diff --git a/PL9fwy3NUQKwa8ZDfSFGn6H8xVFLzqmCZC/0yOo6En_6XI.srt b/PL9fwy3NUQKwa8ZDfSFGn6H8xVFLzqmCZC/0yOo6En_6XI.srt
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index 0000000000000000000000000000000000000000..7d75d5f1533a61c8449911f0fabd1e9dbd7486bd
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+++ b/PL9fwy3NUQKwa8ZDfSFGn6H8xVFLzqmCZC/0yOo6En_6XI.srt
@@ -0,0 +1,2648 @@
+1
+00:00:09,200 --> 00:00:14,260
+المعادلة التفاضلية من خطوة الأولى وهذه السنة
+
+2
+00:00:14,260 --> 00:00:20,760
+أخذنا منها عدة أمثلة من المعادلة سنبدأ بالمعادلة
+
+3
+00:00:20,760 --> 00:00:26,240
+الأولى من linear equations المعادلات الخطية
+
+4
+00:00:26,240 --> 00:00:32,350
+بإنقسام method of integrating factors طريقة عوامل التكامل
+
+5
+00:00:32,350 --> 00:00:37,690
+بالتكامل طبعًا سنعرف بعد قليل ما هو عامل التكامل
+
+6
+00:00:37,690 --> 00:00:44,870
+ولماذا سمي هذا العمل عامل التكامل إذا كنا نعطي
+
+7
+00:00:44,870 --> 00:00:48,970
+تعريف لشكل الـ test of the diffusion equation ثم
+
+8
+00:00:48,970 --> 00:00:56,050
+نضعها على أرض الواقع بمثال ونبدأ عن هذه المعادلة
+
+9
+00:00:58,350 --> 00:01:04,630
+الطيبة العامة للمعادلة التفاضلية من عبارة بالأولى يدفع
+
+10
+00:01:04,630 --> 00:01:09,010
+قضية integration هي عبارة عن integration in general
+
+11
+00:01:09,010 --> 00:01:14,790
+الشكل الثاني dy على dt is a product of dt وy يعني
+
+12
+00:01:14,790 --> 00:01:19,590
+المشتقة الأولى للدالة y بالنسبة إلى t هي عبارة عن 
+
+13
+00:01:19,590 --> 00:01:24,930
+function  في t وy طبعًا ما عنديش معادلة واضحة
+
+14
+00:01:24,930 --> 00:01:29,250
+يمكن أداء حلوة بقى لذلك لذلك روحنا حاطين هذه 
+
+15
+00:01:29,250 --> 00:01:33,590
+المعادلة في الصيغة اللي ممكن نبدأ نشغلها فروحنا 
+
+16
+00:01:33,590 --> 00:01:38,190
+نقول ذاتي أي أن المعادلة هذه كتبت على الشكل التالي
+
+17
+00:01:38,190 --> 00:01:44,500
+في y بيدخل ذات p of t في y سواء مين p of t الآن
+
+18
+00:01:44,500 --> 00:01:47,900
+لو خليت dy على dt في الناحية هذه ونقلنا هذه على 
+
+19
+00:01:47,900 --> 00:01:52,960
+الجهة هذه بيصير طرفي اليمين كله function في y وt
+
+20
+00:01:52,960 --> 00:01:57,300
+زي ما قلنا هنا أو function في t و y إذا الـ
+
+21
+00:01:57,300 --> 00:02:02,040
+function في t و y ساكتبها من الآن فصاعدًا على الشكل
+
+22
+00:02:02,040 --> 00:02:07,240
+التالي dy by dt  زي ال p of t في ال y بيبقى يساوي g 
+
+23
+00:02:07,240 --> 00:02:12,690
+of t ال p of t هي عبارة عن function في t والـ g
+
+24
+00:02:12,690 --> 00:02:17,110
+of t كذلك function أخرى في t والاثنين are continuous
+
+25
+00:02:17,110 --> 00:02:22,590
+على فترة ما يعني هدول دوال متصلة بالنسبة لمين 
+
+26
+00:02:22,590 --> 00:02:29,590
+للمتغير t وكل واحدة فيهم function في t فقط يعني 
+
+27
+00:02:29,590 --> 00:02:34,700
+تكتب بدلالة t بيجي الـ function of t في y بيساوي الـ
+
+28
+00:02:34,700 --> 00:02:40,120
+function of t لوحديها الآن بيجي إلى كيفية حل هذه 
+
+29
+00:02:40,120 --> 00:02:45,920
+المعادلة التفاضلية فبيجي بيقول مشان نحل المعادلة
+
+30
+00:02:45,920 --> 00:02:50,940
+التفاضلية هذه اللي هسميها star بيجي بيختار دالة من 
+
+31
+00:02:50,940 --> 00:02:58,230
+عندي هذه الدالة بيسميها μ of t لـ μ of t بحيث الـ
+
+32
+00:02:58,230 --> 00:03:03,630
+μ of t بدي أتحقق شغل معين يعني أنا لكل مثال بتروح
+
+33
+00:03:03,630 --> 00:03:09,570
+أختار μ of t لأ احنا من هذا سنصل إلى صيغة هذه
+
+34
+00:03:09,570 --> 00:03:15,190
+الصيغة بتعطيني شكل لـ μ of t بدلالة الـ p of t 
+
+35
+00:03:15,190 --> 00:03:19,650
+تبع الـ function الآن يبقى بدنا نختار الـ function 
+
+36
+00:03:19,650 --> 00:03:26,660
+μ of t such that بحيث لو جيت ضربت μ of t في الطرف
+
+37
+00:03:26,660 --> 00:03:37,680
+الأيسر لـ μ of t في dy by dt زائد p of t في ال y
+
+38
+00:03:37,680 --> 00:03:49,240
+هذا الكلام بيساوي لـ μ of t في ال y طبعًا 
+
+39
+00:03:49,900 --> 00:03:55,800
+يبقى احنا الآن بدنا نختار اللي هو ال μ of t اللي
+
+40
+00:03:55,800 --> 00:04:01,360
+هي الدالة الموجودة التي لا تأخذ إلا قيمة موجبة لتحقيق
+
+41
+00:04:01,360 --> 00:04:07,080
+لي هذه العلاقة يبقى هذه العلاقة لأن أنا الـ μ of 
+
+42
+00:04:07,080 --> 00:04:11,580
+t لما أضربها في الطرف الشمال هذا بقدر أجمع الـ μ
+
+43
+00:04:11,580 --> 00:04:18,400
+of t مع ال y وأخد له مشتقة حاصل ضرب بالتكامل طيب الآن
+
+44
+00:04:18,400 --> 00:04:22,960
+بدي أبحث ما هو شكل الـ μ of t إذا مشان أحصل على 
+
+45
+00:04:22,960 --> 00:04:27,420
+شكل ال μ of t بدي أفك الجملة دي وأفك المشتقة 
+
+46
+00:04:27,420 --> 00:04:32,520
+اللي عندنا هذه فلو جيت فكت الجملة دي ال μ of t
+
+47
+00:04:32,520 --> 00:04:38,200
+هذه البنات هسميها μ prime بس لسه هذا الشكل ده
+
+48
+00:04:38,200 --> 00:04:44,720
+دايما من المعادلة زائد ل μ of t
+
+49
+00:05:01,340 --> 00:05:07,240
+طب تعالوا نقارن بين الطرفين في هذه المعادلة طلع لي
+
+50
+00:05:07,240 --> 00:05:12,160
+في ال term هذا وال term هذا إن الاثنين are the same
+
+51
+00:05:12,160 --> 00:05:17,260
+صحيح ولا لأ؟ إذا لما أطرح واحد عند الثاني أو أضيفه
+
+52
+00:05:17,260 --> 00:05:22,820
+إليه بإشارة مخالفة الاثنين هدول بيروحوا وبيبقى عند
+
+53
+00:05:22,820 --> 00:05:31,500
+المعادلة الثانية لـ μ of t ال p of t في ال y يساوي
+
+54
+00:05:31,500 --> 00:05:39,460
+μ prime of t في ال y وسيميلي هذه المعادلة رقم واحد
+
+55
+00:05:41,140 --> 00:05:45,640
+تبقى كويس الآن بدنا نيجي على المعادلة اللي عندنا
+
+56
+00:05:45,640 --> 00:05:51,060
+star هادي بدي أضربها في ال μ of t أضرب طرفيها
+
+57
+00:05:51,060 --> 00:05:56,440
+يفجأة بتروح أضرب طرفي المعادلة star بال μ of t 
+
+58
+00:05:56,440 --> 00:06:03,840
+هروح أقولهم multiply multiply 
+
+59
+00:06:03,840 --> 00:06:13,340
+both sides of equation star اللي احنا بدنا نحلها 
+
+60
+00:06:13,340 --> 00:06:23,060
+by μ of t we get نحصل على يفجأة داشي ده يصير لـ μ 
+
+61
+00:06:23,060 --> 00:06:33,340
+of t ال y prime زائد لـ μ of t ال p of t في ال y 
+
+62
+00:06:33,340 --> 00:06:38,320
+يساوي لـ μ of t ال g of t 
+
+63
+00:06:41,630 --> 00:06:48,230
+طبعًا تلاحظ μ of t μ of t في ال y بقدر 
+
+64
+00:06:48,230 --> 00:06:52,990
+أشيلها وأكتب بدلها مين μ prime of t في ال y
+
+65
+00:06:52,990 --> 00:06:58,910
+يبقى هذه كلها بقدر أشيلها وأكتب بدلها μ prime
+
+66
+00:06:58,910 --> 00:07:04,990
+of t في مين في ال y يبقى هذه بالصيغة μ of t في
+
+67
+00:07:04,990 --> 00:07:11,580
+ال y prime زائد μ prime of t في ال y يساوي μ 
+
+68
+00:07:11,580 --> 00:07:18,860
+of t في ال g of t وهذا الكلام from one يبقى هذا 
+
+69
+00:07:18,860 --> 00:07:23,060
+جبناه من المعادلة اللي تحت اللي عندنا طب أطلعيه
+
+70
+00:07:23,060 --> 00:07:28,440
+للآن في الشكل اللي على الشمال هذا أليس هذا هو 
+
+71
+00:07:28,440 --> 00:07:33,450
+حاصل ضرب دالتين صح ولا لا؟ يبقى بدي أجمع 
+
+72
+00:07:33,450 --> 00:07:40,470
+الدالتين بمشتقة واحدة يبقى بيصير عندي ال μ of t في 
+
+73
+00:07:40,470 --> 00:07:47,950
+ال y كله بده يساوي ال μ of t في ال g of t
+
+74
+00:07:55,290 --> 00:08:01,150
+طبعًا الحقيقة أن استعجلت شوي يعني كان خاطر أحسب من 
+
+75
+00:08:01,150 --> 00:08:07,830
+هذه المعادلة ما هو شكل لـ μ of t قبل ما أضرب هذه طبعًا 
+
+76
+00:08:07,830 --> 00:08:12,310
+يبقى أنا بس استعجلت شوي يبقى من هذه المعادلة يا
+
+77
+00:08:12,310 --> 00:08:19,630
+بنات بقدر أجيب شكل من شكل لـ μ of t وكيف بتروح الـ 
+
+78
+00:08:19,630 --> 00:08:25,770
+y مع ال y لو قسمت الطرفين على ال μ of t ياسي
+
+79
+00:08:25,770 --> 00:08:31,990
+بيصير عندنا هنا بيصير الـ μ prime of t على ال μ
+
+80
+00:08:31,990 --> 00:08:38,050
+of t بده يساوي الـ p of t لما 
+
+81
+00:08:38,050 --> 00:08:39,550
+تروح ال y مع y 
+
+82
+00:08:47,220 --> 00:08:56,350
+μ الـ p of t على μ ال p of t يبقى ال ln تقابل 
+
+83
+00:08:56,350 --> 00:08:59,890
+للمقام لما يكون ال ln تقابل للمقام يبقى التكامل 
+
+84
+00:08:59,890 --> 00:09:05,770
+ل ln absolute value للمقام لكن المقام أنا مختاره 
+
+85
+00:09:05,770 --> 00:09:11,350
+positive يبقى ال ln absolute value لا داعي له يبقى
+
+86
+00:09:11,350 --> 00:09:20,410
+بيصير عندنا ln ال μ of t بده يساوي تكامل p of t dt 
+
+87
+00:09:20,410 --> 00:09:28,270
+زائد كونستانت k مثلاً ال كونستانت k هذا يا بنات بدي
+
+88
+00:09:28,270 --> 00:09:31,050
+آخذه كله بجدّاش  ب صفر
+
+89
+00:09:33,800 --> 00:09:38,640
+طيب يبقى لو أخدت ال constant دي برة عند مين لإن
+
+90
+00:09:38,640 --> 00:09:45,180
+μ of t بده يساوي تكامل p of t dt يبقى بناء عليه 
+
+91
+00:09:45,180 --> 00:09:52,400
+لو رفعت الاثنين كلهم للعدد e بيصير e أس ln μ of t
+
+92
+00:09:52,400 --> 00:10:02,060
+بده يساوي e أس تكامل p of t بناءً على ال e وال ln
+
+93
+00:10:02,060 --> 00:10:05,720
+اللي الاثنين هذول عكس بعض يبقى واحدة بتلغي الثانية
+
+94
+00:10:05,720 --> 00:10:10,240
+يبقى هذا بده يعطينا ال μ of t اللي أنا بدور
+
+95
+00:10:10,240 --> 00:10:18,940
+عليها e أس تكامل p of t dt يبقى 
+
+96
+00:10:18,940 --> 00:10:23,920
+هذا شكل ال μ of t زي ما أنتم شايفين اعتمدت على 
+
+97
+00:10:23,920 --> 00:10:30,870
+مين اعتمدت على المعامل بتاع ال y وهنا المعامل تبع 
+
+98
+00:10:30,870 --> 00:10:36,730
+ال y' هو جدًّا واحد صحيح تمام تمام يبقى من الآن
+
+99
+00:10:36,730 --> 00:10:40,870
+فصاعدًا لما يكون عندي first order differential
+
+100
+00:10:40,870 --> 00:10:47,190
+equation والمعامل تبع ال dy by dt هو الواحد الصحيح
+
+101
+00:10:47,190 --> 00:10:51,450
+بيكون شكل ال integrating factor μ of t هو ال
+
+102
+00:10:51,450 --> 00:10:58,000
+exponential مرفوع للأس تكامل p of t dt وهذا ما 
+
+103
+00:10:58,000 --> 00:11:04,920
+أفعله مع كل سؤال عند الحل طب الآن بدنا نعرف ما هو
+
+104
+00:11:04,920 --> 00:11:10,060
+شكل الحل للمعادلة التفاضلية اللي عندنا طب نروح نقول 
+
+105
+00:11:10,060 --> 00:11:14,500
+نضرب كل term من ال term سبعة المعادلة التفاضلية
+
+106
+00:11:14,500 --> 00:11:19,500
+اللي عندنا في ال μ of t بنستبدل هذا بال μ prime
+
+107
+00:11:19,500 --> 00:11:25,020
+of t في ال y هدول كلهم كمشتقة واحدة يساوي مين؟
+
+108
+00:11:25,020 --> 00:11:32,180
+يساوي لأن لو كاملت الطرفين يبقى by integration
+
+109
+00:11:32,180 --> 00:11:35,480
+بواسطة
+
+110
+00:11:35,480 --> 00:11:42,780
+التكامل بيصير عندنا لـ μ of t في ال y يساوي تكامل لـ 
+
+111
+00:11:42,780 --> 00:11:50,360
+μ of t في g of t dt الزائد كونستانت أنا ما بدي الـ
+
+112
+00:11:50,360 --> 00:11:57,380
+μ of t في y بدي y يبقى بروح بقول هنا the solution
+
+113
+00:11:57,380 --> 00:12:11,380
+of the differential equation star is y تساوي واحد
+
+114
+00:12:11,380 --> 00:12:21,650
+على ال μ of t في تكامل ل μ of t في g of t dt 
+
+115
+00:12:21,650 --> 00:12:29,090
+زائد كونستانت هذا شكل الحل تبع المعادلة التفاضلية 
+
+116
+00:12:29,090 --> 00:12:37,350
+اللي هي star لحد هنا انتهت جزء النظري تبع ال linear
+
+117
+00:12:37,350 --> 00:12:40,890
+first order differential equations لو جاني السؤال 
+
+118
+00:12:40,890 --> 00:12:46,110
+بده يتبع نفس التكتيك بده أروح أجيب له قيمة لـ μ of
+
+119
+00:12:46,110 --> 00:12:51,650
+t بعدين أضرب طرفي المعادلة في ال μ of t وبعدين
+
+120
+00:12:51,650 --> 00:12:58,250
+كده أكامل بأحصل على حل المعادلة التفاضلية بس قبل
+
+121
+00:12:58,250 --> 00:13:01,910
+ما أبدأ الخطوات هكتب ملاحظة حتى ما تنسوهاش بجيبها مكتوبة
+
+122
+00:13:01,910 --> 00:13:08,390
+عندكمشان نأخذ ال μ of t بطريقة صحيحة بدي يكون 
+
+123
+00:13:08,390 --> 00:13:14,090
+المعامل هنا هو واحد صحيح اثنين بدي تبقى المعادلة
+
+124
+00:13:14,090 --> 00:13:17,850
+في نفس الشكل اللي عندنا هذا مش تبقى p of t ثانية 
+
+125
+00:13:17,850 --> 00:13:21,190
+تربيع مثلاً يبقى المستقل أولى ل y 
+
+126
+00:13:27,390 --> 00:13:32,990
+معادلة بتيجي في الشكل هذا والمعامل هنا جدًّا وحطّش
+
+127
+00:13:32,990 --> 00:13:36,450
+إن شاء الله يكون الاثنين بيتجسموا على الاثنين قبل ما
+
+128
+00:13:36,450 --> 00:13:42,170
+تحسب ال μ of t يعني أي معامل هنا ل y prime بدنا
+
+129
+00:13:42,170 --> 00:13:48,110
+نجسم عليه قبل أن نبدأ بالحل أكتب لهذا على شكل 
+
+130
+00:13:48,110 --> 00:13:52,880
+ملاحظة حتى ما تنسوهاش إن شاء الله وتعالوا أثناء
+
+131
+00:13:52,880 --> 00:13:56,300
+الحل 
+
+132
+00:13:56,300 --> 00:14:02,740
+ابقى 
+
+133
+00:14:02,740 --> 00:14:10,500
+not before 
+
+134
+00:14:10,500 --> 00:14:14,480
+confusing 
+
+135
+00:14:14,480 --> 00:14:18,000
+قبل ما تعجبك
+
+136
+00:14:43,680 --> 00:14:51,560
+بتتأكد يعني to make sure that the differential 
+
+137
+00:14:51,560 --> 00:15:03,140
+equation المعادلة التفاضلية is exactly is exactly
+
+138
+00:15:03,140 --> 00:15:15,480
+in the form of star and the coefficient and
+
+139
+00:15:15,480 --> 00:15:25,680
+the the coefficient of
+
+140
+00:15:25,680 --> 00:15:29,740
+y' is واحد صحيح
+
+141
+00:15:47,500 --> 00:15:54,520
+the example one find
+
+142
+00:15:54,520 --> 00:16:08,240
+the general solution of
+
+143
+00:16:08,240 --> 00:16:15,020
+the following differential equation
+
+144
+00:16:19,460 --> 00:16:29,120
+the differential equation and use it and use it to
+
+145
+00:16:29,120 --> 00:16:35,260
+determine عشان
+
+146
+00:16:35,260 --> 00:16:43,180
+نحدد how solutions solutions
+
+147
+00:16:43,180 --> 00:16:46,340
+they behave
+
+148
+00:16:57,690 --> 00:17:06,390
+السؤال الأول نمرة a سؤال ستة من الكتاب تقول dy
+
+149
+00:17:06,390 --> 00:17:16,930
+بـ dt زائد 2y تساوي sin t والتي أكبر من
+
+150
+00:17:16,930 --> 00:17:28,330
+صفر نمرة 2 y' زائد y يساوي ثلاثة
+
+151
+00:17:51,900 --> 00:17:55,600
+السؤال مرة ثانية طبعًا زي ما تشاهدين فيه مطلبين
+
+152
+00:17:55,600 --> 00:17:59,540
+المطلب الأول بيقول هات ال general solution لكل
+
+153
+00:17:59,540 --> 00:18:04,280
+من المعادلات التفاضلية التالية واستخدم الحل اللي
+
+154
+00:18:04,280 --> 00:18:11,300
+جبته مشان تحدد كيف الحل behave بكل سلوكه أو شكله
+
+155
+00:18:11,300 --> 00:18:16,880
+لما t تكبرها بمقدار كبير جدًا يعني تصل إلى ما لا
+
+156
+00:18:16,880 --> 00:18:23,290
+نهاية نقوله solution والنجي للمعادلة الأولى
+
+157
+00:18:23,290 --> 00:18:26,490
+الملاحظة اللي احنا كتبناها هنا لازم يكون معامل y'
+
+158
+00:18:26,730 --> 00:18:31,630
+واحد صحيح إذا ما جاب الكل شيء المعادلة هذه بنروح نقسم
+
+159
+00:18:31,630 --> 00:18:38,010
+الطرفين عالميًا على 2 يبقى باقي بقوله نمرة a 
+
+160
+00:18:41,140 --> 00:18:50,760
+equation s لو جسمنا على 2 بيصير y' زائد 1 على t في 
+
+161
+00:18:50,760 --> 00:19:00,440
+y بده يساوي 5t على 2t وهذه سميها اللي اللي هي 
+
+162
+00:19:00,440 --> 00:19:05,060
+المعادلة الأصلية star اللي بدنا نحلها يبقى الآن 
+
+163
+00:19:05,060 --> 00:19:08,980
+بدنا نروح نجيب عامل التكامل integrating factor
+
+164
+00:19:09,300 --> 00:19:17,220
+يبقى ال μ of t أخذناها قبل قليل e أس تكامل p of t 
+
+165
+00:19:17,220 --> 00:19:23,080
+dt يبقى هذا الكلام اللي يساوي e أس تكامل p of t 
+
+166
+00:19:23,080 --> 00:19:27,560
+صار 2 على t لكن لو ما جسمناش يا بنات 
+
+167
+00:19:27,560 --> 00:19:32,200
+سألجتيها 2 وبالتالي وجعنا في مشكلة عويصة يبقى 
+
+168
+00:19:32,200 --> 00:19:38,950
+باجي بقوله 2 على t في dt هذا الكلام بده
+
+169
+00:19:38,950 --> 00:19:45,050
+يساوي e أس 2 برة التكامل بقول جبات 1 على t
+
+170
+00:19:45,050 --> 00:19:51,950
+dt اللي هي ln t يبقى 2 ln t وليس ln absolute 
+
+171
+00:19:51,950 --> 00:19:57,670
+value ل t لأنه قلنا هنا t مالها greater than zero
+
+172
+00:19:57,670 --> 00:20:04,090
+أكبر من ال zero يبقى هذه e أس ln t تربيع مصبوب
+
+173
+00:20:04,090 --> 00:20:11,280
+هكذا من أين جلبنا هذه المعلومة؟ من الكالكولوس بيه؟ 
+
+174
+00:20:11,280 --> 00:20:15,720
+تمام تمام يبقى يا دكاترة بتساوي t تربيع بيعملوا فيك 
+
+175
+00:20:15,720 --> 00:20:21,060
+برضه؟ لأن ال e وال ln x كل واحدة فيهم inverse
+
+176
+
+216
+00:24:08,950 --> 00:24:17,930
+إذا صار عندي  P تربيع Y يساوي ناقص P P for sin P
+
+217
+00:24:17,930 --> 00:24:25,930
+زائد sin P زائد constant C يبقى بدي ال solution
+
+218
+00:24:25,930 --> 00:24:33,130
+فبروح بقوله the solution is أنا مابدي T تربيع Y
+
+219
+00:24:33,130 --> 00:24:38,850
+وإلا بدي main هي ال Y إذا بقسم كله على مين؟ على T
+
+220
+00:24:38,850 --> 00:24:49,030
+تربيع يبقى Y بدي أساوي C  ذائب  sin T مقسوم  T  مقسوم T  مقسوم T
+
+221
+00:24:49,030 --> 00:24:55,930
+كل هذا على مين؟ على T تربيع يبقى هذا شكل ال general
+
+222
+00:24:55,930 --> 00:25:02,210
+solution لـ  المعادلة التفاضلية لأنها  مام رقم 
+
+223
+00:25:02,210 --> 00:25:07,010
+start خلصنا لسه المطلوب الأول من السؤال المطلوب
+
+224
+00:25:07,010 --> 00:25:11,190
+الثاني قال لي استخدم الحل اللي جيبته هذا
+
+225
+00:25:11,190 --> 00:25:19,110
+ههههههههههههههههههههههههههههههههههههههههههههههههههههههههههههههههههههههههههههههههههههههههههههههههههههههههههههههههههههههههههههههههههههههههههههههههههههههههههههههههههههههههههههههههههههههههههههههههههههههههههه
+
+226
+00:25:35,150 --> 00:25:44,130
+بدا تساوي limit لمن؟ لـ C على T تربيع زائد sin T على
+
+227
+00:25:44,130 --> 00:25:54,630
+T تربيع ناقص cos T على T لما T بدا تروح إلى
+
+228
+00:25:54,630 --> 00:25:59,410
+infinity طيب
+
+229
+00:25:59,410 --> 00:26:02,370
+هذه لما T بدا تروح لمين؟لما لا نهاية
+
+230
+00:26:05,900 --> 00:26:11,860
+أول عدد عملته نهائي بـ0 يفجأها دي بـ0  أجت مشكلتنا مع
+
+231
+00:26:11,860 --> 00:26:19,960
+مين؟ مع sin T على T تربيع طيب نرجع لـ Calculus A طبعا
+
+232
+00:26:19,960 --> 00:26:23,840
+عملناها في Calculus A بس نذكرها بدل A هو sin محصور
+
+233
+00:26:23,840 --> 00:26:32,430
+بين مين ومين؟ سالب واحد وواحد إذا sin T محصور ما
+
+234
+00:26:32,430 --> 00:26:37,090
+بين الواحد وما بين السالب واحد power of  B للفرق
+
+235
+00:26:37,090 --> 00:26:43,530
+انتوا واحد على T تربيع يبقى إيش بيصير سالب واحد على
+
+236
+00:26:43,530 --> 00:26:50,210
+T تربيع sign of T على T تربيع واحد على T تربيع
+
+237
+00:26:51,430 --> 00:26:55,630
+بنروح ناخد ال limit لما T بدها تروح لما لا نهاية
+
+238
+00:26:55,630 --> 00:27:00,870
+يجب عشان نصير عندنا هنا zero أقل من أو يساوي ال
+
+239
+00:27:00,870 --> 00:27:06,810
+limit لما T tends to infinity لـ sin T على T تربيع
+
+240
+00:27:06,810 --> 00:27:12,220
+أقل من أو يساوي ال zero يبقى بـ Sandwich Theorem
+
+241
+00:27:12,220 --> 00:27:15,740
+يبقى
+
+242
+00:27:15,740 --> 00:27:21,980
+بـ Sandwich
+
+243
+00:27:21,980 --> 00:27:31,000
+Theorem يبقى بـ Sandwich
+
+244
+00:27:31,000 --> 00:27:37,020
+Theorem يبقى بـ Sandwich Theorem يبقى بـ Sandwich
+
+245
+00:27:37,020 --> 00:27:37,140
+Theorem يبقى بـ Sandwich Theorem يبقى بـ Sandwich
+
+246
+00:27:37,140 --> 00:27:37,480
+Theorem يبقى بـ Sandwich Theorem يبقى بـ Sandwich
+
+247
+00:27:37,480 --> 00:27:40,720
+Theorem يبقى بـ Sandwich Theorem يبقى بـ 0 كذلك يفجأ
+
+248
+00:27:40,720 --> 00:27:47,340
+هنا بقى يبقى يقول الـ S Y بدأ تروح للـ 0 الـ T بدأ
+
+249
+00:27:47,340 --> 00:27:55,200
+تروح لوين؟ للإنفلي حد لايه سؤال هنا يا ناس؟ فهنا
+
+250
+00:27:55,200 --> 00:27:59,580
+من الحل كاملا نروح للمثال الثاني بس بدنا نشوف إذا
+
+251
+00:27:59,580 --> 00:28:06,800
+فيه تساوي إيه؟ إيه؟ نجي للمثال الثاني
+
+252
+00:28:14,060 --> 00:28:21,840
+يبقى نمر بي المعادلة عند بدايتها نرسم
+
+253
+00:28:21,840 --> 00:28:28,160
+على تمام يبقى المعادلة بالصير اللي نمر بي y prime
+
+254
+00:28:28,160 --> 00:28:37,540
+زائد نصف y يساوي ثلاثة على اتنين في T تربيع كويس
+
+255
+00:28:37,540 --> 00:28:44,870
+بدنا نروح نجيب عامل تكامل اللي هو ال mu of T يساوي
+
+256
+00:28:44,870 --> 00:28:53,190
+E أس تكامل T of T اللي هو نصف DT يبقى هذا الكلام
+
+257
+00:28:53,190 --> 00:28:59,570
+يساوي E أس T على 2  نصف T يعني T على 2 يبقى
+
+258
+00:28:59,570 --> 00:29:04,030
+هذا عامل التكامل لنا يبقى الآن بدنا نروح المعادلة
+
+259
+00:29:04,030 --> 00:29:09,570
+هذه اللي صارت عندنا نسميها double star مشان إنه ما
+
+260
+00:29:09,570 --> 00:29:13,890
+تختلف عن المعادلة L4 يبقى المعادلة هذه بتروح
+
+261
+00:29:13,890 --> 00:29:19,530
+أضربها في مين في E أس E على 2 بروح و أقول لهم
+
+262
+00:29:19,530 --> 00:29:24,270
+multiply both
+
+263
+00:29:24,270 --> 00:29:28,190
+sides of
+
+264
+00:29:28,970 --> 00:29:39,990
+Equation double star by E أس T على اتنين نحصل
+
+265
+00:29:39,990 --> 00:29:40,330
+على
+
+266
+00:30:03,400 --> 00:30:08,220
+يبقى المعادلة دي بيصير على الشكل الساوي E أس T
+
+267
+00:30:08,220 --> 00:30:18,540
+على 2  الـ Y prime زائد نصف E أس T على 2 زائد
+
+268
+00:30:18,540 --> 00:30:26,200
+نصف E أس T على 2 في الـ Y بيبقى ساوي ثلاثة على
+
+269
+00:30:26,200 --> 00:30:30,920
+2 E أس T على 2  تمام fifty
+
+270
+00:30:34,070 --> 00:30:38,850
+طب تعالى نشوف يبقى بناء على الطرف هذا بقدر
+
+271
+00:30:38,850 --> 00:30:43,970
+اتقبله على الشكل الثاني اجمعه بترم واحد اللي هو
+
+272
+00:30:43,970 --> 00:30:51,690
+عامل التكامل مضروبا سواء بكل  prime لو مشتقته وما
+
+273
+00:30:51,690 --> 00:30:56,550
+طلعتش هذا يا بنات معناته حسابك هنا آه غلطي عامل
+
+274
+00:30:56,550 --> 00:31:00,910
+التكامل لازم يطلع المعادلة بالضبط طب عادي لو جيت
+
+275
+00:31:00,910 --> 00:31:06,550
+اشتقها الأولى في مشتقة الثانية هيه مجرد زي دي
+
+276
+00:31:06,550 --> 00:31:11,190
+الثانية اللي هي Y في مشتقة الـ exponential اللي هي
+
+277
+00:31:11,190 --> 00:31:17,010
+نفسها مضروبة في جديد في نصف يبقى هي نصف E أس T على
+
+278
+00:31:17,010 --> 00:31:22,250
+2  تُبين في الـ Y بكلام سليم مائة بالمائة  بادرساه
+
+279
+00:31:22,250 --> 00:31:26,610
+من الفرق الأيمن فهو ثلاثة على اتنين
+
+280
+00:31:55,500 --> 00:31:56,900
+Eac²Eac²Eac²Eac²Eac²Eac²Eac²Eac²Eac²Eac²Eac²Eac²Eac²Eac²Eac²Eac²Eac²Eac²Eac²Eac²Eac²Eac²Eac²Eac²Eac²Eac²Eac²Eac²Eac²Eac²Eac²Eac²Eac²Eac²Eac²Eac²Eac²Eac²Eac²Eac²Eac²Eac²Eac²Eac²Eac²Eac²Eac²Eac²Eac²Eac²Eac²Eac²Eac²Eac²Eac²Eac²Eac²Eac²Eac²Eac²Eac²Eac²Eac²Eac²Eac²Eac²Eac²Eac²Eac²Eac²Eac²Eac²Eac²Eac²Eac²
+
+281
+00:31:57,180 --> 00:32:04,580
+و بدي آخد هنا ال integral يبقى هي ثلاثة على اتنين
+
+282
+00:32:04,580 --> 00:32:13,040
+اللي هو T تربيع هنا E أس T على اتنين بدي اشتق بيصير
+
+283
+00:32:13,040 --> 00:32:19,520
+عندي جداش هنا بنات ثلاثة T فقط مغير لو كامل
+
+284
+00:32:19,520 --> 00:32:25,270
+تكاملها بنفسها مقسومة على جداش على نصف النقطة اللي
+
+285
+00:32:25,270 --> 00:32:31,310
+فوق بيصير اتنين تمام كمان مرة يبقى مشتقتها ثلاثة
+
+286
+00:32:31,310 --> 00:32:36,790
+تكاملها بأربعة E أس T على اتنين يعني اتنين مالكش
+
+287
+00:32:36,790 --> 00:32:40,770
+دعوات وهذه E أس T على اتنين على نصف اللي فوق بيصير
+
+288
+00:32:40,770 --> 00:32:46,490
+اتنين يبقى أربعة E أس T على 2 مشتق كمان مرة اللي
+
+289
+00:32:46,490 --> 00:32:53,970
+هي zero وكمل كمان مرة يبقى ثمانية E أس T على 2 هدف
+
+290
+00:32:53,970 --> 00:32:59,350
+هدف إشارة موجب هدف هدف إشارة سالب هدف هدف إشارة
+
+291
+00:32:59,350 --> 00:33:05,790
+موجب يبقى لو ثمانية بيصير E أس T على 2 في الـ Y
+
+292
+00:33:05,790 --> 00:33:12,630
+يساوي مضروب هذول في بعض النص بتروح مع الاثنين ويصير
+
+293
+00:33:12,630 --> 00:33:18,830
+ثلاثة في ت تربيع E أس T على 2 ثلاثة في ت تربيع E
+
+294
+00:33:18,830 --> 00:33:24,150
+أس T على 2 اللي بعدها ناقص ثلاثة في أربعة بـ 12
+
+295
+00:33:24,150 --> 00:33:31,370
+في E أس T على 2 اللي بعدها زائد أربعة
+
+296
+00:33:31,370 --> 00:33:38,200
+و20 E أس T على 2 زائد constant C
+
+297
+00:33:41,290 --> 00:33:47,650
+بدي أقسم كله على E أس T على 2 يبقى لو قسمت بيصير Y
+
+298
+00:33:47,650 --> 00:33:55,790
+يساوي ثلاثة T تربيع ناقص 12 T زائد 24
+
+299
+00:33:55,790 --> 00:34:04,130
+زائد C على E أس T على 2 هذا هو ال general
+
+300
+00:34:04,130 --> 00:34:13,790
+solution تبع المعادلة التفاضلية طب كويس الآن جاء
+
+301
+00:34:13,790 --> 00:34:18,710
+يشوف لي ما هو سلوك الدالة أو كيف بدها يكون سلوك
+
+302
+00:34:18,710 --> 00:34:23,710
+الدالة لما T بدها تروح لوين؟ لما لا نهاية بقول
+
+303
+00:34:23,710 --> 00:34:29,310
+الآن لو T راحت لما لا نهاية إيه بيصير لترم بيصير؟
+
+304
+00:34:29,310 --> 00:34:38,170
+بيصير؟ لما لا نهاية لما لا نهاية بس بـ0 يبقى هذا term عند
+
+305
+00:34:38,170 --> 00:34:43,170
+لما لا نهاية يروح بـ0 بيظل مين عند هذا term لهم
+
+306
+00:34:43,170 --> 00:34:46,910
+لما لا نهاية ناقص 12 في لما لا نهاية زائد 24
+
+307
+00:34:46,910 --> 00:34:54,410
+يبقى هذا هو الذي سيتحكم في سلوك ابدالة لو رجعنا
+
+308
+00:34:54,410 --> 00:35:00,890
+إلى تمام خلاصة A وليس B بيجينا نقول الدالة من جزئية
+
+309
+00:35:00,890 --> 00:35:06,190
+اللي هي فيه dominated term  أجزاء التحكم لما كنا في
+
+310
+00:35:06,190 --> 00:35:12,610
+الرسم البياني الدالة ما بيجينا نقول لعزيزي التحكم هذا
+
+311
+00:35:12,610 --> 00:35:18,450
+بيتحكم عند T تساوي ما لا نهاية هذا مثلا بيتحكم عند T
+
+312
+00:35:18,450 --> 00:35:22,870
+تساوي Zero كنا بنقول أو T تساوي اتنين أو T تساوي
+
+313
+00:35:22,870 --> 00:35:28,510
+ثلاثة حسب طبيعة مين؟ حسب طبيعة المثل يبقى عند T
+
+314
+00:35:28,510 --> 00:35:31,810
+بيبدأ تساوي ما لا نهاية هذا ال term بيبقى لأنه Zero
+
+315
+00:35:31,810 --> 00:35:37,200
+و بيبقى لعيننا مين؟ ال term هذا يبقى ال term هذا
+
+316
+00:35:37,200 --> 00:35:42,740
+بيكون هو والمنحنى أصحاب بيجيسدوا مع بعض اللي
+
+317
+00:35:42,740 --> 00:35:48,990
+بيجينا نسميهم الـ  asymptotic خط تقارب، مظبوط؟ بس
+
+318
+00:35:48,990 --> 00:35:53,590
+هذا مش خط تقارب هذا منحنى على شكل parabola وماعمله
+
+319
+00:35:53,590 --> 00:35:57,870
+شاف إنه معادلة من الدرجة الثانية في T صحيح ولا
+
+320
+00:35:57,870 --> 00:36:04,850
+لأ؟ يفجأة بيصير المنحنى asymptotic يعني كأنه تقارب
+
+321
+00:36:04,850 --> 00:36:10,830
+مع المنحنى اللي عندنا هذا تمام؟ يفجأة باجي بقوله
+
+322
+00:36:10,830 --> 00:36:17,010
+as T tends to infinity the solution
+
+323
+00:36:21,300 --> 00:36:34,780
+is asymptotic to the curve للمنحنى y تساوي ثلاثة
+
+324
+00:36:34,780 --> 00:36:41,320
+تربيع ناقص 12 P زائد 24 لإن عندي
+
+325
+00:36:41,320 --> 00:36:47,140
+لما لا نهاية هذا كله بيروح جداش P بـ 0 بيضلش إلا هذا
+
+326
+00:36:49,490 --> 00:36:54,230
+حد يلاقي تساؤل هنا؟ لازلنا في نفس الـ section لسه
+
+327
+00:36:54,230 --> 00:37:04,110
+فيه مزيد من الأمثلة آه لأ
+
+328
+00:37:04,110 --> 00:37:09,130
+أنا بفضل تشتغل زي ما اشتغلنا ما بديش تحفظي أنا بدي
+
+329
+00:37:09,130 --> 00:37:14,540
+طريقة الخطوة تكون خطوة سلم للأخرى أنا قادر من عند
+
+330
+00:37:14,540 --> 00:37:18,140
+ما جبت الاسم من عند ما جبت ال integrated factor
+
+331
+00:37:18,140 --> 00:37:21,800
+أقول الـ resolution واحد على الـ mu of t تكامل g of
+
+332
+00:37:21,800 --> 00:37:26,020
+t mu of t dt زائد كنصارى وحطها دموعي أنا بس أنا
+
+333
+00:37:26,020 --> 00:37:31,400
+مدهش بدي الشيء يكون بالترتيب فعلا طيب يا بنات احنا
+
+334
+00:37:31,400 --> 00:37:34,800
+المرة اللي فاتت أعطانا تعريف لـ initial value
+
+335
+00:37:34,800 --> 00:37:40,040
+problem لكن ما حليناش ولا مسألة initial value
+
+336
+00:37:40,040 --> 00:37:46,060
+problem الآن بنتحول نحل مثل initial value of
+
+337
+00:37:46,060 --> 00:37:52,260
+problem ونشوف كيف هتعملوا فيه يبقى المثال رقم
+
+338
+00:37:52,260 --> 00:37:56,400
+اثنين example
+
+339
+00:37:56,400 --> 00:38:04,500
+two solve
+
+340
+00:38:04,500 --> 00:38:07,720
+the
+
+341
+00:38:07,720 --> 00:38:09,380
+following
+
+342
+00:38:18,530 --> 00:38:28,910
+مثل الأولى نمر a y prime زي دي 8 على t في الـ y
+
+343
+00:38:28,910 --> 00:38:37,830
+يساوي cosine t على t تربيع والـ y عند الـ y بدها
+
+344
+00:38:37,830 --> 00:38:48,240
+تساوي  T greater than 0  نمرى D طبعا هذا سؤال 16 من
+
+345
+00:38:48,240 --> 00:38:55,620
+الكتاب وهذا سؤال 20 بيقول الـ T في الـ Y prime زائد
+
+346
+00:38:55,620 --> 00:39:04,860
+T زائد واحد في الـ Y بده يساوي كده؟ بده يساوي T والـ
+
+347
+00:39:04,860 --> 00:39:12,500
+Y عند  pi بده يساوي واحد at T greater than Zero
+
+348
+00:39:12,500 --> 00:39:15,720
+Solution
+
+349
+00:39:15,720 --> 00:39:23,000
+لو
+
+350
+00:39:23,000 --> 00:39:29,760
+نورس للمعادلة رقم A  بناخد A بناخد المعامل يبقى Y'
+
+351
+00:39:30,240 --> 00:39:35,750
+هو واحد طيب جهنا جاهزين يبقى بعدي بقوله لـ mu of T
+
+352
+00:39:35,750 --> 00:39:44,410
+بيساوي E أس كامل 2 على T DT هذا بيساوي E أس
+
+353
+00:39:44,410 --> 00:39:53,050
+2 ln T يبقى E أس ln T تربيع يبقى T تربيع بالضبط
+
+354
+00:39:53,050 --> 00:39:58,970
+تمامًا فبنروح نضرب المعادلة كلها في T تربيع يبقى إيش
+
+355
+00:39:58,970 --> 00:40:12,790
+بيصير عندي T تربيع  وY prime زي دي تربيع
+
+356
+00:40:12,790 --> 00:40:20,090
+الـ y كلها prime يساوي main يساوي cos Tكامل
+
+357
+00:40:20,090 --> 00:40:30,240
+افتراضين يتجه دي تربيع Y تساوي sin T زائد cos C كما
+
+358
+00:40:30,240 --> 00:40:36,200
+عملنا على طول الخط مباشرة يبقى بناء عليه يساوي
+
+359
+00:40:36,200 --> 00:40:44,060
+الـ y يساوي الـ sin الـ T زائد constant C على T
+
+360
+00:40:44,060 --> 00:40:53,420
+تربيع هذا هو مين؟ ال general solution طيب لك أنا
+
+361
+00:40:53,420 --> 00:40:57,580
+راح أفعّل initial condition الـ Initial Condition
+
+362
+00:40:57,580 --> 00:41:04,200
+قال لي Y عند الـ pi تساوي Zero فقلنا لو شيلت كل P
+
+363
+00:41:04,200 --> 00:41:11,100
+وحطيت مكانها pi بيبقى Y prime بـ Zero يبقى Zero
+
+364
+00:41:11,100 --> 00:41:19,220
+بدها تساوي sin pi prime يا بنات بـ Zero زائد  C
+
+365
+00:41:19,220 --> 00:41:30,240
+على من؟ على pi تربيع ومنها C تساوي Zero يبقى سعر شكل
+
+366
+00:41:30,240 --> 00:41:38,020
+الحل على الشكل التالي Y تساوي Sine of T على T
+
+367
+00:41:38,020 --> 00:41:43,280
+تربيع هذا هو main حل ال initial value problem
+
+368
+00:41:43,280 --> 00:41:47,160
+الأولى لجلات ثانية
+
+369
+00:42:10,020 --> 00:42:14,420
+يبقى نمر بيه بلاحظ أن المعامل لـ Y prime هو T
+
+370
+00:42:14,420 --> 00:42:20,940
+إذا حضر نقسم المعادلة كلها علامين على T يبقى بيصير
+
+371
+00:42:20,940 --> 00:42:29,220
+المعادلة Y prime زائد واحد زائد واحد على T في الـ Y
+
+372
+00:42:29,220 --> 00:42:36,080
+بيساوي كده واحد هذه هي المعادلة رقم star اللالي
+
+373
+00:42:38,620 --> 00:42:46,620
+يبقى الـ mu of T يبقى إيه؟ تكامل واحد زائد واحد
+
+374
+00:42:46,620 --> 00:42:53,000
+على T  بـT يبقى هذا الكلام بيساوي إيه؟ تكامل
+
+375
+00:42:53,000 --> 00:43:01,670
+الواحد بـT وادي زائد ln T يعني يا بنات هذه بقدر
+
+376
+00:43:01,670 --> 00:43:11,450
+أقول E أس T في E أس ln T لأن عند ضرب تجمع الأسس
+
+377
+00:43:11,450 --> 00:43:17,290
+مش هتروح تقولي هذه E أس T زائد E أس ln T كلام
+
+378
+00:43:17,290 --> 00:43:22,550
+خاطر يعني هذا ضرب وعند ضرب جمعنا مين؟ جمعنا الأسس
+
+379
+00:43:22,550 --> 00:43:31,440
+هذه كلها بقدرش يبقى صارة المسألة T E أس T يبقى
+
+380
+00:43:31,440 --> 00:43:35,420
+هذا هو عامل التكامل اللي عندنا الآن بنجي على
+
+381
+00:43:35,420 --> 00:43:41,520
+المعادلة star و بنروح نضربها T E
+
+431
+00:49:17,320 --> 00:49:23,720
+n of x y هي واحد صحيح طيب افترضي بالصدر الله إيه
+
+432
+00:49:23,720 --> 00:49:30,510
+لو خلت إن ال M function في X فقط و M function في Y
+
+433
+00:49:30,510 --> 00:49:37,010
+فقط يبقى المعادلة هذه بيبدأ تصير dy by x سوى M of
+
+434
+00:49:37,010 --> 00:49:40,070
+X على N of Y
+
+435
+00:49:44,330 --> 00:49:52,670
+M of y بدي y يساوي M of x مالها دفسي بكيان مفاصلة
+
+436
+00:49:52,670 --> 00:49:57,050
+اللي فيهم y لحال مش ناحية و اللي فيهم ال x where
+
+437
+00:49:57,050 --> 00:50:03,670
+بناحية ثانية كيانة فاصلة متغيرة طيب أنا بدي y تروح
+
+438
+00:50:03,670 --> 00:50:09,550
+بكامل الطرفين تكامل هذه هجيب لي y تكامل هذه هجيب
+
+439
+00:50:09,550 --> 00:50:12,650
+لي دالة بدالة دالة أو هذا بيجيب لي دالة بدالة ال x
+
+440
+00:50:12,910 --> 00:50:18,910
+وهذا بيدل دالة بدلالة Y ومن ثم يكون خلاصنا جيبنا
+
+441
+00:50:18,910 --> 00:50:26,190
+حصل على شكل Y سواء كانت Y صريحة أو ضمنية ضمنيش
+
+442
+00:50:26,190 --> 00:50:30,070
+ضمني إن أنا جلبت جيب Y as a function of it سواء
+
+443
+00:50:30,070 --> 00:50:37,370
+كانت دالة صريحة أو دالة implicit أو غير يعني دالة
+
+444
+00:50:37,370 --> 00:50:42,330
+ضمنية أو دالة صريحة يبقى بالحلها بواصفة ال
+
+445
+00:50:42,330 --> 00:50:47,290
+integration الآن بالتالي ناخد أمثلة توضيحية على
+
+446
+00:50:47,290 --> 00:50:51,190
+الشغل يعني يا بنات الشغل دلوقتي لحد ما أطلع في
+
+447
+00:50:51,190 --> 00:50:55,130
+المعادلة بدي أحاول أفصل ال X لحالي و ال Y لحالي
+
+448
+00:50:55,130 --> 00:51:02,530
+أكمل أنت خلصت أي مسألة ناخد أمثلة يبقى example one
+
+449
+00:51:13,190 --> 00:51:18,270
+and following differential
+
+450
+00:51:18,270 --> 00:51:21,370
+equation
+
+451
+00:51:21,370 --> 00:51:24,890
+المعادلة
+
+452
+00:51:24,890 --> 00:51:37,630
+الأولى نمرا M dy by dx dy by dx يسمى E أس Y أصيني
+
+453
+00:51:37,630 --> 00:51:38,690
+اثنين X
+
+454
+00:51:42,480 --> 00:51:51,160
+E أوسي اثنين Y كله فيه cosine X نمرى به السؤال
+
+455
+00:51:51,160 --> 00:52:02,640
+الثاني إنه X ال Y' يساوي واحد ناقص Y' كله أُس نص
+
+456
+00:52:17,190 --> 00:52:22,490
+السؤال بيقول يحل كل من المعادلات التفاضلية التالية
+
+457
+00:52:22,490 --> 00:52:29,530
+السؤال الأول dy by x يساوي e قُص y cosine من x على y
+
+458
+00:52:29,530 --> 00:52:32,290
+ناقص e قُص 2y cosine من x
+
+459
+00:52:41,640 --> 00:52:45,980
+يجب أن أقول المعادلة هذه هروح أكتبها على الشكل
+
+460
+00:52:45,980 --> 00:52:51,960
+التالي شو هيك لو ضربت في dx مرة واحدة في الطرفين
+
+461
+00:52:51,960 --> 00:52:53,380
+إيش بيصير عندنا
+
+462
+00:53:08,650 --> 00:53:22,070
+كله فيه cos X dx طب أبطال أيه لبنان؟ ال function
+
+463
+00:53:22,070 --> 00:53:25,770
+في Y يعني و الباقي بيبقى ال function بمين؟ X يعني
+
+464
+00:53:25,770 --> 00:53:28,850
+معناه تبقى اللي ده تخلص من هنا يعني بتروح X من
+
+465
+00:53:28,850 --> 00:53:33,770
+الطرفين عليه يعني لو جسمت الطرفين عليه شو بيصير
+
+466
+00:53:33,770 --> 00:53:38,110
+عن الإرمالات؟ Y ناقص E
+
+467
+00:53:42,230 --> 00:53:47,670
+dy يساوي شويه في هذه sin 2X مش هي عبارة عن ما
+
+468
+00:53:47,670 --> 00:53:58,130
+عندنا sin X بيكون sin X على sin X كثير طيب تكتبها
+
+469
+00:53:58,130 --> 00:54:10,220
+بصورة أخرى هذه Y في E-Y ناقص EY كله في dy يبقى هذه
+
+470
+00:54:10,220 --> 00:54:14,300
+على هذه الطلاقة فوق بيشيلت سالف هذه مع هذه تفصل
+
+471
+00:54:14,300 --> 00:54:25,200
+بظل E أس Y cos X مع cos X يبقى 2sin X ب dx يبقى هذه
+
+472
+00:54:25,200 --> 00:54:31,760
+فصلنا يا بنات ال Y لوحدها و ال X لوحدها يبقى
+
+473
+00:54:31,760 --> 00:54:36,340
+الآن بجهة كاملة الطرفين بحصل على مين على ثاني حل
+
+474
+00:54:36,340 --> 00:54:39,080
+يبقى بجهة كاملة هذه
+
+475
+00:54:47,490 --> 00:55:00,210
+يبقى أنا أنا أنا أنا
+
+476
+00:55:00,210 --> 00:55:03,630
+أنا
+
+477
+00:55:03,630 --> 00:55:04,450
+أنا أنا أنا أنا أنا أنا أنا أنا أنا أنا أنا
+
+478
+00:55:04,450 --> 00:55:04,470
+أنا أنا أنا أنا أنا أنا أنا أنا أنا أنا أنا
+
+479
+00:55:04,470 --> 00:55:09,150
+أنا أنا أنا أنا أنا واحد لو كاملها بنفسها مقسمة على
+
+480
+00:55:09,150 --> 00:55:13,550
+سالب واحد مقسمة على سالب واحد والله مضروبة في سالب
+
+481
+00:55:13,550 --> 00:55:21,050
+واحد هي نفسها طيب مشتاق كمان مرة يبقى نفسها مقسمة
+
+482
+00:55:21,050 --> 00:55:26,210
+على سالب واحد بسالب الشّخصية بالموجب يبقى هذه بالهذه
+
+483
+00:55:26,210 --> 00:55:31,230
+بالموجب و هذه بالهذه بالسالب يبقى بالتكامل بسرعة
+
+484
+00:55:31,230 --> 00:55:40,640
+النّهاية بيصير عندنا ناقص Y e قُص ناقص Y ناقص e قُص ناقص Y
+
+485
+00:55:40,640 --> 00:55:47,900
+وهنا وصلنا لناقص هي الناقص وتكامل ال e قُص Y بال e قُص
+
+486
+00:55:47,900 --> 00:55:53,560
+Y itself تمام؟
+
+487
+00:55:53,560 --> 00:55:59,940
+يبقى هاي تكامل التّنّتين وهذه زي ما هي e قُص Y نجي
+
+488
+00:55:59,940 --> 00:56:11,350
+لهذه هذه تكاملت سالب اثنين و sin ال X زائد و sin طب
+
+489
+00:56:11,350 --> 00:56:17,570
+إيش رايح؟ لو ضربت كله في E أُس Y عشان أخلص منها
+
+490
+00:56:17,570 --> 00:56:25,070
+السّوالة ده أو لو ضربت كله في سالب E أُس سالب Y لو
+
+491
+00:56:25,070 --> 00:56:31,740
+ضربت هذه كلها السالب E والسالب E والسالب E والسالب
+
+492
+00:56:31,740 --> 00:56:36,700
+E والسالب E والسالب E والسالب E والسالب E والسالب
+
+493
+00:56:36,700 --> 00:56:37,640
+E والسالب E والسالب E والسالب E والسالب E والسالب
+
+494
+00:56:37,640 --> 00:56:39,480
+E والسالب E والسالب E والسالب E والسالب E والسالب
+
+495
+00:56:39,480 --> 00:56:39,540
+E والسالب E والسالب E والسالب E والسالب E والسالب
+
+496
+00:56:39,540 --> 00:56:41,520
+E والسالب E والسالب E والسالب E والسالب E والسالب
+
+497
+00:56:41,520 --> 00:56:50,100
+E والسالب E والسالب E والسالب
+
+498
+00:56:50,100 --> 00:56:55,900
+E والس
+
+499
+00:56:55,950 --> 00:57:10,650
+يقص يقص يقص يقص يقص يقص يقص يقص يقص يقص يقص يقص
+
+500
+00:57:10,650 --> 00:57:19,950
+يقص يقص يقص يقص يقص يقص
+
+501
+00:57:25,690 --> 00:57:30,310
+مش Y في ناحية و X في ناحية لأن هذه حالة المعادلة
+
+502
+00:57:30,310 --> 00:57:35,530
+الأولى اللي هي عامة نجي للمعادلة الثانية نجي لنمرا
+
+503
+00:57:35,530 --> 00:57:41,770
+B نمرا B لأننا نحاول نفصل المتغيرات فنروح أكثر
+
+504
+00:57:41,770 --> 00:57:50,750
+المعادلة على الشكل التالي X ب dy على dx يساوي جدر
+
+505
+00:57:50,750 --> 00:58:00,680
+التربيعي لو أحد ناقص Y تربيع أول انشرتنا فقلنا E1
+
+506
+00:58:00,680 --> 00:58:06,240
+على الجذر التربيعي العارف واقع صغير التربيع يسمى
+
+507
+00:58:06,240 --> 00:58:13,140
+dx على X فجسمي على هذه dx تطلع هنا و X تنزل تحت
+
+508
+00:58:13,140 --> 00:58:18,100
+الشكل اللي عندنا هذا لأن المعادلة أخذت الشكل
+
+509
+00:58:18,100 --> 00:58:24,920
+الجديد اللي قدامنا هذا كده إيش تكمل المادة الأولى يا
+
+510
+00:58:24,920 --> 00:58:31,100
+بنات؟ Y على الجذر التربيعي لواحد ناقص Y تربيع؟ كده؟
+
+511
+00:58:31,100 --> 00:58:40,280
+sin .. sin إيه؟ كده؟ sin .. sin ألف sin ألف سواء فجو
+
+512
+00:58:40,280 --> 00:58:48,520
+كانت بزايد تحت الجذر؟ تحت الجذر تحت الجذر
+
+513
+00:59:05,040 --> 00:59:12,400
+مش تكامل آخر كل معادلة تفاضلية عندك هي تكاملين يا
+
+514
+00:59:12,400 --> 00:59:20,260
+جلوة كم أنت بيصير عندي Y inverse Y يساوي ln absolute
+
+515
+00:59:20,260 --> 00:59:26,040
+value ل X زي المادة زي ال consistency هذه بقدر
+
+516
+00:59:26,040 --> 00:59:29,500
+أجيب لها Y في دعنّي أو لا بقدر أجيب لها ثاني أو لا
+
+517
+00:59:29,500 --> 00:59:33,300
+بقدر أجيب لها ثاني أو لا بقدر أجيب لها ثاني أو لا
+
+518
+00:59:33,300 --> 00:59:33,620
+بقدر أجيب لها ثاني أو لا بقدر أجيب لها ثاني أو لا
+
+519
+00:59:33,620 --> 00:59:34,600
+بقدر أجيب لها ثاني أو لا بقدر أجيب لها ثاني أو لا
+
+520
+00:59:34,600 --> 00:59:41,340
+بقدر أجيب لها ثاني أو لا بقدر أجيب لها ثاني
+
+521
+00:59:41,340 --> 00:59:45,520
+أو لا بقدر أ
+
+522
+00:59:49,940 --> 00:59:56,740
+لل absolute value ل X زائد constant C هذا هو عبارة
+
+523
+00:59:56,740 --> 00:59:59,640
+عن حل المعادلة التفاضلية
+
+524
+01:00:33,640 --> 01:00:34,700
+ثالث نهار
+
+525
+01:00:53,960 --> 01:01:09,460
+convolution of the following national problems على
+
+526
+01:01:09,460 --> 01:01:20,440
+نمرا إيه؟ نمرا إيه؟ Determine Determine
+
+527
+01:01:20,440 --> 01:01:21,740
+لل interval
+
+528
+01:01:25,900 --> 01:01:37,280
+في الفترة in which the solution
+
+529
+01:01:37,280 --> 01:01:44,240
+is valid
+
+530
+01:01:44,240 --> 01:01:50,000
+أولى
+
+531
+01:01:50,000 --> 01:01:53,860
+وراي ثانوية
+
+532
+01:01:56,460 --> 01:02:11,660
+ناقص x تربيع plus نص dy يساوي sin inverse x dx و y
+
+533
+01:02:11,660 --> 01:02:20,340
+يعني زي رمزية تساوي واحد نقطة ثانية لأن ال y prime
+
+534
+01:02:20,340 --> 01:02:30,740
+هي بساوي XY تكعيب في واحد زائد تكعيب في cos ناقص
+
+535
+01:02:30,740 --> 01:02:39,520
+نصف وY عند Zero كذلك يسمى الواحد
+
+536
+01:03:03,640 --> 01:03:07,860
+يقول يا حل كل مثال كل مثالة تهم الحقيقية
+
+537
+01:03:07,860 --> 01:03:12,620
+أتغلب وهذه الفترة اللي اتحل عليها تكون صحيحة أو
+
+538
+01:03:12,620 --> 01:03:18,140
+اتحل معرفة على هذه الفكرة تظل الدولة اللي عندهم
+
+539
+01:03:18,140 --> 01:03:22,420
+هذه والحمد لله يبقوا عصر ال instance لحال ومغارز لحال
+
+540
+01:03:22,420 --> 01:03:29,730
+بس فيهم هذه هذه ال instance إذا ممكن نفسي مقترفين
+
+541
+01:03:29,730 --> 01:03:36,730
+عليه لأن جبالي مجرده هنا من المفتة الأولى La
+
+542
+01:03:36,730 --> 01:03:50,500
+differential equation SY تربيع Dy Y تربيع Dy يساوي
+
+543
+01:03:50,500 --> 01:03:56,580
+Sine Inverse X على الجذر التربيعي اللي راح يتناقص
+
+544
+01:03:56,580 --> 01:04:04,200
+X تربيع DX اضغط طبعا في الشمال ثانية واتكلم وف
+
+545
+01:04:04,200 --> 01:04:08,000
+أنت سهل
+
+546
+01:04:08,000 --> 01:04:14,370
+أنا عارف ناشيلكن لو جد كلمات قادرين منها تقدر تقول
+
+547
+01:04:14,370 --> 01:04:22,890
+تكامل Y تربيع dy يساوي تكامل ل sin inverse x هذا
+
+548
+01:04:22,890 --> 01:04:28,430
+يقول عارفين منها يعني
+
+549
+01:04:28,430 --> 01:04:36,010
+هذه d ل sin inverse x مظبوط؟ يعني استبدال من
+
+550
+01:04:36,010 --> 01:04:40,780
+المقدار هذا كله بديه ال sin inverse يعني مشتق ال
+
+551
+01:04:40,780 --> 01:04:43,900
+sin inverse يعني مشتق ال sin inverse بيكون واحد
+
+552
+01:04:43,900 --> 01:04:46,100
+نقل تقرير واحد نقل تقرير نقل تقرير نقل تقرير نقل
+
+553
+01:04:46,100 --> 01:04:49,840
+تقرير نقل تقرير نقل تقرير نقل تقرير نقل تقرير نقل
+
+554
+01:04:49,840 --> 01:04:50,560
+تقرير نقل تقرير نقل تقرير نقل تقرير نقل تقرير نقل
+
+555
+01:04:50,560 --> 01:04:51,520
+تقرير نقل تقرير نقل تقرير نقل تقرير نقل تقرير نقل
+
+556
+01:04:51,520 --> 01:04:53,800
+تقرير نقل تقرير نقل تقرير نقل تقرير نقل تقرير نقل
+
+557
+01:04:53,800 --> 01:05:01,380
+تقرير نقل تقرير نقل تقرير نقل تقرير
+
+558
+01:05:05,550 --> 01:05:11,850
+مش مصير إنه هنا مصير إنه Y تكعيب يساوي ثلاثة على
+
+559
+01:05:11,850 --> 01:05:20,390
+اثنين sin inverse x لكل تربيع زائد ثلاثة c طب معقن
+
+560
+01:05:20,390 --> 01:05:26,230
+ياناس ال condition إنه Y عند Zero يساوي جذر واحد
+
+561
+01:05:26,230 --> 01:05:33,010
+يعني لو كانت x ب Zero في Y جذر واحد يبقى واحد إن
+
+562
+01:05:33,010 --> 01:05:47,000
+كنت تكعيب بتساوي ثلاثة على اثنين في sin inverse صفر يبقى
+
+563
+01:05:47,000 --> 01:05:54,440
+هذه Zero كل تربيع زي ثلاثة C يبقى مصير واحد تساوي
+
+564
+01:05:54,440 --> 01:06:01,940
+ثلاثة C وهذا بيعطيك المصير تساوي جذر واحد تساوي الكل
+
+565
+01:06:02,620 --> 01:06:08,620
+يبقى بالإنها العالية بيصير علينا Y تكعيب بدي يساوي
+
+566
+01:06:08,620 --> 01:06:16,260
+ثلاثة على اثنين لـ sin inverse X كل تربيع زائد
+
+567
+01:06:16,260 --> 01:06:28,680
+واحد تمام أو Y تساوي الجذر التّالث لـ Vزي ثلاثة على
+
+568
+01:06:28,680 --> 01:06:35,060
+اثنين ثلاثة على اثنين sin inverse x والتّربية
+
+569
+01:06:35,060 --> 01:06:39,540
+دائرة خلاص
+
+570
+01:06:39,540 --> 01:06:45,640
+لسه المطلوب الأول يومين اللي هو ال solution يبقى
+
+571
+01:06:45,640 --> 01:06:51,720
+من حد ما بدأنا هنا بدأنا في أمريكا والعزل أمريكا
+
+572
+01:06:51,720 --> 01:06:57,940
+دي هذه الفترة اللي الحل عليها هذا بيكون صحيح باجي
+
+573
+01:06:57,940 --> 01:07:03,140
+بسأل نفسي هذا الجذر الثالث جذر الثالث معرف لل Zero
+
+574
+01:07:03,140 --> 01:07:08,900
+والموجب والسالب بدون مشاكل مظبوط؟ صح هاي شو
+
+575
+01:07:08,900 --> 01:07:12,940
+المشكلة وين؟ المشكلة في ال sin inverse ال sin
+
+576
+01:07:12,940 --> 01:07:16,940
+inverse في الدرجة اللي عم نقولها وين؟ من سالب واحد
+
+577
+01:07:16,940 --> 01:07:21,770
+إلى واحد من سالب واحد إلى واحد هذه مظبوط يجب أن
+
+578
+01:07:21,770 --> 01:07:26,730
+أنا أتخذ دائما وأبدا معرضة من سالب واحد إلى واحد
+
+579
+01:07:26,730 --> 01:07:32,550
+وأروح بقول له هنا فاصلة ال X أكبر من أو تساوي سالب
+
+580
+01:07:32,550 --> 01:07:36,790
+واحد أو أقل من أو تساوي سالب واحد أو لأسلوب بل ال X
+
+581
+01:07:36,790 --> 01:07:41,750
+أقل من أو تساوي واحد يبقى هذه ال interval اللي اتحل
+
+582
+01:07:41,750 --> 01:07:50,250
+عليها معرض يبقى هذه جبت من وين كان فلسطين من
+
+583
+01:07:50,250 --> 01:07:55,750
+معلوماتي عن معقوذ اللي هو scientist كان فلسطين طيب
+
+584
+01:07:55,750 --> 01:08:02,050
+نجي لنمرا اثنين نمرا اثنين بيقول y واي فاي يساوي
+
+585
+01:08:02,050 --> 01:08:09,150
+XY تكعيب ده بيعني المثل اللي عندنا يعني ده أقدر أقوله
+
+586
+01:08:09,150 --> 01:08:14,690
+ال equation as تجاهته بالمعادلة على الشكل التالي
+
+587
+01:08:14,690 --> 01:08:24,210
+اللي هو مين؟ dy by dx يساوي هذا X على الجدر
+
+588
+01:08:24,210 --> 01:08:35,210
+التربيعي لواحد زائد X تربيع 8 من Y تكعيب يبقى هذا
+
+589
+01:08:35,210 --> 01:08:39,590
+الجذر كان في الواقع غيبت الإشارة طبعا نزل في
+
+590
+01:08:39,590 --> 01:08:45,620
+المقام وظلت عند X Y تكعيب فوق هذه مدرسة رسمها على
+
+591
+01:08:45,620 --> 01:08:53,140
+الشكل التالي dy على Y تكعيب جسمنا كله على Y تكعيب
+
+592
+01:08:53,140 --> 01:09:01,120
+وضربنا في dx بيصير X في dx على الجذر التربيعي لواحد
+
+593
+01:09:01,120 --> 01:09:07,820
+زائد X تربيع يعني يا بنات كأن الرسم صارت تكامل Y
+
+594
+01:09:07,820 --> 01:09:16,150
+تكعيب dy يساوي تكامل X على جذر تربيعي من واحد زي
+
+595
+01:09:16,150 --> 01:09:24,730
+X تربيع dx أظن الشمال سهل تكمله بقول يا بابا
+
+596
+01:09:24,730 --> 01:09:31,490
+الكل أصين نفرض واحد تربيع إذا
+
+597
+01:09:31,490 --> 01:09:38,190
+أنا لو حطيتي W يساوي واحد زائد X تربيع واش تعطي
+
+598
+01:09:38,190 --> 01:09:43,910
+إنجاز من X dx ما عنديش اثنينات إنجاز نص dw
+
+599
+01:09:47,720 --> 01:09:54,420
+يبقى بيصير المسألة هذه هذه النص برا وهذه تكامل
+
+600
+01:09:54,420 --> 01:10:06,540
+وهنا dw على جذر w أو تكامل dy أثناء تس ثلاثة dy
+
+601
+01:10:06,540 --> 01:10:16,440
+يساوي النص تكامل w أثناء تس نص dw يبقى هذا بالصينية
+
+602
+01:10:16,440 --> 01:10:25,580
+Y أس ناقص اثنين على ناقص اثنين يساوي النص في W أُس
+
+603
+01:10:25,580 --> 01:10:32,180
+أضيف ناقص واحد وأكسب على ناقص الجديد يبقى هذا نص
+
+604
+01:10:32,180 --> 01:10:41,220
+على نص زائد كلستانسيه يبقى نص على نص يبقى هذه صارت
+
+605
+01:10:41,22
+
+646
+01:15:34,850 --> 01:15:40,950
+تكس تربية فالأكبر من Zero ممنوع يسوى Zero لو سوى
+
+647
+01:15:40,950 --> 01:15:46,290
+Zero لأصبح أحد واحد على صفر لما نخلق Seal and Defy
+
+648
+01:15:46,290 --> 01:15:50,770
+يبقى بنات من الحل ال Inquality هذا يبقى لو كان
+
+649
+01:15:50,770 --> 01:15:55,770
+حللها بصير اتنين القدر التربية يلا واحد زائد تكس
+
+650
+01:15:55,770 --> 01:16:04,340
+تربية أقل من مائة أقل من دلالة أوبصير عندنا الجدر
+
+651
+01:16:04,340 --> 01:16:12,160
+التربيع إلى واحد زائد X تربيع أقل من 3 على 2 أقرب
+
+652
+01:16:12,160 --> 01:16:17,280
+الطرفين بصير عندك واحد زائد X تربيع
+
+653
+01:16:34,640 --> 01:16:39,220
+خد الجدر التربيعي يبقى الجدر التربيعي بتطلعلي
+
+654
+01:16:39,220 --> 01:16:45,960
+absolute value لأكس أقل من جدر 5 على 2 يبقى هذه
+
+655
+01:16:45,960 --> 01:16:54,200
+الفترة اللي بحل عليها يكونوا صحيحا طيب
+
+656
+01:16:54,200 --> 01:16:59,000
+ال switch نحن الآن اتذهل منه لكن انا احط زجاج في
+
+657
+01:16:59,000 --> 01:17:03,660
+ال exercises حالة دي اسمها homogeneous function
+
+658
+01:17:04,690 --> 01:17:10,770
+طبعاً بدنا نعطي تعريف لها ونشوف كذا كتاب طبعا حطه
+
+659
+01:17:10,770 --> 01:17:16,830
+حطه لها مجموعة للاسم يبقى موجودة لحالة اسمها ال
+
+660
+01:17:16,830 --> 01:17:23,050
+homogenous situations
+
+661
+01:17:23,050 --> 01:17:33,660
+وهذه موجودة in the exercises اللي هم in exercise دي
+
+662
+01:17:33,660 --> 01:17:38,940
+اتنين اتنين لو كده في التمانين وليس في جزء النظر
+
+663
+01:17:38,940 --> 01:17:48,780
+نعطيها تعريف ونشوف كيف انتجها the first order
+
+664
+01:17:48,780 --> 01:18:03,100
+the first order differential equation dy by dx بنسميه
+
+665
+01:18:03,100 --> 01:18:16,420
+homogeneous if
+
+666
+01:18:16,420 --> 01:18:32,330
+ال F of XY can be written can be written as هي a
+
+667
+01:18:32,330 --> 01:18:42,870
+function of the ratio y على x هو
+
+668
+01:18:42,870 --> 01:18:58,610
+الaccelerator denomination that is a n f dy y dx
+
+669
+01:19:01,200 --> 01:19:11,640
+F of X of Y بدي سوى capital F of Y على X وهذه
+
+670
+01:19:11,640 --> 01:19:20,320
+سبيها المعادلة رقم واحد ويصير
+
+671
+01:19:20,320 --> 01:19:27,720
+question
+
+672
+01:19:27,720 --> 01:19:29,480
+one
+
+673
+01:19:31,690 --> 01:19:32,510
+I was four
+
+674
+01:20:11,720 --> 01:20:18,000
+يقول المقال كذا يقول المعارضة بدا اشيل ال y على x
+
+675
+01:20:18,000 --> 01:20:25,940
+و اضطرها للمتميزة الجديدة والذات من ال V اضطر ال y
+
+676
+01:20:25,940 --> 01:20:34,900
+على x يساوي ال V او المعارضة هذه ممكن اقول Y تساوي
+
+677
+01:20:34,900 --> 01:20:40,880
+X PV بدا نشتقها كاله اشتقناها
+
+678
+01:20:57,930 --> 01:21:04,030
+مرة تانية مشتقة ال y هي dy على dx هذي مشتقة حصل
+
+679
+01:21:04,030 --> 01:21:09,630
+ضغط دقلتين مشتقة الأولى في الثانية زائد الأولى في
+
+680
+01:21:09,630 --> 01:21:14,430
+المشتقة في الضغط الثاني القلب تمسك المعلومة اللي
+
+681
+01:21:14,430 --> 01:21:20,520
+حصلت عليها وعوّضها في المعادلة رقم واحد يعنيبدي
+
+682
+01:21:20,520 --> 01:21:25,080
+أشيل dy على dx مكتوب بدلها main المعادلة اللي
+
+683
+01:21:25,080 --> 01:21:36,540
+عندناها ينجي هنا substitute in equation one we
+
+684
+01:21:36,540 --> 01:21:46,120
+get نقصد علامات dy على dx يكون v زائد x دي v على
+
+685
+01:21:46,120 --> 01:21:55,200
+dx الطرف اليمين بصير F of B المعادلة
+
+686
+01:21:55,200 --> 01:22:02,580
+هذه بقدر اكتبها على الشكل التالي XGB على DX بتساوي
+
+687
+01:22:02,580 --> 01:22:13,200
+F of B ناقص ال B نقدر نفصل المتغيرات يبقى هذه
+
+688
+01:22:13,200 --> 01:22:28,390
+بتصير EVعلى F of V مقص ال V بتساوي DX على X ده
+
+689
+01:22:28,390 --> 01:22:32,750
+شوية وصلة Superbola كلها يبقى بنحل كذلك وكلها بنحل
+
+690
+01:22:32,750 --> 01:22:41,030
+قبل قليل يلقى دي Superbola equation
+
+691
+01:22:41,030 --> 01:22:46,030
+ده كان
+
+692
+01:22:49,090 --> 01:22:58,310
+بsize as before ناخد
+
+693
+01:22:58,310 --> 01:22:59,590
+مثال توضيح عليه
+
+694
+01:23:41,060 --> 01:23:46,320
+ومن ثم Solve
+
+695
+01:23:48,530 --> 01:24:05,890
+إذا تبقى N dy على dx يساوي 4y ناقص 3x على 2x ناقص 
+
+696
+01:24:05,890 --> 01:24:06,190
+y
+
+697
+01:24:35,120 --> 01:24:39,020
+سؤال مرحبا يقول بيبينلي إذا المعادلات التي
+
+698
+01:24:39,020 --> 01:24:45,640
+تستخدمها هي عبارة عن معادلات متجانسة مميزة وبيتم
+
+699
+01:24:45,640 --> 01:24:51,380
+حل هذه المعادلة بيقول الشريف أو الساجل إذا تقدر
+
+700
+01:24:51,380 --> 01:24:57,720
+تقول المعادلة كلها لدلالة y على x أو x على y تصير
+
+701
+01:24:57,720 --> 01:25:02,390
+مميزة بس ممنوع يكون مثلا واحد على X وخمسة على Y
+
+702
+01:25:02,390 --> 01:25:07,150
+ممنوع على كده بدي يكون Y على X أو X على Y لإن لو
+
+703
+01:25:07,150 --> 01:25:11,890
+كنت وصلت لحاله مش مشكلة خالص طبعا يبقى يبقى يبقى
+
+704
+01:25:11,890 --> 01:25:19,190
+كله solution dy على dx يسبب شو رأيك لو جسمت بس
+
+705
+01:25:19,190 --> 01:25:30,310
+والمقام على X كله مش بصير اربع Y على X ناخذ تلاتة
+
+706
+01:25:30,310 --> 01:25:38,750
+على اتنين ناخذ y على x صح ولا لا؟ جسم كله من
+
+707
+01:25:38,750 --> 01:25:42,870
+البصرة والمقام على x الطبعي صارت معادلة لدلالة y
+
+708
+01:25:42,870 --> 01:25:47,650
+على x ولا لا؟ زي ما قلنا صارت function بس احنا
+
+709
+01:25:47,650 --> 01:25:53,490
+صارت function of y على capital F of y على x بنبدأ
+
+710
+01:25:53,490 --> 01:25:57,130
+نعمل عليها المادة homogeneous differential
+
+711
+01:25:57,130 --> 01:26:02,270
+equation يبقى هذا الصغير هو homogeneous
+
+712
+01:26:02,270 --> 01:26:08,850
+differential equation ليشوف كيف نحل ال homogeneous
+
+713
+01:26:08,850 --> 01:26:16,270
+differential equation نيجي نقوله خُد Y على X تساوي
+
+714
+01:26:16,270 --> 01:26:21,630
+Z فانشطرنا تقولنا Y تساوي X
+
+715
+01:26:26,060 --> 01:26:35,600
+DX ممكن نسوي V ذائب X في DV على DX لما عادلتنا
+
+716
+01:26:35,600 --> 01:26:40,940
+هصير على الشكل التالي هشير DY على DX و اكتب قيمتها
+
+717
+01:26:40,940 --> 01:26:50,660
+اللي هي V ذائب X في DV على DX على الطرف
+
+718
+01:26:50,660 --> 01:26:59,660
+الشمال نيجي للطرف اليمين انه أربعة V ناقص تلاتة على
+
+719
+01:26:59,660 --> 01:27:10,540
+اتنين ناقص V نود V على الشجرة التالية يتجسر X بـDV
+
+720
+01:27:10,540 --> 01:27:20,440
+على DX يساوي أربعة V ناقص تلاتة على اتنين ناقص V
+
+721
+01:27:20,440 --> 01:27:28,220
+ناقص V اضافنا للثلاثين لوساوية V هذه بدرة واحدة
+
+722
+01:27:28,220 --> 01:27:36,060
+لهذه المفاهيم يا بنات كبسيل X DV على DX يساوي كله
+
+723
+01:27:36,060 --> 01:27:47,380
+على اتنين ناقص V يظل اربعة V ناقص تلاتة وهذه
+
+724
+01:27:47,380 --> 01:27:57,020
+باعتماد على واحدة تنضرب لناقص V اتنين ناقص V وحتى
+
+725
+01:27:57,020 --> 01:28:05,140
+مقامتنا الكل يبقى X DV على DX يبقى اتنين ناقص V
+
+726
+01:28:05,140 --> 01:28:15,540
+بالمقام هنا اربعة V ناقص تلاتة ناقص اتنين V زائد V
+
+727
+01:28:15,540 --> 01:28:26,670
+تربيع يبقى صارة المثلة اللي هو X DV على dx u7 أي b
+
+728
+01:28:26,670 --> 01:28:36,070
+تربيع وعنفه نقص 2u زائد 4a زائد 2b وغيرها جداش نقص
+
+729
+01:28:36,070 --> 01:28:42,950
+تلاتة مافيش غيرها على الاثنين ناقصين فالشك اللي
+
+730
+01:28:42,950 --> 01:28:47,870
+بيكتبها بدلالة b والشك اسمها بدلالة x وb
+
+731
+01:28:51,860 --> 01:28:58,020
+يبقى هذا شبسيدي اتنين ناقص V على V تربيع زائد
+
+732
+01:28:58,020 --> 01:29:06,320
+اتنين V ناقص تلاتة DV يبقى يسوى DX على X يبقى هذا
+
+733
+01:29:06,320 --> 01:29:14,720
+C Parabol equation يبقى هذا C Parabol equation
+
+734
+01:29:14,720 --> 01:29:24,840
+السؤال هو هذه تقبل very easily يبقى المينكيف نتكلم
+
+735
+01:29:24,840 --> 01:29:34,840
+طبش مدد؟ حالي للمعادلة، مقصود A، مقصود B، مقصود A،
+
+736
+01:29:34,840 --> 01:29:35,480
+مقصود B، مقصود A، مقصود B، مقصود A، مقصود B، مقصود
+
+737
+01:29:35,480 --> 01:29:35,540
+A، مقصود B، مقصود A، مقصود B، مقصود A، مقصود B،
+
+738
+01:29:35,540 --> 01:29:37,520
+B، مقصود A، مقصود B، مقصود A، مقصود B، مقصود A،
+
+739
+01:29:37,520 --> 01:29:42,300
+مقصود A، مقصود B، مقصود A، مقصود A، مقصود B، مقصود
+
+740
+01:29:42,300 --> 01:29:52,310
+A، مقصود A، مقصود A، مقصود هذه بيه وهذه بيه وهذه
+
+741
+01:29:52,310 --> 01:29:58,450
+واحد وهذه ثلاثة وهذه زائد وهذه ناقص ناقص بيه زائد
+
+742
+01:29:58,450 --> 01:30:06,010
+تلاتة بيه زائد اتنين بيه كيف تسرع مع القوة؟ كسور
+
+743
+01:30:06,010 --> 01:30:12,870
+يزمية كسور يزمية ممتازة اتراكتوز يبقى هذا الكلام
+
+744
+01:30:12,870 --> 01:30:20,370
+متساوي هذا قوس اللي هو بيه ناقص واحد و بس تاني D زي
+
+745
+01:30:20,370 --> 01:30:26,950
+التلاتة عاملين كل واحد من القاعدة الأولى و اتنين
+
+746
+01:30:26,950 --> 01:30:33,210
+are different اتنين كولوستان و كمان كولوستان تاني
+
+747
+01:30:33,210 --> 01:30:39,330
+بدنا نتخلص من هذه التسورة و نروح نطلب اتنين في هذا
+
+748
+01:30:39,330 --> 01:30:46,060
+المقام اطلب العربي عندك اطلب اتنين في D ناقص واحد و
+
+749
+01:30:46,060 --> 01:30:53,720
+B زائد تلاتة بنحصل على اتنين ناقص B يساوي A في B
+
+750
+01:30:53,720 --> 01:31:02,120
+زائد تلاتة زائد B في B ناقص واحد يجب اقولك لو كانت
+
+751
+01:31:02,120 --> 01:31:11,360
+ال B تساوي واحد then اتنين ناقص واحد يساوي اربعة A
+
+752
+01:31:11,360 --> 01:31:15,600
+وهذه مع السلامة يبقى هذا بدي اعطيك
+
+753
+01:31:18,560 --> 01:31:27,760
+ناقص واحد يساوي واحد الان لو كان ال V يكون ناقص
+
+754
+01:31:27,760 --> 01:31:35,880
+ثلاثة then يصير اتنين زائد ثلاثة ناقص ناقص ثلاثة
+
+755
+01:31:35,880 --> 01:31:42,340
+يعني زائد ثلاثة ناقص ثلاثة يبقى هنا ناقص ثلاثة
+
+756
+01:31:42,340 --> 01:31:51,740
+ناقص اربع دي يمكن ناقص اربع دي يبقى D مساوى سنة
+
+757
+01:31:51,740 --> 01:31:58,800
+وخمس أربعة يبقى مثلتنا صارت على الشكل التالي اللي
+
+758
+01:31:58,800 --> 01:32:06,060
+هو تكامل نمينا الطلب ثالث الأربعة و الرابعة تانية
+
+759
+01:32:06,060 --> 01:32:17,230
+الرابعة وهنا واحد على V مافس واحد في DV وهنا ناقص
+
+760
+01:32:17,230 --> 01:32:27,590
+بله خمس أربع وهنا واحد على B زائد تلاتة وهي
+
+761
+01:32:27,590 --> 01:32:31,990
+التكامل دي فيها الطرف الشمالي لجهة التكامل هذا
+
+762
+01:32:31,990 --> 01:32:36,530
+ساعطه عليه التكامل اللي اتنين هؤلاء اللي بيساوي
+
+763
+01:32:36,530 --> 01:32:41,350
+تكامل من B X على X
+
+764
+01:32:54,940 --> 01:33:05,160
+طيب لان كله blend يبقى ربع لل absolute value لل V
+
+765
+01:33:05,160 --> 01:33:14,560
+ناقص خمس أربع لل absolute value لل V
+
+766
+01:33:14,560 --> 01:33:21,580
+زائد تلاتة لل V زائد تلاتة بدنا نسوي التلاتة
+
+767
+01:33:21,770 --> 01:33:28,190
+absolute value ل X زائد كل ثانية C شو رايش نموذج
+
+768
+01:33:28,190 --> 01:33:34,970
+أربعة و نتخلص منها؟ شو حسن؟ يبقى بسيطة عندي اللم و
+
+769
+01:33:34,970 --> 01:33:42,690
+ال V اللي هو Y على X ناقص واحد ناقص خمسة لم Y على
+
+770
+01:33:42,690 --> 01:33:49,810
+X زائد تلاتة يساوي أربعة لم absolute value ل X
+
+771
+01:33:49,810 --> 01:34:01,830
+زائد أربعة C one مثلًا طيب هذه بصيها لان absolute
+
+772
+01:34:01,830 --> 01:34:11,570
+value ل Y ناقص X كله على X ناقص خمسة لان Y زائد
+
+773
+01:34:11,570 --> 01:34:19,370
+ثلاثة X كله على X وهنا بتساوي أربعة لان
+
+774
+01:34:23,380 --> 01:34:29,840
+هذا يبقى ناقص بالصير لل absolute value لل Y ناقص X
+
+775
+01:34:29,840 --> 01:34:36,960
+ناقص لل absolute value ل X هذه ناقص خمسة لل
+
+776
+01:34:36,960 --> 01:34:45,720
+absolute value لتلاتة X Y زائد تلاتة X ناقص مع
+
+777
+01:34:45,720 --> 01:34:52,360
+ناقص بالصير زائد خمسةLin Absolute Value of X يساوي
+
+778
+01:34:52,360 --> 01:35:01,380
+4Lin Absolute Value of X زائد 4C1 طيب دعونا نشوف
+
+779
+01:35:01,380 --> 01:35:10,060
+هذي هذي و هذي كتاش مضالين 4Lin X وديها على ناحية
+
+780
+01:35:10,060 --> 01:35:19,240
+التانية تتجهل مع السلم صح؟ طيب هذي بتصير إيش؟ بتصير
+
+781
+01:35:19,240 --> 01:35:27,000
+لل absolute value ل Y ناقص X ناقص لل absolute
+
+782
+01:35:27,000 --> 01:35:36,200
+value ل Y زي 3X خُص 5 يساوي 4Ci
+
+783
+01:35:47,790 --> 01:35:55,530
+هذه جمبسة يبقى اني بصير lamb salute value ل Y ماقص
+
+784
+01:35:55,530 --> 01:36:06,770
+X على Y زائد تلاتة X هذه كل قص خمسة يساوي أربعة
+
+785
+01:36:06,770 --> 01:36:17,060
+سيران كده تخلص من ال lamb يبقى بصير ان solute value
+
+786
+01:36:17,060 --> 01:36:24,120
+of y-x على solute value of y زائد تلاتة كل وصة
+
+787
+01:36:24,120 --> 01:36:32,760
+خمسة يسوى D أربعة C واحد الشرايح هذه كلها بترحبها
+
+788
+01:36:32,760 --> 01:36:38,780
+في C صح ولا لا يبقى بناء علينا solution
+
+789
+01:36:42,800 --> 01:36:51,160
+absolute value لروعي ناقص x يسوى c ان ال absolute
+
+790
+01:36:51,160 --> 01:36:58,620
+value لروعي ثائر ثلاثة و نصف خمسة يجعل هذا الحل
+
+791
+01:36:58,620 --> 01:37:04,420
+الامر لا يزال هناك سؤال كثير موجود 
diff --git a/PL9fwy3NUQKwa8ZDfSFGn6H8xVFLzqmCZC/0yOo6En_6XI_postprocess.srt b/PL9fwy3NUQKwa8ZDfSFGn6H8xVFLzqmCZC/0yOo6En_6XI_postprocess.srt
new file mode 100644
index 0000000000000000000000000000000000000000..1cea2d04e7da557915c1448fea36f6fb02c273b2
--- /dev/null
+++ b/PL9fwy3NUQKwa8ZDfSFGn6H8xVFLzqmCZC/0yOo6En_6XI_postprocess.srt
@@ -0,0 +1,3164 @@
+1
+00:00:09,200 --> 00:00:14,260
+المعادلة التفاصيلية من غطبة الأولى وهذه السنة
+
+2
+00:00:14,260 --> 00:00:20,760
+أخدنا منها عدة أصفر من المعادلة سنبدأ بالمعادلة
+
+3
+00:00:20,760 --> 00:00:26,240
+الأولى من linear equations المعادلات الخطوية
+
+4
+00:00:26,240 --> 00:00:32,350
+بإنقسام مدرسof integrating factors طريقة عواجة
+
+5
+00:00:32,350 --> 00:00:37,690
+بالتكابل طبعا سنعرف بعد قليل ماهو عامل التكابل
+
+6
+00:00:37,690 --> 00:00:44,870
+ولمانه سمى هذا العمل عامل التكابل إذا كنا نعطي
+
+7
+00:00:44,870 --> 00:00:48,970
+تعريف لشكل ال test of the diffusion equation ثم
+
+8
+00:00:48,970 --> 00:00:56,050
+نضعها على أرض الواقع بمعادرة ونبدأ عن هذه المعادرة
+
+9
+00:00:58,350 --> 00:01:04,630
+طيبة عامة للمعادلة التفاظرية من عبارة بالأولى يدفع
+
+10
+00:01:04,630 --> 00:01:09,010
+قضة integration هي عبارة عن integration in default
+
+11
+00:01:09,010 --> 00:01:14,790
+الشكل الثاني dy على d is a product of d وy يعني
+
+12
+00:01:14,790 --> 00:01:19,590
+المشتق الأولى للدالة y بالنسبة الى d هي عبارة عن
+
+13
+00:01:19,590 --> 00:01:24,930
+function demand في d وyطبعا ماعنديش معادلة واضحة
+
+14
+00:01:24,930 --> 00:01:29,250
+يمكن ادى حلوة بقى لذلك لذلك روحنا حاطين هذه
+
+15
+00:01:29,250 --> 00:01:33,590
+المعادلة في الصيغة اللى ممكن نبدأ نشغلها فروحنا
+
+16
+00:01:33,590 --> 00:01:38,190
+نقول ذاتي اي ان المعادلة هذه كتبة على الشكل التالي
+
+17
+00:01:38,190 --> 00:01:44,500
+في Y بيديوين ذات P of P في Y سواء مين P of Pالآن
+
+18
+00:01:44,500 --> 00:01:47,900
+لو خلّيت dy على dt في الناحية هذه ونجمنا هذه على
+
+19
+00:01:47,900 --> 00:01:52,960
+الشجة هذه بصير اطراف اليمين كله function في y وt
+
+20
+00:01:52,960 --> 00:01:57,300
+زي ما قلنا هنا او function في t و y اذا ال
+
+21
+00:01:57,300 --> 00:02:02,040
+function في t و y ساكتبها من الأن فتعيدا على الشكل
+
+22
+00:02:02,040 --> 00:02:07,240
+التالي dy by dt زي ال P of P في ال Y بيبقى سوى G
+
+23
+00:02:07,240 --> 00:02:12,690
+of P ال P of P هي عبارة عن function في Tو ال V of
+
+24
+00:02:12,690 --> 00:02:17,110
+T كذلك function أخرى في T والتنتين are continuous
+
+25
+00:02:17,110 --> 00:02:22,590
+على فترة ما يرجى هدول دوال متصلة بالنسبة لمين
+
+26
+00:02:22,590 --> 00:02:29,590
+للمتغير T وكل واحدة فيهم function في T فقط يعني
+
+27
+00:02:29,590 --> 00:02:34,700
+تكتببدلالة T بيجي ال function of T في Y بيسوي ال
+
+28
+00:02:34,700 --> 00:02:40,120
+function of T لوحديها الان بيجي الى كيفية حل هذه
+
+29
+00:02:40,120 --> 00:02:45,920
+المعادلة التفاضلية فبقى بيقول مشان انحلي المعادلة
+
+30
+00:02:45,920 --> 00:02:50,940
+التفاضلية هذه اللي هسميها star بيذهي اختار دالة من
+
+31
+00:02:50,940 --> 00:02:58,230
+عندى هذه الدالة بيسميها Mu of Zلـ Mu of T بحيث الـ
+
+32
+00:02:58,230 --> 00:03:03,630
+Mu of T بدى اتحقق شغل معين يعني انا لكل مثلة بتروح
+
+33
+00:03:03,630 --> 00:03:09,570
+اختار Mu of T لأ احنا من هذا سنصل الى صيغة هذه
+
+34
+00:03:09,570 --> 00:03:15,190
+الصيغة بتعطينى شكل لـ Mu of T بدلالة الـ P of T
+
+35
+00:03:15,190 --> 00:03:19,650
+تبع ال function الان يبقى بدنا نختار ال function
+
+36
+00:03:19,650 --> 00:03:26,660
+Mu of T such that بحيثو جيب ضربت ميو of P في الطرف
+
+37
+00:03:26,660 --> 00:03:37,680
+الأيسر لميو of P في BY by DT زائد P of P في ال Y
+
+38
+00:03:37,680 --> 00:03:49,240
+هذا الكلام بساوي لميو of P في ال Y طبعا
+
+39
+00:03:49,900 --> 00:03:55,800
+يبقى احنا الان بدنا نختار اللي هو الـ mu of t اللي
+
+40
+00:03:55,800 --> 00:04:01,360
+هي الدالة الموجة التي لا تأخذ الا قيمة موجة تحقيق
+
+41
+00:04:01,360 --> 00:04:07,080
+لي هذه العلاقة يبقى هذه العلاقة لأن انا الـ mu of
+
+42
+00:04:07,080 --> 00:04:11,580
+t لما اضربها في الطرف الشمال هذي بقدر اجمع الـ mu
+
+43
+00:04:11,580 --> 00:04:18,400
+of t مع ال Y واخد له مشتكة حاطم ضرب بالتيلطيب الان
+
+44
+00:04:18,400 --> 00:04:22,960
+بدي ابحث ماهو شكل ال new of T إذا مشان أحصل على
+
+45
+00:04:22,960 --> 00:04:27,420
+شكل ال new of T بدي أفك الجثة ده و أفك المشتقى
+
+46
+00:04:27,420 --> 00:04:32,520
+اللي عندنا هذه فلو جيت فكت الجثة ده ال new of T
+
+47
+00:04:32,520 --> 00:04:38,200
+هذه البنات هسميها wire prime بس لسه هذا الشكل ده
+
+48
+00:04:38,200 --> 00:04:44,720
+دايما من المعادلة زائد ل new of T
+
+49
+00:05:01,340 --> 00:05:07,240
+طب تعالوا نقارن بين الطقسين في هذه المعادلة طلعيلي
+
+50
+00:05:07,240 --> 00:05:12,160
+في ال term هذا و ال term هذاإن إثنين are the same
+
+51
+00:05:12,160 --> 00:05:17,260
+صحيح ولا لأ؟ إذا لما أتقل واحد عند الثاني أو أضيفه
+
+52
+00:05:17,260 --> 00:05:22,820
+إليه بإشارة مخالفة إتنين هدول بضيوف وبيبقى عند
+
+53
+00:05:22,820 --> 00:05:31,500
+المعادلة الثانية ل mu of T ال P of T في ال Y يساوي
+
+54
+00:05:31,500 --> 00:05:39,460
+U prime of T في من Y وسميلي هذه المعادلة رقم أحد
+
+55
+00:05:41,140 --> 00:05:45,640
+تبقى كويس الان بدنا نيجي على المعادلة اللي عندنا
+
+56
+00:05:45,640 --> 00:05:51,060
+star هادي بدي اضربها في ال mu of T اضرب طرفيها
+
+57
+00:05:51,060 --> 00:05:56,440
+يفجأة بتروح اضرب طرفي المعادلة star بال mu of T
+
+58
+00:05:56,440 --> 00:06:03,840
+هروح اقولهم multiply multiply
+
+59
+00:06:03,840 --> 00:06:13,340
+both sides of equationالسعر اللي احنا بدنا نحلها
+
+60
+00:06:13,340 --> 00:06:23,060
+by ميو of P we get نحصل على يفجر داشي ده يصير لميو
+
+61
+00:06:23,060 --> 00:06:33,340
+of P ال Y prime زائد لميو of P ال P of T في ال Y
+
+62
+00:06:33,340 --> 00:06:38,320
+يساوي لميو of P ال D of T
+
+63
+00:06:41,630 --> 00:06:48,230
+طبعا تلاحظ ميو اف تي ميو اف تي في الواي بقدر
+
+64
+00:06:48,230 --> 00:06:52,990
+اشيلها و اكتب بدلها مين ميو برايم اف تي في الواي
+
+65
+00:06:52,990 --> 00:06:58,910
+يبقى هذه كلها بقدر اشيلها و اكتب بدلها ميو برايم
+
+66
+00:06:58,910 --> 00:07:04,990
+اف تي في مين في الواي يبقى هذه بالصيف ميو اف تي في
+
+67
+00:07:04,990 --> 00:07:11,580
+الواي برايم زيدي ميو برايم اف تي في الواييستوي Mu
+
+68
+00:07:11,580 --> 00:07:18,860
+of T بالG of T وهذا الكلام from one يبقى هذا
+
+69
+00:07:18,860 --> 00:07:23,060
+جيبناه من المعادلة اللي تحت اللي عندنا طب أطلعيه
+
+70
+00:07:23,060 --> 00:07:28,440
+للآن في الشكل اللي على الشمال هذا أليس هذا هو
+
+71
+00:07:28,440 --> 00:07:33,450
+مستقل حاصل ضرب ذلتين صح ولا لا؟يبقى بدي أجمع
+
+72
+00:07:33,450 --> 00:07:40,470
+الدلتين بمشتقة واحدة يبقى بصير عندي الـMu of T في
+
+73
+00:07:40,470 --> 00:07:47,950
+الـY Phi كله بده يساوي الـMu of T في الـG of T
+
+74
+00:07:55,290 --> 00:08:01,150
+طبعا الحقيقة ان استعجلت شوية يعني كان خاطر احسب من
+
+75
+00:08:01,150 --> 00:08:07,830
+هذه المعادلة ما هو شكل ل mu of t قبل مضرب هذه طبعا
+
+76
+00:08:07,830 --> 00:08:12,310
+يبقى انا بس استعجلت شوية يبقى من هذه المعادلة يا
+
+77
+00:08:12,310 --> 00:08:19,630
+بنات بقدر اجيب شكل من شكل ل mu of t وكيف بتروح ال
+
+78
+00:08:19,630 --> 00:08:25,770
+y مع ال yلو قسمت الطرفين على الـ mu of t ياسي
+
+79
+00:08:25,770 --> 00:08:31,990
+بيصير عندنا هنا بيصير الـ mu prime of t على الـ mu
+
+80
+00:08:31,990 --> 00:08:38,050
+of t بده يساوي الـ P of T لما
+
+81
+00:08:38,050 --> 00:08:39,550
+تروح ال Y مع Y
+
+82
+00:08:47,220 --> 00:08:56,350
+ميو الـ P of T على ميو الـ P of Tيبقى ال bus تقاضه
+
+83
+00:08:56,350 --> 00:08:59,890
+للمقام لما يكون ال bus تقاضه للمقام يبقى التكامل
+
+84
+00:08:59,890 --> 00:09:05,770
+لن absolute value للمقام لكن المقام انا مختاره
+
+85
+00:09:05,770 --> 00:09:11,350
+positive يبقى ال absolute value لا داعي له يبقى
+
+86
+00:09:11,350 --> 00:09:20,410
+بصير عندنا لن المئة of T بده يساوي تكامل P of T بT
+
+87
+00:09:20,410 --> 00:09:28,270
+زائد كنفة K مثلاالـ Colossal K هذا يا بنات بدي
+
+88
+00:09:28,270 --> 00:09:31,050
+اخده كله بجداش B0
+
+89
+00:09:33,800 --> 00:09:38,640
+طيب يبقى لو أخدت ال constant دي ربوضال عند مين لإن
+
+90
+00:09:38,640 --> 00:09:45,180
+mu of T بده يساوي تكامل P of T dt يبقى بناء عليه
+
+91
+00:09:45,180 --> 00:09:52,400
+لو رفعت اتنين كأس للعدد E بصير E أس لإن mu of T
+
+92
+00:09:52,400 --> 00:10:02,060
+بده يساوي E أس تكامل P of Tبناءً على الـ E والدول
+
+93
+00:10:02,060 --> 00:10:05,720
+اللي اتنين هذول عكس ضبط يبجى واحدة بتنغي الثانية
+
+94
+00:10:05,720 --> 00:10:10,240
+يبجى هذا بده يعطينا الـ Mu of T اللي أنا بدور
+
+95
+00:10:10,240 --> 00:10:18,940
+عليها E أستكامل T of T دي T يبجى
+
+96
+00:10:18,940 --> 00:10:23,920
+هذا شكل الـ Mu of T زي ما انتوا شايفين اعتمدت على
+
+97
+00:10:23,920 --> 00:10:30,870
+مين اعتمدت على المعامل بتابعي ال Yوهنا المعامل تبع
+
+98
+00:10:30,870 --> 00:10:36,730
+ال Y' هو جدّيك واحد صحيح تمام تمام يبقى من الآن
+
+99
+00:10:36,730 --> 00:10:40,870
+فصاعدا لما يكون عندي first order differential
+
+100
+00:10:40,870 --> 00:10:47,190
+equation والمعامل تبع ال dy by dt هو الواحد الصحيح
+
+101
+00:10:47,190 --> 00:10:51,450
+بيكون شكل ال integrating factor mu of t هو ال
+
+102
+00:10:51,450 --> 00:10:58,000
+exponential مرفوه للأس تكامل P of T dtوهذا ما
+
+103
+00:10:58,000 --> 00:11:04,920
+أصنعه مع كل سؤال عند الحل طب الآن بدنا نعرف ما هو
+
+104
+00:11:04,920 --> 00:11:10,060
+شكل الحل للمعادلة التفاضلي اللي عندنا طب نروح نقول
+
+105
+00:11:10,060 --> 00:11:14,500
+نضرب كل term من ال term سبعة المعادلة التفاضلي
+
+106
+00:11:14,500 --> 00:11:19,500
+اللي عندنا في الميو of T بنستبدل هذا بالميو prime
+
+107
+00:11:19,500 --> 00:11:25,020
+of T في ال Yهدول كلهم كمشتقة واحدة يساوي مين؟
+
+108
+00:11:25,020 --> 00:11:32,180
+يساوي لأن لو كاملت الطرفين يبقى by integration
+
+109
+00:11:32,180 --> 00:11:35,480
+بواسطة
+
+110
+00:11:35,480 --> 00:11:42,780
+التكامل بيصير عندنا ل mu of T في ال Y يسوى تكامل ل
+
+111
+00:11:42,780 --> 00:11:50,360
+mu of T في G of T DT الزائد كنستنسيأنا مابدي الـ
+
+112
+00:11:50,360 --> 00:11:57,380
+mu of d في y بدي y يبقى بروح بقول هنا the solution
+
+113
+00:11:57,380 --> 00:12:11,380
+of the differential equation star is y تساوي واحد
+
+114
+00:12:11,380 --> 00:12:21,650
+على ال mu of d فيتكامل لـ Mu of T في G of T DT
+
+115
+00:12:21,650 --> 00:12:29,090
+ذائب كونستانسي هذا شكل الحل تبع المعادلة التفاضلية
+
+116
+00:12:29,090 --> 00:12:37,350
+الهمين Star لحد هنا انتهت جزء النظري تبع ال linear
+
+117
+00:12:37,350 --> 00:12:40,890
+pairs of all differential equationsلو جاني السؤال
+
+118
+00:12:40,890 --> 00:12:46,110
+بده يتبع نفس التكتيك بده أروح أجيب له قيمة لـMU of
+
+119
+00:12:46,110 --> 00:12:51,650
+T بعدين أضرب طرفين المعادلة في الـMU of T وبعدين
+
+120
+00:12:51,650 --> 00:12:58,250
+كده أكامل بحصل على حل المعادلة التفاضلية بس قبل
+
+121
+00:12:58,250 --> 00:13:01,910
+هيكل الخطرة هكتب ملاحظة حتى ماتنسهاش بجهة مكتوبة
+
+122
+00:13:01,910 --> 00:13:08,390
+عندكمشان ناخد الـ mu of t بطريقة صحيحة بدي يكون
+
+123
+00:13:08,390 --> 00:13:14,090
+المعامل هنا هو واحد صحيح اثنين بدي تبقى المعادلة
+
+124
+00:13:14,090 --> 00:13:17,850
+في نفس الشكل اللي عندنا هذا مش تبقى P of T ثوائي
+
+125
+00:13:17,850 --> 00:13:21,190
+تربيع مثلا يبقى المستقل أولى ل Y
+
+126
+00:13:27,390 --> 00:13:32,990
+معادلة يتفجأ في الشكل هذا و المعامل هنا جداش و حطش
+
+127
+00:13:32,990 --> 00:13:36,450
+ان شاء الله يكون اتنين بيتجسم على اتنين قبل ما
+
+128
+00:13:36,450 --> 00:13:42,170
+تحسب ال mu of t يعني اي معامل هنا ل y prime بدنا
+
+129
+00:13:42,170 --> 00:13:48,110
+نجسم عليه قبل ان نبدأ بالحل أكتب لهذا على شكل
+
+130
+00:13:48,110 --> 00:13:52,880
+ملاحظة حتى ما تنسهاشإن شاء الله و تعالى أثناء
+
+131
+00:13:52,880 --> 00:13:56,300
+الحجز
+
+132
+00:13:56,300 --> 00:14:02,740
+ابقى
+
+133
+00:14:02,740 --> 00:14:10,500
+not before
+
+134
+00:14:10,500 --> 00:14:14,480
+confusing
+
+135
+00:14:14,480 --> 00:14:18,000
+قبل ما تعجبك
+
+136
+00:14:43,680 --> 00:14:51,560
+بتتأكد يعني to make sure thatthe differential
+
+137
+00:14:51,560 --> 00:15:03,140
+equation المعادلة التفابلية is exactly is exactly
+
+138
+00:15:03,140 --> 00:15:15,480
+in the form of a star and the coefficient and
+
+139
+00:15:15,480 --> 00:15:25,680
+thethe coefficient of
+
+140
+00:15:25,680 --> 00:15:29,740
+y' is واحد صحيح
+
+141
+00:15:47,500 --> 00:15:54,520
+the example one find
+
+142
+00:15:54,520 --> 00:16:08,240
+the general solution of
+
+143
+00:16:08,240 --> 00:16:15,020
+the following differential equation
+
+144
+00:16:19,460 --> 00:16:29,120
+the differential equation and use it and use it to
+
+145
+00:16:29,120 --> 00:16:35,260
+determine عشان
+
+146
+00:16:35,260 --> 00:16:43,180
+نحدد how solutions solutions
+
+147
+00:16:43,180 --> 00:16:46,340
+they have
+
+148
+00:16:57,690 --> 00:17:06,390
+السؤال الأول نمرة A سؤال ستة من الكتاب تقول تي واي
+
+149
+00:17:06,390 --> 00:17:16,930
+فراين زائد اتنين واي تساوي صين تي والتي أكتر من
+
+150
+00:17:16,930 --> 00:17:28,330
+ازرع نمرة ZY'زائد Y يساوي ثلاثة
+
+151
+00:17:51,900 --> 00:17:55,600
+سؤال مرة تانية طبعا زي ما تشاهدين فيه مطموبين
+
+152
+00:17:55,600 --> 00:17:59,540
+المطموب الأول بيقول هاتل ال general solution لكل
+
+153
+00:17:59,540 --> 00:18:04,280
+من المعادلات التفاغبالية التالية واستخدم الحل اللي
+
+154
+00:18:04,280 --> 00:18:11,300
+جبته مشان تحدد كيف الحل behave بكل سلوكه او شكله
+
+155
+00:18:11,300 --> 00:18:16,880
+لما تي تكبرها بمقدار كبير جدا يعني تصل الى ما لا
+
+156
+00:18:16,880 --> 00:18:23,290
+نهاية نقوله solutionوالنجي للمعادلة الأولى
+
+157
+00:18:23,290 --> 00:18:26,490
+الملاحظة اللى احنا كتبينها هنا لازم يكون معامل y'
+
+158
+00:18:26,730 --> 00:18:31,630
+مجدد اذا من جاب الكل شيء المعادلة هذه بنروح اقسم
+
+159
+00:18:31,630 --> 00:18:38,010
+الطرفين عالميا على C يبقى باقي بقوله نمر ايه
+
+160
+00:18:41,140 --> 00:18:50,760
+Equation S لو جسمت على P بيصير Y' ذائبين على T في
+
+161
+00:18:50,760 --> 00:19:00,440
+Y بده يساوي 5T على 2 على T وهذه سميها اللي اللي هي
+
+162
+00:19:00,440 --> 00:19:05,060
+المعادلة الأصلية Star اللي بدنا نحلها يبقى الأن
+
+163
+00:19:05,060 --> 00:19:08,980
+بدنا نروح نجيب عامل التكامل Integrating factors
+
+164
+00:19:09,300 --> 00:19:17,220
+يبقى الـ Mu of P أخدناها قبل قليل E أستكامل P of T
+
+165
+00:19:17,220 --> 00:19:23,080
+بيتي يبقى هذا الكلام اللي يساوي E أستكامل P of T
+
+166
+00:19:23,080 --> 00:19:27,560
+صارت جباش تين على تين لكن لو ما جسملاش يا بنات
+
+167
+00:19:27,560 --> 00:19:32,200
+سالجتيها تنين وبالتالي وجعنا في مشكلة عويصة يبقى
+
+168
+00:19:32,200 --> 00:19:38,950
+باجي بقوله تنين على تين في بيتيهذا الكلام بده
+
+169
+00:19:38,950 --> 00:19:45,050
+يساوي E أس اتنين برا التكامل بقول جبات واحد على T
+
+170
+00:19:45,050 --> 00:19:51,950
+DT اللي هي لن T يبجى اتنين لن T وليس لن absolute
+
+171
+00:19:51,950 --> 00:19:57,670
+value ل T لأنه قلنا هنا T مالها greater than zero
+
+172
+00:19:57,670 --> 00:20:04,090
+اكبر من ال zero يبجى هذه E أس لن T تربية مصبوب
+
+173
+00:20:04,090 --> 00:20:11,280
+هكذامن أين جلبنا هذا المعلومة؟ من كالكولوز بيه؟
+
+174
+00:20:11,280 --> 00:20:15,720
+تمام تمام يبقى يادروا يتساوي تيتر بيعملوا فيك
+
+175
+00:20:15,720 --> 00:20:21,060
+برضه؟ لأن ال E و S X و L X كل واحدة فيهم inverse
+
+176
+00:20:21,060 --> 00:20:25,380
+لمين للتانية بتلغيها ويظل يتنقل لمين تيتر بيعمل،
+
+177
+00:20:25,380 --> 00:20:29,840
+إذا بناء عليهأصبح الـ integrating factor mu of T
+
+178
+00:20:29,840 --> 00:20:35,400
+بدي ساوي قداش T تربيع الان بنجي للمعادلة star كلها
+
+179
+00:20:35,400 --> 00:20:40,380
+و بنضربها في مام T تربيع يبقى بقى دي بقوله هنا
+
+180
+00:20:40,380 --> 00:20:45,380
+multiply both
+
+181
+00:20:45,380 --> 00:20:59,340
+sides of equation star by T تربيع we getنحصل على I
+
+182
+00:20:59,340 --> 00:21:12,080
+T تربيه Y T تربيه Y زائد 2T في ال Y يساوي T Phi T
+
+183
+00:21:12,080 --> 00:21:18,040
+مرة ثانية بدي أضغط هذه كلها في T تربيه لأن T تربيه
+
+184
+00:21:18,040 --> 00:21:26,520
+Y' T تربيه مع T تختصر ويبقى T فوق ب2 ب2T في ال Yهي
+
+185
+00:21:26,520 --> 00:21:34,120
+تربيعه هنا تي بضل جداش تي صيني تي هي فوق تمام طيب
+
+186
+00:21:34,120 --> 00:21:38,580
+تطلعيلي في هذه شوف الجزء المظري يقول لنا بعد ما
+
+187
+00:21:38,580 --> 00:21:43,880
+نضرب عامل التكامل بصير هذا كله مشتفت حصل ضرب
+
+188
+00:21:43,880 --> 00:21:50,150
+دالتين بقدر أجمعه بدلة واحدة لكل primeطيب اتطلع يا
+
+189
+00:21:50,150 --> 00:21:56,930
+عزيزي أليس هذه هي عاملة تكامل قداش T تربية الدالة
+
+190
+00:21:56,930 --> 00:22:02,210
+الأصليه اليمين Y كله prime شوفيلي مشتقت هذا هو
+
+191
+00:22:02,210 --> 00:22:08,310
+الطرف هذا ولا لا ها T تربية في Y prime زائد Y
+
+192
+00:22:08,310 --> 00:22:14,010
+مشتقت T تربية ب2T يبقى 2TY هي مظبوط بكلامنا سليم
+
+193
+00:22:14,010 --> 00:22:32,460
+100% الشجة اليمينتساوي T في صينيتي تساوي
+
+194
+00:22:32,460 --> 00:22:34,700
+T في صينيتي تساوي T في صينيتي تساوي T في صينيتي
+
+195
+00:22:34,700 --> 00:22:34,820
+تساوي T في صينيتي تساوي T في صينيتي تساوي T في
+
+196
+00:22:34,820 --> 00:22:38,090
+تساوي T في صينيتي تساوي T في صينيتي تساوييبقى تر
+
+197
+00:22:38,090 --> 00:22:42,430
+بي او اي فرايم زي اثنين ت يساوي ت فاين ت كلها مع
+
+198
+00:22:42,430 --> 00:22:53,970
+بعضها ت تر بي او اي في كل فرايم تساوي ت فاين ت تر
+
+199
+00:22:53,970 --> 00:22:59,850
+بي او اي في كل فرايم تساوي ت فاين ت تر بي او اي في
+
+200
+00:22:59,850 --> 00:23:00,130
+كل فرايم ت تر بي او اي في كل فرايم ت تر بي او اي
+
+201
+00:23:00,130 --> 00:23:02,030
+او اي في كل فرايم ت ت تر بي او اي في كل فرايم ت ت
+
+202
+00:23:02,030 --> 00:23:05,190
+تر بي او اي في كل فرايم ت ت تر بي او اي في كل
+
+203
+00:23:05,190 --> 00:23:08,970
+فرايمهذه لسه مكنوية الاصل نفسه بالكونوستانت على
+
+204
+00:23:08,970 --> 00:23:12,950
+الشجة هذه وبعدين احاول على الشجة دي يجي اختصارا
+
+205
+00:23:12,950 --> 00:23:16,250
+بدل ما اعمل خطواتين خطوات واحدة يبقى زائد
+
+206
+00:23:16,250 --> 00:23:20,710
+كونوستانت C يبقى لو جدرت اكمل المعادلة اقدرها دي
+
+207
+00:23:20,710 --> 00:23:24,770
+يكون خلصنا من هذه الشغلات بنعرف نكملها دي يا بنات
+
+208
+00:23:24,770 --> 00:23:30,550
+باشر by part و بنعمللها جدول يبقى باجي بقوله هنا
+
+209
+00:23:30,550 --> 00:23:32,070
+بدي اخد ال derivative
+
+210
+00:23:35,240 --> 00:23:42,960
+وهنا بدى اخد انتجر علينى هذه ال اولى اللى هى T وهى
+
+211
+00:23:42,960 --> 00:23:48,440
+فاينى T يعنى فاينى T بدى اكملها على طول و T بدى
+
+212
+00:23:48,440 --> 00:23:54,700
+افضلها على طول اذا لا افضلها مرة جدش بطلع لو كملت
+
+213
+00:23:54,700 --> 00:24:00,530
+هذه مرة شو بطلع؟بدي أفضلها كمان مرة zero بدي أكمل
+
+214
+00:24:00,530 --> 00:24:04,430
+هذه كمان مرة sin P بعد ذلك بيجي الأقاعدة في
+
+215
+00:24:04,430 --> 00:24:08,950
+الإشارات هذه في هذه بالموجة وهذه في هذه بالسالب
+
+216
+00:24:08,950 --> 00:24:17,930
+إذا صار عندي P تربيه Y يساوي ناقص P P for sin P
+
+217
+00:24:17,930 --> 00:24:25,930
+زائد sin P زائد constant Cيبقى بدي ال solution
+
+218
+00:24:25,930 --> 00:24:33,130
+فبروح بقوله the solution is أنا مابدي T تربية Y
+
+219
+00:24:33,130 --> 00:24:38,850
+وإلا بدي main هي ال Y إذا بقسم كله على مين؟ على T
+
+220
+00:24:38,850 --> 00:24:49,030
+تربية يبقى Y بدي سوى C ذائب صيني T مقص T تقصيني T
+
+221
+00:24:49,030 --> 00:24:55,930
+كل هذا على مين؟ على T تربيةيبقى هذا شكل ال general
+
+222
+00:24:55,930 --> 00:25:02,210
+solution ل مام ل المعادلة التفاضلية لأن مام رقم
+
+223
+00:25:02,210 --> 00:25:07,010
+start خلصنا لسه المطلوب الأول من السؤالالمطلوب
+
+224
+00:25:07,010 --> 00:25:11,190
+التاني قال لي استخدم الحل اللي جيبته هذا
+
+225
+00:25:11,190 --> 00:25:19,110
+ههههههههههههههههههههههههههههههههههههههههههههههههههههههههههههههههههههههههههههههههههههههههههههههههههههههههههههههههههههههههههههههههههههههههههههههههههههههههههههههههههههههههههههههههههههههههههههههههههههههههههه
+
+226
+00:25:35,150 --> 00:25:44,130
+بدا تساوي limit لمن؟ ل C على T تربيع ذات sin T على
+
+227
+00:25:44,130 --> 00:25:54,630
+T تربيع ناقص cos T على T لما T بدا تروح إلى
+
+228
+00:25:54,630 --> 00:25:59,410
+infinity طيب
+
+229
+00:25:59,410 --> 00:26:02,370
+هذه لما T بدا تروح لملنهاف
+
+230
+00:26:05,900 --> 00:26:11,860
+أعدد عمله نهائي بـ0 يفجأها دي بـ0 أجت مشكلتنا مع
+
+231
+00:26:11,860 --> 00:26:19,960
+مين؟ مع sin T على T تربع طيب نرجع لCalculus A طبعا
+
+232
+00:26:19,960 --> 00:26:23,840
+عملناها في Calculus A بس نذكرها بدل A هو sin محصور
+
+233
+00:26:23,840 --> 00:26:32,430
+بين مين ومين؟ سالب واحد وواحد إذا sin Tمحصور ما
+
+234
+00:26:32,430 --> 00:26:37,090
+بين الواحد وما بين السالب واحد power of B للفرق
+
+235
+00:26:37,090 --> 00:26:43,530
+انتوا واحد على T تربيه يبقى اش بيصير سالب واحد على
+
+236
+00:26:43,530 --> 00:26:50,210
+T تربيه sign of T على T تربيه واحد على T تربيه
+
+237
+00:26:51,430 --> 00:26:55,630
+بنروح ناخد ال limit لما T بدها تروح لما لا نهاية
+
+238
+00:26:55,630 --> 00:27:00,870
+يجب عشان نصير عندنا هنا zero أقل من أو يساوي ال
+
+239
+00:27:00,870 --> 00:27:06,810
+limit لما T tends to infinity لصيني T على T تربية
+
+240
+00:27:06,810 --> 00:27:12,220
+أقل من أو يساوي ال zeroيبقى بـSandwich Theorem
+
+241
+00:27:12,220 --> 00:27:15,740
+يبقى
+
+242
+00:27:15,740 --> 00:27:21,980
+بـSandwich
+
+243
+00:27:21,980 --> 00:27:31,000
+Theorem يبقى بـSandwich
+
+244
+00:27:31,000 --> 00:27:37,020
+Theorem يبقى بـSandwich Theorem يبقى بـSandwich
+
+245
+00:27:37,020 --> 00:27:37,140
+Theorem يبقى بـSandwich Theorem يبقى بـSandwich
+
+246
+00:27:37,140 --> 00:27:37,480
+Theorem يبقى بـSandwich Theorem يبقى بـSandwich
+
+247
+00:27:37,480 --> 00:27:40,720
+Theorem يبقى بـSandwich Theorem يبقىبـ 0 كذلك يفجه
+
+248
+00:27:40,720 --> 00:27:47,340
+هنا بقى يبقى يقول الـ S Y بدأ تروح للـ 0 الـ T بدأ
+
+249
+00:27:47,340 --> 00:27:55,200
+تروح لوين؟ للإنفلي حد لايه سؤال هنا يا ناس؟ فهنا
+
+250
+00:27:55,200 --> 00:27:59,580
+من الحل كاملا نروح للمثال الثاني بس بدنا نشوف إذا
+
+251
+00:27:59,580 --> 00:28:06,800
+فيه تساوي ايه؟ ايه؟ نجي للمثال الثاني
+
+252
+00:28:14,060 --> 00:28:21,840
+يبقى نمر بي المعادلة عند بهاية نجسم
+
+253
+00:28:21,840 --> 00:28:28,160
+على تمام يبقى المعادلة بالصير اللي نمر بي y prime
+
+254
+00:28:28,160 --> 00:28:37,540
+زائد نص y يساوي ثلاثة على اتنين في ترابيع كويس
+
+255
+00:28:37,540 --> 00:28:44,870
+بدنا نروح نجيب عامل تكامل اللي هو الميو of Tيساوي
+
+256
+00:28:44,870 --> 00:28:53,190
+E أُس تكامل T of T اللي هو مُص DT يبقى هذا الكلام
+
+257
+00:28:53,190 --> 00:28:59,570
+يساوي E أُس T على تمام مُص T يعني T على تماميبقى
+
+258
+00:28:59,570 --> 00:29:04,030
+هذا عامل التكمل لنا يبقى الأن بدنا نروح المعادلة
+
+259
+00:29:04,030 --> 00:29:09,570
+هذه اللي صارت عندنا نسميها double star مشان أه ما
+
+260
+00:29:09,570 --> 00:29:13,890
+تختلف عن المعادلة L4 يبقى المعادلة هذه بتروح
+
+261
+00:29:13,890 --> 00:29:19,530
+أضربها في مين في E أوش E على 2 بروح و أقول لهم
+
+262
+00:29:19,530 --> 00:29:24,270
+multiply both
+
+263
+00:29:24,270 --> 00:29:28,190
+sides of
+
+264
+00:29:28,970 --> 00:29:39,990
+Equation double star by E أس T على اتنين نحصل
+
+265
+00:29:39,990 --> 00:29:40,330
+على
+
+266
+00:30:03,400 --> 00:30:08,220
+يبقى المعادلة دي بيصير على الشكل الساوي E أُس T
+
+267
+00:30:08,220 --> 00:30:18,540
+على تمام ال Y prime زائد نص E أُس T على تمام زائد
+
+268
+00:30:18,540 --> 00:30:26,200
+نص E أُس T على تمام في ال Y بيبقى ساوي تلاتة على
+
+269
+00:30:26,200 --> 00:30:30,920
+تمام E أُس T على تمام تمام fifty
+
+270
+00:30:34,070 --> 00:30:38,850
+طب تعالى نشوف يبجى بناء ان علي الطرف هذا بقدر
+
+271
+00:30:38,850 --> 00:30:43,970
+اتقبله على الشكل التاني اجمعه بترم واحد اللي هو
+
+272
+00:30:43,970 --> 00:30:51,690
+عامل التكامل مضروفا سواء لكل price لو مشتقته وما
+
+273
+00:30:51,690 --> 00:30:56,550
+طلعتش هذا يا بنات معناته حسابك هنا اه غلطي عامل
+
+274
+00:30:56,550 --> 00:31:00,910
+التكامل لازم يطلع المعادلة بالضباططب عادى لو جيت
+
+275
+00:31:00,910 --> 00:31:06,550
+اشتقها الاولى فى مشتقة الثانية هيه مجرد زي دى
+
+276
+00:31:06,550 --> 00:31:11,190
+التانية اللى هى Y فى مشتقة ال X ponential اللى هى
+
+277
+00:31:11,190 --> 00:31:17,010
+نفسها مضربة فى جديد فى نص يبقى هاى نص E أس T على
+
+278
+00:31:17,010 --> 00:31:22,250
+اتنين تبين فى ال Y بكلام سليم مائة بالمائة بادرساه
+
+279
+00:31:22,250 --> 00:31:26,610
+من الفرق الايمن فهو ثلاثة على اتنين
+
+280
+00:31:55,500 --> 00:31:56,900
+Eac²Eac²Eac²Eac²Eac²Eac²Eac²Eac²Eac²Eac²Eac²Eac²Eac²Eac²Eac²Eac²Eac²Eac²Eac²Eac²Eac²Eac²Eac²Eac²Eac²Eac²Eac²Eac²Eac²Eac²Eac²Eac²Eac²Eac²Eac²Eac²Eac²Eac²Eac²Eac²Eac²Eac²Eac²Eac²Eac²Eac²Eac²Eac²Eac²Eac²Eac²Eac²Eac²Eac²Eac²Eac²Eac²Eac²Eac²Eac²Eac²Eac²Eac²Eac²Eac²Eac²Eac²Eac²Eac²Eac²Eac²Eac²Eac²Eac²Eac
+
+281
+00:31:57,180 --> 00:32:04,580
+و بدي اخد هنا ال integral يبقى هاي ثلاثة على اتنين
+
+282
+00:32:04,580 --> 00:32:13,040
+اللي هو C تربيع هنا E أس T على اتنين بدي اشتق بصير
+
+283
+00:32:13,040 --> 00:32:19,520
+عندي جداش هنا بنات ثلاثة T فقط مغير لو كامل
+
+284
+00:32:19,520 --> 00:32:25,270
+تكاملها بنفسها مقسومة على جداشعلى نص النقطة اللي
+
+285
+00:32:25,270 --> 00:32:31,310
+فوق بصير اتنين تمام كمان مرة يبقى مشتقتها تلاتة
+
+286
+00:32:31,310 --> 00:32:36,790
+تكاملها باربع EOST على اتنين يعني اتنين مالكش
+
+287
+00:32:36,790 --> 00:32:40,770
+دعوات وهذه EOST على اتنين على نص اللي فوق بصير
+
+288
+00:32:40,770 --> 00:32:46,490
+اتنين يبقى اربع EOST على اتنينمشتق كمان مرة اللي
+
+289
+00:32:46,490 --> 00:32:53,970
+هي zero وكمل كمان مرة يبقى تمانية E أس T على 2 هدف
+
+290
+00:32:53,970 --> 00:32:59,350
+هدف إشارة موجب هدف هدف إشارة سالب هدف هدف إشارة
+
+291
+00:32:59,350 --> 00:33:05,790
+موجب يبقى لو تماننا بيصير E أس T على 2 في ال Y
+
+292
+00:33:05,790 --> 00:33:12,630
+يساويمضرب هذول في بعض النص بتروح مع التاني ويصير
+
+293
+00:33:12,630 --> 00:33:18,830
+ثلاثة في تربية E أس T على اتنين ثلاثة في تربية E
+
+294
+00:33:18,830 --> 00:33:24,150
+أس T على اتنين اللي بعدها ناقص ثلاثة في أربعة بطن
+
+295
+00:33:24,150 --> 00:33:31,370
+عشر في E أس T على اتنين اللي بعدها زائد أربعة
+
+296
+00:33:31,370 --> 00:33:38,200
+وعشرين E أس T على اتنينوزائد constant C
+
+297
+00:33:41,290 --> 00:33:47,650
+بدي أقسم كله على E أُس T على 2 يبقى لو قسمت بصير Y
+
+298
+00:33:47,650 --> 00:33:55,790
+يسوى تلاتة T تربية نقص اتناشر T زائد أربعة وعشرين
+
+299
+00:33:55,790 --> 00:34:04,130
+زائد C على E أُس T على 8 هذا هو من ال general
+
+300
+00:34:04,130 --> 00:34:13,790
+solution تبع المعادلة التفابلية طب كويسالان جالى
+
+301
+00:34:13,790 --> 00:34:18,710
+يشوفى ما هو سلوك الدالة او كيف بدى يكون سلوك
+
+302
+00:34:18,710 --> 00:34:23,710
+الدالة لما تى بدها تروح لوين للمالة نهاية بقول
+
+303
+00:34:23,710 --> 00:34:29,310
+الان لو تى راحت للمالة نهاية ايه فجدت ترمى فجدت؟
+
+304
+00:34:29,310 --> 00:34:38,170
+جدت؟ المالة عدد المالة نهاية بس0 يبقى هذا term عند
+
+305
+00:34:38,170 --> 00:34:43,170
+المالة نهائية يروح بـ0 بظل مين عند هذا term لهم
+
+306
+00:34:43,170 --> 00:34:46,910
+مالة نهائية ناقص اتناشر في المالة زاد اربعة وعشرين
+
+307
+00:34:46,910 --> 00:34:54,410
+يبقى هذا هو الذي سيتحكم في سلوك ابدالة لو رجعنا
+
+308
+00:34:54,410 --> 00:35:00,890
+الى تامة خلاصة A وليس B بجينا نقول الدالة من جزية
+
+309
+00:35:00,890 --> 00:35:06,190
+اللي هي فيه dominated term اجزاء التحكملما كنا في
+
+310
+00:35:06,190 --> 00:35:12,610
+الرسم البيانيلدالة ما فجينا نقول لعزيزي التحكم هذا
+
+311
+00:35:12,610 --> 00:35:18,450
+بيتحكم عند T تساوي ما لنهاية هذا مثلا بيتحكم عند T
+
+312
+00:35:18,450 --> 00:35:22,870
+تساوي Zero كنا بنقول او T تساوي اتنين او T تساوي
+
+313
+00:35:22,870 --> 00:35:28,510
+ثلاثة حسب طبيعة مين حسب طبيعة المثلة يبقى عند T
+
+314
+00:35:28,510 --> 00:35:31,810
+بيبدأ تساوي ما لنهاية هذا ال term بيبقى لانه Zero
+
+315
+00:35:31,810 --> 00:35:37,200
+و بيبقى لعيننا مين ال term هذايبقى الterm هذا
+
+316
+00:35:37,200 --> 00:35:42,740
+بيكون هو والمنحنى أصحاب بيجيسدوا مع بعض اللي
+
+317
+00:35:42,740 --> 00:35:48,990
+بيجينا نسميهم ال asymmetric خطور التقارب، مظبوط؟بس
+
+318
+00:35:48,990 --> 00:35:53,590
+هذا مش خط تقارب هذا منحنى على شكل فرابولة وماعمله
+
+319
+00:35:53,590 --> 00:35:57,870
+شيف لإنه معادلة من الدرجة التانية في T صحيح ولا
+
+320
+00:35:57,870 --> 00:36:04,850
+لأ؟ يفجأة بصير المنحنى asymptotic يعني كأنه تقارب
+
+321
+00:36:04,850 --> 00:36:10,830
+مع المنحنى اللي عندنا هذا تمام؟ يفجأة باجي بقوله
+
+322
+00:36:10,830 --> 00:36:17,010
+as T tends to infinity the solution
+
+323
+00:36:21,300 --> 00:36:34,780
+in asymptotic to the curve للمنحنة y تساوي تلاتة
+
+324
+00:36:34,780 --> 00:36:41,320
+تربيع ناقص اتناشر P زائد اربع وعشرين لإن عندي
+
+325
+00:36:41,320 --> 00:36:47,140
+المالة نهاية هذا كله بروح جديش P Zero بضلش الا هذا
+
+326
+00:36:49,490 --> 00:36:54,230
+حد يلاقي تساؤل هنا لازلنا في نفس ال section لسه
+
+327
+00:36:54,230 --> 00:37:04,110
+فيه مزيد من الأمثلة اه لأ
+
+328
+00:37:04,110 --> 00:37:09,130
+انا بفضل تشتغل زي ما اشتغلنا بديش تحفظي انا بدي
+
+329
+00:37:09,130 --> 00:37:14,540
+طريقة الخطوة تكون خطوة سلم للاخرىأنا قادر من عند
+
+330
+00:37:14,540 --> 00:37:18,140
+ما جبت الاسم من عند ما جبت ال integrated factor
+
+331
+00:37:18,140 --> 00:37:21,800
+اقول ال resolution واحد على ال mu of t تكامل g of
+
+332
+00:37:21,800 --> 00:37:26,020
+t mu of t dt ذات كنصارى وحطها دموعي انا بس انا
+
+333
+00:37:26,020 --> 00:37:31,400
+مدهش بد الشيء يكون بالترتيب فعلا طيب يا بنات احنا
+
+334
+00:37:31,400 --> 00:37:34,800
+المرة اللي فتت اعطانا تعريف لل initial value
+
+335
+00:37:34,800 --> 00:37:40,040
+problem لكن ما حللاش ولا مسألة initial value
+
+336
+00:37:40,040 --> 00:37:46,060
+problemالان بنتحول نحل مثلة initial value of
+
+337
+00:37:46,060 --> 00:37:52,260
+problem ونشوف كيف هتعملوا فيه يبقى المثال رقم
+
+338
+00:37:52,260 --> 00:37:56,400
+اتنين example
+
+339
+00:37:56,400 --> 00:38:04,500
+two solve
+
+340
+00:38:04,500 --> 00:38:07,720
+the
+
+341
+00:38:07,720 --> 00:38:09,380
+following
+
+342
+00:38:18,530 --> 00:38:28,910
+مثل الأولى نمر a y prime زي دي 8 على t في ال y
+
+343
+00:38:28,910 --> 00:38:37,830
+يساوي cosine t على t ترابيع و ال y عند ال y بدها
+
+344
+00:38:37,830 --> 00:38:48,240
+تساويو T greater than 0 نمرى D طبعا هذا سؤال 16 من
+
+345
+00:38:48,240 --> 00:38:55,620
+الكتاب وهذا سؤال 20 بيقول ال T في ال Y prime زائد
+
+346
+00:38:55,620 --> 00:39:04,860
+T زائد واحد في ال Y بده يساوي كده؟ بده يساوي T وال
+
+347
+00:39:04,860 --> 00:39:12,500
+Y عند لم تمام بده يساوي واحدAT Greater Than Z
+
+348
+00:39:12,500 --> 00:39:15,720
+Solution
+
+349
+00:39:15,720 --> 00:39:23,000
+لو
+
+350
+00:39:23,000 --> 00:39:29,760
+نورس للمعادلة رقم A بناخد A بناخد المعامل يبقى Y'
+
+351
+00:39:30,240 --> 00:39:35,750
+هو واحد طيب جهنا جاهزينيبقى بعدى بقوله لـ mu of T
+
+352
+00:39:35,750 --> 00:39:44,410
+بيزلزاوى E أُس كامل 2 على T DT هذا بيزلزاوى E أُس
+
+353
+00:39:44,410 --> 00:39:53,050
+2 لن T يبقى E أُس لن T تربيع يبقى T تربيع بالضبط
+
+354
+00:39:53,050 --> 00:39:58,970
+تماما فبنروح نضرب المعادلة كلها في T تربيع يبقى اش
+
+355
+00:39:58,970 --> 00:40:12,790
+بصير عندى T تربيع و I primeزي دي تربيع
+
+356
+00:40:12,790 --> 00:40:20,090
+الـ y كل الـ prime يساوي main يساوي cos T الكامل
+
+357
+00:40:20,090 --> 00:40:30,240
+افتراضين يتجه دي تربيع Y تساوي sin T زائد cos Cكما
+
+358
+00:40:30,240 --> 00:40:36,200
+اعملنا على طول الخط مباشرة يبقى بناء عليه يساوي
+
+359
+00:40:36,200 --> 00:40:44,060
+الـ y يساوي الـ sign الـ T زائد constant C على T
+
+360
+00:40:44,060 --> 00:40:53,420
+تربيع هذا هو مين ال general solution طيب لك انا
+
+361
+00:40:53,420 --> 00:40:57,580
+راح افعل initial conditionالـ Initial Condition
+
+362
+00:40:57,580 --> 00:41:04,200
+قال لي Y عند الـ Pi تساوي Zero فقلنا لو شيلت كل P
+
+363
+00:41:04,200 --> 00:41:11,100
+و حطيت مكانها Pi بيبقى Y مجداش ب Zero يبقى Zero
+
+364
+00:41:11,100 --> 00:41:19,220
+بدها تساوي Final Pi مجداش يا بنات ب Zero زائد 5.C
+
+365
+00:41:19,220 --> 00:41:30,240
+على من على Pi تربيعومنها C تساوي Zero يبقى سعر شكل
+
+366
+00:41:30,240 --> 00:41:38,020
+الحل على الشكل التالي Y تساوي Sine of T على T
+
+367
+00:41:38,020 --> 00:41:43,280
+تربيع هذا هو main حل ال initial value problem
+
+368
+00:41:43,280 --> 00:41:47,160
+الأولى لجلات تانية
+
+369
+00:42:10,020 --> 00:42:14,420
+يبقى نمر بيه بلاحظ ان المعامل السابع y prime هو t
+
+370
+00:42:14,420 --> 00:42:20,940
+إذا حضر أقسم المعادلة كلها علامين على t يبقى بيصير
+
+371
+00:42:20,940 --> 00:42:29,220
+المعادلة y prime زائد واحد زائد واحد على t في ال y
+
+372
+00:42:29,220 --> 00:42:36,080
+بيساوي كده واحد هذه هي المعادلة رقم star اللالي
+
+373
+00:42:38,620 --> 00:42:46,620
+يبقى الميو of T يبقى ايه؟ استكامل واحد زائد واحد
+
+374
+00:42:46,620 --> 00:42:53,000
+على T بـT يبقى هذا الكلام بيساوي ايه؟ استكامل
+
+375
+00:42:53,000 --> 00:43:01,670
+الواحد بـT وادى زائد للـTيعني يا بنات هذه بقدر
+
+376
+00:43:01,670 --> 00:43:11,450
+اقول E أُس T في E أُس لن T لأن عند ضرب تجمع الأسس
+
+377
+00:43:11,450 --> 00:43:17,290
+مش هتروح تقولي هذه E أُس T زائد E أُس لن T كلام
+
+378
+00:43:17,290 --> 00:43:22,550
+خاطر يعني هذا ضرب و عند ضرب جمعنا مين؟ جمعنا الأسس
+
+379
+00:43:22,550 --> 00:43:31,440
+هذه كلها بقدرشيبقى سارة المسألة ت ت إي أس ت يبقى
+
+380
+00:43:31,440 --> 00:43:35,420
+هذا هو عامل التكامل اللي عندنا الآن بنجي على
+
+381
+00:43:35,420 --> 00:43:41,520
+المعادلة star و بنروح نضربها ت ت إي أس ت يبقى باجي
+
+382
+00:43:41,520 --> 00:43:46,980
+بقول multiply situation
+
+383
+00:43:46,980 --> 00:43:57,990
+star by t ت ت إي أس ت we getيبقى هاي هنا ت في E of
+
+384
+00:43:57,990 --> 00:44:09,090
+T في الـ Y prime زائد ت في E of T زائد E of T قول
+
+385
+00:44:09,090 --> 00:44:17,030
+له هذا الكلام في Y يبدو يساوي ت في E of T هذا لأن
+
+386
+00:44:17,030 --> 00:44:23,340
+الطرق الشماليكله بقدر أجمع بمين في عامل التكامل T
+
+387
+00:44:23,340 --> 00:44:29,760
+EOS T في الـY وكله Prime بدي أساوي فرق اليمين T
+
+388
+00:44:29,760 --> 00:44:36,400
+EOS T يعني لو جيت تشتق هذه مشتقة حصل ضرب دالتين
+
+389
+00:44:36,400 --> 00:44:42,500
+هتعطيك T EOS T Y Prime زائد الـY زي ما هي و هذه
+
+390
+00:44:42,500 --> 00:44:49,260
+مشتقة حصل ضرب دالتين اللي T EOS T زاد EOS Tهذه
+
+391
+00:44:49,260 --> 00:44:55,600
+بالضبط تماما يبقى
+
+392
+00:44:55,600 --> 00:45:01,500
+لو كملنا الطرفين تصير تي او سي في ال Y بدر سوى
+
+393
+00:45:01,500 --> 00:45:07,440
+تكامل تي او سي دي تي زائد في نصة ال C يبقى لو
+
+394
+00:45:07,440 --> 00:45:07,540
+سي دي تي زائد في نصة ال C يبقى لو كملنا الطرفين تي
+
+395
+00:45:07,540 --> 00:45:09,040
+او سي دي تي زائد في نصة ال C يبقى لو كملنا الطرفين
+
+396
+00:45:09,040 --> 00:45:12,420
+تي او سي دي تي زائد في نصة ال C يبقى لو كملنا
+
+397
+00:45:12,420 --> 00:45:15,840
+الطرفين تي او سي دي تي زائد في نصة ال C يبقى لو
+
+398
+00:45:15,840 --> 00:45:19,860
+كملنا الطرفين تي او سي دي تي زائأو بدنا نيجي ناخد
+
+399
+00:45:19,860 --> 00:45:28,340
+integral يبقى هنا T وهنا EOS T واحد EOS T Zero EOS
+
+400
+00:45:28,340 --> 00:45:35,120
+T هذي بالموجب وهذه بالمين بالسالب يبقى سعر T EOS T
+
+401
+00:45:35,120 --> 00:45:44,560
+في ال Y بده يساوي T EOS T ماقص EOS T زائد ثلثة C
+
+402
+00:45:45,730 --> 00:45:53,430
+يبقى Y يساوي
+
+403
+00:45:53,430 --> 00:46:03,650
+واحد ناقص واحد على T زائد C على T T E أس T يبقى
+
+404
+00:46:03,650 --> 00:46:12,390
+هذا هو ال general solution
+
+405
+00:46:23,510 --> 00:46:32,110
+الان بدنا نشوف ما هو شكل الحل يبقى
+
+406
+00:46:32,110 --> 00:46:35,170
+بنجي على ال initial condition اللي عنده ال initial
+
+407
+00:46:35,170 --> 00:46:38,350
+condition اللي قال لي y عند ال n اثنين يساوي واحد
+
+408
+00:46:38,670 --> 00:46:44,370
+يعني لو شيلت P وحطيت مكانها لن 2 بتطلع Y أب واحد
+
+409
+00:46:44,370 --> 00:46:53,090
+يبقى واحد يستوي واحد ماقص واحد على لن 2 زائد C على
+
+410
+00:46:53,090 --> 00:47:03,870
+لن 2 في E أس لن 8 أظن لو جبت هذا عند هذا بروح هذا
+
+411
+00:47:03,870 --> 00:47:09,200
+بدي أجيبه هنا بصير بقيمة عموجة بقىيعني واحد على لن
+
+412
+00:47:09,200 --> 00:47:17,460
+اتنين هذا كله باتنين يبقى ال C على اتنين لن اتنين
+
+413
+00:47:17,460 --> 00:47:25,560
+لن اتنين مع لن اتنين يبقى ال C تساوي اتنين يبقى
+
+414
+00:47:25,560 --> 00:47:38,790
+أصبح the solution of the initial value problemY
+
+415
+00:47:38,790 --> 00:47:53,790
+تساوي نقص واحد على T زائد C على T في
+
+416
+00:47:53,790 --> 00:47:54,270
+E
+
+417
+00:47:58,380 --> 00:48:04,140
+يعني المعادلات لازم يمكن حصل المتغيرات في اتحاد
+
+418
+00:48:04,140 --> 00:48:08,620
+يسمى function في اواب لحاله وfunction في اتنى
+
+419
+00:48:08,620 --> 00:48:12,000
+لحاله ينجح هذا المنصور باستخدام ال equation و
+
+420
+00:48:12,000 --> 00:48:16,520
+بعدين يقول هو احسن كام كيف كفتانى فبالي يقول زي
+
+421
+00:48:16,520 --> 00:48:18,420
+جينا مالك يسأل مالك يسأل ال equation
+
+422
+00:48:27,220 --> 00:48:30,900
+يبقى نفس المعادلة توسعة حدام اللي رابط كده لك
+
+423
+00:48:30,900 --> 00:48:35,920
+تقيسها بدلها مبين لك الgenesis equation تاني ممكن
+
+424
+00:48:35,920 --> 00:48:41,960
+تكتب هذه المعادلة على صورة تانية dy by x الطرف
+
+425
+00:48:41,960 --> 00:48:46,680
+الشمالي زي ماقول f of x y ممكن تكتبها على شكل M of
+
+426
+00:48:46,680 --> 00:48:54,300
+x y علي M of x y سؤال هو هل هذا ممكن و لا غير ممكن
+
+427
+00:48:54,300 --> 00:49:01,640
+الإجابة ممكنممكن كيف ممكن f of x y ياخدها كلها بال
+
+428
+00:49:01,640 --> 00:49:07,660
+m of x y و ال n of x y ياخدها بجدال و هذا صحيح إن
+
+429
+00:49:07,660 --> 00:49:13,260
+صارت ما هيش مشكلة إذا صار الكلام هذا ممكن يبقى هذا
+
+430
+00:49:13,260 --> 00:49:17,320
+الكلام ممكن لو حد ال f of x y هي m of x y و حد ال
+
+431
+00:49:17,320 --> 00:49:23,720
+n of x y هي واحد صحيح طيب افترضي بالصدر الله إيه
+
+432
+00:49:23,720 --> 00:49:30,510
+لو خلتإن ال M function في X فقط و M function في Y
+
+433
+00:49:30,510 --> 00:49:37,010
+فقط يبقى المعادلة هذه بيبدأ تصير dy by x سوى M of
+
+434
+00:49:37,010 --> 00:49:40,070
+X على N of Y
+
+435
+00:49:44,330 --> 00:49:52,670
+م of y بدي y يسوى م of x مالها دفسي بكيان مفاصلة
+
+436
+00:49:52,670 --> 00:49:57,050
+اللي فيهم y لحال مش ناحية و اللي فيهم ال x where
+
+437
+00:49:57,050 --> 00:50:03,670
+بناحية تاني كيانة فاصلة متغيرة طيب أنا بدي y تروح
+
+438
+00:50:03,670 --> 00:50:09,550
+بكامل الطرفين تكامل هذه هجيب لي y تكامل هذه هجيب
+
+439
+00:50:09,550 --> 00:50:12,650
+لي دالة بدالة دالة او هذا بيجيب لي دالة بدالة ال x
+
+440
+00:50:12,910 --> 00:50:18,910
+وهذا بيدل دالة بدلالة Y ومن ثم يكون خلاصنا جيبنا
+
+441
+00:50:18,910 --> 00:50:26,190
+حصل على شكل Y سواء كانت Y صريحة أو بيمنية بيمنيش
+
+442
+00:50:26,190 --> 00:50:30,070
+بيمنى انه انا جلبت جيب Y as a function of it سواء
+
+443
+00:50:30,070 --> 00:50:37,370
+كانت دالة صريحة او دالة implicit او غير يعني دالة
+
+444
+00:50:37,370 --> 00:50:42,330
+بيمنية او دالة صريحةيبقى بالحلها بواصفة ال
+
+445
+00:50:42,330 --> 00:50:47,290
+integration الان بالتالي ناخد أمثلة توريحية على
+
+446
+00:50:47,290 --> 00:50:51,190
+الشغل يعني يا بنات الشغل دلوقتي لحد ما أطلع في
+
+447
+00:50:51,190 --> 00:50:55,130
+المعادلة بدي أحاول أفصل ال X لحالي و ال Y لحالي
+
+448
+00:50:55,130 --> 00:51:02,530
+أكمل انت خلصت أي مسألة ناخد أمثلة يبقى example one
+
+449
+00:51:13,190 --> 00:51:18,270
+and following differential
+
+450
+00:51:18,270 --> 00:51:21,370
+equation
+
+451
+00:51:21,370 --> 00:51:24,890
+المعادلة
+
+452
+00:51:24,890 --> 00:51:37,630
+الأولى نمرا M dy by dx dy by dx يسمى E أس Y أصيني
+
+453
+00:51:37,630 --> 00:51:38,690
+اتنين X
+
+454
+00:51:42,480 --> 00:51:51,160
+E أوسى اتنين Y كله فيه أوساين X نمرى بيه السؤال
+
+455
+00:51:51,160 --> 00:52:02,640
+التاني انه X ال Y' يساوي واحد ناقص Y' كله اص نص
+
+456
+00:52:17,190 --> 00:52:22,490
+السؤال بيقول يحل كل من المعاملات التفاعلونية تالية
+
+457
+00:52:22,490 --> 00:52:29,530
+السؤال الأول dy by x يساوي e قص y صينة من x على y
+
+458
+00:52:29,530 --> 00:52:32,290
+ناقص e وسط 2y بكو صينة من x
+
+459
+00:52:41,640 --> 00:52:45,980
+يجب ان اقول المعاملة هذه هروح اكتبها على الشكل
+
+460
+00:52:45,980 --> 00:52:51,960
+التالت شو هيك لو ضربت في DX مرة واحدة في الطرفين
+
+461
+00:52:51,960 --> 00:52:53,380
+ايش بيصير عندنا
+
+462
+00:53:08,650 --> 00:53:22,070
+كله فيه cos X DX طب أبطال أيه لبنان؟ ال function
+
+463
+00:53:22,070 --> 00:53:25,770
+في Y يعني و ال باقي بيبقى ال function بمين؟ X يعني
+
+464
+00:53:25,770 --> 00:53:28,850
+معناه تبقى اللي ده تخلص من هنا يعني بتروح X من
+
+465
+00:53:28,850 --> 00:53:33,770
+الطرفين عليه يعني لو جسمت الطرفين عليها شو بيصير
+
+466
+00:53:33,770 --> 00:53:38,110
+عن الإرمالات؟ Y نقص E
+
+467
+00:53:42,230 --> 00:53:47,670
+DY يساوي شويه في هذه SIN 2X مش هي عبارة عن ما
+
+468
+00:53:47,670 --> 00:53:58,130
+عندنا SIN X بيكون SIN X على SIN X كتير طيب تكتبها
+
+469
+00:53:58,130 --> 00:54:10,220
+بصورة أخرى هذي Y في E-Y ناقص EY كله في DYيبقى هذه
+
+470
+00:54:10,220 --> 00:54:14,300
+على هذه الطلاقة فوق بيشيلت سالف هذه مع هذه تفتصل
+
+471
+00:54:14,300 --> 00:54:25,200
+بظل E أس Y Cos X مع Cos X يبقى 2Sin X بDX يبقى هذه
+
+472
+00:54:25,200 --> 00:54:31,760
+فصلنا يا بنات ال Y لا واحدة و ال X لا واحدة يبقى
+
+473
+00:54:31,760 --> 00:54:36,340
+الأن بجهة كاملة الطرفين بحصل على مين على تاني حل
+
+474
+00:54:36,340 --> 00:54:39,080
+يبقى بجهة كاملة هذه
+
+475
+00:54:47,490 --> 00:55:00,210
+يبقى انا انا انا انا
+
+476
+00:55:00,210 --> 00:55:03,630
+انا
+
+477
+00:55:03,630 --> 00:55:04,450
+انا انا انا انا انا انا انا انا انا انا انا انا
+
+478
+00:55:04,450 --> 00:55:04,470
+انا انا انا انا انا انا انا انا انا انا انا انا
+
+479
+00:55:04,470 --> 00:55:09,150
+انا انا انا انا اناواحد لو كاملها بنفسها مقسمة على
+
+480
+00:55:09,150 --> 00:55:13,550
+سالب واحد مقسمة على سالب واحد والله مضروبة في سالب
+
+481
+00:55:13,550 --> 00:55:21,050
+واحد هي نفسها طيب مشتاق كمان مرة يبقى نفسها مقسمة
+
+482
+00:55:21,050 --> 00:55:26,210
+على سالب واحد بسالب الشصية بالموجة يبقى هذه بالهذه
+
+483
+00:55:26,210 --> 00:55:31,230
+بالموجة و هذه بالهذه بالسالب يبقى بالتكامل بسرع
+
+484
+00:55:31,230 --> 00:55:40,640
+النميمبصير عندنا ناقص Y EOS ناقص Y ناقص EOS ناقص Y
+
+485
+00:55:40,640 --> 00:55:47,900
+وهنا وصلنا لناقص هي الناقص وتكامل ال EOS Y بال EOS
+
+486
+00:55:47,900 --> 00:55:53,560
+Y itself تمام؟
+
+487
+00:55:53,560 --> 00:55:59,940
+يبقى هاي تكامل التنتير وهذه زي ما هي EOS Y نجي
+
+488
+00:55:59,940 --> 00:56:11,350
+لهذههذه تكملت سالب اثنين وصين ال X زائد وخمسين طب
+
+489
+00:56:11,350 --> 00:56:17,570
+ايش رايح؟ لو ضربت كله في E أوس Y عشان اخلص منها
+
+490
+00:56:17,570 --> 00:56:25,070
+السوالة ده او لو ضربت كله في سالب E أوس سالب Y لو
+
+491
+00:56:25,070 --> 00:56:31,740
+ضربت هذه كلهاالسالب E والسالب E والسالب E والسالب
+
+492
+00:56:31,740 --> 00:56:36,700
+E والسالب E والسالب E والسالب E والسالب E والسالب
+
+493
+00:56:36,700 --> 00:56:37,640
+E والسالب E والسالب E والسالب E والسالب E والسالب
+
+494
+00:56:37,640 --> 00:56:39,480
+E والسالب E والسالب E والسالب E والسالب E والسالب
+
+495
+00:56:39,480 --> 00:56:39,540
+E والسالب E والسالب E والسالب E والسالب E والسالب
+
+496
+00:56:39,540 --> 00:56:41,520
+E والسالب E والسالب E والسالب E والسالب E والسالب
+
+497
+00:56:41,520 --> 00:56:50,100
+E والسالب E والسالب E والسالب
+
+498
+00:56:50,100 --> 00:56:55,900
+E والس
+
+499
+00:56:55,950 --> 00:57:10,650
+يقص يقص يقص يقص يقص يقص يقص يقص يقص يقص يقص يقص
+
+500
+00:57:10,650 --> 00:57:19,950
+يقص يقص يقص يقص يقص يقص
+
+501
+00:57:25,690 --> 00:57:30,310
+مش Y في ناحية و X في ناحية لإن هذا حالة المعادلة
+
+502
+00:57:30,310 --> 00:57:35,530
+الأولى اللي هي عامة نجي للمعادلة التانية نجي لنمرة
+
+503
+00:57:35,530 --> 00:57:41,770
+B نمرة B لإننا نحاول نفصل المتغيرات فنروح أكثر
+
+504
+00:57:41,770 --> 00:57:50,750
+المعادلة على الشكل التالي X بDY على DX يساوي جدر
+
+505
+00:57:50,750 --> 00:58:00,680
+التربيعي لو أحد ناقص Y تربيهأول انشرتنا فقلنا E1
+
+506
+00:58:00,680 --> 00:58:06,240
+على الجذر التربيعي العارف واقع صغير التربيع يسمى
+
+507
+00:58:06,240 --> 00:58:13,140
+DX على X فجسمي على هذه DX تطلع هنا و X تنزل تحت
+
+508
+00:58:13,140 --> 00:58:18,100
+الشكل اللي عندنا هذا لأن المعادلة أخدت الشكل
+
+509
+00:58:18,100 --> 00:58:24,920
+الجديد اللي قدامنا هذاكداش تكمل المادة الأولى يا
+
+510
+00:58:24,920 --> 00:58:31,100
+بنادي؟ Y على الجدر التربية لواحد نقص Y تربية؟ كده؟
+
+511
+00:58:31,100 --> 00:58:40,280
+سن .. سن ايه؟ كده؟ سن .. سن الف سن الف سواء فجو
+
+512
+00:58:40,280 --> 00:58:48,520
+كانت بزايد تحت الجدر؟ تحت الجدر تحت الجدر
+
+513
+00:59:05,040 --> 00:59:12,400
+مش تكامل اخر كل معادلة تفضلية عندك هي تكاملين يا
+
+514
+00:59:12,400 --> 00:59:20,260
+جلوة كم انت بصير عندي Y inverse Yيساوي لم absolute
+
+515
+00:59:20,260 --> 00:59:26,040
+value ل X زي المادة زي ال consistency هذي بقدر
+
+516
+00:59:26,040 --> 00:59:29,500
+أجيب لها Y في دعنى و لا بقدر أجيب لها تاني و لا
+
+517
+00:59:29,500 --> 00:59:33,300
+بقدر أجيب لها تاني و لا بقدر أجيب لها تاني و لا
+
+518
+00:59:33,300 --> 00:59:33,620
+بقدر أجيب لها تاني و لا بقدر أجيب لها تاني و لا
+
+519
+00:59:33,620 --> 00:59:34,600
+بقدر أجيب لها تاني و لا بقدر أجيب لها تاني و لا
+
+520
+00:59:34,600 --> 00:59:41,340
+بقدر أجيب لها تاني و لا بقدر أجيب لها تاني
+
+521
+00:59:41,340 --> 00:59:45,520
+و لا بقدر أ
+
+522
+00:59:49,940 --> 00:59:56,740
+لل absolute value ل X زائد constant C هذا هو عبارة
+
+523
+00:59:56,740 --> 00:59:59,640
+عن حل المعادلة التفاغرية
+
+524
+01:00:33,640 --> 01:00:34,700
+ثالث نهار
+
+525
+01:00:53,960 --> 01:01:09,460
+convolution of the following national problems على
+
+526
+01:01:09,460 --> 01:01:20,440
+نمرة إيه؟ نمرة إيه؟ Determine Determine
+
+527
+01:01:20,440 --> 01:01:21,740
+لإنترال
+
+528
+01:01:25,900 --> 01:01:37,280
+فى الفترة in which the solution
+
+529
+01:01:37,280 --> 01:01:44,240
+is بيطار
+
+530
+01:01:44,240 --> 01:01:50,000
+اولى
+
+531
+01:01:50,000 --> 01:01:53,860
+وراى ثانوية
+
+532
+01:01:56,460 --> 01:02:11,660
+نقص x تاريخ plus نص dy يساوي sin inverse x dx و y
+
+533
+01:02:11,660 --> 01:02:20,340
+يعني زي رمزية تساوي واحد نقطة تانية لإن ال y prime
+
+534
+01:02:20,340 --> 01:02:30,740
+هي بيساوي xY تكييب في واحد زائد تكستر في أقص ناقص
+
+535
+01:02:30,740 --> 01:02:39,520
+نصف وY عند Zero كذلك يسمي الواحد
+
+536
+01:03:03,640 --> 01:03:07,860
+يقول يا حل، كل مثال .. كل مثالة تهم الحقيقية
+
+537
+01:03:07,860 --> 01:03:12,620
+أتغلب، وهذه الفترة اللي اتحل عليها تكون صحية أو
+
+538
+01:03:12,620 --> 01:03:18,140
+اتحل معرفة على هذه الفكرة، تظل الدولة اللي عندهم
+
+539
+01:03:18,140 --> 01:03:22,420
+هذه والحمد لله يبقوا عصر الانسس لحال ومغارز لحال،
+
+540
+01:03:22,420 --> 01:03:29,730
+بس فيهم هذه .. هذه الانسسإذا ممكن نفسي مقترفين
+
+541
+01:03:29,730 --> 01:03:36,730
+عليه، لأن جبالي مجرده هنا من المفتة الأولى La
+
+542
+01:03:36,730 --> 01:03:50,500
+differential equation SY تربيع Dy Y تربيع Dy يساوي
+
+543
+01:03:50,500 --> 01:03:56,580
+Sine Inverse X على الجدري التربيعي اللي راح اتناقص
+
+544
+01:03:56,580 --> 01:04:04,200
+X تربيع DX اضغط طبعا في الشمال ثانية و اتكلم و
+
+545
+01:04:04,200 --> 01:04:08,000
+فانت سهل
+
+546
+01:04:08,000 --> 01:04:14,370
+انا عارف ناشيلكن لو جد كلمات قادرين منها تقدر تقول
+
+547
+01:04:14,370 --> 01:04:22,890
+تكامل نواي تربية dy لساوي تكامل لsin inverse x هذا
+
+548
+01:04:22,890 --> 01:04:28,430
+يقول عارفين منها يعني
+
+549
+01:04:28,430 --> 01:04:36,010
+هذي d لsin inverse x، مظبوط؟ يعني استبدال من
+
+550
+01:04:36,010 --> 01:04:40,780
+المقدار هذا كلهبديه ال sign inverse يعني مشتق ال
+
+551
+01:04:40,780 --> 01:04:43,900
+sign inverse يعني مشتق ال sign inverse تقي واحد
+
+552
+01:04:43,900 --> 01:04:46,100
+نقل تقرير واحد نقل تقرير نقل تقرير نقل تقرير نقل
+
+553
+01:04:46,100 --> 01:04:49,840
+تقرير نقل تقرير نقل تقرير نقل تقرير نقل تقرير نقل
+
+554
+01:04:49,840 --> 01:04:50,560
+تقرير نقل تقرير نقل تقرير نقل تقرير نقل تقرير نقل
+
+555
+01:04:50,560 --> 01:04:51,520
+تقرير نقل تقرير نقل تقرير نقل تقرير نقل تقرير نقل
+
+556
+01:04:51,520 --> 01:04:53,800
+تقرير نقل تقرير نقل تقرير نقل تقرير نقل تقرير نقل
+
+557
+01:04:53,800 --> 01:05:01,380
+تقرير نقل تقرير نقل تقرير نقل تقرير
+
+558
+01:05:05,550 --> 01:05:11,850
+مش مصير أنه هنا مصير أنه y تكيب يسوى تلاتة على
+
+559
+01:05:11,850 --> 01:05:20,390
+اتنين sin inverse x لكل تاريخ زائد تلاتة c طب معقن
+
+560
+01:05:20,390 --> 01:05:26,230
+ياناش ال condition انه y عند zero يسوى جدا واحد
+
+561
+01:05:26,230 --> 01:05:33,010
+يعني لو كانت x ب zero في y جدا واحد يبقى واحد ان
+
+562
+01:05:33,010 --> 01:05:47,000
+كنت تكيببتساوي تلاتة على اتنين في صيف المغزيل يبقى
+
+563
+01:05:47,000 --> 01:05:54,440
+هاي Zero كل تربيع زي تلاتة C يبقى مصير واحد تساوي
+
+564
+01:05:54,440 --> 01:06:01,940
+تلاتة C وهذا بيعطيك المصير تساوي جدارك تساوي الكل
+
+565
+01:06:02,620 --> 01:06:08,620
+يبقى بالإنها العالية بصير علينا Y تكيب بدي ساوي
+
+566
+01:06:08,620 --> 01:06:16,260
+تلاتة على اتنين لـsin inverse X القلب الربيع زائد
+
+567
+01:06:16,260 --> 01:06:28,680
+واحد تمام او Y تساوي الجدري التالت لـVزي ثلاثة على
+
+568
+01:06:28,680 --> 01:06:35,060
+اتنين ثلاثة على اتنين sin inverse x والترابية
+
+569
+01:06:35,060 --> 01:06:39,540
+دائرة خلاص
+
+570
+01:06:39,540 --> 01:06:45,640
+لسه المطلوب الأول يومين اللي هو ال solution يبقى
+
+571
+01:06:45,640 --> 01:06:51,720
+من حد ما بدأنا هنا بدأنا في الامريكا والعزل امريكا
+
+572
+01:06:51,720 --> 01:06:57,940
+دي هذه الفترة اللي الحل عليها هذا بيكون صحيحباجي
+
+573
+01:06:57,940 --> 01:07:03,140
+بسأل نفسي هذا الجدر الثالث جدر الثالث معرف لل zero
+
+574
+01:07:03,140 --> 01:07:08,900
+والموجب والسلب بدون مشاكل، مظبوط؟ صح، هاي شو
+
+575
+01:07:08,900 --> 01:07:12,940
+المشكلة وين؟ المشكلة في ال sign inverse، ال sign
+
+576
+01:07:12,940 --> 01:07:16,940
+inverse في الدرجة اللي عم نقولها وين؟ من سلب واحد
+
+577
+01:07:16,940 --> 01:07:21,770
+إلى واحد، من سلب واحد إلى واحد، هاي مظبوطيجب ان
+
+578
+01:07:21,770 --> 01:07:26,730
+انا اتخذ دائما و ابدا معرضة من سالب واحد الى واحد
+
+579
+01:07:26,730 --> 01:07:32,550
+و بروح بقوله هنا فاصلة ال X أكبر من او تسوى سالب
+
+580
+01:07:32,550 --> 01:07:36,790
+واحد او اقل من او تسوى سالب واحد او لأسلوب بل ال X
+
+581
+01:07:36,790 --> 01:07:41,750
+اقل من او تسوى واحد يبقى هذه ال interval اللى اتحل
+
+582
+01:07:41,750 --> 01:07:50,250
+عليها معرض يبقى هذه جبت من وينكان فلسطين من
+
+583
+01:07:50,250 --> 01:07:55,750
+معلوماتي عن معقوذ اللي هو scientist كان فلسطين طيب
+
+584
+01:07:55,750 --> 01:08:02,050
+نجي لنمرة اتنين نمرة اتنين بيقول ي واي فاي يسوى
+
+585
+01:08:02,050 --> 01:08:09,150
+XYKB ده بييزن المثل اللي عندنا يعني ده اقدر اقوله
+
+586
+01:08:09,150 --> 01:08:14,690
+ال equation as تجاهته بالمعادلة على الشكل التالي
+
+587
+01:08:14,690 --> 01:08:24,210
+اللي هو مين؟dy by dx يساوي هذا x على الجدر
+
+588
+01:08:24,210 --> 01:08:35,210
+التربيعي ل1 زائد x تربيع 8 من y تكييف يبقى هذا
+
+589
+01:08:35,210 --> 01:08:39,590
+الجدر كان في الواقع غيبت الإشارة طبعا نزل في
+
+590
+01:08:39,590 --> 01:08:45,620
+المقام وظلت عند x y تكييف فوقهذه مدرسة رسمها على
+
+591
+01:08:45,620 --> 01:08:53,140
+الشكل التالي dy على y تكييف جسمنا كله على y تكييف
+
+592
+01:08:53,140 --> 01:09:01,120
+وضربنا في dx بصير x في dx على الجدرى الترميالي ل1
+
+593
+01:09:01,120 --> 01:09:07,820
+زائر x ترمية يعني يا بنات كأن الرسم صارت تكابر y
+
+594
+01:09:07,820 --> 01:09:16,150
+كسالي 3 dyيساوي تكامل X على جدرى تربية من واحد زي
+
+595
+01:09:16,150 --> 01:09:24,730
+تكس تربية DX أظن الشمال سهل تكملهبقول يا بابا
+
+596
+01:09:24,730 --> 01:09:31,490
+الكلاصين نفرض واحد تربيه اذا
+
+597
+01:09:31,490 --> 01:09:38,190
+انا لو حطيتي w يسوي واحد زائد x تربيه واش تعطي
+
+598
+01:09:38,190 --> 01:09:43,910
+انجاز من x dx ماعنديش اتنينات انجاز نص dw
+
+599
+01:09:47,720 --> 01:09:54,420
+يبقى بصيري المسألة هذه هاي النص برا وهاي تكامل
+
+600
+01:09:54,420 --> 01:10:06,540
+وهنا dw على جذري w أو تكامل dy أثناء تس ثلاثة dy
+
+601
+01:10:06,540 --> 01:10:16,440
+يسوى النص تكامل w أثناء تس نص dwيبقى هذا بالصينيه
+
+602
+01:10:16,440 --> 01:10:25,580
+Y أس ناقص اتنين على ناقص اتنين يساوي النص IEW فهو
+
+603
+01:10:25,580 --> 01:10:32,180
+اضيف نقص واحد و اكسب على نقص الجديد يبقى هذا نص
+
+604
+01:10:32,180 --> 01:10:41,220
+على نص زائد كلستانسيه يبقى نص على نص يبقى هذه صارت
+
+605
+01:10:41,220 --> 01:10:43,840
+ايه صارت ناقص
+
+606
+01:11:00,680 --> 01:11:04,540
+معادلة كل المضروبة في نقص اتنين
+
+607
+01:11:08,630 --> 01:11:14,750
+يعني لو ضربنا في ناقص اتنين نصير واحد على Y تربية
+
+608
+01:11:14,750 --> 01:11:20,610
+يساوي ناقص اتنين الجرهي التربية على واحد زي ال
+
+609
+01:11:20,610 --> 01:11:31,630
+text تربية ناقص اتنين C مش أجلب؟ وضعيا إيش رأيك؟
+
+610
+01:11:31,630 --> 01:11:39,320
+لو شيلت هذه وحطيت بدلها متغير جديد سميلي هذه C1وها
+
+611
+01:11:39,320 --> 01:11:46,940
+دي C1 وها دي C1 بدي أشيل سالب اتنين C1 وقتهم
+
+612
+01:11:46,940 --> 01:11:51,580
+بدالهم C2 أطلع اطلع اطلع اطلع اطلع اطلع اطلع اطلع
+
+613
+01:11:51,580 --> 01:11:51,760
+اطلع اطلع اطلع اطلع اطلع اطلع اطلع اطلع اطلع اطلع
+
+614
+01:11:51,760 --> 01:11:52,020
+اطلع اطلع اطلع اطلع اطلع اطلع اطلع اطلع اطلع اطلع
+
+615
+01:11:52,020 --> 01:11:54,060
+اطلع اطلع اطلع اطلع اطلع اطلع اطلع اطلع اطلع اطلع
+
+616
+01:11:54,060 --> 01:12:05,720
+اطلع اطلع اطلع اطلع اطلع اطلع اطلع اطلع اطلع اط
+
+617
+01:12:06,580 --> 01:12:10,260
+عندي ايش؟ عندي initial condition في الدروحة طبعا
+
+618
+01:12:10,260 --> 01:12:16,620
+عندي y عند zero تساوي واحد الان y عند zero تساوي
+
+619
+01:12:16,620 --> 01:12:24,500
+واحد implies واحد على واحد ترجع له واحد يساوي ناقص
+
+620
+01:12:24,500 --> 01:12:34,100
+اتنين كذر الواحد من ناقص اتنين C1 طبعا يبقى بصير
+
+621
+01:12:34,100 --> 01:12:34,980
+عندي هنا
+
+622
+01:12:39,280 --> 01:12:48,300
+وهنا نقص اتنين C1 يبقى بصير عندنا اللي هو التلاتة
+
+623
+01:12:48,300 --> 01:12:55,600
+سواء سالب اتنين C1 يبقى C1 سالب تلاتة على اتنين
+
+624
+01:12:55,600 --> 01:13:03,980
+لبصير المثل واحد على I تربيع يصير نقص اتنين واحد
+
+625
+01:13:03,980 --> 01:13:08,360
+زاد X تربيعبدي أشيل c1 و أضعه في مكانها ثالث ثلاثة
+
+626
+01:13:08,360 --> 01:13:15,340
+على اتنين يبقى بيصير زائد ثلاث يبقى لو شجلبنا
+
+627
+01:13:15,340 --> 01:13:24,120
+بيصير شكل الحل Y تربيع يسوى واحد على ثلاثة ناقص
+
+628
+01:13:24,120 --> 01:13:31,560
+اتنين الجدرين التربيعي لواحد زائد X تربيع فإذا ما
+
+629
+01:13:31,560 --> 01:13:36,420
+بديش Y تربيع بدي واحد ممكنش ناخدالجدري الترميعي
+
+630
+01:13:36,420 --> 01:13:43,640
+للطرفين يبقى هذا بده يعطينا ان y بساوي زائد او
+
+631
+01:13:43,640 --> 01:13:52,680
+ناقص واحد على الجدري الترميعي لمين لتلاتة ناقص
+
+632
+01:13:52,680 --> 01:13:59,520
+اتنين الجدري الترميعي واحد زائد اكس ترمية طب انا
+
+633
+01:13:59,520 --> 01:14:03,860
+بده اشوف عندي إجابة والله إذا ابتدتبنجر ال
+
+634
+01:14:03,860 --> 01:14:09,640
+condition ال condition اللي عم نقوله y عند ال zero
+
+635
+01:14:09,640 --> 01:14:18,040
+بالساوية ده واحد و اخر واحد موجبه والمساعدة الان y
+
+636
+01:14:18,040 --> 01:14:25,320
+عند ال zero بالساوية واحد هذا يعني ان y اكبر من من
+
+637
+01:14:25,320 --> 01:14:34,510
+ال zero هذا يعني ان yعلى الجدر التربيعي لتلاتة
+
+638
+01:14:34,510 --> 01:14:41,390
+ناقص اتنين بالجدر التربيعي لواحد زائد X التربيعي
+
+639
+01:14:41,390 --> 01:14:46,850
+حتى الآن جيبنا المطبوب الأول فقط لغيره بإننا نروح
+
+640
+01:14:46,850 --> 01:14:52,350
+نجيب المطبوب التالي وهو الفترة اللي حل عليها هذا
+
+641
+01:14:52,350 --> 01:14:54,830
+يقول صحيحا
+
+642
+01:15:04,410 --> 01:15:09,530
+الان الحل صحيح لو الفمية اللى تحت الجدران كانت
+
+643
+01:15:09,530 --> 01:15:16,450
+أكبر من الـ 0 صحيح ولا لا؟ يبقى هنا باجي بقول لا
+
+644
+01:15:16,450 --> 01:15:21,710
+solution is
+
+645
+01:15:21,710 --> 01:15:26,550
+defined معرف if
+
+646
+01:15:34,850 --> 01:15:40,950
+تكس تربية فالأكبر من Zero ممنوع يسوى Zero لو سوى
+
+647
+01:15:40,950 --> 01:15:46,290
+Zero لأصبح أحد واحد على صفر لما نخلق Seal and Defy
+
+648
+01:15:46,290 --> 01:15:50,770
+يبقى بنات من الحل ال Inquality هذا يبقى لو كان
+
+649
+01:15:50,770 --> 01:15:55,770
+حللها بصير اتنين القدر التربية يلا واحد زائد تكس
+
+650
+01:15:55,770 --> 01:16:04,340
+تربية أقل من مائة أقل من دلالة أوبصير عندنا الجدر
+
+651
+01:16:04,340 --> 01:16:12,160
+التربيع إلى واحد زائد X تربيع أقل من 3 على 2 أقرب
+
+652
+01:16:12,160 --> 01:16:17,280
+الطرفين بصير عندك واحد زائد X تربيع
+
+653
+01:16:34,640 --> 01:16:39,220
+خد الجدر التربيهي يبقى الجدر التربيهي بتطلعلي
+
+654
+01:16:39,220 --> 01:16:45,960
+absolute value لأكس أقل من جدر 5 على 2 يبقى هذه
+
+655
+01:16:45,960 --> 01:16:54,200
+الفترة اللي بحل عليها يكونوا صحيحا طيب
+
+656
+01:16:54,200 --> 01:16:59,000
+ال switch نحن الآن اتذهل منه لكن انا احط زجاج في
+
+657
+01:16:59,000 --> 01:17:03,660
+ال exercises حالة دي اسمها homogeneous function
+
+658
+01:17:04,690 --> 01:17:10,770
+طبعاً بدنا نعطي تعريف لها ونشوف كذا كتاب طبعا حطه
+
+659
+01:17:10,770 --> 01:17:16,830
+حطه لها مجموعة للاسم يبقى موجودة لحالة اسمها ال
+
+660
+01:17:16,830 --> 01:17:23,050
+homogenous situations
+
+661
+01:17:23,050 --> 01:17:33,660
+وهذه موجودة in exercises اللي هم inexercise دي
+
+662
+01:17:33,660 --> 01:17:38,940
+اتنين اتنين لو كده في التمانين وليس في جزء النظر
+
+663
+01:17:38,940 --> 01:17:48,780
+نعطيها تعريف ونشوف كيف انتجها the first order
+
+664
+01:17:48,780 --> 01:18:03,100
+the first order dimension equation dy by dxبنسميه
+
+665
+01:18:03,100 --> 01:18:16,420
+homogeneous if
+
+666
+01:18:16,420 --> 01:18:32,330
+ال F of XY can be written can be written asهي a
+
+667
+01:18:32,330 --> 01:18:42,870
+function of the ratio y على x هو
+
+668
+01:18:42,870 --> 01:18:58,610
+الaccelerator denomination that is a n f dy y dx
+
+669
+01:19:01,200 --> 01:19:11,640
+F of X of Y بدي سوى capital F of Y على X وهذه
+
+670
+01:19:11,640 --> 01:19:20,320
+سبيها المعادلة رقم واحد ويصير
+
+671
+01:19:20,320 --> 01:19:27,720
+question
+
+672
+01:19:27,720 --> 01:19:29,480
+one
+
+673
+01:19:31,690 --> 01:19:32,510
+I was four
+
+674
+01:20:11,720 --> 01:20:18,000
+يقول المقال كذا يقول المعارضة بدا اشيل ال y على x
+
+675
+01:20:18,000 --> 01:20:25,940
+و اضطرها للمتميزة الجديدة والذات من ال V اضطر ال y
+
+676
+01:20:25,940 --> 01:20:34,900
+على x يساوي ال V او المعارضة هذه ممكن اقول Y تساوي
+
+677
+01:20:34,900 --> 01:20:40,880
+X PV بدا نشتقها كاله اشتقناها
+
+678
+01:20:57,930 --> 01:21:04,030
+مرة تانية مشتقة ال y هي dy على dx هذي مشتقة حصل
+
+679
+01:21:04,030 --> 01:21:09,630
+ضغط دقلتين مشتقة الأولى في الثانية زائد الأولى في
+
+680
+01:21:09,630 --> 01:21:14,430
+المشتقة في الضغط الثاني القلب تمسك المعلومة اللي
+
+681
+01:21:14,430 --> 01:21:20,520
+حصلت عليها وعوّضها في المعادلة رقم واحد يعنيبدي
+
+682
+01:21:20,520 --> 01:21:25,080
+أشيل dy على dx مكتوب بدلها main المعادلة اللي
+
+683
+01:21:25,080 --> 01:21:36,540
+عندناها ينجي هنا substitute and equation one we
+
+684
+01:21:36,540 --> 01:21:46,120
+get نقصد علامات dy على dx يكون v زائد x دي v على
+
+685
+01:21:46,120 --> 01:21:55,200
+dx الطرف اليمينبصرار F of B المعادلة
+
+686
+01:21:55,200 --> 01:22:02,580
+هذه بقدر اكتبها على الشكل التالي XGB على DX بتساوي
+
+687
+01:22:02,580 --> 01:22:13,200
+F of B ناقص ال B نقدر نفصل المتغيرات يبقى هذه
+
+688
+01:22:13,200 --> 01:22:28,390
+بتصير EVعلى F of D مقص ال V بتساوي DX على X ده
+
+689
+01:22:28,390 --> 01:22:32,750
+شوية وصلة Superbola كلها يبقى بنحل كذلك وكلها بنحل
+
+690
+01:22:32,750 --> 01:22:41,030
+قبل قليل يلقى دي Superbola equation
+
+691
+01:22:41,030 --> 01:22:46,030
+ده كان
+
+692
+01:22:49,090 --> 01:22:58,310
+بsize as before ناخد
+
+693
+01:22:58,310 --> 01:22:59,590
+مثال توضيح عليه
+
+694
+01:23:41,060 --> 01:23:46,320
+ومن ثم Solve
+
+695
+01:23:48,530 --> 01:24:05,890
+إذا تبقى N dy على dx يساوي 4y ناقص 3x على 2x ناقص
+
+696
+01:24:05,890 --> 01:24:06,190
+y
+
+697
+01:24:35,120 --> 01:24:39,020
+سؤال مرحبا يقول بيبينلي إذا المعادلات التي
+
+698
+01:24:39,020 --> 01:24:45,640
+تستخدمها هي عبارة عن معادلات متجانسة مميزة وبيتم
+
+699
+01:24:45,640 --> 01:24:51,380
+حل هذه المعادلة بيقول الشريف أو الساجل إذا تقدر
+
+700
+01:24:51,380 --> 01:24:57,720
+تقول المعادلة كلها لدلالة y على x أو x على y تصير
+
+701
+01:24:57,720 --> 01:25:02,390
+مميزةبس ممنوع يكون مثلا واحد على X وخمسة على Y
+
+702
+01:25:02,390 --> 01:25:07,150
+ممنوع على كده بدي يكون Y على X أو X على Y لإن لو
+
+703
+01:25:07,150 --> 01:25:11,890
+كنت وصلت لحاله مش مشكلة خالص طبعا يبقى يبقى يبقى
+
+704
+01:25:11,890 --> 01:25:19,190
+كله solution dy على dx يسبب شو رأيك لو جسمت بس
+
+705
+01:25:19,190 --> 01:25:30,310
+والمقام على X كله مش بصير اربع Y على Xناخذ تلاتة
+
+706
+01:25:30,310 --> 01:25:38,750
+على اتنين ناخذ y على x صح ولا لا؟ جسم كله من
+
+707
+01:25:38,750 --> 01:25:42,870
+البصرة والمقاب على x الطبعي صارت معادلة لدلالة y
+
+708
+01:25:42,870 --> 01:25:47,650
+على x ولا لا؟ زي ما قلنا صارت function بس احنا
+
+709
+01:25:47,650 --> 01:25:53,490
+صارت function of y على capital F of y على xبنبدأ
+
+710
+01:25:53,490 --> 01:25:57,130
+نعمل عليها المادة homogeneous differential
+
+711
+01:25:57,130 --> 01:26:02,270
+equation يبقى هذا الصغير هو homogeneous
+
+712
+01:26:02,270 --> 01:26:08,850
+differential equation ليشوف كيف نحل ال homogeneous
+
+713
+01:26:08,850 --> 01:26:16,270
+differential equation نيجي نقوله خُد Y على X تساوي
+
+714
+01:26:16,270 --> 01:26:21,630
+Z فانشطرنا تقولنا Y تساوي X
+
+715
+01:26:26,060 --> 01:26:35,600
+DX ممكن نسوي V ذائب X في DV على DX لما عادلتنا
+
+716
+01:26:35,600 --> 01:26:40,940
+هصير على الشكل التالي هشير DY على DX و اكتب قيمتها
+
+717
+01:26:40,940 --> 01:26:50,660
+اللي هي V ذائب V ذائب X في DV على DX على الطرف
+
+718
+01:26:50,660 --> 01:26:59,660
+الشمال نيجي للطرف اليمينأنه أربعة V ناقص تلاتة على
+
+719
+01:26:59,660 --> 01:27:10,540
+اتنين ناقص V نود V على الشجرة التالية يتجسر X بـDP
+
+720
+01:27:10,540 --> 01:27:20,440
+على DX يساوي أربعة V ناقص تلاتة على اتنين ناقص V
+
+721
+01:27:20,440 --> 01:27:28,220
+ناقص Bأضافنا للثلاثين لوساوية V هذه بدرة واحدة
+
+722
+01:27:28,220 --> 01:27:36,060
+لهذه المفاهيم يا بنات كبسيل XDD على DX يساوي كله
+
+723
+01:27:36,060 --> 01:27:47,380
+على اتنين ناقص V يظل اربعة V ناقص تلاتة وهذه
+
+724
+01:27:47,380 --> 01:27:57,020
+باعتماد على واحدة تنضرب لناقص Vتنين ناقص V وحتى
+
+725
+01:27:57,020 --> 01:28:05,140
+مقامتنا الكل يبقى X DV على DX يبقى اتنين ناقص V
+
+726
+01:28:05,140 --> 01:28:15,540
+بالمقام هنا اربعة V ناقص تلاتة ناقص اتنين V زائد V
+
+727
+01:28:15,540 --> 01:28:26,670
+تربية يبقى صارة المثلة اللي هو X DVعلى dx u7 أي b
+
+728
+01:28:26,670 --> 01:28:36,070
+تربيع وعنفه نقص 2u زائد 4a زائد 2b وغيرها جداش نقص
+
+729
+01:28:36,070 --> 01:28:42,950
+تلاتة مافيش غيرها على الاثنين ناقصين فالشك اللي
+
+730
+01:28:42,950 --> 01:28:47,870
+بيكتبها بدلالة b والشك اسمها بدلالة x وb
+
+731
+01:28:51,860 --> 01:28:58,020
+يبقى هذا شبسيدي اتنين ناقص V على V تربية زائد
+
+732
+01:28:58,020 --> 01:29:06,320
+اتنين V ناقص تلاتة DV يبقى يسوى DX على X يبقى هذا
+
+733
+01:29:06,320 --> 01:29:14,720
+C Parabol equation يبقى هذا C Parabol equation
+
+734
+01:29:14,720 --> 01:29:24,840
+السؤال هو هذه تقبل very easily يبقى المينكيف نتكلم
+
+735
+01:29:24,840 --> 01:29:34,840
+طبش مدد؟ حالي للمعادلة، مقصود A، مقصود B، مقصود A،
+
+736
+01:29:34,840 --> 01:29:35,480
+مقصود B، مقصود A، مقصود B، مقصود A، مقصود B، مقصود
+
+737
+01:29:35,480 --> 01:29:35,540
+A، مقصود B، مقصود A، مقصود B، مقصود A، مقصود B،
+
+738
+01:29:35,540 --> 01:29:37,520
+B، مقصود A، مقصود B، مقصود A، مقصود B، مقصود A،
+
+739
+01:29:37,520 --> 01:29:42,300
+مقصود A، مقصود B، مقصود A، مقصود A، مقصود B، مقصود
+
+740
+01:29:42,300 --> 01:29:52,310
+A، مقصود A، مقصود A، مقصودهذه بيه وهذه بيه وهذه
+
+741
+01:29:52,310 --> 01:29:58,450
+واحد وهذه ثلاثة وهذه زائد وهذه ناقص ناقص بيه زائد
+
+742
+01:29:58,450 --> 01:30:06,010
+تلاتة بيه زائد اتنين بيه كيف تسرع مع القوة؟ كسور
+
+743
+01:30:06,010 --> 01:30:12,870
+يزمية كسور يزمية ممتازة اتراكتوز يبقى هذا الكلام
+
+744
+01:30:12,870 --> 01:30:20,370
+متساوي هذا قوس اللي هو بيه ناقص واحدو بس تاني D زي
+
+745
+01:30:20,370 --> 01:30:26,950
+التلاتة عاملين كل واحد من القاعدة الأولى و اتنين
+
+746
+01:30:26,950 --> 01:30:33,210
+are different اتنين كولوستان و كمان كولوستان تاني
+
+747
+01:30:33,210 --> 01:30:39,330
+بدنا نتخلص من هذه التسورة و نروح نطلب اتنين في هذا
+
+748
+01:30:39,330 --> 01:30:46,060
+المقام اطلب العربي عندك اطلب اتنين في D ناقص واحدو
+
+749
+01:30:46,060 --> 01:30:53,720
+B زائد تلاتة بنحصل على اتنين ناقص B يساوي A في B
+
+750
+01:30:53,720 --> 01:31:02,120
+زائد تلاتة زائد B في B ناقص واحد يجب اقولك لو كانت
+
+751
+01:31:02,120 --> 01:31:11,360
+ال B تساوي واحد then اتنين ناقص واحد يساوي اربعة A
+
+752
+01:31:11,360 --> 01:31:15,600
+وهذه مع السلامة يبقى هذا بدي اعطيك
+
+753
+01:31:18,560 --> 01:31:27,760
+نقص واحد يساوي واحد الان لو كان ال V يكون ناقص
+
+754
+01:31:27,760 --> 01:31:35,880
+ثلاثة then يصير اتنين زائد ثلاثة ناقص ناقص ثلاثة
+
+755
+01:31:35,880 --> 01:31:42,340
+يعني زائد ثلاثة ناقص ثلاثة يبقى هنا ناقص ثلاثة
+
+756
+01:31:42,340 --> 01:31:51,740
+ناقص اربع دي يمكن ناقص اربع دييبقى D مساوى سنة
+
+757
+01:31:51,740 --> 01:31:58,800
+وخمس أربعة يبقى مثلتنا صارت على الشكل التالي اللي
+
+758
+01:31:58,800 --> 01:32:06,060
+هو تكامل نمينا الطلب ثالث الأربعة و الرابعة تانية
+
+759
+01:32:06,060 --> 01:32:17,230
+الرابعة وهنا واحد على V مافس واحد في DVوهنا ناطس
+
+760
+01:32:17,230 --> 01:32:27,590
+بله خمس أربع وهنا واحد على بيه زائد تلاتة وهي
+
+761
+01:32:27,590 --> 01:32:31,990
+التكامل دي فيها الطرف الشمالي لجهة التكامل هذا
+
+762
+01:32:31,990 --> 01:32:36,530
+ساعطه عليه التكامل اللي اتنين هؤلاء اللي بيساوي
+
+763
+01:32:36,530 --> 01:32:41,350
+تكامل من بيه X على X
+
+764
+01:32:54,940 --> 01:33:05,160
+طيب لان كله blend يبقى ربع لل absolute value لل V
+
+765
+01:33:05,160 --> 01:33:14,560
+ناقص واحد ناقص خمس أربع لل absolute value لل V
+
+766
+01:33:14,560 --> 01:33:21,580
+زائد تلاتة لل V زائد تلاتة بدنا نسوي التلاتة
+
+767
+01:33:21,770 --> 01:33:28,190
+absolute value ل X زائد كل ثانية C شو رايش نموذج
+
+768
+01:33:28,190 --> 01:33:34,970
+أربعة و نتخلص منها؟ شو حسن؟ يبقى بسيطة عندي اللم و
+
+769
+01:33:34,970 --> 01:33:42,690
+ال V اللي هو Y على X ناقص واحد ناقص خمسة لم Y على
+
+770
+01:33:42,690 --> 01:33:49,810
+X زائد تلاتة يساوي أربعة لم absolute value ل X
+
+771
+01:33:49,810 --> 01:34:01,830
+زائدأربعة C one مثلًا طيب هذه بصيها لان absolute
+
+772
+01:34:01,830 --> 01:34:11,570
+value ل Y ناقص X كله على X ناقص خمسة لان Y زائد
+
+773
+01:34:11,570 --> 01:34:19,370
+ثلاثة X كله على X وهنا بتساوي أربعة لان
+
+774
+01:34:23,380 --> 01:34:29,840
+هذا يبقى ناقص بالصير لل absolute value لل Y ناقص X
+
+775
+01:34:29,840 --> 01:34:36,960
+ناقص لل absolute value ل X هذه ناقص خمسة لل
+
+776
+01:34:36,960 --> 01:34:45,720
+absolute value لتلاتة X Y زائد تلاتة X ناقص مع
+
+777
+01:34:45,720 --> 01:34:52,360
+ناقص بالصير زائد خمسةLin Absolute Value of X يساوي
+
+778
+01:34:52,360 --> 01:35:01,380
+4Lin Absolute Value of X زائد 4C1 طيب دعونا نشوف
+
+779
+01:35:01,380 --> 01:35:10,060
+هذي هذي و هذي كتاش مضالين 4Lin X وديها على ناحية
+
+780
+01:35:10,060 --> 01:35:19,240
+التانية تتجهل مع السلم صح؟ طيب هذي بتصير إيش؟بتصير
+
+781
+01:35:19,240 --> 01:35:27,000
+لل absolute value ل Y ناقص X ناقص لل absolute
+
+782
+01:35:27,000 --> 01:35:36,200
+value ل Y زي 3X خُص 5 يساوي 4Ci
+
+783
+01:35:47,790 --> 01:35:55,530
+هذه جمبسة يبقى اني بصير lamb salute value ل Y ماقص
+
+784
+01:35:55,530 --> 01:36:06,770
+X على Y زائد تلاتة X هذه كل قص خمسة يساوي أربعة
+
+785
+01:36:06,770 --> 01:36:17,060
+سيران كده تخلص من ال lamb يبقى بصير انsolute value
+
+786
+01:36:17,060 --> 01:36:24,120
+of y-x على solute value of y زائد تلاتة كل وصة
+
+787
+01:36:24,120 --> 01:36:32,760
+خمسة يسوى D أربعة C واحد الشرايح هذه كلها بترحبها
+
+788
+01:36:32,760 --> 01:36:38,780
+في C صح ولا لا يبقى بناء علينا solution
+
+789
+01:36:42,800 --> 01:36:51,160
+absolute value لروعي ناقص x يسوى c ان ال absolute
+
+790
+01:36:51,160 --> 01:36:58,620
+value لروعي ثائر ثلاثة و نصف خمسة يجعل هذا الحل
+
+791
+01:36:58,620 --> 01:37:04,420
+الامر لا يزال هناك سؤال كثير موجود
+
diff --git a/PL9fwy3NUQKwa8ZDfSFGn6H8xVFLzqmCZC/0yOo6En_6XI_raw.json b/PL9fwy3NUQKwa8ZDfSFGn6H8xVFLzqmCZC/0yOo6En_6XI_raw.json
new file mode 100644
index 0000000000000000000000000000000000000000..64ef92e3240b8b04682dea811bf9db0edd8eaad9
--- /dev/null
+++ b/PL9fwy3NUQKwa8ZDfSFGn6H8xVFLzqmCZC/0yOo6En_6XI_raw.json
@@ -0,0 +1 @@
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تمام تمام يبقى من الآن فصاعدا لما يكون عندي first order differential equation والمعامل تبع ال dy by dt هو الواحد الصحيح بيكون شكل ال integrating factor mu of t هو ال exponential مرفوه للأس تكامل P of T dt", "tokens": [2407, 3224, 8315, 9673, 3615, 10943, 1211, 6055, 3555, 3615, 2423, 398, 6, 31439, 10874, 3215, 11703, 1829, 4117, 36764, 24401, 20328, 5016, 1829, 5016, 46811, 10943, 46811, 10943, 7251, 3555, 4587, 7578, 9154, 6024, 48506, 6156, 9381, 995, 22488, 995, 5296, 15042, 7251, 30544, 18871, 16254, 700, 1668, 15756, 5367, 4032, 45340, 3615, 10943, 1211, 6055, 3555, 3615, 2423, 14584, 538, 36423, 31439, 2423, 14407, 24401, 31767, 5016, 1829, 5016, 4724, 1829, 30544, 13412, 28820, 2423, 26889, 5952, 2992, 295, 256, 31439, 2423, 21510, 3714, 28480, 2407, 3224, 24976, 10721, 3794, 6055, 4117, 10943, 1211, 430, 295, 314, 36423], "avg_logprob": -0.24613242338199426, "compression_ratio": 1.581896551724138, "no_speech_prob": 0.0, "words": [{"start": 628.61, "end": 629.49, "word": 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657.04, "end": 680.82, "text": "وهذا ما أصنعه مع كل سؤال عند الحل طب الآن بدنا نعرف ما هو شكل الحل للمعادلة التفاضلي اللي عندنا طب نروح نقول نضرب كل term من ال term سبعة المعادلة التفاضلي اللي عندنا في الميو of T بنستبدل هذا بالميو prime of T في ال Y", "tokens": [2407, 3224, 15730, 19446, 5551, 9381, 1863, 3615, 3224, 20449, 28242, 8608, 33604, 6027, 43242, 21542, 1211, 23032, 3555, 6024, 48506, 47525, 8315, 8717, 3615, 28480, 19446, 31439, 13412, 28820, 21542, 1211, 5296, 19528, 3615, 18513, 37977, 16712, 5172, 46958, 20292, 13672, 1829, 43242, 8315, 23032, 3555, 8717, 32887, 5016, 8717, 39648, 8717, 11242, 25513, 28242, 1433, 9154, 2423, 1433, 8608, 3555, 27884, 9673, 3615, 18513, 37977, 16712, 5172, 46958, 20292, 13672, 1829, 43242, 8315, 8978, 9673, 1829, 2407, 295, 314, 44945, 14851, 44510, 1211, 23758, 20666, 2304, 1829, 2407, 5835, 295, 314, 8978, 2423, 398], "avg_logprob": -0.25531571181779056, "compression_ratio": 1.9270833333333333, "no_speech_prob": 0.0, "words": [{"start": 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ما", "probability": 0.8984375}, {"start": 664.48, "end": 664.92, "word": " هو", "probability": 0.654296875}, {"start": 664.92, "end": 665.44, "word": " شكل", "probability": 0.976318359375}, {"start": 665.44, "end": 666.1, "word": " الحل", "probability": 0.991455078125}, {"start": 666.1, "end": 667.58, "word": " للمعادلة", "probability": 0.9216796875}, {"start": 667.58, "end": 668.26, "word": " التفاضلي", "probability": 0.73040771484375}, {"start": 668.26, "end": 668.46, "word": " اللي", "probability": 0.7265625}, {"start": 668.46, "end": 668.94, "word": " عندنا", "probability": 0.982666015625}, {"start": 668.94, "end": 669.46, "word": " طب", "probability": 0.7763671875}, {"start": 669.46, "end": 669.74, "word": " نروح", "probability": 0.781494140625}, {"start": 669.74, "end": 670.06, "word": " نقول", "probability": 0.5008544921875}, {"start": 670.06, "end": 670.52, "word": " نضرب", "probability": 0.8245442708333334}, {"start": 670.52, "end": 671.04, "word": " كل", "probability": 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"word": " Y", "probability": 0.974609375}, {"start": 3028.33, "end": 3028.89, "word": " as", "probability": 0.8359375}, {"start": 3028.89, "end": 3029.09, "word": " a", "probability": 0.96533203125}, {"start": 3029.09, "end": 3029.39, "word": " function", "probability": 0.76953125}, {"start": 3029.39, "end": 3029.63, "word": " of", "probability": 0.97509765625}, {"start": 3029.63, "end": 3029.79, "word": " it", "probability": 0.1590576171875}, {"start": 3029.79, "end": 3030.07, "word": " سواء", "probability": 0.9207356770833334}, {"start": 3030.07, "end": 3030.49, "word": " كانت", "probability": 0.97216796875}, {"start": 3030.49, "end": 3030.75, "word": " دالة", "probability": 0.8470052083333334}, {"start": 3030.75, "end": 3031.43, "word": " صريحة", "probability": 0.9942626953125}, {"start": 3031.43, "end": 3031.95, "word": " او", "probability": 0.91748046875}, {"start": 3031.95, "end": 3032.29, "word": " دالة", "probability": 0.95458984375}, {"start": 3032.29, "end": 3033.57, "word": " implicit", "probability": 0.96044921875}, {"start": 3033.57, "end": 3035.79, "word": " او", "probability": 0.921875}, {"start": 3035.79, "end": 3036.37, "word": " غير", "probability": 0.7242431640625}, {"start": 3036.37, "end": 3036.99, "word": " يعني", "probability": 0.903076171875}, {"start": 3036.99, "end": 3037.37, "word": " دالة", "probability": 0.9705403645833334}, {"start": 3037.37, "end": 3037.81, "word": " بيمنية", "probability": 0.787353515625}, {"start": 3037.81, "end": 3038.15, "word": " او", "probability": 0.93701171875}, {"start": 3038.15, "end": 3038.71, "word": " دالة", "probability": 0.9820963541666666}, {"start": 3038.71, "end": 3039.29, "word": " صريحة", "probability": 0.9931640625}], "temperature": 1.0}, {"id": 117, "seek": 306253, "start": 3039.57, "end": 3062.53, "text": "يبقى بالحلها بواصفة ال integration الان بالتالي ناخد أمثلة توريحية على الشغل يعني يا بنات الشغل دلوقتي لحد ما أطلع في المعادلة بدي أحاول أفصل ال X لحالي و ال Y لحالي أكمل انت خلصت أي مسألة ناخد أمثلة يبقى example one", "tokens": [1829, 3555, 4587, 7578, 20666, 5016, 1211, 11296, 4724, 2407, 33546, 5172, 3660, 2423, 10980, 2423, 7649, 20666, 2655, 6027, 1829, 8717, 47283, 3215, 5551, 2304, 12984, 37977, 6055, 13063, 1829, 5016, 10632, 15844, 25124, 17082, 1211, 37495, 22653, 35186, 4724, 8315, 2655, 25124, 17082, 1211, 11778, 1211, 30543, 31371, 5296, 24401, 19446, 5551, 9566, 1211, 3615, 8978, 9673, 3615, 18513, 37977, 4724, 16254, 5551, 5016, 995, 12610, 5551, 5172, 36520, 2423, 1783, 5296, 5016, 6027, 1829, 4032, 2423, 398, 5296, 5016, 6027, 1829, 5551, 24793, 1211, 16472, 2655, 16490, 1211, 9381, 2655, 36632, 47524, 10721, 37977, 8717, 47283, 3215, 5551, 2304, 12984, 37977, 7251, 3555, 4587, 7578, 1365, 472], "avg_logprob": -0.4850788239960198, "compression_ratio": 1.719626168224299, "no_speech_prob": 5.960464477539063e-08, "words": [{"start": 3039.57, "end": 3040.25, "word": "يبقى", "probability": 0.73468017578125}, {"start": 3040.25, "end": 3040.93, "word": " بالحلها", 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3052.93, "word": " ال", "probability": 0.873046875}, {"start": 3052.93, "end": 3053.21, "word": " X", "probability": 0.41357421875}, {"start": 3053.21, "end": 3054.09, "word": " لحالي", "probability": 0.5411376953125}, {"start": 3054.09, "end": 3054.33, "word": " و", "probability": 0.78173828125}, {"start": 3054.33, "end": 3054.41, "word": " ال", "probability": 0.79443359375}, {"start": 3054.41, "end": 3054.59, "word": " Y", "probability": 0.88037109375}, {"start": 3054.59, "end": 3055.13, "word": " لحالي", "probability": 0.74072265625}, {"start": 3055.13, "end": 3055.75, "word": " أكمل", "probability": 0.8136393229166666}, {"start": 3055.75, "end": 3055.97, "word": " انت", "probability": 0.4207916259765625}, {"start": 3055.97, "end": 3056.67, "word": " خلصت", "probability": 0.5889892578125}, {"start": 3056.67, "end": 3056.91, "word": " أي", "probability": 0.52001953125}, {"start": 3056.91, "end": 3057.93, "word": " مسألة", "probability": 0.88525390625}, {"start": 3057.93, "end": 3059.37, "word": " ناخد", "probability": 0.86669921875}, {"start": 3059.37, "end": 3060.13, "word": " أمثلة", "probability": 0.9742431640625}, {"start": 3060.13, "end": 3061.27, "word": " يبقى", "probability": 0.8824462890625}, {"start": 3061.27, "end": 3061.89, "word": " example", "probability": 0.74853515625}, {"start": 3061.89, "end": 3062.53, "word": " one", "probability": 0.446533203125}], "temperature": 1.0}, {"id": 118, "seek": 309869, "start": 3073.19, "end": 3098.69, "text": "and following differential equation المعادلة الأولى نمرا M dy by dx dy by dx يسمى E أس Y أصيني اتنين X", "tokens": [474, 3480, 15756, 5367, 9673, 3615, 18513, 37977, 16247, 12610, 7578, 8717, 2304, 23557, 376, 14584, 538, 30017, 14584, 538, 30017, 7251, 38251, 7578, 462, 5551, 3794, 398, 5551, 9381, 9957, 1829, 1975, 2655, 1863, 9957, 1783], "avg_logprob": -0.5476973684210527, "compression_ratio": 1.096774193548387, "no_speech_prob": 0.0, "words": [{"start": 3073.19, "end": 3073.75, "word": "and", "probability": 0.08380126953125}, {"start": 3073.75, "end": 3075.25, "word": " following", "probability": 0.66357421875}, {"start": 3075.25, "end": 3078.27, "word": " differential", "probability": 0.7724609375}, {"start": 3078.27, "end": 3081.37, "word": " equation", "probability": 0.6435546875}, {"start": 3081.37, "end": 3084.89, "word": " المعادلة", "probability": 0.8792724609375}, {"start": 3084.89, "end": 3085.57, "word": " الأولى", "probability": 0.986328125}, {"start": 3085.57, "end": 3086.05, "word": " نمرا", "probability": 0.411376953125}, {"start": 3086.05, "end": 3086.71, "word": " M", "probability": 0.51904296875}, {"start": 3086.71, "end": 3088.51, "word": " dy", "probability": 0.41845703125}, {"start": 3088.51, "end": 3088.87, "word": " by", "probability": 0.430908203125}, {"start": 3088.87, "end": 3089.71, "word": " dx", "probability": 0.986328125}, {"start": 3089.71, "end": 3090.71, "word": " dy", "probability": 0.301025390625}, {"start": 3090.71, "end": 3091.89, "word": " by", "probability": 0.76904296875}, {"start": 3091.89, "end": 3092.67, "word": " dx", "probability": 0.99365234375}, {"start": 3092.67, "end": 3094.21, "word": " يسمى", "probability": 0.638916015625}, {"start": 3094.21, "end": 3094.87, "word": " E", "probability": 0.348876953125}, {"start": 3094.87, "end": 3095.45, "word": " أس", "probability": 0.467529296875}, {"start": 3095.45, "end": 3095.97, "word": " Y", "probability": 0.3515625}, {"start": 3095.97, "end": 3097.63, "word": " أصيني", "probability": 0.475341796875}, {"start": 3097.63, "end": 3098.19, "word": " اتنين", "probability": 0.85107421875}, {"start": 3098.19, "end": 3098.69, "word": " X", "probability": 0.91796875}], "temperature": 1.0}, {"id": 119, "seek": 312264, "start": 3102.48, "end": 3122.64, "text": "E أوسى اتنين Y كله فيه أوساين X نمرى بيه السؤال التاني انه X ال Y' يساوي واحد ناقص Y' كله اص نص", "tokens": [36, 34051, 3794, 7578, 1975, 2655, 1863, 9957, 398, 28242, 3224, 8978, 3224, 5551, 41779, 995, 9957, 1783, 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{"start": 3120.92, "end": 3122.04, "word": " كله", "probability": 0.873046875}, {"start": 3122.04, "end": 3122.2, "word": " اص", "probability": 0.504638671875}, {"start": 3122.2, "end": 3122.64, "word": " نص", "probability": 0.716064453125}], "temperature": 1.0}, {"id": 120, "seek": 315229, "start": 3137.19, "end": 3152.29, "text": "السؤال بيقول يحل كل من المعاملات التفاعلونية تالية السؤال الأول dy by x يساوي e قص y صينة من x على y ناقص e وسط 2y بكو صينة من x", "tokens": [6027, 3794, 33604, 6027, 4724, 1829, 39648, 7251, 5016, 1211, 28242, 9154, 9673, 3615, 10943, 1211, 9307, 16712, 5172, 995, 30241, 11536, 10632, 6055, 6027, 10632, 21136, 33604, 6027, 16247, 12610, 14584, 538, 2031, 7251, 3794, 995, 45865, 308, 12174, 9381, 288, 20328, 9957, 3660, 9154, 2031, 15844, 288, 8717, 995, 4587, 9381, 308, 46952, 9566, 568, 88, 4724, 4117, 2407, 20328, 9957, 3660, 9154, 2031], "avg_logprob": -0.59608207887678, "compression_ratio": 1.5851851851851853, "no_speech_prob": 1.7881393432617188e-07, 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" F", "probability": 0.39111328125}, {"start": 4910.32, "end": 4911.18, "word": " of", "probability": 0.395263671875}, {"start": 4911.18, "end": 4911.8, "word": " B", "probability": 0.7900390625}, {"start": 4911.8, "end": 4915.2, "word": " المعادلة", "probability": 0.8721923828125}, {"start": 4915.2, "end": 4915.52, "word": " هذه", "probability": 0.367919921875}, {"start": 4915.52, "end": 4915.88, "word": " بقدر", "probability": 0.7939453125}, {"start": 4915.88, "end": 4916.32, "word": " اكتبها", "probability": 0.85458984375}, {"start": 4916.32, "end": 4916.46, "word": " على", "probability": 0.796875}, {"start": 4916.46, "end": 4916.88, "word": " الشكل", "probability": 0.87744140625}, {"start": 4916.88, "end": 4917.48, "word": " التالي", "probability": 0.8421223958333334}, {"start": 4917.48, "end": 4919.1, "word": " XGB", "probability": 0.54150390625}, {"start": 4919.1, "end": 4920.34, "word": " على", "probability": 0.4111328125}, {"start": 4920.34, "end": 4921.14, "word": " DX", 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القوة؟ كسور يزمية كسور يزمية ممتازة اتراكتوز يبقى هذا الكلام متساوي هذا قوس اللي هو بيه ناقص واحد", "tokens": [3224, 24192, 4724, 1829, 3224, 37037, 24192, 4724, 1829, 3224, 37037, 24192, 36764, 24401, 37037, 24192, 38637, 1211, 5718, 104, 3660, 37037, 24192, 30767, 16373, 3215, 37037, 24192, 8717, 995, 4587, 9381, 8717, 995, 4587, 9381, 4724, 1829, 3224, 30767, 16373, 3215, 6055, 1211, 9307, 3660, 4724, 1829, 3224, 30767, 16373, 3215, 1975, 2655, 1863, 9957, 4724, 1829, 3224, 9122, 33911, 6055, 3794, 2288, 3615, 20449, 25062, 2407, 3660, 22807, 9122, 3794, 13063, 7251, 11622, 2304, 10632, 9122, 3794, 13063, 7251, 11622, 2304, 10632, 3714, 2304, 2655, 31377, 3660, 1975, 2655, 23557, 4117, 2655, 2407, 11622, 7251, 3555, 4587, 7578, 23758, 2423, 28820, 10943, 44650, 3794, 995, 45865, 23758, 12174, 41779, 13672, 1829, 31439, 4724, 1829, 3224, 8717, 995, 4587, 9381, 36764, 24401], "avg_logprob": -0.3581149325736107, "compression_ratio": 2.1882352941176473, "no_speech_prob": 0.0, "words": 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"probability": 0.8522135416666666}, {"start": 5710.84, "end": 5711.92, "word": " تتجهل", "probability": 0.39892578125}, {"start": 5711.92, "end": 5712.3, "word": " مع", "probability": 0.908203125}, {"start": 5712.3, "end": 5712.92, "word": " السلم", "probability": 0.68994140625}, {"start": 5712.92, "end": 5714.94, "word": " صح؟", "probability": 0.7295735677083334}, {"start": 5714.94, "end": 5716.02, "word": " طيب", "probability": 0.8396809895833334}, {"start": 5716.02, "end": 5716.82, "word": " هذي", "probability": 0.8977864583333334}, {"start": 5716.82, "end": 5717.38, "word": " بتصير", "probability": 0.9363606770833334}, {"start": 5717.38, "end": 5717.88, "word": " إيش؟", "probability": 0.8314208984375}], "temperature": 1.0}, {"id": 209, "seek": 573620, "start": 5718.26, "end": 5736.2, "text": "بتصير لل absolute value ل Y ناقص X ناقص لل absolute value ل Y زي 3X خُص 5 يساوي 4Ci", "tokens": [3555, 2655, 9381, 13546, 24976, 8236, 2158, 5296, 398, 8717, 995, 4587, 9381, 1783, 8717, 995, 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5726.16, "word": " لل", "probability": 0.82763671875}, {"start": 5726.16, "end": 5727.0, "word": " absolute", "probability": 0.94091796875}, {"start": 5727.0, "end": 5727.58, "word": " value", "probability": 0.9892578125}, {"start": 5727.58, "end": 5727.82, "word": " ل", "probability": 0.96484375}, {"start": 5727.82, "end": 5728.3, "word": " Y", "probability": 0.9619140625}, {"start": 5728.3, "end": 5728.88, "word": " زي", "probability": 0.83154296875}, {"start": 5728.88, "end": 5730.28, "word": " 3X", "probability": 0.689697265625}, {"start": 5730.28, "end": 5731.18, "word": " خُص", "probability": 0.4748077392578125}, {"start": 5731.18, "end": 5732.06, "word": " 5", "probability": 0.91748046875}, {"start": 5732.06, "end": 5733.74, "word": " يساوي", "probability": 0.92138671875}, {"start": 5733.74, "end": 5736.2, "word": " 4Ci", "probability": 0.6046549479166666}], "temperature": 1.0}, {"id": 210, "seek": 577519, "start": 5747.79, "end": 5775.19, "text": "هذه جمبسة يبقى اني بصير lamb salute value ل Y ماقص X على Y زائد تلاتة X هذه كل قص خمسة يساوي أربعة سيران كده تخلص من ال lamb يبقى بصير ان", "tokens": [3224, 24192, 10874, 2304, 3555, 3794, 3660, 7251, 3555, 4587, 7578, 16472, 1829, 4724, 9381, 13546, 10097, 33673, 2158, 5296, 398, 19446, 4587, 9381, 1783, 15844, 398, 30767, 16373, 3215, 6055, 1211, 9307, 3660, 1783, 29538, 28242, 12174, 9381, 16490, 2304, 3794, 3660, 7251, 3794, 995, 45865, 5551, 25513, 27884, 8608, 13546, 7649, 9122, 3215, 3224, 6055, 9778, 1211, 9381, 9154, 2423, 10097, 7251, 3555, 4587, 7578, 4724, 9381, 13546, 16472], "avg_logprob": -0.5190972056653764, "compression_ratio": 1.4473684210526316, "no_speech_prob": 5.960464477539063e-08, "words": [{"start": 5747.79, "end": 5748.17, "word": "هذه", "probability": 0.26251220703125}, {"start": 5748.17, "end": 5748.97, "word": " جمبسة", "probability": 0.494677734375}, {"start": 5748.97, "end": 5750.85, "word": " يبقى", "probability": 0.74737548828125}, {"start": 5750.85, "end": 5750.99, "word": " اني", "probability": 0.268798828125}, {"start": 5750.99, "end": 5751.73, "word": " بصير", "probability": 0.9729817708333334}, {"start": 5751.73, "end": 5752.61, "word": " lamb", "probability": 0.0499267578125}, {"start": 5752.61, "end": 5753.73, "word": " salute", "probability": 0.1497802734375}, {"start": 5753.73, "end": 5754.19, "word": " value", "probability": 0.347412109375}, {"start": 5754.19, "end": 5754.45, "word": " ل", "probability": 0.544921875}, {"start": 5754.45, "end": 5754.81, "word": " Y", "probability": 0.41064453125}, {"start": 5754.81, "end": 5755.53, "word": " ماقص", "probability": 0.5103352864583334}, {"start": 5755.53, "end": 5756.03, "word": " X", "probability": 0.88916015625}, {"start": 5756.03, "end": 5757.07, "word": " على", "probability": 0.7255859375}, {"start": 5757.07, "end": 5757.89, "word": " Y", "probability": 0.95166015625}, {"start": 5757.89, "end": 5758.75, "word": " زائد", "probability": 0.7985026041666666}, {"start": 5758.75, "end": 5759.73, "word": " تلاتة", "probability": 0.898193359375}, {"start": 5759.73, "end": 5760.21, "word": " X", "probability": 0.96875}, {"start": 5760.21, "end": 5761.09, "word": " هذه", "probability": 0.59912109375}, {"start": 5761.09, "end": 5761.77, "word": " كل", "probability": 0.9599609375}, {"start": 5761.77, "end": 5762.77, "word": " قص", "probability": 0.49737548828125}, {"start": 5762.77, "end": 5764.59, "word": " خمسة", "probability": 0.8570556640625}, {"start": 5764.59, "end": 5765.61, "word": " يساوي", "probability": 0.841552734375}, {"start": 5765.61, "end": 5766.77, "word": " أربعة", "probability": 0.72314453125}, {"start": 5766.77, "end": 5767.71, "word": " سيران", "probability": 0.6985270182291666}, {"start": 5767.71, "end": 5769.41, "word": " كده", "probability": 0.5298665364583334}, {"start": 5769.41, "end": 5770.23, "word": " تخلص", "probability": 0.9376220703125}, {"start": 5770.23, "end": 5770.55, "word": " من", "probability": 0.986328125}, {"start": 5770.55, "end": 5770.85, "word": " ال", "probability": 0.79150390625}, {"start": 5770.85, "end": 5771.35, "word": " lamb", "probability": 0.42626953125}, {"start": 5771.35, "end": 5773.97, "word": " يبقى", "probability": 0.8326416015625}, {"start": 5773.97, "end": 5774.71, "word": " بصير", "probability": 0.9161783854166666}, {"start": 5774.71, "end": 5775.19, "word": " ان", "probability": 0.39306640625}], "temperature": 1.0}, {"id": 211, "seek": 579878, "start": 5775.92, "end": 5798.78, "text": "solute value of y-x على solute value of y زائد تلاتة كل وصة خمسة يسوى D أربعة C واحد الشرايح هذه كلها بترحبها في C صح ولا لا يبقى بناء علينا solution", "tokens": [30926, 1169, 2158, 295, 288, 12, 87, 15844, 1404, 1169, 2158, 295, 288, 30767, 16373, 3215, 6055, 1211, 9307, 3660, 28242, 4032, 9381, 3660, 16490, 2304, 3794, 3660, 7251, 3794, 2407, 7578, 413, 5551, 25513, 27884, 383, 36764, 24401, 25124, 23557, 1829, 5016, 29538, 28242, 11296, 39894, 2288, 5016, 3555, 11296, 8978, 383, 20328, 5016, 49429, 20193, 7251, 3555, 4587, 7578, 44945, 16606, 25894, 8315, 3827], "avg_logprob": -0.597947748739328, "compression_ratio": 1.3865030674846626, "no_speech_prob": 1.1920928955078125e-07, "words": [{"start": 5775.92, "end": 5776.62, "word": "solute", "probability": 0.5802001953125}, {"start": 5776.62, "end": 5777.06, "word": " value", "probability": 0.96923828125}, {"start": 5777.06, "end": 5777.28, "word": " of", "probability": 0.03131103515625}, {"start": 5777.28, "end": 5777.62, "word": " y", "probability": 0.37109375}, {"start": 5777.62, "end": 5778.76, "word": "-x", "probability": 0.4324951171875}, {"start": 5778.76, "end": 5779.3, "word": " على", "probability": 0.335693359375}, {"start": 5779.3, "end": 5780.02, "word": " solute", "probability": 0.753173828125}, {"start": 5780.02, "end": 5780.38, "word": " value", "probability": 0.9892578125}, {"start": 5780.38, "end": 5780.54, "word": " of", "probability": 0.21728515625}, {"start": 5780.54, "end": 5781.02, "word": " y", "probability": 0.83935546875}, {"start": 5781.02, "end": 5781.96, "word": " زائد", "probability": 0.5616048177083334}, {"start": 5781.96, "end": 5782.88, "word": " تلاتة", "probability": 0.7972412109375}, {"start": 5782.88, "end": 5783.64, "word": " كل", "probability": 0.8369140625}, {"start": 5783.64, "end": 5784.12, "word": " وصة", "probability": 0.3486328125}, {"start": 5784.12, "end": 5785.0, "word": " خمسة", "probability": 0.928466796875}, {"start": 5785.0, "end": 5785.76, "word": " يسوى", "probability": 0.6611328125}, {"start": 5785.76, "end": 5786.14, "word": " D", "probability": 0.48876953125}, {"start": 5786.14, "end": 5787.44, "word": " أربعة", "probability": 0.6055501302083334}, {"start": 5787.44, "end": 5788.04, "word": " C", "probability": 0.65966796875}, {"start": 5788.04, "end": 5789.02, "word": " واحد", "probability": 0.583984375}, {"start": 5789.02, "end": 5790.44, "word": " الشرايح", "probability": 0.52972412109375}, {"start": 5790.44, "end": 5790.82, "word": " هذه", "probability": 0.578125}, {"start": 5790.82, "end": 5791.5, "word": " كلها", "probability": 0.964599609375}, {"start": 5791.5, "end": 5792.76, "word": " بترحبها", "probability": 0.64892578125}, {"start": 5792.76, "end": 5792.98, "word": " في", "probability": 0.56396484375}, {"start": 5792.98, "end": 5793.4, "word": " C", "probability": 0.79345703125}, {"start": 5793.4, "end": 5795.4, "word": " صح", "probability": 0.52850341796875}, {"start": 5795.4, "end": 5795.64, "word": " ولا", "probability": 0.94580078125}, {"start": 5795.64, "end": 5796.0, "word": " لا", "probability": 0.65625}, {"start": 5796.0, "end": 5796.7, "word": " يبقى", "probability": 0.514617919921875}, {"start": 5796.7, "end": 5797.08, "word": " بناء", "probability": 0.5859375}, {"start": 5797.08, "end": 5797.76, "word": " علينا", "probability": 0.4422607421875}, {"start": 5797.76, "end": 5798.78, "word": " solution", "probability": 0.8935546875}], "temperature": 1.0}, {"id": 212, "seek": 582442, "start": 5802.8, "end": 5824.42, "text": "absolute value لروعي ناقص x يسوى c ان ال absolute value لروعي ثائر ثلاثة و نصف خمسة يجعل هذا الحل الامر لا يزال هناك سؤال كثير موجود", "tokens": [17243, 401, 1169, 2158, 5296, 32887, 3615, 1829, 8717, 995, 4587, 9381, 2031, 7251, 3794, 2407, 7578, 269, 16472, 2423, 8236, 2158, 5296, 32887, 3615, 1829, 38637, 16373, 2288, 38637, 1211, 5718, 104, 3660, 4032, 8717, 9381, 5172, 16490, 2304, 3794, 3660, 7251, 7435, 30241, 23758, 21542, 1211, 2423, 10943, 2288, 20193, 7251, 11622, 6027, 34105, 4117, 8608, 33604, 6027, 9122, 12984, 13546, 3714, 29245, 23328], "avg_logprob": -0.43097014925373134, "compression_ratio": 1.4583333333333333, "no_speech_prob": 0.0, "words": [{"start": 5802.8, "end": 5803.84, "word": "absolute", "probability": 0.8133138020833334}, {"start": 5803.84, "end": 5804.2, "word": " value", "probability": 0.8896484375}, {"start": 5804.2, "end": 5805.04, "word": " لروعي", "probability": 0.626861572265625}, {"start": 5805.04, "end": 5805.68, "word": " ناقص", "probability": 0.66986083984375}, {"start": 5805.68, "end": 5806.24, "word": " x", "probability": 0.59033203125}, {"start": 5806.24, "end": 5807.58, "word": " يسوى", "probability": 0.75311279296875}, {"start": 5807.58, "end": 5808.38, "word": " c", "probability": 0.412353515625}, {"start": 5808.38, "end": 5809.32, "word": " ان", "probability": 0.1444091796875}, {"start": 5809.32, "end": 5810.24, "word": " ال", "probability": 0.396484375}, {"start": 5810.24, "end": 5811.16, "word": " absolute", "probability": 0.65576171875}, {"start": 5811.16, "end": 5811.82, "word": " value", "probability": 0.97021484375}, {"start": 5811.82, "end": 5812.84, "word": " لروعي", "probability": 0.952880859375}, {"start": 5812.84, "end": 5813.7, "word": " ثائر", "probability": 0.5279134114583334}, {"start": 5813.7, "end": 5814.86, "word": " ثلاثة", "probability": 0.794775390625}, {"start": 5814.86, "end": 5815.46, "word": " و", "probability": 0.7470703125}, {"start": 5815.46, "end": 5816.04, "word": " نصف", "probability": 0.5963541666666666}, {"start": 5816.04, "end": 5817.0, "word": " خمسة", "probability": 0.8968505859375}, {"start": 5817.0, "end": 5817.56, "word": " يجعل", "probability": 0.5709635416666666}, {"start": 5817.56, "end": 5818.0, "word": " هذا", "probability": 0.91552734375}, {"start": 5818.0, "end": 5818.62, "word": " الحل", "probability": 0.9228515625}, {"start": 5818.62, "end": 5819.46, "word": " الامر", "probability": 0.3994954427083333}, {"start": 5819.46, "end": 5822.04, "word": " لا", "probability": 0.55126953125}, {"start": 5822.04, "end": 5822.46, "word": " يزال", "probability": 0.8136393229166666}, {"start": 5822.46, "end": 5822.74, "word": " هناك", "probability": 0.60052490234375}, {"start": 5822.74, "end": 5823.1, "word": " سؤال", "probability": 0.9812825520833334}, {"start": 5823.1, "end": 5823.62, "word": " كثير", "probability": 0.81396484375}, {"start": 5823.62, "end": 5824.42, "word": " موجود", "probability": 0.590576171875}], "temperature": 1.0}], "language": "ar", "language_probability": 1.0, "duration": 5836.4285, "duration_after_vad": 5355.415968750023}
\ No newline at end of file
diff --git a/PL9fwy3NUQKwa8ZDfSFGn6H8xVFLzqmCZC/0yOo6En_6XI_raw.srt b/PL9fwy3NUQKwa8ZDfSFGn6H8xVFLzqmCZC/0yOo6En_6XI_raw.srt
new file mode 100644
index 0000000000000000000000000000000000000000..b269b6cd2f5d7e0a12d54f43853fac1218fc330c
--- /dev/null
+++ b/PL9fwy3NUQKwa8ZDfSFGn6H8xVFLzqmCZC/0yOo6En_6XI_raw.srt
@@ -0,0 +1,3240 @@
+1
+00:00:09,200 --> 00:00:14,260
+المعادلة التفاصيلية من غطبة الأولى وهذه السنة
+
+2
+00:00:14,260 --> 00:00:20,760
+أخدنا منها عدة أصفر من المعادلة سنبدأ بالمعادلة
+
+3
+00:00:20,760 --> 00:00:26,240
+الأولى من linear equations المعادلات الخطوية
+
+4
+00:00:26,240 --> 00:00:32,350
+بإنقسام مدرسof integrating factors طريقة عواجة
+
+5
+00:00:32,350 --> 00:00:37,690
+بالتكابل طبعا سنعرف بعد قليل ماهو عامل التكابل
+
+6
+00:00:37,690 --> 00:00:44,870
+ولمانه سمى هذا العمل عامل التكابل إذا كنا نعطي
+
+7
+00:00:44,870 --> 00:00:48,970
+تعريف لشكل ال test of the diffusion equation ثم
+
+8
+00:00:48,970 --> 00:00:56,050
+نضعها على أرض الواقع بمعادرة ونبدأ عن هذه المعادرة
+
+9
+00:00:58,350 --> 00:01:04,630
+طيبة عامة للمعادلة التفاظرية من عبارة بالأولى يدفع
+
+10
+00:01:04,630 --> 00:01:09,010
+قضة integration هي عبارة عن integration in default
+
+11
+00:01:09,010 --> 00:01:14,790
+الشكل الثاني dy على d is a product of d وy يعني
+
+12
+00:01:14,790 --> 00:01:19,590
+المشتق الأولى للدالة y بالنسبة الى d هي عبارة عن
+
+13
+00:01:19,590 --> 00:01:24,930
+function demand في d وyطبعا ماعنديش معادلة واضحة
+
+14
+00:01:24,930 --> 00:01:29,250
+يمكن ادى حلوة بقى لذلك لذلك روحنا حاطين هذه
+
+15
+00:01:29,250 --> 00:01:33,590
+المعادلة في الصيغة اللى ممكن نبدأ نشغلها فروحنا
+
+16
+00:01:33,590 --> 00:01:38,190
+نقول ذاتي اي ان المعادلة هذه كتبة على الشكل التالي
+
+17
+00:01:38,190 --> 00:01:44,500
+في Y بيديوين ذات P of P في Y سواء مين P of Pالآن
+
+18
+00:01:44,500 --> 00:01:47,900
+لو خلّيت dy على dt في الناحية هذه ونجمنا هذه على
+
+19
+00:01:47,900 --> 00:01:52,960
+الشجة هذه بصير اطراف اليمين كله function في y وt
+
+20
+00:01:52,960 --> 00:01:57,300
+زي ما قلنا هنا او function في t و y اذا ال
+
+21
+00:01:57,300 --> 00:02:02,040
+function في t و y ساكتبها من الأن فتعيدا على الشكل
+
+22
+00:02:02,040 --> 00:02:07,240
+التالي dy by dt زي ال P of P في ال Y بيبقى سوى G
+
+23
+00:02:07,240 --> 00:02:12,690
+of P ال P of P هي عبارة عن function في Tو ال V of
+
+24
+00:02:12,690 --> 00:02:17,110
+T كذلك function أخرى في T والتنتين are continuous
+
+25
+00:02:17,110 --> 00:02:22,590
+على فترة ما يرجى هدول دوال متصلة بالنسبة لمين
+
+26
+00:02:22,590 --> 00:02:29,590
+للمتغير T وكل واحدة فيهم function في T فقط يعني
+
+27
+00:02:29,590 --> 00:02:34,700
+تكتببدلالة T بيجي ال function of T في Y بيسوي ال
+
+28
+00:02:34,700 --> 00:02:40,120
+function of T لوحديها الان بيجي الى كيفية حل هذه
+
+29
+00:02:40,120 --> 00:02:45,920
+المعادلة التفاضلية فبقى بيقول مشان انحلي المعادلة
+
+30
+00:02:45,920 --> 00:02:50,940
+التفاضلية هذه اللي هسميها star بيذهي اختار دالة من
+
+31
+00:02:50,940 --> 00:02:58,230
+عندى هذه الدالة بيسميها Mu of Zلـ Mu of T بحيث الـ
+
+32
+00:02:58,230 --> 00:03:03,630
+Mu of T بدى اتحقق شغل معين يعني انا لكل مثلة بتروح
+
+33
+00:03:03,630 --> 00:03:09,570
+اختار Mu of T لأ احنا من هذا سنصل الى صيغة هذه
+
+34
+00:03:09,570 --> 00:03:15,190
+الصيغة بتعطينى شكل لـ Mu of T بدلالة الـ P of T
+
+35
+00:03:15,190 --> 00:03:19,650
+تبع ال function الان يبقى بدنا نختار ال function
+
+36
+00:03:19,650 --> 00:03:26,660
+Mu of T such that بحيثو جيب ضربت ميو of P في الطرف
+
+37
+00:03:26,660 --> 00:03:37,680
+الأيسر لميو of P في BY by DT زائد P of P في ال Y
+
+38
+00:03:37,680 --> 00:03:49,240
+هذا الكلام بساوي لميو of P في ال Y طبعا
+
+39
+00:03:49,900 --> 00:03:55,800
+يبقى احنا الان بدنا نختار اللي هو الـ mu of t اللي
+
+40
+00:03:55,800 --> 00:04:01,360
+هي الدالة الموجة التي لا تأخذ الا قيمة موجة تحقيق
+
+41
+00:04:01,360 --> 00:04:07,080
+لي هذه العلاقة يبقى هذه العلاقة لأن انا الـ mu of
+
+42
+00:04:07,080 --> 00:04:11,580
+t لما اضربها في الطرف الشمال هذي بقدر اجمع الـ mu
+
+43
+00:04:11,580 --> 00:04:18,400
+of t مع ال Y واخد له مشتكة حاطم ضرب بالتيلطيب الان
+
+44
+00:04:18,400 --> 00:04:22,960
+بدي ابحث ماهو شكل ال new of T إذا مشان أحصل على
+
+45
+00:04:22,960 --> 00:04:27,420
+شكل ال new of T بدي أفك الجثة ده و أفك المشتقى
+
+46
+00:04:27,420 --> 00:04:32,520
+اللي عندنا هذه فلو جيت فكت الجثة ده ال new of T
+
+47
+00:04:32,520 --> 00:04:38,200
+هذه البنات هسميها wire prime بس لسه هذا الشكل ده
+
+48
+00:04:38,200 --> 00:04:44,720
+دايما من المعادلة زائد ل new of T
+
+49
+00:05:01,340 --> 00:05:07,240
+طب تعالوا نقارن بين الطقسين في هذه المعادلة طلعيلي
+
+50
+00:05:07,240 --> 00:05:12,160
+في ال term هذا و ال term هذاإن إثنين are the same
+
+51
+00:05:12,160 --> 00:05:17,260
+صحيح ولا لأ؟ إذا لما أتقل واحد عند الثاني أو أضيفه
+
+52
+00:05:17,260 --> 00:05:22,820
+إليه بإشارة مخالفة إتنين هدول بضيوف وبيبقى عند
+
+53
+00:05:22,820 --> 00:05:31,500
+المعادلة الثانية ل mu of T ال P of T في ال Y يساوي
+
+54
+00:05:31,500 --> 00:05:39,460
+U prime of T في من Y وسميلي هذه المعادلة رقم أحد
+
+55
+00:05:41,140 --> 00:05:45,640
+تبقى كويس الان بدنا نيجي على المعادلة اللي عندنا
+
+56
+00:05:45,640 --> 00:05:51,060
+star هادي بدي اضربها في ال mu of T اضرب طرفيها
+
+57
+00:05:51,060 --> 00:05:56,440
+يفجأة بتروح اضرب طرفي المعادلة star بال mu of T
+
+58
+00:05:56,440 --> 00:06:03,840
+هروح اقولهم multiply multiply
+
+59
+00:06:03,840 --> 00:06:13,340
+both sides of equationالسعر اللي احنا بدنا نحلها
+
+60
+00:06:13,340 --> 00:06:23,060
+by ميو of P we get نحصل على يفجر داشي ده يصير لميو
+
+61
+00:06:23,060 --> 00:06:33,340
+of P ال Y prime زائد لميو of P ال P of T في ال Y
+
+62
+00:06:33,340 --> 00:06:38,320
+يساوي لميو of P ال D of T
+
+63
+00:06:41,630 --> 00:06:48,230
+طبعا تلاحظ ميو اف تي ميو اف تي في الواي بقدر
+
+64
+00:06:48,230 --> 00:06:52,990
+اشيلها و اكتب بدلها مين ميو برايم اف تي في الواي
+
+65
+00:06:52,990 --> 00:06:58,910
+يبقى هذه كلها بقدر اشيلها و اكتب بدلها ميو برايم
+
+66
+00:06:58,910 --> 00:07:04,990
+اف تي في مين في الواي يبقى هذه بالصيف ميو اف تي في
+
+67
+00:07:04,990 --> 00:07:11,580
+الواي برايم زيدي ميو برايم اف تي في الواييستوي Mu
+
+68
+00:07:11,580 --> 00:07:18,860
+of T بالG of T وهذا الكلام from one يبقى هذا
+
+69
+00:07:18,860 --> 00:07:23,060
+جيبناه من المعادلة اللي تحت اللي عندنا طب أطلعيه
+
+70
+00:07:23,060 --> 00:07:28,440
+للآن في الشكل اللي على الشمال هذا أليس هذا هو
+
+71
+00:07:28,440 --> 00:07:33,450
+مستقل حاصل ضرب ذلتين صح ولا لا؟يبقى بدي أجمع
+
+72
+00:07:33,450 --> 00:07:40,470
+الدلتين بمشتقة واحدة يبقى بصير عندي الـMu of T في
+
+73
+00:07:40,470 --> 00:07:47,950
+الـY Phi كله بده يساوي الـMu of T في الـG of T
+
+74
+00:07:55,290 --> 00:08:01,150
+طبعا الحقيقة ان استعجلت شوية يعني كان خاطر احسب من
+
+75
+00:08:01,150 --> 00:08:07,830
+هذه المعادلة ما هو شكل ل mu of t قبل مضرب هذه طبعا
+
+76
+00:08:07,830 --> 00:08:12,310
+يبقى انا بس استعجلت شوية يبقى من هذه المعادلة يا
+
+77
+00:08:12,310 --> 00:08:19,630
+بنات بقدر اجيب شكل من شكل ل mu of t وكيف بتروح ال
+
+78
+00:08:19,630 --> 00:08:25,770
+y مع ال yلو قسمت الطرفين على الـ mu of t ياسي
+
+79
+00:08:25,770 --> 00:08:31,990
+بيصير عندنا هنا بيصير الـ mu prime of t على الـ mu
+
+80
+00:08:31,990 --> 00:08:38,050
+of t بده يساوي الـ P of T لما
+
+81
+00:08:38,050 --> 00:08:39,550
+تروح ال Y مع Y
+
+82
+00:08:47,220 --> 00:08:56,350
+ميو الـ P of T على ميو الـ P of Tيبقى ال bus تقاضه
+
+83
+00:08:56,350 --> 00:08:59,890
+للمقام لما يكون ال bus تقاضه للمقام يبقى التكامل
+
+84
+00:08:59,890 --> 00:09:05,770
+لن absolute value للمقام لكن المقام انا مختاره
+
+85
+00:09:05,770 --> 00:09:11,350
+positive يبقى ال absolute value لا داعي له يبقى
+
+86
+00:09:11,350 --> 00:09:20,410
+بصير عندنا لن المئة of T بده يساوي تكامل P of T بT
+
+87
+00:09:20,410 --> 00:09:28,270
+زائد كنفة K مثلاالـ Colossal K هذا يا بنات بدي
+
+88
+00:09:28,270 --> 00:09:31,050
+اخده كله بجداش B0
+
+89
+00:09:33,800 --> 00:09:38,640
+طيب يبقى لو أخدت ال constant دي ربوضال عند مين لإن
+
+90
+00:09:38,640 --> 00:09:45,180
+mu of T بده يساوي تكامل P of T dt يبقى بناء عليه
+
+91
+00:09:45,180 --> 00:09:52,400
+لو رفعت اتنين كأس للعدد E بصير E أس لإن mu of T
+
+92
+00:09:52,400 --> 00:10:02,060
+بده يساوي E أس تكامل P of Tبناءً على الـ E والدول
+
+93
+00:10:02,060 --> 00:10:05,720
+اللي اتنين هذول عكس ضبط يبجى واحدة بتنغي الثانية
+
+94
+00:10:05,720 --> 00:10:10,240
+يبجى هذا بده يعطينا الـ Mu of T اللي أنا بدور
+
+95
+00:10:10,240 --> 00:10:18,940
+عليها E أستكامل T of T دي T يبجى
+
+96
+00:10:18,940 --> 00:10:23,920
+هذا شكل الـ Mu of T زي ما انتوا شايفين اعتمدت على
+
+97
+00:10:23,920 --> 00:10:30,870
+مين اعتمدت على المعامل بتابعي ال Yوهنا المعامل تبع
+
+98
+00:10:30,870 --> 00:10:36,730
+ال Y' هو جدّيك واحد صحيح تمام تمام يبقى من الآن
+
+99
+00:10:36,730 --> 00:10:40,870
+فصاعدا لما يكون عندي first order differential
+
+100
+00:10:40,870 --> 00:10:47,190
+equation والمعامل تبع ال dy by dt هو الواحد الصحيح
+
+101
+00:10:47,190 --> 00:10:51,450
+بيكون شكل ال integrating factor mu of t هو ال
+
+102
+00:10:51,450 --> 00:10:58,000
+exponential مرفوه للأس تكامل P of T dtوهذا ما
+
+103
+00:10:58,000 --> 00:11:04,920
+أصنعه مع كل سؤال عند الحل طب الآن بدنا نعرف ما هو
+
+104
+00:11:04,920 --> 00:11:10,060
+شكل الحل للمعادلة التفاضلي اللي عندنا طب نروح نقول
+
+105
+00:11:10,060 --> 00:11:14,500
+نضرب كل term من ال term سبعة المعادلة التفاضلي
+
+106
+00:11:14,500 --> 00:11:19,500
+اللي عندنا في الميو of T بنستبدل هذا بالميو prime
+
+107
+00:11:19,500 --> 00:11:25,020
+of T في ال Yهدول كلهم كمشتقة واحدة يساوي مين؟
+
+108
+00:11:25,020 --> 00:11:32,180
+يساوي لأن لو كاملت الطرفين يبقى by integration
+
+109
+00:11:32,180 --> 00:11:35,480
+بواسطة
+
+110
+00:11:35,480 --> 00:11:42,780
+التكامل بيصير عندنا ل mu of T في ال Y يسوى تكامل ل
+
+111
+00:11:42,780 --> 00:11:50,360
+mu of T في G of T DT الزائد كنستنسيأنا مابدي الـ
+
+112
+00:11:50,360 --> 00:11:57,380
+mu of d في y بدي y يبقى بروح بقول هنا the solution
+
+113
+00:11:57,380 --> 00:12:11,380
+of the differential equation star is y تساوي واحد
+
+114
+00:12:11,380 --> 00:12:21,650
+على ال mu of d فيتكامل لـ Mu of T في G of T DT
+
+115
+00:12:21,650 --> 00:12:29,090
+ذائب كونستانسي هذا شكل الحل تبع المعادلة التفاضلية
+
+116
+00:12:29,090 --> 00:12:37,350
+الهمين Star لحد هنا انتهت جزء النظري تبع ال linear
+
+117
+00:12:37,350 --> 00:12:40,890
+pairs of all differential equationsلو جاني السؤال
+
+118
+00:12:40,890 --> 00:12:46,110
+بده يتبع نفس التكتيك بده أروح أجيب له قيمة لـMU of
+
+119
+00:12:46,110 --> 00:12:51,650
+T بعدين أضرب طرفين المعادلة في الـMU of T وبعدين
+
+120
+00:12:51,650 --> 00:12:58,250
+كده أكامل بحصل على حل المعادلة التفاضلية بس قبل
+
+121
+00:12:58,250 --> 00:13:01,910
+هيكل الخطرة هكتب ملاحظة حتى ماتنسهاش بجهة مكتوبة
+
+122
+00:13:01,910 --> 00:13:08,390
+عندكمشان ناخد الـ mu of t بطريقة صحيحة بدي يكون
+
+123
+00:13:08,390 --> 00:13:14,090
+المعامل هنا هو واحد صحيح اثنين بدي تبقى المعادلة
+
+124
+00:13:14,090 --> 00:13:17,850
+في نفس الشكل اللي عندنا هذا مش تبقى P of T ثوائي
+
+125
+00:13:17,850 --> 00:13:21,190
+تربيع مثلا يبقى المستقل أولى ل Y
+
+126
+00:13:27,390 --> 00:13:32,990
+معادلة يتفجأ في الشكل هذا و المعامل هنا جداش و حطش
+
+127
+00:13:32,990 --> 00:13:36,450
+ان شاء الله يكون اتنين بيتجسم على اتنين قبل ما
+
+128
+00:13:36,450 --> 00:13:42,170
+تحسب ال mu of t يعني اي معامل هنا ل y prime بدنا
+
+129
+00:13:42,170 --> 00:13:48,110
+نجسم عليه قبل ان نبدأ بالحل أكتب لهذا على شكل
+
+130
+00:13:48,110 --> 00:13:52,880
+ملاحظة حتى ما تنسهاشإن شاء الله و تعالى أثناء
+
+131
+00:13:52,880 --> 00:13:56,300
+الحجز
+
+132
+00:13:56,300 --> 00:14:02,740
+ابقى
+
+133
+00:14:02,740 --> 00:14:10,500
+not before
+
+134
+00:14:10,500 --> 00:14:14,480
+confusing
+
+135
+00:14:14,480 --> 00:14:18,000
+قبل ما تعجبك
+
+136
+00:14:43,680 --> 00:14:51,560
+بتتأكد يعني to make sure thatthe differential
+
+137
+00:14:51,560 --> 00:15:03,140
+equation المعادلة التفابلية is exactly is exactly
+
+138
+00:15:03,140 --> 00:15:15,480
+in the form of a star and the coefficient and
+
+139
+00:15:15,480 --> 00:15:25,680
+thethe coefficient of
+
+140
+00:15:25,680 --> 00:15:29,740
+y' is واحد صحيح
+
+141
+00:15:47,500 --> 00:15:54,520
+the example one find
+
+142
+00:15:54,520 --> 00:16:08,240
+the general solution of
+
+143
+00:16:08,240 --> 00:16:15,020
+the following differential equation
+
+144
+00:16:19,460 --> 00:16:29,120
+the differential equation and use it and use it to
+
+145
+00:16:29,120 --> 00:16:35,260
+determine عشان
+
+146
+00:16:35,260 --> 00:16:43,180
+نحدد how solutions solutions
+
+147
+00:16:43,180 --> 00:16:46,340
+they have
+
+148
+00:16:57,690 --> 00:17:06,390
+السؤال الأول نمرة A سؤال ستة من الكتاب تقول تي واي
+
+149
+00:17:06,390 --> 00:17:16,930
+فراين زائد اتنين واي تساوي صين تي والتي أكتر من
+
+150
+00:17:16,930 --> 00:17:28,330
+ازرع نمرة ZY'زائد Y يساوي ثلاثة
+
+151
+00:17:51,900 --> 00:17:55,600
+سؤال مرة تانية طبعا زي ما تشاهدين فيه مطموبين
+
+152
+00:17:55,600 --> 00:17:59,540
+المطموب الأول بيقول هاتل ال general solution لكل
+
+153
+00:17:59,540 --> 00:18:04,280
+من المعادلات التفاغبالية التالية واستخدم الحل اللي
+
+154
+00:18:04,280 --> 00:18:11,300
+جبته مشان تحدد كيف الحل behave بكل سلوكه او شكله
+
+155
+00:18:11,300 --> 00:18:16,880
+لما تي تكبرها بمقدار كبير جدا يعني تصل الى ما لا
+
+156
+00:18:16,880 --> 00:18:23,290
+نهاية نقوله solutionوالنجي للمعادلة الأولى
+
+157
+00:18:23,290 --> 00:18:26,490
+الملاحظة اللى احنا كتبينها هنا لازم يكون معامل y'
+
+158
+00:18:26,730 --> 00:18:31,630
+مجدد اذا من جاب الكل شيء المعادلة هذه بنروح اقسم
+
+159
+00:18:31,630 --> 00:18:38,010
+الطرفين عالميا على C يبقى باقي بقوله نمر ايه
+
+160
+00:18:41,140 --> 00:18:50,760
+Equation S لو جسمت على P بيصير Y' ذائبين على T في
+
+161
+00:18:50,760 --> 00:19:00,440
+Y بده يساوي 5T على 2 على T وهذه سميها اللي اللي هي
+
+162
+00:19:00,440 --> 00:19:05,060
+المعادلة الأصلية Star اللي بدنا نحلها يبقى الأن
+
+163
+00:19:05,060 --> 00:19:08,980
+بدنا نروح نجيب عامل التكامل Integrating factors
+
+164
+00:19:09,300 --> 00:19:17,220
+يبقى الـ Mu of P أخدناها قبل قليل E أستكامل P of T
+
+165
+00:19:17,220 --> 00:19:23,080
+بيتي يبقى هذا الكلام اللي يساوي E أستكامل P of T
+
+166
+00:19:23,080 --> 00:19:27,560
+صارت جباش تين على تين لكن لو ما جسملاش يا بنات
+
+167
+00:19:27,560 --> 00:19:32,200
+سالجتيها تنين وبالتالي وجعنا في مشكلة عويصة يبقى
+
+168
+00:19:32,200 --> 00:19:38,950
+باجي بقوله تنين على تين في بيتيهذا الكلام بده
+
+169
+00:19:38,950 --> 00:19:45,050
+يساوي E أس اتنين برا التكامل بقول جبات واحد على T
+
+170
+00:19:45,050 --> 00:19:51,950
+DT اللي هي لن T يبجى اتنين لن T وليس لن absolute
+
+171
+00:19:51,950 --> 00:19:57,670
+value ل T لأنه قلنا هنا T مالها greater than zero
+
+172
+00:19:57,670 --> 00:20:04,090
+اكبر من ال zero يبجى هذه E أس لن T تربية مصبوب
+
+173
+00:20:04,090 --> 00:20:11,280
+هكذامن أين جلبنا هذا المعلومة؟ من كالكولوز بيه؟
+
+174
+00:20:11,280 --> 00:20:15,720
+تمام تمام يبقى يادروا يتساوي تيتر بيعملوا فيك
+
+175
+00:20:15,720 --> 00:20:21,060
+برضه؟ لأن ال E و S X و L X كل واحدة فيهم inverse
+
+176
+00:20:21,060 --> 00:20:25,380
+لمين للتانية بتلغيها ويظل يتنقل لمين تيتر بيعمل،
+
+177
+00:20:25,380 --> 00:20:29,840
+إذا بناء عليهأصبح الـ integrating factor mu of T
+
+178
+00:20:29,840 --> 00:20:35,400
+بدي ساوي قداش T تربيع الان بنجي للمعادلة star كلها
+
+179
+00:20:35,400 --> 00:20:40,380
+و بنضربها في مام T تربيع يبقى بقى دي بقوله هنا
+
+180
+00:20:40,380 --> 00:20:45,380
+multiply both
+
+181
+00:20:45,380 --> 00:20:59,340
+sides of equation star by T تربيع we getنحصل على I
+
+182
+00:20:59,340 --> 00:21:12,080
+T تربيه Y T تربيه Y زائد 2T في ال Y يساوي T Phi T
+
+183
+00:21:12,080 --> 00:21:18,040
+مرة ثانية بدي أضغط هذه كلها في T تربيه لأن T تربيه
+
+184
+00:21:18,040 --> 00:21:26,520
+Y' T تربيه مع T تختصر ويبقى T فوق ب2 ب2T في ال Yهي
+
+185
+00:21:26,520 --> 00:21:34,120
+تربيعه هنا تي بضل جداش تي صيني تي هي فوق تمام طيب
+
+186
+00:21:34,120 --> 00:21:38,580
+تطلعيلي في هذه شوف الجزء المظري يقول لنا بعد ما
+
+187
+00:21:38,580 --> 00:21:43,880
+نضرب عامل التكامل بصير هذا كله مشتفت حصل ضرب
+
+188
+00:21:43,880 --> 00:21:50,150
+دالتين بقدر أجمعه بدلة واحدة لكل primeطيب اتطلع يا
+
+189
+00:21:50,150 --> 00:21:56,930
+عزيزي أليس هذه هي عاملة تكامل قداش T تربية الدالة
+
+190
+00:21:56,930 --> 00:22:02,210
+الأصليه اليمين Y كله prime شوفيلي مشتقت هذا هو
+
+191
+00:22:02,210 --> 00:22:08,310
+الطرف هذا ولا لا ها T تربية في Y prime زائد Y
+
+192
+00:22:08,310 --> 00:22:14,010
+مشتقت T تربية ب2T يبقى 2TY هي مظبوط بكلامنا سليم
+
+193
+00:22:14,010 --> 00:22:32,460
+100% الشجة اليمينتساوي T في صينيتي تساوي
+
+194
+00:22:32,460 --> 00:22:34,700
+T في صينيتي تساوي T في صينيتي تساوي T في صينيتي
+
+195
+00:22:34,700 --> 00:22:34,820
+تساوي T في صينيتي تساوي T في صينيتي تساوي T في
+
+196
+00:22:34,820 --> 00:22:34,820
+صينيتي تساوي T في صينيتي تساوي T في صينيتي تساوي T
+
+197
+00:22:34,820 --> 00:22:34,820
+في صينيتي تساوي T في صينيتي تساوي T في صينيتي
+
+198
+00:22:34,820 --> 00:22:34,820
+تساوي T في صينيتي تساوي T في صينيتي تساوي T في
+
+199
+00:22:34,820 --> 00:22:34,820
+صينيتي تساوي T في صينيتي تساوي T في صينيتي تساوي T
+
+200
+00:22:34,820 --> 00:22:34,820
+في صينيتي تساوي T في صينيتي تساوي T في صينيتي
+
+201
+00:22:34,820 --> 00:22:38,090
+تساوي T في صينيتي تساوي T في صينيتي تساوييبقى تر
+
+202
+00:22:38,090 --> 00:22:42,430
+بي او اي فرايم زي اثنين ت يساوي ت فاين ت كلها مع
+
+203
+00:22:42,430 --> 00:22:53,970
+بعضها ت تر بي او اي في كل فرايم تساوي ت فاين ت تر
+
+204
+00:22:53,970 --> 00:22:59,850
+بي او اي في كل فرايم تساوي ت فاين ت تر بي او اي في
+
+205
+00:22:59,850 --> 00:23:00,130
+كل فرايم ت تر بي او اي في كل فرايم ت تر بي او اي
+
+206
+00:23:00,130 --> 00:23:00,130
+في كل فرايم ت تر بي او اي في كل فرايم ت تر بي او
+
+207
+00:23:00,130 --> 00:23:00,130
+اي في كل فرايم ت تر بي او اي في كل فرايم ت تر بي
+
+208
+00:23:00,130 --> 00:23:02,030
+او اي في كل فرايم ت ت تر بي او اي في كل فرايم ت ت
+
+209
+00:23:02,030 --> 00:23:05,190
+تر بي او اي في كل فرايم ت ت تر بي او اي في كل
+
+210
+00:23:05,190 --> 00:23:08,970
+فرايمهذه لسه مكنوية الاصل نفسه بالكونوستانت على
+
+211
+00:23:08,970 --> 00:23:12,950
+الشجة هذه وبعدين احاول على الشجة دي يجي اختصارا
+
+212
+00:23:12,950 --> 00:23:16,250
+بدل ما اعمل خطواتين خطوات واحدة يبقى زائد
+
+213
+00:23:16,250 --> 00:23:20,710
+كونوستانت C يبقى لو جدرت اكمل المعادلة اقدرها دي
+
+214
+00:23:20,710 --> 00:23:24,770
+يكون خلصنا من هذه الشغلات بنعرف نكملها دي يا بنات
+
+215
+00:23:24,770 --> 00:23:30,550
+باشر by part و بنعمللها جدول يبقى باجي بقوله هنا
+
+216
+00:23:30,550 --> 00:23:32,070
+بدي اخد ال derivative
+
+217
+00:23:35,240 --> 00:23:42,960
+وهنا بدى اخد انتجر علينى هذه ال اولى اللى هى T وهى
+
+218
+00:23:42,960 --> 00:23:48,440
+فاينى T يعنى فاينى T بدى اكملها على طول و T بدى
+
+219
+00:23:48,440 --> 00:23:54,700
+افضلها على طول اذا لا افضلها مرة جدش بطلع لو كملت
+
+220
+00:23:54,700 --> 00:24:00,530
+هذه مرة شو بطلع؟بدي أفضلها كمان مرة zero بدي أكمل
+
+221
+00:24:00,530 --> 00:24:04,430
+هذه كمان مرة sin P بعد ذلك بيجي الأقاعدة في
+
+222
+00:24:04,430 --> 00:24:08,950
+الإشارات هذه في هذه بالموجة وهذه في هذه بالسالب
+
+223
+00:24:08,950 --> 00:24:17,930
+إذا صار عندي P تربيه Y يساوي ناقص P P for sin P
+
+224
+00:24:17,930 --> 00:24:25,930
+زائد sin P زائد constant Cيبقى بدي ال solution
+
+225
+00:24:25,930 --> 00:24:33,130
+فبروح بقوله the solution is أنا مابدي T تربية Y
+
+226
+00:24:33,130 --> 00:24:38,850
+وإلا بدي main هي ال Y إذا بقسم كله على مين؟ على T
+
+227
+00:24:38,850 --> 00:24:49,030
+تربية يبقى Y بدي سوى C ذائب صيني T مقص T تقصيني T
+
+228
+00:24:49,030 --> 00:24:55,930
+كل هذا على مين؟ على T تربيةيبقى هذا شكل ال general
+
+229
+00:24:55,930 --> 00:25:02,210
+solution ل مام ل المعادلة التفاضلية لأن مام رقم
+
+230
+00:25:02,210 --> 00:25:07,010
+start خلصنا لسه المطلوب الأول من السؤالالمطلوب
+
+231
+00:25:07,010 --> 00:25:11,190
+التاني قال لي استخدم الحل اللي جيبته هذا
+
+232
+00:25:11,190 --> 00:25:19,110
+ههههههههههههههههههههههههههههههههههههههههههههههههههههههههههههههههههههههههههههههههههههههههههههههههههههههههههههههههههههههههههههههههههههههههههههههههههههههههههههههههههههههههههههههههههههههههههههههههههههههههههه
+
+233
+00:25:35,150 --> 00:25:44,130
+بدا تساوي limit لمن؟ ل C على T تربيع ذات sin T على
+
+234
+00:25:44,130 --> 00:25:54,630
+T تربيع ناقص cos T على T لما T بدا تروح إلى
+
+235
+00:25:54,630 --> 00:25:59,410
+infinity طيب
+
+236
+00:25:59,410 --> 00:26:02,370
+هذه لما T بدا تروح لملنهاف
+
+237
+00:26:05,900 --> 00:26:11,860
+أعدد عمله نهائي بـ0 يفجأها دي بـ0 أجت مشكلتنا مع
+
+238
+00:26:11,860 --> 00:26:19,960
+مين؟ مع sin T على T تربع طيب نرجع لCalculus A طبعا
+
+239
+00:26:19,960 --> 00:26:23,840
+عملناها في Calculus A بس نذكرها بدل A هو sin محصور
+
+240
+00:26:23,840 --> 00:26:32,430
+بين مين ومين؟ سالب واحد وواحد إذا sin Tمحصور ما
+
+241
+00:26:32,430 --> 00:26:37,090
+بين الواحد وما بين السالب واحد power of B للفرق
+
+242
+00:26:37,090 --> 00:26:43,530
+انتوا واحد على T تربيه يبقى اش بيصير سالب واحد على
+
+243
+00:26:43,530 --> 00:26:50,210
+T تربيه sign of T على T تربيه واحد على T تربيه
+
+244
+00:26:51,430 --> 00:26:55,630
+بنروح ناخد ال limit لما T بدها تروح لما لا نهاية
+
+245
+00:26:55,630 --> 00:27:00,870
+يجب عشان نصير عندنا هنا zero أقل من أو يساوي ال
+
+246
+00:27:00,870 --> 00:27:06,810
+limit لما T tends to infinity لصيني T على T تربية
+
+247
+00:27:06,810 --> 00:27:12,220
+أقل من أو يساوي ال zeroيبقى بـSandwich Theorem
+
+248
+00:27:12,220 --> 00:27:15,740
+يبقى
+
+249
+00:27:15,740 --> 00:27:21,980
+بـSandwich
+
+250
+00:27:21,980 --> 00:27:31,000
+Theorem يبقى بـSandwich
+
+251
+00:27:31,000 --> 00:27:37,020
+Theorem يبقى بـSandwich Theorem يبقى بـSandwich
+
+252
+00:27:37,020 --> 00:27:37,020
+Theorem يبقى بـSandwich Theorem يبقى بـSandwich
+
+253
+00:27:37,020 --> 00:27:37,140
+Theorem يبقى بـSandwich Theorem يبقى بـSandwich
+
+254
+00:27:37,140 --> 00:27:37,140
+Theorem يبقى بـSandwich Theorem يبقى بـSandwich
+
+255
+00:27:37,140 --> 00:27:37,140
+Theorem يبقى بـSandwich Theorem يبقى بـSandwich
+
+256
+00:27:37,140 --> 00:27:37,140
+Theorem يبقى بـSandwich Theorem يبقى بـSandwich
+
+257
+00:27:37,140 --> 00:27:37,140
+Theorem يبقى بـSandwich Theorem يبقى بـSandwich
+
+258
+00:27:37,140 --> 00:27:37,480
+Theorem يبقى بـSandwich Theorem يبقى بـSandwich
+
+259
+00:27:37,480 --> 00:27:40,720
+Theorem يبقى بـSandwich Theorem يبقىبـ 0 كذلك يفجه
+
+260
+00:27:40,720 --> 00:27:47,340
+هنا بقى يبقى يقول الـ S Y بدأ تروح للـ 0 الـ T بدأ
+
+261
+00:27:47,340 --> 00:27:55,200
+تروح لوين؟ للإنفلي حد لايه سؤال هنا يا ناس؟ فهنا
+
+262
+00:27:55,200 --> 00:27:59,580
+من الحل كاملا نروح للمثال الثاني بس بدنا نشوف إذا
+
+263
+00:27:59,580 --> 00:28:06,800
+فيه تساوي ايه؟ ايه؟ نجي للمثال الثاني
+
+264
+00:28:14,060 --> 00:28:21,840
+يبقى نمر بي المعادلة عند بهاية نجسم
+
+265
+00:28:21,840 --> 00:28:28,160
+على تمام يبقى المعادلة بالصير اللي نمر بي y prime
+
+266
+00:28:28,160 --> 00:28:37,540
+زائد نص y يساوي ثلاثة على اتنين في ترابيع كويس
+
+267
+00:28:37,540 --> 00:28:44,870
+بدنا نروح نجيب عامل تكامل اللي هو الميو of Tيساوي
+
+268
+00:28:44,870 --> 00:28:53,190
+E أُس تكامل T of T اللي هو مُص DT يبقى هذا الكلام
+
+269
+00:28:53,190 --> 00:28:59,570
+يساوي E أُس T على تمام مُص T يعني T على تماميبقى
+
+270
+00:28:59,570 --> 00:29:04,030
+هذا عامل التكمل لنا يبقى الأن بدنا نروح المعادلة
+
+271
+00:29:04,030 --> 00:29:09,570
+هذه اللي صارت عندنا نسميها double star مشان أه ما
+
+272
+00:29:09,570 --> 00:29:13,890
+تختلف عن المعادلة L4 يبقى المعادلة هذه بتروح
+
+273
+00:29:13,890 --> 00:29:19,530
+أضربها في مين في E أوش E على 2 بروح و أقول لهم
+
+274
+00:29:19,530 --> 00:29:24,270
+multiply both
+
+275
+00:29:24,270 --> 00:29:28,190
+sides of
+
+276
+00:29:28,970 --> 00:29:39,990
+Equation double star by E أس T على اتنين نحصل
+
+277
+00:29:39,990 --> 00:29:40,330
+على
+
+278
+00:30:03,400 --> 00:30:08,220
+يبقى المعادلة دي بيصير على الشكل الساوي E أُس T
+
+279
+00:30:08,220 --> 00:30:18,540
+على تمام ال Y prime زائد نص E أُس T على تمام زائد
+
+280
+00:30:18,540 --> 00:30:26,200
+نص E أُس T على تمام في ال Y بيبقى ساوي تلاتة على
+
+281
+00:30:26,200 --> 00:30:30,920
+تمام E أُس T على تمام تمام fifty
+
+282
+00:30:34,070 --> 00:30:38,850
+طب تعالى نشوف يبجى بناء ان علي الطرف هذا بقدر
+
+283
+00:30:38,850 --> 00:30:43,970
+اتقبله على الشكل التاني اجمعه بترم واحد اللي هو
+
+284
+00:30:43,970 --> 00:30:51,690
+عامل التكامل مضروفا سواء لكل price لو مشتقته وما
+
+285
+00:30:51,690 --> 00:30:56,550
+طلعتش هذا يا بنات معناته حسابك هنا اه غلطي عامل
+
+286
+00:30:56,550 --> 00:31:00,910
+التكامل لازم يطلع المعادلة بالضباططب عادى لو جيت
+
+287
+00:31:00,910 --> 00:31:06,550
+اشتقها الاولى فى مشتقة الثانية هيه مجرد زي دى
+
+288
+00:31:06,550 --> 00:31:11,190
+التانية اللى هى Y فى مشتقة ال X ponential اللى هى
+
+289
+00:31:11,190 --> 00:31:17,010
+نفسها مضربة فى جديد فى نص يبقى هاى نص E أس T على
+
+290
+00:31:17,010 --> 00:31:22,250
+اتنين تبين فى ال Y بكلام سليم مائة بالمائة بادرساه
+
+291
+00:31:22,250 --> 00:31:26,610
+من الفرق الايمن فهو ثلاثة على اتنين
+
+292
+00:31:55,500 --> 00:31:56,900
+Eac²Eac²Eac²Eac²Eac²Eac²Eac²Eac²Eac²Eac²Eac²Eac²Eac²Eac²Eac²Eac²Eac²Eac²Eac²Eac²Eac²Eac²Eac²Eac²Eac²Eac²Eac²Eac²Eac²Eac²Eac²Eac²Eac²Eac²Eac²Eac²Eac²Eac²Eac²Eac²Eac²Eac²Eac²Eac²Eac²Eac²Eac²Eac²Eac²Eac²Eac²Eac²Eac²Eac²Eac²Eac²Eac²Eac²Eac²Eac²Eac²Eac²Eac²Eac²Eac²Eac²Eac²Eac²Eac²Eac²Eac²Eac²Eac²Eac²Eac
+
+293
+00:31:57,180 --> 00:32:04,580
+و بدي اخد هنا ال integral يبقى هاي ثلاثة على اتنين
+
+294
+00:32:04,580 --> 00:32:13,040
+اللي هو C تربيع هنا E أس T على اتنين بدي اشتق بصير
+
+295
+00:32:13,040 --> 00:32:19,520
+عندي جداش هنا بنات ثلاثة T فقط مغير لو كامل
+
+296
+00:32:19,520 --> 00:32:25,270
+تكاملها بنفسها مقسومة على جداشعلى نص النقطة اللي
+
+297
+00:32:25,270 --> 00:32:31,310
+فوق بصير اتنين تمام كمان مرة يبقى مشتقتها تلاتة
+
+298
+00:32:31,310 --> 00:32:36,790
+تكاملها باربع EOST على اتنين يعني اتنين مالكش
+
+299
+00:32:36,790 --> 00:32:40,770
+دعوات وهذه EOST على اتنين على نص اللي فوق بصير
+
+300
+00:32:40,770 --> 00:32:46,490
+اتنين يبقى اربع EOST على اتنينمشتق كمان مرة اللي
+
+301
+00:32:46,490 --> 00:32:53,970
+هي zero وكمل كمان مرة يبقى تمانية E أس T على 2 هدف
+
+302
+00:32:53,970 --> 00:32:59,350
+هدف إشارة موجب هدف هدف إشارة سالب هدف هدف إشارة
+
+303
+00:32:59,350 --> 00:33:05,790
+موجب يبقى لو تماننا بيصير E أس T على 2 في ال Y
+
+304
+00:33:05,790 --> 00:33:12,630
+يساويمضرب هذول في بعض النص بتروح مع التاني ويصير
+
+305
+00:33:12,630 --> 00:33:18,830
+ثلاثة في تربية E أس T على اتنين ثلاثة في تربية E
+
+306
+00:33:18,830 --> 00:33:24,150
+أس T على اتنين اللي بعدها ناقص ثلاثة في أربعة بطن
+
+307
+00:33:24,150 --> 00:33:31,370
+عشر في E أس T على اتنين اللي بعدها زائد أربعة
+
+308
+00:33:31,370 --> 00:33:38,200
+وعشرين E أس T على اتنينوزائد constant C
+
+309
+00:33:41,290 --> 00:33:47,650
+بدي أقسم كله على E أُس T على 2 يبقى لو قسمت بصير Y
+
+310
+00:33:47,650 --> 00:33:55,790
+يسوى تلاتة T تربية نقص اتناشر T زائد أربعة وعشرين
+
+311
+00:33:55,790 --> 00:34:04,130
+زائد C على E أُس T على 8 هذا هو من ال general
+
+312
+00:34:04,130 --> 00:34:13,790
+solution تبع المعادلة التفابلية طب كويسالان جالى
+
+313
+00:34:13,790 --> 00:34:18,710
+يشوفى ما هو سلوك الدالة او كيف بدى يكون سلوك
+
+314
+00:34:18,710 --> 00:34:23,710
+الدالة لما تى بدها تروح لوين للمالة نهاية بقول
+
+315
+00:34:23,710 --> 00:34:29,310
+الان لو تى راحت للمالة نهاية ايه فجدت ترمى فجدت؟
+
+316
+00:34:29,310 --> 00:34:38,170
+جدت؟ المالة عدد المالة نهاية بس0 يبقى هذا term عند
+
+317
+00:34:38,170 --> 00:34:43,170
+المالة نهائية يروح بـ0 بظل مين عند هذا term لهم
+
+318
+00:34:43,170 --> 00:34:46,910
+مالة نهائية ناقص اتناشر في المالة زاد اربعة وعشرين
+
+319
+00:34:46,910 --> 00:34:54,410
+يبقى هذا هو الذي سيتحكم في سلوك ابدالة لو رجعنا
+
+320
+00:34:54,410 --> 00:35:00,890
+الى تامة خلاصة A وليس B بجينا نقول الدالة من جزية
+
+321
+00:35:00,890 --> 00:35:06,190
+اللي هي فيه dominated term اجزاء التحكملما كنا في
+
+322
+00:35:06,190 --> 00:35:12,610
+الرسم البيانيلدالة ما فجينا نقول لعزيزي التحكم هذا
+
+323
+00:35:12,610 --> 00:35:18,450
+بيتحكم عند T تساوي ما لنهاية هذا مثلا بيتحكم عند T
+
+324
+00:35:18,450 --> 00:35:22,870
+تساوي Zero كنا بنقول او T تساوي اتنين او T تساوي
+
+325
+00:35:22,870 --> 00:35:28,510
+ثلاثة حسب طبيعة مين حسب طبيعة المثلة يبقى عند T
+
+326
+00:35:28,510 --> 00:35:31,810
+بيبدأ تساوي ما لنهاية هذا ال term بيبقى لانه Zero
+
+327
+00:35:31,810 --> 00:35:37,200
+و بيبقى لعيننا مين ال term هذايبقى الterm هذا
+
+328
+00:35:37,200 --> 00:35:42,740
+بيكون هو والمنحنى أصحاب بيجيسدوا مع بعض اللي
+
+329
+00:35:42,740 --> 00:35:48,990
+بيجينا نسميهم ال asymmetric خطور التقارب، مظبوط؟بس
+
+330
+00:35:48,990 --> 00:35:53,590
+هذا مش خط تقارب هذا منحنى على شكل فرابولة وماعمله
+
+331
+00:35:53,590 --> 00:35:57,870
+شيف لإنه معادلة من الدرجة التانية في T صحيح ولا
+
+332
+00:35:57,870 --> 00:36:04,850
+لأ؟ يفجأة بصير المنحنى asymptotic يعني كأنه تقارب
+
+333
+00:36:04,850 --> 00:36:10,830
+مع المنحنى اللي عندنا هذا تمام؟ يفجأة باجي بقوله
+
+334
+00:36:10,830 --> 00:36:17,010
+as T tends to infinity the solution
+
+335
+00:36:21,300 --> 00:36:34,780
+in asymptotic to the curve للمنحنة y تساوي تلاتة
+
+336
+00:36:34,780 --> 00:36:41,320
+تربيع ناقص اتناشر P زائد اربع وعشرين لإن عندي
+
+337
+00:36:41,320 --> 00:36:47,140
+المالة نهاية هذا كله بروح جديش P Zero بضلش الا هذا
+
+338
+00:36:49,490 --> 00:36:54,230
+حد يلاقي تساؤل هنا لازلنا في نفس ال section لسه
+
+339
+00:36:54,230 --> 00:37:04,110
+فيه مزيد من الأمثلة اه لأ
+
+340
+00:37:04,110 --> 00:37:09,130
+انا بفضل تشتغل زي ما اشتغلنا بديش تحفظي انا بدي
+
+341
+00:37:09,130 --> 00:37:14,540
+طريقة الخطوة تكون خطوة سلم للاخرىأنا قادر من عند
+
+342
+00:37:14,540 --> 00:37:18,140
+ما جبت الاسم من عند ما جبت ال integrated factor
+
+343
+00:37:18,140 --> 00:37:21,800
+اقول ال resolution واحد على ال mu of t تكامل g of
+
+344
+00:37:21,800 --> 00:37:26,020
+t mu of t dt ذات كنصارى وحطها دموعي انا بس انا
+
+345
+00:37:26,020 --> 00:37:31,400
+مدهش بد الشيء يكون بالترتيب فعلا طيب يا بنات احنا
+
+346
+00:37:31,400 --> 00:37:34,800
+المرة اللي فتت اعطانا تعريف لل initial value
+
+347
+00:37:34,800 --> 00:37:40,040
+problem لكن ما حللاش ولا مسألة initial value
+
+348
+00:37:40,040 --> 00:37:46,060
+problemالان بنتحول نحل مثلة initial value of
+
+349
+00:37:46,060 --> 00:37:52,260
+problem ونشوف كيف هتعملوا فيه يبقى المثال رقم
+
+350
+00:37:52,260 --> 00:37:56,400
+اتنين example
+
+351
+00:37:56,400 --> 00:38:04,500
+two solve
+
+352
+00:38:04,500 --> 00:38:07,720
+the
+
+353
+00:38:07,720 --> 00:38:09,380
+following
+
+354
+00:38:18,530 --> 00:38:28,910
+مثل الأولى نمر a y prime زي دي 8 على t في ال y
+
+355
+00:38:28,910 --> 00:38:37,830
+يساوي cosine t على t ترابيع و ال y عند ال y بدها
+
+356
+00:38:37,830 --> 00:38:48,240
+تساويو T greater than 0 نمرى D طبعا هذا سؤال 16 من
+
+357
+00:38:48,240 --> 00:38:55,620
+الكتاب وهذا سؤال 20 بيقول ال T في ال Y prime زائد
+
+358
+00:38:55,620 --> 00:39:04,860
+T زائد واحد في ال Y بده يساوي كده؟ بده يساوي T وال
+
+359
+00:39:04,860 --> 00:39:12,500
+Y عند لم تمام بده يساوي واحدAT Greater Than Z
+
+360
+00:39:12,500 --> 00:39:15,720
+Solution
+
+361
+00:39:15,720 --> 00:39:23,000
+لو
+
+362
+00:39:23,000 --> 00:39:29,760
+نورس للمعادلة رقم A بناخد A بناخد المعامل يبقى Y'
+
+363
+00:39:30,240 --> 00:39:35,750
+هو واحد طيب جهنا جاهزينيبقى بعدى بقوله لـ mu of T
+
+364
+00:39:35,750 --> 00:39:44,410
+بيزلزاوى E أُس كامل 2 على T DT هذا بيزلزاوى E أُس
+
+365
+00:39:44,410 --> 00:39:53,050
+2 لن T يبقى E أُس لن T تربيع يبقى T تربيع بالضبط
+
+366
+00:39:53,050 --> 00:39:58,970
+تماما فبنروح نضرب المعادلة كلها في T تربيع يبقى اش
+
+367
+00:39:58,970 --> 00:40:12,790
+بصير عندى T تربيع و I primeزي دي تربيع
+
+368
+00:40:12,790 --> 00:40:20,090
+الـ y كل الـ prime يساوي main يساوي cos T الكامل
+
+369
+00:40:20,090 --> 00:40:30,240
+افتراضين يتجه دي تربيع Y تساوي sin T زائد cos Cكما
+
+370
+00:40:30,240 --> 00:40:36,200
+اعملنا على طول الخط مباشرة يبقى بناء عليه يساوي
+
+371
+00:40:36,200 --> 00:40:44,060
+الـ y يساوي الـ sign الـ T زائد constant C على T
+
+372
+00:40:44,060 --> 00:40:53,420
+تربيع هذا هو مين ال general solution طيب لك انا
+
+373
+00:40:53,420 --> 00:40:57,580
+راح افعل initial conditionالـ Initial Condition
+
+374
+00:40:57,580 --> 00:41:04,200
+قال لي Y عند الـ Pi تساوي Zero فقلنا لو شيلت كل P
+
+375
+00:41:04,200 --> 00:41:11,100
+و حطيت مكانها Pi بيبقى Y مجداش ب Zero يبقى Zero
+
+376
+00:41:11,100 --> 00:41:19,220
+بدها تساوي Final Pi مجداش يا بنات ب Zero زائد 5.C
+
+377
+00:41:19,220 --> 00:41:30,240
+على من على Pi تربيعومنها C تساوي Zero يبقى سعر شكل
+
+378
+00:41:30,240 --> 00:41:38,020
+الحل على الشكل التالي Y تساوي Sine of T على T
+
+379
+00:41:38,020 --> 00:41:43,280
+تربيع هذا هو main حل ال initial value problem
+
+380
+00:41:43,280 --> 00:41:47,160
+الأولى لجلات تانية
+
+381
+00:42:10,020 --> 00:42:14,420
+يبقى نمر بيه بلاحظ ان المعامل السابع y prime هو t
+
+382
+00:42:14,420 --> 00:42:20,940
+إذا حضر أقسم المعادلة كلها علامين على t يبقى بيصير
+
+383
+00:42:20,940 --> 00:42:29,220
+المعادلة y prime زائد واحد زائد واحد على t في ال y
+
+384
+00:42:29,220 --> 00:42:36,080
+بيساوي كده واحد هذه هي المعادلة رقم star اللالي
+
+385
+00:42:38,620 --> 00:42:46,620
+يبقى الميو of T يبقى ايه؟ استكامل واحد زائد واحد
+
+386
+00:42:46,620 --> 00:42:53,000
+على T بـT يبقى هذا الكلام بيساوي ايه؟ استكامل
+
+387
+00:42:53,000 --> 00:43:01,670
+الواحد بـT وادى زائد للـTيعني يا بنات هذه بقدر
+
+388
+00:43:01,670 --> 00:43:11,450
+اقول E أُس T في E أُس لن T لأن عند ضرب تجمع الأسس
+
+389
+00:43:11,450 --> 00:43:17,290
+مش هتروح تقولي هذه E أُس T زائد E أُس لن T كلام
+
+390
+00:43:17,290 --> 00:43:22,550
+خاطر يعني هذا ضرب و عند ضرب جمعنا مين؟ جمعنا الأسس
+
+391
+00:43:22,550 --> 00:43:31,440
+هذه كلها بقدرشيبقى سارة المسألة ت ت إي أس ت يبقى
+
+392
+00:43:31,440 --> 00:43:35,420
+هذا هو عامل التكامل اللي عندنا الآن بنجي على
+
+393
+00:43:35,420 --> 00:43:41,520
+المعادلة star و بنروح نضربها ت ت إي أس ت يبقى باجي
+
+394
+00:43:41,520 --> 00:43:46,980
+بقول multiply situation
+
+395
+00:43:46,980 --> 00:43:57,990
+star by t ت ت إي أس ت we getيبقى هاي هنا ت في E of
+
+396
+00:43:57,990 --> 00:44:09,090
+T في الـ Y prime زائد ت في E of T زائد E of T قول
+
+397
+00:44:09,090 --> 00:44:17,030
+له هذا الكلام في Y يبدو يساوي ت في E of T هذا لأن
+
+398
+00:44:17,030 --> 00:44:23,340
+الطرق الشماليكله بقدر أجمع بمين في عامل التكامل T
+
+399
+00:44:23,340 --> 00:44:29,760
+EOS T في الـY وكله Prime بدي أساوي فرق اليمين T
+
+400
+00:44:29,760 --> 00:44:36,400
+EOS T يعني لو جيت تشتق هذه مشتقة حصل ضرب دالتين
+
+401
+00:44:36,400 --> 00:44:42,500
+هتعطيك T EOS T Y Prime زائد الـY زي ما هي و هذه
+
+402
+00:44:42,500 --> 00:44:49,260
+مشتقة حصل ضرب دالتين اللي T EOS T زاد EOS Tهذه
+
+403
+00:44:49,260 --> 00:44:55,600
+بالضبط تماما يبقى
+
+404
+00:44:55,600 --> 00:45:01,500
+لو كملنا الطرفين تصير تي او سي في ال Y بدر سوى
+
+405
+00:45:01,500 --> 00:45:07,440
+تكامل تي او سي دي تي زائد في نصة ال C يبقى لو
+
+406
+00:45:07,440 --> 00:45:07,440
+كملنا الطرفين تي او سي في ال Y بدر سوى تكامل تي او
+
+407
+00:45:07,440 --> 00:45:07,540
+سي دي تي زائد في نصة ال C يبقى لو كملنا الطرفين تي
+
+408
+00:45:07,540 --> 00:45:09,040
+او سي دي تي زائد في نصة ال C يبقى لو كملنا الطرفين
+
+409
+00:45:09,040 --> 00:45:12,420
+تي او سي دي تي زائد في نصة ال C يبقى لو كملنا
+
+410
+00:45:12,420 --> 00:45:15,840
+الطرفين تي او سي دي تي زائد في نصة ال C يبقى لو
+
+411
+00:45:15,840 --> 00:45:19,860
+كملنا الطرفين تي او سي دي تي زائأو بدنا نيجي ناخد
+
+412
+00:45:19,860 --> 00:45:28,340
+integral يبقى هنا T وهنا EOS T واحد EOS T Zero EOS
+
+413
+00:45:28,340 --> 00:45:35,120
+T هذي بالموجب وهذه بالمين بالسالب يبقى سعر T EOS T
+
+414
+00:45:35,120 --> 00:45:44,560
+في ال Y بده يساوي T EOS T ماقص EOS T زائد ثلثة C
+
+415
+00:45:45,730 --> 00:45:53,430
+يبقى Y يساوي
+
+416
+00:45:53,430 --> 00:46:03,650
+واحد ناقص واحد على T زائد C على T T E أس T يبقى
+
+417
+00:46:03,650 --> 00:46:12,390
+هذا هو ال general solution
+
+418
+00:46:23,510 --> 00:46:32,110
+الان بدنا نشوف ما هو شكل الحل يبقى
+
+419
+00:46:32,110 --> 00:46:35,170
+بنجي على ال initial condition اللي عنده ال initial
+
+420
+00:46:35,170 --> 00:46:38,350
+condition اللي قال لي y عند ال n اثنين يساوي واحد
+
+421
+00:46:38,670 --> 00:46:44,370
+يعني لو شيلت P وحطيت مكانها لن 2 بتطلع Y أب واحد
+
+422
+00:46:44,370 --> 00:46:53,090
+يبقى واحد يستوي واحد ماقص واحد على لن 2 زائد C على
+
+423
+00:46:53,090 --> 00:47:03,870
+لن 2 في E أس لن 8 أظن لو جبت هذا عند هذا بروح هذا
+
+424
+00:47:03,870 --> 00:47:09,200
+بدي أجيبه هنا بصير بقيمة عموجة بقىيعني واحد على لن
+
+425
+00:47:09,200 --> 00:47:17,460
+اتنين هذا كله باتنين يبقى ال C على اتنين لن اتنين
+
+426
+00:47:17,460 --> 00:47:25,560
+لن اتنين مع لن اتنين يبقى ال C تساوي اتنين يبقى
+
+427
+00:47:25,560 --> 00:47:38,790
+أصبح the solution of the initial value problemY
+
+428
+00:47:38,790 --> 00:47:53,790
+تساوي نقص واحد على T زائد C على T في
+
+429
+00:47:53,790 --> 00:47:54,270
+E
+
+430
+00:47:58,380 --> 00:48:04,140
+يعني المعادلات لازم يمكن حصل المتغيرات في اتحاد
+
+431
+00:48:04,140 --> 00:48:08,620
+يسمى function في اواب لحاله وfunction في اتنى
+
+432
+00:48:08,620 --> 00:48:12,000
+لحاله ينجح هذا المنصور باستخدام ال equation و
+
+433
+00:48:12,000 --> 00:48:16,520
+بعدين يقول هو احسن كام كيف كفتانى فبالي يقول زي
+
+434
+00:48:16,520 --> 00:48:18,420
+جينا مالك يسأل مالك يسأل ال equation
+
+435
+00:48:27,220 --> 00:48:30,900
+يبقى نفس المعادلة توسعة حدام اللي رابط كده لك
+
+436
+00:48:30,900 --> 00:48:35,920
+تقيسها بدلها مبين لك الgenesis equation تاني ممكن
+
+437
+00:48:35,920 --> 00:48:41,960
+تكتب هذه المعادلة على صورة تانية dy by x الطرف
+
+438
+00:48:41,960 --> 00:48:46,680
+الشمالي زي ماقول f of x y ممكن تكتبها على شكل M of
+
+439
+00:48:46,680 --> 00:48:54,300
+x y علي M of x y سؤال هو هل هذا ممكن و لا غير ممكن
+
+440
+00:48:54,300 --> 00:49:01,640
+الإجابة ممكنممكن كيف ممكن f of x y ياخدها كلها بال
+
+441
+00:49:01,640 --> 00:49:07,660
+m of x y و ال n of x y ياخدها بجدال و هذا صحيح إن
+
+442
+00:49:07,660 --> 00:49:13,260
+صارت ما هيش مشكلة إذا صار الكلام هذا ممكن يبقى هذا
+
+443
+00:49:13,260 --> 00:49:17,320
+الكلام ممكن لو حد ال f of x y هي m of x y و حد ال
+
+444
+00:49:17,320 --> 00:49:23,720
+n of x y هي واحد صحيح طيب افترضي بالصدر الله إيه
+
+445
+00:49:23,720 --> 00:49:30,510
+لو خلتإن ال M function في X فقط و M function في Y
+
+446
+00:49:30,510 --> 00:49:37,010
+فقط يبقى المعادلة هذه بيبدأ تصير dy by x سوى M of
+
+447
+00:49:37,010 --> 00:49:40,070
+X على N of Y
+
+448
+00:49:44,330 --> 00:49:52,670
+م of y بدي y يسوى م of x مالها دفسي بكيان مفاصلة
+
+449
+00:49:52,670 --> 00:49:57,050
+اللي فيهم y لحال مش ناحية و اللي فيهم ال x where
+
+450
+00:49:57,050 --> 00:50:03,670
+بناحية تاني كيانة فاصلة متغيرة طيب أنا بدي y تروح
+
+451
+00:50:03,670 --> 00:50:09,550
+بكامل الطرفين تكامل هذه هجيب لي y تكامل هذه هجيب
+
+452
+00:50:09,550 --> 00:50:12,650
+لي دالة بدالة دالة او هذا بيجيب لي دالة بدالة ال x
+
+453
+00:50:12,910 --> 00:50:18,910
+وهذا بيدل دالة بدلالة Y ومن ثم يكون خلاصنا جيبنا
+
+454
+00:50:18,910 --> 00:50:26,190
+حصل على شكل Y سواء كانت Y صريحة أو بيمنية بيمنيش
+
+455
+00:50:26,190 --> 00:50:30,070
+بيمنى انه انا جلبت جيب Y as a function of it سواء
+
+456
+00:50:30,070 --> 00:50:37,370
+كانت دالة صريحة او دالة implicit او غير يعني دالة
+
+457
+00:50:37,370 --> 00:50:42,330
+بيمنية او دالة صريحةيبقى بالحلها بواصفة ال
+
+458
+00:50:42,330 --> 00:50:47,290
+integration الان بالتالي ناخد أمثلة توريحية على
+
+459
+00:50:47,290 --> 00:50:51,190
+الشغل يعني يا بنات الشغل دلوقتي لحد ما أطلع في
+
+460
+00:50:51,190 --> 00:50:55,130
+المعادلة بدي أحاول أفصل ال X لحالي و ال Y لحالي
+
+461
+00:50:55,130 --> 00:51:02,530
+أكمل انت خلصت أي مسألة ناخد أمثلة يبقى example one
+
+462
+00:51:13,190 --> 00:51:18,270
+and following differential
+
+463
+00:51:18,270 --> 00:51:21,370
+equation
+
+464
+00:51:21,370 --> 00:51:24,890
+المعادلة
+
+465
+00:51:24,890 --> 00:51:37,630
+الأولى نمرا M dy by dx dy by dx يسمى E أس Y أصيني
+
+466
+00:51:37,630 --> 00:51:38,690
+اتنين X
+
+467
+00:51:42,480 --> 00:51:51,160
+E أوسى اتنين Y كله فيه أوساين X نمرى بيه السؤال
+
+468
+00:51:51,160 --> 00:52:02,640
+التاني انه X ال Y' يساوي واحد ناقص Y' كله اص نص
+
+469
+00:52:17,190 --> 00:52:22,490
+السؤال بيقول يحل كل من المعاملات التفاعلونية تالية
+
+470
+00:52:22,490 --> 00:52:29,530
+السؤال الأول dy by x يساوي e قص y صينة من x على y
+
+471
+00:52:29,530 --> 00:52:32,290
+ناقص e وسط 2y بكو صينة من x
+
+472
+00:52:41,640 --> 00:52:45,980
+يجب ان اقول المعاملة هذه هروح اكتبها على الشكل
+
+473
+00:52:45,980 --> 00:52:51,960
+التالت شو هيك لو ضربت في DX مرة واحدة في الطرفين
+
+474
+00:52:51,960 --> 00:52:53,380
+ايش بيصير عندنا
+
+475
+00:53:08,650 --> 00:53:22,070
+كله فيه cos X DX طب أبطال أيه لبنان؟ ال function
+
+476
+00:53:22,070 --> 00:53:25,770
+في Y يعني و ال باقي بيبقى ال function بمين؟ X يعني
+
+477
+00:53:25,770 --> 00:53:28,850
+معناه تبقى اللي ده تخلص من هنا يعني بتروح X من
+
+478
+00:53:28,850 --> 00:53:33,770
+الطرفين عليه يعني لو جسمت الطرفين عليها شو بيصير
+
+479
+00:53:33,770 --> 00:53:38,110
+عن الإرمالات؟ Y نقص E
+
+480
+00:53:42,230 --> 00:53:47,670
+DY يساوي شويه في هذه SIN 2X مش هي عبارة عن ما
+
+481
+00:53:47,670 --> 00:53:58,130
+عندنا SIN X بيكون SIN X على SIN X كتير طيب تكتبها
+
+482
+00:53:58,130 --> 00:54:10,220
+بصورة أخرى هذي Y في E-Y ناقص EY كله في DYيبقى هذه
+
+483
+00:54:10,220 --> 00:54:14,300
+على هذه الطلاقة فوق بيشيلت سالف هذه مع هذه تفتصل
+
+484
+00:54:14,300 --> 00:54:25,200
+بظل E أس Y Cos X مع Cos X يبقى 2Sin X بDX يبقى هذه
+
+485
+00:54:25,200 --> 00:54:31,760
+فصلنا يا بنات ال Y لا واحدة و ال X لا واحدة يبقى
+
+486
+00:54:31,760 --> 00:54:36,340
+الأن بجهة كاملة الطرفين بحصل على مين على تاني حل
+
+487
+00:54:36,340 --> 00:54:39,080
+يبقى بجهة كاملة هذه
+
+488
+00:54:47,490 --> 00:55:00,210
+يبقى انا انا انا انا
+
+489
+00:55:00,210 --> 00:55:03,630
+انا
+
+490
+00:55:03,630 --> 00:55:04,450
+انا انا انا انا انا انا انا انا انا انا انا انا
+
+491
+00:55:04,450 --> 00:55:04,470
+انا انا انا انا انا انا انا انا انا انا انا انا
+
+492
+00:55:04,470 --> 00:55:04,470
+انا انا انا انا انا انا انا انا انا انا انا انا
+
+493
+00:55:04,470 --> 00:55:04,470
+انا انا انا انا انا انا انا انا انا انا انا انا
+
+494
+00:55:04,470 --> 00:55:09,150
+انا انا انا انا اناواحد لو كاملها بنفسها مقسمة على
+
+495
+00:55:09,150 --> 00:55:13,550
+سالب واحد مقسمة على سالب واحد والله مضروبة في سالب
+
+496
+00:55:13,550 --> 00:55:21,050
+واحد هي نفسها طيب مشتاق كمان مرة يبقى نفسها مقسمة
+
+497
+00:55:21,050 --> 00:55:26,210
+على سالب واحد بسالب الشصية بالموجة يبقى هذه بالهذه
+
+498
+00:55:26,210 --> 00:55:31,230
+بالموجة و هذه بالهذه بالسالب يبقى بالتكامل بسرع
+
+499
+00:55:31,230 --> 00:55:40,640
+النميمبصير عندنا ناقص Y EOS ناقص Y ناقص EOS ناقص Y
+
+500
+00:55:40,640 --> 00:55:47,900
+وهنا وصلنا لناقص هي الناقص وتكامل ال EOS Y بال EOS
+
+501
+00:55:47,900 --> 00:55:53,560
+Y itself تمام؟
+
+502
+00:55:53,560 --> 00:55:59,940
+يبقى هاي تكامل التنتير وهذه زي ما هي EOS Y نجي
+
+503
+00:55:59,940 --> 00:56:11,350
+لهذههذه تكملت سالب اثنين وصين ال X زائد وخمسين طب
+
+504
+00:56:11,350 --> 00:56:17,570
+ايش رايح؟ لو ضربت كله في E أوس Y عشان اخلص منها
+
+505
+00:56:17,570 --> 00:56:25,070
+السوالة ده او لو ضربت كله في سالب E أوس سالب Y لو
+
+506
+00:56:25,070 --> 00:56:31,740
+ضربت هذه كلهاالسالب E والسالب E والسالب E والسالب
+
+507
+00:56:31,740 --> 00:56:31,740
+E والسالب E والسالب E والسالب E والسالب E والسالب
+
+508
+00:56:31,740 --> 00:56:36,700
+E والسالب E والسالب E والسالب E والسالب E والسالب
+
+509
+00:56:36,700 --> 00:56:37,640
+E والسالب E والسالب E والسالب E والسالب E والسالب
+
+510
+00:56:37,640 --> 00:56:39,480
+E والسالب E والسالب E والسالب E والسالب E والسالب
+
+511
+00:56:39,480 --> 00:56:39,540
+E والسالب E والسالب E والسالب E والسالب E والسالب
+
+512
+00:56:39,540 --> 00:56:41,520
+E والسالب E والسالب E والسالب E والسالب E والسالب
+
+513
+00:56:41,520 --> 00:56:50,100
+E والسالب E والسالب E والسالب
+
+514
+00:56:50,100 --> 00:56:55,900
+E والس
+
+515
+00:56:55,950 --> 00:57:10,650
+يقص يقص يقص يقص يقص يقص يقص يقص يقص يقص يقص يقص
+
+516
+00:57:10,650 --> 00:57:19,950
+يقص يقص يقص يقص يقص يقص
+
+517
+00:57:25,690 --> 00:57:30,310
+مش Y في ناحية و X في ناحية لإن هذا حالة المعادلة
+
+518
+00:57:30,310 --> 00:57:35,530
+الأولى اللي هي عامة نجي للمعادلة التانية نجي لنمرة
+
+519
+00:57:35,530 --> 00:57:41,770
+B نمرة B لإننا نحاول نفصل المتغيرات فنروح أكثر
+
+520
+00:57:41,770 --> 00:57:50,750
+المعادلة على الشكل التالي X بDY على DX يساوي جدر
+
+521
+00:57:50,750 --> 00:58:00,680
+التربيعي لو أحد ناقص Y تربيهأول انشرتنا فقلنا E1
+
+522
+00:58:00,680 --> 00:58:06,240
+على الجذر التربيعي العارف واقع صغير التربيع يسمى
+
+523
+00:58:06,240 --> 00:58:13,140
+DX على X فجسمي على هذه DX تطلع هنا و X تنزل تحت
+
+524
+00:58:13,140 --> 00:58:18,100
+الشكل اللي عندنا هذا لأن المعادلة أخدت الشكل
+
+525
+00:58:18,100 --> 00:58:24,920
+الجديد اللي قدامنا هذاكداش تكمل المادة الأولى يا
+
+526
+00:58:24,920 --> 00:58:31,100
+بنادي؟ Y على الجدر التربية لواحد نقص Y تربية؟ كده؟
+
+527
+00:58:31,100 --> 00:58:40,280
+سن .. سن ايه؟ كده؟ سن .. سن الف سن الف سواء فجو
+
+528
+00:58:40,280 --> 00:58:48,520
+كانت بزايد تحت الجدر؟ تحت الجدر تحت الجدر
+
+529
+00:59:05,040 --> 00:59:12,400
+مش تكامل اخر كل معادلة تفضلية عندك هي تكاملين يا
+
+530
+00:59:12,400 --> 00:59:20,260
+جلوة كم انت بصير عندي Y inverse Yيساوي لم absolute
+
+531
+00:59:20,260 --> 00:59:26,040
+value ل X زي المادة زي ال consistency هذي بقدر
+
+532
+00:59:26,040 --> 00:59:29,500
+أجيب لها Y في دعنى و لا بقدر أجيب لها تاني و لا
+
+533
+00:59:29,500 --> 00:59:33,300
+بقدر أجيب لها تاني و لا بقدر أجيب لها تاني و لا
+
+534
+00:59:33,300 --> 00:59:33,620
+بقدر أجيب لها تاني و لا بقدر أجيب لها تاني و لا
+
+535
+00:59:33,620 --> 00:59:33,620
+بقدر أجيب لها تاني و لا بقدر أجيب لها تاني و لا
+
+536
+00:59:33,620 --> 00:59:33,620
+بقدر أجيب لها تاني و لا بقدر أجيب لها تاني و لا
+
+537
+00:59:33,620 --> 00:59:34,600
+بقدر أجيب لها تاني و لا بقدر أجيب لها تاني و لا
+
+538
+00:59:34,600 --> 00:59:41,340
+بقدر أجيب لها تاني و لا بقدر أجيب لها تاني
+
+539
+00:59:41,340 --> 00:59:45,520
+و لا بقدر أ
+
+540
+00:59:49,940 --> 00:59:56,740
+لل absolute value ل X زائد constant C هذا هو عبارة
+
+541
+00:59:56,740 --> 00:59:59,640
+عن حل المعادلة التفاغرية
+
+542
+01:00:33,640 --> 01:00:34,700
+ثالث نهار
+
+543
+01:00:53,960 --> 01:01:09,460
+convolution of the following national problems على
+
+544
+01:01:09,460 --> 01:01:20,440
+نمرة إيه؟ نمرة إيه؟ Determine Determine
+
+545
+01:01:20,440 --> 01:01:21,740
+لإنترال
+
+546
+01:01:25,900 --> 01:01:37,280
+فى الفترة in which the solution
+
+547
+01:01:37,280 --> 01:01:44,240
+is بيطار
+
+548
+01:01:44,240 --> 01:01:50,000
+اولى
+
+549
+01:01:50,000 --> 01:01:53,860
+وراى ثانوية
+
+550
+01:01:56,460 --> 01:02:11,660
+نقص x تاريخ plus نص dy يساوي sin inverse x dx و y
+
+551
+01:02:11,660 --> 01:02:20,340
+يعني زي رمزية تساوي واحد نقطة تانية لإن ال y prime
+
+552
+01:02:20,340 --> 01:02:30,740
+هي بيساوي xY تكييب في واحد زائد تكستر في أقص ناقص
+
+553
+01:02:30,740 --> 01:02:39,520
+نصف وY عند Zero كذلك يسمي الواحد
+
+554
+01:03:03,640 --> 01:03:07,860
+يقول يا حل، كل مثال .. كل مثالة تهم الحقيقية
+
+555
+01:03:07,860 --> 01:03:12,620
+أتغلب، وهذه الفترة اللي اتحل عليها تكون صحية أو
+
+556
+01:03:12,620 --> 01:03:18,140
+اتحل معرفة على هذه الفكرة، تظل الدولة اللي عندهم
+
+557
+01:03:18,140 --> 01:03:22,420
+هذه والحمد لله يبقوا عصر الانسس لحال ومغارز لحال،
+
+558
+01:03:22,420 --> 01:03:29,730
+بس فيهم هذه .. هذه الانسسإذا ممكن نفسي مقترفين
+
+559
+01:03:29,730 --> 01:03:36,730
+عليه، لأن جبالي مجرده هنا من المفتة الأولى La
+
+560
+01:03:36,730 --> 01:03:50,500
+differential equation SY تربيع Dy Y تربيع Dy يساوي
+
+561
+01:03:50,500 --> 01:03:56,580
+Sine Inverse X على الجدري التربيعي اللي راح اتناقص
+
+562
+01:03:56,580 --> 01:04:04,200
+X تربيع DX اضغط طبعا في الشمال ثانية و اتكلم و
+
+563
+01:04:04,200 --> 01:04:08,000
+فانت سهل
+
+564
+01:04:08,000 --> 01:04:14,370
+انا عارف ناشيلكن لو جد كلمات قادرين منها تقدر تقول
+
+565
+01:04:14,370 --> 01:04:22,890
+تكامل نواي تربية dy لساوي تكامل لsin inverse x هذا
+
+566
+01:04:22,890 --> 01:04:28,430
+يقول عارفين منها يعني
+
+567
+01:04:28,430 --> 01:04:36,010
+هذي d لsin inverse x، مظبوط؟ يعني استبدال من
+
+568
+01:04:36,010 --> 01:04:40,780
+المقدار هذا كلهبديه ال sign inverse يعني مشتق ال
+
+569
+01:04:40,780 --> 01:04:43,900
+sign inverse يعني مشتق ال sign inverse تقي واحد
+
+570
+01:04:43,900 --> 01:04:46,100
+نقل تقرير واحد نقل تقرير نقل تقرير نقل تقرير نقل
+
+571
+01:04:46,100 --> 01:04:49,840
+تقرير نقل تقرير نقل تقرير نقل تقرير نقل تقرير نقل
+
+572
+01:04:49,840 --> 01:04:50,560
+تقرير نقل تقرير نقل تقرير نقل تقرير نقل تقرير نقل
+
+573
+01:04:50,560 --> 01:04:51,520
+تقرير نقل تقرير نقل تقرير نقل تقرير نقل تقرير نقل
+
+574
+01:04:51,520 --> 01:04:53,800
+تقرير نقل تقرير نقل تقرير نقل تقرير نقل تقرير نقل
+
+575
+01:04:53,800 --> 01:05:01,380
+تقرير نقل تقرير نقل تقرير نقل تقرير
+
+576
+01:05:05,550 --> 01:05:11,850
+مش مصير أنه هنا مصير أنه y تكيب يسوى تلاتة على
+
+577
+01:05:11,850 --> 01:05:20,390
+اتنين sin inverse x لكل تاريخ زائد تلاتة c طب معقن
+
+578
+01:05:20,390 --> 01:05:26,230
+ياناش ال condition انه y عند zero يسوى جدا واحد
+
+579
+01:05:26,230 --> 01:05:33,010
+يعني لو كانت x ب zero في y جدا واحد يبقى واحد ان
+
+580
+01:05:33,010 --> 01:05:47,000
+كنت تكيببتساوي تلاتة على اتنين في صيف المغزيل يبقى
+
+581
+01:05:47,000 --> 01:05:54,440
+هاي Zero كل تربيع زي تلاتة C يبقى مصير واحد تساوي
+
+582
+01:05:54,440 --> 01:06:01,940
+تلاتة C وهذا بيعطيك المصير تساوي جدارك تساوي الكل
+
+583
+01:06:02,620 --> 01:06:08,620
+يبقى بالإنها العالية بصير علينا Y تكيب بدي ساوي
+
+584
+01:06:08,620 --> 01:06:16,260
+تلاتة على اتنين لـsin inverse X القلب الربيع زائد
+
+585
+01:06:16,260 --> 01:06:28,680
+واحد تمام او Y تساوي الجدري التالت لـVزي ثلاثة على
+
+586
+01:06:28,680 --> 01:06:35,060
+اتنين ثلاثة على اتنين sin inverse x والترابية
+
+587
+01:06:35,060 --> 01:06:39,540
+دائرة خلاص
+
+588
+01:06:39,540 --> 01:06:45,640
+لسه المطلوب الأول يومين اللي هو ال solution يبقى
+
+589
+01:06:45,640 --> 01:06:51,720
+من حد ما بدأنا هنا بدأنا في الامريكا والعزل امريكا
+
+590
+01:06:51,720 --> 01:06:57,940
+دي هذه الفترة اللي الحل عليها هذا بيكون صحيحباجي
+
+591
+01:06:57,940 --> 01:07:03,140
+بسأل نفسي هذا الجدر الثالث جدر الثالث معرف لل zero
+
+592
+01:07:03,140 --> 01:07:08,900
+والموجب والسلب بدون مشاكل، مظبوط؟ صح، هاي شو
+
+593
+01:07:08,900 --> 01:07:12,940
+المشكلة وين؟ المشكلة في ال sign inverse، ال sign
+
+594
+01:07:12,940 --> 01:07:16,940
+inverse في الدرجة اللي عم نقولها وين؟ من سلب واحد
+
+595
+01:07:16,940 --> 01:07:21,770
+إلى واحد، من سلب واحد إلى واحد، هاي مظبوطيجب ان
+
+596
+01:07:21,770 --> 01:07:26,730
+انا اتخذ دائما و ابدا معرضة من سالب واحد الى واحد
+
+597
+01:07:26,730 --> 01:07:32,550
+و بروح بقوله هنا فاصلة ال X أكبر من او تسوى سالب
+
+598
+01:07:32,550 --> 01:07:36,790
+واحد او اقل من او تسوى سالب واحد او لأسلوب بل ال X
+
+599
+01:07:36,790 --> 01:07:41,750
+اقل من او تسوى واحد يبقى هذه ال interval اللى اتحل
+
+600
+01:07:41,750 --> 01:07:50,250
+عليها معرض يبقى هذه جبت من وينكان فلسطين من
+
+601
+01:07:50,250 --> 01:07:55,750
+معلوماتي عن معقوذ اللي هو scientist كان فلسطين طيب
+
+602
+01:07:55,750 --> 01:08:02,050
+نجي لنمرة اتنين نمرة اتنين بيقول ي واي فاي يسوى
+
+603
+01:08:02,050 --> 01:08:09,150
+XYKB ده بييزن المثل اللي عندنا يعني ده اقدر اقوله
+
+604
+01:08:09,150 --> 01:08:14,690
+ال equation as تجاهته بالمعادلة على الشكل التالي
+
+605
+01:08:14,690 --> 01:08:24,210
+اللي هو مين؟dy by dx يساوي هذا x على الجدر
+
+606
+01:08:24,210 --> 01:08:35,210
+التربيعي ل1 زائد x تربيع 8 من y تكييف يبقى هذا
+
+607
+01:08:35,210 --> 01:08:39,590
+الجدر كان في الواقع غيبت الإشارة طبعا نزل في
+
+608
+01:08:39,590 --> 01:08:45,620
+المقام وظلت عند x y تكييف فوقهذه مدرسة رسمها على
+
+609
+01:08:45,620 --> 01:08:53,140
+الشكل التالي dy على y تكييف جسمنا كله على y تكييف
+
+610
+01:08:53,140 --> 01:09:01,120
+وضربنا في dx بصير x في dx على الجدرى الترميالي ل1
+
+611
+01:09:01,120 --> 01:09:07,820
+زائر x ترمية يعني يا بنات كأن الرسم صارت تكابر y
+
+612
+01:09:07,820 --> 01:09:16,150
+كسالي 3 dyيساوي تكامل X على جدرى تربية من واحد زي
+
+613
+01:09:16,150 --> 01:09:24,730
+تكس تربية DX أظن الشمال سهل تكملهبقول يا بابا
+
+614
+01:09:24,730 --> 01:09:31,490
+الكلاصين نفرض واحد تربيه اذا
+
+615
+01:09:31,490 --> 01:09:38,190
+انا لو حطيتي w يسوي واحد زائد x تربيه واش تعطي
+
+616
+01:09:38,190 --> 01:09:43,910
+انجاز من x dx ماعنديش اتنينات انجاز نص dw
+
+617
+01:09:47,720 --> 01:09:54,420
+يبقى بصيري المسألة هذه هاي النص برا وهاي تكامل
+
+618
+01:09:54,420 --> 01:10:06,540
+وهنا dw على جذري w أو تكامل dy أثناء تس ثلاثة dy
+
+619
+01:10:06,540 --> 01:10:16,440
+يسوى النص تكامل w أثناء تس نص dwيبقى هذا بالصينيه
+
+620
+01:10:16,440 --> 01:10:25,580
+Y أس ناقص اتنين على ناقص اتنين يساوي النص IEW فهو
+
+621
+01:10:25,580 --> 01:10:32,180
+اضيف نقص واحد و اكسب على نقص الجديد يبقى هذا نص
+
+622
+01:10:32,180 --> 01:10:41,220
+على نص زائد كلستانسيه يبقى نص على نص يبقى هذه صارت
+
+623
+01:10:41,220 --> 01:10:43,840
+ايه صارت ناقص
+
+624
+01:11:00,680 --> 01:11:04,540
+معادلة كل المضروبة في نقص اتنين
+
+625
+01:11:08,630 --> 01:11:14,750
+يعني لو ضربنا في ناقص اتنين نصير واحد على Y تربية
+
+626
+01:11:14,750 --> 01:11:20,610
+يساوي ناقص اتنين الجرهي التربية على واحد زي ال
+
+627
+01:11:20,610 --> 01:11:31,630
+text تربية ناقص اتنين C مش أجلب؟ وضعيا إيش رأيك؟
+
+628
+01:11:31,630 --> 01:11:39,320
+لو شيلت هذه وحطيت بدلها متغير جديد سميلي هذه C1وها
+
+629
+01:11:39,320 --> 01:11:46,940
+دي C1 وها دي C1 بدي أشيل سالب اتنين C1 وقتهم
+
+630
+01:11:46,940 --> 01:11:51,580
+بدالهم C2 أطلع اطلع اطلع اطلع اطلع اطلع اطلع اطلع
+
+631
+01:11:51,580 --> 01:11:51,760
+اطلع اطلع اطلع اطلع اطلع اطلع اطلع اطلع اطلع اطلع
+
+632
+01:11:51,760 --> 01:11:52,020
+اطلع اطلع اطلع اطلع اطلع اطلع اطلع اطلع اطلع اطلع
+
+633
+01:11:52,020 --> 01:11:54,060
+اطلع اطلع اطلع اطلع اطلع اطلع اطلع اطلع اطلع اطلع
+
+634
+01:11:54,060 --> 01:12:05,720
+اطلع اطلع اطلع اطلع اطلع اطلع اطلع اطلع اطلع اط
+
+635
+01:12:06,580 --> 01:12:10,260
+عندي ايش؟ عندي initial condition في الدروحة طبعا
+
+636
+01:12:10,260 --> 01:12:16,620
+عندي y عند zero تساوي واحد الان y عند zero تساوي
+
+637
+01:12:16,620 --> 01:12:24,500
+واحد implies واحد على واحد ترجع له واحد يساوي ناقص
+
+638
+01:12:24,500 --> 01:12:34,100
+اتنين كذر الواحد من ناقص اتنين C1 طبعا يبقى بصير
+
+639
+01:12:34,100 --> 01:12:34,980
+عندي هنا
+
+640
+01:12:39,280 --> 01:12:48,300
+وهنا نقص اتنين C1 يبقى بصير عندنا اللي هو التلاتة
+
+641
+01:12:48,300 --> 01:12:55,600
+سواء سالب اتنين C1 يبقى C1 سالب تلاتة على اتنين
+
+642
+01:12:55,600 --> 01:13:03,980
+لبصير المثل واحد على I تربيع يصير نقص اتنين واحد
+
+643
+01:13:03,980 --> 01:13:08,360
+زاد X تربيعبدي أشيل c1 و أضعه في مكانها ثالث ثلاثة
+
+644
+01:13:08,360 --> 01:13:15,340
+على اتنين يبقى بيصير زائد ثلاث يبقى لو شجلبنا
+
+645
+01:13:15,340 --> 01:13:24,120
+بيصير شكل الحل Y تربيع يسوى واحد على ثلاثة ناقص
+
+646
+01:13:24,120 --> 01:13:31,560
+اتنين الجدرين التربيعي لواحد زائد X تربيع فإذا ما
+
+647
+01:13:31,560 --> 01:13:36,420
+بديش Y تربيع بدي واحد ممكنش ناخدالجدري الترميعي
+
+648
+01:13:36,420 --> 01:13:43,640
+للطرفين يبقى هذا بده يعطينا ان y بساوي زائد او
+
+649
+01:13:43,640 --> 01:13:52,680
+ناقص واحد على الجدري الترميعي لمين لتلاتة ناقص
+
+650
+01:13:52,680 --> 01:13:59,520
+اتنين الجدري الترميعي واحد زائد اكس ترمية طب انا
+
+651
+01:13:59,520 --> 01:14:03,860
+بده اشوف عندي إجابة والله إذا ابتدتبنجر ال
+
+652
+01:14:03,860 --> 01:14:09,640
+condition ال condition اللي عم نقوله y عند ال zero
+
+653
+01:14:09,640 --> 01:14:18,040
+بالساوية ده واحد و اخر واحد موجبه والمساعدة الان y
+
+654
+01:14:18,040 --> 01:14:25,320
+عند ال zero بالساوية واحد هذا يعني ان y اكبر من من
+
+655
+01:14:25,320 --> 01:14:34,510
+ال zero هذا يعني ان yعلى الجدر التربيعي لتلاتة
+
+656
+01:14:34,510 --> 01:14:41,390
+ناقص اتنين بالجدر التربيعي لواحد زائد X التربيعي
+
+657
+01:14:41,390 --> 01:14:46,850
+حتى الآن جيبنا المطبوب الأول فقط لغيره بإننا نروح
+
+658
+01:14:46,850 --> 01:14:52,350
+نجيب المطبوب التالي وهو الفترة اللي حل عليها هذا
+
+659
+01:14:52,350 --> 01:14:54,830
+يقول صحيحا
+
+660
+01:15:04,410 --> 01:15:09,530
+الان الحل صحيح لو الفمية اللى تحت الجدران كانت
+
+661
+01:15:09,530 --> 01:15:16,450
+أكبر من الـ 0 صحيح ولا لا؟ يبقى هنا باجي بقول لا
+
+662
+01:15:16,450 --> 01:15:21,710
+solution is
+
+663
+01:15:21,710 --> 01:15:26,550
+defined معرف if
+
+664
+01:15:34,850 --> 01:15:40,950
+تكس تربية فالأكبر من Zero ممنوع يسوى Zero لو سوى
+
+665
+01:15:40,950 --> 01:15:46,290
+Zero لأصبح أحد واحد على صفر لما نخلق Seal and Defy
+
+666
+01:15:46,290 --> 01:15:50,770
+يبقى بنات من الحل ال Inquality هذا يبقى لو كان
+
+667
+01:15:50,770 --> 01:15:55,770
+حللها بصير اتنين القدر التربية يلا واحد زائد تكس
+
+668
+01:15:55,770 --> 01:16:04,340
+تربية أقل من مائة أقل من دلالة أوبصير عندنا الجدر
+
+669
+01:16:04,340 --> 01:16:12,160
+التربيع إلى واحد زائد X تربيع أقل من 3 على 2 أقرب
+
+670
+01:16:12,160 --> 01:16:17,280
+الطرفين بصير عندك واحد زائد X تربيع
+
+671
+01:16:34,640 --> 01:16:39,220
+خد الجدر التربيهي يبقى الجدر التربيهي بتطلعلي
+
+672
+01:16:39,220 --> 01:16:45,960
+absolute value لأكس أقل من جدر 5 على 2 يبقى هذه
+
+673
+01:16:45,960 --> 01:16:54,200
+الفترة اللي بحل عليها يكونوا صحيحا طيب
+
+674
+01:16:54,200 --> 01:16:59,000
+ال switch نحن الآن اتذهل منه لكن انا احط زجاج في
+
+675
+01:16:59,000 --> 01:17:03,660
+ال exercises حالة دي اسمها homogeneous function
+
+676
+01:17:04,690 --> 01:17:10,770
+طبعاً بدنا نعطي تعريف لها ونشوف كذا كتاب طبعا حطه
+
+677
+01:17:10,770 --> 01:17:16,830
+حطه لها مجموعة للاسم يبقى موجودة لحالة اسمها ال
+
+678
+01:17:16,830 --> 01:17:23,050
+homogenous situations
+
+679
+01:17:23,050 --> 01:17:33,660
+وهذه موجودة in exercises اللي هم inexercise دي
+
+680
+01:17:33,660 --> 01:17:38,940
+اتنين اتنين لو كده في التمانين وليس في جزء النظر
+
+681
+01:17:38,940 --> 01:17:48,780
+نعطيها تعريف ونشوف كيف انتجها the first order
+
+682
+01:17:48,780 --> 01:18:03,100
+the first order dimension equation dy by dxبنسميه
+
+683
+01:18:03,100 --> 01:18:16,420
+homogeneous if
+
+684
+01:18:16,420 --> 01:18:32,330
+ال F of XY can be written can be written asهي a
+
+685
+01:18:32,330 --> 01:18:42,870
+function of the ratio y على x هو
+
+686
+01:18:42,870 --> 01:18:58,610
+الaccelerator denomination that is a n f dy y dx
+
+687
+01:19:01,200 --> 01:19:11,640
+F of X of Y بدي سوى capital F of Y على X وهذه
+
+688
+01:19:11,640 --> 01:19:20,320
+سبيها المعادلة رقم واحد ويصير
+
+689
+01:19:20,320 --> 01:19:27,720
+question
+
+690
+01:19:27,720 --> 01:19:29,480
+one
+
+691
+01:19:31,690 --> 01:19:32,510
+I was four
+
+692
+01:20:11,720 --> 01:20:18,000
+يقول المقال كذا يقول المعارضة بدا اشيل ال y على x
+
+693
+01:20:18,000 --> 01:20:25,940
+و اضطرها للمتميزة الجديدة والذات من ال V اضطر ال y
+
+694
+01:20:25,940 --> 01:20:34,900
+على x يساوي ال V او المعارضة هذه ممكن اقول Y تساوي
+
+695
+01:20:34,900 --> 01:20:40,880
+X PV بدا نشتقها كاله اشتقناها
+
+696
+01:20:57,930 --> 01:21:04,030
+مرة تانية مشتقة ال y هي dy على dx هذي مشتقة حصل
+
+697
+01:21:04,030 --> 01:21:09,630
+ضغط دقلتين مشتقة الأولى في الثانية زائد الأولى في
+
+698
+01:21:09,630 --> 01:21:14,430
+المشتقة في الضغط الثاني القلب تمسك المعلومة اللي
+
+699
+01:21:14,430 --> 01:21:20,520
+حصلت عليها وعوّضها في المعادلة رقم واحد يعنيبدي
+
+700
+01:21:20,520 --> 01:21:25,080
+أشيل dy على dx مكتوب بدلها main المعادلة اللي
+
+701
+01:21:25,080 --> 01:21:36,540
+عندناها ينجي هنا substitute and equation one we
+
+702
+01:21:36,540 --> 01:21:46,120
+get نقصد علامات dy على dx يكون v زائد x دي v على
+
+703
+01:21:46,120 --> 01:21:55,200
+dx الطرف اليمينبصرار F of B المعادلة
+
+704
+01:21:55,200 --> 01:22:02,580
+هذه بقدر اكتبها على الشكل التالي XGB على DX بتساوي
+
+705
+01:22:02,580 --> 01:22:13,200
+F of B ناقص ال B نقدر نفصل المتغيرات يبقى هذه
+
+706
+01:22:13,200 --> 01:22:28,390
+بتصير EVعلى F of D مقص ال V بتساوي DX على X ده
+
+707
+01:22:28,390 --> 01:22:32,750
+شوية وصلة Superbola كلها يبقى بنحل كذلك وكلها بنحل
+
+708
+01:22:32,750 --> 01:22:41,030
+قبل قليل يلقى دي Superbola equation
+
+709
+01:22:41,030 --> 01:22:46,030
+ده كان
+
+710
+01:22:49,090 --> 01:22:58,310
+بsize as before ناخد
+
+711
+01:22:58,310 --> 01:22:59,590
+مثال توضيح عليه
+
+712
+01:23:41,060 --> 01:23:46,320
+ومن ثم Solve
+
+713
+01:23:48,530 --> 01:24:05,890
+إذا تبقى N dy على dx يساوي 4y ناقص 3x على 2x ناقص
+
+714
+01:24:05,890 --> 01:24:06,190
+y
+
+715
+01:24:35,120 --> 01:24:39,020
+سؤال مرحبا يقول بيبينلي إذا المعادلات التي
+
+716
+01:24:39,020 --> 01:24:45,640
+تستخدمها هي عبارة عن معادلات متجانسة مميزة وبيتم
+
+717
+01:24:45,640 --> 01:24:51,380
+حل هذه المعادلة بيقول الشريف أو الساجل إذا تقدر
+
+718
+01:24:51,380 --> 01:24:57,720
+تقول المعادلة كلها لدلالة y على x أو x على y تصير
+
+719
+01:24:57,720 --> 01:25:02,390
+مميزةبس ممنوع يكون مثلا واحد على X وخمسة على Y
+
+720
+01:25:02,390 --> 01:25:07,150
+ممنوع على كده بدي يكون Y على X أو X على Y لإن لو
+
+721
+01:25:07,150 --> 01:25:11,890
+كنت وصلت لحاله مش مشكلة خالص طبعا يبقى يبقى يبقى
+
+722
+01:25:11,890 --> 01:25:19,190
+كله solution dy على dx يسبب شو رأيك لو جسمت بس
+
+723
+01:25:19,190 --> 01:25:30,310
+والمقام على X كله مش بصير اربع Y على Xناخذ تلاتة
+
+724
+01:25:30,310 --> 01:25:38,750
+على اتنين ناخذ y على x صح ولا لا؟ جسم كله من
+
+725
+01:25:38,750 --> 01:25:42,870
+البصرة والمقاب على x الطبعي صارت معادلة لدلالة y
+
+726
+01:25:42,870 --> 01:25:47,650
+على x ولا لا؟ زي ما قلنا صارت function بس احنا
+
+727
+01:25:47,650 --> 01:25:53,490
+صارت function of y على capital F of y على xبنبدأ
+
+728
+01:25:53,490 --> 01:25:57,130
+نعمل عليها المادة homogeneous differential
+
+729
+01:25:57,130 --> 01:26:02,270
+equation يبقى هذا الصغير هو homogeneous
+
+730
+01:26:02,270 --> 01:26:08,850
+differential equation ليشوف كيف نحل ال homogeneous
+
+731
+01:26:08,850 --> 01:26:16,270
+differential equation نيجي نقوله خُد Y على X تساوي
+
+732
+01:26:16,270 --> 01:26:21,630
+Z فانشطرنا تقولنا Y تساوي X
+
+733
+01:26:26,060 --> 01:26:35,600
+DX ممكن نسوي V ذائب X في DV على DX لما عادلتنا
+
+734
+01:26:35,600 --> 01:26:40,940
+هصير على الشكل التالي هشير DY على DX و اكتب قيمتها
+
+735
+01:26:40,940 --> 01:26:50,660
+اللي هي V ذائب V ذائب X في DV على DX على الطرف
+
+736
+01:26:50,660 --> 01:26:59,660
+الشمال نيجي للطرف اليمينأنه أربعة V ناقص تلاتة على
+
+737
+01:26:59,660 --> 01:27:10,540
+اتنين ناقص V نود V على الشجرة التالية يتجسر X بـDP
+
+738
+01:27:10,540 --> 01:27:20,440
+على DX يساوي أربعة V ناقص تلاتة على اتنين ناقص V
+
+739
+01:27:20,440 --> 01:27:28,220
+ناقص Bأضافنا للثلاثين لوساوية V هذه بدرة واحدة
+
+740
+01:27:28,220 --> 01:27:36,060
+لهذه المفاهيم يا بنات كبسيل XDD على DX يساوي كله
+
+741
+01:27:36,060 --> 01:27:47,380
+على اتنين ناقص V يظل اربعة V ناقص تلاتة وهذه
+
+742
+01:27:47,380 --> 01:27:57,020
+باعتماد على واحدة تنضرب لناقص Vتنين ناقص V وحتى
+
+743
+01:27:57,020 --> 01:28:05,140
+مقامتنا الكل يبقى X DV على DX يبقى اتنين ناقص V
+
+744
+01:28:05,140 --> 01:28:15,540
+بالمقام هنا اربعة V ناقص تلاتة ناقص اتنين V زائد V
+
+745
+01:28:15,540 --> 01:28:26,670
+تربية يبقى صارة المثلة اللي هو X DVعلى dx u7 أي b
+
+746
+01:28:26,670 --> 01:28:36,070
+تربيع وعنفه نقص 2u زائد 4a زائد 2b وغيرها جداش نقص
+
+747
+01:28:36,070 --> 01:28:42,950
+تلاتة مافيش غيرها على الاثنين ناقصين فالشك اللي
+
+748
+01:28:42,950 --> 01:28:47,870
+بيكتبها بدلالة b والشك اسمها بدلالة x وb
+
+749
+01:28:51,860 --> 01:28:58,020
+يبقى هذا شبسيدي اتنين ناقص V على V تربية زائد
+
+750
+01:28:58,020 --> 01:29:06,320
+اتنين V ناقص تلاتة DV يبقى يسوى DX على X يبقى هذا
+
+751
+01:29:06,320 --> 01:29:14,720
+C Parabol equation يبقى هذا C Parabol equation
+
+752
+01:29:14,720 --> 01:29:24,840
+السؤال هو هذه تقبل very easily يبقى المينكيف نتكلم
+
+753
+01:29:24,840 --> 01:29:34,840
+طبش مدد؟ حالي للمعادلة، مقصود A، مقصود B، مقصود A،
+
+754
+01:29:34,840 --> 01:29:35,480
+مقصود B، مقصود A، مقصود B، مقصود A، مقصود B، مقصود
+
+755
+01:29:35,480 --> 01:29:35,540
+A، مقصود B، مقصود A، مقصود B، مقصود A، مقصود B،
+
+756
+01:29:35,540 --> 01:29:35,540
+مقصود A، مقصود B، مقصود A، مقصود B، مقصود A، مقصود
+
+757
+01:29:35,540 --> 01:29:37,520
+B، مقصود A، مقصود B، مقصود A، مقصود B، مقصود A،
+
+758
+01:29:37,520 --> 01:29:42,300
+مقصود A، مقصود B، مقصود A، مقصود A، مقصود B، مقصود
+
+759
+01:29:42,300 --> 01:29:52,310
+A، مقصود A، مقصود A، مقصودهذه بيه وهذه بيه وهذه
+
+760
+01:29:52,310 --> 01:29:58,450
+واحد وهذه ثلاثة وهذه زائد وهذه ناقص ناقص بيه زائد
+
+761
+01:29:58,450 --> 01:30:06,010
+تلاتة بيه زائد اتنين بيه كيف تسرع مع القوة؟ كسور
+
+762
+01:30:06,010 --> 01:30:12,870
+يزمية كسور يزمية ممتازة اتراكتوز يبقى هذا الكلام
+
+763
+01:30:12,870 --> 01:30:20,370
+متساوي هذا قوس اللي هو بيه ناقص واحدو بس تاني D زي
+
+764
+01:30:20,370 --> 01:30:26,950
+التلاتة عاملين كل واحد من القاعدة الأولى و اتنين
+
+765
+01:30:26,950 --> 01:30:33,210
+are different اتنين كولوستان و كمان كولوستان تاني
+
+766
+01:30:33,210 --> 01:30:39,330
+بدنا نتخلص من هذه التسورة و نروح نطلب اتنين في هذا
+
+767
+01:30:39,330 --> 01:30:46,060
+المقام اطلب العربي عندك اطلب اتنين في D ناقص واحدو
+
+768
+01:30:46,060 --> 01:30:53,720
+B زائد تلاتة بنحصل على اتنين ناقص B يساوي A في B
+
+769
+01:30:53,720 --> 01:31:02,120
+زائد تلاتة زائد B في B ناقص واحد يجب اقولك لو كانت
+
+770
+01:31:02,120 --> 01:31:11,360
+ال B تساوي واحد then اتنين ناقص واحد يساوي اربعة A
+
+771
+01:31:11,360 --> 01:31:15,600
+وهذه مع السلامة يبقى هذا بدي اعطيك
+
+772
+01:31:18,560 --> 01:31:27,760
+نقص واحد يساوي واحد الان لو كان ال V يكون ناقص
+
+773
+01:31:27,760 --> 01:31:35,880
+ثلاثة then يصير اتنين زائد ثلاثة ناقص ناقص ثلاثة
+
+774
+01:31:35,880 --> 01:31:42,340
+يعني زائد ثلاثة ناقص ثلاثة يبقى هنا ناقص ثلاثة
+
+775
+01:31:42,340 --> 01:31:51,740
+ناقص اربع دي يمكن ناقص اربع دييبقى D مساوى سنة
+
+776
+01:31:51,740 --> 01:31:58,800
+وخمس أربعة يبقى مثلتنا صارت على الشكل التالي اللي
+
+777
+01:31:58,800 --> 01:32:06,060
+هو تكامل نمينا الطلب ثالث الأربعة و الرابعة تانية
+
+778
+01:32:06,060 --> 01:32:17,230
+الرابعة وهنا واحد على V مافس واحد في DVوهنا ناطس
+
+779
+01:32:17,230 --> 01:32:27,590
+بله خمس أربع وهنا واحد على بيه زائد تلاتة وهي
+
+780
+01:32:27,590 --> 01:32:31,990
+التكامل دي فيها الطرف الشمالي لجهة التكامل هذا
+
+781
+01:32:31,990 --> 01:32:36,530
+ساعطه عليه التكامل اللي اتنين هؤلاء اللي بيساوي
+
+782
+01:32:36,530 --> 01:32:41,350
+تكامل من بيه X على X
+
+783
+01:32:54,940 --> 01:33:05,160
+طيب لان كله blend يبقى ربع لل absolute value لل V
+
+784
+01:33:05,160 --> 01:33:14,560
+ناقص واحد ناقص خمس أربع لل absolute value لل V
+
+785
+01:33:14,560 --> 01:33:21,580
+زائد تلاتة لل V زائد تلاتة بدنا نسوي التلاتة
+
+786
+01:33:21,770 --> 01:33:28,190
+absolute value ل X زائد كل ثانية C شو رايش نموذج
+
+787
+01:33:28,190 --> 01:33:34,970
+أربعة و نتخلص منها؟ شو حسن؟ يبقى بسيطة عندي اللم و
+
+788
+01:33:34,970 --> 01:33:42,690
+ال V اللي هو Y على X ناقص واحد ناقص خمسة لم Y على
+
+789
+01:33:42,690 --> 01:33:49,810
+X زائد تلاتة يساوي أربعة لم absolute value ل X
+
+790
+01:33:49,810 --> 01:34:01,830
+زائدأربعة C one مثلًا طيب هذه بصيها لان absolute
+
+791
+01:34:01,830 --> 01:34:11,570
+value ل Y ناقص X كله على X ناقص خمسة لان Y زائد
+
+792
+01:34:11,570 --> 01:34:19,370
+ثلاثة X كله على X وهنا بتساوي أربعة لان
+
+793
+01:34:23,380 --> 01:34:29,840
+هذا يبقى ناقص بالصير لل absolute value لل Y ناقص X
+
+794
+01:34:29,840 --> 01:34:36,960
+ناقص لل absolute value ل X هذه ناقص خمسة لل
+
+795
+01:34:36,960 --> 01:34:45,720
+absolute value لتلاتة X Y زائد تلاتة X ناقص مع
+
+796
+01:34:45,720 --> 01:34:52,360
+ناقص بالصير زائد خمسةLin Absolute Value of X يساوي
+
+797
+01:34:52,360 --> 01:35:01,380
+4Lin Absolute Value of X زائد 4C1 طيب دعونا نشوف
+
+798
+01:35:01,380 --> 01:35:10,060
+هذي هذي و هذي كتاش مضالين 4Lin X وديها على ناحية
+
+799
+01:35:10,060 --> 01:35:19,240
+التانية تتجهل مع السلم صح؟ طيب هذي بتصير إيش؟بتصير
+
+800
+01:35:19,240 --> 01:35:27,000
+لل absolute value ل Y ناقص X ناقص لل absolute
+
+801
+01:35:27,000 --> 01:35:36,200
+value ل Y زي 3X خُص 5 يساوي 4Ci
+
+802
+01:35:47,790 --> 01:35:55,530
+هذه جمبسة يبقى اني بصير lamb salute value ل Y ماقص
+
+803
+01:35:55,530 --> 01:36:06,770
+X على Y زائد تلاتة X هذه كل قص خمسة يساوي أربعة
+
+804
+01:36:06,770 --> 01:36:17,060
+سيران كده تخلص من ال lamb يبقى بصير انsolute value
+
+805
+01:36:17,060 --> 01:36:24,120
+of y-x على solute value of y زائد تلاتة كل وصة
+
+806
+01:36:24,120 --> 01:36:32,760
+خمسة يسوى D أربعة C واحد الشرايح هذه كلها بترحبها
+
+807
+01:36:32,760 --> 01:36:38,780
+في C صح ولا لا يبقى بناء علينا solution
+
+808
+01:36:42,800 --> 01:36:51,160
+absolute value لروعي ناقص x يسوى c ان ال absolute
+
+809
+01:36:51,160 --> 01:36:58,620
+value لروعي ثائر ثلاثة و نصف خمسة يجعل هذا الحل
+
+810
+01:36:58,620 --> 01:37:04,420
+الامر لا يزال هناك سؤال كثير موجود
+
diff --git a/PL9fwy3NUQKwa8ZDfSFGn6H8xVFLzqmCZC/1myyZiBOvdQ.srt b/PL9fwy3NUQKwa8ZDfSFGn6H8xVFLzqmCZC/1myyZiBOvdQ.srt
new file mode 100644
index 0000000000000000000000000000000000000000..57db5a605970091c73fc396277cea04e9761ad23
--- /dev/null
+++ b/PL9fwy3NUQKwa8ZDfSFGn6H8xVFLzqmCZC/1myyZiBOvdQ.srt
@@ -0,0 +1,2566 @@
+1
+00:00:10,060 --> 00:00:17,020
+بسم الله الرحمن الرحيم، نبدأ اليوم في آخر Chapter في
+
+2
+00:00:17,020 --> 00:00:21,760
+المقرر إن شاء الله، هو Chapter 6، Chapter 6 بتحدث عن 
+
+3
+00:00:21,760 --> 00:00:27,700
+Laplace transforms، تحويلات Laplace، عالم فرنسي اسمه 
+
+4
+00:00:27,700 --> 00:00:33,480
+Laplace، وعمل التحويلات هذه، شو فايدة هذه التحويلات؟
+
+5
+00:00:33,480 --> 00:00:39,760
+تبسيط وضع الدالة اللي عندنا إلى دالة أسهل منها في 
+
+6
+00:00:39,760 --> 00:00:43,020
+التعامل، يبقى هي الفكرة الأساسية، يكون عندها 
+
+7
+00:00:43,020 --> 00:00:46,920
+Function، الـ Function هذا ممكن أستبدلها بـ Function 
+
+8
+00:00:46,920 --> 00:00:52,080
+مكافئة لها، لكن شكل الـ Function الجديدة هي أبسط من 
+
+9
+00:00:52,080 --> 00:00:56,400
+من شكل الـ Function الأصلية، يبقى هذا الفكرة 
+
+10
+00:00:56,400 --> 00:01:03,040
+الأساسية لهذا الموضوع، بعد تعريف لابلاس ترانسفورم 
+
+11
+00:01:03,040 --> 00:01:08,660
+بحل 
+
+12
+00:01:08,660 --> 00:01:13,740
+المعادلات التفاضلية من الرتبة الثانية، من الرتبة 
+
+13
+00:01:13,740 --> 00:01:19,480
+الرابعة، من الرتبة الثالثة، من الرتبة الرابعة، يبقى 
+
+14
+00:01:19,480 --> 00:01:23,200
+هذا موضوع الـ Chapter هذا، in general، لكن أول 
+
+15
+00:01:23,200 --> 00:01:27,080
+Section لـ Laplace transform، مش هندخل فيه في حل 
+
+16
+00:01:27,080 --> 00:01:31,660
+المعادلات التفاضلية، لكن هنشوف كيف عمليا نروح نحسب 
+
+17
+00:01:31,660 --> 00:01:37,000
+Laplace transform لدوال المختلفة، إذا بدنا نعطي 
+
+18
+00:01:37,000 --> 00:01:42,000
+تعريف لـ Laplace transform، نعطي تعريف لنوع جديد من 
+
+19
+00:01:42,000 --> 00:01:46,580
+الـ Functions، نشوف وقت إيش بيكون Laplace transform
+
+20
+00:01:46,580 --> 00:01:53,420
+exist لدالة ما، ثم بعد ذلك نذهب إلى أمثلة لكيفية 
+
+21
+00:01:53,420 --> 00:01:58,480
+حساب Laplace transform للدوال المختلفة، إذا نعود 
+
+22
+00:01:58,480 --> 00:02:02,860
+للتعريف لـ Laplace transform، بيقول: يفترض أن عندك 
+
+23
+00:02:02,860 --> 00:02:09,120
+دالة F small of T، معرفة على الفترة من صفر إلى 
+
+24
+00:02:09,120 --> 00:02:15,080
+Infinity، يعني على كل T الموجبة، يبقى كأننا نص 
+
+25
+00:02:15,080 --> 00:02:21,810
+اليمين تبعها، طبعًا محور X، دي Laplace transform لدالة F 
+
+26
+00:02:21,810 --> 00:02:27,370
+denoted by، يبقى تحويل لبلاس لدالة F، حدها الرمز L 
+
+27
+00:02:27,370 --> 00:02:35,420
+وبين قوسين متوسطتين بحط F of T، هذا رمز أو الرمز اللي 
+
+28
+00:02:35,420 --> 00:02:39,980
+عندنا ده، Capital F of S، مش F small، اللحظة اللي 
+
+29
+00:02:39,980 --> 00:02:44,040
+جوا هنا F small of T، دي F capital of S، يبقى أنا 
+
+30
+00:02:44,040 --> 00:02:51,220
+عندي رمزين لابلاس ترانسفورم لدالة F of T، لابلاس 
+
+31
+00:02:51,220 --> 00:02:58,660
+للـ F of T، أو F of S، هذا 
+
+32
+00:02:58,660 --> 00:03:07,380
+لابلاس الـ Transform is defined by، بقول لابلاس 
+
+33
+00:03:07,380 --> 00:03:14,130
+لدالة F of T، بين قوسين متوسطتين، عمليتها هي تكامل من 
+
+34
+00:03:14,130 --> 00:03:19,230
+Zero إلى Infinity، للـ E أس ST، للـ F of T DT، يعني 
+
+35
+00:03:19,230 --> 00:03:22,430
+إيش؟ يعني الدالة اللي بدي أوجد لها Laplace 
+
+36
+00:03:22,430 --> 00:03:26,110
+Transform، بآخذها بضربها في الـ Exponential Function 
+
+37
+00:03:26,110 --> 00:03:32,490
+E أس ST، وبكامل حاصل ضرب الدالتين من وين لوين؟
+
+38
+00:03:32,940 --> 00:03:38,720
+من صفر إلى Infinity، الآن هذا تكامل محدود، تمام؟ يبقى 
+
+39
+00:03:38,720 --> 00:03:43,440
+لما أكامل الدالة هتطلع عندي دالة بدلالة الـ S، ومن هنا 
+
+40
+00:03:43,440 --> 00:03:49,240
+قلنا Capital F of S، تمام؟ يعني بعد ما أقوم بإجراء 
+
+41
+00:03:49,240 --> 00:03:53,660
+عملية التكامل هتبقى الدالة عندي بدالة S، لأن أنا 
+
+42
+00:03:53,660 --> 00:03:59,260
+عوضت بحدود التكامل بدل T، إذا S هتبقى هي ظهرت في 
+
+43
+00:03:59,260 --> 00:04:00,660
+المثل، ومن هنا بقول 
+
+44
+00:04:05,460 --> 00:04:12,660
+لو جيت واطلعت في هذا التكامل بلاَحظ أن أحد حدود 
+
+45
+00:04:12,660 --> 00:04:17,660
+التكامل Infinity، وإحنا في Calculus بيقولوا، بقولوا عن 
+
+46
+00:04:17,660 --> 00:04:23,140
+التكامل Improper integral، إذا كان أحد حدود التكامل 
+
+47
+00:04:23,370 --> 00:04:29,650
+أو كلاهما Infinity، أو الدالة مش معرفة عند نقطة 
+
+48
+00:04:29,650 --> 00:04:35,190
+وهذه النقطة موجودة داخل فترة التكامل المحدود، 
+
+49
+00:04:35,190 --> 00:04:39,770
+مظبوط؟ نقطة ثانية خلّينا منها، يبقى بدنا نيجي عند 
+
+50
+00:04:39,770 --> 00:04:43,630
+النقطة الأولى، لو كان أحد حدود التكامل أو كلاهما 
+
+51
+00:04:43,630 --> 00:04:49,150
+Infinity، وكمان كلاهما بدنا نشيلها، لو كان أحد حدود 
+
+52
+00:04:49,150 --> 00:04:54,380
+التكامل هو Infinity، يبقى تكامل من وين؟ من Zero إلى 
+
+53
+00:04:54,380 --> 00:04:59,740
+Infinity، يبقى هذا Improper integral فقط بسبب وجود 
+
+54
+00:04:59,740 --> 00:05:04,440
+من الـ Infinity اللي عندنا، لو رجعنا بالذاكرة إلى 
+
+55
+00:05:04,440 --> 00:05:07,900
+الوراء إلى Calculus ب، الـ Improper integral
+
+56
+00:05:07,900 --> 00:05:14,540
+بنحسبه as a limit، فبروح بقول التكامل هذا هو Limit 
+
+57
+00:05:14,540 --> 00:05:20,270
+بشيل الـ Infinity وبحط بدالها Real number A، وبخلي 
+
+58
+00:05:20,270 --> 00:05:23,430
+الـ A آخذ الـ Limit لما الـ A بدأت تروح لـ Infinity
+
+59
+00:05:23,430 --> 00:05:28,470
+يعني أنا بروح بكامل التكامل هذا عادي جدًا بأي طريقة 
+
+60
+00:05:28,470 --> 00:05:32,690
+من طرق التكامل التي سبقت دراستها، بعوّض بحدود 
+
+61
+00:05:32,690 --> 00:05:37,070
+التكامل، وبعد ما عوّضت بآخذ الـ Limit لما A بدأت تروح 
+
+62
+00:05:37,070 --> 00:05:42,050
+لوين؟ للما لا نهاية، لما نأخذ هذه الـ Limit، احتمال 
+
+63
+00:05:42,050 --> 00:05:47,240
+تطلع قيمة عددية، واحتمال تطلع Infinity أو سالب 
+
+64
+00:05:47,240 --> 00:05:52,640
+Infinity، مظبوط؟ إذا طلعت قيمة عددية بقول التكامل 
+
+65
+00:05:52,640 --> 00:05:57,000
+Converge، وإذا ما طلعتش قيمة عددية يطلع Infinity 
+
+66
+00:05:57,000 --> 00:06:01,000
+ولا سالب Infinity بقول التكامل ماله Diverge، هذه 
+
+67
+00:06:01,000 --> 00:06:05,920
+معلوماتنا من Calculus B، التكامل اللي عندنا هو الـ 
+
+68
+00:06:05,920 --> 00:06:09,100
+Improper Integral بنحسبه في الطريقة اللي عندنا، هذا 
+
+69
+00:06:09,100 --> 00:06:13,240
+التكامل هو الـ Converge إذا لم يكن هناك مقاومة
+
+70
+00:06:13,240 --> 00:06:18,420
+وإذا لم يكن هناك مقاومة بقول عنه الـ Diverge، يبقى 
+
+71
+00:06:18,420 --> 00:06:21,100
+هذا الـ Diverge إذا لم يكن هناك مقاومة 
+
+72
+00:06:25,460 --> 00:06:31,520
+يبقى اللي فوق هذا تعريف من Laplace transform، لو 
+
+73
+00:06:31,520 --> 00:06:35,060
+قال لك سواء اتي لـ Laplace transform لدالة، بروح 
+
+74
+00:06:35,060 --> 00:06:40,020
+بضرب الدالة دي في E أس ناقص ST، وبكامل من Zero إلى 
+
+75
+00:06:40,020 --> 00:06:43,780
+Infinity، وبعدين بشغل شغل الـ Improper integral 
+
+76
+00:06:43,780 --> 00:06:48,940
+يعني كأنه، المحاضرة تبعنا هذه هي محاضرة Improper 
+
+77
+00:06:48,940 --> 00:06:54,220
+integrals، يعني كأن إحنا بدنا نعود الـ Improper 
+
+78
+00:06:54,220 --> 00:06:57,800
+integral اللي في Chapter 8، اللي هو آخر Section من 
+
+79
+00:06:57,800 --> 00:07:02,860
+Chapter 8 من Calculus B، طيب في تعريف جديد هذا 
+
+80
+00:07:02,860 --> 00:07:07,900
+ما كناش بنعرفه في Calculus B، Function F is said to 
+
+81
+00:07:07,900 --> 00:07:14,020
+be piecewise continuous، إيش معناه Piece؟ قطعة، يبقى 
+
+82
+00:07:14,020 --> 00:07:19,160
+لما أقول Piecewise continuous، كأنها مقطعة إلى 
+
+83
+00:07:19,160 --> 00:07:24,240
+أجزاء، على كل جزء، الدالة بتبقى دالة متصلة، يبقى 
+
+84
+00:07:24,240 --> 00:07:26,500
+هي المقصود بالـ Piecewise continuous، أنا عندي 
+
+85
+00:07:26,500 --> 00:07:31,300
+فترة، الفترة مقسمة إلى فترتين، إلى ثلاث، إلى أربع، 
+
+86
+00:07:31,300 --> 00:07:35,660
+إلى خمسة، إلى عشرة، إلى أيًّا من الفترات، على كل 
+
+87
+00:07:35,660 --> 00:07:40,660
+فترة من هذه الفترات، الدالة بتبقى معاها Continuous 
+
+88
+00:07:40,660 --> 00:07:44,140
+ما عدا عند النقاط اللي عشان اللي عندها 
+
+89
+00:07:44,140 --> 00:07:50,060
+Discontinuity دي، بجهة دي، بقول كأنها متصلة جزئيًا، ده 
+
+90
+00:07:50,060 --> 00:07:56,640
+لا مقطعة، على كل قطعة بتلاقيها دي لامتصلة، إذا كانت 
+
+91
+00:07:56,640 --> 00:08:00,120
+متصلة 
+
+92
+00:08:00,120 --> 00:08:06,820
+جزئيًا أو على قطع on an interval، على الفترة T من 
+
+93
+00:08:06,820 --> 00:08:13,040
+Alpha إلى Beta، if it is continuous، إذا كانت متصلة 
+
+94
+00:08:13,040 --> 00:08:16,560
+there، هناك يعني على الفترة من Alpha إلى Beta
+
+95
+00:08:16,560 --> 00:08:22,730
+except ما عدا for a finite number لرقم محدود of 
+
+96
+00:08:22,730 --> 00:08:28,130
+Jump discontinuities، يبقى بيكون عندنا عدم اتصال 
+
+97
+00:08:28,130 --> 00:08:34,250
+بقفزة، لأن أنواع الـ Discontinuity وممكن نقول في 
+
+98
+00:08:34,250 --> 00:08:39,670
+Calculus أن الـ Discontinuity ممكن نعمله Removable
+
+99
+00:08:39,670 --> 00:08:46,070
+إزالة، تمام؟ يعني لو كان عند نقطة ما في 
+
+100
+00:08:46,070 --> 00:08:52,480
+Discontinuity مش Jump، مش Jump لا يمكن إزالته، بس لو 
+
+101
+00:08:52,480 --> 00:08:57,020
+كان تجويف عند نقطة بروح بعرف الـ Function بطريقة 
+
+102
+00:08:57,020 --> 00:09:01,180
+جديدة وبآخذ الـ Limit عندما X تروح لهذه النقطة و
+
+103
+00:09:01,180 --> 00:09:05,560
+بعرف الدالة كـ Piecewise function، دالة مكونة من 
+
+104
+00:09:05,560 --> 00:09:09,040
+جزئين، وبالتالي بيخلي الـ Discontinuity بيخلي قيمة 
+
+105
+00:09:09,040 --> 00:09:12,040
+الدالة عند هذه النقطة تساوي الـ Limit، وبالتالي 
+
+106
+00:09:12,040 --> 00:09:15,700
+استطعت إزالة الـ Discontinuity، لكن الـ Discontinuity 
+
+107
+00:09:15,700 --> 00:09:19,700
+اللي أنا معلوم، Jump discontinuity، في كمّة 
+
+108
+00:09:19,700 --> 00:09:24,620
+Discontinuity ثالثة اللي هو Infinite discontinuity
+
+109
+00:09:24,620 --> 00:09:27,460
+يعني الـ Discontinuity اللي بيحصل عند اللي هو 
+
+110
+00:09:27,460 --> 00:09:31,220
+المالها نهاية، يبقى هذا اللي لا يمكن إزالته، والـ 
+
+111
+00:09:31,220 --> 00:09:34,520
+Jump discontinuity اللي لا يمكن إزالته، والنوع 
+
+112
+00:09:34,520 --> 00:09:38,040
+الثالث هو اللي بنزيله، ما لهوش علاقة فيه، إحنا بس 
+
+113
+00:09:38,040 --> 00:09:42,360
+بدنا اللي في النص اللي هو Jump discontinuity، يبقى 
+
+114
+00:09:42,360 --> 00:09:46,840
+في عندنا Jump discontinuity عند عدد محدود، نوضح هذا 
+
+115
+00:09:46,840 --> 00:09:50,840
+الكلام من خلال الرسم اللي قدامنا، بقول الدالة اللي 
+
+116
+00:09:50,840 --> 00:09:59,800
+عندنا هذه اللي هي الـ، الـ F is piecewise
+
+117
+00:10:00,410 --> 00:10:05,650
+الشكل اللي عندنا هو Discontinuous on الفترة من 
+
+118
+00:10:05,650 --> 00:10:11,330
+Alpha لغاية Beta بالشكل اللي عندنا هنا، يبقى عند الـ 
+
+119
+00:10:11,330 --> 00:10:15,330
+Alpha في اتصال من جهة اليمين، و Beta في اتصال من 
+
+120
+00:10:15,330 --> 00:10:19,650
+جهة الشمال، عند T1 و T2 في Discontinuity، و
+
+121
+00:10:19,650 --> 00:10:24,110
+Discontinuity هذا Jump، قفزت من النقطة هذه إلى 
+
+122
+00:10:24,110 --> 00:10:28,690
+النقطة هذه، من هنا قفزت من هنا لهنا، من هنا قفزت 
+
+123
+00:10:28,690 --> 00:10:32,630
+لهنا، بعد هيك صارت اللي اللي هو الـ Continuity هذا، 
+
+124
+00:10:32,630 --> 00:10:38,970
+يبقى على الخط المائل هذا Continuous، على القوس هذا 
+
+125
+00:10:38,970 --> 00:10:43,750
+Continuous، على القوس هذا Continuous، لكن عند T1 و 
+
+126
+00:10:43,750 --> 00:10:48,870
+T2 في عندي Jump discontinuity، يبقى هذه بسميها 
+
+127
+00:10:48,870 --> 00:10:55,150
+Piecewise function، طيب الآن بنجي للنقطة الثانية 
+
+128
+00:10:55,150 --> 00:11:02,750
+وهي متى يمكن نعمل Transform، لدى اللي تمّ شروط 
+
+129
+00:11:02,750 --> 00:11:07,210
+اللازم تتحقق في الـ Function، طبعًا إحنا لن نبحث هذه 
+
+130
+00:11:07,210 --> 00:11:11,950
+الشروط في المسائل، لأن كل المسائل اللي معطية عندنا 
+
+131
+00:11:11,950 --> 00:11:15,500
+في الكتاب فنطبق عليه هذه الشروط وبالتالي، بروح ما 
+
+132
+00:11:15,500 --> 00:11:20,300
+علينا إلا نحسب لابلاس الـ Transform مباشرة، بقول 
+
+133
+00:11:20,300 --> 00:11:25,040
+افترض أن الـ F، شرطين، F بتساوي Continuous يعني 
+
+134
+00:11:25,040 --> 00:11:29,060
+بالشكل اللي عندنا هذا، تمام؟ يبقى وين؟ on the 
+
+135
+00:11:29,060 --> 00:11:33,220
+Interval من Zero لـ A، for any positive number A
+
+136
+00:11:33,220 --> 00:11:39,100
+يعني أخذنا من عند الـ Zero لأي رقم بدك إيّاه موجبه،
+
+137
+00:11:39,100 --> 00:11:44,510
+عند أي رقم جيت الدالة مقطعة إلى جزئين، لثلاث قطع، 
+
+138
+00:11:44,510 --> 00:11:48,210
+لأربع قطع، لعشر قطع، جد ما يكون، يكون Piecewise
+
+139
+00:11:48,210 --> 00:11:53,530
+Continuous، النقطة الثانية، أخدت Absolute value لمين؟ 
+
+140
+00:11:53,530 --> 00:12:01,750
+للـ F of T، ووجدت أقل من أو يساوي K في E أس T، لما أقول 
+
+141
+00:12:01,750 --> 00:12:06,070
+أخذت Absolute value لـ F of T، يعني عمرها ما هتطلع 
+
+142
+00:12:06,070 --> 00:12:11,270
+سلبية، صحيح ولا لا؟ يبقى الرقم اللي على اليمين هذا 
+
+143
+00:12:11,270 --> 00:12:16,630
+ليس يمكن أن يكون سالب، لأن هذه أقل منه، طبعًا أعرف أن 
+
+144
+00:12:16,630 --> 00:12:21,990
+الـ Exponential دائمًا وأبدًا موجب، إذن الـ K دائمًا و 
+
+145
+00:12:21,990 --> 00:12:26,270
+أبدًا إيش بدّه يكون؟ موجب، حتى يكون الكلام صحيح، حتى 
+
+146
+00:12:26,270 --> 00:12:31,450
+الـ Absolute هذا يكون أقل من أو يساوي من هذا الرقم 
+
+147
+00:12:31,450 --> 00:12:36,610
+where T أكبر من أو يساوي M، يعني أنا ممكن آخذ T من 
+
+148
+00:12:36,610 --> 00:12:40,630
+عند حد معين، أخذت الـ T من هنا، من وين؟ من عند الـ 
+
+149
+00:12:40,630 --> 00:12:45,270
+Alpha، يبقى أنا عندي T أكبر من Alpha، يبقى Alpha رقم 
+
+150
+00:12:45,270 --> 00:12:49,270
+موجب، أخذته من عند النقطة هذه، يبقى هذا رقم موجب
+
+151
+00:12:49,270 --> 00:12:53,390
+يبقى M بدأت، تبدأ ترسم من عند النقطة هذه ونمشي وين؟ 
+
+152
+00:12:53,390 --> 00:12:58,710
+على اليمين، يبقى where T أكبر من أو يساوي M، الآن K
+
+153
+00:12:58,710 --> 00:13:03,990
+والـ A والـ M، الـ K والـ A والـ M، اللي T أكبر منها كلهم 
+
+154
+00:13:03,990 --> 00:13:08,690
+Real constants، زيادة على ذلك الـ K والـ M are 
+
+155
+00:13:08,690 --> 00:13:13,290
+necessarily positive، وهذا شرط، له قلت لك هذه 
+
+156
+00:13:13,290 --> 00:13:17,530
+Positive دائمًا وأبدًا، إذا هذه يجب أن تكون Positive
+
+157
+00:13:17,530 --> 00:13:24,130
+لأن هذه Absolute value ما يطلعش إلا قيمة موجبة، طيب إذا 
+
+158
+00:13:24,130 --> 00:13:28,710
+حدث ذلك، تحقق هذان الشرطان، يبقى دي الـ Aplastic 
+
+159
+00:13:28,710 --> 00:13:33,250
+Transform بيكون اللي هو التعريف اللي إحنا حطناه 
+
+160
+00:13:33,250 --> 00:13:38,270
+هنا للـ F of T، هو Capital F of S، يبقى هو E 
+
+161
+00:13:38,270 --> 00:13:42,550
+من التكامل من Zero إلى Infinity للـ E أس ناقص ST
+
+162
+00:13:42,550 --> 00:13:48,490
+للـ F of T DT، بيكون هذا Exist for S greater than A 
+
+163
+00:13:48,490 --> 00:13:52,150
+يبقى هذا الضمان اللي بتخلي 
+
+164
+00:13:56,060 --> 00:14:00,620
+مطلوب في شغلنا نبحث هذه الضمانة، لا، بيقول لك هتيجي بس 
+
+165
+00:14:00,620 --> 00:14:05,160
+Laplace transform لدالة الفلانية، في كل مثال كتابه 
+
+166
+00:14:05,160 --> 00:14:11,060
+بضل عليكي بس تحسب مين؟ الـ Improper integrals، طبعًا 
+
+167
+00:14:11,060 --> 00:14:15,370
+ضايلة خاصية عندي لـ Laplace transform، حشير إليها بعد 
+
+168
+00:14:15,370 --> 00:14:21,830
+قليل بعد أن نأخذ بعض الأمثلة، إذا بدنا نأخذ بعض 
+
+169
+00:14:21,830 --> 00:14:35,330
+الأمثلة لكيفية حساب لابلاس ترانسفورم لدالة ما، حدّ 
+
+170
+00:14:35,330 --> 00:14:40,210
+في كوبونات بتقدر تجيب لي Piecewise continuous يعني 
+
+171
+00:14:40,210 --> 00:14:43,110
+Function، تبقى Piecewise 
+
+172
+00:14:51,960 --> 00:14:59,58
+
+201
+00:18:41,800 --> 00:18:47,440
+itself مقسوما على تفاضل الأس لما الأس يكون من
+
+202
+00:18:47,440 --> 00:18:52,800
+الدرجة الأولى واضح أنه T أس واحد يبقى الأس عندي
+
+203
+00:18:52,800 --> 00:18:57,820
+من الدرجة الأولى يبقى النتيجة الـ exponential كما
+
+204
+00:18:57,820 --> 00:19:04,800
+هي في T مقسوما على نقص الـ S نقص الـ A اللي هو
+
+205
+00:19:04,800 --> 00:19:11,780
+المعامل تبع من تبع الـ T يبقى هاي كاملتها تماما وهذا
+
+206
+00:19:11,780 --> 00:19:17,760
+من وين لوين؟ من عند الـ zero لغاية من الـ a الآن
+
+207
+00:19:17,760 --> 00:19:23,760
+بتعوض بحدود التكامل ومن ثم تروح ناخد الـ limit يبقى
+
+208
+00:19:23,760 --> 00:19:28,000
+هذا الكلام بده يسوي الـ limit لما الـ a tends to
+
+209
+00:19:28,000 --> 00:19:39,830
+infinity لمن؟ للـ E أس ناقص S ناقص A في A على ناقص S
+
+210
+00:19:39,830 --> 00:19:41,770
+ناقص الـ A
+
+211
+00:20:07,350 --> 00:20:15,170
+طلعيني هنا لما الـ a بدها تروح لـ infinity بنزلها 
+
+212
+00:20:15,170 --> 00:20:19,730
+تحت بصير موجّه بـ infinity يعني بصير واحد على
+
+213
+00:20:19,730 --> 00:20:26,370
+infinity يبقى هذا الـ term كله بروح بالسّفارة يبقى
+
+214
+00:20:26,370 --> 00:20:32,670
+هذا بده يصير zero ناقص مع ناقص بالصير زائد واحد على
+
+215
+00:20:32,670 --> 00:20:40,230
+S ناقص الـ A يبقى النتيجة النهائية واحد على S ناقص
+
+216
+00:20:40,230 --> 00:20:47,880
+الـ A والـ S greater than A ليش الـ S greater than A؟
+
+217
+00:20:47,880 --> 00:20:54,720
+لأن لو S كانت أقل من A، لأ صار ناقص فناقص بزائد
+
+218
+00:20:54,720 --> 00:20:59,880
+وظلت هذه في البسط، وبالتالي ما كانت نتيجة زي هيك،
+
+219
+00:20:59,880 --> 00:21:03,600
+يبقى اللي خلّى النتيجة زي هيك أن S دائما وأبدا
+
+220
+00:21:03,600 --> 00:21:10,020
+greater than يبقى من الآن فصاعدا لـ Laplace transform
+
+221
+00:21:10,020 --> 00:21:16,060
+للـ E أس A T هو واحد على S ناقص الـ A واللحظة يا
+
+222
+00:21:16,060 --> 00:21:20,960
+بناتي أن النتيجة طلعت function في main في S كما 
+
+223
+00:21:20,960 --> 00:21:26,120
+زعمنا قبل قليل أن هذه بتطلع function في main في S
+
+224
+00:21:26,120 --> 00:21:32,230
+وبضلّش عندي T نهائي بالمرة بعد إجراء عملية التكامل
+
+225
+00:21:32,230 --> 00:21:38,070
+يصبح النتيجة 1 على S نقص اللي قد نقل عليها لو قلت
+
+226
+00:21:38,070 --> 00:21:44,050
+جدّيش لـ Laplace transform لـ E أس ثلاثة T تقوليني 1 على
+
+227
+00:21:44,050 --> 00:21:45,090
+S نقص 3
+
+228
+00:21:50,040 --> 00:21:57,760
+بنص T بيصير 1 على S ناقص نص وهكذا يبقى خلاص ما عليه
+
+229
+00:21:57,760 --> 00:22:02,800
+إلا أشيل A وأحط الرقم اللي عندنا هذا بناء عليه
+
+230
+00:22:02,800 --> 00:22:08,300
+حروح أجيب اللي هو B وC يبقى هذا اللي هو A بده يجي
+
+231
+00:22:08,300 --> 00:22:14,840
+لـ B بده لـ Laplace transform لـ مين؟ هلّأ الواحد صحيح ولا
+
+232
+00:22:14,840 --> 00:22:21,260
+لا طيب هل ممكن احصل على الواحد من الدالة هذه لو
+
+233
+00:22:21,260 --> 00:22:27,860
+كانت الـ a بـ zero يبقى بصير e أس zero له بواحد يبقى
+
+234
+00:22:27,860 --> 00:22:36,460
+باجي بقوله if الـ a تساوي zero then e أس at بده
+
+235
+00:22:36,460 --> 00:22:44,260
+يساوي e أس zero اللي هو واحد يبقى لـ Laplace transform
+
+236
+00:22:44,260 --> 00:22:52,240
+يبقى لـ Laplace transform للواحد هو لـ Laplace transform لـ
+
+237
+00:22:52,240 --> 00:23:00,120
+E أس زيرو في T يبقى مكان الـ E كده شجّعني؟ Zero يبقى
+
+238
+00:23:00,120 --> 00:23:08,410
+هنا واحد على S ناقص الـ Zero يعني واحد على S والـ S
+
+239
+00:23:08,410 --> 00:23:14,190
+greater than Zero يبقى من الآن فصاعدا يا بنات بدك
+
+240
+00:23:14,190 --> 00:23:19,230
+تعرفيه Automatic أن لابلاس ترانسفورم للواحد الصحيح
+
+241
+00:23:19,230 --> 00:23:25,190
+يساوي كده بعد قليل هقولي قدّيش لـ Laplace للـ إتنين، قدّيش لـ
+
+242
+00:23:25,190 --> 00:23:29,510
+Laplace لـ تلاتة، قدّيش لـ Laplace لـ نص، قدّيش لـ Laplace لـ مية وهكذا تمام؟ بس خليها المعلومة هذه عندك وسنرجع لها
+
+243
+00:23:29,510 --> 00:23:33,810
+كثيرا خلال شغلنا طيب نروح الآن لنمرّسي
+
+244
+00:23:33,810 --> 00:23:39,090
+كثيرا خلال شغلنا طيب نروح الأن لنمرسى 
+
+245
+00:23:53,800 --> 00:24:02,100
+نمرّسي بدي لابلاس ترانسفورم للإي والسالب اتي ايش
+
+246
+00:24:02,100 --> 00:24:07,880
+أفرجت عن السؤال اللي عندي بس الـ a صارت بالسالب
+
+247
+00:24:07,880 --> 00:24:13,380
+يبقى أنا بدي اجي على النتيجة دي واستبدل كل a بسالب
+
+248
+00:24:13,380 --> 00:24:21,280
+a بكون وصلت للنتيجة يبقى هذه باجي بقوله from part
+
+249
+00:24:21,280 --> 00:24:31,240
+a نحن لدينا لابلاس ترانسفورم للـ E أس ناقص AT يساوي
+
+250
+00:24:31,240 --> 00:24:39,740
+واحد على S ناقص ناقص A يبقى 
+
+251
+00:24:39,740 --> 00:24:47,580
+نتيجة واحد على S زائد A أنا بقولش أكبر من إيه ولا
+
+252
+00:24:47,580 --> 00:24:51,900
+أصغر من إيه، مدام جامع يبقى معنا مشكلة في هذه
+
+253
+00:24:51,900 --> 00:24:57,940
+الحالة، تمام؟ طبعا هذا من أبسط أنواع الأمثلة إلا
+
+254
+00:24:57,940 --> 00:25:02,840
+لابد اللي لف ولا درم مباشر، مفيش فيه تعب، انتجلي
+
+255
+00:25:02,840 --> 00:25:09,760
+شوية مثال اتنين بدنا 
+
+256
+00:25:09,760 --> 00:25:23,420
+نعيّن له لابلاس ترانسفورم لدالة ساين اي تي بس
+
+257
+00:25:23,420 --> 00:25:28,460
+هذا مش كتير يبقى بده احط التعريف يبقى باجي بقوله
+
+258
+00:25:28,460 --> 00:25:33,620
+solution بدلا
+
+259
+00:25:33,620 --> 00:25:40,160
+لابلاس لساين اي تي يبقى sin at هي الـ f of t الـ
+
+260
+00:25:40,160 --> 00:25:44,860
+function اللي عندنا يبقى طبّق لي التعريف integration
+
+261
+00:25:44,860 --> 00:25:55,000
+من zero لـ infinity للـ E أس ناقص ST لـ sin at dt
+
+262
+00:25:57,900 --> 00:26:02,200
+هذا الـ Improper Integral يبقى بيطبّق خاصية الـ
+
+263
+00:26:02,200 --> 00:26:06,880
+Improper Integral يبقى الـ Limit تكامل من Zero لـ
+
+264
+00:26:06,880 --> 00:26:13,420
+A لما الـ A بده تروح لـ Infinity للـ E أس ناقص ST
+
+265
+00:26:13,420 --> 00:26:23,860
+لـ Sin ATDT إذا بروح أكمل هذه المسألة كيف بنكمل
+
+266
+00:26:23,860 --> 00:26:29,720
+هذه يا بنات؟ بتتجزّأ integration by parts يبقى بداخل U
+
+267
+00:26:29,720 --> 00:26:35,380
+ده اللي هو والباقي كله بيكون DV طبعا هذه زي ما
+
+268
+00:26:35,380 --> 00:26:39,700
+بيقولوا ضرب العميان صيب اش ما تاخد صح إن اخدت الـ U
+
+269
+00:26:39,700 --> 00:26:44,400
+الـ exponential والـ DV الـ sign ماشي إن اخدت الـ U
+
+270
+00:26:44,400 --> 00:26:47,970
+الـ sign والـ DV الـ exponential ماشي ليش؟ لأن
+
+271
+00:26:47,970 --> 00:26:52,850
+الاشتقاق أو التكامل لـ Sin هو Sin Cos Sin Cos والـ
+
+272
+00:26:52,850 --> 00:26:56,030
+Exponential تكامل الله تعالى بفضل كيف ما يكون الـ
+
+273
+00:26:56,030 --> 00:27:00,490
+Exponential كمية بيبقى يا بضرب في رقم يا بِجْسَمْ على 
+
+274
+00:27:00,490 --> 00:27:04,890
+رقم  يك بإيش ما تاخده صحيح يبقى أنا لو روحت في الأمش
+
+275
+00:27:04,890 --> 00:27:12,030
+قلت خد الـ U تساوي E أس ناقص ST وخد الـ DV اللي هو
+
+276
+00:27:12,030 --> 00:27:14,870
+Sin ATDT
+
+277
+00:27:18,590 --> 00:27:25,470
+كويس يبقى الـ DU بتبدأ تساوي الـ E ما ننشل زي ما هو
+
+278
+00:27:25,470 --> 00:27:33,130
+مضروب في تفاضل الـ S يبقى ناقص S في E أس ناقص ST في ال
+
+279
+00:27:33,130 --> 00:27:39,550
+DT يبقى الـ exponential زي ما هي ضرب مشتقة الـ S
+
+280
+00:27:39,550 --> 00:27:45,390
+بالنسبة إلى T اللي هو بناقص S فمين في DT هذه بدي
+
+281
+00:27:45,390 --> 00:27:52,950
+أكاملها تكامل الـ sin بقدّيش؟ سالب cos يبقى سالب V
+
+282
+00:27:52,950 --> 00:28:01,670
+تساوي سالب cos AT على مين؟ على A والزائد كونصت 
+
+283
+00:28:01,670 --> 00:28:05,250
+أنت ما تكتبش وبتاخديه بـ zero دائما وأبدا لسهولة
+
+284
+00:28:05,250 --> 00:28:10,130
+كما درسنا في Calculus B طيب الآن هذا الكلام بده
+
+285
+00:28:10,130 --> 00:28:18,280
+يساوي Limit لما الـ A tends to infinity بدا اجي اخد U
+
+286
+00:28:18,280 --> 00:28:26,820
+في V طاليل هنا هي ناقص U في V يبقى ناقص واحد على A
+
+287
+00:28:26,820 --> 00:28:39,040
+لـ E أس ناقص ST في cos AT تمام هذا U في V ناقص 
+
+288
+00:28:39,540 --> 00:28:51,520
+تكامل من Zero إلى V داليو V ناقص Cos A T على A في 
+
+289
+00:28:51,520 --> 00:29:01,960
+داليو ناقص S E أس ناقص S T في DT تمام؟ بدي أعيد
+
+290
+00:29:01,960 --> 00:29:03,340
+ترتيب المسألة 
+
+291
+00:29:05,780 --> 00:29:10,300
+هذا لو السّلب بقدر أنقله تحت وأخليه موجب يبقى 
+
+292
+00:29:10,300 --> 00:29:16,420
+high limit لما الـ a tends to infinity لمن؟ لـ ناقص
+
+293
+00:29:16,420 --> 00:29:24,440
+cos at على a في الـ E أس S T والحكي هذا من ولا وين؟ من zero لغاية a يبقى من zero لغاية a بنجي
+
+294
+00:29:24,440 --> 00:29:33,390
+لبعدها عندك سالب وسالب وسالب تلاتة سالب بسالب
+
+295
+00:29:33,390 --> 00:29:39,470
+واحد يبقى هاي السالب عندك S مقدار ثابت وإيه مقدار
+
+296
+00:29:39,470 --> 00:29:45,110
+ثابت برة التكامل يبقى ناقص S على A تكامل من zero
+
+297
+00:29:45,110 --> 00:29:52,830
+إلى A للـ E أس ناقص ST لـ cos ATDT
+
+298
+00:29:52,830 --> 00:30:01,670
+طيب نجي للمقدار اللي عندنا هذا بدي أشيل كل T وأحط
+
+299
+00:30:05,400 --> 00:30:12,760
+مكانها A يبقى هذا الكلام بده يساوي Limit لما الـ A 
+
+300
+00:30:12,760 --> 00:30:20,140
+tends to infinity لـ ناقص cos AA على A E أس SA
+
+301
+00:30:20,140 --> 00:30:30,480
+ناقص مع ناقص بيصير زائد بدي أشيل الـ T وأضع مكانها 
+
+302
+00:30:31,630 --> 00:30:37,170
+واحد بدي أشيل الـ T وأضع مكانها
+
+303
+00:30:37,170 --> 00:30:41,990
+واحد يبقى إيش بيصير هنا بدي أشيل الـ T وأضع مكانها
+
+304
+00:30:41,990 --> 00:30:45,990
+zero بيصير cos صفر اللي بيبقى dash بواحد
+
+305
+00:30:45,990 --> 00:30:55,160
+يبقى واحد E أس Zero واحد في A بـ A يبقى زائد واحد
+
+306
+00:30:55,160 --> 00:31:03,780
+على A الـ Limit للمقدار هذا كله ووصلنا ناقص S على A 
+
+307
+00:31:03,780 --> 00:31:10,280
+في Limit لما الـ A tends to infinity لتكامل من Zero
+
+308
+00:31:10,280 --> 00:31:17,740
+إلى A للـ E أس ناقص ST لـ cos ATDT
+
+309
+00:31:36,770 --> 00:31:41,990
+طيب تعال نشوف المقدار الأول إيه بده تروح لوين؟
+
+310
+00:31:41,990 --> 00:31:49,390
+للمالْنهاية بسالب والبسط هذا محصور من وين لوين البسط
+
+311
+00:31:49,390 --> 00:31:55,630
+cos محصور من وين لوين؟ سالب واحد يعني رقم محصور ما
+
+312
+00:31:55,630 --> 00:32:01,010
+بين الاتنين مظبوط ولا لا المقام هذا لما إيه بده
+
+313
+00:32:01,010 --> 00:32:02,850
+تروح للمالْنهاية قدّيش؟ بالسيارة
+
+314
+00:32:18,650 --> 00:32:23,350
+ممكن اجيبه بطريقة تانية أروح أقول اه الـ cos
+
+315
+00:32:23,350 --> 00:32:29,120
+محصور بين سالب واحد وواحد أضرب الطرفين في 1 على a
+
+316
+00:32:29,120 --> 00:32:35,860
+في e أس s على a يبقى 1 على a e أس s في a يبقى 
+
+317
+00:32:35,860 --> 00:32:41,000
+بيصير 1 على ما لا نهاية بـ zero أقل من أو يساوي الـ
+
+318
+00:32:41,000 --> 00:32:46,550
+Limit الـ cos على المقدرة ده أقل من أو يساوي 1 على
+
+319
+00:32:46,550 --> 00:32:50,650
+ما لا نهاية بـ 0 بساندوش تيرام يبقى اللي في النص
+
+320
+00:32:50,650 --> 00:32:56,230
+بقدّيش؟ بـ 0 إذا الـ Limit هذا كله بـ 0 مع السلامة
+
+321
+00:32:56,230 --> 00:33:02,130
+غير مأسوف عليه بظلمينا عندنا هنا 1 على إيه ناقص
+
+322
+00:33:02,130 --> 00:33:09,270
+المقدار هذا يبقى هذا بده يساوي لابلاس لـ sin AT
+
+323
+00:33:09,270 --> 00:33:19,400
+بده يساوي 1 على إيه ناقص أو لا مش ناقص ناقص S على F
+
+324
+00:33:19,400 --> 00:33:29,180
+E هذا نفس القصة زي اللي فوق يبقى بيدّروح اخذ له الـ U
+
+325
+00:33:29,180 --> 00:33:41,070
+تساوي E أس ناقص ST وبدي اخدي الـ DV Cos ATDT يبقى
+
+326
+00:33:41,070 --> 00:33:51,890
+بدنا الـ DU بناقص S E أس ناقص ST DT والـ V بـ sin A T 
+
+327
+00:33:51,890 --> 00:34:01,650
+على A تمام يبقى U في V يبقى همّاش خلاص ما كتبناش الـ
+
+328
+00:34:01,650 --> 00:34:06,610
+Limit بدنا نكتب الـ Limit قبل هذا يبقى هذا الـ Limit
+
+329
+00:34:07,390 --> 00:34:13,990
+لما a tends to infinity لمن؟ للنتيجة اللي عندنا U
+
+330
+00:34:13,990 --> 00:34:24,050
+في V يبقى E أس ناقص ST E أس ناقص ST sin AT كله على 
+
+331
+00:34:24,050 --> 00:34:31,900
+من؟ على A وبالموجب ناقص تكامل من zero لغاية الـ a
+
+332
+00:34:31,900 --> 00:34:38,540
+طبعا التكامل هذا من zero إلى a لمين؟ للـ VW الـ V
+
+333
+00:34:38,540 --> 00:34:49,340
+اللي هو sin AT على A اللي هو ناقص S في E أو ناقص
+
+334
+00:34:49,340 --> 00:34:55,360
+ST في DT يساوي
+
+335
+00:34:56,450 --> 00:35:05,610
+1 على a ناقص s على a وهذا الـ Limit لما a tends to
+
+336
+00:35:05,610 --> 00:35:10,370
+infinity وهي الـ ghost بدنا نعوّض بالقيمة اللي فوق
+
+337
+00:35:10,370 --> 00:35:19,750
+ناقص اللي تحت يبقى sin a a على a في e أس s a
+
+338
+00:35:19,750 --> 00:35:29,150
+أو انزلها تحت سرتّمين بالموجب ناقص zero في أي شغلة
+
+339
+00:35:29,150 --> 00:35:35,570
+اللي هو بـ zero اللي بعدها ناقص مع ناقص اللي هي
+
+340
+00:35:35,570 --> 00:35:44,990
+بزائد واحد عاللّٰه S على A في تكامل من Zero إلى 
+
+341
+00:35:44,990 --> 00:35:55,440
+A للـ E أس ناقص ST لـ sin ATDT وهيجفلنا الجوز يبقى
+
+342
+00:35:55,440 --> 00:36:01,880
+هذا الكلام بده يساوي مين؟ الـ F of S لابلاس لهذه
+
+343
+00:36:01,880 --> 00:36:11,920
+هديها رمز مين؟ F of S يساوي 1 على a ناقص S على
+
+344
+00:36:11,920 --> 00:36:15,560
+A طلعولي يا بنات الـ Limit هنا لما الـ A بده تروح لـ
+
+345
+00:36:15,560 --> 00:36:21,920
+infinity المقام بالـ infinity وهنا واحد عمل نهاية
+
+346
+00:36:21,920 --> 00:36:27,500
+يبقى هذا بروح كله بالزيرو يبقى سلم مع السّلمة يبقى 
+
+347
+00:36:27,500 --> 00:36:33,400
+أنا ناقص S على A ووصلنا الى S عليه بظل قدّيش S على A
+
+348
+00:36:33,400 --> 00:36:41,220
+لكل تربيع وهذه شعر ثمان الناقص ووصلنا الى الـ Limit
+
+349
+00:36:41,220 --> 00:36:48,160
+لما الـ A بده تروح لـ infinity لمين؟ لتكامل من 0 إلى A
+
+350
+00:36:48,160 --> 00:36:53,820
+للـ E أس ناقص ST لـ sin ATDT
+
+351
+00:36:56,340 --> 00:37:02,820
+طيب صار Capital F of S يساوي 1 على إيه ناقص
+
+352
+00:37:02,820 --> 00:37:09,060
+استربيع على إيه تربيع هذا بنات لو رجعته الى أصله
+
+353
+00:37:09,060 --> 00:37:14,220
+مش هو عبارة عن تكامل من zero لـ infinity للـ E OS
+
+354
+00:37:14,220 --> 00:37:22,130
+ناقص ST للـ sin ATDT صحيح ولا لأ؟ يعني صار Capital
+
+355
+00:37:22,130 --> 00:37:28,830
+F of S يساوي 1 على إيه ناقص S تربيع على إيه
+
+356
+00:37:28,830 --> 00:37:34,230
+تربيع وهذا F of S صحيح ولا لأ؟ طيب شو رايك بدي
+
+357
+00:37:34,230 --> 00:37:38,600
+أجيب هادي على الشجّة التانية؟ هذه من التكاملات
+
+358
+00:37:38,600 --> 00:37:42,940
+الدورية بنات لبعض مرتين بطلع رأس المسألة زكريين
+
+359
+00:37:42,940 --> 00:37:46,460
+integration by parts علّّين عليها كتير إذا هذه بدي
+
+360
+00:37:46,460 --> 00:37:49,800
+وديها على الشجّة تاني لو وديتها على الشجّة تاني بصير
+
+361
+00:37:49,800 --> 00:37:56,580
+واحد زائد S تربيع على A تربيع في Capital F of S 
+
+362
+00:37:56,580 --> 00:38:03,790
+بدّه يساوي مين؟ واحد على A أو بمعنى آخر هذي بقدر أقول
+
+363
+00:38:03,790 --> 00:38:12,630
+A تربيع زائد S تربيع على A تربيع كل هذا في Capital 
+
+364
+00:38:12,630 --> 00:38:18,820
+F of S بده يساوي كده إيه؟ واحد على A فأنا بدي أقف
+
+365
+00:38:18,820 --> 00:38:26,400
+فوق S اللي بدي
+
+401
+00:42:42,880 --> 00:42:49,560
+نقول هذا هو limit للتكامل
+
+402
+00:42:49,560 --> 00:42:55,140
+من zero إلى a لما a tends to infinity لـ T to the 
+
+403
+00:42:55,140 --> 00:43:03,570
+power n E<sup>−ST</sup> في DT بدي أعملها integration by
+
+404
+00:43:03,570 --> 00:43:08,590
+parts عادي بدون جدول وأشوف لوين بده توصلنا كيف
+
+405
+00:43:08,590 --> 00:43:13,190
+الخطوة واحدة وبعدين ممكن نستنتج الخطوة الثانية
+
+406
+00:43:13,190 --> 00:43:23,650
+يبقى بدي آخذ الـ U هي T to the power N وDV = E<sup>−ST</sup> DT
+
+407
+00:43:23,650 --> 00:43:33,970
+الآن بدنا DU يبقى N T<sup>N−1</sup> في الـ DT بدنا 
+
+408
+00:43:33,970 --> 00:43:41,690
+الـ V يساوي E<sup>−ST</sup> كما هي مقسومة على تفاضل
+
+409
+00:43:41,690 --> 00:43:49,350
+الأس لأن الأس من الدرجة الأولى يبقى هذه U وهذه V
+
+410
+00:43:49,350 --> 00:43:54,130
+اللي عندنا إذا النتيجة التكامل كتالي هذه الـ limit
+
+411
+00:43:54,540 --> 00:44:01,680
+لما a tends to infinity بنا نيجي لـ U في V يبقى T
+
+412
+00:44:01,680 --> 00:44:12,240
+to the power N E<sup>−ST</sup> على ناقص S والحكي هذا
+
+413
+00:44:12,240 --> 00:44:20,510
+من Zero لغاية الـ A ناقص تكامل من zero إلى a للـ V
+
+414
+00:44:20,510 --> 00:44:30,510
+دال U الـ V هي E<sup>−ST</sup> على ناقص S دال U لـ N T
+
+415
+00:44:30,510 --> 00:44:37,630
+أس N ناقص واحد DT وهذا الـ limit لمين؟ للمقدار هذا
+
+416
+00:44:37,630 --> 00:44:38,410
+كله
+
+417
+00:44:40,730 --> 00:44:47,570
+طيب يساوي limit لما الـ a tends to infinity بتعوض
+
+418
+00:44:47,570 --> 00:44:51,750
+بالقيمة اللي فوق ناقص القيمة اللي تحت يعني يا شباب
+
+419
+00:44:51,750 --> 00:45:00,250
+هذه T والله هذه بتصير A<sup>N</sup> وهذه خليني أنزلها تحت
+
+420
+00:45:00,250 --> 00:45:09,050
+ناقص S في E<sup>−SA</sup> ناقص
+
+421
+00:45:13,380 --> 00:45:19,940
+أي مقدار يبقى بزيرو على أي رقم يبقى بزيرو خلصنا
+
+422
+00:45:19,940 --> 00:45:26,980
+منها الآن بقي عندي الناقص مع ناقص بصير زائد عندك
+
+423
+00:45:26,980 --> 00:45:34,180
+N على S مقدار ثابت خليك برا بظل تكامل من Zero إلى 
+
+424
+00:45:34,180 --> 00:45:34,740
+A
+
+425
+00:45:44,120 --> 00:45:47,900
+آخر حاجة توصلنا لها هي limit لما الـ a tends to 
+
+426
+00:45:47,900 --> 00:45:53,880
+infinity للـ A to the power N E<sup>−SA</sup> بنجيب 
+
+427
+00:45:53,880 --> 00:45:59,880
+نزلها تحت بالشكل اللي أن هذا ناقص هنا Zero على 
+
+428
+00:45:59,880 --> 00:46:04,640
+المقدار بـ Zero N على S بإشارة سالب مع سالب بصير
+
+429
+00:46:04,640 --> 00:46:05,960
+موجب وبره التكامل
+
+430
+01:00:43,560 --> 01:00:51,060
+بعد مرتين بيخلص الـ bus مظبوط؟ بيصير واحد صحيح،
+
+431
+01:00:51,060 --> 01:00:57,420
+كويس؟ وهذا بيظل A<sup>2</sup> أس، جداش بتشتق كل مرة
+
+432
+01:00:57,420 --> 01:01:00,880
+بتضرب اتنين والـ exponential زي ما هي طب لما لاقيت
+
+433
+01:01:00,880 --> 01:01:06,220
+روح للمالا نهاية بيصير واحد على مالا نهاية بـ Zero
+
+434
+01:01:06,220 --> 01:01:09,700
+هذا عند التربيع وعند التكعيب وعند الأربعة و
+
+435
+01:01:09,700 --> 01:01:14,020
+القسمة والستة والـ N كله بيصير الـ limit هذا بـ
+
+436
+01:01:14,020 --> 01:01:22,750
+Zero هذا بيصير بـ Zero مرة واحدة كان في انكوا سؤال في
+
+437
+01:01:22,750 --> 01:01:29,910
+calculus B في الـ section اللي هو مين greater than
+
+438
+01:01:29,910 --> 01:01:33,410
+مين من الدوال اللي بنعمر مقارنة بين relative
+
+439
+01:01:33,410 --> 01:01:37,970
+rates of growth وكان انكوا في سؤال بيقول زي هيك
+
+440
+01:01:37,970 --> 01:01:43,870
+high limit لما الـ X بده تروح للـ infinity للـ X to 
+
+441
+01:01:43,870 --> 01:01:54,680
+the power N على E of X الحين اضغط على الرقم 
+
+442
+01:01:54,680 --> 01:01:58,180
+اللي بديكي ياه يبقى هذا لو جينا في خضرنه ايش بيصير
+
+443
+01:01:58,180 --> 01:02:03,520
+إن X<sup>N</sup> N−1 على U<sup>6</sup> N في N−1 في
+
+444
+01:02:03,520 --> 01:02:07,620
+X<sup>N−2</sup> على U<sup>6</sup> يبقى في الآخر ايش بيطلع
+
+445
+01:02:07,620 --> 01:02:12,840
+عندي N factorial لأن N في N−1 لأن N 
+
+446
+01:02:12,840 --> 01:02:19,540
+factorial على U<sup>6</sup> مظبوط يبقى هذه بعد عدة مرات بدي
+
+447
+01:02:19,540 --> 01:02:24,640
+يصير limit لما الـ X tends to infinity للـ N 
+
+448
+01:02:24,640 --> 01:02:31,840
+factorial على E<sup>6</sup> و N factorial هي ده رقم و E<sup>6</sup> و
+
+449
+01:02:31,840 --> 01:02:35,840
+الـ 6 لما الـ X بتروح للمالا نهاية بجديش المقام عدد
+
+450
+01:02:35,840 --> 01:02:41,080
+على مالا نهاية Zero يبقى النتيجة هذه تساوي Zero
+
+451
+01:02:41,080 --> 01:02:47,570
+تمام؟ يبقى بناء عليه هذه زيها بس بدل الـ A أجانبين
+
+452
+01:02:47,570 --> 01:02:52,630
+اللي هو الـ X يبقى هذه بـ Zero مع السلامة يبقى صارت
+
+453
+01:02:52,630 --> 01:02:59,770
+النتيجة تساوي N على S في limit لما الـ A tends to
+
+454
+01:02:59,770 --> 01:03:07,030
+infinity لمين؟ لتكامل من Zero إلى A ل T to the
+
+455
+01:03:07,030 --> 01:03:16,890
+power N−1 ل E<sup>−ST</sup> DT يعني ايش؟
+
+456
+01:03:16,890 --> 01:03:24,530
+يعني اللي هو N على S ثمين في تاكامل من Zero لـ
+
+457
+01:03:24,530 --> 01:03:30,090
+Infinity ل T to the power N−1 E<sup>−ST</sup>
+
+458
+01:03:30,090 --> 01:03:39,140
+T DTوالمسألة هذه صارت نفس المسألة اللي بدأنا
+
+459
+01:03:39,140 --> 01:03:46,420
+فيها اللهم إلا الأس تبع الـ T نقص جداش طيب تتوقعوا
+
+460
+01:03:46,420 --> 01:03:52,720
+لو روحت كاملت كمان مرة انسى اللي برا جداش تتوقعوا 
+
+461
+01:03:52,720 --> 01:04:01,140
+الجواب يكون؟ لما كانت N صارت N على S إذا الـ term
+
+462
+01:04:01,140 --> 01:04:08,160
+اللي بعدها بتكون N−1 على S في تكامل ل T أس
+
+463
+01:04:08,160 --> 01:04:12,860
+N−2 في الـ exponential صحيح ولا لا؟ يعني
+
+464
+01:04:12,860 --> 01:04:19,330
+هذه الخطوة اللي بعدها اختصارا بتصير N فإن نقص واحد 
+
+465
+01:04:19,330 --> 01:04:27,410
+على S في S فإن في تكامل من Zero إلى Infinity لـ T 
+
+466
+01:04:27,410 --> 01:04:36,170
+أس N−2 E<sup>−ST</sup> D T تمام؟ 
+
+467
+01:04:36,170 --> 01:04:42,930
+طب لو عملنا كمان خطوة بصير N في N−1 في N−
+
+468
+01:04:42,930 --> 01:04:48,010
+2 على S في S في S في تكامل من Zero ل Infinity
+
+469
+01:04:48,010 --> 01:04:53,230
+ل T أس N−3 
+
+470
+01:04:53,230 --> 01:05:00,130
+في مين في E<sup>−ST</sup> D T إذا لو ضلنا مستمرين على 
+
+471
+01:05:00,130 --> 01:05:03,150
+هالشغل هذه هنوصل لما يأتي
+
+472
+01:05:21,490 --> 01:05:25,690
+إذا لو ضلنا مستمرين على الشغل هذه هنوصل لـ Laplace
+
+473
+01:05:25,690 --> 01:05:31,690
+transform لـ T to the power N بده يساوي الـ N في N 
+
+474
+01:05:31,690 --> 01:05:38,730
+ناقص واحد في N ناقص اتنين لغاية تلاتة اتنين في 
+
+475
+01:05:38,730 --> 01:05:55,870
+واحد على S في S في في S فاس فاس فاس فاس فاس فاس
+
+476
+01:05:55,870 --> 01:06:01,200
+فاس فاس فاس فاس فاس فاس الشركة بنات هلا وصل ت و ال
+
+477
+01:06:01,200 --> 01:06:04,740
+سن ت و ال سن نقص واحد ت و ال سن نقص اتنين ت و ال
+
+478
+01:06:04,740 --> 01:06:10,020
+سن نقص تلاتة ت تربيع ت و ال واحد ت و ال zero يبقى
+
+479
+01:06:10,020 --> 01:06:14,740
+وصي لـ plus لـ T و ال zero يبقى هذا الكلام بده يساوي
+
+480
+01:06:14,740 --> 01:06:21,780
+اللي فوق اللي هو n factorial واللي تحت S أُس قداش N
+
+481
+01:06:21,780 --> 01:06:27,900
+في Laplace Transform لمين؟ للواحد أظن جيبنا Laplace 
+
+482
+01:06:27,900 --> 01:06:32,320
+Transform للواحد قبل قليل وبواحد على S يبقى ده
+
+483
+01:06:32,320 --> 01:06:38,160
+صار N factorial على S to the power N في Laplace 
+
+484
+01:06:38,160 --> 01:06:43,620
+للواحد اللي هو واحد على S إذا النتيجة النهائية N 
+
+485
+01:06:43,620 --> 01:06:53,260
+factorial على S to the power N+1 طب
+
+486
+01:06:53,260 --> 01:07:01,030
+ايش رايك؟ أحنا قبل قليل استنتجنا Laplace للواحد من ال
+
+487
+01:07:01,030 --> 01:07:07,510
+E أُس AT بقدر أجيب Laplace للواحد من المسألة هذه 
+
+488
+01:07:07,510 --> 01:07:12,530
+الهين وصلنا أن Laplace ل T to the power N هي N
+
+489
+01:07:12,530 --> 01:07:18,550
+factorial على S أُس N+1 لو بدي Laplace
+
+490
+01:07:18,550 --> 01:07:19,510
+للواحد
+
+491
+01:07:35,360 --> 01:07:42,640
+بناء عليه لو سألتكوا وقلتلكوا بدنا الـ Laplace
+
+492
+01:07:42,640 --> 01:07:45,960
+transform لـ T تكعيب
+
+493
+01:07:54,640 --> 01:08:05,100
+تلاتة+واحد أربعة مباشرة تلاتة
+
+494
+01:08:05,100 --> 01:08:09,380
++واحد أربعة مباشرة تلاتة+واحد أربعة
+
+495
+01:08:09,380 --> 01:08:15,940
+مباشرة تلاتة+واحد أربعة مباشرة
+
+496
+01:08:37,550 --> 01:08:43,130
+الآن بدنا نضيف الـ بارة النظرية اللي قلنا عليها قبل
+
+497
+01:08:43,130 --> 01:08:48,840
+قليل إن الـ Laplace الـ transform is a linear function
+
+498
+01:08:48,840 --> 01:08:55,800
+ده اللي خطية يبقى بدنا نكتب العلاقة هذه ونحاول
+
+499
+01:08:55,800 --> 01:09:02,160
+نبين شو معناها بالضبط وكيف سنستخدم هذا المعنى في
+
+500
+01:09:02,160 --> 01:09:13,420
+حل بعض المسائل يبقى remark if الـ F1 of T
+
+501
+01:09:16,120 --> 01:09:25,100
+F2 of T are functions that have Laplace transform
+
+502
+01:09:25,100 --> 01:09:33,480
+and if C1 and C2 are any constants Laplace
+
+503
+01:09:33,480 --> 01:09:44,020
+transform لـ C1 في الـ F1 of T زائد زائد C2 F2 of T بده 
+
+504
+01:09:44,020 --> 01:09:53,380
+يساوي و C1 Laplace transform للـ F1 زائد C2 Laplace 
+
+505
+01:09:53,380 --> 01:10:02,980
+transform للـ F2 of T F1 of T الشكل اللي عندنا
+
+506
+01:10:11,690 --> 01:10:16,270
+مرة ثانية بقول لو عندي دالتين واحدة F1 of T
+
+507
+01:10:16,270 --> 01:10:21,090
+و الثانية F2 of T والتنتين هذول Laplace transform 
+
+508
+01:10:21,090 --> 01:10:26,040
+اللي هم exist تمام يبقى اتنين that have Laplace 
+
+509
+01:10:26,040 --> 01:10:31,560
+transform ولو كان C1 وC2 ثوابت أي ثوابت ما عنديش 
+
+510
+01:10:31,560 --> 01:10:37,320
+قيود عضات صحيحة موجبة سالبة كسرية ما عندنا مشكلة يبقى
+
+511
+01:10:37,320 --> 01:10:40,920
+Laplace transform لـ C1 في الدالة الأولى زائد C2 في
+
+512
+01:10:40,920 --> 01:10:45,320
+الدالة الثانية تساوي C1 Laplace للأولى زائد C2
+
+513
+01:10:45,320 --> 01:10:48,760
+Laplace للدالة الثانية وهذا اللي بيسميها الخاصية
+
+514
+01:10:48,760 --> 01:10:53,570
+الخطية لـ Laplace transform يبقى هذه الـ Linear 
+
+515
+01:10:53,570 --> 01:10:58,810
+Property لـ Laplace Transform لما أوضح لك كيف اجت 
+
+516
+01:10:58,810 --> 01:11:06,670
+هذه سأقول لك الآن لو جيت لـ Laplace Transform لـ C1
+
+517
+01:11:06,670 --> 01:11:15,530
+F1 of T زي C2 F2 of T حسب تعريف Laplace Transform يبقى 
+
+518
+01:11:15,530 --> 01:11:24,120
+بتكامل من Zero إلى Infinity للـ E<sup>−ST</sup> في C1
+
+519
+01:11:24,120 --> 01:11:32,440
+F1 of T زائد C2 F2
+
+520
+01:11:32,440 --> 01:11:40,050
+of T كله بالنسبة الى DT بقدر أوزع هذا التكامل إلى
+
+521
+01:11:40,050 --> 01:11:45,290
+تكاملين يبقى هذا الكلام يساوي تكامل من zero لـ 
+
+522
+01:11:45,290 --> 01:11:54,250
+infinity للـ E<sup>−ST</sup> في C1 F1 of T DT زائد 
+
+523
+01:11:54,250 --> 01:12:02,110
+تكامل من zero لـ infinity للـ E<sup>−ST</sup> في C2 F2
+
+524
+01:12:02,110 --> 01:12:10,030
+of T DT ويساوي أظن C1 مقدار ثابت بقدر أقوله برة
+
+525
+01:12:10,030 --> 01:12:15,630
+التكامل يبقى هذا الكلام بده يساوي C1 تكامل من 
+
+526
+01:12:15,630 --> 01:12:25,230
+0 إلى infinity للـ E<sup>−ST</sup> للـ F1 of T DT هذا
+
+527
+01:12:25,230 --> 01:12:29,770
+زيّه ياسي اتنين برة التكامل من zero إلى 
+
+528
+01:12:29,770 --> 01:12:38,850
+infinity للـ E<sup>−ST</sup> E<sup>−ST</sup> للـ F2 of T
+
+529
+01:12:38,850 --> 01:12:47,280
+في DT سؤال هذا تعريف من يا بنات لبلة الـ F1 يبقى هذا
+
+530
+01:12:47,280 --> 01:12:55,560
+الكلام يساوي C1 Laplace للـ F1 of T زائد C2 الثاني 
+
+531
+01:12:55,560 --> 01:13:02,440
+Laplace للـ F2 of T أظن وهو المطلوب هذا إذا من
+
+532
+01:13:02,440 --> 01:13:05,900
+الآن فا صدر لو كان عندي Laplace لمجموع ده الاتنين
+
+533
+01:13:05,900 --> 01:13:09,280
+بقدر آخذ Laplace الأولى زائد Laplace الثانية
+
+534
+01:13:09,280 --> 01:13:15,160
+بالزائد أو بالنقص لكن ضرب ما اتكلمناش فيه عند الضرب
+
+535
+01:13:15,160 --> 01:13:19,560
+كلامنا غلط آه أنا بتكلم للجمع أو الطرح فقط ده
+
+536
+01:13:19,560 --> 01:13:24,560
+غيره وإذا في مقدار ثابت باخده برة هذا نعطي
+
+537
+01:13:24,560 --> 01:13:40,260
+مثال توضيحي على ذلك يبقى example امرأ
+
+538
+01:13:40,260 --> 01:13:40,780
+واحد
+
+539
+01:13:43,310 --> 01:13:53,610
+Find Laplace transform لنصف T تربيع زائد ثمانية
+
+540
+01:13:53,610 --> 01:14:03,910
+زائد اتنين sin 3T Laplace 
+
+541
+01:14:03,910 --> 01:14:09,670
+transform لهذه الدالة تمام؟ بقدر أقوله والله كويس
+
+542
+01:14:09,990 --> 01:14:14,370
+اللي أنا بدي أطبق الآن قاعدة اللي فوق نظرا ل
+
+543
+01:14:14,370 --> 01:14:17,410
+إنها linear يقبل Laplace للدالة الأولى زائد الـ 
+
+544
+01:14:17,410 --> 01:14:21,590
+Laplace للدالة الثانية زائد الـ Laplace للدالة الثالثة
+
+545
+01:14:21,590 --> 01:14:26,390
+يبقى solution هذه
+
+546
+01:14:26,390 --> 01:14:31,690
+بقدر أكتبها على الشكل التالي Laplace transform
+
+547
+01:14:31,690 --> 01:14:40,470
+الـ main لـ T تربيع زائد Laplace transform لمين لـ
+
+548
+01:14:40,470 --> 01:14:45,810
+ثمانية اللي بقدر أكتبها ثمانية في قداش في واحد مش 
+
+549
+01:14:45,810 --> 01:14:50,490
+ثمانية واحد من عشرة لأ ثمانية مضروبة في واحد تمام
+
+550
+01:14:50,490 --> 01:14:58,130
+زائد اتنين Laplace transform لـ sin 3T جبتها
+
+551
+01:14:58,130 --> 01:15:01,990
+من وين؟ من خاصية الـ linearity اللي فوق اللي عندنا
+
+552
+01:15:01,990 --> 01:15:09,140
+هذا تطبيق مباشر يبقى هذا الكلام بده يساوي النص ليه؟
+
+553
+01:15:09,140 --> 01:15:15,740
+Laplace لـ T تربيع آه هي T تكعيب يبقى بقدر أقول
+
+554
+01:15:15,740 --> 01:15:26,060
+اللي هي 2! على مين؟ على S تكعيب زائد
+
+555
+01:15:26,060 --> 01:15:34,940
+هذه ثمانية في Laplace لمين؟ للواحد الصحيح وهذه زائد
+
+556
+01:15:34,940 --> 01:15:42,800
+اتنين في Laplace لـ sin 3T قبل قليل sin AT كان
+
+557
+01:15:42,800 --> 01:15:50,380
+A على S تربيع+A تربيع يبقى هذه 3 على S
+
+558
+01:15:50,380 --> 01:15:54,940
+تربيع+3 تربيع اللي يبقى جداش اللي هو
+
+559
+01:15:54,940 --> 01:16:00,620
+بتسعة طيب أظن نص مع 2! مع السلامة
+
+560
+01:16:00,620 --> 01:16:04,600
+2! 2×1 يبقى ضالة النتيجة
+
+561
+01:16:04,600 --> 01:16:12,760
+تساوي 1 على S تكعيب زائد هذه 1 على S يبقى
+
+562
+01:16:12,760 --> 01:16:21,420
+بصير 8 على S هذه زائد 2×3 بـ 6
+
+563
+01:16:21,420 --> 01:16:27,360
+على S تربيع+9 بدك تخليها زي ما هي كان بها 
+
+564
+01:16:27,360 --> 01:16:31,500
+بس لو كان هذا السؤال في الكتاب لسمح الله و روحت 
+
+565
+01:16:31,500 --> 01:16:35,460
+بتلاقيش الإجابة زي هيك بتلاقي الإجابة على الشكل
+
+566
+01:16:35,460 --> 01:16:42,500
+التالي بدنا نوحد المقامات كله يبقى S تكعيب في S
+
+567
+01:16:42,500 --> 01:16:47,920
+تربيع+9 طبعا S تكعيب اشتمت على مين؟ على S
+
+568
+01:16:47,920 --> 01:16:54,400
+يبقى لو جسمت هذه على هذه بصير عندي S تربيع+
+
+569
+01:16:54,400 --> 01:17:03,450
+9 الآن زائد 8 S تربيع في مين؟ في S تربيع
+
+570
+01:17:03,450 --> 01:17:13,650
+زائد 9 اللي بعدها زائد 6 S تكعيب تمام؟ طيب
+
+571
+01:17:13,650 --> 01:17:20,290
+هذه عبارة عن ايش؟ عبارة عن عندك أظن 8 S أس
+
+572
+01:17:20,290 --> 01:17:27,920
+أربعة في الشغيرها يبقى هاي
+
+601
+01:06:52,230 --> 01:06:57,930
+أظن النص بقدر أقوله طلع برا تمام؟ يبقى إيش بصير؟
+
+602
+01:06:57,930 --> 01:07:09,010
+بصير هذا النص هو يتكمل من zero إلى A لل E أس لو
+
+603
+01:07:09,010 --> 01:07:14,190
+جيت أخد هذه و هذه مع بعض و أخد هذه و هذه مع بعض
+
+604
+01:07:14,470 --> 01:07:19,490
+يبقى بقدر أقول هذه بدي أجمع لإثنين يبقى ناقص S
+
+605
+01:07:19,490 --> 01:07:27,530
+زائد B أو ناقص S ناقص B في T term الأول هي ناقص S
+
+606
+01:07:27,530 --> 01:07:32,570
+هي في T و ناقص فناقص بزائد BT اللي هو الجزء الأول
+
+607
+01:07:32,570 --> 01:07:40,150
+الجزء الثاني زائد بدي أخد هذه و هذه مع بعض بقدر أخد
+
+608
+01:07:40,150 --> 01:07:46,730
+ناقص T عامل مشترك بيبقى S زائد ال B يبقى زائد E
+
+609
+01:07:46,730 --> 01:07:58,710
+وهي ناقص برا و S زائد ال B كله في T في DT مظبوط؟
+
+610
+01:07:58,710 --> 01:08:04,930
+limit ولا يهمك مديش limit from zero to infinity
+
+611
+01:08:04,930 --> 01:08:13,910
+ماشي؟ بدول limit يساوي هذا الآن limit للأولى زائد
+
+612
+01:08:13,910 --> 01:08:19,210
+limit للثانية أو هنا لا plus للأولى زائد لا plus
+
+613
+01:08:19,210 --> 01:08:25,470
+للثانية يبقى هذا الكلام نص حسب ال linearity يبقى
+
+614
+01:08:25,470 --> 01:08:34,730
+نص اللي هو لا plus لمين؟ لل E أس ناقص S ناقص ال B
+
+615
+01:08:34,730 --> 01:08:48,080
+في T زائد نص لابلاس لإي أس ناقص S زائد B في T لابد
+
+616
+01:08:48,080 --> 01:08:53,040
+نستخدم المثال الأول اللي جاهز عندنا يبقى هذا نص
+
+617
+01:08:53,040 --> 01:09:03,110
+فيه الـ plus لهذه اللي هو واحد على S زائد S ناقص ال
+
+618
+01:09:03,110 --> 01:09:12,210
+B يبقى S ناقص ال B، مظبوط؟
+
+619
+01:09:12,210 --> 01:09:21,430
+هذه جوش، استنى جوش وحطينا لها S يبقى S لا استنى
+
+620
+01:09:21,430 --> 01:09:29,770
+شوية، السؤال هو بيقول جوش بي تي جوش بي تي و حطيناها
+
+621
+01:09:29,770 --> 01:09:36,100
+بي تي آآ احنا حطيناها دغري ليش حطيناها؟ استنى شوية
+
+622
+01:09:36,100 --> 01:09:42,760
+استنى يا بناتنا احنا هنا حطينا التعريف لكن هذه بقدر
+
+623
+01:09:42,760 --> 01:09:46,840
+أقول بالشكل التالي مباشرة نفس الفكرة اللي احنا
+
+624
+01:09:46,840 --> 01:09:52,320
+ماشينا فيها يعني أنا ما بديش أعمل التكامل هذا بدي
+
+625
+01:09:52,320 --> 01:10:00,140
+أسهل شوية يبقى هذه لا plus لا نص في مين؟ في ال E أس
+
+626
+01:10:00,140 --> 01:10:07,960
+BT زائد E أس ناقص BT مظبوط؟ يبقى كأنه عندي دالتين
+
+627
+01:10:07,960 --> 01:10:18,700
+يبقى هذا نص لابلاس لمين؟ لل EOS BT زائد نص لابلاس 
+
+628
+01:10:18,700 --> 01:10:25,020
+لل EOS ناقص BT طبعًا؟ يبقى ما قلنا شاكر الجوالات
+
+629
+01:10:25,020 --> 01:10:28,560
+من أول ما دخلنا وبعدين أول ما دخلنا قلنا جاف
+
+630
+01:10:28,560 --> 01:10:36,630
+لجوال المنبه ولا جوال اسمه جوال يبقى نصف لابلاس لل E
+
+631
+01:10:36,630 --> 01:10:41,610
+أس BT زائد نصف لابلاس لل E أس نقص BT هذه حسبناها
+
+632
+01:10:41,610 --> 01:10:50,350
+قبل قليل النصف في واحد على S ناقص ال B و هذه كمان
+
+633
+01:10:50,350 --> 01:11:01,850
+نصف في واحد على S زائد ال B هذا الكلام يساوي نص في
+
+634
+01:11:01,850 --> 01:11:11,230
+واحد على S نقص ال B واحد على S زائد ال B يبقى هذا
+
+635
+01:11:11,230 --> 01:11:18,010
+الكلام يساوي نص بدا واحد المقامات S نقص ال B في S
+
+636
+01:11:18,010 --> 01:11:25,610
+زائد ال B بشير عند S زائد ال B زائد ال S نقص ال B
+
+637
+01:11:28,210 --> 01:11:34,070
+نقص بي وزائد بي مع السلامة يبقى اللي صار عندي نص في
+
+638
+01:11:34,070 --> 01:11:41,450
+إثنين اس هذا تحليل مين؟ فرق بين المربعين يبقى هذا
+
+639
+01:11:41,450 --> 01:11:48,590
+اس تربيع ناقص بي تربيع نص مع إثنين مع السلامة يبقى
+
+640
+01:11:48,590 --> 01:11:54,010
+اس على اس تربيع ناقص مين؟ بي تربيع قبل شوية قلت لكم
+
+641
+01:11:54,010 --> 01:12:01,030
+good exercise لابلاس ل cosine ا ت قلت لكم S على S
+
+642
+01:12:01,030 --> 01:12:05,850
+تربيع زائد ب تربيع مش ناقص في حال تلاقوش ناقص في
+
+643
+01:12:05,850 --> 01:12:07,930
+حال تلاقوش cosine زائد
+
+644
+01:12:13,040 --> 01:12:19,340
+نمرا بيج أخد حاصل ضرب الإثنين يبقى أنا بدي لابلاسي
+
+645
+01:12:19,340 --> 01:12:28,960
+ترانسفورم لل E أس AT في مين؟ في E أس BT زائد E أس
+
+646
+01:12:28,960 --> 01:12:36,020
+ناقص BT كله على جداش على الإثنين يبقى هذا الكلام
+
+647
+01:12:36,020 --> 01:12:44,280
+بده يساوي لابلاس ترانسفورم لنص في ال E أس A زائد
+
+648
+01:12:44,280 --> 01:12:54,880
+ال B يبقى A زائد ال B في T زائد نص في E أس A ناقص
+
+649
+01:12:54,880 --> 01:13:04,140
+ال B كله في من؟ في T هذا الكلام يساوي نص لابلاس
+
+650
+01:13:04,140 --> 01:13:11,640
+ترانسفورم لل E أس A زائد ال B في T من خاصية ال
+
+651
+01:13:11,640 --> 01:13:19,960
+linearity زائد نص لابلاس ترانسفورم لل E أس A ناقص
+
+652
+01:13:19,960 --> 01:13:30,830
+ال B في T هذا الكلام يساوي نص في طلعيني من هذه يبقى
+
+653
+01:13:30,830 --> 01:13:37,730
+هذه أول مثال أخذناه اليوم واحد على مين؟ على S ناقص
+
+654
+01:13:37,730 --> 01:13:48,590
+ال A زائد ال B تمام اللي بعده زائد نص في واحد على
+
+655
+01:13:48,590 --> 01:14:00,710
+S زائد اللي هو ال A ناقص ال B هذه موجبة وهذه بيبقى
+
+656
+01:14:00,710 --> 01:14:07,750
+هذه بالموجب يبقى تكون سالب يبقى سالب بالشكل اللي
+
+657
+01:14:07,750 --> 01:14:12,530
+عندنا هنا تمام؟ لأن الأس عندي هنا موجب وهنا موجب
+
+658
+01:14:12,530 --> 01:14:17,650
+إيه ناقص ال B؟ طيب هنعيد ترتيب اللي هو النتيجة
+
+659
+01:14:17,650 --> 01:14:19,170
+اللي وصلنا لها هذه
+
+660
+01:14:39,050 --> 01:14:48,830
+إذا صار عندي لابلاس ترانسفورم لل E أس AT في جوش BT
+
+661
+01:14:48,830 --> 01:14:55,130
+بده يساوي، بده أخد ابناء النص عامل مشترك من الكل،
+
+662
+01:14:55,130 --> 01:15:03,250
+مظل واحد على شو رايك هذه بدي أكتبها S ناقص ال A و
+
+663
+01:15:03,250 --> 01:15:07,450
+هنا من وهنا والله خليها زي ما هي وبعض الخطوات
+
+664
+01:15:07,450 --> 01:15:14,010
+التالية بنعملها يبقى S ناقص ال A زائد ال B هذا ال
+
+665
+01:15:14,010 --> 01:15:21,230
+term الأول بعدها زائد أخذنا النص برا يبقى واحد على
+
+666
+01:15:21,230 --> 01:15:28,730
+S ناقص ال A ناقص ال B بشكل عندنا هنا يبقى هذه
+
+667
+01:15:28,730 --> 01:15:35,790
+تساوي نص فين؟ بدا وحد المقامات اللي هدول كلهم يبقى
+
+668
+01:15:35,790 --> 01:15:46,750
+بصير S ناقص ال A زائد ال B في S ناقص ال A ناقص ال
+
+669
+01:15:46,750 --> 01:15:55,510
+B هنا هذا بصير S ناقص ال A زائد ال B وهنا زائد ال
+
+670
+01:15:55,510 --> 01:16:04,120
+S ناقص ال A ناقص ال B وحط المقامات للكل يبقى بصير S
+
+671
+01:16:04,120 --> 01:16:08,880
+وهذا فكته S ناقص ال A زائد ال B وهذا الثاني فكته
+
+672
+01:16:08,880 --> 01:16:14,980
+بصير S ناقص ال A ناقص ال B أظن ناقص ال B وزائد ال
+
+673
+01:16:14,980 --> 01:16:20,640
+B مع السلامة هذا ال term هو هذا ال term يبقى هذا
+
+674
+01:16:20,640 --> 01:16:28,420
+النص وهنا بصير 2 في S ناقص ال A شو رايكوا هذه؟ بدأ
+
+675
+01:16:28,420 --> 01:16:34,750
+أكتب الجثة ده على الشكل التالي لو ال S ناقص ال A
+
+676
+01:16:34,750 --> 01:16:44,190
+ناقص ال B هذا جوس لحاله هذا كمان بدي أكتبه S ناقص
+
+677
+01:16:44,190 --> 01:16:49,790
+ال A وناقص ناقص بصير زائد ال B بالشكل اللي عندنا
+
+678
+01:16:49,790 --> 01:16:56,230
+طيب الإثنين هذه مع الإثنين هذه يبقى إيش بصير عندنا
+
+679
+01:16:56,230 --> 01:17:03,720
+بصير S ناقص ال A طب اتطلعيلي علي هدول فرق بين
+
+680
+01:17:03,720 --> 01:17:11,560
+المربعين صح؟ يبقى ده بيصير ال S ناقص ال A لكل تربيع
+
+681
+01:17:11,560 --> 01:17:18,280
+ناقص ب تربيع إذا هذا هو الابلاس ترانسفورم لل E S
+
+682
+01:17:18,280 --> 01:17:25,900
+A T في جوش B T DT وعدناكم بوعد قبل قليل ولم ننفذه
+
+683
+01:17:26,410 --> 01:17:29,190
+شو الوعد اللي وعدناكم فيه؟ قلنا بنجيبلكوا ال
+
+684
+01:17:29,190 --> 01:17:35,290
+sign AT بطريقة أخرى طب نيجي للطريقة الأخرى اللي
+
+685
+01:17:35,290 --> 01:17:40,550
+وعدناكم فيها و بها ننهي المحاضرة أصلًا مرت علينا
+
+686
+01:17:40,550 --> 01:17:45,170
+صيغة أويلر مش أويلر ديفرنشال ايكويشن تبع في
+
+687
+01:17:45,170 --> 01:17:45,690
+الكملة
+
+688
+01:17:50,020 --> 01:17:59,720
+يبقى مرة علينا a cos θ زائد i sin
+
+689
+01:17:59,720 --> 01:18:00,660
+θ
+
+690
+01:18:05,110 --> 01:18:11,830
+الآن بدنا نيجي نقيس عليها لو جينا قلنا لك قداش
+
+691
+01:18:11,830 --> 01:18:24,730
+اللي هو E أس I a T إيش بتقولي له؟ cosine a T زائد
+
+692
+01:18:24,730 --> 01:18:33,490
+I sine a T صح؟ يعني شيلنا θ وحطينا مكانها مين؟
+
+693
+01:18:52,650 --> 01:19:01,420
+طب إيش رايك لو طرحنا الإثنين من بعض طرحناهم طرح إذا
+
+694
+01:19:01,420 --> 01:19:11,700
+بصير عندي E أس I A T ناقص E أس ناقص I A T يبقى
+
+695
+01:19:11,700 --> 01:19:17,180
+بصير هنا ناقص وهنا ذات بروحة هدول وبصير عندنا
+
+696
+01:19:17,180 --> 01:19:29,680
+إثنين I في Sin A T وكأنه SinAT بدها تساوي واحد
+
+697
+01:19:29,680 --> 01:19:39,900
+على إثنين I في مين؟ في E أس I AT ناقص E أس ناقص I
+
+698
+01:19:39,900 --> 01:19:47,330
+AT طبعًا الكتاب حاطط هذا سؤال في التمرين وجاي لك
+
+699
+01:19:47,330 --> 01:19:51,750
+sign AT يساوي هذا هي جابينالك من أين؟ من وين جابها
+
+700
+01:19:51,750 --> 01:19:56,530
+جابها من أويلر فورميولا من صيغة أويلر وهي جيبنا
+
+701
+01:19:56,530 --> 01:20:02,870
+sign AT يبقى احنا لو بدنا نحسب لابلاس لهذه الدالة
+
+702
+01:20:02,870 --> 01:20:07,290
+كأنه بدنا نحسب لابلاس لطرف اليمين
+
+703
+01:20:09,690 --> 01:20:15,130
+يعني هذا يا بنات كأنه حل ثاني لتاني سؤال أخذناه
+
+704
+01:20:15,130 --> 01:20:23,130
+اليوم مظبوط إذا بدي أحسب لابلاس ل sign eighty
+
+705
+01:20:24,880 --> 01:20:31,220
+يبقى هو لابلاس لخطار في اليمين يبقى هو لابلاس ل
+
+706
+01:20:31,220 --> 01:20:42,600
+1 على 2 I تمين في E أس I A T ناقص E أس ناقص I A T
+
+707
+01:20:42,600 --> 01:20:47,420
+بالشكل اللي عندنا هذا اللي قلته هناك مقولة كويس
+
+708
+01:20:47,420 --> 01:20:52,780
+إذا هذا الكلام بدي يساوي أظن 1 على 2 I مقدار ثابت
+
+709
+01:20:53,540 --> 01:21:01,420
+يبقى شرف برا يبقى هذا واحد على إثنين I لابلاس ل E
+
+710
+01:21:01,420 --> 01:21:10,160
+أس I A T ناقص واحد على إثنين I لمين؟ ليه لابلاس
+
+711
+01:21:10,160 --> 01:21:18,240
+ترانسفورم ل E أس ناقص A I T يبقى هذا الكلام بدي
+
+712
+01:21:18,240 --> 01:21:29,250
+اسمه واحد على إثنين I يبقى هذه واحد على S ناقص AI
+
+713
+01:21:29,250 --> 01:21:38,090
+طبق الأول مثال أخذناه اليوم ناقص
+
+714
+01:21:38,090 --> 01:21:48,790
+واحد على إثنين I لمين؟ لواحد على S زائد AI يعني يا
+
+715
+01:21:48,790 --> 01:21:54,030
+بنات هذه بيصير واحد على إثنين I عامل مشترك بيظل
+
+716
+01:21:54,030 --> 01:22:03,710
+أدنا واحد على S ناقص AI ناقص واحد على S زائد AI لو
+
+717
+01:22:03,710 --> 01:22:09,870
+وحدنا المقامات للكل يبقى واحد على إثنين I وهنا
+
+718
+01:22:09,870 --> 01:22:16,390
+بيصير S ناقص AI في S زائد AI
+
+719
+01:22:19,040 --> 01:22:31,220
+تمام بيصير عندك S زائد AI ناقص S زائد AI هذا
+
+720
+01:22:31,220 --> 01:22:38,580
+الكلام يساوي واحد على إثنين I فيه أظن ناقص S وزائد
+
+721
+01:22:38,580 --> 01:22:47,520
+S مع السلامة بيضلي إثنين AI على أليس هذا الفرق بين
+
+722
+01:22:47,520 --> 01:22:56,050
+المربعين؟ يبقى مربع الكمية الأولى ناقص مربع الكمية
+
+723
+01:22:56,050 --> 01:23:02,210
+الثانية يبقى A تربيع في I تربيع I تربيع يبقى سالب
+
+724
+01:23:02,210 --> 01:23:08,310
+واحد يبقى سالب A تربيع يبقى سالب A تربيع بالشكل
+
+725
+01:23:08,310 --> 01:23:14,120
+اللي عندنا هذا يبقى إثنين اي مع إثنين ومع الاي
+
+726
+01:23:14,120 --> 01:23:22,000
+بيبقى القداش اي هذه S تربيع زائد A تربيع نفس
+
+727
+01:23:22,000 --> 01:23:26,620
+النتيجة اللي حصلنا عليها قبل قليل في المثال رقم
+
+728
+01:23:26,620 --> 01:23:31,640
+إثنين ولا لا يبقى هذا السؤال موجود عندك في الكتاب
+
+729
+01:23:31,640 --> 01:23:39,010
+ومش هجدكم بس بدوا كمان لابلاس ل cosine AT لو
+
+730
+01:23:39,010 --> 01:23:44,230
+أخذنا لابلاي سا كوسين بيطلع هذه بالضبط بس بدل 2I
+
+731
+01:23:44,230 --> 01:23:49,350
+بيصير النص فقط ما عنديش I وهذه بدل النقص مش بيصير
+
+732
+01:23:49,350 --> 01:23:55,590
+بيصير زائد تمرين سؤال موجود في الكتاب أندي لحد هنا
+
+733
+01:23:55,590 --> 01:24:00,790
+stop بنكمل إن شاء الله المرة القادمة
diff --git a/PL9fwy3NUQKwa8ZDfSFGn6H8xVFLzqmCZC/1myyZiBOvdQ_raw.json b/PL9fwy3NUQKwa8ZDfSFGn6H8xVFLzqmCZC/1myyZiBOvdQ_raw.json
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index 0000000000000000000000000000000000000000..c50615a35404c3004e7d54b869c9c35bfa9a7f7f
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@@ -0,0 +1 @@
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Improper Integral بحسبه في الطريقة اللي عندنا هذا التكامل هو الـ Converge إذا لم يكن هناك مقاومة وإذا لم يكن هناك مقاومة بقول عنه الـ Diverge يبقى هذا الـ Diverge إذا لم يكن هناك مقاومة", "tokens": [6027, 2655, 4117, 10943, 1211, 13672, 1829, 43242, 8315, 31439, 2423, 39184, 8270, 340, 610, 23894, 304, 4724, 5016, 35457, 3224, 8978, 41950, 16572, 28671, 13672, 1829, 43242, 8315, 23758, 16712, 4117, 10943, 1211, 31439, 2423, 39184, 2656, 331, 432, 11933, 15730, 32767, 7251, 19452, 34105, 4117, 3714, 4587, 995, 20498, 3660, 4032, 28814, 15730, 32767, 7251, 19452, 34105, 4117, 3714, 4587, 995, 20498, 3660, 4724, 39648, 18871, 3224, 2423, 39184, 413, 1837, 432, 7251, 3555, 4587, 7578, 23758, 2423, 39184, 413, 1837, 432, 11933, 15730, 32767, 7251, 19452, 34105, 4117, 3714, 4587, 995, 20498, 3660], "avg_logprob": -0.4278350417146978, "compression_ratio": 2.0414201183431953, "no_speech_prob": 0.0, "words": [{"start": 364.24, "end": 365.0, "word": "التكامل", "probability": 0.709130859375}, 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إذا كانت متصلة there هناك يعني على الفترة من Alpha إلى Beta except", "tokens": [28814, 15730, 25961, 2655, 44650, 36520, 3660, 10874, 11622, 19986, 25528, 34051, 15844, 12174, 9566, 3615, 322, 364, 15035, 15844, 27188, 2655, 25720, 314, 9154, 20588, 30731, 33286, 498, 309, 307, 10957, 11933, 15730, 25961, 2655, 44650, 36520, 3660, 456, 34105, 4117, 37495, 22653, 15844, 27188, 2655, 25720, 9154, 20588, 30731, 33286, 3993], "avg_logprob": -0.24956596394379935, "compression_ratio": 1.5290322580645161, "no_speech_prob": 0.0, "words": [{"start": 474.66, "end": 475.6, "word": "إذا", "probability": 0.57965087890625}, {"start": 475.6, "end": 476.64, "word": " كانت", "probability": 0.7646484375}, {"start": 476.64, "end": 480.12, "word": " متصلة", "probability": 0.7381184895833334}, {"start": 480.12, "end": 481.08, "word": " جزئيا", "probability": 0.668365478515625}, {"start": 481.08, "end": 481.78, "word": " أو", "probability": 0.57568359375}, {"start": 481.78, "end": 482.2, "word": " على", 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0.7626953125}, {"start": 568.7, "end": 569.48, "word": " يبقى", "probability": 0.94677734375}, {"start": 569.48, "end": 569.68, "word": " هذا", "probability": 0.93359375}, {"start": 569.68, "end": 569.86, "word": " اللي", "probability": 0.970703125}, {"start": 569.86, "end": 569.98, "word": " لا", "probability": 0.794921875}, {"start": 569.98, "end": 570.32, "word": " يمكن", "probability": 0.827392578125}, {"start": 570.32, "end": 570.9, "word": " ازالته", "probability": 0.873046875}, {"start": 570.9, "end": 571.08, "word": " و", "probability": 0.52783203125}, {"start": 571.08, "end": 571.22, "word": " ال", "probability": 0.51171875}, {"start": 571.22, "end": 571.52, "word": " jump", "probability": 0.91552734375}, {"start": 571.52, "end": 572.4, "word": " discontinuity", "probability": 0.966552734375}, {"start": 572.4, "end": 572.64, "word": " اللي", "probability": 0.767333984375}, {"start": 572.64, "end": 572.64, "word": " لا", "probability": 0.8564453125}, {"start": 572.64, "end": 572.92, "word": " يمكن", "probability": 0.90966796875}, {"start": 572.92, "end": 573.66, "word": " ازالته", "probability": 0.991455078125}, {"start": 573.66, "end": 574.18, "word": " و", "probability": 0.66357421875}, {"start": 574.18, "end": 574.52, "word": " النوع", "probability": 0.94091796875}, {"start": 574.52, "end": 574.98, "word": " التالت", "probability": 0.9557291666666666}, {"start": 574.98, "end": 575.16, "word": " هو", "probability": 0.626953125}, {"start": 575.16, "end": 575.3, "word": " اللي", "probability": 0.96435546875}, {"start": 575.3, "end": 575.76, "word": " بنزيله", "probability": 0.81353759765625}, {"start": 575.76, "end": 576.38, "word": " مالناهش", "probability": 0.737158203125}, {"start": 576.38, "end": 576.86, "word": " علاقة", "probability": 0.9803059895833334}, {"start": 576.86, "end": 577.12, "word": " فيه", "probability": 0.931884765625}, {"start": 577.12, "end": 577.64, "word": " احنا", "probability": 0.90625}, {"start": 577.64, "end": 578.04, "word": " بس", "probability": 0.9716796875}, {"start": 578.04, "end": 578.4, "word": " بدنا", "probability": 0.94580078125}, {"start": 578.4, "end": 578.58, "word": " اللي", "probability": 0.990234375}, {"start": 578.58, "end": 578.68, "word": " في", "probability": 0.5625}, {"start": 578.68, "end": 579.12, "word": " النص", "probability": 0.833251953125}, {"start": 579.12, "end": 579.66, "word": " اللي", "probability": 0.98974609375}, {"start": 579.66, "end": 579.8, "word": " هو", "probability": 0.93896484375}, {"start": 579.8, "end": 580.28, "word": " jump", "probability": 0.58203125}, {"start": 580.28, "end": 581.4, "word": " discontinuity", "probability": 0.961181640625}], "temperature": 1.0}, {"id": 26, "seek": 59979, "start": 581.8, "end": 599.8, "text": "يبقى فينا jump discontinuity عند عدد محدود نوضح هذا الكلام من خلال الرصم اللي قدامنا بقول الدالة اللي عندنا هذه اللي هي ال ال F is piecewise", "tokens": [1829, 3555, 4587, 7578, 8978, 8315, 3012, 31420, 21757, 43242, 6225, 3215, 3215, 3714, 24401, 23328, 8717, 2407, 11242, 5016, 23758, 2423, 28820, 10943, 9154, 16490, 1211, 6027, 34892, 9381, 2304, 13672, 1829, 12174, 3215, 10943, 8315, 4724, 39648, 32748, 6027, 3660, 13672, 1829, 43242, 8315, 29538, 13672, 1829, 39896, 2423, 2423, 479, 307, 2522, 3711], "avg_logprob": -0.2286184273268047, "compression_ratio": 1.4705882352941178, "no_speech_prob": 0.0, "words": [{"start": 581.8, "end": 582.36, "word": "يبقى", "probability": 0.777099609375}, {"start": 582.36, "end": 582.78, "word": " فينا", "probability": 0.4815673828125}, {"start": 582.78, "end": 583.32, "word": " jump", "probability": 0.330810546875}, {"start": 583.32, "end": 584.32, "word": " discontinuity", "probability": 0.92333984375}, {"start": 584.32, "end": 584.7, "word": " عند", "probability": 0.8349609375}, {"start": 584.7, "end": 585.24, "word": " عدد", "probability": 0.9166666666666666}, {"start": 585.24, "end": 585.92, "word": " محدود", "probability": 0.99072265625}, {"start": 585.92, "end": 586.58, "word": " نوضح", "probability": 0.89111328125}, {"start": 586.58, "end": 586.84, "word": " هذا", "probability": 0.939453125}, {"start": 586.84, "end": 587.38, "word": " الكلام", "probability": 0.9423828125}, {"start": 587.38, "end": 587.56, "word": " من", "probability": 0.98779296875}, {"start": 587.56, "end": 587.9, "word": " خلال", "probability": 0.97998046875}, {"start": 587.9, "end": 588.34, "word": " الرصم", "probability": 0.713134765625}, {"start": 588.34, "end": 588.48, "word": " اللي", "probability": 0.888671875}, {"start": 588.48, "end": 589.18, "word": " قدامنا", "probability": 0.9056396484375}, {"start": 589.18, "end": 590.18, "word": " بقول", "probability": 0.9580078125}, {"start": 590.18, "end": 590.7, "word": " الدالة", "probability": 0.8670247395833334}, {"start": 590.7, "end": 590.84, "word": " اللي", "probability": 0.927001953125}, {"start": 590.84, "end": 591.44, "word": " عندنا", "probability": 0.9853515625}, {"start": 591.44, "end": 591.9, "word": " هذه", "probability": 0.564453125}, {"start": 591.9, "end": 592.68, "word": " اللي", "probability": 0.6553955078125}, {"start": 592.68, "end": 593.24, "word": " هي", "probability": 0.90576171875}, {"start": 593.24, "end": 593.82, "word": " ال", "probability": 0.8466796875}, {"start": 593.82, "end": 594.94, "word": " ال", "probability": 0.52490234375}, {"start": 594.94, "end": 595.6, "word": " F", "probability": 0.421630859375}, {"start": 595.6, "end": 596.48, "word": " is", "probability": 0.73388671875}, {"start": 596.48, "end": 599.8, "word": " piecewise", "probability": 0.759033203125}], "temperature": 1.0}, {"id": 27, "seek": 62180, "start": 600.41, "end": 621.81, "text": "الشكل اللي عندنا هو discontinuous on الفترة من alpha لغاية beta بالشكل اللي عندنا هنا يبقى عند ال alpha في اتصال من جهة اليمنان و beta في اتصال من جهة الشمال عند T1 و T2 في discontinuity و discontinuity هذا jump", "tokens": [6027, 8592, 28820, 13672, 1829, 43242, 8315, 31439, 31420, 12549, 322, 27188, 2655, 25720, 9154, 8961, 5296, 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"end": 604.99, "word": " الفترة", "probability": 0.9490559895833334}, {"start": 604.99, "end": 605.65, "word": " من", "probability": 0.88134765625}, {"start": 605.65, "end": 606.27, "word": " alpha", "probability": 0.27685546875}, {"start": 606.27, "end": 607.79, "word": " لغاية", "probability": 0.9732666015625}, {"start": 607.79, "end": 608.35, "word": " beta", "probability": 0.79736328125}, {"start": 608.35, "end": 608.99, "word": " بالشكل", "probability": 0.771484375}, {"start": 608.99, "end": 609.13, "word": " اللي", "probability": 0.983642578125}, {"start": 609.13, "end": 609.61, "word": " عندنا", "probability": 0.905029296875}, {"start": 609.61, "end": 609.89, "word": " هنا", "probability": 0.36181640625}, {"start": 609.89, "end": 610.93, "word": " يبقى", "probability": 0.9161376953125}, {"start": 610.93, "end": 611.19, "word": " عند", "probability": 0.93505859375}, {"start": 611.19, "end": 611.33, "word": " ال", "probability": 0.8876953125}, {"start": 611.33, "end": 611.67, "word": " alpha", "probability": 0.8154296875}, {"start": 611.67, "end": 611.93, "word": " في", "probability": 0.8740234375}, {"start": 611.93, "end": 612.57, "word": " اتصال", "probability": 0.9439697265625}, {"start": 612.57, "end": 612.79, "word": " من", "probability": 0.9853515625}, {"start": 612.79, "end": 613.17, "word": " جهة", "probability": 0.9733072916666666}, {"start": 613.17, "end": 613.83, "word": " اليمنان", "probability": 0.6979166666666666}, {"start": 613.83, "end": 613.99, "word": " و", "probability": 0.6640625}, {"start": 613.99, "end": 614.29, "word": " beta", "probability": 0.36767578125}, {"start": 614.29, "end": 614.55, "word": " في", "probability": 0.95556640625}, {"start": 614.55, "end": 615.13, "word": " اتصال", "probability": 0.991943359375}, {"start": 615.13, "end": 615.33, "word": " من", "probability": 0.97998046875}, {"start": 615.33, "end": 615.65, "word": " جهة", "probability": 0.93017578125}, {"start": 615.65, "end": 616.17, "word": " الشمال", "probability": 0.9894205729166666}, {"start": 616.17, "end": 616.79, "word": " عند", "probability": 0.59326171875}, {"start": 616.79, "end": 617.39, "word": " T1", "probability": 0.75927734375}, {"start": 617.39, "end": 617.59, "word": " و", "probability": 0.95947265625}, {"start": 617.59, "end": 618.13, "word": " T2", "probability": 0.8408203125}, {"start": 618.13, "end": 618.39, "word": " في", "probability": 0.83056640625}, {"start": 618.39, "end": 619.43, "word": " discontinuity", "probability": 0.9384765625}, {"start": 619.43, "end": 619.65, "word": " و", "probability": 0.386474609375}, {"start": 619.65, "end": 620.81, "word": " discontinuity", "probability": 0.662841796875}, {"start": 620.81, "end": 621.23, "word": " هذا", "probability": 0.83935546875}, {"start": 621.23, "end": 621.81, "word": " jump", "probability": 0.685546875}], "temperature": 1.0}, {"id": 28, "seek": 64441, "start": 621.99, "end": 644.41, "text": "قفزت من النقطة هذه إلى النقطة هذه، من هنا قفزت من هنا لهنا، من هنا قفزت لهنا، بعد هيك صارت اللي اللي هو ال continuity هذا، يبقى على الخط المائل هذا continuous على القوس هذا continuous على القوس هذا continuous، لكن عند T1 و T2", "tokens": [4587, 5172, 11622, 2655, 9154, 28239, 47432, 3660, 29538, 30731, 28239, 47432, 3660, 29538, 12399, 9154, 34105, 12174, 5172, 11622, 2655, 9154, 34105, 46740, 8315, 12399, 9154, 34105, 12174, 5172, 11622, 2655, 46740, 8315, 12399, 39182, 39896, 4117, 20328, 9640, 2655, 13672, 1829, 13672, 1829, 31439, 2423, 23807, 23758, 12399, 7251, 3555, 4587, 7578, 15844, 33962, 9566, 9673, 16373, 1211, 23758, 10957, 15844, 25062, 41779, 23758, 10957, 15844, 25062, 41779, 23758, 10957, 12399, 44381, 43242, 314, 16, 4032, 314, 17], "avg_logprob": -0.20428241035084665, "compression_ratio": 2.104651162790698, "no_speech_prob": 0.0, "words": [{"start": 621.99, "end": 623.01, "word": "قفزت", "probability": 0.8641357421875}, {"start": 623.01, "end": 623.15, "word": " من", "probability": 0.94091796875}, {"start": 623.15, "end": 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"probability": 0.99462890625}, {"start": 627.99, "end": 628.69, "word": " قفزت", "probability": 0.99609375}, {"start": 628.69, "end": 629.49, "word": " لهنا،", "probability": 0.92236328125}, {"start": 629.49, "end": 629.83, "word": " بعد", "probability": 0.79150390625}, {"start": 629.83, "end": 630.25, "word": " هيك", "probability": 0.68798828125}, {"start": 630.25, "end": 630.67, "word": " صارت", "probability": 0.82421875}, {"start": 630.67, "end": 631.13, "word": " اللي", "probability": 0.588134765625}, {"start": 631.13, "end": 631.23, "word": " اللي", "probability": 0.797607421875}, {"start": 631.23, "end": 631.37, "word": " هو", "probability": 0.8583984375}, {"start": 631.37, "end": 631.45, "word": " ال", "probability": 0.8681640625}, {"start": 631.45, "end": 631.91, "word": " continuity", "probability": 0.64404296875}, {"start": 631.91, "end": 632.63, "word": " هذا،", "probability": 0.6455078125}, {"start": 632.63, "end": 632.93, "word": " يبقى", "probability": 0.8824462890625}, {"start": 632.93, "end": 633.15, "word": " على", "probability": 0.966796875}, {"start": 633.15, "end": 633.55, "word": " الخط", "probability": 0.955322265625}, {"start": 633.55, "end": 634.47, "word": " المائل", "probability": 0.8260091145833334}, {"start": 634.47, "end": 634.75, "word": " هذا", "probability": 0.91357421875}, {"start": 634.75, "end": 635.59, "word": " continuous", "probability": 0.364501953125}, {"start": 635.59, "end": 637.89, "word": " على", "probability": 0.71240234375}, {"start": 637.89, "end": 638.73, "word": " القوس", "probability": 0.783935546875}, {"start": 638.73, "end": 638.97, "word": " هذا", "probability": 0.95458984375}, {"start": 638.97, "end": 639.79, "word": " continuous", "probability": 0.97607421875}, {"start": 639.79, "end": 640.31, "word": " على", "probability": 0.70849609375}, {"start": 640.31, "end": 640.81, "word": " القوس", "probability": 0.974609375}, {"start": 640.81, "end": 641.23, "word": " هذا", "probability": 0.9775390625}, {"start": 641.23, "end": 642.55, "word": " continuous،", "probability": 0.8525390625}, {"start": 642.55, "end": 642.81, "word": " لكن", "probability": 0.953125}, {"start": 642.81, "end": 643.09, "word": " عند", "probability": 0.73828125}, {"start": 643.09, "end": 643.57, "word": " T1", "probability": 0.812255859375}, {"start": 643.57, "end": 643.75, "word": " و", "probability": 0.951171875}, {"start": 643.75, "end": 644.41, "word": " T2", "probability": 0.8056640625}], "temperature": 1.0}, {"id": 29, "seek": 67449, "start": 644.81, "end": 674.49, "text": "في عندي jump discontinuity يبقى هذه بسميها piecewise function طيب الآن بنجي للنقطة الثانية وهي متى يمكن نعمل transform لدى اللى تم شروط اللازم تتحقق في ال function طبعا احنا لن نبحث هذه الشروط في المسائل لأن كل المسائل اللى معطيه عندنا في الكتاب فنطبق عليه هذه الشروط وبالتالي", "tokens": [41185, 18871, 16254, 3012, 31420, 21757, 7251, 3555, 4587, 7578, 29538, 4724, 38251, 1829, 11296, 2522, 3711, 2445, 23032, 1829, 3555, 6024, 48506, 44945, 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"probability": 0.814697265625}, {"start": 671.01, "end": 671.63, "word": " معطيه", "probability": 0.6514892578125}, {"start": 671.63, "end": 671.95, "word": " عندنا", "probability": 0.879150390625}, {"start": 671.95, "end": 672.05, "word": " في", "probability": 0.779296875}, {"start": 672.05, "end": 672.47, "word": " الكتاب", "probability": 0.9588216145833334}, {"start": 672.47, "end": 673.05, "word": " فنطبق", "probability": 0.7703125}, {"start": 673.05, "end": 673.29, "word": " عليه", "probability": 0.88916015625}, {"start": 673.29, "end": 673.51, "word": " هذه", "probability": 0.71435546875}, {"start": 673.51, "end": 673.85, "word": " الشروط", "probability": 0.9656575520833334}, {"start": 673.85, "end": 674.49, "word": " وبالتالي", "probability": 0.944921875}], "temperature": 1.0}, {"id": 30, "seek": 70212, "start": 674.78, "end": 702.12, "text": "بروح ما علينا إلا نحسب لبلاس ال transform مباشرة بقول افترض ان ال F شرطين F بيسوازي continuous يعني بالشكل اللي عندنا هذا تمام يبقى وين on the interval من zero ل A for any positive number A يعني أخدنا من عند ال zero لأي رقم بدكي يوجه فيه عند أي رقم لجيت الدالة مقطعة إلى جزئين", "tokens": [3555, 32887, 5016, 19446, 25894, 8315, 11933, 15040, 8717, 5016, 35457, 5296, 3555, 15040, 3794, 2423, 4088, 3714, 3555, 33599, 25720, 4724, 39648, 1975, 5172, 2655, 43042, 16472, 2423, 479, 13412, 2288, 9566, 9957, 479, 4724, 1829, 3794, 2407, 31377, 1829, 10957, 37495, 22653, 20666, 8592, 28820, 13672, 1829, 43242, 8315, 23758, 46811, 10943, 7251, 3555, 4587, 7578, 4032, 9957, 322, 264, 15035, 9154, 4018, 5296, 316, 337, 604, 3353, 1230, 316, 37495, 22653, 5551, 9778, 3215, 8315, 9154, 43242, 2423, 4018, 5296, 10721, 1829, 12602, 4587, 2304, 47525, 4117, 1829, 7251, 29245, 3224, 8978, 3224, 43242, 36632, 12602, 4587, 2304, 5296, 7435, 36081, 32748, 6027, 3660, 3714, 47432, 27884, 30731, 10874, 11622, 19986, 9957], "avg_logprob": -0.2654902893921425, "compression_ratio": 1.5940959409594095, "no_speech_prob": 0.0, "words": [{"start": 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{"id": 67, "seek": 158470, "start": 1557.9, "end": 1584.7, "text": "هذا الـ Improper Integral يبقى بيطبق خاصية الـ Improper Integral يبقى الـ Limit تكامل من Zero لـ A لما الـ A بده تروح ل Infinity للـ E أُس ناقص ST لـ Sin ATDT إذا بروح أكمل هذه المسألة كيف بنكمل هذه يا بنات؟", "tokens": [3224, 15730, 2423, 39184, 8270, 340, 610, 23894, 304, 7251, 3555, 4587, 7578, 4724, 1829, 9566, 3555, 4587, 16490, 33546, 10632, 2423, 39184, 8270, 340, 610, 23894, 304, 7251, 3555, 4587, 7578, 2423, 39184, 16406, 270, 6055, 4117, 10943, 1211, 9154, 17182, 5296, 39184, 316, 5296, 15042, 2423, 39184, 316, 47525, 3224, 6055, 32887, 5016, 5296, 34762, 24976, 39184, 462, 5551, 10859, 3794, 8717, 995, 4587, 9381, 4904, 5296, 39184, 11187, 8872, 35, 51, 11933, 15730, 4724, 32887, 5016, 5551, 24793, 1211, 29538, 9673, 3794, 10721, 37977, 9122, 33911, 44945, 24793, 1211, 29538, 35186, 4724, 8315, 2655, 22807], "avg_logprob": -0.3355429389260032, "compression_ratio": 1.5707070707070707, "no_speech_prob": 0.0, 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{"start": 3306.06, "end": 3306.94, "word": " if", "probability": 0.53564453125}, {"start": 3306.94, "end": 3307.72, "word": " C1", "probability": 0.84033203125}, {"start": 3307.72, "end": 3308.5, "word": " and", "probability": 0.91162109375}, {"start": 3308.5, "end": 3309.46, "word": " C2", "probability": 0.9912109375}, {"start": 3309.46, "end": 3310.34, "word": " are", "probability": 0.9404296875}, {"start": 3310.34, "end": 3311.06, "word": " any", "probability": 0.849609375}, {"start": 3311.06, "end": 3312.64, "word": " constants", "probability": 0.72607421875}, {"start": 3312.64, "end": 3313.48, "word": " Laplace", "probability": 0.8154296875}, {"start": 3313.48, "end": 3314.58, "word": " transform", "probability": 0.83251953125}, {"start": 3314.58, "end": 3315.88, "word": " لC1", "probability": 0.802734375}], "temperature": 1.0}, {"id": 139, "seek": 334298, "start": 3316.58, "end": 3342.98, "text": "فى ال F of T زائد زائد C2 F2 of T بده ساوي و C1 ل plus transform لل F1 زائد C2 ل plus transform لل F2 of T F1 of T الشكل اللى عندنا", "tokens": [5172, 7578, 2423, 479, 295, 314, 30767, 16373, 3215, 30767, 16373, 3215, 383, 17, 479, 17, 295, 314, 47525, 3224, 8608, 995, 45865, 4032, 383, 16, 5296, 1804, 4088, 24976, 479, 16, 30767, 16373, 3215, 383, 17, 5296, 1804, 4088, 24976, 479, 17, 295, 314, 479, 16, 295, 314, 25124, 28820, 13672, 7578, 43242, 8315], "avg_logprob": -0.2960379421710968, "compression_ratio": 1.4830508474576272, "no_speech_prob": 5.960464477539063e-08, "words": [{"start": 3316.58, "end": 3316.8, "word": "فى", "probability": 0.57098388671875}, {"start": 3316.8, "end": 3316.96, "word": " ال", "probability": 0.568359375}, {"start": 3316.96, "end": 3317.32, "word": " F", "probability": 0.7529296875}, {"start": 3317.32, "end": 3317.84, "word": " of", "probability": 0.65966796875}, {"start": 3317.84, "end": 3318.24, "word": " T", "probability": 0.953125}, {"start": 3318.24, "end": 3319.38, "word": " زائد", "probability": 0.573486328125}, {"start": 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"probability": 0.974609375}, {"start": 3339.56, "end": 3340.02, "word": " T", "probability": 0.99462890625}, {"start": 3340.02, "end": 3342.58, "word": " الشكل", "probability": 0.841064453125}, {"start": 3342.58, "end": 3342.82, "word": " اللى", "probability": 0.5567626953125}, {"start": 3342.82, "end": 3342.98, "word": " عندنا", "probability": 0.76220703125}], "temperature": 1.0}, {"id": 140, "seek": 336235, "start": 3351.69, "end": 3362.35, "text": "مرة تانية بقول لو عندي دلتين واحدة F1 of T والتانية F2 of T والتنتين هذول Laplace transform اللي هم exist", "tokens": [2304, 25720, 6055, 7649, 10632, 4724, 39648, 45164, 18871, 16254, 11778, 1211, 2655, 9957, 36764, 24401, 3660, 479, 16, 295, 314, 16070, 2655, 7649, 10632, 479, 17, 295, 314, 16070, 2655, 29399, 9957, 8032, 8848, 12610, 2369, 6742, 4088, 13672, 1829, 8032, 2304, 2514], "avg_logprob": -0.21666666401757134, "compression_ratio": 1.2325581395348837, "no_speech_prob": 0.0, "words": [{"start": 3351.69, "end": 3352.13, "word": 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كله بالنسبة الى DT", "tokens": [1211, 1211, 39184, 462, 5551, 10859, 3794, 8717, 995, 4587, 9381, 4904, 8978, 383, 16, 479, 16, 295, 314, 30767, 16373, 3215, 383, 17, 479, 17, 295, 314, 28242, 3224, 20666, 1863, 35457, 3660, 2423, 7578, 413, 51], "avg_logprob": -0.2289663438613598, "compression_ratio": 1.021505376344086, "no_speech_prob": 0.0, "words": [{"start": 3418.92, "end": 3419.58, "word": "للـ", "probability": 0.6432291666666666}, {"start": 3419.58, "end": 3419.8, "word": " E", "probability": 0.8046875}, {"start": 3419.8, "end": 3420.36, "word": " أُس", "probability": 0.649169921875}, {"start": 3420.36, "end": 3421.06, "word": " ناقص", "probability": 0.8421630859375}, {"start": 3421.06, "end": 3421.82, "word": " ST", "probability": 0.544921875}, {"start": 3421.82, "end": 3422.18, "word": " في", "probability": 0.7900390625}, {"start": 3422.18, "end": 3424.12, "word": " C1", "probability": 0.623046875}, {"start": 3424.12, "end": 3425.16, "word": " F1", "probability": 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"word": " النص", "probability": 0.855712890625}, {"start": 3647.38, "end": 3649.14, "word": " ليه؟", "probability": 0.6160481770833334}, {"start": 3649.14, "end": 3649.7, "word": " Laplace", "probability": 0.5299072265625}, {"start": 3649.7, "end": 3650.46, "word": " لتيتا", "probability": 0.6353759765625}, {"start": 3650.46, "end": 3651.08, "word": " ربيع", "probability": 0.8855794270833334}, {"start": 3651.08, "end": 3653.04, "word": " اه", "probability": 0.52423095703125}, {"start": 3653.04, "end": 3653.42, "word": " هي", "probability": 0.1527099609375}, {"start": 3653.42, "end": 3654.34, "word": " تيتا", "probability": 0.8133138020833334}, {"start": 3654.34, "end": 3654.7, "word": " كيب", "probability": 0.8592122395833334}, {"start": 3654.7, "end": 3655.0, "word": " يبقى", "probability": 0.89697265625}, {"start": 3655.0, "end": 3655.44, "word": " بقدر", "probability": 0.8914388020833334}, {"start": 3655.44, "end": 3655.74, "word": " اقول", "probability": 0.882568359375}, {"start": 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{"start": 4307.61, "end": 4308.59, "word": " يبقى", "probability": 0.99365234375}, {"start": 4308.59, "end": 4308.99, "word": " اس", "probability": 0.91650390625}, {"start": 4308.99, "end": 4309.43, "word": " على", "probability": 0.599609375}, {"start": 4309.43, "end": 4309.85, "word": " اس", "probability": 0.95068359375}, {"start": 4309.85, "end": 4310.43, "word": " تربية", "probability": 0.97607421875}, {"start": 4310.43, "end": 4310.97, "word": " ناقص", "probability": 0.989013671875}, {"start": 4310.97, "end": 4311.37, "word": " مين", "probability": 0.948974609375}], "temperature": 1.0}, {"id": 178, "seek": 432793, "start": 4311.81, "end": 4327.93, "text": "ب تربية قبل شوية قولتلكم good exercise ل plus ل cosine ا ت قولتلكم S على S تربية زائد ب تربية مش ناقص في حال تلاقوش ناقص في حال تلاقوش cosine زائد", "tokens": [3555, 6055, 25513, 10632, 12174, 36150, 13412, 2407, 10632, 12174, 12610, 2655, 23275, 2304, 665, 5380, 5296, 1804, 5296, 23565, 1975, 6055, 12174, 12610, 2655, 23275, 2304, 318, 15844, 318, 6055, 25513, 10632, 30767, 16373, 3215, 4724, 6055, 25513, 10632, 37893, 8717, 995, 4587, 9381, 8978, 11331, 6027, 6055, 15040, 4587, 2407, 8592, 8717, 995, 4587, 9381, 8978, 11331, 6027, 6055, 15040, 4587, 2407, 8592, 23565, 30767, 16373, 3215], "avg_logprob": -0.2573660578046526, "compression_ratio": 1.686131386861314, "no_speech_prob": 0.0, "words": [{"start": 4311.81, "end": 4312.05, "word": "ب", "probability": 0.180419921875}, {"start": 4312.05, "end": 4312.59, "word": " تربية", "probability": 0.6603190104166666}, {"start": 4312.59, "end": 4312.97, "word": " قبل", "probability": 0.822509765625}, {"start": 4312.97, "end": 4313.39, "word": " شوية", "probability": 0.7892252604166666}, {"start": 4313.39, "end": 4314.01, "word": " قولتلكم", "probability": 0.74072265625}, {"start": 4314.01, "end": 4314.25, "word": " good", "probability": 0.75341796875}, {"start": 4314.25, "end": 4315.47, "word": " exercise", "probability": 0.94873046875}, {"start": 4315.47, "end": 4316.03, "word": " ل", "probability": 0.5224609375}, {"start": 4316.03, "end": 4316.51, "word": " plus", "probability": 0.464111328125}, {"start": 4316.51, "end": 4316.81, "word": " ل", "probability": 0.94970703125}, {"start": 4316.81, "end": 4317.73, "word": " cosine", "probability": 0.876953125}, {"start": 4317.73, "end": 4318.43, "word": " ا", "probability": 0.2431640625}, {"start": 4318.43, "end": 4318.69, "word": " ت", "probability": 0.4248046875}, {"start": 4318.69, "end": 4319.83, "word": " قولتلكم", "probability": 0.9119140625}, {"start": 4319.83, "end": 4320.23, "word": " S", "probability": 0.37158203125}, {"start": 4320.23, "end": 4320.65, "word": " على", "probability": 0.76611328125}, {"start": 4320.65, "end": 4321.03, "word": " S", "probability": 0.90966796875}, {"start": 4321.03, "end": 4321.65, "word": " تربية", "probability": 0.9305013020833334}, {"start": 4321.65, "end": 4322.67, "word": " زائد", "probability": 0.9078776041666666}, {"start": 4322.67, "end": 4322.85, "word": " ب", "probability": 0.9150390625}, {"start": 4322.85, "end": 4323.35, "word": " تربية", "probability": 0.8834635416666666}, {"start": 4323.35, "end": 4323.57, "word": " مش", "probability": 0.90185546875}, {"start": 4323.57, "end": 4324.21, "word": " ناقص", "probability": 0.98193359375}, {"start": 4324.21, "end": 4324.59, "word": " في", "probability": 0.89111328125}, {"start": 4324.59, "end": 4324.77, "word": " حال", "probability": 0.99072265625}, {"start": 4324.77, "end": 4325.17, "word": " تلاقوش", "probability": 0.721533203125}, {"start": 4325.17, "end": 4325.69, "word": " ناقص", "probability": 0.9925537109375}, {"start": 4325.69, "end": 4325.85, "word": " في", "probability": 0.89013671875}, {"start": 4325.85, "end": 4326.11, "word": " حال", "probability": 0.99609375}, {"start": 4326.11, "end": 4326.35, "word": " تلاقوش", "probability": 0.87861328125}, {"start": 4326.35, "end": 4327.01, "word": " cosine", "probability": 0.50927734375}, {"start": 4327.01, "end": 4327.93, "word": " زائد", "probability": 0.9671223958333334}], "temperature": 1.0}, {"id": 179, "seek": 435358, "start": 4333.04, "end": 4353.58, "text": "نمرابيج أخد حاصل ضرب الإتنين يبجى أنا بدى لابلاسي ترانسفورم لل E أس AT في مين؟ في E أس BT زائد E أس ناقص BT كله على جداش على الإتنين", "tokens": [1863, 29973, 16758, 1829, 7435, 5551, 9778, 3215, 11331, 33546, 1211, 48812, 25513, 33688, 2655, 1863, 9957, 7251, 3555, 7435, 7578, 41850, 47525, 7578, 5296, 16758, 15040, 3794, 1829, 6055, 2288, 7649, 3794, 5172, 13063, 2304, 24976, 462, 5551, 3794, 8872, 8978, 3714, 9957, 22807, 8978, 462, 5551, 3794, 31144, 30767, 16373, 3215, 462, 5551, 3794, 8717, 995, 4587, 9381, 31144, 28242, 3224, 15844, 10874, 3215, 33599, 15844, 33688, 2655, 1863, 9957], "avg_logprob": -0.2705479419394715, "compression_ratio": 1.527027027027027, "no_speech_prob": 0.0, "words": [{"start": 4333.04, "end": 4334.08, "word": "نمرابيج", "probability": 0.6048828125}, {"start": 4334.08, "end": 4334.56, "word": " أخد", "probability": 0.7898763020833334}, {"start": 4334.56, "end": 4335.26, "word": " حاصل", "probability": 0.8444010416666666}, {"start": 4335.26, "end": 4335.64, "word": " ضرب", "probability": 0.971923828125}, {"start": 4335.64, "end": 4336.38, "word": " الإتنين", "probability": 0.7899169921875}, {"start": 4336.38, "end": 4337.4, "word": " يبجى", "probability": 0.650146484375}, {"start": 4337.4, "end": 4337.78, "word": " أنا", "probability": 0.6923828125}, {"start": 4337.78, "end": 4338.38, "word": " بدى", "probability": 0.697021484375}, {"start": 4338.38, "end": 4339.34, "word": " لابلاسي", "probability": 0.73154296875}, {"start": 4339.34, "end": 4340.74, "word": " ترانسفورم", "probability": 0.7581612723214286}, {"start": 4340.74, "end": 4341.36, "word": " لل", "probability": 0.845703125}, {"start": 4341.36, "end": 4342.06, "word": " E", "probability": 0.634765625}, {"start": 4342.06, "end": 4342.58, "word": " أس", "probability": 0.5587158203125}, {"start": 4342.58, "end": 4343.64, "word": " AT", "probability": 0.8212890625}, {"start": 4343.64, "end": 4344.24, "word": " في", "probability": 0.78369140625}, {"start": 4344.24, "end": 4345.06, "word": " مين؟", "probability": 0.6412760416666666}, {"start": 4345.06, "end": 4345.32, "word": " في", "probability": 0.82666015625}, {"start": 4345.32, "end": 4345.76, "word": " E", "probability": 0.9541015625}, {"start": 4345.76, "end": 4346.44, "word": " أس", "probability": 0.973388671875}, {"start": 4346.44, "end": 4347.2, "word": " BT", "probability": 0.8994140625}, {"start": 4347.2, "end": 4348.28, "word": " زائد", "probability": 0.7605794270833334}, {"start": 4348.28, "end": 4348.6, "word": " E", "probability": 0.9873046875}, {"start": 4348.6, "end": 4348.96, "word": " أس", "probability": 0.949462890625}, {"start": 4348.96, "end": 4349.5, "word": " ناقص", "probability": 0.975830078125}, {"start": 4349.5, "end": 4350.34, "word": " BT", "probability": 0.8876953125}, {"start": 4350.34, "end": 4350.98, "word": " كله", "probability": 0.92236328125}, {"start": 4350.98, "end": 4351.12, "word": " على", "probability": 0.78515625}, {"start": 4351.12, "end": 4351.8, "word": " جداش", "probability": 0.8068033854166666}, {"start": 4351.8, "end": 4352.76, "word": " على", "probability": 0.433837890625}, {"start": 4352.76, "end": 4353.58, "word": " الإتنين", "probability": 0.9720458984375}], "temperature": 1.0}, {"id": 180, "seek": 437814, "start": 4354.44, "end": 4378.14, "text": "يبقى هذا الكلام بده يساوي ل plus transform ل نص في ال E أس A زائد ال B يبقى A زائد ال B في T زائد نص في E أس A ناقص ال B كله في من؟ في T", "tokens": [1829, 3555, 4587, 7578, 23758, 2423, 28820, 10943, 47525, 3224, 7251, 3794, 995, 45865, 5296, 1804, 4088, 5296, 8717, 9381, 8978, 2423, 462, 5551, 3794, 316, 30767, 16373, 3215, 2423, 363, 7251, 3555, 4587, 7578, 316, 30767, 16373, 3215, 2423, 363, 8978, 314, 30767, 16373, 3215, 8717, 9381, 8978, 462, 5551, 3794, 316, 8717, 995, 4587, 9381, 2423, 363, 28242, 3224, 8978, 9154, 22807, 8978, 314], "avg_logprob": -0.1607975790749735, "compression_ratio": 1.5289855072463767, "no_speech_prob": 0.0, "words": [{"start": 4354.44, "end": 4355.04, "word": "يبقى", "probability": 0.915283203125}, {"start": 4355.04, "end": 4355.32, "word": " هذا", "probability": 0.91455078125}, {"start": 4355.32, "end": 4356.02, "word": " الكلام", "probability": 0.93408203125}, {"start": 4356.02, "end": 4356.54, "word": " بده", "probability": 0.50006103515625}, {"start": 4356.54, "end": 4357.28, "word": " يساوي", "probability": 0.9710693359375}, {"start": 4357.28, "end": 4357.76, "word": " ل", "probability": 0.85693359375}, {"start": 4357.76, "end": 4358.32, "word": " plus", "probability": 0.2320556640625}, {"start": 4358.32, "end": 4359.4, "word": " transform", "probability": 0.6240234375}, {"start": 4359.4, "end": 4359.76, "word": " ل", "probability": 0.93896484375}, {"start": 4359.76, "end": 4360.32, "word": " نص", "probability": 0.925048828125}, {"start": 4360.32, "end": 4361.22, "word": " في", "probability": 0.8427734375}, {"start": 4361.22, "end": 4361.54, "word": " ال", "probability": 0.462890625}, {"start": 4361.54, "end": 4361.94, "word": " E", "probability": 0.61865234375}, {"start": 4361.94, "end": 4362.68, "word": " أس", "probability": 0.644775390625}, {"start": 4362.68, "end": 4363.12, "word": " A", "probability": 0.45068359375}, {"start": 4363.12, "end": 4364.28, "word": " زائد", "probability": 0.765869140625}, {"start": 4364.28, "end": 4364.54, "word": " ال", "probability": 0.74267578125}, {"start": 4364.54, "end": 4364.8, "word": " B", "probability": 0.9296875}, {"start": 4364.8, "end": 4366.18, "word": " يبقى", "probability": 0.9722900390625}, {"start": 4366.18, "end": 4366.68, "word": " A", "probability": 0.81494140625}, {"start": 4366.68, "end": 4367.66, "word": " زائد", "probability": 0.9723307291666666}, {"start": 4367.66, "end": 4367.98, "word": " ال", "probability": 0.818359375}, {"start": 4367.98, "end": 4368.34, "word": " B", "probability": 0.9853515625}, {"start": 4368.34, "end": 4368.8, "word": " في", "probability": 0.9091796875}, {"start": 4368.8, "end": 4369.44, "word": " T", "probability": 0.89501953125}, {"start": 4369.44, "end": 4370.76, "word": " زائد", "probability": 0.97607421875}, {"start": 4370.76, "end": 4371.4, "word": " نص", "probability": 0.985595703125}, {"start": 4371.4, "end": 4372.2, "word": " في", "probability": 0.96484375}, {"start": 4372.2, "end": 4372.72, "word": " E", "probability": 0.97705078125}, {"start": 4372.72, "end": 4373.46, "word": " أس", "probability": 0.98486328125}, {"start": 4373.46, "end": 4373.94, "word": " A", "probability": 0.9814453125}, {"start": 4373.94, "end": 4374.88, "word": " ناقص", "probability": 0.9466552734375}, {"start": 4374.88, "end": 4375.18, "word": " ال", "probability": 0.97119140625}, {"start": 4375.18, "end": 4375.62, "word": " B", "probability": 0.9755859375}, {"start": 4375.62, "end": 4376.56, "word": " كله", "probability": 0.97412109375}, {"start": 4376.56, "end": 4376.7, "word": " في", "probability": 0.97509765625}, {"start": 4376.7, "end": 4377.52, "word": " من؟", "probability": 0.74560546875}, {"start": 4377.52, "end": 4377.74, "word": " في", "probability": 0.9697265625}, {"start": 4377.74, "end": 4378.14, "word": " T", "probability": 0.95263671875}], "temperature": 1.0}, {"id": 181, "seek": 440968, "start": 4380.28, "end": 4409.68, "text": "هذا الكلام يساوي نص لبلاس ترانس فورم لل E أس A زائد ال B في T من خاصية ال linearity زائد نص لبلاس ترانس فورم لل E أس A ناقص ال B في T هذا الكلام يساوي نص في طلعيني من هذه", "tokens": [3224, 15730, 2423, 28820, 10943, 7251, 3794, 995, 45865, 8717, 9381, 5296, 3555, 15040, 3794, 6055, 2288, 7649, 3794, 6156, 13063, 2304, 24976, 462, 5551, 3794, 316, 30767, 16373, 3215, 2423, 363, 8978, 314, 9154, 16490, 33546, 10632, 2423, 8213, 507, 30767, 16373, 3215, 8717, 9381, 5296, 3555, 15040, 3794, 6055, 2288, 7649, 3794, 6156, 13063, 2304, 24976, 462, 5551, 3794, 316, 8717, 995, 4587, 9381, 2423, 363, 8978, 314, 23758, 2423, 28820, 10943, 7251, 3794, 995, 45865, 8717, 9381, 8978, 23032, 1211, 3615, 9957, 1829, 9154, 29538], "avg_logprob": -0.15335322497935777, "compression_ratio": 1.88, "no_speech_prob": 0.0, "words": [{"start": 4380.28, "end": 4380.68, "word": "هذا", "probability": 0.84423828125}, {"start": 4380.68, "end": 4381.18, "word": " الكلام", "probability": 0.9363606770833334}, {"start": 4381.18, "end": 4382.0, "word": " يساوي", "probability": 0.9564208984375}, {"start": 4382.0, "end": 4382.98, "word": " نص", "probability": 0.951416015625}, {"start": 4382.98, "end": 4384.14, "word": " لبلاس", "probability": 0.76708984375}, {"start": 4384.14, "end": 4384.86, "word": " ترانس", "probability": 0.77197265625}, {"start": 4384.86, "end": 4385.38, "word": " فورم", "probability": 0.7732747395833334}, {"start": 4385.38, "end": 4386.14, "word": " لل", "probability": 0.72900390625}, {"start": 4386.14, "end": 4386.5, "word": " E", "probability": 0.7197265625}, {"start": 4386.5, "end": 4387.06, "word": " أس", "probability": 0.6337890625}, {"start": 4387.06, "end": 4387.48, "word": " A", "probability": 0.7900390625}, {"start": 4387.48, "end": 4388.36, "word": " زائد", "probability": 0.87939453125}, {"start": 4388.36, "end": 4388.68, "word": " ال", "probability": 0.8115234375}, {"start": 4388.68, "end": 4389.22, "word": " B", "probability": 0.80224609375}, {"start": 4389.22, "end": 4389.64, "word": " في", "probability": 0.8759765625}, {"start": 4389.64, "end": 4390.1, "word": " T", "probability": 0.89990234375}, {"start": 4390.1, "end": 4390.9, "word": " من", "probability": 0.87353515625}, {"start": 4390.9, "end": 4391.44, "word": " خاصية", "probability": 0.9913736979166666}, {"start": 4391.44, "end": 4391.64, "word": " ال", "probability": 0.93603515625}, {"start": 4391.64, "end": 4392.36, "word": " linearity", "probability": 0.794677734375}, {"start": 4392.36, "end": 4393.66, "word": " زائد", "probability": 0.8753255208333334}, {"start": 4393.66, "end": 4394.38, 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\ No newline at end of file
diff --git a/PL9fwy3NUQKwa8ZDfSFGn6H8xVFLzqmCZC/1myyZiBOvdQ_raw.srt b/PL9fwy3NUQKwa8ZDfSFGn6H8xVFLzqmCZC/1myyZiBOvdQ_raw.srt
new file mode 100644
index 0000000000000000000000000000000000000000..671196293f02e10b69b41d2c3493f2f82702ed27
--- /dev/null
+++ b/PL9fwy3NUQKwa8ZDfSFGn6H8xVFLzqmCZC/1myyZiBOvdQ_raw.srt
@@ -0,0 +1,2936 @@
+1
+00:00:10,060 --> 00:00:17,020
+بسم الله الرحمن الرحيمنبدأ اليوم في آخر chapter في
+
+2
+00:00:17,020 --> 00:00:21,760
+المقرر ان شاء الله هو chapter 6 chapter 6 بتحدث عن
+
+3
+00:00:21,760 --> 00:00:27,700
+Laplace transforms تحويلات Laplace عالم فرنسي اسمه
+
+4
+00:00:27,700 --> 00:00:33,480
+Laplace وعمل التحويلات هذه شو فايدة هذه التحويلات
+
+5
+00:00:33,480 --> 00:00:39,760
+تبسيط وضع الدالة اللي عندنا إلى دالة أسهل منهافي
+
+6
+00:00:39,760 --> 00:00:43,020
+التعامل يبقى هي الفكرة الأساسية يكون عندها
+
+7
+00:00:43,020 --> 00:00:46,920
+function ال function هذا ممكن أستبدلها ب function
+
+8
+00:00:46,920 --> 00:00:52,080
+مكافئة لها لكن شكل ال function الجديدة هي أبسط من
+
+9
+00:00:52,080 --> 00:00:56,400
+من شكل ال function الأصلية يبقى هذا الفكرة
+
+10
+00:00:56,400 --> 00:01:03,040
+الأساسية لهذا الموضوعبعد تعريف للابلاس ترانسفورم
+
+11
+00:01:03,040 --> 00:01:08,660
+بحل
+
+12
+00:01:08,660 --> 00:01:13,740
+المعادلات التفاضلية من الرتبة التانية من الرتبة
+
+13
+00:01:13,740 --> 00:01:19,480
+الرابعة من الرتبة التالتة من الرتبة الرابعةيبقى
+
+14
+00:01:19,480 --> 00:01:23,200
+هذا موضوع ال chapter هذا in general لكن اول
+
+15
+00:01:23,200 --> 00:01:27,080
+section ل Laplace transform مش هندخل فيه في حل
+
+16
+00:01:27,080 --> 00:01:31,660
+المعادلات التفاضلية لكن هنشوف كيف عمليا روح نحسب
+
+17
+00:01:31,660 --> 00:01:37,000
+Laplace transform لدوال المختلفة اذا بدا نعطي
+
+18
+00:01:37,000 --> 00:01:42,000
+تعريف ل Laplace transform نعطي تعريف لنوع جديد من
+
+19
+00:01:42,000 --> 00:01:46,580
+ال functions نشوف وقت ايش بيكون Laplace transform
+
+20
+00:01:46,580 --> 00:01:53,420
+exist لدالةما ثم بعد ذلك نذهب الى أمثلة لكيفية
+
+21
+00:01:53,420 --> 00:01:58,480
+حساب Laplace transform للدوال المختلفة اذا نعود
+
+22
+00:01:58,480 --> 00:02:02,860
+للتعريف لـ Laplace transform يقول يفترض ان عندك
+
+23
+00:02:02,860 --> 00:02:09,120
+دالة F small of T معرفة على الفترة من صفر الى
+
+24
+00:02:09,120 --> 00:02:15,080
+infinity يعني على كل T الموجبة يبقى كأننا نص
+
+25
+00:02:15,080 --> 00:02:21,810
+اليمين تبعينطبعا محور X دي لبلاس transform لدالة F
+
+26
+00:02:21,810 --> 00:02:27,370
+denoted by يبقى تحويل لبلاس لدالة F حديها الرمز L
+
+27
+00:02:27,370 --> 00:02:35,420
+وبين جثيم متوسطات بحط F of Tهذا رمز او الرمز اللي
+
+28
+00:02:35,420 --> 00:02:39,980
+عندنا ده capital F of S مش F small ،اللحظة اللي
+
+29
+00:02:39,980 --> 00:02:44,040
+جوا هنا F small of T دي F capital of S يبقى انا
+
+30
+00:02:44,040 --> 00:02:51,220
+عندي رمزين للابلاسات transform لدالة F of Tلأ بلاس
+
+31
+00:02:51,220 --> 00:02:58,660
+لل F of T أو F of S هذا
+
+32
+00:02:58,660 --> 00:03:07,380
+لأ بلاس ال transform is defined by بقول لأ بلاس
+
+33
+00:03:07,380 --> 00:03:14,130
+لدلة F of T بين قوسين متوسطين عملياهي تكامل من
+
+34
+00:03:14,130 --> 00:03:19,230
+zero إلى infinity لل E اصناق ST لل F of T DT يعني
+
+35
+00:03:19,230 --> 00:03:22,430
+ايش؟ يعني الدلة اللى بدي اوجد لها Laplace
+
+36
+00:03:22,430 --> 00:03:26,110
+Transform بادرح بدربها في ال exponential function
+
+37
+00:03:26,110 --> 00:03:32,490
+E اصناق ST وبكامل حصل ضرب الدلتين من وين اللي وين
+
+38
+00:03:32,940 --> 00:03:38,720
+من صفر إلى infinity الآن هذا تكامل محدود تمام يبقى
+
+39
+00:03:38,720 --> 00:03:43,440
+لما اكمل الدالة هتطلع عندي دلة بدلالة ال S ومن هنا
+
+40
+00:03:43,440 --> 00:03:49,240
+قلنا capital F of S تمام يعني بعد ما اقوم باجراء
+
+41
+00:03:49,240 --> 00:03:53,660
+عملية التكامل هتبقى الدالة عند بني بدلة S لإن احا
+
+42
+00:03:53,660 --> 00:03:59,260
+عوض بحدود التكامل بدل T إذا S هتبقى هي ظهر في
+
+43
+00:03:59,260 --> 00:04:00,660
+المثل ومن هنا بقول
+
+44
+00:04:05,460 --> 00:04:12,660
+لو جت واطلعت في هذا التكامل بلاحظ أن أحد حدود
+
+45
+00:04:12,660 --> 00:04:17,660
+التكامل infinity واحنا في calculus بيقولنا بقول عن
+
+46
+00:04:17,660 --> 00:04:23,140
+التكامل improper integral إذا كان أحد حدود التكامل
+
+47
+00:04:23,370 --> 00:04:29,650
+أو كلاهما infinity أو الدالة مش معرفة عند نقطة
+
+48
+00:04:29,650 --> 00:04:35,190
+وهذه النقطة موجودة داخل فترة التكامل المحدود،
+
+49
+00:04:35,190 --> 00:04:39,770
+مظبوط؟ نقطة تانية خلّينا منها يبقى بدنا نيجي عند
+
+50
+00:04:39,770 --> 00:04:43,630
+النقطة الأولى لو كان أحد حدود التكامل أو كلاهما
+
+51
+00:04:43,630 --> 00:04:49,150
+infinity وكمان كلاهما بدنا نشييها لو كان أحد حدود
+
+52
+00:04:49,150 --> 00:04:54,380
+التكامل هو infinityيبقى تكامل من وين من zero إلى
+
+53
+00:04:54,380 --> 00:04:59,740
+infinity يبقى هذا improper integral فقط بسبب وجود
+
+54
+00:04:59,740 --> 00:05:04,440
+من ال infinity اللي عندنا لو رجعنا بالذاكرة إلى
+
+55
+00:05:04,440 --> 00:05:07,900
+الوراء إلى calculus بيه ال improper integral
+
+56
+00:05:07,900 --> 00:05:14,540
+بنحسبه as a limit فبروح بقول التكامل هذا هو limit
+
+57
+00:05:14,540 --> 00:05:20,270
+بشيل ال infinity و بحط بدالها real number aوبخلّي
+
+58
+00:05:20,270 --> 00:05:23,430
+ال a لاخد ال limit لما ال a بدأ تروح ل infinity
+
+59
+00:05:23,430 --> 00:05:28,470
+يعني انا بروح بكامل التكامل هذا عادي جدا بأي طريقة
+
+60
+00:05:28,470 --> 00:05:32,690
+من طرق التكامل التي سبقت دراستها بعوب بحدود
+
+61
+00:05:32,690 --> 00:05:37,070
+التكامل وبعد ما عوب باخد ال limit لما a بدأ تروح
+
+62
+00:05:37,070 --> 00:05:42,050
+لوين لل ما لا نهاية لما ناخد هذه ال limit احتمال
+
+63
+00:05:42,050 --> 00:05:47,240
+تطلع قيمة عدديةوإحتمال تطلع infinity أو سالب
+
+64
+00:05:47,240 --> 00:05:52,640
+infinity، مظبوط؟ إذا طلعت قيمة عددية بقول التكامل
+
+65
+00:05:52,640 --> 00:05:57,000
+converge، وإذا ما طلعتش قيمة عددية يطلع infinity
+
+66
+00:05:57,000 --> 00:06:01,000
+ولا سالب infinity بقول التكامل ماله diverge، هذه
+
+67
+00:06:01,000 --> 00:06:05,920
+معلوماتنا من Calculus Bالتكامل اللي عندنا هو الـ
+
+68
+00:06:05,920 --> 00:06:09,100
+Improper Integral بحسبه في الطريقة اللي عندنا هذا
+
+69
+00:06:09,100 --> 00:06:13,240
+التكامل هو الـ Converge إذا لم يكن هناك مقاومة
+
+70
+00:06:13,240 --> 00:06:18,420
+وإذا لم يكن هناك مقاومة بقول عنه الـ Diverge يبقى
+
+71
+00:06:18,420 --> 00:06:21,100
+هذا الـ Diverge إذا لم يكن هناك مقاومة
+
+72
+00:06:25,460 --> 00:06:31,520
+يبقى اللي فوق هذا تعريف من Laplace transform لو
+
+73
+00:06:31,520 --> 00:06:35,060
+قال لك سواء اتي ل Laplace transform لدالة بروح
+
+74
+00:06:35,060 --> 00:06:40,020
+بضرب الدالة دي في E وسنقص ST و بكامل من zero إلى
+
+75
+00:06:40,020 --> 00:06:43,780
+infinity و بعدين بشغل شغل ال improper integral
+
+76
+00:06:43,780 --> 00:06:48,940
+يعني كأنهالمحاضرة تبعتنا هذه هي محاضرة improper
+
+77
+00:06:48,940 --> 00:06:54,220
+integrals يعني كأن احنا بدنا نعود الـ improper
+
+78
+00:06:54,220 --> 00:06:57,800
+integral اللي في chapter 8 اللي هو اخر section من
+
+79
+00:06:57,800 --> 00:07:02,860
+chapter 8 من calculus B طيب في تعريف جديد هذا
+
+80
+00:07:02,860 --> 00:07:07,900
+ماكناش بنعرفه في calculus B function f is said to
+
+81
+00:07:07,900 --> 00:07:14,020
+be piecewise continuous ايش معناه piece؟ قطةيبقى
+
+82
+00:07:14,020 --> 00:07:19,160
+لما أقول piecewise continuous كأنها مقطعة إلى
+
+83
+00:07:19,160 --> 00:07:24,240
+أجزاء على كل جزء، الدالة بتبقى دالة متاصلة، يبقى
+
+84
+00:07:24,240 --> 00:07:26,500
+هي المقصود بال piecewise continuous، أنا عندي
+
+85
+00:07:26,500 --> 00:07:31,300
+فترة، الفترة مجزة إلى فترتين، إلى تلاتة، إلى أربع،
+
+86
+00:07:31,300 --> 00:07:35,660
+إلى خمسة، إلى عشرة، إلى إيه من الفترات، على كل
+
+87
+00:07:35,660 --> 00:07:40,660
+فترة من هذه الفترات، الدالة بتبقى معاهاcontinuous
+
+88
+00:07:40,660 --> 00:07:44,140
+مايعادى عند النقاط اللى عشان اللى عندها
+
+89
+00:07:44,140 --> 00:07:50,060
+discontinuity دى بجهة دى بقول كإنها متصلة جزئيا ده
+
+90
+00:07:50,060 --> 00:07:56,640
+لامقطعة على كل قطعة بتفجيها ده لامتصلةإذا كانت
+
+91
+00:07:56,640 --> 00:08:00,120
+متصلة
+
+92
+00:08:00,120 --> 00:08:06,820
+جزئيا أو على قطع on an interval على الفترة T من
+
+93
+00:08:06,820 --> 00:08:13,040
+Alpha إلى Beta if it is continuous إذا كانت متصلة
+
+94
+00:08:13,040 --> 00:08:16,560
+there هناك يعني على الفترة من Alpha إلى Beta
+
+95
+00:08:16,560 --> 00:08:22,730
+exceptما عدا for a finite number لرقم محدود of
+
+96
+00:08:22,730 --> 00:08:28,130
+jump discontinuities يبقى بيكون عندنا عدم اتصال
+
+97
+00:08:28,130 --> 00:08:34,250
+بقفزة لأن انواع ال discontinuity وممكن نقول في
+
+98
+00:08:34,250 --> 00:08:39,670
+calculus ان ال discontinuity ممكن نعمله removable
+
+99
+00:08:39,670 --> 00:08:46,070
+إزالة تمام؟ يعني لو كان عند نقطة ما في
+
+100
+00:08:46,070 --> 00:08:52,480
+discontinuityمش jump مش jump لا يمكن ازالته بس لو
+
+101
+00:08:52,480 --> 00:08:57,020
+كان تجويف عند نقطة بروح بعرف ال function بطريقة
+
+102
+00:08:57,020 --> 00:09:01,180
+جديدة و باخد ال limit عندما x تروح لهذه النقطة و
+
+103
+00:09:01,180 --> 00:09:05,560
+بعرف الدالة ك piecewise function دالة مكونة من
+
+104
+00:09:05,560 --> 00:09:09,040
+جزئين وبالتالي بيخلي ال discontinuity بيخلي قيمة
+
+105
+00:09:09,040 --> 00:09:12,040
+الدالة عند هذه النقطة تساوي ال limit وبالتالي
+
+106
+00:09:12,040 --> 00:09:15,700
+استطعت ازالة ال discontinuity لكن ال discontinuity
+
+107
+00:09:15,700 --> 00:09:19,700
+اللي انا معلومJump discontinuity في كمة
+
+108
+00:09:19,700 --> 00:09:24,620
+discontinuity تالت اللي هو infinite discontinuity
+
+109
+00:09:24,620 --> 00:09:27,460
+يعني ال discontinuity اللي بيحصل عند اللي هو
+
+110
+00:09:27,460 --> 00:09:31,220
+المالة نهاية يبقى هذا اللي لا يمكن ازالته و ال
+
+111
+00:09:31,220 --> 00:09:34,520
+jump discontinuity اللي لا يمكن ازالته و النوع
+
+112
+00:09:34,520 --> 00:09:38,040
+التالت هو اللي بنزيله مالناهش علاقة فيه احنا بس
+
+113
+00:09:38,040 --> 00:09:42,360
+بدنا اللي في النص اللي هو jump discontinuityيبقى
+
+114
+00:09:42,360 --> 00:09:46,840
+فينا jump discontinuity عند عدد محدود نوضح هذا
+
+115
+00:09:46,840 --> 00:09:50,840
+الكلام من خلال الرصم اللي قدامنا بقول الدالة اللي
+
+116
+00:09:50,840 --> 00:09:59,800
+عندنا هذه اللي هي ال ال F is piecewise
+
+117
+00:10:00,410 --> 00:10:05,650
+الشكل اللي عندنا هو discontinuous on الفترة من
+
+118
+00:10:05,650 --> 00:10:11,330
+alpha لغاية beta بالشكل اللي عندنا هنا يبقى عند ال
+
+119
+00:10:11,330 --> 00:10:15,330
+alpha في اتصال من جهة اليمنان و beta في اتصال من
+
+120
+00:10:15,330 --> 00:10:19,650
+جهة الشمال عند T1 و T2 في discontinuity و
+
+121
+00:10:19,650 --> 00:10:24,110
+discontinuity هذا jumpقفزت من النقطة هذه إلى
+
+122
+00:10:24,110 --> 00:10:28,690
+النقطة هذه، من هنا قفزت من هنا لهنا، من هنا قفزت
+
+123
+00:10:28,690 --> 00:10:32,630
+لهنا، بعد هيك صارت اللي اللي هو ال continuity هذا،
+
+124
+00:10:32,630 --> 00:10:38,970
+يبقى على الخط المائل هذا continuous على القوس هذا
+
+125
+00:10:38,970 --> 00:10:43,750
+continuous على القوس هذا continuous، لكن عند T1 و
+
+126
+00:10:43,750 --> 00:10:48,870
+T2في عندي jump discontinuity يبقى هذه بسميها
+
+127
+00:10:48,870 --> 00:10:55,150
+piecewise function طيب الآن بنجي للنقطة الثانية
+
+128
+00:10:55,150 --> 00:11:02,750
+وهي متى يمكن نعمل transform لدى اللى تم شروط
+
+129
+00:11:02,750 --> 00:11:07,210
+اللازم تتحقق في ال function طبعا احنا لن نبحث هذه
+
+130
+00:11:07,210 --> 00:11:11,950
+الشروط في المسائل لأن كل المسائل اللى معطيه عندنا
+
+131
+00:11:11,950 --> 00:11:15,500
+في الكتاب فنطبق عليه هذه الشروط وبالتاليبروح ما
+
+132
+00:11:15,500 --> 00:11:20,300
+علينا إلا نحسب لبلاس ال transform مباشرة بقول
+
+133
+00:11:20,300 --> 00:11:25,040
+افترض ان ال F شرطين F بيسوازي continuous يعني
+
+134
+00:11:25,040 --> 00:11:29,060
+بالشكل اللي عندنا هذا تمام يبقى وين on the
+
+135
+00:11:29,060 --> 00:11:33,220
+interval من zero ل A for any positive number A
+
+136
+00:11:33,220 --> 00:11:39,100
+يعني أخدنا من عند ال zero لأي رقم بدكي يوجه فيه
+
+137
+00:11:39,100 --> 00:11:44,510
+عند أي رقم لجيت الدالة مقطعة إلى جزئينلثلاث قطع
+
+138
+00:11:44,510 --> 00:11:48,210
+لاربع قطع لعشر قطع جد ما يكون يكون piecewise
+
+139
+00:11:48,210 --> 00:11:53,530
+continuous النقطة الثانية أخدت absolute value لمين
+
+140
+00:11:53,530 --> 00:12:01,750
+لل F of T وجدت أقل من أو يسوى K في E أس Tلما أقول
+
+141
+00:12:01,750 --> 00:12:06,070
+أخدت absolute value ل F of T يعني عمرها ما هتطلع
+
+142
+00:12:06,070 --> 00:12:11,270
+سالبة صحيح ولا لا؟ يبقى الرقم اللي على اليمين هذا
+
+143
+00:12:11,270 --> 00:12:16,630
+ليس يمكن أن يكون سالب لأن هذه أقل منه طبعا أعرف أن
+
+144
+00:12:16,630 --> 00:12:21,990
+ال exponential دائما و أبدا موجب إذن ال Kدائما و
+
+145
+00:12:21,990 --> 00:12:26,270
+أبدا اش بدى يكون موجب حتى يكون الكلام الصحيح حتى
+
+146
+00:12:26,270 --> 00:12:31,450
+ال absolute هذا يكون أقل من أو يسوى من هذا الرقم
+
+147
+00:12:31,450 --> 00:12:36,610
+where T أكبر من أو يسوى M يعني انا ممكن اخد T من
+
+148
+00:12:36,610 --> 00:12:40,630
+عند حد معين اخدت ال T من هنا من وين؟ من عند ال
+
+149
+00:12:40,630 --> 00:12:45,270
+alpha يبقى انا عندي T أكبر من alphaيبقى Alpha رقم
+
+150
+00:12:45,270 --> 00:12:49,270
+موجب أخدته من عند النقطة هذه يبقى هذا رقم موجب
+
+151
+00:12:49,270 --> 00:12:53,390
+يبقى M بدأ تبدأ ترسم من عند النقطة هذه و نمشي وين؟
+
+152
+00:12:53,390 --> 00:12:58,710
+على اليمين يبقى where T أكبر من ما يسوى M الان K
+
+153
+00:12:58,710 --> 00:13:03,990
+والA والM ال K والA والM اللي T أكبر منها كلهم
+
+154
+00:13:03,990 --> 00:13:08,690
+real constantsزيادة على ذلك ال K و ال M are
+
+155
+00:13:08,690 --> 00:13:13,290
+necessarily positive وهذا شرط له قلت لك هذه
+
+156
+00:13:13,290 --> 00:13:17,530
+positive دائما و أبدا إذا هذه يجب أن تكون positive
+
+157
+00:13:17,530 --> 00:13:24,130
+لأن هذه absolute value مطلعش إلا قيمة موجبةطيب إذا
+
+158
+00:13:24,130 --> 00:13:28,710
+حدث ذلك تحقق قضان الشرطان يبقى دي ال aplastic
+
+159
+00:13:28,710 --> 00:13:33,250
+transform بيكون اللي هو التعريف اللي احنا حطناه
+
+160
+00:13:33,250 --> 00:13:38,270
+هنا لدى ال F of T هو capital F of this يبقى هو E
+
+161
+00:13:38,270 --> 00:13:42,550
+من التكامل من zero الى infinity لل E واس ناقص ST
+
+162
+00:13:42,550 --> 00:13:48,490
+لل F of T DT بيكون هذا exist for S greater than A
+
+163
+00:13:48,490 --> 00:13:52,150
+يبقى هذا الضمان اللي بتخلي
+
+164
+00:13:56,060 --> 00:14:00,620
+مطلوب في شغلنا نبحث هذه الضمنة لأ بيقولك هتيلي بس
+
+165
+00:14:00,620 --> 00:14:05,160
+Laplace transform لدالة الفلانية في كل مثال كتابه
+
+166
+00:14:05,160 --> 00:14:11,060
+بضل عليكي بس تحسب مين ال improper integrals طبعا
+
+167
+00:14:11,060 --> 00:14:15,370
+ضايلة خاصية عندي لLaplace transformحشير إليها بعد
+
+168
+00:14:15,370 --> 00:14:21,830
+قليل بعد أن ناخد بعض الأمثلة إذا بدأ ناخد بعض
+
+169
+00:14:21,830 --> 00:14:35,330
+الأمثلة لكيفية حساب لبلاس ترانسفورم لدالة ما حد
+
+170
+00:14:35,330 --> 00:14:40,210
+في كوبنات بتقدر تجيب لي piecewise continuous يعني
+
+171
+00:14:40,210 --> 00:14:43,110
+function تبقى piecewise
+
+172
+00:14:51,960 --> 00:14:59,580
+نقسم الـ real line الى فترة اتنين ونقسم
+
+173
+00:14:59,580 --> 00:15:04,860
+الـ real line الى فترة اتنين ونقسم الـ real line
+
+174
+00:15:04,860 --> 00:15:10,400
+الى فترة اتنين ونقسم الـ real line الى فترة اتنين
+
+175
+00:15:10,420 --> 00:15:14,540
+Positive Integer يبقى زادة أو ناقص الانبعي ما شاء
+
+176
+00:15:14,540 --> 00:15:18,380
+الله عليها مالة نهاية من الفترات لكن مااخدش مالة
+
+177
+00:15:18,380 --> 00:15:21,820
+نهاية من الفترات باخد من عند السفر إلى infinity
+
+178
+00:15:21,820 --> 00:15:27,360
+طبقا للتعريف تبعنا تمام و هكذا طيب نبدأ ناخد بعض
+
+179
+00:15:27,360 --> 00:15:38,480
+الأمثلة يبقى examples find
+
+180
+00:15:40,120 --> 00:15:50,100
+the Laplace transform for
+
+181
+00:15:50,100 --> 00:16:07,680
+each of the following functions أول سؤال بدنا نمرأ
+
+182
+00:16:07,680 --> 00:16:19,030
+أيه؟الـ F of T تساوي E أُس AT والـ T greater than
+
+183
+00:16:19,030 --> 00:16:28,590
+or equal to zero وكمان نمرة B بدنا ال F of T يساوي
+
+184
+00:16:28,590 --> 00:16:35,750
+واحد صحيح نمرة C بدنا ال F of T يساوي E أُس ناقص
+
+185
+00:16:35,750 --> 00:16:36,350
+AT
+
+186
+00:16:38,930 --> 00:16:43,950
+بنجيب لبلاس ترانسفورب لكل ذالب من الدوال السلال
+
+187
+00:16:43,950 --> 00:16:48,370
+هذول يعتبروا ثلاثة أسئلة منفصلة لكن في الحقيقة
+
+188
+00:16:48,370 --> 00:16:52,270
+سؤال واحد و هذول بنستخدم تيجيهم من مين من شكل
+
+189
+00:16:52,270 --> 00:16:58,940
+السؤال اللي عندنا يبقى باجي ل solutionوبدي اخد
+
+190
+00:16:58,940 --> 00:17:00,160
+نمرة A
+
+191
+00:17:28,440 --> 00:17:34,680
+يبقى انا طبقت التعريف تطبيقا حرفيا EOS-ST كتبتها
+
+192
+00:17:34,680 --> 00:17:39,500
+شيلت ال F of T و حطيت قيمتها ل EOSAT
+
+193
+00:17:44,420 --> 00:17:50,840
+انتجرال يبقى بده اعسبه as a limit limit وهي تكامل
+
+194
+00:17:50,840 --> 00:17:56,180
+zero بخليها زي ما هي infinity ماهواش رقم فبستبدله
+
+195
+00:17:56,180 --> 00:18:02,040
+بالرقم a و بخلي ال a تروح ل infinity هدول اللي جوا
+
+196
+00:18:02,040 --> 00:18:07,470
+يا بنات حاصل ضرب يبقاش بيحصل في الأسسمش معها جامعة
+
+197
+00:18:07,470 --> 00:18:14,290
+يعني هذه ناقص ST زائد AT ممكن أخد T عامل مشترك
+
+198
+00:18:14,290 --> 00:18:21,310
+وبالتالي يصير E أس ناقص S ناقص ATDT
+
+199
+00:18:31,310 --> 00:18:36,930
+نرجع لهذا الكلام يساوي ال limit لما ال a tends to
+
+200
+00:18:36,930 --> 00:18:41,800
+infinityتكامل الـ exponential بالـ exponential
+
+201
+00:18:41,800 --> 00:18:47,440
+itself مقسوما على تفاضل الأُس لما الأُس يكون من
+
+202
+00:18:47,440 --> 00:18:52,800
+الدرجة الأولى واضح أنه T أُس واحد يبقى الأُس عندي
+
+203
+00:18:52,800 --> 00:18:57,820
+من الدرجة الأولى يبقى النتيجة ال exponential كما
+
+204
+00:18:57,820 --> 00:19:04,800
+هي في T مقسوما على نقص ال S نقص ال A اللي هو
+
+205
+00:19:04,800 --> 00:19:11,780
+المعامل تبع من تبع ال Tيبقى هاي كاملتها تماما وهذا
+
+206
+00:19:11,780 --> 00:19:17,760
+من وين لوين من عند ال zero لغاية من ال a الآن
+
+207
+00:19:17,760 --> 00:19:23,760
+بتعوض بحدود التكامل ومن ثم تروح ناخد ال limit يبقى
+
+208
+00:19:23,760 --> 00:19:28,000
+هذا الكلام بده يسوي ال limit لما ال a tends to
+
+209
+00:19:28,000 --> 00:19:39,830
+infinity لمن؟ لل E أس ناقص S ناقص Aفي A على ناقص S
+
+210
+00:19:39,830 --> 00:19:41,770
+ناقص ال A
+
+211
+00:20:07,350 --> 00:20:15,170
+طلعيني هنا لما ال a بدها تروح ل infinity بنزلها
+
+212
+00:20:15,170 --> 00:20:19,730
+تحت بصير موجة ب infinity يعني بصير واحد على
+
+213
+00:20:19,730 --> 00:20:26,370
+infinity يبجى هذا ال term كله بروح بالسفارةيبقى
+
+214
+00:20:26,370 --> 00:20:32,670
+هذا بده صير zero ناقص مع ناقص بالصير زائد واحد على
+
+215
+00:20:32,670 --> 00:20:40,230
+S ناقص ال A يبقى النتيجة النهائية واحد على S ناقص
+
+216
+00:20:40,230 --> 00:20:47,880
+ال A وال S greater than Aليش ال S greater than A؟
+
+217
+00:20:47,880 --> 00:20:54,720
+لأن لو S كانت أقل من A، لأ صار ناقص فناقص بزائد
+
+218
+00:20:54,720 --> 00:20:59,880
+وظلت هذه في البص، وبالتالي ماكنتش نتيجة زي هيك،
+
+219
+00:20:59,880 --> 00:21:03,600
+يبقى اللي خلى النتيجة زي هيك أن S دائما و أبدا
+
+220
+00:21:03,600 --> 00:21:10,020
+greater thanيبقى من الآن فصاعدا ل plus transform
+
+221
+00:21:10,020 --> 00:21:16,060
+لل E أُس A T هو واحد على S ناقص ال A و اللحظة يا
+
+222
+00:21:16,060 --> 00:21:20,960
+بناتي ان النتيجة طلعت function في main في S كما
+
+223
+00:21:20,960 --> 00:21:26,120
+زعمنا قبل قليل ان هذه بتطلع function في main في S
+
+224
+00:21:26,120 --> 00:21:32,230
+و بضلش عندي T نهائي بالمرةبعد إجراء عملية التكامل
+
+225
+00:21:32,230 --> 00:21:38,070
+يصبح النتيجة 1 على S نقص اللي قد نقل عليها لو قلت
+
+226
+00:21:38,070 --> 00:21:44,050
+جدش ل plus transform ل E أس ثلاثة T تقوليني 1 على
+
+227
+00:21:44,050 --> 00:21:45,090
+S نقص 3
+
+228
+00:21:50,040 --> 00:21:57,760
+بنص T بيصير 1 على S ناقص نص وهكذا يبقى خلاص ماعليه
+
+229
+00:21:57,760 --> 00:22:02,800
+إلا أشيل A و أحط الرقم اللي عندنا هذا بناء عليه
+
+230
+00:22:02,800 --> 00:22:08,300
+حروح أجيب اللي هو B وC يبقى هذا اللي هو A بده يجي
+
+231
+00:22:08,300 --> 00:22:14,840
+ل B بده ل plus transform ل مين هوللواحد صحيح ولا
+
+232
+00:22:14,840 --> 00:22:21,260
+لا طيب هل ممكن احصل على الواحد من الدالة هذه لو
+
+233
+00:22:21,260 --> 00:22:27,860
+كانت ال a ب zero يبقى بصير e أس zero له بواحد يبقى
+
+234
+00:22:27,860 --> 00:22:36,460
+باجي بقوله if ال a تساوي zero then e أس at بده
+
+235
+00:22:36,460 --> 00:22:44,260
+يساوي e أس zero اللي هو واحديبقى لبلاسي ترانسفورم
+
+236
+00:22:44,260 --> 00:22:52,240
+يبقى لبلاسي ترانسفورم للواحد هو لبلاسي ترانسفورم ل
+
+237
+00:22:52,240 --> 00:23:00,120
+E أس زيرو في T يبقى مكان ال E كده شجعني؟ Zero يبقى
+
+238
+00:23:00,120 --> 00:23:08,410
+هنا واحدعلى S ناقص الـ Zero يعني واحد على S والـ S
+
+239
+00:23:08,410 --> 00:23:14,190
+greater than Zero يبقى من الأن فصاعدا يا بنات بدك
+
+240
+00:23:14,190 --> 00:23:19,230
+تعرفيه Automatic ان لابلاس ترانسفورم للواحد الصحيح
+
+241
+00:23:19,230 --> 00:23:25,190
+يسوي كدهبعد قليل هقولي قدش ل plus لل إتنين قدش ل
+
+242
+00:23:25,190 --> 00:23:29,510
+plus ل تلاتة قدش ل plus ل نص قدش ل plus ل مية و
+
+243
+00:23:29,510 --> 00:23:33,810
+هكذا تمام؟ بس خليها المعلومة هذه عندك وسنرجع لها
+
+244
+00:23:33,810 --> 00:23:39,090
+كثيرا خلال شغلنا طيب نروح الأن لنمرسى
+
+245
+00:23:53,800 --> 00:24:02,100
+نمرسى بدي لابلاس ترانسفورم للإي والسالب اتي ايش
+
+246
+00:24:02,100 --> 00:24:07,880
+افرجت عن السؤال اللى عندي بس ال a صارت بالسالب
+
+247
+00:24:07,880 --> 00:24:13,380
+يبقى انا بدي اجي على النتيجة دى واستبدل كل a بسالب
+
+248
+00:24:13,380 --> 00:24:21,280
+a بكون وصلت للنتيجة يبقى هذه باجي بقوله from part
+
+249
+00:24:21,280 --> 00:24:31,240
+aنحن لدينا لبلاس ترانسفورم لل E اص ناقص AT يسوى
+
+250
+00:24:31,240 --> 00:24:39,740
+واحد على S ناقص ناقص A يبقى
+
+251
+00:24:39,740 --> 00:24:47,580
+نتيجة واحد على S زائد Aأنا بقولش أكبر من إيه و لا
+
+252
+00:24:47,580 --> 00:24:51,900
+أصغر من إيه، مدام جامع يبقى معنا مشكلة في هذه
+
+253
+00:24:51,900 --> 00:24:57,940
+الحالة، تمام؟ طبعا هذا من أبسط أنواع الأمثلة إلا
+
+254
+00:24:57,940 --> 00:25:02,840
+لابد اللي لف ولا درم مباشر، مفيش فيه تعب، انتجلي
+
+255
+00:25:02,840 --> 00:25:09,760
+شوية مثال اتنين بدنا
+
+256
+00:25:09,760 --> 00:25:23,420
+فعينلو لا بلاس ترانسفورم لدالا صين اي تي بس
+
+257
+00:25:23,420 --> 00:25:28,460
+هذا مش كتير يبقى بده احط التعريف يبقى باجي بقوله
+
+258
+00:25:28,460 --> 00:25:33,620
+solution بدلا
+
+259
+00:25:33,620 --> 00:25:40,160
+بلاس لصين اي تييبقى sin at هي ال f of t ال
+
+260
+00:25:40,160 --> 00:25:44,860
+function اللي عندنا يبقى طبقة للتعريف integration
+
+261
+00:25:44,860 --> 00:25:55,000
+من zero ل infinity لل E أس ناقص ST ل sin at dt
+
+262
+00:25:57,900 --> 00:26:02,200
+هذا الـ Improper Integral يبقى بيطبق خاصية الـ
+
+263
+00:26:02,200 --> 00:26:06,880
+Improper Integral يبقى الـ Limit تكامل من Zero لـ
+
+264
+00:26:06,880 --> 00:26:13,420
+A لما الـ A بده تروح ل Infinity للـ E أُس ناقص ST
+
+265
+00:26:13,420 --> 00:26:23,860
+لـ Sin ATDT إذا بروح أكمل هذه المسألة كيف بنكمل
+
+266
+00:26:23,860 --> 00:26:29,720
+هذه يا بنات؟بتتجزى integration bypass يبقى بداخل U
+
+267
+00:26:29,720 --> 00:26:35,380
+ده اللى و الباقى كله بيكون DV طبعا هذه زى ما
+
+268
+00:26:35,380 --> 00:26:39,700
+بيقولوا ضرب العميان صيب اش ما تاخد صح ان اخدت ال U
+
+269
+00:26:39,700 --> 00:26:44,400
+ال exponential و ال DV ال sign ماشى ان اخدت ال U
+
+270
+00:26:44,400 --> 00:26:47,970
+ال sign و ال DV ال exponential ماشى ليش؟لأن
+
+271
+00:26:47,970 --> 00:26:52,850
+الاشتقاق أو التكامل لـSin هو Sin Cos Sin Cos و الـ
+
+272
+00:26:52,850 --> 00:26:56,030
+Exponential تكامل الله تعالى بفضل كيف ما يكون الـ
+
+273
+00:26:56,030 --> 00:27:00,490
+Exponential كمية بيبقى يا بضرب في رقم يا بجسم على
+
+274
+00:27:00,490 --> 00:27:04,890
+رقميك بإيش ماتاخده صحيح يبقى انا لو روحت في الامش
+
+275
+00:27:04,890 --> 00:27:12,030
+قولت خد ال U تساوي E أس ناقص ST و خد ال DV اللي هو
+
+276
+00:27:12,030 --> 00:27:14,870
+Sin ATDT
+
+277
+00:27:18,590 --> 00:27:25,470
+كويس يبقى ال D يبدأ تساوي ال X ما ننشل زي ما هو
+
+278
+00:27:25,470 --> 00:27:33,130
+مضروب في تفاضل ال S يبقى ناقص S في ناقص ST في ال
+
+279
+00:27:33,130 --> 00:27:39,550
+DTيبقى الـ exponential زي ما هي ضرب مشتقة الـ S
+
+280
+00:27:39,550 --> 00:27:45,390
+بالنسبة إلى T اللي هو بناقص S فمين في DT هذه بدي
+
+281
+00:27:45,390 --> 00:27:52,950
+أكاملها تكامل الصين بقداشسالب كوصين يبقى سائل V
+
+282
+00:27:52,950 --> 00:28:01,670
+تساوي سالب كوصين AT على مين على اين والزائد كونصة
+
+283
+00:28:01,670 --> 00:28:05,250
+انت ما تكتبش و بتاخديه ب zero دائما و أبدا لسهولة
+
+284
+00:28:05,250 --> 00:28:10,130
+كما درسنا في calculus B طيب الآن هذا الكلام بده
+
+285
+00:28:10,130 --> 00:28:18,280
+يساوي limit لما ال A tends to infinityبدا جى اخد U
+
+286
+00:28:18,280 --> 00:28:26,820
+في V طاليل هنا هي ناقص U في V يبقى ناقص واحد على A
+
+287
+00:28:26,820 --> 00:28:39,040
+ل E أس ناقص ST في cosine AT تمام هذا U في V ناقص
+
+288
+00:28:39,540 --> 00:28:51,520
+تكامل من Zero إلى Vداليو V ناقص Cos A T على A في
+
+289
+00:28:51,520 --> 00:29:01,960
+داليو ناقص S E أس ناقص S T في DT تمام؟ بدي أعيد
+
+290
+00:29:01,960 --> 00:29:03,340
+ترتيب المسألة
+
+291
+00:29:05,780 --> 00:29:10,300
+هذا لو السلب بقدر اناسله تحت و اخليه موجب يبقى
+
+292
+00:29:10,300 --> 00:29:16,420
+high limit لما ال a tends to infinity لمن لناقص
+
+293
+00:29:16,420 --> 00:29:24,440
+cosine at على a في ال E أُس S T و الحكي هذا من و
+
+294
+00:29:24,440 --> 00:29:33,390
+لا وين من zero لغاية a يبقى من zero لغاية aبنجي
+
+295
+00:29:33,390 --> 00:29:39,470
+لبعدها عندك سالب و سالب و سالب تلاتة سالب بسالب
+
+296
+00:29:39,470 --> 00:29:45,110
+واحد يبقى هاي السالب عندك S مقدر ثابت و ايه مقدر
+
+297
+00:29:45,110 --> 00:29:52,830
+ثابت برا التكامل يبقى ناقص S على A تكامل من zero
+
+298
+00:29:52,830 --> 00:30:01,670
+إلى A لل E أس ناقص ST ل cosine ATDT
+
+299
+00:30:05,400 --> 00:30:12,760
+طيب نجي للمقدار اللى عندنا هذا بدي أشيل كل T و أحط
+
+300
+00:30:12,760 --> 00:30:20,140
+مكانهاش A يبقى هذا الكلام بده يساوي limit لما ال A
+
+301
+00:30:20,140 --> 00:30:30,480
+tends to infinity لناقص cosine AA على AEOSSA
+
+302
+00:30:31,630 --> 00:30:37,170
+نقص مع نقص بيصير زاد بدي اشيل ال T و اضع مكانها
+
+303
+00:30:37,170 --> 00:30:41,990
+واحد يبقى ايش بيصير هنا بدي اشيل ال T و اضع مكانها
+
+304
+00:30:41,990 --> 00:30:45,990
+zero بيصير cosine صفر اللي بيبقى ال dash بواحد
+
+305
+00:30:45,990 --> 00:30:55,160
+يبقى واحدE أُس Zero واحد في A بـ A يبقى زائد واحد
+
+306
+00:30:55,160 --> 00:31:03,780
+على A ال limit للمقدار هذا كله ووصلنا ناقص S على A
+
+307
+00:31:03,780 --> 00:31:10,280
+في limit لما ال A tends to infinity لتكامل من Zero
+
+308
+00:31:10,280 --> 00:31:17,740
+إلى A لل E أس ناقص ST ل cosine ATDT
+
+309
+00:31:36,770 --> 00:31:41,990
+طيب تعالى نشوف المقدار الأول ايه بده تروح لوين؟
+
+310
+00:31:41,990 --> 00:31:49,390
+للملنها بسلب والبسط هذا محصور من وين لوين البسط
+
+311
+00:31:49,390 --> 00:31:55,630
+cos محصور من وين لوين سلب واحد يعني رقم محصور ما
+
+312
+00:31:55,630 --> 00:32:01,010
+بين الاتنين مظبوط ولا لا المقام هذا لما ايه بده
+
+313
+00:32:01,010 --> 00:32:02,850
+تروح للملنها جديش بالسيارة
+
+314
+00:32:18,650 --> 00:32:23,350
+ممكن اجيبه بطريقة تانية اروح اقول اه ال cosine
+
+315
+00:32:23,350 --> 00:32:29,120
+محصور بين سالب واحد و واحدأضرب الطرفين في 1 على a
+
+316
+00:32:29,120 --> 00:32:35,860
+في e أس s على a يبقى 1 على a e أس s في a يبقى
+
+317
+00:32:35,860 --> 00:32:41,000
+بيصير 1 على ما لا نهاية ب zero أقل من أو يسوي ال
+
+318
+00:32:41,000 --> 00:32:46,550
+limit ال cosine على المقدرة ده أقل من أو يسوي1 على
+
+319
+00:32:46,550 --> 00:32:50,650
+ما لديها بـ 000 بساندوش تيرام يبقى اللي فى النص
+
+320
+00:32:50,650 --> 00:32:56,230
+بقداش بـ 0 إذا ال limit هذا كله بـ 0 مع السلامة
+
+321
+00:32:56,230 --> 00:33:02,130
+غير مأسوف عليه بظلمينا عندنا هنا 1 على ايه ناقص
+
+322
+00:33:02,130 --> 00:33:09,270
+المقدار هذا يبقى هذا بده يساوي ل plus ل sign AT
+
+323
+00:33:09,270 --> 00:33:19,400
+بده يساوي 1 على ايهناقص او لا مش ناقص ناقص S على F
+
+324
+00:33:19,400 --> 00:33:29,180
+E هذا نفس القصة زي اللي فوق يبقى بيدروح اخدله ال U
+
+325
+00:33:29,180 --> 00:33:41,070
+تساوي E أس ناقص ST و بدي اخدي ال DV Cos ATDT يبقى
+
+326
+00:33:41,070 --> 00:33:51,890
+بدنا ال DU بناقص S E أس ناقص ST DT وال V بصين A T
+
+327
+00:33:51,890 --> 00:34:01,650
+على A تمام يبقى U في V يبقى هماش خلاص ما كتبناش ال
+
+328
+00:34:01,650 --> 00:34:06,610
+limit بدنا نكتب ال limit قبل هذا يبقى هذا ال limit
+
+329
+00:34:07,390 --> 00:34:13,990
+لما a tends to infinity لمن؟ للنتيجة اللى عندنا U
+
+330
+00:34:13,990 --> 00:34:24,050
+في V يبقى E أص ناقص ST E أص ناقص ST sin AT كله على
+
+331
+00:34:24,050 --> 00:34:31,900
+من؟ على A و بالموجةناقص تكامل من zero لغاية الـ a
+
+332
+00:34:31,900 --> 00:34:38,540
+طبعا التكامل هذا من zero إلى a لمين لل VW ال V
+
+333
+00:34:38,540 --> 00:34:49,340
+اللي هو sign AT على AW اللي هو ناقص S في E او ناقص
+
+334
+00:34:49,340 --> 00:34:55,360
+ST في DT يساوي
+
+335
+00:34:56,450 --> 00:35:05,610
+1 على a ناقص s على a وهذا ال limit لما a tends to
+
+336
+00:35:05,610 --> 00:35:10,370
+infinity وهي ال ghost بدنا نعوض بالقيمة اللى فوق
+
+337
+00:35:10,370 --> 00:35:19,750
+ناقص اللى تحت يبقى sign a a على a في e أس s a
+
+338
+00:35:19,750 --> 00:35:29,150
+اواطنزلها تحت سرتمين بالموجة ناقصزيرو في أي شغلة
+
+339
+00:35:29,150 --> 00:35:35,570
+اللي هو بزيرو اللي بعدها ناقص مع ناقص اللي هي
+
+340
+00:35:35,570 --> 00:35:44,990
+بزايد واحد عالي والله S على A في تكامل من Zero إلى
+
+341
+00:35:44,990 --> 00:35:55,440
+A لل E أس ناقص ST ل sign ATDT وهيجفلنا الجوزيبقى
+
+342
+00:35:55,440 --> 00:36:01,880
+هذا الكلام بده يساوي مين؟ ال F of S لا plus لهذه
+
+343
+00:36:01,880 --> 00:36:11,920
+هديها رمز مين؟ F of S يساوي واحد على A ناقص S على
+
+344
+00:36:11,920 --> 00:36:15,560
+A طلعولي يا بنات ال limit هنا لما ال A بده تروح ل
+
+345
+00:36:15,560 --> 00:36:21,920
+infinityالمقام بالإنفينيتي وهنا واحد عمل نهاية
+
+346
+00:36:21,920 --> 00:36:27,500
+يبقى هذا بروح كله بالزيرو يبقى سلم مع السلمة يبقى
+
+347
+00:36:27,500 --> 00:36:33,400
+اناقص S على A ووصلنا الى S عليه بظل جداش S على A
+
+348
+00:36:33,400 --> 00:36:41,220
+لكل تربيه وهذه شعر ثمان الناقص ووصلنا الى ال limit
+
+349
+00:36:41,220 --> 00:36:48,160
+لما ال A بده تروح لإنفينيتيلمين لتكامل من 0 إلى A
+
+350
+00:36:48,160 --> 00:36:53,820
+لل E أس ناقص ST لصين ATDT
+
+351
+00:36:56,340 --> 00:37:02,820
+طيب صار capital F of S يساوي واحد على ايه ناقص
+
+352
+00:37:02,820 --> 00:37:09,060
+استربيع على ايه تربيع هذا بنات لو رجعته الى أصله
+
+353
+00:37:09,060 --> 00:37:14,220
+مش هو عبارة عن تكامل من zero ل infinity لل EOS
+
+354
+00:37:14,220 --> 00:37:22,130
+ناقص ST لل sign ATDTصحيح ولا لأ؟ يعني صار capital
+
+355
+00:37:22,130 --> 00:37:28,830
+F of S يسوى واحد على إيه ناقص S تربية على إيه
+
+356
+00:37:28,830 --> 00:37:34,230
+تربية وهذا F of S صحيح ولا لأ؟ طيب شو رايك بدي
+
+357
+00:37:34,230 --> 00:37:38,600
+أجيب هادي على الشجة التانية؟هذه من التكاملات
+
+358
+00:37:38,600 --> 00:37:42,940
+الدورية بنات لبعض مرتين بطلع رأس المسألة زكريين
+
+359
+00:37:42,940 --> 00:37:46,460
+integration by parts علّين عليها كتير إذا هذه بدي
+
+360
+00:37:46,460 --> 00:37:49,800
+وديها على الشجة تاني لو وديتها على الشجة تاني بصير
+
+361
+00:37:49,800 --> 00:37:56,580
+واحد زائد S تربيع على A تربيع في capital F of S
+
+362
+00:37:56,580 --> 00:38:03,790
+بديه سوى مين؟ واحد على Aأو بمعنى آخر هذي بقدر اقول
+
+363
+00:38:03,790 --> 00:38:12,630
+A تربيع زائد S تربيع على A تربيع كل هذا في capital
+
+364
+00:38:12,630 --> 00:38:18,820
+F of S بده يساوي كده ايه؟ واحد على Aفانا بدي اقف
+
+365
+00:38:18,820 --> 00:38:26,400
+فوق S اللي بدي دور عليها يبقى F of S بده يسوي قداش
+
+366
+00:38:26,400 --> 00:38:35,160
+اضرب فوق بصير A تربيع على A في S تربيع زائد من A
+
+367
+00:38:35,160 --> 00:38:44,420
+تربيعيبقى صار عندي لابلاسي ترانسفورم لصين AT بده
+
+368
+00:38:44,420 --> 00:38:49,940
+يساوي نختصر ال M على ال A يبقى هذا بده يساوي
+
+369
+00:38:49,940 --> 00:38:59,140
+capital F of S وهذا بده يصير A على S تربيع زائد A
+
+370
+00:38:59,140 --> 00:38:59,980
+تربيع
+
+371
+00:39:04,400 --> 00:39:10,440
+يبقى صار بناء على لبلاس ال transform ل sign AT
+
+372
+00:39:10,440 --> 00:39:17,160
+يساوي A على S تربيع زائد A تربيع بعد قليل هحسب
+
+373
+00:39:17,160 --> 00:39:22,460
+الكيها بطريقة أخرى و طلع الكمين نفس النتيجة اللي
+
+374
+00:39:22,460 --> 00:39:28,580
+هي A على S تربيع زائد A تربيع طب خليني أسأل السؤال
+
+375
+00:39:28,580 --> 00:39:35,200
+التالي تتوقعلـ plus transform لـ cosine a t ايش
+
+376
+00:39:35,200 --> 00:39:42,860
+يكون بدل صين مدحوط cosine حد بتقدر قولي شو النتيجة
+
+377
+00:39:42,860 --> 00:39:51,600
+نفس هذه بالضبط بس بدل ال a بتجي مكانها s بصير s
+
+378
+00:39:51,600 --> 00:39:56,440
+على s تربيه زي a تربيه فقط لا غير وهذه check
+
+379
+00:39:56,440 --> 00:39:58,700
+اعمليها في البيت
+
+380
+00:40:05,990 --> 00:40:13,150
+بعدها نعطيها لك good exercise نفس
+
+381
+00:40:13,150 --> 00:40:17,010
+التكتيك اللي تبعنا في ال sign بدك تتبعي في ال
+
+382
+00:40:17,010 --> 00:40:24,930
+cosine حرفيا يبقى هنا بروح نقول good exercise ا
+
+383
+00:40:24,930 --> 00:40:36,710
+checkthat Laplace transform لcos At ساوي S على S
+
+384
+00:40:36,710 --> 00:40:44,530
+تربيع زائد A تربيع هذا
+
+385
+00:40:44,530 --> 00:40:51,270
+كان المثال رقم اتنين بدنا نروح للمثال رقم تلاتة
+
+386
+00:40:59,930 --> 00:41:12,670
+لت ال F of T بده تسوي T to the power N where ال N
+
+387
+00:41:12,670 --> 00:41:22,210
+is a positive integer find
+
+388
+00:41:26,020 --> 00:41:30,080
+لا بلا تترانسفرم ال T to the power N
+
+389
+00:41:40,350 --> 00:41:44,630
+يبقى انا في عندي function جديدة هذه ال function f
+
+390
+00:41:44,630 --> 00:41:50,470
+of t يسوى t to the power n و ال n عدد صحيح موجب
+
+391
+00:41:50,470 --> 00:41:55,150
+كاسرى او سالب ماعناهش علاقة فيه يبقى الشرط أساسي
+
+392
+00:41:55,150 --> 00:42:00,150
+ان عدد صحيح موجب جالي هادلي لف لسه transform ل t
+
+393
+00:42:00,150 --> 00:42:05,650
+to the power n دججوا معايا كويس هذه المثلة مثيرة
+
+394
+00:42:05,650 --> 00:42:10,860
+شوية كيف مثيرة تعالوا نشوفيبقى احنا بدنا نبقى
+
+395
+00:42:10,860 --> 00:42:16,520
+place لـT to the power N حسب التعريف يبقى تكامل من
+
+396
+00:42:16,520 --> 00:42:22,480
+Zero إلى Infinity لـE أص ناقص ST لـT to the power
+
+397
+00:42:22,480 --> 00:42:26,960
+N DT تمام؟
+
+398
+00:42:26,960 --> 00:42:30,920
+كيف بنكمل مثلا زي هذه exponential في T to the
+
+399
+00:42:30,920 --> 00:42:37,820
+power N؟بالجدول ممتاز ان بس احنا هنا بدنا اشين
+
+400
+00:42:37,820 --> 00:42:42,880
+جدول ليش ان هذا improper integral يبقى بدنا نروح
+
+401
+00:42:42,880 --> 00:42:49,560
+نقول هذا هو limit لتكامل
+
+402
+00:42:49,560 --> 00:42:55,140
+من zero إلى a لما a tends to infinity ل T to the
+
+403
+00:42:55,140 --> 00:43:03,570
+power n E أصناق ST في DTبدي اعملها integration by
+
+404
+00:43:03,570 --> 00:43:08,590
+parts عادي بدون جدول واشوف لوين بده توصلنا كفين
+
+405
+00:43:08,590 --> 00:43:13,190
+الخطوة واحدة وبعدين ممكن نستنتج الخطوة الثانية
+
+406
+00:43:13,190 --> 00:43:23,650
+يبقى بدي اخدي ال U هي T to the power N وDVE-STDT
+
+407
+00:43:23,650 --> 00:43:33,970
+الان بدنا DUيبقى N T أس N ناقص واحد في الـ DT بدنا
+
+408
+00:43:33,970 --> 00:43:41,690
+ال V يساوي E أس ناقص ST كما هي مقسومة على تفاضل
+
+409
+00:43:41,690 --> 00:43:49,350
+الأس لأن الأس من الدرجة الأولى يبقى هذه U وهذه V
+
+410
+00:43:49,350 --> 00:43:54,130
+اللي عندنا إذا النتيجة التكامل كتالي هذه ال limit
+
+411
+00:43:54,540 --> 00:44:01,680
+لما a tends to infinity بنا نيجي ل U في V يبقى T
+
+412
+00:44:01,680 --> 00:44:12,240
+to the power N E أس ناقص ST على ناقص S و الحكي هذا
+
+413
+00:44:12,240 --> 00:44:20,510
+من Zero لغاية ال Aناقص تكامل من zero إلى a لل V
+
+414
+00:44:20,510 --> 00:44:30,510
+دال U ال V هي E أس ناقص ST على ناقص S دال U ل N T
+
+415
+00:44:30,510 --> 00:44:37,630
+أس N ناقص واحد DT وهذا ال limit لمين؟ للمقدار هذا
+
+416
+00:44:37,630 --> 00:44:38,410
+كله
+
+417
+00:44:40,730 --> 00:44:47,570
+طيب يساوي limit لما ال a tends to infinity بتعوض
+
+418
+00:44:47,570 --> 00:44:51,750
+بالقيمة اللى فوق ناقص القيمة اللى تحت يعني يا شباب
+
+419
+00:44:51,750 --> 00:45:00,250
+هذه T والله هذه بتصير A أس N وهذه خليني أنزلها تحت
+
+420
+00:45:00,250 --> 00:45:09,050
+ناقص S في E أس S في A ناقص
+
+421
+00:45:13,380 --> 00:45:19,940
+أي مقدار يبقى بزيرو على أي رقم يبقى بزيرو خلصنا
+
+422
+00:45:19,940 --> 00:45:26,980
+منها الآن بقال عندي الناقص مع ناقص بصغير زائد عندك
+
+423
+00:45:26,980 --> 00:45:34,180
+N على S مقدار ثابت خليك برا بظل تكامل من Zero إلى
+
+424
+00:45:34,180 --> 00:45:34,740
+A
+
+425
+00:45:44,120 --> 00:45:47,900
+أخر حاجة توصلنا لها هي limit لما ال a tends to
+
+426
+00:45:47,900 --> 00:45:53,880
+infinityللـ A to the power N EOS ناقص S A بجبن
+
+427
+00:45:53,880 --> 00:45:59,880
+نزلها تحت بالشكل اللي أن هذا ناقص هنا Zero على
+
+428
+00:45:59,880 --> 00:46:04,640
+المقدار B Zero N على S بإشارة سالب مع سالب بصير
+
+429
+00:46:04,640 --> 00:46:05,960
+موجب و برة التكامل
+
+430
+00:46:23,560 --> 00:46:31,060
+بعد مرتين بيخلص ال busمظبوط؟ بيصير واحد صحيح،
+
+431
+00:46:31,060 --> 00:46:37,420
+كويس؟ و هذا بيظل A أس اتنين أس، جداش بتشتقى كل مرة
+
+432
+00:46:37,420 --> 00:46:40,880
+بتضرب اتنين و ال exponential زي ماني طب لما لاقيت
+
+433
+00:46:40,880 --> 00:46:46,220
+روح للمالة نهاية بيصير واحد ع مالة نهاية ب zero
+
+434
+00:46:46,220 --> 00:46:49,700
+هذا عند التربية و عند التكيب و عند الأربعة و
+
+435
+00:46:49,700 --> 00:46:54,020
+القمسة و الستة و ال N كله بيصير ال limit هذا ب
+
+436
+00:46:54,020 --> 00:47:02,750
+zeroهذا بيصير بزيرو مرة واحدة كان في انكوا سؤال في
+
+437
+00:47:02,750 --> 00:47:09,910
+calculus B في ال section اللي هو مين greater than
+
+438
+00:47:09,910 --> 00:47:13,410
+مين من الدوال اللي بنعمر مقارنة between relative
+
+439
+00:47:13,410 --> 00:47:17,970
+rates of growth وكان انكوا في سؤال بيقول زي هيك
+
+440
+00:47:17,970 --> 00:47:23,870
+high limit لما ال X بده تروح لل infinityللـ X to
+
+441
+00:47:23,870 --> 00:47:34,680
+the power N على E of Xالحين اضغط على الرقم
+
+442
+00:47:34,680 --> 00:47:38,180
+اللى بديكى ياه يبقى هذا لو جينا في خضرنه ايش بيصير
+
+443
+00:47:38,180 --> 00:47:43,520
+ان اكسوس ان ناقص واحد على U6 ان في ان ناقص واحد في
+
+444
+00:47:43,520 --> 00:47:47,620
+اكسوس ان ناقص اتنين على U6 يبقى في الآخر ايش بيطلع
+
+445
+00:47:47,620 --> 00:47:52,840
+عندي ان فاكتوريال لان ان في ان ناقص واحد لان ان
+
+446
+00:47:52,840 --> 00:47:59,540
+فاكتوريال على U6مظبوط يبقى هذه بعد عدة مرات بدي
+
+447
+00:47:59,540 --> 00:48:04,640
+يصير limit لما ال X tends to infinity لل N
+
+448
+00:48:04,640 --> 00:48:11,840
+factorial على E و ال 6 N factorial هي ده رقم و E و
+
+449
+00:48:11,840 --> 00:48:15,840
+ال 6 لما ال X بتروح للمالة نهاية بجديش المقام عدد
+
+450
+00:48:15,840 --> 00:48:21,080
+ع مالة نهاية Zero يبقى النتيجة هذه تساوي Zero
+
+451
+00:48:21,080 --> 00:48:27,570
+تمام؟يبقى بناء عليه هذه زيها بس بدل ال A أجانبين
+
+452
+00:48:27,570 --> 00:48:32,630
+اللي هو ال X يبقى هذه ب Zero مع السلامة يبقى صارة
+
+453
+00:48:32,630 --> 00:48:39,770
+النتيجة تساوي N على S في limit لما ال A tends to
+
+454
+00:48:39,770 --> 00:48:47,030
+infinity لمين؟ لتكامل من Zero إلى Aللتى to the
+
+455
+00:48:47,030 --> 00:48:56,890
+power n minus one لل E أس ناقص S T DT يعني إيش؟
+
+456
+00:48:56,890 --> 00:49:04,530
+يعني اللى هو N على S ثمين فيتا كامل من Zero ل
+
+457
+00:49:04,530 --> 00:49:10,090
+Infinity لتى to the power n minus one E أس ناقص S
+
+458
+00:49:10,090 --> 00:49:19,140
+T DTوان المسألة هذه صارت نفس المسألة اللى بدأنا
+
+459
+00:49:19,140 --> 00:49:26,420
+فيها اللهم إلا الأس تبع ال T نقص جداش طيب تتوقعوا
+
+460
+00:49:26,420 --> 00:49:32,720
+لو روحت كاملت كمان مرة انسى اللى برا جداش تتوقعوا
+
+461
+00:49:32,720 --> 00:49:41,140
+الجواب يكون؟لما كانت N صارت N على S إذا ال term
+
+462
+00:49:41,140 --> 00:49:48,160
+اللي بعدش بتكون N ناقص واحد على S في تكامل ل T أس
+
+463
+00:49:48,160 --> 00:49:52,860
+N ناقص اتنين في ال exponential صحيح ولا لا؟ يعني
+
+464
+00:49:52,860 --> 00:49:59,330
+هذه الخطوة اللي بعدها اختصارا بتصير Nفإن نقص واحد
+
+465
+00:49:59,330 --> 00:50:07,410
+على S في S فمين في تكامل من Zero إلى Infinity ل T
+
+466
+00:50:07,410 --> 00:50:16,170
+أس N نقص اتنين E أس نقص S T D T تمام؟
+
+467
+00:50:16,170 --> 00:50:22,930
+طب لو عملنا كمان خطوةبصير N فى النقص واحد فى النقص
+
+468
+00:50:22,930 --> 00:50:28,010
+اتنين على S فى S فى S فى تكامل من Zero ل Infinity
+
+469
+00:50:28,010 --> 00:50:33,230
+اللى T أس N نقص تلاتة
+
+470
+00:50:33,230 --> 00:50:40,130
+فى مين فى E أس نقص S T D T إذا لو ضلنا مستمرين على
+
+471
+00:50:40,130 --> 00:50:43,150
+هالشغل هذه هنوصل لما يأتي
+
+472
+00:51:01,490 --> 00:51:05,690
+إذا لو ضلنا مستمرين على الشغل هذه هنوصل لـ Laplace
+
+473
+00:51:05,690 --> 00:51:11,690
+transform ل T to the power N بده يسوى ال N في N
+
+474
+00:51:11,690 --> 00:51:18,730
+ناقص واحد في N ناقص اتنين لغاية تلاتة اتنين في
+
+475
+00:51:18,730 --> 00:51:35,870
+واحد على S في S في في Sفاس فاس فاس فاس فاس فاس
+
+476
+00:51:35,870 --> 00:51:41,200
+فاس فاس فاس فاس فاس فاسالشركة بنات هلا وصل ت و ال
+
+477
+00:51:41,200 --> 00:51:44,740
+سن ت و ال سن نقص واحد ت و ال سن نقص اتنين ت و ال
+
+478
+00:51:44,740 --> 00:51:50,020
+سن نقص تلاتة ت تربية ت و ال واحد ت و ال zero يبقى
+
+479
+00:51:50,020 --> 00:51:54,740
+وصي ل plus ل ت و ال zero يبقى هذا الكلام بده يساوي
+
+480
+00:51:54,740 --> 00:52:01,780
+اللي فوق اللي هو n factorialواللي تحت S أُس قداش N
+
+481
+00:52:01,780 --> 00:52:07,900
+في لبلاس ترانسفورم لمين؟ للواحد أظن جيبنا لبلاس
+
+482
+00:52:07,900 --> 00:52:12,320
+ترانسفورم للواحد قبل قليل و بواحد على S يبقى ده
+
+483
+00:52:12,320 --> 00:52:18,160
+صار N factorial على S to the power N في لبلاس
+
+484
+00:52:18,160 --> 00:52:23,620
+للواحد اللي هو واحد على S إذا النتيجة النهائية N
+
+485
+00:52:23,620 --> 00:52:33,260
+factorialعلى S to the power N plus one طب
+
+486
+00:52:33,260 --> 00:52:41,030
+إيش رايك؟أحنا قبل قليل استنتجنا لبلاس للواحد من ال
+
+487
+00:52:41,030 --> 00:52:47,510
+E أُس AT بقدر أجيب لبلاس للواحد من المسألة هذه
+
+488
+00:52:47,510 --> 00:52:52,530
+الهين وصلنا أن لبلاس التي to the power N هي N
+
+489
+00:52:52,530 --> 00:52:58,550
+factorial على S أُس N زائد واحد لو بدي لبلاس
+
+490
+00:52:58,550 --> 00:52:59,510
+للواحد
+
+491
+00:53:15,360 --> 00:53:22,640
+بناء عليه لو سألتكوا و قلتلكوا بدنا ال place
+
+492
+00:53:22,640 --> 00:53:25,960
+transform ل T تكيب
+
+493
+00:53:34,640 --> 00:53:45,100
+تلاتة زائد واحد واربعة مباشرة تلاتة
+
+494
+00:53:45,100 --> 00:53:49,380
+زائد واحد واربعة مباشرة تلاتة زائد واحد واربعة
+
+495
+00:53:49,380 --> 00:53:55,940
+مباشرة تلاتة زائد واحد واربعة مباشرة
+
+496
+00:54:17,550 --> 00:54:23,130
+الان بدنا نضيف الابارة النظرية اللى قلنا عليها قبل
+
+497
+00:54:23,130 --> 00:54:28,840
+قليلإن الابلاس الـ transform is a linear function
+
+498
+00:54:28,840 --> 00:54:35,800
+ده اللي خطية يبقى بدنا نكتب العلاقة هذه و نحاول
+
+499
+00:54:35,800 --> 00:54:42,160
+نبين شو معناها بالضبط و كيف سنستخدم هذا المعنى في
+
+500
+00:54:42,160 --> 00:54:53,420
+حل بعض المسائل يبقى remark if ال F one of T
+
+501
+00:54:56,120 --> 00:55:05,100
+F2 of T are functions that have Laplace transform
+
+502
+00:55:05,100 --> 00:55:13,480
+and if C1 and C2 are any constants Laplace
+
+503
+00:55:13,480 --> 00:55:24,020
+transform لC1فى ال F of T زائد زائد C2 F2 of T بده
+
+504
+00:55:24,020 --> 00:55:33,380
+ساوي و C1 ل plus transform لل F1 زائد C2 ل plus
+
+505
+00:55:33,380 --> 00:55:42,980
+transform لل F2 of T F1 of T الشكل اللى عندنا
+
+506
+00:55:51,690 --> 00:55:56,270
+مرة تانية بقول لو عندي دلتين واحدة F1 of T
+
+507
+00:55:56,270 --> 00:56:01,090
+والتانية F2 of T والتنتين هذول Laplace transform
+
+508
+00:56:01,090 --> 00:56:06,040
+اللي هم existتمام يبقى اتنين that have Laplace
+
+509
+00:56:06,040 --> 00:56:11,560
+transform ولو كان C1 وC2 ثوابت اي ثوابت ماعنديش
+
+510
+00:56:11,560 --> 00:56:17,320
+قيود عضات صحيحة موجبة سالبة كسرية ماعنا مشكلة يبقى
+
+511
+00:56:17,320 --> 00:56:20,920
+Laplace transform ل C1 في الدالة الأولى زائد C2 في
+
+512
+00:56:20,920 --> 00:56:25,320
+الدالة الثانية تساوي C1 Laplace للأولى زائد C2
+
+513
+00:56:25,320 --> 00:56:28,760
+Laplace للدالة الثانية وهذا اللي بيسميها الخاصية
+
+514
+00:56:28,760 --> 00:56:33,570
+الخطية لLaplace transformيبقى هذه الـ Linear
+
+515
+00:56:33,570 --> 00:56:38,810
+Property لـ Laplace Transform لما أوضح لك كيف أجت
+
+516
+00:56:38,810 --> 00:56:46,670
+هذه سأقول لك الآن لو جيت لـ Laplace Transform ل C1
+
+517
+00:56:46,670 --> 00:56:55,530
+F1 of T زي C2 F2 of T حسب تعريف Laplace Transformي
+
+518
+00:56:55,530 --> 00:57:04,120
+بتكامل من Zero إلى Infinityللـ E أُس ناقص ST في C1
+
+519
+00:57:04,120 --> 00:57:12,440
+F1 of T زائد C2 F2
+
+520
+00:57:12,440 --> 00:57:20,050
+of T كله بالنسبة الى DTبقدر اوزع هذا التكامل الى
+
+521
+00:57:20,050 --> 00:57:25,290
+تكاملين يبقى هذا الكلام يساوي تكامل من zero ل
+
+522
+00:57:25,290 --> 00:57:34,250
+infinity لل E أص ناقص ST في C1 F1 of T DT زائد
+
+523
+00:57:34,250 --> 00:57:42,110
+تكامل من zero ل infinity لل E أص ناقص ST في C2 F2
+
+524
+00:57:42,110 --> 00:57:50,030
+of T DT ويساويأظن C1 مقدار ثابت بقدر أقوله الشرف
+
+525
+00:57:50,030 --> 00:57:55,630
+برا التكامل يبقى هذا الكلام بده يساوي C1 تكامل من
+
+526
+00:57:55,630 --> 00:58:05,230
+0 إلى infinity لل E أص ناقص ST لل F1 of T DTهذا
+
+527
+00:58:05,230 --> 00:58:09,770
+زيه ياسي اتنين شرف برا التكامل من zero إلى
+
+528
+00:58:09,770 --> 00:58:18,850
+infinity لل E أس ناقص ST E أس ناقص ST لل F2 of T
+
+529
+00:58:18,850 --> 00:58:27,280
+في DT سؤال هذا تعريف من يا بنات لبلة ال F1يبقى هذا
+
+530
+00:58:27,280 --> 00:58:35,560
+الكلام يساوي C1 Laplace لل F1 of T زائد C2 التاني
+
+531
+00:58:35,560 --> 00:58:42,440
+Laplace لل F2 of T أظن و هو المطلوب هذا إذا من
+
+532
+00:58:42,440 --> 00:58:45,900
+الآن فا صادر لو كان عندي Laplace لمجموع ده الإتين
+
+533
+00:58:45,900 --> 00:58:49,280
+بقدر أخد Laplace الأولى زائد Laplace التانية
+
+534
+00:58:49,280 --> 00:58:55,160
+بالزائد أوبالنقص لكن ضرب ما اتكلمناش فيه عند الضرب
+
+535
+00:58:55,160 --> 00:58:59,560
+كلامنا غلط اه انا بتكلم للجامع او الطرح فقط ده
+
+536
+00:58:59,560 --> 00:59:04,560
+غيره و اذا في مقدار ثابت باخده ايه ضرة هذا نعطي
+
+537
+00:59:04,560 --> 00:59:20,260
+مثال توضيحي على ذلك يبقى example امرا
+
+538
+00:59:20,260 --> 00:59:20,780
+واحد
+
+539
+00:59:23,310 --> 00:59:33,610
+Find Laplace transform لنص T تربيع زائد تمانية
+
+540
+00:59:33,610 --> 00:59:43,910
+زائد اتنين sin تلاتة T Laplace
+
+541
+00:59:43,910 --> 00:59:49,670
+transform لهذه الدالة تمام؟ بقدر اقوله والله كويس
+
+542
+00:59:49,990 --> 00:59:54,370
+اللي انا بدى اطبق الان قاعد اللى فوق نظرا اللى
+
+543
+00:59:54,370 --> 00:59:57,410
+انها linear يقبل ال plus للدالة الاولى زايد ال
+
+544
+00:59:57,410 --> 01:00:01,590
+plus للدالة التانية زايد ال plus للدالة التالتة
+
+545
+01:00:01,590 --> 01:00:06,390
+يبقى solution هذه
+
+546
+01:00:06,390 --> 01:00:11,690
+بقدر اكتبها على الشكل التالي مص ال plus transform
+
+547
+01:00:11,690 --> 01:00:20,470
+ال main ل T تربيعزائد Laplace transform لمين ل
+
+548
+01:00:20,470 --> 01:00:25,810
+تمانية اللى بقدر اكتبها تمانية في قداش في واحد مش
+
+549
+01:00:25,810 --> 01:00:30,490
+تمانية واحد من عشرة لأ تمانية مضروبة في واحد تمام
+
+550
+01:00:30,490 --> 01:00:38,130
+زائد اتنين Laplace transform ل sign تلاتة T جبتها
+
+551
+01:00:38,130 --> 01:00:41,990
+من وين من خاصية ال linearity اللى فوق اللى عندنا
+
+552
+01:00:41,990 --> 01:00:49,140
+هذا تطبيق مباشريبقى هذا الكلام بده يساوي النص ليه؟
+
+553
+01:00:49,140 --> 01:00:55,740
+Laplace لتيتا ربيع اه هي تيتا كيب يبقى بقدر اقول
+
+554
+01:00:55,740 --> 01:01:06,060
+اللي هي اتنين factorial على مين على اس تكيب زائد
+
+555
+01:01:06,060 --> 01:01:14,940
+هذه تمانية في Laplace لمين للواحد الصحيحو هذه زائد
+
+556
+01:01:14,940 --> 01:01:22,800
+اتنين في ل plus ل sin تلاتة T قبل قليل sin A T كان
+
+557
+01:01:22,800 --> 01:01:30,380
+A على S تربية زائد A تربية يبقى هذه تلاتة على S
+
+558
+01:01:30,380 --> 01:01:34,940
+تربية زائد تلاتة تربية اللي يبقى داشر اللي هو
+
+559
+01:01:34,940 --> 01:01:40,620
+بتسعة طيب اظن نص مع اتنين factorial مع السلامة
+
+560
+01:01:40,620 --> 01:01:44,600
+اتنين factorial اتنين في واحديبقى ضالة النتيجة
+
+561
+01:01:44,600 --> 01:01:52,760
+تساوي واحد على اس تكيب زائد هذه واحد على اس يبقى
+
+562
+01:01:52,760 --> 01:02:01,420
+بصير تمانية على اس هذه زائد اتنين في تلاتة بستة
+
+563
+01:02:01,420 --> 01:02:07,360
+على اس ترابيع زائد تسعة بدك تخليها زي ما كان بها
+
+564
+01:02:07,360 --> 01:02:11,500
+بس لو كان هذا السؤال في الكتاب لصمح اللهو روحت
+
+565
+01:02:11,500 --> 01:02:15,460
+بتلاقيش الإجابة زي هيك بتلاقي الإجابة على الشكل
+
+566
+01:02:15,460 --> 01:02:22,500
+التالي بدنا نوحد المقامات كله يبقى S تكيب في S
+
+567
+01:02:22,500 --> 01:02:27,920
+تربية زائد تسعة طبعا S تكيب اشتمت على مين؟ على S
+
+568
+01:02:27,920 --> 01:02:34,400
+يبقى لو جسمت هذه على هذه بصير عندي S تربية زائد
+
+569
+01:02:34,400 --> 01:02:43,450
+تسعةالان زائد تمانية أس تربيع في مين في أس تربيع
+
+570
+01:02:43,450 --> 01:02:53,650
+زائد تسعة اللي بعدها زائد ستة أس تكيبة تمام؟ طيب
+
+571
+01:02:53,650 --> 01:03:00,290
+هذه عبارة عن إيش؟ عبارة عن عندك أظن تمانية أس أس
+
+572
+01:03:00,290 --> 01:03:07,920
+أربعة في الشغيرهايبقى هاي تمانية S أص أربعة أظنه
+
+573
+01:03:07,920 --> 01:03:15,060
+تكييب مافيش غيرها يبقى زائد ستة S تكييب نيجي
+
+574
+01:03:15,060 --> 01:03:21,460
+للتربيع تسعة في تمانية بتنين وسبعين S تربيع و عندك
+
+575
+01:03:21,460 --> 01:03:28,360
+S تربيع يبقى تلاتة وسبعين S تربيعيبقى زائد تلاتة و
+
+576
+01:03:28,360 --> 01:03:32,400
+سبعين استربيع مش طايل عندى الا ال constant اللى
+
+577
+01:03:32,400 --> 01:03:39,960
+همين تسعة يبقى زائد تسعة كله على استكعيب في
+
+578
+01:03:39,960 --> 01:03:47,480
+استربيع زائد تسعة طب خلينى أسأل السؤال التالى
+
+579
+01:03:47,480 --> 01:03:53,340
+افترض اعطانى هذه هيك تقدر ترجعيها لهذه
+
+580
+01:03:57,180 --> 01:04:03,200
+وكيف؟ نقدر؟ يعني
+
+581
+01:04:03,200 --> 01:04:06,960
+بنقول هذا على هذا و هذا على هذا و هذا على هذا و
+
+582
+01:04:06,960 --> 01:04:12,920
+هذا على هذا طيب هيك يعني اتعلمنا؟ يعني من الهيئة
+
+583
+01:04:15,950 --> 01:04:20,730
+القصور الجزئية نعمل لها partial fractions وبالتالي
+
+584
+01:04:20,730 --> 01:04:24,690
+بنقدر نرجع هذه إلى أصلها
+
+585
+01:04:33,520 --> 01:04:36,520
+ماشي تيجي يقولي و الله طلعت هيك هذه بتخلف عن هذه،
+
+586
+01:04:36,520 --> 01:04:39,960
+لأ و الله حللي غلط، لأ الحل صح، بس واحدة المقامات،
+
+587
+01:04:39,960 --> 01:04:58,260
+وشوفي كده بتطلع النتيجة اللي عندك طيب،
+
+588
+01:04:58,260 --> 01:05:09,390
+ناخد كمان مثال آخرثالث من هنا نمر
+
+589
+01:05:09,390 --> 01:05:19,070
+A نمر B
+
+590
+01:05:19,070 --> 01:05:24,250
+نمر B نمر B
+
+591
+01:05:24,250 --> 01:05:30,950
+نمر B نمر B نمر B نمر B نمر B نمر B نمر B نمر B
+
+592
+01:05:30,950 --> 01:05:30,950
+نمر B
+
+593
+01:05:43,370 --> 01:05:49,590
+واللي بالك معناه كويسة الان بدنا لبلاس ترانسفورم
+
+594
+01:05:49,590 --> 01:05:58,090
+لجوش بي ت كيف نجيب هذا دي بناه؟ بدي اقول E وص ناقص
+
+595
+01:05:58,090 --> 01:06:06,370
+ST في جوش بي ت لكن في عندي رأي غير هيك شوف يبقى لو
+
+596
+01:06:06,370 --> 01:06:13,520
+جيت للتعريف وتكامل من Zero إلى Infinityللإي أس
+
+597
+01:06:13,520 --> 01:06:22,800
+ناقص ST لجوش BTDT كتعريف ما عنده مشكلة طيب هذا
+
+598
+01:06:22,800 --> 01:06:29,340
+الكلام تكامل من zero إلى infinity لminimum لإي أس
+
+599
+01:06:29,340 --> 01:06:34,800
+ناقص ST الجوش هذه مش مقدر اكتبها بدالة ال
+
+600
+01:06:34,800 --> 01:06:41,990
+exponential من آخر section في شبطار تمانيةاللي كان
+
+601
+01:06:41,990 --> 01:06:50,370
+E أُس BT زائد E أُس ناقص BT على 2DT
+
+602
+01:06:52,230 --> 01:06:57,930
+أظن النُص بقدر أقوله طلع برا تمام؟ يبقى إيش بصير؟
+
+603
+01:06:57,930 --> 01:07:09,010
+بصير هذا النُص هو يتكمل من zero إلى A لل E أُس لو
+
+604
+01:07:09,010 --> 01:07:14,190
+جيت أخد هذه و هذه مع بعض و أخد هذه و هذه مع بعض
+
+605
+01:07:14,470 --> 01:07:19,490
+يبقى بقدر أقول هذه بدي أجمع لإتنين يبقى ناقص S
+
+606
+01:07:19,490 --> 01:07:27,530
+زائد B أو ناقص S ناقص B في T term الأول هي ناقص S
+
+607
+01:07:27,530 --> 01:07:32,570
+هي في T و ناقص فناقص بزائد BT اللي هو الجزء الأول
+
+608
+01:07:32,570 --> 01:07:40,150
+الجزء الثاني زائدبدي اخد هدى و هدى مع بعض بقدر اخد
+
+609
+01:07:40,150 --> 01:07:46,730
+ناقص T عامل مشترك بيبقى S زائد ال B يبقى زائد E
+
+610
+01:07:46,730 --> 01:07:58,710
+وهي ناقص برا و S زائد ال B كله في T في DT مظبوط؟
+
+611
+01:07:58,710 --> 01:08:04,930
+limit ولا يهمك مديش limit from zero to infinity
+
+612
+01:08:04,930 --> 01:08:13,910
+ماشي؟بدول limit يسوى هذا الان limit للأولى زائد
+
+613
+01:08:13,910 --> 01:08:19,210
+limit للثانية او هنا لا plus للأولى زائد لا plus
+
+614
+01:08:19,210 --> 01:08:25,470
+للثانية يبقى هذا الكلام نص حسب ال linearity يبقى
+
+615
+01:08:25,470 --> 01:08:34,730
+نص اللي هو لا plus لمين لل E أس ناقص S ناقص ال B
+
+616
+01:08:34,730 --> 01:08:48,080
+في Tزائد نص لبلاس لإي أس ناقص S زائد B في T لابد
+
+617
+01:08:48,080 --> 01:08:53,040
+استخدم المثال الأول اللي جاهز عندنا يبقى هذا نص
+
+618
+01:08:53,040 --> 01:09:03,110
+فيهالـ plus لهذه اللي هو واحد على S زائد S ناقص ال
+
+619
+01:09:03,110 --> 01:09:12,210
+B يبقى S ناقص ال B، مصبوط؟
+
+620
+01:09:12,210 --> 01:09:21,430
+هذه جوش، استنى جوش وحطنا لها S يبقى S لا استنى
+
+621
+01:09:21,430 --> 01:09:29,770
+شوية، السؤال هوبيقول جوش بي تي جوش بي تي و حطناها
+
+622
+01:09:29,770 --> 01:09:36,100
+بي تي ا ا احنا حطناها دغري ليش حطناها؟استنى شوية
+
+623
+01:09:36,100 --> 01:09:42,760
+استنى يا بناتي احنا هنا حطينا التعريف لكن هذه بقدر
+
+624
+01:09:42,760 --> 01:09:46,840
+اقول بالشكل التالي مباشرة نفس الفكرة اللى احنا
+
+625
+01:09:46,840 --> 01:09:52,320
+ماشينا فيها يعني انا مابديش اعمل التكامل هذا بدي
+
+626
+01:09:52,320 --> 01:10:00,140
+اسهل شوية يبقى هذه لا plus لا نص فى مين فى ال E أس
+
+627
+01:10:00,140 --> 01:10:07,960
+BT زاد E أس ناقص BTمصبوط؟ يبقى كأنه عندي دالتين
+
+628
+01:10:07,960 --> 01:10:18,700
+يبقى هذا نص ل plus لمن؟ لل EOS BT زائد نص ل plus
+
+629
+01:10:18,700 --> 01:10:25,020
+لل EOS ناقص BT طبعا؟ يبقى ما جولنا شاكر الجوالات
+
+630
+01:10:25,020 --> 01:10:28,560
+من أول ما دخلنا و بعدين أول ما دخلنا جولنا جاف
+
+631
+01:10:28,560 --> 01:10:36,630
+للجوالمنبه ولا جوال اسمه جوال يبقى نصف لبلاس لل E
+
+632
+01:10:36,630 --> 01:10:41,610
+أس BT زائد نصف لبلاس لل E أس نقص BT هذه حسبناها
+
+633
+01:10:41,610 --> 01:10:50,350
+قبل قليل النصف في واحد على S ناقص ال B و هذه كمان
+
+634
+01:10:50,350 --> 01:11:01,850
+نصف في واحد على S زائد ال Bهذا الكلام يساوي نص في
+
+635
+01:11:01,850 --> 01:11:11,230
+واحد على S نقص ال B واحد على S زائد ال B يبقى هذا
+
+636
+01:11:11,230 --> 01:11:18,010
+الكلام يساوي نص بدا واحد المقامات S نقص ال B في S
+
+637
+01:11:18,010 --> 01:11:25,610
+زائد ال B بشير عند S زائد ال B زائد ال S نقص ال B
+
+638
+01:11:28,210 --> 01:11:34,070
+نقص بي وزائد بي مع السلامة يبقى الصار عندي مص في
+
+639
+01:11:34,070 --> 01:11:41,450
+اتنين اس هذا تحليل مين فرق بين المربعين يبقى هذا
+
+640
+01:11:41,450 --> 01:11:48,590
+اس تربية ناقص بي تربية مص مع اتنين مع السلامة يبقى
+
+641
+01:11:48,590 --> 01:11:54,010
+اس على اس تربية ناقص مينب تربية قبل شوية قولتلكم
+
+642
+01:11:54,010 --> 01:12:01,030
+good exercise ل plus ل cosine ا ت قولتلكم S على S
+
+643
+01:12:01,030 --> 01:12:05,850
+تربية زائد ب تربية مش ناقص في حال تلاقوش ناقص في
+
+644
+01:12:05,850 --> 01:12:07,930
+حال تلاقوش cosine زائد
+
+645
+01:12:13,040 --> 01:12:19,340
+نمرابيج أخد حاصل ضرب الإتنين يبجى أنا بدى لابلاسي
+
+646
+01:12:19,340 --> 01:12:28,960
+ترانسفورم لل E أس AT في مين؟ في E أس BT زائد E أس
+
+647
+01:12:28,960 --> 01:12:36,020
+ناقص BT كله على جداش على الإتنينيبقى هذا الكلام
+
+648
+01:12:36,020 --> 01:12:44,280
+بده يساوي ل plus transform ل نص في ال E أس A زائد
+
+649
+01:12:44,280 --> 01:12:54,880
+ال B يبقى A زائد ال B في T زائد نص في E أس A ناقص
+
+650
+01:12:54,880 --> 01:13:04,140
+ال B كله في من؟ في Tهذا الكلام يساوي نص لبلاس
+
+651
+01:13:04,140 --> 01:13:11,640
+ترانس فورم لل E أس A زائد ال B في T من خاصية ال
+
+652
+01:13:11,640 --> 01:13:19,960
+linearity زائد نص لبلاس ترانس فورم لل E أس A ناقص
+
+653
+01:13:19,960 --> 01:13:30,830
+ال B في T هذا الكلام يساوي نص في طلعيني من هذهيبقى
+
+654
+01:13:30,830 --> 01:13:37,730
+هذه أول مثال أخدنا اليوم واحد على مين على S ناقص
+
+655
+01:13:37,730 --> 01:13:48,590
+ال A زائد ال B تمام اللي بعده زائد نص في واحد على
+
+656
+01:13:48,590 --> 01:14:00,710
+S زائد اللي هو ال A ناقص ال Bهذه موجبة وهذه بيبقى
+
+657
+01:14:00,710 --> 01:14:07,750
+هذه بالموجب يبقى تكون سالب يبقى سالب بالشكل اللي
+
+658
+01:14:07,750 --> 01:14:12,530
+عندنا هنا تمام؟ لإن الأس عندى هنا موجب وهنا موجب
+
+659
+01:14:12,530 --> 01:14:17,650
+ايه ناقص البيت؟ طيب هنعيد ترتيب اللي هو النتيجة
+
+660
+01:14:17,650 --> 01:14:19,170
+اللي وصلنا لها هذه
+
+661
+01:14:39,050 --> 01:14:48,830
+إذا صار عندى لبلاس transform لل E أس AT في جوش BT
+
+662
+01:14:48,830 --> 01:14:55,130
+بده يساوي، بده أخد أبناط المُص عامل مشترك من الكل،
+
+663
+01:14:55,130 --> 01:15:03,250
+مظل واحد علىشو رايك هذه بدي اكتبها S ناقص ال A و
+
+664
+01:15:03,250 --> 01:15:07,450
+هنا من و هنا و الله خليها زي ما هي و بعض الخطوات
+
+665
+01:15:07,450 --> 01:15:14,010
+التالية بنعملها يبقى S ناقص ال A زائد ال B هذا ال
+
+666
+01:15:14,010 --> 01:15:21,230
+term الأولبعدها زائد أخدنا النص برا يبقى واحد على
+
+667
+01:15:21,230 --> 01:15:28,730
+S ناقص ال A ناقص ال B بشكل عندنا هنا يبقى هذه
+
+668
+01:15:28,730 --> 01:15:35,790
+تساوي نص فين؟ بدا وحد المقامات اللي هدول كلهميبقى
+
+669
+01:15:35,790 --> 01:15:46,750
+بصير S ناقص ال A زائد ال B في S ناقص ال A ناقص ال
+
+670
+01:15:46,750 --> 01:15:55,510
+B هنا هذا بصير S ناقص ال A زائد ال B وهنا زائد ال
+
+671
+01:15:55,510 --> 01:16:04,120
+S ناقص ال A ناقص ال B وحط المقامات للكليبقى بصير S
+
+672
+01:16:04,120 --> 01:16:08,880
+وهذا فكته S ناقص ال A زائد ال B وهذا التاني فكته
+
+673
+01:16:08,880 --> 01:16:14,980
+بصير S ناقص ال A ناقص ال B أظن ناقص ال B وزائد ال
+
+674
+01:16:14,980 --> 01:16:20,640
+B مع السلامة هذا ال term هو هذا ال term يبقى هذا
+
+675
+01:16:20,640 --> 01:16:28,420
+النص وهنا بصير 2 في S ناقص ال A شو رايكوا هذي؟ بدأ
+
+676
+01:16:28,420 --> 01:16:34,750
+اكتب الجثة ده على الشكل التاليلو ال S ناقص ال A
+
+677
+01:16:34,750 --> 01:16:44,190
+ناقص ال B هذا جوس لحاله هذا كمان بدي اكتبه S ناقص
+
+678
+01:16:44,190 --> 01:16:49,790
+ال A وناقص ناقص بصير زائد ال B بالشكل اللي عندنا
+
+679
+01:16:49,790 --> 01:16:56,230
+طيب الاتنين هذه مع الاتنين هذه يبقى ايش بصير عندنا
+
+680
+01:16:56,230 --> 01:17:03,720
+بصير S ناقص ال Aطب اتطلعيلي علي هدول فرق بين
+
+681
+01:17:03,720 --> 01:17:11,560
+المربعين صح يبقى ده بيصير ال S ناقص ال A لكل تربيع
+
+682
+01:17:11,560 --> 01:17:18,280
+ناقص بيه تربيع اذا هذا هو ال plus transform لل E S
+
+683
+01:17:18,280 --> 01:17:25,900
+A T في جوش B T DT وعدناكوا بوعد قبل قليل ولم ننفذه
+
+684
+01:17:26,410 --> 01:17:29,190
+شو الوعد اللى وعدناكوا فيه؟ قولنا بنجيبلكوا ال
+
+685
+01:17:29,190 --> 01:17:35,290
+sign AT بطريقة أخرى طب نيجي للطريقة الأخرى اللى
+
+686
+01:17:35,290 --> 01:17:40,550
+وعدناكوا فيها و بيها ننهي المحاضرة اصلا مرت علينا
+
+687
+01:17:40,550 --> 01:17:45,170
+صيغة Euler مش Euler differential equation تبع في
+
+688
+01:17:45,170 --> 01:17:45,690
+الكملة
+
+689
+01:17:50,020 --> 01:17:59,720
+يبقى مرة علينا a cos theta cos theta زائد i sin
+
+690
+01:17:59,720 --> 01:18:00,660
+theta
+
+691
+01:18:05,110 --> 01:18:11,830
+الان بدنا نيجي نقيس عليها لو جينا قولنا لك قداش
+
+692
+01:18:11,830 --> 01:18:24,730
+اللي هو E اص I a T ايش بتقولي ليه؟ cosine a T زائد
+
+693
+01:18:24,730 --> 01:18:33,490
+I sine a T صح؟ يعني شيلنا θ و حطينا مكانها مين؟
+
+694
+01:18:52,650 --> 01:19:01,420
+طب ايش رايك لو طرحنا الاتنين من بعضطرحناهم طرح إذا
+
+695
+01:19:01,420 --> 01:19:11,700
+بصير عندي E أس I A T ناقص E أس ناقص I A T يبقى
+
+696
+01:19:11,700 --> 01:19:17,180
+بصير هنا ناقص و هنا ذات بروحة هدول و بصير عندنا
+
+697
+01:19:17,180 --> 01:19:29,680
+اتنين I في Sin A T و كأنه SinAT بدها تساوي واحد
+
+698
+01:19:29,680 --> 01:19:39,900
+على اتنين I في مين؟ في E أس I AT ناقص E أس ناقص I
+
+699
+01:19:39,900 --> 01:19:47,330
+ATطبعا الكتاب حاطط هذا سؤال في التمرين و جايلك
+
+700
+01:19:47,330 --> 01:19:51,750
+sign AT يساوي هذا هاي جيبنالك من اين من وين جابها
+
+701
+01:19:51,750 --> 01:19:56,530
+جابها من Euler formula من صيغة Euler وهي جيبنا
+
+702
+01:19:56,530 --> 01:20:02,870
+sign AT يبقى احنا لو بدنا نحسب Laplace لهذه الدالة
+
+703
+01:20:02,870 --> 01:20:07,290
+كأنه بدنا نحسب Laplace لطرف اليمين
+
+704
+01:20:09,690 --> 01:20:15,130
+يعني هذا يا بنات كأنه حل ثاني لتاني سؤال أخدناه
+
+705
+01:20:15,130 --> 01:20:23,130
+اليوم مظبوط إذا بدي أحسب ل plus ل sign eighty
+
+706
+01:20:24,880 --> 01:20:31,220
+يبقى هو لـ plus لاخطار في اليمين يبقى هو ل plus ل
+
+707
+01:20:31,220 --> 01:20:42,600
+1 على 2 I تمين في E أس I A T ناقص E أس ناقص I A T
+
+708
+01:20:42,600 --> 01:20:47,420
+بالشكل اللي عندنا هذا اللي قلته هناك مقوله كويس
+
+709
+01:20:47,420 --> 01:20:52,780
+اذا هذا الكلام بدي يساوي اظن 1 على 2 I مقدار ثابت
+
+710
+01:20:53,540 --> 01:21:01,420
+يبقى شرف برا يبقى هذا واحد على اتنين I ل plus ل E
+
+711
+01:21:01,420 --> 01:21:10,160
+أس I A T ناقص واحد على اتنين I ل مين ليه ل plus
+
+712
+01:21:10,160 --> 01:21:18,240
+transform ل E أس ناقص A I T يبقى هذا الكلام بدي
+
+713
+01:21:18,240 --> 01:21:29,250
+اسمه واحد على اتنين Iيبقى هذه واحد على S ناقص AI
+
+714
+01:21:29,250 --> 01:21:38,090
+طبق الأول مثال أخدنا اليوم ناقص
+
+715
+01:21:38,090 --> 01:21:48,790
+واحد على اتنين I لمين لواحد على S زائد AIيعني يا
+
+716
+01:21:48,790 --> 01:21:54,030
+بنات هذي بيصير واحد على اتنين I عامل مشترك بيظل
+
+717
+01:21:54,030 --> 01:22:03,710
+ادنا واحد على S ناقص AI ناقص واحد على S زائد AI لو
+
+718
+01:22:03,710 --> 01:22:09,870
+وحدنا المقامات للكل يبقى واحد على اتنين I وهنا
+
+719
+01:22:09,870 --> 01:22:16,390
+بيصير S ناقص AI في S زائد AI
+
+720
+01:22:19,040 --> 01:22:31,220
+تمام بيصير عندك S زائد AI ناقص S زائد AI هذا
+
+721
+01:22:31,220 --> 01:22:38,580
+الكلام يساوي واحد على اتنين I فيه اظن ناقص S وزائد
+
+722
+01:22:38,580 --> 01:22:47,520
+S مع السلامة بيضلي اتنين AI على أليس هذا الفرق بين
+
+723
+01:22:47,520 --> 01:22:56,050
+المربعين؟يبقى مربع الكمية الأولى ناقص مربع الكمية
+
+724
+01:22:56,050 --> 01:23:02,210
+التانية يبقى A تربيع في I تربيع I تربيع يبقى سالب
+
+725
+01:23:02,210 --> 01:23:08,310
+واحد يبقى سالب A تربيع يبقى سالب A تربيع بالشكل
+
+726
+01:23:08,310 --> 01:23:14,120
+اللي عندنا هذايبقى اتنين اي مع اتنين ومع الاي
+
+727
+01:23:14,120 --> 01:23:22,000
+بيبقى القداش اي هذي S تربيع زائد A تربيع نفس
+
+728
+01:23:22,000 --> 01:23:26,620
+النتيجة اللي حصلنا عليها قبل قليل في المثال رقم
+
+729
+01:23:26,620 --> 01:23:31,640
+اتنين ولا لا يبقى هذا السؤال موجود عندك في الكتاب
+
+730
+01:23:31,640 --> 01:23:39,010
+ومش هجدكوا بس بدوا كمان ل place ل cosine ATلو
+
+731
+01:23:39,010 --> 01:23:44,230
+أخدنا لبلاي سا كوسين بيطلع هذه بالضبط بس بدل 2I
+
+732
+01:23:44,230 --> 01:23:49,350
+بيصير النص فقط ماعنديش I وهذه بدل النقص مش بيصير
+
+733
+01:23:49,350 --> 01:23:55,590
+بيصير زائد تمرين سؤال موجود في الكتاب أندي لحد هنا
+
+734
+01:23:55,590 --> 01:24:00,790
+stop بنكمل ان شاء الله المرة القادمة
+
diff --git a/PL9fwy3NUQKwa8ZDfSFGn6H8xVFLzqmCZC/5tytEs18MlY.srt b/PL9fwy3NUQKwa8ZDfSFGn6H8xVFLzqmCZC/5tytEs18MlY.srt
new file mode 100644
index 0000000000000000000000000000000000000000..73ff49131db8f8bb5052a8a9bdae1edbb9fc2b27
--- /dev/null
+++ b/PL9fwy3NUQKwa8ZDfSFGn6H8xVFLzqmCZC/5tytEs18MlY.srt
@@ -0,0 +1,2703 @@
+1
+00:00:10,540 --> 00:00:15,240
+المرة الماضية انتهينا من سكشن ستة اثنين اللي هو
+
+2
+00:00:15,240 --> 00:00:19,840
+يتحدث عن استخدام the Laplace transform لحل المعادلة
+
+3
+00:00:19,840 --> 00:00:24,280
+التفاضلية أو حل الـ initial value problem اليوم إن
+
+4
+00:00:24,280 --> 00:00:28,240
+شاء الله هناخد  function جديدة نسميها unit step
+
+5
+00:00:28,240 --> 00:00:33,630
+function أو اختصارا الـ step function نقطة تعريف الـ
+
+6
+00:00:33,630 --> 00:00:37,550
+step function  ولاحظ أن الـ step function بتلعب دور
+
+7
+00:00:37,550 --> 00:00:42,830
+كبير في موضوع the Laplace transform بل سنحسبها كمان
+
+8
+00:00:42,830 --> 00:00:47,670
+the Laplace transform بجي بقول the unit step function
+
+9
+00:00:47,670 --> 00:00:52,050
+is denoted by يبقى هنرمز للـ unit step function
+
+10
+00:00:52,050 --> 00:00:58,870
+بيبدأ لـ U c as a function of T الـ undefined as
+
+11
+00:00:58,870 --> 00:01:04,090
+ونعرفها بالشكل التالي كـ piecewise function يبقى U
+
+12
+00:01:04,090 --> 00:01:09,430
+c of T بيبدأ تساوي صفر لما T تبقى دائما وأبدا أقل 
+
+13
+00:01:09,430 --> 00:01:14,280
+من c وإذا كانت تساوي c أو أكبر من c فالـ unit step
+
+14
+00:01:14,280 --> 00:01:19,500
+function بتساوي كده واحد صحيح ممكن نتعرف على شكل
+
+15
+00:01:19,500 --> 00:01:24,040
+الـ unit step function اللي عندنا كالتالي لو جيت
+
+16
+00:01:24,040 --> 00:01:30,520
+أخذت محاور بالشكل هذا وقلت هذا محور T وهذا محور Y
+
+17
+00:01:30,520 --> 00:01:33,280
+أو محور f يبقى هذا محور Y
+
+18
+00:01:38,500 --> 00:01:45,360
+افترضوا أن هذا رقم الـ main الرقم c لأن اشترط c
+
+19
+00:01:45,360 --> 00:01:53,180
+ما لها أكبر من صفر إذا لما تبقى الدالة قبل c يعني
+
+20
+00:01:53,180 --> 00:01:58,540
+أي قيمة قبل c قيمة الدالة عندها جداش تبقى بصفر
+
+21
+00:01:58,540 --> 00:02:02,860
+يبقى الدالة بدأت تكون مغطية المنطقة هذه كلها
+
+22
+00:02:02,860 --> 00:02:07,640
+بالشكل اللي عندها تمام لكن من هنا بنات بدأت تبقى
+
+23
+00:02:07,640 --> 00:02:12,180
+فترة مفتوحة أو النقطة هذه عندها معرفة دالة غير
+
+24
+00:02:12,180 --> 00:02:17,180
+معرفة دالة هادي عند النقطة معرفة وين بيصير قيمتها
+
+25
+00:02:17,180 --> 00:02:21,420
+فوق اللى بواحد عندما c إذا بيجي على القيمة اللى
+
+26
+00:02:21,420 --> 00:02:26,260
+عندنا اللي واحد صحيح وطلع قبالها وبالتالي الدالة
+
+27
+00:02:26,260 --> 00:02:31,680
+بعد ذلك دالة ثابتة لكل القيم اللي بعد c قيمة
+
+28
+00:02:31,680 --> 00:02:35,810
+الدالة مقدار ثابت اللي واحد يبقى لو رسمنا هذه الـ
+
+29
+00:02:35,810 --> 00:02:41,110
+function هتصير بالشكل اللي عندنا هذا يبقى هنا حصلت
+
+30
+00:02:41,110 --> 00:02:46,910
+قفزة من النقطة لأن هذه لم نقطة اللي فوق وما من هنا
+
+31
+00:02:46,910 --> 00:02:51,570
+سميناها الـ step function اللي هي دالة القفزة أو
+
+32
+00:02:51,570 --> 00:02:56,810
+الدالة السلمية تمام بس ما طلعتش درجات كتير درجة
+
+33
+00:02:56,810 --> 00:02:59,740
+واحدة مش أكثر السلمية اللي أخذناها في الـ calculus
+
+34
+00:02:59,740 --> 00:03:05,360
+إيه نطلع عدة درجات وها كده الآن بنحاول نستخدم هذه
+
+35
+00:03:05,360 --> 00:03:10,400
+الدالة في رسم بعض الـ functions نبدأ ناخد بعض
+
+36
+00:03:10,400 --> 00:03:19,720
+الأمثلة على كيفية الرسم يبقى example sketch
+
+37
+00:03:19,720 --> 00:03:26,160
+the graph of 
+
+38
+00:03:27,860 --> 00:03:38,240
+the function f of t بدي يساوي واحد ناقص u c of t
+
+39
+00:03:43,120 --> 00:03:47,240
+قال ارسم لي شكل الدالة اللي عندنا هذه بنقوله
+
+40
+00:03:47,240 --> 00:03:51,620
+بقصتنا بسيطة جدا بنحاول نرسم هذه الدالة إذا لو
+
+41
+00:03:51,620 --> 00:03:57,320
+جينا رسمنا هذه الدالة بقوله هذه الـ function هذه T
+
+42
+00:03:57,320 --> 00:04:03,000
+وهذه هنا main الـ F of T ونختار الرقم هذا اللي
+
+43
+00:04:03,000 --> 00:04:07,300
+عندنا اللي هو main الرقم c اللي هو greater than
+
+44
+00:04:07,300 --> 00:04:14,050
+zero دائما وأبدا طيب بنا نتعرف على شكل الدالة بدي
+
+45
+00:04:14,050 --> 00:04:18,910
+بقوله أنا مش هانرسم بدي أعرف شو شكلها يبقى F of T
+
+46
+00:04:18,910 --> 00:04:27,650
+بديه يساوي واحد ناقص الـ U c of T أما صفر لما T أقل
+
+47
+00:04:27,650 --> 00:04:35,100
+من c أما واحد لما T greater than or equal to c يبقى
+
+48
+00:04:35,100 --> 00:04:41,340
+هذه بدها تساوي بشكل إن إذا واحد ناقص صفر بواحد
+
+49
+00:04:41,340 --> 00:04:47,400
+يبقى هاي واحد لما T أقل من c واحد ناقص واحد يساوي
+
+50
+00:04:47,400 --> 00:04:55,380
+صفر لما T greater than or equal to c إذا كان T أقل
+
+51
+00:04:55,380 --> 00:05:01,120
+من c فقيمة الدالة كم واحد يبقى على المنطقة هذه
+
+52
+00:05:01,120 --> 00:05:05,200
+بتبقى قيمة الدالة كل واحد إذا لو طلعت هنا عند
+
+53
+00:05:05,200 --> 00:05:10,060
+الواحد يبقى بدها تبقى الـ function عنها معرفة بهذا
+
+54
+00:05:10,060 --> 00:05:16,060
+الشكل كل المنطقة بس عندها دي  مفتوحة لأنها أقل من
+
+55
+00:05:16,060 --> 00:05:23,580
+c هي تحتها دوري هيك هي نقطة c تمام يبقى هذا إذا
+
+56
+00:05:23,580 --> 00:05:28,740
+كان T أقل من c فقيمة الدالة واحد لكن عندما T تساوي
+
+57
+00:05:28,740 --> 00:05:34,880
+c فما فوق تصير قيمة الدالة صفر يبقى هنا بدأ تصير
+
+58
+00:05:34,880 --> 00:05:41,340
+هنا بصفر مغلقة ونظل ماشيين إلى ما شاء الله يبقى
+
+59
+00:05:41,340 --> 00:05:45,780
+هذه كلها تعتبر من رسمة الـ function اللي عندنا
+
+60
+00:05:45,780 --> 00:05:50,230
+وكأنه إن هي إيه اللي عملنا جبنا اللي فوق تحت واللي
+
+61
+00:05:50,230 --> 00:05:55,690
+تحت فوق بالضبط تماما يبقى هذا مثال هذا يعتبر مثال
+
+62
+00:05:55,690 --> 00:06:01,390
+بسيط انتجليه شوية يبقى بنجي نقول example two
+
+63
+00:06:01,390 --> 00:06:08,530
+example two يبقى هذا كان example one وهذا example
+
+64
+00:06:08,530 --> 00:06:15,150
+two برضه sketch the graph of the function sketch
+
+65
+00:06:15,150 --> 00:06:17,670
+the graph
+
+66
+00:06:27,820 --> 00:06:38,800
+y تساوي T ناقص ثلاثة في U اثنين as a function of T
+
+67
+00:06:40,000 --> 00:06:49,500
+ناقص T ناقص اثنين T ناقص اثنين في U ثلاثة as a
+
+68
+00:06:49,500 --> 00:06:58,000
+function of T on the interval on the interval T
+
+69
+00:06:58,000 --> 00:07:05,160
+greater than or equal to zero كويس
+
+70
+00:07:05,160 --> 00:07:10,830
+قال لي ارسم لي شكل الدالة اللي عندنا هذه على الفترة
+
+71
+00:07:10,830 --> 00:07:16,010
+من صفر لغاية infinity بيطلع في السؤال و بيطلع في
+
+72
+00:07:16,010 --> 00:07:22,470
+اللي عندي بعد عن بعض مظبوط الشكل هو بعد عن بعض لكن
+
+73
+00:07:22,470 --> 00:07:27,050
+أنا بدي أحاول أحط الـ function اللي عندنا هذه على
+
+74
+00:07:27,050 --> 00:07:31,470
+الصيغة اللي عندنا هذه وبالتالي بيصير عملية الرسم
+
+75
+00:07:31,470 --> 00:07:37,370
+عملية سهلة لحظة يا إخواننا جايبين هنا U 2 و U 3 يعني
+
+76
+00:07:37,370 --> 00:07:42,930
+أنا دخلت رقمين على الخط إذا أنا بدي أدرس الفترة من
+
+77
+00:07:42,930 --> 00:07:48,030
+صفر لغاية اثنين ومن اثنين لغاية الثلاثة ومن الثلاثة
+
+78
+00:07:48,030 --> 00:07:51,830
+فما فوق يعني صار عندي ثلاث فترات من خلال السؤال
+
+79
+00:07:51,830 --> 00:07:57,770
+اللي عندنا هذا تمام فأروح بقول له دل هادي y تساوي
+
+80
+00:07:57,770 --> 00:08:04,470
+أحد ثلاث أمور الأمر الأول بدي آخد لما T تبقى أقل
+
+81
+00:08:04,470 --> 00:08:11,270
+من اثنين لما T تبقى أقل من اثنين يبقى هادي T ناقص
+
+82
+00:08:11,270 --> 00:08:14,230
+ثلاثة كم تكون قيمة الدال هادي
+
+83
+00:08:18,690 --> 00:08:24,290
+يبقى نقص T نقص 2 U 3 قداش قبل اثنين
+
+84
+00:08:30,130 --> 00:08:34,510
+صفر برضه قبل اثنين ونص بصفر وقبل اثنين وتسعة
+
+85
+00:08:34,510 --> 00:08:39,010
+وتسعة وقبل الثلاثة بصفر اثنين قبل الثلاثة إذا 
+
+86
+00:08:39,010 --> 00:08:46,590
+هذه صفر طبعا فلو كانت الـ T أكبر من أو تساوي اثنين
+
+87
+00:08:46,590 --> 00:08:53,980
+وأقل من ثلاثة يبقى بجي بقول له هادي T ناقص ثلاثة
+
+88
+00:08:53,980 --> 00:08:59,680
+في U اثنين هالحساس بعد اثنين مظبوط بعد اثنين
+
+89
+00:08:59,680 --> 00:09:02,700
+على طول بواحد إذا من اثنين لثلاثة جيبتها في
+
+90
+00:09:02,700 --> 00:09:11,290
+الجداش بواحد نقص T نقص اثنين في قبل الثلاثة اللي
+
+91
+00:09:11,290 --> 00:09:17,550
+همين بصفر تمام نيجي الآن ناخد الفترة T greater
+
+92
+00:09:17,550 --> 00:09:22,810
+than or equal to ثلاثة يبقى U اثنين بقداش بتكون
+
+93
+00:09:22,810 --> 00:09:30,410
+بعد الثلاثة بواحد يبقى بيصير T ناقص ثلاثة في واحد
+
+94
+00:09:30,800 --> 00:09:36,720
+نقص T نقص اثنين في قداش كمان بواحد تمام تمام
+
+95
+00:09:36,720 --> 00:09:41,980
+الآن نروح نتعرف على شكل الدالة اللي عندنا هذه يبقى
+
+96
+00:09:41,980 --> 00:09:48,940
+دي صار شكلها بالشكل التالي هذا ثلاثة أجزاء الجزء
+
+97
+00:09:48,940 --> 00:09:53,000
+الأول صفر في رقم صفر صفر في رقم صفر صفر نقص
+
+98
+00:09:53,000 --> 00:09:59,620
+صفر يبقى بصفر لما T أقل من اثنين هذا الـ term
+
+99
+00:09:59,620 --> 00:10:05,100
+بيزير وبيظلش عندنا إلا main T ناقص ثلاثة يبقى T
+
+100
+00:10:05,100 --> 00:10:10,540
+ناقص ثلاثة لما T أكبر من أو يساوي اثنين وأقل من
+
+101
+00:10:10,540 --> 00:10:18,380
+الثلاثة نيجي لهذه تصير T ناقص ثلاثة ناقص T 
+
+102
+00:10:18,380 --> 00:10:23,800
+زائد اثنين ناقص T وزائد T مع السلامة ناقص ثلاثة
+
+103
+00:10:23,800 --> 00:10:29,620
+وزائد اثنين بيظل قداش ناقص واحد يبقى ناقص واحد لما
+
+104
+00:10:29,620 --> 00:10:33,760
+T greater than or equal to ثلاثة إذا من الـ
+
+105
+00:10:33,760 --> 00:10:39,240
+function الأصلية اللي عند هذه استطعت كتابتها على
+
+106
+00:10:39,240 --> 00:10:45,420
+الشكل اللي عندنا هذا إلا لو رسمت هذه بكون رسمت الـ
+
+107
+00:10:45,420 --> 00:10:50,520
+function الأصلية طيب تعالوا نرسم ونشوف كيف بدو
+
+108
+00:10:50,520 --> 00:10:58,220
+يكون شكلها إذا لو جيت قلت هذا محور T وهذا محور Y
+
+109
+00:11:00,050 --> 00:11:05,730
+الآن هيا عندي هنا اثنين وهي عندي هنا إيش اللي هي
+
+110
+00:11:05,730 --> 00:11:10,610
+الثلاثة وهذا ما بعدها الآن جاب لي اثنين جداش قيمة
+
+111
+00:11:10,610 --> 00:11:17,050
+الدالة صفر يبقى مفتوحة عندي اثنين هيك هي مفتوحة
+
+112
+00:11:17,050 --> 00:11:23,190
+ونغطي المنطقة هذه كلها كل المنطقة اللي عندنا هذه
+
+113
+00:11:23,190 --> 00:11:27,970
+ليه قيمة من قيمة الـ dollar الآن بدنا نيجي من
+
+114
+00:11:27,970 --> 00:11:34,730
+اثنين لغاية ثلاثة يبقى y تساوي T ناقص ثلاثة يعني
+
+115
+00:11:34,730 --> 00:11:42,210
+معادلة خطية الآن قداش قيمتها عندي اثنين T أكبر من
+
+116
+00:11:42,210 --> 00:11:47,290
+يساوي اثنين لو حطيت اثنين بيصير كده إذا عند اثنين
+
+117
+00:11:47,290 --> 00:11:54,090
+هذه بدها تنزل هنا لمين لسالب واحد تمام يبقى بيجيني
+
+118
+00:11:54,090 --> 00:11:59,750
+هنا بنزل رأسي لغاية ما أجي عند السالب واحد و
+
+119
+00:11:59,750 --> 00:12:07,370
+بيصير مغلقة بسبب اليساوي طيب لو وصلت لثلاثة لا سمح
+
+120
+00:12:07,370 --> 00:12:10,250
+الله طبعا أقل من ثلاثة بيقول لو صارت ثلاثة إيش
+
+121
+00:12:10,250 --> 00:12:15,790
+بيصير صفر يبقى عندي الثلاثة بدأ تطلع لصفر بس
+
+122
+00:12:15,790 --> 00:12:20,830
+عند صفر بيكون مالها مفتوحة إذا هذا يمثل الخط
+
+123
+00:12:20,830 --> 00:12:26,730
+المستقيم T ناقص ثلاثة يبقى بدو يصير شكل دالة
+
+124
+00:12:26,730 --> 00:12:30,430
+بالشكل اللي يعني هذا الخط المستقيم الغامق هذا
+
+125
+00:12:34,560 --> 00:12:40,560
+يبقى هذا رسمة لـ T ناقص ثلاثة تمام بعد ذلك بدو يجيب
+
+126
+00:12:40,560 --> 00:12:45,300
+بعد الثلاثة بعد الثلاثة قيمة الدالة كده سالب واحد
+
+127
+00:12:45,300 --> 00:12:51,880
+إذا هذه بدها تنزل automatic عند السالب واحد وبعد
+
+128
+00:12:51,880 --> 00:12:56,880
+الثلاثة قيمتها على محور الخط كده سالب واحد يبقى
+
+129
+00:12:56,880 --> 00:13:02,820
+هذه الدالة بالشكل الثاني هنا يبقى هاي رسمنا اللي هو
+
+130
+00:13:02,820 --> 00:13:07,020
+الدالة في المقاطع الثلاثة اللي هي piecewise
+
+131
+00:13:07,020 --> 00:13:13,340
+continuous طبعا يبقى هاه لو الشكل استشكل علينا هذا
+
+132
+00:13:13,340 --> 00:13:17,960
+بأحاول أحطه في شكل جديد هاي الشكل الجديد الشكل
+
+133
+00:13:17,960 --> 00:13:21,040
+الجديد الساهر رسمه يبقى بدون اسم وبالتالي يكون
+
+134
+00:13:21,040 --> 00:13:25,660
+رسمنا من الدالة الأصلية اللي عندنا
+
+135
+00:13:41,980 --> 00:13:48,980
+بنحاول نجيب the Laplace transform لمن لـ U c of T يبقى
+
+136
+00:13:48,980 --> 00:13:56,380
+example كمان find the Laplace
+
+137
+00:13:56,380 --> 00:14:03,020
+transform for
+
+138
+00:14:03,020 --> 00:14:10,180
+the function U c of T
+
+139
+00:14:20,470 --> 00:14:23,970
+الورقة الجادة اللي اقنعكوا هي المرة اللي فاتت أو
+
+140
+00:14:23,970 --> 00:14:29,050
+في الكتاب صفحة 319 لو فتحنا بنعرف النتيجة مباشرة
+
+141
+00:14:29,050 --> 00:14:35,370
+لكن بنعرف من أين جاءت هذه النتيجة يبقى عندك U c
+
+142
+00:14:35,370 --> 00:14:40,830
+و T هي رقم مقماشرقم 12 للبلايس ترانسفورم إيه إيه
+
+143
+00:14:40,830 --> 00:14:42,290
+إيه إيه إيه إيه إيه إيه إيه إيه إيه إيه إيه إيه
+
+144
+00:14:42,290 --> 00:14:45,750
+إيه إيه إيه إيه إيه إيه إيه 
+
+145
+00:14:45,750 --> 00:14:51,830
+إيه إيه
+
+146
+00:14:53,060 --> 00:15:00,320
+أنا بروح بقول له the plus transform لـ U c of T بدو يساوي
+
+147
+00:15:00,320 --> 00:15:08,100
+تكامل من صفر لـ infinity لـ E أس ناقص ST لـ U c of T
+
+148
+00:15:08,100 --> 00:15:17,250
+DT طيب هذا الكلام يساوي ما يعني هذه U c of T عبارة
+
+149
+00:15:17,250 --> 00:15:22,730
+عن جزئين تمام إذن بالدجاجة للجزء الأول يبقى هذا
+
+150
+00:15:22,730 --> 00:15:29,910
+integration من صفر إلى c للـ E أس ناقص ST في
+
+151
+00:15:29,910 --> 00:15:36,550
+الفترة هذه U c of T بقداش صفر ممتاز جدا يبقى في
+
+152
+00:15:36,550 --> 00:15:44,560
+صفر في DT إزاي تكامل من c إلى Infinity للـ E أُس
+
+153
+00:15:44,560 --> 00:15:51,780
+ناقص ST في الـ use of U بواحد في الـ DT إذا هذا كله
+
+154
+00:15:51,780 --> 00:15:57,720
+بيروح بقداش بصفر هذا improper integral يبقى بيروح
+
+155
+00:15:57,720 --> 00:16:04,720
+اعمل له as a limit يبقى هذا الـ limit تكامل من c إلى
+
+156
+00:16:04,720 --> 00:16:11,980
+a لما a tends to infinity للـ E أس ناقص STDT
+
+157
+00:16:14,720 --> 00:16:19,980
+هذا الكلام يساوي limit لما الـ a tends to infinity
+
+158
+00:16:19,980 --> 00:16:25,760
+تكامل الـ exponential بالـ exponential itself على
+
+159
+00:16:25,760 --> 00:16:31,200
+مشتقة الأس لما يكون الأس as a linear function يعني
+
+160
+00:16:31,200 --> 00:16:36,840
+معادلة من الدرجة الأولى يبقى عالمين على ناقص الـ s
+
+161
+00:16:36,840 --> 00:16:44,640
+من c لغاية الـ a يبقى هذا الكلام بدو يساوي limit لما
+
+162
+00:16:44,640 --> 00:16:48,920
+a tends to infinity بتعوض فيه نتيجة التكامل
+
+163
+00:16:48,920 --> 00:16:53,660
+بالقيمة اللي فوق نقص اللي تحت لإنه finite integral
+
+164
+00:16:53,660 --> 00:17:03,440
+تكامل محدود يبقى هذا E أس ناقص S A على ناقص S ناقص
+
+165
+00:17:03,440 --> 00:17:11,820
+E أس بدي أشيل هذه وأحط مكانها c يبقى ناقص S في c
+
+166
+00:17:11,820 --> 00:17:22,130
+على مين على ناقص S والـ limit للمقدار هذا كله طب
+
+167
+00:17:22,130 --> 00:17:25,450
+لما الـ E بدها تروح لـ infinity هذا الـ أس بالسالب
+
+168
+00:17:25,450 --> 00:17:30,150
+يبقى بنزل وين تحت بيصير واحد على ما له نهاية اللي
+
+169
+00:17:30,150 --> 00:17:34,530
+هو الجداش يبقى هذا الله يسهل عليه غير مأسوف عليه
+
+170
+00:17:34,530 --> 00:17:39,930
+بصفر هذا كله له دعوة باللمتة مافيش فيه capital E
+
+171
+00:17:39,930 --> 00:17:44,990
+نهاية يبقى هذا يعتبر كونستان يبقى ناقص على ناقص
+
+172
+00:17:44,990 --> 00:17:52,210
+بالزائد بيظل E أس الـ CS على S هي النتيجة اللي
+
+173
+00:17:52,210 --> 00:17:56,290
+عندنا يبقى هذا الـ plus transform للـ unit step
+
+174
+00:17:56,290 --> 00:18:00,850
+function اللي ذكرناها قبل قليل أظن هي نفس النتيجة
+
+175
+00:18:00,850 --> 00:18:05,330
+اللي عندكوا في الجدول يبقى هي نفس النتيجة بالضبط
+
+176
+00
+
+216
+00:23:15,660 --> 00:23:26,980
+بقول هنا F F of S هو لابلاس ترانسفورم لدالة F of T
+
+217
+00:23:26,980 --> 00:23:37,220
+ماله هذا exists لو كان هذا موجود for S which is
+
+218
+00:23:37,220 --> 00:23:44,740
+greater than C و C دائما وأبدا ما لها موجبة than
+
+219
+00:23:44,740 --> 00:23:56,600
+النقطة الأولى لابلاس ترانسفورم لـ U C of T في الـ F
+
+220
+00:23:56,600 --> 00:24:04,100
+of T ناقص الـ C في الـ F of T ناقص الـ C يبقى هذا
+
+221
+00:24:04,100 --> 00:24:12,700
+يساوي E أس ناقص CS فاهمين؟ في لابلاس ترانسفورم للـ
+
+222
+00:24:12,700 --> 00:24:20,240
+F of T واللي بده يساوي E أس ناقص CS في capital F
+
+223
+00:24:20,240 --> 00:24:25,020
+of S وهذه سميها رقم 1
+
+224
+00:24:27,700 --> 00:24:33,480
+ممكن أعمل عملية عكسية آخذ معكوس لابلاس ترانسفورم
+
+225
+00:24:33,480 --> 00:24:38,900
+للدالة هذه يبقى مين بده يعطيني الدالة بين القوسين يبقى
+
+226
+00:24:38,900 --> 00:24:50,890
+لو قلت لكم conversely على العكس لابلاس انفرس لمن؟
+
+227
+00:24:50,890 --> 00:24:58,150
+للـ E أس ناقص CS في capital F of S بده يساوي من
+
+228
+00:24:58,150 --> 00:25:02,350
+لابلاس انفرس لـ لابلاس هذه لابلاس انفرس مع لابلاس
+
+229
+00:25:02,350 --> 00:25:06,350
+هتلقوا بعضها بظالمين الدالة اللي عندها دي فجأة ده
+
+230
+00:25:06,350 --> 00:25:18,430
+بده يساوي U C of T في الـ F of T ناقص الـ C تمام
+
+231
+00:25:18,430 --> 00:25:24,480
+نأتي الآن للنقطة الثانية النقطة الثانية بيقول لابلاس
+
+232
+00:25:24,480 --> 00:25:34,180
+ترانسفورم لـ E of C في T في الـ F of T في الـ F of T
+
+233
+00:25:34,180 --> 00:25:44,000
+بده يساوي الـ F of S ناقص الـ C والـ S greater than C
+
+234
+00:25:44,000 --> 00:25:46,920
+وإلا كمان الـ S
+
+235
+00:25:50,450 --> 00:25:57,670
+لو عملت العملية العكسية يبقى هنا conversely
+
+236
+00:26:00,350 --> 00:26:09,270
+لابلاس انفرس لمين؟ لـ capital F of S ناقص الـ C بده
+
+237
+00:26:09,270 --> 00:26:18,890
+يساوي E of CT في الـ F of T بالشكل اللي عندنا سميها 
+
+238
+00:26:18,890 --> 00:26:24,480
+هذه رقم اثنين يبقى واحد واثنين هما النقطتين
+
+239
+00:26:24,480 --> 00:26:28,860
+الأساسيتين تبعات النظريتين اللي عندنا في الكتاب
+
+240
+00:26:28,860 --> 00:26:35,520
+بنا نرجع لكل واحدة فيهم ونروح نبرهن صحتها وبعدين
+
+241
+00:26:35,520 --> 00:26:42,900
+نستخدمها كخواص لحل المسائل المختلفة الـ proof
+
+242
+00:26:54,670 --> 00:26:55,870
+هذه هي النقطة الأولى
+
+243
+00:26:58,620 --> 00:27:05,820
+لو كان لابلاس ترانسفورم لدالة exist then لابلاس
+
+244
+00:27:05,820 --> 00:27:10,920
+ترانسفورم لهذه الدالة بعد ما عمل لها shift مضروبا
+
+245
+00:27:10,920 --> 00:27:16,000
+في الـ U C of T بيساوي E أس ناقص CS في لابلاس الـ F
+
+246
+00:27:16,000 --> 00:27:20,600
+of T أو إن شئتم فقولوا E أس ناقص CS فاهمين في 
+
+247
+00:27:20,600 --> 00:27:26,150
+capital F of S يبقى أنا بالدرجة آخذه منين؟ الدالة
+
+248
+00:27:26,150 --> 00:27:30,270
+اللي عندنا هذه فبأجي بقوله أنا بدي آخذ Laplace
+
+249
+00:27:30,270 --> 00:27:37,930
+transform لـ U C of T فمين في الـ F of T ناقص الـ C
+
+250
+00:27:37,930 --> 00:27:43,110
+بدي أعرف إنه هل هو القيمة اللي هناك والله ما هيش
+
+251
+00:27:43,520 --> 00:27:47,500
+بقوله كويس بدي أرجع لتعريف الـ Laplace transform اللي 
+
+252
+00:27:47,500 --> 00:27:52,020
+اتعلمناه يبقى هذا integration من zero لغاية
+
+253
+00:27:52,020 --> 00:28:02,000
+infinity لـ E أس ناقص ST فاهمين؟ في الـ U C of
+
+254
+00:28:02,000 --> 00:28:11,430
+T في الـ F of T ناقص الـ C كله دي تمام الـ unit step
+
+255
+00:28:11,430 --> 00:28:17,370
+function عبارة عن جزء إما صفريا إما كده هيكون واحد
+
+256
+00:28:17,370 --> 00:28:22,410
+ممتاز جدا إذا هذه بدها تساوي integration من zero
+
+257
+00:28:22,410 --> 00:28:31,670
+للـ C للـ E أس ناقص ST في zero في الـ F of T ناقص الـ
+
+258
+00:28:31,670 --> 00:28:38,230
+C في DT زائد integration من C إلى infinity للـ E 
+
+259
+00:28:38,230 --> 00:28:46,270
+أس ناقص ST في واحد في الـ F of T ناقص الـ C DT يبقى
+
+260
+00:28:46,270 --> 00:28:49,750
+شيلت الـ unit step function وحطيتها مرة بزيرو على
+
+261
+00:28:49,750 --> 00:28:55,190
+الفترة من zero لـ C ومرة بواحد من C لغاية infinity
+
+262
+00:28:55,190 --> 00:29:00,790
+الـ term الأول هذا ماله Zero معاه سلامة نأتي للـ
+
+263
+00:29:00,790 --> 00:29:04,770
+term الثاني اللي عندنا هذا يبقى هذا الكلام بده
+
+264
+00:29:04,770 --> 00:29:12,310
+يساوي integration من C لغاية infinity للـ E أس ناقص
+
+265
+00:29:12,310 --> 00:29:18,510
+ST في الـ F of T ناقص الـ C في DT
+
+266
+00:29:27,760 --> 00:29:33,480
+إذا بدي أعتبر هذا كله بمين؟ بمتغير جديد، إذا بدي 
+
+267
+00:29:33,480 --> 00:29:37,320
+أعمل تعويض زي ما كنا بنعوض عادي في التكاملات
+
+268
+00:29:37,320 --> 00:29:41,340
+العادية integration by substitution إذا أنا لو
+
+269
+00:29:41,340 --> 00:29:54,090
+رحت حطيت الـ η تساوي تساوي T ناقص C يبقى دي إي تا
+
+270
+00:29:54,090 --> 00:30:00,070
+بده يساوي دي تي والـ C ما هو مقدار ثابت مش تكتب مين
+
+271
+00:30:00,070 --> 00:30:06,790
+بزيرو تمام؟ هذا المثال ها دي هتصبح على الشكل التالي
+
+272
+00:30:06,790 --> 00:30:13,050
+يبقى صار لابلاس ترانسفورم لـ U C as a function of T
+
+273
+00:30:13,050 --> 00:30:20,530
+في الـ F of T ناقص الـ C بده يساوي تكامل تعالوا نشوف
+
+274
+00:30:20,530 --> 00:30:28,930
+هنا يبقى E أس ناقص S نجي لمين؟ التي قدشتي يا بنات
+
+275
+00:30:28,930 --> 00:30:39,250
+η زائد C يبقى هذه بـ η زائد C η زائد C طبعا
+
+276
+00:30:39,250 --> 00:30:49,400
+الآن هذه F of η الـ D T دي η طبعا بظالمين عن
+
+277
+00:30:49,400 --> 00:30:56,410
+حدود التكامل بأجي بقول لو كانت T بـ Infinity يبقى
+
+278
+00:30:56,410 --> 00:31:02,470
+بـ η Infinity ناقص يعني Infinity يبقى بقى الحد
+
+279
+00:31:02,470 --> 00:31:09,510
+العلوي كما هو الآن لو كان الحد الـ T تساوي الـ C
+
+280
+00:31:09,510 --> 00:31:15,350
+بيصير C ناقص C لو بـ Zero يبقى η تساوي قداش
+
+281
+00:31:15,350 --> 00:31:20,910
+تساوي Zero تمام تمام يبقى هذا تكامل من Zero لـ
+
+282
+00:31:20,910 --> 00:31:30,760
+Infinity هذا بنات E أس ناقص S η زائد في إيه من
+
+283
+00:31:30,760 --> 00:31:39,740
+في E أس ناقص CS في الـ F of η في D η،
+
+284
+00:31:39,740 --> 00:31:46,230
+مظبوط؟ هذا إيه اللي هو علاقة بالتكامل؟ ما ليش علاقة
+
+285
+00:31:46,230 --> 00:31:50,530
+في η يبقى هذا مقدار ثابت شرفنا برا يبقى هذا
+
+286
+00:31:50,530 --> 00:32:00,270
+بيصير E أس ناقص CS CS تكامل من Zero لـ Infinity لـ E
+
+287
+00:32:00,270 --> 00:32:10,150
+أس ناقص S η في الـ F of η في D η طب إيش 
+
+288
+00:32:10,150 --> 00:32:16,180
+رأيكم هذا مين يا بنات؟ تعريف مين؟ Laplace transform
+
+289
+00:32:16,180 --> 00:32:22,480
+لدالة F of η يعني مين؟ له capital F of S صحيح ولا
+
+290
+00:32:22,480 --> 00:32:28,800
+لأ؟ يعني هذا بقول له E أس ناقص CS في Laplace
+
+291
+00:32:28,800 --> 00:32:35,560
+transform للـ F of η تمام؟ اللي هو مين؟ capital F
+
+292
+00:32:35,560 --> 00:32:42,920
+of S يبقى E أس ناقص CS في capital F of S أظن وهو 
+
+293
+00:32:42,920 --> 00:32:43,720
+المطلوب؟
+
+294
+00:32:52,490 --> 00:33:01,130
+إذا أثبتنا المطلوب الأول جاء لي conversely يعني آخذ
+
+295
+00:33:01,130 --> 00:33:04,790
+الـ Laplace inverse هنا بده يساوي الـ Laplace inverse هنا
+
+296
+00:33:04,790 --> 00:33:09,310
+تماما بأجي بقوله الآن بده أجي للـ conversely بتاعتها
+
+297
+00:33:10,030 --> 00:33:17,330
+يبقى بدأ آخذ Laplace inverse لمين؟ لـ Laplace لـ U C
+
+298
+00:33:17,330 --> 00:33:23,690
+of T في F of T ناقص C بده يساوي Laplace inverse
+
+299
+00:33:23,690 --> 00:33:29,270
+لنتيجة اللي طلعت عندنا هذه E أس ناقص CS في capital
+
+300
+00:33:29,270 --> 00:33:37,690
+F of S طبعا يبقى بناء على أساس لابلاس انفرس لمن؟ 
+
+301
+00:33:37,690 --> 00:33:47,790
+للـ E أس ناقص CS في capital F of S بده يساوي U C of 
+
+302
+00:33:47,790 --> 00:33:56,250
+T في F of T ناقص C طيب إيش رأيكم هذه موجودة عندكم في
+
+303
+00:33:56,250 --> 00:34:01,090
+الجدول؟ موجودة؟
+
+304
+00:34:05,760 --> 00:34:12,740
+رقم كم؟ رقم ثلاثة عشر اللي هو شبهها بالضبط تماما. هذا
+
+305
+00:34:12,740 --> 00:34:16,840
+يا لي وE أس ناقص CS في capital F of S يبقى هذه
+
+306
+00:34:16,840 --> 00:34:20,980
+الثلاثة عشر اللي عندكم وين؟ في الجدول اللي إحنا أثبتناها
+
+307
+00:34:20,980 --> 00:34:26,260
+عمليا. هذه هي النقطة الأولى. نأتي لمين؟ للنقطة 
+
+308
+00:34:26,260 --> 00:34:30,800
+الثانية؟ النقطة الثانية قال اللي بده لابلاس
+
+309
+00:34:30,800 --> 00:34:39,660
+transform لـ الـ E أس ناقص CT للـ F of T بالشكل اللي 
+
+310
+00:34:39,660 --> 00:34:45,600
+عندنا يبقى نروح لتعريف لابلاس ترانسفورم لتعريف
+
+311
+00:34:45,600 --> 00:34:50,660
+لابلاس ترانسفورم إذا بدي النتيجة تطلع F of S ناقص 
+
+312
+00:34:50,660 --> 00:34:56,840
+الـ C E of CT بالموجب وليست بالسالب تمام؟ يبقى هذه
+
+313
+00:34:56,840 --> 00:35:03,640
+بدها تساوي تكامل من Zero لـ Infinity للـ E أس ناقص
+
+314
+00:35:03,640 --> 00:35:10,800
+ST في مين؟ في الدالة اللي عندنا هذه E of CT في الـ F
+
+315
+00:35:10,800 --> 00:35:12,580
+of T في الـ DT
+
+316
+00:35:15,340 --> 00:35:20,180
+يبقى هذه بدها تساوي integration من zero إلى
+
+317
+00:35:20,180 --> 00:35:26,100
+infinity هذا الأساسات زي بعض يبقى عند الضرب تجمع
+
+318
+00:35:26,100 --> 00:35:35,920
+الأسس يبقى هذا الكلام بده يساوي E في ناقص S ناقص C
+
+319
+00:35:35,920 --> 00:35:39,940
+في T في F of T DT
+
+320
+00:35:48,130 --> 00:35:54,770
+هذا هو تعريف لابلاس ترانسفورم للدالة اللي عندنا
+
+321
+00:35:54,770 --> 00:36:00,490
+اللي هي الـ F of T بس بشرط مش F of S الـ S أجاب
+
+322
+00:36:00,490 --> 00:36:05,070
+دالة مين؟ S ناقص الـ C يبقى من خلال الـ definition
+
+323
+00:36:05,070 --> 00:36:11,650
+تبع لابلاس ترانسفورم هذا بده يساوي لو capital F of
+
+324
+00:36:11,650 --> 00:36:17,810
+S ناقص الـ C من تعريف لابلاس ترانسفورم لمين؟ لهذه
+
+325
+00:36:17,810 --> 00:36:23,710
+الدالة الآن الآن العملية اللي هو conversely بقدر
+
+326
+00:36:23,710 --> 00:36:28,930
+آخذ لابلاس ترانسفورم لمين؟ للطرفين يبقى بأجي بقوله
+
+327
+00:36:28,930 --> 00:36:31,130
+conversely
+
+328
+00:36:32,420 --> 00:36:41,580
+Laplace inverse لمين؟ لـ capital F of S ناقص الـ C بده
+
+329
+00:36:41,580 --> 00:36:45,660
+يساوي Laplace inverse لـ Laplace بتلغيها بظالمين 
+
+330
+00:36:45,660 --> 00:36:53,520
+الدالة اللي في النص اللي هو E أس CT E أس S CT في
+
+331
+00:36:53,520 --> 00:37:00,080
+من؟ في الـ F of T أظن لو طلعت في الجدول الموجودة
+
+332
+00:37:00,080 --> 00:37:05,560
+هذه برضه اللي هي رقم قداش يا بنات؟ طلع لي في الجدول
+
+333
+00:37:05,560 --> 00:37:11,800
+اللي بين إيديكم أربعة عشر يبقى هي سعرب بتقول رقم
+
+334
+00:37:11,800 --> 00:37:18,040
+أربعة عشر مظبوط يبقى دي رقم أربعة عشر الـ F of S ناقص 
+
+335
+00:37:18,040 --> 00:37:24,860
+من؟ ناقص الـ C الآن شرحنا كيف نستخدم النقطتين 
+
+336
+00:37:24,860 --> 00:37:30,730
+الاثنين اللي عندنا دول في حل المسائل المختلفة يبقى
+
+337
+00:37:30,730 --> 00:37:38,190
+الآن بدنا هذه رقم واحد هذه تماما وبدنا رقم اثنين
+
+338
+00:37:38,190 --> 00:37:43,010
+هذه نكون ملمين بهم ومن خلالهم بدنا نحاول نحل
+
+339
+00:37:43,010 --> 00:37:50,230
+أمثلة مختلفة بأشكال مختلفة كما سترون بعد أن
+
+340
+00:37:50,230 --> 00:37:54,410
+انتهينا من برهان النظرية بدنا نجي ناخذ بعض 
+
+341
+00:37:54,410 --> 00:38:00,500
+الأمثلة حد بدها العمود هذا؟ أنا بدي أترك العمود هنا
+
+342
+00:38:00,500 --> 00:38:23,740
+مش هذول الاثنين هدول لازمات هنا example
+
+343
+00:38:23,740 --> 00:38:24,800
+one
+
+344
+00:38:28,570 --> 00:38:35,730
+أول مثال بقول compute the following compute the
+
+345
+00:38:35,730 --> 00:38:45,770
+following عسبي لي ما يأتي نمرة a بدي لابلاس
+
+346
+00:38:45,770 --> 00:38:55,490
+transform لـ U 2π by as a function of T لصين تي
+
+347
+00:39:02,750 --> 00:39:07,870
+يبقى بأجي بطلع وبيدخل هذه المثال يبقى بأجي بقوله 
+
+348
+00:39:07,870 --> 00:39:14,130
+والـ U C of T هي في F of T ناقص الـ C مقدار الـ
+
+349
+00:39:14,130 --> 00:39:18,950
+shift اللي هنا هو المقدار تبع الـ U C بالضبط تماما
+
+350
+00:39:18,950 --> 00:39:24,570
+بأجي بطلع في مثلي 2π by هنا ما عنديش 2π by
+
+351
+00:39:25,010 --> 00:39:30,890
+مظبوط؟ اه لكن طلب لابلاس ترانسفورم بقول أنا هاه لو
+
+352
+00:39:30,890 --> 00:39:36,550
+قدرت أحطها على الصيغة هذه بجي الجواب عندي مظبوط
+
+353
+00:39:36,550 --> 00:39:42,250
+برجع لذاكرتي من ورق الـ sin T periodic function
+
+354
+00:39:42,250 --> 00:39:47,610
+يعني ده اللي دورية كل قداش؟ تتكرر الدورة كل 2π 
+
+355
+00:39:47,610 --> 00:39:53,760
+by يعني لو أضفت 2π by أو طرحت 2π by لا تتغير
+
+356
+00:39:53,760 --> 00:39:58,260
+قيمة الـ function على الإطلاق تمام؟ يبقى بأجي
+
+357
+00:39:58,260 --> 00:40:05,500
+بقوله solution اتدالى
+
+358
+00:40:05,500 --> 00:40:10,420
+Laplace transform لـ U 2π by as a function of T
+
+359
+00:40:10,420 --> 00:40:16,300
+لصين تي بده يساوي Laplace transform لـ U 2π by
+
+360
+00:40:16,300 --> 00:40:22,920
+as a function of T لصين تي زائد أو ناقص اللي بدك 
+
+361
+00:40:22,920 --> 00:40:27,600
+إياها 2π by لكن إحنا نعيش بالزمن هنا تبقى ناقص
+
+362
+00:40:27,600 --> 00:40:31,620
+يبقى زائد مش لازمالي يبقى بطرح اللي دورة كاملة
+
+363
+00:40:31,620 --> 00:40:37,320
+2π by بالشكل اللي عندنا إذا صارت هذه ها هي الشكل
+
+364
+00:40:37,320 --> 00:40:42,460
+اللي عندنا هذا بالضبط صحيح ولا لأ؟ إذا الجواب E أس
+
+365
+00:40:42,460 --> 00:40:49,060
+ناقص CS يبقى automatic من part one الجواب E أس
+
+366
+00:40:49,060 --> 00:40:58,600
+ناقص C بـ 2π by S في مين؟ في لابلاس ترانسفورم للـ F
+
+367
+00:40:58,600 --> 00:41:05,460
+of T هذه F of T ناقص 2π by يبقى shift انسى
+
+368
+00:41:05,460 --> 00:41:11,980
+يبقى في لابلاس ترانسفورم للـ F of T اللي هي sin T
+
+369
+00:41:16,290 --> 00:41:23,090
+هذا الكلام بده يساوي الو E أس ناقص 2π by S بده 
+
+370
+00:41:23,090 --> 00:41:28,670
+لفلس لصين تي بروح على الجدول تمام بأجي على الجدول
+
+371
+00:41:28,670 --> 00:41:34,630
+الصين تي طبعا اللي هي رقم خمسة لـ A على S تربيع زائد 
+
+372
+00:41:34,630 --> 00:41:42,280
+A تربيع إيه عندي هنا بقداش؟ بواحد يبقى في واحد على 
+
+373
+00:41:42,280 --> 00:41:47,720
+S تربيع زائد واحد تربيع الهمين بواحد يبقى النتيجة 
+
+374
+00:41:47,720 --> 00:41:54,600
+E أس ناقص 2π by S على S تربيع زائد واحد
+
+375
+00:41:57,900 --> 00:42:03,000
+يبقى هذه النظرية ريحتني بدل لسه أشيل الـ UCT وأحطها 
+
+376
+00:42:03,000 --> 00:42:07,100
+مرة بـ Zero ومرة بواحد وأضرب فيه وأس ناقص 
+
+377
+00:42:07,100 --> 00:42:12,250
+CT وE و أس 2T في الـ sin T ولسه أعمل 
+
+378
+00:42:12,250 --> 00:42:16,730
+integration by parts مرتين لأجبتها في سطرين بدل ما
+
+379
+00:42:16,730 --> 00:42:20,130
+بدي بدي صفحة كاملة وجهة في سطرين إذا النظرية هذه
+
+380
+00:42:20,130 --> 00:42:26,510
+سهلت لي عملية حساب لابلاس ترانسفورم للدوال المختلفة
+
+381
+00:42:26,510 --> 00:42:30,790
+طبعا هذا السؤال يعتبر سؤالا مباشرا ده في لف ولا
+
+382
+00:42:30,790 --> 00:42:38,010
+دوران تمام ننتقل شوية Laplace transform بدنا لمين؟ لـ
+
+383
+00:42
+
+431
+00:48:22,530 --> 00:48:28,850
+بده يخلق الـ T ين بده يخلق اثنين T ناقص واحد فبقى
+
+432
+00:48:28,850 --> 00:48:35,710
+بيقول لو كتبت اثنين T ناقص اثنين أضفت للمعادلة 
+
+433
+00:48:35,710 --> 00:48:36,430
+قداش؟
+
+434
+00:48:42,520 --> 00:48:51,520
+اثنين T ناقص اثنين زائد خمسة اثنين T زائد ثلاثة
+
+435
+00:49:00,860 --> 00:49:04,620
+بقول له تمام والله ما عقول العفرة دي ضرورية دي 
+
+436
+00:49:04,620 --> 00:49:09,620
+ربالك مشان أوصل مسألة لصورة من النظرية حتى أقدر
+
+437
+00:49:09,620 --> 00:49:14,200
+أطبقها أكبر أجي بقول هذا الكلام يساوي لبلاسي
+
+438
+00:49:14,200 --> 00:49:20,020
+ترانسفورم ليه؟ لو أخذت اثنين عامل مشترك بضل قداش؟
+
+439
+00:49:20,020 --> 00:49:27,640
+ناقص واحد في مين في الـ U1 as a function of T زائد
+
+440
+00:49:27,640 --> 00:49:35,400
+خمسة في الـ U1 of T بالشكل اللي عندنا طبعًا الحين
+
+441
+00:49:35,400 --> 00:49:39,000
+هذا لابلاس ترانسفورم لـ Linear Function
+
+442
+00:49:46,380 --> 00:49:53,420
+يبقى هذا الكلام يساوي اثنين Laplace Transform لـ T
+
+443
+00:49:53,420 --> 00:50:02,380
+ناقص واحد في U1 of T زائد خمسة Laplace Transform لـ
+
+444
+00:50:02,380 --> 00:50:10,380
+U1 of T طبعًا يبقى هذا الكلام يساوي اثنين بالدالي
+
+445
+00:50:10,380 --> 00:50:16,080
+لابلاس ترانسفورم للمثال اللي عندنا يبقى هي U C of 
+
+446
+00:50:16,080 --> 00:50:22,560
+T اللي هو بقداش U واحد وهنا F of T ناقص الـ C الـ F 
+
+447
+00:50:22,560 --> 00:50:27,450
+of T هي T بس معمولة لشيء في جهة اليمين بمقدار إذا
+
+448
+00:50:27,450 --> 00:50:34,130
+هذه قداش ما تحطوا يا بنات اثنين في E أس ناقص واحد 
+
+449
+00:50:34,130 --> 00:50:42,430
+في S تمام في لابلاس ترانسفورم لمين للـ T يبقى هذه
+
+450
+00:50:42,430 --> 00:50:47,350
+أصلها قبل الـ Shift هو عبارة عن مين؟ عبارة عن T بجهاد
+
+451
+00:50:47,350 --> 00:50:54,190
+الـ F of T خلصنا منها زائد من زائد خمسة لأ
+
+452
+00:50:54,190 --> 00:50:59,310
+لابلاس ترانسفورم لـ U one of T حسبناها توسع لـ U C of T 
+
+453
+00:50:59,310 --> 00:51:04,970
+فقولنا هنا زائد خمسة E أس ناقص C S
+
+454
+00:51:12,410 --> 00:51:19,290
+طيب نجي لهذه يبقى اثنين E أس ناقص S لابلاس
+
+455
+00:51:19,290 --> 00:51:25,880
+ترانسفورم لـ T من الجدول واحد Factorial على مين؟
+
+456
+00:51:25,880 --> 00:51:33,600
+على S تربيع يبقى هذه واحد Factorial على S تربيع
+
+457
+00:51:33,600 --> 00:51:40,040
+اللي هي من الجدول رقم كده؟ ثلاثة، رقم ثلاثة من
+
+458
+00:51:40,040 --> 00:51:47,710
+الجدول، بس إن عندي قداش بواحد، صحيح بنضل هنا زائد 
+
+459
+00:51:47,710 --> 00:51:57,110
+خمسة E أس ناقص S على مين؟ على S أو لو رح نرتبها 
+
+460
+00:51:57,110 --> 00:52:07,010
+بنقول اثنين E أس ناقص S على S تربيع زائد خمسة E أس 
+
+461
+00:52:07,010 --> 00:52:13,950
+ناقص S على S هذا لابلاس ترانسفورم لمين؟ لهذه الـ
+
+462
+00:52:13,950 --> 00:52:14,690
+Function
+
+463
+00:52:29,140 --> 00:52:39,740
+بناخد كمان نقطة يبقى نمر دي نمر دي بدنا لابلاس 
+
+464
+00:52:39,740 --> 00:52:48,060
+ترانسفورم لـ T ناقص ثلاثة في الـ U اثنين as a
+
+465
+00:52:48,060 --> 00:52:56,760
+Function of T ناقص T ناقص اثنين ثمين في الـ U ثلاثة 
+
+466
+00:52:56,760 --> 00:53:10,900
+as a Function of T يبقى
+
+467
+00:53:10,900 --> 00:53:15,380
+بدي أعرف قداش الـ F لسه ترانسفورم لمين؟ لهذه الدالة 
+
+468
+00:53:15,380 --> 00:53:20,200
+بقوله بسيطة جدا بطلع الرقم اللي هنا بيختلف عن الرقم
+
+469
+00:53:20,200 --> 00:53:24,460
+اثنين عكس بعض وهنا عكس بعض اثنين اللي كانت برا 
+
+470
+00:53:24,460 --> 00:53:28,580
+صارت جوه واللي جوه ايش اللي قعدت برا تدبر حالك 
+
+471
+00:53:28,580 --> 00:53:33,540
+اعمل أي عمل رياضي بحت تتخلى الرقم اللي جوه زي
+
+472
+00:53:33,540 --> 00:53:38,800
+الرقم اللي برا تمام فباجي بقول هذه لابلاس 
+
+473
+00:53:38,800 --> 00:53:45,690
+ترانسفورم ليه؟ هذه ايش بكتبها يا بنات؟ ناقص اثنين ناقص
+
+474
+00:53:45,690 --> 00:53:50,230
+واحد ما عنديش مشكلة في هذه الحالة يبقى لـ T ناقص
+
+475
+00:53:50,230 --> 00:53:57,890
+اثنين ناقص واحد في الـ U اثنين of T وصلنا ناقص هذه 
+
+476
+00:53:57,890 --> 00:54:04,090
+بنفس الطريقة بدي أضيف واحد وأطرح واحد يمشي بالصير 
+
+477
+00:54:04,090 --> 00:54:11,530
+T ناقص ثلاثة زائد واحد في U ثلاثة as a Function of
+
+478
+00:54:11,530 --> 00:54:18,890
+T طيب هذه بتاخدها مع بعض وتضرب في U2 يبقى Laplace 
+
+479
+00:54:18,890 --> 00:54:24,390
+Transform لـ T ناقص اثنين في U2 of T
+
+480
+00:54:31,820 --> 00:54:39,040
+ناقص T ناقص ثلاثة في الـ U ثلاثة of T ناقص في زائد 
+
+481
+00:54:39,040 --> 00:54:46,860
+بناقص U ثلاثة as a Function of T الآن لابلاس هذه الـ
+
+482
+00:54:46,860 --> 00:54:50,080
+Linear Function
+
+483
+00:54:50,400 --> 00:54:58,600
+لابلاس لمين؟ لـ T ناقص اثنين لـ U اثنين of T ناقص لا
+
+484
+00:54:58,600 --> 00:55:05,700
+بلس Transform لـ U اثنين of T ناقص لابلاس Transform 
+
+485
+00:55:05,700 --> 00:55:14,000
+لـ T ناقص ثلاثة لـ U ثلاثة as a Function of T ناقص 
+
+486
+00:55:14,000 --> 00:55:20,780
+لابلاس Transform لـ U ثلاثة as a Function of T يبقى 
+
+487
+00:55:20,780 --> 00:55:25,080
+هذا الكلام يساوي أظن هذه هي النظرية اللي فوق هناك
+
+488
+00:55:25,080 --> 00:55:33,040
+حرفيًا تمام يبقى النتيجة E أس ناقص C S يعني E أس ناقص 
+
+489
+00:55:33,040 --> 00:55:42,160
+اثنين S في لابلاس ترانسفورم لمين؟ للدالة قبل الـ
+
+490
+00:55:42,160 --> 00:55:49,510
+Shift يبقى لابلاس ترانسفورم لـ T ناقص هذه جاهزة
+
+491
+00:55:49,510 --> 00:55:57,830
+اللي هو قداش؟ منها E أس ناقص اثنين S على S حسبناها 
+
+492
+00:55:57,830 --> 00:56:02,570
+أول ثالث مثال اليوم بعد مثلنا الرسم حسبناها لابلاس
+
+493
+00:56:02,570 --> 00:56:08,610
+لـ U C of T قد ما يكون C بها يكون قيمة موجبة بنجي
+
+494
+00:56:08,610 --> 00:56:13,550
+اللي بعدها يبقى وصلنا لناقص هذه الـ C عندك بقداش؟
+
+495
+00:56:13,550 --> 00:56:21,730
+بثلاثة يبقى E أس ناقص ثلاثة S ثمين في لابلاس
+
+496
+00:56:21,730 --> 00:56:29,810
+ترانسفورم للدالة قبل الـ Shift هذه ناقص E أس ناقص
+
+497
+00:56:29,810 --> 00:56:36,710
+ثلاثة S على مين؟ على S إذًا هذه بدها تساوي E أس 
+
+498
+00:56:36,710 --> 00:56:42,170
+ناقص اثنين S هذه واحد Factorial على مين؟ على S
+
+499
+00:56:42,170 --> 00:56:47,720
+تربيع يعني يبقى على S تربيع دوري وهذه ناقص E وناقص
+
+500
+00:56:47,720 --> 00:56:55,540
+2S على S وهذه ناقص E أس ناقص ثلاثة S على S تربيع
+
+501
+00:56:55,540 --> 00:57:02,320
+كذلك وهذه ناقص E أس ناقص ثلاثة S على S
+
+502
+00:57:17,780 --> 00:57:24,060
+يبقى هذا النوع الأول من أنواع الأمثلة بدنا نيجي
+
+503
+00:57:24,060 --> 00:57:27,700
+لنوع ثاني يبقى Example Two
+
+504
+00:57:46,110 --> 00:57:52,450
+Example 2 Find Laplace
+
+505
+00:57:52,450 --> 00:58:01,750
+Transform For
+
+506
+00:58:01,750 --> 00:58:09,390
+The Following Functions
+
+507
+00:58:16,040 --> 00:58:23,280
+الـ F of T بده يساوي مين؟ بده يساوي أحد أمرين يا
+
+508
+00:58:23,280 --> 00:58:31,940
+إما Zero لما T أقل من الواحد يا إما T تربيع ناقص
+
+509
+00:58:31,940 --> 00:58:43,220
+اثنين T زائد اثنين ناقص اثنين T زائد اثنين لما T
+
+510
+00:58:45,100 --> 00:58:54,820
+أكبر من أو تساوي من أو تساوي الواحد قال
+
+511
+00:58:54,820 --> 00:58:57,700
+لي هاتي لي لابلاس ترانسفورم للدالة اللي عندنا هنا
+
+512
+00:58:57,700 --> 00:59:07,340
+بقول له Solution سي
+
+513
+00:59:07,340 --> 00:59:11,680
+عندنا هنا بقدر شمانات يبقى بدي Shift هنا بمقدار 
+
+514
+00:59:11,680 --> 00:59:18,030
+كده؟ مقدار واحد أنا لازم أخلق
+
+515
+00:59:18,030 --> 00:59:23,170
+في المسألة Shift بمقدار واحد إذا بروح بقوله F of T
+
+516
+00:59:23,170 --> 00:59:28,430
+بدي أعيد صياغتها على الشكل التالي يا إما Zero لما
+
+517
+00:59:28,430 --> 00:59:34,510
+T أقل من واحد يا إما T تربيع ناقص اثنين قداش بده
+
+518
+00:59:34,510 --> 00:59:39,810
+لما أصير مربع كامل يبقى الواحد بياخده من عندي
+
+519
+00:59:39,810 --> 00:59:43,990
+الجيران يبقى الواحد يبقى الواحد يبقى الواحد يبقى
+
+520
+00:59:43,990 --> 00:59:44,230
+الواحد يبقى الواحد يبقى الواحد يبقى
+
+521
+00:59:44,230 --> 00:59:45,830
+الواحد يبقى الواحد يبقى الواحد يبقى
+
+522
+00:59:45,830 --> 00:59:47,090
+الواحد يبقى الواحد يبقى الواحد يبقى
+
+523
+00:59:47,090 --> 00:59:47,930
+الواحد يبقى الواحد يبقى الواحد يبقى
+
+524
+00:59:47,930 --> 00:59:48,950
+الواحد يبقى الواحد يبقى الواحد يبقى
+
+525
+00:59:48,950 --> 00:59:53,890
+الواحد يبقى الواحد يبقى الواحد يبقى
+
+526
+00:59:53,890 --> 01:00:01,890
+الواحد يبقى الواحد يبقى الـ T ناقص واحد الكل تربيع 
+
+527
+01:00:01,890 --> 01:00:08,630
+يبقى هذه T ناقص واحد الكل تربيع زائد واحد لما T
+
+528
+01:00:08,630 --> 01:00:16,150
+Greater Than or Equal to One طيب
+
+529
+01:00:16,150 --> 01:00:22,850
+أليست هذه بقدر أكتبها على شكل الـ Unit Step Function
+
+530
+01:00:22,850 --> 01:00:29,210
+صحيح ولا لأ؟ يعني هذه بقدر أكتب الدالة اللي عندناها
+
+531
+01:00:29,210 --> 01:00:34,950
+دي في الـ U1 of T يعني هذه بقدر أكتبها على الشكل
+
+532
+01:00:34,950 --> 01:00:43,630
+التالي U1 as a Function of T في مين؟ في الـ T ناقص 
+
+533
+01:00:43,630 --> 01:00:52,350
+واحد الكل تربيع زائد واحد السؤال قال لي هاتي Laplace
+
+534
+01:00:52,350 --> 01:00:56,750
+Transform لهذه الدالة، إذا الآن بقدر أجد له
+
+535
+01:00:56,750 --> 01:01:02,590
+Laplace Transform لأنه غيرت شكل الـ Function الأصلي
+
+536
+01:01:02,590 --> 01:01:08,810
+بالشكل المكافئ له المتعرف عليه طبق النظرية اللي
+
+537
+01:01:08,810 --> 01:01:14,320
+عندنا يبقى أنا لو أخدت لابلاس ترانسفورم للـ F of T
+
+538
+01:01:14,320 --> 01:01:18,980
+بدي يساوي لابلاس ترانسفورم لمين؟ للدالة اللي عندنا
+
+539
+01:01:18,980 --> 01:01:25,660
+هذه يبقى بناء عليه لابلاس ترانسفورم للدالة F of T بدي
+
+540
+01:01:25,660 --> 01:01:32,740
+يساوي لابلاس ترانسفورم لمين؟ للـ U1 as a Function of
+
+541
+01:01:32,740 --> 01:01:40,980
+T في T ناقص واحد الكل تربيع زائد واحد هيجفلنا U C
+
+542
+01:01:40,980 --> 01:01:47,300
+of T في F of T ناقص الـ C يبقى E أس ناقص S في لابلاس
+
+543
+01:01:47,300 --> 01:01:53,480
+للـ F of T قبل الـ Shift يبقى هذا ايش؟ هذا بيبقى 
+
+544
+01:01:53,480 --> 01:02:01,360
+تساوي مين؟ بيبقى تساوي E أس ناقص واحد في S لـ ناقص C S 
+
+545
+01:02:01,360 --> 01:02:07,600
+يبقى بناقص S في لابلاس ترانسفورم للدالة قبل الـ Shift
+
+546
+01:02:07,600 --> 01:02:12,970
+مين الدالة قبل الـ Shift؟ T تربيع زائد واحد يبقى هذه
+
+547
+01:02:12,970 --> 01:02:18,190
+T تربيع زائد واحد بالشكل اللي عندنا هذا طيب هذا
+
+548
+01:02:18,190 --> 01:02:23,850
+الكلام يساوي E أس ناقص S فيه هذه لابلاس فده عبارة
+
+549
+01:02:23,850 --> 01:02:28,350
+عن لابلاس للأول زائد لابلاس للثاني لأنها Linear
+
+550
+01:02:28,350 --> 01:02:35,670
+يبقى لابلاس لـ T تربيع زائد لابلاس للواحد بالشكل
+
+551
+01:02:35,670 --> 01:02:42,820
+اللي عندنا هذا يبقى هذه ناقص S E أس ناقص S فيه نجي لـ
+
+552
+01:02:42,820 --> 01:02:49,780
+T تربيع من الجدول رقم ثلاثة ثم يبقى هذه اثنين 
+
+553
+01:02:49,780 --> 01:02:56,700
+Factorial على S تكعيب زي الواحد اللي هو واحد على S 
+
+554
+01:02:56,700 --> 01:03:02,560
+عملناها قبل هيك واحد على S بالشكل اللي عندنا يعني 
+
+555
+01:03:02,560 --> 01:03:10,540
+كأن النتيجة هي اثنين E أس ناقص S على S تكعيب زائد E 
+
+556
+01:03:10,540 --> 01:03:13,200
+أس ناقص S على S 
+
+557
+01:03:32,870 --> 01:03:39,590
+نمر بيه بيقول الـ F of T بدها تساوي أحد ثلاثة أمور
+
+558
+01:03:39,590 --> 01:03:49,270
+يا إما Zero لما T أقل من باي يا إما T ناقص باي لما
+
+559
+01:03:49,270 --> 01:03:55,990
+T أكبر من أو يساوي باي وأقل من اثنين باي يا إما 
+
+560
+01:03:55,990 --> 01:04:01,390
+Zero لما T Greater Than or Equal to Two Pi
+
+561
+01:04:22,140 --> 01:04:29,140
+مش جزءين زي المثلة اللي فاتت بسهولة، لأ هذه ثلاثة
+
+562
+01:04:29,140 --> 01:04:33,880
+أجزاء وأنا مشان أجيبلها لابلاس ترانسفورم بدي 
+
+563
+01:04:33,880 --> 01:04:41,840
+أكتبها بدلالة Unit Step Function الـ U C of T بقول
+
+564
+01:04:41,840 --> 01:04:46,280
+Okay بدي أكتبها بالـ Unit Step Function هذه مش
+
+565
+01:04:46,280 --> 01:04:50,680
+مباشرة زيها دي هذيك أخذت هذيك عمل مشترك وضرب في U C
+
+566
+01:04:50,680 --> 01:04:55,980
+وكتير لو يطلع الدوري إذا أنا بدأ أفكر تفكيري كويس
+
+567
+01:04:55,980 --> 01:05:00,120
+طبعًا من خلال الـ Domain تبع الدالة دي ملاحظة إنه
+
+568
+01:05:00,120 --> 01:05:05,300
+جسمها لكم فترة لثلاث فترات من Zero لـ Pi ومن Pi لـ
+
+569
+01:05:05,300 --> 01:05:09,380
+اثنين Pi ومن اثنين Pi لـ Infinity يعني لازم يطلع 
+
+570
+01:05:09,380 --> 01:05:15,820
+في المثل عندي U Pi of T و U اثنين Pi of T مظبوط
+
+571
+01:05:15,820 --> 01:05:20,920
+يبقى هي استنتجته لواحدة من خلال من من خلال شكل 
+
+572
+01:05:20,920 --> 01:05:26,240
+الدالة طيب تعالوا نفهم هيك ونشوف على شكل لو رحت
+
+573
+01:05:26,240 --> 01:05:32,580
+مدام U Pi و U اثنين Pi والـ Pi باجت في الأول و 2Pi
+
+574
+01:05:32,580 --> 01:05:38,680
+في الآخر باجي لو قلت له Consider خد لي هيك اللي هو
+
+575
+01:05:38,680 --> 01:05:47,300
+U Pi of T ناقص U 2Pi as a Function of T وشوف لقداش 
+
+576
+01:05:47,300 --> 01:05:52,780
+هذول بدهم يزاوز لو طرحت اثنين من بعض على مين؟ على 
+
+577
+01:05:52,780 --> 01:05:57,680
+الثلاث فترات هذه إن شوف شو بتعطيني باجي بقوله والله
+
+578
+01:05:57,680 --> 01:05:58,340
+كويس
+
+579
+01:06:05,460 --> 01:06:14,420
+عندما تبقى T أقل من Pi تبقى T ناقص 
+
+580
+01:06:15,630 --> 01:06:21,850
+طيب بدنا نيجي ناخد الفترة T أكبر من أو يساوي Pi و 
+
+581
+01:06:21,850 --> 01:06:29,530
+أقل من اثنين Pi قداش قيمة الـ U Pi واحد تمام يبقى 
+
+582
+01:06:29,530 --> 01:06:36,840
+هذه واحد ناقص الـ U اثنين Pi تمام التمام طيب بداجي
+
+583
+01:06:36,840 --> 01:06:42,500
+الآن T أكبر من أو يساوي اثنين Pi قداش قيمة الدالة
+
+584
+01:06:42,500 --> 01:06:50,090
+الأولى والثانية يعني واحد ناقص واحد يبقى صورة هذه
+
+585
+01:06:50,090 --> 01:06:58,210
+الـ U Pi ناقص U 2Pi كله as a Function of T و as a 
+
+586
+01:06:58,210 --> 01:07:04,950
+Function of T يبقى هذه الـ U Pi as a Function of T
+
+587
+01:07:04,950 --> 01:07:12,070
+ناقص U 2Pi as a Function of T يساوي أحد ثلاثة أمور
+
+588
+01:07:12,480 --> 01:07:20,060
+يا إما Zero لما T أقل من Pi، يا إما واحد لما T
+
+589
+01:07:20,060 --> 01:07:25,940
+أكبر من أو يساوي Pi وأقل من اثنين Pi، يا إما 
+
+590
+01:07:25,940 --> 01:07:32,460
+Zero لما T Greater Than or Equal to Two Pi بقول
+
+591
+01:07:32,460 --> 01:07:36,540
+كويس، طب احنا جبنا الفرق طلع هذول، ايش بتفرج هدي
+
+592
+01:07:36,540 --> 01:07:44,590
+عن اللي فوق؟ لو ضربت اللي فوق في T ناقص Pi تطلع
+
+593
+01:07:44,590 --> 01:07:50,910
+هذه هذي طيب ممتاز إذا هروح أضرب الطرفين في T ناقص 
+
+594
+01:07:50,910 --> 01:07:57,730
+Pi إذا لو ضربت في T ناقص Pi بيصير U Pi of T في 
+
+595
+01:07:57,730 --> 01:08:07,310
+T ناقص الـ Pi ناقص U 2Pi as a Function of T في T
+
+596
+01:08:07,310 --> 01:08:14,750
+ناقص الـ Pi كله بده يساوي ما يتيه يا إما Zero لما 
+
+597
+01:08:14,750 --> 01:08:22,230
+T أقل من Pi يا إما T ن
+
+646
+01:14:07,010 --> 01:14:18,350
+أيه؟ capital F of S بده يساوي E أس ناقص اتنين S
+
+647
+01:14:18,350 --> 01:14:26,630
+على مين؟ على S تربيع زائد الـ S ناقص اتنين
+
+648
+01:14:37,230 --> 01:14:43,070
+عشان نحاول نستفيد من جدول اللي قدامنا بقدر الإمكان
+
+649
+01:14:43,070 --> 01:14:46,950
+طبعا لو أروح للجدول بشوفش ولا شغل زي هيك بلاقيش
+
+650
+01:14:46,950 --> 01:14:48,670
+ولا حاجة زي هيك بالشكل هذا
+
+651
+01:15:00,200 --> 01:15:09,460
+هذا واحد على هذه لو حللته كحاصل ضرب قوسين يبقى هنا
+
+652
+01:15:09,460 --> 01:15:18,040
+S هنا S هنا واحد هنا اتنين هنا زائد هنا ناقص ناقص
+
+653
+01:15:18,040 --> 01:15:24,460
+S بزائد اتنين S بظل زائد S بعد هيك بدي أروح أعمل
+
+654
+01:15:24,460 --> 01:15:29,750
+partial fraction لهذه وهي قسور جزئية بحيث أفصلها
+
+655
+01:15:29,750 --> 01:15:34,250
+هائلة، لماذا؟ لأنه أنا ما بعرف الـ place لحاصل ضرب
+
+656
+01:15:34,250 --> 01:15:38,530
+قيمتين، ما أخذناهاش، ما نعرفهاش، تمام؟ إذن بدل ما هي
+
+657
+01:15:38,530 --> 01:15:42,930
+ضرب بدي أخليها مجموعة، جمع يعني كأنه هنا موحدة،
+
+658
+01:15:42,930 --> 01:15:47,340
+مقدرة، عاملة ومشتركة بدي أردها إلى أصلها قبل أخذ
+
+659
+01:15:47,340 --> 01:15:53,000
+العامل المشترك بقوله بسيطة المقام محلل إلى أبسط 
+
+660
+01:15:53,000 --> 01:15:58,780
+العوامل الأولية والأقواس are different ولا واحد زي
+
+661
+01:15:58,780 --> 01:16:04,030
+التاني وكل واحد فيهم من الدرجات الأولى فبروح بقول
+
+662
+01:16:04,030 --> 01:16:12,230
+له هذه واحد على S ناقص واحد في S زائد اتنين يساوي
+
+663
+01:16:12,230 --> 01:16:18,310
+constant على القوس الأول constant ثاني على القوس
+
+664
+01:16:18,310 --> 01:16:23,670
+الثاني بعد هيك بروح أضرب في المقام تبع الطرف
+
+665
+01:16:23,670 --> 01:16:29,050
+الشمال زي ما كنا بنعمل في calculus بيبقى الواحد
+
+666
+01:16:29,050 --> 01:16:30,810
+بده يساوي A
+
+667
+01:16:38,930 --> 01:16:45,910
+يبقى بطل يصير عندنا كثور إنما صارت كل المسألة في
+
+668
+01:16:45,910 --> 01:16:46,710
+البسط
+
+669
+01:17:01,440 --> 01:17:09,100
+طيب حط قيم لـ S من عندك فباجي بقول لو كانت الـ S
+
+670
+01:17:09,100 --> 01:17:16,900
+تساوي واحد then الواحد بده يساوي تلاتة A يبقى
+
+671
+01:17:16,900 --> 01:17:24,300
+تلاتة A ومنها الـ A تساوي قد إيش؟ تساوي طول الآن لو
+
+672
+01:17:24,300 --> 01:17:31,170
+كانت الـ S تساوي ناقص اتنين نقص اتنين يبقى تقير الـ a
+
+673
+01:17:31,170 --> 01:17:39,170
+وبظل then الواحد يساوي ناقص تلاتة b ناقص اتنين ناقص
+
+674
+01:17:39,170 --> 01:17:46,510
+واحد يكون ناقص تلاتة b ومنها b تساوي كم؟ سالب تلت
+
+675
+01:17:46,510 --> 01:17:54,950
+إذا صار capital F of S أصبح على الشكل التالي هو
+
+676
+01:17:54,950 --> 01:17:59,290
+أيه؟ هذا بدي استبدله بمين؟ بالمقدار اللي عندنا
+
+677
+01:17:59,290 --> 01:18:05,150
+يبقى بدي يجي هنا تلت وهنا سالب تلت يبقى هذا تلت
+
+678
+01:18:05,150 --> 01:18:11,270
+خذيه برة عامل مشترك بيظل E أس ناقص اتنين S في
+
+679
+01:18:11,270 --> 01:18:20,590
+جداش في واحد على S ناقص واحد ناقص واحد على S زائد
+
+680
+01:18:20,590 --> 01:18:29,260
+اتنين يعني أيه؟ يعني هذا تلت في E أس ناقص اتنين S
+
+681
+01:18:29,260 --> 01:18:38,400
+في واحد على S ناقص الواحد ناقص تلت في E أس ناقص
+
+682
+01:18:38,400 --> 01:18:43,680
+اتنين S في واحد على S زائد اتنين
+
+683
+01:18:49,000 --> 01:18:54,480
+نرجع لمين؟ نرجع للنظرية تبعنا اللي كنا نشتغل
+
+684
+01:18:54,480 --> 01:18:59,740
+عليها اللي روحناها مسحناها طلعنا النظرية مرة
+
+685
+01:18:59,740 --> 01:19:08,630
+ثانية شوفوا ليش بيقول هنا طبعا
+
+686
+01:19:08,630 --> 01:19:16,510
+عندك E أس ناقص 2S في capital F of S هذه بتروح أردها
+
+687
+01:19:16,510 --> 01:19:20,870
+لمين للمعكوس تبعها طلع لي في كلمة conversely
+
+688
+01:19:20,870 --> 01:19:27,590
+للنقطة الأولى عندك الـ plus inverse لـ E أس ناقص CS في
+
+689
+01:19:27,590 --> 01:19:35,230
+capital F of SUC of T في F of T ناقص الـ C
+
+690
+01:19:56,010 --> 01:20:03,690
+تلت صف على شجة بدي الـ plus inverse لمين؟ للـ E أس
+
+691
+01:20:03,690 --> 01:20:11,090
+ناقص اتنين S واحد على S ناقص الواحد ناقص تلت الـ
+
+692
+01:20:11,090 --> 01:20:19,010
+plus inverse لمين؟ لـ E أس ناقص اتنين S واحد على S
+
+693
+01:20:19,010 --> 01:20:23,890
+زائد اتنين هذا الكلام بده يساوي هي تلت
+
+694
+01:20:29,720 --> 01:20:33,880
+النقطة الأولى المعكوزة تبعها اللي على اليمين الـ
+
+695
+01:20:33,880 --> 01:20:40,000
+plus inverse لـ E أس نق الـ CS في capital F of S هي
+
+696
+01:20:40,000 --> 01:20:46,180
+capital F of S وهي E أس نق الـ CS يبقى بده أرجعها
+
+697
+01:20:46,180 --> 01:20:51,320
+لمين؟ إلى أصلها يبقى أصلها شو بده يكون يا بنت؟ U C
+
+698
+01:20:51,320 --> 01:21:00,080
+of T C عندي هنا في قد إيش يبقى أنا بقول U2 as a
+
+699
+01:21:00,080 --> 01:21:08,240
+function of T طيب هذه مين؟ هذه E أس T بس بدي أعمل
+
+700
+01:21:08,240 --> 01:21:17,360
+لها shift بمقدار كتير لتنين يبقى E أس T ناقص اتنين
+
+701
+01:21:17,360 --> 01:21:26,220
+مرة ثانية افتحي بافترك على النظرية، يلا فارجي على
+
+702
+01:21:26,220 --> 01:21:31,390
+ثلاث صفحات للخلف، والله أربعة النظرية بتقول لـ Plus
+
+703
+01:21:31,390 --> 01:21:36,450
+لـ UC of T للـ F of T ناقص C والساوي E أس نق الـ Cs
+
+704
+01:21:36,450 --> 01:21:42,770
+في كابتل F of S احنا اللي موجود عند مين E أس نق
+
+705
+01:21:42,770 --> 01:21:49,110
+الـ Cs في كابتل F of S إذن بتدرجع على الأصل تبعها
+
+706
+01:21:49,110 --> 01:21:53,110
+قبل نأخذ Laplace transform فبأخذ Laplace inverse
+
+707
+01:21:53,110 --> 01:21:59,410
+للطرفين يبقى بالأسفل إن لأ plus inverse لإي أس ناقص
+
+708
+01:21:59,410 --> 01:22:10,620
+CS في capital F of S هذه الـ F of S وهذه E أس ناقص
+
+709
+01:22:10,620 --> 01:22:14,700
+CS بالدرجة العاصلة يبقى الـ C عندي هنا بقد إيش
+
+710
+01:22:14,700 --> 01:22:22,340
+بإتمام يبقى بقوله تلت U2 of T هذه E أس T لكن هو
+
+711
+01:22:22,340 --> 01:22:27,500
+قال لي F of T ناقص الـ C يبقى بدي أعمل الـ Shift
+
+712
+01:22:27,500 --> 01:22:35,610
+مقدار الـ C فبقول T ناقص 2 واضحة؟ اللي عملناها لهذه
+
+713
+01:22:35,610 --> 01:22:42,850
+هأعملها للتانية يبقى هي كمان ناقص طول طلّها لهذه
+
+714
+01:22:42,850 --> 01:22:51,710
+يس ناقص اتنين اس يبقى U اتنين as a function of T
+
+715
+01:22:52,300 --> 01:22:57,980
+تمام؟ ضال plus لهذه ده رجع على أصلها، شو أصلها؟
+
+716
+01:22:57,980 --> 01:23:05,600
+E أس ناقص اتنين T و بدي اخذ ناقص اتنين shift منها،
+
+717
+01:23:05,600 --> 01:23:10,280
+يبقى ما بصيرش E أس،
+
+718
+01:23:10,280 --> 01:23:17,280
+هدف الأصل ناقص اتنين T مظبوط أو لا؟ إذا بدي أعمل لها
+
+719
+01:23:17,280 --> 01:23:21,940
+shift بمقدار كده مقدار اتنين كمان نفس النتيجة اللي
+
+720
+01:23:21,940 --> 01:23:27,000
+احنا احنا عملناها لها يبقى لما نعمل الـ shift اللي
+
+721
+01:23:27,000 --> 01:23:32,680
+عندنا هذا لها بيبقى تصير على مين؟ على الشكل التالي
+
+722
+01:23:32,680 --> 01:23:41,760
+اللي هو مين؟ اللي هو E أس ناقص اتنين T نقص بيصير
+
+723
+01:23:41,760 --> 01:23:48,440
+زائد اتنين لماذا؟ لأنه في الأصل ناقص يبقى ناقص
+
+724
+01:23:48,440 --> 01:23:56,100
+يبقى ناقص يبقى ناقص
+
+725
+01:23:56,100 --> 01:23:59,920
+يبقى ناقص يبقى ناقص يبقى ناقص يبقى ناقص يبقى ناقص
+
+726
+01:23:59,920 --> 01:24:06,000
+يبقى ناقص يبقى ناقص يبقى ناقص يبقى ناقص يبقى ناقص
+
+727
+01:24:06,000 --> 01:24:09,500
+يبقى ناقص يبقى ناقص يبقى ناقص يبقى ناقص يبقى ناقص
+
+728
+01:24:09,500 --> 01:24:09,620
+يبقى ناقص يبقى
+
+729
+01:24:14,570 --> 01:24:18,190
+لأ، لأ، لأ، في غلطة يا بنات، في غلطة، في غلطة،
+
+730
+01:24:18,190 --> 01:24:24,390
+الغلطة كيف؟ إن هذه ناقص اتنين، وهنا بدأت أقول T
+
+731
+01:24:24,390 --> 01:24:29,530
+زائد اتنين، بيصير أربعة، يعني هذه زائد أربعة وليست
+
+732
+01:24:29,530 --> 01:24:35,480
+اتنين، لما نأخذ اتنين، بيصير T ناقص اتنين يعني القصة
+
+733
+01:24:35,480 --> 01:24:38,660
+اللي هنا هو نفس القصة اللي بين قوسين هنا بالضبط
+
+734
+01:24:38,660 --> 01:24:44,020
+تمامًا، تمام؟ بس اجعليها قد إيش؟ اللي هو سالب اتنين، مرة
+
+735
+01:24:44,020 --> 01:24:49,420
+ثانية بتعيدها مرة ثانية بدأنا هذه الدالة قبل الـ
+
+736
+01:24:49,420 --> 01:24:55,780
+shift اللي هو قد إيش؟ E أس ناقص اتنين تمام الـ T بدي
+
+737
+01:24:55,780 --> 01:25:01,120
+أعمل لها الـ shift بمقدار اتنين يبقى بالداخل أقوله
+
+738
+01:25:01,120 --> 01:25:07,660
+E أس ناقص اتنين في T ناقص اتنين مش هه بلاش تقولي
+
+739
+01:25:07,660 --> 01:25:12,260
+كيف هذه الأربعة اجت نصف المسألة ولا لا؟ بقول لك ايه
+
+740
+01:25:12,260 --> 01:25:19,270
+على طول هي ناقص تلت هذي درة هي ناقص الـ T و اتنين
+
+741
+01:25:19,270 --> 01:25:24,470
+of T E و ناقص اتنين الـ T عندي هذي بدي أعمله الـ
+
+742
+01:25:24,470 --> 01:25:30,510
+shift مقدار اتنين فبقول T ناقص اتنين مباشرة فهو
+
+743
+01:25:30,510 --> 01:25:38,790
+رايح دماغك طيب هذا كان هو السؤال الأول نمرة A بنجي
+
+744
+01:25:38,790 --> 01:25:39,610
+لنمرة V
+
+745
+01:25:48,310 --> 01:25:52,390
+خذوا لنمرة ب طبعا السؤال الأول هو السؤال
+
+746
+01:25:52,390 --> 01:25:58,610
+الرابع عشر من الكتاب نمرة ب سؤال الخامس عشر من الكتاب
+
+747
+01:26:02,380 --> 01:26:09,180
+بدي أساوي اتنين في اس ناقص واحد اتنين في اس ناقص
+
+748
+01:26:09,180 --> 01:26:16,860
+واحد في اي أس ناقص اتنين اس على اس تربيع ناقص
+
+749
+01:26:16,860 --> 01:26:22,760
+اتنين اس زائد اللي هو اتنين زائد اتنين
+
+750
+01:26:32,740 --> 01:26:38,840
+بنرتب وضع المثلة قبل أيه؟ قبل ما نبدأ الحل قبل ما
+
+751
+01:26:38,840 --> 01:26:44,220
+نبدأ معكوس لبلاي transform فباجي بقوله capital F
+
+752
+01:26:44,220 --> 01:26:50,400
+of S بده يساوي أظن إن اتنين مقدار ثابت ما له دعوة
+
+753
+01:26:50,400 --> 01:26:56,420
+و E أس ناقص اتنين S كمان ما له دعوة بضل عندي قد إيش
+
+754
+01:26:56,420 --> 01:27:03,700
+S ناقص واحد هذا بقدر أعمله أيه؟ مربع كامل يبقى S
+
+755
+01:27:03,700 --> 01:27:10,580
+تربيع ناقص اتنين S زائد واحد بضل جداش؟ زائد واحد
+
+756
+01:27:10,580 --> 01:27:15,820
+بالشكل اللي عندنا أنا أو بقدر أكتبها اتنين ما لكش
+
+757
+01:27:15,820 --> 01:27:22,520
+دعوة E أس ناقص اتنين S فاهمين؟ في الـ S ناقص واحد
+
+758
+01:27:22,520 --> 01:27:28,940
+على S ناقص واحد لكل تربيع زائد واحد بالشكل اللي
+
+759
+01:27:28,940 --> 01:27:37,790
+عندنا أنا إذا بتأخذ الـ plus inverse لمين؟ لـ F of S
+
+760
+01:27:37,790 --> 01:27:45,710
+يساوي اتنين
+
+761
+01:27:45,710 --> 01:27:54,970
+الـ plus inverse لمين؟ لـ E أثناء قصة 2S في الـ S ناقص
+
+762
+01:27:54,970 --> 01:28:03,810
+واحد الـ S ناقص واحد ناقص واحد الكل تربيع زائد واحد
+
+763
+01:28:03,810 --> 01:28:05,610
+بالشكل اللي عندنا هذا
+
+764
+01:28:13,100 --> 01:28:18,520
+بارجع لمين؟ كمان للنظرية، نرجع للنظرية تبعنا هذه
+
+765
+01:28:18,520 --> 01:28:24,980
+مرة ثانية، اللي كنا بنشغل بهاتف والساعة أنا عندي
+
+766
+01:28:24,980 --> 01:28:31,720
+هي E أس نقص اتنين S يبقى C يبقى 12 ب 2 هذه
+
+767
+01:28:31,720 --> 01:28:37,760
+capital F of S بدي أرجع لهذه وأشوف من أصلها من
+
+768
+01:28:37,760 --> 01:28:45,320
+وين؟ من الجدول تمام؟ لو رجعت لهذه الدالة اللي هي الـ
+
+769
+01:28:45,320 --> 01:28:48,560
+S ناقص واحد على S ناقص واحد كل تربيع اللي هي عبارة
+
+770
+01:28:48,560 --> 01:28:54,060
+عن مين؟ رقم كده 10 بالضبط تمامًا اللي هو S ناقص
+
+771
+01:28:54,060 --> 01:28:57,220
+الـ A على S ناقص L كل تربيع زائد B تربيع يعني الـ A
+
+772
+01:28:57,220 --> 01:29:03,400
+بواحد يا بنات والـ B بواحد كذلك يبقى أصلها E أس AT
+
+773
+01:29:03,400 --> 01:29:10,480
+Cos BT يعني E أس T Cos T لإنه الـ A والـ B بواحد
+
+774
+01:29:10,820 --> 01:29:16,080
+يبقى في الهام الشيخ بقول أنا عند الـ F of T بده
+
+775
+01:29:16,080 --> 01:29:22,600
+يساوي E أس تي كوساين T تمام؟ لكن بدي أرجع للنظرية
+
+776
+01:29:22,600 --> 01:29:29,480
+تبعي وأقول هذا الكلام يساوي اتنين في جداش؟ هذه U
+
+777
+01:29:29,480 --> 01:29:34,560
+اتنين as a function of T برجع للنظرية هي تبعنا
+
+778
+01:29:35,870 --> 01:29:42,270
+يبقى أنا
+
+779
+01:29:42,270 --> 01:29:49,250
+أعمل shift لكل واحدة منهم بمقدار اتنين يبقى هذه في
+
+780
+01:29:49,250 --> 01:29:59,610
+الـ E of T ناقص اتنين في cosine T ناقص اتنين كذلك
+
+781
+01:29:59,610 --> 01:30:04,310
+يبقى هي طبقت النظرية وعملت main وعملت shift اللي
+
+782
+01:30:04,310 --> 01:30:09,070
+بدي إياها الروح لنمرسى من المسألة
+
+783
+01:30:30,830 --> 01:30:39,370
+بيقول لي F of S نمرة C capital F of S بده يساوي
+
+784
+01:30:39,370 --> 01:30:50,350
+مين؟ E أس ناقص S زائد E أس ناقص اتنين S ناقص E أس
+
+785
+01:30:50,350 --> 01:30:56,030
+ناقص تلاتة S ناقص E أس ناقص
+
+786
+01:31:06,240 --> 01:31:11,180
+خلينا نعيد ترتيب المثلة قبل ما نبدأ يبقى باجي
+
+787
+01:31:11,180 --> 01:31:18,050
+بقوله solution بعد كتابة F of S بقدر أكتبها على
+
+788
+01:31:18,050 --> 01:31:25,470
+الشكل التالي بقدر أوزع البسط على المقام يبقى هذا E
+
+789
+01:31:25,470 --> 01:31:37,680
+أس ناقص S على S هذه زائد E أس ناقص اتنين S على من؟
+
+790
+01:31:37,680 --> 01:31:46,240
+على S هذه ناقص E أس ناقص تلاتة S على S هذه ناقص E أس
+
+791
+01:31:46,240 --> 01:31:50,540
+ناقص أربعة S على S
+
+792
+01:31:54,190 --> 01:31:59,650
+أول مثال أخذناه في جدول لبلاس ترانسفورم كان لبلاس
+
+793
+01:31:59,650 --> 01:32:08,710
+ترانسفورم لـ U C of T قد إيش طالعة؟ U أس ناقص C S على
+
+794
+01:32:08,710 --> 01:32:13,030
+S اللي هو في الجدول واللي عندنا بنات رقم قد إيش؟ رقم
+
+795
+01:32:13,030 --> 01:32:20,430
+12 إذا أنا بدي أطبق رقم 12 كام مرة؟ أربع مرات يبقى
+
+796
+01:32:20,430 --> 01:32:26,930
+لما يكون عندي U C of T بتشويه أصلها C S على F يبقى
+
+797
+01:32:26,930 --> 01:32:31,650
+بناءً أنا عليه بأخذ Laplace inverse للطرفين يبقى
+
+798
+01:32:31,650 --> 01:32:39,450
+Laplace inverse لـ capital F of S يساوي Laplace
+
+799
+01:32:39,450 --> 01:32:46,070
+inverse لمين؟ للـ E أس ناقص S على S زائد Laplace
+
+800
+01:32:46,070 --> 01:32:53,490
+inverse للـ E أس ناقص اتنين S على S معقص Laplace
+
+801
+01:32:53,490 --> 01:33:02,120
+inverse لمين؟ للـ إي أس ناقص ثلاثة S على S ناقص لـ plus
+
+802
+01:33:02,120 --> 01:33:09,940
+inverse للـ إي أس ناقص أربعة S على S يبقى لـ plus
+
+803
+01:33:09,940 --> 01:33:17,360
+inverse لـ capital F of S بده يساوي هذه C هنا بقد إيش
+
+804
+01:33:17,360 --> 01:33:25,380
+يا بنات؟ بواحد يبقى هذه باعتبارها من U one of T طب
+
+805
+01:33:25,380 --> 01:33:32,680
+هذه U2 of D فقط لغير مظبوط طبقا لرقم 12 اللي عندنا
+
+806
+01:33:32,680 --> 01:33:41,190
+يبقى زائد U2 as a function of D طب هذه ناقص U تلاتة
+
+807
+01:33:41,190 --> 01:33:47,010
+يبقى ناقص U تلاتة as a function of T لأن C تتسبب في
+
+808
+01:33:47,010 --> 01:33:54,490
+قدرات تلاتة ناقص U أربعة as a function of T
+
+809
+01:33:57,330 --> 01:34:02,630
+يبقى هذا إيش؟ أعطانا عدة أمثلة نجيب كيف معكوس
+
+810
+01:34:02,630 --> 01:34:06,730
+Laplace transform يعني بيعطيني Laplace transform و
+
+811
\ No newline at end of file
diff --git a/PL9fwy3NUQKwa8ZDfSFGn6H8xVFLzqmCZC/5tytEs18MlY_postprocess.srt b/PL9fwy3NUQKwa8ZDfSFGn6H8xVFLzqmCZC/5tytEs18MlY_postprocess.srt
new file mode 100644
index 0000000000000000000000000000000000000000..2456b1c5925901fdcd61faa887e0a6f0f60a3f6b
--- /dev/null
+++ b/PL9fwy3NUQKwa8ZDfSFGn6H8xVFLzqmCZC/5tytEs18MlY_postprocess.srt
@@ -0,0 +1,3276 @@
+1
+00:00:10,540 --> 00:00:15,240
+المرة الماضية انتهينا من سكتشن ستة اتنين اللي هو
+
+2
+00:00:15,240 --> 00:00:19,840
+بيتحدث عن استخدام laplace transform لحل المعادلة
+
+3
+00:00:19,840 --> 00:00:24,280
+التفاضلية او حل ال initial value problem اليوم ان
+
+4
+00:00:24,280 --> 00:00:28,240
+شاء الله هناخد function جديدة نسميها unit step
+
+5
+00:00:28,240 --> 00:00:33,630
+functionأو اختصارا ال step function نقطة تعريف ال
+
+6
+00:00:33,630 --> 00:00:37,550
+step function وحلاحظ ان ال step function بتلعب دور
+
+7
+00:00:37,550 --> 00:00:42,830
+كبير في موضوع Laplace transform بل سنحسبها كمان
+
+8
+00:00:42,830 --> 00:00:47,670
+Laplace transformبجي بقول the unit step function
+
+9
+00:00:47,670 --> 00:00:52,050
+is denoted by يبجى حنرمز لل unit step function
+
+10
+00:00:52,050 --> 00:00:58,870
+بيبدأ ل U C as a function of T ال undefined as
+
+11
+00:00:58,870 --> 00:01:04,090
+وبنعرفها بالشكل التالي ك piecewise function يبجى U
+
+12
+00:01:04,090 --> 00:01:09,430
+C of T بيبدأ تساوي زيرو لما T تبجى دائما وابدا أقل
+
+13
+00:01:09,430 --> 00:01:14,280
+من Cوإذا كانت تساوي C أو أكبر من C فال unit step
+
+14
+00:01:14,280 --> 00:01:19,500
+function بتساوي كده؟ واحد صحيح ممكن نتعرف على شكل
+
+15
+00:01:19,500 --> 00:01:24,040
+ال unit step function اللي عندنا كالتالي لو جيت
+
+16
+00:01:24,040 --> 00:01:30,520
+أخدت محاور بالشكل هذا وقلت هذا محور T و هذا محور Y
+
+17
+00:01:30,520 --> 00:01:33,280
+أو محور F يبقى هذا محور Y
+
+18
+00:01:38,500 --> 00:01:45,360
+أفترضوا أن هذا رقم الـ main الرقم Cلأن اشترط C
+
+19
+00:01:45,360 --> 00:01:53,180
+مالها اكبر من Zero اذا لما تبقى الدالة قبل C يعني
+
+20
+00:01:53,180 --> 00:01:58,540
+اي قيمة قبل C قيمة الدالة عندها جداش تبقى ب Zero
+
+21
+00:01:58,540 --> 00:02:02,860
+يبقى الدالة بدأت تكون مغطية المنطقة هذه كلها
+
+22
+00:02:02,860 --> 00:02:07,640
+بالشكل اللي عندها تمام؟ لكن من هنا بنات بدأت تبقى
+
+23
+00:02:07,640 --> 00:02:12,180
+فترة مفتوحة او النقطة هذه عندهامعرفة دالة غير
+
+24
+00:02:12,180 --> 00:02:17,180
+معرفة دالة هادى عند النقطة معرفة وين بيصير قيمتها
+
+25
+00:02:17,180 --> 00:02:21,420
+فوق اللى بواحد عندما سيه اذا بيجي على القيمة اللى
+
+26
+00:02:21,420 --> 00:02:26,260
+عندنا اللى واحد صحيح واطلع اقبالها وبالتالي الدالة
+
+27
+00:02:26,260 --> 00:02:31,680
+بعد ذلك دالة ثابتة لكل القيم اللى بعد سيه قيمة
+
+28
+00:02:31,680 --> 00:02:35,810
+الدالة مقدر ثابت اللى واحديبقى لو رسمنا هذه ال
+
+29
+00:02:35,810 --> 00:02:41,110
+function هتصير بالشكل اللي عندنا هذا يبقى هنا حصلت
+
+30
+00:02:41,110 --> 00:02:46,910
+قفزة من النقطة لأن هذه لم نقطة اللي فوق وما من هنا
+
+31
+00:02:46,910 --> 00:02:51,570
+سمناها ال step function اللي هي دالة القفزة أو
+
+32
+00:02:51,570 --> 00:02:56,810
+الدالة السلمية تمام؟ بس ماطلعش درجات كتير درجة
+
+33
+00:02:56,810 --> 00:02:59,740
+واحدة مش أكترالسلامية اللى أخدناها في ال calculus
+
+34
+00:02:59,740 --> 00:03:05,360
+ايه نطلع عدة درجات وها كده الان بنحاول نستخدم هذه
+
+35
+00:03:05,360 --> 00:03:10,400
+الدالة في رسم بعض ال functions نبدأ ناخد بعض
+
+36
+00:03:10,400 --> 00:03:19,720
+الأمثلة على كيفية الرسم يبقى example sketch
+
+37
+00:03:19,720 --> 00:03:26,160
+the graph of
+
+38
+00:03:27,860 --> 00:03:38,240
+the function f of t بدى يسوى واحد ناقص u c of t
+
+39
+00:03:43,120 --> 00:03:47,240
+قال ارسم لي شكل الدالة اللى عندنا هذه بنقوله
+
+40
+00:03:47,240 --> 00:03:51,620
+بقصتنا بسيطة جدا بنحاول نرسم هذه الدالة اذا لو
+
+41
+00:03:51,620 --> 00:03:57,320
+جينا رسمنا هذه الدالة بقوله هذا ال function هذه T
+
+42
+00:03:57,320 --> 00:04:03,000
+وهذه هنا main ال F of T ونختار الرقم هذا اللى
+
+43
+00:04:03,000 --> 00:04:07,300
+عندنا اللى هو main الرقم C اللى هو greater than
+
+44
+00:04:07,300 --> 00:04:14,050
+zero دائما وأبداطيب بنا نتعرف على شكل الدالة بدي
+
+45
+00:04:14,050 --> 00:04:18,910
+بقوله انا مش هانرسوم بدي اعرف شو شكلها يبقى F of T
+
+46
+00:04:18,910 --> 00:04:27,650
+بديه سوى واحد ناقص ال U C of T اما Zero لما T اقل
+
+47
+00:04:27,650 --> 00:04:35,100
+من C اما واحد لما T greater than or equal to Cيبقى
+
+48
+00:04:35,100 --> 00:04:41,340
+هذه بدها تساوي بشكل ان اذا واحد ناقص zero بواحد
+
+49
+00:04:41,340 --> 00:04:47,400
+يبقى هاي واحد لما T اقل من C واحد ناقص واحد يساوي
+
+50
+00:04:47,400 --> 00:04:55,380
+zero لما T greater than or equal to Cإذا كان T أقل
+
+51
+00:04:55,380 --> 00:05:01,120
+من C فقيمة الدالة كم؟ واحد يبقى على المنطقة هذه
+
+52
+00:05:01,120 --> 00:05:05,200
+بتبقى قيمة الدالة كل واحد إذا لو طلعت هنا عند
+
+53
+00:05:05,200 --> 00:05:10,060
+الواحد يبقى بدها تبقى ال function عنها معرفة بهذا
+
+54
+00:05:10,060 --> 00:05:16,060
+الشكل كل المنطقة بس عندها دياش مفتوحة لأنها أقل من
+
+55
+00:05:16,060 --> 00:05:23,580
+C هي تحتها دوري هيك هي نقطة C تمام؟يبقى هذا إذا
+
+56
+00:05:23,580 --> 00:05:28,740
+كان T أقل من C فقيمة الدالة واحد لكن عندما T تسوى
+
+57
+00:05:28,740 --> 00:05:34,880
+C فما فوق تصير قيمة الدالة Zero يبقى هنا بدأ تصير
+
+58
+00:05:34,880 --> 00:05:41,340
+هنا ب Zero مغلقة ونظل ماشيين إلى ما شاء الله يبقى
+
+59
+00:05:41,340 --> 00:05:45,780
+هذه الكلة تعتبر من رسمة ال function اللي عندنا
+
+60
+00:05:45,780 --> 00:05:50,230
+وكأنه انها ايه اللي عملنا جلبنا اللي فوق تحتواللي
+
+61
+00:05:50,230 --> 00:05:55,690
+تحت فوق بالضبط تماما يبقى هذا مثال هذا يعتبر مثال
+
+62
+00:05:55,690 --> 00:06:01,390
+بسيط انتجليه شوية يبقى بنيجي نقول example two
+
+63
+00:06:01,390 --> 00:06:08,530
+example two يبقى هذا كان example one وهذا example
+
+64
+00:06:08,530 --> 00:06:15,150
+two برضه sketch the graph of the function sketch
+
+65
+00:06:15,150 --> 00:06:17,670
+the graph
+
+66
+00:06:27,820 --> 00:06:38,800
+Y تساوي T ناقص تلاتة في U اتنين as a function of T
+
+67
+00:06:40,000 --> 00:06:49,500
+ناقص T ناقص اتنين T ناقص اتنين في U تلاتة as a
+
+68
+00:06:49,500 --> 00:06:58,000
+function of T on the interval on the interval T
+
+69
+00:06:58,000 --> 00:07:05,160
+greater than or equal to zero كويس
+
+70
+00:07:05,160 --> 00:07:10,830
+قال لي ارسمليشكل الدالة اللى عندنا هذه على الفترة
+
+71
+00:07:10,830 --> 00:07:16,010
+من صفر لغاية infinity بطلع في السؤال و بطلع في
+
+72
+00:07:16,010 --> 00:07:22,470
+اللى عنديبعد عن بعض مظبوط الشكل هو بعد عن بعض لكن
+
+73
+00:07:22,470 --> 00:07:27,050
+انا بدي احاول احط ال function اللي عندنا هذه على
+
+74
+00:07:27,050 --> 00:07:31,470
+الصيغة اللي عندنا هذه وبالتالي بصير العملية الرسم
+
+75
+00:07:31,470 --> 00:07:37,370
+عملية سهلة لحظة يا اخناش جالين هنا U2 و U3 يعني
+
+76
+00:07:37,370 --> 00:07:42,930
+انا دخلت رقمين على الخط اذا انا بدي ادرس الفترة من
+
+77
+00:07:42,930 --> 00:07:48,030
+صفر لغاية اتنينومن اتنين لغاية التلاتة ومن التلاتة
+
+78
+00:07:48,030 --> 00:07:51,830
+فما فوق يعني صار عندي تلت فترات من خلال السؤال
+
+79
+00:07:51,830 --> 00:07:57,770
+اللي عندنا هذا تمام فبروح بقول له دل هادي Y تساوي
+
+80
+00:07:57,770 --> 00:08:04,470
+أحد ثلاثة أمور الأمر الأول بدي أخد لما T تبقى أقل
+
+81
+00:08:04,470 --> 00:08:11,270
+من اتنين لما T تبقى أقل من اتنين يبقى هادي T ناقص
+
+82
+00:08:11,270 --> 00:08:14,230
+ثلاثة كم تكون قيمة الدل هادي؟
+
+83
+00:08:18,690 --> 00:08:24,290
+يبقى نقص T نقص 2 U تلاتة قداش قبل اتنين
+
+84
+00:08:30,130 --> 00:08:34,510
+زيرو برضه قبل اتنين و نص بزيرو و قبل اتنين و تسعة
+
+85
+00:08:34,510 --> 00:08:39,010
+و تسعة و قبل التلاتة بزيرو اتنين قبل التلاتة اذا
+
+86
+00:08:39,010 --> 00:08:46,590
+هذه زيرو طبعا فلو كانت ال T اكبر من او تساوي اتنين
+
+87
+00:08:46,590 --> 00:08:53,980
+و اقل من تلاتةيبقى باجي بقول له هدى تى ناقص ثلاثة
+
+88
+00:08:53,980 --> 00:08:59,680
+فيه يو اتنين هالحساس بعد اتنين، مظبوط؟ بعد اتنين
+
+89
+00:08:59,680 --> 00:09:02,700
+على طول بواحد، اذا من اتنين لتلاتة جيبتها في
+
+90
+00:09:02,700 --> 00:09:11,290
+الجداش بواحدنقص ا ت نقص اتنين في قبل التلاتة اللي
+
+91
+00:09:11,290 --> 00:09:17,550
+همين ب zero تمام نيجي الان ناخد الفترة T greater
+
+92
+00:09:17,550 --> 00:09:22,810
+than or equal to تلاتة يبقى U اتنين بقداش بتكون
+
+93
+00:09:22,810 --> 00:09:30,410
+بعد التلاتة بواحد يبقى بصير T ناقص تلاتة في واحد
+
+94
+00:09:30,800 --> 00:09:36,720
+نقص T نقص اتنين في قداش كمان بواحد تمام التمام
+
+95
+00:09:36,720 --> 00:09:41,980
+الأن نروح نتعرف على شكل الدالة اللي عندنا هذه يبقى
+
+96
+00:09:41,980 --> 00:09:48,940
+دي صار شكلها بالشكل التالي هذا ثلاثة أجزاء الجزء
+
+97
+00:09:48,940 --> 00:09:53,000
+الأول Zero في رقم Zero Zero في رقم Zero Zero نقص
+
+98
+00:09:53,000 --> 00:09:59,620
+Zero يبقى ب Zero لما T أقل من اتنينهذا الـ term
+
+99
+00:09:59,620 --> 00:10:05,100
+بيزير و بيظلش عندنا الا main ت ناقص ثلاثة يبقى T
+
+100
+00:10:05,100 --> 00:10:10,540
+ناقص ثلاثة لما T أكبر من أو يسوى اتنين وأقل من
+
+101
+00:10:10,540 --> 00:10:18,380
+الmain من ثلاثةنجي لهذه تصير T ناقص تلاتة ناقص T
+
+102
+00:10:18,380 --> 00:10:23,800
+زائد اتنين ناقص T وزائد T مع السلامة ناقص تلاتة
+
+103
+00:10:23,800 --> 00:10:29,620
+وزائد اتنين بيظل قداش ناقص واحد يبقى ناقص واحد لما
+
+104
+00:10:29,620 --> 00:10:33,760
+T greater than or equal to تلاتة اذا من ال
+
+105
+00:10:33,760 --> 00:10:39,240
+function الأصلي اللي عند هذه استطعتكتابتها على
+
+106
+00:10:39,240 --> 00:10:45,420
+الشكل اللي عندنا هذا إلا لو رسمت هذه بكون رسمت الـ
+
+107
+00:10:45,420 --> 00:10:50,520
+function الأصلية طيب تعالوا نرسم و نشوف كيف بدو
+
+108
+00:10:50,520 --> 00:10:58,220
+يكون شكلها إذا لو جيت قلت هذا محور T و هذا محور Y
+
+109
+00:11:00,050 --> 00:11:05,730
+الان هيا عندى هنا اتنين وهي عندى هنا اش اللى هى
+
+110
+00:11:05,730 --> 00:11:10,610
+التلاتة وهذا ما بعدها الان جابلى اتنين جديش قيمة
+
+111
+00:11:10,610 --> 00:11:17,050
+الدالة؟ Zero يبقى مفتوحة عندى اتنين هيك هي مفتوحة
+
+112
+00:11:17,050 --> 00:11:23,190
+ونغطى المنطقة هذه كلهاكل المنطقة اللي عندنا هذه
+
+113
+00:11:23,190 --> 00:11:27,970
+ليه قيمة من؟ قيمة ال dollar الان بدنا نيجي من
+
+114
+00:11:27,970 --> 00:11:34,730
+اتنين لغاية تلاتة يبقى Y تساوي T ناقص تلاتة يعني
+
+115
+00:11:34,730 --> 00:11:42,210
+معادلة خطية الان قداش قيمتها عندي اتنينT أكبر من
+
+116
+00:11:42,210 --> 00:11:47,290
+يساوي اتنين لو حطيت اتنين بيصير كده اذا عند اتنين
+
+117
+00:11:47,290 --> 00:11:54,090
+هذي بدها تنزل هنا لمين لسالب واحد تمام يبقى بيجيني
+
+118
+00:11:54,090 --> 00:11:59,750
+هنا بنزل رأسي لغاية ما جوان عند السالب واحد و
+
+119
+00:11:59,750 --> 00:12:07,370
+بيصير مغلقة بسبب اليساويطيب لو وصلت لتلاتة لا سمح
+
+120
+00:12:07,370 --> 00:12:10,250
+الله، طبعا أقل من تلاتة، بيقول لو صارت تلاتة إيش
+
+121
+00:12:10,250 --> 00:12:15,790
+بيصير؟ Zero، يبقى عندي التلاتة بدأ تطلع ل Zero، بس
+
+122
+00:12:15,790 --> 00:12:20,830
+عند Zero بيكون مالها مفتوحة، إذا هذا يمثل الخط
+
+123
+00:12:20,830 --> 00:12:26,730
+المستقيم T ناقص تلاتة، يبقى بده يصير شكل دالة
+
+124
+00:12:26,730 --> 00:12:30,430
+بالشكل اللي يعني هذا الخط المستقيم الغامق هذا
+
+125
+00:12:34,560 --> 00:12:40,560
+يبقى هذا رسمة لطي ناقص تلاتة تمام بعد ذلك بده يجيب
+
+126
+00:12:40,560 --> 00:12:45,300
+بعد التلاتة بعد التلاتة قيمة الدلة كده؟ سالب واحد
+
+127
+00:12:45,300 --> 00:12:51,880
+اذا هذه بدها تنزل automatic عند السالب واحد و بعد
+
+128
+00:12:51,880 --> 00:12:56,880
+التلاتة قيمتها على خور الخط كده؟ سالب واحد يبقى
+
+129
+00:12:56,880 --> 00:13:02,820
+هذه الدلة بالشكل التاني هنايبقى هاي رسمنا اللي هو
+
+130
+00:13:02,820 --> 00:13:07,020
+الدالة في المقاطع الثلاثة اللي هي piecewise
+
+131
+00:13:07,020 --> 00:13:13,340
+continuous طبعا يبقى هاه لو الشكل استشكل علينا هذا
+
+132
+00:13:13,340 --> 00:13:17,960
+بحاول أحطه في شكل جديد هاي الشكل الجديد الشكل
+
+133
+00:13:17,960 --> 00:13:21,040
+الجديد الساهر رسمه يبقى بدون اسم وبالتالي يكون
+
+134
+00:13:21,040 --> 00:13:25,660
+رسمنا من الدالة الأصلية اللي عندنا
+
+135
+00:13:41,980 --> 00:13:48,980
+بنحاول نجيب Laplace transform لمن؟ ل UC of T يبقى
+
+136
+00:13:48,980 --> 00:13:56,380
+example كمان find Laplace
+
+137
+00:13:56,380 --> 00:14:03,020
+transform for
+
+138
+00:14:03,020 --> 00:14:10,180
+the function UC of T
+
+139
+00:14:20,470 --> 00:14:23,970
+الورقة الجادة اللى اقنعكوا هي المرة اللى فاتت او
+
+140
+00:14:23,970 --> 00:14:29,050
+في الكتاب صفحة 319 لو فتحنا بنعرف النتيجة مباشرة
+
+141
+00:14:29,050 --> 00:14:35,370
+لكن بنعرف من اين جاءت هذه النتيجة يبقى عندك يو سي
+
+142
+00:14:35,370 --> 00:14:40,830
+و تي هي رقم مقماشرقم 12 لبلايس ترانسفورم إيه إيه
+
+143
+00:14:40,830 --> 00:14:42,290
+إيه إيه إيه إيه إيه إيه إيه إيه إيه إيه إيه إيه
+
+144
+00:14:42,290 --> 00:14:45,750
+إيه إيه إيه إيه إيه إيه إيه
+
+145
+00:14:45,750 --> 00:14:51,830
+إيه إيه
+
+146
+00:14:53,060 --> 00:15:00,320
+أنا بروح بقول له plus transform ل UC of T بده سوى
+
+147
+00:15:00,320 --> 00:15:08,100
+تكامل من zero ل infinity ل E اصنعقص ST ل UC of T
+
+148
+00:15:08,100 --> 00:15:17,250
+DTطيب هذا الكلام يساوي ما يعني هذي U C of T عبارة
+
+149
+00:15:17,250 --> 00:15:22,730
+عن جزئين تمام؟ إذن بالداجة للجزء الأول يبقى هذا
+
+150
+00:15:22,730 --> 00:15:29,910
+integration من Zero إلى C لل E أس ناقص ST في
+
+151
+00:15:29,910 --> 00:15:36,550
+الفترة هذه U C of T بقدرش؟ Zero ممتاز جدا يبقى في
+
+152
+00:15:36,550 --> 00:15:44,560
+Zero في DT إزاي؟تكامل من C إلى Infinity لل E أُس
+
+153
+00:15:44,560 --> 00:15:51,780
+ناقص ST في ال use of U بواحد في ال DTأذا هذا كله
+
+154
+00:15:51,780 --> 00:15:57,720
+بيروح بقداش بزيرو هذا improper integral يبقى بيروح
+
+155
+00:15:57,720 --> 00:16:04,720
+اعمله as a limit يبقى هذا ال limit تكامل من C إلى
+
+156
+00:16:04,720 --> 00:16:11,980
+A لما A tends to infinity لل E أصناق STDT
+
+157
+00:16:14,720 --> 00:16:19,980
+هذا الكلام يساوي limit لما ال a tends to infinity
+
+158
+00:16:19,980 --> 00:16:25,760
+تكمل ال exponential بال exponential itself على
+
+159
+00:16:25,760 --> 00:16:31,200
+مشتقة الأس لما يكون الأس as a linear function يعني
+
+160
+00:16:31,200 --> 00:16:36,840
+معدلة من الدرجة الأولى يبقى عالمين على ناقص ال s
+
+161
+00:16:36,840 --> 00:16:44,640
+من c لغاية ال aيبقى هذا الكلام بده يساوي limit لما
+
+162
+00:16:44,640 --> 00:16:48,920
+a tends to infinity بتدعوض فيه نتيجة التكامل
+
+163
+00:16:48,920 --> 00:16:53,660
+بالقيمة اللي فوق نقص اللي تحت لإنه finite integral
+
+164
+00:16:53,660 --> 00:17:03,440
+تكامل محدوديبقى هذا E أس ناقص S A على ناقص S ناقص
+
+165
+00:17:03,440 --> 00:17:11,820
+E أس بدي أشيل هذه و أحط مكانها C يبقى ناقص S في C
+
+166
+00:17:11,820 --> 00:17:22,130
+على مين على ناقص S و ال limit للمقدار هذا كلهطب
+
+167
+00:17:22,130 --> 00:17:25,450
+لما ال E بده تروح ل infinity هذا ال أس بالسالب
+
+168
+00:17:25,450 --> 00:17:30,150
+يبقى بنزل وين؟ تحت بصير واحد على ماله نهايه اللي
+
+169
+00:17:30,150 --> 00:17:34,530
+هو الجداش يبقى هذا الله يسهل عليه غير مأسوف عليه
+
+170
+00:17:34,530 --> 00:17:39,930
+بزيره هذا كله له دعوة باللمتة مافيش فيه capital E
+
+171
+00:17:39,930 --> 00:17:44,990
+نهاية يبقى هذا يعتبر كونستان يبقى ناقص على ناقص
+
+172
+00:17:44,990 --> 00:17:52,210
+بالزائدبظل E أصناع ال CS على S هي النتيجة اللى
+
+173
+00:17:52,210 --> 00:17:56,290
+عندنا يبقى هذا ال plus transform لل unit step
+
+174
+00:17:56,290 --> 00:18:00,850
+function اللى ذكرناها قبل قليل أظن هي نفس النتيجة
+
+175
+00:18:00,850 --> 00:18:05,330
+اللى عندكوا في الجدول يبقى هي نفس النتيجة بالضبط
+
+176
+00:18:05,330 --> 00:18:06,370
+تماما
+
+177
+00:18:16,550 --> 00:18:22,370
+الان بدنا نروح نعطي تعريف ل function جديدة تعتمد
+
+178
+00:18:22,370 --> 00:18:32,210
+على function أخرى فبجي بقول definition from
+
+179
+00:18:32,210 --> 00:18:40,670
+a given function if
+
+180
+00:18:40,670 --> 00:18:43,550
+we define
+
+181
+00:18:45,840 --> 00:18:55,000
+define a related function
+
+182
+00:18:55,000 --> 00:19:07,200
+g مثلا byG of T بده يساوي أحد أمرين، يا إما Zero
+
+183
+00:19:07,200 --> 00:19:17,240
+لما T أقل من C، يا إما ال F of T ناقص الـC لما T
+
+184
+00:19:17,240 --> 00:19:20,400
+greater than or equal to C
+
+185
+00:19:30,010 --> 00:19:34,910
+بنرجع للتعريف اللي احنا جايلينه هذا مرة ثانية بقول
+
+186
+00:19:34,910 --> 00:19:40,190
+from a given function f يبقى f دي مالها function
+
+187
+00:19:40,190 --> 00:19:45,230
+معطاعة تمام ال function المعطاعة بدي اعرف من
+
+188
+00:19:45,230 --> 00:19:49,850
+خلالها function تانية مرتبطة معاها related
+
+189
+00:19:49,850 --> 00:19:54,710
+function g بدي أسميها g جي بتعتمد على مين؟ اذا
+
+190
+00:19:54,710 --> 00:20:00,330
+مرتبطة معاها برابط ما ما هو الرابط هذا بيقول بايG
+
+191
+00:20:00,330 --> 00:20:06,250
+of T بدي يساوي أحد أمرين، يا إما Zero لما T أقل من
+
+192
+00:20:06,250 --> 00:20:12,390
+C، يا إما ال F of T ناقص الـC لما T أكبر من أو
+
+193
+00:20:12,390 --> 00:20:16,310
+يساوي C، لو جيت سؤالكوا السؤال التالت، و أنتم
+
+194
+00:20:16,310 --> 00:20:22,010
+دارسين Calculus A بنجاحبظبط وزيادة على ذلك P وربما
+
+195
+00:20:22,010 --> 00:20:27,190
+C كمان تمام لما اقول ان في عندي function F of T
+
+196
+00:20:27,190 --> 00:20:34,570
+ماذا تعني F of T ناقص ال C علم انه C positive ايه
+
+197
+00:20:34,570 --> 00:20:37,630
+زيها يعني بنعمل لل function shift
+
+198
+00:20:42,220 --> 00:20:59,000
+يبقى هذه إزاحة جهة اليمين بمقدار C يبقى
+
+199
+00:20:59,000 --> 00:21:02,700
+هذه الـG عبارة عن shift للدالة اليمين
+
+200
+00:21:06,030 --> 00:21:12,230
+طب ماهي رأيك و هذي بقدر أصيغها صياغة أخرى ممكن أخد
+
+201
+00:21:12,230 --> 00:21:17,990
+f of t ناقص c عامل مشترك برا من الكل بنفع ولا لا؟
+
+202
+00:21:17,990 --> 00:21:22,310
+بصير هنا zero زي ما هو هنا جداش لأن ال f of t
+
+203
+00:21:22,310 --> 00:21:26,110
+ناقصه ضرب ال zero ب zero في ولا حد بتطلع هذي
+
+204
+00:21:26,110 --> 00:21:31,630
+بالضبط تماما يعني هذي بقدر أقول بالضبط هي عبارة عن
+
+205
+00:21:31,630 --> 00:21:39,150
+fof T ناقص الـC أحد أمرين، يا إما Zero لما T أقل
+
+206
+00:21:39,150 --> 00:21:45,010
+من C، يا إما واحد لما T أكبر من أو تساوي C، صحيح
+
+207
+00:21:45,010 --> 00:21:51,850
+ولا لا؟ طيب، ممتاز، هذه هها، هي حد ذاتها هذه، مين
+
+208
+00:21:51,850 --> 00:21:57,300
+هي؟الـ unit step function يعني معناه هذا الكلام
+
+209
+00:21:57,300 --> 00:22:07,420
+بقدر اكتب هذه U C of T في ال F of T ناقص ال C يبقى
+
+210
+00:22:07,420 --> 00:22:13,140
+G of T صغرها صياغة أخرى غير الصياغة اللي عندنا هذه
+
+211
+00:22:13,140 --> 00:22:18,440
+روحت قلت هي ال unit step function U C of T مضروبة
+
+212
+00:22:18,440 --> 00:22:29,350
+في ال Fمعلومة مهمة لها ما بعدها نأخذ
+
+213
+00:22:29,350 --> 00:22:32,810
+بعض الخواص لـ plus transform
+
+214
+00:23:04,510 --> 00:23:10,660
+الكتاب حاطط القواص على شكل نظريتينأنا هخلهم نظرية
+
+215
+00:23:10,660 --> 00:23:15,660
+واحدة بس بنقطتين عشان ما نكررش الكلام اكتر فجباجي
+
+216
+00:23:15,660 --> 00:23:26,980
+بقول هنا F F of S هو لبلاس ترانسفورم لدالة F of T
+
+217
+00:23:26,980 --> 00:23:37,220
+ماله هذا exists لو كان هذا موجود forS which is
+
+218
+00:23:37,220 --> 00:23:44,740
+greater than C و C دائما و أبدا ما لها موجبة than
+
+219
+00:23:44,740 --> 00:23:56,600
+النقطة الأولى لابلاس ترانسفورم ل UC of T في ال F
+
+220
+00:23:56,600 --> 00:24:04,100
+of Tناقص الـ C في ال F of T ناقص الـ C يبقى هذا
+
+221
+00:24:04,100 --> 00:24:12,700
+يسوي E أس ناقص CS فاهمين؟ في لابلاس ترانسفورم للـ
+
+222
+00:24:12,700 --> 00:24:20,240
+F of T و اللي بده يسوي E أس ناقص CS في capital F
+
+223
+00:24:20,240 --> 00:24:25,020
+of S وهذه سمونيها رقم 1
+
+224
+00:24:27,700 --> 00:24:33,480
+ممكن اعمل عملية عكسية اخد معكوس ل place transform
+
+225
+00:24:33,480 --> 00:24:38,900
+للدل هذي يبقى مين بدي يعطيني الدل بين القوسين يبقى
+
+226
+00:24:38,900 --> 00:24:50,890
+لو قلتلكوا converselyعلى العكس لأبلاس انفرس لمن؟
+
+227
+00:24:50,890 --> 00:24:58,150
+لل E أصناع ال CS في capital F of S بده يساوي من
+
+228
+00:24:58,150 --> 00:25:02,350
+لأبلاس انفرس ل لأبلاس هذه لأبلاس انفرس مع لأبلاس
+
+229
+00:25:02,350 --> 00:25:06,350
+هتلقوا بعضها بظالمين الدالة اللي عندها دي فجأة ده
+
+230
+00:25:06,350 --> 00:25:18,430
+بده يساوي UC of Tفى ال F of T ناقص ال C تمام
+
+231
+00:25:18,430 --> 00:25:24,480
+نيجى الآن للنقطة الثانيةالنقطة الثانية بيقول لبلاس
+
+232
+00:25:24,480 --> 00:25:34,180
+ترانس فورب لل E of C في T فال F of T فال F of T
+
+233
+00:25:34,180 --> 00:25:44,000
+بده ساوي ال F of S ناقص ال C والS greater than C
+
+234
+00:25:44,000 --> 00:25:46,920
+وإلا كمان ال S
+
+235
+00:25:50,450 --> 00:25:57,670
+لو عملت العملية العكسية يبقى هنا conversely
+
+236
+00:26:00,350 --> 00:26:09,270
+لابلاس انفرس لمين ليه capital F of S ناقص ال C بده
+
+237
+00:26:09,270 --> 00:26:18,890
+يساوي E of CT في ال F of T بالشكل اللي عندنا سميلي
+
+238
+00:26:18,890 --> 00:26:24,480
+هذه رقم اتنينيبقى واحد واثنين هما النقطتين
+
+239
+00:26:24,480 --> 00:26:28,860
+الأساسيتين تبعات النظريتين اللى عندنا فى الكتاب
+
+240
+00:26:28,860 --> 00:26:35,520
+بنا نرجع لكل واحدة فىهم ونروح نبرهن صحتها و بعدين
+
+241
+00:26:35,520 --> 00:26:42,900
+نستخدمها كخواص يحل المسائل المختلفة ال proof
+
+242
+00:26:54,670 --> 00:26:55,870
+هذه هي النقطة الأولى
+
+243
+00:26:58,620 --> 00:27:05,820
+لو كان لبلاس ترانسفورم لدالة exist then لبلاس
+
+244
+00:27:05,820 --> 00:27:10,920
+ترانسفورم لهذه الدالة بعد ما عمل لها shift مضروبا
+
+245
+00:27:10,920 --> 00:27:16,000
+في ال U C of T بيسوي E وصناعة ال CS في لبلاس ال F
+
+246
+00:27:16,000 --> 00:27:20,600
+of T او ان شئتم فقولوا E وصناعة ال CS فهمين في
+
+247
+00:27:20,600 --> 00:27:26,150
+capital F of S يبقى انا بالدرجة اخدله منين؟الدالة
+
+248
+00:27:26,150 --> 00:27:30,270
+اللى عندنا هذه فباجي بقوله انا بدي اخد Laplace
+
+249
+00:27:30,270 --> 00:27:37,930
+transform ل U C of T فمين فى ال F of T ناقص ال C
+
+250
+00:27:37,930 --> 00:27:43,110
+بدي اعرف انه هل هو القيمة اللى هناك و الله ما هيشى
+
+251
+00:27:43,520 --> 00:27:47,500
+بقوله كويس بدي ارجع لتعريف ال class transform اللي
+
+252
+00:27:47,500 --> 00:27:52,020
+اتعلمناه يبقى هذا integration من zero لغاية
+
+253
+00:27:52,020 --> 00:28:02,000
+infinity ل E أس ناقص ST فاهمين؟ في ال U C of
+
+254
+00:28:02,000 --> 00:28:11,430
+T في ال F of T ناقص ال C كله ديتمام ال unit step
+
+255
+00:28:11,430 --> 00:28:17,370
+function عبارة عن جزء اما صفريا اما كدهش واحد
+
+256
+00:28:17,370 --> 00:28:22,410
+ممتاز جدا اذا هذه بدها تساوي integration من zero
+
+257
+00:28:22,410 --> 00:28:31,670
+لل C لل E أُس ناقص ST في zero في ال F of T ناقص ال
+
+258
+00:28:31,670 --> 00:28:38,230
+C في DT زائد integration من C إلى infinity لل E
+
+259
+00:28:38,230 --> 00:28:46,270
+أُس ناقص ST في واحد في ال F of T ناقص ال C DTيبقى
+
+260
+00:28:46,270 --> 00:28:49,750
+شيلت ال unit step function وحطيتها مرة بزيرو على
+
+261
+00:28:49,750 --> 00:28:55,190
+الفترة من zero ل C ومرة بواحد من C لغاية infinity
+
+262
+00:28:55,190 --> 00:29:00,790
+ال term الأول هذا ماله Zero معاه سلامة نيجي لل
+
+263
+00:29:00,790 --> 00:29:04,770
+term التان اللي عندنا هذا يبقى هذا الكلام بده
+
+264
+00:29:04,770 --> 00:29:12,310
+يساوي integration من C لغاية infinity لل E أس ناقص
+
+265
+00:29:12,310 --> 00:29:18,510
+STفى الـ F of T ناقص الـ C فى DT
+
+266
+00:29:27,760 --> 00:29:33,480
+إذا بدى اعتبر هذا كله بمين بمتغير جديد، إذا بدى
+
+267
+00:29:33,480 --> 00:29:37,320
+أعمل تعويض زي ما كنا بنعوض عادي في التكاملات
+
+268
+00:29:37,320 --> 00:29:41,340
+العادية integration by substitution إذا أنا لو
+
+269
+00:29:41,340 --> 00:29:54,090
+روحت حطيت ال eta تساوي تساوي T ناقص Cيبقى دي إي تا
+
+270
+00:29:54,090 --> 00:30:00,070
+بده يساوي دي تي والسي ما هو مقدار ثابت مش تكتب مين
+
+271
+00:30:00,070 --> 00:30:06,790
+بزيرو تمام؟ هذا المثل ها دي هتصبح على الشكل التالي
+
+272
+00:30:06,790 --> 00:30:13,050
+يبقى صار ل plus transform ل U C as a function of T
+
+273
+00:30:13,050 --> 00:30:20,530
+في ال F of T ناقص ال C بده يساوي تكاملتعالى نشوف
+
+274
+00:30:20,530 --> 00:30:28,930
+هنا يبقى E أس ناقص S نجي لمين التي قدشتي يا بنات
+
+275
+00:30:28,930 --> 00:30:39,250
+إيتا زائد C يبقى هذه بإيتا زائد C إيتا زائد C طبعا
+
+276
+00:30:39,250 --> 00:30:49,400
+الان هذه F of إيتا ال D تيب دي إيتاطبعاً ضالمين عن
+
+277
+00:30:49,400 --> 00:30:56,410
+حدود التكامل باجي بقول لو كانت T ب Infinityيبقى
+
+278
+00:30:56,410 --> 00:31:02,470
+بإي تا infinity ناقص يعني infinity يبقى بقى الحد
+
+279
+00:31:02,470 --> 00:31:09,510
+العلوي كما هو الآن لو كان الحد ال T تساوي ال C
+
+280
+00:31:09,510 --> 00:31:15,350
+بيصير C ناقص C لو ب Zero يبقى إي تا تساوي قداش
+
+281
+00:31:15,350 --> 00:31:20,910
+تساوي Zero تمام تمام يبقى هذا تكمل من Zero ل
+
+282
+00:31:20,910 --> 00:31:30,760
+Infinityهذا بنات E أس ناقص S إيتاه زائد في إيمين
+
+283
+00:31:30,760 --> 00:31:39,740
+في E أس ناقص CS في ال F of إيتاه في D إيتاه،
+
+284
+00:31:39,740 --> 00:31:46,230
+مظبوط؟ هذا إيه اللي هو علاقة بالتكامل؟ماليش علاقش
+
+285
+00:31:46,230 --> 00:31:50,530
+في إيته يبقى هذا مقدار ثابت تشرفنا برا يبقى هذا
+
+286
+00:31:50,530 --> 00:32:00,270
+بيصير E أس ناقص CS CS تكامل من Zero ل Infinity ل E
+
+287
+00:32:00,270 --> 00:32:10,150
+أس ناقص S إيته في ال F of إيته في D إيته طب إيش
+
+288
+00:32:10,150 --> 00:32:16,180
+رايكوا هذا مين يا بنات تعريف مين؟Laplace transform
+
+289
+00:32:16,180 --> 00:32:22,480
+لدالة F of Eta يعني مين له capital F of S صحيح ولا
+
+290
+00:32:22,480 --> 00:32:28,800
+لأ؟يعني هدا بقول له E أصناق ال CS في Laplace
+
+291
+00:32:28,800 --> 00:32:35,560
+transform لل F of Eta تمام؟ اللي هو مين؟ capital F
+
+292
+00:32:35,560 --> 00:32:42,920
+of S يبقى E أصناق ال CS في capital F of S أظن و هو
+
+293
+00:32:42,920 --> 00:32:43,720
+المطلوب؟
+
+294
+00:32:52,490 --> 00:33:01,130
+أذا اثبتنا المطلوب الأول جالي conversely يعني خد
+
+295
+00:33:01,130 --> 00:33:04,790
+ال plus inverse هنا بده يسوي ال plus inverse هنا
+
+296
+00:33:04,790 --> 00:33:09,310
+تماما باجي بقوله الآن بده اجي لل conversely بتاعته
+
+297
+00:33:10,030 --> 00:33:17,330
+يبقى بدأ أخد Laplace inverse لمين؟ لLaplace ل U C
+
+298
+00:33:17,330 --> 00:33:23,690
+of T في F of T ناقص C بده يسوي Laplace inverse
+
+299
+00:33:23,690 --> 00:33:29,270
+لنتيجة اللي طلعت عندنا هذه E أس ناقص CS في capital
+
+300
+00:33:29,270 --> 00:33:37,690
+F of Sطبعا يبقى بناء علي أسار ل class inverse لمن؟
+
+301
+00:33:37,690 --> 00:33:47,790
+لل E أس ناقص CS في capital F of S بده يساوي UC of
+
+302
+00:33:47,790 --> 00:33:56,250
+T في F of T ناقص C طيب إيش رأيك هذه موجودة عندك في
+
+303
+00:33:56,250 --> 00:34:01,090
+الجدول؟ موجودة؟
+
+304
+00:34:05,760 --> 00:34:12,740
+رقم كم؟ رقم تلتاشر اللي هو شبهها بالضبط تماما. هذا
+
+305
+00:34:12,740 --> 00:34:16,840
+يالي و إيه أصناق ال CS في capital F of S يبقى هذه
+
+306
+00:34:16,840 --> 00:34:20,980
+تلتاشر اللي عندك وين في الجدولة اللي احنا أثبتناها
+
+307
+00:34:20,980 --> 00:34:26,260
+عمليا. هذه هي النقطة الأولى.بنجي لمين للنقطة
+
+308
+00:34:26,260 --> 00:34:30,800
+الثانية؟النقوة الثانية قال اللي بده ل plus
+
+309
+00:34:30,800 --> 00:34:39,660
+transform ل ال E أصناع ال CT لل F of T بالشكل اللي
+
+310
+00:34:39,660 --> 00:34:45,600
+عندنايبقى نروح لتعريف لابلاسي ترانسفورم لتعريف
+
+311
+00:34:45,600 --> 00:34:50,660
+لابلاسي ترانسفورم اذا بد النتيجة تقضع F of S ناقص
+
+312
+00:34:50,660 --> 00:34:56,840
+الـC E of CT بالموجب وليست بالثالث تمام؟ يبقى هذه
+
+313
+00:34:56,840 --> 00:35:03,640
+بدها تساوي تكامل من Zero ل Infinity لل E أُس ناقص
+
+314
+00:35:03,640 --> 00:35:10,800
+ST في مين؟ في الدالة اللي عندنا هذه E of CTفى ال F
+
+315
+00:35:10,800 --> 00:35:12,580
+of T فى ال DT
+
+316
+00:35:15,340 --> 00:35:20,180
+يبقى هذه بدها تساوي integration من zero إلى
+
+317
+00:35:20,180 --> 00:35:26,100
+infinity هذا الأساسات زي بعض يبقى عند الضرب تجمع
+
+318
+00:35:26,100 --> 00:35:35,920
+الأسس يبقى هذا الكلام بد يساوي E في ناقص S ناقص C
+
+319
+00:35:35,920 --> 00:35:39,940
+في T في F of T DT
+
+320
+00:35:48,130 --> 00:35:54,770
+هذا هو تعريف لبلاس ترانسفورم للدالة اللى عندنا
+
+321
+00:35:54,770 --> 00:36:00,490
+اللى هى ال F of D بس بشرط مش F of S ال S أجاب
+
+322
+00:36:00,490 --> 00:36:05,070
+دالها مين؟ S ناقص ال Cيبقى من خلال ال definition
+
+323
+00:36:05,070 --> 00:36:11,650
+تبع لبلاس ترانسفورم هذا بده يساوي لو capital F of
+
+324
+00:36:11,650 --> 00:36:17,810
+S ناقص ال C من تعريف لبلاس ترانسفورم لمين لهذه
+
+325
+00:36:17,810 --> 00:36:23,710
+الدالة الان الان العملية اللي هو conversely بقدر
+
+326
+00:36:23,710 --> 00:36:28,930
+اخد لبلاس ترانسفورم لمين للطرفين يبقى باجي بقوله
+
+327
+00:36:28,930 --> 00:36:31,130
+conversely
+
+328
+00:36:32,420 --> 00:36:41,580
+Laplace inverse لمن؟ لcapital F of S ناقص الـC بده
+
+329
+00:36:41,580 --> 00:36:45,660
+يساوي Laplace inverse لLaplace بتلغيها بظلمين
+
+330
+00:36:45,660 --> 00:36:53,520
+الدالة اللي في النص اللي هو E أس CT E أس S CT في
+
+331
+00:36:53,520 --> 00:37:00,080
+من؟ في ال F of T اظن لو اطلعت في الجدوة الموجودة
+
+332
+00:37:00,080 --> 00:37:05,560
+هذه برضهاللي هي رقم قداش يا بنات طلعلي في الجدول
+
+333
+00:37:05,560 --> 00:37:11,800
+اللي بين إيداكي اربعتاش يبقى هي سعرب بتقول رقم
+
+334
+00:37:11,800 --> 00:37:18,040
+اربعتاش مظبوط يبقى دي رقم اربعتاش ال F of S ناقص
+
+335
+00:37:18,040 --> 00:37:24,860
+من ناقص ال C الان شطرتنا كيف نستخدم النقطتين
+
+336
+00:37:24,860 --> 00:37:30,730
+الاتنين اللي عندنا دول في حل المسائل المختلفةيبقى
+
+337
+00:37:30,730 --> 00:37:38,190
+الآن بدنا هذه رقم واحد هذه تماما وبدنا رقم اتنين
+
+338
+00:37:38,190 --> 00:37:43,010
+هذه نكون ملمين ابهم ومن خلالهم بدنا نحاول نحل
+
+339
+00:37:43,010 --> 00:37:50,230
+أمثلة مختلفة بأشكال مختلفة كما ستراهن بعد أن
+
+340
+00:37:50,230 --> 00:37:54,410
+انتهينا من برهان النظرية بدنا نيجي ناخد بعض
+
+341
+00:37:54,410 --> 00:38:00,500
+الأمثلة حد بدها العمود هذاأنا بدى أترك العمود هنا
+
+342
+00:38:00,500 --> 00:38:23,740
+مش هالاتنين هدول لازمات هنا example
+
+343
+00:38:23,740 --> 00:38:24,800
+one
+
+344
+00:38:28,570 --> 00:38:35,730
+أول مثال بقول compute the following compute the
+
+345
+00:38:35,730 --> 00:38:45,770
+following عسبي لي ما يأتي نمرة a بدلا plus
+
+346
+00:38:45,770 --> 00:38:55,490
+transform ل U اتنين by as a function of T لصيني T
+
+347
+00:39:02,750 --> 00:39:07,870
+يبقى باجي بطلع و بيدحل هذه المثلة يبقى باجي بقوله
+
+348
+00:39:07,870 --> 00:39:14,130
+و ال U C of T هي في F of T ناقص ال C مقدار ال
+
+349
+00:39:14,130 --> 00:39:18,950
+shift اللي هنا هو المقدار تبع ال U C بالضبط تماما
+
+350
+00:39:18,950 --> 00:39:24,570
+باجي بطلع في مثلتي اتنين by هنا ماعنديش اتنين by
+
+351
+00:39:25,010 --> 00:39:30,890
+مظبوط؟ اه لكن طلب لبلاس ترانسفورم بقول انا هاه لو
+
+352
+00:39:30,890 --> 00:39:36,550
+قدرت احطها على الصيغة هذه بجهي الجواب عندي مظبوط
+
+353
+00:39:36,550 --> 00:39:42,250
+برجع لذاكرة من الوراق sign T periodic function
+
+354
+00:39:42,250 --> 00:39:47,610
+يعني ده اللي دورية كل قداش تتكرر الدورة كل اتنين
+
+355
+00:39:47,610 --> 00:39:53,760
+by يعني لو اضفت اتنين by او طرحت اتنين byلا تتغير
+
+356
+00:39:53,760 --> 00:39:58,260
+قيمة الـ function على الإطلاق تمام؟ يبقى باجي
+
+357
+00:39:58,260 --> 00:40:05,500
+بقوله solution اتدالى
+
+358
+00:40:05,500 --> 00:40:10,420
+Laplace transform ل U اتنين by as a function of T
+
+359
+00:40:10,420 --> 00:40:16,300
+لصينة T بده يساوي Laplace transform ل U اتنين by
+
+360
+00:40:16,300 --> 00:40:22,920
+as a function of Tلصين تي زائد او ناقص اللي بدك
+
+361
+00:40:22,920 --> 00:40:27,600
+اياها اتنين باي لكن احنا نعيش بالزمن هنا تبقى ناقص
+
+362
+00:40:27,600 --> 00:40:31,620
+يبقى زائد مش لازمالي يبقى بطرح اللي دورة كاملة
+
+363
+00:40:31,620 --> 00:40:37,320
+اتنين باي بالشكل اللي عندناإذا صرت هذه ها هي الشكل
+
+364
+00:40:37,320 --> 00:40:42,460
+اللي عندنا هذا بالضبط صحيح ولا لأ إذا الجواب E أس
+
+365
+00:40:42,460 --> 00:40:49,060
+ناقص CS يبقى automatic من part one الجواب E أس
+
+366
+00:40:49,060 --> 00:40:58,600
+ناقص C بإتنين by Sفي مين؟ في لبلاس ترانسفورم لل F
+
+367
+00:40:58,600 --> 00:41:05,460
+of T هذه F of T ناقص اتنين باي يبقى shift انسى
+
+368
+00:41:05,460 --> 00:41:11,980
+يبقى في لبلاس ترانسفورم لل F of T اللي هي صيني T
+
+369
+00:41:16,290 --> 00:41:23,090
+هذا الكلام بده يساوي الو E أس ناقص اتنين by S بده
+
+370
+00:41:23,090 --> 00:41:28,670
+لفلس لصينة T بروح على الجدول تمام باجي على الجدول
+
+371
+00:41:28,670 --> 00:41:34,630
+الصين T طبعا اللي هي رقم خمسة ل A على S تربيع زائد
+
+372
+00:41:34,630 --> 00:41:42,280
+A تربيعأيه عندي هنا بقداش؟ بواحد يبقى في واحد على
+
+373
+00:41:42,280 --> 00:41:47,720
+S تربيع زائد واحد تربيع الهمين بواحد يبقى النتيجة
+
+374
+00:41:47,720 --> 00:41:54,600
+E اص ناقص اتنين by S على S تربيع زائد واحد
+
+375
+00:41:57,900 --> 00:42:03,000
+يبقى هذه النظرية ريحتني بدل لسه أشيل ال UCT و
+
+376
+00:42:03,000 --> 00:42:07,100
+أحطها مرة ب Zero و مرة بواحد و أضرب فيه و أس ناقص
+
+377
+00:42:07,100 --> 00:42:12,250
+CT و E و أس اتنين Tفي الـ signet و لسه اعمل
+
+378
+00:42:12,250 --> 00:42:16,730
+integration by parts مرتين لأجبتها في سطرين بدل ما
+
+379
+00:42:16,730 --> 00:42:20,130
+بدي بدي صفحة كاملة وجهة في سطرين إذا النظرية هذه
+
+380
+00:42:20,130 --> 00:42:26,510
+سهلتلي عملية حساب لف لاس ترانسفورم للدوال المختلفة
+
+381
+00:42:26,510 --> 00:42:30,790
+طبعا هذا السؤال يعتبر سؤالا مباشرا ده في لف ولا
+
+382
+00:42:30,790 --> 00:42:38,010
+دوران تمامنتقل شوية Laplace transform بدنا لمين ل
+
+383
+00:42:38,010 --> 00:42:48,910
+U by of T لصينة T أقوله
+
+384
+00:42:48,910 --> 00:42:56,910
+كويس هذا الكلام بده يسمى Laplace transform لمين ل
+
+385
+00:42:56,910 --> 00:43:04,470
+U by as a function of Tهذه بدّيها تكون لو كانت T
+
+386
+00:43:04,470 --> 00:43:11,750
+ناقص باي لكان مشكلة محلولة تمام ماقدرش أحط T ناقص
+
+387
+00:43:11,750 --> 00:43:18,270
+باي مباشرة إلا إذا كنت عارف قداش نتيجتها لكن أنا
+
+388
+00:43:18,270 --> 00:43:22,750
+مش عارف لو بدي أحط T ناقص ال باي بقول أه بدي أقول
+
+389
+00:43:22,750 --> 00:43:31,950
+sin T cos باينقص cosine t sin pi تطلع فعلا sin t
+
+390
+00:43:31,950 --> 00:43:37,890
+بس بإشارة قدر سالم نسيت القانون هذا يبقى ضيعة
+
+391
+00:43:37,890 --> 00:43:42,310
+المسألة تمام؟ لا هو ضيقة المسألة ولا حاجة نعمل
+
+392
+00:43:42,310 --> 00:43:50,270
+عملية تحايل كيف عملية تحايل؟ بقول هذه sin t ناقص
+
+393
+00:43:50,270 --> 00:43:56,890
+2pi مافيها مشكلة هذه اظن هذه عملناها فوقانا بديش
+
+394
+00:43:56,890 --> 00:44:01,290
+بدي باي بديش اتنين باي بقول بسيط يا اخي تدبر حالك
+
+395
+00:44:01,290 --> 00:44:08,790
+فبعدين بقول هذه لابلاس ترانسفورم ليه باي of T في
+
+396
+00:44:08,790 --> 00:44:19,870
+مين في ال sign T ناقص باي ناقص باي مش بنفعك يبقى
+
+397
+00:44:19,870 --> 00:44:26,420
+ناقص باي لدالة اللي عندنالو جبتها من الأول و قلت
+
+398
+00:44:26,420 --> 00:44:32,040
+سالب sin t ناقص by ماعناش مشكلة بقولك صحيح طيب
+
+399
+00:44:32,040 --> 00:44:38,100
+الان لما عملناها بالشكل هذا هذه كأنه هذه زاوية و
+
+400
+00:44:38,100 --> 00:44:43,380
+هذه زاوية تانية إذا بقدر أفكها كاش ل sin زاويتها
+
+401
+00:44:43,380 --> 00:44:48,820
+يبقى هذه ل plus transform ل you by as a function
+
+402
+00:44:48,820 --> 00:44:58,630
+of t في sinت ناقص ال by في cosine ال by وصلنا
+
+403
+00:44:58,630 --> 00:45:10,150
+للناقص يبقى cosine ت ناقص ال by في main في sign ال
+
+404
+00:45:10,150 --> 00:45:10,570
+by
+
+405
+00:45:13,530 --> 00:45:18,550
+بقول انا مرة تانية لو بدل ما سويتك لو بدل هذه حطيت
+
+406
+00:45:18,550 --> 00:45:23,410
+T ناقص باي وحطيت اشارة سالب برا نفس النتيجة ماعنا
+
+407
+00:45:23,410 --> 00:45:27,570
+مشكلة واحنا هنا سنوصلها قداش sign ال bye يا بناتي
+
+408
+00:45:27,570 --> 00:45:32,590
+يبقى ال term هذا اجر الفات حالي قداش cosine 180
+
+409
+00:45:33,380 --> 00:45:38,060
+سالب واحد يبقى بيضل سالب sign يبقى أسارة هذه هي
+
+410
+00:45:38,060 --> 00:45:47,300
+عبارة عن هذه هي عبارة عن ل plus transform لمن ل U
+
+411
+00:45:47,300 --> 00:45:56,400
+by of T في من في سالب sign T ناقص by بالشكل اللي
+
+412
+00:45:56,400 --> 00:46:03,480
+عندناأظن اللينيار يبقى السالب هذا بقوله شرفنا برا
+
+413
+00:46:03,480 --> 00:46:11,400
+يبقى هاي سالب ل place transform ل U باي of T ل
+
+414
+00:46:11,400 --> 00:46:17,940
+sign اللي هو T ناقص باي الشكل اللي عندنا هذا أظن
+
+415
+00:46:17,940 --> 00:46:20,660
+صارت هذه هي صيغة رقم واحد اللي هناك
+
+416
+00:46:25,960 --> 00:46:35,800
+يبقى هذا السالب اللي برا وهذا E أس ناقص C في S بدي
+
+417
+00:46:35,800 --> 00:46:42,700
+لبلاس ترانسفورم لمين لصينة T في لبلاس ترانسفورم
+
+418
+00:46:42,700 --> 00:46:50,760
+لصينة Tوهذه وجدناها قبل قليل من الجدول يبقى ناقص E
+
+419
+00:46:50,760 --> 00:46:58,460
+أس ناقص CS على S تربيع زائد واحد كما كانت في نمرة
+
+420
+00:46:58,460 --> 00:47:12,440
+B طيب
+
+421
+00:47:12,440 --> 00:47:23,910
+نمرة Cنمر الـ C بدلا بلاس ترانسفورم لمن؟ لـ 2T
+
+422
+00:47:23,910 --> 00:47:34,210
+زائد 3 في U1 of T بالشكل اللي عندنا، solution
+
+423
+00:47:40,720 --> 00:47:47,600
+أنا عندي هنا لو كان ال T ناقص واحد و هنا U one of
+
+424
+00:47:47,600 --> 00:47:51,700
+T كان قصتي محلولة بس إيش عندي؟ عندي اتنين T و
+
+425
+00:47:51,700 --> 00:47:55,700
+تلاتة يعني لا هي T على شجة ولا حتى واحد على شجة
+
+426
+00:47:55,700 --> 00:48:01,460
+لكن دبر حالك، اظبط أمورك بحيث فعلا نوصل لمين
+
+427
+00:48:01,460 --> 00:48:04,400
+للصيغة اللي قدامنا هذه إذا وصلنا للصيغة هذه بصير
+
+428
+00:48:04,400 --> 00:48:09,470
+قصتنا بسيطة جدا قلصبقول له ماشي هذه Laplace
+
+429
+00:48:09,470 --> 00:48:16,150
+transform لدالة اتنين T زائد تلاتة في ال U one of
+
+430
+00:48:16,150 --> 00:48:22,530
+T بده يساوي Laplace transform ليه؟ مكان اتنين T
+
+431
+00:48:22,530 --> 00:48:28,850
+بده يخلق الهمين بده يخلق اتنين T ناقص واحد فبقى
+
+432
+00:48:28,850 --> 00:48:35,710
+بيقول لو كتبت اتنين T ناقص اتنين اضفت للمعادلة
+
+433
+00:48:35,710 --> 00:48:36,430
+جداش؟
+
+434
+00:48:42,520 --> 00:48:51,520
+تنين T ناقص اتنين زائد خمسة تنين T زائد تلاتة
+
+435
+00:49:00,860 --> 00:49:04,620
+بقول له تمام و الله ماعقول العفرة دي ضرورية دي
+
+436
+00:49:04,620 --> 00:49:09,620
+ربالك مشان اوصل مسألة لصورة من النظرية حتى اقدر
+
+437
+00:49:09,620 --> 00:49:14,200
+اطبقها اكبراجي بقول هذا الكلام يساوي لبلاسي
+
+438
+00:49:14,200 --> 00:49:20,020
+ترانسفورم ليه؟ لو خدت اتنين عامل مشرك بضل قداش؟ت
+
+439
+00:49:20,020 --> 00:49:27,640
+ناقص واحد في مين في ال U1 as a function of T زائد
+
+440
+00:49:27,640 --> 00:49:35,400
+خمسة في ال U1 of T بالشكل اللي عندنا طبعا الحين
+
+441
+00:49:35,400 --> 00:49:39,000
+هذا لابلس تترانسوفوم لينيار فانكشن
+
+442
+00:49:46,380 --> 00:49:53,420
+يبقى هذا الكلام يسوى اتنين Laplace transform ل T
+
+443
+00:49:53,420 --> 00:50:02,380
+ناقص واحد في U1 of T زائد خمسة Laplace transform ل
+
+444
+00:50:02,380 --> 00:50:10,380
+U1 of Tطبعا يبقى هذا الكلام يساوي اتنين بالدالي
+
+445
+00:50:10,380 --> 00:50:16,080
+لبلايس ترانسفورم للمثال اللي عندنا يبقى هي U C of
+
+446
+00:50:16,080 --> 00:50:22,560
+T اللي هو بقداش U واحد وهنا F of T ناقص ال C ال F
+
+447
+00:50:22,560 --> 00:50:27,450
+of T هي T بس معمولة لشيء في جهة اليمين بمقدارإذا
+
+448
+00:50:27,450 --> 00:50:34,130
+هذه قداش ما تحطن يا بنات اتنين في اي أس ناقص واحد
+
+449
+00:50:34,130 --> 00:50:42,430
+في اس تمام في لابلاسي transform لمين التي يبقى هذه
+
+450
+00:50:42,430 --> 00:50:47,350
+أصلها قبل ال shift هو عبارة عن مينعبارة عن T بجهاد
+
+451
+00:50:47,350 --> 00:50:54,190
+ال F of T خلصنا منها زائد من زائد خمسة لأ
+
+452
+00:50:54,190 --> 00:50:59,310
+بلاسترانسفارم ل U one of T حسبناها توسع ل U C of T
+
+453
+00:50:59,310 --> 00:51:04,970
+فقولنا هنا زائد خمسة E أس ناقص CS
+
+454
+00:51:12,410 --> 00:51:19,290
+طيب نجي لهذه يبقى اتنين اي اس ناقص اس لكلاس
+
+455
+00:51:19,290 --> 00:51:25,880
+ترانسفورم لاتيمن الجدول واحد factorial على مين؟
+
+456
+00:51:25,880 --> 00:51:33,600
+على S تربية يبقى هذه واحد factorial على S تربية
+
+457
+00:51:33,600 --> 00:51:40,040
+اللي هي من الجدول رقم كده؟ تلاتة، رقم تلاتة من
+
+458
+00:51:40,040 --> 00:51:47,710
+الجدول، بس ان عندي مقداش بواحد، صحيحبنضل هنا زائد
+
+459
+00:51:47,710 --> 00:51:57,110
+خمسة E أس ناقص S على مين على S أو لو رح نرتبناها
+
+460
+00:51:57,110 --> 00:52:07,010
+بنقول اتنين E أس ناقص S على S تربيع زائد خمسة E أس
+
+461
+00:52:07,010 --> 00:52:13,950
+ناقص S على S هذا لأ plus ال transform لمين لهذه ال
+
+462
+00:52:13,950 --> 00:52:14,690
+function
+
+463
+00:52:29,140 --> 00:52:39,740
+بناخد كمان نقطة يبقى نمر دي نمر دي بدنا laplace
+
+464
+00:52:39,740 --> 00:52:48,060
+transform لتي ناقص ثلاثةفى ال U اتنين as a
+
+465
+00:52:48,060 --> 00:52:56,760
+function of T ناقص T ناقص اتنين ثمين فى ال U تلاتة
+
+466
+00:52:56,760 --> 00:53:10,900
+as a function of T يبقى
+
+467
+00:53:10,900 --> 00:53:15,380
+بدى عرف جديش ال F لسه transform لمينلهذه الدلة
+
+468
+00:53:15,380 --> 00:53:20,200
+بقوله بسيطة جدا بطلع الرقم اللي هنا بختلف عن الرقم
+
+469
+00:53:20,200 --> 00:53:24,460
+اتنين عكس بعض و هنا عكس بعض اتنين اللي كانت برا
+
+470
+00:53:24,460 --> 00:53:28,580
+صارت جوه و اللي جوه ايش اللي قعدت برا تدبر حالك
+
+471
+00:53:28,580 --> 00:53:33,540
+اعمل اي عمل رياضي بحت تتخلى الرقم اللي جوه زي
+
+472
+00:53:33,540 --> 00:53:38,800
+الرقم اللي برا تمام فباجي بقول هذه la place
+
+473
+00:53:38,800 --> 00:53:45,690
+transform ليه هذه ايش بكتبها بناتنقص اتنين ناقص
+
+474
+00:53:45,690 --> 00:53:50,230
+واحد ماعنديش مشكلة في هذه الحالة يبقى ل T ناقص
+
+475
+00:53:50,230 --> 00:53:57,890
+اتنين ناقص واحد في ال U اتنين of T وصلنا ناقص هذه
+
+476
+00:53:57,890 --> 00:54:04,090
+بنفس الطريقة بدي اضيف واحد و اطرح واحد يمشي بالصير
+
+477
+00:54:04,090 --> 00:54:11,530
+T ناقص تلاتة زائد واحد في U تلاتة as a function of
+
+478
+00:54:11,530 --> 00:54:18,890
+Tطيب هذه بتاخدها مع بعض و تضرب في U2 يبقى Laplace
+
+479
+00:54:18,890 --> 00:54:24,390
+transform ل T ناقص اتنين في U2 of T
+
+480
+00:54:31,820 --> 00:54:39,040
+ناقص T ناقص تلاتة في ال U تلاتة of T ناقص في زائد
+
+481
+00:54:39,040 --> 00:54:46,860
+بناقص U تلاتة as a function of T الان لابلس هذه ال
+
+482
+00:54:46,860 --> 00:54:50,080
+linear function
+
+483
+00:54:50,400 --> 00:54:58,600
+لا بلس لمين لت ناقص اتنين ل U اتنين of T ناقص لا
+
+484
+00:54:58,600 --> 00:55:05,700
+بلس transform ل U اتنين of T ناقص لا بلس transform
+
+485
+00:55:05,700 --> 00:55:14,000
+ل T ناقص تلاتة ل U تلاتة as a function of T ناقص
+
+486
+00:55:14,000 --> 00:55:20,780
+لا بلس transform ل U تلاتة as a function of Tيبقى
+
+487
+00:55:20,780 --> 00:55:25,080
+هذا الكلام يساوي أظن هذه هي النظرية اللي فوق هناك
+
+488
+00:55:25,080 --> 00:55:33,040
+حرفيا تمام يبقى النتيجة EOS ناقص CS يعني EOS ناقص
+
+489
+00:55:33,040 --> 00:55:42,160
+اتنين S في Laplace ترانسفورم لمين؟ ل T لدلة قبل ال
+
+490
+00:55:42,160 --> 00:55:49,510
+shift يبقى Laplace ترانسفورم ل T ناقصهذه جاهزة
+
+491
+00:55:49,510 --> 00:55:57,830
+اللي هو قداشر منها E أس ناقص اتنين S على S حسبناها
+
+492
+00:55:57,830 --> 00:56:02,570
+اول تالت مثال اليوم بعد مثلنا الرسم حسبناها ل plus
+
+493
+00:56:02,570 --> 00:56:08,610
+ل U C of T قد ما يكون C بها يكون قيمة موجبةبنجي
+
+494
+00:56:08,610 --> 00:56:13,550
+اللي بعدها يبقى وصلنا لناقص هذي الـC عندك بقداش؟
+
+495
+00:56:13,550 --> 00:56:21,730
+بتلاتة يبقى E أُس ناقص تلاتة S ثمين في لابلاس
+
+496
+00:56:21,730 --> 00:56:29,810
+ترانسفورم لدلة قبل ال shiftهذه ناقص E أس ناقص
+
+497
+00:56:29,810 --> 00:56:36,710
+تلاتة S على مين؟ على S إذاً هذه بدها تساوي E أس
+
+498
+00:56:36,710 --> 00:56:42,170
+ناقص اتنين S هذه واحد factorial على مين؟ على S
+
+499
+00:56:42,170 --> 00:56:47,720
+تربية يعني يبقى على S تربية دوريوهذه ناقص E وناقص
+
+500
+00:56:47,720 --> 00:56:55,540
+2S على S وهذه ناقص E أس ناقص تلاتة S على S تربية
+
+501
+00:56:55,540 --> 00:57:02,320
+كذلك وهذه ناقص E أس ناقص تلاتة S على S
+
+502
+00:57:17,780 --> 00:57:24,060
+يبقى هذا النوع الأول من أنواع الأمثلة بدنا نيجي
+
+503
+00:57:24,060 --> 00:57:27,700
+لنوعتين يبقى example two
+
+504
+00:57:46,110 --> 00:57:52,450
+Example 2 Find Laplace
+
+505
+00:57:52,450 --> 00:58:01,750
+Transform For
+
+506
+00:58:01,750 --> 00:58:09,390
+The Following Functions
+
+507
+00:58:16,040 --> 00:58:23,280
+الـ F of T بده يساوي مين؟ بده يساوي أحد أمرين يا
+
+508
+00:58:23,280 --> 00:58:31,940
+إما Zero لما T أقل من الواحد يا إما T تربيع ناقص
+
+509
+00:58:31,940 --> 00:58:43,220
+اتنين T زائد اتنين ناقص اتنين T زائد اتنين لما T
+
+510
+00:58:45,100 --> 00:58:54,820
+أكبر من أو تساوي من أو تساوي الواحد قال
+
+511
+00:58:54,820 --> 00:58:57,700
+لي هاتي لي بلاسة transform للدالة اللي عندنا هنا
+
+512
+00:58:57,700 --> 00:59:07,340
+بقول له solution سي
+
+513
+00:59:07,340 --> 00:59:11,680
+عندنا هنا بقدر شمانات يبقى بدي shift هنا بمقدار
+
+514
+00:59:11,680 --> 00:59:18,030
+كده؟ مقدار واحدأنا لازم أخلق
+
+515
+00:59:18,030 --> 00:59:23,170
+في المسألة shift بمقدار واحد اذا بروح بقوله f of t
+
+516
+00:59:23,170 --> 00:59:28,430
+بدي أعيد صياغتها على الشكل التالي يا إما zero لما
+
+517
+00:59:28,430 --> 00:59:34,510
+ت أقل من واحد يا إما ت تربية نقص اتنين تجداش بده
+
+518
+00:59:34,510 --> 00:59:39,810
+لما أصير مربع كامليبقى الواحد بياخده من عندي
+
+519
+00:59:39,810 --> 00:59:43,990
+الجيران يبقى الواحد يبقى الواحد يبقى الواحد يبقى
+
+520
+00:59:43,990 --> 00:59:44,230
+الواحد يبقى الواحد يبقى الواحد يبقى الواحد يبقى
+
+521
+00:59:44,230 --> 00:59:45,830
+الواحد يبقى الواحد يبقى الواحد يبقى الواحد يبقى
+
+522
+00:59:45,830 --> 00:59:47,090
+الواحد يبقى الواحد يبقى الواحد يبقى الواحد يبقى
+
+523
+00:59:47,090 --> 00:59:47,930
+الواحد يبقى الواحد يبقى الواحد يبقى الواحد يبقى
+
+524
+00:59:47,930 --> 00:59:48,950
+الواحد يبقى الواحد يبقى الواحد يبقى الواحد يبقى
+
+525
+00:59:48,950 --> 00:59:53,890
+الواحد يبقى الواحد يبقى الواحد يبقى الواحد يبقى
+
+526
+00:59:53,890 --> 01:00:01,890
+الواحد يبقى الواحد يبقالـ T ناقص واحد لكل تربية
+
+527
+01:00:01,890 --> 01:00:08,630
+يبقى هذه T ناقص واحد لكل تربية زائد واحد لما T
+
+528
+01:00:08,630 --> 01:00:16,150
+greater than or equal to one طيب
+
+529
+01:00:16,150 --> 01:00:22,850
+أليست هذهبقدر اكتبها على شكل ال unit step function
+
+530
+01:00:22,850 --> 01:00:29,210
+صحيح ولا لأ يعني هذه بقدر اكتب الدالة اللي عناها
+
+531
+01:00:29,210 --> 01:00:34,950
+دي في ال U1 of T يعني هذه بقدر اكتبها على الشكل
+
+532
+01:00:34,950 --> 01:00:43,630
+التالي U1 as a function of T في من؟ في ال T ناقص
+
+533
+01:00:43,630 --> 01:00:52,350
+واحد لكل تربيع زائد واحدالسؤال قال لي هاتي Laplace
+
+534
+01:00:52,350 --> 01:00:56,750
+transform لهذه الدالة، إذا الأن بقدر أجد له
+
+535
+01:00:56,750 --> 01:01:02,590
+Laplace transform لأنه غيرت شكل ال function الأصلي
+
+536
+01:01:02,590 --> 01:01:08,810
+بالشكل المكافئ له المتعرف عليه طبق النظرية اللي
+
+537
+01:01:08,810 --> 01:01:14,320
+عندنايبقى انا لو أخدت لبلاس ترانسفورم لل F of T
+
+538
+01:01:14,320 --> 01:01:18,980
+بدي يساوي لبلاس ترانسفورم لمين؟ لدلة اللي عندنا
+
+539
+01:01:18,980 --> 01:01:25,660
+هذه يبقى بناء عليه لبلاس ترانسفورم لدلة F of T بدي
+
+540
+01:01:25,660 --> 01:01:32,740
+يساوي لبلاس ترانسفورم لمين؟ لل U1 as a function of
+
+541
+01:01:32,740 --> 01:01:40,980
+T في T الناقص واحد لكل تربية زائد واحد هيجفلناUC
+
+542
+01:01:40,980 --> 01:01:47,300
+of T فى F of T ناقص الـC يبقى EOS ناقص S فى لبلاس
+
+543
+01:01:47,300 --> 01:01:53,480
+للـF of T قبل الـShift يبقى هذا إيش؟ هذا بيبقى
+
+544
+01:01:53,480 --> 01:02:01,360
+تساوي مين؟ بيبقى تساوي EOS ناقص واحد فى S لناقص CS
+
+545
+01:02:01,360 --> 01:02:07,600
+يبقى بناقص S فى لبلاس يترانسفورم لدلة قبل الـShift
+
+546
+01:02:07,600 --> 01:02:12,970
+مين الدلة قبل الـShift؟T تربية زائد واحد يبقى هذه
+
+547
+01:02:12,970 --> 01:02:18,190
+T تربية زائد واحد بالشكل اللي عندنا هذا طيب هذا
+
+548
+01:02:18,190 --> 01:02:23,850
+الكلام يساوي E أص ناقص S فيه هذه Laplace فده عبارة
+
+549
+01:02:23,850 --> 01:02:28,350
+عن Laplace للأول زائد Laplace للثاني لأنها Linear
+
+550
+01:02:28,350 --> 01:02:35,670
+يبقى Laplace ل T تربية زائد Laplace للواحد بالشكل
+
+551
+01:02:35,670 --> 01:02:42,820
+اللي عندنا هذايبقى هذه ناقص S يوس ناقص S فيه نجي ل
+
+552
+01:02:42,820 --> 01:02:49,780
+T ترابيع من الجدوة الرقم تلاتة ثم يبقى هذه اتنين
+
+553
+01:02:49,780 --> 01:02:56,700
+factorial على S تكيب زي الواحد اللي هو واحد على S
+
+554
+01:02:56,700 --> 01:03:02,560
+عملناها قبل هيك واحد على S بالشكل اللي عندنايعني
+
+555
+01:03:02,560 --> 01:03:10,540
+كأن النتيجة هي اتنين E أس ناقص S على S تكيب زائد E
+
+556
+01:03:10,540 --> 01:03:13,200
+أس ناقص S على S
+
+557
+01:03:32,870 --> 01:03:39,590
+نمر بيه بيقول ال F of T بدها تسوي أحد ثلاثة أمور
+
+558
+01:03:39,590 --> 01:03:49,270
+يا إما Zero لما T أقل من باي يا إما T ناقص باي لما
+
+559
+01:03:49,270 --> 01:03:55,990
+T أكبر من أو يسوي بايه أقل من اتنين باي يا إما
+
+560
+01:03:55,990 --> 01:04:01,390
+Zero لما T greater than or equal to two pi
+
+561
+01:04:22,140 --> 01:04:29,140
+مش جزءين زي المثلة اللي فاتت بسهولة، لأ هذه ثلاثة
+
+562
+01:04:29,140 --> 01:04:33,880
+أجزاءوانا مشان اجيبلها ل placid transform بدي
+
+563
+01:04:33,880 --> 01:04:41,840
+اكتبها بدلالة unit step function اله u c of t بقول
+
+564
+01:04:41,840 --> 01:04:46,280
+okay بدي اكتبها بال unit step functionهذه مش
+
+565
+01:04:46,280 --> 01:04:50,680
+مباشرة زيها دي هذيك خدت هذيك عمل مشترك وضرب في UC
+
+566
+01:04:50,680 --> 01:04:55,980
+و كتير لو يطلع الدوري اذا انا بدأ افكر تفكيري كويس
+
+567
+01:04:55,980 --> 01:05:00,120
+طبعا من حلال ال domain تبع الدالة دي ملاحظة انه
+
+568
+01:05:00,120 --> 01:05:05,300
+جسمها لكم فترةلثلاث فترات من zero ل by و من by ل
+
+569
+01:05:05,300 --> 01:05:09,380
+اتنين by و من اتنين by ل infinity يعني لازم يطلع
+
+570
+01:05:09,380 --> 01:05:15,820
+في المثل عندى u by of t و u اتنين by of t مظبوط
+
+571
+01:05:15,820 --> 01:05:20,920
+يبقى هى استنتجته ل واحدة من خلال من من خلال شكل
+
+572
+01:05:20,920 --> 01:05:26,240
+الدلال طيب تعالوا نتفهم هيك و نشوف على شكل لو روحت
+
+573
+01:05:26,240 --> 01:05:32,580
+مدام u by و u اتنين byوالـ pi باجت في الأول و 2pi
+
+574
+01:05:32,580 --> 01:05:38,680
+في الآخر باجي لو قلت له consider خد لي هيك اللي هو
+
+575
+01:05:38,680 --> 01:05:47,300
+u pi of t ناقص u2pi as a function of t وشوف لقداش
+
+576
+01:05:47,300 --> 01:05:52,780
+هذول بدهم يزاوز لو طرحت لاتنين من بعض على مين على
+
+577
+01:05:52,780 --> 01:05:57,680
+التلت فترات هذه انشوف شو بتعطيني باجي بقوله والله
+
+578
+01:05:57,680 --> 01:05:58,340
+كويس
+
+579
+01:06:05,460 --> 01:06:14,420
+عندما تبقى T أقل من Y تبقى T نقص
+
+580
+01:06:15,630 --> 01:06:21,850
+طيب بدنا نيجي ناخد الفترة T اكبر من او يساوي باي و
+
+581
+01:06:21,850 --> 01:06:29,530
+اقل من اتنين باي قداش قيمة ال U باي واحد تمام يبقى
+
+582
+01:06:29,530 --> 01:06:36,840
+هذه واحد ناقص ال U اتنين بايتمام التمام طيب بداجي
+
+583
+01:06:36,840 --> 01:06:42,500
+الان T اكبر من او يسوى اتنين باي جداش قيمة الدالة
+
+584
+01:06:42,500 --> 01:06:50,090
+الاولى والتانية يعني واحد ناقص واحديبقى صورة هذه
+
+585
+01:06:50,090 --> 01:06:58,210
+ال U by ماقص U2 by كله as a function of T و as a
+
+586
+01:06:58,210 --> 01:07:04,950
+function of T يبقى هذه ال U by as a function of T
+
+587
+01:07:04,950 --> 01:07:12,070
+ماقص U2 by as a function of T يساوي أحد ثلاثة أمور
+
+588
+01:07:12,480 --> 01:07:20,060
+يا اما zero لما T اقل من باي، يا اما واحد لما T
+
+589
+01:07:20,060 --> 01:07:25,940
+اكبر من او يساوي باي و اقل من اتنين باي، يا اما
+
+590
+01:07:25,940 --> 01:07:32,460
+zero لما T greater than or equal to two باي بقول
+
+591
+01:07:32,460 --> 01:07:36,540
+كويس، طب احنا جيبنا الفرق طلع هدول، ايش بتفرج هدي
+
+592
+01:07:36,540 --> 01:07:44,590
+عن اللي فوق؟لو ضربت اللي فوق في T ناقص باي تطلع
+
+593
+01:07:44,590 --> 01:07:50,910
+هذه هذي طيب ممتاز إذا هروح أضرب الطرفين في T ناقص
+
+594
+01:07:50,910 --> 01:07:57,730
+باي إذا لو ضربت في T ناقص باي بيصير U باي of T في
+
+595
+01:07:57,730 --> 01:08:07,310
+T ناقص البي ناقص U2 باي as a function of Tفى T
+
+596
+01:08:07,310 --> 01:08:14,750
+ناقص الـ Pi كله بده يساوي ما يتيه يا إما Zero لما
+
+597
+01:08:14,750 --> 01:08:22,230
+T أقل من Pi يا إما T ناقص Pi لما T أكبر من أو
+
+598
+01:08:22,230 --> 01:08:28,410
+يساوي Pi و أقل من 2 Pi يا إما Zero لما T greater
+
+599
+01:08:28,410 --> 01:08:35,810
+than or equal to 2 Piمظبوط يبقى عملت عملية تحايل
+
+600
+01:08:35,810 --> 01:08:40,770
+على مين على ال function اللي أعطاها لهذه و جبتها
+
+601
+01:08:40,770 --> 01:08:45,050
+روحت بدللة مين ال U باي و U اتنين باي إذا لابلاس
+
+602
+01:08:45,050 --> 01:08:50,750
+ترانسفورم لهذه الدلة هو لابلاس ترانسفورم لمين لهذه
+
+603
+01:08:50,750 --> 01:08:54,730
+الدلة و مش عارف يمكن لسه بدأ فبركة كمانويمكن جهزة
+
+604
+01:08:54,730 --> 01:08:59,410
+الله أعلم إذا بدنا نروح ناخد the place transform
+
+605
+01:08:59,410 --> 01:09:05,150
+لمين لهذه الدالة أظن نمسح عارفين الحين صارنا الشغل
+
+606
+01:09:05,150 --> 01:09:05,770
+هذه؟
+
+607
+01:09:16,950 --> 01:09:26,710
+طيب إذا أصار عندي لبلاس transform لدلة f of t بده
+
+608
+01:09:26,710 --> 01:09:36,390
+يسوى لبلاس transform لمن؟ ل U بي of T في T ناقص بي
+
+609
+01:09:37,240 --> 01:09:48,120
+ناقص U2 باي as a function of T فمين؟ في T ناقص باي
+
+610
+01:09:48,120 --> 01:09:53,100
+الشكل اللي عالي هناتمام تمام لابلاس هو linear
+
+611
+01:09:53,100 --> 01:09:56,100
+function هو هيخش على ال term الأول و هيخش على ال
+
+612
+01:09:56,100 --> 01:10:04,300
+term التاني يبقى هذا لابلاس transform ل U by of T
+
+613
+01:10:04,300 --> 01:10:14,180
+في T ناقص ال by ناقص لابلاس transform ل U اتنين by
+
+614
+01:10:14,180 --> 01:10:19,560
+as a function of T بس هذه لابلاس مش هتظبط معاها
+
+615
+01:10:20,420 --> 01:10:28,360
+يعني بدها فشون يعمل؟ بنضيف باي و بنطرح باي تمام
+
+616
+01:10:28,360 --> 01:10:36,980
+يبقى هذه بقدر اقول في تي ناقص اتنين باي زائد باي
+
+617
+01:10:36,980 --> 01:10:46,790
+كلها يقفلناهذه المرحلة ستكون مين؟ او هذه المعروفة
+
+618
+01:10:46,790 --> 01:10:56,550
+اي اس ناقص by اس في ال place transform لمين؟ لـT
+
+619
+01:10:56,550 --> 01:11:04,160
+قبل ال shiftتمام هذه يا بنات هجزئها إلى جزئين يبقى
+
+620
+01:11:04,160 --> 01:11:10,640
+ناقص ل plus transform ل U2 by as a function of T
+
+621
+01:11:10,640 --> 01:11:22,760
+في T ناقص اتنين by ناقص by في U2 U2 by as a
+
+622
+01:11:22,760 --> 01:11:30,410
+function of T بالشكل اللي قلناطيب هدى E أس ناقص by
+
+623
+01:11:30,410 --> 01:11:37,190
+S هدى اللى واحد factorial على S تربيع من الجدول
+
+624
+01:11:37,190 --> 01:11:46,350
+اللى بعدها هدى نفس القصة لأمين A أس سالب اتنين by
+
+625
+01:11:46,350 --> 01:11:56,780
+S في لك less transform لدالها قبل ال shiftهذا بي
+
+626
+01:11:56,780 --> 01:12:02,480
+مقدار ثابت ليس لديه دعوة برا لبلاس يبقى ناقص بي في
+
+627
+01:12:02,480 --> 01:12:11,220
+لبلاس ال transform ل U2 بي as a function of T هذا
+
+628
+01:12:11,220 --> 01:12:20,020
+يسوى E أس ناقص بي S على S تربيع هذا بنفس الطريقة E
+
+629
+01:12:20,020 --> 01:12:32,120
+أس ناقص 2 بي S على S تربيعناقص باي وهذه EOS ناقص
+
+630
+01:12:32,120 --> 01:12:39,560
+اتنين by S على Sيبقى هاي قدرنا نعمل تحوير يا عم
+
+631
+01:12:39,560 --> 01:12:44,720
+السؤال اللى تجيلي شوية دى ربانى يعنى كل سؤال مدلة
+
+632
+01:12:44,720 --> 01:12:49,260
+مجزة من جزئيا من تلاتة من أربعة جد ما يكون بتروح
+
+633
+01:12:49,260 --> 01:12:55,200
+اكتبها بدلالة ال U C of T حسب التجزيق اللى عندي لو
+
+634
+01:12:55,200 --> 01:12:59,340
+كان جزة واحد اتنين تلاتة بيبدأ أقوله U one و بعدين
+
+635
+01:12:59,340 --> 01:13:04,170
+U two و بعدين U threeوشوف كيف بما يناسب طبيعة مين
+
+636
+01:13:04,170 --> 01:13:09,170
+طبيعة المصنع يبقى هاي جيبنا Laplace transform لهذه
+
+637
+01:13:09,170 --> 01:13:14,030
+الدوال طيب بدي أعمل عملية عكسية شو العملية
+
+638
+01:13:14,030 --> 01:13:18,550
+العكسية؟ مش هنتقل سابقا نقول conversely نجيب معكس
+
+639
+01:13:18,550 --> 01:13:23,130
+Laplace transform بدي أعطي Laplace transform لبعض
+
+640
+01:13:23,130 --> 01:13:31,020
+الدوال و أعرف ما هو أصل هذه الدوالطبعا يبقى مثال
+
+641
+01:13:31,020 --> 01:13:40,580
+رقم كده ايش؟ تلاتة مثال رقم تلاتة find the
+
+642
+01:13:40,580 --> 01:13:54,240
+inverse of the plus transform of
+
+643
+01:13:54,240 --> 01:13:56,780
+the
+
+644
+01:13:58,190 --> 01:14:02,890
+following functions
+
+645
+01:14:02,890 --> 01:14:07,010
+نمر
+
+646
+01:14:07,010 --> 01:14:18,350
+ايه؟ capital F of S بده يساوي E اص ناقص اتنين S
+
+647
+01:14:18,350 --> 01:14:26,630
+على مين؟ على S تربيع زائد ال S ناقص اتنين
+
+648
+01:14:37,230 --> 01:14:43,070
+عشان نحاول نستفيد من جدول اللي قدامنا بقدر الإمكان
+
+649
+01:14:43,070 --> 01:14:46,950
+طبعا لو أروح الجدول بشوفش ولا شغل زي هيك بلاقيش
+
+650
+01:14:46,950 --> 01:14:48,670
+ولا حاجة زي هيك بالشكل هذا
+
+651
+01:15:00,200 --> 01:15:09,460
+هذا واحد على هذه لو حللته كحاصل ضرب قوسين يبقى هنا
+
+652
+01:15:09,460 --> 01:15:18,040
+S هنا S هنا واحد هنا اتنين هنا زائد هنا ناقص ناقص
+
+653
+01:15:18,040 --> 01:15:24,460
+S بزائد اتنين S بظل زائد S بعد هيك بدى اروح اعمل
+
+654
+01:15:24,460 --> 01:15:29,750
+partial fraction لهذهوهي قصور جزية بحيث أفصلها
+
+655
+01:15:29,750 --> 01:15:34,250
+هائلة، لماذا؟ لأنه أنا ماعرفش ل place لحصل ضرب
+
+656
+01:15:34,250 --> 01:15:38,530
+قيمتين، ماخدنهاش، مانعرفهاش، تمام؟ إذن بدل ما هي
+
+657
+01:15:38,530 --> 01:15:42,930
+ضرب بدي أخليها مجموعة، جمع يعني كأنه هنا موحدة،
+
+658
+01:15:42,930 --> 01:15:47,340
+مقدرة، عاملة ومشتركةبدي أردها إلى أصلها قبل أخذ
+
+659
+01:15:47,340 --> 01:15:53,000
+العامل المشترك بقوله بسيطة المقام محلل إلى أبسط
+
+660
+01:15:53,000 --> 01:15:58,780
+العوامل الأولية والأقواس are different ولا واحد زي
+
+661
+01:15:58,780 --> 01:16:04,030
+التاني وكل واحد فيهم من الدرجات الأولىفبروح بقول
+
+662
+01:16:04,030 --> 01:16:12,230
+له هذه واحد على S ناقص واحد في S زائد اتنين يساوي
+
+663
+01:16:12,230 --> 01:16:18,310
+constant على الجوس الاول constant تاني على الجوس
+
+664
+01:16:18,310 --> 01:16:23,670
+التاني بعد هيك بروح اضرب في المقام تبع الطرف
+
+665
+01:16:23,670 --> 01:16:29,050
+الشمال زي ما كنا بنعمل في calculus بيبقى الواحد
+
+666
+01:16:29,050 --> 01:16:30,810
+بده يساوي A
+
+667
+01:16:38,930 --> 01:16:45,910
+يبقى بطل يصير عندنا كثور وانما صارت كل المسألة في
+
+668
+01:16:45,910 --> 01:16:46,710
+البصد
+
+669
+01:17:01,440 --> 01:17:09,100
+طيب حط قيم ل S من عندك فباجي بقول لو كانت ال S
+
+670
+01:17:09,100 --> 01:17:16,900
+تساوي واحد then الواحد بده يساوي تلاتة A يبقى
+
+671
+01:17:16,900 --> 01:17:24,300
+تلاتة A ومنها ال A تساوي قدراش تساوي طول الان لو
+
+672
+01:17:24,300 --> 01:17:31,170
+كانت ال S تساوي ناقص اتنيننقص اتنين يبقى تقير ال a
+
+673
+01:17:31,170 --> 01:17:39,170
+وبظل then الواحد يسوى ناقص تلاتة b ناقص اتنين ناقص
+
+674
+01:17:39,170 --> 01:17:46,510
+واحد يكون ناقص تلاتة b ومنها b تسوى كم؟ سالب تلت
+
+675
+01:17:46,510 --> 01:17:54,950
+اذا صار capital F of S أصبح على الشكل التاليوين هو
+
+676
+01:17:54,950 --> 01:17:59,290
+ايه؟ هذا بدي استبدله بمين؟ بالمقدار اللي عندنا
+
+677
+01:17:59,290 --> 01:18:05,150
+يبقى بدي جيني هنا تلت و هنا سالب تلت يبقى هذا تلت
+
+678
+01:18:05,150 --> 01:18:11,270
+خديه برا عام المشترك بيظل E أس ناقص اتنين S في
+
+679
+01:18:11,270 --> 01:18:20,590
+جداش في واحد على S ناقص واحد ناقص واحد على S زائد
+
+680
+01:18:20,590 --> 01:18:29,260
+اتنينيعني ايه؟ يعني هذا تلت في E أس ناقص اتنين S
+
+681
+01:18:29,260 --> 01:18:38,400
+في واحد على S ناقص الواحد ناقص تلت في E أس ناقص
+
+682
+01:18:38,400 --> 01:18:43,680
+اتنين S في واحد على S زائد اتنين
+
+683
+01:18:49,000 --> 01:18:54,480
+نرجع لمين؟ نرجع للنظرية تبعتنا اللى كنا نشتغل
+
+684
+01:18:54,480 --> 01:18:59,740
+عليها اللى روحناها مسحناها طلعينا النظرية مرة
+
+685
+01:18:59,740 --> 01:19:08,630
+تانيةشوفي ليش بيقول هنا طبعا
+
+686
+01:19:08,630 --> 01:19:16,510
+عندك EOS ناقص 2S في capital F of S هذه بتروح اردها
+
+687
+01:19:16,510 --> 01:19:20,870
+لمين للمعكوس تبعها طلعيلي في كلمة conversely
+
+688
+01:19:20,870 --> 01:19:27,590
+للنقطة الأولى عندك ل plus inverse ل EOS ناقص CS في
+
+689
+01:19:27,590 --> 01:19:35,230
+capital F of SUC of T في F of T ناقص الـC
+
+690
+01:19:56,010 --> 01:20:03,690
+تلت صف على شجة بدي ل plus inverse لمن؟ لل E أس
+
+691
+01:20:03,690 --> 01:20:11,090
+ناقص اتنين S واحد على S ناقص الواحد ناقص تلت ل
+
+692
+01:20:11,090 --> 01:20:19,010
+plus inverse لمن؟ ل E أس ناقص اتنين S واحد على S
+
+693
+01:20:19,010 --> 01:20:23,890
+زائد اتنين هذا الكلام بده يساوي هاي تلت
+
+694
+01:20:29,720 --> 01:20:33,880
+النقطة الأولى المعكوزة تبعها اللى على اليمين ل
+
+695
+01:20:33,880 --> 01:20:40,000
+plus inverse ل E أسنق ال CS في capital F of S هي
+
+696
+01:20:40,000 --> 01:20:46,180
+capital F of S وهي E أسنق ال CS يبقى بده أرجعها
+
+697
+01:20:46,180 --> 01:20:51,320
+لمن؟ إلى أصلها يبقى أصلها شو بده يكون يا بنت؟ U C
+
+698
+01:20:51,320 --> 01:21:00,080
+of T C عندي هنا في قداشيبقى انا بقول U2 as a
+
+699
+01:21:00,080 --> 01:21:08,240
+function of T طيب هذي مين؟ هذي E أس T بس بدي اعمل
+
+700
+01:21:08,240 --> 01:21:17,360
+لها shift بمقدار كتير لتنين يبقى E أس T ناقص اتنين
+
+701
+01:21:17,360 --> 01:21:26,220
+مرة تانيةأفتحي بافترك على النظرية، يلّا فارجي على
+
+702
+01:21:26,220 --> 01:21:31,390
+ثلاث صفحات للخلف، والله أربعةالنظرية بتقول لـPlus
+
+703
+01:21:31,390 --> 01:21:36,450
+لـUC of T للـF of T ناقصة C والساوي E أثناق الـCs
+
+704
+01:21:36,450 --> 01:21:42,770
+في كابتل F of S احنا اللي موجود عند مين E أثناق
+
+705
+01:21:42,770 --> 01:21:49,110
+الـCs في كابتل F of S إذن بتدرجع على الأصل تبعها
+
+706
+01:21:49,110 --> 01:21:53,110
+قبل ناخد Laplace transform فباخد Laplace inverse
+
+707
+01:21:53,110 --> 01:21:59,410
+للطرفينيبقى بالاسفل ان لأ plus inverse لإي أس ناقص
+
+708
+01:21:59,410 --> 01:22:10,620
+CS في capital F of Sهذه لـ F of S و هذه E أُس ناقص
+
+709
+01:22:10,620 --> 01:22:14,700
+CS بالدرجة العاصلة يبقى الـ C عندى هنا بقداش
+
+710
+01:22:14,700 --> 01:22:22,340
+بإتمام يبقى بقوله تلت U2 of T هذه E أُس T لكن هو
+
+711
+01:22:22,340 --> 01:22:27,500
+قال لي F of T ناقص الـ C يبقى بدي أعمل الـ Shift
+
+712
+01:22:27,500 --> 01:22:35,610
+مقدار الـ C فبقول T ناقص 2 واضحة؟اللي عملناها لهذه
+
+713
+01:22:35,610 --> 01:22:42,850
+هعملها للتانية يبقى هاي كمان ناقص طول طلّها لهذه
+
+714
+01:22:42,850 --> 01:22:51,710
+يس ناقص اتنين اس يبقى U اتنين as a function of T
+
+715
+01:22:52,300 --> 01:22:57,980
+تمام؟ ضال plus لهذه ده رجع على أصلها، شو أصلها؟
+
+716
+01:22:57,980 --> 01:23:05,600
+EOS ناقص اتنين T و بدي اخد ناقص اتنين shift منها،
+
+717
+01:23:05,600 --> 01:23:10,280
+يبقاش بصير EOS،
+
+718
+01:23:10,280 --> 01:23:17,280
+هدف الأصل ناقص اتنين Tمظبوط او لا اذا بدي اعمل لها
+
+719
+01:23:17,280 --> 01:23:21,940
+shift بمقدار كده مقدار اتنين كمان نفس النتيجة اللي
+
+720
+01:23:21,940 --> 01:23:27,000
+احنا احنا عملناها لها يبقى لما نعمل ال shift اللي
+
+721
+01:23:27,000 --> 01:23:32,680
+عندنا هذا لها بيبقى تصير على مين على الشكل التالي
+
+722
+01:23:32,680 --> 01:23:41,760
+اللي هو مين اللي هو E أس ناقص اتنين Tنقص بيصير
+
+723
+01:23:41,760 --> 01:23:48,440
+زائد اتنين لماذا؟ لأنه في الأصل ناقص يبقى ناقص
+
+724
+01:23:48,440 --> 01:23:56,100
+يبقى ناقص يبقى ناقص
+
+725
+01:23:56,100 --> 01:23:59,920
+يبقى ناقص يبقى ناقص يبقى ناقص يبقى ناقص يبقى ناقص
+
+726
+01:23:59,920 --> 01:24:06,000
+يبقى ناقص يبقى ناقص يبقى ناقص يبقى ناقص يبقى ناقص
+
+727
+01:24:06,000 --> 01:24:09,500
+يبقى ناقص يبقى ناقص يبقى ناقص يبقى ناقص يبقى ناقص
+
+728
+01:24:09,500 --> 01:24:09,620
+يبقى ناقص يبقى
+
+729
+01:24:14,570 --> 01:24:18,190
+لأ، لأ، لأ، في غلطة يا بنات، في غلطة، في غلطة،
+
+730
+01:24:18,190 --> 01:24:24,390
+الغلطة كيف؟ ان هذه ناقص اتنين، وهنا بدأ اقول T
+
+731
+01:24:24,390 --> 01:24:29,530
+زائد اتنين، بصير اربع، يعني هذه زائد اربع وليست
+
+732
+01:24:29,530 --> 01:24:35,480
+اتنين، لما ناخد اتنين، بصير T ناقص اتنينيعني القصة
+
+733
+01:24:35,480 --> 01:24:38,660
+اللي هنا هو نفس القصة اللي بين قصين هنا بالضبط
+
+734
+01:24:38,660 --> 01:24:44,020
+تماما، تمام؟ بس اجعله قداش اللي هو سالب اتنين، مرة
+
+735
+01:24:44,020 --> 01:24:49,420
+تانية بتعيدهامرة تانية بدأينا هذه الدالة قبل ال
+
+736
+01:24:49,420 --> 01:24:55,780
+shift اللي هو قد ياش E أس ناقص اتنين تمام ال T بدي
+
+737
+01:24:55,780 --> 01:25:01,120
+اعمل لها ال shift بمقدار اتنين يبقى بالداجي اقوله
+
+738
+01:25:01,120 --> 01:25:07,660
+E أس ناقص اتنين في T ناقص اتنين مش هه بلاش تقولي
+
+739
+01:25:07,660 --> 01:25:12,260
+كيف هذه الأربعة أجت نصف المسمة ولا لا بقولك ايها
+
+740
+01:25:12,260 --> 01:25:19,270
+على طولهي ناقص تلت هذي دره هاي ناقص ال T و اتنين
+
+741
+01:25:19,270 --> 01:25:24,470
+of T E و ناقص اتنين ال T عندي هذي بدي اعمله ال
+
+742
+01:25:24,470 --> 01:25:30,510
+shift مقدر اتنين فبقول T ناقص اتنين مباشرة فهو
+
+743
+01:25:30,510 --> 01:25:38,790
+رايح دماغك طيب هذا كان هو السؤال الأول نمرة A بنجي
+
+744
+01:25:38,790 --> 01:25:39,610
+لنمرة V
+
+745
+01:25:48,310 --> 01:25:52,390
+خودي لنمرى بيه طبعا السؤال الأول هو السؤال
+
+746
+01:25:52,390 --> 01:25:58,610
+الاربعتاش من الكتاب نمرى بيه سؤال خمستاش من الكتاب
+
+747
+01:26:02,380 --> 01:26:09,180
+بدي أساوي اتنين في اس ناقص واحد اتنين في اس ناقص
+
+748
+01:26:09,180 --> 01:26:16,860
+واحد في اي أس ناقص اتنين اس على اس تربيع ناقص
+
+749
+01:26:16,860 --> 01:26:22,760
+اتنين اس زائد اللي هو اتنين زائد اتنين
+
+750
+01:26:32,740 --> 01:26:38,840
+بنرتب وضع المثلة قبل ايه قبل ما نبدأ الحل قبل ما
+
+751
+01:26:38,840 --> 01:26:44,220
+نبدأ معكوس لبلاي transform فباجي بقوله capital F
+
+752
+01:26:44,220 --> 01:26:50,400
+of S بده يساوي اظن ان اتنين مقدار ثابت مالوش دعوة
+
+753
+01:26:50,400 --> 01:26:56,420
+و E أس ناقص اتنين S كمان مالوش دعوة بضل عندي قداش
+
+754
+01:26:56,420 --> 01:27:03,700
+S ناقص واحد هذا بقدر اعمله ايه مربع كامليبقى S
+
+755
+01:27:03,700 --> 01:27:10,580
+تربية ناقص اتنين S زائد واحد بضل جداج زائد واحد
+
+756
+01:27:10,580 --> 01:27:15,820
+بالشكل اللي عندنا انا او بقدر اكتبها اتنين مالكش
+
+757
+01:27:15,820 --> 01:27:22,520
+دعوة E أس ناقص اتنين S فاهمين في ال S ناقص واحد
+
+758
+01:27:22,520 --> 01:27:28,940
+على S ناقص واحد لكل تربية زائد واحد بالشكل اللي
+
+759
+01:27:28,940 --> 01:27:37,790
+عندنا اناأذا بتاخد ل plus inverse ل مين؟ ل F of S
+
+760
+01:27:37,790 --> 01:27:45,710
+يساوي اتنين
+
+761
+01:27:45,710 --> 01:27:54,970
+ل plus inverse ل مين؟ ل E أثناء قصة 2Sفي ال S ناقص
+
+762
+01:27:54,970 --> 01:28:03,810
+واحد ال S ناقص واحد ناقص واحد الكل تربيع زائد واحد
+
+763
+01:28:03,810 --> 01:28:05,610
+بالشكل اللي عندنا هذا
+
+764
+01:28:13,100 --> 01:28:18,520
+بارجع لمين؟ كمان للنظرية، نرجع للنظرية تبعتنا هذه
+
+765
+01:28:18,520 --> 01:28:24,980
+مرة ثانية، اللي كنا بنشغل بهاتف والساعةأنا عندي
+
+766
+01:28:24,980 --> 01:28:31,720
+هاي E أس نقص اتنين S يبقى C يبقى 12 ب 2 هذه
+
+767
+01:28:31,720 --> 01:28:37,760
+capital F of S بدي أرجع لهذه و أشوف من أصلها من
+
+768
+01:28:37,760 --> 01:28:45,320
+وين من الجدول تمام؟ لو رجعت لهذه الدالةاللي هي ال
+
+769
+01:28:45,320 --> 01:28:48,560
+S ناقص واحد على S ناقص واحد كل تربية اللي هي عبارة
+
+770
+01:28:48,560 --> 01:28:54,060
+عن مين رقم كدهش عشرة بالضبط تماما اللي هو S ناقص
+
+771
+01:28:54,060 --> 01:28:57,220
+ال A على S ناقص L كل تربية زاد B تربية يعني ال A
+
+772
+01:28:57,220 --> 01:29:03,400
+بواحد يا بنات و ال B بواحد كذلك يبقى أصلها E أس AT
+
+773
+01:29:03,400 --> 01:29:10,480
+Cos BT يعني E أس T Cos T لإنه ال A و ال B بواحد
+
+774
+01:29:10,820 --> 01:29:16,080
+يبقى في الهام الشيخ بقول انا عند ال F of T بده
+
+775
+01:29:16,080 --> 01:29:22,600
+يساوي E أس تي كوصينة T تمام؟ لكن بدي ارجع للنظرية
+
+776
+01:29:22,600 --> 01:29:29,480
+تبعتي و اقول هذا الكلام يساوي اتنين في جداش هذه U
+
+777
+01:29:29,480 --> 01:29:34,560
+اتنين as a function of T برجع للنظرية ها تبعتنا
+
+778
+01:29:35,870 --> 01:29:42,270
+يبقى انا
+
+779
+01:29:42,270 --> 01:29:49,250
+اعمل shift لكل واحدة منهم بمقدار اتنين يبقى هذه في
+
+780
+01:29:49,250 --> 01:29:59,610
+ال E of T ناقص اتنين في cosine T ناقص اتنين كذلك
+
+781
+01:29:59,610 --> 01:30:04,310
+يبقى هي طبقت النظرية وعملت main وعملت shift اللي
+
+782
+01:30:04,310 --> 01:30:09,070
+بديهاالروح لنمرسى من المسألة
+
+783
+01:30:30,830 --> 01:30:39,370
+بيقول لي F of S نمرى C capital F of S بده يساوي
+
+784
+01:30:39,370 --> 01:30:50,350
+مين E أس ناقص S زائد E أس ناقص اتنين S ناقص E أس
+
+785
+01:30:50,350 --> 01:30:56,030
+ناقص تلاتة S ناقص E أس ناقص
+
+786
+01:31:06,240 --> 01:31:11,180
+خلّينا نعيد ترتيب المثلة قبل ما نبدأ يبقى باجي
+
+787
+01:31:11,180 --> 01:31:18,050
+بقوله solutionبعد كتابة F of S بقدر اكتبها على
+
+788
+01:31:18,050 --> 01:31:25,470
+الشكل التالف بقدر اوزع البسط على المقال يبقى هذا E
+
+789
+01:31:25,470 --> 01:31:37,680
+أس ناقص S على Sهذه زائد EOS ناقص اتنين S على من؟
+
+790
+01:31:37,680 --> 01:31:46,240
+على S هذه ناقص EOS ناقص تلاتة S على S هذه ناقص EOS
+
+791
+01:31:46,240 --> 01:31:50,540
+ناقص اربعة S على S
+
+792
+01:31:54,190 --> 01:31:59,650
+أول مثال أخدناه في جد لبلاس ترانسفورم كان لبلاس
+
+793
+01:31:59,650 --> 01:32:08,710
+ترانسفورم ل U C of T قداش طالعة؟ U أس ناقص C S على
+
+794
+01:32:08,710 --> 01:32:13,030
+S اللي هو في الجد و اللي عندنا بنات رقم قداش؟ رقم
+
+795
+01:32:13,030 --> 01:32:20,430
+12 إذا أنا بدي أطبق رقم 12 كام مرات؟ أربع مراتيبقى
+
+796
+01:32:20,430 --> 01:32:26,930
+لما يكون عندي U C of T بتشويه أصلاق C S على F يبقى
+
+797
+01:32:26,930 --> 01:32:31,650
+بناء انا عليه بتاخد Laplace inverse للطرفين يبقى
+
+798
+01:32:31,650 --> 01:32:39,450
+Laplace inverse لcapital F of Sيساوي Laplace
+
+799
+01:32:39,450 --> 01:32:46,070
+inverse لمين لل E أس ناقص S على S زائد Laplace
+
+800
+01:32:46,070 --> 01:32:53,490
+inverse لل E أس ناقص اتنين S على S معقص Laplace
+
+801
+01:32:53,490 --> 01:33:02,120
+inverse لمينللإي أس ناقص ثلاثة S على S ناقص ل plus
+
+802
+01:33:02,120 --> 01:33:09,940
+inverse للإي أس ناقص أربعة S على S يبقى ل plus
+
+803
+01:33:09,940 --> 01:33:17,360
+inverse لcapital F of S بده يساوي هذه C هنا بقداش
+
+804
+01:33:17,360 --> 01:33:25,380
+يا بنات بواحد يبقى هذه باعتبارها من U one of Tطب
+
+805
+01:33:25,380 --> 01:33:32,680
+هذه U2 of D فقط لغير مظبوط طبقا لرقم 12 اللي عندنا
+
+806
+01:33:32,680 --> 01:33:41,190
+يبقى زائد U2 as a function of D طب هذهنقص U تلاتة
+
+807
+01:33:41,190 --> 01:33:47,010
+يبقى نقص U تلاتة as a function of T لأن C تتسبب في
+
+808
+01:33:47,010 --> 01:33:54,490
+قدرات تلاتة نقص U أربعة as a function of T
+
+809
+01:33:57,330 --> 01:34:02,630
+يبقى هذا إيش اعطانكه عدة أمثلة نجيب كيف معكوس
+
+810
+01:34:02,630 --> 01:34:06,730
+Laplace transform يعني بيعطيني Laplace transform و
+
+811
+01:34:06,730 --> 01:34:11,810
+بطلب ما هو شكل الدالة الأصلي انت لو روحت خدت
+
+812
+01:34:11,810 --> 01:34:15,430
+الدالة دي و خدتي لها Laplace transform لازم يطلع
+
+813
+01:34:15,430 --> 01:34:21,390
+منين؟أو بيطلع هذا و توحدله المقام بيطلع مين بيطلع
+
+814
+01:34:21,390 --> 01:34:27,050
+ده اللي فوق لحد هنا stop بيعطيكوا العافية انتهى
+
+815
+01:34:27,050 --> 01:34:33,990
+هذا ال section إلى يكون أرقام المسائل يبقى من واحد
+
+816
+01:34:33,990 --> 01:34:42,290
+يبقى exercises ستة تلاتة من واحد لغاية اتنين و
+
+817
+01:34:42,290 --> 01:34:44,270
+تلاتين الأد
+
+818
+01:34:46,920 --> 01:34:54,240
+المحاضرة القادمة ان شاء الله تعالى اللي
+
+819
+01:34:54,240 --> 01:35:00,880
+هو اخر section اللي هو ستة اربع وبه ينتهي المقرر
+
diff --git a/PL9fwy3NUQKwa8ZDfSFGn6H8xVFLzqmCZC/5tytEs18MlY_raw.json b/PL9fwy3NUQKwa8ZDfSFGn6H8xVFLzqmCZC/5tytEs18MlY_raw.json
new file mode 100644
index 0000000000000000000000000000000000000000..7110b88fafb8da0bf31e20b9ba67e48a110ee12b
--- /dev/null
+++ b/PL9fwy3NUQKwa8ZDfSFGn6H8xVFLzqmCZC/5tytEs18MlY_raw.json
@@ -0,0 +1 @@
+{"segments": [{"id": 1, "seek": 2886, "start": 10.54, "end": 28.86, "text": "المرة الماضية انتهينا من سكتشن ستة اتنين اللي هو بيتحدث عن استخدام laplace transform لحل المعادلة التفاضلية او حل ال initial value problem اليوم ان شاء الله هناخد function جديدة نسميها unit step function", "tokens": [45340, 25720, 9673, 46958, 10632, 16472, 47395, 1829, 8315, 9154, 8608, 4117, 2655, 8592, 1863, 8608, 2655, 3660, 1975, 2655, 1863, 9957, 13672, 1829, 31439, 4724, 36081, 24401, 12984, 18871, 44713, 9778, 3215, 10943, 635, 6742, 4088, 5296, 5016, 1211, 9673, 3615, 18513, 37977, 16712, 5172, 46958, 1211, 10632, 1975, 2407, 11331, 1211, 2423, 5883, 2158, 1154, 45595, 20498, 16472, 13412, 16606, 21984, 8032, 1863, 47283, 3215, 2445, 10874, 16254, 41891, 8717, 38251, 1829, 11296, 4985, 1823, 2445], "avg_logprob": -0.21261866786811925, "compression_ratio": 1.5242718446601942, "no_speech_prob": 5.960464477539063e-08, "words": [{"start": 10.54, "end": 11.66, "word": "المرة", "probability": 0.5771484375}, {"start": 11.66, "end": 12.28, "word": " الماضية", "probability": 0.9806315104166666}, {"start": 12.28, "end": 12.92, "word": " انتهينا", "probability": 0.9122314453125}, {"start": 12.92, "end": 13.08, "word": " من", "probability": 0.9794921875}, {"start": 13.08, "end": 13.58, "word": " سكتشن", "probability": 0.5904296875}, {"start": 13.58, "end": 14.14, "word": " ستة", "probability": 0.6062825520833334}, {"start": 14.14, "end": 14.6, "word": " اتنين", "probability": 0.9635009765625}, {"start": 14.6, "end": 15.16, "word": " اللي", "probability": 0.69921875}, {"start": 15.16, "end": 15.24, "word": " هو", "probability": 0.65478515625}, {"start": 15.24, "end": 15.96, "word": " بيتحدث", "probability": 0.880126953125}, {"start": 15.96, "end": 16.26, "word": " عن", "probability": 0.95556640625}, {"start": 16.26, "end": 16.84, "word": " استخدام", "probability": 0.9794921875}, {"start": 16.84, "end": 17.28, "word": " laplace", "probability": 0.48870849609375}, {"start": 17.28, "end": 18.14, "word": " transform", "probability": 0.96044921875}, {"start": 18.14, "end": 19.22, "word": " لحل", "probability": 0.9734700520833334}, {"start": 19.22, "end": 19.84, "word": " المعادلة", "probability": 0.97802734375}, {"start": 19.84, "end": 20.54, "word": " التفاضلية", "probability": 0.806494140625}, {"start": 20.54, "end": 20.84, "word": " او", "probability": 0.9013671875}, {"start": 20.84, "end": 21.3, "word": " حل", "probability": 0.931396484375}, {"start": 21.3, "end": 21.44, "word": " ال", "probability": 0.974609375}, {"start": 21.44, "end": 21.92, "word": " initial", "probability": 0.703125}, {"start": 21.92, "end": 22.56, "word": " value", "probability": 0.96337890625}, {"start": 22.56, "end": 23.18, "word": " problem", "probability": 0.93896484375}, {"start": 23.18, "end": 24.12, "word": " اليوم", "probability": 0.934326171875}, {"start": 24.12, "end": 24.28, "word": " ان", "probability": 0.828125}, {"start": 24.28, "end": 24.54, "word": " شاء", "probability": 0.909423828125}, {"start": 24.54, "end": 24.68, "word": " الله", "probability": 0.95458984375}, {"start": 24.68, "end": 25.48, "word": " هناخد", "probability": 0.88134765625}, {"start": 25.48, "end": 26.26, "word": " function", "probability": 0.81689453125}, {"start": 26.26, "end": 26.74, "word": " جديدة", "probability": 0.9710286458333334}, {"start": 26.74, "end": 27.44, "word": " نسميها", "probability": 0.8382568359375}, {"start": 27.44, "end": 27.78, "word": " unit", "probability": 0.411865234375}, {"start": 27.78, "end": 28.24, "word": " step", "probability": 0.95458984375}, {"start": 28.24, "end": 28.86, "word": " function", "probability": 0.96142578125}], "temperature": 1.0}, {"id": 2, "seek": 4423, "start": 29.17, "end": 44.23, "text": "أو اختصارا ال step function نقطة تعريف ال step function وحلاحظ ان ال step function بتلعب دور كبير في موضوع Laplace transform بل سنحسبها كمان Laplace transform", "tokens": [10721, 2407, 1975, 46456, 9381, 9640, 995, 2423, 1823, 2445, 8717, 47432, 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67.25, "end": 67.73, "word": " تبجى", "probability": 0.9100341796875}, {"start": 67.73, "end": 68.15, "word": " دائما", "probability": 0.91796875}, {"start": 68.15, "end": 68.63, "word": " وابدا", "probability": 0.7506510416666666}, {"start": 68.63, "end": 69.43, "word": " أقل", "probability": 0.9342447916666666}, {"start": 69.43, "end": 69.69, "word": " من", "probability": 0.98974609375}, {"start": 69.69, "end": 70.03, "word": " C", "probability": 0.96240234375}], "temperature": 1.0}, {"id": 4, "seek": 9328, "start": 70.2, "end": 93.28, "text": "وإذا كانت تساوي C أو أكبر من C فال unit step function بتساوي كده؟ واحد صحيح ممكن نتعرف على شكل ال unit step function اللي عندنا كالتالي لو جيت أخدت محاور بالشكل هذا وقلت هذا محور T و هذا محور Y أو محور F يبقى هذا محور Y", "tokens": [2407, 28814, 15730, 25961, 2655, 6055, 3794, 995, 45865, 383, 34051, 5551, 4117, 26890, 9154, 383, 6156, 6027, 4985, 1823, 2445, 39894, 3794, 995, 45865, 9122, 3215, 3224, 22807, 36764, 24401, 20328, 5016, 1829, 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"probability": 0.93408203125}, {"start": 2057.54, "end": 2057.68, "word": " اللي", "probability": 0.981689453125}, {"start": 2057.68, "end": 2058.02, "word": " عندك", "probability": 0.928955078125}, {"start": 2058.02, "end": 2058.34, "word": " وين", "probability": 0.5216064453125}, {"start": 2058.34, "end": 2058.78, "word": " في", "probability": 0.8369140625}, {"start": 2058.78, "end": 2059.48, "word": " الجدولة", "probability": 0.8077392578125}, {"start": 2059.48, "end": 2059.48, "word": " اللي", "probability": 0.942138671875}, {"start": 2059.48, "end": 2060.02, "word": " احنا", "probability": 0.8634440104166666}, {"start": 2060.02, "end": 2060.98, "word": " أثبتناها", "probability": 0.954345703125}, {"start": 2060.98, "end": 2062.16, "word": " عمليا.", "probability": 0.8118896484375}, {"start": 2062.5, "end": 2062.98, "word": " هذه", "probability": 0.89697265625}, {"start": 2062.98, "end": 2063.24, "word": " هي", "probability": 0.88427734375}, {"start": 2063.24, "end": 2063.84, "word": " النقطة", "probability": 0.9869791666666666}, {"start": 2063.84, "end": 2064.54, "word": " الأولى", "probability": 0.98291015625}, {"start": 2064.54, "end": 2065.08, "word": ".بنجي", "probability": 0.7890380859375}, {"start": 2065.08, "end": 2065.42, "word": " لمين", "probability": 0.7919921875}, {"start": 2065.42, "end": 2066.26, "word": " للنقطة", "probability": 0.951904296875}, {"start": 2066.26, "end": 2067.08, "word": " الثانية؟", "probability": 0.95244140625}], "temperature": 1.0}, {"id": 90, "seek": 208014, "start": 2067.96, "end": 2080.14, "text": "النقوة الثانية قال اللي بده ل plus transform ل ال E أصناع ال CT لل F of T بالشكل اللي عندنا", "tokens": [6027, 1863, 4587, 2407, 3660, 6024, 104, 7649, 10632, 50239, 13672, 1829, 47525, 3224, 5296, 1804, 4088, 5296, 2423, 462, 5551, 9381, 8315, 3615, 2423, 19529, 24976, 479, 295, 314, 20666, 8592, 28820, 13672, 1829, 43242, 8315], "avg_logprob": -0.291118428895348, "compression_ratio": 1.2566371681415929, "no_speech_prob": 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{"start": 2075.04, "end": 2075.28, "word": " ال", "probability": 0.57763671875}, {"start": 2075.28, "end": 2076.16, "word": " CT", "probability": 0.8056640625}, {"start": 2076.16, "end": 2077.08, "word": " لل", "probability": 0.5185546875}, {"start": 2077.08, "end": 2077.7, "word": " F", "probability": 0.919921875}, {"start": 2077.7, "end": 2078.4, "word": " of", "probability": 0.7705078125}, {"start": 2078.4, "end": 2078.86, "word": " T", "probability": 0.95068359375}, {"start": 2078.86, "end": 2079.5, "word": " بالشكل", "probability": 0.9342447916666666}, {"start": 2079.5, "end": 2079.66, "word": " اللي", "probability": 0.97216796875}, {"start": 2079.66, "end": 2080.14, "word": " عندنا", "probability": 0.670654296875}], "temperature": 1.0}, {"id": 91, "seek": 210930, "start": 2081.04, "end": 2109.3, "text": "يبقى نروح لتعريف لابلاسي ترانسفورم لتعريف لابلاسي ترانسفورم اذا بد النتيجة تقضع F of S ناقص الـC E of CT بالموجب وليست بالثالث تمام؟ يبقى هذه بدها تساوي تكامل من Zero ل Infinity لل E أُس ناقص ST في مين؟ في الدالة اللي عندنا هذه E of CT", "tokens": [1829, 3555, 4587, 7578, 8717, 32887, 5016, 5296, 2655, 3615, 16572, 5172, 5296, 16758, 15040, 3794, 1829, 6055, 2288, 7649, 3794, 5172, 13063, 2304, 5296, 2655, 3615, 16572, 5172, 5296, 16758, 15040, 3794, 1829, 6055, 2288, 7649, 3794, 5172, 13063, 2304, 1975, 15730, 47525, 28239, 31371, 7435, 3660, 6055, 4587, 11242, 3615, 479, 295, 318, 8717, 995, 4587, 9381, 2423, 39184, 34, 462, 295, 19529, 20666, 2304, 29245, 3555, 4032, 20292, 14851, 20666, 12984, 6027, 12984, 46811, 10943, 22807, 7251, 3555, 4587, 7578, 29538, 47525, 11296, 6055, 3794, 995, 45865, 6055, 4117, 10943, 1211, 9154, 17182, 5296, 34762, 24976, 462, 5551, 10859, 3794, 8717, 995, 4587, 9381, 4904, 8978, 3714, 9957, 22807, 8978, 32748, 6027, 3660, 13672, 1829, 43242, 8315, 29538, 462, 295, 19529], "avg_logprob": -0.3060000038146973, "compression_ratio": 1.7623318385650224, "no_speech_prob": 0.0, "words": [{"start": 2081.04, "end": 2081.38, "word": 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0.793212890625}, {"start": 2247.02, "end": 2247.98, "word": " المسائل", "probability": 0.935791015625}, {"start": 2247.98, "end": 2249.78, "word": " المختلفة", "probability": 0.9952392578125}], "temperature": 1.0}, {"id": 98, "seek": 227803, "start": 2250.09, "end": 2278.03, "text": "يبقى الآن بدنا هذه رقم واحد هذه تماما وبدنا رقم اتنين هذه نكون ملمين ابهم ومن خلالهم بدنا نحاول نحل أمثلة مختلفة بأشكال مختلفة كما ستراهن بعد أن انتهينا من برهان النظرية بدنا نيجي ناخد بعض الأمثلة حد بدها العمود هذا", "tokens": [1829, 3555, 4587, 7578, 6024, 48506, 47525, 8315, 29538, 12602, 4587, 2304, 36764, 24401, 29538, 46811, 10943, 995, 4032, 44510, 8315, 12602, 4587, 2304, 1975, 2655, 1863, 9957, 29538, 8717, 30544, 3714, 19528, 9957, 48127, 16095, 4032, 27842, 16490, 1211, 6027, 16095, 47525, 8315, 8717, 5016, 995, 12610, 8717, 5016, 1211, 5551, 2304, 12984, 37977, 3714, 46456, 46538, 3660, 4724, 10721, 8592, 4117, 6027, 3714, 46456, 46538, 3660, 9122, 15042, 8608, 2655, 23557, 3224, 1863, 39182, 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"word": " نحل", "probability": 0.9527994791666666}, {"start": 2263.01, "end": 2263.99, "word": " أمثلة", "probability": 0.8614501953125}, {"start": 2263.99, "end": 2264.75, "word": " مختلفة", "probability": 0.993896484375}, {"start": 2264.75, "end": 2265.53, "word": " بأشكال", "probability": 0.96015625}, {"start": 2265.53, "end": 2267.25, "word": " مختلفة", "probability": 0.9844970703125}, {"start": 2267.25, "end": 2268.21, "word": " كما", "probability": 0.98193359375}, {"start": 2268.21, "end": 2269.55, "word": " ستراهن", "probability": 0.862158203125}, {"start": 2269.55, "end": 2270.03, "word": " بعد", "probability": 0.90283203125}, {"start": 2270.03, "end": 2270.23, "word": " أن", "probability": 0.413330078125}, {"start": 2270.23, "end": 2270.67, "word": " انتهينا", "probability": 0.8095703125}, {"start": 2270.67, "end": 2270.85, "word": " من", "probability": 0.98779296875}, {"start": 2270.85, "end": 2271.31, "word": " برهان", "probability": 0.794677734375}, {"start": 2271.31, 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لازمات", "probability": 0.8494873046875}, {"start": 2282.44, "end": 2283.08, "word": " هنا", "probability": 0.921875}, {"start": 2283.08, "end": 2303.74, "word": " example", "probability": 0.1346435546875}, {"start": 2303.74, "end": 2304.8, "word": " one", "probability": 0.5888671875}], "temperature": 1.0}, {"id": 100, "seek": 233548, "start": 2308.57, "end": 2335.49, "text": "أول مثال بقول compute the following compute the following عسبي لي ما يأتي نمرة a بدلا plus transform ل U اتنين by as a function of T لصيني T", "tokens": [10721, 12610, 50113, 6027, 4724, 39648, 14722, 264, 3480, 14722, 264, 3480, 6225, 35457, 1829, 32239, 19446, 7251, 10721, 31371, 8717, 2304, 25720, 257, 47525, 15040, 1804, 4088, 5296, 624, 1975, 2655, 1863, 9957, 538, 382, 257, 2445, 295, 314, 5296, 9381, 9957, 1829, 314], "avg_logprob": -0.3488451015690099, "compression_ratio": 1.2638888888888888, "no_speech_prob": 0.0, "words": [{"start": 2308.57, "end": 2309.01, "word": "أول", "probability": 0.801025390625}, 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3437.78, "end": 3447.7, "text": "يبقى هذا النوع الأول من أنواع الأمثلة بدنا نيجي لنوعتين يبقى example two", "tokens": [1829, 3555, 4587, 7578, 23758, 28239, 45367, 16247, 12610, 9154, 14739, 14407, 3615, 16247, 2304, 12984, 37977, 47525, 8315, 8717, 1829, 7435, 1829, 5296, 1863, 2407, 34268, 9957, 7251, 3555, 4587, 7578, 1365, 732], "avg_logprob": -0.2812499931880406, "compression_ratio": 1.2448979591836735, "no_speech_prob": 5.960464477539063e-08, "words": [{"start": 3437.78, "end": 3438.98, "word": "يبقى", "probability": 0.62152099609375}, {"start": 3438.98, "end": 3439.28, "word": " هذا", "probability": 0.57080078125}, {"start": 3439.28, "end": 3439.66, "word": " النوع", "probability": 0.889892578125}, {"start": 3439.66, "end": 3440.24, "word": " الأول", "probability": 0.862060546875}, {"start": 3440.24, "end": 3440.72, "word": " من", "probability": 0.96142578125}, {"start": 3440.72, "end": 3441.82, "word": " أنواع", "probability": 0.93798828125}, {"start": 3441.82, "end": 3443.06, 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و جبتها روحت بدللة مين ال U باي و U اتنين باي إذا لابلاس ترانسفورم لهذه الدلة هو لابلاس ترانسفورم لمين لهذه الدلة و مش عارف يمكن لسه بدأ فبركة كمان", "tokens": [2304, 19913, 3555, 2407, 9566, 7251, 3555, 4587, 7578, 6225, 42213, 2655, 6225, 42213, 10632, 6055, 5016, 995, 26895, 15844, 3714, 9957, 15844, 2423, 2445, 13672, 1829, 5551, 3615, 9566, 995, 11296, 46740, 24192, 4032, 10874, 3555, 2655, 11296, 12602, 2407, 33753, 47525, 1211, 37977, 3714, 9957, 2423, 624, 4724, 47302, 4032, 624, 1975, 2655, 1863, 9957, 4724, 47302, 11933, 15730, 5296, 16758, 15040, 3794, 6055, 2288, 7649, 3794, 5172, 13063, 2304, 46740, 24192, 32748, 37977, 31439, 5296, 16758, 15040, 3794, 6055, 2288, 7649, 3794, 5172, 13063, 2304, 5296, 2304, 9957, 46740, 24192, 32748, 37977, 4032, 37893, 6225, 9640, 5172, 7251, 43020, 5296, 3794, 3224, 47525, 10721, 6156, 26890, 4117, 3660, 9122, 2304, 7649], "avg_logprob": -0.2858695678088976, "compression_ratio": 1.8762376237623761, "no_speech_prob": 0.0, "words": 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4168.99, "end": 4170.05, "word": " لمن؟", "probability": 0.6284993489583334}, {"start": 4170.05, "end": 4170.39, "word": " ل", "probability": 0.69189453125}, {"start": 4170.39, "end": 4170.99, "word": " U", "probability": 0.322021484375}, {"start": 4170.99, "end": 4171.93, "word": " بي", "probability": 0.326904296875}, {"start": 4171.93, "end": 4172.55, "word": " of", "probability": 0.794921875}, {"start": 4172.55, "end": 4173.11, "word": " T", "probability": 0.4140625}, {"start": 4173.11, "end": 4173.77, "word": " في", "probability": 0.712890625}, {"start": 4173.77, "end": 4174.57, "word": " T", "probability": 0.8095703125}, {"start": 4174.57, "end": 4175.93, "word": " ناقص", "probability": 0.963134765625}, {"start": 4175.93, "end": 4176.39, "word": " بي", "probability": 0.86572265625}], "temperature": 1.0}, {"id": 177, "seek": 418934, "start": 4177.24, "end": 4189.34, "text": "ناقص U2 باي as a function of T فمين؟ في T ناقص باي الشكل اللي عالي هنا", "tokens": [1863, 995, 4587, 9381, 624, 17, 4724, 47302, 382, 257, 2445, 295, 314, 6156, 2304, 9957, 22807, 8978, 314, 8717, 995, 4587, 9381, 4724, 47302, 25124, 28820, 13672, 1829, 6225, 6027, 1829, 34105], "avg_logprob": -0.4568014688351575, "compression_ratio": 1.2159090909090908, "no_speech_prob": 0.0, "words": [{"start": 4177.24, "end": 4178.46, "word": "ناقص", "probability": 0.6798095703125}, {"start": 4178.46, "end": 4180.4, "word": " U2", "probability": 0.5816650390625}, {"start": 4180.4, "end": 4181.02, "word": " باي", "probability": 0.43115234375}, {"start": 4181.02, "end": 4181.48, "word": " as", "probability": 0.5869140625}, {"start": 4181.48, "end": 4181.84, "word": " a", "probability": 0.904296875}, {"start": 4181.84, "end": 4182.7, "word": " function", "probability": 0.978515625}, {"start": 4182.7, "end": 4183.34, "word": " of", "probability": 0.97412109375}, {"start": 4183.34, "end": 4183.92, "word": " T", "probability": 0.8955078125}, {"start": 4183.92, "end": 4185.44, "word": " فمين؟", "probability": 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معاها", "tokens": [2655, 15042, 2304, 46811, 10943, 5296, 16758, 15040, 3794, 31439, 8213, 2445, 31439, 39896, 9778, 8592, 15844, 2423, 1433, 16247, 12610, 4032, 39896, 9778, 8592, 15844, 2423, 1433, 16712, 7649, 1829, 7251, 3555, 4587, 7578, 23758, 5296, 16758, 15040, 3794, 4088, 5296, 624, 538, 295, 314, 8978, 314, 8717, 995, 4587, 9381, 2423, 538, 8717, 995, 4587, 9381, 5296, 16758, 15040, 3794, 4088, 5296, 624, 1975, 2655, 1863, 9957, 538, 382, 257, 2445, 295, 314, 4724, 3794, 29538, 5296, 16758, 15040, 3794, 37893, 8032, 2655, 19913, 3555, 9566, 20449, 995, 11296], "avg_logprob": -0.2574728144251782, "compression_ratio": 1.819672131147541, "no_speech_prob": 0.0, "words": [{"start": 4190.38, "end": 4190.94, "word": "تمام", "probability": 0.5242106119791666}, {"start": 4190.94, "end": 4191.84, "word": " تمام", "probability": 0.890869140625}, {"start": 4191.84, "end": 4192.64, "word": " لابلاس", "probability": 0.56365966796875}, {"start": 4192.64, "end": 4192.8, "word": " هو", 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"end": 4215.54, "word": " a", "probability": 0.9287109375}, {"start": 4215.54, "end": 4216.06, "word": " function", "probability": 0.97119140625}, {"start": 4216.06, "end": 4216.46, "word": " of", "probability": 0.974609375}, {"start": 4216.46, "end": 4216.68, "word": " T", "probability": 0.96337890625}, {"start": 4216.68, "end": 4217.42, "word": " بس", "probability": 0.773193359375}, {"start": 4217.42, "end": 4217.68, "word": " هذه", "probability": 0.6865234375}, {"start": 4217.68, "end": 4218.14, "word": " لابلاس", "probability": 0.8944091796875}, {"start": 4218.14, "end": 4218.32, "word": " مش", "probability": 0.93115234375}, {"start": 4218.32, "end": 4219.02, "word": " هتظبط", "probability": 0.9658203125}, {"start": 4219.02, "end": 4219.56, "word": " معاها", "probability": 0.9173177083333334}], "temperature": 1.0}, {"id": 179, "seek": 423985, "start": 4220.42, "end": 4239.86, "text": "يعني بدها فشون يعمل؟ بنضيف باي و بنطرح باي تمام يبقى هذه بقدر اقول في تي ناقص اتنين باي زائد باي 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"probability": 0.6112060546875}, {"start": 4226.2, "end": 4226.38, "word": " و", "probability": 0.5693359375}, {"start": 4226.38, "end": 4227.14, "word": " بنطرح", "probability": 0.8934326171875}, {"start": 4227.14, "end": 4227.56, "word": " باي", "probability": 0.845703125}, {"start": 4227.56, "end": 4228.36, "word": " تمام", "probability": 0.68212890625}, {"start": 4228.36, "end": 4229.38, "word": " يبقى", "probability": 0.873291015625}, {"start": 4229.38, "end": 4229.74, "word": " هذه", "probability": 0.66796875}, {"start": 4229.74, "end": 4230.32, "word": " بقدر", "probability": 0.9713541666666666}, {"start": 4230.32, "end": 4231.06, "word": " اقول", "probability": 0.78076171875}, {"start": 4231.06, "end": 4231.72, "word": " في", "probability": 0.66796875}, {"start": 4231.72, "end": 4233.06, "word": " تي", "probability": 0.54052734375}, {"start": 4233.06, "end": 4233.76, "word": " ناقص", "probability": 0.893310546875}, {"start": 4233.76, "end": 4234.4, "word": " اتنين", "probability": 0.9385986328125}, {"start": 4234.4, "end": 4234.98, "word": " باي", "probability": 0.798583984375}, {"start": 4234.98, "end": 4236.34, "word": " زائد", "probability": 0.9295247395833334}, {"start": 4236.34, "end": 4236.98, "word": " باي", "probability": 0.813232421875}, {"start": 4236.98, "end": 4238.9, "word": " كلها", "probability": 0.717041015625}, {"start": 4238.9, "end": 4239.86, "word": " يقفلنا", "probability": 0.87099609375}], "temperature": 1.0}, {"id": 180, "seek": 425793, "start": 4241.51, "end": 4257.93, "text": "هذه المرحلة ستكون مين؟ او هذه المعروفة اي اس ناقص by اس في ال place transform لمين؟ لـT قبل ال shift", "tokens": [3224, 24192, 9673, 2288, 5016, 37977, 8608, 2655, 30544, 3714, 9957, 22807, 1975, 2407, 29538, 9673, 3615, 32887, 5172, 3660, 1975, 1829, 1975, 3794, 8717, 995, 4587, 9381, 538, 24525, 8978, 2423, 1081, 4088, 32767, 9957, 22807, 5296, 39184, 51, 12174, 36150, 2423, 5513], "avg_logprob": -0.6163194285498725, "compression_ratio": 1.234375, "no_speech_prob": 5.960464477539063e-08, "words": [{"start": 4241.51, "end": 4242.71, "word": "هذه", "probability": 0.674560546875}, {"start": 4242.71, "end": 4242.81, "word": " المرحلة", "probability": 0.47039794921875}, {"start": 4242.81, "end": 4243.19, "word": " ستكون", "probability": 0.4706217447916667}, {"start": 4243.19, "end": 4243.87, "word": " مين؟", "probability": 0.3542887369791667}, {"start": 4243.87, "end": 4245.51, "word": " او", "probability": 0.495849609375}, {"start": 4245.51, "end": 4245.91, "word": " هذه", "probability": 0.65087890625}, {"start": 4245.91, "end": 4246.79, "word": " المعروفة", "probability": 0.95869140625}, {"start": 4246.79, "end": 4247.35, "word": " اي", "probability": 0.17022705078125}, {"start": 4247.35, "end": 4249.57, "word": " اس", "probability": 0.4117431640625}, {"start": 4249.57, "end": 4250.79, "word": " ناقص", "probability": 0.900634765625}, {"start": 4250.79, "end": 4251.29, "word": " by", "probability": 0.411865234375}, {"start": 4251.29, "end": 4251.89, "word": " اس", "probability": 0.51171875}, {"start": 4251.89, "end": 4252.65, "word": " في", "probability": 0.82421875}, {"start": 4252.65, "end": 4252.95, "word": " ال", "probability": 0.61376953125}, {"start": 4252.95, "end": 4253.61, "word": " place", "probability": 0.22607421875}, {"start": 4253.61, "end": 4254.81, "word": " transform", "probability": 0.7900390625}, {"start": 4254.81, "end": 4255.99, "word": " لمين؟", "probability": 0.7025553385416666}, {"start": 4255.99, "end": 4256.55, "word": " لـT", "probability": 0.4458821614583333}, {"start": 4256.55, "end": 4257.13, "word": " قبل", "probability": 0.987548828125}, {"start": 4257.13, "end": 4257.37, "word": " ال", "probability": 0.62451171875}, {"start": 4257.37, "end": 4257.93, "word": " shift", "probability": 0.8310546875}], "temperature": 1.0}, {"id": 181, "seek": 428585, "start": 4258.84, "end": 4285.86, "text": "تمام هذه يا بنات هجزئها إلى جزئين يبقى ناقص ل plus transform ل U2 by as a function of 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"probability": 0.97216796875}, {"start": 5648.39, "end": 5648.99, "word": " الدالة", "probability": 0.8787434895833334}, {"start": 5648.99, "end": 5649.41, "word": " الأصلي", "probability": 0.71435546875}, {"start": 5649.41, "end": 5649.97, "word": " انت", "probability": 0.6806640625}, {"start": 5649.97, "end": 5650.27, "word": " لو", "probability": 0.34423828125}, {"start": 5650.27, "end": 5651.35, "word": " روحت", "probability": 0.8126627604166666}, {"start": 5651.35, "end": 5651.81, "word": " خدت", "probability": 0.777099609375}, {"start": 5651.81, "end": 5652.27, "word": " الدالة", "probability": 0.9498697916666666}, {"start": 5652.27, "end": 5652.39, "word": " دي", "probability": 0.7861328125}, {"start": 5652.39, "end": 5652.49, "word": " و", "probability": 0.95751953125}, {"start": 5652.49, "end": 5652.85, "word": " خدتي", "probability": 0.6585286458333334}, {"start": 5652.85, "end": 5653.09, "word": " لها", "probability": 0.4010009765625}, {"start": 5653.09, "end": 5653.71, 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"word": " بيطلع", "probability": 0.855859375}, {"start": 5660.33, "end": 5660.65, "word": " مين", "probability": 0.60528564453125}, {"start": 5660.65, "end": 5661.39, "word": " بيطلع", "probability": 0.861376953125}, {"start": 5661.39, "end": 5661.85, "word": " ده", "probability": 0.8349609375}, {"start": 5661.85, "end": 5662.57, "word": " اللي", "probability": 0.6591796875}, {"start": 5662.57, "end": 5662.93, "word": " فوق", "probability": 0.97119140625}, {"start": 5662.93, "end": 5663.61, "word": " لحد", "probability": 0.877197265625}, {"start": 5663.61, "end": 5663.89, "word": " هنا", "probability": 0.97607421875}, {"start": 5663.89, "end": 5664.35, "word": " stop", "probability": 0.427001953125}, {"start": 5664.35, "end": 5665.05, "word": " بيعطيكوا", "probability": 0.7718912760416666}, {"start": 5665.05, "end": 5665.73, "word": " العافية", "probability": 0.7704264322916666}, {"start": 5665.73, "end": 5667.05, "word": " انتهى", "probability": 0.93115234375}, {"start": 5667.05, 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5694.88, "word": " اخر", "probability": 0.6763916015625}, {"start": 5694.88, "end": 5695.44, "word": " section", "probability": 0.84521484375}, {"start": 5695.44, "end": 5695.76, "word": " اللي", "probability": 0.9072265625}, {"start": 5695.76, "end": 5695.94, "word": " هو", "probability": 0.92041015625}, {"start": 5695.94, "end": 5696.5, "word": " ستة", "probability": 0.7718912760416666}, {"start": 5696.5, "end": 5697.1, "word": " اربع", "probability": 0.80615234375}, {"start": 5697.1, "end": 5698.14, "word": " وبه", "probability": 0.5953369140625}, {"start": 5698.14, "end": 5699.36, "word": " ينتهي", "probability": 0.9312744140625}, {"start": 5699.36, "end": 5700.88, "word": " المقرر", "probability": 0.9915771484375}], "temperature": 1.0}], "language": "ar", "language_probability": 1.0, "duration": 5702.496, "duration_after_vad": 5424.177218750008}
\ No newline at end of file
diff --git a/PL9fwy3NUQKwa8ZDfSFGn6H8xVFLzqmCZC/5tytEs18MlY_raw.srt b/PL9fwy3NUQKwa8ZDfSFGn6H8xVFLzqmCZC/5tytEs18MlY_raw.srt
new file mode 100644
index 0000000000000000000000000000000000000000..e74e0c7b107403db7ceb0080856bd32da583e81a
--- /dev/null
+++ b/PL9fwy3NUQKwa8ZDfSFGn6H8xVFLzqmCZC/5tytEs18MlY_raw.srt
@@ -0,0 +1,3280 @@
+1
+00:00:10,540 --> 00:00:15,240
+المرة الماضية انتهينا من سكتشن ستة اتنين اللي هو
+
+2
+00:00:15,240 --> 00:00:19,840
+بيتحدث عن استخدام laplace transform لحل المعادلة
+
+3
+00:00:19,840 --> 00:00:24,280
+التفاضلية او حل ال initial value problem اليوم ان
+
+4
+00:00:24,280 --> 00:00:28,240
+شاء الله هناخد function جديدة نسميها unit step
+
+5
+00:00:28,240 --> 00:00:33,630
+functionأو اختصارا ال step function نقطة تعريف ال
+
+6
+00:00:33,630 --> 00:00:37,550
+step function وحلاحظ ان ال step function بتلعب دور
+
+7
+00:00:37,550 --> 00:00:42,830
+كبير في موضوع Laplace transform بل سنحسبها كمان
+
+8
+00:00:42,830 --> 00:00:47,670
+Laplace transformبجي بقول the unit step function
+
+9
+00:00:47,670 --> 00:00:52,050
+is denoted by يبجى حنرمز لل unit step function
+
+10
+00:00:52,050 --> 00:00:58,870
+بيبدأ ل U C as a function of T ال undefined as
+
+11
+00:00:58,870 --> 00:01:04,090
+وبنعرفها بالشكل التالي ك piecewise function يبجى U
+
+12
+00:01:04,090 --> 00:01:09,430
+C of T بيبدأ تساوي زيرو لما T تبجى دائما وابدا أقل
+
+13
+00:01:09,430 --> 00:01:14,280
+من Cوإذا كانت تساوي C أو أكبر من C فال unit step
+
+14
+00:01:14,280 --> 00:01:19,500
+function بتساوي كده؟ واحد صحيح ممكن نتعرف على شكل
+
+15
+00:01:19,500 --> 00:01:24,040
+ال unit step function اللي عندنا كالتالي لو جيت
+
+16
+00:01:24,040 --> 00:01:30,520
+أخدت محاور بالشكل هذا وقلت هذا محور T و هذا محور Y
+
+17
+00:01:30,520 --> 00:01:33,280
+أو محور F يبقى هذا محور Y
+
+18
+00:01:38,500 --> 00:01:45,360
+أفترضوا أن هذا رقم الـ main الرقم Cلأن اشترط C
+
+19
+00:01:45,360 --> 00:01:53,180
+مالها اكبر من Zero اذا لما تبقى الدالة قبل C يعني
+
+20
+00:01:53,180 --> 00:01:58,540
+اي قيمة قبل C قيمة الدالة عندها جداش تبقى ب Zero
+
+21
+00:01:58,540 --> 00:02:02,860
+يبقى الدالة بدأت تكون مغطية المنطقة هذه كلها
+
+22
+00:02:02,860 --> 00:02:07,640
+بالشكل اللي عندها تمام؟ لكن من هنا بنات بدأت تبقى
+
+23
+00:02:07,640 --> 00:02:12,180
+فترة مفتوحة او النقطة هذه عندهامعرفة دالة غير
+
+24
+00:02:12,180 --> 00:02:17,180
+معرفة دالة هادى عند النقطة معرفة وين بيصير قيمتها
+
+25
+00:02:17,180 --> 00:02:21,420
+فوق اللى بواحد عندما سيه اذا بيجي على القيمة اللى
+
+26
+00:02:21,420 --> 00:02:26,260
+عندنا اللى واحد صحيح واطلع اقبالها وبالتالي الدالة
+
+27
+00:02:26,260 --> 00:02:31,680
+بعد ذلك دالة ثابتة لكل القيم اللى بعد سيه قيمة
+
+28
+00:02:31,680 --> 00:02:35,810
+الدالة مقدر ثابت اللى واحديبقى لو رسمنا هذه ال
+
+29
+00:02:35,810 --> 00:02:41,110
+function هتصير بالشكل اللي عندنا هذا يبقى هنا حصلت
+
+30
+00:02:41,110 --> 00:02:46,910
+قفزة من النقطة لأن هذه لم نقطة اللي فوق وما من هنا
+
+31
+00:02:46,910 --> 00:02:51,570
+سمناها ال step function اللي هي دالة القفزة أو
+
+32
+00:02:51,570 --> 00:02:56,810
+الدالة السلمية تمام؟ بس ماطلعش درجات كتير درجة
+
+33
+00:02:56,810 --> 00:02:59,740
+واحدة مش أكترالسلامية اللى أخدناها في ال calculus
+
+34
+00:02:59,740 --> 00:03:05,360
+ايه نطلع عدة درجات وها كده الان بنحاول نستخدم هذه
+
+35
+00:03:05,360 --> 00:03:10,400
+الدالة في رسم بعض ال functions نبدأ ناخد بعض
+
+36
+00:03:10,400 --> 00:03:19,720
+الأمثلة على كيفية الرسم يبقى example sketch
+
+37
+00:03:19,720 --> 00:03:26,160
+the graph of
+
+38
+00:03:27,860 --> 00:03:38,240
+the function f of t بدى يسوى واحد ناقص u c of t
+
+39
+00:03:43,120 --> 00:03:47,240
+قال ارسم لي شكل الدالة اللى عندنا هذه بنقوله
+
+40
+00:03:47,240 --> 00:03:51,620
+بقصتنا بسيطة جدا بنحاول نرسم هذه الدالة اذا لو
+
+41
+00:03:51,620 --> 00:03:57,320
+جينا رسمنا هذه الدالة بقوله هذا ال function هذه T
+
+42
+00:03:57,320 --> 00:04:03,000
+وهذه هنا main ال F of T ونختار الرقم هذا اللى
+
+43
+00:04:03,000 --> 00:04:07,300
+عندنا اللى هو main الرقم C اللى هو greater than
+
+44
+00:04:07,300 --> 00:04:14,050
+zero دائما وأبداطيب بنا نتعرف على شكل الدالة بدي
+
+45
+00:04:14,050 --> 00:04:18,910
+بقوله انا مش هانرسوم بدي اعرف شو شكلها يبقى F of T
+
+46
+00:04:18,910 --> 00:04:27,650
+بديه سوى واحد ناقص ال U C of T اما Zero لما T اقل
+
+47
+00:04:27,650 --> 00:04:35,100
+من C اما واحد لما T greater than or equal to Cيبقى
+
+48
+00:04:35,100 --> 00:04:41,340
+هذه بدها تساوي بشكل ان اذا واحد ناقص zero بواحد
+
+49
+00:04:41,340 --> 00:04:47,400
+يبقى هاي واحد لما T اقل من C واحد ناقص واحد يساوي
+
+50
+00:04:47,400 --> 00:04:55,380
+zero لما T greater than or equal to Cإذا كان T أقل
+
+51
+00:04:55,380 --> 00:05:01,120
+من C فقيمة الدالة كم؟ واحد يبقى على المنطقة هذه
+
+52
+00:05:01,120 --> 00:05:05,200
+بتبقى قيمة الدالة كل واحد إذا لو طلعت هنا عند
+
+53
+00:05:05,200 --> 00:05:10,060
+الواحد يبقى بدها تبقى ال function عنها معرفة بهذا
+
+54
+00:05:10,060 --> 00:05:16,060
+الشكل كل المنطقة بس عندها دياش مفتوحة لأنها أقل من
+
+55
+00:05:16,060 --> 00:05:23,580
+C هي تحتها دوري هيك هي نقطة C تمام؟يبقى هذا إذا
+
+56
+00:05:23,580 --> 00:05:28,740
+كان T أقل من C فقيمة الدالة واحد لكن عندما T تسوى
+
+57
+00:05:28,740 --> 00:05:34,880
+C فما فوق تصير قيمة الدالة Zero يبقى هنا بدأ تصير
+
+58
+00:05:34,880 --> 00:05:41,340
+هنا ب Zero مغلقة ونظل ماشيين إلى ما شاء الله يبقى
+
+59
+00:05:41,340 --> 00:05:45,780
+هذه الكلة تعتبر من رسمة ال function اللي عندنا
+
+60
+00:05:45,780 --> 00:05:50,230
+وكأنه انها ايه اللي عملنا جلبنا اللي فوق تحتواللي
+
+61
+00:05:50,230 --> 00:05:55,690
+تحت فوق بالضبط تماما يبقى هذا مثال هذا يعتبر مثال
+
+62
+00:05:55,690 --> 00:06:01,390
+بسيط انتجليه شوية يبقى بنيجي نقول example two
+
+63
+00:06:01,390 --> 00:06:08,530
+example two يبقى هذا كان example one وهذا example
+
+64
+00:06:08,530 --> 00:06:15,150
+two برضه sketch the graph of the function sketch
+
+65
+00:06:15,150 --> 00:06:17,670
+the graph
+
+66
+00:06:27,820 --> 00:06:38,800
+Y تساوي T ناقص تلاتة في U اتنين as a function of T
+
+67
+00:06:40,000 --> 00:06:49,500
+ناقص T ناقص اتنين T ناقص اتنين في U تلاتة as a
+
+68
+00:06:49,500 --> 00:06:58,000
+function of T on the interval on the interval T
+
+69
+00:06:58,000 --> 00:07:05,160
+greater than or equal to zero كويس
+
+70
+00:07:05,160 --> 00:07:10,830
+قال لي ارسمليشكل الدالة اللى عندنا هذه على الفترة
+
+71
+00:07:10,830 --> 00:07:16,010
+من صفر لغاية infinity بطلع في السؤال و بطلع في
+
+72
+00:07:16,010 --> 00:07:22,470
+اللى عنديبعد عن بعض مظبوط الشكل هو بعد عن بعض لكن
+
+73
+00:07:22,470 --> 00:07:27,050
+انا بدي احاول احط ال function اللي عندنا هذه على
+
+74
+00:07:27,050 --> 00:07:31,470
+الصيغة اللي عندنا هذه وبالتالي بصير العملية الرسم
+
+75
+00:07:31,470 --> 00:07:37,370
+عملية سهلة لحظة يا اخناش جالين هنا U2 و U3 يعني
+
+76
+00:07:37,370 --> 00:07:42,930
+انا دخلت رقمين على الخط اذا انا بدي ادرس الفترة من
+
+77
+00:07:42,930 --> 00:07:48,030
+صفر لغاية اتنينومن اتنين لغاية التلاتة ومن التلاتة
+
+78
+00:07:48,030 --> 00:07:51,830
+فما فوق يعني صار عندي تلت فترات من خلال السؤال
+
+79
+00:07:51,830 --> 00:07:57,770
+اللي عندنا هذا تمام فبروح بقول له دل هادي Y تساوي
+
+80
+00:07:57,770 --> 00:08:04,470
+أحد ثلاثة أمور الأمر الأول بدي أخد لما T تبقى أقل
+
+81
+00:08:04,470 --> 00:08:11,270
+من اتنين لما T تبقى أقل من اتنين يبقى هادي T ناقص
+
+82
+00:08:11,270 --> 00:08:14,230
+ثلاثة كم تكون قيمة الدل هادي؟
+
+83
+00:08:18,690 --> 00:08:24,290
+يبقى نقص T نقص 2 U تلاتة قداش قبل اتنين
+
+84
+00:08:30,130 --> 00:08:34,510
+زيرو برضه قبل اتنين و نص بزيرو و قبل اتنين و تسعة
+
+85
+00:08:34,510 --> 00:08:39,010
+و تسعة و قبل التلاتة بزيرو اتنين قبل التلاتة اذا
+
+86
+00:08:39,010 --> 00:08:46,590
+هذه زيرو طبعا فلو كانت ال T اكبر من او تساوي اتنين
+
+87
+00:08:46,590 --> 00:08:53,980
+و اقل من تلاتةيبقى باجي بقول له هدى تى ناقص ثلاثة
+
+88
+00:08:53,980 --> 00:08:59,680
+فيه يو اتنين هالحساس بعد اتنين، مظبوط؟ بعد اتنين
+
+89
+00:08:59,680 --> 00:09:02,700
+على طول بواحد، اذا من اتنين لتلاتة جيبتها في
+
+90
+00:09:02,700 --> 00:09:11,290
+الجداش بواحدنقص ا ت نقص اتنين في قبل التلاتة اللي
+
+91
+00:09:11,290 --> 00:09:17,550
+همين ب zero تمام نيجي الان ناخد الفترة T greater
+
+92
+00:09:17,550 --> 00:09:22,810
+than or equal to تلاتة يبقى U اتنين بقداش بتكون
+
+93
+00:09:22,810 --> 00:09:30,410
+بعد التلاتة بواحد يبقى بصير T ناقص تلاتة في واحد
+
+94
+00:09:30,800 --> 00:09:36,720
+نقص T نقص اتنين في قداش كمان بواحد تمام التمام
+
+95
+00:09:36,720 --> 00:09:41,980
+الأن نروح نتعرف على شكل الدالة اللي عندنا هذه يبقى
+
+96
+00:09:41,980 --> 00:09:48,940
+دي صار شكلها بالشكل التالي هذا ثلاثة أجزاء الجزء
+
+97
+00:09:48,940 --> 00:09:53,000
+الأول Zero في رقم Zero Zero في رقم Zero Zero نقص
+
+98
+00:09:53,000 --> 00:09:59,620
+Zero يبقى ب Zero لما T أقل من اتنينهذا الـ term
+
+99
+00:09:59,620 --> 00:10:05,100
+بيزير و بيظلش عندنا الا main ت ناقص ثلاثة يبقى T
+
+100
+00:10:05,100 --> 00:10:10,540
+ناقص ثلاثة لما T أكبر من أو يسوى اتنين وأقل من
+
+101
+00:10:10,540 --> 00:10:18,380
+الmain من ثلاثةنجي لهذه تصير T ناقص تلاتة ناقص T
+
+102
+00:10:18,380 --> 00:10:23,800
+زائد اتنين ناقص T وزائد T مع السلامة ناقص تلاتة
+
+103
+00:10:23,800 --> 00:10:29,620
+وزائد اتنين بيظل قداش ناقص واحد يبقى ناقص واحد لما
+
+104
+00:10:29,620 --> 00:10:33,760
+T greater than or equal to تلاتة اذا من ال
+
+105
+00:10:33,760 --> 00:10:39,240
+function الأصلي اللي عند هذه استطعتكتابتها على
+
+106
+00:10:39,240 --> 00:10:45,420
+الشكل اللي عندنا هذا إلا لو رسمت هذه بكون رسمت الـ
+
+107
+00:10:45,420 --> 00:10:50,520
+function الأصلية طيب تعالوا نرسم و نشوف كيف بدو
+
+108
+00:10:50,520 --> 00:10:58,220
+يكون شكلها إذا لو جيت قلت هذا محور T و هذا محور Y
+
+109
+00:11:00,050 --> 00:11:05,730
+الان هيا عندى هنا اتنين وهي عندى هنا اش اللى هى
+
+110
+00:11:05,730 --> 00:11:10,610
+التلاتة وهذا ما بعدها الان جابلى اتنين جديش قيمة
+
+111
+00:11:10,610 --> 00:11:17,050
+الدالة؟ Zero يبقى مفتوحة عندى اتنين هيك هي مفتوحة
+
+112
+00:11:17,050 --> 00:11:23,190
+ونغطى المنطقة هذه كلهاكل المنطقة اللي عندنا هذه
+
+113
+00:11:23,190 --> 00:11:27,970
+ليه قيمة من؟ قيمة ال dollar الان بدنا نيجي من
+
+114
+00:11:27,970 --> 00:11:34,730
+اتنين لغاية تلاتة يبقى Y تساوي T ناقص تلاتة يعني
+
+115
+00:11:34,730 --> 00:11:42,210
+معادلة خطية الان قداش قيمتها عندي اتنينT أكبر من
+
+116
+00:11:42,210 --> 00:11:47,290
+يساوي اتنين لو حطيت اتنين بيصير كده اذا عند اتنين
+
+117
+00:11:47,290 --> 00:11:54,090
+هذي بدها تنزل هنا لمين لسالب واحد تمام يبقى بيجيني
+
+118
+00:11:54,090 --> 00:11:59,750
+هنا بنزل رأسي لغاية ما جوان عند السالب واحد و
+
+119
+00:11:59,750 --> 00:12:07,370
+بيصير مغلقة بسبب اليساويطيب لو وصلت لتلاتة لا سمح
+
+120
+00:12:07,370 --> 00:12:10,250
+الله، طبعا أقل من تلاتة، بيقول لو صارت تلاتة إيش
+
+121
+00:12:10,250 --> 00:12:15,790
+بيصير؟ Zero، يبقى عندي التلاتة بدأ تطلع ل Zero، بس
+
+122
+00:12:15,790 --> 00:12:20,830
+عند Zero بيكون مالها مفتوحة، إذا هذا يمثل الخط
+
+123
+00:12:20,830 --> 00:12:26,730
+المستقيم T ناقص تلاتة، يبقى بده يصير شكل دالة
+
+124
+00:12:26,730 --> 00:12:30,430
+بالشكل اللي يعني هذا الخط المستقيم الغامق هذا
+
+125
+00:12:34,560 --> 00:12:40,560
+يبقى هذا رسمة لطي ناقص تلاتة تمام بعد ذلك بده يجيب
+
+126
+00:12:40,560 --> 00:12:45,300
+بعد التلاتة بعد التلاتة قيمة الدلة كده؟ سالب واحد
+
+127
+00:12:45,300 --> 00:12:51,880
+اذا هذه بدها تنزل automatic عند السالب واحد و بعد
+
+128
+00:12:51,880 --> 00:12:56,880
+التلاتة قيمتها على خور الخط كده؟ سالب واحد يبقى
+
+129
+00:12:56,880 --> 00:13:02,820
+هذه الدلة بالشكل التاني هنايبقى هاي رسمنا اللي هو
+
+130
+00:13:02,820 --> 00:13:07,020
+الدالة في المقاطع الثلاثة اللي هي piecewise
+
+131
+00:13:07,020 --> 00:13:13,340
+continuous طبعا يبقى هاه لو الشكل استشكل علينا هذا
+
+132
+00:13:13,340 --> 00:13:17,960
+بحاول أحطه في شكل جديد هاي الشكل الجديد الشكل
+
+133
+00:13:17,960 --> 00:13:21,040
+الجديد الساهر رسمه يبقى بدون اسم وبالتالي يكون
+
+134
+00:13:21,040 --> 00:13:25,660
+رسمنا من الدالة الأصلية اللي عندنا
+
+135
+00:13:41,980 --> 00:13:48,980
+بنحاول نجيب Laplace transform لمن؟ ل UC of T يبقى
+
+136
+00:13:48,980 --> 00:13:56,380
+example كمان find Laplace
+
+137
+00:13:56,380 --> 00:14:03,020
+transform for
+
+138
+00:14:03,020 --> 00:14:10,180
+the function UC of T
+
+139
+00:14:20,470 --> 00:14:23,970
+الورقة الجادة اللى اقنعكوا هي المرة اللى فاتت او
+
+140
+00:14:23,970 --> 00:14:29,050
+في الكتاب صفحة 319 لو فتحنا بنعرف النتيجة مباشرة
+
+141
+00:14:29,050 --> 00:14:35,370
+لكن بنعرف من اين جاءت هذه النتيجة يبقى عندك يو سي
+
+142
+00:14:35,370 --> 00:14:40,830
+و تي هي رقم مقماشرقم 12 لبلايس ترانسفورم إيه إيه
+
+143
+00:14:40,830 --> 00:14:42,290
+إيه إيه إيه إيه إيه إيه إيه إيه إيه إيه إيه إيه
+
+144
+00:14:42,290 --> 00:14:45,750
+إيه إيه إيه إيه إيه إيه إيه
+
+145
+00:14:45,750 --> 00:14:51,830
+إيه إيه
+
+146
+00:14:53,060 --> 00:15:00,320
+أنا بروح بقول له plus transform ل UC of T بده سوى
+
+147
+00:15:00,320 --> 00:15:08,100
+تكامل من zero ل infinity ل E اصنعقص ST ل UC of T
+
+148
+00:15:08,100 --> 00:15:17,250
+DTطيب هذا الكلام يساوي ما يعني هذي U C of T عبارة
+
+149
+00:15:17,250 --> 00:15:22,730
+عن جزئين تمام؟ إذن بالداجة للجزء الأول يبقى هذا
+
+150
+00:15:22,730 --> 00:15:29,910
+integration من Zero إلى C لل E أس ناقص ST في
+
+151
+00:15:29,910 --> 00:15:36,550
+الفترة هذه U C of T بقدرش؟ Zero ممتاز جدا يبقى في
+
+152
+00:15:36,550 --> 00:15:44,560
+Zero في DT إزاي؟تكامل من C إلى Infinity لل E أُس
+
+153
+00:15:44,560 --> 00:15:51,780
+ناقص ST في ال use of U بواحد في ال DTأذا هذا كله
+
+154
+00:15:51,780 --> 00:15:57,720
+بيروح بقداش بزيرو هذا improper integral يبقى بيروح
+
+155
+00:15:57,720 --> 00:16:04,720
+اعمله as a limit يبقى هذا ال limit تكامل من C إلى
+
+156
+00:16:04,720 --> 00:16:11,980
+A لما A tends to infinity لل E أصناق STDT
+
+157
+00:16:14,720 --> 00:16:19,980
+هذا الكلام يساوي limit لما ال a tends to infinity
+
+158
+00:16:19,980 --> 00:16:25,760
+تكمل ال exponential بال exponential itself على
+
+159
+00:16:25,760 --> 00:16:31,200
+مشتقة الأس لما يكون الأس as a linear function يعني
+
+160
+00:16:31,200 --> 00:16:36,840
+معدلة من الدرجة الأولى يبقى عالمين على ناقص ال s
+
+161
+00:16:36,840 --> 00:16:44,640
+من c لغاية ال aيبقى هذا الكلام بده يساوي limit لما
+
+162
+00:16:44,640 --> 00:16:48,920
+a tends to infinity بتدعوض فيه نتيجة التكامل
+
+163
+00:16:48,920 --> 00:16:53,660
+بالقيمة اللي فوق نقص اللي تحت لإنه finite integral
+
+164
+00:16:53,660 --> 00:17:03,440
+تكامل محدوديبقى هذا E أس ناقص S A على ناقص S ناقص
+
+165
+00:17:03,440 --> 00:17:11,820
+E أس بدي أشيل هذه و أحط مكانها C يبقى ناقص S في C
+
+166
+00:17:11,820 --> 00:17:22,130
+على مين على ناقص S و ال limit للمقدار هذا كلهطب
+
+167
+00:17:22,130 --> 00:17:25,450
+لما ال E بده تروح ل infinity هذا ال أس بالسالب
+
+168
+00:17:25,450 --> 00:17:30,150
+يبقى بنزل وين؟ تحت بصير واحد على ماله نهايه اللي
+
+169
+00:17:30,150 --> 00:17:34,530
+هو الجداش يبقى هذا الله يسهل عليه غير مأسوف عليه
+
+170
+00:17:34,530 --> 00:17:39,930
+بزيره هذا كله له دعوة باللمتة مافيش فيه capital E
+
+171
+00:17:39,930 --> 00:17:44,990
+نهاية يبقى هذا يعتبر كونستان يبقى ناقص على ناقص
+
+172
+00:17:44,990 --> 00:17:52,210
+بالزائدبظل E أصناع ال CS على S هي النتيجة اللى
+
+173
+00:17:52,210 --> 00:17:56,290
+عندنا يبقى هذا ال plus transform لل unit step
+
+174
+00:17:56,290 --> 00:18:00,850
+function اللى ذكرناها قبل قليل أظن هي نفس النتيجة
+
+175
+00:18:00,850 --> 00:18:05,330
+اللى عندكوا في الجدول يبقى هي نفس النتيجة بالضبط
+
+176
+00:18:05,330 --> 00:18:06,370
+تماما
+
+177
+00:18:16,550 --> 00:18:22,370
+الان بدنا نروح نعطي تعريف ل function جديدة تعتمد
+
+178
+00:18:22,370 --> 00:18:32,210
+على function أخرى فبجي بقول definition from
+
+179
+00:18:32,210 --> 00:18:40,670
+a given function if
+
+180
+00:18:40,670 --> 00:18:43,550
+we define
+
+181
+00:18:45,840 --> 00:18:55,000
+define a related function
+
+182
+00:18:55,000 --> 00:19:07,200
+g مثلا byG of T بده يساوي أحد أمرين، يا إما Zero
+
+183
+00:19:07,200 --> 00:19:17,240
+لما T أقل من C، يا إما ال F of T ناقص الـC لما T
+
+184
+00:19:17,240 --> 00:19:20,400
+greater than or equal to C
+
+185
+00:19:30,010 --> 00:19:34,910
+بنرجع للتعريف اللي احنا جايلينه هذا مرة ثانية بقول
+
+186
+00:19:34,910 --> 00:19:40,190
+from a given function f يبقى f دي مالها function
+
+187
+00:19:40,190 --> 00:19:45,230
+معطاعة تمام ال function المعطاعة بدي اعرف من
+
+188
+00:19:45,230 --> 00:19:49,850
+خلالها function تانية مرتبطة معاها related
+
+189
+00:19:49,850 --> 00:19:54,710
+function g بدي أسميها g جي بتعتمد على مين؟ اذا
+
+190
+00:19:54,710 --> 00:20:00,330
+مرتبطة معاها برابط ما ما هو الرابط هذا بيقول بايG
+
+191
+00:20:00,330 --> 00:20:06,250
+of T بدي يساوي أحد أمرين، يا إما Zero لما T أقل من
+
+192
+00:20:06,250 --> 00:20:12,390
+C، يا إما ال F of T ناقص الـC لما T أكبر من أو
+
+193
+00:20:12,390 --> 00:20:16,310
+يساوي C، لو جيت سؤالكوا السؤال التالت، و أنتم
+
+194
+00:20:16,310 --> 00:20:22,010
+دارسين Calculus A بنجاحبظبط وزيادة على ذلك P وربما
+
+195
+00:20:22,010 --> 00:20:27,190
+C كمان تمام لما اقول ان في عندي function F of T
+
+196
+00:20:27,190 --> 00:20:34,570
+ماذا تعني F of T ناقص ال C علم انه C positive ايه
+
+197
+00:20:34,570 --> 00:20:37,630
+زيها يعني بنعمل لل function shift
+
+198
+00:20:42,220 --> 00:20:59,000
+يبقى هذه إزاحة جهة اليمين بمقدار C يبقى
+
+199
+00:20:59,000 --> 00:21:02,700
+هذه الـG عبارة عن shift للدالة اليمين
+
+200
+00:21:06,030 --> 00:21:12,230
+طب ماهي رأيك و هذي بقدر أصيغها صياغة أخرى ممكن أخد
+
+201
+00:21:12,230 --> 00:21:17,990
+f of t ناقص c عامل مشترك برا من الكل بنفع ولا لا؟
+
+202
+00:21:17,990 --> 00:21:22,310
+بصير هنا zero زي ما هو هنا جداش لأن ال f of t
+
+203
+00:21:22,310 --> 00:21:26,110
+ناقصه ضرب ال zero ب zero في ولا حد بتطلع هذي
+
+204
+00:21:26,110 --> 00:21:31,630
+بالضبط تماما يعني هذي بقدر أقول بالضبط هي عبارة عن
+
+205
+00:21:31,630 --> 00:21:39,150
+fof T ناقص الـC أحد أمرين، يا إما Zero لما T أقل
+
+206
+00:21:39,150 --> 00:21:45,010
+من C، يا إما واحد لما T أكبر من أو تساوي C، صحيح
+
+207
+00:21:45,010 --> 00:21:51,850
+ولا لا؟ طيب، ممتاز، هذه هها، هي حد ذاتها هذه، مين
+
+208
+00:21:51,850 --> 00:21:57,300
+هي؟الـ unit step function يعني معناه هذا الكلام
+
+209
+00:21:57,300 --> 00:22:07,420
+بقدر اكتب هذه U C of T في ال F of T ناقص ال C يبقى
+
+210
+00:22:07,420 --> 00:22:13,140
+G of T صغرها صياغة أخرى غير الصياغة اللي عندنا هذه
+
+211
+00:22:13,140 --> 00:22:18,440
+روحت قلت هي ال unit step function U C of T مضروبة
+
+212
+00:22:18,440 --> 00:22:29,350
+في ال Fمعلومة مهمة لها ما بعدها نأخذ
+
+213
+00:22:29,350 --> 00:22:32,810
+بعض الخواص لـ plus transform
+
+214
+00:23:04,510 --> 00:23:10,660
+الكتاب حاطط القواص على شكل نظريتينأنا هخلهم نظرية
+
+215
+00:23:10,660 --> 00:23:15,660
+واحدة بس بنقطتين عشان ما نكررش الكلام اكتر فجباجي
+
+216
+00:23:15,660 --> 00:23:26,980
+بقول هنا F F of S هو لبلاس ترانسفورم لدالة F of T
+
+217
+00:23:26,980 --> 00:23:37,220
+ماله هذا exists لو كان هذا موجود forS which is
+
+218
+00:23:37,220 --> 00:23:44,740
+greater than C و C دائما و أبدا ما لها موجبة than
+
+219
+00:23:44,740 --> 00:23:56,600
+النقطة الأولى لابلاس ترانسفورم ل UC of T في ال F
+
+220
+00:23:56,600 --> 00:24:04,100
+of Tناقص الـ C في ال F of T ناقص الـ C يبقى هذا
+
+221
+00:24:04,100 --> 00:24:12,700
+يسوي E أس ناقص CS فاهمين؟ في لابلاس ترانسفورم للـ
+
+222
+00:24:12,700 --> 00:24:20,240
+F of T و اللي بده يسوي E أس ناقص CS في capital F
+
+223
+00:24:20,240 --> 00:24:25,020
+of S وهذه سمونيها رقم 1
+
+224
+00:24:27,700 --> 00:24:33,480
+ممكن اعمل عملية عكسية اخد معكوس ل place transform
+
+225
+00:24:33,480 --> 00:24:38,900
+للدل هذي يبقى مين بدي يعطيني الدل بين القوسين يبقى
+
+226
+00:24:38,900 --> 00:24:50,890
+لو قلتلكوا converselyعلى العكس لأبلاس انفرس لمن؟
+
+227
+00:24:50,890 --> 00:24:58,150
+لل E أصناع ال CS في capital F of S بده يساوي من
+
+228
+00:24:58,150 --> 00:25:02,350
+لأبلاس انفرس ل لأبلاس هذه لأبلاس انفرس مع لأبلاس
+
+229
+00:25:02,350 --> 00:25:06,350
+هتلقوا بعضها بظالمين الدالة اللي عندها دي فجأة ده
+
+230
+00:25:06,350 --> 00:25:18,430
+بده يساوي UC of Tفى ال F of T ناقص ال C تمام
+
+231
+00:25:18,430 --> 00:25:24,480
+نيجى الآن للنقطة الثانيةالنقطة الثانية بيقول لبلاس
+
+232
+00:25:24,480 --> 00:25:34,180
+ترانس فورب لل E of C في T فال F of T فال F of T
+
+233
+00:25:34,180 --> 00:25:44,000
+بده ساوي ال F of S ناقص ال C والS greater than C
+
+234
+00:25:44,000 --> 00:25:46,920
+وإلا كمان ال S
+
+235
+00:25:50,450 --> 00:25:57,670
+لو عملت العملية العكسية يبقى هنا conversely
+
+236
+00:26:00,350 --> 00:26:09,270
+لابلاس انفرس لمين ليه capital F of S ناقص ال C بده
+
+237
+00:26:09,270 --> 00:26:18,890
+يساوي E of CT في ال F of T بالشكل اللي عندنا سميلي
+
+238
+00:26:18,890 --> 00:26:24,480
+هذه رقم اتنينيبقى واحد واثنين هما النقطتين
+
+239
+00:26:24,480 --> 00:26:28,860
+الأساسيتين تبعات النظريتين اللى عندنا فى الكتاب
+
+240
+00:26:28,860 --> 00:26:35,520
+بنا نرجع لكل واحدة فىهم ونروح نبرهن صحتها و بعدين
+
+241
+00:26:35,520 --> 00:26:42,900
+نستخدمها كخواص يحل المسائل المختلفة ال proof
+
+242
+00:26:54,670 --> 00:26:55,870
+هذه هي النقطة الأولى
+
+243
+00:26:58,620 --> 00:27:05,820
+لو كان لبلاس ترانسفورم لدالة exist then لبلاس
+
+244
+00:27:05,820 --> 00:27:10,920
+ترانسفورم لهذه الدالة بعد ما عمل لها shift مضروبا
+
+245
+00:27:10,920 --> 00:27:16,000
+في ال U C of T بيسوي E وصناعة ال CS في لبلاس ال F
+
+246
+00:27:16,000 --> 00:27:20,600
+of T او ان شئتم فقولوا E وصناعة ال CS فهمين في
+
+247
+00:27:20,600 --> 00:27:26,150
+capital F of S يبقى انا بالدرجة اخدله منين؟الدالة
+
+248
+00:27:26,150 --> 00:27:30,270
+اللى عندنا هذه فباجي بقوله انا بدي اخد Laplace
+
+249
+00:27:30,270 --> 00:27:37,930
+transform ل U C of T فمين فى ال F of T ناقص ال C
+
+250
+00:27:37,930 --> 00:27:43,110
+بدي اعرف انه هل هو القيمة اللى هناك و الله ما هيشى
+
+251
+00:27:43,520 --> 00:27:47,500
+بقوله كويس بدي ارجع لتعريف ال class transform اللي
+
+252
+00:27:47,500 --> 00:27:52,020
+اتعلمناه يبقى هذا integration من zero لغاية
+
+253
+00:27:52,020 --> 00:28:02,000
+infinity ل E أس ناقص ST فاهمين؟ في ال U C of
+
+254
+00:28:02,000 --> 00:28:11,430
+T في ال F of T ناقص ال C كله ديتمام ال unit step
+
+255
+00:28:11,430 --> 00:28:17,370
+function عبارة عن جزء اما صفريا اما كدهش واحد
+
+256
+00:28:17,370 --> 00:28:22,410
+ممتاز جدا اذا هذه بدها تساوي integration من zero
+
+257
+00:28:22,410 --> 00:28:31,670
+لل C لل E أُس ناقص ST في zero في ال F of T ناقص ال
+
+258
+00:28:31,670 --> 00:28:38,230
+C في DT زائد integration من C إلى infinity لل E
+
+259
+00:28:38,230 --> 00:28:46,270
+أُس ناقص ST في واحد في ال F of T ناقص ال C DTيبقى
+
+260
+00:28:46,270 --> 00:28:49,750
+شيلت ال unit step function وحطيتها مرة بزيرو على
+
+261
+00:28:49,750 --> 00:28:55,190
+الفترة من zero ل C ومرة بواحد من C لغاية infinity
+
+262
+00:28:55,190 --> 00:29:00,790
+ال term الأول هذا ماله Zero معاه سلامة نيجي لل
+
+263
+00:29:00,790 --> 00:29:04,770
+term التان اللي عندنا هذا يبقى هذا الكلام بده
+
+264
+00:29:04,770 --> 00:29:12,310
+يساوي integration من C لغاية infinity لل E أس ناقص
+
+265
+00:29:12,310 --> 00:29:18,510
+STفى الـ F of T ناقص الـ C فى DT
+
+266
+00:29:27,760 --> 00:29:33,480
+إذا بدى اعتبر هذا كله بمين بمتغير جديد، إذا بدى
+
+267
+00:29:33,480 --> 00:29:37,320
+أعمل تعويض زي ما كنا بنعوض عادي في التكاملات
+
+268
+00:29:37,320 --> 00:29:41,340
+العادية integration by substitution إذا أنا لو
+
+269
+00:29:41,340 --> 00:29:54,090
+روحت حطيت ال eta تساوي تساوي T ناقص Cيبقى دي إي تا
+
+270
+00:29:54,090 --> 00:30:00,070
+بده يساوي دي تي والسي ما هو مقدار ثابت مش تكتب مين
+
+271
+00:30:00,070 --> 00:30:06,790
+بزيرو تمام؟ هذا المثل ها دي هتصبح على الشكل التالي
+
+272
+00:30:06,790 --> 00:30:13,050
+يبقى صار ل plus transform ل U C as a function of T
+
+273
+00:30:13,050 --> 00:30:20,530
+في ال F of T ناقص ال C بده يساوي تكاملتعالى نشوف
+
+274
+00:30:20,530 --> 00:30:28,930
+هنا يبقى E أس ناقص S نجي لمين التي قدشتي يا بنات
+
+275
+00:30:28,930 --> 00:30:39,250
+إيتا زائد C يبقى هذه بإيتا زائد C إيتا زائد C طبعا
+
+276
+00:30:39,250 --> 00:30:49,400
+الان هذه F of إيتا ال D تيب دي إيتاطبعاً ضالمين عن
+
+277
+00:30:49,400 --> 00:30:56,410
+حدود التكامل باجي بقول لو كانت T ب Infinityيبقى
+
+278
+00:30:56,410 --> 00:31:02,470
+بإي تا infinity ناقص يعني infinity يبقى بقى الحد
+
+279
+00:31:02,470 --> 00:31:09,510
+العلوي كما هو الآن لو كان الحد ال T تساوي ال C
+
+280
+00:31:09,510 --> 00:31:15,350
+بيصير C ناقص C لو ب Zero يبقى إي تا تساوي قداش
+
+281
+00:31:15,350 --> 00:31:20,910
+تساوي Zero تمام تمام يبقى هذا تكمل من Zero ل
+
+282
+00:31:20,910 --> 00:31:30,760
+Infinityهذا بنات E أس ناقص S إيتاه زائد في إيمين
+
+283
+00:31:30,760 --> 00:31:39,740
+في E أس ناقص CS في ال F of إيتاه في D إيتاه،
+
+284
+00:31:39,740 --> 00:31:46,230
+مظبوط؟ هذا إيه اللي هو علاقة بالتكامل؟ماليش علاقش
+
+285
+00:31:46,230 --> 00:31:50,530
+في إيته يبقى هذا مقدار ثابت تشرفنا برا يبقى هذا
+
+286
+00:31:50,530 --> 00:32:00,270
+بيصير E أس ناقص CS CS تكامل من Zero ل Infinity ل E
+
+287
+00:32:00,270 --> 00:32:10,150
+أس ناقص S إيته في ال F of إيته في D إيته طب إيش
+
+288
+00:32:10,150 --> 00:32:16,180
+رايكوا هذا مين يا بنات تعريف مين؟Laplace transform
+
+289
+00:32:16,180 --> 00:32:22,480
+لدالة F of Eta يعني مين له capital F of S صحيح ولا
+
+290
+00:32:22,480 --> 00:32:28,800
+لأ؟يعني هدا بقول له E أصناق ال CS في Laplace
+
+291
+00:32:28,800 --> 00:32:35,560
+transform لل F of Eta تمام؟ اللي هو مين؟ capital F
+
+292
+00:32:35,560 --> 00:32:42,920
+of S يبقى E أصناق ال CS في capital F of S أظن و هو
+
+293
+00:32:42,920 --> 00:32:43,720
+المطلوب؟
+
+294
+00:32:52,490 --> 00:33:01,130
+أذا اثبتنا المطلوب الأول جالي conversely يعني خد
+
+295
+00:33:01,130 --> 00:33:04,790
+ال plus inverse هنا بده يسوي ال plus inverse هنا
+
+296
+00:33:04,790 --> 00:33:09,310
+تماما باجي بقوله الآن بده اجي لل conversely بتاعته
+
+297
+00:33:10,030 --> 00:33:17,330
+يبقى بدأ أخد Laplace inverse لمين؟ لLaplace ل U C
+
+298
+00:33:17,330 --> 00:33:23,690
+of T في F of T ناقص C بده يسوي Laplace inverse
+
+299
+00:33:23,690 --> 00:33:29,270
+لنتيجة اللي طلعت عندنا هذه E أس ناقص CS في capital
+
+300
+00:33:29,270 --> 00:33:37,690
+F of Sطبعا يبقى بناء علي أسار ل class inverse لمن؟
+
+301
+00:33:37,690 --> 00:33:47,790
+لل E أس ناقص CS في capital F of S بده يساوي UC of
+
+302
+00:33:47,790 --> 00:33:56,250
+T في F of T ناقص C طيب إيش رأيك هذه موجودة عندك في
+
+303
+00:33:56,250 --> 00:34:01,090
+الجدول؟ موجودة؟
+
+304
+00:34:05,760 --> 00:34:12,740
+رقم كم؟ رقم تلتاشر اللي هو شبهها بالضبط تماما. هذا
+
+305
+00:34:12,740 --> 00:34:16,840
+يالي و إيه أصناق ال CS في capital F of S يبقى هذه
+
+306
+00:34:16,840 --> 00:34:20,980
+تلتاشر اللي عندك وين في الجدولة اللي احنا أثبتناها
+
+307
+00:34:20,980 --> 00:34:26,260
+عمليا. هذه هي النقطة الأولى.بنجي لمين للنقطة
+
+308
+00:34:26,260 --> 00:34:30,800
+الثانية؟النقوة الثانية قال اللي بده ل plus
+
+309
+00:34:30,800 --> 00:34:39,660
+transform ل ال E أصناع ال CT لل F of T بالشكل اللي
+
+310
+00:34:39,660 --> 00:34:45,600
+عندنايبقى نروح لتعريف لابلاسي ترانسفورم لتعريف
+
+311
+00:34:45,600 --> 00:34:50,660
+لابلاسي ترانسفورم اذا بد النتيجة تقضع F of S ناقص
+
+312
+00:34:50,660 --> 00:34:56,840
+الـC E of CT بالموجب وليست بالثالث تمام؟ يبقى هذه
+
+313
+00:34:56,840 --> 00:35:03,640
+بدها تساوي تكامل من Zero ل Infinity لل E أُس ناقص
+
+314
+00:35:03,640 --> 00:35:10,800
+ST في مين؟ في الدالة اللي عندنا هذه E of CTفى ال F
+
+315
+00:35:10,800 --> 00:35:12,580
+of T فى ال DT
+
+316
+00:35:15,340 --> 00:35:20,180
+يبقى هذه بدها تساوي integration من zero إلى
+
+317
+00:35:20,180 --> 00:35:26,100
+infinity هذا الأساسات زي بعض يبقى عند الضرب تجمع
+
+318
+00:35:26,100 --> 00:35:35,920
+الأسس يبقى هذا الكلام بد يساوي E في ناقص S ناقص C
+
+319
+00:35:35,920 --> 00:35:39,940
+في T في F of T DT
+
+320
+00:35:48,130 --> 00:35:54,770
+هذا هو تعريف لبلاس ترانسفورم للدالة اللى عندنا
+
+321
+00:35:54,770 --> 00:36:00,490
+اللى هى ال F of D بس بشرط مش F of S ال S أجاب
+
+322
+00:36:00,490 --> 00:36:05,070
+دالها مين؟ S ناقص ال Cيبقى من خلال ال definition
+
+323
+00:36:05,070 --> 00:36:11,650
+تبع لبلاس ترانسفورم هذا بده يساوي لو capital F of
+
+324
+00:36:11,650 --> 00:36:17,810
+S ناقص ال C من تعريف لبلاس ترانسفورم لمين لهذه
+
+325
+00:36:17,810 --> 00:36:23,710
+الدالة الان الان العملية اللي هو conversely بقدر
+
+326
+00:36:23,710 --> 00:36:28,930
+اخد لبلاس ترانسفورم لمين للطرفين يبقى باجي بقوله
+
+327
+00:36:28,930 --> 00:36:31,130
+conversely
+
+328
+00:36:32,420 --> 00:36:41,580
+Laplace inverse لمن؟ لcapital F of S ناقص الـC بده
+
+329
+00:36:41,580 --> 00:36:45,660
+يساوي Laplace inverse لLaplace بتلغيها بظلمين
+
+330
+00:36:45,660 --> 00:36:53,520
+الدالة اللي في النص اللي هو E أس CT E أس S CT في
+
+331
+00:36:53,520 --> 00:37:00,080
+من؟ في ال F of T اظن لو اطلعت في الجدوة الموجودة
+
+332
+00:37:00,080 --> 00:37:05,560
+هذه برضهاللي هي رقم قداش يا بنات طلعلي في الجدول
+
+333
+00:37:05,560 --> 00:37:11,800
+اللي بين إيداكي اربعتاش يبقى هي سعرب بتقول رقم
+
+334
+00:37:11,800 --> 00:37:18,040
+اربعتاش مظبوط يبقى دي رقم اربعتاش ال F of S ناقص
+
+335
+00:37:18,040 --> 00:37:24,860
+من ناقص ال C الان شطرتنا كيف نستخدم النقطتين
+
+336
+00:37:24,860 --> 00:37:30,730
+الاتنين اللي عندنا دول في حل المسائل المختلفةيبقى
+
+337
+00:37:30,730 --> 00:37:38,190
+الآن بدنا هذه رقم واحد هذه تماما وبدنا رقم اتنين
+
+338
+00:37:38,190 --> 00:37:43,010
+هذه نكون ملمين ابهم ومن خلالهم بدنا نحاول نحل
+
+339
+00:37:43,010 --> 00:37:50,230
+أمثلة مختلفة بأشكال مختلفة كما ستراهن بعد أن
+
+340
+00:37:50,230 --> 00:37:54,410
+انتهينا من برهان النظرية بدنا نيجي ناخد بعض
+
+341
+00:37:54,410 --> 00:38:00,500
+الأمثلة حد بدها العمود هذاأنا بدى أترك العمود هنا
+
+342
+00:38:00,500 --> 00:38:23,740
+مش هالاتنين هدول لازمات هنا example
+
+343
+00:38:23,740 --> 00:38:24,800
+one
+
+344
+00:38:28,570 --> 00:38:35,730
+أول مثال بقول compute the following compute the
+
+345
+00:38:35,730 --> 00:38:45,770
+following عسبي لي ما يأتي نمرة a بدلا plus
+
+346
+00:38:45,770 --> 00:38:55,490
+transform ل U اتنين by as a function of T لصيني T
+
+347
+00:39:02,750 --> 00:39:07,870
+يبقى باجي بطلع و بيدحل هذه المثلة يبقى باجي بقوله
+
+348
+00:39:07,870 --> 00:39:14,130
+و ال U C of T هي في F of T ناقص ال C مقدار ال
+
+349
+00:39:14,130 --> 00:39:18,950
+shift اللي هنا هو المقدار تبع ال U C بالضبط تماما
+
+350
+00:39:18,950 --> 00:39:24,570
+باجي بطلع في مثلتي اتنين by هنا ماعنديش اتنين by
+
+351
+00:39:25,010 --> 00:39:30,890
+مظبوط؟ اه لكن طلب لبلاس ترانسفورم بقول انا هاه لو
+
+352
+00:39:30,890 --> 00:39:36,550
+قدرت احطها على الصيغة هذه بجهي الجواب عندي مظبوط
+
+353
+00:39:36,550 --> 00:39:42,250
+برجع لذاكرة من الوراق sign T periodic function
+
+354
+00:39:42,250 --> 00:39:47,610
+يعني ده اللي دورية كل قداش تتكرر الدورة كل اتنين
+
+355
+00:39:47,610 --> 00:39:53,760
+by يعني لو اضفت اتنين by او طرحت اتنين byلا تتغير
+
+356
+00:39:53,760 --> 00:39:58,260
+قيمة الـ function على الإطلاق تمام؟ يبقى باجي
+
+357
+00:39:58,260 --> 00:40:05,500
+بقوله solution اتدالى
+
+358
+00:40:05,500 --> 00:40:10,420
+Laplace transform ل U اتنين by as a function of T
+
+359
+00:40:10,420 --> 00:40:16,300
+لصينة T بده يساوي Laplace transform ل U اتنين by
+
+360
+00:40:16,300 --> 00:40:22,920
+as a function of Tلصين تي زائد او ناقص اللي بدك
+
+361
+00:40:22,920 --> 00:40:27,600
+اياها اتنين باي لكن احنا نعيش بالزمن هنا تبقى ناقص
+
+362
+00:40:27,600 --> 00:40:31,620
+يبقى زائد مش لازمالي يبقى بطرح اللي دورة كاملة
+
+363
+00:40:31,620 --> 00:40:37,320
+اتنين باي بالشكل اللي عندناإذا صرت هذه ها هي الشكل
+
+364
+00:40:37,320 --> 00:40:42,460
+اللي عندنا هذا بالضبط صحيح ولا لأ إذا الجواب E أس
+
+365
+00:40:42,460 --> 00:40:49,060
+ناقص CS يبقى automatic من part one الجواب E أس
+
+366
+00:40:49,060 --> 00:40:58,600
+ناقص C بإتنين by Sفي مين؟ في لبلاس ترانسفورم لل F
+
+367
+00:40:58,600 --> 00:41:05,460
+of T هذه F of T ناقص اتنين باي يبقى shift انسى
+
+368
+00:41:05,460 --> 00:41:11,980
+يبقى في لبلاس ترانسفورم لل F of T اللي هي صيني T
+
+369
+00:41:16,290 --> 00:41:23,090
+هذا الكلام بده يساوي الو E أس ناقص اتنين by S بده
+
+370
+00:41:23,090 --> 00:41:28,670
+لفلس لصينة T بروح على الجدول تمام باجي على الجدول
+
+371
+00:41:28,670 --> 00:41:34,630
+الصين T طبعا اللي هي رقم خمسة ل A على S تربيع زائد
+
+372
+00:41:34,630 --> 00:41:42,280
+A تربيعأيه عندي هنا بقداش؟ بواحد يبقى في واحد على
+
+373
+00:41:42,280 --> 00:41:47,720
+S تربيع زائد واحد تربيع الهمين بواحد يبقى النتيجة
+
+374
+00:41:47,720 --> 00:41:54,600
+E اص ناقص اتنين by S على S تربيع زائد واحد
+
+375
+00:41:57,900 --> 00:42:03,000
+يبقى هذه النظرية ريحتني بدل لسه أشيل ال UCT و
+
+376
+00:42:03,000 --> 00:42:07,100
+أحطها مرة ب Zero و مرة بواحد و أضرب فيه و أس ناقص
+
+377
+00:42:07,100 --> 00:42:12,250
+CT و E و أس اتنين Tفي الـ signet و لسه اعمل
+
+378
+00:42:12,250 --> 00:42:16,730
+integration by parts مرتين لأجبتها في سطرين بدل ما
+
+379
+00:42:16,730 --> 00:42:20,130
+بدي بدي صفحة كاملة وجهة في سطرين إذا النظرية هذه
+
+380
+00:42:20,130 --> 00:42:26,510
+سهلتلي عملية حساب لف لاس ترانسفورم للدوال المختلفة
+
+381
+00:42:26,510 --> 00:42:30,790
+طبعا هذا السؤال يعتبر سؤالا مباشرا ده في لف ولا
+
+382
+00:42:30,790 --> 00:42:38,010
+دوران تمامنتقل شوية Laplace transform بدنا لمين ل
+
+383
+00:42:38,010 --> 00:42:48,910
+U by of T لصينة T أقوله
+
+384
+00:42:48,910 --> 00:42:56,910
+كويس هذا الكلام بده يسمى Laplace transform لمين ل
+
+385
+00:42:56,910 --> 00:43:04,470
+U by as a function of Tهذه بدّيها تكون لو كانت T
+
+386
+00:43:04,470 --> 00:43:11,750
+ناقص باي لكان مشكلة محلولة تمام ماقدرش أحط T ناقص
+
+387
+00:43:11,750 --> 00:43:18,270
+باي مباشرة إلا إذا كنت عارف قداش نتيجتها لكن أنا
+
+388
+00:43:18,270 --> 00:43:22,750
+مش عارف لو بدي أحط T ناقص ال باي بقول أه بدي أقول
+
+389
+00:43:22,750 --> 00:43:31,950
+sin T cos باينقص cosine t sin pi تطلع فعلا sin t
+
+390
+00:43:31,950 --> 00:43:37,890
+بس بإشارة قدر سالم نسيت القانون هذا يبقى ضيعة
+
+391
+00:43:37,890 --> 00:43:42,310
+المسألة تمام؟ لا هو ضيقة المسألة ولا حاجة نعمل
+
+392
+00:43:42,310 --> 00:43:50,270
+عملية تحايل كيف عملية تحايل؟ بقول هذه sin t ناقص
+
+393
+00:43:50,270 --> 00:43:56,890
+2pi مافيها مشكلة هذه اظن هذه عملناها فوقانا بديش
+
+394
+00:43:56,890 --> 00:44:01,290
+بدي باي بديش اتنين باي بقول بسيط يا اخي تدبر حالك
+
+395
+00:44:01,290 --> 00:44:08,790
+فبعدين بقول هذه لابلاس ترانسفورم ليه باي of T في
+
+396
+00:44:08,790 --> 00:44:19,870
+مين في ال sign T ناقص باي ناقص باي مش بنفعك يبقى
+
+397
+00:44:19,870 --> 00:44:26,420
+ناقص باي لدالة اللي عندنالو جبتها من الأول و قلت
+
+398
+00:44:26,420 --> 00:44:32,040
+سالب sin t ناقص by ماعناش مشكلة بقولك صحيح طيب
+
+399
+00:44:32,040 --> 00:44:38,100
+الان لما عملناها بالشكل هذا هذه كأنه هذه زاوية و
+
+400
+00:44:38,100 --> 00:44:43,380
+هذه زاوية تانية إذا بقدر أفكها كاش ل sin زاويتها
+
+401
+00:44:43,380 --> 00:44:48,820
+يبقى هذه ل plus transform ل you by as a function
+
+402
+00:44:48,820 --> 00:44:58,630
+of t في sinت ناقص ال by في cosine ال by وصلنا
+
+403
+00:44:58,630 --> 00:45:10,150
+للناقص يبقى cosine ت ناقص ال by في main في sign ال
+
+404
+00:45:10,150 --> 00:45:10,570
+by
+
+405
+00:45:13,530 --> 00:45:18,550
+بقول انا مرة تانية لو بدل ما سويتك لو بدل هذه حطيت
+
+406
+00:45:18,550 --> 00:45:23,410
+T ناقص باي وحطيت اشارة سالب برا نفس النتيجة ماعنا
+
+407
+00:45:23,410 --> 00:45:27,570
+مشكلة واحنا هنا سنوصلها قداش sign ال bye يا بناتي
+
+408
+00:45:27,570 --> 00:45:32,590
+يبقى ال term هذا اجر الفات حالي قداش cosine 180
+
+409
+00:45:33,380 --> 00:45:38,060
+سالب واحد يبقى بيضل سالب sign يبقى أسارة هذه هي
+
+410
+00:45:38,060 --> 00:45:47,300
+عبارة عن هذه هي عبارة عن ل plus transform لمن ل U
+
+411
+00:45:47,300 --> 00:45:56,400
+by of T في من في سالب sign T ناقص by بالشكل اللي
+
+412
+00:45:56,400 --> 00:46:03,480
+عندناأظن اللينيار يبقى السالب هذا بقوله شرفنا برا
+
+413
+00:46:03,480 --> 00:46:11,400
+يبقى هاي سالب ل place transform ل U باي of T ل
+
+414
+00:46:11,400 --> 00:46:17,940
+sign اللي هو T ناقص باي الشكل اللي عندنا هذا أظن
+
+415
+00:46:17,940 --> 00:46:20,660
+صارت هذه هي صيغة رقم واحد اللي هناك
+
+416
+00:46:25,960 --> 00:46:35,800
+يبقى هذا السالب اللي برا وهذا E أس ناقص C في S بدي
+
+417
+00:46:35,800 --> 00:46:42,700
+لبلاس ترانسفورم لمين لصينة T في لبلاس ترانسفورم
+
+418
+00:46:42,700 --> 00:46:50,760
+لصينة Tوهذه وجدناها قبل قليل من الجدول يبقى ناقص E
+
+419
+00:46:50,760 --> 00:46:58,460
+أس ناقص CS على S تربيع زائد واحد كما كانت في نمرة
+
+420
+00:46:58,460 --> 00:47:12,440
+B طيب
+
+421
+00:47:12,440 --> 00:47:23,910
+نمرة Cنمر الـ C بدلا بلاس ترانسفورم لمن؟ لـ 2T
+
+422
+00:47:23,910 --> 00:47:34,210
+زائد 3 في U1 of T بالشكل اللي عندنا، solution
+
+423
+00:47:40,720 --> 00:47:47,600
+أنا عندي هنا لو كان ال T ناقص واحد و هنا U one of
+
+424
+00:47:47,600 --> 00:47:51,700
+T كان قصتي محلولة بس إيش عندي؟ عندي اتنين T و
+
+425
+00:47:51,700 --> 00:47:55,700
+تلاتة يعني لا هي T على شجة ولا حتى واحد على شجة
+
+426
+00:47:55,700 --> 00:48:01,460
+لكن دبر حالك، اظبط أمورك بحيث فعلا نوصل لمين
+
+427
+00:48:01,460 --> 00:48:04,400
+للصيغة اللي قدامنا هذه إذا وصلنا للصيغة هذه بصير
+
+428
+00:48:04,400 --> 00:48:09,470
+قصتنا بسيطة جدا قلصبقول له ماشي هذه Laplace
+
+429
+00:48:09,470 --> 00:48:16,150
+transform لدالة اتنين T زائد تلاتة في ال U one of
+
+430
+00:48:16,150 --> 00:48:22,530
+T بده يساوي Laplace transform ليه؟ مكان اتنين T
+
+431
+00:48:22,530 --> 00:48:28,850
+بده يخلق الهمين بده يخلق اتنين T ناقص واحد فبقى
+
+432
+00:48:28,850 --> 00:48:35,710
+بيقول لو كتبت اتنين T ناقص اتنين اضفت للمعادلة
+
+433
+00:48:35,710 --> 00:48:36,430
+جداش؟
+
+434
+00:48:42,520 --> 00:48:51,520
+تنين T ناقص اتنين زائد خمسة تنين T زائد تلاتة
+
+435
+00:49:00,860 --> 00:49:04,620
+بقول له تمام و الله ماعقول العفرة دي ضرورية دي
+
+436
+00:49:04,620 --> 00:49:09,620
+ربالك مشان اوصل مسألة لصورة من النظرية حتى اقدر
+
+437
+00:49:09,620 --> 00:49:14,200
+اطبقها اكبراجي بقول هذا الكلام يساوي لبلاسي
+
+438
+00:49:14,200 --> 00:49:20,020
+ترانسفورم ليه؟ لو خدت اتنين عامل مشرك بضل قداش؟ت
+
+439
+00:49:20,020 --> 00:49:27,640
+ناقص واحد في مين في ال U1 as a function of T زائد
+
+440
+00:49:27,640 --> 00:49:35,400
+خمسة في ال U1 of T بالشكل اللي عندنا طبعا الحين
+
+441
+00:49:35,400 --> 00:49:39,000
+هذا لابلس تترانسوفوم لينيار فانكشن
+
+442
+00:49:46,380 --> 00:49:53,420
+يبقى هذا الكلام يسوى اتنين Laplace transform ل T
+
+443
+00:49:53,420 --> 00:50:02,380
+ناقص واحد في U1 of T زائد خمسة Laplace transform ل
+
+444
+00:50:02,380 --> 00:50:10,380
+U1 of Tطبعا يبقى هذا الكلام يساوي اتنين بالدالي
+
+445
+00:50:10,380 --> 00:50:16,080
+لبلايس ترانسفورم للمثال اللي عندنا يبقى هي U C of
+
+446
+00:50:16,080 --> 00:50:22,560
+T اللي هو بقداش U واحد وهنا F of T ناقص ال C ال F
+
+447
+00:50:22,560 --> 00:50:27,450
+of T هي T بس معمولة لشيء في جهة اليمين بمقدارإذا
+
+448
+00:50:27,450 --> 00:50:34,130
+هذه قداش ما تحطن يا بنات اتنين في اي أس ناقص واحد
+
+449
+00:50:34,130 --> 00:50:42,430
+في اس تمام في لابلاسي transform لمين التي يبقى هذه
+
+450
+00:50:42,430 --> 00:50:47,350
+أصلها قبل ال shift هو عبارة عن مينعبارة عن T بجهاد
+
+451
+00:50:47,350 --> 00:50:54,190
+ال F of T خلصنا منها زائد من زائد خمسة لأ
+
+452
+00:50:54,190 --> 00:50:59,310
+بلاسترانسفارم ل U one of T حسبناها توسع ل U C of T
+
+453
+00:50:59,310 --> 00:51:04,970
+فقولنا هنا زائد خمسة E أس ناقص CS
+
+454
+00:51:12,410 --> 00:51:19,290
+طيب نجي لهذه يبقى اتنين اي اس ناقص اس لكلاس
+
+455
+00:51:19,290 --> 00:51:25,880
+ترانسفورم لاتيمن الجدول واحد factorial على مين؟
+
+456
+00:51:25,880 --> 00:51:33,600
+على S تربية يبقى هذه واحد factorial على S تربية
+
+457
+00:51:33,600 --> 00:51:40,040
+اللي هي من الجدول رقم كده؟ تلاتة، رقم تلاتة من
+
+458
+00:51:40,040 --> 00:51:47,710
+الجدول، بس ان عندي مقداش بواحد، صحيحبنضل هنا زائد
+
+459
+00:51:47,710 --> 00:51:57,110
+خمسة E أس ناقص S على مين على S أو لو رح نرتبناها
+
+460
+00:51:57,110 --> 00:52:07,010
+بنقول اتنين E أس ناقص S على S تربيع زائد خمسة E أس
+
+461
+00:52:07,010 --> 00:52:13,950
+ناقص S على S هذا لأ plus ال transform لمين لهذه ال
+
+462
+00:52:13,950 --> 00:52:14,690
+function
+
+463
+00:52:29,140 --> 00:52:39,740
+بناخد كمان نقطة يبقى نمر دي نمر دي بدنا laplace
+
+464
+00:52:39,740 --> 00:52:48,060
+transform لتي ناقص ثلاثةفى ال U اتنين as a
+
+465
+00:52:48,060 --> 00:52:56,760
+function of T ناقص T ناقص اتنين ثمين فى ال U تلاتة
+
+466
+00:52:56,760 --> 00:53:10,900
+as a function of T يبقى
+
+467
+00:53:10,900 --> 00:53:15,380
+بدى عرف جديش ال F لسه transform لمينلهذه الدلة
+
+468
+00:53:15,380 --> 00:53:20,200
+بقوله بسيطة جدا بطلع الرقم اللي هنا بختلف عن الرقم
+
+469
+00:53:20,200 --> 00:53:24,460
+اتنين عكس بعض و هنا عكس بعض اتنين اللي كانت برا
+
+470
+00:53:24,460 --> 00:53:28,580
+صارت جوه و اللي جوه ايش اللي قعدت برا تدبر حالك
+
+471
+00:53:28,580 --> 00:53:33,540
+اعمل اي عمل رياضي بحت تتخلى الرقم اللي جوه زي
+
+472
+00:53:33,540 --> 00:53:38,800
+الرقم اللي برا تمام فباجي بقول هذه la place
+
+473
+00:53:38,800 --> 00:53:45,690
+transform ليه هذه ايش بكتبها بناتنقص اتنين ناقص
+
+474
+00:53:45,690 --> 00:53:50,230
+واحد ماعنديش مشكلة في هذه الحالة يبقى ل T ناقص
+
+475
+00:53:50,230 --> 00:53:57,890
+اتنين ناقص واحد في ال U اتنين of T وصلنا ناقص هذه
+
+476
+00:53:57,890 --> 00:54:04,090
+بنفس الطريقة بدي اضيف واحد و اطرح واحد يمشي بالصير
+
+477
+00:54:04,090 --> 00:54:11,530
+T ناقص تلاتة زائد واحد في U تلاتة as a function of
+
+478
+00:54:11,530 --> 00:54:18,890
+Tطيب هذه بتاخدها مع بعض و تضرب في U2 يبقى Laplace
+
+479
+00:54:18,890 --> 00:54:24,390
+transform ل T ناقص اتنين في U2 of T
+
+480
+00:54:31,820 --> 00:54:39,040
+ناقص T ناقص تلاتة في ال U تلاتة of T ناقص في زائد
+
+481
+00:54:39,040 --> 00:54:46,860
+بناقص U تلاتة as a function of T الان لابلس هذه ال
+
+482
+00:54:46,860 --> 00:54:50,080
+linear function
+
+483
+00:54:50,400 --> 00:54:58,600
+لا بلس لمين لت ناقص اتنين ل U اتنين of T ناقص لا
+
+484
+00:54:58,600 --> 00:55:05,700
+بلس transform ل U اتنين of T ناقص لا بلس transform
+
+485
+00:55:05,700 --> 00:55:14,000
+ل T ناقص تلاتة ل U تلاتة as a function of T ناقص
+
+486
+00:55:14,000 --> 00:55:20,780
+لا بلس transform ل U تلاتة as a function of Tيبقى
+
+487
+00:55:20,780 --> 00:55:25,080
+هذا الكلام يساوي أظن هذه هي النظرية اللي فوق هناك
+
+488
+00:55:25,080 --> 00:55:33,040
+حرفيا تمام يبقى النتيجة EOS ناقص CS يعني EOS ناقص
+
+489
+00:55:33,040 --> 00:55:42,160
+اتنين S في Laplace ترانسفورم لمين؟ ل T لدلة قبل ال
+
+490
+00:55:42,160 --> 00:55:49,510
+shift يبقى Laplace ترانسفورم ل T ناقصهذه جاهزة
+
+491
+00:55:49,510 --> 00:55:57,830
+اللي هو قداشر منها E أس ناقص اتنين S على S حسبناها
+
+492
+00:55:57,830 --> 00:56:02,570
+اول تالت مثال اليوم بعد مثلنا الرسم حسبناها ل plus
+
+493
+00:56:02,570 --> 00:56:08,610
+ل U C of T قد ما يكون C بها يكون قيمة موجبةبنجي
+
+494
+00:56:08,610 --> 00:56:13,550
+اللي بعدها يبقى وصلنا لناقص هذي الـC عندك بقداش؟
+
+495
+00:56:13,550 --> 00:56:21,730
+بتلاتة يبقى E أُس ناقص تلاتة S ثمين في لابلاس
+
+496
+00:56:21,730 --> 00:56:29,810
+ترانسفورم لدلة قبل ال shiftهذه ناقص E أس ناقص
+
+497
+00:56:29,810 --> 00:56:36,710
+تلاتة S على مين؟ على S إذاً هذه بدها تساوي E أس
+
+498
+00:56:36,710 --> 00:56:42,170
+ناقص اتنين S هذه واحد factorial على مين؟ على S
+
+499
+00:56:42,170 --> 00:56:47,720
+تربية يعني يبقى على S تربية دوريوهذه ناقص E وناقص
+
+500
+00:56:47,720 --> 00:56:55,540
+2S على S وهذه ناقص E أس ناقص تلاتة S على S تربية
+
+501
+00:56:55,540 --> 00:57:02,320
+كذلك وهذه ناقص E أس ناقص تلاتة S على S
+
+502
+00:57:17,780 --> 00:57:24,060
+يبقى هذا النوع الأول من أنواع الأمثلة بدنا نيجي
+
+503
+00:57:24,060 --> 00:57:27,700
+لنوعتين يبقى example two
+
+504
+00:57:46,110 --> 00:57:52,450
+Example 2 Find Laplace
+
+505
+00:57:52,450 --> 00:58:01,750
+Transform For
+
+506
+00:58:01,750 --> 00:58:09,390
+The Following Functions
+
+507
+00:58:16,040 --> 00:58:23,280
+الـ F of T بده يساوي مين؟ بده يساوي أحد أمرين يا
+
+508
+00:58:23,280 --> 00:58:31,940
+إما Zero لما T أقل من الواحد يا إما T تربيع ناقص
+
+509
+00:58:31,940 --> 00:58:43,220
+اتنين T زائد اتنين ناقص اتنين T زائد اتنين لما T
+
+510
+00:58:45,100 --> 00:58:54,820
+أكبر من أو تساوي من أو تساوي الواحد قال
+
+511
+00:58:54,820 --> 00:58:57,700
+لي هاتي لي بلاسة transform للدالة اللي عندنا هنا
+
+512
+00:58:57,700 --> 00:59:07,340
+بقول له solution سي
+
+513
+00:59:07,340 --> 00:59:11,680
+عندنا هنا بقدر شمانات يبقى بدي shift هنا بمقدار
+
+514
+00:59:11,680 --> 00:59:18,030
+كده؟ مقدار واحدأنا لازم أخلق
+
+515
+00:59:18,030 --> 00:59:23,170
+في المسألة shift بمقدار واحد اذا بروح بقوله f of t
+
+516
+00:59:23,170 --> 00:59:28,430
+بدي أعيد صياغتها على الشكل التالي يا إما zero لما
+
+517
+00:59:28,430 --> 00:59:34,510
+ت أقل من واحد يا إما ت تربية نقص اتنين تجداش بده
+
+518
+00:59:34,510 --> 00:59:39,810
+لما أصير مربع كامليبقى الواحد بياخده من عندي
+
+519
+00:59:39,810 --> 00:59:43,990
+الجيران يبقى الواحد يبقى الواحد يبقى الواحد يبقى
+
+520
+00:59:43,990 --> 00:59:44,230
+الواحد يبقى الواحد يبقى الواحد يبقى الواحد يبقى
+
+521
+00:59:44,230 --> 00:59:45,830
+الواحد يبقى الواحد يبقى الواحد يبقى الواحد يبقى
+
+522
+00:59:45,830 --> 00:59:47,090
+الواحد يبقى الواحد يبقى الواحد يبقى الواحد يبقى
+
+523
+00:59:47,090 --> 00:59:47,930
+الواحد يبقى الواحد يبقى الواحد يبقى الواحد يبقى
+
+524
+00:59:47,930 --> 00:59:48,950
+الواحد يبقى الواحد يبقى الواحد يبقى الواحد يبقى
+
+525
+00:59:48,950 --> 00:59:53,890
+الواحد يبقى الواحد يبقى الواحد يبقى الواحد يبقى
+
+526
+00:59:53,890 --> 01:00:01,890
+الواحد يبقى الواحد يبقالـ T ناقص واحد لكل تربية
+
+527
+01:00:01,890 --> 01:00:08,630
+يبقى هذه T ناقص واحد لكل تربية زائد واحد لما T
+
+528
+01:00:08,630 --> 01:00:16,150
+greater than or equal to one طيب
+
+529
+01:00:16,150 --> 01:00:22,850
+أليست هذهبقدر اكتبها على شكل ال unit step function
+
+530
+01:00:22,850 --> 01:00:29,210
+صحيح ولا لأ يعني هذه بقدر اكتب الدالة اللي عناها
+
+531
+01:00:29,210 --> 01:00:34,950
+دي في ال U1 of T يعني هذه بقدر اكتبها على الشكل
+
+532
+01:00:34,950 --> 01:00:43,630
+التالي U1 as a function of T في من؟ في ال T ناقص
+
+533
+01:00:43,630 --> 01:00:52,350
+واحد لكل تربيع زائد واحدالسؤال قال لي هاتي Laplace
+
+534
+01:00:52,350 --> 01:00:56,750
+transform لهذه الدالة، إذا الأن بقدر أجد له
+
+535
+01:00:56,750 --> 01:01:02,590
+Laplace transform لأنه غيرت شكل ال function الأصلي
+
+536
+01:01:02,590 --> 01:01:08,810
+بالشكل المكافئ له المتعرف عليه طبق النظرية اللي
+
+537
+01:01:08,810 --> 01:01:14,320
+عندنايبقى انا لو أخدت لبلاس ترانسفورم لل F of T
+
+538
+01:01:14,320 --> 01:01:18,980
+بدي يساوي لبلاس ترانسفورم لمين؟ لدلة اللي عندنا
+
+539
+01:01:18,980 --> 01:01:25,660
+هذه يبقى بناء عليه لبلاس ترانسفورم لدلة F of T بدي
+
+540
+01:01:25,660 --> 01:01:32,740
+يساوي لبلاس ترانسفورم لمين؟ لل U1 as a function of
+
+541
+01:01:32,740 --> 01:01:40,980
+T في T الناقص واحد لكل تربية زائد واحد هيجفلناUC
+
+542
+01:01:40,980 --> 01:01:47,300
+of T فى F of T ناقص الـC يبقى EOS ناقص S فى لبلاس
+
+543
+01:01:47,300 --> 01:01:53,480
+للـF of T قبل الـShift يبقى هذا إيش؟ هذا بيبقى
+
+544
+01:01:53,480 --> 01:02:01,360
+تساوي مين؟ بيبقى تساوي EOS ناقص واحد فى S لناقص CS
+
+545
+01:02:01,360 --> 01:02:07,600
+يبقى بناقص S فى لبلاس يترانسفورم لدلة قبل الـShift
+
+546
+01:02:07,600 --> 01:02:12,970
+مين الدلة قبل الـShift؟T تربية زائد واحد يبقى هذه
+
+547
+01:02:12,970 --> 01:02:18,190
+T تربية زائد واحد بالشكل اللي عندنا هذا طيب هذا
+
+548
+01:02:18,190 --> 01:02:23,850
+الكلام يساوي E أص ناقص S فيه هذه Laplace فده عبارة
+
+549
+01:02:23,850 --> 01:02:28,350
+عن Laplace للأول زائد Laplace للثاني لأنها Linear
+
+550
+01:02:28,350 --> 01:02:35,670
+يبقى Laplace ل T تربية زائد Laplace للواحد بالشكل
+
+551
+01:02:35,670 --> 01:02:42,820
+اللي عندنا هذايبقى هذه ناقص S يوس ناقص S فيه نجي ل
+
+552
+01:02:42,820 --> 01:02:49,780
+T ترابيع من الجدوة الرقم تلاتة ثم يبقى هذه اتنين
+
+553
+01:02:49,780 --> 01:02:56,700
+factorial على S تكيب زي الواحد اللي هو واحد على S
+
+554
+01:02:56,700 --> 01:03:02,560
+عملناها قبل هيك واحد على S بالشكل اللي عندنايعني
+
+555
+01:03:02,560 --> 01:03:10,540
+كأن النتيجة هي اتنين E أس ناقص S على S تكيب زائد E
+
+556
+01:03:10,540 --> 01:03:13,200
+أس ناقص S على S
+
+557
+01:03:32,870 --> 01:03:39,590
+نمر بيه بيقول ال F of T بدها تسوي أحد ثلاثة أمور
+
+558
+01:03:39,590 --> 01:03:49,270
+يا إما Zero لما T أقل من باي يا إما T ناقص باي لما
+
+559
+01:03:49,270 --> 01:03:55,990
+T أكبر من أو يسوي بايه أقل من اتنين باي يا إما
+
+560
+01:03:55,990 --> 01:04:01,390
+Zero لما T greater than or equal to two pi
+
+561
+01:04:22,140 --> 01:04:29,140
+مش جزءين زي المثلة اللي فاتت بسهولة، لأ هذه ثلاثة
+
+562
+01:04:29,140 --> 01:04:33,880
+أجزاءوانا مشان اجيبلها ل placid transform بدي
+
+563
+01:04:33,880 --> 01:04:41,840
+اكتبها بدلالة unit step function اله u c of t بقول
+
+564
+01:04:41,840 --> 01:04:46,280
+okay بدي اكتبها بال unit step functionهذه مش
+
+565
+01:04:46,280 --> 01:04:50,680
+مباشرة زيها دي هذيك خدت هذيك عمل مشترك وضرب في UC
+
+566
+01:04:50,680 --> 01:04:55,980
+و كتير لو يطلع الدوري اذا انا بدأ افكر تفكيري كويس
+
+567
+01:04:55,980 --> 01:05:00,120
+طبعا من حلال ال domain تبع الدالة دي ملاحظة انه
+
+568
+01:05:00,120 --> 01:05:05,300
+جسمها لكم فترةلثلاث فترات من zero ل by و من by ل
+
+569
+01:05:05,300 --> 01:05:09,380
+اتنين by و من اتنين by ل infinity يعني لازم يطلع
+
+570
+01:05:09,380 --> 01:05:15,820
+في المثل عندى u by of t و u اتنين by of t مظبوط
+
+571
+01:05:15,820 --> 01:05:20,920
+يبقى هى استنتجته ل واحدة من خلال من من خلال شكل
+
+572
+01:05:20,920 --> 01:05:26,240
+الدلال طيب تعالوا نتفهم هيك و نشوف على شكل لو روحت
+
+573
+01:05:26,240 --> 01:05:32,580
+مدام u by و u اتنين byوالـ pi باجت في الأول و 2pi
+
+574
+01:05:32,580 --> 01:05:38,680
+في الآخر باجي لو قلت له consider خد لي هيك اللي هو
+
+575
+01:05:38,680 --> 01:05:47,300
+u pi of t ناقص u2pi as a function of t وشوف لقداش
+
+576
+01:05:47,300 --> 01:05:52,780
+هذول بدهم يزاوز لو طرحت لاتنين من بعض على مين على
+
+577
+01:05:52,780 --> 01:05:57,680
+التلت فترات هذه انشوف شو بتعطيني باجي بقوله والله
+
+578
+01:05:57,680 --> 01:05:58,340
+كويس
+
+579
+01:06:05,460 --> 01:06:14,420
+عندما تبقى T أقل من Y تبقى T نقص
+
+580
+01:06:15,630 --> 01:06:21,850
+طيب بدنا نيجي ناخد الفترة T اكبر من او يساوي باي و
+
+581
+01:06:21,850 --> 01:06:29,530
+اقل من اتنين باي قداش قيمة ال U باي واحد تمام يبقى
+
+582
+01:06:29,530 --> 01:06:36,840
+هذه واحد ناقص ال U اتنين بايتمام التمام طيب بداجي
+
+583
+01:06:36,840 --> 01:06:42,500
+الان T اكبر من او يسوى اتنين باي جداش قيمة الدالة
+
+584
+01:06:42,500 --> 01:06:50,090
+الاولى والتانية يعني واحد ناقص واحديبقى صورة هذه
+
+585
+01:06:50,090 --> 01:06:58,210
+ال U by ماقص U2 by كله as a function of T و as a
+
+586
+01:06:58,210 --> 01:07:04,950
+function of T يبقى هذه ال U by as a function of T
+
+587
+01:07:04,950 --> 01:07:12,070
+ماقص U2 by as a function of T يساوي أحد ثلاثة أمور
+
+588
+01:07:12,480 --> 01:07:20,060
+يا اما zero لما T اقل من باي، يا اما واحد لما T
+
+589
+01:07:20,060 --> 01:07:25,940
+اكبر من او يساوي باي و اقل من اتنين باي، يا اما
+
+590
+01:07:25,940 --> 01:07:32,460
+zero لما T greater than or equal to two باي بقول
+
+591
+01:07:32,460 --> 01:07:36,540
+كويس، طب احنا جيبنا الفرق طلع هدول، ايش بتفرج هدي
+
+592
+01:07:36,540 --> 01:07:44,590
+عن اللي فوق؟لو ضربت اللي فوق في T ناقص باي تطلع
+
+593
+01:07:44,590 --> 01:07:50,910
+هذه هذي طيب ممتاز إذا هروح أضرب الطرفين في T ناقص
+
+594
+01:07:50,910 --> 01:07:57,730
+باي إذا لو ضربت في T ناقص باي بيصير U باي of T في
+
+595
+01:07:57,730 --> 01:08:07,310
+T ناقص البي ناقص U2 باي as a function of Tفى T
+
+596
+01:08:07,310 --> 01:08:14,750
+ناقص الـ Pi كله بده يساوي ما يتيه يا إما Zero لما
+
+597
+01:08:14,750 --> 01:08:22,230
+T أقل من Pi يا إما T ناقص Pi لما T أكبر من أو
+
+598
+01:08:22,230 --> 01:08:28,410
+يساوي Pi و أقل من 2 Pi يا إما Zero لما T greater
+
+599
+01:08:28,410 --> 01:08:35,810
+than or equal to 2 Piمظبوط يبقى عملت عملية تحايل
+
+600
+01:08:35,810 --> 01:08:40,770
+على مين على ال function اللي أعطاها لهذه و جبتها
+
+601
+01:08:40,770 --> 01:08:45,050
+روحت بدللة مين ال U باي و U اتنين باي إذا لابلاس
+
+602
+01:08:45,050 --> 01:08:50,750
+ترانسفورم لهذه الدلة هو لابلاس ترانسفورم لمين لهذه
+
+603
+01:08:50,750 --> 01:08:54,730
+الدلة و مش عارف يمكن لسه بدأ فبركة كمانويمكن جهزة
+
+604
+01:08:54,730 --> 01:08:59,410
+الله أعلم إذا بدنا نروح ناخد the place transform
+
+605
+01:08:59,410 --> 01:09:05,150
+لمين لهذه الدالة أظن نمسح عارفين الحين صارنا الشغل
+
+606
+01:09:05,150 --> 01:09:05,770
+هذه؟
+
+607
+01:09:16,950 --> 01:09:26,710
+طيب إذا أصار عندي لبلاس transform لدلة f of t بده
+
+608
+01:09:26,710 --> 01:09:36,390
+يسوى لبلاس transform لمن؟ ل U بي of T في T ناقص بي
+
+609
+01:09:37,240 --> 01:09:48,120
+ناقص U2 باي as a function of T فمين؟ في T ناقص باي
+
+610
+01:09:48,120 --> 01:09:53,100
+الشكل اللي عالي هناتمام تمام لابلاس هو linear
+
+611
+01:09:53,100 --> 01:09:56,100
+function هو هيخش على ال term الأول و هيخش على ال
+
+612
+01:09:56,100 --> 01:10:04,300
+term التاني يبقى هذا لابلاس transform ل U by of T
+
+613
+01:10:04,300 --> 01:10:14,180
+في T ناقص ال by ناقص لابلاس transform ل U اتنين by
+
+614
+01:10:14,180 --> 01:10:19,560
+as a function of T بس هذه لابلاس مش هتظبط معاها
+
+615
+01:10:20,420 --> 01:10:28,360
+يعني بدها فشون يعمل؟ بنضيف باي و بنطرح باي تمام
+
+616
+01:10:28,360 --> 01:10:36,980
+يبقى هذه بقدر اقول في تي ناقص اتنين باي زائد باي
+
+617
+01:10:36,980 --> 01:10:46,790
+كلها يقفلناهذه المرحلة ستكون مين؟ او هذه المعروفة
+
+618
+01:10:46,790 --> 01:10:56,550
+اي اس ناقص by اس في ال place transform لمين؟ لـT
+
+619
+01:10:56,550 --> 01:11:04,160
+قبل ال shiftتمام هذه يا بنات هجزئها إلى جزئين يبقى
+
+620
+01:11:04,160 --> 01:11:10,640
+ناقص ل plus transform ل U2 by as a function of T
+
+621
+01:11:10,640 --> 01:11:22,760
+في T ناقص اتنين by ناقص by في U2 U2 by as a
+
+622
+01:11:22,760 --> 01:11:30,410
+function of T بالشكل اللي قلناطيب هدى E أس ناقص by
+
+623
+01:11:30,410 --> 01:11:37,190
+S هدى اللى واحد factorial على S تربيع من الجدول
+
+624
+01:11:37,190 --> 01:11:46,350
+اللى بعدها هدى نفس القصة لأمين A أس سالب اتنين by
+
+625
+01:11:46,350 --> 01:11:56,780
+S في لك less transform لدالها قبل ال shiftهذا بي
+
+626
+01:11:56,780 --> 01:12:02,480
+مقدار ثابت ليس لديه دعوة برا لبلاس يبقى ناقص بي في
+
+627
+01:12:02,480 --> 01:12:11,220
+لبلاس ال transform ل U2 بي as a function of T هذا
+
+628
+01:12:11,220 --> 01:12:20,020
+يسوى E أس ناقص بي S على S تربيع هذا بنفس الطريقة E
+
+629
+01:12:20,020 --> 01:12:32,120
+أس ناقص 2 بي S على S تربيعناقص باي وهذه EOS ناقص
+
+630
+01:12:32,120 --> 01:12:39,560
+اتنين by S على Sيبقى هاي قدرنا نعمل تحوير يا عم
+
+631
+01:12:39,560 --> 01:12:44,720
+السؤال اللى تجيلي شوية دى ربانى يعنى كل سؤال مدلة
+
+632
+01:12:44,720 --> 01:12:49,260
+مجزة من جزئيا من تلاتة من أربعة جد ما يكون بتروح
+
+633
+01:12:49,260 --> 01:12:55,200
+اكتبها بدلالة ال U C of T حسب التجزيق اللى عندي لو
+
+634
+01:12:55,200 --> 01:12:59,340
+كان جزة واحد اتنين تلاتة بيبدأ أقوله U one و بعدين
+
+635
+01:12:59,340 --> 01:13:04,170
+U two و بعدين U threeوشوف كيف بما يناسب طبيعة مين
+
+636
+01:13:04,170 --> 01:13:09,170
+طبيعة المصنع يبقى هاي جيبنا Laplace transform لهذه
+
+637
+01:13:09,170 --> 01:13:14,030
+الدوال طيب بدي أعمل عملية عكسية شو العملية
+
+638
+01:13:14,030 --> 01:13:18,550
+العكسية؟ مش هنتقل سابقا نقول conversely نجيب معكس
+
+639
+01:13:18,550 --> 01:13:23,130
+Laplace transform بدي أعطي Laplace transform لبعض
+
+640
+01:13:23,130 --> 01:13:31,020
+الدوال و أعرف ما هو أصل هذه الدوالطبعا يبقى مثال
+
+641
+01:13:31,020 --> 01:13:40,580
+رقم كده ايش؟ تلاتة مثال رقم تلاتة find the
+
+642
+01:13:40,580 --> 01:13:54,240
+inverse of the plus transform of
+
+643
+01:13:54,240 --> 01:13:56,780
+the
+
+644
+01:13:58,190 --> 01:14:02,890
+following functions
+
+645
+01:14:02,890 --> 01:14:07,010
+نمر
+
+646
+01:14:07,010 --> 01:14:18,350
+ايه؟ capital F of S بده يساوي E اص ناقص اتنين S
+
+647
+01:14:18,350 --> 01:14:26,630
+على مين؟ على S تربيع زائد ال S ناقص اتنين
+
+648
+01:14:37,230 --> 01:14:43,070
+عشان نحاول نستفيد من جدول اللي قدامنا بقدر الإمكان
+
+649
+01:14:43,070 --> 01:14:46,950
+طبعا لو أروح الجدول بشوفش ولا شغل زي هيك بلاقيش
+
+650
+01:14:46,950 --> 01:14:48,670
+ولا حاجة زي هيك بالشكل هذا
+
+651
+01:15:00,200 --> 01:15:09,460
+هذا واحد على هذه لو حللته كحاصل ضرب قوسين يبقى هنا
+
+652
+01:15:09,460 --> 01:15:18,040
+S هنا S هنا واحد هنا اتنين هنا زائد هنا ناقص ناقص
+
+653
+01:15:18,040 --> 01:15:24,460
+S بزائد اتنين S بظل زائد S بعد هيك بدى اروح اعمل
+
+654
+01:15:24,460 --> 01:15:29,750
+partial fraction لهذهوهي قصور جزية بحيث أفصلها
+
+655
+01:15:29,750 --> 01:15:34,250
+هائلة، لماذا؟ لأنه أنا ماعرفش ل place لحصل ضرب
+
+656
+01:15:34,250 --> 01:15:38,530
+قيمتين، ماخدنهاش، مانعرفهاش، تمام؟ إذن بدل ما هي
+
+657
+01:15:38,530 --> 01:15:42,930
+ضرب بدي أخليها مجموعة، جمع يعني كأنه هنا موحدة،
+
+658
+01:15:42,930 --> 01:15:47,340
+مقدرة، عاملة ومشتركةبدي أردها إلى أصلها قبل أخذ
+
+659
+01:15:47,340 --> 01:15:53,000
+العامل المشترك بقوله بسيطة المقام محلل إلى أبسط
+
+660
+01:15:53,000 --> 01:15:58,780
+العوامل الأولية والأقواس are different ولا واحد زي
+
+661
+01:15:58,780 --> 01:16:04,030
+التاني وكل واحد فيهم من الدرجات الأولىفبروح بقول
+
+662
+01:16:04,030 --> 01:16:12,230
+له هذه واحد على S ناقص واحد في S زائد اتنين يساوي
+
+663
+01:16:12,230 --> 01:16:18,310
+constant على الجوس الاول constant تاني على الجوس
+
+664
+01:16:18,310 --> 01:16:23,670
+التاني بعد هيك بروح اضرب في المقام تبع الطرف
+
+665
+01:16:23,670 --> 01:16:29,050
+الشمال زي ما كنا بنعمل في calculus بيبقى الواحد
+
+666
+01:16:29,050 --> 01:16:30,810
+بده يساوي A
+
+667
+01:16:38,930 --> 01:16:45,910
+يبقى بطل يصير عندنا كثور وانما صارت كل المسألة في
+
+668
+01:16:45,910 --> 01:16:46,710
+البصد
+
+669
+01:17:01,440 --> 01:17:09,100
+طيب حط قيم ل S من عندك فباجي بقول لو كانت ال S
+
+670
+01:17:09,100 --> 01:17:16,900
+تساوي واحد then الواحد بده يساوي تلاتة A يبقى
+
+671
+01:17:16,900 --> 01:17:24,300
+تلاتة A ومنها ال A تساوي قدراش تساوي طول الان لو
+
+672
+01:17:24,300 --> 01:17:31,170
+كانت ال S تساوي ناقص اتنيننقص اتنين يبقى تقير ال a
+
+673
+01:17:31,170 --> 01:17:39,170
+وبظل then الواحد يسوى ناقص تلاتة b ناقص اتنين ناقص
+
+674
+01:17:39,170 --> 01:17:46,510
+واحد يكون ناقص تلاتة b ومنها b تسوى كم؟ سالب تلت
+
+675
+01:17:46,510 --> 01:17:54,950
+اذا صار capital F of S أصبح على الشكل التاليوين هو
+
+676
+01:17:54,950 --> 01:17:59,290
+ايه؟ هذا بدي استبدله بمين؟ بالمقدار اللي عندنا
+
+677
+01:17:59,290 --> 01:18:05,150
+يبقى بدي جيني هنا تلت و هنا سالب تلت يبقى هذا تلت
+
+678
+01:18:05,150 --> 01:18:11,270
+خديه برا عام المشترك بيظل E أس ناقص اتنين S في
+
+679
+01:18:11,270 --> 01:18:20,590
+جداش في واحد على S ناقص واحد ناقص واحد على S زائد
+
+680
+01:18:20,590 --> 01:18:29,260
+اتنينيعني ايه؟ يعني هذا تلت في E أس ناقص اتنين S
+
+681
+01:18:29,260 --> 01:18:38,400
+في واحد على S ناقص الواحد ناقص تلت في E أس ناقص
+
+682
+01:18:38,400 --> 01:18:43,680
+اتنين S في واحد على S زائد اتنين
+
+683
+01:18:49,000 --> 01:18:54,480
+نرجع لمين؟ نرجع للنظرية تبعتنا اللى كنا نشتغل
+
+684
+01:18:54,480 --> 01:18:59,740
+عليها اللى روحناها مسحناها طلعينا النظرية مرة
+
+685
+01:18:59,740 --> 01:19:08,630
+تانيةشوفي ليش بيقول هنا طبعا
+
+686
+01:19:08,630 --> 01:19:16,510
+عندك EOS ناقص 2S في capital F of S هذه بتروح اردها
+
+687
+01:19:16,510 --> 01:19:20,870
+لمين للمعكوس تبعها طلعيلي في كلمة conversely
+
+688
+01:19:20,870 --> 01:19:27,590
+للنقطة الأولى عندك ل plus inverse ل EOS ناقص CS في
+
+689
+01:19:27,590 --> 01:19:35,230
+capital F of SUC of T في F of T ناقص الـC
+
+690
+01:19:56,010 --> 01:20:03,690
+تلت صف على شجة بدي ل plus inverse لمن؟ لل E أس
+
+691
+01:20:03,690 --> 01:20:11,090
+ناقص اتنين S واحد على S ناقص الواحد ناقص تلت ل
+
+692
+01:20:11,090 --> 01:20:19,010
+plus inverse لمن؟ ل E أس ناقص اتنين S واحد على S
+
+693
+01:20:19,010 --> 01:20:23,890
+زائد اتنين هذا الكلام بده يساوي هاي تلت
+
+694
+01:20:29,720 --> 01:20:33,880
+النقطة الأولى المعكوزة تبعها اللى على اليمين ل
+
+695
+01:20:33,880 --> 01:20:40,000
+plus inverse ل E أسنق ال CS في capital F of S هي
+
+696
+01:20:40,000 --> 01:20:46,180
+capital F of S وهي E أسنق ال CS يبقى بده أرجعها
+
+697
+01:20:46,180 --> 01:20:51,320
+لمن؟ إلى أصلها يبقى أصلها شو بده يكون يا بنت؟ U C
+
+698
+01:20:51,320 --> 01:21:00,080
+of T C عندي هنا في قداشيبقى انا بقول U2 as a
+
+699
+01:21:00,080 --> 01:21:08,240
+function of T طيب هذي مين؟ هذي E أس T بس بدي اعمل
+
+700
+01:21:08,240 --> 01:21:17,360
+لها shift بمقدار كتير لتنين يبقى E أس T ناقص اتنين
+
+701
+01:21:17,360 --> 01:21:26,220
+مرة تانيةأفتحي بافترك على النظرية، يلّا فارجي على
+
+702
+01:21:26,220 --> 01:21:31,390
+ثلاث صفحات للخلف، والله أربعةالنظرية بتقول لـPlus
+
+703
+01:21:31,390 --> 01:21:36,450
+لـUC of T للـF of T ناقصة C والساوي E أثناق الـCs
+
+704
+01:21:36,450 --> 01:21:42,770
+في كابتل F of S احنا اللي موجود عند مين E أثناق
+
+705
+01:21:42,770 --> 01:21:49,110
+الـCs في كابتل F of S إذن بتدرجع على الأصل تبعها
+
+706
+01:21:49,110 --> 01:21:53,110
+قبل ناخد Laplace transform فباخد Laplace inverse
+
+707
+01:21:53,110 --> 01:21:59,410
+للطرفينيبقى بالاسفل ان لأ plus inverse لإي أس ناقص
+
+708
+01:21:59,410 --> 01:22:10,620
+CS في capital F of Sهذه لـ F of S و هذه E أُس ناقص
+
+709
+01:22:10,620 --> 01:22:14,700
+CS بالدرجة العاصلة يبقى الـ C عندى هنا بقداش
+
+710
+01:22:14,700 --> 01:22:22,340
+بإتمام يبقى بقوله تلت U2 of T هذه E أُس T لكن هو
+
+711
+01:22:22,340 --> 01:22:27,500
+قال لي F of T ناقص الـ C يبقى بدي أعمل الـ Shift
+
+712
+01:22:27,500 --> 01:22:35,610
+مقدار الـ C فبقول T ناقص 2 واضحة؟اللي عملناها لهذه
+
+713
+01:22:35,610 --> 01:22:42,850
+هعملها للتانية يبقى هاي كمان ناقص طول طلّها لهذه
+
+714
+01:22:42,850 --> 01:22:51,710
+يس ناقص اتنين اس يبقى U اتنين as a function of T
+
+715
+01:22:52,300 --> 01:22:57,980
+تمام؟ ضال plus لهذه ده رجع على أصلها، شو أصلها؟
+
+716
+01:22:57,980 --> 01:23:05,600
+EOS ناقص اتنين T و بدي اخد ناقص اتنين shift منها،
+
+717
+01:23:05,600 --> 01:23:10,280
+يبقاش بصير EOS،
+
+718
+01:23:10,280 --> 01:23:17,280
+هدف الأصل ناقص اتنين Tمظبوط او لا اذا بدي اعمل لها
+
+719
+01:23:17,280 --> 01:23:21,940
+shift بمقدار كده مقدار اتنين كمان نفس النتيجة اللي
+
+720
+01:23:21,940 --> 01:23:27,000
+احنا احنا عملناها لها يبقى لما نعمل ال shift اللي
+
+721
+01:23:27,000 --> 01:23:32,680
+عندنا هذا لها بيبقى تصير على مين على الشكل التالي
+
+722
+01:23:32,680 --> 01:23:41,760
+اللي هو مين اللي هو E أس ناقص اتنين Tنقص بيصير
+
+723
+01:23:41,760 --> 01:23:48,440
+زائد اتنين لماذا؟ لأنه في الأصل ناقص يبقى ناقص
+
+724
+01:23:48,440 --> 01:23:56,100
+يبقى ناقص يبقى ناقص
+
+725
+01:23:56,100 --> 01:23:59,920
+يبقى ناقص يبقى ناقص يبقى ناقص يبقى ناقص يبقى ناقص
+
+726
+01:23:59,920 --> 01:24:06,000
+يبقى ناقص يبقى ناقص يبقى ناقص يبقى ناقص يبقى ناقص
+
+727
+01:24:06,000 --> 01:24:09,500
+يبقى ناقص يبقى ناقص يبقى ناقص يبقى ناقص يبقى ناقص
+
+728
+01:24:09,500 --> 01:24:09,500
+يبقى ناقص يبقى ناقص يبقى ناقص يبقى ناقص يبقى ناقص
+
+729
+01:24:09,500 --> 01:24:09,620
+يبقى ناقص يبقى
+
+730
+01:24:14,570 --> 01:24:18,190
+لأ، لأ، لأ، في غلطة يا بنات، في غلطة، في غلطة،
+
+731
+01:24:18,190 --> 01:24:24,390
+الغلطة كيف؟ ان هذه ناقص اتنين، وهنا بدأ اقول T
+
+732
+01:24:24,390 --> 01:24:29,530
+زائد اتنين، بصير اربع، يعني هذه زائد اربع وليست
+
+733
+01:24:29,530 --> 01:24:35,480
+اتنين، لما ناخد اتنين، بصير T ناقص اتنينيعني القصة
+
+734
+01:24:35,480 --> 01:24:38,660
+اللي هنا هو نفس القصة اللي بين قصين هنا بالضبط
+
+735
+01:24:38,660 --> 01:24:44,020
+تماما، تمام؟ بس اجعله قداش اللي هو سالب اتنين، مرة
+
+736
+01:24:44,020 --> 01:24:49,420
+تانية بتعيدهامرة تانية بدأينا هذه الدالة قبل ال
+
+737
+01:24:49,420 --> 01:24:55,780
+shift اللي هو قد ياش E أس ناقص اتنين تمام ال T بدي
+
+738
+01:24:55,780 --> 01:25:01,120
+اعمل لها ال shift بمقدار اتنين يبقى بالداجي اقوله
+
+739
+01:25:01,120 --> 01:25:07,660
+E أس ناقص اتنين في T ناقص اتنين مش هه بلاش تقولي
+
+740
+01:25:07,660 --> 01:25:12,260
+كيف هذه الأربعة أجت نصف المسمة ولا لا بقولك ايها
+
+741
+01:25:12,260 --> 01:25:19,270
+على طولهي ناقص تلت هذي دره هاي ناقص ال T و اتنين
+
+742
+01:25:19,270 --> 01:25:24,470
+of T E و ناقص اتنين ال T عندي هذي بدي اعمله ال
+
+743
+01:25:24,470 --> 01:25:30,510
+shift مقدر اتنين فبقول T ناقص اتنين مباشرة فهو
+
+744
+01:25:30,510 --> 01:25:38,790
+رايح دماغك طيب هذا كان هو السؤال الأول نمرة A بنجي
+
+745
+01:25:38,790 --> 01:25:39,610
+لنمرة V
+
+746
+01:25:48,310 --> 01:25:52,390
+خودي لنمرى بيه طبعا السؤال الأول هو السؤال
+
+747
+01:25:52,390 --> 01:25:58,610
+الاربعتاش من الكتاب نمرى بيه سؤال خمستاش من الكتاب
+
+748
+01:26:02,380 --> 01:26:09,180
+بدي أساوي اتنين في اس ناقص واحد اتنين في اس ناقص
+
+749
+01:26:09,180 --> 01:26:16,860
+واحد في اي أس ناقص اتنين اس على اس تربيع ناقص
+
+750
+01:26:16,860 --> 01:26:22,760
+اتنين اس زائد اللي هو اتنين زائد اتنين
+
+751
+01:26:32,740 --> 01:26:38,840
+بنرتب وضع المثلة قبل ايه قبل ما نبدأ الحل قبل ما
+
+752
+01:26:38,840 --> 01:26:44,220
+نبدأ معكوس لبلاي transform فباجي بقوله capital F
+
+753
+01:26:44,220 --> 01:26:50,400
+of S بده يساوي اظن ان اتنين مقدار ثابت مالوش دعوة
+
+754
+01:26:50,400 --> 01:26:56,420
+و E أس ناقص اتنين S كمان مالوش دعوة بضل عندي قداش
+
+755
+01:26:56,420 --> 01:27:03,700
+S ناقص واحد هذا بقدر اعمله ايه مربع كامليبقى S
+
+756
+01:27:03,700 --> 01:27:10,580
+تربية ناقص اتنين S زائد واحد بضل جداج زائد واحد
+
+757
+01:27:10,580 --> 01:27:15,820
+بالشكل اللي عندنا انا او بقدر اكتبها اتنين مالكش
+
+758
+01:27:15,820 --> 01:27:22,520
+دعوة E أس ناقص اتنين S فاهمين في ال S ناقص واحد
+
+759
+01:27:22,520 --> 01:27:28,940
+على S ناقص واحد لكل تربية زائد واحد بالشكل اللي
+
+760
+01:27:28,940 --> 01:27:37,790
+عندنا اناأذا بتاخد ل plus inverse ل مين؟ ل F of S
+
+761
+01:27:37,790 --> 01:27:45,710
+يساوي اتنين
+
+762
+01:27:45,710 --> 01:27:54,970
+ل plus inverse ل مين؟ ل E أثناء قصة 2Sفي ال S ناقص
+
+763
+01:27:54,970 --> 01:28:03,810
+واحد ال S ناقص واحد ناقص واحد الكل تربيع زائد واحد
+
+764
+01:28:03,810 --> 01:28:05,610
+بالشكل اللي عندنا هذا
+
+765
+01:28:13,100 --> 01:28:18,520
+بارجع لمين؟ كمان للنظرية، نرجع للنظرية تبعتنا هذه
+
+766
+01:28:18,520 --> 01:28:24,980
+مرة ثانية، اللي كنا بنشغل بهاتف والساعةأنا عندي
+
+767
+01:28:24,980 --> 01:28:31,720
+هاي E أس نقص اتنين S يبقى C يبقى 12 ب 2 هذه
+
+768
+01:28:31,720 --> 01:28:37,760
+capital F of S بدي أرجع لهذه و أشوف من أصلها من
+
+769
+01:28:37,760 --> 01:28:45,320
+وين من الجدول تمام؟ لو رجعت لهذه الدالةاللي هي ال
+
+770
+01:28:45,320 --> 01:28:48,560
+S ناقص واحد على S ناقص واحد كل تربية اللي هي عبارة
+
+771
+01:28:48,560 --> 01:28:54,060
+عن مين رقم كدهش عشرة بالضبط تماما اللي هو S ناقص
+
+772
+01:28:54,060 --> 01:28:57,220
+ال A على S ناقص L كل تربية زاد B تربية يعني ال A
+
+773
+01:28:57,220 --> 01:29:03,400
+بواحد يا بنات و ال B بواحد كذلك يبقى أصلها E أس AT
+
+774
+01:29:03,400 --> 01:29:10,480
+Cos BT يعني E أس T Cos T لإنه ال A و ال B بواحد
+
+775
+01:29:10,820 --> 01:29:16,080
+يبقى في الهام الشيخ بقول انا عند ال F of T بده
+
+776
+01:29:16,080 --> 01:29:22,600
+يساوي E أس تي كوصينة T تمام؟ لكن بدي ارجع للنظرية
+
+777
+01:29:22,600 --> 01:29:29,480
+تبعتي و اقول هذا الكلام يساوي اتنين في جداش هذه U
+
+778
+01:29:29,480 --> 01:29:34,560
+اتنين as a function of T برجع للنظرية ها تبعتنا
+
+779
+01:29:35,870 --> 01:29:42,270
+يبقى انا
+
+780
+01:29:42,270 --> 01:29:49,250
+اعمل shift لكل واحدة منهم بمقدار اتنين يبقى هذه في
+
+781
+01:29:49,250 --> 01:29:59,610
+ال E of T ناقص اتنين في cosine T ناقص اتنين كذلك
+
+782
+01:29:59,610 --> 01:30:04,310
+يبقى هي طبقت النظرية وعملت main وعملت shift اللي
+
+783
+01:30:04,310 --> 01:30:09,070
+بديهاالروح لنمرسى من المسألة
+
+784
+01:30:30,830 --> 01:30:39,370
+بيقول لي F of S نمرى C capital F of S بده يساوي
+
+785
+01:30:39,370 --> 01:30:50,350
+مين E أس ناقص S زائد E أس ناقص اتنين S ناقص E أس
+
+786
+01:30:50,350 --> 01:30:56,030
+ناقص تلاتة S ناقص E أس ناقص
+
+787
+01:31:06,240 --> 01:31:11,180
+خلّينا نعيد ترتيب المثلة قبل ما نبدأ يبقى باجي
+
+788
+01:31:11,180 --> 01:31:18,050
+بقوله solutionبعد كتابة F of S بقدر اكتبها على
+
+789
+01:31:18,050 --> 01:31:25,470
+الشكل التالف بقدر اوزع البسط على المقال يبقى هذا E
+
+790
+01:31:25,470 --> 01:31:37,680
+أس ناقص S على Sهذه زائد EOS ناقص اتنين S على من؟
+
+791
+01:31:37,680 --> 01:31:46,240
+على S هذه ناقص EOS ناقص تلاتة S على S هذه ناقص EOS
+
+792
+01:31:46,240 --> 01:31:50,540
+ناقص اربعة S على S
+
+793
+01:31:54,190 --> 01:31:59,650
+أول مثال أخدناه في جد لبلاس ترانسفورم كان لبلاس
+
+794
+01:31:59,650 --> 01:32:08,710
+ترانسفورم ل U C of T قداش طالعة؟ U أس ناقص C S على
+
+795
+01:32:08,710 --> 01:32:13,030
+S اللي هو في الجد و اللي عندنا بنات رقم قداش؟ رقم
+
+796
+01:32:13,030 --> 01:32:20,430
+12 إذا أنا بدي أطبق رقم 12 كام مرات؟ أربع مراتيبقى
+
+797
+01:32:20,430 --> 01:32:26,930
+لما يكون عندي U C of T بتشويه أصلاق C S على F يبقى
+
+798
+01:32:26,930 --> 01:32:31,650
+بناء انا عليه بتاخد Laplace inverse للطرفين يبقى
+
+799
+01:32:31,650 --> 01:32:39,450
+Laplace inverse لcapital F of Sيساوي Laplace
+
+800
+01:32:39,450 --> 01:32:46,070
+inverse لمين لل E أس ناقص S على S زائد Laplace
+
+801
+01:32:46,070 --> 01:32:53,490
+inverse لل E أس ناقص اتنين S على S معقص Laplace
+
+802
+01:32:53,490 --> 01:33:02,120
+inverse لمينللإي أس ناقص ثلاثة S على S ناقص ل plus
+
+803
+01:33:02,120 --> 01:33:09,940
+inverse للإي أس ناقص أربعة S على S يبقى ل plus
+
+804
+01:33:09,940 --> 01:33:17,360
+inverse لcapital F of S بده يساوي هذه C هنا بقداش
+
+805
+01:33:17,360 --> 01:33:25,380
+يا بنات بواحد يبقى هذه باعتبارها من U one of Tطب
+
+806
+01:33:25,380 --> 01:33:32,680
+هذه U2 of D فقط لغير مظبوط طبقا لرقم 12 اللي عندنا
+
+807
+01:33:32,680 --> 01:33:41,190
+يبقى زائد U2 as a function of D طب هذهنقص U تلاتة
+
+808
+01:33:41,190 --> 01:33:47,010
+يبقى نقص U تلاتة as a function of T لأن C تتسبب في
+
+809
+01:33:47,010 --> 01:33:54,490
+قدرات تلاتة نقص U أربعة as a function of T
+
+810
+01:33:57,330 --> 01:34:02,630
+يبقى هذا إيش اعطانكه عدة أمثلة نجيب كيف معكوس
+
+811
+01:34:02,630 --> 01:34:06,730
+Laplace transform يعني بيعطيني Laplace transform و
+
+812
+01:34:06,730 --> 01:34:11,810
+بطلب ما هو شكل الدالة الأصلي انت لو روحت خدت
+
+813
+01:34:11,810 --> 01:34:15,430
+الدالة دي و خدتي لها Laplace transform لازم يطلع
+
+814
+01:34:15,430 --> 01:34:21,390
+منين؟أو بيطلع هذا و توحدله المقام بيطلع مين بيطلع
+
+815
+01:34:21,390 --> 01:34:27,050
+ده اللي فوق لحد هنا stop بيعطيكوا العافية انتهى
+
+816
+01:34:27,050 --> 01:34:33,990
+هذا ال section إلى يكون أرقام المسائل يبقى من واحد
+
+817
+01:34:33,990 --> 01:34:42,290
+يبقى exercises ستة تلاتة من واحد لغاية اتنين و
+
+818
+01:34:42,290 --> 01:34:44,270
+تلاتين الأد
+
+819
+01:34:46,920 --> 01:34:54,240
+المحاضرة القادمة ان شاء الله تعالى اللي
+
+820
+01:34:54,240 --> 01:35:00,880
+هو اخر section اللي هو ستة اربع وبه ينتهي المقرر
+
diff --git a/PL9fwy3NUQKwa8ZDfSFGn6H8xVFLzqmCZC/6jXOnqsn_jg.srt b/PL9fwy3NUQKwa8ZDfSFGn6H8xVFLzqmCZC/6jXOnqsn_jg.srt
new file mode 100644
index 0000000000000000000000000000000000000000..fdb2e4abb48ec7b800d8c1da038a265185ca4df2
--- /dev/null
+++ b/PL9fwy3NUQKwa8ZDfSFGn6H8xVFLzqmCZC/6jXOnqsn_jg.srt
@@ -0,0 +1,3265 @@
+1
+00:00:10,220 --> 00:00:14,300
+بسم الله الرحمن الرحيم بنكمل ال section اللي 
+
+2
+00:00:14,300 --> 00:00:19,500
+ابتدأنا المرة الماضية وهى ال serious solutions يعني
+
+3
+00:00:19,500 --> 00:00:22,940
+باستخدام ال power series فابتدأنا المرة اللي فاتت 
+
+4
+00:00:22,940 --> 00:00:27,440
+بالتذكير بمعنى ال power series و ال convergence لل
+
+5
+00:00:27,440 --> 00:00:34,600
+power series في calculus B أخدنا اللي هو في نهاية
+
+6
+00:00:34,600 --> 00:00:39,880
+chapter ال power series أخدنا اللي هو ال McLaurin
+
+7
+00:00:39,880 --> 00:00:44,320
+series و ال Taylor series فكان ال Taylor series
+
+8
+00:00:44,320 --> 00:00:49,280
+على شكل ال Taylor اللي عندنا هنا يبقى بنتابع النقاط
+
+9
+00:00:49,280 --> 00:00:53,640
+الطبيعية للمرأة اللي فتحناها باجي بقوله the Taylor
+
+10
+00:00:53,640 --> 00:01:03,340
+series as summation من n equal zero to infinity
+
+11
+00:01:03,340 --> 00:01:12,060
+لمين؟ للتفاضل لرقم n عند النقطة a أو عند النقطة x
+
+12
+00:01:12,060 --> 00:01:20,200
+node لمين؟ للـ x ناقص الـ x node to the power n على n
+
+13
+00:01:20,200 --> 00:01:21,260
+factorial
+
+14
+00:01:23,260 --> 00:01:29,380
+على N factorial بالشكل اللي عندنا هذا أو بقدر
+
+15
+00:01:29,380 --> 00:01:35,700
+أحطها بالشكل المفكوك الطويل هي عبارة عن اللي هو ال
+
+16
+00:01:35,700 --> 00:01:43,720
+F of X node زائد ال F prime of X node في ال X ناقص
+
+17
+00:01:43,720 --> 00:01:50,000
+ال X node على واحد factorial زائد المشتقة الثانية
+
+18
+00:01:50,000 --> 00:01:56,200
+عند ال X node ناقص ال X node الكل تربيع على 2
+
+19
+00:01:56,200 --> 00:02:00,620
+factorial زائد زائد ونظل ماشين لغاية ما نوصل
+
+20
+00:02:00,620 --> 00:02:06,860
+للتفاضل رقم N لل X node في ال X ناقص ال X node to
+
+21
+00:02:06,860 --> 00:02:13,390
+the power N على N factorial زائد إلى آخره هذا مين
+
+22
+00:02:13,390 --> 00:02:18,490
+اللي هو Taylor series اللي قال لو كانت x node
+
+23
+00:02:18,490 --> 00:02:24,130
+يساوي زيرو بنحصل على مين؟ على McLaurin series يبقى
+
+24
+00:02:24,130 --> 00:02:32,770
+باجي بقوله هنا اف ال اكس نود تساوي زيرو we get the
+
+25
+00:02:32,770 --> 00:02:38,350
+McLaurin series
+
+26
+00:02:38,350 --> 00:02:41,230
+and
+
+27
+00:02:43,710 --> 00:02:50,890
+الشكل التالي هو summation من n equal zero to
+
+28
+00:02:50,890 --> 00:02:58,930
+infinity للتفاضل رقم N عند 0 للـ X to the power N على N
+
+29
+00:02:58,930 --> 00:03:03,350
+factorial يعني يا بنات بدي أشيل كل X node وأحط
+
+30
+00:03:03,350 --> 00:03:07,350
+مكانه 0 يبقى ال summation اللي فوق بصير على
+
+31
+00:03:07,350 --> 00:03:13,610
+الشكل اللي عندنا هذا يبقى بناء عليه هذا هيساوي F
+
+32
+00:03:13,610 --> 00:03:19,690
+of 0 زائد F prime of 0 X على 1 factorial
+
+33
+00:03:28,310 --> 00:03:38,550
+المفكوك الأول هو عبارة عن مفكوك Taylor أو متسلسلة
+
+34
+00:03:38,550 --> 00:03:44,470
+Taylor والثانية متسلسلة Maclaurin اثنين علماء في مجال
+
+35
+00:03:44,470 --> 00:03:49,240
+الرياضيات اكتشف الـTaylor العلاقة الأولى وMaclaurin
+
+36
+00:03:49,240 --> 00:03:56,160
+العلاقة الثانية وسميت باسمه ما تمام طيب شو قصة ال
+
+37
+00:03:56,160 --> 00:04:01,900
+series هذه؟ أنا بقول لك اه خدي مارك كويس أي function
+
+38
+00:04:01,900 --> 00:04:07,560
+اللي لها مالانهاية من ال derivatives بقدر أكتبها
+
+39
+00:04:07,560 --> 00:04:12,740
+على شكل Taylor series أو Maclaurin series طيب في أن
+
+40
+00:04:12,740 --> 00:04:17,620
+دوال فعلًا اللي هم مالانهاية المشتقات يعني بيكملوش
+
+41
+00:04:17,620 --> 00:04:22,340
+مثلًا تجد واحد يقول F of X يساوي X عشان عشرين،
+
+42
+00:04:22,340 --> 00:04:26,480
+بقول بعد عشرين المشتقة بتكمل المسألة هذه، الهدف
+
+43
+00:04:26,480 --> 00:04:31,050
+ماهي مشتقات للمالانهاية لكن لو أخدت F of X يساوي
+
+44
+00:04:31,050 --> 00:04:42,010
+e أوس X أو E أوس X أو Cos X أو Sin X أو Ln X أو
+
+45
+00:04:42,010 --> 00:04:48,310
+Tan inverse X أو 1 على X أو 1 على X كل هذه الدوال
+
+46
+00:04:48,310 --> 00:04:53,730
+مهما تشتقيها هي بتكملش حتى لو قلت لك x أوس نص أو
+
+47
+00:04:53,730 --> 00:04:58,790
+x أوس تلت أربع واشتق إلى مالانهاية بتخلصش نهائي
+
+48
+00:04:58,790 --> 00:05:03,030
+يبقى مثل هذه الدوال هي التي بقدر أكتبها على شكل
+
+49
+00:05:03,030 --> 00:05:08,390
+Taylor أو McLaurin series زي ما كنا بنحسب في
+
+50
+00:05:08,390 --> 00:05:12,830
+calculus بي في calculus بي اللي هو Taylor أو
+
+51
+00:05:12,830 --> 00:05:18,070
+McLaurin series للدوال المختلفة وكنا بنزهقنا أحيان
+
+52
+00:05:18,070 --> 00:05:23,640
+بشكل الحد النوني لكن in general بنجيب كل الدوال
+
+53
+00:05:23,640 --> 00:05:31,420
+اللي عندنا هذه يبقى كل دالة لها مالانهاية من
+
+54
+00:05:31,420 --> 00:05:38,060
+المشتقات يعني كل ال derivatives تبعاتها are exist
+
+55
+00:05:38,060 --> 00:05:44,280
+بقدر أكتب علي شكل Taylor series أو Maclaurin series
+
+56
+00:05:44,280 --> 00:05:53,040
+طيب إن أنا آجي لتعريف بسيط جدًا يبقى تعريف جديد هذا
+
+57
+00:05:53,040 --> 00:06:02,300
+ما شفناهوش قبل هيك يبقى باجي بقول definition a
+
+58
+00:06:02,300 --> 00:06:13,280
+function f a function f is called analytic
+
+59
+00:06:13,280 --> 00:06:17,200
+دة 
+
+60
+00:06:17,200 --> 00:06:19,880
+اللي تحليلية at
+
+61
+00:06:21,530 --> 00:06:25,810
+أو أو
+
+62
+00:06:25,810 --> 00:06:29,030
+أو
+
+63
+00:06:29,030 --> 00:06:33,410
+أو
+
+64
+00:06:33,410 --> 00:06:33,430
+أو أو أو أو أو
+
+65
+00:06:58,910 --> 00:07:04,830
+إذا كنا نستطيع أن نكتبها على شكل power series فهي 
+
+66
+00:07:04,830 --> 00:07:08,110
+F
+
+67
+00:07:08,110 --> 00:07:14,250
+of X بدي أكتبها على شكل summation من N equal zero
+
+68
+00:07:14,250 --> 00:07:21,880
+to infinity للتفاضل رقم N عند الـ x node للـ x 
+
+69
+00:07:21,880 --> 00:07:28,320
+ناقص الـ x node to the power n على n factorial
+
+70
+00:07:28,320 --> 00:07:44,240
+with radius of convergence with radius of
+
+71
+00:07:44,240 --> 00:07:47,680
+convergence
+
+72
+00:07:49,410 --> 00:07:59,970
+اللي هو راه راه greater than zero
+
+73
+00:08:12,850 --> 00:08:16,890
+تعريف هذا جديد ما شفناهوش في calculus بي على
+
+74
+00:08:16,890 --> 00:08:22,390
+الأطلاع وإنما لزمناه هنا في المعادلات التفاضلية
+
+75
+00:08:22,390 --> 00:08:26,530
+التعريف بيقول مياتي الدالة if بقدر أقول عنها
+
+76
+00:08:26,530 --> 00:08:33,490
+analytic function يعني دالة تحليلية at a point عند
+
+77
+00:08:33,490 --> 00:08:38,390
+نقطة x ساوي x node if it can be written as a power
+
+78
+00:08:38,390 --> 00:08:43,670
+series إذا جئت تكتب على شكل power series that is f
+
+79
+00:08:43,670 --> 00:08:47,670
+of x بدي أساوي summation من n equal zero to
+
+80
+00:08:47,670 --> 00:08:52,280
+infinity للتفاضل رقم n عند ال x node في الـ X نقص
+
+81
+00:08:52,280 --> 00:08:56,620
+الـ X naught to the power N على N factorial with
+
+82
+00:08:56,620 --> 00:09:00,840
+radius of convergence rho greater than zero يعني
+
+83
+00:09:00,840 --> 00:09:04,720
+أي power series المرة اللي فاتت قلنا اللي أحد
+
+84
+00:09:04,720 --> 00:09:09,000
+ثلاثة احتمالات يا إما convergence عند نقطة واحدة
+
+85
+00:09:09,000 --> 00:09:13,360
+فقط وفي هذه الحالة ال radius of convergence بده
+
+86
+00:09:13,360 --> 00:09:17,760
+يساوي zero يا إما convergence على كل ال real line
+
+87
+00:09:18,090 --> 00:09:21,110
+وبالتالي ال interval of convergence من سالب
+
+88
+00:09:21,110 --> 00:09:25,250
+infinity ل infinity وال radius of convergence بده
+
+89
+00:09:25,250 --> 00:09:26,910
+يساوي infinity
+
+90
+00:09:29,510 --> 00:09:33,810
+ممكن تبقى ال convergence على فترة و diverge خارج
+
+91
+00:09:33,810 --> 00:09:37,390
+هذه الفترة ال radius of convergence يساوي طول
+
+92
+00:09:37,390 --> 00:09:42,630
+الفترة اللي عندنا هذه وهذا كتبناه المرة الماضية
+
+93
+00:09:42,630 --> 00:09:49,390
+طيب أنا إلى خاطر أعيد صياغة التعريف بطريقة أخرى كي
+
+94
+00:09:49,390 --> 00:09:52,590
+أبقى أتصيبه بطريقة أخرى بجيب تطلع الكلام اللي عندنا
+
+95
+00:09:52,590 --> 00:09:59,060
+هذا مش هو هذا ولا لا صح؟ يبقى دا اللي بقدر أقول
+
+96
+00:09:59,060 --> 00:10:04,580
+إنها أنا analytic إذا كتبتها على صيغة Taylor series
+
+97
+00:10:04,580 --> 00:10:10,280
+أو McLaurin series صح ولا لا؟ مصبوط يبقى من انفصال
+
+98
+00:10:10,280 --> 00:10:15,580
+أن إذا بقدر أحط ال function اللي عندي على شكل صيغة
+
+99
+00:10:15,580 --> 00:10:19,840
+Taylor series أو McLaurin series إذا هي analytic
+
+100
+00:10:19,840 --> 00:10:25,890
+function كل الدوال التي ذكرتها قبل قليل هي analytic
+
+101
+00:10:25,890 --> 00:10:30,810
+functions يعني كل الدوال اللي إلها مالانهاية من
+
+102
+00:10:30,810 --> 00:10:37,170
+المشتقات هي عبارة عن analytic functions إذا Sin X
+
+103
+00:10:37,170 --> 00:10:45,270
+و Cos X و Sin X و Cos X و E أوس X و E ناقص X و Ln X و 1
+
+104
+00:10:45,270 --> 00:10:49,930
+على X و Tan inverse X كل هذه are analytic functions
+
+105
+00:10:49,930 --> 00:10:52,850
+يعني هي دوال تحليلية
+
+106
+00:10:54,680 --> 00:11:00,080
+نأخذ ملاحظة بسيطة هذه هتهمنا عند حل الكثير من
+
+107
+00:11:00,080 --> 00:11:03,440
+المسائل خلال هذا ال section وخلال ال section
+
+108
+00:11:03,440 --> 00:11:09,300
+القادم إن شاء الله اللي هتتعرضه اليوم هذه هكتبها
+
+109
+00:11:09,300 --> 00:11:16,500
+على شكل ال remark التالية ال remark بتقول ما يأتي
+
+110
+00:11:16,500 --> 00:11:26,300
+if summation من n equal zero to infinity لل a n في ال
+
+111
+00:11:26,300 --> 00:11:32,760
+X ناقص X node to the power N بدي أساوي summation من
+
+112
+00:11:32,760 --> 00:11:38,740
+N equal 0 to infinity لل b n في ال X ناقص ال X node
+
+113
+00:11:38,740 --> 00:11:50,700
+to the power N for each X لكل X then الآن
+
+114
+00:11:51,670 --> 00:11:59,510
+بدي أساوي ال b n وال n بدها تساوي 0 و1 و2 
+
+115
+00:11:59,510 --> 00:12:06,210
+و3  0 و1 و2 و3 وتظلك ماشية إلى ما
+
+116
+00:12:06,210 --> 00:12:07,370
+شاء الله
+
+117
+00:12:11,800 --> 00:12:18,660
+الـ a 0 بدي أساوي ال b 0 وال a 1 بدي أساوي ال b 1 وال
+
+118
+00:12:18,660 --> 00:12:26,320
+a n بدي أساوي ال b n إلى مالانهاية in particular
+
+119
+00:12:26,320 --> 00:12:33,160
+كحالة خاصة if
+
+120
+00:12:33,160 --> 00:12:42,280
+summation من n equal zero to infinity لل a n لل x
+
+121
+00:12:42,280 --> 00:12:50,300
+ناقص ال x not to the power n بدي أساوي zero for each
+
+122
+00:12:50,300 --> 00:13:00,420
+x لكل x then بنستنتج ما يأتي أن ال a n بده يساوي
+
+123
+00:13:00,420 --> 00:13:06,960
+zero that is أن ال a naught بده يساوي ال a one بده
+
+124
+00:13:06,960 --> 00:13:12,240
+يساوي ال a two بده يساوي ال a n بده يساوي بدها
+
+125
+00:13:12,240 --> 00:13:15,900
+يساوي كله جذاش اللي هو zero
+
+126
+00:13:19,560 --> 00:13:24,100
+بنرجع للـ remark هذه مرة ثانية وصحيح اسمها معايا 
+
+127
+00:13:24,100 --> 00:13:28,820
+كويسة إنها very important في الحسابات الآن وكذلك
+
+128
+00:13:28,820 --> 00:13:34,400
+لل section القادم بيقول لو كان summation من n
+
+129
+00:13:34,400 --> 00:13:38,280
+equals zero to infinity لل a n في ال X ناقص ال X
+
+130
+00:13:38,280 --> 00:13:42,350
+node to the power n بدي أساوي ال summation من n
+
+131
+00:13:42,350 --> 00:13:45,550
+equal zero to infinity لل b n في ال x نقص ال x
+
+132
+00:13:45,550 --> 00:13:51,870
+not to the power n for each x لكل x then ال a n
+
+133
+00:13:51,870 --> 00:13:56,390
+بدي أساوي ال b n اثبتي شوية طلعي هنا يا بنات ال
+
+134
+00:13:56,390 --> 00:13:59,990
+summation هذا هو ال summation هذا ببدأ من عند zero
+
+135
+00:13:59,990 --> 00:14:04,850
+وبنتهي وين؟ في مالانهاية اثنين ال x نقص ال x not
+
+136
+00:14:04,850 --> 00:14:08,310
+to the power n هي نفس ال x نقص ال x not to the
+
+137
+00:14:08,310 --> 00:14:13,080
+power n لأنه يقول for each x تمام يبقى هذه هي هذه
+
+138
+00:14:13,080 --> 00:14:18,860
+بيضلش عندي إلا ما عدا إلا a n و b n إذا إن حدث ذلك
+
+139
+00:14:18,860 --> 00:14:22,240
+إذا ال summation هو ال summation وال axis هي ال
+
+140
+00:14:22,240 --> 00:14:27,880
+axis بيضلش عندي إلا ال a n يساوي ما عدا ال b n وال
+
+141
+00:14:27,880 --> 00:14:35,960
+n 0 1 2 3 4 إلى آخره يبقى لحد مالانهاية that is
+
+142
+00:14:35,960 --> 00:14:40,660
+بدي أعيد صياغة هذا الكلام مرة أقرأ لو كانت n ب
+
+143
+00:14:40,660 --> 00:14:48,480
+0 بصير a 0 و b 0 لو كانت n ب1 بصير a 1 و b 1 لو
+
+144
+00:14:48,480 --> 00:14:53,180
+كانت n ب2 بصير a 2 تساوي b 2 لو كانت 3 يبقى 
+
+145
+00:14:53,180 --> 00:14:58,140
+a 3 بدي أساوي b 3 وهكذا يبقى هضل ماشي لغاية a n بدي
+
+146
+00:14:58,140 --> 00:15:03,540
+أساوي b n وفوت كمان نزيد واحد يساوي بنزيد واحد نزيد
+
+147
+00:15:03,540 --> 00:15:07,840
+اثنين يساوي بنزيد اثنين إلى مالانهاية يعني القصد
+
+148
+00:15:07,840 --> 00:15:11,640
+من ذلك إذا ال summation هنا بيساوي ال summation هنا
+
+149
+00:15:11,640 --> 00:15:15,840
+يبقى المعامل هنا هو نفس المعامل هنا باختصار هي
+
+150
+00:15:15,840 --> 00:15:20,320
+اللي قصد يقوله الآن لو جينا أخذنا حالة خاصة ايش
+
+151
+00:15:20,320 --> 00:15:24,280
+الحالة الخاصة نفترض هذا المقدار هذا حطينا بداله
+
+152
+00:15:24,280 --> 00:15:28,480
+0 يبقى ال summation هذا بيساوي 0 يبقى إن حدث
+
+153
+00:15:28,480 --> 00:15:32,880
+أن ال summation هذا بده يساوي 0 يبقى في هذه
+
+154
+00:15:32,880 --> 00:15:37,720
+الحالة ال a n هي اللي بدها تساوي 0 لما ال a n
+
+155
+00:15:37,720 --> 00:15:42,100
+بدها تساوي 0 يبقى ال a naught بدها تساوي 0 وال
+
+156
+00:15:42,100 --> 00:15:48,080
+a one وال a 2 وال a 3 وال a 4 وال n كله بيصفر
+
+157
+00:15:48,080 --> 00:15:51,960
+يبقى في هذه الحالة بصير كل المعاملات اللي عند مين
+
+158
+00:15:51,960 --> 00:15:58,930
+بيصفر طيب هذه نقطة مهمة جدًا لزمان مضايق كمان نقطة
+
+159
+00:15:58,930 --> 00:16:02,010
+لازمانة من هذه ال section اللي هو حاجة نسميها
+
+160
+00:16:02,010 --> 00:16:07,370
+shift of index لما أكتب ال summation بدي أغير
+
+161
+00:16:07,370 --> 00:16:12,170
+الدليل اللي تحت ال summation هنا ممكن أغيره زي ما
+
+162
+00:16:12,170 --> 00:16:18,030
+بدي دون أن أغير في قيمة ال summation أخذناها في
+
+163
+00:16:18,030 --> 00:16:25,530
+calculus B في section تلاتة من calculus B يبقى بدنا
+
+164
+00:16:25,530 --> 00:16:31,290
+نعيدها هنا نظرًا لأهميتها أثناء الحسابات يبقى نحط
+
+165
+00:16:31,290 --> 00:16:37,330
+عنوان صغير حاجة اسمه shift of index of summation
+
+166
+00:16:37,330 --> 00:16:43,950
+of index of summation
+
+167
+00:16:49,880 --> 00:16:58,160
+بدنا نوضح هذا الكلام بمثال example example
+
+168
+00:16:58,160 --> 00:17:07,040
+one let y تساوي ال summation من n equal zero to
+
+169
+00:17:07,040 --> 00:17:14,540
+infinity لل a n x to the power n compute
+
+170
+00:17:16,020 --> 00:17:31,280
+احسب لي y prime و y double prime واكتبهم
+
+171
+00:17:31,280 --> 00:17:40,540
+لي in terms of x to the power n
+
+172
+00:18:14,470 --> 00:18:19,770
+عشان احسب المشتقة الأولى والمشتقة الثانية واكتب
+
+173
+00:18:19,770 --> 00:18:24,600
+لي الناتج كله بدلالة X to the power N إذا تعالوا
+
+174
+00:18:24,600 --> 00:18:29,300
+نشوف شكل ال Y وبعدين نجيب المشتقة الأولى والثانية
+
+175
+00:18:29,300 --> 00:18:34,300
+لها إذا لو جيت أشوف شكل ال Y يبقى Y تساوي ال
+
+176
+00:18:34,300 --> 00:18:39,880
+summation من N equal zero to infinity لل A N لل X
+
+177
+00:18:39,880 --> 00:18:46,320
+to the power M هذا شكل ال series باستخدام الحد
+
+178
+00:18:46,320 --> 00:18:49,580
+النوني هذا اسمه الحد النوني لل series لو أنا بدي
+
+179
+00:18:49,580 --> 00:18:56,140
+أشوفها على طبيعتها يبقى ببدأ أحط n تساوي 0 بصير ايش
+
+180
+00:18:56,140 --> 00:19:04,100
+عندي a 0 x أس 0 بواحد بعد 0 شو بيجيني 1 يبقى
+
+181
+00:19:04,100 --> 00
+
+216
+00:22:42,830 --> 00:22:49,110
+عند الـ main من عند الـ zero قبل ما أكمل بدي أشوف إيش
+
+217
+00:22:49,110 --> 00:22:54,950
+بيقول يوم قال لي افترض Y احسب لي Y' و YW' واكتب لي كل
+
+218
+00:22:54,950 --> 00:23:01,730
+واحد فيهم بدلالة X to the power N احنا هنا X بدلالة 
+
+219
+00:23:01,730 --> 00:23:07,850
+مين الناقص واحد يبقى أنا بدي أروح أكتب الـ summation
+
+220
+00:23:07,850 --> 00:23:14,910
+هذا بدلالة X to the power N دون أن أغير في قيمة الـ
+
+221
+00:23:14,910 --> 00:23:21,450
+summation بقول له والله كويس يبقى هذا ههه بقدر أكتبه 
+
+222
+00:23:21,450 --> 00:23:26,150
+summation على الشكل اللي عندنا ده وأستنى شوية هنا
+
+223
+00:23:26,150 --> 00:23:31,730
+إذا بدي أبدأ أخلي هذا x to the power n يعني لو
+
+224
+00:23:31,730 --> 00:23:40,430
+شيلت كل n وحطيت مكانها n زائد واحد عندما أحصل على
+
+225
+00:23:40,430 --> 00:23:45,110
+ناقص واحدة بصير X to the power of N
+
+226
+00:23:56,150 --> 00:24:01,350
+يعني N تساوي كده؟ Zero ممتاز جدا يبقى هذا بيصير من
+
+227
+00:24:01,350 --> 00:24:06,270
+عند N تساوي Zero إلى Infinity بده أشيل هذه وأكتف
+
+228
+00:24:06,270 --> 00:24:10,830
+بدلها N زاد واحد تساوي واحد وجينا أيما كل ما 
+
+229
+00:24:10,830 --> 00:24:15,790
+اشتقينا طار كمان term حذفنا كمان term يبقى صارت من 
+
+230
+00:24:15,790 --> 00:24:20,730
+عند N تساوي اتنين طب اطلعي لي هنا اتنين
+
+231
+00:24:26,710 --> 00:24:32,550
+يبقى اتنين اتنين اتنين اتنين اتنين اتنين اتنين
+
+232
+00:24:32,550 --> 00:24:33,970
+اتنين اتنين اتنين اتنين اتنين اتنين اتنين اتنين
+
+233
+00:24:33,970 --> 00:24:34,070
+اتنين اتنين اتنين اتنين اتنين اتنين اتنين اتنين
+
+234
+00:24:34,070 --> 00:24:43,470
+اتنين اتنين اتنين اتنين
+
+235
+00:24:46,840 --> 00:24:53,240
+ب6A3X1 يبقى 6A3X1
+
+236
+00:24:53,240 --> 00:24:57,720
+مظبوط والباقي كله مظبوط يبقى هاي كتبناها كتابة
+
+237
+00:24:57,720 --> 00:25:02,870
+سليمة تمام نجي للمطلوب الثاني جالي بدي تكتبها لي
+
+238
+00:25:02,870 --> 00:25:08,550
+بدلالة x to the power n بقول له اه مش أنا أكتبها x
+
+239
+00:25:08,550 --> 00:25:15,090
+to the power n بدي أشيل كل n وأحط مكانها n زائد
+
+240
+00:25:15,090 --> 00:25:19,870
+اثنين إذا لما أحط هنا بنات n زائد اثنين يساوي
+
+241
+00:25:19,870 --> 00:25:23,720
+اثنين بصير الـ submission من وين من عند الـ zero
+
+242
+00:25:23,720 --> 00:25:28,480
+يبقى هذا الكلام بيصير summation من عند الـ zero
+
+243
+00:25:28,480 --> 00:25:34,420
+لغاية الـ infinity إذا بدي أشيل كل N وأضع مكانها N
+
+244
+00:25:34,420 --> 00:25:41,040
+زي 2 بيصير هذه N زي 2 وهذه إن زائد اثنين ناقص واحد
+
+245
+00:25:41,040 --> 00:25:48,360
+يعني ان زائد واحد يبقى هاي ان زائد اثنين في ان 
+
+246
+00:25:48,360 --> 00:25:55,980
+زائد واحد في ان زائد اثنين في الـ X to the power ان
+
+247
+00:25:55,980 --> 00:26:02,380
+اثنين ناقص اثنين ما بتدلش عندي إلا ان يبقى هاي غيرت
+
+248
+00:26:02,380 --> 00:26:06,500
+الـ index تبع الـ summation بدل ما كان عند ان يساوي
+
+249
+00:26:06,500 --> 00:26:06,980
+اثنين
+
+250
+00:26:10,400 --> 00:26:15,900
+اللي كتبته هذا جديد فعلا بيعطيني هذا ولا لا؟ أقول
+
+251
+00:26:15,900 --> 00:26:19,900
+تعالى نشوف من هنا بده يبدأ من وين؟ من عند الـ Zero
+
+252
+00:26:19,900 --> 00:26:24,920
+Zero بيبقى هنا اثنين Zero بيبقى هنا واحد Zero بيبقى
+
+253
+00:26:24,920 --> 00:26:30,580
+هنا اثنين يبقى اثنين اثنين اكس Zero بواحد اثنين
+
+254
+00:26:30,580 --> 00:26:36,740
+اثنين والله مظبوط بعد الـ zero بيجي مين واحد يبقى
+
+255
+00:26:36,740 --> 00:26:43,120
+واحد واثنين تلاتة في اثنين اللي هو بستة ا واحد زي
+
+256
+00:26:43,120 --> 00:26:49,700
+اثنين يبقى a تلاتة x يبقى هاي ستة a تلاتة x وهكذا
+
+257
+00:26:49,700 --> 00:26:53,060
+بالنسبة للباقي يبقى غيرنا الـ index تبع الـ
+
+258
+00:26:53,060 --> 00:26:57,860
+summation لكن المعلومات بقيت كما هي إذا يا بنات لو
+
+259
+00:26:57,860 --> 00:27:03,000
+غيرت الـ index تبع الـ summation لا يتغير قيمة السيرة
+
+260
+00:27:03,000 --> 00:27:08,040
+صحيح شكلا بصير شكلها مش زيها لكن في الحقيقة عندي
+
+261
+00:27:08,040 --> 00:27:14,200
+الحسابات كل term هو نظيره الأساسي لا يتغير وهذا
+
+262
+00:27:14,200 --> 00:27:20,900
+حط المعلومة في دماغك لزمان الآن وفورا كمان يبقى
+
+263
+00:27:20,900 --> 00:27:25,760
+بنجي لـ example two example
+
+264
+00:27:25,760 --> 00:27:30,400
+two له سنة أربعة وعشرين من التمرين بيقول ما يا
+
+265
+00:27:30,400 --> 00:27:31,620
+تيريا الرعي
+
+266
+00:27:51,370 --> 00:28:00,610
+الحد العام involves يشتمل على الـ X to the power N
+
+267
+00:28:01,590 --> 00:28:09,330
+هو ما عطيني واحد ناقص X تربيع summation من عند الـ
+
+268
+00:28:09,330 --> 00:28:18,190
+N تساوي اثنين الى infinity للـ N في الـ N ناقص واحد
+
+269
+00:28:18,190 --> 00:28:23,470
+في الـ AN في الـ X قص N ناقص اثنين
+
+270
+00:28:35,270 --> 00:28:39,610
+السؤال مرة ثانية السؤال اللي بيقول يعني rewrite
+
+271
+00:28:39,610 --> 00:28:45,270
+قعد كتابة أو قعد صياغة the given expression الصيغة
+
+272
+00:28:45,270 --> 00:28:51,150
+المعطاة as a sum كمجموع يعني كـ summation whose
+
+273
+00:28:51,150 --> 00:28:57,520
+generic term الحد العام تبعه involves x to the
+
+274
+00:28:57,520 --> 00:29:03,380
+power n يعني أنا عندي x هنا بيقوس قداش الناقص
+
+275
+00:29:03,380 --> 00:29:06,280
+اثنين أنا ما بديش إيه الناقص اثنين بدي أتخلص من
+
+276
+00:29:06,280 --> 00:29:10,340
+الناقص اثنين بدي إياها بدلالة الـ x to the power n
+
+277
+00:29:10,340 --> 00:29:15,700
+فقط بقول لكم إيه تعال نشوف بطلع هذه مش زي اللي جاب
+
+278
+00:29:15,700 --> 00:29:17,600
+الكمّان مضروب وغرق مين
+
+279
+00:29:23,610 --> 00:29:29,070
+يبقى اتصرف بمخك وشوف كيف بدك تسويه بقول له بسيطة هذا
+
+280
+00:29:29,070 --> 00:29:33,830
+الـ term اللي عندك هو واحد ناقص X تربيع مضروب في
+
+281
+00:29:33,830 --> 00:29:39,310
+summation من N equal to infinity للـ N في X ناقص
+
+282
+00:29:39,310 --> 00:29:47,830
+واحد للـ A N للـ X ناقص اثنين طبعا طيب شو رأيكم يا
+
+283
+00:29:47,830 --> 00:29:51,990
+بنات بدي أتلح لحظة بقول لو كتبو بـ summation واحد
+
+284
+00:29:51,990 --> 00:29:55,490
+هذه اللي جوه اللي برا لو كانت زي اللي جوه كان
+
+285
+00:29:55,490 --> 00:30:00,270
+ضربتها جوه واتريحت مظبوط لكن هذه مجموعة إيه؟
+
+286
+00:30:00,270 --> 00:30:04,870
+كميتين إذا بقول الكمية الأولى في الـ summation ناقص
+
+287
+00:30:04,870 --> 00:30:07,510
+الكمية الثانية في الـ summation وبالتالي فكتي
+
+288
+00:30:07,510 --> 00:30:13,150
+العقدة الأولى مظبوط؟ يبقى هذا الكلام بده يساوي واحد
+
+289
+00:30:13,150 --> 00:30:17,550
+في الـ summation بالـ summation زي ما هو من اثنين
+
+290
+00:30:17,550 --> 00:30:23,030
+لغاية infinity للـ N في الـ N ناقص واحد في الـ A N في
+
+291
+00:30:23,030 --> 00:30:29,190
+الـ X أس N ناقص اثنين ناقص الـ X تربيع هذه بانت
+
+292
+00:30:29,190 --> 00:30:33,850
+تدخلها جوه يبقى لو دخلت جوه إيش بصير عندنا هنا؟
+
+293
+00:30:34,020 --> 00:30:40,450
+ناقص summation من N equal two to infinity للـ ان في
+
+294
+00:30:40,450 --> 00:30:46,690
+الان ناقص واحد هذه ان ناقص واحد مش اكس ما ان في
+
+295
+00:30:46,690 --> 00:30:54,350
+الان ناقص واحد أيوة في الان في الان في جداش هذه
+
+296
+00:30:54,350 --> 00:31:00,870
+بصيها اكسوس ان فقط لأن ان زائد اثنين وناقص اثنين
+
+297
+00:31:00,870 --> 00:31:08,910
+بصير الـ X to the power N مظهر طيب نرجع مرة ثانية
+
+298
+00:31:08,910 --> 00:31:15,170
+بقول لي اكتب هذا كـ summation واحد مش اثنين وبشرط أن
+
+299
+00:31:15,170 --> 00:31:21,090
+الاص يكون X to the power N بقول له والله هي جاهزة
+
+300
+00:31:21,090 --> 00:31:26,590
+مكتوبة بس هذه مش مكتوبة بدلالة الـ N يبقى الشغل
+
+301
+00:31:26,590 --> 00:31:32,970
+عندنا بقدر أشيل كل N وأحط مكانها بس مشان تكتبوا
+
+302
+00:31:32,970 --> 00:31:37,930
+يتغير كل الـ index هدول يبقى بروح بقول له ماشي مافي
+
+303
+00:31:37,930 --> 00:31:43,230
+مشكلة هذي يساوي إذا أنا هشيل كل N وأكتب مكانة N
+
+304
+00:31:43,230 --> 00:31:49,850
+زاد اثنين بصير N تساوي جداش Zero الى Infinity للـ N
+
+305
+00:31:50,230 --> 00:31:57,230
+زائد اثنين في الـ N زائد اثنين نقص واحد يعني N زائد
+
+306
+00:31:57,230 --> 00:32:07,230
+واحد للـ A N زائد اثنين للـ X to the power N نجي
+
+307
+00:32:07,230 --> 00:32:12,270
+لبعدها ناقص summation من N equal to تبقى نزلها زي
+
+308
+00:32:12,270 --> 00:32:16,630
+ما هي لأن هجازة S هتلعب في المكتسبات الوطنية
+
+309
+00:32:16,630 --> 00:32:20,910
+المكتسبة اللي عندك بدأ تحافظ عليه لأنه مطلوب نخلي
+
+310
+00:32:20,910 --> 00:32:26,850
+المسألة بدلالة X to the power N يبقى N في N ناقص
+
+311
+00:32:26,850 --> 00:32:33,870
+واحد في N في X to the power N أول ساعة في الخواص
+
+312
+00:32:33,870 --> 00:32:37,970
+قلنا إذا summation بسوى summation بتطلع في
+
+313
+00:32:37,970 --> 00:32:41,390
+المعاملات يبقى المعامل هنا بده يساوي المعامل هنا
+
+314
+00:32:41,390 --> 00:32:46,550
+مظبوط اللي كتبناها قبل شوية بجي بتطلع هذي X و XN
+
+315
+00:32:46,550 --> 00:32:52,030
+هذي X و XN ممتاز هذا summation .. اه الـ summation
+
+316
+00:32:52,030 --> 00:32:56,250
+مش زي بعضه بده الـ summation النقطة اللي يبده هنا
+
+317
+00:32:56,250 --> 00:33:00,990
+فيها هي النقطة اللي يبده هنا فيها بالضبط تمام مش
+
+318
+00:33:00,990 --> 00:33:04,090
+هنقدر نجمعهم وإلا بقدرش أجمعهم وإلا بدي يكون الـ
+
+319
+00:33:04,090 --> 00:33:06,850
+index اللي هنا زي الـ index هنا واللي فوق ما هو
+
+320
+00:33:06,850 --> 00:33:09,750
+المالة نهائية تطرح منه واحد والله أضيف له خمسة
+
+321
+00:33:09,750 --> 00:33:14,510
+كله مالة نهائية تمام؟ بقول له كويس إذا بدي أخلي الـ
+
+322
+00:33:14,510 --> 00:33:19,430
+index اللي هنا زي الـ index اللي هنا بقول له بسيطة
+
+323
+00:33:19,430 --> 00:33:24,590
+جدا تغلبش حالك كثير إيش رأيكم لو طلعت أول term
+
+324
+00:33:24,590 --> 00:33:30,180
+هنا؟ حسب تجدش الـ summation عند الـ zero وعند الـ
+
+325
+00:33:30,180 --> 00:33:34,260
+واحد بيظل بعدها الـ summation يقول لي إيه بدا بيصير
+
+326
+00:33:34,260 --> 00:33:39,160
+زي هذا إذا بقدر أجبلهم مع بعض مظبوط يبقى بقدر أقول
+
+327
+00:33:39,160 --> 00:33:45,060
+هذا الكلام يساوي لو كانت الـ n بيزيرو بيظل اثنين في
+
+328
+00:33:45,060 --> 00:33:51,870
+واحد اللي هو بجدش اثنين اه دي اثنين ن بزيرو بصير
+
+329
+00:33:51,870 --> 00:33:58,010
+اثنين هنا ن بزيرو بصير اكس Zero بواحد يبقى الحد
+
+330
+00:33:58,010 --> 00:34:03,990
+الأول اثنين اثنين يبقى هاي فلت زيرو بدي أفلت كمان
+
+331
+00:34:03,990 --> 00:34:09,130
+الواحد يبقى بقول له ز صمشي يبقى جامع بدي أشيله لأنه
+
+332
+00:34:09,130 --> 00:34:14,050
+وأحط مكانه واحد يبقى بصير تلاتة في اثنين بدي أكتب
+
+333
+00:34:14,050 --> 00:34:21,060
+هلك بدي أكتب تلاتة في اثنين بس مشان تعرفك إيه فجأت
+
+334
+00:34:21,060 --> 00:34:27,560
+ثاني في مين؟ في a واحد زائد اثنين ل a تلاتة في
+
+335
+00:34:27,560 --> 00:34:37,430
+مين؟ في الـ X أس واحد طبعا انتقل نقل نقل نقل نقل نقل
+
+336
+00:34:37,430 --> 00:34:45,310
+نقل نقل نقل نقل نقل
+
+337
+00:35:12,460 --> 00:35:23,280
+هذه بدها تساوي اثنين اثنين زائد ستة ات تلاتة X زائد
+
+338
+00:35:23,280 --> 00:35:27,300
+إيش رايك؟ هذا الـ summation هو الـ summation إذا
+
+339
+00:35:27,300 --> 00:35:33,840
+بآخذ summation مشترك للكل يبقى هذا summation من N
+
+340
+00:35:33,840 --> 00:35:40,760
+equal two to infinity لمن؟ للـ N زائد اثنين في الـ N
+
+341
+00:36:07,870 --> 00:36:12,670
+مرة ثانية بقول الخطوة الأخيرة الخطوة اللي قدامي هذه
+
+342
+00:36:12,670 --> 00:36:18,230
+هكتبها بشكل آخر الـ two terms هذول نزلتهم زي ما هم
+
+343
+00:36:18,230 --> 00:36:22,790
+بدون مشاكل جيت هنا هذا الـ summation هو نفس الـ
+
+344
+00:36:22,790 --> 00:36:27,730
+summation إذا بدي أخذ عامل مشترك x to the power n
+
+345
+00:36:27,730 --> 00:36:31,230
+هي نفس الـ x to the power n بدي أخذها عامل مشترك
+
+346
+00:36:31,230 --> 00:36:36,140
+برا يبقى بدلش عندي إلا هذا المعامل والمعامل اللي
+
+347
+00:36:36,140 --> 00:36:41,480
+عندنا هذا وشرط السالب بينهما إذا المعامل هذا
+
+348
+00:36:41,480 --> 00:36:47,620
+نزلته زي ما هو وسالب المعامل هذا نزلته زي ما هو وهي
+
+349
+00:36:47,620 --> 00:36:53,740
+هي الـ X to the power N والـ summation هيه برا تمام
+
+350
+00:36:53,740 --> 00:36:58,860
+إيش بقول يعيد كتاب لك كصم whose generic term X to
+
+351
+00:36:58,860 --> 00:37:04,170
+the power N اه كتبت له إيه طيب إيش رايك يا بنات
+
+352
+00:37:04,170 --> 00:37:10,850
+تعالى نشوف هل لو حطيت للـ summation جوه هذا اللي هو
+
+353
+00:37:10,850 --> 00:37:17,670
+n بواحد بطلع الـ term هذا ولو حطيت n بـ zero بطلع
+
+354
+00:37:17,670 --> 00:37:22,470
+الـ term هذا انطلع الـ term بقدر أهمل هدول وأكتب الـ
+
+355
+00:37:22,470 --> 00:37:26,090
+summation عند n equal zero وأخلي اللي جوه زي ما
+
+356
+00:37:26,090 --> 00:37:31,510
+هو مظبوط؟ يعني بدل ما يكون مبعتر طويل هيك ممكن
+
+357
+00:37:31,510 --> 00:37:36,270
+أجمعه بـ submission واحد تعال نشوف بدل اثنين لو
+
+358
+00:37:36,270 --> 00:37:43,910
+حطيت واحد إيش بيصير عندي؟ تلاتة في اثنين ستة اتلتا
+
+359
+00:37:43,910 --> 00:37:51,750
+ستة اتلتا حط هنا بواحد بطير هذا بصفر مظبوط؟ يبقى
+
+360
+00:37:51,750 --> 00:37:55,790
+هنا بصير 6A3F1
+
+361
+00:37:55,790 --> 00:37:59,570
+6A3F1
+
+362
+00:37:59,570 --> 00:38:04,030
+إذا لو رجعت الـ summation وخلّيته هنا من انتوا ساوي
+
+363
+00:38:04,030 --> 00:38:09,230
+واحد ما عندي مشكلة طيب هل بنفع أخليه من عند انتوا
+
+364
+00:38:09,230 --> 00:38:14,590
+ساوي زيرو تعال شوف حط انتوا ساوي زيرو بضلي اثنين
+
+365
+00:38:14,590 --> 00:38:23,750
+في واحد باتنين A2 تعمل البرنامج
+
+366
+00:38:23,750 --> 00:38:31,740
+باستخدام البرنامج إذا بقدر أدخل هدول مع الـ
+
+367
+00:38:31,740 --> 00:38:38,560
+summation هذا وأخليه summation من عند n equal 0 to
+
+368
+00:38:38,560 --> 00:38:43,840
+infinity نفس هذا زي ما هو مش هغيره يا بنات يبقى n
+
+369
+00:38:43,840 --> 00:38:53,300
+زائد 2 في n زائد 1 في الـ a n زائد 2 ناقص n في n
+
+370
+00:38:53,300 --> 00:39:00,380
+ناقص 1 في الـ a n في x to the power n يبقى جماعة
+
+371
+00:39:00,380 --> 00:39:06,580
+لهذا هذا كله خلّيته summation واحد مرة واحدة
+
+372
+00:39:06,580 --> 00:39:11,660
+without problems بدون مشاكل والـ index بدل ما كان
+
+373
+00:39:11,660 --> 00:39:16,520
+عندي اثنين خلّيته له من وين؟ من عندي الـ zero كويسة
+
+374
+00:39:16,520 --> 00:39:20,040
+الفكرة هذه؟ هنشتغل فيها كثير دي ربالكم
+
+375
+00:39:25,790 --> 00:39:29,810
+نأخذ مثال حول نفس المفهوم.
+
+376
+00:39:53,110 --> 00:39:56,790
+مثال ثلاثة اللي هو سؤال ثمانية وعشرين من الكتاب
+
+377
+00:39:56,790 --> 00:40:03,150
+ثلاثة سؤال ثمانية وعشرين هو آخر سؤال في التمرين
+
+378
+00:40:03,150 --> 00:40:15,770
+بيقول لي دي تيرمين حدد لي اللي هو the a n so that
+
+379
+00:40:15,770 --> 00:40:19,450
+equation so that
+
+380
+00:40:22,260 --> 00:40:28,140
+بحيث أن المعادلة summation من n equal one to
+
+381
+00:40:28,140 --> 00:40:37,460
+infinity للـ n a n x أس n ناقص واحد زائد اثنين
+
+382
+00:40:37,460 --> 00:40:44,420
+summation من عند n equal zero to infinity للـ a in
+
+383
+00:40:44,420 --> 00:40:55,340
+x to the power n بده يساوي من 0 is satisfied is
+
+384
+00:40:55,340 --> 00:41:04,040
+satisfied try حاول to identify
+
+385
+00:41:04,040 --> 00:41:11,600
+try to identify the function represented
+
+386
+00:41:26
+
+431
+00:45:17,980 --> 00:45:22,540
+إذا الآن هي اللي في Zero مش الـ X ده بارن صحيح ولا
+
+432
+00:45:22,540 --> 00:45:26,520
+لأ؟ يبقى مادام هذه تساوي Zero شو اللي خلاها Zero؟
+
+433
+00:45:26,520 --> 00:45:32,480
+هذه ليست Zero يبقى اللي بين قوسين هو Zero يبقى هذا
+
+434
+00:45:32,480 --> 00:45:40,300
+بده يخليلي مين؟ بده يخليلي أن n زائد واحد  n زائد
+
+435
+00:45:40,300 --> 00:45:48,310
+واحد زائد 2 n هي Zero أو بمعنى آخر بقدر أقول
+
+436
+00:45:48,310 --> 00:45:57,810
+n زائد واحد تساوي ناقص 2 n على من على n زائد
+
+437
+00:45:57,810 --> 00:46:04,270
+واحد الشكل اللي عندنا طيب الآن هنا تبدأ من وين؟
+
+438
+00:46:06,250 --> 00:46:12,570
+يبقى عندي الـ zero يبقى باجي بقول له هذا هيك و الـ n
+
+439
+00:46:12,570 --> 00:46:18,730
+تساوي zero و واحد و اثنين و إلى ما شاء الله عارفين
+
+440
+00:46:18,730 --> 00:46:24,470
+هذه شو اسمها يا بنات؟ هذه اسمها recurrence relation
+
+441
+00:46:24,470 --> 00:46:31,050
+المعادلة التكرارية يبقى هذه اسمها recurrence
+
+442
+00:46:31,050 --> 00:46:33,110
+relation
+
+443
+00:46:38,230 --> 00:46:43,070
+ماذا يعني Recurrent؟ ماذا يعني معادلة تكرارية؟ ماذا
+
+444
+00:46:43,070 --> 00:46:49,290
+يعني Recurrent؟ ماذا يعني Recurrent؟ ماذا يعني
+
+445
+00:46:49,290 --> 00:46:53,690
+Recurrent؟ ماذا
+
+446
+00:46:53,690 --> 00:46:57,570
+يعني Recurrent؟
+
+447
+00:46:58,020 --> 00:47:03,520
+فأجي أقول له قلي الـ n من وين بتبدأ؟ عند الـ zero إذا هنا
+
+448
+00:47:03,520 --> 00:47:12,020
+بيصير a one تساوي ناقص 2 a نود على a يبقى
+
+449
+00:47:12,020 --> 00:47:16,180
+هجيب له a one ممكن أجيب المعادلة أرجع لها ثاني و
+
+450
+00:47:16,180 --> 00:47:20,180
+أجيب a اثنين ممكن أرجع لها و أجيب a ثلاثة و أرجع
+
+451
+00:47:20,180 --> 00:47:25,760
+لها و أجيب a أربعة و كذا و منها أجيب له صيغة a n
+
+452
+00:47:25,760 --> 00:47:31,640
+اللي طلبها تمام لما طلب جالي هاتي الشكل الـ a n
+
+453
+00:47:31,640 --> 00:47:37,420
+بقول له والله تمام إذا أنا بدي آخذ لو كانت الـ n
+
+454
+00:47:37,420 --> 00:47:43,240
+تساوي الـ zero then حط zero zero زائد واحد يصير
+
+455
+00:47:43,240 --> 00:47:49,800
+واحد يبقى a واحد تساوي ناقص 2 a naught على
+
+456
+00:47:49,800 --> 00:47:58,080
+واحد يعني جداش يعني ناقص 2 a naught  بادي بقول له
+
+457
+00:47:58,080 --> 00:48:05,700
+لو كانت الـ N تساوي واحد then بدل الـ واحد A واحد
+
+458
+00:48:05,700 --> 00:48:12,900
+زائد واحد يعني اللي هم اثنين يبقى بده أشيل كل N
+
+459
+00:48:12,900 --> 00:48:19,640
+و أحط مكانها واحد يبقى بده يساوي ناقص 2 A واحد
+
+460
+00:48:19,640 --> 00:48:27,390
+على واحد زائد واحد يبقى هذا معناه أن اثنين تساوي
+
+461
+00:48:27,390 --> 00:48:33,090
+ناقص 2 ا واحد على 2 طب a واحد موجود عندي
+
+462
+00:48:33,090 --> 00:48:40,790
+فوق مظبوط يبقى هذا معناه ناقص 2 على 2 في
+
+463
+00:48:40,790 --> 00:48:49,320
+ناقص 2 and odd يعني هذا معناه ناقص 2 لكل
+
+464
+00:48:49,320 --> 00:48:55,600
+تربيع إنه اد على 2 شرطة 2 هذا مش هي 2
+
+465
+00:48:55,600 --> 00:49:01,200
+factorial كمان يعني مضروب 2 يبقى بقدر أكتبها
+
+466
+00:49:01,200 --> 00:49:05,740
+2 factorial طبعا هتسأل واحدة طب ليش
+
+467
+00:49:05,740 --> 00:49:11,120
+ما تختصرها مع اللي فوق بنقول لك لحاجة في نفسي يا عقوبة
+
+468
+00:49:11,120 --> 00:49:17,740
+ستعرفونها بعد قليل طبعا يعني ليش ما اختصرتش إليها سرح
+
+469
+00:49:17,740 --> 00:49:22,500
+أنا عايز أخليها تظل بها ده الشكل باجي بقول له لو
+
+470
+00:49:22,500 --> 00:49:28,520
+كانت الـ N تساوي 2 then يبقى بدي أشيل الـ N و أحط
+
+471
+00:49:28,520 --> 00:49:36,620
+مكانها وين 2 يبقى بيصير 3 تساوي 2 زائد
+
+472
+00:49:36,620 --> 00:49:42,960
+واحد يبقى N عندي هنا مقدارها 2 يبقى هذه تساوي
+
+473
+00:49:42,960 --> 00:49:50,460
+ناقص 2 اثنين على 2 زائد واحد يعني هذه
+
+474
+00:49:50,460 --> 00:49:57,420
+تساوي ناقص 2 على 3 في 2 وين 2 هي
+
+475
+00:49:57,420 --> 00:50:04,320
+يبقى هذه 2 اللي هو ناقص 2 لكل تربيع a
+
+476
+00:50:04,320 --> 00:50:11,030
+node على 2 factorial ناقص 2 فنقص 2 تربيع
+
+477
+00:50:11,030 --> 00:50:17,910
+فنقص 2 تكعيب و a not زي ما هو هذا 3 في
+
+478
+00:50:17,910 --> 00:50:22,350
+2 factorial اللي يبقى جداش 3 factorial
+
+479
+00:50:22,350 --> 00:50:29,170
+يبقى هذه 3 factorial طب حد فيكم تقدر تقول لي لو
+
+480
+00:50:29,170 --> 00:50:35,690
+كانت الـ into ساوي 3 يبقى بحصل على مين؟ على ايه
+
+481
+00:50:35,690 --> 00:50:40,910
+4 حد فيكم بتقدر يقدرش 4 من خلال النتائج هذه
+
+482
+00:50:40,910 --> 00:50:45,630
+اللي هو سالب 2 أس 4 a nod على 4
+
+483
+00:50:45,630 --> 00:50:52,790
+factorial تمام؟ إذا أنا لو ظليت مستمر هوصل إلى
+
+484
+00:50:52,790 --> 00:51:01,350
+أين؟ 3 يبقى 3 3 يبقى ناقص 2 to the
+
+485
+00:51:01,350 --> 00:51:10,650
+power n لل a node على n factorial تمام يبقى هذا
+
+486
+00:51:10,650 --> 00:51:15,050
+الصيغة اللي هو ايه؟ اللي هو بده ياها قال هات لي شكل
+
+487
+00:51:15,050 --> 00:51:21,640
+الـ a n يبقى قدرت أحصل على شكل الـ a n من خلال
+
+488
+00:51:21,640 --> 00:51:25,920
+المعادلة التكرارية أو الـ recurrence relation اللي
+
+489
+00:51:25,920 --> 00:51:31,400
+أنا يبقى أنا جبت له main المطلوب الأول شكل الـ a n
+
+490
+00:51:31,400 --> 00:51:37,060
+كله بدلالة main الـ a note يبقى أجيب له على سؤال
+
+491
+00:51:37,060 --> 00:51:42,150
+ايش بيقول لي؟ try حاول ان قدرت اهلا وسهلا ما لقيتش بلاش
+
+492
+00:51:42,150 --> 00:51:47,930
+بس هذه مشان أقدر بدي أفتح calculus V و روح تشوف ايه
+
+493
+00:51:47,930 --> 00:51:52,810
+الشكل اللي هو الـ factorial أو ايه الشكل الـ power
+
+494
+00:51:52,810 --> 00:51:58,610
+series لدوال المختلفة بقول try to identify the
+
+495
+00:51:58,610 --> 00:52:03,470
+function represented by هذه بقول له خليني أشوف الشكل
+
+496
+00:52:03,470 --> 00:52:08,450
+هذه المطلوب الثاني فبروح بقول له أنا عندي summation
+
+497
+00:52:09,590 --> 00:52:14,550
+من n equal zero to infinity لل a n لل x to the
+
+498
+00:52:14,550 --> 00:52:20,090
+power n a n هي قيمتها إذا هشيلها و أحط قيمتها
+
+499
+00:52:20,090 --> 00:52:25,150
+يبقى بيصير عندي بيصير عندي summation من n equal
+
+500
+00:52:25,150 --> 00:52:31,310
+zero to infinity لمين؟ لـ ناقص 2 to the power n لل
+
+501
+00:52:31,310 --> 00:52:39,360
+a node على n factorial في ال x to the power n يساوي
+
+502
+00:52:39,360 --> 00:52:44,240
+ال summation من n equal zero to infinity ال a node
+
+503
+00:52:44,240 --> 00:52:49,000
+هذا مقدار ثابت ما له دعوة نيجي هذا الأس تبعه قداش
+
+504
+00:52:49,000 --> 00:52:56,000
+n و هذا الأس تبعه قداش يعني هذا كأنه ناقص 2 x
+
+505
+00:52:56,000 --> 00:53:04,410
+كله to the power n على n factorial تمام طب حد فيكوا
+
+506
+00:53:04,410 --> 00:53:12,550
+مذاكرة McLaurin series لده لإيه؟ و الـ six؟ لده لإيه
+
+507
+00:53:12,550 --> 00:53:21,150
+و الـ six؟ حد فيكوا بتحلم؟ طب حد فيكوا بتعلم؟ ولا
+
+508
+00:53:21,150 --> 00:53:25,960
+واحدة طبعا طبعا خدنا مثال هذا أول مثال على مكلورين
+
+509
+00:53:25,960 --> 00:53:30,460
+سيريز في Calculus B بجي نقول إن الـ E X تساوي
+
+510
+00:53:30,460 --> 00:53:34,480
+الصميم من N equal zero to infinity إلى X to the
+
+511
+00:53:34,480 --> 00:53:40,820
+power N على N factorial تمام يبقى E أس X كانت
+
+512
+00:53:40,820 --> 00:53:47,340
+عندنا زمان E أس X يساوي X to the power N على N
+
+513
+00:53:47,340 --> 00:53:53,000
+factorial وصميم من N equal zero to infinity في شبه
+
+514
+00:53:53,000 --> 00:53:59,880
+بينها وبين هذه يبقى هذه مين هي؟ E أس ناقص 2 X
+
+515
+00:53:59,880 --> 00:54:05,820
+يبقى هذا الكلام بده يساوي summation من N equal zero
+
+516
+00:54:05,820 --> 00:54:11,660
+to infinity لل A node E لأ بدون summation يا بنات
+
+517
+00:54:11,660 --> 00:54:17,040
+خلاص كـ function هذه يبقى A node في الـ E أس سالب
+
+518
+00:54:17,040 --> 00:54:24,750
+2 X فقط بغي يبقى هذه الدالة التي تمثل من الـ
+
+519
+00:54:24,750 --> 00:54:29,130
+power series اللي عندنا هذه وهو هذا المطلوب الثاني
+
+520
+00:54:29,130 --> 00:54:33,730
+يجب أن أحاول أن أعرف الـ functions التي تمثل الـ
+
+521
+00:54:33,730 --> 00:54:38,290
+power series اللي عندنا ماشي يبقى هذه اعتمدت وين
+
+522
+00:54:38,290 --> 00:54:44,430
+على معلوماتنا من calculus b طيب لحد هنا stop انتهى
+
+523
+00:54:44,430 --> 00:54:48,970
+هذا الـ section إلى يكون أرقام المسائل
+
+524
+00:54:50,890 --> 00:54:58,990
+يبقى exercises خمسة واحد المسائل التالية من واحد
+
+525
+00:54:58,990 --> 00:55:04,010
+لغاية ثمانية و عشرين الفضل وطبعا هذه السؤال ثمانية
+
+526
+00:55:04,010 --> 00:55:11,350
+وعشرين قدامكم وأربعة و عشرين حلناها قبل شوية حد
+
+527
+00:55:11,350 --> 00:55:15,990
+فيكم اللي يتسائل هنا بنات؟ تغيير الـ index هرجع له
+
+528
+00:55:15,990 --> 00:55:20,030
+الآن في section خمسة اثنين اللي بدنا نبدأ حالا
+
+529
+00:55:45,390 --> 00:55:50,350
+بنتنقل الآن للـ section اللي بعده برضه اللي فوق
+
+530
+00:55:50,350 --> 00:55:51,250
+انتهينا منها
+
+531
+00:56:06,240 --> 00:56:12,840
+بنتقل الآن لـ Section 5-2 اللي هو بيتحدث عن Series
+
+532
+00:56:12,840 --> 00:56:18,840
+Solution Series Solution
+
+533
+00:56:18,840 --> 00:56:22,360
+Near
+
+534
+00:56:22,360 --> 00:56:25,520
+An
+
+535
+00:56:25,520 --> 00:56:28,900
+Ordinary
+
+536
+00:56:28,900 --> 00:56:34,180
+Point Art
+
+537
+00:56:35,570 --> 00:56:42,970
+One Consider
+
+538
+00:56:42,970 --> 00:56:46,410
+the
+
+539
+00:56:46,410 --> 00:56:51,310
+differential equation
+
+540
+00:56:53,100 --> 00:56:59,880
+Capital P of X في الـ Y W Prime Capital Q of X في
+
+541
+00:56:59,880 --> 00:57:06,360
+الـ Y Prime Capital R of X في الـ Y بده يساوي Zero
+
+542
+00:57:06,360 --> 00:57:10,260
+وهذا بده يسميها المعادلة رقم 1
+
+543
+00:57:14,420 --> 00:57:25,140
+P of X with a Q of X and R of X are polynomials
+
+544
+00:57:25,140 --> 00:57:33,640
+with
+
+545
+00:57:33,640 --> 00:57:37,200
+no common factors
+
+546
+00:57:45,800 --> 00:57:55,480
+ما فيش بينهم عوامل مشتركة نعطي تعريف رقم واحد a
+
+547
+00:57:55,480 --> 00:58:08,260
+point a point x0 is called an ordinary point an
+
+548
+00:58:08,260 --> 00:58:13,280
+ordinary point
+
+549
+00:58:15,450 --> 00:58:20,070
+for the differential equation one for the
+
+550
+00:58:20,070 --> 00:58:26,230
+differential equation
+
+551
+00:58:26,230 --> 00:58:40,310
+one if ال P of X not لا يساوي ال zero لو كانت هذه
+
+552
+00:58:40,310 --> 00:58:46,450
+لا تساوي ال zero نمر اثنين عن طريق الوصول إلى موقع
+
+553
+00:58:46,450 --> 00:58:55,910
+X0 هو موقع عشان يسمى موقع عشان يسمى موقع عشان يسمى
+
+554
+00:58:55,910 --> 00:59:08,730
+موقع عشان يسمى موقع عشان يسمى موقع عشان
+
+555
+00:59:08,730 --> 00:59:12,910
+يسمى
+
+556
+00:59:13,010 --> 00:59:22,210
+الـ P of X0 بده يساوي مين؟ بده يساوي Zero Now
+
+557
+00:59:22,210 --> 00:59:25,370
+We
+
+558
+00:59:25,370 --> 00:59:37,850
+Look For We Look For A Solution Of The
+
+559
+00:59:37,850 --> 00:59:44,080
+Differential Equation 1 Of That differential
+
+560
+00:59:44,080 --> 00:59:51,240
+equation one
+
+561
+00:59:51,240 --> 01:00:05,440
+in the form في الشكل y تساوي ال summation من n
+
+562
+01:00:05,440 --> 01:00:12,880
+equal zero to infinity لل a nx نقص x node to the
+
+563
+01:00:12,880 --> 01:00:28,960
+power m where ال x node is an ordinary point and
+
+564
+01:00:28,960 --> 01:00:32,120
+the
+
+565
+01:00:32,120 --> 01:00:37,960
+series and the series
+
+566
+01:00:44,720 --> 01:00:55,260
+converge and the series converge in the interval
+
+567
+01:00:55,260 --> 01:01:04,680
+in the interval absolute value ال X نقص ال X أقل
+
+568
+01:01:04,680 --> 01:01:09,920
+من رو for some
+
+569
+01:01:11,320 --> 01:01:15,680
+أقرأ اللي أكبر من مين؟ من أزيمة
+
+570
+01:02:10,840 --> 01:02:16,720
+بنحاول نفهم كل كلمة مكتوبة قدامنا هنا على السطر
+
+571
+01:02:16,720 --> 01:02:19,900
+لأنه خلاص هاي الكلمتين النظرية تبع الـ section هذا
+
+572
+01:02:19,900 --> 01:02:24,640
+وبعد هيك بتذكروا عندنا شغل كيف نحل المعادلة
+
+573
+01:02:24,640 --> 01:02:28,720
+التفاضلية العنوان اللي أحنا عارفينه section 5-2
+
+574
+01:02:28,720 --> 01:02:34,460
+serious solution near an ordinary point of part
+
+575
+01:02:34,460 --> 01:02:39,540
+one يبقى احنا الآن يا بنات بدنا نحاول نستخدم
+
+576
+01:02:39,540 --> 01:02:45,840
+المتسلسلات في حل المعادلة التفاضلية المتجانسة من
+
+577
+01:02:45,840 --> 01:02:50,740
+الرتبة الثانية ما احنا كنا بنحلها سابقا لكن بدون
+
+578
+01:02:50,740 --> 01:02:56,040
+متسلسلات مظبوط الآن هنحاول نحلها مرة ثانية
+
+579
+01:02:56,040 --> 01:03:00,200
+باستخدام اللي هو الـ power series أو باستخدام
+
+580
+01:03:00,200 --> 01:03:04,110
+المتسلسلات بقول اعتبر الصيغة العامة للمعادلة
+
+581
+01:03:04,110 --> 01:03:09,050
+التفاضلية للصيغة رقم واحد المتعرف عليها قبل ذلك بس
+
+582
+01:03:09,050 --> 01:03:13,750
+بشرط قل الدول الثلاثة الـ P و الـ Q و الـ R هدول ما
+
+583
+01:03:13,750 --> 01:03:18,950
+لهم بديهم كثيرات حدود مش حيالها يعني إذا كانوا
+
+584
+01:03:18,950 --> 01:03:22,330
+كثيرات حدود قولهم كلام وإذا مش كثيرات حدود قولهم
+
+585
+01:03:22,330 --> 01:03:28,050
+كلام ثاني تمام؟ احنا اليوم سنقتصر دراستنا على إن
+
+586
+01:03:28,050 --> 01:03:33,650
+لو كانوا المعاملات هدول كثيرات حدود يبقى الـ P و الـ
+
+587
+01:03:33,650 --> 01:03:37,350
+Q و الـ R كثيرات حدود من الرتبة الأولى والرتبة
+
+588
+01:03:37,350 --> 01:03:40,090
+التالية والدرجة الأولى والدرجة الثانية والدرجة
+
+589
+01:03:40,090 --> 01:03:41,130
+التالية والدرجة التالية والدرجة التالية والدرجة
+
+590
+01:03:41,130 --> 01:03:41,530
+التالية والدرجة التالية والدرجة التالية والدرجة
+
+591
+01:03:41,530 --> 01:03:42,430
+التالية والدرجة التالية والدرجة التالية والدرجة
+
+592
+01:03:42,430 --> 01:03:44,990
+التالية والدرجة التالية والدرجة التالية والدرجة
+
+593
+01:03:44,990 --> 01:03:45,050
+التالية والدرجة التالية والدرجة التالية والدرجة
+
+594
+01:03:45,050 --> 01:03:45,870
+التالية والدرجة التالية والدرجة التالية والدرجة
+
+595
+01:03:45,870 --> 01:03:46,750
+التالية والدرجة التالية والدرجة التالية والدرجة
+
+596
+01:03:46,750 --> 01:03:48,930
+التالية والدرجة التالية والدرجة التالية والدرجة
+
+597
+01:03:48,930 --> 01:03:52,320
+التالية والدي يعني هذه وهذه يمكن يكون بينهم عامل
+
+598
+01:03:52,320 --> 01:03:56,980
+مشترك لكن مع الثالثة لأ وهكذا يعني لا يوجد
+
+599
+01:03:56,980 --> 01:04:01,520
+للثلاثة مع بعض بينهم عامل مشترك لو وجد بدنا نتخلص
+
+600
+01:04:01,520 --> 01:04:06,580
+منه و نتخلص منه تمام ولا يؤثر على شكل الحل
+
+601
+01:04:06,580 --> 01:04:11,720
+المعادلة التفاضلية يبقى الـ P و الـ QR have no
+
+602
+01:04:11,720 --> 01:04:17,420
+common factors لا توجد بينهم أي عوامل مشتركة بدنا
+
+603
+01:04:17,420 --> 01:04:21,200
+نعطي تعريف جديد هذا كلام برضه جديد علينا
+
+604
+01:04:21,200 --> 01:04:25,100
+ما شوفناهوش قبل اليوم بدنا نعطي تعريف للـ ordinary
+
+605
+01:04:25,100 --> 01:04:28,580
+point اللي هي النقطة العادية و الـ singular point
+
+606
+01:04:28,580 --> 01:04:33,840
+اللي هي النقطة الشاذة أو النقطة المنفردة أو النقطة
+
+607
+01:04:33,840 --> 01:04:38,420
+المنعزلة لكن الدارج النقطة الشاذة singular point
+
+608
+01:04:39,220 --> 01:04:43,560
+طبعا singular اللغة الأدبية أعزب في اللغة
+
+609
+01:04:43,560 --> 01:04:46,980
+الإنجليزية لكن احنا ما قلناش دعوة
+
+646
+01:07:59,680 --> 01:08:05,620
+نصف قطر التقارب كذلك إذا النقطة هذه عبارة عن X
+
+647
+01:08:05,620 --> 01:08:14,680
+x<sub>0</sub> ناقص ρ والنقطة هذه x<sub>0</sub> زائد ρ النقطة هذه
+
+648
+01:08:14,680 --> 01:08:18,180
+وقبل النقطة هذه ال series diverges مليش علاقة فيها
+
+649
+01:08:18,180 --> 01:08:22,880
+يبقى أنا مقيد في الفترة اللي ال series هذه تبعت
+
+650
+01:08:22,880 --> 01:08:27,580
+الحل اللي بتكون عليها مالها تقاربية و نصف القطر
+
+651
+01:08:27,580 --> 01:08:32,340
+هنا دائما و أبدا موجب لأنه مسافة مسافة بين
+
+652
+01:08:32,340 --> 01:08:36,020
+النقطتين يبقى مضحكتش المقصود بالعبارة اللي عندنا
+
+653
+01:08:36,020 --> 01:08:41,560
+هذه تمام يبقى هي كل ما في الأمر يبقى بنات الحل
+
+654
+01:08:41,560 --> 01:08:48,860
+عندي في حالة المعادلات هذه بوصفة المتسلسلات ممكن
+
+655
+01:08:48,860 --> 01:08:53,740
+يكون على الشكل اللي عندنا هذا و ممكن يكون لو كانت x
+
+656
+01:08:53,740 --> 01:08:58,300
+<sub>0</sub> بزيرو لو اعطاني x<sub>0</sub> بزيرو بصير الحل على
+
+657
+01:08:58,300 --> 01:09:05,540
+اسم a<sub>n</sub> x<sup>n</sup> تمام إذا جالي عند x<sub>0</sub>
+
+658
+01:09:05,540 --> 01:09:09,500
+تسوى واحد أو ال ordinary point تسوى واحد أو اتنين
+
+659
+01:09:09,500 --> 01:09:14,900
+أو تلاتة بدي اتقيد فيها وبالتالي احسب ايه الحل
+
+660
+01:09:14,900 --> 01:09:20,410
+عندها هذا كل الجزء النظري تبع ال section لكن الحل
+
+661
+01:09:20,410 --> 01:09:25,430
+طويل شوية للمثال نبدأ ناخد مثال فوضيح على الشغل
+
+662
+01:09:25,430 --> 01:09:40,110
+هذه أول مثال يقول ما يأتي example one يقول
+
+663
+01:09:40,110 --> 01:09:41,910
+find the series solution
+
+664
+01:09:49,750 --> 01:10:00,110
+الحل اللي بيكون على شكل متسلسلة and the recurrence
+
+665
+01:10:00,110 --> 01:10:06,470
+relation and
+
+666
+01:10:06,470 --> 01:10:12,330
+recurrence relation for the
+
+667
+01:10:14,680 --> 01:10:23,100
+differential equation للمعادلة التفاضلية y''
+
+668
+01:10:23,100 --> 01:10:33,460
+زائد x في y' زائد 2 y تساوي zero about
+
+669
+01:10:33,460 --> 01:10:36,580
+the
+
+670
+01:10:36,580 --> 01:10:40,460
+point حوالين النقطة
+
+671
+01:11:00,900 --> 01:11:08,100
+نرجع لسؤال مرة ثانية طالب شغلتين طالب الحل و
+
+672
+01:11:08,100 --> 01:11:12,720
+recurrence relation طبعا أنا مش هقدر اوصل للحل الا
+
+673
+01:11:12,720 --> 01:11:16,840
+احسب له a recurrence relation find the series
+
+674
+01:11:16,840 --> 01:11:21,180
+solution and the recurrence relation for the
+
+675
+01:11:21,180 --> 01:11:26,160
+differential equation هذه about the point x<sub>0</sub> يساوي
+
+676
+01:11:26,160 --> 01:11:32,020
+0 هل قلل x<sub>0</sub> يساوي 0 هذه ordinary point ولا singular
+
+677
+01:11:32,020 --> 01:11:37,920
+point ما جليش لكن أنا لحالي هاكتشف انه هادي ordinary
+
+678
+01:11:37,920 --> 01:11:41,320
+point من دون ما يقولي بقول .. بقولك كده، بقولك
+
+679
+01:11:41,320 --> 01:11:45,940
+كتالة، هالحين مين ان ال P of X تبعت المعادلة هاد
+
+680
+01:11:45,940 --> 01:11:54,950
+يا بنات؟ جدير؟ واحدهل هناك قيمة ل X بتخلي النتيجة
+
+681
+01:11:54,950 --> 01:12:00,090
+هذه صفر ولا قيمة؟ يبقى هذا مقدار ثابت جد ما
+
+682
+01:12:00,090 --> 01:12:04,810
+تتغير ال X بتبقى مقدار ثابت أيش ما تصير ال X يبقى
+
+683
+01:12:04,810 --> 01:12:12,010
+هذا معناته هذا طبعا سوى واحد for all X هذا معناته
+
+684
+01:12:12,010 --> 01:12:19,230
+every point is an ordinary 
+
+685
+01:12:25,800 --> 01:12:30,500
+ببنان عليه ال X not to zero هو ordinary ولا
+
+686
+01:12:30,500 --> 01:12:39,600
+singular؟ ordinary يبقى ال X not to zero is an
+
+687
+01:12:39,600 --> 01:12:46,020
+ordinary point تمام
+
+688
+01:12:47,200 --> 01:12:55,200
+يبقى الحل بيكون على شكل y تساوي a<sub>0</sub> في x ناقص
+
+689
+01:12:55,200 --> 01:13:01,940
+zero يعني a<sub>n</sub> x<sup>n</sup> يبقى هنا باجي بقول
+
+690
+01:13:01,940 --> 01:13:08,400
+let y تساوي ال summation من n equal zero ل
+
+691
+01:13:08,400 --> 01:13:20,560
+infinity لل a<sub>n</sub> x<sup>n</sup> be a solution of
+
+692
+01:13:20,560 --> 01:13:28,020
+the differential equation 1 سميلي هذا بنات اللي هي
+
+693
+01:13:28,020 --> 01:13:34,980
+المعادلة رقم 1 اللي تبعت السؤال كويس
+
+694
+01:13:34,980 --> 01:13:47,750
+نشتاق يبقى بدنا y' يساوي summation لل n a<sub>n</sub> x
+
+695
+01:13:47,750 --> 01:13:51,950
+to the power n minus one و ال summation بيبدأ من
+
+696
+01:13:51,950 --> 01:13:58,410
+وين ان عند n تساوي واحد لإنه أول حد هنا هو a<sub>0</sub>
+
+697
+01:13:58,820 --> 01:14:04,800
+هيضير مع الاشتقاق طيب هذا بده يعطيك ان y''
+
+698
+01:14:04,800 --> 01:14:13,000
+يساوي summation n في n ناقص واحد في a<sub>n</sub> في ال x أس
+
+699
+01:14:13,000 --> 01:14:20,940
+n ناقص 2 تمام ال summation من وان بده يبدأ من
+
+700
+01:14:20,940 --> 01:14:26,560
+عند n تساوي 2 الى infinity يبقى هاي جيبته
+
+701
+01:14:26,560 --> 01:14:30,940
+المشتقة الأولى و المشتقة الثانية بتروح اعوض وين في
+
+702
+01:14:30,940 --> 01:14:39,180
+المعادلة رقم واحد يبقى باجي بقول له substitute in
+
+703
+01:14:39,180 --> 01:14:49,200
+the differential equation one we get نحصل علاماتي
+
+704
+01:14:49,900 --> 01:14:55,100
+الأول شي y'' يبقى بدي أنزل هذا ال summation زي ما
+
+705
+01:14:55,100 --> 01:15:00,380
+هو يبقى ما يصير عندي summation من N equal two to
+
+706
+01:15:00,380 --> 01:15:06,580
+infinity ما دها زائد X في summation بدنا المشتقة
+
+707
+01:15:06,580 --> 01:15:14,300
+الأولى من عند N equal one to infinity لمن؟ لل N a<sub>N</sub> 
+
+708
+01:15:14,300 --> 01:15:21,290
+X<sup>N-1</sup> أيه بيخلصنا ال term الثاني زائد
+
+709
+01:15:21,290 --> 01:15:26,990
+2 في summation من عند ال N equal zero to
+
+710
+01:15:26,990 --> 01:15:36,050
+infinity لمين لـ X<sup>N</sup> كل هذا بده
+
+711
+01:15:36,050 --> 01:15:42,620
+يساوي كده؟ بده يساوي Zero مشان اجيب له recurrence
+
+712
+01:15:42,620 --> 01:15:49,540
+relation بدي كله يصير بدلالة X<sup>M</sup> هاي
+
+713
+01:15:49,540 --> 01:15:54,900
+واحدة 2 بدي ال index اللي تحت ال summation كله
+
+714
+01:15:54,900 --> 01:16:00,820
+يصير زي بعضه كويس؟ بنقوله بسيطة يبقى هذا الكلام
+
+715
+01:16:00,820 --> 01:16:06,140
+بدنا نرجع لمين؟ زي شغلنا اللي توقبل قليل في ال
+
+716
+01:16:06,140 --> 01:16:11,480
+section الماضي صحيح ولا لا؟ إذا ال section الماضي
+
+717
+01:16:11,480 --> 01:16:16,780
+كان ضروري جدا مشان نعرف نشتغل في هذا ال section
+
+718
+01:16:16,780 --> 01:16:23,370
+فباجي بقول هذه بقدر أخليها x<sup>n</sup> لو
+
+719
+01:16:23,370 --> 01:16:28,890
+خلّيت ال index يبدأ من وين إذا بدأ أشيل كل n و أحط
+
+720
+01:16:28,890 --> 01:16:37,590
+مكانها n زائد 2 يبقى بصير المسألة summation من n
+
+721
+01:16:37,590 --> 01:16:46,290
+equal zero to infinity وهذه بصير n زائد 2 في n
+
+722
+01:16:46,290 --> 01:16:55,350
+زائد 1 في a<sub>n+2</sub> في ال x<sup>n</sup>
+
+723
+01:16:55,350 --> 01:17:01,370
+طيب هذه بسيطة دخل هذه جوا بصير x<sup>n</sup>
+
+724
+01:17:01,370 --> 01:17:06,490
+يبقى ال x بروح بدخلها جوا يبقى لما ندخلها جوا ال
+
+725
+01:17:06,490 --> 01:17:11,950
+summation زائد summation من n equal one to
+
+726
+01:17:11,950 --> 01:17:21,390
+infinity لل a<sub>n</sub> x<sup>n+1</sup> ونقص
+
+727
+01:17:21,390 --> 01:17:26,650
+واحد مع السلامة يبقى زائد x<sup>n</sup> 2
+
+728
+01:17:26,650 --> 01:17:31,210
+هذه بقدر أدخلها جوا ال summation يبقى زائد
+
+729
+01:17:31,210 --> 01:17:37,390
+summation من n equal zero to infinity للـ 2 a<sub>n</sub>
+
+730
+01:17:37,390 --> 01:17:43,310
+x<sup>n</sup> كله بده يساوي قداش يساوي zero بقول
+
+731
+01:17:43,310 --> 01:17:48,810
+كويس تعالى نطلع في ال X's هنا to the power N هنا
+
+732
+01:17:48,810 --> 01:17:53,070
+to the power N to the power N يبقى بدنا نحافظ على
+
+733
+01:17:53,070 --> 01:17:57,510
+المكتسبات الوطنية أصحى تلعبي فيها إن احنا هذه
+
+734
+01:17:57,510 --> 01:18:00,610
+بيتنا ياها لازمنا نطلع في دلالة X<sup>N</sup>
+
+735
+01:18:00,610 --> 01:18:05,830
+طيب نجي لها ال summation N تساوي Zero N تساوي واحد
+
+736
+01:18:05,830 --> 01:18:13,460
+N تساوي Zero مظبوط يبقى أنا يا بخليهم كلهم zero يا
+
+737
+01:18:13,460 --> 01:18:19,000
+بخليهم كلهم واحد مظبوط مش هنقدر نجمعهم مع بعض بقول
+
+738
+01:18:19,000 --> 01:18:24,680
+أه لو هذه بده أخليها zero أيش بيصير عندي؟ بده أشيل
+
+739
+01:18:24,680 --> 01:18:29,020
+كل N و أحط مكانها N زاد واحد بيصير N زائد واحد a<sub>N+1</sub>
+
+740
+01:18:29,020 --> 01:18:34,820
+زائد واحد X<sup>N+1</sup> خربنا الدنيا ما حافظناش على
+
+741
+01:18:34,820 --> 01:18:40,240
+المكتسبات الوطنية تمام؟ يبقى اصحى تلعب فيها طيب
+
+742
+01:18:40,240 --> 01:18:46,140
+تعالى نحول ال summation كله بدلالة 2 هذا سهل جدا و
+
+743
+01:18:46,140 --> 01:18:51,760
+بيصيرش مشاكل في ال index كيف؟ بقى يبقى فلت أول حد
+
+744
+01:18:51,760 --> 01:18:55,820
+هنا و هنا فلت أول حد من هنا من ال summation يبقى
+
+745
+01:18:55,820 --> 01:18:59,500
+انحلت مشكلتك بيصير كل ال summation زي ما هو و ال
+
+746
+01:18:59,500 --> 01:19:05,300
+index بقيت كما هي تمام كيف نجي نقول حط n ب zero
+
+747
+01:19:05,300 --> 01:19:13,820
+zero zero بظلي 2 في 1 ب 2 X<sup>0</sup> ب واحد
+
+748
+01:19:13,820 --> 01:19:18,550
+يبقى هذا لما ال n تساوي zero بالا عندنا زائد
+
+749
+01:19:18,550 --> 01:19:24,570
+summation لما ال N تساوي واحد لل infinity لل N زائد
+
+750
+01:19:24,570 --> 01:19:29,770
+2 في N زائد 1 في ال a<sub>N+2</sub> في ال
+
+751
+01:19:29,770 --> 01:19:36,040
+X<sup>N</sup> هذه يا بناتفش فيها تلعب بنزلها زي
+
+752
+01:19:36,040 --> 01:19:41,940
+ما هي 1 الى infinity لل N a<sub>N</sub> X<sup>N</sup>
+
+753
+01:19:41,940 --> 01:19:47,420
+زائد هذه كمان بده أطلع منها الحد الأول يعني لو
+
+754
+01:19:47,420 --> 01:19:54,120
+كانت N تساوي Zero بيصير 2 a<sub>0</sub> زائد summation
+
+755
+01:19:54,120 --> 01:20:01,140
+من N equal Zero to infinity للـ 2 من عند N تساوي
+
+756
+01:20:01,140 --> 01:20:09,650
+واحد للـ 2 a<sub>n</sub> x<sup>n</sup> يساوي Zero ن إذا ال
+
+757
+01:20:09,650 --> 01:20:14,110
+term هذا و ال term هذا بيقولوا مخليكي أنتوا على
+
+758
+01:20:14,110 --> 01:20:20,070
+الشك ده اطلعوا برا يبقى بيصير عندي قداش 2 2
+
+759
+01:20:20,070 --> 01:20:27,690
+زائد 2 a<sub>0</sub> لحالهم باقي ال Summations كله
+
+760
+01:20:27,690 --> 01:20:31,850
+مضروب في X<sup>N</sup> وكله بيبدأ من عند الواحد
+
+761
+01:20:31,850 --> 01:20:36,870
+يبقى بقدر أجمعهم مع بعض بـ Summation واحد يبقى بقدر
+
+762
+01:20:36,870 --> 01:20:42,550
+أقول هذا زائد summation من N equal one to infinity
+
+763
+01:20:42,550 --> 01:20:49,610
+للـ N زائد 2 في N زائد 1 في ال a<sub>N+2</sub> زائد
+
+764
+01:20:49,610 --> 01:21:00,740
+N في ال a<sub>N</sub> زائد 2 a<sub>n</sub> وكل هذا
+
+765
+01:21:00,740 --> 01:21:07,600
+الكلام مضروب في main في ال x<sup>n</sup> و يساوي
+
+766
+01:21:07,600 --> 01:21:11,320
+zero الآن
+
+767
+01:21:11,320 --> 01:21:16,060
+عندنا polynomial على الشمال بده يساوي zero شو خلها
+
+768
+01:21:16,060 --> 01:21:22,250
+zero؟ معاملات إذا كل المعاملات بيصير صفر يبقى بناء
+
+769
+01:21:22,250 --> 01:21:27,910
+عليه بيصير عندي 2 2 زائد 2 a<sub>0</sub> يساوي
+
+770
+01:21:27,910 --> 01:21:40,650
+كده؟ Zero ومنها الـ 2 يساوي ناقص a<sub>0</sub> تمام؟ طيب
+
+771
+01:21:40,650 --> 01:21:49,750
+نيجي ثانية and هذه يا بنات N زائد 2 في N زائد
+
+772
+01:21:49,750 --> 01:21:57,370
+1 في a<sub>N+2</sub> زائد شو رأيك ندخل فيها a<sub>N</sub> عمل
+
+773
+01:21:57,370 --> 01:22:05,990
+مشترك بيظل قد ايش N زائد 2 يبقى N زائد 2 في
+
+774
+01:22:05,990 --> 01:22:14,970
+a<sub>N</sub> بده يساوي Zero بنقدر نجزئ كله على مين؟ على N زائد
+
+775
+01:22:14,970 --> 01:22:23,730
+2 لو جزئنا على N زائد 2 أيش بيضل عندنا؟ بيضل عندنا
+
+776
+01:22:23,730 --> 01:22:37,090
+N زائد 1 في ال a<sub>N+2</sub> يساوي ناقص a<sub>N</sub> أو بيصير
+
+777
+01:22:37,090 --> 01:22:44,190
+عندنا مين؟ بيصير عندنا a<sub>n+2</sub> يساوي ناقص a<sub> </sub>
+
+778
+01:22:44,190 --> 01:22:54,400
+n على مين على n زائد 1 طب a<sub>2</sub> بقد ايش؟ سالب
+
+779
+01:22:54,400 --> 01:23:05,000
+a<sub>0</sub> يبقى هذا معناته سالب سالب a<sub>0</sub> على N زائد
+
+780
+01:23:05,000 --> 01:23:10,920
+1 استنى
+
+781
+01:23:10,920 --> 01:23:15,620
+استنى شوية هذه N زائد اه هذه a<sub>N</sub> كيش خلها a<sub>2</sub>
+
+782
+01:23:16,110 --> 01:23:20,910
+أصابة امرأة و أخطأ عمر بس كلام مظبوط كلامك صحيح
+
+783
+01:23:20,910 --> 01:23:28,230
+يبقى هذه a<sub>n</sub> بس كلام مظبوط أصابة امرأة و أخطأ عمر
+
+784
+01:23:28,230 --> 01:23:34,310
+تمام؟ طب شو اسم هذه يا بنات؟ هذا ال recurrence
+
+785
+01:23:34,310 --> 01:23:40,650
+relation يبقى هذه هي ال recurrence relation بس a<sub>n</sub>
+
+786
+01:23:40,650 --> 01:23:43,450
+بتبدأ من n zero ولا من n الواحد؟
+
+787
+01:23:46,330 --> 01:23:54,110
+هذه لو قلنا من عند ال zero بيصير 2 هذه zero
+
+788
+01:23:54,110 --> 01:24:01,550
+وهذه zero مظبوط بيصير ناقص a<sub>0</sub> على 1 اللي فوق
+
+789
+01:24:01,550 --> 01:24:01,950
+هذه
+
+790
+01:24:07,790 --> 01:24:13,230
+عندما قلت n تساوي زيرو لكن عندما قلت n تساوي
+
+791
+01:24:13,230 --> 01:24:18,030
+واحد لبقى اللي فوق فقلت لحاله إذا بجمع 2 مع
+
+792
+01:24:18,030 --> 01:24:22,870
+بعض و بقول n تساوي زيرو و 1 و 2 و 3
+
+793
+01:24:22,870 --> 01:24:28,930
+إلى ما شاء الله يبقى اجتملت على اللي فوق لو كانت ها
+
+794
+01:24:28,930 --> 01:24:32,210
+عوقة عند الـ 0 وما طلعتش اللي فوق يبقى بيخلي اللي
+
+795
+01:24:32,210 --> 01:24:36,490
+فوق لحالها وها دي لحالها وها دي اللي بسميها
+
+796
+01:24:36,490 --> 01:24:41,890
+reconciliation و بقول إن بتبدأ من عند الواحد تمام
+
+797
+01:24:41,890 --> 01:24:49,430
+بعيد كلامي هذا مرة ثانية احنا هنا سمينا ثابت سوينا
+
+798
+01:24:49,430 --> 01:24:55,340
+ثابت بالـ 0 طالع عند a<sub>2</sub> يساوي ناقص a<sub>0</sub> نأخذ
+
+799
+01:24:55,340 --> 01:24:58,320
+المعامل هذا و أقوم به بالـ zero و أخرجه عند الـ
+
+800
+01:24:58,320 --> 01:25:01,920
+recurrence relation الـ recurrence relation يبقى
+
+801
+01:25:01,920 --> 01:25:07,720
+ممكن تجتمل على المقدار اللي فوق و ممكن ألا تجتمل
+
+802
+01:25:07,720 --> 01:25:12,700
+إذا هذه لم تجتمل على اللي فوق بجي بقول n تساوي
+
+803
+01:25:12,700 --> 01:25:17,440
+1 و 2 و 3 و لا أكتب ال zero إذا جمعت
+
+804
+01:25:17,440 --> 01:25:21,220
+على اللي فوق بجي بخليها تبدأ من عند ال zero بسبنجي
+
+805
+01:25:21,220 --> 01:25:25,860
+بقول لو حطينا zero لل N فعلا بتجيب اللي فوق ولا
+
+806
+01:25:25,860 --> 01:25:31,720
+بتجيبوش بنقول يطلع هنا حط زيرو بيصير 2 حط زيرو
+
+807
+01:25:31,720 --> 01:25:36,940
+بيصير a<sub>0</sub> حط زيرو بيصير ناقص a<sub>0</sub> على 1 يبقى
+
+808
+01:25:36,940 --> 01:25:41,420
+مظبوط يبقى هه خلاص n تساوي zero بدل ال N استغنت عن
+
+809
+01:25:41,420 --> 01:25:46,440
+هذه و صرت هذه هي ال recurrence relation اللي عندنا
+
+810
+01:25:46,440 --> 01:25:54,790
+طيب الأن بدنا نبدأ نحسب a<sub>2</sub> موجودة بدي أحسب a<sub>3</sub> و a<sub>4</sub>
+
+811
+01:25:54,790 --> 01:26:01,030
+و a<sub>5</sub> مشان أجيب شكل الحل اللي عندنا فباجي بقول له الأن
+
+812
+01:26:01,030 --> 01:26:07,270
+بدي أجي آخذ اللي هو مين a<sub>2</sub> موجودة يبقى بدي أجي آخذ
+
+813
+01:26:07,270 --> 01:26:14,520
+له a<sub>3</sub> و n زائد 2 التلاتة اللي بقدر أكتبها 1 زي
+
+814
+01:26:14,520 --> 01:26:18,580
+2 يبقى لما أقارنها مع ال reconciliation يبقى
+
+815
+01:26:18,580 --> 01:26:23,320
+ال N هنا بقدرش يبقى بده أشيل كل N و أحط مكانها
+
+816
+01:26:23,320 --> 01:26:30,360
+1
+
+861
+01:31:50,590 --> 01:31:57,290
+سبعة أقل منه بمقدار واحد يبقى 2n زائد واحد أقل منه
+
+862
+01:31:57,290 --> 01:32:04,200
+بمقدار واحد يبقى 2n يبقى بضل ماشي لغاية 2n بس
+
+863
+01:32:04,200 --> 01:32:08,160
+ضايل علينا واحد نشوف هل الإشارة هذه صحيحة اللي
+
+864
+01:32:08,160 --> 01:32:13,280
+كتبناها والله ما يجرى إذا صحيحة بصمنا إذا مش صحيحة
+
+865
+01:32:13,280 --> 01:32:18,280
+بص بتقول n زائد واحد أو n زائد واحد بتصير مالها
+
+866
+01:32:18,280 --> 01:32:24,760
+صحيحة بعدين بقولي كويس لو حطيت n بواحد يبقى بصير
+
+867
+01:32:24,760 --> 01:32:32,190
+ايش 2n بواحد بصير سالب a0 و الواحدة كله
+
+868
+01:32:32,190 --> 01:32:36,370
+بطير و بضلش عندي إلا مين إلا واحد يبقى سالب a0
+
+869
+01:32:36,370 --> 01:32:43,970
+هي صحيحة طب لو حطيت n باتنين بصير a4 سالب
+
+870
+01:32:43,970 --> 01:32:49,470
+واحد تربيع يبقى بضل بس a0 على 1 في 3
+
+871
+01:32:49,830 --> 01:32:56,690
+4 a0 1 في 3 هي 4 طب اه 6 بنفس
+
+872
+01:32:56,690 --> 01:33:01,790
+الطريقة يبقى إشرتنا صحيحة و بالمثل هنا صحيحة تماما
+
+873
+01:33:01,790 --> 01:33:07,590
+ما عندنا مشكلة مدام جبت هذا الكلام إذا بقدر أشوف
+
+874
+01:33:07,590 --> 01:33:15,600
+شكل الـ solution أنا فارضه شو شكله مسحناه مع
+
+875
+01:33:15,600 --> 01:33:23,020
+السلامة احنا فرضنا أن ال summation للـ a n في x to
+
+876
+01:33:23,020 --> 01:33:31,530
+the power n يبقى عندنا الـ solution y كان a0
+
+877
+01:33:31,530 --> 01:33:43,250
+زائد a1 x زائد a2 x تربيع a3 x تكعيب a4 x أس 4 a5
+
+878
+01:33:43,250 --> 01:33:51,150
+x أس 5 a6 x أس 6 عن طريق الوصول إلى الـ a7x7 زائد
+
+879
+01:33:51,150 --> 01:33:58,390
+زائد a n x to the power n زائد الآخرين يصمش من n
+
+880
+01:33:58,390 --> 01:34:03,530
+equal zero to infinity للـ a n x to the power n مش
+
+881
+01:34:03,530 --> 01:34:08,570
+هيك كان شكله؟ طيب نيجي نعوض يبقى ايه الـ solution y
+
+882
+01:34:08,570 --> 01:34:16,010
+سوى a0 زائد a1 x خليتهم زي ما هم ليش؟ لأن كل الحلول
+
+883
+01:34:16,010 --> 01:34:24,110
+طلعت بـ a0 و a1 وصلنا لمين؟ للـ a2 الـ a2 بقدرش
+
+884
+01:34:24,110 --> 01:34:32,190
+عندنا؟ بناقص a0 يبقى ناقص a0 x تربيع وصلنا
+
+885
+01:34:32,190 --> 01:34:37,480
+للـ a3 الـ a3 هو ناقص a1 على 2
+
+886
+01:34:45,910 --> 01:34:50,930
+لـ x تكعيب ايه 3 يبقى هذه x تكعيب لأن هاي
+
+887
+01:34:50,930 --> 01:34:55,130
+الـ x تربيع أخدناها يبقى خلاصة من مين من الـ a3
+
+888
+01:34:55,130 --> 01:35:04,490
+بنيجي للـ a4 يعني زائد a0 على 1 في 3 يبقى
+
+889
+01:35:04,490 --> 01:35:13,250
+هذه a4 في الـ x أس 4 الآن اللي بعدها زائد وصلنا
+
+890
+01:35:13,250 --> 01:35:21,910
+مين للـ a5 الـ a5 هي فوق اللي هو a1 على 2 في 4 في
+
+891
+01:35:21,910 --> 01:35:30,250
+x أس 5 تمام وصلنا لـ a6 a6 اللي هو ناقص a0
+
+892
+01:35:30,250 --> 01:35:40,330
+على 1 في 3 في 5 في من؟ في الـ x أس قديش هذه a
+
+893
+01:35:40,330 --> 01:35:47,170
+في الـ x أس 6 وصلنا للـ a7 هي الـ a7 اللي
+
+894
+01:35:47,170 --> 01:35:53,950
+هو ناقص a1 على 2 4 6 في الـ x أس 7
+
+895
+01:35:53,950 --> 01:36:02,070
+زائد a n بعرفهاش لكن أنا بعرف a 2n يبقى بقوله
+
+896
+01:36:02,070 --> 01:36:09,250
+زائد هذا بتظل ماشية وبعدين بقوله الـ a2n اللي هي
+
+897
+01:36:09,250 --> 01:36:16,170
+مين اللي هو ناقص 1 to the power n a1 على 2
+
+898
+01:36:16,170 --> 01:36:24,470
+4 a n اللي قبلها اللي قبلها يبقى a0 a
+
+899
+01:36:24,470 --> 01:36:31,480
+0 على 1 في 3 في 5 1 في 3 في
+
+900
+01:36:31,480 --> 01:36:38,460
+5 في 2 n ناقص 1 في الـ x أس 2 n
+
+901
+01:36:42,370 --> 01:36:49,430
+اللي بعده زائد ناقص 1 to the power n للـ a1
+
+902
+01:36:49,430 --> 01:36:59,430
+على 2 4 6 للـ 2 n زائد x x 2
+
+903
+01:36:59,430 --> 01:37:07,350
+n زائد 1 زائد إلى ما شاء الله طيب بدنا نكتب
+
+904
+01:37:07,350 --> 01:37:09,090
+الجواب النهائي
+
+905
+01:37:20,350 --> 01:37:27,550
+الجواب النهائي y تساوي اللي فيهم a0 بدي أخدهم
+
+906
+01:37:27,550 --> 01:37:31,770
+مع بعض و اللي فيهم a1 بدي أخدهم مع بعض بس الـ a0
+
+907
+01:37:31,770 --> 01:37:38,070
+بدي أخدها برة عامل مشترك يبقى هذه a0 من الكل
+
+908
+01:37:38,070 --> 01:37:48,470
+وظل عندي 1 بعد هيك ناقص x تربيع ناقص x تربيع بعد
+
+909
+01:37:48,470 --> 01:37:56,890
+ذلك زائد x أس 4 زائد x أس 4 على 1 في
+
+910
+01:37:56,890 --> 01:38:02,050
+3 هذه باعتبارها على جداش على 1 اللي بعدها
+
+911
+01:38:02,050 --> 01:38:11,630
+ناقص x أس 6 يبقى ناقص x أس 6 على 1 في 3
+
+912
+01:38:11,630 --> 01:38:17,930
+في 5 ونبقى نمشي لغاية
+
+913
+01:38:17,930 --> 01:38:21,530
+سالب
+
+914
+01:38:21,530 --> 01:38:27,030
+1 to the power n لـ x قديش ناخدها عامل مشترك
+
+915
+01:38:27,030 --> 01:38:34,630
+للـ x أس 2 n على 1 في 3 في 5 في
+
+916
+01:38:34,630 --> 01:38:42,530
+2 n ناقص 1 زائد إلى ما شاء الله أخذ هذول
+
+917
+01:38:42,530 --> 01:38:49,550
+منهم زائد الباقي أخذ منهم a1 عامل مشترك يبقى
+
+918
+01:38:49,550 --> 01:38:57,930
+ايش بطلع عندي؟ x وبعد الـ x بيجينا ناقص x تكعيب
+
+919
+01:38:57,930 --> 01:38:59,050
+على 2
+
+920
+01:39:03,900 --> 01:39:13,480
+واللي بعدها ناقص x تكعيب على a2 بصير عندي زائد x
+
+921
+01:39:13,480 --> 01:39:17,940
+أس
+
+922
+01:39:17,940 --> 01:39:25,730
+5 على 2 في 4 وبعدها بيصير ناقص x أو
+
+923
+01:39:25,730 --> 01:39:32,890
+الـ 7 ناقص x أو الـ 7 على 2 في 4 في 6
+
+924
+01:39:32,890 --> 01:39:39,410
+وزائد زائد ناقص 1 to the power n للـ x أس 2
+
+925
+01:39:39,410 --> 01:39:46,690
+n زائد 1 على 2 4 6 2 n زائد إلى
+
+926
+01:39:46,690 --> 01:39:52,780
+ما شاء الله يعني يا بنات بقدر أكتب هذه على الشكل
+
+927
+01:39:52,780 --> 01:40:00,460
+التالي a0 summation لشكل الحد النوني to the
+
+928
+01:40:00,460 --> 01:40:08,080
+power n للـ x أس 2 n 1 3 5 2 n
+
+929
+01:40:08,080 --> 01:40:17,420
+ناقص 1 من عند n تساوي 0 إلى ∞ يبقى
+
+930
+01:40:17,420 --> 01:40:25,230
+هنا زائد اللي هو الحد النوني هذا هذا a1 summation
+
+931
+01:40:25,230 --> 01:40:32,030
+من n equal 0 to ∞ لمين لشكل الحد النوني
+
+932
+01:40:32,030 --> 01:40:40,670
+n x أس 2 n زائد 1 2 4 6 لغاية
+
+933
+01:40:40,670 --> 01:40:47,930
+2 n بس تعالى نشوف شغل هذا صح ولا غلط تعالى
+
+934
+01:40:47,930 --> 01:40:55,580
+نشوف صح هذا ولا غلط الآن لو قلت أن n تساوي 0
+
+935
+01:40:55,580 --> 01:40:59,720
+إذا n تساوي 0 إذا n تساوي 0 إذا n تساوي
+
+936
+01:40:59,720 --> 01:41:00,140
+0
+
+937
+01:41:12,100 --> 01:41:18,260
+و أقول له a0 زائد a0 و أقول له من عند الـ n
+
+938
+01:41:18,260 --> 01:41:23,080
+تساوي 1 اه هيك بيصير كلامي صحيح لو حطيت n بواحد
+
+939
+01:41:23,080 --> 01:41:27,320
+بيصير 2 ناقص 1 اللي هو 1 الحد الأول حط
+
+940
+01:41:27,320 --> 01:41:32,980
+هنا 1 و هنا x أس 2 يبقى بيصير ناقص x تربيع
+
+941
+01:41:32,980 --> 01:41:38,760
+هيو مظبوط تمام؟ و الـ 1 ده في a0 هيو طلعته
+
+942
+01:41:38,760 --> 01:41:43,230
+بره إذا ما عندي مشكلة في هذه الحالة هذا بالنسبة
+
+943
+01:41:43,230 --> 01:41:48,450
+للـ term الأول الـ term الثاني نفس القصة يبقى بالداج
+
+944
+01:41:48,450 --> 01:41:56,850
+أقول له من عند n تساوي 1 وهذه a1x زائد a1 يعني
+
+945
+01:41:56,850 --> 01:42:02,870
+يا بنات خلت الحد الأول هذا كمان برة وبالتالي ما
+
+946
+01:42:02,870 --> 01:42:06,990
+عنده مشكلة في هذه الحالة بيصير شونه سليم 100
+
+947
+01:42:06,990 --> 01:42:13,160
+بالمائة أو إن شئنا فقلنا a0 مقدار ثابت زائد a
+
+948
+01:42:13,160 --> 01:42:26,160
+0 y1 زائد a1 x زائد a1 y2 أو a0 زائد a1 x
+
+949
+01:42:26,160 --> 01:42:36,180
+زائد a0 y1 زائد a1 y2 هذا الـ general solution
+
+950
+01:42:38,330 --> 01:42:42,450
+يعني يا بنات لو غطيت هدول بصينا الصيغة اللي عندنا
+
+951
+01:42:42,450 --> 01:42:46,930
+هذه هي الصيغة اللي احنا عارفينها قبل هيك لما كنا
+
+952
+01:42:46,930 --> 01:42:53,350
+نحلها بالطريقة العادية في chapter 3 حد يلاقي تساؤل
+
+953
+01:42:53,350 --> 01:42:58,830
+هنا لسه لا يزال عندنا مثال أتعقد من هذا كثير هذا
+
+954
+01:42:58,830 --> 01:43:06,450
+كله حسابات مباشرة وسهلة أيوة ماشي لحد هنا تمام؟
+
+955
+01:43:07,280 --> 01:43:13,100
+هذه زائد هذه يبقى هذا يعتبر الحل الأول وهذا يعتبر
+
+956
+01:43:13,100 --> 01:43:18,860
+الحل الثاني تمام؟ بدي أحاول أكتب كل واحد فيهم بس
+
+957
+01:43:18,860 --> 01:43:23,280
+على شكل summation ليس إلا لو قلت a0 في الـ
+
+958
+01:43:23,280 --> 01:43:27,560
+summation الأول بالشكل هذا وخليته يبدأ من عند الـ
+
+959
+01:43:27,560 --> 01:43:32,480
+0 بصير كلامي غلط ليش؟ لأن لو حطيت n بـ 0
+
+960
+01:43:32,480 --> 01:43:37,200
+بطلع عندي هذا term جداش احنا ما عنديش سالب 1 عندي
+
+961
+01:43:37,200 --> 01:43:41,880
+جداش عندي 1 إذا لا يمكن يصير الكلام هذا عندي
+
+962
+01:43:41,880 --> 01:43:47,560
+الصح تمام؟ لكن لو كانت هذه 2 n زائد 1 مش
+
+963
+01:43:47,560 --> 01:43:52,160
+الكلام صحيح بس نظرا لـ 2 n نقص وعاد كلام مش
+
+964
+01:43:52,160 --> 01:43:57,910
+صحيح إذا انطلعت الحد الأول اللي هو n خليته على
+
+965
+01:43:57,910 --> 01:44:03,070
+الشكل وهذا خليته على الشكل والباقي خدت منه a0
+
+966
+01:44:03,070 --> 01:44:07,530
+عامل مشترك و خدت a1 عامل مشترك فطلع الـ series
+
+967
+01:44:07,530 --> 01:44:11,570
+اللي عندنا هذه والـ series اللي عندنا هذه يبقى هذا
+
+968
+01:44:11,570 --> 01:44:16,390
+الشكل الـ general solution لمين للمعادلة التفاضلية
+
+969
+01:44:16,390 --> 01:44:21,010
+هذا يا بنات شوفي إذا جبتي الـ recurrence relation
+
+970
+01:44:21,010 --> 01:44:26,440
+هذه الصحيحة بصير الباقي كله تعويض عادي ما فيش فيه أي
+
+971
+01:44:26,440 --> 01:44:32,920
+صعوبة لكن إذا جبتيها غلط ضيعتي سؤالك لذلك كل
+
+972
+01:44:32,920 --> 01:44:37,500
+امتحانها بنيجب فيه سؤال على هذا الـ section كل
+
+973
+01:44:37,500 --> 01:44:42,740
+امتحانها أي ورقة امتحان نهائي بتلاقي فيها سؤال على
+
+974
+01:44:42,740 --> 01:44:47,580
+هذا الـ section لسه أبدا أعطيك مثال المرة القادمة
+
+975
+01:44:47,580 --> 01:44:49,940
+إن شاء الله حد فيكوا لايه تساؤل هنا؟ 
diff --git a/PL9fwy3NUQKwa8ZDfSFGn6H8xVFLzqmCZC/6jXOnqsn_jg_postprocess.srt b/PL9fwy3NUQKwa8ZDfSFGn6H8xVFLzqmCZC/6jXOnqsn_jg_postprocess.srt
new file mode 100644
index 0000000000000000000000000000000000000000..f5173da841a0acf4b4895d36c48ae38f5d68b63d
--- /dev/null
+++ b/PL9fwy3NUQKwa8ZDfSFGn6H8xVFLzqmCZC/6jXOnqsn_jg_postprocess.srt
@@ -0,0 +1,3900 @@
+1
+00:00:10,220 --> 00:00:14,300
+بسم الله الرحمن الرحيم بنكمل ال section اللى
+
+2
+00:00:14,300 --> 00:00:19,500
+ابتدأنا المرة الماضية وهى ال serious solutionيعني
+
+3
+00:00:19,500 --> 00:00:22,940
+باستخدام ال power series فابتدأنا المرة اللي فاكرة
+
+4
+00:00:22,940 --> 00:00:27,440
+بالتذكير بمعنى ال power series و ال convergence لل
+
+5
+00:00:27,440 --> 00:00:34,600
+power series في calculus B أخدنا اللي هو في نهاية
+
+6
+00:00:34,600 --> 00:00:39,880
+chapter ال power series أخدنا اللي هو ال McLaurin
+
+7
+00:00:39,880 --> 00:00:44,320
+series و ال taylor series فكان ال taylor series
+
+8
+00:00:44,320 --> 00:00:49,280
+على شكل ال tail اللي عندنا هنايبقى بنتابع النقاط
+
+9
+00:00:49,280 --> 00:00:53,640
+طبيعية المرأة اللي فتحتها باجي بقولهthe Taylor
+
+10
+00:00:53,640 --> 00:01:03,340
+series as summation من n equal zero to infinity
+
+11
+00:01:03,340 --> 00:01:12,060
+لمين للتفاضل لرقم n عند النقطة a أو عند النقطة x
+
+12
+00:01:12,060 --> 00:01:20,200
+node لمين لل x ناقص ال x node to the power n على n
+
+13
+00:01:20,200 --> 00:01:21,260
+factorial
+
+14
+00:01:23,260 --> 00:01:29,380
+على N factorial بالشكل اللي عندنا هذا او بقدر
+
+15
+00:01:29,380 --> 00:01:35,700
+احطها بالشكل المفكوك الطويل هي عبارة عن اللي هو ال
+
+16
+00:01:35,700 --> 00:01:43,720
+F of X node زائد ال F prime of X node في ال X ناقص
+
+17
+00:01:43,720 --> 00:01:50,000
+ال X node على واحد factorial زائد المشتقة الثانية
+
+18
+00:01:50,000 --> 00:01:56,200
+عند ال X nodeنقص ال X node لكل تربية على 2
+
+19
+00:01:56,200 --> 00:02:00,620
+factorial زائد زائد و نظل ماشي لغاية ما نوصل
+
+20
+00:02:00,620 --> 00:02:06,860
+لتفاضل رقم N لل X node في ال X نقص ال X node to
+
+21
+00:02:06,860 --> 00:02:13,390
+the power N على N factorial زائد إلى آخرينهذا مين
+
+22
+00:02:13,390 --> 00:02:18,490
+اللي هو تايلور سيريز اللي قال لو كانت اكس نود
+
+23
+00:02:18,490 --> 00:02:24,130
+يساوي زيرو بنحصل على مين على مكلورين سيريز يبقى
+
+24
+00:02:24,130 --> 00:02:32,770
+باجي بقوله هنا اف ال اكس نود تساوي زيرو we get the
+
+25
+00:02:32,770 --> 00:02:38,350
+McLaurin series
+
+26
+00:02:38,350 --> 00:02:41,230
+and
+
+27
+00:02:43,710 --> 00:02:50,890
+الشكل التالي هو summation من n equal zero to
+
+28
+00:02:50,890 --> 00:02:58,930
+infinityلتفضل رقم N عند 0 ل X to the power N على N
+
+29
+00:02:58,930 --> 00:03:03,350
+factorial يعني يا بنات بده اشيل كل X node و احط
+
+30
+00:03:03,350 --> 00:03:07,350
+مكانه من 0 يبقى ال summation اللي فوق بصير على
+
+31
+00:03:07,350 --> 00:03:13,610
+الشكل اللي عندنا هذا يبقى بناء عليه هذا هيساوي F
+
+32
+00:03:13,610 --> 00:03:19,690
+of 0 زائد F prime of 0 X على 1 factorial
+
+33
+00:03:28,310 --> 00:03:38,550
+المفكوك الأول هو عبارة عن مفكوك تايلور أو متسلسل
+
+34
+00:03:38,550 --> 00:03:44,470
+تايلور والتانية متسلسل ماكلون اتنين علماء في مجال
+
+35
+00:03:44,470 --> 00:03:49,240
+الرياضياتاكتشف الـTaylor العلاقة الأولى وMaclaurin
+
+36
+00:03:49,240 --> 00:03:56,160
+العلاقة الثانية وسميت باسمه ما تمام طيب شو قصة ال
+
+37
+00:03:56,160 --> 00:04:01,900
+series هذه؟ انا بقولك اه خدي مارك كويس اي function
+
+38
+00:04:01,900 --> 00:04:07,560
+اللي لها مالة نهاية من ال derivatives بقدر اكتبها
+
+39
+00:04:07,560 --> 00:04:12,740
+على شكل Taylor series او Maclaurin seriesطيب فى أن
+
+40
+00:04:12,740 --> 00:04:17,620
+دوال فعلًا اللي هم مالة نهام المشتقات يعني بيكملوش
+
+41
+00:04:17,620 --> 00:04:22,340
+مثلًا تجد واحد يقول F of X يساوي X عشان عشرين،
+
+42
+00:04:22,340 --> 00:04:26,480
+بقول بعد عشرين المشتقة بتكمل المسألة هذه، الهدف
+
+43
+00:04:26,480 --> 00:04:31,050
+ماهياش مشتقات للمالة نهائيةلكن لو أخدت F of X يسوى
+
+44
+00:04:31,050 --> 00:04:42,010
+E أوس X أو E أوس X أو Cos X أو Sin X أو Ln X أو
+
+45
+00:04:42,010 --> 00:04:48,310
+Tan inverse X أو 1 على X أو 1 على X كل هذه الدوال
+
+46
+00:04:48,310 --> 00:04:53,730
+مهما تشتقيها هي بتكملشحتى لو قولتلك اكسوس نص او
+
+47
+00:04:53,730 --> 00:04:58,790
+اكسوس تلت اربع واشتق إلى مال نهاية بتخلصش نهائي
+
+48
+00:04:58,790 --> 00:05:03,030
+يبقى مثل هذه الدواليه اللتي بقدر اكتبها على شكل
+
+49
+00:05:03,030 --> 00:05:08,390
+تايلور او مكلورين سيريز زي ما كنا بنحسب في
+
+50
+00:05:08,390 --> 00:05:12,830
+calculus بي في calculus بي اللي هو تايلور او
+
+51
+00:05:12,830 --> 00:05:18,070
+مكلورين سيريز للدوال المختلفة وكنا بزهجنا أحيان
+
+52
+00:05:18,070 --> 00:05:23,640
+بشكل الحد النونيلكن in general بنجيب كل الدوال
+
+53
+00:05:23,640 --> 00:05:31,420
+اللي عندنا هادي يبقى كل دالة لها مالة نهاية من
+
+54
+00:05:31,420 --> 00:05:38,060
+المشتقات يعني كل ال derivatives تبعاتها are exist
+
+55
+00:05:38,060 --> 00:05:44,280
+بقدر اكتب علي شكل taylor series او mclaren series
+
+56
+00:05:44,280 --> 00:05:53,040
+طيب ان انا اجي لتعريف بسيط جدايبقى تعريف جديد هذا
+
+57
+00:05:53,040 --> 00:06:02,300
+ماشفنهوش قبل هيك يبقى باجي بقول definition a
+
+58
+00:06:02,300 --> 00:06:13,280
+function f a function f is called analytic
+
+59
+00:06:13,280 --> 00:06:17,200
+ده
+
+60
+00:06:17,200 --> 00:06:19,880
+اللي تحليلية at
+
+61
+00:06:21,530 --> 00:06:25,810
+او او
+
+62
+00:06:25,810 --> 00:06:29,030
+او
+
+63
+00:06:29,030 --> 00:06:33,410
+او
+
+64
+00:06:33,410 --> 00:06:33,430
+او او او او او
+
+65
+00:06:58,910 --> 00:07:04,830
+إذا كنا نستطيع أن نكتبها على شكل power series فهي
+
+66
+00:07:04,830 --> 00:07:08,110
+F
+
+67
+00:07:08,110 --> 00:07:14,250
+of X بدي أكتبها على شكل summation من N equal zero
+
+68
+00:07:14,250 --> 00:07:21,880
+to infinity لتفاضل رقم Nللأند الـ x node للـ x
+
+69
+00:07:21,880 --> 00:07:28,320
+ناقص الـ x node to the power n على n factorial
+
+70
+00:07:28,320 --> 00:07:44,240
+with radius of convergence with radius of
+
+71
+00:07:44,240 --> 00:07:47,680
+convergence
+
+72
+00:07:49,410 --> 00:07:59,970
+اللي هو راه راه greater than zero
+
+73
+00:08:12,850 --> 00:08:16,890
+تعريف هذا جديد ماشوفنهوش في calculus بي على
+
+74
+00:08:16,890 --> 00:08:22,390
+الأطلاع وإنما لزمناه هنا في المعادلات التفاضليه
+
+75
+00:08:22,390 --> 00:08:26,530
+التعريف بيقول مياتي الدالة if بقدر اقول عنها
+
+76
+00:08:26,530 --> 00:08:33,490
+analytic function يعني دالة تحليلية at a point عند
+
+77
+00:08:33,490 --> 00:08:38,390
+نقطة x ساوي x node if it can be written as a power
+
+78
+00:08:38,390 --> 00:08:43,670
+seriesإذا جئت تكتب على شكل power series that is f
+
+79
+00:08:43,670 --> 00:08:47,670
+of x بدي ساوي summation من n equal zero to
+
+80
+00:08:47,670 --> 00:08:52,280
+infinity لتفاضل رقم n عند ال x nodeفى الـ X نقص
+
+81
+00:08:52,280 --> 00:08:56,620
+الـ X naught to the power N على N factorial with
+
+82
+00:08:56,620 --> 00:09:00,840
+radius of convergence rho greater than zero يعني
+
+83
+00:09:00,840 --> 00:09:04,720
+any power series المرة اللى فاتة قولنا اللى أحد
+
+84
+00:09:04,720 --> 00:09:09,000
+ثلاثة احتمالات يا إما convergence عند نقطة واحدة
+
+85
+00:09:09,000 --> 00:09:13,360
+فقط وفي هذه الحالة ال radius of convergence بده
+
+86
+00:09:13,360 --> 00:09:17,760
+يساوي zero يا إما convergence على كل ال real line
+
+87
+00:09:18,090 --> 00:09:21,110
+وبالتالي ال interval of convergence من سلب
+
+88
+00:09:21,110 --> 00:09:25,250
+infinity ل infinity وال radius of convergence بده
+
+89
+00:09:25,250 --> 00:09:26,910
+يساوي infinity
+
+90
+00:09:29,510 --> 00:09:33,810
+ممكن تبقى ال convergence على فترة و diverge خارج
+
+91
+00:09:33,810 --> 00:09:37,390
+هذه الفترة ال radius of convergence يسوى المص
+
+92
+00:09:37,390 --> 00:09:42,630
+الفترة اللى عندنا هذه و هذا كتبناه المرة الماضية
+
+93
+00:09:42,630 --> 00:09:49,390
+طيب انا الى خاطر اعيد صياغة التعريف بطريقة اخرى كي
+
+94
+00:09:49,390 --> 00:09:52,590
+ابك تصيبه بطريقة اخرى بجبه تطلع الكلام اللى عندنا
+
+95
+00:09:52,590 --> 00:09:59,060
+هذا مش هو هذا ولا لا صح؟يبقى دا اللي بقدر اقول
+
+96
+00:09:59,060 --> 00:10:04,580
+انها انا analytic اذا كتبتها على صيغة تايلور سيريز
+
+97
+00:10:04,580 --> 00:10:10,280
+او مكلورن سيريز صح ولا لا مصبوط يبقى من الانفصال
+
+98
+00:10:10,280 --> 00:10:15,580
+ان اذا بقدر احط ال function اللي عندي على شكل صيغة
+
+99
+00:10:15,580 --> 00:10:19,840
+تايلور سيريز او مكلورن سيريز اذا هي analytic
+
+100
+00:10:19,840 --> 00:10:25,890
+functionكل الدول التي ذكرتها قبل قليل هي analytic
+
+101
+00:10:25,890 --> 00:10:30,810
+functions يعني كل الدول اللي إلها مال نهاية من
+
+102
+00:10:30,810 --> 00:10:37,170
+المشتاقات هي عبارة عن analytic functionsأذا sin X
+
+103
+00:10:37,170 --> 00:10:45,270
+وcos X وsin X وcos X وEOS X وEOS ناقص X وLin X و1
+
+104
+00:10:45,270 --> 00:10:49,930
+على X و10 انفرسيس كل هذه are analytic functions
+
+105
+00:10:49,930 --> 00:10:52,850
+يعني هي دوال تحليلية
+
+106
+00:10:54,680 --> 00:11:00,080
+نأخد ملاحظة بسيطة هذه هتهمنا عند حل الكثير من
+
+107
+00:11:00,080 --> 00:11:03,440
+المسائل خلال هذا ال section و خلال ال section
+
+108
+00:11:03,440 --> 00:11:09,300
+القادم ان شاء الله اللي هتتعرضه اليوم هذه هكتبها
+
+109
+00:11:09,300 --> 00:11:16,500
+على شكل ال remark التالية ال remark بتقول ما يأتي
+
+110
+00:11:16,500 --> 00:11:26,300
+if summation من n equal zero to infinityللأن في ال
+
+111
+00:11:26,300 --> 00:11:32,760
+X ناقص X node to the power N بدي سوى summation من
+
+112
+00:11:32,760 --> 00:11:38,740
+N equal 0 to infinity للبن في ال X ناقص ال X node
+
+113
+00:11:38,740 --> 00:11:50,700
+to the power N for each X لكل X then الان
+
+114
+00:11:51,670 --> 00:11:59,510
+بدي ساوي ال BN و ال N بدها تساوي Zero واحد و اتنين
+
+115
+00:11:59,510 --> 00:12:06,210
+و تلاتة واحد و اتنين و تلاتة و تظلك ماشية الى ما
+
+116
+00:12:06,210 --> 00:12:07,370
+شاء الله
+
+117
+00:12:11,800 --> 00:12:18,660
+الـ A0 بدي سوى الـ B0 والـ A1 بدي سوى الـ B1 والـ
+
+118
+00:12:18,660 --> 00:12:26,320
+A N بدي سوى الـ B N إلى ما لا نهايةin particular
+
+119
+00:12:26,320 --> 00:12:33,160
+كحالة خاصة if
+
+120
+00:12:33,160 --> 00:12:42,280
+summation من n equal zero to infinity لل a n لل x
+
+121
+00:12:42,280 --> 00:12:50,300
+نقص ال x not to the power n بده يسوى zero for each
+
+122
+00:12:50,300 --> 00:13:00,420
+x لكل x thenبنستنتج مع اياتي ان ال a n بده يساوي
+
+123
+00:13:00,420 --> 00:13:06,960
+zero that is ان ال a naught بده يساوي ال a one بده
+
+124
+00:13:06,960 --> 00:13:12,240
+يساوي ال a two بده يساوي ال a n بده يساوي بده
+
+125
+00:13:12,240 --> 00:13:15,900
+يساوي كله جداش اللي هو zero
+
+126
+00:13:19,560 --> 00:13:24,100
+بنرجع للـ remark هذه مرة ثانية و صح اسمها معايا
+
+127
+00:13:24,100 --> 00:13:28,820
+كويسة انها very important في الحسابات الآن و كذلك
+
+128
+00:13:28,820 --> 00:13:34,400
+لل section القادر بيقول لو كان summation من n
+
+129
+00:13:34,400 --> 00:13:38,280
+equals zero to infinity لل a n في ال X ناقص ال X
+
+130
+00:13:38,280 --> 00:13:42,350
+node to the power nبدى يساوي ال summation من n
+
+131
+00:13:42,350 --> 00:13:45,550
+equal zero to infinity لل b in في ال x نقص ال x
+
+132
+00:13:45,550 --> 00:13:51,870
+not to the power n for each x لكل x then ال a in
+
+133
+00:13:51,870 --> 00:13:56,390
+بدى يساوي ال b in اتنى شوية طلعى هنا يا بنات ال
+
+134
+00:13:56,390 --> 00:13:59,990
+summation هذا هو ال summation هذا ببدأ من عند zero
+
+135
+00:13:59,990 --> 00:14:04,850
+و بنتهي وين في مالة نهاية اتنين ال x نقص ال x not
+
+136
+00:14:04,850 --> 00:14:08,310
+to the power n هي نفس ال x نقص ال x not to the
+
+137
+00:14:08,310 --> 00:14:13,080
+power n لأنه يقول for each xتمام يبقى هذه هي هذه
+
+138
+00:14:13,080 --> 00:14:18,860
+بيضلش عندى إلا main إلا a n و b n إذا إن حدث ذلك
+
+139
+00:14:18,860 --> 00:14:22,240
+إذا ال summation هو ال summation و ال axis هي ال
+
+140
+00:14:22,240 --> 00:14:27,880
+axis بيضلش عندى إلا ال a n يساوي main ال b n و ال
+
+141
+00:14:27,880 --> 00:14:35,960
+n 0 1 2 3 4 إلى آخرينيبقى لحد المالانهية that is
+
+142
+00:14:35,960 --> 00:14:40,660
+بدي أعيد صياغة هذا الكلام مرة أقرأ لو كانت N ب
+
+143
+00:14:40,660 --> 00:14:48,480
+Zero بصير A0 وB0 لو كانت N بواحد بصير A1 وB1 لو
+
+144
+00:14:48,480 --> 00:14:53,180
+كانت N باتنين بصير A2 تسوى B2 لو كانت تلاتة يبقى
+
+145
+00:14:53,180 --> 00:14:58,140
+A3 بدي سوى B3 و هكذا يبقى هضل ماشي لغاية AN بدي
+
+146
+00:14:58,140 --> 00:15:03,540
+سوى BN وفوت كمانانزد واحد يسوى بنزد واحد انزد
+
+147
+00:15:03,540 --> 00:15:07,840
+اتنين يسوى بنزد اتنين الى ما لا نهاية يعني القصد
+
+148
+00:15:07,840 --> 00:15:11,640
+من ذلك اذا ال summation هنا بيسوى ال summation هنا
+
+149
+00:15:11,640 --> 00:15:15,840
+يبقى المعامل هنا هو نفس المعامل هنا باختصار هاي
+
+150
+00:15:15,840 --> 00:15:20,320
+اللي قصد يقوله الان لو جينا خدنا حالة خاصة ايش
+
+151
+00:15:20,320 --> 00:15:24,280
+الحالة الخاصة نفترض هذا المقدر هذا حطينا بدأله
+
+152
+00:15:24,280 --> 00:15:28,480
+Zero يبقى ال summation هذا بيسوى Zeroيبقى ان حدث
+
+153
+00:15:28,480 --> 00:15:32,880
+ان ال summation هذا بده يساوي zero يبقى في هذه
+
+154
+00:15:32,880 --> 00:15:37,720
+الحالة ال a n هي اللي بده تساوي zero لما ال a n
+
+155
+00:15:37,720 --> 00:15:42,100
+بده يساوي zero يبقى ال a naught بده يساوي zero وال
+
+156
+00:15:42,100 --> 00:15:48,080
+a oneو ال A2 و ال A3 و ال A4 و ال N كله بيأسفار
+
+157
+00:15:48,080 --> 00:15:51,960
+يبقى في هذه الحالة بصير كل الكهات اللي عند مين
+
+158
+00:15:51,960 --> 00:15:58,930
+بيأسفار طيب هذه نقطة مهمة جدا لزمانمضايق كمان نقطة
+
+159
+00:15:58,930 --> 00:16:02,010
+لازمانة من هذه ال section اللي هو حاجة نسميها
+
+160
+00:16:02,010 --> 00:16:07,370
+shift of index لما أكتب ال summation بدي أغير
+
+161
+00:16:07,370 --> 00:16:12,170
+الدليل اللي تحت ال summation هنا ممكن أغيره زي ما
+
+162
+00:16:12,170 --> 00:16:18,030
+بدي دون أن أغير في قيمة ال summation خدناها في
+
+163
+00:16:18,030 --> 00:16:25,530
+calculus Bفي section تلاتة من calculus B يبقى بدنا
+
+164
+00:16:25,530 --> 00:16:31,290
+نعيدها هنا نظرا لأهميتها أثناء الحسابات يبقى نحط
+
+165
+00:16:31,290 --> 00:16:37,330
+عنوان صغير حاجة اسمه shift of index of summation
+
+166
+00:16:37,330 --> 00:16:43,950
+of index of summation
+
+167
+00:16:49,880 --> 00:16:58,160
+بدنا نوضح هذا الكلام بمثال example example
+
+168
+00:16:58,160 --> 00:17:07,040
+one let y تساوي ال summation من n equal zero to
+
+169
+00:17:07,040 --> 00:17:14,540
+infinity لل a n x to the power n compute
+
+170
+00:17:16,020 --> 00:17:31,280
+احسبلي y prime و yw prime و اكتبهم
+
+171
+00:17:31,280 --> 00:17:40,540
+لي in terms of x to the power n
+
+172
+00:18:14,470 --> 00:18:19,770
+عشان احسب المشتقة الأولى و المشتقة الثانية و اكتب
+
+173
+00:18:19,770 --> 00:18:24,600
+لي الناتج كله بدلالة X to the power Nأذا تعالوا
+
+174
+00:18:24,600 --> 00:18:29,300
+نشوف شكل ال Y و بعدين نجيب المشتقة الأولى والثانية
+
+175
+00:18:29,300 --> 00:18:34,300
+لها إذا لو جيت أشوف شكل ال Y يبقى Y تساوي ال
+
+176
+00:18:34,300 --> 00:18:39,880
+summation من N equal zero to infinity لل A N لل X
+
+177
+00:18:39,880 --> 00:18:46,320
+to the power M هذا شكل ال series باستخدام الحد
+
+178
+00:18:46,320 --> 00:18:49,580
+نوني هذا اسمه الحد نوني لل series لو أنا بدي
+
+179
+00:18:49,580 --> 00:18:56,140
+أشوفها على طبيعتهايبقى ببدأ احط n تساوي 0 بصير ايش
+
+180
+00:18:56,140 --> 00:19:04,100
+عندي a0 x أس 0 بواحد بعد zero شو بيجيني واحد يبقى
+
+181
+00:19:04,100 --> 00:19:12,860
+بصير a1 x أس واحد يعني a1x يبقى زائد a1x لو حطيت n
+
+182
+00:19:12,860 --> 00:19:21,420
+باتنين بصير a2x تربيعيبقى زائد a2 x تربية زائد a3
+
+183
+00:19:21,420 --> 00:19:28,480
+x تقعيب a4 x to the power 4 ونظل ماشيين لغاية ال a
+
+184
+00:19:28,480 --> 00:19:33,660
+in x to the power n زائد إلى ما لا نهاية يبقى هذه
+
+185
+00:19:33,660 --> 00:19:40,500
+مين يا بنات؟ اللي هي y بدنا احنا مين؟ y w prime
+
+186
+00:19:48,790 --> 00:19:54,020
+هذا الـ A1 هو مشتقة الـ Xيبقى بيطلع عشان دي الامين
+
+187
+00:19:54,020 --> 00:20:01,580
+a1 يبقى a المشتقة الأولى اللى هى a1 نجى اللى بعدها
+
+188
+00:20:01,580 --> 00:20:09,820
+الشقة دى اتنين a اتنين x يبقى زائد اتنين a اتنين x
+
+189
+00:20:09,820 --> 00:20:16,870
+اللى بعده زائد تلاتة a تلاتة x تربيعزائد اربعة
+
+190
+00:20:16,870 --> 00:20:26,170
+اربعة اكس تكيب زائد زائد هوصل لمين لا زائد اللي
+
+191
+00:20:26,170 --> 00:20:34,490
+همين N A N X أس N ناقص واحد زائد الى اخرى شو رايك
+
+192
+00:20:34,490 --> 00:20:39,470
+اكتب هذه على شكل summation طبعا ال summation هنا
+
+193
+00:20:39,470 --> 00:20:44,810
+لما تطلع هناكتبينه احنا هنا بدلالة main بدلالة
+
+194
+00:20:44,810 --> 00:20:50,390
+الحد النوني تمام اذا هذا الطويل بقدر اكتبه دلالة
+
+195
+00:20:50,390 --> 00:20:57,850
+الحد النوني يبقى هذا الكلام بدرساوي summationمن
+
+196
+00:20:57,850 --> 00:21:02,790
+عند أبساطوري اللى وين للحد نونى وين الحد نونى هى
+
+197
+00:21:02,790 --> 00:21:11,090
+الحد نونى اللى هو N A N X plus N ناقص واحد نجى
+
+198
+00:21:11,090 --> 00:21:15,550
+نشوف ال summation من وين بيبدأ هل الحدود اللى عندى
+
+199
+00:21:15,550 --> 00:21:20,910
+جد الحدود اللى فوق بالضبط ولا اقل منهم اقلب واحد
+
+200
+00:21:20,910 --> 00:21:24,590
+لان انا اختار واحد لان ال summation هدا بيبدأ من
+
+201
+00:21:24,590 --> 00:21:28,410
+عند ال zero ولا من عند ال واحدمن عند الواحد لأنه
+
+202
+00:21:28,410 --> 00:21:33,730
+نقص ال summation يبقى هذا من عند n تساوي واحد الى
+
+203
+00:21:33,730 --> 00:21:38,210
+infinity طيب تعالى نشوف كلامنا هذا صح ولا غلط يبقى
+
+204
+00:21:38,210 --> 00:21:40,890
+ماقدرش ابدا من عند zero بدأ ابدا من عند الواحد
+
+205
+00:21:40,890 --> 00:21:46,670
+يبقى بصير واحد في a واحد ب a واحد x اص واحد ناقص
+
+206
+00:21:46,670 --> 00:21:51,570
+واحد اص زيرو اللي هو واحد في a واحد ب a واحد يبقى
+
+207
+00:21:51,570 --> 00:21:57,640
+الحد الأول a one بعد الواحد بدي احط n بقداشيبقى
+
+208
+00:21:57,640 --> 00:22:04,320
+اتنين اتنين اكس اوس اتنين اكس اكس اكس اكس اكس اكس
+
+209
+00:22:04,320 --> 00:22:09,220
+اكس اكس
+
+210
+00:22:09,220 --> 00:22:17,360
+اكس اكس اكس اكس اكس اكس اكس اكس اكس اكس اكس اكس
+
+211
+00:22:17,360 --> 00:22:22,670
+اكسعشان يا بنات لما كنت ال summation و أشتق مرة
+
+212
+00:22:22,670 --> 00:22:28,570
+واحدة إذا طار أحد ال terms بدي أنقص ال index اللي
+
+213
+00:22:28,570 --> 00:22:33,510
+تحت ال summation بمقدار واحد تمام؟ يبقى من هنا ال
+
+214
+00:22:33,510 --> 00:22:38,370
+summation بمقدار واحد لكن لو ما طارش ولا term بيضل
+
+215
+00:22:38,370 --> 00:22:42,830
+ايه؟ مانحذفش ولا term بيضل ال summation كما هو من
+
+216
+00:22:42,830 --> 00:22:49,110
+عند ال main من عند ال zeroقبل ما اكمل بدي اشوف ايش
+
+217
+00:22:49,110 --> 00:22:54,950
+بيقول يوم قاللي افترض Y احسبلي Y' وYW' واكتبلي كل
+
+218
+00:22:54,950 --> 00:23:01,730
+واحد فيهم بدللة X to the power N احنا هنا X بدللة
+
+219
+00:23:01,730 --> 00:23:07,850
+مين الناقص واحد يبقى انا بدروح اكتب ال summation
+
+220
+00:23:07,850 --> 00:23:14,910
+هذا بدللة X to the power N دون ان اغير في قيمة ال
+
+221
+00:23:14,910 --> 00:23:21,450
+summationبقوله والله كويس يبقى هذا هه بقدر اكتبه
+
+222
+00:23:21,450 --> 00:23:26,150
+summation على الشكل اللي عندنا ده واستنى شوية هنا
+
+223
+00:23:26,150 --> 00:23:31,730
+اذا بدى ابدأ اخلي هذا x to the power n يعني لو
+
+224
+00:23:31,730 --> 00:23:40,430
+شيلت كل n وحطيت مكانها n زائد واحدعندما أحصل على
+
+225
+00:23:40,430 --> 00:23:45,110
+ناقص واحدة بصير X to the power of N
+
+226
+00:23:56,150 --> 00:24:01,350
+يعني N تساوي كده؟ Zero ممتاز جدا يبقى هذا بيصير من
+
+227
+00:24:01,350 --> 00:24:06,270
+عند N تساوي Zero إلى Infinity بده اشيل هذه و اكتف
+
+228
+00:24:06,270 --> 00:24:10,830
+بدلها N زاد واحد تساوي واحد و جينا ايما كل ما
+
+229
+00:24:10,830 --> 00:24:15,790
+اشتقنا طار كمان term حذفنا كمان term يبقى صارت من
+
+230
+00:24:15,790 --> 00:24:20,730
+عند N تساوي اتنين طب اطلعي لي هنا اتنين
+
+231
+00:24:26,710 --> 00:24:32,550
+يبقى اتنين اتنين اتنين اتنين اتنين اتنين اتنين
+
+232
+00:24:32,550 --> 00:24:33,970
+اتنين اتنين اتنين اتنين اتنين اتنين اتنين اتنين
+
+233
+00:24:33,970 --> 00:24:34,070
+اتنين اتنين اتنين اتنين اتنين اتنين اتنين اتنين
+
+234
+00:24:34,070 --> 00:24:43,470
+اتنين اتنين اتنين اتنين
+
+235
+00:24:46,840 --> 00:24:53,240
+ب6A3X1 يبقى 6A3X1
+
+236
+00:24:53,240 --> 00:24:57,720
+مظبوط و الباقي كله مظبوط يبقى هاي كتبناها كتابة
+
+237
+00:24:57,720 --> 00:25:02,870
+سليمة تمامنجي للمطلوب التاني جالي بدي تكتبها لي
+
+238
+00:25:02,870 --> 00:25:08,550
+بدلالة x to the power n بقول له اه مش انا اكتبها x
+
+239
+00:25:08,550 --> 00:25:15,090
+to the power n بدي اشيل كل n و احط مكانها n زائد
+
+240
+00:25:15,090 --> 00:25:19,870
+اتنين اذا لما احط هنا بنات n زائد اتنين يساوي
+
+241
+00:25:19,870 --> 00:25:23,720
+اتنين بصير ال submission من وينمن عند الـ zero
+
+242
+00:25:23,720 --> 00:25:28,480
+يبقى هذا الكلام بيصير summation من عند ال zero
+
+243
+00:25:28,480 --> 00:25:34,420
+لغاية ال infinity إذا بدي أشيل كل N و أضع مكانها N
+
+244
+00:25:34,420 --> 00:25:41,040
+زي 2 بيصير هذه N زي 2 وهذهإن زائد اتنين ناقص واحد
+
+245
+00:25:41,040 --> 00:25:48,360
+يعني ان زائد واحد يبقى هاي ان زائد اتنين في ان
+
+246
+00:25:48,360 --> 00:25:55,980
+زائد واحد في ان زائد اتنين في ال X to the power ان
+
+247
+00:25:55,980 --> 00:26:02,380
+اتنين ناقص اتنين مابتدلش عندى الا ان يبقى هاي غيرت
+
+248
+00:26:02,380 --> 00:26:06,500
+ال index تبع ال summation بدل ما كان عند ان يساوي
+
+249
+00:26:06,500 --> 00:26:06,980
+اتنين
+
+250
+00:26:10,400 --> 00:26:15,900
+اللي كتبته هذا جديد فعلا بيعطيني هذا ولا لا؟ اقول
+
+251
+00:26:15,900 --> 00:26:19,900
+تعالى نشوف من هنا بده يبدأ من وين؟ من عند الـ Zero
+
+252
+00:26:19,900 --> 00:26:24,920
+Zero بيبقى هنا اتنين Zero بيبقى هنا احد Zero بيبقى
+
+253
+00:26:24,920 --> 00:26:30,580
+هنا اتنين يبقى اتنين اتنين اكسه Zero بواحد اتنين
+
+254
+00:26:30,580 --> 00:26:36,740
+اتنين والله مظبوطبعد الـ zero بيجي نمين واحد يبقى
+
+255
+00:26:36,740 --> 00:26:43,120
+واحد و اتنين تلاتة في اتنين اللي هو بستة ا واحد زي
+
+256
+00:26:43,120 --> 00:26:49,700
+اتنين يبقى a تلاتة x يبقى هاي ستة a تلاتة x و هكذا
+
+257
+00:26:49,700 --> 00:26:53,060
+بالنسبة للباقي يبقى غيرنا ال index تبع ال
+
+258
+00:26:53,060 --> 00:26:57,860
+summation لكن المعلومات بقيت كما هي إذا يا بنات لو
+
+259
+00:26:57,860 --> 00:27:03,000
+غيرت ال index تبع ال summation لا يتغيرقيمة السيرة
+
+260
+00:27:03,000 --> 00:27:08,040
+صحيح شكلا بصير شكلها مش زيها لكن في الحقيقة عندي
+
+261
+00:27:08,040 --> 00:27:14,200
+الحسابات كل term هو نظيره الأساسي لا يتغير و هذا
+
+262
+00:27:14,200 --> 00:27:20,900
+حط المعلومة في دماغك لزمان الآن و فورا كمان يبقى
+
+263
+00:27:20,900 --> 00:27:25,760
+بنجي ل example two example
+
+264
+00:27:25,760 --> 00:27:30,400
+two له سنة اربعة و عشرين من التمرين بيقول ما يا
+
+265
+00:27:30,400 --> 00:27:31,620
+تيريا الرعي
+
+266
+00:27:51,370 --> 00:28:00,610
+الحد العام involves يشتمل على ال X to the power N
+
+267
+00:28:01,590 --> 00:28:09,330
+هو ماعطيني واحد ناقص X ترابيع summation من عند ال
+
+268
+00:28:09,330 --> 00:28:18,190
+N تساوي اتنين الى infinity لل N في ال N ناقص واحد
+
+269
+00:28:18,190 --> 00:28:23,470
+في ال AN في ال X قص N ناقص اتنين
+
+270
+00:28:35,270 --> 00:28:39,610
+السؤال مرة ثانية السؤال اللي بيقول يعني rewrite
+
+271
+00:28:39,610 --> 00:28:45,270
+قعد كتابة أو قعد صياغة the given expression الصيغة
+
+272
+00:28:45,270 --> 00:28:51,150
+المعطاة as a sum كمجموع يعني ك summation whose
+
+273
+00:28:51,150 --> 00:28:57,520
+generic term الحد العام تبعهinvolves x to the
+
+274
+00:28:57,520 --> 00:29:03,380
+power n يعني انا عندى x هنا بيقوس قداش الناقص
+
+275
+00:29:03,380 --> 00:29:06,280
+اتنين انا مابديش ايه الناقص اتنين بدي اتخلص من
+
+276
+00:29:06,280 --> 00:29:10,340
+الناقص اتنين بدي اياها بدلات ال x to the power n
+
+277
+00:29:10,340 --> 00:29:15,700
+فقط بقولكوا ايه تعالى نشوف بطلع هذه مش زى اللى جاب
+
+278
+00:29:15,700 --> 00:29:17,600
+الكمان مضروب وغرق مين
+
+279
+00:29:23,610 --> 00:29:29,070
+يبقى اتصرف بمخك وشوف كيف بدك تسويه بقوله بسيطة هذا
+
+280
+00:29:29,070 --> 00:29:33,830
+ال term اللي عندك هو واحد ناقص X تربية مضروب في
+
+281
+00:29:33,830 --> 00:29:39,310
+summation من N equal to infinity لل N في X ناقص
+
+282
+00:29:39,310 --> 00:29:47,830
+واحد لل A N لل X ناقص اتنينطبعا طيب شو رأيكوا يا
+
+283
+00:29:47,830 --> 00:29:51,990
+بنات بدي أتلح لحظة بقول لو كتبوا ب summation واحد
+
+284
+00:29:51,990 --> 00:29:55,490
+هذه اللي جوه اللي برا لو كانت زي اللي جوه كان
+
+285
+00:29:55,490 --> 00:30:00,270
+ضربتها جوه و اتريحت مظبوط لكن هذه مجموعة إيه؟
+
+286
+00:30:00,270 --> 00:30:04,870
+كميتين إذا بقول الكمية الأولى في ال summation ناقص
+
+287
+00:30:04,870 --> 00:30:07,510
+الكمية التانية في ال summation وبالتالي فكتي
+
+288
+00:30:07,510 --> 00:30:13,150
+العقدة الأولىمظبوط؟ يبقى هذا الكلام بده يساوي واحد
+
+289
+00:30:13,150 --> 00:30:17,550
+في ال summation بال summation زي ما هو من اتنين
+
+290
+00:30:17,550 --> 00:30:23,030
+لغاية infinity لل N في ال N ناقص واحد في ال A N في
+
+291
+00:30:23,030 --> 00:30:29,190
+ال X أس N ناقص اتنين ناقص ال X تربية هذه بانت
+
+292
+00:30:29,190 --> 00:30:33,850
+تدخلها جوه يبقى لو دخلت جوه إيش بصير عندنا هنا؟
+
+293
+00:30:34,020 --> 00:30:40,450
+ناقص summation من N equal two to infinityللان في
+
+294
+00:30:40,450 --> 00:30:46,690
+الان ناقص واحد هذه ان ناقص واحد مش اكسما ان في
+
+295
+00:30:46,690 --> 00:30:54,350
+الان ناقص واحد ايوة في الان في الان في جداش هذه
+
+296
+00:30:54,350 --> 00:31:00,870
+بصيها اكسوس ان فقط لان ان زائد اتنين وناقص اتنين
+
+297
+00:31:00,870 --> 00:31:08,910
+بصير ال X to the power N مظهرطيب نرجع مرة تانية
+
+298
+00:31:08,910 --> 00:31:15,170
+بقولي اكتب هذا ك summation واحد مش اتنين وبشرط ان
+
+299
+00:31:15,170 --> 00:31:21,090
+الاص يكون X to the power N بقوله والله هي جاهزة
+
+300
+00:31:21,090 --> 00:31:26,590
+مكتوبة بس هذه مش مكتوبة بدلالة ال N يبقى الشغل
+
+301
+00:31:26,590 --> 00:31:32,970
+عندنا بقدر اشيل كل N و احط مكانهابس مشان تكتبوا
+
+302
+00:31:32,970 --> 00:31:37,930
+يتغير كل ال index هدول يبقى بروح بقوله ماشي مافي
+
+303
+00:31:37,930 --> 00:31:43,230
+مشكلة هذي يساوي اذا انا هشيل كل N و اكتب مكانة N
+
+304
+00:31:43,230 --> 00:31:49,850
+زاد اتنين بصير N تساوي جداش Zero الى Infinity لل N
+
+305
+00:31:50,230 --> 00:31:57,230
+زائد اتنين في ال N زائد اتنين نقص واحد يعني N زائد
+
+306
+00:31:57,230 --> 00:32:07,230
+واحد لل A N زائد اتنين لل X to the power Nنجي
+
+307
+00:32:07,230 --> 00:32:12,270
+لبعدها ناقص summation من N equal to تبقى نزلها زي
+
+308
+00:32:12,270 --> 00:32:16,630
+ما هي لأن هجازة S هتلعب في المكتسبات الوطنية
+
+309
+00:32:16,630 --> 00:32:20,910
+المكتسبة اللي عندك بدأ تحافظ عليه لأنه مطلوب نخلي
+
+310
+00:32:20,910 --> 00:32:26,850
+المسألة بدلالة X to the power N يبقى N في N ناقص
+
+311
+00:32:26,850 --> 00:32:33,870
+واحد في N في X to the power Nأول ساعة في الخواص
+
+312
+00:32:33,870 --> 00:32:37,970
+قلنا إذا summation بسوى summation بتطلع في
+
+313
+00:32:37,970 --> 00:32:41,390
+المعاملات يبقى المعامل هنا بده يسوى المعامل هنا
+
+314
+00:32:41,390 --> 00:32:46,550
+مظبوط اللي كتبناها قبل شوية بجي بتطلع هذي X و XN
+
+315
+00:32:46,550 --> 00:32:52,030
+هذي X و XN ممتاز هذا summation .. اه ال summation
+
+316
+00:32:52,030 --> 00:32:56,250
+مش زي بعضه بده ال summation النقطة اللي يبده هنا
+
+317
+00:32:56,250 --> 00:33:00,990
+فيها هي النقطة اللي يبده هنا فيها بالضبط تمامامش
+
+318
+00:33:00,990 --> 00:33:04,090
+هنقدر أجمعهم و إلا بقدرش أجمعهم و إلا بدي يكون ال
+
+319
+00:33:04,090 --> 00:33:06,850
+index اللي هنا زي ال index هنا و اللي فوق ما هو
+
+320
+00:33:06,850 --> 00:33:09,750
+المالة نهائية تطرح منه واحد و الله اضيفيله خمسة
+
+321
+00:33:09,750 --> 00:33:14,510
+كله مالة نهائية تمام؟ بقوله كويس إذا بدي أخلي ال
+
+322
+00:33:14,510 --> 00:33:19,430
+index اللي هنا زي ال index اللي هنا بقوله بسيطة
+
+323
+00:33:19,430 --> 00:33:24,590
+جدا تغلبش حالك كتير إيش رأيكوا لو طلعت أول term
+
+324
+00:33:24,590 --> 00:33:30,180
+هنا؟حسب تجدش ال summation عند ال zero و عند ال
+
+325
+00:33:30,180 --> 00:33:34,260
+واحد بيظل بعدها ال summation يقولني ايه بدا بيصير
+
+326
+00:33:34,260 --> 00:33:39,160
+زي هذا اذا بقدر اجبلهم مع بعض مظبوط يبقى بقدر اقول
+
+327
+00:33:39,160 --> 00:33:45,060
+هذا الكلام يسوي لو كانت ال n بيزيرو بيظل اتنين في
+
+328
+00:33:45,060 --> 00:33:51,870
+واحد اللي هو بجدش اتنين اه دي اتنينن بزيرو بصير
+
+329
+00:33:51,870 --> 00:33:58,010
+اتنين هنا ن بزيرو بصير اكس وزيرو بواحد يبقى الحد
+
+330
+00:33:58,010 --> 00:34:03,990
+الاول اتنين اتنين يبقى هاي فلت زيرو بدي افلت كمان
+
+331
+00:34:03,990 --> 00:34:09,130
+الواحد يبقى بقوله ز صمشي يبقى جامع بدي اشيله لانه
+
+332
+00:34:09,130 --> 00:34:14,050
+و احط مكانه واحد يبقى بصير تلاتة في اتنين بدي اكتب
+
+333
+00:34:14,050 --> 00:34:21,060
+هلك بدي اكتب تلاتةفي اتنين بس مشان تعرفك ايه فجأت
+
+334
+00:34:21,060 --> 00:34:27,560
+تاني في مين؟ في a واحد زائد اتنين ل a تلاتة في
+
+335
+00:34:27,560 --> 00:34:37,430
+مين؟ في ال X أس واحدطبعا انتقل نقل نقل نقل نقل نقل
+
+336
+00:34:37,430 --> 00:34:45,310
+نقل نقل نقل نقل نقل
+
+337
+00:35:12,460 --> 00:35:23,280
+هذه بدها تساوي اتنين اتنينزائد ستة ات تلاتة X زائد
+
+338
+00:35:23,280 --> 00:35:27,300
+ايش رايك؟ هذا ال summation هو ال summation اذا
+
+339
+00:35:27,300 --> 00:35:33,840
+باخده summation مشترك للكل يبقى هذا summation من N
+
+340
+00:35:33,840 --> 00:35:40,760
+equal two to infinity لمن؟ لل N زائد اتنين في ال N
+
+341
+00:36:07,870 --> 00:36:12,670
+مرة تانية بقول الخطوة الأخيرةالخطوة اللي قدامي هذه
+
+342
+00:36:12,670 --> 00:36:18,230
+هكتبها بشكل آخر ال two terms هذول نزلتهم زي ما هم
+
+343
+00:36:18,230 --> 00:36:22,790
+بدون مشاكل جيت هنا هذا ال summation هو نفس ال
+
+344
+00:36:22,790 --> 00:36:27,730
+summation إذا بدي أخد عامل مشترك x to the power n
+
+345
+00:36:27,730 --> 00:36:31,230
+هي نفس ال x to the power n بدي أخدها عامل مشترك
+
+346
+00:36:31,230 --> 00:36:36,140
+برايبقى بدلش عندى الا هذا المعامل والمعامل اللى
+
+347
+00:36:36,140 --> 00:36:41,480
+عندنا هذا و شرط السالب بينهما إذا المعامل هذا
+
+348
+00:36:41,480 --> 00:36:47,620
+نزلته زي ما هو و سالب المعامل هذا نزلته زي ما هو و
+
+349
+00:36:47,620 --> 00:36:53,740
+هي ال X to the power N و ال summation هيه برا تمام
+
+350
+00:36:53,740 --> 00:36:58,860
+ايش بقول يعيد كتاب لك كصم whose generic term X to
+
+351
+00:36:58,860 --> 00:37:04,170
+the power N اه كتبتله هيهطيب ايش رايك يا بنات
+
+352
+00:37:04,170 --> 00:37:10,850
+تعالى نشوف هل لو حطيت لل summation جوه هذا اللي هو
+
+353
+00:37:10,850 --> 00:37:17,670
+n بواحد بطلع ال term هذا و لو حطيت n ب zero بطلع
+
+354
+00:37:17,670 --> 00:37:22,470
+ال term هذا انطلع ال term بقدر اهمل هدول و اكتب ال
+
+355
+00:37:22,470 --> 00:37:26,090
+summation عند n equal zero و اخلي اللي جوه زي ما
+
+356
+00:37:26,090 --> 00:37:31,510
+هومظبوط؟ يعني بدل ما يكون مبعتر طويل هيك ممكن
+
+357
+00:37:31,510 --> 00:37:36,270
+اجمعه ب submission واحد تعالى نشوف بدل اتنين لو
+
+358
+00:37:36,270 --> 00:37:43,910
+حطيت واحد ايش بيصير عندي؟ تلاتة في اتنين ستة اتلتا
+
+359
+00:37:43,910 --> 00:37:51,750
+ستة اتلتا حط هنا بواحد بطير هذا بصفر مظبوط؟يبقى
+
+360
+00:37:51,750 --> 00:37:55,790
+هنا بصير 6A3F1
+
+361
+00:37:55,790 --> 00:37:59,570
+6A3F1
+
+362
+00:37:59,570 --> 00:38:04,030
+إذا لو رجعت ال summation و خلته هنا من انتوا ساوي
+
+363
+00:38:04,030 --> 00:38:09,230
+واحد ماعندي مشكلة طيب هل بنفع أخليه من عند انتوا
+
+364
+00:38:09,230 --> 00:38:14,590
+ساوي زيرو تعالي شوف حط انتوا ساوي زيرو بضلي اتنين
+
+365
+00:38:14,590 --> 00:38:23,750
+في واحد باتنين A2تعمل البرنامج
+
+366
+00:38:23,750 --> 00:38:31,740
+باستخدام البرنامجاذا بقدر ادخل هدول مع ال
+
+367
+00:38:31,740 --> 00:38:38,560
+summation هدا واخليه summation من عند n equal 0 to
+
+368
+00:38:38,560 --> 00:38:43,840
+infinity نفس هدا زي ما هو مش هغيره يا بنات يبقى n
+
+369
+00:38:43,840 --> 00:38:53,300
+زائد 2 في n زائد 1 في ال a n زائد 2 ناقص n في n
+
+370
+00:38:53,300 --> 00:39:00,380
+ناقص 1 في ال a n في x to the power nيبقى جماعة
+
+371
+00:39:00,380 --> 00:39:06,580
+لهذا هذا كله خلّيته summation واحد مرة واحدة
+
+372
+00:39:06,580 --> 00:39:11,660
+without problems بدون مشاكل وال index بدل ما كان
+
+373
+00:39:11,660 --> 00:39:16,520
+عندي اتنين خلّيته له من وين؟ من عندي ال zero كويسة
+
+374
+00:39:16,520 --> 00:39:20,040
+الفكرة هذه؟ هنشتغل فيها كتير دي ربالكم
+
+375
+00:39:25,790 --> 00:39:29,810
+نأخد مثال حول نفس المفهوم.
+
+376
+00:39:53,110 --> 00:39:56,790
+مثال ثلاثة اللي هو سؤال تمانية و عشرين من الكتاب
+
+377
+00:39:56,790 --> 00:40:03,150
+ثلاثة سؤال تمانية و عشرين هو آخر سؤال في التمرين
+
+378
+00:40:03,150 --> 00:40:15,770
+بيقول لي دي تيرمين حددلي اللي هو the a n so that
+
+379
+00:40:15,770 --> 00:40:19,450
+equation so that
+
+380
+00:40:22,260 --> 00:40:28,140
+بحيث ان المعادلة summation من n equal one to
+
+381
+00:40:28,140 --> 00:40:37,460
+infinity لل n a n x أس n ناقص واحد زائد اتنين
+
+382
+00:40:37,460 --> 00:40:44,420
+summation من عند n equal zero to infinityللـ a in
+
+383
+00:40:44,420 --> 00:40:55,340
+x to the power n بده يساوي من 0 is satisfied is
+
+384
+00:40:55,340 --> 00:41:04,040
+satisfied try حاول to identify
+
+385
+00:41:04,040 --> 00:41:11,600
+try to identify the function represented
+
+386
+00:41:26,020 --> 00:41:29,220
+بالمتسلسل بالمتسلسل بالمتسلسل بالمتسلسل بالمتسلسل
+
+387
+00:41:29,220 --> 00:41:29,520
+بالمتسلسل بالمتسلسل بالمتسلسل بالمتسلسل بالمتسلسل
+
+388
+00:41:29,520 --> 00:41:29,940
+بالمتسلسل بالمتسلسل بالمتسلسل بالمتسلسل بالمتسلسل
+
+389
+00:41:29,940 --> 00:41:32,600
+بالمتسلسل بالمتسلسل بالمتسلسل بالمتسلسل بالمتسلسل
+
+390
+00:41:32,600 --> 00:41:33,900
+بالمتسلسل بالمتسلسل بالمتسلسل بالمتسلسل بالمتسلسل
+
+391
+00:41:33,900 --> 00:41:33,920
+بالمتسلسل بالمتسلسل بالمتسلسل بالمتسلسل بالمتسلسل
+
+392
+00:41:33,920 --> 00:41:36,880
+بالمتسلسل بالمتسلسل
+
+393
+00:42:13,900 --> 00:42:20,540
+سؤال مرة تانية تقولي حددلي شكل الان يعني المعامل
+
+394
+00:42:20,540 --> 00:42:25,220
+تبع الحد انه ان بتعرف ايه شكله بحيث المعادلة اللي
+
+395
+00:42:25,220 --> 00:42:29,920
+عندنا هذه ما لها is satisfied تبقى صحيحة يعني
+
+396
+00:42:29,920 --> 00:42:33,500
+مجموع اتنين هدول بده يساوي zero بعد ما تخلص هذه
+
+397
+00:42:33,500 --> 00:42:40,600
+الشغلة ا try to identify حاول تعرفلي ما هي الدالة
+
+398
+00:42:40,600 --> 00:42:44,720
+التي تمثل بال power series اللي عندنا هذهإذا كنتوا
+
+399
+00:42:44,720 --> 00:42:48,440
+من ذاكرية في ال power series section قسمناها إلى
+
+400
+00:42:48,440 --> 00:42:53,480
+جزئين تمام الجزء الأول بقينا ناخد ال function
+
+401
+00:42:53,480 --> 00:42:59,780
+بقينا نصف الأول نجيب فترة التقارب و نصف فترة
+
+402
+00:42:59,780 --> 00:43:04,320
+التقاربوالجزء الثاني في نفس ال section في calculus
+
+403
+00:43:04,320 --> 00:43:08,900
+بيجينا نكتف الدالة as a power series او العكس لو
+
+404
+00:43:08,900 --> 00:43:11,800
+عندى power series اكتبها على شكل main شكل function
+
+405
+00:43:11,800 --> 00:43:15,720
+وبعدها خشينا في taylor وmaclaurin طيب اليوم بتذكر
+
+406
+00:43:15,720 --> 00:43:18,960
+تذكير الله يساقل بالجزء اللى خلاكه الجزء الاولى من
+
+407
+00:43:18,960 --> 00:43:23,650
+الشغل تبع اليومالان انا عندى هنا summation ببدأ من
+
+408
+00:43:23,650 --> 00:43:27,770
+عند الواحد و هنا summation ببدأ من عند ال zero اذا
+
+409
+00:43:27,770 --> 00:43:33,490
+ماقدرش اجمعهم مع بعض لان عندي هنا a n و a n وانا
+
+410
+00:43:33,490 --> 00:43:39,560
+بدي اعرف ماهو شكل ال a n بنقول تمامالمعادلة دي بده
+
+411
+00:43:39,560 --> 00:43:43,140
+ايد كتابتها اتنين بقدر ادخلها جوا بتاعة ال
+
+412
+00:43:43,140 --> 00:43:48,140
+summation هذا بقدر اخلي ال summation يبدأ من وين
+
+413
+00:43:48,140 --> 00:43:52,600
+من وين ال zero اذا بدي اشيل كل n و احط مكانها n
+
+414
+00:43:52,600 --> 00:43:57,520
+زائد واحد يبقى ده ايش بيصير يا منات summation من n
+
+415
+00:43:57,520 --> 00:44:06,400
+equal zero to infinityللإن زائد واحد a n زائد واحد
+
+416
+00:44:06,400 --> 00:44:12,200
+x to the power n ناقص summation من n equal zero to
+
+417
+00:44:12,200 --> 00:44:18,840
+infinity للإتنين a n x to the power n يساوي زيرو
+
+418
+00:44:18,840 --> 00:44:27,460
+مرة تانيةهذا زاد وهذا زاد وهذا زاد وهذا زاد وهذا
+
+419
+00:44:27,460 --> 00:44:29,960
+زاد وهذا زاد وهذا زاد وهذا زاد وهذا زاد وهذا زاد
+
+420
+00:44:29,960 --> 00:44:34,000
+وهذا زاد وهذا زاد وهذا زاد وهذا زاد وهذا زاد وهذا
+
+421
+00:44:34,000 --> 00:44:35,140
+زاد وهذا زاد وهذا زاد وهذا زاد وهذا زاد وهذا زاد
+
+422
+00:44:35,140 --> 00:44:35,200
+وهذا زاد وهذا زاد وهذا زاد وهذا زاد وهذا زاد وهذا
+
+423
+00:44:35,200 --> 00:44:36,380
+زاد وهذا زاد وهذا زاد وهذا زاد وهذا زاد وهذا زاد
+
+424
+00:44:36,380 --> 00:44:36,900
+وهذا زاد وهذا زاد وهذا زاد وهذا زاد وهذا زاد وهذا
+
+425
+00:44:36,900 --> 00:44:44,340
+زاد وهذا زاد وهذا زاد وهذا زاد
+
+426
+00:44:44,340 --> 00:44:55,940
+وهذا زلمن؟ لل n زائد واحد a n زائد واحد زائد اتنين
+
+427
+00:44:55,940 --> 00:45:02,860
+a n كل هذا الكلام في مينابلات next to the power n
+
+428
+00:45:02,860 --> 00:45:08,760
+يساوي zero اخدنا
+
+429
+00:45:08,760 --> 00:45:14,580
+في الخواص قبل قليللو كان عند الصميش اللي الان في
+
+430
+00:45:14,580 --> 00:45:17,980
+ال X ناقص ال X not to the power N بده يساوي Zero
+
+431
+00:45:17,980 --> 00:45:22,540
+إذا الان هي اللي في Zeroمش ال X ده بارن صحيح ولا
+
+432
+00:45:22,540 --> 00:45:26,520
+لأ؟ يبقى مادام هذه تساوي Zero شو اللي خلاها Zero؟
+
+433
+00:45:26,520 --> 00:45:32,480
+هذه ليست Zero يبقى اللي بين جثين هو Zero يبقى هذا
+
+434
+00:45:32,480 --> 00:45:40,300
+بده يخليلي مين؟ بده يخليلي ان ان زائد واحد ان زائد
+
+435
+00:45:40,300 --> 00:45:48,310
+واحد زائدي اتنين ان هي Zeroاو بمعنى اخر بقدر اقول
+
+436
+00:45:48,310 --> 00:45:57,810
+ان زائد واحد تسوى نقص اتنين ان على من على ان زائد
+
+437
+00:45:57,810 --> 00:46:04,270
+واحد الشكل اللي عندنا طيب الان هنا تبدأ من وين؟
+
+438
+00:46:06,250 --> 00:46:12,570
+يبقى عندي ال zero يبقى باجي بقول له هذا هك و ال n
+
+439
+00:46:12,570 --> 00:46:18,730
+تسوى zero و واحد و اتنين و الى ما شاء الله عارفين
+
+440
+00:46:18,730 --> 00:46:24,470
+هذه شو اسمها يا بنات هذه اسمها recurrence relation
+
+441
+00:46:24,470 --> 00:46:31,050
+المعادلة التيارية يبقى هذه اسمها recurrence
+
+442
+00:46:31,050 --> 00:46:33,110
+relation
+
+443
+00:46:38,230 --> 00:46:43,070
+ماذا يعني Recurrent؟ ماذا يعني معادلة تيارية؟ ماذا
+
+444
+00:46:43,070 --> 00:46:49,290
+يعني Recurrent؟ ماذا يعني Recurrent؟ ماذا يعني
+
+445
+00:46:49,290 --> 00:46:53,690
+Recurrent؟ ماذا
+
+446
+00:46:53,690 --> 00:46:57,570
+يعني Recurrent؟
+
+447
+00:46:58,020 --> 00:47:03,520
+فاجيب أقوله قلي n من ون بتبدأ عند ال zero إذا هنا
+
+448
+00:47:03,520 --> 00:47:12,020
+بصير a one يسوى ناقص اتنين a نود على a يبقى
+
+449
+00:47:12,020 --> 00:47:16,180
+هجيبتله a one ممكن أجيب المعادلة أرجع لها تاني و
+
+450
+00:47:16,180 --> 00:47:20,180
+أجيب a اتنين ممكن أرجع لها و أجيب a تلاتة و أرجع
+
+451
+00:47:20,180 --> 00:47:25,760
+لها و أجيب a أربعة و كذا و منها أجيب له صيغة a n
+
+452
+00:47:25,760 --> 00:47:31,640
+اللي طلبها هذهتمام لما طلب جالي هاتي الشكل ال a n
+
+453
+00:47:31,640 --> 00:47:37,420
+بقوله والله تمام اذا انا بدي اخد لو كانت ال n
+
+454
+00:47:37,420 --> 00:47:43,240
+تساوي ال zero then حط zero zero زائد واحد يصير
+
+455
+00:47:43,240 --> 00:47:49,800
+واحد يبقى a واحد ساوية ناقص اتنين a naught على
+
+456
+00:47:49,800 --> 00:47:58,080
+واحد يعني جداش يعني ناقص اتنين a naughtبادى بقوله
+
+457
+00:47:58,080 --> 00:48:05,700
+لو كانت ال N تساوي واحد then بدل ال واحد A واحد
+
+458
+00:48:05,700 --> 00:48:12,900
+زائد واحد يعني اللي همين اتنين يبقى بده أشيل كل N
+
+459
+00:48:12,900 --> 00:48:19,640
+و أحط مكانها واحد يبقى بده يساوي نقص اتنين A واحد
+
+460
+00:48:19,640 --> 00:48:27,390
+على واحد زائد واحديبقى هذا معناه ان اتنين يساوي
+
+461
+00:48:27,390 --> 00:48:33,090
+ناقص اتنين ا واحد على اتنين طب ا واحد موجود عندى
+
+462
+00:48:33,090 --> 00:48:40,790
+فوق مظبوط يبقى هذا معناته ناقص اتنين على اتنين في
+
+463
+00:48:40,790 --> 00:48:49,320
+ناقص اتنين and oddيعني هذا معناه نقص اتنين لكل
+
+464
+00:48:49,320 --> 00:48:55,600
+تربيه انه اد على اتنين شرك اتنين هذا مش هي اتنين
+
+465
+00:48:55,600 --> 00:49:01,200
+factorial كمان يعني مضروب اتنين يبقى بقدر اكتبها
+
+466
+00:49:01,200 --> 00:49:05,740
+اتنين factorial طبعا هتسأل واحدة ده طب ليش
+
+467
+00:49:05,740 --> 00:49:11,120
+ماتختصرها مع اللي فوق بنقولك لحاجة في نفسي يا عقوب
+
+468
+00:49:11,120 --> 00:49:17,740
+ستعرفونها بعد قليلطبعا يعني ليش ماختصرتش إليها سرح
+
+469
+00:49:17,740 --> 00:49:22,500
+أنا عايز أخليها تظل بيها ده الشكل باجي بقوله لو
+
+470
+00:49:22,500 --> 00:49:28,520
+كانت ال N تساوي 2 then يبقى بدي أشيل ال N و أحط
+
+471
+00:49:28,520 --> 00:49:36,620
+مكانها وين اتنين يبقى بصير اتلاتة يساوي اتنين زائد
+
+472
+00:49:36,620 --> 00:49:42,960
+واحد يبقى N عندي هنا مقداشباتنين يبقى هذه تساوي
+
+473
+00:49:42,960 --> 00:49:50,460
+ناقص اتنين اتنين على اتنين زائد واحد يعني هذه
+
+474
+00:49:50,460 --> 00:49:57,420
+تساوي ناقص اتنين على تلاتة في اتنين وين اتنين هي
+
+475
+00:49:57,420 --> 00:50:04,320
+يبقى هذه اتنين اللي هو ناقص اتنين لكل ترابيع a
+
+476
+00:50:04,320 --> 00:50:11,030
+node على اتنين factorialنقص اتنين فنقص اتنين تربية
+
+477
+00:50:11,030 --> 00:50:17,910
+فنقص اتنين تكعيب و a not زي ما هو هذا تلاتة في
+
+478
+00:50:17,910 --> 00:50:22,350
+اتنين factorial اللي يبقى دهاش تلاتة factorial
+
+479
+00:50:22,350 --> 00:50:29,170
+يبقى هذه تلاتة factorial طب حد فيكم تقدر تقوللي لو
+
+480
+00:50:29,170 --> 00:50:35,690
+كانت ال into ساوي تلاتة يبقى بحصل على مين على ايه
+
+481
+00:50:35,690 --> 00:50:40,910
+اربعةحد فيكم بتقدر يقدرش اربعة من خلال النتائج هذه
+
+482
+00:50:40,910 --> 00:50:45,630
+اللي هو سالب اتمين اقصى اربعة انود على اربعة
+
+483
+00:50:45,630 --> 00:50:52,790
+factorial تمام؟ اذا انا لو ضليت مستمر هوصل الى
+
+484
+00:50:52,790 --> 00:51:01,350
+اين؟تلاتة يبقى تلاتة تلاتة يبقى ناقص اتنين to the
+
+485
+00:51:01,350 --> 00:51:10,650
+power n لل a node على n factorial تمام يبقى هذا
+
+486
+00:51:10,650 --> 00:51:15,050
+الصيغة اللي هو ايه اللي هو بده ياها قال هاتلي شكل
+
+487
+00:51:15,050 --> 00:51:21,640
+ال a nيبقى قدرت احصل على شكل ال a n من خلال
+
+488
+00:51:21,640 --> 00:51:25,920
+المعادلة التيارية او ال recurrence relation اللي
+
+489
+00:51:25,920 --> 00:51:31,400
+انا يبقى انا جبتله main المطلوب الاول شكل ال a n
+
+490
+00:51:31,400 --> 00:51:37,060
+كله بدلالة main ال a note يبقى اجبناله على سؤال
+
+491
+00:51:37,060 --> 00:51:42,150
+ايش بيقوللي try حاولان قدرت اهلا وسهلا ماجدتش بلاش
+
+492
+00:51:42,150 --> 00:51:47,930
+بس هذه مشان اقدر بدي افتح calculus V وروح تشوف ايه
+
+493
+00:51:47,930 --> 00:51:52,810
+الشكل اللي هو ال factorial او ايه الشكل ال power
+
+494
+00:51:52,810 --> 00:51:58,610
+series لدوال المختلفة بقول try to identify the
+
+495
+00:51:58,610 --> 00:52:03,470
+function represented by هذه بقوله خليني اشوف الشكل
+
+496
+00:52:03,470 --> 00:52:08,450
+هذه المطلوب التاني فبروح بقوله انا عندي summation
+
+497
+00:52:09,590 --> 00:52:14,550
+من n equal zero to infinity لل a n لل x to the
+
+498
+00:52:14,550 --> 00:52:20,090
+power n a n هي قيمتها إذا هشيلها و أحط قيمتها
+
+499
+00:52:20,090 --> 00:52:25,150
+يبقاش بصير عندي بصير عندي summation من n equal
+
+500
+00:52:25,150 --> 00:52:31,310
+zero to infinity لمين لنقص اتنين to the power n لل
+
+501
+00:52:31,310 --> 00:52:39,360
+a node على n factorial في ال x to the power nيسوي
+
+502
+00:52:39,360 --> 00:52:44,240
+ال summation من n equal zero to infinity ال a node
+
+503
+00:52:44,240 --> 00:52:49,000
+هذا مقدر ثابت مالوش دعوة نيجي هذا ال أس تبعه قداش
+
+504
+00:52:49,000 --> 00:52:56,000
+n و هذا الأس تبعه قداش يعني هذا كأنه ناقص اتنين x
+
+505
+00:52:56,000 --> 00:53:04,410
+كله to the power n على n factorial تمامطب حد فيكوا
+
+506
+00:53:04,410 --> 00:53:12,550
+مذاكرة McLaurin series لده لإيه و ال six؟ لده لإيه
+
+507
+00:53:12,550 --> 00:53:21,150
+و ال six؟ حد فيكوا بتحلم؟ طب حد فيكوا بتعلم؟ ولا
+
+508
+00:53:21,150 --> 00:53:25,960
+واحدة طبعاطبعا خدنا مثال هذا اول مثال على مكلورين
+
+509
+00:53:25,960 --> 00:53:30,460
+سيريز في Calculus B بجي نقول ان ال E X تساوي
+
+510
+00:53:30,460 --> 00:53:34,480
+الصميم من N equal zero to infinity إلى X to the
+
+511
+00:53:34,480 --> 00:53:40,820
+power N على N factorial تمام يبقى E أس X كانت
+
+512
+00:53:40,820 --> 00:53:47,340
+عندنا زمان E أس X يساوي X to the power N على N
+
+513
+00:53:47,340 --> 00:53:53,000
+factorial وصميم من N equal zero to infinityفى شبه
+
+514
+00:53:53,000 --> 00:53:59,880
+بينها وبين هذه يبقى هذه مين هى E أس سالب اتنين X
+
+515
+00:53:59,880 --> 00:54:05,820
+يبقى هذا الكلام بده ساوي summation من N equal zero
+
+516
+00:54:05,820 --> 00:54:11,660
+to infinity لل A node E لأ بدون summation يا بنات
+
+517
+00:54:11,660 --> 00:54:17,040
+خلاص ك function هذه يبقى A node فى ال E أس سالب
+
+518
+00:54:17,040 --> 00:54:24,750
+اتنين X فقط بغىيبقى هذه الدالة التي تمثل من ال
+
+519
+00:54:24,750 --> 00:54:29,130
+power series اللى عندنا هذى وهو هذا المطلوب الثاني
+
+520
+00:54:29,130 --> 00:54:33,730
+يجب ان احاول ان اعنف ال functions التي تمثل ال
+
+521
+00:54:33,730 --> 00:54:38,290
+power series اللى عندنا ماشي يبقى هذه اعتمدت وين
+
+522
+00:54:38,290 --> 00:54:44,430
+على معلوماتنا من calculus b طيب لحد هنا stop انتهى
+
+523
+00:54:44,430 --> 00:54:48,970
+هذا ال section الى يكون أرقام المسائل
+
+524
+00:54:50,890 --> 00:54:58,990
+يبقى exercises خمسة واحد المسائل التالية من واحد
+
+525
+00:54:58,990 --> 00:55:04,010
+لغاية تمانية وعشرين الفضل وطبعا هذه السؤال تمانية
+
+526
+00:55:04,010 --> 00:55:11,350
+وعشرين قدامكوا واربعة وعشرين حلناها قبل شوية حد
+
+527
+00:55:11,350 --> 00:55:15,990
+فيكوا اللي يتساول هنا بنات؟ تغيير ال index هرجعله
+
+528
+00:55:15,990 --> 00:55:20,030
+الآن في section خمسة اتنين اللي بدنا نبدأ حالا
+
+529
+00:55:45,390 --> 00:55:50,350
+بننتقل الان لل section اللى بعده برضه اللى فوق
+
+530
+00:55:50,350 --> 00:55:51,250
+انتهينا منها
+
+531
+00:56:06,240 --> 00:56:12,840
+بنتقل الأن لـ Section 5-2 اللي هو بتحدث عن Series
+
+532
+00:56:12,840 --> 00:56:18,840
+Solution Series Solution
+
+533
+00:56:18,840 --> 00:56:22,360
+Near
+
+534
+00:56:22,360 --> 00:56:25,520
+An
+
+535
+00:56:25,520 --> 00:56:28,900
+Ordinary
+
+536
+00:56:28,900 --> 00:56:34,180
+Point Art
+
+537
+00:56:35,570 --> 00:56:42,970
+One Consider
+
+538
+00:56:42,970 --> 00:56:46,410
+the
+
+539
+00:56:46,410 --> 00:56:51,310
+differential equation
+
+540
+00:56:53,100 --> 00:56:59,880
+Capital P of X في الـ Y W Prime Capital Q of X في
+
+541
+00:56:59,880 --> 00:57:06,360
+الـ Y Prime Capital R of X في الـ Y بده يساوي Zero
+
+542
+00:57:06,360 --> 00:57:10,260
+وهذا بده يسميها المعادلة رقم 1
+
+543
+00:57:14,420 --> 00:57:25,140
+P of X with a Q of X and R of X are polynomials
+
+544
+00:57:25,140 --> 00:57:33,640
+with
+
+545
+00:57:33,640 --> 00:57:37,200
+no common factors
+
+546
+00:57:45,800 --> 00:57:55,480
+مافيش بينهم عوامل مشتركة نعطي تعريف رقم واحد a
+
+547
+00:57:55,480 --> 00:58:08,260
+point a point x0 is called an ordinary point an
+
+548
+00:58:08,260 --> 00:58:13,280
+ordinary point
+
+549
+00:58:15,450 --> 00:58:20,070
+for the differential equation one for the
+
+550
+00:58:20,070 --> 00:58:26,230
+differential equation
+
+551
+00:58:26,230 --> 00:58:40,310
+one if ال P of X not لا يساوي ال zero لو كانت هذه
+
+552
+00:58:40,310 --> 00:58:46,450
+لا تساوي ال zero نمري اتنينعن طريق الوصول إلى موقع
+
+553
+00:58:46,450 --> 00:58:55,910
+X0 هو موقع عشان يسمى موقع عشان يسمى موقع عشان يسمى
+
+554
+00:58:55,910 --> 00:59:08,730
+موقع عشان يسمى موقع عشان يسمى موقع عشان
+
+555
+00:59:08,730 --> 00:59:12,910
+يسمى
+
+556
+00:59:13,010 --> 00:59:22,210
+الـ P of X0 بده يساوي مين؟ بده يساوي Zero Now
+
+557
+00:59:22,210 --> 00:59:25,370
+We
+
+558
+00:59:25,370 --> 00:59:37,850
+Look For We Look For A Solution Of The
+
+559
+00:59:37,850 --> 00:59:44,080
+Differential Equation 1 Of Thatdifferential
+
+560
+00:59:44,080 --> 00:59:51,240
+equation one
+
+561
+00:59:51,240 --> 01:00:05,440
+in the form في الشكل y تساوي ال summation من n
+
+562
+01:00:05,440 --> 01:00:12,880
+equal zero to infinity لل a nx نقص x node to the
+
+563
+01:00:12,880 --> 01:00:28,960
+power m where ال x node is an ordinary point and
+
+564
+01:00:28,960 --> 01:00:32,120
+the
+
+565
+01:00:32,120 --> 01:00:37,960
+series and the series
+
+566
+01:00:44,720 --> 01:00:55,260
+converge and the series converge in the interval
+
+567
+01:00:55,260 --> 01:01:04,680
+in the interval absolute value ال X نقص ال X أقل
+
+568
+01:01:04,680 --> 01:01:09,920
+من رو for some
+
+569
+01:01:11,320 --> 01:01:15,680
+أقرأ اللي أكبر من مين من أزيمة
+
+570
+01:02:10,840 --> 01:02:16,720
+بنحاول نفهم كل كلمة مكتوبة قدامنا هنا على السطورة
+
+571
+01:02:16,720 --> 01:02:19,900
+لإنه خلاص هاي الكلمتين النظرية تبع ال section هدا
+
+572
+01:02:19,900 --> 01:02:24,640
+و بعد هيك بتذكروا عندنا شغل كيف نحل المعادلة
+
+573
+01:02:24,640 --> 01:02:28,720
+التفاضلي العنوان اللي أحنا عارفينه section 5-2
+
+574
+01:02:28,720 --> 01:02:34,460
+serious solution near an ordinary point of part
+
+575
+01:02:34,460 --> 01:02:39,540
+oneيبقى احنا الآن يا بنات بدنا نحاول نستخدم
+
+576
+01:02:39,540 --> 01:02:45,840
+المتسلسلات فى حل المعادلة التفاضلية المتجانسة من
+
+577
+01:02:45,840 --> 01:02:50,740
+الرتبة الثانية ماحنا كنا بنحلها سابقا لكن بدون
+
+578
+01:02:50,740 --> 01:02:56,040
+متسلسلات مظبوط الآن هنحاول نحلها مرة ثانية
+
+579
+01:02:56,040 --> 01:03:00,200
+باستخدام اللى هو ال power series او باستخدام
+
+580
+01:03:00,200 --> 01:03:04,110
+المتسلسلاتبقول اعتبر الصيغة العامة للمعادلة
+
+581
+01:03:04,110 --> 01:03:09,050
+التفاضلية للصيغة رقم واحد المتعرف عليها قبل ذلك بس
+
+582
+01:03:09,050 --> 01:03:13,750
+بشرط قل الدول التلاتة ال P و ال Q و ال R هدول ما
+
+583
+01:03:13,750 --> 01:03:18,950
+لهم بديهم كثيرات حدود مش حيالها يعني إذا كانوا
+
+584
+01:03:18,950 --> 01:03:22,330
+كثيرات حدود قلهم كلام و إذا مش كثيرات حدود قلهم
+
+585
+01:03:22,330 --> 01:03:28,050
+كلام ثاني تمام؟ احنا اليوم سنقتصر دراستنا على إن
+
+586
+01:03:28,050 --> 01:03:33,650
+لو كانوا المعاملات هدول كثيرات حدوديبقى ال P و ال
+
+587
+01:03:33,650 --> 01:03:37,350
+Q و ال R كثيرات حدود من الرتبة الأولى و الرتبة
+
+588
+01:03:37,350 --> 01:03:40,090
+التالية و الدرجة الأولى و الدرجة التانية و الدرجة
+
+589
+01:03:40,090 --> 01:03:41,130
+التالية و الدرجة التالية و الدرجة التالية و الدرجة
+
+590
+01:03:41,130 --> 01:03:41,530
+التالية و الدرجة التالية و الدرجة التالية و الدرجة
+
+591
+01:03:41,530 --> 01:03:42,430
+التالية و الدرجة التالية و الدرجة التالية و الدرجة
+
+592
+01:03:42,430 --> 01:03:44,990
+التالية و الدرجة التالية و الدرجة التالية و الدرجة
+
+593
+01:03:44,990 --> 01:03:45,050
+التالية و الدرجة التالية و الدرجة التالية و الدرجة
+
+594
+01:03:45,050 --> 01:03:45,870
+التالية و الدرجة التالية و الدرجة التالية و الدرجة
+
+595
+01:03:45,870 --> 01:03:46,750
+التالية و الدرجة التالية و الدرجة التالية و الدرجة
+
+596
+01:03:46,750 --> 01:03:48,930
+التالية و الدرجة التالية و الدرجة التالية و الدرجة
+
+597
+01:03:48,930 --> 01:03:52,320
+التالية و الديعني هذه و هذه يمكن يكون بينهم عامل
+
+598
+01:03:52,320 --> 01:03:56,980
+مشترك لكن مع التالتة لأ و هكذا يعني لا يوجد
+
+599
+01:03:56,980 --> 01:04:01,520
+للتلاتة مع بعض بينهم عامل مشترك لو وجد بدنا نكسب
+
+600
+01:04:01,520 --> 01:04:06,580
+عليه و نتخلص منه تمام ولا يؤثر على شكل الحل
+
+601
+01:04:06,580 --> 01:04:11,720
+المعادلة التفاضلية يبقى ال P و ال QR have no
+
+602
+01:04:11,720 --> 01:04:17,420
+common factors لاتوجد بينهم أي عوامل مشتركةبدنا
+
+603
+01:04:17,420 --> 01:04:21,200
+نعطي تعريف جديد، هذا كلام برضه جديد علينا
+
+604
+01:04:21,200 --> 01:04:25,100
+ماشوفنهوش قبل اليوم بدنا نعطي تعريف لل ordinary
+
+605
+01:04:25,100 --> 01:04:28,580
+point اللي هي النقطة العادية و ال singular point
+
+606
+01:04:28,580 --> 01:04:33,840
+اللي هي النقطة الشاذة أو النقطة المنفردة أو النقطة
+
+607
+01:04:33,840 --> 01:04:38,420
+المنعزلة لكن الدارج النقطة الشاذة singular point
+
+608
+01:04:39,220 --> 01:04:43,560
+طبعا singular اللغة الأدبية اعزب في اللغة
+
+609
+01:04:43,560 --> 01:04:46,980
+الإنجليزية لكن احنا ماقلناش دعوة هنا بيقول مفرد،
+
+610
+01:04:46,980 --> 01:04:52,260
+منفرد، أو شاذر، النقطة الشاذة اللي عندنا هنا يبقى
+
+611
+01:04:52,260 --> 01:04:57,160
+النقطة x0 is called an ordinary point بسميها نقطة
+
+612
+01:04:57,160 --> 01:05:00,600
+عادية for the differential equation one اللي عندنا
+
+613
+01:05:00,600 --> 01:05:07,130
+إذا كان ال P of x0 لا يساوي زي V يعني أي نقطةبعوضه
+
+614
+01:05:07,130 --> 01:05:12,930
+بقى في الـP بيكون الناتج لا يساوي 0 بسميها .. طب
+
+615
+01:05:12,930 --> 01:05:17,350
+لو ساوى 0 يصير singular point اللي هي النقطة
+
+616
+01:05:17,350 --> 01:05:21,050
+الثانية يبقى التعريف تاني النقطة X1 بقول عنها
+
+617
+01:05:21,050 --> 01:05:24,430
+singular point نقطة شدى for the differential
+
+618
+01:05:24,430 --> 01:05:29,530
+equation 1 إذا عوضت بها في الدالة P وطلع الناتج
+
+619
+01:05:29,530 --> 01:05:34,910
+يساوي 0يبقى من حد ما يعطيني معادلة تفاضلية بروح
+
+620
+01:05:34,910 --> 01:05:40,260
+بتطلع للمعامل تبع واي باطل ال primeكل النقاط اللي
+
+621
+01:05:40,260 --> 01:05:44,740
+بتخليه زيرو بسميها singular points والنقاط اللي
+
+622
+01:05:44,740 --> 01:05:50,640
+بتخليش زيرو بسميها ordinary points احنا في هذا ال
+
+623
+01:05:50,640 --> 01:05:54,380
+section بدنا نشتغل على ال ordinary points وليس على
+
+624
+01:05:54,380 --> 01:05:59,420
+ال singular points تمام؟ طيب تعالوا نشوف اللي
+
+625
+01:05:59,420 --> 01:06:03,360
+بعدها يبقى هذا التعريف الأول والتعريف التانييبقى
+
+626
+01:06:03,360 --> 01:06:14,760
+نبحث عن حلول من الاختلافية 1 على الشكل التالي نبحث
+
+627
+01:06:14,760 --> 01:06:20,300
+عن حل على الشكل متسلسلة للمعادلة اللى فوق على
+
+628
+01:06:20,300 --> 01:06:25,480
+الصيغة هذه حيث ال X node هذه مالها ordinary point
+
+629
+01:06:25,480 --> 01:06:29,710
+singular point لسه ماليش دعوة فيهاand the series،
+
+630
+01:06:29,710 --> 01:06:34,010
+ال series هذه تبقى تقريبية على الفترة اللي عندنا
+
+631
+01:06:34,010 --> 01:06:38,410
+هذه، يبقى مين هو روية بنات؟ ال radius of
+
+632
+01:06:38,410 --> 01:06:41,790
+convergence اللي حكينا عليه المرة اللي فاتتيبقى
+
+633
+01:06:41,790 --> 01:06:46,790
+لما أقول هذه هذه بقدر أحلها على الشكل التالي لما
+
+634
+01:06:46,790 --> 01:06:52,090
+أقول هذه absolutely يبقى x ناقص ال x node أقل من
+
+635
+01:06:52,090 --> 01:06:57,650
+row و أكبر من سالب row لو أضفنا x node للتلاتة
+
+636
+01:06:57,650 --> 01:07:03,650
+الأطراف بيصير x node ناقص row أقل من x أقل من x
+
+637
+01:07:03,650 --> 01:07:10,750
+node زائد row كيف يعني هذه؟بنقولك اه لو جيت قولت
+
+638
+01:07:10,750 --> 01:07:16,950
+هذا ال real life تمام وعندي هذه النقطة وهذه النقطة
+
+639
+01:07:16,950 --> 01:07:22,890
+هذه الفترة اللي ال P of X او الدوال اللي عندنا
+
+640
+01:07:22,890 --> 01:07:27,520
+عليها يكون realيبقى هنا point of the series
+
+641
+01:07:27,520 --> 01:07:35,160
+converge على الفترة اللي عندنا هنا ال X node نقطة
+
+642
+01:07:35,160 --> 01:07:42,120
+موجودة وين؟ داخل هذه الفترة يبقى هنا النقطة هذه من
+
+643
+01:07:42,120 --> 01:07:48,560
+X node اللي هي ال ordinary point يبقى هذه هي ال
+
+644
+01:07:48,560 --> 01:07:51,780
+ordinary point
+
+645
+01:07:53,740 --> 01:07:59,680
+يبقى هذا كله طول تبع رو نصف قطر التقارب وهذا رو
+
+646
+01:07:59,680 --> 01:08:05,620
+نصف قطر التقارب كذلك إذا النقطة هذه عبارة عن X
+
+647
+01:08:05,620 --> 01:08:14,680
+node ناقص رو والنقطة هذه X node زائد روالنقطة هذه
+
+648
+01:08:14,680 --> 01:08:18,180
+وقبل النقطة هذه ال series diverse مليش علاقة فيها
+
+649
+01:08:18,180 --> 01:08:22,880
+يبقى أنا مقيد في الفترة اللي ال series هذه تبعت
+
+650
+01:08:22,880 --> 01:08:27,580
+الحل اللي بتكون عليها مالها تقاربية و نصف القطر
+
+651
+01:08:27,580 --> 01:08:32,340
+هنا دائما و أبدا موجب لأنه مسافة مسافة بين
+
+652
+01:08:32,340 --> 01:08:36,020
+النقطتين يبقى مضحكتش المقصود بالعبارة اللي عندنا
+
+653
+01:08:36,020 --> 01:08:41,560
+هذه تمام يبقى هي كل ما في الأمر يبقى بنات الحل
+
+654
+01:08:41,560 --> 01:08:48,860
+عنديفي حالة المعادلات هذه بوصفة المتسلسلات ممكن
+
+655
+01:08:48,860 --> 01:08:53,740
+يكون على الشكل اللي عندنا هذاو ممكن يكون لو كانت x
+
+656
+01:08:53,740 --> 01:08:58,300
+node بيزيرو لو اعطاني x node بزيرو بصير الحل على
+
+657
+01:08:58,300 --> 01:09:05,540
+اسم a in x to the power n تمام اذا جالي عند x node
+
+658
+01:09:05,540 --> 01:09:09,500
+تسوى واحد او ال ordinary point تسوى واحد او اتنين
+
+659
+01:09:09,500 --> 01:09:14,900
+او تلاتة بدي اتقيد فيها وبالتالي احسب ايه الحل
+
+660
+01:09:14,900 --> 01:09:20,410
+عندهاهذا كل الجزء النظري تبع ال section لكن الحل
+
+661
+01:09:20,410 --> 01:09:25,430
+طويل شوية للمثال نبدأ ناخد مثال فوضيح على الشغل
+
+662
+01:09:25,430 --> 01:09:40,110
+هذه أول مثال يقول ما يأتي example one يقول
+
+663
+01:09:40,110 --> 01:09:41,910
+find the serious solution
+
+664
+01:09:49,750 --> 01:10:00,110
+الحل اللي بيكون على شكل متسلسلة and the recurrence
+
+665
+01:10:00,110 --> 01:10:06,470
+relation and
+
+666
+01:10:06,470 --> 01:10:12,330
+recurrence relation for the
+
+667
+01:10:14,680 --> 01:10:23,100
+differential equation للمعادلة التفاغلية yw prime
+
+668
+01:10:23,100 --> 01:10:33,460
+زائد x في y prime زائد اتنين y تساوي zero about
+
+669
+01:10:33,460 --> 01:10:36,580
+the
+
+670
+01:10:36,580 --> 01:10:40,460
+point حوالين النقطة
+
+671
+01:11:00,900 --> 01:11:08,100
+نرجع لسؤال مرة ثانيةطالب شغلتين طالب الحل و
+
+672
+01:11:08,100 --> 01:11:12,720
+recurrence relation طبعا انا مش هقدر اوصل للحل الا
+
+673
+01:11:12,720 --> 01:11:16,840
+احسبله a recurrence relation find the serious
+
+674
+01:11:16,840 --> 01:11:21,180
+solution and the recurrence relation for the
+
+675
+01:11:21,180 --> 01:11:26,160
+differential equation هذه about the point x0 يسوى
+
+676
+01:11:26,160 --> 01:11:32,020
+0 هل قلل x0 يسوى 0 هذه ordinary point ولا singular
+
+677
+01:11:32,020 --> 01:11:37,920
+pointماجليش لكن انا لحالي هاكتشف انه هادي ordinary
+
+678
+01:11:37,920 --> 01:11:41,320
+point من دون ما يقولي بقول .. بقولك كده، بقولك
+
+679
+01:11:41,320 --> 01:11:45,940
+كتالة، هالحين مين ان ال P of X تبعت المعادلة هاد
+
+680
+01:11:45,940 --> 01:11:54,950
+يا بنات؟ جدير؟ واحدهل هناك قيمة ل X بتخلي النتيجة
+
+681
+01:11:54,950 --> 01:12:00,090
+هذه السفر ولا قيمة؟ يبقى هذا مقدار ثابت جد ما
+
+682
+01:12:00,090 --> 01:12:04,810
+تتغير ال X بتبقى مقدار ثابت أيش ما تصير ال X يبقى
+
+683
+01:12:04,810 --> 01:12:12,010
+هذا معناته هذا طبعا سوى واحد for all X هذا معناته
+
+684
+01:12:12,010 --> 01:12:19,230
+every point is an ordinary
+
+685
+01:12:25,800 --> 01:12:30,500
+ببنان عليه ال X not to zero هو ordinary ولا
+
+686
+01:12:30,500 --> 01:12:39,600
+singular؟ ordinary يبقى ال X not to zero is an
+
+687
+01:12:39,600 --> 01:12:46,020
+ordinary point تمام
+
+688
+01:12:47,200 --> 01:12:55,200
+يبقى الحل بيكون على شكل y تساوي a node في x ناقص
+
+689
+01:12:55,200 --> 01:13:01,940
+zero يعني a n x to the power n يبقى هنا باجي بقول
+
+690
+01:13:01,940 --> 01:13:08,400
+let y تساوي ال summation من n equal zero ل
+
+691
+01:13:08,400 --> 01:13:20,560
+infinity لل a nx to the power n be a solution of
+
+692
+01:13:20,560 --> 01:13:28,020
+the differential equation 1 سميلي هذا بنات اللي هي
+
+693
+01:13:28,020 --> 01:13:34,980
+المعادلة رقم 1 اللي تبعت السؤال كويس
+
+694
+01:13:34,980 --> 01:13:47,750
+نشتاقيبقى بدنا y prime يسوى summation لل n a n x
+
+695
+01:13:47,750 --> 01:13:51,950
+to the power n minus one و ال summation بيبدأ من
+
+696
+01:13:51,950 --> 01:13:58,410
+وين ان عند n تسوى واحد لإنه أول حد هنا هو a note
+
+697
+01:13:58,820 --> 01:14:04,800
+هيطير مع الاشتقاء طيب هذا بده يعطيك ان y w prime
+
+698
+01:14:04,800 --> 01:14:13,000
+يساوي summation n في الناقص واحد في a n في ال x أس
+
+699
+01:14:13,000 --> 01:14:20,940
+n ناقص اتنين تمام ال summation من وان بده يبدأ من
+
+700
+01:14:20,940 --> 01:14:26,560
+عند n يساوي اتنين الى infinityيبقى هاي جيبته
+
+701
+01:14:26,560 --> 01:14:30,940
+المشتقة الأولى و المشتقة التانية بتروح اعوض وين في
+
+702
+01:14:30,940 --> 01:14:39,180
+المعادلة رقم واحد يبقى باجي بقوله substitute in
+
+703
+01:14:39,180 --> 01:14:49,200
+the differential equation one we get نحصل علاماتي
+
+704
+01:14:49,900 --> 01:14:55,100
+الأول شي YW' يبقى بدي أنزل هذا ال summation زي ما
+
+705
+01:14:55,100 --> 01:15:00,380
+هو يبقاش بصير عندي summation من N equal two to
+
+706
+01:15:00,380 --> 01:15:06,580
+infinity مادها زائد X في summation بدنا المشتقة
+
+707
+01:15:06,580 --> 01:15:14,300
+الأولى من عند N equal one to infinity لمن؟ لل N A
+
+708
+01:15:14,300 --> 01:15:21,290
+N X أس N ناقص واحدأيه بيخلصنا ال term التاني زائد
+
+709
+01:15:21,290 --> 01:15:26,990
+اتنين في summation من عند ال N equal zero to
+
+710
+01:15:26,990 --> 01:15:36,050
+infinity لمين لان X to the power N كل هذا بده
+
+711
+01:15:36,050 --> 01:15:42,620
+يساوي كده؟ بده يساوي Zeroمشان اجيب له recurrence
+
+712
+01:15:42,620 --> 01:15:49,540
+relation بدي كله يصير بدلالة X to the power M هاي
+
+713
+01:15:49,540 --> 01:15:54,900
+واحدة اتنين بدي ال index اللي تحت ال summation كله
+
+714
+01:15:54,900 --> 01:16:00,820
+يصير زي بعضهكويس؟ بنقوله بسيطة يبقى هذا الكلام
+
+715
+01:16:00,820 --> 01:16:06,140
+بدنا نرجع لمين؟ زي شغلنا اللي توقبل قليل في ال
+
+716
+01:16:06,140 --> 01:16:11,480
+section الماضي صحيح ولا لا؟ إذا ال section الماضي
+
+717
+01:16:11,480 --> 01:16:16,780
+كان ضروري جدا مشان نعرف نشتغل في هذا ال section
+
+718
+01:16:16,780 --> 01:16:23,370
+فباجي بقولهذه بقدر أخليها x to the power n لو
+
+719
+01:16:23,370 --> 01:16:28,890
+خلّيت ال index يبدأ من وين إذا بدأ أشيل كل n و أحط
+
+720
+01:16:28,890 --> 01:16:37,590
+مكانها n زائد 2 يبقى بصير المسألة summation من n
+
+721
+01:16:37,590 --> 01:16:46,290
+equal zero to infinity وهذه بصير nزائد اتنين في n
+
+722
+01:16:46,290 --> 01:16:55,350
+زائد واحد في a n زائد اتنين في ال x to the power n
+
+723
+01:16:55,350 --> 01:17:01,370
+طيب هذه بسيطة دخل هذه جوا بصير x to the power n
+
+724
+01:17:01,370 --> 01:17:06,490
+يبقى ال x بروح بدخلها جوا يبقى لما ندخلها جوا ال
+
+725
+01:17:06,490 --> 01:17:11,950
+summation زائد summation من n equal one to
+
+726
+01:17:11,950 --> 01:17:21,390
+infinityللإن a n x to the power n زائد واحد ونقص
+
+727
+01:17:21,390 --> 01:17:26,650
+واحد مع السلامة يبقى زائد x to the power n اتنين
+
+728
+01:17:26,650 --> 01:17:31,210
+هذه بقدر ادخلها جوا ال summation يبقى زائد
+
+729
+01:17:31,210 --> 01:17:37,390
+summation من n equal zero to infinity للإتنين a n
+
+730
+01:17:37,390 --> 01:17:43,310
+x to the power n كله بده يساوي قداش يساوي zeroبقول
+
+731
+01:17:43,310 --> 01:17:48,810
+كويس تعالى نطلع فى ال X's هنا to the power N هنا
+
+732
+01:17:48,810 --> 01:17:53,070
+to the power N to the power N يبقى بدنا نحافظ على
+
+733
+01:17:53,070 --> 01:17:57,510
+المكتسبات الموطنية أصحى تلعبي فيها ان احنا هذه
+
+734
+01:17:57,510 --> 01:18:00,610
+بيتناياها لازمنا نطلع فى دلاله X to the power N
+
+735
+01:18:00,610 --> 01:18:05,830
+طيب نجي لها ال summation N تساوي Zero N تساوي واحد
+
+736
+01:18:05,830 --> 01:18:13,460
+N تساوي Zeroمظبوط يبقى انا يا بخليهم كلهم zero يا
+
+737
+01:18:13,460 --> 01:18:19,000
+بخليهم كلهم واحد مظبوط مش هنقدر اجمعهم مع بعض بقول
+
+738
+01:18:19,000 --> 01:18:24,680
+اه لو هذه بده اخليها zero ايش بصير عندي؟ بده اشيل
+
+739
+01:18:24,680 --> 01:18:29,020
+كل N و احط مكانها N زاد واحد بيصير N زاد واحد A N
+
+740
+01:18:29,020 --> 01:18:34,820
+زاد واحد Xو سن زاد واحد خربنا الدنيا ماحافظلاش على
+
+741
+01:18:34,820 --> 01:18:40,240
+المكتسبات الوطنية تمام؟ يبقى اصحى تلعب فيها طيب
+
+742
+01:18:40,240 --> 01:18:46,140
+تعالى نحول ال summation كله بدلالة 2 هذا سهل جدا و
+
+743
+01:18:46,140 --> 01:18:51,760
+بصيرش مشاكل في ال excess كيف؟ بقى يبقى فلت أول حد
+
+744
+01:18:51,760 --> 01:18:55,820
+هنا و هنا فلت أول حد من هنا من ال summation يبقى
+
+745
+01:18:55,820 --> 01:18:59,500
+انحلت مشكلتكبصير كل ال summation زي ما هو و ال
+
+746
+01:18:59,500 --> 01:19:05,300
+excess بقيت كما هي تمام كيف نجي نقول حط n ب zero
+
+747
+01:19:05,300 --> 01:19:13,820
+zero zero بظلي 2 في 1 ب 2 اتنين اكس و zero ب واحد
+
+748
+01:19:13,820 --> 01:19:18,550
+يبقى هذا لما ال n تسوي zeroبالا عندنا زائد
+
+749
+01:19:18,550 --> 01:19:24,570
+summation لما ال N تسوى واحد لل infinity لل N زائد
+
+750
+01:19:24,570 --> 01:19:29,770
+اتنين في ال N زائد واحد في ال A N زائد اتنين في ال
+
+751
+01:19:29,770 --> 01:19:36,040
+X to the power Nهذه يا بنادفش فيها تلعب بنزلها زي
+
+752
+01:19:36,040 --> 01:19:41,940
+ما هي واحد الى infinity لل N A N X to the power N
+
+753
+01:19:41,940 --> 01:19:47,420
+زائد هذه كمان بده اطلع منها الحد الاول يعني لو
+
+754
+01:19:47,420 --> 01:19:54,120
+كانت N يساوي Zero بصير اتنين A نقعد زائد summation
+
+755
+01:19:54,120 --> 01:20:01,140
+من N equal Zero to infinity للاتنين من عند N تساوي
+
+756
+01:20:01,140 --> 01:20:09,650
+واحدللإتنين a n x to the power n ساوي زيرون إذا ال
+
+757
+01:20:09,650 --> 01:20:14,110
+term هذا و ال term هذا بيقولوا مخليكوا أنتوا على
+
+758
+01:20:14,110 --> 01:20:20,070
+الشك ده اطلعوا برا يبقى بصير عندي جداش اتنين اتنين
+
+759
+01:20:20,070 --> 01:20:27,690
+زائد اتنين a naught لحالهمباقي الـ Summations كله
+
+760
+01:20:27,690 --> 01:20:31,850
+مضروف في X to the power N وكله بيبدأ من عند الواحد
+
+761
+01:20:31,850 --> 01:20:36,870
+يبقى بقدر أجمعهم مع بعض بSummation واحد يبقى بقدر
+
+762
+01:20:36,870 --> 01:20:42,550
+أقول هذا زائد summation من N equal one to infinity
+
+763
+01:20:42,550 --> 01:20:49,610
+لل N زائد اتنين في ال N زائد واحد في ال A N زائد
+
+764
+01:20:49,610 --> 01:21:00,740
+اتنين زائد N في ال A Nزائد اتنين a n وكل هذا
+
+765
+01:21:00,740 --> 01:21:07,600
+الكلام مضروب في main في ال x to the power n ويساوي
+
+766
+01:21:07,600 --> 01:21:11,320
+zero الان
+
+767
+01:21:11,320 --> 01:21:16,060
+عندنا polynomial على الشمال بده يساوي zero شو خلها
+
+768
+01:21:16,060 --> 01:21:22,250
+zero؟معاملات إذا كل المعاملات بيبقى أصفر يبقى بناء
+
+769
+01:21:22,250 --> 01:21:27,910
+عليه بيصير عندي اتنين اتنين زائد اتنين ا نوت يسوى
+
+770
+01:21:27,910 --> 01:21:40,650
+كده؟ Zero ومنها ال اتنين يسوى ناقص ا نوت تمام؟ طيب
+
+771
+01:21:40,650 --> 01:21:49,750
+نيجي تانية andهذه يا بنات N زائد اتنين في N زائد
+
+772
+01:21:49,750 --> 01:21:57,370
+واحد في AN زائد اتنين زائد شو رايك هد فيها AN عمل
+
+773
+01:21:57,370 --> 01:22:05,990
+مشترك بيظل جديش N زائد اتنين يبقى N زائد اتنين في
+
+774
+01:22:05,990 --> 01:22:14,970
+AN بده ساوي Zeroبنقدر نجسم كله على مين؟ على N زائد
+
+775
+01:22:14,970 --> 01:22:23,730
+2 لو جسمنا على N زائد 2 ايش بيضل عندنا؟ بيضل عندنا
+
+776
+01:22:23,730 --> 01:22:37,090
+N زائد 1 في ال A N زائد 2 يسوى ناقص A Nأو بيصير
+
+777
+01:22:37,090 --> 01:22:44,190
+عندنا مين؟ بيصير عندنا a n زيدي اتنين يسوى ناقص a
+
+778
+01:22:44,190 --> 01:22:54,400
+اتنين على مين على n زائد واحد طب a اتنين بقدش؟سالب
+
+779
+01:22:54,400 --> 01:23:05,000
+A نوت يبقى هذا معناته سالب سالب A نوت على N زائد
+
+780
+01:23:05,000 --> 01:23:10,920
+واحد استنى
+
+781
+01:23:10,920 --> 01:23:15,620
+استنى شوية هذه N زائد اه هذه A N كيش خلها A اتنين
+
+782
+01:23:16,110 --> 01:23:20,910
+أصابة امرأة و أخطأ عمر بس كلام مظبوط كلامك صحيح
+
+783
+01:23:20,910 --> 01:23:28,230
+يبقى هذه ان بس كلام مظبوط أصابة امرأة و أخطأ عمر
+
+784
+01:23:28,230 --> 01:23:34,310
+تمام؟ طب شو اسم هذه يا بنات؟ هذا ال recurrence
+
+785
+01:23:34,310 --> 01:23:40,650
+relation يبقى هذه هي ال recurrence relation بس ان
+
+786
+01:23:40,650 --> 01:23:43,450
+بتبدأ من أندي zero ولا من أندي الواحد؟
+
+787
+01:23:46,330 --> 01:23:54,110
+هذه لو قلنا من عند ال zero بيصير اتنين هذه zero
+
+788
+01:23:54,110 --> 01:24:01,550
+وهذه zero مظبوط بيصير ناقص ا نود على واحد اللي فوق
+
+789
+01:24:01,550 --> 01:24:01,950
+هذه
+
+790
+01:24:07,790 --> 01:24:13,230
+عندما قلت انته ساوي زيرو لكن عندما قلت انته ساوي
+
+791
+01:24:13,230 --> 01:24:18,030
+واحد لبقى اللي فوق فقلت لحاله اذا بجمع اتنين مع
+
+792
+01:24:18,030 --> 01:24:22,870
+بعض و بقول انته ساوي زيرو و واحد و اتنين و تلاتة
+
+793
+01:24:22,870 --> 01:24:28,930
+الى ما شاء الله يبقى اجتملت على اللي فوقلو كانت ها
+
+794
+01:24:28,930 --> 01:24:32,210
+عوقة عند الـ 0 وماطلعتش اللي فوق يبقى بيخل اللي
+
+795
+01:24:32,210 --> 01:24:36,490
+فوق لحالها وها دي لحاله وها دي اللي بسميها
+
+796
+01:24:36,490 --> 01:24:41,890
+reconciliation وبقول ان بتبدأ من عند الواحد تمام
+
+797
+01:24:41,890 --> 01:24:49,430
+بعيد كلامي هذا مرة تانية احنا هنا سمينا ثابت سوينا
+
+798
+01:24:49,430 --> 01:24:55,340
+ثابت بالـ 0 طالع عند ا اتنين يسوى ناقص ا نونأخذ
+
+799
+01:24:55,340 --> 01:24:58,320
+المعامل هذا و أقوم به بالـ zero و أخرجه عند الـ
+
+800
+01:24:58,320 --> 01:25:01,920
+recurrence relation الـ recurrence relation يبقى
+
+801
+01:25:01,920 --> 01:25:07,720
+ممكن تجتمل على المقدار اللي فوق و ممكن ألا تجتمل
+
+802
+01:25:07,720 --> 01:25:12,700
+إذا هذه لم تجتمل على اللي فوق بجه بقول ان تسوى
+
+803
+01:25:12,700 --> 01:25:17,440
+واحد و اتنين و تلاتة و لا أكتب ال zero إذا جمعت
+
+804
+01:25:17,440 --> 01:25:21,220
+على اللي فوق بجه بخليها تبدأ من عند ال zero بسبنجي
+
+805
+01:25:21,220 --> 01:25:25,860
+بقول لو حطينا zero لل N فعلا بتجيب اللي فوق ولا
+
+806
+01:25:25,860 --> 01:25:31,720
+بتجيبوش بنقول يطلع هنا حط زيرو بصير اتنين حط زيرو
+
+807
+01:25:31,720 --> 01:25:36,940
+بصير انود حط زيرو بصير ناقص انود على one يبقى
+
+808
+01:25:36,940 --> 01:25:41,420
+مظبوط يبقى هه خلاص انت سوى zero بدل ال N استغنت عن
+
+809
+01:25:41,420 --> 01:25:46,440
+هذه وصرت هذه هي ال recurrence relation اللي عندنا
+
+810
+01:25:46,440 --> 01:25:54,790
+طيب الأن بدنا نبدأ نحسبE2 موجودة بدي أحسب E3 وE4
+
+811
+01:25:54,790 --> 01:26:01,030
+وE5 مشان أجيب شكل الحل اللي عندنا فباجي بقوله الأن
+
+812
+01:26:01,030 --> 01:26:07,270
+بدي أجي أخد اللي هو مين E2 موجودة يبقى بدي أجي أخد
+
+813
+01:26:07,270 --> 01:26:14,520
+له E3 وE1 زائد 2التلاتة اللي بقدر اكتبها واحد زي
+
+814
+01:26:14,520 --> 01:26:18,580
+اتنين يبقى لما اقارنها مع ال reconciliation يبقى
+
+815
+01:26:18,580 --> 01:26:23,320
+ال N هنا بقدرش يبقى بده أشيل كل N و أحط مكانها
+
+816
+01:26:23,320 --> 01:26:30,360
+واحد يبقى ناقص A واحد على واحد زائد واحد يبقى ناقص
+
+817
+01:26:30,360 --> 01:26:37,000
+A واحد على مين على الاتنين يبقى جيبناله هيمين A
+
+818
+01:26:37,000 --> 01:26:42,680
+تلاتة بده أجيب له مينأربع يبقى بدى اروح اجيب له
+
+819
+01:26:42,680 --> 01:26:51,040
+اربع اتنين زي ايدي اتنين ويساوي اذا بدى اشيل كل ان
+
+820
+01:26:51,040 --> 01:26:59,360
+و احط مكانها اتنين يبقى ناقص اتنين على الاتنين زي
+
+821
+01:26:59,360 --> 01:27:03,480
+اتنين واحد طيب اتنين عندي معروف اللي هيبقى كده؟
+
+822
+01:27:03,650 --> 01:27:13,890
+بناقص a node يبقى هذا ناقص ناقص a node على من؟ على
+
+823
+01:27:13,890 --> 01:27:20,710
+تلاتة يبقى a node على تلاتة تلاتة ايش رايك اكتبها
+
+824
+01:27:20,710 --> 01:27:24,970
+واحد في تلاتة او لا كتبتيها تلاتة مافيش مشكلة
+
+825
+01:27:24,970 --> 01:27:30,490
+تلاتة في واحد والله تلاتة سيئان طيب ليش؟ اقولك انا
+
+826
+01:27:30,490 --> 01:27:37,110
+قصد هيك متعمدلازم تتعامل بلاش، خلّيها تلاتة زي ما
+
+827
+01:27:37,110 --> 01:27:50,450
+هي جيبنا
+
+828
+01:27:50,450 --> 01:27:56,640
+ايه؟ تلاتة، اربع، خلّينا نجيب ايه؟ خمسةيبقى a خمسة
+
+829
+01:27:56,640 --> 01:28:03,380
+يساوي اللي هي a تلاتة زائد اتنين اذا هشيل كل n وحط
+
+830
+01:28:03,380 --> 01:28:11,000
+مكانها تلاتة يبقى سالب a تلاتة على تلاتة زائد واحد
+
+831
+01:28:11,320 --> 01:28:16,820
+هو يسوي سالب اظن ا تلاتة عسبناها لو سالب ا واحد
+
+832
+01:28:16,820 --> 01:28:24,800
+على اتنين يبقى سالب ا واحد على اتنين على مين على
+
+833
+01:28:24,800 --> 01:28:32,940
+اربعة يعني صارت ا one على اتنين في اربعةطب نجيب a6
+
+834
+01:28:32,940 --> 01:28:43,120
+a6 ل a4 زائد 2 يبقى سالب a4 على 4 زائد من زائد
+
+835
+01:28:43,120 --> 01:28:53,560
+واحد يبقى هنا سالب واحد على خمسة في a4 a4 ل a نود
+
+836
+01:28:53,560 --> 01:29:19,600
+a نود على من على واحد في تلاتةيبقى A7 يساوي
+
+837
+01:29:19,600 --> 01:29:31,040
+A5 زائد 2 يبقى A5 على 5 زائد 1يبقى هاي سالب واحد
+
+838
+01:29:31,040 --> 01:29:39,460
+على ستة اخمسة هيها فوق اللي هو ا one على اتنين في
+
+839
+01:29:39,460 --> 01:29:46,460
+اربع يعني سالب ا one على اتنين في اربع في ستة طيب
+
+840
+01:29:46,460 --> 01:29:51,780
+حد فيكم بتقدر تقولي قداش ا تمانية
+
+841
+01:29:55,220 --> 01:30:01,060
+بغض النظر على السنب اي نوت واحد تلاتة خمسة سبعة و
+
+842
+01:30:01,060 --> 01:30:07,400
+هكذا تمام اذا بدأ اجي اعوض في المعلومات هذه تبع دي
+
+843
+01:30:07,400 --> 01:30:13,960
+بس قبل اعوض في المعلومات لو جيت قولتك طيب اتنين ان
+
+844
+01:30:16,740 --> 01:30:24,940
+زوجين يساوي تعالى تطلعى ستة يبقى واحد تلاتة خمسة
+
+845
+01:30:24,940 --> 01:30:30,180
+اقل من الستة بمقدار واحد و هنا سالب ايه نوت تمام
+
+846
+01:30:30,180 --> 01:30:38,180
+اربع ايه اربع ايه نوت واحد في تلاتة لما تبقى اربع
+
+847
+01:30:38,180 --> 01:30:42,180
+تبقى واحد في تلاتة اقل منها و هنا بس هذه موجب و
+
+848
+01:30:42,180 --> 01:30:43,780
+هذه كمين سالب
+
+849
+01:31:05,570 --> 01:31:07,490
+أتنين اتنين اتنين اتنين اتنين اتنين اتنين اتنين
+
+850
+01:31:07,490 --> 01:31:07,530
+اتنين اتنين اتنين اتنين اتنين اتنين اتنين اتنين
+
+851
+01:31:07,530 --> 01:31:07,570
+اتنين اتنين اتنين اتنين اتنين اتنين اتنين اتنين
+
+852
+01:31:07,570 --> 01:31:08,670
+اتنين اتنين اتنين اتنين اتنين اتنين اتنين اتنين
+
+853
+01:31:08,670 --> 01:31:10,170
+اتنين اتنين اتنين اتنين اتنين اتنين اتنين اتنين
+
+854
+01:31:10,170 --> 01:31:13,090
+اتنين اتنين اتنين اتنين اتنين اتنين اتنين اتنينطلع
+
+855
+01:31:13,090 --> 01:31:17,750
+الستة صارت أقل منها بواحد اللي هو الخمسة يبقى
+
+856
+01:31:17,750 --> 01:31:24,530
+اتنين اين اتنين اين اقل منها مين بواحد طيب حد فيكم
+
+857
+01:31:24,530 --> 01:31:30,710
+تقدر تقولي قداش اتنين اين زائد واحد يعني ال term
+
+858
+01:31:30,710 --> 01:31:37,030
+اللي بيجي بعدهيجب ان نختار الفرديات 2n زائد 1 يعني
+
+859
+01:31:37,030 --> 01:31:43,550
+رقم فردي بقول السبعة اللي هو كمان سالب واحد to the
+
+860
+01:31:43,550 --> 01:31:50,590
+power n لل a one اتنين اربع ستة ونظل ماشيين هنا
+
+861
+01:31:50,590 --> 01:31:57,290
+سبعة اقل منه بمقدار واحد يبقى 2n زائد واحد اقل منه
+
+862
+01:31:57,290 --> 01:32:04,200
+بمقدار واحد يبقى 2nيبقى بضل ماشي لغاية اتنين ان بس
+
+863
+01:32:04,200 --> 01:32:08,160
+ضايل علينا واحد نشوف هل الإشارة هذه صحيحة اللي
+
+864
+01:32:08,160 --> 01:32:13,280
+كتبناها والله مايجرى إذا صحيحة بصمنا إذا مش صحيحة
+
+865
+01:32:13,280 --> 01:32:18,280
+بص بتقول ان زائد واحد او ان زائد واحد بتصير مالها
+
+866
+01:32:18,280 --> 01:32:24,760
+صحيحة بعدين بقولي كويس لو حطيت ان بواحد يبقى بصير
+
+867
+01:32:24,760 --> 01:32:32,190
+ايش اتنينن بواحد بصير سالب a نود و الواحدة كله
+
+868
+01:32:32,190 --> 01:32:36,370
+بطير و بضلش عندى الا مين الا واحد يبقى سالب a نود
+
+869
+01:32:36,370 --> 01:32:43,970
+هي صحيحة طب لو حطيت n باتنين بصير a أربعة سالب
+
+870
+01:32:43,970 --> 01:32:49,470
+واحد ترابيع يبقى بضل بس a نود على واحد في تلاتة
+
+871
+01:32:49,830 --> 01:32:56,690
+أربع ا نون واحد في تلاتة هي اربع طب اه ستة بنفس
+
+872
+01:32:56,690 --> 01:33:01,790
+الطريقة يبقى إشرتنا صحيحة و بالمثل هنا صحيحة تماما
+
+873
+01:33:01,790 --> 01:33:07,590
+ما عندنا مشكلة مدام جبت هذا الكلام إذا بقدر أشوف
+
+874
+01:33:07,590 --> 01:33:15,600
+شكل السيل ال solution أنا فارضه شو شكلهمسحناه مع
+
+875
+01:33:15,600 --> 01:33:23,020
+السلامة احنا فرضنا ان ال summation لل a n في x to
+
+876
+01:33:23,020 --> 01:33:31,530
+the power nيبقى عندنا ال solution y كان a node
+
+877
+01:33:31,530 --> 01:33:43,250
+زائد a1 x زائد a2 x تربية a3 x تكيب a4 x أربعة a5
+
+878
+01:33:43,250 --> 01:33:51,150
+x خمسة a6 x ستةعن طريق الوصول إلى الـ a7x7 زائد
+
+879
+01:33:51,150 --> 01:33:58,390
+زائد a n x to the power n زائد الاخرين يصمش من n
+
+880
+01:33:58,390 --> 01:34:03,530
+equal zero to infinity لل a n x to the power n مش
+
+881
+01:34:03,530 --> 01:34:08,570
+هيك كان شكله؟ طيب نيجي نعوض يبقى ايه ال solution y
+
+882
+01:34:08,570 --> 01:34:16,010
+سوى a0زائد a1 x خلّيتهم زي مهمة ليش؟ لأن كل الحلول
+
+883
+01:34:16,010 --> 01:34:24,110
+طلعت ب a node و a1 وصلنا لمين؟ لل a2 ال a2 بقدرش
+
+884
+01:34:24,110 --> 01:34:32,190
+عندنا؟ بناقص a node يبقى ناقص a node x تربيع وصلنا
+
+885
+01:34:32,190 --> 01:34:37,480
+لل a3الـ A3 هو ناقص A1 على 2
+
+886
+01:34:45,910 --> 01:34:50,930
+لأكس تكييبا ايه تلاتة يبقى هذه اكس تكييب لإن هاي
+
+887
+01:34:50,930 --> 01:34:55,130
+ال X تربية أخدناها يبقى خلاصة من مين من ال A3
+
+888
+01:34:55,130 --> 01:35:04,490
+بنيجي لل A4 يعني زائد A ناد على واحد في تلاتة يبقى
+
+889
+01:35:04,490 --> 01:35:13,250
+هذه A4 في ال X أُس 4 الآن اللي بعدها زائد وصلنا
+
+890
+01:35:13,250 --> 01:35:21,910
+مين ال A5الـ A5 هي فوق اللي هو A1 على 2 في 4 في
+
+891
+01:35:21,910 --> 01:35:30,250
+إكسوس خمسة تمام وصلنا لـ A6 A6 اللي هو الناقص A0
+
+892
+01:35:30,250 --> 01:35:40,330
+على 1 في 3في خمسة في من؟ في ال X أُس مقدّش هذه A
+
+893
+01:35:40,330 --> 01:35:47,170
+في ال X أُس ستة وصلنا لل A سبعة هي ال A سبعة اللي
+
+894
+01:35:47,170 --> 01:35:53,950
+هو ناقص A one على اتنين اربعة ستة في ال X أس سبعة
+
+895
+01:35:53,950 --> 01:36:02,070
+زائد A N بعرفهاش لكن أنا بعرف A تنين Nيبقى بقوله
+
+896
+01:36:02,070 --> 01:36:09,250
+زائب هذا بتظل ماشية وبعدين بقوله ال a2n اللي هي
+
+897
+01:36:09,250 --> 01:36:16,170
+مين اللي هو ناقص واحد to the power n a1 على اتنين
+
+898
+01:36:16,170 --> 01:36:24,470
+اربع ل a n اللي قبلها اللي قبلها يبقى a node a
+
+899
+01:36:24,470 --> 01:36:31,480
+node على واحد في تلاتة في خمسة واحدفى تلاتة فى
+
+900
+01:36:31,480 --> 01:36:38,460
+خمسة فى اتنين N ناقص واحد فى ال X أوسى اتنين N
+
+901
+01:36:42,370 --> 01:36:49,430
+اللي بعده زائد ناقص واحد to the power n لل a one
+
+902
+01:36:49,430 --> 01:36:59,430
+على اتنين اربعة ستة لل اتنين n زائد اكس اكس اتنين
+
+903
+01:36:59,430 --> 01:37:07,350
+n زائد واحد زائد الى ما شاء الله طيب بدنا نكتب
+
+904
+01:37:07,350 --> 01:37:09,090
+الجواب النهائي
+
+905
+01:37:20,350 --> 01:37:27,550
+الجواب النهائي Y تساوي اللي فيهم A نوت بدي أخدهم
+
+906
+01:37:27,550 --> 01:37:31,770
+مع بعض و اللي فيهم A1 بدي أخدهم مع بعض بس ال A نوت
+
+907
+01:37:31,770 --> 01:37:38,070
+بدي أخدها بره عامل مشترك يبقى هذه A نوت من الكل
+
+908
+01:37:38,070 --> 01:37:48,470
+وظل عندي واحد بعد هيك ناقص X تربيةنقص X تربية بعد
+
+909
+01:37:48,470 --> 01:37:56,890
+ذلك زائد X أس أربعة زائد X أس أربعة على واحد في
+
+910
+01:37:56,890 --> 01:38:02,050
+تلاتة هذه باعتبارها على جداش على واحد اللي بعدها
+
+911
+01:38:02,050 --> 01:38:11,630
+ناقص X أس ستة يبقى ناقص X أس ستة على واحد في تلاتة
+
+912
+01:38:11,630 --> 01:38:17,930
+في خمسةونبقى نمشي لغاية
+
+913
+01:38:17,930 --> 01:38:21,530
+سالب
+
+914
+01:38:21,530 --> 01:38:27,030
+واحد to the power N لمن X نقطة ناخدها عامل مشترك
+
+915
+01:38:27,030 --> 01:38:34,630
+لل X أسوا اتنين N على واحد في تلاتة في خمسة في
+
+916
+01:38:34,630 --> 01:38:42,530
+اتنين N ناقص واحد زائد إلى ما شاء اللهأخذ هذول
+
+917
+01:38:42,530 --> 01:38:49,550
+منهم زائد الباقي أخذ منهم a one عامل مشترك يبقى
+
+918
+01:38:49,550 --> 01:38:57,930
+ايش بطلع عندي؟ X وبعد ال X بجينا من ناقص X تكييب
+
+919
+01:38:57,930 --> 01:38:59,050
+على اتنين
+
+920
+01:39:03,900 --> 01:39:13,480
+واللي بعدها ناقص x تكييب على a2 بصير عندى زائد x
+
+921
+01:39:13,480 --> 01:39:17,940
+أس
+
+922
+01:39:17,940 --> 01:39:25,730
+خمسة ع اتنين في أربعوبعدها بيصير الناقص x أو
+
+923
+01:39:25,730 --> 01:39:32,890
+السبعة ناقص x أو السبعة على اتنين في اربعة في ستة
+
+924
+01:39:32,890 --> 01:39:39,410
+وزائد زائد ناقص واحد to the power n لل x أوس اتنين
+
+925
+01:39:39,410 --> 01:39:46,690
+n زائد واحد على اتنين اربعة ستة اتنين n زائد إلى
+
+926
+01:39:46,690 --> 01:39:52,780
+ما شاء اللهيعني يا بنات بقدر اكتب هذه على الشكل
+
+927
+01:39:52,780 --> 01:40:00,460
+التالي a node summation لشكل الحد النوني to the
+
+928
+01:40:00,460 --> 01:40:08,080
+power n لل X أُس اتنين N واحد تلاتة خمسة اتنين N
+
+929
+01:40:08,080 --> 01:40:17,420
+ناقص واحد من عند N تساوي Zero إلى Infinity يبقى
+
+930
+01:40:17,420 --> 01:40:25,230
+هنا زائداللي هو الحد النوني هذا هذا a1 summation
+
+931
+01:40:25,230 --> 01:40:32,030
+من n equal zero to infinity لمين لشكل الحد النوني
+
+932
+01:40:32,030 --> 01:40:40,670
+n x أس اتنين n زائد واحد اتنين اربع ستة لغاية
+
+933
+01:40:40,670 --> 01:40:47,930
+اتنين n بس تعالى نشوف شغل هذا صح ولا غلط تعالى
+
+934
+01:40:47,930 --> 01:40:55,580
+نشوف صح هذا ولا غلطالان لو قلت ان انت ساوي زيرو
+
+935
+01:40:55,580 --> 01:40:59,720
+اذا انت ساوي زيرو اذا انت ساوي زيرو اذا انت ساوي
+
+936
+01:40:59,720 --> 01:41:00,140
+زيرو
+
+937
+01:41:12,100 --> 01:41:18,260
+و اقول له a node زائد a node و اقول له من عند ال N
+
+938
+01:41:18,260 --> 01:41:23,080
+تساوي واحد اه هيك بيصير كلامي صحيح لو حطيت N بواحد
+
+939
+01:41:23,080 --> 01:41:27,320
+بيصير اتنين ناقص واحد اللي هو واحد الحد الأول حط
+
+940
+01:41:27,320 --> 01:41:32,980
+هنا واحد و هنا X أس تربية يبقى بيصير ناقص X تربية
+
+941
+01:41:32,980 --> 01:41:38,760
+هيو مظبوط تمام؟ و الواحدة ده في a node هيو طلعته
+
+942
+01:41:38,760 --> 01:41:43,230
+برا إذا ماعندي مشكلةفي هذه الحالة هذا بالنسبة
+
+943
+01:41:43,230 --> 01:41:48,450
+للterm الأول الterm التاني نفس القصة يبقى بالداج
+
+944
+01:41:48,450 --> 01:41:56,850
+أقول له من عند انت ساوي واحد وهذه a1x زائد a1 يعني
+
+945
+01:41:56,850 --> 01:42:02,870
+يا بنات خلت الحد الأول هذا كمان برة وبالتالي ما
+
+946
+01:42:02,870 --> 01:42:06,990
+عنده مشكلة في هذه الحالة بيصير شونه سليم مائة
+
+947
+01:42:06,990 --> 01:42:13,160
+بالمائةأو ان شئتنا فقلنا a node مقدار ثابت زائد a
+
+948
+01:42:13,160 --> 01:42:26,160
+node y1 زائد a1 x زائد a1 y2 او a node زائد a1 x
+
+949
+01:42:26,160 --> 01:42:36,180
+زائد a node y1 زائد a1 y2 هذا ال general solution
+
+950
+01:42:38,330 --> 01:42:42,450
+يعني يا بنات لو غطيت هدول، بصينا الصيغة اللي عندنا
+
+951
+01:42:42,450 --> 01:42:46,930
+هذه هي الصيغة اللي احنا عارفينها قبل هيك لما كنا
+
+952
+01:42:46,930 --> 01:42:53,350
+نحلب الطريقة العادية في chapter 3 حد يلاقي تساؤل
+
+953
+01:42:53,350 --> 01:42:58,830
+هنا، لسه لا يزال عندنا مثال أتقل من هذا كتير، هذا
+
+954
+01:42:58,830 --> 01:43:06,450
+كله حسابات مباشرة وسهلة، أيوة، ماشي، لحد هنا تمام؟
+
+955
+01:43:07,280 --> 01:43:13,100
+هذه زائد هذه يبقى هذا يعتبر الحل الأول وهذا يعتبر
+
+956
+01:43:13,100 --> 01:43:18,860
+الحل الثاني تمام؟ بدي أحاول أكتب كل واحد فيهم بس
+
+957
+01:43:18,860 --> 01:43:23,280
+على شكل summation ليس الا لو قلت a node في ال
+
+958
+01:43:23,280 --> 01:43:27,560
+summation الأول بالشكل هذا وخليته يبدأ من عند ال
+
+959
+01:43:27,560 --> 01:43:32,480
+zero بصير كلامي غلط ليش؟ لأن لو حطيت in ب zero
+
+960
+01:43:32,480 --> 01:43:37,200
+بطلع عندي هذا term جداشأنا ماعنديش سالب واحد، عندي
+
+961
+01:43:37,200 --> 01:43:41,880
+جديش، عندي واحد، إذا لا يمكن يصير الكلام هذا عندي
+
+962
+01:43:41,880 --> 01:43:47,560
+الصح، تمام؟ لكن لو كانت هذه اتنين N زائد واحد، مش
+
+963
+01:43:47,560 --> 01:43:52,160
+الكلام صحيح، بس نظرا لإتنين N نقص وعاد كلام مش
+
+964
+01:43:52,160 --> 01:43:57,910
+صحيح، إذا انطلعت الحد الأول اللي هو Nخلته على
+
+965
+01:43:57,910 --> 01:44:03,070
+الشجة و هذا خلته على الشجة و الباقى خدت منه a نود
+
+966
+01:44:03,070 --> 01:44:07,530
+عامل مشترك و خدت a one عامل مشترك فطلع ال series
+
+967
+01:44:07,530 --> 01:44:11,570
+اللى عندنا هذه و ال series اللى عندنا هذه يبقى هذا
+
+968
+01:44:11,570 --> 01:44:16,390
+الشكل ال general solution لمين للمعادلة التفاضلية
+
+969
+01:44:16,390 --> 01:44:21,010
+هذا يا مناطش شوفي إذا جبت ال recurrence relation
+
+970
+01:44:21,010 --> 01:44:26,440
+هذه الصحيحة بصير الباقى كله تعويض عاديمافيش فيه اي
+
+971
+01:44:26,440 --> 01:44:32,920
+صعوبة لكن اذا جبتيها غلط ضيعتي سؤالك لذلك كل
+
+972
+01:44:32,920 --> 01:44:37,500
+امتحانها بنجيب فيه سؤال على هذا ال section كل
+
+973
+01:44:37,500 --> 01:44:42,740
+امتحانها اي ورقة امتحان نهائي بتلاقي فيها سؤال على
+
+974
+01:44:42,740 --> 01:44:47,580
+هذا ال section لسه ابدا اعطيك مثال المرة القادمة
+
+975
+01:44:47,580 --> 01:44:49,940
+ان شاء الله حد فيكوا لايه تساؤل هنا؟
+
diff --git a/PL9fwy3NUQKwa8ZDfSFGn6H8xVFLzqmCZC/6jXOnqsn_jg_raw.json b/PL9fwy3NUQKwa8ZDfSFGn6H8xVFLzqmCZC/6jXOnqsn_jg_raw.json
new file mode 100644
index 0000000000000000000000000000000000000000..aa3fe4b3691f1d28ea79196feb52f64c627620d3
--- /dev/null
+++ b/PL9fwy3NUQKwa8ZDfSFGn6H8xVFLzqmCZC/6jXOnqsn_jg_raw.json
@@ -0,0 +1 @@
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"probability": 0.9559326171875}, {"start": 66.84, "end": 67.36, "word": " n", "probability": 0.68603515625}, {"start": 67.36, "end": 68.38, "word": " عند", "probability": 0.9716796875}, {"start": 68.38, "end": 69.42, "word": " النقطة", "probability": 0.97509765625}, {"start": 69.42, "end": 69.82, "word": " a", "probability": 0.75048828125}, {"start": 69.82, "end": 70.32, "word": " أو", "probability": 0.60400390625}, {"start": 70.32, "end": 70.64, "word": " عند", "probability": 0.98193359375}, {"start": 70.64, "end": 71.54, "word": " النقطة", "probability": 0.9788411458333334}, {"start": 71.54, "end": 72.06, "word": " x", "probability": 0.904296875}, {"start": 72.06, "end": 72.88, "word": " node", "probability": 0.89599609375}, {"start": 72.88, "end": 73.98, "word": " لمين", "probability": 0.848388671875}, {"start": 73.98, "end": 74.52, "word": " لل", "probability": 0.80322265625}, {"start": 74.52, "end": 75.08, "word": " x", "probability": 0.4892578125}, {"start": 75.08, "end": 75.84, "word": " ناقص", "probability": 0.96533203125}, {"start": 75.84, "end": 76.08, "word": " ال", "probability": 0.85498046875}, {"start": 76.08, "end": 76.46, "word": " x", "probability": 0.81982421875}, {"start": 76.46, "end": 76.94, "word": " node", "probability": 0.9384765625}, {"start": 76.94, "end": 77.22, "word": " to", "probability": 0.95654296875}, {"start": 77.22, "end": 77.48, "word": " the", "probability": 0.8974609375}, {"start": 77.48, "end": 78.06, "word": " power", "probability": 0.8759765625}, {"start": 78.06, "end": 78.62, "word": " n", "probability": 0.90966796875}, {"start": 78.62, "end": 79.58, "word": " على", "probability": 0.72802734375}, {"start": 79.58, "end": 80.2, "word": " n", "probability": 0.90478515625}, {"start": 80.2, "end": 81.26, "word": " factorial", "probability": 0.6962890625}], "temperature": 1.0}, {"id": 5, "seek": 11154, "start": 83.26, "end": 111.54, "text": "على N factorial بالشكل اللي عندنا هذا او بقدر احطها بالشكل المفكوك الطويل هي عبارة عن اللي هو ال F of X node زائد ال F prime of X node في ال X ناقص ال X node على واحد factorial زائد المشتقة الثانية عند ال X node", "tokens": [3615, 23942, 426, 36916, 20666, 8592, 28820, 13672, 1829, 43242, 8315, 23758, 1975, 2407, 4724, 28543, 2288, 1975, 5016, 9566, 11296, 20666, 8592, 28820, 9673, 5172, 4117, 2407, 4117, 41950, 2407, 26895, 39896, 6225, 3555, 9640, 3660, 18871, 13672, 1829, 31439, 2423, 479, 295, 1783, 9984, 30767, 16373, 3215, 2423, 479, 5835, 295, 1783, 9984, 8978, 2423, 1783, 8717, 995, 4587, 9381, 2423, 1783, 9984, 15844, 36764, 24401, 36916, 30767, 16373, 3215, 9673, 8592, 2655, 28671, 6024, 104, 7649, 10632, 43242, 2423, 1783, 9984], "avg_logprob": -0.1636948543436387, "compression_ratio": 1.766304347826087, "no_speech_prob": 4.172325134277344e-07, "words": [{"start": 83.26, "end": 83.84, "word": "على", "probability": 0.654052734375}, {"start": 83.84, "end": 84.26, "word": " N", "probability": 0.178466796875}, {"start": 84.26, "end": 85.24, "word": " factorial", 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{"start": 93.64, "end": 94.64, "word": " عن", "probability": 0.99267578125}, {"start": 94.64, "end": 95.14, "word": " اللي", "probability": 0.766357421875}, {"start": 95.14, "end": 95.4, "word": " هو", "probability": 0.97265625}, {"start": 95.4, "end": 95.7, "word": " ال", "probability": 0.477294921875}, {"start": 95.7, "end": 96.22, "word": " F", "probability": 0.7890625}, {"start": 96.22, "end": 96.76, "word": " of", "probability": 0.8828125}, {"start": 96.76, "end": 97.32, "word": " X", "probability": 0.9453125}, {"start": 97.32, "end": 97.86, "word": " node", "probability": 0.85107421875}, {"start": 97.86, "end": 98.88, "word": " زائد", "probability": 0.861328125}, {"start": 98.88, "end": 99.16, "word": " ال", "probability": 0.59521484375}, {"start": 99.16, "end": 99.56, "word": " F", "probability": 0.96337890625}, {"start": 99.56, "end": 100.4, "word": " prime", "probability": 0.7578125}, {"start": 100.4, "end": 100.88, "word": " of", "probability": 0.962890625}, {"start": 100.88, "end": 101.26, "word": " X", "probability": 0.99365234375}, {"start": 101.26, "end": 101.78, "word": " node", "probability": 0.93408203125}, {"start": 101.78, "end": 102.34, "word": " في", "probability": 0.7900390625}, {"start": 102.34, "end": 102.62, "word": " ال", "probability": 0.6474609375}, {"start": 102.62, "end": 103.0, "word": " X", "probability": 0.94580078125}, {"start": 103.0, "end": 103.72, "word": " ناقص", "probability": 0.9071044921875}, {"start": 103.72, "end": 103.94, "word": " ال", "probability": 0.837890625}, {"start": 103.94, "end": 104.28, "word": " X", "probability": 0.98193359375}, {"start": 104.28, "end": 104.72, "word": " node", "probability": 0.9560546875}, {"start": 104.72, "end": 105.04, "word": " على", "probability": 0.775390625}, {"start": 105.04, "end": 105.52, "word": " واحد", "probability": 0.811767578125}, {"start": 105.52, "end": 106.32, "word": " factorial", "probability": 0.6875}, {"start": 106.32, "end": 107.94, "word": " زائد", "probability": 0.9578450520833334}, {"start": 107.94, "end": 109.24, "word": " المشتقة", "probability": 0.919677734375}, {"start": 109.24, "end": 110.0, "word": " الثانية", "probability": 0.940673828125}, {"start": 110.0, "end": 110.42, "word": " عند", "probability": 0.978515625}, {"start": 110.42, "end": 110.66, "word": " ال", "probability": 0.78759765625}, {"start": 110.66, "end": 111.06, "word": " X", "probability": 0.98291015625}, {"start": 111.06, "end": 111.54, "word": " node", "probability": 0.927734375}], "temperature": 1.0}, {"id": 6, "seek": 13166, "start": 112.58, "end": 131.66, "text": "نقص ال X node لكل تربية على 2 factorial زائد زائد و نظل ماشي لغاية ما نوصل لتفاضل رقم N لل X node في ال X نقص ال X node to the power N على N factorial زائد إلى آخرين", "tokens": [1863, 4587, 9381, 2423, 1783, 9984, 5296, 28820, 6055, 25513, 10632, 15844, 568, 36916, 30767, 16373, 3215, 30767, 16373, 3215, 4032, 8717, 19913, 1211, 3714, 33599, 1829, 5296, 17082, 995, 10632, 19446, 8717, 2407, 36520, 5296, 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" factorial", "probability": 0.5634765625}, {"start": 117.12, "end": 118.34, "word": " زائد", "probability": 0.6272786458333334}, {"start": 118.34, "end": 118.82, "word": " زائد", "probability": 0.9454752604166666}, {"start": 118.82, "end": 118.92, "word": " و", "probability": 0.81787109375}, {"start": 118.92, "end": 119.28, "word": " نظل", "probability": 0.5521647135416666}, {"start": 119.28, "end": 119.68, "word": " ماشي", "probability": 0.7981770833333334}, {"start": 119.68, "end": 120.08, "word": " لغاية", "probability": 0.81640625}, {"start": 120.08, "end": 120.24, "word": " ما", "probability": 0.91943359375}, {"start": 120.24, "end": 120.62, "word": " نوصل", "probability": 0.9775390625}, {"start": 120.62, "end": 121.52, "word": " لتفاضل", "probability": 0.8064453125}, {"start": 121.52, "end": 122.46, "word": " رقم", "probability": 0.9822591145833334}, {"start": 122.46, "end": 122.8, "word": " N", "probability": 0.474365234375}, {"start": 122.8, "end": 123.52, "word": " لل", "probability": 0.66064453125}, {"start": 123.52, "end": 124.02, "word": " X", "probability": 0.91650390625}, {"start": 124.02, "end": 124.5, "word": " node", "probability": 0.970703125}, {"start": 124.5, "end": 124.7, "word": " في", "probability": 0.60009765625}, {"start": 124.7, "end": 124.9, "word": " ال", "probability": 0.427490234375}, {"start": 124.9, "end": 125.24, "word": " X", "probability": 0.96630859375}, {"start": 125.24, "end": 125.82, "word": " نقص", "probability": 0.9482421875}, {"start": 125.82, "end": 125.98, "word": " ال", "probability": 0.7158203125}, {"start": 125.98, "end": 126.26, "word": " X", "probability": 0.98974609375}, {"start": 126.26, "end": 126.64, "word": " node", "probability": 0.9541015625}, {"start": 126.64, "end": 126.86, "word": " to", "probability": 0.93701171875}, {"start": 126.86, "end": 127.08, "word": " the", "probability": 0.896484375}, {"start": 127.08, "end": 127.48, "word": " power", "probability": 0.87158203125}, {"start": 127.48, "end": 127.88, "word": " N", "probability": 0.7568359375}, {"start": 127.88, "end": 128.26, "word": " على", "probability": 0.7939453125}, {"start": 128.26, "end": 128.68, "word": " N", "probability": 0.89794921875}, {"start": 128.68, "end": 129.5, "word": " factorial", "probability": 0.87060546875}, {"start": 129.5, "end": 130.54, "word": " زائد", "probability": 0.9361979166666666}, {"start": 130.54, "end": 130.84, "word": " إلى", "probability": 0.83544921875}, {"start": 130.84, "end": 131.66, "word": " آخرين", "probability": 0.9724934895833334}], "temperature": 1.0}, {"id": 7, "seek": 16122, "start": 132.57, "end": 161.23, "text": "هذا مين اللي هو تايلور سيريز اللي قال لو كانت اكس نود يساوي زيرو بنحصل على مين على مكلورين سيريز يبقى باجي بقوله هنا اف ال اكس نود تساوي زيرو we get the McLaurin series and", "tokens": [3224, 15730, 3714, 9957, 13672, 1829, 31439, 6055, 995, 26895, 13063, 8608, 13546, 1829, 11622, 13672, 1829, 50239, 45164, 25961, 2655, 1975, 4117, 3794, 8717, 23328, 7251, 3794, 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"probability": 0.706298828125}, {"start": 136.95, "end": 137.13, "word": " قال", "probability": 0.9775390625}, {"start": 137.13, "end": 137.39, "word": " لو", "probability": 0.9169921875}, {"start": 137.39, "end": 137.89, "word": " كانت", "probability": 0.855224609375}, {"start": 137.89, "end": 138.25, "word": " اكس", "probability": 0.6764729817708334}, {"start": 138.25, "end": 138.49, "word": " نود", "probability": 0.783935546875}, {"start": 138.49, "end": 139.35, "word": " يساوي", "probability": 0.9090576171875}, {"start": 139.35, "end": 139.77, "word": " زيرو", "probability": 0.7327473958333334}, {"start": 139.77, "end": 140.29, "word": " بنحصل", "probability": 0.9542643229166666}, {"start": 140.29, "end": 140.53, "word": " على", "probability": 0.79052734375}, {"start": 140.53, "end": 140.95, "word": " مين", "probability": 0.942138671875}, {"start": 140.95, "end": 141.71, "word": " على", "probability": 0.681640625}, {"start": 141.71, "end": 142.59, "word": " مكلورين", "probability": 0.713134765625}, {"start": 142.59, "end": 143.33, "word": " سيريز", "probability": 0.9683837890625}, {"start": 143.33, "end": 144.13, "word": " يبقى", "probability": 0.9442138671875}, {"start": 144.13, "end": 144.51, "word": " باجي", "probability": 0.8484700520833334}, {"start": 144.51, "end": 145.19, "word": " بقوله", "probability": 0.8551432291666666}, {"start": 145.19, "end": 145.65, "word": " هنا", "probability": 0.96240234375}, {"start": 145.65, "end": 146.41, "word": " اف", "probability": 0.6202392578125}, {"start": 146.41, "end": 147.35, "word": " ال", "probability": 0.90380859375}, {"start": 147.35, "end": 147.89, "word": " اكس", "probability": 0.721923828125}, {"start": 147.89, "end": 148.19, "word": " نود", "probability": 0.92529296875}, {"start": 148.19, "end": 148.93, "word": " تساوي", "probability": 0.9730224609375}, {"start": 148.93, "end": 149.59, "word": " زيرو", "probability": 0.9541015625}, {"start": 149.59, "end": 150.37, "word": " we", "probability": 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393.41, "end": 393.41, "word": " او", "probability": 0.898193359375}, {"start": 393.41, "end": 393.41, "word": " او", "probability": 0.939453125}, {"start": 393.41, "end": 393.41, "word": " او", "probability": 0.957763671875}, {"start": 393.41, "end": 393.43, "word": " او", "probability": 0.966064453125}, {"start": 393.43, "end": 393.43, "word": " او", "probability": 0.97021484375}], "temperature": 1.0}, {"id": 18, "seek": 43849, "start": 418.91, "end": 438.49, "text": "إذا كنا نستطيع أن نكتبها على شكل power series فهي F of X بدي أكتبها على شكل summation من N equal zero to infinity لتفاضل رقم N", "tokens": [28814, 15730, 9122, 8315, 8717, 14851, 9566, 40228, 14739, 8717, 4117, 2655, 3555, 11296, 15844, 13412, 28820, 1347, 2638, 6156, 3224, 1829, 479, 295, 1783, 4724, 16254, 5551, 4117, 2655, 3555, 11296, 15844, 13412, 28820, 28811, 9154, 426, 2681, 4018, 281, 13202, 5296, 2655, 5172, 46958, 1211, 12602, 4587, 2304, 426], "avg_logprob": -0.44561299165854085, "compression_ratio": 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of", "probability": 0.3779296875}, {"start": 428.59, "end": 429.17, "word": " X", "probability": 0.955078125}, {"start": 429.17, "end": 429.99, "word": " بدي", "probability": 0.25848388671875}, {"start": 429.99, "end": 430.51, "word": " أكتبها", "probability": 0.884765625}, {"start": 430.51, "end": 430.73, "word": " على", "probability": 0.9375}, {"start": 430.73, "end": 431.19, "word": " شكل", "probability": 0.968017578125}, {"start": 431.19, "end": 432.05, "word": " summation", "probability": 0.7705078125}, {"start": 432.05, "end": 433.03, "word": " من", "probability": 0.8994140625}, {"start": 433.03, "end": 433.39, "word": " N", "probability": 0.40576171875}, {"start": 433.39, "end": 433.81, "word": " equal", "probability": 0.2138671875}, {"start": 433.81, "end": 434.25, "word": " zero", "probability": 0.4130859375}, {"start": 434.25, "end": 434.59, "word": " to", "probability": 0.939453125}, {"start": 434.59, "end": 435.49, "word": " infinity", "probability": 0.81201171875}, {"start": 435.49, "end": 437.19, "word": " لتفاضل", "probability": 0.87861328125}, {"start": 437.19, "end": 438.05, "word": " رقم", "probability": 0.9806315104166666}, {"start": 438.05, "end": 438.49, "word": " N", "probability": 0.8349609375}], "temperature": 1.0}, {"id": 19, "seek": 46768, "start": 439.0, "end": 467.68, "text": "للأند الـ x node للـ x ناقص الـ x node to the power n على n factorial with radius of convergence with radius of convergence", "tokens": [1211, 1211, 10721, 41260, 2423, 39184, 2031, 9984, 24976, 39184, 2031, 8717, 995, 4587, 9381, 2423, 39184, 2031, 9984, 281, 264, 1347, 297, 15844, 297, 36916, 365, 15845, 295, 32181, 365, 15845, 295, 32181], "avg_logprob": -0.40580357483455115, "compression_ratio": 1.3846153846153846, "no_speech_prob": 0.0, "words": [{"start": 439.0, "end": 439.98, "word": "للأند", "probability": 0.295318603515625}, {"start": 439.98, "end": 440.32, "word": " الـ", "probability": 0.5338134765625}, {"start": 440.32, "end": 440.54, "word": " 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"end": 446.94, "word": " n", "probability": 0.77099609375}, {"start": 446.94, "end": 448.32, "word": " factorial", "probability": 0.68359375}, {"start": 448.32, "end": 450.5, "word": " with", "probability": 0.78857421875}, {"start": 450.5, "end": 451.0, "word": " radius", "probability": 0.88330078125}, {"start": 451.0, "end": 451.26, "word": " of", "probability": 0.96826171875}, {"start": 451.26, "end": 452.38, "word": " convergence", "probability": 0.95751953125}, {"start": 452.38, "end": 453.6, "word": " with", "probability": 0.63134765625}, {"start": 453.6, "end": 455.98, "word": " radius", "probability": 0.86767578125}, {"start": 455.98, "end": 464.24, "word": " of", "probability": 0.92138671875}, {"start": 464.24, "end": 467.68, "word": " convergence", "probability": 0.9296875}], "temperature": 1.0}, {"id": 20, "seek": 47997, "start": 469.41, "end": 479.97, "text": "اللي هو راه راه greater than zero", "tokens": [6027, 20292, 31439, 12602, 40294, 12602, 40294, 5044, 813, 4018], "avg_logprob": -0.48721589825370093, "compression_ratio": 0.9782608695652174, "no_speech_prob": 0.0, "words": [{"start": 469.41, "end": 469.89, "word": "اللي", "probability": 0.5050048828125}, {"start": 469.89, "end": 470.45, "word": " هو", "probability": 0.9755859375}, {"start": 470.45, "end": 472.59, "word": " راه", "probability": 0.528564453125}, {"start": 472.59, "end": 475.47, "word": " راه", "probability": 0.628173828125}, {"start": 475.47, "end": 477.89, "word": " greater", "probability": 0.54736328125}, {"start": 477.89, "end": 478.97, "word": " than", "probability": 0.92041015625}, {"start": 478.97, "end": 479.97, "word": " zero", "probability": 0.64599609375}], "temperature": 1.0}, {"id": 21, "seek": 51911, "start": 492.85, "end": 519.11, "text": "تعريف هذا جديد ماشوفنهوش في calculus بي على الأطلاع وإنما لزمناه هنا في المعادلات التفاضليه التعريف بيقول مياتي الدالة if بقدر اقول عنها analytic function يعني دالة تحليلية at a point عند نقطة x ساوي x node if it can be written as a power series", "tokens": [2655, 3615, 16572, 5172, 23758, 10874, 16254, 3215, 19446, 8592, 38688, 1863, 3224, 2407, 8592, 8978, 33400, 4724, 1829, 15844, 16247, 9566, 15040, 3615, 4032, 28814, 1863, 15042, 5296, 11622, 2304, 8315, 3224, 34105, 8978, 9673, 3615, 18513, 1211, 9307, 16712, 5172, 46958, 20292, 3224, 16712, 3615, 16572, 5172, 4724, 1829, 39648, 3714, 25528, 31371, 32748, 6027, 3660, 498, 4724, 28543, 2288, 1975, 39648, 18871, 11296, 40358, 2445, 37495, 22653, 11778, 6027, 3660, 6055, 5016, 20292, 1211, 10632, 412, 257, 935, 43242, 8717, 47432, 3660, 2031, 8608, 995, 45865, 2031, 9984, 498, 309, 393, 312, 3720, 382, 257, 1347, 2638], "avg_logprob": -0.2172029697068847, "compression_ratio": 1.524390243902439, "no_speech_prob": 0.0, "words": [{"start": 492.85, "end": 493.35, "word": "تعريف", "probability": 0.797119140625}, {"start": 493.35, "end": 493.57, "word": " هذا", "probability": 0.84375}, {"start": 493.57, "end": 494.07, "word": " جديد", "probability": 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0.9700520833333334}, {"start": 510.41, "end": 511.65, "word": " تحليلية", "probability": 0.93349609375}, {"start": 511.65, "end": 512.39, "word": " at", "probability": 0.94189453125}, {"start": 512.39, "end": 512.79, "word": " a", "probability": 0.9326171875}, {"start": 512.79, "end": 513.19, "word": " point", "probability": 0.9912109375}, {"start": 513.19, "end": 513.49, "word": " عند", "probability": 0.9736328125}, {"start": 513.49, "end": 513.99, "word": " نقطة", "probability": 0.9191080729166666}, {"start": 513.99, "end": 514.19, "word": " x", "probability": 0.59375}, {"start": 514.19, "end": 514.71, "word": " ساوي", "probability": 0.5847981770833334}, {"start": 514.71, "end": 514.97, "word": " x", "probability": 0.900390625}, {"start": 514.97, "end": 515.31, "word": " node", "probability": 0.499267578125}, {"start": 515.31, "end": 515.93, "word": " if", "probability": 0.95361328125}, {"start": 515.93, "end": 516.21, "word": " it", "probability": 0.9755859375}, {"start": 516.21, "end": 516.51, "word": " can", "probability": 0.95654296875}, {"start": 516.51, "end": 516.75, "word": " be", "probability": 0.9453125}, {"start": 516.75, "end": 517.13, "word": " written", "probability": 0.9267578125}, {"start": 517.13, "end": 517.55, "word": " as", "probability": 0.97412109375}, {"start": 517.55, "end": 518.01, "word": " a", "probability": 0.96240234375}, {"start": 518.01, "end": 518.39, "word": " power", "probability": 0.88427734375}, {"start": 518.39, "end": 519.11, "word": " series", "probability": 0.88671875}], "temperature": 1.0}, {"id": 22, "seek": 53095, "start": 519.43, "end": 530.95, "text": "إذا جئت تكتب على شكل power series that is f of x بدي ساوي summation من n equal zero to infinity لتفاضل رقم n عند ال x node", "tokens": [28814, 15730, 10874, 19986, 2655, 6055, 4117, 2655, 3555, 15844, 13412, 28820, 1347, 2638, 300, 307, 283, 295, 2031, 4724, 16254, 8608, 995, 45865, 28811, 9154, 297, 2681, 4018, 281, 13202, 5296, 2655, 5172, 46958, 1211, 12602, 4587, 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773.44, "text": "in particular كحالة خاصة if summation من n equal zero to infinity لل a n لل x نقص ال x not to the power n بده يسوى zero for each x لكل x then", "tokens": [259, 1729, 9122, 5016, 6027, 3660, 16490, 33546, 3660, 498, 28811, 9154, 297, 2681, 4018, 281, 13202, 24976, 257, 297, 24976, 2031, 8717, 4587, 9381, 2423, 2031, 406, 281, 264, 1347, 297, 47525, 3224, 7251, 3794, 2407, 7578, 4018, 337, 1184, 2031, 5296, 28820, 2031, 550], "avg_logprob": -0.3570478710722416, "compression_ratio": 1.2214285714285715, "no_speech_prob": 0.0, "words": [{"start": 744.98, "end": 745.44, "word": "in", "probability": 0.1639404296875}, {"start": 745.44, "end": 746.32, "word": " particular", "probability": 0.904296875}, {"start": 746.32, "end": 747.52, "word": " كحالة", "probability": 0.83856201171875}, {"start": 747.52, "end": 748.66, "word": " خاصة", "probability": 0.9697265625}, {"start": 748.66, "end": 753.16, "word": " if", "probability": 0.53515625}, {"start": 753.16, "end": 755.36, 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" جداش", "probability": 0.7262369791666666}, {"start": 793.82, "end": 794.68, "word": " اللي", "probability": 0.90283203125}, {"start": 794.68, "end": 795.18, "word": " هو", "probability": 0.98583984375}, {"start": 795.18, "end": 795.9, "word": " zero", "probability": 0.78564453125}], "temperature": 1.0}, {"id": 35, "seek": 82004, "start": 799.56, "end": 820.04, "text": "بنرجع للـ remark هذه مرة ثانية و صح اسمها معايا كويسة انها very important في الحسابات الآن و كذلك لل section القادر بيقول لو كان summation من n equals zero to infinity لل a n في ال X ناقص ال X node to the power n", "tokens": [3555, 1863, 47341, 3615, 24976, 39184, 7942, 29538, 3714, 25720, 38637, 7649, 10632, 4032, 20328, 5016, 24525, 2304, 11296, 20449, 995, 25528, 9122, 45865, 3794, 3660, 16472, 11296, 588, 1021, 8978, 21542, 3794, 16758, 9307, 6024, 48506, 4032, 9122, 8848, 23275, 24976, 3541, 25062, 18513, 2288, 4724, 1829, 39648, 45164, 25961, 28811, 9154, 297, 6915, 4018, 281, 13202, 24976, 257, 297, 8978, 2423, 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هنا ممكن أغيره زي ما بدي دون أن أغير في قيمة ال summation خدناها في calculus B", "tokens": [2304, 11242, 47302, 4587, 9122, 2304, 7649, 8717, 47432, 3660, 5296, 31377, 2304, 7649, 3660, 9154, 29538, 2423, 3541, 13672, 1829, 31439, 11331, 26108, 3660, 8717, 38251, 1829, 11296, 5513, 295, 8186, 5296, 15042, 5551, 4117, 2655, 3555, 2423, 28811, 4724, 16254, 5551, 17082, 13546, 32748, 20292, 1211, 13672, 1829, 6055, 33753, 2423, 28811, 34105, 3714, 43020, 5551, 17082, 13546, 3224, 30767, 1829, 19446, 4724, 16254, 11778, 11536, 14739, 5551, 17082, 13546, 8978, 12174, 32640, 3660, 2423, 28811, 16490, 3215, 8315, 11296, 8978, 33400, 363], "avg_logprob": -0.21348110205212303, "compression_ratio": 1.6567164179104477, "no_speech_prob": 0.0, "words": [{"start": 957.59, "end": 958.13, "word": "مضايق", "probability": 0.4227142333984375}, {"start": 958.13, "end": 958.55, "word": " كمان", "probability": 0.8287760416666666}, {"start": 958.55, "end": 958.93, "word": " نقطة", "probability": 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{"start": 969.77, "end": 970.65, "word": " ممكن", "probability": 0.968017578125}, {"start": 970.65, "end": 971.55, "word": " أغيره", "probability": 0.97216796875}, {"start": 971.55, "end": 971.95, "word": " زي", "probability": 0.937255859375}, {"start": 971.95, "end": 972.17, "word": " ما", "probability": 0.94189453125}, {"start": 972.17, "end": 972.61, "word": " بدي", "probability": 0.758544921875}, {"start": 972.61, "end": 973.37, "word": " دون", "probability": 0.96044921875}, {"start": 973.37, "end": 973.73, "word": " أن", "probability": 0.81640625}, {"start": 973.73, "end": 974.53, "word": " أغير", "probability": 0.9586588541666666}, {"start": 974.53, "end": 974.93, "word": " في", "probability": 0.93359375}, {"start": 974.93, "end": 975.69, "word": " قيمة", "probability": 0.9967447916666666}, {"start": 975.69, "end": 976.07, "word": " ال", "probability": 0.9140625}, {"start": 976.07, "end": 976.77, "word": " summation", "probability": 0.96630859375}, {"start": 976.77, "end": 977.77, "word": " خدناها", "probability": 0.9263916015625}, {"start": 977.77, "end": 978.03, "word": " في", "probability": 0.93798828125}, {"start": 978.03, "end": 978.51, "word": " calculus", "probability": 0.8857421875}, {"start": 978.51, "end": 979.21, "word": " B", "probability": 0.37255859375}], "temperature": 1.0}, {"id": 43, "seek": 100395, "start": 979.51, "end": 1003.95, "text": "في section تلاتة من calculus B يبقى بدنا نعيدها هنا نظرا لأهميتها أثناء الحسابات يبقى نحط عنوان صغير حاجة اسمه shift of index of summation of index of summation", "tokens": [41185, 3541, 6055, 1211, 9307, 3660, 9154, 33400, 363, 7251, 3555, 4587, 7578, 47525, 8315, 8717, 3615, 25708, 11296, 34105, 8717, 19913, 23557, 5296, 10721, 16095, 36081, 11296, 5551, 12984, 1863, 16606, 21542, 3794, 16758, 9307, 7251, 3555, 4587, 7578, 8717, 5016, 9566, 18871, 2407, 7649, 20328, 17082, 13546, 11331, 26108, 3660, 24525, 2304, 3224, 5513, 295, 8186, 295, 28811, 295, 8186, 295, 28811], "avg_logprob": 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اتنين اللي هو بستة ا واحد زي اتنين يبقى a تلاتة x يبقى هاي ستة a تلاتة x و هكذا بالنسبة للباقي يبقى غيرنا ال index تبع ال summation لكن المعلومات بقيت كما هي إذا يا بنات لو غيرت ال index تبع ال summation لا يتغير", "tokens": [3555, 22488, 2423, 39184, 4018, 4724, 1829, 7435, 1829, 8717, 2304, 9957, 36764, 24401, 7251, 3555, 4587, 7578, 36764, 24401, 4032, 1975, 2655, 1863, 9957, 6055, 1211, 9307, 3660, 8978, 1975, 2655, 1863, 9957, 13672, 1829, 31439, 4724, 14851, 3660, 1975, 36764, 24401, 30767, 1829, 1975, 2655, 1863, 9957, 7251, 3555, 4587, 7578, 257, 6055, 1211, 9307, 3660, 2031, 7251, 3555, 4587, 7578, 8032, 47302, 8608, 2655, 3660, 257, 6055, 1211, 9307, 3660, 2031, 4032, 8032, 4117, 15730, 20666, 1863, 35457, 3660, 24976, 3555, 995, 38436, 7251, 3555, 4587, 7578, 32771, 13546, 8315, 2423, 8186, 6055, 3555, 3615, 2423, 28811, 44381, 9673, 30241, 20498, 9307, 4724, 4587, 36081, 9122, 15042, 39896, 11933, 15730, 35186, 4724, 8315, 2655, 45164, 32771, 13546, 2655, 2423, 8186, 6055, 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بالمتسلسل بالمتسلسل بالمتسلسل بالمتسلسل بالمتسلسل بالمتسلسل بالمتسلسل", "tokens": [3555, 45340, 2655, 3794, 1211, 3794, 1211, 20666, 2304, 2655, 3794, 1211, 3794, 1211, 20666, 2304, 2655, 3794, 1211, 3794, 1211, 20666, 2304, 2655, 3794, 1211, 3794, 1211, 20666, 2304, 2655, 3794, 1211, 3794, 1211, 20666, 2304, 2655, 3794, 1211, 3794, 1211, 20666, 2304, 2655, 3794, 1211, 3794, 1211, 20666, 2304, 2655, 3794, 1211, 3794, 1211, 20666, 2304, 2655, 3794, 1211, 3794, 1211, 20666, 2304, 2655, 3794, 1211, 3794, 1211, 20666, 2304, 2655, 3794, 1211, 3794, 1211, 20666, 2304, 2655, 3794, 1211, 3794, 1211, 20666, 2304, 2655, 3794, 1211, 3794, 1211, 20666, 2304, 2655, 3794, 1211, 3794, 1211, 20666, 2304, 2655, 3794, 1211, 3794, 1211, 20666, 2304, 2655, 3794, 1211, 3794, 1211, 20666, 2304, 2655, 3794, 1211, 3794, 1211, 20666, 2304, 2655, 3794, 1211, 3794, 1211, 20666, 2304, 2655, 3794, 1211, 3794, 1211, 20666, 2304, 2655, 3794, 1211, 3794, 1211, 20666, 2304, 2655, 3794, 1211, 3794, 1211, 20666, 2304, 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series", "probability": 0.90087890625}, {"start": 2566.2, "end": 2566.94, "word": " section", "probability": 0.654296875}, {"start": 2566.94, "end": 2568.2, "word": " قسمناها", "probability": 0.69561767578125}, {"start": 2568.2, "end": 2568.44, "word": " إلى", "probability": 0.896484375}, {"start": 2568.44, "end": 2569.36, "word": " جزئين", "probability": 0.892578125}, {"start": 2569.36, "end": 2570.4, "word": " تمام", "probability": 0.707763671875}, {"start": 2570.4, "end": 2571.28, "word": " الجزء", "probability": 0.9036458333333334}, {"start": 2571.28, "end": 2571.82, "word": " الأول", "probability": 0.959716796875}, {"start": 2571.82, "end": 2572.48, "word": " بقينا", "probability": 0.6036376953125}, {"start": 2572.48, "end": 2572.86, "word": " ناخد", "probability": 0.9552408854166666}, {"start": 2572.86, "end": 2572.96, "word": " ال", "probability": 0.94677734375}, {"start": 2572.96, "end": 2573.48, "word": " function", "probability": 0.92529296875}, {"start": 2573.48, "end": 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العكس لو عندى power series اكتبها على شكل main شكل function وبعدها خشينا في taylor وmaclaurin طيب اليوم بتذكر تذكير الله يساقل بالجزء اللى خلاكه الجزء الاولى من الشغل تبع اليوم", "tokens": [2407, 6027, 7435, 11622, 38207, 6024, 104, 7649, 1829, 8978, 8717, 36178, 2423, 3541, 8978, 33400, 4724, 1829, 7435, 1829, 8315, 8717, 4117, 2655, 5172, 32748, 6027, 3660, 382, 257, 1347, 2638, 1975, 2407, 18863, 4117, 3794, 45164, 43242, 7578, 1347, 2638, 1975, 4117, 2655, 3555, 11296, 15844, 13412, 28820, 2135, 13412, 28820, 2445, 46599, 22488, 11296, 16490, 8592, 1829, 8315, 8978, 39224, 6746, 4032, 37065, 875, 374, 259, 23032, 1829, 3555, 45595, 20498, 39894, 8848, 37983, 6055, 8848, 4117, 13546, 21984, 7251, 3794, 995, 4587, 1211, 20666, 7435, 11622, 38207, 13672, 7578, 16490, 15040, 4117, 3224, 25724, 11622, 38207, 42963, 12610, 7578, 9154, 25124, 17082, 1211, 6055, 3555, 3615, 45595, 20498], "avg_logprob": -0.29894911926404566, "compression_ratio": 1.7393162393162394, "no_speech_prob": 0.0, 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108, "seek": 261741, "start": 2601.09, "end": 2617.41, "text": "الان انا عندى هنا summation ببدأ من عند الواحد و هنا summation ببدأ من عند ال zero اذا ماقدرش اجمعهم مع بعض لان عندي هنا a n و a n وانا بدي اعرف ماهو شكل ال a n بنقول تمام", "tokens": [6027, 7649, 1975, 8315, 43242, 7578, 34105, 28811, 4724, 44510, 10721, 9154, 43242, 2423, 14407, 24401, 4032, 34105, 28811, 4724, 44510, 10721, 9154, 43242, 2423, 4018, 1975, 15730, 19446, 28543, 2288, 8592, 1975, 7435, 2304, 3615, 16095, 20449, 45030, 11242, 5296, 7649, 18871, 16254, 34105, 257, 297, 4032, 257, 297, 4032, 7649, 995, 4724, 16254, 1975, 3615, 28480, 19446, 3224, 2407, 13412, 28820, 2423, 257, 297, 44945, 39648, 46811, 10943], "avg_logprob": -0.2722271143550604, "compression_ratio": 1.71875, "no_speech_prob": 0.0, "words": [{"start": 2601.09, "end": 2601.57, "word": "الان", "probability": 0.79052734375}, {"start": 2601.57, "end": 2601.77, "word": " انا", "probability": 0.5994873046875}, {"start": 2601.77, "end": 2602.15, 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"word": " a", "probability": 0.544921875}, {"start": 3075.99, "end": 3076.51, "word": " n", "probability": 0.72265625}], "temperature": 1.0}, {"id": 128, "seek": 309956, "start": 3076.92, "end": 3099.56, "text": "يبقى قدرت احصل على شكل ال a n من خلال المعادلة التيارية او ال recurrence relation اللي انا يبقى انا جبتله main المطلوب الاول شكل ال a n كله بدلالة main ال a note يبقى اجبناله على سؤال ايش بيقوللي try حاول", "tokens": [1829, 3555, 4587, 7578, 12174, 3215, 43500, 1975, 5016, 36520, 15844, 13412, 28820, 2423, 257, 297, 9154, 16490, 1211, 6027, 9673, 3615, 18513, 37977, 38392, 9640, 10632, 1975, 2407, 2423, 18680, 10760, 9721, 13672, 1829, 1975, 8315, 7251, 3555, 4587, 7578, 1975, 8315, 10874, 3555, 2655, 43761, 2135, 9673, 9566, 1211, 37746, 42963, 12610, 13412, 28820, 2423, 257, 297, 28242, 3224, 47525, 1211, 6027, 3660, 2135, 2423, 257, 3637, 7251, 3555, 4587, 7578, 1975, 7435, 3555, 1863, 6027, 3224, 15844, 8608, 33604, 6027, 1975, 1829, 8592, 4724, 1829, 39648, 20292, 853, 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387842, "start": 3857.0, "end": 3878.42, "text": "بدنا نعطي تعريف جديد، هذا كلام برضه جديد علينا ماشوفنهوش قبل اليوم بدنا نعطي تعريف لل ordinary point اللي هي النقطة العادية و ال singular point اللي هي النقطة الشاذة أو النقطة المنفردة أو النقطة المنعزلة لكن الدارج النقطة الشاذة singular point", "tokens": [44510, 8315, 8717, 3615, 9566, 1829, 37279, 16572, 5172, 10874, 16254, 3215, 12399, 23758, 28242, 10943, 4724, 43042, 3224, 10874, 16254, 3215, 11203, 9957, 995, 19446, 8592, 38688, 1863, 3224, 2407, 8592, 12174, 36150, 45595, 20498, 47525, 8315, 8717, 3615, 9566, 1829, 37279, 16572, 5172, 24976, 10547, 935, 13672, 1829, 39896, 28239, 47432, 3660, 18863, 18513, 10632, 4032, 2423, 20010, 935, 13672, 1829, 39896, 28239, 47432, 3660, 25124, 45636, 3660, 34051, 28239, 47432, 3660, 9673, 1863, 5172, 2288, 41891, 34051, 28239, 47432, 3660, 9673, 1863, 3615, 11622, 37977, 44381, 32748, 9640, 7435, 28239, 47432, 3660, 25124, 45636, 3660, 20010, 935], "avg_logprob": -0.19709158061754586, 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substitute in the differential equation one we get نحصل علاماتي", "tokens": [1829, 3555, 4587, 7578, 8032, 47302, 10874, 1829, 3555, 47395, 9673, 8592, 2655, 28671, 16247, 12610, 7578, 4032, 9673, 8592, 2655, 28671, 16712, 7649, 10632, 39894, 32887, 5016, 1975, 3615, 2407, 11242, 4032, 9957, 8978, 9673, 3615, 18513, 37977, 12602, 4587, 2304, 36764, 24401, 7251, 3555, 4587, 7578, 4724, 26108, 1829, 4724, 39648, 3224, 15802, 294, 264, 15756, 5367, 472, 321, 483, 8717, 5016, 36520, 11203, 10943, 9307, 1829], "avg_logprob": -0.22901785394975116, "compression_ratio": 1.471264367816092, "no_speech_prob": 0.0, "words": [{"start": 4465.7, "end": 4466.08, "word": "يبقى", "probability": 0.8048095703125}, {"start": 4466.08, "end": 4466.22, "word": " هاي", "probability": 0.4495849609375}, {"start": 4466.22, "end": 4466.56, "word": " جيبته", "probability": 0.7445068359375}, {"start": 4466.56, "end": 4467.16, "word": " المشتقة", "probability": 0.94873046875}, {"start": 4467.16, "end": 4467.5, 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"probability": 0.78759765625}, {"start": 4734.94, "end": 4735.44, "word": " summation", "probability": 0.95556640625}, {"start": 4735.44, "end": 4735.82, "word": " يبقى", "probability": 0.780731201171875}, {"start": 4735.82, "end": 4736.36, "word": " انحلت", "probability": 0.84765625}, {"start": 4736.36, "end": 4737.04, "word": " مشكلتك", "probability": 0.91015625}], "temperature": 1.0}, {"id": 192, "seek": 475618, "start": 4737.3, "end": 4756.18, "text": "بصير كل ال summation زي ما هو و ال excess بقيت كما هي تمام كيف نجي نقول حط n ب zero zero zero بظلي 2 في 1 ب 2 اتنين اكس و zero ب واحد يبقى هذا لما ال n تسوي zero", "tokens": [3555, 9381, 13546, 28242, 2423, 28811, 30767, 1829, 19446, 31439, 4032, 2423, 9310, 4724, 4587, 36081, 9122, 15042, 39896, 46811, 10943, 9122, 33911, 8717, 7435, 1829, 8717, 39648, 11331, 9566, 297, 4724, 4018, 4018, 4018, 4724, 19913, 20292, 568, 8978, 502, 4724, 568, 1975, 2655, 1863, 9957, 1975, 4117, 3794, 4032, 4018, 4724, 36764, 24401, 7251, 3555, 4587, 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series اللى عندنا هذه يبقى هذا الشكل ال general solution لمين للمعادلة التفاضلية هذا يا مناطش شوفي إذا جبت ال recurrence relation هذه الصحيحة بصير الباقى كله تعويض عادي", "tokens": [9778, 1211, 47395, 15844, 25124, 7435, 3660, 4032, 23758, 16490, 1211, 47395, 15844, 25124, 7435, 3660, 4032, 29739, 995, 4587, 7578, 16490, 3215, 2655, 9154, 3224, 257, 8717, 23328, 6225, 10943, 1211, 37893, 2655, 31747, 4032, 16490, 3215, 2655, 257, 472, 6225, 10943, 1211, 37893, 2655, 31747, 6156, 9566, 1211, 3615, 2423, 2638, 13672, 7578, 43242, 8315, 29538, 4032, 2423, 2638, 13672, 7578, 43242, 8315, 29538, 7251, 3555, 4587, 7578, 23758, 25124, 28820, 2423, 2674, 3827, 5296, 2304, 9957, 5296, 19528, 3615, 18513, 37977, 16712, 5172, 46958, 1211, 10632, 23758, 35186, 3714, 8315, 9566, 8592, 13412, 38688, 1829, 11933, 15730, 10874, 3555, 2655, 2423, 18680, 10760, 9721, 29538, 31767, 5016, 1829, 5016, 3660, 4724, 9381, 13546, 29739, 995, 4587, 7578, 28242, 3224, 37279, 45865, 11242, 6225, 995, 16254], 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"probability": 0.63226318359375}, {"start": 6251.33, "end": 6251.57, "word": " هذا", "probability": 0.8232421875}, {"start": 6251.57, "end": 6252.19, "word": " الشكل", "probability": 0.952392578125}, {"start": 6252.19, "end": 6252.47, "word": " ال", "probability": 0.9501953125}, {"start": 6252.47, "end": 6252.89, "word": " general", "probability": 0.91162109375}, {"start": 6252.89, "end": 6253.63, "word": " solution", "probability": 0.984375}, {"start": 6253.63, "end": 6254.15, "word": " لمين", "probability": 0.3890787760416667}, {"start": 6254.15, "end": 6255.35, "word": " للمعادلة", "probability": 0.909375}, {"start": 6255.35, "end": 6256.39, "word": " التفاضلية", "probability": 0.8833984375}, {"start": 6256.39, "end": 6256.99, "word": " هذا", "probability": 0.437744140625}, {"start": 6256.99, "end": 6257.23, "word": " يا", "probability": 0.63818359375}, {"start": 6257.23, "end": 6257.65, "word": " مناطش", "probability": 0.56964111328125}, {"start": 6257.65, "end": 6258.59, "word": " شوفي", "probability": 0.7215983072916666}, {"start": 6258.59, "end": 6258.79, "word": " إذا", "probability": 0.76220703125}, {"start": 6258.79, "end": 6259.17, "word": " جبت", "probability": 0.94287109375}, {"start": 6259.17, "end": 6259.35, "word": " ال", "probability": 0.93212890625}, {"start": 6259.35, "end": 6260.23, "word": " recurrence", "probability": 0.6539306640625}, {"start": 6260.23, "end": 6261.01, "word": " relation", "probability": 0.97412109375}, {"start": 6261.01, "end": 6261.51, "word": " هذه", "probability": 0.77685546875}, {"start": 6261.51, "end": 6262.69, "word": " الصحيحة", "probability": 0.98525390625}, {"start": 6262.69, "end": 6263.25, "word": " بصير", "probability": 0.85791015625}, {"start": 6263.25, "end": 6263.65, "word": " الباقى", "probability": 0.883544921875}, {"start": 6263.65, "end": 6264.07, "word": " كله", "probability": 0.985107421875}, {"start": 6264.07, "end": 6264.67, "word": " تعويض", "probability": 0.880859375}, {"start": 6264.67, "end": 6265.11, "word": " عادي", "probability": 0.8850911458333334}], "temperature": 1.0}, {"id": 254, "seek": 628994, "start": 6265.48, "end": 6289.94, "text": "مافيش فيه اي صعوبة لكن اذا جبتيها غلط ضيعتي سؤالك لذلك كل امتحانها بنجيب فيه سؤال على هذا ال section كل امتحانها اي ورقة امتحان نهائي بتلاقي فيها سؤال على هذا ال section لسه ابدا اعطيك مثال المرة القادمة ان شاء الله حد فيكوا لايه تساؤل هنا؟", "tokens": [15042, 41185, 8592, 8978, 3224, 1975, 1829, 20328, 3615, 37746, 3660, 44381, 1975, 15730, 10874, 3555, 31371, 11296, 32771, 1211, 9566, 48812, 1829, 34268, 1829, 8608, 33604, 6027, 4117, 5296, 8848, 23275, 28242, 1975, 2304, 2655, 5016, 7649, 11296, 44945, 7435, 1829, 3555, 8978, 3224, 8608, 33604, 6027, 15844, 23758, 2423, 3541, 28242, 1975, 2304, 2655, 5016, 7649, 11296, 1975, 1829, 4032, 2288, 28671, 1975, 2304, 2655, 5016, 7649, 8717, 3224, 16373, 1829, 39894, 15040, 38436, 8978, 11296, 8608, 33604, 6027, 15844, 23758, 2423, 3541, 5296, 3794, 3224, 48127, 28259, 1975, 3615, 9566, 1829, 4117, 50113, 6027, 9673, 25720, 25062, 18513, 46007, 16472, 13412, 16606, 21984, 11331, 3215, 8978, 4117, 14407, 20193, 1829, 3224, 6055, 3794, 5718, 97, 1211, 34105, 22807], "avg_logprob": -0.17200307364835113, "compression_ratio": 1.9090909090909092, "no_speech_prob": 5.960464477539063e-08, "words": [{"start": 6265.48, "end": 6265.98, "word": "مافيش", "probability": 0.81298828125}, {"start": 6265.98, "end": 6266.2, "word": " فيه", "probability": 0.839599609375}, {"start": 6266.2, "end": 6266.44, "word": " اي", "probability": 0.6702880859375}, {"start": 6266.44, "end": 6267.08, "word": " صعوبة", "probability": 0.9923095703125}, {"start": 6267.08, "end": 6267.54, "word": " لكن", "probability": 0.499267578125}, {"start": 6267.54, "end": 6267.78, "word": " اذا", "probability": 0.899169921875}, {"start": 6267.78, "end": 6268.34, "word": " جبتيها", "probability": 0.8431396484375}, {"start": 6268.34, "end": 6268.76, "word": " غلط", "probability": 0.9905598958333334}, {"start": 6268.76, "end": 6269.62, "word": " ضيعتي", "probability": 0.72796630859375}, {"start": 6269.62, "end": 6270.74, "word": " سؤالك", "probability": 0.99169921875}, {"start": 6270.74, "end": 6272.2, "word": " لذلك", "probability": 0.9129231770833334}, {"start": 6272.2, "end": 6272.92, "word": " كل", "probability": 0.91162109375}, {"start": 6272.92, "end": 6273.88, "word": " امتحانها", "probability": 0.8587646484375}, {"start": 6273.88, "end": 6274.64, "word": " بنجيب", "probability": 0.9306640625}, {"start": 6274.64, "end": 6274.88, "word": " فيه", "probability": 0.814208984375}, {"start": 6274.88, "end": 6275.26, "word": " سؤال", "probability": 0.9944661458333334}, {"start": 6275.26, "end": 6275.5, "word": " على", "probability": 0.8525390625}, {"start": 6275.5, "end": 6275.92, "word": " هذا", "probability": 0.94189453125}, {"start": 6275.92, "end": 6276.1, "word": " ال", "probability": 0.71875}, {"start": 6276.1, "end": 6276.58, "word": " section", "probability": 0.87939453125}, {"start": 6276.58, "end": 6277.5, "word": " كل", "probability": 0.7216796875}, {"start": 6277.5, "end": 6278.38, "word": " امتحانها", "probability": 0.9173990885416666}, {"start": 6278.38, "end": 6279.28, "word": " اي", "probability": 0.453125}, {"start": 6279.28, "end": 6279.74, "word": " ورقة", "probability": 0.9329427083333334}, {"start": 6279.74, "end": 6280.3, "word": " امتحان", "probability": 0.885302734375}, {"start": 6280.3, "end": 6280.86, "word": " نهائي", "probability": 0.86865234375}, {"start": 6280.86, "end": 6281.64, "word": " بتلاقي", "probability": 0.91748046875}, {"start": 6281.64, "end": 6281.96, "word": " فيها", "probability": 0.94775390625}, {"start": 6281.96, "end": 6282.5, "word": " سؤال", "probability": 0.9952799479166666}, {"start": 6282.5, "end": 6282.74, "word": " على", "probability": 0.9140625}, {"start": 6282.74, "end": 6283.34, "word": " هذا", "probability": 0.9765625}, {"start": 6283.34, "end": 6283.68, "word": " ال", "probability": 0.9306640625}, {"start": 6283.68, "end": 6284.24, "word": " section", "probability": 0.85791015625}, {"start": 6284.24, "end": 6285.34, "word": " لسه", "probability": 0.9627278645833334}, {"start": 6285.34, "end": 6285.54, "word": " ابدا", "probability": 0.482421875}, {"start": 6285.54, "end": 6285.92, "word": " اعطيك", "probability": 0.89931640625}, {"start": 6285.92, "end": 6286.66, "word": " مثال", "probability": 0.4864501953125}, {"start": 6286.66, "end": 6287.04, "word": " المرة", "probability": 0.855224609375}, {"start": 6287.04, "end": 6287.58, "word": " القادمة", "probability": 0.9845377604166666}, {"start": 6287.58, "end": 6287.76, "word": " ان", "probability": 0.78076171875}, {"start": 6287.76, "end": 6287.94, "word": " شاء", "probability": 0.93212890625}, {"start": 6287.94, "end": 6288.02, "word": " الله", "probability": 0.953125}, {"start": 6288.02, "end": 6288.38, "word": " حد", "probability": 0.778564453125}, {"start": 6288.38, "end": 6288.74, "word": " فيكوا", "probability": 0.8466796875}, {"start": 6288.74, "end": 6288.98, "word": " لايه", "probability": 0.8134765625}, {"start": 6288.98, "end": 6289.46, "word": " تساؤل", "probability": 0.8671875}, {"start": 6289.46, "end": 6289.94, "word": " هنا؟", "probability": 0.92578125}], "temperature": 1.0}], "language": "ar", "language_probability": 1.0, "duration": 6291.4465, "duration_after_vad": 5969.989093750046}
\ No newline at end of file
diff --git a/PL9fwy3NUQKwa8ZDfSFGn6H8xVFLzqmCZC/6nKiDvoO6MU.srt b/PL9fwy3NUQKwa8ZDfSFGn6H8xVFLzqmCZC/6nKiDvoO6MU.srt
new file mode 100644
index 0000000000000000000000000000000000000000..381b1d43c4b4cde9b98f2f5ee86afce71802f916
--- /dev/null
+++ b/PL9fwy3NUQKwa8ZDfSFGn6H8xVFLzqmCZC/6nKiDvoO6MU.srt
@@ -0,0 +1,3112 @@
+1
+00:00:09,980 --> 00:00:15,580
+بسم الله الرحمن الرحيم بنواصل ما ابتدأنا به المرة 
+
+2
+00:00:15,580 --> 00:00:20,420
+الماضية وهو series solution near an ordinary point
+
+3
+00:00:20,420 --> 00:00:24,760
+وسميناها part one وبعد قليل إن شاء الله خلال هذه
+
+4
+00:00:24,760 --> 00:00:29,000
+المحاضرة حناخد part 2 ونشوف شو العلاقة ما بين
+
+5
+00:00:29,000 --> 00:00:34,220
+الأتنين على أي حال مرة اللي فاتت أخدنا مثال واحد
+
+6
+00:00:34,220 --> 00:00:38,840
+على كيفية استخدام المتسلسلات في حل المعادلة
+
+7
+00:00:38,840 --> 00:00:43,800
+التفاضلية من الرتبة الثانية والآن بناخد مثلًا
+
+8
+00:00:43,800 --> 00:00:48,940
+المثال أسهل شوية من ناحية الإجراءات العملية واحنا 
+
+9
+00:00:48,940 --> 00:00:54,900
+بنشتغل ما كانش هيكون مباشر زي مثال المرة الماضية
+
+10
+00:00:54,900 --> 00:00:59,900
+المثال بيقول find the series solution هات إن شكل
+
+11
+00:00:59,900 --> 00:01:04,080
+الحل اللي على شكل متسلسلة and the recurrence
+
+12
+00:01:04,080 --> 00:01:07,520
+relation والمعادلة التكرارية للـ differential
+
+13
+00:01:07,520 --> 00:01:13,550
+equation اللي عندنا about the point x يساوي 2
+
+14
+00:01:13,550 --> 00:01:16,650
+اثنين هذا أنا مش عارف هي singular point ولا
+
+15
+00:01:16,650 --> 00:01:20,850
+ordinary point لكن احنا موضوعنا حتى هذه اللحظة
+
+16
+00:01:20,850 --> 00:01:25,130
+الدراسة عند من عند الـ ordinary points وليس عند 
+
+17
+00:01:25,130 --> 00:01:29,430
+الـ singular points لكن بدنا نبين إن هذه النقطة هي 
+
+18
+00:01:29,430 --> 00:01:35,150
+عبارة عن ordinary point فلو جيت بدي أقول له الـ P of
+
+19
+00:01:35,150 --> 00:01:42,270
+x يبقى الـ P of x اللي هي من 2 لا يمكن أن تساوي
+
+20
+00:01:42,270 --> 00:01:48,130
+zero مهما تغيرت الـ x يبقى كل النقاط عبارة عن
+
+21
+00:01:48,130 --> 00:01:52,770
+ordinary points يعني لا يوجد عندي singular points
+
+22
+00:01:52,770 --> 00:02:01,070
+يبقى هذا معناه إن الـ x يساوي 2 is an ordinary 
+
+23
+00:02:01,070 --> 00:02:06,670
+point يبقى هذه عبارة عن نقطة عادية
+
+24
+00:02:11,740 --> 00:02:20,980
+احنا بنبحث على ايه؟ الـ solution Y في الصيغة التالية
+
+25
+00:02:20,980 --> 00:02:27,200
+summation من N equal zero to infinity للـ A N المرة 
+
+26
+00:02:27,200 --> 00:02:30,940
+اللي فاتت المثال الماضي منها كانت النقطة x يساوي
+
+27
+00:02:30,940 --> 00:02:36,280
+زيرو وليس x يساوي 2 فكان summation للـ A N X to
+
+28
+00:02:36,280 --> 00:02:43,230
+the power N لكن مدام احنا الحل هيكون حوالين النقطة
+
+29
+00:02:43,230 --> 00:02:49,350
+هذه كما بنقول x ناقص 2 كله to the power n
+
+30
+00:02:49,350 --> 00:02:55,610
+which converge
+
+31
+00:02:55,610 --> 00:03:05,230
+for اللي هو absolute value للـ x ناقص 2 أقل من
+
+32
+00:03:05,230 --> 00:03:11,340
+رو و رو greater than zero يبقى هذه الـ series تبقى
+
+33
+00:03:11,340 --> 00:03:15,520
+تقاربية خلال الفترة اللي عندنا اللي هو absolute
+
+34
+00:03:15,520 --> 00:03:20,000
+value للـ X ناقص 2 أقل من رو و رو greater than
+
+35
+00:03:20,000 --> 00:03:24,520
+zero بس مجرد التذكير اللي ليس اللي بتذكركم بكل
+
+36
+00:03:24,520 --> 00:03:29,380
+كلام بيه هذه الـ absolute value للـ X ناقص 2 أقل
+
+37
+00:03:29,380 --> 00:03:37,760
+من رو وأكبر من رو أول X أقل من رو زائد 2 وأقل 
+
+38
+00:03:37,760 --> 00:03:44,460
+من 2 ناقص رو يعني لو جيت قلت هذا الـ real line 
+
+39
+00:03:44,460 --> 00:03:50,360
+تمام؟ وهذه النقطة اللي هي 2 النقطة هذه 2
+
+40
+00:03:50,360 --> 00:03:56,320
+زائد رو النقطة هادي ها ها اللي هي 2 ناقص رو
+
+41
+00:03:56,320 --> 00:04:00,660
+وبالتالي هذا نصف القطر أو radius of convergence
+
+42
+00:04:00,660 --> 00:04:05,280
+اللي هي رو وهذا radius of convergence برضه مين
+
+43
+00:04:05,280 --> 00:04:11,960
+اللي هي رو طيب ممتاز ايش رأيكم نتعرف على شكل الحل
+
+44
+00:04:11,960 --> 00:04:15,440
+لأنه مش هنعوض في المعادلة دي بالزمن المشتقة الأولى 
+
+45
+00:04:15,440 --> 00:04:22,140
+والمشتقة الثانية يبقى أنا عندي y تساوي الـ summation
+
+46
+00:04:22,140 --> 00:04:28,600
+من n equal zero to infinity للـ a n في الـ x ناقص
+
+47
+00:04:28,600 --> 00:04:35,120
+2 كله to the power m هذا بده يعطينا إن المشتقة 
+
+48
+00:04:35,120 --> 00:04:42,490
+الأولى y prime يساوي summation لمن؟ للـ N in
+
+49
+00:04:42,490 --> 00:04:48,770
+constant x ناقص 2 to the power N ناقص 1 الـ 
+
+50
+00:04:48,770 --> 00:04:51,630
+summation هذا لما أشتق المشتق اللي هو اللي بيبدأ 
+
+51
+00:04:51,630 --> 00:04:56,570
+من وين؟ من عند N تساوي 1 من عند N تساوي 1 إلى
+
+52
+00:04:56,570 --> 00:05:02,670
+infinity هذا بده يعطينا إن المشتق الثاني Y double prime
+
+53
+00:05:03,210 --> 00:05:09,510
+هذا كله مقدار ثابت إذا بدي أشتق هذه كمان مرة يبقى 
+
+54
+00:05:09,510 --> 00:05:17,030
+summation للـ N في الـ N ناقص 1 في الـ A M في الـ X
+
+55
+00:05:17,030 --> 00:05:22,150
+ناقص 2 to the power N ناقص 2 طبعًا مشتقة 
+
+56
+00:05:22,150 --> 00:05:26,050
+مداخل القصة اللي هو بقداش؟ بواحد صحيح يبقى بروحش 
+
+57
+00:05:26,050 --> 00:05:29,710
+باكتبها الـ summation هنا ابتدأ من عند N يساوي 
+
+58
+00:05:29,710 --> 00:05:35,050
+واحد يبقى من هنا من عند N تساوي 2 زي ما كنا 
+
+59
+00:05:35,050 --> 00:05:39,470
+شفنا في الـ section الماضي وزي ما شفنا في مثال
+
+60
+00:05:39,470 --> 00:05:51,830
+المرة الماضية الآن عندي Y و Y'' و Y'' و Y'' و Y''
+
+61
+00:05:51,830 --> 00:05:53,050
+و Y'' و Y'' و Y'' و Y'' و Y'' و Y'' و Y'' و Y'' و
+
+62
+00:05:53,050 --> 00:05:53,490
+Y'' و Y'' و Y'' و Y'' و Y'' و Y'' و Y'' و Y'' و
+
+63
+00:05:53,490 --> 00:05:53,630
+Y'' و Y'' و Y'' و Y'' و Y'' و Y'' و Y'' و Y'' و
+
+64
+00:05:53,630 --> 00:05:53,670
+Y'' و Y'' و Y'' و Y'' و Y'' و Y'' و Y'' و Y'' و
+
+65
+00:05:53,670 --> 00:05:54,070
+Y'' و Y'' و Y'' و Y'' و Y'' و Y'' و Y'' و Y'' و
+
+66
+00:05:54,070 --> 00:05:56,190
+Y'' و Y'' و Y'' و Y'' و Y'' و Y'' و Y'' و Y'' و
+
+67
+00:05:56,190 --> 00:06:01,710
+Y'' و Y'' و Y'' و Y'' و Y''
+
+68
+00:06:04,550 --> 00:06:09,970
+بنجعلها 2 Y double prime يبقى هذه بدي اروح اضربها في بينامنات بدي
+
+69
+00:06:09,970 --> 00:06:14,470
+اضربها في 2 الاثنين هذه لو خليتها برة الـ
+
+70
+00:06:14,470 --> 00:06:18,340
+summation والله حطيتها جوا الـ summation بتفرق لكم
+
+71
+00:06:18,340 --> 00:06:22,560
+مالوش دعوة بالصميشن يعني مالوش دعوة بالـ N إذا هذه
+
+72
+00:06:22,560 --> 00:06:29,300
+ستصبح summation من N equal to infinity لـ 2 اللي
+
+73
+00:06:29,300 --> 00:06:37,580
+عندنا N في من؟ في الـ N ناقص 1 في الـ A N في الـ X
+
+74
+00:06:37,580 --> 00:06:43,620
+ناقص 2 to the power N ناقص 2 يبقى خلصها من 
+
+75
+00:06:43,620 --> 00:06:49,830
+من؟ من الـ term الأول بدنا نيجي للـ term التاني اللي
+
+76
+00:06:49,830 --> 00:06:54,470
+هو الـ X زائد 1 مالكش دعوة يخليك برة لأنك مش زي 
+
+77
+00:06:54,470 --> 00:06:57,910
+اللي جوا، لو كان زي اللي جوا هذا كان دخلناه
+
+78
+00:06:57,910 --> 00:07:02,520
+مباشرة، لكن خليكي لما نتفاهم عليكي شوية يبقى x زاد
+
+79
+00:07:02,520 --> 00:07:06,360
+واحد في الـ y prime وين الـ y prime؟ ها هي يبقى
+
+80
+00:07:06,360 --> 00:07:13,320
+summation من n equal one to infinity للـ n a n x
+
+81
+00:07:13,320 --> 00:07:18,440
+ناقص 2 to the power n ناقص الـ 1 قلصنا الـ
+
+82
+00:07:18,440 --> 00:07:21,980
+term التاني بدنا نروح للـ term التالت يبقى هذه بدنا
+
+83
+00:07:21,980 --> 00:07:25,700
+نروح نضربها وين؟ 3 3 كتبتها برة الـ 
+
+84
+00:07:25,700 --> 00:07:29,200
+summation ولا جوا الـ summation نسيتني يبقى بالداخل
+
+85
+00:07:29,200 --> 00:07:34,800
+3 جوا الـ summation يبقى زائد summation من n 
+
+86
+00:07:34,800 --> 00:07:41,440
+equal zero to infinity لـ 3 a n في الـ x ناقص
+
+87
+00:07:41,440 --> 00:07:46,780
+2 to the power n كله بده يساوي مين؟ بده يساوي 
+
+88
+00:07:46,780 --> 00:07:53,460
+zero يبقى احنا الآن بدنا نعيد ترتيب أوراق المسألة
+
+89
+00:07:53,460 --> 00:07:58,860
+في شغلتين الشغل الأولى هادي x to the power n x نقص
+
+90
+00:07:58,860 --> 00:08:03,460
+2 to the power n بدي الباقي هادي الأسس كلها to
+
+91
+00:08:03,460 --> 00:08:08,860
+the power n هي واحدة الثانية بدي الـ index لتحت الـ
+
+92
+00:08:08,860 --> 00:08:13,900
+summation يكون كله موحد مشان أقدر أجمع وأعمل ايه
+
+93
+00:08:13,900 --> 00:08:19,040
+ب summation واحد فقط فبجي بقول هادي مشان أخليها
+
+94
+00:08:19,040 --> 00:08:25,330
+بدلالة الـ n يبقى بدي يشيل كل N ويحط مكانه N زائد
+
+95
+00:08:25,330 --> 00:08:30,610
+2 يبقى دي بدها تصير على الشكل التالي يبقى 
+
+96
+00:08:30,610 --> 00:08:40,820
+summation من عند N equal zero ولا لأ؟ هذا يعني
+
+97
+00:08:40,820 --> 00:08:48,140
+إن تساوي 0 لمن؟ للـ infinity وبالتالي 2 بدي
+
+98
+00:08:48,140 --> 00:08:54,140
+أشيل الـ N وأحط مكانها N زائد 2 وهذا يعني إن
+
+99
+00:08:54,140 --> 00:09:01,560
+زائد 2 ناقص 1 يعني N زائد 1 هذه A N زائد
+
+100
+00:09:01,560 --> 00:09:08,100
+2 كله في x ناقص 2 كله to the power m
+
+101
+00:09:08,100 --> 00:09:13,700
+يبقى هذه زبطناها الخطوة الأولى خلينا الأس تبعها to 
+
+102
+00:09:13,700 --> 00:09:18,960
+the power m اه هنا في جوا x وفي برة x بدي 
+
+103
+00:09:18,960 --> 00:09:24,690
+أدخل اللي جوا برة بس مش زي بعض ورتنا مظبوط هذه x زي
+
+104
+00:09:24,690 --> 00:09:29,970
+واحد وهذه x نقص 2 طيب كيف بدي أدخل؟ أدخل الـ x
+
+105
+00:09:29,970 --> 00:09:33,790
+هنا برضه لحاله بتضبطش أدخل الـ 1 لحاله بتضبطش
+
+106
+00:09:33,790 --> 00:09:38,410
+إذا بدي أشتغل شغل فعلًا يكون رياضي سليم وماحدش 
+
+107
+00:09:38,410 --> 00:09:42,170
+يقول لي كلامك مش صحيح ايش بتقترحي علينا نعمة اللي
+
+108
+00:09:42,170 --> 00:09:46,110
+بتعرفي ترفعي دي أبو جاه شيفها؟ أيوة x زي 1 هيفرع
+
+109
+00:09:46,110 --> 00:09:53,110
+x نقص 2 ميل ميل شو اسمك أنت؟ ايه حنين حنين
+
+110
+00:09:53,110 --> 00:09:56,510
+حنين
+
+111
+00:09:56,510 --> 00:10:01,050
+حنين حنين حنين حنين حنين حنين حنين حنين حنين حنين
+
+112
+00:10:01,050 --> 00:10:09,530
+حنين حنين حنين حنين حنين حنين حنين حنين حنين حنين
+
+113
+00:10:09,530 --> 00:10:09,550
+حنين حنين حنين حنين حنين حنين حنين حنين حنين حنين
+
+114
+00:10:09,550 --> 00:10:09,590
+حنين حنين حنين حنين حنين حنين حنين حنين حنين حنين
+
+115
+00:10:09,590 --> 00:10:19,450
+حنين
+
+116
+00:10:19,450 --> 00:10:27,840
+لكن هذه حلت لي معضلة كبيرة جدًا ايش صار عندي x نقص
+
+117
+00:10:27,840 --> 00:10:32,000
+2 مضروبة في الجواب بقدر اضربها بدون مشاكل و
+
+118
+00:10:32,000 --> 00:10:35,480
+بظل عندي 3 مضروبة في الـ summation يعني حاسين
+
+119
+00:10:35,480 --> 00:10:40,240
+عندي كم double summations؟ واحد مضروب في x نقص 
+
+120
+00:10:40,240 --> 00:10:44,580
+2 واحد مضروب في مام في 3 ايه بجهائي أول 
+
+121
+00:10:44,580 --> 00:10:49,530
+معضلة موجودة في المسألة تغلبنا عليها بتفكير سليم كيف
+
+122
+00:10:49,530 --> 00:10:54,370
+أكتب اللي هو الـ term اللي برة بدلالة main بدلالة
+
+123
+00:10:54,370 --> 00:10:57,330
+term اللي جوا، بالتالي بيكون خلصنا من المسألة هذه
+
+124
+00:10:57,330 --> 00:11:03,230
+يبقى يا بنات هذه الـ x ناقص 2 بدي أدخلها جوا الـ
+
+125
+00:11:03,230 --> 00:11:07,090
+summation وبعد ذلك زائد 3 كمان أدخلها جوا الـ
+
+126
+00:11:07,090 --> 00:11:11,350
+summation وبالتالي هيظهر term main وليس term واحد
+
+127
+00:11:11,710 --> 00:11:17,890
+يبقى حنيجي هنا زائد هي عندنا summation من وين؟ من 
+
+128
+00:11:17,890 --> 00:11:25,110
+عند الـ N equal one to infinity لمين؟ للـ N A N X 
+
+129
+00:11:25,110 --> 00:11:30,310
+ناقص 2 x ناقص 2 بدأت تيجي هذه أس قداش يا 
+
+130
+00:11:30,310 --> 00:11:38,350
+بنات؟ أس 1 يبقى هذا مع السلامة بظل هذا أس N فاضل
+
+131
+00:11:38,350 --> 00:11:41,950
+علينا مين؟ فاضل علينا الـ 3 تدخل على الـ 
+
+132
+00:11:41,950 --> 00:11:47,330
+summation يبقى زائد summation من n equal one to 
+
+133
+00:11:47,330 --> 00:11:56,810
+infinity لـ 3 n a n x ناقص 2 أس قداش؟ ناقص
+
+134
+00:11:56,810 --> 00:12:01,910
+واحد هذه الـ 3 مالهاش دعوة بتضيعش الأس بيظل الأس
+
+135
+00:12:01,910 --> 00:12:06,380
+زي ما هو يبقى الترمين اللي كتبتهم عبارة عن الـ term
+
+136
+00:12:06,380 --> 00:12:11,600
+هذا فقط وبقى اللي عندنا مين؟ الـ term الأخير يبقى 
+
+137
+00:12:11,600 --> 00:12:20,140
+زائد summation من n equal zero to infinity لـ 3 
+
+138
+00:12:20,140 --> 00:12:25,380
+a n في الـ X ناقص 2 to the power n كل هذا بدي
+
+139
+00:12:25,380 --> 00:12:32,260
+يساوي مان؟ بدي يساوي زيرو طيب، حتى الآن فكنا مهضومة 
+
+140
+00:12:32,260 --> 00:12:38,640
+واحدة، اللي هو هذه كتبناها بدلالة اللي جوا، الآن 
+
+141
+00:12:38,640 --> 00:12:49,490
+نرجع لشغلنا المرة الماضية هيبقى أول
+
+142
+00:12:49,490 --> 00:12:54,710
+خطوة بنعملها بنوحد الأسس تبع main الـ x اللي عندنا 
+
+143
+00:12:54,710 --> 00:13:00,370
+هذه بعدين بطلها هذي أس n جاهزة هذي أس n جاهزة
+
+144
+00:13:00,370 --> 00:13:04,890
+هذي أس n جاهزة يبقى هذي اللي ما هيش جاهزة يبقى
+
+145
+00:13:04,890 --> 00:13:10,910
+مشان أجهزها هذي بدي أشيل كل n وأحط مكانه n زائد
+
+146
+00:13:10,910 --> 00:13:14,630
+واحد يبقى هذه يا بنات بدي أعكس كتابة أنت بدي 
+
+147
+00:13:14,630 --> 00:13:20,550
+أنزلها زي ما هي وهذه بدي أنزلها زي ما هي وهذه زائد
+
+148
+00:13:20,550 --> 00:13:26,510
+summation من n equal zero to infinity لـ 3 n 
+
+149
+00:13:26,510 --> 00:13:34,190
+زائد 1 a n زائد 1 x ناقص 2 to the power
+
+150
+00:13:34,190 --> 00:13:40,750
+n يبقى شيلت كل n للـ term التالت ده وحطيت مكانه n 
+
+151
+00:13:40,750 --> 00:13:47,430
+زائد 1 هذا كمان زائد بدي أنزله مانو زي ما هو 
+
+152
+00:13:47,430 --> 00:13:54,570
+ماعنديش مشكلة فيه إذا ايش اللي حصل الآن؟ وحتى الأسس
+
+153
+00:13:54,570 --> 00:13:59,090
+كلها تبعت من؟ تبعت الـ x ناقص 2 إذا حلّينا 
+
+154
+00:13:59,090 --> 00:14:03,530
+المعضلة الثانية فاضل مين علينا؟ المعضلة الثالثة 
+
+155
+00:14:03,530 --> 00:14:07,290
+المعضلة الثالثة بدي أخلّي الـ index لتحت الـ
+
+156
+00:14:07,290 --> 00:14:12,990
+summation هذا كله زي بعضه دون أن أضيع الشغل اللي
+
+157
+00:14:12,990 --> 00:14:16,010
+اشتغلته بالنسبة للـ x ناقص 2 to the power n
+
+158
+00:14:16,010 --> 00:14:20,510
+يعني اصحي تعملي شغل تخربيه اللي اشتغلت يقول لنا 
+
+159
+00:14:20,510 --> 00:14:24,070
+بالبلدي انحافظ على المكتسبات الوطنية المرة اللي 
+
+160
+00:14:24,070 --> 00:14:26,870
+فاتت، يبقى احنا هنا نفس القصة بدنا نحافظ على 
+
+161
+00:14:26,870 --> 00:14:30,590
+المكتسبات الوطنية، معناته بدي أشتغل شغل رياضي
+
+162
+00:14:30,590 --> 00:14:34,610
+سليم، ماحدش يقول لي فيه حاجة، وأخلّي الأس تبع الـ x
+
+163
+00:14:34,610 --> 00:14:40,080
+ناقص 2 هو هو في الأربع terms، بقول لك كويس احنا 
+
+164
+00:14:40,080 --> 00:14:44,740
+عندنا ده من عند الـ 1 يبقى أنا ماقدرش ألعب فيه 
+
+165
+00:14:44,740 --> 00:14:49,420
+طيب باجي بقول ممكن أخلي الباجي كله من عند الـ 1
+
+166
+00:14:49,420 --> 00:14:53,780
+يبدأ كيف؟ بطلع أول term في الـ series اللي عندنا 
+
+167
+00:14:53,780 --> 00:14:57,980
+ضارة الـ summation وبالتالي بصير بوحد الـ index هذه 
+
+168
+00:14:57,980 --> 00:15:04,200
+فمثلا لو حطيت الـ n يساوي 0 بصير 2 في 2
+
+169
+00:15:04,200 --> 00:15:10,450
+في 1 يعني 4 2 فقط
+
+216
+00:19:58,460 --> 00:20:05,780
+معناته أن الـ A2 بده يساوي ثلاثة أرباع بإشارة سالب
+
+217
+00:20:06,000 --> 00:20:13,580
+لمن؟ للـ A1 زائد A نقطة من هنا بدأ يظهر أول اختلاف
+
+218
+00:20:13,580 --> 00:20:17,660
+بين سؤالنا هذا وبين سؤالي المرة الماضية المرة
+
+219
+00:20:17,660 --> 00:20:23,120
+الماضية طلعت a2 بدلالة main a node فقط المرة هذه
+
+220
+00:20:23,120 --> 00:20:28,560
+طلعت بدلالة a node و a1 وبالتالي ما عندناش مشكلة برضه
+
+221
+00:20:28,560 --> 00:20:33,660
+يعني إيش ما تطلع بسجلها زي ما هي كويس هذه الآن في
+
+222
+00:20:33,660 --> 00:20:40,550
+عوامل مشتركة ممكن يعني أجسم عليها في جوس عامل مشارك
+
+223
+00:20:40,550 --> 00:20:43,630
+من الـ term الأول و الـ term الثاني و الثاني بيقولي
+
+224
+00:20:43,630 --> 00:20:46,990
+هنا n زاد واحد هنا n زاد واحد بس هنا ما فيش n زاد
+
+225
+00:20:46,990 --> 00:20:53,160
+واحد مصغر يبقى بخلي كل شيء زي ما هو إذا هذا و هذا
+
+226
+00:20:53,160 --> 00:20:58,260
+هوديهم على الشجة الثانية و أقسم على هذا المعامل
+
+227
+00:20:58,260 --> 00:21:05,160
+بيصير عندنا الـ a n زائد اثنين يساوي ناقص هيخليه 
+
+228
+00:21:05,160 --> 00:21:11,900
+برا بيظل عندنا مين ثلاثة في n زائد واحد a n زائد
+
+229
+00:21:11,900 --> 00:21:20,640
+واحد زائد n زائد ثلاثة a n كل هذا مقسوم على الاثنين
+
+230
+00:21:36,190 --> 00:21:42,090
+عن طريق الـ Recurrence relation اللي طلبها عندي
+
+231
+00:21:42,090 --> 00:21:47,120
+وين في رأس المثلثة جالسة لـ Recurrence relation طب
+
+232
+00:21:47,120 --> 00:21:54,160
+بدي أشوف هدي بدي تبدأ in من وين يبقى in تساوي أبدأ
+
+233
+00:21:54,160 --> 00:21:59,400
+من عند الـ zero لو قلنا من عند الـ zero شو بيعطيني 
+
+234
+00:21:59,400 --> 00:22:05,580
+اثنين ما اثنين هي جاهزة صح؟ يبقى الصحة ده من وين؟
+
+235
+00:22:05,580 --> 00:22:11,720
+من عند الواحد يبقى إنتوا ساوية واحد واثنين وثلاثة
+
+236
+00:22:11,720 --> 00:22:16,720
+وإلى ما شاء الله يبقى هذه يا بنات الـ recurrence
+
+237
+00:22:16,720 --> 00:22:21,320
+relation اللي بدها إياها اللي هو المطلوب الأول من
+
+238
+00:22:21,320 --> 00:22:27,680
+المسألة طيب بعد هيك الآن احكي قولي
+
+239
+00:22:31,340 --> 00:22:36,340
+ممتاز، إذا جربنا إيش؟ إذا جربنا n بي زيرو، إذا
+
+240
+00:22:36,340 --> 00:22:40,580
+جربنا n بي زيرو، إذا جربنا n بي زيرو، إذا جربنا n
+
+241
+00:22:40,580 --> 00:22:42,440
+إذا جربنا n بي زيرو، إذا جربنا n بي زيرو، إذا 
+
+242
+00:22:42,440 --> 00:22:43,380
+جربنا n بي زيرو، إذا جربنا n بي زيرو، إذا جربنا n
+
+243
+00:22:43,380 --> 00:22:46,960
+بي زيرو، إذا جربنا n بي زيرو، إذا جربنا n بي زيرو،
+
+244
+00:22:46,960 --> 00:22:48,940
+إذا جربنا n بي زيرو، إذا جربنا n بي زيرو، إذا
+
+245
+00:22:48,940 --> 00:22:56,640
+جربنا n بي زيرو، إذا جربنا n بي زيرو، إذا 
+
+246
+00:22:56,640 --> 00:23:03,380
+جربنا نخلص وبقول هي الـ record اللي بتشمل الأولى
+
+247
+00:23:03,380 --> 00:23:07,800
+و الثانية بمشي الحال ما عندنا مشكلة بيخلي هذه الحال
+
+248
+00:23:07,800 --> 00:23:11,760
+و هذه الحال و أقول عندي إنت سوا عادي ماشي الحال بدي
+
+249
+00:23:11,760 --> 00:23:15,280
+أجمع الـ 22 بصيغة اللي عندي و أخلي N تبدأ من عند
+
+250
+00:23:15,280 --> 00:23:20,080
+الظهور و ما عنديش مشكلة تمام؟ ليش؟ لأن لو حطيت N ب
+
+251
+00:23:20,080 --> 00:23:23,660
+zero في الـ recurrence relation هذا بيطلع منين؟ بيطلع
+
+252
+00:23:23,660 --> 00:23:29,660
+الـ term اللي عنها ده إذا ممكن أن أستغني عن هذه هيك
+
+253
+00:23:29,660 --> 00:23:37,260
+و اروح أقول هذه الـ N تساوي Zero واحد و اثنين و ثلاثة
+
+254
+00:23:37,260 --> 00:23:42,080
+إلى مالها نهاية كتبت هيك ولا كتب هيك اثنين صح تكتب
+
+255
+00:23:42,080 --> 00:23:46,300
+الصيغة اللي تشوفيها مناسبة بالنسبة لك ماشي لأن راح
+
+256
+00:23:46,300 --> 00:23:49,880
+أحط N تساوي Zero في المستطيل هذا بيطلع المستطيل
+
+257
+00:23:49,880 --> 00:23:54,230
+الأول عنها و الـ term الأول اللي عنها ما علينا اثنين
+
+258
+00:23:54,230 --> 00:23:58,110
+جاهزة عندي بدل الـ a اي ون و اي نود بدي أجيب من
+
+259
+00:23:58,110 --> 00:24:05,590
+إيه ثلاثة يبقى بدي ثلاثة اي اي ون زي اثنين إذا
+
+260
+00:24:05,590 --> 00:24:11,130
+بدي أشيل كل n و أحط مكانها واحد صحيح يبقى هذا
+
+261
+00:24:11,130 --> 00:24:15,410
+الكلام هي الناقص برا وهي الجوز بصير هذه يا بنات
+
+262
+00:24:15,410 --> 00:24:22,540
+ثلاثة في اثنين اللي هو كده؟ ستة اثنين ستة اثنين
+
+263
+00:24:22,540 --> 00:24:31,260
+زائد أربعة a واحد هذا كل البسط على المقام المقام
+
+264
+00:24:31,260 --> 00:24:36,940
+ده أحط هذه بواحد بيصير ثلاثة في اثنين بستة ستة في
+
+265
+00:24:36,940 --> 00:24:43,080
+اثنين باطمعش يبقى هذه كلها على أطمعش بالشكل اللي
+
+266
+00:24:43,080 --> 00:24:45,040
+عندنا تمام؟
+
+267
+00:24:46,600 --> 00:24:54,400
+هذه يا بنات تساوي ناقص نصف في مين في الاثنين ستة على 
+
+268
+00:24:54,400 --> 00:24:58,300
+اثنا عشر ناقص نصف في الاثنين أربعة على اثنا عشر اللي هو
+
+269
+00:24:58,300 --> 00:25:07,480
+بقد إيش؟ ثلث يبقى ناقص ثلث في أربعة يعني أربعة أثلاث لا
+
+270
+00:25:07,480 --> 00:25:10,780
+ثلث بس ثلث اللي هو الـ
+
+271
+00:25:14,230 --> 00:25:20,910
+طب اثنين مقطع يبقى بقدر أشيل اثنين وحقمتها بيصير
+
+272
+00:25:20,910 --> 00:25:26,530
+المثلثة كلها بدلالة a node و a one يبقى هذا الكلام
+
+273
+00:25:26,530 --> 00:25:34,270
+بده يساوي ناقص نصف و اثنين هيقلب ناقص ثلث ربع a
+
+274
+00:25:34,270 --> 00:25:42,630
+one في ناقص ثلث ربع a one ناقص ثلث ربع
+
+275
+00:25:44,980 --> 00:25:51,080
+هذا كله بيكون ناقص
+
+276
+00:25:51,080 --> 00:26:00,050
+ثلث A1 يبقى هذه تساوي بيطلع لي كويس هنا بدي أفكر بيصير
+
+277
+00:26:00,050 --> 00:26:07,050
+هذا قد إيش؟ ثلاثة أثمان بالموجب يبقى ثلاثة على ثمانية
+
+278
+00:26:07,050 --> 00:26:16,930
+a one ناقص فنقصه بيزيد برضه ثلاثة أثمان ثلاثة أثمان a
+
+279
+00:26:16,930 --> 00:26:24,650
+naught ناقص ثلث a one بيطلع لي الـ term الأول و الأخير
+
+280
+00:26:26,110 --> 00:26:31,170
+يجب أن تجمع الموضوع في المشتركة الـ 3 و 8، 4 و 20،
+
+281
+00:26:31,170 --> 00:26:38,090
+يبقى لو قلنا على 4 و 20 بنضيف كده 24 على
+
+282
+00:26:38,090 --> 00:26:45,030
+ثمانية فيها الثلاثة في ثلاثة بتسعة a تسعة a وان
+
+283
+00:26:45,030 --> 00:26:48,870
+تمام و نيجي هنا 24 على ثلاثة فيها
+
+284
+00:26:48,870 --> 00:26:55,130
+ثمانية في واحد بسالب ثمانية a وان سالب ثمانية a
+
+285
+00:26:55,130 --> 00:27:00,320
+وان هذا الـ term هنا الأخير ثلاثة أثمان a note ما لهوش 
+
+286
+00:27:00,320 --> 00:27:08,000
+دعوة لحاله يبقى زائد ثلاثة أثمان a note و يساوي ها
+
+287
+00:27:08,000 --> 00:27:14,460
+بيصبح a one بس على 24 يبقى a one على
+
+288
+00:27:14,460 --> 00:27:21,120
+24 زائد ثلاثة a note على مين؟ على ثمانية
+
+289
+00:27:21,120 --> 00:27:29,910
+إذا تمكنا من كتابة من من كتابة الـ A ثلاثة بدلالة
+
+290
+00:27:29,910 --> 00:27:38,390
+A1 و A0 بالمثل بدنا نروح نجيب A4 اللي عبارة عن A2
+
+291
+00:27:38,390 --> 00:27:43,630
+زائد 2 يبقى بدها أرجع و أشيل كل N و أحط مكانها
+
+292
+00:27:43,630 --> 00:27:50,240
+اثنين يبقى هاي السالب برا و بدي أحط اثنين بيصير
+
+293
+00:27:50,240 --> 00:27:58,460
+اثنين واحد ثلاثة ثلاثة في ثلاثة بتسعة ثلاثة يبقى
+
+294
+00:27:58,460 --> 00:28:08,620
+هذه تسعة ثلاثة زائد خمسة اثنين على مين؟ على حاطين
+
+295
+00:28:08,620 --> 00:28:14,540
+اثنين أربعة في اثنين بثمانية ثمانية في ثلاثة بـ 24
+
+296
+00:28:14,540 --> 00:28:20,180
+يبقى على 24 طب إيش بدي أسوي فيه
+
+297
+00:28:20,180 --> 00:28:25,740
+هذه يا بنات؟ بدي أشيل A ثلاثة و أكتب قيمتها هذه
+
+298
+00:28:25,740 --> 00:28:31,580
+بتصير بدلالة A1 و A1 و بدي أشيل A2 و أكتبها هنا إذا
+
+299
+00:28:31,580 --> 00:28:34,680
+أنا بدي أعطيك النتيجة ما بديش أضايق وقتي و أنا بسوي
+
+300
+00:28:34,680 --> 00:28:40,620
+كسور يبقى النتيجة النهائية على الشكل التالي بعد ما
+
+301
+00:28:40,620 --> 00:28:47,120
+تحسب الحسابات هذه بتطلع النتيجة عندك اللي هو A4
+
+302
+00:28:47,120 --> 00:28:52,780
+يساوي 9A1
+
+303
+00:28:52,780 --> 00:29:01,880
+على 64 زائد A node على 64
+
+304
+00:29:06,650 --> 00:29:12,570
+الآن يكفينا هذا للحصول على مين؟ على شكل الحل احنا 
+
+305
+00:29:12,570 --> 00:29:16,830
+فرضنا الحل على الشكل اللي عندنا هذا إذا بدّك فيك هذا
+
+306
+00:29:16,830 --> 00:29:23,990
+مش هنعوض في a1 و a2 و a3 إلى آخره يبقى باجي بقوله
+
+307
+00:29:23,990 --> 00:29:27,890
+الـ solution سيكون على الشكل التالي
+
+308
+00:29:48,260 --> 00:29:54,740
+يبقى the solution is
+
+309
+00:29:54,740 --> 00:30:01,900
+y يساوي summation من n equal zero to infinity للـ a
+
+310
+00:30:01,900 --> 00:30:07,130
+n x ناقص اثنين to the power n اللي كتبناها على 
+
+311
+00:30:07,130 --> 00:30:15,650
+الشكل التالي a0 زائد a1 في الـ X ناقص اثنين زائد a2
+
+312
+00:30:15,650 --> 00:30:23,910
+في الـ X ناقص اثنين الكل تربيع زائد اللي هو a3 X ناقص
+
+313
+00:30:23,910 --> 00:30:30,770
+اثنين الكل تكعيب زائد a4 X ناقص اثنين أس أربعة زائد
+
+314
+00:30:30,770 --> 00:30:38,940
+إلى ما شاء الله هذا الكلام يبدو يساوي a نود ما لهوش
+
+315
+00:30:38,940 --> 00:30:44,400
+دعوة الحل بده يظل بدللتها كمان a1 في الـ X ناقص 
+
+316
+00:30:44,400 --> 00:30:49,640
+اثنين بتبقى كما هي الحل بيكون بدللتها الآن بده
+
+317
+00:30:49,640 --> 00:30:54,920
+نيجي لمين؟ وصلنا لـ a اثنين اثنين اللي هو ناقص ثلث ربع
+
+318
+00:30:54,920 --> 00:31:03,120
+a1 ناقص ثلث ربع a نود يبقى ناقص أو زائد ناقص ثلث ربع
+
+319
+00:31:03,280 --> 00:31:11,500
+أول ناقص ثلث ربع a نوت كل هذا مضروب في مين؟ في الـ
+
+320
+00:31:11,500 --> 00:31:18,720
+X ناقص اثنين لكل تربيع جينا لـ A ثلاثة يبقى وصلنا لـ
+
+321
+00:31:18,720 --> 00:31:26,900
+A ثلاثة وين A ثلاثة؟ هي A3 اللي هو A1 على 24 يبقى
+
+322
+00:31:26,900 --> 00:31:38,060
+زائد A1 على 24 زائد اللي هو ثلاثة A node ثلاثة A
+
+323
+00:31:38,060 --> 00:31:45,020
+node على مين؟ على ثمانية كله هدف مين؟ في الـ X ناقص
+
+324
+00:31:45,020 --> 00:31:53,440
+اثنين لكل تكعيب زائد جينا لـ A4 اللي هو 9A1 على 64
+
+325
+00:31:53,440 --> 00:32:08,240
+9A1 على 64 زائد A node على 64 على 64 في الـ X ناقص 2
+
+326
+00:32:08,240 --> 00:32:16,380
+كله أربعة زائد إلى ما شاء الله طيب
+
+327
+00:32:16,380 --> 00:32:22,260
+هذا الكلام يساوي بتاخد اللي فيهم a node مع بعض
+
+328
+00:32:22,260 --> 00:32:28,320
+والباقي اللي فيهم a one مع بعض يبقى هذا a node مين
+
+329
+00:32:28,320 --> 00:32:34,380
+بيظل إن يعمل اثنين واحد هنا هذه a node بيصير ناقص 
+
+330
+00:32:34,380 --> 00:32:41,720
+ثلث أربع ناقص ثلث أربع في الـ X ناقص اثنين لكل
+
+331
+00:32:41,720 --> 00:32:48,480
+تربيع أخذ الـ term هذا فقط تمام نجي ل بعده بدي اخذ
+
+332
+00:32:48,480 --> 00:32:56,020
+الـ term هذا يبقى زائد ثلث أثمان في الـ X ناقص اثنين
+
+333
+00:32:56,020 --> 00:33:04,600
+لكل تكعيب زائد واحد على 64 يعني X ناقص اثنين 
+
+334
+00:33:04,600 --> 00:33:13,600
+كله أس أربعة على 64 زائد إلى ما شاء الله
+
+335
+00:33:13,600 --> 00:33:21,090
+زائد بتروح تاخد a one عامل مشترك إيش بيظل عندي؟ x
+
+336
+00:33:21,090 --> 00:33:28,490
+ناقص اثنين بيضاعف هذه ناقص ثلث ربع يبقى ناقص ثلث
+
+337
+00:33:28,490 --> 00:33:34,710
+ربع في من؟ في الـ x ناقص اثنين لكل تربيع خلصنا
+
+338
+00:33:34,710 --> 00:33:41,770
+منها و الـ a نود هي برا نجي ل بعدها زائد x ناقص
+
+339
+00:33:41,770 --> 00:33:48,170
+اثنين الكل تكعيب على 24 نجي اللي بعدها
+
+340
+00:33:48,170 --> 00:33:56,150
+زائد تسعة في الـ X ناقص اثنين أس أربعة على أربع
+
+341
+00:33:56,150 --> 00:33:59,590
+و ستين زائد إلى ما شاء الله
+
+342
+00:34:06,460 --> 00:34:11,780
+هذا هو الحل الأول و هذا هو الحل الثاني لـ second
+
+343
+00:34:11,780 --> 00:34:19,140
+order differential equation اللي عندنا
+
+344
+00:34:29,160 --> 00:34:33,760
+في أي حتة في السؤال اللي فات يعني أحيانا بنكتب إيش
+
+345
+00:34:33,760 --> 00:34:38,320
+find the first three terms of the series solution
+
+346
+00:34:38,320 --> 00:34:43,300
+يعني ما يهمناش الشكل العام اللي هو شكل الحد النوني في 
+
+347
+00:34:43,300 --> 00:34:47,120
+الـ summation لكن بيهمنا نجيب الأول ثلاثة أربعة termات
+
+348
+00:34:47,120 --> 00:34:51,720
+أو أول ثلاثة termات مما يدل على أن هذه ما لها عبارة
+
+349
+00:34:51,720 --> 00:34:56,260
+عن series حد فيكم اللي يتساءل هنا؟
+
+350
+00:35:07,760 --> 00:35:16,060
+لحد هنا stop بدنا منكم المسائل التالية يبقى
+
+351
+00:35:16,060 --> 00:35:23,640
+exercises خمسة اثنين بدنا المسائل من واحد لغاية 
+
+352
+00:35:23,640 --> 00:35:33,740
+ثلاثة عشر الأد و بدنا من خمسة عشر لغاية ثمانية عشر part
+
+353
+00:35:33,740 --> 00:35:38,880
+اللي هو إيه فقط اللي باقي بدنا إياه شيء اللي متعلق
+
+354
+00:35:38,880 --> 00:35:45,160
+بالرسم و ما إلى ذلك كله مش لازم بس هاتون هذا الجزء
+
+355
+00:35:45,160 --> 00:35:48,720
+الموضوع
+
+356
+00:35:48,720 --> 00:35:51,240
+هذا الـ section اللي انتهينا منه كان serious
+
+357
+00:35:51,240 --> 00:35:56,800
+solution near an ordinary point part one بدنا نيجي 
+
+358
+00:35:56,800 --> 00:35:59,140
+لـ section اللي بعده الـ section اللي بعده برضه
+
+359
+00:35:59,140 --> 00:36:03,880
+serious solution near an ordinary point part two
+
+360
+00:36:03,880 --> 00:36:06,100
+يبقى الجزء الثاني
+
+361
+00:36:34,050 --> 00:36:37,690
+حد أبيض أي كلمة من هنا اللي على اللوحة ده أمسح
+
+362
+00:36:58,660 --> 00:37:11,260
+يبقى section خمسة ثلاثة series solution near an
+
+363
+00:37:11,260 --> 00:37:19,040
+ordinary point part
+
+364
+00:37:19,040 --> 00:37:20,720
+two
+
+365
+00:37:28,670 --> 00:37:33,510
+الفكرة في هذه المقالة هي أن إذا كنا نشتغل شغل لو
+
+366
+00:37:33,510 --> 00:37:39,130
+روح نجيب شكل الـ an أو العلاقة بتربط من بين الـ an
+
+367
+00:37:39,130 --> 00:37:44,190
+و الـ an زائد واحد أو الـ an زائد اثنين و الـ an زائد واحد مع
+
+368
+00:37:44,190 --> 00:37:48,420
+الـ an هو ده كنا نسميها recurrence relation بنبطل
+
+369
+00:37:48,420 --> 00:37:52,720
+نجيب الـ reference relation لكن بدي أجيب صيغة أخرى
+
+370
+00:37:52,720 --> 00:37:59,800
+للـ an كيف هذا ما سنشير إليه الآن إن شاء الله بدنا
+
+371
+00:37:59,800 --> 00:38:02,660
+نُشير للمعادلة التفاضلية اللي بدأنا فيها المرة اللي
+
+372
+00:38:02,660 --> 00:38:07,200
+فاتت و اللي حلينا فيها الآن و بعدين بنشوف كيف بنجيب
+
+373
+00:38:07,200 --> 00:38:15,180
+الـ an يبقى بيقول y suppose that افترض أنه الـ
+
+374
+00:38:15,180 --> 00:38:16,500
+differential equation
+
+375
+00:38:21,770 --> 00:38:27,290
+المعادلة التفاضلية P of X في الـ Y double prime P
+
+376
+00:38:27,290 --> 00:38:29,510
+of X في الـ Y double prime P of X في الـ Y double
+
+377
+00:38:29,510 --> 00:38:30,310
+prime P of X في الـ Y double prime P of X في الـ Y
+
+378
+00:38:30,310 --> 00:38:32,630
+double prime P of X في الـ Y double prime P of X في
+
+379
+00:38:32,630 --> 00:38:38,530
+الـ Y double prime P of X في الـ Y double prime
+
+380
+00:38:44,330 --> 00:38:54,390
+هذه المعادلة لها حل على صيغة Y تساوي Phi of X and
+
+381
+00:38:54,390 --> 00:39:03,890
+that Phi of X has a Taylor series
+
+382
+00:39:10,600 --> 00:39:18,180
+متسلسلة تايلور اللي على الشكل التالي Y تساوي فاي of
+
+383
+00:39:18,180 --> 00:39:25,760
+X سم من N equal zero to infinity للـ A N في
+
+431
+00:44:17,620 --> 00:44:24,280
+الكلام بدي يعطينا five prime of the X node بدي أساعده
+
+432
+00:44:24,280 --> 00:44:29,640
+حط هنا X node بطير وكلهم شو بظل عنده يبقى هذه A1
+
+433
+00:44:29,640 --> 00:44:35,710
+طيب خلوا هذول عندك في الذاكرة بالزمن أن نرجع لهم
+
+434
+00:44:35,710 --> 00:44:42,930
+بعد قليل وبنواصل المشي تبعنا بدي أروح أجيب مين مشتقة
+
+435
+00:44:42,930 --> 00:44:50,730
+أ ثانية يبقى five w prime of x هذا مع السلامة هذا
+
+436
+00:44:50,730 --> 00:44:58,680
+بيبقى قداش اثنين اثنين بواحد يبقى هذا بيصير اثنين
+
+437
+00:44:58,680 --> 00:45:06,940
+في ثلاثة بستة ثلاثة x ناقص x node أس واحد زائد
+
+438
+00:45:06,940 --> 00:45:14,320
+ثلاثة في أربعة باثنا عشر أربعة في مين في ال x ناقص x
+
+439
+00:45:14,320 --> 00:45:21,560
+node الكل تربيع زائد إلى ما شاء الله اللي خاطر أعيد
+
+440
+00:45:21,560 --> 00:45:26,380
+صياغة هذا term مرة ثانية فبروح بقول هذا الكلام
+
+441
+00:45:26,380 --> 00:45:30,720
+يساوي اثنين هذه يا بنات مش بقدر أكتبها اثنين
+
+442
+00:45:30,720 --> 00:45:38,340
+factorial مضروب اثنين في اثنين يبقى هذا اثنين
+
+443
+00:45:38,340 --> 00:45:45,780
+factorial في اثنين طيب ايش ستة مضروب ثلاثة يبقى
+
+444
+00:45:45,780 --> 00:45:54,410
+هذا ثلاثة factorial ثلاثة في ال x ناقص ال x node
+
+445
+00:45:54,410 --> 00:46:00,930
+هذه لسه ما قدرتش خليكي مرتاحة شوية يبقى هذا الكلام
+
+446
+00:46:00,930 --> 00:46:08,590
+زائد اللي هو اثنا عشر أربعة x ناقص x node لكل تربيع
+
+447
+00:46:08,590 --> 00:46:16,450
+زائد إلى ما شاء الله طب لو بده أجيب المشتقة في w
+
+448
+00:46:16,450 --> 00:46:25,730
+prime of x node هذا كله بيروح بظل قداش بس يبقى هنا
+
+449
+00:46:25,730 --> 00:46:32,870
+لو بده أجيب في بابلي prime of x node يبقى النتيجة
+
+450
+00:46:32,870 --> 00:46:39,870
+2 factorial اثنين بس حط هنا x node ب 0 والباقي كله
+
+451
+00:46:39,870 --> 00:46:44,590
+بيروح مرة ثانية طيب ايش رأيك أن نجيب المشتقة
+
+452
+00:46:44,590 --> 00:46:50,650
+الثالثة؟ يبقى لو جبت المشتقة الثالثة as a function
+
+453
+00:46:50,650 --> 00:46:56,110
+of x يبقى ايش بتعطينا هذا مع السلامة وبيبقى لنا
+
+454
+00:46:56,110 --> 00:47:02,350
+مين؟ اللي هو الثلاثة factorial a ثلاثة بدي أشتق
+
+455
+00:47:02,350 --> 00:47:07,130
+هذه السلة هذه بتروح هذه ثلاثة factorial a ثلاثة
+
+456
+00:47:07,130 --> 00:47:10,990
+هذه ايش بيصير؟ نفس اتماشي بأربعة وعشرين الهمين
+
+457
+00:47:11,760 --> 00:47:18,620
+أربعة factorial أربعة يبقى زائد أربعة factorial
+
+458
+00:47:18,620 --> 00:47:28,200
+أربعة بظل معنا أن ال x ناقص ال x node أس واحد زائد
+
+459
+00:47:28,200 --> 00:47:29,980
+إلى آخره
+
+460
+00:47:32,430 --> 00:47:39,110
+طيب، هذه مش بتعطيني يا بنات، كمان المشتقة الرقم
+
+461
+00:47:39,110 --> 00:47:44,610
+ثلاثة عند ال x node قد ايش تساوي؟ ثلاثة factorial
+
+462
+00:47:44,610 --> 00:47:49,750
+a ثلاثة ثلاثة factorial a ثلاثة
+
+463
+00:47:52,290 --> 00:47:59,130
+طب لو ضليت مستمرة عليها الشكل هذه بوصل
+
+464
+00:47:59,130 --> 00:48:06,570
+للمشتقة رقم m مثلا يبقى لو ضليت مستمرة هوصل للمشتقة
+
+465
+00:48:06,570 --> 00:48:15,470
+رقم m عند ال x هشوف قداش تساوي طلع يا ابنك المشتقة
+
+466
+00:48:15,470 --> 00:48:22,780
+الثانية يبقى 2 factorial ايه اثنين؟ زائد ثلاثة
+
+467
+00:48:22,780 --> 00:48:27,540
+factorial أكبر منها ب ثلاثة في x ناقص x node
+
+468
+00:48:27,540 --> 00:48:34,200
+زائد طيب لو جت المشتقة الثالثة ثلاثة factorial a
+
+469
+00:48:34,200 --> 00:48:40,280
+ثلاثة أربعة factorial ها x ناقص x node x واحد
+
+470
+00:48:40,280 --> 00:48:45,660
+زائد إلى آخره يبقى أنا بدي أروح أعّمم هذه وأقول لو
+
+471
+00:48:45,660 --> 00:48:54,960
+وصلت لمشتقة رقم m ثلاثة ثلاثة ثلاثة ثلاثة
+
+472
+00:48:54,960 --> 00:48:57,580
+ثلاثة ثلاثة ثلاثة ثلاثة ثلاثة ثلاثة ثلاثة ثلاثة
+
+473
+00:48:57,580 --> 00:48:57,660
+ثلاثة ثلاثة ثلاثة ثلاثة ثلاثة ثلاثة ثلاثة ثلاثة
+
+474
+00:48:57,660 --> 00:49:01,080
+ثلاثة ثلاثة ثلاثة ثلاثة ثلاثة ثلاثة ثلاثة ثلاثة
+
+475
+00:49:01,080 --> 00:49:03,700
+ثلاثة ثلاثة ثلاثة ثلاثة ثلاثة ثلاثة ثلاثة ثلاثة
+
+476
+00:49:03,700 --> 00:49:06,760
+ثلاثة
+
+477
+00:49:06,760 --> 00:49:06,780
+ثلاثة ثلاثة ثلاثة ثلاثة ثلاثة ثلاثة ثلاثة ثلاثة
+
+478
+00:49:06,780 --> 00:49:11,360
+ثلاثة ثلاثة ثلاثة
+
+479
+00:49:12,280 --> 00:49:16,920
+يبقى ايش بيكون m زائد واحد factorial في m في m
+
+480
+00:49:16,920 --> 00:49:20,820
+ناقص واحد في m ناقص اثنين لغاية ما نوصل لثلاثة في
+
+481
+00:49:20,820 --> 00:49:27,440
+اثنين في واحد يبقى زائد ه اللي هو ال m زائد واحد
+
+482
+00:49:27,440 --> 00:49:34,320
+في ال m في ال m ناقص واحد في ال m ناقص اثنين ونظل
+
+483
+00:49:34,320 --> 00:49:40,430
+ماشي لغاية ما نوصل للاثنين في واحد يبقى هذا من ال
+
+484
+00:49:40,430 --> 00:49:44,050
+factorial اللي كتبته لسه ال factorial بيجينا هد
+
+485
+00:49:44,050 --> 00:49:50,990
+مين؟ a m زائد واحد لأنه أكبر منه بواحد فاهمين؟ في
+
+486
+00:49:50,990 --> 00:50:05,190
+ال a m زائد واحد فاهمين؟ في ال x ناقص x node زائد
+
+487
+00:50:05,190 --> 00:50:06,810
+إلى ما شاء الله
+
+488
+00:50:11,590 --> 00:50:17,910
+بناء عليه لو جت تقول في to the derivative m عند
+
+489
+00:50:17,910 --> 00:50:18,570
+ال x
+
+490
+00:50:21,210 --> 00:50:26,530
+ال m factorial في ال a m وهذا بروح لكم لو قداش
+
+491
+00:50:26,530 --> 00:50:33,530
+بصفر طب أنا بدي أوصل ل a n فباجي بقوله بكل بساطة
+
+492
+00:50:33,530 --> 00:50:41,030
+لو وصلت للمشتقة رقم n عند ال x node بده يساوي n
+
+493
+00:50:41,030 --> 00:50:48,830
+factorial في ال a n صحيح ولا لأ؟ يبقى هذه الصيغة
+
+494
+00:50:48,830 --> 00:50:53,370
+تبعنا ليها تحت الوضع بدي a n لحالها بقوله بسيطة
+
+495
+00:50:53,370 --> 00:50:59,790
+يبقى هذا بدي يعطينا أن a n بدي يساوي المشتقة رقم n
+
+496
+00:50:59,790 --> 00:51:07,040
+عند ال ordinary point x node على n factorial هذه
+
+497
+00:51:07,040 --> 00:51:17,470
+لاثنين أرض نفس الشيء يبقى هذه لو factorial طيب هيك
+
+498
+00:51:17,470 --> 00:51:22,970
+أنا جبت له مين؟ جبت له المشتقة جبت له a n بدلالة
+
+499
+00:51:22,970 --> 00:51:27,870
+المشتقة النونية للحل اللي هو مين؟ اللي هو five لكن
+
+500
+00:51:27,870 --> 00:51:32,170
+هنا بعد ما كنا نجيب ال recurrence relation روح
+
+501
+00:51:32,170 --> 00:51:39,410
+تواصل الحل وجيب الحل بدلالة a node و a one مظبوط؟
+
+502
+00:51:39,410 --> 00:51:44,280
+شكله غير مسوء المثال اللي جابني شوية يبقى أنا بدي أروح
+
+503
+00:51:44,280 --> 00:51:49,220
+أجيب ال a n بدلالة ال a node و ال a one وإذا
+
+504
+00:51:49,220 --> 00:51:54,480
+جبتهم بكون خلصت ماشي يبقى الآن بدأ نكتب الكلمتين
+
+505
+00:51:54,480 --> 00:51:58,980
+والاثنين هذول سمي لي هذه رقم اثنين الصيغة هذه أو
+
+506
+00:51:58,980 --> 00:52:05,120
+هذه سميها رقم اثنين أكتب
+
+507
+00:52:05,120 --> 00:52:08,340
+now we shall
+
+508
+00:52:13,700 --> 00:52:22,840
+write an in terms
+
+509
+00:52:22,840 --> 00:52:36,580
+of a node and a one as follows يبقى كتالي since
+
+510
+00:52:40,720 --> 00:52:46,100
+is a solution
+
+511
+00:52:46,100 --> 00:53:04,480
+of the differential equation when we have طلعيني
+
+512
+00:53:04,480 --> 00:53:11,600
+كويس احنا فرضنا أن phi of x هي حل المعادلة التفاضلية
+
+513
+00:53:11,600 --> 00:53:15,160
+إذا المعادلة التفاضلية رقم واحد بقدر أكتبها على
+
+514
+00:53:15,160 --> 00:53:20,540
+الشكل التالي بقدر أشيل كل y وأكتب phi of
+
+515
+00:53:20,540 --> 00:53:28,000
+x لأنها تحققها يصبح يصير أن p of x في phi prime
+
+516
+00:53:28,000 --> 00:53:28,740
+of x
+
+517
+00:53:50,100 --> 00:53:57,610
+ممكن أجسم كله على capital p of x بيصير ال phi w
+
+518
+00:53:57,610 --> 00:54:06,210
+prime of x زائد p small of x في ال phi prime of x
+
+519
+00:54:06,210 --> 00:54:12,970
+زائد ل q small of x في ال phi of x بده يساوي صفر
+
+520
+00:54:12,970 --> 00:54:23,720
+where حيث ال p of x small هي عبارة عن ل q of x على
+
+521
+00:54:23,720 --> 00:54:32,740
+capital p of x and ل q of x هي عبارة عن r of x
+
+522
+00:54:32,740 --> 00:54:38,100
+capital على capital p of x وهذول are analytic
+
+523
+00:54:38,100 --> 00:54:39,320
+functions
+
+524
+00:54:50,060 --> 00:54:55,560
+يبقى دول تحليلات بقدر أكتبهم على شكل تايلور سيريز
+
+525
+00:54:55,560 --> 00:55:03,620
+يبقى ال phi ممكن أعيد كتابة المعادلة هذه مرة ثانية
+
+526
+00:55:03,620 --> 00:55:09,440
+وأروح أقول five w prime of x ببدأ يساوي only هذول
+
+527
+00:55:09,440 --> 00:55:12,500
+على الشجة الثانية يبقى بيصير سالب
+
+528
+00:55:28,850 --> 00:55:35,970
+من فوق بالزمن المشتقة عند من عند ال ordinary point
+
+529
+00:55:35,970 --> 00:55:42,600
+x0 إذا بناء عليها بقدر أحسب هذه عند ال x0 يبقى باجي
+
+530
+00:55:42,600 --> 00:55:47,780
+بقوله هذه سميها للمعادلة رقم ثلاثة منها لأن هذه
+
+531
+00:55:47,780 --> 00:55:52,860
+أساسية عندنا الآن ايش رأيك؟ بدأ أكتب هذه الآن
+
+532
+00:55:52,860 --> 00:55:58,860
+بدلالة a0 و a1 إذا بروح أعوض في phi عند ال
+
+533
+00:55:58,860 --> 00:56:04,560
+ordinary point ل x0 يبقى بيصير عندنا phi w prime of
+
+534
+00:56:04,560 --> 00:56:12,090
+x0 يساوي ناقص p of x node في ال phi prime of x
+
+535
+00:56:12,090 --> 00:56:18,950
+node ناقص ل q of x node في ال phi of x node و
+
+536
+00:56:18,950 --> 00:56:27,310
+يساوي طب قداش ال phi prime of x node one
+
+537
+00:56:27,310 --> 00:56:35,520
+يبقى بقدر أشيل وأكتب بدالها مين يبقى هنا ناقص p of x
+
+538
+00:56:35,520 --> 00:56:44,760
+node في ال a1 تمام؟ وهنا ناقص ل q of x node في ال
+
+539
+00:56:44,760 --> 00:56:48,980
+phi of x node phi of x node اللي هي قداش؟ a node
+
+540
+00:56:48,980 --> 00:56:55,420
+يبقى هنا في ال a node يبقى بناء عليه كتابة phi w
+
+541
+00:56:55,420 --> 00:57:09,220
+prime بدل من a node أو x node بدل من a node أو
+
+542
+00:57:09,220 --> 00:57:21,600
+اثنين
+
+543
+00:57:21,990 --> 00:57:25,730
+طيب ايش رأيك الآن بدي أروح أجيب كمان المشتقة
+
+544
+00:57:25,730 --> 00:57:31,670
+الثالثة والرابعة والخامسة كله بدلالة a node و a1
+
+545
+00:57:31,670 --> 00:57:37,270
+يبقى بدي أجي على الاثنين هذه شو أعملها بدي أشتقها
+
+546
+00:57:37,270 --> 00:57:44,310
+كمان مرة يبقى باجي بقوله five triple prime of x
+
+547
+00:57:44,310 --> 00:57:51,560
+أوه هذه يا عزيزي لأن كلها مشتقة حصل ضرب دالتين يبقى
+
+548
+00:57:51,560 --> 00:57:57,960
+بدي أكتبها باختصار يبقى سالب p في ال fi w prime
+
+549
+00:57:57,960 --> 00:58:03,840
+سالب p prime في ال fi prime هاي اشتقينا ال term
+
+550
+00:58:03,840 --> 00:58:10,700
+الأول بدي أجي ل term الثاني سالب q في ال fi prime
+
+551
+00:58:10,700 --> 00:58:20,280
+سالب q prime في ال fi زي ما هي طيب شو رأيك هذه و
+
+552
+00:58:20,280 --> 00:58:25,500
+هذه؟ مش كلهم مضروبات في ال fi prime إذا ما بقدر
+
+553
+00:58:25,500 --> 00:58:33,220
+آخذهم مين مع بعض يبقى هذا الكلام بده يساوي سالب p
+
+554
+00:58:33,220 --> 00:58:41,540
+في ال fi double prime سالب وهي goes بظهر p prime
+
+555
+00:58:43,330 --> 00:58:53,370
+ال q كله في مين؟ في ال phi a' سالب a q' في مين؟ في
+
+556
+00:58:53,370 --> 00:58:58,430
+ال phi بتفهم أن هذه function في x وهذه function في
+
+557
+00:58:58,430 --> 00:59:04,590
+x وهذه function في x وكله functions of x تمام؟ إذا
+
+558
+00:59:04,590 --> 00:59:10,100
+بقدر أحسب المشتقة الثانية هذه وين؟ عند ال x node
+
+559
+00:59:10,100 --> 00:59:15,740
+يبقى بروح بقوله يبقى phi triple prime عند ال x
+
+560
+00:59:15,740 --> 00:59:25,140
+node يساوي ناقص p of x node مين هذه؟ phi double
+
+561
+00:59:25,140 --> 00:59:31,560
+prime of x node موجودة؟ هيها فوق إذا بقدر أجيبها
+
+562
+00:59:31,560 --> 00:59:37,960
+من فوق ونزلها هيها يبقى هذه بيصير في مين؟ في سالب
+
+563
+00:59:37,960 --> 00:59:47,680
+p of x node في ال a1 سالب eq of x node في ال a0
+
+564
+00:59:51,170 --> 00:59:56,730
+طيب خلص لسه ال term الأول بدي أجي لل term الثاني
+
+565
+00:59:56,730 --> 01:00:07,750
+ناقص p prime of x node of x node زائد ل q of x
+
+566
+01:00:07,750 --> 01:00:14,130
+node كله في من؟ في ال phi prime phi prime of x node
+
+567
+01:00:14,130 --> 01:00:19,790
+phi prime of x node اللي هو كده؟ a1 يبقى هذا كله
+
+568
+01:00:19,790 --> 01:00:26,170
+في ال a1 ناقص iq prime of x node في ال phi of
+
+569
+01:00:26,170 --> 01:00:33,840
+x node اللي هو كده؟ a0 وهي كتبنا المشتقة
+
+570
+01:00:33,840 --> 01:00:40,100
+الثالثة عند x node ليس بدلالة ال a3 وإنما بدلالة ال
+
+571
+01:00:40,100 --> 01:00:46,980
+a0 و a1 بنفس الطريقة نشتغل نفس الشغل
+
+572
+01:01:05,640 --> 01:01:13,300
+يبقى هنا so we write روحنا كتبنا five triple a
+
+573
+01:01:13,300 --> 01:01:23,280
+prime of x node in terms of a node and a one
+
+574
+01:01:23,280 --> 01:01:27,300
+similarly بنفس الطريقة
+
+575
+01:01:30,190 --> 01:01:39,430
+Similarly, we can write نصاتية كتابة المشتقة
+
+576
+01:01:39,430 --> 01:01:46,290
+الرابعة عند ال x node والمشتقة الخامسة عند ال x
+
+577
+01:01:46,290 --> 01:01:56,270
+node  و و و إلى آخره in terms of هو بنقدر نقول كتبنا
+
+578
+01:01:56,270 --> 01:02:04,930
+ال a n a similarly we can write in terms of ..
+
+579
+01:02:04,930 --> 01:02:15,330
+استني شوية استني شوية that is that is
+
+580
+01:02:15,330 --> 01:02:30,520
+we write we write كتبنا a n in terms of اللي هو a
+
+581
+01:02:30,520 --> 01:02:39,600
+naught and a one ليش؟ لأن هنا لو قلنا المشتقة
+
+582
+01:02:39,600 --> 01:02:44,120
+الثانية يبقى اثنين factorial a n يبقى بيصير هذه
+
+583
+01:02:44,120 --> 01:02:49,500
+مجسومة على اثنين هي يبقى هاي اثنين ثلاثة أربعة
+
+584
+01:02:49,500 --> 01:02:59,060
+هكذا كتبناها بدلالة ثانية طيب similarly we
+
+585
+01:02:59,060 --> 01:03:00,980
+can
+
+586
+01:03:04,200 --> 01:03:10,580
+right similarly we can هذه كتبنا a ثلاثة يا بنات
+
+587
+01:03:10,580 --> 01:03:15,800
+مش أكثر يبقى a ثلاثة بدلالة انه ليش؟ لأن جه
+
+588
+01:03:15,800 --> 01:03:20,700
+المشتقة هادي هادي بناء عليه تبقى a ثلاثة يساوي
+
+589
+01:03:20,700 --> 01:03:25,800
+المشتقة الثالثة على ثلاثة factorial مظبوط؟ يبقى هنا
+
+590
+01:03:25,800 --> 01:03:29,920
+بقدر أقول كتبنا a ثلاثة in terms similarly we
+
+591
+01:03:29,920 --> 01:03:31,380
+can write
+
+592
+01:03:34,560 --> 01:03:41,120
+in terms of
+
+593
+01:03:41,120 --> 01:03:55,180
+in terms of الحمد لله and a one طيب
+
+594
+01:03:55,180 --> 01:03:59,720
+ده رجع الكلام هذا فقط مشان بس يثبت المعنى احنا
+
+595
+01:03:59,720 --> 01:04:03,900
+خلصنا بس مشان نثبت المعلومات وبعد كده بناخد أمثلة
+
+596
+01:04:03,900 --> 01:04:09,560
+مشان نشوف كيف بدنا نطبق هذا الكلام اللي قلناه احنا
+
+597
+01:04:09,560 --> 01:04:15,260
+وصلنا إلى هذه الصيغة تمام وسمينا وصلنا ل ال main
+
+598
+01:04:15,260 --> 01:04:18,560
+معادلة هذه وروحنا كتبناها في الصيغة اللي عندنا هي
+
+599
+01:04:18,560 --> 01:04:20,720
+رقم ثلاثة
+
+600
+01:04:23,910 --> 01:04:29,090
+قلنا نذهب ونحسب المشتقة الثانية عند ال point
+
+601
+01:04:29,090 --> 01:04:34,130
+ordinary يبقى شيلنا كل x وكتبنا بدلها x node
+
+602
+01:04:34,130 --> 01:04:38,570
+صارت هنا ناقص p of x node في prime of x node ناقص
+
+603
+01:04:38,570 --> 01:04:42,250
+q of x node في prime of x node الآن شيلنا five
+
+604
+01:04:42,250 --> 01:04:45,170
+prime of x node وحطينا قيمتها اللي طلعناها قبل
+
+605
+01:04:45,170 --> 01:04:49,130
+قليل a1 وشيلنا five of x node وطلعنا قيمتها اللي
+
+606
+01:04:49,130 --> 01:04:54,130
+هي main a node يبقى صار هذه قيمة المشتقة الثانية
+
+607
+01:04:
+
+646
+01:09:07,600 --> 01:09:11,660
+في تربله prime of one و المشتق الرابع برضه under
+
+647
+01:09:11,660 --> 01:09:15,690
+one و الله يعطيك العافية بدنا قيم عددية من خلال الـ
+
+648
+01:09:15,690 --> 01:09:20,150
+initial conditions اللي عندك نقوله بسيطة خلاص بدنا
+
+649
+01:09:20,150 --> 01:09:23,890
+نيجي لكلام اللي أنا بقى بطل على المعادلة اللي عندي
+
+650
+01:09:23,890 --> 01:09:27,710
+المعادلة X ترميها YW prime دالة في Y prime دالة في
+
+651
+01:09:27,710 --> 01:09:33,930
+Y يبقى هنا المعامل هو احنا بنشتغل روحنا جسمنا على
+
+652
+01:09:33,930 --> 01:09:38,330
+capital P of X مش عارف ده على دهرة لأ المساحات على
+
+653
+01:09:38,330 --> 01:09:42,190
+أي حال إذا لما نيجي نشتغل الشغل هاد يا بنات بديك
+
+654
+01:09:42,190 --> 01:09:47,410
+تروح أتي جسمي على المعامل تبع YWY حتى وإن كان رقم
+
+655
+01:09:47,650 --> 01:09:51,210
+بدي أقسم عليه بحيث أخلي المعامل دائما أو أبدا هو
+
+656
+01:09:51,210 --> 01:09:55,690
+main واحد صحيح يبقى المعادلة دي بصير على الشكل
+
+657
+01:09:55,690 --> 01:10:02,090
+التالي y double prime زائد واحد زائد x على x
+
+658
+01:10:02,090 --> 01:10:11,510
+تربية في ال y prime زائد تلاتة لن ال x على x
+
+659
+01:10:11,510 --> 01:10:19,330
+تربية كله في ال y بده يساوي zero تمام، إذا هذا بده
+
+660
+01:10:19,330 --> 01:10:26,690
+يعطي كمين إن ال P of X يساوي، إيش رأيك؟ واحد على X
+
+661
+01:10:26,690 --> 01:10:31,150
+تربية، مش عبارة عن X نقص اثنين؟ أسهل اللي في الشغل
+
+662
+01:10:31,150 --> 01:10:37,090
+يبقى باجي بقوله هذه X ناقص اثنين X على X تربيع بضل
+
+663
+01:10:37,090 --> 01:10:43,490
+واحد على X يعني X أس سالب واحد زائد X أس سالب واحد
+
+664
+01:10:43,490 --> 01:10:52,570
+يبقى أنا كتبت ال P of X في ثوب جديد وال Q of X
+
+665
+01:10:52,570 --> 01:10:57,120
+بذاسر خليها زي ما هي مش مشكلة تمام؟ لأن إذا طلعتها
+
+666
+01:10:57,120 --> 01:11:02,600
+فوق بيصير x أس ناقص اثنين تمام؟ بدك تطلعها فوق
+
+667
+01:11:02,600 --> 01:11:06,660
+بنتطلعها فوق بنتريها بيصير x ناقص اثنين لن ال x و
+
+668
+01:11:06,660 --> 01:11:10,520
+ايه الحساب بيصير؟ لمش تقعد حصل ضرب دلتين بزهجني
+
+669
+01:11:10,520 --> 01:11:14,180
+شوية لو كانت خارج قسم الدلتين بس حصل ضرب سلي، إذا
+
+670
+01:11:14,180 --> 01:11:21,850
+بقدر أقول هذه التلاتة x أس ناقص اثنين لن ال x طب
+
+671
+01:11:21,850 --> 01:11:28,350
+ليش سويتك؟ آه بقولك ليش سويتك؟ هنا لازم ل بعد شوية
+
+672
+01:11:28,350 --> 01:11:34,250
+بلزم ل من؟ بلزم ل P prime و Q prime و P double
+
+673
+01:11:34,250 --> 01:11:38,950
+prime و Q .. إذا بلزم ل الشغلات هذه إذا قبل مشتغل
+
+674
+01:11:38,950 --> 01:11:43,470
+ولا شغل بنروح نحسب قداش قيمة كل واحدة من هدول قبل
+
+675
+01:11:43,470 --> 01:11:49,950
+المبدأ طبعا بقوله كويس إذا أنا لو جيت قولتله ال P
+
+676
+01:11:49,950 --> 01:11:56,430
+prime of X بدي أشتقها يبقى ناقص اثنين X أس ناقص
+
+677
+01:11:56,430 --> 01:12:06,410
+تلاتة ناقص X أس ناقص اثنين طبعا لو بدي PW prime as
+
+678
+01:12:06,410 --> 01:12:12,690
+a function of X يبقى إيش بصير عندي هنا ستة اكس اص
+
+679
+01:12:12,690 --> 01:12:19,510
+ناقص أربعة زيدي اثنين اكس اص ناقص تلاتة أظن مش
+
+680
+01:12:19,510 --> 01:12:24,570
+هيلزمني أكثر من هيك المشتقة التالتة فيها المشتقة
+
+681
+01:12:24,570 --> 01:12:27,790
+الأولى فقط يبقى لو جيبنا الرابع بيجيب المشتقة
+
+682
+01:12:27,790 --> 01:12:32,180
+الثاني ويمكفها الله يعطيك العافية يبقى بناء عليه لو
+
+683
+01:12:32,180 --> 01:12:36,840
+بدي أحسبه P of 1 لأنه ليش ال condition المحسبات
+
+684
+01:12:36,840 --> 01:12:42,000
+عند ال one إيش بدي يكون هنا بناه واحد زائد واحد
+
+685
+01:12:42,000 --> 01:12:47,000
+مظبوط يبقى اللي هو اثنين يبقى P of one بدي يساوي
+
+686
+01:12:47,000 --> 01:12:52,760
+اثنين بدي ال P prime of one يبقى هذا واحد ما بصير
+
+687
+01:12:52,760 --> 01:12:57,440
+سالب اثنين سالب واحد اللي هو قداش سالب تلاتة بدي
+
+688
+01:12:57,440 --> 01:13:03,080
+ال P double prime of one يبقى ستة زائد اثنين اللي
+
+689
+01:13:03,080 --> 01:13:08,960
+هو قداش ثمانية سيب المعلومات هذه بدنا نروح لمين
+
+690
+01:13:08,960 --> 01:13:15,800
+للي Q يبقى بدي أشتقها يبقى بدي ل Q prime of X هذه
+
+691
+01:13:15,800 --> 01:13:22,630
+مشتقة حاصل ضرب دالة تانية يبقى دالة الأولى في ناقص
+
+692
+01:13:22,630 --> 01:13:28,490
+اثنين في مشتقة الدالة الثانية اللي همين واحد على X
+
+693
+01:13:28,490 --> 01:13:39,550
+ناقص ستة X أس ناقص تلاتة ناقص طبعا ستة X أس ناقص
+
+694
+01:13:39,550 --> 01:13:46,530
+تلاتة في لن ال X يعني هذا إيش بيصير؟ بيصير تلاتة
+
+695
+01:13:46,530 --> 01:13:51,730
+اكس اص ناقص تلاتة طلعتها فوق بيصير بإشارة سالب
+
+696
+01:13:51,730 --> 01:14:01,370
+وهنا ناقص اللي هو ستة اكس اص ناقص تلاتة في لن ال X
+
+697
+01:14:02,090 --> 01:14:07,090
+هنجيب المشتقة الثانية يبقى المشتقة ثانية q double
+
+698
+01:14:07,090 --> 01:14:16,430
+prime of x يبقى بالصيرة ناقص تسعة x أس ناقص أربعة
+
+699
+01:14:16,430 --> 01:14:22,910
+اللي بعدها مشتقة حاصل ضارب دالتين يبقى ناقص ستة x
+
+700
+01:14:22,910 --> 01:14:29,570
+أس ناقص تلاتة في واحد على x ناقص فناقص بزايد ستة
+
+701
+01:14:29,570 --> 01:14:40,930
+في تلاتة ثمانتاشرx²-4x²-4
+
+702
+01:14:40,930 --> 01:14:44,570
+-15
+
+703
+01:14:44,570 --> 01:14:48,530
+-15x²
+
+704
+01:14:48,530 --> 01:14:49,690
+-4
+
+705
+01:15:02,380 --> 01:15:09,700
+إذا ما بقدر أجيب له اكيو of one تعالى شوفي بدل من
+
+706
+01:15:09,700 --> 01:15:15,140
+الواحد بقداش بصفر في أي رقم بصفر يبقى ب zero مع
+
+707
+01:15:15,140 --> 01:15:20,100
+السلامة غير مأسوف عليك اكيو prime of one وايه ال
+
+708
+01:15:20,100 --> 01:15:26,880
+اكيو prime هاي ب one بطلع هنا تلاتة وهذا ب zero مع
+
+709
+01:15:26,880 --> 01:15:34,240
+السلامة يبقى تلاتة يساوي تلاتة الآن بدنا لـ q
+
+710
+01:15:34,240 --> 01:15:42,660
+double prime of one لأن الواحد بزير و بطير يبقى
+
+711
+01:15:42,660 --> 01:15:49,910
+فضل قداش سالب خمسة عشر يساوي سالب خمسة عشر طيب خلّي هذه
+
+712
+01:15:49,910 --> 01:15:55,890
+المعلومات جاهزة يعني هذه وين ما لزمتل الآن بدي
+
+713
+01:15:55,890 --> 01:16:02,810
+أبدأ آخد منها و أعوّض و هذه زيها كمان بنفس الطريقة
+
+714
+01:16:02,810 --> 01:16:08,050
+طيب نبدأ في مسألتنا يبقى قال لي أول شغلة بده مين
+
+715
+01:16:08,050 --> 01:16:13,210
+بده five double prime of one وين five double prime
+
+716
+01:16:13,210 --> 01:16:17,720
+of x هي يبقى هذه المعادلة الأساسية اللي بدأ أبدأ
+
+717
+01:16:17,720 --> 01:16:23,180
+أشتغل بها
+
+718
+01:16:23,180 --> 01:16:36,120
+يبقى
+
+719
+01:16:36,120 --> 01:16:44,850
+بروح أقول we know that we know احنا بنعرف أن الـ
+
+720
+01:16:44,850 --> 01:16:55,470
+Phi W' of X يساوي ناقص P of X في Phi' of X ناقص ل
+
+721
+01:16:55,470 --> 01:17:02,870
+Q of X ناقص في Phi of X هذه اللي كنا نسميها
+
+722
+01:17:02,870 --> 01:17:08,370
+المعادلة رقم قداش تلاتة يبقى هذه تلاتة وليست اثنين
+
+723
+01:17:09,590 --> 01:17:20,970
+إذا لتحت هذا كله بدنا نمسحه ما لهوش لزوم طيب
+
+724
+01:17:20,970 --> 01:17:24,990
+إيه شرايك من المعادلة هذه بقدر أجيب المطلوب الأول
+
+725
+01:17:24,990 --> 01:17:30,330
+صح يبقى بدي أحسب هذا المقدار عند مين عند النقطة
+
+726
+01:17:30,330 --> 01:17:35,350
+واحدة هو five double prime of one يبقى باجي بقوله
+
+727
+01:17:35,350 --> 01:17:42,350
+في دابلة prime of one بده يساوي ناقص P of one فيه
+
+728
+01:17:42,350 --> 01:17:49,590
+prime of one ناقص Q of one في ال في of one ويساوي
+
+729
+01:17:49,590 --> 01:17:55,530
+ال P of one يبقى كده شبنات باثنين يبقى هاي سالب
+
+730
+01:17:55,530 --> 01:18:01,200
+قبلها يبقى هاي سالب باثنين ال Phi prime of one
+
+731
+01:18:01,200 --> 01:18:06,520
+طلع لي هذا مش Y عبارة عن حل هو Phi يبقى Y prime of
+
+732
+01:18:06,520 --> 01:18:11,760
+one بقداش ب Zero جبتم ال initial condition يبقى في
+
+733
+01:18:11,760 --> 01:18:17,840
+Zero ناقص ال Q of one اللي هو Zero يبقى هاي Zero
+
+734
+01:18:17,840 --> 01:18:23,920
+في ال Phi of one Phi of one هايها اللي هو بقداش
+
+735
+01:18:23,920 --> 01:18:33,500
+باثنين يبقى في اثنين يبقى الحمد لله بقداش ريحنا بده
+
+736
+01:18:33,500 --> 01:18:37,560
+أجيب المشتقة التالتة عند الواحد إذا بده أجي على
+
+737
+01:18:37,560 --> 01:18:43,260
+الاثنين شو أعملها بده أشتقها يبقى بده أجي للي فوق
+
+738
+01:18:43,260 --> 01:18:50,500
+هادي هيك و اروح أشتقها في triple prime of x يبقى بدي
+
+739
+01:18:50,500 --> 01:18:56,460
+أختصر يا بنات يبقى ناقص P في ال Phi W Prime ناقص
+
+740
+01:18:56,460 --> 01:19:02,240
+P Prime في ال Phi Prime هذا ال term الأول ناقص Q
+
+741
+01:19:02,240 --> 01:19:09,480
+في ال Phi Prime ناقص Q Prime في ال Phi زي ما هي
+
+742
+01:19:09,480 --> 01:19:16,200
+بدي أحسب هذا عند الواحد يبقى بصير Phi Triple Prime
+
+743
+01:19:16,200 --> 01:19:23,300
+عند الواحد ناقص P of واحد في W prime of واحد ناقص P
+
+744
+01:19:23,300 --> 01:19:30,880
+prime of واحد في F prime of واحد ناقص Q of واحد في
+
+745
+01:19:30,880 --> 01:19:38,020
+F prime of واحد ناقص Q prime of واحد في F prime of
+
+746
+01:19:38,020 --> 01:19:42,220
+واحد ناقص
+
+747
+01:19:42,220 --> 01:19:50,550
+P1 يبقى هاي ناقص اثنين five double prime of one هاي
+
+748
+01:19:50,550 --> 01:19:56,590
+اللي أوجدناها فوق من البداية بقداش ب zero يبقى هاي
+
+749
+01:19:56,590 --> 01:20:03,220
+zero نقص P' of one P' of one اللي هي سالب تلاتة
+
+750
+01:20:03,220 --> 01:20:10,360
+يبقى سالب لسالب تلاتة five prime of one اللي هو
+
+751
+01:20:10,360 --> 01:20:19,220
+مقداش ب zero يبقى هذا كمان ب zero نقص Q of one ل Q
+
+752
+01:20:19,220 --> 01:20:24,710
+of one اللي هو ب zero ال Q of 1 بـ 0 فايه Prime of
+
+753
+01:20:24,710 --> 01:20:31,410
+1 فايه Prime of 1 كمان بـ 0 ناقص ال Q Prime of 1
+
+754
+01:20:31,410 --> 01:20:36,810
+اللي هو قداش تلاتة يبقى ناقص تلاتة في ال Phi 1
+
+755
+01:20:36,810 --> 01:20:48,020
+اللي هو قداش 2 0 0 0 يبقى الجواب قداش سالب ستة كمان
+
+756
+01:20:48,020 --> 01:20:53,040
+طيب قال لي هات المشتقة الرابعة إذا بده أجي على هذه
+
+757
+01:20:53,040 --> 01:20:58,900
+اللي اشتقتها و أشتقها كمان إيه كمان مرة يبقى بده
+
+758
+01:20:58,900 --> 01:21:05,320
+أجيب له المشتقة الرابعة as a function of X برضه
+
+759
+01:21:05,320 --> 01:21:10,240
+اختصار بديش أكتب ال X's للسولة هذه المشتقة اتحصل
+
+760
+01:21:10,240 --> 01:21:15,320
+دور بدلتين يبقى ناقص P في ال Phi Tripoli Prime
+
+761
+01:21:15,640 --> 01:21:23,820
+ناقص P' Phi W' خلصنا منها اللي بعدها ناقص P' Phi
+
+762
+01:21:23,820 --> 01:21:33,160
+W' ناقص P W' Phi' خلصنا منها اللي بعدها ناقص Q Phi
+
+763
+01:21:33,160 --> 01:21:43,720
+W' نقص Q' في قلصنا منها اللي بعدها نقص Q' في قلصنا
+
+764
+01:21:43,720 --> 01:21:50,060
+منها نقص Q'' في قلصنا منها اللي بعدها نقص Q' في
+
+765
+01:21:50,060 --> 01:21:53,720
+بعدها نقص Q'' في قلصنا منها اللي بعدها نقص Q'' في
+
+766
+01:21:53,720 --> 01:21:53,780
+قلصنا منها اللي بعدها نقص Q'' في قلصنا منها اللي
+
+767
+01:21:53,780 --> 01:21:57,160
+بعدها نقص Q'' في قلصنا منها اللي بعدها نقص Q'' في
+
+768
+01:21:57,160 --> 01:22:01,240
+قلصنا منها اللي بعدها نقص بتروح تدور ناقص P of one
+
+769
+01:22:01,240 --> 01:22:07,480
+P of one اللي هو قداش باثنين يبقى هاي ناقص اثنين
+
+770
+01:22:07,480 --> 01:22:11,440
+المشتقة التالتة عند الواحد هي جاهزة اللي هي قداش
+
+771
+01:22:11,440 --> 01:22:18,380
+سالب ستة والله رايحتنا هذه اللي بعدها ناقص P prime
+
+772
+01:22:18,380 --> 01:22:24,390
+of one P prime of one اللي هي قداش سالب تلاتة يبقى
+
+773
+01:22:24,390 --> 01:22:31,770
+هاي سالب تلاتة ال five double prime زيرو الله يسهل
+
+774
+01:22:31,770 --> 01:22:37,330
+عليها يبقى هاي زيرو خلصنا أول two terms نجي ال
+
+775
+01:22:37,330 --> 01:22:42,550
+term التالت ناقص P prime of one P prime of one
+
+776
+01:22:42,550 --> 01:22:47,630
+اللي هو بقداش بسالب تلاتة يبقى هاي سالب تلاتة ال
+
+777
+01:22:47,630 --> 01:22:53,000
+five double prime اللي هو بزيرو ريعتنا نقص ال PW
+
+778
+01:22:53,000 --> 01:23:00,560
+prime ال PW prime هو 8 نقص 8 في ال Phi prime
+
+779
+01:23:00,560 --> 01:23:09,080
+ال Phi prime هو 0 يبقى هنا بـ 0 نقص ال Q of 1 ال Q
+
+780
+01:23:09,080 --> 01:23:15,460
+of 1 هو 0 يبقى هذه 0 في 0 في ال Phi W prime نقص
+
+781
+01:23:15,460 --> 01:23:21,780
+ال EQ prime ال EQ prime هو 3 في ال Phi prime فايه
+
+782
+01:23:21,780 --> 01:23:27,340
+البرم اللي هي بالزرع ناقص كي و دابلي برم كي و
+
+783
+01:23:27,340 --> 01:23:32,540
+دابلي برم بناقص خمسة عشر ناقص خمسة عشر في الفاية
+
+784
+01:23:32,540 --> 01:23:41,420
+اللي هي بالتنين بالتنين يساوي هذا بالاطمعش زرع زرع
+
+785
+01:23:41,420 --> 01:23:45,440
+زرع زرع زرع زرع زرع زرع زرع زرع زرع زرع زرع زرع
+
+786
+01:23:45,440 --> 01:23:45,560
+زرع زرع زرع زرع زرع زرع زرع زرع زرع زرع زرع زرع
+
+787
+01:23:45,560 --> 01:23:45,580
+زرع زرع زرع زرع زرع زرع زرع زرع زرع زرع زرع زرع
+
+788
+01:23:45,580 --> 01:23:47,330
+زرع زرع زرع زرع زرع زرع زرع زرع زرع زرع زيبقى زائد
+
+789
+01:23:47,330 --> 01:23:54,370
+ثلاثين ويساوي قداش اثنين وأربعين الشغل بتطول تروح
+
+790
+01:23:54,370 --> 01:24:00,110
+يعني بدأي زهج أزهجان بضيع إيه؟ بضيع المسألة دوريا
+
+791
+01:24:00,110 --> 01:24:04,950
+حدا فيكم بتسأل أي سؤال هنا بنات؟ إذا العمود الفقري
+
+792
+01:24:04,950 --> 01:24:10,090
+عندنا له المعادلة رقم تلاتة كل الشغل بدي يكون منها
+
+793
+01:24:10,090 --> 01:24:16,550
+من عندها بنبدأ نجيب أربعة وخمسة وستة وكله هذا سؤال
+
+794
+01:24:16,550 --> 01:24:20,290
+هو رقم تلاتة من أسئلة الكتابة في عندك أظن ما بّارة
+
+795
+01:24:20,290 --> 01:24:25,130
+أربعة أسئلة أو خمس أسئلة بالشكل هذا هذا هو أحدهم
+
+796
+01:24:25,130 --> 01:24:38,670
+و الباقي بنفس الطريقة اللي 
+
+797
+01:24:38,670 --> 01:24:43,790
+أنا بدأ أعطي تعريف لل analytic function مرة ثانية
+
+798
+01:24:44,600 --> 01:24:54,700
+ونشوف نظرية عليها وبعد ذلك نأخذ بعض الأمثلة يبقى
+
+799
+01:24:54,700 --> 01:25:01,780
+التعريف بيقول ما يأتي definition تعريف
+
+800
+01:25:01,780 --> 01:25:07,160
+رقم واحد بيقول for the differential equation for
+
+801
+01:25:07,160 --> 01:25:10,120
+the differential
+
+802
+01:25:24,000 --> 01:25:35,200
+النقطة x0 هي نقطة
+
+803
+01:25:35,200 --> 01:25:37,440
+عامة
+
+804
+01:25:42,790 --> 01:25:56,130
+ordinary point نقطة عادية if ال P of X and ال Q of
+
+805
+01:25:56,130 --> 01:26:04,290
+X ما لهم are analytic are analytic
+
+806
+01:26:04,290 --> 01:26:17,780
+at X node نمر اثنين if ال P of X and the Q of X
+
+807
+01:26:17,780 --> 01:26:28,360
+are not analytic are not analytic يبقى لو ما كناش
+
+808
+01:26:28,360 --> 01:26:38,520
+دوال تحليلية at X node then اللي هو ال X node then
+
+809
+01:26:43,520 --> 01:26:56,120
+ال x0 is called is called a singular point a
+
+810
+01:26:56,120 --> 01:27:05,140
+singular point آخر نظرية في هذا ال section بتقول
+
+811
+01:27:05,140 --> 01:27:06,160
+ما يأتي
+
+812
+01:27:12,360 --> 01:27:24,880
+ال X naught is an ordinary point نقطة عادية of
+
+813
+01:27:24,880 --> 01:27:28,620
+the differential
+
+814
+01:27:30,210 --> 01:27:
+
+861
+01:34:32,520 --> 01:34:35,900
+الـ analytic function وهو مرتبط بالتعريف السابق
+
+862
+01:34:35,900 --> 01:34:41,890
+بتدخل المعامل y double prime هو a وحظ صحيح إذا بدأ
+
+863
+01:34:41,890 --> 01:34:46,250
+أروح على الدوال الـ P of X والـ Q of X هل هم
+
+864
+01:34:46,250 --> 01:34:50,870
+analytic functions ولا لأ؟ إذا لقيتهم يعني بقدر 
+
+865
+01:34:50,870 --> 01:34:55,090
+أكتبهم على شكل تايلور أو ماكلورين سيريز ولا؟ إذا قدرت
+
+866
+01:34:55,090 --> 01:34:59,290
+عند النقطة المعطاة، مش حكاية عند أي نقطة، يبقى إذا 
+
+867
+01:34:59,290 --> 01:35:03,270
+قدرت عند هذه النقطة بسمي هذه ordinary point، ما قدرت
+
+868
+01:35:03,270 --> 01:35:08,500
+يبقى هذه singular point. نمرّة اثنين بيقول إذا هدول
+
+869
+01:35:08,500 --> 01:35:13,580
+هدول مش analytic يعني ما قدرت أكتب أي واحدة
+
+870
+01:35:13,580 --> 01:35:17,360
+فيهم على شكل تايلور أو ماكلورين سيريز، يبقى النقطة 
+
+871
+01:35:17,360 --> 01:35:23,720
+هذه بيصير معاها singular point. طيب، يمكن ييجي في 
+
+872
+01:35:23,720 --> 01:35:28,060
+بالأحدكم السؤال التالي، هدول two functions افترض
+
+873
+01:35:28,060 --> 01:35:32,620
+إن الأولى قدرت أكتبها على شكل تايلور سيريز، بس
+
+874
+01:35:32,620 --> 01:35:36,930
+التانية ما قدرت، يعني ما بنفع أكتبها على شكل taylor
+
+875
+01:35:36,930 --> 01:35:40,970
+series، إذا بيكون الدوال الاثنين هدول analytic عند 
+
+876
+01:35:40,970 --> 01:35:46,700
+هذه النقطة، لأ، يعني أنا بدي الاثنتين في نفس الوقت
+
+877
+01:35:46,700 --> 01:35:49,540
+يكونوا analytic عند نفس النقطة، واحدة analytic
+
+878
+01:35:49,540 --> 01:35:53,820
+والثانية لأ، يبقى خلاص مرفوض، بدي الاثنتين أو الـ two 
+
+879
+01:35:53,820 --> 01:35:57,500
+functions الـ P of X small  و P of X small of X يكونوا
+
+880
+01:35:57,500 --> 01:36:02,160
+analytic عند نفس النقطة، في أي واحد إن حدث ذلك بقول 
+
+881
+01:36:02,160 --> 01:36:06,260
+النقطة هذه معناها ordinary point، ما حدث يبقى بقول
+
+882
+01:36:06,260 --> 01:36:10,760
+هذه singular point. خلي هذه المعلومة في دماغك و
+
+883
+01:36:10,760 --> 01:36:14,000
+نذهب نستخدمها في النص التابع للنظرية اللي قدامنا.
+
+884
+01:36:14,000 --> 01:36:18,520
+بقول لو كانت الـ X node عبارة عن ordinary point
+
+885
+01:36:18,520 --> 01:36:23,520
+للمعادلة هذه، يبقى جسمها هذه على هذه بتطلع 
+
+886
+01:36:23,520 --> 01:36:27,940
+analytic، جسمها هذه على هذه بتطلع analytic عشان تكون
+
+887
+01:36:27,940 --> 01:36:28,700
+هذه مالها؟
+
+888
+01:36:47,610 --> 01:36:52,690
+الحل تبع المعادلة رقم واحد بقدرة وعلى سير الـ
+
+889
+01:36:52,690 --> 01:36:57,910
+solution يعني لو كان هدول الاثنتين analytic بأقمن
+
+890
+01:36:57,910 --> 01:37:04,150
+وجود حل على شكل متسلسلة للمعادلة هذه، ومش عجبه جدًّا
+
+891
+01:37:04,150 --> 01:37:08,810
+هيكوب بس لأ، هو عبارة عن مجموع حلين، كونصا في الحل 
+
+892
+01:37:08,810 --> 01:37:12,190
+الأول وكونصا في الحل الثاني، وأنت شوفت في section
+
+893
+01:37:12,190 --> 01:37:17,260
+خمسة اثنين، بقينا نطلع حل constant a node في series
+
+894
+01:37:17,260 --> 01:37:20,620
+زائد a1 في series ثانية، لسه اليوم معناه مظبوط ولا
+
+895
+01:37:20,620 --> 01:37:24,580
+لأ، يبقى هي اللي بقوله بشكل هذا حيث الـ a node والـ
+
+896
+01:37:24,580 --> 01:37:28,660
+a1 عبارة عن ثوابت والـ y1 والـ y2 linearly
+
+897
+01:37:28,660 --> 01:37:33,420
+independent series solution وركز على series حل
+
+898
+01:37:33,420 --> 01:37:36,560
+لإن إحنا بنشتغل في series، بنشتغلش بالحلال اللي كنا في
+
+899
+01:37:36,560 --> 01:37:41,380
+chapter ثلاثة أو أربعة، يبقى see the solution that
+
+900
+01:37:41,380 --> 01:37:45,660
+are analytic at each node يعني الحلّين هدول كمان
+
+901
+01:37:45,660 --> 01:37:50,320
+analytic وين يعني كل واحد فيهم مكتوب على شكل تايلور 
+
+902
+01:37:50,490 --> 01:37:55,970
+سيريز عند هذه النقطة، طب كويس إحنا صار عندنا حلين
+
+903
+01:37:55,970 --> 01:38:00,510
+و الاثنين linearly independent في عندنا حاجة اسمها
+
+904
+01:38:00,510 --> 01:38:05,950
+نصف قطر التقارب لكل من Y واحد و Y اثنين، مش هذه series، إذا 
+
+905
+01:38:05,950 --> 01:38:10,310
+بتكون تقاربي على فترة، إذا نقلتها نصف تقارب، هذه
+
+906
+01:38:10,310 --> 01:38:16,130
+التقاربات ستكون مرتبطة على فترة يبقى لها نصف قطر 
+
+907
+01:38:16,130 --> 01:38:21,130
+تقارب قد يكون مثل نصف التقارب الأول وقد يختلف عنه
+
+908
+01:38:21,520 --> 01:38:25,520
+طيب، إن اتفقوا بأخذ واحد، يوم، إن اختلفوا بأخذ اللي
+
+909
+01:38:25,520 --> 01:38:30,720
+صغير فيهم، إيش بقول هنا؟ الـ radius of convergence
+
+910
+01:38:30,720 --> 01:38:36,140
+for each y1 and y2 is the minimum الأصغر of the
+
+911
+01:38:36,140 --> 01:38:40,660
+radius، radii جمع radius اللي هو نصف القطر of
+
+912
+01:38:40,660 --> 01:38:46,430
+convergence for the series for P and Q يبقى الأصغر 
+
+913
+01:38:46,430 --> 01:38:51,090
+فيهم ها بيكون هو نصف القطر إيه؟ لإيه؟ خاطر أعطي مثال
+
+914
+01:38:51,090 --> 01:38:57,070
+صغير على هذه لأ، لا سطرين بس، سطرين على الأخرى بس
+
+915
+01:38:57,070 --> 01:38:59,750
+مشان أثبت المعلومة، والمرة جايب نحل بدل المثال
+
+916
+01:38:59,750 --> 01:39:09,670
+ثلاثة يبقى مثال صغير، المثال بيقول ما يأتي، يبقى مش
+
+917
+01:39:09,670 --> 01:39:14,450
+ضايل إلا مجموعة من الأمثلة على هذا الـ section بدنا
+
+918
+01:39:14,450 --> 01:39:22,390
+نيجي لأول مثال، بقول determine أو بلا شوف خليه أي 
+
+919
+01:39:22,390 --> 01:39:26,870
+determine a lower bound
+
+920
+01:39:33,560 --> 01:39:41,620
+for the radius of convergence for the radius of
+
+921
+01:39:41,620 --> 01:39:45,340
+convergence
+
+922
+01:39:45,340 --> 01:39:50,080
+of
+
+923
+01:39:50,080 --> 01:39:58,780
+series solutions of series solutions series
+
+924
+01:39:58,780 --> 01:40:00,820
+solutions about
+
+925
+01:40:29,360 --> 01:40:31,520
+المعادلة الأولى
+
+926
+01:40:49,090 --> 01:40:50,490
+Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''
+
+927
+01:41:03,170 --> 01:41:09,470
+كويس، المعادلة جاهزة مجسومة وخالصة، يبقى capital P
+
+928
+01:41:09,470 --> 01:41:15,990
+هنا بقدرش يا بنات؟ واحد، يبقى الـ capital P of X
+
+929
+01:41:15,990 --> 01:41:22,170
+بده يساوي واحد، في عندنا نقطة في الدنيا بدها تغير
+
+930
+01:41:22,170 --> 01:41:26,590
+القيمة هذه تخليها صفر؟ ما عنديش، يبقى كل النقاط اللي
+
+931
+01:41:26,590 --> 01:41:33,410
+عندي are ordinary points يبقى هذه لا يمكن أن تساوي 0
+
+932
+01:41:33,410 --> 01:41:42,110
+for all x يبقى هذا بدي أقول لك all the points are
+
+933
+01:41:42,110 --> 01:41:47,070
+ordinary points
+
+934
+01:41:48,390 --> 01:41:52,670
+يبقى بناء عليه الـ zero والـ أربعة مالهم؟ ordinary
+
+935
+01:41:52,670 --> 01:42:00,610
+points، الـ X naught يساوي zero والـ X naught يساوي
+
+936
+01:42:00,610 --> 01:42:11,890
+أربعة are ordinary points هذا كويس، ما عنديش ولا 
+
+937
+01:42:11,890 --> 01:42:16,890
+singular point تمامًا بقول لكم، يبقى لو جيت للـ real
+
+938
+01:42:16,890 --> 01:42:21,810
+line، هذا الـ real line وهذا النقطة zero وهذا النقطة
+
+939
+01:42:21,810 --> 01:42:28,570
+أربعة ما عنديش singular point بدي أوقف عندها، يبقى
+
+940
+01:42:28,570 --> 01:42:33,390
+الـ radius الأولى اللي بدي يكون من وين لوين؟ من صفر
+
+941
+01:42:33,390 --> 01:42:38,730
+إلى مالانهاية، طول قداش؟ تبعه مالانهاية، يعني الـ radius
+
+942
+01:42:38,730 --> 01:42:43,130
+الثاني بدي يكون من وين؟ من أربعة إلى مالانهاية، قداش؟
+
+943
+01:42:44,370 --> 01:42:47,490
+عشان إذا الـ raw one بده يساوي مالانهاية والـ raw
+
+944
+01:42:47,490 --> 01:42:50,850
+two بده يساوي مالانهاية فيهم واحد صغير وواحد
+
+945
+01:42:50,850 --> 01:42:55,970
+كبير لأ يبقى الـ radius مالانهاية، يبقى بأجي بقوله
+
+946
+01:42:55,970 --> 01:43:02,930
+الـ raw one بده يساوي infinity والـ raw two بده يساوي
+
+947
+01:43:02,930 --> 01:43:08,530
+infinity، قالي هات لي الـ lower bound للـ radius of 
+
+948
+01:43:08,530 --> 01:43:16,690
+convergence، يبقى بأجي بقوله هنا the lower bound
+
+949
+01:43:16,690 --> 01:43:26,150
+for the radius of convergence
+
+950
+01:43:26,150 --> 01:43:36,490
+is r تساوي قداش؟ infinity ما فيش غيرها، طبعًا هذا أتفه
+
+951
+01:43:36,490 --> 01:43:41,410
+أنواع المسائل، لكن اسمها في الكتاب، تمام؟ مرة جا
+
+952
+01:43:41,410 --> 01:43:44,950
+إن شاء الله تصير مش روتين في الهلاب، تطلع قيم
+
+953
+01:43:44,950 --> 01:43:51,170
+عددية، وحنلقى في العديد من الأمثلة، وقد تكون النقطة 
+
+954
+01:43:51,170 --> 01:43:56,710
+singular point حقيقية وقد تكون تخيلية، يبقى على كل
+
+955
+01:43:56,710 --> 01:44:01,750
+الأمرين، بدنا نحسب هذا إن شاء الله المرة القادمة
+
+
+
diff --git a/PL9fwy3NUQKwa8ZDfSFGn6H8xVFLzqmCZC/6nKiDvoO6MU_postprocess.srt b/PL9fwy3NUQKwa8ZDfSFGn6H8xVFLzqmCZC/6nKiDvoO6MU_postprocess.srt
new file mode 100644
index 0000000000000000000000000000000000000000..195688e369a75c9cc1a86a656d9289f1d718d83e
--- /dev/null
+++ b/PL9fwy3NUQKwa8ZDfSFGn6H8xVFLzqmCZC/6nKiDvoO6MU_postprocess.srt
@@ -0,0 +1,3820 @@
+1
+00:00:09,980 --> 00:00:15,580
+بسم الله الرحمن الرحيم بنواصل ما ابتدأنا به المرة
+
+2
+00:00:15,580 --> 00:00:20,420
+الماضية وهو series solution near an ordinary point
+
+3
+00:00:20,420 --> 00:00:24,760
+وسميناها part one وبعد قليل ان شاء الله خلال هذه
+
+4
+00:00:24,760 --> 00:00:29,000
+المحاضرةحناخذ part 2 ونشوف شو العلاقة ما بين
+
+5
+00:00:29,000 --> 00:00:34,220
+الأتنين على أي حال مرة اللي فاتت أخدنا مثال واحد
+
+6
+00:00:34,220 --> 00:00:38,840
+على كيفية استخدام المتسلسلات في حل المعادلة
+
+7
+00:00:38,840 --> 00:00:43,800
+التفاضلية من الرتبة الثانية والآن بناخد مثلك
+
+8
+00:00:43,800 --> 00:00:48,940
+المثال أتقل شوية من ناحيةالاجراءات العملية و احنا
+
+9
+00:00:48,940 --> 00:00:54,900
+بنشتغل ماكانش مش هيكون مباشر زي مثال المرة الماضية
+
+10
+00:00:54,900 --> 00:00:59,900
+المثال بيقول find the serious solution هات ان شكل
+
+11
+00:00:59,900 --> 00:01:04,080
+الحل اللي على شكل متسلسلة and the recurrence
+
+12
+00:01:04,080 --> 00:01:07,520
+relation والمعادلة التيارية لل differential
+
+13
+00:01:07,520 --> 00:01:13,550
+equationاللي عندنا about the point X يسوى من اتنين
+
+14
+00:01:13,550 --> 00:01:16,650
+اتنين هذا انا مش عارف هي singular point ولا
+
+15
+00:01:16,650 --> 00:01:20,850
+ordinary point لكن احنا موضوعنا حتى هذه اللحظة
+
+16
+00:01:20,850 --> 00:01:25,130
+الدراسة عند من عند ال ordinary points لأ وليس عند
+
+17
+00:01:25,130 --> 00:01:29,430
+ال singular points لكن بدنا نبين ان هذه النقطة هي
+
+18
+00:01:29,430 --> 00:01:35,150
+عبارة عن ordinary point فلو جيت بدى اقوله ال P of
+
+19
+00:01:35,150 --> 00:01:42,270
+X يبقى ال P of X اللي هي منإتنين لا يمكن أن تساوي
+
+20
+00:01:42,270 --> 00:01:48,130
+zero مهما تغيرت ال X يبقى كل النقاط عبارة عن
+
+21
+00:01:48,130 --> 00:01:52,770
+ordinary points يعني لا يوجد عندي singular points
+
+22
+00:01:52,770 --> 00:02:01,070
+يبقى هذا معناه إن ال X يساوي 2 is an ordinary
+
+23
+00:02:01,070 --> 00:02:06,670
+point يبقى هذه عبارة عن نقطة عادية
+
+24
+00:02:11,740 --> 00:02:20,980
+أحنا بنبحث على إيه ال solutionY في الصيغة التالية
+
+25
+00:02:20,980 --> 00:02:27,200
+summation من N equal zero to infinity لل A N المرة
+
+26
+00:02:27,200 --> 00:02:30,940
+اللي فاتت المثال الماضي منها كانت النقطة X يساوي
+
+27
+00:02:30,940 --> 00:02:36,280
+زيرو وليس X يساوي اتنين فكان summation لل A N X to
+
+28
+00:02:36,280 --> 00:02:43,230
+the power N لكن مدام احناالحل هيكون حوالين النقطة
+
+29
+00:02:43,230 --> 00:02:49,350
+هذه كما بنقول x ناقص اتنين كله to the power n
+
+30
+00:02:49,350 --> 00:02:55,610
+which converge
+
+31
+00:02:55,610 --> 00:03:05,230
+for اللي هو absolute value لل x ناقص اتنين اقل من
+
+32
+00:03:05,230 --> 00:03:11,340
+رو و رو greater than zeroيبقى هذه ال series تبقى
+
+33
+00:03:11,340 --> 00:03:15,520
+تقاربية خلال الفترة اللى عندنا اللى هو absolute
+
+34
+00:03:15,520 --> 00:03:20,000
+value لل X ناقص اتنين اقل من رو و رو greater than
+
+35
+00:03:20,000 --> 00:03:24,520
+zero بس مجرد التذكير اللى ليس اللى بتذكركوا بكل
+
+36
+00:03:24,520 --> 00:03:29,380
+كلاص بيه هذه ال absolute value لل X ناقص اتنين اقل
+
+37
+00:03:29,380 --> 00:03:37,760
+من رو و اكبر من روأول X أقل من رو زائد اتنين و اقل
+
+38
+00:03:37,760 --> 00:03:44,460
+من اتنين ناقص رو يعني لو جيت قولت هذا ال real line
+
+39
+00:03:44,460 --> 00:03:50,360
+تمام؟ و هذه النقطة اللي هي اتنين النقطة هذه اتنين
+
+40
+00:03:50,360 --> 00:03:56,320
+زائد روالنقطة ها دي ها ها اللي هي اتنين ناقص رو
+
+41
+00:03:56,320 --> 00:04:00,660
+وبالتالي هذا نصف القطر او radius of convergence
+
+42
+00:04:00,660 --> 00:04:05,280
+اللي هي رو وهذا radius of convergence برضه مين
+
+43
+00:04:05,280 --> 00:04:11,960
+اللي هي رو طيب ممتاز ايش رايكوا اتعرف على شكل الحل
+
+44
+00:04:11,960 --> 00:04:15,440
+لإنه مش هنعوض في المعادلة دي بالزمن المشتقة الأولى
+
+45
+00:04:15,440 --> 00:04:22,140
+والمشتقة الثانيةيبقى انا عندي y تساوي ال summation
+
+46
+00:04:22,140 --> 00:04:28,600
+من n equal zero to infinity لل a n في ال x ناقص
+
+47
+00:04:28,600 --> 00:04:35,120
+اتنين كله to the power m هذا بده يعطينا ان المشتقة
+
+48
+00:04:35,120 --> 00:04:42,490
+الاولى y prime يساويSummation لمن؟ لل N in
+
+49
+00:04:42,490 --> 00:04:48,770
+constant X ناقص اتنين to the power N minus one ال
+
+50
+00:04:48,770 --> 00:04:51,630
+summation هذا لما اشتق المشتق اللي هو اللي بيبدأ
+
+51
+00:04:51,630 --> 00:04:56,570
+من وين؟ من عند N تسوى واحد من عند N تسوى واحد الى
+
+52
+00:04:56,570 --> 00:05:02,670
+infinity هذا بده يعطينا ان المشتق الثاني YW prime
+
+53
+00:05:03,210 --> 00:05:09,510
+هذا كله مقدار ثابت إذا بدى أشتاق هذه كمان مرة يبقى
+
+54
+00:05:09,510 --> 00:05:17,030
+summation لل N في ال N ناقص واحد في ال AMفى الـ X
+
+55
+00:05:17,030 --> 00:05:22,150
+ناقص اتنين to the power in minus اتنين طبعا مشتقة
+
+56
+00:05:22,150 --> 00:05:26,050
+مداخل القصة اللى هو بقداش بواحد صحيح يبقى بروحاش
+
+57
+00:05:26,050 --> 00:05:29,710
+باكتبها ال summation هنا ابتدا من عند ان يساوي
+
+58
+00:05:29,710 --> 00:05:35,050
+واحد يبقى من هنا من عند ان تساوي اتنين زى ما كنا
+
+59
+00:05:35,050 --> 00:05:39,470
+شفنا فى ال section الماضى وزى ما شفنا فى مثال
+
+60
+00:05:39,470 --> 00:05:51,830
+المرة الماضىالان عندي Y و Y'' و Y'' و Y'' و Y''
+
+61
+00:05:51,830 --> 00:05:53,050
+و Y'' و Y'' و Y'' و Y'' و Y'' و Y'' و Y'' و Y'' و
+
+62
+00:05:53,050 --> 00:05:53,490
+Y'' و Y'' و Y'' و Y'' و Y'' و Y'' و Y'' و Y'' و
+
+63
+00:05:53,490 --> 00:05:53,630
+Y'' و Y'' و Y'' و Y'' و Y'' و Y'' و Y'' و Y'' و
+
+64
+00:05:53,630 --> 00:05:53,670
+Y'' و Y'' و Y'' و Y'' و Y'' و Y'' و Y'' و Y'' و
+
+65
+00:05:53,670 --> 00:05:54,070
+Y'' و Y'' و Y'' و Y'' و Y'' و Y'' و Y'' و Y'' و
+
+66
+00:05:54,070 --> 00:05:56,190
+Y'' و Y'' و Y'' و Y'' و Y'' و Y'' و Y'' و Y'' و
+
+67
+00:05:56,190 --> 00:06:01,710
+Y'' و Y'' و Y'' و Y'' و Y''
+
+68
+00:06:04,550 --> 00:06:09,970
+بنجعلها 2YWP يبقى هذه بدروح اضربها في بينامنات بده
+
+69
+00:06:09,970 --> 00:06:14,470
+اضربها في اتنين الاتنين هذه لو خلتها برا ال
+
+70
+00:06:14,470 --> 00:06:18,340
+summation والله حطيتها جوا ال summation بتفرجكونوا
+
+71
+00:06:18,340 --> 00:06:22,560
+مالوش دعوة بالصميشن يعني مالوش دعوة بال N إذا هذه
+
+72
+00:06:22,560 --> 00:06:29,300
+ستصبح summation من N equal to infinity لإتنين اللي
+
+73
+00:06:29,300 --> 00:06:37,580
+عندنا N في من؟ في ال N ناقص واحد في ال A N في ال X
+
+74
+00:06:37,580 --> 00:06:43,620
+ناقص اتنين to the power N ناقص اتنين يبقى خلصها من
+
+75
+00:06:43,620 --> 00:06:49,830
+من؟ من ال term الأولبدنا نيجي لل term التاني اللي
+
+76
+00:06:49,830 --> 00:06:54,470
+هو ال X زائد واحد مالكش دعوة يخليك برا لإنك مش زي
+
+77
+00:06:54,470 --> 00:06:57,910
+اللي جوا، لو كان زي اللي جوا هذا كان دخلناه
+
+78
+00:06:57,910 --> 00:07:02,520
+مباشرة، لكن خليكي لما نتفاهم عليكي شويةيبقى x زاد
+
+79
+00:07:02,520 --> 00:07:06,360
+واحد في ال y prime وين ال y prime؟ هايها يبقى
+
+80
+00:07:06,360 --> 00:07:13,320
+summation من n equal one to infinity لل n a n x
+
+81
+00:07:13,320 --> 00:07:18,440
+ناقص اتنين to the power n minus ال one قلصنا ال
+
+82
+00:07:18,440 --> 00:07:21,980
+term التاني بدنا نروح لل term التالت يبقى هذه بدنا
+
+83
+00:07:21,980 --> 00:07:25,700
+نروح نضربها وين؟ تلاتة تلاتة كتبتها برا ال
+
+84
+00:07:25,700 --> 00:07:29,200
+summation ولا جوا ال summation نسيانيبقى بالداخل
+
+85
+00:07:29,200 --> 00:07:34,800
+تلاتة جوا ال summation يبقى زائد summation من n
+
+86
+00:07:34,800 --> 00:07:41,440
+equal zero to infinity لتلاتة a n في ال x ناقص
+
+87
+00:07:41,440 --> 00:07:46,780
+اتنين to the power n كله بده يساوي مين؟ بده يساوي
+
+88
+00:07:46,780 --> 00:07:53,460
+zero يبقى احنا الآن بدنا نعيد ترتيب أوراق المثلة
+
+89
+00:07:53,460 --> 00:07:58,860
+في شغلتينالشغل الأولى هدى x to the power n x نقص
+
+90
+00:07:58,860 --> 00:08:03,460
+اتنين to the power n بدى الباقى هدى الأسس كلها to
+
+91
+00:08:03,460 --> 00:08:08,860
+the power n هى واحدة الثانية بدى ال index لتحت ال
+
+92
+00:08:08,860 --> 00:08:13,900
+summation يكون كله موحد مشان اقدر اجمع و اعمل ايه
+
+93
+00:08:13,900 --> 00:08:19,040
+ب summation واحد فقط فبجى بقول هدى مشان اخليها
+
+94
+00:08:19,040 --> 00:08:25,330
+بدلالة ال nيبقى بده يشيل كل N ويحط مكانها N زائد
+
+95
+00:08:25,330 --> 00:08:30,610
+اتنين يبقى دي بدها تصير على الشكل التالي يبقى
+
+96
+00:08:30,610 --> 00:08:40,820
+summation من عند N equal to zero ولا لأ؟هذا يعني
+
+97
+00:08:40,820 --> 00:08:48,140
+ان تساوي 0 لمن؟ لل infinity وبالتالي اتنين بده
+
+98
+00:08:48,140 --> 00:08:54,140
+اشيل الان وحط مكانها ان زائد اتنين وهذا يعني ان
+
+99
+00:08:54,140 --> 00:09:01,560
+زائد اتنين ناقص واحد يعني ان زائد واحدهذه a n زائد
+
+100
+00:09:01,560 --> 00:09:08,100
+اتنين كله في اكس ناقص اتنين كله to the power m
+
+101
+00:09:08,100 --> 00:09:13,700
+يبقى هذه زبطناها الخطوة الأولى خلينا الأس تبعها to
+
+102
+00:09:13,700 --> 00:09:18,960
+the power m اه هنا في جوا اكس و في برا اكس بده
+
+103
+00:09:18,960 --> 00:09:24,690
+ادخل اللي جوا برا بس مش زي بعض ورطنامظبوط هذه X زي
+
+104
+00:09:24,690 --> 00:09:29,970
+واحد وهذه X نقص اتنين طيب كي بدى ادخل ادخل ال X
+
+105
+00:09:29,970 --> 00:09:33,790
+هنا برضه لحاله بتظبطش ادخل ال واحد لحاله بتظبطش
+
+106
+00:09:33,790 --> 00:09:38,410
+اذا بدي اشتغل شغل فعلا يكون رياضي سليم وماحدش
+
+107
+00:09:38,410 --> 00:09:42,170
+يقولي كلامك مش صحيح ايش بتقترحه علينا نعمة اللي
+
+108
+00:09:42,170 --> 00:09:46,110
+بتعرفي ترفعي دي ابو جا شيفها ايوة X زي واحد هيفرع
+
+109
+00:09:46,110 --> 00:09:53,110
+X نقص اتنين ميال ميال شو اسمك انت ايهحنين حنين
+
+110
+00:09:53,110 --> 00:09:56,510
+حنين
+
+111
+00:09:56,510 --> 00:10:01,050
+حنين حنين حنين حنين حنين حنين حنين حنين حنين حنين
+
+112
+00:10:01,050 --> 00:10:09,530
+حنين حنين حنين حنين حنين حنين حنين حنين حنين حنين
+
+113
+00:10:09,530 --> 00:10:09,550
+حنين حنين حنين حنين حنين حنين حنين حنين حنين حنين
+
+114
+00:10:09,550 --> 00:10:09,590
+حنين حنين حنين حنين حنين حنين حنين حنين حنين حنين
+
+115
+00:10:09,590 --> 00:10:19,450
+حنين
+
+116
+00:10:19,450 --> 00:10:27,840
+حنلكن هذه حلتلي معضلة كبيرة جدا ايش صار عندي x نقص
+
+117
+00:10:27,840 --> 00:10:32,000
+اتنين مضروبة في الاجابة بقدر اضربها بدون مشاكل و
+
+118
+00:10:32,000 --> 00:10:35,480
+بضل عندي تلاتة مضروبة في ال summation يعني حاسين
+
+119
+00:10:35,480 --> 00:10:40,240
+عندي كم double summations واحد مضروب في x نقص
+
+120
+00:10:40,240 --> 00:10:44,580
+اتنين واحد مضروب في مام في تلاتة ايه بجهاي اول
+
+121
+00:10:44,580 --> 00:10:49,530
+معضلة موجودة في المثلة تغلبنا عليها بتفكير سليمكيف
+
+122
+00:10:49,530 --> 00:10:54,370
+اكتب اللي هو ال term اللي برا بدلالة main بدلالة
+
+123
+00:10:54,370 --> 00:10:57,330
+term اللي جوا، بالتالي بيكون خلصنا من المثل هذه
+
+124
+00:10:57,330 --> 00:11:03,230
+يبقى يا بنات هذه ال X ناقص اتنين بدي دخلها جوا ال
+
+125
+00:11:03,230 --> 00:11:07,090
+summation وبعد ذلك زائد تلاتة كمان ادخلها جوا ال
+
+126
+00:11:07,090 --> 00:11:11,350
+summation وبالتالي هيظهر term main وليس term واحد
+
+127
+00:11:11,710 --> 00:11:17,890
+يبقى هانيجي هنا زائد هي عندنا summation من وين؟ من
+
+128
+00:11:17,890 --> 00:11:25,110
+عند ال N equal one to infinity لمين؟ لل N A N X
+
+129
+00:11:25,110 --> 00:11:30,310
+ناقص اتنين X ناقص اتنين بدا تيجي هذه أس قداش يا
+
+130
+00:11:30,310 --> 00:11:38,350
+بنات أس واحد يبقى هذا مع السلامة بظل هذا أس Nضايل
+
+131
+00:11:38,350 --> 00:11:41,950
+علينا مين؟ ضايل علينا التلاتة تدخل على ال
+
+132
+00:11:41,950 --> 00:11:47,330
+summation يبقى زائد summation من n equal one to
+
+133
+00:11:47,330 --> 00:11:56,810
+infinity لتلاتة n a n x ناقص اتنين أس قداش ناقص
+
+134
+00:11:56,810 --> 00:12:01,910
+واحد هذه التلاتة مالاش دعوة بتضيعش الأس بيظل الأس
+
+135
+00:12:01,910 --> 00:12:06,380
+زي ما هويبقى الترمين اللي كتبتهم عبارة عن الترم
+
+136
+00:12:06,380 --> 00:12:11,600
+هذا فقط و بقى اللي عندنا مين؟ الترم الأخير يبقى
+
+137
+00:12:11,600 --> 00:12:20,140
+زائد summation من n equal zero to infinity لثلاثة
+
+138
+00:12:20,140 --> 00:12:25,380
+a n في ال X لقص اتنين to the power n كل هذا بده
+
+139
+00:12:25,380 --> 00:12:32,260
+ساوي مان؟ بده ساوي زيروطيب، حتى الآن فكنا مهضلة
+
+140
+00:12:32,260 --> 00:12:38,640
+واحدة، اللي هو هذه كتبناها بدلالة اللي جوا، الآن
+
+141
+00:12:38,640 --> 00:12:49,490
+نرجع لشغلنا المرة الماضيةهيبقى اول
+
+142
+00:12:49,490 --> 00:12:54,710
+خطوة بنعملها بنوحد الاص تبع main ال X اللي عندنا
+
+143
+00:12:54,710 --> 00:13:00,370
+هذه بعدين بطلها هذي أس ان جاهزة هذي أس ان جاهزة
+
+144
+00:13:00,370 --> 00:13:04,890
+هذي أس ان جاهزة يبقى هذي اللي ماهياش جاهزة يبقى
+
+145
+00:13:04,890 --> 00:13:10,910
+مشان أجهزها هذي بدي أشيل كل ان و أحط مكانهان زائد
+
+146
+00:13:10,910 --> 00:13:14,630
+واحد يبقى هذه يا بنات بديش اعكس كتابة انت بدي
+
+147
+00:13:14,630 --> 00:13:20,550
+نزلها زي ما هي وهذه بدي نزلها زي ما هي وهذه زائد
+
+148
+00:13:20,550 --> 00:13:26,510
+summation من n equal zero to infinity لتلاتة n
+
+149
+00:13:26,510 --> 00:13:34,190
+زائد واحد a n زائد واحد x ناقص اتنين to the power
+
+150
+00:13:34,190 --> 00:13:40,750
+nيبقى شيلت كل in لل term التالت ده وحطيت مكانه in
+
+151
+00:13:40,750 --> 00:13:47,430
+زائد واحد هذا كمان زائد بدي أنزله مانه زي ما هو
+
+152
+00:13:47,430 --> 00:13:54,570
+ماعنديش مشكلة فيهإذا إيش اللي حصل الآن وحتى الأسس
+
+153
+00:13:54,570 --> 00:13:59,090
+كلها تبعت من؟ تبعت ال X ناقص اتنين إذا حلّينا
+
+154
+00:13:59,090 --> 00:14:03,530
+المعضلة التانية ضايل مين علينا؟ المعضلة التالتة
+
+155
+00:14:03,530 --> 00:14:07,290
+المعضلة التالتة بدي أخلّي ال index لتحت ال
+
+156
+00:14:07,290 --> 00:14:12,990
+summation هذا كله زي بعضه دون أن أضيع الشغل اللي
+
+157
+00:14:12,990 --> 00:14:16,010
+اشتغلته بالنسبة لل X ناقص اتنين to the power n
+
+158
+00:14:16,010 --> 00:14:20,510
+يعني اصحي تعملي شغل تخربيهاللي اشتغلت يقولنا
+
+159
+00:14:20,510 --> 00:14:24,070
+بالبلد انحافظ على المكتسبات الوطنية المرة اللي
+
+160
+00:14:24,070 --> 00:14:26,870
+فاتت، يبقى احنا هنا نفس القصة بدنا نحافظ على
+
+161
+00:14:26,870 --> 00:14:30,590
+المكتسبات الوطنية، معناته بدي اشتغل شغل رياضي
+
+162
+00:14:30,590 --> 00:14:34,610
+سليم، ماحدش يقوللي فيه حاجة، واخل الأس تبع ال X
+
+163
+00:14:34,610 --> 00:14:40,080
+ناقص اتنين هو هو في الأربع تيرمان، بقولك كويسأحنا
+
+164
+00:14:40,080 --> 00:14:44,740
+عندنا ده من عند الواحد يبقى أنا ماقدرش ألعب فيه
+
+165
+00:14:44,740 --> 00:14:49,420
+طيب باجي بقول ممكن أخلي الباجي كله من عند الواحد
+
+166
+00:14:49,420 --> 00:14:53,780
+يبدأ كيف؟ بطلع أول term في ال series اللي عندنا
+
+167
+00:14:53,780 --> 00:14:57,980
+ضارة ال summation وبالتالي بصير بوحد ال index هذه
+
+168
+00:14:57,980 --> 00:15:04,200
+فمثلا لو حطيت ال n يساوي zero بصير اتنين في اتنين
+
+169
+00:15:04,200 --> 00:15:10,450
+في واحد يعني اربعة اتنين فقطيبقى بصيري عندي هنا اي
+
+170
+00:15:10,450 --> 00:15:17,990
+اربعة اتنين مفيش غيرها زي summation من n equal one
+
+171
+00:15:17,990 --> 00:15:24,370
+to infinity للتنين في ال n زائد اتنين في ال n زائد
+
+172
+00:15:24,370 --> 00:15:30,150
+واحد في ال a n زائد اتنين في ال x ناقص اتنين to
+
+173
+00:15:30,150 --> 00:15:36,180
+the power n يبقى هاي ال term الأول خلصنا منهالترم
+
+174
+00:15:36,180 --> 00:15:40,240
+التاني بنزله زي ما هو لإنه ما عندهوش مشكلة مادي من
+
+175
+00:15:40,240 --> 00:15:45,340
+عند الواحد يبقى زائد summation من n equal one to
+
+176
+00:15:45,340 --> 00:15:53,660
+infinity لل n a n x ناقص اتنين to the power n اللي
+
+177
+00:15:53,660 --> 00:15:58,180
+بعد هو اللي عنده المشكلةيبقى بيطلع كمان term زي
+
+178
+00:15:58,180 --> 00:16:04,380
+مين؟ زي الأولاني يبقى باجي بقوله زائد بدي أضع N بـ
+
+179
+00:16:04,380 --> 00:16:11,780
+00 بيبقى تلاتة A1 يبقى هاي تلاتة A1 أقص Zero اللي
+
+180
+00:16:11,780 --> 00:16:17,300
+هو بواحد زائد summation من N equal one to infinity
+
+181
+00:16:17,300 --> 00:16:22,840
+لتلاتة في N زائد واحد A N زائد واحد
+
+182
+00:16:27,900 --> 00:16:36,220
+ماحدش أحسن من حد يبقى زائد تلاتة a نوت وها دي راحة
+
+183
+00:16:36,220 --> 00:16:41,000
+الله سهل عليها زائد summation من n equal one to
+
+184
+00:16:41,000 --> 00:16:47,420
+infinity لتلاتة a n x نقص اتنين to the power n كله
+
+185
+00:16:47,420 --> 00:16:53,300
+بده يساويهذه الخطوة اللى عملتها خلصتها بنديت على
+
+186
+00:16:53,300 --> 00:16:59,300
+ال term الأول و ال term التالت
+
+187
+00:16:59,300 --> 00:17:03,680
+و الرابع طلعت بس أول حد من الصمشي و البجي خلته زى
+
+188
+00:17:03,680 --> 00:17:08,460
+ما هوالان لو طلعت في مسألتي من أولها إلى آخرها
+
+189
+00:17:08,460 --> 00:17:13,700
+بلاحظ ان ال index اللى تحت ال summation موحد كله
+
+190
+00:17:13,700 --> 00:17:19,320
+بيبدأ من أند الواحد اتنين ال X ناقص اتنين to the
+
+191
+00:17:19,320 --> 00:17:24,680
+power N كلها موحدة للكل تمام؟ اذا بقدر اجمل هذه
+
+192
+00:17:24,680 --> 00:17:31,230
+بمعادلة واحدةبدي اخدي ثوابت هدول مع بعض لحال و
+
+193
+00:17:31,230 --> 00:17:35,930
+الباقي لحال يبقى هذا ايش؟ بصي يا بنات هاي اربعة
+
+194
+00:17:35,930 --> 00:17:43,960
+اتنين زائد تلاتة في ا واحد زائد ا نولهي عندك تلاتة
+
+195
+00:17:43,960 --> 00:17:47,720
+a واحد و تلاتة a نوت اخدتهم مع بعض تلاتة عامل
+
+196
+00:17:47,720 --> 00:17:52,500
+مشترك من الكل نجي لبعدها زائد هاي ال summation
+
+197
+00:17:52,500 --> 00:17:58,960
+مشترك للكل من عند n equal one to infinity تمام؟
+
+198
+00:17:58,960 --> 00:18:05,000
+وهذا جوز كبير الآن هنا ايش بضالة عندى اتنين في n
+
+199
+00:18:05,350 --> 00:18:12,130
+زائد اتنين في N زائد واحد في AN زائد اتنين هذي
+
+200
+00:18:12,130 --> 00:18:18,190
+يخليها عمل مشارك من الكل general اللي بعدها زائد N
+
+201
+00:18:18,190 --> 00:18:25,790
+في ANجينا للي بعدها زائد تلاتة في N زائد واحد في
+
+202
+00:18:25,790 --> 00:18:33,770
+ال A N زائد واحد وصلنا هذه يبقى زائد تلاتة A N
+
+203
+00:18:33,770 --> 00:18:39,690
+خلصنا كله مضروب في ال X ناقص اتنين to the power N
+
+204
+00:18:39,690 --> 00:18:41,050
+يساوي Zero
+
+205
+00:18:44,500 --> 00:18:49,660
+الان عندي polynomial تساوي زيرو إذا معاملات ال
+
+206
+00:18:49,660 --> 00:18:53,540
+polynomial كلهم بأصفر هم اللي خلولي ال polynomial
+
+207
+00:18:53,540 --> 00:18:57,980
+تساوي زيرو إذا هذا ال term بده يساوي زيرو والباقي
+
+208
+00:18:57,980 --> 00:19:03,580
+بده يساوي زيرو يبقى بيصير عندي اربعة اتنين زائد
+
+209
+00:19:03,580 --> 00:19:09,990
+تلاتة ا وان زائد ا نوت بده يساوي زيرووبعدها كل
+
+210
+00:19:09,990 --> 00:19:15,730
+معامل هذا بين القوسين بده يساوي zero المعامل هذا
+
+211
+00:19:15,730 --> 00:19:24,470
+اتنين اتنين في n زائد اتنين في n زائد واحد في a n
+
+212
+00:19:24,470 --> 00:19:33,510
+زائد اتنين زائد تلاتة in زائد واحد في a n زائد
+
+213
+00:19:33,510 --> 00:19:41,400
+واحد طلعيلي هذه وهذهمش في بينهم AN عامل مشترك بيظل
+
+214
+00:19:41,400 --> 00:19:51,100
+جديش N زائد تلاتة يبقى زائد N زائد تلاتة كله في AN
+
+215
+00:19:51,100 --> 00:19:58,460
+هذا بده يساوي من؟ بده يساوي Zero طيب لو جيت لهذه
+
+216
+00:19:58,460 --> 00:20:05,780
+معناته ان ال A2 بده يساوي تلات تربع بإشارة سالب
+
+217
+00:20:06,000 --> 00:20:13,580
+لمن؟ لل A1 زائد A نقطةمن هنا بدأ يظهر اول اختلاف
+
+218
+00:20:13,580 --> 00:20:17,660
+بين سؤالنا هذا وبين سؤالي المرة الماضية المرة
+
+219
+00:20:17,660 --> 00:20:23,120
+الماضية طلعت a2 بدلالة main a node فقط المرة هذه
+
+220
+00:20:23,120 --> 00:20:28,560
+طلعت بدلالة a node و a1 وبالتالي ماعناش مشكلة برضه
+
+221
+00:20:28,560 --> 00:20:33,660
+يعني ايش ما تطلع بسجلها زي ما هي كويس هذه الآن في
+
+222
+00:20:33,660 --> 00:20:40,550
+عوامل مشتركةممكن يعني اجسم عليها في جوس عامل مشارك
+
+223
+00:20:40,550 --> 00:20:43,630
+من ال term الأول و ال term التاني و التاني بيقولي
+
+224
+00:20:43,630 --> 00:20:46,990
+هنا n زاد واحد هنا n زاد واحد بس هنا مافيش n زاد
+
+225
+00:20:46,990 --> 00:20:53,160
+واحد مصغر يبقى بخلي كل شي زي ما هواذا هذا و هذا
+
+226
+00:20:53,160 --> 00:20:58,260
+هوديهم على الشجة التانية و اقسم على هذا المعامل
+
+227
+00:20:58,260 --> 00:21:05,160
+بيصير عندنا ال a n زائد اتنين يساوي ناقص هيخليه
+
+228
+00:21:05,160 --> 00:21:11,900
+برا بيظل عندنا مين تلاتة في n زائد واحد a n زائد
+
+229
+00:21:11,900 --> 00:21:20,640
+واحد زائد n زائد تلاتة a n كل هذا مقسم على الاتنين
+
+230
+00:21:36,190 --> 00:21:42,090
+عن طريق الـ Recurrence relation اللى طلبها عندى
+
+231
+00:21:42,090 --> 00:21:47,120
+وين فى رأس المثلة جالسة لـ Recurrence relationطب
+
+232
+00:21:47,120 --> 00:21:54,160
+بدى اشوف هدى بدى تبدأ in من وين يبقى in تساوي ابدا
+
+233
+00:21:54,160 --> 00:21:59,400
+من عند ال zero لو قليه من عند ال zero شو بيعطيني
+
+234
+00:21:59,400 --> 00:22:05,580
+اتنين ما اتنين هي جاهزةصح؟ يبقى الصحة ده من وين؟
+
+235
+00:22:05,580 --> 00:22:11,720
+من عند الواحد يبقى انتوا ساوية واحد واتنين وتلاتة
+
+236
+00:22:11,720 --> 00:22:16,720
+وإلى ما شاء الله يبقى هذه يا بنات ال recurrence
+
+237
+00:22:16,720 --> 00:22:21,320
+relation اللي بدّوياها اللي هو المطلوب الأول من
+
+238
+00:22:21,320 --> 00:22:27,680
+المسألة طيب بعد هيك الآن احكي قولي
+
+239
+00:22:31,340 --> 00:22:36,340
+ممتاز، اذا جربنا ايش؟ اذا جربنا ن بي زيرو، اذا
+
+240
+00:22:36,340 --> 00:22:40,580
+جربنا ن بي زيرو، اذا جربنا ن بي زيرو، اذا جربنا ن
+
+241
+00:22:40,580 --> 00:22:42,440
+اذا جربنا ن بي زيرو، اذا جربنا ن بي زيرو، اذا
+
+242
+00:22:42,440 --> 00:22:43,380
+جربنا ن بي زيرو، اذا جربنا ن بي زيرو، اذا جربنا ن
+
+243
+00:22:43,380 --> 00:22:46,960
+بي زيرو، اذا جربنا ن بي زيرو، اذا جربنا ن بي زيرو،
+
+244
+00:22:46,960 --> 00:22:48,940
+اذا جربنا ن بي زيرو، اذا جربنا ن بي زيرو، اذا
+
+245
+00:22:48,940 --> 00:22:56,640
+جربنا ن بي زيرو، اذا جربنا ن بي زيرو، اذا
+
+246
+00:22:56,640 --> 00:23:03,380
+جربنا نخلاص و بقول هي ال record اللى بتشمل الأولى
+
+247
+00:23:03,380 --> 00:23:07,800
+و الثانية بمشي الحال ماعناه مشكلة بيخلي هذه الحال
+
+248
+00:23:07,800 --> 00:23:11,760
+و هذه الحال و اقول عندى انت سوا عاد ماشي الحال بدي
+
+249
+00:23:11,760 --> 00:23:15,280
+أجمع ال 22 بصيغة اللى عندي و أخلي N تبدأ من عند
+
+250
+00:23:15,280 --> 00:23:20,080
+الذهور و ماعنديش مشكلة تمام؟ ليش؟ لأن لو حطيت N ب
+
+251
+00:23:20,080 --> 00:23:23,660
+zero في ال recurrence relation هذا بطلع منين؟بطلع
+
+252
+00:23:23,660 --> 00:23:29,660
+ال term اللي عنها ده إذا ممكن أن استغني عن هذه هيك
+
+253
+00:23:29,660 --> 00:23:37,260
+وروح أقول هذه ال N تساوي Zero واحد و اتنين و تلاتة
+
+254
+00:23:37,260 --> 00:23:42,080
+إلى مالها نهاية كتبت هيك ولا كتب هيك اتنين صح تكتب
+
+255
+00:23:42,080 --> 00:23:46,300
+الصيغة اللي تشوفيها مناسبة بالنسبة لك ماشي لإن راح
+
+256
+00:23:46,300 --> 00:23:49,880
+احطت N تساوي Zero في المستطيل هذا بطلع المستطيل
+
+257
+00:23:49,880 --> 00:23:54,230
+الأول عنها و ال term الأول اللي عنهاما علينا اتنين
+
+258
+00:23:54,230 --> 00:23:58,110
+جاهزة عندي بدلا الات اي ون و اي نود بدي اجيب من
+
+259
+00:23:58,110 --> 00:24:05,590
+ايه اتلاتة يبقى بدي اتلاتة اي اي ون زي اتنين اذا
+
+260
+00:24:05,590 --> 00:24:11,130
+بدي اشيل كل ان و احط مكانها واحد صحيح يبقى هذا
+
+261
+00:24:11,130 --> 00:24:15,410
+الكلام هي الناقص برا وهي الجوز بصير هذه يا بنات
+
+262
+00:24:15,410 --> 00:24:22,540
+تلاتة في اتنين اللي هو كده؟ ستة اتنينستة اتنين
+
+263
+00:24:22,540 --> 00:24:31,260
+زائد اربع اي واحد هذا كل البسطة على المقام المقام
+
+264
+00:24:31,260 --> 00:24:36,940
+ده احط هذه بواحد بصير تلاتة في اتنين بستة ستة في
+
+265
+00:24:36,940 --> 00:24:43,080
+اتنين باطمعش يبقى هذه كلها على اقمعش بالشكل اللي
+
+266
+00:24:43,080 --> 00:24:45,040
+عندنا تمام؟
+
+267
+00:24:46,600 --> 00:24:54,400
+هذه البنات تساوي ناقص نص فى مين فى الاتنين ستة على
+
+268
+00:24:54,400 --> 00:24:58,300
+اتناش بناقص نص فى الاتنين اربع على اتناش اللى هو
+
+269
+00:24:58,300 --> 00:25:07,480
+بقداش تلت يبقى ناقص تلت فى اربع يعني اربع اتلت لا
+
+270
+00:25:07,480 --> 00:25:10,780
+تلت بس تلت اللى هو ال
+
+271
+00:25:14,230 --> 00:25:20,910
+طب اتنين مقطع يبقى بقدر اشيل اتنين وحقمتها بصير
+
+272
+00:25:20,910 --> 00:25:26,530
+المثلة كلها بدلالة a node و a one يبقى هذا الكلام
+
+273
+00:25:26,530 --> 00:25:34,270
+بده يساوي ناقص نص و اتنين هيقلوب ناقص تلت ربع a
+
+274
+00:25:34,270 --> 00:25:42,630
+one في ناقص تلت ربع a one ناقص تلت ربع
+
+275
+00:25:44,980 --> 00:25:51,080
+هذا كله يكون ناقص
+
+276
+00:25:51,080 --> 00:26:00,050
+تلت A1 يبقى هذه تساويطلعيلي كويس هنا بدى افكر بصير
+
+277
+00:26:00,050 --> 00:26:07,050
+هذا قداش تلات اتمان بالموجب يبقى تلاتة على تمانية
+
+278
+00:26:07,050 --> 00:26:16,930
+ا one نقص فنقصه بزايد برضه تلات اتمان تلات اتمان a
+
+279
+00:26:16,930 --> 00:26:24,650
+naught ناقص تلت ا one طلعيلي ال term الأول و الأخر
+
+280
+00:26:26,110 --> 00:26:31,170
+يجب أن تجمع الموضوع في المشتركة الـ 3 و 8، 4 و 20،
+
+281
+00:26:31,170 --> 00:26:38,090
+يبقى لو قلت على 4 و 20بنضيف كدهش اربعة و عشرين على
+
+282
+00:26:38,090 --> 00:26:45,030
+تمانية فيها التلاتة في تلاتة بتسعة اي تسعة ا وان
+
+283
+00:26:45,030 --> 00:26:48,870
+تمام و نيجي هنا اربعة و عشرين على تلاتة فيها
+
+284
+00:26:48,870 --> 00:26:55,130
+تمانية في واحد بسالب تمانية ا وان سالب تمانية ا
+
+285
+00:26:55,130 --> 00:27:00,320
+وان هذا ال term هناالاخير تلاتة اثمان a note مالوش
+
+286
+00:27:00,320 --> 00:27:08,000
+دعوة لحاله يبقى زائد تلاتة اثمان a note ويساوي ها
+
+287
+00:27:08,000 --> 00:27:14,460
+بيبقى a one بس على اربعة وعشرين يبقى a one على
+
+288
+00:27:14,460 --> 00:27:21,120
+اربعة وعشرين زائد تلاتة a note على مين على تمانية
+
+289
+00:27:21,120 --> 00:27:29,910
+اذا تمكنا من كتابة من من كتابةالـ A تلاتة بدلالة
+
+290
+00:27:29,910 --> 00:27:38,390
+A1 و A0 بالمثل بدنا نروح نجيب A4 اللي عبارة عن A2
+
+291
+00:27:38,390 --> 00:27:43,630
+زائد 2 يبقى بدها اجع و اشيل كل N و احط مكانها
+
+292
+00:27:43,630 --> 00:27:50,240
+اتنين يبقى هاي السالب براو بدي احط اتنين بصير
+
+293
+00:27:50,240 --> 00:27:58,460
+اتنين واحد تلاتة تلاتة في تلاتة بتسعة اتلاتة يبقى
+
+294
+00:27:58,460 --> 00:28:08,620
+هذه تسعة اتلاتة زائد خمس اتنين على مين على حاطين
+
+295
+00:28:08,620 --> 00:28:14,540
+اتنينأربعة فى اتنين بتمانية تمانية فى تلاتة باربعة
+
+296
+00:28:14,540 --> 00:28:20,180
+وعشرين يبقى عالة أربعة وعشرين طب إيش بدى أسوي فيه
+
+297
+00:28:20,180 --> 00:28:25,740
+هذه يا بنات؟ بدى أشيل A تلاتة و أكتب قيمتها هذه
+
+298
+00:28:25,740 --> 00:28:31,580
+تصير بدلالة A1 و A1 و بدى أشيل A2 و أكتبها هنا إذا
+
+299
+00:28:31,580 --> 00:28:34,680
+أنا بدى أعطيك النتيجة بديش أضايق وقتي و أنا بسوي
+
+300
+00:28:34,680 --> 00:28:40,620
+كسوريبقى النتيجة النهائية على الشكل التالي بعد ما
+
+301
+00:28:40,620 --> 00:28:47,120
+تحسب الحسابات هذه بتطلع النتيجة عندك اللي هو A4
+
+302
+00:28:47,120 --> 00:28:52,780
+يساوي 9A1
+
+303
+00:28:52,780 --> 00:29:01,880
+على 64 زائد A node على 64
+
+304
+00:29:06,650 --> 00:29:12,570
+الان يكفينا هذا للحصول على مين؟ على شكل الحل احنا
+
+305
+00:29:12,570 --> 00:29:16,830
+فرضين الحل على الشكل اللى عندنا هذا اذا بد فيك هذا
+
+306
+00:29:16,830 --> 00:29:23,990
+مش هنعوض في a1 و a2 و a3 الى اخره يبقى باجي بقوله
+
+307
+00:29:23,990 --> 00:29:27,890
+ال solution سيكون على الشكل التالي
+
+308
+00:29:48,260 --> 00:29:54,740
+يبقى the solution is
+
+309
+00:29:54,740 --> 00:30:01,900
+y يساوي summation من n equal zero to infinity لل a
+
+310
+00:30:01,900 --> 00:30:07,130
+n x ناقص اتنين to the power nاللي كتبناها على
+
+311
+00:30:07,130 --> 00:30:15,650
+الشكل التالي a0 زائد a1 في ال X نقص اتنين زائد a2
+
+312
+00:30:15,650 --> 00:30:23,910
+في ال X نقص اتنين الكل تربيع زائد اللي هو a3 X نقص
+
+313
+00:30:23,910 --> 00:30:30,770
+اتنين الكل تكيب زائد a4 X نقص اتنين أس أربعة زائد
+
+314
+00:30:30,770 --> 00:30:38,940
+إلى ما شاء اللههذا الكلام يبدو يساوي ا نود مالاش
+
+315
+00:30:38,940 --> 00:30:44,400
+دعوة الحل بده يظل بدللتها كمان a1 في ال X ناقص
+
+316
+00:30:44,400 --> 00:30:49,640
+اتنين بتبقى كما هي الحل هيكون بدللتها الان بده
+
+317
+00:30:49,640 --> 00:30:54,920
+نيجي لمين وصلنا لا اتنين اتنين اللي هو ناقص تلتربع
+
+318
+00:30:54,920 --> 00:31:03,120
+a1 ناقص تلتربع a نود يبقى ناقص او زائد ناقص تلتربع
+
+319
+00:31:03,280 --> 00:31:11,500
+أول ناقص تلت تربع ا نوت كل هذا مضروب في مين؟ في ال
+
+320
+00:31:11,500 --> 00:31:18,720
+X ناقص اتنين لكل تربية جينا ل A تلاتة يبقى وصلنا ل
+
+321
+00:31:18,720 --> 00:31:26,900
+A تلاتة وين A تلاتة؟هي A3 اللي هو A1 على 24 يبقى
+
+322
+00:31:26,900 --> 00:31:38,060
+زائد A1 على 24 زائد اللي هو تلاتة A node تلاتة A
+
+323
+00:31:38,060 --> 00:31:45,020
+node على مين على تمانية كله هدف مين في ال X نقص
+
+324
+00:31:45,020 --> 00:31:53,440
+اتنين لكل تكييف زائد جينا ل A4اللي هو 9A1 على 64
+
+325
+00:31:53,440 --> 00:32:08,240
+9A1 على 64 زائد A node على 64 على 64 في ال X نقص 2
+
+326
+00:32:08,240 --> 00:32:16,380
+كله أربعة زائد إلى ما شاء الله طيب
+
+327
+00:32:16,380 --> 00:32:22,260
+هذا الكلام يساويبتاخد اللي فيهم a node مع بعض
+
+328
+00:32:22,260 --> 00:32:28,320
+والباقي اللي فيهم a one مع بعض يبقى هذا a node مين
+
+329
+00:32:28,320 --> 00:32:34,380
+بيظل ان يعمل اتنين واحد هنا هذه a node بصير ناقص
+
+330
+00:32:34,380 --> 00:32:41,720
+تلت اربع ناقص تلت اربعفي ال X ناقص اتنين لكل
+
+331
+00:32:41,720 --> 00:32:48,480
+ترابيع خدت ال term هذا فقط تمام نجي ل بعده بدي اخد
+
+332
+00:32:48,480 --> 00:32:56,020
+ال term هذا يبقى زائد تلت أتمان في ال X ناقص اتنين
+
+333
+00:32:56,020 --> 00:33:04,600
+لكل تكيبزائد واحد على اربعة وستين يعني X نقص اتنين
+
+334
+00:33:04,600 --> 00:33:13,600
+كله أس اربعة على اربعة وستين زائد إلى ما شاء الله
+
+335
+00:33:13,600 --> 00:33:21,090
+زائدبتروح اخد a one عامل مشترك ايش بيظل عندي؟ x
+
+336
+00:33:21,090 --> 00:33:28,490
+ناقص اتنين بيداجي هذه ناقص تلت تربع يبقى ناقص تلت
+
+337
+00:33:28,490 --> 00:33:34,710
+تربع في من؟ في ال x ناقص اتنين لكل تربيع خلصنا
+
+338
+00:33:34,710 --> 00:33:41,770
+منها و ال a نود هي برا نجي لبعدهازائد اكس ناقص
+
+339
+00:33:41,770 --> 00:33:48,170
+اتنين الكل تكعيب على اربع وعشرين نجي اللي بعدها
+
+340
+00:33:48,170 --> 00:33:56,150
+زائد تسعة في ال X ناقص اتنين اص اربع على اربع
+
+341
+00:33:56,150 --> 00:33:59,590
+وستين زائد الى ما شاء الله
+
+342
+00:34:06,460 --> 00:34:11,780
+هذا هو الحل الأول وهذا هو الحل الثاني لـ second
+
+343
+00:34:11,780 --> 00:34:19,140
+order differential equation اللي عندنا
+
+344
+00:34:29,160 --> 00:34:33,760
+في أي حتة في السؤال اللي فات يعني أحيانا بنكتب ايش
+
+345
+00:34:33,760 --> 00:34:38,320
+find the first three terms of the series solution
+
+346
+00:34:38,320 --> 00:34:43,300
+يعني بهمناش الشكل العام اللي هو شكل الحد النوني في
+
+347
+00:34:43,300 --> 00:34:47,120
+ال summation لكن بهم نجيب الأول تلات أربعة termات
+
+348
+00:34:47,120 --> 00:34:51,720
+أو أول تلات termات مما يدل على أن هذه مالها عبارة
+
+349
+00:34:51,720 --> 00:34:56,260
+عن series حد فيكوا اللي يتساؤل هنا؟
+
+350
+00:35:07,760 --> 00:35:16,060
+لحد هنا stop بدنا منكوا المسائل التاليةيبقى
+
+351
+00:35:16,060 --> 00:35:23,640
+exercises خمسة اتنين بدنا المساهل من واحد لغاية
+
+352
+00:35:23,640 --> 00:35:33,740
+تلتاش الأد و بدنا من خمستاش لغاية تمانتاش part
+
+353
+00:35:33,740 --> 00:35:38,880
+اللي هو ايه فقط اللي باجي بدناه شي اللي متعلق
+
+354
+00:35:38,880 --> 00:35:45,160
+بالرسم و ما إلى ذلك كله مش لازمنبس هاتون هذا الجزء
+
+355
+00:35:45,160 --> 00:35:48,720
+الموضوع
+
+356
+00:35:48,720 --> 00:35:51,240
+هذا ال section اللي انتهينا منه كان serious
+
+357
+00:35:51,240 --> 00:35:56,800
+solution near an ordinary point part one بدنا نيجي
+
+358
+00:35:56,800 --> 00:35:59,140
+ل section اللي بعده ال section اللي بعده برضه
+
+359
+00:35:59,140 --> 00:36:03,880
+serious solution near an ordinary point part two
+
+360
+00:36:03,880 --> 00:36:06,100
+يبقى الجزء الثاني
+
+361
+00:36:34,050 --> 00:36:37,690
+حد ابيض اي كلمة من هنا اللي على اللوحة ده امسح
+
+362
+00:36:58,660 --> 00:37:11,260
+يبقى section خمسة تلاتة series solution near an
+
+363
+00:37:11,260 --> 00:37:19,040
+ordinary point part
+
+364
+00:37:19,040 --> 00:37:20,720
+two
+
+365
+00:37:28,670 --> 00:37:33,510
+الفكرة في هذه المقالة هي ان اذا كنا نشتغل شغل لو
+
+366
+00:37:33,510 --> 00:37:39,130
+روح نجيب شكل الان او العلاقة بترمض من بين الان
+
+367
+00:37:39,130 --> 00:37:44,190
+والان زاد واحد او الان زاد اتنين والان زاد واحد مع
+
+368
+00:37:44,190 --> 00:37:48,420
+الان هو ده كنا نسميها recurrence relationبنبطل
+
+369
+00:37:48,420 --> 00:37:52,720
+نجيب ال reference relation لكن بدي أجيب صيغة أخرى
+
+370
+00:37:52,720 --> 00:37:59,800
+للان كيف هذا ما سنشير إليه الآن ان شاء الله بدنا
+
+371
+00:37:59,800 --> 00:38:02,660
+نشير للمعادلة التفاضل اللي بدأنا فيها المرة اللي
+
+372
+00:38:02,660 --> 00:38:07,200
+فاتت و اللي حد فيها الآن و بعدين بنشوف كيف بنجيب
+
+373
+00:38:07,200 --> 00:38:15,180
+الان يبقى بيقول ي suppose that افترض أنه ال
+
+374
+00:38:15,180 --> 00:38:16,500
+differential equation
+
+375
+00:38:21,770 --> 00:38:27,290
+المعادلة التفاضلية P of X في الـ Y double prime P
+
+376
+00:38:27,290 --> 00:38:29,510
+of X في ال Y double prime P of X في ال Y double
+
+377
+00:38:29,510 --> 00:38:30,310
+prime P of X في ال Y double prime P of X في ال Y
+
+378
+00:38:30,310 --> 00:38:32,630
+double prime P of X في ال Y double prime P of X في
+
+379
+00:38:32,630 --> 00:38:38,530
+ال Y double prime P of X في ال Y double prime
+
+380
+00:38:44,330 --> 00:38:54,390
+هذه المعادلة لها حل على صيغة Y تساوي Phi of X and
+
+381
+00:38:54,390 --> 00:39:03,890
+that Phi of X has a Taylor series
+
+382
+00:39:10,600 --> 00:39:18,180
+متسلسل التالور اللي على الشكل التالي Y تسوى فاي of
+
+383
+00:39:18,180 --> 00:39:25,760
+X سم من N equal zero to infinity لل A N في ال X
+
+384
+00:39:25,760 --> 00:39:32,720
+نقص ال X not to the power N which converge
+
+385
+00:39:33,280 --> 00:39:40,280
+واللي بتكون تقاربية for absolute value لل X نقص ال
+
+386
+00:39:40,280 --> 00:39:46,280
+X node أقل من ال raw و ال raw greater than zero
+
+387
+00:39:46,280 --> 00:39:59,300
+and ال X node is an ordinary point تبقى هذه نقطة
+
+388
+00:39:59,300 --> 00:40:08,650
+عادية we shall findwe shall find بنحاول نوجد a
+
+389
+00:40:08,650 --> 00:40:12,550
+formula صيغة
+
+390
+00:40:12,550 --> 00:40:27,650
+for ال a n نرجع
+
+391
+00:40:27,650 --> 00:40:32,340
+لكلام اللي احنا كاتبينه هذا مرة ثانيةجالي افترض ان
+
+392
+00:40:32,340 --> 00:40:35,500
+عند المعادلة التفاضلية اللى سميتها المعادلة 1 نفس
+
+393
+00:40:35,500 --> 00:40:39,320
+المعادلة تابعة المرة اللى فاتت لم نغير فيها شيئا
+
+394
+00:40:39,320 --> 00:40:44,500
+ده افترض المعادلة دى لها حل على الشكل y تساوي phi
+
+395
+00:40:44,500 --> 00:40:48,940
+of x حيث phi of x has a taylor series شو يعني
+
+396
+00:40:48,940 --> 00:40:56,590
+taylor series يعني معناته ان هذه analyticتمام طيب
+
+397
+00:40:56,590 --> 00:41:00,770
+يعني في of x هذه انا لاتكيبها في of x كتبتها على
+
+398
+00:41:00,770 --> 00:41:04,650
+شكل تايلور سيريز بالشكل اللي عندنا هذا which
+
+399
+00:41:04,650 --> 00:41:09,010
+converge والتي تكون تقاربية على الفترة هذه وهذا
+
+400
+00:41:09,010 --> 00:41:13,430
+رسمتلكوا قبل قليل بس ال X node حاطيتها عنده نقطة
+
+401
+00:41:13,430 --> 00:41:18,770
+يساوي اتنين وال X node عبارة عن an ordinary point
+
+402
+00:41:18,770 --> 00:41:25,150
+بنحاول نجيب شكل ال a انتوفي المثال هذا والمثال
+
+403
+00:41:25,150 --> 00:41:29,070
+المراري فاتة نجيب الـ Recurrence relation اللي
+
+404
+00:41:29,070 --> 00:41:34,210
+بتربط ما بين الان زائد اتنين والان او الان زائد
+
+405
+00:41:34,210 --> 00:41:40,630
+واحد والانالان بنحاول نوجد هذه بطريقة اخرى او
+
+406
+00:41:40,630 --> 00:41:46,030
+بصيغة اخرى غير اللى اتعودنا عليها قبل ذلك الان كيف
+
+407
+00:41:46,030 --> 00:41:51,790
+كالتالي هي عندي فاي of X اللى هو ال summation من N
+
+408
+00:41:51,790 --> 00:41:57,810
+equal zero to infinity لل A N في ال X نقص ال X not
+
+409
+00:41:57,810 --> 00:42:04,120
+to the power Nلو كتبتها بالشكل الطويل يبقى هذا إيش
+
+410
+00:42:04,120 --> 00:42:09,880
+بده تساوي a naught حط zero بصير هذا كله term واحد
+
+411
+00:42:10,270 --> 00:42:18,210
+حط بواحد بصير a1 في ال X ناقص ال X node a2 في ال X
+
+412
+00:42:18,210 --> 00:42:25,910
+ناقص X node لكل تربيع a3 في ال X ناقص ال X node
+
+413
+00:42:25,910 --> 00:42:33,750
+لكل تكييب زائد a4 X ناقص X node to the power 4
+
+414
+00:42:33,750 --> 00:42:38,370
+زائد إلى ما شاء الله لغاية ما نوصل لشكل الحد
+
+415
+00:42:38,370 --> 00:42:43,000
+النونيفبحنا عندنا المشتقة الأولى والثانية إذا بدي
+
+416
+00:42:43,000 --> 00:42:48,260
+أروح أجيب المشتقة الأولى والمشتقة الثانية بس قبلها
+
+417
+00:42:48,260 --> 00:42:53,280
+يا بنات لو بدي أجيب five of X node بدي أعرف قداش
+
+418
+00:42:53,280 --> 00:43:00,080
+تساوي هديها منها لو بدي أجيب five of X node يعني
+
+419
+00:43:00,080 --> 00:43:05,440
+قداش قيمة الحل هذا عند ال X node يبقى بدي أشيل كل
+
+420
+00:43:05,440 --> 00:43:11,050
+X و أحط مكانهاالحمد لله كلهم بروحوا مع دمين term
+
+421
+00:43:11,050 --> 00:43:17,530
+الأول يبقى هاي ظهر عندي اللي هو ال a node اللي انا
+
+422
+00:43:17,530 --> 00:43:22,100
+بقى يظهر معايا تابو جتابو قبل شوية في الحلطب بدى
+
+423
+00:43:22,100 --> 00:43:28,300
+اروح اجيبله file prime of x يبقى بده داشتق هدى مع
+
+424
+00:43:28,300 --> 00:43:34,380
+السلامة ايش بطلع عندى هنا اي one يبقى هدى اي one
+
+425
+00:43:34,380 --> 00:43:38,880
+ومشتقة ال X node انه رقم ثابت ب zero ومشتقة هدى
+
+426
+00:43:38,880 --> 00:43:47,230
+بقدرش بواحدمع السلامة يبقى زائد اتنين اتنين اتنين
+
+427
+00:43:47,230 --> 00:43:54,670
+اتنين في ال X ناقص ال X node أسواحى زائد تلاتة
+
+428
+00:43:54,670 --> 00:44:02,330
+اتلاتة في ال X ناقص X node الكل تربيع زائد أربعة
+
+429
+00:44:02,330 --> 00:44:11,840
+اربعة X ناقص X node الكل تكيب زائد إلى آخرينطب ايش
+
+430
+00:44:11,840 --> 00:44:17,620
+رأيك احسب المشتق هذي كذلك عند X node يبقى هذا
+
+431
+00:44:17,620 --> 00:44:24,280
+الكلام بدي يعطينا five prime of X node بدي ساعده
+
+432
+00:44:24,280 --> 00:44:29,640
+حط هنا X node بطير و كلهم شو بظل عنده يبقى هذي A1
+
+433
+00:44:29,640 --> 00:44:35,710
+طيب خلوا هذول عندك في الذاكرةبالزمن ان نرجع لهم
+
+434
+00:44:35,710 --> 00:44:42,930
+بعد قليل و بنواصل المشي تبعنا بدروح اجيب مين مشتقة
+
+435
+00:44:42,930 --> 00:44:50,730
+ا ثانية يبقى five w prime of x هذا مع السلامة هذا
+
+436
+00:44:50,730 --> 00:44:58,680
+بيبقى قداش اتنين اتنينبواحد يبقى هذا بيصير اتنين
+
+437
+00:44:58,680 --> 00:45:06,940
+في تلاتة بستة اتلاتة اكس ناقص اكس نود أس واحد زائد
+
+438
+00:45:06,940 --> 00:45:14,320
+تلاتة في أربع باطماشر اربعة في مين في ال X ناقص X
+
+439
+00:45:14,320 --> 00:45:21,560
+نود الكل تربية زائد إلى ما شاء الله اللي خاطر اعيد
+
+440
+00:45:21,560 --> 00:45:26,380
+صياغة هذا term مرة تانيةفبروح بقول هذا الكلام
+
+441
+00:45:26,380 --> 00:45:30,720
+يساوي اتنين هذه يا بنات مش بقدر اكتبها اتنين
+
+442
+00:45:30,720 --> 00:45:38,340
+factorial مضروب اتنين في اتنين يبقى هذا اتنين
+
+443
+00:45:38,340 --> 00:45:45,780
+factorial في اتنين طيب ايش ستة مضروب تلاتة يبقى
+
+444
+00:45:45,780 --> 00:45:54,410
+هذا تلاتة factorialأتلاتة في ال X ناقص ال X node
+
+445
+00:45:54,410 --> 00:46:00,930
+هذه لسه مقدرش خليكي ماتريحة شوية يبقى هذا الكلام
+
+446
+00:46:00,930 --> 00:46:08,590
+زائد اللي هو اتناشر اربع X ناقص X node لكل تربية
+
+447
+00:46:08,590 --> 00:46:16,450
+زائد إلى ما شاء الله طب لو بده اجيب امانات في W
+
+448
+00:46:16,450 --> 00:46:25,730
+prime of X nodeهذا كله بروح بظل قداش بس يبقى هانها
+
+449
+00:46:25,730 --> 00:46:32,870
+لو بده اجيب في بابلي prime of X node يبقى النتيجة
+
+450
+00:46:32,870 --> 00:46:39,870
+2 factorial اتنين بس حط هنا X node ب 00 والبقى كله
+
+451
+00:46:39,870 --> 00:46:44,590
+بروح مرة ثانية طيب ايش رأيك ان نجيب المشتقة
+
+452
+00:46:44,590 --> 00:46:50,650
+التالتة؟يبقى لو جبت المشتقة التالتة as a function
+
+453
+00:46:50,650 --> 00:46:56,110
+of X يبقى إيش بتعطينا هذا مع السلامة و بيبقى لنا
+
+454
+00:46:56,110 --> 00:47:02,350
+مين؟ اللي هو التلاتة factorial a تلاتة بدي أشتق
+
+455
+00:47:02,350 --> 00:47:07,130
+هذه السلة هذه بتروح هذه تلاتة factorial a تلاتة
+
+456
+00:47:07,130 --> 00:47:10,990
+هذه إيش بيصير؟ نفس اتماشي باربعة و عشرين الهمين
+
+457
+00:47:11,760 --> 00:47:18,620
+أربعة factorial اربعة يبقى زائد اربعة factorial
+
+458
+00:47:18,620 --> 00:47:28,200
+اربعة بظلمينا ان ال X نقص ال X node أس واحد زائد
+
+459
+00:47:28,200 --> 00:47:29,980
+إلى آخرين
+
+460
+00:47:32,430 --> 00:47:39,110
+طيب، هذه مش بتعطيني يا بنات، كمان المشتقة الرقم
+
+461
+00:47:39,110 --> 00:47:44,610
+تلاتة عند ال X note قد إيش تساوي؟ تلاتة factorial
+
+462
+00:47:44,610 --> 00:47:49,750
+A تلاتة تلاتة factorial A تلاتة
+
+463
+00:47:52,290 --> 00:47:59,130
+طب لو ضليت مستمر عليها الشكل هذه بوصل
+
+464
+00:47:59,130 --> 00:48:06,570
+للمشتقة رقم M مثلا يبقى لو ضليت مستمر هوصل للمشتقة
+
+465
+00:48:06,570 --> 00:48:15,470
+رقم M عند ال X هشوف قداش تساوي طلع يا ابنك المشتقة
+
+466
+00:48:15,470 --> 00:48:22,780
+الثانية يبقى 2 factorial ايه اتنين؟زائد ثلاثة
+
+467
+00:48:22,780 --> 00:48:27,540
+factorial أكبر منها ا ثلاثة في اكس نقص اكس نوت
+
+468
+00:48:27,540 --> 00:48:34,200
+زائد طيب لو جت المشتقة التالتة ثلاثة factorial ا
+
+469
+00:48:34,200 --> 00:48:40,280
+ثلاثة اربعة factorial ها اكس نقص اكس نوت اكس واحد
+
+470
+00:48:40,280 --> 00:48:45,660
+زائد الى اخره يبقى انا بدروح اعمم هذه و اقول لو
+
+471
+00:48:45,660 --> 00:48:54,960
+وصلت لمشتقة رقم Mتلاتة تلاتة تلاتة تلاتة
+
+472
+00:48:54,960 --> 00:48:57,580
+تلاتة تلاتة تلاتة تلاتة تلاتة تلاتة تلاتة تلاتة
+
+473
+00:48:57,580 --> 00:48:57,660
+تلاتة تلاتة تلاتة تلاتة تلاتة تلاتة تلاتة تلاتة
+
+474
+00:48:57,660 --> 00:49:01,080
+تلاتة تلاتة تلاتة تلاتة تلاتة تلاتة تلاتة تلاتة
+
+475
+00:49:01,080 --> 00:49:03,700
+تلاتة تلاتة تلاتة تلاتة تلاتة تلاتة تلاتة تلاتة
+
+476
+00:49:03,700 --> 00:49:06,760
+تلاتة
+
+477
+00:49:06,760 --> 00:49:06,780
+تلاتة تلاتة تلاتة تلاتة تلاتة تلاتة تلاتة تلاتة
+
+478
+00:49:06,780 --> 00:49:11,360
+تلاتة تلاتة تلاتة
+
+479
+00:49:12,280 --> 00:49:16,920
+يبقى ايش بيكون M زائد واحد factorial في M في M
+
+480
+00:49:16,920 --> 00:49:20,820
+ناقص واحد في M ناقص اتنين لغاية ما نوصل لتلاتة في
+
+481
+00:49:20,820 --> 00:49:27,440
+اتنين في واحد يبقى زائد ه اللي هو ال M زائد واحد
+
+482
+00:49:27,440 --> 00:49:34,320
+في ال M في ال M ناقص واحد في ال M ناقص اتنين ونظل
+
+483
+00:49:34,320 --> 00:49:40,430
+ماشي لغاية ما نوصل لاتنين في واحد يبقى هذا منالـ
+
+484
+00:49:40,430 --> 00:49:44,050
+factorial اللي كتبته لسه ال factorial بيجينا هد
+
+485
+00:49:44,050 --> 00:49:50,990
+مين؟ ا م زائد واحد لأنه أكبر منه بواحد فاهمين؟ في
+
+486
+00:49:50,990 --> 00:50:05,190
+ال a m زائد واحد فاهمين؟ في ال x ناقص x node زائد
+
+487
+00:50:05,190 --> 00:50:06,810
+إلى ما شاء الله
+
+488
+00:50:11,590 --> 00:50:17,910
+بناء عليه لو جيها تقول في to the derivative M عند
+
+489
+00:50:17,910 --> 00:50:18,570
+ال X
+
+490
+00:50:21,210 --> 00:50:26,530
+الـ M factorial في الـ A M و هذا بروحكوا لو قداش
+
+491
+00:50:26,530 --> 00:50:33,530
+بزيرو طب انا بده اوصل ل A N فباجي بقوله بكل بساطة
+
+492
+00:50:33,530 --> 00:50:41,030
+لو وصلت للمشتقى الرقم N عند ال X node بده يساوي N
+
+493
+00:50:41,030 --> 00:50:48,830
+factorial في ال A Mصحيح ولا لأ؟ يبقى هذه الصيغة
+
+494
+00:50:48,830 --> 00:50:53,370
+تبعتي ليها تحت الوضع بدي AN لحالها بقوله بسيطة
+
+495
+00:50:53,370 --> 00:50:59,790
+يبقى هذا بدي يعطينا ان AN بدي ساوي المشتق الرقم N
+
+496
+00:50:59,790 --> 00:51:07,040
+عند ال ordinary point X node على N factorialهذه
+
+497
+00:51:07,040 --> 00:51:17,470
+لإتنين أرض نفس الشيء يبقى هذه لو فاكتورياطيب هك
+
+498
+00:51:17,470 --> 00:51:22,970
+انا جبتله مين؟ جبتله المشتقة جبتله a n بدلالة
+
+499
+00:51:22,970 --> 00:51:27,870
+المشتقة النونية للحل اللي هو مين؟ اللي هو five لكن
+
+500
+00:51:27,870 --> 00:51:32,170
+هنا بعد ما كنا نجيب ال recurrence relation روح
+
+501
+00:51:32,170 --> 00:51:39,410
+تواصل الحل وجيب الحل بدلالة a node و a one مظبوط؟
+
+502
+00:51:39,410 --> 00:51:44,280
+شك بغير مسوء المثال اللي جابني شويةيبقى انا بيدروح
+
+503
+00:51:44,280 --> 00:51:49,220
+اجيب ال a in بدلات ال a node و ال a one و اذا
+
+504
+00:51:49,220 --> 00:51:54,480
+جبتهم بكون خلصت ماشي يبقى الان بدأ نكتب الكلمتين
+
+505
+00:51:54,480 --> 00:51:58,980
+والاتنين هذول سميلي هذه رقم اتنين الصيغة هذه او
+
+506
+00:51:58,980 --> 00:52:05,120
+هذه سميها لرقم اتنين اكتب
+
+507
+00:52:05,120 --> 00:52:08,340
+now we shall
+
+508
+00:52:13,700 --> 00:52:22,840
+write an in terms
+
+509
+00:52:22,840 --> 00:52:36,580
+of a node and a ion as follows يبقى كتالي since
+
+510
+00:52:40,720 --> 00:52:46,100
+is a solution
+
+511
+00:52:46,100 --> 00:53:04,480
+of the differential equation when we have طلعيني
+
+512
+00:53:04,480 --> 00:53:11,600
+كويسأحنا فرضنا أن في of x هي حل المعادلة التفاضلية
+
+513
+00:53:11,600 --> 00:53:15,160
+إذا المعادلة التفاضلية رقم واحد بقدر أكتبها على
+
+514
+00:53:15,160 --> 00:53:20,540
+الشكل التالف بقدر أشيل كل y و أكتب هذا أيضا في of
+
+515
+00:53:20,540 --> 00:53:28,000
+x لإنها تحققها يبقاش بصير أن P of x في في w prime
+
+516
+00:53:28,000 --> 00:53:28,740
+of x
+
+517
+00:53:50,100 --> 00:53:57,610
+ممكن اجسم كله على capital P of Xبصير الـ phi w
+
+518
+00:53:57,610 --> 00:54:06,210
+prime of x زائد p small of x في الـ phi prime of x
+
+519
+00:54:06,210 --> 00:54:12,970
+زائد ل q small of x في الـ phi of x بده يساوي zero
+
+520
+00:54:12,970 --> 00:54:23,720
+whereحيث ال P of X small هي عبارة عن ل Q of X على
+
+521
+00:54:23,720 --> 00:54:32,740
+capital P of X and ل Q of X هي عبارة عن R of X
+
+522
+00:54:32,740 --> 00:54:38,100
+capital على capital P of X وهدول are analytic
+
+523
+00:54:38,100 --> 00:54:39,320
+functions
+
+524
+00:54:50,060 --> 00:54:55,560
+يبقى دول تحلية بقدر اكتبهم على شكل تايلور سيريز
+
+525
+00:54:55,560 --> 00:55:03,620
+يبقى السا ممكن اعيد كتابة المعادلة هذه مرة ثانية
+
+526
+00:55:03,620 --> 00:55:09,440
+واروح اقول five w prime of x بدا اساوي only هدول
+
+527
+00:55:09,440 --> 00:55:12,500
+على الشجة التانية يبقى بصير سالب
+
+528
+00:55:28,850 --> 00:55:35,970
+من فوق بالزمن المشتقة عند من عند ال ordinary point
+
+529
+00:55:35,970 --> 00:55:42,600
+x0 إذا بناء عليها بقدر أحسب هذه عند ال x0يبقى باجي
+
+530
+00:55:42,600 --> 00:55:47,780
+بقوله هذه سميها للمعادلة رقم تلاتة منها لأن هذه
+
+531
+00:55:47,780 --> 00:55:52,860
+أساسية عندنا الآن إيش رأيك؟ بدأ اكتب هذه الآن
+
+532
+00:55:52,860 --> 00:55:58,860
+بدللة a0 و a1 إذا بروح أعوض في mean عند ال
+
+533
+00:55:58,860 --> 00:56:04,560
+ordinary point ل X0 يبقى بصير عندنا Phi W prime of
+
+534
+00:56:04,560 --> 00:56:12,090
+X0يساوي ناقص P of X node في الـ Phi prime of X
+
+535
+00:56:12,090 --> 00:56:18,950
+node ناقص ل Q of X node في ال Phi of X node و
+
+536
+00:56:18,950 --> 00:56:27,310
+يساوي طب قداش ال Phi prime of X node one
+
+537
+00:56:27,310 --> 00:56:35,520
+يبقى بقدر اشيل و اكتب دلها مينيبقى هنا ناقص P of X
+
+538
+00:56:35,520 --> 00:56:44,760
+node في ال A1 تمام؟ وهنا ناقص ل Q of X node في ال
+
+539
+00:56:44,760 --> 00:56:48,980
+Phi of X node Phi of X node اللي هي قداشر؟ A node
+
+540
+00:56:48,980 --> 00:56:55,420
+يبقى هنا في ال A node يبقى بناء عليه كتابة Phi W
+
+541
+00:56:55,420 --> 00:57:09,220
+primeبدل من اي نود او اكس نود بدل من اي نود او
+
+542
+00:57:09,220 --> 00:57:21,600
+اتنين
+
+543
+00:57:21,990 --> 00:57:25,730
+طيب ايش رايك الان بدي اروح اجيب كمان المشتقة
+
+544
+00:57:25,730 --> 00:57:31,670
+التالتة و الرابعة و الخامسة كله بدلالة a node و a1
+
+545
+00:57:31,670 --> 00:57:37,270
+يبقى بدي اجي على الاتنين هذي شو اعملها بدي اشتقها
+
+546
+00:57:37,270 --> 00:57:44,310
+كمان مرة يبقى باجي بقوله five triple prime of x
+
+547
+00:57:44,310 --> 00:57:51,560
+اوه هذه يا عزيزي لان كلها مشتقة حصل ضرب دلتينيبقى
+
+548
+00:57:51,560 --> 00:57:57,960
+بدي اكتبها باختصار يبقى سالب P في الـ Fi W Prime
+
+549
+00:57:57,960 --> 00:58:03,840
+سالب P Prime في ال Fi Prime هاي اشتقنا ال term
+
+550
+00:58:03,840 --> 00:58:10,700
+الأول بدي اجي لterm التاني سالبي Q في ال Fi Prime
+
+551
+00:58:10,700 --> 00:58:20,280
+سالبي Q Prime في ال Fi زي ما هي طيب شرايك هذه و
+
+552
+00:58:20,280 --> 00:58:25,500
+هذه؟مش كلهم مضربات في الـ fi prime إذا ما بقدر
+
+553
+00:58:25,500 --> 00:58:33,220
+أخدهم مين مع بعض يبقى هذا الكلام بده يساوي سالب P
+
+554
+00:58:33,220 --> 00:58:41,540
+في ال fi double prime سالب و هي goes بظهر P prime
+
+555
+00:58:43,330 --> 00:58:53,370
+الـ Q كله في مين؟ في الـPhi A' سالب AQ' في مين؟ في
+
+556
+00:58:53,370 --> 00:58:58,430
+الـPhi بتفهم ان هذه function في X وهذه function في
+
+557
+00:58:58,430 --> 00:59:04,590
+X وهذه function في X وكله functions of X تمام؟ إذا
+
+558
+00:59:04,590 --> 00:59:10,100
+بقدر أحسب المشتقة الثاني هذي وين؟عند ال X node
+
+559
+00:59:10,100 --> 00:59:15,740
+يبقى بروح بقوله يبقى Phi triple prime عند ال X
+
+560
+00:59:15,740 --> 00:59:25,140
+node يساوي ناقص P of X node مين هذه؟ Phi double
+
+561
+00:59:25,140 --> 00:59:31,560
+prime of X node موجودة؟ هيها فوق إذا بقدر أجيبها
+
+562
+00:59:31,560 --> 00:59:37,960
+من فوق و نزلها هيها يبقى هذه بالصير في مين؟في سالب
+
+563
+00:59:37,960 --> 00:59:47,680
+P of X node في ال A1 سالب EQ of X node في ال A0
+
+564
+00:59:51,170 --> 00:59:56,730
+طيب هيخلص لسه ال term الأول بداجي لل term التاني
+
+565
+00:59:56,730 --> 01:00:07,750
+ناقص P prime of X node of X node زائد ل Q of X
+
+566
+01:00:07,750 --> 01:00:14,130
+node كله في من؟ في ال 5 primeفاي برايم اف اكس نود
+
+567
+01:00:14,130 --> 01:00:19,790
+فاي برايم اف اكس نود اللي هو كده؟ اون يبقى هذا كله
+
+568
+01:00:19,790 --> 01:00:26,170
+في ال اون ناقص يكيو برايم اف اكس نود في الفاي اف
+
+569
+01:00:26,170 --> 01:00:33,840
+اكس نود اللي هو كده؟ ا نودوهي كتبنا المشتقة
+
+570
+01:00:33,840 --> 01:00:40,100
+التالتة عند X node ليس بدلات ال A3 وانما بدلات ال
+
+571
+01:00:40,100 --> 01:00:46,980
+A node وA1 بنفس الطريقة نشتغل نفس الشغل
+
+572
+01:01:05,640 --> 01:01:13,300
+يبقى هنا سا وي رايت روحنا كتبنا five triple a
+
+573
+01:01:13,300 --> 01:01:23,280
+prime of x node in terms of a node and a one
+
+574
+01:01:23,280 --> 01:01:27,300
+similarly بنفس الطريقة
+
+575
+01:01:30,190 --> 01:01:39,430
+Similarly, we can write نصاتية كتابة المشتقة
+
+576
+01:01:39,430 --> 01:01:46,290
+الرابعة عند ال X node و المشتقة الخامسة عند ال X
+
+577
+01:01:46,290 --> 01:01:56,270
+node و و و إلى آخره in terms ofهو بنقدر نقول كتبنا
+
+578
+01:01:56,270 --> 01:02:04,930
+ال a in a similarly we can write in terms of ..
+
+579
+01:02:04,930 --> 01:02:15,330
+استني شوية استني شوية that is that is
+
+580
+01:02:15,330 --> 01:02:30,520
+we write we writeكتبنا a in in terms of اللي هو a
+
+581
+01:02:30,520 --> 01:02:39,600
+naught and a oneليش؟ لأن هنا لو قلنا المشتقة
+
+582
+01:02:39,600 --> 01:02:44,120
+الثاني يبقى اتنين factorial a in يبقى بصير هذه
+
+583
+01:02:44,120 --> 01:02:49,500
+مجسومة على اتنين هي يبقى هاي اتنين اتلاتة اربعة
+
+584
+01:02:49,500 --> 01:02:59,060
+هكذا كتبناها بدلالة تانية طيب similarly we
+
+585
+01:02:59,060 --> 01:03:00,980
+can
+
+586
+01:03:04,200 --> 01:03:10,580
+right similarly we can هذه كتبنا ايه تلاتة يا بنا
+
+587
+01:03:10,580 --> 01:03:15,800
+مش اكتر يبقى ايه تلاتة بدلالة انه ليش لان جه
+
+588
+01:03:15,800 --> 01:03:20,700
+المشتقة هادي هادي بناء عليه تبقى ايه تلاتة يسوى
+
+589
+01:03:20,700 --> 01:03:25,800
+المشتقة التالتة على تلاتة factorial مظبوط يبقى هنا
+
+590
+01:03:25,800 --> 01:03:29,920
+بقدر اقول كتبنا ايه تلاتة in terms similarly we
+
+591
+01:03:29,920 --> 01:03:31,380
+can write
+
+592
+01:03:34,560 --> 01:03:41,120
+in terms of
+
+593
+01:03:41,120 --> 01:03:55,180
+in terms of الحمد لله and a one طيب
+
+594
+01:03:55,180 --> 01:03:59,720
+ده رجع الكلام هذا فقط مشان بس يثبت المعنى احنا
+
+595
+01:03:59,720 --> 01:04:03,900
+خلصنابس مشان نثبت المعلومات و بعد كده بناخد أمثلة
+
+596
+01:04:03,900 --> 01:04:09,560
+مشان نشوف كيف بدنا نطبق هذا الكلام اللي قلناه احنا
+
+597
+01:04:09,560 --> 01:04:15,260
+وصلنا الى هذه الصيغة تمام و سمينا وصلنا ل ال mail
+
+598
+01:04:15,260 --> 01:04:18,560
+معادلة هذه و روحنا كتبناها فى الصيغة اللى عندنا هي
+
+599
+01:04:18,560 --> 01:04:20,720
+رقم تلاتة
+
+600
+01:04:23,910 --> 01:04:29,090
+قلنا نذهب و نحسب المشتقة الثانية عند ال point
+
+601
+01:04:29,090 --> 01:04:34,130
+ordinary يبقى اشيلنا كل X و كتبنا بدلها من X node
+
+602
+01:04:34,130 --> 01:04:38,570
+صارت هنا ناقص P of X node في Prime of X node ناقص
+
+603
+01:04:38,570 --> 01:04:42,250
+Q of X node في Prime of X nodeالان شيلنا fire
+
+604
+01:04:42,250 --> 01:04:45,170
+prime of x node و حطينا قيمتها اللي طلعناها قبل
+
+605
+01:04:45,170 --> 01:04:49,130
+قليل a1 و شيلنا fire of x node و طلعنا قيمتها اللي
+
+606
+01:04:49,130 --> 01:04:54,130
+هي main a node يبقى صار هذه قيمة المشتقة الثانية
+
+607
+01:04:54,130 --> 01:05:01,290
+لكن يا بنات أليست هذه هي اتنين factorial في ال a2
+
+608
+01:05:03,960 --> 01:05:09,220
+أتنين فاكتوريال في ال A2 لأننا مجتقة ثانية صحيح
+
+609
+01:05:09,220 --> 01:05:16,060
+ولا لأ؟ كويس يعني معناته أنا جدرت أكتب A2 بذللة A1
+
+610
+01:05:16,060 --> 01:05:21,580
+و A2 صحيح ولا لأ؟ طيب نيجي للي بعدها روحنا جيبنا
+
+611
+01:05:21,580 --> 01:05:25,580
+المجتقة التالتة لما جيبنا المجتقة التالتة صارت
+
+612
+01:05:25,580 --> 01:05:29,540
+بالشكل هذا اختصرناها و كتبناها بالشكل هذا طيب
+
+613
+01:05:29,970 --> 01:05:33,850
+المشتقة التالتة عند الاكسود روحنا كتبناها بيه بقى
+
+614
+01:05:33,850 --> 01:05:41,110
+لم يظهر عندي الا a1 و a0 المشتقة التالتة عند
+
+615
+01:05:41,110 --> 01:05:46,370
+الاكسود هي تلاتة factorial a3 يعني هذه تلاتة
+
+616
+01:05:46,370 --> 01:05:53,090
+factorial a3 يعني معنى هذا الكلام انه جدرنا نكتب
+
+617
+01:05:53,090 --> 01:05:58,050
+a3 يعني لو جسمنا كله على تلاتة factorialبكون جبت
+
+618
+01:05:58,050 --> 01:06:04,770
+a3 بدلالة a node و a1 يبقى فهمنا هذا السطر كيف
+
+619
+01:06:04,770 --> 01:06:09,990
+كتبت a3 in terms of a node و a1 هيها من هناك هذه
+
+620
+01:06:09,990 --> 01:06:13,510
+اللي كانت يعني حسيت أنها مغبشة عندكوا شوية يبقى
+
+621
+01:06:13,510 --> 01:06:17,370
+هاي روحنا و أضبحناها لكوا تاني يبقى الشلط هذا و
+
+622
+01:06:17,370 --> 01:06:21,970
+حطيت قيمته اللي هي 3 factorial a3 لو جسمت كله على
+
+623
+01:06:21,970 --> 01:06:29,370
+a factorial بصير a3 بدلالة a nodeهنا بنفس الطريقة
+
+624
+01:06:29,370 --> 01:06:37,690
+بنكتب a4 و a5 و a6 و كده in terms of a node and a1
+
+625
+01:06:37,690 --> 01:06:43,810
+تمام؟ الكلام اللي بقوله هوضحه بمثال عملي الآن قبل
+
+626
+01:06:43,810 --> 01:06:48,810
+ان ندخل المثال، حد فيكم بتحب تسأل اي نقطة هنا؟
+
+627
+01:06:48,810 --> 01:06:54,230
+ناخد مثال توضحي على ذلك
+
+628
+01:06:59,220 --> 01:07:07,780
+هذه المفتاح الحل الباقى يجب أن تكون معروفة لأن
+
+629
+01:07:07,780 --> 01:07:11,300
+منها سأجلب المشتقة التالتة ومنها سأجلب المشتقة
+
+630
+01:07:11,300 --> 01:07:15,460
+الرابعة ومنها سأجلب المشتقة الخامسة وكذلك تمام
+
+631
+01:07:15,460 --> 01:07:22,720
+يبقى مثال هذا
+
+632
+01:07:22,720 --> 01:07:32,980
+سؤال تلاتة من الكتاببيقول لي if الـ phi of x is a
+
+633
+01:07:32,980 --> 01:07:43,340
+solution of the initial value problem للـ x تربيع
+
+634
+01:07:43,340 --> 01:07:50,760
+yw prime زائد واحد زائد x في الـ y prime
+
+635
+01:07:53,480 --> 01:08:02,520
+زائد تلاتة في لن ال X كل هذا الكلام في ال Y بدر
+
+636
+01:08:02,520 --> 01:08:07,840
+ساوي Zero و ال condition الأولاني Y عند ال واحد
+
+637
+01:08:07,840 --> 01:08:12,480
+بدر ساوي اتنين و ال condition التاني Y prime عند
+
+638
+01:08:12,480 --> 01:08:14,420
+ال واحد بدر ساوي Zero
+
+639
+01:08:18,180 --> 01:08:25,580
+حددونا قداش قيمة لـ Phi double prime of one Phi
+
+640
+01:08:25,580 --> 01:08:33,260
+triple prime of one and المشتقة الرابعة عند الواحد
+
+641
+01:08:33,260 --> 01:08:39,740
+بدي أعرف قداش قيمة كل term من هذه الترمات solution
+
+642
+01:08:51,200 --> 01:08:55,820
+خلّيني أقول لكم اذا كان في او فيكس ما شكله انا مش
+
+643
+01:08:55,820 --> 01:08:59,620
+عارف مش راح قالي هاتلي في او فيكس لأ هم عطيني رمز
+
+644
+01:08:59,620 --> 01:09:03,400
+في او فيكس يعتبر حل لل initial value problem اللي
+
+645
+01:09:03,400 --> 01:09:07,600
+عندنا قالي من خلالك بس بدنا في دابله prime of one
+
+646
+01:09:07,600 --> 01:09:11,660
+في تربله prime of one و المشتق الرابع برضه under
+
+647
+01:09:11,660 --> 01:09:15,690
+one و الله يعطيك العافية بدنا قيم عددية من خلالالـ
+
+648
+01:09:15,690 --> 01:09:20,150
+initial conditions اللي عندك نقوله بسيطة خلاص بدنا
+
+649
+01:09:20,150 --> 01:09:23,890
+نيجي لكلام اللي أنا بقى بطل على المعادلة اللي عندى
+
+650
+01:09:23,890 --> 01:09:27,710
+المعادلة X ترميها YW prime دالة في Y prime دالة في
+
+651
+01:09:27,710 --> 01:09:33,930
+Y يبقى هنا المعامل هو احنا بنشتغل روحنا جسمنا على
+
+652
+01:09:33,930 --> 01:09:38,330
+capital P of X مش عارف ده على دهرة لأ المساحات على
+
+653
+01:09:38,330 --> 01:09:42,190
+اي حال إذا لما نيجي نشتغل الشغل هاد يا بناتبديك
+
+654
+01:09:42,190 --> 01:09:47,410
+تروح اتيه جسمي على المعامل تبع YWY حتى وإن كان رقم
+
+655
+01:09:47,650 --> 01:09:51,210
+بدي اقسم عليه بحيث اخلي المعامل دائما او ابدا هو
+
+656
+01:09:51,210 --> 01:09:55,690
+main واحد صحيح يبقى المعادلة دي بصير على الشكل
+
+657
+01:09:55,690 --> 01:10:02,090
+التالي y double prime زائد واحد زائد x على x
+
+658
+01:10:02,090 --> 01:10:11,510
+ترابية في ال y prime زائد تلاتة لن ال x على x
+
+659
+01:10:11,510 --> 01:10:19,330
+ترابية كله في ال y بده ساوي zeroتمام، إذا هذا بده
+
+660
+01:10:19,330 --> 01:10:26,690
+يعطي كمين إن ال P of X يساوي، إيش رأيك؟ واحد على X
+
+661
+01:10:26,690 --> 01:10:31,150
+تربية، مش عبارة عن X نقص اتنين؟أسهل اللي في الشغل
+
+662
+01:10:31,150 --> 01:10:37,090
+يبقى باجي بقوله هذي X ناقص اتنين X على X تربية بضل
+
+663
+01:10:37,090 --> 01:10:43,490
+واحد على X يعني X أسالب واحد زائد X أسالب واحد
+
+664
+01:10:43,490 --> 01:10:52,570
+يبقى أنا كتبت ال P of X في ثوب جديد وال Q of X
+
+665
+01:10:52,570 --> 01:10:57,120
+بذاسر خليها زي ما هي مش مشكلة تمام؟لان اذا طلعتها
+
+666
+01:10:57,120 --> 01:11:02,600
+فوق بيصير x أس ناقص اتنين تمام؟ بدك تطلعها فوق
+
+667
+01:11:02,600 --> 01:11:06,660
+بنتطلعها فوق بنتريها بيصير x ناقص اتنين فلن ال x و
+
+668
+01:11:06,660 --> 01:11:10,520
+ايه الحساب بيصير؟ لمش تقعد حصل ضرب دلتين بزهجني
+
+669
+01:11:10,520 --> 01:11:14,180
+شوية لو كانت خارج قسم الدلتين بس حصل ضرب سلي، اذا
+
+670
+01:11:14,180 --> 01:11:21,850
+بقدر اقول هذه التلاتة x أس ناقص اتنين فلن ال xطب
+
+671
+01:11:21,850 --> 01:11:28,350
+ليش سويتك؟ اه بقولك ليش سويتك؟ هنا لازم ل بعد شوية
+
+672
+01:11:28,350 --> 01:11:34,250
+بلزم ل من؟ بلزم ل P prime و Q prime و P double
+
+673
+01:11:34,250 --> 01:11:38,950
+prime و Q .. إذا بلزم ل الشغلات هذه إذا قبل مشتغل
+
+674
+01:11:38,950 --> 01:11:43,470
+ولا شغل بنروح أحسب قداش قيمة كل واحدة من هدول قبل
+
+675
+01:11:43,470 --> 01:11:49,950
+المبدأطبعا بقوله كويس اذا انا لو جيت قولتله ال P
+
+676
+01:11:49,950 --> 01:11:56,430
+prime of X بدي اشتقها يبقى ناقص اتنين X أس ناقص
+
+677
+01:11:56,430 --> 01:12:06,410
+تلاتة ناقص X أس ناقص اتنين طبعا لو بدي PW prime as
+
+678
+01:12:06,410 --> 01:12:12,690
+a function of Xيبقى ايش بصير عندى هنا ستة اكس اص
+
+679
+01:12:12,690 --> 01:12:19,510
+ناقص اربعة زيدي اتنين اكس اص ناقص تلاتة اظن مش
+
+680
+01:12:19,510 --> 01:12:24,570
+هيلزمني اكتر من هيك المشتقة التالتة فيها المشتقة
+
+681
+01:12:24,570 --> 01:12:27,790
+الاولى فقط يبقى لو جيبنا الرابع بيجيب المشتقة
+
+682
+01:12:27,790 --> 01:12:32,180
+التانى ويمكفها الله يعطيك العافيةيبقى بناء عليه لو
+
+683
+01:12:32,180 --> 01:12:36,840
+بدى احسبله P of 1 لانه ليش ال condition المحسبات
+
+684
+01:12:36,840 --> 01:12:42,000
+عند ال one ايش بدى يكون هنا بناه واحد زائد واحد
+
+685
+01:12:42,000 --> 01:12:47,000
+مظبوط يبقى اللي هو اتنين يبقى P of one بدى يساوي
+
+686
+01:12:47,000 --> 01:12:52,760
+اتنين بدى ال P prime of oneيبقى هذا واحد مابصير
+
+687
+01:12:52,760 --> 01:12:57,440
+سالب اتنين سالب واحد اللي هو قداش سالب تلاتة بدي
+
+688
+01:12:57,440 --> 01:13:03,080
+ال P double prime of one يبقى ستة زائد اتنين اللي
+
+689
+01:13:03,080 --> 01:13:08,960
+هو قداش تمانية سيب المعلومات هذه بدنا نروح لمين
+
+690
+01:13:08,960 --> 01:13:15,800
+للي Q يبقى بدي اشتقها يبقى بدي ل Q prime of X هذه
+
+691
+01:13:15,800 --> 01:13:22,630
+مشتقة تحصل ضرب دالة تانية يبقى دالة الأولىفي ناقص
+
+692
+01:13:22,630 --> 01:13:28,490
+اتنين في مشتقة الدالة الثانية اللي همين واحد على X
+
+693
+01:13:28,490 --> 01:13:39,550
+ناقص ستة X أس ناقص تلاتة ناقص طبعا ستة X أس ناقص
+
+694
+01:13:39,550 --> 01:13:46,530
+تلاتة في لن ال Xيعني هذا ايش بيصير؟ بيصير تلاتة
+
+695
+01:13:46,530 --> 01:13:51,730
+اكس اص ناقص تلاتة طلعتها فوق بيصير بإشارة سالب
+
+696
+01:13:51,730 --> 01:14:01,370
+وهنا ناقص اللي هو ستة اكس اص ناقص تلاتة في لن ال X
+
+697
+01:14:02,090 --> 01:14:07,090
+هنجيب المشتقة الثانية يبقى المشتقة ثانية q double
+
+698
+01:14:07,090 --> 01:14:16,430
+prime of x يبقى بالصيرة ناقص تسعة x أس ناقص أربعة
+
+699
+01:14:16,430 --> 01:14:22,910
+اللي بعدها مشتقة حصل ضارب دالتين يبقى ناقص ستة x
+
+700
+01:14:22,910 --> 01:14:29,570
+أس ناقص تلاتة في واحد على x ناقص فناقص بزايد ستة
+
+701
+01:14:29,570 --> 01:14:40,930
+في تلاتة تمانتاشرx²-4x²-4
+
+702
+01:14:40,930 --> 01:14:44,570
+-15
+
+703
+01:14:44,570 --> 01:14:48,530
+-15x²
+
+704
+01:14:48,530 --> 01:14:49,690
+-4
+
+705
+01:15:02,380 --> 01:15:09,700
+إذا ما بقدر اجيب له اكيو of one تعالى شوفى بدل من
+
+706
+01:15:09,700 --> 01:15:15,140
+الواحد بقداش بصفر في اي رقم بصفر يبقى ب zero مع
+
+707
+01:15:15,140 --> 01:15:20,100
+السلامة غير مأسوف عليك اكيو prime of one وايه ال
+
+708
+01:15:20,100 --> 01:15:26,880
+اكيو prime هاى ب one بطلع هنا تلاتة وهذا ب zero مع
+
+709
+01:15:26,880 --> 01:15:34,240
+السلامة يبقى تلاتة يساوي تلاتةالان بدنا لـ q
+
+710
+01:15:34,240 --> 01:15:42,660
+double prime of one لان الواحد بزير و بطير يبقى
+
+711
+01:15:42,660 --> 01:15:49,910
+فضل قداش سالب خمستاش يساوي سالب خمستاشطيب خلّي هذه
+
+712
+01:15:49,910 --> 01:15:55,890
+المعلومات جاهزة يعني هذه وين ما لزمتل الآن بدي
+
+713
+01:15:55,890 --> 01:16:02,810
+أبدأ أخد منها و أعوّب و هذه زيها كمان بنفس الطريقة
+
+714
+01:16:02,810 --> 01:16:08,050
+طيب نبدأ في مسألتنا يبقى قاللي أول شغلة بده مين
+
+715
+01:16:08,050 --> 01:16:13,210
+بده five double prime of one وين five double prime
+
+716
+01:16:13,210 --> 01:16:17,720
+of x هييبقى هذه المعادلة الأساسية اللي بدأ أبدأ
+
+717
+01:16:17,720 --> 01:16:23,180
+أشتغل بها
+
+718
+01:16:23,180 --> 01:16:36,120
+يبقى
+
+719
+01:16:36,120 --> 01:16:44,850
+بروح أقول we know that we knowأحنا بنعرف أن الـ
+
+720
+01:16:44,850 --> 01:16:55,470
+Phi W' of X يساوي ناقص P of X في Phi' of X ناقص ل
+
+721
+01:16:55,470 --> 01:17:02,870
+Q of X ناقص في Phi of X هذه اللي كنا نسميها
+
+722
+01:17:02,870 --> 01:17:08,370
+المعادلة رقم قداشر تلاتة يبقى هذه تلاتة وليست اتنى
+
+723
+01:17:09,590 --> 01:17:20,970
+إذا لتحت هذا كله بدنا نمسحه مالهوش لزوم طيب
+
+724
+01:17:20,970 --> 01:17:24,990
+إيه شرايك من المعادلة هذه بقدر أجيب المطلوب الأول
+
+725
+01:17:24,990 --> 01:17:30,330
+صح يبقى بدى أحسب هذا المقدار عند مين أن النقطة
+
+726
+01:17:30,330 --> 01:17:35,350
+واحدة هو five double prime of oneيبقى باجي بقوله
+
+727
+01:17:35,350 --> 01:17:42,350
+في دابلة prime of one بده يساوي ناقص P of one فيه
+
+728
+01:17:42,350 --> 01:17:49,590
+prime of one ناقص Q of one في ال في of one ويساوي
+
+729
+01:17:49,590 --> 01:17:55,530
+ال P of one يبقى كده شبنات باتنين يبقى هاي سالف
+
+730
+01:17:55,530 --> 01:18:01,200
+قبلها يبقى هاي سالي باتنينالـ Phi prime of one
+
+731
+01:18:01,200 --> 01:18:06,520
+طلعيلي هذا مش Y عبارة عن حل هو Phi يبقى Y prime of
+
+732
+01:18:06,520 --> 01:18:11,760
+one بقداش ب Zero جبتم ال initial condition يبقى في
+
+733
+01:18:11,760 --> 01:18:17,840
+Zero ناقص ال Q of one اللي هو Zero يبقى هاي Zero
+
+734
+01:18:17,840 --> 01:18:23,920
+في ال Phi of one Phi of one هايها اللي هو بقداش
+
+735
+01:18:23,920 --> 01:18:33,500
+باتنينيبقى في اتنين يبقى الحمد لله بقداش ريحنا بده
+
+736
+01:18:33,500 --> 01:18:37,560
+اجيب المشتقة التالتة عند الواحد اذا بده اجي على
+
+737
+01:18:37,560 --> 01:18:43,260
+الاتنين شو اعملها بده اشتقها يبقى بده اجي للي فوق
+
+738
+01:18:43,260 --> 01:18:50,500
+هادي هيك واروح اشتقها في triple prime of xيبقى بدي
+
+739
+01:18:50,500 --> 01:18:56,460
+اختصر يا بنات يبقى ناقص P في الـ Phi W Prime ناقص
+
+740
+01:18:56,460 --> 01:19:02,240
+P Prime في ال Phi Prime هذا ال term الأول ناقص Q
+
+741
+01:19:02,240 --> 01:19:09,480
+في ال Phi Prime ناقص Q Prime في ال Phi زي ما هي
+
+742
+01:19:09,480 --> 01:19:16,200
+بدي احسب هذا عند الواحد يبقى بصير Phi Triple Prime
+
+743
+01:19:16,200 --> 01:19:23,300
+عند الواحدناقص P of واحد في W prime of واحد ناقص P
+
+744
+01:19:23,300 --> 01:19:30,880
+prime of واحد في F prime of واحد ناقص Q of واحد في
+
+745
+01:19:30,880 --> 01:19:38,020
+F prime of واحد ناقص Q prime of واحد في F prime of
+
+746
+01:19:38,020 --> 01:19:42,220
+واحد ناقص
+
+747
+01:19:42,220 --> 01:19:50,550
+P1يبقى هاي ناقص اتنين five double prime of one هاي
+
+748
+01:19:50,550 --> 01:19:56,590
+اللي اوجدناها فوق من البداية بقدرش ب zero يبقى هاي
+
+749
+01:19:56,590 --> 01:20:03,220
+zeroنقص P' of one P' of one اللي هي سالب تلاتة
+
+750
+01:20:03,220 --> 01:20:10,360
+يبقى سالب لسالب تلاتة five prime of one اللي هو
+
+751
+01:20:10,360 --> 01:20:19,220
+مقدش ب zero يبقى هذا كمان ب zero نقص Q of one ل Q
+
+752
+01:20:19,220 --> 01:20:24,710
+of one اللي هو ب zeroالـ Q of 1 بـ 0 فاية Prime of
+
+753
+01:20:24,710 --> 01:20:31,410
+1 فاية Prime of 1 كمان بـ 0 ناقص الـ Q Prime of 1
+
+754
+01:20:31,410 --> 01:20:36,810
+اللي هو قداش تلاتة يبقى ناقص تلاتة في الـ Phi 1
+
+755
+01:20:36,810 --> 01:20:48,020
+اللي هو قداش 2 0 0 0 يبقى الجواب قداش سالب ستةكمان
+
+756
+01:20:48,020 --> 01:20:53,040
+طيب قال لي هات المشتقة الرابع اذا بده اجي على هذه
+
+757
+01:20:53,040 --> 01:20:58,900
+اللي اشتقتها و اشتقها كمان ايه كمان مرة يبقى بده
+
+758
+01:20:58,900 --> 01:21:05,320
+اجيب له المشتقة الرابع as a function of X برضه
+
+759
+01:21:05,320 --> 01:21:10,240
+اختصار بديش اكتب ال X's للسولة هذه المشتقة اتحصل
+
+760
+01:21:10,240 --> 01:21:15,320
+دور بدلتين يبقى ناقص P في الـ Phi Tripoli Prime
+
+761
+01:21:15,640 --> 01:21:23,820
+ناقص P' Phi W' خلصنا منها اللي بعدها ناقص P' Phi
+
+762
+01:21:23,820 --> 01:21:33,160
+W' ناقص P W' Phi' خلصنا منها اللي بعدها ناقص Q Phi
+
+763
+01:21:33,160 --> 01:21:43,720
+W'نقص Q' فى قلصنا منها اللى بعدها نقص Q' فى قلصنا
+
+764
+01:21:43,720 --> 01:21:50,060
+منها نقص Q'' فى قلصنا منها اللى بعدها نقص Q' فى
+
+765
+01:21:50,060 --> 01:21:53,720
+بعدها نقص Q'' فى قلصنا منها اللى بعدها نقص Q'' فى
+
+766
+01:21:53,720 --> 01:21:53,780
+قلصنا منها اللى بعدها نقص Q'' فى قلصنا منها اللى
+
+767
+01:21:53,780 --> 01:21:57,160
+بعدها نقص Q'' فى قلصنا منها اللى بعدها نقص Q'' فى
+
+768
+01:21:57,160 --> 01:22:01,240
+قلصنا منها اللى بعدها نقصبتروح ادور ناقص P of one
+
+769
+01:22:01,240 --> 01:22:07,480
+P of one اللي هو قداش باتنين يبقى هاي ناقص اتنين
+
+770
+01:22:07,480 --> 01:22:11,440
+المشتقة التالتة عند الواحد هي جاهزة اللي هي قداش
+
+771
+01:22:11,440 --> 01:22:18,380
+سالب ستة والله رايحتنا هذه اللي بعدها ناقص P prime
+
+772
+01:22:18,380 --> 01:22:24,390
+of one P prime of one اللي هي قداش سالب تلاتةيبقى
+
+773
+01:22:24,390 --> 01:22:31,770
+هاي سالب تلاتة ال five double prime زيرو الله يسهل
+
+774
+01:22:31,770 --> 01:22:37,330
+عليها يبقى هاي زيرو خلصنا اول two terms نجي ال
+
+775
+01:22:37,330 --> 01:22:42,550
+term التالت ناقص P prime of one P prime of one
+
+776
+01:22:42,550 --> 01:22:47,630
+اللي هو بقداش بسالب تلاتة يبقى هاي سالب تلاتة ال
+
+777
+01:22:47,630 --> 01:22:53,000
+five double prime اللي هو بزيرو ريعتنانقص الـPW
+
+778
+01:22:53,000 --> 01:23:00,560
+prime الـPW prime هو 8 نقص 8 في الـPhi prime
+
+779
+01:23:00,560 --> 01:23:09,080
+الـPhi prime هو 0 يبقى هنا بـ0 نقص الـQ of 1 الـQ
+
+780
+01:23:09,080 --> 01:23:15,460
+of 1 هو 0 يبقى هذه 0 في 0 في الـPhi W prime نقص
+
+781
+01:23:15,460 --> 01:23:21,780
+الـEQ prime الـEQ prime هو 3 في الـPhi primeفاية
+
+782
+01:23:21,780 --> 01:23:27,340
+البرامي اللي هي بالزرع ناقص كي و دابلي برامي كي و
+
+783
+01:23:27,340 --> 01:23:32,540
+دابلي برامي بناقص خمستاش ناقص خمستاش في الفاية
+
+784
+01:23:32,540 --> 01:23:41,420
+اللي هي بالتنين بالتنين يساوي هذا بالاطمعش زرع زرع
+
+785
+01:23:41,420 --> 01:23:45,440
+زرع زرع زرع زرع زرع زرع زرع زرع زرع زرع زرع زرع
+
+786
+01:23:45,440 --> 01:23:45,560
+زرع زرع زرع زرع زرع زرع زرع زرع زرع زرع زرع زرع
+
+787
+01:23:45,560 --> 01:23:45,580
+زرع زرع زرع زرع زرع زرع زرع زرع زرع زرع زرع زرع
+
+788
+01:23:45,580 --> 01:23:47,330
+زرع زرع زرع زرع زرع زرع زرع زرع زرع زرع زيبقى زائد
+
+789
+01:23:47,330 --> 01:23:54,370
+تلاتين ويساوي قداش اتنين واربعين الشغل بتطول اتروح
+
+790
+01:23:54,370 --> 01:24:00,110
+يعني بدأي زهج ازهجان بضيع ايه؟ بضيع المسألة دوريا
+
+791
+01:24:00,110 --> 01:24:04,950
+حدا فيكم بتسأل اي سؤال هنا بنان؟ اذا العمود الفقري
+
+792
+01:24:04,950 --> 01:24:10,090
+عندنا له المعادلة رقم تلاتة كل الشغل بدي يكون منها
+
+793
+01:24:10,090 --> 01:24:16,550
+من عندها بنبدأ نجيب اربعة وخمسة وستة وكلههذا سؤال
+
+794
+01:24:16,550 --> 01:24:20,290
+هو رقم تلاتة من أسئلة الكتابة في عندك أظن مابارة
+
+795
+01:24:20,290 --> 01:24:25,130
+أربعة أسئلة أو خمس أسئلة بالشكل هذا هذا هو أحدهم
+
+796
+01:24:25,130 --> 01:24:38,670
+والباقي بنفس الطريقة اللي
+
+797
+01:24:38,670 --> 01:24:43,790
+انا بدأ نعطي تعريف لل analytic function مرة ثانية
+
+798
+01:24:44,600 --> 01:24:54,700
+ونشوف نظرية عليها وبعد ذلك ناخد بعض الأمثلة يبقى
+
+799
+01:24:54,700 --> 01:25:01,780
+التعريف بيقول ما يأتي definition تعريف
+
+800
+01:25:01,780 --> 01:25:07,160
+رقم واحد بيقول for the differential equation for
+
+801
+01:25:07,160 --> 01:25:10,120
+the differential
+
+802
+01:25:24,000 --> 01:25:35,200
+النقطة x0 هي نقطة
+
+803
+01:25:35,200 --> 01:25:37,440
+عامة
+
+804
+01:25:42,790 --> 01:25:56,130
+ordinary point نقطة عادية if ال P of X and ال Q of
+
+805
+01:25:56,130 --> 01:26:04,290
+X ما لهم are analytic are analytic
+
+806
+01:26:04,290 --> 01:26:17,780
+at X node نمر اتنين ifالـ P of X and the Q of X
+
+807
+01:26:17,780 --> 01:26:28,360
+are not analytic are not analytic يبقى لو ماكناش
+
+808
+01:26:28,360 --> 01:26:38,520
+دوال تحليلية at X node then اللي هو ال X node then
+
+809
+01:26:43,520 --> 01:26:56,120
+الـ x0 is called is called a singular point a
+
+810
+01:26:56,120 --> 01:27:05,140
+singular point آخر نظرية في هذا ال section بتقول
+
+811
+01:27:05,140 --> 01:27:06,160
+ما يأتي
+
+812
+01:27:12,360 --> 01:27:24,880
+الـ X naught is an ordinary point نقطة عادية of
+
+813
+01:27:24,880 --> 01:27:28,620
+the differential
+
+814
+01:27:30,210 --> 01:27:36,490
+equation للمعادلة التفاضلية capital P of X في ال
+
+815
+01:27:36,490 --> 01:27:44,250
+YW prime Q of X Y prime R of X في ال Y تساوي Zero
+
+816
+01:27:44,250 --> 01:27:54,810
+وهذه سامعها المعادلة رقم واحد that is INF ال P
+
+817
+01:27:54,810 --> 01:28:04,300
+لتساويالـ Q على كابتل P and الـ Q بده يساوي ال R
+
+818
+01:28:04,300 --> 01:28:18,040
+على كابتل P R أنا لاتك at X node then the general
+
+819
+01:28:18,040 --> 01:28:23,460
+solution then general
+
+820
+01:28:23,460 --> 01:28:24,540
+solution
+
+821
+01:28:31,510 --> 01:28:39,650
+الحل العام للإيقاع
+
+822
+01:28:39,650 --> 01:28:45,990
+الواحد هو y
+
+823
+01:28:45,990 --> 01:28:53,450
+تساوي summation من n equal zero to infinity لل a n
+
+824
+01:28:53,450 --> 01:28:58,830
+في ال x ناقص ال x not to the power nواللي بقدر
+
+825
+01:28:58,830 --> 01:29:06,810
+اكتب عليه شكل a0 في ال y1 of x زائد a1 في ال y2 of
+
+826
+01:29:06,810 --> 01:29:19,970
+x where ال a0 and ال
+
+827
+01:29:19,970 --> 01:29:23,590
+a1 are constants
+
+828
+01:29:31,880 --> 01:29:37,840
+وY1 وY2 هم
+
+829
+01:29:37,840 --> 01:29:49,060
+نقاط مستقلين ومستقلين نقاط
+
+830
+01:29:49,060 --> 01:29:51,320
+مستقلين
+
+831
+01:29:59,000 --> 01:30:08,940
+analytic at x0 the
+
+832
+01:30:08,940 --> 01:30:21,700
+radius of convergence the
+
+833
+01:30:21,700 --> 01:30:25,140
+radius of convergence of
+
+834
+01:30:45,090 --> 01:30:57,370
+Y1 Y2 Y3
+
+835
+01:30:57,370 --> 01:30:57,630
+Y4 Y5 Y6 Y7 Y8 Y9 Y10 Y11 Y12 Y13 Y12 Y13 Y12 Y12
+
+836
+01:30:57,630 --> 01:31:01,120
+Y12 Y12 Y12 Y12 Y12 Y12 Y12 Y12 Y12 Y12 Y12of the
+
+837
+01:31:01,120 --> 01:31:11,620
+radia of the radia of convergence
+
+838
+01:31:11,620 --> 01:31:26,280
+of convergence of the series of the series for P
+
+839
+01:31:26,280 --> 01:31:29,320
+andThank you
+
+840
+01:32:57,990 --> 01:33:03,950
+طيب نجي لتعريف اللى ماتيه ليه التعريف بيقول ليش
+
+841
+01:33:03,950 --> 01:33:06,850
+for the differential equation اللى قدامنا دى the
+
+842
+01:33:06,850 --> 01:33:11,830
+point X node is called an ordinary point if P of X
+
+843
+01:33:11,830 --> 01:33:17,310
+and Q of X are analytic at X node تبصرنا شوية وإيش
+
+844
+01:33:17,310 --> 01:33:21,840
+تعريف ال analytic كتبناه المرة اللى فاتةتعريف ال
+
+845
+01:33:21,840 --> 01:33:24,640
+analytic بيقول function analytic إذا جدر تكتب على
+
+846
+01:33:24,640 --> 01:33:28,640
+شكل taylor series أو maclaurin series، مظبوط ولا
+
+847
+01:33:28,640 --> 01:33:34,020
+مش هيك هنا بنقول؟ بنقول تمام تمام، يبقى إذا والله
+
+848
+01:33:34,020 --> 01:33:40,380
+ال function جدر تكتب على شكل taylor series أو
+
+849
+01:33:40,380 --> 01:33:43,660
+maclaurin series، يبقى هذه بيسميها analytic
+
+850
+01:33:43,660 --> 01:33:49,450
+function، إيش بيقول هنا؟بقول المعادلة هذه النقطة x
+
+851
+01:33:49,450 --> 01:33:54,850
+note بقول عنها ordinary point إذا ال P small و ال
+
+852
+01:33:54,850 --> 01:33:58,950
+K small يعني جسمت على المعامل اللي هنا هايه جاهز و
+
+853
+01:33:58,950 --> 01:34:03,410
+خالص إذا كانت هذه و هذه كانوا انالتكي يعني إذا كل
+
+854
+01:34:03,410 --> 01:34:07,670
+واحدة فيهم جدرت أكتب على شكل taylor series أو
+
+855
+01:34:08,030 --> 01:34:12,750
+مكلورين سيريز بيكون النقطة هذه ordinary point يبقى
+
+856
+01:34:12,750 --> 01:34:16,410
+هذا التعريف جديد لمين؟ ال ordinary point احنا
+
+857
+01:34:16,410 --> 01:34:20,200
+المرة اللي فاتتبجي نقول ان ال ordinary point بشوف
+
+858
+01:34:20,200 --> 01:34:24,380
+المعامل تبع y double prime من النقط اللي بتخليها
+
+859
+01:34:24,380 --> 01:34:27,740
+أصفر بسميها singular points والباجي كله بيصيروا
+
+860
+01:34:27,740 --> 01:34:32,520
+ordinary points تمام؟ الآن أعطينا تعريف جديد لأن
+
+861
+01:34:32,520 --> 01:34:35,900
+ال analytic function و هو مرتبط بالتعريف السابق
+
+862
+01:34:35,900 --> 01:34:41,890
+بتدخل المعامل y double prime هو aوحظ صحيح إذا بدى
+
+863
+01:34:41,890 --> 01:34:46,250
+أروح على الدوال ال P of X و ال Q of X هل هم
+
+864
+01:34:46,250 --> 01:34:50,870
+analytic functions ولا لأ إذا لجيتهم يعني بقدر
+
+865
+01:34:50,870 --> 01:34:55,090
+أكتبهم على شكل تايلور أو ماكرون سيريز ولا إذا جدرت
+
+866
+01:34:55,090 --> 01:34:59,290
+عند النقطة المعطاة مش حيالة عند أي نقطة يبقى إذا
+
+867
+01:34:59,290 --> 01:35:03,270
+جدرت عند هذه النقطة بسمي هذه ordinary point ماجدرت
+
+868
+01:35:03,270 --> 01:35:08,500
+يبقى هذه singular pointنمر اتنين بيقول اذا هدول
+
+869
+01:35:08,500 --> 01:35:13,580
+هدول ارنقت انالاتيكي يعني ماقدرتش اكتب اي واحدة
+
+870
+01:35:13,580 --> 01:35:17,360
+فيهم على شكل تايلور او ماكرون سيريز يبقى النقطة
+
+871
+01:35:17,360 --> 01:35:23,720
+هذه بيصير معاها singular point طيب يمكن ييجي في
+
+872
+01:35:23,720 --> 01:35:28,060
+بال أحدكم السؤال التالف هدول two functions افترض
+
+873
+01:35:28,060 --> 01:35:32,620
+ان الأولى قدرت اكتبها على شكل تايلور سيريز بس
+
+874
+01:35:32,620 --> 01:35:36,930
+التانية ماقدرتشيعني بنفعش نكتب على شكل taylor
+
+875
+01:35:36,930 --> 01:35:40,970
+series، إذا بيكون الدوال الأثنين هدول Analytic عند
+
+876
+01:35:40,970 --> 01:35:46,700
+هذه النقطة، لأيعني انا بدي التنتين في نفس الوقت
+
+877
+01:35:46,700 --> 01:35:49,540
+يكونوا analytic عند نفس النقطة واحدة analytic
+
+878
+01:35:49,540 --> 01:35:53,820
+والتانية لأ يبقى خلاص مرفوض بدي التنتين او ال two
+
+879
+01:35:53,820 --> 01:35:57,500
+functional P of X small و P of X small of X يكونوا
+
+880
+01:35:57,500 --> 01:36:02,160
+analytic عند نفس النقطة في اي واحد ان حدث ذلك بقول
+
+881
+01:36:02,160 --> 01:36:06,260
+النقطة هذه معناها ordinary point ما حدث يبقى بقول
+
+882
+01:36:06,260 --> 01:36:10,760
+هذه singular pointخلّي هذه المعلومة في دماغك و
+
+883
+01:36:10,760 --> 01:36:14,000
+نذهب نستخدمها في النص التابع للنظرية اللي قدامنا
+
+884
+01:36:14,000 --> 01:36:18,520
+بقول لو كانت ال X node عبارة عن ordinary point
+
+885
+01:36:18,520 --> 01:36:23,520
+للمعادلة هادي يبقى جسمنا هادي على هادي بتطلع
+
+886
+01:36:23,520 --> 01:36:27,940
+أنالتك جسمنا هادي على هادي بتطلع أنالتك عشان تكون
+
+887
+01:36:27,940 --> 01:36:28,700
+هادي مالها
+
+888
+01:36:47,610 --> 01:36:52,690
+الحل تبع المعادلة رقم واحد بقدرة وعلى سير ال
+
+889
+01:36:52,690 --> 01:36:57,910
+solution يعني لو كان هدول التنتين analyticبأقمن
+
+890
+01:36:57,910 --> 01:37:04,150
+وجود حل على شكل متسلسلة للمعادلة هذه ومش عجبه جد
+
+891
+01:37:04,150 --> 01:37:08,810
+هيكوب بس لأ هو عبارة عن مجموع حلين كونصا في الحل
+
+892
+01:37:08,810 --> 01:37:12,190
+الأول و كونصا في الحل الثاني وانت شوفت في section
+
+893
+01:37:12,190 --> 01:37:17,260
+خمسة اتنينبقينا نطلع حل constant a node في series
+
+894
+01:37:17,260 --> 01:37:20,620
+زايد a1 في series تانية لسه اليوم معناه مظبوط ولا
+
+895
+01:37:20,620 --> 01:37:24,580
+لأ يبقى هاي اللي بقوله بشكل هذا حيث ال a node و ال
+
+896
+01:37:24,580 --> 01:37:28,660
+a1 عبارة عن ثوابت و ال y1 و ال y2 linearly
+
+897
+01:37:28,660 --> 01:37:33,420
+independent series solution و ركز على series حل
+
+898
+01:37:33,420 --> 01:37:36,560
+لإن احنا بنشتغل في series بنشتغلش بالحلاللي كنا في
+
+899
+01:37:36,560 --> 01:37:41,380
+chapter تلاتة او اربعة يبقى see the solution that
+
+900
+01:37:41,380 --> 01:37:45,660
+are analytic at each node يعني الحالين هدول كمان
+
+901
+01:37:45,660 --> 01:37:50,320
+analytic وين يعني كل واحد يهم مكتوب على شكل تايلور
+
+902
+01:37:50,490 --> 01:37:55,970
+سيريز عند هذه النقطة طب كويس احنا صار عندنا حالين
+
+903
+01:37:55,970 --> 01:38:00,510
+و اتنين linearly independent في عندنا حاجة اسمها
+
+904
+01:38:00,510 --> 01:38:05,950
+نصف قطر التقارب لكل من Y واحد و مش هذه سيريز إذا
+
+905
+01:38:05,950 --> 01:38:10,310
+بتكون تقاربي على فترة إذا نقلها نصف تقاربهذه
+
+906
+01:38:10,310 --> 01:38:16,130
+التقاربات ستكون مرتبطة على فترة يبقى لها نصف قطر
+
+907
+01:38:16,130 --> 01:38:21,130
+تقارب قد يكون مثل نصف التقارب الأول وقد يختلف عنه
+
+908
+01:38:21,520 --> 01:38:25,520
+طيب إن اتفقوا باخد واحد يوم، إن اختلفوا باخد اللي
+
+909
+01:38:25,520 --> 01:38:30,720
+صغير فيهم، إيش بقول هنا؟ ال radius of convergence
+
+910
+01:38:30,720 --> 01:38:36,140
+for each y1 and y2 is the minimum الأصغر of the
+
+911
+01:38:36,140 --> 01:38:40,660
+radius, radius جمع radius اللي هو نصف القطر of
+
+912
+01:38:40,660 --> 01:38:46,430
+convergence for the series for P and Qيبقى الاصغير
+
+913
+01:38:46,430 --> 01:38:51,090
+فيهم ها بيكون هو نصف القطر إيه لإيه خاطر أعطي مثال
+
+914
+01:38:51,090 --> 01:38:57,070
+صغير على هذه لأ لا سطرين بس سطرين على الأخرى بس
+
+915
+01:38:57,070 --> 01:38:59,750
+مشان أثبت المعلومة و المرة جايب نحل بدل المثال
+
+916
+01:38:59,750 --> 01:39:09,670
+تلاتة يبقى مثال صغير المثال بيقول ما يأتي يبقىمش
+
+917
+01:39:09,670 --> 01:39:14,450
+ضايل إلا مجموعة من الأمثلة على هذا ال section بدنا
+
+918
+01:39:14,450 --> 01:39:22,390
+نيجي لأول مثال بقول determine او بلا شوف خليه اي
+
+919
+01:39:22,390 --> 01:39:26,870
+determine a lower bound
+
+920
+01:39:33,560 --> 01:39:41,620
+for the radius of convergence for the radius of
+
+921
+01:39:41,620 --> 01:39:45,340
+convergence
+
+922
+01:39:45,340 --> 01:39:50,080
+of
+
+923
+01:39:50,080 --> 01:39:58,780
+serious solutions of serious solutions serious
+
+924
+01:39:58,780 --> 01:40:00,820
+solutions about
+
+925
+01:40:29,360 --> 01:40:31,520
+المعادلة الأولى
+
+926
+01:40:49,090 --> 01:40:50,490
+Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''
+
+927
+01:41:03,170 --> 01:41:09,470
+كويس المعادلة جاهزة مجسومة و خالصة يبقى capital P
+
+928
+01:41:09,470 --> 01:41:15,990
+هنا بقدرش يا بنات؟ واحد يبقى الان capital P of X
+
+929
+01:41:15,990 --> 01:41:22,170
+بده ساوي واحد في عندنا نقطة في الدنيا بدها تغير
+
+930
+01:41:22,170 --> 01:41:26,590
+القيمة هذا تخليها صفر ماعنديش يبقى كل النقاط اللي
+
+931
+01:41:26,590 --> 01:41:33,410
+عندي are ordinary pointsيبقى هذه ليمكن أن تساوي 0
+
+932
+01:41:33,410 --> 01:41:42,110
+for all x يبقى هذا بدي أقول لك all the points are
+
+933
+01:41:42,110 --> 01:41:47,070
+ordinary points
+
+934
+01:41:48,390 --> 01:41:52,670
+يبقى بناء عليه الـ zero والاربعة مالهم ordinary
+
+935
+01:41:52,670 --> 01:42:00,610
+points ال X naught ساوي zero and ال X naught ساوي
+
+936
+01:42:00,610 --> 01:42:11,890
+أربعة are ordinary points هذا كويس ماعنديش ولا
+
+937
+01:42:11,890 --> 01:42:16,890
+singular point تماما بقولكوا يبقى لو جيت لل real
+
+938
+01:42:16,890 --> 01:42:21,810
+lineهذا الريال لاني و هذا النقطة zero و هذا النقطة
+
+939
+01:42:21,810 --> 01:42:28,570
+أربعة ماعنديش singular point بدي أوقف عندها يبقى
+
+940
+01:42:28,570 --> 01:42:33,390
+ال radius الأولى اللي بدي يكون من وين لوين من صفر
+
+941
+01:42:33,390 --> 01:42:38,730
+إلى مالنها طول قداش تبعه مالنها يعني ال radius
+
+942
+01:42:38,730 --> 01:42:43,130
+التاني بدي يكون من وين من أربعة إلى مالنها قداش
+
+943
+01:42:44,370 --> 01:42:47,490
+عشان اذا ال raw one بده يسوي مالة نهاية و ال raw
+
+944
+01:42:47,490 --> 01:42:50,850
+two بده يسوي مالة نهاية فى هم واحد صغير و واحد
+
+945
+01:42:50,850 --> 01:42:55,970
+كبير لأ يبقى ال radius مالة نهاية يبقى باجي بقوله
+
+946
+01:42:55,970 --> 01:43:02,930
+ال raw one بده يسوي infinity و ال raw two بده يسوي
+
+947
+01:43:02,930 --> 01:43:08,530
+infinityقالي هاتلي ال lower bound لل radius of
+
+948
+01:43:08,530 --> 01:43:16,690
+convergence يبقى باجي بقوله هنا the lower bound
+
+949
+01:43:16,690 --> 01:43:26,150
+for the radius of convergence
+
+950
+01:43:26,150 --> 01:43:36,490
+is ر تساوي قداش infinity مافيش غيرهاطبعا هذا أتفه
+
+951
+01:43:36,490 --> 01:43:41,410
+أنواع المسائل، لكن اسمها في الكتاب، تمام؟ مرة جا
+
+952
+01:43:41,410 --> 01:43:44,950
+ان شاء الله تصير مش روين في الهلاب، تطلع قيم
+
+953
+01:43:44,950 --> 01:43:51,170
+عددية، وحنق في العديد من الأمثلة، وقد تكون النقطة
+
+954
+01:43:51,170 --> 01:43:56,710
+singular point حقيقية وقد تكون تخيلية، يبقى على كل
+
+955
+01:43:56,710 --> 01:44:01,750
+الأمرين، بدنا نحسب هذا ان شاء الله المرة القادمة
+
diff --git a/PL9fwy3NUQKwa8ZDfSFGn6H8xVFLzqmCZC/6nKiDvoO6MU_raw.json b/PL9fwy3NUQKwa8ZDfSFGn6H8xVFLzqmCZC/6nKiDvoO6MU_raw.json
new file mode 100644
index 0000000000000000000000000000000000000000..4b0955f8d6177b96c9113a0b02ab2799410d8ff4
--- /dev/null
+++ b/PL9fwy3NUQKwa8ZDfSFGn6H8xVFLzqmCZC/6nKiDvoO6MU_raw.json
@@ -0,0 +1 @@
+{"segments": [{"id": 1, "seek": 2538, "start": 9.98, "end": 25.38, "text": "بسم الله الرحمن الرحيم بنواصل ما ابتدأنا به المرة الماضية وهو series solution near an ordinary point وسميناها part one وبعد قليل ان شاء الله خلال هذه المحاضرة", "tokens": [3555, 38251, 21984, 34892, 5016, 27842, 34892, 5016, 32640, 44945, 2407, 33546, 1211, 19446, 48127, 2655, 3215, 10721, 8315, 39627, 9673, 25720, 9673, 46958, 10632, 37037, 2407, 2638, 3827, 2651, 364, 10547, 935, 4032, 38251, 1829, 8315, 11296, 644, 472, 46599, 22488, 12174, 20292, 1211, 16472, 13412, 16606, 21984, 16490, 1211, 6027, 29538, 9673, 5016, 46958, 25720], "avg_logprob": -0.1293103494520845, "compression_ratio": 1.439306358381503, "no_speech_prob": 1.7881393432617188e-07, "words": [{"start": 9.979999999999999, "end": 10.96, "word": "بسم", "probability": 0.842041015625}, {"start": 10.96, "end": 11.18, "word": " الله", "probability": 0.96044921875}, {"start": 11.18, "end": 11.62, "word": " الرحمن", "probability": 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infinity هذا بده يعطينا ان المشتق الثاني YW prime", "tokens": [50, 40879, 399, 5296, 27842, 22807, 24976, 426, 294, 5754, 1783, 8717, 995, 4587, 9381, 1975, 2655, 1863, 9957, 281, 264, 1347, 426, 3175, 472, 2423, 28811, 23758, 5296, 15042, 1975, 8592, 2655, 4587, 9673, 8592, 2655, 4587, 13672, 1829, 31439, 13672, 1829, 4724, 1829, 44510, 10721, 9154, 4032, 9957, 22807, 9154, 43242, 426, 6055, 3794, 2407, 7578, 36764, 24401, 9154, 43242, 426, 6055, 3794, 2407, 7578, 36764, 24401, 2423, 7578, 13202, 23758, 47525, 3224, 37495, 9566, 1829, 8315, 16472, 9673, 8592, 2655, 4587, 6024, 104, 7649, 1829, 398, 54, 5835], "avg_logprob": -0.31691576961589896, "compression_ratio": 1.6336633663366336, "no_speech_prob": 0.0, "words": [{"start": 278.72999999999996, "end": 279.65, "word": "Summation", "probability": 0.6220296223958334}, {"start": 279.65, "end": 280.57, "word": " لمن؟", "probability": 0.537841796875}, {"start": 280.57, "end": 281.01, "word": " لل", "probability": 0.2218017578125}, 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summation من n equal one to infinity لتلاتة a n x نقص اتنين to the power n كله بده يساوي", "tokens": [15042, 24401, 8592, 5551, 5016, 3794, 1863, 9154, 11331, 3215, 7251, 3555, 4587, 7578, 30767, 16373, 3215, 6055, 1211, 9307, 3660, 257, 8717, 35473, 4032, 11296, 11778, 1829, 12602, 39319, 3660, 21984, 8608, 3224, 1211, 25894, 11296, 30767, 16373, 3215, 28811, 9154, 297, 2681, 472, 281, 13202, 5296, 2655, 1211, 9307, 3660, 257, 297, 2031, 8717, 4587, 9381, 1975, 2655, 1863, 9957, 281, 264, 1347, 297, 28242, 3224, 47525, 3224, 7251, 3794, 995, 45865], "avg_logprob": -0.28812501112620037, "compression_ratio": 1.3872832369942196, "no_speech_prob": 0.0, "words": [{"start": 987.9, "end": 988.76, "word": "ماحدش", "probability": 0.4278157552083333}, {"start": 988.76, "end": 989.14, "word": " أحسن", "probability": 0.9134521484375}, {"start": 989.14, "end": 989.32, "word": " من", "probability": 0.95263671875}, {"start": 989.32, "end": 989.74, "word": " حد", "probability": 0.948486328125}, 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1296.19, "end": 1306.35, "text": "عن طريق الـ Recurrence relation اللى طلبها عندى وين فى رأس المثلة جالسة لـ Recurrence relation", "tokens": [3615, 1863, 23032, 16572, 4587, 2423, 39184, 9647, 374, 10760, 9721, 13672, 7578, 23032, 46152, 11296, 43242, 7578, 4032, 9957, 6156, 7578, 12602, 10721, 3794, 9673, 12984, 37977, 10874, 6027, 3794, 3660, 5296, 39184, 9647, 374, 10760, 9721], "avg_logprob": -0.4979967826452011, "compression_ratio": 1.2924528301886793, "no_speech_prob": 0.0, "words": [{"start": 1296.1899999999998, "end": 1297.3899999999999, "word": "عن", "probability": 0.18133544921875}, {"start": 1297.3899999999999, "end": 1298.59, "word": " طريق", "probability": 0.86376953125}, {"start": 1298.59, "end": 1298.59, "word": " الـ", "probability": 0.3258056640625}, {"start": 1298.59, "end": 1299.87, "word": " Recurrence", "probability": 0.79541015625}, {"start": 1299.87, "end": 1300.49, "word": " relation", "probability": 0.70849609375}, {"start": 1300.49, "end": 1300.67, "word": " 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من وين يبقى in تساوي ابدا من عند ال zero لو قليه من عند ال zero شو بيعطيني اتنين ما اتنين هي جاهزة", "tokens": [9566, 3555, 47525, 7578, 1975, 8592, 38688, 8032, 3215, 7578, 47525, 7578, 6055, 44510, 10721, 294, 9154, 4032, 9957, 7251, 3555, 4587, 7578, 294, 6055, 3794, 995, 45865, 48127, 28259, 9154, 43242, 2423, 4018, 45164, 12174, 20292, 3224, 9154, 43242, 2423, 4018, 13412, 2407, 4724, 1829, 3615, 9566, 1829, 22653, 1975, 2655, 1863, 9957, 19446, 1975, 2655, 1863, 9957, 39896, 10874, 40294, 11622, 3660], "avg_logprob": -0.2980769230769231, "compression_ratio": 1.586466165413534, "no_speech_prob": 0.0, "words": [{"start": 1306.8, "end": 1307.12, "word": "طب", "probability": 0.439300537109375}, {"start": 1307.12, "end": 1307.38, "word": " بدى", "probability": 0.65478515625}, {"start": 1307.38, "end": 1307.64, "word": " اشوف", "probability": 0.7003580729166666}, {"start": 1307.64, "end": 1307.96, "word": " هدى", "probability": 0.6500651041666666}, {"start": 1307.96, "end": 1308.26, 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A", "probability": 0.93603515625}, {"start": 3640.38, "end": 3641.0, "word": " node", "probability": 0.73876953125}, {"start": 3641.0, "end": 3642.24, "word": " وA1", "probability": 0.7168782552083334}, {"start": 3642.24, "end": 3643.2, "word": " بنفس", "probability": 0.9365234375}, {"start": 3643.2, "end": 3644.04, "word": " الطريقة", "probability": 0.98095703125}, {"start": 3644.04, "end": 3645.8, "word": " نشتغل", "probability": 0.7677734375}, {"start": 3645.8, "end": 3646.18, "word": " نفس", "probability": 0.97216796875}, {"start": 3646.18, "end": 3646.98, "word": " الشغل", "probability": 0.9812825520833334}], "temperature": 1.0}, {"id": 153, "seek": 368730, "start": 3665.64, "end": 3687.3, "text": "يبقى هنا سا وي رايت روحنا كتبنا five triple a prime of x node in terms of a node and a one similarly بنفس الطريقة", "tokens": [1829, 3555, 4587, 7578, 34105, 8608, 995, 4032, 1829, 12602, 995, 36081, 12602, 2407, 5016, 8315, 9122, 2655, 3555, 8315, 1732, 15508, 257, 5835, 295, 2031, 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{"start": 3683.28, "end": 3685.56, "word": " similarly", "probability": 0.5380859375}, {"start": 3685.56, "end": 3686.44, "word": " بنفس", "probability": 0.971435546875}, {"start": 3686.44, "end": 3687.3, "word": " الطريقة", "probability": 0.9783528645833334}], "temperature": 1.0}, {"id": 154, "seek": 371343, "start": 3690.19, "end": 3713.43, "text": "Similarly, we can write نصاتية كتابة المشتقة الرابعة عند ال X node و المشتقة الخامسة عند ال X node و و و إلى آخره in terms of", "tokens": [39392, 2202, 356, 11, 321, 393, 2464, 8717, 9381, 9307, 10632, 9122, 2655, 16758, 3660, 9673, 8592, 2655, 28671, 34892, 16758, 27884, 43242, 2423, 1783, 9984, 4032, 9673, 8592, 2655, 28671, 33962, 10943, 3794, 3660, 43242, 2423, 1783, 9984, 4032, 4032, 4032, 30731, 19753, 34740, 3224, 294, 2115, 295], "avg_logprob": -0.2765624922513962, "compression_ratio": 1.4453125, "no_speech_prob": 0.0, "words": [{"start": 3690.19, "end": 3691.59, "word": "Similarly,", "probability": 0.6782023111979166}, {"start": 3691.67, "end": 3692.25, "word": " we", "probability": 0.8330078125}, {"start": 3692.25, "end": 3693.69, "word": " can", "probability": 0.947265625}, {"start": 3693.69, "end": 3695.41, "word": " write", "probability": 0.92529296875}, {"start": 3695.41, "end": 3696.87, "word": " نصاتية", "probability": 0.57806396484375}, {"start": 3696.87, "end": 3698.21, "word": " كتابة", "probability": 0.9891357421875}, {"start": 3698.21, "end": 3699.43, "word": " المشتقة", "probability": 0.789306640625}, {"start": 3699.43, "end": 3700.17, "word": " الرابعة", "probability": 0.9466145833333334}, {"start": 3700.17, "end": 3700.65, "word": " عند", "probability": 0.8779296875}, {"start": 3700.65, "end": 3700.85, "word": " ال", "probability": 0.75830078125}, {"start": 3700.85, "end": 3701.07, "word": " X", "probability": 0.58056640625}, {"start": 3701.07, "end": 3701.53, "word": " node", "probability": 0.426025390625}, {"start": 3701.53, "end": 3702.23, "word": " و", "probability": 0.6123046875}, {"start": 3702.23, "end": 3703.25, "word": " المشتقة", "probability": 0.8787841796875}, {"start": 3703.25, "end": 3704.71, "word": " الخامسة", "probability": 0.9766845703125}, {"start": 3704.71, "end": 3705.63, "word": " عند", "probability": 0.951171875}, {"start": 3705.63, "end": 3705.91, "word": " ال", "probability": 0.7138671875}, {"start": 3705.91, "end": 3706.29, "word": " X", "probability": 0.9501953125}, {"start": 3706.29, "end": 3706.83, "word": " node", "probability": 0.9150390625}, {"start": 3706.83, "end": 3707.33, "word": " و", "probability": 0.83447265625}, {"start": 3707.33, "end": 3707.57, "word": " و", "probability": 0.7177734375}, {"start": 3707.57, "end": 3707.97, "word": " و", "probability": 0.9677734375}, {"start": 3707.97, "end": 3708.25, "word": " إلى", "probability": 0.217041015625}, {"start": 3708.25, "end": 3709.01, "word": " آخره", "probability": 0.9020182291666666}, {"start": 3709.01, "end": 3710.05, "word": " in", "probability": 0.8076171875}, {"start": 3710.05, 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هذا الكلام اللي قلناه احنا وصلنا الى هذه الصيغة تمام و سمينا وصلنا ل ال mail معادلة هذه و روحنا كتبناها فى الصيغة اللى عندنا هي رقم تلاتة", "tokens": [3555, 3794, 37893, 7649, 8717, 12984, 3555, 2655, 9673, 30241, 20498, 9307, 4032, 39182, 9122, 3215, 3224, 44945, 47283, 3215, 5551, 2304, 12984, 37977, 37893, 7649, 8717, 8592, 38688, 9122, 33911, 47525, 8315, 8717, 9566, 3555, 4587, 23758, 2423, 28820, 10943, 13672, 1829, 12174, 1211, 8315, 3224, 1975, 5016, 8315, 4032, 36520, 8315, 2423, 7578, 29538, 31767, 1829, 17082, 3660, 46811, 10943, 4032, 8608, 2304, 1829, 8315, 4032, 36520, 8315, 5296, 2423, 10071, 20449, 18513, 37977, 29538, 4032, 12602, 2407, 5016, 8315, 9122, 2655, 3555, 8315, 11296, 6156, 7578, 31767, 1829, 17082, 3660, 13672, 7578, 43242, 8315, 39896, 12602, 4587, 2304, 6055, 1211, 9307, 3660], "avg_logprob": -0.1939858559448764, "compression_ratio": 1.8629441624365481, "no_speech_prob": 0.0, "words": [{"start": 3840.98, "end": 3841.28, "word": "بس", "probability": 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18863, 16254, 3215, 9154, 16247, 2304, 12984, 37977, 12399, 4032, 28543, 6055, 30544, 28239, 47432, 3660, 20010, 935, 11331, 38436, 4587, 10632, 4032, 28543, 6055, 30544, 6055, 9778, 26895, 10632, 12399, 7251, 3555, 4587, 7578, 15844, 28242, 16247, 29973, 9957, 12399, 47525, 8315, 8717, 5016, 35457, 23758, 16472, 13412, 16606, 21984, 9673, 25720, 25062, 18513, 46007], "avg_logprob": -0.24593496177254653, "compression_ratio": 1.7834645669291338, "no_speech_prob": 5.960464477539063e-08, "words": [{"start": 6214.69, "end": 6215.19, "word": "طبعا", "probability": 0.9593505859375}, {"start": 6215.19, "end": 6215.67, "word": " هذا", "probability": 0.62353515625}, {"start": 6215.67, "end": 6216.49, "word": " أتفه", "probability": 0.7237548828125}, {"start": 6216.49, "end": 6217.03, "word": " أنواع", "probability": 0.94482421875}, {"start": 6217.03, "end": 6217.83, "word": " المسائل،", "probability": 0.802392578125}, {"start": 6217.83, "end": 6218.09, "word": " لكن", "probability": 0.93896484375}, {"start": 6218.09, "end": 6218.53, "word": " اسمها", "probability": 0.4806722005208333}, {"start": 6218.53, "end": 6218.77, "word": " في", "probability": 0.478759765625}, {"start": 6218.77, "end": 6219.71, "word": " الكتاب،", "probability": 0.83416748046875}, {"start": 6219.71, "end": 6220.71, "word": " تمام؟", "probability": 0.82568359375}, {"start": 6220.71, "end": 6221.11, "word": " مرة", "probability": 0.4542236328125}, {"start": 6221.11, "end": 6221.41, "word": " جا", "probability": 0.656494140625}, {"start": 6221.41, "end": 6221.53, "word": " ان", "probability": 0.251953125}, {"start": 6221.53, "end": 6221.87, "word": " شاء", "probability": 0.909423828125}, {"start": 6221.87, "end": 6222.03, "word": " الله", "probability": 0.95068359375}, {"start": 6222.03, "end": 6222.67, "word": " تصير", "probability": 0.67431640625}, {"start": 6222.67, "end": 6223.05, "word": " مش", "probability": 0.94921875}, {"start": 6223.05, "end": 6223.51, "word": " روين", "probability": 0.6053059895833334}, {"start": 6223.51, "end": 6223.67, "word": " في", "probability": 0.462158203125}, {"start": 6223.67, "end": 6224.11, "word": " الهلاب،", "probability": 0.639404296875}, {"start": 6224.11, "end": 6224.55, "word": " تطلع", "probability": 0.88525390625}, {"start": 6224.55, "end": 6224.95, "word": " قيم", "probability": 0.97998046875}, {"start": 6224.95, "end": 6226.05, "word": " عددية،", "probability": 0.863916015625}, {"start": 6226.05, "end": 6226.75, "word": " وحنق", "probability": 0.69781494140625}, {"start": 6226.75, "end": 6226.93, "word": " في", "probability": 0.29541015625}, {"start": 6226.93, "end": 6227.53, "word": " العديد", "probability": 0.970703125}, {"start": 6227.53, "end": 6227.75, "word": " من", "probability": 0.9931640625}, {"start": 6227.75, "end": 6228.97, "word": " الأمثلة،", "probability": 0.88896484375}, {"start": 6228.97, "end": 6229.49, "word": " وقد", "probability": 0.966796875}, {"start": 6229.49, "end": 6230.23, "word": " تكون", 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\ No newline at end of file
diff --git a/PL9fwy3NUQKwa8ZDfSFGn6H8xVFLzqmCZC/6nKiDvoO6MU_raw.srt b/PL9fwy3NUQKwa8ZDfSFGn6H8xVFLzqmCZC/6nKiDvoO6MU_raw.srt
new file mode 100644
index 0000000000000000000000000000000000000000..fb281059e480c38d33295ffd9d68c287b7de4de3
--- /dev/null
+++ b/PL9fwy3NUQKwa8ZDfSFGn6H8xVFLzqmCZC/6nKiDvoO6MU_raw.srt
@@ -0,0 +1,3880 @@
+1
+00:00:09,980 --> 00:00:15,580
+بسم الله الرحمن الرحيم بنواصل ما ابتدأنا به المرة
+
+2
+00:00:15,580 --> 00:00:20,420
+الماضية وهو series solution near an ordinary point
+
+3
+00:00:20,420 --> 00:00:24,760
+وسميناها part one وبعد قليل ان شاء الله خلال هذه
+
+4
+00:00:24,760 --> 00:00:29,000
+المحاضرةحناخذ part 2 ونشوف شو العلاقة ما بين
+
+5
+00:00:29,000 --> 00:00:34,220
+الأتنين على أي حال مرة اللي فاتت أخدنا مثال واحد
+
+6
+00:00:34,220 --> 00:00:38,840
+على كيفية استخدام المتسلسلات في حل المعادلة
+
+7
+00:00:38,840 --> 00:00:43,800
+التفاضلية من الرتبة الثانية والآن بناخد مثلك
+
+8
+00:00:43,800 --> 00:00:48,940
+المثال أتقل شوية من ناحيةالاجراءات العملية و احنا
+
+9
+00:00:48,940 --> 00:00:54,900
+بنشتغل ماكانش مش هيكون مباشر زي مثال المرة الماضية
+
+10
+00:00:54,900 --> 00:00:59,900
+المثال بيقول find the serious solution هات ان شكل
+
+11
+00:00:59,900 --> 00:01:04,080
+الحل اللي على شكل متسلسلة and the recurrence
+
+12
+00:01:04,080 --> 00:01:07,520
+relation والمعادلة التيارية لل differential
+
+13
+00:01:07,520 --> 00:01:13,550
+equationاللي عندنا about the point X يسوى من اتنين
+
+14
+00:01:13,550 --> 00:01:16,650
+اتنين هذا انا مش عارف هي singular point ولا
+
+15
+00:01:16,650 --> 00:01:20,850
+ordinary point لكن احنا موضوعنا حتى هذه اللحظة
+
+16
+00:01:20,850 --> 00:01:25,130
+الدراسة عند من عند ال ordinary points لأ وليس عند
+
+17
+00:01:25,130 --> 00:01:29,430
+ال singular points لكن بدنا نبين ان هذه النقطة هي
+
+18
+00:01:29,430 --> 00:01:35,150
+عبارة عن ordinary point فلو جيت بدى اقوله ال P of
+
+19
+00:01:35,150 --> 00:01:42,270
+X يبقى ال P of X اللي هي منإتنين لا يمكن أن تساوي
+
+20
+00:01:42,270 --> 00:01:48,130
+zero مهما تغيرت ال X يبقى كل النقاط عبارة عن
+
+21
+00:01:48,130 --> 00:01:52,770
+ordinary points يعني لا يوجد عندي singular points
+
+22
+00:01:52,770 --> 00:02:01,070
+يبقى هذا معناه إن ال X يساوي 2 is an ordinary
+
+23
+00:02:01,070 --> 00:02:06,670
+point يبقى هذه عبارة عن نقطة عادية
+
+24
+00:02:11,740 --> 00:02:20,980
+أحنا بنبحث على إيه ال solutionY في الصيغة التالية
+
+25
+00:02:20,980 --> 00:02:27,200
+summation من N equal zero to infinity لل A N المرة
+
+26
+00:02:27,200 --> 00:02:30,940
+اللي فاتت المثال الماضي منها كانت النقطة X يساوي
+
+27
+00:02:30,940 --> 00:02:36,280
+زيرو وليس X يساوي اتنين فكان summation لل A N X to
+
+28
+00:02:36,280 --> 00:02:43,230
+the power N لكن مدام احناالحل هيكون حوالين النقطة
+
+29
+00:02:43,230 --> 00:02:49,350
+هذه كما بنقول x ناقص اتنين كله to the power n
+
+30
+00:02:49,350 --> 00:02:55,610
+which converge
+
+31
+00:02:55,610 --> 00:03:05,230
+for اللي هو absolute value لل x ناقص اتنين اقل من
+
+32
+00:03:05,230 --> 00:03:11,340
+رو و رو greater than zeroيبقى هذه ال series تبقى
+
+33
+00:03:11,340 --> 00:03:15,520
+تقاربية خلال الفترة اللى عندنا اللى هو absolute
+
+34
+00:03:15,520 --> 00:03:20,000
+value لل X ناقص اتنين اقل من رو و رو greater than
+
+35
+00:03:20,000 --> 00:03:24,520
+zero بس مجرد التذكير اللى ليس اللى بتذكركوا بكل
+
+36
+00:03:24,520 --> 00:03:29,380
+كلاص بيه هذه ال absolute value لل X ناقص اتنين اقل
+
+37
+00:03:29,380 --> 00:03:37,760
+من رو و اكبر من روأول X أقل من رو زائد اتنين و اقل
+
+38
+00:03:37,760 --> 00:03:44,460
+من اتنين ناقص رو يعني لو جيت قولت هذا ال real line
+
+39
+00:03:44,460 --> 00:03:50,360
+تمام؟ و هذه النقطة اللي هي اتنين النقطة هذه اتنين
+
+40
+00:03:50,360 --> 00:03:56,320
+زائد روالنقطة ها دي ها ها اللي هي اتنين ناقص رو
+
+41
+00:03:56,320 --> 00:04:00,660
+وبالتالي هذا نصف القطر او radius of convergence
+
+42
+00:04:00,660 --> 00:04:05,280
+اللي هي رو وهذا radius of convergence برضه مين
+
+43
+00:04:05,280 --> 00:04:11,960
+اللي هي رو طيب ممتاز ايش رايكوا اتعرف على شكل الحل
+
+44
+00:04:11,960 --> 00:04:15,440
+لإنه مش هنعوض في المعادلة دي بالزمن المشتقة الأولى
+
+45
+00:04:15,440 --> 00:04:22,140
+والمشتقة الثانيةيبقى انا عندي y تساوي ال summation
+
+46
+00:04:22,140 --> 00:04:28,600
+من n equal zero to infinity لل a n في ال x ناقص
+
+47
+00:04:28,600 --> 00:04:35,120
+اتنين كله to the power m هذا بده يعطينا ان المشتقة
+
+48
+00:04:35,120 --> 00:04:42,490
+الاولى y prime يساويSummation لمن؟ لل N in
+
+49
+00:04:42,490 --> 00:04:48,770
+constant X ناقص اتنين to the power N minus one ال
+
+50
+00:04:48,770 --> 00:04:51,630
+summation هذا لما اشتق المشتق اللي هو اللي بيبدأ
+
+51
+00:04:51,630 --> 00:04:56,570
+من وين؟ من عند N تسوى واحد من عند N تسوى واحد الى
+
+52
+00:04:56,570 --> 00:05:02,670
+infinity هذا بده يعطينا ان المشتق الثاني YW prime
+
+53
+00:05:03,210 --> 00:05:09,510
+هذا كله مقدار ثابت إذا بدى أشتاق هذه كمان مرة يبقى
+
+54
+00:05:09,510 --> 00:05:17,030
+summation لل N في ال N ناقص واحد في ال AMفى الـ X
+
+55
+00:05:17,030 --> 00:05:22,150
+ناقص اتنين to the power in minus اتنين طبعا مشتقة
+
+56
+00:05:22,150 --> 00:05:26,050
+مداخل القصة اللى هو بقداش بواحد صحيح يبقى بروحاش
+
+57
+00:05:26,050 --> 00:05:29,710
+باكتبها ال summation هنا ابتدا من عند ان يساوي
+
+58
+00:05:29,710 --> 00:05:35,050
+واحد يبقى من هنا من عند ان تساوي اتنين زى ما كنا
+
+59
+00:05:35,050 --> 00:05:39,470
+شفنا فى ال section الماضى وزى ما شفنا فى مثال
+
+60
+00:05:39,470 --> 00:05:51,830
+المرة الماضىالان عندي Y و Y'' و Y'' و Y'' و Y''
+
+61
+00:05:51,830 --> 00:05:53,050
+و Y'' و Y'' و Y'' و Y'' و Y'' و Y'' و Y'' و Y'' و
+
+62
+00:05:53,050 --> 00:05:53,490
+Y'' و Y'' و Y'' و Y'' و Y'' و Y'' و Y'' و Y'' و
+
+63
+00:05:53,490 --> 00:05:53,630
+Y'' و Y'' و Y'' و Y'' و Y'' و Y'' و Y'' و Y'' و
+
+64
+00:05:53,630 --> 00:05:53,630
+Y'' و Y'' و Y'' و Y'' و Y'' و Y'' و Y'' و Y'' و
+
+65
+00:05:53,630 --> 00:05:53,670
+Y'' و Y'' و Y'' و Y'' و Y'' و Y'' و Y'' و Y'' و
+
+66
+00:05:53,670 --> 00:05:53,670
+Y'' و Y'' و Y'' و Y'' و Y'' و Y'' و Y'' و Y'' و
+
+67
+00:05:53,670 --> 00:05:54,070
+Y'' و Y'' و Y'' و Y'' و Y'' و Y'' و Y'' و Y'' و
+
+68
+00:05:54,070 --> 00:05:56,190
+Y'' و Y'' و Y'' و Y'' و Y'' و Y'' و Y'' و Y'' و
+
+69
+00:05:56,190 --> 00:06:01,710
+Y'' و Y'' و Y'' و Y'' و Y''
+
+70
+00:06:04,550 --> 00:06:09,970
+بنجعلها 2YWP يبقى هذه بدروح اضربها في بينامنات بده
+
+71
+00:06:09,970 --> 00:06:14,470
+اضربها في اتنين الاتنين هذه لو خلتها برا ال
+
+72
+00:06:14,470 --> 00:06:18,340
+summation والله حطيتها جوا ال summation بتفرجكونوا
+
+73
+00:06:18,340 --> 00:06:22,560
+مالوش دعوة بالصميشن يعني مالوش دعوة بال N إذا هذه
+
+74
+00:06:22,560 --> 00:06:29,300
+ستصبح summation من N equal to infinity لإتنين اللي
+
+75
+00:06:29,300 --> 00:06:37,580
+عندنا N في من؟ في ال N ناقص واحد في ال A N في ال X
+
+76
+00:06:37,580 --> 00:06:43,620
+ناقص اتنين to the power N ناقص اتنين يبقى خلصها من
+
+77
+00:06:43,620 --> 00:06:49,830
+من؟ من ال term الأولبدنا نيجي لل term التاني اللي
+
+78
+00:06:49,830 --> 00:06:54,470
+هو ال X زائد واحد مالكش دعوة يخليك برا لإنك مش زي
+
+79
+00:06:54,470 --> 00:06:57,910
+اللي جوا، لو كان زي اللي جوا هذا كان دخلناه
+
+80
+00:06:57,910 --> 00:07:02,520
+مباشرة، لكن خليكي لما نتفاهم عليكي شويةيبقى x زاد
+
+81
+00:07:02,520 --> 00:07:06,360
+واحد في ال y prime وين ال y prime؟ هايها يبقى
+
+82
+00:07:06,360 --> 00:07:13,320
+summation من n equal one to infinity لل n a n x
+
+83
+00:07:13,320 --> 00:07:18,440
+ناقص اتنين to the power n minus ال one قلصنا ال
+
+84
+00:07:18,440 --> 00:07:21,980
+term التاني بدنا نروح لل term التالت يبقى هذه بدنا
+
+85
+00:07:21,980 --> 00:07:25,700
+نروح نضربها وين؟ تلاتة تلاتة كتبتها برا ال
+
+86
+00:07:25,700 --> 00:07:29,200
+summation ولا جوا ال summation نسيانيبقى بالداخل
+
+87
+00:07:29,200 --> 00:07:34,800
+تلاتة جوا ال summation يبقى زائد summation من n
+
+88
+00:07:34,800 --> 00:07:41,440
+equal zero to infinity لتلاتة a n في ال x ناقص
+
+89
+00:07:41,440 --> 00:07:46,780
+اتنين to the power n كله بده يساوي مين؟ بده يساوي
+
+90
+00:07:46,780 --> 00:07:53,460
+zero يبقى احنا الآن بدنا نعيد ترتيب أوراق المثلة
+
+91
+00:07:53,460 --> 00:07:58,860
+في شغلتينالشغل الأولى هدى x to the power n x نقص
+
+92
+00:07:58,860 --> 00:08:03,460
+اتنين to the power n بدى الباقى هدى الأسس كلها to
+
+93
+00:08:03,460 --> 00:08:08,860
+the power n هى واحدة الثانية بدى ال index لتحت ال
+
+94
+00:08:08,860 --> 00:08:13,900
+summation يكون كله موحد مشان اقدر اجمع و اعمل ايه
+
+95
+00:08:13,900 --> 00:08:19,040
+ب summation واحد فقط فبجى بقول هدى مشان اخليها
+
+96
+00:08:19,040 --> 00:08:25,330
+بدلالة ال nيبقى بده يشيل كل N ويحط مكانها N زائد
+
+97
+00:08:25,330 --> 00:08:30,610
+اتنين يبقى دي بدها تصير على الشكل التالي يبقى
+
+98
+00:08:30,610 --> 00:08:40,820
+summation من عند N equal to zero ولا لأ؟هذا يعني
+
+99
+00:08:40,820 --> 00:08:48,140
+ان تساوي 0 لمن؟ لل infinity وبالتالي اتنين بده
+
+100
+00:08:48,140 --> 00:08:54,140
+اشيل الان وحط مكانها ان زائد اتنين وهذا يعني ان
+
+101
+00:08:54,140 --> 00:09:01,560
+زائد اتنين ناقص واحد يعني ان زائد واحدهذه a n زائد
+
+102
+00:09:01,560 --> 00:09:08,100
+اتنين كله في اكس ناقص اتنين كله to the power m
+
+103
+00:09:08,100 --> 00:09:13,700
+يبقى هذه زبطناها الخطوة الأولى خلينا الأس تبعها to
+
+104
+00:09:13,700 --> 00:09:18,960
+the power m اه هنا في جوا اكس و في برا اكس بده
+
+105
+00:09:18,960 --> 00:09:24,690
+ادخل اللي جوا برا بس مش زي بعض ورطنامظبوط هذه X زي
+
+106
+00:09:24,690 --> 00:09:29,970
+واحد وهذه X نقص اتنين طيب كي بدى ادخل ادخل ال X
+
+107
+00:09:29,970 --> 00:09:33,790
+هنا برضه لحاله بتظبطش ادخل ال واحد لحاله بتظبطش
+
+108
+00:09:33,790 --> 00:09:38,410
+اذا بدي اشتغل شغل فعلا يكون رياضي سليم وماحدش
+
+109
+00:09:38,410 --> 00:09:42,170
+يقولي كلامك مش صحيح ايش بتقترحه علينا نعمة اللي
+
+110
+00:09:42,170 --> 00:09:46,110
+بتعرفي ترفعي دي ابو جا شيفها ايوة X زي واحد هيفرع
+
+111
+00:09:46,110 --> 00:09:53,110
+X نقص اتنين ميال ميال شو اسمك انت ايهحنين حنين
+
+112
+00:09:53,110 --> 00:09:56,510
+حنين
+
+113
+00:09:56,510 --> 00:10:01,050
+حنين حنين حنين حنين حنين حنين حنين حنين حنين حنين
+
+114
+00:10:01,050 --> 00:10:09,530
+حنين حنين حنين حنين حنين حنين حنين حنين حنين حنين
+
+115
+00:10:09,530 --> 00:10:09,550
+حنين حنين حنين حنين حنين حنين حنين حنين حنين حنين
+
+116
+00:10:09,550 --> 00:10:09,550
+حنين حنين حنين حنين حنين حنين حنين حنين حنين حنين
+
+117
+00:10:09,550 --> 00:10:09,550
+حنين حنين حنين حنين حنين حنين حنين حنين حنين حنين
+
+118
+00:10:09,550 --> 00:10:09,550
+حنين حنين حنين حنين حنين حنين حنين حنين حنين حنين
+
+119
+00:10:09,550 --> 00:10:09,590
+حنين حنين حنين حنين حنين حنين حنين حنين حنين حنين
+
+120
+00:10:09,590 --> 00:10:19,450
+حنين
+
+121
+00:10:19,450 --> 00:10:27,840
+حنلكن هذه حلتلي معضلة كبيرة جدا ايش صار عندي x نقص
+
+122
+00:10:27,840 --> 00:10:32,000
+اتنين مضروبة في الاجابة بقدر اضربها بدون مشاكل و
+
+123
+00:10:32,000 --> 00:10:35,480
+بضل عندي تلاتة مضروبة في ال summation يعني حاسين
+
+124
+00:10:35,480 --> 00:10:40,240
+عندي كم double summations واحد مضروب في x نقص
+
+125
+00:10:40,240 --> 00:10:44,580
+اتنين واحد مضروب في مام في تلاتة ايه بجهاي اول
+
+126
+00:10:44,580 --> 00:10:49,530
+معضلة موجودة في المثلة تغلبنا عليها بتفكير سليمكيف
+
+127
+00:10:49,530 --> 00:10:54,370
+اكتب اللي هو ال term اللي برا بدلالة main بدلالة
+
+128
+00:10:54,370 --> 00:10:57,330
+term اللي جوا، بالتالي بيكون خلصنا من المثل هذه
+
+129
+00:10:57,330 --> 00:11:03,230
+يبقى يا بنات هذه ال X ناقص اتنين بدي دخلها جوا ال
+
+130
+00:11:03,230 --> 00:11:07,090
+summation وبعد ذلك زائد تلاتة كمان ادخلها جوا ال
+
+131
+00:11:07,090 --> 00:11:11,350
+summation وبالتالي هيظهر term main وليس term واحد
+
+132
+00:11:11,710 --> 00:11:17,890
+يبقى هانيجي هنا زائد هي عندنا summation من وين؟ من
+
+133
+00:11:17,890 --> 00:11:25,110
+عند ال N equal one to infinity لمين؟ لل N A N X
+
+134
+00:11:25,110 --> 00:11:30,310
+ناقص اتنين X ناقص اتنين بدا تيجي هذه أس قداش يا
+
+135
+00:11:30,310 --> 00:11:38,350
+بنات أس واحد يبقى هذا مع السلامة بظل هذا أس Nضايل
+
+136
+00:11:38,350 --> 00:11:41,950
+علينا مين؟ ضايل علينا التلاتة تدخل على ال
+
+137
+00:11:41,950 --> 00:11:47,330
+summation يبقى زائد summation من n equal one to
+
+138
+00:11:47,330 --> 00:11:56,810
+infinity لتلاتة n a n x ناقص اتنين أس قداش ناقص
+
+139
+00:11:56,810 --> 00:12:01,910
+واحد هذه التلاتة مالاش دعوة بتضيعش الأس بيظل الأس
+
+140
+00:12:01,910 --> 00:12:06,380
+زي ما هويبقى الترمين اللي كتبتهم عبارة عن الترم
+
+141
+00:12:06,380 --> 00:12:11,600
+هذا فقط و بقى اللي عندنا مين؟ الترم الأخير يبقى
+
+142
+00:12:11,600 --> 00:12:20,140
+زائد summation من n equal zero to infinity لثلاثة
+
+143
+00:12:20,140 --> 00:12:25,380
+a n في ال X لقص اتنين to the power n كل هذا بده
+
+144
+00:12:25,380 --> 00:12:32,260
+ساوي مان؟ بده ساوي زيروطيب، حتى الآن فكنا مهضلة
+
+145
+00:12:32,260 --> 00:12:38,640
+واحدة، اللي هو هذه كتبناها بدلالة اللي جوا، الآن
+
+146
+00:12:38,640 --> 00:12:49,490
+نرجع لشغلنا المرة الماضيةهيبقى اول
+
+147
+00:12:49,490 --> 00:12:54,710
+خطوة بنعملها بنوحد الاص تبع main ال X اللي عندنا
+
+148
+00:12:54,710 --> 00:13:00,370
+هذه بعدين بطلها هذي أس ان جاهزة هذي أس ان جاهزة
+
+149
+00:13:00,370 --> 00:13:04,890
+هذي أس ان جاهزة يبقى هذي اللي ماهياش جاهزة يبقى
+
+150
+00:13:04,890 --> 00:13:10,910
+مشان أجهزها هذي بدي أشيل كل ان و أحط مكانهان زائد
+
+151
+00:13:10,910 --> 00:13:14,630
+واحد يبقى هذه يا بنات بديش اعكس كتابة انت بدي
+
+152
+00:13:14,630 --> 00:13:20,550
+نزلها زي ما هي وهذه بدي نزلها زي ما هي وهذه زائد
+
+153
+00:13:20,550 --> 00:13:26,510
+summation من n equal zero to infinity لتلاتة n
+
+154
+00:13:26,510 --> 00:13:34,190
+زائد واحد a n زائد واحد x ناقص اتنين to the power
+
+155
+00:13:34,190 --> 00:13:40,750
+nيبقى شيلت كل in لل term التالت ده وحطيت مكانه in
+
+156
+00:13:40,750 --> 00:13:47,430
+زائد واحد هذا كمان زائد بدي أنزله مانه زي ما هو
+
+157
+00:13:47,430 --> 00:13:54,570
+ماعنديش مشكلة فيهإذا إيش اللي حصل الآن وحتى الأسس
+
+158
+00:13:54,570 --> 00:13:59,090
+كلها تبعت من؟ تبعت ال X ناقص اتنين إذا حلّينا
+
+159
+00:13:59,090 --> 00:14:03,530
+المعضلة التانية ضايل مين علينا؟ المعضلة التالتة
+
+160
+00:14:03,530 --> 00:14:07,290
+المعضلة التالتة بدي أخلّي ال index لتحت ال
+
+161
+00:14:07,290 --> 00:14:12,990
+summation هذا كله زي بعضه دون أن أضيع الشغل اللي
+
+162
+00:14:12,990 --> 00:14:16,010
+اشتغلته بالنسبة لل X ناقص اتنين to the power n
+
+163
+00:14:16,010 --> 00:14:20,510
+يعني اصحي تعملي شغل تخربيهاللي اشتغلت يقولنا
+
+164
+00:14:20,510 --> 00:14:24,070
+بالبلد انحافظ على المكتسبات الوطنية المرة اللي
+
+165
+00:14:24,070 --> 00:14:26,870
+فاتت، يبقى احنا هنا نفس القصة بدنا نحافظ على
+
+166
+00:14:26,870 --> 00:14:30,590
+المكتسبات الوطنية، معناته بدي اشتغل شغل رياضي
+
+167
+00:14:30,590 --> 00:14:34,610
+سليم، ماحدش يقوللي فيه حاجة، واخل الأس تبع ال X
+
+168
+00:14:34,610 --> 00:14:40,080
+ناقص اتنين هو هو في الأربع تيرمان، بقولك كويسأحنا
+
+169
+00:14:40,080 --> 00:14:44,740
+عندنا ده من عند الواحد يبقى أنا ماقدرش ألعب فيه
+
+170
+00:14:44,740 --> 00:14:49,420
+طيب باجي بقول ممكن أخلي الباجي كله من عند الواحد
+
+171
+00:14:49,420 --> 00:14:53,780
+يبدأ كيف؟ بطلع أول term في ال series اللي عندنا
+
+172
+00:14:53,780 --> 00:14:57,980
+ضارة ال summation وبالتالي بصير بوحد ال index هذه
+
+173
+00:14:57,980 --> 00:15:04,200
+فمثلا لو حطيت ال n يساوي zero بصير اتنين في اتنين
+
+174
+00:15:04,200 --> 00:15:10,450
+في واحد يعني اربعة اتنين فقطيبقى بصيري عندي هنا اي
+
+175
+00:15:10,450 --> 00:15:17,990
+اربعة اتنين مفيش غيرها زي summation من n equal one
+
+176
+00:15:17,990 --> 00:15:24,370
+to infinity للتنين في ال n زائد اتنين في ال n زائد
+
+177
+00:15:24,370 --> 00:15:30,150
+واحد في ال a n زائد اتنين في ال x ناقص اتنين to
+
+178
+00:15:30,150 --> 00:15:36,180
+the power n يبقى هاي ال term الأول خلصنا منهالترم
+
+179
+00:15:36,180 --> 00:15:40,240
+التاني بنزله زي ما هو لإنه ما عندهوش مشكلة مادي من
+
+180
+00:15:40,240 --> 00:15:45,340
+عند الواحد يبقى زائد summation من n equal one to
+
+181
+00:15:45,340 --> 00:15:53,660
+infinity لل n a n x ناقص اتنين to the power n اللي
+
+182
+00:15:53,660 --> 00:15:58,180
+بعد هو اللي عنده المشكلةيبقى بيطلع كمان term زي
+
+183
+00:15:58,180 --> 00:16:04,380
+مين؟ زي الأولاني يبقى باجي بقوله زائد بدي أضع N بـ
+
+184
+00:16:04,380 --> 00:16:11,780
+00 بيبقى تلاتة A1 يبقى هاي تلاتة A1 أقص Zero اللي
+
+185
+00:16:11,780 --> 00:16:17,300
+هو بواحد زائد summation من N equal one to infinity
+
+186
+00:16:17,300 --> 00:16:22,840
+لتلاتة في N زائد واحد A N زائد واحد
+
+187
+00:16:27,900 --> 00:16:36,220
+ماحدش أحسن من حد يبقى زائد تلاتة a نوت وها دي راحة
+
+188
+00:16:36,220 --> 00:16:41,000
+الله سهل عليها زائد summation من n equal one to
+
+189
+00:16:41,000 --> 00:16:47,420
+infinity لتلاتة a n x نقص اتنين to the power n كله
+
+190
+00:16:47,420 --> 00:16:53,300
+بده يساويهذه الخطوة اللى عملتها خلصتها بنديت على
+
+191
+00:16:53,300 --> 00:16:59,300
+ال term الأول و ال term التالت
+
+192
+00:16:59,300 --> 00:17:03,680
+و الرابع طلعت بس أول حد من الصمشي و البجي خلته زى
+
+193
+00:17:03,680 --> 00:17:08,460
+ما هوالان لو طلعت في مسألتي من أولها إلى آخرها
+
+194
+00:17:08,460 --> 00:17:13,700
+بلاحظ ان ال index اللى تحت ال summation موحد كله
+
+195
+00:17:13,700 --> 00:17:19,320
+بيبدأ من أند الواحد اتنين ال X ناقص اتنين to the
+
+196
+00:17:19,320 --> 00:17:24,680
+power N كلها موحدة للكل تمام؟ اذا بقدر اجمل هذه
+
+197
+00:17:24,680 --> 00:17:31,230
+بمعادلة واحدةبدي اخدي ثوابت هدول مع بعض لحال و
+
+198
+00:17:31,230 --> 00:17:35,930
+الباقي لحال يبقى هذا ايش؟ بصي يا بنات هاي اربعة
+
+199
+00:17:35,930 --> 00:17:43,960
+اتنين زائد تلاتة في ا واحد زائد ا نولهي عندك تلاتة
+
+200
+00:17:43,960 --> 00:17:47,720
+a واحد و تلاتة a نوت اخدتهم مع بعض تلاتة عامل
+
+201
+00:17:47,720 --> 00:17:52,500
+مشترك من الكل نجي لبعدها زائد هاي ال summation
+
+202
+00:17:52,500 --> 00:17:58,960
+مشترك للكل من عند n equal one to infinity تمام؟
+
+203
+00:17:58,960 --> 00:18:05,000
+وهذا جوز كبير الآن هنا ايش بضالة عندى اتنين في n
+
+204
+00:18:05,350 --> 00:18:12,130
+زائد اتنين في N زائد واحد في AN زائد اتنين هذي
+
+205
+00:18:12,130 --> 00:18:18,190
+يخليها عمل مشارك من الكل general اللي بعدها زائد N
+
+206
+00:18:18,190 --> 00:18:25,790
+في ANجينا للي بعدها زائد تلاتة في N زائد واحد في
+
+207
+00:18:25,790 --> 00:18:33,770
+ال A N زائد واحد وصلنا هذه يبقى زائد تلاتة A N
+
+208
+00:18:33,770 --> 00:18:39,690
+خلصنا كله مضروب في ال X ناقص اتنين to the power N
+
+209
+00:18:39,690 --> 00:18:41,050
+يساوي Zero
+
+210
+00:18:44,500 --> 00:18:49,660
+الان عندي polynomial تساوي زيرو إذا معاملات ال
+
+211
+00:18:49,660 --> 00:18:53,540
+polynomial كلهم بأصفر هم اللي خلولي ال polynomial
+
+212
+00:18:53,540 --> 00:18:57,980
+تساوي زيرو إذا هذا ال term بده يساوي زيرو والباقي
+
+213
+00:18:57,980 --> 00:19:03,580
+بده يساوي زيرو يبقى بيصير عندي اربعة اتنين زائد
+
+214
+00:19:03,580 --> 00:19:09,990
+تلاتة ا وان زائد ا نوت بده يساوي زيرووبعدها كل
+
+215
+00:19:09,990 --> 00:19:15,730
+معامل هذا بين القوسين بده يساوي zero المعامل هذا
+
+216
+00:19:15,730 --> 00:19:24,470
+اتنين اتنين في n زائد اتنين في n زائد واحد في a n
+
+217
+00:19:24,470 --> 00:19:33,510
+زائد اتنين زائد تلاتة in زائد واحد في a n زائد
+
+218
+00:19:33,510 --> 00:19:41,400
+واحد طلعيلي هذه وهذهمش في بينهم AN عامل مشترك بيظل
+
+219
+00:19:41,400 --> 00:19:51,100
+جديش N زائد تلاتة يبقى زائد N زائد تلاتة كله في AN
+
+220
+00:19:51,100 --> 00:19:58,460
+هذا بده يساوي من؟ بده يساوي Zero طيب لو جيت لهذه
+
+221
+00:19:58,460 --> 00:20:05,780
+معناته ان ال A2 بده يساوي تلات تربع بإشارة سالب
+
+222
+00:20:06,000 --> 00:20:13,580
+لمن؟ لل A1 زائد A نقطةمن هنا بدأ يظهر اول اختلاف
+
+223
+00:20:13,580 --> 00:20:17,660
+بين سؤالنا هذا وبين سؤالي المرة الماضية المرة
+
+224
+00:20:17,660 --> 00:20:23,120
+الماضية طلعت a2 بدلالة main a node فقط المرة هذه
+
+225
+00:20:23,120 --> 00:20:28,560
+طلعت بدلالة a node و a1 وبالتالي ماعناش مشكلة برضه
+
+226
+00:20:28,560 --> 00:20:33,660
+يعني ايش ما تطلع بسجلها زي ما هي كويس هذه الآن في
+
+227
+00:20:33,660 --> 00:20:40,550
+عوامل مشتركةممكن يعني اجسم عليها في جوس عامل مشارك
+
+228
+00:20:40,550 --> 00:20:43,630
+من ال term الأول و ال term التاني و التاني بيقولي
+
+229
+00:20:43,630 --> 00:20:46,990
+هنا n زاد واحد هنا n زاد واحد بس هنا مافيش n زاد
+
+230
+00:20:46,990 --> 00:20:53,160
+واحد مصغر يبقى بخلي كل شي زي ما هواذا هذا و هذا
+
+231
+00:20:53,160 --> 00:20:58,260
+هوديهم على الشجة التانية و اقسم على هذا المعامل
+
+232
+00:20:58,260 --> 00:21:05,160
+بيصير عندنا ال a n زائد اتنين يساوي ناقص هيخليه
+
+233
+00:21:05,160 --> 00:21:11,900
+برا بيظل عندنا مين تلاتة في n زائد واحد a n زائد
+
+234
+00:21:11,900 --> 00:21:20,640
+واحد زائد n زائد تلاتة a n كل هذا مقسم على الاتنين
+
+235
+00:21:36,190 --> 00:21:42,090
+عن طريق الـ Recurrence relation اللى طلبها عندى
+
+236
+00:21:42,090 --> 00:21:47,120
+وين فى رأس المثلة جالسة لـ Recurrence relationطب
+
+237
+00:21:47,120 --> 00:21:54,160
+بدى اشوف هدى بدى تبدأ in من وين يبقى in تساوي ابدا
+
+238
+00:21:54,160 --> 00:21:59,400
+من عند ال zero لو قليه من عند ال zero شو بيعطيني
+
+239
+00:21:59,400 --> 00:22:05,580
+اتنين ما اتنين هي جاهزةصح؟ يبقى الصحة ده من وين؟
+
+240
+00:22:05,580 --> 00:22:11,720
+من عند الواحد يبقى انتوا ساوية واحد واتنين وتلاتة
+
+241
+00:22:11,720 --> 00:22:16,720
+وإلى ما شاء الله يبقى هذه يا بنات ال recurrence
+
+242
+00:22:16,720 --> 00:22:21,320
+relation اللي بدّوياها اللي هو المطلوب الأول من
+
+243
+00:22:21,320 --> 00:22:27,680
+المسألة طيب بعد هيك الآن احكي قولي
+
+244
+00:22:31,340 --> 00:22:36,340
+ممتاز، اذا جربنا ايش؟ اذا جربنا ن بي زيرو، اذا
+
+245
+00:22:36,340 --> 00:22:40,580
+جربنا ن بي زيرو، اذا جربنا ن بي زيرو، اذا جربنا ن
+
+246
+00:22:40,580 --> 00:22:40,580
+بي زيرو، اذا جربنا ن بي زيرو، اذا جربنا ن بي زيرو،
+
+247
+00:22:40,580 --> 00:22:42,440
+اذا جربنا ن بي زيرو، اذا جربنا ن بي زيرو، اذا
+
+248
+00:22:42,440 --> 00:22:43,380
+جربنا ن بي زيرو، اذا جربنا ن بي زيرو، اذا جربنا ن
+
+249
+00:22:43,380 --> 00:22:46,960
+بي زيرو، اذا جربنا ن بي زيرو، اذا جربنا ن بي زيرو،
+
+250
+00:22:46,960 --> 00:22:48,940
+اذا جربنا ن بي زيرو، اذا جربنا ن بي زيرو، اذا
+
+251
+00:22:48,940 --> 00:22:56,640
+جربنا ن بي زيرو، اذا جربنا ن بي زيرو، اذا
+
+252
+00:22:56,640 --> 00:23:03,380
+جربنا نخلاص و بقول هي ال record اللى بتشمل الأولى
+
+253
+00:23:03,380 --> 00:23:07,800
+و الثانية بمشي الحال ماعناه مشكلة بيخلي هذه الحال
+
+254
+00:23:07,800 --> 00:23:11,760
+و هذه الحال و اقول عندى انت سوا عاد ماشي الحال بدي
+
+255
+00:23:11,760 --> 00:23:15,280
+أجمع ال 22 بصيغة اللى عندي و أخلي N تبدأ من عند
+
+256
+00:23:15,280 --> 00:23:20,080
+الذهور و ماعنديش مشكلة تمام؟ ليش؟ لأن لو حطيت N ب
+
+257
+00:23:20,080 --> 00:23:23,660
+zero في ال recurrence relation هذا بطلع منين؟بطلع
+
+258
+00:23:23,660 --> 00:23:29,660
+ال term اللي عنها ده إذا ممكن أن استغني عن هذه هيك
+
+259
+00:23:29,660 --> 00:23:37,260
+وروح أقول هذه ال N تساوي Zero واحد و اتنين و تلاتة
+
+260
+00:23:37,260 --> 00:23:42,080
+إلى مالها نهاية كتبت هيك ولا كتب هيك اتنين صح تكتب
+
+261
+00:23:42,080 --> 00:23:46,300
+الصيغة اللي تشوفيها مناسبة بالنسبة لك ماشي لإن راح
+
+262
+00:23:46,300 --> 00:23:49,880
+احطت N تساوي Zero في المستطيل هذا بطلع المستطيل
+
+263
+00:23:49,880 --> 00:23:54,230
+الأول عنها و ال term الأول اللي عنهاما علينا اتنين
+
+264
+00:23:54,230 --> 00:23:58,110
+جاهزة عندي بدلا الات اي ون و اي نود بدي اجيب من
+
+265
+00:23:58,110 --> 00:24:05,590
+ايه اتلاتة يبقى بدي اتلاتة اي اي ون زي اتنين اذا
+
+266
+00:24:05,590 --> 00:24:11,130
+بدي اشيل كل ان و احط مكانها واحد صحيح يبقى هذا
+
+267
+00:24:11,130 --> 00:24:15,410
+الكلام هي الناقص برا وهي الجوز بصير هذه يا بنات
+
+268
+00:24:15,410 --> 00:24:22,540
+تلاتة في اتنين اللي هو كده؟ ستة اتنينستة اتنين
+
+269
+00:24:22,540 --> 00:24:31,260
+زائد اربع اي واحد هذا كل البسطة على المقام المقام
+
+270
+00:24:31,260 --> 00:24:36,940
+ده احط هذه بواحد بصير تلاتة في اتنين بستة ستة في
+
+271
+00:24:36,940 --> 00:24:43,080
+اتنين باطمعش يبقى هذه كلها على اقمعش بالشكل اللي
+
+272
+00:24:43,080 --> 00:24:45,040
+عندنا تمام؟
+
+273
+00:24:46,600 --> 00:24:54,400
+هذه البنات تساوي ناقص نص فى مين فى الاتنين ستة على
+
+274
+00:24:54,400 --> 00:24:58,300
+اتناش بناقص نص فى الاتنين اربع على اتناش اللى هو
+
+275
+00:24:58,300 --> 00:25:07,480
+بقداش تلت يبقى ناقص تلت فى اربع يعني اربع اتلت لا
+
+276
+00:25:07,480 --> 00:25:10,780
+تلت بس تلت اللى هو ال
+
+277
+00:25:14,230 --> 00:25:20,910
+طب اتنين مقطع يبقى بقدر اشيل اتنين وحقمتها بصير
+
+278
+00:25:20,910 --> 00:25:26,530
+المثلة كلها بدلالة a node و a one يبقى هذا الكلام
+
+279
+00:25:26,530 --> 00:25:34,270
+بده يساوي ناقص نص و اتنين هيقلوب ناقص تلت ربع a
+
+280
+00:25:34,270 --> 00:25:42,630
+one في ناقص تلت ربع a one ناقص تلت ربع
+
+281
+00:25:44,980 --> 00:25:51,080
+هذا كله يكون ناقص
+
+282
+00:25:51,080 --> 00:26:00,050
+تلت A1 يبقى هذه تساويطلعيلي كويس هنا بدى افكر بصير
+
+283
+00:26:00,050 --> 00:26:07,050
+هذا قداش تلات اتمان بالموجب يبقى تلاتة على تمانية
+
+284
+00:26:07,050 --> 00:26:16,930
+ا one نقص فنقصه بزايد برضه تلات اتمان تلات اتمان a
+
+285
+00:26:16,930 --> 00:26:24,650
+naught ناقص تلت ا one طلعيلي ال term الأول و الأخر
+
+286
+00:26:26,110 --> 00:26:31,170
+يجب أن تجمع الموضوع في المشتركة الـ 3 و 8، 4 و 20،
+
+287
+00:26:31,170 --> 00:26:38,090
+يبقى لو قلت على 4 و 20بنضيف كدهش اربعة و عشرين على
+
+288
+00:26:38,090 --> 00:26:45,030
+تمانية فيها التلاتة في تلاتة بتسعة اي تسعة ا وان
+
+289
+00:26:45,030 --> 00:26:48,870
+تمام و نيجي هنا اربعة و عشرين على تلاتة فيها
+
+290
+00:26:48,870 --> 00:26:55,130
+تمانية في واحد بسالب تمانية ا وان سالب تمانية ا
+
+291
+00:26:55,130 --> 00:27:00,320
+وان هذا ال term هناالاخير تلاتة اثمان a note مالوش
+
+292
+00:27:00,320 --> 00:27:08,000
+دعوة لحاله يبقى زائد تلاتة اثمان a note ويساوي ها
+
+293
+00:27:08,000 --> 00:27:14,460
+بيبقى a one بس على اربعة وعشرين يبقى a one على
+
+294
+00:27:14,460 --> 00:27:21,120
+اربعة وعشرين زائد تلاتة a note على مين على تمانية
+
+295
+00:27:21,120 --> 00:27:29,910
+اذا تمكنا من كتابة من من كتابةالـ A تلاتة بدلالة
+
+296
+00:27:29,910 --> 00:27:38,390
+A1 و A0 بالمثل بدنا نروح نجيب A4 اللي عبارة عن A2
+
+297
+00:27:38,390 --> 00:27:43,630
+زائد 2 يبقى بدها اجع و اشيل كل N و احط مكانها
+
+298
+00:27:43,630 --> 00:27:50,240
+اتنين يبقى هاي السالب براو بدي احط اتنين بصير
+
+299
+00:27:50,240 --> 00:27:58,460
+اتنين واحد تلاتة تلاتة في تلاتة بتسعة اتلاتة يبقى
+
+300
+00:27:58,460 --> 00:28:08,620
+هذه تسعة اتلاتة زائد خمس اتنين على مين على حاطين
+
+301
+00:28:08,620 --> 00:28:14,540
+اتنينأربعة فى اتنين بتمانية تمانية فى تلاتة باربعة
+
+302
+00:28:14,540 --> 00:28:20,180
+وعشرين يبقى عالة أربعة وعشرين طب إيش بدى أسوي فيه
+
+303
+00:28:20,180 --> 00:28:25,740
+هذه يا بنات؟ بدى أشيل A تلاتة و أكتب قيمتها هذه
+
+304
+00:28:25,740 --> 00:28:31,580
+تصير بدلالة A1 و A1 و بدى أشيل A2 و أكتبها هنا إذا
+
+305
+00:28:31,580 --> 00:28:34,680
+أنا بدى أعطيك النتيجة بديش أضايق وقتي و أنا بسوي
+
+306
+00:28:34,680 --> 00:28:40,620
+كسوريبقى النتيجة النهائية على الشكل التالي بعد ما
+
+307
+00:28:40,620 --> 00:28:47,120
+تحسب الحسابات هذه بتطلع النتيجة عندك اللي هو A4
+
+308
+00:28:47,120 --> 00:28:52,780
+يساوي 9A1
+
+309
+00:28:52,780 --> 00:29:01,880
+على 64 زائد A node على 64
+
+310
+00:29:06,650 --> 00:29:12,570
+الان يكفينا هذا للحصول على مين؟ على شكل الحل احنا
+
+311
+00:29:12,570 --> 00:29:16,830
+فرضين الحل على الشكل اللى عندنا هذا اذا بد فيك هذا
+
+312
+00:29:16,830 --> 00:29:23,990
+مش هنعوض في a1 و a2 و a3 الى اخره يبقى باجي بقوله
+
+313
+00:29:23,990 --> 00:29:27,890
+ال solution سيكون على الشكل التالي
+
+314
+00:29:48,260 --> 00:29:54,740
+يبقى the solution is
+
+315
+00:29:54,740 --> 00:30:01,900
+y يساوي summation من n equal zero to infinity لل a
+
+316
+00:30:01,900 --> 00:30:07,130
+n x ناقص اتنين to the power nاللي كتبناها على
+
+317
+00:30:07,130 --> 00:30:15,650
+الشكل التالي a0 زائد a1 في ال X نقص اتنين زائد a2
+
+318
+00:30:15,650 --> 00:30:23,910
+في ال X نقص اتنين الكل تربيع زائد اللي هو a3 X نقص
+
+319
+00:30:23,910 --> 00:30:30,770
+اتنين الكل تكيب زائد a4 X نقص اتنين أس أربعة زائد
+
+320
+00:30:30,770 --> 00:30:38,940
+إلى ما شاء اللههذا الكلام يبدو يساوي ا نود مالاش
+
+321
+00:30:38,940 --> 00:30:44,400
+دعوة الحل بده يظل بدللتها كمان a1 في ال X ناقص
+
+322
+00:30:44,400 --> 00:30:49,640
+اتنين بتبقى كما هي الحل هيكون بدللتها الان بده
+
+323
+00:30:49,640 --> 00:30:54,920
+نيجي لمين وصلنا لا اتنين اتنين اللي هو ناقص تلتربع
+
+324
+00:30:54,920 --> 00:31:03,120
+a1 ناقص تلتربع a نود يبقى ناقص او زائد ناقص تلتربع
+
+325
+00:31:03,280 --> 00:31:11,500
+أول ناقص تلت تربع ا نوت كل هذا مضروب في مين؟ في ال
+
+326
+00:31:11,500 --> 00:31:18,720
+X ناقص اتنين لكل تربية جينا ل A تلاتة يبقى وصلنا ل
+
+327
+00:31:18,720 --> 00:31:26,900
+A تلاتة وين A تلاتة؟هي A3 اللي هو A1 على 24 يبقى
+
+328
+00:31:26,900 --> 00:31:38,060
+زائد A1 على 24 زائد اللي هو تلاتة A node تلاتة A
+
+329
+00:31:38,060 --> 00:31:45,020
+node على مين على تمانية كله هدف مين في ال X نقص
+
+330
+00:31:45,020 --> 00:31:53,440
+اتنين لكل تكييف زائد جينا ل A4اللي هو 9A1 على 64
+
+331
+00:31:53,440 --> 00:32:08,240
+9A1 على 64 زائد A node على 64 على 64 في ال X نقص 2
+
+332
+00:32:08,240 --> 00:32:16,380
+كله أربعة زائد إلى ما شاء الله طيب
+
+333
+00:32:16,380 --> 00:32:22,260
+هذا الكلام يساويبتاخد اللي فيهم a node مع بعض
+
+334
+00:32:22,260 --> 00:32:28,320
+والباقي اللي فيهم a one مع بعض يبقى هذا a node مين
+
+335
+00:32:28,320 --> 00:32:34,380
+بيظل ان يعمل اتنين واحد هنا هذه a node بصير ناقص
+
+336
+00:32:34,380 --> 00:32:41,720
+تلت اربع ناقص تلت اربعفي ال X ناقص اتنين لكل
+
+337
+00:32:41,720 --> 00:32:48,480
+ترابيع خدت ال term هذا فقط تمام نجي ل بعده بدي اخد
+
+338
+00:32:48,480 --> 00:32:56,020
+ال term هذا يبقى زائد تلت أتمان في ال X ناقص اتنين
+
+339
+00:32:56,020 --> 00:33:04,600
+لكل تكيبزائد واحد على اربعة وستين يعني X نقص اتنين
+
+340
+00:33:04,600 --> 00:33:13,600
+كله أس اربعة على اربعة وستين زائد إلى ما شاء الله
+
+341
+00:33:13,600 --> 00:33:21,090
+زائدبتروح اخد a one عامل مشترك ايش بيظل عندي؟ x
+
+342
+00:33:21,090 --> 00:33:28,490
+ناقص اتنين بيداجي هذه ناقص تلت تربع يبقى ناقص تلت
+
+343
+00:33:28,490 --> 00:33:34,710
+تربع في من؟ في ال x ناقص اتنين لكل تربيع خلصنا
+
+344
+00:33:34,710 --> 00:33:41,770
+منها و ال a نود هي برا نجي لبعدهازائد اكس ناقص
+
+345
+00:33:41,770 --> 00:33:48,170
+اتنين الكل تكعيب على اربع وعشرين نجي اللي بعدها
+
+346
+00:33:48,170 --> 00:33:56,150
+زائد تسعة في ال X ناقص اتنين اص اربع على اربع
+
+347
+00:33:56,150 --> 00:33:59,590
+وستين زائد الى ما شاء الله
+
+348
+00:34:06,460 --> 00:34:11,780
+هذا هو الحل الأول وهذا هو الحل الثاني لـ second
+
+349
+00:34:11,780 --> 00:34:19,140
+order differential equation اللي عندنا
+
+350
+00:34:29,160 --> 00:34:33,760
+في أي حتة في السؤال اللي فات يعني أحيانا بنكتب ايش
+
+351
+00:34:33,760 --> 00:34:38,320
+find the first three terms of the series solution
+
+352
+00:34:38,320 --> 00:34:43,300
+يعني بهمناش الشكل العام اللي هو شكل الحد النوني في
+
+353
+00:34:43,300 --> 00:34:47,120
+ال summation لكن بهم نجيب الأول تلات أربعة termات
+
+354
+00:34:47,120 --> 00:34:51,720
+أو أول تلات termات مما يدل على أن هذه مالها عبارة
+
+355
+00:34:51,720 --> 00:34:56,260
+عن series حد فيكوا اللي يتساؤل هنا؟
+
+356
+00:35:07,760 --> 00:35:16,060
+لحد هنا stop بدنا منكوا المسائل التاليةيبقى
+
+357
+00:35:16,060 --> 00:35:23,640
+exercises خمسة اتنين بدنا المساهل من واحد لغاية
+
+358
+00:35:23,640 --> 00:35:33,740
+تلتاش الأد و بدنا من خمستاش لغاية تمانتاش part
+
+359
+00:35:33,740 --> 00:35:38,880
+اللي هو ايه فقط اللي باجي بدناه شي اللي متعلق
+
+360
+00:35:38,880 --> 00:35:45,160
+بالرسم و ما إلى ذلك كله مش لازمنبس هاتون هذا الجزء
+
+361
+00:35:45,160 --> 00:35:48,720
+الموضوع
+
+362
+00:35:48,720 --> 00:35:51,240
+هذا ال section اللي انتهينا منه كان serious
+
+363
+00:35:51,240 --> 00:35:56,800
+solution near an ordinary point part one بدنا نيجي
+
+364
+00:35:56,800 --> 00:35:59,140
+ل section اللي بعده ال section اللي بعده برضه
+
+365
+00:35:59,140 --> 00:36:03,880
+serious solution near an ordinary point part two
+
+366
+00:36:03,880 --> 00:36:06,100
+يبقى الجزء الثاني
+
+367
+00:36:34,050 --> 00:36:37,690
+حد ابيض اي كلمة من هنا اللي على اللوحة ده امسح
+
+368
+00:36:58,660 --> 00:37:11,260
+يبقى section خمسة تلاتة series solution near an
+
+369
+00:37:11,260 --> 00:37:19,040
+ordinary point part
+
+370
+00:37:19,040 --> 00:37:20,720
+two
+
+371
+00:37:28,670 --> 00:37:33,510
+الفكرة في هذه المقالة هي ان اذا كنا نشتغل شغل لو
+
+372
+00:37:33,510 --> 00:37:39,130
+روح نجيب شكل الان او العلاقة بترمض من بين الان
+
+373
+00:37:39,130 --> 00:37:44,190
+والان زاد واحد او الان زاد اتنين والان زاد واحد مع
+
+374
+00:37:44,190 --> 00:37:48,420
+الان هو ده كنا نسميها recurrence relationبنبطل
+
+375
+00:37:48,420 --> 00:37:52,720
+نجيب ال reference relation لكن بدي أجيب صيغة أخرى
+
+376
+00:37:52,720 --> 00:37:59,800
+للان كيف هذا ما سنشير إليه الآن ان شاء الله بدنا
+
+377
+00:37:59,800 --> 00:38:02,660
+نشير للمعادلة التفاضل اللي بدأنا فيها المرة اللي
+
+378
+00:38:02,660 --> 00:38:07,200
+فاتت و اللي حد فيها الآن و بعدين بنشوف كيف بنجيب
+
+379
+00:38:07,200 --> 00:38:15,180
+الان يبقى بيقول ي suppose that افترض أنه ال
+
+380
+00:38:15,180 --> 00:38:16,500
+differential equation
+
+381
+00:38:21,770 --> 00:38:27,290
+المعادلة التفاضلية P of X في الـ Y double prime P
+
+382
+00:38:27,290 --> 00:38:29,510
+of X في ال Y double prime P of X في ال Y double
+
+383
+00:38:29,510 --> 00:38:30,310
+prime P of X في ال Y double prime P of X في ال Y
+
+384
+00:38:30,310 --> 00:38:32,630
+double prime P of X في ال Y double prime P of X في
+
+385
+00:38:32,630 --> 00:38:38,530
+ال Y double prime P of X في ال Y double prime
+
+386
+00:38:44,330 --> 00:38:54,390
+هذه المعادلة لها حل على صيغة Y تساوي Phi of X and
+
+387
+00:38:54,390 --> 00:39:03,890
+that Phi of X has a Taylor series
+
+388
+00:39:10,600 --> 00:39:18,180
+متسلسل التالور اللي على الشكل التالي Y تسوى فاي of
+
+389
+00:39:18,180 --> 00:39:25,760
+X سم من N equal zero to infinity لل A N في ال X
+
+390
+00:39:25,760 --> 00:39:32,720
+نقص ال X not to the power N which converge
+
+391
+00:39:33,280 --> 00:39:40,280
+واللي بتكون تقاربية for absolute value لل X نقص ال
+
+392
+00:39:40,280 --> 00:39:46,280
+X node أقل من ال raw و ال raw greater than zero
+
+393
+00:39:46,280 --> 00:39:59,300
+and ال X node is an ordinary point تبقى هذه نقطة
+
+394
+00:39:59,300 --> 00:40:08,650
+عادية we shall findwe shall find بنحاول نوجد a
+
+395
+00:40:08,650 --> 00:40:12,550
+formula صيغة
+
+396
+00:40:12,550 --> 00:40:27,650
+for ال a n نرجع
+
+397
+00:40:27,650 --> 00:40:32,340
+لكلام اللي احنا كاتبينه هذا مرة ثانيةجالي افترض ان
+
+398
+00:40:32,340 --> 00:40:35,500
+عند المعادلة التفاضلية اللى سميتها المعادلة 1 نفس
+
+399
+00:40:35,500 --> 00:40:39,320
+المعادلة تابعة المرة اللى فاتت لم نغير فيها شيئا
+
+400
+00:40:39,320 --> 00:40:44,500
+ده افترض المعادلة دى لها حل على الشكل y تساوي phi
+
+401
+00:40:44,500 --> 00:40:48,940
+of x حيث phi of x has a taylor series شو يعني
+
+402
+00:40:48,940 --> 00:40:56,590
+taylor series يعني معناته ان هذه analyticتمام طيب
+
+403
+00:40:56,590 --> 00:41:00,770
+يعني في of x هذه انا لاتكيبها في of x كتبتها على
+
+404
+00:41:00,770 --> 00:41:04,650
+شكل تايلور سيريز بالشكل اللي عندنا هذا which
+
+405
+00:41:04,650 --> 00:41:09,010
+converge والتي تكون تقاربية على الفترة هذه وهذا
+
+406
+00:41:09,010 --> 00:41:13,430
+رسمتلكوا قبل قليل بس ال X node حاطيتها عنده نقطة
+
+407
+00:41:13,430 --> 00:41:18,770
+يساوي اتنين وال X node عبارة عن an ordinary point
+
+408
+00:41:18,770 --> 00:41:25,150
+بنحاول نجيب شكل ال a انتوفي المثال هذا والمثال
+
+409
+00:41:25,150 --> 00:41:29,070
+المراري فاتة نجيب الـ Recurrence relation اللي
+
+410
+00:41:29,070 --> 00:41:34,210
+بتربط ما بين الان زائد اتنين والان او الان زائد
+
+411
+00:41:34,210 --> 00:41:40,630
+واحد والانالان بنحاول نوجد هذه بطريقة اخرى او
+
+412
+00:41:40,630 --> 00:41:46,030
+بصيغة اخرى غير اللى اتعودنا عليها قبل ذلك الان كيف
+
+413
+00:41:46,030 --> 00:41:51,790
+كالتالي هي عندي فاي of X اللى هو ال summation من N
+
+414
+00:41:51,790 --> 00:41:57,810
+equal zero to infinity لل A N في ال X نقص ال X not
+
+415
+00:41:57,810 --> 00:42:04,120
+to the power Nلو كتبتها بالشكل الطويل يبقى هذا إيش
+
+416
+00:42:04,120 --> 00:42:09,880
+بده تساوي a naught حط zero بصير هذا كله term واحد
+
+417
+00:42:10,270 --> 00:42:18,210
+حط بواحد بصير a1 في ال X ناقص ال X node a2 في ال X
+
+418
+00:42:18,210 --> 00:42:25,910
+ناقص X node لكل تربيع a3 في ال X ناقص ال X node
+
+419
+00:42:25,910 --> 00:42:33,750
+لكل تكييب زائد a4 X ناقص X node to the power 4
+
+420
+00:42:33,750 --> 00:42:38,370
+زائد إلى ما شاء الله لغاية ما نوصل لشكل الحد
+
+421
+00:42:38,370 --> 00:42:43,000
+النونيفبحنا عندنا المشتقة الأولى والثانية إذا بدي
+
+422
+00:42:43,000 --> 00:42:48,260
+أروح أجيب المشتقة الأولى والمشتقة الثانية بس قبلها
+
+423
+00:42:48,260 --> 00:42:53,280
+يا بنات لو بدي أجيب five of X node بدي أعرف قداش
+
+424
+00:42:53,280 --> 00:43:00,080
+تساوي هديها منها لو بدي أجيب five of X node يعني
+
+425
+00:43:00,080 --> 00:43:05,440
+قداش قيمة الحل هذا عند ال X node يبقى بدي أشيل كل
+
+426
+00:43:05,440 --> 00:43:11,050
+X و أحط مكانهاالحمد لله كلهم بروحوا مع دمين term
+
+427
+00:43:11,050 --> 00:43:17,530
+الأول يبقى هاي ظهر عندي اللي هو ال a node اللي انا
+
+428
+00:43:17,530 --> 00:43:22,100
+بقى يظهر معايا تابو جتابو قبل شوية في الحلطب بدى
+
+429
+00:43:22,100 --> 00:43:28,300
+اروح اجيبله file prime of x يبقى بده داشتق هدى مع
+
+430
+00:43:28,300 --> 00:43:34,380
+السلامة ايش بطلع عندى هنا اي one يبقى هدى اي one
+
+431
+00:43:34,380 --> 00:43:38,880
+ومشتقة ال X node انه رقم ثابت ب zero ومشتقة هدى
+
+432
+00:43:38,880 --> 00:43:47,230
+بقدرش بواحدمع السلامة يبقى زائد اتنين اتنين اتنين
+
+433
+00:43:47,230 --> 00:43:54,670
+اتنين في ال X ناقص ال X node أسواحى زائد تلاتة
+
+434
+00:43:54,670 --> 00:44:02,330
+اتلاتة في ال X ناقص X node الكل تربيع زائد أربعة
+
+435
+00:44:02,330 --> 00:44:11,840
+اربعة X ناقص X node الكل تكيب زائد إلى آخرينطب ايش
+
+436
+00:44:11,840 --> 00:44:17,620
+رأيك احسب المشتق هذي كذلك عند X node يبقى هذا
+
+437
+00:44:17,620 --> 00:44:24,280
+الكلام بدي يعطينا five prime of X node بدي ساعده
+
+438
+00:44:24,280 --> 00:44:29,640
+حط هنا X node بطير و كلهم شو بظل عنده يبقى هذي A1
+
+439
+00:44:29,640 --> 00:44:35,710
+طيب خلوا هذول عندك في الذاكرةبالزمن ان نرجع لهم
+
+440
+00:44:35,710 --> 00:44:42,930
+بعد قليل و بنواصل المشي تبعنا بدروح اجيب مين مشتقة
+
+441
+00:44:42,930 --> 00:44:50,730
+ا ثانية يبقى five w prime of x هذا مع السلامة هذا
+
+442
+00:44:50,730 --> 00:44:58,680
+بيبقى قداش اتنين اتنينبواحد يبقى هذا بيصير اتنين
+
+443
+00:44:58,680 --> 00:45:06,940
+في تلاتة بستة اتلاتة اكس ناقص اكس نود أس واحد زائد
+
+444
+00:45:06,940 --> 00:45:14,320
+تلاتة في أربع باطماشر اربعة في مين في ال X ناقص X
+
+445
+00:45:14,320 --> 00:45:21,560
+نود الكل تربية زائد إلى ما شاء الله اللي خاطر اعيد
+
+446
+00:45:21,560 --> 00:45:26,380
+صياغة هذا term مرة تانيةفبروح بقول هذا الكلام
+
+447
+00:45:26,380 --> 00:45:30,720
+يساوي اتنين هذه يا بنات مش بقدر اكتبها اتنين
+
+448
+00:45:30,720 --> 00:45:38,340
+factorial مضروب اتنين في اتنين يبقى هذا اتنين
+
+449
+00:45:38,340 --> 00:45:45,780
+factorial في اتنين طيب ايش ستة مضروب تلاتة يبقى
+
+450
+00:45:45,780 --> 00:45:54,410
+هذا تلاتة factorialأتلاتة في ال X ناقص ال X node
+
+451
+00:45:54,410 --> 00:46:00,930
+هذه لسه مقدرش خليكي ماتريحة شوية يبقى هذا الكلام
+
+452
+00:46:00,930 --> 00:46:08,590
+زائد اللي هو اتناشر اربع X ناقص X node لكل تربية
+
+453
+00:46:08,590 --> 00:46:16,450
+زائد إلى ما شاء الله طب لو بده اجيب امانات في W
+
+454
+00:46:16,450 --> 00:46:25,730
+prime of X nodeهذا كله بروح بظل قداش بس يبقى هانها
+
+455
+00:46:25,730 --> 00:46:32,870
+لو بده اجيب في بابلي prime of X node يبقى النتيجة
+
+456
+00:46:32,870 --> 00:46:39,870
+2 factorial اتنين بس حط هنا X node ب 00 والبقى كله
+
+457
+00:46:39,870 --> 00:46:44,590
+بروح مرة ثانية طيب ايش رأيك ان نجيب المشتقة
+
+458
+00:46:44,590 --> 00:46:50,650
+التالتة؟يبقى لو جبت المشتقة التالتة as a function
+
+459
+00:46:50,650 --> 00:46:56,110
+of X يبقى إيش بتعطينا هذا مع السلامة و بيبقى لنا
+
+460
+00:46:56,110 --> 00:47:02,350
+مين؟ اللي هو التلاتة factorial a تلاتة بدي أشتق
+
+461
+00:47:02,350 --> 00:47:07,130
+هذه السلة هذه بتروح هذه تلاتة factorial a تلاتة
+
+462
+00:47:07,130 --> 00:47:10,990
+هذه إيش بيصير؟ نفس اتماشي باربعة و عشرين الهمين
+
+463
+00:47:11,760 --> 00:47:18,620
+أربعة factorial اربعة يبقى زائد اربعة factorial
+
+464
+00:47:18,620 --> 00:47:28,200
+اربعة بظلمينا ان ال X نقص ال X node أس واحد زائد
+
+465
+00:47:28,200 --> 00:47:29,980
+إلى آخرين
+
+466
+00:47:32,430 --> 00:47:39,110
+طيب، هذه مش بتعطيني يا بنات، كمان المشتقة الرقم
+
+467
+00:47:39,110 --> 00:47:44,610
+تلاتة عند ال X note قد إيش تساوي؟ تلاتة factorial
+
+468
+00:47:44,610 --> 00:47:49,750
+A تلاتة تلاتة factorial A تلاتة
+
+469
+00:47:52,290 --> 00:47:59,130
+طب لو ضليت مستمر عليها الشكل هذه بوصل
+
+470
+00:47:59,130 --> 00:48:06,570
+للمشتقة رقم M مثلا يبقى لو ضليت مستمر هوصل للمشتقة
+
+471
+00:48:06,570 --> 00:48:15,470
+رقم M عند ال X هشوف قداش تساوي طلع يا ابنك المشتقة
+
+472
+00:48:15,470 --> 00:48:22,780
+الثانية يبقى 2 factorial ايه اتنين؟زائد ثلاثة
+
+473
+00:48:22,780 --> 00:48:27,540
+factorial أكبر منها ا ثلاثة في اكس نقص اكس نوت
+
+474
+00:48:27,540 --> 00:48:34,200
+زائد طيب لو جت المشتقة التالتة ثلاثة factorial ا
+
+475
+00:48:34,200 --> 00:48:40,280
+ثلاثة اربعة factorial ها اكس نقص اكس نوت اكس واحد
+
+476
+00:48:40,280 --> 00:48:45,660
+زائد الى اخره يبقى انا بدروح اعمم هذه و اقول لو
+
+477
+00:48:45,660 --> 00:48:54,960
+وصلت لمشتقة رقم Mتلاتة تلاتة تلاتة تلاتة
+
+478
+00:48:54,960 --> 00:48:57,580
+تلاتة تلاتة تلاتة تلاتة تلاتة تلاتة تلاتة تلاتة
+
+479
+00:48:57,580 --> 00:48:57,660
+تلاتة تلاتة تلاتة تلاتة تلاتة تلاتة تلاتة تلاتة
+
+480
+00:48:57,660 --> 00:49:01,080
+تلاتة تلاتة تلاتة تلاتة تلاتة تلاتة تلاتة تلاتة
+
+481
+00:49:01,080 --> 00:49:03,700
+تلاتة تلاتة تلاتة تلاتة تلاتة تلاتة تلاتة تلاتة
+
+482
+00:49:03,700 --> 00:49:06,760
+تلاتة
+
+483
+00:49:06,760 --> 00:49:06,780
+تلاتة تلاتة تلاتة تلاتة تلاتة تلاتة تلاتة تلاتة
+
+484
+00:49:06,780 --> 00:49:06,780
+تلاتة تلاتة تلاتة تلاتة تلاتة تلاتة تلاتة تلاتة
+
+485
+00:49:06,780 --> 00:49:11,360
+تلاتة تلاتة تلاتة
+
+486
+00:49:12,280 --> 00:49:16,920
+يبقى ايش بيكون M زائد واحد factorial في M في M
+
+487
+00:49:16,920 --> 00:49:20,820
+ناقص واحد في M ناقص اتنين لغاية ما نوصل لتلاتة في
+
+488
+00:49:20,820 --> 00:49:27,440
+اتنين في واحد يبقى زائد ه اللي هو ال M زائد واحد
+
+489
+00:49:27,440 --> 00:49:34,320
+في ال M في ال M ناقص واحد في ال M ناقص اتنين ونظل
+
+490
+00:49:34,320 --> 00:49:40,430
+ماشي لغاية ما نوصل لاتنين في واحد يبقى هذا منالـ
+
+491
+00:49:40,430 --> 00:49:44,050
+factorial اللي كتبته لسه ال factorial بيجينا هد
+
+492
+00:49:44,050 --> 00:49:50,990
+مين؟ ا م زائد واحد لأنه أكبر منه بواحد فاهمين؟ في
+
+493
+00:49:50,990 --> 00:50:05,190
+ال a m زائد واحد فاهمين؟ في ال x ناقص x node زائد
+
+494
+00:50:05,190 --> 00:50:06,810
+إلى ما شاء الله
+
+495
+00:50:11,590 --> 00:50:17,910
+بناء عليه لو جيها تقول في to the derivative M عند
+
+496
+00:50:17,910 --> 00:50:18,570
+ال X
+
+497
+00:50:21,210 --> 00:50:26,530
+الـ M factorial في الـ A M و هذا بروحكوا لو قداش
+
+498
+00:50:26,530 --> 00:50:33,530
+بزيرو طب انا بده اوصل ل A N فباجي بقوله بكل بساطة
+
+499
+00:50:33,530 --> 00:50:41,030
+لو وصلت للمشتقى الرقم N عند ال X node بده يساوي N
+
+500
+00:50:41,030 --> 00:50:48,830
+factorial في ال A Mصحيح ولا لأ؟ يبقى هذه الصيغة
+
+501
+00:50:48,830 --> 00:50:53,370
+تبعتي ليها تحت الوضع بدي AN لحالها بقوله بسيطة
+
+502
+00:50:53,370 --> 00:50:59,790
+يبقى هذا بدي يعطينا ان AN بدي ساوي المشتق الرقم N
+
+503
+00:50:59,790 --> 00:51:07,040
+عند ال ordinary point X node على N factorialهذه
+
+504
+00:51:07,040 --> 00:51:17,470
+لإتنين أرض نفس الشيء يبقى هذه لو فاكتورياطيب هك
+
+505
+00:51:17,470 --> 00:51:22,970
+انا جبتله مين؟ جبتله المشتقة جبتله a n بدلالة
+
+506
+00:51:22,970 --> 00:51:27,870
+المشتقة النونية للحل اللي هو مين؟ اللي هو five لكن
+
+507
+00:51:27,870 --> 00:51:32,170
+هنا بعد ما كنا نجيب ال recurrence relation روح
+
+508
+00:51:32,170 --> 00:51:39,410
+تواصل الحل وجيب الحل بدلالة a node و a one مظبوط؟
+
+509
+00:51:39,410 --> 00:51:44,280
+شك بغير مسوء المثال اللي جابني شويةيبقى انا بيدروح
+
+510
+00:51:44,280 --> 00:51:49,220
+اجيب ال a in بدلات ال a node و ال a one و اذا
+
+511
+00:51:49,220 --> 00:51:54,480
+جبتهم بكون خلصت ماشي يبقى الان بدأ نكتب الكلمتين
+
+512
+00:51:54,480 --> 00:51:58,980
+والاتنين هذول سميلي هذه رقم اتنين الصيغة هذه او
+
+513
+00:51:58,980 --> 00:52:05,120
+هذه سميها لرقم اتنين اكتب
+
+514
+00:52:05,120 --> 00:52:08,340
+now we shall
+
+515
+00:52:13,700 --> 00:52:22,840
+write an in terms
+
+516
+00:52:22,840 --> 00:52:36,580
+of a node and a ion as follows يبقى كتالي since
+
+517
+00:52:40,720 --> 00:52:46,100
+is a solution
+
+518
+00:52:46,100 --> 00:53:04,480
+of the differential equation when we have طلعيني
+
+519
+00:53:04,480 --> 00:53:11,600
+كويسأحنا فرضنا أن في of x هي حل المعادلة التفاضلية
+
+520
+00:53:11,600 --> 00:53:15,160
+إذا المعادلة التفاضلية رقم واحد بقدر أكتبها على
+
+521
+00:53:15,160 --> 00:53:20,540
+الشكل التالف بقدر أشيل كل y و أكتب هذا أيضا في of
+
+522
+00:53:20,540 --> 00:53:28,000
+x لإنها تحققها يبقاش بصير أن P of x في في w prime
+
+523
+00:53:28,000 --> 00:53:28,740
+of x
+
+524
+00:53:50,100 --> 00:53:57,610
+ممكن اجسم كله على capital P of Xبصير الـ phi w
+
+525
+00:53:57,610 --> 00:54:06,210
+prime of x زائد p small of x في الـ phi prime of x
+
+526
+00:54:06,210 --> 00:54:12,970
+زائد ل q small of x في الـ phi of x بده يساوي zero
+
+527
+00:54:12,970 --> 00:54:23,720
+whereحيث ال P of X small هي عبارة عن ل Q of X على
+
+528
+00:54:23,720 --> 00:54:32,740
+capital P of X and ل Q of X هي عبارة عن R of X
+
+529
+00:54:32,740 --> 00:54:38,100
+capital على capital P of X وهدول are analytic
+
+530
+00:54:38,100 --> 00:54:39,320
+functions
+
+531
+00:54:50,060 --> 00:54:55,560
+يبقى دول تحلية بقدر اكتبهم على شكل تايلور سيريز
+
+532
+00:54:55,560 --> 00:55:03,620
+يبقى السا ممكن اعيد كتابة المعادلة هذه مرة ثانية
+
+533
+00:55:03,620 --> 00:55:09,440
+واروح اقول five w prime of x بدا اساوي only هدول
+
+534
+00:55:09,440 --> 00:55:12,500
+على الشجة التانية يبقى بصير سالب
+
+535
+00:55:28,850 --> 00:55:35,970
+من فوق بالزمن المشتقة عند من عند ال ordinary point
+
+536
+00:55:35,970 --> 00:55:42,600
+x0 إذا بناء عليها بقدر أحسب هذه عند ال x0يبقى باجي
+
+537
+00:55:42,600 --> 00:55:47,780
+بقوله هذه سميها للمعادلة رقم تلاتة منها لأن هذه
+
+538
+00:55:47,780 --> 00:55:52,860
+أساسية عندنا الآن إيش رأيك؟ بدأ اكتب هذه الآن
+
+539
+00:55:52,860 --> 00:55:58,860
+بدللة a0 و a1 إذا بروح أعوض في mean عند ال
+
+540
+00:55:58,860 --> 00:56:04,560
+ordinary point ل X0 يبقى بصير عندنا Phi W prime of
+
+541
+00:56:04,560 --> 00:56:12,090
+X0يساوي ناقص P of X node في الـ Phi prime of X
+
+542
+00:56:12,090 --> 00:56:18,950
+node ناقص ل Q of X node في ال Phi of X node و
+
+543
+00:56:18,950 --> 00:56:27,310
+يساوي طب قداش ال Phi prime of X node one
+
+544
+00:56:27,310 --> 00:56:35,520
+يبقى بقدر اشيل و اكتب دلها مينيبقى هنا ناقص P of X
+
+545
+00:56:35,520 --> 00:56:44,760
+node في ال A1 تمام؟ وهنا ناقص ل Q of X node في ال
+
+546
+00:56:44,760 --> 00:56:48,980
+Phi of X node Phi of X node اللي هي قداشر؟ A node
+
+547
+00:56:48,980 --> 00:56:55,420
+يبقى هنا في ال A node يبقى بناء عليه كتابة Phi W
+
+548
+00:56:55,420 --> 00:57:09,220
+primeبدل من اي نود او اكس نود بدل من اي نود او
+
+549
+00:57:09,220 --> 00:57:21,600
+اتنين
+
+550
+00:57:21,990 --> 00:57:25,730
+طيب ايش رايك الان بدي اروح اجيب كمان المشتقة
+
+551
+00:57:25,730 --> 00:57:31,670
+التالتة و الرابعة و الخامسة كله بدلالة a node و a1
+
+552
+00:57:31,670 --> 00:57:37,270
+يبقى بدي اجي على الاتنين هذي شو اعملها بدي اشتقها
+
+553
+00:57:37,270 --> 00:57:44,310
+كمان مرة يبقى باجي بقوله five triple prime of x
+
+554
+00:57:44,310 --> 00:57:51,560
+اوه هذه يا عزيزي لان كلها مشتقة حصل ضرب دلتينيبقى
+
+555
+00:57:51,560 --> 00:57:57,960
+بدي اكتبها باختصار يبقى سالب P في الـ Fi W Prime
+
+556
+00:57:57,960 --> 00:58:03,840
+سالب P Prime في ال Fi Prime هاي اشتقنا ال term
+
+557
+00:58:03,840 --> 00:58:10,700
+الأول بدي اجي لterm التاني سالبي Q في ال Fi Prime
+
+558
+00:58:10,700 --> 00:58:20,280
+سالبي Q Prime في ال Fi زي ما هي طيب شرايك هذه و
+
+559
+00:58:20,280 --> 00:58:25,500
+هذه؟مش كلهم مضربات في الـ fi prime إذا ما بقدر
+
+560
+00:58:25,500 --> 00:58:33,220
+أخدهم مين مع بعض يبقى هذا الكلام بده يساوي سالب P
+
+561
+00:58:33,220 --> 00:58:41,540
+في ال fi double prime سالب و هي goes بظهر P prime
+
+562
+00:58:43,330 --> 00:58:53,370
+الـ Q كله في مين؟ في الـPhi A' سالب AQ' في مين؟ في
+
+563
+00:58:53,370 --> 00:58:58,430
+الـPhi بتفهم ان هذه function في X وهذه function في
+
+564
+00:58:58,430 --> 00:59:04,590
+X وهذه function في X وكله functions of X تمام؟ إذا
+
+565
+00:59:04,590 --> 00:59:10,100
+بقدر أحسب المشتقة الثاني هذي وين؟عند ال X node
+
+566
+00:59:10,100 --> 00:59:15,740
+يبقى بروح بقوله يبقى Phi triple prime عند ال X
+
+567
+00:59:15,740 --> 00:59:25,140
+node يساوي ناقص P of X node مين هذه؟ Phi double
+
+568
+00:59:25,140 --> 00:59:31,560
+prime of X node موجودة؟ هيها فوق إذا بقدر أجيبها
+
+569
+00:59:31,560 --> 00:59:37,960
+من فوق و نزلها هيها يبقى هذه بالصير في مين؟في سالب
+
+570
+00:59:37,960 --> 00:59:47,680
+P of X node في ال A1 سالب EQ of X node في ال A0
+
+571
+00:59:51,170 --> 00:59:56,730
+طيب هيخلص لسه ال term الأول بداجي لل term التاني
+
+572
+00:59:56,730 --> 01:00:07,750
+ناقص P prime of X node of X node زائد ل Q of X
+
+573
+01:00:07,750 --> 01:00:14,130
+node كله في من؟ في ال 5 primeفاي برايم اف اكس نود
+
+574
+01:00:14,130 --> 01:00:19,790
+فاي برايم اف اكس نود اللي هو كده؟ اون يبقى هذا كله
+
+575
+01:00:19,790 --> 01:00:26,170
+في ال اون ناقص يكيو برايم اف اكس نود في الفاي اف
+
+576
+01:00:26,170 --> 01:00:33,840
+اكس نود اللي هو كده؟ ا نودوهي كتبنا المشتقة
+
+577
+01:00:33,840 --> 01:00:40,100
+التالتة عند X node ليس بدلات ال A3 وانما بدلات ال
+
+578
+01:00:40,100 --> 01:00:46,980
+A node وA1 بنفس الطريقة نشتغل نفس الشغل
+
+579
+01:01:05,640 --> 01:01:13,300
+يبقى هنا سا وي رايت روحنا كتبنا five triple a
+
+580
+01:01:13,300 --> 01:01:23,280
+prime of x node in terms of a node and a one
+
+581
+01:01:23,280 --> 01:01:27,300
+similarly بنفس الطريقة
+
+582
+01:01:30,190 --> 01:01:39,430
+Similarly, we can write نصاتية كتابة المشتقة
+
+583
+01:01:39,430 --> 01:01:46,290
+الرابعة عند ال X node و المشتقة الخامسة عند ال X
+
+584
+01:01:46,290 --> 01:01:56,270
+node و و و إلى آخره in terms ofهو بنقدر نقول كتبنا
+
+585
+01:01:56,270 --> 01:02:04,930
+ال a in a similarly we can write in terms of ..
+
+586
+01:02:04,930 --> 01:02:15,330
+استني شوية استني شوية that is that is
+
+587
+01:02:15,330 --> 01:02:30,520
+we write we writeكتبنا a in in terms of اللي هو a
+
+588
+01:02:30,520 --> 01:02:39,600
+naught and a oneليش؟ لأن هنا لو قلنا المشتقة
+
+589
+01:02:39,600 --> 01:02:44,120
+الثاني يبقى اتنين factorial a in يبقى بصير هذه
+
+590
+01:02:44,120 --> 01:02:49,500
+مجسومة على اتنين هي يبقى هاي اتنين اتلاتة اربعة
+
+591
+01:02:49,500 --> 01:02:59,060
+هكذا كتبناها بدلالة تانية طيب similarly we
+
+592
+01:02:59,060 --> 01:03:00,980
+can
+
+593
+01:03:04,200 --> 01:03:10,580
+right similarly we can هذه كتبنا ايه تلاتة يا بنا
+
+594
+01:03:10,580 --> 01:03:15,800
+مش اكتر يبقى ايه تلاتة بدلالة انه ليش لان جه
+
+595
+01:03:15,800 --> 01:03:20,700
+المشتقة هادي هادي بناء عليه تبقى ايه تلاتة يسوى
+
+596
+01:03:20,700 --> 01:03:25,800
+المشتقة التالتة على تلاتة factorial مظبوط يبقى هنا
+
+597
+01:03:25,800 --> 01:03:29,920
+بقدر اقول كتبنا ايه تلاتة in terms similarly we
+
+598
+01:03:29,920 --> 01:03:31,380
+can write
+
+599
+01:03:34,560 --> 01:03:41,120
+in terms of
+
+600
+01:03:41,120 --> 01:03:55,180
+in terms of الحمد لله and a one طيب
+
+601
+01:03:55,180 --> 01:03:59,720
+ده رجع الكلام هذا فقط مشان بس يثبت المعنى احنا
+
+602
+01:03:59,720 --> 01:04:03,900
+خلصنابس مشان نثبت المعلومات و بعد كده بناخد أمثلة
+
+603
+01:04:03,900 --> 01:04:09,560
+مشان نشوف كيف بدنا نطبق هذا الكلام اللي قلناه احنا
+
+604
+01:04:09,560 --> 01:04:15,260
+وصلنا الى هذه الصيغة تمام و سمينا وصلنا ل ال mail
+
+605
+01:04:15,260 --> 01:04:18,560
+معادلة هذه و روحنا كتبناها فى الصيغة اللى عندنا هي
+
+606
+01:04:18,560 --> 01:04:20,720
+رقم تلاتة
+
+607
+01:04:23,910 --> 01:04:29,090
+قلنا نذهب و نحسب المشتقة الثانية عند ال point
+
+608
+01:04:29,090 --> 01:04:34,130
+ordinary يبقى اشيلنا كل X و كتبنا بدلها من X node
+
+609
+01:04:34,130 --> 01:04:38,570
+صارت هنا ناقص P of X node في Prime of X node ناقص
+
+610
+01:04:38,570 --> 01:04:42,250
+Q of X node في Prime of X nodeالان شيلنا fire
+
+611
+01:04:42,250 --> 01:04:45,170
+prime of x node و حطينا قيمتها اللي طلعناها قبل
+
+612
+01:04:45,170 --> 01:04:49,130
+قليل a1 و شيلنا fire of x node و طلعنا قيمتها اللي
+
+613
+01:04:49,130 --> 01:04:54,130
+هي main a node يبقى صار هذه قيمة المشتقة الثانية
+
+614
+01:04:54,130 --> 01:05:01,290
+لكن يا بنات أليست هذه هي اتنين factorial في ال a2
+
+615
+01:05:03,960 --> 01:05:09,220
+أتنين فاكتوريال في ال A2 لأننا مجتقة ثانية صحيح
+
+616
+01:05:09,220 --> 01:05:16,060
+ولا لأ؟ كويس يعني معناته أنا جدرت أكتب A2 بذللة A1
+
+617
+01:05:16,060 --> 01:05:21,580
+و A2 صحيح ولا لأ؟ طيب نيجي للي بعدها روحنا جيبنا
+
+618
+01:05:21,580 --> 01:05:25,580
+المجتقة التالتة لما جيبنا المجتقة التالتة صارت
+
+619
+01:05:25,580 --> 01:05:29,540
+بالشكل هذا اختصرناها و كتبناها بالشكل هذا طيب
+
+620
+01:05:29,970 --> 01:05:33,850
+المشتقة التالتة عند الاكسود روحنا كتبناها بيه بقى
+
+621
+01:05:33,850 --> 01:05:41,110
+لم يظهر عندي الا a1 و a0 المشتقة التالتة عند
+
+622
+01:05:41,110 --> 01:05:46,370
+الاكسود هي تلاتة factorial a3 يعني هذه تلاتة
+
+623
+01:05:46,370 --> 01:05:53,090
+factorial a3 يعني معنى هذا الكلام انه جدرنا نكتب
+
+624
+01:05:53,090 --> 01:05:58,050
+a3 يعني لو جسمنا كله على تلاتة factorialبكون جبت
+
+625
+01:05:58,050 --> 01:06:04,770
+a3 بدلالة a node و a1 يبقى فهمنا هذا السطر كيف
+
+626
+01:06:04,770 --> 01:06:09,990
+كتبت a3 in terms of a node و a1 هيها من هناك هذه
+
+627
+01:06:09,990 --> 01:06:13,510
+اللي كانت يعني حسيت أنها مغبشة عندكوا شوية يبقى
+
+628
+01:06:13,510 --> 01:06:17,370
+هاي روحنا و أضبحناها لكوا تاني يبقى الشلط هذا و
+
+629
+01:06:17,370 --> 01:06:21,970
+حطيت قيمته اللي هي 3 factorial a3 لو جسمت كله على
+
+630
+01:06:21,970 --> 01:06:29,370
+a factorial بصير a3 بدلالة a nodeهنا بنفس الطريقة
+
+631
+01:06:29,370 --> 01:06:37,690
+بنكتب a4 و a5 و a6 و كده in terms of a node and a1
+
+632
+01:06:37,690 --> 01:06:43,810
+تمام؟ الكلام اللي بقوله هوضحه بمثال عملي الآن قبل
+
+633
+01:06:43,810 --> 01:06:48,810
+ان ندخل المثال، حد فيكم بتحب تسأل اي نقطة هنا؟
+
+634
+01:06:48,810 --> 01:06:54,230
+ناخد مثال توضحي على ذلك
+
+635
+01:06:59,220 --> 01:07:07,780
+هذه المفتاح الحل الباقى يجب أن تكون معروفة لأن
+
+636
+01:07:07,780 --> 01:07:11,300
+منها سأجلب المشتقة التالتة ومنها سأجلب المشتقة
+
+637
+01:07:11,300 --> 01:07:15,460
+الرابعة ومنها سأجلب المشتقة الخامسة وكذلك تمام
+
+638
+01:07:15,460 --> 01:07:22,720
+يبقى مثال هذا
+
+639
+01:07:22,720 --> 01:07:32,980
+سؤال تلاتة من الكتاببيقول لي if الـ phi of x is a
+
+640
+01:07:32,980 --> 01:07:43,340
+solution of the initial value problem للـ x تربيع
+
+641
+01:07:43,340 --> 01:07:50,760
+yw prime زائد واحد زائد x في الـ y prime
+
+642
+01:07:53,480 --> 01:08:02,520
+زائد تلاتة في لن ال X كل هذا الكلام في ال Y بدر
+
+643
+01:08:02,520 --> 01:08:07,840
+ساوي Zero و ال condition الأولاني Y عند ال واحد
+
+644
+01:08:07,840 --> 01:08:12,480
+بدر ساوي اتنين و ال condition التاني Y prime عند
+
+645
+01:08:12,480 --> 01:08:14,420
+ال واحد بدر ساوي Zero
+
+646
+01:08:18,180 --> 01:08:25,580
+حددونا قداش قيمة لـ Phi double prime of one Phi
+
+647
+01:08:25,580 --> 01:08:33,260
+triple prime of one and المشتقة الرابعة عند الواحد
+
+648
+01:08:33,260 --> 01:08:39,740
+بدي أعرف قداش قيمة كل term من هذه الترمات solution
+
+649
+01:08:51,200 --> 01:08:55,820
+خلّيني أقول لكم اذا كان في او فيكس ما شكله انا مش
+
+650
+01:08:55,820 --> 01:08:59,620
+عارف مش راح قالي هاتلي في او فيكس لأ هم عطيني رمز
+
+651
+01:08:59,620 --> 01:09:03,400
+في او فيكس يعتبر حل لل initial value problem اللي
+
+652
+01:09:03,400 --> 01:09:07,600
+عندنا قالي من خلالك بس بدنا في دابله prime of one
+
+653
+01:09:07,600 --> 01:09:11,660
+في تربله prime of one و المشتق الرابع برضه under
+
+654
+01:09:11,660 --> 01:09:15,690
+one و الله يعطيك العافية بدنا قيم عددية من خلالالـ
+
+655
+01:09:15,690 --> 01:09:20,150
+initial conditions اللي عندك نقوله بسيطة خلاص بدنا
+
+656
+01:09:20,150 --> 01:09:23,890
+نيجي لكلام اللي أنا بقى بطل على المعادلة اللي عندى
+
+657
+01:09:23,890 --> 01:09:27,710
+المعادلة X ترميها YW prime دالة في Y prime دالة في
+
+658
+01:09:27,710 --> 01:09:33,930
+Y يبقى هنا المعامل هو احنا بنشتغل روحنا جسمنا على
+
+659
+01:09:33,930 --> 01:09:38,330
+capital P of X مش عارف ده على دهرة لأ المساحات على
+
+660
+01:09:38,330 --> 01:09:42,190
+اي حال إذا لما نيجي نشتغل الشغل هاد يا بناتبديك
+
+661
+01:09:42,190 --> 01:09:47,410
+تروح اتيه جسمي على المعامل تبع YWY حتى وإن كان رقم
+
+662
+01:09:47,650 --> 01:09:51,210
+بدي اقسم عليه بحيث اخلي المعامل دائما او ابدا هو
+
+663
+01:09:51,210 --> 01:09:55,690
+main واحد صحيح يبقى المعادلة دي بصير على الشكل
+
+664
+01:09:55,690 --> 01:10:02,090
+التالي y double prime زائد واحد زائد x على x
+
+665
+01:10:02,090 --> 01:10:11,510
+ترابية في ال y prime زائد تلاتة لن ال x على x
+
+666
+01:10:11,510 --> 01:10:19,330
+ترابية كله في ال y بده ساوي zeroتمام، إذا هذا بده
+
+667
+01:10:19,330 --> 01:10:26,690
+يعطي كمين إن ال P of X يساوي، إيش رأيك؟ واحد على X
+
+668
+01:10:26,690 --> 01:10:31,150
+تربية، مش عبارة عن X نقص اتنين؟أسهل اللي في الشغل
+
+669
+01:10:31,150 --> 01:10:37,090
+يبقى باجي بقوله هذي X ناقص اتنين X على X تربية بضل
+
+670
+01:10:37,090 --> 01:10:43,490
+واحد على X يعني X أسالب واحد زائد X أسالب واحد
+
+671
+01:10:43,490 --> 01:10:52,570
+يبقى أنا كتبت ال P of X في ثوب جديد وال Q of X
+
+672
+01:10:52,570 --> 01:10:57,120
+بذاسر خليها زي ما هي مش مشكلة تمام؟لان اذا طلعتها
+
+673
+01:10:57,120 --> 01:11:02,600
+فوق بيصير x أس ناقص اتنين تمام؟ بدك تطلعها فوق
+
+674
+01:11:02,600 --> 01:11:06,660
+بنتطلعها فوق بنتريها بيصير x ناقص اتنين فلن ال x و
+
+675
+01:11:06,660 --> 01:11:10,520
+ايه الحساب بيصير؟ لمش تقعد حصل ضرب دلتين بزهجني
+
+676
+01:11:10,520 --> 01:11:14,180
+شوية لو كانت خارج قسم الدلتين بس حصل ضرب سلي، اذا
+
+677
+01:11:14,180 --> 01:11:21,850
+بقدر اقول هذه التلاتة x أس ناقص اتنين فلن ال xطب
+
+678
+01:11:21,850 --> 01:11:28,350
+ليش سويتك؟ اه بقولك ليش سويتك؟ هنا لازم ل بعد شوية
+
+679
+01:11:28,350 --> 01:11:34,250
+بلزم ل من؟ بلزم ل P prime و Q prime و P double
+
+680
+01:11:34,250 --> 01:11:38,950
+prime و Q .. إذا بلزم ل الشغلات هذه إذا قبل مشتغل
+
+681
+01:11:38,950 --> 01:11:43,470
+ولا شغل بنروح أحسب قداش قيمة كل واحدة من هدول قبل
+
+682
+01:11:43,470 --> 01:11:49,950
+المبدأطبعا بقوله كويس اذا انا لو جيت قولتله ال P
+
+683
+01:11:49,950 --> 01:11:56,430
+prime of X بدي اشتقها يبقى ناقص اتنين X أس ناقص
+
+684
+01:11:56,430 --> 01:12:06,410
+تلاتة ناقص X أس ناقص اتنين طبعا لو بدي PW prime as
+
+685
+01:12:06,410 --> 01:12:12,690
+a function of Xيبقى ايش بصير عندى هنا ستة اكس اص
+
+686
+01:12:12,690 --> 01:12:19,510
+ناقص اربعة زيدي اتنين اكس اص ناقص تلاتة اظن مش
+
+687
+01:12:19,510 --> 01:12:24,570
+هيلزمني اكتر من هيك المشتقة التالتة فيها المشتقة
+
+688
+01:12:24,570 --> 01:12:27,790
+الاولى فقط يبقى لو جيبنا الرابع بيجيب المشتقة
+
+689
+01:12:27,790 --> 01:12:32,180
+التانى ويمكفها الله يعطيك العافيةيبقى بناء عليه لو
+
+690
+01:12:32,180 --> 01:12:36,840
+بدى احسبله P of 1 لانه ليش ال condition المحسبات
+
+691
+01:12:36,840 --> 01:12:42,000
+عند ال one ايش بدى يكون هنا بناه واحد زائد واحد
+
+692
+01:12:42,000 --> 01:12:47,000
+مظبوط يبقى اللي هو اتنين يبقى P of one بدى يساوي
+
+693
+01:12:47,000 --> 01:12:52,760
+اتنين بدى ال P prime of oneيبقى هذا واحد مابصير
+
+694
+01:12:52,760 --> 01:12:57,440
+سالب اتنين سالب واحد اللي هو قداش سالب تلاتة بدي
+
+695
+01:12:57,440 --> 01:13:03,080
+ال P double prime of one يبقى ستة زائد اتنين اللي
+
+696
+01:13:03,080 --> 01:13:08,960
+هو قداش تمانية سيب المعلومات هذه بدنا نروح لمين
+
+697
+01:13:08,960 --> 01:13:15,800
+للي Q يبقى بدي اشتقها يبقى بدي ل Q prime of X هذه
+
+698
+01:13:15,800 --> 01:13:22,630
+مشتقة تحصل ضرب دالة تانية يبقى دالة الأولىفي ناقص
+
+699
+01:13:22,630 --> 01:13:28,490
+اتنين في مشتقة الدالة الثانية اللي همين واحد على X
+
+700
+01:13:28,490 --> 01:13:39,550
+ناقص ستة X أس ناقص تلاتة ناقص طبعا ستة X أس ناقص
+
+701
+01:13:39,550 --> 01:13:46,530
+تلاتة في لن ال Xيعني هذا ايش بيصير؟ بيصير تلاتة
+
+702
+01:13:46,530 --> 01:13:51,730
+اكس اص ناقص تلاتة طلعتها فوق بيصير بإشارة سالب
+
+703
+01:13:51,730 --> 01:14:01,370
+وهنا ناقص اللي هو ستة اكس اص ناقص تلاتة في لن ال X
+
+704
+01:14:02,090 --> 01:14:07,090
+هنجيب المشتقة الثانية يبقى المشتقة ثانية q double
+
+705
+01:14:07,090 --> 01:14:16,430
+prime of x يبقى بالصيرة ناقص تسعة x أس ناقص أربعة
+
+706
+01:14:16,430 --> 01:14:22,910
+اللي بعدها مشتقة حصل ضارب دالتين يبقى ناقص ستة x
+
+707
+01:14:22,910 --> 01:14:29,570
+أس ناقص تلاتة في واحد على x ناقص فناقص بزايد ستة
+
+708
+01:14:29,570 --> 01:14:40,930
+في تلاتة تمانتاشرx²-4x²-4
+
+709
+01:14:40,930 --> 01:14:44,570
+-15
+
+710
+01:14:44,570 --> 01:14:48,530
+-15x²
+
+711
+01:14:48,530 --> 01:14:49,690
+-4
+
+712
+01:15:02,380 --> 01:15:09,700
+إذا ما بقدر اجيب له اكيو of one تعالى شوفى بدل من
+
+713
+01:15:09,700 --> 01:15:15,140
+الواحد بقداش بصفر في اي رقم بصفر يبقى ب zero مع
+
+714
+01:15:15,140 --> 01:15:20,100
+السلامة غير مأسوف عليك اكيو prime of one وايه ال
+
+715
+01:15:20,100 --> 01:15:26,880
+اكيو prime هاى ب one بطلع هنا تلاتة وهذا ب zero مع
+
+716
+01:15:26,880 --> 01:15:34,240
+السلامة يبقى تلاتة يساوي تلاتةالان بدنا لـ q
+
+717
+01:15:34,240 --> 01:15:42,660
+double prime of one لان الواحد بزير و بطير يبقى
+
+718
+01:15:42,660 --> 01:15:49,910
+فضل قداش سالب خمستاش يساوي سالب خمستاشطيب خلّي هذه
+
+719
+01:15:49,910 --> 01:15:55,890
+المعلومات جاهزة يعني هذه وين ما لزمتل الآن بدي
+
+720
+01:15:55,890 --> 01:16:02,810
+أبدأ أخد منها و أعوّب و هذه زيها كمان بنفس الطريقة
+
+721
+01:16:02,810 --> 01:16:08,050
+طيب نبدأ في مسألتنا يبقى قاللي أول شغلة بده مين
+
+722
+01:16:08,050 --> 01:16:13,210
+بده five double prime of one وين five double prime
+
+723
+01:16:13,210 --> 01:16:17,720
+of x هييبقى هذه المعادلة الأساسية اللي بدأ أبدأ
+
+724
+01:16:17,720 --> 01:16:23,180
+أشتغل بها
+
+725
+01:16:23,180 --> 01:16:36,120
+يبقى
+
+726
+01:16:36,120 --> 01:16:44,850
+بروح أقول we know that we knowأحنا بنعرف أن الـ
+
+727
+01:16:44,850 --> 01:16:55,470
+Phi W' of X يساوي ناقص P of X في Phi' of X ناقص ل
+
+728
+01:16:55,470 --> 01:17:02,870
+Q of X ناقص في Phi of X هذه اللي كنا نسميها
+
+729
+01:17:02,870 --> 01:17:08,370
+المعادلة رقم قداشر تلاتة يبقى هذه تلاتة وليست اتنى
+
+730
+01:17:09,590 --> 01:17:20,970
+إذا لتحت هذا كله بدنا نمسحه مالهوش لزوم طيب
+
+731
+01:17:20,970 --> 01:17:24,990
+إيه شرايك من المعادلة هذه بقدر أجيب المطلوب الأول
+
+732
+01:17:24,990 --> 01:17:30,330
+صح يبقى بدى أحسب هذا المقدار عند مين أن النقطة
+
+733
+01:17:30,330 --> 01:17:35,350
+واحدة هو five double prime of oneيبقى باجي بقوله
+
+734
+01:17:35,350 --> 01:17:42,350
+في دابلة prime of one بده يساوي ناقص P of one فيه
+
+735
+01:17:42,350 --> 01:17:49,590
+prime of one ناقص Q of one في ال في of one ويساوي
+
+736
+01:17:49,590 --> 01:17:55,530
+ال P of one يبقى كده شبنات باتنين يبقى هاي سالف
+
+737
+01:17:55,530 --> 01:18:01,200
+قبلها يبقى هاي سالي باتنينالـ Phi prime of one
+
+738
+01:18:01,200 --> 01:18:06,520
+طلعيلي هذا مش Y عبارة عن حل هو Phi يبقى Y prime of
+
+739
+01:18:06,520 --> 01:18:11,760
+one بقداش ب Zero جبتم ال initial condition يبقى في
+
+740
+01:18:11,760 --> 01:18:17,840
+Zero ناقص ال Q of one اللي هو Zero يبقى هاي Zero
+
+741
+01:18:17,840 --> 01:18:23,920
+في ال Phi of one Phi of one هايها اللي هو بقداش
+
+742
+01:18:23,920 --> 01:18:33,500
+باتنينيبقى في اتنين يبقى الحمد لله بقداش ريحنا بده
+
+743
+01:18:33,500 --> 01:18:37,560
+اجيب المشتقة التالتة عند الواحد اذا بده اجي على
+
+744
+01:18:37,560 --> 01:18:43,260
+الاتنين شو اعملها بده اشتقها يبقى بده اجي للي فوق
+
+745
+01:18:43,260 --> 01:18:50,500
+هادي هيك واروح اشتقها في triple prime of xيبقى بدي
+
+746
+01:18:50,500 --> 01:18:56,460
+اختصر يا بنات يبقى ناقص P في الـ Phi W Prime ناقص
+
+747
+01:18:56,460 --> 01:19:02,240
+P Prime في ال Phi Prime هذا ال term الأول ناقص Q
+
+748
+01:19:02,240 --> 01:19:09,480
+في ال Phi Prime ناقص Q Prime في ال Phi زي ما هي
+
+749
+01:19:09,480 --> 01:19:16,200
+بدي احسب هذا عند الواحد يبقى بصير Phi Triple Prime
+
+750
+01:19:16,200 --> 01:19:23,300
+عند الواحدناقص P of واحد في W prime of واحد ناقص P
+
+751
+01:19:23,300 --> 01:19:30,880
+prime of واحد في F prime of واحد ناقص Q of واحد في
+
+752
+01:19:30,880 --> 01:19:38,020
+F prime of واحد ناقص Q prime of واحد في F prime of
+
+753
+01:19:38,020 --> 01:19:42,220
+واحد ناقص
+
+754
+01:19:42,220 --> 01:19:50,550
+P1يبقى هاي ناقص اتنين five double prime of one هاي
+
+755
+01:19:50,550 --> 01:19:56,590
+اللي اوجدناها فوق من البداية بقدرش ب zero يبقى هاي
+
+756
+01:19:56,590 --> 01:20:03,220
+zeroنقص P' of one P' of one اللي هي سالب تلاتة
+
+757
+01:20:03,220 --> 01:20:10,360
+يبقى سالب لسالب تلاتة five prime of one اللي هو
+
+758
+01:20:10,360 --> 01:20:19,220
+مقدش ب zero يبقى هذا كمان ب zero نقص Q of one ل Q
+
+759
+01:20:19,220 --> 01:20:24,710
+of one اللي هو ب zeroالـ Q of 1 بـ 0 فاية Prime of
+
+760
+01:20:24,710 --> 01:20:31,410
+1 فاية Prime of 1 كمان بـ 0 ناقص الـ Q Prime of 1
+
+761
+01:20:31,410 --> 01:20:36,810
+اللي هو قداش تلاتة يبقى ناقص تلاتة في الـ Phi 1
+
+762
+01:20:36,810 --> 01:20:48,020
+اللي هو قداش 2 0 0 0 يبقى الجواب قداش سالب ستةكمان
+
+763
+01:20:48,020 --> 01:20:53,040
+طيب قال لي هات المشتقة الرابع اذا بده اجي على هذه
+
+764
+01:20:53,040 --> 01:20:58,900
+اللي اشتقتها و اشتقها كمان ايه كمان مرة يبقى بده
+
+765
+01:20:58,900 --> 01:21:05,320
+اجيب له المشتقة الرابع as a function of X برضه
+
+766
+01:21:05,320 --> 01:21:10,240
+اختصار بديش اكتب ال X's للسولة هذه المشتقة اتحصل
+
+767
+01:21:10,240 --> 01:21:15,320
+دور بدلتين يبقى ناقص P في الـ Phi Tripoli Prime
+
+768
+01:21:15,640 --> 01:21:23,820
+ناقص P' Phi W' خلصنا منها اللي بعدها ناقص P' Phi
+
+769
+01:21:23,820 --> 01:21:33,160
+W' ناقص P W' Phi' خلصنا منها اللي بعدها ناقص Q Phi
+
+770
+01:21:33,160 --> 01:21:43,720
+W'نقص Q' فى قلصنا منها اللى بعدها نقص Q' فى قلصنا
+
+771
+01:21:43,720 --> 01:21:50,060
+منها نقص Q'' فى قلصنا منها اللى بعدها نقص Q' فى
+
+772
+01:21:50,060 --> 01:21:50,060
+قلصنا منها اللى بعدها نقص Q'' فى قلصنا منها اللى
+
+773
+01:21:50,060 --> 01:21:53,720
+بعدها نقص Q'' فى قلصنا منها اللى بعدها نقص Q'' فى
+
+774
+01:21:53,720 --> 01:21:53,780
+قلصنا منها اللى بعدها نقص Q'' فى قلصنا منها اللى
+
+775
+01:21:53,780 --> 01:21:57,160
+بعدها نقص Q'' فى قلصنا منها اللى بعدها نقص Q'' فى
+
+776
+01:21:57,160 --> 01:22:01,240
+قلصنا منها اللى بعدها نقصبتروح ادور ناقص P of one
+
+777
+01:22:01,240 --> 01:22:07,480
+P of one اللي هو قداش باتنين يبقى هاي ناقص اتنين
+
+778
+01:22:07,480 --> 01:22:11,440
+المشتقة التالتة عند الواحد هي جاهزة اللي هي قداش
+
+779
+01:22:11,440 --> 01:22:18,380
+سالب ستة والله رايحتنا هذه اللي بعدها ناقص P prime
+
+780
+01:22:18,380 --> 01:22:24,390
+of one P prime of one اللي هي قداش سالب تلاتةيبقى
+
+781
+01:22:24,390 --> 01:22:31,770
+هاي سالب تلاتة ال five double prime زيرو الله يسهل
+
+782
+01:22:31,770 --> 01:22:37,330
+عليها يبقى هاي زيرو خلصنا اول two terms نجي ال
+
+783
+01:22:37,330 --> 01:22:42,550
+term التالت ناقص P prime of one P prime of one
+
+784
+01:22:42,550 --> 01:22:47,630
+اللي هو بقداش بسالب تلاتة يبقى هاي سالب تلاتة ال
+
+785
+01:22:47,630 --> 01:22:53,000
+five double prime اللي هو بزيرو ريعتنانقص الـPW
+
+786
+01:22:53,000 --> 01:23:00,560
+prime الـPW prime هو 8 نقص 8 في الـPhi prime
+
+787
+01:23:00,560 --> 01:23:09,080
+الـPhi prime هو 0 يبقى هنا بـ0 نقص الـQ of 1 الـQ
+
+788
+01:23:09,080 --> 01:23:15,460
+of 1 هو 0 يبقى هذه 0 في 0 في الـPhi W prime نقص
+
+789
+01:23:15,460 --> 01:23:21,780
+الـEQ prime الـEQ prime هو 3 في الـPhi primeفاية
+
+790
+01:23:21,780 --> 01:23:27,340
+البرامي اللي هي بالزرع ناقص كي و دابلي برامي كي و
+
+791
+01:23:27,340 --> 01:23:32,540
+دابلي برامي بناقص خمستاش ناقص خمستاش في الفاية
+
+792
+01:23:32,540 --> 01:23:41,420
+اللي هي بالتنين بالتنين يساوي هذا بالاطمعش زرع زرع
+
+793
+01:23:41,420 --> 01:23:45,440
+زرع زرع زرع زرع زرع زرع زرع زرع زرع زرع زرع زرع
+
+794
+01:23:45,440 --> 01:23:45,560
+زرع زرع زرع زرع زرع زرع زرع زرع زرع زرع زرع زرع
+
+795
+01:23:45,560 --> 01:23:45,580
+زرع زرع زرع زرع زرع زرع زرع زرع زرع زرع زرع زرع
+
+796
+01:23:45,580 --> 01:23:47,330
+زرع زرع زرع زرع زرع زرع زرع زرع زرع زرع زيبقى زائد
+
+797
+01:23:47,330 --> 01:23:54,370
+تلاتين ويساوي قداش اتنين واربعين الشغل بتطول اتروح
+
+798
+01:23:54,370 --> 01:24:00,110
+يعني بدأي زهج ازهجان بضيع ايه؟ بضيع المسألة دوريا
+
+799
+01:24:00,110 --> 01:24:04,950
+حدا فيكم بتسأل اي سؤال هنا بنان؟ اذا العمود الفقري
+
+800
+01:24:04,950 --> 01:24:10,090
+عندنا له المعادلة رقم تلاتة كل الشغل بدي يكون منها
+
+801
+01:24:10,090 --> 01:24:16,550
+من عندها بنبدأ نجيب اربعة وخمسة وستة وكلههذا سؤال
+
+802
+01:24:16,550 --> 01:24:20,290
+هو رقم تلاتة من أسئلة الكتابة في عندك أظن مابارة
+
+803
+01:24:20,290 --> 01:24:25,130
+أربعة أسئلة أو خمس أسئلة بالشكل هذا هذا هو أحدهم
+
+804
+01:24:25,130 --> 01:24:38,670
+والباقي بنفس الطريقة اللي
+
+805
+01:24:38,670 --> 01:24:43,790
+انا بدأ نعطي تعريف لل analytic function مرة ثانية
+
+806
+01:24:44,600 --> 01:24:54,700
+ونشوف نظرية عليها وبعد ذلك ناخد بعض الأمثلة يبقى
+
+807
+01:24:54,700 --> 01:25:01,780
+التعريف بيقول ما يأتي definition تعريف
+
+808
+01:25:01,780 --> 01:25:07,160
+رقم واحد بيقول for the differential equation for
+
+809
+01:25:07,160 --> 01:25:10,120
+the differential
+
+810
+01:25:24,000 --> 01:25:35,200
+النقطة x0 هي نقطة
+
+811
+01:25:35,200 --> 01:25:37,440
+عامة
+
+812
+01:25:42,790 --> 01:25:56,130
+ordinary point نقطة عادية if ال P of X and ال Q of
+
+813
+01:25:56,130 --> 01:26:04,290
+X ما لهم are analytic are analytic
+
+814
+01:26:04,290 --> 01:26:17,780
+at X node نمر اتنين ifالـ P of X and the Q of X
+
+815
+01:26:17,780 --> 01:26:28,360
+are not analytic are not analytic يبقى لو ماكناش
+
+816
+01:26:28,360 --> 01:26:38,520
+دوال تحليلية at X node then اللي هو ال X node then
+
+817
+01:26:43,520 --> 01:26:56,120
+الـ x0 is called is called a singular point a
+
+818
+01:26:56,120 --> 01:27:05,140
+singular point آخر نظرية في هذا ال section بتقول
+
+819
+01:27:05,140 --> 01:27:06,160
+ما يأتي
+
+820
+01:27:12,360 --> 01:27:24,880
+الـ X naught is an ordinary point نقطة عادية of
+
+821
+01:27:24,880 --> 01:27:28,620
+the differential
+
+822
+01:27:30,210 --> 01:27:36,490
+equation للمعادلة التفاضلية capital P of X في ال
+
+823
+01:27:36,490 --> 01:27:44,250
+YW prime Q of X Y prime R of X في ال Y تساوي Zero
+
+824
+01:27:44,250 --> 01:27:54,810
+وهذه سامعها المعادلة رقم واحد that is INF ال P
+
+825
+01:27:54,810 --> 01:28:04,300
+لتساويالـ Q على كابتل P and الـ Q بده يساوي ال R
+
+826
+01:28:04,300 --> 01:28:18,040
+على كابتل P R أنا لاتك at X node then the general
+
+827
+01:28:18,040 --> 01:28:23,460
+solution then general
+
+828
+01:28:23,460 --> 01:28:24,540
+solution
+
+829
+01:28:31,510 --> 01:28:39,650
+الحل العام للإيقاع
+
+830
+01:28:39,650 --> 01:28:45,990
+الواحد هو y
+
+831
+01:28:45,990 --> 01:28:53,450
+تساوي summation من n equal zero to infinity لل a n
+
+832
+01:28:53,450 --> 01:28:58,830
+في ال x ناقص ال x not to the power nواللي بقدر
+
+833
+01:28:58,830 --> 01:29:06,810
+اكتب عليه شكل a0 في ال y1 of x زائد a1 في ال y2 of
+
+834
+01:29:06,810 --> 01:29:19,970
+x where ال a0 and ال
+
+835
+01:29:19,970 --> 01:29:23,590
+a1 are constants
+
+836
+01:29:31,880 --> 01:29:37,840
+وY1 وY2 هم
+
+837
+01:29:37,840 --> 01:29:49,060
+نقاط مستقلين ومستقلين نقاط
+
+838
+01:29:49,060 --> 01:29:51,320
+مستقلين
+
+839
+01:29:59,000 --> 01:30:08,940
+analytic at x0 the
+
+840
+01:30:08,940 --> 01:30:21,700
+radius of convergence the
+
+841
+01:30:21,700 --> 01:30:25,140
+radius of convergence of
+
+842
+01:30:45,090 --> 01:30:57,370
+Y1 Y2 Y3
+
+843
+01:30:57,370 --> 01:30:57,630
+Y4 Y5 Y6 Y7 Y8 Y9 Y10 Y11 Y12 Y13 Y12 Y13 Y12 Y12
+
+844
+01:30:57,630 --> 01:30:57,630
+Y12 Y12 Y12 Y12 Y12 Y12 Y12 Y12 Y12 Y12 Y12 Y12
+
+845
+01:30:57,630 --> 01:30:57,630
+Y12 Y12 Y12 Y12 Y12 Y12 Y12 Y12 Y12 Y12 Y12 Y12
+
+846
+01:30:57,630 --> 01:30:57,630
+Y12 Y12 Y12 Y12 Y12 Y12 Y12 Y12 Y12 Y12 Y12 Y12
+
+847
+01:30:57,630 --> 01:30:57,630
+Y12 Y12 Y12 Y12 Y12 Y12 Y12 Y12 Y12 Y12 Y12 Y12
+
+848
+01:30:57,630 --> 01:30:57,630
+Y12 Y12 Y12 Y12 Y12 Y12 Y12 Y12 Y12 Y12 Y12 Y12
+
+849
+01:30:57,630 --> 01:30:57,630
+Y12 Y12 Y12 Y12 Y12 Y12 Y12 Y12 Y12 Y12 Y12 Y12
+
+850
+01:30:57,630 --> 01:30:57,630
+Y12 Y12 Y12 Y12 Y12 Y12 Y12 Y12 Y12 Y12 Y12 Y12
+
+851
+01:30:57,630 --> 01:31:01,120
+Y12 Y12 Y12 Y12 Y12 Y12 Y12 Y12 Y12 Y12 Y12of the
+
+852
+01:31:01,120 --> 01:31:11,620
+radia of the radia of convergence
+
+853
+01:31:11,620 --> 01:31:26,280
+of convergence of the series of the series for P
+
+854
+01:31:26,280 --> 01:31:29,320
+andThank you
+
+855
+01:32:57,990 --> 01:33:03,950
+طيب نجي لتعريف اللى ماتيه ليه التعريف بيقول ليش
+
+856
+01:33:03,950 --> 01:33:06,850
+for the differential equation اللى قدامنا دى the
+
+857
+01:33:06,850 --> 01:33:11,830
+point X node is called an ordinary point if P of X
+
+858
+01:33:11,830 --> 01:33:17,310
+and Q of X are analytic at X node تبصرنا شوية وإيش
+
+859
+01:33:17,310 --> 01:33:21,840
+تعريف ال analytic كتبناه المرة اللى فاتةتعريف ال
+
+860
+01:33:21,840 --> 01:33:24,640
+analytic بيقول function analytic إذا جدر تكتب على
+
+861
+01:33:24,640 --> 01:33:28,640
+شكل taylor series أو maclaurin series، مظبوط ولا
+
+862
+01:33:28,640 --> 01:33:34,020
+مش هيك هنا بنقول؟ بنقول تمام تمام، يبقى إذا والله
+
+863
+01:33:34,020 --> 01:33:40,380
+ال function جدر تكتب على شكل taylor series أو
+
+864
+01:33:40,380 --> 01:33:43,660
+maclaurin series، يبقى هذه بيسميها analytic
+
+865
+01:33:43,660 --> 01:33:49,450
+function، إيش بيقول هنا؟بقول المعادلة هذه النقطة x
+
+866
+01:33:49,450 --> 01:33:54,850
+note بقول عنها ordinary point إذا ال P small و ال
+
+867
+01:33:54,850 --> 01:33:58,950
+K small يعني جسمت على المعامل اللي هنا هايه جاهز و
+
+868
+01:33:58,950 --> 01:34:03,410
+خالص إذا كانت هذه و هذه كانوا انالتكي يعني إذا كل
+
+869
+01:34:03,410 --> 01:34:07,670
+واحدة فيهم جدرت أكتب على شكل taylor series أو
+
+870
+01:34:08,030 --> 01:34:12,750
+مكلورين سيريز بيكون النقطة هذه ordinary point يبقى
+
+871
+01:34:12,750 --> 01:34:16,410
+هذا التعريف جديد لمين؟ ال ordinary point احنا
+
+872
+01:34:16,410 --> 01:34:20,200
+المرة اللي فاتتبجي نقول ان ال ordinary point بشوف
+
+873
+01:34:20,200 --> 01:34:24,380
+المعامل تبع y double prime من النقط اللي بتخليها
+
+874
+01:34:24,380 --> 01:34:27,740
+أصفر بسميها singular points والباجي كله بيصيروا
+
+875
+01:34:27,740 --> 01:34:32,520
+ordinary points تمام؟ الآن أعطينا تعريف جديد لأن
+
+876
+01:34:32,520 --> 01:34:35,900
+ال analytic function و هو مرتبط بالتعريف السابق
+
+877
+01:34:35,900 --> 01:34:41,890
+بتدخل المعامل y double prime هو aوحظ صحيح إذا بدى
+
+878
+01:34:41,890 --> 01:34:46,250
+أروح على الدوال ال P of X و ال Q of X هل هم
+
+879
+01:34:46,250 --> 01:34:50,870
+analytic functions ولا لأ إذا لجيتهم يعني بقدر
+
+880
+01:34:50,870 --> 01:34:55,090
+أكتبهم على شكل تايلور أو ماكرون سيريز ولا إذا جدرت
+
+881
+01:34:55,090 --> 01:34:59,290
+عند النقطة المعطاة مش حيالة عند أي نقطة يبقى إذا
+
+882
+01:34:59,290 --> 01:35:03,270
+جدرت عند هذه النقطة بسمي هذه ordinary point ماجدرت
+
+883
+01:35:03,270 --> 01:35:08,500
+يبقى هذه singular pointنمر اتنين بيقول اذا هدول
+
+884
+01:35:08,500 --> 01:35:13,580
+هدول ارنقت انالاتيكي يعني ماقدرتش اكتب اي واحدة
+
+885
+01:35:13,580 --> 01:35:17,360
+فيهم على شكل تايلور او ماكرون سيريز يبقى النقطة
+
+886
+01:35:17,360 --> 01:35:23,720
+هذه بيصير معاها singular point طيب يمكن ييجي في
+
+887
+01:35:23,720 --> 01:35:28,060
+بال أحدكم السؤال التالف هدول two functions افترض
+
+888
+01:35:28,060 --> 01:35:32,620
+ان الأولى قدرت اكتبها على شكل تايلور سيريز بس
+
+889
+01:35:32,620 --> 01:35:36,930
+التانية ماقدرتشيعني بنفعش نكتب على شكل taylor
+
+890
+01:35:36,930 --> 01:35:40,970
+series، إذا بيكون الدوال الأثنين هدول Analytic عند
+
+891
+01:35:40,970 --> 01:35:46,700
+هذه النقطة، لأيعني انا بدي التنتين في نفس الوقت
+
+892
+01:35:46,700 --> 01:35:49,540
+يكونوا analytic عند نفس النقطة واحدة analytic
+
+893
+01:35:49,540 --> 01:35:53,820
+والتانية لأ يبقى خلاص مرفوض بدي التنتين او ال two
+
+894
+01:35:53,820 --> 01:35:57,500
+functional P of X small و P of X small of X يكونوا
+
+895
+01:35:57,500 --> 01:36:02,160
+analytic عند نفس النقطة في اي واحد ان حدث ذلك بقول
+
+896
+01:36:02,160 --> 01:36:06,260
+النقطة هذه معناها ordinary point ما حدث يبقى بقول
+
+897
+01:36:06,260 --> 01:36:10,760
+هذه singular pointخلّي هذه المعلومة في دماغك و
+
+898
+01:36:10,760 --> 01:36:14,000
+نذهب نستخدمها في النص التابع للنظرية اللي قدامنا
+
+899
+01:36:14,000 --> 01:36:18,520
+بقول لو كانت ال X node عبارة عن ordinary point
+
+900
+01:36:18,520 --> 01:36:23,520
+للمعادلة هادي يبقى جسمنا هادي على هادي بتطلع
+
+901
+01:36:23,520 --> 01:36:27,940
+أنالتك جسمنا هادي على هادي بتطلع أنالتك عشان تكون
+
+902
+01:36:27,940 --> 01:36:28,700
+هادي مالها
+
+903
+01:36:47,610 --> 01:36:52,690
+الحل تبع المعادلة رقم واحد بقدرة وعلى سير ال
+
+904
+01:36:52,690 --> 01:36:57,910
+solution يعني لو كان هدول التنتين analyticبأقمن
+
+905
+01:36:57,910 --> 01:37:04,150
+وجود حل على شكل متسلسلة للمعادلة هذه ومش عجبه جد
+
+906
+01:37:04,150 --> 01:37:08,810
+هيكوب بس لأ هو عبارة عن مجموع حلين كونصا في الحل
+
+907
+01:37:08,810 --> 01:37:12,190
+الأول و كونصا في الحل الثاني وانت شوفت في section
+
+908
+01:37:12,190 --> 01:37:17,260
+خمسة اتنينبقينا نطلع حل constant a node في series
+
+909
+01:37:17,260 --> 01:37:20,620
+زايد a1 في series تانية لسه اليوم معناه مظبوط ولا
+
+910
+01:37:20,620 --> 01:37:24,580
+لأ يبقى هاي اللي بقوله بشكل هذا حيث ال a node و ال
+
+911
+01:37:24,580 --> 01:37:28,660
+a1 عبارة عن ثوابت و ال y1 و ال y2 linearly
+
+912
+01:37:28,660 --> 01:37:33,420
+independent series solution و ركز على series حل
+
+913
+01:37:33,420 --> 01:37:36,560
+لإن احنا بنشتغل في series بنشتغلش بالحلاللي كنا في
+
+914
+01:37:36,560 --> 01:37:41,380
+chapter تلاتة او اربعة يبقى see the solution that
+
+915
+01:37:41,380 --> 01:37:45,660
+are analytic at each node يعني الحالين هدول كمان
+
+916
+01:37:45,660 --> 01:37:50,320
+analytic وين يعني كل واحد يهم مكتوب على شكل تايلور
+
+917
+01:37:50,490 --> 01:37:55,970
+سيريز عند هذه النقطة طب كويس احنا صار عندنا حالين
+
+918
+01:37:55,970 --> 01:38:00,510
+و اتنين linearly independent في عندنا حاجة اسمها
+
+919
+01:38:00,510 --> 01:38:05,950
+نصف قطر التقارب لكل من Y واحد و مش هذه سيريز إذا
+
+920
+01:38:05,950 --> 01:38:10,310
+بتكون تقاربي على فترة إذا نقلها نصف تقاربهذه
+
+921
+01:38:10,310 --> 01:38:16,130
+التقاربات ستكون مرتبطة على فترة يبقى لها نصف قطر
+
+922
+01:38:16,130 --> 01:38:21,130
+تقارب قد يكون مثل نصف التقارب الأول وقد يختلف عنه
+
+923
+01:38:21,520 --> 01:38:25,520
+طيب إن اتفقوا باخد واحد يوم، إن اختلفوا باخد اللي
+
+924
+01:38:25,520 --> 01:38:30,720
+صغير فيهم، إيش بقول هنا؟ ال radius of convergence
+
+925
+01:38:30,720 --> 01:38:36,140
+for each y1 and y2 is the minimum الأصغر of the
+
+926
+01:38:36,140 --> 01:38:40,660
+radius, radius جمع radius اللي هو نصف القطر of
+
+927
+01:38:40,660 --> 01:38:46,430
+convergence for the series for P and Qيبقى الاصغير
+
+928
+01:38:46,430 --> 01:38:51,090
+فيهم ها بيكون هو نصف القطر إيه لإيه خاطر أعطي مثال
+
+929
+01:38:51,090 --> 01:38:57,070
+صغير على هذه لأ لا سطرين بس سطرين على الأخرى بس
+
+930
+01:38:57,070 --> 01:38:59,750
+مشان أثبت المعلومة و المرة جايب نحل بدل المثال
+
+931
+01:38:59,750 --> 01:39:09,670
+تلاتة يبقى مثال صغير المثال بيقول ما يأتي يبقىمش
+
+932
+01:39:09,670 --> 01:39:14,450
+ضايل إلا مجموعة من الأمثلة على هذا ال section بدنا
+
+933
+01:39:14,450 --> 01:39:22,390
+نيجي لأول مثال بقول determine او بلا شوف خليه اي
+
+934
+01:39:22,390 --> 01:39:26,870
+determine a lower bound
+
+935
+01:39:33,560 --> 01:39:41,620
+for the radius of convergence for the radius of
+
+936
+01:39:41,620 --> 01:39:45,340
+convergence
+
+937
+01:39:45,340 --> 01:39:50,080
+of
+
+938
+01:39:50,080 --> 01:39:58,780
+serious solutions of serious solutions serious
+
+939
+01:39:58,780 --> 01:40:00,820
+solutions about
+
+940
+01:40:29,360 --> 01:40:31,520
+المعادلة الأولى
+
+941
+01:40:49,090 --> 01:40:50,490
+Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''
+
+942
+01:41:03,170 --> 01:41:09,470
+كويس المعادلة جاهزة مجسومة و خالصة يبقى capital P
+
+943
+01:41:09,470 --> 01:41:15,990
+هنا بقدرش يا بنات؟ واحد يبقى الان capital P of X
+
+944
+01:41:15,990 --> 01:41:22,170
+بده ساوي واحد في عندنا نقطة في الدنيا بدها تغير
+
+945
+01:41:22,170 --> 01:41:26,590
+القيمة هذا تخليها صفر ماعنديش يبقى كل النقاط اللي
+
+946
+01:41:26,590 --> 01:41:33,410
+عندي are ordinary pointsيبقى هذه ليمكن أن تساوي 0
+
+947
+01:41:33,410 --> 01:41:42,110
+for all x يبقى هذا بدي أقول لك all the points are
+
+948
+01:41:42,110 --> 01:41:47,070
+ordinary points
+
+949
+01:41:48,390 --> 01:41:52,670
+يبقى بناء عليه الـ zero والاربعة مالهم ordinary
+
+950
+01:41:52,670 --> 01:42:00,610
+points ال X naught ساوي zero and ال X naught ساوي
+
+951
+01:42:00,610 --> 01:42:11,890
+أربعة are ordinary points هذا كويس ماعنديش ولا
+
+952
+01:42:11,890 --> 01:42:16,890
+singular point تماما بقولكوا يبقى لو جيت لل real
+
+953
+01:42:16,890 --> 01:42:21,810
+lineهذا الريال لاني و هذا النقطة zero و هذا النقطة
+
+954
+01:42:21,810 --> 01:42:28,570
+أربعة ماعنديش singular point بدي أوقف عندها يبقى
+
+955
+01:42:28,570 --> 01:42:33,390
+ال radius الأولى اللي بدي يكون من وين لوين من صفر
+
+956
+01:42:33,390 --> 01:42:38,730
+إلى مالنها طول قداش تبعه مالنها يعني ال radius
+
+957
+01:42:38,730 --> 01:42:43,130
+التاني بدي يكون من وين من أربعة إلى مالنها قداش
+
+958
+01:42:44,370 --> 01:42:47,490
+عشان اذا ال raw one بده يسوي مالة نهاية و ال raw
+
+959
+01:42:47,490 --> 01:42:50,850
+two بده يسوي مالة نهاية فى هم واحد صغير و واحد
+
+960
+01:42:50,850 --> 01:42:55,970
+كبير لأ يبقى ال radius مالة نهاية يبقى باجي بقوله
+
+961
+01:42:55,970 --> 01:43:02,930
+ال raw one بده يسوي infinity و ال raw two بده يسوي
+
+962
+01:43:02,930 --> 01:43:08,530
+infinityقالي هاتلي ال lower bound لل radius of
+
+963
+01:43:08,530 --> 01:43:16,690
+convergence يبقى باجي بقوله هنا the lower bound
+
+964
+01:43:16,690 --> 01:43:26,150
+for the radius of convergence
+
+965
+01:43:26,150 --> 01:43:36,490
+is ر تساوي قداش infinity مافيش غيرهاطبعا هذا أتفه
+
+966
+01:43:36,490 --> 01:43:41,410
+أنواع المسائل، لكن اسمها في الكتاب، تمام؟ مرة جا
+
+967
+01:43:41,410 --> 01:43:44,950
+ان شاء الله تصير مش روين في الهلاب، تطلع قيم
+
+968
+01:43:44,950 --> 01:43:51,170
+عددية، وحنق في العديد من الأمثلة، وقد تكون النقطة
+
+969
+01:43:51,170 --> 01:43:56,710
+singular point حقيقية وقد تكون تخيلية، يبقى على كل
+
+970
+01:43:56,710 --> 01:44:01,750
+الأمرين، بدنا نحسب هذا ان شاء الله المرة القادمة
+
diff --git a/PL9fwy3NUQKwa8ZDfSFGn6H8xVFLzqmCZC/Bx_N_tiknzs_raw.srt b/PL9fwy3NUQKwa8ZDfSFGn6H8xVFLzqmCZC/Bx_N_tiknzs_raw.srt
new file mode 100644
index 0000000000000000000000000000000000000000..34b06b8a7651e9e7b53cf82cb957ff0a8c895021
--- /dev/null
+++ b/PL9fwy3NUQKwa8ZDfSFGn6H8xVFLzqmCZC/Bx_N_tiknzs_raw.srt
@@ -0,0 +1,3936 @@
+1
+00:00:10,800 --> 00:00:15,160
+بسم الله الرحمن الرحيم نبدأ اليوم في section 55
+
+2
+00:00:15,160 --> 00:00:21,700
+بتكلم فقط عن Euler equation معادلة Euler طبعا
+
+3
+00:00:21,700 --> 00:00:25,540
+معادلة Euler إلها أكثر من صيغة هناخد الصيغة الأولى
+
+4
+00:00:25,540 --> 00:00:29,840
+و بعدين هناخد الصيغة الثانيةthe Euler differential
+
+5
+00:00:29,840 --> 00:00:33,460
+equation معادلة التفاظلية تبعت العالم Euler is an
+
+6
+00:00:33,460 --> 00:00:37,160
+equation in the form طبعا لو ماسكت اي كتاب غير
+
+7
+00:00:37,160 --> 00:00:41,740
+كتابنا بسميها Cauchy-Euler equation يعني اسم مركّم
+
+8
+00:00:41,740 --> 00:00:44,880
+احنا Cauchy-Euler هو ال Euler يبقى هي Euler وهي
+
+9
+00:00:44,880 --> 00:00:49,700
+المعادلة قدامنابغض النظر على التسمية يبقى معادلة
+
+10
+00:00:49,700 --> 00:00:54,080
+Euler على صيغة X تربية YW prime زائد Alpha XY
+
+11
+00:00:54,080 --> 00:01:00,100
+prime زائد Beta Y تساوي Zero يعني معادلة من الرتبة
+
+12
+00:01:00,100 --> 00:01:06,760
+الثانية المعامل تبع YW prime معادلة من الدرجة
+
+13
+00:01:06,760 --> 00:01:10,420
+الثانية ومافيش فيها إلا X تربية مش X تربية زائد
+
+14
+00:01:10,420 --> 00:01:15,260
+شغلة بس X تربية هنا Alpha X ال Alpha مقدار ثابت
+
+15
+00:01:22,350 --> 00:01:28,150
+يبقى الصيغة اللى قدامك صيغة Euler equation in
+
+16
+00:01:28,150 --> 00:01:34,170
+general ال alpha و ال beta constant ال X يساوي 0
+
+17
+00:01:34,170 --> 00:01:39,030
+طبعا هي هادئاش singular point و في نفس الوقت بتكون
+
+18
+00:01:39,030 --> 00:01:43,310
+regular singular pointلأن ال singular ممكن تبقى
+
+19
+00:01:43,310 --> 00:01:47,650
+regular وممكن تكون irregular يبقى ان هذه دائما هو
+
+20
+00:01:47,650 --> 00:01:52,550
+بال regular singular point الحال تبع هذه المعادلة
+
+21
+00:01:52,550 --> 00:01:59,150
+على interval لا تحتوي عالميا على ال singular point
+
+22
+00:01:59,150 --> 00:02:02,590
+ان عند ال singular point x يساوي zero يبقى احنا
+
+23
+00:02:02,590 --> 00:02:06,110
+على فترة لا تشتمل not including
+
+24
+00:02:10,180 --> 00:02:14,720
+يبقى في هذه الحالة شكل الحل بيكون على الصيغة y
+
+25
+00:02:14,720 --> 00:02:18,880
+ساوي c واحد y واحد زايد c اتنين y اتنين حيث y واحد
+
+26
+00:02:18,880 --> 00:02:22,540
+و y اتنين are two linearly independent solutions
+
+27
+00:02:22,540 --> 00:02:27,610
+لمن؟ لل equation oneعادي linearly independent
+
+28
+00:02:27,610 --> 00:02:33,110
+solution لل equation 1 و C1 و C2 عبارة عن ثوابت
+
+29
+00:02:33,110 --> 00:02:37,950
+طبعا يا بنات لما بتلاحظوا لما اقول X ساوي Zero هي
+
+30
+00:02:37,950 --> 00:02:41,490
+singular point يبقى ريا الله انقسم لك كام فترة
+
+31
+00:02:41,490 --> 00:02:45,950
+انقسم لفترتين من Zero إلى Infinity و من سلب
+
+32
+00:02:45,950 --> 00:02:50,440
+Infinity إلى Zeroبعد قليل ممكن تبقى ال singular
+
+33
+00:02:50,440 --> 00:02:54,080
+point مش zero يمكن تبقى واحد يمكن اتنين يمكن تلاتة
+
+34
+00:02:54,080 --> 00:02:58,120
+يبقى هذا الرقم برضه بيجسم ال interval اللي هو الى
+
+35
+00:02:58,120 --> 00:03:02,380
+فترتين يبقى احنا بدنا ندرس الحل على فترة واحدة
+
+36
+00:03:02,380 --> 00:03:07,930
+وبعد هيك بنشوف على الفترة الثانيةفبجيب اقول to
+
+37
+00:03:07,930 --> 00:03:11,910
+solve equation one we have two intervals هي الفترة
+
+38
+00:03:11,910 --> 00:03:15,010
+اللى عندنا من سلب infinity الى zero ومن zero الى
+
+39
+00:03:15,010 --> 00:03:19,810
+infinity هنا x بتبقى اقل من zero و هنا x معناها
+
+40
+00:03:19,810 --> 00:03:23,900
+greater than zero اذا انا بدأ اخد الحلعلى الفترة
+
+41
+00:03:23,900 --> 00:03:28,740
+اللي عندنا هذه يبقى بدي أخد الحالة الأولى if ال X
+
+42
+00:03:28,740 --> 00:03:32,820
+greater than 0 لو كانت ال X أكبر من 0 يعني بدي
+
+43
+00:03:32,820 --> 00:03:37,520
+أدرس على نص الفترة تبع ال real line شو بدي أعمل
+
+44
+00:03:37,520 --> 00:03:43,160
+بدي أفرض الحل على صيغة مازي ما كنا قبل هيك
+
+45
+00:03:43,160 --> 00:03:46,220
+المعادلة ده من الرتبة الثانية بنقول لأ بس بشرط
+
+46
+00:03:46,220 --> 00:03:50,640
+يكون هذا الثوابت بقين اقول let Y تساوي E أُس RT is
+
+47
+00:03:50,640 --> 00:03:54,160
+a solution هنا بنفس الفكرة بس بدناش نفرضها
+
+48
+00:03:54,160 --> 00:03:58,520
+exponential بدنا نفرضها polynomial يبقى بداجي
+
+49
+00:03:58,520 --> 00:04:07,700
+اقوله let Y تساوي X أُس R be a solution
+
+50
+00:04:14,910 --> 00:04:20,830
+بعد ذلك اشتق
+
+51
+00:04:20,830 --> 00:04:25,130
+هذه مرتين و اعوضه في المعادلة اللى فوق و نشوف اللى
+
+52
+00:04:25,130 --> 00:04:29,050
+وين بدنا نوصل في هذه الحالة اذا مبدأش الى ال Y'
+
+53
+00:04:29,750 --> 00:04:36,250
+يبقى هذه بالساوية R في X أس R ناقص واحدالأُس هذا
+
+54
+00:04:36,250 --> 00:04:41,050
+يا بنات اللي هو اري ممكن يكون integer سالب او موجب
+
+55
+00:04:41,050 --> 00:04:46,150
+و ممكن يكون zero و ممكن يكون كسري سالب او موجب
+
+56
+00:04:46,150 --> 00:04:51,970
+كذلك يعني any real number تمام الان بدنا نجيب main
+
+57
+00:04:51,970 --> 00:04:59,110
+yw prime يبقى r في مين في r ناقص واحد في x أس r
+
+58
+00:04:59,110 --> 00:05:04,750
+ناقص اتنينبناخد المعلومات هذه ونروح نعوض وين في
+
+59
+00:05:04,750 --> 00:05:12,930
+المعادلة واحد يبقى بالداجي اقوله هنا substitute of
+
+60
+00:05:12,930 --> 00:05:22,250
+an equation when we get بنحصل على ما يأتي هاي ال X
+
+61
+00:05:22,250 --> 00:05:27,190
+تربيع في مين؟ في ال YW prime اللي هي R
+
+62
+00:05:32,410 --> 00:05:39,030
+اللي بعدها زائد alpha x في ال y prime ال y prime
+
+63
+00:05:39,030 --> 00:05:47,090
+اللي هى r في x أس r minus ال one زائد beta y, y
+
+64
+00:05:47,090 --> 00:05:53,820
+اللي هى x أس r, x أس r كله بده يساوي zeroبدا داخل
+
+65
+00:05:53,820 --> 00:05:59,640
+ال X تربية داخل القوس يبقاش بيصير R في R ناقص واحد
+
+66
+00:05:59,640 --> 00:06:08,420
+في X أُس R زائد Alpha R X أُس R زائد Beta X أُس R
+
+67
+00:06:08,420 --> 00:06:14,240
+يسوى كده؟ يسوى Zero إيش رأيك؟ بدي أجسم كله على X
+
+68
+00:06:14,240 --> 00:06:19,600
+أُس R، بنفع؟ليش نقص أكبر من Zero لا يمكن أن تساوي
+
+69
+00:06:19,600 --> 00:06:23,520
+Zero وبالتالي بقدر اقسم عليها يبقى هذه المعادلة
+
+70
+00:06:23,520 --> 00:06:29,180
+بيصير على الشكل التالي R في R ناقص واحد زائد Alpha
+
+71
+00:06:29,180 --> 00:06:37,040
+R زائد Beta يساوي Zero المعادلة هذه بيصير R تربيع
+
+72
+00:06:37,040 --> 00:06:46,310
+ناقص R زائد Alpha R زائد Beta يساوي Zero اوهي ال R
+
+73
+00:06:46,310 --> 00:06:52,190
+تربية هذه فيها R و فيها R بتاخد R عامل مشترك بضل
+
+74
+00:06:52,190 --> 00:07:00,210
+زائد Alpha ناقص واحد في R زائد Beta يساوي من يساوي
+
+75
+00:07:00,210 --> 00:07:07,230
+Zero هل هذه معادلة تفاضلية؟هذه معادلة تفاضلية؟ لأ
+
+76
+00:07:07,230 --> 00:07:11,190
+هذه معادلة من الدرجة الثانية عادية يبقى هذه بدي
+
+77
+00:07:11,190 --> 00:07:15,910
+أسميها زي ما كنا بنفرض قبل هي Y تساوي E أس RT
+
+78
+00:07:15,910 --> 00:07:20,230
+عبارة عن solution إذا هذه بدي أسميها ايه؟ ال
+
+79
+00:07:20,230 --> 00:07:26,010
+characteristic equation يبقى دي بنوزها هك و بقول
+
+80
+00:07:26,010 --> 00:07:28,730
+هذه ال characteristic equation ال differential
+
+81
+00:07:28,730 --> 00:07:34,880
+equation manيبقى هذه بدي أسميها ال characteristic
+
+82
+00:07:34,880 --> 00:07:46,160
+equation of the differential equation one إذا هذه
+
+83
+00:07:46,160 --> 00:07:50,820
+لها جذور صحيح ولا لأ؟ لها معادلة من الضررية
+
+84
+00:07:50,820 --> 00:07:58,190
+التانية لها جذرينالجذران قد يكونان حقيقيا ومختلفا
+
+85
+00:07:58,190 --> 00:08:05,490
+او حقيقيا ومتساويا او two complex conjugate تخيليا
+
+86
+00:08:05,490 --> 00:08:10,710
+ومترافقا بدنا ندرس الحالات الثلاث اللي هذول اللي
+
+87
+00:08:10,710 --> 00:08:15,330
+عندنا يبقى هذه بدنا نسميها بنات سميها لل equation
+
+88
+00:08:15,330 --> 00:08:26,320
+رقم اتنينيبقى هنا باجي بقول يبقى
+
+89
+00:08:26,320 --> 00:08:36,520
+the roots of the differential the roots of the
+
+90
+00:08:36,520 --> 00:08:43,640
+equation اتنين R يكونوا على الشكل التالي نمرحل
+
+91
+00:08:44,960 --> 00:08:59,680
+R1 and R2 are real and different يعني حقيقياني
+
+92
+00:08:59,680 --> 00:09:09,600
+ومختلفان يبقى باجي بقوله يعني هذه that is أي أن R1
+
+93
+00:09:09,600 --> 00:09:12,200
+لا تساوي R2
+
+94
+00:09:33,020 --> 00:09:38,320
+يبقى انا اقول معاهمحالين للمعادلة اللي قلناها دي
+
+95
+00:09:38,320 --> 00:09:43,660
+لو طلعوا لإتنين are linearly independent يبجي هدول
+
+96
+00:09:43,660 --> 00:09:47,120
+بيكونوا لماين fundamental set of solutions
+
+97
+00:09:47,120 --> 00:09:51,860
+وبالتالي شكل الحل بيصير على الشكل اللي قدامنا هذا
+
+98
+00:09:51,860 --> 00:09:58,850
+c1 y1 زائد c2 y2 ويكون خلصة من المثلة هذهأذا بدي
+
+99
+00:09:58,850 --> 00:10:02,070
+ابحث الـ Runnerskin تبع من الاتنين إذا طلع الـ
+
+100
+00:10:02,070 --> 00:10:05,710
+Runnerskin ليه يساوي Zero بيطولوا يصير الاتنين دول
+
+101
+00:10:05,710 --> 00:10:09,470
+Linearly Dependent بس Independent بيصيروا الاتنين
+
+102
+00:10:09,470 --> 00:10:14,770
+دول بيكونوا لمين ال general solution إذا بدي أبحث
+
+103
+00:10:14,770 --> 00:10:22,570
+ال Runnerskin تبع X أُس R1 و X أُس R2 وهي المحدد
+
+104
+00:10:22,570 --> 00:10:29,880
+وهذا X أُس R1وهذا ال X أُس R2 بضعوها اشتق مشان
+
+105
+00:10:29,880 --> 00:10:36,120
+أجيب الصف الثاني من المحدد يبقى R1 X أس R1 ناقص
+
+106
+00:10:36,120 --> 00:10:45,460
+واحد R2 X أس R2 ناقص واحد وهي المحدد بدأ فك المحدد
+
+107
+00:10:45,460 --> 00:10:50,500
+هذايبقى حاصل ضرب عناصر القطر الرئيسي ناقص حاصل ضرب
+
+108
+00:10:50,500 --> 00:11:01,420
+عناصر القطر الثانوي يبقى R2 Fix أس R1 زائد R2 ناقص
+
+109
+00:11:01,420 --> 00:11:06,900
+واحد عند الضرب تجمع الأسس خلصنا الرئيسي بدأ نيجي
+
+110
+00:11:06,900 --> 00:11:18,350
+للثانويناقص R1 في من؟ في X أُس R1 زائد R2 ناقص 1
+
+111
+00:11:18,350 --> 00:11:23,630
+إيش بتلاحظوا بنات؟ في عام المشترك ما بيقل اتنين
+
+112
+00:11:23,630 --> 00:11:32,580
+يبقى هذا الكلام R2 ناقص R1في ال X أُس R1 زائد R2
+
+113
+00:11:32,580 --> 00:11:39,920
+ناقص واحد السؤال هو هل يمكن لهذه القيمة أن تساوي
+
+114
+00:11:39,920 --> 00:11:46,900
+صفرا في يوم من الأيام لأ لأن R1 بسويش R2 اتنين ال
+
+115
+00:11:46,900 --> 00:11:51,040
+X دائما وامد greater than zero إذا لا يمكن لهذا
+
+116
+00:11:51,040 --> 00:11:56,250
+المقدر أن يساوي zeroيبقى هذا الكلام لا يمكن أن
+
+117
+00:11:56,250 --> 00:12:04,390
+يساوي zero since اللي هو R1 لا يساوي R2 وال X من
+
+118
+00:12:04,390 --> 00:12:09,450
+البداية هي هجيلين greater than zeroيبقى هذا الكلام
+
+119
+00:12:09,450 --> 00:12:14,070
+لا يمكن أن يساوي zero يبقى اتنين هدول linearly
+
+120
+00:12:14,070 --> 00:12:24,770
+independent يبقى هنا ال X أس R1 و X أس R2 رتو
+
+121
+00:12:24,770 --> 00:12:31,810
+linearly independent solutions of
+
+122
+00:12:31,810 --> 00:12:38,350
+the equation oneمعناته بقدر اجيب ال general
+
+123
+00:12:38,350 --> 00:12:41,370
+solution يبقى باجي بقوله
+
+124
+00:12:49,410 --> 00:12:59,730
+equation one is y تساوي c واحد x أس r واحد c اتنين
+
+125
+00:12:59,730 --> 00:13:08,190
+x أس r اتنين بالشكل اللي عندنا هنا x أس r اتنين
+
+126
+00:13:08,190 --> 00:13:12,310
+اذا المعادلة اللي عندى في ال characteristic
+
+127
+00:13:12,310 --> 00:13:19,600
+equation لو حلتها وطلع الجذران حقيقيا ومختلفابكون
+
+128
+00:13:19,600 --> 00:13:26,480
+شكل الحل في صيغته العامة Y يساوي C1 X أُس R1 زاد
+
+129
+00:13:26,480 --> 00:13:32,480
+C2 X أُس R2 وبالتالي بيكون خلصنا من مين؟ خلصنا من
+
+130
+00:13:32,480 --> 00:13:37,520
+الحالة الأولى، بدروح لوين؟ للحالة الثانية
+
+131
+00:13:52,000 --> 00:14:01,660
+يبقى الحالة الثانية if R1 يسوى R2 يسوى R مثلا say
+
+132
+00:14:01,660 --> 00:14:09,780
+يعني ال two roots are real and equal يعني that is
+
+133
+00:14:09,780 --> 00:14:13,060
+the
+
+134
+00:14:13,060 --> 00:14:20,480
+two roots of equation اتنين
+
+135
+00:14:22,860 --> 00:14:31,520
+are real and repeated حد
+
+136
+00:14:31,520 --> 00:14:34,740
+ماذا يذكر فيك عندما يقول الـ two roots are real
+
+137
+00:14:34,740 --> 00:14:39,560
+and repeatedزمان لمعادلة رتبة تانية لما كنا نقول X
+
+138
+00:14:39,560 --> 00:14:47,260
+يساوي Us RT شو شكل الحلم الذاكرين؟ C1 زائد C2 في T
+
+139
+00:14:47,260 --> 00:14:52,400
+كله في ال exponential مظبوط هنا نفس الفكرة بس مش T
+
+140
+00:14:52,400 --> 00:14:59,060
+بديجي مكانها اللي انتييعني C1 زي C2 لين T يعني بال
+
+141
+00:14:59,060 --> 00:15:02,620
+reduction of order لما يعطيني حل بقدر أجيب شكل
+
+142
+00:15:02,620 --> 00:15:06,360
+الحل تاني المرة اللي فات جيبناها فكان شكله T المرة
+
+143
+00:15:06,360 --> 00:15:12,340
+هذه لو روحنا نحاسب يكون شكله لين T يبقى real and
+
+144
+00:15:12,340 --> 00:15:15,500
+repeated then
+
+145
+00:15:16,940 --> 00:15:27,160
+we have one solution حل واحد اللي هو ماين؟ اللي هو
+
+146
+00:15:27,160 --> 00:15:33,060
+Y يساوي اللي هو ماين؟ X أس
+
+147
+00:15:39,700 --> 00:15:47,640
+الثانية الحلول هي
+
+148
+00:15:47,640 --> 00:15:55,620
+Y
+
+149
+00:15:55,620 --> 00:16:05,300
+تساوي X أُس R في لن Xالان بدنا نشوف هل اتنين هدول
+
+150
+00:16:05,300 --> 00:16:09,760
+are linearly independent ولا لا يبقى بدي اخد
+
+151
+00:16:09,760 --> 00:16:17,820
+الرونسكين تبع ال X أُس R و X أُس R في لن ال X يبقى
+
+152
+00:16:17,820 --> 00:16:25,180
+هذا بدي يعطيني المحدد X أُس RX أُس R فى لن X هدى
+
+153
+00:16:25,180 --> 00:16:32,120
+مشتقتها R X أُس R ناقص واحد هدى مشتقت حاصل ضرب ده
+
+154
+00:16:32,120 --> 00:16:40,060
+اللى تانى يبقى R X أُس R ناقص واحد فى لن X زائد
+
+155
+00:16:40,060 --> 00:16:49,540
+قداش مشتقت لن Xوحد على X مع ال X أُس R بصير X أُس
+
+156
+00:16:49,540 --> 00:16:55,740
+R ناقص واحد يم على طول يبقى هذه A كتبها عندك على
+
+157
+00:16:55,740 --> 00:17:01,300
+شجعك مشتقة هذه X أُس R في واحد على X يبقى تختصر
+
+158
+00:17:01,300 --> 00:17:06,320
+بصير X أُس R ناقص واحد يبقى هاي المحدد الآن بدنا
+
+159
+00:17:06,320 --> 00:17:11,520
+نحسب قيمة هذا المحدد يبقى هذا الكلام بده يساوي هذه
+
+160
+00:17:11,520 --> 00:17:20,760
+Aوهذا X أس اتنين R ناقص واحد في لن ال X زائد X أس
+
+161
+00:17:20,760 --> 00:17:25,640
+اتنين R ناقص واحد يبقى هذا حاصل ضرب عناصر قطر
+
+162
+00:17:25,640 --> 00:17:31,080
+رئيسي الناقص حاصل ضرب عناصر قطر الثانوي يبقى ناقص
+
+163
+00:17:31,080 --> 00:17:40,940
+R و X أس اتنين R ناقص واحد في لن ال Xطلعيني للterm
+
+164
+00:17:40,940 --> 00:17:44,800
+الأول والterm الأخير الاتنين are the same اتنين
+
+165
+00:17:44,800 --> 00:17:45,940
+نفسي يبقى هذا
+
+166
+00:17:45,940 --> 00:17:56,260
+ههههههههههههههههههههههههههههههههههههههههههههههههههههههههههههههههههههههههههههههههههههههههههههههههههههههههههههههههههههههههههههههههههههههههههههههههههههههههههههههههههههههههههههههههههههههههههههههه
+
+167
+00:17:58,950 --> 00:18:04,030
+يبقى هذه اللي لا يمكن أن تساوي zero يبقى الاتنين
+
+168
+00:18:04,030 --> 00:18:08,070
+هذول ما لهم linearly independent بيكوّنون ال
+
+169
+00:18:08,070 --> 00:18:13,670
+fundamental set of solutions يبقى سوء ال XO's are
+
+170
+00:18:13,670 --> 00:18:20,490
+andالإكسوس R في لين ال X are linearly independent
+
+171
+00:18:20,490 --> 00:18:29,670
+solutions of equation 1 يبقى بناء عليه the general
+
+172
+00:18:29,670 --> 00:18:35,030
+solution
+
+173
+00:18:35,030 --> 00:18:50,920
+is Y تسوىC1 زائد C2 في لن ال X كله في X أُس R شكل
+
+174
+00:18:50,920 --> 00:18:57,780
+لنا هنا يبقى هذا شكل الحل لو كان real and repeated
+
+175
+00:18:57,780 --> 00:19:04,900
+نيجي لوين للحالة التالتة لو كان روس R complex
+
+176
+00:19:04,900 --> 00:19:18,500
+conjugate يبقى Fthe roots of equation two are
+
+177
+00:19:18,500 --> 00:19:28,020
+complex conjugate يعني
+
+178
+00:19:28,020 --> 00:19:33,460
+اللي هم عبارة عن lambda زائد او ناقص I mu
+
+179
+00:19:36,220 --> 00:19:39,480
+يبقى بدي شكل الحل بديش اروح اقعد احسب الوصف كمان
+
+180
+00:19:39,480 --> 00:19:53,640
+اجدي قصة بتطول يبقى then the general solution is y
+
+181
+00:19:53,640 --> 00:20:03,200
+تساوي x أُس لاندا تفتح اجازة c1 cosine mu في لن ال
+
+182
+00:20:03,200 --> 00:20:03,660
+x
+
+183
+00:20:13,800 --> 00:20:23,700
+ما هو الحل الأول؟ الحل الأول x أسلن في cos Mu لن X
+
+184
+00:20:23,700 --> 00:20:30,800
+الحل الثاني x أسلن في sin Mu لن Xهذا يجب ان تشكل
+
+185
+00:20:30,800 --> 00:20:36,940
+الرونسكين يبقى تقوليلي الرونسكين هذا تبع الحل
+
+186
+00:20:36,940 --> 00:20:44,680
+الأول الو X أُس لاندا في cosine ميو لن ال X و X
+
+187
+00:20:44,680 --> 00:20:53,260
+أُس لاندا في sine ميو لن ال X لو حسبت الرونسكين
+
+188
+00:20:53,260 --> 00:20:58,480
+هذا يبقى النتيجة عبارة عن ميو في
+
+189
+00:21:01,840 --> 00:21:10,880
+يبقى النتيجة اللي هي الميو 8 في اكس أس اتنين لاندا
+
+190
+00:21:10,880 --> 00:21:17,500
+ناقص واحد وهذا لا يمكن أن يساوي zero طب حدا فيكوا
+
+191
+00:21:17,500 --> 00:21:21,520
+بتقول ليه هذا لا يمكن أن يساوي zero؟
+
+192
+00:21:24,120 --> 00:21:30,740
+هذه أصلا بتسويش zero اكسبوننتشر لميو ممكن يتساوي
+
+193
+00:21:30,740 --> 00:21:37,830
+zero لو ساوت zero ببطل يصير الحل complexبصير real
+
+194
+00:21:37,830 --> 00:21:42,670
+مظبوط و احنا ماش ترضيه انه حل ماله complex يبقى
+
+195
+00:21:42,670 --> 00:21:46,590
+هذا الكلام لا يمكن ان يساوي zero يبقى الاتنين هذا
+
+196
+00:21:46,590 --> 00:21:49,930
+طبعا هذا بيجي تعمله هي ت check في البيت مش تقري
+
+197
+00:21:49,930 --> 00:21:52,810
+تحصل ضرب دالتين ومش تقري تحصل ضرب و تروح تفك
+
+198
+00:21:52,810 --> 00:21:57,610
+المحدد و أي نتيجة عندك بتتأكد منهايبقى هذا الشكل
+
+199
+00:21:57,610 --> 00:22:03,110
+الحل في حالة مين؟ في حالة اللي هو لو كان ال roots
+
+200
+00:22:03,110 --> 00:22:08,050
+are complex conjugate يبقى هذه مين؟ هذه الحالات
+
+201
+00:22:08,050 --> 00:22:15,390
+الثلاث لل equation هي مين؟لإتنين وبالتالي عرفنا
+
+202
+00:22:15,390 --> 00:22:20,810
+شكل الحل في كل حالة من الحالات التلاتة لو طلع ال
+
+203
+00:22:20,810 --> 00:22:24,270
+roads real and different الحالة التانية لو طلع
+
+204
+00:22:24,270 --> 00:22:28,950
+real and repeated الحالة التالتة لو طلع complex
+
+205
+00:22:46,050 --> 00:22:50,390
+الحلول التلاتة تبقى كما هي بس بدل ال X بنقول
+
+206
+00:22:50,390 --> 00:22:57,070
+absoluteيبقى value ل X لأن X ليس معرف إلا للقيمة
+
+207
+00:22:57,070 --> 00:23:02,210
+الموجبة يبقى
+
+208
+00:23:02,210 --> 00:23:06,270
+on the
+
+209
+00:23:06,270 --> 00:23:16,230
+interval على الفترة X less than zero يبقى
+
+210
+00:23:27,800 --> 00:23:36,300
+الحل الأول Y تساوي C1 absolute value ل X أُس R1
+
+211
+00:23:36,300 --> 00:23:45,630
+زائد C2 absolute value ل X أُس R2الحل الثاني Y
+
+212
+00:23:45,630 --> 00:23:54,430
+يساوي C1 زي C2 لن absolute value ل X في absolute
+
+213
+00:23:54,430 --> 00:24:03,430
+value ل X أُسالحل الثالث والاخير Y تساوي absolute
+
+214
+00:24:03,430 --> 00:24:13,310
+value ل X أسلن ده فيه C1 cos Mu ln absolute value
+
+215
+00:24:13,310 --> 00:24:23,030
+ل X زائد C2 sin Mu اللي هو ln absolute value ل X
+
+216
+00:24:23,030 --> 00:24:28,570
+بالشكل اللي عندنايبقى هذا شكل الحل في الأمور
+
+217
+00:24:28,570 --> 00:24:36,470
+الثلاثة طب افترض انه طلعت عندنا ال singular point
+
+218
+00:24:36,470 --> 00:24:42,450
+هي X يساوي Zero وما جليش ل X أكبر من Zero و ل X
+
+219
+00:24:42,450 --> 00:24:47,310
+أقل من Zero يعني بدى أحل الحل هنا و أعود أحله على
+
+220
+00:24:47,310 --> 00:24:52,120
+الشجرة تانية لا لا ولا حاجةبتقول من البداية if x
+
+221
+00:24:52,120 --> 00:24:56,560
+greater than zero و بشتغل شغل لغاية مخلص في الآخر
+
+222
+00:24:56,560 --> 00:25:01,120
+بقوله the general solution is و بكتبه بس بدل ال x
+
+223
+00:25:01,120 --> 00:25:05,800
+بحطه ب value x و بقول كف الله المؤمنين القتاللكن
+
+224
+00:25:05,800 --> 00:25:09,560
+ان حددني من البداية ان X أكبر من Zero بيكون ريحني
+
+225
+00:25:09,560 --> 00:25:14,540
+ما حددلي بفرضها انا أكبر من Zero لغاية ماجي بشكل
+
+226
+00:25:14,540 --> 00:25:18,420
+الحل العام بس بشيل كل X و بحط مكان Absolute بل ال
+
+227
+00:25:18,420 --> 00:25:25,140
+X بيكون حالينا الإشكالية بالكامل طيب ال Euler
+
+228
+00:25:25,140 --> 00:25:31,390
+equation هذه يا بنات في لها حالة خاصةالحالة الخاصة
+
+229
+00:25:31,390 --> 00:25:36,260
+ليست بالضرورة تكون X تربية و Y double primeممكن
+
+230
+00:25:36,260 --> 00:25:40,920
+تبقى x ناقص واحد و y double prime ممكن تبقى x زائد
+
+231
+00:25:40,920 --> 00:25:46,760
+تلاتة تربية في y double prime و هكذا يعني ليس
+
+232
+00:25:46,760 --> 00:25:50,820
+بالضرورة ان تبقى x لأ ممكن ال x معمول لها shift
+
+233
+00:25:50,820 --> 00:25:55,480
+مقدار واحد اتنين تلاتة نص نقل يقدر ما يكون يبقى
+
+234
+00:25:55,480 --> 00:25:59,600
+هذه بتسميها special case من الحالة الأولى يبقى
+
+235
+00:25:59,600 --> 00:26:09,570
+بداجة اقوله special case حالة خاصةإذا كانت الـ
+
+236
+00:26:09,570 --> 00:26:16,130
+Euler Equation
+
+237
+00:26:16,130 --> 00:26:26,350
+في الـ Formفي الشكل التالي اللي هو x ناقص x node
+
+238
+00:26:26,350 --> 00:26:32,310
+لكل تربية في ال y double prime زائد alpha في x
+
+239
+00:26:32,310 --> 00:26:39,270
+ناقص x node في ال y prime زائد beta y تساوي zero
+
+240
+00:26:39,270 --> 00:26:46,150
+then we look
+
+241
+00:26:46,150 --> 00:26:56,250
+forنبحث عن حلوة A على
+
+242
+00:26:56,250 --> 00:27:01,870
+حل في شكل
+
+243
+00:27:01,870 --> 00:27:12,370
+Y يساوي X ناقص X نوت كله to the power R لذلك نحصل
+
+244
+00:27:12,370 --> 00:27:15,790
+نحصل نفس
+
+245
+00:27:38,460 --> 00:27:42,940
+بعد ما نستبدل
+
+246
+00:28:19,210 --> 00:28:23,750
+مرة تانية بقول يبقى لو كانت ال X أخدناها على
+
+247
+00:28:23,750 --> 00:28:28,530
+الفترة السالبة بشتغل كأنه أنا بشتغل على الموجبة و
+
+248
+00:28:28,530 --> 00:28:32,230
+في الآخر بس بشيل X و بحط مكانها absolute value ل X
+
+249
+00:28:32,230 --> 00:28:37,110
+بعد هيك الحلول بتاخد اللي هو أي شكل من الأشكال
+
+250
+00:28:37,110 --> 00:28:41,430
+التلاتة اللي عندنابعد ذلك لا يمكن أن تكون المعادلة
+
+251
+00:28:41,430 --> 00:28:45,650
+x تربيع y double prime يمكن أن تكون x ناقص ثلاثة
+
+252
+00:28:45,650 --> 00:28:49,410
+لكل تربيع y double prime و التانية مثلها يبقى على
+
+253
+00:28:49,410 --> 00:28:53,570
+الشكل المين على الشكل اللي عندنا هنا يبقى هاي
+
+254
+00:28:53,570 --> 00:28:56,650
+معادلة تربيع y double prime معادلة من الدرجة
+
+255
+00:28:56,650 --> 00:28:59,250
+الأولى y double prime في constant و constant في y
+
+256
+00:28:59,250 --> 00:29:04,570
+يبقى الشكل الحلبي ده نفسه ضلية y تساوي مش x plus r
+
+257
+00:29:05,080 --> 00:29:09,960
+بقول X ناقص ال X node اللي عندها ده كله to the
+
+258
+00:29:09,960 --> 00:29:14,560
+power R يبقى بفترض الحل على الشكل أن هذا بشتغط مرة
+
+259
+00:29:14,560 --> 00:29:18,760
+و مرتين و بروح بعوض في المعادلة لغاية بنحصل على
+
+260
+00:29:18,760 --> 00:29:22,940
+main على ال characteristic equation بروح بحل ال
+
+261
+00:29:22,940 --> 00:29:25,920
+characteristic equation و بجي بشوف هل ال real and
+
+262
+00:29:25,920 --> 00:29:29,240
+different هل ال real and repeated هل ال complex أي
+
+263
+00:29:29,240 --> 00:29:34,770
+واحدة بتطلع فيهم بقوله تمامأذا بشيل كل X موجودة
+
+264
+00:29:34,770 --> 00:29:39,910
+عند هنا و هحط بدل X ناقص ال X نور و يبقى كل شيء
+
+265
+00:29:39,910 --> 00:29:44,670
+كما هو واضح كلامنا طبعا هعطيكم مثال عملي الآن بعد
+
+266
+00:29:44,670 --> 00:29:52,390
+قليل على هذا الكلام حدا فيكم اي تساول هنا طالش
+
+267
+00:29:52,390 --> 00:29:59,570
+اللي شوية أمثلة يعني طيب نبدأ المثال الأولعندنا
+
+268
+00:29:59,570 --> 00:30:04,270
+مجموعة اللي بقى اسمها من الأمثلة تقول examples
+
+269
+00:30:04,270 --> 00:30:08,570
+determine
+
+270
+00:30:08,570 --> 00:30:20,530
+the general solution of
+
+271
+00:30:20,530 --> 00:30:23,810
+the
+
+272
+00:30:23,810 --> 00:30:27,870
+given differential equation of the
+
+273
+00:30:43,470 --> 00:30:55,130
+الحل هذا بيكون صحيح in any interval على أي فترة
+
+274
+00:31:13,070 --> 00:31:20,490
+أول سؤال هو السؤال الاطمعش من التمرينيقول الـ x
+
+275
+00:31:20,490 --> 00:31:30,170
+تربيع y double prime ناقص 4x في y prime زائد 4y
+
+276
+00:31:30,170 --> 00:31:35,810
+كلها بدأت تساوي 0 وهذه هي المعادلة رقم 1
+
+277
+00:32:24,750 --> 00:32:30,210
+يبقى فترة عندنا فترتين يا اما من ال zero اطالة يا
+
+278
+00:32:30,210 --> 00:32:31,070
+اما جاب ال main
+
+279
+00:32:38,250 --> 00:32:44,530
+أفرض X أكبر من 0 أفرض X أكبر من 0 أفرض X أكبر من 0
+
+280
+00:32:44,530 --> 00:32:50,070
+أفرض X أكبر من 0 أفرض X أكبر من 0 أفرض X أكبر من 0
+
+281
+00:32:50,070 --> 00:32:54,150
+أفرض X أكبر من 0 أفرض X أكبر من 0 أفرض X أكبر من 0
+
+282
+00:32:54,150 --> 00:33:00,490
+أفرض X أكبر من 0 أفرض X أكبر من 0 أفرض X أكبر من 0
+
+283
+00:33:00,490 --> 00:33:00,490
+أفرض X أكبر من 0 أفرض X أكبر من 0 أفرض X أكبر من 0
+
+284
+00:33:00,490 --> 00:33:00,490
+أفرض X أكبر من 0 أفرض X أكبر من 0 أفرض X أكبر من 0
+
+285
+00:33:00,490 --> 00:33:00,490
+أفرض X أكبر من 0 أفرض X أكبر من 0 أفرض X أكبر من 0
+
+286
+00:33:00,490 --> 00:33:00,490
+أفرض X أكبر من 0 أفرض X أكبر من 0 أفرض X أكبر من 0
+
+287
+00:33:00,490 --> 00:33:00,510
+أفرض X أكبر من
+
+288
+00:33:10,890 --> 00:33:18,330
+يبقى then y prime r x أس r ناقص واحد y w prime
+
+289
+00:33:18,330 --> 00:33:24,540
+يسوى r في r ناقص واحد في x أس r ناقص اتنينبناخد
+
+290
+00:33:24,540 --> 00:33:30,140
+المعلومات هذه ونعوضها في المعادلة رقم واحد يبقى
+
+291
+00:33:30,140 --> 00:33:40,580
+substitute in equation one we get نحصل على ما يأتي
+
+292
+00:33:40,580 --> 00:33:50,040
+هاي ال X تربية اللي براYW'RR-1XSR
+
+293
+00:33:50,040 --> 00:33:55,880
+-2-4XY
+
+294
+00:33:55,880 --> 00:33:59,860
+'RXSR
+
+295
+00:33:59,860 --> 00:34:06,040
+-1 4XSR0
+
+296
+00:34:08,980 --> 00:34:14,240
+مضاب اللي برا الجوس جوا الجوس يبقى R في R ناقص
+
+297
+00:34:14,240 --> 00:34:19,920
+واحد في X أُس R ناقص اتنين بيصير مع الاتنين اللي
+
+298
+00:34:19,920 --> 00:34:29,120
+برا بيصير X أُس R ناقص أربعة R X أُس R زائد أربعة
+
+299
+00:34:29,120 --> 00:34:36,190
+X أُس R تساوي Zeroنقسم كله على اكسوس R يبقى لو
+
+300
+00:34:36,190 --> 00:34:43,390
+قسمنا R في R ناقص واحد ناقص اربعة R زائد اربعة
+
+301
+00:34:43,390 --> 00:34:51,510
+تساوي Zero قبل ما اكمل لو جينا بنات قولنا افترض
+
+302
+00:34:51,510 --> 00:34:55,170
+الحل على الصيغة اللي عندنا وجيبنا المشتقة الأولى
+
+303
+00:34:55,170 --> 00:35:00,660
+وجيبنا المشتقة الثانيةوقلنا له substitute then the
+
+304
+00:35:00,660 --> 00:35:04,400
+characteristic equation is الشكل اللي عندنا هنا
+
+305
+00:35:04,400 --> 00:35:09,980
+فيه مشكلة؟ لأ أبنى طالع هذا بتطير ال X تربية والله
+
+306
+00:35:09,980 --> 00:35:14,080
+ده بتطير بصير R في R ناقص واحد بديجي مكانها هذه
+
+307
+00:35:14,080 --> 00:35:18,960
+بصير ناقص أربعة R هذه أربعة زي ما هي تساوي Zero
+
+308
+00:35:19,380 --> 00:35:23,720
+ببقى لإننا نرتب وضع مين المعادلة هذه لكن هذه اللي
+
+309
+00:35:23,720 --> 00:35:27,740
+بصير هي ال characteristic equation تمام؟ زي ما كنا
+
+310
+00:35:27,740 --> 00:35:30,800
+هناك نفرض كذا إذا ال characteristic equation كذا،
+
+311
+00:35:30,800 --> 00:35:37,060
+مصبوط؟ يبقى هنا بصير R في R ناقص واحد زائد Alpha R
+
+312
+00:35:37,060 --> 00:35:42,490
+زائد Beta كله بده يساوي مين؟ بده يساوي Zeroهذه ال
+
+313
+00:35:42,490 --> 00:35:47,570
+L لو جينا رتبناها، ايش بصير عندنا؟ R تربيع بصير
+
+314
+00:35:47,570 --> 00:35:57,030
+عندنا هنا ناقص R وناقص 4R ناقص 5R يبقى هاي ناقص 5R
+
+315
+00:35:57,030 --> 00:36:04,270
+زائد كده؟ زائد 4 كله يساوي 0أظن بنقدر نحلل هذه
+
+316
+00:36:04,270 --> 00:36:11,930
+كقوسين كتالي يساوي zero هذي R هذي R هذي واحد هذي
+
+317
+00:36:11,930 --> 00:36:18,570
+اربعة هذي ناقص هذي ناقص يبقى معنى هذا الكلام ان R
+
+318
+00:36:18,570 --> 00:36:24,770
+واحد تساوي واحد وR اتنين يساوي قداشر اربعة يبقى
+
+319
+00:36:24,770 --> 00:36:31,090
+two real and different roots مظبوط اليمينالحالة
+
+320
+00:36:31,090 --> 00:36:35,890
+الأولى يبقى بناء عليه بصير ال general solution
+
+321
+00:36:35,890 --> 00:36:47,190
+يبقى the general solution is y تساوي c واحد في x
+
+322
+00:36:47,190 --> 00:36:52,870
+بس ايش بدي احطها absolute value of x بتنفع للي
+
+323
+00:36:52,870 --> 00:36:59,780
+اكبر من zero ولي اقل من zero أس قداش أس واحدزائد
+
+324
+00:36:59,780 --> 00:37:06,680
+C2 absolute value of X أُس كده؟ أُس أربعة يبقى هذا
+
+325
+00:37:06,680 --> 00:37:12,760
+هو ال general solution للمعادلة التفاضلية التكتيكي
+
+326
+00:37:12,760 --> 00:37:18,400
+اللي تبقى بدك تتبعيه مع كل معادلة بعد ذلك بنفس
+
+327
+00:37:18,400 --> 00:37:21,140
+الطريقة السؤال الثاني
+
+328
+00:37:23,850 --> 00:37:30,350
+الو سؤال ستة من الكتاب بقول X ناقص واحد لكل ترابيع
+
+329
+00:37:30,350 --> 00:37:37,990
+في ال Y double prime زائد تمانية في ال X ناقص واحد
+
+330
+00:37:37,990 --> 00:37:46,510
+prime زائد اتناشر Y يساوي Zero هذه هي المعادلة رقم
+
+331
+00:37:46,510 --> 00:37:51,110
+واحد و بدنا نحلها خليني
+
+332
+00:37:51,110 --> 00:37:55,860
+أسهل السؤال التاليالحين هذه ابنات لو قلت زي هيك
+
+333
+00:37:55,860 --> 00:38:00,460
+هدف Zero مش موجود وضلت المعادلة بالشكل هذا هذه
+
+334
+00:38:00,460 --> 00:38:07,220
+معادلة Euler ولا مياشي Euler Euler
+
+335
+00:38:07,220 --> 00:38:12,180
+ولا لا؟أولار ليش نجلة Alpha و Beta constants ولم
+
+336
+00:38:12,180 --> 00:38:17,120
+يحددهم هل بأسفار و لا غير الأسفار يعني لو كان عندي
+
+337
+00:38:17,120 --> 00:38:21,540
+ترمين بس المعامل هذا بدي يكون هذا بالضبط هذا تربية
+
+338
+00:38:21,540 --> 00:38:26,760
+و هذا من وين من الدرجة الأولى طب لو قلت هذا هيك
+
+339
+00:38:26,760 --> 00:38:32,380
+هذه أولار لأ مش أولار لازم يكون هذه تربية حتى تبقى
+
+340
+00:38:32,380 --> 00:38:37,340
+أولار طيب ده أسأل كمان مرة لو الترمين الأثنين هدول
+
+341
+00:38:37,340 --> 00:38:42,960
+طارواو بس ضلت هذه العالة boiler على طول الخط طبعا
+
+342
+00:38:42,960 --> 00:38:46,800
+يعني ليس بالضرورة أن كل مقادير التلاتة موجودة لأن
+
+343
+00:38:46,800 --> 00:38:50,900
+ال alphabet أقل ال constants ولم يحدد أصفرهم يعني
+
+344
+00:38:50,900 --> 00:38:55,120
+لو كانوا أصفر ماشي مش أصفر ماشي، كويس؟ يبقى أنا
+
+345
+00:38:55,120 --> 00:38:58,600
+عندي question بالشكل .. أه هذه اللي قلنا عليها قبل
+
+346
+00:38:58,600 --> 00:39:04,120
+قليل special case، طبعا السؤال هو وين ال singular
+
+347
+00:39:04,120 --> 00:39:10,890
+point؟يعني انقسمت الـ real line إلى فترتين، من أين
+
+348
+00:39:10,890 --> 00:39:17,810
+إلى أين؟ من سالب infinity لغاية ومن الواحد مش عند
+
+349
+00:39:17,810 --> 00:39:25,390
+ال zero تمام؟ يبقى باجي بقوله solution يبقى
+
+350
+00:39:25,390 --> 00:39:32,470
+باجي بقوله ال X سوى واحد is a singular point
+
+351
+00:39:34,560 --> 00:39:38,480
+ما دام singular point يبقى انا بدي اخد x اكبر من
+
+352
+00:39:38,480 --> 00:39:43,860
+ال zero والله اكبر من ال واحد اكبر من ال واحد مش
+
+353
+00:39:43,860 --> 00:39:49,960
+من ال zero يبقى باجي بقوله هنا بدي اخد لو كانت ال
+
+354
+00:39:49,960 --> 00:39:57,580
+x اكبر من ال واحد افترض ان y يسوى x وصر
+
+355
+00:40:01,810 --> 00:40:12,230
+يبقى انا بدك تقولي X ماقص واحد كله أس R تمام زي
+
+356
+00:40:12,230 --> 00:40:17,090
+مين زي هدا بالضبط تمام طب لو كانت زائد بده اقوله
+
+357
+00:40:17,090 --> 00:40:22,590
+هنا X زائد واحد أس R على طول الخط يبقى Y تساوي X ر
+
+358
+00:40:22,590 --> 00:40:29,310
+با solution of the
+
+359
+00:40:31,380 --> 00:40:38,280
+differential equation one then اعمل الخطوات هذه و
+
+360
+00:40:38,280 --> 00:40:40,960
+الله اقول ال characteristic equation دوري زي ما هي
+
+361
+00:40:40,960 --> 00:40:48,180
+هنا هيطلع عندك x ناقص واحد أس R هنا x ناقص واحد أس
+
+362
+00:40:48,180 --> 00:40:52,580
+R هنا x ناقص واحد أس R يبقى بقسم عليها وبالتالي
+
+363
+00:40:52,580 --> 00:40:57,200
+ايه بصير معنا مشكلة في هذه الحالة يبقى بقدر اجيب
+
+364
+00:40:57,200 --> 00:41:00,710
+له من ال characteristic equation دورييبقى باجي
+
+365
+00:41:00,710 --> 00:41:11,290
+بقوله then the characteristic equation is R في R
+
+366
+00:41:11,290 --> 00:41:16,730
+ناقص واحد نرجع للمعادلة تانية خلصنا من هنا يبقى
+
+367
+00:41:16,730 --> 00:41:24,030
+زائد تمانية R وهنا زائد اتناشر يساوي كده؟ يساوي
+
+368
+00:41:24,030 --> 00:41:30,690
+Zeroيبقى بيصير R في R في R تربيع ناقص R وزائد
+
+369
+00:41:30,690 --> 00:41:37,610
+تمانية R بظهر قدر؟ سبعة R يبقى زائد سبعة R زائد
+
+370
+00:41:37,610 --> 00:41:44,030
+اتناشر يساوي Zero هذه لو روحت حللتها بيصير X زائد
+
+371
+00:41:44,030 --> 00:41:49,250
+تلاتة في X زائد اربعة يساوي Zero تلاتة في اربعة
+
+372
+00:41:49,250 --> 00:41:53,990
+عليهم اتناشر وتلاتة X واربعة X اللي هي مين؟ سبعة X
+
+373
+00:41:54,190 --> 00:42:00,710
+يبقى بناء عليه ال X بدأ تساوي سالب تلاتة وهي أقصد
+
+374
+00:42:00,710 --> 00:42:08,430
+ال R يا بنات مش X R زائد تلاتة وR زائد أربعة يبقى
+
+375
+00:42:08,430 --> 00:42:14,970
+R تساوي سالب تلاتة وR تساوي من اللي هو سالب أربعة
+
+376
+00:42:14,970 --> 00:42:19,590
+يبقى ال general solution سيكون على الشكل التالي
+
+377
+00:42:19,590 --> 00:42:21,110
+يبقى ذا
+
+378
+00:42:35,720 --> 00:42:45,420
+على فرض الحل X ناقص واحد اس Rيبقى c1 في ال x ناقص
+
+379
+00:42:45,420 --> 00:42:51,400
+واحد أس ناقص تلاتة و بدي أخدله من ال absolute
+
+380
+00:42:51,400 --> 00:42:58,400
+value بالشكل اللي عندنا هذا زائد c2 absolute value
+
+381
+00:42:58,400 --> 00:43:05,480
+لل x ناقص واحد كله أس قدر أس ناقص أربعةيبقى هذا
+
+382
+00:43:05,480 --> 00:43:10,160
+شكل ال general solution لمين للمعادلة التفاضلية
+
+383
+00:43:10,160 --> 00:43:15,480
+اللي هي رقم واحد لكن لو كان يعطيني فترة باقتصر
+
+384
+00:43:15,480 --> 00:43:21,660
+الحل اللي عندي على الفترة المعطاة ناخد كمان مثال
+
+385
+00:43:21,660 --> 00:43:27,700
+تلاتة تلاتة
+
+386
+00:43:27,700 --> 00:43:36,850
+بقول solveذا ال initial value problem اللي هو x
+
+387
+00:43:36,850 --> 00:43:42,810
+تربيع في ال y double prime ناقص تلاتة x في ال y
+
+388
+00:43:42,810 --> 00:43:51,050
+prime زائد أربعة y تساوي zeroو ال y عند السلب واحد
+
+389
+00:43:51,050 --> 00:43:56,490
+يسوي كده؟ يسوي اتنين و ال y prime عند السلب واحد
+
+390
+00:43:56,490 --> 00:44:02,930
+يسوي كده؟ يسوي تلاتة واعتبر هذه المثلة رقم واحد
+
+391
+00:44:02,930 --> 00:44:08,750
+كويس
+
+392
+00:44:08,750 --> 00:44:14,850
+يبقى هذه المثلة قدامنا بالشكل اللي عندنا هذابنجي
+
+393
+00:44:14,850 --> 00:44:22,130
+نحل المثال واضح انه اكس تساوي زيرو هو عبارة عن
+
+394
+00:44:22,130 --> 00:44:28,770
+singular point يبقى هنا الاكس تساوي زيرو is a
+
+395
+00:44:28,770 --> 00:44:35,790
+singular point تمام
+
+396
+00:44:35,790 --> 00:44:42,530
+اتمام؟ما دام singular point يبقى انجسمت الفترة من
+
+397
+00:44:42,530 --> 00:44:47,090
+zero لغاية infinity او من zero لغاية سالب infinity
+
+398
+00:44:47,090 --> 00:44:52,470
+وما جاليش وين لكن انا بقدر احدد ما دام initial
+
+399
+00:44:52,470 --> 00:44:58,750
+value problem النقطة وين سالب واحد سالب واحد يبقى
+
+400
+00:44:58,750 --> 00:45:02,390
+معناه اتاخد وين الفترة اللى علي الشمال مش الفترة
+
+401
+00:45:02,390 --> 00:45:10,010
+اللى علي اليمين يبقى عندنا x اقل من 100يبقى هنا
+
+402
+00:45:10,010 --> 00:45:16,090
+since the
+
+403
+00:45:16,090 --> 00:45:20,490
+initial point
+
+404
+00:45:21,730 --> 00:45:28,170
+النقطة الابتدائية EX يساوي سالب واحد موجودة في
+
+405
+00:45:28,170 --> 00:45:36,530
+الفترة من سالب infinity لغاية Zero و X
+
+406
+00:45:36,530 --> 00:45:42,910
+أقل من Zero كويس
+
+407
+00:45:42,910 --> 00:45:50,240
+يبقى بنفع افترض ان الحل Y تساوي X أسارلأ هتقولي
+
+408
+00:45:50,240 --> 00:46:14,440
+absolute value لمن لل X أُس R يبقى
+
+409
+00:46:14,440 --> 00:46:22,740
+باجي بقوله هناطبعا x اساوي زيرو هي ال singular
+
+410
+00:46:22,740 --> 00:46:30,860
+point يبقى باجي بقوله let y تساوي x أس ا ر be a
+
+411
+00:46:30,860 --> 00:46:40,080
+solution of the differential equationولكن بدي أفهم
+
+412
+00:46:40,080 --> 00:46:44,760
+إن X هذه سالبة، صحيح؟ يعني في الجهة الوين؟ في
+
+413
+00:46:44,760 --> 00:46:47,880
+الجهة الشمال، إذا بدي أمشيها زي ما هي و في الآخر
+
+414
+00:46:47,880 --> 00:46:51,260
+بدي أحط مين؟ أبسطي بدي أمشي بخاطر، بدي أحطها
+
+415
+00:46:51,260 --> 00:46:59,210
+إجباري غصب عني، تمام؟ طيب تعالى نشوف يبقى thenThe
+
+416
+00:46:59,210 --> 00:47:08,430
+characteristic equation is R في R ناقص واحد ايش
+
+417
+00:47:08,430 --> 00:47:17,830
+عندي هنا ناقص تلاتة R زائد اربعة تساوي زيروالان
+
+418
+00:47:17,830 --> 00:47:24,250
+صار عندنا R تربيع ناقص R و ناقص تلاتة R ناقص أربعة
+
+419
+00:47:24,250 --> 00:47:32,010
+R زائد أربعة تساوي كم؟ Zero هذا معناه ايه؟ ان ال R
+
+420
+00:47:32,010 --> 00:47:38,380
+ناقص اتنين لكل تربيع يسوى مين؟زيرو يبقى really
+
+421
+00:47:38,380 --> 00:47:45,020
+repeated roots يبقى هذا معناه ان R واحد تسوي R
+
+422
+00:47:45,020 --> 00:47:54,340
+اتنين تسوي كده يبقى صار ده general solution
+
+423
+00:47:54,340 --> 00:48:05,780
+of equation one is Y يسوى C واحد زائد C اتنين لان
+
+424
+00:48:06,860 --> 00:48:13,780
+أبسلوت فاليو ل X في قلت X تربية والله أبسلوت فاليو
+
+425
+00:48:13,780 --> 00:48:18,550
+ل X تربية ليه اتنين اربع سيم لان كميةمربع مصبور
+
+426
+00:48:18,550 --> 00:48:22,690
+يبقى صار الحل على الشكل اللي ان انا يبقى انا عندي
+
+427
+00:48:22,690 --> 00:48:28,930
+حلين الحل الأولاني هو X تربية والحل الثاني هو X
+
+428
+00:48:28,930 --> 00:48:36,030
+تربية في ال absolute value ل X تمام طيب قال لي في
+
+429
+00:48:36,030 --> 00:48:41,860
+عندك two initial conditions يبقى بدي احاولأستخدم
+
+430
+00:48:41,860 --> 00:48:49,280
+ال two initial conditions للحلول للحصول على C1 وC2
+
+431
+00:48:49,280 --> 00:48:58,980
+يبقى أي Y C1 X تربية C2 X تربية لين absolute value
+
+432
+00:48:58,980 --> 00:49:04,720
+ل X خلّيني أجيب المشتقة مشان أروح أنعوضيبقى
+
+433
+00:49:04,720 --> 00:49:12,040
+بالداجي لل Y' يساوي 2C1X
+
+434
+00:49:12,040 --> 00:49:18,440
+زائد 2C2X
+
+435
+00:49:18,440 --> 00:49:26,950
+لل absolute value X هذا مشتقة الأول في الثانيسي
+
+436
+00:49:26,950 --> 00:49:34,230
+اتنين اكس تربية في مشتقة لن absolute value ل X انا
+
+437
+00:49:34,230 --> 00:49:41,370
+ازعم انها واحد على X فقط لغير بدون absolute طبعا
+
+438
+00:49:41,370 --> 00:49:44,690
+هوريكوا ياها طبعا اخدناها في كلكلاص بيه بس بدها
+
+439
+00:49:44,690 --> 00:49:48,490
+تذكر بها تذكر بس خليني ارتبها وبعدين بتبينلكوا
+
+440
+00:49:48,490 --> 00:49:49,970
+ياها يبقى اتنين
+
+441
+00:50:00,770 --> 00:50:06,910
+تعالوا في الهامش نبينكم كيف مشتقة لن absolute
+
+442
+00:50:06,910 --> 00:50:14,670
+value ل X احنا بنات عندنا D على DX ل لن X سالب و
+
+443
+00:50:14,670 --> 00:50:47,790
+الله موجباهلأ X يجب أن نختار X أقل من Zero سالب
+
+444
+00:50:47,890 --> 00:50:53,210
+يبقى هاي المشتقة زي قلتلكوا الزعم و أثبت انه فعلا
+
+445
+00:50:53,210 --> 00:50:56,810
+مشتقة تواعى على ال X يبقى صارت بالشكل اللي عندنا
+
+446
+00:50:56,810 --> 00:51:02,770
+هذا بدأجي لل initial condition الأول جالي Y عند
+
+447
+00:51:02,770 --> 00:51:07,970
+سالب واحد يساوي اتنين اذا انا هشيل ال Y و احط مكان
+
+448
+00:51:07,970 --> 00:51:16,940
+اقدر اتنينوشيل كل X وحط مكانها سالب واحد يبقى C1
+
+449
+00:51:16,940 --> 00:51:24,620
+في سالب واحد الكل تاربيع نجي هنا لن لسالب واحد
+
+450
+00:51:24,620 --> 00:51:29,560
+يعني لن الواحد لن الواحد في Zero مع السلامة يبقى
+
+451
+00:51:29,560 --> 00:51:35,820
+زائد Zero هذا بدي يعطيك ان C1 يسوى كده؟ يسوى اتنين
+
+452
+00:51:36,360 --> 00:51:39,880
+بنجي ال condition التاني يقل ال y prime عند السلب
+
+453
+00:51:39,880 --> 00:51:45,160
+واحد يساوي تلاتة ال y prime عند السلب واحد يساوي
+
+454
+00:51:45,160 --> 00:51:50,240
+تلاتة يساوي تلاتة نجي نشوف هذا شو بده يعطينا
+
+455
+00:51:50,240 --> 00:51:54,880
+طلعيني ليه كويس هنابدي اجي ال wire prime هي wire
+
+456
+00:51:54,880 --> 00:52:02,400
+prime يبقى هاي ثلاثة بده يساوي اتنين C واحد في مين
+
+457
+00:52:02,400 --> 00:52:10,880
+في سالب واحد تمام نيجي هنا هذا Zero يبقى زائد Zero
+
+458
+00:52:10,880 --> 00:52:18,980
+خلصنا منه ضل عنا زائد C اتنين في سالب واحديبقى
+
+459
+00:52:18,980 --> 00:52:26,260
+النتيجة تلاتة تساوي سالب اتنين C واحد و سالب C
+
+460
+00:52:26,260 --> 00:52:32,480
+اتنين C واحد بقدراش باتنين يبقى هذا بدري اعطيكوا
+
+461
+00:52:32,480 --> 00:52:42,490
+انه تلاتةتساوي سالب اربعة تساوي
+
+462
+00:52:42,490 --> 00:52:54,950
+سالب
+
+463
+00:52:54,950 --> 00:53:02,090
+اربعة تساويزاد اربعة و تلاتة سبعة يبقى C2 تساوي
+
+464
+00:53:02,090 --> 00:53:10,670
+سالب سبعة يبقى هذه سالب سبعة تمام هذا شكل C2 يبقى
+
+465
+00:53:10,670 --> 00:53:15,050
+بناء عليه ال solution هيكون عالمين على الشكل
+
+466
+00:53:15,050 --> 00:53:19,130
+التالي يبقى بقى دي بقول له ده solution
+
+467
+00:53:21,500 --> 00:53:31,780
+Y تساوي C1 ب2 يبقى 2X تربيع C2 بسالب سبعة يبقى
+
+468
+00:53:31,780 --> 00:53:38,960
+سالب سبعة X تربيع لين absolute value ل X هذه يا
+
+469
+00:53:38,960 --> 00:53:42,680
+بنات التربيع حاطيت ال absolute والله خلتيه بتفرجش
+
+470
+00:53:42,680 --> 00:53:47,390
+عنها لإنه كميةمربعة فهي دائما و أبدا موجبة سواء
+
+471
+00:53:47,390 --> 00:54:07,450
+كانت ال X موجبة أو سالبة طيب
+
+472
+00:54:07,450 --> 00:54:14,090
+كان هذا هو المثال رقم 3 له سؤال 15 من الكتابمثال
+
+473
+00:54:14,090 --> 00:54:21,290
+رقم أربعة له سؤال عشرة من الكتاب بيقول ال X ناقص
+
+474
+00:54:21,290 --> 00:54:28,710
+اتنين الكل تربية في ال Y W prime زائد خمسة في ال X
+
+475
+00:54:28,710 --> 00:54:35,390
+ناقص اتنين في ال Y prime زائد تمانية Y يساوي Zero
+
+476
+00:54:35,390 --> 00:54:42,810
+هذه هي المعادلة رقم واحد قدش ال singular point؟
+
+477
+00:54:43,280 --> 00:54:49,300
+يبقى X يساوي اتنين يبقى solution يبقى
+
+478
+00:54:49,300 --> 00:55:01,560
+X يساوي اتنين is a singular point تمام؟ إذا الحل
+
+479
+00:55:01,560 --> 00:55:05,840
+اللي عندي بده أفضل على الشكل التالي يبقى باجي بقول
+
+480
+00:55:05,840 --> 00:55:15,480
+له letمن Y تساوي X ناقص اتنين to the power R بيه
+
+481
+00:55:15,480 --> 00:55:26,000
+solution of equation one then the characteristic
+
+482
+00:55:26,000 --> 00:55:31,200
+equation is R
+
+483
+00:55:32,270 --> 00:55:39,950
+ار ناقص واحد زائد خمسة ار زائد تمانية يساوي كم؟
+
+484
+00:55:39,950 --> 00:55:46,430
+يساوي Zero هذه يا بنات بصير R تربيع وعندك ناقص R
+
+485
+00:55:46,430 --> 00:55:53,370
+زائد خمسة ار مضال زائد كم؟ اربع ار زائد تمانية
+
+486
+00:55:53,370 --> 00:56:00,810
+يساوي Zero هل بنقدر نحلها هذه بالاقواز؟ مش امكانية
+
+487
+00:56:01,730 --> 00:56:06,470
+مش ممكنية على الإطلاق إذا مدى حلها بمين؟ بالقانون
+
+488
+00:56:06,470 --> 00:56:14,090
+العام يبقى R يساوي ناقص با زائد أو ناقص الجذر
+
+489
+00:56:14,090 --> 00:56:20,390
+التربيع إلى با تربيع ناقص أربع ألف اللي هي بواحد
+
+490
+00:56:20,390 --> 00:56:27,410
+جيم اللي هي بتمانية كله على اتنين في واحدهذا
+
+491
+00:56:27,410 --> 00:56:32,750
+الكلام يساوي ناقص اربعة زايد او ناقص اربعة في
+
+492
+00:56:32,750 --> 00:56:38,210
+تمانية باتنين و تلاتين شيله منهم ستاشر بستاشر
+
+493
+00:56:38,210 --> 00:56:45,070
+سالبة تحت الجدر تطلع بزايد او ناقص اربعة اي كله
+
+494
+00:56:45,070 --> 00:56:51,590
+على اتنين يبقى ناقص اتنين زايد او ناقص اتنين اي
+
+495
+00:56:51,590 --> 00:56:55,090
+يبقى بناء ان عليه قداش لانده يا بنات
+
+496
+00:57:00,600 --> 00:57:06,420
+يبقى الشكل الحل بيكون على الشكل التالي the
+
+497
+00:57:06,420 --> 00:57:14,060
+solution of question one is
+
+498
+00:57:36,370 --> 00:57:41,640
+طب لو شلت ال absolute value فيه مشكلة هنا؟لأ لإن
+
+499
+00:57:41,640 --> 00:57:45,320
+هذا باعتبارها واحد ع الاكس نقص اتنين كل تربية كمية
+
+500
+00:57:45,320 --> 00:57:49,160
+هي موجبة كتبتها والله شيلتها هنا مابتفرقش عندها
+
+501
+00:57:49,160 --> 00:57:55,900
+خليها مش مشكلة طيب يبقى هذا X أُس لامدة في C واحد
+
+502
+00:57:55,900 --> 00:58:04,560
+في cosine لميو لميو بقدراشباتنين يبقى اتنين لين
+
+503
+00:58:04,560 --> 00:58:14,360
+absolute value ل X زائد C اتنين صين اتنين لين
+
+504
+00:58:14,360 --> 00:58:21,120
+absolute value ل X كيف؟
+
+505
+00:58:21,120 --> 00:58:27,560
+اه X نقص اتنين مظبوط أصابة امرأة و أختها عمريبقى
+
+506
+00:58:27,560 --> 00:58:38,760
+هذه absolute value ل x ناقص اتنين زائد c2 sin a2 ل
+
+507
+00:58:38,760 --> 00:58:44,260
+absolute value ل x ناقص اتنين بالشكل اللي عندنا
+
+508
+00:58:44,260 --> 00:58:50,430
+هناإذا أعطينا مثلة على الحالة الأولى لو كان ال
+
+509
+00:58:50,430 --> 00:58:54,810
+roots real and different وعطينا مثال على الحالة
+
+510
+00:58:54,810 --> 00:58:58,230
+الثانية لو كان ال roots real and repeated وعطينا
+
+511
+00:58:58,230 --> 00:59:02,190
+مثال على الحالة الثالثة لو كان ال roots are
+
+512
+00:59:02,190 --> 00:59:09,910
+complex طيب نواصل برضه في نفس الموضوع وإلى يكون
+
+513
+00:59:09,910 --> 00:59:16,790
+المثال التالي وبدنا نشوف شو رأيكوا فيهانتوا
+
+514
+00:59:16,790 --> 00:59:24,410
+بتلاحظوا ان كل أسئلتنا حتى هذه اللحظة مالها كل طرف
+
+515
+00:59:24,410 --> 00:59:29,270
+اليمين zero يعنياش homogeneous differential
+
+516
+00:59:29,270 --> 00:59:33,050
+equation طيب لو بطلت الصير homogeneous
+
+517
+00:59:33,050 --> 00:59:37,170
+differential equation كيف بدنا نسويه؟ يبقى مثال
+
+518
+00:59:37,170 --> 00:59:43,400
+خمسة اللي بيجي زيه في الامتحاناتبقول Solve يعني
+
+519
+00:59:43,400 --> 00:59:47,380
+إذا بنجيبكوا على Euler تبقى هذا السؤال هدية مباشرة
+
+520
+00:59:47,380 --> 00:59:51,900
+لكن ممكن أجيبه على Euler مع شغل تاني أصيد عصفرين
+
+521
+00:59:51,900 --> 00:59:59,320
+بحجرين واحد بقول Solve the differential equation
+
+522
+00:59:59,320 --> 01:00:04,420
+حل المعادلة التفاضليةاللي هي ال X في ال Y double
+
+523
+01:00:04,420 --> 01:00:13,400
+prime زائد Y prime يساوى اتناشر لإن ال X على X وال
+
+524
+01:00:13,400 --> 01:00:18,860
+X greater than zero وهذا نسميها اللي هي المعادلة
+
+525
+01:00:18,860 --> 01:00:24,220
+رقم واحد حد
+
+526
+01:00:24,220 --> 01:00:30,120
+بده ال channel على اليمين ضايلة هذه؟ خلاص نمسح؟
+
+527
+01:00:30,120 --> 01:00:30,780
+ماشي
+
+528
+01:00:45,180 --> 01:00:48,280
+نرجع لسؤالنا اللى قدامنا هذا بقول solve the
+
+529
+01:00:48,280 --> 01:00:51,220
+differential equation وعطانى معادلة بالشكل هذا و
+
+530
+01:00:51,220 --> 01:00:57,720
+سكت ماقالليش ولا حل و بس و انت حر باجيب القلانة x
+
+531
+01:00:57,720 --> 01:01:03,420
+y double prime طب هدى مش Euler واحنا بنعرف انه لما
+
+532
+01:01:03,420 --> 01:01:08,180
+تبقى المعادلة المعاملات
+
+533
+01:01:08,180 --> 01:01:12,380
+متغيرات بده يعطينى أحد الحلول وانا بجيب الحل
+
+534
+01:01:12,380 --> 01:01:16,230
+التانى بال reduction of orderمظبوط، لكن بنقوله
+
+535
+01:01:16,230 --> 01:01:22,970
+بسيطة جدا، روحه ضرب لكله في X، تمام؟ إذا لو ضربت
+
+536
+01:01:22,970 --> 01:01:28,770
+في X، بصير المعادلة X تربيه و Y double prime زائد
+
+537
+01:01:28,770 --> 01:01:35,050
+X في Y prime يسوا اتناشر لإن ال X، صحيح ولا لا؟
+
+538
+01:01:35,050 --> 01:01:40,750
+يبقى هذه شو اسمها؟Homogeneous ولا Non-homogeneous؟
+
+539
+01:01:40,750 --> 01:01:44,870
+Non-homogeneous differential equation لإن الطرف
+
+540
+01:01:44,870 --> 01:01:48,430
+اليمين صار فيه function ما هوش ال zero طب مادام
+
+541
+01:01:48,430 --> 01:01:52,890
+non-homogeneous أنا تعلمت قبل هيك من chapter تلاتة
+
+542
+01:01:52,890 --> 01:01:57,050
+حل ال non-homogeneous بطريقتين يا إما ال
+
+543
+01:01:57,050 --> 01:02:00,550
+undetermined coefficients يا إما ال variations of
+
+544
+01:02:00,550 --> 01:02:05,800
+parameters مظبوط؟أذا بدي ألجأ إلى إحدى الطريقتين
+
+545
+01:02:05,800 --> 01:02:10,780
+لحل المعادلة إذا هجز المعادلة إلى homogeneous وإلى
+
+546
+01:02:10,780 --> 01:02:14,880
+non homogeneous بدي أجي أقول لو افترض هذا zero
+
+547
+01:02:14,880 --> 01:02:19,780
+بتظل المعادلة هذه، مين هي هذه؟ Euler ولا لا؟ رغم
+
+548
+01:02:19,780 --> 01:02:23,840
+أن ال term التالف طائر، مش موجود، إذا هذه ما لها؟
+
+549
+01:02:23,840 --> 01:02:28,560
+Euler equation مدام Euler equation بفترض إن الحل
+
+550
+01:02:28,560 --> 01:02:29,500
+على الصيغة
+
+551
+01:02:41,450 --> 01:02:54,170
+يبقى الـ x يساوي 0 is a singular point for the
+
+552
+01:02:54,170 --> 01:03:00,910
+differentialEquation x تربية y double a prime زائد
+
+553
+01:03:00,910 --> 01:03:06,830
+x y prime يساوي zero يعني ال mainly ال homogenous
+
+554
+01:03:06,830 --> 01:03:18,620
+مش ال non homogenousإذا بناء عليه بقوله let Y
+
+555
+01:03:18,620 --> 01:03:25,600
+تساوي X أس آر بحطش absolute لإن هو X greater than
+
+556
+01:03:25,600 --> 01:03:31,280
+0طبعا لو ماقلش x greater than zero أنا بستنتجها
+
+557
+01:03:31,280 --> 01:03:36,600
+لحالي ليش ان ال len مش معرف إلا لقيمة موجبة إذا لا
+
+558
+01:03:36,600 --> 01:03:41,780
+يمكن x أن تكون zero ولا حتى قيمة سالبة طبعا يبقى
+
+559
+01:03:41,780 --> 01:03:51,160
+باجي بقول y تسوي x أصار بي اي solution of the
+
+560
+01:03:51,160 --> 01:03:58,100
+differential equation one والأتنينتنين وين اتنين
+
+561
+01:03:58,100 --> 01:04:02,880
+هي اتنين يبقى لل homogenous مش لل non homogenous
+
+562
+01:04:02,880 --> 01:04:15,040
+يبقى then the characteristic equation is R في R
+
+563
+01:04:15,040 --> 01:04:22,380
+ناقص واحد زائد R كله بده يسوي zeroماعنديش ال term
+
+564
+01:04:22,380 --> 01:04:28,380
+التالث طب هدى R تربية ناقص R وزائد R مع السلامة
+
+565
+01:04:28,380 --> 01:04:34,700
+يبقى دهش بيعطيني R تربية بديه ساوي قداش أكم حل إيه
+
+566
+01:04:34,700 --> 01:04:41,340
+المعادلة هدى حلين وكل واحد فيهم بديه ساوي zero
+
+567
+01:04:41,340 --> 01:04:46,120
+يعني ال real repeated roots يبقى هدى بديه يعطينا
+
+568
+01:04:46,120 --> 01:04:51,870
+ورا واحد بديه ساوي R اتنين بديه ساوي zeroبناء عليه
+
+569
+01:04:51,870 --> 01:05:03,930
+solution yc حل الهوموجينيه بده يساوي c1 زائد c2
+
+570
+01:05:03,930 --> 01:05:11,970
+لإن ال x في اكتر من هيك في x أُس 0 بالطيارة اللي
+
+571
+01:05:11,970 --> 01:05:18,910
+بواحد يبقى هذا بس شكل الحل بار الباقي يبقى هي حلنا
+
+572
+01:05:18,910 --> 01:05:25,140
+مين؟الهوموجينس بدي جي لمين؟ لأ non homogeneous بطل
+
+573
+01:05:25,140 --> 01:05:28,560
+على ال non homogeneous يبقى هي ال non homogeneous
+
+574
+01:05:28,560 --> 01:05:34,460
+بقدر أحلها بال undetermined coefficients لإن انا
+
+575
+01:05:34,460 --> 01:05:39,640
+عندي شرطين ولا واحد الحمد لله اتحققالمعاملات ما
+
+576
+01:05:39,640 --> 01:05:46,200
+هيش توابط اتنين هذه ليست على اي شكل من الجدول يبقى
+
+577
+01:05:46,200 --> 01:05:51,300
+اصلا اللي ماضلش قدامي الا طريق واحد اللي همين ال
+
+578
+01:05:51,300 --> 01:05:54,680
+variation of parameter مش انا حل بال variation of
+
+579
+01:05:54,680 --> 01:06:00,910
+parameterبدي أروح أحط المعادلة هذه في شكل جديد
+
+580
+01:06:00,910 --> 01:06:06,010
+يبقى المعادلة واحدة هذه ضلت زي ما هي واحد ماتغيرتش
+
+581
+01:06:06,010 --> 01:06:10,990
+بس ضربت في X يبقى المعادلة هتروح أجسم على مين على
+
+582
+01:06:10,990 --> 01:06:16,490
+X تربية كويس يبقى باجي بقوله the differential
+
+583
+01:06:36,730 --> 01:06:41,470
+يبقى هذه اللي صار شكلها g of x يا بنات مش هذه اللي
+
+584
+01:06:41,470 --> 01:06:46,960
+فوقو دي ربالكوا يعني خلينا متواضعين الربع فيكوا هو
+
+585
+01:06:46,960 --> 01:06:50,660
+بيغلطوا في عين سيقسم عليها و يوحي يحط لها دي
+
+586
+01:06:50,660 --> 01:06:55,000
+GeoVex و تيجي تعاقبس و ماتقدرش تحل ايه المثل بسبب
+
+587
+01:06:55,000 --> 01:06:59,820
+خطأ انه الناس يتقسم علي مين؟ علي X تربية طيب انا
+
+588
+01:06:59,820 --> 01:07:04,360
+مشان استخدم ال variation of parameters بلزمني
+
+589
+01:07:04,360 --> 01:07:10,990
+الرنسكين تبعي الحالين قداش الحل الأول هناوالحل
+
+590
+01:07:10,990 --> 01:07:15,790
+التاني، إذا بدي أجيب الرونسك، انقلهم لهم، لازمني
+
+591
+01:07:16,250 --> 01:07:20,770
+يبقى باجي بيقوله هنا بدي أجيب له ال رونسكين as a
+
+592
+01:07:20,770 --> 01:07:26,050
+function of X بقول الحل الأول واحد والحل التاني
+
+593
+01:07:26,050 --> 01:07:31,630
+لإن ال X مشتقة ال واحد ب Zero ومشتقة لإن ال X
+
+594
+01:07:31,630 --> 01:07:40,130
+بواحد على X الرئيسي ناقصي الثانوي يبقى بقداش واحد
+
+595
+01:07:40,130 --> 01:07:46,260
+على X فقط لا غير يبقى جيبنا قيمة من ال رونسكينيبقى
+
+596
+01:07:46,260 --> 01:07:53,940
+باجي بقول by the variation
+
+597
+01:07:53,940 --> 01:07:58,360
+of
+
+598
+01:07:58,360 --> 01:08:05,260
+parameters method
+
+599
+01:08:05,260 --> 01:08:08,400
+we
+
+600
+01:08:08,400 --> 01:08:13,740
+get the particular
+
+601
+01:08:22,730 --> 01:08:34,450
+Solution of equation one in the form في الشكل
+
+602
+01:08:34,450 --> 01:08:37,850
+capital Y of X
+
+603
+01:08:45,880 --> 01:08:54,580
+وحط مكانها U1 of X U1 of X ده شيل ال C2 وحط بدالها
+
+604
+01:08:54,580 --> 01:09:02,660
+U2 of X في من؟ في لن ال X where حيثه بدنا نيجي
+
+605
+01:09:02,660 --> 01:09:13,810
+نجيب U1 of X لسالب تكامل Y2الـ G of X على الـ
+
+606
+01:09:13,810 --> 01:09:22,810
+Ronskin of X DX سالب تكامل Y طولهمين لن ال X يبقى
+
+607
+01:09:22,810 --> 01:09:25,070
+I لن ال X
+
+608
+01:09:33,300 --> 01:09:40,760
+يبقى اتناشر لن ال X على X ترابيع كله على ال
+
+609
+01:09:40,760 --> 01:09:46,720
+رونسكين اللي هو طولة جداش واحد على X بالنسبة إلى
+
+610
+01:09:46,720 --> 01:09:53,820
+DXطيب هاي السالب برا وهي التكامل اظن ان لو جلبتها
+
+611
+01:09:53,820 --> 01:09:59,160
+بتطلع ال X فوق مع X تربيه يفضل X في المقام يبقى
+
+612
+01:09:59,160 --> 01:10:06,400
+هاي 12 وهذا ال link X الكل تربيه على X DX
+
+613
+01:10:08,930 --> 01:10:15,110
+مرة تانية طلعوا ليه كويس اتناشر لن اكس تربية هي
+
+614
+01:10:15,110 --> 01:10:19,150
+اتناشر وهي لن اكس تربية والسالب هي السالب بقى واحد
+
+615
+01:10:19,150 --> 01:10:22,170
+على اكس واحد على اكس تربية تنجلي بعدها تطلع اكس
+
+616
+01:10:22,170 --> 01:10:27,610
+فوق واكس تربية تحت بقى واحد على اكس طيب السؤال هذي
+
+617
+01:10:27,610 --> 01:10:34,580
+واحد على اكس DXمشتقت من؟ من ال X إذا بقدر أقول هذا
+
+618
+01:10:34,580 --> 01:10:44,320
+ناقص اتناشر تكامل من X الكل تربية مشتقت من Xيعني
+
+619
+01:10:44,320 --> 01:10:54,180
+كأنه أنا بكامل T تربيع DT تكيب على تلاتة يعني هذا
+
+620
+01:10:54,180 --> 01:11:02,760
+يساوي ناقص اتناشر لان X الكل تكيب على من؟ على
+
+621
+01:11:02,760 --> 01:11:07,530
+تلاتةوالكون اصلا هنفرض بعضها قليل بـ0 بدنا اشيها
+
+622
+01:11:07,530 --> 01:11:14,490
+من البداية يبقى النتيجة صارت ناقص 4 لن X الكل
+
+623
+01:11:14,490 --> 01:11:21,890
+تكييب طيب بدنا نيجي ناخد U2 as a function of X
+
+624
+01:11:21,890 --> 01:11:30,090
+يبقى تكامل Y1 في G of X على رنسكين of X DX يبقى
+
+625
+01:11:30,090 --> 01:11:37,710
+تكامل الحل الأولاني واحدزي ما هو التاني اتناشر لان
+
+626
+01:11:37,710 --> 01:11:44,550
+ال X على X تربيع يبقى اتناشر لان ال X على X تربيع
+
+627
+01:11:44,550 --> 01:11:51,370
+على الرمز كل واحد على X DX يساوي اتناشر خليكي برا
+
+628
+01:11:51,370 --> 01:11:56,540
+وهي تكاملهذه ال X بتطلع فوق بتروح مع ال X هذه
+
+629
+01:11:56,540 --> 01:12:04,360
+بيصير لن ال X على X في ال DX بنفس الطريقة هذه
+
+630
+01:12:04,360 --> 01:12:12,940
+عبارة عن لن ال X يبقى يساوي 12 تكامل لن ال X مشتقة
+
+631
+01:12:12,940 --> 01:12:23,290
+لن ال X يبقى تربيع على 2يبقى بده يساوي 6 لن X الكل
+
+632
+01:12:23,290 --> 01:12:29,810
+تربية إذا ما بقدر أجيب له particular solution Y of
+
+633
+01:12:29,810 --> 01:12:36,610
+X Y of X يقال يو واحد of X يو واحد هيها جاهزة اللي
+
+634
+01:12:36,610 --> 01:12:46,160
+هو قداش ناقص أربعة لن X الكل تكيباللي بعدها زائد U
+
+635
+01:12:46,160 --> 01:12:54,100
+اتنين يبقى زائد ستة لن ال X الكل تربيع مضروب في
+
+636
+01:12:54,100 --> 01:13:02,780
+من؟ في لن ال X يعني لن ال X الكل تكعيب بصير ناقص
+
+637
+01:13:02,780 --> 01:13:10,940
+اربعة و هنا زائد ستة بقى الجداش اتنين لن ال X الكل
+
+638
+01:13:10,940 --> 01:13:16,920
+تكعيبجبنا ال particular solution وعندي حل ال
+
+639
+01:13:16,920 --> 01:13:21,540
+homogeneous يبقى باجي مع اتنين بكون جبت حلمين
+
+640
+01:13:21,540 --> 01:13:27,640
+المسألة الأولى يبقى باجي بقوله the general
+
+641
+01:13:27,640 --> 01:13:41,640
+solution of the differentialيبقى y يساوي
+
+642
+01:13:41,640 --> 01:13:53,040
+yc زائد capital y of x يبقى y يساوي c1 c2 لإن ال x
+
+643
+01:13:53,040 --> 01:14:01,940
+زائد 2 لإن ال x الكل تكعيببالرابعية في الامتحانات
+
+644
+01:14:01,940 --> 01:14:06,260
+بنجيب زي هيك كتير بنكرر هذه الطريقة ليش؟ لأنها
+
+645
+01:14:06,260 --> 01:14:09,360
+بتدي بعدة طرق حل ال homogeneous و ال non
+
+646
+01:14:09,360 --> 01:14:14,500
+homogeneous حل ال Euler بعد هيك اللي هو حل ال non
+
+647
+01:14:14,500 --> 01:14:18,000
+homogeneous differential equation وبالتالي بنجيب
+
+648
+01:14:18,000 --> 01:14:21,220
+أكتر من موضوع بسؤال انه عجيب، هي جيبنا ال
+
+649
+01:14:21,220 --> 01:14:28,460
+variation مع مين؟ مع ال Euler حد فيكوا لايه تساوي
+
+650
+01:14:28,460 --> 01:14:42,220
+هنا؟حاجة بتسأل؟ ماشي طب
+
+651
+01:14:42,220 --> 01:14:48,680
+أحيانا يا بنات معادلة Euler هذه ممكن نروح نحلها
+
+652
+01:14:48,680 --> 01:14:53,900
+بال undetermined coefficients وليس بال variation
+
+653
+01:14:53,900 --> 01:15:00,820
+of parametersكيف بعد ما نتحيل على المعادلة و بدل
+
+654
+01:15:00,820 --> 01:15:06,400
+المعاملات اللي هم متغيرات بحولهم إلى ثوابت؟ ان
+
+655
+01:15:06,400 --> 01:15:10,600
+حولناهم إلى ثوابت بقدر أستخدمين ال undetermined
+
+656
+01:15:10,600 --> 01:15:14,640
+coefficients بسمين بشرط الطرف اليمين يكون
+
+657
+01:15:14,640 --> 01:15:17,400
+polynomial يا polynomial في exponential يا
+
+658
+01:15:17,400 --> 01:15:21,600
+polynomial في exponential في sine او cosine او
+
+659
+01:15:21,600 --> 01:15:26,680
+مجموعهما او الفرق فيما بينهمأذا هحطلك هذا الكلام
+
+660
+01:15:26,680 --> 01:15:36,060
+على صورة ال remark التالية يبقى remark بيقول
+
+661
+01:15:36,060 --> 01:15:46,600
+لي any Euler equation لل X تربيع في ال YW prime
+
+662
+01:15:46,600 --> 01:15:54,600
+زائد Alpha X في ال Y primeزائد بيتا واي تساوي زيرو
+
+663
+01:15:54,600 --> 01:16:08,540
+can always can always can always be written as be
+
+664
+01:16:08,540 --> 01:16:17,940
+written as من هناك درستهم دائما و أبدا as a linear
+
+665
+01:16:19,490 --> 01:16:24,450
+مقارنة مع
+
+666
+01:16:24,450 --> 01:16:29,490
+مقارنة
+
+667
+01:16:29,490 --> 01:16:31,110
+مع مقارنة مع مقارنة مع مقارنة مع مقارنة مع مقارنة
+
+668
+01:16:31,110 --> 01:16:40,530
+مع مقارنة مع مقارنة مع مقارنة مع مقارنة مع مقارنة
+
+669
+01:16:40,530 --> 01:16:45,910
+مع مقارنة مع مقارنة مع
+
+670
+01:16:50,760 --> 01:16:56,380
+بالتحديد X يساوي E أساسي كتابة
+
+671
+01:17:20,860 --> 01:17:24,880
+إذا زي طريقتنا اللي تاومت طريقت أستخدم ال
+
+672
+01:17:24,880 --> 01:17:29,040
+variation of parameters في حل معادلة euler ممكن
+
+673
+01:17:29,040 --> 01:17:32,600
+أضطر أستخدم اللي هو ال undetermined coefficients
+
+674
+01:17:32,600 --> 01:17:36,980
+في حل معادلة euler كمان، إيش بيقوللي؟ بيقوللي
+
+675
+01:17:36,980 --> 01:17:42,970
+معادلة euler هذه ممكن دائما وأبدانحولها إلى معادلة
+
+676
+01:17:42,970 --> 01:17:49,470
+خطية بمعاملات ثابتة لو استخدمنا التعويض X يساوي E
+
+677
+01:17:49,470 --> 01:17:56,870
+أوس T السؤال كيف؟ بنقولك التالي عندك X يساوي E أوس
+
+678
+01:17:56,870 --> 01:18:06,300
+T خديني لن للطرفين يبقى بصير T تساوي لن Xلن ال X
+
+679
+01:18:06,300 --> 01:18:10,780
+يسوي T في لن ال E لن ال E بواحد يبقى بيضالش إلا T
+
+680
+01:18:10,780 --> 01:18:16,740
+طب لو اشتقنا هذه بالنسبة ل X بيصير DT على DX يسوى
+
+681
+01:18:16,740 --> 01:18:22,560
+جدار يسوى واحد على X خلّي لي هالمعلومة هذه عندك و
+
+682
+01:18:22,560 --> 01:18:28,440
+تعالى نشوف كيف بدنا نسوي الان أنا عند مين Y prime
+
+683
+01:18:28,440 --> 01:18:35,800
+اللي هي مين DY على DX صحيح ولا لأطيب، أليس تهادي
+
+684
+01:18:35,800 --> 01:18:42,660
+فيها أي علاقة في دلة بتربط T و X، يعني X دلة في T،
+
+685
+01:18:42,660 --> 01:18:50,420
+إذا بقدر أقولها دي Dy على Dt في Dt على Dx، صحيح
+
+686
+01:18:50,420 --> 01:18:55,880
+ولا لا؟طيب دي تي على دي إكس بجداش واحد على إكس إذا
+
+687
+01:18:55,880 --> 01:19:02,420
+صار تدى واحد على إكس في دي واي على دي تي إذا صارت
+
+688
+01:19:02,420 --> 01:19:08,080
+المشتقة الأولى تبعت المعادلة y prime بقدر أكتبها
+
+689
+01:19:08,080 --> 01:19:13,390
+بالشكل اللى قدامنا هذهفلما تضرب في X تذهب و لا
+
+690
+01:19:13,390 --> 01:19:18,010
+تبقى المعاملة ثابتة اللي هو Alpha صحيح ولا لأ؟ كما
+
+691
+01:19:18,010 --> 01:19:24,790
+غيرنا هذه سأغير أيضا ال YW' بجي بقول يبقى ال YW'
+
+692
+01:19:25,550 --> 01:19:35,750
+يبقى هي D على DX ده 1 على X في DY على DT مظبوط؟
+
+693
+01:19:35,750 --> 01:19:44,630
+إذا أنا مشتقتش حاصل ضرب دلتينمش تقتلوله بقداش سالب
+
+694
+01:19:44,630 --> 01:19:49,790
+واحد على X تربيع يبقى هاي سالب واحد على X تربيع
+
+695
+01:19:49,790 --> 01:19:58,910
+ودالة تانية كما هي Z الواحد على X زي ما هي وهذا D
+
+696
+01:19:58,910 --> 01:20:10,210
+على DX لمين؟ لDY على DTطبعا يساوي هذا زي ما هو
+
+697
+01:20:10,210 --> 01:20:17,030
+واحد على X تربية بالثالث في DY على DT زائد واحد
+
+698
+01:20:17,030 --> 01:20:22,370
+على X احنا جميعا توسعنا لكسة دي function في من؟ في
+
+699
+01:20:22,370 --> 01:20:27,990
+T لأن X هنا بدأت تساوي U of T إذا أنا ده مقدر
+
+700
+01:20:27,990 --> 01:20:35,840
+اكتبه D على DT في DT على DXيبقى هذا بده يصير 1 على
+
+701
+01:20:35,840 --> 01:20:47,230
+X في D على DT لDY على DT في DT على DXتمام؟ يبقى ما
+
+702
+01:20:47,230 --> 01:20:52,350
+سويتش اشي و على الاكس هيها هذه دي على دي اكس
+
+703
+01:20:52,350 --> 01:20:56,950
+عملتها دي على دي تي في دي تي على دي اكس وظل دي على
+
+704
+01:20:56,950 --> 01:21:01,490
+دي تي لمين؟ للمقدار اللي عنها هذا يبقى هذا الكلام
+
+705
+01:21:01,490 --> 01:21:07,890
+يساوي سالم واحد على اكس تربية في دي واي على دي تي
+
+706
+01:21:07,890 --> 01:21:13,650
+زائد كداش هذا المقدار يا بنات؟دى تى على دى اكس
+
+707
+01:21:13,650 --> 01:21:18,630
+واحد على اكس واندك واحد على اكس مضروب فيه يصير
+
+708
+01:21:18,630 --> 01:21:24,130
+واحد على اكس تربية يبقى هاي واحد على اكس تربية طيب
+
+709
+01:21:24,130 --> 01:21:28,810
+هدى شو تعنى المتغير هدى هو المتغير هدى تعنى
+
+710
+01:21:28,810 --> 01:21:37,520
+المشتقة الثانية اللى Y بالنسبةالان يبقى في d²y على
+
+711
+01:21:37,520 --> 01:21:44,840
+dt² شو رايك لو أخدت 1 على x تربية عامل مشترك بيظل
+
+712
+01:21:44,840 --> 01:21:55,880
+d²y على dt² ناقص dy على dt خلصنا
+
+713
+01:21:57,040 --> 01:22:01,760
+يبقى احنا تطلع يواءي prime شو شكلها و تطلع يواءي
+
+714
+01:22:01,760 --> 01:22:06,620
+double prime شو شكلها بدي اخد هالمعلومتين هدول و
+
+715
+01:22:06,620 --> 01:22:09,420
+ارجع اعوض في المعادلة الخاصة و اشوف طاروا
+
+716
+01:22:09,420 --> 01:22:14,800
+المعاملات هدول و صاروا معاملات ثابتة ولا لأ يبقى
+
+717
+01:22:14,800 --> 01:22:19,980
+باجي بقول هنا substitute سميني هذه اللي هي
+
+718
+01:22:19,980 --> 01:22:23,220
+المعادلة رقم واحد يبقى substitute
+
+719
+01:22:26,620 --> 01:22:36,400
+Equation one we get هدا ال X تربية Y فتحنا جوش وي
+
+720
+01:22:36,400 --> 01:22:41,800
+دابل هرام هي اللي تحت واحد على X تربية فيه دي
+
+721
+01:22:41,800 --> 01:22:50,420
+سكوير Y على دي تي سكوير ناقص DY على دي تي جف للجوش
+
+722
+01:22:50,420 --> 01:22:56,340
+الزغير و جف للجوش الكبيرزائد alpha x في main في ال
+
+723
+01:22:56,340 --> 01:23:03,360
+y prime y prime اللي هو واحد على x في dy على dt
+
+724
+01:23:03,360 --> 01:23:10,580
+خلصنا منها زائد beta y كله بده يساوي قداش zero اظن
+
+725
+01:23:10,580 --> 01:23:19,420
+هذه بتروح مع هذهيبقى صار d2y على dt2 ناقص dy على
+
+726
+01:23:19,420 --> 01:23:27,120
+dt زائد هذه برضه بتروح مع هذه يبقى alpha dy على dt
+
+727
+01:23:27,120 --> 01:23:36,810
+زائد beta y ساوي zero صحيح؟طيب هذا الحينها هو d²y
+
+728
+01:23:36,810 --> 01:23:45,710
+على dt² هذه هذه يبقى زائد alpha ناقص واحد في dy
+
+729
+01:23:45,710 --> 01:23:54,320
+على dt زائد beta y يسوى zeroالمعامل واحد صحيح
+
+730
+01:23:54,320 --> 01:23:59,920
+Alpha رقم ناقص واحد رقم Beta رقم يبقى صارت
+
+731
+01:23:59,920 --> 01:24:05,000
+equation with constant coefficients يبقى هذه
+
+732
+01:24:05,000 --> 01:24:15,660
+second order linear differential equation with
+
+733
+01:24:15,660 --> 01:24:19,360
+constant coefficients
+
+734
+01:24:25,360 --> 01:24:30,440
+هذه المعادلة حولناها إلى معادلة بمعاملات ثابتة
+
+735
+01:24:30,440 --> 01:24:35,260
+يبقى مضالش عليها إلا تطلع على شكل g of x إذا بنتبق
+
+736
+01:24:35,260 --> 01:24:38,420
+عليها ال undetermined coefficients بحلها بال
+
+737
+01:24:38,420 --> 01:24:42,840
+undetermined coefficients لا ينطبق برجع لمين لل
+
+738
+01:24:42,840 --> 01:24:47,580
+variation of parameters يبقى بقدر أحل بالشكل هذا
+
+739
+01:24:47,580 --> 01:24:51,310
+أو بالشكل هذاطب لو بنقدر نحلها بال undetermined
+
+740
+01:24:51,310 --> 01:24:54,030
+coefficients و رح نحلناها بال variational
+
+741
+01:24:54,030 --> 01:24:58,470
+parameters غلط؟ لأ مش غلط صح ايه لأ و بتالي
+
+742
+01:24:58,470 --> 01:25:03,730
+ماعنديش مشكلة بدنا ناخد مثال فقط على الشغل هذه
+
+743
+01:25:41,820 --> 01:25:44,480
+معادلة التفاضلية
+
+744
+01:25:49,070 --> 01:25:59,130
+زائد x في ال y prime ناقص y يساوي تسعة x ترابيع في
+
+745
+01:25:59,130 --> 01:26:04,030
+لن ال x و ال x greater than zero وسميلي هذه
+
+746
+01:26:04,030 --> 01:26:12,850
+المعادلة رقم واحدuse the
+
+747
+01:26:12,850 --> 01:26:16,630
+substitution
+
+748
+01:26:16,630 --> 01:26:28,250
+استخدم التعويضة اللي هو من X تساوي E أس T to solve
+
+749
+01:26:28,250 --> 01:26:31,750
+equation
+
+750
+01:26:31,750 --> 01:26:36,010
+one نمر بيه
+
+751
+01:26:39,560 --> 01:27:00,760
+solve the differential equation one directly يعني
+
+752
+01:27:00,760 --> 01:27:06,320
+كأن احنا بنحل السؤال ده كام مرةمارتين تمام و مكفف
+
+753
+01:27:06,320 --> 01:27:10,160
+نحله مرتين و مكفف اليوم و نخلص ال section طيب
+
+754
+01:27:10,160 --> 01:27:12,960
+تعالى نشوف كيف نحله ايش بيقولى فى الأول استخدمى
+
+755
+01:27:12,960 --> 01:27:17,360
+التعويضة هذه عشان اتحل المعادلة التفاضلية اللى
+
+756
+01:27:17,360 --> 01:27:21,500
+عندك كده يبقى انا بدي اخد ال homogeneous هل ال
+
+757
+01:27:21,500 --> 01:27:26,280
+homogeneous هدى Euler ولا ماهياش Eulerعشان انا
+
+758
+01:27:26,280 --> 01:27:31,960
+لحالي بدي اعرف شكل ال oiler عشان اعرف احلها ب
+
+759
+01:27:31,960 --> 01:27:39,660
+oiler ولا يبدا بجي بقوله نمرة a مضاجي اقول ال X
+
+760
+01:27:39,660 --> 01:27:48,820
+يساوي E أس T يبقى T تساوي لنا ال X يبقى DT على DX
+
+761
+01:27:48,820 --> 01:27:56,220
+يساوي كده؟ واحد على X andوالـ y prime يا بنات
+
+762
+01:27:56,220 --> 01:28:03,700
+حسبناها تواحد على x في dy على dt و ال y double
+
+763
+01:28:03,700 --> 01:28:10,660
+prime واحد على x تربيع في d square y على dt square
+
+764
+01:28:10,660 --> 01:28:21,260
+ناقص dy على dt هذه ما بعدتش مظبوط؟ مدام هيك يبقى
+
+765
+01:28:21,260 --> 01:28:23,460
+بدنا نبدأ نشتغل شغلنا
+
+766
+01:28:26,580 --> 01:28:31,020
+لحظة الشغل اللى اشتغلناه نظري ايه بنعيده كمان مرة
+
+767
+01:28:31,020 --> 01:28:36,480
+الان بتاخد هالمعلومة تدى وعوض وين فى المعادلة رقم
+
+768
+01:28:36,480 --> 01:28:38,920
+واحد يبقى باجى بقوله
+
+769
+01:28:48,520 --> 01:28:55,800
+هذا ال X تربيع وهذا واحد على X تربيع في D2Y على
+
+770
+01:28:55,800 --> 01:29:07,590
+DT2 ناقص DY على DTاللي بعده زائد X في واحد على X
+
+771
+01:29:07,590 --> 01:29:17,510
+في DY على DT اللي بعده ناقص Y كما هي يساوي هي
+
+772
+01:29:17,510 --> 01:29:24,960
+التسعة طلعوا لقبلات X تربيع كداش X؟Eost ربيع بصير
+
+773
+01:29:24,960 --> 01:29:30,600
+Eost لكل تربية يعني E أس اتنين T يبجى ال X تربية
+
+774
+01:29:30,600 --> 01:29:39,280
+صارت E أس اتنين T لإن ال X بجداش بي تي يبجى صارت
+
+775
+01:29:39,280 --> 01:29:42,840
+بي تي مش هتروح تسوي الشجة الشمال و تنسي الشجة
+
+776
+01:29:42,840 --> 01:29:49,080
+اليمين وصلت خبسة عندك تلت متغيرات X Y و T لأ هاي
+
+777
+01:29:49,080 --> 01:29:53,200
+المعادلة من أول لآخره مافيش الا متغيرينو I و T
+
+778
+01:29:53,200 --> 01:29:57,720
+بتنسي الأخيرة بصير تخبيصك على كيفك تلت متغيرات
+
+779
+01:29:57,720 --> 01:30:01,660
+بصير تشتغلي و أنت مش ذارع او فاضل و عقبص و عوض و
+
+780
+01:30:01,660 --> 01:30:05,400
+مش راضي اتطلع و بصير الصاحب يا أستاذ تعالي أستاذ
+
+781
+01:30:05,400 --> 01:30:08,480
+بقولك ماليش دعوة في الحل اسأليني بس في السؤال اللي
+
+782
+01:30:08,480 --> 01:30:12,920
+في الإجابة ماليش علاقة فيه تمام حلك إلك هيك بقولك
+
+783
+01:30:12,920 --> 01:30:13,140
+أه
+
+784
+01:30:19,530 --> 01:30:24,890
+هذه مع هذه الله يسهل عليها وهذه مع هذه الله يسهل
+
+785
+01:30:24,890 --> 01:30:31,750
+عليها يبقى صلة المثلة d²y على dt² هذا بالنقص وهذا
+
+786
+01:30:31,750 --> 01:30:39,050
+بالزادمع السلامة غير محسوف عليهم ناقص
+
+787
+01:30:39,050 --> 01:30:49,450
+Y يساوي تسعة تسعة T E أس اتنين T ايش رايك فيها
+
+788
+01:30:49,450 --> 01:30:54,970
+equation with constant coefficients يبقى هذه
+
+789
+01:30:54,970 --> 01:31:01,530
+equation with constant coefficients
+
+790
+01:31:09,900 --> 01:31:14,300
+بتنفع معاها ال undetermined coefficients ولا لأ؟
+
+791
+01:31:14,300 --> 01:31:17,400
+هذه مش مشكلة الطرف اليمين بلانوميل بيكون
+
+792
+01:31:17,400 --> 01:31:20,220
+exponential إذا بتنفع معاها ال undetermined
+
+793
+01:31:20,220 --> 01:31:24,740
+coefficients لو بينفعش بروح عالميا على ال
+
+794
+01:31:24,740 --> 01:31:27,980
+variation و ال parameter لكن مادام بينفع خلاص بجيب
+
+795
+01:31:27,980 --> 01:31:37,880
+شكل ال .. بيبقى بداجي أقولهY تساوي E أُس RT بأي
+
+796
+01:31:37,880 --> 01:31:44,480
+solution of the homogeneous differential equation
+
+797
+01:31:44,480 --> 01:31:51,980
+D squared Y على DT squared ناقص Y يسوى Zero وهي ال
+
+798
+01:31:51,980 --> 01:32:00,200
+homogenous يبقى then the characteristic
+
+799
+01:32:03,380 --> 01:32:10,880
+Equation is R ترابية ناقص واحد يساوي كم؟ يساوي
+
+800
+01:32:10,880 --> 01:32:17,340
+Zeroيبقى هذا يعطيك ان R ناقص واحد في R زائد واحد
+
+801
+01:32:17,340 --> 01:32:23,340
+يساوي Zero يبقى هذا يعطيك ان R يساوي ناقص واحد وR
+
+802
+01:32:23,340 --> 01:32:32,740
+اتنين تساوي قداش واحد اذا اصبح الحل YC يساوي C
+
+803
+01:32:32,740 --> 01:32:41,240
+واحد في E أس ناقص T زائد C اتنين في E أس قداش أس T
+
+804
+01:32:41,710 --> 01:32:48,490
+الروح نجيب مين ال particular solution لإن هاد الآن
+
+805
+01:32:48,490 --> 01:32:53,650
+مالها مانه
+
+806
+01:32:53,650 --> 01:32:57,510
+homogenous لكن المعاملات ثوابت مش متغيرات زي راس
+
+807
+01:32:57,510 --> 01:33:03,650
+المسألة يبقى هاد اللي بده بروزها ورجعلها بعد قليل
+
+808
+01:33:03,650 --> 01:33:13,210
+يبقى باجي بقوله the partتكيولر solution of
+
+809
+01:33:13,210 --> 01:33:19,050
+equation هذي يبقى نسميها الاتنين اللي فوق كانت
+
+810
+01:33:19,050 --> 01:33:24,950
+واحد يبقى هذي .. هذي لأ وين؟ هذي اللي هي وين
+
+811
+01:33:24,950 --> 01:33:31,310
+اختصرناها صارت هذي هذي بتسميها الاتنين يبقى of the
+
+812
+01:33:31,310 --> 01:33:40,210
+differential equation اتنينY of T بيبقى Y of T
+
+813
+01:33:40,210 --> 01:33:49,010
+بيبقى Y of T بيبقى Y of
+
+814
+01:33:49,010 --> 01:34:00,010
+T بيبقى Y of T بيبقى Y of
+
+815
+01:34:00,010 --> 01:34:05,440
+T بيبقى Y of T بيبقى Y of T بيبقى Y of T بيبقىو
+
+816
+01:34:05,440 --> 01:34:10,540
+بعد هي كده بقول غطي ال T و أس S و بعد هي بتطلع ال
+
+817
+01:34:10,540 --> 01:34:16,600
+باقي هل اي term هنا يشبه اي term هنا لأ لإن هذه E
+
+818
+01:34:16,600 --> 01:34:20,940
+أس T و هذه E أس 2T بختلفوا عن بعض يبقى ال S هنا
+
+819
+01:34:20,940 --> 01:34:28,780
+بجدية ب Zero يبقى هنا ال S تساوي Zero مدام Zero
+
+820
+01:34:28,780 --> 01:34:33,200
+اذا capital Y of T يساوي
+
+821
+01:34:42,580 --> 01:34:50,130
+طيب بدنا نجيب قداش a نوت و قداش a oneيبقى باجي
+
+822
+01:34:50,130 --> 01:34:58,250
+بقوله y prime يساوي a node في e أس اتنين t زائد
+
+823
+01:34:58,250 --> 01:35:07,150
+اتنين a node t زائد اتنين a one كله في e أس اتنين
+
+824
+01:35:07,150 --> 01:35:17,400
+tع رايحك بالمرة يبقى هذا كله بيساوي a0 زائد اتنين
+
+825
+01:35:17,400 --> 01:35:26,180
+a0t زائد اتنين a1 كله في ال E أس اتنين T مش شاكر
+
+826
+01:35:26,180 --> 01:35:33,710
+يا أهلي؟ خلاصطيب بدنا نجيب yw prime نشتغل كمان مرة
+
+827
+01:35:33,710 --> 01:35:42,090
+هذه ب zero وهذه ب zero وهذه ب 2 a naught يبقى 2 a
+
+828
+01:35:42,090 --> 01:35:51,830
+naught في e أوس 2t زائد a2 في a naught 2 a naught
+
+829
+01:35:51,830 --> 01:35:57,210
+t 2 a1 في e أوس 2t
+
+830
+01:35:59,320 --> 01:36:04,580
+بدي اخد E أس اتنين T عام المشترك يبقى بظل قداش
+
+831
+01:36:04,580 --> 01:36:13,400
+اتنين A نوت وزائد كمان اتنين A نوت بمش وهي زائد
+
+832
+01:36:13,400 --> 01:36:21,640
+اتنين في اتنين باربع A نوت T وزائد اربع A one كل
+
+833
+01:36:21,640 --> 01:36:31,330
+هذا في E أس اتنين Tيعني كداش يعني اربع a نوت زائد
+
+834
+01:36:31,330 --> 01:36:41,750
+اربع a one زائد اربع a نوت T كله هدا وين؟ في E أس
+
+835
+01:36:41,750 --> 01:36:48,750
+اتنين T كويس؟ يبقى الأن بتروح عوض وين؟ في المعادلة
+
+836
+01:36:48,750 --> 01:36:54,070
+رقم اتنين يبقى باجي بقوله substitute
+
+837
+01:37:08,530 --> 01:37:17,750
+يبقى الهيمين هذه كلها يبقى اربع a نوت زائد اربع a
+
+838
+01:37:17,750 --> 01:37:23,320
+one اربع a note Tو بدي أخلّي الـ exponential للكل
+
+839
+01:37:23,320 --> 01:37:30,660
+بعد هيش ناقص Y وين Y هيو يبقى بدي أحط لها ناقص
+
+840
+01:37:30,660 --> 01:37:41,160
+يبقى ناقص A نقص T ناقص N كله في ال E أس اتنين T
+
+841
+01:37:41,160 --> 01:37:49,120
+بدي أساوي الطرف اليمين اللي هو تسعة T E أس اتنين T
+
+842
+01:37:49,860 --> 01:37:56,440
+أظن ممكن اقسم الطرفين على E أس اتنين T ويظل انما
+
+843
+01:37:56,440 --> 01:38:04,200
+يأتي اربع A نود مفيش غيرها يبقى هاي اربع A نود
+
+844
+01:38:04,200 --> 01:38:13,120
+وعندك اربع A one وناقص A one يبقى زائد تلاتة A one
+
+845
+01:38:13,790 --> 01:38:21,290
+أربعة A نوت T ونقص A نوت T يبقى زائد تلاتة A نوت T
+
+846
+01:38:21,290 --> 01:38:29,750
+كله بده يساوي تسعة T نقد مقارنة ما بين الطرفين
+
+847
+01:38:29,750 --> 01:38:37,290
+يبقى هذا بده يعطيلك انه تلاتة A نوت بده يساوي قداش
+
+848
+01:38:37,290 --> 01:38:44,380
+تسعة يعني هذا بده يعطيلك انه A نوت يساوي قداشتلاتة
+
+849
+01:38:44,380 --> 01:38:51,980
+and هذا كله مافيش فيه T يبقى كده بده يساوي؟ Zero
+
+850
+01:38:51,980 --> 01:38:59,120
+and أربعة a naught زائد تلاتة a one بده يساوي Zero
+
+851
+01:38:59,120 --> 01:39:06,380
+هذا بده يعطيناالـ A نوله كم؟ بتلاتة يبقى هاي أربعة
+
+852
+01:39:06,380 --> 01:39:14,080
+في تلاتة زائد تلاتة A1 بده ساوي Zero يبقى A1 كم
+
+853
+01:39:14,080 --> 01:39:21,180
+بده ساوي يا بنات؟ سالب أربعةيبقى اذا اصبح capital
+
+854
+01:39:21,180 --> 01:39:30,780
+Y of T بده يساوي E naught اللي هي تلاتة يبقى تلاتة
+
+855
+01:39:30,780 --> 01:39:40,400
+T ناقص اربعة في E اوس اتنين T اذا هذا ال
+
+856
+01:39:40,400 --> 01:39:45,560
+particular solutionيبقى بناء عليه صار ال general
+
+857
+01:39:45,560 --> 01:39:54,920
+solution y يساوي yc زائد capital Y of T يبقى y
+
+858
+01:39:54,920 --> 01:40:04,120
+يساوي yc هيها فوق يبقى c واحد e أس ناقص T زائد c
+
+859
+01:40:04,120 --> 01:40:14,200
+اتنين e أس Tزائد تلاتة T ناقص أربعة في E أوس اتنين
+
+860
+01:40:14,200 --> 01:40:20,720
+T خليني أسأل السؤال التالي هل المعادلة من أولها
+
+861
+01:40:20,720 --> 01:40:26,220
+إلى آخرها فيها T إذا بيدروح أحولها كلها بدلالة من؟
+
+862
+01:40:26,220 --> 01:40:32,060
+بدلالة X إذا لو حولتها بدلالة X بدها تصبح على
+
+863
+01:40:32,060 --> 01:40:38,980
+الشكل التالي يعني بده أشيلالـ E أُس T وحُط مكانها
+
+864
+01:40:38,980 --> 01:40:46,440
+X طيب ال E أُس ناقص T واحد
+
+865
+01:40:46,440 --> 01:40:51,280
+على X يعني X أُس سالب واحد طبعا يبقى هذه بدها تصير
+
+866
+01:40:51,280 --> 01:40:57,060
+على الشكل التالي طيب نمسح هذا وخلّي المعادلة هي
+
+867
+01:40:57,060 --> 01:41:04,860
+فوق و هذا كله بدنا نشيلههنقول لك هذا على الشكل
+
+868
+01:41:04,860 --> 01:41:11,940
+التالي يبقى solution of
+
+869
+01:41:11,940 --> 01:41:20,380
+equation one is y يساوي عندك هنا c واحد
+
+870
+01:41:26,150 --> 01:41:40,430
+يبقى اكس أسالي بواحد تمام زائد C تلاتة
+
+871
+01:41:40,430 --> 01:41:45,610
+تلاتة
+
+872
+01:41:45,610 --> 01:41:55,680
+لان ال X ناقص أربعةالـ A أُس T بلن ال X يعني ايه
+
+873
+01:41:55,680 --> 01:42:03,860
+نكتبه لك هتوتين يبقى E أُسي اتنين و T اليمين لن ال
+
+874
+01:42:03,860 --> 01:42:10,580
+X يبقى صار عندنا Y يسوي C واحد X أُس ناقص واحد C
+
+875
+01:42:10,580 --> 01:42:17,900
+اتنين X زائد تلاتة لن ال X ناقص أربعة فيهطلعيني
+
+876
+01:42:17,900 --> 01:42:21,720
+هنا اتنين بتجي كواصل ال X تربيع ال E و L عكس بعض
+
+877
+01:42:21,720 --> 01:42:29,900
+يبقى هذي بصير X تربيع فقط لا غير تمام؟ بدك تفكيها
+
+878
+01:42:29,900 --> 01:42:34,100
+الحين فش مشكلة تخليها زي ما هي فش مشكلة يبقى واعي
+
+879
+01:42:34,100 --> 01:42:42,080
+C1 X ناقص واحد C2 X تلاتة X تربيع لن ال X ناقص
+
+880
+01:42:42,080 --> 01:42:48,150
+أربعة X تربيعبريوزيها و بدنا الحل التاني يطلع زي
+
+881
+01:42:48,150 --> 01:42:53,130
+هذا بس الحل التاني قصير مش زي هذا لإن لا بدنا نحور
+
+882
+01:42:53,130 --> 01:43:00,350
+ولا حاجة حتى
+
+883
+01:43:00,350 --> 01:43:05,090
+الآن خلصنا إيه من المثلة بدنا نيجي اللي بيه بيه
+
+884
+01:43:05,090 --> 01:43:10,650
+هاي المثلة قدامي زي مهين يبقى أنا بدي أخد Euler
+
+885
+01:43:10,650 --> 01:43:15,940
+لحاله وبعد هيك بروح باخد ال homogeneousتمام يبقى
+
+886
+01:43:15,940 --> 01:43:25,100
+باجي بقوله هنا let او هنا باجي بقوله ال X تساوي
+
+887
+01:43:25,100 --> 01:43:36,980
+zero is a singular point for the Euler
+
+888
+01:43:36,980 --> 01:43:46,500
+differential equation اللي هي mainx تربيع yw prime
+
+889
+01:43:46,500 --> 01:43:55,280
+زائد x y prime ناقص y تساوي zero يبقى باجي بقوله
+
+890
+01:43:55,280 --> 01:44:04,820
+let y تساوي x أسار بي ا solution هذه واحدة سمينا
+
+891
+01:44:04,820 --> 01:44:10,620
+اثنين هذه تكون تلاتة بي ا solution of equation
+
+892
+01:44:11,270 --> 01:44:23,170
+تلاتة then the characteristic equation is R في R
+
+893
+01:44:23,170 --> 01:44:33,110
+ناقص واحد زائد R وهنا ناقص واحد كله بده يساوي كده؟
+
+894
+01:44:33,110 --> 01:44:38,920
+بده يساوي Zeroيبقى هذا الكلام بده يعطيك انه R
+
+895
+01:44:38,920 --> 01:44:45,180
+تربيه هنا ناقص R وزائد R مع السلامة ناقص واحد
+
+896
+01:44:45,180 --> 01:44:51,940
+يساوي Zero يبقى ال R تساوي زائد او ناقص واحد يبقى
+
+897
+01:44:51,940 --> 01:45:01,080
+صار YC يساوي C واحد Fixed ناقص واحد C اتنين Fixed
+
+898
+01:45:04,180 --> 01:45:09,040
+يبقى هاي جيبنا أحل ال homogenous بنا نيجي لمين ال
+
+899
+01:45:09,040 --> 01:45:13,860
+non-homogenous بنفعش غير أروح أخلي المعامل تبع Y''
+
+900
+01:45:13,860 --> 01:45:14,660
+هو مين
+
+901
+01:45:35,320 --> 01:45:43,760
+وأحد صحيح يبقى بروح باقسم كله على مين؟ على
+
+902
+01:45:43,760 --> 01:45:50,900
+X تربيعكله في ال Y بده يساوي تسعة في ال N ال X
+
+903
+01:45:50,900 --> 01:45:56,460
+يبقى هادي G يا بنات طيب إذا حاطينا المعادلة في
+
+904
+01:45:56,460 --> 01:46:02,580
+مين؟ في الشكل الجديد اللي عندنا المعادلة هذهيبقى
+
+905
+01:46:02,580 --> 01:46:06,420
+واضح المعاملات متغيرات إذا لا يمكن أقدر أحلها بالـ
+
+906
+01:46:06,420 --> 01:46:09,900
+Undetermined coefficients يبقى بيذهب لمين؟
+
+907
+01:46:09,900 --> 01:46:13,240
+للvariation of parameters مشان واخد الvariation of
+
+908
+01:46:13,240 --> 01:46:16,960
+parameters بيذهب أحسب ال runoff skin تبع من؟ تبع
+
+909
+01:46:16,960 --> 01:46:21,040
+الحالين الأثنين هدول إذا بدي أجهزة أقول ال runoff
+
+910
+01:46:21,040 --> 01:46:27,690
+skin as a function of x يساويالحل الأول x أوص ناقص
+
+911
+01:46:27,690 --> 01:46:34,270
+واحد والحل التاني x مشتقته السالب x أوص سالب اتنين
+
+912
+01:46:34,270 --> 01:46:41,010
+وهنا واحد ويساوي حصل ضرب عناصر القطر الرئيسي ناقص
+
+913
+01:46:41,010 --> 01:46:46,570
+مع ناقص بالسير الزائد حصل ضرب عناصر القطر الثانوي
+
+914
+01:46:46,570 --> 01:46:54,260
+يبقى اتنين x أوص ناقص واحدأو اتنين على X طبعا
+
+915
+01:46:54,260 --> 01:46:59,060
+اشترطلي في الاول X لا تساوي ال zero يبقى هذا لا
+
+916
+01:46:59,060 --> 01:47:05,920
+يمكن ان يساوي من ال zero يبقى باجي بقوله هنا the
+
+917
+01:47:05,920 --> 01:47:11,760
+particular solution
+
+918
+01:47:11,760 --> 01:47:19,780
+of equation
+
+919
+01:47:21,050 --> 01:47:25,670
+هذه تسميها تلاتة وهذه تسميها أربعة يا بنات of
+
+920
+01:47:25,670 --> 01:47:34,230
+equation أربعة is capital Y of X ماعنديش T هنا
+
+921
+01:47:34,230 --> 01:47:40,630
+يبقى capital Y of X يساوي U one of X في ال X
+
+922
+01:47:40,630 --> 01:47:49,090
+السالب واحد زائد U اتنين of X في ال X itselfالان
+
+923
+01:47:49,090 --> 01:47:56,330
+بدنا نجي الى u1 as a function of x سالب تكامل y2
+
+924
+01:47:56,330 --> 01:48:04,110
+في g of x على رونسكين of x dx سالب تكامل y2 اللي
+
+925
+01:48:04,110 --> 01:48:11,870
+هي بx وال g of x اللي هي بتسعى لإن ال xتسعة لان ال
+
+926
+01:48:11,870 --> 01:48:17,790
+X مقسم على ال رونسكين ال رونسكين هو كم؟ اتنين على
+
+927
+01:48:17,790 --> 01:48:26,290
+X DX تمام؟ يبقى هذي بيصير سالب تسعة على اتنين وال
+
+928
+01:48:26,290 --> 01:48:34,090
+X هذي تطلع فوق بصير تكامل لل X تربيع لان ال X في
+
+929
+01:48:34,090 --> 01:48:43,580
+DX كيف بنكمل هذه؟بس الجدول لا بيجيبهاش الجدول لإن
+
+930
+01:48:43,580 --> 01:48:48,700
+هذه لن ال X مش شهيدة لتانية تمام اذا بتروح اقول يا
+
+931
+01:48:48,700 --> 01:48:57,760
+بنات ال U تساوي لن ال X و ال DV بتساوي ال X تربية
+
+932
+01:48:57,760 --> 01:49:04,580
+في DX يبقى ال DU بواحد على X DX و ال V ب X تكييب
+
+933
+01:49:04,580 --> 01:49:14,280
+على تلاتة يبقى هذهيبقى النتيجة يساوي ناقص تسعة على
+
+934
+01:49:14,280 --> 01:49:22,380
+اتنين هيها برا U في V اللي هو تالت X تكييب في لن X
+
+935
+01:49:22,380 --> 01:49:25,240
+ناقص تكامل V
+
+936
+01:49:34,280 --> 01:49:42,400
+يبقى هذا الكلام ناقص تسعة على اتنين فيطالت X تكيب
+
+937
+01:49:42,400 --> 01:49:51,740
+لان X مع X تربيع بتروح بظهر بس X تربيع تكاملة X
+
+938
+01:49:51,740 --> 01:49:59,300
+تكيب على تلاتة يبقى ناقص X تكيب على تسعة بالشكل
+
+939
+01:49:59,300 --> 01:50:05,630
+اللي عنها دهندخل التسعين عليها بالسالب يبقى سالب
+
+940
+01:50:05,630 --> 01:50:12,950
+بظل تلاتة على اتنين سالب تلاتة على اتنين اكس تكيب
+
+941
+01:50:12,950 --> 01:50:18,590
+للنل اكس سالب مع سالب بيصير موجب تسعة مع تسعة مع
+
+942
+01:50:18,590 --> 01:50:27,650
+السلامة يبقى نص اكس تكيب بدنا ال U اتنين ال U
+
+943
+01:50:27,650 --> 01:50:35,450
+تكاملللـ Y1 في الـ G of X على رونسكين of X في الـ
+
+944
+01:50:35,450 --> 01:50:42,430
+DX هو يسوي تكامل Y1 اللي هو في كده؟ X أوص ناقص
+
+945
+01:50:42,430 --> 01:50:49,510
+واحد X أوص ناقص واحد الـ G of X اللي هو التسعة في
+
+946
+01:50:49,510 --> 01:50:56,470
+لن ال X على مين؟ على رونسكين كده طلعناه؟هي موجودة
+
+947
+01:50:56,470 --> 01:51:04,110
+عندنا 2 على X 2 على X كله في ال DX يبقى يساوي 9
+
+948
+01:51:04,110 --> 01:51:09,410
+على 2 في تكامل هذا ال X تطلع فوق مع ال X سالب واحد
+
+949
+01:51:09,410 --> 01:51:16,510
+مع السلامة بظل تكامل لإن ال X في ال DX بنفس
+
+950
+01:51:16,510 --> 01:51:20,190
+الطريقة اللي اتبعناها فوق وهذا مثال موجود معاكم في
+
+951
+01:51:20,190 --> 01:51:28,200
+calculus Bيبقى النتيجة 9 على 2 في X لأن X ناقص X
+
+952
+01:51:28,200 --> 01:51:40,850
+يعني تسعة على اتنين X لأن X ناقص 9 على 2 في Xطيب
+
+953
+01:51:40,850 --> 01:51:47,830
+جبنا U1 و U2 إذا بقدر أجيب شكل ال Y of X يبقى شكل
+
+954
+01:51:47,830 --> 01:51:53,590
+ال Y of X بده يساوي U1 هي ال U1 مضروبة في الحل
+
+955
+01:51:53,590 --> 01:52:00,940
+الأول الحل الأول هو X وسالب 1يبقى هنا وراها تهيأ
+
+956
+01:52:00,940 --> 01:52:07,840
+هي اللي هو ناقص تلاتة على اتنين X تكييب لإن ال X
+
+957
+01:52:07,840 --> 01:52:16,500
+زائد نص X تكييب كله هذا في ال X و ناقص واحد زائد
+
+958
+01:52:16,500 --> 01:52:23,880
+U2 اللي هو تسعة على اتنين X لإن ال X ناقص تسعة على
+
+959
+01:52:23,880 --> 01:52:26,980
+اتنين في جداش في ال X
+
+960
+01:52:33,020 --> 01:52:40,800
+يبقى النتيجة دغري بعد ما جيبنا U1 و U2 يبقى
+
+961
+01:52:40,800 --> 01:52:48,280
+النتيجة بتطلع يا ست في الآخر اللي هي تساوي تلاتة X
+
+962
+01:52:48,280 --> 01:52:57,560
+تربيع فلن ال X ناقص أربعة X تربيعيبقى بناء ان
+
+963
+01:52:57,560 --> 01:53:02,400
+عليها بقدر اجيب ال general solution يبقى بقى اللي
+
+964
+01:53:02,400 --> 01:53:11,380
+بقوله ال general solution يبقى
+
+965
+01:53:11,380 --> 01:53:24,100
+the general solution of the differential equation
+
+966
+01:53:24,100 --> 01:53:33,690
+1SY تساوي YC زائد capital Y of X يبقى هذا بدي
+
+967
+01:53:33,690 --> 01:53:40,930
+أقولك ان Y تساوي YC هيها يبقى C واحد X اصلاقص واحد
+
+968
+01:53:40,930 --> 01:53:46,950
+C اتنين X زائد capital Y of X اللي طلع اللي هو
+
+969
+01:53:46,950 --> 01:53:59,470
+زائد تلاتة X تربيةوالن ال X ناقص 4X تربيع شوفي لي
+
+970
+01:53:59,470 --> 01:54:04,250
+هي هذه النتيجة اللي طلعناها في part A نفسها يبقى
+
+971
+01:54:04,250 --> 01:54:09,130
+سواء كان ب directly مباشرة او بالتحويل ال
+
+972
+01:54:09,130 --> 01:54:12,170
+undetermined coefficients كله بوصلني الى نفس
+
+973
+01:54:12,170 --> 01:54:18,110
+النتيجة وصلنا الان ل exercises 55
+
+974
+01:54:19,820 --> 01:54:28,480
+خمسة خمسة المسائل من واحد لغاية ستة عشر ال even و
+
+975
+01:54:28,480 --> 01:54:36,440
+من اربعة و عشرين لغاية تسعة و عشرينترى بالك يمكن
+
+976
+01:54:36,440 --> 01:54:39,480
+لو جيبنا سؤال في الامتحان المقيدك نقولك use the
+
+977
+01:54:39,480 --> 01:54:43,880
+substitution X تساوي E وC to solve the
+
+978
+01:54:43,880 --> 01:54:46,780
+differential equation او to change the
+
+979
+01:54:46,780 --> 01:54:49,360
+differential equation into a differential equation
+
+980
+01:54:49,360 --> 01:54:53,000
+with constant coefficients then solve the new
+
+981
+01:54:53,000 --> 01:54:57,680
+equation حل المعادلة الجديدة يبقى اما بطلب الطريقة
+
+982
+01:54:57,680 --> 01:55:01,240
+الأولى يبقى اعطيك المعادلة لو بسكت وانت حل
+
+983
+01:55:01,240 --> 01:55:04,000
+بالطريقة الأولى و بالطريقة التانية اللى بدك إياها
+
+984
+01:55:04,200 --> 01:55:06,220
+سيانة مابتفرجش عنها
+
diff --git a/PL9fwy3NUQKwa8ZDfSFGn6H8xVFLzqmCZC/MCBJ_x7Y0Bg_postprocess.srt b/PL9fwy3NUQKwa8ZDfSFGn6H8xVFLzqmCZC/MCBJ_x7Y0Bg_postprocess.srt
new file mode 100644
index 0000000000000000000000000000000000000000..370cf9717e21ab56fa6cbbac06c5598d84709f7a
--- /dev/null
+++ b/PL9fwy3NUQKwa8ZDfSFGn6H8xVFLzqmCZC/MCBJ_x7Y0Bg_postprocess.srt
@@ -0,0 +1,3252 @@
+1
+00:00:09,840 --> 00:00:16,100
+بسم الله الرحمن الرحيم المرة الماضية كنا نتكلم في
+
+2
+00:00:16,100 --> 00:00:21,820
+المسائل العامة على الشابتر اتنين وكنا في هذه
+
+3
+00:00:21,820 --> 00:00:26,100
+المسائل العامة حاطط ليه تلت نقاطالمرة الفاتة
+
+4
+00:00:26,100 --> 00:00:31,120
+اتعرضنا للنقطة الأولى ركات equation والان بقى
+
+5
+00:00:31,120 --> 00:00:35,600
+لدينا نقطتين النقطة الأولى ال equation with the
+
+6
+00:00:35,600 --> 00:00:40,440
+dependent variable y missing يعني معادلة فيها
+
+7
+00:00:40,440 --> 00:00:44,960
+الرمز الواي مفقود missing مفقود مش موجود في
+
+8
+00:00:44,960 --> 00:00:49,320
+المعادلة والنقطة التالتة ال equation with the
+
+9
+00:00:49,320 --> 00:00:54,590
+independent variable t missingطبعا هناخد الأولى
+
+10
+00:00:54,590 --> 00:00:59,690
+اللى هي equations with a dependent variable y
+
+11
+00:00:59,690 --> 00:01:04,430
+missing يعني معادلات تفاضلية فيها اللى هو المجهول
+
+12
+00:01:04,430 --> 00:01:10,050
+y مش موجود في المعادلة و بدنا نشوف كيف هنحل هذه
+
+13
+00:01:10,050 --> 00:01:16,210
+المعادلةالنوع هذا بنات من المعادلات بصير عندنا
+
+14
+00:01:16,210 --> 00:01:22,110
+معادلة من رتبتي الثانية و بننزل رتبتها الى الرتبة
+
+15
+00:01:22,110 --> 00:01:26,730
+الأولى و بنحلها زى ما كنا نحل في الشرط الرمضى يعنى
+
+16
+00:01:26,730 --> 00:01:30,970
+ممكن تطلع المعادلة بعد تنزيل رتبتهايمكن linear
+
+17
+00:01:30,970 --> 00:01:35,610
+يمكن Bernoulli يمكن exact يمكن exact بس بدأ
+
+18
+00:01:35,610 --> 00:01:40,190
+integrating factor يمكن separable يمكن homogeneous
+
+19
+00:01:40,190 --> 00:01:44,370
+الاخري يبقى لبعد ما نحولها من الرتبة الثانية الى
+
+20
+00:01:44,370 --> 00:01:48,390
+الرتبة الأولىأي معادلة من المعادلات السابقة بنقدر
+
+21
+00:01:48,390 --> 00:01:53,730
+نحلها ونخلص منها الشغلة يبقى these equations are
+
+22
+00:01:53,730 --> 00:01:58,750
+in the form الشكل العام للمعادلات اللي فيها y
+
+23
+00:01:58,750 --> 00:02:03,810
+variable او ال variable y missing مفقود مش موجود
+
+24
+00:02:03,810 --> 00:02:10,670
+يعني الشكل y'' يسوى f of t وy' y مش موجودة لكن y'
+
+25
+00:02:11,030 --> 00:02:16,740
+موجودة وy'' موجودةيبقى هذه المعادلة فيها y مفقودة
+
+26
+00:02:16,740 --> 00:02:22,020
+مش موجودة في المعادلة.مشان انحل المعادلة هذه بدنا
+
+27
+00:02:22,020 --> 00:02:27,200
+نعمل تعويضة معينة شو التعويضة هذه؟ بدأ احط ان v
+
+28
+00:02:27,200 --> 00:02:32,000
+بدوا يساوي y prime يعني المشتق اللي قول احديها رمز
+
+29
+00:02:32,000 --> 00:02:36,760
+جديد وليكن v و بدأ اشتقها كمان مرة فبصير v prime
+
+30
+00:02:36,760 --> 00:02:41,130
+هي y double primeبتاخد المعلومتين اللي اتنين هدول
+
+31
+00:02:41,130 --> 00:02:46,210
+و اعوض في المعادل اللي عندها default يبقى yw prime
+
+32
+00:02:46,210 --> 00:02:50,930
+بدها تصير مين؟ بدها تصير v prime ال y prime بدها
+
+33
+00:02:50,930 --> 00:02:54,570
+تصير v يبقى المعادلة رقم واحد صارت على الشكل اللي
+
+34
+00:02:54,570 --> 00:02:58,950
+عندنا هذا يبقى مش شايفين الا مشتقة واحدة في المثل
+
+35
+00:02:58,950 --> 00:03:03,250
+بس ايش صارت؟ first order differential equation
+
+36
+00:03:03,250 --> 00:03:07,400
+يمكن linear يمكن exactيمكن هموجينياص يمكن
+
+37
+00:03:07,400 --> 00:03:10,960
+سيفارابول يمكن تقول هموجينياص يمكن تقول ال exact
+
+38
+00:03:10,960 --> 00:03:15,120
+يمكن تقول ال linear الله أعلم مين ما كانت تكون
+
+39
+00:03:15,120 --> 00:03:21,680
+بنروح نحلها زي ما كنا بنحل في الشبتر
+
+40
+00:03:21,680 --> 00:03:24,980
+اللي بين إيدينا اللي احنا في المسائل العامة عليه
+
+41
+00:03:26,180 --> 00:03:28,780
+بنبدأ نعطي أمثلة بقول solve the differential
+
+42
+00:03:28,780 --> 00:03:32,520
+equation هو بقول ليش ان Y missing ولا T missing
+
+43
+00:03:32,520 --> 00:03:34,100
+انا بده لاحظها
+
+44
+00:03:34,100 --> 00:03:41,900
+ههههههههههههههههههههههههههههههههههههههههههههههههههههههههههههههههههههههههههههههههههههههههههههههههههههههههههههههههههههههههههههههههههههههههههههههههههههههههههههههههههههههههههههههههههههههههههه
+
+45
+00:03:51,300 --> 00:03:55,320
+أثانية و احنا موضوعنا هو الرتبة الأولى إذا بدى
+
+46
+00:03:55,320 --> 00:03:59,640
+ننزل الرتبة من الرتبة الثانية إلى الرتبة الأولى بس
+
+47
+00:03:59,640 --> 00:04:03,700
+بعدى باطلع في المعادلة اللى عندنا هذه هل المعادلة
+
+48
+00:04:03,700 --> 00:04:09,060
+هذه فيها Y ماعنديش Y كل اللى عندى Y prime وY
+
+49
+00:04:09,060 --> 00:04:13,900
+double prime يبقى هذه equation with Y missing يبقى
+
+50
+00:04:13,900 --> 00:04:26,610
+solution يبقى equation oneis an equation with y
+
+51
+00:04:26,610 --> 00:04:34,270
+missing يبقى هذه فيها y مفقودة بناء عليه هروح افرب
+
+52
+00:04:34,270 --> 00:04:44,470
+ان اللي هو v تساوي من y prime يبقى putV تساوي Y'
+
+53
+00:04:44,990 --> 00:04:53,050
+هذا بيعطينا ان V' يساوي YW' يبقى المعادلة هذه تصير
+
+54
+00:04:53,050 --> 00:05:00,670
+T تربية V' زائد اتنين T في ال V بده يساوي كده؟ بده
+
+55
+00:05:00,670 --> 00:05:05,070
+يساوي واحد نجلة الواحد على الشجة التانية صارت هداش
+
+56
+00:05:05,070 --> 00:05:10,990
+First Order والسؤال هل هي Linear ولا غير Linear؟
+
+57
+00:05:11,540 --> 00:05:20,980
+برضه linear يبقى هذه بقدر لو جسمت على T اقول هذه V
+
+58
+00:05:20,980 --> 00:05:28,920
+prime زائد اتنين على T كل هذا الكلام في V بده
+
+59
+00:05:28,920 --> 00:05:34,660
+يساوي واحد على مين على T تربيع اللي هي linear
+
+60
+00:05:34,660 --> 00:05:37,860
+first
+
+61
+00:05:37,860 --> 00:05:39,840
+order
+
+62
+00:05:47,160 --> 00:05:49,400
+معادلة المعادلة
+
+63
+00:05:53,770 --> 00:05:59,930
+يبقى بتروح أخد من عامل التكامل فبدأ أخد ل mu of T
+
+64
+00:05:59,930 --> 00:06:11,610
+E أس تكامل من اتنين على T dt يبقى E أس اتنين ل T
+
+65
+00:06:11,610 --> 00:06:16,170
+ولا داعي لل absolute value لأن T greater than zero
+
+66
+00:06:17,270 --> 00:06:23,050
+يبقى هذه بدأت تساوي T تربيع الان بنجي على المعادلة
+
+67
+00:06:23,050 --> 00:06:28,230
+هذه سميه للمعادلة هذه رقم اتنين يبقى بتقولي لي
+
+68
+00:06:28,230 --> 00:06:33,290
+multiply equation
+
+69
+00:06:33,290 --> 00:06:42,290
+اتنين by T تربيع we get نحصل على يبقى ايش بيصير T
+
+70
+00:06:42,290 --> 00:06:50,910
+تربيع في ال V primeزائد اتنين T في ال V يسوي واحد
+
+71
+00:06:50,910 --> 00:06:58,210
+صحيح او ممكن نقول ت تربيه في V لكل Prime يسوي واحد
+
+72
+00:06:58,210 --> 00:07:05,450
+صحيح لو جينا كملناها يا بنات ت تربيه في V يسوي T
+
+73
+00:07:05,450 --> 00:07:13,430
+زائد constant Cطب انا بديش هذه بدي V اذا بجسم كله
+
+74
+00:07:13,430 --> 00:07:20,190
+على مين على T تربيع يبقى صارت V عندي اللي هي مين
+
+75
+00:07:20,190 --> 00:07:30,050
+واحد على T زائد C على T تربيع هذا بدي اعطيلك مية T
+
+76
+00:07:30,050 --> 00:07:32,870
+V هذه انا فرضها هي مين
+
+77
+00:07:38,990 --> 00:07:48,290
+يبقى هذا يجب ان اعطيك ان V تساوي DY على DT يجب ان
+
+78
+00:07:48,290 --> 00:07:56,080
+تساوي من 1 على T زائد C على T ترابيعأو ان شئتوا
+
+79
+00:07:56,080 --> 00:08:04,680
+نفقوا ندى الـ dy بده يساوي اللى هو من واحد عالى T
+
+80
+00:08:04,680 --> 00:08:11,990
+زائد C عالى T تربيع كله بالنسبة لمان لدى Tبدنا
+
+81
+00:08:11,990 --> 00:08:23,370
+نكامل يبقى Y تساوي لنت ناقص C عالة Z كنصة جديد
+
+82
+00:08:23,370 --> 00:08:31,710
+وليكن C1 يبقى هذا ال solution تبع المعادلة الأصلية
+
+83
+00:08:31,710 --> 00:08:38,130
+يبقى اضطرنا لتكامل كم مرة مرتين حتى نصل إلى
+
+84
+00:08:38,130 --> 00:08:42,580
+الإجابةيبقى هذا النوع الأول equations with y
+
+85
+00:08:42,580 --> 00:08:46,760
+missing بدنا نيجي للنوع ثاني equations with c
+
+86
+00:08:46,760 --> 00:08:55,360
+missing يبقى بدنا نيجي الآن لل equations with
+
+87
+00:08:55,360 --> 00:09:06,220
+the independent variable
+
+88
+00:09:09,310 --> 00:09:13,690
+T missing يبقى
+
+89
+00:09:13,690 --> 00:09:17,790
+T هي المفقودة
+
+90
+00:09:17,790 --> 00:09:22,310
+These equations
+
+91
+00:09:22,310 --> 00:09:36,150
+هذه المعادلات are in the form are in the form YW
+
+92
+00:09:36,150 --> 00:09:51,330
+primey double prime بدا تساوي f of y و y prime for
+
+93
+00:09:51,330 --> 00:10:01,530
+these equations بهذه المعادلات for these equations
+
+94
+00:10:01,530 --> 00:10:17,160
+we think of y وthink of Y as independent
+
+95
+00:10:17,160 --> 00:10:20,260
+variable
+
+96
+00:10:38,090 --> 00:10:42,910
+بنجي الآن للنوع الثاني ال equations with the
+
+97
+00:10:42,910 --> 00:10:46,710
+independent variable t missing يبقى في الناحية
+
+98
+00:10:46,710 --> 00:10:50,230
+الأولى كان المتغير التابع اللي هو y missing في
+
+99
+00:10:50,230 --> 00:10:53,050
+الناحية اللي عندنا هذه بيكون ال independent
+
+100
+00:10:53,050 --> 00:10:58,490
+variable المتغير المستقل هو اللي مفقود و غير موجود
+
+101
+00:10:58,490 --> 00:11:03,420
+في المعادلةيبقى المعادلات من هذا النوع بتبقى على
+
+102
+00:11:03,420 --> 00:11:08,440
+الشكل التالي y double prime يسوى f of y و y prime
+
+103
+00:11:08,440 --> 00:11:12,940
+اطلع هنا شو كان شكلها كان y double prime اصلا f of
+
+104
+00:11:12,940 --> 00:11:18,780
+t و y prime t موجودة و y مفقودة هنا الحمد لله y
+
+105
+00:11:18,780 --> 00:11:23,750
+موجودة و اللي مفقودة هي mainهي T ، T مش ظاهرة في
+
+106
+00:11:23,750 --> 00:11:28,450
+المعادلة يبقى شو بدنا نعمل في هذه الحالة فبقى بقول
+
+107
+00:11:28,450 --> 00:11:34,850
+له لهذه المعادلة بروح بعتبر ان المتغير المستقل هو
+
+108
+00:11:34,850 --> 00:11:42,430
+Y وليس T تمام؟ يبقى كأنه بعتبر ها we think of Y
+
+109
+00:11:42,430 --> 00:11:46,730
+بروح نعتقد ان Y هو ال independent variable
+
+110
+00:11:46,730 --> 00:11:52,120
+وبالتالي بدأ يصير الشغل على الشكل التالفباجي بقوله
+
+111
+00:11:52,120 --> 00:12:01,560
+put v تساوي y prime اللى هى main اللى هى dy على dt
+
+112
+00:12:01,560 --> 00:12:09,920
+طب احنا بدنا v prime كويس يبقى باجي بقوله v prime
+
+113
+00:12:09,920 --> 00:12:17,570
+تساويبقدرش اقول dy اللي هو ال .. ال .. اللي هو y
+
+114
+00:12:17,570 --> 00:12:24,650
+double prime دغري انا بده ادخل y كمتغير مستقل يبقى
+
+115
+00:12:24,650 --> 00:12:30,810
+هذا بصير dy ا .. ا .. ا .. بده اجيب المشتقة هذه
+
+116
+00:12:30,810 --> 00:12:38,980
+اللي هو dv اللي بدها تساوي dv على dtالان انا
+
+117
+00:12:38,980 --> 00:12:43,820
+باعتقد ان مش T هو المتغير المستقل بدي اعتقد ان Y
+
+118
+00:12:43,820 --> 00:12:51,420
+هو المتغير المستقل اذا بقدر اقول هذه DV على DY في
+
+119
+00:12:51,420 --> 00:12:58,970
+DY على DT عملنا حاجة؟ ماعملناش اشيطب ال DIY على DT
+
+120
+00:12:58,970 --> 00:13:05,630
+هذه هي من V يبقى بقدر أشيل هذه و أكتب بدالها V
+
+121
+00:13:05,630 --> 00:13:10,190
+يبقى صارت V في DV على DY
+
+122
+00:13:13,280 --> 00:13:19,720
+بناء عليها كأنك مفقودة مش مبينة، يبقى لو أخدت
+
+123
+00:13:19,720 --> 00:13:24,380
+المعلومات هذه و جيت عوّط في المعادلة اللي فوق،
+
+124
+00:13:24,380 --> 00:13:30,840
+بصير عندنا V prime اللي هي عبارة من YW prime صح
+
+125
+00:13:30,840 --> 00:13:39,580
+ولا لأ؟يبقى V' بيجي بدل V في DV على DY يبقى بصير
+
+126
+00:13:39,580 --> 00:13:48,700
+المعادل V في DV على DY بيسوي F of Y وV
+
+127
+00:13:54,480 --> 00:14:06,200
+يبقى هذه ايش صارت first order
+
+128
+00:14:06,200 --> 00:14:17,860
+differential equation that can be solved
+
+129
+00:14:27,580 --> 00:14:35,790
+زي ما كنت بحل في بداية هذا الشبطةيبجى هذه امانات
+
+130
+00:14:35,790 --> 00:14:40,690
+تي missing بتفرج شوية عن من عن ال y missing ال y
+
+131
+00:14:40,690 --> 00:14:46,870
+missing أسهل في الحساب من من من ال T missing طيب
+
+132
+00:14:46,870 --> 00:14:52,890
+نعطيكم مثال و نشوف كيف نشتغل الشغلة هذه يبجى
+
+133
+00:14:52,890 --> 00:14:53,450
+example
+
+134
+00:15:06,550 --> 00:15:18,310
+Solve the differential equation yw prime زائد y
+
+135
+00:15:18,310 --> 00:15:25,950
+prime لكل ترابيع يساوي اتنين E اصناق ال Y واعتبر
+
+136
+00:15:25,950 --> 00:15:32,420
+هذه المعادلة رقم واحدالسؤال هو هل شايفين في
+
+137
+00:15:32,420 --> 00:15:38,680
+المعادلة عندنا فيه T يبقى equation with T missing
+
+138
+00:15:38,680 --> 00:15:44,340
+يبقى solution this
+
+139
+00:15:44,340 --> 00:15:57,280
+is an equation with T missing يبقى T مفقودة لذلك
+
+140
+00:15:57,280 --> 00:16:09,360
+بتروح أقوله potV تساوي الـ Y' يعني DY على DT هذا
+
+141
+00:16:09,360 --> 00:16:21,040
+بده يعطينا انه DV او ال V' بده يساوي او ال V هذه
+
+142
+00:16:21,040 --> 00:16:29,750
+بحط هنا DY بجيبنا V' اللي هو DV على DT DV على DTلو
+
+143
+00:16:29,750 --> 00:16:39,210
+DV على DY في DY على DT يبقى V في DVعلى دي Y يعني
+
+144
+00:16:39,210 --> 00:16:44,750
+كأنه احنا بنشتق بالنسبة الى Y يبقى بنا نعتقد ان Y
+
+145
+00:16:44,750 --> 00:16:51,270
+هو المتغير المستقل وليس المتغير التابع بنا نمسك
+
+146
+00:16:51,270 --> 00:16:54,950
+المعلومات هذه ونروح نعوض في المعادلة 1 اللي فوق
+
+147
+00:16:54,950 --> 00:17:01,160
+يبقى الان V Prime هذه عبارة عن مينالـ y double
+
+148
+00:17:01,160 --> 00:17:06,740
+prime يبقى هذه كأنها y double prime بالضبط يبقى
+
+149
+00:17:06,740 --> 00:17:12,220
+أنا بدي أشيل y double prime و بدي أحط مكانها v في
+
+150
+00:17:12,220 --> 00:17:23,260
+dv على dy زائد y prime هي v ترابيع يساوي اتنين e
+
+151
+00:17:23,260 --> 00:17:29,970
+اثناقص yيبقى المعادلة هذه صارت first order
+
+152
+00:17:29,970 --> 00:17:34,170
+differential equation لكن مش مبينة لا linear ولا
+
+153
+00:17:34,170 --> 00:17:38,330
+exact ولا absurd الشو لكن احنا لو روحنا رتبناها
+
+154
+00:17:38,330 --> 00:17:43,490
+هيك وشوفنا ايش كيف ممكن نكتبها يبقى هذه المعادلة
+
+155
+00:17:43,490 --> 00:17:47,410
+بقدر اقول DV على DY
+
+156
+00:18:01,940 --> 00:18:13,140
+ممتاز يبقى هذه معادلة Bernoulli equation
+
+157
+00:18:13,140 --> 00:18:19,160
+يبقى هذه معادلة Bernoulli equationمدام هك يبقى أول
+
+158
+00:18:19,160 --> 00:18:24,260
+شغلة بدها تخلص من مين؟ من ال V اللي عندي إذا بروح
+
+159
+00:18:24,260 --> 00:18:29,700
+بضرب كله في مين؟ في V يبقى لو ضربت في V بصير
+
+160
+00:18:29,700 --> 00:18:36,660
+المعادلة دي كما كانت يبقى V في DV على DY زائد V
+
+161
+00:18:36,660 --> 00:18:45,380
+تربيع يساوي اتنين E أس ناقص Y بعد هيكبعدها أهالي
+
+162
+00:18:45,380 --> 00:18:51,580
+هذه كلها و بفرضها بماذا؟ بمتغير جديد يبقى بقوله
+
+163
+00:18:51,580 --> 00:19:02,970
+put مثلا z تساوي v تربيعإذا بدنا دي زد على مين؟
+
+164
+00:19:02,970 --> 00:19:09,030
+على دي واي لإن احنا بنفضل بنسبة لمين؟ لواي يبقى
+
+165
+00:19:09,030 --> 00:19:19,330
+يساوي اتنين V في دي V على دي Yإذا DV على DY هي
+
+166
+00:19:19,330 --> 00:19:26,950
+عبارة عن نص DZ على DY يبقى V في DV على DY هي عبارة
+
+167
+00:19:26,950 --> 00:19:39,870
+عن نص في DZ على DY زائد Z يساوى 2 U ناقص Yأو لو
+
+168
+00:19:39,870 --> 00:19:46,970
+ضربنا كله في اتنين يبقى معنا هذا الكلام ان دي زد
+
+169
+00:19:46,970 --> 00:19:53,850
+على دي واي زائد اتنين زد يساوي اربعة اي واس ناقص
+
+170
+00:19:53,850 --> 00:20:00,870
+واي ايش صار شكل هذه المعادلة linear يبقى هذه صارت
+
+171
+00:20:00,870 --> 00:20:05,510
+linear first order
+
+172
+00:20:13,120 --> 00:20:18,740
+بنحل المعادلة هادى زى ما كنا بنحل قبل ذلك يبقى بدي
+
+173
+00:20:18,740 --> 00:20:21,460
+اخد لم يقومين يا بنات
+
+174
+00:20:24,050 --> 00:20:31,250
+متغير المستقل هو Y يبقى الميور of Y يبقى E أس
+
+175
+00:20:31,250 --> 00:20:38,990
+تكامل اتنين DY يبقى E أس اتنين Y الآن بنجي
+
+176
+00:20:38,990 --> 00:20:44,270
+للمعادلة هذه كلها وبضربها في قداشبإي أس اتنين واي
+
+177
+00:20:44,270 --> 00:20:52,110
+يبقاش بصير عندي اي أس اتنين واي في دي زد على دي
+
+178
+00:20:52,110 --> 00:20:58,810
+واي زائد اتنين اي أس اتنين واي في زد بده يساوي
+
+179
+00:20:58,810 --> 00:21:06,540
+اربع اي أس واييوز اتنين واي و اي اث ناقص واي بيبقى
+
+180
+00:21:06,540 --> 00:21:12,040
+الاربعة اي اث واي هذه المناط اللي هي عبارة عن اي
+
+181
+00:21:12,040 --> 00:21:20,040
+اث اتنين واي في من في دي زد على دي واي لكل prime
+
+182
+00:21:20,040 --> 00:21:27,540
+والله في زد بس في زد يبقى هذه في زد كلها بيبقى
+
+183
+00:21:27,540 --> 00:21:35,210
+تسوى من اربعة اي اث وايالروحان كامل يبقى لو كملنا
+
+184
+00:21:35,210 --> 00:21:43,570
+بصير عندي A أس اتنين Y في Z بده ساوي تكامل هذه
+
+185
+00:21:43,570 --> 00:21:52,490
+بنفسها زائد كونستان C خلصناه؟ لا ماخلصناش انت وين
+
+186
+00:21:52,490 --> 00:21:53,170
+لسه؟
+
+187
+00:22:13,020 --> 00:22:18,780
+طيب يبقى بقدر اجيب z من هذه المعادلة لو ضربت
+
+188
+00:22:18,780 --> 00:22:24,860
+الطرفين في e أس ناقص اتنين y يبقى هذه بدها تعطيك
+
+189
+00:22:24,860 --> 00:22:36,220
+ما يأتي ان ال z تساوي اربعة e أس ناقص y زائد c e
+
+190
+00:22:36,220 --> 00:22:45,490
+أس ناقص اتنين y طب مين z هذه امانات؟V تربية يعني
+
+191
+00:22:45,490 --> 00:22:55,630
+هذا بده يعطيكي ان V تربية تساوي لخاطر
+
+192
+00:22:55,630 --> 00:23:03,390
+واحد وساطة بخليها هاي اربعة على E اص Y زائد C على
+
+193
+00:23:03,390 --> 00:23:11,760
+E اص اتنين Y او ان شيتم فقولوا E اص اتنين Yباربع E
+
+194
+00:23:11,760 --> 00:23:20,560
+اص Y زائد constant C طيب هذا مين؟ هذا V تربيع احنا
+
+195
+00:23:20,560 --> 00:23:29,480
+بدنا مين؟ بدنا V اذا V تساوي الجدري التربيعي لاربع
+
+196
+00:23:29,480 --> 00:23:37,480
+E اص Y زائد constant C على E اص اتنين Y ال V عند
+
+197
+00:23:37,480 --> 00:23:42,800
+مين هذا ياولادة؟و اين راحت ال V ال V اللي عبارة عن
+
+198
+00:23:42,800 --> 00:23:48,900
+Y prime اللي هي DY على DT يبقى هذا بدي اعطيكي انه
+
+199
+00:23:48,900 --> 00:23:57,420
+DY على DT يسوى الجدر التربيع ل 4 E أص Y زائد
+
+200
+00:23:57,420 --> 00:24:06,260
+constant C على E أص Y E أص 2Y تحت الجدر بصير E أص
+
+201
+00:24:06,260 --> 00:24:13,970
+Yبنروح نكتب المعادلة هذه بشكل اخر فهذه بدها تصير E
+
+202
+00:24:13,970 --> 00:24:19,930
+أوس Y على الجدرى التربية ل 4E أوس Y زائد constant
+
+203
+00:24:19,930 --> 00:24:28,290
+C في Dy بد يساوي DTمرضنا هذا و جسمنا و دي تي
+
+204
+00:24:28,290 --> 00:24:33,850
+ودناها على الشجاعة التانية. بدنا نروح نكامل هذه
+
+205
+00:24:33,850 --> 00:24:39,130
+الدلة. إن كملنا، بيكون خلصنا، بيكون جيبنا الحل. طب
+
+206
+00:24:39,130 --> 00:24:41,390
+كيف بدنا نكامل هذه الدلة يا بناتي؟
+
+207
+00:24:44,000 --> 00:24:49,480
+أه الطرف الشمال تعويض يعني بدي أشيل كل القيمة لتحت
+
+208
+00:24:49,480 --> 00:24:53,760
+الجدر و أحطها ب variable جديد حط أي variable يجي
+
+209
+00:24:53,760 --> 00:24:58,780
+في بالك إذا لو قلنا حط ال w يسوى أربعة e أسواي
+
+210
+00:24:58,780 --> 00:25:06,780
+زائد constant c يبقى ال dw بأربعة e أسواي dy والc
+
+211
+00:25:06,780 --> 00:25:14,500
+مع السلامةإذاً ال E أس Y في ال D Y عبارة عن ربع DW
+
+212
+00:25:14,500 --> 00:25:22,400
+إذا بصير المثل هذه على الشكل التالي هاي ربع و هنا
+
+213
+00:25:22,400 --> 00:25:32,480
+كمان اللي هو الجدر التربيعي ل W وهذه E أس Y DY بDW
+
+214
+00:25:38,100 --> 00:25:46,660
+أو لو ضربت في أربعة بيصير عندك main بيصير عندك w
+
+215
+00:25:46,660 --> 00:25:55,550
+أقص نص دي دابليو بده يساوي أربعة دي تإن كامل
+
+216
+00:25:55,550 --> 00:26:05,530
+الطرفين يبقى W أص نص على نص بده ساوي 4T زائد
+
+217
+00:26:05,530 --> 00:26:08,030
+constant وليكن C1
+
+218
+00:26:11,420 --> 00:26:17,720
+طيب هذا معناه ايش؟ معناته ان اتنين الجذر التربيه
+
+219
+00:26:17,720 --> 00:26:26,840
+الى W لاربع E اص Y زائد constant C بده ساوي اربعة
+
+220
+00:26:26,840 --> 00:26:30,260
+T زائد constant C1
+
+221
+00:26:34,960 --> 00:26:40,960
+بنقدر نجسم كله على الاتنين يبقى الجذر التربيعي
+
+222
+00:26:40,960 --> 00:26:47,580
+لأربعة E اصوي زائد constant C يساوي نصف مين في
+
+223
+00:26:47,580 --> 00:26:55,580
+أربعة T زائد C oneبنقدر نربع الطرفين إذا لو ربعنا
+
+224
+00:26:55,580 --> 00:27:04,820
+الطرفين بصير 4EY زائد constant C بدي ساوي ربع في
+
+225
+00:27:04,820 --> 00:27:15,090
+4T زائد C1 لكل تربيعممكن ننقل C1 على الشجة التانية
+
+226
+00:27:15,090 --> 00:27:26,110
+يبقى بصير 4E وY بده يساوي الرابع في مين في 4T زائد
+
+227
+00:27:26,110 --> 00:27:31,010
+C1 لكل تربية ناقص constant C
+
+228
+00:27:35,420 --> 00:27:43,660
+يبقى هنا هذا الكلام بده يعطيلك ان e اص y بده يسوى
+
+229
+00:27:43,660 --> 00:27:54,780
+واحد على ستاشر في اربعة تزايد c one لكل تربيع ماقص
+
+230
+00:27:57,490 --> 00:28:01,750
+هذا اللى جوا الـ C1 همانات ولا C .. لأ لأ C1 همان
+
+231
+00:28:01,750 --> 00:28:08,990
+يبقى ناقص الرابع C بالشكل اللى عندنا هذا فلاص
+
+232
+00:28:08,990 --> 00:28:13,710
+يكفينا اخلى الحل زي هيك بدك تقوله Y سوى لإن الطرف
+
+233
+00:28:13,710 --> 00:28:18,430
+اليمين مافيش مشكلةلحد هنا والله يعطيك العافية لحظة
+
+234
+00:28:18,430 --> 00:28:22,390
+ان هذا النوع من السؤال أصعب من اللي قبله شوية طب
+
+235
+00:28:22,390 --> 00:28:27,650
+ايش رأيك نجيبلك الفكرتين بسؤال واحد يعني ممكن
+
+236
+00:28:27,650 --> 00:28:32,910
+نجيبلك سؤال T missing وY missing اتنين مرة واحدة
+
+237
+00:28:56,740 --> 00:29:03,880
+طيب ممكن نجيب لك example كتالي
+
+238
+00:29:03,880 --> 00:29:12,560
+solve
+
+239
+00:29:12,560 --> 00:29:14,260
+initial value problem
+
+240
+00:29:20,720 --> 00:29:27,640
+الـ y prime و y double prime يساوي اتنين و ال y
+
+241
+00:29:27,640 --> 00:29:32,960
+عند ال zero بدها تساوي الواحد و ال y prime عند ال
+
+242
+00:29:32,960 --> 00:29:39,580
+zero بدها تساوي اتنين
+
+243
+00:29:39,580 --> 00:29:46,500
+طالعي
+
+244
+00:29:46,500 --> 00:29:53,300
+في المسألة هي مسألة فيها yفيها T يبقى اتنين
+
+245
+00:29:53,300 --> 00:30:05,800
+مفقودين يبقى this is an equation with Y missing
+
+246
+00:30:05,800 --> 00:30:14,960
+and T missing اتنين مفقودين مش موجودين في المثلة
+
+247
+00:30:14,960 --> 00:30:20,460
+يبقى أحلى على الطريقة الأولى والتانيةاللي بدك
+
+248
+00:30:20,460 --> 00:30:24,620
+إياها اللي بتشوفيها أسهل بالنسبالك مين الأولى
+
+249
+00:30:24,620 --> 00:30:31,460
+أسهل؟ خلاص الأولى الأولى يبقى باجي بقوله pot V
+
+250
+00:30:31,460 --> 00:30:38,360
+تساوي Y prime هذا بده يعطينا ان V prime بدها تساوي
+
+251
+00:30:38,360 --> 00:30:44,100
+Y double prime اذا المثل صارت على الشكل التالي V
+
+252
+00:30:44,100 --> 00:30:51,700
+في ال V prime سوى قداشيساوي تمام كويس بدنا هذه
+
+253
+00:30:51,700 --> 00:31:00,120
+المثلة نحاول نكتبها بطريقة أخرى يبقى هذه V وهذه DV
+
+254
+00:31:00,120 --> 00:31:06,180
+على DT بده يساوي كده؟ بده يساوي اتنين يبقى بناء
+
+255
+00:31:06,180 --> 00:31:15,500
+عليها السعر V DV بده يساوي اتنين DTإن كامل الطرفين
+
+256
+00:31:15,500 --> 00:31:25,260
+يبقى V تربيع على 2 يساوي 2 زائد constant C 2T زائد
+
+257
+00:31:25,260 --> 00:31:32,580
+constant C لو ضربتي كله في 2 بصير عندنا مين هنا V
+
+258
+00:31:32,580 --> 00:31:43,750
+تربيع بده يساوي 4T زائد 2C طب مين هي V هذه؟واللي
+
+259
+00:31:43,750 --> 00:31:52,490
+هي Y' يعني صار عندنا Y' لكل ترابيع يساوي اتنين T
+
+260
+00:31:52,490 --> 00:32:00,910
+او الله اربعة T اربعة T زائد اتنين C upon initial
+
+261
+00:32:00,910 --> 00:32:06,070
+condition المشتقة عندها Zero بدأت ساوي قداش اتنين
+
+262
+00:32:06,480 --> 00:32:12,880
+أذا المشتقة ان زيرو بده تساوي اتنين implies
+
+263
+00:32:12,880 --> 00:32:19,340
+المشتقة تساوي قداشها دي اتنين يبقى اتنين تربيه
+
+264
+00:32:19,340 --> 00:32:27,400
+واجتاش لما T تساوي زيرو زائد اتنين C اذا صار عند
+
+265
+00:32:27,400 --> 00:32:29,260
+هنا اربع
+
+266
+00:32:35,190 --> 00:32:40,750
+يبقى صارة المثال اللي عندي على الشكل التالي اللي
+
+267
+00:32:40,750 --> 00:32:50,410
+هو y prime الكل ترابيع بدر ساوي اربعة t زائد اربعة
+
+268
+00:32:50,410 --> 00:32:56,350
+لأن c عندي بقدرش باتنين تمام طبعا بديش y prime بدي
+
+269
+00:32:56,350 --> 00:33:02,770
+y prime شو بنعمل؟بناخد الجذر التربيعي للطرفين يبقى
+
+270
+00:33:02,770 --> 00:33:12,470
+بصير ان y prime بده ساوي الجذر التربيعي لل 4t زائد
+
+271
+00:33:12,470 --> 00:33:19,110
+4 طبعا الجذر ممكن يكون سالب او موجب لكن لما كانت
+
+272
+00:33:19,110 --> 00:33:25,200
+المشتقة عندناقيمة موجبة إذا بنحمله سلبة وبصير بس
+
+273
+00:33:25,200 --> 00:33:30,000
+بالشكل اللي عامله هذا يعني هذه كأنها سارة مين؟ dy
+
+274
+00:33:30,000 --> 00:33:38,740
+على dt يساوي الجذر التربية ل 4t زائد 4 أو ال dy
+
+275
+00:33:38,740 --> 00:33:49,410
+بده يساوي الجذر التربية ل 4t زائد 4 dtتمام بدنا
+
+276
+00:33:49,410 --> 00:33:56,650
+نكامل الطرفين يبقى هذا معناه ان Y يساوي تكامل
+
+277
+00:33:56,650 --> 00:34:05,210
+الجدرى التربية ل 4T زائد 4 كله بالنسبة الى DT كيف
+
+278
+00:34:05,210 --> 00:34:11,550
+بدنا نكامل الدالة هذه يا بنات عادي
+
+279
+00:34:11,550 --> 00:34:17,760
+جدا كل كمية اللى تحت الجدرى بحطها ب Wيبقى هاي W
+
+280
+00:34:17,760 --> 00:34:23,620
+بده يساوي اربعة T زائد اربعة يبقى DW بده يساوي
+
+281
+00:34:23,620 --> 00:34:32,360
+اربعة DT والاربعة دي كبير Zero إذا صار ربع DW بده
+
+282
+00:34:32,360 --> 00:34:41,400
+يساوي من DT إذا صار عندنا Y تساويهي التكامل و هذا
+
+283
+00:34:41,400 --> 00:34:51,060
+ال W أص نص و ال DT بربع دي W يبقى بناء عليه صار Y
+
+284
+00:34:51,060 --> 00:34:59,840
+يساوي الرابع و هذه بصير W أص تلاتة على اتنين على
+
+285
+00:34:59,840 --> 00:35:06,870
+تلاتة على اتنين زائد constant واليكن C1هذه يا بنات
+
+286
+00:35:06,870 --> 00:35:13,970
+بتصير ال y يساوي هذي بتشجل فوق بظل هنا اتنين بصير
+
+287
+00:35:13,970 --> 00:35:22,250
+six اللي هو W أس ثلاثة على اتنين زائد constant C1
+
+288
+00:35:23,750 --> 00:35:28,270
+بتطلع اتنين فوق اتنين مع اربعة بيبقى النص في تلت
+
+289
+00:35:28,270 --> 00:35:34,150
+اللي هو ب 6 و W أستلاتة على اتنين زائد constant C1
+
+290
+00:35:34,150 --> 00:35:38,250
+طب في ان ال initial condition تاني Y عند Zero يسوى
+
+291
+00:35:38,250 --> 00:35:44,090
+الواحد يبقى لو جينا هنا جينا نحسب ال condition او
+
+292
+00:35:44,090 --> 00:35:48,870
+نستخدم ال initial condition التاني مشان حساب ال
+
+293
+00:35:48,870 --> 00:35:50,570
+constant الثاني
+
+294
+00:35:57,060 --> 00:36:01,020
+يبقى بناء ان علي اباجي بقوله احنا عندنا y عند ال
+
+295
+00:36:01,020 --> 00:36:07,740
+zero تساوي واحد implies ان واحد بده يساوي
+
+296
+00:36:12,540 --> 00:36:17,040
+الـ W قدش اللي هي أربعة T زائد أربعة يعني هذه
+
+297
+00:36:17,040 --> 00:36:21,760
+تساوي ال swords الأربعة
+
+298
+00:36:21,760 --> 00:36:27,980
+T زائد أربعة كله أس تلاتة على اتنين زائد constant
+
+299
+00:36:27,980 --> 00:36:34,950
+C1 إذا أصار واحد بده يساوي ال swordsوايه ال ghost
+
+300
+00:36:34,950 --> 00:36:42,310
+تي بي زيرو بيضل أربعة أس تلاتة على اتنين زائد
+
+301
+00:36:42,310 --> 00:36:48,870
+constant C1 يفكر هذا بده يعطينا ان واحد يساوي هذا
+
+302
+00:36:48,870 --> 00:36:53,350
+مناقش الجدر التربيع يلاقى اربعة تكييب اربعة تكييب
+
+303
+00:36:53,350 --> 00:36:59,900
+اللي هي باربعة وستين تحت الجدر التربيع بتمانيةيبقى
+
+304
+00:36:59,900 --> 00:37:08,860
+هاي تمانية على ستة زائد constant C1 او الواحد بده
+
+305
+00:37:08,860 --> 00:37:15,960
+يساوي اربع اتلات زائد constant C1 يبقى C1 بده
+
+306
+00:37:15,960 --> 00:37:26,670
+يساوي سالب تلتإذا بصير الحل اللي عندنا y تساوي هي
+
+307
+00:37:26,670 --> 00:37:35,790
+السُدس برا وهذا أربعة T زائد أربعة أس تلاتة على
+
+308
+00:37:35,790 --> 00:37:43,310
+اتنين وناقص تلت بالشكل اللي عندنا هذا يبقى هذا شكل
+
+309
+00:37:43,310 --> 00:37:47,370
+ال general solution للمعادلة شايفينها صغيرة مش
+
+310
+00:37:47,370 --> 00:37:48,430
+مستهلة يعني
+
+311
+00:37:51,420 --> 00:37:56,960
+أيب عليك بكون انتهى هذا ال chapter وإلى يكون أرقام
+
+312
+00:37:56,960 --> 00:38:03,640
+المسائل التالية اللي هو التمرين العامة تمرين
+
+313
+00:38:03,640 --> 00:38:15,120
+العامة أو مسائل عامة على chapter اتنين
+
+314
+00:38:17,060 --> 00:38:22,920
+المثال من واحد لغاية اتنين و تلاتين اللي هو
+
+315
+00:38:22,920 --> 00:38:31,640
+multiple of three ايش يعني مضعفات تلاتة تلاتة ستة
+
+316
+00:38:31,640 --> 00:38:38,120
+تسعة الاخرين كويس وبنضيف عليها السؤال اربعة و
+
+317
+00:38:38,120 --> 00:38:44,580
+تلاتين تبع recate equationحلنا احنا نمرة A انت بدك
+
+318
+00:38:44,580 --> 00:38:52,560
+تحلي نمرة B و كذلك نمرة C و بعد هيك المسائل تاعة
+
+319
+00:38:52,560 --> 00:38:57,780
+ال Y missing و ال T missing من ستة و تلاتين لغاية
+
+320
+00:38:57,780 --> 00:39:06,880
+خمسين اللي هي ال odd حد
+
+321
+00:39:06,880 --> 00:39:11,750
+لا يتسول في هذا ال chapterأي تساول في هذا ال
+
+322
+00:39:11,750 --> 00:39:17,350
+chapter ننتقل الآن على ال chapter رقم تلاتة اللي
+
+323
+00:39:17,350 --> 00:39:20,570
+هو second order differential equations
+
+324
+00:40:03,180 --> 00:40:15,360
+شبتر تلاتة second order
+
+325
+00:40:15,360 --> 00:40:20,840
+linear differential
+
+326
+00:40:20,840 --> 00:40:24,020
+equations
+
+327
+00:40:27,330 --> 00:40:32,650
+أول section في هذا ال chapter تلاتة واحد اللي هو
+
+328
+00:40:32,650 --> 00:40:40,070
+ال homogeneous differential equations
+
+329
+00:40:40,070 --> 00:40:47,430
+with constant coefficients with constant
+
+330
+00:40:47,430 --> 00:40:49,130
+coefficients
+
+331
+00:41:19,590 --> 00:41:23,780
+خلّي بالكم معنا هنايبقى احنا انتهينا من ال first
+
+332
+00:41:23,780 --> 00:41:28,440
+order differential equation وبنتقل ال second order
+
+333
+00:41:28,440 --> 00:41:32,760
+differential equation كاتبين احنا second order
+
+334
+00:41:32,760 --> 00:41:36,980
+linear differential equation اه احنا في اول
+
+335
+00:41:36,980 --> 00:41:42,020
+chapter ماعرفناش الا ال first order linear
+
+336
+00:41:42,020 --> 00:41:45,140
+differential equation لكن ال second order ماعرفنوش
+
+337
+00:41:45,140 --> 00:41:49,360
+يبقى اول شغلة بنروح انعرف ال second order linear
+
+338
+00:41:49,360 --> 00:41:53,670
+differential equationو بعد هيك نبدأ نفصل في مهم في
+
+339
+00:41:53,670 --> 00:41:59,210
+هذه المعادلة اذا بتروح اكتب التعريف تبعها كتالي
+
+340
+00:41:59,210 --> 00:42:05,850
+definition و بدى اعتبره التعريف الاول a second
+
+341
+00:42:05,850 --> 00:42:11,330
+order
+
+342
+00:42:11,330 --> 00:42:14,430
+ordinary
+
+343
+00:42:14,430 --> 00:42:17,950
+differential
+
+344
+00:42:17,950 --> 00:42:19,850
+equation
+
+345
+00:42:21,390 --> 00:42:29,510
+is an equation in the form is an equation in the
+
+346
+00:42:29,510 --> 00:42:39,410
+form بالشكل التالي اللي هو yw prime او d square y
+
+347
+00:42:39,410 --> 00:42:50,750
+by dt square بدل سوى f of t و y و dy على dt
+
+348
+00:42:51,240 --> 00:42:57,240
+واعتبرين ان هذه المعادلة رقم واحد تعالى فى الثانى
+
+349
+00:42:57,240 --> 00:43:07,660
+الـ differential equation one is called linear is
+
+350
+00:43:07,660 --> 00:43:19,260
+called linear سميها معادلة خطية if it can
+
+351
+00:43:44,270 --> 00:43:45,670
+Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''
+
+352
+00:43:47,120 --> 00:43:54,360
+سميه لهذه كمان المعادلة رقم اتنين where ال P of T
+
+353
+00:43:54,360 --> 00:44:06,360
+وال Q of T and ال G of T are continuous functions
+
+354
+00:44:06,360 --> 00:44:13,240
+of
+
+355
+00:44:13,240 --> 00:44:13,660
+T
+
+356
+00:44:18,320 --> 00:44:28,880
+ملاحظة بسيطة sometimes أحيانا the differential
+
+357
+00:44:28,880 --> 00:44:38,780
+equation اتنين appears تظهر
+
+358
+00:44:38,780 --> 00:44:43,240
+in the form الشكل
+
+359
+00:44:43,240 --> 00:44:54,470
+التالياللي هو P of T في ال YW prime زائد ل Q of T
+
+360
+00:44:54,470 --> 00:45:05,710
+في ال Y prime زائد R of T في ال Y بدها تساوي G of
+
+361
+00:45:05,710 --> 00:45:22,390
+T where حيث ال Pحيث ال P of T بدر ساوي ال Q of T
+
+362
+00:45:22,390 --> 00:45:35,750
+على capital P of T و ال Q of T بدر ساوي ال R of T
+
+363
+00:45:35,750 --> 00:45:40,390
+على capital P of T and
+
+364
+00:45:42,560 --> 00:45:53,400
+الـ G of T بدر ساوي أو الـ G small of T الـ G of T
+
+365
+00:45:53,400 --> 00:46:07,580
+بدر ساوي الـ G of T على capital P of T command
+
+366
+00:46:07,580 --> 00:46:09,120
+definition تالت
+
+367
+00:46:17,530 --> 00:46:32,890
+if the second order differential equation is
+
+368
+00:46:32,890 --> 00:46:47,730
+not in the form في الشكل اتنين orفالشكل اتنين او
+
+369
+00:46:47,730 --> 00:46:54,370
+تلاتة تلاتة طبعا اللي هو الشكل تبع ال G of T هذا
+
+370
+00:46:54,370 --> 00:47:00,650
+الشكل اللي هو تلاتة اذا ماكنتش في اتنين او تلاتة
+
+371
+00:47:00,650 --> 00:47:14,110
+then it is called nonlinear ماهياش
+
+372
+00:47:14,110 --> 00:47:14,730
+خطية
+
+373
+00:47:17,280 --> 00:47:23,640
+أخر definition هو أربعة بيقول ال differential
+
+374
+00:47:23,640 --> 00:47:33,720
+equation the differential equation اتنين or تلاتة
+
+375
+00:47:33,720 --> 00:47:42,160
+is called homogeneous is called homogeneous
+
+376
+00:47:43,660 --> 00:47:54,660
+فالـ G of T بدها تساوي زيرو or G of T بدها تساوي
+
+377
+00:47:54,660 --> 00:48:02,220
+زيرو and non homogeneous
+
+378
+00:48:07,410 --> 00:48:17,410
+الـ G of T لا تساوي Zero أو G of T لا تساوي Zero
+
+379
+00:48:22,230 --> 00:48:27,710
+بنرجع لهذه التعريف مرة ثانية من بدايتها يعني
+
+380
+00:48:27,710 --> 00:48:32,250
+دراستنا في هذا الشتر بدأت تكون مصابة على هذه
+
+381
+00:48:32,250 --> 00:48:38,070
+التعريف second order linear differential equation
+
+382
+00:48:38,070 --> 00:48:42,070
+يبقى احنا بدأ نشتل على معادلات خطية من الرتبة
+
+383
+00:48:42,070 --> 00:48:45,670
+الثانية homogeneous differential equation with
+
+384
+00:48:45,670 --> 00:48:49,710
+constant coefficients بدنا نبدأ بمابالـ
+
+385
+00:48:49,710 --> 00:48:52,550
+homogeneous differential equations المعادلات
+
+386
+00:48:52,550 --> 00:49:00,290
+القطية المتجانسة بمعاملات ثابتة اللي بدنا ناخد
+
+387
+00:49:00,290 --> 00:49:03,450
+المعادلة ال general لغاية ما نوصل لل homogenous
+
+388
+00:49:03,450 --> 00:49:05,970
+يبقى ال second order ordinary differential
+
+389
+00:49:05,970 --> 00:49:08,910
+equation هي عبارة عن المعادلة في الشكل التالي
+
+390
+00:49:08,910 --> 00:49:15,310
+مشتقة ثانية تظهر F ك function في T و Y و Y prime
+
+391
+00:49:17,380 --> 00:49:25,120
+يبقى هذه الدالة بيكون فيها YW' Y' Y وTبنتعرف على
+
+392
+00:49:25,120 --> 00:49:30,340
+شكلها العملي ماهو الشكل العملي للمعادلة واحد فبقى
+
+393
+00:49:30,340 --> 00:49:33,900
+جيب اقول differential equation one is called
+
+394
+00:49:33,900 --> 00:49:38,980
+linear بسميها ده المعادلة الخطية if it can be
+
+395
+00:49:38,980 --> 00:49:42,860
+written as إذا جدرنا نكتب هذه على الشكل التالي
+
+396
+00:49:42,860 --> 00:49:48,040
+اللي عندنا yw prime زي p small of t في y prime
+
+397
+00:49:55,280 --> 00:49:59,100
+لو جدرنا نكتبها على الشكل اللي عندنا هذا بقول
+
+398
+00:49:59,100 --> 00:50:02,520
+الشكل اللي هذا عبارة عن مين linear first or
+
+399
+00:50:02,520 --> 00:50:06,890
+differential equation بشرطان دوال P of T و Q of T
+
+400
+00:50:06,890 --> 00:50:11,190
+و G of T يكونوا continuous functions of T دوال
+
+401
+00:50:11,190 --> 00:50:16,770
+متصلة بالنسبة لمين إلا T أحيانا المعادلة تظهرش على
+
+402
+00:50:16,770 --> 00:50:22,310
+الشكل لأنها ليس بالضرورةيمكن أن يكون المعامل يكون
+
+403
+00:50:22,310 --> 00:50:28,730
+الواتر صحيح ممكن يكون function في T فلو ظهرت as a
+
+404
+00:50:28,730 --> 00:50:34,030
+function في T تظهر على الشكل التالي كابتل P of T
+
+405
+00:50:34,030 --> 00:50:36,830
+هذي small وهذه كابتل
+
+406
+00:50:41,770 --> 00:50:46,330
+زيدي Q of T كابتل في ال wire prime زيدي R of T
+
+407
+00:50:46,330 --> 00:50:51,530
+طبعا كتبتم كابتل مشان اميز المعادلات الاتنين هدول
+
+408
+00:50:51,530 --> 00:50:58,950
+عن بعض R of T بدي تسوي G of T وكأنه هذا هو الأصل
+
+409
+00:50:58,950 --> 00:51:04,630
+هذا هو أصل المعادلة لما روحت جسمت كله على P
+
+410
+00:51:04,630 --> 00:51:10,470
+capital of Tحصلت على P small of T هي Q of T على P
+
+411
+00:51:10,470 --> 00:51:15,730
+of T والـ Q of T small هي R of T على P of T والـ G
+
+412
+00:51:15,730 --> 00:51:20,170
+small of T هي G capital of T على P of T يبقى هذا
+
+413
+00:51:20,170 --> 00:51:25,170
+الأصل اجسمي كله على P capital of T بحصل على مين؟
+
+414
+00:51:25,170 --> 00:51:29,270
+على المعادلة اللي فوق يبقى المعادلة رقم اتنين او
+
+415
+00:51:29,270 --> 00:51:34,950
+المعادلة رقم تلاتة اتنتين بقول عنهم linearاو
+
+416
+00:51:34,950 --> 00:51:40,670
+second order linear differential equations طيب
+
+417
+00:51:40,670 --> 00:51:46,830
+تمام الان if the second order differential is not
+
+418
+00:51:46,830 --> 00:51:52,510
+in the form 2 او 3 يعني لو انا عندي معادلة من
+
+419
+00:51:52,510 --> 00:51:57,490
+الرتبة الثانية ليست على هذا الشكل ولا على الشكل
+
+420
+00:51:57,490 --> 00:52:01,130
+هذا كيف يعني يعني حاطيتلك هنا مثلا تربيع
+
+421
+00:52:28,850 --> 00:52:30,550
+تركيب تركيب تركيب تركيب تركيب تركيب تركيب تركيب
+
+422
+00:52:30,550 --> 00:52:33,610
+تركيب تركيب تركيبهذا البرنامج هو البرنامج
+
+423
+00:52:33,610 --> 00:52:37,990
+الهوموجيني والهوموجيني واللانهوموجيني
+
+424
+00:52:47,880 --> 00:52:51,920
+لاتساوي 0 او لاتساوي 0 يبقى non homogeneous
+
+425
+00:52:51,920 --> 00:52:54,840
+differential equation يبقى ال differential
+
+426
+00:52:54,840 --> 00:52:58,160
+equation اتنين او تلاتة بيقول عنها homogeneous اذا
+
+427
+00:52:58,160 --> 00:53:03,280
+كان g s one of t بده ساوي 0 او g capital of t بده
+
+428
+00:53:03,280 --> 00:53:10,960
+ساوي 0 non homogeneous اذا كانت لاتساوي 0 في ال
+
+429
+00:53:10,960 --> 00:53:15,620
+section اللي بين ادينا احنا شو بناخد؟يعني G of T
+
+430
+00:53:15,620 --> 00:53:19,800
+small او G capital of T بقداش ب zero يبقى هاي اللي
+
+431
+00:53:19,800 --> 00:53:25,080
+بدنا نشتغل عليه خلال مين خلال هذا section لو جايلي
+
+432
+00:53:25,080 --> 00:53:29,380
+كمان كلام زيادة with constant coefficients مش
+
+433
+00:53:29,380 --> 00:53:33,580
+حياله يبقى انا بداخد اللي هو ال homogeneous
+
+434
+00:53:33,580 --> 00:53:38,160
+differential equation و بعدك بداخد حلقة خاصة منها
+
+435
+00:53:38,160 --> 00:53:43,190
+لو كانوا المعاملات ثوابتوبدأ اشتغل عليها و بعد هيك
+
+436
+00:53:43,190 --> 00:53:49,970
+برجع لو كان المعاملات متغيرات تمام يبقى بدل ال
+
+437
+00:53:49,970 --> 00:53:54,630
+section تلاتة هنشتغل علامين على ال homogeneous
+
+438
+00:53:54,630 --> 00:53:58,070
+differential equation وبعد هيك بنرجع لل non
+
+439
+00:53:58,070 --> 00:54:02,140
+homogeneous differential equationبنضغطهم في آخر
+
+440
+00:54:02,140 --> 00:54:07,320
+two sections من هذا ال chapter اللي هو section
+
+441
+00:54:07,320 --> 00:54:13,460
+تلاتة ستة و تلاتة سبعة يبقى بدنا نبدأ بماين بال
+
+442
+00:54:13,460 --> 00:54:19,460
+homogeneous اللي هو differential equation يبقى
+
+443
+00:54:19,460 --> 00:54:26,560
+بدني أخد solution بدنا
+
+444
+00:54:26,560 --> 00:54:35,740
+الحل ofThe homogeneous differential
+
+445
+00:54:35,740 --> 00:54:37,820
+equation
+
+446
+00:54:38,760 --> 00:54:45,640
+اللي capital P of T في ال YW prime زائد capital Q
+
+447
+00:54:45,640 --> 00:54:53,860
+of T في ال Y prime زائد ال R capital of T في ال Y
+
+448
+00:54:53,860 --> 00:54:58,920
+بدها تساوي Zero وهذه يا بنات ساموها للمعادلة رقم
+
+449
+00:54:58,920 --> 00:55:05,420
+واحد هذه اللي بنبدأ نشتغل عليها بدأت أخد الحالة
+
+450
+00:55:05,420 --> 00:55:13,710
+الخاصة اللي احنا جالين عليها FP of T والـ Q of T
+
+451
+00:55:13,710 --> 00:55:30,990
+and ال R of T are constants then equation 1 as ال
+
+452
+00:55:30,990 --> 00:55:31,530
+A
+
+453
+00:55:47,130 --> 00:55:48,530
+Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''
+
+454
+00:55:56,350 --> 00:56:02,230
+يبقى احنا الان وصلنا لمين للعلوم اللي احنا رافعينه
+
+455
+00:56:02,230 --> 00:56:07,370
+هذا يبقى
+
+456
+00:56:07,370 --> 00:56:12,290
+هذا اللي فات كان كله مقدمة عشان نعرف ما هو شكل ال
+
+457
+00:56:12,290 --> 00:56:16,890
+second order lineardifferential equation الان
+
+458
+00:56:16,890 --> 00:56:21,090
+وصلنا الى معادلة بهذا الشكل with constant
+
+459
+00:56:21,090 --> 00:56:25,210
+coefficients يعني المعاملات ال a و ال b و ال c
+
+460
+00:56:25,210 --> 00:56:30,410
+كلهم ثوابت طب كويس صح اصحى الان كيف بدنا نحل
+
+461
+00:56:30,410 --> 00:56:35,710
+المعادلة دى بتروح افترض حل من عندي لهذه المعادلة
+
+462
+00:56:35,710 --> 00:56:41,250
+يبقى بداجي اقول له لات هداش سامينا حاجة ولا لسه دي
+
+463
+00:56:41,250 --> 00:56:43,530
+واحد ساميه لهذه اتنين
+
+464
+00:57:04,410 --> 00:57:11,850
+افترض ان هذا حل مادام حل اذا لازم له حقق المعادلة
+
+465
+00:57:11,850 --> 00:57:18,600
+يبقى thenما دام هيك بده اجيب المشتقة الأولى
+
+466
+00:57:18,600 --> 00:57:23,080
+والمشتقة الثانية وانعوض في المعادلة وانشوف وين
+
+467
+00:57:23,080 --> 00:57:29,300
+بدنا نوصل يبقى لو جيت قول y prime اظن مشتقة ال X
+
+468
+00:57:29,300 --> 00:57:37,380
+بننشل بنفسها ضرب مشتقة الأس كدهش مشتقة الأس؟هذا
+
+469
+00:57:37,380 --> 00:57:41,780
+رقم
+
+470
+00:57:41,780 --> 00:57:48,340
+ثابت يبقى رقم ثابت يبقى رقم ثابت يبقى رقم ثابت
+
+471
+00:57:48,340 --> 00:57:55,840
+يبقى رقم ثابت يبقىبدا امسك المعلومات اللي حصلت
+
+472
+00:57:55,840 --> 00:58:00,620
+عليها و اروح اعوض في المعادلة اتنين يبقى بداجي
+
+473
+00:58:00,620 --> 00:58:12,180
+اقوله هنا Substitute and equation اتنين و جيت نحصل
+
+474
+00:58:12,180 --> 00:58:25,130
+على ما ياتي هذا ال A YR تربيع و E أس RTزائد PR E
+
+475
+00:58:25,130 --> 00:58:37,930
+أُس RT زائد C في E أُس RT سؤال
+
+476
+00:58:37,930 --> 00:58:44,470
+هذا الكلام كله بده يساوي قداش؟ بده يساوي Zero هل
+
+477
+00:58:44,470 --> 00:58:48,610
+ال exponential function في يوم من الأيام ممكن
+
+478
+00:58:48,610 --> 00:58:49,890
+تساوي Zero؟
+
+479
+00:58:53,590 --> 00:58:56,870
+الـ Exponential EOS RT ممكن تساوي 0 في يوم من
+
+480
+00:58:56,870 --> 00:59:01,270
+الأيام؟ عمر ما الـ Exponential بتساوي 0 ولا حتى
+
+481
+00:59:01,270 --> 00:59:05,630
+قيمة سالمة، الـ Exponential دائما و أبدا قيمة
+
+482
+00:59:05,630 --> 00:59:10,070
+موجبة زي ما اتعرفنا عليها، اذا كنتوا بتذكروا في
+
+483
+00:59:10,070 --> 00:59:15,570
+calculus B رسمنا الـ Exponential function فكانت
+
+484
+00:59:15,570 --> 00:59:21,380
+على الشكل التالي اللي عندنايعني هذه A أقصر T لو
+
+485
+00:59:21,380 --> 00:59:26,420
+كانت بالسالب بتجي من وايا من الناحية التانية يبقى
+
+486
+00:59:26,420 --> 00:59:33,240
+هذا محور T و هذا محور Y لو كانت بالسالب بتجي كهك
+
+487
+00:59:35,090 --> 00:59:42,070
+هذا الـ A أُس ناقص RT فهذه النقطة اللي هي الـ Zero
+
+488
+00:59:42,070 --> 00:59:47,290
+وهذه واحدة يبقى دائما و أبدا الرسمة المنحنة تبعها
+
+489
+00:59:47,290 --> 00:59:52,880
+كله أعلى الـ X axis يعني لا تأخذ إلا قيمةمعجبة
+
+490
+00:59:52,880 --> 00:59:59,180
+تمام تمام طيب شو رايك بنقدر نجسم المعادلة كلها على
+
+491
+00:59:59,180 --> 01:00:04,460
+E أُس RT بدون مشاكل مدام لا يساوي Zero بقدر اجسم
+
+492
+01:00:04,460 --> 01:00:12,760
+عليها يبقى لو جسمت طرفين على E أُس RT بنحصل على
+
+493
+01:00:12,760 --> 01:00:14,740
+المعادلة التالية
+
+494
+01:00:30,200 --> 01:00:35,060
+يبقى لو قسمنا على a و اقصرتي بصرا ان ال a في ال
+
+495
+01:00:35,060 --> 01:00:42,780
+RTR تربية زائد PR زائد C يساوي Zero ايش رايكوا هذه
+
+496
+01:00:42,780 --> 01:00:44,220
+معادلة افاضلية
+
+497
+01:00:49,350 --> 01:00:53,910
+لأ، يبقى احنا كنا بنشتغل على معادلة تفاضلية
+
+498
+01:00:53,910 --> 01:00:58,310
+وانتقلنا إلى معادلة عادية، كنا بنشتغل على معادلة
+
+499
+01:00:58,310 --> 01:01:01,810
+تفاضلية من الرتبة الثانية، انتقلنا إلى معادلة
+
+500
+01:01:01,810 --> 01:01:06,510
+عادية من الدرجة الثانية، مظبوط ولا لأ؟ إذا بدنا
+
+501
+01:01:06,510 --> 01:01:13,030
+نحل المعادلة هذه، حل المعادلة هذه كتالة يبقى هذه
+
+502
+01:01:13,030 --> 01:01:18,970
+بنسميها يا بنات The Characteristic
+
+503
+01:01:21,670 --> 01:01:25,370
+المعادلة المميزة أو ال accelerator equation
+
+504
+01:01:25,370 --> 01:01:29,030
+المعادلة المساعدة كتابنا بيقول ال characteristic
+
+505
+01:01:29,030 --> 01:01:34,310
+يبقى the characteristic equation of the
+
+506
+01:01:34,310 --> 01:01:41,230
+differential equation اللي أعطناها الرقمين الرقم
+
+507
+01:01:41,230 --> 01:01:42,090
+اتنين
+
+508
+01:01:44,470 --> 01:01:49,390
+يبقى يادم يسميها المعادلة المميزة للمعادلة رقم
+
+509
+01:01:49,390 --> 01:01:55,630
+اتنين او المعادلة المساعدة للمعادلة رقم اتنينطب
+
+510
+01:01:55,630 --> 01:01:59,630
+بدنا نحلها بقول مضارة تانية بحلها عادي جدا
+
+511
+01:01:59,630 --> 01:02:05,630
+بالاقواس بالقانون يبقى in general R تساوي ناقص
+
+512
+01:02:05,630 --> 01:02:12,130
+بزايد او ناقص الجدر التربيهي لبقى تربيه ناقص 4000
+
+513
+01:02:12,130 --> 01:02:21,430
+جيم كله على 2000 يبقى كام قيمة صار عندى لR؟يعني
+
+514
+01:02:21,430 --> 01:02:28,750
+كام حل صار عندى؟ حلين، يعني هذا بده يعطينا ان R1
+
+515
+01:02:28,750 --> 01:02:35,710
+بده ساوي ناقص B زائد الجدر التربية ل B تربية ناقص
+
+516
+01:02:35,710 --> 01:02:44,840
+4AC على 2Aوالـ R2 يسوى ناقص B ناقص الجذر التربية
+
+517
+01:02:44,840 --> 01:02:54,900
+لB تربية ناقص 4AC كله على 2A تبقى
+
+518
+01:02:54,900 --> 01:03:00,280
+صاروا عندي جذرين طب استنى شوية كيف؟ مين اللي افتح
+
+519
+01:03:00,280 --> 01:03:01,760
+كشوفي شفت سهل؟ ايوة
+
+520
+01:03:12,520 --> 01:03:18,520
+او ايش؟ مركبين يعني تخيلين اه في ان الجذرين هدول
+
+521
+01:03:18,520 --> 01:03:23,040
+يا بنات the roots اللي هم احد ثلاثة احتمالات
+
+522
+01:03:23,040 --> 01:03:28,240
+الاحتمال الاول ان اتنين are different ولا واحد زي
+
+523
+01:03:28,240 --> 01:03:36,090
+التانيالاحتمال الثاني ان اتنين هدول يكونوا متساوين
+
+524
+01:03:36,090 --> 01:03:42,290
+R1 يساوي R2الاحتمال الثالث ان هؤلاء يكونوا are
+
+525
+01:03:42,290 --> 01:03:46,390
+conjugate complex او complex conjugate اتنين
+
+526
+01:03:46,390 --> 01:03:52,930
+يكونوا تخيليين ومترافقين في نفس الوقت اللي بده
+
+527
+01:03:52,930 --> 01:03:59,610
+يتحكم في هذا الكلام المميز من المميز اللي هو
+
+528
+01:03:59,610 --> 01:04:03,430
+القيمة اللي تحت الجذر هذه إذا القيمة اللي تحت
+
+529
+01:04:03,430 --> 01:04:10,390
+الجذر موجبة يبقى اتنين are real and differentيبقى
+
+530
+01:04:10,390 --> 01:04:16,430
+R1 لا يساوي R2 إذا والله المميز يساوي 0 يبقى طار
+
+531
+01:04:16,430 --> 01:04:21,450
+الجدر هذا وطار الجدر السار R1 نقص بيها ع 2 ايه و
+
+532
+01:04:21,450 --> 01:04:27,150
+هنا نقص بيه نفس الشيء يبقى 2R equal R1 بده يساوي
+
+533
+01:04:27,150 --> 01:04:31,470
+R2 الاحتمال الثالث ان لو كانت الكمية اللي تحت
+
+534
+01:04:31,470 --> 01:04:37,110
+الجدر كمية سالبة بيصيروا 2R complex conjugate
+
+535
+01:04:40,420 --> 01:04:47,980
+طيب يبقى هاي طلعنا الجذور اللي هى R1 وR2 يبقى فيها
+
+536
+01:04:47,980 --> 01:04:58,280
+ان الاحتمال الاول انه if ال B تربية ناقص 4AC
+
+537
+01:04:58,280 --> 01:05:11,100
+greater than 0 then the roots are realand
+
+538
+01:05:11,100 --> 01:05:16,500
+different يبقى
+
+539
+01:05:16,500 --> 01:05:24,660
+اتنين حقيقيين ومختلفين that is اي ان R واحد
+
+540
+01:05:24,660 --> 01:05:36,380
+لاتساوي R اتنين R واحد لاتساوي R اتنين نمل اتنين F
+
+541
+01:05:37,100 --> 01:05:45,480
+الـ B تربيع ناقص أربعة AC بده يساوي Zero then the
+
+542
+01:05:45,480 --> 01:05:57,840
+roots are real repeated ايش يعني حقيقية و مكررة
+
+543
+01:05:57,840 --> 01:06:01,920
+يعني اتنين are coincide اتنين بنطبق على بعض يعني
+
+544
+01:06:01,920 --> 01:06:06,720
+اتنين are equal يبقى بقوله that is
+
+545
+01:06:09,170 --> 01:06:19,950
+أنه R1 يسوى R2 نمرة تلاتة F الـ B تربيع نقص أربعة
+
+546
+01:06:19,950 --> 01:06:32,330
+AC أقل من Zero يبقى then they roots are complex
+
+547
+01:06:32,330 --> 01:06:34,670
+conjugate
+
+548
+01:06:38,460 --> 01:06:45,740
+يبقى كمية تخيولية ومترافقة، ايش الكمية التخيولية
+
+549
+01:06:45,740 --> 01:06:50,320
+والمترافقة؟ حد بتقدر تجيبلي عدد تخيولي يا بنات؟
+
+550
+01:06:50,320 --> 01:06:54,880
+عدد كم، عطيني بس، اي حاجة تقول، بس الواحد ترفع
+
+551
+01:06:54,880 --> 01:07:05,290
+يداه وتحكي، اهجذر سالب تلاتة جذر
+
+552
+01:07:05,290 --> 01:07:10,830
+تلاتة I I الحرف الأول من كلمة imaginary
+
+553
+01:07:14,300 --> 01:07:20,360
+لسالب واحد لكن in general الرقم التخيلي او العدد
+
+554
+01:07:20,360 --> 01:07:26,080
+التخيلي بنقول a زائد ib كنتوا في الثانوية بيقولوا
+
+555
+01:07:26,080 --> 01:07:32,060
+سين زائد فاتر حيث اتها الحرف الأول من كلمات تخيلي
+
+556
+01:07:32,060 --> 01:07:38,200
+احنا اننا نقل جهة بيقول a زائد bi او ibحيث I هو
+
+557
+01:07:38,200 --> 01:07:44,080
+الجذر التربيهي لمنين؟ لسالب واحد يبقى لو كان الرقم
+
+558
+01:07:44,080 --> 01:07:50,160
+الأول او العدد الأول يتخيل A زائد B في I التاني
+
+559
+01:07:50,160 --> 01:07:54,960
+ايش بيكون؟ كنجج التابع المرافق يبقى المرافق للجزء
+
+560
+01:07:54,960 --> 01:08:01,620
+التخيلي وليس للجزء الحقيقي بيكون التخيلي A ناقص B
+
+561
+01:08:01,620 --> 01:08:08,730
+في Iتمام؟ طب احنا اليوم بنااخد بس الحالة الأولى و
+
+562
+01:08:08,730 --> 01:08:13,210
+بعد هيك الحالات التانية و التالتة هنحط كل واحدة في
+
+563
+01:08:13,210 --> 01:08:19,810
+section منفصل عن الثاني يبقى بالداج ياخد الان if
+
+564
+01:08:19,810 --> 01:08:29,450
+the roots are real and different
+
+565
+01:08:33,460 --> 01:08:47,220
+then the two solutions of the differential
+
+566
+01:08:47,220 --> 01:09:00,930
+equation two Rالأول هسمي Y1 يسوى E أُس R1T وY2
+
+567
+01:09:00,930 --> 01:09:10,550
+يسوى E أُس R2T لإن R1 وR2 ليسوا إيقال بيسووش بعض
+
+568
+01:09:10,550 --> 01:09:15,840
+طيب إذا صار عندي حلينطب لكن احنا بدنا اشرها بدنا
+
+569
+01:09:15,840 --> 01:09:23,080
+ال general solution يبقى هذا يا بنات لو جيت عوقب
+
+570
+01:09:23,080 --> 01:09:28,880
+في المعادلة رقم اتنين بده يحققها و هذا كمان لو جيت
+
+571
+01:09:28,880 --> 01:09:34,500
+عوقب في المعادلة رقم اتنين بده يحققها لكن في عندي
+
+572
+01:09:34,500 --> 01:09:43,140
+the general solution of
+
+573
+01:09:44,040 --> 01:09:54,720
+the differential equation اتنين is y يسوى c1y1
+
+574
+01:09:54,720 --> 01:10:06,720
+زائد c2y2 يعني y تسوى c1 في e أس r1t زائد c2 في e
+
+575
+01:10:06,720 --> 01:10:09,200
+أس r2t
+
+576
+01:10:11,510 --> 01:10:16,250
+يبقى الامباروز في المستطيل هذا يعتبر ال general
+
+577
+01:10:16,250 --> 01:10:23,850
+solution للمعادلة رقم 2 إذا كانت الجذور حقيقية
+
+578
+01:10:23,850 --> 01:10:29,390
+ومختلفة، لو كان الجذور حقيقية ومختلفة، إلا الشكل
+
+579
+01:10:29,390 --> 01:10:34,010
+غير هذا الشكل، ولو كانت complex إلا شكل غير هذا
+
+580
+01:10:34,010 --> 01:10:39,480
+الشكل، إذا نمنات من الآن فصاعدامن حد ملاقي الجذور
+
+581
+01:10:39,480 --> 01:10:43,100
+تبع تلقى ال characteristic equation اللى فوق are
+
+582
+01:10:43,100 --> 01:10:47,980
+real and different automatic الحل العام للمعادلة
+
+583
+01:10:47,980 --> 01:10:52,240
+رقم اتنين على الشكل اللى عندنا هذا يبقى بس عليك
+
+584
+01:10:52,240 --> 01:10:58,500
+توش دي are واحد و are اتنين طب السؤال هو طب لو
+
+585
+01:10:58,500 --> 01:11:02,800
+اعطانى مثلك كيف بدى ابدأ بقول كويس ان اعطاك مثلة
+
+586
+01:11:02,800 --> 01:11:08,950
+بيعطيك مثلة زى هذهالخطوة الأولى let y تساوي usrtba
+
+587
+01:11:08,950 --> 01:11:12,910
+solution بجيب المشتقة الأولى والمشتقة الثانية
+
+588
+01:11:12,910 --> 01:11:17,010
+ومنها بجيب ال characteristic equation جيبنا ال
+
+589
+01:11:17,010 --> 01:11:22,070
+characteristic equation بروح بحلها عادي جدا زي
+
+590
+01:11:22,070 --> 01:11:26,110
+الاعدادية زي الصف التامن اللي كنا نشتغل فيها هو
+
+591
+01:11:26,110 --> 01:11:29,470
+الصف السابع والله لا أدري ماكان الصف التامن تمام
+
+592
+01:11:29,470 --> 01:11:33,940
+بروح نحل المعادلة هذه ونجيب الجذور R1وهر اتنين
+
+593
+01:11:33,940 --> 01:11:37,780
+اللي جيتهم مختلفين اذا ال general solution على طول
+
+594
+01:11:37,780 --> 01:11:43,400
+القطب الشكل اللي عندنا هذا تمام؟ حد بتسألي سؤال
+
+595
+01:11:43,400 --> 01:11:50,920
+قبل ان ندخل الى الأمثلة؟ انا أمثلة كتير، اه، هي عم
+
+596
+01:11:50,920 --> 01:11:55,760
+بتسأل؟ طيب، ندخل الى الأمثلة
+
+597
+01:12:24,080 --> 01:12:26,480
+المثال الأول examples
+
+598
+01:12:41,730 --> 01:12:49,350
+solve the following differential
+
+599
+01:12:49,350 --> 01:12:52,410
+equation
+
+600
+01:12:52,410 --> 01:13:06,490
+equation z نمرا a y double prime زائد خمسة y prime
+
+601
+01:13:06,490 --> 01:13:16,350
+يساوي زيرو نمرا bY double prime ناقص اتنين Y prime
+
+602
+01:13:16,350 --> 01:13:23,850
+ناقص اتنين Y بده يستوي كده؟ بده يستوي Zero هذا
+
+603
+01:13:23,850 --> 01:13:29,130
+سؤال تمانية من الكتاب وهذا سؤال خمسة من الكتاب
+
+604
+01:13:29,130 --> 01:13:34,110
+يبقى solution اخد
+
+605
+01:13:34,110 --> 01:13:39,360
+المثلة رقم Aبطلع في المثل رقم ايه بلاقي
+
+606
+01:13:39,360 --> 01:13:43,000
+homogeneous differential equation with constant
+
+607
+01:13:43,000 --> 01:13:47,440
+coefficients يبقى automatic بروح بفرض الحل على
+
+608
+01:13:47,440 --> 01:13:58,020
+صيغة E Os RT يبقى let Y بده يتساوي E Os RT بيه
+
+609
+01:13:58,020 --> 01:14:06,890
+solution لل equation اللي عندنا هنا يبقى thenالـ
+
+610
+01:14:06,890 --> 01:14:14,330
+Y' يكون R في E أُس RT والـ YW' يكون R تربية في E
+
+611
+01:14:14,330 --> 01:14:20,770
+أُس RT بعد ذلك بتعوض في المعادلة بيصير R تربية في
+
+612
+01:14:20,770 --> 01:14:29,320
+E أُس RT زائد 5R في E أُس RT يساوي 0بعد هيك بروح
+
+613
+01:14:29,320 --> 01:14:36,280
+نجسم كله على مين على E و أس أرتي بصير R تربيع زائد
+
+614
+01:14:36,280 --> 01:14:42,840
+خمسة R كله بده يسوى مين Zero طيب ايش رايك بدل ما
+
+615
+01:14:42,840 --> 01:14:44,480
+نقعد نفضل و نسوي
+
+616
+01:14:54,100 --> 01:14:59,140
+بنفع على بنفعش بس إيش بدك تقولي؟ تقولي left Y تسوى
+
+617
+01:14:59,140 --> 01:15:01,920
+U RT بيه إيه ال solution then the characteristic
+
+618
+01:15:01,920 --> 01:15:06,580
+equation is كذا تمام؟ يبقى بقى فاهم إن أنت فعلا
+
+619
+01:15:06,580 --> 01:15:09,930
+فاهم الكلام الشتغليهمش حطيت المعادلة فضل غيري و ان
+
+620
+01:15:09,930 --> 01:15:13,350
+كنت كتبتي هذه تحتها دوري من وين أجدت هذه الله أعلم
+
+621
+01:15:13,350 --> 01:15:18,930
+يبقى
+
+622
+01:15:18,930 --> 01:15:27,190
+بنات هذه اللي هي ال characteristic equation وسميلي
+
+623
+01:15:27,190 --> 01:15:34,830
+هذه المعادلة رقم واحد of equation oneيبقى هذه هي
+
+624
+01:15:34,830 --> 01:15:39,470
+المعادلة المميزة أو المعادلة المساعدة للمعادلة
+
+625
+01:15:39,470 --> 01:15:43,450
+العرقموها يبقى الأن بدي أحلي المعادلة هذه بأي
+
+626
+01:15:43,450 --> 01:15:49,410
+طريقة كانت بلجة للتحليل مثلا يبقى فيها R عام
+
+627
+01:15:49,410 --> 01:15:54,810
+المشترك بقدر أخدها يبقى R عام المشترك بظل R زائد
+
+628
+01:15:54,810 --> 01:16:01,650
+خمسة يساوي Zero ومنها R one تساوي Zero وR two كده
+
+629
+01:16:01,650 --> 01:16:07,960
+شو ساوي؟سالب خمسة ممتاز جدا جبت R1 و R2 يبقى هاي
+
+630
+01:16:07,960 --> 01:16:15,460
+ال general solution يبقى بروح بقوله the general
+
+631
+01:16:15,460 --> 01:16:22,920
+solution of equation
+
+632
+01:16:23,890 --> 01:16:32,490
+وان ازم why you say constant C1 في E أُس R one T
+
+633
+01:16:32,490 --> 01:16:38,350
+يعني E أُس جداش E أُس Zero T بدي اكتبها بس المرة
+
+634
+01:16:38,350 --> 01:16:40,790
+دي وبعدين ببطل اكتبها بس عشان اول مرة
+
+635
+01:16:58,800 --> 01:17:06,090
+بنجي للمسألة Bبنفس التكتيك الكلام اللي قلتلكوا
+
+636
+01:17:06,090 --> 01:17:12,790
+الشفوي حصيرا كتبوهله مباشرة يبقاش بدهجة اقول let Y
+
+637
+01:17:12,790 --> 01:17:22,970
+تساوي E أس RT be a solution of the differential
+
+638
+01:17:22,970 --> 01:17:29,570
+equation اتنين وهي هذه سمناها اللي هي الاتنين
+
+639
+01:17:29,570 --> 01:17:37,200
+المثل التانييبقى لو قلتلي هيك دغري then the
+
+640
+01:17:37,200 --> 01:17:50,180
+characteristic equation is R تربيع نقص اتنين R
+
+641
+01:17:50,180 --> 01:17:55,920
+يساوي زيرا ممتاز جدا يبقى ان قلت بالطريقة الاولى
+
+642
+01:17:55,920 --> 01:18:01,580
+ماشي هيك ماشي و ماعناه مشكلة تمامابس السؤال هو
+
+643
+01:18:01,580 --> 01:18:10,060
+بنقدر نحلل المعادلة هذه؟ نقدر؟
+
+644
+01:18:10,060 --> 01:18:16,600
+نقدر؟ لأ بنقدرش يبقى مليش الامانالقانون العام يبقى
+
+645
+01:18:16,600 --> 01:18:22,760
+بناء عليه بروح بقوله هذا بدي يعطينا R يساوي ناقص
+
+646
+01:18:22,760 --> 01:18:28,320
+باله قداش اتنين زائدة وناقص الجدر التربية اللي بات
+
+647
+01:18:28,320 --> 01:18:37,640
+تربية اللي هو اربعة ناقص اربعة الف اللي هو بواحد
+
+648
+01:18:38,040 --> 01:18:46,240
+جيم اللي هو بسالب اتنين كله على اتنين في واحد يبقى
+
+649
+01:18:46,240 --> 01:18:51,260
+احصار هذه يا بناتي اتنين زائد او ناقص اتطلعي هذه
+
+650
+01:18:51,260 --> 01:18:57,940
+بقداش موجة بتمانية موجة بتمانية او اربعة باطماش
+
+651
+01:18:57,940 --> 01:19:03,970
+اطماش اللي هو اتنين جدر تلاتة يبقى اتنينجذر تلاتة
+
+652
+01:19:03,970 --> 01:19:08,330
+على اتنين، تلاحظ القيمة التي تحت الجذر التالية
+
+653
+01:19:08,330 --> 01:19:13,200
+عليها تموج بقىيبقى الجذور اتنين are real and
+
+654
+01:19:13,200 --> 01:19:20,620
+different يبقى صار عند ال R يساوي واحد زائد او
+
+655
+01:19:20,620 --> 01:19:26,380
+ناقص جذر تلاتة يبقى صار R واحد يساوي واحد زائد جذر
+
+656
+01:19:26,380 --> 01:19:33,780
+تلاتة وR اتنين واحد ناقص جذر تلاتة يبقى باجي بقوله
+
+657
+01:19:33,780 --> 01:19:36,720
+the solution
+
+658
+01:19:38,790 --> 01:19:48,070
+Y تساوي C1 في E أس واحد زائد جذر تلاتة كله في T
+
+659
+01:19:48,070 --> 01:20:00,030
+زائد C2 في E أس واحد ناقص جذر تلاتة كله في من؟ كله
+
+660
+01:20:00,030 --> 01:20:00,870
+في T
+
+661
+01:20:09,710 --> 01:20:16,130
+يبقى هاي كتبتله الحل تبع من تبع المعادلة هذه رقم
+
+662
+01:20:16,130 --> 01:20:16,690
+اتنين
+
+663
+01:20:39,390 --> 01:20:51,070
+ناخد كمان مثال example
+
+664
+01:20:51,070 --> 01:20:57,270
+2 solve the
+
+665
+01:20:57,270 --> 01:21:03,090
+following initial
+
+666
+01:21:03,090 --> 01:21:14,040
+value of problems and describeand describe اوصف
+
+667
+01:21:14,040 --> 01:21:24,420
+ليه its behavior its behavior describe
+
+668
+01:21:24,420 --> 01:21:33,580
+its behavior as T increases as T increases
+
+669
+01:21:38,730 --> 01:21:46,650
+سؤال عشرة من الكتاب يقول yw prime زائد اربع y
+
+670
+01:21:46,650 --> 01:21:54,870
+prime زائد تلاتة y تساوي زيرو و ال y عند ال zero
+
+671
+01:21:54,870 --> 01:22:00,030
+بده يساوي اتنين و ال y prime عند ال zero بده يساوي
+
+672
+01:22:00,030 --> 01:22:05,730
+سالب واحد نمرأ بإيه اللي هو سؤال ستة عشر من الكتاب
+
+673
+01:22:06,520 --> 01:22:15,340
+بقول اربعة y double prime ناقص y تساوي zero وال y
+
+674
+01:22:15,340 --> 01:22:22,380
+عند السلب اتنين بده ساوي واحد وال y prime عند
+
+675
+01:22:22,380 --> 01:22:28,760
+السلب اتنين بال y prime عند السلب اتنين بده ساوي
+
+676
+01:22:28,760 --> 01:22:30,320
+سالب واحد
+
+677
+01:23:04,330 --> 01:23:08,950
+سؤال زي ما تشايفين initial value problem و بدل
+
+678
+01:23:08,950 --> 01:23:13,670
+المطلوب اتنين و ليس مطلوبا واحد بيقول حل ال
+
+679
+01:23:13,670 --> 01:23:18,030
+initial value problem و هاتلي ما هو شكل الحل او
+
+680
+01:23:18,030 --> 01:23:23,670
+وصفلي سلوك الحل لما T increases يعني لما T تكبر و
+
+681
+01:23:23,670 --> 01:23:29,330
+تروح لوينللمالة نهاية اذا انا بدي امسك المثلة رقم
+
+682
+01:23:29,330 --> 01:23:34,650
+واحد يبقى هذه اعتبارها المثلة رقم واحد وهذه المثلة
+
+683
+01:23:34,650 --> 01:23:42,390
+رقم اتنين يبقى بيناجي لنمر ايه لت Y تساوي E أس RT
+
+684
+01:23:42,390 --> 01:23:55,390
+ب solution of the differential equation oneيبقى
+
+685
+01:23:55,390 --> 01:24:00,230
+automatic بروح بقوله ايه؟ the characteristic
+
+686
+01:24:00,230 --> 01:24:06,350
+equation is R
+
+687
+01:24:06,350 --> 01:24:14,490
+تربيع زائد اربعة R زائد تلاتة تساوي Zero اظن
+
+688
+01:24:14,490 --> 01:24:20,710
+بتتحلل هذه يا بناتتتحلل مافيش مشكلة يبقى هذا جوس
+
+689
+01:24:20,710 --> 01:24:28,310
+هذا جوس تاني بده يتساوي zero هنا R هنا R هنا 1 هنا
+
+690
+01:24:28,310 --> 01:24:35,070
+3 هنا زائد هنا زائديبقى ZR وزائد تلاتة R زائد
+
+691
+01:24:35,070 --> 01:24:42,510
+أربعة R ومنها ال R بدها تساوي سالب واحد وال R بدها
+
+692
+01:24:42,510 --> 01:24:48,650
+تساوي سالب تلاتة real and different يبقى باجي
+
+693
+01:24:48,650 --> 01:24:54,450
+بقوله the general solution
+
+694
+01:24:57,010 --> 01:25:09,550
+Y تساوي C1 Eوص ناقص T زائد C2 Eوص ناقص تلاتة T طيب
+
+695
+01:25:09,550 --> 01:25:12,650
+ماعطيني ال initial conditions ال initial
+
+696
+01:25:12,650 --> 01:25:19,030
+conditions فايديتهم ان اقدر اجيب قيمة C1 و قيمة C2
+
+697
+01:25:19,030 --> 01:25:23,610
+طب موجودة ال Y و موجودة Y prime اذا خليني اشتقها و
+
+698
+01:25:23,610 --> 01:25:29,150
+بعدين بنعوضيبقى لو روحنا اشتقنا هذه مانتش بصير Y'
+
+699
+01:25:29,810 --> 01:25:40,410
+يسوى ناقص C1 EOS ناقص T ناقص تلاتة C2 EOS ناقص
+
+700
+01:25:40,410 --> 01:25:46,610
+تلاتة T ال exponential زي ما هي ضرب مشتقة الاس
+
+701
+01:25:46,610 --> 01:25:53,410
+تمام نيجي لل initial condition الأوليبقى ال
+
+702
+01:25:53,410 --> 01:25:57,150
+initial condition الأول بيقول لي y عند zero بده
+
+703
+01:25:57,150 --> 01:26:04,390
+يساوي كدهش لإتنين يبقى هذا بده يعطينا لإتنين بدها
+
+704
+01:26:04,390 --> 01:26:12,230
+تساوي c1 زائد c2 لإنه e of zero بواحد و e of zero
+
+705
+01:26:12,230 --> 01:26:16,370
+بواحد نيجي ال condition التاني يقول لي y prime عند
+
+706
+01:26:16,370 --> 01:26:24,810
+zero بقدهش سالب واحد بده يساويحط zero بصير سالب C1
+
+707
+01:26:24,810 --> 01:26:31,990
+سالب تلاتة C2 شو رايك نجمع طب لو جمعنا هدول مع
+
+708
+01:26:31,990 --> 01:26:40,950
+السلامة بضل عندي واحد يساوي النقص اتنين C2 يبقى C2
+
+709
+01:26:40,950 --> 01:26:49,020
+يساوي سالب نصإذا نجيبنا C2، لما نجيبنا C2، مين
+
+710
+01:26:49,020 --> 01:26:54,460
+ضايل علينا؟ C1، روح أعوض في أي من المعادلة تانية،
+
+711
+01:26:54,460 --> 01:26:59,480
+الأسهل لمين؟ المعادلة الأولى، فبعدي بقول المعادلة
+
+712
+01:26:59,480 --> 01:27:09,830
+الأولى على الشكل التاليتساوي C واحد ناقص نص هذا
+
+713
+01:27:09,830 --> 01:27:17,230
+يعني ان C واحد بده يساوي كده اش اتنين و نص يعني
+
+714
+01:27:17,230 --> 01:27:25,650
+خمسة على اتنين اذا صار solution is
+
+715
+01:27:26,860 --> 01:27:38,160
+هي ال Y يساوي C1 خمسة على اتنين E أس ناقص T الان
+
+716
+01:27:38,160 --> 01:27:47,760
+C2 اللي هو ناقص نص E أس ناقص تلاتة T حدا فيكم اي
+
+717
+01:27:47,760 --> 01:27:52,020
+تساؤل هنا اي
+
+718
+01:27:52,020 --> 01:27:59,780
+تساؤلطيب بروح لنمرى بيه من المثلة نمرى بيه برضه
+
+719
+01:27:59,780 --> 01:28:14,220
+let Y تساوي E أس RT بيه solution of equation 2 من
+
+720
+01:28:14,220 --> 01:28:18,340
+اللي بتحكي؟ اه
+
+721
+01:28:18,340 --> 01:28:24,670
+يبقى يقولنا من بدأ تسأل طيب قولوا انت ناسيينأه هذه
+
+722
+01:28:24,670 --> 01:28:31,030
+بدري عليها شوية إذا هذا جانبين له شكل الحل تبع
+
+723
+01:28:31,030 --> 01:28:36,910
+المعادلة هذه يبقى هذه بقدر اكتبها بنات خمسة على
+
+724
+01:28:36,910 --> 01:28:44,610
+اتنين E أس T ناقص واحد على اتنين E أس تلاتة T
+
+725
+01:28:45,770 --> 01:28:51,350
+المطلب التاني من السؤال قال لي وصفلي سلوك الحل لما
+
+726
+01:28:51,350 --> 01:28:55,930
+T increases increases يعني وين بدها تروح يعني
+
+727
+01:28:55,930 --> 01:28:59,610
+معناه كأني بقولي خد ال limit لما T بدها تروح لما
+
+728
+01:28:59,610 --> 01:29:06,050
+لا نهايةاذا بروح بقوله limit ال Y لما T بدها تروح
+
+729
+01:29:06,050 --> 01:29:10,690
+ل infinity بده يساوي limit لما T بدها تروح ل
+
+730
+01:29:10,690 --> 01:29:17,410
+infinity لخمس عالة اتنين E أس T ناقص واحد على
+
+731
+01:29:17,410 --> 01:29:23,550
+اتنين E أس تلاتة T لما T بدها تروح ل المقام هذا
+
+732
+01:29:23,550 --> 01:29:24,850
+كله بقداش
+
+733
+01:29:47,770 --> 01:29:53,390
+يبقى هذا إجابة الشطر الثاني من السؤال ننتقل الآن
+
+734
+01:29:53,390 --> 01:29:54,730
+إلى نمربي
+
+735
+01:29:57,980 --> 01:30:03,040
+علي صوتك شوية والله
+
+736
+01:30:03,040 --> 01:30:08,700
+ماانا فاهم شو اقول ال missing مالها؟ في ان هنا
+
+737
+01:30:08,700 --> 01:30:13,520
+missing و ان هي المعادلة هذه المعادلة بتقدر
+
+738
+01:30:13,520 --> 01:30:19,420
+تعتبريها function with T missing تمام؟ اللي الصعبة
+
+739
+01:30:19,420 --> 01:30:23,210
+مش السهلةانجرب يا عزيزي اذا بتقدري اهلا و اهلا
+
+740
+01:30:23,210 --> 01:30:28,370
+بتقدريش انت حرار لا بتقدري من حقك اه من حقك نسأل و
+
+741
+01:30:28,370 --> 01:30:32,530
+هذا سؤال عادي جدا equation with T missing بس مين
+
+742
+01:30:32,530 --> 01:30:36,650
+أسهل هذي ولا ال T missing هذي أسهل كتير يبقى انا
+
+743
+01:30:36,650 --> 01:30:40,830
+كنت بحل بتلك الطريقة اللي ماكنت بعرفش اتنين هذي
+
+744
+01:30:40,830 --> 01:30:45,030
+linear يعني السهلة يعني ال T missing او ال Y
+
+745
+01:30:45,030 --> 01:30:48,590
+missing بيعطيكي function ماهياش linear يعني مكلقة
+
+746
+01:30:48,590 --> 01:30:52,970
+عشوية هيكتمام و انت بدك تروح و تحليها بس هو بيقولش
+
+747
+01:30:52,970 --> 01:30:56,050
+لك ليه T missing ولا Y missing بيخليك لحالك و
+
+748
+01:30:56,050 --> 01:31:01,850
+يشتغل اللي بدك هيه في حد بتسأل تاني طيب ننتقل الان
+
+749
+01:31:01,850 --> 01:31:07,510
+الى نمرا بيه يبقى باجي بقوله little y تساوي E أُس
+
+750
+01:31:07,510 --> 01:31:17,690
+RTBA solution of the differential
+
+751
+01:31:32,170 --> 01:31:39,610
+بنجي على المعادلة التانية هاي أربعة أربعة ناقص كذا
+
+752
+01:31:39,610 --> 01:31:47,490
+شبناها ناقص واحد يساوي زيروهذا سيعطيك ان R تربيه
+
+753
+01:31:47,490 --> 01:31:54,890
+تساوي قداش يعني هذا سيعطيك ان R تساوي زائد او ناقص
+
+754
+01:31:54,890 --> 01:32:01,750
+نصتمام؟ يعني في عندي كم إجابة؟ جابتين و اتنين are
+
+755
+01:32:01,750 --> 01:32:08,250
+real and different واحد نص والتاني سالف نص يبقى
+
+756
+01:32:08,250 --> 01:32:14,690
+باجي بقوله the general solution is
+
+757
+01:32:26,690 --> 01:32:36,150
+اللي هو Y سوى C1 في E أُس T على 2 زائد C2 في E أُس
+
+758
+01:32:36,150 --> 01:32:45,350
+ناقص T على 2 يبقى هذا هو من الحلبنروح ندور على مين
+
+759
+01:32:45,350 --> 01:32:54,450
+على C1 وC2 إذا خلّينا نشتق بالمرة يبقى Y' يساوي نص
+
+760
+01:32:54,450 --> 01:33:06,210
+C1 إيص T على 2 ناقص نص C2 إيص ناقص T على 2نمسك ال
+
+761
+01:33:06,210 --> 01:33:11,110
+condition الأول ال condition الأول بقول لي why عند
+
+762
+01:33:11,110 --> 01:33:20,170
+السالب اتنين يساوي واحد اذا واحد بده يساوي سي واحد
+
+763
+01:33:20,170 --> 01:33:26,930
+ده حط هنا سالب اتنين بصير ايه السالب واحد يبقى ايه
+
+764
+01:33:26,930 --> 01:33:35,070
+السالب واحدزاد سي اتنين سالي باتنين مع سالي بيصير
+
+765
+01:33:35,070 --> 01:33:42,590
+موجة باتنين يبجأي فقط لا غير هذا ال condition
+
+766
+01:33:42,590 --> 01:33:48,590
+الأولcondition التاني بيقول لي y prime عند السلب
+
+767
+01:33:48,590 --> 01:33:57,330
+اتنين يسوى قداش يسوى السلب واحد هذا بده يعطينا ان
+
+768
+01:33:57,330 --> 01:34:09,130
+السلب واحد يسوى هذا نصوهذا C و C واحد نص C واحد في
+
+769
+01:34:09,130 --> 01:34:20,590
+E أس سالب واحد وهنا ناقص نص وهنا C اتنين في E أس
+
+770
+01:34:20,590 --> 01:34:30,350
+واحد يعني ايه دوري شو رايك نتخلص من انصاص هذه لو
+
+771
+01:34:30,350 --> 01:34:37,520
+ضربنا في اتنينكويس؟ و الله بدنا نضرب في ناقص اتنين
+
+772
+01:34:37,520 --> 01:34:44,780
+حتى نختصر بالمرء هذه بده اخليها زي ما هي هذه ها
+
+773
+01:34:44,780 --> 01:34:50,140
+بده انزلها زي ما هي هذه مش فيها كسور واحد يساوي C
+
+774
+01:34:50,140 --> 01:34:55,360
+واحد في يوس ناقص واحد زائد C اتنين A هذه بده
+
+775
+01:34:55,360 --> 01:35:00,900
+اضربها في سلب اتنين ايش بصير موجة باتنينيساوي
+
+776
+01:35:00,900 --> 01:35:09,760
+السالب C1E والسالب واحد السالب بصير موجب C2E لو
+
+777
+01:35:09,760 --> 01:35:18,460
+جمعنا بروحوا هدول مع بعض وهذا بدي يطلع لي انه 2C2E
+
+778
+01:35:18,460 --> 01:35:27,100
+بدي يساوي قداشيساوي تلاتة يبقى ومنها C2 يساوي
+
+779
+01:35:27,100 --> 01:35:35,460
+تلاتة على اتنين E والسالب واحد هذا
+
+780
+01:35:35,460 --> 01:35:41,800
+جيبنا من اللي هو الـC2 بدنا نروح نجيب C1 بنرجع
+
+781
+01:35:41,800 --> 01:35:45,040
+نعوض في المعادلة هذه خليني اكتب هذا فوق
+
+782
+01:36:04,110 --> 01:36:09,610
+طيب الان بدى امسك المعلومة اللى حصلت عليها هذه هيك
+
+783
+01:36:09,610 --> 01:36:16,150
+واجع وضبان في المعادلة الأولى يعني ماشي بصير عندي
+
+784
+01:36:16,150 --> 01:36:27,070
+واحد يساوي C واحد في E أسالب واحد واحد في C واحد E
+
+785
+01:36:27,070 --> 01:36:32,050
+أسالب واحد الان C اتنين بتلاتة على اتنين E أسالب
+
+786
+01:36:32,050 --> 01:36:40,830
+واحدزائد تلاتة على اتنين E أسالب واحد في ال E يبقى
+
+787
+01:36:40,830 --> 01:36:46,490
+هذه و هذه بروح الله سهل عليهم بصير ان C واحد E
+
+788
+01:36:46,490 --> 01:36:51,690
+أسالب واحد يساوي بدون تلاتة على اتنين يعني واحد و
+
+789
+01:36:51,690 --> 01:37:00,150
+نص بجيب يصير ناقص نصناقص نص اضرب كله في E بيصير C1
+
+790
+01:37:00,150 --> 01:37:09,690
+C1 بده يساوي سالب نص E تمام اذا اصبح الحل على
+
+791
+01:37:09,690 --> 01:37:20,180
+الشكل التالي يبقى ده solution is y تساويY تساوي C
+
+792
+01:37:20,180 --> 01:37:30,580
+واحد اللي يبقى داشر ناقص نص E ناقص نص E في E أس T
+
+793
+01:37:30,580 --> 01:37:38,590
+على اتنين وزائد C اتنين بالموجة بظنزائد تلاتة على
+
+794
+01:37:38,590 --> 01:37:44,610
+اتنين E والسالب واحد تلاتة على اتنين E والسالب
+
+795
+01:37:44,610 --> 01:37:53,900
+واحد في جداش في E والسالب T على اتنينيا بتخليها زي
+
+796
+01:37:53,900 --> 01:37:58,660
+ما هي يا بدك تخليها اي واحدة ماعناش مشكلة تقدر
+
+797
+01:37:58,660 --> 01:38:06,400
+تقولي هذا الكلام يساوي الناقص نص وهذه A أس T على
+
+798
+01:38:06,400 --> 01:38:13,480
+اتنين زائد واحد وهنا زائد تلاتة على اتنين
+
+799
+01:38:22,080 --> 01:38:29,060
+بشارة مخالفة يبقى هذا شكل الحل ال initial value
+
+800
+01:38:29,060 --> 01:38:34,800
+problem لا يزال عن المزيد من الأمثلة بدل المثال
+
+801
+01:38:34,800 --> 01:38:40,810
+اتنينحاجة بتسأل اه ضل عندنا بس شغلة الشغلة بده شوف
+
+802
+01:38:40,810 --> 01:38:46,560
+كيف سلوك الحل هذا لما ت بدها تروح للمالة نهايةيبقى
+
+803
+01:38:46,560 --> 01:38:52,620
+بتروح اخد ال limit لما T بدها تروح للملة نهاية ل Y
+
+804
+01:38:52,620 --> 01:38:59,380
+يبقى limit لما T بدها تروح للملة نهاية لمن لناقص
+
+805
+01:38:59,380 --> 01:39:06,080
+نص E أس T على اتنين زائد واحد زائد تلاتة على اتنين
+
+806
+01:39:06,080 --> 01:39:11,940
+E أس ناقص T على اتنين زائد واحد لما T بدها تروح
+
+807
+01:39:11,940 --> 01:39:16,150
+للملة نهاية ال term هذا كله بجداشة منهازيرو لإن
+
+808
+01:39:16,150 --> 01:39:20,710
+هذا بنزل تحت بصير عدد على مالة نهاية بزيرو لكن هذا
+
+809
+01:39:20,710 --> 01:39:27,470
+كده؟ سالب مالة نهاية هي السالب برا وهذا مالة نهاية
+
+810
+01:39:27,470 --> 01:39:33,830
+هذا سالب مالة نهاية زائد زيرو فبجي بقول the
+
+811
+01:39:33,830 --> 01:39:35,010
+solution
+
+812
+01:39:46,980 --> 01:39:52,520
+يبقى بنقول يازال هناك المزيد من الأمثلة للمرة
+
+813
+01:39:52,520 --> 01:39:56,200
+القادمة ان شاء الله تعالى، أعطيكوا العافية
+
diff --git a/PL9fwy3NUQKwa8ZDfSFGn6H8xVFLzqmCZC/MCBJ_x7Y0Bg_raw.json b/PL9fwy3NUQKwa8ZDfSFGn6H8xVFLzqmCZC/MCBJ_x7Y0Bg_raw.json
new file mode 100644
index 0000000000000000000000000000000000000000..0d47c6825c852ff698ba9199216fd19021166cb5
--- /dev/null
+++ b/PL9fwy3NUQKwa8ZDfSFGn6H8xVFLzqmCZC/MCBJ_x7Y0Bg_raw.json
@@ -0,0 +1 @@
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"word": " يمكن", "probability": 0.79296875}, {"start": 91.85, "end": 92.63, "word": " Bernoulli", "probability": 0.90771484375}, {"start": 92.63, "end": 93.21, "word": " يمكن", "probability": 0.931396484375}, {"start": 93.21, "end": 93.95, "word": " exact", "probability": 0.96337890625}, {"start": 93.95, "end": 94.55, "word": " يمكن", "probability": 0.869873046875}, {"start": 94.55, "end": 94.99, "word": " exact", "probability": 0.923828125}, {"start": 94.99, "end": 95.33, "word": " بس", "probability": 0.985107421875}, {"start": 95.33, "end": 95.61, "word": " بدأ", "probability": 0.65673828125}, {"start": 95.61, "end": 96.07, "word": " integrating", "probability": 0.72998046875}, {"start": 96.07, "end": 96.95, "word": " factor", "probability": 0.8388671875}, {"start": 96.95, "end": 97.95, "word": " يمكن", "probability": 0.953125}, {"start": 97.95, "end": 98.73, "word": " separable", "probability": 0.951416015625}, {"start": 98.73, "end": 99.27, "word": " يمكن", "probability": 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{"start": 151.0, "end": 151.58, "word": " احديها", "probability": 0.69512939453125}, {"start": 151.58, "end": 152.0, "word": " رمز", "probability": 0.9938151041666666}, {"start": 152.0, "end": 152.48, "word": " جديد", "probability": 0.98974609375}, {"start": 152.48, "end": 153.08, "word": " وليكن", "probability": 0.4913736979166667}, {"start": 153.08, "end": 153.26, "word": " v", "probability": 0.7607421875}, {"start": 153.26, "end": 153.38, "word": " و", "probability": 0.66455078125}, {"start": 153.38, "end": 153.6, "word": " بدأ", "probability": 0.6405029296875}, {"start": 153.6, "end": 154.16, "word": " اشتقها", "probability": 0.980078125}, {"start": 154.16, "end": 154.6, "word": " كمان", "probability": 0.9435221354166666}, {"start": 154.6, "end": 155.06, "word": " مرة", "probability": 0.982666015625}, {"start": 155.06, "end": 156.0, "word": " فبصير", "probability": 0.876220703125}, {"start": 156.0, "end": 156.28, "word": " v", "probability": 0.93701171875}, {"start": 156.28, "end": 156.76, "word": " prime", "probability": 0.86328125}, {"start": 156.76, "end": 157.02, "word": " هي", "probability": 0.9482421875}, {"start": 157.02, "end": 157.62, "word": " y", "probability": 0.953125}, {"start": 157.62, "end": 158.0, "word": " double", "probability": 0.52490234375}, {"start": 158.0, "end": 158.58, "word": " prime", "probability": 0.88916015625}], "temperature": 1.0}, {"id": 8, "seek": 18545, "start": 159.01, "end": 185.45, "text": "بتاخد المعلومتين اللي اتنين هدول و اعوض في المعادل اللي عندها default يبقى yw prime بدها تصير مين؟ بدها تصير v prime ال y prime بدها تصير v يبقى المعادلة رقم واحد صارت على الشكل اللي عندنا هذا يبقى مش شايفين الا مشتقة واحدة في المثل بس ايش صارت؟ first order differential equation يمكن linear يمكن exact", "tokens": [3555, 2655, 47283, 3215, 9673, 30241, 20498, 2655, 9957, 13672, 1829, 1975, 2655, 1863, 9957, 8032, 3215, 12610, 4032, 1975, 3615, 2407, 11242, 8978, 9673, 3615, 18513, 1211, 13672, 1829, 43242, 11296, 7576, 7251, 3555, 4587, 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المعادلات are in the form are in the form YW prime", "tokens": [51, 5361, 7251, 3555, 4587, 7578, 314, 39896, 9673, 5172, 4587, 23328, 3660, 1981, 11787, 29538, 9673, 3615, 18513, 1211, 9307, 366, 294, 264, 1254, 366, 294, 264, 1254, 398, 54, 5835], "avg_logprob": -0.34422348484848486, "compression_ratio": 1.146788990825688, "no_speech_prob": 0.0, "words": [{"start": 549.31, "end": 549.67, "word": "T", "probability": 0.1260986328125}, {"start": 549.67, "end": 550.51, "word": " missing", "probability": 0.42578125}, {"start": 550.51, "end": 553.69, "word": " يبقى", "probability": 0.885986328125}, {"start": 553.69, "end": 554.01, "word": " T", "probability": 0.91943359375}, {"start": 554.01, "end": 554.41, "word": " هي", "probability": 0.61865234375}, {"start": 554.41, "end": 557.79, "word": " المفقودة", "probability": 0.976171875}, {"start": 557.79, "end": 558.93, "word": " These", "probability": 0.26708984375}, {"start": 558.93, "end": 562.31, "word": " equations", "probability": 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"temperature": 1.0}, {"id": 36, "seek": 85786, "start": 834.48, "end": 857.86, "text": "يبقى هذه ايش صارت first order differential equation that can be solved", "tokens": [1829, 3555, 4587, 7578, 29538, 1975, 1829, 8592, 20328, 9640, 2655, 700, 1668, 15756, 5367, 300, 393, 312, 13041], "avg_logprob": -0.4624999910593033, "compression_ratio": 0.9655172413793104, "no_speech_prob": 0.0, "words": [{"start": 834.48, "end": 835.88, "word": "يبقى", "probability": 0.7321014404296875}, {"start": 835.88, "end": 836.16, "word": " هذه", "probability": 0.4951171875}, {"start": 836.16, "end": 836.4, "word": " ايش", "probability": 0.4034016927083333}, {"start": 836.4, "end": 836.98, "word": " صارت", "probability": 0.8473307291666666}, {"start": 836.98, "end": 838.24, "word": " first", "probability": 0.2415771484375}, {"start": 838.24, "end": 846.2, "word": " order", "probability": 0.931640625}, {"start": 846.2, "end": 848.22, "word": " differential", "probability": 0.91259765625}, {"start": 848.22, 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نجسم كله على الاتنين يبقى الجذر التربيعي لأربعة E اصوي زائد constant C يساوي نصف مين في أربعة T زائد C one", "tokens": [3555, 1863, 28543, 2288, 8717, 7435, 38251, 28242, 3224, 15844, 2423, 9307, 1863, 9957, 7251, 3555, 4587, 7578, 25724, 8848, 2288, 16712, 2288, 21292, 3615, 1829, 5296, 10721, 25513, 27884, 462, 1975, 9381, 45865, 30767, 16373, 3215, 5754, 383, 7251, 3794, 995, 45865, 8717, 9381, 5172, 3714, 9957, 8978, 5551, 25513, 27884, 314, 30767, 16373, 3215, 383, 472], "avg_logprob": -0.3567266999664953, "compression_ratio": 1.355072463768116, "no_speech_prob": 0.0, "words": [{"start": 1594.96, "end": 1595.5, "word": "بنقدر", "probability": 0.596435546875}, {"start": 1595.5, "end": 1595.92, "word": " نجسم", "probability": 0.9353841145833334}, {"start": 1595.92, "end": 1596.24, "word": " كله", "probability": 0.95068359375}, {"start": 1596.24, "end": 1596.36, "word": " على", "probability": 0.59716796875}, {"start": 1596.36, "end": 1598.56, "word": " الاتنين", "probability": 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165101, "start": 1631.27, "end": 1651.01, "text": "ممكن ننقل C1 على الشجة التانية يبقى بصير 4E وY بده يساوي الرابع في مين في 4T زائد C1 لكل تربية ناقص constant C", "tokens": [2304, 43020, 8717, 1863, 4587, 1211, 383, 16, 15844, 25124, 7435, 3660, 16712, 7649, 10632, 7251, 3555, 4587, 7578, 4724, 9381, 13546, 1017, 36, 4032, 56, 47525, 3224, 7251, 3794, 995, 45865, 34892, 16758, 3615, 8978, 3714, 9957, 8978, 1017, 51, 30767, 16373, 3215, 383, 16, 5296, 28820, 6055, 25513, 10632, 8717, 995, 4587, 9381, 5754, 383], "avg_logprob": -0.2578125123319955, "compression_ratio": 1.2517482517482517, "no_speech_prob": 0.0, "words": [{"start": 1631.27, "end": 1631.93, "word": "ممكن", "probability": 0.76220703125}, {"start": 1631.93, "end": 1632.51, "word": " ننقل", "probability": 0.934814453125}, {"start": 1632.51, "end": 1633.17, "word": " C1", "probability": 0.67333984375}, {"start": 1633.17, "end": 1633.81, "word": " على", "probability": 0.70166015625}, {"start": 1633.81, "end": 1634.47, "word": 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"end": 1694.43, "word": " مافيش", "probability": 0.7098795572916666}, {"start": 1694.43, "end": 1694.95, "word": " مشكلة", "probability": 0.9835611979166666}], "temperature": 1.0}, {"id": 73, "seek": 171291, "start": 1695.21, "end": 1712.91, "text": "لحد هنا والله يعطيك العافية لحظة ان هذا النوع من السؤال أصعب من اللي قبله شوية طب ايش رأيك نجيبلك الفكرتين بسؤال واحد يعني ممكن نجيبلك سؤال T missing وY missing اتنين مرة واحدة", "tokens": [1211, 24401, 34105, 16070, 43761, 37495, 9566, 1829, 4117, 18863, 31845, 10632, 5296, 5016, 19913, 3660, 16472, 23758, 28239, 45367, 9154, 21136, 33604, 6027, 5551, 9381, 3615, 3555, 9154, 13672, 1829, 12174, 36150, 3224, 13412, 2407, 10632, 23032, 3555, 1975, 1829, 8592, 12602, 10721, 1829, 4117, 8717, 7435, 1829, 3555, 23275, 27188, 4117, 43500, 9957, 4724, 3794, 33604, 6027, 36764, 24401, 37495, 22653, 3714, 43020, 8717, 7435, 1829, 3555, 23275, 8608, 33604, 6027, 314, 5361, 4032, 56, 5361, 1975, 2655, 1863, 9957, 3714, 25720, 36764, 24401, 3660], "avg_logprob": -0.15243252654644576, "compression_ratio": 1.702247191011236, "no_speech_prob": 5.960464477539063e-08, "words": [{"start": 1695.21, "end": 1695.71, "word": "لحد", "probability": 0.850341796875}, {"start": 1695.71, "end": 1696.01, "word": " هنا", "probability": 0.982421875}, {"start": 1696.01, "end": 1696.27, "word": " والله", "probability": 0.7332763671875}, {"start": 1696.27, "end": 1696.67, "word": " يعطيك", "probability": 0.97900390625}, {"start": 1696.67, "end": 1697.19, "word": " العافية", "probability": 0.9466145833333334}, {"start": 1697.19, "end": 1698.43, "word": " لحظة", "probability": 0.764251708984375}, {"start": 1698.43, "end": 1698.63, "word": " ان", "probability": 0.56103515625}, {"start": 1698.63, "end": 1698.99, "word": " هذا", "probability": 0.84423828125}, {"start": 1698.99, "end": 1699.23, "word": " النوع", "probability": 0.883544921875}, {"start": 1699.23, "end": 1699.37, "word": " من", "probability": 0.91015625}, {"start": 1699.37, "end": 1699.61, 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{"id": 74, "seek": 175426, "start": 1736.74, "end": 1754.26, "text": "طيب ممكن نجيب لك example كتالي solve initial value problem", "tokens": [9566, 1829, 3555, 3714, 43020, 8717, 7435, 1829, 3555, 5296, 4117, 1365, 9122, 2655, 6027, 1829, 5039, 5883, 2158, 1154], "avg_logprob": -0.27864583900996615, "compression_ratio": 0.9620253164556962, "no_speech_prob": 0.0, "words": [{"start": 1736.74, "end": 1737.64, "word": "طيب", "probability": 0.8623046875}, {"start": 1737.64, "end": 1738.38, "word": " ممكن", "probability": 0.962158203125}, {"start": 1738.38, "end": 1738.9, "word": " نجيب", "probability": 0.8602294921875}, {"start": 1738.9, "end": 1739.12, "word": " لك", "probability": 0.6868896484375}, {"start": 1739.12, "end": 1739.9, "word": " example", "probability": 0.830078125}, {"start": 1739.9, "end": 1743.88, "word": " كتالي", "probability": 0.748291015625}, {"start": 1743.88, "end": 1752.56, "word": " solve", "probability": 0.69287109375}, {"start": 1752.56, "end": 1753.14, "word": " initial", "probability": 0.47412109375}, {"start": 1753.14, "end": 1753.56, "word": " value", "probability": 0.98779296875}, {"start": 1753.56, "end": 1754.26, "word": " problem", "probability": 0.94921875}], "temperature": 1.0}, {"id": 75, "seek": 178970, "start": 1760.72, "end": 1789.7, "text": "الـ y prime و y double prime يساوي اتنين و ال y عند ال zero بدها تساوي الواحد و ال y prime عند ال zero بدها تساوي اتنين طالعي في المسألة هي مسألة فيها y", "tokens": [6027, 39184, 288, 5835, 4032, 288, 3834, 5835, 7251, 3794, 995, 45865, 1975, 2655, 1863, 9957, 4032, 2423, 288, 43242, 2423, 4018, 47525, 11296, 6055, 3794, 995, 45865, 2423, 14407, 24401, 4032, 2423, 288, 5835, 43242, 2423, 4018, 47525, 11296, 6055, 3794, 995, 45865, 1975, 2655, 1863, 9957, 23032, 6027, 3615, 1829, 8978, 9673, 3794, 10721, 37977, 39896, 47524, 10721, 37977, 8978, 11296, 288], "avg_logprob": -0.275, "compression_ratio": 1.7611940298507462, "no_speech_prob": 0.0, "words": [{"start": 1760.72, "end": 1761.16, 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T missing اتنين مفقودين مش موجودين في المثلة يبقى أحلى على الطريقة الأولى والتانية", "tokens": [41185, 11296, 314, 7251, 3555, 4587, 7578, 1975, 2655, 1863, 9957, 3714, 5172, 4587, 23328, 9957, 7251, 3555, 4587, 7578, 341, 307, 364, 5367, 365, 398, 5361, 293, 314, 5361, 1975, 2655, 1863, 9957, 3714, 5172, 4587, 23328, 9957, 37893, 3714, 29245, 23328, 9957, 8978, 9673, 12984, 37977, 7251, 3555, 4587, 7578, 5551, 5016, 23942, 15844, 41950, 16572, 28671, 16247, 12610, 7578, 16070, 2655, 7649, 10632], "avg_logprob": -0.136077424038702, "compression_ratio": 1.5592105263157894, "no_speech_prob": 0.0, "words": [{"start": 1790.82, "end": 1791.4, "word": "فيها", "probability": 0.537353515625}, {"start": 1791.4, "end": 1791.7, "word": " T", "probability": 0.6962890625}, {"start": 1791.7, "end": 1792.94, "word": " يبقى", "probability": 0.9580078125}, {"start": 1792.94, "end": 1793.3, "word": " اتنين", "probability": 0.93896484375}, {"start": 1793.3, "end": 1794.16, "word": " مفقودين", 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"seek": 184702, "start": 1819.44, "end": 1847.02, "text": "اللي بدك إياها اللي بتشوفيها أسهل بالنسبالك مين الأولى أسهل؟ خلاص الأولى الأولى يبقى باجي بقوله pot V تساوي Y prime هذا بده يعطينا ان V prime بدها تساوي Y double prime اذا المثل صارت على الشكل التالي V في ال V prime سوى قداش", "tokens": [6027, 20292, 47525, 4117, 11933, 25528, 11296, 13672, 1829, 39894, 8592, 38688, 1829, 11296, 5551, 3794, 3224, 1211, 20666, 1863, 35457, 6027, 4117, 3714, 9957, 16247, 12610, 7578, 5551, 3794, 3224, 1211, 22807, 16490, 1211, 33546, 16247, 12610, 7578, 16247, 12610, 7578, 7251, 3555, 4587, 7578, 4724, 26108, 1829, 4724, 39648, 3224, 1847, 691, 6055, 3794, 995, 45865, 398, 5835, 23758, 47525, 3224, 37495, 9566, 1829, 8315, 16472, 691, 5835, 47525, 11296, 6055, 3794, 995, 45865, 398, 3834, 5835, 1975, 15730, 9673, 12984, 1211, 20328, 9640, 2655, 15844, 25124, 28820, 16712, 6027, 1829, 691, 8978, 2423, 691, 5835, 8608, 2407, 7578, 12174, 3215, 33599], "avg_logprob": -0.25669642630077544, 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0.9459228515625}, {"start": 2802.91, "end": 2803.73, "word": " or", "probability": 0.6142578125}], "temperature": 1.0}, {"id": 113, "seek": 283473, "start": 2805.37, "end": 2834.73, "text": "فالشكل اتنين او تلاتة تلاتة طبعا اللي هو الشكل تبع ال G of T هذا الشكل اللي هو تلاتة اذا ماكنتش في اتنين او تلاتة then it is called nonlinear ماهياش خطية", "tokens": [5172, 6027, 8592, 28820, 1975, 2655, 1863, 9957, 1975, 2407, 6055, 1211, 9307, 3660, 6055, 1211, 9307, 3660, 23032, 3555, 3615, 995, 13672, 1829, 31439, 25124, 28820, 6055, 3555, 3615, 2423, 460, 295, 314, 23758, 25124, 28820, 13672, 1829, 31439, 6055, 1211, 9307, 3660, 1975, 15730, 19446, 19452, 2655, 8592, 8978, 1975, 2655, 1863, 9957, 1975, 2407, 6055, 1211, 9307, 3660, 550, 309, 307, 1219, 2107, 28263, 19446, 3224, 1829, 33599, 16490, 9566, 10632], "avg_logprob": -0.19010417143503824, "compression_ratio": 1.6644295302013423, "no_speech_prob": 0.0, "words": [{"start": 2805.37, "end": 2806.29, "word": "فالشكل", "probability": 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0.740234375}, {"start": 2813.15, "end": 2813.49, "word": " T", "probability": 0.97509765625}, {"start": 2813.49, "end": 2814.37, "word": " هذا", "probability": 0.88671875}, {"start": 2814.37, "end": 2815.07, "word": " الشكل", "probability": 0.978271484375}, {"start": 2815.07, "end": 2815.73, "word": " اللي", "probability": 0.978759765625}, {"start": 2815.73, "end": 2816.17, "word": " هو", "probability": 0.99169921875}, {"start": 2816.17, "end": 2817.03, "word": " تلاتة", "probability": 0.9765625}, {"start": 2817.03, "end": 2817.85, "word": " اذا", "probability": 0.7626953125}, {"start": 2817.85, "end": 2818.43, "word": " ماكنتش", "probability": 0.9661865234375}, {"start": 2818.43, "end": 2818.61, "word": " في", "probability": 0.5439453125}, {"start": 2818.61, "end": 2819.05, "word": " اتنين", "probability": 0.9649658203125}, {"start": 2819.05, "end": 2819.41, "word": " او", "probability": 0.97509765625}, {"start": 2819.41, "end": 2820.65, "word": " تلاتة", "probability": 0.990478515625}, {"start": 2820.65, "end": 2821.59, "word": " then", "probability": 0.462646484375}, {"start": 2821.59, "end": 2823.79, "word": " it", "probability": 0.96875}, {"start": 2823.79, "end": 2825.31, "word": " is", "probability": 0.9443359375}, {"start": 2825.31, "end": 2828.03, "word": " called", "probability": 0.89990234375}, {"start": 2828.03, "end": 2830.47, "word": " nonlinear", "probability": 0.763671875}, {"start": 2830.47, "end": 2834.11, "word": " ماهياش", "probability": 0.9547119140625}, {"start": 2834.11, "end": 2834.73, "word": " خطية", "probability": 0.9737955729166666}], "temperature": 1.0}, {"id": 114, "seek": 286216, "start": 2837.28, "end": 2862.16, "text": "أخر definition هو أربعة بيقول ال differential equation the differential equation اتنين or تلاتة is called homogeneous is called homogeneous", "tokens": [10721, 34740, 7123, 31439, 5551, 25513, 27884, 4724, 1829, 39648, 2423, 15756, 5367, 264, 15756, 5367, 1975, 2655, 1863, 9957, 420, 6055, 1211, 9307, 3660, 307, 1219, 42632, 307, 1219, 42632], "avg_logprob": -0.28588866628706455, "compression_ratio": 1.3833333333333333, "no_speech_prob": 0.0, "words": [{"start": 2837.28, "end": 2837.96, "word": "أخر", "probability": 0.6728515625}, {"start": 2837.96, "end": 2838.74, "word": " definition", "probability": 0.204345703125}, {"start": 2838.74, "end": 2840.14, "word": " هو", "probability": 0.299560546875}, {"start": 2840.14, "end": 2840.94, "word": " أربعة", "probability": 0.7901204427083334}, {"start": 2840.94, "end": 2843.18, "word": " بيقول", "probability": 0.85498046875}, {"start": 2843.18, "end": 2843.3, "word": " ال", "probability": 0.69970703125}, {"start": 2843.3, "end": 2843.64, "word": " differential", "probability": 0.78759765625}, {"start": 2843.64, "end": 2844.8, "word": " equation", "probability": 0.986328125}, {"start": 2844.8, "end": 2846.62, "word": " the", "probability": 0.328125}, {"start": 2846.62, "end": 2848.66, "word": " differential", "probability": 0.86376953125}, {"start": 2848.66, "end": 2850.64, "word": " equation", "probability": 0.98193359375}, {"start": 2850.64, "end": 2851.64, "word": " اتنين", "probability": 0.931640625}, {"start": 2851.64, "end": 2852.2, "word": " or", "probability": 0.61181640625}, {"start": 2852.2, "end": 2853.72, "word": " تلاتة", "probability": 0.94677734375}, {"start": 2853.72, "end": 2855.34, "word": " is", "probability": 0.86767578125}, {"start": 2855.34, "end": 2855.72, "word": " called", "probability": 0.935546875}, {"start": 2855.72, "end": 2856.48, "word": " homogeneous", "probability": 0.90771484375}, {"start": 2856.48, "end": 2857.84, "word": " is", "probability": 0.8525390625}, {"start": 2857.84, "end": 2859.6, "word": " called", "probability": 0.931640625}, {"start": 2859.6, "end": 2862.16, "word": " homogeneous", "probability": 0.9560546875}], "temperature": 1.0}, {"id": 115, "seek": 288222, "start": 2863.66, "end": 2882.22, "text": "فالـ G of T بدها تساوي زيرو or G of T بدها تساوي زيرو and non homogeneous", "tokens": [5172, 6027, 39184, 460, 295, 314, 47525, 11296, 6055, 3794, 995, 45865, 30767, 13546, 2407, 420, 460, 295, 314, 47525, 11296, 6055, 3794, 995, 45865, 30767, 13546, 2407, 293, 2107, 42632], "avg_logprob": -0.42626954335719347, "compression_ratio": 1.3205128205128205, "no_speech_prob": 5.960464477539063e-08, "words": [{"start": 2863.66, "end": 2865.06, "word": "فالـ", "probability": 0.3854166666666667}, {"start": 2865.06, "end": 2865.38, "word": " G", "probability": 0.51806640625}, {"start": 2865.38, "end": 2865.88, "word": " of", "probability": 0.4873046875}, {"start": 2865.88, "end": 2866.16, "word": " T", "probability": 0.9638671875}, {"start": 2866.16, "end": 2866.66, "word": " بدها", "probability": 0.84326171875}, {"start": 2866.66, "end": 2867.34, "word": " تساوي", "probability": 0.964599609375}, {"start": 2867.34, "end": 2868.06, "word": " زيرو", "probability": 0.614501953125}, {"start": 2868.06, "end": 2869.74, "word": " or", "probability": 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314, 20193, 6055, 3794, 995, 45865, 17182], "avg_logprob": -0.27414773404598236, "compression_ratio": 1.3137254901960784, "no_speech_prob": 0.0, "words": [{"start": 2887.41, "end": 2887.83, "word": "الـ", "probability": 0.75390625}, {"start": 2887.83, "end": 2888.05, "word": " G", "probability": 0.5419921875}, {"start": 2888.05, "end": 2888.49, "word": " of", "probability": 0.420166015625}, {"start": 2888.49, "end": 2888.93, "word": " T", "probability": 0.97119140625}, {"start": 2888.93, "end": 2889.85, "word": " لا", "probability": 0.708984375}, {"start": 2889.85, "end": 2890.83, "word": " تساوي", "probability": 0.9666748046875}, {"start": 2890.83, "end": 2891.51, "word": " Zero", "probability": 0.415283203125}, {"start": 2891.51, "end": 2892.45, "word": " أو", "probability": 0.2392578125}, {"start": 2892.45, "end": 2893.83, "word": " G", "probability": 0.56689453125}, {"start": 2893.83, "end": 2894.65, "word": " of", "probability": 0.82080078125}, {"start": 2894.65, "end": 2895.11, "word": " T", "probability": 0.97412109375}, {"start": 2895.11, "end": 2896.05, "word": " لا", "probability": 0.8369140625}, {"start": 2896.05, "end": 2896.97, "word": " تساوي", "probability": 0.990234375}, {"start": 2896.97, "end": 2897.41, "word": " Zero", "probability": 0.9365234375}], "temperature": 1.0}, {"id": 117, "seek": 292883, "start": 2902.23, "end": 2928.83, "text": "بنرجع لهذه التعريف مرة ثانية من بدايتها يعني دراستنا في هذا الشتر بدأت تكون مصابة على هذه التعريف second order linear differential equation يبقى احنا بدأ نشتل على معادلات خطية من الرتبة الثانية homogeneous differential equation with constant coefficients بدنا نبدأ بما", "tokens": [3555, 1863, 47341, 3615, 46740, 24192, 16712, 3615, 16572, 5172, 3714, 25720, 38637, 7649, 10632, 9154, 4724, 28259, 36081, 11296, 37495, 22653, 11778, 23557, 14851, 8315, 8978, 23758, 25124, 2655, 2288, 47525, 10721, 2655, 6055, 30544, 3714, 9381, 16758, 3660, 15844, 29538, 16712, 3615, 16572, 5172, 1150, 1668, 8213, 15756, 5367, 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2916.45, "word": " order", "probability": 0.8828125}, {"start": 2916.45, "end": 2916.85, "word": " linear", "probability": 0.8486328125}, {"start": 2916.85, "end": 2917.45, "word": " differential", "probability": 0.91357421875}, {"start": 2917.45, "end": 2918.07, "word": " equation", "probability": 0.9580078125}, {"start": 2918.07, "end": 2918.31, "word": " يبقى", "probability": 0.637451171875}, {"start": 2918.31, "end": 2918.69, "word": " احنا", "probability": 0.8587239583333334}, {"start": 2918.69, "end": 2919.03, "word": " بدأ", "probability": 0.748046875}, {"start": 2919.03, "end": 2919.39, "word": " نشتل", "probability": 0.77716064453125}, {"start": 2919.39, "end": 2919.61, "word": " على", "probability": 0.89306640625}, {"start": 2919.61, "end": 2920.27, "word": " معادلات", "probability": 0.9437255859375}, {"start": 2920.27, "end": 2921.03, "word": " خطية", "probability": 0.9305013020833334}, {"start": 2921.03, "end": 2921.33, "word": " من", "probability": 0.98974609375}, {"start": 2921.33, "end": 2922.07, "word": " الرتبة", "probability": 0.8997395833333334}, {"start": 2922.07, "end": 2922.99, "word": " الثانية", "probability": 0.9713134765625}, {"start": 2922.99, "end": 2924.09, "word": " homogeneous", "probability": 0.9462890625}, {"start": 2924.09, "end": 2924.83, "word": " differential", "probability": 0.90673828125}, {"start": 2924.83, "end": 2925.37, "word": " equation", "probability": 0.8740234375}, {"start": 2925.37, "end": 2925.67, "word": " with", "probability": 0.9248046875}, {"start": 2925.67, "end": 2926.45, "word": " constant", "probability": 0.9423828125}, {"start": 2926.45, "end": 2927.45, "word": " coefficients", "probability": 0.77001953125}, {"start": 2927.45, "end": 2927.97, "word": " بدنا", "probability": 0.876220703125}, {"start": 2927.97, "end": 2928.49, "word": " نبدأ", "probability": 0.9856770833333334}, {"start": 2928.49, "end": 2928.83, "word": " بما", "probability": 0.6663818359375}], "temperature": 1.0}, {"id": 118, "seek": 295531, "start": 2929.35, "end": 2955.31, "text": "بالـ homogeneous differential equations المعادلات القطية المتجانسة بمعاملات ثابتة اللي بدنا ناخد المعادلة ال general لغاية ما نوصل لل homogenous يبقى ال second order ordinary differential equation هي عبارة عن المعادلة في الشكل التالي مشتقة ثانية تظهر F ك function في T و Y و Y prime", "tokens": [3555, 6027, 39184, 42632, 15756, 11787, 9673, 3615, 18513, 1211, 9307, 25062, 9566, 10632, 9673, 2655, 7435, 7649, 3794, 3660, 4724, 2304, 3615, 10943, 1211, 9307, 38637, 16758, 2655, 3660, 13672, 1829, 47525, 8315, 8717, 47283, 3215, 9673, 3615, 18513, 37977, 2423, 2674, 5296, 17082, 995, 10632, 19446, 8717, 2407, 36520, 24976, 3655, 45519, 7251, 3555, 4587, 7578, 2423, 1150, 1668, 10547, 15756, 5367, 39896, 6225, 3555, 9640, 3660, 18871, 9673, 3615, 18513, 37977, 8978, 25124, 28820, 16712, 6027, 1829, 37893, 2655, 28671, 38637, 7649, 10632, 6055, 19913, 3224, 2288, 479, 9122, 2445, 8978, 314, 4032, 398, 4032, 398, 5835], "avg_logprob": 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0.96142578125}, {"start": 3802.08, "end": 3803.04, "word": " احتمالات", "probability": 0.97958984375}, {"start": 3803.04, "end": 3804.56, "word": " الاحتمال", "probability": 0.9716796875}, {"start": 3804.56, "end": 3805.0, "word": " الاول", "probability": 0.818359375}, {"start": 3805.0, "end": 3805.22, "word": " ان", "probability": 0.90234375}, {"start": 3805.22, "end": 3805.94, "word": " اتنين", "probability": 0.9102783203125}, {"start": 3805.94, "end": 3806.26, "word": " are", "probability": 0.8935546875}, {"start": 3806.26, "end": 3806.96, "word": " different", "probability": 0.95556640625}, {"start": 3806.96, "end": 3807.42, "word": " ولا", "probability": 0.8623046875}, {"start": 3807.42, "end": 3807.88, "word": " واحد", "probability": 0.9892578125}, {"start": 3807.88, "end": 3808.24, "word": " زي", "probability": 0.956298828125}, {"start": 3808.24, "end": 3808.86, "word": " التاني", "probability": 0.88623046875}], "temperature": 1.0}, {"id": 156, "seek": 381821, "start": 3810.63, "end": 3818.21, "text": "الاحتمال الثاني ان اتنين هدول يكونوا متساوين R1 يساوي R2", "tokens": [6027, 995, 33753, 2304, 6027, 6024, 104, 7649, 1829, 16472, 1975, 2655, 1863, 9957, 8032, 3215, 12610, 7251, 30544, 14407, 44650, 3794, 995, 2407, 9957, 497, 16, 7251, 3794, 995, 45865, 497, 17], "avg_logprob": -0.24793197302257314, "compression_ratio": 1.2692307692307692, "no_speech_prob": 0.0, "words": [{"start": 3810.6299999999997, "end": 3811.91, "word": "الاحتمال", "probability": 0.7484375}, {"start": 3811.91, "end": 3812.51, "word": " الثاني", "probability": 0.8819580078125}, {"start": 3812.51, "end": 3812.75, "word": " ان", "probability": 0.6484375}, {"start": 3812.75, "end": 3813.57, "word": " اتنين", "probability": 0.8394775390625}, {"start": 3813.57, "end": 3814.17, "word": " هدول", "probability": 0.7296549479166666}, {"start": 3814.17, "end": 3814.75, "word": " يكونوا", "probability": 0.8055013020833334}, {"start": 3814.75, "end": 3816.09, "word": " متساوين", "probability": 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0.9642333984375}, {"start": 3845.95, "end": 3846.29, "word": " are", "probability": 0.9150390625}, {"start": 3846.29, "end": 3846.69, "word": " real", "probability": 0.9462890625}, {"start": 3846.69, "end": 3847.23, "word": " and", "probability": 0.9638671875}, {"start": 3847.23, "end": 3847.93, "word": " different", "probability": 0.92529296875}], "temperature": 1.0}, {"id": 158, "seek": 387711, "start": 3849.43, "end": 3877.11, "text": "يبقى R1 لا يساوي R2 إذا والله المميز يساوي 0 يبقى طار الجدر هذا وطار الجدر السار R1 نقص بيها ع 2 ايه و هنا نقص بيه نفس الشيء يبقى 2R equal R1 بده يساوي R2 الاحتمال الثالث ان لو كانت الكمية اللي تحت الجدر كمية سالبة بيصيروا 2R complex conjugate", "tokens": [1829, 3555, 4587, 7578, 497, 16, 20193, 7251, 3794, 995, 45865, 497, 17, 11933, 15730, 16070, 43761, 9673, 2304, 1829, 11622, 7251, 3794, 995, 45865, 1958, 7251, 3555, 4587, 7578, 23032, 9640, 25724, 3215, 2288, 23758, 4032, 9566, 9640, 25724, 3215, 2288, 21136, 9640, 497, 16, 8717, 4587, 9381, 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الجذور اللي هى R1 وR2 يبقى فيها ان الاحتمال الاول انه if ال B تربية ناقص 4AC greater than 0 then the roots are real", "tokens": [9566, 1829, 3555, 7251, 3555, 4587, 7578, 8032, 47302, 23032, 1211, 3615, 8315, 25724, 8848, 13063, 13672, 1829, 8032, 7578, 497, 16, 4032, 49, 17, 7251, 3555, 4587, 7578, 8978, 11296, 16472, 42963, 33753, 2304, 6027, 42963, 12610, 16472, 3224, 498, 2423, 363, 6055, 25513, 10632, 8717, 995, 4587, 9381, 1017, 4378, 5044, 813, 1958, 550, 264, 10669, 366, 957], "avg_logprob": -0.28790983997407504, "compression_ratio": 1.3092105263157894, "no_speech_prob": 0.0, "words": [{"start": 3880.42, "end": 3880.86, "word": "طيب", "probability": 0.7466634114583334}, {"start": 3880.86, "end": 3882.38, "word": " يبقى", "probability": 0.924072265625}, {"start": 3882.38, "end": 3882.6, "word": " هاي", "probability": 0.507568359375}, {"start": 3882.6, "end": 3883.42, "word": " طلعنا", "probability": 0.96875}, {"start": 3883.42, "end": 3884.24, "word": " الجذور", "probability": 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"probability": 0.9742431640625}, {"start": 3962.32, "end": 3962.68, "word": " are", "probability": 0.93115234375}, {"start": 3962.68, "end": 3963.34, "word": " equal", "probability": 0.865234375}, {"start": 3963.34, "end": 3964.6, "word": " يبقى", "probability": 0.974609375}, {"start": 3964.6, "end": 3965.34, "word": " بقوله", "probability": 0.9137369791666666}, {"start": 3965.34, "end": 3965.58, "word": " that", "probability": 0.794921875}, {"start": 3965.58, "end": 3966.72, "word": " is", "probability": 0.958984375}], "temperature": 1.0}, {"id": 162, "seek": 399467, "start": 3969.17, "end": 3994.67, "text": "أنه R1 يسوى R2 نمرة تلاتة F الـ B تربيع نقص أربعة AC أقل من Zero يبقى then they roots are complex conjugate", "tokens": [33456, 3224, 497, 16, 7251, 3794, 2407, 7578, 497, 17, 8717, 2304, 25720, 6055, 1211, 9307, 3660, 479, 2423, 39184, 363, 6055, 25513, 40228, 8717, 4587, 9381, 5551, 25513, 27884, 8157, 5551, 4587, 1211, 9154, 17182, 7251, 3555, 4587, 7578, 550, 436, 10669, 366, 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"probability": 0.899609375}, {"start": 4007.78, "end": 4008.04, "word": " عدد", "probability": 0.9679361979166666}, {"start": 4008.04, "end": 4008.72, "word": " تخيولي", "probability": 0.904296875}, {"start": 4008.72, "end": 4008.84, "word": " يا", "probability": 0.9755859375}, {"start": 4008.84, "end": 4010.32, "word": " بنات؟", "probability": 0.738037109375}, {"start": 4010.32, "end": 4011.54, "word": " عدد", "probability": 0.9612630208333334}, {"start": 4011.54, "end": 4012.02, "word": " كم،", "probability": 0.5919189453125}, {"start": 4012.02, "end": 4012.94, "word": " عطيني", "probability": 0.7666015625}, {"start": 4012.94, "end": 4013.32, "word": " بس،", "probability": 0.9031575520833334}, {"start": 4013.32, "end": 4013.42, "word": " اي", "probability": 0.77587890625}, {"start": 4013.42, "end": 4013.76, "word": " حاجة", "probability": 0.9951171875}, {"start": 4013.76, "end": 4014.16, "word": " تقول،", "probability": 0.7950846354166666}, {"start": 4014.16, "end": 4014.28, "word": " بس", "probability": 0.95654296875}, {"start": 4014.28, "end": 4014.5, "word": " الواحد", "probability": 0.8956705729166666}, {"start": 4014.5, "end": 4014.88, "word": " ترفع", "probability": 0.9659830729166666}, {"start": 4014.88, "end": 4015.14, "word": " يداه", "probability": 0.4486490885416667}, {"start": 4015.14, "end": 4015.9, "word": " وتحكي،", "probability": 0.866748046875}, {"start": 4015.9, "end": 4016.18, "word": " اه", "probability": 0.903076171875}], "temperature": 1.0}, {"id": 164, "seek": 403083, "start": 4018.81, "end": 4030.83, "text": "جذر سالب تلاتة جذر تلاتة I I الحرف الأول من كلمة imaginary", "tokens": [7435, 8848, 2288, 8608, 6027, 3555, 6055, 1211, 9307, 3660, 10874, 8848, 2288, 6055, 1211, 9307, 3660, 286, 286, 21542, 28480, 16247, 12610, 9154, 9122, 19528, 3660, 26164], "avg_logprob": -0.38685344005453176, "compression_ratio": 1.1604938271604939, "no_speech_prob": 1.7881393432617188e-07, "words": [{"start": 4018.8100000000004, "end": 4020.01, "word": "جذر", 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4344.08, "end": 4345.32, "word": "المثال", "probability": 0.9207356770833334}, {"start": 4345.32, "end": 4345.86, "word": " الأول", "probability": 0.811767578125}, {"start": 4345.86, "end": 4346.48, "word": " examples", "probability": 0.677734375}], "temperature": 1.0}, {"id": 177, "seek": 438949, "start": 4361.73, "end": 4389.49, "text": "solve the following differential equation equation z نمرا a y double prime زائد خمسة y prime يساوي زيرو نمرا b", "tokens": [30926, 303, 264, 3480, 15756, 5367, 5367, 710, 8717, 2304, 23557, 257, 288, 3834, 5835, 30767, 16373, 3215, 16490, 2304, 3794, 3660, 288, 5835, 7251, 3794, 995, 45865, 30767, 13546, 2407, 8717, 2304, 23557, 272], "avg_logprob": -0.3936631936166022, "compression_ratio": 1.1842105263157894, "no_speech_prob": 0.0, "words": [{"start": 4361.73, "end": 4362.75, "word": "solve", "probability": 0.539794921875}, {"start": 4362.75, "end": 4364.25, "word": " the", "probability": 0.72900390625}, {"start": 4364.25, "end": 4365.29, "word": " following", "probability": 0.8828125}, {"start": 4365.29, "end": 4369.35, "word": " differential", "probability": 0.86572265625}, {"start": 4369.35, "end": 4372.41, "word": " equation", "probability": 0.77880859375}, {"start": 4372.41, "end": 4374.81, "word": " equation", "probability": 0.2120361328125}, {"start": 4374.81, "end": 4375.95, "word": " z", "probability": 0.457763671875}, {"start": 4375.95, "end": 4377.73, "word": " نمرا", "probability": 0.429443359375}, {"start": 4377.73, "end": 4378.33, "word": " a", "probability": 0.83056640625}, {"start": 4378.33, "end": 4380.63, "word": " y", "probability": 0.8271484375}, {"start": 4380.63, "end": 4381.13, "word": " double", "probability": 0.382080078125}, {"start": 4381.13, "end": 4382.03, "word": " prime", "probability": 0.85888671875}, {"start": 4382.03, "end": 4383.99, "word": " زائد", "probability": 0.8543294270833334}, {"start": 4383.99, "end": 4385.17, "word": " خمسة", "probability": 0.949462890625}, {"start": 4385.17, "end": 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كتبوهله مباشرة يبقاش بدهجة اقول let Y تساوي E أس RT be a solution of the differential equation اتنين وهي هذه سمناها اللي هي الاتنين المثل التاني", "tokens": [3555, 1863, 36178, 16712, 4117, 31371, 4117, 2423, 28820, 10943, 13672, 1829, 12174, 1211, 2655, 23275, 14407, 25124, 5172, 45865, 11331, 9381, 13546, 995, 9122, 2655, 3555, 2407, 3224, 43761, 3714, 3555, 33599, 25720, 7251, 3555, 4587, 33599, 47525, 3224, 7435, 3660, 1975, 39648, 718, 398, 6055, 3794, 995, 45865, 462, 5551, 3794, 21797, 312, 257, 3827, 295, 264, 15756, 5367, 1975, 2655, 1863, 9957, 37037, 1829, 29538, 8608, 27842, 995, 11296, 13672, 1829, 39896, 2423, 9307, 1863, 9957, 9673, 12984, 1211, 16712, 7649, 1829], "avg_logprob": -0.29051597381747046, "compression_ratio": 1.4757281553398058, "no_speech_prob": 0.0, "words": [{"start": 4622.99, "end": 4623.55, "word": "بنفس", "probability": 0.9554036458333334}, {"start": 4623.55, "end": 4624.39, "word": " التكتيك", "probability": 0.79681396484375}, {"start": 4624.39, 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"word": " then", "probability": 0.405517578125}, {"start": 4656.08, "end": 4657.2, "word": " the", "probability": 0.833984375}, {"start": 4657.2, "end": 4659.04, "word": " characteristic", "probability": 0.86767578125}, {"start": 4659.04, "end": 4661.68, "word": " equation", "probability": 0.97509765625}, {"start": 4661.68, "end": 4663.44, "word": " is", "probability": 0.953125}, {"start": 4663.44, "end": 4665.88, "word": " R", "probability": 0.378662109375}, {"start": 4665.88, "end": 4667.5, "word": " تربيع", "probability": 0.8387451171875}, {"start": 4667.5, "end": 4669.14, "word": " نقص", "probability": 0.8108723958333334}, {"start": 4669.14, "end": 4669.72, "word": " اتنين", "probability": 0.8829345703125}, {"start": 4669.72, "end": 4670.18, "word": " R", "probability": 0.8076171875}, {"start": 4670.18, "end": 4671.84, "word": " يساوي", "probability": 0.8468017578125}, {"start": 4671.84, "end": 4672.14, "word": " زيرا", "probability": 0.5174967447916666}, {"start": 4672.14, "end": 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4678.5, "end": 4679.0, "word": " مشكلة", "probability": 0.9778645833333334}, {"start": 4679.0, "end": 4679.5, "word": " تماما", "probability": 0.9949544270833334}], "temperature": 1.0}, {"id": 190, "seek": 469374, "start": 4680.58, "end": 4693.74, "text": "بس السؤال هو بنقدر نحلل المعادلة هذه؟ نقدر؟ نقدر؟ لأ بنقدرش يبقى مليش الامان", "tokens": [3555, 3794, 21136, 33604, 6027, 31439, 44945, 28543, 2288, 8717, 5016, 1211, 1211, 9673, 3615, 18513, 37977, 29538, 22807, 8717, 28543, 2288, 22807, 8717, 28543, 2288, 22807, 5296, 10721, 4724, 1863, 28543, 2288, 8592, 7251, 3555, 4587, 7578, 3714, 20292, 8592, 2423, 10943, 7649], "avg_logprob": -0.26388889948527017, "compression_ratio": 1.4329896907216495, "no_speech_prob": 0.0, "words": [{"start": 4680.58, "end": 4680.96, "word": "بس", "probability": 0.4752197265625}, {"start": 4680.96, "end": 4681.24, "word": " السؤال", "probability": 0.9671223958333334}, {"start": 4681.24, "end": 4681.58, "word": " هو", "probability": 0.93408203125}, 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"end": 4717.64, "text": "القانون العام يبقى بناء عليه بروح بقوله هذا بدي يعطينا R يساوي ناقص باله قداش اتنين زائدة وناقص الجدر التربية اللي بات تربية اللي هو اربعة ناقص اربعة الف اللي هو بواحد", "tokens": [6027, 4587, 7649, 11536, 18863, 10943, 7251, 3555, 4587, 7578, 44945, 16606, 47356, 4724, 32887, 5016, 4724, 39648, 3224, 23758, 4724, 16254, 37495, 9566, 1829, 8315, 497, 7251, 3794, 995, 45865, 8717, 995, 4587, 9381, 20666, 3224, 12174, 3215, 33599, 1975, 2655, 1863, 9957, 30767, 16373, 41891, 4032, 8315, 4587, 9381, 25724, 3215, 2288, 16712, 25513, 10632, 13672, 1829, 4724, 9307, 6055, 25513, 10632, 13672, 1829, 31439, 1975, 25513, 27884, 8717, 995, 4587, 9381, 1975, 25513, 27884, 27188, 13672, 1829, 31439, 4724, 14407, 24401], "avg_logprob": -0.20680147689931533, "compression_ratio": 1.819277108433735, "no_speech_prob": 0.0, "words": [{"start": 4694.22, "end": 4695.08, "word": "القانون", "probability": 0.8480224609375}, {"start": 4695.08, "end": 4695.68, "word": " العام", 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11296, 6055, 32887, 5016, 5296, 19528, 37977, 8717, 3224, 995, 10632, 5296, 398, 7251, 3555, 4587, 7578, 4948, 5296, 15042, 314, 47525, 11296, 6055, 32887, 5016, 5296, 19528, 37977, 8717, 3224, 995, 10632, 5296, 27842, 5296, 8315, 4587, 9381, 8717, 9381, 462, 5551, 3794, 314, 15844, 1975, 2655, 1863, 9957, 30767, 16373, 3215, 36764, 24401, 30767, 16373, 3215, 6055, 1211, 9307, 3660, 15844, 1975, 2655, 1863, 9957, 462, 5551, 3794, 8717, 995, 4587, 9381, 314, 15844, 1975, 2655, 1863, 9957, 30767, 16373, 3215, 36764, 24401, 5296, 15042, 314, 47525, 11296, 6055, 32887, 5016, 5296, 19528, 37977, 8717, 3224, 995, 10632, 2423, 1433, 23758, 28242, 3224, 4724, 7435, 3215, 33599, 3660, 9154, 11296], "avg_logprob": -0.19815891472868216, "compression_ratio": 2.3699421965317917, "no_speech_prob": 0.0, "words": [{"start": 5926.06, "end": 5926.56, "word": "يبقى", "probability": 0.7470703125}, {"start": 5926.56, "end": 5926.96, "word": " بتروح", "probability": 0.7392578125}, {"start": 5926.96, "end": 5927.6, "word": " اخد", "probability": 0.8225911458333334}, {"start": 5927.6, "end": 5927.92, "word": " ال", "probability": 0.919921875}, {"start": 5927.92, "end": 5928.48, "word": " limit", "probability": 0.88525390625}, {"start": 5928.48, "end": 5929.56, "word": " لما", "probability": 0.932373046875}, {"start": 5929.56, "end": 5929.88, "word": " T", "probability": 0.58935546875}, {"start": 5929.88, "end": 5930.26, "word": " بدها", "probability": 0.82861328125}, {"start": 5930.26, "end": 5930.68, "word": " تروح", "probability": 0.99462890625}, {"start": 5930.68, "end": 5931.18, "word": " للملة", "probability": 0.5138346354166666}, {"start": 5931.18, "end": 5931.66, "word": " نهاية", "probability": 0.7469482421875}, {"start": 5931.66, "end": 5931.94, "word": " ل", "probability": 0.60009765625}, {"start": 5931.94, "end": 5932.62, "word": " Y", "probability": 0.53369140625}, {"start": 5932.62, "end": 5933.64, "word": " يبقى", "probability": 0.9376220703125}, {"start": 5933.64, "end": 5934.22, "word": " limit", "probability": 0.892578125}, {"start": 5934.22, "end": 5935.04, "word": " لما", "probability": 0.944091796875}, {"start": 5935.04, "end": 5935.3, "word": " T", "probability": 0.89892578125}, {"start": 5935.3, "end": 5935.62, "word": " بدها", "probability": 0.978271484375}, {"start": 5935.62, "end": 5936.06, "word": " تروح", "probability": 0.9949544270833334}, {"start": 5936.06, "end": 5936.62, "word": " للملة", "probability": 0.9659830729166666}, {"start": 5936.62, "end": 5937.34, "word": " نهاية", "probability": 0.941650390625}, {"start": 5937.34, "end": 5938.3, "word": " لمن", "probability": 0.54962158203125}, {"start": 5938.3, "end": 5939.38, "word": " لناقص", "probability": 0.6903076171875}, {"start": 5939.38, "end": 5939.94, "word": " نص", "probability": 0.981201171875}, {"start": 5939.94, "end": 5940.6, "word": " E", "probability": 0.611328125}, {"start": 5940.6, "end": 5940.98, "word": " أس", "probability": 0.333892822265625}, {"start": 5940.98, "end": 5941.18, "word": " T", "probability": 0.9658203125}, {"start": 5941.18, "end": 5941.48, "word": " على", "probability": 0.7216796875}, {"start": 5941.48, "end": 5942.06, "word": " اتنين", "probability": 0.84271240234375}, {"start": 5942.06, "end": 5943.0, "word": " زائد", "probability": 0.9456380208333334}, {"start": 5943.0, "end": 5943.6, "word": " واحد", "probability": 0.983642578125}, {"start": 5943.6, "end": 5944.56, "word": " زائد", "probability": 0.98583984375}, {"start": 5944.56, "end": 5945.18, "word": " تلاتة", "probability": 0.9302978515625}, {"start": 5945.18, "end": 5945.42, "word": " على", "probability": 0.8857421875}, {"start": 5945.42, "end": 5946.08, "word": " اتنين", "probability": 0.98779296875}, {"start": 5946.08, "end": 5946.68, "word": " E", "probability": 0.97021484375}, {"start": 5946.68, "end": 5947.02, "word": " أس", "probability": 0.880126953125}, {"start": 5947.02, "end": 5947.48, "word": " ناقص", "probability": 0.98681640625}, {"start": 5947.48, "end": 5947.76, "word": " T", "probability": 0.966796875}, {"start": 5947.76, "end": 5948.06, "word": " على", "probability": 0.92626953125}, {"start": 5948.06, "end": 5948.76, "word": " اتنين", "probability": 0.9898681640625}, {"start": 5948.76, "end": 5949.72, "word": " زائد", "probability": 0.984375}, {"start": 5949.72, "end": 5950.16, "word": " واحد", "probability": 0.983154296875}, {"start": 5950.16, "end": 5951.22, "word": " لما", "probability": 0.8271484375}, {"start": 5951.22, "end": 5951.42, "word": " T", "probability": 0.84912109375}, {"start": 5951.42, "end": 5951.66, "word": " بدها", "probability": 0.957275390625}, {"start": 5951.66, "end": 5951.94, "word": " تروح", "probability": 0.9970703125}, {"start": 5951.94, "end": 5952.4, "word": " للملة", "probability": 0.94970703125}, {"start": 5952.4, "end": 5952.76, "word": " نهاية", "probability": 0.9700927734375}, {"start": 5952.76, "end": 5952.94, "word": " ال", "probability": 0.458251953125}, {"start": 5952.94, "end": 5953.1, "word": " term", "probability": 0.8408203125}, {"start": 5953.1, "end": 5953.34, "word": " هذا", "probability": 0.80029296875}, {"start": 5953.34, "end": 5953.64, "word": " كله", "probability": 0.953857421875}, {"start": 5953.64, "end": 5954.2, "word": " بجداشة", "probability": 0.6802734375}, {"start": 5954.2, "end": 5954.48, "word": " منها", "probability": 0.658447265625}], "temperature": 1.0}, {"id": 242, "seek": 597501, "start": 5955.25, "end": 5975.01, "text": "زيرو لإن هذا بنزل تحت بصير عدد على مالة نهاية بزيرو لكن هذا كده؟ سالب مالة نهاية هي السالب برا وهذا مالة نهاية هذا سالب مالة نهاية زائد زيرو فبجي بقول the solution", "tokens": [11622, 1829, 32887, 5296, 28814, 1863, 23758, 44945, 11622, 1211, 6055, 33753, 4724, 9381, 13546, 6225, 3215, 3215, 15844, 3714, 6027, 3660, 8717, 11296, 10632, 4724, 11622, 13546, 2407, 44381, 23758, 9122, 3215, 3224, 22807, 8608, 6027, 3555, 3714, 6027, 3660, 8717, 11296, 10632, 39896, 21136, 6027, 3555, 4724, 23557, 37037, 15730, 3714, 6027, 3660, 8717, 11296, 10632, 23758, 8608, 6027, 3555, 3714, 6027, 3660, 8717, 11296, 10632, 30767, 16373, 3215, 30767, 13546, 2407, 6156, 3555, 7435, 1829, 4724, 39648, 264, 3827], "avg_logprob": -0.2611069363283824, "compression_ratio": 1.8496732026143792, "no_speech_prob": 5.960464477539062e-07, "words": [{"start": 5955.25, "end": 5955.83, "word": "زيرو", "probability": 0.3638509114583333}, {"start": 5955.83, "end": 5956.15, "word": " لإن", "probability": 0.5618489583333334}, {"start": 5956.15, "end": 5956.35, "word": " هذا", "probability": 0.7109375}, {"start": 5956.35, "end": 5956.87, "word": " بنزل", "probability": 0.9405924479166666}, {"start": 5956.87, "end": 5957.25, "word": " تحت", "probability": 0.875244140625}, {"start": 5957.25, "end": 5957.89, "word": " بصير", "probability": 0.6866048177083334}, {"start": 5957.89, "end": 5958.23, "word": " عدد", "probability": 0.9609375}, {"start": 5958.23, "end": 5958.49, "word": " على", "probability": 0.900390625}, {"start": 5958.49, "end": 5958.83, "word": " مالة", "probability": 0.7744140625}, {"start": 5958.83, "end": 5959.23, "word": " نهاية", "probability": 0.8956705729166666}, {"start": 5959.23, "end": 5959.77, "word": " بزيرو", "probability": 0.6566162109375}, {"start": 5959.77, "end": 5960.35, "word": " لكن", "probability": 0.66796875}, {"start": 5960.35, "end": 5960.71, "word": " هذا", "probability": 0.890625}, {"start": 5960.71, "end": 5961.63, "word": " كده؟", "probability": 0.629913330078125}, {"start": 5961.63, "end": 5963.59, "word": " سالب", "probability": 0.8336588541666666}, {"start": 5963.59, "end": 5964.17, "word": " مالة", "probability": 0.9619140625}, {"start": 5964.17, "end": 5964.57, "word": " نهاية", "probability": 0.95166015625}, {"start": 5964.57, "end": 5964.81, "word": " هي", "probability": 0.60009765625}, {"start": 5964.81, "end": 5965.39, "word": " السالب", "probability": 0.8772786458333334}, {"start": 5965.39, "end": 5965.85, "word": " برا", "probability": 0.87890625}, {"start": 5965.85, "end": 5966.33, "word": " وهذا", "probability": 0.62548828125}, {"start": 5966.33, "end": 5966.91, "word": " مالة", "probability": 0.9427083333333334}, {"start": 5966.91, "end": 5967.47, "word": " نهاية", "probability": 0.958984375}, {"start": 5967.47, "end": 5968.15, "word": " هذا", "probability": 0.7958984375}, {"start": 5968.15, "end": 5968.79, "word": " سالب", "probability": 0.9763997395833334}, {"start": 5968.79, "end": 5969.23, "word": " مالة", "probability": 0.9869791666666666}, {"start": 5969.23, "end": 5969.89, "word": " نهاية", "probability": 0.9685872395833334}, {"start": 5969.89, "end": 5971.53, "word": " زائد", "probability": 0.90869140625}, {"start": 5971.53, "end": 5972.05, "word": " زيرو", "probability": 0.89697265625}, {"start": 5972.05, "end": 5972.79, "word": " فبجي", "probability": 0.7359619140625}, {"start": 5972.79, "end": 5973.41, "word": " بقول", "probability": 0.98583984375}, {"start": 5973.41, "end": 5973.83, "word": " the", "probability": 0.5126953125}, {"start": 5973.83, "end": 5975.01, "word": " solution", "probability": 0.95849609375}], "temperature": 1.0}, {"id": 243, "seek": 599620, "start": 5986.98, "end": 5996.2, "text": "يبقى بنقول يازال هناك المزيد من الأمثلة للمرة القادمة ان شاء الله تعالى، أعطيكوا العافية", "tokens": [1829, 3555, 4587, 7578, 44945, 39648, 7251, 31377, 6027, 34105, 4117, 9673, 11622, 25708, 9154, 16247, 2304, 12984, 37977, 5296, 19528, 25720, 25062, 18513, 46007, 16472, 13412, 16606, 21984, 37279, 6027, 7578, 12399, 5551, 3615, 9566, 1829, 4117, 14407, 18863, 31845, 10632], "avg_logprob": -0.249454936315847, "compression_ratio": 1.4727272727272727, "no_speech_prob": 5.960464477539063e-08, "words": [{"start": 5986.9800000000005, "end": 5988.02, "word": "يبقى", "probability": 0.6138763427734375}, {"start": 5988.02, "end": 5988.48, "word": " بنقول", "probability": 0.62451171875}, {"start": 5988.48, "end": 5989.08, "word": " يازال", "probability": 0.689208984375}, {"start": 5989.08, "end": 5989.56, "word": " هناك", "probability": 0.958740234375}, {"start": 5989.56, "end": 5990.18, "word": " المزيد", "probability": 0.9744466145833334}, {"start": 5990.18, "end": 5990.48, "word": " من", "probability": 0.9697265625}, {"start": 5990.48, "end": 5991.34, "word": " الأمثلة", "probability": 0.9716796875}, {"start": 5991.34, "end": 5992.52, "word": " للمرة", "probability": 0.94482421875}, {"start": 5992.52, "end": 5993.44, "word": " القادمة", "probability": 0.9939778645833334}, {"start": 5993.44, "end": 5993.86, "word": " ان", "probability": 0.72998046875}, {"start": 5993.86, "end": 5994.38, "word": " شاء", "probability": 0.966552734375}, {"start": 5994.38, "end": 5994.76, "word": " الله", "probability": 0.9482421875}, {"start": 5994.76, "end": 5995.42, "word": " تعالى،", "probability": 0.8140869140625}, {"start": 5995.42, "end": 5995.74, "word": " أعطيكوا", "probability": 0.7936197916666666}, {"start": 5995.74, "end": 5996.2, "word": " العافية", "probability": 0.904296875}], "temperature": 1.0}], "language": "ar", "language_probability": 1.0, "duration": 5998.4575, "duration_after_vad": 5555.13534375003}
\ No newline at end of file
diff --git a/PL9fwy3NUQKwa8ZDfSFGn6H8xVFLzqmCZC/MCBJ_x7Y0Bg_raw.srt b/PL9fwy3NUQKwa8ZDfSFGn6H8xVFLzqmCZC/MCBJ_x7Y0Bg_raw.srt
new file mode 100644
index 0000000000000000000000000000000000000000..370cf9717e21ab56fa6cbbac06c5598d84709f7a
--- /dev/null
+++ b/PL9fwy3NUQKwa8ZDfSFGn6H8xVFLzqmCZC/MCBJ_x7Y0Bg_raw.srt
@@ -0,0 +1,3252 @@
+1
+00:00:09,840 --> 00:00:16,100
+بسم الله الرحمن الرحيم المرة الماضية كنا نتكلم في
+
+2
+00:00:16,100 --> 00:00:21,820
+المسائل العامة على الشابتر اتنين وكنا في هذه
+
+3
+00:00:21,820 --> 00:00:26,100
+المسائل العامة حاطط ليه تلت نقاطالمرة الفاتة
+
+4
+00:00:26,100 --> 00:00:31,120
+اتعرضنا للنقطة الأولى ركات equation والان بقى
+
+5
+00:00:31,120 --> 00:00:35,600
+لدينا نقطتين النقطة الأولى ال equation with the
+
+6
+00:00:35,600 --> 00:00:40,440
+dependent variable y missing يعني معادلة فيها
+
+7
+00:00:40,440 --> 00:00:44,960
+الرمز الواي مفقود missing مفقود مش موجود في
+
+8
+00:00:44,960 --> 00:00:49,320
+المعادلة والنقطة التالتة ال equation with the
+
+9
+00:00:49,320 --> 00:00:54,590
+independent variable t missingطبعا هناخد الأولى
+
+10
+00:00:54,590 --> 00:00:59,690
+اللى هي equations with a dependent variable y
+
+11
+00:00:59,690 --> 00:01:04,430
+missing يعني معادلات تفاضلية فيها اللى هو المجهول
+
+12
+00:01:04,430 --> 00:01:10,050
+y مش موجود في المعادلة و بدنا نشوف كيف هنحل هذه
+
+13
+00:01:10,050 --> 00:01:16,210
+المعادلةالنوع هذا بنات من المعادلات بصير عندنا
+
+14
+00:01:16,210 --> 00:01:22,110
+معادلة من رتبتي الثانية و بننزل رتبتها الى الرتبة
+
+15
+00:01:22,110 --> 00:01:26,730
+الأولى و بنحلها زى ما كنا نحل في الشرط الرمضى يعنى
+
+16
+00:01:26,730 --> 00:01:30,970
+ممكن تطلع المعادلة بعد تنزيل رتبتهايمكن linear
+
+17
+00:01:30,970 --> 00:01:35,610
+يمكن Bernoulli يمكن exact يمكن exact بس بدأ
+
+18
+00:01:35,610 --> 00:01:40,190
+integrating factor يمكن separable يمكن homogeneous
+
+19
+00:01:40,190 --> 00:01:44,370
+الاخري يبقى لبعد ما نحولها من الرتبة الثانية الى
+
+20
+00:01:44,370 --> 00:01:48,390
+الرتبة الأولىأي معادلة من المعادلات السابقة بنقدر
+
+21
+00:01:48,390 --> 00:01:53,730
+نحلها ونخلص منها الشغلة يبقى these equations are
+
+22
+00:01:53,730 --> 00:01:58,750
+in the form الشكل العام للمعادلات اللي فيها y
+
+23
+00:01:58,750 --> 00:02:03,810
+variable او ال variable y missing مفقود مش موجود
+
+24
+00:02:03,810 --> 00:02:10,670
+يعني الشكل y'' يسوى f of t وy' y مش موجودة لكن y'
+
+25
+00:02:11,030 --> 00:02:16,740
+موجودة وy'' موجودةيبقى هذه المعادلة فيها y مفقودة
+
+26
+00:02:16,740 --> 00:02:22,020
+مش موجودة في المعادلة.مشان انحل المعادلة هذه بدنا
+
+27
+00:02:22,020 --> 00:02:27,200
+نعمل تعويضة معينة شو التعويضة هذه؟ بدأ احط ان v
+
+28
+00:02:27,200 --> 00:02:32,000
+بدوا يساوي y prime يعني المشتق اللي قول احديها رمز
+
+29
+00:02:32,000 --> 00:02:36,760
+جديد وليكن v و بدأ اشتقها كمان مرة فبصير v prime
+
+30
+00:02:36,760 --> 00:02:41,130
+هي y double primeبتاخد المعلومتين اللي اتنين هدول
+
+31
+00:02:41,130 --> 00:02:46,210
+و اعوض في المعادل اللي عندها default يبقى yw prime
+
+32
+00:02:46,210 --> 00:02:50,930
+بدها تصير مين؟ بدها تصير v prime ال y prime بدها
+
+33
+00:02:50,930 --> 00:02:54,570
+تصير v يبقى المعادلة رقم واحد صارت على الشكل اللي
+
+34
+00:02:54,570 --> 00:02:58,950
+عندنا هذا يبقى مش شايفين الا مشتقة واحدة في المثل
+
+35
+00:02:58,950 --> 00:03:03,250
+بس ايش صارت؟ first order differential equation
+
+36
+00:03:03,250 --> 00:03:07,400
+يمكن linear يمكن exactيمكن هموجينياص يمكن
+
+37
+00:03:07,400 --> 00:03:10,960
+سيفارابول يمكن تقول هموجينياص يمكن تقول ال exact
+
+38
+00:03:10,960 --> 00:03:15,120
+يمكن تقول ال linear الله أعلم مين ما كانت تكون
+
+39
+00:03:15,120 --> 00:03:21,680
+بنروح نحلها زي ما كنا بنحل في الشبتر
+
+40
+00:03:21,680 --> 00:03:24,980
+اللي بين إيدينا اللي احنا في المسائل العامة عليه
+
+41
+00:03:26,180 --> 00:03:28,780
+بنبدأ نعطي أمثلة بقول solve the differential
+
+42
+00:03:28,780 --> 00:03:32,520
+equation هو بقول ليش ان Y missing ولا T missing
+
+43
+00:03:32,520 --> 00:03:34,100
+انا بده لاحظها
+
+44
+00:03:34,100 --> 00:03:41,900
+ههههههههههههههههههههههههههههههههههههههههههههههههههههههههههههههههههههههههههههههههههههههههههههههههههههههههههههههههههههههههههههههههههههههههههههههههههههههههههههههههههههههههههههههههههههههههههه
+
+45
+00:03:51,300 --> 00:03:55,320
+أثانية و احنا موضوعنا هو الرتبة الأولى إذا بدى
+
+46
+00:03:55,320 --> 00:03:59,640
+ننزل الرتبة من الرتبة الثانية إلى الرتبة الأولى بس
+
+47
+00:03:59,640 --> 00:04:03,700
+بعدى باطلع في المعادلة اللى عندنا هذه هل المعادلة
+
+48
+00:04:03,700 --> 00:04:09,060
+هذه فيها Y ماعنديش Y كل اللى عندى Y prime وY
+
+49
+00:04:09,060 --> 00:04:13,900
+double prime يبقى هذه equation with Y missing يبقى
+
+50
+00:04:13,900 --> 00:04:26,610
+solution يبقى equation oneis an equation with y
+
+51
+00:04:26,610 --> 00:04:34,270
+missing يبقى هذه فيها y مفقودة بناء عليه هروح افرب
+
+52
+00:04:34,270 --> 00:04:44,470
+ان اللي هو v تساوي من y prime يبقى putV تساوي Y'
+
+53
+00:04:44,990 --> 00:04:53,050
+هذا بيعطينا ان V' يساوي YW' يبقى المعادلة هذه تصير
+
+54
+00:04:53,050 --> 00:05:00,670
+T تربية V' زائد اتنين T في ال V بده يساوي كده؟ بده
+
+55
+00:05:00,670 --> 00:05:05,070
+يساوي واحد نجلة الواحد على الشجة التانية صارت هداش
+
+56
+00:05:05,070 --> 00:05:10,990
+First Order والسؤال هل هي Linear ولا غير Linear؟
+
+57
+00:05:11,540 --> 00:05:20,980
+برضه linear يبقى هذه بقدر لو جسمت على T اقول هذه V
+
+58
+00:05:20,980 --> 00:05:28,920
+prime زائد اتنين على T كل هذا الكلام في V بده
+
+59
+00:05:28,920 --> 00:05:34,660
+يساوي واحد على مين على T تربيع اللي هي linear
+
+60
+00:05:34,660 --> 00:05:37,860
+first
+
+61
+00:05:37,860 --> 00:05:39,840
+order
+
+62
+00:05:47,160 --> 00:05:49,400
+معادلة المعادلة
+
+63
+00:05:53,770 --> 00:05:59,930
+يبقى بتروح أخد من عامل التكامل فبدأ أخد ل mu of T
+
+64
+00:05:59,930 --> 00:06:11,610
+E أس تكامل من اتنين على T dt يبقى E أس اتنين ل T
+
+65
+00:06:11,610 --> 00:06:16,170
+ولا داعي لل absolute value لأن T greater than zero
+
+66
+00:06:17,270 --> 00:06:23,050
+يبقى هذه بدأت تساوي T تربيع الان بنجي على المعادلة
+
+67
+00:06:23,050 --> 00:06:28,230
+هذه سميه للمعادلة هذه رقم اتنين يبقى بتقولي لي
+
+68
+00:06:28,230 --> 00:06:33,290
+multiply equation
+
+69
+00:06:33,290 --> 00:06:42,290
+اتنين by T تربيع we get نحصل على يبقى ايش بيصير T
+
+70
+00:06:42,290 --> 00:06:50,910
+تربيع في ال V primeزائد اتنين T في ال V يسوي واحد
+
+71
+00:06:50,910 --> 00:06:58,210
+صحيح او ممكن نقول ت تربيه في V لكل Prime يسوي واحد
+
+72
+00:06:58,210 --> 00:07:05,450
+صحيح لو جينا كملناها يا بنات ت تربيه في V يسوي T
+
+73
+00:07:05,450 --> 00:07:13,430
+زائد constant Cطب انا بديش هذه بدي V اذا بجسم كله
+
+74
+00:07:13,430 --> 00:07:20,190
+على مين على T تربيع يبقى صارت V عندي اللي هي مين
+
+75
+00:07:20,190 --> 00:07:30,050
+واحد على T زائد C على T تربيع هذا بدي اعطيلك مية T
+
+76
+00:07:30,050 --> 00:07:32,870
+V هذه انا فرضها هي مين
+
+77
+00:07:38,990 --> 00:07:48,290
+يبقى هذا يجب ان اعطيك ان V تساوي DY على DT يجب ان
+
+78
+00:07:48,290 --> 00:07:56,080
+تساوي من 1 على T زائد C على T ترابيعأو ان شئتوا
+
+79
+00:07:56,080 --> 00:08:04,680
+نفقوا ندى الـ dy بده يساوي اللى هو من واحد عالى T
+
+80
+00:08:04,680 --> 00:08:11,990
+زائد C عالى T تربيع كله بالنسبة لمان لدى Tبدنا
+
+81
+00:08:11,990 --> 00:08:23,370
+نكامل يبقى Y تساوي لنت ناقص C عالة Z كنصة جديد
+
+82
+00:08:23,370 --> 00:08:31,710
+وليكن C1 يبقى هذا ال solution تبع المعادلة الأصلية
+
+83
+00:08:31,710 --> 00:08:38,130
+يبقى اضطرنا لتكامل كم مرة مرتين حتى نصل إلى
+
+84
+00:08:38,130 --> 00:08:42,580
+الإجابةيبقى هذا النوع الأول equations with y
+
+85
+00:08:42,580 --> 00:08:46,760
+missing بدنا نيجي للنوع ثاني equations with c
+
+86
+00:08:46,760 --> 00:08:55,360
+missing يبقى بدنا نيجي الآن لل equations with
+
+87
+00:08:55,360 --> 00:09:06,220
+the independent variable
+
+88
+00:09:09,310 --> 00:09:13,690
+T missing يبقى
+
+89
+00:09:13,690 --> 00:09:17,790
+T هي المفقودة
+
+90
+00:09:17,790 --> 00:09:22,310
+These equations
+
+91
+00:09:22,310 --> 00:09:36,150
+هذه المعادلات are in the form are in the form YW
+
+92
+00:09:36,150 --> 00:09:51,330
+primey double prime بدا تساوي f of y و y prime for
+
+93
+00:09:51,330 --> 00:10:01,530
+these equations بهذه المعادلات for these equations
+
+94
+00:10:01,530 --> 00:10:17,160
+we think of y وthink of Y as independent
+
+95
+00:10:17,160 --> 00:10:20,260
+variable
+
+96
+00:10:38,090 --> 00:10:42,910
+بنجي الآن للنوع الثاني ال equations with the
+
+97
+00:10:42,910 --> 00:10:46,710
+independent variable t missing يبقى في الناحية
+
+98
+00:10:46,710 --> 00:10:50,230
+الأولى كان المتغير التابع اللي هو y missing في
+
+99
+00:10:50,230 --> 00:10:53,050
+الناحية اللي عندنا هذه بيكون ال independent
+
+100
+00:10:53,050 --> 00:10:58,490
+variable المتغير المستقل هو اللي مفقود و غير موجود
+
+101
+00:10:58,490 --> 00:11:03,420
+في المعادلةيبقى المعادلات من هذا النوع بتبقى على
+
+102
+00:11:03,420 --> 00:11:08,440
+الشكل التالي y double prime يسوى f of y و y prime
+
+103
+00:11:08,440 --> 00:11:12,940
+اطلع هنا شو كان شكلها كان y double prime اصلا f of
+
+104
+00:11:12,940 --> 00:11:18,780
+t و y prime t موجودة و y مفقودة هنا الحمد لله y
+
+105
+00:11:18,780 --> 00:11:23,750
+موجودة و اللي مفقودة هي mainهي T ، T مش ظاهرة في
+
+106
+00:11:23,750 --> 00:11:28,450
+المعادلة يبقى شو بدنا نعمل في هذه الحالة فبقى بقول
+
+107
+00:11:28,450 --> 00:11:34,850
+له لهذه المعادلة بروح بعتبر ان المتغير المستقل هو
+
+108
+00:11:34,850 --> 00:11:42,430
+Y وليس T تمام؟ يبقى كأنه بعتبر ها we think of Y
+
+109
+00:11:42,430 --> 00:11:46,730
+بروح نعتقد ان Y هو ال independent variable
+
+110
+00:11:46,730 --> 00:11:52,120
+وبالتالي بدأ يصير الشغل على الشكل التالفباجي بقوله
+
+111
+00:11:52,120 --> 00:12:01,560
+put v تساوي y prime اللى هى main اللى هى dy على dt
+
+112
+00:12:01,560 --> 00:12:09,920
+طب احنا بدنا v prime كويس يبقى باجي بقوله v prime
+
+113
+00:12:09,920 --> 00:12:17,570
+تساويبقدرش اقول dy اللي هو ال .. ال .. اللي هو y
+
+114
+00:12:17,570 --> 00:12:24,650
+double prime دغري انا بده ادخل y كمتغير مستقل يبقى
+
+115
+00:12:24,650 --> 00:12:30,810
+هذا بصير dy ا .. ا .. ا .. بده اجيب المشتقة هذه
+
+116
+00:12:30,810 --> 00:12:38,980
+اللي هو dv اللي بدها تساوي dv على dtالان انا
+
+117
+00:12:38,980 --> 00:12:43,820
+باعتقد ان مش T هو المتغير المستقل بدي اعتقد ان Y
+
+118
+00:12:43,820 --> 00:12:51,420
+هو المتغير المستقل اذا بقدر اقول هذه DV على DY في
+
+119
+00:12:51,420 --> 00:12:58,970
+DY على DT عملنا حاجة؟ ماعملناش اشيطب ال DIY على DT
+
+120
+00:12:58,970 --> 00:13:05,630
+هذه هي من V يبقى بقدر أشيل هذه و أكتب بدالها V
+
+121
+00:13:05,630 --> 00:13:10,190
+يبقى صارت V في DV على DY
+
+122
+00:13:13,280 --> 00:13:19,720
+بناء عليها كأنك مفقودة مش مبينة، يبقى لو أخدت
+
+123
+00:13:19,720 --> 00:13:24,380
+المعلومات هذه و جيت عوّط في المعادلة اللي فوق،
+
+124
+00:13:24,380 --> 00:13:30,840
+بصير عندنا V prime اللي هي عبارة من YW prime صح
+
+125
+00:13:30,840 --> 00:13:39,580
+ولا لأ؟يبقى V' بيجي بدل V في DV على DY يبقى بصير
+
+126
+00:13:39,580 --> 00:13:48,700
+المعادل V في DV على DY بيسوي F of Y وV
+
+127
+00:13:54,480 --> 00:14:06,200
+يبقى هذه ايش صارت first order
+
+128
+00:14:06,200 --> 00:14:17,860
+differential equation that can be solved
+
+129
+00:14:27,580 --> 00:14:35,790
+زي ما كنت بحل في بداية هذا الشبطةيبجى هذه امانات
+
+130
+00:14:35,790 --> 00:14:40,690
+تي missing بتفرج شوية عن من عن ال y missing ال y
+
+131
+00:14:40,690 --> 00:14:46,870
+missing أسهل في الحساب من من من ال T missing طيب
+
+132
+00:14:46,870 --> 00:14:52,890
+نعطيكم مثال و نشوف كيف نشتغل الشغلة هذه يبجى
+
+133
+00:14:52,890 --> 00:14:53,450
+example
+
+134
+00:15:06,550 --> 00:15:18,310
+Solve the differential equation yw prime زائد y
+
+135
+00:15:18,310 --> 00:15:25,950
+prime لكل ترابيع يساوي اتنين E اصناق ال Y واعتبر
+
+136
+00:15:25,950 --> 00:15:32,420
+هذه المعادلة رقم واحدالسؤال هو هل شايفين في
+
+137
+00:15:32,420 --> 00:15:38,680
+المعادلة عندنا فيه T يبقى equation with T missing
+
+138
+00:15:38,680 --> 00:15:44,340
+يبقى solution this
+
+139
+00:15:44,340 --> 00:15:57,280
+is an equation with T missing يبقى T مفقودة لذلك
+
+140
+00:15:57,280 --> 00:16:09,360
+بتروح أقوله potV تساوي الـ Y' يعني DY على DT هذا
+
+141
+00:16:09,360 --> 00:16:21,040
+بده يعطينا انه DV او ال V' بده يساوي او ال V هذه
+
+142
+00:16:21,040 --> 00:16:29,750
+بحط هنا DY بجيبنا V' اللي هو DV على DT DV على DTلو
+
+143
+00:16:29,750 --> 00:16:39,210
+DV على DY في DY على DT يبقى V في DVعلى دي Y يعني
+
+144
+00:16:39,210 --> 00:16:44,750
+كأنه احنا بنشتق بالنسبة الى Y يبقى بنا نعتقد ان Y
+
+145
+00:16:44,750 --> 00:16:51,270
+هو المتغير المستقل وليس المتغير التابع بنا نمسك
+
+146
+00:16:51,270 --> 00:16:54,950
+المعلومات هذه ونروح نعوض في المعادلة 1 اللي فوق
+
+147
+00:16:54,950 --> 00:17:01,160
+يبقى الان V Prime هذه عبارة عن مينالـ y double
+
+148
+00:17:01,160 --> 00:17:06,740
+prime يبقى هذه كأنها y double prime بالضبط يبقى
+
+149
+00:17:06,740 --> 00:17:12,220
+أنا بدي أشيل y double prime و بدي أحط مكانها v في
+
+150
+00:17:12,220 --> 00:17:23,260
+dv على dy زائد y prime هي v ترابيع يساوي اتنين e
+
+151
+00:17:23,260 --> 00:17:29,970
+اثناقص yيبقى المعادلة هذه صارت first order
+
+152
+00:17:29,970 --> 00:17:34,170
+differential equation لكن مش مبينة لا linear ولا
+
+153
+00:17:34,170 --> 00:17:38,330
+exact ولا absurd الشو لكن احنا لو روحنا رتبناها
+
+154
+00:17:38,330 --> 00:17:43,490
+هيك وشوفنا ايش كيف ممكن نكتبها يبقى هذه المعادلة
+
+155
+00:17:43,490 --> 00:17:47,410
+بقدر اقول DV على DY
+
+156
+00:18:01,940 --> 00:18:13,140
+ممتاز يبقى هذه معادلة Bernoulli equation
+
+157
+00:18:13,140 --> 00:18:19,160
+يبقى هذه معادلة Bernoulli equationمدام هك يبقى أول
+
+158
+00:18:19,160 --> 00:18:24,260
+شغلة بدها تخلص من مين؟ من ال V اللي عندي إذا بروح
+
+159
+00:18:24,260 --> 00:18:29,700
+بضرب كله في مين؟ في V يبقى لو ضربت في V بصير
+
+160
+00:18:29,700 --> 00:18:36,660
+المعادلة دي كما كانت يبقى V في DV على DY زائد V
+
+161
+00:18:36,660 --> 00:18:45,380
+تربيع يساوي اتنين E أس ناقص Y بعد هيكبعدها أهالي
+
+162
+00:18:45,380 --> 00:18:51,580
+هذه كلها و بفرضها بماذا؟ بمتغير جديد يبقى بقوله
+
+163
+00:18:51,580 --> 00:19:02,970
+put مثلا z تساوي v تربيعإذا بدنا دي زد على مين؟
+
+164
+00:19:02,970 --> 00:19:09,030
+على دي واي لإن احنا بنفضل بنسبة لمين؟ لواي يبقى
+
+165
+00:19:09,030 --> 00:19:19,330
+يساوي اتنين V في دي V على دي Yإذا DV على DY هي
+
+166
+00:19:19,330 --> 00:19:26,950
+عبارة عن نص DZ على DY يبقى V في DV على DY هي عبارة
+
+167
+00:19:26,950 --> 00:19:39,870
+عن نص في DZ على DY زائد Z يساوى 2 U ناقص Yأو لو
+
+168
+00:19:39,870 --> 00:19:46,970
+ضربنا كله في اتنين يبقى معنا هذا الكلام ان دي زد
+
+169
+00:19:46,970 --> 00:19:53,850
+على دي واي زائد اتنين زد يساوي اربعة اي واس ناقص
+
+170
+00:19:53,850 --> 00:20:00,870
+واي ايش صار شكل هذه المعادلة linear يبقى هذه صارت
+
+171
+00:20:00,870 --> 00:20:05,510
+linear first order
+
+172
+00:20:13,120 --> 00:20:18,740
+بنحل المعادلة هادى زى ما كنا بنحل قبل ذلك يبقى بدي
+
+173
+00:20:18,740 --> 00:20:21,460
+اخد لم يقومين يا بنات
+
+174
+00:20:24,050 --> 00:20:31,250
+متغير المستقل هو Y يبقى الميور of Y يبقى E أس
+
+175
+00:20:31,250 --> 00:20:38,990
+تكامل اتنين DY يبقى E أس اتنين Y الآن بنجي
+
+176
+00:20:38,990 --> 00:20:44,270
+للمعادلة هذه كلها وبضربها في قداشبإي أس اتنين واي
+
+177
+00:20:44,270 --> 00:20:52,110
+يبقاش بصير عندي اي أس اتنين واي في دي زد على دي
+
+178
+00:20:52,110 --> 00:20:58,810
+واي زائد اتنين اي أس اتنين واي في زد بده يساوي
+
+179
+00:20:58,810 --> 00:21:06,540
+اربع اي أس واييوز اتنين واي و اي اث ناقص واي بيبقى
+
+180
+00:21:06,540 --> 00:21:12,040
+الاربعة اي اث واي هذه المناط اللي هي عبارة عن اي
+
+181
+00:21:12,040 --> 00:21:20,040
+اث اتنين واي في من في دي زد على دي واي لكل prime
+
+182
+00:21:20,040 --> 00:21:27,540
+والله في زد بس في زد يبقى هذه في زد كلها بيبقى
+
+183
+00:21:27,540 --> 00:21:35,210
+تسوى من اربعة اي اث وايالروحان كامل يبقى لو كملنا
+
+184
+00:21:35,210 --> 00:21:43,570
+بصير عندي A أس اتنين Y في Z بده ساوي تكامل هذه
+
+185
+00:21:43,570 --> 00:21:52,490
+بنفسها زائد كونستان C خلصناه؟ لا ماخلصناش انت وين
+
+186
+00:21:52,490 --> 00:21:53,170
+لسه؟
+
+187
+00:22:13,020 --> 00:22:18,780
+طيب يبقى بقدر اجيب z من هذه المعادلة لو ضربت
+
+188
+00:22:18,780 --> 00:22:24,860
+الطرفين في e أس ناقص اتنين y يبقى هذه بدها تعطيك
+
+189
+00:22:24,860 --> 00:22:36,220
+ما يأتي ان ال z تساوي اربعة e أس ناقص y زائد c e
+
+190
+00:22:36,220 --> 00:22:45,490
+أس ناقص اتنين y طب مين z هذه امانات؟V تربية يعني
+
+191
+00:22:45,490 --> 00:22:55,630
+هذا بده يعطيكي ان V تربية تساوي لخاطر
+
+192
+00:22:55,630 --> 00:23:03,390
+واحد وساطة بخليها هاي اربعة على E اص Y زائد C على
+
+193
+00:23:03,390 --> 00:23:11,760
+E اص اتنين Y او ان شيتم فقولوا E اص اتنين Yباربع E
+
+194
+00:23:11,760 --> 00:23:20,560
+اص Y زائد constant C طيب هذا مين؟ هذا V تربيع احنا
+
+195
+00:23:20,560 --> 00:23:29,480
+بدنا مين؟ بدنا V اذا V تساوي الجدري التربيعي لاربع
+
+196
+00:23:29,480 --> 00:23:37,480
+E اص Y زائد constant C على E اص اتنين Y ال V عند
+
+197
+00:23:37,480 --> 00:23:42,800
+مين هذا ياولادة؟و اين راحت ال V ال V اللي عبارة عن
+
+198
+00:23:42,800 --> 00:23:48,900
+Y prime اللي هي DY على DT يبقى هذا بدي اعطيكي انه
+
+199
+00:23:48,900 --> 00:23:57,420
+DY على DT يسوى الجدر التربيع ل 4 E أص Y زائد
+
+200
+00:23:57,420 --> 00:24:06,260
+constant C على E أص Y E أص 2Y تحت الجدر بصير E أص
+
+201
+00:24:06,260 --> 00:24:13,970
+Yبنروح نكتب المعادلة هذه بشكل اخر فهذه بدها تصير E
+
+202
+00:24:13,970 --> 00:24:19,930
+أوس Y على الجدرى التربية ل 4E أوس Y زائد constant
+
+203
+00:24:19,930 --> 00:24:28,290
+C في Dy بد يساوي DTمرضنا هذا و جسمنا و دي تي
+
+204
+00:24:28,290 --> 00:24:33,850
+ودناها على الشجاعة التانية. بدنا نروح نكامل هذه
+
+205
+00:24:33,850 --> 00:24:39,130
+الدلة. إن كملنا، بيكون خلصنا، بيكون جيبنا الحل. طب
+
+206
+00:24:39,130 --> 00:24:41,390
+كيف بدنا نكامل هذه الدلة يا بناتي؟
+
+207
+00:24:44,000 --> 00:24:49,480
+أه الطرف الشمال تعويض يعني بدي أشيل كل القيمة لتحت
+
+208
+00:24:49,480 --> 00:24:53,760
+الجدر و أحطها ب variable جديد حط أي variable يجي
+
+209
+00:24:53,760 --> 00:24:58,780
+في بالك إذا لو قلنا حط ال w يسوى أربعة e أسواي
+
+210
+00:24:58,780 --> 00:25:06,780
+زائد constant c يبقى ال dw بأربعة e أسواي dy والc
+
+211
+00:25:06,780 --> 00:25:14,500
+مع السلامةإذاً ال E أس Y في ال D Y عبارة عن ربع DW
+
+212
+00:25:14,500 --> 00:25:22,400
+إذا بصير المثل هذه على الشكل التالي هاي ربع و هنا
+
+213
+00:25:22,400 --> 00:25:32,480
+كمان اللي هو الجدر التربيعي ل W وهذه E أس Y DY بDW
+
+214
+00:25:38,100 --> 00:25:46,660
+أو لو ضربت في أربعة بيصير عندك main بيصير عندك w
+
+215
+00:25:46,660 --> 00:25:55,550
+أقص نص دي دابليو بده يساوي أربعة دي تإن كامل
+
+216
+00:25:55,550 --> 00:26:05,530
+الطرفين يبقى W أص نص على نص بده ساوي 4T زائد
+
+217
+00:26:05,530 --> 00:26:08,030
+constant وليكن C1
+
+218
+00:26:11,420 --> 00:26:17,720
+طيب هذا معناه ايش؟ معناته ان اتنين الجذر التربيه
+
+219
+00:26:17,720 --> 00:26:26,840
+الى W لاربع E اص Y زائد constant C بده ساوي اربعة
+
+220
+00:26:26,840 --> 00:26:30,260
+T زائد constant C1
+
+221
+00:26:34,960 --> 00:26:40,960
+بنقدر نجسم كله على الاتنين يبقى الجذر التربيعي
+
+222
+00:26:40,960 --> 00:26:47,580
+لأربعة E اصوي زائد constant C يساوي نصف مين في
+
+223
+00:26:47,580 --> 00:26:55,580
+أربعة T زائد C oneبنقدر نربع الطرفين إذا لو ربعنا
+
+224
+00:26:55,580 --> 00:27:04,820
+الطرفين بصير 4EY زائد constant C بدي ساوي ربع في
+
+225
+00:27:04,820 --> 00:27:15,090
+4T زائد C1 لكل تربيعممكن ننقل C1 على الشجة التانية
+
+226
+00:27:15,090 --> 00:27:26,110
+يبقى بصير 4E وY بده يساوي الرابع في مين في 4T زائد
+
+227
+00:27:26,110 --> 00:27:31,010
+C1 لكل تربية ناقص constant C
+
+228
+00:27:35,420 --> 00:27:43,660
+يبقى هنا هذا الكلام بده يعطيلك ان e اص y بده يسوى
+
+229
+00:27:43,660 --> 00:27:54,780
+واحد على ستاشر في اربعة تزايد c one لكل تربيع ماقص
+
+230
+00:27:57,490 --> 00:28:01,750
+هذا اللى جوا الـ C1 همانات ولا C .. لأ لأ C1 همان
+
+231
+00:28:01,750 --> 00:28:08,990
+يبقى ناقص الرابع C بالشكل اللى عندنا هذا فلاص
+
+232
+00:28:08,990 --> 00:28:13,710
+يكفينا اخلى الحل زي هيك بدك تقوله Y سوى لإن الطرف
+
+233
+00:28:13,710 --> 00:28:18,430
+اليمين مافيش مشكلةلحد هنا والله يعطيك العافية لحظة
+
+234
+00:28:18,430 --> 00:28:22,390
+ان هذا النوع من السؤال أصعب من اللي قبله شوية طب
+
+235
+00:28:22,390 --> 00:28:27,650
+ايش رأيك نجيبلك الفكرتين بسؤال واحد يعني ممكن
+
+236
+00:28:27,650 --> 00:28:32,910
+نجيبلك سؤال T missing وY missing اتنين مرة واحدة
+
+237
+00:28:56,740 --> 00:29:03,880
+طيب ممكن نجيب لك example كتالي
+
+238
+00:29:03,880 --> 00:29:12,560
+solve
+
+239
+00:29:12,560 --> 00:29:14,260
+initial value problem
+
+240
+00:29:20,720 --> 00:29:27,640
+الـ y prime و y double prime يساوي اتنين و ال y
+
+241
+00:29:27,640 --> 00:29:32,960
+عند ال zero بدها تساوي الواحد و ال y prime عند ال
+
+242
+00:29:32,960 --> 00:29:39,580
+zero بدها تساوي اتنين
+
+243
+00:29:39,580 --> 00:29:46,500
+طالعي
+
+244
+00:29:46,500 --> 00:29:53,300
+في المسألة هي مسألة فيها yفيها T يبقى اتنين
+
+245
+00:29:53,300 --> 00:30:05,800
+مفقودين يبقى this is an equation with Y missing
+
+246
+00:30:05,800 --> 00:30:14,960
+and T missing اتنين مفقودين مش موجودين في المثلة
+
+247
+00:30:14,960 --> 00:30:20,460
+يبقى أحلى على الطريقة الأولى والتانيةاللي بدك
+
+248
+00:30:20,460 --> 00:30:24,620
+إياها اللي بتشوفيها أسهل بالنسبالك مين الأولى
+
+249
+00:30:24,620 --> 00:30:31,460
+أسهل؟ خلاص الأولى الأولى يبقى باجي بقوله pot V
+
+250
+00:30:31,460 --> 00:30:38,360
+تساوي Y prime هذا بده يعطينا ان V prime بدها تساوي
+
+251
+00:30:38,360 --> 00:30:44,100
+Y double prime اذا المثل صارت على الشكل التالي V
+
+252
+00:30:44,100 --> 00:30:51,700
+في ال V prime سوى قداشيساوي تمام كويس بدنا هذه
+
+253
+00:30:51,700 --> 00:31:00,120
+المثلة نحاول نكتبها بطريقة أخرى يبقى هذه V وهذه DV
+
+254
+00:31:00,120 --> 00:31:06,180
+على DT بده يساوي كده؟ بده يساوي اتنين يبقى بناء
+
+255
+00:31:06,180 --> 00:31:15,500
+عليها السعر V DV بده يساوي اتنين DTإن كامل الطرفين
+
+256
+00:31:15,500 --> 00:31:25,260
+يبقى V تربيع على 2 يساوي 2 زائد constant C 2T زائد
+
+257
+00:31:25,260 --> 00:31:32,580
+constant C لو ضربتي كله في 2 بصير عندنا مين هنا V
+
+258
+00:31:32,580 --> 00:31:43,750
+تربيع بده يساوي 4T زائد 2C طب مين هي V هذه؟واللي
+
+259
+00:31:43,750 --> 00:31:52,490
+هي Y' يعني صار عندنا Y' لكل ترابيع يساوي اتنين T
+
+260
+00:31:52,490 --> 00:32:00,910
+او الله اربعة T اربعة T زائد اتنين C upon initial
+
+261
+00:32:00,910 --> 00:32:06,070
+condition المشتقة عندها Zero بدأت ساوي قداش اتنين
+
+262
+00:32:06,480 --> 00:32:12,880
+أذا المشتقة ان زيرو بده تساوي اتنين implies
+
+263
+00:32:12,880 --> 00:32:19,340
+المشتقة تساوي قداشها دي اتنين يبقى اتنين تربيه
+
+264
+00:32:19,340 --> 00:32:27,400
+واجتاش لما T تساوي زيرو زائد اتنين C اذا صار عند
+
+265
+00:32:27,400 --> 00:32:29,260
+هنا اربع
+
+266
+00:32:35,190 --> 00:32:40,750
+يبقى صارة المثال اللي عندي على الشكل التالي اللي
+
+267
+00:32:40,750 --> 00:32:50,410
+هو y prime الكل ترابيع بدر ساوي اربعة t زائد اربعة
+
+268
+00:32:50,410 --> 00:32:56,350
+لأن c عندي بقدرش باتنين تمام طبعا بديش y prime بدي
+
+269
+00:32:56,350 --> 00:33:02,770
+y prime شو بنعمل؟بناخد الجذر التربيعي للطرفين يبقى
+
+270
+00:33:02,770 --> 00:33:12,470
+بصير ان y prime بده ساوي الجذر التربيعي لل 4t زائد
+
+271
+00:33:12,470 --> 00:33:19,110
+4 طبعا الجذر ممكن يكون سالب او موجب لكن لما كانت
+
+272
+00:33:19,110 --> 00:33:25,200
+المشتقة عندناقيمة موجبة إذا بنحمله سلبة وبصير بس
+
+273
+00:33:25,200 --> 00:33:30,000
+بالشكل اللي عامله هذا يعني هذه كأنها سارة مين؟ dy
+
+274
+00:33:30,000 --> 00:33:38,740
+على dt يساوي الجذر التربية ل 4t زائد 4 أو ال dy
+
+275
+00:33:38,740 --> 00:33:49,410
+بده يساوي الجذر التربية ل 4t زائد 4 dtتمام بدنا
+
+276
+00:33:49,410 --> 00:33:56,650
+نكامل الطرفين يبقى هذا معناه ان Y يساوي تكامل
+
+277
+00:33:56,650 --> 00:34:05,210
+الجدرى التربية ل 4T زائد 4 كله بالنسبة الى DT كيف
+
+278
+00:34:05,210 --> 00:34:11,550
+بدنا نكامل الدالة هذه يا بنات عادي
+
+279
+00:34:11,550 --> 00:34:17,760
+جدا كل كمية اللى تحت الجدرى بحطها ب Wيبقى هاي W
+
+280
+00:34:17,760 --> 00:34:23,620
+بده يساوي اربعة T زائد اربعة يبقى DW بده يساوي
+
+281
+00:34:23,620 --> 00:34:32,360
+اربعة DT والاربعة دي كبير Zero إذا صار ربع DW بده
+
+282
+00:34:32,360 --> 00:34:41,400
+يساوي من DT إذا صار عندنا Y تساويهي التكامل و هذا
+
+283
+00:34:41,400 --> 00:34:51,060
+ال W أص نص و ال DT بربع دي W يبقى بناء عليه صار Y
+
+284
+00:34:51,060 --> 00:34:59,840
+يساوي الرابع و هذه بصير W أص تلاتة على اتنين على
+
+285
+00:34:59,840 --> 00:35:06,870
+تلاتة على اتنين زائد constant واليكن C1هذه يا بنات
+
+286
+00:35:06,870 --> 00:35:13,970
+بتصير ال y يساوي هذي بتشجل فوق بظل هنا اتنين بصير
+
+287
+00:35:13,970 --> 00:35:22,250
+six اللي هو W أس ثلاثة على اتنين زائد constant C1
+
+288
+00:35:23,750 --> 00:35:28,270
+بتطلع اتنين فوق اتنين مع اربعة بيبقى النص في تلت
+
+289
+00:35:28,270 --> 00:35:34,150
+اللي هو ب 6 و W أستلاتة على اتنين زائد constant C1
+
+290
+00:35:34,150 --> 00:35:38,250
+طب في ان ال initial condition تاني Y عند Zero يسوى
+
+291
+00:35:38,250 --> 00:35:44,090
+الواحد يبقى لو جينا هنا جينا نحسب ال condition او
+
+292
+00:35:44,090 --> 00:35:48,870
+نستخدم ال initial condition التاني مشان حساب ال
+
+293
+00:35:48,870 --> 00:35:50,570
+constant الثاني
+
+294
+00:35:57,060 --> 00:36:01,020
+يبقى بناء ان علي اباجي بقوله احنا عندنا y عند ال
+
+295
+00:36:01,020 --> 00:36:07,740
+zero تساوي واحد implies ان واحد بده يساوي
+
+296
+00:36:12,540 --> 00:36:17,040
+الـ W قدش اللي هي أربعة T زائد أربعة يعني هذه
+
+297
+00:36:17,040 --> 00:36:21,760
+تساوي ال swords الأربعة
+
+298
+00:36:21,760 --> 00:36:27,980
+T زائد أربعة كله أس تلاتة على اتنين زائد constant
+
+299
+00:36:27,980 --> 00:36:34,950
+C1 إذا أصار واحد بده يساوي ال swordsوايه ال ghost
+
+300
+00:36:34,950 --> 00:36:42,310
+تي بي زيرو بيضل أربعة أس تلاتة على اتنين زائد
+
+301
+00:36:42,310 --> 00:36:48,870
+constant C1 يفكر هذا بده يعطينا ان واحد يساوي هذا
+
+302
+00:36:48,870 --> 00:36:53,350
+مناقش الجدر التربيع يلاقى اربعة تكييب اربعة تكييب
+
+303
+00:36:53,350 --> 00:36:59,900
+اللي هي باربعة وستين تحت الجدر التربيع بتمانيةيبقى
+
+304
+00:36:59,900 --> 00:37:08,860
+هاي تمانية على ستة زائد constant C1 او الواحد بده
+
+305
+00:37:08,860 --> 00:37:15,960
+يساوي اربع اتلات زائد constant C1 يبقى C1 بده
+
+306
+00:37:15,960 --> 00:37:26,670
+يساوي سالب تلتإذا بصير الحل اللي عندنا y تساوي هي
+
+307
+00:37:26,670 --> 00:37:35,790
+السُدس برا وهذا أربعة T زائد أربعة أس تلاتة على
+
+308
+00:37:35,790 --> 00:37:43,310
+اتنين وناقص تلت بالشكل اللي عندنا هذا يبقى هذا شكل
+
+309
+00:37:43,310 --> 00:37:47,370
+ال general solution للمعادلة شايفينها صغيرة مش
+
+310
+00:37:47,370 --> 00:37:48,430
+مستهلة يعني
+
+311
+00:37:51,420 --> 00:37:56,960
+أيب عليك بكون انتهى هذا ال chapter وإلى يكون أرقام
+
+312
+00:37:56,960 --> 00:38:03,640
+المسائل التالية اللي هو التمرين العامة تمرين
+
+313
+00:38:03,640 --> 00:38:15,120
+العامة أو مسائل عامة على chapter اتنين
+
+314
+00:38:17,060 --> 00:38:22,920
+المثال من واحد لغاية اتنين و تلاتين اللي هو
+
+315
+00:38:22,920 --> 00:38:31,640
+multiple of three ايش يعني مضعفات تلاتة تلاتة ستة
+
+316
+00:38:31,640 --> 00:38:38,120
+تسعة الاخرين كويس وبنضيف عليها السؤال اربعة و
+
+317
+00:38:38,120 --> 00:38:44,580
+تلاتين تبع recate equationحلنا احنا نمرة A انت بدك
+
+318
+00:38:44,580 --> 00:38:52,560
+تحلي نمرة B و كذلك نمرة C و بعد هيك المسائل تاعة
+
+319
+00:38:52,560 --> 00:38:57,780
+ال Y missing و ال T missing من ستة و تلاتين لغاية
+
+320
+00:38:57,780 --> 00:39:06,880
+خمسين اللي هي ال odd حد
+
+321
+00:39:06,880 --> 00:39:11,750
+لا يتسول في هذا ال chapterأي تساول في هذا ال
+
+322
+00:39:11,750 --> 00:39:17,350
+chapter ننتقل الآن على ال chapter رقم تلاتة اللي
+
+323
+00:39:17,350 --> 00:39:20,570
+هو second order differential equations
+
+324
+00:40:03,180 --> 00:40:15,360
+شبتر تلاتة second order
+
+325
+00:40:15,360 --> 00:40:20,840
+linear differential
+
+326
+00:40:20,840 --> 00:40:24,020
+equations
+
+327
+00:40:27,330 --> 00:40:32,650
+أول section في هذا ال chapter تلاتة واحد اللي هو
+
+328
+00:40:32,650 --> 00:40:40,070
+ال homogeneous differential equations
+
+329
+00:40:40,070 --> 00:40:47,430
+with constant coefficients with constant
+
+330
+00:40:47,430 --> 00:40:49,130
+coefficients
+
+331
+00:41:19,590 --> 00:41:23,780
+خلّي بالكم معنا هنايبقى احنا انتهينا من ال first
+
+332
+00:41:23,780 --> 00:41:28,440
+order differential equation وبنتقل ال second order
+
+333
+00:41:28,440 --> 00:41:32,760
+differential equation كاتبين احنا second order
+
+334
+00:41:32,760 --> 00:41:36,980
+linear differential equation اه احنا في اول
+
+335
+00:41:36,980 --> 00:41:42,020
+chapter ماعرفناش الا ال first order linear
+
+336
+00:41:42,020 --> 00:41:45,140
+differential equation لكن ال second order ماعرفنوش
+
+337
+00:41:45,140 --> 00:41:49,360
+يبقى اول شغلة بنروح انعرف ال second order linear
+
+338
+00:41:49,360 --> 00:41:53,670
+differential equationو بعد هيك نبدأ نفصل في مهم في
+
+339
+00:41:53,670 --> 00:41:59,210
+هذه المعادلة اذا بتروح اكتب التعريف تبعها كتالي
+
+340
+00:41:59,210 --> 00:42:05,850
+definition و بدى اعتبره التعريف الاول a second
+
+341
+00:42:05,850 --> 00:42:11,330
+order
+
+342
+00:42:11,330 --> 00:42:14,430
+ordinary
+
+343
+00:42:14,430 --> 00:42:17,950
+differential
+
+344
+00:42:17,950 --> 00:42:19,850
+equation
+
+345
+00:42:21,390 --> 00:42:29,510
+is an equation in the form is an equation in the
+
+346
+00:42:29,510 --> 00:42:39,410
+form بالشكل التالي اللي هو yw prime او d square y
+
+347
+00:42:39,410 --> 00:42:50,750
+by dt square بدل سوى f of t و y و dy على dt
+
+348
+00:42:51,240 --> 00:42:57,240
+واعتبرين ان هذه المعادلة رقم واحد تعالى فى الثانى
+
+349
+00:42:57,240 --> 00:43:07,660
+الـ differential equation one is called linear is
+
+350
+00:43:07,660 --> 00:43:19,260
+called linear سميها معادلة خطية if it can
+
+351
+00:43:44,270 --> 00:43:45,670
+Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''
+
+352
+00:43:47,120 --> 00:43:54,360
+سميه لهذه كمان المعادلة رقم اتنين where ال P of T
+
+353
+00:43:54,360 --> 00:44:06,360
+وال Q of T and ال G of T are continuous functions
+
+354
+00:44:06,360 --> 00:44:13,240
+of
+
+355
+00:44:13,240 --> 00:44:13,660
+T
+
+356
+00:44:18,320 --> 00:44:28,880
+ملاحظة بسيطة sometimes أحيانا the differential
+
+357
+00:44:28,880 --> 00:44:38,780
+equation اتنين appears تظهر
+
+358
+00:44:38,780 --> 00:44:43,240
+in the form الشكل
+
+359
+00:44:43,240 --> 00:44:54,470
+التالياللي هو P of T في ال YW prime زائد ل Q of T
+
+360
+00:44:54,470 --> 00:45:05,710
+في ال Y prime زائد R of T في ال Y بدها تساوي G of
+
+361
+00:45:05,710 --> 00:45:22,390
+T where حيث ال Pحيث ال P of T بدر ساوي ال Q of T
+
+362
+00:45:22,390 --> 00:45:35,750
+على capital P of T و ال Q of T بدر ساوي ال R of T
+
+363
+00:45:35,750 --> 00:45:40,390
+على capital P of T and
+
+364
+00:45:42,560 --> 00:45:53,400
+الـ G of T بدر ساوي أو الـ G small of T الـ G of T
+
+365
+00:45:53,400 --> 00:46:07,580
+بدر ساوي الـ G of T على capital P of T command
+
+366
+00:46:07,580 --> 00:46:09,120
+definition تالت
+
+367
+00:46:17,530 --> 00:46:32,890
+if the second order differential equation is
+
+368
+00:46:32,890 --> 00:46:47,730
+not in the form في الشكل اتنين orفالشكل اتنين او
+
+369
+00:46:47,730 --> 00:46:54,370
+تلاتة تلاتة طبعا اللي هو الشكل تبع ال G of T هذا
+
+370
+00:46:54,370 --> 00:47:00,650
+الشكل اللي هو تلاتة اذا ماكنتش في اتنين او تلاتة
+
+371
+00:47:00,650 --> 00:47:14,110
+then it is called nonlinear ماهياش
+
+372
+00:47:14,110 --> 00:47:14,730
+خطية
+
+373
+00:47:17,280 --> 00:47:23,640
+أخر definition هو أربعة بيقول ال differential
+
+374
+00:47:23,640 --> 00:47:33,720
+equation the differential equation اتنين or تلاتة
+
+375
+00:47:33,720 --> 00:47:42,160
+is called homogeneous is called homogeneous
+
+376
+00:47:43,660 --> 00:47:54,660
+فالـ G of T بدها تساوي زيرو or G of T بدها تساوي
+
+377
+00:47:54,660 --> 00:48:02,220
+زيرو and non homogeneous
+
+378
+00:48:07,410 --> 00:48:17,410
+الـ G of T لا تساوي Zero أو G of T لا تساوي Zero
+
+379
+00:48:22,230 --> 00:48:27,710
+بنرجع لهذه التعريف مرة ثانية من بدايتها يعني
+
+380
+00:48:27,710 --> 00:48:32,250
+دراستنا في هذا الشتر بدأت تكون مصابة على هذه
+
+381
+00:48:32,250 --> 00:48:38,070
+التعريف second order linear differential equation
+
+382
+00:48:38,070 --> 00:48:42,070
+يبقى احنا بدأ نشتل على معادلات خطية من الرتبة
+
+383
+00:48:42,070 --> 00:48:45,670
+الثانية homogeneous differential equation with
+
+384
+00:48:45,670 --> 00:48:49,710
+constant coefficients بدنا نبدأ بمابالـ
+
+385
+00:48:49,710 --> 00:48:52,550
+homogeneous differential equations المعادلات
+
+386
+00:48:52,550 --> 00:49:00,290
+القطية المتجانسة بمعاملات ثابتة اللي بدنا ناخد
+
+387
+00:49:00,290 --> 00:49:03,450
+المعادلة ال general لغاية ما نوصل لل homogenous
+
+388
+00:49:03,450 --> 00:49:05,970
+يبقى ال second order ordinary differential
+
+389
+00:49:05,970 --> 00:49:08,910
+equation هي عبارة عن المعادلة في الشكل التالي
+
+390
+00:49:08,910 --> 00:49:15,310
+مشتقة ثانية تظهر F ك function في T و Y و Y prime
+
+391
+00:49:17,380 --> 00:49:25,120
+يبقى هذه الدالة بيكون فيها YW' Y' Y وTبنتعرف على
+
+392
+00:49:25,120 --> 00:49:30,340
+شكلها العملي ماهو الشكل العملي للمعادلة واحد فبقى
+
+393
+00:49:30,340 --> 00:49:33,900
+جيب اقول differential equation one is called
+
+394
+00:49:33,900 --> 00:49:38,980
+linear بسميها ده المعادلة الخطية if it can be
+
+395
+00:49:38,980 --> 00:49:42,860
+written as إذا جدرنا نكتب هذه على الشكل التالي
+
+396
+00:49:42,860 --> 00:49:48,040
+اللي عندنا yw prime زي p small of t في y prime
+
+397
+00:49:55,280 --> 00:49:59,100
+لو جدرنا نكتبها على الشكل اللي عندنا هذا بقول
+
+398
+00:49:59,100 --> 00:50:02,520
+الشكل اللي هذا عبارة عن مين linear first or
+
+399
+00:50:02,520 --> 00:50:06,890
+differential equation بشرطان دوال P of T و Q of T
+
+400
+00:50:06,890 --> 00:50:11,190
+و G of T يكونوا continuous functions of T دوال
+
+401
+00:50:11,190 --> 00:50:16,770
+متصلة بالنسبة لمين إلا T أحيانا المعادلة تظهرش على
+
+402
+00:50:16,770 --> 00:50:22,310
+الشكل لأنها ليس بالضرورةيمكن أن يكون المعامل يكون
+
+403
+00:50:22,310 --> 00:50:28,730
+الواتر صحيح ممكن يكون function في T فلو ظهرت as a
+
+404
+00:50:28,730 --> 00:50:34,030
+function في T تظهر على الشكل التالي كابتل P of T
+
+405
+00:50:34,030 --> 00:50:36,830
+هذي small وهذه كابتل
+
+406
+00:50:41,770 --> 00:50:46,330
+زيدي Q of T كابتل في ال wire prime زيدي R of T
+
+407
+00:50:46,330 --> 00:50:51,530
+طبعا كتبتم كابتل مشان اميز المعادلات الاتنين هدول
+
+408
+00:50:51,530 --> 00:50:58,950
+عن بعض R of T بدي تسوي G of T وكأنه هذا هو الأصل
+
+409
+00:50:58,950 --> 00:51:04,630
+هذا هو أصل المعادلة لما روحت جسمت كله على P
+
+410
+00:51:04,630 --> 00:51:10,470
+capital of Tحصلت على P small of T هي Q of T على P
+
+411
+00:51:10,470 --> 00:51:15,730
+of T والـ Q of T small هي R of T على P of T والـ G
+
+412
+00:51:15,730 --> 00:51:20,170
+small of T هي G capital of T على P of T يبقى هذا
+
+413
+00:51:20,170 --> 00:51:25,170
+الأصل اجسمي كله على P capital of T بحصل على مين؟
+
+414
+00:51:25,170 --> 00:51:29,270
+على المعادلة اللي فوق يبقى المعادلة رقم اتنين او
+
+415
+00:51:29,270 --> 00:51:34,950
+المعادلة رقم تلاتة اتنتين بقول عنهم linearاو
+
+416
+00:51:34,950 --> 00:51:40,670
+second order linear differential equations طيب
+
+417
+00:51:40,670 --> 00:51:46,830
+تمام الان if the second order differential is not
+
+418
+00:51:46,830 --> 00:51:52,510
+in the form 2 او 3 يعني لو انا عندي معادلة من
+
+419
+00:51:52,510 --> 00:51:57,490
+الرتبة الثانية ليست على هذا الشكل ولا على الشكل
+
+420
+00:51:57,490 --> 00:52:01,130
+هذا كيف يعني يعني حاطيتلك هنا مثلا تربيع
+
+421
+00:52:28,850 --> 00:52:30,550
+تركيب تركيب تركيب تركيب تركيب تركيب تركيب تركيب
+
+422
+00:52:30,550 --> 00:52:33,610
+تركيب تركيب تركيبهذا البرنامج هو البرنامج
+
+423
+00:52:33,610 --> 00:52:37,990
+الهوموجيني والهوموجيني واللانهوموجيني
+
+424
+00:52:47,880 --> 00:52:51,920
+لاتساوي 0 او لاتساوي 0 يبقى non homogeneous
+
+425
+00:52:51,920 --> 00:52:54,840
+differential equation يبقى ال differential
+
+426
+00:52:54,840 --> 00:52:58,160
+equation اتنين او تلاتة بيقول عنها homogeneous اذا
+
+427
+00:52:58,160 --> 00:53:03,280
+كان g s one of t بده ساوي 0 او g capital of t بده
+
+428
+00:53:03,280 --> 00:53:10,960
+ساوي 0 non homogeneous اذا كانت لاتساوي 0 في ال
+
+429
+00:53:10,960 --> 00:53:15,620
+section اللي بين ادينا احنا شو بناخد؟يعني G of T
+
+430
+00:53:15,620 --> 00:53:19,800
+small او G capital of T بقداش ب zero يبقى هاي اللي
+
+431
+00:53:19,800 --> 00:53:25,080
+بدنا نشتغل عليه خلال مين خلال هذا section لو جايلي
+
+432
+00:53:25,080 --> 00:53:29,380
+كمان كلام زيادة with constant coefficients مش
+
+433
+00:53:29,380 --> 00:53:33,580
+حياله يبقى انا بداخد اللي هو ال homogeneous
+
+434
+00:53:33,580 --> 00:53:38,160
+differential equation و بعدك بداخد حلقة خاصة منها
+
+435
+00:53:38,160 --> 00:53:43,190
+لو كانوا المعاملات ثوابتوبدأ اشتغل عليها و بعد هيك
+
+436
+00:53:43,190 --> 00:53:49,970
+برجع لو كان المعاملات متغيرات تمام يبقى بدل ال
+
+437
+00:53:49,970 --> 00:53:54,630
+section تلاتة هنشتغل علامين على ال homogeneous
+
+438
+00:53:54,630 --> 00:53:58,070
+differential equation وبعد هيك بنرجع لل non
+
+439
+00:53:58,070 --> 00:54:02,140
+homogeneous differential equationبنضغطهم في آخر
+
+440
+00:54:02,140 --> 00:54:07,320
+two sections من هذا ال chapter اللي هو section
+
+441
+00:54:07,320 --> 00:54:13,460
+تلاتة ستة و تلاتة سبعة يبقى بدنا نبدأ بماين بال
+
+442
+00:54:13,460 --> 00:54:19,460
+homogeneous اللي هو differential equation يبقى
+
+443
+00:54:19,460 --> 00:54:26,560
+بدني أخد solution بدنا
+
+444
+00:54:26,560 --> 00:54:35,740
+الحل ofThe homogeneous differential
+
+445
+00:54:35,740 --> 00:54:37,820
+equation
+
+446
+00:54:38,760 --> 00:54:45,640
+اللي capital P of T في ال YW prime زائد capital Q
+
+447
+00:54:45,640 --> 00:54:53,860
+of T في ال Y prime زائد ال R capital of T في ال Y
+
+448
+00:54:53,860 --> 00:54:58,920
+بدها تساوي Zero وهذه يا بنات ساموها للمعادلة رقم
+
+449
+00:54:58,920 --> 00:55:05,420
+واحد هذه اللي بنبدأ نشتغل عليها بدأت أخد الحالة
+
+450
+00:55:05,420 --> 00:55:13,710
+الخاصة اللي احنا جالين عليها FP of T والـ Q of T
+
+451
+00:55:13,710 --> 00:55:30,990
+and ال R of T are constants then equation 1 as ال
+
+452
+00:55:30,990 --> 00:55:31,530
+A
+
+453
+00:55:47,130 --> 00:55:48,530
+Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''
+
+454
+00:55:56,350 --> 00:56:02,230
+يبقى احنا الان وصلنا لمين للعلوم اللي احنا رافعينه
+
+455
+00:56:02,230 --> 00:56:07,370
+هذا يبقى
+
+456
+00:56:07,370 --> 00:56:12,290
+هذا اللي فات كان كله مقدمة عشان نعرف ما هو شكل ال
+
+457
+00:56:12,290 --> 00:56:16,890
+second order lineardifferential equation الان
+
+458
+00:56:16,890 --> 00:56:21,090
+وصلنا الى معادلة بهذا الشكل with constant
+
+459
+00:56:21,090 --> 00:56:25,210
+coefficients يعني المعاملات ال a و ال b و ال c
+
+460
+00:56:25,210 --> 00:56:30,410
+كلهم ثوابت طب كويس صح اصحى الان كيف بدنا نحل
+
+461
+00:56:30,410 --> 00:56:35,710
+المعادلة دى بتروح افترض حل من عندي لهذه المعادلة
+
+462
+00:56:35,710 --> 00:56:41,250
+يبقى بداجي اقول له لات هداش سامينا حاجة ولا لسه دي
+
+463
+00:56:41,250 --> 00:56:43,530
+واحد ساميه لهذه اتنين
+
+464
+00:57:04,410 --> 00:57:11,850
+افترض ان هذا حل مادام حل اذا لازم له حقق المعادلة
+
+465
+00:57:11,850 --> 00:57:18,600
+يبقى thenما دام هيك بده اجيب المشتقة الأولى
+
+466
+00:57:18,600 --> 00:57:23,080
+والمشتقة الثانية وانعوض في المعادلة وانشوف وين
+
+467
+00:57:23,080 --> 00:57:29,300
+بدنا نوصل يبقى لو جيت قول y prime اظن مشتقة ال X
+
+468
+00:57:29,300 --> 00:57:37,380
+بننشل بنفسها ضرب مشتقة الأس كدهش مشتقة الأس؟هذا
+
+469
+00:57:37,380 --> 00:57:41,780
+رقم
+
+470
+00:57:41,780 --> 00:57:48,340
+ثابت يبقى رقم ثابت يبقى رقم ثابت يبقى رقم ثابت
+
+471
+00:57:48,340 --> 00:57:55,840
+يبقى رقم ثابت يبقىبدا امسك المعلومات اللي حصلت
+
+472
+00:57:55,840 --> 00:58:00,620
+عليها و اروح اعوض في المعادلة اتنين يبقى بداجي
+
+473
+00:58:00,620 --> 00:58:12,180
+اقوله هنا Substitute and equation اتنين و جيت نحصل
+
+474
+00:58:12,180 --> 00:58:25,130
+على ما ياتي هذا ال A YR تربيع و E أس RTزائد PR E
+
+475
+00:58:25,130 --> 00:58:37,930
+أُس RT زائد C في E أُس RT سؤال
+
+476
+00:58:37,930 --> 00:58:44,470
+هذا الكلام كله بده يساوي قداش؟ بده يساوي Zero هل
+
+477
+00:58:44,470 --> 00:58:48,610
+ال exponential function في يوم من الأيام ممكن
+
+478
+00:58:48,610 --> 00:58:49,890
+تساوي Zero؟
+
+479
+00:58:53,590 --> 00:58:56,870
+الـ Exponential EOS RT ممكن تساوي 0 في يوم من
+
+480
+00:58:56,870 --> 00:59:01,270
+الأيام؟ عمر ما الـ Exponential بتساوي 0 ولا حتى
+
+481
+00:59:01,270 --> 00:59:05,630
+قيمة سالمة، الـ Exponential دائما و أبدا قيمة
+
+482
+00:59:05,630 --> 00:59:10,070
+موجبة زي ما اتعرفنا عليها، اذا كنتوا بتذكروا في
+
+483
+00:59:10,070 --> 00:59:15,570
+calculus B رسمنا الـ Exponential function فكانت
+
+484
+00:59:15,570 --> 00:59:21,380
+على الشكل التالي اللي عندنايعني هذه A أقصر T لو
+
+485
+00:59:21,380 --> 00:59:26,420
+كانت بالسالب بتجي من وايا من الناحية التانية يبقى
+
+486
+00:59:26,420 --> 00:59:33,240
+هذا محور T و هذا محور Y لو كانت بالسالب بتجي كهك
+
+487
+00:59:35,090 --> 00:59:42,070
+هذا الـ A أُس ناقص RT فهذه النقطة اللي هي الـ Zero
+
+488
+00:59:42,070 --> 00:59:47,290
+وهذه واحدة يبقى دائما و أبدا الرسمة المنحنة تبعها
+
+489
+00:59:47,290 --> 00:59:52,880
+كله أعلى الـ X axis يعني لا تأخذ إلا قيمةمعجبة
+
+490
+00:59:52,880 --> 00:59:59,180
+تمام تمام طيب شو رايك بنقدر نجسم المعادلة كلها على
+
+491
+00:59:59,180 --> 01:00:04,460
+E أُس RT بدون مشاكل مدام لا يساوي Zero بقدر اجسم
+
+492
+01:00:04,460 --> 01:00:12,760
+عليها يبقى لو جسمت طرفين على E أُس RT بنحصل على
+
+493
+01:00:12,760 --> 01:00:14,740
+المعادلة التالية
+
+494
+01:00:30,200 --> 01:00:35,060
+يبقى لو قسمنا على a و اقصرتي بصرا ان ال a في ال
+
+495
+01:00:35,060 --> 01:00:42,780
+RTR تربية زائد PR زائد C يساوي Zero ايش رايكوا هذه
+
+496
+01:00:42,780 --> 01:00:44,220
+معادلة افاضلية
+
+497
+01:00:49,350 --> 01:00:53,910
+لأ، يبقى احنا كنا بنشتغل على معادلة تفاضلية
+
+498
+01:00:53,910 --> 01:00:58,310
+وانتقلنا إلى معادلة عادية، كنا بنشتغل على معادلة
+
+499
+01:00:58,310 --> 01:01:01,810
+تفاضلية من الرتبة الثانية، انتقلنا إلى معادلة
+
+500
+01:01:01,810 --> 01:01:06,510
+عادية من الدرجة الثانية، مظبوط ولا لأ؟ إذا بدنا
+
+501
+01:01:06,510 --> 01:01:13,030
+نحل المعادلة هذه، حل المعادلة هذه كتالة يبقى هذه
+
+502
+01:01:13,030 --> 01:01:18,970
+بنسميها يا بنات The Characteristic
+
+503
+01:01:21,670 --> 01:01:25,370
+المعادلة المميزة أو ال accelerator equation
+
+504
+01:01:25,370 --> 01:01:29,030
+المعادلة المساعدة كتابنا بيقول ال characteristic
+
+505
+01:01:29,030 --> 01:01:34,310
+يبقى the characteristic equation of the
+
+506
+01:01:34,310 --> 01:01:41,230
+differential equation اللي أعطناها الرقمين الرقم
+
+507
+01:01:41,230 --> 01:01:42,090
+اتنين
+
+508
+01:01:44,470 --> 01:01:49,390
+يبقى يادم يسميها المعادلة المميزة للمعادلة رقم
+
+509
+01:01:49,390 --> 01:01:55,630
+اتنين او المعادلة المساعدة للمعادلة رقم اتنينطب
+
+510
+01:01:55,630 --> 01:01:59,630
+بدنا نحلها بقول مضارة تانية بحلها عادي جدا
+
+511
+01:01:59,630 --> 01:02:05,630
+بالاقواس بالقانون يبقى in general R تساوي ناقص
+
+512
+01:02:05,630 --> 01:02:12,130
+بزايد او ناقص الجدر التربيهي لبقى تربيه ناقص 4000
+
+513
+01:02:12,130 --> 01:02:21,430
+جيم كله على 2000 يبقى كام قيمة صار عندى لR؟يعني
+
+514
+01:02:21,430 --> 01:02:28,750
+كام حل صار عندى؟ حلين، يعني هذا بده يعطينا ان R1
+
+515
+01:02:28,750 --> 01:02:35,710
+بده ساوي ناقص B زائد الجدر التربية ل B تربية ناقص
+
+516
+01:02:35,710 --> 01:02:44,840
+4AC على 2Aوالـ R2 يسوى ناقص B ناقص الجذر التربية
+
+517
+01:02:44,840 --> 01:02:54,900
+لB تربية ناقص 4AC كله على 2A تبقى
+
+518
+01:02:54,900 --> 01:03:00,280
+صاروا عندي جذرين طب استنى شوية كيف؟ مين اللي افتح
+
+519
+01:03:00,280 --> 01:03:01,760
+كشوفي شفت سهل؟ ايوة
+
+520
+01:03:12,520 --> 01:03:18,520
+او ايش؟ مركبين يعني تخيلين اه في ان الجذرين هدول
+
+521
+01:03:18,520 --> 01:03:23,040
+يا بنات the roots اللي هم احد ثلاثة احتمالات
+
+522
+01:03:23,040 --> 01:03:28,240
+الاحتمال الاول ان اتنين are different ولا واحد زي
+
+523
+01:03:28,240 --> 01:03:36,090
+التانيالاحتمال الثاني ان اتنين هدول يكونوا متساوين
+
+524
+01:03:36,090 --> 01:03:42,290
+R1 يساوي R2الاحتمال الثالث ان هؤلاء يكونوا are
+
+525
+01:03:42,290 --> 01:03:46,390
+conjugate complex او complex conjugate اتنين
+
+526
+01:03:46,390 --> 01:03:52,930
+يكونوا تخيليين ومترافقين في نفس الوقت اللي بده
+
+527
+01:03:52,930 --> 01:03:59,610
+يتحكم في هذا الكلام المميز من المميز اللي هو
+
+528
+01:03:59,610 --> 01:04:03,430
+القيمة اللي تحت الجذر هذه إذا القيمة اللي تحت
+
+529
+01:04:03,430 --> 01:04:10,390
+الجذر موجبة يبقى اتنين are real and differentيبقى
+
+530
+01:04:10,390 --> 01:04:16,430
+R1 لا يساوي R2 إذا والله المميز يساوي 0 يبقى طار
+
+531
+01:04:16,430 --> 01:04:21,450
+الجدر هذا وطار الجدر السار R1 نقص بيها ع 2 ايه و
+
+532
+01:04:21,450 --> 01:04:27,150
+هنا نقص بيه نفس الشيء يبقى 2R equal R1 بده يساوي
+
+533
+01:04:27,150 --> 01:04:31,470
+R2 الاحتمال الثالث ان لو كانت الكمية اللي تحت
+
+534
+01:04:31,470 --> 01:04:37,110
+الجدر كمية سالبة بيصيروا 2R complex conjugate
+
+535
+01:04:40,420 --> 01:04:47,980
+طيب يبقى هاي طلعنا الجذور اللي هى R1 وR2 يبقى فيها
+
+536
+01:04:47,980 --> 01:04:58,280
+ان الاحتمال الاول انه if ال B تربية ناقص 4AC
+
+537
+01:04:58,280 --> 01:05:11,100
+greater than 0 then the roots are realand
+
+538
+01:05:11,100 --> 01:05:16,500
+different يبقى
+
+539
+01:05:16,500 --> 01:05:24,660
+اتنين حقيقيين ومختلفين that is اي ان R واحد
+
+540
+01:05:24,660 --> 01:05:36,380
+لاتساوي R اتنين R واحد لاتساوي R اتنين نمل اتنين F
+
+541
+01:05:37,100 --> 01:05:45,480
+الـ B تربيع ناقص أربعة AC بده يساوي Zero then the
+
+542
+01:05:45,480 --> 01:05:57,840
+roots are real repeated ايش يعني حقيقية و مكررة
+
+543
+01:05:57,840 --> 01:06:01,920
+يعني اتنين are coincide اتنين بنطبق على بعض يعني
+
+544
+01:06:01,920 --> 01:06:06,720
+اتنين are equal يبقى بقوله that is
+
+545
+01:06:09,170 --> 01:06:19,950
+أنه R1 يسوى R2 نمرة تلاتة F الـ B تربيع نقص أربعة
+
+546
+01:06:19,950 --> 01:06:32,330
+AC أقل من Zero يبقى then they roots are complex
+
+547
+01:06:32,330 --> 01:06:34,670
+conjugate
+
+548
+01:06:38,460 --> 01:06:45,740
+يبقى كمية تخيولية ومترافقة، ايش الكمية التخيولية
+
+549
+01:06:45,740 --> 01:06:50,320
+والمترافقة؟ حد بتقدر تجيبلي عدد تخيولي يا بنات؟
+
+550
+01:06:50,320 --> 01:06:54,880
+عدد كم، عطيني بس، اي حاجة تقول، بس الواحد ترفع
+
+551
+01:06:54,880 --> 01:07:05,290
+يداه وتحكي، اهجذر سالب تلاتة جذر
+
+552
+01:07:05,290 --> 01:07:10,830
+تلاتة I I الحرف الأول من كلمة imaginary
+
+553
+01:07:14,300 --> 01:07:20,360
+لسالب واحد لكن in general الرقم التخيلي او العدد
+
+554
+01:07:20,360 --> 01:07:26,080
+التخيلي بنقول a زائد ib كنتوا في الثانوية بيقولوا
+
+555
+01:07:26,080 --> 01:07:32,060
+سين زائد فاتر حيث اتها الحرف الأول من كلمات تخيلي
+
+556
+01:07:32,060 --> 01:07:38,200
+احنا اننا نقل جهة بيقول a زائد bi او ibحيث I هو
+
+557
+01:07:38,200 --> 01:07:44,080
+الجذر التربيهي لمنين؟ لسالب واحد يبقى لو كان الرقم
+
+558
+01:07:44,080 --> 01:07:50,160
+الأول او العدد الأول يتخيل A زائد B في I التاني
+
+559
+01:07:50,160 --> 01:07:54,960
+ايش بيكون؟ كنجج التابع المرافق يبقى المرافق للجزء
+
+560
+01:07:54,960 --> 01:08:01,620
+التخيلي وليس للجزء الحقيقي بيكون التخيلي A ناقص B
+
+561
+01:08:01,620 --> 01:08:08,730
+في Iتمام؟ طب احنا اليوم بنااخد بس الحالة الأولى و
+
+562
+01:08:08,730 --> 01:08:13,210
+بعد هيك الحالات التانية و التالتة هنحط كل واحدة في
+
+563
+01:08:13,210 --> 01:08:19,810
+section منفصل عن الثاني يبقى بالداج ياخد الان if
+
+564
+01:08:19,810 --> 01:08:29,450
+the roots are real and different
+
+565
+01:08:33,460 --> 01:08:47,220
+then the two solutions of the differential
+
+566
+01:08:47,220 --> 01:09:00,930
+equation two Rالأول هسمي Y1 يسوى E أُس R1T وY2
+
+567
+01:09:00,930 --> 01:09:10,550
+يسوى E أُس R2T لإن R1 وR2 ليسوا إيقال بيسووش بعض
+
+568
+01:09:10,550 --> 01:09:15,840
+طيب إذا صار عندي حلينطب لكن احنا بدنا اشرها بدنا
+
+569
+01:09:15,840 --> 01:09:23,080
+ال general solution يبقى هذا يا بنات لو جيت عوقب
+
+570
+01:09:23,080 --> 01:09:28,880
+في المعادلة رقم اتنين بده يحققها و هذا كمان لو جيت
+
+571
+01:09:28,880 --> 01:09:34,500
+عوقب في المعادلة رقم اتنين بده يحققها لكن في عندي
+
+572
+01:09:34,500 --> 01:09:43,140
+the general solution of
+
+573
+01:09:44,040 --> 01:09:54,720
+the differential equation اتنين is y يسوى c1y1
+
+574
+01:09:54,720 --> 01:10:06,720
+زائد c2y2 يعني y تسوى c1 في e أس r1t زائد c2 في e
+
+575
+01:10:06,720 --> 01:10:09,200
+أس r2t
+
+576
+01:10:11,510 --> 01:10:16,250
+يبقى الامباروز في المستطيل هذا يعتبر ال general
+
+577
+01:10:16,250 --> 01:10:23,850
+solution للمعادلة رقم 2 إذا كانت الجذور حقيقية
+
+578
+01:10:23,850 --> 01:10:29,390
+ومختلفة، لو كان الجذور حقيقية ومختلفة، إلا الشكل
+
+579
+01:10:29,390 --> 01:10:34,010
+غير هذا الشكل، ولو كانت complex إلا شكل غير هذا
+
+580
+01:10:34,010 --> 01:10:39,480
+الشكل، إذا نمنات من الآن فصاعدامن حد ملاقي الجذور
+
+581
+01:10:39,480 --> 01:10:43,100
+تبع تلقى ال characteristic equation اللى فوق are
+
+582
+01:10:43,100 --> 01:10:47,980
+real and different automatic الحل العام للمعادلة
+
+583
+01:10:47,980 --> 01:10:52,240
+رقم اتنين على الشكل اللى عندنا هذا يبقى بس عليك
+
+584
+01:10:52,240 --> 01:10:58,500
+توش دي are واحد و are اتنين طب السؤال هو طب لو
+
+585
+01:10:58,500 --> 01:11:02,800
+اعطانى مثلك كيف بدى ابدأ بقول كويس ان اعطاك مثلة
+
+586
+01:11:02,800 --> 01:11:08,950
+بيعطيك مثلة زى هذهالخطوة الأولى let y تساوي usrtba
+
+587
+01:11:08,950 --> 01:11:12,910
+solution بجيب المشتقة الأولى والمشتقة الثانية
+
+588
+01:11:12,910 --> 01:11:17,010
+ومنها بجيب ال characteristic equation جيبنا ال
+
+589
+01:11:17,010 --> 01:11:22,070
+characteristic equation بروح بحلها عادي جدا زي
+
+590
+01:11:22,070 --> 01:11:26,110
+الاعدادية زي الصف التامن اللي كنا نشتغل فيها هو
+
+591
+01:11:26,110 --> 01:11:29,470
+الصف السابع والله لا أدري ماكان الصف التامن تمام
+
+592
+01:11:29,470 --> 01:11:33,940
+بروح نحل المعادلة هذه ونجيب الجذور R1وهر اتنين
+
+593
+01:11:33,940 --> 01:11:37,780
+اللي جيتهم مختلفين اذا ال general solution على طول
+
+594
+01:11:37,780 --> 01:11:43,400
+القطب الشكل اللي عندنا هذا تمام؟ حد بتسألي سؤال
+
+595
+01:11:43,400 --> 01:11:50,920
+قبل ان ندخل الى الأمثلة؟ انا أمثلة كتير، اه، هي عم
+
+596
+01:11:50,920 --> 01:11:55,760
+بتسأل؟ طيب، ندخل الى الأمثلة
+
+597
+01:12:24,080 --> 01:12:26,480
+المثال الأول examples
+
+598
+01:12:41,730 --> 01:12:49,350
+solve the following differential
+
+599
+01:12:49,350 --> 01:12:52,410
+equation
+
+600
+01:12:52,410 --> 01:13:06,490
+equation z نمرا a y double prime زائد خمسة y prime
+
+601
+01:13:06,490 --> 01:13:16,350
+يساوي زيرو نمرا bY double prime ناقص اتنين Y prime
+
+602
+01:13:16,350 --> 01:13:23,850
+ناقص اتنين Y بده يستوي كده؟ بده يستوي Zero هذا
+
+603
+01:13:23,850 --> 01:13:29,130
+سؤال تمانية من الكتاب وهذا سؤال خمسة من الكتاب
+
+604
+01:13:29,130 --> 01:13:34,110
+يبقى solution اخد
+
+605
+01:13:34,110 --> 01:13:39,360
+المثلة رقم Aبطلع في المثل رقم ايه بلاقي
+
+606
+01:13:39,360 --> 01:13:43,000
+homogeneous differential equation with constant
+
+607
+01:13:43,000 --> 01:13:47,440
+coefficients يبقى automatic بروح بفرض الحل على
+
+608
+01:13:47,440 --> 01:13:58,020
+صيغة E Os RT يبقى let Y بده يتساوي E Os RT بيه
+
+609
+01:13:58,020 --> 01:14:06,890
+solution لل equation اللي عندنا هنا يبقى thenالـ
+
+610
+01:14:06,890 --> 01:14:14,330
+Y' يكون R في E أُس RT والـ YW' يكون R تربية في E
+
+611
+01:14:14,330 --> 01:14:20,770
+أُس RT بعد ذلك بتعوض في المعادلة بيصير R تربية في
+
+612
+01:14:20,770 --> 01:14:29,320
+E أُس RT زائد 5R في E أُس RT يساوي 0بعد هيك بروح
+
+613
+01:14:29,320 --> 01:14:36,280
+نجسم كله على مين على E و أس أرتي بصير R تربيع زائد
+
+614
+01:14:36,280 --> 01:14:42,840
+خمسة R كله بده يسوى مين Zero طيب ايش رايك بدل ما
+
+615
+01:14:42,840 --> 01:14:44,480
+نقعد نفضل و نسوي
+
+616
+01:14:54,100 --> 01:14:59,140
+بنفع على بنفعش بس إيش بدك تقولي؟ تقولي left Y تسوى
+
+617
+01:14:59,140 --> 01:15:01,920
+U RT بيه إيه ال solution then the characteristic
+
+618
+01:15:01,920 --> 01:15:06,580
+equation is كذا تمام؟ يبقى بقى فاهم إن أنت فعلا
+
+619
+01:15:06,580 --> 01:15:09,930
+فاهم الكلام الشتغليهمش حطيت المعادلة فضل غيري و ان
+
+620
+01:15:09,930 --> 01:15:13,350
+كنت كتبتي هذه تحتها دوري من وين أجدت هذه الله أعلم
+
+621
+01:15:13,350 --> 01:15:18,930
+يبقى
+
+622
+01:15:18,930 --> 01:15:27,190
+بنات هذه اللي هي ال characteristic equation وسميلي
+
+623
+01:15:27,190 --> 01:15:34,830
+هذه المعادلة رقم واحد of equation oneيبقى هذه هي
+
+624
+01:15:34,830 --> 01:15:39,470
+المعادلة المميزة أو المعادلة المساعدة للمعادلة
+
+625
+01:15:39,470 --> 01:15:43,450
+العرقموها يبقى الأن بدي أحلي المعادلة هذه بأي
+
+626
+01:15:43,450 --> 01:15:49,410
+طريقة كانت بلجة للتحليل مثلا يبقى فيها R عام
+
+627
+01:15:49,410 --> 01:15:54,810
+المشترك بقدر أخدها يبقى R عام المشترك بظل R زائد
+
+628
+01:15:54,810 --> 01:16:01,650
+خمسة يساوي Zero ومنها R one تساوي Zero وR two كده
+
+629
+01:16:01,650 --> 01:16:07,960
+شو ساوي؟سالب خمسة ممتاز جدا جبت R1 و R2 يبقى هاي
+
+630
+01:16:07,960 --> 01:16:15,460
+ال general solution يبقى بروح بقوله the general
+
+631
+01:16:15,460 --> 01:16:22,920
+solution of equation
+
+632
+01:16:23,890 --> 01:16:32,490
+وان ازم why you say constant C1 في E أُس R one T
+
+633
+01:16:32,490 --> 01:16:38,350
+يعني E أُس جداش E أُس Zero T بدي اكتبها بس المرة
+
+634
+01:16:38,350 --> 01:16:40,790
+دي وبعدين ببطل اكتبها بس عشان اول مرة
+
+635
+01:16:58,800 --> 01:17:06,090
+بنجي للمسألة Bبنفس التكتيك الكلام اللي قلتلكوا
+
+636
+01:17:06,090 --> 01:17:12,790
+الشفوي حصيرا كتبوهله مباشرة يبقاش بدهجة اقول let Y
+
+637
+01:17:12,790 --> 01:17:22,970
+تساوي E أس RT be a solution of the differential
+
+638
+01:17:22,970 --> 01:17:29,570
+equation اتنين وهي هذه سمناها اللي هي الاتنين
+
+639
+01:17:29,570 --> 01:17:37,200
+المثل التانييبقى لو قلتلي هيك دغري then the
+
+640
+01:17:37,200 --> 01:17:50,180
+characteristic equation is R تربيع نقص اتنين R
+
+641
+01:17:50,180 --> 01:17:55,920
+يساوي زيرا ممتاز جدا يبقى ان قلت بالطريقة الاولى
+
+642
+01:17:55,920 --> 01:18:01,580
+ماشي هيك ماشي و ماعناه مشكلة تمامابس السؤال هو
+
+643
+01:18:01,580 --> 01:18:10,060
+بنقدر نحلل المعادلة هذه؟ نقدر؟
+
+644
+01:18:10,060 --> 01:18:16,600
+نقدر؟ لأ بنقدرش يبقى مليش الامانالقانون العام يبقى
+
+645
+01:18:16,600 --> 01:18:22,760
+بناء عليه بروح بقوله هذا بدي يعطينا R يساوي ناقص
+
+646
+01:18:22,760 --> 01:18:28,320
+باله قداش اتنين زائدة وناقص الجدر التربية اللي بات
+
+647
+01:18:28,320 --> 01:18:37,640
+تربية اللي هو اربعة ناقص اربعة الف اللي هو بواحد
+
+648
+01:18:38,040 --> 01:18:46,240
+جيم اللي هو بسالب اتنين كله على اتنين في واحد يبقى
+
+649
+01:18:46,240 --> 01:18:51,260
+احصار هذه يا بناتي اتنين زائد او ناقص اتطلعي هذه
+
+650
+01:18:51,260 --> 01:18:57,940
+بقداش موجة بتمانية موجة بتمانية او اربعة باطماش
+
+651
+01:18:57,940 --> 01:19:03,970
+اطماش اللي هو اتنين جدر تلاتة يبقى اتنينجذر تلاتة
+
+652
+01:19:03,970 --> 01:19:08,330
+على اتنين، تلاحظ القيمة التي تحت الجذر التالية
+
+653
+01:19:08,330 --> 01:19:13,200
+عليها تموج بقىيبقى الجذور اتنين are real and
+
+654
+01:19:13,200 --> 01:19:20,620
+different يبقى صار عند ال R يساوي واحد زائد او
+
+655
+01:19:20,620 --> 01:19:26,380
+ناقص جذر تلاتة يبقى صار R واحد يساوي واحد زائد جذر
+
+656
+01:19:26,380 --> 01:19:33,780
+تلاتة وR اتنين واحد ناقص جذر تلاتة يبقى باجي بقوله
+
+657
+01:19:33,780 --> 01:19:36,720
+the solution
+
+658
+01:19:38,790 --> 01:19:48,070
+Y تساوي C1 في E أس واحد زائد جذر تلاتة كله في T
+
+659
+01:19:48,070 --> 01:20:00,030
+زائد C2 في E أس واحد ناقص جذر تلاتة كله في من؟ كله
+
+660
+01:20:00,030 --> 01:20:00,870
+في T
+
+661
+01:20:09,710 --> 01:20:16,130
+يبقى هاي كتبتله الحل تبع من تبع المعادلة هذه رقم
+
+662
+01:20:16,130 --> 01:20:16,690
+اتنين
+
+663
+01:20:39,390 --> 01:20:51,070
+ناخد كمان مثال example
+
+664
+01:20:51,070 --> 01:20:57,270
+2 solve the
+
+665
+01:20:57,270 --> 01:21:03,090
+following initial
+
+666
+01:21:03,090 --> 01:21:14,040
+value of problems and describeand describe اوصف
+
+667
+01:21:14,040 --> 01:21:24,420
+ليه its behavior its behavior describe
+
+668
+01:21:24,420 --> 01:21:33,580
+its behavior as T increases as T increases
+
+669
+01:21:38,730 --> 01:21:46,650
+سؤال عشرة من الكتاب يقول yw prime زائد اربع y
+
+670
+01:21:46,650 --> 01:21:54,870
+prime زائد تلاتة y تساوي زيرو و ال y عند ال zero
+
+671
+01:21:54,870 --> 01:22:00,030
+بده يساوي اتنين و ال y prime عند ال zero بده يساوي
+
+672
+01:22:00,030 --> 01:22:05,730
+سالب واحد نمرأ بإيه اللي هو سؤال ستة عشر من الكتاب
+
+673
+01:22:06,520 --> 01:22:15,340
+بقول اربعة y double prime ناقص y تساوي zero وال y
+
+674
+01:22:15,340 --> 01:22:22,380
+عند السلب اتنين بده ساوي واحد وال y prime عند
+
+675
+01:22:22,380 --> 01:22:28,760
+السلب اتنين بال y prime عند السلب اتنين بده ساوي
+
+676
+01:22:28,760 --> 01:22:30,320
+سالب واحد
+
+677
+01:23:04,330 --> 01:23:08,950
+سؤال زي ما تشايفين initial value problem و بدل
+
+678
+01:23:08,950 --> 01:23:13,670
+المطلوب اتنين و ليس مطلوبا واحد بيقول حل ال
+
+679
+01:23:13,670 --> 01:23:18,030
+initial value problem و هاتلي ما هو شكل الحل او
+
+680
+01:23:18,030 --> 01:23:23,670
+وصفلي سلوك الحل لما T increases يعني لما T تكبر و
+
+681
+01:23:23,670 --> 01:23:29,330
+تروح لوينللمالة نهاية اذا انا بدي امسك المثلة رقم
+
+682
+01:23:29,330 --> 01:23:34,650
+واحد يبقى هذه اعتبارها المثلة رقم واحد وهذه المثلة
+
+683
+01:23:34,650 --> 01:23:42,390
+رقم اتنين يبقى بيناجي لنمر ايه لت Y تساوي E أس RT
+
+684
+01:23:42,390 --> 01:23:55,390
+ب solution of the differential equation oneيبقى
+
+685
+01:23:55,390 --> 01:24:00,230
+automatic بروح بقوله ايه؟ the characteristic
+
+686
+01:24:00,230 --> 01:24:06,350
+equation is R
+
+687
+01:24:06,350 --> 01:24:14,490
+تربيع زائد اربعة R زائد تلاتة تساوي Zero اظن
+
+688
+01:24:14,490 --> 01:24:20,710
+بتتحلل هذه يا بناتتتحلل مافيش مشكلة يبقى هذا جوس
+
+689
+01:24:20,710 --> 01:24:28,310
+هذا جوس تاني بده يتساوي zero هنا R هنا R هنا 1 هنا
+
+690
+01:24:28,310 --> 01:24:35,070
+3 هنا زائد هنا زائديبقى ZR وزائد تلاتة R زائد
+
+691
+01:24:35,070 --> 01:24:42,510
+أربعة R ومنها ال R بدها تساوي سالب واحد وال R بدها
+
+692
+01:24:42,510 --> 01:24:48,650
+تساوي سالب تلاتة real and different يبقى باجي
+
+693
+01:24:48,650 --> 01:24:54,450
+بقوله the general solution
+
+694
+01:24:57,010 --> 01:25:09,550
+Y تساوي C1 Eوص ناقص T زائد C2 Eوص ناقص تلاتة T طيب
+
+695
+01:25:09,550 --> 01:25:12,650
+ماعطيني ال initial conditions ال initial
+
+696
+01:25:12,650 --> 01:25:19,030
+conditions فايديتهم ان اقدر اجيب قيمة C1 و قيمة C2
+
+697
+01:25:19,030 --> 01:25:23,610
+طب موجودة ال Y و موجودة Y prime اذا خليني اشتقها و
+
+698
+01:25:23,610 --> 01:25:29,150
+بعدين بنعوضيبقى لو روحنا اشتقنا هذه مانتش بصير Y'
+
+699
+01:25:29,810 --> 01:25:40,410
+يسوى ناقص C1 EOS ناقص T ناقص تلاتة C2 EOS ناقص
+
+700
+01:25:40,410 --> 01:25:46,610
+تلاتة T ال exponential زي ما هي ضرب مشتقة الاس
+
+701
+01:25:46,610 --> 01:25:53,410
+تمام نيجي لل initial condition الأوليبقى ال
+
+702
+01:25:53,410 --> 01:25:57,150
+initial condition الأول بيقول لي y عند zero بده
+
+703
+01:25:57,150 --> 01:26:04,390
+يساوي كدهش لإتنين يبقى هذا بده يعطينا لإتنين بدها
+
+704
+01:26:04,390 --> 01:26:12,230
+تساوي c1 زائد c2 لإنه e of zero بواحد و e of zero
+
+705
+01:26:12,230 --> 01:26:16,370
+بواحد نيجي ال condition التاني يقول لي y prime عند
+
+706
+01:26:16,370 --> 01:26:24,810
+zero بقدهش سالب واحد بده يساويحط zero بصير سالب C1
+
+707
+01:26:24,810 --> 01:26:31,990
+سالب تلاتة C2 شو رايك نجمع طب لو جمعنا هدول مع
+
+708
+01:26:31,990 --> 01:26:40,950
+السلامة بضل عندي واحد يساوي النقص اتنين C2 يبقى C2
+
+709
+01:26:40,950 --> 01:26:49,020
+يساوي سالب نصإذا نجيبنا C2، لما نجيبنا C2، مين
+
+710
+01:26:49,020 --> 01:26:54,460
+ضايل علينا؟ C1، روح أعوض في أي من المعادلة تانية،
+
+711
+01:26:54,460 --> 01:26:59,480
+الأسهل لمين؟ المعادلة الأولى، فبعدي بقول المعادلة
+
+712
+01:26:59,480 --> 01:27:09,830
+الأولى على الشكل التاليتساوي C واحد ناقص نص هذا
+
+713
+01:27:09,830 --> 01:27:17,230
+يعني ان C واحد بده يساوي كده اش اتنين و نص يعني
+
+714
+01:27:17,230 --> 01:27:25,650
+خمسة على اتنين اذا صار solution is
+
+715
+01:27:26,860 --> 01:27:38,160
+هي ال Y يساوي C1 خمسة على اتنين E أس ناقص T الان
+
+716
+01:27:38,160 --> 01:27:47,760
+C2 اللي هو ناقص نص E أس ناقص تلاتة T حدا فيكم اي
+
+717
+01:27:47,760 --> 01:27:52,020
+تساؤل هنا اي
+
+718
+01:27:52,020 --> 01:27:59,780
+تساؤلطيب بروح لنمرى بيه من المثلة نمرى بيه برضه
+
+719
+01:27:59,780 --> 01:28:14,220
+let Y تساوي E أس RT بيه solution of equation 2 من
+
+720
+01:28:14,220 --> 01:28:18,340
+اللي بتحكي؟ اه
+
+721
+01:28:18,340 --> 01:28:24,670
+يبقى يقولنا من بدأ تسأل طيب قولوا انت ناسيينأه هذه
+
+722
+01:28:24,670 --> 01:28:31,030
+بدري عليها شوية إذا هذا جانبين له شكل الحل تبع
+
+723
+01:28:31,030 --> 01:28:36,910
+المعادلة هذه يبقى هذه بقدر اكتبها بنات خمسة على
+
+724
+01:28:36,910 --> 01:28:44,610
+اتنين E أس T ناقص واحد على اتنين E أس تلاتة T
+
+725
+01:28:45,770 --> 01:28:51,350
+المطلب التاني من السؤال قال لي وصفلي سلوك الحل لما
+
+726
+01:28:51,350 --> 01:28:55,930
+T increases increases يعني وين بدها تروح يعني
+
+727
+01:28:55,930 --> 01:28:59,610
+معناه كأني بقولي خد ال limit لما T بدها تروح لما
+
+728
+01:28:59,610 --> 01:29:06,050
+لا نهايةاذا بروح بقوله limit ال Y لما T بدها تروح
+
+729
+01:29:06,050 --> 01:29:10,690
+ل infinity بده يساوي limit لما T بدها تروح ل
+
+730
+01:29:10,690 --> 01:29:17,410
+infinity لخمس عالة اتنين E أس T ناقص واحد على
+
+731
+01:29:17,410 --> 01:29:23,550
+اتنين E أس تلاتة T لما T بدها تروح ل المقام هذا
+
+732
+01:29:23,550 --> 01:29:24,850
+كله بقداش
+
+733
+01:29:47,770 --> 01:29:53,390
+يبقى هذا إجابة الشطر الثاني من السؤال ننتقل الآن
+
+734
+01:29:53,390 --> 01:29:54,730
+إلى نمربي
+
+735
+01:29:57,980 --> 01:30:03,040
+علي صوتك شوية والله
+
+736
+01:30:03,040 --> 01:30:08,700
+ماانا فاهم شو اقول ال missing مالها؟ في ان هنا
+
+737
+01:30:08,700 --> 01:30:13,520
+missing و ان هي المعادلة هذه المعادلة بتقدر
+
+738
+01:30:13,520 --> 01:30:19,420
+تعتبريها function with T missing تمام؟ اللي الصعبة
+
+739
+01:30:19,420 --> 01:30:23,210
+مش السهلةانجرب يا عزيزي اذا بتقدري اهلا و اهلا
+
+740
+01:30:23,210 --> 01:30:28,370
+بتقدريش انت حرار لا بتقدري من حقك اه من حقك نسأل و
+
+741
+01:30:28,370 --> 01:30:32,530
+هذا سؤال عادي جدا equation with T missing بس مين
+
+742
+01:30:32,530 --> 01:30:36,650
+أسهل هذي ولا ال T missing هذي أسهل كتير يبقى انا
+
+743
+01:30:36,650 --> 01:30:40,830
+كنت بحل بتلك الطريقة اللي ماكنت بعرفش اتنين هذي
+
+744
+01:30:40,830 --> 01:30:45,030
+linear يعني السهلة يعني ال T missing او ال Y
+
+745
+01:30:45,030 --> 01:30:48,590
+missing بيعطيكي function ماهياش linear يعني مكلقة
+
+746
+01:30:48,590 --> 01:30:52,970
+عشوية هيكتمام و انت بدك تروح و تحليها بس هو بيقولش
+
+747
+01:30:52,970 --> 01:30:56,050
+لك ليه T missing ولا Y missing بيخليك لحالك و
+
+748
+01:30:56,050 --> 01:31:01,850
+يشتغل اللي بدك هيه في حد بتسأل تاني طيب ننتقل الان
+
+749
+01:31:01,850 --> 01:31:07,510
+الى نمرا بيه يبقى باجي بقوله little y تساوي E أُس
+
+750
+01:31:07,510 --> 01:31:17,690
+RTBA solution of the differential
+
+751
+01:31:32,170 --> 01:31:39,610
+بنجي على المعادلة التانية هاي أربعة أربعة ناقص كذا
+
+752
+01:31:39,610 --> 01:31:47,490
+شبناها ناقص واحد يساوي زيروهذا سيعطيك ان R تربيه
+
+753
+01:31:47,490 --> 01:31:54,890
+تساوي قداش يعني هذا سيعطيك ان R تساوي زائد او ناقص
+
+754
+01:31:54,890 --> 01:32:01,750
+نصتمام؟ يعني في عندي كم إجابة؟ جابتين و اتنين are
+
+755
+01:32:01,750 --> 01:32:08,250
+real and different واحد نص والتاني سالف نص يبقى
+
+756
+01:32:08,250 --> 01:32:14,690
+باجي بقوله the general solution is
+
+757
+01:32:26,690 --> 01:32:36,150
+اللي هو Y سوى C1 في E أُس T على 2 زائد C2 في E أُس
+
+758
+01:32:36,150 --> 01:32:45,350
+ناقص T على 2 يبقى هذا هو من الحلبنروح ندور على مين
+
+759
+01:32:45,350 --> 01:32:54,450
+على C1 وC2 إذا خلّينا نشتق بالمرة يبقى Y' يساوي نص
+
+760
+01:32:54,450 --> 01:33:06,210
+C1 إيص T على 2 ناقص نص C2 إيص ناقص T على 2نمسك ال
+
+761
+01:33:06,210 --> 01:33:11,110
+condition الأول ال condition الأول بقول لي why عند
+
+762
+01:33:11,110 --> 01:33:20,170
+السالب اتنين يساوي واحد اذا واحد بده يساوي سي واحد
+
+763
+01:33:20,170 --> 01:33:26,930
+ده حط هنا سالب اتنين بصير ايه السالب واحد يبقى ايه
+
+764
+01:33:26,930 --> 01:33:35,070
+السالب واحدزاد سي اتنين سالي باتنين مع سالي بيصير
+
+765
+01:33:35,070 --> 01:33:42,590
+موجة باتنين يبجأي فقط لا غير هذا ال condition
+
+766
+01:33:42,590 --> 01:33:48,590
+الأولcondition التاني بيقول لي y prime عند السلب
+
+767
+01:33:48,590 --> 01:33:57,330
+اتنين يسوى قداش يسوى السلب واحد هذا بده يعطينا ان
+
+768
+01:33:57,330 --> 01:34:09,130
+السلب واحد يسوى هذا نصوهذا C و C واحد نص C واحد في
+
+769
+01:34:09,130 --> 01:34:20,590
+E أس سالب واحد وهنا ناقص نص وهنا C اتنين في E أس
+
+770
+01:34:20,590 --> 01:34:30,350
+واحد يعني ايه دوري شو رايك نتخلص من انصاص هذه لو
+
+771
+01:34:30,350 --> 01:34:37,520
+ضربنا في اتنينكويس؟ و الله بدنا نضرب في ناقص اتنين
+
+772
+01:34:37,520 --> 01:34:44,780
+حتى نختصر بالمرء هذه بده اخليها زي ما هي هذه ها
+
+773
+01:34:44,780 --> 01:34:50,140
+بده انزلها زي ما هي هذه مش فيها كسور واحد يساوي C
+
+774
+01:34:50,140 --> 01:34:55,360
+واحد في يوس ناقص واحد زائد C اتنين A هذه بده
+
+775
+01:34:55,360 --> 01:35:00,900
+اضربها في سلب اتنين ايش بصير موجة باتنينيساوي
+
+776
+01:35:00,900 --> 01:35:09,760
+السالب C1E والسالب واحد السالب بصير موجب C2E لو
+
+777
+01:35:09,760 --> 01:35:18,460
+جمعنا بروحوا هدول مع بعض وهذا بدي يطلع لي انه 2C2E
+
+778
+01:35:18,460 --> 01:35:27,100
+بدي يساوي قداشيساوي تلاتة يبقى ومنها C2 يساوي
+
+779
+01:35:27,100 --> 01:35:35,460
+تلاتة على اتنين E والسالب واحد هذا
+
+780
+01:35:35,460 --> 01:35:41,800
+جيبنا من اللي هو الـC2 بدنا نروح نجيب C1 بنرجع
+
+781
+01:35:41,800 --> 01:35:45,040
+نعوض في المعادلة هذه خليني اكتب هذا فوق
+
+782
+01:36:04,110 --> 01:36:09,610
+طيب الان بدى امسك المعلومة اللى حصلت عليها هذه هيك
+
+783
+01:36:09,610 --> 01:36:16,150
+واجع وضبان في المعادلة الأولى يعني ماشي بصير عندي
+
+784
+01:36:16,150 --> 01:36:27,070
+واحد يساوي C واحد في E أسالب واحد واحد في C واحد E
+
+785
+01:36:27,070 --> 01:36:32,050
+أسالب واحد الان C اتنين بتلاتة على اتنين E أسالب
+
+786
+01:36:32,050 --> 01:36:40,830
+واحدزائد تلاتة على اتنين E أسالب واحد في ال E يبقى
+
+787
+01:36:40,830 --> 01:36:46,490
+هذه و هذه بروح الله سهل عليهم بصير ان C واحد E
+
+788
+01:36:46,490 --> 01:36:51,690
+أسالب واحد يساوي بدون تلاتة على اتنين يعني واحد و
+
+789
+01:36:51,690 --> 01:37:00,150
+نص بجيب يصير ناقص نصناقص نص اضرب كله في E بيصير C1
+
+790
+01:37:00,150 --> 01:37:09,690
+C1 بده يساوي سالب نص E تمام اذا اصبح الحل على
+
+791
+01:37:09,690 --> 01:37:20,180
+الشكل التالي يبقى ده solution is y تساويY تساوي C
+
+792
+01:37:20,180 --> 01:37:30,580
+واحد اللي يبقى داشر ناقص نص E ناقص نص E في E أس T
+
+793
+01:37:30,580 --> 01:37:38,590
+على اتنين وزائد C اتنين بالموجة بظنزائد تلاتة على
+
+794
+01:37:38,590 --> 01:37:44,610
+اتنين E والسالب واحد تلاتة على اتنين E والسالب
+
+795
+01:37:44,610 --> 01:37:53,900
+واحد في جداش في E والسالب T على اتنينيا بتخليها زي
+
+796
+01:37:53,900 --> 01:37:58,660
+ما هي يا بدك تخليها اي واحدة ماعناش مشكلة تقدر
+
+797
+01:37:58,660 --> 01:38:06,400
+تقولي هذا الكلام يساوي الناقص نص وهذه A أس T على
+
+798
+01:38:06,400 --> 01:38:13,480
+اتنين زائد واحد وهنا زائد تلاتة على اتنين
+
+799
+01:38:22,080 --> 01:38:29,060
+بشارة مخالفة يبقى هذا شكل الحل ال initial value
+
+800
+01:38:29,060 --> 01:38:34,800
+problem لا يزال عن المزيد من الأمثلة بدل المثال
+
+801
+01:38:34,800 --> 01:38:40,810
+اتنينحاجة بتسأل اه ضل عندنا بس شغلة الشغلة بده شوف
+
+802
+01:38:40,810 --> 01:38:46,560
+كيف سلوك الحل هذا لما ت بدها تروح للمالة نهايةيبقى
+
+803
+01:38:46,560 --> 01:38:52,620
+بتروح اخد ال limit لما T بدها تروح للملة نهاية ل Y
+
+804
+01:38:52,620 --> 01:38:59,380
+يبقى limit لما T بدها تروح للملة نهاية لمن لناقص
+
+805
+01:38:59,380 --> 01:39:06,080
+نص E أس T على اتنين زائد واحد زائد تلاتة على اتنين
+
+806
+01:39:06,080 --> 01:39:11,940
+E أس ناقص T على اتنين زائد واحد لما T بدها تروح
+
+807
+01:39:11,940 --> 01:39:16,150
+للملة نهاية ال term هذا كله بجداشة منهازيرو لإن
+
+808
+01:39:16,150 --> 01:39:20,710
+هذا بنزل تحت بصير عدد على مالة نهاية بزيرو لكن هذا
+
+809
+01:39:20,710 --> 01:39:27,470
+كده؟ سالب مالة نهاية هي السالب برا وهذا مالة نهاية
+
+810
+01:39:27,470 --> 01:39:33,830
+هذا سالب مالة نهاية زائد زيرو فبجي بقول the
+
+811
+01:39:33,830 --> 01:39:35,010
+solution
+
+812
+01:39:46,980 --> 01:39:52,520
+يبقى بنقول يازال هناك المزيد من الأمثلة للمرة
+
+813
+01:39:52,520 --> 01:39:56,200
+القادمة ان شاء الله تعالى، أعطيكوا العافية
+
diff --git a/PL9fwy3NUQKwa8ZDfSFGn6H8xVFLzqmCZC/PY1U7lboILA_postprocess.srt b/PL9fwy3NUQKwa8ZDfSFGn6H8xVFLzqmCZC/PY1U7lboILA_postprocess.srt
new file mode 100644
index 0000000000000000000000000000000000000000..c8c91668e6d712c7629142ca5c08139a7a587cab
--- /dev/null
+++ b/PL9fwy3NUQKwa8ZDfSFGn6H8xVFLzqmCZC/PY1U7lboILA_postprocess.srt
@@ -0,0 +1,3400 @@
+1
+00:00:09,580 --> 00:00:15,820
+بسم الله الرحمن الرحيم المرة الماضية كنا بنتحدث في
+
+2
+00:00:15,820 --> 00:00:20,460
+chapter 3 عن ال second order differential equation
+
+3
+00:00:20,460 --> 00:00:25,060
+وجزّانها إلى جزئين ال homogeneous linear
+
+4
+00:00:25,060 --> 00:00:29,160
+differential equationوالـ Non-homogeneous linear
+
+5
+00:00:29,160 --> 00:00:33,720
+differential equation ودرسنا التنتين كل واحدة فيهم
+
+6
+00:00:33,720 --> 00:00:38,320
+على حده وعرفنا ان حل الـ Non-homogeneous يعتمد على
+
+7
+00:00:38,320 --> 00:00:41,240
+حال مياه الـ homogeneous differential equation
+
+8
+00:00:41,240 --> 00:00:46,220
+Chapter 4 اللي بين أدينا هو تعميم لـ Chapter 3
+
+9
+00:00:46,220 --> 00:00:50,880
+يعني مافيش فيه معلومات جديدة ولذلك سنحاول أن نختصر
+
+10
+00:00:50,880 --> 00:00:55,540
+بقدر الإمكانمابنعش نمشي بالتفصيل اللي مشينا فيه في
+
+11
+00:00:55,540 --> 00:01:01,340
+chapter 3 وإنما سنختصر بحيث يكون نأتي بالزبدة أو
+
+12
+00:01:01,340 --> 00:01:05,660
+الفائدة من هذا ال chapterلذلك شرط الرابعة بيقول لي
+
+13
+00:01:05,660 --> 00:01:09,440
+higher order linear differential equation يعني
+
+14
+00:01:09,440 --> 00:01:14,300
+المعادلة التفاضل الخطية من الرتب العليا او من
+
+15
+00:01:14,300 --> 00:01:18,660
+الرتب العليا يعني ايش؟يعني رتبة التالتة الرابعة
+
+16
+00:01:18,660 --> 00:01:23,620
+الخامسة السادسة السابعة التمنة الاخرين يعني انسي
+
+17
+00:01:23,620 --> 00:01:27,840
+الاتنين بعد اتنين فما فوق، من الرتبة التالتة فما
+
+18
+00:01:27,840 --> 00:01:32,790
+فوقأول section يعتبر إزاي مقدمة لهذا الشرطر يعني
+
+19
+00:01:32,790 --> 00:01:37,750
+بيجيبلي بعض المعلومات الأساسية اللازمة للدراسة
+
+20
+00:01:37,750 --> 00:01:42,690
+فيما بعد فجالي ال general theory النظرية العامة of
+
+21
+00:01:42,690 --> 00:01:45,250
+the nth order linear differential equation
+
+22
+00:01:45,250 --> 00:01:50,710
+للمعادلة التفاضلية من الرتبة النونية nth order
+
+23
+00:01:50,710 --> 00:01:56,900
+يبقى الرتبة النونية رتبة الرقم nان قداش الله علم
+
+24
+00:01:56,900 --> 00:02:04,500
+ثلاثة ماشي اربعة ماشي خمسة ماشي الى اخره الان نجي
+
+25
+00:02:04,500 --> 00:02:09,240
+لأول تعريف عند هنا بيقولي an nth order linear
+
+26
+00:02:09,240 --> 00:02:12,240
+differential equation is an equation in the form
+
+27
+00:02:12,740 --> 00:02:18,880
+يبقى الشكل العام لهذه المعادلة y to the مش أُس in
+
+28
+00:02:18,880 --> 00:02:22,920
+هذه المعادلة لأ y to the derivative in يعني هذا
+
+29
+00:02:22,920 --> 00:02:27,260
+رمز يدل على المشتقة نونية لما هطلق رقم وبين جثين
+
+30
+00:02:27,260 --> 00:02:31,800
+يبقى هذا معناته مشتقة لكن مافيش جثين يبقى هذا
+
+31
+00:02:31,800 --> 00:02:37,120
+يعتبر أُس فباجي بقول هذه y to the derivative in
+
+32
+00:02:37,120 --> 00:02:43,020
+زائد function في T P1 of Tفي y to the derivative
+
+33
+00:02:43,020 --> 00:02:48,180
+of n minus one زائد P2 of t برضه function of y to
+
+34
+00:02:48,180 --> 00:02:51,840
+the derivative of n minus two زائد زائد زائد زائد
+
+35
+00:02:51,840 --> 00:02:58,260
+زائد زائد زائد
+
+36
+00:02:58,260 --> 00:02:58,880
+زائد زائد زائد زائد زائد زائد زائد زائد زائد زائد
+
+37
+00:02:58,880 --> 00:02:58,900
+زائد زائد زائد زائد زائد زائد زائد زائد زائد زائد
+
+38
+00:02:58,900 --> 00:02:59,000
+زائد زائد زائد زائد زائد زائد زائد زائد زائد زائد
+
+39
+00:02:59,000 --> 00:02:59,220
+زائد زائد زائد زائد زائد زائد زائد زائد زائد زائد
+
+40
+00:02:59,220 --> 00:02:59,300
+زائد زائد زائد زائد زائد زائد زائد زائد زائد زائد
+
+41
+00:02:59,300 --> 00:03:03,290
+زائد زائد زائد زائد زائد زائد زائد زائدبدى يسوى
+
+42
+00:03:03,290 --> 00:03:08,970
+مين؟ G of T يبقى هذه المعادلة اللى سافين بالتسلسل
+
+43
+00:03:08,970 --> 00:03:13,790
+بنزل مشتقة نونية الناقص واحد الناقص اتنين الناقص
+
+44
+00:03:13,790 --> 00:03:17,430
+ثلاثة لغاية نص المشتقة التانية المشتقة الاولى Y
+
+45
+00:03:17,430 --> 00:03:24,190
+بدون مشتقة يسوى مين؟ يسوى G of T بقولش هنا دراسة
+
+46
+00:03:24,190 --> 00:03:29,970
+المعادلة واحد تشبه دراسة من ال second order linear
+
+47
+00:03:29,970 --> 00:03:34,820
+differential equationيعني دراسة المعادلة دي تماما
+
+48
+00:03:34,820 --> 00:03:39,300
+مثل دراسة من دراسة اللي هو second order
+
+49
+00:03:39,300 --> 00:03:43,830
+differential equation ذاتي بدنا نذكر تذكيرفبجي
+
+50
+00:03:43,830 --> 00:03:48,850
+بقول لو كان y1 و y2 و y3 لغاية yn are linearly
+
+51
+00:03:48,850 --> 00:03:52,750
+independent solutions of the homogeneous
+
+52
+00:03:52,750 --> 00:03:56,350
+differential equation اللي عندنا دي بجي الشكل ال
+
+53
+00:03:56,350 --> 00:04:01,610
+general solution لهذه المعادلة كنا بنديله رمز c في
+
+54
+00:04:01,610 --> 00:04:05,490
+ال second دولة بجي انا جينا نقول yc تساوي c1 و y1
+
+55
+00:04:05,490 --> 00:04:12,720
+زي c2 و y2 هنا عند انثمن ال solutions يبقى باجي
+
+56
+00:04:12,720 --> 00:04:18,280
+يقول c1 y1 زي ال c2 y2 ويظل ماشي لغاية cn yn و ال
+
+57
+00:04:18,280 --> 00:04:23,520
+c هات هدول كله مالهم ثابت تمام يبقى لو عندي
+
+58
+00:04:23,520 --> 00:04:27,160
+linearly independent solutions بهذا الشكل بدي يكون
+
+59
+00:04:27,160 --> 00:04:31,360
+ال fundamental set of solutions او ال general
+
+60
+00:04:31,360 --> 00:04:36,280
+solution للمعادل عالمين على الشكل اللي عندنا هذا
+
+61
+00:04:36,280 --> 00:04:42,950
+بعد احتياط الأخرىلو أخدت رونسك لمين لكل الحلول هذه
+
+62
+00:04:42,950 --> 00:04:47,250
+as a function of T كتبته بالشكل هذا او بالشكل هذا
+
+63
+00:04:47,250 --> 00:04:51,630
+و لاجئت ان رونسك الهدف معله لا يساوي zero
+
+64
+00:04:51,630 --> 00:04:56,170
+اتوماتيكي يبقى ال general solution نفس اللي عندنا
+
+65
+00:04:56,170 --> 00:04:59,390
+هناك اللي هو الشكل اللي عندنا هذا و طبعا في ال
+
+66
+00:04:59,390 --> 00:05:06,020
+second order قلنا في اربع شغلات بتكافئبعض، مجموعة
+
+67
+00:05:06,020 --> 00:05:09,360
+الحل اللي بتكونولي fundamental set هنا بقول مجموعة
+
+68
+00:05:09,360 --> 00:05:14,400
+الحلول بتكونولي fundamental set of solutions او
+
+69
+00:05:14,400 --> 00:05:17,820
+بيجيبولي ال general solution او الرنس كان عنده
+
+70
+00:05:17,820 --> 00:05:22,500
+نقطة يساوي لا يساوي zero او الرنس كان على كل ال
+
+71
+00:05:22,500 --> 00:05:27,740
+interval ماله لا يساوي zero يبقى هيه يبقى بيكون
+
+72
+00:05:27,740 --> 00:05:32,460
+شكل الحل على الصيغة اللي عندنا هذهأخدنا كمان في
+
+73
+00:05:32,460 --> 00:05:39,520
+حالة second order إيجاد صيغة أخرى لقيمة
+
+74
+00:05:39,520 --> 00:05:43,580
+الرونسكين باستخدام able theorem able theorem في
+
+75
+00:05:43,580 --> 00:05:49,920
+حالة مجموعة من الحلول بنفس الطريقة باجي بقول ال
+
+76
+00:05:49,920 --> 00:05:53,620
+رونسكين تبع ال Y1 لغاية ال YN as a function of T
+
+77
+00:05:53,620 --> 00:06:00,160
+هو كونسان في أسناق استكامل P1 of T DT مين هو ال P1
+
+78
+00:06:00,160 --> 00:06:06,590
+of T؟يبقى هو المعامل تبع y to the derivative n
+
+79
+00:06:06,590 --> 00:06:11,170
+minus one و بشرط أن يكون معامل y to the derivative
+
+80
+00:06:11,170 --> 00:06:16,410
+n هو main يعني لو ماكانش وعصاهم بدي أجسم على هذا
+
+81
+00:06:16,410 --> 00:06:20,490
+المعامل وهذا خليه واعد صحيح وبالتالي P1 of t بتاخد
+
+82
+00:06:20,490 --> 00:06:24,710
+شكل غير الشكل اللي ظهرت فيه لأول مرة يبقى بناء
+
+83
+00:06:24,710 --> 00:06:29,450
+عليه ههه بدي يكون P1 هو المعامل تبع y to the
+
+84
+00:06:29,450 --> 00:06:33,770
+derivative n minus oneوفي نفس الوقت المعامل تبع yn
+
+85
+00:06:33,770 --> 00:06:39,330
+يجب أن يكون واحد صحيح بعد ذلك هذه نظرية أخدناها
+
+86
+00:06:39,330 --> 00:06:42,570
+كمان في second order أنه لو عند ال particular
+
+87
+00:06:42,570 --> 00:06:45,750
+solution لل non homogeneous differential equation
+
+88
+00:06:45,750 --> 00:06:49,490
+وعند ال general solution لل homogeneous
+
+89
+00:06:49,490 --> 00:06:53,270
+differential equation أجمع الأثنين بيعطيني ال
+
+90
+00:06:53,270 --> 00:06:57,580
+general solution أمامللـ second order linear
+
+91
+00:06:57,580 --> 00:07:00,300
+differential equation هذه في حالة ال second نفس
+
+92
+00:07:00,300 --> 00:07:04,740
+الكلام في حالة ال nth order فلو كان capital YT هو
+
+93
+00:07:04,740 --> 00:07:08,640
+ال particular solution لل differential equation
+
+94
+00:07:08,640 --> 00:07:14,420
+one وكان YC اللي حاكين عليه هذا هو ال general
+
+95
+00:07:14,420 --> 00:07:17,580
+solution لل homogeneous differential equation إذا
+
+96
+00:07:17,580 --> 00:07:23,670
+لو جمعنا الاتنين هدولبيعطيني ال general solution
+
+97
+00:07:23,670 --> 00:07:30,830
+لمن؟ للمعادلة رقم واحد يعني كإن Y بده يساوي C1Y1
+
+98
+00:07:30,830 --> 00:07:39,810
+C2Y2 زائد CNYN زائد ال particular solution capital
+
+99
+00:07:39,810 --> 00:07:47,010
+Y of Tأكتر منها الكلمتين اللي قدامك اللي أحب ناش
+
+100
+00:07:47,010 --> 00:07:51,750
+من الجزء النظري التابع هذا ال section حد بتحب تسأل
+
+101
+00:07:51,750 --> 00:07:59,270
+ليه سؤال هنا قبل أن ندخل إلى الأمثلة حد
+
+102
+00:07:59,270 --> 00:08:06,130
+بتحب تسأل ليه سؤال طيب
+
+103
+00:08:06,130 --> 00:08:10,370
+نأتي إلى الأمثلة هذه هي هي ورا
+
+104
+00:08:13,470 --> 00:08:18,730
+اللي ما كتبتش اسمها يا بنات تكتب اسمها يبقى بإننا
+
+105
+00:08:18,730 --> 00:08:27,730
+نيجي للأمثلة examples المثال
+
+106
+00:08:27,730 --> 00:08:37,190
+الأول بيقول determine the intervals determine the
+
+107
+00:08:37,190 --> 00:08:40,030
+intervals
+
+108
+00:08:43,280 --> 00:08:51,500
+in which solutions
+
+109
+00:08:51,500 --> 00:08:54,920
+are
+
+110
+00:08:54,920 --> 00:09:01,440
+sure to exist
+
+111
+00:09:09,890 --> 00:09:18,990
+بيقول لي X ناقص واحد Y to the derivative four زائد
+
+112
+00:09:18,990 --> 00:09:26,210
+X زائد واحد Y to the derivative two المشتقة
+
+113
+00:09:26,210 --> 00:09:35,670
+الثانية زائد تان ال X كلها في Y بده ساوي زيرو
+
+114
+00:09:59,380 --> 00:10:04,980
+سؤال مرة تانية بيقول لحدد الفترات اللي الحل عليها
+
+115
+00:10:04,980 --> 00:10:10,580
+sure بتأكيد to exist يعني موجود على هذه الفترة
+
+116
+00:10:10,580 --> 00:10:14,460
+احنا لما كنا نقول المعاملة هو رقم واحد بجي انا
+
+117
+00:10:14,460 --> 00:10:19,800
+اشترق ان المعاملات هي دوال متاصلة، مظبوط؟ اذا انا
+
+118
+00:10:19,800 --> 00:10:24,740
+بدي اشوف شكل المعاملة و اكتشف ان هذه دوال متاصلة
+
+119
+00:10:24,740 --> 00:10:30,720
+فبجي الحل كالتالي solutionيبقى المعادلة اللى عندى
+
+120
+00:10:30,720 --> 00:10:38,920
+بدى اكتبها بشكل جديد y to the derivative 4 زائد x
+
+121
+00:10:38,920 --> 00:10:45,760
+زائد 1 على x ناقص 1 في y to the derivative 2
+
+122
+00:10:45,760 --> 00:10:54,300
+المشتقة الثانية زائد 10 ال x على مين على x ناقص 1
+
+123
+00:10:54,300 --> 00:11:05,070
+كله في y يساوي 0الاول لو جيت لل P1 of T P1 of X
+
+124
+00:11:05,070 --> 00:11:12,310
+اليمين يا بنات X زائد واحد على X ناقص واحد ال
+
+125
+00:11:12,310 --> 00:11:17,990
+discontinuity حصل وين؟ عند الواحد يبقى هذه is
+
+126
+00:11:17,990 --> 00:11:22,270
+discontinuous
+
+127
+00:11:22,270 --> 00:11:32,440
+at X يساوي واحد تمام؟نجي التانية اللي بعديها P2 of
+
+128
+00:11:32,440 --> 00:11:40,400
+X اللي هي تان ال X على مين؟ على X is discontinuous
+
+129
+00:11:40,400 --> 00:11:47,780
+at X ساوين ال discontinuity حصل وين؟ عند الواحد بس
+
+130
+00:11:47,780 --> 00:11:53,020
+بجي للتان ال X و اكتشف ال discontinuity للتان X
+
+131
+00:11:53,020 --> 00:11:58,820
+عند مين؟ باية اتنين وسلب باية اتنينتلاتة باية على
+
+132
+00:11:58,820 --> 00:12:02,040
+اتنين سالب تلاتة باية على اتنين خمسة باية على
+
+133
+00:12:02,040 --> 00:12:06,580
+اتنين سالب خمسة باية على اتنين و هكذا نظل ماشيين
+
+134
+00:12:06,580 --> 00:12:16,780
+يبقى و زائد او ناقص N باية على اتنين و ال N is odd
+
+135
+00:12:18,400 --> 00:12:21,980
+يعني بايع اتنين ثلاثة بايع اتنين خمسة بايع اتنين
+
+136
+00:12:21,980 --> 00:12:26,520
+سبعة بايع اتنين الى اخر يوم تمام يبقى تعالوا لو
+
+137
+00:12:26,520 --> 00:12:32,440
+حطيت خط احدد هذه الفترات لو جيت قلت هذا ال real
+
+138
+00:12:32,440 --> 00:12:42,620
+life عندك هنا بتيجي له سالب خمسة سالب خمسة by على
+
+139
+00:12:42,620 --> 00:12:49,230
+اتنينبعدها بدها تجيكي هنا سالب تلاتة by على اتنين
+
+140
+00:12:49,230 --> 00:12:56,290
+هنا بدها تجيكي سالب by على اتنين هنا بدها تجيكي
+
+141
+00:12:56,290 --> 00:13:03,530
+موجب by على اتنين هنا موجب تلاتة by على اتنين ده
+
+142
+00:13:03,530 --> 00:13:10,850
+الماشيين موجب خمسة by على اتنين and so on نيجي
+
+143
+00:13:10,850 --> 00:13:15,850
+للواحد نشوف وين موقع الواحدبدي اجي الواحد ال by
+
+144
+00:13:15,850 --> 00:13:20,630
+قداش هي هنا تلاتة صحيح و اربتاشر من مية مظبوط لو
+
+145
+00:13:20,630 --> 00:13:26,130
+جسمتها على اتنين بطلع واحد و نص و كمان كسر بسيط
+
+146
+00:13:26,130 --> 00:13:31,850
+يعني تقريبا واحد و نص مظبوط واحد و نص يبقى ال by
+
+147
+00:13:31,850 --> 00:13:37,010
+على اتنين هدى قداش واحد و نص يبقى الواحد بدي اجي
+
+148
+00:13:37,010 --> 00:13:43,350
+وين جابلها يبقى الواحد ممكن يجي هنا هذا الواحديبقى
+
+149
+00:13:43,350 --> 00:13:47,070
+النقاط اللي احنا راسمينهم دول هما نقاط ال
+
+150
+00:13:47,070 --> 00:13:52,210
+discontinuity لل functions P1 و P2 إذا الدوال اللي
+
+151
+00:13:52,210 --> 00:13:56,890
+عندى هذا الدوال متصل على كل real line ما عدمين
+
+152
+00:13:56,890 --> 00:14:04,050
+الخطوط اللي عندنا يبقى باجي بقوله هنا the solution
+
+153
+00:14:04,050 --> 00:14:17,000
+exists on theintervals على الفترات من هنا جايين من
+
+154
+00:14:17,000 --> 00:14:23,620
+سلب infinity وصلنا لمين؟ لأ سالب خمسة by على اتنين
+
+155
+00:14:23,620 --> 00:14:30,300
+و سالب تلاتة by على اتنين و بعدها سالب تلاتة by
+
+156
+00:14:30,300 --> 00:14:37,740
+على اتنين و سالب by على اتنين و بعدها سالب by على
+
+157
+00:14:37,740 --> 00:14:44,360
+اتنين أجانب الطريق من؟عنده بدي اوغف يبقى وا واحد
+
+158
+00:14:44,360 --> 00:14:52,060
+وعندك كمان واحد ومين و باي على اتنين ونظل ماشيين
+
+159
+00:14:52,060 --> 00:14:59,400
+باي على اتنين و تلاتة باي على اتنين تلاتة باي على
+
+160
+00:14:59,400 --> 00:15:05,080
+اتنين و خمسة باي على اتنين و لسه ماشيين الى ما شاء
+
+161
+00:15:05,080 --> 00:15:11,020
+الله تمام؟ يبقى هذا كلها مين؟هذا كله ال interval
+
+162
+00:15:11,020 --> 00:15:15,820
+اللي اللي اللي ده اللي اللي اللي اللي اللي اللي
+
+163
+00:15:15,820 --> 00:15:16,160
+اللي اللي اللي اللي اللي اللي اللي اللي اللي اللي
+
+164
+00:15:16,160 --> 00:15:17,000
+اللي اللي اللي اللي اللي اللي اللي اللي اللي اللي
+
+165
+00:15:17,000 --> 00:15:17,680
+اللي اللي اللي اللي اللي اللي اللي اللي اللي اللي
+
+166
+00:15:17,680 --> 00:15:17,720
+اللي اللي اللي اللي اللي اللي اللي اللي اللي اللي
+
+167
+00:15:17,720 --> 00:15:17,880
+اللي اللي اللي اللي اللي اللي اللي اللي اللي اللي
+
+168
+00:15:17,880 --> 00:15:17,940
+اللي اللي اللي اللي اللي اللي اللي اللي اللي اللي
+
+169
+00:15:17,940 --> 00:15:22,840
+اللي اللي اللي اللي اللي اللي اللي اللي اللي اللي
+
+170
+00:15:22,840 --> 00:15:27,320
+اللي اللي
+
+171
+00:15:27,320 --> 00:15:27,340
+اللي اللي اللي اللي اللي اللي اللي اللي اللي اللي
+
+172
+00:15:27,340 --> 00:15:36,780
+اللي اللي اللي اللي اللي اللي
+
+173
+00:15:36,780 --> 00:15:48,020
+الليسؤال التاني بيقول ما يأتي determine whether
+
+174
+00:15:48,020 --> 00:15:51,720
+the
+
+175
+00:15:51,720 --> 00:15:58,260
+following set determine
+
+176
+00:15:58,260 --> 00:16:06,540
+the following set of functions are
+
+177
+00:16:07,440 --> 00:16:16,700
+Linearly Dependent او Linearly Independent هذا
+
+178
+00:16:16,700 --> 00:16:24,820
+المطلب الأول المطلب التاني if they are linearly
+
+179
+00:16:24,820 --> 00:16:29,500
+dependent find a linear relation
+
+180
+00:16:39,860 --> 00:16:50,280
+reinheralation among them
+
+181
+00:16:50,280 --> 00:16:54,160
+نمر
+
+182
+00:16:54,160 --> 00:17:03,860
+ايه سؤال سبعة من الكتاب بيقول F1 of T بدي ساوي
+
+183
+00:17:03,860 --> 00:17:11,500
+اتنين T ناقص تلاتةوال F2 as a function of T بدر
+
+184
+00:17:11,500 --> 00:17:22,440
+ساوي T ترابيع زائد واحد وال F3 of T بدر
+
+185
+00:17:22,440 --> 00:17:28,340
+ساوي اتنين T ترابيع ناقص T
+
+186
+00:17:37,690 --> 00:17:42,570
+نرجع لأسئلتنا مرة تانية يقول دي determine whether
+
+187
+00:17:42,570 --> 00:17:47,570
+the following set
+
+188
+00:17:47,570 --> 00:17:53,870
+of functions
+
+189
+00:17:53,870 --> 00:17:58,370
+are linearly dependent or linearly independent
+
+190
+00:17:58,370 --> 00:18:02,670
+يعني مجموعة الدول التالية شوفوا هل هي linearly
+
+191
+00:18:02,670 --> 00:18:07,690
+dependent ولا linearly independentلو كانت linearly
+
+192
+00:18:07,690 --> 00:18:13,550
+dependent find a linear relation هتيلي علاقة خاطية
+
+193
+00:18:13,550 --> 00:18:18,070
+among them يعني بتربط هذه الدول التلاتة مع بعض
+
+194
+00:18:18,070 --> 00:18:23,730
+بنذكركم بجينا نقول ان لو في عندي مجموعة من ال
+
+195
+00:18:23,730 --> 00:18:28,930
+functions تنتين تلاتة أربعة خمسة جد ما يكونوا لو
+
+196
+00:18:28,930 --> 00:18:33,130
+ضربت كل واحدة فيهم في constant وقلت يساوي صفر
+
+197
+00:18:33,650 --> 00:18:38,250
+ولاقيته ان C1 يساوي C2 يساوي C3 يساوي يساوي C ان
+
+198
+00:18:38,250 --> 00:18:45,050
+يساوي Zero بقول هدول linearly independent فالمقابل
+
+199
+00:18:45,050 --> 00:18:49,150
+لو أخدت رونسكين لهذه الدولة ولاقيته لا يساوي Zero
+
+200
+00:18:49,150 --> 00:18:54,150
+يبقى هدول كمان linearly independent النقطة الثانية
+
+201
+00:18:54,860 --> 00:18:59,480
+لو جيت للدوال اللي عندي هذه اها او constant في
+
+202
+00:18:59,480 --> 00:19:02,660
+الدالة الأولى زاد constant في التانية زاد constant
+
+203
+00:19:02,660 --> 00:19:06,520
+في التالتة زاد زاد constant في الأخرى يسوى zero
+
+204
+00:19:06,520 --> 00:19:11,680
+لجيت ال constants هدول ممنوع كلهم يسوى zero على
+
+205
+00:19:11,680 --> 00:19:16,720
+الأقل ولو لجيت واحد فيهم لا يسوى zero اذا هذه ال
+
+206
+00:19:16,720 --> 00:19:22,310
+function ما لها linearly dependent اولو أخدت لها
+
+207
+00:19:22,310 --> 00:19:25,530
+المحدد و طلع يساوي zero يبقى هدول linearly
+
+208
+00:19:25,530 --> 00:19:30,330
+dependent إذا إن كانت linearly dependent بدي يكون
+
+209
+00:19:30,330 --> 00:19:33,390
+constant في الأول زائد constant في التاني زائد
+
+210
+00:19:33,390 --> 00:19:36,830
+constant في الزائد زائد بدي يساوي zero بدوا إيه
+
+211
+00:19:36,830 --> 00:19:41,930
+شكل هذه العلاقة الخطية هذا هو المطلوب الثاني من
+
+212
+00:19:41,930 --> 00:19:46,830
+السؤال طيب نجي لنا النقطة الأولى مايعطيني هذه تلات
+
+213
+00:19:46,830 --> 00:19:51,240
+دوالوبدي اشوف هالها دي linearly dependent ولا
+
+214
+00:19:51,240 --> 00:19:56,060
+linearly independent اظن ابسط حاجة ناخد ال runoff
+
+215
+00:19:56,060 --> 00:20:04,060
+skin تبعها تمام يبقى انا لو جيت جولت solution بدي
+
+216
+00:20:04,060 --> 00:20:11,680
+اخد ال runoff skin تبع ال F1 و F2 و F3 كله as a
+
+217
+00:20:11,680 --> 00:20:17,040
+function of Tيبقى ماعليه إلا إيه إلا هات يحط
+
+218
+00:20:17,040 --> 00:20:22,120
+الدالة الأولى الدالة الأولى اللى هى لإتنين T ناقص
+
+219
+00:20:22,120 --> 00:20:29,140
+تلاتة الدالة التانية T تربيع زائد واحد الدالة
+
+220
+00:20:29,140 --> 00:20:36,480
+التالتة اللى هتنين T تربيع ناقص T الأن بدي أبدأ
+
+221
+00:20:36,480 --> 00:20:40,720
+أشتقكم توجبلي شوية في الجزء النظر يا بنات لما
+
+222
+00:20:40,720 --> 00:20:45,610
+كتبنا المحدد كتبنا الصف الأولصف التاني اللي هو
+
+223
+00:20:45,610 --> 00:20:50,050
+المشتقة الأولى صف التالت المشتقة الثانية ضالين
+
+224
+00:20:50,050 --> 00:20:55,010
+المشي لغاية المشتقة النونية ناقص واحد، مظبوط؟ هدول
+
+225
+00:20:55,010 --> 00:20:58,910
+تلت دوال يبقى بيضل أناشي لغاية ما وصل المشتقة رقم
+
+226
+00:20:58,910 --> 00:21:05,110
+اتنين أقل من ال order اللي عندنا بمقدار واحد يبقى
+
+227
+00:21:05,110 --> 00:21:09,790
+.. طب لو كانوا أربع دوال؟بدي أصير عندي مش محدد
+
+228
+00:21:09,790 --> 00:21:14,030
+بتلات صفوف و تلات أعمدة بدي
+
+229
+00:21:14,030 --> 00:21:20,930
+أصل لغاية المشتقة التالتة و هكذا فبدنا نشتق الدالة
+
+230
+00:21:20,930 --> 00:21:26,570
+الأولى بالنسبة ل T بقداش اتنين مشتقة هذه اتنين T
+
+231
+00:21:26,570 --> 00:21:32,590
+مشتقة هذه اربعة T ناقص واحد نشتق كمان مرة Zero
+
+232
+00:21:32,590 --> 00:21:39,880
+كمان مرة اتنين كمان مرة اربعبدنا نعرف قداش قيمة
+
+233
+00:21:39,880 --> 00:21:45,000
+هذا المحدد يبقى هذا الكلام يساوي بدا فكه باستخدام
+
+234
+00:21:45,000 --> 00:21:51,200
+عناصر الصف الأول والله أسهل لي باستخدام العمود
+
+235
+00:21:51,200 --> 00:21:57,700
+الأول ليش؟ لأن في صفر بفصلة التلت، مظبوط؟ أو
+
+236
+00:21:57,700 --> 00:22:02,160
+باستخدام الصف التالت، سيارة بتفرقش عنها، إذا خلينا
+
+237
+00:22:02,160 --> 00:22:08,020
+بالعمود الأوليبقى باجي بقوله اتنين تين ناقص تلاتة
+
+238
+00:22:08,020 --> 00:22:13,340
+فيه بروح نشطه بصفه و عموده لناسيه اتفك المحدد هنا
+
+239
+00:22:13,340 --> 00:22:17,020
+اللي بذكركم بنجي للعنصر اللي عنده اللي هو العنصر
+
+240
+00:22:17,020 --> 00:22:22,370
+هذاو بنشطه بصف و عمود و بضال مين عندى المحدد
+
+241
+00:22:22,370 --> 00:22:26,870
+الأصغر هذا بدى أفكه حاصل ضرب عناصر القطر الرئيسى
+
+242
+00:22:26,870 --> 00:22:32,570
+ناقص حاصل ضرب عناصر القطر الثانوي حاصل ضرب عناصر
+
+243
+00:22:32,570 --> 00:22:41,340
+القطر الرئيسى ب 4 ف 2 ب 8 Tماقص حاصل ضرب عناصر
+
+244
+00:22:41,340 --> 00:22:50,420
+القطر الثانوي يبقى ماقص تمانيته زائد اتنين خلصنا
+
+245
+00:22:50,420 --> 00:22:55,140
+منه بالدالي للعواصر اللي بعده حسب قاعدة الإشارات
+
+246
+00:22:55,140 --> 00:23:05,090
+شرط هذا مالها سالب يبقى سالب اتنين في اشط بصفههو
+
+247
+00:23:05,090 --> 00:23:10,530
+عموده بيبقى المحدد هذا أربعة في T تربية وزايد واحد
+
+248
+00:23:10,530 --> 00:23:18,650
+يبقى أربعة T تربية زايد أربعة ناقص أربعة T تربية
+
+249
+00:23:18,650 --> 00:23:26,470
+زايد اتنين T تمام اللي بعده زايد صفر في محدده اللي
+
+250
+00:23:26,470 --> 00:23:31,830
+هو الصفر طيب نجي نشوفها أظن هذه و هذه مع السلامة
+
+251
+00:23:32,540 --> 00:23:36,540
+طيب غير مصوف عليهم بيظل اتنين بيضربها في قداش
+
+252
+00:23:36,540 --> 00:23:43,160
+اربعة تي ناقص ستة بالداجة لان اربعة تي تربيع
+
+253
+00:23:43,160 --> 00:23:46,980
+بالموجة واربعة تي تربيع بالسالب دول شاندي الا
+
+254
+00:23:46,980 --> 00:23:51,660
+اربعة زائد اتنين تي بيضربها في قداش ناقص اتنين
+
+255
+00:23:51,660 --> 00:24:01,500
+يبقى ناقص تمانية ناقص اربعة تيماقص 4T وزاد 4T مع
+
+256
+00:24:01,500 --> 00:24:08,220
+السلام وطلع الجواب جدا ماقص 14 هذا الكلام ماله لا
+
+257
+00:24:08,220 --> 00:24:14,020
+يمكن أن يساوي 0 for all T مهما كان شكل ال T
+
+258
+00:24:35,720 --> 00:24:42,540
+خلصنا حل السؤال ولا لسه مطلوب تاني؟الله سبحانه و
+
+259
+00:24:42,540 --> 00:24:46,920
+تعالى بيقول لو كان linearly dependent بد ال linear
+
+260
+00:24:46,920 --> 00:24:50,580
+combination يبقى هدول linearly independent لو ضربت
+
+261
+00:24:50,580 --> 00:24:52,920
+constant في الأول و constant في التاني و constant
+
+262
+00:24:52,920 --> 00:24:57,860
+في التاني كله بده يقلع بأصفر السيطاني إذا أنا
+
+263
+00:24:57,860 --> 00:25:02,040
+مطلوب التاني الله ينطبق عالمين على هذا الجزء من
+
+264
+00:25:02,040 --> 00:25:07,380
+السؤال طيب فنروح لنمرى بيه اللي هو السؤال تمانية
+
+265
+00:25:07,380 --> 00:25:16,380
+من الكتاب وراه مباشرةبقول ايش F1 of T بده يساوي
+
+266
+00:25:16,380 --> 00:25:26,460
+اتنين T ناقص تلاتة نفس الدالة اللي فوق وال F2 of T
+
+267
+00:25:26,460 --> 00:25:34,440
+بده يساوي اتنين T ترابيع زائد واحد اتنين T ترابيع
+
+268
+00:25:34,440 --> 00:25:45,280
+زائد واحد وال F3 of Tبدو يساوي تلاتة T تربيع زائد
+
+269
+00:25:45,280 --> 00:25:51,860
+T الان قال لي شوف لي هدول linearly dependent و لا
+
+270
+00:25:51,860 --> 00:25:56,280
+linearly independent احنا هدول طلعنا مالهم
+
+271
+00:25:56,280 --> 00:26:01,000
+linearly independent يعني نتوقع هدول كمان يطلعوا
+
+272
+00:26:01,000 --> 00:26:07,690
+زيهم معناته انا قاعد بكرريبقى .. يبقى .. بمعناته
+
+273
+00:26:07,690 --> 00:26:10,970
+احنا قاعدين بنكرر الرسالة، يبقى المتوقع ان يكون
+
+274
+00:26:10,970 --> 00:26:16,010
+ماله linearly dependent، بس ماينفعش هيك إلا أروح
+
+275
+00:26:16,010 --> 00:26:22,150
+أثبت هذا الكلامبإمكاني أثبت ذلك بأكثر من طريقة
+
+276
+00:26:22,150 --> 00:26:26,890
+إحدى الطرق زي اللي فات أجيب ال runoff skin تبعه و
+
+277
+00:26:26,890 --> 00:26:33,170
+أجيب يساوي 0 و يبقى linearly dependent طريقة تانية
+
+278
+00:26:33,170 --> 00:26:36,970
+أني أقول كون الصين في الأول و كون الصين في التاني
+
+279
+00:26:36,970 --> 00:26:39,710
+و كون الصين في التالت و أجمع و أساوي ب 0 و أروح
+
+280
+00:26:39,710 --> 00:26:44,210
+أجيب قيمسي واحد و سي اتنين و سي تلتة على الاقل
+
+281
+00:26:44,210 --> 00:26:50,490
+لازم نلاقي واحد فيهم لا يساوي ال zero طبعا طريقة
+
+282
+00:26:50,490 --> 00:26:55,030
+تالتة تعتمد على دقة النظر عندك تعالي تطلعي كويس
+
+283
+00:26:55,030 --> 00:27:01,150
+انا عندي تلت دوال ايش رايكش لو جيت هنا T تربيع و
+
+284
+00:27:01,150 --> 00:27:06,010
+هنا T و هنا constant هادف اش فيه اقل انه جاب ال T
+
+285
+00:27:06,010 --> 00:27:11,840
+تربيع و T و كأنه هاديبتعتمد على مين؟ على الاتنين،
+
+286
+00:27:11,840 --> 00:27:17,000
+بس بتعتمد كيف أنا مش عارف، كويس؟ بنقولك كيف تعتمد،
+
+287
+00:27:17,000 --> 00:27:24,460
+الآن لو جيت قولت أنا كتالي solution، بديش أسوي زي
+
+288
+00:27:24,460 --> 00:27:28,780
+قبل اللي هو المحدد اللي عندي، بدي أفكر بطريقة أخرى
+
+289
+00:27:29,190 --> 00:27:33,850
+باجي بقول هذه وهذه هذه فيها constant وهذه فيها
+
+290
+00:27:33,850 --> 00:27:39,790
+constant لكن هذه يبقى انا لو فكرت تخلص من ال two
+
+291
+00:27:39,790 --> 00:27:46,630
+constants ممكن تبقى foraged مظبوط بقولها كيف تتخلص
+
+292
+00:27:46,630 --> 00:27:52,700
+بقولها ده سالم تلاتة يبقى ممكن اضرب هذه في طولو
+
+293
+00:27:52,700 --> 00:27:56,700
+اجمع التنتين يا بضرب هذه في تلاتة و اجمع التنين
+
+294
+00:27:56,700 --> 00:28:01,580
+صحيح ولا لا بيكون الكون استنطار و يمكن اوصل لهذه
+
+295
+00:28:01,580 --> 00:28:06,020
+او جربتها او شغل من هذا القبيل طيب تعالوا نجرب
+
+296
+00:28:06,020 --> 00:28:14,970
+يبقى انا لو جيت اخد F1 of Tزائد تلاتة F2 of T
+
+297
+00:28:41,100 --> 00:28:50,540
+زائد تلاتة في اتنين بستة T تربيع زائد تلاتة بقول I
+
+298
+00:28:50,540 --> 00:28:56,560
+سالب تلاتة وزائد تلاتة مع السلامة هذا الكلام يساوي
+
+299
+00:28:56,560 --> 00:29:04,070
+بقى اللي عندي ستة T تربيع زائد اتنين Tفي عامل
+
+300
+00:29:04,070 --> 00:29:10,150
+مشترك فيبا بينهم اه فيلي اتنين يبجى اي اتنين و اي
+
+301
+00:29:10,150 --> 00:29:19,030
+تيتك اجداش اتنين هنا تلاتةتلاتة T تكيب زائد T
+
+302
+00:29:19,030 --> 00:29:25,350
+تلاتة T تربيع زائد T تلاتة T تربيع زائد T تلاتة T
+
+303
+00:29:25,350 --> 00:29:26,830
+تربيع زائد T تلاتة T تربيع زائد T تلاتة T تربيع
+
+304
+00:29:26,830 --> 00:29:27,170
+تلاتة T تربيع زائد T تلاتة T تربيع زائد T تلاتة T
+
+305
+00:29:27,170 --> 00:29:32,470
+تلاتة T تربيع زائد T تلاتة T تربيع
+
+306
+00:29:32,470 --> 00:29:40,680
+زائد T تلاتصحيح ولا لأ؟ يبقى الصيارة عندي F1 of T
+
+307
+00:29:40,680 --> 00:29:49,660
+زائد تلاتة F2 of T مقصة اتنين F تلاتة of T يشبه
+
+308
+00:29:49,660 --> 00:29:57,940
+جداش الآن هل المعاملات هدول أصفر؟أصفار هدول؟ لأ
+
+309
+00:29:57,940 --> 00:30:02,900
+مدام مش أصفار يبقى هذا شو يعني ان هدول linearly
+
+310
+00:30:02,900 --> 00:30:07,900
+dependent وهيرناش اللي بديها يبقى انا لما اشتغلت
+
+311
+00:30:07,900 --> 00:30:12,380
+بالطريقة ده ستة أصفرين بحجر لو بدي أشغل زي قبل لسه
+
+312
+00:30:12,380 --> 00:30:14,840
+بدي أروح أحسب اللي هو ممكن و أثبت انهم linearly
+
+313
+00:30:14,840 --> 00:30:18,890
+dependentو بعد هيك أروح أدور على علاقة هذه لكن
+
+314
+00:30:18,890 --> 00:30:24,090
+شغلي بهذه الطريقة تفكيري ست عصفرين بحجر واحد و
+
+315
+00:30:24,090 --> 00:30:35,750
+بأقصر وقت ممكن يبقى هذا معناته ان ال F1 و F2 و F3
+
+316
+00:30:35,750 --> 00:30:40,350
+are linearly dependent because
+
+317
+00:30:43,270 --> 00:30:51,430
+ان الـC1 بده يساوي واحد وC2 بده يساوي تلاتة وC3
+
+318
+00:30:51,430 --> 00:31:00,810
+بده يساوي سالب اتنين يبقى not zeros ماهياش أصفات
+
+319
+00:31:00,810 --> 00:31:05,650
+يبقى هدول linearly dependent وهي ال relation اللى
+
+320
+00:31:05,650 --> 00:31:10,010
+بتربط المعادلات التلاتة هدول او الدول التلاتة من
+
+321
+00:31:10,010 --> 00:31:15,310
+مينمع بعضهم البعض طبق للمطلوب التاني المطلوب
+
+322
+00:31:15,310 --> 00:31:19,880
+التاني قال find a linear relation among themهتلرّي
+
+323
+00:31:19,880 --> 00:31:24,180
+لإن الناس بتربطهم إن كانوا linearly dependent
+
+324
+00:31:24,180 --> 00:31:30,240
+واضحة الصورة يبقى هذا اختصرنا فيها الحل بدل مثبت
+
+325
+00:31:30,240 --> 00:31:34,860
+انهم linearly dependent وروح أدور على هذه العلاقة
+
+326
+00:31:34,860 --> 00:31:38,120
+يبقى هذه العلاقة بيانات لإنهم linearly dependent
+
+327
+00:31:38,120 --> 00:31:43,920
+لإن الثوابت ماهياش أصفر اتنين جيبنا العلاقة اللي
+
+328
+00:31:43,920 --> 00:31:48,380
+عندناها دي وبالتالي صدنا أصفرين بحجر واحد
+
+329
+00:32:06,740 --> 00:32:12,340
+ناخد كمان مثال مثال
+
+330
+00:32:12,340 --> 00:32:22,020
+تلاتة سؤال سبعتاش من الكتاب بيقول show that بييني
+
+331
+00:32:22,020 --> 00:32:32,280
+أن رونسكين تبع الخمسة و ال sign تربيع T و
+
+332
+00:32:32,280 --> 00:32:42,140
+cosine اتنين Tبدو يساوي zero for all T كمان مطلوب
+
+333
+00:32:42,140 --> 00:32:53,420
+can you establish this
+
+334
+00:32:53,420 --> 00:32:58,440
+result هذه
+
+335
+00:32:58,440 --> 00:33:00,680
+النتيجة without
+
+336
+00:33:13,420 --> 00:33:17,180
+Evolution of the runnerskin
+
+337
+00:34:02,470 --> 00:34:06,810
+السؤال مرة ثانية السؤال زي ما انت شايفين مطلبين
+
+338
+00:34:07,460 --> 00:34:10,340
+المطلوب الأول بيقول بيبين لي أن ال neurons can
+
+339
+00:34:10,340 --> 00:34:14,200
+remain للثلاث دوال هذول الخمسة و ال sign تربيه T و
+
+340
+00:34:14,200 --> 00:34:18,220
+ال cosine اتنين T بده يساوي Zero يعني هذول
+
+341
+00:34:18,220 --> 00:34:25,420
+Linearly Dependent ما علينا بعدين المطلوب التاني
+
+342
+00:34:25,420 --> 00:34:30,520
+بيقول Can you establish بتقدر تثبتلي هذه النتيجة
+
+343
+00:34:30,520 --> 00:34:36,920
+without direct evolution بدون حسابات مباشرةيعني
+
+344
+00:34:36,920 --> 00:34:41,220
+بدون ما تحطها المحدد وتروح تحسب اللي هو ال one
+
+345
+00:34:41,220 --> 00:34:46,220
+skin هذول ام لا تقوله تعالى نشوف مطلوب مطلوب نمشي
+
+346
+00:34:46,220 --> 00:34:49,900
+step by step دي اول شئ بدأت بتقول ان هذا الكلام
+
+347
+00:34:49,900 --> 00:34:57,940
+يساوي zeroهذه الرنسة تتبع الخمسة والصين تربيتي
+
+348
+00:34:57,940 --> 00:35:04,480
+والكوصين اتنين تي تتبع المحدد هذه الخمسة وهذه
+
+349
+00:35:04,480 --> 00:35:12,960
+الصين تربيتي وهذه الكوصين اتنين تي نجيب الصفين
+
+350
+00:35:12,960 --> 00:35:20,000
+التانيات في المحدد مشتقة الخمسة بقداش؟ مشتقة الصين
+
+351
+00:35:20,000 --> 00:35:33,760
+تربيةحد بتعرف؟ كدهش؟ 2 sin t في cos t يعني 2 sin t
+
+352
+00:35:33,760 --> 00:35:40,160
+في cos t هذه يا بنات بقدر استبدلها ب sin 2t مش
+
+353
+00:35:40,160 --> 00:35:43,420
+هحصل ايه؟ هسلي في الحسابات لإن لو بده الشقة اللي
+
+354
+00:35:43,420 --> 00:35:47,730
+بقعد افضل مشتقة تحصل ضربده اللي تانه هذا بتكبر
+
+355
+00:35:47,730 --> 00:35:52,510
+الموضوع طيب هذا ال cosine بيسالب sin فيه اتنين
+
+356
+00:35:52,510 --> 00:35:59,250
+يبقى سالب اتنين sin اتنين T الصف اللي بعده مشتاقة
+
+357
+00:35:59,250 --> 00:36:06,170
+ال zero ب zero اتنين cosine اتنين T هذه كمان مرة
+
+358
+00:36:06,170 --> 00:36:13,960
+بسالب اربع cosine اتنين Tبدي أفك المحدد هذا و أشوف
+
+359
+00:36:13,960 --> 00:36:19,020
+كده شو ساوي بدي أفكه باستخدام عناصر العمود الأول
+
+360
+00:36:19,020 --> 00:36:24,820
+لإنه فيه أسفار بسهل الشغل يبقى باجي بقوله خمسة في
+
+361
+00:36:24,820 --> 00:36:33,460
+أشق بصفه و عموده بصير هذا اللي هو ناقص أربع sign
+
+362
+00:36:33,460 --> 00:36:42,600
+اتنين Tcos 2t هذا الرئيسي ناقص الثانوي ناقص مع
+
+363
+00:36:42,600 --> 00:36:52,200
+ناقص بيصير زائد اربع sin 2t cos 2t بعدها zero في
+
+364
+00:36:52,200 --> 00:36:56,720
+محدده ب zero zero في محدده ب zero يبقى زائد zero
+
+365
+00:36:56,720 --> 00:37:02,000
+زائد zero طلعيلي في ال term هذا و ال term هذا نفسه
+
+366
+00:37:02,000 --> 00:37:06,470
+كل واحد بإشارةمخالفة يبجي عن الجامعة بطلع كمان
+
+367
+00:37:06,470 --> 00:37:13,270
+جداش Zero في خمسة Zero زائد Zero زائد Zero بطلع
+
+368
+00:37:13,270 --> 00:37:16,110
+جداش اظن و هو المطلوب
+
+369
+00:37:23,120 --> 00:37:27,860
+خلص المطلوب الأول المطلوب التاني بيقول Can you
+
+370
+00:37:27,860 --> 00:37:32,940
+establish بتقدر تثبت أو توصل للنتيجة هذه بدون ما
+
+371
+00:37:32,940 --> 00:37:41,940
+تعمل حسابتك هذه أم لا الإجابة نعم موافقة يعني طيب
+
+372
+00:37:41,940 --> 00:37:42,980
+ماشي كيف؟
+
+373
+00:37:50,490 --> 00:37:54,210
+طيب انا بالحسابات بالنظر يعنى كيف يعنى؟انه دولة
+
+374
+00:37:54,210 --> 00:38:02,210
+ثالث اكيد العمل الاول حكيم زى يعنى ايوة حساب
+
+375
+00:38:02,210 --> 00:38:05,450
+مثلثات يا بنت الفكرة الموضوع حساب مثلثة اه الحين
+
+376
+00:38:05,450 --> 00:38:09,970
+قطعين اتنين فيه دلوقتي واحد ناقص اتنين واحد ناقص
+
+377
+00:38:09,970 --> 00:38:16,850
+تايتر بقىماشي موافق واحد ناقص sin تربية T يعني
+
+378
+00:38:16,850 --> 00:38:22,570
+باختصار sin تربية T يسوى نص في واحد ناقص cosine
+
+379
+00:38:22,570 --> 00:38:28,430
+اتنين T صح؟ وبالتالي ممكن اجيب خلق الخمسة في
+
+380
+00:38:28,430 --> 00:38:33,350
+الموضوع و ال cosine صارت موجودةيبقى بداجة للمطلوب
+
+381
+00:38:33,350 --> 00:38:40,710
+الثاني لو جيت قلت sin تربيع ال T يساوي النص في
+
+382
+00:38:40,710 --> 00:38:46,830
+واحد ناقص cosine اتنين T يبقى cosine اتنين T ظهرت
+
+383
+00:38:46,830 --> 00:38:51,530
+في العلاقة اللي عندها ذاك اللي مظهرت شمين الخامسة
+
+384
+00:38:51,530 --> 00:38:55,770
+طيب بدنا نخلق الخمسة في هذه العلاقة بقولك بسيطة
+
+385
+00:38:55,770 --> 00:39:05,190
+جداهذه عبارة عن نص ناقص نص cosine اتنين T طب النص
+
+386
+00:39:05,190 --> 00:39:11,130
+هذه مش عبارة عن خمسة على عشرة يعني خلجت الخمسة في
+
+387
+00:39:11,130 --> 00:39:19,930
+الموضوع يعني بقدر اقول هذه تساوي عشر في خمسة ناقص
+
+388
+00:39:19,930 --> 00:39:27,400
+نص cosine اتنين Tمظبوط؟ طب إيش رأيك أعملها معادلة
+
+389
+00:39:27,400 --> 00:39:35,700
+صفرية؟ يبقاش بصير عندي I sine تربية T زائد نص
+
+390
+00:39:35,700 --> 00:39:43,000
+كوسين اتنين T ناقص عشر في خمسة يساوي زرع
+
+391
+00:39:47,350 --> 00:39:54,890
+لحظة هي دالة وهي التانية وهي التالتة constant في
+
+392
+00:39:54,890 --> 00:39:58,950
+الأولى اللى هو واحد صحية constant في التانية
+
+393
+00:39:58,950 --> 00:40:03,170
+constant في التالتة اللى هو السالب عشور ساوة zero
+
+394
+00:40:03,720 --> 00:40:09,540
+الثابت هدول التلاتة ولا واحد فيهم zero يبقى معناه
+
+395
+00:40:09,540 --> 00:40:14,400
+هدول ان التلاتة دول linearly إذا الورس كنت باعهم ب
+
+396
+00:40:14,400 --> 00:40:19,570
+zeroصحيح ولا لأ؟ بدون ما نحسب الroneskin أبدا،
+
+397
+00:40:19,570 --> 00:40:29,590
+يبقى هذا معناه إن ال sign تربية T و cosine إتنين T
+
+398
+00:40:29,590 --> 00:40:38,170
+and الخمسة are linearly dependentلأنه التلاتة
+
+399
+00:40:38,170 --> 00:40:42,110
+ضربناهم في cononsense و ال cononsense هدول طوله
+
+400
+00:40:42,110 --> 00:40:44,410
+اللي هيوز سوى zero يبجى هدول ماله linearly
+
+401
+00:40:44,410 --> 00:40:48,430
+dependent مادام linearly dependent ايه ده نيرو
+
+402
+00:40:48,430 --> 00:40:54,110
+نيسكين تبعهم بقداش؟ ب zero يبجى هذا بده يعطيني ال
+
+403
+00:40:54,110 --> 00:41:01,210
+نيرو نيسكين تبع الخمسةوSin تربيه T وCos تربيه T
+
+404
+00:41:01,210 --> 00:41:06,130
+تربيه T تربيه T تربيه T تربيه T تربيه T تربيه T
+
+405
+00:41:06,130 --> 00:41:06,190
+تربيه T تربيه T تربيه T تربيه T تربيه T تربيه T
+
+406
+00:41:06,190 --> 00:41:07,190
+تربيه T تربيه T تربيه T تربيه T تربيه T تربيه T
+
+407
+00:41:07,190 --> 00:41:11,610
+تربيه T تربيه T تربيه T تربيه T تربيه T تربيه T
+
+408
+00:41:11,610 --> 00:41:16,950
+تربيه T تربيه T تربيه T تربيه
+
+409
+00:41:16,950 --> 00:41:24,350
+T تربيه T تربيه T تربيه T تربيه T تربيه T تربيه T
+
+410
+00:41:24,350 --> 00:41:30,500
+تربيه T تربيكمان مثال مثال أربعة اللي هو سؤال
+
+411
+00:41:30,500 --> 00:41:39,740
+أربعة و عشرين من الكتاب بيقول use able's formula
+
+412
+00:41:39,740 --> 00:41:42,840
+able
+
+413
+00:41:42,840 --> 00:41:50,440
+to find the wrong skin to find the wrong skin
+
+414
+00:41:54,120 --> 00:42:02,120
+of a fundamental
+
+415
+00:42:02,120 --> 00:42:08,880
+set of
+
+416
+00:42:08,880 --> 00:42:16,240
+solutions of
+
+417
+00:42:16,240 --> 00:42:22,480
+the differential equation
+
+418
+00:42:24,230 --> 00:42:33,750
+تربيع y to the derivative 4 زائد ty triple prime
+
+419
+00:42:33,750 --> 00:42:41,830
+زائد y double prime ناقص 4y تساوي 0
+
+420
+00:42:54,140 --> 00:42:58,200
+سؤال مرة ثانية طبعا كتبنا ايه بال formula قبل قليل
+
+421
+00:42:58,200 --> 00:43:02,760
+في الجزء النظري؟ مظبوط في اخر الجزء النظري قال
+
+422
+00:43:02,760 --> 00:43:06,460
+يستخدم الصيغة اللي عندك كده مشان تجيب ال runescan
+
+423
+00:43:06,460 --> 00:43:09,400
+تبع ال fundamental set of solutions لماين؟
+
+424
+00:43:09,400 --> 00:43:14,550
+للمعادلة اللي عندنا؟ هل طلب مني إيجاد الحلول؟لو
+
+425
+00:43:14,550 --> 00:43:17,930
+طلبش جامعه لكن بقدر ايجي برونسكين تبع الحلول بدون
+
+426
+00:43:17,930 --> 00:43:23,190
+معرف ما هو شكل الحلول بواسطة able theorem يبقى
+
+427
+00:43:23,190 --> 00:43:28,370
+باجي بقوله لما كتبنا ال able لازم يكون المعامل تبع
+
+428
+00:43:28,370 --> 00:43:33,220
+وليو سبعة بجداشيبقى بده أجسب لمعادلة كلها علامين
+
+429
+00:43:33,220 --> 00:43:38,720
+على T تربية يبقى المعادلة بيصير على الشكل التالي
+
+430
+00:43:38,720 --> 00:43:46,560
+زائد واحد على T في Y triple prime زائد اللي هو
+
+431
+00:43:46,560 --> 00:43:52,380
+واحد على T تربية في ال Y double primeنقص اربعة
+
+432
+00:43:52,380 --> 00:43:58,240
+التي تربية في ال Y بده يساوي من Zero يبقى الرمز
+
+433
+00:43:58,240 --> 00:44:03,720
+كان اللي بدهيه as a function of T وعبارة عن
+
+434
+00:44:03,720 --> 00:44:12,190
+كونستانسي في اسناقس تكامل P1 of T دي Tمش كتبناها
+
+435
+00:44:12,190 --> 00:44:19,210
+قبل قليل؟ طيب تمام يبقى هذا الكلام بدي ساوي C في E
+
+436
+00:44:19,210 --> 00:44:27,860
+وصناعة استكامل P1 اللي هو واحد على T دي Tماعطانيش
+
+437
+00:44:27,860 --> 00:44:32,780
+شروط على T لكن لو اعطاني اكبر من ال zero ولا اقل
+
+438
+00:44:32,780 --> 00:44:38,080
+من ال zero كانت خلاصنا من من من ال absolute value
+
+439
+00:44:38,080 --> 00:44:46,240
+يبقى E أس ناقص لن absolute value لمين التي يبقى C
+
+440
+00:44:46,240 --> 00:44:53,290
+E أس لن absolute value ل T أس قداشوالسالب واحد
+
+441
+00:44:53,290 --> 00:45:00,910
+يبقى هذا C على absolute value لمين التي هذا شكل
+
+442
+00:45:00,910 --> 00:45:06,530
+الرونسكين اللي طلبه بدون معرفة من شكل الحلول اللي
+
+443
+00:45:06,530 --> 00:45:11,870
+عندي لمين لهذه المعادلة طيب الان انتهى ال section
+
+444
+00:45:11,870 --> 00:45:16,680
+الأول زى ما تشوفين section بسيطبدنا ال exercises
+
+445
+00:45:16,680 --> 00:45:26,820
+تبعات section 4-1 اللي هي من ال 1 ل 16 ال even و
+
+446
+00:45:26,820 --> 00:45:32,320
+من 21 لغاية كداش لغاية 24
+
+447
+00:45:44,770 --> 00:45:45,470
+مش عارف
+
+448
+00:46:03,420 --> 00:46:10,780
+بتقدر تحليها انت هذهك بالشكل هذا؟ لسه لم نتكلم في
+
+449
+00:46:10,780 --> 00:46:15,120
+الحل الحل ابتدا من section 4.2 لنهاية ال chapter
+
+450
+00:46:15,120 --> 00:46:19,700
+كيف هنحل المعادلة في أوضاعها المختلفة مش هطول عليك
+
+451
+00:46:19,700 --> 00:46:24,400
+هدخل فيها دوري الهيل مباشرة ان شاء الله يبقى بنجي
+
+452
+00:46:24,400 --> 00:46:30,280
+ل section 4.2 اللي هو ال homogeneous
+
+453
+00:46:35,080 --> 00:46:45,180
+المقارنة مع مقارنة مستمردة مع مقارنة
+
+454
+00:46:45,180 --> 00:46:57,400
+مستمردة اعتنوا
+
+455
+00:47:04,560 --> 00:47:11,020
+Order Linear Homogeneous
+
+456
+00:47:11,020 --> 00:47:20,680
+Differential Equation لعل الشكل a0 y to the
+
+457
+00:47:20,680 --> 00:47:26,640
+derivative nزائد a1 y to the derivative of n minus
+
+458
+00:47:26,640 --> 00:47:32,520
+one زائد a2 y to the derivative of n minus two
+
+459
+00:47:32,520 --> 00:47:42,080
+زائد a n minus واحد y prime زائد a n y بده يساوي
+
+460
+00:47:42,080 --> 00:47:49,820
+zero وسميلي هذه المعادلة رقم واحد where
+
+461
+00:47:49,820 --> 00:48:04,470
+حيثالـ A0 والـ A1 والـ A2 والـ ANR real constants
+
+462
+00:48:04,470 --> 00:48:14,130
+ثوابت حقيقية الآن بدنا نحلها يبقى بدنا نجاوبها
+
+463
+00:48:14,130 --> 00:48:18,800
+سواء الأخت قبل قليل اللي قالت كيف بدنا نحلهابنقول
+
+464
+00:48:18,800 --> 00:48:23,380
+الحل كالتالية لحظة المعادلة هذه المعاملات ثوابت
+
+465
+00:48:23,380 --> 00:48:28,260
+لسه ما اتكلمناش المعادلة لو كان المعاملات متغيرات
+
+466
+00:48:28,260 --> 00:48:37,940
+يبقى بداجي اقوله let Y تساوي E أس RT be a solution
+
+467
+00:48:37,940 --> 00:48:47,420
+of the differential equation one then they
+
+468
+00:48:50,920 --> 00:48:58,640
+كاركترستيك اكويشن از ال a نود r to the power n
+
+469
+00:48:58,640 --> 00:49:00,380
+زائد a1
+
+470
+00:49:05,330 --> 00:49:13,150
+R⁻¹ R⁻¹ R⁻¹ R⁻¹ R⁻¹
+
+471
+00:49:13,150 --> 00:49:17,490
+R⁻¹ R⁻¹
+
+472
+00:49:17,490 --> 00:49:21,690
+R⁻¹
+
+473
+00:49:42,410 --> 00:49:49,370
+أول ما بدأنا هذا الشبتر هو تعميم لشبتر ثلاثة يبقى
+
+474
+00:49:49,370 --> 00:49:55,230
+هنا نعمم نفس المعلومات في شبتر ثلاثة كان عندي y
+
+475
+00:49:55,230 --> 00:50:00,010
+double prime زاد p of t في ال y prime زاد q of t
+
+476
+00:50:00,010 --> 00:50:05,250
+في ال y بدي ساويزيوم تلت ترماتهذا الحمد لله ترمت
+
+477
+00:50:05,250 --> 00:50:09,770
+كثيرا عشرة خمسة عشر عشرين جد ما يكونوا يبقى أنا
+
+478
+00:50:09,770 --> 00:50:13,770
+عندي معادلة بالشكل لأن هذا معادلة homogeneous
+
+479
+00:50:13,770 --> 00:50:18,930
+linear differential equation with constant
+
+480
+00:50:18,930 --> 00:50:26,370
+coefficients المعاملات هذول كلهم ثابتبتفرض Y تساوي
+
+481
+00:50:26,370 --> 00:50:32,690
+U RT كما كان في حالة ثانوية order بيه solution of
+
+482
+00:50:32,690 --> 00:50:35,210
+the differential equation one then the
+
+483
+00:50:35,210 --> 00:50:40,330
+characteristic equation على الشكل أن a not RN زائد
+
+484
+00:50:40,330 --> 00:50:46,990
+a1RN-1 زائد a2RN زائد زائد aN-1R زائد aN يساوي
+
+485
+00:50:46,990 --> 00:50:53,580
+zeroانتقلنا من معادلة تفاضلية إلى معادلة عادية
+
+486
+00:50:53,580 --> 00:50:58,800
+معادلة تفاضلية من الرتبة النونية إلى معادلة عادية
+
+487
+00:50:58,800 --> 00:51:04,440
+من الدرجة النونية وليست معادلة تفاضلية الآن هذه
+
+488
+00:51:04,440 --> 00:51:12,960
+المعادلة كم جذر لها يا بنات؟ كدوش يعني؟ معادلة من
+
+489
+00:51:12,960 --> 00:51:18,210
+الدرجة التانية كم جذر لها؟ من الدرجة التالتةالجذور
+
+490
+00:51:18,210 --> 00:51:23,810
+والرابع مضاجة نونية ان من الجذور يبقى هذه المعادلة
+
+491
+00:51:23,810 --> 00:51:29,650
+انها ان من الجذور تعالى قبل ما نكتب ولا كلمة نتكلم
+
+492
+00:51:29,650 --> 00:51:33,690
+كلام شافه وبعد هيك بنروح نكتب لو روحت حسبت هذه
+
+493
+00:51:33,690 --> 00:51:38,170
+الجذور يمكن يطلع كلهم جذور حقيقية أولى واحد زي
+
+494
+00:51:38,170 --> 00:51:48,060
+التاني صح؟ممكن يطلعوا جذور كلهم تخيلية وولا واحد
+
+495
+00:51:48,060 --> 00:51:57,340
+زي التاني صح؟ ممكن يطلعوا جذور مكررة وكلهم حقيقية
+
+496
+00:51:57,340 --> 00:52:05,480
+يمكن يطلعوا شوية حقيقية وشوية complex تمام؟ وإذا
+
+497
+00:52:05,480 --> 00:52:09,600
+كانوا complex بيكونوا complex conjugateطب انا
+
+498
+00:52:09,600 --> 00:52:13,980
+هتقولي معقول؟ بقولها اه معقول كيف؟ بقولها افترض ان
+
+499
+00:52:13,980 --> 00:52:20,020
+المعادلة دي كانت من الدرجة الخامسة طلعوا تلت جذور
+
+500
+00:52:20,020 --> 00:52:26,840
+حقيقية اتنين اش بطلعوا؟ تخيلين و مترافقين لان ال
+
+501
+00:52:26,840 --> 00:52:31,460
+complex دايما بطلع الجدر و المرافق له يعني لا يمكن
+
+502
+00:52:31,460 --> 00:52:38,030
+ان يكون في المعادلة تلت جذور complexصح؟ ولا
+
+503
+00:52:38,030 --> 00:52:41,370
+معادلة، سواء كان من الرتبة الزوجية أو من الرتبة
+
+504
+00:52:41,370 --> 00:52:45,870
+الفردية، سيان، مافيش تلاتة complex، فيه اتنين، صح؟
+
+505
+00:52:45,870 --> 00:52:49,730
+فيه اربعة ماشي، فيه ستة ماشي، فيه تمانية ماشية،
+
+506
+00:52:49,730 --> 00:52:54,610
+ممكن يكون ال complex repeated وممكن مايكونوش
+
+507
+00:52:54,610 --> 00:52:59,190
+repeated كمان، يبقى هذا كل ما يتعلق بالمعادلة اللي
+
+508
+00:52:59,190 --> 00:53:05,490
+عندنا هذه، تمام؟إذا هنختصر هذه في ثلاث حالات،
+
+509
+00:53:05,490 --> 00:53:11,150
+الجذور حقيقية ومختلفة، الجذور complex، وبعد ذلك
+
+510
+00:53:11,150 --> 00:53:17,810
+الجذور مكررة وسنفصلها إلى حقيقية مكررة أو تخيلية
+
+511
+00:53:17,810 --> 00:53:24,030
+ومكررةونشوف كيف تفجر صيغة الحل في كل حالة من
+
+512
+00:53:24,030 --> 00:53:28,530
+الحياة تلاني يعني إحنا قاعدين بنعمم ال second
+
+513
+00:53:28,530 --> 00:53:33,350
+order linear homogeneous differential equation مش
+
+514
+00:53:33,350 --> 00:53:36,810
+بنكتشف شغلات جديدة، لأ إحنا قاعدين بنعمم تعميم ليس
+
+515
+00:53:36,810 --> 00:53:45,370
+إلا يبقى باجي بقول هذه المعادلة اتنين this this
+
+516
+00:53:46,400 --> 00:53:54,640
+Equation has N roots هذي لها N من الجذور بدأ أخد
+
+517
+00:53:54,640 --> 00:54:02,120
+الحالة الأولى The roots are
+
+518
+00:54:02,120 --> 00:54:07,600
+real and
+
+519
+00:54:07,600 --> 00:54:10,660
+different
+
+520
+00:54:10,660 --> 00:54:26,420
+غير متساويتمام فهاجي بقول if the roots of equation
+
+521
+00:54:26,420 --> 00:54:41,080
+الاتنين are real and no two are
+
+522
+00:54:41,080 --> 00:54:42,860
+equal
+
+523
+00:54:47,340 --> 00:54:59,420
+أي أن R1 لا يمكن أن يسوى R2 لا يمكن أن يسوى R3 لا
+
+524
+00:54:59,420 --> 00:55:04,220
+يمكن أن يسوى RN ثم
+
+525
+00:55:29,680 --> 00:55:36,980
+يجب ان نقوم باستخدام الاسئلة
+
+526
+00:55:36,980 --> 00:55:38,760
+الواتس او الاسئلة الواتس او الاسئلة الواتس او
+
+527
+00:55:38,760 --> 00:55:38,880
+الاسئلة الواتس او الاسئلة الواتس او الاسئلة الواتس
+
+528
+00:55:38,880 --> 00:55:38,940
+او الاسئلة الواتس او الاسئلة الواتس او الاسئلة
+
+529
+00:55:38,940 --> 00:55:42,240
+الواتس او الاسئلة الواتسيبقى هذا الشكل الحل في هذه
+
+530
+00:55:42,240 --> 00:55:47,320
+الحالة كنا في حالة ال second order نقول C1EOSR1T
+
+531
+00:55:47,320 --> 00:55:55,020
+C2EOSR2T ونوقف N يبقى بدنا نوصل لمين لل N بدنا
+
+532
+00:55:55,020 --> 00:56:07,220
+نيجي للحالة الثانية the roots are
+
+533
+00:56:07,220 --> 00:56:18,100
+complex conjugateare complex conjugate يبقى
+
+534
+00:56:18,100 --> 00:56:30,300
+الجذور تخيّلية ومترافقة if the roots of
+
+535
+00:56:30,300 --> 00:56:36,300
+equation 2 are
+
+536
+00:56:38,810 --> 00:56:45,910
+complex conjugate تحيولية
+
+537
+00:56:45,910 --> 00:56:52,310
+مترافقة then these
+
+538
+00:56:52,310 --> 00:57:07,050
+roots هذه الجذور are in the form الشكل التاليlanda
+
+539
+00:57:07,050 --> 00:57:15,190
+one زائد او ناقص imu one وlanda
+
+540
+00:57:15,190 --> 00:57:23,410
+two زائد او ناقص imu two ونظل ماشين لعيط ما نوصل ل
+
+541
+00:57:23,410 --> 00:57:33,470
+landa s زائد او ناقص imu s يبقى
+
+542
+00:57:33,470 --> 00:57:38,820
+theوالخيار الأساسي
+
+543
+00:57:38,820 --> 00:57:44,160
+للإدارة
+
+544
+00:57:44,160 --> 00:57:48,440
+1S
+
+545
+00:57:48,440 --> 00:57:50,540
+Y
+
+546
+00:57:53,030 --> 00:58:10,310
+A أُس لاندا وان T في A1 Cos Mu 1T زائد B1 Sin Mu
+
+547
+00:58:10,310 --> 00:58:21,850
+1T زائد A أُس لاندا 2T في A2
+
+548
+00:58:27,300 --> 00:58:34,560
+بتو صين ميو تي تي زائد زائد
+
+549
+00:58:58,020 --> 00:59:03,680
+الحالة التالتة والاخيرة The Roots
+
+550
+00:59:06,650 --> 00:59:16,650
+are repeated لو كانت الجذور مكررة بدي أقسمها إلى
+
+551
+00:59:16,650 --> 00:59:33,310
+جزئين نمر A if the roots of equation 2 are real
+
+552
+00:59:33,310 --> 00:59:34,930
+repeated
+
+553
+00:59:36,960 --> 00:59:49,640
+لو كانت حقيقية و مكررة that is IN R1 يسوى R2 يسوى
+
+554
+00:59:49,640 --> 01:00:05,740
+RN يسوى RC مثلا then the general solution
+
+555
+01:00:09,110 --> 01:00:19,510
+والسؤال الواضح هو Y
+
+556
+01:00:19,510 --> 01:00:34,770
+تساوي C1 زائد C2T C3T تربيع زائد CN T أس N ناقص
+
+557
+01:00:34,770 --> 01:00:46,850
+واحدكله في E أس RT نمر
+
+558
+01:00:46,850 --> 01:00:51,290
+بي if
+
+559
+01:00:51,290 --> 01:00:57,970
+the roots of
+
+560
+01:00:57,970 --> 01:01:03,910
+equation 2 are
+
+561
+01:01:09,680 --> 01:01:23,520
+repeated complex conjugate repeated
+
+562
+01:01:23,520 --> 01:01:33,920
+complex conjugate then the general solution
+
+563
+01:01:41,460 --> 01:01:48,200
+Y تساوي C1
+
+564
+01:01:48,200 --> 01:01:57,260
+C2 T زائد زائد CS
+
+565
+01:01:57,260 --> 01:02:02,980
+T أُس S ناقص واحد
+
+566
+01:02:05,390 --> 01:02:17,810
+فى E أُس لامدة T كوسين ميو T زائد بي واحد بيتنين T
+
+567
+01:02:17,810 --> 01:02:29,970
+بي S تي أُس S ناقص واحد كله في sign والله فى E أُس
+
+568
+01:02:29,970 --> 01:02:40,400
+لامدة T فى Eحُس لندتي فى صين لميوتى
+
+569
+01:03:25,170 --> 01:03:27,170
+ماذا بحق الجحيم
+
+570
+01:04:11,950 --> 01:04:15,570
+نرجع لكلام اللي احنا كاتبينه على بنات من أول و
+
+571
+01:04:15,570 --> 01:04:20,300
+جديديبقى سيكشن أربعة اتنين بتتكلم فقط عن ال
+
+572
+01:04:20,300 --> 01:04:25,240
+homogenous linear differential equations تمام
+
+573
+01:04:25,240 --> 01:04:28,640
+بيقول يعتبر ال nth order linear differential
+
+574
+01:04:28,640 --> 01:04:32,580
+equation اللي عندنا هذه بالمعاملات الثابتة هذه
+
+575
+01:04:32,580 --> 01:04:37,440
+بدنا نيجي نحلها زي ما كنا بنعمل في شبتر تلاتة
+
+576
+01:04:37,440 --> 01:04:42,780
+بنفترض ان هو يسوي EOSRT عبارة عن solution اشتق مرة
+
+577
+01:04:42,780 --> 01:04:47,410
+و اتنين و تلاتة و اين من المراتوبنرجع بنعود في
+
+578
+01:04:47,410 --> 01:04:52,470
+المعادلة التفاضلية وبعدين بنقسم على EOSRT بنحسب
+
+579
+01:04:52,470 --> 01:04:57,270
+نحصل على مين؟ على المعادلة لأن من الدرجة النونية
+
+580
+01:04:57,270 --> 01:05:03,050
+بدل ما كانت معادلة تفاضلية من الرتبة النونية صارت
+
+581
+01:05:03,050 --> 01:05:07,710
+معادلة عادية من الدرجة النونية بدنا نيجي نحل
+
+582
+01:05:07,710 --> 01:05:13,660
+المعادلة هذه، هذه المعادلة لها N من الجذورلما يكون
+
+583
+01:05:13,660 --> 01:05:18,180
+لها ان من الجذور، فهناك احتمالات تعدى لهذه الجذور،
+
+584
+01:05:18,180 --> 01:05:23,480
+الاحتمال الاول ان الجذور تبقى حقيقية وغير متساوية،
+
+585
+01:05:23,480 --> 01:05:27,760
+real and different، ولا واحد فيهم زي التاني،
+
+586
+01:05:27,760 --> 01:05:31,560
+مختلفات عن بعض تماما، يبقى if the roots of a
+
+587
+01:05:31,560 --> 01:05:35,920
+question are real and not two are equal، مافيش يوم
+
+588
+01:05:35,920 --> 01:05:41,410
+اتنين بيسووا بعضالرقم 1 لا يمكن يسوى رقم 2 ولا
+
+589
+01:05:41,410 --> 01:05:48,230
+يمكن يسوى رقم 3ن حدث ذلك يبقى ال general solution
+
+590
+01:05:48,230 --> 01:05:53,410
+للمعادلة رقم واحد بدي يكون على الشكل التالي Y تسوى
+
+591
+01:05:53,410 --> 01:06:01,890
+C1 في E أُس R1T زائد C2 في E أُس R2T زائد زائد وCN
+
+592
+01:06:01,890 --> 01:06:08,030
+E أُس RNT بالشكل اللي عندنا هذا الحالة الأولى لو
+
+593
+01:06:08,030 --> 01:06:12,860
+كان ال real and different unequal الحالة الثانيةلو
+
+594
+01:06:12,860 --> 01:06:16,640
+كان الجذور هذه complex و إذا كانوا complex كل
+
+595
+01:06:16,640 --> 01:06:24,300
+اتنين يكونوا معاهممترافقين يبقى باجي بقول الشكل ال
+
+596
+01:06:24,300 --> 01:06:29,020
+roots هذه بدأ تبقى على الشكل التالي لاندا زائد او
+
+597
+01:06:29,020 --> 01:06:34,500
+ناقص imu1 يبقى هي الترافق ممكن يكون لاندا 2 زائد
+
+598
+01:06:34,500 --> 01:06:39,480
+imu2 الترافق ما بين الاتنين انضل مشيل لغاية لاندا
+
+599
+01:06:39,480 --> 01:06:47,520
+S زائد او ناقص imuS طبعاربما يتبضر الى ذهنك السؤال
+
+600
+01:06:47,520 --> 01:06:53,220
+التالي او الى البعض منكم ليش ماهياش lambda n زيد
+
+601
+01:06:53,220 --> 01:07:01,420
+او ناقص imun مظبوط صح ولا لأ مش هالت سؤال بقولكوا
+
+602
+01:07:01,420 --> 01:07:06,420
+ياسه هذول اتنين مترافقين انا عندي درجة نونيةمظبوط
+
+603
+01:07:06,420 --> 01:07:11,640
+إذا اتنين مترافقين بدي يكونوا النصيك و النصيك يعني
+
+604
+01:07:11,640 --> 01:07:16,100
+لو كان عشرة بديهم يطلعوا خمسة و الخمسة مرافقتهم
+
+605
+01:07:16,100 --> 01:07:23,020
+يبقى S تبقى N على 2 صحيح ولا لأ؟ تبقى N على 2 يمكن
+
+606
+01:07:23,020 --> 01:07:28,280
+شوية فيهم حقيقي و شوية فيهم complex يبقى الحقيقي
+
+607
+01:07:28,280 --> 01:07:32,600
+بدي أعملهم زي الحقيقي و ال complex بطلوا يصيروا
+
+608
+01:07:32,600 --> 01:07:38,630
+عشرة يمكن يطلعوا ستةيمكن يطلع أربع مظبوط بقدرش
+
+609
+01:07:38,630 --> 01:07:43,650
+اقول ان على اتنات من هنا روحنا جولنا يبقى land s و
+
+610
+01:07:43,650 --> 01:07:48,830
+I and me و S جد ما يطلع يطلع تمام طب ان حد ذلك ما
+
+611
+01:07:48,830 --> 01:07:54,310
+هو شكل ال general solution بقوله كل واحد فيهم بدي
+
+612
+01:07:54,310 --> 01:07:58,430
+يكون على الشكل هذه يبقى ايه اصل يعني هذا كان شكل
+
+613
+01:07:58,430 --> 01:08:03,440
+مين؟لو كانت من ال second order مش كنا نقول E وصل
+
+614
+01:08:03,440 --> 01:08:09,220
+لاندا C1 Cos Mu T زائد C2 Sin Mu T بس احنا عندنا
+
+615
+01:08:09,220 --> 01:08:13,820
+ميوهات عددهم S وفي عندنا لاندات عددهم S يبقى فبروح
+
+616
+01:08:13,820 --> 01:08:22,000
+بقولوا E وصل لاندا 1T A1 Cos Mu 1T زائد B1 Sin Mu
+
+617
+01:08:22,000 --> 01:08:28,340
+1Tاللي بعده E أس لاندا تو T في E أس لاندا تو E أس
+
+618
+01:08:28,340 --> 01:08:28,860
+لاندا تو E أس لاندا تو E أس لاندا تو E أس لاندا تو
+
+619
+01:08:28,860 --> 01:08:32,720
+E أس لاندا تو E أس لاندا تو E أس لاندا تو E أس
+
+620
+01:08:32,720 --> 01:08:37,220
+لاندا تو E أس لاندا تو E أس لاندا تو E أس لاندا تو
+
+621
+01:08:37,220 --> 01:08:37,900
+E أس لاندا تو E أس لاندا تو E أس لاندا تو E أس
+
+622
+01:08:37,900 --> 01:08:38,140
+E أس لاندا تو E أس لاندا تو E أس لاندا تو E أس
+
+623
+01:08:38,140 --> 01:08:45,360
+لاندا تو E أس لاندا تو E أس لاندا تو E أس لاندا تو
+
+624
+01:08:45,360 --> 01:08:48,300
+E أاولا اتنين اثنين اثنين اثنين اثنين اثنين اثنين
+
+625
+01:08:48,300 --> 01:08:49,320
+اثنين اثنين اثنين اثنين اثنين اثنين اثنين اثنين
+
+626
+01:08:49,320 --> 01:08:53,740
+اثنين اثنين اثنين اثنين اثنين اثنين اثنين اثنين
+
+627
+01:08:53,740 --> 01:08:55,660
+اثنين اثنين اثنين اثنين اثنين اثنين اثنين اثنين
+
+628
+01:08:55,660 --> 01:08:56,480
+اثنين اثنين اثنين اثنين اثنين اثنين اثنين اثنين
+
+629
+01:08:56,480 --> 01:09:00,080
+اثنين اثنين اثنين اثنين اثنين اثنين اثنين اثنين
+
+630
+01:09:00,080 --> 01:09:04,140
+اثنين اثنين اثنين اثنين اثنين اثنين اثنين اثنين ا
+
+631
+01:09:04,180 --> 01:09:09,120
+ما كتبناش N على 2 N على 2 لو كانوا كلهم complex
+
+632
+01:09:09,120 --> 01:09:12,960
+لكن ممكن يطلع بعضهم ريالوا بعضهم complex يبقى
+
+633
+01:09:12,960 --> 01:09:17,140
+فباجي بقول ال complex بكتبهم الشكل اللي عندنا هذا
+
+634
+01:09:17,140 --> 01:09:22,640
+يبقى هذا لو كان كله complex طيب لو كانوا كلهم
+
+635
+01:09:22,640 --> 01:09:29,120
+repeated مكررينفي احتمال ان يكون الـ real و
+
+636
+01:09:29,120 --> 01:09:32,220
+repeated و في احتمال يكون complex و repeated
+
+637
+01:09:32,220 --> 01:09:35,540
+مظبوطة او لا؟ يبقى شو بينا نعمل شو بيكون الشكل
+
+638
+01:09:35,540 --> 01:09:39,080
+الحالي في هذه الحالة بقول ما ياتي if the roots of
+
+639
+01:09:39,080 --> 01:09:42,820
+equations in R are really repeated يعني راحة بدي
+
+640
+01:09:42,820 --> 01:09:47,620
+سوى R اتنين بدي سوى بدي سوى RN اختصارا بدي اسميها
+
+641
+01:09:47,620 --> 01:09:53,900
+R مثل Rc يعني مثلاتمام؟ يبقى شكل ال general
+
+642
+01:09:53,900 --> 01:09:57,940
+solution بيكون على الشكل التالي في حالة ال second
+
+643
+01:09:57,940 --> 01:10:02,900
+order بيجي نقول C1 زي C2 في T كله في ال
+
+644
+01:10:02,900 --> 01:10:09,140
+exponential هنا أحنا بدنا نعممها صار C1 زي C2T زي
+
+645
+01:10:09,140 --> 01:10:17,130
+C3T تربيع زي زي CNT أس N ناقص واحدأخر T بتكون أقل
+
+646
+01:10:17,130 --> 01:10:20,490
+بقداش لإن في ال second و اذا كان كروص ازايد
+
+647
+01:10:20,490 --> 01:10:25,150
+كروستان في T و احنا عندنا second اتنين فبتبقى T
+
+648
+01:10:25,150 --> 01:10:29,750
+اقص واحد اقل من القرص تبع المعادلة بقداش بواحد
+
+649
+01:10:29,750 --> 01:10:35,630
+يبقى صارت المعادلة دي في مين في E Os RT على اللي
+
+650
+01:10:35,630 --> 01:10:39,510
+طلعت عندنا هذه تمام يبقى هذا الشكل ال general
+
+651
+01:10:39,510 --> 01:10:43,770
+solution لو كانوا really repeatedطب لو كانوا
+
+652
+01:10:43,770 --> 01:10:48,530
+complex و repeated يبقى سمنها النقطة رقم B يبقى
+
+653
+01:10:48,530 --> 01:10:52,010
+اذا روح سباقية كونجة R repeated complex conjugate
+
+654
+01:10:52,010 --> 01:10:58,050
+ترافق و مكرر ما هم نصين صاروا الجذور نص و نص
+
+655
+01:10:58,050 --> 01:11:02,570
+المرافق يبقى هدول اللي مشاكله هدول اللي لهمالشكل
+
+656
+01:11:02,570 --> 01:11:06,190
+اللي بيبقى الشكل ال general solution بيكون c1 زاد
+
+657
+01:11:06,190 --> 01:11:13,470
+c2t زاد زاد c st أس s minus ال one فاللي a أس
+
+658
+01:11:13,470 --> 01:11:19,610
+لاندا t cos ميو t وهذا التكرار هيه مضروف a أس
+
+659
+01:11:19,610 --> 01:11:26,260
+لاندا في ال cosineب1 ب2t زائد زائد بست to the
+
+660
+01:11:26,260 --> 01:11:30,980
+power of s minus one في أصلة نتيفة sign immunity
+
+661
+01:11:30,980 --> 01:11:36,900
+يبقى هذا complex conjugate ومكرر طبعا هذا الشكل
+
+662
+01:11:36,900 --> 01:11:42,180
+قليل الحدوث اللي لم يكن نادرا في كتابنا في مسائل
+
+663
+01:11:42,180 --> 01:11:47,320
+كتاب تبعتنا لكن البجيات بتكرر واش كتيرحد في كل اي
+
+664
+01:11:47,320 --> 01:11:51,000
+تساؤل هنا قبل ان ندخل الامثلة، هذا كل جزء النظرية
+
+665
+01:11:51,000 --> 01:11:54,760
+تبع الـ Section، قال له قدام، قال له حد بتسأل اي
+
+666
+01:11:54,760 --> 01:11:59,120
+سؤال هنا، ناخد امثلة طوبيحية على الحالات اللي
+
+667
+01:11:59,120 --> 01:12:05,800
+عندنا هنا، اه، في اي تساؤل؟ طيب، نيجي للامثلة
+
+668
+01:12:43,020 --> 01:12:44,860
+تبقى مثال
+
+669
+01:12:51,550 --> 01:12:55,770
+أول مثال بيقول
+
+670
+01:12:55,770 --> 01:13:00,210
+ي determine the
+
+671
+01:13:00,210 --> 01:13:04,070
+general
+
+672
+01:13:04,070 --> 01:13:07,650
+solution
+
+673
+01:13:07,650 --> 01:13:12,550
+of
+
+674
+01:13:12,550 --> 01:13:16,170
+the following
+
+675
+01:13:21,590 --> 01:13:28,010
+differential equations نمره
+
+676
+01:13:28,010 --> 01:13:31,530
+A الوثائق
+
+677
+01:13:31,530 --> 01:13:38,710
+الاتناشر من الكتاب بيقول مشتقة التالتة لو I ناقص
+
+678
+01:13:38,710 --> 01:13:47,170
+تلاتة المشتقة الثانيةزائد ثلاثة y prime ناقص y
+
+679
+01:13:47,170 --> 01:14:04,070
+تساوي zero هذه المعادلة رقم واحد التكتيك
+
+680
+01:14:04,070 --> 01:14:08,050
+اللي اتبعناه في ال second order اللي اتبعه هناأو
+
+681
+01:14:08,050 --> 01:14:11,990
+اللى شرحناته فى الجزء النظري بدنا نعيده فى كل سؤال
+
+682
+01:14:11,990 --> 01:14:18,870
+من هذه المثال فبجى بقوله let Y تساوي E أُس RT بيه
+
+683
+01:14:18,870 --> 01:14:29,850
+solution of the differential equation 2The
+
+684
+01:14:29,850 --> 01:14:41,050
+characteristic equation is R تكيب ناقص ثلاثة R
+
+685
+01:14:41,050 --> 01:14:50,350
+تربيع زائد تلاتة R ناقص واحد بده يساوي زينة لما
+
+686
+01:14:50,350 --> 01:14:54,990
+كانت المعادلة من الدرجة الثانية قصتنا سهلةيا بحل
+
+687
+01:14:54,990 --> 01:14:59,250
+القسين، يا بروح على القانون العام، مظبوط، بس هنا
+
+688
+01:14:59,250 --> 01:15:04,110
+ماتظبطش معناه لا قانون عام ولا حاجة، يبقى في عندي
+
+689
+01:15:04,110 --> 01:15:10,310
+أكثر من طريقة لحل هذه المعادلة، هدول أربع termات،
+
+690
+01:15:10,310 --> 01:15:14,370
+إذا ممكن أخد كل term مع بعض و أخد عاملهم عامل
+
+691
+01:15:14,370 --> 01:15:21,670
+مشترك، كان بيعني ماجدرتش بشوف من الرقم اللي بيقسم
+
+692
+01:15:21,670 --> 01:15:26,400
+سالب واحد،طبعا ماحيش عندنا إلا ميان رقمين اللي هو
+
+693
+01:15:26,400 --> 01:15:32,940
+واحد وسالف واحد يبقى بيكون واحد فيهم على الأقل هو
+
+694
+01:15:32,940 --> 01:15:38,040
+أحد عوامل المعادلة يبقى بروح باجسم المعادلة هذه
+
+695
+01:15:38,040 --> 01:15:43,940
+على R ناقص واحد أو R زائد واحد حسب المعامل
+
+696
+01:15:43,940 --> 01:15:48,160
+وبالتالي بنزل الرتبة من الرتبة التالتة إلى الرتبة
+
+697
+01:15:48,160 --> 01:15:53,950
+وخلاص بصير قصدي سهل بعد هيك مظبوطلكن اذا جيت قولت
+
+698
+01:15:53,950 --> 01:15:59,870
+هذه يا مانان بقدر اقول هذه R تكيب ناقص واحد هدول
+
+699
+01:15:59,870 --> 01:16:05,110
+التان تان فيهم عامل مشترك اللي همين سالب تلاتة R
+
+700
+01:16:05,110 --> 01:16:13,760
+بظل قداش R ناقص واحد يساوي Zeroأخذ سالب ثلاثة R من
+
+701
+01:16:13,760 --> 01:16:18,420
+التنتين هذول برا من المشاركة هنا بيظل R و هنا بيظل
+
+702
+01:16:18,420 --> 01:16:24,460
+سالب واحد هذه فيها كمان R ناقص واحد إذا بدى أحلل
+
+703
+01:16:24,460 --> 01:16:31,500
+هذه كفارق بين المكعبين يبقى هذه بدها تعطينا فتحة
+
+704
+01:16:31,500 --> 01:16:36,800
+كويس بدى ذاكرك بتحليل الفرق بين المكعبين ابتخد
+
+705
+01:16:36,800 --> 01:16:42,390
+الجذر التالت للقيمة الأولى اللي هو G11و ناقص كما
+
+706
+01:16:42,390 --> 01:16:47,110
+هي و بتاخد الجذر التالت للقيمة التانية اللى قداش
+
+707
+01:16:47,110 --> 01:16:51,570
+واحد ايه اخدنا الجذر التالت للأولى و الجذر التالت
+
+708
+01:16:51,570 --> 01:16:57,670
+للتالت بالمثل لو كان مجموع مكعبين بنسوي نفس القصة
+
+709
+01:16:57,670 --> 01:17:03,970
+تمام؟ طيب بعد كده بقول قوس مربع الأول R تربين
+
+710
+01:17:03,970 --> 01:17:09,370
+الإشارة هذه ناقص بحط عكسها تماما و بضرب القيمتان
+
+711
+01:17:09,370 --> 01:17:16,110
+في بعضواحد في R بقداش ب R زائد مربع القيمة التانية
+
+712
+01:17:16,110 --> 01:17:20,710
+اللي هو جداش، إذاً هذا هو تحليل الفرق بين المكعبين
+
+713
+01:17:20,710 --> 01:17:21,610
+القيمة الأولى
+
+714
+01:17:24,450 --> 01:17:30,430
+يبقى باجي بقوله ناقص تلاتة R في R ناقص واحد يساوي
+
+715
+01:17:30,430 --> 01:17:34,530
+Zero انا عندي هذه كمية و هذه كمية فيه بينهم عامل
+
+716
+01:17:34,530 --> 01:17:38,850
+مشترك اللي همين R ناقص واحد بقوله يا R ناقص واحد
+
+717
+01:17:38,850 --> 01:17:43,340
+خليك برا انتيبقى لما أخد عمل مشترك بيظل عندي R
+
+718
+01:17:43,340 --> 01:17:51,500
+تربية زائد R زائد واحد ناقص تلاتة R فقط لغير يبقى
+
+719
+01:17:51,500 --> 01:17:58,080
+بده يساوي Zero هذه بتصير R ناقص واحد فيه هذه يا
+
+720
+01:17:58,080 --> 01:18:03,960
+بنات اللي هى R تربية عندك R وناقص تلاتة R اللي هي
+
+721
+01:18:03,960 --> 01:18:09,930
+بناقص اتنين R زائد واحد كله بده يساوي Zeroهذه
+
+722
+01:18:09,930 --> 01:18:20,130
+عبارة عن مين؟ R ناقص واحد لكل تكييب
+
+723
+01:18:20,130 --> 01:18:26,610
+هذا معناته أن R ناقص واحد لكل تكييب يساوي Zero هذه
+
+724
+01:18:26,610 --> 01:18:32,250
+محددة من أي درجة تالتة يبقى لك كم جذر والتلاتة
+
+725
+01:18:32,250 --> 01:18:39,660
+مالهمحقيقية ومتساوية repeated roots اللي هو الحالة
+
+726
+01:18:39,660 --> 01:18:45,380
+الأخيرة اللي عندنا نمر أيه يبقى هنا معناته أن R1
+
+727
+01:18:45,380 --> 01:18:51,420
+بديه يسوي R2 بديه يسوي R3 بديه يسوي كده؟ واحد
+
+728
+01:18:51,420 --> 01:19:00,000
+صحيح، تمام؟ يعني هذه real repeated roots
+
+729
+01:19:02,350 --> 01:19:12,770
+يبقى بناء عليه the solution of the differential
+
+730
+01:19:12,770 --> 01:19:26,890
+equation 1 as y تساوي c1 زي c2t زي c3t تربيه امشي
+
+731
+01:19:26,890 --> 01:19:32,310
+كمان ولا خلاصلأ خلاص لحظة الأس هنا كده اش اتنين
+
+732
+01:19:32,310 --> 01:19:37,650
+رغم ان المعادلة على رقم تلاتة كله في إيه أس اعرف
+
+733
+01:19:37,650 --> 01:19:44,290
+انت بقداش؟ بواحد في T الـT itself يبقى هذا شكل ال
+
+734
+01:19:44,290 --> 01:19:51,210
+solution تبع المعادلة إلا أن حد إلا يتساول هنا أظن
+
+735
+01:19:51,210 --> 01:19:56,170
+بسيطة مش صعبة طيب نشوف غيرها نمر بيه
+
+736
+01:19:58,790 --> 01:20:07,170
+نمرى بيه اللي هو سؤال تمانتاشر من الكتاب بيقول لي
+
+737
+01:20:07,170 --> 01:20:13,430
+y أس to the derivative ستة ناقص y double prime
+
+738
+01:20:13,430 --> 01:20:19,630
+يساوي زيرو بسيط شغل بسيط مش كتير بدنا نجينا على
+
+739
+01:20:19,630 --> 01:20:23,710
+solution اللي هي المعادلة الصغيرة هذه نفس التكتيك
+
+740
+01:20:23,710 --> 01:20:26,670
+اللي اتبع بعدين بقوله solution
+
+741
+01:20:30,160 --> 01:20:38,680
+لت Y تساوي E أس R T بيسميها للمعادلة الرقم 1 بيه
+
+742
+01:20:38,680 --> 01:20:52,080
+solution of the differential equation 1 then the
+
+743
+01:20:52,080 --> 01:20:56,060
+characteristic
+
+744
+01:20:56,060 --> 01:21:08,190
+equation isأرقص 6 ناقص R تربيع يساوي 0 صح؟
+
+745
+01:21:08,190 --> 01:21:14,710
+في عامل مشترك؟ اللي هو مين؟ هذا بدي يعطينا أن R
+
+746
+01:21:14,710 --> 01:21:21,950
+تربيع في أرقص 4 ناقص 1 يساوي 0 هذه فرق بين
+
+747
+01:21:21,950 --> 01:21:27,470
+المربعين بقدر أحللها فرق بين المربعين يبقى هاي R
+
+748
+01:21:27,470 --> 01:21:34,780
+تربيع اللي براوهنا R تربيع ناقص واحد في R تربيع
+
+749
+01:21:34,780 --> 01:21:41,720
+زاد واحد بده يساوي Zero صحيح؟ هذه كمان فرق بين
+
+750
+01:21:41,720 --> 01:21:51,530
+المربعين يبقى هذه R تربيع في R ناقص واحدفى R زائد
+
+751
+01:21:51,530 --> 01:21:58,610
+واحد فى R ترابيع زائد واحد كله بده يساوي قداش بده
+
+752
+01:21:58,610 --> 01:22:04,630
+يساوي Zero طيب الحلال لو خلصنا هذا ايش معناها ان
+
+753
+01:22:04,630 --> 01:22:12,530
+الجدر هذا مكرر مرتين يبقى R واحد تساوي R اتنين
+
+754
+01:22:12,530 --> 01:22:19,080
+تساوي Zeroوهذه معناها ان ال R تلاتة بواحد وال R
+
+755
+01:22:19,080 --> 01:22:25,300
+أربعة بسالب واحد خلصنا هدول شو رايك في هذه R تربية
+
+756
+01:22:25,300 --> 01:22:29,400
+تساوي ناقص واحد يبقى complex يعني R تساوي زايد او
+
+757
+01:22:29,400 --> 01:22:39,400
+ناقص I يبقى هنا هذا معناه ان R خمسة تساوي I وR ستة
+
+758
+01:22:39,400 --> 01:22:44,900
+تساوي سالب Iوالعيط طبعا معروف اللي هو الجذر
+
+759
+01:22:44,900 --> 01:22:50,780
+التربيهي ل سالب واحد يبقى اتنين complex و اتنين
+
+760
+01:22:50,780 --> 01:22:55,260
+conjugate و الباقى real يبقى اتصار مشترك من اتنين
+
+761
+01:22:55,260 --> 01:23:00,660
+complex و main و real كذلك يبقى بناء عليه the
+
+762
+01:23:00,660 --> 01:23:08,720
+general solution is بدي اشوف ال general solution
+
+763
+01:23:08,720 --> 01:23:17,540
+اللي عندنا هنا y تساويهي يا بنات C1 زائد C2 في T
+
+764
+01:23:17,540 --> 01:23:24,680
+المكرر في E أس Zero T يعني بواحد يبقى مافيش غير
+
+765
+01:23:24,680 --> 01:23:33,480
+هدول اتنين لحالهم زائد نيجي اللي بعده C3 E Os T
+
+766
+01:23:33,480 --> 01:23:42,620
+زائد C4 E Os ناقص T نيجي اللي هدول لاندا بقداشزائر
+
+767
+01:23:42,620 --> 01:23:48,680
+وماعنديش لانه يبقى E و Zero لبعد يبقى زائد C خمسة
+
+768
+01:23:48,680 --> 01:23:58,980
+cosine T زائد C ستة sine T يعني
+
+769
+01:23:58,980 --> 01:24:04,080
+سؤال صغير لكن برضه بدنا نفكر كيف نحله حتى الآن
+
+770
+01:24:04,080 --> 01:24:11,970
+برضه كله تحليل سهل هذهمافيش فيها أي فكرة ناخد مثال
+
+771
+01:24:11,970 --> 01:24:17,690
+اخر في محاضرة اليوم و المرة الجاية بنكمل و بدنا
+
+772
+01:24:17,690 --> 01:24:23,830
+نشوف ايش الفكرة اللي فيه يبقى نمره الـC نمره الـC
+
+773
+01:24:23,830 --> 01:24:31,350
+سؤال تسعة عشر من الكتاب بيقول لي why to the
+
+774
+01:24:31,350 --> 01:24:38,480
+derivative fiveناقص تلاتة y to the derivative four
+
+775
+01:24:38,480 --> 01:24:47,560
+زائد تلاتة to the triple derivative ناقص تلاتة y w
+
+776
+01:24:47,560 --> 01:24:57,320
+prime زائد اتنين y prime بده يساوي من zero يبقى
+
+777
+01:24:57,320 --> 01:25:02,560
+باجي بقول له solution let
+
+778
+01:25:03,320 --> 01:25:11,680
+Y تساوي E أُس RT بإيه سوليوشن
+
+779
+01:25:11,680 --> 01:25:15,100
+Of
+
+780
+01:25:15,100 --> 01:25:26,720
+The Differential Equation 1 High Equation 1 Then
+
+781
+01:25:26,720 --> 01:25:32,000
+The Characteristic
+
+782
+01:25:32,780 --> 01:25:44,300
+Equation is R أُس خمسة ناقص تلاتة R أُس أربع زائد
+
+783
+01:25:44,300 --> 01:25:52,820
+تلاتة R تكريم ناقص تلاتة R تربيع زائد اتنين R بده
+
+784
+01:25:52,820 --> 01:25:59,400
+يسوى قداش Zero هذه معادلة من الدرجةيعني لها خمسة
+
+785
+01:25:59,400 --> 01:26:06,300
+جذور تمام طيب نبدأ نشوف كيف بدنا نحللها و نيفر أظن
+
+786
+01:26:06,300 --> 01:26:10,840
+في R عامل مشترك يبقى التحليل بإخراج العامل المشترك
+
+787
+01:26:10,840 --> 01:26:18,880
+هاي R ضالان دمين R أُس أربع ناقص تلاتة R تكيب زائد
+
+788
+01:26:18,880 --> 01:26:24,880
+تلاتة R تربيع ناقص تلاتة R زائد اتنين يساوي زير
+
+789
+01:26:28,050 --> 01:26:31,450
+الان بنطلع فى المعادلة اللى عندنا دى كيبنا حلل
+
+790
+01:26:31,450 --> 01:26:37,250
+المعادلة اللى بين قسمنا الدرجة الرابعة اخد كل
+
+791
+01:26:37,250 --> 01:26:41,050
+اتنين مع بعض واصبطش اشي فى تلاتة واشي فى اتنين
+
+792
+01:26:41,050 --> 01:26:46,470
+تمام يبقى ممكن نعمل قسمة مطولة كيف بدى اجيب القسمة
+
+793
+01:26:46,470 --> 01:26:52,070
+المطولة شوف يا بنات بروح على المقدار الثابت مين هو
+
+794
+01:26:53,010 --> 01:27:00,190
+وبدور على قواسمه اتنين سالب اتنين واحد سالب واحد
+
+795
+01:27:00,190 --> 01:27:04,930
+امسك اي رقم فيهم و اعوضه في المعدل اللي بيخليه
+
+796
+01:27:04,930 --> 01:27:11,270
+اللي بيخليه صفر بيكون هو احد العوامل تمام باقسم
+
+797
+01:27:11,270 --> 01:27:15,890
+عليه بنزل الدرجة من الدرجة التالتة لوين لمن الدرجة
+
+798
+01:27:15,890 --> 01:27:21,030
+الرابعة للدرجة وبعدها يمكن تنحله يمكن اسوي نفس ال
+
+799
+01:27:21,030 --> 01:27:25,940
+tacticتمام؟ واحدة اشتر شوية قالتلي طب اشترك استنى
+
+800
+01:27:25,940 --> 01:27:31,100
+شوية انت عندك تلاتات كتير قلتله والله مظبوط قالتلي
+
+801
+01:27:31,100 --> 01:27:36,340
+بتقدر تخلي هذه تلاتة بقولك ايه؟ قال ضيف واحد واطرح
+
+802
+01:27:36,340 --> 01:27:41,240
+واحد تبقى حلية المشكلة كلها ولا تقسم جسمها مطول
+
+803
+01:27:41,240 --> 01:27:46,800
+ولا غيره دقة نظر بقولك ايه؟ قالت هذه بالشكل التالي
+
+804
+01:27:46,800 --> 01:27:59,000
+IRوهذا R أس أربع وناقص تلاتة R تربيع وناقص تلاتة R
+
+805
+01:27:59,000 --> 01:28:09,800
+تكيب وزائد تلاتة R تربيع وناقص تلاتة R وزائد تلاتة
+
+806
+01:28:09,800 --> 01:28:16,040
+ناقص واحد كله يسوى زيرو يعني ايش عاملينأضافت واحد
+
+807
+01:28:16,040 --> 01:28:20,000
+واطرحت واحد لما اضافت واحد لاتنين صار تلاتة قام
+
+808
+01:28:20,000 --> 01:28:24,600
+اطرحت واحد قلتلها و بعدين قالت تعالي شوف ايش اللي
+
+809
+01:28:24,600 --> 01:28:30,160
+صار هاي اتنين اربع ستة قلتلها مظبوط قال بدي ااخد
+
+810
+01:28:30,160 --> 01:28:34,040
+كل اتنين مع بعض في الأول كانوا خمسة الحين صاروا
+
+811
+01:28:34,040 --> 01:28:39,860
+ستة كيف بتقولي هاي ار و هذا ارقص اربعة ناقص واحد
+
+812
+01:28:39,860 --> 01:28:46,960
+مع الأخيرو هدول اتنين بداخد منهم ناقص تلاتة R تربي
+
+813
+01:28:46,960 --> 01:28:52,800
+عامل مشترك بظل R ناقص واحد قلنا لها مظبوط و قالت
+
+814
+01:28:52,800 --> 01:28:58,660
+هدول كمان ناقص تلاتة بظل R ناقص واحد يساوي Zero
+
+815
+01:28:58,660 --> 01:29:05,700
+قلنا لها ان قالت هدى كمان بتحللها فرق بين المربعين
+
+816
+01:29:06,100 --> 01:29:12,000
+يبقى بنجي بنقولها أو بناخد منها دول are ناقص واحد
+
+817
+01:29:12,000 --> 01:29:18,010
+كمان يبقى هذا اهفى R تربية ناقص واحد فى R تربية
+
+818
+01:29:18,010 --> 01:29:22,890
+زائد واحد عامل مشترك هى حللنا الجوس الاول كفرق بين
+
+819
+01:29:22,890 --> 01:29:29,890
+المربعين جالتلى هذا ناقص تلاتة عامل مشترك مابل
+
+820
+01:29:29,890 --> 01:29:36,830
+اتنين وR ناقص واحد عامل مشترك مابل اتنين بظل R
+
+821
+01:29:36,830 --> 01:29:40,730
+تربية زائد واحد كلها يساوي زير وقلنا لها مظبوط
+
+822
+01:29:43,930 --> 01:29:49,150
+بعد مرة تانية الخطوة اللي عملناها هذه أضفنا فوق
+
+823
+01:29:49,150 --> 01:29:54,010
+واحد و طرحنا واحد صار عندي ست ترمات بدي أخد كل
+
+824
+01:29:54,010 --> 01:29:59,050
+ترمين مع بعض يبقى أخد الأول والأخر مع بعض هذول
+
+825
+01:29:59,050 --> 01:30:02,870
+اتنين أخد منهم سالب تلاتة R تربي عام المشترك هذه
+
+826
+01:30:02,870 --> 01:30:08,010
+أخد سالب تلاتة عام المشترك بعدين هذه حللت فرق من
+
+827
+01:30:08,010 --> 01:30:13,090
+المربعين هذه أخد ناقص تلاتة في R ناقص واحد كل عام
+
+828
+01:30:13,090 --> 01:30:18,400
+المشتركطلع عند هنا R ثربية وطلع عند هنا ايش؟ واحد
+
+829
+01:30:18,400 --> 01:30:22,920
+فقط لان اخدت ناقص تلاتة في R ناقص واحد دي بيصرت
+
+830
+01:30:22,920 --> 01:30:28,460
+بالشكل هذا اطلع الي هدتين و هدتين في بينهم عامل
+
+831
+01:30:28,460 --> 01:30:37,820
+مشترك؟ شرفنا برايبقى هذا R في R تربيه زائد واحد بل
+
+832
+01:30:37,820 --> 01:30:43,100
+مين عندنا هذا كمان بنحلل الفرق بين المربعين اللي
+
+833
+01:30:43,100 --> 01:30:50,940
+هو مين R ناقص واحد في R زائد واحد تمام هذا راح
+
+834
+01:30:50,940 --> 01:30:56,580
+يبقى ناقص تلاتة في R ناقص واحد كله بده يساوي Zero
+
+835
+01:30:57,420 --> 01:31:01,720
+طيب ايش رأيك ار ناقص واحد و ار ناقص واحد شرفنا برا
+
+836
+01:31:01,720 --> 01:31:07,920
+كمان يبقى اي ار في ار ناقص واحد في ار تربيه زائد
+
+837
+01:31:07,920 --> 01:31:15,380
+واحد بل ار زائد واحد و هنا قداش ناقص ثلاثة بس بده
+
+838
+01:31:15,380 --> 01:31:21,600
+يساوي ال zero يبقى هذا بصير main ار في ار ناقص
+
+839
+01:31:21,600 --> 01:31:29,600
+واحد في ار ناقص اتنينفئة ترابية زائد واحد بده
+
+840
+01:31:29,600 --> 01:31:35,980
+يساوي zero اصلا هدول تلاتة real and different و
+
+841
+01:31:35,980 --> 01:31:39,920
+هدول اتنين complex conjugate يبقى بقدر اجيب ال
+
+842
+01:31:39,920 --> 01:31:45,920
+general solution يبقى بروح بقوله the general
+
+843
+01:31:45,920 --> 01:32:00,400
+solution of the differentialEquation 1 is Y تساوي
+
+844
+01:32:00,400 --> 01:32:12,600
+C1 في E أُس 0 مظبوط يبقى C1 زائد C2 في E أُس T
+
+845
+01:32:12,600 --> 01:32:25,420
+زائد C3 في E أُس 2T هدول Complexيبقى زائد C4 في
+
+846
+01:32:25,420 --> 01:32:34,540
+Cos T زائد C5 في Sin T هذا هو ال general solution
+
+847
+01:32:34,540 --> 01:32:39,260
+للمعادلة اللي يعني لازلنا في نفس ال section في
+
+848
+01:32:39,260 --> 01:32:45,400
+هناك مزيد من الأمثلة و خاصة لما يكون كله complex
+
+849
+01:32:45,400 --> 01:32:49,830
+لكسة ماجيبناش عليه ولا مثال كله complexيبقى للمرة
+
+850
+01:32:49,830 --> 01:32:52,530
+القادمة ان شاء الله ابنكم
+
diff --git a/PL9fwy3NUQKwa8ZDfSFGn6H8xVFLzqmCZC/PY1U7lboILA_raw.json b/PL9fwy3NUQKwa8ZDfSFGn6H8xVFLzqmCZC/PY1U7lboILA_raw.json
new file mode 100644
index 0000000000000000000000000000000000000000..3b5f191cca95ca368460b3ede46f563a78e8f850
--- /dev/null
+++ b/PL9fwy3NUQKwa8ZDfSFGn6H8xVFLzqmCZC/PY1U7lboILA_raw.json
@@ -0,0 +1 @@
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927.36, "end": 927.38, "word": " اللي", "probability": 0.91943359375}, {"start": 927.38, "end": 927.98, "word": " اللي", "probability": 0.91455078125}, {"start": 927.98, "end": 936.78, "word": " اللي", "probability": 0.9140625}, {"start": 936.78, "end": 936.82, "word": " اللي", "probability": 0.9111328125}], "temperature": 1.0}, {"id": 36, "seek": 96654, "start": 938.48, "end": 966.54, "text": "سؤال التاني بيقول ما يأتي determine whether the following set determine the following set of functions are", "tokens": [3794, 33604, 6027, 16712, 7649, 1829, 4724, 1829, 39648, 19446, 7251, 10721, 31371, 6997, 1968, 264, 3480, 992, 6997, 264, 3480, 992, 295, 6828, 366], "avg_logprob": -0.21063702610822824, "compression_ratio": 1.2574257425742574, "no_speech_prob": 0.0, "words": [{"start": 938.48, "end": 939.06, "word": "سؤال", "probability": 0.746337890625}, {"start": 939.06, "end": 939.58, "word": " التاني", "probability": 0.7877604166666666}, {"start": 939.58, "end": 940.16, "word": " بيقول", "probability": 0.9513346354166666}, {"start": 940.16, "end": 940.5, "word": " ما", "probability": 0.9560546875}, {"start": 940.5, "end": 941.12, "word": " يأتي", "probability": 0.8937174479166666}, {"start": 941.12, "end": 943.04, "word": " determine", "probability": 0.54931640625}, {"start": 943.04, "end": 948.02, "word": " whether", "probability": 0.7744140625}, {"start": 948.02, "end": 951.72, "word": " the", "probability": 0.82763671875}, {"start": 951.72, "end": 952.36, "word": " following", "probability": 0.904296875}, {"start": 952.36, "end": 953.16, "word": " set", "probability": 0.95068359375}, {"start": 953.16, "end": 958.26, "word": " determine", "probability": 0.399169921875}, {"start": 958.26, "end": 958.98, "word": " the", "probability": 0.9404296875}, {"start": 958.98, "end": 959.48, "word": " following", "probability": 0.91015625}, {"start": 959.48, "end": 960.28, "word": " set", "probability": 0.95556640625}, {"start": 960.28, "end": 961.98, "word": " of", "probability": 0.9716796875}, {"start": 961.98, "end": 963.46, "word": " functions", "probability": 0.8828125}, {"start": 963.46, "end": 966.54, "word": " are", "probability": 0.80712890625}], "temperature": 1.0}, {"id": 37, "seek": 98950, "start": 967.44, "end": 989.5, "text": "Linearly Dependent او Linearly Independent هذا المطلب الأول المطلب التاني if they are linearly dependent find a linear relation", "tokens": [43, 533, 289, 356, 4056, 521, 317, 1975, 2407, 14670, 289, 356, 40310, 23758, 9673, 9566, 46152, 16247, 12610, 9673, 9566, 46152, 16712, 7649, 1829, 498, 436, 366, 43586, 12334, 915, 257, 8213, 9721], "avg_logprob": -0.4562499863760812, "compression_ratio": 1.4220183486238531, "no_speech_prob": 0.0, "words": [{"start": 967.44, "end": 968.62, "word": "Linearly", "probability": 0.7093658447265625}, {"start": 968.62, "end": 970.32, "word": " Dependent", "probability": 0.7237141927083334}, {"start": 970.32, "end": 971.2, "word": " او", "probability": 0.5838623046875}, {"start": 971.2, "end": 972.76, "word": " Linearly", "probability": 0.92578125}, {"start": 972.76, "end": 973.72, "word": " Independent", "probability": 0.88720703125}, {"start": 973.72, "end": 976.7, "word": " هذا", "probability": 0.11627197265625}, {"start": 976.7, "end": 977.08, "word": " المطلب", "probability": 0.671630859375}, {"start": 977.08, "end": 977.48, "word": " الأول", "probability": 0.891357421875}, {"start": 977.48, "end": 977.96, "word": " المطلب", "probability": 0.738037109375}, {"start": 977.96, "end": 978.74, "word": " التاني", "probability": 0.8302408854166666}, {"start": 978.74, "end": 979.52, "word": " if", "probability": 0.271240234375}, {"start": 979.52, "end": 981.32, "word": " they", "probability": 0.88623046875}, {"start": 981.32, "end": 983.12, "word": " are", "probability": 0.94775390625}, {"start": 983.12, "end": 984.82, "word": " linearly", "probability": 0.77978515625}, {"start": 984.82, "end": 986.24, "word": " dependent", "probability": 0.8310546875}, {"start": 986.24, "end": 987.94, "word": " find", "probability": 0.8154296875}, {"start": 987.94, "end": 988.26, "word": " a", "probability": 0.970703125}, {"start": 988.26, "end": 988.58, "word": " linear", "probability": 0.919921875}, {"start": 988.58, "end": 989.5, "word": " relation", "probability": 0.96630859375}], "temperature": 1.0}, {"id": 38, "seek": 102696, "start": 999.86, "end": 1026.96, "text": "reinheralation among them نمر ايه سؤال سبعة من الكتاب بيقول F1 of T بدي ساوي اتنين T ناقص تلاتة", "tokens": [265, 259, 511, 304, 399, 3654, 552, 8717, 29973, 1975, 1829, 3224, 8608, 33604, 6027, 8608, 3555, 27884, 9154, 33251, 2655, 16758, 4724, 1829, 39648, 479, 16, 295, 314, 4724, 16254, 8608, 995, 45865, 1975, 2655, 1863, 9957, 314, 8717, 995, 4587, 9381, 6055, 1211, 9307, 3660], "avg_logprob": -0.3860677170256774, "compression_ratio": 1.125984251968504, "no_speech_prob": 0.0, "words": [{"start": 999.86, "end": 1001.26, "word": "reinheralation", "probability": 0.454248046875}, {"start": 1001.26, "end": 1002.66, "word": " among", "probability": 0.91650390625}, {"start": 1002.66, "end": 1010.28, "word": " them", "probability": 0.9111328125}, {"start": 1010.28, "end": 1014.16, "word": " نمر", "probability": 0.48345947265625}, {"start": 1014.16, "end": 1015.26, "word": " ايه", "probability": 0.6886393229166666}, {"start": 1015.26, "end": 1016.6, "word": " سؤال", "probability": 0.74560546875}, {"start": 1016.6, "end": 1017.06, "word": " سبعة", "probability": 0.8487955729166666}, {"start": 1017.06, "end": 1017.34, "word": " من", "probability": 0.98388671875}, {"start": 1017.34, "end": 1018.06, "word": " الكتاب", "probability": 0.9757486979166666}, {"start": 1018.06, "end": 1019.46, "word": " بيقول", "probability": 0.9222005208333334}, {"start": 1019.46, "end": 1020.6, "word": " F1", "probability": 0.5556640625}, {"start": 1020.6, "end": 1021.66, "word": " of", "probability": 0.69873046875}, {"start": 1021.66, "end": 1022.1, "word": " T", "probability": 0.876953125}, {"start": 1022.1, "end": 1023.18, "word": " بدي", "probability": 0.547607421875}, {"start": 1023.18, "end": 1023.86, "word": " ساوي", "probability": 0.6737467447916666}, {"start": 1023.86, "end": 1024.6, "word": " اتنين", "probability": 0.847900390625}, {"start": 1024.6, "end": 1025.12, "word": " T", "probability": 0.75390625}, {"start": 1025.12, "end": 1026.28, "word": " ناقص", "probability": 0.9339599609375}, {"start": 1026.28, "end": 1026.96, "word": " تلاتة", "probability": 0.778228759765625}], "temperature": 1.0}, {"id": 39, "seek": 104833, "start": 1027.3, "end": 1048.34, "text": "وال F2 as a function of T بدر ساوي T ترابيع زائد واحد وال F3 of T بدر ساوي اتنين T ترابيع ناقص T", "tokens": [2407, 6027, 479, 17, 382, 257, 2445, 295, 314, 47525, 2288, 8608, 995, 45865, 314, 6055, 2288, 16758, 40228, 30767, 16373, 3215, 36764, 24401, 16070, 479, 18, 295, 314, 47525, 2288, 8608, 995, 45865, 1975, 2655, 1863, 9957, 314, 6055, 2288, 16758, 40228, 8717, 995, 4587, 9381, 314], "avg_logprob": -0.2256058624812535, "compression_ratio": 1.3679245283018868, "no_speech_prob": 0.0, "words": [{"start": 1027.3, "end": 1027.7, "word": "وال", "probability": 0.32452392578125}, {"start": 1027.7, "end": 1028.36, "word": " F2", "probability": 0.6654052734375}, {"start": 1028.36, "end": 1028.74, "word": " as", "probability": 0.5751953125}, {"start": 1028.74, "end": 1029.02, "word": " a", "probability": 0.91259765625}, {"start": 1029.02, "end": 1029.58, "word": " function", "probability": 0.97021484375}, {"start": 1029.58, "end": 1030.08, "word": " of", "probability": 0.9755859375}, {"start": 1030.08, "end": 1030.5, "word": " T", "probability": 0.8525390625}, {"start": 1030.5, "end": 1031.5, "word": " بدر", "probability": 0.43145751953125}, {"start": 1031.5, "end": 1032.2, "word": " ساوي", "probability": 0.8665364583333334}, {"start": 1032.2, "end": 1032.88, "word": " T", "probability": 0.76123046875}, {"start": 1032.88, "end": 1033.76, "word": " ترابيع", "probability": 0.8486328125}, {"start": 1033.76, "end": 1034.88, "word": " زائد", "probability": 0.6590983072916666}, {"start": 1034.88, "end": 1035.48, "word": " واحد", "probability": 0.939697265625}, {"start": 1035.48, "end": 1036.16, "word": " وال", "probability": 0.405029296875}, {"start": 1036.16, "end": 1037.22, "word": " F3", "probability": 0.87890625}, {"start": 1037.22, "end": 1037.88, "word": " of", "probability": 0.955078125}, {"start": 1037.88, "end": 1038.42, "word": " T", "probability": 0.9892578125}, {"start": 1038.42, "end": 1042.44, "word": " بدر", "probability": 0.748779296875}, {"start": 1042.44, "end": 1043.16, "word": " ساوي", "probability": 0.9537760416666666}, {"start": 1043.16, "end": 1044.94, "word": " اتنين", "probability": 0.943359375}, {"start": 1044.94, "end": 1045.32, "word": " T", "probability": 0.94140625}, {"start": 1045.32, "end": 1046.42, "word": " ترابيع", "probability": 0.977294921875}, {"start": 1046.42, "end": 1048.04, "word": " ناقص", "probability": 0.9765625}, {"start": 1048.04, "end": 1048.34, "word": " T", "probability": 0.95458984375}], "temperature": 1.0}, {"id": 40, "seek": 108558, "start": 1057.69, "end": 1085.59, "text": "نرجع لأسئلتنا مرة تانية يقول دي determine whether the following set of functions are linearly dependent or linearly independent يعني مجموعة الدول التالية شوفوا هل هي linearly dependent ولا linearly independent", "tokens": [1863, 47341, 3615, 5296, 10721, 3794, 19986, 1211, 2655, 8315, 3714, 25720, 6055, 7649, 10632, 7251, 39648, 11778, 1829, 6997, 1968, 264, 3480, 992, 295, 6828, 366, 43586, 12334, 420, 43586, 6695, 37495, 22653, 3714, 7435, 2304, 2407, 27884, 32748, 12610, 16712, 6027, 10632, 13412, 38688, 14407, 8032, 1211, 39896, 43586, 12334, 49429, 43586, 6695], "avg_logprob": -0.29631697439721655, "compression_ratio": 1.5371428571428571, "no_speech_prob": 0.0, "words": [{"start": 1057.69, "end": 1058.13, "word": "نرجع", "probability": 0.5885416666666666}, {"start": 1058.13, "end": 1058.63, "word": " لأسئلتنا", "probability": 0.7595563616071429}, {"start": 1058.63, "end": 1058.93, "word": " مرة", "probability": 0.960693359375}, {"start": 1058.93, "end": 1059.39, "word": " تانية", "probability": 0.9619140625}, {"start": 1059.39, "end": 1061.43, "word": " يقول", "probability": 0.40667724609375}, {"start": 1061.43, "end": 1061.75, "word": " دي", "probability": 0.35723876953125}, {"start": 1061.75, "end": 1062.17, "word": " determine", "probability": 0.2481689453125}, {"start": 1062.17, "end": 1062.57, "word": " whether", "probability": 0.7890625}, {"start": 1062.57, "end": 1062.87, "word": " the", "probability": 0.85791015625}, {"start": 1062.87, "end": 1063.57, "word": " following", "probability": 0.90087890625}, {"start": 1063.57, "end": 1067.57, "word": " set", "probability": 0.7666015625}, {"start": 1067.57, "end": 1067.97, "word": " of", "probability": 0.97509765625}, {"start": 1067.97, "end": 1073.87, "word": " functions", "probability": 0.83349609375}, {"start": 1073.87, "end": 1075.11, "word": " are", "probability": 0.3466796875}, {"start": 1075.11, "end": 1075.65, "word": " linearly", "probability": 0.91552734375}, {"start": 1075.65, "end": 1076.51, "word": " dependent", "probability": 0.70947265625}, {"start": 1076.51, "end": 1077.05, "word": " or", "probability": 0.94921875}, {"start": 1077.05, "end": 1077.71, "word": " linearly", "probability": 0.96240234375}, {"start": 1077.71, "end": 1078.37, "word": " independent", "probability": 0.947265625}, {"start": 1078.37, "end": 1078.77, "word": " يعني", "probability": 0.731689453125}, {"start": 1078.77, "end": 1079.45, "word": " مجموعة", "probability": 0.93603515625}, {"start": 1079.45, "end": 1079.91, "word": " الدول", "probability": 0.96533203125}, {"start": 1079.91, "end": 1080.61, "word": " التالية", "probability": 0.9889322916666666}, {"start": 1080.61, "end": 1081.47, "word": " شوفوا", "probability": 0.80615234375}, {"start": 1081.47, "end": 1081.71, "word": " هل", "probability": 0.861328125}, {"start": 1081.71, "end": 1082.15, "word": " هي", "probability": 0.92236328125}, {"start": 1082.15, "end": 1082.67, "word": " linearly", "probability": 0.9775390625}, {"start": 1082.67, "end": 1083.47, "word": " dependent", "probability": 0.85693359375}, {"start": 1083.47, "end": 1083.83, "word": " ولا", "probability": 0.7216796875}, {"start": 1083.83, "end": 1084.47, "word": " linearly", "probability": 0.982421875}, {"start": 1084.47, "end": 1085.59, "word": " independent", "probability": 0.9541015625}], "temperature": 1.0}, {"id": 41, "seek": 111313, "start": 1086.21, "end": 1113.13, "text": "لو كانت linearly dependent find a linear relation هتيلي علاقة خاطية among them يعني بتربط هذه الدول التلاتة مع بعض بنذكركم بجينا نقول ان لو في عندي مجموعة من ال functions تنتين تلاتة أربعة خمسة جد ما يكونوا لو ضربت كل واحدة فيهم في constant وقلت يساوي صفر", "tokens": [1211, 2407, 25961, 2655, 43586, 12334, 915, 257, 8213, 9721, 8032, 31371, 20292, 11203, 995, 28671, 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"probability": 0.6905110677083334}, {"start": 1812.74, "end": 1813.06, "word": " أحسب", "probability": 0.8570963541666666}, {"start": 1813.06, "end": 1813.18, "word": " اللي", "probability": 0.682373046875}, {"start": 1813.18, "end": 1813.28, "word": " هو", "probability": 0.338134765625}, {"start": 1813.28, "end": 1813.46, "word": " ممكن", "probability": 0.866943359375}, {"start": 1813.46, "end": 1813.64, "word": " و", "probability": 0.90625}, {"start": 1813.64, "end": 1814.0, "word": " أثبت", "probability": 0.9144287109375}, {"start": 1814.0, "end": 1814.24, "word": " انهم", "probability": 0.731201171875}, {"start": 1814.24, "end": 1814.84, "word": " linearly", "probability": 0.9755859375}, {"start": 1814.84, "end": 1815.8, "word": " dependent", "probability": 0.93017578125}], "temperature": 1.0}, {"id": 72, "seek": 184035, "start": 1816.15, "end": 1840.35, "text": "و بعد هيك أروح أدور على علاقة هذه لكن شغلي بهذه الطريقة تفكيري ست عصفرين بحجر واحد و بأقصر وقت ممكن يبقى هذا معناته ان ال F1 و F2 و F3 are linearly dependent because", "tokens": [2407, 39182, 39896, 4117, 5551, 32887, 5016, 5551, 3215, 13063, 15844, 11203, 995, 28671, 29538, 44381, 13412, 17082, 20292, 39627, 24192, 41950, 16572, 28671, 6055, 5172, 4117, 13546, 1829, 8608, 2655, 6225, 9381, 5172, 2288, 9957, 4724, 5016, 7435, 2288, 36764, 24401, 4032, 4724, 10721, 4587, 9381, 2288, 4032, 38149, 3714, 43020, 7251, 3555, 4587, 7578, 23758, 20449, 8315, 47395, 16472, 2423, 479, 16, 4032, 479, 17, 4032, 479, 18, 366, 43586, 12334, 570], "avg_logprob": -0.21260416905085247, "compression_ratio": 1.398936170212766, "no_speech_prob": 0.0, "words": [{"start": 1816.15, "end": 1816.41, "word": "و", "probability": 0.420166015625}, {"start": 1816.41, "end": 1816.75, "word": " بعد", "probability": 0.8291015625}, {"start": 1816.75, "end": 1817.11, "word": " هيك", "probability": 0.6641845703125}, {"start": 1817.11, "end": 1817.37, "word": " أروح", "probability": 0.6337076822916666}, {"start": 1817.37, "end": 1817.73, 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"word": " واحد", "probability": 0.912841796875}, {"start": 1823.61, "end": 1824.09, "word": " و", "probability": 0.40869140625}, {"start": 1824.09, "end": 1825.21, "word": " بأقصر", "probability": 0.97978515625}, {"start": 1825.21, "end": 1825.57, "word": " وقت", "probability": 0.9560546875}, {"start": 1825.57, "end": 1826.11, "word": " ممكن", "probability": 0.9892578125}, {"start": 1826.11, "end": 1827.03, "word": " يبقى", "probability": 0.9468994140625}, {"start": 1827.03, "end": 1827.39, "word": " هذا", "probability": 0.85205078125}, {"start": 1827.39, "end": 1828.09, "word": " معناته", "probability": 0.9798177083333334}, {"start": 1828.09, "end": 1828.37, "word": " ان", "probability": 0.365966796875}, {"start": 1828.37, "end": 1829.85, "word": " ال", "probability": 0.52880859375}, {"start": 1829.85, "end": 1830.81, "word": " F1", "probability": 0.763427734375}, {"start": 1830.81, "end": 1831.43, "word": " و", "probability": 0.7216796875}, {"start": 1831.43, "end": 1832.69, "word": " F2", "probability": 0.8056640625}, {"start": 1832.69, "end": 1833.63, "word": " و", "probability": 0.830078125}, {"start": 1833.63, "end": 1835.75, "word": " F3", "probability": 0.838134765625}, {"start": 1835.75, "end": 1836.63, "word": " are", "probability": 0.284423828125}, {"start": 1836.63, "end": 1837.63, "word": " linearly", "probability": 0.94287109375}, {"start": 1837.63, "end": 1839.09, "word": " dependent", "probability": 0.88134765625}, {"start": 1839.09, "end": 1840.35, "word": " because", "probability": 0.81982421875}], "temperature": 1.0}, {"id": 73, "seek": 187033, "start": 1843.27, "end": 1870.33, "text": "ان الـC1 بده يساوي واحد وC2 بده يساوي تلاتة وC3 بده يساوي سالب اتنين يبقى not zeros ماهياش أصفات يبقى هدول linearly dependent وهي ال relation اللى بتربط المعادلات التلاتة هدول او الدول التلاتة من مين", "tokens": [7649, 2423, 39184, 34, 16, 47525, 3224, 7251, 3794, 995, 45865, 36764, 24401, 4032, 34, 17, 47525, 3224, 7251, 3794, 995, 45865, 6055, 1211, 9307, 3660, 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"end": 1848.09, "word": " وC2", "probability": 0.7047526041666666}, {"start": 1848.09, "end": 1848.65, "word": " بده", "probability": 0.89794921875}, {"start": 1848.65, "end": 1849.09, "word": " يساوي", "probability": 0.9869384765625}, {"start": 1849.09, "end": 1849.89, "word": " تلاتة", "probability": 0.834716796875}, {"start": 1849.89, "end": 1851.43, "word": " وC3", "probability": 0.9171549479166666}, {"start": 1851.43, "end": 1852.01, "word": " بده", "probability": 0.954833984375}, {"start": 1852.01, "end": 1852.49, "word": " يساوي", "probability": 0.9866943359375}, {"start": 1852.49, "end": 1853.53, "word": " سالب", "probability": 0.7493489583333334}, {"start": 1853.53, "end": 1854.27, "word": " اتنين", "probability": 0.9569091796875}, {"start": 1854.27, "end": 1855.83, "word": " يبقى", "probability": 0.919189453125}, {"start": 1855.83, "end": 1856.93, "word": " not", "probability": 0.2464599609375}, {"start": 1856.93, "end": 1858.41, "word": " zeros", "probability": 0.705078125}, {"start": 1858.41, "end": 1860.07, "word": " ماهياش", "probability": 0.9114990234375}, {"start": 1860.07, "end": 1860.81, "word": " أصفات", "probability": 0.7659912109375}, {"start": 1860.81, "end": 1861.53, "word": " يبقى", "probability": 0.955810546875}, {"start": 1861.53, "end": 1861.85, "word": " هدول", "probability": 0.77685546875}, {"start": 1861.85, "end": 1862.29, "word": " linearly", "probability": 0.86083984375}, {"start": 1862.29, "end": 1862.97, "word": " dependent", "probability": 0.8046875}, {"start": 1862.97, "end": 1864.01, "word": " وهي", "probability": 0.850830078125}, {"start": 1864.01, "end": 1864.25, "word": " ال", "probability": 0.40576171875}, {"start": 1864.25, "end": 1864.87, "word": " relation", "probability": 0.75732421875}, {"start": 1864.87, "end": 1865.65, "word": " اللى", "probability": 0.760009765625}, {"start": 1865.65, "end": 1866.43, "word": " بتربط", "probability": 0.9737955729166666}, {"start": 1866.43, "end": 1867.49, "word": " المعادلات", 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0.477294921875}, {"start": 1876.43, "end": 1876.85, "word": " a", "probability": 0.9482421875}, {"start": 1876.85, "end": 1877.31, "word": " linear", "probability": 0.921875}, {"start": 1877.31, "end": 1878.01, "word": " relation", "probability": 0.97802734375}, {"start": 1878.01, "end": 1878.51, "word": " among", "probability": 0.88232421875}, {"start": 1878.51, "end": 1878.91, "word": " them", "probability": 0.93212890625}], "temperature": 1.0}, {"id": 75, "seek": 190838, "start": 1879.16, "end": 1908.38, "text": "هتلرّي لإن الناس بتربطهم إن كانوا linearly dependent واضحة الصورة يبقى هذا اختصرنا فيها الحل بدل مثبت انهم linearly dependent وروح أدور على هذه العلاقة يبقى هذه العلاقة بيانات لإنهم linearly dependent لإن الثوابت ماهياش أصفر اتنين جيبنا العلاقة اللي عندناها دي وبالتالي صدنا أصفرين بحجر واحد", "tokens": [3224, 2655, 1211, 2288, 11703, 1829, 5296, 28814, 1863, 2423, 8315, 3794, 39894, 25513, 9566, 16095, 36145, 25961, 14407, 43586, 12334, 4032, 46958, 5016, 3660, 31767, 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شئ بدأت بتقول ان هذا الكلام يساوي zero", "tokens": [40228, 22653, 47525, 11536, 19446, 6055, 5016, 9566, 11296, 9673, 24401, 3215, 34683, 32887, 5016, 6055, 5016, 35457, 13672, 1829, 31439, 2423, 472, 3178, 8032, 8848, 12610, 1975, 2304, 20193, 6055, 39648, 3224, 37279, 6027, 7578, 8717, 8592, 38688, 3714, 9566, 1211, 37746, 3714, 9566, 1211, 37746, 8717, 2304, 8592, 1829, 1823, 538, 1823, 11778, 1829, 1975, 12610, 13412, 19986, 47525, 10721, 2655, 39894, 39648, 16472, 23758, 2423, 28820, 10943, 7251, 3794, 995, 45865, 4018], "avg_logprob": -0.22964638314749064, "compression_ratio": 1.5465116279069768, "no_speech_prob": 0.0, "words": [{"start": 2076.48, "end": 2076.92, "word": "يعني", "probability": 0.815673828125}, {"start": 2076.92, "end": 2077.38, "word": " بدون", "probability": 0.9951171875}, {"start": 2077.38, "end": 2077.48, "word": " ما", "probability": 0.6376953125}, {"start": 2077.48, "end": 2078.08, "word": " تحطها", "probability": 0.7642822265625}, {"start": 2078.08, "end": 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"text": "cos 2t هذا الرئيسي ناقص الثانوي ناقص مع ناقص بيصير زائد اربع sin 2t cos 2t بعدها zero في محدده ب zero zero في محدده ب zero يبقى زائد zero زائد zero طلعيلي في ال term هذا و ال term هذا نفسه كل واحد بإشارة", "tokens": [6877, 568, 83, 23758, 34892, 19986, 1829, 3794, 1829, 8717, 995, 4587, 9381, 6024, 104, 7649, 45865, 8717, 995, 4587, 9381, 20449, 8717, 995, 4587, 9381, 4724, 1829, 9381, 13546, 30767, 16373, 3215, 1975, 25513, 3615, 3343, 568, 83, 3792, 568, 83, 39182, 11296, 4018, 8978, 3714, 24401, 3215, 3224, 4724, 4018, 4018, 8978, 3714, 24401, 3215, 3224, 4724, 4018, 7251, 3555, 4587, 7578, 30767, 16373, 3215, 4018, 30767, 16373, 3215, 4018, 23032, 1211, 3615, 1829, 20292, 8978, 2423, 1433, 23758, 4032, 2423, 1433, 23758, 8717, 36178, 3224, 28242, 36764, 24401, 4724, 28814, 8592, 9640, 3660], "avg_logprob": -0.21665593275089853, "compression_ratio": 1.8, "no_speech_prob": 0.0, "words": [{"start": 2195.4, "end": 2195.96, "word": "cos", "probability": 0.0675048828125}, {"start": 2195.96, "end": 2197.74, "word": " 2t", "probability": 0.5872802734375}, {"start": 2197.74, "end": 2198.68, "word": " هذا", "probability": 0.6591796875}, {"start": 2198.68, "end": 2199.6, "word": " الرئيسي", "probability": 0.9587890625}, {"start": 2199.6, "end": 2200.54, "word": " ناقص", "probability": 0.8919677734375}, {"start": 2200.54, "end": 2201.42, "word": " الثانوي", "probability": 0.805419921875}, {"start": 2201.42, "end": 2202.42, "word": " ناقص", "probability": 0.93310546875}, {"start": 2202.42, "end": 2202.6, "word": " مع", "probability": 0.96240234375}, {"start": 2202.6, "end": 2203.1, "word": " ناقص", "probability": 0.99072265625}, {"start": 2203.1, "end": 2203.56, "word": " بيصير", "probability": 0.7869873046875}, {"start": 2203.56, "end": 2204.36, "word": " زائد", "probability": 0.7574055989583334}, {"start": 2204.36, "end": 2205.58, "word": " اربع", "probability": 0.5892740885416666}, {"start": 2205.58, "end": 2206.4, "word": " sin", "probability": 0.431396484375}, {"start": 2206.4, "end": 2207.72, "word": " 2t", "probability": 0.894287109375}, {"start": 2207.72, "end": 2208.48, "word": " cos", "probability": 0.5615234375}, {"start": 2208.48, "end": 2210.32, "word": " 2t", "probability": 0.935791015625}, {"start": 2210.32, "end": 2211.62, "word": " بعدها", "probability": 0.9462890625}, {"start": 2211.62, "end": 2211.94, "word": " zero", "probability": 0.350341796875}, {"start": 2211.94, "end": 2212.2, "word": " في", "probability": 0.95849609375}, {"start": 2212.2, "end": 2212.98, "word": " محدده", "probability": 0.9327392578125}, {"start": 2212.98, "end": 2213.06, "word": " ب", "probability": 0.52587890625}, {"start": 2213.06, "end": 2213.32, "word": " zero", "probability": 0.5517578125}, {"start": 2213.32, "end": 2213.6, "word": " zero", "probability": 0.3349609375}, {"start": 2213.6, "end": 2213.78, "word": " في", "probability": 0.810546875}, {"start": 2213.78, "end": 2214.46, "word": " محدده", "probability": 0.9927978515625}, {"start": 2214.46, "end": 2214.6, "word": " ب", "probability": 0.9140625}, {"start": 2214.6, "end": 2214.98, "word": " zero", "probability": 0.90380859375}, {"start": 2214.98, "end": 2215.82, "word": " يبقى", "probability": 0.95361328125}, {"start": 2215.82, "end": 2216.32, "word": " زائد", "probability": 0.92236328125}, {"start": 2216.32, "end": 2216.72, "word": " zero", "probability": 0.68994140625}, {"start": 2216.72, "end": 2217.3, "word": " زائد", "probability": 0.9664713541666666}, {"start": 2217.3, "end": 2217.78, "word": " zero", "probability": 0.861328125}, {"start": 2217.78, "end": 2218.8, "word": " طلعيلي", "probability": 0.82578125}, {"start": 2218.8, "end": 2218.96, "word": " في", "probability": 0.9013671875}, {"start": 2218.96, "end": 2219.08, "word": " ال", "probability": 0.73095703125}, {"start": 2219.08, "end": 2219.3, "word": " term", "probability": 0.8935546875}, {"start": 2219.3, "end": 2219.6, "word": " هذا", "probability": 0.765625}, {"start": 2219.6, "end": 2219.74, "word": " و", "probability": 0.755859375}, {"start": 2219.74, "end": 2219.88, "word": " ال", "probability": 0.4697265625}, {"start": 2219.88, "end": 2220.16, "word": " term", "probability": 0.89599609375}, {"start": 2220.16, "end": 2220.56, "word": " هذا", "probability": 0.9482421875}, {"start": 2220.56, "end": 2222.0, "word": " نفسه", "probability": 0.8732096354166666}, {"start": 2222.0, "end": 2222.24, "word": " كل", "probability": 0.92236328125}, {"start": 2222.24, "end": 2222.5, "word": " واحد", "probability": 0.990966796875}, {"start": 2222.5, "end": 2223.18, "word": " بإشارة", "probability": 0.9009765625}], "temperature": 1.0}, {"id": 87, "seek": 223611, "start": 2223.75, "end": 2236.11, "text": "مخالفة يبجي عن الجامعة بطلع كمان جداش Zero في خمسة Zero زائد Zero زائد Zero بطلع جداش اظن و هو المطلوب", "tokens": [2304, 9778, 6027, 5172, 3660, 7251, 3555, 7435, 1829, 18871, 25724, 10943, 27884, 4724, 9566, 1211, 3615, 9122, 2304, 7649, 10874, 3215, 33599, 17182, 8978, 16490, 2304, 3794, 3660, 17182, 30767, 16373, 3215, 17182, 30767, 16373, 3215, 17182, 4724, 9566, 1211, 3615, 10874, 3215, 33599, 1975, 19913, 1863, 4032, 31439, 9673, 9566, 1211, 37746], "avg_logprob": -0.2133522781458768, "compression_ratio": 1.5135135135135136, "no_speech_prob": 0.0, "words": [{"start": 2223.75, "end": 2224.73, "word": "مخالفة", "probability": 0.82841796875}, {"start": 2224.73, "end": 2225.05, "word": " يبجي", "probability": 0.6458740234375}, {"start": 2225.05, "end": 2225.19, "word": " عن", "probability": 0.90771484375}, {"start": 2225.19, "end": 2225.61, "word": " الجامعة", "probability": 0.9708658854166666}, {"start": 2225.61, "end": 2226.07, "word": " بطلع", "probability": 0.8275146484375}, {"start": 2226.07, "end": 2226.47, "word": " كمان", "probability": 0.9029947916666666}, {"start": 2226.47, "end": 2227.17, "word": " جداش", "probability": 0.635986328125}, {"start": 2227.17, "end": 2228.09, "word": " Zero", "probability": 0.25341796875}, {"start": 2228.09, "end": 2228.31, "word": " في", "probability": 0.83251953125}, {"start": 2228.31, "end": 2229.25, "word": " خمسة", "probability": 0.9598388671875}, {"start": 2229.25, "end": 2230.31, "word": " Zero", "probability": 0.65576171875}, {"start": 2230.31, "end": 2230.89, "word": " زائد", "probability": 0.7980143229166666}, {"start": 2230.89, "end": 2231.21, "word": " Zero", "probability": 0.8984375}, {"start": 2231.21, "end": 2231.79, "word": " زائد", "probability": 0.8636067708333334}, {"start": 2231.79, "end": 2232.37, "word": " Zero", "probability": 0.9580078125}, {"start": 2232.37, "end": 2233.27, "word": " بطلع", "probability": 0.924560546875}, {"start": 2233.27, "end": 2233.93, "word": " جداش", "probability": 0.9742838541666666}, {"start": 2233.93, "end": 2235.13, "word": " اظن", "probability": 0.79443359375}, {"start": 2235.13, "end": 2235.25, "word": " و", "probability": 0.52392578125}, {"start": 2235.25, "end": 2235.41, "word": " هو", "probability": 0.86328125}, {"start": 2235.41, "end": 2236.11, "word": " المطلوب", "probability": 0.9886474609375}], "temperature": 1.0}, {"id": 88, "seek": 226298, "start": 2243.12, "end": 2262.98, "text": "خلص المطلوب الأول المطلوب التاني بيقول Can you establish بتقدر تثبت أو توصل للنتيجة هذه بدون ما تعمل حسابتك هذه أم لا الإجابة نعم موافقة يعني طيب ماشي كيف؟", "tokens": [9778, 1211, 9381, 9673, 9566, 1211, 37746, 16247, 12610, 9673, 9566, 1211, 37746, 16712, 7649, 1829, 4724, 1829, 39648, 1664, 291, 8327, 39894, 28543, 2288, 6055, 12984, 3555, 2655, 34051, 33427, 36520, 24976, 29399, 1829, 7435, 3660, 29538, 47525, 11536, 19446, 6055, 25957, 1211, 11331, 3794, 16758, 2655, 4117, 29538, 5551, 2304, 20193, 33688, 7435, 16758, 3660, 8717, 25957, 3714, 14407, 5172, 28671, 37495, 22653, 23032, 1829, 3555, 3714, 33599, 1829, 9122, 33911, 22807], "avg_logprob": -0.2564583412806193, "compression_ratio": 1.5, "no_speech_prob": 0.0, "words": [{"start": 2243.12, "end": 2244.4, "word": "خلص", "probability": 0.5765177408854166}, {"start": 2244.4, 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{"start": 2251.04, "end": 2251.8, "word": " للنتيجة", "probability": 0.96279296875}, {"start": 2251.8, "end": 2252.1, "word": " هذه", "probability": 0.365234375}, {"start": 2252.1, "end": 2252.78, "word": " بدون", "probability": 0.98779296875}, {"start": 2252.78, "end": 2252.94, "word": " ما", "probability": 0.6376953125}, {"start": 2252.94, "end": 2253.5, "word": " تعمل", "probability": 0.98583984375}, {"start": 2253.5, "end": 2254.46, "word": " حسابتك", "probability": 0.91708984375}, {"start": 2254.46, "end": 2254.92, "word": " هذه", "probability": 0.63037109375}, {"start": 2254.92, "end": 2255.56, "word": " أم", "probability": 0.763671875}, {"start": 2255.56, "end": 2256.22, "word": " لا", "probability": 0.85693359375}, {"start": 2256.22, "end": 2258.06, "word": " الإجابة", "probability": 0.828369140625}, {"start": 2258.06, "end": 2259.5, "word": " نعم", "probability": 0.8330078125}, {"start": 2259.5, "end": 2260.74, "word": " موافقة", "probability": 0.8134765625}, {"start": 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2282.21, "end": 2282.77, "word": " مثلثات", "probability": 0.8525390625}, {"start": 2282.77, "end": 2282.89, "word": " يا", "probability": 0.7890625}, {"start": 2282.89, "end": 2283.09, "word": " بنت", "probability": 0.6177978515625}, {"start": 2283.09, "end": 2283.57, "word": " الفكرة", "probability": 0.8474934895833334}, {"start": 2283.57, "end": 2283.91, "word": " الموضوع", "probability": 0.8677978515625}, {"start": 2283.91, "end": 2284.23, "word": " حساب", "probability": 0.9630533854166666}, {"start": 2284.23, "end": 2284.75, "word": " مثلثة", "probability": 0.85382080078125}, {"start": 2284.75, "end": 2285.07, "word": " اه", "probability": 0.89208984375}, {"start": 2285.07, "end": 2285.45, "word": " الحين", "probability": 0.38287353515625}, {"start": 2285.45, "end": 2285.87, "word": " قطعين", "probability": 0.69647216796875}, {"start": 2285.87, "end": 2286.15, "word": " اتنين", "probability": 0.942138671875}, {"start": 2286.15, "end": 2286.41, "word": " فيه", "probability": 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{"id": 140, "seek": 354368, "start": 3538.02, "end": 3543.68, "text": "الحالة التالتة والاخيرة The Roots", "tokens": [6027, 5016, 6027, 3660, 16712, 6027, 2655, 3660, 16070, 47283, 48923, 440, 3101, 1971], "avg_logprob": -0.35546875, "compression_ratio": 1.125, "no_speech_prob": 0.0, "words": [{"start": 3538.02, "end": 3539.42, "word": "الحالة", "probability": 0.648681640625}, {"start": 3539.42, "end": 3540.02, "word": " التالتة", "probability": 0.90869140625}, {"start": 3540.02, "end": 3541.18, "word": " والاخيرة", "probability": 0.8683268229166666}, {"start": 3541.18, "end": 3543.08, "word": " The", "probability": 0.26904296875}, {"start": 3543.08, "end": 3543.68, "word": " Roots", "probability": 0.699951171875}], "temperature": 1.0}, {"id": 141, "seek": 357493, "start": 3546.65, "end": 3574.93, "text": "are repeated لو كانت الجذور مكررة بدي أقسمها إلى جزئين نمر A if the roots of equation 2 are real repeated", "tokens": [543, 10477, 45164, 25961, 2655, 25724, 8848, 13063, 3714, 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5495.12, "word": " different", "probability": 0.8720703125}, {"start": 5495.12, "end": 5495.98, "word": " و", "probability": 0.5830078125}, {"start": 5495.98, "end": 5496.52, "word": " هدول", "probability": 0.9163411458333334}, {"start": 5496.52, "end": 5497.12, "word": " اتنين", "probability": 0.94970703125}, {"start": 5497.12, "end": 5497.86, "word": " complex", "probability": 0.91064453125}, {"start": 5497.86, "end": 5498.52, "word": " conjugate", "probability": 0.728515625}, {"start": 5498.52, "end": 5498.92, "word": " يبقى", "probability": 0.8763427734375}, {"start": 5498.92, "end": 5499.36, "word": " بقدر", "probability": 0.9505208333333334}, {"start": 5499.36, "end": 5499.74, "word": " اجيب", "probability": 0.9085693359375}, {"start": 5499.74, "end": 5499.92, "word": " ال", "probability": 0.96435546875}, {"start": 5499.92, "end": 5500.32, "word": " general", "probability": 0.86376953125}, {"start": 5500.32, "end": 5501.3, "word": " solution", "probability": 0.970703125}, {"start": 5501.3, "end": 5502.18, "word": " يبقى", "probability": 0.9447021484375}, {"start": 5502.18, "end": 5502.64, "word": " بروح", "probability": 0.9485677083333334}, {"start": 5502.64, "end": 5503.5, "word": " بقوله", "probability": 0.8447265625}, {"start": 5503.5, "end": 5504.08, "word": " the", "probability": 0.54638671875}, {"start": 5504.08, "end": 5505.92, "word": " general", "probability": 0.90185546875}, {"start": 5505.92, "end": 5508.64, "word": " solution", "probability": 0.96044921875}, {"start": 5508.64, "end": 5510.96, "word": " of", "probability": 0.96435546875}, {"start": 5510.96, "end": 5512.26, "word": " the", "probability": 0.8955078125}, {"start": 5512.26, "end": 5514.02, "word": " differential", "probability": 0.87890625}], "temperature": 1.0}, {"id": 217, "seek": 554010, "start": 5514.78, "end": 5540.1, "text": "Equation 1 is Y تساوي C1 في E أُس 0 مظبوط يبقى C1 زائد C2 في E أُس T زائد C3 في E أُس 2T هدول Complex", "tokens": [36, 358, 399, 502, 307, 398, 6055, 3794, 995, 45865, 383, 16, 8978, 462, 5551, 10859, 3794, 1958, 3714, 19913, 3555, 2407, 9566, 7251, 3555, 4587, 7578, 383, 16, 30767, 16373, 3215, 383, 17, 8978, 462, 5551, 10859, 3794, 314, 30767, 16373, 3215, 383, 18, 8978, 462, 5551, 10859, 3794, 568, 51, 8032, 3215, 12610, 41184], "avg_logprob": -0.18804824561403508, "compression_ratio": 1.2456140350877194, "no_speech_prob": 0.0, "words": [{"start": 5514.78, "end": 5515.94, "word": "Equation", "probability": 0.7342936197916666}, {"start": 5515.94, "end": 5516.82, "word": " 1", "probability": 0.400146484375}, {"start": 5516.82, "end": 5517.62, "word": " is", "probability": 0.68408203125}, {"start": 5517.62, "end": 5519.5, "word": " Y", "probability": 0.478271484375}, {"start": 5519.5, "end": 5520.4, "word": " تساوي", "probability": 0.69696044921875}, {"start": 5520.4, "end": 5521.9, "word": " C1", "probability": 0.821533203125}, {"start": 5521.9, "end": 5522.96, "word": " في", "probability": 0.82861328125}, {"start": 5522.96, "end": 5523.6, "word": " E", "probability": 0.82421875}, {"start": 5523.6, "end": 5524.16, "word": " أُس", "probability": 0.5980631510416666}, {"start": 5524.16, "end": 5524.9, "word": " 0", "probability": 0.63134765625}, {"start": 5524.9, "end": 5526.2, "word": " مظبوط", "probability": 0.86669921875}, {"start": 5526.2, "end": 5527.08, "word": " يبقى", "probability": 0.884765625}, {"start": 5527.08, "end": 5527.9, "word": " C1", "probability": 0.93115234375}, {"start": 5527.9, "end": 5529.0, "word": " زائد", "probability": 0.826171875}, {"start": 5529.0, "end": 5530.18, "word": " C2", "probability": 0.979248046875}, {"start": 5530.18, "end": 5530.9, "word": " في", "probability": 0.9912109375}, {"start": 5530.9, "end": 5531.58, "word": " E", "probability": 0.99658203125}, {"start": 5531.58, "end": 5532.14, "word": " أُس", "probability": 0.9676106770833334}, {"start": 5532.14, "end": 5532.6, "word": " T", "probability": 0.85791015625}, {"start": 5532.6, "end": 5534.18, "word": " زائد", "probability": 0.9288736979166666}, {"start": 5534.18, "end": 5535.38, "word": " C3", "probability": 0.98681640625}, {"start": 5535.38, "end": 5535.88, "word": " في", "probability": 0.994140625}, {"start": 5535.88, "end": 5536.5, "word": " E", "probability": 0.998046875}, {"start": 5536.5, "end": 5536.92, "word": " أُس", "probability": 0.9674479166666666}, {"start": 5536.92, "end": 5538.12, "word": " 2T", "probability": 0.890625}, {"start": 5538.12, "end": 5539.48, "word": " هدول", "probability": 0.88671875}, {"start": 5539.48, "end": 5540.1, "word": " Complex", "probability": 0.474365234375}], "temperature": 1.0}, {"id": 218, "seek": 556840, "start": 5540.62, "end": 5568.4, "text": "يبقى زائد C4 في Cos T زائد C5 في Sin T هذا هو ال general solution للمعادلة اللي يعني لازلنا في نفس ال section في هناك مزيد من الأمثلة و خاصة لما يكون كله complex لكسة ماجيبناش عليه ولا مثال كله complex", "tokens": [1829, 3555, 4587, 7578, 30767, 16373, 3215, 383, 19, 8978, 15855, 314, 30767, 16373, 3215, 383, 20, 8978, 11187, 314, 23758, 31439, 2423, 2674, 3827, 5296, 19528, 3615, 18513, 37977, 13672, 1829, 37495, 22653, 5296, 31377, 1211, 8315, 8978, 8717, 36178, 2423, 3541, 8978, 34105, 4117, 3714, 11622, 25708, 9154, 16247, 2304, 12984, 37977, 4032, 16490, 33546, 3660, 5296, 15042, 7251, 30544, 28242, 3224, 3997, 5296, 4117, 3794, 3660, 19446, 7435, 1829, 3555, 1863, 33599, 47356, 49429, 50113, 6027, 28242, 3224, 3997], "avg_logprob": -0.22289155980190598, "compression_ratio": 1.526829268292683, "no_speech_prob": 0.0, "words": [{"start": 5540.62, "end": 5541.56, "word": "يبقى", "probability": 0.8319091796875}, {"start": 5541.56, "end": 5542.92, "word": " زائد", "probability": 0.5910746256510416}, {"start": 5542.92, "end": 5544.58, "word": " C4", "probability": 0.6124267578125}, {"start": 5544.58, "end": 5545.42, "word": " في", "probability": 0.7587890625}, {"start": 5545.42, "end": 5545.9, "word": " Cos", "probability": 0.2529296875}, {"start": 5545.9, "end": 5546.88, "word": " T", "probability": 0.75927734375}, {"start": 5546.88, "end": 5548.06, "word": " زائد", "probability": 0.8640950520833334}, {"start": 5548.06, "end": 5549.28, "word": " C5", "probability": 0.968017578125}, {"start": 5549.28, "end": 5550.12, "word": " في", "probability": 0.98193359375}, {"start": 5550.12, "end": 5550.64, "word": " Sin", "probability": 0.87158203125}, {"start": 5550.64, "end": 5551.16, "word": " T", "probability": 0.97265625}, {"start": 5551.16, "end": 5551.98, "word": " هذا", "probability": 0.77978515625}, {"start": 5551.98, "end": 5552.46, "word": " هو", "probability": 0.990234375}, {"start": 5552.46, "end": 5552.68, "word": " ال", "probability": 0.818359375}, {"start": 5552.68, "end": 5553.2, "word": " general", "probability": 0.41796875}, {"start": 5553.2, "end": 5554.54, "word": " solution", "probability": 0.97265625}, {"start": 5554.54, "end": 5555.56, "word": " للمعادلة", "probability": 0.9375}, {"start": 5555.56, "end": 5555.88, "word": " اللي", "probability": 0.71875}, {"start": 5555.88, "end": 5556.26, "word": " يعني", "probability": 0.6005859375}, {"start": 5556.26, "end": 5557.46, "word": " لازلنا", "probability": 0.9346923828125}, {"start": 5557.46, "end": 5557.7, "word": " في", "probability": 0.96923828125}, {"start": 5557.7, "end": 5558.0, "word": " نفس", "probability": 0.99609375}, {"start": 5558.0, "end": 5558.18, "word": " ال", "probability": 0.93505859375}, {"start": 5558.18, "end": 5558.66, "word": " section", "probability": 0.90478515625}, {"start": 5558.66, "end": 5559.26, "word": " في", "probability": 0.7421875}, {"start": 5559.26, "end": 5559.84, "word": " هناك", "probability": 0.853271484375}, {"start": 5559.84, "end": 5560.88, "word": " مزيد", "probability": 0.9793294270833334}, {"start": 5560.88, "end": 5561.28, "word": " من", "probability": 0.98486328125}, {"start": 5561.28, "end": 5562.36, "word": " الأمثلة", "probability": 0.9620361328125}, {"start": 5562.36, "end": 5562.9, "word": " و", "probability": 0.97119140625}, {"start": 5562.9, "end": 5563.48, "word": " خاصة", "probability": 0.8946940104166666}, {"start": 5563.48, "end": 5563.74, "word": " لما", "probability": 0.89990234375}, {"start": 5563.74, "end": 5564.14, "word": " يكون", "probability": 0.990478515625}, {"start": 5564.14, "end": 5564.82, "word": " كله", "probability": 0.986572265625}, {"start": 5564.82, "end": 5565.4, "word": " complex", "probability": 0.8671875}, {"start": 5565.4, "end": 5565.88, "word": " لكسة", "probability": 0.52294921875}, {"start": 5565.88, "end": 5566.44, "word": " ماجيبناش", "probability": 0.778564453125}, {"start": 5566.44, "end": 5566.72, "word": " عليه", "probability": 0.96240234375}, {"start": 5566.72, "end": 5567.1, "word": " ولا", "probability": 0.495849609375}, {"start": 5567.1, "end": 5567.62, "word": " مثال", "probability": 0.95068359375}, {"start": 5567.62, "end": 5568.06, "word": " كله", "probability": 0.954345703125}, {"start": 5568.06, "end": 5568.4, "word": " complex", "probability": 0.923828125}], "temperature": 1.0}, {"id": 219, "seek": 557253, "start": 5568.87, "end": 5572.53, "text": "يبقى للمرة القادمة ان شاء الله ابنكم", "tokens": [1829, 3555, 4587, 7578, 5296, 19528, 25720, 25062, 18513, 46007, 16472, 13412, 16606, 21984, 48127, 1863, 24793], "avg_logprob": -0.1382378488779068, "compression_ratio": 1.0819672131147542, "no_speech_prob": 0.0, "words": [{"start": 5568.87, "end": 5569.31, "word": "يبقى", "probability": 0.92041015625}, {"start": 5569.31, "end": 5569.83, "word": " للمرة", "probability": 0.9733072916666666}, {"start": 5569.83, "end": 5570.65, "word": " القادمة", "probability": 0.9928385416666666}, {"start": 5570.65, "end": 5571.15, "word": " ان", "probability": 0.650390625}, {"start": 5571.15, "end": 5571.47, "word": " شاء", "probability": 0.959716796875}, {"start": 5571.47, "end": 5571.83, "word": " الله", "probability": 0.97265625}, {"start": 5571.83, "end": 5572.53, "word": " ابنكم", "probability": 0.7210286458333334}], "temperature": 1.0}], "language": "ar", "language_probability": 1.0, "duration": 5573.4855, "duration_after_vad": 5227.4128437500185}
\ No newline at end of file
diff --git a/PL9fwy3NUQKwa8ZDfSFGn6H8xVFLzqmCZC/PY1U7lboILA_raw.srt b/PL9fwy3NUQKwa8ZDfSFGn6H8xVFLzqmCZC/PY1U7lboILA_raw.srt
new file mode 100644
index 0000000000000000000000000000000000000000..2414f2a9e6902c33dbeba06bf104cf559a10deb6
--- /dev/null
+++ b/PL9fwy3NUQKwa8ZDfSFGn6H8xVFLzqmCZC/PY1U7lboILA_raw.srt
@@ -0,0 +1,3428 @@
+1
+00:00:09,580 --> 00:00:15,820
+بسم الله الرحمن الرحيم المرة الماضية كنا بنتحدث في
+
+2
+00:00:15,820 --> 00:00:20,460
+chapter 3 عن ال second order differential equation
+
+3
+00:00:20,460 --> 00:00:25,060
+وجزّانها إلى جزئين ال homogeneous linear
+
+4
+00:00:25,060 --> 00:00:29,160
+differential equationوالـ Non-homogeneous linear
+
+5
+00:00:29,160 --> 00:00:33,720
+differential equation ودرسنا التنتين كل واحدة فيهم
+
+6
+00:00:33,720 --> 00:00:38,320
+على حده وعرفنا ان حل الـ Non-homogeneous يعتمد على
+
+7
+00:00:38,320 --> 00:00:41,240
+حال مياه الـ homogeneous differential equation
+
+8
+00:00:41,240 --> 00:00:46,220
+Chapter 4 اللي بين أدينا هو تعميم لـ Chapter 3
+
+9
+00:00:46,220 --> 00:00:50,880
+يعني مافيش فيه معلومات جديدة ولذلك سنحاول أن نختصر
+
+10
+00:00:50,880 --> 00:00:55,540
+بقدر الإمكانمابنعش نمشي بالتفصيل اللي مشينا فيه في
+
+11
+00:00:55,540 --> 00:01:01,340
+chapter 3 وإنما سنختصر بحيث يكون نأتي بالزبدة أو
+
+12
+00:01:01,340 --> 00:01:05,660
+الفائدة من هذا ال chapterلذلك شرط الرابعة بيقول لي
+
+13
+00:01:05,660 --> 00:01:09,440
+higher order linear differential equation يعني
+
+14
+00:01:09,440 --> 00:01:14,300
+المعادلة التفاضل الخطية من الرتب العليا او من
+
+15
+00:01:14,300 --> 00:01:18,660
+الرتب العليا يعني ايش؟يعني رتبة التالتة الرابعة
+
+16
+00:01:18,660 --> 00:01:23,620
+الخامسة السادسة السابعة التمنة الاخرين يعني انسي
+
+17
+00:01:23,620 --> 00:01:27,840
+الاتنين بعد اتنين فما فوق، من الرتبة التالتة فما
+
+18
+00:01:27,840 --> 00:01:32,790
+فوقأول section يعتبر إزاي مقدمة لهذا الشرطر يعني
+
+19
+00:01:32,790 --> 00:01:37,750
+بيجيبلي بعض المعلومات الأساسية اللازمة للدراسة
+
+20
+00:01:37,750 --> 00:01:42,690
+فيما بعد فجالي ال general theory النظرية العامة of
+
+21
+00:01:42,690 --> 00:01:45,250
+the nth order linear differential equation
+
+22
+00:01:45,250 --> 00:01:50,710
+للمعادلة التفاضلية من الرتبة النونية nth order
+
+23
+00:01:50,710 --> 00:01:56,900
+يبقى الرتبة النونية رتبة الرقم nان قداش الله علم
+
+24
+00:01:56,900 --> 00:02:04,500
+ثلاثة ماشي اربعة ماشي خمسة ماشي الى اخره الان نجي
+
+25
+00:02:04,500 --> 00:02:09,240
+لأول تعريف عند هنا بيقولي an nth order linear
+
+26
+00:02:09,240 --> 00:02:12,240
+differential equation is an equation in the form
+
+27
+00:02:12,740 --> 00:02:18,880
+يبقى الشكل العام لهذه المعادلة y to the مش أُس in
+
+28
+00:02:18,880 --> 00:02:22,920
+هذه المعادلة لأ y to the derivative in يعني هذا
+
+29
+00:02:22,920 --> 00:02:27,260
+رمز يدل على المشتقة نونية لما هطلق رقم وبين جثين
+
+30
+00:02:27,260 --> 00:02:31,800
+يبقى هذا معناته مشتقة لكن مافيش جثين يبقى هذا
+
+31
+00:02:31,800 --> 00:02:37,120
+يعتبر أُس فباجي بقول هذه y to the derivative in
+
+32
+00:02:37,120 --> 00:02:43,020
+زائد function في T P1 of Tفي y to the derivative
+
+33
+00:02:43,020 --> 00:02:48,180
+of n minus one زائد P2 of t برضه function of y to
+
+34
+00:02:48,180 --> 00:02:51,840
+the derivative of n minus two زائد زائد زائد زائد
+
+35
+00:02:51,840 --> 00:02:58,260
+زائد زائد زائد
+
+36
+00:02:58,260 --> 00:02:58,880
+زائد زائد زائد زائد زائد زائد زائد زائد زائد زائد
+
+37
+00:02:58,880 --> 00:02:58,900
+زائد زائد زائد زائد زائد زائد زائد زائد زائد زائد
+
+38
+00:02:58,900 --> 00:02:59,000
+زائد زائد زائد زائد زائد زائد زائد زائد زائد زائد
+
+39
+00:02:59,000 --> 00:02:59,220
+زائد زائد زائد زائد زائد زائد زائد زائد زائد زائد
+
+40
+00:02:59,220 --> 00:02:59,300
+زائد زائد زائد زائد زائد زائد زائد زائد زائد زائد
+
+41
+00:02:59,300 --> 00:03:03,290
+زائد زائد زائد زائد زائد زائد زائد زائدبدى يسوى
+
+42
+00:03:03,290 --> 00:03:08,970
+مين؟ G of T يبقى هذه المعادلة اللى سافين بالتسلسل
+
+43
+00:03:08,970 --> 00:03:13,790
+بنزل مشتقة نونية الناقص واحد الناقص اتنين الناقص
+
+44
+00:03:13,790 --> 00:03:17,430
+ثلاثة لغاية نص المشتقة التانية المشتقة الاولى Y
+
+45
+00:03:17,430 --> 00:03:24,190
+بدون مشتقة يسوى مين؟ يسوى G of T بقولش هنا دراسة
+
+46
+00:03:24,190 --> 00:03:29,970
+المعادلة واحد تشبه دراسة من ال second order linear
+
+47
+00:03:29,970 --> 00:03:34,820
+differential equationيعني دراسة المعادلة دي تماما
+
+48
+00:03:34,820 --> 00:03:39,300
+مثل دراسة من دراسة اللي هو second order
+
+49
+00:03:39,300 --> 00:03:43,830
+differential equation ذاتي بدنا نذكر تذكيرفبجي
+
+50
+00:03:43,830 --> 00:03:48,850
+بقول لو كان y1 و y2 و y3 لغاية yn are linearly
+
+51
+00:03:48,850 --> 00:03:52,750
+independent solutions of the homogeneous
+
+52
+00:03:52,750 --> 00:03:56,350
+differential equation اللي عندنا دي بجي الشكل ال
+
+53
+00:03:56,350 --> 00:04:01,610
+general solution لهذه المعادلة كنا بنديله رمز c في
+
+54
+00:04:01,610 --> 00:04:05,490
+ال second دولة بجي انا جينا نقول yc تساوي c1 و y1
+
+55
+00:04:05,490 --> 00:04:12,720
+زي c2 و y2 هنا عند انثمن ال solutions يبقى باجي
+
+56
+00:04:12,720 --> 00:04:18,280
+يقول c1 y1 زي ال c2 y2 ويظل ماشي لغاية cn yn و ال
+
+57
+00:04:18,280 --> 00:04:23,520
+c هات هدول كله مالهم ثابت تمام يبقى لو عندي
+
+58
+00:04:23,520 --> 00:04:27,160
+linearly independent solutions بهذا الشكل بدي يكون
+
+59
+00:04:27,160 --> 00:04:31,360
+ال fundamental set of solutions او ال general
+
+60
+00:04:31,360 --> 00:04:36,280
+solution للمعادل عالمين على الشكل اللي عندنا هذا
+
+61
+00:04:36,280 --> 00:04:42,950
+بعد احتياط الأخرىلو أخدت رونسك لمين لكل الحلول هذه
+
+62
+00:04:42,950 --> 00:04:47,250
+as a function of T كتبته بالشكل هذا او بالشكل هذا
+
+63
+00:04:47,250 --> 00:04:51,630
+و لاجئت ان رونسك الهدف معله لا يساوي zero
+
+64
+00:04:51,630 --> 00:04:56,170
+اتوماتيكي يبقى ال general solution نفس اللي عندنا
+
+65
+00:04:56,170 --> 00:04:59,390
+هناك اللي هو الشكل اللي عندنا هذا و طبعا في ال
+
+66
+00:04:59,390 --> 00:05:06,020
+second order قلنا في اربع شغلات بتكافئبعض، مجموعة
+
+67
+00:05:06,020 --> 00:05:09,360
+الحل اللي بتكونولي fundamental set هنا بقول مجموعة
+
+68
+00:05:09,360 --> 00:05:14,400
+الحلول بتكونولي fundamental set of solutions او
+
+69
+00:05:14,400 --> 00:05:17,820
+بيجيبولي ال general solution او الرنس كان عنده
+
+70
+00:05:17,820 --> 00:05:22,500
+نقطة يساوي لا يساوي zero او الرنس كان على كل ال
+
+71
+00:05:22,500 --> 00:05:27,740
+interval ماله لا يساوي zero يبقى هيه يبقى بيكون
+
+72
+00:05:27,740 --> 00:05:32,460
+شكل الحل على الصيغة اللي عندنا هذهأخدنا كمان في
+
+73
+00:05:32,460 --> 00:05:39,520
+حالة second order إيجاد صيغة أخرى لقيمة
+
+74
+00:05:39,520 --> 00:05:43,580
+الرونسكين باستخدام able theorem able theorem في
+
+75
+00:05:43,580 --> 00:05:49,920
+حالة مجموعة من الحلول بنفس الطريقة باجي بقول ال
+
+76
+00:05:49,920 --> 00:05:53,620
+رونسكين تبع ال Y1 لغاية ال YN as a function of T
+
+77
+00:05:53,620 --> 00:06:00,160
+هو كونسان في أسناق استكامل P1 of T DT مين هو ال P1
+
+78
+00:06:00,160 --> 00:06:06,590
+of T؟يبقى هو المعامل تبع y to the derivative n
+
+79
+00:06:06,590 --> 00:06:11,170
+minus one و بشرط أن يكون معامل y to the derivative
+
+80
+00:06:11,170 --> 00:06:16,410
+n هو main يعني لو ماكانش وعصاهم بدي أجسم على هذا
+
+81
+00:06:16,410 --> 00:06:20,490
+المعامل وهذا خليه واعد صحيح وبالتالي P1 of t بتاخد
+
+82
+00:06:20,490 --> 00:06:24,710
+شكل غير الشكل اللي ظهرت فيه لأول مرة يبقى بناء
+
+83
+00:06:24,710 --> 00:06:29,450
+عليه ههه بدي يكون P1 هو المعامل تبع y to the
+
+84
+00:06:29,450 --> 00:06:33,770
+derivative n minus oneوفي نفس الوقت المعامل تبع yn
+
+85
+00:06:33,770 --> 00:06:39,330
+يجب أن يكون واحد صحيح بعد ذلك هذه نظرية أخدناها
+
+86
+00:06:39,330 --> 00:06:42,570
+كمان في second order أنه لو عند ال particular
+
+87
+00:06:42,570 --> 00:06:45,750
+solution لل non homogeneous differential equation
+
+88
+00:06:45,750 --> 00:06:49,490
+وعند ال general solution لل homogeneous
+
+89
+00:06:49,490 --> 00:06:53,270
+differential equation أجمع الأثنين بيعطيني ال
+
+90
+00:06:53,270 --> 00:06:57,580
+general solution أمامللـ second order linear
+
+91
+00:06:57,580 --> 00:07:00,300
+differential equation هذه في حالة ال second نفس
+
+92
+00:07:00,300 --> 00:07:04,740
+الكلام في حالة ال nth order فلو كان capital YT هو
+
+93
+00:07:04,740 --> 00:07:08,640
+ال particular solution لل differential equation
+
+94
+00:07:08,640 --> 00:07:14,420
+one وكان YC اللي حاكين عليه هذا هو ال general
+
+95
+00:07:14,420 --> 00:07:17,580
+solution لل homogeneous differential equation إذا
+
+96
+00:07:17,580 --> 00:07:23,670
+لو جمعنا الاتنين هدولبيعطيني ال general solution
+
+97
+00:07:23,670 --> 00:07:30,830
+لمن؟ للمعادلة رقم واحد يعني كإن Y بده يساوي C1Y1
+
+98
+00:07:30,830 --> 00:07:39,810
+C2Y2 زائد CNYN زائد ال particular solution capital
+
+99
+00:07:39,810 --> 00:07:47,010
+Y of Tأكتر منها الكلمتين اللي قدامك اللي أحب ناش
+
+100
+00:07:47,010 --> 00:07:51,750
+من الجزء النظري التابع هذا ال section حد بتحب تسأل
+
+101
+00:07:51,750 --> 00:07:59,270
+ليه سؤال هنا قبل أن ندخل إلى الأمثلة حد
+
+102
+00:07:59,270 --> 00:08:06,130
+بتحب تسأل ليه سؤال طيب
+
+103
+00:08:06,130 --> 00:08:10,370
+نأتي إلى الأمثلة هذه هي هي ورا
+
+104
+00:08:13,470 --> 00:08:18,730
+اللي ما كتبتش اسمها يا بنات تكتب اسمها يبقى بإننا
+
+105
+00:08:18,730 --> 00:08:27,730
+نيجي للأمثلة examples المثال
+
+106
+00:08:27,730 --> 00:08:37,190
+الأول بيقول determine the intervals determine the
+
+107
+00:08:37,190 --> 00:08:40,030
+intervals
+
+108
+00:08:43,280 --> 00:08:51,500
+in which solutions
+
+109
+00:08:51,500 --> 00:08:54,920
+are
+
+110
+00:08:54,920 --> 00:09:01,440
+sure to exist
+
+111
+00:09:09,890 --> 00:09:18,990
+بيقول لي X ناقص واحد Y to the derivative four زائد
+
+112
+00:09:18,990 --> 00:09:26,210
+X زائد واحد Y to the derivative two المشتقة
+
+113
+00:09:26,210 --> 00:09:35,670
+الثانية زائد تان ال X كلها في Y بده ساوي زيرو
+
+114
+00:09:59,380 --> 00:10:04,980
+سؤال مرة تانية بيقول لحدد الفترات اللي الحل عليها
+
+115
+00:10:04,980 --> 00:10:10,580
+sure بتأكيد to exist يعني موجود على هذه الفترة
+
+116
+00:10:10,580 --> 00:10:14,460
+احنا لما كنا نقول المعاملة هو رقم واحد بجي انا
+
+117
+00:10:14,460 --> 00:10:19,800
+اشترق ان المعاملات هي دوال متاصلة، مظبوط؟ اذا انا
+
+118
+00:10:19,800 --> 00:10:24,740
+بدي اشوف شكل المعاملة و اكتشف ان هذه دوال متاصلة
+
+119
+00:10:24,740 --> 00:10:30,720
+فبجي الحل كالتالي solutionيبقى المعادلة اللى عندى
+
+120
+00:10:30,720 --> 00:10:38,920
+بدى اكتبها بشكل جديد y to the derivative 4 زائد x
+
+121
+00:10:38,920 --> 00:10:45,760
+زائد 1 على x ناقص 1 في y to the derivative 2
+
+122
+00:10:45,760 --> 00:10:54,300
+المشتقة الثانية زائد 10 ال x على مين على x ناقص 1
+
+123
+00:10:54,300 --> 00:11:05,070
+كله في y يساوي 0الاول لو جيت لل P1 of T P1 of X
+
+124
+00:11:05,070 --> 00:11:12,310
+اليمين يا بنات X زائد واحد على X ناقص واحد ال
+
+125
+00:11:12,310 --> 00:11:17,990
+discontinuity حصل وين؟ عند الواحد يبقى هذه is
+
+126
+00:11:17,990 --> 00:11:22,270
+discontinuous
+
+127
+00:11:22,270 --> 00:11:32,440
+at X يساوي واحد تمام؟نجي التانية اللي بعديها P2 of
+
+128
+00:11:32,440 --> 00:11:40,400
+X اللي هي تان ال X على مين؟ على X is discontinuous
+
+129
+00:11:40,400 --> 00:11:47,780
+at X ساوين ال discontinuity حصل وين؟ عند الواحد بس
+
+130
+00:11:47,780 --> 00:11:53,020
+بجي للتان ال X و اكتشف ال discontinuity للتان X
+
+131
+00:11:53,020 --> 00:11:58,820
+عند مين؟ باية اتنين وسلب باية اتنينتلاتة باية على
+
+132
+00:11:58,820 --> 00:12:02,040
+اتنين سالب تلاتة باية على اتنين خمسة باية على
+
+133
+00:12:02,040 --> 00:12:06,580
+اتنين سالب خمسة باية على اتنين و هكذا نظل ماشيين
+
+134
+00:12:06,580 --> 00:12:16,780
+يبقى و زائد او ناقص N باية على اتنين و ال N is odd
+
+135
+00:12:18,400 --> 00:12:21,980
+يعني بايع اتنين ثلاثة بايع اتنين خمسة بايع اتنين
+
+136
+00:12:21,980 --> 00:12:26,520
+سبعة بايع اتنين الى اخر يوم تمام يبقى تعالوا لو
+
+137
+00:12:26,520 --> 00:12:32,440
+حطيت خط احدد هذه الفترات لو جيت قلت هذا ال real
+
+138
+00:12:32,440 --> 00:12:42,620
+life عندك هنا بتيجي له سالب خمسة سالب خمسة by على
+
+139
+00:12:42,620 --> 00:12:49,230
+اتنينبعدها بدها تجيكي هنا سالب تلاتة by على اتنين
+
+140
+00:12:49,230 --> 00:12:56,290
+هنا بدها تجيكي سالب by على اتنين هنا بدها تجيكي
+
+141
+00:12:56,290 --> 00:13:03,530
+موجب by على اتنين هنا موجب تلاتة by على اتنين ده
+
+142
+00:13:03,530 --> 00:13:10,850
+الماشيين موجب خمسة by على اتنين and so on نيجي
+
+143
+00:13:10,850 --> 00:13:15,850
+للواحد نشوف وين موقع الواحدبدي اجي الواحد ال by
+
+144
+00:13:15,850 --> 00:13:20,630
+قداش هي هنا تلاتة صحيح و اربتاشر من مية مظبوط لو
+
+145
+00:13:20,630 --> 00:13:26,130
+جسمتها على اتنين بطلع واحد و نص و كمان كسر بسيط
+
+146
+00:13:26,130 --> 00:13:31,850
+يعني تقريبا واحد و نص مظبوط واحد و نص يبقى ال by
+
+147
+00:13:31,850 --> 00:13:37,010
+على اتنين هدى قداش واحد و نص يبقى الواحد بدي اجي
+
+148
+00:13:37,010 --> 00:13:43,350
+وين جابلها يبقى الواحد ممكن يجي هنا هذا الواحديبقى
+
+149
+00:13:43,350 --> 00:13:47,070
+النقاط اللي احنا راسمينهم دول هما نقاط ال
+
+150
+00:13:47,070 --> 00:13:52,210
+discontinuity لل functions P1 و P2 إذا الدوال اللي
+
+151
+00:13:52,210 --> 00:13:56,890
+عندى هذا الدوال متصل على كل real line ما عدمين
+
+152
+00:13:56,890 --> 00:14:04,050
+الخطوط اللي عندنا يبقى باجي بقوله هنا the solution
+
+153
+00:14:04,050 --> 00:14:17,000
+exists on theintervals على الفترات من هنا جايين من
+
+154
+00:14:17,000 --> 00:14:23,620
+سلب infinity وصلنا لمين؟ لأ سالب خمسة by على اتنين
+
+155
+00:14:23,620 --> 00:14:30,300
+و سالب تلاتة by على اتنين و بعدها سالب تلاتة by
+
+156
+00:14:30,300 --> 00:14:37,740
+على اتنين و سالب by على اتنين و بعدها سالب by على
+
+157
+00:14:37,740 --> 00:14:44,360
+اتنين أجانب الطريق من؟عنده بدي اوغف يبقى وا واحد
+
+158
+00:14:44,360 --> 00:14:52,060
+وعندك كمان واحد ومين و باي على اتنين ونظل ماشيين
+
+159
+00:14:52,060 --> 00:14:59,400
+باي على اتنين و تلاتة باي على اتنين تلاتة باي على
+
+160
+00:14:59,400 --> 00:15:05,080
+اتنين و خمسة باي على اتنين و لسه ماشيين الى ما شاء
+
+161
+00:15:05,080 --> 00:15:11,020
+الله تمام؟ يبقى هذا كلها مين؟هذا كله ال interval
+
+162
+00:15:11,020 --> 00:15:15,820
+اللي اللي اللي ده اللي اللي اللي اللي اللي اللي
+
+163
+00:15:15,820 --> 00:15:16,160
+اللي اللي اللي اللي اللي اللي اللي اللي اللي اللي
+
+164
+00:15:16,160 --> 00:15:17,000
+اللي اللي اللي اللي اللي اللي اللي اللي اللي اللي
+
+165
+00:15:17,000 --> 00:15:17,680
+اللي اللي اللي اللي اللي اللي اللي اللي اللي اللي
+
+166
+00:15:17,680 --> 00:15:17,720
+اللي اللي اللي اللي اللي اللي اللي اللي اللي اللي
+
+167
+00:15:17,720 --> 00:15:17,880
+اللي اللي اللي اللي اللي اللي اللي اللي اللي اللي
+
+168
+00:15:17,880 --> 00:15:17,940
+اللي اللي اللي اللي اللي اللي اللي اللي اللي اللي
+
+169
+00:15:17,940 --> 00:15:22,840
+اللي اللي اللي اللي اللي اللي اللي اللي اللي اللي
+
+170
+00:15:22,840 --> 00:15:27,320
+اللي اللي
+
+171
+00:15:27,320 --> 00:15:27,320
+اللي اللي اللي اللي اللي اللي اللي اللي اللي اللي
+
+172
+00:15:27,320 --> 00:15:27,340
+اللي اللي اللي اللي اللي اللي اللي اللي اللي اللي
+
+173
+00:15:27,340 --> 00:15:36,780
+اللي اللي اللي اللي اللي اللي
+
+174
+00:15:36,780 --> 00:15:48,020
+الليسؤال التاني بيقول ما يأتي determine whether
+
+175
+00:15:48,020 --> 00:15:51,720
+the
+
+176
+00:15:51,720 --> 00:15:58,260
+following set determine
+
+177
+00:15:58,260 --> 00:16:06,540
+the following set of functions are
+
+178
+00:16:07,440 --> 00:16:16,700
+Linearly Dependent او Linearly Independent هذا
+
+179
+00:16:16,700 --> 00:16:24,820
+المطلب الأول المطلب التاني if they are linearly
+
+180
+00:16:24,820 --> 00:16:29,500
+dependent find a linear relation
+
+181
+00:16:39,860 --> 00:16:50,280
+reinheralation among them
+
+182
+00:16:50,280 --> 00:16:54,160
+نمر
+
+183
+00:16:54,160 --> 00:17:03,860
+ايه سؤال سبعة من الكتاب بيقول F1 of T بدي ساوي
+
+184
+00:17:03,860 --> 00:17:11,500
+اتنين T ناقص تلاتةوال F2 as a function of T بدر
+
+185
+00:17:11,500 --> 00:17:22,440
+ساوي T ترابيع زائد واحد وال F3 of T بدر
+
+186
+00:17:22,440 --> 00:17:28,340
+ساوي اتنين T ترابيع ناقص T
+
+187
+00:17:37,690 --> 00:17:42,570
+نرجع لأسئلتنا مرة تانية يقول دي determine whether
+
+188
+00:17:42,570 --> 00:17:47,570
+the following set
+
+189
+00:17:47,570 --> 00:17:53,870
+of functions
+
+190
+00:17:53,870 --> 00:17:58,370
+are linearly dependent or linearly independent
+
+191
+00:17:58,370 --> 00:18:02,670
+يعني مجموعة الدول التالية شوفوا هل هي linearly
+
+192
+00:18:02,670 --> 00:18:07,690
+dependent ولا linearly independentلو كانت linearly
+
+193
+00:18:07,690 --> 00:18:13,550
+dependent find a linear relation هتيلي علاقة خاطية
+
+194
+00:18:13,550 --> 00:18:18,070
+among them يعني بتربط هذه الدول التلاتة مع بعض
+
+195
+00:18:18,070 --> 00:18:23,730
+بنذكركم بجينا نقول ان لو في عندي مجموعة من ال
+
+196
+00:18:23,730 --> 00:18:28,930
+functions تنتين تلاتة أربعة خمسة جد ما يكونوا لو
+
+197
+00:18:28,930 --> 00:18:33,130
+ضربت كل واحدة فيهم في constant وقلت يساوي صفر
+
+198
+00:18:33,650 --> 00:18:38,250
+ولاقيته ان C1 يساوي C2 يساوي C3 يساوي يساوي C ان
+
+199
+00:18:38,250 --> 00:18:45,050
+يساوي Zero بقول هدول linearly independent فالمقابل
+
+200
+00:18:45,050 --> 00:18:49,150
+لو أخدت رونسكين لهذه الدولة ولاقيته لا يساوي Zero
+
+201
+00:18:49,150 --> 00:18:54,150
+يبقى هدول كمان linearly independent النقطة الثانية
+
+202
+00:18:54,860 --> 00:18:59,480
+لو جيت للدوال اللي عندي هذه اها او constant في
+
+203
+00:18:59,480 --> 00:19:02,660
+الدالة الأولى زاد constant في التانية زاد constant
+
+204
+00:19:02,660 --> 00:19:06,520
+في التالتة زاد زاد constant في الأخرى يسوى zero
+
+205
+00:19:06,520 --> 00:19:11,680
+لجيت ال constants هدول ممنوع كلهم يسوى zero على
+
+206
+00:19:11,680 --> 00:19:16,720
+الأقل ولو لجيت واحد فيهم لا يسوى zero اذا هذه ال
+
+207
+00:19:16,720 --> 00:19:22,310
+function ما لها linearly dependent اولو أخدت لها
+
+208
+00:19:22,310 --> 00:19:25,530
+المحدد و طلع يساوي zero يبقى هدول linearly
+
+209
+00:19:25,530 --> 00:19:30,330
+dependent إذا إن كانت linearly dependent بدي يكون
+
+210
+00:19:30,330 --> 00:19:33,390
+constant في الأول زائد constant في التاني زائد
+
+211
+00:19:33,390 --> 00:19:36,830
+constant في الزائد زائد بدي يساوي zero بدوا إيه
+
+212
+00:19:36,830 --> 00:19:41,930
+شكل هذه العلاقة الخطية هذا هو المطلوب الثاني من
+
+213
+00:19:41,930 --> 00:19:46,830
+السؤال طيب نجي لنا النقطة الأولى مايعطيني هذه تلات
+
+214
+00:19:46,830 --> 00:19:51,240
+دوالوبدي اشوف هالها دي linearly dependent ولا
+
+215
+00:19:51,240 --> 00:19:56,060
+linearly independent اظن ابسط حاجة ناخد ال runoff
+
+216
+00:19:56,060 --> 00:20:04,060
+skin تبعها تمام يبقى انا لو جيت جولت solution بدي
+
+217
+00:20:04,060 --> 00:20:11,680
+اخد ال runoff skin تبع ال F1 و F2 و F3 كله as a
+
+218
+00:20:11,680 --> 00:20:17,040
+function of Tيبقى ماعليه إلا إيه إلا هات يحط
+
+219
+00:20:17,040 --> 00:20:22,120
+الدالة الأولى الدالة الأولى اللى هى لإتنين T ناقص
+
+220
+00:20:22,120 --> 00:20:29,140
+تلاتة الدالة التانية T تربيع زائد واحد الدالة
+
+221
+00:20:29,140 --> 00:20:36,480
+التالتة اللى هتنين T تربيع ناقص T الأن بدي أبدأ
+
+222
+00:20:36,480 --> 00:20:40,720
+أشتقكم توجبلي شوية في الجزء النظر يا بنات لما
+
+223
+00:20:40,720 --> 00:20:45,610
+كتبنا المحدد كتبنا الصف الأولصف التاني اللي هو
+
+224
+00:20:45,610 --> 00:20:50,050
+المشتقة الأولى صف التالت المشتقة الثانية ضالين
+
+225
+00:20:50,050 --> 00:20:55,010
+المشي لغاية المشتقة النونية ناقص واحد، مظبوط؟ هدول
+
+226
+00:20:55,010 --> 00:20:58,910
+تلت دوال يبقى بيضل أناشي لغاية ما وصل المشتقة رقم
+
+227
+00:20:58,910 --> 00:21:05,110
+اتنين أقل من ال order اللي عندنا بمقدار واحد يبقى
+
+228
+00:21:05,110 --> 00:21:09,790
+.. طب لو كانوا أربع دوال؟بدي أصير عندي مش محدد
+
+229
+00:21:09,790 --> 00:21:14,030
+بتلات صفوف و تلات أعمدة بدي
+
+230
+00:21:14,030 --> 00:21:20,930
+أصل لغاية المشتقة التالتة و هكذا فبدنا نشتق الدالة
+
+231
+00:21:20,930 --> 00:21:26,570
+الأولى بالنسبة ل T بقداش اتنين مشتقة هذه اتنين T
+
+232
+00:21:26,570 --> 00:21:32,590
+مشتقة هذه اربعة T ناقص واحد نشتق كمان مرة Zero
+
+233
+00:21:32,590 --> 00:21:39,880
+كمان مرة اتنين كمان مرة اربعبدنا نعرف قداش قيمة
+
+234
+00:21:39,880 --> 00:21:45,000
+هذا المحدد يبقى هذا الكلام يساوي بدا فكه باستخدام
+
+235
+00:21:45,000 --> 00:21:51,200
+عناصر الصف الأول والله أسهل لي باستخدام العمود
+
+236
+00:21:51,200 --> 00:21:57,700
+الأول ليش؟ لأن في صفر بفصلة التلت، مظبوط؟ أو
+
+237
+00:21:57,700 --> 00:22:02,160
+باستخدام الصف التالت، سيارة بتفرقش عنها، إذا خلينا
+
+238
+00:22:02,160 --> 00:22:08,020
+بالعمود الأوليبقى باجي بقوله اتنين تين ناقص تلاتة
+
+239
+00:22:08,020 --> 00:22:13,340
+فيه بروح نشطه بصفه و عموده لناسيه اتفك المحدد هنا
+
+240
+00:22:13,340 --> 00:22:17,020
+اللي بذكركم بنجي للعنصر اللي عنده اللي هو العنصر
+
+241
+00:22:17,020 --> 00:22:22,370
+هذاو بنشطه بصف و عمود و بضال مين عندى المحدد
+
+242
+00:22:22,370 --> 00:22:26,870
+الأصغر هذا بدى أفكه حاصل ضرب عناصر القطر الرئيسى
+
+243
+00:22:26,870 --> 00:22:32,570
+ناقص حاصل ضرب عناصر القطر الثانوي حاصل ضرب عناصر
+
+244
+00:22:32,570 --> 00:22:41,340
+القطر الرئيسى ب 4 ف 2 ب 8 Tماقص حاصل ضرب عناصر
+
+245
+00:22:41,340 --> 00:22:50,420
+القطر الثانوي يبقى ماقص تمانيته زائد اتنين خلصنا
+
+246
+00:22:50,420 --> 00:22:55,140
+منه بالدالي للعواصر اللي بعده حسب قاعدة الإشارات
+
+247
+00:22:55,140 --> 00:23:05,090
+شرط هذا مالها سالب يبقى سالب اتنين في اشط بصفههو
+
+248
+00:23:05,090 --> 00:23:10,530
+عموده بيبقى المحدد هذا أربعة في T تربية وزايد واحد
+
+249
+00:23:10,530 --> 00:23:18,650
+يبقى أربعة T تربية زايد أربعة ناقص أربعة T تربية
+
+250
+00:23:18,650 --> 00:23:26,470
+زايد اتنين T تمام اللي بعده زايد صفر في محدده اللي
+
+251
+00:23:26,470 --> 00:23:31,830
+هو الصفر طيب نجي نشوفها أظن هذه و هذه مع السلامة
+
+252
+00:23:32,540 --> 00:23:36,540
+طيب غير مصوف عليهم بيظل اتنين بيضربها في قداش
+
+253
+00:23:36,540 --> 00:23:43,160
+اربعة تي ناقص ستة بالداجة لان اربعة تي تربيع
+
+254
+00:23:43,160 --> 00:23:46,980
+بالموجة واربعة تي تربيع بالسالب دول شاندي الا
+
+255
+00:23:46,980 --> 00:23:51,660
+اربعة زائد اتنين تي بيضربها في قداش ناقص اتنين
+
+256
+00:23:51,660 --> 00:24:01,500
+يبقى ناقص تمانية ناقص اربعة تيماقص 4T وزاد 4T مع
+
+257
+00:24:01,500 --> 00:24:08,220
+السلام وطلع الجواب جدا ماقص 14 هذا الكلام ماله لا
+
+258
+00:24:08,220 --> 00:24:14,020
+يمكن أن يساوي 0 for all T مهما كان شكل ال T
+
+259
+00:24:35,720 --> 00:24:42,540
+خلصنا حل السؤال ولا لسه مطلوب تاني؟الله سبحانه و
+
+260
+00:24:42,540 --> 00:24:46,920
+تعالى بيقول لو كان linearly dependent بد ال linear
+
+261
+00:24:46,920 --> 00:24:50,580
+combination يبقى هدول linearly independent لو ضربت
+
+262
+00:24:50,580 --> 00:24:52,920
+constant في الأول و constant في التاني و constant
+
+263
+00:24:52,920 --> 00:24:57,860
+في التاني كله بده يقلع بأصفر السيطاني إذا أنا
+
+264
+00:24:57,860 --> 00:25:02,040
+مطلوب التاني الله ينطبق عالمين على هذا الجزء من
+
+265
+00:25:02,040 --> 00:25:07,380
+السؤال طيب فنروح لنمرى بيه اللي هو السؤال تمانية
+
+266
+00:25:07,380 --> 00:25:16,380
+من الكتاب وراه مباشرةبقول ايش F1 of T بده يساوي
+
+267
+00:25:16,380 --> 00:25:26,460
+اتنين T ناقص تلاتة نفس الدالة اللي فوق وال F2 of T
+
+268
+00:25:26,460 --> 00:25:34,440
+بده يساوي اتنين T ترابيع زائد واحد اتنين T ترابيع
+
+269
+00:25:34,440 --> 00:25:45,280
+زائد واحد وال F3 of Tبدو يساوي تلاتة T تربيع زائد
+
+270
+00:25:45,280 --> 00:25:51,860
+T الان قال لي شوف لي هدول linearly dependent و لا
+
+271
+00:25:51,860 --> 00:25:56,280
+linearly independent احنا هدول طلعنا مالهم
+
+272
+00:25:56,280 --> 00:26:01,000
+linearly independent يعني نتوقع هدول كمان يطلعوا
+
+273
+00:26:01,000 --> 00:26:07,690
+زيهم معناته انا قاعد بكرريبقى .. يبقى .. بمعناته
+
+274
+00:26:07,690 --> 00:26:10,970
+احنا قاعدين بنكرر الرسالة، يبقى المتوقع ان يكون
+
+275
+00:26:10,970 --> 00:26:16,010
+ماله linearly dependent، بس ماينفعش هيك إلا أروح
+
+276
+00:26:16,010 --> 00:26:22,150
+أثبت هذا الكلامبإمكاني أثبت ذلك بأكثر من طريقة
+
+277
+00:26:22,150 --> 00:26:26,890
+إحدى الطرق زي اللي فات أجيب ال runoff skin تبعه و
+
+278
+00:26:26,890 --> 00:26:33,170
+أجيب يساوي 0 و يبقى linearly dependent طريقة تانية
+
+279
+00:26:33,170 --> 00:26:36,970
+أني أقول كون الصين في الأول و كون الصين في التاني
+
+280
+00:26:36,970 --> 00:26:39,710
+و كون الصين في التالت و أجمع و أساوي ب 0 و أروح
+
+281
+00:26:39,710 --> 00:26:44,210
+أجيب قيمسي واحد و سي اتنين و سي تلتة على الاقل
+
+282
+00:26:44,210 --> 00:26:50,490
+لازم نلاقي واحد فيهم لا يساوي ال zero طبعا طريقة
+
+283
+00:26:50,490 --> 00:26:55,030
+تالتة تعتمد على دقة النظر عندك تعالي تطلعي كويس
+
+284
+00:26:55,030 --> 00:27:01,150
+انا عندي تلت دوال ايش رايكش لو جيت هنا T تربيع و
+
+285
+00:27:01,150 --> 00:27:06,010
+هنا T و هنا constant هادف اش فيه اقل انه جاب ال T
+
+286
+00:27:06,010 --> 00:27:11,840
+تربيع و T و كأنه هاديبتعتمد على مين؟ على الاتنين،
+
+287
+00:27:11,840 --> 00:27:17,000
+بس بتعتمد كيف أنا مش عارف، كويس؟ بنقولك كيف تعتمد،
+
+288
+00:27:17,000 --> 00:27:24,460
+الآن لو جيت قولت أنا كتالي solution، بديش أسوي زي
+
+289
+00:27:24,460 --> 00:27:28,780
+قبل اللي هو المحدد اللي عندي، بدي أفكر بطريقة أخرى
+
+290
+00:27:29,190 --> 00:27:33,850
+باجي بقول هذه وهذه هذه فيها constant وهذه فيها
+
+291
+00:27:33,850 --> 00:27:39,790
+constant لكن هذه يبقى انا لو فكرت تخلص من ال two
+
+292
+00:27:39,790 --> 00:27:46,630
+constants ممكن تبقى foraged مظبوط بقولها كيف تتخلص
+
+293
+00:27:46,630 --> 00:27:52,700
+بقولها ده سالم تلاتة يبقى ممكن اضرب هذه في طولو
+
+294
+00:27:52,700 --> 00:27:56,700
+اجمع التنتين يا بضرب هذه في تلاتة و اجمع التنين
+
+295
+00:27:56,700 --> 00:28:01,580
+صحيح ولا لا بيكون الكون استنطار و يمكن اوصل لهذه
+
+296
+00:28:01,580 --> 00:28:06,020
+او جربتها او شغل من هذا القبيل طيب تعالوا نجرب
+
+297
+00:28:06,020 --> 00:28:14,970
+يبقى انا لو جيت اخد F1 of Tزائد تلاتة F2 of T
+
+298
+00:28:41,100 --> 00:28:50,540
+زائد تلاتة في اتنين بستة T تربيع زائد تلاتة بقول I
+
+299
+00:28:50,540 --> 00:28:56,560
+سالب تلاتة وزائد تلاتة مع السلامة هذا الكلام يساوي
+
+300
+00:28:56,560 --> 00:29:04,070
+بقى اللي عندي ستة T تربيع زائد اتنين Tفي عامل
+
+301
+00:29:04,070 --> 00:29:10,150
+مشترك فيبا بينهم اه فيلي اتنين يبجى اي اتنين و اي
+
+302
+00:29:10,150 --> 00:29:19,030
+تيتك اجداش اتنين هنا تلاتةتلاتة T تكيب زائد T
+
+303
+00:29:19,030 --> 00:29:25,350
+تلاتة T تربيع زائد T تلاتة T تربيع زائد T تلاتة T
+
+304
+00:29:25,350 --> 00:29:26,830
+تربيع زائد T تلاتة T تربيع زائد T تلاتة T تربيع
+
+305
+00:29:26,830 --> 00:29:26,830
+زائد T تلاتة T تربيع زائد T تلاتة T تربيع زائد T
+
+306
+00:29:26,830 --> 00:29:27,170
+تلاتة T تربيع زائد T تلاتة T تربيع زائد T تلاتة T
+
+307
+00:29:27,170 --> 00:29:27,170
+تربيع زائد T تلاتة T تربيع زائد T تلاتة T تربيع
+
+308
+00:29:27,170 --> 00:29:27,170
+زائد T تلاتة T تربيع زائد T تلاتة T تربيع زائد T
+
+309
+00:29:27,170 --> 00:29:32,470
+تلاتة T تربيع زائد T تلاتة T تربيع
+
+310
+00:29:32,470 --> 00:29:40,680
+زائد T تلاتصحيح ولا لأ؟ يبقى الصيارة عندي F1 of T
+
+311
+00:29:40,680 --> 00:29:49,660
+زائد تلاتة F2 of T مقصة اتنين F تلاتة of T يشبه
+
+312
+00:29:49,660 --> 00:29:57,940
+جداش الآن هل المعاملات هدول أصفر؟أصفار هدول؟ لأ
+
+313
+00:29:57,940 --> 00:30:02,900
+مدام مش أصفار يبقى هذا شو يعني ان هدول linearly
+
+314
+00:30:02,900 --> 00:30:07,900
+dependent وهيرناش اللي بديها يبقى انا لما اشتغلت
+
+315
+00:30:07,900 --> 00:30:12,380
+بالطريقة ده ستة أصفرين بحجر لو بدي أشغل زي قبل لسه
+
+316
+00:30:12,380 --> 00:30:14,840
+بدي أروح أحسب اللي هو ممكن و أثبت انهم linearly
+
+317
+00:30:14,840 --> 00:30:18,890
+dependentو بعد هيك أروح أدور على علاقة هذه لكن
+
+318
+00:30:18,890 --> 00:30:24,090
+شغلي بهذه الطريقة تفكيري ست عصفرين بحجر واحد و
+
+319
+00:30:24,090 --> 00:30:35,750
+بأقصر وقت ممكن يبقى هذا معناته ان ال F1 و F2 و F3
+
+320
+00:30:35,750 --> 00:30:40,350
+are linearly dependent because
+
+321
+00:30:43,270 --> 00:30:51,430
+ان الـC1 بده يساوي واحد وC2 بده يساوي تلاتة وC3
+
+322
+00:30:51,430 --> 00:31:00,810
+بده يساوي سالب اتنين يبقى not zeros ماهياش أصفات
+
+323
+00:31:00,810 --> 00:31:05,650
+يبقى هدول linearly dependent وهي ال relation اللى
+
+324
+00:31:05,650 --> 00:31:10,010
+بتربط المعادلات التلاتة هدول او الدول التلاتة من
+
+325
+00:31:10,010 --> 00:31:15,310
+مينمع بعضهم البعض طبق للمطلوب التاني المطلوب
+
+326
+00:31:15,310 --> 00:31:19,880
+التاني قال find a linear relation among themهتلرّي
+
+327
+00:31:19,880 --> 00:31:24,180
+لإن الناس بتربطهم إن كانوا linearly dependent
+
+328
+00:31:24,180 --> 00:31:30,240
+واضحة الصورة يبقى هذا اختصرنا فيها الحل بدل مثبت
+
+329
+00:31:30,240 --> 00:31:34,860
+انهم linearly dependent وروح أدور على هذه العلاقة
+
+330
+00:31:34,860 --> 00:31:38,120
+يبقى هذه العلاقة بيانات لإنهم linearly dependent
+
+331
+00:31:38,120 --> 00:31:43,920
+لإن الثوابت ماهياش أصفر اتنين جيبنا العلاقة اللي
+
+332
+00:31:43,920 --> 00:31:48,380
+عندناها دي وبالتالي صدنا أصفرين بحجر واحد
+
+333
+00:32:06,740 --> 00:32:12,340
+ناخد كمان مثال مثال
+
+334
+00:32:12,340 --> 00:32:22,020
+تلاتة سؤال سبعتاش من الكتاب بيقول show that بييني
+
+335
+00:32:22,020 --> 00:32:32,280
+أن رونسكين تبع الخمسة و ال sign تربيع T و
+
+336
+00:32:32,280 --> 00:32:42,140
+cosine اتنين Tبدو يساوي zero for all T كمان مطلوب
+
+337
+00:32:42,140 --> 00:32:53,420
+can you establish this
+
+338
+00:32:53,420 --> 00:32:58,440
+result هذه
+
+339
+00:32:58,440 --> 00:33:00,680
+النتيجة without
+
+340
+00:33:13,420 --> 00:33:17,180
+Evolution of the runnerskin
+
+341
+00:34:02,470 --> 00:34:06,810
+السؤال مرة ثانية السؤال زي ما انت شايفين مطلبين
+
+342
+00:34:07,460 --> 00:34:10,340
+المطلوب الأول بيقول بيبين لي أن ال neurons can
+
+343
+00:34:10,340 --> 00:34:14,200
+remain للثلاث دوال هذول الخمسة و ال sign تربيه T و
+
+344
+00:34:14,200 --> 00:34:18,220
+ال cosine اتنين T بده يساوي Zero يعني هذول
+
+345
+00:34:18,220 --> 00:34:25,420
+Linearly Dependent ما علينا بعدين المطلوب التاني
+
+346
+00:34:25,420 --> 00:34:30,520
+بيقول Can you establish بتقدر تثبتلي هذه النتيجة
+
+347
+00:34:30,520 --> 00:34:36,920
+without direct evolution بدون حسابات مباشرةيعني
+
+348
+00:34:36,920 --> 00:34:41,220
+بدون ما تحطها المحدد وتروح تحسب اللي هو ال one
+
+349
+00:34:41,220 --> 00:34:46,220
+skin هذول ام لا تقوله تعالى نشوف مطلوب مطلوب نمشي
+
+350
+00:34:46,220 --> 00:34:49,900
+step by step دي اول شئ بدأت بتقول ان هذا الكلام
+
+351
+00:34:49,900 --> 00:34:57,940
+يساوي zeroهذه الرنسة تتبع الخمسة والصين تربيتي
+
+352
+00:34:57,940 --> 00:35:04,480
+والكوصين اتنين تي تتبع المحدد هذه الخمسة وهذه
+
+353
+00:35:04,480 --> 00:35:12,960
+الصين تربيتي وهذه الكوصين اتنين تي نجيب الصفين
+
+354
+00:35:12,960 --> 00:35:20,000
+التانيات في المحدد مشتقة الخمسة بقداش؟ مشتقة الصين
+
+355
+00:35:20,000 --> 00:35:33,760
+تربيةحد بتعرف؟ كدهش؟ 2 sin t في cos t يعني 2 sin t
+
+356
+00:35:33,760 --> 00:35:40,160
+في cos t هذه يا بنات بقدر استبدلها ب sin 2t مش
+
+357
+00:35:40,160 --> 00:35:43,420
+هحصل ايه؟ هسلي في الحسابات لإن لو بده الشقة اللي
+
+358
+00:35:43,420 --> 00:35:47,730
+بقعد افضل مشتقة تحصل ضربده اللي تانه هذا بتكبر
+
+359
+00:35:47,730 --> 00:35:52,510
+الموضوع طيب هذا ال cosine بيسالب sin فيه اتنين
+
+360
+00:35:52,510 --> 00:35:59,250
+يبقى سالب اتنين sin اتنين T الصف اللي بعده مشتاقة
+
+361
+00:35:59,250 --> 00:36:06,170
+ال zero ب zero اتنين cosine اتنين T هذه كمان مرة
+
+362
+00:36:06,170 --> 00:36:13,960
+بسالب اربع cosine اتنين Tبدي أفك المحدد هذا و أشوف
+
+363
+00:36:13,960 --> 00:36:19,020
+كده شو ساوي بدي أفكه باستخدام عناصر العمود الأول
+
+364
+00:36:19,020 --> 00:36:24,820
+لإنه فيه أسفار بسهل الشغل يبقى باجي بقوله خمسة في
+
+365
+00:36:24,820 --> 00:36:33,460
+أشق بصفه و عموده بصير هذا اللي هو ناقص أربع sign
+
+366
+00:36:33,460 --> 00:36:42,600
+اتنين Tcos 2t هذا الرئيسي ناقص الثانوي ناقص مع
+
+367
+00:36:42,600 --> 00:36:52,200
+ناقص بيصير زائد اربع sin 2t cos 2t بعدها zero في
+
+368
+00:36:52,200 --> 00:36:56,720
+محدده ب zero zero في محدده ب zero يبقى زائد zero
+
+369
+00:36:56,720 --> 00:37:02,000
+زائد zero طلعيلي في ال term هذا و ال term هذا نفسه
+
+370
+00:37:02,000 --> 00:37:06,470
+كل واحد بإشارةمخالفة يبجي عن الجامعة بطلع كمان
+
+371
+00:37:06,470 --> 00:37:13,270
+جداش Zero في خمسة Zero زائد Zero زائد Zero بطلع
+
+372
+00:37:13,270 --> 00:37:16,110
+جداش اظن و هو المطلوب
+
+373
+00:37:23,120 --> 00:37:27,860
+خلص المطلوب الأول المطلوب التاني بيقول Can you
+
+374
+00:37:27,860 --> 00:37:32,940
+establish بتقدر تثبت أو توصل للنتيجة هذه بدون ما
+
+375
+00:37:32,940 --> 00:37:41,940
+تعمل حسابتك هذه أم لا الإجابة نعم موافقة يعني طيب
+
+376
+00:37:41,940 --> 00:37:42,980
+ماشي كيف؟
+
+377
+00:37:50,490 --> 00:37:54,210
+طيب انا بالحسابات بالنظر يعنى كيف يعنى؟انه دولة
+
+378
+00:37:54,210 --> 00:38:02,210
+ثالث اكيد العمل الاول حكيم زى يعنى ايوة حساب
+
+379
+00:38:02,210 --> 00:38:05,450
+مثلثات يا بنت الفكرة الموضوع حساب مثلثة اه الحين
+
+380
+00:38:05,450 --> 00:38:09,970
+قطعين اتنين فيه دلوقتي واحد ناقص اتنين واحد ناقص
+
+381
+00:38:09,970 --> 00:38:16,850
+تايتر بقىماشي موافق واحد ناقص sin تربية T يعني
+
+382
+00:38:16,850 --> 00:38:22,570
+باختصار sin تربية T يسوى نص في واحد ناقص cosine
+
+383
+00:38:22,570 --> 00:38:28,430
+اتنين T صح؟ وبالتالي ممكن اجيب خلق الخمسة في
+
+384
+00:38:28,430 --> 00:38:33,350
+الموضوع و ال cosine صارت موجودةيبقى بداجة للمطلوب
+
+385
+00:38:33,350 --> 00:38:40,710
+الثاني لو جيت قلت sin تربيع ال T يساوي النص في
+
+386
+00:38:40,710 --> 00:38:46,830
+واحد ناقص cosine اتنين T يبقى cosine اتنين T ظهرت
+
+387
+00:38:46,830 --> 00:38:51,530
+في العلاقة اللي عندها ذاك اللي مظهرت شمين الخامسة
+
+388
+00:38:51,530 --> 00:38:55,770
+طيب بدنا نخلق الخمسة في هذه العلاقة بقولك بسيطة
+
+389
+00:38:55,770 --> 00:39:05,190
+جداهذه عبارة عن نص ناقص نص cosine اتنين T طب النص
+
+390
+00:39:05,190 --> 00:39:11,130
+هذه مش عبارة عن خمسة على عشرة يعني خلجت الخمسة في
+
+391
+00:39:11,130 --> 00:39:19,930
+الموضوع يعني بقدر اقول هذه تساوي عشر في خمسة ناقص
+
+392
+00:39:19,930 --> 00:39:27,400
+نص cosine اتنين Tمظبوط؟ طب إيش رأيك أعملها معادلة
+
+393
+00:39:27,400 --> 00:39:35,700
+صفرية؟ يبقاش بصير عندي I sine تربية T زائد نص
+
+394
+00:39:35,700 --> 00:39:43,000
+كوسين اتنين T ناقص عشر في خمسة يساوي زرع
+
+395
+00:39:47,350 --> 00:39:54,890
+لحظة هي دالة وهي التانية وهي التالتة constant في
+
+396
+00:39:54,890 --> 00:39:58,950
+الأولى اللى هو واحد صحية constant في التانية
+
+397
+00:39:58,950 --> 00:40:03,170
+constant في التالتة اللى هو السالب عشور ساوة zero
+
+398
+00:40:03,720 --> 00:40:09,540
+الثابت هدول التلاتة ولا واحد فيهم zero يبقى معناه
+
+399
+00:40:09,540 --> 00:40:14,400
+هدول ان التلاتة دول linearly إذا الورس كنت باعهم ب
+
+400
+00:40:14,400 --> 00:40:19,570
+zeroصحيح ولا لأ؟ بدون ما نحسب الroneskin أبدا،
+
+401
+00:40:19,570 --> 00:40:29,590
+يبقى هذا معناه إن ال sign تربية T و cosine إتنين T
+
+402
+00:40:29,590 --> 00:40:38,170
+and الخمسة are linearly dependentلأنه التلاتة
+
+403
+00:40:38,170 --> 00:40:42,110
+ضربناهم في cononsense و ال cononsense هدول طوله
+
+404
+00:40:42,110 --> 00:40:44,410
+اللي هيوز سوى zero يبجى هدول ماله linearly
+
+405
+00:40:44,410 --> 00:40:48,430
+dependent مادام linearly dependent ايه ده نيرو
+
+406
+00:40:48,430 --> 00:40:54,110
+نيسكين تبعهم بقداش؟ ب zero يبجى هذا بده يعطيني ال
+
+407
+00:40:54,110 --> 00:41:01,210
+نيرو نيسكين تبع الخمسةوSin تربيه T وCos تربيه T
+
+408
+00:41:01,210 --> 00:41:06,130
+تربيه T تربيه T تربيه T تربيه T تربيه T تربيه T
+
+409
+00:41:06,130 --> 00:41:06,190
+تربيه T تربيه T تربيه T تربيه T تربيه T تربيه T
+
+410
+00:41:06,190 --> 00:41:07,190
+تربيه T تربيه T تربيه T تربيه T تربيه T تربيه T
+
+411
+00:41:07,190 --> 00:41:11,610
+تربيه T تربيه T تربيه T تربيه T تربيه T تربيه T
+
+412
+00:41:11,610 --> 00:41:16,950
+تربيه T تربيه T تربيه T تربيه
+
+413
+00:41:16,950 --> 00:41:24,350
+T تربيه T تربيه T تربيه T تربيه T تربيه T تربيه T
+
+414
+00:41:24,350 --> 00:41:24,350
+تربيه T تربيه T تربيه T تربيه T تربيه T تربيه T
+
+415
+00:41:24,350 --> 00:41:30,500
+تربيه T تربيكمان مثال مثال أربعة اللي هو سؤال
+
+416
+00:41:30,500 --> 00:41:39,740
+أربعة و عشرين من الكتاب بيقول use able's formula
+
+417
+00:41:39,740 --> 00:41:42,840
+able
+
+418
+00:41:42,840 --> 00:41:50,440
+to find the wrong skin to find the wrong skin
+
+419
+00:41:54,120 --> 00:42:02,120
+of a fundamental
+
+420
+00:42:02,120 --> 00:42:08,880
+set of
+
+421
+00:42:08,880 --> 00:42:16,240
+solutions of
+
+422
+00:42:16,240 --> 00:42:22,480
+the differential equation
+
+423
+00:42:24,230 --> 00:42:33,750
+تربيع y to the derivative 4 زائد ty triple prime
+
+424
+00:42:33,750 --> 00:42:41,830
+زائد y double prime ناقص 4y تساوي 0
+
+425
+00:42:54,140 --> 00:42:58,200
+سؤال مرة ثانية طبعا كتبنا ايه بال formula قبل قليل
+
+426
+00:42:58,200 --> 00:43:02,760
+في الجزء النظري؟ مظبوط في اخر الجزء النظري قال
+
+427
+00:43:02,760 --> 00:43:06,460
+يستخدم الصيغة اللي عندك كده مشان تجيب ال runescan
+
+428
+00:43:06,460 --> 00:43:09,400
+تبع ال fundamental set of solutions لماين؟
+
+429
+00:43:09,400 --> 00:43:14,550
+للمعادلة اللي عندنا؟ هل طلب مني إيجاد الحلول؟لو
+
+430
+00:43:14,550 --> 00:43:17,930
+طلبش جامعه لكن بقدر ايجي برونسكين تبع الحلول بدون
+
+431
+00:43:17,930 --> 00:43:23,190
+معرف ما هو شكل الحلول بواسطة able theorem يبقى
+
+432
+00:43:23,190 --> 00:43:28,370
+باجي بقوله لما كتبنا ال able لازم يكون المعامل تبع
+
+433
+00:43:28,370 --> 00:43:33,220
+وليو سبعة بجداشيبقى بده أجسب لمعادلة كلها علامين
+
+434
+00:43:33,220 --> 00:43:38,720
+على T تربية يبقى المعادلة بيصير على الشكل التالي
+
+435
+00:43:38,720 --> 00:43:46,560
+زائد واحد على T في Y triple prime زائد اللي هو
+
+436
+00:43:46,560 --> 00:43:52,380
+واحد على T تربية في ال Y double primeنقص اربعة
+
+437
+00:43:52,380 --> 00:43:58,240
+التي تربية في ال Y بده يساوي من Zero يبقى الرمز
+
+438
+00:43:58,240 --> 00:44:03,720
+كان اللي بدهيه as a function of T وعبارة عن
+
+439
+00:44:03,720 --> 00:44:12,190
+كونستانسي في اسناقس تكامل P1 of T دي Tمش كتبناها
+
+440
+00:44:12,190 --> 00:44:19,210
+قبل قليل؟ طيب تمام يبقى هذا الكلام بدي ساوي C في E
+
+441
+00:44:19,210 --> 00:44:27,860
+وصناعة استكامل P1 اللي هو واحد على T دي Tماعطانيش
+
+442
+00:44:27,860 --> 00:44:32,780
+شروط على T لكن لو اعطاني اكبر من ال zero ولا اقل
+
+443
+00:44:32,780 --> 00:44:38,080
+من ال zero كانت خلاصنا من من من ال absolute value
+
+444
+00:44:38,080 --> 00:44:46,240
+يبقى E أس ناقص لن absolute value لمين التي يبقى C
+
+445
+00:44:46,240 --> 00:44:53,290
+E أس لن absolute value ل T أس قداشوالسالب واحد
+
+446
+00:44:53,290 --> 00:45:00,910
+يبقى هذا C على absolute value لمين التي هذا شكل
+
+447
+00:45:00,910 --> 00:45:06,530
+الرونسكين اللي طلبه بدون معرفة من شكل الحلول اللي
+
+448
+00:45:06,530 --> 00:45:11,870
+عندي لمين لهذه المعادلة طيب الان انتهى ال section
+
+449
+00:45:11,870 --> 00:45:16,680
+الأول زى ما تشوفين section بسيطبدنا ال exercises
+
+450
+00:45:16,680 --> 00:45:26,820
+تبعات section 4-1 اللي هي من ال 1 ل 16 ال even و
+
+451
+00:45:26,820 --> 00:45:32,320
+من 21 لغاية كداش لغاية 24
+
+452
+00:45:44,770 --> 00:45:45,470
+مش عارف
+
+453
+00:46:03,420 --> 00:46:10,780
+بتقدر تحليها انت هذهك بالشكل هذا؟ لسه لم نتكلم في
+
+454
+00:46:10,780 --> 00:46:15,120
+الحل الحل ابتدا من section 4.2 لنهاية ال chapter
+
+455
+00:46:15,120 --> 00:46:19,700
+كيف هنحل المعادلة في أوضاعها المختلفة مش هطول عليك
+
+456
+00:46:19,700 --> 00:46:24,400
+هدخل فيها دوري الهيل مباشرة ان شاء الله يبقى بنجي
+
+457
+00:46:24,400 --> 00:46:30,280
+ل section 4.2 اللي هو ال homogeneous
+
+458
+00:46:35,080 --> 00:46:45,180
+المقارنة مع مقارنة مستمردة مع مقارنة
+
+459
+00:46:45,180 --> 00:46:57,400
+مستمردة اعتنوا
+
+460
+00:46:57,400 --> 00:46:57,400
+ان
+
+461
+00:47:04,560 --> 00:47:11,020
+Order Linear Homogeneous
+
+462
+00:47:11,020 --> 00:47:20,680
+Differential Equation لعل الشكل a0 y to the
+
+463
+00:47:20,680 --> 00:47:26,640
+derivative nزائد a1 y to the derivative of n minus
+
+464
+00:47:26,640 --> 00:47:32,520
+one زائد a2 y to the derivative of n minus two
+
+465
+00:47:32,520 --> 00:47:42,080
+زائد a n minus واحد y prime زائد a n y بده يساوي
+
+466
+00:47:42,080 --> 00:47:49,820
+zero وسميلي هذه المعادلة رقم واحد where
+
+467
+00:47:49,820 --> 00:48:04,470
+حيثالـ A0 والـ A1 والـ A2 والـ ANR real constants
+
+468
+00:48:04,470 --> 00:48:14,130
+ثوابت حقيقية الآن بدنا نحلها يبقى بدنا نجاوبها
+
+469
+00:48:14,130 --> 00:48:18,800
+سواء الأخت قبل قليل اللي قالت كيف بدنا نحلهابنقول
+
+470
+00:48:18,800 --> 00:48:23,380
+الحل كالتالية لحظة المعادلة هذه المعاملات ثوابت
+
+471
+00:48:23,380 --> 00:48:28,260
+لسه ما اتكلمناش المعادلة لو كان المعاملات متغيرات
+
+472
+00:48:28,260 --> 00:48:37,940
+يبقى بداجي اقوله let Y تساوي E أس RT be a solution
+
+473
+00:48:37,940 --> 00:48:47,420
+of the differential equation one then they
+
+474
+00:48:50,920 --> 00:48:58,640
+كاركترستيك اكويشن از ال a نود r to the power n
+
+475
+00:48:58,640 --> 00:49:00,380
+زائد a1
+
+476
+00:49:05,330 --> 00:49:13,150
+R⁻¹ R⁻¹ R⁻¹ R⁻¹ R⁻¹
+
+477
+00:49:13,150 --> 00:49:17,490
+R⁻¹ R⁻¹
+
+478
+00:49:17,490 --> 00:49:21,690
+R⁻¹
+
+479
+00:49:42,410 --> 00:49:49,370
+أول ما بدأنا هذا الشبتر هو تعميم لشبتر ثلاثة يبقى
+
+480
+00:49:49,370 --> 00:49:55,230
+هنا نعمم نفس المعلومات في شبتر ثلاثة كان عندي y
+
+481
+00:49:55,230 --> 00:50:00,010
+double prime زاد p of t في ال y prime زاد q of t
+
+482
+00:50:00,010 --> 00:50:05,250
+في ال y بدي ساويزيوم تلت ترماتهذا الحمد لله ترمت
+
+483
+00:50:05,250 --> 00:50:09,770
+كثيرا عشرة خمسة عشر عشرين جد ما يكونوا يبقى أنا
+
+484
+00:50:09,770 --> 00:50:13,770
+عندي معادلة بالشكل لأن هذا معادلة homogeneous
+
+485
+00:50:13,770 --> 00:50:18,930
+linear differential equation with constant
+
+486
+00:50:18,930 --> 00:50:26,370
+coefficients المعاملات هذول كلهم ثابتبتفرض Y تساوي
+
+487
+00:50:26,370 --> 00:50:32,690
+U RT كما كان في حالة ثانوية order بيه solution of
+
+488
+00:50:32,690 --> 00:50:35,210
+the differential equation one then the
+
+489
+00:50:35,210 --> 00:50:40,330
+characteristic equation على الشكل أن a not RN زائد
+
+490
+00:50:40,330 --> 00:50:46,990
+a1RN-1 زائد a2RN زائد زائد aN-1R زائد aN يساوي
+
+491
+00:50:46,990 --> 00:50:53,580
+zeroانتقلنا من معادلة تفاضلية إلى معادلة عادية
+
+492
+00:50:53,580 --> 00:50:58,800
+معادلة تفاضلية من الرتبة النونية إلى معادلة عادية
+
+493
+00:50:58,800 --> 00:51:04,440
+من الدرجة النونية وليست معادلة تفاضلية الآن هذه
+
+494
+00:51:04,440 --> 00:51:12,960
+المعادلة كم جذر لها يا بنات؟ كدوش يعني؟ معادلة من
+
+495
+00:51:12,960 --> 00:51:18,210
+الدرجة التانية كم جذر لها؟ من الدرجة التالتةالجذور
+
+496
+00:51:18,210 --> 00:51:23,810
+والرابع مضاجة نونية ان من الجذور يبقى هذه المعادلة
+
+497
+00:51:23,810 --> 00:51:29,650
+انها ان من الجذور تعالى قبل ما نكتب ولا كلمة نتكلم
+
+498
+00:51:29,650 --> 00:51:33,690
+كلام شافه وبعد هيك بنروح نكتب لو روحت حسبت هذه
+
+499
+00:51:33,690 --> 00:51:38,170
+الجذور يمكن يطلع كلهم جذور حقيقية أولى واحد زي
+
+500
+00:51:38,170 --> 00:51:48,060
+التاني صح؟ممكن يطلعوا جذور كلهم تخيلية وولا واحد
+
+501
+00:51:48,060 --> 00:51:57,340
+زي التاني صح؟ ممكن يطلعوا جذور مكررة وكلهم حقيقية
+
+502
+00:51:57,340 --> 00:52:05,480
+يمكن يطلعوا شوية حقيقية وشوية complex تمام؟ وإذا
+
+503
+00:52:05,480 --> 00:52:09,600
+كانوا complex بيكونوا complex conjugateطب انا
+
+504
+00:52:09,600 --> 00:52:13,980
+هتقولي معقول؟ بقولها اه معقول كيف؟ بقولها افترض ان
+
+505
+00:52:13,980 --> 00:52:20,020
+المعادلة دي كانت من الدرجة الخامسة طلعوا تلت جذور
+
+506
+00:52:20,020 --> 00:52:26,840
+حقيقية اتنين اش بطلعوا؟ تخيلين و مترافقين لان ال
+
+507
+00:52:26,840 --> 00:52:31,460
+complex دايما بطلع الجدر و المرافق له يعني لا يمكن
+
+508
+00:52:31,460 --> 00:52:38,030
+ان يكون في المعادلة تلت جذور complexصح؟ ولا
+
+509
+00:52:38,030 --> 00:52:41,370
+معادلة، سواء كان من الرتبة الزوجية أو من الرتبة
+
+510
+00:52:41,370 --> 00:52:45,870
+الفردية، سيان، مافيش تلاتة complex، فيه اتنين، صح؟
+
+511
+00:52:45,870 --> 00:52:49,730
+فيه اربعة ماشي، فيه ستة ماشي، فيه تمانية ماشية،
+
+512
+00:52:49,730 --> 00:52:54,610
+ممكن يكون ال complex repeated وممكن مايكونوش
+
+513
+00:52:54,610 --> 00:52:59,190
+repeated كمان، يبقى هذا كل ما يتعلق بالمعادلة اللي
+
+514
+00:52:59,190 --> 00:53:05,490
+عندنا هذه، تمام؟إذا هنختصر هذه في ثلاث حالات،
+
+515
+00:53:05,490 --> 00:53:11,150
+الجذور حقيقية ومختلفة، الجذور complex، وبعد ذلك
+
+516
+00:53:11,150 --> 00:53:17,810
+الجذور مكررة وسنفصلها إلى حقيقية مكررة أو تخيلية
+
+517
+00:53:17,810 --> 00:53:24,030
+ومكررةونشوف كيف تفجر صيغة الحل في كل حالة من
+
+518
+00:53:24,030 --> 00:53:28,530
+الحياة تلاني يعني إحنا قاعدين بنعمم ال second
+
+519
+00:53:28,530 --> 00:53:33,350
+order linear homogeneous differential equation مش
+
+520
+00:53:33,350 --> 00:53:36,810
+بنكتشف شغلات جديدة، لأ إحنا قاعدين بنعمم تعميم ليس
+
+521
+00:53:36,810 --> 00:53:45,370
+إلا يبقى باجي بقول هذه المعادلة اتنين this this
+
+522
+00:53:46,400 --> 00:53:54,640
+Equation has N roots هذي لها N من الجذور بدأ أخد
+
+523
+00:53:54,640 --> 00:54:02,120
+الحالة الأولى The roots are
+
+524
+00:54:02,120 --> 00:54:07,600
+real and
+
+525
+00:54:07,600 --> 00:54:10,660
+different
+
+526
+00:54:10,660 --> 00:54:26,420
+غير متساويتمام فهاجي بقول if the roots of equation
+
+527
+00:54:26,420 --> 00:54:41,080
+الاتنين are real and no two are
+
+528
+00:54:41,080 --> 00:54:42,860
+equal
+
+529
+00:54:47,340 --> 00:54:59,420
+أي أن R1 لا يمكن أن يسوى R2 لا يمكن أن يسوى R3 لا
+
+530
+00:54:59,420 --> 00:55:04,220
+يمكن أن يسوى RN ثم
+
+531
+00:55:29,680 --> 00:55:36,980
+يجب ان نقوم باستخدام الاسئلة
+
+532
+00:55:36,980 --> 00:55:38,760
+الواتس او الاسئلة الواتس او الاسئلة الواتس او
+
+533
+00:55:38,760 --> 00:55:38,880
+الاسئلة الواتس او الاسئلة الواتس او الاسئلة الواتس
+
+534
+00:55:38,880 --> 00:55:38,940
+او الاسئلة الواتس او الاسئلة الواتس او الاسئلة
+
+535
+00:55:38,940 --> 00:55:42,240
+الواتس او الاسئلة الواتسيبقى هذا الشكل الحل في هذه
+
+536
+00:55:42,240 --> 00:55:47,320
+الحالة كنا في حالة ال second order نقول C1EOSR1T
+
+537
+00:55:47,320 --> 00:55:55,020
+C2EOSR2T ونوقف N يبقى بدنا نوصل لمين لل N بدنا
+
+538
+00:55:55,020 --> 00:56:07,220
+نيجي للحالة الثانية the roots are
+
+539
+00:56:07,220 --> 00:56:18,100
+complex conjugateare complex conjugate يبقى
+
+540
+00:56:18,100 --> 00:56:30,300
+الجذور تخيّلية ومترافقة if the roots of
+
+541
+00:56:30,300 --> 00:56:36,300
+equation 2 are
+
+542
+00:56:38,810 --> 00:56:45,910
+complex conjugate تحيولية
+
+543
+00:56:45,910 --> 00:56:52,310
+مترافقة then these
+
+544
+00:56:52,310 --> 00:57:07,050
+roots هذه الجذور are in the form الشكل التاليlanda
+
+545
+00:57:07,050 --> 00:57:15,190
+one زائد او ناقص imu one وlanda
+
+546
+00:57:15,190 --> 00:57:23,410
+two زائد او ناقص imu two ونظل ماشين لعيط ما نوصل ل
+
+547
+00:57:23,410 --> 00:57:33,470
+landa s زائد او ناقص imu s يبقى
+
+548
+00:57:33,470 --> 00:57:38,820
+theوالخيار الأساسي
+
+549
+00:57:38,820 --> 00:57:44,160
+للإدارة
+
+550
+00:57:44,160 --> 00:57:48,440
+1S
+
+551
+00:57:48,440 --> 00:57:50,540
+Y
+
+552
+00:57:53,030 --> 00:58:10,310
+A أُس لاندا وان T في A1 Cos Mu 1T زائد B1 Sin Mu
+
+553
+00:58:10,310 --> 00:58:21,850
+1T زائد A أُس لاندا 2T في A2
+
+554
+00:58:27,300 --> 00:58:34,560
+بتو صين ميو تي تي زائد زائد
+
+555
+00:58:58,020 --> 00:59:03,680
+الحالة التالتة والاخيرة The Roots
+
+556
+00:59:06,650 --> 00:59:16,650
+are repeated لو كانت الجذور مكررة بدي أقسمها إلى
+
+557
+00:59:16,650 --> 00:59:33,310
+جزئين نمر A if the roots of equation 2 are real
+
+558
+00:59:33,310 --> 00:59:34,930
+repeated
+
+559
+00:59:36,960 --> 00:59:49,640
+لو كانت حقيقية و مكررة that is IN R1 يسوى R2 يسوى
+
+560
+00:59:49,640 --> 01:00:05,740
+RN يسوى RC مثلا then the general solution
+
+561
+01:00:09,110 --> 01:00:19,510
+والسؤال الواضح هو Y
+
+562
+01:00:19,510 --> 01:00:34,770
+تساوي C1 زائد C2T C3T تربيع زائد CN T أس N ناقص
+
+563
+01:00:34,770 --> 01:00:46,850
+واحدكله في E أس RT نمر
+
+564
+01:00:46,850 --> 01:00:51,290
+بي if
+
+565
+01:00:51,290 --> 01:00:57,970
+the roots of
+
+566
+01:00:57,970 --> 01:01:03,910
+equation 2 are
+
+567
+01:01:09,680 --> 01:01:23,520
+repeated complex conjugate repeated
+
+568
+01:01:23,520 --> 01:01:33,920
+complex conjugate then the general solution
+
+569
+01:01:41,460 --> 01:01:48,200
+Y تساوي C1
+
+570
+01:01:48,200 --> 01:01:57,260
+C2 T زائد زائد CS
+
+571
+01:01:57,260 --> 01:02:02,980
+T أُس S ناقص واحد
+
+572
+01:02:05,390 --> 01:02:17,810
+فى E أُس لامدة T كوسين ميو T زائد بي واحد بيتنين T
+
+573
+01:02:17,810 --> 01:02:29,970
+بي S تي أُس S ناقص واحد كله في sign والله فى E أُس
+
+574
+01:02:29,970 --> 01:02:40,400
+لامدة T فى Eحُس لندتي فى صين لميوتى
+
+575
+01:03:25,170 --> 01:03:27,170
+ماذا بحق الجحيم
+
+576
+01:04:11,950 --> 01:04:15,570
+نرجع لكلام اللي احنا كاتبينه على بنات من أول و
+
+577
+01:04:15,570 --> 01:04:20,300
+جديديبقى سيكشن أربعة اتنين بتتكلم فقط عن ال
+
+578
+01:04:20,300 --> 01:04:25,240
+homogenous linear differential equations تمام
+
+579
+01:04:25,240 --> 01:04:28,640
+بيقول يعتبر ال nth order linear differential
+
+580
+01:04:28,640 --> 01:04:32,580
+equation اللي عندنا هذه بالمعاملات الثابتة هذه
+
+581
+01:04:32,580 --> 01:04:37,440
+بدنا نيجي نحلها زي ما كنا بنعمل في شبتر تلاتة
+
+582
+01:04:37,440 --> 01:04:42,780
+بنفترض ان هو يسوي EOSRT عبارة عن solution اشتق مرة
+
+583
+01:04:42,780 --> 01:04:47,410
+و اتنين و تلاتة و اين من المراتوبنرجع بنعود في
+
+584
+01:04:47,410 --> 01:04:52,470
+المعادلة التفاضلية وبعدين بنقسم على EOSRT بنحسب
+
+585
+01:04:52,470 --> 01:04:57,270
+نحصل على مين؟ على المعادلة لأن من الدرجة النونية
+
+586
+01:04:57,270 --> 01:05:03,050
+بدل ما كانت معادلة تفاضلية من الرتبة النونية صارت
+
+587
+01:05:03,050 --> 01:05:07,710
+معادلة عادية من الدرجة النونية بدنا نيجي نحل
+
+588
+01:05:07,710 --> 01:05:13,660
+المعادلة هذه، هذه المعادلة لها N من الجذورلما يكون
+
+589
+01:05:13,660 --> 01:05:18,180
+لها ان من الجذور، فهناك احتمالات تعدى لهذه الجذور،
+
+590
+01:05:18,180 --> 01:05:23,480
+الاحتمال الاول ان الجذور تبقى حقيقية وغير متساوية،
+
+591
+01:05:23,480 --> 01:05:27,760
+real and different، ولا واحد فيهم زي التاني،
+
+592
+01:05:27,760 --> 01:05:31,560
+مختلفات عن بعض تماما، يبقى if the roots of a
+
+593
+01:05:31,560 --> 01:05:35,920
+question are real and not two are equal، مافيش يوم
+
+594
+01:05:35,920 --> 01:05:41,410
+اتنين بيسووا بعضالرقم 1 لا يمكن يسوى رقم 2 ولا
+
+595
+01:05:41,410 --> 01:05:48,230
+يمكن يسوى رقم 3ن حدث ذلك يبقى ال general solution
+
+596
+01:05:48,230 --> 01:05:53,410
+للمعادلة رقم واحد بدي يكون على الشكل التالي Y تسوى
+
+597
+01:05:53,410 --> 01:06:01,890
+C1 في E أُس R1T زائد C2 في E أُس R2T زائد زائد وCN
+
+598
+01:06:01,890 --> 01:06:08,030
+E أُس RNT بالشكل اللي عندنا هذا الحالة الأولى لو
+
+599
+01:06:08,030 --> 01:06:12,860
+كان ال real and different unequal الحالة الثانيةلو
+
+600
+01:06:12,860 --> 01:06:16,640
+كان الجذور هذه complex و إذا كانوا complex كل
+
+601
+01:06:16,640 --> 01:06:24,300
+اتنين يكونوا معاهممترافقين يبقى باجي بقول الشكل ال
+
+602
+01:06:24,300 --> 01:06:29,020
+roots هذه بدأ تبقى على الشكل التالي لاندا زائد او
+
+603
+01:06:29,020 --> 01:06:34,500
+ناقص imu1 يبقى هي الترافق ممكن يكون لاندا 2 زائد
+
+604
+01:06:34,500 --> 01:06:39,480
+imu2 الترافق ما بين الاتنين انضل مشيل لغاية لاندا
+
+605
+01:06:39,480 --> 01:06:47,520
+S زائد او ناقص imuS طبعاربما يتبضر الى ذهنك السؤال
+
+606
+01:06:47,520 --> 01:06:53,220
+التالي او الى البعض منكم ليش ماهياش lambda n زيد
+
+607
+01:06:53,220 --> 01:07:01,420
+او ناقص imun مظبوط صح ولا لأ مش هالت سؤال بقولكوا
+
+608
+01:07:01,420 --> 01:07:06,420
+ياسه هذول اتنين مترافقين انا عندي درجة نونيةمظبوط
+
+609
+01:07:06,420 --> 01:07:11,640
+إذا اتنين مترافقين بدي يكونوا النصيك و النصيك يعني
+
+610
+01:07:11,640 --> 01:07:16,100
+لو كان عشرة بديهم يطلعوا خمسة و الخمسة مرافقتهم
+
+611
+01:07:16,100 --> 01:07:23,020
+يبقى S تبقى N على 2 صحيح ولا لأ؟ تبقى N على 2 يمكن
+
+612
+01:07:23,020 --> 01:07:28,280
+شوية فيهم حقيقي و شوية فيهم complex يبقى الحقيقي
+
+613
+01:07:28,280 --> 01:07:32,600
+بدي أعملهم زي الحقيقي و ال complex بطلوا يصيروا
+
+614
+01:07:32,600 --> 01:07:38,630
+عشرة يمكن يطلعوا ستةيمكن يطلع أربع مظبوط بقدرش
+
+615
+01:07:38,630 --> 01:07:43,650
+اقول ان على اتنات من هنا روحنا جولنا يبقى land s و
+
+616
+01:07:43,650 --> 01:07:48,830
+I and me و S جد ما يطلع يطلع تمام طب ان حد ذلك ما
+
+617
+01:07:48,830 --> 01:07:54,310
+هو شكل ال general solution بقوله كل واحد فيهم بدي
+
+618
+01:07:54,310 --> 01:07:58,430
+يكون على الشكل هذه يبقى ايه اصل يعني هذا كان شكل
+
+619
+01:07:58,430 --> 01:08:03,440
+مين؟لو كانت من ال second order مش كنا نقول E وصل
+
+620
+01:08:03,440 --> 01:08:09,220
+لاندا C1 Cos Mu T زائد C2 Sin Mu T بس احنا عندنا
+
+621
+01:08:09,220 --> 01:08:13,820
+ميوهات عددهم S وفي عندنا لاندات عددهم S يبقى فبروح
+
+622
+01:08:13,820 --> 01:08:22,000
+بقولوا E وصل لاندا 1T A1 Cos Mu 1T زائد B1 Sin Mu
+
+623
+01:08:22,000 --> 01:08:28,340
+1Tاللي بعده E أس لاندا تو T في E أس لاندا تو E أس
+
+624
+01:08:28,340 --> 01:08:28,860
+لاندا تو E أس لاندا تو E أس لاندا تو E أس لاندا تو
+
+625
+01:08:28,860 --> 01:08:32,720
+E أس لاندا تو E أس لاندا تو E أس لاندا تو E أس
+
+626
+01:08:32,720 --> 01:08:37,220
+لاندا تو E أس لاندا تو E أس لاندا تو E أس لاندا تو
+
+627
+01:08:37,220 --> 01:08:37,900
+E أس لاندا تو E أس لاندا تو E أس لاندا تو E أس
+
+628
+01:08:37,900 --> 01:08:37,900
+لاندا تو E أس لاندا تو E أس لاندا تو E أس لاندا تو
+
+629
+01:08:37,900 --> 01:08:38,140
+E أس لاندا تو E أس لاندا تو E أس لاندا تو E أس
+
+630
+01:08:38,140 --> 01:08:45,360
+لاندا تو E أس لاندا تو E أس لاندا تو E أس لاندا تو
+
+631
+01:08:45,360 --> 01:08:48,300
+E أاولا اتنين اثنين اثنين اثنين اثنين اثنين اثنين
+
+632
+01:08:48,300 --> 01:08:49,320
+اثنين اثنين اثنين اثنين اثنين اثنين اثنين اثنين
+
+633
+01:08:49,320 --> 01:08:53,740
+اثنين اثنين اثنين اثنين اثنين اثنين اثنين اثنين
+
+634
+01:08:53,740 --> 01:08:55,660
+اثنين اثنين اثنين اثنين اثنين اثنين اثنين اثنين
+
+635
+01:08:55,660 --> 01:08:56,480
+اثنين اثنين اثنين اثنين اثنين اثنين اثنين اثنين
+
+636
+01:08:56,480 --> 01:09:00,080
+اثنين اثنين اثنين اثنين اثنين اثنين اثنين اثنين
+
+637
+01:09:00,080 --> 01:09:04,140
+اثنين اثنين اثنين اثنين اثنين اثنين اثنين اثنين ا
+
+638
+01:09:04,180 --> 01:09:09,120
+ما كتبناش N على 2 N على 2 لو كانوا كلهم complex
+
+639
+01:09:09,120 --> 01:09:12,960
+لكن ممكن يطلع بعضهم ريالوا بعضهم complex يبقى
+
+640
+01:09:12,960 --> 01:09:17,140
+فباجي بقول ال complex بكتبهم الشكل اللي عندنا هذا
+
+641
+01:09:17,140 --> 01:09:22,640
+يبقى هذا لو كان كله complex طيب لو كانوا كلهم
+
+642
+01:09:22,640 --> 01:09:29,120
+repeated مكررينفي احتمال ان يكون الـ real و
+
+643
+01:09:29,120 --> 01:09:32,220
+repeated و في احتمال يكون complex و repeated
+
+644
+01:09:32,220 --> 01:09:35,540
+مظبوطة او لا؟ يبقى شو بينا نعمل شو بيكون الشكل
+
+645
+01:09:35,540 --> 01:09:39,080
+الحالي في هذه الحالة بقول ما ياتي if the roots of
+
+646
+01:09:39,080 --> 01:09:42,820
+equations in R are really repeated يعني راحة بدي
+
+647
+01:09:42,820 --> 01:09:47,620
+سوى R اتنين بدي سوى بدي سوى RN اختصارا بدي اسميها
+
+648
+01:09:47,620 --> 01:09:53,900
+R مثل Rc يعني مثلاتمام؟ يبقى شكل ال general
+
+649
+01:09:53,900 --> 01:09:57,940
+solution بيكون على الشكل التالي في حالة ال second
+
+650
+01:09:57,940 --> 01:10:02,900
+order بيجي نقول C1 زي C2 في T كله في ال
+
+651
+01:10:02,900 --> 01:10:09,140
+exponential هنا أحنا بدنا نعممها صار C1 زي C2T زي
+
+652
+01:10:09,140 --> 01:10:17,130
+C3T تربيع زي زي CNT أس N ناقص واحدأخر T بتكون أقل
+
+653
+01:10:17,130 --> 01:10:20,490
+بقداش لإن في ال second و اذا كان كروص ازايد
+
+654
+01:10:20,490 --> 01:10:25,150
+كروستان في T و احنا عندنا second اتنين فبتبقى T
+
+655
+01:10:25,150 --> 01:10:29,750
+اقص واحد اقل من القرص تبع المعادلة بقداش بواحد
+
+656
+01:10:29,750 --> 01:10:35,630
+يبقى صارت المعادلة دي في مين في E Os RT على اللي
+
+657
+01:10:35,630 --> 01:10:39,510
+طلعت عندنا هذه تمام يبقى هذا الشكل ال general
+
+658
+01:10:39,510 --> 01:10:43,770
+solution لو كانوا really repeatedطب لو كانوا
+
+659
+01:10:43,770 --> 01:10:48,530
+complex و repeated يبقى سمنها النقطة رقم B يبقى
+
+660
+01:10:48,530 --> 01:10:52,010
+اذا روح سباقية كونجة R repeated complex conjugate
+
+661
+01:10:52,010 --> 01:10:58,050
+ترافق و مكرر ما هم نصين صاروا الجذور نص و نص
+
+662
+01:10:58,050 --> 01:11:02,570
+المرافق يبقى هدول اللي مشاكله هدول اللي لهمالشكل
+
+663
+01:11:02,570 --> 01:11:06,190
+اللي بيبقى الشكل ال general solution بيكون c1 زاد
+
+664
+01:11:06,190 --> 01:11:13,470
+c2t زاد زاد c st أس s minus ال one فاللي a أس
+
+665
+01:11:13,470 --> 01:11:19,610
+لاندا t cos ميو t وهذا التكرار هيه مضروف a أس
+
+666
+01:11:19,610 --> 01:11:26,260
+لاندا في ال cosineب1 ب2t زائد زائد بست to the
+
+667
+01:11:26,260 --> 01:11:30,980
+power of s minus one في أصلة نتيفة sign immunity
+
+668
+01:11:30,980 --> 01:11:36,900
+يبقى هذا complex conjugate ومكرر طبعا هذا الشكل
+
+669
+01:11:36,900 --> 01:11:42,180
+قليل الحدوث اللي لم يكن نادرا في كتابنا في مسائل
+
+670
+01:11:42,180 --> 01:11:47,320
+كتاب تبعتنا لكن البجيات بتكرر واش كتيرحد في كل اي
+
+671
+01:11:47,320 --> 01:11:51,000
+تساؤل هنا قبل ان ندخل الامثلة، هذا كل جزء النظرية
+
+672
+01:11:51,000 --> 01:11:54,760
+تبع الـ Section، قال له قدام، قال له حد بتسأل اي
+
+673
+01:11:54,760 --> 01:11:59,120
+سؤال هنا، ناخد امثلة طوبيحية على الحالات اللي
+
+674
+01:11:59,120 --> 01:12:05,800
+عندنا هنا، اه، في اي تساؤل؟ طيب، نيجي للامثلة
+
+675
+01:12:43,020 --> 01:12:44,860
+تبقى مثال
+
+676
+01:12:51,550 --> 01:12:55,770
+أول مثال بيقول
+
+677
+01:12:55,770 --> 01:13:00,210
+ي determine the
+
+678
+01:13:00,210 --> 01:13:04,070
+general
+
+679
+01:13:04,070 --> 01:13:07,650
+solution
+
+680
+01:13:07,650 --> 01:13:12,550
+of
+
+681
+01:13:12,550 --> 01:13:16,170
+the following
+
+682
+01:13:21,590 --> 01:13:28,010
+differential equations نمره
+
+683
+01:13:28,010 --> 01:13:31,530
+A الوثائق
+
+684
+01:13:31,530 --> 01:13:38,710
+الاتناشر من الكتاب بيقول مشتقة التالتة لو I ناقص
+
+685
+01:13:38,710 --> 01:13:47,170
+تلاتة المشتقة الثانيةزائد ثلاثة y prime ناقص y
+
+686
+01:13:47,170 --> 01:14:04,070
+تساوي zero هذه المعادلة رقم واحد التكتيك
+
+687
+01:14:04,070 --> 01:14:08,050
+اللي اتبعناه في ال second order اللي اتبعه هناأو
+
+688
+01:14:08,050 --> 01:14:11,990
+اللى شرحناته فى الجزء النظري بدنا نعيده فى كل سؤال
+
+689
+01:14:11,990 --> 01:14:18,870
+من هذه المثال فبجى بقوله let Y تساوي E أُس RT بيه
+
+690
+01:14:18,870 --> 01:14:29,850
+solution of the differential equation 2The
+
+691
+01:14:29,850 --> 01:14:41,050
+characteristic equation is R تكيب ناقص ثلاثة R
+
+692
+01:14:41,050 --> 01:14:50,350
+تربيع زائد تلاتة R ناقص واحد بده يساوي زينة لما
+
+693
+01:14:50,350 --> 01:14:54,990
+كانت المعادلة من الدرجة الثانية قصتنا سهلةيا بحل
+
+694
+01:14:54,990 --> 01:14:59,250
+القسين، يا بروح على القانون العام، مظبوط، بس هنا
+
+695
+01:14:59,250 --> 01:15:04,110
+ماتظبطش معناه لا قانون عام ولا حاجة، يبقى في عندي
+
+696
+01:15:04,110 --> 01:15:10,310
+أكثر من طريقة لحل هذه المعادلة، هدول أربع termات،
+
+697
+01:15:10,310 --> 01:15:14,370
+إذا ممكن أخد كل term مع بعض و أخد عاملهم عامل
+
+698
+01:15:14,370 --> 01:15:21,670
+مشترك، كان بيعني ماجدرتش بشوف من الرقم اللي بيقسم
+
+699
+01:15:21,670 --> 01:15:26,400
+سالب واحد،طبعا ماحيش عندنا إلا ميان رقمين اللي هو
+
+700
+01:15:26,400 --> 01:15:32,940
+واحد وسالف واحد يبقى بيكون واحد فيهم على الأقل هو
+
+701
+01:15:32,940 --> 01:15:38,040
+أحد عوامل المعادلة يبقى بروح باجسم المعادلة هذه
+
+702
+01:15:38,040 --> 01:15:43,940
+على R ناقص واحد أو R زائد واحد حسب المعامل
+
+703
+01:15:43,940 --> 01:15:48,160
+وبالتالي بنزل الرتبة من الرتبة التالتة إلى الرتبة
+
+704
+01:15:48,160 --> 01:15:53,950
+وخلاص بصير قصدي سهل بعد هيك مظبوطلكن اذا جيت قولت
+
+705
+01:15:53,950 --> 01:15:59,870
+هذه يا مانان بقدر اقول هذه R تكيب ناقص واحد هدول
+
+706
+01:15:59,870 --> 01:16:05,110
+التان تان فيهم عامل مشترك اللي همين سالب تلاتة R
+
+707
+01:16:05,110 --> 01:16:13,760
+بظل قداش R ناقص واحد يساوي Zeroأخذ سالب ثلاثة R من
+
+708
+01:16:13,760 --> 01:16:18,420
+التنتين هذول برا من المشاركة هنا بيظل R و هنا بيظل
+
+709
+01:16:18,420 --> 01:16:24,460
+سالب واحد هذه فيها كمان R ناقص واحد إذا بدى أحلل
+
+710
+01:16:24,460 --> 01:16:31,500
+هذه كفارق بين المكعبين يبقى هذه بدها تعطينا فتحة
+
+711
+01:16:31,500 --> 01:16:36,800
+كويس بدى ذاكرك بتحليل الفرق بين المكعبين ابتخد
+
+712
+01:16:36,800 --> 01:16:42,390
+الجذر التالت للقيمة الأولى اللي هو G11و ناقص كما
+
+713
+01:16:42,390 --> 01:16:47,110
+هي و بتاخد الجذر التالت للقيمة التانية اللى قداش
+
+714
+01:16:47,110 --> 01:16:51,570
+واحد ايه اخدنا الجذر التالت للأولى و الجذر التالت
+
+715
+01:16:51,570 --> 01:16:57,670
+للتالت بالمثل لو كان مجموع مكعبين بنسوي نفس القصة
+
+716
+01:16:57,670 --> 01:17:03,970
+تمام؟ طيب بعد كده بقول قوس مربع الأول R تربين
+
+717
+01:17:03,970 --> 01:17:09,370
+الإشارة هذه ناقص بحط عكسها تماما و بضرب القيمتان
+
+718
+01:17:09,370 --> 01:17:16,110
+في بعضواحد في R بقداش ب R زائد مربع القيمة التانية
+
+719
+01:17:16,110 --> 01:17:20,710
+اللي هو جداش، إذاً هذا هو تحليل الفرق بين المكعبين
+
+720
+01:17:20,710 --> 01:17:21,610
+القيمة الأولى
+
+721
+01:17:24,450 --> 01:17:30,430
+يبقى باجي بقوله ناقص تلاتة R في R ناقص واحد يساوي
+
+722
+01:17:30,430 --> 01:17:34,530
+Zero انا عندي هذه كمية و هذه كمية فيه بينهم عامل
+
+723
+01:17:34,530 --> 01:17:38,850
+مشترك اللي همين R ناقص واحد بقوله يا R ناقص واحد
+
+724
+01:17:38,850 --> 01:17:43,340
+خليك برا انتيبقى لما أخد عمل مشترك بيظل عندي R
+
+725
+01:17:43,340 --> 01:17:51,500
+تربية زائد R زائد واحد ناقص تلاتة R فقط لغير يبقى
+
+726
+01:17:51,500 --> 01:17:58,080
+بده يساوي Zero هذه بتصير R ناقص واحد فيه هذه يا
+
+727
+01:17:58,080 --> 01:18:03,960
+بنات اللي هى R تربية عندك R وناقص تلاتة R اللي هي
+
+728
+01:18:03,960 --> 01:18:09,930
+بناقص اتنين R زائد واحد كله بده يساوي Zeroهذه
+
+729
+01:18:09,930 --> 01:18:20,130
+عبارة عن مين؟ R ناقص واحد لكل تكييب
+
+730
+01:18:20,130 --> 01:18:26,610
+هذا معناته أن R ناقص واحد لكل تكييب يساوي Zero هذه
+
+731
+01:18:26,610 --> 01:18:32,250
+محددة من أي درجة تالتة يبقى لك كم جذر والتلاتة
+
+732
+01:18:32,250 --> 01:18:39,660
+مالهمحقيقية ومتساوية repeated roots اللي هو الحالة
+
+733
+01:18:39,660 --> 01:18:45,380
+الأخيرة اللي عندنا نمر أيه يبقى هنا معناته أن R1
+
+734
+01:18:45,380 --> 01:18:51,420
+بديه يسوي R2 بديه يسوي R3 بديه يسوي كده؟ واحد
+
+735
+01:18:51,420 --> 01:19:00,000
+صحيح، تمام؟ يعني هذه real repeated roots
+
+736
+01:19:02,350 --> 01:19:12,770
+يبقى بناء عليه the solution of the differential
+
+737
+01:19:12,770 --> 01:19:26,890
+equation 1 as y تساوي c1 زي c2t زي c3t تربيه امشي
+
+738
+01:19:26,890 --> 01:19:32,310
+كمان ولا خلاصلأ خلاص لحظة الأس هنا كده اش اتنين
+
+739
+01:19:32,310 --> 01:19:37,650
+رغم ان المعادلة على رقم تلاتة كله في إيه أس اعرف
+
+740
+01:19:37,650 --> 01:19:44,290
+انت بقداش؟ بواحد في T الـT itself يبقى هذا شكل ال
+
+741
+01:19:44,290 --> 01:19:51,210
+solution تبع المعادلة إلا أن حد إلا يتساول هنا أظن
+
+742
+01:19:51,210 --> 01:19:56,170
+بسيطة مش صعبة طيب نشوف غيرها نمر بيه
+
+743
+01:19:58,790 --> 01:20:07,170
+نمرى بيه اللي هو سؤال تمانتاشر من الكتاب بيقول لي
+
+744
+01:20:07,170 --> 01:20:13,430
+y أس to the derivative ستة ناقص y double prime
+
+745
+01:20:13,430 --> 01:20:19,630
+يساوي زيرو بسيط شغل بسيط مش كتير بدنا نجينا على
+
+746
+01:20:19,630 --> 01:20:23,710
+solution اللي هي المعادلة الصغيرة هذه نفس التكتيك
+
+747
+01:20:23,710 --> 01:20:26,670
+اللي اتبع بعدين بقوله solution
+
+748
+01:20:30,160 --> 01:20:38,680
+لت Y تساوي E أس R T بيسميها للمعادلة الرقم 1 بيه
+
+749
+01:20:38,680 --> 01:20:52,080
+solution of the differential equation 1 then the
+
+750
+01:20:52,080 --> 01:20:56,060
+characteristic
+
+751
+01:20:56,060 --> 01:21:08,190
+equation isأرقص 6 ناقص R تربيع يساوي 0 صح؟
+
+752
+01:21:08,190 --> 01:21:14,710
+في عامل مشترك؟ اللي هو مين؟ هذا بدي يعطينا أن R
+
+753
+01:21:14,710 --> 01:21:21,950
+تربيع في أرقص 4 ناقص 1 يساوي 0 هذه فرق بين
+
+754
+01:21:21,950 --> 01:21:27,470
+المربعين بقدر أحللها فرق بين المربعين يبقى هاي R
+
+755
+01:21:27,470 --> 01:21:34,780
+تربيع اللي براوهنا R تربيع ناقص واحد في R تربيع
+
+756
+01:21:34,780 --> 01:21:41,720
+زاد واحد بده يساوي Zero صحيح؟ هذه كمان فرق بين
+
+757
+01:21:41,720 --> 01:21:51,530
+المربعين يبقى هذه R تربيع في R ناقص واحدفى R زائد
+
+758
+01:21:51,530 --> 01:21:58,610
+واحد فى R ترابيع زائد واحد كله بده يساوي قداش بده
+
+759
+01:21:58,610 --> 01:22:04,630
+يساوي Zero طيب الحلال لو خلصنا هذا ايش معناها ان
+
+760
+01:22:04,630 --> 01:22:12,530
+الجدر هذا مكرر مرتين يبقى R واحد تساوي R اتنين
+
+761
+01:22:12,530 --> 01:22:19,080
+تساوي Zeroوهذه معناها ان ال R تلاتة بواحد وال R
+
+762
+01:22:19,080 --> 01:22:25,300
+أربعة بسالب واحد خلصنا هدول شو رايك في هذه R تربية
+
+763
+01:22:25,300 --> 01:22:29,400
+تساوي ناقص واحد يبقى complex يعني R تساوي زايد او
+
+764
+01:22:29,400 --> 01:22:39,400
+ناقص I يبقى هنا هذا معناه ان R خمسة تساوي I وR ستة
+
+765
+01:22:39,400 --> 01:22:44,900
+تساوي سالب Iوالعيط طبعا معروف اللي هو الجذر
+
+766
+01:22:44,900 --> 01:22:50,780
+التربيهي ل سالب واحد يبقى اتنين complex و اتنين
+
+767
+01:22:50,780 --> 01:22:55,260
+conjugate و الباقى real يبقى اتصار مشترك من اتنين
+
+768
+01:22:55,260 --> 01:23:00,660
+complex و main و real كذلك يبقى بناء عليه the
+
+769
+01:23:00,660 --> 01:23:08,720
+general solution is بدي اشوف ال general solution
+
+770
+01:23:08,720 --> 01:23:17,540
+اللي عندنا هنا y تساويهي يا بنات C1 زائد C2 في T
+
+771
+01:23:17,540 --> 01:23:24,680
+المكرر في E أس Zero T يعني بواحد يبقى مافيش غير
+
+772
+01:23:24,680 --> 01:23:33,480
+هدول اتنين لحالهم زائد نيجي اللي بعده C3 E Os T
+
+773
+01:23:33,480 --> 01:23:42,620
+زائد C4 E Os ناقص T نيجي اللي هدول لاندا بقداشزائر
+
+774
+01:23:42,620 --> 01:23:48,680
+وماعنديش لانه يبقى E و Zero لبعد يبقى زائد C خمسة
+
+775
+01:23:48,680 --> 01:23:58,980
+cosine T زائد C ستة sine T يعني
+
+776
+01:23:58,980 --> 01:24:04,080
+سؤال صغير لكن برضه بدنا نفكر كيف نحله حتى الآن
+
+777
+01:24:04,080 --> 01:24:11,970
+برضه كله تحليل سهل هذهمافيش فيها أي فكرة ناخد مثال
+
+778
+01:24:11,970 --> 01:24:17,690
+اخر في محاضرة اليوم و المرة الجاية بنكمل و بدنا
+
+779
+01:24:17,690 --> 01:24:23,830
+نشوف ايش الفكرة اللي فيه يبقى نمره الـC نمره الـC
+
+780
+01:24:23,830 --> 01:24:31,350
+سؤال تسعة عشر من الكتاب بيقول لي why to the
+
+781
+01:24:31,350 --> 01:24:38,480
+derivative fiveناقص تلاتة y to the derivative four
+
+782
+01:24:38,480 --> 01:24:47,560
+زائد تلاتة to the triple derivative ناقص تلاتة y w
+
+783
+01:24:47,560 --> 01:24:57,320
+prime زائد اتنين y prime بده يساوي من zero يبقى
+
+784
+01:24:57,320 --> 01:25:02,560
+باجي بقول له solution let
+
+785
+01:25:03,320 --> 01:25:11,680
+Y تساوي E أُس RT بإيه سوليوشن
+
+786
+01:25:11,680 --> 01:25:15,100
+Of
+
+787
+01:25:15,100 --> 01:25:26,720
+The Differential Equation 1 High Equation 1 Then
+
+788
+01:25:26,720 --> 01:25:32,000
+The Characteristic
+
+789
+01:25:32,780 --> 01:25:44,300
+Equation is R أُس خمسة ناقص تلاتة R أُس أربع زائد
+
+790
+01:25:44,300 --> 01:25:52,820
+تلاتة R تكريم ناقص تلاتة R تربيع زائد اتنين R بده
+
+791
+01:25:52,820 --> 01:25:59,400
+يسوى قداش Zero هذه معادلة من الدرجةيعني لها خمسة
+
+792
+01:25:59,400 --> 01:26:06,300
+جذور تمام طيب نبدأ نشوف كيف بدنا نحللها و نيفر أظن
+
+793
+01:26:06,300 --> 01:26:10,840
+في R عامل مشترك يبقى التحليل بإخراج العامل المشترك
+
+794
+01:26:10,840 --> 01:26:18,880
+هاي R ضالان دمين R أُس أربع ناقص تلاتة R تكيب زائد
+
+795
+01:26:18,880 --> 01:26:24,880
+تلاتة R تربيع ناقص تلاتة R زائد اتنين يساوي زير
+
+796
+01:26:28,050 --> 01:26:31,450
+الان بنطلع فى المعادلة اللى عندنا دى كيبنا حلل
+
+797
+01:26:31,450 --> 01:26:37,250
+المعادلة اللى بين قسمنا الدرجة الرابعة اخد كل
+
+798
+01:26:37,250 --> 01:26:41,050
+اتنين مع بعض واصبطش اشي فى تلاتة واشي فى اتنين
+
+799
+01:26:41,050 --> 01:26:46,470
+تمام يبقى ممكن نعمل قسمة مطولة كيف بدى اجيب القسمة
+
+800
+01:26:46,470 --> 01:26:52,070
+المطولة شوف يا بنات بروح على المقدار الثابت مين هو
+
+801
+01:26:53,010 --> 01:27:00,190
+وبدور على قواسمه اتنين سالب اتنين واحد سالب واحد
+
+802
+01:27:00,190 --> 01:27:04,930
+امسك اي رقم فيهم و اعوضه في المعدل اللي بيخليه
+
+803
+01:27:04,930 --> 01:27:11,270
+اللي بيخليه صفر بيكون هو احد العوامل تمام باقسم
+
+804
+01:27:11,270 --> 01:27:15,890
+عليه بنزل الدرجة من الدرجة التالتة لوين لمن الدرجة
+
+805
+01:27:15,890 --> 01:27:21,030
+الرابعة للدرجة وبعدها يمكن تنحله يمكن اسوي نفس ال
+
+806
+01:27:21,030 --> 01:27:25,940
+tacticتمام؟ واحدة اشتر شوية قالتلي طب اشترك استنى
+
+807
+01:27:25,940 --> 01:27:31,100
+شوية انت عندك تلاتات كتير قلتله والله مظبوط قالتلي
+
+808
+01:27:31,100 --> 01:27:36,340
+بتقدر تخلي هذه تلاتة بقولك ايه؟ قال ضيف واحد واطرح
+
+809
+01:27:36,340 --> 01:27:41,240
+واحد تبقى حلية المشكلة كلها ولا تقسم جسمها مطول
+
+810
+01:27:41,240 --> 01:27:46,800
+ولا غيره دقة نظر بقولك ايه؟ قالت هذه بالشكل التالي
+
+811
+01:27:46,800 --> 01:27:59,000
+IRوهذا R أس أربع وناقص تلاتة R تربيع وناقص تلاتة R
+
+812
+01:27:59,000 --> 01:28:09,800
+تكيب وزائد تلاتة R تربيع وناقص تلاتة R وزائد تلاتة
+
+813
+01:28:09,800 --> 01:28:16,040
+ناقص واحد كله يسوى زيرو يعني ايش عاملينأضافت واحد
+
+814
+01:28:16,040 --> 01:28:20,000
+واطرحت واحد لما اضافت واحد لاتنين صار تلاتة قام
+
+815
+01:28:20,000 --> 01:28:24,600
+اطرحت واحد قلتلها و بعدين قالت تعالي شوف ايش اللي
+
+816
+01:28:24,600 --> 01:28:30,160
+صار هاي اتنين اربع ستة قلتلها مظبوط قال بدي ااخد
+
+817
+01:28:30,160 --> 01:28:34,040
+كل اتنين مع بعض في الأول كانوا خمسة الحين صاروا
+
+818
+01:28:34,040 --> 01:28:39,860
+ستة كيف بتقولي هاي ار و هذا ارقص اربعة ناقص واحد
+
+819
+01:28:39,860 --> 01:28:46,960
+مع الأخيرو هدول اتنين بداخد منهم ناقص تلاتة R تربي
+
+820
+01:28:46,960 --> 01:28:52,800
+عامل مشترك بظل R ناقص واحد قلنا لها مظبوط و قالت
+
+821
+01:28:52,800 --> 01:28:58,660
+هدول كمان ناقص تلاتة بظل R ناقص واحد يساوي Zero
+
+822
+01:28:58,660 --> 01:29:05,700
+قلنا لها ان قالت هدى كمان بتحللها فرق بين المربعين
+
+823
+01:29:06,100 --> 01:29:12,000
+يبقى بنجي بنقولها أو بناخد منها دول are ناقص واحد
+
+824
+01:29:12,000 --> 01:29:18,010
+كمان يبقى هذا اهفى R تربية ناقص واحد فى R تربية
+
+825
+01:29:18,010 --> 01:29:22,890
+زائد واحد عامل مشترك هى حللنا الجوس الاول كفرق بين
+
+826
+01:29:22,890 --> 01:29:29,890
+المربعين جالتلى هذا ناقص تلاتة عامل مشترك مابل
+
+827
+01:29:29,890 --> 01:29:36,830
+اتنين وR ناقص واحد عامل مشترك مابل اتنين بظل R
+
+828
+01:29:36,830 --> 01:29:40,730
+تربية زائد واحد كلها يساوي زير وقلنا لها مظبوط
+
+829
+01:29:43,930 --> 01:29:49,150
+بعد مرة تانية الخطوة اللي عملناها هذه أضفنا فوق
+
+830
+01:29:49,150 --> 01:29:54,010
+واحد و طرحنا واحد صار عندي ست ترمات بدي أخد كل
+
+831
+01:29:54,010 --> 01:29:59,050
+ترمين مع بعض يبقى أخد الأول والأخر مع بعض هذول
+
+832
+01:29:59,050 --> 01:30:02,870
+اتنين أخد منهم سالب تلاتة R تربي عام المشترك هذه
+
+833
+01:30:02,870 --> 01:30:08,010
+أخد سالب تلاتة عام المشترك بعدين هذه حللت فرق من
+
+834
+01:30:08,010 --> 01:30:13,090
+المربعين هذه أخد ناقص تلاتة في R ناقص واحد كل عام
+
+835
+01:30:13,090 --> 01:30:18,400
+المشتركطلع عند هنا R ثربية وطلع عند هنا ايش؟ واحد
+
+836
+01:30:18,400 --> 01:30:22,920
+فقط لان اخدت ناقص تلاتة في R ناقص واحد دي بيصرت
+
+837
+01:30:22,920 --> 01:30:28,460
+بالشكل هذا اطلع الي هدتين و هدتين في بينهم عامل
+
+838
+01:30:28,460 --> 01:30:37,820
+مشترك؟ شرفنا برايبقى هذا R في R تربيه زائد واحد بل
+
+839
+01:30:37,820 --> 01:30:43,100
+مين عندنا هذا كمان بنحلل الفرق بين المربعين اللي
+
+840
+01:30:43,100 --> 01:30:50,940
+هو مين R ناقص واحد في R زائد واحد تمام هذا راح
+
+841
+01:30:50,940 --> 01:30:56,580
+يبقى ناقص تلاتة في R ناقص واحد كله بده يساوي Zero
+
+842
+01:30:57,420 --> 01:31:01,720
+طيب ايش رأيك ار ناقص واحد و ار ناقص واحد شرفنا برا
+
+843
+01:31:01,720 --> 01:31:07,920
+كمان يبقى اي ار في ار ناقص واحد في ار تربيه زائد
+
+844
+01:31:07,920 --> 01:31:15,380
+واحد بل ار زائد واحد و هنا قداش ناقص ثلاثة بس بده
+
+845
+01:31:15,380 --> 01:31:21,600
+يساوي ال zero يبقى هذا بصير main ار في ار ناقص
+
+846
+01:31:21,600 --> 01:31:29,600
+واحد في ار ناقص اتنينفئة ترابية زائد واحد بده
+
+847
+01:31:29,600 --> 01:31:35,980
+يساوي zero اصلا هدول تلاتة real and different و
+
+848
+01:31:35,980 --> 01:31:39,920
+هدول اتنين complex conjugate يبقى بقدر اجيب ال
+
+849
+01:31:39,920 --> 01:31:45,920
+general solution يبقى بروح بقوله the general
+
+850
+01:31:45,920 --> 01:32:00,400
+solution of the differentialEquation 1 is Y تساوي
+
+851
+01:32:00,400 --> 01:32:12,600
+C1 في E أُس 0 مظبوط يبقى C1 زائد C2 في E أُس T
+
+852
+01:32:12,600 --> 01:32:25,420
+زائد C3 في E أُس 2T هدول Complexيبقى زائد C4 في
+
+853
+01:32:25,420 --> 01:32:34,540
+Cos T زائد C5 في Sin T هذا هو ال general solution
+
+854
+01:32:34,540 --> 01:32:39,260
+للمعادلة اللي يعني لازلنا في نفس ال section في
+
+855
+01:32:39,260 --> 01:32:45,400
+هناك مزيد من الأمثلة و خاصة لما يكون كله complex
+
+856
+01:32:45,400 --> 01:32:49,830
+لكسة ماجيبناش عليه ولا مثال كله complexيبقى للمرة
+
+857
+01:32:49,830 --> 01:32:52,530
+القادمة ان شاء الله ابنكم
+
diff --git a/PL9fwy3NUQKwa8ZDfSFGn6H8xVFLzqmCZC/Q2YiEyS2_gY.srt b/PL9fwy3NUQKwa8ZDfSFGn6H8xVFLzqmCZC/Q2YiEyS2_gY.srt
new file mode 100644
index 0000000000000000000000000000000000000000..f118b319cc41c60fee2ea1d95d7663f2d8e9ccad
--- /dev/null
+++ b/PL9fwy3NUQKwa8ZDfSFGn6H8xVFLzqmCZC/Q2YiEyS2_gY.srt
@@ -0,0 +1,2810 @@
+1
+00:00:09,660 --> 00:00:14,080
+بسم الله الرحمن الرحيم المرة اللي فاتت بدينا في
+
+2
+00:00:14,080 --> 00:00:18,660
+section ثلاثة وعطينا تعريف ل linearly
+
+3
+00:00:18,660 --> 00:00:23,420
+independent و linearly dependent functions أقول أن 
+
+4
+00:00:23,420 --> 00:00:26,140
+لو في عندي functions بقول عنهم linearly
+
+5
+00:00:26,140 --> 00:00:30,570
+independent إذا كان ال constants اللي كانت تبعهم ما له لا
+
+6
+00:00:30,570 --> 00:00:35,930
+يساوي صفر أما إذا كانت ال functions linearly dependent
+
+7
+00:00:35,930 --> 00:00:41,190
+فال constants اللي كانت تبعهم ما له بده يساوي صفر اثنين
+
+8
+00:00:41,190 --> 00:00:46,230
+قلنا أن ال two functions بقول عنهم linearly 
+
+9
+00:00:46,230 --> 00:00:51,290
+independent لو جيت تلاقي two constants في 
+
+10
+00:00:51,290 --> 00:00:53,930
+الدالة الأولى في الدالة الثانية بده يساوي 
+
+11
+00:00:53,930 --> 00:00:54,870
+صفر كان
+
+12
+00:01:00,290 --> 00:01:04,950
+لكن لو كان على الأقل واحد من ال constants  لا 
+
+13
+00:01:04,950 --> 00:01:10,620
+يساوي صفر ممكن اثنين ما يكونوش بصفر كذلك يبقى في
+
+14
+00:01:10,620 --> 00:01:13,900
+هذه الحالة بقول ال two functions f and g are
+
+15
+00:01:13,900 --> 00:01:20,120
+linearly dependent تمام؟ بعد هيك روحنا لنظرية و
+
+16
+00:01:20,120 --> 00:01:24,040
+النظرية هذه اللي هي أول نظرية أو هي النظرية الوحيدة
+
+17
+00:01:24,040 --> 00:01:28,680
+اللي أخذناها المرة اللي فاتت اللي هو بنحكم على ال
+
+18
+00:01:28,680 --> 00:01:32,600
+two functions أو ال two solutions ل second order
+
+19
+00:01:32,600 --> 00:01:36,220
+differential equation بينهم linearly dependent أو
+
+20
+00:01:36,220 --> 00:01:41,640
+linearly independent من خلال ال wronskian يعني لو
+
+21
+00:01:41,640 --> 00:01:47,580
+جينا وجدنا أن ال wronskian عند نقطة ما لا يساوي صفر
+
+22
+00:01:47,580 --> 00:01:51,040
+إذا ال two functions بقول عنهم linearly
+
+23
+00:01:51,040 --> 00:01:57,930
+independent ولو كانوا اثنين linearly dependent
+
+24
+00:01:57,930 --> 00:02:03,550
+يكون ال wronskian يساوي صفر هذه النظرية الجاهزة
+
+25
+00:02:03,550 --> 00:02:09,650
+نظرية أقوى منها وتبقى في اتجاهين لكن بعد قليل في
+
+26
+00:02:09,650 --> 00:02:14,870
+محاضرتنا هذه بس قبلها هنجيب ال wronskian بطريقة
+
+27
+00:02:14,870 --> 00:02:18,910
+أخرى غير اللي احنا متعودين عليها أو اللي عارفين
+
+28
+00:02:18,910 --> 00:02:22,530
+تبعت المحدد الدالة الأولى الثانية مشتقة الأولى
+
+29
+00:02:22,530 --> 00:02:27,010
+ومشتقة الثانية فهذه اكتشفها العالم Abel وبالتالي
+
+30
+00:02:27,010 --> 00:02:32,850
+سميت باسمه ف Abel's theorem يبقى نظرية العالم Abel
+
+31
+00:02:33,460 --> 00:02:37,500
+بتقول لو كان Y1 وY2 هو عبارة عن solutions لل
+
+32
+00:02:37,500 --> 00:02:40,220
+differential equation من ال second order اللي
+
+33
+00:02:40,220 --> 00:02:44,460
+قدامنا هذه حيث ال P وQ و R continuous functions
+
+34
+00:02:44,460 --> 00:02:52,740
+على الفترة المفتوحة I يبقى ال wronskian كمغلة Y1 وY2
+
+35
+00:02:52,740 --> 00:03:01,060
+كمغلة T يساوي C في E أس ناقص تكامل P of T DT يبقى
+
+36
+00:03:01,060 --> 00:03:05,440
+من الآن وفصاعدا طبقا لهذه النظر يبقى ال wronskian له
+
+37
+00:03:05,440 --> 00:03:10,340
+كم شكل؟ شكلين الشكل الأولاني شكل المحدد اللي احنا
+
+38
+00:03:10,340 --> 00:03:13,860
+عرفناه قبل كده والشكل الثاني مقدار ثابت في ال
+
+39
+00:03:13,860 --> 00:03:18,360
+exponential لـ P of T هو المعامل تبع مين؟ هو
+
+40
+00:03:18,360 --> 00:03:23,520
+المعامل  Y double prime بشرط أن يكون معامل Y double prime هو الواحد
+
+41
+00:03:23,520 --> 00:03:27,400
+الصحيح يعني لو كان معامل Y double prime هو 
+
+42
+00:03:27,400 --> 00:03:33,020
+رقم ثاني أو دالة ثانية بدي أقسم الطرفين عليه ومن ثم
+
+43
+00:03:33,020 --> 00:03:40,730
+بروح بحسب مين؟ يبقى C مقدار ثابت يعتمد على الحلّين
+
+44
+00:03:40,730 --> 00:03:48,850
+Y1 وY2 ولا يعتمد على شكل ال Main شكل ال T طب نروح 
+
+45
+00:03:48,850 --> 00:03:52,650
+نثبت صحة هذا الكلام بس قبل أن نثبت صحة هذا الكلام 
+
+46
+00:03:52,650 --> 00:03:56,090
+احنا ما نقول مش هنجيب linearly dependent و
+
+47
+00:03:56,090 --> 00:03:59,750
+independent بل ال wronskian هذا يستوي ال صفر وما يستويش 
+
+48
+00:03:59,750 --> 00:04:05,070
+الصفر بدي بسأل هل ال exponential هذه عمرها بده
+
+49
+00:04:05,070 --> 00:04:08,550
+تساوي صفر في يوم من الأيام اللي هي؟ لا لأنه أخذنا في
+
+50
+00:04:08,550 --> 00:04:13,150
+calculus بأن ال exponential دائما وأبدا ده لا
+
+51
+00:04:13,150 --> 00:04:17,390
+أكبر من صفر بتاخد قيمة أكبر من صفر عمرها بتاخد 
+
+52
+00:04:17,390 --> 00:04:20,770
+صفر ولا بتاخد قيمة سالبة، إذا شو اللي بده يخليه
+
+53
+00:04:20,770 --> 00:04:28,290
+صفر؟ يبقى C لو كانت هذا الكلام لا يمكن أن يساوي
+
+54
+00:04:28,290 --> 00:04:33,310
+صفر إلا إذا كانت C تساوي صفر فقط لكن إذا C 
+
+55
+00:04:33,310 --> 00:04:38,250
+ما تساويش صفر يبقى ال wronskian هذا ما له لا يمكن أن
+
+56
+00:04:38,250 --> 00:04:43,890
+يساوي صفر على الإطلاق نجي نثبت صحة هذه النظرية
+
+57
+00:04:43,890 --> 00:04:49,230
+طيب نجي للماضية قليل اثنين هدول حلل المعادلة هذه
+
+58
+00:04:49,230 --> 00:04:53,910
+يبقى اثنين هدول ما لهم؟ بيحققوا المعادلة دي يبقى باجي
+
+59
+00:04:53,910 --> 00:05:08,870
+بقوله بما أن since Y1 and Y2 are two solutions of 
+
+60
+00:05:08,870 --> 00:05:11,890
+equation one
+
+61
+00:05:15,630 --> 00:05:19,710
+يبقى كل واحد فيهم هيحقق المعادلة اللي عندنا يبقى بيصير
+
+62
+00:05:19,710 --> 00:05:20,270
+بيصير
+
+63
+00:05:23,800 --> 00:05:30,900
+زائد P of T في ال Y واحد prime زائد Q of T في 
+
+64
+00:05:30,900 --> 00:05:38,780
+ال Y واحد يساوي كده؟ يساوي صفر اثنين and ال Y2
+
+65
+00:05:38,780 --> 00:05:46,000
+double prime زائد P of T في ال Y2 prime زائد Q of T
+
+66
+00:05:46,000 --> 00:05:52,490
+في ال Y2 يساوي كده؟ يساوي صفر طيب أنا بدي آجي
+
+67
+00:05:52,490 --> 00:05:56,770
+إلى المعادلتين هدول بدي أحاول أطيّر ال term الأخير 
+
+68
+00:05:56,770 --> 00:06:04,090
+فلو جيت للمعادلة الأولى هذه روحت ضربتها في سالب Y2
+
+69
+00:06:04,090 --> 00:06:10,890
+والمعادلة الثانية ضربتها في موجب Y1
+
+70
+00:06:12,180 --> 00:06:16,220
+المعادلة كلها من أولها لآخرها يبقى المعادلة الأولى
+
+71
+00:06:16,220 --> 00:06:21,260
+بتضربها في سالب Y2 والمعادلة الثانية بتضربها في 
+
+72
+00:06:21,260 --> 00:06:26,740
+موجب Y1 يبقى كل من المعادلتين هتصبح على الشكل 
+
+73
+00:06:26,740 --> 00:06:40,310
+التالي سالب Y1 double prime Y2 سالب P of T في Y1 prime Y2
+
+74
+00:06:40,310 --> 00:06:51,030
+سالب Q of T في Y1 Y2 يساوي صفر المعادلة الثانية
+
+75
+00:06:51,030 --> 00:06:57,410
+هضربها في Y1 يبقى Y1 double prime Y2 
+
+76
+00:06:59,260 --> 00:07:09,520
+زائد P of T في Y1 prime Y2 زائد Q of T في Y1 Y2 زائد P
+
+77
+00:07:09,520 --> 00:07:11,080
+of T في Y1 Y2 زائد P of T في Y1 Y2 زائد P of T في 
+
+78
+00:07:11,080 --> 00:07:16,440
+Y1 Y2 زائد
+
+79
+00:07:16,440 --> 00:07:22,350
+Q of T في Y1 Y2 زائد Q of T في Y1 Y2 وبعد ما ضربنا
+
+80
+00:07:22,350 --> 00:07:27,450
+المعادلة الثانية في Y1 شويه نجمع يبقى لو جمعنا
+
+81
+00:07:27,450 --> 00:07:32,100
+هدول الله سهّل عليهم مع السلامة غير ما يصير عليهم يبقى
+
+82
+00:07:32,100 --> 00:07:38,400
+بيصير مجموع المعادلتين على الشكل التالي يبقى Y1
+
+83
+00:07:38,400 --> 00:07:46,240
+Y2 double prime ناقص Y1 double prime Y2 مجموع
+
+84
+00:07:46,240 --> 00:07:51,120
+ال termين هذول يا بنات بياخدوا P of T عامل مشترك 
+
+85
+00:07:51,120 --> 00:07:58,940
+منهم يبقى زائد P of T عامل مشترك بظل عندي Y1 Y2 
+
+86
+00:07:58,940 --> 00:08:06,790
+prime ناقص Y1 prime Y2 
+
+87
+00:08:06,790 --> 00:08:11,810
+Y1 Y2 Y1 Y2 Y2 Y2 Y2 Y2 Y2 Y2 Y2 Y2 Y2 Y2 Y2 Y2 Y2
+
+88
+00:08:11,810 --> 00:08:15,810
+Y2 Y2 Y2 Y2 Y2 Y2 Y2 Y2 Y2 Y2 Y2 Y2 Y2 Y2 Y2 Y2 Y2
+
+89
+00:08:15,810 --> 00:08:18,610
+Y2 Y2 Y2 Y2 Y2 Y2 Y2 Y2 Y2 Y2 Y2 Y2 Y2 Y2 Y2 Y2 Y2
+
+90
+00:08:18,610 --> 00:08:23,550
+Y2 Y2 Y2 Y2 Y2 Y2 Y2 Y2 Y2
+
+91
+00:08:23,550 --> 00:08:32,250
+Y2 Y2 Y أنا بدي أعرف ال W of T ال wronskian W of T يا
+
+92
+00:08:32,250 --> 00:08:40,170
+بنات مش هو عبارة عن Y1 Y2 Y1 prime Y2 prime صح
+
+93
+00:08:40,170 --> 00:08:46,810
+يبقى هذا لو جيت فكّيته شو بيعطيني؟ بيعطيني Y1 Y2
+
+94
+00:08:46,810 --> 00:08:56,440
+prime ناقص Y1 prime Y2 الرئيسي ناقص الثانوي طيب بدي 
+
+95
+00:08:56,440 --> 00:09:02,100
+أشتقه وأشوف شو بيعطينا يبقى لو جيت لـ W prime as a
+
+96
+00:09:02,100 --> 00:09:07,820
+function of t يعني dW على dt هذه مشتقة حاصل ضرب
+
+97
+00:09:07,820 --> 00:09:13,620
+دالتين وهذه مشتقة حاصل ضرب دالتين يبقى الدالة
+
+98
+00:09:13,620 --> 00:09:20,140
+الأولى في مشتقة الدالة الثانية زائد مشتقة الدالة
+
+99
+00:09:20,140 --> 00:09:25,410
+الأولى في الدالة الثانية كما هي اللي عملته لحاصل
+
+100
+00:09:25,410 --> 00:09:29,810
+الضرب الأول هروح أعمله لمين؟ لحاصل الضرب الثاني
+
+101
+00:09:29,810 --> 00:09:35,950
+الناقص الدالة الأولى في مشتقة الدالة الثانية زائد
+
+102
+00:09:35,950 --> 00:09:46,650
+مع ناقص بيصير ناقص اللي هو من اشتقينا اللي هو Y1 prime Y2 
+
+103
+00:09:46,650 --> 00:09:51,510
+فالليلة في هذه وهذه مش الاثنين أرض واحدة 
+
+104
+00:09:51,510 --> 00:09:56,180
+موجبة وواحدة سالبة يبقى مع السلامة يبقى صارت
+
+105
+00:09:56,180 --> 00:10:04,800
+النتيجة هي Y1 Y2 double prime ناقص Y1 double prime
+
+106
+00:10:04,800 --> 00:10:12,280
+Y2 طيب أبطال الليلة لهذه هل ليست هذه هي بالضبط ولا
+
+107
+00:10:12,280 --> 00:10:18,390
+لا؟ إذا هذه بقدر أشيلها وأكتب بدالها من؟ و بدّالها W و
+
+108
+00:10:18,390 --> 00:10:25,510
+هذه بقدر أشيلها وأكتب بدالها من W إذا باجي بقوله 
+
+109
+00:10:25,510 --> 00:10:37,130
+substitute في equation اثنين ونحصل على W prime و
+
+110
+00:10:37,130 --> 00:10:45,640
+أكتب بدالها من W زائد P of T في W as a function of
+
+111
+00:10:45,640 --> 00:10:51,930
+T بده يساوي صفر يبقى من second order linear
+
+112
+00:10:51,930 --> 00:10:56,190
+differential equation تحولنا إلى first order
+
+113
+00:10:56,190 --> 00:11:01,470
+differential equation هذه بنحلها بسيطة يبقى هذه يا 
+
+114
+00:11:01,470 --> 00:11:09,030
+بنات بقدر أقول W prime of t بده يساوي سالب P of t 
+
+115
+00:11:09,030 --> 00:11:20,050
+في W of t ممكن نقسم كلّه على W يبقى هنا بيصير W prime of
+
+116
+00:11:20,050 --> 00:11:26,990
+T على W of T بيكون ناقص P of T
+
+117
+00:11:30,810 --> 00:11:36,250
+يبقى لو كملنا الطرفين إيش بيصير عندنا هنا؟ لين
+
+118
+00:11:36,250 --> 00:11:45,270
+absolute value لـ W of T لـ W of T بده يساوي ناقص
+
+119
+00:11:45,270 --> 00:11:53,170
+تكامل P of T dt زائد constant وليكن C1 أنا ما بدي
+
+120
+00:11:53,170 --> 00:11:56,950
+الليّن ل W بدي ال W itself يبقى لما نرفع
+
+121
+00:11:56,950 --> 00:12:01,930
+الطرفين كأس العدد E لو رفعناها كأس العدد E
+
+122
+00:12:01,930 --> 00:12:08,510
+بيبقى ال absolute value ل W of T يساوي E أس 
+
+123
+00:12:08,510 --> 00:12:19,070
+تكامل لـ P of T dt زائد ال constant C1 سؤال هو هل هذه في
+
+124
+00:12:19,070 --> 00:12:27,250
+يوم من الأيام بتاخد قيمة سالبة أو صفر؟ يبقى هذا 
+
+125
+00:12:27,250 --> 00:12:30,570
+الكلام ال absolute value أشيلناه والله خليناها
+
+126
+00:12:30,570 --> 00:12:38,030
+سيّانة يبقى هذه positive وبالتالي W of T بده يساوي E
+
+127
+00:12:38,030 --> 00:12:47,090
+of T ناقص تكامل P of T dt في E of C1 وزّعت الأسس
+
+128
+00:12:47,090 --> 00:12:53,310
+عند ضرب تجمع الأسس مظبوط أيه؟ طيب إيش رأيك هذه 
+
+129
+00:12:53,310 --> 00:12:59,800
+كلها constant؟ ال E بـ 2 و 7 من عشرة وال C1 كل
+
+130
+00:12:59,800 --> 00:13:01,160
+صحيح يبقى هذا كلّ صحيح يبقى هذا كل صحيح يبقى هذا كل 
+
+131
+00:13:01,160 --> 00:13:03,000
+صحيح يبقى هذا كل صحيح يبقى هذا كل صحيح يبقى هذا كل
+
+132
+00:13:03,000 --> 00:13:03,800
+صحيح يبقى هذا كل صحيح يبقى هذا كل صحيح يبقى هذا كل
+
+133
+00:13:03,800 --> 00:13:07,360
+صحيح يبقى هذا كل صحيح يبقى هذا كل صحيح يبقى هذا كل
+
+134
+00:13:07,360 --> 00:13:08,880
+صحيح يبقى هذا كل صحيح يبقى هذا كل صحيح يبقى هذا كل
+
+135
+00:13:08,880 --> 00:13:11,080
+صحيح يبقى هذا كل صحيح يبقى هذا كل صحيح يبقى هذا كل
+
+136
+00:13:11,080 --> 00:13:19,380
+صحيح يبقى هذا كل صحيح يبقى هذا
+
+137
+00:13:19,380 --> 00:13:26,490
+كل صحيح يبقى خلاصنا؟ يبقى الآن عندي طريقتان أو عندي
+
+138
+00:13:26,490 --> 00:13:33,750
+طريقتين أو توجد طريقتان لمين؟ لحساب ال wronskian، 
+
+139
+00:13:33,750 --> 00:13:40,170
+تمام؟ طيب، حدّ فيكن يتساءل هنا؟ آه البرهان صحيح، 
+
+140
+00:13:40,170 --> 00:13:45,510
+والله صحيح ضربنا وجمعنا واشتقينا ال wronskian طلع
+
+141
+00:13:45,510 --> 00:13:51,110
+الجواب دغري كامل وطلع الجواب حليّ باللي بدّكِ..
+
+142
+00:13:51,110 --> 00:13:54,750
+الحين هأعطيكِ مدّة للمثال ثلاثة وتشوفي حالك حتى
+
+143
+00:13:54,750 --> 00:13:55,990
+اللي بتنتيني
+
+144
+00:14:19,140 --> 00:14:27,440
+يبقى أول مثال example one أول
+
+145
+00:14:27,440 --> 00:14:38,120
+مثال let Y1 بده يساوي جذر ال T وال Y2 بده يساوي 
+
+146
+00:14:38,120 --> 00:14:46,140
+واحد على T بي two solutions
+
+147
+00:14:47,270 --> 00:14:56,650
+بتو solutions of the differential equation of the
+
+148
+00:14:56,650 --> 00:15:05,690
+differential equation للمعادلة التفاضلية اثنين T
+
+149
+00:15:05,690 --> 00:15:14,070
+تربيع Y double prime زائد ثلاثة T Y prime ناقص Y
+
+150
+00:15:14,070 --> 00:15:23,540
+تساوي صفر وال T greater than zero find بدنا
+
+151
+00:15:23,540 --> 00:15:31,080
+ال wronskian تبع ال Y واحد وال Y اثنين as a function
+
+152
+00:15:31,080 --> 00:15:40,940
+of T also وكذلك find the constant C on the 
+
+153
+00:15:40,940 --> 00:15:42,580
+constant
+
+154
+00:16:09,120 --> 00:16:15,550
+الاخت لواء بتسألته قبل قليل بتقول إيش؟ بتقول طب أنا
+
+155
+00:16:15,550 --> 00:16:18,570
+إيش احنا نستخدم هال wronskian اللي أخذناها قبل
+
+156
+00:16:18,570 --> 00:16:23,190
+المحدد والله تبعي بالطريقة اللي نقول هي يمكن يلزم الاثنين
+
+157
+00:16:23,190 --> 00:16:28,380
+ونحن الإجابة على جدّ السؤال نشوف شو اللي بدها طيب
+
+158
+00:16:28,380 --> 00:16:32,820
+السؤال بيقول ما يلي الكلام الـ... الإجابة على لغة
+
+159
+00:16:32,820 --> 00:16:37,460
+لواء والكلام للسامعين بتقول افترض أو المثال اللي 
+
+160
+00:16:37,460 --> 00:16:41,160
+بتقول افترض أن Y1 هو جذر ال T وال Y2 و1 على T وهم
+
+161
+00:16:41,160 --> 00:16:45,020
+عبارة عن حلّين للمعادلة التفاضلية لأنه قال هات لي 
+
+162
+00:16:45,020 --> 00:16:49,000
+ال wronskian تبعهم بقوله بسيط أول شيء هنجيب ال wronskian
+
+163
+00:16:49,240 --> 00:16:56,900
+as a function of T مباشرة فبجب أقول الحل الأول جذر 
+
+164
+00:16:56,900 --> 00:17:05,540
+ال T والحل الثاني 1 على T بدنا نشتقه يبقى 1 على 2
+
+165
+00:17:05,540 --> 00:17:12,920
+جذر ال T وهذا سالب 1 على T تربيع هذا الكلام بده
+
+166
+00:17:12,920 --> 00:17:18,180
+يساوي حاصل ضرب عناصر القطر الرئيسي ناقص حاصل ضرب
+
+167
+00:17:18,180 --> 00:17:24,380
+عناصر القطر الثانوي أظن ناقص T أس ثلاثة على
+
+168
+00:17:24,380 --> 00:17:31,070
+اثنين بنفع يبقى T أس سالب اثنين ضرب T أس نص يبقى T 
+
+169
+00:17:31,070 --> 00:17:34,970
+أس سالب واحد ونص يعني T أس سالب ثلاثة على اثنين
+
+170
+00:17:34,970 --> 00:17:41,770
+هذا الرئيسي ناقصي الثانوي كله في المقام يبقى ما 
+
+171
+00:17:41,770 --> 00:17:47,430
+نطلعه فوق بيصير T أس سالب واحد ونص T أس سالب نص
+
+172
+00:17:47,430 --> 00:17:55,030
+يبقى هذا بيصير ناقص نص T أس سالب ثلاثة على اثنين
+
+173
+00:17:56,
+
+216
+00:22:54,220 --> 00:23:01,720
+وإذا كان الـ Wronskian تبع الحل الأول والحل الثاني عند
+
+217
+00:23:01,720 --> 00:23:08,580
+الواحد بده يساوي واحد أو دونه اللي هو الـ Wronskian
+
+218
+00:23:08,580 --> 00:23:14,420
+تبع الحل الأول والحل الثاني عند الثمان
+
+219
+00:23:29,110 --> 00:23:32,610
+لو مسكت ورقة الامتحان تبع الفصل الماضي تبع أعمال 
+
+220
+00:23:32,610 --> 00:23:37,970
+الفصل بتلاقي هذا السؤال موجود فيها طيب بقول افترض
+
+221
+00:23:37,970 --> 00:23:42,670
+أنه عندي حلين واثنين linearly independent يبقى 
+
+222
+00:23:42,670 --> 00:23:47,570
+لو جيتك وحسبت الـ Wronskian تبعهم ممكن يساوي صفر؟ مش 
+
+223
+00:23:47,570 --> 00:23:50,770
+إمكانية يبقى مدام جالي linearly independent يبقى
+
+224
+00:23:50,770 --> 00:23:55,770
+الـ Wronskian لا يمكن أن يساوي صفر بأي حالة من الأحوال
+
+225
+00:23:55,770 --> 00:24:00,600
+وبالتالي الـ C تبعت الـ Abel theorem لا يمكن أن تكون
+
+226
+00:24:00,600 --> 00:24:05,660
+بصفر على الإطلاق طيب قال لي ماشي لها اثنين linearly 
+
+227
+00:24:05,660 --> 00:24:08,600
+independent solution للمعادلة هذه قال لي هات لي الـ
+
+228
+00:24:08,600 --> 00:24:12,360
+Wronskian وإذا كان الـ Wronskian عند الواحد بدي يساوي عدد
+
+229
+00:24:12,360 --> 00:24:16,400
+هات لي الـ Wronskian وأنا عندي اثنين بقول لكم يا شباب باجي 
+
+230
+00:24:16,400 --> 00:24:19,040
+للـ differential equation هذه بدي أحطها في الـ
+
+231
+00:24:19,040 --> 00:24:23,690
+standard form مشان أجيب P of T بالظبط أنا بدي
+
+232
+00:24:23,690 --> 00:24:28,850
+المعامل هنا بقدرش إذا بتروح أقسم كلّه على  وبقدر 
+
+233
+00:24:28,850 --> 00:24:32,870
+أقسم بكل سهولة لإن T greater than zero لإن يمكن أن
+
+234
+00:24:32,870 --> 00:24:36,790
+تساوي صفر إذا بناء على المعادلة دي بتصير على
+
+235
+00:24:36,790 --> 00:24:45,200
+الشكل التالي Y ناقص أربعة على T في الـ Y prime زائد
+
+236
+00:24:45,200 --> 00:24:52,440
+اللي هو ستة على T تربيع في الـ Y بدّه يساوي كده؟ بده
+
+237
+00:24:52,440 --> 00:24:58,620
+يساوي صفر تمام تمام يبقى الآن بقدر أجيب الـ Wronskian
+
+238
+00:24:58,620 --> 00:25:02,340
+تبعها طبعًا احنا من ضمن الـ Wronskian لازم تبقى الدوال
+
+239
+00:25:02,340 --> 00:25:07,460
+دوال متصلة لـ P ولـ Q طبعًا الـ discontinuity بيحصل
+
+240
+00:25:07,460 --> 00:25:12,170
+وين؟ عند الـ Zero لكن احنا مش مهتمين يبقى دول
+
+241
+00:25:12,170 --> 00:25:16,490
+continuous متحقق على طول الخط بدون أي إشكالية يبقى
+
+242
+00:25:16,490 --> 00:25:20,210
+مناقيش عليها بقدر أجيب الـ Wronskian تبع الحل الأول والحل 
+
+243
+00:25:20,210 --> 00:25:26,390
+الثاني يبقى الـ Wronskian تبع الحل الأول والحل الثاني as
+
+244
+00:25:26,390 --> 00:25:36,200
+a function of T يساوي C في E أس ناقص أصلًا تنسوش ناقص 
+
+245
+00:25:36,200 --> 00:25:40,480
+القانون يبقى
+
+246
+00:25:40,480 --> 00:25:51,440
+بيصير زائد تكامل أربعة على T DT يبقى هذا الكلام ساوي C
+
+247
+00:25:51,440 --> 00:25:58,880
+في E أس أربعة لين T لغاية لأن T أكبر من زمّن من Zero
+
+248
+00:26:00,560 --> 00:26:09,320
+يبقى C في E أس لين T أس أربعة يبقى C في T أس أربعة
+
+249
+00:26:09,320 --> 00:26:18,500
+هذا شكل من الـ Wronskian جالي إن الـ Wronskian عند الواحد بدّه
+
+250
+00:26:18,500 --> 00:26:23,520
+يساوي واحد M plus يعني بده أشيل كل T وأحط مكانها
+
+251
+00:26:24,160 --> 00:26:31,580
+واحد يبقى هنا واحد بده يساوي C في واحد أس أربعة يعني 
+
+252
+00:26:31,580 --> 00:26:37,700
+بتطلع C بقد ايش؟ لما C تساوي واحد يبقى أصبح in 
+
+253
+00:26:37,700 --> 00:26:44,800
+general الـ Wronskian الحل الأول والحل الثاني بدّه يساوي
+
+254
+00:26:44,800 --> 00:26:52,640
+بقد ايش؟ E ولا بدّه يساوي دور T وأربعة دور جالي هات لي الـ
+
+255
+00:26:52,640 --> 00:26:58,240
+Wronskian تبع الحل الأول والحل الثاني عندي اثنين
+
+256
+00:26:58,240 --> 00:27:04,620
+يبقى ما عليّ إلا أشيل T وأحط مكانها اثنين أس أربعة
+
+257
+00:27:04,620 --> 00:27:11,980
+يبقى الجواب بقد ايش؟ 16 صحيح؟ مباشر هذا اجى في
+
+258
+00:27:11,980 --> 00:27:17,420
+الامتحان الفصل الماضي طيب خذي الـ example تلاتة
+
+259
+00:27:20,860 --> 00:27:33,360
+بقول إنّ Y1 and Y2 بيكونوا solutions
+
+260
+00:27:33,360 --> 00:27:39,880
+of the
+
+261
+00:27:39,880 --> 00:27:47,960
+differential equation للمعادلة التفاضلية واحد ناقص
+
+262
+00:27:47,960 --> 00:27:49,040
+T تربيع
+
+263
+00:28:03,230 --> 00:28:04,630
+Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''
+
+264
+00:28:05,370 --> 00:28:12,870
+قال إذا كان F الـ Wronskian تبع الـ Y واحد والـ Y اثنين
+
+265
+00:28:12,870 --> 00:28:22,550
+عند النص بده يساوي ثلاثة find الـ Wronskian
+
+266
+00:28:22,550 --> 00:28:29,130
+تبع الحل الأول والحل الثاني as a function of T for 
+
+267
+00:28:29,130 --> 00:28:39,750
+all T or all T لجميع قيم T in the interval in the
+
+268
+00:28:39,750 --> 00:28:52,830
+interval على الفترة in which بحيث أن in which the
+
+269
+00:28:52,830 --> 00:29:01,190
+solution exists
+
+270
+00:29:42,830 --> 00:29:48,150
+نرجع لسؤالنا مرة ثانية بقول افترض عندي حلين
+
+271
+00:29:48,150 --> 00:29:51,990
+للمعادلة التفاضلية اللي قدامنا هذه وإذا كان
+
+272
+00:29:51,990 --> 00:29:55,970
+الـ Wronskian عنده نص بده يساوي ثلاثة هات لي الـ Wronskian in 
+
+273
+00:29:55,970 --> 00:30:01,630
+general as a function of T in the interval على
+
+274
+00:30:01,630 --> 00:30:05,130
+الفترة اللي الحل بيكون عليها صياني أنا بدي أحسب 
+
+275
+00:30:05,130 --> 00:30:08,570
+بقد ايش نص كدالة للـ T وبدي أعرف اللي الـ interval
+
+276
+00:30:08,570 --> 00:30:12,410
+اللي الكلام عليها هذا معنى صحيح يبقى العبارة الأخرى 
+
+277
+00:30:12,410 --> 00:30:15,990
+هي اللي أتي اللي اجت زيادة على مين؟ الحال الأول 
+
+278
+00:30:15,990 --> 00:30:19,610
+حال الأول قال لي تيجريفر دان زيرو فهو طان الفترة،
+
+279
+00:30:19,610 --> 00:30:23,830
+بس هنا ما اطنش الفترة أنا اللي بدي أجيب مين؟ الفترة
+
+280
+00:30:23,830 --> 00:30:28,680
+التابعة لذلك المعادلة التفاضلية دي بدي أنقلها 
+
+281
+00:30:28,680 --> 00:30:32,660
+إلى وضع آخر غير الوضع اللي هو فيه بدي اخلّي المعامل
+
+282
+00:30:32,660 --> 00:30:38,520
+هذا Y double prime يبقى بدأ أقسم كلّه على مين؟ على واحد ناقص T
+
+283
+00:30:38,520 --> 00:30:44,520
+تربيع يبقى solution the
+
+284
+00:30:44,520 --> 00:30:52,700
+differential equation S بدي أكتبها على الشكل 
+
+285
+00:30:52,700 --> 00:30:53,960
+التالي Y
+
+286
+00:31:17,930 --> 00:31:24,270
+أظنّ المقام نقدر نحلله كفرق بين مربعين يبقى هذا لو
+
+287
+00:31:24,270 --> 00:31:30,930
+جينا حللنا بيصير Y double prime زائد واحد زائد T
+
+288
+00:31:30,930 --> 00:31:38,050
+واحد ناقص T في واحد زائد T كله في الـ Y prime واحد
+
+289
+00:31:38,050 --> 00:31:45,490
+ناقص T واحد ناقص T في واحد زائد T كلّه في الـ Y بدّه
+
+290
+00:31:45,490 --> 00:31:51,410
+يساوي بقد ايش؟ صفر نختصر الاختصارات اللي موجودة يبقى
+
+291
+00:31:51,410 --> 00:31:55,770
+المعادلة التفاضلية أصبحت على الشكل التالي
+
+292
+00:32:07,510 --> 00:32:11,090
+مشان نحسب الـ Wronskian لازم يكون معامل P of T
+
+293
+00:32:11,090 --> 00:32:17,350
+والـ Q of T دوال متصلة على نفس الفترة مظبوط طيب
+
+294
+00:32:17,350 --> 00:32:22,950
+هنا الآن باجي أقوله الـ P of T اللي هي واحد على 
+
+295
+00:32:22,950 --> 00:32:33,230
+واحد ناقص T هذه continuous for all T اللي بتساويش
+
+296
+00:32:33,230 --> 00:32:40,760
+الواحد صحيح ولا لأ؟ طيب لـ Q of T اللي هي واحد على 
+
+297
+00:32:40,760 --> 00:32:46,740
+واحد زائد T continuous لكل الـ T اللي بتساويش مين؟
+
+298
+00:32:46,740 --> 00:32:53,020
+سالب واحد طيب تعالوا نشوف هذا الـ real line وهذه 
+
+299
+00:32:53,020 --> 00:32:56,680
+النقطة اللي عندي سالب واحد وهذه النقطة اللي عندي 
+
+300
+00:32:56,680 --> 00:33:03,480
+اللي واحد الدالة له continuity و discontinuity حصل عند
+
+301
+00:33:03,480 --> 00:33:10,020
+الواحد يعني هنا open وبعدها continuous وقبلها 
+
+302
+00:33:10,020 --> 00:33:16,080
+continuous بنجي ثاني لـ Q of T الـ discontinuity حصل 
+
+303
+00:33:16,080 --> 00:33:22,620
+وين؟ عند السالب واحد يبقى هنا مفتوحة وبنجي هيك 
+
+304
+00:33:22,620 --> 00:33:28,220
+continuous على طول وهيك continuous كذلك على طول
+
+305
+00:33:28,220 --> 00:33:37,610
+يبقى في عندي كم منطقة مشتركة بينهم؟ ثلاث مناطق من
+
+306
+00:33:37,610 --> 00:33:42,930
+سالب ما لا نهاية إلى سالب واحد ومن سالب واحد إلى واحد
+
+307
+00:33:42,930 --> 00:33:47,630
+ومن واحد إلى ما لا نهاية يبقى احنا قسمنا الـ real line
+
+308
+00:33:47,630 --> 00:33:55,070
+إلى three open intervals من أخد منهم تعالى نشوف 
+
+309
+00:33:55,070 --> 00:34:00,710
+ايش بيقول هنا الـ Wronskian وين؟ عند النص يبقى النص بيجي 
+
+310
+00:34:00,710 --> 00:34:06,500
+وين في الفترة من سالب واحد إلى واحد يعني هذه هنا
+
+311
+00:34:06,500 --> 00:34:13,100
+تبقى الـ Zero وهنا تجينا النص هي نقطة لأن هذه إذا 
+
+312
+00:34:13,100 --> 00:34:18,600
+أنا بتاخد الفترة من وين لوين؟ من سالب واحد إلى واحد
+
+313
+00:34:18,600 --> 00:34:30,880
+يبقى هنا الـ functions الـ P of T and لـ Q of T
+
+314
+00:34:34,950 --> 00:34:42,910
+continuous واللي موجودة في الـ interval من
+
+315
+00:34:42,910 --> 00:34:47,630
+سالب واحد إلى واحد يعني احنا شغلنا هيكون على الفترة 
+
+316
+00:34:47,630 --> 00:34:53,110
+هذه وباقي الفترات ما ليّ دعوة فيهم بنقول له كويس
+
+317
+00:34:53,110 --> 00:34:57,470
+طيب احنا لسه قاعدين بنبحث بس في الـ continuity لكن 
+
+318
+00:34:57,470 --> 00:35:02,290
+ما تكلمناش في الحل اللي هو بده إياه حتى اللحظة أشجلجل
+
+319
+00:35:02,290 --> 00:35:06,210
+هات لي الـ Wronskian أو إذا كان الـ Wronskian عنده نصف بدّه
+
+320
+00:35:06,210 --> 00:35:11,050
+يساوي ثلاثة هات لي الـ Wronskian على الفترة اللي الحل
+
+321
+00:35:11,050 --> 00:35:15,720
+عليها صحيح يبقى الحل عنده صيانة في فترة من سالب
+
+322
+00:35:15,720 --> 00:35:19,640
+واحد إلى واحد والفترات الثانية ما ليّ علاقة فيها
+
+323
+00:35:19,640 --> 00:35:24,060
+يعني أخدت الفترة الممكنة على مين؟ على النص إذا 
+
+324
+00:35:24,060 --> 00:35:28,920
+بدنا نروح نحسب مين الـ Wronskian تبعنا يبقى باجي
+
+325
+00:35:28,920 --> 00:35:35,240
+أقوله الـ Wronskian as a function of T يساوي C في E 
+
+326
+00:35:35,240 --> 00:35:44,320
+والسالب تكامل P of T DT يعني يساوي C في E والسالب 
+
+327
+00:35:44,320 --> 00:35:50,280
+تكامل وين الـ P اللي عندنا هي واحد على واحد ناقص T
+
+328
+00:35:50,280 --> 00:35:59,760
+يبقى هي سالب واحد على واحد ناقص T DT أظنّ البسط 
+
+329
+00:35:59,760 --> 00:36:08,460
+فاضل المقام يبقى بيصير عندنا C في E أس لين absolute
+
+330
+00:36:08,460 --> 00:36:17,040
+value للواحد ناقص T يعني مين؟ يعني C absolute value
+
+331
+00:36:17,040 --> 00:36:24,100
+للواحد ناقص T طيب بدنا نشوف هل الـ absolute هذا 
+
+332
+00:36:24,100 --> 00:36:30,440
+بيظلّ ولا بيروح احنا بنشتغل ما بين من سالب واحد إلى
+
+333
+00:36:30,440 --> 00:36:34,660
+واحد ممنوع الواحد وممنوع السالب واحد يبقى ايش؟ 
+
+334
+00:36:34,660 --> 00:36:40,240
+ما تحط هنا عمرها بيصير سالب هات حط الرقم اللي بدّك 
+
+335
+00:36:40,240 --> 00:36:43,660
+يعني بعيد عن السالب واحد والواحد وخد أي شغلة بينهم
+
+336
+00:36:43,660 --> 00:36:48,410
+عمرها بيصير سالب يبقى هذه موجبة دائمًا وأبدًا إذا لا 
+
+337
+00:36:48,410 --> 00:36:54,630
+داعي للـ absolute value يبقى بهذا بدّه يساوي C في 
+
+338
+00:36:54,630 --> 00:37:01,590
+واحد ناقص T لكل T اللي موجودة في الـ interval من
+
+339
+00:37:01,590 --> 00:37:05,330
+سالب واحد إلى واحد للـ open interval
+
+340
+00:37:08,010 --> 00:37:16,210
+الـ Wronskian عند النص بده يساوي ثلاثة implies يبقى
+
+341
+00:37:16,210 --> 00:37:22,390
+بده يشيل كل T ويحط مكانها نص يبقى هاي ثلاثة بدّه 
+
+342
+00:37:22,390 --> 00:37:23,190
+يساوي
+
+343
+00:37:48,540 --> 00:37:49,940
+Y1Y2Y3Y4Y5Y6Y7Y8Y9Y10Y11Y12Y13Y14Y15Y16Y17Y18Y19Y20Y21Y22Y22Y22Y23Y23Y23Y23Y23Y23Y23Y23Y23Y23Y23Y23Y23Y23Y23Y23Y23Y23Y23Y23Y23Y23Y23Y23Y23Y23Y23Y23Y23Y23Y23Y23Y23Y23Y23Y23Y23Y23Y23Y23Y23Y23Y23Y23Y23Y23Y23Y23Y23Y23Y23Y23Y23Y23Y23Y23Y23Y23Y23Y23Y23Y23Y23Y23Y23Y23Y23Y23Y23Y23Y23Y23Y23Y23
+
+344
+00:37:50,110 --> 00:37:58,370
+بدّه يساوي ستة في الـ Wronskian اللي هو واحد ناقص T، ده اللي 
+
+345
+00:37:58,370 --> 00:38:04,910
+هو الحل المطلوب، حد فيكم بيحب يسأل لي سؤال هنا؟
+
+346
+00:38:04,910 --> 00:38:08,530
+أيوه، دي ايش؟
+
+347
+00:38:15,940 --> 00:38:23,000
+هذه الفترة اللي لازم تختار ت سالب نص وسالب تصبح
+
+348
+00:38:23,000 --> 00:38:26,600
+واحد زائد نص ثلاثة على اثنين موجبة يبقى هذا على الـ 
+
+349
+00:38:26,600 --> 00:38:31,500
+absolute value بيغيرها تاخدها نص موجبة تصبح واحد
+
+350
+00:38:31,500 --> 00:38:35,360
+ناقص نص تبقى نص موجبة يبقى هذا على الـ absolute
+
+351
+00:38:35,360 --> 00:38:40,340
+value أي رقم تاخده أيّه بعيد عن سالب واحد اخد أي
+
+352
+00:38:40,340 --> 00:38:45,060
+رقم بينهم تظل بين جثين هذه الكمية يبقى لا داعي للـ
+
+353
+00:38:45,060 --> 00:38:51,200
+absolute value تمام؟ اتلاحظت قولت لك هذا for all T 
+
+354
+00:38:51,200 --> 00:38:55,180
+يعني شيلت الـ absolute value قولت لك C في واحد ناقص
+
+355
+00:38:55,180 --> 00:38:57,940
+T ليا كل الـ T اللي موجود في الـ interval بس لو طلعت
+
+356
+00:38:57,940 --> 00:39:03,320
+برة هذى بيصير كلامي مش صحيح تمام؟ حد يسأل ثاني؟
+
+357
+00:39:04,360 --> 00:39:11,280
+ننتقل الآن إلى النقطة اللي بعدها اللي هي نظرية وهذه
+
+358
+00:39:11,280 --> 00:39:15,860
+النظرية طبعًا أقوى من النظرية اللي أخذناها المرة 
+
+359
+00:39:15,860 --> 00:39:19,200
+الماضية المرة الماضية فأخذناها نظرية واحدة وكان
+
+360
+00:39:19,200 --> 00:39:23,560
+بنمشي في اتجاه واحد إذا الـ Wronskian لا يساوي صفر
+
+361
+00:39:23,560 --> 00:39:28,340
+عند نقطة بنقول linearly independent والعكس لو كانت
+
+362
+00:39:28,340 --> 00:39:31,920
+هي linearly dependent بنقول الـ Wronskian يساوي صفر
+
+363
+00:39:32,180 --> 00:39:37,460
+الآن بدنا نجيب نظرية أقوى منها في الاتجاهين if and
+
+364
+00:39:37,460 --> 00:39:49,860
+only if النظرية بتقول ما يأتي فيرم 
+
+365
+00:39:49,860 --> 00:39:55,440
+let 
+
+366
+00:39:55,440 --> 00:40:01,380
+الـ Y واحد and Y اثنين 
+
+367
+00:40:06,080 --> 00:40:14,720
+be solutions be solutions of the differential equation
+
+368
+00:40:14,720 --> 00:40:25,940
+للمعادلة التفاضلية L of Y بدّه يساوي Y double prime
+
+369
+00:40:25,940 --> 00:40:28,700
+زائد P of T في Y prime
+
+370
+00:40:33,730 --> 00:40:48,350
+الـ P of T and Q of T are continuous functions
+
+371
+00:40:49,320 --> 00:41:01,180
+دوال متصلة on an interval I on an open interval I 
+
+372
+00:41:01,180 --> 00:41:11,060
+then then 
+
+373
+00:41:11,060 --> 00:41:26,010
+Y واحد and Y اثنين are linearly dependent on I if
+
+374
+00:41:26,010 --> 00:41:33,270
+and only if if and only if الـ Wronskian تبع الـ Y
+
+375
+00:41:33,270 --> 00:41:41,310
+واحد والـ Y اثنين as a function of T linearly
+
+376
+00:41:41,310 --> 00:41:51,080
+dependent on I linearly dependent on if and only if
+
+377
+00:41:51,080 --> 00:41:54,380
+الـ Wronskian
+
+3
+
+431
+00:48:36,110 --> 00:48:40,450
+كانت في اتجاه واحد لكن سرعتها في اتجاهين إلى
+
+432
+00:48:40,450 --> 00:48:43,970
+الاتجاه الصحيح و لجميع قيم T التي موجودة في ال
+
+433
+00:48:43,970 --> 00:48:48,510
+interval مش هندقق على نقطة واحدة وإنما على كل ال
+
+434
+00:48:48,510 --> 00:48:51,870
+interval التي الحل عليها صحيح أو للدوال التي
+
+435
+00:48:51,870 --> 00:48:58,000
+عليها متصلة التي P وQ والخيار هو من ناحية أخرى يعني
+
+436
+00:48:58,000 --> 00:49:02,620
+كانوا بالداخل يمشي العكس أن Y1 وY2 are linearly 
+
+437
+00:49:02,620 --> 00:49:08,680
+independent إذا الوضع نفسه كان لا يساوي zero لكل 
+
+438
+00:49:08,680 --> 00:49:13,160
+الـ T التي موجودة في الـ I، جالي on I يعني على كل ال
+
+439
+00:49:13,160 --> 00:49:17,900
+I بلا استثناء، لكن هناك في النظرية يقول لمن؟ عندنا 
+
+440
+00:49:17,900 --> 00:49:21,740
+نقطة واحدة، إذا من الآن فصاعدًا، لأن لو عندي
+
+441
+00:49:21,740 --> 00:49:25,400
+معادلة تفاضلية يجيب تحليل ويقول لي شوفهم لينيار أو
+
+442
+00:49:25,400 --> 00:49:29,160
+independent، والله independent لقيت عند نقطة لقيت
+
+443
+00:49:29,160 --> 00:49:33,880
+عند نقطتين لقيت عند كل نقاط الاتنين are the same
+
+444
+00:49:33,880 --> 00:49:37,380
+linearly independent تعني أن الوضع كان لا يساوي
+
+445
+00:49:37,380 --> 00:49:41,860
+zero والعكس صحيح linearly dependent تعني أن الوضع 
+
+446
+00:49:41,860 --> 00:49:46,580
+كان يساوي zero والعكس صحيح طب الـ remark هذه يا بنات
+
+447
+00:49:46,580 --> 00:49:51,900
+لأنها شملت كل ما سبق في الـ section الذي فات، تمام؟
+
+448
+00:49:51,900 --> 00:49:55,840
+يعني جمعته كله وحطته في النقاط الأربع التي قدامها
+
+449
+00:49:55,840 --> 00:49:59,880
+ده إيش بتقولي remark؟ لو كان هدول حلول المعادلة 
+
+450
+00:49:59,880 --> 00:50:03,680
+ال تفاضلية يبقى then the following are equivalent
+
+451
+00:50:03,680 --> 00:50:07,320
+في عندي أربع جمل التي يمكن تشيلي أي واحدة منهم و
+
+452
+00:50:07,320 --> 00:50:12,460
+تحطي الثانية بدلًا منها الأولى بتقولي أن y1 و y2 are
+
+453
+00:50:12,460 --> 00:50:16,540
+fundamental set of solutions عالميًا على ال
+
+454
+00:50:16,540 --> 00:50:22,300
+interval I للمعادلة التفاضلية التي عندنا، يبقى
+
+455
+00:50:22,300 --> 00:50:26,300
+هذول اتنين بيكونولي fundamentals أو الـ general
+
+456
+00:50:26,300 --> 00:50:30,380
+solution تمام سي واحد الأول زائد سي اتنين هو الـ general
+
+457
+00:50:30,380 --> 00:50:36,380
+اتنين مكافئين لبعض، هذا بكافئ إيش؟ بكافئ لو حدث 
+
+458
+00:50:36,380 --> 00:50:39,540
+ذلك أن هذول كانوا اتنين fundamental set of
+
+459
+00:50:39,540 --> 00:50:45,960
+solutions يبقى حاليًا linearly independent مظبوط؟
+
+460
+00:50:46,320 --> 00:50:52,960
+ممكن كمان أن رونسكين تمام عند نقطة لا يساوي zero
+
+461
+00:50:52,960 --> 00:51:00,060
+تمام؟ طيب ممكن رونسكين عند كل النقاط يكون لا يساوي
+
+462
+00:51:00,060 --> 00:51:05,380
+zero يعني أن ثبت أن عند نقطة واحدة على الأقل كان
+
+463
+00:51:05,380 --> 00:51:09,640
+لا يساوي zero في الـ interval إذا رونسكين لا يساوي
+
+464
+00:51:09,640 --> 00:51:14,120
+zero على كل الـ interval مرة واحدة هيبقى ده جمع
+
+465
+00:51:14,120 --> 00:51:19,500
+النظريتين مع بعض بشغل هيبقى نقولش لك اثبتلي والله
+
+466
+00:51:19,500 --> 00:51:22,460
+اتنين هدول بيكونولي fundamental set of solutions
+
+467
+00:51:22,460 --> 00:51:23,700
+بتروح تاخديلهم
+
+468
+01:00:00,225 --> 01:00:04,605
+أو اتنين بيكونولي fundamental set of solutions
+
+469
+01:00:04,605 --> 01:00:08,285
+للمسألة التي عندي عند نقطة والله عن جميع النقاط
+
+470
+01:00:08,285 --> 01:00:15,765
+كله سيئة، حد فيكم بتسأل أسئلة قبل أن آخذ مثال طيب 
+
+471
+01:00:15,765 --> 01:00:20,125
+إيه الأمثلة والله إيه المثال example
+
+472
+01:00:27,635 --> 01:00:32,115
+بقول لك Y1 
+
+473
+01:00:32,115 --> 01:00:36,135
+بيه
+
+474
+01:00:36,135 --> 01:00:46,155
+solution of the initial value problem YW prime
+
+475
+01:00:46,155 --> 01:00:56,515
+زائد T تربيع Y prime زائد T تكعيب Y تساوي Zero وال
+
+476
+01:00:56,515 --> 01:01:03,655
+y واحد عند الـ واحد يساوي واحد والـ y prime عند الـ
+
+477
+01:01:03,655 --> 01:01:15,915
+واحد بده يساوي كده؟ بده يساوي تلاتة الآن let y2 be
+
+478
+01:01:15,915 --> 01:01:22,555
+a solution of the initial value problem والشرط أن 
+
+479
+01:01:22,555 --> 01:01:31,095
+y2 عند الواحد y2 عند الواحد يساوي سالب واحد و y2 a
+
+480
+01:01:31,095 --> 01:01:38,255
+prime عند الواحد يساوي قداش اتنين، المطلوب الأول 
+
+481
+01:01:38,255 --> 01:01:46,815
+نمر ايه بيقول show that show that بيقول أن y واحد
+
+482
+01:01:46,815 --> 01:02:01,835
+عند y اتنين form a fundamental set 
+
+483
+01:02:01,835 --> 01:02:10,935
+of solutions
+
+484
+01:02:10,935 --> 01:02:15,995
+of the differential equation
+
+485
+01:02:27,695 --> 01:02:36,495
+of the differential equation للمعادلة التفاضلية 
+
+486
+01:02:36,495 --> 01:02:43,735
+التي هي Y double prime زائد T تربيع Y prime زائد T
+
+487
+01:02:43,735 --> 01:02:52,055
+تكعيب Y بده يساوي قداش بده يساوي Zero نمر بي find
+
+488
+01:02:52,055 --> 01:02:56,375
+constants find constants
+
+489
+01:02:59,335 --> 01:03:16,475
+C1 and C2 such that بحيث أن Y تساوي C1 Y1 زائد C2 Y2 زائد C2
+
+490
+01:03:16,475 --> 01:03:30,885
+Y2 is the general solution of الـ initial value
+
+491
+01:03:30,885 --> 01:03:39,445
+problem الـ y double prime زائد الـ T تربيع y prime
+
+492
+01:03:39,445 --> 01:03:47,325
+زائد الـ T تكعيب y بدو يساوي zero والـ Y عند الواحد 
+
+493
+01:03:47,325 --> 01:03:53,665
+بدو يساوي اتنين والـ Y prime عند الواحد بدو يساوي
+
+494
+01:03:53,665 --> 01:03:56,445
+كده؟ بدو يساوي zero 
+
+495
+01:04:10,065 --> 01:04:16,025
+نرجع لسؤالنا مرة ثانية بقول لو كان Y1 هو solution
+
+496
+01:04:16,025 --> 01:04:21,885
+للـ initial value problem التي عندنا هذا Y2 هو 
+
+497
+01:04:21,885 --> 01:04:25,245
+solution لنفس الـ initial value problem المعادلة
+
+498
+01:04:25,245 --> 01:04:29,725
+نفسها بس غيرنا مين؟ غيرنا الـ initial conditions
+
+499
+01:04:29,725 --> 01:04:37,165
+يبقى أنا عندي Y1 و Y1' و Y2 و Y2' بقول المطبق الذي
+
+500
+01:04:37,165 --> 01:04:40,105
+هو الـ Bayley أن أي واحد أو أي اتنين form a
+
+501
+01:04:40,105 --> 01:04:42,605
+fundamental set of solutions للـ differential
+
+502
+01:04:42,605 --> 01:04:47,625
+equation التي عندنا هذه بقوله والله كويس إذا والله
+
+503
+01:04:47,625 --> 01:04:52,625
+المحدد تبعهم لا يساوي zero إذا الأتنين بيكونوا
+
+504
+01:04:52,625 --> 01:04:55,165
+fundamental set of solutions طبقا للـ remark التي 
+
+505
+01:04:55,165 --> 01:05:00,075
+مسحناها قبل قليل أو الـ band in Y1 وY2 before my
+
+506
+01:05:00,075 --> 01:05:03,075
+fundamental system solution إذا الورونس كان عند 
+
+507
+01:05:03,075 --> 01:05:07,495
+نقطة أو على طول كان ماله؟ لا يستوزن، إذا بدنا نروح 
+
+508
+01:05:07,495 --> 01:05:11,355
+نحسب الورونس كان، تمام؟ إذا لو رحت حسبت الورونس 
+
+509
+01:05:11,355 --> 01:05:16,735
+عند نقطة أو عند كل النقاط، كلسيا أي واحدة فيهم، طب
+
+510
+01:05:16,735 --> 01:05:19,815
+احنا بلاحظ أن الـ initial conditions محسبات، كلهم
+
+511
+01:05:19,815 --> 01:05:24,085
+عند مين؟ إذا خليني أحسب الورونسكين عند الواحد صح
+
+512
+01:05:24,085 --> 01:05:29,765
+ولا لأ يبقى باجي بقوله solution نمر ايه؟ بدي أحسب
+
+513
+01:05:29,765 --> 01:05:36,845
+الورونسكين عند الواحد يبقى هذا الكلام بدي يساوي y
+
+514
+01:05:36,845 --> 01:05:44,465
+واحد عند الواحد y اتنين عند الواحد y اتنين وواحد
+
+515
+01:05:44,465 --> 01:05:52,475
+prime عند الواحد y اتنين prime عند الواحد صح؟ كويس
+
+516
+01:05:52,475 --> 01:05:57,815
+هذه يعني T node يا بنات تبعت الـ remark هي التي هي 
+
+517
+01:05:57,815 --> 01:06:03,355
+واحد طب هذا الكلام بده يساوي Y واحد عند الواحد هي 
+
+518
+01:06:03,355 --> 01:06:10,655
+بواحد Y اتنين عند الواحد هي بسالب واحد Y واحد الـ 
+
+519
+01:06:10,655 --> 01:06:16,495
+prime عند الواحد هي بتلاتة Y اتنين الـ prime عند
+
+520
+01:06:16,495 --> 01:06:22,625
+الواحد اللي هو باتنين، يبقى نفك المحددة ده اتنين
+
+521
+01:06:22,625 --> 01:06:29,705
+زائد تلاتة اتنين زائد تلاتة هو يساوي خمسة لا يساوي
+
+522
+01:06:29,705 --> 01:06:34,095
+Zero ما دام لا يساوي zero يبقى الحالين هدول بقالهم
+
+523
+01:06:34,095 --> 01:06:38,295
+بيكونولي fundamental set وأنا مش عارف شو شكلهم ولا 
+
+524
+01:06:38,295 --> 01:06:42,935
+مطلوب أعرف شكلهم ماجليش هاتل الحالين تمام يبقى 
+
+525
+01:06:42,935 --> 01:06:56,515
+باجي بقول له so y1 and y2 form a fundamental set
+
+526
+01:07:28,845 --> 01:07:34,475
+خلصنا المطلب الأول نعود لمطلب الثاني، المطلوب الثاني
+
+527
+01:07:34,475 --> 01:07:41,015
+هو find constants C1 وC2 يبقى مادام هذول كوّنولي 
+
+528
+01:07:41,015 --> 01:07:44,815
+fundamental set of solutions يبقى الـ general
+
+529
+01:07:44,815 --> 01:07:48,955
+solution يكون constant في الحل الأول زائد constant
+
+530
+01:07:48,955 --> 01:07:56,915
+في الحل الثاني، إذا باجي بقول له general solution
+
+531
+01:08:08,965 --> 01:08:10,365
+YYYYYYYYYYYYYYYYYY
+
+532
+01:08:28,835 --> 01:08:35,375
+إذا بقدر أستخدم الشروط التي عندي فيه إيجاد c1 و c2
+
+533
+01:08:35,375 --> 01:08:40,000
+مظبوط ولا لا باجي بقوله والله كويس يبقى بدي أشتق
+
+534
+01:08:40,000 --> 01:08:45,300
+هذه أمانة، إذا لو اشتقت هذه إيش بصير y prime c1 
+
+535
+01:08:45,300 --> 01:08:54,210
+مقدار ثابت مالوش دهوة وهذه y1 prime زائد c2 y2 prime عند 
+
+536
+01:08:54,210 --> 01:08:58,510
+الواحد يجب أن يجي إلى الـ condition الأول يجي إلى 
+
+537
+01:08:58,510 --> 01:09:00,630
+الـ condition الواحد يجي إلى الـ condition الواحد
+
+538
+01:09:00,630 --> 01:09:01,370
+يجي إلى الـ condition الواحد يجي إلى الـ condition
+
+539
+01:09:01,370 --> 01:09:02,690
+الواحد يجي إلى الـ condition الواحد يجي إلى الـ
+
+540
+01:09:02,690 --> 01:09:04,410
+condition الواحد يجي إلى الـ condition الواحد يجي 
+
+541
+01:09:04,410 --> 01:09:06,670
+إلى الـ condition الواحد يجي إلى الـ condition
+
+542
+01:09:06,670 --> 01:09:07,550
+الواحد يجي إلى الـ condition الواحد يجي إلى الـ
+
+543
+01:09:07,550 --> 01:09:08,010
+condition الواحد يجي إلى الـ condition الواحد يجي
+
+544
+01:09:08,010 --> 01:09:09,090
+الواحد يجي إلى الـ condition الواحد يجي إلى الـ 
+
+545
+01:09:09,090 --> 01:09:15,410
+condition الواحد يجي إلى الـ condition الواحد يجي
+
+546
+01:09:15,410 --> 01:09:20,930
+إلى الـ condition الواحد والواحد of واحد بيبقى قداش
+
+547
+01:09:20,930 --> 01:09:26,910
+الذي هو واحد، يبقى صارت هذه C والله بلاش أكتب عليك
+
+548
+01:09:26,910 --> 01:09:33,050
+على خطين بلاش تقولي كيف هذه اجت الآن
+
+549
+01:09:33,050 --> 01:09:41,500
+من هدول اتنين، بقدر أقول ما يلي أن y عند الواحد بده
+
+550
+01:09:41,500 --> 01:09:47,760
+يساوي c واحد في y واحد عند الواحد زائد c اتنين في
+
+551
+01:09:47,760 --> 01:09:54,460
+y اتنين عند الواحد، y a prime عند الواحد بده يساوي
+
+552
+01:09:54,460 --> 01:09:59,880
+c واحد في y واحد a prime عند الواحد زائد c اتنين 
+
+553
+01:09:59,880 --> 01:10:07,530
+في y اتنين a prime عند الواحد تمام؟ هكتبهم لك فوق 
+
+554
+01:10:07,530 --> 01:10:15,930
+الآن احنا عندنا واللي عندك y واحد عند الواحد
+
+555
+01:10:15,930 --> 01:10:21,470
+معطيني إياها بقداش باتنين، implies ليه اتنين بدها 
+
+556
+01:10:21,470 --> 01:10:27,490
+تساوي و y واحد ايه الـ prime التي هي main بقداش و
+
+557
+01:10:27,490 --> 01:10:34,250
+واحد التي هي بقداش بواحد يبقى بـ c واحد و y اتنين
+
+558
+01:10:34,250 --> 01:10:39,950
+عند الواحد بناقص واحد يبقى ناقص c اتنين، الـ 
+
+559
+01:10:39,950 --> 01:10:43,150
+condition الثاني يجب أن يعطينا main يجب أن يعطينا
+
+560
+01:10:43,150 --> 01:10:50,000
+y1 prime y prime عند الواحد بده يساوي الـ zero يبقى 
+
+561
+01:10:50,000 --> 01:10:56,340
+zero بده يساوي y1 prime عند الواحد التي هو الثلاثة
+
+562
+01:10:56,540 --> 01:11:03,880
+يبقى تلاتة C واحد و Y اتنين عند الواحد الـ prime هو
+
+563
+01:11:03,880 --> 01:11:10,860
+بقداش بـ اتنين يبقى زائد اتنين C اتنين، شو رأيك يا
+
+564
+01:11:10,860 --> 01:11:15,960
+بنات لو ضربت المعادلة التي فوق في اتنين بصير اربع
+
+565
+01:11:15,960 --> 01:11:21,960
+يساوي اتنين C واحد ناقص اتنين C اتنين، هذه خلتها زي 
+
+566
+01:11:21,960 --> 01:11:27,860
+مين تلاتة C واحد زائد اتنين C اتنين، وروح الجماعة
+
+567
+01:11:27,860 --> 01:11:34,080
+هذه مع السلامة أربع يساوي خمسة C واحد يبقى C واحد
+
+568
+01:11:34,080 --> 01:11:40,200
+يبقى دي أربع أخماس، ما دام أربع أخماس يبقى نعود في
+
+569
+01:11:40,200 --> 01:11:48,880
+أي من المعادلتين، يبقى بصير اتنين تساوي أربع أخماس 
+
+570
+01:11:48,880 --> 01:11:58,620
+ناقص اتنين يبقى C2 تساوي أربع أخماس ناقص اتنين طبعًا
+
+571
+01:11:58,620 --> 01:12:05,880
+كله على قداش على خمسة بصير أربع ناقص عشرة يبقى
+
+572
+01:12:05,880 --> 01:12:11,120
+ناقص ستة أخماس يبقى بناء على الـ general 
+
+573
+01:12:13,320 --> 01:12:21,090
+Solution General solution of the العامة الولادة 
+
+574
+01:12:21,090 --> 01:12:31,210
+التي بديها هي Y27 C1 طلعناها بـ 4 أخماس يبقى 4 أخماس
+
+575
+01:12:31,210 --> 01:12:39,270
+Y1 و C2 بناقص 6 أخماس Y2 يبقى هذا الـ general
+
+576
+01:12:39,270 --> 01:12:44,770
+solution التي بديها، انتهى
+
+577
+01:12:44,770 --> 01:12:52,130
+الـ section بنجي لـ exercises تلاتة تلاتة ومن جول
+
+578
+01:12:52,130 --> 01:13:04,530
+المسائل من واحد لغاية تلاتاشر والأد ومن خمسة عشر لغاية
+
+579
+01:13:04,530 --> 01:13:15,510
+واحد وعشرين وسؤال تلاتة وعشرين حد
+
+580
+01:13:15,510 --> 01:13:17,530
+فيك وبتحب تسأل أي سؤال هنا يا بنات؟
+
+581
+01:13:26,750 --> 01:13:31,170
+الآن ننتقل إلى الـ section الذي بعده بعد ما
+
+582
+01:13:31,170 --> 01:13:37,870
+دوخناكوا شوية بدنا نرجع للأصل الذي ابتدينا فيه 
+
+583
+01:13:37,870 --> 01:13:42,670
+الذي هو الـ homogeneous differential equation with
+
+584
+01:13:42,670 --> 01:13:44,610
+constant coefficients
+
+585
+01:13:55,380 --> 01:14:01,800
+يبقى بدنا نيجي لـ section تلاتة أربعة section تلاتة
+
+586
+01:14:01,800 --> 01:14:12,120
+أربعة بتكلم عن الـ complex roots complex roots of
+
+587
+01:14:12,120 --> 01:14:18,140
+the characteristic equation
+
+588
+01:14:29,620 --> 01:14:35,430
+نبدأ بـ section تلاتة واحد أول section، أخذنا الـ
+
+589
+01:14:35,430 --> 01:14:39,930
+second order linear differential equation وروحنا 
+
+590
+01:14:39,930 --> 01:14:44,670
+أخذنا حالة خاصة منها لما يكونوا الـ coefficients are
+
+591
+01:14:44,670 --> 01:14:49,450
+constants يبقى لو كانوا المعاملات ما لهم ثوابت
+
+592
+01:14:49,450 --> 01:14:53,470
+بقولنا بنفرض أن EOSRT هو عبارة عن حل، وبالتالي
+
+593
+01:14:53,470 --> 01:14:58,050
+بنجيب الـ characteristic equation لـ AR تربيع زائد BR
+
+594
+01:14:58,050 --> 01:15:06,850
+زائد C، وقلنا الحل له أحد ثلاثة احتمالات، الاحتمال
+
+595
+01:15:06,850 --> 01:15:13,770
+الأول أن اتنين are real and different وأخذنا أمثلة 
+
+596
+01:15:13,770 --> 01:15:19,050
+عليها، وبعد هيك صبرنا شوية وغطسنا وين في شُجْعَة ثانية
+
+597
+01:15:19,050 --> 01:15:24,330
+الآن بدنا نرجع بعد section تلاتة اتنين وتلاتة
+
+598
+01:15:24,330 --> 01:15:28,130
+تلاتة بدنا نرجع لكلام الذي ابتدأنا فيه في section
+
+599
+01:15:28,130 --> 01:15:32,330
+تلاتة واحد بداخل تلاتة أربع أن لو كان اتنين are
+
+600
+01:15:32,330 --> 01:15:36,920
+complex roots الاتنين كانوا complex roots and 
+
+601
+01:15:36,920 --> 01:15:40,860
+conjugate اتنين تخيلين ومترافقين وبعد ذلك الـ
+
+602
+01:15:40,860 --> 01:15:44,600
+section الذي بعد بناخد لو كانوا اتنين are real
+
+603
+01:15:44,600 --> 01:15:49,580
+repeated roots جذور حقيقية ومكررة يخلينا مع الـ
+
+604
+01:15:49,580 --> 01:15:53,760
+
+646
+01:12:52,240 --> 01:12:57,970
+التربية إلى سالب واحد يعني كمية تخيّلية إذا صار
+
+647
+01:12:57,970 --> 01:13:02,450
+الجدرين R1 وR2 بدل الكلكة الكبيرة هذه بدي أكتبها 
+
+648
+01:13:02,450 --> 01:13:06,970
+بشكل ألطف بالشكل اللي أنا هنا تمام؟ مدام صاروا
+
+649
+01:13:06,970 --> 01:13:10,310
+هذول الجدرين اللي يبقى لو رجعنا ل section تلاتة
+
+650
+01:13:10,310 --> 01:13:18,050
+واحد بقين أقول إذا الحل C1 في E أس R1 زائد C2 في E
+
+651
+01:13:18,050 --> 01:13:21,570
+أس R2 صحيح ولا لأ؟ يبقى باجي بقول
+
+652
+01:13:31,990 --> 01:13:44,910
+Y1 يساوي E أُس لاندا زائد IMU و Y2 يساوي E أُس 
+
+653
+01:13:44,910 --> 01:13:54,320
+لاندا ناقص IMU هي اصلا ده ناقص IU وبالتالي the 
+
+654
+01:13:54,320 --> 01:14:02,800
+general solution of 
+
+655
+01:14:02,800 --> 01:14:16,580
+the differential equation star is y تساوي C1 في E 
+
+656
+01:14:16,580 --> 01:14:24,320
+أُس لاندا زائد I ميو في T طبعا هذه في T يا بنات
+
+657
+01:14:24,320 --> 01:14:32,600
+هذه كله في T وهذا كله في T زائد
+
+658
+01:14:32,600 --> 01:14:43,550
+C2 في E أُس لاندا ناقص I ميو كله في T يبقى هذا شكل
+
+659
+01:14:43,550 --> 01:14:51,630
+الحل اللي عندنا هذا طيب الحل زي ما تشوفين مكتوب
+
+660
+01:14:51,630 --> 01:14:56,170
+بدل ال complex numbers وغالبيتكوا مادرسوش complex
+
+661
+01:14:56,170 --> 01:15:00,470
+number فى حد درست مادة ال complex يا بنات يعني هي
+
+662
+01:15:00,470 --> 01:15:06,740
+واحدة ويمكن هي اتنين طيب الغالبية مادرسوش لكن لذلك
+
+663
+01:15:06,740 --> 01:15:11,080
+بدل ما الحل مكتوب واصل complex numbers بدي احاول 
+
+664
+01:15:11,080 --> 01:15:15,100
+اكتب بدلالة main بدلالة ال real number فيها ان
+
+665
+01:15:15,100 --> 01:15:19,660
+معادلة اسم معادلة Euler اللي بكتب ال exponential
+
+666
+01:15:19,660 --> 01:15:25,420
+function بدلالة ال sign و ال cosine يبقى باجي بقول
+
+667
+01:15:25,420 --> 01:15:30,200
+ما يأتي now we shall
+
+668
+01:15:37,200 --> 01:15:49,480
+write this solution هذا الحل in a
+
+669
+01:15:49,480 --> 01:16:02,880
+real form في شكل حقيقي by using by using Euler's
+
+670
+01:16:10,000 --> 01:16:21,280
+شي أولرز فورملة بيقول E أُس I T يساوي Cos T زائد I
+
+671
+01:16:21,280 --> 01:16:26,140
+Sin T خلي 
+
+672
+01:16:26,140 --> 01:16:30,060
+دراسة ال complex طبعا حدوها هذه واحنا بنحطها 
+
+673
+01:16:30,060 --> 01:16:36,390
+كقاعدة ونشتغل عليها يبقى E أُس I T هي عبارة عن Cos
+
+674
+01:16:36,390 --> 01:16:41,810
+T زائد I Sin T طبعا لو جينا فاكينا يا بنات هنا 
+
+675
+01:16:41,810 --> 01:16:49,630
+بصير Lambda T و I Mu T مظبوط هنا بصير Lambda T و
+
+676
+01:16:49,630 --> 01:16:54,990
+ناقص I ميو T ناقص إذا بدنا نشوف E أس ناقص I T
+
+677
+01:16:54,990 --> 01:17:00,050
+عبارة عن مين إذا بناء عليه لو بدي أجي أخد E أس
+
+678
+01:17:00,050 --> 01:17:08,170
+ناقص I T بقدر أقول E أس I في ناقص T يبقى معنى كلمة
+
+679
+01:17:08,170 --> 01:17:13,320
+T مين أجي مكانها يا بنات؟ سالب T يبقى بصير كوساين
+
+680
+01:17:13,320 --> 01:17:20,520
+لسالب T زائد I سين لسالب T ويساوي ال cosine odd
+
+681
+01:17:20,520 --> 01:17:24,280
+function و لا even function؟ even يبقى السالب مع
+
+682
+01:17:24,280 --> 01:17:29,080
+السلامة يبقى ال cosine T والسين odd يبقى السالب 
+
+683
+01:17:29,080 --> 01:17:36,170
+يطلع برا سالب I سين T خلي المعلومة اللي عندك هذه 
+
+684
+01:17:36,170 --> 01:17:43,070
+لزمان لو كان الأس بالسالب يبقى زي الأس بالموجب بس
+
+685
+01:17:43,070 --> 01:17:49,670
+بيفرقوا عن بعضهم بمية بشارة سالب يعني كأنه العدد 
+
+686
+01:17:49,670 --> 01:17:54,870
+والعدد المرافق لهم، مش كنت أقول سين زائد سات ته
+
+687
+01:17:54,870 --> 01:17:58,950
+بالعربي المرافق لو السين ناقص سات ته يعني بنغير 
+
+688
+01:17:58,950 --> 01:18:05,030
+إشارة الجزء التخيلي، طلع cosine T ما فيش فيها تخيلي
+
+689
+01:18:05,030 --> 01:18:10,870
+sin T فيها تخيلي، cosine T ما فيهاش، sin T هي فيها
+
+690
+01:18:10,870 --> 01:18:16,010
+سالب، يبقى صار هذا العدد وهذا هو العدد المرافق له 
+
+691
+01:18:16,290 --> 01:18:20,130
+في ال complex numbers في الأعداد المركبة أو 
+
+692
+01:18:20,130 --> 01:18:26,750
+الأعداد التخيلية تمام تمام يبقى هذه Euler formula 
+
+693
+01:18:26,750 --> 01:18:35,250
+يبقى بناء عليه لو بدي أجيبها بنات E أس I mu T بناء 
+
+694
+01:18:35,250 --> 01:18:43,050
+عليه يبقى بدل الثيمين أجانب يبقى بصير cosine mu t
+
+695
+01:18:43,050 --> 01:18:54,830
+كلها زائد I sine mu t وفي نفس الوقت E أس سالب I mu t
+
+696
+01:18:54,830 --> 01:19:02,710
+cosine mu t ناقص I sine mu t
+
+697
+01:19:05,060 --> 01:19:09,820
+طيب كويس يبقى عرفنا كل واحدة فيهم يبقى لو جينا
+
+698
+01:19:09,820 --> 01:19:16,840
+بدنا ناخد المجموع تبعهم، لو جيت أخد E أُس I لميو T 
+
+699
+01:19:16,840 --> 01:19:23,980
+زائد E أُس ناقص I ميو T بده يساوي يبقى بدي أجمع 
+
+700
+01:19:23,980 --> 01:19:29,340
+الاتنين، إيش رأيك في هذه وهذه؟ يبقى بضل قداش؟
+
+701
+01:19:29,340 --> 01:19:39,550
+اتنين Cos mu t لو بدل ما أجمعهم بدي أطرحهم طرح يبقى 
+
+702
+01:19:39,550 --> 01:19:48,230
+إيش بصير E أس I mute ناقص E أس ناقص I mute يبقى
+
+703
+01:19:48,230 --> 01:19:54,990
+هذه بصير سالب بتروح مع الموجب وهذه بصير موجب مع
+
+704
+01:19:54,990 --> 01:20:02,230
+الموجب بصير اتنين I sign ل mute
+
+705
+01:20:04,950 --> 01:20:12,610
+تمام؟ يبقى هذا الجمع تبعهم والطرح تبعهم هذا احنا
+
+706
+01:20:12,610 --> 01:20:18,030
+قلنا الحل يا بنات الحل هذا سميليه المعادلة رقم
+
+707
+01:20:18,030 --> 01:20:26,930
+اتنين سميليه المعادلة رقم اتنين الآن هذا يمثل حل
+
+708
+01:20:26,930 --> 01:20:32,070
+المعادلة الأصلية اللي هو star هل هناك قيود على C1 
+
+709
+01:20:32,070 --> 01:20:38,820
+و C2؟ في قيود عندي؟ لأ ما عنديش قيود، ما عنديش قيود لأ 
+
+710
+01:20:38,820 --> 01:20:44,460
+على C1 ولا على C يعني خد زي ما بدك فباجي بقول لو
+
+711
+01:20:44,460 --> 01:20:57,620
+أخدت الآن ترك C1 يساوي C2 يساوي 1 مثلا then equation
+
+712
+01:21:01,830 --> 01:21:18,830
+Y تساوي E أس لامدة T في E أس I ميو T زائد E أس
+
+713
+01:21:18,830 --> 01:21:23,970
+لامدة T في E أس ناقص I ميو T
+
+714
+01:21:27,690 --> 01:21:38,150
+يبقى Y تساوي اللي هسميه الحل الأول يبقى
+
+715
+01:21:38,150 --> 01:21:45,430
+Y واحد بده يساوي E Os Lambda T عامل مشترك بظل ان
+
+716
+01:21:45,430 --> 01:21:58,740
+E Os IMUT زائد E Os ناقص IMUT موجودة فوق؟ يبقى بقدر
+
+717
+01:21:58,740 --> 01:22:05,060
+أقول هذه تساوي اتنين E اصلا ده تي كوساين ميوتي
+
+718
+01:22:05,060 --> 01:22:12,020
+صحيح ولا لأ؟ يبقى هذا صار أحد الحلول للمعادلة طيب
+
+719
+01:22:12,020 --> 01:22:18,920
+لو جيت قلت لك take C واحد يساوي واحد and C اتنين
+
+720
+01:22:18,920 --> 01:22:27,550
+يساوي سالب واحد مش بحصل عليه حل تاني؟ يبقى ان
+
+721
+01:22:27,550 --> 01:22:30,810
+اكويشن تو
+
+722
+01:22:41,000 --> 01:23:04,340
+Y2 يبدو يساوي يبقى
+
+723
+01:23:04,340 --> 01:23:12,810
+يصير عندي Y2 يساوي بتاخد E Os Lambda T عامل مشترك
+
+724
+01:23:12,810 --> 01:23:24,280
+بظل E Os IMUT ناقص E Os ناقص IMUT ويساوي يطلع لي في
+
+725
+01:23:24,280 --> 01:23:30,960
+هذه قداش؟ اتنين اي صين ميو تي يبقى بصير
+
+726
+01:23:30,960 --> 01:23:42,300
+اتنين اي اصلا ده تي صين ميو تي يبقى أنا عندي الحل 
+
+727
+01:23:42,300 --> 01:23:48,600
+الأول والحل الثاني طلع لي هذا اتنين مقدار ثابت و
+
+728
+01:23:48,600 --> 01:23:54,650
+اتنين اي مقدار ثابت اللي هم تأثير على الحل ثابت
+
+729
+01:23:54,650 --> 01:24:01,190
+مالهم تأثير لأ يبقى كأن الحل الأول هو E أس لاندا T
+
+730
+01:24:01,190 --> 01:24:06,630
+Cos Mu T و الحل الثاني E أس لاندا T Sin Mu T بكوز
+
+731
+01:24:06,630 --> 01:24:16,410
+اتنين و اتنين I as are constants يبقى thus we have
+
+732
+01:24:16,410 --> 01:24:17,850
+to
+
+733
+01:24:19,600 --> 01:24:28,280
+Linearly Independent Solutions اللي هم أميم E 
+
+734
+01:24:28,280 --> 01:24:41,080
+أسلندة T Cos M U T and E أسلندة T Sin M U T
+
+735
+01:24:41,080 --> 01:24:42,120
+because
+
+736
+01:24:46,380 --> 01:24:51,980
+ليه هدول linearly independent solutions؟ علشان 
+
+737
+01:24:51,980 --> 01:24:59,200
+المحدد تبعهم ماله؟ ممنوع يساوي zero دعونا نشوف
+
+738
+01:24:59,200 --> 01:25:04,700
+المحدد تبعهم، بده يساوي zero وما بيساويش ال zero
+
+739
+01:25:07,490 --> 01:25:15,450
+يبقى بدي اخذ الرونسكين تبع ال E أسلندة T cosine 
+
+740
+01:25:15,450 --> 01:25:23,870
+لميوتي و E أسلندة T sine لميوتي يبقى هذا الكلام
+
+741
+01:25:23,870 --> 01:25:32,130
+بده يساوي هاي المحدد E أسلندة T cosine لميوتي و E
+
+742
+01:25:32,130 --> 01:25:36,910
+أسلندة T sine لميوتي
+
+743
+01:25:38,960 --> 01:25:46,280
+بدا اشتق هذه، مشتقة مين؟ حاصل ضرب دالتين، بدا اشتق
+
+744
+01:25:46,280 --> 01:25:49,860
+الدالة الأولى ال exponential زي ما هي مضروبة في
+
+745
+01:25:49,860 --> 01:25:57,260
+تفاضل مين؟ الاس يبقى لاندا اي اس لاندا ت كوساين ميو
+
+746
+01:25:57,260 --> 01:26:03,960
+ت، الأولى مشتقة التانية، التانية بسالب ساين في مشتقة
+
+747
+01:26:03,960 --> 01:26:05,620
+الزاوية اللي ميو 
+
+748
+01:26:11,740 --> 01:26:15,800
+اللي عملنا الدالة الأولى بدنا نروح نعمل الدالة
+
+749
+01:26:15,800 --> 01:26:24,490
+الثانية يبقى lambdaE Os Lambda T Sine Mu T زائد
+
+750
+01:26:24,490 --> 01:26:31,270
+لميو E Os Lambda T Cos Lambda T لميو T وتعالى نفكر
+
+751
+01:26:31,270 --> 01:26:37,630
+محدد ونشوف على إيش بده يصفى حاصل ضرب على ناطر 
+
+752
+01:26:37,630 --> 01:26:45,290
+القطر الرئيسية يبقى Lambda في E Os 2 Lambda T في 
+
+753
+01:26:45,290 --> 01:26:55,060
+مين؟ في Sine T Cos في sign ميو تي كوسين ميو تى زائد
+
+754
+01:26:55,060 --> 01:27:06,900
+لميو فى E أس اتنين لاندا تى فى كوسين تربيع لميو تى
+
+755
+01:27:06,900 --> 01:27:15,240
+خلصنا الرئيسي بداجي الناقص الثانوي ناقص لاندا
+
+756
+01:27:25,720 --> 01:27:38,700
+مقص مع نقص بصير زائد شو
+
+757
+01:27:38,700 --> 01:27:44,820
+رأيك هذه هي هذه؟ وحدة موجبة بواحدة سالبة مع السلامة
+
+758
+01:27:44,820 --> 01:27:52,840
+فما هي رأيك هذه وهذه؟ فيها لم يُ في E أس اتنين
+
+759
+01:27:52,840 --> 01:27:59,890
+لامدة T عامل مشترك بضلك cosine تربية لميو T زائد 
+
+760
+01:27:59,890 --> 01:28:06,990
+sin تربية لميو T اللي بين قوسانه بقداش؟ يبقى صار 
+
+761
+01:28:06,990 --> 01:28:14,570
+عندك ميو في E أس اتنين لاند T عمر هذا بده يساوي 
+
+762
+01:28:14,570 --> 01:28:21,020
+zero يا بنات؟ لأ يبقى هذا الكلام لا يمكن أن يساوي
+
+763
+01:28:21,020 --> 01:28:27,980
+zero because ما هو السبب؟ ان E أس اثنين لامدة T
+
+764
+01:28:27,980 --> 01:28:39,000
+دائما وأبدا أكبر من ال zero and لم يو لا يمكن أن 
+
+765
+01:28:39,000 --> 01:28:42,400
+تساوي zero ليش؟ sense
+
+766
+01:28:44,960 --> 01:28:51,080
+لو كانت ميو بزيرو بصير 
+
+767
+01:28:51,080 --> 01:28:56,040
+الحل كله بلانبا ال root بصير حقيقي وليس complex
+
+768
+01:28:56,040 --> 01:29:04,500
+يبقى and هذا لا يمكن يساوي zero since the 
+
+769
+01:29:04,500 --> 01:29:08,520
+roots are complex
+
+770
+01:29:10,400 --> 01:29:15,580
+لأنه لو سا وزيره بيصير الجذور حقيقية وليست مركبة
+
+771
+01:29:15,580 --> 01:29:21,180
+يبقى بناء عليها اتنين هدول كونولي the fundamental
+
+772
+01:29:21,180 --> 01:29:25,740
+set of solutions يبقى هدول بيجيبولي ال general 
+
+773
+01:29:25,740 --> 01:29:32,580
+solution يبقى باجي بقول ال sir the general 
+
+774
+01:29:32,580 --> 01:29:38,620
+solution of the
+
+775
+01:29:58,050 --> 01:29:59,330
+الشكل اللي عندنا
+
+776
+01:30:06,510 --> 01:30:12,130
+يبقى من الآن فصاعدا بهمن لو كان R واحد يساوي R 
+
+777
+01:30:12,130 --> 01:30:15,990
+اتنين اتنين أعداد حقيقية كما في section تلاتة واحد 
+
+778
+01:30:15,990 --> 01:30:19,710
+تقول الحل العام هو C واحد في E Os R واحد T زائد C
+
+779
+01:30:19,710 --> 01:30:24,730
+اتنين في E Os R اتنين T لو طلع الجذور complex يبقى
+
+780
+01:30:24,730 --> 01:30:29,750
+شكل الحل E Os لاندا T C واحد كوساين ميو T زائد C 
+
+781
+01:30:29,750 --> 01:30:35,960
+اتنين ساين ميو T قبل ما أضحي بالمعلومة هذه منك بدنا
+
+782
+01:30:35,960 --> 01:30:40,280
+نعطيكي أمثلة، ديرا بالك هذا حساب الورس كان محطوط 
+
+783
+01:30:40,280 --> 01:30:44,120
+عندك سؤال في الكتاب محطوط اللي كنت تعسبيه، احنا دي
+
+784
+01:30:44,120 --> 01:30:46,920
+احنا حلينا السؤال وانت ما انتش داري أريحناكي منه
+
+785
+01:31:05,270 --> 01:31:09,190
+يبقى أمثلة بسيطة جدا ما فيهاش لحمة كتير زي النظر
+
+786
+01:31:09,190 --> 01:31:14,910
+يعني تلت امثلة ما بيعدلوش حساب الورونسكين هذا تمام 
+
+787
+01:31:14,910 --> 01:31:22,210
+يبقى examples solve 
+
+788
+01:31:22,210 --> 01:31:28,350
+the following differential 
+
+789
+01:31:28,350 --> 01:31:31,770
+equations
+
+790
+01:31:36,510 --> 01:31:46,810
+أول سؤال بيقول أربعة وي دابلي قرام زائد تسعة وي 
+
+791
+01:31:46,810 --> 01:31:53,870
+بده يساوي زيرو solution بدأ ابدأ زي ما بدأت ال
+
+792
+01:31:53,870 --> 01:31:59,750
+نظري بدأ اقول له let Y
+
+793
+01:31:59,750 --> 01:32:05,910
+تساوي E أس RT ب A solution
+
+794
+01:32:07,240 --> 01:32:13,400
+then the characteristic 
+
+795
+01:32:13,400 --> 01:32:19,160
+equation is أربع
+
+796
+01:32:20,330 --> 01:32:26,750
+ار تربيع زائد تسعة يساوي زيرو أو ان شئتم فاقولوا
+
+797
+01:32:26,750 --> 01:32:34,010
+أربع ار تربيع يساوي قداش؟ ناقص تسعة يبقى ار يساوي
+
+798
+01:32:34,010 --> 01:32:40,430
+الجذر التربيعي اللي ناقص تسعة على مين؟ على أربع يعني
+
+799
+01:32:40,430 --> 01:32:46,410
+زائد أو ناقص تلاتة على اتنين الجذر التربيعي إلى سالب
+
+800
+01:32:46,410 --> 01:32:53,610
+واحد سالب واحد بقداش؟ قلنا اي يبقى هنا زائد أو ناقص 
+
+801
+01:32:53,610 --> 01:33:01,510
+تلاتة على اتنين اي يبقى بناء عليها بناء كداش لاندا
+
+802
+01:33:01,510 --> 01:33:11,830
+هنا كداش لاندا؟ Zero و كداش لميو؟ تلاتة على اتنين،
+
+803
+01:33:11,830 --> 01:33:15,850
+صحيح ولا لا؟ زائد ونقص عن اتنين، مترافقين، يعني 
+
+804
+01:33:15,850 --> 01:33:19,190
+الإشارتين بيختلفوا للجزء التخيلي، الجزء الحقيقي عن
+
+805
+01:33:19,190 --> 01:33:23,810
+الـ Zero، يبقى بناء عليه أصبح The Solution
+
+806
+01:33:26,450 --> 01:33:37,450
+Y تساوي C إيه؟ قداش؟ Zero مش Lambda ب Zero في C
+
+807
+01:33:37,450 --> 01:33:42,520
+واحد cosine ليه ميو عندي تلاتة على اتنين؟ يبقى
+
+808
+01:33:42,520 --> 01:33:48,440
+تلاتة على اتنين T زائد C اتنين Sine تلاتة على 
+
+809
+01:33:48,440 --> 01:33:55,940
+اتنين T وانتهينا من المثلة يبقى Y C واحد Cos تلاتة 
+
+810
+01:33:55,940 --> 01:34:03,100
+T على اتنين زائد C اتنين Sine تلاتة T على اتنين
+
+811
+01:34:03,100 --> 01:34:10,400
+بسيط المثال الثاني المثال الثاني طبعا الأول هذا 
+
+812
+01:34:10,400 --> 01:34:17,120
+بلغة سؤال 12 من الكتاب هذا سؤال 12 من الكتاب وهذا
+
+813
+01:34:17,120 --> 01:34:24,620
+سؤال 15 من الكتاب بيقول يو اي دابلي برايم زائد واي
+
+814
+01:34:24,620 --> 01:34:31,460
+برايم زائد واحد وربع واي بده يساوي كده؟ بده يساوي
+
+815
+01:34:31,460 --> 01:34:40,610
+زيرو واحد ربع يعني كده؟ مش خمس أرباع، واحد وربع يبقى
+
+816
+01:34:40,610 --> 01:34:47,450
+هذا بده يعطيلك ان yw prime زائد y prime خمس أرباع y
+
+817
+01
+
+861
+01:40:18,440 --> 01:40:25,480
+في الثانية زائد الدالة الأولى E أس ناقص اثنين T في
+
+862
+01:40:25,480 --> 01:40:32,360
+مشتقة الثانية اللي هو السالب C واحد sine T وزائد C
+
+863
+01:40:32,360 --> 01:40:39,050
+اثنين cosine T نمسك ال initial condition الأول و
+
+864
+01:40:39,050 --> 01:40:44,490
+قال لي y عند ال zero بدها تساوي واحد إذا هاي واحد
+
+865
+01:40:44,490 --> 01:40:50,110
+بده أشيل كل T و أحط مكانها zero بصير E  و ال zero
+
+866
+01:40:50,110 --> 01:40:55,810
+اللي هو بواحد في cosine صفر اللي هو بواحد sin صفر
+
+867
+01:40:55,810 --> 01:41:00,870
+بصفر يبقى بالشكل اللي عندنا هذا يبقى هذه المعادلة
+
+868
+01:41:00,870 --> 01:41:06,250
+بتعطينا ان c1 يساوي كده؟ يساوي 1 نجي ال initial
+
+869
+01:41:06,250 --> 01:41:12,490
+condition الثاني y prime عند 0 بدر تساوي 0 implies
+
+870
+01:41:12,490 --> 01:41:24,420
+ان 0 بدر تساوي ناقص 2 وهذه بقدرش؟ ب1 في c1 لأن هذا
+
+871
+01:41:24,420 --> 01:41:31,780
+في هنا بزيرو هنا بواحد هنا بزيرو يبقى بس C واحد
+
+872
+01:41:31,780 --> 01:41:39,140
+اللي بعده زائد واحد فيه sine زيرو بزيرو cosine صفر
+
+873
+01:41:39,140 --> 01:41:46,700
+بواحد يبقى زائد C اثنين يبقى C اثنين بناء عليه صار
+
+874
+01:41:46,700 --> 01:41:54,270
+عندنا C اثنين بده يساوي اثنين C واحد C واحد عندي
+
+875
+01:41:54,270 --> 01:42:01,350
+بقداش يبقى هادول اثنين مع بعض بدي خليلي انه C2
+
+876
+01:42:01,350 --> 01:42:06,730
+يساوي قداش اثنين يبقى صار ال solution
+
+877
+01:42:12,490 --> 01:42:23,970
+C1-C2T C1-C2T C1-C2T C1
+
+878
+01:42:23,970 --> 01:42:26,470
+-C2T
+
+879
+01:42:34,410 --> 01:42:39,490
+احنا نظري انتهينا منه ال section لكن راح احط بشغلة
+
+880
+01:42:39,490 --> 01:42:44,290
+very important في ال exercises تبقى المرة الجاية
+
+881
+01:42:44,290 --> 01:42:48,810
+بنشرح هذه النقطة و بناخد بعض الأمثلة عليها و بعدين
+
+882
+01:42:48,810 --> 01:42:52,530
+بنخش في ال section اللي بعده ان شاء الله
diff --git a/PL9fwy3NUQKwa8ZDfSFGn6H8xVFLzqmCZC/Q2YiEyS2_gY_postprocess.srt b/PL9fwy3NUQKwa8ZDfSFGn6H8xVFLzqmCZC/Q2YiEyS2_gY_postprocess.srt
new file mode 100644
index 0000000000000000000000000000000000000000..872b7ec42ab59cc25830fbe5c8d5fcb71a523240
--- /dev/null
+++ b/PL9fwy3NUQKwa8ZDfSFGn6H8xVFLzqmCZC/Q2YiEyS2_gY_postprocess.srt
@@ -0,0 +1,3528 @@
+1
+00:00:09,660 --> 00:00:14,080
+بسم الله الرحمن الرحيم المرة اللي فاتت بدينا في
+
+2
+00:00:14,080 --> 00:00:18,660
+section تلاتة تلاتة وعطينا تعريف ل linearly
+
+3
+00:00:18,660 --> 00:00:23,420
+independent و linearly dependent functions اقول ان
+
+4
+00:00:23,420 --> 00:00:26,140
+لو في عنده functions بقول عنهم linearly
+
+5
+00:00:26,140 --> 00:00:30,570
+independentإذا كان الغنوز اللي كانت تبعهم ماله لا
+
+6
+00:00:30,570 --> 00:00:35,930
+يساوي زيرو اما إذا كانت التنتين linearly dependent
+
+7
+00:00:35,930 --> 00:00:41,190
+فالغنوز اللي كانت تبعهم ماله بده يساوي زيرو اتنين
+
+8
+00:00:41,190 --> 00:00:46,230
+قلنا ان ال two functions بقول عنهم linearly
+
+9
+00:00:46,230 --> 00:00:51,290
+independent لو جدت تلاقي two constants كونستان في
+
+10
+00:00:51,290 --> 00:00:53,930
+الدالة الأولى كونستان في الدالة التانية بده يساوي
+
+11
+00:00:53,930 --> 00:00:54,870
+زيرو كان
+
+12
+00:01:00,290 --> 00:01:04,950
+لكن لو كان على الأقل واحد من كواحد او كاتنين لا
+
+13
+00:01:04,950 --> 00:01:10,620
+يساوي زيروو ممكن اتنين مايكونوش بأصفر كذلك يبقى في
+
+14
+00:01:10,620 --> 00:01:13,900
+هذه الحالة بقول ال two functions f and g are
+
+15
+00:01:13,900 --> 00:01:20,120
+linearly dependent تمام؟ بعد هيك روحنا لنظرية و
+
+16
+00:01:20,120 --> 00:01:24,040
+النظرية هذه اللي اول نظرية او هي النظرية الوحيدة
+
+17
+00:01:24,040 --> 00:01:28,680
+اللي أخدناها المرة اللي فاتت اللي هو بنحكم على ال
+
+18
+00:01:28,680 --> 00:01:32,600
+two functions او ال two solutions ل second order
+
+19
+00:01:32,600 --> 00:01:36,220
+differential equationبينهم linearly dependent او
+
+20
+00:01:36,220 --> 00:01:41,640
+linearly independent من خلال الورنسكين يعني لو
+
+21
+00:01:41,640 --> 00:01:47,580
+جينا وجينا ان الورنسكين عند نقطة ما لا يساوي zero
+
+22
+00:01:47,580 --> 00:01:51,040
+اذا ال two functions بقول عنهم linearly
+
+23
+00:01:51,040 --> 00:01:57,930
+independentولو كانوا تنتهيوا linearly dependent
+
+24
+00:01:57,930 --> 00:02:03,550
+يكون ال goal skin يساوي zero هذه النظرية الحجيبة
+
+25
+00:02:03,550 --> 00:02:09,650
+نظرية أقوى منها وتبقى في اتجاهينلكن بعد قليل في
+
+26
+00:02:09,650 --> 00:02:14,870
+محاضرتنا هذه بس قبلها هنجيب ال worn skin بطريقة
+
+27
+00:02:14,870 --> 00:02:18,910
+أخرى غير اللي احنا اتعودنا عليها أو اللي عارفين
+
+28
+00:02:18,910 --> 00:02:22,530
+تبعة المحدد الدالة الأولى التانية مشتقة الأولى
+
+29
+00:02:22,530 --> 00:02:27,010
+ومشتقة الثانية فهذه اكتشافها العالم Abel وبالتالي
+
+30
+00:02:27,010 --> 00:02:32,850
+سميت باسمه فables theorem يبقى نظرية العالم Abel
+
+31
+00:02:33,460 --> 00:02:37,500
+بتقول لو كان Y1 وY2 هو عبارة عن solutions لل
+
+32
+00:02:37,500 --> 00:02:40,220
+differential equation من ال second order اللي
+
+33
+00:02:40,220 --> 00:02:44,460
+قدامنا هذه حيث ال P و P و R continuous functions
+
+34
+00:02:44,460 --> 00:02:52,740
+على الفترة المفتوحة Iيبقى الورونسكين كمشكلة Y1 وY2
+
+35
+00:02:52,740 --> 00:03:01,060
+كمشكلة T يساوي C في E أس ناقص تكامل P of T DT يبقى
+
+36
+00:03:01,060 --> 00:03:05,440
+من الأن و فسادا طبقا لهذه النظر يبقى الورونسكين له
+
+37
+00:03:05,440 --> 00:03:10,340
+كم شكلشكلين الشكل الأولاني شكل المحدد اللي احنا
+
+38
+00:03:10,340 --> 00:03:13,860
+عرفناه قبل ايه والشكل التالي مقدار ثابت في ال
+
+39
+00:03:13,860 --> 00:03:18,360
+exponential لنا ال P of T هو المعامل تبع مين هو
+
+40
+00:03:18,360 --> 00:03:23,520
+البنات بشرط ان يكون معامل Y double prime هو الواحد
+
+41
+00:03:23,520 --> 00:03:27,400
+الصحيح يعني لو كان المعامل تبع Y double prime هو
+
+42
+00:03:27,400 --> 00:03:33,020
+رقم تاني او دلة تانية بدي اجسم الطرفين عليه ومن ثم
+
+43
+00:03:33,020 --> 00:03:40,730
+بروح بحسب مينيبقى C مقدار ثابت يعتمد على الحالين
+
+44
+00:03:40,730 --> 00:03:48,850
+Y1 وY2 ولا يعتمد على شكل الـMain شكل الـT طب نروح
+
+45
+00:03:48,850 --> 00:03:52,650
+نثبت صحة هذا الكلام بس قبل ان نثبت صحة هذا الكلام
+
+46
+00:03:52,650 --> 00:03:56,090
+احنا مانقول مش هنجيب linearly dependent و
+
+47
+00:03:56,090 --> 00:03:59,750
+independent بد الoneskin هذا يستوي الـ0 ومايستويش
+
+48
+00:03:59,750 --> 00:04:05,070
+الـ0بدي بسأل هل ال exponential هادي عمرها بده
+
+49
+00:04:05,070 --> 00:04:08,550
+تساوي zero في يومنا اللي هي؟ لأ لإنه أخدنا في
+
+50
+00:04:08,550 --> 00:04:13,150
+calculus بإن ال exponential دائما و أبدا ده لأ
+
+51
+00:04:13,150 --> 00:04:17,390
+أكبر من zero بتاخد قيمة أكبر من zero لعمرها بتاخد
+
+52
+00:04:17,390 --> 00:04:20,770
+zero ولا بتاخد قيمة سليمة، إذا شو اللي بده يخليه
+
+53
+00:04:20,770 --> 00:04:28,290
+zero؟ اليبقى C لو كانت هذا الكلام لا يمكن أن يساوي
+
+54
+00:04:28,290 --> 00:04:33,310
+Zero إلا إذا كانت C تساوي Zero فقط لكن إذا C
+
+55
+00:04:33,310 --> 00:04:38,250
+بتسويش Zero يبقى الورونسكين هذا ما له لا يمكن أن
+
+56
+00:04:38,250 --> 00:04:43,890
+يساوي Zero على الإطلاق نجي نثبت صحة هذه النظرية
+
+57
+00:04:43,890 --> 00:04:49,230
+طيب نجي الماضية قلي اتنين هدول حلل المعادلة هذه
+
+58
+00:04:49,230 --> 00:04:53,910
+يبقى اتنين هدول ما لهمبحقق المعادلة دي يبقى باجي
+
+59
+00:04:53,910 --> 00:05:08,870
+بقوله بما أن since Y1 and Y2 are two solutions of
+
+60
+00:05:08,870 --> 00:05:11,890
+equation one
+
+61
+00:05:15,630 --> 00:05:19,710
+يبقى كل واحد فيهم هيحقق المعادلة اللي عندنا يبقاش
+
+62
+00:05:19,710 --> 00:05:20,270
+بصير
+
+63
+00:05:23,800 --> 00:05:30,900
+زائد P of T في ال Y واحد ال prime زائد Q of T في
+
+64
+00:05:30,900 --> 00:05:38,780
+ال Y واحد بيساوي كده؟ بيساوي Zero اتنين and ال Y2
+
+65
+00:05:38,780 --> 00:05:46,000
+بابلي prime زائد P of T في ال Y2 prime زائد Q of T
+
+66
+00:05:46,000 --> 00:05:52,490
+في ال Y2 بيساوي كده؟ بيساوي Zero طيب انابدي اجي
+
+67
+00:05:52,490 --> 00:05:56,770
+الى المعادلتين هذول بدي احاول اطيّر ال term الأخير
+
+68
+00:05:56,770 --> 00:06:04,090
+فلو جيت المعادلة الأولى هذه روحت ضربتها في سالب Y2
+
+69
+00:06:04,090 --> 00:06:10,890
+والمعادلة الثانية ضربتها في موجب Y1
+
+70
+00:06:12,180 --> 00:06:16,220
+المعادلة كلها من أولها لآخرها يبقى المعادلة الأولى
+
+71
+00:06:16,220 --> 00:06:21,260
+بتضربها في سالب Y2 والمعادلة التانية بتضربها في
+
+72
+00:06:21,260 --> 00:06:26,740
+موجب Y1 يبقى كل من المعادلتين هتصبح على الشكل
+
+73
+00:06:26,740 --> 00:06:40,310
+التالي سالب Y1 double prime Y2سالب P of T في Y1 Y2
+
+74
+00:06:40,310 --> 00:06:51,030
+سالب EQ of T في Y1 Y2 يبقى 0 المعادلة التانية
+
+75
+00:06:51,030 --> 00:06:57,410
+هضربها في Y1 يبقى Y1 Y2
+
+76
+00:06:59,260 --> 00:07:09,520
+زائد P of T في Y1 Y2 زائد P of T في Y1 Y2 زائد P
+
+77
+00:07:09,520 --> 00:07:11,080
+of T في Y1 Y2 زائد P of T في Y1 Y2 زائد P of T في
+
+78
+00:07:11,080 --> 00:07:16,440
+Y1 Y2 زائد
+
+79
+00:07:16,440 --> 00:07:22,350
+P of T في Y1 Y2 زائد P of T في Y1 Y2وبعد ما ضربنا
+
+80
+00:07:22,350 --> 00:07:27,450
+المعادلة التانية في Y1 شويك نجمع يبقى لو جمعنا
+
+81
+00:07:27,450 --> 00:07:32,100
+هذول الله سهل عليهم مع السلام غير ماسوف عليهميبقى
+
+82
+00:07:32,100 --> 00:07:38,400
+بيصير مجموع المعادلاتين على الشكل التالي يبقى y1
+
+83
+00:07:38,400 --> 00:07:46,240
+y2 double prime ناقص y1 double prime y2 مجموع
+
+84
+00:07:46,240 --> 00:07:51,120
+الترمين هذول هذول يا بنات بيداخد P of T عامل مشترك
+
+85
+00:07:51,120 --> 00:07:58,940
+منهم يبقى زائد P of T عامل مشترك بظل عندي y1 y2
+
+86
+00:07:58,940 --> 00:08:06,790
+primeنقص Y1 Y2 Y1 Y2 Y1 Y2 Y2 Y2 Y2 Y2 Y2 Y2 Y2 Y2
+
+87
+00:08:06,790 --> 00:08:11,810
+Y2 Y2 Y2 Y2 Y2 Y2 Y2 Y2 Y2 Y2 Y2 Y2 Y2 Y2 Y2 Y2 Y2
+
+88
+00:08:11,810 --> 00:08:15,810
+Y2 Y2 Y2 Y2 Y2 Y2 Y2 Y2 Y2 Y2 Y2 Y2 Y2 Y2 Y2 Y2 Y2
+
+89
+00:08:15,810 --> 00:08:18,610
+Y2 Y2 Y2 Y2 Y2 Y2 Y2 Y2 Y2 Y2 Y2 Y2 Y2 Y2 Y2 Y2 Y2
+
+90
+00:08:18,610 --> 00:08:23,550
+Y2 Y2 Y2 Y2 Y2 Y2 Y2 Y2 Y2
+
+91
+00:08:23,550 --> 00:08:32,250
+Y2 Y2 Yأنا بدي أعرف ال W of T الرونسكين W of T يا
+
+92
+00:08:32,250 --> 00:08:40,170
+بنات مش هو عبارة عن Y1 Y2 Y1 prime Y2 prime صح
+
+93
+00:08:40,170 --> 00:08:46,810
+يبقى هذا لو جيت فاكته شو بيعطيني بيعطيني Y1 Y2
+
+94
+00:08:46,810 --> 00:08:56,440
+prime ناقص Y1 prime Y2 الرئيسي ناقص الثانويطب بدي
+
+95
+00:08:56,440 --> 00:09:02,100
+أشتقه و أشوف شو بيعطينا يبقى لو جيت ل w prime as a
+
+96
+00:09:02,100 --> 00:09:07,820
+function of t يعني dw على dt هذه مشتقة حصل ضرب
+
+97
+00:09:07,820 --> 00:09:13,620
+دالتين وهذه مشتقة حصل ضرب دالتين يبقى الدالة
+
+98
+00:09:13,620 --> 00:09:20,140
+الأولى في مشتقة الدالة الثانية زائد مشتقة الدالة
+
+99
+00:09:20,140 --> 00:09:25,410
+الأولى في الدالة الثانية كما هياللي عملته لحاصل
+
+100
+00:09:25,410 --> 00:09:29,810
+الضرب الأول هروح اعمله لمين؟ لحاصل الضرب الثاني
+
+101
+00:09:29,810 --> 00:09:35,950
+الناقص الدالة الأولى في مشتقة الدالة الثانية زائد
+
+102
+00:09:35,950 --> 00:09:46,650
+مع ناقص بصير ناقص اللي هو من اشتقل اللي هو Y1W'Y2
+
+103
+00:09:46,650 --> 00:09:51,510
+فالليلة في هذه و هذه مش الأثنين أرض سان واحدة
+
+104
+00:09:51,510 --> 00:09:56,180
+موجبة و واحدة سالبةيبقى مع السلامة يبقى صارة
+
+105
+00:09:56,180 --> 00:10:04,800
+النتيجة هي y1 y2 double prime ناقص y1 double prime
+
+106
+00:10:04,800 --> 00:10:12,280
+y2 طب أبطال الليلة لهذه هل ليست هذه هي بالضبط ولا
+
+107
+00:10:12,280 --> 00:10:18,390
+لا؟ إذا هذه بقدر أشيل وقت بدالها من؟و برامج W و
+
+108
+00:10:18,390 --> 00:10:25,510
+هذه بقدر اشيلها و اكتب دبالها من W اذا باجي بقوله
+
+109
+00:10:25,510 --> 00:10:37,130
+substitute and equation اتنين و نحصل على W برامج و
+
+110
+00:10:37,130 --> 00:10:45,640
+اكتب دبالها من Wزائد P of T في W as a function of
+
+111
+00:10:45,640 --> 00:10:51,930
+T بده ساوي Zeroيبقى من second order linear
+
+112
+00:10:51,930 --> 00:10:56,190
+differential equation تحولنا إلى first order
+
+113
+00:10:56,190 --> 00:11:01,470
+differential equation هذه بنحلها بسيطة يبقى هذه يا
+
+114
+00:11:01,470 --> 00:11:09,030
+بنات بقدر اقول w prime of t بده يساوي سالب p of t
+
+115
+00:11:09,030 --> 00:11:20,050
+في w of t ممكن نجسم كله على w يبقى هنا بصير wA' of
+
+116
+00:11:20,050 --> 00:11:26,990
+T على W of T بيكون ناقص P of T
+
+117
+00:11:30,810 --> 00:11:36,250
+يبقى لو كملة الطرفين ايش بصير عننا هنا لين
+
+118
+00:11:36,250 --> 00:11:45,270
+absolute value ل W of T ل W of T بده ساوي ناقص
+
+119
+00:11:45,270 --> 00:11:53,170
+تكامل P of T دي T زاد constant وليكن C1أنا ما بدّي
+
+120
+00:11:53,170 --> 00:11:56,950
+اللي ان الـW بدّي الـW itself يبقى لما نرفع
+
+121
+00:11:56,950 --> 00:12:01,930
+الطرفين كوصل العدد A لو رفعناها كوصل العدد دي
+
+122
+00:12:01,930 --> 00:12:08,510
+بيبقى ال absolute value لW of T يساوي E أساليب
+
+123
+00:12:08,510 --> 00:12:19,070
+تكامل لP of T DT زي الconstant C1سؤال هو هل هذه في
+
+124
+00:12:19,070 --> 00:12:27,250
+يوم من الأيام تاخد قيمة سالبة أو صفة؟ يبقى هذا
+
+125
+00:12:27,250 --> 00:12:30,570
+الكلام ال absolute value، اشيلناه والله خلناها
+
+126
+00:12:30,570 --> 00:12:38,030
+سيانةيبقى هذه positive وبالتالي W of T بده يساوي E
+
+127
+00:12:38,030 --> 00:12:47,090
+of T ناقص تكامل P of T DT في E of C1 وزعت الأسس
+
+128
+00:12:47,090 --> 00:12:53,310
+عند برب تجمع الأسس مظبوط ايه طب ايه اش رايك هذه
+
+129
+00:12:53,310 --> 00:12:59,800
+كلها constant؟الـ E بـ 2 و 7 من عشرة و الـ C 1 كل
+
+130
+00:12:59,800 --> 00:13:01,160
+صحيح يبقى هذا كل صحيح يبقى هذا كل صحيح يبقى هذا كل
+
+131
+00:13:01,160 --> 00:13:03,000
+صحيح يبقى هذا كل صحيح يبقى هذا كل صحيح يبقى هذا كل
+
+132
+00:13:03,000 --> 00:13:03,800
+صحيح يبقى هذا كل صحيح يبقى هذا كل صحيح يبقى هذا كل
+
+133
+00:13:03,800 --> 00:13:07,360
+صحيح يبقى هذا كل صحيح يبقى هذا كل صحيح يبقى هذا كل
+
+134
+00:13:07,360 --> 00:13:08,880
+صحيح يبقى هذا كل صحيح يبقى هذا كل صحيح يبقى هذا كل
+
+135
+00:13:08,880 --> 00:13:11,080
+صحيح يبقى هذا كل صحيح يبقى هذا كل صحيح يبقى هذا كل
+
+136
+00:13:11,080 --> 00:13:19,380
+صحيح يبقى هذا كل صحيح يبقى هذا
+
+137
+00:13:19,380 --> 00:13:26,490
+كل صحيح يبخلاصنا؟ يبقى الأن عندي طريقتان أو عندي
+
+138
+00:13:26,490 --> 00:13:33,750
+طريقتين أو توجد طريقتين لمين لا حساب رونسكين،
+
+139
+00:13:33,750 --> 00:13:40,170
+تمام؟ طيب، حد فيكن لا يتساؤل هنا؟ أه البرهان صحيح،
+
+140
+00:13:40,170 --> 00:13:45,510
+والله صحيح ضربنا وجمعنا واشتقنا رونسكين، طلع
+
+141
+00:13:45,510 --> 00:13:51,110
+الجواب دغري كامل وطلع الجوابحلّي باللي بدكي ..
+
+142
+00:13:51,110 --> 00:13:54,750
+الحين هعطيكي مدى للمثال تلاتة و تشوفي حالك حتى
+
+143
+00:13:54,750 --> 00:13:55,990
+اللي بتنتين
+
+144
+00:14:19,140 --> 00:14:27,440
+يبقى اول مثال example one اول
+
+145
+00:14:27,440 --> 00:14:38,120
+مثال let y1 بده يسوي جذر ال T و ال y2 بده يسوي
+
+146
+00:14:38,120 --> 00:14:46,140
+واحد عال T بي two solutions
+
+147
+00:14:47,270 --> 00:14:56,650
+بتو solutions of the differential equation of the
+
+148
+00:14:56,650 --> 00:15:05,690
+differential equation للمعادلة التفاضلية اتنين T
+
+149
+00:15:05,690 --> 00:15:14,070
+ترابيع Y double prime زائد تلاتة T Y prime ناقص Y
+
+150
+00:15:14,070 --> 00:15:23,540
+تساوي Zeroو الـ T greater than zero find بدنا
+
+151
+00:15:23,540 --> 00:15:31,080
+الرنسكان تبع ال Y واحد و ال Y اتنين as a function
+
+152
+00:15:31,080 --> 00:15:40,940
+of T also و كذلك find the constant C on the
+
+153
+00:15:40,940 --> 00:15:42,580
+constant
+
+154
+00:16:09,120 --> 00:16:15,550
+الاخت لواء بتسألته قبل قليلبتقول ايش؟ بتقول طب اني
+
+155
+00:16:15,550 --> 00:16:18,570
+اتي احنا نستخدم هال runnerskin اللي أخدناها قبل
+
+156
+00:16:18,570 --> 00:16:23,190
+المحدد و الله تبعي بالما نقول هي يمكن يلزم الأثنان
+
+157
+00:16:23,190 --> 00:16:28,380
+و احنا الإجابة على جد السؤال نشوف شو اللي بديهاطيب
+
+158
+00:16:28,380 --> 00:16:32,820
+السؤال بيقول ما ياتي الكلام ال .. الإجابة على لغة
+
+159
+00:16:32,820 --> 00:16:37,460
+لواء و الكلام للسامعين بتقول افترض او المثل اللي
+
+160
+00:16:37,460 --> 00:16:41,160
+بتقول افترض ان Y1 هو جدر ال T و Y2 و 1 على T و هم
+
+161
+00:16:41,160 --> 00:16:45,020
+عبارة عن حليل المعادلة التفاضلية لأنه قال هاتل
+
+162
+00:16:45,020 --> 00:16:49,000
+الرونسكين تبعهم بقوله بسيط اول شي هبجيب الرونسكين
+
+163
+00:16:49,240 --> 00:16:56,900
+As a function of T مباشرة فبجب أقول الحل الأول جذر
+
+164
+00:16:56,900 --> 00:17:05,540
+ال T و الحل التاني 1 على T بدنا نشتقه يبقى 1 على 2
+
+165
+00:17:05,540 --> 00:17:12,920
+جذر ال T و هذا سالب 1 على T تربيعهذا الكلام بده
+
+166
+00:17:12,920 --> 00:17:18,180
+يساوي حاصل ضرب عناصر القطر الرئيسي ناقص حاصل ضرب
+
+167
+00:17:18,180 --> 00:17:24,380
+عناصر القطر الثانوي اظن ناقص T أساليب تلاتة على
+
+168
+00:17:24,380 --> 00:17:31,070
+اتنين بنفعليبقى T أس سالب اتنين ضرب T أس نص يبقى T
+
+169
+00:17:31,070 --> 00:17:34,970
+أس سالب واحد و نص يعني T أس سالب تلاتة على اتنين
+
+170
+00:17:34,970 --> 00:17:41,770
+هذا الرئيسي ناقصي الثانوي كله في المقام يبقى ما
+
+171
+00:17:41,770 --> 00:17:47,430
+نطلعه فوق يصير T أس سالب واحد و نص T أس سالب نص
+
+172
+00:17:47,430 --> 00:17:55,030
+يبقى هذا يصير ناقص نص T أس سالب تلاتة على اتنين
+
+173
+00:17:56,050 --> 00:18:02,110
+مظبوط هيك يا بناد؟ طيب واحد صحيح وكمان نص، واحد و
+
+174
+00:18:02,110 --> 00:18:08,210
+نص يعني الإجابة السالب تلاتة على اتنين، T السالب
+
+175
+00:18:08,210 --> 00:18:14,660
+تلاتة على اتنينوT أكبر من Zero إذا لا يمكن هذا أنه
+
+176
+00:18:14,660 --> 00:18:20,820
+يساوي Zero فاش إمكانية يساوي Zero ليش؟ لأنه T
+
+177
+00:18:20,820 --> 00:18:25,060
+greater than Zero يبقى جيب نيروليسكن اللي هو
+
+178
+00:18:25,060 --> 00:18:30,220
+المقلوب الأول تبع المثلة المقلوب التاني بيقول ليش؟
+
+179
+00:18:30,220 --> 00:18:34,660
+وكذلك هتل مقدار الثابت C تبع A بال Theorem
+
+180
+00:18:34,660 --> 00:18:40,440
+نيروليسكن عندها أيه كمان؟ إذا هذا بدي يساوي مين؟
+
+181
+00:18:41,510 --> 00:18:46,710
+بدي أسألك اللعنة صحيح ولا لأ بس بشرط ان المعامل
+
+182
+00:18:46,710 --> 00:18:50,890
+هذا بدي يكون واحد صحيح بديش يكون اتنين تي تاربيع
+
+183
+00:18:50,890 --> 00:18:57,030
+اذا بروح نحط المعادلة هذه في الصيغة الجديدة كتالة
+
+184
+00:18:57,030 --> 00:19:03,950
+يبقى باجي بقوله the differential equation is y
+
+185
+00:19:03,950 --> 00:19:11,290
+double prime زائد تلاتة على اتنين تي تي في المقادة
+
+186
+00:19:11,500 --> 00:19:20,700
+تمام في من؟ في الـY' وهنا ناقص 1 على 2T تربيع كله
+
+187
+00:19:20,700 --> 00:19:22,820
+في الـY بده يساوي 0
+
+188
+00:19:29,790 --> 00:19:34,010
+يبقى اشتراك مع انه لازم يكون ال Y'' المعامل تبعها
+
+189
+00:19:34,010 --> 00:19:40,250
+واحد صحيح الحين هذا أصبح هو P of T تبع able
+
+190
+00:19:40,250 --> 00:19:46,790
+theorem اذا باجي بقوله ال رونسكين تبع able theorem
+
+191
+00:19:46,790 --> 00:19:55,130
+هو C فيه اصناع استكامل 3 على 2TDT
+
+192
+00:19:57,060 --> 00:20:03,480
+يبقى هذا الكلام بده يساوي C في E أس ناقص ثلاثة على
+
+193
+00:20:03,480 --> 00:20:10,460
+اتنين برا و هذه بيصير Lin absolute value ل T لكن
+
+194
+00:20:10,460 --> 00:20:15,640
+لما كان ال T أكبر من ال zero فبنقول Lin T و بنسكت
+
+195
+00:20:15,640 --> 00:20:24,120
+تمام؟ يبقى هذه C في E أس Lin T أس سالب تلاتة على
+
+196
+00:20:24,120 --> 00:20:31,220
+اتنينيعني يا بنات بالصغير هذه C في T أس سالب تلاتة
+
+197
+00:20:31,220 --> 00:20:37,960
+على اتنين فدرونسكن هذا مش ورونسكن هذا يبقى اتنين
+
+198
+00:20:37,960 --> 00:20:45,290
+هدول لازم يساووا بعضيبقى بنسويهم بعض بناء عليه
+
+199
+00:20:45,290 --> 00:20:51,110
+بصير C في T أساليب تلاتة على اتنين بده يساوي
+
+200
+00:20:51,110 --> 00:20:55,930
+أساليب تلاتة على اتنين T أساليب تلاتة على اتنين
+
+201
+00:20:55,930 --> 00:21:01,670
+الان T أكبر من ال zero يعني رقم لا يساوي zero إذا
+
+202
+00:21:01,670 --> 00:21:05,950
+بنجسم نقدر نجسم الطرفين على T أساليب تلاتة على
+
+203
+00:21:05,950 --> 00:21:13,950
+اتنين ومنها ال C بده يساوي أساليب تلاتةعلى اتنى
+
+204
+00:21:13,950 --> 00:21:21,110
+يبقى هى ويا لي واق استخدمنا الشجتين في نفس السؤال
+
+205
+00:21:21,110 --> 00:21:25,770
+يعنى الشكلين تبع الرنس كان استخدمناهم في حل
+
+206
+00:21:25,770 --> 00:21:31,310
+المسألة اللى بين ايدينه يبقى احلى من الصرف حسب ما
+
+207
+00:21:31,310 --> 00:21:33,690
+هو مطلوب في المسألة
+
+208
+00:21:44,250 --> 00:21:49,390
+نأخد ايضا مثال اتنين
+
+209
+00:21:49,390 --> 00:21:53,950
+هذا اجى في الامتحان الفاصل اللى فات هذا فاصل فات
+
+210
+00:21:53,950 --> 00:21:59,130
+يعني قبل شهرين و نص تقريبا بيقول suppose that
+
+211
+00:21:59,130 --> 00:22:02,950
+suppose
+
+212
+00:22:02,950 --> 00:22:11,890
+that ان y واحد and y اتنين are
+
+213
+00:22:32,860 --> 00:22:41,170
+للمعادلة التفاضليةاللي هي T تربية YW prime ناقص
+
+214
+00:22:41,170 --> 00:22:48,310
+أربعة T Y prime زائد ستة Y تساوي زيرو T greater
+
+215
+00:22:48,310 --> 00:22:49,830
+than zero
+
+216
+00:22:54,220 --> 00:23:01,720
+وإذا كان الرنسكين تبع الحل الأول والحل الثاني عند
+
+217
+00:23:01,720 --> 00:23:08,580
+الواحد بده يساوي واحد اوش دونه اللي هو الرنسكين
+
+218
+00:23:08,580 --> 00:23:14,420
+تبع الحل الأول والحل الثاني عند الثمان
+
+219
+00:23:29,110 --> 00:23:32,610
+لو مسكت ورقة الامتحان تبع الفصل الماضي تبع تعمال
+
+220
+00:23:32,610 --> 00:23:37,970
+الفصل بتلاقي هذا السؤال موجود فيها طيب بقول افترض
+
+221
+00:23:37,970 --> 00:23:42,670
+انه عندي حالين و اتنين linearly independent يبقى
+
+222
+00:23:42,670 --> 00:23:47,570
+لو جيتك و حسبت نونسكين تبعهم ممكن يساوي zero؟ مش
+
+223
+00:23:47,570 --> 00:23:50,770
+إمكانية يبقى مدام جالي linearly independent يبقى
+
+224
+00:23:50,770 --> 00:23:55,770
+نونسكين لايمكن أن يساوي zero بأي حالة من الحواله
+
+225
+00:23:55,770 --> 00:24:00,600
+وبالتالي ال C تبعت ال able theoremلا يمكن أن تكون
+
+226
+00:24:00,600 --> 00:24:05,660
+بصفر على الإطلاق طيب قال لي ماشي لها اتنين لينيرا
+
+227
+00:24:05,660 --> 00:24:08,600
+independent solution للمعادلة هذه قال لي هاتلي ال
+
+228
+00:24:08,600 --> 00:24:12,360
+رونسكين وإذا كان رونسكين عند الواحد بدي يساوي عدد
+
+229
+00:24:12,360 --> 00:24:16,400
+هاتلي ال رونسكين وانا عندي اتنين بقولكوا ياسي باجي
+
+230
+00:24:16,400 --> 00:24:19,040
+لل differential equation هذه بدي أحطها في ال
+
+231
+00:24:19,040 --> 00:24:23,690
+standard fourمشان اجيب P of T بالظبط انا بدى
+
+232
+00:24:23,690 --> 00:24:28,850
+المعامل هنا بقدرش اذا بتروح اقسم كله على و بقدر
+
+233
+00:24:28,850 --> 00:24:32,870
+اقسم بكل سهولة لإن T greater than zero لإن يمكن ان
+
+234
+00:24:32,870 --> 00:24:36,790
+تساوي zero اذا بناء على المعادلة دى بتصير على
+
+235
+00:24:36,790 --> 00:24:45,200
+الشكل التالي Y ناقص اربع على T في ال Y primeزائد
+
+236
+00:24:45,200 --> 00:24:52,440
+اللي هو 6 على T تربيع في ال Y بده يساوي كده؟ بده
+
+237
+00:24:52,440 --> 00:24:58,620
+يساوي Zero تمام تمام يبقى الان بقدر اجيب الرونسكين
+
+238
+00:24:58,620 --> 00:25:02,340
+تبعها طبعا احنا من ضمن الرونسكين لازم تبقى الدوال
+
+239
+00:25:02,340 --> 00:25:07,460
+دوال متاصلة لل P و لQ طبعا ال discontinuity بيحصل
+
+240
+00:25:07,460 --> 00:25:12,170
+وين؟ عند ال Zero لكن احنا مش ترطينيبقى دول
+
+241
+00:25:12,170 --> 00:25:16,490
+continuous متحقق على طول الخط بدون أي إشكالية يبقى
+
+242
+00:25:16,490 --> 00:25:20,210
+مناقن عليها بقدر أجيب رونسكين تبع الحل الأول والحل
+
+243
+00:25:20,210 --> 00:25:26,390
+التاني يبقى رونسكين تبع الحل الأول والحل التاني as
+
+244
+00:25:26,390 --> 00:25:36,200
+a function of T يساوي C في E أص ناقصزاد تنسوش ناقص
+
+245
+00:25:36,200 --> 00:25:40,480
+القانون يبقى
+
+246
+00:25:40,480 --> 00:25:51,440
+بصير زاد تكامل 4 على T DT يبقى هذا الكلام ساوي C
+
+247
+00:25:51,440 --> 00:25:58,880
+في E أُص 4 لأن T لغرى لأن T أكبر من زمين من Zero
+
+248
+00:26:00,560 --> 00:26:09,320
+يبقى C في E أس لين T أس أربع يبقى C في T أس أربع
+
+249
+00:26:09,320 --> 00:26:18,500
+هذا شكل من رونسكان جالي ان رونسكان عند الواحد بده
+
+250
+00:26:18,500 --> 00:26:23,520
+يسوي واحد M plus يعني بده أشيل كل T و أحط مكانها
+
+251
+00:26:24,160 --> 00:26:31,580
+يبقى هنا واحد بده يساوي C في واحد وص أربعة يعني
+
+252
+00:26:31,580 --> 00:26:37,700
+بتطلع C بقداش لما C تساوي واحد يبقى أصبح in
+
+253
+00:26:37,700 --> 00:26:44,800
+general رونسكين الحل الأول والحل الثاني بده يساوي
+
+254
+00:26:44,800 --> 00:26:52,640
+قداش E ولا بده يساوي دورة T و أربعة دورجالي هاتلر
+
+255
+00:26:52,640 --> 00:26:58,240
+رونسكين تبع الحل الأول والحل التاني عندي اتنين
+
+256
+00:26:58,240 --> 00:27:04,620
+يبقى ماعلي الا أشيل T و أحط مكانها اتنين أس أربع
+
+257
+00:27:04,620 --> 00:27:11,980
+يبقى الجواب جداش ابت سبعاش صحيح؟ مباشر هذا أجى في
+
+258
+00:27:11,980 --> 00:27:17,420
+الامتحان الفصل الماضي طيب خدي ال example تلاتة
+
+259
+00:27:20,860 --> 00:27:33,360
+بقول الات Y1 and Y2 بيتو solutions
+
+260
+00:27:33,360 --> 00:27:39,880
+of the
+
+261
+00:27:39,880 --> 00:27:47,960
+differential equation للمعادلة التفاضلية واحد ناقص
+
+262
+00:27:47,960 --> 00:27:49,040
+T تربيع
+
+263
+00:28:03,230 --> 00:28:04,630
+Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''
+
+264
+00:28:05,370 --> 00:28:12,870
+قال إذا كان F الرنسكين تبع ال Y واحد وال Y اتنين
+
+265
+00:28:12,870 --> 00:28:22,550
+عند المص بده يساوي تلاتة find الرنسكين
+
+266
+00:28:22,550 --> 00:28:29,130
+تبع الحل الأول والحل التاني as a function of T for
+
+267
+00:28:29,130 --> 00:28:39,750
+all Tor all T لجميع قيم T in the interval in the
+
+268
+00:28:39,750 --> 00:28:52,830
+interval على الفترة in which بحيث أن in which the
+
+269
+00:28:52,830 --> 00:29:01,190
+solution exists
+
+270
+00:29:42,830 --> 00:29:48,150
+نرجع لسؤالنا مرة ثانيةبقول افترض عندي حلين
+
+271
+00:29:48,150 --> 00:29:51,990
+للمعادلة التفاضلية اللى قدامنا هذه وإذا كان
+
+272
+00:29:51,990 --> 00:29:55,970
+رونوسكين عنده نقص بده يساوي تلاتة هاته رونوسكين in
+
+273
+00:29:55,970 --> 00:30:01,630
+general as a function of T in the interval على
+
+274
+00:30:01,630 --> 00:30:05,130
+الفترة اللى الحل بيكون عليها صياني أنا بدي أحسب
+
+275
+00:30:05,130 --> 00:30:08,570
+جداشة نقص كمدالة لل T و بدي أعرف اللى ال interval
+
+276
+00:30:08,570 --> 00:30:12,410
+اللى الكلام عليها هذا معنىصحيح يبقى العبارة الأخرى
+
+277
+00:30:12,410 --> 00:30:15,990
+هي اللي أتي اللي أجت زيادة على مين، الحال الأول
+
+278
+00:30:15,990 --> 00:30:19,610
+حال الأول قال لي تيجريفر دانزيرو فهو طان الفترة،
+
+279
+00:30:19,610 --> 00:30:23,830
+بس هنا مااطنش الفترة أنا اللي بدي أجيب مين الفترة
+
+280
+00:30:23,830 --> 00:30:28,680
+التابعتنالذلك المعادلة التفاضليها دي بدي أنقلها
+
+281
+00:30:28,680 --> 00:30:32,660
+الى وضع اخر غير الوضع اللي هو فيه بدي اخل المعامل
+
+282
+00:30:32,660 --> 00:30:38,520
+هذا جداش يبقى بدأ اقسم كله على مين على واحد نقص T
+
+283
+00:30:38,520 --> 00:30:44,520
+تربيع يبقى solution the
+
+284
+00:30:44,520 --> 00:30:52,700
+differential equation S بدي اكتبها على الشكل
+
+285
+00:30:52,700 --> 00:30:53,960
+التالي Y
+
+286
+00:31:17,930 --> 00:31:24,270
+أظن المقام نقدر نحلله كفرق بين المربعينيبقى هذا لو
+
+287
+00:31:24,270 --> 00:31:30,930
+جينا حللنا بصير y double prime زائد واحد زائد T
+
+288
+00:31:30,930 --> 00:31:38,050
+واحد ناقص T في واحد زائد T كله في ال Y prime واحد
+
+289
+00:31:38,050 --> 00:31:45,490
+ناقص T واحد ناقص T في واحد زائد T كله في ال Y بده
+
+290
+00:31:45,490 --> 00:31:51,410
+يساوي قداش Zeroنختصر الاختصارات اللي موجودة يبقى
+
+291
+00:31:51,410 --> 00:31:55,770
+المعادلة التفاضلية أصبحت على الشكل التالي
+
+292
+00:32:07,510 --> 00:32:11,090
+مشان نحسب الـ one of skin لازم يكون معاملة P of T
+
+293
+00:32:11,090 --> 00:32:17,350
+والـ Q of T دوال متصلة على نفس الفترة مظبوط طيب
+
+294
+00:32:17,350 --> 00:32:22,950
+هنا الأن بداجي أقوله ال P of T اللي هي واحد على
+
+295
+00:32:22,950 --> 00:32:33,230
+واحد ناقص T هذه continuous for all T اللي بتسويش
+
+296
+00:32:33,230 --> 00:32:40,760
+الواحد صحيح ولا لأ؟طيب لك U of T اللي هي واحد على
+
+297
+00:32:40,760 --> 00:32:46,740
+واحد زائد T continuous لكل ال T اللي بتسويه شمين
+
+298
+00:32:46,740 --> 00:32:53,020
+سالب واحد طيب تعالوا نشوف هذا ال real line وهذه
+
+299
+00:32:53,020 --> 00:32:56,680
+النقطة اللي عندي سالب واحد وهذه النقطة اللي عندي
+
+300
+00:32:56,680 --> 00:33:03,480
+اللي واحدالدالة له purity و discontinuity حصل عند
+
+301
+00:33:03,480 --> 00:33:10,020
+الواحد يعني هنا open و بعدها continuous و قبلها
+
+302
+00:33:10,020 --> 00:33:16,080
+continuousبنجي تاني ل Q of T ال discontinuity حصل
+
+303
+00:33:16,080 --> 00:33:22,620
+وين عند السالب واحد يبقى هنا مفتوحة وبنجي هيك
+
+304
+00:33:22,620 --> 00:33:28,220
+continuous على طول و هيك continuous كذلك على طول
+
+305
+00:33:28,220 --> 00:33:37,610
+يبقى في عندي كام منطقة مشتركة بينهمتلت مناطق من
+
+306
+00:33:37,610 --> 00:33:42,930
+سالب infinity إلى سالب واحد ومن سالب واحد إلى واحد
+
+307
+00:33:42,930 --> 00:33:47,630
+ومن واحد إلى infinity يبقى احنا جسمنا ال real line
+
+308
+00:33:47,630 --> 00:33:55,070
+إلى three open intervals من اخد منهم تعالى نشوف
+
+309
+00:33:55,070 --> 00:34:00,710
+ايش بيقول هنا رونسكان وين عند النص يبقى النص بيجي
+
+310
+00:34:00,710 --> 00:34:06,500
+وين في الفترة من سالب واحد إلى واحديعني هذه هنا
+
+311
+00:34:06,500 --> 00:34:13,100
+تبقى ال zero وهنا تجينا النص عين نقطة لان هذه اذا
+
+312
+00:34:13,100 --> 00:34:18,600
+انا بتاخد الفترة من وين لوين من سلب واحد الى واحد
+
+313
+00:34:18,600 --> 00:34:30,880
+يبقى هنا ال functions ال P of T and ل Q of T
+
+314
+00:34:34,950 --> 00:34:42,910
+أركنتنيواص أت مص اللي موجودة في ال interval من
+
+315
+00:34:42,910 --> 00:34:47,630
+سالب واحد إلى واحد يعني احنا شغل هيكون على الفترة
+
+316
+00:34:47,630 --> 00:34:53,110
+يادى وباقى الفترات ماليش دعوة فيهمبنقول له كويس
+
+317
+00:34:53,110 --> 00:34:57,470
+طيب احنا لسه جاعدين بنبحث بس في ال continuity لكن
+
+318
+00:34:57,470 --> 00:35:02,290
+ماتكلمناش في الحل اللي هو بدهيه حتى اللحظة اشجلجل
+
+319
+00:35:02,290 --> 00:35:06,210
+هتل ال ورنسكين او اذا كان ورنسكين عنده نصف بده
+
+320
+00:35:06,210 --> 00:35:11,050
+يساوي تلاتة هتل ال ورنسكين على الفترة اللي الحل
+
+321
+00:35:11,050 --> 00:35:15,720
+عليها صحيح يبقى الحل عنده صيعانيات فترةمن سالب
+
+322
+00:35:15,720 --> 00:35:19,640
+واحد إلى واحد والفترات التانية ماليش علاقة فيها
+
+323
+00:35:19,640 --> 00:35:24,060
+يعني أخدت الفترة المجتملة على مين؟ على النصف إذا
+
+324
+00:35:24,060 --> 00:35:28,920
+بدنا نروح نحسب مين الرونسكين تبعنا يبقى بداجي
+
+325
+00:35:28,920 --> 00:35:35,240
+أقوله الرونسكين as a function of T يساوي C في E
+
+326
+00:35:35,240 --> 00:35:44,320
+والسالب تكاملP of T D T يعني يسوي C في A والسالب
+
+327
+00:35:44,320 --> 00:35:50,280
+تكامل وين ال P اللي عندنا هي واحد على واحد ناقص T
+
+328
+00:35:50,280 --> 00:35:59,760
+يبقى هي سالب واحد على واحد سالب T D Tأظن البسطى
+
+329
+00:35:59,760 --> 00:36:08,460
+فاضل المقام يبقاش بيصير عندنا C في E أسلن absolute
+
+330
+00:36:08,460 --> 00:36:17,040
+value للواحد ناقص T يعني مين يعني C absolute value
+
+331
+00:36:17,040 --> 00:36:24,100
+للواحد ناقص T طيب بدنا نشوف هل ال absolute هذا
+
+332
+00:36:24,100 --> 00:36:30,440
+بيظل ولا بيروح احنا بنشغل علامينمن سالب واحد الى
+
+333
+00:36:30,440 --> 00:36:34,660
+واحد ممنوع الواحد وممنوع السالب واحد يبقى ايش
+
+334
+00:36:34,660 --> 00:36:40,240
+ماتحط هنا عمرها بصير سالب ها حط الرقم اللي بدك
+
+335
+00:36:40,240 --> 00:36:43,660
+يعني بعيد عن السالب واحد والواحد وخد أي شغلة بينهم
+
+336
+00:36:43,660 --> 00:36:48,410
+عمرها بصير سالبيبقى هذه موجبة دائما و أبدا إذا لا
+
+337
+00:36:48,410 --> 00:36:54,630
+داعي لل absolute value يبقى بهذا بده يساوي C في
+
+338
+00:36:54,630 --> 00:37:01,590
+واحد ناقص T لكل T اللي موجودة في ال interval من
+
+339
+00:37:01,590 --> 00:37:05,330
+سالب واحد إلى واحد لل open interval
+
+340
+00:37:08,010 --> 00:37:16,210
+الرونس كان عند النص بده يساوي تلاتة implies يبقى
+
+341
+00:37:16,210 --> 00:37:22,390
+بده يشيل كل تي ويحط مكانها نص يبقى هاي تلاتة بده
+
+342
+00:37:22,390 --> 00:37:23,190
+يساوي
+
+343
+00:37:48,540 --> 00:37:49,940
+Y1Y2Y3Y4Y5Y6Y7Y8Y9Y10Y11Y12Y13Y14Y15Y16Y17Y18Y19Y20Y21Y22Y22Y22Y23Y23Y23Y23Y23Y23Y23Y23Y23Y23Y23Y23Y23Y23Y23Y23Y23Y23Y23Y23Y23Y23Y23Y23Y23Y23Y23Y23Y23Y23Y23Y23Y23Y23Y23Y23Y23Y23Y23Y23Y23Y23Y23Y23Y23Y23Y23Y23Y23Y23Y23Y23Y23Y23Y23Y23Y23Y23Y23Y23Y23Y23Y23Y23Y23Y23Y23Y23Y23Y23Y23Y23Y23Y23Y23Y23Y23Y23Y23Y23Y23Y23Y23Y23Y23Y23Y23Y23
+
+344
+00:37:50,110 --> 00:37:58,370
+بدي ساوي ستة فرنسكان اللي هو واحد ناقصتي، ده اللي
+
+345
+00:37:58,370 --> 00:38:04,910
+هو الحل المطلوب، حد فيكم بتحب تسألي سؤال هنا؟
+
+346
+00:38:04,910 --> 00:38:08,530
+ايوة، ديش ايش؟
+
+347
+00:38:15,940 --> 00:38:23,000
+هذه الفترة اللي لازم تختار ت سالب نص و سالب تصبح
+
+348
+00:38:23,000 --> 00:38:26,600
+واحد زاد نص تلاتة ع اتنين موجة يبقى هذا على ال
+
+349
+00:38:26,600 --> 00:38:31,500
+absolute value تغيرها تاخدها نص موجة تصبح واحد
+
+350
+00:38:31,500 --> 00:38:35,360
+ناقص نص تبقى نص موجة يبقى هذا على ال absolute
+
+351
+00:38:35,360 --> 00:38:40,340
+value اي رقم تاخده ايه بعيد عن سالب واحد اخد اي
+
+352
+00:38:40,340 --> 00:38:45,060
+رقم بينهم تظل بين جثين هذه الكميةيبقى لا داعي لل
+
+353
+00:38:45,060 --> 00:38:51,200
+absolute value تمام؟ اتلاحظى قولتلك هذا for all T
+
+354
+00:38:51,200 --> 00:38:55,180
+يعني اشيلت ال absolute value قولتلك C في واحد ناقص
+
+355
+00:38:55,180 --> 00:38:57,940
+تيليا كل ال T اللى موجود فى ال internet بس لو طلعت
+
+356
+00:38:57,940 --> 00:39:03,320
+برا هذى بيصير كلامى مش صحى تمام؟ حد تسأل تانى؟
+
+357
+00:39:04,360 --> 00:39:11,280
+ننتقل الان الى النقطة اللى بعدها اللى هي نظرية و
+
+358
+00:39:11,280 --> 00:39:15,860
+هذه النظرية طبعا اقوى من النظرية اللى خدناها المرة
+
+359
+00:39:15,860 --> 00:39:19,200
+الماضية المرة الماضية فماخدناها نظرية واحدة وكان
+
+360
+00:39:19,200 --> 00:39:23,560
+بنمشي في اتجاه واحد اذا الورنس كان لا يساوي zero
+
+361
+00:39:23,560 --> 00:39:28,340
+عند نقطة بنقول nearly independent والعكس لو كانت
+
+362
+00:39:28,340 --> 00:39:31,920
+انتها nearly dependent بنقول الورنس كان يساوي zero
+
+363
+00:39:32,180 --> 00:39:37,460
+الان بدنا نجيب نظرية اقوى منها في الاتجاهين if and
+
+364
+00:39:37,460 --> 00:39:49,860
+only if النظرية بتقول ما يأتي فيرم
+
+365
+00:39:49,860 --> 00:39:55,440
+let
+
+366
+00:39:55,440 --> 00:40:01,380
+ال y واحد and y اتنين
+
+367
+00:40:06,080 --> 00:40:14,720
+بسوليوشنز بسوليوشنز of the differential equation
+
+368
+00:40:14,720 --> 00:40:25,940
+للمعادلة التفاضلية L of Y بدا تساوي Y double prime
+
+369
+00:40:25,940 --> 00:40:28,700
+زي P of T في Y prime
+
+370
+00:40:33,730 --> 00:40:48,350
+الـ P of T and Q of T are continuous functions
+
+371
+00:40:49,320 --> 00:41:01,180
+دوال متصلة on an interval I on an open interval I
+
+372
+00:41:01,180 --> 00:41:11,060
+then then
+
+373
+00:41:11,060 --> 00:41:26,010
+Y واحد and Y اتنين arelinearly dependent on I if
+
+374
+00:41:26,010 --> 00:41:33,270
+and only if if and only if الورنس كان تبع ال Y
+
+375
+00:41:33,270 --> 00:41:41,310
+واحد وال Y اتنين as a function of T linearly
+
+376
+00:41:41,310 --> 00:41:51,080
+dependent on I linearly dependent on If and only f
+
+377
+00:41:51,080 --> 00:41:54,380
+الهونسكين
+
+378
+00:41:54,380 --> 00:42:00,520
+تبعهم بده يساوي zero لكل ال T اللي موجودة في ال
+
+379
+00:42:00,520 --> 00:42:05,540
+interval I alternatively
+
+380
+00:42:05,540 --> 00:42:11,660
+ال Y
+
+381
+00:42:11,660 --> 00:42:22,360
+واحد and Y اتنين areLinearly Independent if and
+
+382
+00:42:22,360 --> 00:42:29,420
+only if الرنس كان تبع الحل الأول والحل التاني as a
+
+383
+00:42:29,420 --> 00:42:37,540
+function of t لا يساوي zero on ال interval I
+
+384
+00:42:37,540 --> 00:42:40,720
+remark
+
+385
+00:42:40,720 --> 00:42:41,980
+let
+
+386
+00:42:51,140 --> 00:42:58,520
+Y1 وY2 بصوليوشنز
+
+387
+00:42:58,520 --> 00:43:02,280
+بصوليوشنز
+
+388
+00:43:02,280 --> 00:43:12,000
+of the differential equation للمعادلة التفاضلية YW
+
+389
+00:43:12,000 --> 00:43:18,340
+prime P of Tفى الـ y prime q of t فى ال y بده
+
+390
+00:43:18,340 --> 00:43:28,720
+يساوي zero then the following the
+
+391
+00:43:28,720 --> 00:43:38,540
+following are equivalent النمرة
+
+392
+00:43:38,540 --> 00:43:42,540
+واحد the functions
+
+393
+00:43:45,210 --> 00:43:59,330
+ي واحد وي اتنين are fundamental
+
+394
+00:43:59,330 --> 00:44:02,490
+set
+
+395
+00:44:02,490 --> 00:44:07,370
+of solutions
+
+396
+00:44:07,370 --> 00:44:19,400
+of solutions on the interval Iنمر اتنين ال
+
+397
+00:44:19,400 --> 00:44:28,900
+functions y1 و y2 are linearly independent on the
+
+398
+00:44:28,900 --> 00:44:38,480
+interval I نمر تلاتة الورنسكين تبقى الحل الأول
+
+399
+00:44:38,480 --> 00:44:51,500
+والحل الثاني عند نقطة T nodeلا يساوي zero for some
+
+400
+00:44:51,500 --> 00:45:03,780
+t naught اللي موجودة في ال I نمرا أربعة ال
+
+401
+00:45:03,780 --> 00:45:07,020
+one is can تبع الحل الأول
+
+402
+00:45:09,580 --> 00:45:19,240
+والحل الثاني as a function of t لا يساوي zero for
+
+403
+00:45:19,240 --> 00:45:25,420
+all t اللي موجودة في ال interval I
+
+404
+00:46:15,500 --> 00:46:21,340
+طيب نعود إلى نظرية تبعتنا هنا لأن انتوا افتحولي
+
+405
+00:46:21,340 --> 00:46:28,340
+على المحاضرة اللى فاتت اخر محاضرة اخر نظرية اخر
+
+406
+00:46:28,340 --> 00:46:31,580
+نظرية كتبناها في محاضرة المرة الماضية
+
+407
+00:46:44,440 --> 00:46:50,850
+أه فتحته؟ طيبالنظرية كانت بتقول ما ياتي في عندي
+
+408
+00:46:50,850 --> 00:46:55,930
+دلتين F وG الدلتين كانوا دوال قابلة للاشتقاق مادام
+
+409
+00:46:55,930 --> 00:47:00,210
+قابلة الاشتقاق يبقى تعني ايه؟ متاصلة تمام لك العكس
+
+410
+00:47:00,210 --> 00:47:04,190
+ما لو مش صحيح يبقى متاص على ال open interval I and
+
+411
+00:47:04,190 --> 00:47:08,150
+if there exists T node in I يعني لو لجأت نقطة
+
+412
+00:47:08,150 --> 00:47:11,850
+واحدة T node موجودة في ال interval I بحيث الرنوس
+
+413
+00:47:11,850 --> 00:47:14,830
+كان عندها لا يستوي Zero يبقى الدلتين هذول بقول
+
+414
+00:47:14,830 --> 00:47:21,040
+عنهملنيرلي اندبندنت يبقى لو كان الرنسكين I أساوي
+
+415
+00:47:21,040 --> 00:47:25,720
+زيرو يبقى الدلاتين هدول لينيرلي اندبندنت فقط يبقى
+
+416
+00:47:25,720 --> 00:47:29,540
+السير وين في اتجاه واحد روحنا قولنا in the other
+
+417
+00:47:29,540 --> 00:47:33,160
+hand مشينا في الاتجاه الثاني قولنا لو ال F و G
+
+418
+00:47:33,160 --> 00:47:38,040
+كانوا لينيرلي dependent يبقى الرنسكين تبعهم أساوي
+
+419
+00:47:38,040 --> 00:47:43,370
+زيرو عن كل T موجودة في ال Iإذا هذه معلوماتها بسيطة
+
+420
+00:47:43,370 --> 00:47:48,210
+بمشيش في الاتجاهين لكن أجت النظرية هذه اللي بين
+
+421
+00:47:48,210 --> 00:47:54,150
+إيدنا عمّمت النظرية هذه وصارت أهم منها وأقوى منها
+
+422
+00:47:54,150 --> 00:47:58,110
+يبقى هذه ال theorem stronger than the first
+
+423
+00:47:58,110 --> 00:48:02,290
+theorem الأولانية تعالوا نشوف إيش بتقولبقول لو كان
+
+424
+00:48:02,290 --> 00:48:06,990
+هدول حالين يبقى احنا قايدنا
+
+425
+00:48:06,990 --> 00:48:12,810
+حالنا بحالين لمعادلة تفاضلية يبقى Y1 وY2 حالين
+
+426
+00:48:12,810 --> 00:48:16,070
+للمعادلة التفاضلية اللي عندنا و ال P و ال Q ده هو
+
+427
+00:48:16,070 --> 00:48:21,630
+المتصل على ال interval I them ال Y1 و Y2 are
+
+428
+00:48:21,630 --> 00:48:26,210
+linearly dependent if and only if ال honors can
+
+429
+00:48:26,210 --> 00:48:31,770
+بدوا يساوي Zero لكل ال T اللي موجودة في ال Iكلمة
+
+430
+00:48:31,770 --> 00:48:36,110
+on the other hand في النظرية الأولى اللى قبل شوية
+
+431
+00:48:36,110 --> 00:48:40,450
+كانت في اتجاه واحد لكنها سرعتاش في اتجاهين الى
+
+432
+00:48:40,450 --> 00:48:43,970
+اتجاه الصحيح و لجميع قيم T اللى موجودة فى ال
+
+433
+00:48:43,970 --> 00:48:48,510
+interval مش هندق نقطة واحدة وانما على كل ال
+
+434
+00:48:48,510 --> 00:48:51,870
+interval اللى الحل هادي عليها صحيح أو للدوا اللى
+
+435
+00:48:51,870 --> 00:48:58,000
+عليها متصلة اللى P وQالخيار هو من ناحية أخرى يعني
+
+436
+00:48:58,000 --> 00:49:02,620
+كانوا بالداخل يمشي العكس أن Y1 وY2 are linearly
+
+437
+00:49:02,620 --> 00:49:08,680
+independent إذا الوضع نفسه كان لا يساوي zero لكل
+
+438
+00:49:08,680 --> 00:49:13,160
+ال T اللي موجود في ال I، جالي on I يعني على كل ال
+
+439
+00:49:13,160 --> 00:49:17,900
+I بلا استثناءلكن هناك في النظرية يقول لمن؟ عندنا
+
+440
+00:49:17,900 --> 00:49:21,740
+نقطة واحدة، إذا من الأن فا صاعد، لإن لو عندي
+
+441
+00:49:21,740 --> 00:49:25,400
+معادلة فاضل يجيب تحليل و يقول لي شوفهم لينيار او
+
+442
+00:49:25,400 --> 00:49:29,160
+independent، والله independentلقيت عند نقطة لقيت
+
+443
+00:49:29,160 --> 00:49:33,880
+عند نقطتين لقيت عند كل نقاط الاتنين are the same
+
+444
+00:49:33,880 --> 00:49:37,380
+linearly independent تعني ان الوضع كان لايساوي
+
+445
+00:49:37,380 --> 00:49:41,860
+zero والعكسه صحيح linearly dependent تعني ان الوضع
+
+446
+00:49:41,860 --> 00:49:46,580
+كان يساوي zero والعكسه صحيح طب ال remark هذه بنات
+
+447
+00:49:46,580 --> 00:49:51,900
+لأنها شملت كل ما سبق في ال section اللي فاتتمام؟
+
+448
+00:49:51,900 --> 00:49:55,840
+يعني جمعته كله و حطته في النقاط الأربع اللي قدامها
+
+449
+00:49:55,840 --> 00:49:59,880
+ده إيش بتقولي remark؟ لو كان هدول حلل المعادلة
+
+450
+00:49:59,880 --> 00:50:03,680
+التفاضلية يبقى then the following are equivalent
+
+451
+00:50:03,680 --> 00:50:07,320
+في عندي أربع جملة اللي يمكن تشيلي أي واحدة منهم و
+
+452
+00:50:07,320 --> 00:50:12,460
+تحط التانية بدلها الأولى بتقولي ان y1 و y2 are
+
+453
+00:50:12,460 --> 00:50:16,540
+fundamental set of solutions عالميا على ال
+
+454
+00:50:16,540 --> 00:50:22,300
+interval I لمياة للمعادلة التفاضلية اللي عندنايبقى
+
+455
+00:50:22,300 --> 00:50:26,300
+هذول اتنين بيكونولي fundamentals او ال general
+
+456
+00:50:26,300 --> 00:50:30,380
+solution تمام سي واحد الاول زي اتنين هو ال general
+
+457
+00:50:30,380 --> 00:50:36,380
+اتنين مكافئبين لبعض هذا بكافئ ايش؟ بكافئ لو حدث
+
+458
+00:50:36,380 --> 00:50:39,540
+ذلك ان هذول كانوا اتنين fundamental set of
+
+459
+00:50:39,540 --> 00:50:45,960
+solutions يبقى الحاليا linearly independent مظبوط؟
+
+460
+00:50:46,320 --> 00:50:52,960
+ممكن كمان ان رونسكين تمام عند نقطة لا يساوي zero
+
+461
+00:50:52,960 --> 00:51:00,060
+تمام؟ طيب ممكن رونسكين عند كل النقاط يكون لا يساوي
+
+462
+00:51:00,060 --> 00:51:05,380
+zero يعني ان ثبت ان عند نقطة واحدة على الأقل كان
+
+463
+00:51:05,380 --> 00:51:09,640
+لا يساوي zero في ال interval اذا رونسكين لا يساوي
+
+464
+00:51:09,640 --> 00:51:14,120
+zero على كل ال interval مرةواحد هيبقى ده جمع
+
+465
+00:51:14,120 --> 00:51:19,500
+النظريتين مع بعض بشغل هيبقى نقولش لك اثبتلي والله
+
+466
+00:51:19,500 --> 00:51:22,460
+اتنين هدول بتكونولي fundamental set of solutions
+
+467
+00:51:22,460 --> 00:51:23,700
+بتروح تاخديلهم
+
+468
+00:51:29,850 --> 00:51:34,890
+أو اتنين بيكونولي fundamental set of solutions
+
+469
+00:51:34,890 --> 00:51:38,570
+للمسألة اللي عندي عند نقطة والله عن جميع النقاط
+
+470
+00:51:38,570 --> 00:51:46,050
+كله سيئة حد فيكم بتسأل أسئلة قبل أن أخد مثال طيب
+
+471
+00:51:46,050 --> 00:51:50,410
+إيه الأمثلة والله إيه المثال example
+
+472
+00:51:58,410 --> 00:52:02,890
+بقول لك Y1
+
+473
+00:52:02,890 --> 00:52:06,910
+بيه
+
+474
+00:52:06,910 --> 00:52:16,930
+solution of the initial value problem YW prime
+
+475
+00:52:16,930 --> 00:52:27,290
+زائد T تربيع Y prime زائد T تكييب Y تساوي Zeroو ال
+
+476
+00:52:27,290 --> 00:52:34,430
+y واحد عند ال واحد يساوي واحد و ال y prime عند ال
+
+477
+00:52:34,430 --> 00:52:46,690
+واحد بده يساوي كده؟ بده يساوي تلاتة الان let y2 be
+
+478
+00:52:46,690 --> 00:52:53,330
+a solution of the initial value problem والشرط ان
+
+479
+00:52:53,330 --> 00:53:01,870
+y2 عند الواحد y2 عند الواحد ساوي سالب واحد و y2 a
+
+480
+00:53:01,870 --> 00:53:09,030
+prime عند الواحد ساوي قداش اتنين المصطلوب الأول
+
+481
+00:53:09,030 --> 00:53:17,590
+نمر ايه بيقول show that show that بيقول ان y واحد
+
+482
+00:53:17,590 --> 00:53:32,610
+عند y اتنينForm a fundamental set
+
+483
+00:53:32,610 --> 00:53:41,710
+of solutions
+
+484
+00:53:41,710 --> 00:53:46,770
+of the differential equation
+
+485
+00:53:58,460 --> 00:54:07,260
+of the differential equation للمعادلة التفاضلية
+
+486
+00:54:07,260 --> 00:54:14,500
+الهي Y double prime زائد T تربية Y prime زائد T
+
+487
+00:54:14,500 --> 00:54:22,820
+تكييب Y بده يساوي قداش بده يساوي Zero نمر بي find
+
+488
+00:54:22,820 --> 00:54:27,140
+constants find constants
+
+489
+00:54:30,100 --> 00:54:47,240
+C1 and C2 such that بحيث ان Y تساوي C1 Y1 C2 Y2 C2
+
+490
+00:54:47,240 --> 00:55:01,650
+Y2 is the general solution ofالـ initial value
+
+491
+00:55:01,650 --> 00:55:10,210
+problem الـ y double prime زي ال T تربيع y prime
+
+492
+00:55:10,210 --> 00:55:18,090
+زي ال T تكييب y بدو يساوي zero وال Y عند الواحد
+
+493
+00:55:18,090 --> 00:55:24,430
+بدو يساوي اتنين وال Y prime عند الواحد بدو يساوي
+
+494
+00:55:24,430 --> 00:55:27,210
+كده؟ بدو يساوي zero
+
+495
+00:56:02,040 --> 00:56:08,000
+نرجع لسؤالنا مرة ثانية بقول لو كان Y1 هو solution
+
+496
+00:56:08,000 --> 00:56:13,860
+لل initial value problem اللي عندنا هذا Y2 هو
+
+497
+00:56:13,860 --> 00:56:17,220
+solution لنفس ال initial value problem المعادلة
+
+498
+00:56:17,220 --> 00:56:21,700
+نفسها بس غيرنا مين؟ غيرنا ال initial conditions
+
+499
+00:56:21,700 --> 00:56:29,140
+يبقى انا عندي Y1 و Y1' و Y2 و Y2'بقول المطبق اللي
+
+500
+00:56:29,140 --> 00:56:32,080
+هو ال Bayley ان اي واحد او اي اتنين form a
+
+501
+00:56:32,080 --> 00:56:34,580
+fundamental set of solutions لل differential
+
+502
+00:56:34,580 --> 00:56:39,600
+equation اللي عندنا هذه بقوله والله كويس اذا والله
+
+503
+00:56:39,600 --> 00:56:44,600
+المحدد تبعهم لا يساوي zero إذا الأتنين بيكونوا
+
+504
+00:56:44,600 --> 00:56:47,140
+fundamental set of solutions طبقا لل remark اللي
+
+505
+00:56:47,140 --> 00:56:52,050
+مسحناها قبل قليلأو الـ band in Y1 وY2 before my
+
+506
+00:56:52,050 --> 00:56:55,050
+fundamental system solution إذا الورونس كان عند
+
+507
+00:56:55,050 --> 00:56:59,470
+نقطة أو على طول كان ماله، لا يستوزن، إذا بدنا نروح
+
+508
+00:56:59,470 --> 00:57:03,330
+نحسب الورونس كان، تمام؟ إذا لو رحت حسبت الورونس
+
+509
+00:57:03,330 --> 00:57:08,710
+عند نقطة أو عند كل النقاط، كلسيا أي واحدة فيهم، طب
+
+510
+00:57:08,710 --> 00:57:11,790
+احنا بلاحظ ان ال initial conditions محسبات، كلهم
+
+511
+00:57:11,790 --> 00:57:16,060
+عند مين؟إذا خلّيني أحسب الورونسكين عند الواحد صح
+
+512
+00:57:16,060 --> 00:57:21,740
+ولا لأ يبقى باجي بقوله solution نمر ايه؟ بدي أحسب
+
+513
+00:57:21,740 --> 00:57:28,820
+الورونسكين عند الواحد يبقى هذا الكلام بدي يساوي y
+
+514
+00:57:28,820 --> 00:57:36,440
+واحد عند الواحد y اتنين عند الواحد y اتنين وواحد
+
+515
+00:57:36,440 --> 00:57:44,450
+prime عند الواحد y اتنين prime عند الواحدصح؟ كويس
+
+516
+00:57:44,450 --> 00:57:49,790
+هذه يعني T node يا بنات تبعت ال remark هي اللي هي
+
+517
+00:57:49,790 --> 00:57:55,330
+واحد طب هذا الكلام بده يساوي Y واحد عند الواحد هي
+
+518
+00:57:55,330 --> 00:58:02,630
+بواحد Y اتنين عند الواحد هي بسالب واحد Y واحد ال
+
+519
+00:58:02,630 --> 00:58:08,470
+prime عند الواحد هي بتلاتة Y اتنين ال prime عند
+
+520
+00:58:08,470 --> 00:58:14,600
+الواحد اللي هو باتنينيبقى نفك المحددة ده اتنين
+
+521
+00:58:14,600 --> 00:58:21,680
+زائد تلاتة اتنين زائد تلاتة هو يساوي خمسة لا يساوي
+
+522
+00:58:21,680 --> 00:58:26,070
+Zeroما دام لا يساوي zero يبقى الحالين هدول بقالهم
+
+523
+00:58:26,070 --> 00:58:30,270
+بيكونولي fundamental set واني مش عارف شو شكلهم ولا
+
+524
+00:58:30,270 --> 00:58:34,910
+مطلوب اعرف شكلهم ماجليش هاتل الحالين تمام يبقى
+
+525
+00:58:34,910 --> 00:58:48,490
+باجي بقول له so y1 and y2 form a fundamental set
+
+526
+00:59:09,820 --> 00:59:15,450
+خلصنا المطلب الأول نعود لمطلب الثانيالمطلوب التاني
+
+527
+00:59:15,450 --> 00:59:21,990
+هو find constants C1 وC2 يبقى مادام هذول كوّنولي
+
+528
+00:59:21,990 --> 00:59:25,790
+fundamental set of solutions يبقى ال general
+
+529
+00:59:25,790 --> 00:59:29,930
+solution يكون constant في الحل الأول زاد constant
+
+530
+00:59:29,930 --> 00:59:37,890
+في الحل التاني اذا باجي بقول له general solution
+
+531
+00:59:50,940 --> 00:59:52,340
+YYYYYYYYYYYYYYYYYY
+
+532
+01:00:09,810 --> 01:00:16,350
+إذا بقدر استخدم الشروط اللي عندي فيه إيجاد c1 و c2
+
+533
+01:00:16,350 --> 01:00:20,810
+مظبوط ولا لا باجي بقوله والله كويس يبقى بدي أشتق
+
+534
+01:00:20,810 --> 01:00:26,110
+هذه امانة إذا لو اشتقت هذه إيش بصير y prime c1
+
+535
+01:00:26,110 --> 01:00:35,020
+مقدار ثابت مالوش دهوة وهذه y1 prime c2 y2 primeعند
+
+536
+01:00:35,020 --> 01:00:39,320
+الواحد يجب أن يجي إلى ال condition الأول يجي إلى
+
+537
+01:00:39,320 --> 01:00:41,440
+ال condition الواحد يجي إلى ال condition الواحد
+
+538
+01:00:41,440 --> 01:00:42,180
+يجي إلى ال condition الواحد يجي إلى ال condition
+
+539
+01:00:42,180 --> 01:00:43,500
+الواحد يجي إلى ال condition الواحد يجي إلى ال
+
+540
+01:00:43,500 --> 01:00:45,220
+condition الواحد يجي إلى ال condition الواحد يجي
+
+541
+01:00:45,220 --> 01:00:47,480
+إلى ال condition الواحد يجي إلى ال condition
+
+542
+01:00:47,480 --> 01:00:48,360
+الواحد يجي إلى ال condition الواحد يجي إلى ال
+
+543
+01:00:48,360 --> 01:00:48,820
+condition الواحد يجي إلى ال condition الواحد يجي
+
+544
+01:00:48,820 --> 01:00:49,900
+الواحد يجي إلى ال condition الواحد يجي إلى ال
+
+545
+01:00:49,900 --> 01:00:56,220
+condition الواحد يجي إلى ال condition الواحد يجي
+
+546
+01:00:56,220 --> 01:01:01,740
+إلى ال condition الواحدوالواحد of واحد بيبقى اداش
+
+547
+01:01:01,740 --> 01:01:07,720
+اللي هو واحد يبقى صارت هذه C والله بلاش اكتب عليك
+
+548
+01:01:07,720 --> 01:01:13,860
+على خطتين بلاش تقولي كيف هذه اجت الان
+
+549
+01:01:13,860 --> 01:01:22,310
+من هدول اتنينبقدر اقول ما ياتي ان y عند الواحد بده
+
+550
+01:01:22,310 --> 01:01:28,570
+يساوي c واحد في y واحد عند الواحد زائد c اتنين في
+
+551
+01:01:28,570 --> 01:01:35,270
+y اتنين عند الواحد y a prime عند الواحد بده يساوي
+
+552
+01:01:35,270 --> 01:01:40,690
+c واحد في y واحد a prime عند الواحد زائد c اتنين
+
+553
+01:01:40,690 --> 01:01:48,340
+في y اتنين a prime عند الواحدتمام؟ هكتبهم لك فوق
+
+554
+01:01:48,340 --> 01:01:56,740
+الآن احنا عندناواللي عندك y واحد عند الواحد
+
+555
+01:01:56,740 --> 01:02:02,280
+ماعطينيها بقداش باتنين implies ليه اتنين بدها
+
+556
+01:02:02,280 --> 01:02:08,300
+تساوي وي واحد ايه ال prime اللي هي main بقداش وي
+
+557
+01:02:08,300 --> 01:02:15,060
+واحد اللي هي بقداش بواحد يبقى ب c واحد وي اتنين
+
+558
+01:02:15,060 --> 01:02:20,970
+عند الواحد بناقص واحد يبقى ناقص c اتنينالـ
+
+559
+01:02:20,970 --> 01:02:24,170
+condition التاني يجب أن يعطينا main يجب أن يعطينا
+
+560
+01:02:24,170 --> 01:02:31,010
+y1 prime y prime عند الواحد بده يساوي ال zero يبقى
+
+561
+01:02:31,010 --> 01:02:37,350
+zero بده يساوي y1 prime عند الواحد اللي هو الثلاثة
+
+562
+01:02:37,570 --> 01:02:44,910
+يبقى تلاتة C واحد و Y اتنين عند الواحد ال prime هو
+
+563
+01:02:44,910 --> 01:02:51,890
+بقداش ب اتنين يبقى زائد اتنين C اتنين شو رأيك يا
+
+564
+01:02:51,890 --> 01:02:56,990
+بنات لو ضربت المعادل اللي فوق في اتنين بصير اربع
+
+565
+01:02:56,990 --> 01:03:02,990
+يساوي اتنين C واحد نقص اتنين C اتنين هذه خلتها زي
+
+566
+01:03:02,990 --> 01:03:08,890
+مينتلاتة C واحد زائد اتنين C اتنين وروح الجماعة
+
+567
+01:03:08,890 --> 01:03:15,110
+هذه مع السلامة اربع يسوى خمسة C واحد يبقى C واحد
+
+568
+01:03:15,110 --> 01:03:21,230
+يبقى دياشر اربع احمس مدام اربع احمس يبقى نعود في
+
+569
+01:03:21,230 --> 01:03:29,910
+اي من المعادلتينيبقى بصير اتنين تساوي اربع اخمس
+
+570
+01:03:29,910 --> 01:03:39,650
+ناقص اتنين يبقى C2 تساوي اربع اخمس ناقص اتنين طبعا
+
+571
+01:03:39,650 --> 01:03:46,910
+كله على قداش على حمسة بصير اربع ناقص عشرة يبقى
+
+572
+01:03:46,910 --> 01:03:52,150
+ناقص ست اخمس يبقى بناء على ال general
+
+573
+01:03:55,350 --> 01:04:03,120
+Solution General solution of theالعامة الوالدة
+
+574
+01:04:03,120 --> 01:04:13,240
+اللي بديها هي Y27 C1 طلعناها ب4 أخمس يبقى 4 أخمس
+
+575
+01:04:13,240 --> 01:04:21,300
+Y1 و C2 بناقص 6 أخمس Y2 يبقى هذا ال general
+
+576
+01:04:21,300 --> 01:04:26,800
+solution اللي بديها انتهى
+
+577
+01:04:26,800 --> 01:04:34,160
+ال section بنجي ل exercisesتلاتة تلاتة ومن جول
+
+578
+01:04:34,160 --> 01:04:46,560
+المسائل من واحد لغاية تلتاش الأد ومن خمستاش لغاية
+
+579
+01:04:46,560 --> 01:04:57,540
+واحد وعشرين وسؤال تلاتة وعشرين حد
+
+580
+01:04:57,540 --> 01:04:59,560
+فيك و بتحب تسأل أي سؤال هنا يا بنات؟
+
+581
+01:05:08,740 --> 01:05:13,160
+الان بنتقل الى ال section اللى بعده بعد ما
+
+582
+01:05:13,160 --> 01:05:19,860
+دوخناكوا شوية بدنا نرجع للاصل اللى ابتدينا فيه
+
+583
+01:05:19,860 --> 01:05:24,660
+اللى هو ال homogeneous differential equation with
+
+584
+01:05:24,660 --> 01:05:26,600
+constant coefficients
+
+585
+01:05:37,370 --> 01:05:43,790
+يبقى بدنا نيجي ل section تلاتة أربعة section تلاتة
+
+586
+01:05:43,790 --> 01:05:54,110
+أربعة بتكلم عن ال complex roots complex roots of
+
+587
+01:05:54,110 --> 01:06:00,130
+the characteristic equation
+
+588
+01:06:11,610 --> 01:06:17,420
+بنبدأ ب section تلاتة واحد اول sectionواخدنا ال
+
+589
+01:06:17,420 --> 01:06:21,920
+second order linear differential equation وروحنا
+
+590
+01:06:21,920 --> 01:06:26,660
+خدنا حالة خاصة منها لما يكونوا ال coefficients are
+
+591
+01:06:26,660 --> 01:06:31,440
+colostants يبقى لو كانوا المعاملات ما لهم ثوابت
+
+592
+01:06:31,440 --> 01:06:35,460
+بقولنا بنفرض ان EOSRT هو عبارة عن حلوة وبالتالي
+
+593
+01:06:35,460 --> 01:06:40,040
+بنجيب ال characteristic equation لAR ثربيه زائد BR
+
+594
+01:06:40,040 --> 01:06:48,840
+زائد Cوقلنا الحل له أحد ثلاثة احتمالات الاحتمال
+
+595
+01:06:48,840 --> 01:06:55,760
+الاول ان اتنين are real and different واخدنا امثلة
+
+596
+01:06:55,760 --> 01:07:01,040
+عليهاو بعد هيك صبرنا شوية و غطسنا وين في شجة تانية
+
+597
+01:07:01,040 --> 01:07:06,320
+الان بدنا نرجع بعد section تلاتة اتنين و تلاتة
+
+598
+01:07:06,320 --> 01:07:10,120
+تلاتة بدنا نرجع لكلام اللي ابتدأنا فيه في section
+
+599
+01:07:10,120 --> 01:07:14,320
+تلاتة واحد بداخل تلاتة اربع ان لو كان اتنين are
+
+600
+01:07:14,320 --> 01:07:18,910
+complex rootsالاتنين كانوا complex roots and
+
+601
+01:07:18,910 --> 01:07:22,850
+conjugate اتنين تخيلين ومترافقين وبعد ذلك ال
+
+602
+01:07:22,850 --> 01:07:26,590
+section اللي بعد بناخد لو كانوا اتنين are real
+
+603
+01:07:26,590 --> 01:07:31,570
+repeated roots جذور حقيقية ومقريبة يخلينا مع ال
+
+604
+01:07:31,570 --> 01:07:35,750
+complex اتنين ونذكر تذكير بالمعادة اللي بدأنا فيها
+
+605
+01:07:35,750 --> 01:07:39,830
+وال characteristic equation يبقى باجي بقول هنا
+
+606
+01:07:39,830 --> 01:07:40,610
+consider
+
+607
+01:07:47,460 --> 01:07:57,680
+Homogenous Differential Equation لـ AYW' زائد BY'
+
+608
+01:07:58,560 --> 01:08:04,760
+زائد CY بده يساوي Zero وهذه سمنها المعادلة Star
+
+609
+01:08:06,110 --> 01:08:14,150
+قلنا لو كان ال Y تساوي E أس RT if لهذا is a
+
+610
+01:08:14,150 --> 01:08:19,430
+solution
+
+611
+01:08:19,430 --> 01:08:31,190
+of the differential equation star
+
+612
+01:08:31,190 --> 01:08:32,550
+then
+
+613
+01:08:36,900 --> 01:08:47,440
+كاركترستيك إيكوشن S الهمين AR ثرابية زايد PR زايد
+
+614
+01:08:47,440 --> 01:08:54,380
+C بده يساوي Zero وهذه سمناها المعادلة واحدة هذه
+
+615
+01:08:54,380 --> 01:08:59,920
+البنات بدنا نروح نحلها بواسطة القانون يبقى باجي
+
+616
+01:08:59,920 --> 01:09:01,960
+بقوله The Roots
+
+617
+01:09:04,670 --> 01:09:15,890
+Equation 1R R1 بده يساوي ناقص با زي الجدرى التربية
+
+618
+01:09:15,890 --> 01:09:22,070
+لبا التربية ناقص أربعة ألف جيم كله على اتنين ألف
+
+619
+01:09:24,920 --> 01:09:31,900
+ار اتنين تسوى ناقص با ناقص الجدر التربية لبا تربية
+
+620
+01:09:31,900 --> 01:09:36,640
+ناقص اربع ا سي على اتنين ا
+
+621
+01:09:56,320 --> 01:10:01,400
+كويس المرة اللى فاتت كتبنا الشغل هذه في section
+
+622
+01:10:01,400 --> 01:10:05,700
+تلاتة واحد ابنجلان اخدنا لو كان ال b تربية نقص
+
+623
+01:10:05,700 --> 01:10:10,520
+اربعة ac اكبر من ال zero يبقى قولنا الجدران حقيقيا
+
+624
+01:10:10,520 --> 01:10:15,380
+ومختلفا تمام؟المرة هذه لو كانت القيمة تحت الجدران
+
+625
+01:10:15,380 --> 01:10:21,440
+الهميز أقل من ال zero يبقى باجي بقوله if ال b
+
+626
+01:10:21,440 --> 01:10:28,680
+تربيع ناقص أربع a c أقل من ال zero يبقى الجدران
+
+627
+01:10:28,680 --> 01:10:40,540
+تخيليا مظبوط then the roots are
+
+628
+01:10:42,050 --> 01:10:48,930
+complex conjugate يبقى
+
+629
+01:10:48,930 --> 01:11:02,950
+complex conjugate and we write it
+
+630
+01:11:02,950 --> 01:11:04,770
+in the form
+
+631
+01:11:08,310 --> 01:11:16,230
+ممكن نكتبها على شكل ر واحد يساوي لاندا زائد IMU
+
+632
+01:11:16,230 --> 01:11:27,670
+and ر اتنين يساوي لاندا ناقص IMU واللاندا والميو
+
+633
+01:11:27,670 --> 01:11:32,970
+أعداد حقيقية موجودة في ال set of real numbers
+
+634
+01:11:49,250 --> 01:11:53,910
+مرة تانية بقول عند المعادلة التفاضلية بالشكل هذا
+
+635
+01:11:53,910 --> 01:11:58,070
+رد نوعي تساوي ART عبارة عن حل هذه المعادلة
+
+636
+01:11:58,070 --> 01:12:01,870
+التفاضلية حصلنا على ال characteristic equation
+
+637
+01:12:01,870 --> 01:12:05,150
+بالشكل اللي عندنا هذا جيبنا حل ال characteristic
+
+638
+01:12:05,150 --> 01:12:11,850
+equation وطلع عندي R1 وR2 بقول لو الكمية اللي تحت
+
+639
+01:12:11,850 --> 01:12:16,960
+الجدر هذه كانت كمية سالبةإذا أصبح R واحد و R اتنين
+
+640
+01:12:16,960 --> 01:12:23,440
+كمية تخيلية، يعني إيش بيصير؟ ناقص B على 2A زيدي
+
+641
+01:12:23,440 --> 01:12:30,200
+الجدر على 2A، وهنا ناقص B على 2A ناقص الجدر على 2A
+
+642
+01:12:30,540 --> 01:12:35,280
+ناقص بى او ناقص بى على اتنين ايه بدي اسميها لاندا
+
+643
+01:12:35,280 --> 01:12:41,200
+والجذر على اتنين ايه بدي اسميه ميو وال I هذه الحرف
+
+644
+01:12:41,200 --> 01:12:47,700
+الأول من كلمة imaginary تخيلي يعني I تساوي سالب او
+
+645
+01:12:47,700 --> 01:12:52,240
+الجذر التربية إلى سالب واحد وال I تساوي الجذر
+
+646
+01:12:52,240 --> 01:12:57,970
+التربية إلى سالب واحديعني كمية تخيّلية إذا صار
+
+647
+01:12:57,970 --> 01:13:02,450
+الجدرين R1 وR2 بدل الكلكة الكبيرة هذه بدي أكتبها
+
+648
+01:13:02,450 --> 01:13:06,970
+بشكل ألطف بالشكل اللي أنا هنا تمام؟ مدام صاروا
+
+649
+01:13:06,970 --> 01:13:10,310
+هذول الجدرين اللي يبقى لو رجعنا ل section تلاتة
+
+650
+01:13:10,310 --> 01:13:18,050
+واحد بقين أقول إذا الحل C1 في E أس R1 زاد C2 في E
+
+651
+01:13:18,050 --> 01:13:21,570
+أس R2 صحيح ولا لأ؟ يبقى باجي بقول
+
+652
+01:13:31,990 --> 01:13:44,910
+Y1 يساوي E أُس لاندا زائد IMU و Y2 يساوي E أُس
+
+653
+01:13:44,910 --> 01:13:54,320
+لاندا ناقص IMUهي اصلا ده ناقص IU وبالتالي the
+
+654
+01:13:54,320 --> 01:14:02,800
+general solution of
+
+655
+01:14:02,800 --> 01:14:16,580
+the differential equation star is y تساويC1 في A
+
+656
+01:14:16,580 --> 01:14:24,320
+أُس لاندا زائد I ميو في T طبعا هذه في T يا بنات
+
+657
+01:14:24,320 --> 01:14:32,600
+هذه كله في T وهذا كله في T زائد
+
+658
+01:14:32,600 --> 01:14:43,550
+C2 في A أُس لاندا ناقص I ميو كله في Tيبقى هذا شكل
+
+659
+01:14:43,550 --> 01:14:51,630
+الحل اللى عندنا هذا طيب الحل زى ما تشايفين مكتوب
+
+660
+01:14:51,630 --> 01:14:56,170
+بدل ال complex numbers وغالبيتكوا مادرسوش complex
+
+661
+01:14:56,170 --> 01:15:00,470
+number فى حد درست مادة ال complex يا بنات يعنى هى
+
+662
+01:15:00,470 --> 01:15:06,740
+واحدة ويمكن هى تنتين طيب الغالبية مادرسوشلكن لذلك
+
+663
+01:15:06,740 --> 01:15:11,080
+بدل مالحل مكتوب واصل complex numbers بدي احاول
+
+664
+01:15:11,080 --> 01:15:15,100
+اكتب بدلالة main بدلالة ال real number فيها ان
+
+665
+01:15:15,100 --> 01:15:19,660
+معادلة اسم معادلة Euler اللي بكتب ال exponential
+
+666
+01:15:19,660 --> 01:15:25,420
+function بدلالة ال sign و ال cosine يبقى باجي بقول
+
+667
+01:15:25,420 --> 01:15:30,200
+ما يأتي now we shall
+
+668
+01:15:37,200 --> 01:15:49,480
+write this solution هذا الحل in a
+
+669
+01:15:49,480 --> 01:16:02,880
+real form في شكل حقيقي by using by using oilers
+
+670
+01:16:10,000 --> 01:16:21,280
+شي أولرز فورملة بيقول E أُس I T يساوي Cos T زائد I
+
+671
+01:16:21,280 --> 01:16:26,140
+Sin T خلي
+
+672
+01:16:26,140 --> 01:16:30,060
+دراسة ال complex طبعا حدوها هذه و احنا بنحطها
+
+673
+01:16:30,060 --> 01:16:36,390
+كقاعدة و نشتغل عليهايبقى E أُس I T هي عبارة عن Cos
+
+674
+01:16:36,390 --> 01:16:41,810
+T زائد I Sin T طبعا لو جينا فاكينا يا بنات هنا
+
+675
+01:16:41,810 --> 01:16:49,630
+بصير Lambda T و I Mu T مظبوط هنا بصير Lambda Tو
+
+676
+01:16:49,630 --> 01:16:54,990
+ناقص I ميو T ناقص إذا بدنا نشوف E أس ناقص I T
+
+677
+01:16:54,990 --> 01:17:00,050
+عبارة عن مين إذا بناء عليه لو بدي أجي أخد E أس
+
+678
+01:17:00,050 --> 01:17:08,170
+ناقص I T بقدر أقول E أس I في ناقص T يبقى معنى كلمة
+
+679
+01:17:08,170 --> 01:17:13,320
+T مين أجي مكانها يا بناتيسالب T يبقى بالصير كوصين
+
+680
+01:17:13,320 --> 01:17:20,520
+لسلب T زائد I سين لسلب T ويساوي ال cosine odd
+
+681
+01:17:20,520 --> 01:17:24,280
+function و لا even function even يبقى سلب مع
+
+682
+01:17:24,280 --> 01:17:29,080
+السلامة يبقى ال cosine T والسين odd يبقى السلب
+
+683
+01:17:29,080 --> 01:17:36,170
+يطلع برا سلب I سين Tخلّي المعلومة اللي عندك هذه
+
+684
+01:17:36,170 --> 01:17:43,070
+لزمان لو كان الأس بالسالب يبقى زي الأس بالموجة بس
+
+685
+01:17:43,070 --> 01:17:49,670
+بيفرقوا عن بعضهم بمية بشارة سالب يعني كأنه العدد
+
+686
+01:17:49,670 --> 01:17:54,870
+والعدد المرافق لهمش كنت أقول سين زائد سات ته
+
+687
+01:17:54,870 --> 01:17:58,950
+بالعربي المرافق لو السين ناقص سات ته يعني بنغير
+
+688
+01:17:58,950 --> 01:18:05,030
+انشارة الجزء التخيلة طلع cosine T مافيش فيها تخيلة
+
+689
+01:18:05,030 --> 01:18:10,870
+sin T فيها تخيلة cosine T مافيهاش sin T هي فيها
+
+690
+01:18:10,870 --> 01:18:16,010
+سالب يبقاش صار هذا العدد وهذا هو العدد المرافق له
+
+691
+01:18:16,290 --> 01:18:20,130
+في ال complex numbers في الأعداد المركبة أو
+
+692
+01:18:20,130 --> 01:18:26,750
+الأعداد التخيلية تمام تمام يبقى هذي Euler formula
+
+693
+01:18:26,750 --> 01:18:35,250
+يبقى بناء عليه لو بدى أجيبها بنات E أس I mu T بناء
+
+694
+01:18:35,250 --> 01:18:43,050
+عليهيبقى بدل الثيمين أجانب يبقى باصير cosine mu t
+
+695
+01:18:43,050 --> 01:18:54,830
+كلها زائد I sine mu t وفي نفس الوقت E أسالب I mu t
+
+696
+01:18:54,830 --> 01:19:02,710
+cosine mu t ناقص I sine mu t
+
+697
+01:19:05,060 --> 01:19:09,820
+طيب كويس يبقى عرفنا كل واحدة فيهم يبقى لو جينا
+
+698
+01:19:09,820 --> 01:19:16,840
+بدنا ناخد المجموع تبعهم لو جيت أخد E أُس I لميو T
+
+699
+01:19:16,840 --> 01:19:23,980
+زائد E أُس ناقص I ميو T بده يساوي يبقى بدي أجمع
+
+700
+01:19:23,980 --> 01:19:29,340
+الإتنين، إيش رأيك في هذه و هذه؟ يبقى بضل قداش؟
+
+701
+01:19:29,340 --> 01:19:39,550
+إتنينCos mu tلو بدل مدجمعهم بدي اطرحهم طرح يبقى
+
+702
+01:19:39,550 --> 01:19:48,230
+ايش بصير E أس I mute ناقص E أس ناقص I mute يبقى
+
+703
+01:19:48,230 --> 01:19:54,990
+هذه بصير سالب بتروح مع الموجب وهذه بصير موجب مع
+
+704
+01:19:54,990 --> 01:20:02,230
+الموجب بصير اتنين I sign ل mute
+
+705
+01:20:04,950 --> 01:20:12,610
+تمام؟ يبقى هذا الجمع تبعهم والطرح تبعهم هذا احنا
+
+706
+01:20:12,610 --> 01:20:18,030
+قلنا الحل يا بنات الحل هذا سميليه المعادلة رقم
+
+707
+01:20:18,030 --> 01:20:26,930
+اتنين سميليه المعادلة رقم اتنين الان هذا يمثل حل
+
+708
+01:20:26,930 --> 01:20:32,070
+المعادلة الأصلية اللي هو star هل هناك قيود على C1
+
+709
+01:20:32,070 --> 01:20:38,820
+وC2؟فى قيود عندى؟ لأ ماعنديش قيود، ماعنديش قيود لأ
+
+710
+01:20:38,820 --> 01:20:44,460
+على C1 ولا على C يعني خد زى ما بدك فباجي بقول لو
+
+711
+01:20:44,460 --> 01:20:57,620
+أخدت الآن ترك C1 يسوى C2 يسوى 1 مثلا then equation
+
+712
+01:21:01,830 --> 01:21:18,830
+Y تساوي E أس لامدة T في E أس I ميو T زائد E أس
+
+713
+01:21:18,830 --> 01:21:23,970
+لامدة T في E أس ناقص I ميو T
+
+714
+01:21:27,690 --> 01:21:38,150
+يبقى Y تساوي اللي هسميه الحل الأول يبقى
+
+715
+01:21:38,150 --> 01:21:45,430
+Y واحد بده يساوي EOS Lambda T عامل مشترك بظل ان
+
+716
+01:21:45,430 --> 01:21:58,740
+EOS IMUT زاد EOS ناقص IMUT موجودة فوق؟يبقى بقدر
+
+717
+01:21:58,740 --> 01:22:05,060
+اقول هذه تساوي اتنين E اصلا ده تي كوساين ميوتي
+
+718
+01:22:05,060 --> 01:22:12,020
+صحيح ولا لأ؟ يبقى هذا صار احد الحلول للمعادلة طيب
+
+719
+01:22:12,020 --> 01:22:18,920
+لو جيت قولتلك take C واحد يساوي واحد and C اتنين
+
+720
+01:22:18,920 --> 01:22:27,550
+يساوي سالب واحد مش بحصل عليه حل تاني؟ يبقىان
+
+721
+01:22:27,550 --> 01:22:30,810
+اكويشن تو
+
+722
+01:22:41,000 --> 01:23:04,340
+Y2 يبدو يساوي يبقى
+
+723
+01:23:04,340 --> 01:23:12,810
+يصير عندي Y2 يساويبتاخد EOS Lambda T عامل مشترك
+
+724
+01:23:12,810 --> 01:23:24,280
+بظل EOS IMUT ناقص EOS ناقص IMUT ويساويطلعيلي فى
+
+725
+01:23:24,280 --> 01:23:30,960
+هذه قداش ثلاثانه اتنين اي صين ميو تي يبقى بصير
+
+726
+01:23:30,960 --> 01:23:42,300
+اتنين اي اصلا ده تي صين ميو تي يبقى انا عندي الحل
+
+727
+01:23:42,300 --> 01:23:48,600
+الاول و الحل التانى طلعيلي هذا اتنين مقدار ثابت و
+
+728
+01:23:48,600 --> 01:23:54,650
+اتنين اي مقدار ثابت اللي هم تأثير على الحلثابت
+
+729
+01:23:54,650 --> 01:24:01,190
+مالهم تأثير لأ يبقى كأن الحل الأول هو E أس لاندا T
+
+730
+01:24:01,190 --> 01:24:06,630
+Cos Mu T و الحل الثاني E أس لاندا T Sin Mu T بكوز
+
+731
+01:24:06,630 --> 01:24:16,410
+اتنين و اتنين I as are constants يبقى thus we have
+
+732
+01:24:16,410 --> 01:24:17,850
+to
+
+733
+01:24:19,600 --> 01:24:28,280
+Linearly Independent Solutions اللي هم أميم E
+
+734
+01:24:28,280 --> 01:24:41,080
+أسلندة T Cos M U T and E أسلندة T Sin M U T
+
+735
+01:24:41,080 --> 01:24:42,120
+because
+
+736
+01:24:46,380 --> 01:24:51,980
+ليش هدول linearly independent solutions؟ علشان
+
+737
+01:24:51,980 --> 01:24:59,200
+المحدد تبعهم ماله ممنوع يساوي zero دعونا نشوف
+
+738
+01:24:59,200 --> 01:25:04,700
+المحدد تبعهم، بده يساوي zero وما بيسويش ال zero
+
+739
+01:25:07,490 --> 01:25:15,450
+يبقى بدى اخد الرونسكين تبع ال E أسلندة T cosine
+
+740
+01:25:15,450 --> 01:25:23,870
+لميوتي و E أسلندة T sine لميوتي يبقى هذا الكلام
+
+741
+01:25:23,870 --> 01:25:32,130
+بدى يسوي هاي المحدد E أسلندة T cosine لميوتي و E
+
+742
+01:25:32,130 --> 01:25:36,910
+أسلندة T sine لميوتي
+
+743
+01:25:38,960 --> 01:25:46,280
+بدا اشتق هذه مجتقة مين حاصن ضرب دالتين بدا اشتق
+
+744
+01:25:46,280 --> 01:25:49,860
+الدالة الاولى ال exponential زي ما هي مضروبة في
+
+745
+01:25:49,860 --> 01:25:57,260
+تفاضل مين الاس يبقى لاندا اي اس لاندا ت كوصين ميو
+
+746
+01:25:57,260 --> 01:26:03,960
+ت الاولى مجتقة التانية التانية بسالب ساين في مجتقة
+
+747
+01:26:03,960 --> 01:26:05,620
+الزاوية اللى ميو
+
+748
+01:26:11,740 --> 01:26:15,800
+اللي عملنا الدالة الأولى بدنا نروح نعمل الدالة
+
+749
+01:26:15,800 --> 01:26:24,490
+الثانية يبقى lambdaE Os Lambda T Sine Mu T زيد
+
+750
+01:26:24,490 --> 01:26:31,270
+لميو E Os Lambda T Cos Lambda T لميو T وتعالى نفكر
+
+751
+01:26:31,270 --> 01:26:37,630
+محدد ونشوف على إيش بده يصف حاصل ضرب على ناطر
+
+752
+01:26:37,630 --> 01:26:45,290
+القطرة الرئيسية يبقى Lambda في E Os 2 Lambda T في
+
+753
+01:26:45,290 --> 01:26:55,060
+مين في Sine T Cosفى sign ميو تي كوسين ميو تى زاد
+
+754
+01:26:55,060 --> 01:27:06,900
+لميو فى E أس اتنين لاندا تى فى كوسين تربيع لميو تى
+
+755
+01:27:06,900 --> 01:27:15,240
+خلصنا الرئيسى بداجى الناقص الثانوي ناقص لاندا
+
+756
+01:27:25,720 --> 01:27:38,700
+مقص مع نقص بصير زائد شو
+
+757
+01:27:38,700 --> 01:27:44,820
+رايك هذه هي هذه؟وحدة موجة بواحدة سلبة مع السلامة
+
+758
+01:27:44,820 --> 01:27:52,840
+فما هي رأيك هذه و هذه؟ فيها لم يُ في E أس اتنية
+
+759
+01:27:52,840 --> 01:27:59,890
+لامدة T عامل مشتركبضلك cosine تربية لميو T زائد
+
+760
+01:27:59,890 --> 01:28:06,990
+sin تربية لميو T اللي بين قصانه بقداش يبقى سارة
+
+761
+01:28:06,990 --> 01:28:14,570
+عندك ميو في E أس اتنين لاند T عمر هذا بده يساوي
+
+762
+01:28:14,570 --> 01:28:21,020
+zero يا بنات؟ لأيبقى هذا الكلام لا يمكن أن يساوي
+
+763
+01:28:21,020 --> 01:28:27,980
+zero because ما هو السبب ان E أس اثنية لامدة T
+
+764
+01:28:27,980 --> 01:28:39,000
+دائما و أبدا أكبر من ال zero and لم يو لا يمكن أن
+
+765
+01:28:39,000 --> 01:28:42,400
+تساوي zero ليش sense
+
+766
+01:28:44,960 --> 01:28:51,080
+لو كانت ميو بزيرو بصير
+
+767
+01:28:51,080 --> 01:28:56,040
+الحل كله بلانبا ال root بصير حقيقي و ليس complex
+
+768
+01:28:56,040 --> 01:29:04,500
+يبقى and هذا لا يمكن يسوى zero since the
+
+769
+01:29:04,500 --> 01:29:08,520
+roots are complex
+
+770
+01:29:10,400 --> 01:29:15,580
+لأنه لو سا وزيره بيصير الجذور حقيقية وليستاش مركبة
+
+771
+01:29:15,580 --> 01:29:21,180
+يبقى بناء عليها اتنين هدول كوّنولي the fundamental
+
+772
+01:29:21,180 --> 01:29:25,740
+set of solutions يبقى هدول بيجيبولي ال general
+
+773
+01:29:25,740 --> 01:29:32,580
+solution يبقى باجي بقول ال sir the general
+
+774
+01:29:32,580 --> 01:29:38,620
+solution of the
+
+775
+01:29:58,050 --> 01:29:59,330
+الشكل اللي عندنا
+
+776
+01:30:06,510 --> 01:30:12,130
+يبقى من الآن فصاعدا بهمن لو كان R واحد يساوي R
+
+777
+01:30:12,130 --> 01:30:15,990
+اتنين اتنين اعداد حقيقية كما في section تلاتة واحد
+
+778
+01:30:15,990 --> 01:30:19,710
+تقول الحل العام هو C واحد في EOS R واحد T زائد C
+
+779
+01:30:19,710 --> 01:30:24,730
+اتنين في EOS R اتنين T لو طلع الجذور complex يبقى
+
+780
+01:30:24,730 --> 01:30:29,750
+شكل الحل EOS لاندا T C واحد كوساين ميو T زايد C
+
+781
+01:30:29,750 --> 01:30:35,960
+اتنين ساين ميو T قبل مضيح المعلومة هذه منكبدنا
+
+782
+01:30:35,960 --> 01:30:40,280
+نعطيكي أمثلة، ديرا بالك هذا حساب الورس كان محطوط
+
+783
+01:30:40,280 --> 01:30:44,120
+عندك سؤال في الكتاب محطوط اللي كنت تعسبيه، احنا دي
+
+784
+01:30:44,120 --> 01:30:46,920
+احنا حلينا السؤال و انت ماانتش داري اريحناكي منه
+
+785
+01:31:05,270 --> 01:31:09,190
+يبقى امثلة بسيطة جدا مادهاش لحمة كتير زي النظر
+
+786
+01:31:09,190 --> 01:31:14,910
+يعني تلت امثلة بيعدلوش حساب الورونسكين هذا تمام
+
+787
+01:31:14,910 --> 01:31:22,210
+يبقى examples solve
+
+788
+01:31:22,210 --> 01:31:28,350
+the following differential
+
+789
+01:31:28,350 --> 01:31:31,770
+equations
+
+790
+01:31:36,510 --> 01:31:46,810
+أول سؤال بيقول اربعة وي دابلي قرام زائد تسعة وي
+
+791
+01:31:46,810 --> 01:31:53,870
+بده يساوي زيرو solution بدأ ابدأ زي ما بدأت ال
+
+792
+01:31:53,870 --> 01:31:59,750
+user النظري بدأ اقول له let Y
+
+793
+01:31:59,750 --> 01:32:05,910
+تساوي E أس RT ب A solution
+
+794
+01:32:07,240 --> 01:32:13,400
+then the characteristic
+
+795
+01:32:13,400 --> 01:32:19,160
+equation is هاربع
+
+796
+01:32:20,330 --> 01:32:26,750
+ار تربيع زائد تسعة يساوي زيرو او ان شئتم فاقولوا
+
+797
+01:32:26,750 --> 01:32:34,010
+اربع ار تربيع يساوي قداش ناقص تسعة يبقى ار يساوي
+
+798
+01:32:34,010 --> 01:32:40,430
+الجدر التربيع اللي ناقص تسعة على مين على اربع يعني
+
+799
+01:32:40,430 --> 01:32:46,410
+زائد او ناقص تلاتة على اتنين الجدر التربيع إلى سلب
+
+800
+01:32:46,410 --> 01:32:53,610
+واحد سلب واحد بقداش قولنااي يبقى هنا زائد او ناقص
+
+801
+01:32:53,610 --> 01:33:01,510
+تلاتة على اتنين اي يبقى بنان عليها بنان كداش لاندا
+
+802
+01:33:01,510 --> 01:33:11,830
+هنا كداش لاندا؟ Zero و كداش لميو؟تلاتة على اتنين،
+
+803
+01:33:11,830 --> 01:33:15,850
+صحيح ولا لا؟ زاد ونقص عن اتنين، مترافقين، يعني
+
+804
+01:33:15,850 --> 01:33:19,190
+الإشارتين بيختلفوا للجزء التخيلي، الجزء الحقيقي عن
+
+805
+01:33:19,190 --> 01:33:23,810
+الـ Zero، يبقى بناء عليه أصبح The Solution
+
+806
+01:33:26,450 --> 01:33:37,450
+Y تساوي C إيه؟ قداش؟ Zero مش Lambda ب Zero في C
+
+807
+01:33:37,450 --> 01:33:42,520
+واحد cosine ليه ميو عندي تلاتة على اتنين؟يبقى
+
+808
+01:33:42,520 --> 01:33:48,440
+تلاتة على اتنين T زائد C اتنين Sine تلاتة على
+
+809
+01:33:48,440 --> 01:33:55,940
+اتنين T وانتهينا من المثلة يبقى Y C واحد Cos تلاتة
+
+810
+01:33:55,940 --> 01:34:03,100
+T على اتنين زائد C اتنين Sine تلاتة T على اتنين
+
+811
+01:34:03,100 --> 01:34:10,400
+بسيط المثال الثانيالمثال الثاني طبعا الأول هذا
+
+812
+01:34:10,400 --> 01:34:17,120
+بلغة سؤال 12 من الكتاب هذا سؤال 12 من الكتاب و هذا
+
+813
+01:34:17,120 --> 01:34:24,620
+سؤال 15 من الكتاب بيقول يو اي دابلي برايم زائد واي
+
+814
+01:34:24,620 --> 01:34:31,460
+برايم زائد واحد وربع واي بده يساوي كده؟ بده يساوي
+
+815
+01:34:31,460 --> 01:34:40,610
+زيو واحد ربع يعني كده؟مش خمس أرباع واحد وربع يبقى
+
+816
+01:34:40,610 --> 01:34:47,450
+هذا بده يعطيلك ان yw prime زاد y prime خمس أرباع y
+
+817
+01:34:47,450 --> 01:34:52,770
+يساوي zero او لو ضربت كله في أربعة بصير أربعة yw
+
+818
+01:34:52,770 --> 01:35:00,130
+prime زاد أربعة y prime زاد خمسة y يساوي zeroيبقى
+
+819
+01:35:00,130 --> 01:35:06,430
+بالانهيجة نقول لو افترض ان Y يسوى E اصارتي ب A
+
+820
+01:35:06,430 --> 01:35:15,330
+solution then the characteristic equation is
+
+821
+01:35:17,660 --> 01:35:27,920
+ار تساوي او اربع ار تربية زاد اربع ار زاد خمسة
+
+822
+01:35:27,920 --> 01:35:32,960
+يساوي zero لا يمكن نقدر نحللها بالاقوازيبقى ماليش
+
+823
+01:35:32,960 --> 01:35:39,440
+اللي ليهاش القانون يبقى بناء عليه R تساوي اللي هو
+
+824
+01:35:39,440 --> 01:35:46,080
+ناقص با زادة وناقص الجذر التربيعي لبا تربيع ناقص
+
+825
+01:35:46,080 --> 01:35:53,140
+أربعة ألف اللي هي أربعة جيم اللي هي خمسة كله على
+
+826
+01:35:53,140 --> 01:36:00,530
+اتنين ألف اتنين في أربعةيبقى بناء ان عليها R تساوي
+
+827
+01:36:00,530 --> 01:36:06,910
+نقص اربعة زادة او نقص اربعة فى اربعة بستاش ستاش فى
+
+828
+01:36:06,910 --> 01:36:13,030
+خمسة بتمانين شيله منها ستاش يبقى اربعة وستين الجدر
+
+829
+01:36:13,030 --> 01:36:19,710
+التربيه اللى سالب اربعة وستينكله على قداش تمانية
+
+830
+01:36:19,710 --> 01:36:27,070
+يبقى ناقص اربع زائد او ناقص تمانية اي على تمانية
+
+831
+01:36:27,070 --> 01:36:34,990
+يعني ناقص نص زائد او ناقص اي يبقى ناقص نص عبارة عن
+
+832
+01:36:34,990 --> 01:36:44,030
+ايش هذا بناتوهنا هذا باعتبار واحد يبقى لم يوتوا
+
+833
+01:36:44,030 --> 01:36:47,170
+ساوي واحد يبقى صار ال solution
+
+834
+01:36:50,020 --> 01:36:57,220
+Y تساوي E أس لاندا لامبدا اللي هو ناقص نص T يعني
+
+835
+01:36:57,220 --> 01:37:05,900
+ناقص T على اتنين في C واحد cosine T زاد C اتنين في
+
+836
+01:37:05,900 --> 01:37:12,840
+sine T كمان مثال زيهم هيك صغير وننهي المحاضرة
+
+837
+01:37:12,840 --> 01:37:17,000
+بايروبوس
+
+838
+01:37:17,000 --> 01:37:18,880
+يعطوني خمسة واخدوا العشرة
+
+839
+01:37:32,130 --> 01:37:35,430
+السؤال بيقول solve the initial value problem
+
+840
+01:37:50,070 --> 01:37:58,070
+اللي هي y w prime زائد أربع y prime زائد خمسة y
+
+841
+01:37:58,070 --> 01:38:04,290
+يساوي zero و ال y عند ال zero يساوي واحد و ال pi
+
+842
+01:38:04,290 --> 01:38:12,490
+prime عند ال zero بده يساوي zero يبقى هذه جاهزة
+
+843
+01:38:12,490 --> 01:38:13,410
+solution
+
+844
+01:38:15,770 --> 01:38:24,430
+يبقى باجي بقوله let Y تساوي E أُس RT ب A solution
+
+845
+01:38:24,430 --> 01:38:30,770
+then the characteristic
+
+846
+01:38:30,770 --> 01:38:42,450
+equation is R تربيع زائد أربعة R زائد حمسة يساوي
+
+847
+01:38:42,450 --> 01:38:49,550
+زيرطبعا لا يمكن نقدر نحلل هذه يبقى ماليش إلا أحلها
+
+848
+01:38:49,550 --> 01:38:55,990
+بالقانون ناقص أربعة زيد أو ناقص الجذر التربيعي
+
+849
+01:38:55,990 --> 01:39:01,790
+لبقى تربيعي لبس أتاشر ناقص أربعة ألف اللي هي بواحد
+
+850
+01:39:01,790 --> 01:39:09,010
+جيم اللي هي بخمسة كله على قداش على اتنين في واحد
+
+851
+01:39:09,500 --> 01:39:15,400
+يساوي ناقص اربع زائد او ناقص اربع في خمسة بعشرين
+
+852
+01:39:15,400 --> 01:39:20,360
+بنشيل منه من ستاش مضال قداش ناقص اربع يعني اتنين
+
+853
+01:39:20,360 --> 01:39:26,880
+ايه اتنين ايه كله على قداش على اتنين يبقى ناقص
+
+854
+01:39:26,880 --> 01:39:33,620
+اتنين زائد او ناقص ايه يبقى هذه كلها من أبلاندة
+
+855
+01:39:33,620 --> 01:39:38,280
+وليم يوت تساوي قداش كمان واحد يبقى
+
+856
+01:39:41,240 --> 01:39:52,120
+Solution is Y تساوي E أس لاندا T لإيه E أس ناقص
+
+857
+01:39:52,120 --> 01:40:00,840
+اتنين T C واحد cosine T زايد C اتنين sine ت كونه
+
+858
+01:40:00,840 --> 01:40:05,200
+upon initial conditions خلينا فضلها بالمرةيبقى لو
+
+859
+01:40:05,200 --> 01:40:12,380
+جبت y' تساوي ناقص اتنين EOS ناقص اتنين T C واحد
+
+860
+01:40:12,380 --> 01:40:18,440
+cosine T C اتنين cosine T هذه مشتقة الدالة الأولى
+
+861
+01:40:18,440 --> 01:40:25,480
+في الثانيةزائد الدالة الأولى E أس ناقص اتنين T في
+
+862
+01:40:25,480 --> 01:40:32,360
+مشتقة الثانية اللي هو السالب C واحد sine T وزائد C
+
+863
+01:40:32,360 --> 01:40:39,050
+اتنين cosine Tنمسك ال initial condition الأول و
+
+864
+01:40:39,050 --> 01:40:44,490
+قال لي y عند ال zero بدها تساوي واحد إذا هاي واحد
+
+865
+01:40:44,490 --> 01:40:50,110
+بده أشيل كل T و أحط مكانها zero بصير E و ال zero
+
+866
+01:40:50,110 --> 01:40:55,810
+اللي هو بواحد في cosine صفر اللي هو بواحد sin صفر
+
+867
+01:40:55,810 --> 01:41:00,870
+بصفر يبقى بالشكل اللي عندنا هذايبقى هذه المعادلة
+
+868
+01:41:00,870 --> 01:41:06,250
+بتعطينا ان c1 يساوي كده؟ يساوي 1 نجي ال initial
+
+869
+01:41:06,250 --> 01:41:12,490
+condition الثاني y prime عند 0 بدر ساوي 0 implies
+
+870
+01:41:12,490 --> 01:41:24,420
+ان 0 بدر ساوي ناقص 2 وهذه بقدرش؟ ب1 في c1لأن هذا
+
+871
+01:41:24,420 --> 01:41:31,780
+في هنا بزيرو هنا بواحد هنا بزيرو يبقى بس C واحد
+
+872
+01:41:31,780 --> 01:41:39,140
+اللي بعده زائد واحد فيه صين زيرو بزيرو كوصين صفر
+
+873
+01:41:39,140 --> 01:41:46,700
+واحد يبقى زائد C اتنين يبقى C اتنين بناء عليه صار
+
+874
+01:41:46,700 --> 01:41:54,270
+عندنا C اتنين بده يساوي اتنين C واحدسي واحد عندى
+
+875
+01:41:54,270 --> 01:42:01,350
+بقداش يبقى هادول اتنين مع بعض بدي خليلي انه C2
+
+876
+01:42:01,350 --> 01:42:06,730
+يساوي قداش اتنين يبقى صار ال solution
+
+877
+01:42:12,490 --> 01:42:23,970
+C1-C2T C1-C2T C1-C2T C1
+
+878
+01:42:23,970 --> 01:42:26,470
+-C2T
+
+879
+01:42:34,410 --> 01:42:39,490
+احنا نظري انتهينا منه ال section لكن راح حط بشغلة
+
+880
+01:42:39,490 --> 01:42:44,290
+very important في ال exercises تبقى المرة الجاية
+
+881
+01:42:44,290 --> 01:42:48,810
+بنشرح هذه النقطة و بناخد بعض الأمثلة عليها و بعدين
+
+882
+01:42:48,810 --> 01:42:52,530
+بنخش في ال section اللي بعده ان شاء الله
+
diff --git a/PL9fwy3NUQKwa8ZDfSFGn6H8xVFLzqmCZC/Q2YiEyS2_gY_raw.json b/PL9fwy3NUQKwa8ZDfSFGn6H8xVFLzqmCZC/Q2YiEyS2_gY_raw.json
new file mode 100644
index 0000000000000000000000000000000000000000..20fd9aea0297e97297c8c27657ec6cdf9a8bb255
--- /dev/null
+++ b/PL9fwy3NUQKwa8ZDfSFGn6H8xVFLzqmCZC/Q2YiEyS2_gY_raw.json
@@ -0,0 +1 @@
+{"segments": [{"id": 1, "seek": 2714, "start": 9.66, "end": 27.14, "text": "بسم الله الرحمن الرحيم المرة اللي فاتت بدينا في section تلاتة تلاتة وعطينا تعريف ل linearly independent و linearly dependent functions اقول ان لو في عنده functions بقول عنهم linearly independent", "tokens": [3555, 38251, 21984, 34892, 5016, 27842, 34892, 5016, 32640, 9673, 25720, 13672, 1829, 6156, 9307, 2655, 47525, 1829, 8315, 8978, 3541, 6055, 1211, 9307, 3660, 6055, 1211, 9307, 3660, 4032, 3615, 9566, 1829, 8315, 37279, 16572, 5172, 5296, 43586, 6695, 4032, 43586, 12334, 6828, 1975, 39648, 16472, 45164, 8978, 43242, 3224, 6828, 4724, 39648, 18871, 16095, 43586, 6695], "avg_logprob": -0.22139831215648328, "compression_ratio": 1.7267080745341614, "no_speech_prob": 5.960464477539063e-08, "words": [{"start": 9.659999999999998, "end": 10.62, "word": "بسم", "probability": 0.7138671875}, {"start": 10.62, "end": 10.8, "word": " الله", "probability": 0.9677734375}, {"start": 10.8, "end": 11.24, "word": " الرحمن", "probability": 0.9697265625}, {"start": 11.24, "end": 11.8, "word": " الرحيم", "probability": 0.9933268229166666}, {"start": 11.8, "end": 13.1, "word": " المرة", "probability": 0.6805419921875}, {"start": 13.1, "end": 13.26, "word": " اللي", "probability": 0.6097412109375}, {"start": 13.26, "end": 13.54, "word": " فاتت", "probability": 0.8777669270833334}, {"start": 13.54, "end": 13.92, "word": " بدينا", "probability": 0.740478515625}, {"start": 13.92, "end": 14.08, "word": " في", "probability": 0.91015625}, {"start": 14.08, "end": 14.56, "word": " section", "probability": 0.7099609375}, {"start": 14.56, "end": 15.48, "word": " تلاتة", "probability": 0.79400634765625}, {"start": 15.48, "end": 16.18, "word": " تلاتة", "probability": 0.9727783203125}, {"start": 16.18, "end": 17.22, "word": " وعطينا", "probability": 0.85625}, {"start": 17.22, "end": 17.98, "word": " تعريف", "probability": 0.98876953125}, {"start": 17.98, "end": 18.18, "word": " ل", "probability": 0.56591796875}, {"start": 18.18, "end": 18.66, "word": " linearly", "probability": 0.71240234375}, {"start": 18.66, "end": 19.68, "word": " independent", "probability": 0.919921875}, {"start": 19.68, "end": 20.14, "word": " و", "probability": 0.8310546875}, {"start": 20.14, "end": 20.66, "word": " linearly", "probability": 0.8720703125}, {"start": 20.66, "end": 21.46, "word": " dependent", "probability": 0.8623046875}, {"start": 21.46, "end": 22.46, "word": " functions", "probability": 0.8251953125}, {"start": 22.46, "end": 23.26, "word": " اقول", "probability": 0.5216064453125}, {"start": 23.26, "end": 23.42, "word": " ان", "probability": 0.4970703125}, {"start": 23.42, "end": 23.6, "word": " لو", "probability": 0.7509765625}, {"start": 23.6, "end": 23.76, "word": " في", "probability": 0.73193359375}, {"start": 23.76, "end": 24.16, "word": " عنده", "probability": 0.815673828125}, {"start": 24.16, "end": 24.7, "word": " functions", "probability": 0.57421875}, {"start": 24.7, "end": 25.1, "word": " بقول", "probability": 0.917724609375}, {"start": 25.1, "end": 25.52, "word": " عنهم", "probability": 0.978515625}, {"start": 25.52, "end": 26.14, "word": " linearly", "probability": 0.97216796875}, {"start": 26.14, "end": 27.14, "word": " independent", "probability": 0.9541015625}], "temperature": 1.0}, {"id": 2, "seek": 5487, "start": 27.69, "end": 54.87, "text": "إذا كان الغنوز اللي كانت تبعهم ماله لا يساوي زيرو اما إذا كانت التنتين linearly dependent فالغنوز اللي كانت تبعهم ماله بده يساوي زيرو اتنين قلنا ان ال two functions بقول عنهم linearly independent لو جدت تلاقي two constants كونستان في الدالة الأولى كونستان في الدالة التانية بده يساوي زيرو كان", "tokens": [28814, 15730, 25961, 6024, 118, 1863, 2407, 11622, 13672, 1829, 25961, 2655, 6055, 3555, 3615, 16095, 3714, 6027, 3224, 20193, 7251, 3794, 995, 45865, 30767, 13546, 2407, 1975, 15042, 11933, 15730, 25961, 2655, 16712, 29399, 9957, 43586, 12334, 6156, 6027, 17082, 1863, 2407, 11622, 13672, 1829, 25961, 2655, 6055, 3555, 3615, 16095, 3714, 6027, 3224, 47525, 3224, 7251, 3794, 995, 45865, 30767, 13546, 2407, 1975, 2655, 1863, 9957, 12174, 1211, 8315, 16472, 2423, 732, 6828, 4724, 39648, 18871, 16095, 43586, 6695, 45164, 10874, 3215, 2655, 6055, 15040, 38436, 732, 35870, 9122, 11536, 14851, 7649, 8978, 32748, 6027, 3660, 16247, 12610, 7578, 9122, 11536, 14851, 7649, 8978, 32748, 6027, 3660, 16712, 7649, 10632, 47525, 3224, 7251, 3794, 995, 45865, 30767, 13546, 2407, 25961], "avg_logprob": -0.26346544715447157, "compression_ratio": 2.1743119266055047, "no_speech_prob": 0.0, "words": [{"start": 27.69, "end": 28.11, "word": "إذا", "probability": 0.66845703125}, {"start": 28.11, "end": 28.47, "word": " كان", "probability": 0.9453125}, {"start": 28.47, "end": 28.87, "word": " الغنوز", "probability": 0.6367431640625}, {"start": 28.87, "end": 29.05, "word": " اللي", "probability": 0.52618408203125}, {"start": 29.05, "end": 29.19, "word": " كانت", "probability": 0.62255859375}, {"start": 29.19, "end": 29.51, "word": " تبعهم", "probability": 0.7960205078125}, {"start": 29.51, "end": 29.95, "word": " ماله", "probability": 0.81982421875}, {"start": 29.95, "end": 30.57, "word": " لا", "probability": 0.322509765625}, {"start": 30.57, "end": 31.43, "word": " يساوي", "probability": 0.8675537109375}, {"start": 31.43, "end": 31.89, "word": " زيرو", "probability": 0.587890625}, {"start": 31.89, "end": 32.65, "word": " اما", "probability": 0.6353759765625}, {"start": 32.65, "end": 32.97, "word": " إذا", "probability": 0.810791015625}, {"start": 32.97, "end": 33.49, "word": " كانت", "probability": 0.9560546875}, {"start": 33.49, "end": 34.15, "word": " التنتين", "probability": 0.8287760416666666}, {"start": 34.15, "end": 34.83, "word": " linearly", "probability": 0.7978515625}, {"start": 34.83, "end": 35.93, "word": " dependent", "probability": 0.603515625}, {"start": 35.93, "end": 37.71, "word": " فالغنوز", "probability": 0.9462890625}, {"start": 37.71, "end": 37.89, "word": " اللي", "probability": 0.9814453125}, {"start": 37.89, "end": 38.07, "word": " كانت", "probability": 0.954345703125}, {"start": 38.07, "end": 38.73, "word": " تبعهم", "probability": 0.9776611328125}, {"start": 38.73, "end": 39.67, "word": " ماله", "probability": 0.9695638020833334}, {"start": 39.67, "end": 39.99, "word": " بده", "probability": 0.403076171875}, {"start": 39.99, "end": 40.33, "word": " يساوي", "probability": 0.9560546875}, {"start": 40.33, "end": 40.67, "word": " زيرو", "probability": 0.9283854166666666}, {"start": 40.67, "end": 41.19, "word": " اتنين", "probability": 0.7861328125}, {"start": 41.19, "end": 42.43, "word": " قلنا", "probability": 0.84228515625}, {"start": 42.43, "end": 43.29, "word": " ان", "probability": 0.7294921875}, {"start": 43.29, "end": 43.87, "word": " ال", "probability": 0.90625}, {"start": 43.87, "end": 44.07, "word": " two", "probability": 0.6494140625}, {"start": 44.07, "end": 44.87, "word": " functions", "probability": 0.86181640625}, {"start": 44.87, "end": 45.45, 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"probability": 0.93896484375}, {"start": 51.99, "end": 52.47, "word": " كونستان", "probability": 0.83795166015625}, {"start": 52.47, "end": 52.63, "word": " في", "probability": 0.97412109375}, {"start": 52.63, "end": 52.99, "word": " الدالة", "probability": 0.99072265625}, {"start": 52.99, "end": 53.25, "word": " التانية", "probability": 0.9676106770833334}, {"start": 53.25, "end": 53.57, "word": " بده", "probability": 0.925537109375}, {"start": 53.57, "end": 53.93, "word": " يساوي", "probability": 0.98095703125}, {"start": 53.93, "end": 54.31, "word": " زيرو", "probability": 0.9549153645833334}, {"start": 54.31, "end": 54.87, "word": " كان", "probability": 0.828125}], "temperature": 1.0}, {"id": 3, "seek": 6623, "start": 60.29, "end": 66.23, "text": "لكن لو كان على الأقل واحد من كواحد او كاتنين لا يساوي زيرو", "tokens": [1211, 19452, 45164, 25961, 15844, 16247, 4587, 1211, 36764, 24401, 9154, 9122, 14407, 24401, 1975, 2407, 9122, 9307, 1863, 9957, 20193, 7251, 3794, 995, 45865, 30767, 13546, 2407], "avg_logprob": -0.48491378488211795, "compression_ratio": 1.2839506172839505, "no_speech_prob": 0.0, "words": [{"start": 60.29, "end": 61.21, "word": "لكن", "probability": 0.2733154296875}, {"start": 61.21, "end": 61.39, "word": " لو", "probability": 0.48388671875}, {"start": 61.39, "end": 61.69, "word": " كان", "probability": 0.83251953125}, {"start": 61.69, "end": 61.91, "word": " على", "probability": 0.72509765625}, {"start": 61.91, "end": 62.53, "word": " الأقل", "probability": 0.8986002604166666}, {"start": 62.53, "end": 63.07, "word": " واحد", "probability": 0.6162109375}, {"start": 63.07, "end": 63.27, "word": " من", "probability": 0.92236328125}, {"start": 63.27, "end": 63.93, "word": " كواحد", "probability": 0.6923828125}, {"start": 63.93, "end": 64.17, "word": " او", "probability": 0.7388916015625}, {"start": 64.17, "end": 64.63, "word": " كاتنين", "probability": 0.7755126953125}, {"start": 64.63, "end": 64.95, "word": " لا", "probability": 0.61328125}, 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0.7314453125}, {"start": 82.82, "end": 83.34, "word": " النظرية", "probability": 0.9775390625}, {"start": 83.34, "end": 84.04, "word": " الوحيدة", "probability": 0.97705078125}, {"start": 84.04, "end": 84.54, "word": " اللي", "probability": 0.865234375}, {"start": 84.54, "end": 85.04, "word": " أخدناها", "probability": 0.880810546875}, {"start": 85.04, "end": 85.44, "word": " المرة", "probability": 0.971435546875}, {"start": 85.44, "end": 85.64, "word": " اللي", "probability": 0.952880859375}, {"start": 85.64, "end": 86.2, "word": " فاتت", "probability": 0.9840494791666666}, {"start": 86.2, "end": 86.68, "word": " اللي", "probability": 0.963134765625}, {"start": 86.68, "end": 86.86, "word": " هو", "probability": 0.9609375}, {"start": 86.86, "end": 87.52, "word": " بنحكم", "probability": 0.8566080729166666}, {"start": 87.52, "end": 88.46, "word": " على", "probability": 0.91748046875}, {"start": 88.46, "end": 88.68, "word": " ال", "probability": 0.642578125}, {"start": 88.68, "end": 88.9, "word": " two", "probability": 0.939453125}, {"start": 88.9, "end": 89.7, "word": " functions", "probability": 0.90234375}, {"start": 89.7, "end": 90.1, "word": " او", "probability": 0.86279296875}, {"start": 90.1, "end": 90.28, "word": " ال", "probability": 0.96923828125}, {"start": 90.28, "end": 90.52, "word": " two", "probability": 0.9599609375}, {"start": 90.52, "end": 91.44, "word": " solutions", "probability": 0.9296875}, {"start": 91.44, "end": 91.68, "word": " ل", "probability": 0.55078125}, {"start": 91.68, "end": 92.06, "word": " second", "probability": 0.73193359375}, {"start": 92.06, "end": 92.6, "word": " order", "probability": 0.916015625}, {"start": 92.6, "end": 93.06, "word": " differential", "probability": 0.89404296875}, {"start": 93.06, "end": 93.74, "word": " equation", "probability": 0.884765625}], "temperature": 1.0}, {"id": 5, "seek": 11286, "start": 94.14, "end": 112.86, "text": "بينهم linearly dependent او linearly independent من خلال الورنسكين يعني لو جينا وجينا ان الورنسكين عند نقطة ما لا يساوي zero اذا ال two functions بقول عنهم linearly independent", "tokens": [3555, 9957, 16095, 43586, 12334, 1975, 2407, 43586, 6695, 9154, 16490, 1211, 6027, 2423, 13063, 1863, 3794, 4117, 9957, 37495, 22653, 45164, 10874, 1829, 8315, 49610, 1829, 8315, 16472, 2423, 13063, 1863, 3794, 4117, 9957, 43242, 8717, 47432, 3660, 19446, 20193, 7251, 3794, 995, 45865, 4018, 1975, 15730, 2423, 732, 6828, 4724, 39648, 18871, 16095, 43586, 6695], "avg_logprob": -0.20932112762640262, "compression_ratio": 1.6012658227848102, "no_speech_prob": 0.0, "words": [{"start": 94.14, "end": 94.58, "word": "بينهم", "probability": 0.7124837239583334}, {"start": 94.58, "end": 95.06, "word": " linearly", "probability": 0.8701171875}, {"start": 95.06, "end": 95.74, "word": " dependent", "probability": 0.634765625}, {"start": 95.74, "end": 96.22, "word": " او", "probability": 0.6729736328125}, {"start": 96.22, "end": 96.88, "word": " linearly", "probability": 0.96337890625}, {"start": 96.88, "end": 97.74, "word": " independent", "probability": 0.94091796875}, {"start": 97.74, "end": 98.3, "word": " من", "probability": 0.90771484375}, {"start": 98.3, "end": 99.28, "word": " خلال", "probability": 0.9933268229166666}, {"start": 99.28, "end": 100.22, "word": " الورنسكين", "probability": 0.73486328125}, {"start": 100.22, "end": 100.62, "word": " يعني", "probability": 0.7451171875}, {"start": 100.62, "end": 101.64, "word": " لو", "probability": 0.86865234375}, {"start": 101.64, "end": 102.0, "word": " جينا", "probability": 0.9440104166666666}, {"start": 102.0, "end": 102.44, "word": " وجينا", "probability": 0.7615559895833334}, {"start": 102.44, "end": 102.66, "word": " ان", "probability": 0.8388671875}, {"start": 102.66, "end": 103.34, "word": " الورنسكين", "probability": 0.9668782552083334}, {"start": 103.34, "end": 103.64, "word": " عند", "probability": 0.986328125}, {"start": 103.64, "end": 104.58, "word": " نقطة", "probability": 0.8427734375}, {"start": 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"seek": 12705, "start": 113.57, "end": 127.05, "text": "ولو كانوا تنتهيوا linearly dependent يكون ال goal skin يساوي zero هذه النظرية الحجيبة نظرية أقوى منها وتبقى في اتجاهين", "tokens": [2407, 1211, 2407, 25961, 14407, 6055, 29399, 3224, 1829, 14407, 43586, 12334, 7251, 30544, 2423, 3387, 3178, 7251, 3794, 995, 45865, 4018, 29538, 28239, 19913, 2288, 10632, 21542, 7435, 1829, 49401, 8717, 19913, 2288, 10632, 5551, 4587, 2407, 7578, 9154, 11296, 34683, 3555, 4587, 7578, 8978, 1975, 2655, 7435, 40294, 9957], "avg_logprob": -0.4654447121115831, "compression_ratio": 1.296551724137931, "no_speech_prob": 0.0, "words": [{"start": 113.57, "end": 114.11, "word": "ولو", "probability": 0.5575358072916666}, {"start": 114.11, "end": 116.09, "word": " كانوا", "probability": 0.92529296875}, {"start": 116.09, "end": 116.59, "word": " تنتهيوا", "probability": 0.6359130859375}, {"start": 116.59, "end": 116.95, "word": " linearly", "probability": 0.12939453125}, {"start": 116.95, "end": 117.93, "word": " dependent", "probability": 0.7177734375}, {"start": 117.93, "end": 118.67, "word": " يكون", "probability": 0.28765869140625}, {"start": 118.67, "end": 118.87, "word": " ال", "probability": 0.485107421875}, {"start": 118.87, "end": 119.05, "word": " goal", "probability": 0.2030029296875}, {"start": 119.05, "end": 119.29, "word": " skin", "probability": 0.376220703125}, {"start": 119.29, "end": 120.71, "word": " يساوي", "probability": 0.7156982421875}, {"start": 120.71, "end": 120.95, "word": " zero", "probability": 0.153564453125}, {"start": 120.95, "end": 121.29, "word": " هذه", "probability": 0.300537109375}, {"start": 121.29, "end": 122.27, "word": " النظرية", "probability": 0.8843994140625}, {"start": 122.27, "end": 123.55, "word": " الحجيبة", "probability": 0.52508544921875}, {"start": 123.55, "end": 124.25, "word": " نظرية", "probability": 0.8546142578125}, {"start": 124.25, "end": 125.05, "word": " أقوى", "probability": 0.8544921875}, {"start": 125.05, "end": 125.47, "word": " 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{"start": 137.29, "end": 137.83, "word": " عليها", "probability": 0.989501953125}, {"start": 137.83, "end": 138.35, "word": " أو", "probability": 0.5087890625}, {"start": 138.35, "end": 138.51, "word": " اللي", "probability": 0.9833984375}, {"start": 138.51, "end": 138.91, "word": " عارفين", "probability": 0.9766845703125}, {"start": 138.91, "end": 139.33, "word": " تبعة", "probability": 0.549560546875}, {"start": 139.33, "end": 140.01, "word": " المحدد", "probability": 0.9537760416666666}, {"start": 140.01, "end": 140.47, "word": " الدالة", "probability": 0.9015299479166666}, {"start": 140.47, "end": 140.83, "word": " الأولى", "probability": 0.9597981770833334}, {"start": 140.83, "end": 141.33, "word": " التانية", "probability": 0.7508951822916666}, {"start": 141.33, "end": 142.19, "word": " مشتقة", "probability": 0.7771809895833334}, {"start": 142.19, "end": 142.53, "word": " الأولى", "probability": 0.9558919270833334}, {"start": 142.53, "end": 143.15, "word": " ومشتقة", 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هو هل هذه في يوم من الأيام تاخد قيمة سالبة أو صفة؟ يبقى هذا الكلام ال absolute value، اشيلناه والله خلناها سيانة", "tokens": [3794, 33604, 6027, 31439, 8032, 1211, 29538, 8978, 7251, 20498, 9154, 16247, 1829, 10943, 6055, 47283, 3215, 12174, 32640, 3660, 8608, 6027, 49401, 34051, 20328, 5172, 3660, 22807, 7251, 3555, 4587, 7578, 23758, 2423, 28820, 10943, 2423, 8236, 2158, 12399, 1975, 8592, 26895, 8315, 3224, 16070, 43761, 16490, 1211, 8315, 11296, 8608, 1829, 7649, 3660], "avg_logprob": -0.23395647693957602, "compression_ratio": 1.3819444444444444, "no_speech_prob": 0.0, "words": [{"start": 735.81, "end": 736.79, "word": "سؤال", "probability": 0.9313151041666666}, {"start": 736.79, "end": 737.11, "word": " هو", "probability": 0.9423828125}, {"start": 737.11, "end": 738.33, "word": " هل", "probability": 0.8349609375}, {"start": 738.33, "end": 738.79, "word": " هذه", "probability": 0.373779296875}, {"start": 738.79, "end": 739.07, "word": " في", "probability": 0.8525390625}, {"start": 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بتنتين", "probability": 0.9103190104166666}], "temperature": 1.0}, {"id": 39, "seek": 88614, "start": 859.14, "end": 886.14, "text": "يبقى اول مثال example one اول مثال let y1 بده يسوي جذر ال T و ال y2 بده يسوي واحد عال T بي two solutions", "tokens": [1829, 3555, 4587, 7578, 1975, 12610, 50113, 6027, 1365, 472, 1975, 12610, 50113, 6027, 718, 288, 16, 47525, 3224, 7251, 3794, 45865, 10874, 8848, 2288, 2423, 314, 4032, 2423, 288, 17, 47525, 3224, 7251, 3794, 45865, 36764, 24401, 6225, 6027, 314, 4724, 1829, 732, 6547], "avg_logprob": -0.4177989227616269, "compression_ratio": 1.3076923076923077, "no_speech_prob": 0.0, "words": [{"start": 859.14, "end": 859.54, "word": "يبقى", "probability": 0.678985595703125}, {"start": 859.54, "end": 859.9, "word": " اول", "probability": 0.672607421875}, {"start": 859.9, "end": 860.52, "word": " مثال", "probability": 0.986572265625}, {"start": 860.52, "end": 860.88, "word": " example", "probability": 0.447265625}, {"start": 860.88, "end": 861.7, "word": " one", "probability": 0.60986328125}, {"start": 861.7, "end": 867.44, "word": " اول", "probability": 0.694091796875}, {"start": 867.44, "end": 868.26, "word": " مثال", "probability": 0.977783203125}, {"start": 868.26, "end": 870.1, "word": " let", "probability": 0.548828125}, {"start": 870.1, "end": 872.5, "word": " y1", "probability": 0.68994140625}, {"start": 872.5, "end": 872.92, "word": " بده", "probability": 0.26690673828125}, {"start": 872.92, "end": 873.36, "word": " يسوي", "probability": 0.8072916666666666}, {"start": 873.36, "end": 874.2, "word": " جذر", "probability": 0.5247395833333334}, {"start": 874.2, "end": 874.54, "word": " ال", "probability": 0.56591796875}, {"start": 874.54, "end": 874.9, "word": " T", "probability": 0.65869140625}, {"start": 874.9, "end": 876.06, "word": " و", "probability": 0.56689453125}, {"start": 876.06, "end": 876.26, "word": " ال", "probability": 0.469970703125}, {"start": 876.26, "end": 877.06, "word": " y2", "probability": 0.807373046875}, 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stronger than the first theorem الأولانية تعالوا نشوف إيش بتقول", "tokens": [28814, 15730, 29538, 20449, 1211, 20498, 9307, 11296, 4724, 3794, 1829, 9566, 3660, 4724, 2304, 8592, 1829, 8592, 8978, 2423, 9307, 7435, 40294, 9957, 44381, 5551, 7435, 2655, 28239, 19913, 2288, 10632, 29538, 13672, 1829, 49374, 11933, 25708, 8315, 6225, 2304, 11703, 2304, 2655, 28239, 19913, 2288, 10632, 29538, 4032, 9381, 9640, 2655, 5551, 16095, 9154, 11296, 36725, 4587, 2407, 7578, 9154, 11296, 7251, 3555, 4587, 7578, 29538, 2423, 20904, 7249, 813, 264, 700, 20904, 16247, 12610, 7649, 10632, 37279, 6027, 14407, 8717, 8592, 38688, 11933, 1829, 8592, 39894, 39648], "avg_logprob": -0.16328983418234103, "compression_ratio": 1.6634146341463414, "no_speech_prob": 0.0, "words": [{"start": 2861.51, "end": 2861.93, "word": "إذا", "probability": 0.590576171875}, {"start": 2861.93, "end": 2862.23, "word": " هذه", "probability": 0.83203125}, {"start": 2862.23, "end": 2862.91, "word": " معلوماتها", "probability": 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"text": "لكن هناك في النظرية يقول لمن؟ عندنا نقطة واحدة، إذا من الأن فا صاعد، لإن لو عندي معادلة فاضل يجيب تحليل و يقول لي شوفهم لينيار او independent، والله independent", "tokens": [1211, 19452, 34105, 4117, 8978, 28239, 19913, 2288, 10632, 7251, 39648, 5296, 27842, 22807, 43242, 8315, 8717, 47432, 3660, 36764, 24401, 3660, 12399, 11933, 15730, 9154, 16247, 1863, 6156, 995, 20328, 995, 22488, 12399, 5296, 28814, 1863, 45164, 18871, 16254, 20449, 18513, 37977, 6156, 46958, 1211, 7251, 7435, 1829, 3555, 6055, 5016, 1211, 26895, 4032, 7251, 39648, 32239, 13412, 38688, 16095, 5296, 9957, 1829, 9640, 1975, 2407, 6695, 12399, 16070, 43761, 6695], "avg_logprob": -0.4113869895673778, "compression_ratio": 1.5459770114942528, "no_speech_prob": 0.0, "words": [{"start": 2955.0, "end": 2955.42, "word": "لكن", "probability": 0.6446533203125}, {"start": 2955.42, "end": 2955.82, "word": " هناك", "probability": 0.900146484375}, {"start": 2955.82, "end": 2955.88, "word": " في", "probability": 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"probability": 0.6744791666666666}, {"start": 2961.44, "end": 2961.54, "word": " لو", "probability": 0.8115234375}, {"start": 2961.54, "end": 2961.74, "word": " عندي", "probability": 0.842041015625}, {"start": 2961.74, "end": 2962.2, "word": " معادلة", "probability": 0.8138020833333334}, {"start": 2962.2, "end": 2962.76, "word": " فاضل", "probability": 0.6783854166666666}, {"start": 2962.76, "end": 2963.26, "word": " يجيب", "probability": 0.8240966796875}, {"start": 2963.26, "end": 2963.7, "word": " تحليل", "probability": 0.7586669921875}, {"start": 2963.7, "end": 2963.82, "word": " و", "probability": 0.470458984375}, {"start": 2963.82, "end": 2964.02, "word": " يقول", "probability": 0.5792236328125}, {"start": 2964.02, "end": 2964.12, "word": " لي", "probability": 0.6494140625}, {"start": 2964.12, "end": 2964.58, "word": " شوفهم", "probability": 0.8610026041666666}, {"start": 2964.58, "end": 2965.16, "word": " لينيار", "probability": 0.59185791015625}, {"start": 2965.16, "end": 2965.4, "word": " او", "probability": 0.400909423828125}, {"start": 2965.4, "end": 2966.02, "word": " independent،", "probability": 0.654541015625}, {"start": 2966.02, "end": 2966.32, "word": " والله", "probability": 0.746337890625}, {"start": 2966.32, "end": 2966.8, "word": " independent", "probability": 0.740234375}], "temperature": 1.0}, {"id": 122, "seek": 299072, "start": 2967.42, "end": 2990.72, "text": "لقيت عند نقطة لقيت عند نقطتين لقيت عند كل نقاط الاتنين are the same linearly independent تعني ان الوضع كان لايساوي zero والعكسه صحيح linearly dependent تعني ان الوضع كان يساوي zero والعكسه صحيح طب ال remark هذه بنات لأنها شملت كل ما سبق في ال section اللي فات", "tokens": [1211, 4587, 36081, 43242, 8717, 47432, 3660, 5296, 4587, 36081, 43242, 8717, 47432, 2655, 9957, 5296, 4587, 36081, 43242, 28242, 8717, 4587, 41193, 2423, 9307, 1863, 9957, 366, 264, 912, 43586, 6695, 37279, 22653, 16472, 2423, 2407, 11242, 3615, 25961, 20193, 1829, 3794, 995, 45865, 4018, 16070, 3615, 4117, 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2988.78, "word": " ما", "probability": 0.9404296875}, {"start": 2988.78, "end": 2989.28, "word": " سبق", "probability": 0.9864908854166666}, {"start": 2989.28, "end": 2989.46, "word": " في", "probability": 0.8544921875}, {"start": 2989.46, "end": 2989.52, "word": " ال", "probability": 0.75439453125}, {"start": 2989.52, "end": 2989.92, "word": " section", "probability": 0.8515625}, {"start": 2989.92, "end": 2990.28, "word": " اللي", "probability": 0.8505859375}, {"start": 2990.28, "end": 2990.72, "word": " فات", "probability": 0.988037109375}], "temperature": 1.0}, {"id": 123, "seek": 302040, "start": 2991.02, "end": 3020.4, "text": "تمام؟ يعني جمعته كله و حطته في النقاط الأربع اللي قدامها ده إيش بتقولي remark؟ لو كان هدول حلل المعادلة التفاضلية يبقى then the following are equivalent في عندي أربع جملة اللي يمكن تشيلي أي واحدة منهم و تحط التانية بدلها الأولى بتقولي ان y1 و y2 are fundamental set of solutions عالميا على ال interval I لمياة للمعادلة التفاضلية اللي عندنا", "tokens": [2655, 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"end": 3006.9, "word": " واحدة", "probability": 0.9817708333333334}, {"start": 3006.9, "end": 3007.14, "word": " منهم", "probability": 0.951171875}, {"start": 3007.14, "end": 3007.32, "word": " و", "probability": 0.5732421875}, {"start": 3007.32, "end": 3007.62, "word": " تحط", "probability": 0.9876302083333334}, {"start": 3007.62, "end": 3008.28, "word": " التانية", "probability": 0.9363606770833334}, {"start": 3008.28, "end": 3009.02, "word": " بدلها", "probability": 0.857421875}, {"start": 3009.02, "end": 3010.2, "word": " الأولى", "probability": 0.9295247395833334}, {"start": 3010.2, "end": 3010.82, "word": " بتقولي", "probability": 0.8785807291666666}, {"start": 3010.82, "end": 3011.02, "word": " ان", "probability": 0.443115234375}, {"start": 3011.02, "end": 3011.58, "word": " y1", "probability": 0.4598388671875}, {"start": 3011.58, "end": 3011.8, "word": " و", "probability": 0.9619140625}, {"start": 3011.8, "end": 3012.2, "word": " y2", "probability": 0.914306640625}, {"start": 3012.2, "end": 3012.46, "word": " are", "probability": 0.91015625}, {"start": 3012.46, "end": 3013.04, "word": " fundamental", "probability": 0.69580078125}, {"start": 3013.04, "end": 3013.56, "word": " set", "probability": 0.84423828125}, {"start": 3013.56, "end": 3013.86, "word": " of", "probability": 0.97900390625}, {"start": 3013.86, "end": 3014.88, "word": " solutions", "probability": 0.9287109375}, {"start": 3014.88, "end": 3015.7, "word": " عالميا", "probability": 0.85546875}, {"start": 3015.7, "end": 3016.38, "word": " على", "probability": 0.82177734375}, {"start": 3016.38, "end": 3016.54, "word": " ال", "probability": 0.98046875}, {"start": 3016.54, "end": 3017.04, "word": " interval", "probability": 0.75634765625}, {"start": 3017.04, "end": 3017.34, "word": " I", "probability": 0.67138671875}, {"start": 3017.34, "end": 3017.96, "word": " لمياة", "probability": 0.5738118489583334}, {"start": 3017.96, "end": 3018.72, "word": " للمعادلة", "probability": 0.8673828125}, {"start": 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{"start": 3913.16, "end": 3914.08, "word": " دوخناكوا", "probability": 0.8511555989583334}, {"start": 3914.08, "end": 3914.68, "word": " شوية", "probability": 0.9412434895833334}, {"start": 3914.68, "end": 3915.76, "word": " بدنا", "probability": 0.779296875}, {"start": 3915.76, "end": 3916.22, "word": " نرجع", "probability": 0.9622395833333334}, {"start": 3916.22, "end": 3917.3, "word": " للاصل", "probability": 0.8631184895833334}, {"start": 3917.3, "end": 3917.98, "word": " اللى", "probability": 0.99072265625}, {"start": 3917.98, "end": 3918.76, "word": " ابتدينا", "probability": 0.8907470703125}, {"start": 3918.76, "end": 3919.86, "word": " فيه", "probability": 0.929931640625}, {"start": 3919.86, "end": 3920.36, "word": " اللى", "probability": 0.9072265625}, {"start": 3920.36, "end": 3920.88, "word": " هو", "probability": 0.92578125}, {"start": 3920.88, "end": 3921.28, "word": " ال", "probability": 0.82275390625}, {"start": 3921.28, "end": 3921.94, "word": " homogeneous", "probability": 0.57666015625}, {"start": 3921.94, "end": 3922.84, "word": " differential", "probability": 0.8544921875}, {"start": 3922.84, "end": 3923.9, "word": " equation", "probability": 0.95849609375}, {"start": 3923.9, "end": 3924.66, "word": " with", "probability": 0.9306640625}, {"start": 3924.66, "end": 3925.52, "word": " constant", "probability": 0.94384765625}, {"start": 3925.52, "end": 3926.6, "word": " coefficients", "probability": 0.8154296875}], "temperature": 1.0}, {"id": 159, "seek": 396013, "start": 3937.37, "end": 3960.13, "text": "يبقى بدنا نيجي ل section تلاتة أربعة section تلاتة أربعة بتكلم عن ال complex roots complex roots of the characteristic equation", "tokens": [1829, 3555, 4587, 7578, 47525, 8315, 8717, 1829, 7435, 1829, 5296, 3541, 6055, 1211, 9307, 3660, 5551, 25513, 27884, 3541, 6055, 1211, 9307, 3660, 5551, 25513, 27884, 39894, 4117, 19528, 18871, 2423, 3997, 10669, 3997, 10669, 295, 264, 16282, 5367], "avg_logprob": -0.2187500058150873, "compression_ratio": 1.3852459016393444, "no_speech_prob": 0.0, "words": [{"start": 3937.37, "end": 3937.89, "word": "يبقى", "probability": 0.674835205078125}, {"start": 3937.89, "end": 3938.23, "word": " بدنا", "probability": 0.9345703125}, {"start": 3938.23, "end": 3938.65, "word": " نيجي", "probability": 0.932861328125}, {"start": 3938.65, "end": 3938.79, "word": " ل", "probability": 0.9228515625}, {"start": 3938.79, "end": 3939.27, "word": " section", "probability": 0.6025390625}, {"start": 3939.27, "end": 3940.17, "word": " تلاتة", "probability": 0.8409423828125}, {"start": 3940.17, "end": 3940.71, "word": " أربعة", "probability": 0.7897135416666666}, {"start": 3940.71, "end": 3942.39, "word": " section", "probability": 0.2333984375}, {"start": 3942.39, "end": 3943.79, "word": " تلاتة", "probability": 0.97509765625}, {"start": 3943.79, "end": 3944.53, "word": " أربعة", "probability": 0.9677734375}, {"start": 3944.53, "end": 3945.95, "word": " بتكلم", "probability": 0.8914388020833334}, {"start": 3945.95, "end": 3946.41, "word": " عن", "probability": 0.99609375}, {"start": 3946.41, "end": 3946.81, "word": " ال", "probability": 0.89306640625}, {"start": 3946.81, "end": 3947.83, "word": " complex", "probability": 0.7861328125}, {"start": 3947.83, "end": 3950.15, "word": " roots", "probability": 0.89453125}, {"start": 3950.15, "end": 3951.81, "word": " complex", "probability": 0.3955078125}, {"start": 3951.81, "end": 3953.11, "word": " roots", "probability": 0.931640625}, {"start": 3953.11, "end": 3954.11, "word": " of", "probability": 0.9677734375}, {"start": 3954.11, "end": 3955.67, "word": " the", "probability": 0.7958984375}, {"start": 3955.67, "end": 3958.41, "word": " characteristic", "probability": 0.869140625}, {"start": 3958.41, "end": 3960.13, "word": " equation", "probability": 0.9306640625}], "temperature": 1.0}, {"id": 160, "seek": 397511, "start": 3971.61, "end": 3975.11, "text": "بنبدأ ب section تلاتة واحد اول section", "tokens": [3555, 1863, 44510, 10721, 4724, 3541, 6055, 1211, 9307, 3660, 36764, 24401, 1975, 12610, 3541], "avg_logprob": -0.50537109375, "compression_ratio": 0.9333333333333333, "no_speech_prob": 0.0, "words": [{"start": 3971.61, "end": 3972.13, "word": "بنبدأ", "probability": 0.579132080078125}, {"start": 3972.13, "end": 3972.25, "word": " ب", "probability": 0.53125}, {"start": 3972.25, "end": 3972.57, "word": " section", "probability": 0.1053466796875}, {"start": 3972.57, "end": 3973.11, "word": " تلاتة", "probability": 0.82666015625}, {"start": 3973.11, "end": 3973.51, "word": " واحد", "probability": 0.943603515625}, {"start": 3973.51, "end": 3974.57, "word": " اول", "probability": 0.7269287109375}, {"start": 3974.57, "end": 3975.11, "word": " section", "probability": 0.76123046875}], "temperature": 1.0}, {"id": 161, "seek": 400070, "start": 3976.08, "end": 4000.7, "text": "واخدنا ال second order linear differential equation وروحنا خدنا حالة خاصة منها لما يكونوا ال coefficients are colostants يبقى لو كانوا المعاملات ما لهم ثوابت بقولنا بنفرض ان EOSRT هو عبارة عن حلوة وبالتالي بنجيب ال characteristic equation لAR ثربيه زائد BR زائد C", "tokens": [2407, 47283, 3215, 8315, 2423, 1150, 1668, 8213, 15756, 5367, 4032, 32887, 5016, 8315, 16490, 3215, 8315, 11331, 6027, 3660, 16490, 33546, 3660, 9154, 11296, 5296, 15042, 7251, 30544, 14407, 2423, 31994, 366, 1173, 555, 1719, 7251, 3555, 4587, 7578, 45164, 25961, 14407, 9673, 3615, 10943, 1211, 9307, 19446, 5296, 16095, 38637, 14407, 3555, 2655, 4724, 39648, 8315, 44945, 5172, 43042, 16472, 462, 4367, 49, 51, 31439, 6225, 3555, 9640, 3660, 18871, 11331, 1211, 2407, 3660, 46599, 6027, 2655, 6027, 1829, 44945, 7435, 1829, 3555, 2423, 16282, 5367, 5296, 1899, 38637, 2288, 21292, 3224, 30767, 16373, 3215, 10262, 30767, 16373, 3215, 383], "avg_logprob": -0.27229976364709796, "compression_ratio": 1.51953125, "no_speech_prob": 5.960464477539063e-08, "words": [{"start": 3976.08, "end": 3976.98, "word": "واخدنا", "probability": 0.79632568359375}, {"start": 3976.98, "end": 3977.42, "word": " ال", "probability": 0.51611328125}, {"start": 3977.42, "end": 3977.72, "word": " second", "probability": 0.3564453125}, {"start": 3977.72, "end": 3978.28, "word": " order", "probability": 0.927734375}, {"start": 3978.28, "end": 3979.08, "word": " linear", "probability": 0.8291015625}, {"start": 3979.08, "end": 3980.14, "word": " differential", "probability": 0.85693359375}, {"start": 3980.14, "end": 3980.98, "word": " equation", "probability": 0.970703125}, {"start": 3980.98, "end": 3981.92, "word": " وروحنا", "probability": 0.7872314453125}, {"start": 3981.92, "end": 3982.3, "word": " خدنا", "probability": 0.8507486979166666}, {"start": 3982.3, "end": 3982.76, "word": " حالة", "probability": 0.96044921875}, {"start": 3982.76, "end": 3983.28, "word": " خاصة", "probability": 0.970703125}, {"start": 3983.28, "end": 3983.7, "word": " منها", "probability": 0.985595703125}, {"start": 3983.7, "end": 3984.4, "word": " لما", "probability": 0.92041015625}, {"start": 3984.4, "end": 3985.08, "word": " يكونوا", "probability": 0.9309895833333334}, {"start": 3985.08, "end": 3985.3, "word": " ال", "probability": 0.93115234375}, {"start": 3985.3, "end": 3986.02, "word": " coefficients", "probability": 0.9873046875}, {"start": 3986.02, "end": 3986.66, "word": " are", "probability": 0.8916015625}, {"start": 3986.66, "end": 3987.46, "word": " colostants", "probability": 0.4461263020833333}, {"start": 3987.46, "end": 3988.22, "word": " يبقى", "probability": 0.91552734375}, {"start": 3988.22, "end": 3988.42, "word": " لو", "probability": 0.98095703125}, {"start": 3988.42, "end": 3988.8, "word": " كانوا", "probability": 0.976806640625}, {"start": 3988.8, "end": 3989.6, "word": " المعاملات", "probability": 0.99140625}, {"start": 3989.6, "end": 3989.8, "word": " ما", "probability": 0.54345703125}, {"start": 3989.8, "end": 3990.2, "word": " لهم", "probability": 0.803466796875}, {"start": 3990.2, "end": 3991.44, "word": " ثوابت", "probability": 0.82861328125}, {"start": 3991.44, "end": 3992.02, "word": " بقولنا", "probability": 0.6144205729166666}, {"start": 3992.02, "end": 3992.46, "word": " بنفرض", "probability": 0.82861328125}, {"start": 3992.46, "end": 3992.78, "word": " ان", "probability": 0.6728515625}, {"start": 3992.78, "end": 3993.88, "word": " EOSRT", "probability": 0.5615234375}, {"start": 3993.88, "end": 3994.12, "word": " هو", "probability": 0.84521484375}, {"start": 3994.12, "end": 3994.46, "word": " عبارة", "probability": 0.973388671875}, {"start": 3994.46, "end": 3994.66, "word": " عن", "probability": 0.99169921875}, {"start": 3994.66, "end": 3995.1, "word": " حلوة", "probability": 0.9437255859375}, {"start": 3995.1, "end": 3995.46, "word": " وبالتالي", "probability": 0.8119384765625}, {"start": 3995.46, "end": 3995.9, "word": " بنجيب", "probability": 0.9744873046875}, {"start": 3995.9, "end": 3995.98, "word": " ال", "probability": 0.9384765625}, {"start": 3995.98, "end": 3996.5, "word": " characteristic", "probability": 0.908203125}, {"start": 3996.5, "end": 3997.46, "word": " equation", "probability": 0.97802734375}, {"start": 3997.46, "end": 3998.64, "word": " لAR", "probability": 0.410400390625}, {"start": 3998.64, "end": 3999.28, "word": " ثربيه", "probability": 0.6220703125}, {"start": 3999.28, "end": 3999.6, "word": " زائد", "probability": 0.6643880208333334}, {"start": 3999.6, "end": 4000.04, "word": " BR", "probability": 0.47509765625}, {"start": 4000.04, "end": 4000.48, "word": " زائد", "probability": 0.8538411458333334}, {"start": 4000.48, "end": 4000.7, "word": " C", "probability": 0.96728515625}], "temperature": 1.0}, {"id": 162, "seek": 401626, "start": 4003.42, "end": 4016.26, "text": "وقلنا الحل له أحد ثلاثة احتمالات الاحتمال الاول ان اتنين are real and different واخدنا امثلة عليها", "tokens": [2407, 4587, 1211, 8315, 21542, 1211, 46740, 5551, 24401, 38637, 1211, 5718, 104, 3660, 1975, 33753, 2304, 6027, 9307, 42963, 33753, 2304, 6027, 42963, 12610, 16472, 1975, 2655, 1863, 9957, 366, 957, 293, 819, 4032, 47283, 3215, 8315, 1975, 2304, 12984, 37977, 25894, 11296], "avg_logprob": -0.23923611243565876, "compression_ratio": 1.3416666666666666, "no_speech_prob": 0.0, "words": [{"start": 4003.42, "end": 4003.94, "word": "وقلنا", "probability": 0.60955810546875}, {"start": 4003.94, "end": 4004.38, "word": " الحل", "probability": 0.77880859375}, {"start": 4004.38, "end": 4004.88, "word": " له", "probability": 0.26025390625}, {"start": 4004.88, "end": 4005.48, "word": " أحد", "probability": 0.83056640625}, {"start": 4005.48, "end": 4006.64, "word": " ثلاثة", "probability": 0.87890625}, {"start": 4006.64, "end": 4007.6, "word": " احتمالات", "probability": 0.96953125}, {"start": 4007.6, "end": 4008.84, "word": " الاحتمال", "probability": 0.9136962890625}, {"start": 4008.84, "end": 4009.84, "word": " الاول", "probability": 0.64794921875}, {"start": 4009.84, "end": 4010.14, "word": " ان", "probability": 0.76318359375}, {"start": 4010.14, "end": 4010.86, "word": " اتنين", "probability": 0.7783203125}, {"start": 4010.86, "end": 4011.38, "word": " are", "probability": 0.67333984375}, {"start": 4011.38, "end": 4012.04, "word": " real", "probability": 0.89990234375}, {"start": 4012.04, "end": 4012.62, "word": " and", "probability": 0.91064453125}, {"start": 4012.62, "end": 4013.76, "word": " different", "probability": 0.89599609375}, {"start": 4013.76, "end": 4015.14, "word": " واخدنا", "probability": 0.869140625}, {"start": 4015.14, "end": 4015.76, "word": " امثلة", "probability": 0.8609619140625}, {"start": 4015.76, "end": 4016.26, "word": " عليها", "probability": 0.9677734375}], "temperature": 1.0}, {"id": 163, "seek": 403572, "start": 4016.7, "end": 4035.72, "text": "و بعد هيك صبرنا شوية و غطسنا وين في شجة تانية الان بدنا نرجع بعد section تلاتة اتنين و تلاتة تلاتة بدنا نرجع لكلام اللي ابتدأنا فيه في section تلاتة واحد بداخل تلاتة اربع ان لو كان اتنين are complex roots", "tokens": [2407, 39182, 39896, 4117, 20328, 26890, 8315, 13412, 2407, 10632, 4032, 32771, 9566, 3794, 8315, 4032, 9957, 8978, 13412, 7435, 3660, 6055, 7649, 10632, 2423, 7649, 47525, 8315, 8717, 47341, 3615, 39182, 3541, 6055, 1211, 9307, 3660, 1975, 2655, 1863, 9957, 4032, 6055, 1211, 9307, 3660, 6055, 1211, 9307, 3660, 47525, 8315, 8717, 47341, 3615, 5296, 28820, 10943, 13672, 1829, 48127, 2655, 3215, 10721, 8315, 8978, 3224, 8978, 3541, 6055, 1211, 9307, 3660, 36764, 24401, 47525, 47283, 1211, 6055, 1211, 9307, 3660, 1975, 25513, 3615, 16472, 45164, 25961, 1975, 2655, 1863, 9957, 366, 3997, 10669], "avg_logprob": -0.20670572218174735, "compression_ratio": 1.8225806451612903, "no_speech_prob": 0.0, "words": [{"start": 4016.7, "end": 4016.9, "word": "و", "probability": 0.32275390625}, {"start": 4016.9, "end": 4017.2, "word": " بعد", "probability": 0.73828125}, {"start": 4017.2, "end": 4017.6, "word": " هيك", "probability": 0.46044921875}, {"start": 4017.6, "end": 4018.2, "word": " صبرنا", "probability": 0.88671875}, {"start": 4018.2, "end": 4018.62, "word": " شوية", "probability": 0.9070638020833334}, {"start": 4018.62, "end": 4018.82, "word": " و", "probability": 0.9609375}, {"start": 4018.82, "end": 4019.92, "word": " غطسنا", "probability": 0.7161865234375}, {"start": 4019.92, "end": 4020.14, "word": " وين", "probability": 0.580322265625}, {"start": 4020.14, "end": 4020.24, "word": " في", "probability": 0.7529296875}, {"start": 4020.24, "end": 4020.6, "word": " شجة", "probability": 0.7939453125}, {"start": 4020.6, "end": 4021.04, "word": " تانية", "probability": 0.9918619791666666}, {"start": 4021.04, "end": 4021.82, "word": " الان", "probability": 0.5574951171875}, {"start": 4021.82, "end": 4022.16, "word": " بدنا", "probability": 0.92431640625}, {"start": 4022.16, "end": 4022.68, "word": " نرجع", "probability": 0.92578125}, {"start": 4022.68, "end": 4023.36, "word": " بعد", "probability": 0.7978515625}, {"start": 4023.36, "end": 4023.78, "word": " section", "probability": 0.463623046875}, {"start": 4023.78, "end": 4025.52, "word": " تلاتة", "probability": 0.8460693359375}, {"start": 4025.52, "end": 4025.74, "word": " اتنين", "probability": 0.8887939453125}, {"start": 4025.74, "end": 4025.9, "word": " و", "probability": 0.9365234375}, {"start": 4025.9, "end": 4026.32, "word": " تلاتة", "probability": 0.9576416015625}, {"start": 4026.32, "end": 4026.74, "word": " تلاتة", "probability": 0.97998046875}, {"start": 4026.74, "end": 4027.12, "word": " بدنا", "probability": 0.76123046875}, {"start": 4027.12, "end": 4027.46, "word": " نرجع", "probability": 0.9742838541666666}, {"start": 4027.46, "end": 4028.28, "word": " لكلام", "probability": 0.7405598958333334}, {"start": 4028.28, "end": 4028.76, "word": " اللي", "probability": 0.80419921875}, {"start": 4028.76, "end": 4029.32, "word": " ابتدأنا", "probability": 0.9146484375}, {"start": 4029.32, "end": 4029.62, "word": " فيه", "probability": 0.973388671875}, {"start": 4029.62, "end": 4029.7, "word": " في", "probability": 0.8740234375}, {"start": 4029.7, "end": 4030.12, "word": " section", "probability": 0.76708984375}, {"start": 4030.12, "end": 4030.64, "word": " تلاتة", "probability": 0.9793701171875}, {"start": 4030.64, "end": 4031.04, "word": " واحد", "probability": 0.962890625}, {"start": 4031.04, "end": 4031.84, "word": " بداخل", "probability": 0.681884765625}, {"start": 4031.84, "end": 4032.26, "word": " تلاتة", "probability": 0.93994140625}, {"start": 4032.26, "end": 4032.54, "word": " اربع", "probability": 0.7581380208333334}, {"start": 4032.54, "end": 4032.72, "word": " ان", "probability": 0.7587890625}, {"start": 4032.72, "end": 4033.0, "word": " لو", "probability": 0.83447265625}, {"start": 4033.0, "end": 4033.44, "word": " كان", "probability": 0.97607421875}, {"start": 4033.44, "end": 4034.02, "word": " اتنين", "probability": 0.9586181640625}, {"start": 4034.02, "end": 4034.32, "word": " are", "probability": 0.76806640625}, {"start": 4034.32, "end": 4035.08, "word": " complex", "probability": 0.89697265625}, {"start": 4035.08, "end": 4035.72, "word": " roots", "probability": 0.91064453125}], "temperature": 1.0}, {"id": 164, "seek": 406061, "start": 4036.13, "end": 4060.61, "text": "الاتنين كانوا complex roots and conjugate اتنين تخيلين ومترافقين وبعد ذلك ال section اللي بعد بناخد لو كانوا اتنين are real repeated roots جذور حقيقية ومقريبة يخلينا مع ال complex اتنين ونذكر تذكير بالمعادة اللي بدأنا فيها وال characteristic equation يبقى باجي بقول هنا consider", "tokens": [6027, 9307, 1863, 9957, 25961, 14407, 3997, 10669, 293, 45064, 1975, 2655, 1863, 9957, 6055, 9778, 26895, 9957, 4032, 2304, 2655, 23557, 5172, 4587, 9957, 46599, 22488, 29910, 23275, 2423, 3541, 13672, 1829, 39182, 44945, 47283, 3215, 45164, 25961, 14407, 1975, 2655, 1863, 9957, 366, 957, 10477, 10669, 10874, 8848, 13063, 11331, 38436, 4587, 10632, 4032, 2304, 4587, 16572, 49401, 7251, 9778, 1211, 9957, 995, 20449, 2423, 3997, 1975, 2655, 1863, 9957, 4032, 1863, 8848, 37983, 6055, 8848, 4117, 13546, 20666, 2304, 3615, 18513, 3660, 13672, 1829, 47525, 10721, 8315, 8978, 11296, 16070, 16282, 5367, 7251, 3555, 4587, 7578, 4724, 26108, 1829, 4724, 39648, 34105, 1949], "avg_logprob": -0.24634929962247332, "compression_ratio": 1.7377049180327868, "no_speech_prob": 5.960464477539063e-08, "words": [{"start": 4036.13, "end": 4036.81, "word": "الاتنين", "probability": 0.5762939453125}, {"start": 4036.81, "end": 4037.59, "word": " كانوا", "probability": 0.879638671875}, {"start": 4037.59, "end": 4038.15, "word": " complex", "probability": 0.31787109375}, {"start": 4038.15, "end": 4038.55, "word": " roots", "probability": 0.67431640625}, {"start": 4038.55, "end": 4038.91, "word": " and", "probability": 0.625}, {"start": 4038.91, "end": 4039.43, "word": " conjugate", "probability": 0.4482421875}, {"start": 4039.43, "end": 4039.93, "word": " اتنين", "probability": 0.80255126953125}, {"start": 4039.93, "end": 4040.51, "word": " تخيلين", "probability": 0.8343505859375}, {"start": 4040.51, "end": 4041.45, "word": " ومترافقين", "probability": 0.8820452008928571}, {"start": 4041.45, "end": 4042.51, "word": " وبعد", "probability": 0.6934814453125}, {"start": 4042.51, "end": 4042.67, "word": " ذلك", "probability": 0.4901123046875}, {"start": 4042.67, "end": 4042.85, "word": " ال", "probability": 0.86474609375}, {"start": 4042.85, "end": 4043.11, "word": " section", "probability": 0.779296875}, {"start": 4043.11, "end": 4043.37, "word": " اللي", "probability": 0.786376953125}, {"start": 4043.37, "end": 4043.59, "word": " بعد", "probability": 0.75146484375}, {"start": 4043.59, "end": 4044.07, "word": " بناخد", "probability": 0.7897135416666666}, {"start": 4044.07, "end": 4044.29, "word": " لو", "probability": 0.890625}, {"start": 4044.29, "end": 4044.63, "word": " كانوا", "probability": 0.822998046875}, {"start": 4044.63, "end": 4045.19, "word": " اتنين", "probability": 0.9544677734375}, {"start": 4045.19, "end": 4045.97, "word": " are", "probability": 0.740234375}, {"start": 4045.97, "end": 4046.59, "word": " real", "probability": 0.7265625}, {"start": 4046.59, "end": 4047.39, "word": " repeated", "probability": 0.83740234375}, {"start": 4047.39, "end": 4047.97, "word": " roots", "probability": 0.9130859375}, {"start": 4047.97, "end": 4048.77, "word": " جذور", "probability": 0.9759114583333334}, {"start": 4048.77, "end": 4049.69, "word": " حقيقية", "probability": 0.98876953125}, {"start": 4049.69, "end": 4050.83, "word": " ومقريبة", "probability": 0.87041015625}, {"start": 4050.83, "end": 4051.31, "word": " يخلينا", "probability": 0.68623046875}, {"start": 4051.31, "end": 4051.45, "word": " مع", "probability": 0.98046875}, {"start": 4051.45, "end": 4051.57, "word": " ال", "probability": 0.96337890625}, {"start": 4051.57, "end": 4051.99, "word": " complex", "probability": 0.88916015625}, {"start": 4051.99, "end": 4052.57, "word": " اتنين", "probability": 0.9150390625}, {"start": 4052.57, "end": 4053.57, "word": " ونذكر", "probability": 0.9058837890625}, {"start": 4053.57, "end": 4054.11, "word": " تذكير", "probability": 0.8626708984375}, {"start": 4054.11, "end": 4054.73, "word": " بالمعادة", "probability": 0.8939453125}, {"start": 4054.73, "end": 4054.91, "word": " اللي", "probability": 0.91015625}, {"start": 4054.91, "end": 4055.37, "word": " بدأنا", "probability": 0.8400065104166666}, {"start": 4055.37, "end": 4055.75, "word": " فيها", "probability": 0.732666015625}, {"start": 4055.75, "end": 4055.93, "word": " وال", "probability": 0.46484375}, {"start": 4055.93, "end": 4056.49, "word": " characteristic", "probability": 0.841796875}, {"start": 4056.49, "end": 4057.85, "word": " equation", "probability": 0.9755859375}, {"start": 4057.85, "end": 4058.75, "word": " يبقى", "probability": 0.8983154296875}, {"start": 4058.75, "end": 4059.13, "word": " باجي", "probability": 0.7928059895833334}, {"start": 4059.13, "end": 4059.59, "word": " بقول", "probability": 0.959228515625}, {"start": 4059.59, "end": 4059.83, "word": " هنا", "probability": 0.94482421875}, {"start": 4059.83, "end": 4060.61, "word": " consider", "probability": 0.93896484375}], "temperature": 1.0}, {"id": 165, "seek": 408476, "start": 4067.46, "end": 4084.76, "text": "Homogenous Differential Equation لـ AYW' زائد BY' زائد CY بده يساوي Zero وهذه سمنها المعادلة Star", "tokens": [39, 13395, 1766, 563, 413, 12612, 2549, 15624, 399, 5296, 39184, 316, 56, 54, 6, 30767, 16373, 3215, 26930, 6, 30767, 16373, 3215, 383, 56, 47525, 3224, 7251, 3794, 995, 45865, 17182, 37037, 24192, 8608, 27842, 11296, 9673, 3615, 18513, 37977, 5705], "avg_logprob": -0.48909883443699326, "compression_ratio": 1.056, "no_speech_prob": 0.0, "words": [{"start": 4067.46, "end": 4068.86, "word": "Homogenous", "probability": 0.511566162109375}, {"start": 4068.86, "end": 4070.26, "word": " Differential", "probability": 0.6803385416666666}, {"start": 4070.26, "end": 4072.42, "word": " Equation", "probability": 0.857421875}, {"start": 4072.42, "end": 4073.76, "word": " لـ", "probability": 0.28369140625}, {"start": 4073.76, "end": 4075.52, "word": " AYW'", "probability": 0.4320475260416667}, {"start": 4076.22, "end": 4077.26, "word": " زائد", "probability": 0.48455810546875}, {"start": 4077.26, "end": 4077.68, "word": " BY'", "probability": 0.939453125}, {"start": 4078.56, "end": 4079.66, "word": " زائد", "probability": 0.9231770833333334}, {"start": 4079.66, "end": 4080.24, "word": " CY", "probability": 0.848388671875}, {"start": 4080.24, "end": 4080.6, "word": " بده", "probability": 0.30963134765625}, {"start": 4080.6, "end": 4081.04, "word": " يساوي", "probability": 0.802734375}, {"start": 4081.04, "end": 4081.54, "word": " Zero", "probability": 0.435302734375}, {"start": 4081.54, "end": 4082.56, "word": " وهذه", "probability": 0.670654296875}, {"start": 4082.56, "end": 4083.34, "word": " سمنها", "probability": 0.7384440104166666}, {"start": 4083.34, "end": 4084.16, "word": " المعادلة", "probability": 0.97314453125}, {"start": 4084.16, "end": 4084.76, "word": " Star", "probability": 0.49755859375}], "temperature": 1.0}, {"id": 166, "seek": 411255, "start": 4086.11, "end": 4112.55, "text": "قلنا لو كان ال Y تساوي E أس RT if لهذا is a solution of the differential equation star then", "tokens": [4587, 1211, 8315, 45164, 25961, 2423, 398, 6055, 3794, 995, 45865, 462, 5551, 3794, 21797, 498, 46740, 15730, 307, 257, 3827, 295, 264, 15756, 5367, 3543, 550], "avg_logprob": -0.48716515941279276, "compression_ratio": 1.0462962962962963, "no_speech_prob": 0.0, "words": [{"start": 4086.11, "end": 4086.81, "word": "قلنا", "probability": 0.5349324544270834}, {"start": 4086.81, "end": 4087.07, "word": " لو", "probability": 0.92333984375}, {"start": 4087.07, "end": 4087.75, "word": " كان", "probability": 0.9638671875}, {"start": 4087.75, "end": 4088.33, "word": " ال", "probability": 0.896484375}, {"start": 4088.33, "end": 4088.63, "word": " Y", "probability": 0.41748046875}, {"start": 4088.63, "end": 4089.33, "word": " تساوي", "probability": 0.65582275390625}, {"start": 4089.33, 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"compression_ratio": 1.4838709677419355, "no_speech_prob": 0.0, "words": [{"start": 4116.900000000001, "end": 4118.3, "word": "كاركترستيك", "probability": 0.6551666259765625}, {"start": 4118.3, "end": 4119.54, "word": " إيكوشن", "probability": 0.5584920247395834}, {"start": 4119.54, "end": 4120.32, "word": " S", "probability": 0.2332763671875}, {"start": 4120.32, "end": 4122.64, "word": " الهمين", "probability": 0.489990234375}, {"start": 4122.64, "end": 4123.7, "word": " AR", "probability": 0.32666015625}, {"start": 4123.7, "end": 4124.82, "word": " ثرابية", "probability": 0.57489013671875}, {"start": 4124.82, "end": 4125.6, "word": " زايد", "probability": 0.4991861979166667}, {"start": 4125.6, "end": 4126.36, "word": " PR", "probability": 0.5283203125}, {"start": 4126.36, "end": 4127.44, "word": " زايد", "probability": 0.9508463541666666}, {"start": 4127.44, "end": 4127.72, "word": " C", "probability": 0.88623046875}, {"start": 4127.72, "end": 4128.14, "word": " بده", "probability": 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"probability": 0.86572265625}, {"start": 4155.89, "end": 4156.37, "word": " لبا", "probability": 0.8382161458333334}, {"start": 4156.37, "end": 4156.93, "word": " التربية", "probability": 0.90087890625}, {"start": 4156.93, "end": 4157.73, "word": " ناقص", "probability": 0.97802734375}, {"start": 4157.73, "end": 4158.39, "word": " أربعة", "probability": 0.7386067708333334}, {"start": 4158.39, "end": 4158.93, "word": " ألف", "probability": 0.843505859375}, {"start": 4158.93, "end": 4159.43, "word": " جيم", "probability": 0.9208984375}, {"start": 4159.43, "end": 4160.43, "word": " كله", "probability": 0.928466796875}, {"start": 4160.43, "end": 4160.67, "word": " على", "probability": 0.8076171875}, {"start": 4160.67, "end": 4161.61, "word": " اتنين", "probability": 0.8984375}, {"start": 4161.61, "end": 4162.07, "word": " ألف", "probability": 0.881103515625}], "temperature": 1.0}, {"id": 169, "seek": 417664, "start": 4164.92, "end": 4176.64, "text": "ار اتنين تسوى ناقص با ناقص الجدر التربية لبا تربية ناقص اربع ا سي على اتنين ا", "tokens": [9640, 1975, 2655, 1863, 9957, 6055, 3794, 2407, 7578, 8717, 995, 4587, 9381, 4724, 995, 8717, 995, 4587, 9381, 25724, 3215, 2288, 16712, 25513, 10632, 5296, 3555, 995, 6055, 25513, 10632, 8717, 995, 4587, 9381, 1975, 25513, 3615, 1975, 8608, 1829, 15844, 1975, 2655, 1863, 9957, 1975], "avg_logprob": -0.32584635727107525, "compression_ratio": 1.6235294117647059, "no_speech_prob": 0.0, "words": [{"start": 4164.92, "end": 4165.4, "word": "ار", "probability": 0.1490478515625}, {"start": 4165.4, "end": 4166.22, "word": " اتنين", "probability": 0.7762451171875}, {"start": 4166.22, "end": 4167.22, "word": " تسوى", "probability": 0.60833740234375}, {"start": 4167.22, "end": 4168.04, "word": " ناقص", "probability": 0.85614013671875}, {"start": 4168.04, "end": 4168.56, "word": " با", "probability": 0.348876953125}, {"start": 4168.56, "end": 4169.54, "word": " ناقص", "probability": 0.910888671875}, {"start": 4169.54, "end": 4170.06, "word": " 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الشغل هذه في section تلاتة واحد ابنجلان اخدنا لو كان ال b تربية نقص اربعة ac اكبر من ال zero يبقى قولنا الجدران حقيقيا ومختلفا تمام؟", "tokens": [4117, 45865, 3794, 9673, 25720, 13672, 7578, 6156, 9307, 2655, 9122, 2655, 3555, 8315, 25124, 17082, 1211, 29538, 8978, 3541, 6055, 1211, 9307, 3660, 36764, 24401, 48127, 1863, 7435, 1211, 7649, 1975, 9778, 3215, 8315, 45164, 25961, 2423, 272, 6055, 25513, 10632, 8717, 4587, 9381, 1975, 25513, 27884, 696, 1975, 4117, 26890, 9154, 2423, 4018, 7251, 3555, 4587, 7578, 12174, 12610, 8315, 25724, 3215, 2288, 7649, 11331, 38436, 4587, 25528, 4032, 2304, 46456, 46538, 995, 46811, 10943, 22807], "avg_logprob": -0.2935126499284672, "compression_ratio": 1.5393258426966292, "no_speech_prob": 0.0, "words": [{"start": 4196.32, "end": 4197.2, "word": "كويس", "probability": 0.4529215494791667}, {"start": 4197.2, "end": 4198.08, "word": " المرة", "probability": 0.7330322265625}, {"start": 4198.08, "end": 4198.26, "word": " اللى", "probability": 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"word": " and", "probability": 0.82470703125}, {"start": 4252.45, "end": 4255.15, "word": " we", "probability": 0.81494140625}, {"start": 4255.15, "end": 4257.27, "word": " write", "probability": 0.9482421875}, {"start": 4257.27, "end": 4262.95, "word": " it", "probability": 0.97216796875}, {"start": 4262.95, "end": 4264.03, "word": " in", "probability": 0.472900390625}, {"start": 4264.03, "end": 4264.33, "word": " the", "probability": 0.84228515625}, {"start": 4264.33, "end": 4264.77, "word": " form", "probability": 0.88134765625}], "temperature": 1.0}, {"id": 173, "seek": 429297, "start": 4268.31, "end": 4292.97, "text": "ممكن نكتبها على شكل ر واحد يساوي لاندا زائد IMU and ر اتنين يساوي لاندا ناقص IMU واللاندا والميو أعداد حقيقية موجودة في ال set of real numbers", "tokens": [2304, 43020, 8717, 4117, 2655, 3555, 11296, 15844, 13412, 28820, 12602, 36764, 24401, 7251, 3794, 995, 45865, 5296, 7649, 28259, 30767, 16373, 3215, 21463, 52, 293, 12602, 1975, 2655, 1863, 9957, 7251, 3794, 995, 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الجدر هذه كانت كمية سالبة", "tokens": [2304, 25720, 6055, 7649, 10632, 4724, 39648, 43242, 9673, 3615, 18513, 37977, 16712, 5172, 46958, 1211, 10632, 20666, 8592, 28820, 23758, 12602, 3215, 8717, 2407, 3615, 1829, 6055, 3794, 995, 45865, 8943, 51, 6225, 3555, 9640, 3660, 18871, 11331, 1211, 29538, 9673, 3615, 18513, 37977, 16712, 5172, 46958, 1211, 10632, 11331, 36520, 8315, 15844, 2423, 16282, 5367, 20666, 8592, 28820, 13672, 1829, 43242, 8315, 23758, 10874, 1829, 3555, 8315, 11331, 1211, 2423, 16282, 5367, 4032, 9566, 1211, 3615, 18871, 16254, 497, 16, 4032, 49, 17, 4724, 39648, 45164, 33251, 2304, 10632, 13672, 1829, 6055, 33753, 25724, 3215, 2288, 29538, 25961, 2655, 9122, 2304, 10632, 8608, 6027, 49401], "avg_logprob": -0.19849536650710636, "compression_ratio": 1.9111111111111112, "no_speech_prob": 0.0, "words": [{"start": 4309.25, "end": 4309.61, "word": "مرة", "probability": 0.5970458984375}, {"start": 4309.61, "end": 4309.91, "word": " تانية", "probability": 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"probability": 0.98583984375}], "temperature": 1.0}, {"id": 181, "seek": 450518, "start": 4482.37, "end": 4505.19, "text": "يبقى هذا شكل الحل اللى عندنا هذا طيب الحل زى ما تشايفين مكتوب بدل ال complex numbers وغالبيتكوا مادرسوش complex number فى حد درست مادة ال complex يا بنات يعنى هى واحدة ويمكن هى تنتين طيب الغالبية مادرسوش", "tokens": [1829, 3555, 4587, 7578, 23758, 13412, 28820, 21542, 1211, 13672, 7578, 43242, 8315, 23758, 23032, 1829, 3555, 21542, 1211, 30767, 7578, 19446, 6055, 8592, 995, 33911, 9957, 3714, 4117, 2655, 37746, 47525, 1211, 2423, 3997, 3547, 4032, 17082, 6027, 3555, 36081, 4117, 14407, 19446, 3215, 2288, 3794, 2407, 8592, 3997, 1230, 6156, 7578, 11331, 3215, 11778, 2288, 14851, 3714, 18513, 3660, 2423, 3997, 35186, 4724, 8315, 2655, 37495, 1863, 7578, 8032, 7578, 36764, 24401, 3660, 4032, 32640, 19452, 8032, 7578, 6055, 29399, 9957, 23032, 1829, 3555, 6024, 118, 6027, 3555, 10632, 19446, 3215, 2288, 3794, 2407, 8592], "avg_logprob": -0.1650191323489559, "compression_ratio": 1.8206521739130435, "no_speech_prob": 0.0, "words": [{"start": 4482.37, "end": 4482.85, "word": "يبقى", "probability": 0.8177490234375}, {"start": 4482.85, "end": 4483.13, "word": " هذا", "probability": 0.841796875}, {"start": 4483.13, "end": 4483.55, "word": " شكل", "probability": 0.915771484375}, {"start": 4483.55, "end": 4484.19, "word": " الحل", "probability": 0.982177734375}, {"start": 4484.19, "end": 4484.69, "word": " اللى", "probability": 0.707275390625}, {"start": 4484.69, "end": 4485.39, "word": " عندنا", "probability": 0.825439453125}, {"start": 4485.39, "end": 4485.97, "word": " هذا", "probability": 0.73681640625}, {"start": 4485.97, "end": 4488.25, "word": " طيب", "probability": 0.6924641927083334}, {"start": 4488.25, "end": 4490.25, "word": " الحل", "probability": 0.963623046875}, {"start": 4490.25, "end": 4490.41, "word": " زى", "probability": 0.94384765625}, {"start": 4490.41, "end": 4490.51, "word": " ما", "probability": 0.88134765625}, {"start": 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تنتين", "probability": 0.8922526041666666}, {"start": 4503.01, "end": 4503.89, "word": " طيب", "probability": 0.9142252604166666}, {"start": 4503.89, "end": 4504.47, "word": " الغالبية", "probability": 0.96220703125}, {"start": 4504.47, "end": 4505.19, "word": " مادرسوش", "probability": 0.93310546875}], "temperature": 1.0}, {"id": 182, "seek": 453020, "start": 4505.72, "end": 4530.2, "text": "لكن لذلك بدل مالحل مكتوب واصل complex numbers بدي احاول اكتب بدلالة main بدلالة ال real number فيها ان معادلة اسم معادلة Euler اللي بكتب ال exponential function بدلالة ال sign و ال cosine يبقى باجي بقول ما يأتي now we shall", "tokens": [1211, 19452, 5296, 8848, 23275, 47525, 1211, 3714, 6027, 5016, 1211, 3714, 4117, 2655, 37746, 4032, 33546, 1211, 3997, 3547, 4724, 16254, 1975, 5016, 995, 12610, 1975, 4117, 2655, 3555, 47525, 1211, 6027, 3660, 2135, 47525, 1211, 6027, 3660, 2423, 957, 1230, 8978, 11296, 16472, 20449, 18513, 37977, 24525, 2304, 20449, 18513, 37977, 462, 26318, 13672, 1829, 4724, 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"temperature": 1.0}, {"id": 221, "seek": 549177, "start": 5465.27, "end": 5491.77, "text": "يبقى امثلة بسيطة جدا مادهاش لحمة كتير زي النظر يعني تلت امثلة بيعدلوش حساب الورونسكين هذا تمام يبقى examples solve the following differential equations", "tokens": [1829, 3555, 4587, 7578, 1975, 2304, 12984, 37977, 4724, 3794, 1829, 9566, 3660, 10874, 28259, 3714, 18513, 3224, 33599, 5296, 35571, 3660, 9122, 2655, 13546, 30767, 1829, 28239, 19913, 2288, 37495, 22653, 6055, 1211, 2655, 1975, 2304, 12984, 37977, 4724, 1829, 22488, 1211, 2407, 8592, 11331, 3794, 16758, 2423, 13063, 11536, 3794, 4117, 9957, 23758, 46811, 10943, 7251, 3555, 4587, 7578, 5110, 5039, 264, 3480, 15756, 11787], "avg_logprob": -0.29641543241108165, "compression_ratio": 1.346820809248555, "no_speech_prob": 0.0, "words": [{"start": 5465.27, "end": 5465.69, "word": "يبقى", "probability": 0.6754608154296875}, {"start": 5465.69, "end": 5466.27, "word": " امثلة", "probability": 0.7520904541015625}, {"start": 5466.27, "end": 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" the", "probability": 0.8818359375}, {"start": 5853.97, "end": 5854.33, "word": " initial", "probability": 0.95263671875}, {"start": 5854.33, "end": 5854.73, "word": " value", "probability": 0.97509765625}, {"start": 5854.73, "end": 5855.43, "word": " problem", "probability": 0.92626953125}], "temperature": 1.0}, {"id": 239, "seek": 589341, "start": 5870.07, "end": 5893.41, "text": "اللي هي y w prime زائد أربع y prime زائد خمسة y يساوي zero و ال y عند ال zero يساوي واحد و ال pi prime عند ال zero بده يساوي zero يبقى هذه جاهزة solution", "tokens": [6027, 20292, 39896, 288, 261, 5835, 30767, 16373, 3215, 5551, 25513, 3615, 288, 5835, 30767, 16373, 3215, 16490, 2304, 3794, 3660, 288, 7251, 3794, 995, 45865, 4018, 4032, 2423, 288, 43242, 2423, 4018, 7251, 3794, 995, 45865, 36764, 24401, 4032, 2423, 3895, 5835, 43242, 2423, 4018, 47525, 3224, 7251, 3794, 995, 45865, 4018, 7251, 3555, 4587, 7578, 29538, 10874, 40294, 11622, 3660, 3827], "avg_logprob": -0.24401854793541133, 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"end": 5878.07, "word": " y", "probability": 0.94677734375}, {"start": 5878.07, "end": 5878.87, "word": " يساوي", "probability": 0.9293212890625}, {"start": 5878.87, "end": 5879.47, "word": " zero", "probability": 0.360595703125}, {"start": 5879.47, "end": 5880.45, "word": " و", "probability": 0.415283203125}, {"start": 5880.45, "end": 5880.69, "word": " ال", "probability": 0.80322265625}, {"start": 5880.69, "end": 5881.15, "word": " y", "probability": 0.85888671875}, {"start": 5881.15, "end": 5881.65, "word": " عند", "probability": 0.99169921875}, {"start": 5881.65, "end": 5881.91, "word": " ال", "probability": 0.78125}, {"start": 5881.91, "end": 5882.27, "word": " zero", "probability": 0.9072265625}, {"start": 5882.27, "end": 5882.99, "word": " يساوي", "probability": 0.98388671875}, {"start": 5882.99, "end": 5883.65, "word": " واحد", "probability": 0.989013671875}, {"start": 5883.65, "end": 5883.83, "word": " و", "probability": 0.70458984375}, {"start": 5883.83, "end": 5884.01, "word": " ال", "probability": 0.9404296875}, {"start": 5884.01, "end": 5884.29, "word": " pi", "probability": 0.466796875}, {"start": 5884.29, "end": 5884.99, "word": " prime", "probability": 0.90185546875}, {"start": 5884.99, "end": 5885.35, "word": " عند", "probability": 0.98779296875}, {"start": 5885.35, "end": 5885.61, "word": " ال", "probability": 0.90966796875}, {"start": 5885.61, "end": 5886.05, "word": " zero", "probability": 0.9169921875}, {"start": 5886.05, "end": 5887.19, "word": " بده", "probability": 0.713623046875}, {"start": 5887.19, "end": 5888.09, "word": " يساوي", "probability": 0.9107666015625}, {"start": 5888.09, "end": 5889.03, "word": " zero", "probability": 0.73486328125}, {"start": 5889.03, "end": 5891.37, "word": " يبقى", "probability": 0.9215087890625}, {"start": 5891.37, "end": 5891.71, "word": " هذه", "probability": 0.2144775390625}, {"start": 5891.71, "end": 5892.49, "word": " جاهزة", "probability": 0.98291015625}, {"start": 5892.49, "end": 5893.41, "word": " solution", "probability": 0.869140625}], "temperature": 1.0}, {"id": 240, "seek": 592291, "start": 5895.77, "end": 5922.91, "text": "يبقى باجي بقوله let Y تساوي E أُس RT ب A solution then the characteristic equation is R تربيع زائد أربعة R زائد حمسة يساوي زير", "tokens": [1829, 3555, 4587, 7578, 4724, 26108, 1829, 4724, 39648, 3224, 718, 398, 6055, 3794, 995, 45865, 462, 5551, 10859, 3794, 21797, 4724, 316, 3827, 550, 264, 16282, 5367, 307, 497, 6055, 2288, 21292, 3615, 30767, 16373, 3215, 5551, 25513, 27884, 497, 30767, 16373, 3215, 11331, 2304, 3794, 3660, 7251, 3794, 995, 45865, 30767, 13546], "avg_logprob": -0.27443182468414307, "compression_ratio": 1.2191780821917808, "no_speech_prob": 0.0, "words": [{"start": 5895.77, "end": 5896.23, "word": "يبقى", "probability": 0.7799072265625}, {"start": 5896.23, "end": 5896.69, "word": " باجي", "probability": 0.70361328125}, {"start": 5896.69, "end": 5897.25, "word": " بقوله", "probability": 0.8473307291666666}, {"start": 5897.25, "end": 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5912.81, "word": " equation", "probability": 0.982421875}, {"start": 5912.81, "end": 5913.71, "word": " is", "probability": 0.94384765625}, {"start": 5913.71, "end": 5916.09, "word": " R", "probability": 0.385009765625}, {"start": 5916.09, "end": 5917.09, "word": " تربيع", "probability": 0.7802734375}, {"start": 5917.09, "end": 5918.19, "word": " زائد", "probability": 0.81884765625}, {"start": 5918.19, "end": 5918.99, "word": " أربعة", "probability": 0.7887369791666666}, {"start": 5918.99, "end": 5919.39, "word": " R", "probability": 0.923828125}, {"start": 5919.39, "end": 5920.03, "word": " زائد", "probability": 0.9720052083333334}, {"start": 5920.03, "end": 5921.39, "word": " حمسة", "probability": 0.92919921875}, {"start": 5921.39, "end": 5922.45, "word": " يساوي", "probability": 0.9755859375}, {"start": 5922.45, "end": 5922.91, "word": " زير", "probability": 0.465087890625}], "temperature": 1.0}, {"id": 241, "seek": 594901, "start": 5923.55, "end": 5949.01, "text": "طبعا لا يمكن نقدر نحلل هذه يبقى ماليش إلا أحلها بالقانون ناقص أربعة زيد أو ناقص الجذر التربيعي لبقى تربيعي لبس أتاشر ناقص أربعة ألف اللي هي بواحد جيم اللي هي بخمسة كله على قداش على اتنين في واحد", "tokens": [9566, 3555, 3615, 995, 20193, 7251, 43020, 8717, 28543, 2288, 8717, 5016, 1211, 1211, 29538, 7251, 3555, 4587, 7578, 3714, 6027, 1829, 8592, 11933, 15040, 5551, 5016, 1211, 11296, 20666, 4587, 7649, 11536, 8717, 995, 4587, 9381, 5551, 25513, 27884, 30767, 25708, 34051, 8717, 995, 4587, 9381, 25724, 8848, 2288, 16712, 2288, 21292, 3615, 1829, 5296, 3555, 4587, 7578, 6055, 2288, 21292, 3615, 1829, 5296, 3555, 3794, 5551, 2655, 33599, 2288, 8717, 995, 4587, 9381, 5551, 25513, 27884, 5551, 46538, 13672, 1829, 39896, 4724, 14407, 24401, 10874, 32640, 13672, 1829, 39896, 4724, 9778, 2304, 3794, 3660, 28242, 3224, 15844, 12174, 3215, 33599, 15844, 1975, 2655, 1863, 9957, 8978, 36764, 24401], "avg_logprob": -0.23662725547412494, "compression_ratio": 1.9230769230769231, "no_speech_prob": 0.0, "words": 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C اتنين بناء عليه صار عندنا C اتنين بده يساوي اتنين C واحد", "tokens": [1211, 33456, 23758, 8978, 34105, 4724, 11622, 13546, 2407, 34105, 4724, 14407, 24401, 34105, 4724, 11622, 13546, 2407, 7251, 3555, 4587, 7578, 4724, 3794, 383, 36764, 24401, 13672, 1829, 39182, 3224, 30767, 16373, 3215, 36764, 24401, 8978, 3224, 20328, 9957, 30767, 13546, 2407, 4724, 11622, 13546, 2407, 9122, 2407, 9381, 9957, 20328, 5172, 2288, 36764, 24401, 7251, 3555, 4587, 7578, 30767, 16373, 3215, 383, 1975, 2655, 1863, 9957, 7251, 3555, 4587, 7578, 383, 1975, 2655, 1863, 9957, 44945, 16606, 47356, 20328, 9640, 43242, 8315, 383, 1975, 2655, 1863, 9957, 47525, 3224, 7251, 3794, 995, 45865, 1975, 2655, 1863, 9957, 383, 36764, 24401], "avg_logprob": -0.2016080027645074, "compression_ratio": 2.1538461538461537, "no_speech_prob": 5.960464477539063e-08, "words": [{"start": 6083.2, "end": 6083.9, "word": "لأن", "probability": 0.53271484375}, {"start": 6083.9, "end": 6084.42, "word": " هذا", "probability": 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{"start": 6092.9, "end": 6093.72, "word": " بعده", "probability": 0.716796875}, {"start": 6093.72, "end": 6094.54, "word": " زائد", "probability": 0.8396809895833334}, {"start": 6094.54, "end": 6095.3, "word": " واحد", "probability": 0.98681640625}, {"start": 6095.3, "end": 6096.0, "word": " فيه", "probability": 0.7200927734375}, {"start": 6096.0, "end": 6096.94, "word": " صين", "probability": 0.57208251953125}, {"start": 6096.94, "end": 6097.4, "word": " زيرو", "probability": 0.8701171875}, {"start": 6097.4, "end": 6098.06, "word": " بزيرو", "probability": 0.96435546875}, {"start": 6098.06, "end": 6098.76, "word": " كوصين", "probability": 0.732666015625}, {"start": 6098.76, "end": 6099.14, "word": " صفر", "probability": 0.9456380208333334}, {"start": 6099.14, "end": 6099.4, "word": " واحد", "probability": 0.9951171875}, {"start": 6099.4, "end": 6099.7, "word": " يبقى", "probability": 0.9840087890625}, {"start": 6099.7, "end": 6100.36, "word": " زائد", "probability": 0.97705078125}, 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19913, 16572, 16472, 47395, 1829, 8315, 9154, 3224, 2423, 3541, 44381, 12602, 39319, 11331, 9566, 4724, 8592, 17082, 37977, 588, 1021, 8978, 2423, 11900, 6055, 3555, 4587, 7578, 9673, 25720, 25724, 995, 10632, 44945, 46309, 5016, 29538, 28239, 47432, 3660, 4032, 44945, 47283, 3215, 45030, 11242, 16247, 2304, 12984, 37977, 25894, 11296, 4032, 39182, 9957, 44945, 9778, 8592, 8978, 2423, 3541, 13672, 1829, 39182, 3224, 16472, 13412, 16606, 21984], "avg_logprob": -0.15625000653201587, "compression_ratio": 1.5634517766497462, "no_speech_prob": 2.384185791015625e-07, "words": [{"start": 6154.41, "end": 6154.89, "word": "احنا", "probability": 0.90869140625}, {"start": 6154.89, "end": 6155.49, "word": " نظري", "probability": 0.97607421875}, {"start": 6155.49, "end": 6156.31, "word": " انتهينا", "probability": 0.9356689453125}, {"start": 6156.31, "end": 6156.69, "word": " منه", "probability": 0.780029296875}, {"start": 6156.69, "end": 6156.79, "word": " ال", "probability": 0.445068359375}, {"start": 6156.79, "end": 6157.15, "word": " section", "probability": 0.87060546875}, {"start": 6157.15, "end": 6157.87, "word": " لكن", "probability": 0.744140625}, {"start": 6157.87, "end": 6158.37, "word": " راح", "probability": 0.916259765625}, {"start": 6158.37, "end": 6158.77, "word": " حط", "probability": 0.92529296875}, {"start": 6158.77, "end": 6159.49, "word": " بشغلة", "probability": 0.65313720703125}, {"start": 6159.49, "end": 6159.91, "word": " very", "probability": 0.88623046875}, {"start": 6159.91, "end": 6161.13, "word": " important", "probability": 0.9609375}, {"start": 6161.13, "end": 6161.49, "word": " في", "probability": 0.736328125}, {"start": 6161.49, "end": 6161.57, "word": " ال", "probability": 0.97900390625}, {"start": 6161.57, "end": 6162.57, "word": " exercises", "probability": 0.99462890625}, {"start": 6162.57, "end": 6163.47, "word": " تبقى", "probability": 0.782958984375}, {"start": 6163.47, "end": 6163.85, "word": " المرة", "probability": 0.86376953125}, {"start": 6163.85, "end": 6164.29, "word": " الجاية", "probability": 0.9122721354166666}, {"start": 6164.29, "end": 6164.85, "word": " بنشرح", "probability": 0.9627278645833334}, {"start": 6164.85, "end": 6165.11, "word": " هذه", "probability": 0.8916015625}, {"start": 6165.11, "end": 6165.71, "word": " النقطة", "probability": 0.9840494791666666}, {"start": 6165.71, "end": 6166.13, "word": " و", "probability": 0.66015625}, {"start": 6166.13, "end": 6166.55, "word": " بناخد", "probability": 0.9488932291666666}, {"start": 6166.55, "end": 6166.83, "word": " بعض", "probability": 0.979248046875}, {"start": 6166.83, "end": 6167.35, "word": " الأمثلة", "probability": 0.8671875}, {"start": 6167.35, "end": 6167.87, "word": " عليها", "probability": 0.982666015625}, {"start": 6167.87, "end": 6168.39, "word": " و", "probability": 0.85205078125}, {"start": 6168.39, "end": 6168.81, "word": " بعدين", "probability": 0.81298828125}, {"start": 6168.81, "end": 6169.31, "word": " بنخش", "probability": 0.79345703125}, {"start": 6169.31, "end": 6169.43, "word": " في", "probability": 0.85205078125}, {"start": 6169.43, "end": 6169.55, "word": " ال", "probability": 0.93359375}, {"start": 6169.55, "end": 6170.13, "word": " section", "probability": 0.89794921875}, {"start": 6170.13, "end": 6171.13, "word": " اللي", "probability": 0.840087890625}, {"start": 6171.13, "end": 6171.67, "word": " بعده", "probability": 0.9482421875}, {"start": 6171.67, "end": 6171.91, "word": " ان", "probability": 0.81005859375}, {"start": 6171.91, "end": 6172.29, "word": " شاء", "probability": 0.98974609375}, {"start": 6172.29, "end": 6172.53, "word": " الله", "probability": 0.9541015625}], "temperature": 1.0}], "language": "ar", "language_probability": 1.0, "duration": 6175.695, "duration_after_vad": 5762.103468750034}
\ No newline at end of file
diff --git a/PL9fwy3NUQKwa8ZDfSFGn6H8xVFLzqmCZC/Q2YiEyS2_gY_raw.srt b/PL9fwy3NUQKwa8ZDfSFGn6H8xVFLzqmCZC/Q2YiEyS2_gY_raw.srt
new file mode 100644
index 0000000000000000000000000000000000000000..69b27e9a23fa57ac7e2bf5bd07328424ad0d5ce9
--- /dev/null
+++ b/PL9fwy3NUQKwa8ZDfSFGn6H8xVFLzqmCZC/Q2YiEyS2_gY_raw.srt
@@ -0,0 +1,3552 @@
+1
+00:00:09,660 --> 00:00:14,080
+بسم الله الرحمن الرحيم المرة اللي فاتت بدينا في
+
+2
+00:00:14,080 --> 00:00:18,660
+section تلاتة تلاتة وعطينا تعريف ل linearly
+
+3
+00:00:18,660 --> 00:00:23,420
+independent و linearly dependent functions اقول ان
+
+4
+00:00:23,420 --> 00:00:26,140
+لو في عنده functions بقول عنهم linearly
+
+5
+00:00:26,140 --> 00:00:30,570
+independentإذا كان الغنوز اللي كانت تبعهم ماله لا
+
+6
+00:00:30,570 --> 00:00:35,930
+يساوي زيرو اما إذا كانت التنتين linearly dependent
+
+7
+00:00:35,930 --> 00:00:41,190
+فالغنوز اللي كانت تبعهم ماله بده يساوي زيرو اتنين
+
+8
+00:00:41,190 --> 00:00:46,230
+قلنا ان ال two functions بقول عنهم linearly
+
+9
+00:00:46,230 --> 00:00:51,290
+independent لو جدت تلاقي two constants كونستان في
+
+10
+00:00:51,290 --> 00:00:53,930
+الدالة الأولى كونستان في الدالة التانية بده يساوي
+
+11
+00:00:53,930 --> 00:00:54,870
+زيرو كان
+
+12
+00:01:00,290 --> 00:01:04,950
+لكن لو كان على الأقل واحد من كواحد او كاتنين لا
+
+13
+00:01:04,950 --> 00:01:10,620
+يساوي زيروو ممكن اتنين مايكونوش بأصفر كذلك يبقى في
+
+14
+00:01:10,620 --> 00:01:13,900
+هذه الحالة بقول ال two functions f and g are
+
+15
+00:01:13,900 --> 00:01:20,120
+linearly dependent تمام؟ بعد هيك روحنا لنظرية و
+
+16
+00:01:20,120 --> 00:01:24,040
+النظرية هذه اللي اول نظرية او هي النظرية الوحيدة
+
+17
+00:01:24,040 --> 00:01:28,680
+اللي أخدناها المرة اللي فاتت اللي هو بنحكم على ال
+
+18
+00:01:28,680 --> 00:01:32,600
+two functions او ال two solutions ل second order
+
+19
+00:01:32,600 --> 00:01:36,220
+differential equationبينهم linearly dependent او
+
+20
+00:01:36,220 --> 00:01:41,640
+linearly independent من خلال الورنسكين يعني لو
+
+21
+00:01:41,640 --> 00:01:47,580
+جينا وجينا ان الورنسكين عند نقطة ما لا يساوي zero
+
+22
+00:01:47,580 --> 00:01:51,040
+اذا ال two functions بقول عنهم linearly
+
+23
+00:01:51,040 --> 00:01:57,930
+independentولو كانوا تنتهيوا linearly dependent
+
+24
+00:01:57,930 --> 00:02:03,550
+يكون ال goal skin يساوي zero هذه النظرية الحجيبة
+
+25
+00:02:03,550 --> 00:02:09,650
+نظرية أقوى منها وتبقى في اتجاهينلكن بعد قليل في
+
+26
+00:02:09,650 --> 00:02:14,870
+محاضرتنا هذه بس قبلها هنجيب ال worn skin بطريقة
+
+27
+00:02:14,870 --> 00:02:18,910
+أخرى غير اللي احنا اتعودنا عليها أو اللي عارفين
+
+28
+00:02:18,910 --> 00:02:22,530
+تبعة المحدد الدالة الأولى التانية مشتقة الأولى
+
+29
+00:02:22,530 --> 00:02:27,010
+ومشتقة الثانية فهذه اكتشافها العالم Abel وبالتالي
+
+30
+00:02:27,010 --> 00:02:32,850
+سميت باسمه فables theorem يبقى نظرية العالم Abel
+
+31
+00:02:33,460 --> 00:02:37,500
+بتقول لو كان Y1 وY2 هو عبارة عن solutions لل
+
+32
+00:02:37,500 --> 00:02:40,220
+differential equation من ال second order اللي
+
+33
+00:02:40,220 --> 00:02:44,460
+قدامنا هذه حيث ال P و P و R continuous functions
+
+34
+00:02:44,460 --> 00:02:52,740
+على الفترة المفتوحة Iيبقى الورونسكين كمشكلة Y1 وY2
+
+35
+00:02:52,740 --> 00:03:01,060
+كمشكلة T يساوي C في E أس ناقص تكامل P of T DT يبقى
+
+36
+00:03:01,060 --> 00:03:05,440
+من الأن و فسادا طبقا لهذه النظر يبقى الورونسكين له
+
+37
+00:03:05,440 --> 00:03:10,340
+كم شكلشكلين الشكل الأولاني شكل المحدد اللي احنا
+
+38
+00:03:10,340 --> 00:03:13,860
+عرفناه قبل ايه والشكل التالي مقدار ثابت في ال
+
+39
+00:03:13,860 --> 00:03:18,360
+exponential لنا ال P of T هو المعامل تبع مين هو
+
+40
+00:03:18,360 --> 00:03:23,520
+البنات بشرط ان يكون معامل Y double prime هو الواحد
+
+41
+00:03:23,520 --> 00:03:27,400
+الصحيح يعني لو كان المعامل تبع Y double prime هو
+
+42
+00:03:27,400 --> 00:03:33,020
+رقم تاني او دلة تانية بدي اجسم الطرفين عليه ومن ثم
+
+43
+00:03:33,020 --> 00:03:40,730
+بروح بحسب مينيبقى C مقدار ثابت يعتمد على الحالين
+
+44
+00:03:40,730 --> 00:03:48,850
+Y1 وY2 ولا يعتمد على شكل الـMain شكل الـT طب نروح
+
+45
+00:03:48,850 --> 00:03:52,650
+نثبت صحة هذا الكلام بس قبل ان نثبت صحة هذا الكلام
+
+46
+00:03:52,650 --> 00:03:56,090
+احنا مانقول مش هنجيب linearly dependent و
+
+47
+00:03:56,090 --> 00:03:59,750
+independent بد الoneskin هذا يستوي الـ0 ومايستويش
+
+48
+00:03:59,750 --> 00:04:05,070
+الـ0بدي بسأل هل ال exponential هادي عمرها بده
+
+49
+00:04:05,070 --> 00:04:08,550
+تساوي zero في يومنا اللي هي؟ لأ لإنه أخدنا في
+
+50
+00:04:08,550 --> 00:04:13,150
+calculus بإن ال exponential دائما و أبدا ده لأ
+
+51
+00:04:13,150 --> 00:04:17,390
+أكبر من zero بتاخد قيمة أكبر من zero لعمرها بتاخد
+
+52
+00:04:17,390 --> 00:04:20,770
+zero ولا بتاخد قيمة سليمة، إذا شو اللي بده يخليه
+
+53
+00:04:20,770 --> 00:04:28,290
+zero؟ اليبقى C لو كانت هذا الكلام لا يمكن أن يساوي
+
+54
+00:04:28,290 --> 00:04:33,310
+Zero إلا إذا كانت C تساوي Zero فقط لكن إذا C
+
+55
+00:04:33,310 --> 00:04:38,250
+بتسويش Zero يبقى الورونسكين هذا ما له لا يمكن أن
+
+56
+00:04:38,250 --> 00:04:43,890
+يساوي Zero على الإطلاق نجي نثبت صحة هذه النظرية
+
+57
+00:04:43,890 --> 00:04:49,230
+طيب نجي الماضية قلي اتنين هدول حلل المعادلة هذه
+
+58
+00:04:49,230 --> 00:04:53,910
+يبقى اتنين هدول ما لهمبحقق المعادلة دي يبقى باجي
+
+59
+00:04:53,910 --> 00:05:08,870
+بقوله بما أن since Y1 and Y2 are two solutions of
+
+60
+00:05:08,870 --> 00:05:11,890
+equation one
+
+61
+00:05:15,630 --> 00:05:19,710
+يبقى كل واحد فيهم هيحقق المعادلة اللي عندنا يبقاش
+
+62
+00:05:19,710 --> 00:05:20,270
+بصير
+
+63
+00:05:23,800 --> 00:05:30,900
+زائد P of T في ال Y واحد ال prime زائد Q of T في
+
+64
+00:05:30,900 --> 00:05:38,780
+ال Y واحد بيساوي كده؟ بيساوي Zero اتنين and ال Y2
+
+65
+00:05:38,780 --> 00:05:46,000
+بابلي prime زائد P of T في ال Y2 prime زائد Q of T
+
+66
+00:05:46,000 --> 00:05:52,490
+في ال Y2 بيساوي كده؟ بيساوي Zero طيب انابدي اجي
+
+67
+00:05:52,490 --> 00:05:56,770
+الى المعادلتين هذول بدي احاول اطيّر ال term الأخير
+
+68
+00:05:56,770 --> 00:06:04,090
+فلو جيت المعادلة الأولى هذه روحت ضربتها في سالب Y2
+
+69
+00:06:04,090 --> 00:06:10,890
+والمعادلة الثانية ضربتها في موجب Y1
+
+70
+00:06:12,180 --> 00:06:16,220
+المعادلة كلها من أولها لآخرها يبقى المعادلة الأولى
+
+71
+00:06:16,220 --> 00:06:21,260
+بتضربها في سالب Y2 والمعادلة التانية بتضربها في
+
+72
+00:06:21,260 --> 00:06:26,740
+موجب Y1 يبقى كل من المعادلتين هتصبح على الشكل
+
+73
+00:06:26,740 --> 00:06:40,310
+التالي سالب Y1 double prime Y2سالب P of T في Y1 Y2
+
+74
+00:06:40,310 --> 00:06:51,030
+سالب EQ of T في Y1 Y2 يبقى 0 المعادلة التانية
+
+75
+00:06:51,030 --> 00:06:57,410
+هضربها في Y1 يبقى Y1 Y2
+
+76
+00:06:59,260 --> 00:07:09,520
+زائد P of T في Y1 Y2 زائد P of T في Y1 Y2 زائد P
+
+77
+00:07:09,520 --> 00:07:11,080
+of T في Y1 Y2 زائد P of T في Y1 Y2 زائد P of T في
+
+78
+00:07:11,080 --> 00:07:16,440
+Y1 Y2 زائد
+
+79
+00:07:16,440 --> 00:07:22,350
+P of T في Y1 Y2 زائد P of T في Y1 Y2وبعد ما ضربنا
+
+80
+00:07:22,350 --> 00:07:27,450
+المعادلة التانية في Y1 شويك نجمع يبقى لو جمعنا
+
+81
+00:07:27,450 --> 00:07:32,100
+هذول الله سهل عليهم مع السلام غير ماسوف عليهميبقى
+
+82
+00:07:32,100 --> 00:07:38,400
+بيصير مجموع المعادلاتين على الشكل التالي يبقى y1
+
+83
+00:07:38,400 --> 00:07:46,240
+y2 double prime ناقص y1 double prime y2 مجموع
+
+84
+00:07:46,240 --> 00:07:51,120
+الترمين هذول هذول يا بنات بيداخد P of T عامل مشترك
+
+85
+00:07:51,120 --> 00:07:58,940
+منهم يبقى زائد P of T عامل مشترك بظل عندي y1 y2
+
+86
+00:07:58,940 --> 00:08:06,790
+primeنقص Y1 Y2 Y1 Y2 Y1 Y2 Y2 Y2 Y2 Y2 Y2 Y2 Y2 Y2
+
+87
+00:08:06,790 --> 00:08:11,810
+Y2 Y2 Y2 Y2 Y2 Y2 Y2 Y2 Y2 Y2 Y2 Y2 Y2 Y2 Y2 Y2 Y2
+
+88
+00:08:11,810 --> 00:08:15,810
+Y2 Y2 Y2 Y2 Y2 Y2 Y2 Y2 Y2 Y2 Y2 Y2 Y2 Y2 Y2 Y2 Y2
+
+89
+00:08:15,810 --> 00:08:18,610
+Y2 Y2 Y2 Y2 Y2 Y2 Y2 Y2 Y2 Y2 Y2 Y2 Y2 Y2 Y2 Y2 Y2
+
+90
+00:08:18,610 --> 00:08:18,610
+Y2 Y2 Y2 Y2 Y2 Y2 Y2 Y2 Y2 Y2 Y2 Y2 Y2 Y2 Y2 Y2 Y2
+
+91
+00:08:18,610 --> 00:08:18,610
+Y2 Y2 Y2 Y2 Y2 Y2 Y2 Y2 Y2 Y2 Y2 Y2 Y2 Y2 Y2 Y2 Y2
+
+92
+00:08:18,610 --> 00:08:23,550
+Y2 Y2 Y2 Y2 Y2 Y2 Y2 Y2 Y2
+
+93
+00:08:23,550 --> 00:08:32,250
+Y2 Y2 Yأنا بدي أعرف ال W of T الرونسكين W of T يا
+
+94
+00:08:32,250 --> 00:08:40,170
+بنات مش هو عبارة عن Y1 Y2 Y1 prime Y2 prime صح
+
+95
+00:08:40,170 --> 00:08:46,810
+يبقى هذا لو جيت فاكته شو بيعطيني بيعطيني Y1 Y2
+
+96
+00:08:46,810 --> 00:08:56,440
+prime ناقص Y1 prime Y2 الرئيسي ناقص الثانويطب بدي
+
+97
+00:08:56,440 --> 00:09:02,100
+أشتقه و أشوف شو بيعطينا يبقى لو جيت ل w prime as a
+
+98
+00:09:02,100 --> 00:09:07,820
+function of t يعني dw على dt هذه مشتقة حصل ضرب
+
+99
+00:09:07,820 --> 00:09:13,620
+دالتين وهذه مشتقة حصل ضرب دالتين يبقى الدالة
+
+100
+00:09:13,620 --> 00:09:20,140
+الأولى في مشتقة الدالة الثانية زائد مشتقة الدالة
+
+101
+00:09:20,140 --> 00:09:25,410
+الأولى في الدالة الثانية كما هياللي عملته لحاصل
+
+102
+00:09:25,410 --> 00:09:29,810
+الضرب الأول هروح اعمله لمين؟ لحاصل الضرب الثاني
+
+103
+00:09:29,810 --> 00:09:35,950
+الناقص الدالة الأولى في مشتقة الدالة الثانية زائد
+
+104
+00:09:35,950 --> 00:09:46,650
+مع ناقص بصير ناقص اللي هو من اشتقل اللي هو Y1W'Y2
+
+105
+00:09:46,650 --> 00:09:51,510
+فالليلة في هذه و هذه مش الأثنين أرض سان واحدة
+
+106
+00:09:51,510 --> 00:09:56,180
+موجبة و واحدة سالبةيبقى مع السلامة يبقى صارة
+
+107
+00:09:56,180 --> 00:10:04,800
+النتيجة هي y1 y2 double prime ناقص y1 double prime
+
+108
+00:10:04,800 --> 00:10:12,280
+y2 طب أبطال الليلة لهذه هل ليست هذه هي بالضبط ولا
+
+109
+00:10:12,280 --> 00:10:18,390
+لا؟ إذا هذه بقدر أشيل وقت بدالها من؟و برامج W و
+
+110
+00:10:18,390 --> 00:10:25,510
+هذه بقدر اشيلها و اكتب دبالها من W اذا باجي بقوله
+
+111
+00:10:25,510 --> 00:10:37,130
+substitute and equation اتنين و نحصل على W برامج و
+
+112
+00:10:37,130 --> 00:10:45,640
+اكتب دبالها من Wزائد P of T في W as a function of
+
+113
+00:10:45,640 --> 00:10:51,930
+T بده ساوي Zeroيبقى من second order linear
+
+114
+00:10:51,930 --> 00:10:56,190
+differential equation تحولنا إلى first order
+
+115
+00:10:56,190 --> 00:11:01,470
+differential equation هذه بنحلها بسيطة يبقى هذه يا
+
+116
+00:11:01,470 --> 00:11:09,030
+بنات بقدر اقول w prime of t بده يساوي سالب p of t
+
+117
+00:11:09,030 --> 00:11:20,050
+في w of t ممكن نجسم كله على w يبقى هنا بصير wA' of
+
+118
+00:11:20,050 --> 00:11:26,990
+T على W of T بيكون ناقص P of T
+
+119
+00:11:30,810 --> 00:11:36,250
+يبقى لو كملة الطرفين ايش بصير عننا هنا لين
+
+120
+00:11:36,250 --> 00:11:45,270
+absolute value ل W of T ل W of T بده ساوي ناقص
+
+121
+00:11:45,270 --> 00:11:53,170
+تكامل P of T دي T زاد constant وليكن C1أنا ما بدّي
+
+122
+00:11:53,170 --> 00:11:56,950
+اللي ان الـW بدّي الـW itself يبقى لما نرفع
+
+123
+00:11:56,950 --> 00:12:01,930
+الطرفين كوصل العدد A لو رفعناها كوصل العدد دي
+
+124
+00:12:01,930 --> 00:12:08,510
+بيبقى ال absolute value لW of T يساوي E أساليب
+
+125
+00:12:08,510 --> 00:12:19,070
+تكامل لP of T DT زي الconstant C1سؤال هو هل هذه في
+
+126
+00:12:19,070 --> 00:12:27,250
+يوم من الأيام تاخد قيمة سالبة أو صفة؟ يبقى هذا
+
+127
+00:12:27,250 --> 00:12:30,570
+الكلام ال absolute value، اشيلناه والله خلناها
+
+128
+00:12:30,570 --> 00:12:38,030
+سيانةيبقى هذه positive وبالتالي W of T بده يساوي E
+
+129
+00:12:38,030 --> 00:12:47,090
+of T ناقص تكامل P of T DT في E of C1 وزعت الأسس
+
+130
+00:12:47,090 --> 00:12:53,310
+عند برب تجمع الأسس مظبوط ايه طب ايه اش رايك هذه
+
+131
+00:12:53,310 --> 00:12:59,800
+كلها constant؟الـ E بـ 2 و 7 من عشرة و الـ C 1 كل
+
+132
+00:12:59,800 --> 00:13:01,160
+صحيح يبقى هذا كل صحيح يبقى هذا كل صحيح يبقى هذا كل
+
+133
+00:13:01,160 --> 00:13:03,000
+صحيح يبقى هذا كل صحيح يبقى هذا كل صحيح يبقى هذا كل
+
+134
+00:13:03,000 --> 00:13:03,800
+صحيح يبقى هذا كل صحيح يبقى هذا كل صحيح يبقى هذا كل
+
+135
+00:13:03,800 --> 00:13:07,360
+صحيح يبقى هذا كل صحيح يبقى هذا كل صحيح يبقى هذا كل
+
+136
+00:13:07,360 --> 00:13:08,880
+صحيح يبقى هذا كل صحيح يبقى هذا كل صحيح يبقى هذا كل
+
+137
+00:13:08,880 --> 00:13:11,080
+صحيح يبقى هذا كل صحيح يبقى هذا كل صحيح يبقى هذا كل
+
+138
+00:13:11,080 --> 00:13:19,380
+صحيح يبقى هذا كل صحيح يبقى هذا
+
+139
+00:13:19,380 --> 00:13:26,490
+كل صحيح يبخلاصنا؟ يبقى الأن عندي طريقتان أو عندي
+
+140
+00:13:26,490 --> 00:13:33,750
+طريقتين أو توجد طريقتين لمين لا حساب رونسكين،
+
+141
+00:13:33,750 --> 00:13:40,170
+تمام؟ طيب، حد فيكن لا يتساؤل هنا؟ أه البرهان صحيح،
+
+142
+00:13:40,170 --> 00:13:45,510
+والله صحيح ضربنا وجمعنا واشتقنا رونسكين، طلع
+
+143
+00:13:45,510 --> 00:13:51,110
+الجواب دغري كامل وطلع الجوابحلّي باللي بدكي ..
+
+144
+00:13:51,110 --> 00:13:54,750
+الحين هعطيكي مدى للمثال تلاتة و تشوفي حالك حتى
+
+145
+00:13:54,750 --> 00:13:55,990
+اللي بتنتين
+
+146
+00:14:19,140 --> 00:14:27,440
+يبقى اول مثال example one اول
+
+147
+00:14:27,440 --> 00:14:38,120
+مثال let y1 بده يسوي جذر ال T و ال y2 بده يسوي
+
+148
+00:14:38,120 --> 00:14:46,140
+واحد عال T بي two solutions
+
+149
+00:14:47,270 --> 00:14:56,650
+بتو solutions of the differential equation of the
+
+150
+00:14:56,650 --> 00:15:05,690
+differential equation للمعادلة التفاضلية اتنين T
+
+151
+00:15:05,690 --> 00:15:14,070
+ترابيع Y double prime زائد تلاتة T Y prime ناقص Y
+
+152
+00:15:14,070 --> 00:15:23,540
+تساوي Zeroو الـ T greater than zero find بدنا
+
+153
+00:15:23,540 --> 00:15:31,080
+الرنسكان تبع ال Y واحد و ال Y اتنين as a function
+
+154
+00:15:31,080 --> 00:15:40,940
+of T also و كذلك find the constant C on the
+
+155
+00:15:40,940 --> 00:15:42,580
+constant
+
+156
+00:16:09,120 --> 00:16:15,550
+الاخت لواء بتسألته قبل قليلبتقول ايش؟ بتقول طب اني
+
+157
+00:16:15,550 --> 00:16:18,570
+اتي احنا نستخدم هال runnerskin اللي أخدناها قبل
+
+158
+00:16:18,570 --> 00:16:23,190
+المحدد و الله تبعي بالما نقول هي يمكن يلزم الأثنان
+
+159
+00:16:23,190 --> 00:16:28,380
+و احنا الإجابة على جد السؤال نشوف شو اللي بديهاطيب
+
+160
+00:16:28,380 --> 00:16:32,820
+السؤال بيقول ما ياتي الكلام ال .. الإجابة على لغة
+
+161
+00:16:32,820 --> 00:16:37,460
+لواء و الكلام للسامعين بتقول افترض او المثل اللي
+
+162
+00:16:37,460 --> 00:16:41,160
+بتقول افترض ان Y1 هو جدر ال T و Y2 و 1 على T و هم
+
+163
+00:16:41,160 --> 00:16:45,020
+عبارة عن حليل المعادلة التفاضلية لأنه قال هاتل
+
+164
+00:16:45,020 --> 00:16:49,000
+الرونسكين تبعهم بقوله بسيط اول شي هبجيب الرونسكين
+
+165
+00:16:49,240 --> 00:16:56,900
+As a function of T مباشرة فبجب أقول الحل الأول جذر
+
+166
+00:16:56,900 --> 00:17:05,540
+ال T و الحل التاني 1 على T بدنا نشتقه يبقى 1 على 2
+
+167
+00:17:05,540 --> 00:17:12,920
+جذر ال T و هذا سالب 1 على T تربيعهذا الكلام بده
+
+168
+00:17:12,920 --> 00:17:18,180
+يساوي حاصل ضرب عناصر القطر الرئيسي ناقص حاصل ضرب
+
+169
+00:17:18,180 --> 00:17:24,380
+عناصر القطر الثانوي اظن ناقص T أساليب تلاتة على
+
+170
+00:17:24,380 --> 00:17:31,070
+اتنين بنفعليبقى T أس سالب اتنين ضرب T أس نص يبقى T
+
+171
+00:17:31,070 --> 00:17:34,970
+أس سالب واحد و نص يعني T أس سالب تلاتة على اتنين
+
+172
+00:17:34,970 --> 00:17:41,770
+هذا الرئيسي ناقصي الثانوي كله في المقام يبقى ما
+
+173
+00:17:41,770 --> 00:17:47,430
+نطلعه فوق يصير T أس سالب واحد و نص T أس سالب نص
+
+174
+00:17:47,430 --> 00:17:55,030
+يبقى هذا يصير ناقص نص T أس سالب تلاتة على اتنين
+
+175
+00:17:56,050 --> 00:18:02,110
+مظبوط هيك يا بناد؟ طيب واحد صحيح وكمان نص، واحد و
+
+176
+00:18:02,110 --> 00:18:08,210
+نص يعني الإجابة السالب تلاتة على اتنين، T السالب
+
+177
+00:18:08,210 --> 00:18:14,660
+تلاتة على اتنينوT أكبر من Zero إذا لا يمكن هذا أنه
+
+178
+00:18:14,660 --> 00:18:20,820
+يساوي Zero فاش إمكانية يساوي Zero ليش؟ لأنه T
+
+179
+00:18:20,820 --> 00:18:25,060
+greater than Zero يبقى جيب نيروليسكن اللي هو
+
+180
+00:18:25,060 --> 00:18:30,220
+المقلوب الأول تبع المثلة المقلوب التاني بيقول ليش؟
+
+181
+00:18:30,220 --> 00:18:34,660
+وكذلك هتل مقدار الثابت C تبع A بال Theorem
+
+182
+00:18:34,660 --> 00:18:40,440
+نيروليسكن عندها أيه كمان؟ إذا هذا بدي يساوي مين؟
+
+183
+00:18:41,510 --> 00:18:46,710
+بدي أسألك اللعنة صحيح ولا لأ بس بشرط ان المعامل
+
+184
+00:18:46,710 --> 00:18:50,890
+هذا بدي يكون واحد صحيح بديش يكون اتنين تي تاربيع
+
+185
+00:18:50,890 --> 00:18:57,030
+اذا بروح نحط المعادلة هذه في الصيغة الجديدة كتالة
+
+186
+00:18:57,030 --> 00:19:03,950
+يبقى باجي بقوله the differential equation is y
+
+187
+00:19:03,950 --> 00:19:11,290
+double prime زائد تلاتة على اتنين تي تي في المقادة
+
+188
+00:19:11,500 --> 00:19:20,700
+تمام في من؟ في الـY' وهنا ناقص 1 على 2T تربيع كله
+
+189
+00:19:20,700 --> 00:19:22,820
+في الـY بده يساوي 0
+
+190
+00:19:29,790 --> 00:19:34,010
+يبقى اشتراك مع انه لازم يكون ال Y'' المعامل تبعها
+
+191
+00:19:34,010 --> 00:19:40,250
+واحد صحيح الحين هذا أصبح هو P of T تبع able
+
+192
+00:19:40,250 --> 00:19:46,790
+theorem اذا باجي بقوله ال رونسكين تبع able theorem
+
+193
+00:19:46,790 --> 00:19:55,130
+هو C فيه اصناع استكامل 3 على 2TDT
+
+194
+00:19:57,060 --> 00:20:03,480
+يبقى هذا الكلام بده يساوي C في E أس ناقص ثلاثة على
+
+195
+00:20:03,480 --> 00:20:10,460
+اتنين برا و هذه بيصير Lin absolute value ل T لكن
+
+196
+00:20:10,460 --> 00:20:15,640
+لما كان ال T أكبر من ال zero فبنقول Lin T و بنسكت
+
+197
+00:20:15,640 --> 00:20:24,120
+تمام؟ يبقى هذه C في E أس Lin T أس سالب تلاتة على
+
+198
+00:20:24,120 --> 00:20:31,220
+اتنينيعني يا بنات بالصغير هذه C في T أس سالب تلاتة
+
+199
+00:20:31,220 --> 00:20:37,960
+على اتنين فدرونسكن هذا مش ورونسكن هذا يبقى اتنين
+
+200
+00:20:37,960 --> 00:20:45,290
+هدول لازم يساووا بعضيبقى بنسويهم بعض بناء عليه
+
+201
+00:20:45,290 --> 00:20:51,110
+بصير C في T أساليب تلاتة على اتنين بده يساوي
+
+202
+00:20:51,110 --> 00:20:55,930
+أساليب تلاتة على اتنين T أساليب تلاتة على اتنين
+
+203
+00:20:55,930 --> 00:21:01,670
+الان T أكبر من ال zero يعني رقم لا يساوي zero إذا
+
+204
+00:21:01,670 --> 00:21:05,950
+بنجسم نقدر نجسم الطرفين على T أساليب تلاتة على
+
+205
+00:21:05,950 --> 00:21:13,950
+اتنين ومنها ال C بده يساوي أساليب تلاتةعلى اتنى
+
+206
+00:21:13,950 --> 00:21:21,110
+يبقى هى ويا لي واق استخدمنا الشجتين في نفس السؤال
+
+207
+00:21:21,110 --> 00:21:25,770
+يعنى الشكلين تبع الرنس كان استخدمناهم في حل
+
+208
+00:21:25,770 --> 00:21:31,310
+المسألة اللى بين ايدينه يبقى احلى من الصرف حسب ما
+
+209
+00:21:31,310 --> 00:21:33,690
+هو مطلوب في المسألة
+
+210
+00:21:44,250 --> 00:21:49,390
+نأخد ايضا مثال اتنين
+
+211
+00:21:49,390 --> 00:21:53,950
+هذا اجى في الامتحان الفاصل اللى فات هذا فاصل فات
+
+212
+00:21:53,950 --> 00:21:59,130
+يعني قبل شهرين و نص تقريبا بيقول suppose that
+
+213
+00:21:59,130 --> 00:22:02,950
+suppose
+
+214
+00:22:02,950 --> 00:22:11,890
+that ان y واحد and y اتنين are
+
+215
+00:22:32,860 --> 00:22:41,170
+للمعادلة التفاضليةاللي هي T تربية YW prime ناقص
+
+216
+00:22:41,170 --> 00:22:48,310
+أربعة T Y prime زائد ستة Y تساوي زيرو T greater
+
+217
+00:22:48,310 --> 00:22:49,830
+than zero
+
+218
+00:22:54,220 --> 00:23:01,720
+وإذا كان الرنسكين تبع الحل الأول والحل الثاني عند
+
+219
+00:23:01,720 --> 00:23:08,580
+الواحد بده يساوي واحد اوش دونه اللي هو الرنسكين
+
+220
+00:23:08,580 --> 00:23:14,420
+تبع الحل الأول والحل الثاني عند الثمان
+
+221
+00:23:29,110 --> 00:23:32,610
+لو مسكت ورقة الامتحان تبع الفصل الماضي تبع تعمال
+
+222
+00:23:32,610 --> 00:23:37,970
+الفصل بتلاقي هذا السؤال موجود فيها طيب بقول افترض
+
+223
+00:23:37,970 --> 00:23:42,670
+انه عندي حالين و اتنين linearly independent يبقى
+
+224
+00:23:42,670 --> 00:23:47,570
+لو جيتك و حسبت نونسكين تبعهم ممكن يساوي zero؟ مش
+
+225
+00:23:47,570 --> 00:23:50,770
+إمكانية يبقى مدام جالي linearly independent يبقى
+
+226
+00:23:50,770 --> 00:23:55,770
+نونسكين لايمكن أن يساوي zero بأي حالة من الحواله
+
+227
+00:23:55,770 --> 00:24:00,600
+وبالتالي ال C تبعت ال able theoremلا يمكن أن تكون
+
+228
+00:24:00,600 --> 00:24:05,660
+بصفر على الإطلاق طيب قال لي ماشي لها اتنين لينيرا
+
+229
+00:24:05,660 --> 00:24:08,600
+independent solution للمعادلة هذه قال لي هاتلي ال
+
+230
+00:24:08,600 --> 00:24:12,360
+رونسكين وإذا كان رونسكين عند الواحد بدي يساوي عدد
+
+231
+00:24:12,360 --> 00:24:16,400
+هاتلي ال رونسكين وانا عندي اتنين بقولكوا ياسي باجي
+
+232
+00:24:16,400 --> 00:24:19,040
+لل differential equation هذه بدي أحطها في ال
+
+233
+00:24:19,040 --> 00:24:23,690
+standard fourمشان اجيب P of T بالظبط انا بدى
+
+234
+00:24:23,690 --> 00:24:28,850
+المعامل هنا بقدرش اذا بتروح اقسم كله على و بقدر
+
+235
+00:24:28,850 --> 00:24:32,870
+اقسم بكل سهولة لإن T greater than zero لإن يمكن ان
+
+236
+00:24:32,870 --> 00:24:36,790
+تساوي zero اذا بناء على المعادلة دى بتصير على
+
+237
+00:24:36,790 --> 00:24:45,200
+الشكل التالي Y ناقص اربع على T في ال Y primeزائد
+
+238
+00:24:45,200 --> 00:24:52,440
+اللي هو 6 على T تربيع في ال Y بده يساوي كده؟ بده
+
+239
+00:24:52,440 --> 00:24:58,620
+يساوي Zero تمام تمام يبقى الان بقدر اجيب الرونسكين
+
+240
+00:24:58,620 --> 00:25:02,340
+تبعها طبعا احنا من ضمن الرونسكين لازم تبقى الدوال
+
+241
+00:25:02,340 --> 00:25:07,460
+دوال متاصلة لل P و لQ طبعا ال discontinuity بيحصل
+
+242
+00:25:07,460 --> 00:25:12,170
+وين؟ عند ال Zero لكن احنا مش ترطينيبقى دول
+
+243
+00:25:12,170 --> 00:25:16,490
+continuous متحقق على طول الخط بدون أي إشكالية يبقى
+
+244
+00:25:16,490 --> 00:25:20,210
+مناقن عليها بقدر أجيب رونسكين تبع الحل الأول والحل
+
+245
+00:25:20,210 --> 00:25:26,390
+التاني يبقى رونسكين تبع الحل الأول والحل التاني as
+
+246
+00:25:26,390 --> 00:25:36,200
+a function of T يساوي C في E أص ناقصزاد تنسوش ناقص
+
+247
+00:25:36,200 --> 00:25:40,480
+القانون يبقى
+
+248
+00:25:40,480 --> 00:25:51,440
+بصير زاد تكامل 4 على T DT يبقى هذا الكلام ساوي C
+
+249
+00:25:51,440 --> 00:25:58,880
+في E أُص 4 لأن T لغرى لأن T أكبر من زمين من Zero
+
+250
+00:26:00,560 --> 00:26:09,320
+يبقى C في E أس لين T أس أربع يبقى C في T أس أربع
+
+251
+00:26:09,320 --> 00:26:18,500
+هذا شكل من رونسكان جالي ان رونسكان عند الواحد بده
+
+252
+00:26:18,500 --> 00:26:23,520
+يسوي واحد M plus يعني بده أشيل كل T و أحط مكانها
+
+253
+00:26:24,160 --> 00:26:31,580
+يبقى هنا واحد بده يساوي C في واحد وص أربعة يعني
+
+254
+00:26:31,580 --> 00:26:37,700
+بتطلع C بقداش لما C تساوي واحد يبقى أصبح in
+
+255
+00:26:37,700 --> 00:26:44,800
+general رونسكين الحل الأول والحل الثاني بده يساوي
+
+256
+00:26:44,800 --> 00:26:52,640
+قداش E ولا بده يساوي دورة T و أربعة دورجالي هاتلر
+
+257
+00:26:52,640 --> 00:26:58,240
+رونسكين تبع الحل الأول والحل التاني عندي اتنين
+
+258
+00:26:58,240 --> 00:27:04,620
+يبقى ماعلي الا أشيل T و أحط مكانها اتنين أس أربع
+
+259
+00:27:04,620 --> 00:27:11,980
+يبقى الجواب جداش ابت سبعاش صحيح؟ مباشر هذا أجى في
+
+260
+00:27:11,980 --> 00:27:17,420
+الامتحان الفصل الماضي طيب خدي ال example تلاتة
+
+261
+00:27:20,860 --> 00:27:33,360
+بقول الات Y1 and Y2 بيتو solutions
+
+262
+00:27:33,360 --> 00:27:39,880
+of the
+
+263
+00:27:39,880 --> 00:27:47,960
+differential equation للمعادلة التفاضلية واحد ناقص
+
+264
+00:27:47,960 --> 00:27:49,040
+T تربيع
+
+265
+00:28:03,230 --> 00:28:04,630
+Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''
+
+266
+00:28:05,370 --> 00:28:12,870
+قال إذا كان F الرنسكين تبع ال Y واحد وال Y اتنين
+
+267
+00:28:12,870 --> 00:28:22,550
+عند المص بده يساوي تلاتة find الرنسكين
+
+268
+00:28:22,550 --> 00:28:29,130
+تبع الحل الأول والحل التاني as a function of T for
+
+269
+00:28:29,130 --> 00:28:39,750
+all Tor all T لجميع قيم T in the interval in the
+
+270
+00:28:39,750 --> 00:28:52,830
+interval على الفترة in which بحيث أن in which the
+
+271
+00:28:52,830 --> 00:29:01,190
+solution exists
+
+272
+00:29:42,830 --> 00:29:48,150
+نرجع لسؤالنا مرة ثانيةبقول افترض عندي حلين
+
+273
+00:29:48,150 --> 00:29:51,990
+للمعادلة التفاضلية اللى قدامنا هذه وإذا كان
+
+274
+00:29:51,990 --> 00:29:55,970
+رونوسكين عنده نقص بده يساوي تلاتة هاته رونوسكين in
+
+275
+00:29:55,970 --> 00:30:01,630
+general as a function of T in the interval على
+
+276
+00:30:01,630 --> 00:30:05,130
+الفترة اللى الحل بيكون عليها صياني أنا بدي أحسب
+
+277
+00:30:05,130 --> 00:30:08,570
+جداشة نقص كمدالة لل T و بدي أعرف اللى ال interval
+
+278
+00:30:08,570 --> 00:30:12,410
+اللى الكلام عليها هذا معنىصحيح يبقى العبارة الأخرى
+
+279
+00:30:12,410 --> 00:30:15,990
+هي اللي أتي اللي أجت زيادة على مين، الحال الأول
+
+280
+00:30:15,990 --> 00:30:19,610
+حال الأول قال لي تيجريفر دانزيرو فهو طان الفترة،
+
+281
+00:30:19,610 --> 00:30:23,830
+بس هنا مااطنش الفترة أنا اللي بدي أجيب مين الفترة
+
+282
+00:30:23,830 --> 00:30:28,680
+التابعتنالذلك المعادلة التفاضليها دي بدي أنقلها
+
+283
+00:30:28,680 --> 00:30:32,660
+الى وضع اخر غير الوضع اللي هو فيه بدي اخل المعامل
+
+284
+00:30:32,660 --> 00:30:38,520
+هذا جداش يبقى بدأ اقسم كله على مين على واحد نقص T
+
+285
+00:30:38,520 --> 00:30:44,520
+تربيع يبقى solution the
+
+286
+00:30:44,520 --> 00:30:52,700
+differential equation S بدي اكتبها على الشكل
+
+287
+00:30:52,700 --> 00:30:53,960
+التالي Y
+
+288
+00:31:17,930 --> 00:31:24,270
+أظن المقام نقدر نحلله كفرق بين المربعينيبقى هذا لو
+
+289
+00:31:24,270 --> 00:31:30,930
+جينا حللنا بصير y double prime زائد واحد زائد T
+
+290
+00:31:30,930 --> 00:31:38,050
+واحد ناقص T في واحد زائد T كله في ال Y prime واحد
+
+291
+00:31:38,050 --> 00:31:45,490
+ناقص T واحد ناقص T في واحد زائد T كله في ال Y بده
+
+292
+00:31:45,490 --> 00:31:51,410
+يساوي قداش Zeroنختصر الاختصارات اللي موجودة يبقى
+
+293
+00:31:51,410 --> 00:31:55,770
+المعادلة التفاضلية أصبحت على الشكل التالي
+
+294
+00:32:07,510 --> 00:32:11,090
+مشان نحسب الـ one of skin لازم يكون معاملة P of T
+
+295
+00:32:11,090 --> 00:32:17,350
+والـ Q of T دوال متصلة على نفس الفترة مظبوط طيب
+
+296
+00:32:17,350 --> 00:32:22,950
+هنا الأن بداجي أقوله ال P of T اللي هي واحد على
+
+297
+00:32:22,950 --> 00:32:33,230
+واحد ناقص T هذه continuous for all T اللي بتسويش
+
+298
+00:32:33,230 --> 00:32:40,760
+الواحد صحيح ولا لأ؟طيب لك U of T اللي هي واحد على
+
+299
+00:32:40,760 --> 00:32:46,740
+واحد زائد T continuous لكل ال T اللي بتسويه شمين
+
+300
+00:32:46,740 --> 00:32:53,020
+سالب واحد طيب تعالوا نشوف هذا ال real line وهذه
+
+301
+00:32:53,020 --> 00:32:56,680
+النقطة اللي عندي سالب واحد وهذه النقطة اللي عندي
+
+302
+00:32:56,680 --> 00:33:03,480
+اللي واحدالدالة له purity و discontinuity حصل عند
+
+303
+00:33:03,480 --> 00:33:10,020
+الواحد يعني هنا open و بعدها continuous و قبلها
+
+304
+00:33:10,020 --> 00:33:16,080
+continuousبنجي تاني ل Q of T ال discontinuity حصل
+
+305
+00:33:16,080 --> 00:33:22,620
+وين عند السالب واحد يبقى هنا مفتوحة وبنجي هيك
+
+306
+00:33:22,620 --> 00:33:28,220
+continuous على طول و هيك continuous كذلك على طول
+
+307
+00:33:28,220 --> 00:33:37,610
+يبقى في عندي كام منطقة مشتركة بينهمتلت مناطق من
+
+308
+00:33:37,610 --> 00:33:42,930
+سالب infinity إلى سالب واحد ومن سالب واحد إلى واحد
+
+309
+00:33:42,930 --> 00:33:47,630
+ومن واحد إلى infinity يبقى احنا جسمنا ال real line
+
+310
+00:33:47,630 --> 00:33:55,070
+إلى three open intervals من اخد منهم تعالى نشوف
+
+311
+00:33:55,070 --> 00:34:00,710
+ايش بيقول هنا رونسكان وين عند النص يبقى النص بيجي
+
+312
+00:34:00,710 --> 00:34:06,500
+وين في الفترة من سالب واحد إلى واحديعني هذه هنا
+
+313
+00:34:06,500 --> 00:34:13,100
+تبقى ال zero وهنا تجينا النص عين نقطة لان هذه اذا
+
+314
+00:34:13,100 --> 00:34:18,600
+انا بتاخد الفترة من وين لوين من سلب واحد الى واحد
+
+315
+00:34:18,600 --> 00:34:30,880
+يبقى هنا ال functions ال P of T and ل Q of T
+
+316
+00:34:34,950 --> 00:34:42,910
+أركنتنيواص أت مص اللي موجودة في ال interval من
+
+317
+00:34:42,910 --> 00:34:47,630
+سالب واحد إلى واحد يعني احنا شغل هيكون على الفترة
+
+318
+00:34:47,630 --> 00:34:53,110
+يادى وباقى الفترات ماليش دعوة فيهمبنقول له كويس
+
+319
+00:34:53,110 --> 00:34:57,470
+طيب احنا لسه جاعدين بنبحث بس في ال continuity لكن
+
+320
+00:34:57,470 --> 00:35:02,290
+ماتكلمناش في الحل اللي هو بدهيه حتى اللحظة اشجلجل
+
+321
+00:35:02,290 --> 00:35:06,210
+هتل ال ورنسكين او اذا كان ورنسكين عنده نصف بده
+
+322
+00:35:06,210 --> 00:35:11,050
+يساوي تلاتة هتل ال ورنسكين على الفترة اللي الحل
+
+323
+00:35:11,050 --> 00:35:15,720
+عليها صحيح يبقى الحل عنده صيعانيات فترةمن سالب
+
+324
+00:35:15,720 --> 00:35:19,640
+واحد إلى واحد والفترات التانية ماليش علاقة فيها
+
+325
+00:35:19,640 --> 00:35:24,060
+يعني أخدت الفترة المجتملة على مين؟ على النصف إذا
+
+326
+00:35:24,060 --> 00:35:28,920
+بدنا نروح نحسب مين الرونسكين تبعنا يبقى بداجي
+
+327
+00:35:28,920 --> 00:35:35,240
+أقوله الرونسكين as a function of T يساوي C في E
+
+328
+00:35:35,240 --> 00:35:44,320
+والسالب تكاملP of T D T يعني يسوي C في A والسالب
+
+329
+00:35:44,320 --> 00:35:50,280
+تكامل وين ال P اللي عندنا هي واحد على واحد ناقص T
+
+330
+00:35:50,280 --> 00:35:59,760
+يبقى هي سالب واحد على واحد سالب T D Tأظن البسطى
+
+331
+00:35:59,760 --> 00:36:08,460
+فاضل المقام يبقاش بيصير عندنا C في E أسلن absolute
+
+332
+00:36:08,460 --> 00:36:17,040
+value للواحد ناقص T يعني مين يعني C absolute value
+
+333
+00:36:17,040 --> 00:36:24,100
+للواحد ناقص T طيب بدنا نشوف هل ال absolute هذا
+
+334
+00:36:24,100 --> 00:36:30,440
+بيظل ولا بيروح احنا بنشغل علامينمن سالب واحد الى
+
+335
+00:36:30,440 --> 00:36:34,660
+واحد ممنوع الواحد وممنوع السالب واحد يبقى ايش
+
+336
+00:36:34,660 --> 00:36:40,240
+ماتحط هنا عمرها بصير سالب ها حط الرقم اللي بدك
+
+337
+00:36:40,240 --> 00:36:43,660
+يعني بعيد عن السالب واحد والواحد وخد أي شغلة بينهم
+
+338
+00:36:43,660 --> 00:36:48,410
+عمرها بصير سالبيبقى هذه موجبة دائما و أبدا إذا لا
+
+339
+00:36:48,410 --> 00:36:54,630
+داعي لل absolute value يبقى بهذا بده يساوي C في
+
+340
+00:36:54,630 --> 00:37:01,590
+واحد ناقص T لكل T اللي موجودة في ال interval من
+
+341
+00:37:01,590 --> 00:37:05,330
+سالب واحد إلى واحد لل open interval
+
+342
+00:37:08,010 --> 00:37:16,210
+الرونس كان عند النص بده يساوي تلاتة implies يبقى
+
+343
+00:37:16,210 --> 00:37:22,390
+بده يشيل كل تي ويحط مكانها نص يبقى هاي تلاتة بده
+
+344
+00:37:22,390 --> 00:37:23,190
+يساوي
+
+345
+00:37:48,540 --> 00:37:49,940
+Y1Y2Y3Y4Y5Y6Y7Y8Y9Y10Y11Y12Y13Y14Y15Y16Y17Y18Y19Y20Y21Y22Y22Y22Y23Y23Y23Y23Y23Y23Y23Y23Y23Y23Y23Y23Y23Y23Y23Y23Y23Y23Y23Y23Y23Y23Y23Y23Y23Y23Y23Y23Y23Y23Y23Y23Y23Y23Y23Y23Y23Y23Y23Y23Y23Y23Y23Y23Y23Y23Y23Y23Y23Y23Y23Y23Y23Y23Y23Y23Y23Y23Y23Y23Y23Y23Y23Y23Y23Y23Y23Y23Y23Y23Y23Y23Y23Y23Y23Y23Y23Y23Y23Y23Y23Y23Y23Y23Y23Y23Y23Y23
+
+346
+00:37:50,110 --> 00:37:58,370
+بدي ساوي ستة فرنسكان اللي هو واحد ناقصتي، ده اللي
+
+347
+00:37:58,370 --> 00:38:04,910
+هو الحل المطلوب، حد فيكم بتحب تسألي سؤال هنا؟
+
+348
+00:38:04,910 --> 00:38:08,530
+ايوة، ديش ايش؟
+
+349
+00:38:15,940 --> 00:38:23,000
+هذه الفترة اللي لازم تختار ت سالب نص و سالب تصبح
+
+350
+00:38:23,000 --> 00:38:26,600
+واحد زاد نص تلاتة ع اتنين موجة يبقى هذا على ال
+
+351
+00:38:26,600 --> 00:38:31,500
+absolute value تغيرها تاخدها نص موجة تصبح واحد
+
+352
+00:38:31,500 --> 00:38:35,360
+ناقص نص تبقى نص موجة يبقى هذا على ال absolute
+
+353
+00:38:35,360 --> 00:38:40,340
+value اي رقم تاخده ايه بعيد عن سالب واحد اخد اي
+
+354
+00:38:40,340 --> 00:38:45,060
+رقم بينهم تظل بين جثين هذه الكميةيبقى لا داعي لل
+
+355
+00:38:45,060 --> 00:38:51,200
+absolute value تمام؟ اتلاحظى قولتلك هذا for all T
+
+356
+00:38:51,200 --> 00:38:55,180
+يعني اشيلت ال absolute value قولتلك C في واحد ناقص
+
+357
+00:38:55,180 --> 00:38:57,940
+تيليا كل ال T اللى موجود فى ال internet بس لو طلعت
+
+358
+00:38:57,940 --> 00:39:03,320
+برا هذى بيصير كلامى مش صحى تمام؟ حد تسأل تانى؟
+
+359
+00:39:04,360 --> 00:39:11,280
+ننتقل الان الى النقطة اللى بعدها اللى هي نظرية و
+
+360
+00:39:11,280 --> 00:39:15,860
+هذه النظرية طبعا اقوى من النظرية اللى خدناها المرة
+
+361
+00:39:15,860 --> 00:39:19,200
+الماضية المرة الماضية فماخدناها نظرية واحدة وكان
+
+362
+00:39:19,200 --> 00:39:23,560
+بنمشي في اتجاه واحد اذا الورنس كان لا يساوي zero
+
+363
+00:39:23,560 --> 00:39:28,340
+عند نقطة بنقول nearly independent والعكس لو كانت
+
+364
+00:39:28,340 --> 00:39:31,920
+انتها nearly dependent بنقول الورنس كان يساوي zero
+
+365
+00:39:32,180 --> 00:39:37,460
+الان بدنا نجيب نظرية اقوى منها في الاتجاهين if and
+
+366
+00:39:37,460 --> 00:39:49,860
+only if النظرية بتقول ما يأتي فيرم
+
+367
+00:39:49,860 --> 00:39:55,440
+let
+
+368
+00:39:55,440 --> 00:40:01,380
+ال y واحد and y اتنين
+
+369
+00:40:06,080 --> 00:40:14,720
+بسوليوشنز بسوليوشنز of the differential equation
+
+370
+00:40:14,720 --> 00:40:25,940
+للمعادلة التفاضلية L of Y بدا تساوي Y double prime
+
+371
+00:40:25,940 --> 00:40:28,700
+زي P of T في Y prime
+
+372
+00:40:33,730 --> 00:40:48,350
+الـ P of T and Q of T are continuous functions
+
+373
+00:40:49,320 --> 00:41:01,180
+دوال متصلة on an interval I on an open interval I
+
+374
+00:41:01,180 --> 00:41:11,060
+then then
+
+375
+00:41:11,060 --> 00:41:26,010
+Y واحد and Y اتنين arelinearly dependent on I if
+
+376
+00:41:26,010 --> 00:41:33,270
+and only if if and only if الورنس كان تبع ال Y
+
+377
+00:41:33,270 --> 00:41:41,310
+واحد وال Y اتنين as a function of T linearly
+
+378
+00:41:41,310 --> 00:41:51,080
+dependent on I linearly dependent on If and only f
+
+379
+00:41:51,080 --> 00:41:54,380
+الهونسكين
+
+380
+00:41:54,380 --> 00:42:00,520
+تبعهم بده يساوي zero لكل ال T اللي موجودة في ال
+
+381
+00:42:00,520 --> 00:42:05,540
+interval I alternatively
+
+382
+00:42:05,540 --> 00:42:11,660
+ال Y
+
+383
+00:42:11,660 --> 00:42:22,360
+واحد and Y اتنين areLinearly Independent if and
+
+384
+00:42:22,360 --> 00:42:29,420
+only if الرنس كان تبع الحل الأول والحل التاني as a
+
+385
+00:42:29,420 --> 00:42:37,540
+function of t لا يساوي zero on ال interval I
+
+386
+00:42:37,540 --> 00:42:40,720
+remark
+
+387
+00:42:40,720 --> 00:42:41,980
+let
+
+388
+00:42:51,140 --> 00:42:58,520
+Y1 وY2 بصوليوشنز
+
+389
+00:42:58,520 --> 00:43:02,280
+بصوليوشنز
+
+390
+00:43:02,280 --> 00:43:12,000
+of the differential equation للمعادلة التفاضلية YW
+
+391
+00:43:12,000 --> 00:43:18,340
+prime P of Tفى الـ y prime q of t فى ال y بده
+
+392
+00:43:18,340 --> 00:43:28,720
+يساوي zero then the following the
+
+393
+00:43:28,720 --> 00:43:38,540
+following are equivalent النمرة
+
+394
+00:43:38,540 --> 00:43:42,540
+واحد the functions
+
+395
+00:43:45,210 --> 00:43:59,330
+ي واحد وي اتنين are fundamental
+
+396
+00:43:59,330 --> 00:44:02,490
+set
+
+397
+00:44:02,490 --> 00:44:07,370
+of solutions
+
+398
+00:44:07,370 --> 00:44:19,400
+of solutions on the interval Iنمر اتنين ال
+
+399
+00:44:19,400 --> 00:44:28,900
+functions y1 و y2 are linearly independent on the
+
+400
+00:44:28,900 --> 00:44:38,480
+interval I نمر تلاتة الورنسكين تبقى الحل الأول
+
+401
+00:44:38,480 --> 00:44:51,500
+والحل الثاني عند نقطة T nodeلا يساوي zero for some
+
+402
+00:44:51,500 --> 00:45:03,780
+t naught اللي موجودة في ال I نمرا أربعة ال
+
+403
+00:45:03,780 --> 00:45:07,020
+one is can تبع الحل الأول
+
+404
+00:45:09,580 --> 00:45:19,240
+والحل الثاني as a function of t لا يساوي zero for
+
+405
+00:45:19,240 --> 00:45:25,420
+all t اللي موجودة في ال interval I
+
+406
+00:46:15,500 --> 00:46:21,340
+طيب نعود إلى نظرية تبعتنا هنا لأن انتوا افتحولي
+
+407
+00:46:21,340 --> 00:46:28,340
+على المحاضرة اللى فاتت اخر محاضرة اخر نظرية اخر
+
+408
+00:46:28,340 --> 00:46:31,580
+نظرية كتبناها في محاضرة المرة الماضية
+
+409
+00:46:44,440 --> 00:46:50,850
+أه فتحته؟ طيبالنظرية كانت بتقول ما ياتي في عندي
+
+410
+00:46:50,850 --> 00:46:55,930
+دلتين F وG الدلتين كانوا دوال قابلة للاشتقاق مادام
+
+411
+00:46:55,930 --> 00:47:00,210
+قابلة الاشتقاق يبقى تعني ايه؟ متاصلة تمام لك العكس
+
+412
+00:47:00,210 --> 00:47:04,190
+ما لو مش صحيح يبقى متاص على ال open interval I and
+
+413
+00:47:04,190 --> 00:47:08,150
+if there exists T node in I يعني لو لجأت نقطة
+
+414
+00:47:08,150 --> 00:47:11,850
+واحدة T node موجودة في ال interval I بحيث الرنوس
+
+415
+00:47:11,850 --> 00:47:14,830
+كان عندها لا يستوي Zero يبقى الدلتين هذول بقول
+
+416
+00:47:14,830 --> 00:47:21,040
+عنهملنيرلي اندبندنت يبقى لو كان الرنسكين I أساوي
+
+417
+00:47:21,040 --> 00:47:25,720
+زيرو يبقى الدلاتين هدول لينيرلي اندبندنت فقط يبقى
+
+418
+00:47:25,720 --> 00:47:29,540
+السير وين في اتجاه واحد روحنا قولنا in the other
+
+419
+00:47:29,540 --> 00:47:33,160
+hand مشينا في الاتجاه الثاني قولنا لو ال F و G
+
+420
+00:47:33,160 --> 00:47:38,040
+كانوا لينيرلي dependent يبقى الرنسكين تبعهم أساوي
+
+421
+00:47:38,040 --> 00:47:43,370
+زيرو عن كل T موجودة في ال Iإذا هذه معلوماتها بسيطة
+
+422
+00:47:43,370 --> 00:47:48,210
+بمشيش في الاتجاهين لكن أجت النظرية هذه اللي بين
+
+423
+00:47:48,210 --> 00:47:54,150
+إيدنا عمّمت النظرية هذه وصارت أهم منها وأقوى منها
+
+424
+00:47:54,150 --> 00:47:58,110
+يبقى هذه ال theorem stronger than the first
+
+425
+00:47:58,110 --> 00:48:02,290
+theorem الأولانية تعالوا نشوف إيش بتقولبقول لو كان
+
+426
+00:48:02,290 --> 00:48:06,990
+هدول حالين يبقى احنا قايدنا
+
+427
+00:48:06,990 --> 00:48:12,810
+حالنا بحالين لمعادلة تفاضلية يبقى Y1 وY2 حالين
+
+428
+00:48:12,810 --> 00:48:16,070
+للمعادلة التفاضلية اللي عندنا و ال P و ال Q ده هو
+
+429
+00:48:16,070 --> 00:48:21,630
+المتصل على ال interval I them ال Y1 و Y2 are
+
+430
+00:48:21,630 --> 00:48:26,210
+linearly dependent if and only if ال honors can
+
+431
+00:48:26,210 --> 00:48:31,770
+بدوا يساوي Zero لكل ال T اللي موجودة في ال Iكلمة
+
+432
+00:48:31,770 --> 00:48:36,110
+on the other hand في النظرية الأولى اللى قبل شوية
+
+433
+00:48:36,110 --> 00:48:40,450
+كانت في اتجاه واحد لكنها سرعتاش في اتجاهين الى
+
+434
+00:48:40,450 --> 00:48:43,970
+اتجاه الصحيح و لجميع قيم T اللى موجودة فى ال
+
+435
+00:48:43,970 --> 00:48:48,510
+interval مش هندق نقطة واحدة وانما على كل ال
+
+436
+00:48:48,510 --> 00:48:51,870
+interval اللى الحل هادي عليها صحيح أو للدوا اللى
+
+437
+00:48:51,870 --> 00:48:58,000
+عليها متصلة اللى P وQالخيار هو من ناحية أخرى يعني
+
+438
+00:48:58,000 --> 00:49:02,620
+كانوا بالداخل يمشي العكس أن Y1 وY2 are linearly
+
+439
+00:49:02,620 --> 00:49:08,680
+independent إذا الوضع نفسه كان لا يساوي zero لكل
+
+440
+00:49:08,680 --> 00:49:13,160
+ال T اللي موجود في ال I، جالي on I يعني على كل ال
+
+441
+00:49:13,160 --> 00:49:17,900
+I بلا استثناءلكن هناك في النظرية يقول لمن؟ عندنا
+
+442
+00:49:17,900 --> 00:49:21,740
+نقطة واحدة، إذا من الأن فا صاعد، لإن لو عندي
+
+443
+00:49:21,740 --> 00:49:25,400
+معادلة فاضل يجيب تحليل و يقول لي شوفهم لينيار او
+
+444
+00:49:25,400 --> 00:49:29,160
+independent، والله independentلقيت عند نقطة لقيت
+
+445
+00:49:29,160 --> 00:49:33,880
+عند نقطتين لقيت عند كل نقاط الاتنين are the same
+
+446
+00:49:33,880 --> 00:49:37,380
+linearly independent تعني ان الوضع كان لايساوي
+
+447
+00:49:37,380 --> 00:49:41,860
+zero والعكسه صحيح linearly dependent تعني ان الوضع
+
+448
+00:49:41,860 --> 00:49:46,580
+كان يساوي zero والعكسه صحيح طب ال remark هذه بنات
+
+449
+00:49:46,580 --> 00:49:51,900
+لأنها شملت كل ما سبق في ال section اللي فاتتمام؟
+
+450
+00:49:51,900 --> 00:49:55,840
+يعني جمعته كله و حطته في النقاط الأربع اللي قدامها
+
+451
+00:49:55,840 --> 00:49:59,880
+ده إيش بتقولي remark؟ لو كان هدول حلل المعادلة
+
+452
+00:49:59,880 --> 00:50:03,680
+التفاضلية يبقى then the following are equivalent
+
+453
+00:50:03,680 --> 00:50:07,320
+في عندي أربع جملة اللي يمكن تشيلي أي واحدة منهم و
+
+454
+00:50:07,320 --> 00:50:12,460
+تحط التانية بدلها الأولى بتقولي ان y1 و y2 are
+
+455
+00:50:12,460 --> 00:50:16,540
+fundamental set of solutions عالميا على ال
+
+456
+00:50:16,540 --> 00:50:22,300
+interval I لمياة للمعادلة التفاضلية اللي عندنايبقى
+
+457
+00:50:22,300 --> 00:50:26,300
+هذول اتنين بيكونولي fundamentals او ال general
+
+458
+00:50:26,300 --> 00:50:30,380
+solution تمام سي واحد الاول زي اتنين هو ال general
+
+459
+00:50:30,380 --> 00:50:36,380
+اتنين مكافئبين لبعض هذا بكافئ ايش؟ بكافئ لو حدث
+
+460
+00:50:36,380 --> 00:50:39,540
+ذلك ان هذول كانوا اتنين fundamental set of
+
+461
+00:50:39,540 --> 00:50:45,960
+solutions يبقى الحاليا linearly independent مظبوط؟
+
+462
+00:50:46,320 --> 00:50:52,960
+ممكن كمان ان رونسكين تمام عند نقطة لا يساوي zero
+
+463
+00:50:52,960 --> 00:51:00,060
+تمام؟ طيب ممكن رونسكين عند كل النقاط يكون لا يساوي
+
+464
+00:51:00,060 --> 00:51:05,380
+zero يعني ان ثبت ان عند نقطة واحدة على الأقل كان
+
+465
+00:51:05,380 --> 00:51:09,640
+لا يساوي zero في ال interval اذا رونسكين لا يساوي
+
+466
+00:51:09,640 --> 00:51:14,120
+zero على كل ال interval مرةواحد هيبقى ده جمع
+
+467
+00:51:14,120 --> 00:51:19,500
+النظريتين مع بعض بشغل هيبقى نقولش لك اثبتلي والله
+
+468
+00:51:19,500 --> 00:51:22,460
+اتنين هدول بتكونولي fundamental set of solutions
+
+469
+00:51:22,460 --> 00:51:23,700
+بتروح تاخديلهم
+
+470
+00:51:29,850 --> 00:51:34,890
+أو اتنين بيكونولي fundamental set of solutions
+
+471
+00:51:34,890 --> 00:51:38,570
+للمسألة اللي عندي عند نقطة والله عن جميع النقاط
+
+472
+00:51:38,570 --> 00:51:46,050
+كله سيئة حد فيكم بتسأل أسئلة قبل أن أخد مثال طيب
+
+473
+00:51:46,050 --> 00:51:50,410
+إيه الأمثلة والله إيه المثال example
+
+474
+00:51:58,410 --> 00:52:02,890
+بقول لك Y1
+
+475
+00:52:02,890 --> 00:52:06,910
+بيه
+
+476
+00:52:06,910 --> 00:52:16,930
+solution of the initial value problem YW prime
+
+477
+00:52:16,930 --> 00:52:27,290
+زائد T تربيع Y prime زائد T تكييب Y تساوي Zeroو ال
+
+478
+00:52:27,290 --> 00:52:34,430
+y واحد عند ال واحد يساوي واحد و ال y prime عند ال
+
+479
+00:52:34,430 --> 00:52:46,690
+واحد بده يساوي كده؟ بده يساوي تلاتة الان let y2 be
+
+480
+00:52:46,690 --> 00:52:53,330
+a solution of the initial value problem والشرط ان
+
+481
+00:52:53,330 --> 00:53:01,870
+y2 عند الواحد y2 عند الواحد ساوي سالب واحد و y2 a
+
+482
+00:53:01,870 --> 00:53:09,030
+prime عند الواحد ساوي قداش اتنين المصطلوب الأول
+
+483
+00:53:09,030 --> 00:53:17,590
+نمر ايه بيقول show that show that بيقول ان y واحد
+
+484
+00:53:17,590 --> 00:53:32,610
+عند y اتنينForm a fundamental set
+
+485
+00:53:32,610 --> 00:53:41,710
+of solutions
+
+486
+00:53:41,710 --> 00:53:46,770
+of the differential equation
+
+487
+00:53:58,460 --> 00:54:07,260
+of the differential equation للمعادلة التفاضلية
+
+488
+00:54:07,260 --> 00:54:14,500
+الهي Y double prime زائد T تربية Y prime زائد T
+
+489
+00:54:14,500 --> 00:54:22,820
+تكييب Y بده يساوي قداش بده يساوي Zero نمر بي find
+
+490
+00:54:22,820 --> 00:54:27,140
+constants find constants
+
+491
+00:54:30,100 --> 00:54:47,240
+C1 and C2 such that بحيث ان Y تساوي C1 Y1 C2 Y2 C2
+
+492
+00:54:47,240 --> 00:55:01,650
+Y2 is the general solution ofالـ initial value
+
+493
+00:55:01,650 --> 00:55:10,210
+problem الـ y double prime زي ال T تربيع y prime
+
+494
+00:55:10,210 --> 00:55:18,090
+زي ال T تكييب y بدو يساوي zero وال Y عند الواحد
+
+495
+00:55:18,090 --> 00:55:24,430
+بدو يساوي اتنين وال Y prime عند الواحد بدو يساوي
+
+496
+00:55:24,430 --> 00:55:27,210
+كده؟ بدو يساوي zero
+
+497
+00:56:02,040 --> 00:56:08,000
+نرجع لسؤالنا مرة ثانية بقول لو كان Y1 هو solution
+
+498
+00:56:08,000 --> 00:56:13,860
+لل initial value problem اللي عندنا هذا Y2 هو
+
+499
+00:56:13,860 --> 00:56:17,220
+solution لنفس ال initial value problem المعادلة
+
+500
+00:56:17,220 --> 00:56:21,700
+نفسها بس غيرنا مين؟ غيرنا ال initial conditions
+
+501
+00:56:21,700 --> 00:56:29,140
+يبقى انا عندي Y1 و Y1' و Y2 و Y2'بقول المطبق اللي
+
+502
+00:56:29,140 --> 00:56:32,080
+هو ال Bayley ان اي واحد او اي اتنين form a
+
+503
+00:56:32,080 --> 00:56:34,580
+fundamental set of solutions لل differential
+
+504
+00:56:34,580 --> 00:56:39,600
+equation اللي عندنا هذه بقوله والله كويس اذا والله
+
+505
+00:56:39,600 --> 00:56:44,600
+المحدد تبعهم لا يساوي zero إذا الأتنين بيكونوا
+
+506
+00:56:44,600 --> 00:56:47,140
+fundamental set of solutions طبقا لل remark اللي
+
+507
+00:56:47,140 --> 00:56:52,050
+مسحناها قبل قليلأو الـ band in Y1 وY2 before my
+
+508
+00:56:52,050 --> 00:56:55,050
+fundamental system solution إذا الورونس كان عند
+
+509
+00:56:55,050 --> 00:56:59,470
+نقطة أو على طول كان ماله، لا يستوزن، إذا بدنا نروح
+
+510
+00:56:59,470 --> 00:57:03,330
+نحسب الورونس كان، تمام؟ إذا لو رحت حسبت الورونس
+
+511
+00:57:03,330 --> 00:57:08,710
+عند نقطة أو عند كل النقاط، كلسيا أي واحدة فيهم، طب
+
+512
+00:57:08,710 --> 00:57:11,790
+احنا بلاحظ ان ال initial conditions محسبات، كلهم
+
+513
+00:57:11,790 --> 00:57:16,060
+عند مين؟إذا خلّيني أحسب الورونسكين عند الواحد صح
+
+514
+00:57:16,060 --> 00:57:21,740
+ولا لأ يبقى باجي بقوله solution نمر ايه؟ بدي أحسب
+
+515
+00:57:21,740 --> 00:57:28,820
+الورونسكين عند الواحد يبقى هذا الكلام بدي يساوي y
+
+516
+00:57:28,820 --> 00:57:36,440
+واحد عند الواحد y اتنين عند الواحد y اتنين وواحد
+
+517
+00:57:36,440 --> 00:57:44,450
+prime عند الواحد y اتنين prime عند الواحدصح؟ كويس
+
+518
+00:57:44,450 --> 00:57:49,790
+هذه يعني T node يا بنات تبعت ال remark هي اللي هي
+
+519
+00:57:49,790 --> 00:57:55,330
+واحد طب هذا الكلام بده يساوي Y واحد عند الواحد هي
+
+520
+00:57:55,330 --> 00:58:02,630
+بواحد Y اتنين عند الواحد هي بسالب واحد Y واحد ال
+
+521
+00:58:02,630 --> 00:58:08,470
+prime عند الواحد هي بتلاتة Y اتنين ال prime عند
+
+522
+00:58:08,470 --> 00:58:14,600
+الواحد اللي هو باتنينيبقى نفك المحددة ده اتنين
+
+523
+00:58:14,600 --> 00:58:21,680
+زائد تلاتة اتنين زائد تلاتة هو يساوي خمسة لا يساوي
+
+524
+00:58:21,680 --> 00:58:26,070
+Zeroما دام لا يساوي zero يبقى الحالين هدول بقالهم
+
+525
+00:58:26,070 --> 00:58:30,270
+بيكونولي fundamental set واني مش عارف شو شكلهم ولا
+
+526
+00:58:30,270 --> 00:58:34,910
+مطلوب اعرف شكلهم ماجليش هاتل الحالين تمام يبقى
+
+527
+00:58:34,910 --> 00:58:48,490
+باجي بقول له so y1 and y2 form a fundamental set
+
+528
+00:59:09,820 --> 00:59:15,450
+خلصنا المطلب الأول نعود لمطلب الثانيالمطلوب التاني
+
+529
+00:59:15,450 --> 00:59:21,990
+هو find constants C1 وC2 يبقى مادام هذول كوّنولي
+
+530
+00:59:21,990 --> 00:59:25,790
+fundamental set of solutions يبقى ال general
+
+531
+00:59:25,790 --> 00:59:29,930
+solution يكون constant في الحل الأول زاد constant
+
+532
+00:59:29,930 --> 00:59:37,890
+في الحل التاني اذا باجي بقول له general solution
+
+533
+00:59:50,940 --> 00:59:52,340
+YYYYYYYYYYYYYYYYYY
+
+534
+01:00:09,810 --> 01:00:16,350
+إذا بقدر استخدم الشروط اللي عندي فيه إيجاد c1 و c2
+
+535
+01:00:16,350 --> 01:00:20,810
+مظبوط ولا لا باجي بقوله والله كويس يبقى بدي أشتق
+
+536
+01:00:20,810 --> 01:00:26,110
+هذه امانة إذا لو اشتقت هذه إيش بصير y prime c1
+
+537
+01:00:26,110 --> 01:00:35,020
+مقدار ثابت مالوش دهوة وهذه y1 prime c2 y2 primeعند
+
+538
+01:00:35,020 --> 01:00:39,320
+الواحد يجب أن يجي إلى ال condition الأول يجي إلى
+
+539
+01:00:39,320 --> 01:00:41,440
+ال condition الواحد يجي إلى ال condition الواحد
+
+540
+01:00:41,440 --> 01:00:42,180
+يجي إلى ال condition الواحد يجي إلى ال condition
+
+541
+01:00:42,180 --> 01:00:43,500
+الواحد يجي إلى ال condition الواحد يجي إلى ال
+
+542
+01:00:43,500 --> 01:00:45,220
+condition الواحد يجي إلى ال condition الواحد يجي
+
+543
+01:00:45,220 --> 01:00:47,480
+إلى ال condition الواحد يجي إلى ال condition
+
+544
+01:00:47,480 --> 01:00:48,360
+الواحد يجي إلى ال condition الواحد يجي إلى ال
+
+545
+01:00:48,360 --> 01:00:48,820
+condition الواحد يجي إلى ال condition الواحد يجي
+
+546
+01:00:48,820 --> 01:00:48,820
+إلى ال condition الواحد يجي إلى ال condition
+
+547
+01:00:48,820 --> 01:00:48,820
+الواحد يجي إلى ال condition الواحد يجي إلى ال
+
+548
+01:00:48,820 --> 01:00:48,820
+condition الواحد يجي إلى ال condition الواحد يجي
+
+549
+01:00:48,820 --> 01:00:48,820
+إلى ال condition الواحد يجي إلى ال condition
+
+550
+01:00:48,820 --> 01:00:49,900
+الواحد يجي إلى ال condition الواحد يجي إلى ال
+
+551
+01:00:49,900 --> 01:00:56,220
+condition الواحد يجي إلى ال condition الواحد يجي
+
+552
+01:00:56,220 --> 01:01:01,740
+إلى ال condition الواحدوالواحد of واحد بيبقى اداش
+
+553
+01:01:01,740 --> 01:01:07,720
+اللي هو واحد يبقى صارت هذه C والله بلاش اكتب عليك
+
+554
+01:01:07,720 --> 01:01:13,860
+على خطتين بلاش تقولي كيف هذه اجت الان
+
+555
+01:01:13,860 --> 01:01:22,310
+من هدول اتنينبقدر اقول ما ياتي ان y عند الواحد بده
+
+556
+01:01:22,310 --> 01:01:28,570
+يساوي c واحد في y واحد عند الواحد زائد c اتنين في
+
+557
+01:01:28,570 --> 01:01:35,270
+y اتنين عند الواحد y a prime عند الواحد بده يساوي
+
+558
+01:01:35,270 --> 01:01:40,690
+c واحد في y واحد a prime عند الواحد زائد c اتنين
+
+559
+01:01:40,690 --> 01:01:48,340
+في y اتنين a prime عند الواحدتمام؟ هكتبهم لك فوق
+
+560
+01:01:48,340 --> 01:01:56,740
+الآن احنا عندناواللي عندك y واحد عند الواحد
+
+561
+01:01:56,740 --> 01:02:02,280
+ماعطينيها بقداش باتنين implies ليه اتنين بدها
+
+562
+01:02:02,280 --> 01:02:08,300
+تساوي وي واحد ايه ال prime اللي هي main بقداش وي
+
+563
+01:02:08,300 --> 01:02:15,060
+واحد اللي هي بقداش بواحد يبقى ب c واحد وي اتنين
+
+564
+01:02:15,060 --> 01:02:20,970
+عند الواحد بناقص واحد يبقى ناقص c اتنينالـ
+
+565
+01:02:20,970 --> 01:02:24,170
+condition التاني يجب أن يعطينا main يجب أن يعطينا
+
+566
+01:02:24,170 --> 01:02:31,010
+y1 prime y prime عند الواحد بده يساوي ال zero يبقى
+
+567
+01:02:31,010 --> 01:02:37,350
+zero بده يساوي y1 prime عند الواحد اللي هو الثلاثة
+
+568
+01:02:37,570 --> 01:02:44,910
+يبقى تلاتة C واحد و Y اتنين عند الواحد ال prime هو
+
+569
+01:02:44,910 --> 01:02:51,890
+بقداش ب اتنين يبقى زائد اتنين C اتنين شو رأيك يا
+
+570
+01:02:51,890 --> 01:02:56,990
+بنات لو ضربت المعادل اللي فوق في اتنين بصير اربع
+
+571
+01:02:56,990 --> 01:03:02,990
+يساوي اتنين C واحد نقص اتنين C اتنين هذه خلتها زي
+
+572
+01:03:02,990 --> 01:03:08,890
+مينتلاتة C واحد زائد اتنين C اتنين وروح الجماعة
+
+573
+01:03:08,890 --> 01:03:15,110
+هذه مع السلامة اربع يسوى خمسة C واحد يبقى C واحد
+
+574
+01:03:15,110 --> 01:03:21,230
+يبقى دياشر اربع احمس مدام اربع احمس يبقى نعود في
+
+575
+01:03:21,230 --> 01:03:29,910
+اي من المعادلتينيبقى بصير اتنين تساوي اربع اخمس
+
+576
+01:03:29,910 --> 01:03:39,650
+ناقص اتنين يبقى C2 تساوي اربع اخمس ناقص اتنين طبعا
+
+577
+01:03:39,650 --> 01:03:46,910
+كله على قداش على حمسة بصير اربع ناقص عشرة يبقى
+
+578
+01:03:46,910 --> 01:03:52,150
+ناقص ست اخمس يبقى بناء على ال general
+
+579
+01:03:55,350 --> 01:04:03,120
+Solution General solution of theالعامة الوالدة
+
+580
+01:04:03,120 --> 01:04:13,240
+اللي بديها هي Y27 C1 طلعناها ب4 أخمس يبقى 4 أخمس
+
+581
+01:04:13,240 --> 01:04:21,300
+Y1 و C2 بناقص 6 أخمس Y2 يبقى هذا ال general
+
+582
+01:04:21,300 --> 01:04:26,800
+solution اللي بديها انتهى
+
+583
+01:04:26,800 --> 01:04:34,160
+ال section بنجي ل exercisesتلاتة تلاتة ومن جول
+
+584
+01:04:34,160 --> 01:04:46,560
+المسائل من واحد لغاية تلتاش الأد ومن خمستاش لغاية
+
+585
+01:04:46,560 --> 01:04:57,540
+واحد وعشرين وسؤال تلاتة وعشرين حد
+
+586
+01:04:57,540 --> 01:04:59,560
+فيك و بتحب تسأل أي سؤال هنا يا بنات؟
+
+587
+01:05:08,740 --> 01:05:13,160
+الان بنتقل الى ال section اللى بعده بعد ما
+
+588
+01:05:13,160 --> 01:05:19,860
+دوخناكوا شوية بدنا نرجع للاصل اللى ابتدينا فيه
+
+589
+01:05:19,860 --> 01:05:24,660
+اللى هو ال homogeneous differential equation with
+
+590
+01:05:24,660 --> 01:05:26,600
+constant coefficients
+
+591
+01:05:37,370 --> 01:05:43,790
+يبقى بدنا نيجي ل section تلاتة أربعة section تلاتة
+
+592
+01:05:43,790 --> 01:05:54,110
+أربعة بتكلم عن ال complex roots complex roots of
+
+593
+01:05:54,110 --> 01:06:00,130
+the characteristic equation
+
+594
+01:06:11,610 --> 01:06:17,420
+بنبدأ ب section تلاتة واحد اول sectionواخدنا ال
+
+595
+01:06:17,420 --> 01:06:21,920
+second order linear differential equation وروحنا
+
+596
+01:06:21,920 --> 01:06:26,660
+خدنا حالة خاصة منها لما يكونوا ال coefficients are
+
+597
+01:06:26,660 --> 01:06:31,440
+colostants يبقى لو كانوا المعاملات ما لهم ثوابت
+
+598
+01:06:31,440 --> 01:06:35,460
+بقولنا بنفرض ان EOSRT هو عبارة عن حلوة وبالتالي
+
+599
+01:06:35,460 --> 01:06:40,040
+بنجيب ال characteristic equation لAR ثربيه زائد BR
+
+600
+01:06:40,040 --> 01:06:48,840
+زائد Cوقلنا الحل له أحد ثلاثة احتمالات الاحتمال
+
+601
+01:06:48,840 --> 01:06:55,760
+الاول ان اتنين are real and different واخدنا امثلة
+
+602
+01:06:55,760 --> 01:07:01,040
+عليهاو بعد هيك صبرنا شوية و غطسنا وين في شجة تانية
+
+603
+01:07:01,040 --> 01:07:06,320
+الان بدنا نرجع بعد section تلاتة اتنين و تلاتة
+
+604
+01:07:06,320 --> 01:07:10,120
+تلاتة بدنا نرجع لكلام اللي ابتدأنا فيه في section
+
+605
+01:07:10,120 --> 01:07:14,320
+تلاتة واحد بداخل تلاتة اربع ان لو كان اتنين are
+
+606
+01:07:14,320 --> 01:07:18,910
+complex rootsالاتنين كانوا complex roots and
+
+607
+01:07:18,910 --> 01:07:22,850
+conjugate اتنين تخيلين ومترافقين وبعد ذلك ال
+
+608
+01:07:22,850 --> 01:07:26,590
+section اللي بعد بناخد لو كانوا اتنين are real
+
+609
+01:07:26,590 --> 01:07:31,570
+repeated roots جذور حقيقية ومقريبة يخلينا مع ال
+
+610
+01:07:31,570 --> 01:07:35,750
+complex اتنين ونذكر تذكير بالمعادة اللي بدأنا فيها
+
+611
+01:07:35,750 --> 01:07:39,830
+وال characteristic equation يبقى باجي بقول هنا
+
+612
+01:07:39,830 --> 01:07:40,610
+consider
+
+613
+01:07:47,460 --> 01:07:57,680
+Homogenous Differential Equation لـ AYW' زائد BY'
+
+614
+01:07:58,560 --> 01:08:04,760
+زائد CY بده يساوي Zero وهذه سمنها المعادلة Star
+
+615
+01:08:06,110 --> 01:08:14,150
+قلنا لو كان ال Y تساوي E أس RT if لهذا is a
+
+616
+01:08:14,150 --> 01:08:19,430
+solution
+
+617
+01:08:19,430 --> 01:08:31,190
+of the differential equation star
+
+618
+01:08:31,190 --> 01:08:32,550
+then
+
+619
+01:08:36,900 --> 01:08:47,440
+كاركترستيك إيكوشن S الهمين AR ثرابية زايد PR زايد
+
+620
+01:08:47,440 --> 01:08:54,380
+C بده يساوي Zero وهذه سمناها المعادلة واحدة هذه
+
+621
+01:08:54,380 --> 01:08:59,920
+البنات بدنا نروح نحلها بواسطة القانون يبقى باجي
+
+622
+01:08:59,920 --> 01:09:01,960
+بقوله The Roots
+
+623
+01:09:04,670 --> 01:09:15,890
+Equation 1R R1 بده يساوي ناقص با زي الجدرى التربية
+
+624
+01:09:15,890 --> 01:09:22,070
+لبا التربية ناقص أربعة ألف جيم كله على اتنين ألف
+
+625
+01:09:24,920 --> 01:09:31,900
+ار اتنين تسوى ناقص با ناقص الجدر التربية لبا تربية
+
+626
+01:09:31,900 --> 01:09:36,640
+ناقص اربع ا سي على اتنين ا
+
+627
+01:09:56,320 --> 01:10:01,400
+كويس المرة اللى فاتت كتبنا الشغل هذه في section
+
+628
+01:10:01,400 --> 01:10:05,700
+تلاتة واحد ابنجلان اخدنا لو كان ال b تربية نقص
+
+629
+01:10:05,700 --> 01:10:10,520
+اربعة ac اكبر من ال zero يبقى قولنا الجدران حقيقيا
+
+630
+01:10:10,520 --> 01:10:15,380
+ومختلفا تمام؟المرة هذه لو كانت القيمة تحت الجدران
+
+631
+01:10:15,380 --> 01:10:21,440
+الهميز أقل من ال zero يبقى باجي بقوله if ال b
+
+632
+01:10:21,440 --> 01:10:28,680
+تربيع ناقص أربع a c أقل من ال zero يبقى الجدران
+
+633
+01:10:28,680 --> 01:10:40,540
+تخيليا مظبوط then the roots are
+
+634
+01:10:42,050 --> 01:10:48,930
+complex conjugate يبقى
+
+635
+01:10:48,930 --> 01:11:02,950
+complex conjugate and we write it
+
+636
+01:11:02,950 --> 01:11:04,770
+in the form
+
+637
+01:11:08,310 --> 01:11:16,230
+ممكن نكتبها على شكل ر واحد يساوي لاندا زائد IMU
+
+638
+01:11:16,230 --> 01:11:27,670
+and ر اتنين يساوي لاندا ناقص IMU واللاندا والميو
+
+639
+01:11:27,670 --> 01:11:32,970
+أعداد حقيقية موجودة في ال set of real numbers
+
+640
+01:11:49,250 --> 01:11:53,910
+مرة تانية بقول عند المعادلة التفاضلية بالشكل هذا
+
+641
+01:11:53,910 --> 01:11:58,070
+رد نوعي تساوي ART عبارة عن حل هذه المعادلة
+
+642
+01:11:58,070 --> 01:12:01,870
+التفاضلية حصلنا على ال characteristic equation
+
+643
+01:12:01,870 --> 01:12:05,150
+بالشكل اللي عندنا هذا جيبنا حل ال characteristic
+
+644
+01:12:05,150 --> 01:12:11,850
+equation وطلع عندي R1 وR2 بقول لو الكمية اللي تحت
+
+645
+01:12:11,850 --> 01:12:16,960
+الجدر هذه كانت كمية سالبةإذا أصبح R واحد و R اتنين
+
+646
+01:12:16,960 --> 01:12:23,440
+كمية تخيلية، يعني إيش بيصير؟ ناقص B على 2A زيدي
+
+647
+01:12:23,440 --> 01:12:30,200
+الجدر على 2A، وهنا ناقص B على 2A ناقص الجدر على 2A
+
+648
+01:12:30,540 --> 01:12:35,280
+ناقص بى او ناقص بى على اتنين ايه بدي اسميها لاندا
+
+649
+01:12:35,280 --> 01:12:41,200
+والجذر على اتنين ايه بدي اسميه ميو وال I هذه الحرف
+
+650
+01:12:41,200 --> 01:12:47,700
+الأول من كلمة imaginary تخيلي يعني I تساوي سالب او
+
+651
+01:12:47,700 --> 01:12:52,240
+الجذر التربية إلى سالب واحد وال I تساوي الجذر
+
+652
+01:12:52,240 --> 01:12:57,970
+التربية إلى سالب واحديعني كمية تخيّلية إذا صار
+
+653
+01:12:57,970 --> 01:13:02,450
+الجدرين R1 وR2 بدل الكلكة الكبيرة هذه بدي أكتبها
+
+654
+01:13:02,450 --> 01:13:06,970
+بشكل ألطف بالشكل اللي أنا هنا تمام؟ مدام صاروا
+
+655
+01:13:06,970 --> 01:13:10,310
+هذول الجدرين اللي يبقى لو رجعنا ل section تلاتة
+
+656
+01:13:10,310 --> 01:13:18,050
+واحد بقين أقول إذا الحل C1 في E أس R1 زاد C2 في E
+
+657
+01:13:18,050 --> 01:13:21,570
+أس R2 صحيح ولا لأ؟ يبقى باجي بقول
+
+658
+01:13:31,990 --> 01:13:44,910
+Y1 يساوي E أُس لاندا زائد IMU و Y2 يساوي E أُس
+
+659
+01:13:44,910 --> 01:13:54,320
+لاندا ناقص IMUهي اصلا ده ناقص IU وبالتالي the
+
+660
+01:13:54,320 --> 01:14:02,800
+general solution of
+
+661
+01:14:02,800 --> 01:14:16,580
+the differential equation star is y تساويC1 في A
+
+662
+01:14:16,580 --> 01:14:24,320
+أُس لاندا زائد I ميو في T طبعا هذه في T يا بنات
+
+663
+01:14:24,320 --> 01:14:32,600
+هذه كله في T وهذا كله في T زائد
+
+664
+01:14:32,600 --> 01:14:43,550
+C2 في A أُس لاندا ناقص I ميو كله في Tيبقى هذا شكل
+
+665
+01:14:43,550 --> 01:14:51,630
+الحل اللى عندنا هذا طيب الحل زى ما تشايفين مكتوب
+
+666
+01:14:51,630 --> 01:14:56,170
+بدل ال complex numbers وغالبيتكوا مادرسوش complex
+
+667
+01:14:56,170 --> 01:15:00,470
+number فى حد درست مادة ال complex يا بنات يعنى هى
+
+668
+01:15:00,470 --> 01:15:06,740
+واحدة ويمكن هى تنتين طيب الغالبية مادرسوشلكن لذلك
+
+669
+01:15:06,740 --> 01:15:11,080
+بدل مالحل مكتوب واصل complex numbers بدي احاول
+
+670
+01:15:11,080 --> 01:15:15,100
+اكتب بدلالة main بدلالة ال real number فيها ان
+
+671
+01:15:15,100 --> 01:15:19,660
+معادلة اسم معادلة Euler اللي بكتب ال exponential
+
+672
+01:15:19,660 --> 01:15:25,420
+function بدلالة ال sign و ال cosine يبقى باجي بقول
+
+673
+01:15:25,420 --> 01:15:30,200
+ما يأتي now we shall
+
+674
+01:15:37,200 --> 01:15:49,480
+write this solution هذا الحل in a
+
+675
+01:15:49,480 --> 01:16:02,880
+real form في شكل حقيقي by using by using oilers
+
+676
+01:16:10,000 --> 01:16:21,280
+شي أولرز فورملة بيقول E أُس I T يساوي Cos T زائد I
+
+677
+01:16:21,280 --> 01:16:26,140
+Sin T خلي
+
+678
+01:16:26,140 --> 01:16:30,060
+دراسة ال complex طبعا حدوها هذه و احنا بنحطها
+
+679
+01:16:30,060 --> 01:16:36,390
+كقاعدة و نشتغل عليهايبقى E أُس I T هي عبارة عن Cos
+
+680
+01:16:36,390 --> 01:16:41,810
+T زائد I Sin T طبعا لو جينا فاكينا يا بنات هنا
+
+681
+01:16:41,810 --> 01:16:49,630
+بصير Lambda T و I Mu T مظبوط هنا بصير Lambda Tو
+
+682
+01:16:49,630 --> 01:16:54,990
+ناقص I ميو T ناقص إذا بدنا نشوف E أس ناقص I T
+
+683
+01:16:54,990 --> 01:17:00,050
+عبارة عن مين إذا بناء عليه لو بدي أجي أخد E أس
+
+684
+01:17:00,050 --> 01:17:08,170
+ناقص I T بقدر أقول E أس I في ناقص T يبقى معنى كلمة
+
+685
+01:17:08,170 --> 01:17:13,320
+T مين أجي مكانها يا بناتيسالب T يبقى بالصير كوصين
+
+686
+01:17:13,320 --> 01:17:20,520
+لسلب T زائد I سين لسلب T ويساوي ال cosine odd
+
+687
+01:17:20,520 --> 01:17:24,280
+function و لا even function even يبقى سلب مع
+
+688
+01:17:24,280 --> 01:17:29,080
+السلامة يبقى ال cosine T والسين odd يبقى السلب
+
+689
+01:17:29,080 --> 01:17:36,170
+يطلع برا سلب I سين Tخلّي المعلومة اللي عندك هذه
+
+690
+01:17:36,170 --> 01:17:43,070
+لزمان لو كان الأس بالسالب يبقى زي الأس بالموجة بس
+
+691
+01:17:43,070 --> 01:17:49,670
+بيفرقوا عن بعضهم بمية بشارة سالب يعني كأنه العدد
+
+692
+01:17:49,670 --> 01:17:54,870
+والعدد المرافق لهمش كنت أقول سين زائد سات ته
+
+693
+01:17:54,870 --> 01:17:58,950
+بالعربي المرافق لو السين ناقص سات ته يعني بنغير
+
+694
+01:17:58,950 --> 01:18:05,030
+انشارة الجزء التخيلة طلع cosine T مافيش فيها تخيلة
+
+695
+01:18:05,030 --> 01:18:10,870
+sin T فيها تخيلة cosine T مافيهاش sin T هي فيها
+
+696
+01:18:10,870 --> 01:18:16,010
+سالب يبقاش صار هذا العدد وهذا هو العدد المرافق له
+
+697
+01:18:16,290 --> 01:18:20,130
+في ال complex numbers في الأعداد المركبة أو
+
+698
+01:18:20,130 --> 01:18:26,750
+الأعداد التخيلية تمام تمام يبقى هذي Euler formula
+
+699
+01:18:26,750 --> 01:18:35,250
+يبقى بناء عليه لو بدى أجيبها بنات E أس I mu T بناء
+
+700
+01:18:35,250 --> 01:18:43,050
+عليهيبقى بدل الثيمين أجانب يبقى باصير cosine mu t
+
+701
+01:18:43,050 --> 01:18:54,830
+كلها زائد I sine mu t وفي نفس الوقت E أسالب I mu t
+
+702
+01:18:54,830 --> 01:19:02,710
+cosine mu t ناقص I sine mu t
+
+703
+01:19:05,060 --> 01:19:09,820
+طيب كويس يبقى عرفنا كل واحدة فيهم يبقى لو جينا
+
+704
+01:19:09,820 --> 01:19:16,840
+بدنا ناخد المجموع تبعهم لو جيت أخد E أُس I لميو T
+
+705
+01:19:16,840 --> 01:19:23,980
+زائد E أُس ناقص I ميو T بده يساوي يبقى بدي أجمع
+
+706
+01:19:23,980 --> 01:19:29,340
+الإتنين، إيش رأيك في هذه و هذه؟ يبقى بضل قداش؟
+
+707
+01:19:29,340 --> 01:19:39,550
+إتنينCos mu tلو بدل مدجمعهم بدي اطرحهم طرح يبقى
+
+708
+01:19:39,550 --> 01:19:48,230
+ايش بصير E أس I mute ناقص E أس ناقص I mute يبقى
+
+709
+01:19:48,230 --> 01:19:54,990
+هذه بصير سالب بتروح مع الموجب وهذه بصير موجب مع
+
+710
+01:19:54,990 --> 01:20:02,230
+الموجب بصير اتنين I sign ل mute
+
+711
+01:20:04,950 --> 01:20:12,610
+تمام؟ يبقى هذا الجمع تبعهم والطرح تبعهم هذا احنا
+
+712
+01:20:12,610 --> 01:20:18,030
+قلنا الحل يا بنات الحل هذا سميليه المعادلة رقم
+
+713
+01:20:18,030 --> 01:20:26,930
+اتنين سميليه المعادلة رقم اتنين الان هذا يمثل حل
+
+714
+01:20:26,930 --> 01:20:32,070
+المعادلة الأصلية اللي هو star هل هناك قيود على C1
+
+715
+01:20:32,070 --> 01:20:38,820
+وC2؟فى قيود عندى؟ لأ ماعنديش قيود، ماعنديش قيود لأ
+
+716
+01:20:38,820 --> 01:20:44,460
+على C1 ولا على C يعني خد زى ما بدك فباجي بقول لو
+
+717
+01:20:44,460 --> 01:20:57,620
+أخدت الآن ترك C1 يسوى C2 يسوى 1 مثلا then equation
+
+718
+01:21:01,830 --> 01:21:18,830
+Y تساوي E أس لامدة T في E أس I ميو T زائد E أس
+
+719
+01:21:18,830 --> 01:21:23,970
+لامدة T في E أس ناقص I ميو T
+
+720
+01:21:27,690 --> 01:21:38,150
+يبقى Y تساوي اللي هسميه الحل الأول يبقى
+
+721
+01:21:38,150 --> 01:21:45,430
+Y واحد بده يساوي EOS Lambda T عامل مشترك بظل ان
+
+722
+01:21:45,430 --> 01:21:58,740
+EOS IMUT زاد EOS ناقص IMUT موجودة فوق؟يبقى بقدر
+
+723
+01:21:58,740 --> 01:22:05,060
+اقول هذه تساوي اتنين E اصلا ده تي كوساين ميوتي
+
+724
+01:22:05,060 --> 01:22:12,020
+صحيح ولا لأ؟ يبقى هذا صار احد الحلول للمعادلة طيب
+
+725
+01:22:12,020 --> 01:22:18,920
+لو جيت قولتلك take C واحد يساوي واحد and C اتنين
+
+726
+01:22:18,920 --> 01:22:27,550
+يساوي سالب واحد مش بحصل عليه حل تاني؟ يبقىان
+
+727
+01:22:27,550 --> 01:22:30,810
+اكويشن تو
+
+728
+01:22:41,000 --> 01:23:04,340
+Y2 يبدو يساوي يبقى
+
+729
+01:23:04,340 --> 01:23:12,810
+يصير عندي Y2 يساويبتاخد EOS Lambda T عامل مشترك
+
+730
+01:23:12,810 --> 01:23:24,280
+بظل EOS IMUT ناقص EOS ناقص IMUT ويساويطلعيلي فى
+
+731
+01:23:24,280 --> 01:23:30,960
+هذه قداش ثلاثانه اتنين اي صين ميو تي يبقى بصير
+
+732
+01:23:30,960 --> 01:23:42,300
+اتنين اي اصلا ده تي صين ميو تي يبقى انا عندي الحل
+
+733
+01:23:42,300 --> 01:23:48,600
+الاول و الحل التانى طلعيلي هذا اتنين مقدار ثابت و
+
+734
+01:23:48,600 --> 01:23:54,650
+اتنين اي مقدار ثابت اللي هم تأثير على الحلثابت
+
+735
+01:23:54,650 --> 01:24:01,190
+مالهم تأثير لأ يبقى كأن الحل الأول هو E أس لاندا T
+
+736
+01:24:01,190 --> 01:24:06,630
+Cos Mu T و الحل الثاني E أس لاندا T Sin Mu T بكوز
+
+737
+01:24:06,630 --> 01:24:16,410
+اتنين و اتنين I as are constants يبقى thus we have
+
+738
+01:24:16,410 --> 01:24:17,850
+to
+
+739
+01:24:19,600 --> 01:24:28,280
+Linearly Independent Solutions اللي هم أميم E
+
+740
+01:24:28,280 --> 01:24:41,080
+أسلندة T Cos M U T and E أسلندة T Sin M U T
+
+741
+01:24:41,080 --> 01:24:42,120
+because
+
+742
+01:24:46,380 --> 01:24:51,980
+ليش هدول linearly independent solutions؟ علشان
+
+743
+01:24:51,980 --> 01:24:59,200
+المحدد تبعهم ماله ممنوع يساوي zero دعونا نشوف
+
+744
+01:24:59,200 --> 01:25:04,700
+المحدد تبعهم، بده يساوي zero وما بيسويش ال zero
+
+745
+01:25:07,490 --> 01:25:15,450
+يبقى بدى اخد الرونسكين تبع ال E أسلندة T cosine
+
+746
+01:25:15,450 --> 01:25:23,870
+لميوتي و E أسلندة T sine لميوتي يبقى هذا الكلام
+
+747
+01:25:23,870 --> 01:25:32,130
+بدى يسوي هاي المحدد E أسلندة T cosine لميوتي و E
+
+748
+01:25:32,130 --> 01:25:36,910
+أسلندة T sine لميوتي
+
+749
+01:25:38,960 --> 01:25:46,280
+بدا اشتق هذه مجتقة مين حاصن ضرب دالتين بدا اشتق
+
+750
+01:25:46,280 --> 01:25:49,860
+الدالة الاولى ال exponential زي ما هي مضروبة في
+
+751
+01:25:49,860 --> 01:25:57,260
+تفاضل مين الاس يبقى لاندا اي اس لاندا ت كوصين ميو
+
+752
+01:25:57,260 --> 01:26:03,960
+ت الاولى مجتقة التانية التانية بسالب ساين في مجتقة
+
+753
+01:26:03,960 --> 01:26:05,620
+الزاوية اللى ميو
+
+754
+01:26:11,740 --> 01:26:15,800
+اللي عملنا الدالة الأولى بدنا نروح نعمل الدالة
+
+755
+01:26:15,800 --> 01:26:24,490
+الثانية يبقى lambdaE Os Lambda T Sine Mu T زيد
+
+756
+01:26:24,490 --> 01:26:31,270
+لميو E Os Lambda T Cos Lambda T لميو T وتعالى نفكر
+
+757
+01:26:31,270 --> 01:26:37,630
+محدد ونشوف على إيش بده يصف حاصل ضرب على ناطر
+
+758
+01:26:37,630 --> 01:26:45,290
+القطرة الرئيسية يبقى Lambda في E Os 2 Lambda T في
+
+759
+01:26:45,290 --> 01:26:55,060
+مين في Sine T Cosفى sign ميو تي كوسين ميو تى زاد
+
+760
+01:26:55,060 --> 01:27:06,900
+لميو فى E أس اتنين لاندا تى فى كوسين تربيع لميو تى
+
+761
+01:27:06,900 --> 01:27:15,240
+خلصنا الرئيسى بداجى الناقص الثانوي ناقص لاندا
+
+762
+01:27:25,720 --> 01:27:38,700
+مقص مع نقص بصير زائد شو
+
+763
+01:27:38,700 --> 01:27:44,820
+رايك هذه هي هذه؟وحدة موجة بواحدة سلبة مع السلامة
+
+764
+01:27:44,820 --> 01:27:52,840
+فما هي رأيك هذه و هذه؟ فيها لم يُ في E أس اتنية
+
+765
+01:27:52,840 --> 01:27:59,890
+لامدة T عامل مشتركبضلك cosine تربية لميو T زائد
+
+766
+01:27:59,890 --> 01:28:06,990
+sin تربية لميو T اللي بين قصانه بقداش يبقى سارة
+
+767
+01:28:06,990 --> 01:28:14,570
+عندك ميو في E أس اتنين لاند T عمر هذا بده يساوي
+
+768
+01:28:14,570 --> 01:28:21,020
+zero يا بنات؟ لأيبقى هذا الكلام لا يمكن أن يساوي
+
+769
+01:28:21,020 --> 01:28:27,980
+zero because ما هو السبب ان E أس اثنية لامدة T
+
+770
+01:28:27,980 --> 01:28:39,000
+دائما و أبدا أكبر من ال zero and لم يو لا يمكن أن
+
+771
+01:28:39,000 --> 01:28:42,400
+تساوي zero ليش sense
+
+772
+01:28:44,960 --> 01:28:51,080
+لو كانت ميو بزيرو بصير
+
+773
+01:28:51,080 --> 01:28:56,040
+الحل كله بلانبا ال root بصير حقيقي و ليس complex
+
+774
+01:28:56,040 --> 01:29:04,500
+يبقى and هذا لا يمكن يسوى zero since the
+
+775
+01:29:04,500 --> 01:29:08,520
+roots are complex
+
+776
+01:29:10,400 --> 01:29:15,580
+لأنه لو سا وزيره بيصير الجذور حقيقية وليستاش مركبة
+
+777
+01:29:15,580 --> 01:29:21,180
+يبقى بناء عليها اتنين هدول كوّنولي the fundamental
+
+778
+01:29:21,180 --> 01:29:25,740
+set of solutions يبقى هدول بيجيبولي ال general
+
+779
+01:29:25,740 --> 01:29:32,580
+solution يبقى باجي بقول ال sir the general
+
+780
+01:29:32,580 --> 01:29:38,620
+solution of the
+
+781
+01:29:58,050 --> 01:29:59,330
+الشكل اللي عندنا
+
+782
+01:30:06,510 --> 01:30:12,130
+يبقى من الآن فصاعدا بهمن لو كان R واحد يساوي R
+
+783
+01:30:12,130 --> 01:30:15,990
+اتنين اتنين اعداد حقيقية كما في section تلاتة واحد
+
+784
+01:30:15,990 --> 01:30:19,710
+تقول الحل العام هو C واحد في EOS R واحد T زائد C
+
+785
+01:30:19,710 --> 01:30:24,730
+اتنين في EOS R اتنين T لو طلع الجذور complex يبقى
+
+786
+01:30:24,730 --> 01:30:29,750
+شكل الحل EOS لاندا T C واحد كوساين ميو T زايد C
+
+787
+01:30:29,750 --> 01:30:35,960
+اتنين ساين ميو T قبل مضيح المعلومة هذه منكبدنا
+
+788
+01:30:35,960 --> 01:30:40,280
+نعطيكي أمثلة، ديرا بالك هذا حساب الورس كان محطوط
+
+789
+01:30:40,280 --> 01:30:44,120
+عندك سؤال في الكتاب محطوط اللي كنت تعسبيه، احنا دي
+
+790
+01:30:44,120 --> 01:30:46,920
+احنا حلينا السؤال و انت ماانتش داري اريحناكي منه
+
+791
+01:31:05,270 --> 01:31:09,190
+يبقى امثلة بسيطة جدا مادهاش لحمة كتير زي النظر
+
+792
+01:31:09,190 --> 01:31:14,910
+يعني تلت امثلة بيعدلوش حساب الورونسكين هذا تمام
+
+793
+01:31:14,910 --> 01:31:22,210
+يبقى examples solve
+
+794
+01:31:22,210 --> 01:31:28,350
+the following differential
+
+795
+01:31:28,350 --> 01:31:31,770
+equations
+
+796
+01:31:36,510 --> 01:31:46,810
+أول سؤال بيقول اربعة وي دابلي قرام زائد تسعة وي
+
+797
+01:31:46,810 --> 01:31:53,870
+بده يساوي زيرو solution بدأ ابدأ زي ما بدأت ال
+
+798
+01:31:53,870 --> 01:31:59,750
+user النظري بدأ اقول له let Y
+
+799
+01:31:59,750 --> 01:32:05,910
+تساوي E أس RT ب A solution
+
+800
+01:32:07,240 --> 01:32:13,400
+then the characteristic
+
+801
+01:32:13,400 --> 01:32:19,160
+equation is هاربع
+
+802
+01:32:20,330 --> 01:32:26,750
+ار تربيع زائد تسعة يساوي زيرو او ان شئتم فاقولوا
+
+803
+01:32:26,750 --> 01:32:34,010
+اربع ار تربيع يساوي قداش ناقص تسعة يبقى ار يساوي
+
+804
+01:32:34,010 --> 01:32:40,430
+الجدر التربيع اللي ناقص تسعة على مين على اربع يعني
+
+805
+01:32:40,430 --> 01:32:46,410
+زائد او ناقص تلاتة على اتنين الجدر التربيع إلى سلب
+
+806
+01:32:46,410 --> 01:32:53,610
+واحد سلب واحد بقداش قولنااي يبقى هنا زائد او ناقص
+
+807
+01:32:53,610 --> 01:33:01,510
+تلاتة على اتنين اي يبقى بنان عليها بنان كداش لاندا
+
+808
+01:33:01,510 --> 01:33:11,830
+هنا كداش لاندا؟ Zero و كداش لميو؟تلاتة على اتنين،
+
+809
+01:33:11,830 --> 01:33:15,850
+صحيح ولا لا؟ زاد ونقص عن اتنين، مترافقين، يعني
+
+810
+01:33:15,850 --> 01:33:19,190
+الإشارتين بيختلفوا للجزء التخيلي، الجزء الحقيقي عن
+
+811
+01:33:19,190 --> 01:33:23,810
+الـ Zero، يبقى بناء عليه أصبح The Solution
+
+812
+01:33:26,450 --> 01:33:37,450
+Y تساوي C إيه؟ قداش؟ Zero مش Lambda ب Zero في C
+
+813
+01:33:37,450 --> 01:33:42,520
+واحد cosine ليه ميو عندي تلاتة على اتنين؟يبقى
+
+814
+01:33:42,520 --> 01:33:48,440
+تلاتة على اتنين T زائد C اتنين Sine تلاتة على
+
+815
+01:33:48,440 --> 01:33:55,940
+اتنين T وانتهينا من المثلة يبقى Y C واحد Cos تلاتة
+
+816
+01:33:55,940 --> 01:34:03,100
+T على اتنين زائد C اتنين Sine تلاتة T على اتنين
+
+817
+01:34:03,100 --> 01:34:10,400
+بسيط المثال الثانيالمثال الثاني طبعا الأول هذا
+
+818
+01:34:10,400 --> 01:34:17,120
+بلغة سؤال 12 من الكتاب هذا سؤال 12 من الكتاب و هذا
+
+819
+01:34:17,120 --> 01:34:24,620
+سؤال 15 من الكتاب بيقول يو اي دابلي برايم زائد واي
+
+820
+01:34:24,620 --> 01:34:31,460
+برايم زائد واحد وربع واي بده يساوي كده؟ بده يساوي
+
+821
+01:34:31,460 --> 01:34:40,610
+زيو واحد ربع يعني كده؟مش خمس أرباع واحد وربع يبقى
+
+822
+01:34:40,610 --> 01:34:47,450
+هذا بده يعطيلك ان yw prime زاد y prime خمس أرباع y
+
+823
+01:34:47,450 --> 01:34:52,770
+يساوي zero او لو ضربت كله في أربعة بصير أربعة yw
+
+824
+01:34:52,770 --> 01:35:00,130
+prime زاد أربعة y prime زاد خمسة y يساوي zeroيبقى
+
+825
+01:35:00,130 --> 01:35:06,430
+بالانهيجة نقول لو افترض ان Y يسوى E اصارتي ب A
+
+826
+01:35:06,430 --> 01:35:15,330
+solution then the characteristic equation is
+
+827
+01:35:17,660 --> 01:35:27,920
+ار تساوي او اربع ار تربية زاد اربع ار زاد خمسة
+
+828
+01:35:27,920 --> 01:35:32,960
+يساوي zero لا يمكن نقدر نحللها بالاقوازيبقى ماليش
+
+829
+01:35:32,960 --> 01:35:39,440
+اللي ليهاش القانون يبقى بناء عليه R تساوي اللي هو
+
+830
+01:35:39,440 --> 01:35:46,080
+ناقص با زادة وناقص الجذر التربيعي لبا تربيع ناقص
+
+831
+01:35:46,080 --> 01:35:53,140
+أربعة ألف اللي هي أربعة جيم اللي هي خمسة كله على
+
+832
+01:35:53,140 --> 01:36:00,530
+اتنين ألف اتنين في أربعةيبقى بناء ان عليها R تساوي
+
+833
+01:36:00,530 --> 01:36:06,910
+نقص اربعة زادة او نقص اربعة فى اربعة بستاش ستاش فى
+
+834
+01:36:06,910 --> 01:36:13,030
+خمسة بتمانين شيله منها ستاش يبقى اربعة وستين الجدر
+
+835
+01:36:13,030 --> 01:36:19,710
+التربيه اللى سالب اربعة وستينكله على قداش تمانية
+
+836
+01:36:19,710 --> 01:36:27,070
+يبقى ناقص اربع زائد او ناقص تمانية اي على تمانية
+
+837
+01:36:27,070 --> 01:36:34,990
+يعني ناقص نص زائد او ناقص اي يبقى ناقص نص عبارة عن
+
+838
+01:36:34,990 --> 01:36:44,030
+ايش هذا بناتوهنا هذا باعتبار واحد يبقى لم يوتوا
+
+839
+01:36:44,030 --> 01:36:47,170
+ساوي واحد يبقى صار ال solution
+
+840
+01:36:50,020 --> 01:36:57,220
+Y تساوي E أس لاندا لامبدا اللي هو ناقص نص T يعني
+
+841
+01:36:57,220 --> 01:37:05,900
+ناقص T على اتنين في C واحد cosine T زاد C اتنين في
+
+842
+01:37:05,900 --> 01:37:12,840
+sine T كمان مثال زيهم هيك صغير وننهي المحاضرة
+
+843
+01:37:12,840 --> 01:37:17,000
+بايروبوس
+
+844
+01:37:17,000 --> 01:37:18,880
+يعطوني خمسة واخدوا العشرة
+
+845
+01:37:32,130 --> 01:37:35,430
+السؤال بيقول solve the initial value problem
+
+846
+01:37:50,070 --> 01:37:58,070
+اللي هي y w prime زائد أربع y prime زائد خمسة y
+
+847
+01:37:58,070 --> 01:38:04,290
+يساوي zero و ال y عند ال zero يساوي واحد و ال pi
+
+848
+01:38:04,290 --> 01:38:12,490
+prime عند ال zero بده يساوي zero يبقى هذه جاهزة
+
+849
+01:38:12,490 --> 01:38:13,410
+solution
+
+850
+01:38:15,770 --> 01:38:24,430
+يبقى باجي بقوله let Y تساوي E أُس RT ب A solution
+
+851
+01:38:24,430 --> 01:38:30,770
+then the characteristic
+
+852
+01:38:30,770 --> 01:38:42,450
+equation is R تربيع زائد أربعة R زائد حمسة يساوي
+
+853
+01:38:42,450 --> 01:38:49,550
+زيرطبعا لا يمكن نقدر نحلل هذه يبقى ماليش إلا أحلها
+
+854
+01:38:49,550 --> 01:38:55,990
+بالقانون ناقص أربعة زيد أو ناقص الجذر التربيعي
+
+855
+01:38:55,990 --> 01:39:01,790
+لبقى تربيعي لبس أتاشر ناقص أربعة ألف اللي هي بواحد
+
+856
+01:39:01,790 --> 01:39:09,010
+جيم اللي هي بخمسة كله على قداش على اتنين في واحد
+
+857
+01:39:09,500 --> 01:39:15,400
+يساوي ناقص اربع زائد او ناقص اربع في خمسة بعشرين
+
+858
+01:39:15,400 --> 01:39:20,360
+بنشيل منه من ستاش مضال قداش ناقص اربع يعني اتنين
+
+859
+01:39:20,360 --> 01:39:26,880
+ايه اتنين ايه كله على قداش على اتنين يبقى ناقص
+
+860
+01:39:26,880 --> 01:39:33,620
+اتنين زائد او ناقص ايه يبقى هذه كلها من أبلاندة
+
+861
+01:39:33,620 --> 01:39:38,280
+وليم يوت تساوي قداش كمان واحد يبقى
+
+862
+01:39:41,240 --> 01:39:52,120
+Solution is Y تساوي E أس لاندا T لإيه E أس ناقص
+
+863
+01:39:52,120 --> 01:40:00,840
+اتنين T C واحد cosine T زايد C اتنين sine ت كونه
+
+864
+01:40:00,840 --> 01:40:05,200
+upon initial conditions خلينا فضلها بالمرةيبقى لو
+
+865
+01:40:05,200 --> 01:40:12,380
+جبت y' تساوي ناقص اتنين EOS ناقص اتنين T C واحد
+
+866
+01:40:12,380 --> 01:40:18,440
+cosine T C اتنين cosine T هذه مشتقة الدالة الأولى
+
+867
+01:40:18,440 --> 01:40:25,480
+في الثانيةزائد الدالة الأولى E أس ناقص اتنين T في
+
+868
+01:40:25,480 --> 01:40:32,360
+مشتقة الثانية اللي هو السالب C واحد sine T وزائد C
+
+869
+01:40:32,360 --> 01:40:39,050
+اتنين cosine Tنمسك ال initial condition الأول و
+
+870
+01:40:39,050 --> 01:40:44,490
+قال لي y عند ال zero بدها تساوي واحد إذا هاي واحد
+
+871
+01:40:44,490 --> 01:40:50,110
+بده أشيل كل T و أحط مكانها zero بصير E و ال zero
+
+872
+01:40:50,110 --> 01:40:55,810
+اللي هو بواحد في cosine صفر اللي هو بواحد sin صفر
+
+873
+01:40:55,810 --> 01:41:00,870
+بصفر يبقى بالشكل اللي عندنا هذايبقى هذه المعادلة
+
+874
+01:41:00,870 --> 01:41:06,250
+بتعطينا ان c1 يساوي كده؟ يساوي 1 نجي ال initial
+
+875
+01:41:06,250 --> 01:41:12,490
+condition الثاني y prime عند 0 بدر ساوي 0 implies
+
+876
+01:41:12,490 --> 01:41:24,420
+ان 0 بدر ساوي ناقص 2 وهذه بقدرش؟ ب1 في c1لأن هذا
+
+877
+01:41:24,420 --> 01:41:31,780
+في هنا بزيرو هنا بواحد هنا بزيرو يبقى بس C واحد
+
+878
+01:41:31,780 --> 01:41:39,140
+اللي بعده زائد واحد فيه صين زيرو بزيرو كوصين صفر
+
+879
+01:41:39,140 --> 01:41:46,700
+واحد يبقى زائد C اتنين يبقى C اتنين بناء عليه صار
+
+880
+01:41:46,700 --> 01:41:54,270
+عندنا C اتنين بده يساوي اتنين C واحدسي واحد عندى
+
+881
+01:41:54,270 --> 01:42:01,350
+بقداش يبقى هادول اتنين مع بعض بدي خليلي انه C2
+
+882
+01:42:01,350 --> 01:42:06,730
+يساوي قداش اتنين يبقى صار ال solution
+
+883
+01:42:12,490 --> 01:42:23,970
+C1-C2T C1-C2T C1-C2T C1
+
+884
+01:42:23,970 --> 01:42:26,470
+-C2T
+
+885
+01:42:34,410 --> 01:42:39,490
+احنا نظري انتهينا منه ال section لكن راح حط بشغلة
+
+886
+01:42:39,490 --> 01:42:44,290
+very important في ال exercises تبقى المرة الجاية
+
+887
+01:42:44,290 --> 01:42:48,810
+بنشرح هذه النقطة و بناخد بعض الأمثلة عليها و بعدين
+
+888
+01:42:48,810 --> 01:42:52,530
+بنخش في ال section اللي بعده ان شاء الله
+
diff --git a/PL9fwy3NUQKwa8ZDfSFGn6H8xVFLzqmCZC/QjmVIa7skBA.srt b/PL9fwy3NUQKwa8ZDfSFGn6H8xVFLzqmCZC/QjmVIa7skBA.srt
new file mode 100644
index 0000000000000000000000000000000000000000..3feba3e6684547ff111ba632e2607bf54629d07e
--- /dev/null
+++ b/PL9fwy3NUQKwa8ZDfSFGn6H8xVFLzqmCZC/QjmVIa7skBA.srt
@@ -0,0 +1,2684 @@
+1
+00:00:10,000 --> 00:00:12,200
+بسم الله الرحمن الرحيم
+
+2
+00:00:14,730 --> 00:00:20,350
+لازلنا في نفس الشفرة تلاتة ابتدأنا من section تلاتة
+
+3
+00:00:20,350 --> 00:00:25,730
+واحد بالمعادلة a y double prime زائد b y prime زائد c y
+
+4
+00:00:25,730 --> 00:00:30,390
+بده يساوي zero فرضنا انه عندي حل على الصيغة y
+
+5
+00:00:30,390 --> 00:00:35,710
+تساوي e أس r t وصلنا لل characteristic equation على
+
+6
+00:00:35,710 --> 00:00:40,640
+شكل ar تربيع زائد br زائد c يساوي zero و روحنا
+
+7
+00:00:40,640 --> 00:00:45,720
+جيبنا جذور هذه المعادلة فكانت على الشكل التالي
+
+8
+00:00:45,720 --> 00:00:49,820
+ناقص b زائد أو ناقص الجذر التربيعي لـ b تربيع ناقص 
+
+9
+00:00:49,820 --> 00:00:55,400
+أربعة ac على اثنين a واخدنا اللي هو حالتين
+
+10
+00:00:55,400 --> 00:01:00,400
+الحالة الأولى لو كان المميز هذا اللي هو b تربيع
+
+11
+00:01:00,400 --> 00:01:05,840
+ناقص أربعة ac greater than zero وعرفنا انه بطلع
+
+12
+00:01:05,840 --> 00:01:12,100
+عندي قيمتين لـ r و اتنتين are real وصار الحل in
+
+13
+00:01:12,100 --> 00:01:16,820
+general c واحد e r واحد t زائد c اثنين e r اثنين t
+
+14
+00:01:16,820 --> 00:01:21,840
+والمحاضرة الماضية اللي كان section تلاتة
+
+15
+00:01:21,840 --> 00:01:26,240
+أربعة قلنا لو طلعت القيمة اللي تحت الجذر اللي هو
+
+16
+00:01:26,240 --> 00:01:31,480
+المميز b تربيع ناقص أربعة ac أقل من ال zero
+
+17
+00:01:31,480 --> 00:01:37,410
+وقلنا هذا بيصير كمية تخيلية أو الحل بيكون عدد
+
+18
+00:01:37,410 --> 00:01:43,010
+تخيلي وبالتالي عملنا شوية اختصارات وحطينا الحل على
+
+19
+00:01:43,010 --> 00:01:50,650
+صيغة e أس lambda t افتحه c1 cos mu t زائد c2 sin mu t
+
+20
+00:01:50,650 --> 00:01:56,710
+يبقى أخدنا حالتين أن الجذور حقيقية ومختلفة الجذور
+
+21
+00:01:56,710 --> 00:02:02,560
+اثنين تخيليين ومترافقين الآن بنجي للحالة الثالثة
+
+22
+00:02:02,560 --> 00:02:08,360
+والأخيرة لو كان المميز اللي هو b تربيع ناقص 4ac بده
+
+23
+00:02:08,360 --> 00:02:13,360
+يساوي zero إذا الجذر هذا كله بطير بالزائد والنقص
+
+24
+00:02:13,360 --> 00:02:19,100
+ولا يبقى عندي إلا ناقص b على 2a يبقى بصير
+
+25
+00:02:19,100 --> 00:02:24,920
+الجذور حقيقية ومكررة من هنا كان عنوان ال section
+
+26
+00:02:24,920 --> 00:02:32,110
+بيدينا repeated roots الجذور المكررة يعني لو حصل
+
+27
+00:02:32,110 --> 00:02:38,530
+أن الجذور تبع المعادلة المميزة هذه اثنين جذران
+
+28
+00:02:38,530 --> 00:02:45,270
+حقيقيان ومكرران بدنا نعرف شو شكل الحل للمعادلة
+
+29
+00:02:45,270 --> 00:02:49,830
+ال تفاضلية إذا اثنين بيتساوى معناته ماعنديش إلا مين
+
+30
+00:02:49,830 --> 00:02:56,200
+حلا واحدا يبقى مادام r واحد يساوي r اثنين هما
+
+31
+00:02:56,200 --> 00:03:04,560
+الجذران يساوي e أس ناقص b على اثنين a we have
+
+32
+00:03:04,560 --> 00:03:15,160
+one solution حل واحد اللي هو y واحد يساوي e أس
+
+33
+00:03:15,160 --> 00:03:23,900
+ناقص b على اثنين a كله مضروب في من؟ في t طيب كويس
+
+34
+00:03:23,900 --> 00:03:27,940
+هذه معادلة من الرتبة الثانية إذا لها حلين وليس
+
+35
+00:03:27,940 --> 00:03:33,600
+حلا واحدة إذا بنروح نبحث عن حل ثاني الحل الثاني
+
+36
+00:03:33,600 --> 00:03:39,940
+بنحاول نحصل عليه بدلالة من؟ بدلالة الحل الأول يبقى
+
+37
+00:03:39,940 --> 00:03:46,480
+بداجي أقول suppose that افترضوا أنه we have
+
+38
+00:03:46,480 --> 00:03:49,460
+another
+
+39
+00:04:06,910 --> 00:04:17,410
+على الشكل التالي هسمي y يساوي v of t في y1 of t من
+
+40
+00:04:17,410 --> 00:04:24,820
+الـ y1 اللي هي هذه يعني اللي هو بده يساوي v of t في
+
+41
+00:04:24,820 --> 00:04:36,080
+من في ال e أس ناقص b على اثنين a كله في من في t
+
+42
+00:04:36,080 --> 00:04:41,700
+يبقى هذا شكل الحل الثاني بالشكل اللي قدامنا هذا
+
+43
+00:04:41,700 --> 00:04:47,960
+طيب مين هي v of t هذه function of t بدنا نحاول نجد
+
+44
+00:04:47,960 --> 00:04:56,700
+شو شكلها الآن نحن سنجد
+
+45
+00:04:56,700 --> 00:05:00,200
+طريقة
+
+46
+00:05:00,200 --> 00:05:04,080
+نحو
+
+47
+00:05:04,080 --> 00:05:14,420
+v of t كالتالي
+
+48
+00:05:19,830 --> 00:05:28,510
+y تساوي v of t في e أس ناقص b على اثنين a كله في
+
+49
+00:05:28,510 --> 00:05:28,750
+t
+
+50
+00:05:34,330 --> 00:05:39,810
+هذا الحل مرتين وأعوضه في المعادلة الأصلية
+
+51
+00:05:39,810 --> 00:05:45,490
+وبالتالي سنصل إلى شكل v of t إيش بدي يكون إذا بروح
+
+52
+00:05:45,490 --> 00:05:49,930
+أشتق هذا مرتين المرة الأولى بداجي أقول y prime
+
+53
+00:05:49,930 --> 00:05:58,550
+يساوي المشتقة الأولى v prime of t في e أس ناقص b
+
+54
+00:05:58,550 --> 00:06:04,910
+على اثنين a في t هذا مشتقة الأولى في الدالة الثانية
+
+55
+00:06:04,910 --> 00:06:10,870
+زائد الأولى في v of t مشتقة الثانية بناقص
+
+56
+00:06:10,870 --> 00:06:19,810
+فبتيجي ناقص v of t في مين؟ في ال b على 2a في ال e
+
+57
+00:06:19,810 --> 00:06:28,760
+أس ناقص b على 2a كله في t أو لو أخذنا ال
+
+58
+00:06:28,760 --> 00:06:34,820
+exponential هذه عامل مشترك بصير المثل كالتالي اللي
+
+59
+00:06:34,820 --> 00:06:38,940
+هو باختصاره ما بديش أكتب v of t بدي أكتب v prime
+
+60
+00:06:38,940 --> 00:06:45,420
+دوري يبقى بدي أكتب هذا ال v prime وهنا بضل عندي
+
+61
+00:06:45,420 --> 00:06:55,200
+ناقص b على 2a كله في v في ال e أس ناقص b على 2a في
+
+62
+00:06:55,200 --> 00:07:00,820
+t يبقى أخدت ال exponential كعامل مشترك أو common
+
+63
+00:07:00,820 --> 00:07:04,820
+factor من الشجتين وخليته برا وبظل عندي هنا v
+
+64
+00:07:04,820 --> 00:07:10,940
+prime وبظل هنا v بس في ال b على 2a الآن بدنا نروح
+
+65
+00:07:10,940 --> 00:07:17,340
+نجيب المشتقة الثانية ال y double prime إذا مشتقة حاصل ضرب
+
+66
+00:07:17,340 --> 00:07:22,620
+دالتين مشتقة الأولى v prime
+
+67
+00:07:23,520 --> 00:07:30,640
+في الدالة الثانية في e أس ناقص b على اثنين a في t
+
+68
+00:07:31,520 --> 00:07:38,620
+بنشتق كمان مرة يبقى ناقص هي ال v double prime زي ما هي وال
+
+69
+00:07:38,620 --> 00:07:46,260
+أس اللي هو b على 2a في ال exponential e أس ناقص b
+
+70
+00:07:46,260 --> 00:07:54,340
+على 2a في t هيشتق الأولى ومشتقت حاصل ضرب دالتين
+
+71
+00:07:55,050 --> 00:08:00,650
+ناقص بإن نشتق ثانية كمان حاصل ضرب دالتين يبقى هذا
+
+72
+00:08:00,650 --> 00:08:11,880
+v double prime في b على 2a في e أس ناقص b على 2a كله في t هي
+
+73
+00:08:11,880 --> 00:08:16,000
+مشتقة الأولى في الثانية زائد لكن الإشارة ناقص هتخش
+
+74
+00:08:16,000 --> 00:08:23,620
+على الاثنين يبقى بتجيني ناقص v زي ما هي هذه هيجي
+
+75
+00:08:23,620 --> 00:08:29,180
+كمان ناقص فبصير زائد ويجي الأس كمان مرة يبقى b
+
+76
+00:08:29,180 --> 00:08:36,280
+تربيع على أربعة a تربيع في ال e أس ناقص b على
+
+77
+00:08:36,280 --> 00:08:44,600
+اثنين a كله في t طيب هذا الكلام بده يساوي بده آخد
+
+78
+00:08:44,600 --> 00:08:50,580
+ال exponential برا عامل مشترك هذه هي هذه بالضبط
+
+79
+00:08:50,580 --> 00:08:56,200
+تمامًا صحيح ولا لا يبقى اثنين مضروبة في واحدة فيهم
+
+80
+00:08:56,200 --> 00:09:01,640
+اثنين مع اثنين اللي تحت يتم اختصارها إذا بضل أن ال
+
+81
+00:09:01,640 --> 00:09:11,270
+v double prime ناقص b على a في ال v prime هيحذفان الاثنتين
+
+82
+00:09:11,270 --> 00:09:18,170
+هدول مرة واحدة زائد v في ال b تربيع على أربعة a
+
+83
+00:09:18,170 --> 00:09:22,710
+تربيع وكل هذا ههه في main في ال exponential
+
+84
+00:09:22,710 --> 00:09:31,140
+function e أس ناقص b على اثنين a كله في t الآن جبت
+
+85
+00:09:31,140 --> 00:09:35,480
+y prime و y double prime بدي أرجع أعوض في المعادلة
+
+86
+00:09:35,480 --> 00:09:43,500
+main star يبقى substitute in
+
+87
+00:09:43,500 --> 00:09:53,840
+the differential equation star نحصل على يبقى عندي
+
+88
+00:09:53,840 --> 00:09:59,580
+إيش؟ a في ال y double prime مظبوط؟ يعني يا بنات a
+
+89
+00:09:59,580 --> 00:10:03,200
+بدي أضربها في المقدار هذا كله يبقى إيش بيصير
+
+90
+00:10:03,200 --> 00:10:12,660
+عندنا a في ال v double prime ناقص b في ال v prime
+
+91
+00:10:12,660 --> 00:10:22,000
+زائد b تربيع على أربعة a فقط بدون تربيع في ال v
+
+92
+00:10:23,480 --> 00:10:27,560
+ضربتها في a بطير a مع ال a تربيع بيبقى ال a بس
+
+93
+00:10:27,560 --> 00:10:33,280
+في المقام يبقى هذا كله من ال a في ال y double
+
+94
+00:10:33,280 --> 00:10:38,740
+prime طبعًا ال exponential هخليها للأخر خلاص للكل
+
+95
+00:10:38,740 --> 00:10:43,980
+الآن b في ال y prime وين ال y prime هيها هضربها
+
+96
+00:10:43,980 --> 00:10:53,580
+في b يبقى إيش بيصير زائد b في ال v prime ناقص b تربيع على
+
+97
+00:10:53,580 --> 00:11:00,110
+اثنين a في ال v خلصنا منها بقى ال exponential للأخر
+
+98
+00:11:00,110 --> 00:11:05,710
+هاخده عامل مشترك من الكل قال زائد c في ال y هي ال
+
+99
+00:11:05,710 --> 00:11:12,030
+y اللي هي v في ال exponential يبقى زائد c في ال v
+
+100
+00:11:12,030 --> 00:11:19,410
+وهذا كله مضروب في ال exponential e أس ناقص b على
+
+101
+00:11:19,410 --> 00:11:26,930
+2a في t كله بده يساوي zero سؤال هل يمكن للـ
+
+102
+00:11:26,930 --> 00:11:30,990
+exponential في يوم من الأيام أنه يساوي zero إذا
+
+103
+00:11:30,990 --> 00:11:36,510
+بنقدر نقسم عليه الطرفين بدون مشاكل صفر على أي رقم
+
+104
+00:11:36,510 --> 00:11:41,890
+يساوي صفر طارت هذه طيب يطلعي لهذه bv prime وهذه
+
+105
+00:11:41,890 --> 00:11:47,830
+السالب bv prime يبقى مع السلامة طيب نيجي نشوف شو
+
+106
+00:11:47,830 --> 00:11:55,440
+اللي حصل عندنا صار عندنا مين av double prime الباقي هذه
+
+107
+00:11:55,440 --> 00:12:01,340
+فيها v وهذه فيها v وهذه فيها v إذا بقدر آخد v
+
+108
+00:12:01,340 --> 00:12:09,740
+عامل مشترك من مين؟ من الكل بس اطلعيلي لهذه وهذه مش
+
+109
+00:12:09,740 --> 00:12:15,170
+هي بس الفرق في ال coefficients هذه ربع المقدار وهذه
+
+110
+00:12:15,170 --> 00:12:21,570
+نصف المقدار إذا بضل ربع المقدار بإشارة سالب يبقى
+
+111
+00:12:21,570 --> 00:12:31,790
+زائد سالب b تربيع على أربعة a زائد c كل هذا
+
+112
+00:12:31,790 --> 00:12:37,550
+الكلام في v بده يساوي zero مرة ثانية بده أقولها
+
+113
+00:12:37,550 --> 00:12:44,470
+هذه هي نزلنا هذه كما هي اختصرنا هذه مع هذه نيجي هذه
+
+114
+00:12:44,470 --> 00:12:50,790
+و هذه ربع b تربيع على a في v ونقص نصف b تربيع على
+
+115
+00:12:50,790 --> 00:12:58,410
+a في v معناته هذا بيبقى سالب ربع b تربيع على a في
+
+116
+00:12:58,410 --> 00:13:03,370
+v يبقى هاي سالب ربع b تربيع على a في v وهي ال v
+
+117
+00:13:03,370 --> 00:13:09,580
+بزائد constant c يبقى هاي زائد من c إيه لخاطر أوحد
+
+118
+00:13:09,580 --> 00:13:14,140
+المقامات لهدول وأشوف لوين بده توصلني يبقى لو
+
+119
+00:13:14,140 --> 00:13:21,020
+وحدنا المقامات لهدول إيش بصير عندنا av double prime زائد
+
+120
+00:13:21,020 --> 00:13:27,720
+كله يا بنات على قداش على 4a إيش رأيك آخد سالب برا
+
+121
+00:13:28,380 --> 00:13:35,900
+أريحلي يبقى بصير عندي أنا كداش b تربيع ناقص أربعة
+
+122
+00:13:35,900 --> 00:13:42,360
+ac كله في ال v بده يساوي zero صحيح؟ طب إيه شو
+
+123
+00:13:42,360 --> 00:13:49,050
+رأيك هنا؟ b تربيع ناقص أربعة ac يبقى كم؟ يبقى ال
+
+124
+00:13:49,050 --> 00:13:54,470
+term الأخير هذا مع السلامة يبقى هذا كمان بيروح ب
+
+125
+00:13:54,470 --> 00:14:00,790
+zero because إن b تربيع ناقص أربعة ac تفاجئنا
+
+126
+00:14:00,790 --> 00:14:05,950
+علينا صفر من مين؟ من البداية يبقى إيش ضلّ
+
+127
+00:14:05,950 --> 00:14:11,810
+النتيجة؟ av double prime بده يساوي zero يبقى لو
+
+128
+00:14:11,810 --> 00:14:17,470
+قسمنا على a بصير v double prime يساوي zero بنفع
+
+129
+00:14:17,470 --> 00:14:22,750
+نقسم على a؟ بنفع لأن a لا يمكن أن تساوي zero لو
+
+130
+00:14:22,750 --> 00:14:27,310
+كانت ال a ب zero لانزل رتبة المعادلة لما الرتبة
+
+131
+00:14:27,310 --> 00:14:30,530
+الثانية إلى الرتبة الأولى واحنا شغلنا في الرتبة
+
+132
+00:14:30,530 --> 00:14:34,870
+الثانية يبقى a لا يمكن أن تساوي zero بأي حالة من
+
+133
+00:14:34,870 --> 00:14:39,290
+الأحوال يبقى بنجسم عليها without problems بدون أي
+
+134
+00:14:39,290 --> 00:14:45,110
+مشكلة طيب يبقى لو كملنا مرتين بنحصل على شكل ال v of
+
+135
+00:14:45,110 --> 00:14:49,830
+t اللي روحنا قلنا هنا we shall find الشكل تبعها
+
+136
+00:14:49,830 --> 00:14:53,830
+بدي أكمل مرتين بحصل على الشكل اللي بدي إياه يبقى
+
+137
+00:14:53,830 --> 00:14:59,250
+بناء على لو كملت مرة واحدة بصير v prime of t يساوي
+
+138
+00:14:59,250 --> 00:15:05,390
+كده؟ c1 إن كملت كمان مرة يبقى لو كملنا كمان مرة
+
+139
+00:15:05,390 --> 00:15:14,070
+بصير v of t بدي يساوي c1 t زائد c2 طيب تعال نتفهم
+
+140
+00:15:14,070 --> 00:15:20,870
+على ال constants هدول c2 عبارة عن رقم لو أنا أخده
+
+141
+00:15:20,870 --> 00:15:29,170
+هذا رقم غير الصفر بصير v c1 t زائد رقم الرقم هذا لما
+
+142
+00:15:29,170 --> 00:15:33,790
+أرجع أضربه في الحل اللي فوق برقم يعني إيش يعني
+
+143
+00:15:33,790 --> 00:15:38,970
+كررتي الحل اللي عندي صحيح ولا لا تكرار لا فائدة
+
+144
+00:15:38,970 --> 00:15:45,550
+منه إذا ممكن آخد c2 بقداش بصفر حتى لا يحدث تكرار
+
+145
+00:15:45,860 --> 00:15:52,440
+يبقى اتفاقنا c2 بـ 0 v of t قال لي constant في t هل
+
+146
+00:15:52,440 --> 00:15:56,860
+ال constant له تأثير على الحل؟ لا ما عنديش يبقى لو
+
+147
+00:15:56,860 --> 00:16:01,340
+عندي حل أضربه في constant والله مية constant بظل
+
+148
+00:16:01,340 --> 00:16:07,300
+هو حل يبقى هنا v of t in general هي t وبالتالي
+
+149
+00:16:07,300 --> 00:16:18,100
+بقدر آخد c1 بـ 1 و c2 بـ 0 يبقى باجي بقول i take خدلي c1
+
+150
+00:16:18,100 --> 00:16:29,000
+تساوي 1 and c2 تساوي 0 we get بنحصل على v of t بده
+
+151
+00:16:29,000 --> 00:16:36,480
+يساوي t فقط  ده غير يبقى باجي بقول the second
+
+152
+00:16:36,480 --> 00:16:39,560
+solution
+
+153
+00:16:59,270 --> 00:17:09,260
+السؤال هو هل هذا الحل مع الحل الأولاني y1 of t
+
+154
+00:17:09,260 --> 00:17:17,840
+بيكونولي مجموعة الحلول الأساسية الإجابة الله أعلم عن
+
+155
+00:17:17,840 --> 00:17:23,280
+الـ wronskian إذا كان wronskian لا يساوي 0 يبقى اثنين
+
+156
+00:17:23,280 --> 00:17:26,300
+هذول يجيبولي ال fundamental set of solutions
+
+157
+00:17:26,300 --> 00:17:31,020
+وبالتالي يجيبولي شكل ال general solution إذا بدنا
+
+158
+00:17:31,020 --> 00:17:36,240
+نروح نحسب wronskian تبع من تبع الحلّين هذول
+
+159
+00:17:36,240 --> 00:17:42,180
+ونشوف هل بيقدر الغرض أم لا إذا قدّوا الغرض بكونوا
+
+160
+00:17:42,180 --> 00:17:47,640
+انتهينا من مسألتنا وإذا ما قدّوش بصير فيه كلام ثاني
+
+161
+00:17:50,210 --> 00:17:56,290
+طيب إذا بادروح آخد ال wronskian تبع الحل الأول والحل
+
+162
+00:17:56,290 --> 00:18:01,870
+الثاني as a function of t الحل الأول e أس ناقص b
+
+163
+00:18:01,870 --> 00:18:09,230
+على اثنين a في t والحل الثاني t في e أس ناقص b على
+
+164
+00:18:09,230 --> 00:18:15,770
+اثنين a في t بنشتغل الحل الأول يبقى ناقص b على
+
+165
+00:18:15,770 --> 00:18:24,410
+اثنين a في ال e أس ناقص b على اثنين a في t b على
+
+166
+00:18:24,410 --> 00:18:31,010
+اثنين a كله في t exponential مشتقتها نفسها ضرب
+
+167
+00:18:31,010 --> 00:18:37,770
+مشتقة الأس هذه مشتقة حاصل ضرب دالتين يبقى مشتقة
+
+168
+00:18:37,770 --> 00:18:43,370
+الدالة الأولى واحد بيظل ال exponential فقط لا غير
+
+169
+00:18:43,370 --> 00:18:52,470
+ناقص b على اثنين a في t في e أس ناقص b على اثنين a
+
+170
+00:18:52,470 --> 00:18:56,860
+في t اللي هي مشتقة الدالة الثانية في الدالة
+
+171
+00:18:56,860 --> 00:19:03,660
+الأولى اللي هي t نفك المحدد هذا يبقى بطل عندنا e أس
+
+172
+00:19:03,660 --> 00:19:12,180
+ناقص b على a كله في t مظبوط؟ نصف زائد نصف اللي هو حاصل
+
+17
+
+201
+00:22:43,290 --> 00:22:48,990
+words فحطينا 2 في الـmain في section 1 طيب نبدأ الآن
+
+202
+00:22:48,990 --> 00:22:55,050
+ناخد أمثلة على هذا الـsection أو على repeat تدرس
+
+203
+00:22:55,050 --> 00:23:03,330
+تطبيق عملي لشيء اللي شفناه هنا اللي 
+
+204
+00:23:03,330 --> 00:23:06,870
+بتسأل مين وماذا تقول وأين السائلة
+
+205
+00:23:09,370 --> 00:23:13,970
+بعد نهاية هذا الـsection بيعطيك اتنين قول ليعقوب
+
+206
+00:23:13,970 --> 00:23:20,070
+عليه السلام فصبر جميل عصى الله أن يأتيني بهم جميعًا
+
+207
+00:23:20,070 --> 00:23:27,090
+يعني يأتِي بيوسف وأخوه بنيامين تمام؟ يبقى بناجي لا 
+
+208
+00:23:27,090 --> 00:23:27,690
+examples
+
+209
+00:23:39,510 --> 00:23:45,650
+السؤال الأول هو
+
+210
+00:23:45,650 --> 00:23:47,850
+سؤال 8 من الكتاب
+
+211
+00:24:04,520 --> 00:24:16,680
+16y double prime زائد 24y prime زائد 9y يساوي 0
+
+212
+00:24:25,580 --> 00:24:30,420
+سؤال مرة ثانية، ماطيني معادلة تفاضلية من الرتبة
+
+213
+00:24:30,420 --> 00:24:35,060
+الثانية والـconstant coefficients بمعاملات ثابتة
+
+214
+00:24:35,060 --> 00:24:40,530
+وطلب مني إيجاد الحل العام لهذه المعادلة يبقى
+
+215
+00:24:40,530 --> 00:24:44,390
+التكتيك كما مشينا في حالة الـcomplex roots وكما
+
+216
+00:24:44,390 --> 00:24:48,530
+مشينا في حالة الـreal different roots يبقى بداجة
+
+217
+00:24:48,530 --> 00:24:56,790
+أقول له افترض let Y تساوي E أس R T مالهاش
+
+218
+00:24:56,790 --> 00:25:01,610
+solution then
+
+219
+00:25:06,290 --> 00:25:17,690
+A characteristic equation is يبقى على الشكل التالي
+
+220
+00:25:17,690 --> 00:25:30,130
+وراعط لي 16R تربيع زائد 24R زائد 9 بدها تساوي 0
+
+221
+00:25:30,130 --> 00:25:37,060
+أولًا جينا حللناها إلى قوسين هالشكل لأن هذا بيصير
+
+222
+00:25:37,060 --> 00:25:45,010
+4R وهنا 4R وهنا 3 وهنا 3 2 زائد
+
+223
+00:25:45,010 --> 00:25:50,290
+3 و 4 واطماش واطماش 24 وطلع نفس
+
+224
+00:25:50,290 --> 00:25:55,630
+القوس يعني بدها تساوي 0 هذا معناه أنه 4R
+
+225
+00:25:55,630 --> 00:26:01,850
+زائد 3 لكل تربيع بدها تساوي 0 يبقى صار
+
+226
+00:26:01,850 --> 00:26:07,610
+هنا repeated roots يبقى بصير عندنا هنا الـR1
+
+227
+00:26:07,610 --> 00:26:15,160
+تساوي R2 تساوي سالب 3/4 يبقى طالع عندنا
+
+228
+00:26:15,160 --> 00:26:20,280
+real repeated roots يبقى هذه اللي بنسميها الـreal
+
+229
+00:26:20,280 --> 00:26:29,680
+repeated roots جذور حقيقية ومكررة يبقى بصير الـ
+
+230
+00:26:29,680 --> 00:26:35,000
+general solution على الشكل التالي يبقى الـthe general
+
+231
+00:26:35,000 --> 00:26:37,480
+solution
+
+232
+00:26:38,920 --> 00:26:50,700
+is y تساوي c1 زائد c2t في E أس r تي  r بـ3/4 
+
+233
+00:26:50,700 --> 00:26:59,660
+بـ4 يبقى بـالسالب 3/4 اللي هو كله في من في T
+
+234
+00:26:59,660 --> 00:27:07,520
+هذا الحل العام للمعادلة التفاضلية ناخد كمان مثال
+
+235
+00:27:08,230 --> 00:27:17,270
+يبقى example 2 سؤال 14 من الكتاب بيقول solve the
+
+236
+00:27:17,270 --> 00:27:24,610
+initial value problem اللي هو مين؟ y double prime
+
+237
+00:27:24,610 --> 00:27:32,510
+زائد 4y prime زائد 4y تساوي 0 ومعطيني
+
+238
+00:27:32,510 --> 00:27:37,430
+two initial conditions y عند الـ-1 يساوي 
+
+239
+00:27:37,430 --> 00:27:44,800
+2 و y prime عند الـ-1 يساوي مين؟ 1
+
+240
+00:27:44,800 --> 00:27:48,300
+قال لي solve الـinitial condition الـinitial value
+
+241
+00:27:48,300 --> 00:27:51,860
+problem اللي عندنا يبقى اللي بقوله solution
+
+242
+00:27:56,700 --> 00:28:02,340
+يبقى تكتيك الحل يا بنات زي المثال السابق تمامًا بس
+
+243
+00:28:02,340 --> 00:28:07,880
+بعد ما نجيب الـC1 والـC2 بدنا نروح باستخدام
+
+244
+00:28:07,880 --> 00:28:14,300
+الشروط الابتدائية اللي معطيني إياها إن أروح أجيب من
+
+245
+00:28:14,300 --> 00:28:18,810
+أجيب الحلبقى بقى بقى بقى بقى بقى بقى بقى بقى بقى
+
+246
+00:28:18,810 --> 00:28:24,590
+بقى
+
+247
+00:28:39,130 --> 00:28:45,490
+المعادلة المميزة R تربيع زائد 4R زائد 4R
+
+248
+00:28:46,920 --> 00:28:53,820
+0 هذي اللي هي عبارة عن (R زائد 2) لكل تربيع
+
+249
+00:28:53,820 --> 00:29:01,340
+بدها تساوي 0 هذا معناه أن R1 بدها تساوي R
+
+250
+00:29:01,340 --> 00:29:06,160
+2 بدها تساوي -2 اللي هي repeated roots
+
+251
+00:29:06,160 --> 00:29:13,440
+يبقى بيصير هنا الـthe general solution
+
+252
+00:29:16,620 --> 00:29:29,720
+Y تساوي C1 زائد C2T في E أس -2T نشتاقها بالمرة
+
+253
+00:29:29,720 --> 00:29:36,720
+نشتاقها بالمرة يلا هاي الـy prime يساعد هذه مشتقة
+
+254
+00:29:36,720 --> 00:29:44,480
+حاصل ضرب دالتين يبقى مشتقة c1 بـ0 ومشتقة c2t بـ
+
+255
+00:29:44,480 --> 00:29:54,500
+c2 يبقى هاي c2 في E أس -2t مشتقة الدالة الأولى
+
+256
+00:29:54,500 --> 00:29:58,220
+في الثانية زائد الدالة الثانية اللي هو الجواز في
+
+257
+00:29:58,220 --> 00:30:05,300
+مشتقة E أس -2T اللي هي -2 E أس -2T يبقى
+
+258
+00:30:05,300 --> 00:30:16,820
+-2 في C1 زائد C2T في E أس -2T هي جيبنا الدالة
+
+259
+00:30:16,820 --> 00:30:22,060
+ومشتقتها الآن بدنا نروح للـinitial condition اللي
+
+260
+00:30:22,060 --> 00:30:27,800
+قال الـY عند الـ-1 يساوي 2 Y عند الـ-
+
+261
+00:30:27,800 --> 00:30:33,580
+1 بدها تساوي 2 implies يبقى بدي أشيل الـY و
+
+262
+00:30:33,580 --> 00:30:35,220
+أكتب مكانها قداش
+
+263
+00:30:40,460 --> 00:30:54,300
+يبقى بيصير C1-C2 يبقى هنا C1-C2 كلها في E وسالب 2
+
+264
+00:30:54,300 --> 00:31:00,600
+في -1 يعني بيصير E تربيع فقط لا غير يبقى بـE
+
+265
+00:31:00,600 --> 00:31:06,600
+تربيع أيش رأيك أنا ما بديش الـE تربيع عادي بدي أضغط في
+
+266
+00:31:06,600 --> 00:31:10,900
+E سالب 2 مشان أخلي الكونوستانس لحالهم يبقى
+
+267
+00:31:10,900 --> 00:31:16,680
+بناء عليه بيصير عندنا هنا C1 ناقص C2 يساوي
+
+268
+00:31:16,680 --> 00:31:22,650
+2 E سالب 2 الآن بدنا نجي للـinitial condition
+
+269
+00:31:22,650 --> 00:31:27,170
+الثاني الـy prime عند الـ-1 بدها تساوي 1
+
+270
+00:31:27,170 --> 00:31:33,150
+إذا بدنا نجي نشيل المشتقة الأولى ونكتب لها قداش 1
+
+271
+00:31:33,150 --> 00:31:39,190
+ونشيل كل T ونحط مكانها -1 يبقى هاي 1
+
+272
+00:31:39,190 --> 00:31:46,250
+يساوي C2 هاي C2 في E تربيع
+
+273
+00:31:50,790 --> 00:31:56,490
+وصلنا لـ-2C1
+
+274
+00:31:56,490 --> 00:31:59,530
+-C2
+
+275
+00:32:07,240 --> 00:32:13,040
+يبقى هذه يا بنات بصير 1 تساوي C2 E تربيع ناقص
+
+276
+00:32:13,040 --> 00:32:22,100
+2C1 E تربيع زائد 2C2 E تربيع يعني صارت
+
+277
+00:32:22,100 --> 00:32:32,960
+1 تساوي 3C2 أو 3C2 ناقص
+
+278
+00:32:32,960 --> 00:32:39,620
+2C1 كله في الـE تربيع يعني صار عندنا مين؟
+
+279
+00:32:39,620 --> 00:32:46,960
+صار عندنا 3C2 ناقص 2C1 كله بدها
+
+280
+00:32:46,960 --> 00:32:54,750
+تساوي E سالب 2 تمام شو رأيك لو جيت ضربت
+
+281
+00:32:54,750 --> 00:33:00,610
+المعادلة الأولى في 2 المعادلة الأولى في 2
+
+282
+00:33:00,610 --> 00:33:05,610
+اللي فوق هذه يبقى هذه بدنا نضربها في 2 لو ضربتها
+
+283
+00:33:05,610 --> 00:33:12,090
+في 2 بصير عند مين بصير -2C2
+
+284
+00:33:12,090 --> 00:33:18,810
+زائد 2C1 بدها تساوي 4 أو 2 ناقص
+
+285
+00:33:18,810 --> 00:33:24,330
+2 ضربت المعادلة فوق كلها في 2 طيب نجمع بصير
+
+286
+00:33:24,330 --> 00:33:32,030
+هدول مع السلامة بضل أنا قداش يا بنات بضل C2 تساوي
+
+287
+00:33:32,030 --> 00:33:39,620
+5 E ناقص 2 بدي C1 برجع أعوض في المعادلة اللي
+
+288
+00:33:39,620 --> 00:33:51,120
+فوق هذا بدها تعطيك أن C1-5E^-2 تساوي 2 E^-2 هذا
+
+289
+00:33:51,120 --> 00:34:00,500
+بدها تعطيك أن C1 تساوي 7 E^-2 جبت له C1 و C2 إذا 
+
+290
+00:34:00,500 --> 00:34:06,040
+بجيب أقول له solution of
+
+291
+00:34:12,250 --> 00:34:22,040
+يبقى هاي Y تساوي جالي C1 يبقى C1 وينك يا C1 اللي هي
+
+292
+00:34:22,040 --> 00:34:31,320
+7 E أس -2 C1 7 E أس -2 و C2
+
+293
+00:34:31,320 --> 00:34:40,700
+اللي هي بزايد 5 E أس -2 في T كلها في
+
+294
+00:34:40,700 --> 00:34:48,750
+قداش في E أس -2 T شو رأيك بدي أطلع E أس -
+
+295
+00:34:48,750 --> 00:34:54,990
+2 برة يبقى لو طلعناها برة بصير الحل Y يساوي
+
+296
+00:34:54,990 --> 00:35:05,090
+7 زائد 5T في E أس -2T -2
+
+297
+00:35:05,090 --> 00:35:08,370
+أو إن شئتم تحطوها بشكل آخر
+
+298
+00:35:27,380 --> 00:35:34,560
+أما ما طلبته عن أرقام المسائل ففي نهاية هذا
+
+299
+00:35:34,560 --> 00:35:38,520
+الـsection بعد ما ناخد النقطة الثانية اللي هي 
+
+300
+00:35:38,520 --> 00:35:45,740
+reduction of order حد فيكن أي سؤال فيما سبق 
+
+301
+00:35:45,740 --> 00:35:51,480
+دراسته حول الـrepeated roots يا بناتها؟ أي تساؤل
+
+302
+00:35:51,480 --> 00:35:55,360
+احنا جاهزين؟
+
+303
+00:35:55,360 --> 00:36:02,480
+في
+
+304
+00:36:02,480 --> 00:36:09,740
+أي تساؤل؟ طب نجي لطريقة جديدة اسمها reduction of
+
+305
+00:36:09,740 --> 00:36:24,780
+order reduction of order reduction 
+
+306
+00:36:24,780 --> 00:36:30,200
+of order يعني اختزال للرتبة بدل من الرتبة تبقى رتبة
+
+307
+00:36:30,200 --> 00:36:35,320
+ثانية ننزلها لمن؟ لرتبة أولى، هذه بنستخدمها وإذا 
+
+308
+00:36:35,320 --> 00:36:41,620
+إذا أعطاني أحد الحلول وطلب مني؟ وطلب الحل الثاني 
+
+309
+00:36:41,620 --> 00:36:47,550
+طبعًا السؤال عن معادلة من الرتبة الثانية سواء كانت
+
+310
+00:36:47,550 --> 00:36:51,290
+الـdifferential equation بمعاملات ثابتة أو بغير 
+
+311
+00:36:51,290 --> 00:36:56,130
+المعاملات الثابتة بنفعل هالخطوات بس in general أن
+
+312
+00:36:56,130 --> 00:37:03,030
+نطلع أحد الحلول بحط المعاملات functions وليست
+
+313
+00:37:03,030 --> 00:37:08,090
+constants تمام الكلام اللي قلته هشوفه عمليًا هروح نحطه 
+
+314
+00:37:08,090 --> 00:37:15,970
+عمليًا الآن إن شاء الله فنجيب نقول consider consider
+
+315
+00:37:15,970 --> 00:37:24,650
+the homogeneous differential 
+
+316
+00:37:24,650 --> 00:37:34,290
+equation المعادلة التفاضلية اللي هي Y W prime P of T
+
+317
+00:37:34,290 --> 00:37:41,270
+في Y prime Q of T في Y بدها تساوي 0 وسمينا هذه
+
+318
+00:37:41,270 --> 00:37:43,070
+المعادلة Star
+
+319
+00:37:48,790 --> 00:37:59,770
+نفترض أن الـY1 هي حلول 
+
+320
+00:37:59,770 --> 00:38:11,050
+تبدأ من المقارنة الاختصارية المسألة
+
+321
+00:38:11,050 --> 00:38:11,870
+هو
+
+322
+00:38:15,890 --> 00:38:22,390
+السؤال هو can
+
+323
+00:38:22,390 --> 00:38:30,050
+we determine هل
+
+324
+00:38:30,050 --> 00:38:35,570
+بنقدر نحدد a function
+
+325
+00:38:37,100 --> 00:38:45,940
+v of t such that بحيث أن can have function v of t
+
+326
+00:38:45,940 --> 00:38:56,320
+such that الـy تساوي الـv of t في y one of t is 
+
+327
+00:38:56,320 --> 00:39:01,020
+another solution
+
+328
+00:39:03,530 --> 00:39:14,950
+is another solution of equation  أستاذ ممكن الـthe
+
+329
+00:39:14,950 --> 00:39:19,310
+answer is
+
+330
+00:39:19,310 --> 00:39:30,630
+yes كيف؟ as follows كتالوج علكة
+
+331
+00:39:30,630 --> 00:39:36,120
+الآن من خلال هالسطرين اللي كتبناهم أدركتم مدى
+
+332
+00:39:36,120 --> 00:39:41,160
+العلاقة ما بين موضوع الـreduction of order مع مين؟
+
+333
+00:39:41,160 --> 00:39:45,920
+مع الـrepeated roots نرجع الكلام اللي احنا كاتبينه
+
+334
+00:39:45,920 --> 00:39:51,300
+من جديد نفهم شو اللي احنا كاتبينه وما علاقته بالـ
+
+335
+00:39:51,300 --> 00:39:55,980
+repeated roots التي درسناها قبل قليل
+
+336
+00:40:03,220 --> 00:40:07,840
+يبقى موضوعنا الآن لدراسة المعادلة التفاضلية ستار
+
+337
+00:40:07,840 --> 00:40:12,300
+هو موضوع reduction of order اختزال الرتبة أو تنزيل
+
+338
+00:40:12,300 --> 00:40:16,260
+الرتبة من الرتبة الثانية إلى الرتبة الأولى هذه
+
+339
+00:40:16,260 --> 00:40:20,660
+المعادلة التفاضلية اللي عندنا لم نشترط أن P و Q
+
+340
+00:40:20,660 --> 00:40:25,080
+يكونوا constants لكن في section 3.1 3.2
+
+341
+00:40:25,080 --> 00:40:29,500
+3 3 4 3 5 حتى
+
+342
+00:40:29,500 --> 00:40:34,000
+اللحظة هذه اشترط أن يكون مالهم الـcoefficients are
+
+343
+00:40:34,000 --> 00:40:38,660
+real، المعاملات ثوابت وليست continuous functions،
+
+344
+00:40:38,660 --> 00:40:42,620
+ماهياش دوال متغيرة وإنما دوال كلها ثوابت، الـA
+
+345
+00:40:42,620 --> 00:40:46,000
+constant، الـB constant والـC constant، لكننا لما
+
+346
+00:40:46,000 --> 00:40:51,340
+اشترطنا للـP و للـQ لكن هذا بتعتمد أنه بيعطيني حل
+
+347
+00:40:51,340 --> 00:40:55,680
+وأنا بروح بدور على مين؟ على الحل الثاني لهذه
+
+348
+00:40:55,680 --> 00:41:00,480
+المعادلة التفاضلية بقول افترض أن هو Y1 هو حل
+
+349
+00:41:00,480 --> 00:41:04,780
+المعادلة التفاضلية اللي عندنا Star السؤال هو the
+
+350
+00:41:04,780 --> 00:41:10,500
+question is can we determine بنقدر نحدد دالة V of T
+
+351
+00:41:10,500 --> 00:41:15,540
+بحيث Y تساوي V of T في Y1 of T is another 
+
+352
+00:41:15,540 --> 00:41:21,560
+solution حل آخر للمعادلة Star الإجابة نعم كيف
+
+353
+00:41:21,560 --> 00:41:25,250
+كالتالي يبقى يا بنات احنا الشغل اللي بنشتغله الآن
+
+354
+00:41:25,250 --> 00:41:29,930
+هو نفس الشغل اللي اشتغلناه تو الساعة في حالة
+
+355
+00:41:29,930 --> 00:41:35,290
+repeated roots مع الفارق شو الفارق؟ هناك طلعت R1
+
+356
+00:41:35,290 --> 00:41:39,890
+معروفة ليه -B على 8A واشتغلنا عليها، هنا أنا 
+
+357
+00:41:39,890 --> 00:41:44,770
+مش عارفاها، خليتها بدلالة مين؟ Y1، جد ما يطلع يطلع 
+
+358
+00:41:44,770 --> 00:41:48,850
+أو أيش ما يطلع يطلع أو أيش معطيني إياها خلاص هو
+
+359
+00:41:48,850 --> 00:41:52,670
+معطيني إياها بدأ استخدم وامشي مش يعني E أس -P على
+
+360
+00:41:52,670 --> 00:41:57,090
+2A في T زي ما طلع قبل قليل لا ليس بالضرورة
+
+361
+00:41:58,880 --> 00:42:02,760
+يبقى اللي طلع قبل قليل كان حلقة خاصة لأن المعاملات
+
+362
+00:42:02,760 --> 00:42:06,900
+ثوابت بس هنا المعاملات لم نشترط أنها ثوابت أي 
+
+363
+00:42:06,900 --> 00:42:12,420
+continuous functions تمام؟ يبقى افتراضنا أن الحل 
+
+364
+00:42:12,420 --> 00:42:19,130
+الثاني على الشكل هو Y تساوي V of T في Y1 بدي أعرف ما هو
+
+365
+00:42:19,130 --> 00:42:25,690
+شكل الـV of T واللي بيخليه للـV في Y1 هو عبارة عن
+
+366
+00:42:25,690 --> 00:42:31,390
+حل آخر لمين؟ للمعادلة Star إذا التكتيك اللي اتبعته
+
+367
+00:42:31,390 --> 00:42:36,100
+قبل قليل بيتبعه هنا يبقى الآن بروح أجيب مين اللي هو
+
+368
+00:42:36,100 --> 00:42:40,300
+المشتقة الأولى والمشتقة الثانية ونروح نعوض وإن في
+
+369
+00:42:40,300 --> 00:42:43,180
+المعادلة الصغيرة وبعدها الله بفرجها إن شاء الله
+
+370
+00:42:43,180 --> 00:42:50,200
+يبقى بدنا نجي نقول احنا عندنا اللي هو الـY تساوي V of 
+
+371
+00:42:50,200 --> 00:42:57,500
+T في Y1 of T بدنا نشتق المشتقة الأولى يبقى الـY
+
+372
+00:42:57,500 --> 00:43:06,140
+prime بدها تساوي V of T في الـY1 prime زائد V prime
+
+373
+00:43:06,140 --> 00:43:10,840
+في الـY1 بدنا نكتب الـT هذه خلاص مفهومة كل واحدة 
+
+374
+00
+
+401
+00:46:30,800 --> 00:46:36,440
+التلاتة هدول بقى لنا مين؟ بقى للثنتين هدول مظبوط
+
+402
+00:46:36,440 --> 00:46:46,920
+يبقى زائد اثنين y one prime في ال v prime زائد y 
+
+403
+00:46:46,920 --> 00:46:52,740
+one في ال v double prime كل هذا الكلام بده يساوي
+
+404
+00:46:52,740 --> 00:46:58,490
+كده؟ بده يساوي zero ماذا رأيك في المقدار بين
+
+405
+00:46:58,490 --> 00:47:08,650
+القوسين هذا يبقى
+
+406
+00:47:08,650 --> 00:47:19,230
+هذا بزيرو يبقى
+
+407
+00:47:19,230 --> 00:47:28,260
+المعادلة ألت إلى الشكل التالي اللي هو Y1 VW prime
+
+408
+00:47:28,260 --> 00:47:36,960
+زائد اثنين Y1 prime زائد اثنين Y1 في ال VW زائد
+
+409
+00:47:36,960 --> 00:47:43,320
+اثنين Y1 prime في ال V prime بده يساوي Zero شو
+
+410
+00:47:43,320 --> 00:47:45,660
+رأيك نقسم على Y1
+
+411
+00:47:50,220 --> 00:47:57,000
+لحظة شوية اتأني اتأني شوية ضلت هذه و اه في عندنا P
+
+412
+00:47:57,000 --> 00:48:05,660
+اه اثنين اتأني اتأني شوية هذه عندنا هنا هذه و هذه
+
+413
+00:48:05,660 --> 00:48:10,560
+و هذه مظبوطة هذه مافيها مشكلة ضل عندنا term اه
+
+414
+00:48:10,560 --> 00:48:15,340
+ثلاث تيرمات ضايل مش تيرمين ثلاث تيرمات بنصلحها
+
+415
+00:48:15,340 --> 00:48:24,420
+بسيطة جدا يبقى اثنين و اثنين و اثنين و اثنين و
+
+416
+00:48:24,420 --> 00:48:26,200
+اثنين و اثنين و اثنين و اثنين و 
+
+417
+00:48:26,200 --> 00:48:33,600
+اثنين و اثنين و اثنين
+
+418
+00:48:35,240 --> 00:48:46,240
+زائد اثنين Y1 prime زائد PY1 كل هذا في ال V prime
+
+419
+00:48:46,240 --> 00:48:56,560
+مظبوط زائد Y1 VW prime كل هذا الكلام بده يساوي
+
+420
+00:48:56,560 --> 00:49:06,260
+مين؟ بده يساوي Zero الآن بقدر اقسم كله على Y1 يبقى
+
+421
+00:49:06,260 --> 00:49:15,600
+لو قسمت على Y1 بيصير المعادلة VW prime زائد الهمين
+
+422
+00:49:15,600 --> 00:49:26,080
+اثنين Y1 prime على Y1 زائد P of T كله في ال V
+
+423
+00:49:26,080 --> 00:49:32,370
+prime يساوي Zero ماذا رأيك في المعادلة هذه اللي بين
+
+424
+00:49:32,370 --> 00:49:40,530
+أعطينا فيها V يعني equation with V مفقودة V مفقودة
+
+425
+00:49:40,530 --> 00:49:53,040
+يبقى هذه equation with V مفقودة يبقى هذه مفقودة إذا 
+
+426
+00:49:53,040 --> 00:50:00,580
+بقدر أشيل ال V' و أضع بدلها Z مثلا يبقى pot و
+
+427
+00:50:00,580 --> 00:50:09,880
+أضعنا Z تساوي V' هذا بدي أخبرك أن Z' تساوي VW' لأن V
+
+428
+00:50:09,880 --> 00:50:16,680
+تعادل Y هناك بصير المعادلة هادية على الشكل التالي
+
+429
+00:50:16,680 --> 00:50:27,400
+بصير z prime زائد 2y prime على y1 2y prime على y1
+
+430
+00:50:33,090 --> 00:50:38,390
+نزلنا الرتبة من الرتبة الثانية إلى الرتبة الأولى 
+
+431
+00:50:51,840 --> 00:51:01,920
+that can be solved as before نقدر نحلها كما كنا 
+
+432
+00:51:01,920 --> 00:51:06,100
+نحل من قبل يبقى هذه اللي اسمها الطريقة يا بنات 
+
+433
+00:51:06,100 --> 00:51:11,620
+طريقة مين ال reduction of order عند حل هذه الأنواع
+
+434
+00:51:11,620 --> 00:51:15,620
+من المسائل بدنا نمشي بنفس التكتيك النظري اللي
+
+435
+00:51:15,620 --> 00:51:21,320
+مشينا فيه هنا قدامنا تماما يبقى حد في كل أي تساؤل
+
+436
+00:51:21,320 --> 00:51:25,860
+هنا هنبدأ ناخد أمثلة توضحها بس قوليلي ها في تساؤل 
+
+437
+00:51:25,860 --> 00:51:32,260
+على الكلام هنا او في نقطة مش مفهومة كده طبعا 
+
+438
+00:51:32,260 --> 00:51:36,080
+function نفس التكتيك اللي كنا مش أخذنا equation
+
+439
+00:51:36,080 --> 00:51:40,740
+with y missing وt missing is z هنا مكان ال y هناك
+
+440
+00:51:40,740 --> 00:51:45,120
+بالضبط تماما ها في أي تساؤل آخر ايوة 
+
+441
+00:51:48,470 --> 00:51:53,190
+الـ Q متغير والـ P متغير واخدناهم ثابت ما عناه 
+
+442
+00:51:53,190 --> 00:51:57,150
+مشكلة المهم يعطينا حل و الحل اللي بيعطيناه سواء 
+
+443
+00:51:57,150 --> 00:52:00,470
+كانت ده او لا بمعاملة الـ differential equation 
+
+444
+00:52:00,470 --> 00:52:03,370
+بمعاملات ثابتة أو ما هيش معاملة ثابتة ما عناه 
+
+445
+00:52:03,370 --> 00:52:08,810
+مشكلة ماشي اكتبها الملاحظة دي اكتب ملاحظة بالعربي 
+
+446
+00:52:08,810 --> 00:52:15,750
+نستخدم هذه الطريقة إذا 
+
+447
+00:52:15,750 --> 00:52:16,670
+أعطينا 
+
+448
+00:52:19,390 --> 00:52:24,750
+أحد الحلول للمعادلة 
+
+449
+00:52:24,750 --> 00:52:30,210
+التفاضلية إلى
+
+450
+00:52:30,210 --> 00:52:37,110
+اللي قدامك هذى y w prime زائد p of t y prime زائد q 
+
+451
+00:52:37,110 --> 00:52:46,490
+of t في y بده يساوي zero where ال
+
+452
+00:52:46,490 --> 00:53:03,070
+p of tand the Q of T are constants or not يعني
+
+453
+00:53:03,070 --> 00:53:05,570
+كانوا ثوابت و الله ما له ايه ثوابت مش مشكلة لما 
+
+454
+00:53:05,570 --> 00:53:10,210
+يعطاني حل هو الطريقة دي وسطها بجيب من؟ بجيب الحل
+
+455
+00:53:10,210 --> 00:53:16,330
+الثاني إذا أروح ناخد مثال على هذا الكلام يبقى
+
+456
+00:53:16,330 --> 00:53:16,890
+example
+
+457
+00:53:23,900 --> 00:53:34,060
+سؤال خمسة و عشرين من الكتاب بيقول if Y1 دو سوء
+
+458
+00:53:34,060 --> 00:53:45,780
+واحد على T و T greater than zero is a solution of
+
+459
+00:53:45,780 --> 00:53:51,940
+the differential equation
+
+460
+00:53:52,590 --> 00:54:01,790
+للمعادلة التفاضلية لـ T تربيع YW prime زائد ثلاثة 
+
+461
+00:54:01,790 --> 00:54:13,330
+T في Y prime زائد Y تساوي Zero Find a second
+
+462
+00:54:13,330 --> 00:54:19,810
+linearly independent solution
+
+463
+00:54:22,930 --> 00:54:48,430
+of the given differential equation زي
+
+464
+00:54:48,430 --> 00:54:51,470
+ما تشوفين هنا Y1 حل المعادلة 
+
+465
+00:54:58,470 --> 00:55:01,510
+المعادلة اللي عنها second order differential
+
+466
+00:55:01,510 --> 00:55:05,390
+equation سواء كمعامل T تربيع او المعامل واحد صحيح
+
+467
+00:55:05,390 --> 00:55:09,710
+لو جسمنا على T تربيع بصير المعامل main واحد صحيح
+
+468
+00:55:09,710 --> 00:55:14,890
+لكن هل لازم لي شكل P of T وقل Q of T؟ مش لازم لي
+
+469
+00:55:14,890 --> 00:55:20,090
+وبالتالي لا داعي للقسمة مش ده القسم بهمنا مين بهمنا
+
+470
+00:55:20,090 --> 00:55:24,790
+الشغل اللي عندنا ده ما تيني واحد على T هو حل يبقى
+
+471
+00:55:24,790 --> 00:55:28,830
+الحل الثاني V of T في واحد على T و بتجديه بشكل مين
+
+472
+00:55:28,830 --> 00:55:37,710
+ال V of T يبقى بعدي بقوله هنا suppose that
+
+473
+00:55:37,710 --> 00:55:43,650
+افرض انه the other solution
+
+474
+00:55:45,910 --> 00:55:55,730
+Y تساوي V of T في مين؟ في واحد على T والآن بدنا
+
+475
+00:55:55,730 --> 00:56:00,030
+نروح نجيب له مين؟ شكل ال V of T إذا بدنا نروح
+
+476
+00:56:00,030 --> 00:56:08,830
+نشتقها يا بنات يبقى هنش بيصير Y prime بده يساوي V
+
+477
+00:56:08,830 --> 00:56:19,620
+prime في واحد على T زائد و لا ناقص V في واحد على T
+
+478
+00:56:19,620 --> 00:56:26,180
+تربيع مشتقة واحد على T بسالب واحد على T تربيع نجيب
+
+479
+00:56:26,180 --> 00:56:38,280
+المشتقة الثانية يبقى YW' يساوي VW' في 1 على T ناقص
+
+480
+00:56:38,280 --> 00:56:44,060
+V' في 1 على T تربيع
+
+481
+00:56:47,810 --> 00:56:53,730
+يبقى الآن اشتقت اثنين هذول كمشتقت حصل ضرب دلتين
+
+482
+00:56:53,730 --> 00:56:59,210
+يبقى
+
+483
+00:56:59,210 --> 00:57:08,120
+ناقص V' في 1 على T تربيع جنة ناقص من ثابت ال V
+
+484
+00:57:08,120 --> 00:57:14,120
+ومشتقت هذه كان T والسلب ثاني يبقى سالب اثنين T
+
+485
+00:57:14,120 --> 00:57:21,220
+والسلب ثلاثة مع السلب بصير موجب اثنين V على T تكعيب
+
+486
+00:57:21,220 --> 00:57:30,380
+يبقى موجب V في اثنين على T تكعيب
+
+487
+00:57:36,150 --> 00:57:42,750
+تمام يبقى هاي جيبت Y' وYW' الآن بدي ارجع اعوض وين
+
+488
+00:57:42,750 --> 00:57:47,710
+في المعادلة الاصلية سميها ليها دي كنا بنسميها قبل
+
+489
+00:57:47,710 --> 00:57:56,490
+هيك مين ليه star يبقى بنجي نقول هنا substitute and
+
+490
+00:57:56,490 --> 00:58:04,690
+the differential equation star we get
+
+491
+00:58:35,520 --> 00:58:43,960
+الآن تربيع في الـ
+
+492
+00:58:43,960 --> 00:58:52,300
+v double prime على t وهذه عبارة عن ثنتين ناقص
+
+493
+00:58:52,300 --> 00:58:53,500
+اثنين
+
+494
+00:59:04,390 --> 00:59:10,830
+V على T تكعيب هذا ال term الأول ال term الثاني 
+
+495
+00:59:10,830 --> 00:59:16,470
+زائد ثلاثة T في ال Y prime Y prime اللي هو الأولى
+
+496
+00:59:16,470 --> 00:59:27,340
+V prime على T V' على T ناقص V على T تربيع اللي
+
+497
+00:59:27,340 --> 00:59:34,240
+بعدها زائد Y زائد V على T كل هذا الكلام بده يساوي 
+
+498
+00:59:34,240 --> 00:59:41,240
+من؟ بده يساوي Zero طبعا Y هي اللي فرضناها V في 1
+
+499
+00:59:41,240 --> 00:59:47,210
+على T يعني V على T هي V على T طيب انفك الأقواس هذه
+
+500
+00:59:47,210 --> 00:59:54,450
+بصير أنا mean T في ال V Double Prime ناقص اثنين V 
+
+501
+00:59:54,450 --> 01:00:03,130
+Prime زائد اثنين على T كله في ال V زائد ثلاثة في V
+
+502
+01:00:03,130 --> 01:00:13,650
+Prime ناقص ثلاثة V على T نقص ثلاثة V على T زائد V
+
+503
+01:00:13,650 --> 01:00:20,450
+على T كله بده يساوي Zero اتطلع لي الى ناقص اثنين V
+
+504
+01:00:20,450 --> 01:00:29,410
+Prime و ثلاثة V Prime و ثلاثة V' في غيرهم و مش
+
+505
+01:00:29,410 --> 01:00:35,870
+غيرهم طيب بظل عندنا T في ال V Double Prime و بظل
+
+506
+01:00:35,870 --> 01:00:45,170
+عندنا هنا زائد V Prime اثنين على T واحدة يبقى هذه مع 
+
+507
+01:00:45,170 --> 01:00:51,190
+هذه بيصيروا ثلاثة مع سالب ثلاثة مع السلامة بيروحوا
+
+508
+01:00:51,190 --> 01:00:56,650
+هذا الكلام بده يساوي مين بده يساوي صفر زي ما أنت 
+
+509
+01:00:56,650 --> 01:01:02,930
+شايف ال equation with v missing يبقى هذه equation
+
+510
+01:01:02,930 --> 01:01:15,430
+with v missing طيب تمام إذا بدي اقول let z تساوي v
+
+511
+01:01:15,430 --> 01:01:20,810
+prime هذا بدي أعطيك إن z prime بدي تساوي v double
+
+512
+01:01:20,810 --> 01:01:29,610
+prime يبقى لتصبح المعادلة T z prime زائد z بدي تساوي
+
+513
+01:01:29,610 --> 01:01:38,450
+قداش zero أو بقدر اقول لو z prime زائد واحد على T
+
+514
+01:01:38,450 --> 01:01:46,710
+في z يبدو يساوي zero أو بقدر اقول z prime على z
+
+515
+01:01:46,710 --> 01:01:58,390
+يساوي ناقص واحد على T إن كامل يبقى هذا الكلام لين
+
+516
+01:01:58,390 --> 01:02:07,490
+absolute value ل z يساوي ناقص لين absolute value ل T 
+
+517
+01:02:07,490 --> 01:02:15,680
+زائد constant C1 شو رأيك أجيب اللي ناتج عن بعض يبقى 
+
+518
+01:02:15,680 --> 01:02:22,220
+لو جبت بتيجي بشارات موجب يبقى هنا إيش بصير بصير لن
+
+519
+01:02:22,220 --> 01:02:28,800
+absolute value ل Z لن absolute value ل T تساوي C1
+
+520
+01:02:28,800 --> 01:02:36,780
+أظن لن زائد لن تعني لن حاصل الضرب يبقى بصير عندنا
+
+521
+01:02:36,780 --> 01:02:43,560
+لن absolute value ل ZT يساوي C1 أضايق ال
+
+522
+01:02:43,560 --> 01:02:49,420
+exponential نضيع ال line و ندخل ال exponential يبقى 
+
+523
+01:02:49,420 --> 01:02:55,920
+absolute value ل ZT يساوي E وال C1 عمر ال
+
+524
+01:02:55,920 --> 01:02:59,940
+exponential بياخد قيمة سالبة يبقى ال absolute هو
+
+525
+01:02:59,940 --> 01:03:10,690
+guilt يبقى باجي بقول يبقى Z T يساوي C و R C تساوي E
+
+526
+01:03:10,690 --> 01:03:17,170
+و C1 مش E و C1 مقدار ثابت بده نسميها C أسهل يبقى
+
+527
+01:03:17,170 --> 01:03:23,150
+بناء عليه بصير Z اللي هي تساوي مين يا بنات فرضناها 
+
+528
+01:03:24,570 --> 01:03:24,970
+V'
+
+529
+01:03:27,610 --> 01:03:36,280
+بده يساوي C على T طبعا هذه Z زي ما شايفين يبقى C
+
+530
+01:03:36,280 --> 01:03:45,560
+على T طيب إن كامل الطرفين يبقى هذا بده يعطينا V of
+
+531
+01:03:45,560 --> 01:03:53,920
+T بده يساوي C لإن T بدون absolute value ليش؟ لأنه
+
+532
+01:03:53,920 --> 01:03:58,880
+قال هنا في المثال T greater than 0 طبعا يبقى لا
+
+533
+01:03:58,880 --> 01:04:05,670
+داعي لل absolute value طيب هذه مين؟ V of T يبقى C 
+
+534
+01:04:05,670 --> 01:04:14,000
+لإن T زائد constant لمن C ثابث التكامل بنات
+
+535
+01:04:14,000 --> 01:04:19,080
+عليه بقدر آخذ c بواحد و بقدر آخذ c باثنين يبقى دايسر
+
+536
+01:04:19,080 --> 01:04:30,380
+بصفر يبقى هنا take c تساوي واحد صحيح and c باثنين
+
+537
+01:04:30,380 --> 01:04:39,420
+يساوي صفر we get بنحصل على اثنين على v of t بده 
+
+538
+01:04:39,420 --> 01:04:45,510
+يساوي لن ال t يبقى هذا بده يعطيلك the other
+
+539
+01:04:45,510 --> 01:04:51,410
+solution is
+
+540
+01:04:51,410 --> 01:05:05,030
+هه ال Y2 بده يساوي V of T في 1 على T يبقى لن T على
+
+541
+01:05:05,030 --> 01:05:05,430
+T
+
+542
+01:05:08,160 --> 01:05:12,700
+السؤال هو جالي هاتلي solution ثاني collinearly
+
+543
+01:05:12,700 --> 01:05:16,360
+independent مع الحل اللي عندنا هذا يبقى شو بدنا 
+
+544
+01:05:16,360 --> 01:05:21,900
+نعمل؟ بدنا نجيب الرونسكين تبع الحلّين يبقى بده
+
+545
+01:05:21,900 --> 01:05:27,880
+أجيب له الآن الرونسكين تبع الحل الأول اللي هو 1 على 
+
+546
+01:05:27,880 --> 01:05:35,790
+T و الحل الثاني لن T على T يبقى هاي المحدد واحد و 
+
+547
+01:05:35,790 --> 01:05:40,970
+الله ايش رأيك ليه السهولة بدي أقول T السالب واحد و
+
+548
+01:05:40,970 --> 01:05:47,210
+هنا T السالب واحد في لنة T بدل ما اخليها كثور 
+
+549
+01:05:47,210 --> 01:05:54,430
+هيكسلي بس في الكتابة بدنا نشتق يبقى سالب T السالب
+
+550
+01:05:54,430 --> 01:06:01,410
+اثنين هذه المشتقة حاصل ضرب دلتين تي و السالب واحد في
+
+551
+01:06:01,410 --> 01:06:08,310
+واحد على تي تمام يعني تي و السالب اثنين صح ولا لا
+
+552
+01:06:08,310 --> 01:06:13,430
+يبقى هذه والله خليها على خطوطين يبقى تي و السالب
+
+553
+01:06:13,430 --> 01:06:21,890
+واحد في واحد على تين سالب اللي هو تي و السالب اثنين
+
+554
+01:06:21,890 --> 01:06:29,190
+في لن التيمرة ثانية أنا اقعد واحد على ت ماذا
+
+555
+01:06:29,190 --> 01:06:33,360
+أكتبته و السالب واحد لن ال T على T بالكتابة T
+
+556
+01:06:33,360 --> 01:06:35,780
+و السالب واحد لن T 
+
+557
+01:07:01,870 --> 01:07:09,790
+يبقى هذه في هذه بيصير T أسالب اثنين في واحد على T 
+
+558
+01:07:09,790 --> 01:07:17,150
+يعني T أسالب ثلاثة يبقى هاي T أسالب ثلاثة خلاصنا
+
+559
+01:07:17,150 --> 01:07:23,870
+الترمينات ناقص T أسالب واحد في هذه بيصير T أسالب
+
+560
+01:07:23,870 --> 01:07:31,620
+ثلاثة في لن TT السالب ثلاثة في الآن ال T هذا 
+
+561
+01:07:31,620 --> 01:07:38,680
+الرئيسي ناقص الثانوي مع النقص بيصير زائد T السالب
+
+562
+01:07:38,680 --> 01:07:45,670
+ثلاثة في من؟ في لن ال T هذول اثنين بيروحوا مع بعض
+
+563
+01:07:45,670 --> 01:07:53,370
+بيظل عندي قداش T أس سالب ثلاثة وهذا لا يساوي صفر 
+
+564
+01:07:53,370 --> 01:08:01,070
+السبب because انه T greater than zero مدام هيك
+
+565
+01:08:01,070 --> 01:08:03,950
+يبقى اثنين هذول شو بيعملوا ليه؟ linearly 
+
+566
+01:08:03,950 --> 01:08:12,880
+independent solution لمين للمعادلة اللي عندنا يبقى
+
+567
+01:08:12,880 --> 01:08:22,060
+هنا الواحد على التي and الانتيالات
+
+568
+01:08:22,060 --> 01:08:29,680
+are linearly independent solutions
+
+569
+01:08:29,680 --> 01:08:31,100
+of
+
+570
+01:08:42,010 --> 01:08:53,990
+يبقى بيناه يعني صار the general solution is Y
+
+571
+01:08:53,990 --> 01:09:07,190
+تساوي C1 في 1 على T زائد C2 في 1 على T في لنة T
+
+572
+01:09:07,590 --> 01:09:12,450
+يبقى هذا حل المعادلة التفاضلية يبقى طريقة ال 
+
+573
+01:09:12,450 --> 01:09:16,270
+reduction of order دائما و أبدا منالجة لها إذا 
+
+574
+01:09:16,270 --> 01:09:22,870
+أعطانا مين
+
+601
+01:11:48,080 --> 01:11:52,520
+coefficients يبقى سيكشن تلاتة ستة
+
+602
+01:12:10,660 --> 01:12:19,040
+Undetermined coefficients طريقة المعاملات المجهولة
+
+603
+01:12:22,370 --> 01:12:26,830
+الـ Non-homogeneous هنحلها بطريقتين بدنا ناخد
+
+604
+01:12:26,830 --> 01:12:29,490
+الطريقة الأولى والـ section اللى جاى إن شاء الله
+
+605
+01:12:29,490 --> 01:12:36,470
+بناخد الطريقة الثانية يبقى هنُمهّد لذلك بنظريتين بدنا 
+
+606
+01:12:36,470 --> 01:12:49,310
+ناخد النظرية الأولى بيقول if Y1 and Y2 are two
+
+607
+01:12:49,310 --> 01:12:50,390
+solutions
+
+608
+01:13:13,920 --> 01:13:24,610
+تساوي y double prime زائد p of t في y زائد q of t في y بده
+
+609
+01:13:24,610 --> 01:13:36,050
+ساوي g of t بده ساوي g of t وهذه سامعوني المعادلة
+
+610
+01:13:36,050 --> 01:13:56,600
+رقم واحد then اللي هو مين؟ Y1-Y2 is a solution of
+
+611
+01:13:56,600 --> 01:14:06,690
+the homogeneous differential equation اللي هو ال L
+
+612
+01:14:06,690 --> 01:14:13,870
+of Y بده يساوي y double prime زائد p of t في ال y
+
+613
+01:14:13,870 --> 01:14:19,950
+prime زائد q of t في ال y بده يساوي Zero وسميها
+
+614
+01:14:19,950 --> 01:14:31,690
+للمعادلة رقم اتنين Also وكذلك if Y واحد and Y
+
+615
+01:14:31,690 --> 01:14:40,660
+اتنين small هما مجموعات حلول مجموعات
+
+616
+01:14:40,660 --> 01:14:49,620
+حلول
+
+617
+01:14:49,620 --> 01:15:00,000
+مجموعات حلول مجموعات حلول مجموعات
+
+618
+01:15:22,390 --> 01:15:23,790
+Y1Y2Y1Y2Y2Y2Y2Y2Y2Y2Y2Y2Y2Y2Y2Y2Y2Y2Y2
+
+619
+01:15:25,650 --> 01:15:34,290
+حيث C1 and C2
+
+620
+01:15:34,290 --> 01:15:40,090
+are constants يبقى دول ثابت
+
+621
+01:16:00,210 --> 01:16:13,590
+النظرية بتقول لو عندي capital Y1 و capital Y2 هما
+
+622
+01:16:13,590 --> 01:16:17,370
+حلّين لمن؟ للـ non homogeneous differential
+
+623
+01:16:17,370 --> 01:16:24,430
+equation طيب هذا ما قطعت يبقى then الفرق في ما
+
+624
+01:16:24,430 --> 01:16:28,270
+بينهما يعني الفرق ما بين الحلين تبعين ال non
+
+625
+01:16:28,270 --> 01:16:34,550
+homogeneous هو عبارة عن حل ال homogeneous حلّين لل
+
+626
+01:16:34,550 --> 01:16:38,870
+non homogeneous الفرق بينهما هو حل ال homogeneous
+
+627
+01:16:38,870 --> 01:16:43,170
+differential equation يعني لو كان g of t بقد إيش ب
+
+628
+01:16:43,170 --> 01:16:48,810
+zero هذا المطلوب الأول قال also وكذلك لو كان y1
+
+629
+01:16:48,810 --> 01:16:52,250
+small و y2 small fundamental set of solutions
+
+630
+01:16:52,250 --> 01:16:57,610
+للمعادلة رقم اتنين اللي عندنا هنا يبقى ال y واحد و
+
+631
+01:16:57,610 --> 01:17:01,210
+y اتنين مادام حل بدي يكونوا على الشكل c واحد y
+
+632
+01:17:01,210 --> 01:17:04,610
+واحد زائد c اتنين y اتنين اللي هو ال general
+
+633
+01:17:04,610 --> 01:17:08,970
+solution لمن؟ لل differential equation اتنين اللي
+
+634
+01:17:08,970 --> 01:17:14,510
+عندنا هذه العجيلة البرهة يبقى لأن أنا لدي معادلة
+
+635
+01:17:14,510 --> 01:17:21,130
+تفاضلية ولها حلّان إذا الحلّان الاتنين هذول بيحققوا
+
+636
+01:17:21,130 --> 01:17:27,470
+من المعادلة التفاضلية يبقى باجي بقوله since بما أن
+
+637
+01:17:27,470 --> 01:17:40,430
+Y1 وY2 are two solutions of the
+
+638
+01:18:04,550 --> 01:18:05,950
+Y1Y1Y1Y1Y1Y1Y1Y1Y1Y1Y1Y1Y1Y1Y1Y1
+
+639
+01:18:07,860 --> 01:18:19,390
+الـ L of Y2 يساوي كذلك g of T يعني ال differential
+
+640
+01:18:19,390 --> 01:18:23,550
+linear operator لما يأثر على الحل الأول بده يساوي
+
+641
+01:18:23,550 --> 01:18:28,150
+g of T وكذلك لما يأثر على الحل الثاني بده يساوي g
+
+642
+01:18:28,150 --> 01:18:34,370
+of T طيب تعال نشوف ال linear operator لو أثر على
+
+643
+01:18:34,370 --> 01:18:41,510
+capital Y1 ناقص capital Y2 شو بده يعطينا؟ الآن هذا
+
+644
+01:18:41,510 --> 01:18:47,670
+linear مادام linear إذا بده يؤدي للنتيجة المطلوبة
+
+645
+01:18:47,670 --> 01:18:55,790
+ماشي يا بنا ماعندناش مشكلة يبقى L of Y1 minus Y2 بده
+
+646
+01:18:55,790 --> 01:19:02,370
+يساوي هذا الآن مؤثر خطي مادام مؤثر خطي إذا بقدر
+
+647
+01:19:02,370 --> 01:19:09,410
+أقول L of Y1 ناقص L of Y2
+
+648
+01:19:11,520 --> 01:19:19,660
+طيب هذا ليش؟ since ال L is linear لكن لو ما كانش
+
+649
+01:19:19,660 --> 01:19:23,840
+linear ما أقدرش أكتب الشكل هذا منه يبقى هذا الكلام
+
+650
+01:19:23,840 --> 01:19:32,740
+بدّه يساوي L of Y one هايو قديش؟ g of T والتاني g of
+
+651
+01:19:32,740 --> 01:19:39,500
+T يبقى النتيجة قديش؟ يبقى أصبح كأن y1 ناقص y2 هو
+
+652
+01:19:39,500 --> 01:19:44,520
+solution لمين؟ للمعادلة رقم 2 اللي بدها تساوي 0
+
+653
+01:19:44,520 --> 01:19:53,860
+يبقى اللي بقول له this means that هذا يعني أن y1
+
+654
+01:19:53,860 --> 01:19:59,840
+minus y2 is a solution
+
+655
+01:20:10,660 --> 01:20:15,360
+يبقى الفرق بينهما هو حل مين؟ لل homogenous
+
+656
+01:20:15,360 --> 01:20:20,820
+differential equation رقم اتنين بيقولي أيضًا لو كان
+
+657
+01:20:20,820 --> 01:20:25,700
+هدول بيكونوا لي fundamental set of solutions يبقى
+
+658
+01:20:25,700 --> 01:20:34,960
+باجي بقوله since بما أن y1 and y2 form a
+
+659
+01:20:34,960 --> 01:20:40,540
+fundamental set
+
+660
+01:20:40,540 --> 01:20:45,460
+of solutions
+
+661
+01:20:45,460 --> 01:20:47,560
+of
+
+662
+01:20:48,590 --> 01:20:58,330
+the differential equation اتنين the general
+
+663
+01:20:58,330 --> 01:21:11,510
+solution is Y تساوي C1Y1 زائد C2Y2
+
+664
+01:21:14,540 --> 01:21:18,720
+مصبور يبقى هذول اتنين بيكونوا fundamental set of 
+
+665
+01:21:18,720 --> 01:21:21,660
+solution للمعادلة رقم اتنين يبقى ال general
+
+666
+01:21:21,660 --> 01:21:30,060
+solution بيجي of equation اتنين as يبقى على الشكل
+
+667
+01:21:30,060 --> 01:21:36,440
+التالي يبقى هذا شكل الحل العام للمعادلة رقم 2 يبقى
+
+668
+01:21:36,440 --> 01:21:41,020
+بناء عليه أي حل للمعادلة رقم 2 بدّه يكون على مين؟
+
+669
+01:21:41,020 --> 01:21:44,400
+على الشكل اللي عندنا هذا لكن إحنا في المطلوب الأول
+
+670
+01:21:44,400 --> 01:21:50,000
+أثبتنا أن y1-y2 هو عبارة عن solution للمعادلة 2
+
+671
+01:21:50,000 --> 01:21:55,450
+صحيح ولا لا؟ إذا ال y1-y2 بدّه ياخد مين؟ الشكل هذا
+
+672
+01:21:55,450 --> 01:22:01,230
+يبقى بقى بقول since بما أن capital Y1 minus
+
+673
+01:22:01,230 --> 01:22:11,490
+capital Y2 is a solution of equation two we have
+
+674
+01:22:12,290 --> 01:22:19,430
+يبقى بدّه يصير capital Y1 ناقص capital Y2 بدّه يساوي
+
+675
+01:22:19,430 --> 01:22:28,130
+C1Y1 زائد C2Y2 وهو المطلوب في أنا كمان نظرية ثانية 
+
+676
+01:22:28,130 --> 01:22:33,370
+بس أصغر من النظرية هذه وبتعتمد عليها مباشرة
+
+677
+01:22:44,980 --> 01:22:55,580
+يبقى بدنا نيجي لنظرية رقم اتنين theorem two بتقول
+
+678
+01:22:55,580 --> 01:23:07,700
+ما يلي let L of Y بدّه يساوي y double prime زائد p of t في y
+
+679
+01:23:07,700 --> 01:23:14,580
+prime زائد q of t في y بدّه يساوي g of T وهذه اللي
+
+680
+01:23:14,580 --> 01:23:21,680
+هي المعادلة رقم 1 تبعت المرة الماضية ب a non
+
+681
+01:23:21,680 --> 01:23:31,440
+homogeneous differential equation F
+
+682
+01:23:31,440 --> 01:23:40,780
+capital Y of T is a particular solution is a
+
+683
+01:23:40,780 --> 01:23:46,060
+particular solution
+
+684
+01:23:46,060 --> 01:23:55,620
+is a particular solution of the differential
+
+685
+01:23:55,620 --> 01:24:02,500
+equation one and
+
+686
+01:24:02,500 --> 01:24:12,580
+y one و y too small are
+
+687
+01:24:12,580 --> 01:24:15,720
+fundamental
+
+688
+01:24:15,720 --> 01:24:19,920
+set
+
+689
+01:24:19,920 --> 01:24:30,560
+of solutions of
+
+690
+01:24:30,560 --> 01:24:34,220
+the homogeneous
+
+691
+01:24:37,620 --> 01:24:44,400
+differential equation إلى y double prime زائد p
+
+692
+01:24:44,400 --> 01:24:49,700
+of t في ال y prime زائد q of t في ال y بدّه يساوي
+
+693
+01:24:49,700 --> 01:24:55,760
+زيرو وهذه المعادلة رقم اتنين then the general
+
+694
+01:24:55,760 --> 01:24:56,840
+solution
+
+695
+01:25:05,060 --> 01:25:14,420
+the general solution of the differential equation
+
+696
+01:25:14,420 --> 01:25:18,640
+one has the form
+
+697
+01:25:34,530 --> 01:25:41,670
+C1Y1T زائد C2Y2T زائد YT
+
+698
+01:26:06,310 --> 01:26:11,250
+مرة ثانية نظرية يا بنات زي ما تشوفين بتعتمد بشكل
+
+699
+01:26:11,250 --> 01:26:15,550
+مباشر على النظرية اللي قبلها بيقول افترض أنه عندي
+
+700
+01:26:15,550 --> 01:26:18,070
+non homogeneous differential equation اللي هي one
+
+701
+01:26:18,070 --> 01:26:25,250
+هاديلو فرضت أن capital Y of T هو حل خاص particular
+
+702
+01:26:25,250 --> 01:26:29,750
+solution يعني حل خاص لمن؟ لل homogenous
+
+703
+01:26:29,750 --> 01:26:34,590
+differential equation 1 وفي نفس الوقت كان Y1 صغير
+
+704
+01:26:34,590 --> 01:26:39,150
+و Y2 صغير حلّين أو اتنين بشكل fundamental set of
+
+705
+01:26:39,150 --> 01:26:41,330
+solutions لل homogenous
+
+706
+01:26:47,540 --> 01:26:52,220
+يبقى ال general solution لل equation 1 مجموعة حل
+
+707
+01:26:52,220 --> 01:26:56,920
+ال homogenous الخاص وحل ال non homogenous يبقى f
+
+708
+01:26:56,920 --> 01:27:02,140
+of t حل المعادلة التفاضلية بيكون c1y1 زائد c2 y2 هذا
+
+709
+01:27:02,140 --> 01:27:04,360
+حل من ال homogenous
+
+710
+01:27:14,220 --> 01:27:23,880
+برهان بسيط جدًا بدي أقوله let phi of t and capital
+
+711
+01:27:23,880 --> 01:27:31,040
+Y of T be two solutions
+
+712
+01:27:31,040 --> 01:27:36,420
+of equation one
+
+713
+01:27:38,940 --> 01:27:45,800
+إذا الفرق فيما بينهما حل مين؟ لل equation 2 بواسطة
+
+714
+01:27:45,800 --> 01:27:53,260
+النظرية اللي فوق صحيح ولا لا؟ يبقى by the first
+
+715
+01:27:53,260 --> 01:28:00,560
+theorem بالنظرية الأولى اللي أخذناها اللي هو Phi
+
+716
+01:28:00,560 --> 01:28:12,560
+of T ناقص capital Y of T is a solution of the
+
+717
+01:28:12,560 --> 01:28:17,200
+differential equation two
+
+718
+01:28:33,560 --> 01:28:38,880
+طب كويس إذا الفرق في ما بينهما هو حل ال equation
+
+719
+01:28:38,880 --> 01:28:43,260
+2 طب داير ال equation 2 مين ال general solution
+
+720
+01:28:43,260 --> 01:28:49,060
+تبعها؟ وأي واحد هو ال fundamental set of 
+
+721
+01:28:49,060 --> 01:28:53,080
+solutions قال لي لو كان واحد واي واحد باجي
+
+722
+01:28:53,080 --> 01:29:01,620
+بقوله هنا since the fundamental set
+
+723
+01:29:03,640 --> 01:29:17,280
+of solutions of equation أو since y1
+
+724
+01:29:17,280 --> 01:29:24,300
+and y2 since y1
+
+725
+01:29:24,300 --> 01:29:32,220
+and y2 are fundamental set of solution of equation
+
+726
+01:29:32,810 --> 01:29:42,690
+to the general solution
+
+727
+01:29:42,690 --> 01:29:58,370
+of equation 2 is y تساوي c1 y1 زائد c2 y2 يبقى 
+
+728
+01:29:58,370 --> 01:30:02,790
+الآن الفرق في ما بين هذا اللي قلنا solution لل
+
+729
+01:30:02,790 --> 01:30:05,990
+equation اتنين وهذا ال general solution يبقى
+
+730
+01:30:05,990 --> 01:30:13,230
+اتنين هذول يبقى Phi of T ناقص capital Y of T بدّه
+
+731
+01:30:13,230 --> 01:30:18,250
+يساوي C1Y1 زائد C2Y2
+
+732
+01:30:19,250 --> 01:30:27,350
+نضيف Y of T  للطرفين يبقى بصير Y of T زائد C1 Y1
+
+733
+01:30:27,350 --> 01:30:36,630
+زائد C2 Y2 زائد Y of T هذا شكل main and non
+
+734
+01:30:36,630 --> 01:30:47,150
+homogeneous هذا is the solution of the non
+
+735
+01:30:50,420 --> 01:30:59,520
+Homogenous Differential Equation 1 لحد
+
+736
+01:30:59,520 --> 01:31:02,620
+هنا أصبحنا أكثر من نظرياتك ما عنديش في هذا ال
+
+737
+01:31:02,620 --> 01:31:07,960
+section يبقى من الآن فصاعدًا لما بنحل مثلًا non
+
+738
+01:31:07,960 --> 01:31:13,020
+homogeneous differential equation بدّ من بدي
+
+739
+01:31:13,020 --> 01:31:18,510
+particular solution وبدي الحل العام لل homogenous
+
+740
+01:31:18,510 --> 01:31:21,930
+differential equation بجمع الحلين بيعطينا الحل
+
+741
+01:31:21,930 --> 01:31:25,570
+العام لل non homogenous differential equation يبقى
+
+742
+01:31:25,570 --> 01:31:29,570
+المرة القادمة إن شاء الله بدنا نبدأ في أول طريقة
+
+743
+01:31:29,570 --> 01:31:33,960
+من طرق الحل Homogeneous differential equation هي
+
+744
+01:31:33,960 --> 01:31:38,520
+طريقة الـ Undetermined coefficients والطريقة
+
+745
+01:31:38,520 --> 01:31:42,860
+الثانية الى section 3-6 بنسميها طريقة ال variation
+
+746
+01:31:42,860 --> 01:31:48,320
+of parameters تغيير المتغيرات أو الوسيطات اللي
+
+747
+01:31:48,320 --> 01:31:52,880
+موجودة وين؟ في المسألة ال Undetermined coefficients
+
+748
+01:31:52,880 --> 01:31:57,600
+بتعتمد على المعادلة التفاضلية اللي المعاملات
+
+749
+01:31:57,600 --> 01:32:01,880
+تبعها ثابت أما ال variation المعاملات ليست
+
+750
+01:32:01,880 --> 01:32:05,920
+بالضرورة أن تكون ثوابت، ثوابت ماشي ماهي ثوابت،
+
+751
+01:32:05,920 --> 01:32:09,100
+ماشي؟ فالمرة القادمة إن شاء الله تعالى
diff --git a/PL9fwy3NUQKwa8ZDfSFGn6H8xVFLzqmCZC/RDSrZpOLp38.srt b/PL9fwy3NUQKwa8ZDfSFGn6H8xVFLzqmCZC/RDSrZpOLp38.srt
new file mode 100644
index 0000000000000000000000000000000000000000..a6d0bd38fff9d0a9b29889dd2d74294dce1e88f5
--- /dev/null
+++ b/PL9fwy3NUQKwa8ZDfSFGn6H8xVFLzqmCZC/RDSrZpOLp38.srt
@@ -0,0 +1,2785 @@
+1
+00:00:09,340 --> 00:00:14,560
+بسم الله الرحمن الرحيم  المرة اللي فاتت بدأنا
+
+2
+00:00:14,560 --> 00:00:19,320
+بتعريف لابلاس ترانسفورم وحسبنا لابلاس ترانسفورم 
+
+3
+00:00:19,320 --> 00:00:24,160
+مجموعة من الدوال اليوم إن شاء الله هنعطيكم مجموعة
+
+4
+00:00:24,160 --> 00:00:28,040
+من الدوال و لابلاس ترانسفورم اللي موجودة قبالك في 
+
+5
+00:00:28,040 --> 00:00:28,560
+جدول
+
+6
+00:00:39,960 --> 00:00:45,300
+موضوع اليوم موضوع solution of initial value 
+
+7
+00:00:45,300 --> 00:00:48,770
+problems يبقى احنا عندنا initial value problem
+
+8
+00:00:48,770 --> 00:00:54,230
+بنحاول نوجد الحل هذا تبع المعادلة باستخدام Laplace
+
+9
+00:00:54,230 --> 00:01:00,770
+transform احنا في البداية حلينها حل عادي زمان ثم
+
+10
+00:01:00,770 --> 00:01:05,730
+بعد ذلك حلينها بالـ C resolution ثم الآن بنحل نفس
+
+11
+00:01:05,730 --> 00:01:09,650
+المعادلة بـ Laplace transform بس Laplace transform
+
+12
+00:01:09,880 --> 00:01:14,180
+فقط هنستخدمه للدوال with constant coefficient
+
+13
+00:01:14,180 --> 00:01:18,240
+للمعادلات التفاضلية و with constant coefficients
+
+14
+00:01:18,240 --> 00:01:23,420
+يبقى المعاملات كلها لهم ثوابت وليست أي معاملة 
+
+15
+00:01:24,270 --> 00:01:27,370
+فبجي بقول في هذا الـ section we shall use Laplace
+
+16
+00:01:27,370 --> 00:01:31,290
+transform لنستخدم تحويلات لابلاس مشان الحل الـ 
+
+17
+00:01:31,290 --> 00:01:36,490
+initial value problems مسائل القيم الحدية for 
+
+18
+00:01:36,490 --> 00:01:40,310
+linear differential equations للمعادلات الخطية
+
+19
+00:01:40,310 --> 00:01:46,620
+with constant coefficients بمعاملات ثابتة ذات يعني
+
+20
+00:01:46,620 --> 00:01:51,220
+بدنا نترجم الكلام اللي قولناه قبل بصيغة أخرى that
+
+21
+00:01:51,220 --> 00:01:54,580
+is we shall solve the differential equation a y
+
+22
+00:01:54,580 --> 00:01:58,720
+double prime زيادة b y prime زيادة c y يساوي zero
+
+23
+00:01:58,720 --> 00:02:02,660
+طبعا الـ a و الـ b و الـ c constant لإن احنا جايلين
+
+24
+00:02:02,660 --> 00:02:07,020
+with constant coefficients ما لها by Laplace
+
+25
+00:02:07,020 --> 00:02:12,020
+transform بتحويلات Laplace نحاول نحل المعادلات اللي
+
+26
+00:02:12,020 --> 00:02:15,580
+بتكون على الشكل اللي قدامنا هذه باستخدام أو
+
+27
+00:02:15,580 --> 00:02:20,180
+باستخدام التحويلات لابلاس لكن احنا المرة اللي فاتت
+
+28
+00:02:20,180 --> 00:02:26,680
+أخدنا لابلاس للدوال ولم نأخذ لابلاس للمشتقات مظبوط 
+
+29
+00:02:26,680 --> 00:02:30,780
+أخدنا لابلاس للدوال العادية وشوفنا كيف بناخد اسمه بدنا
+
+30
+00:02:30,780 --> 00:02:36,300
+نيجي الآن نعطي نظرية تتحدث عن كيفية إيجاد لابلاس
+
+31
+00:02:36,300 --> 00:02:40,000
+للمشتقة الأولى لابلاس للمشتقة الثانية لابلاس
+
+32
+00:02:40,000 --> 00:02:43,800
+ترانسفورم للمشتقة الثالثة لابلاس ترانسفورم للمشتقة
+
+33
+00:02:43,800 --> 00:02:50,000
+الـ nونية يبقى النظرية بتقول لو كان لابلاس الـ F prime
+
+34
+00:02:50,000 --> 00:02:54,460
+exist يبقى في هذه الحالة لكل الـ S اللي أكبر من A
+
+35
+00:02:54,460 --> 00:03:00,960
+then لابلاس ترانسفورم للـ F prime of T عمليا سيساوي 
+
+36
+00:03:00,960 --> 00:03:06,220
+S في لابلاس الـ F of T ناقص الـ F of Zero أثناء
+
+37
+00:03:06,220 --> 00:03:09,900
+الكتابة واحنا بنحلممكن ما نكتبش الكلام اللي عندنا،
+
+38
+00:03:09,900 --> 00:03:14,940
+هنروح نكتب S في capital Y of S مين capital Y of S؟
+
+39
+00:03:14,940 --> 00:03:19,040
+هو لا بلاس لمين؟ للي F of T لإن احنا قولنا لا بلاس 
+
+40
+00:03:19,040 --> 00:03:24,000
+للي F of T بقطعة دالة في S تمام؟ ولما كانت
+
+41
+00:03:24,000 --> 00:03:30,730
+المسألة بدلالة Y كلها فبروح بقول capital Y of S 
+
+42
+00:03:30,730 --> 00:03:34,330
+ناقص F of zero اللي هي قيمة الدالة عند الـ zero
+
+43
+00:03:34,330 --> 00:03:39,550
+يعني قيمة الـ Y عند الـ zero F هذي هذي لبالك مش F
+
+44
+00:03:39,550 --> 00:03:45,270
+هذي هه هذي هه ممكن أقولك هذي G of T مش هم
+
+45
+00:03:45,270 --> 00:03:50,030
+ما تلخبطيش يبقى هذي G of T يبقى الـ F of T تبعتنا
+
+46
+00:03:50,030 --> 00:03:57,950
+هذي هي Y تمام؟ إذا بقول مرة ثانية Laplace transform
+
+47
+00:03:57,950 --> 00:04:04,450
+للـ F prime of T هو S في Laplace للـ F of T نقص F of
+
+48
+00:04:04,450 --> 00:04:10,310
+Zero عمليا هكتب S في capital Y of S نقص Y of Zero
+
+49
+00:04:10,310 --> 00:04:13,310
+طبعا في الكتاب مكتوب هيكفي احنا بنكتب هذا الكتاب و
+
+50
+00:04:13,310 --> 00:04:16,730
+هذا الكتاب لكن عند الشغل العملي ممكن اكتب هذه 
+
+51
+00:04:16,730 --> 00:04:20,370
+مباشرة و ما بديش اللي جابلها لإن أنا شغلي بده يجيب
+
+52
+00:04:20,370 --> 00:04:28,220
+capital Y of S Y of S هو Laplace تبع F of T يعني
+
+53
+00:04:28,220 --> 00:04:32,480
+أنا بس بأعد كتابة المعادلة من جديد يعني بده اكتب
+
+54
+00:04:32,480 --> 00:04:37,240
+هذه دغري و اكتب مين اكتب هذه طيب هذا Laplace 
+
+55
+00:04:37,240 --> 00:04:40,940
+للمشتقة الأولى تعالوا خذوا Laplace للمشتقة الثانية
+
+56
+00:04:40,940 --> 00:04:46,460
+as a function of T يبقى الأولى بعدين بمين بـ S ثانية 
+
+57
+00:04:47,880 --> 00:04:52,140
+الثالثة اسكيب الرابعة S أس أربعة وبتبدأ الأس
+
+58
+00:04:52,140 --> 00:04:57,180
+ينقص كل ten بنقص من الأس واحد طلع لي هنا يبقى S
+
+59
+00:04:57,180 --> 00:05:02,800
+تربيع في الـ plus للـ F of T كله بناقص بعده ناقص 
+
+60
+00:05:02,800 --> 00:05:07,380
+الـ S تربيع صارت هنا ايش S أجاني F of Zero بعدها
+
+61
+00:05:07,380 --> 00:05:13,590
+مشتقة الـ F and Man and Zero أو عمليا هقول S تربيع 
+
+62
+00:05:13,590 --> 00:05:20,090
+في capital Y of S ناقص S في Y عند الـ zero ناقص Y
+
+63
+00:05:20,090 --> 00:05:26,540
+prime عند الـ zero عليها بنروح نجيب لابلاس المشتقة
+
+64
+00:05:26,540 --> 00:05:31,160
+الثالثة لابلاس المشتقة الرابعة in general بروح بقول
+
+65
+00:05:31,160 --> 00:05:36,880
+لابلاس للمشتقة الـ nونية يبقى بده أبدأ S أس N S أس
+
+66
+00:05:36,880 --> 00:05:40,840
+N ناقص واحد S أس N ناقص اثنين وضل نزل لغاية موصل
+
+67
+00:05:40,840 --> 00:05:47,260
+لـ S وآخر term ما يوجد فيه S تمام مرة ثانية يبقى 
+
+68
+00:05:47,260 --> 00:05:52,340
+لابلاس للتفاضل رقم N عند T بده يساوي S أس N في
+
+69
+00:05:52,340 --> 00:05:56,860
+لابلاس F of T أو لسهولة N's that fold سأبدأ فيها دي
+
+70
+00:05:56,860 --> 00:06:03,000
+دوري يبقى S أس N في capital Y of S ناقص S أس N
+
+71
+00:06:03,000 --> 00:06:08,320
+ناقص واحد في Y and Zero وبعد هيك باب المشتقة 
+
+72
+00:06:08,320 --> 00:06:11,740
+الأولى المشتقة دي يعني المشتقة بتطلع و S مالها 
+
+73
+00:06:11,740 --> 00:06:16,020
+بتنزل عكس بعض هذه الأس تبعها بنزل وهذه المشتقة
+
+74
+00:06:16,020 --> 00:06:19,120
+تبعها بتطلع، المشتقة الأولى، المشتقة الثانية،
+
+75
+00:06:19,120 --> 00:06:24,520
+الثالثة، الرابعة إلى آخرها يبقى S أس N كابيتال Y of 
+
+76
+00:06:24,520 --> 00:06:30,440
+S ناقص S أس N ناقص واحد Y عند الـ zero ناقص S أس N
+
+77
+00:06:30,440 --> 00:06:35,620
+ناقص اثنين Y prime عند الـ zero اللي بعدها يبقى S
+
+78
+00:06:35,620 --> 00:06:40,640
+أس N ناقص ثلاثة و Y double Prime and Zero أظل ماشي
+
+79
+00:06:40,640 --> 00:06:45,720
+لغاية S Y to the derivative N ناقص اثنين and Zero
+
+80
+00:06:45,720 --> 00:06:50,580
+آخر term مافيش فيه S زي ما كان آخر term هنا كله 
+
+81
+00:06:50,580 --> 00:06:54,900
+مافيش فيه S تمين في Y to the derivative N minus الـ
+
+82
+00:06:54,900 --> 00:07:01,480
+one and Zero يعني آخر term هنا بيكون هو المشتقة
+
+83
+00:07:01,480 --> 00:07:07,290
+الـ N ناقص واحد مشتقة ثانية آخر ترم بيكون مين؟ مشتقة الأولى
+
+84
+00:07:07,290 --> 00:07:12,270
+يعني لو كانت المشتقة الثالثة بيصير آخر ترم مشتقة 
+
+85
+00:07:12,270 --> 00:07:18,510
+الثانية وهكذا تمام؟ طيب الآن بدنا نروح نشتغل عملي 
+
+86
+00:07:18,510 --> 00:07:22,730
+يعني بنشوف كيف التطبيق العملي لصيغة اللي موجودة
+
+87
+00:07:22,730 --> 00:07:26,910
+هذه طيب السؤال قبل ما تبدأ هذه الصيغة بدنا نحفظها؟
+
+88
+00:07:27,050 --> 00:07:31,690
+لا ما بدناش يجيك تحفظيها تمام؟ هعطيك إياها في جدول
+
+89
+00:07:31,690 --> 00:07:36,850
+موجود الصيغة عندك هنا المهم بدي كيف أستخدمها بعد
+
+90
+00:07:36,850 --> 00:07:42,890
+قليل هأقول لكم كيف بدنا نشتغل بالجدول هذا الـ .. الآن
+
+91
+00:07:42,890 --> 00:07:47,890
+بدنا نيجي نحل مثال على هذا الكلام طيب قال لي حل
+
+92
+00:07:47,890 --> 00:07:53,620
+المعادلة التفاضلية ولم يتكلم كلمة سأخبرك أن أنا
+
+93
+00:07:53,620 --> 00:08:02,160
+ممكن أحل الطريقة القديمة باستخدام 
+
+94
+00:08:02,160 --> 00:08:07,660
+لابلاس ترانسفورم لتحل الاختصار الاختصار الاختصار
+
+95
+00:08:07,660 --> 00:08:12,380
+الاختصار الاختصار الاختصار الاختصار الاختصار
+
+96
+00:08:12,380 --> 00:08:19,260
+الاختصار الاختصار الاختصار الاختصار الاختصار
+
+97
+00:08:19,260 --> 00:08:20,040
+الاختصار الاختصار الاختصار الاختصار الاختصار
+
+98
+00:08:20,040 --> 00:08:22,410
+الاختصار الاختصار الاختصار الاختص طريقتنا القديمة
+
+99
+00:08:22,410 --> 00:08:26,490
+وبالطريقة من؟ لجديدة لإنه ما قال لي قال لي solve the
+
+100
+00:08:26,490 --> 00:08:32,950
+following initial value problems بس تمام إذا أنا
+
+101
+00:08:32,950 --> 00:08:36,890
+لو أجاني السؤال بهذا الشكل لامتحان ليه الحرية أحل
+
+102
+00:08:36,890 --> 00:08:40,610
+بالطريقة اللي بدي إياها يبقى أنا لو بده أحل بالطريقة
+
+103
+00:08:40,610 --> 00:08:50,700
+القديمة بقوله هيك solution لت يساوي E of RT be a 
+
+104
+00:08:50,700 --> 00:09:01,180
+solution of equation one then the characteristic
+
+105
+00:09:01,180 --> 00:09:04,520
+equation is 
+
+106
+00:09:06,610 --> 00:09:12,430
+أر تربيع ناقص أر ناقص اثنين يساوي زيرو هذه لو جيت
+
+107
+00:09:12,430 --> 00:09:18,750
+أحلها كحاصل ضرب قوسين ويساوي زيرو يبقى هنا أر هنا
+
+108
+00:09:18,750 --> 00:09:25,510
+أر هنا واحد هنا اثنين هنا ناقص هنا زائد هي ناقص أر
+
+109
+00:09:25,510 --> 00:09:30,630
+وناقص اثنين أر بضل ناقص أر هي في النص ومنها أر one
+
+110
+00:09:30,630 --> 00:09:37,770
+تساوي سالب واحد و R2 تساوي كده؟ تساوي اثنين، تمام؟
+
+111
+00:09:37,770 --> 00:09:45,350
+إذا صار إن الحل هو Y يساوي C1 في E أس ناقص T زائد
+
+112
+00:09:45,350 --> 00:09:53,610
+C2 في E أس اثنين T يبقى هذا الحل اللي احنا اتعلمناه
+
+113
+00:09:53,610 --> 00:09:59,570
+قبل طبعا الحين ما بديش الحل هذا بدي اروح لحل آخر
+
+114
+00:09:59,570 --> 00:10:02,990
+بواسط الـ initial value problem أو بـ الـ series
+
+115
+00:10:02,990 --> 00:10:06,810
+solution بس إن كان بده series solution بدي يعطيني 
+
+116
+00:10:06,810 --> 00:10:10,710
+نقطة مظبوط هذا ما اعطانيش نقطة يبقى in series
+
+117
+00:10:10,710 --> 00:10:16,910
+solution طبعا ايه كويس يبقى بداجي ايش بداجي اقوله
+
+118
+00:10:16,910 --> 00:10:19,010
+هنا another solution 
+
+119
+00:10:24,860 --> 00:10:30,200
+بناخد محل آخر يبقى نأخذ Laplace transform للطرفين 
+
+120
+00:10:30,200 --> 00:10:35,440
+يبقى بدي أجيك عندك هنا Laplace transform لـ Y 
+
+121
+00:10:35,440 --> 00:10:41,120
+double prime ناقص Y prime زائد اثنين Y بده يساوي
+
+122
+00:10:41,120 --> 00:10:48,040
+Laplace لـ Zero تكامل
+
+123
+00:10:48,040 --> 00:10:53,380
+EOS ناقص T ضرب Zero في DT يبقى Zero كويس يبقى هذا 
+
+124
+00:10:53,380 --> 00:10:58,460
+بده يساوي Zero طيب هذا الآن linear لـ plus linear
+
+125
+00:10:58,460 --> 00:11:03,100
+function مظبوط إذا هذا شو بده يعطينا بده يعطينا لـ 
+
+126
+00:11:03,100 --> 00:11:10,480
+plus للـ y double prime ناقص لـ plus للـ y prime زي 
+
+127
+00:11:10,480 --> 00:11:16,080
+دي اثنين لـ plus للـ y كله بده يساوي مان؟ بده يساوي
+
+128
+00:11:16,080 --> 00:11:23,860
+زيرو ايش فيه؟ اه هذه ناقص المثلة خلاص يبقى هذه 
+
+129
+00:11:23,860 --> 00:11:30,850
+ناقص تمام هنا كتبت اه وهنا نقص تمام يبقى كله بالشكل
+
+130
+00:11:30,850 --> 00:11:33,890
+اللي عنه هذا الآن بدي أشيل الـ plus للـ y double
+
+131
+00:11:33,890 --> 00:11:39,530
+prime و أحط القيمة بتاعته و أشيل الـ plus لمن؟ للـ y
+
+132
+00:11:39,530 --> 00:11:43,170
+prime و الـ y و أحط القيمة بتاعته من وين؟ من الكلام
+
+133
+00:11:43,170 --> 00:11:47,250
+اللي قعدنا عنه هذا بدي نمسك الأولى الـ plus للـ y
+
+134
+00:11:47,250 --> 00:11:52,610
+double prime يبقى هي عبارة عن s تربيع في capital Y
+
+135
+00:11:52,610 --> 00:12:01,350
+of s ناقص s في main في الـ y عند الـ zero ناقص y
+
+136
+00:12:01,350 --> 00:12:07,800
+prime عند الـ zero يبقى يخلصنا من الجزء الأول اللي
+
+137
+00:12:07,800 --> 00:12:13,520
+بعده هاي ناقص وبتفتح قوس حتى ما تخلطي بده يجي الـ 
+
+138
+00:12:13,520 --> 00:12:18,860
+Y prime هي موجودة عند أول واحدة يبقى هي S في
+
+139
+00:12:18,860 --> 00:12:28,430
+capital Y of S ناقص Y عند الـ zero وصلنا لبعدها ناقص
+
+140
+00:12:28,430 --> 00:12:34,850
+اثنين capital Y of S كل هذا الكلام بده يساوي كده؟ 
+
+141
+00:12:34,850 --> 00:12:42,110
+بده يساوي Zero إذا بدي أعرف بعد هيك ماهو شكل 
+
+142
+00:12:42,110 --> 00:12:47,170
+capital Y of S بنقولك بسيطة، إذا خلينا نفك هذه
+
+143
+00:12:47,170 --> 00:12:54,310
+يبقى هذه S تربيع في capital Y of S ناقص S في Y عند
+
+144
+00:12:54,310 --> 00:12:59,910
+الـ zero معطاة، بقداش؟ بواحد يبقى ما بديش لو أحط
+
+145
+00:12:59,910 --> 00:13:07,110
+مكانها واحد الآن ناقص Y' عند الـ zero بقداش بزيرو 
+
+146
+00:13:07,110 --> 00:13:13,870
+مع السلامة خلصنا الـ term الأول بداجي هذا ناقص S في 
+
+147
+00:13:13,870 --> 00:13:20,170
+capital Y of S ناقص في ناقص بزائد Y عند الـ zero
+
+148
+00:13:20,170 --> 00:13:28,230
+بقداش بواحد اللي بعدها ناقص اثنين capital Y of S بده
+
+149
+00:13:28,230 --> 00:13:34,530
+يساوي Zero طلع لي الـ term هذا و الـ term هذا و الـ
+
+150
+00:13:34,530 --> 00:13:40,050
+term هذا فيهم capital Y of S، صحيح ولا لأ؟ إذا
+
+151
+00:13:40,050 --> 00:13:44,170
+بتاخدوا عامل مشترك من الكل شو، بيبقى لدي هنا، بيبقى
+
+152
+00:13:44,170 --> 00:13:53,390
+لدي S تربيع، ناقص S، ناقصي 2، كله في capital Y of
+
+153
+00:13:53,390 --> 00:14:01,440
+S هذه ناقص S في واحد بناقص S هذه Zero مع السلام
+
+154
+00:14:01,440 --> 00:14:06,540
+الله يسهل عليها هذه زائد واحد قلصت كله بده يساوي
+
+155
+00:14:06,540 --> 00:14:12,800
+كده؟ بده يساوي Zero اللي فيها capital Y of S بده
+
+156
+00:14:12,800 --> 00:14:17,720
+أخليها في جهة و الباقي وين؟ في جهة ثانية أنا ما بديش
+
+157
+00:14:17,720 --> 00:14:23,220
+هذه أنا بدي capital Y of S فبروح بقوله capital Y
+
+158
+00:14:23,220 --> 00:14:32,360
+of S بدي أساوي S ناقص واحد تقسيم S زائد واحد في مين
+
+159
+00:14:32,360 --> 00:14:41,580
+في S ناقص اثنين واضح أن اختصارات ما عنديش طيب كيف
+
+160
+00:14:41,580 --> 00:14:43,060
+بدي أسوي فيها هذه 
+
+161
+00:14:45,990 --> 00:14:49,470
+بقول بسيطة جدا سمعنا بالـ partial fractions في
+
+162
+00:14:49,470 --> 00:14:55,250
+Calculus B كسور الجزئية إذا بروح بأحلل هذا الكسر
+
+163
+00:14:55,250 --> 00:15:01,090
+إلى مجموع كسرين أو ثلاثة أو أربعة حسب طبيعة المثلة
+
+164
+00:15:01,090 --> 00:15:07,830
+بجيب أطلع أنا عند المقام اللي هو قوسين وقوس الثاني
+
+165
+00:15:07,830 --> 00:15:13,400
+يبقى Different coefficients، معاملات مختلفة، إذا
+
+166
+00:15:13,400 --> 00:15:18,080
+باجي بقوله هذا الكلام يساوي، هذا قوس، اللي هو 
+
+167
+00:15:18,080 --> 00:15:24,060
+الـ S زائد واحد، القوس اللي هو زائد وهذا كسر وهذا
+
+168
+00:15:24,060 --> 00:15:30,980
+الثاني بعد هيك باجي بقول كل واحد من المقامات مختلف 
+
+169
+00:15:30,980 --> 00:15:35,920
+عن الثاني وكل واحد من الدرجة الأولى إذا بقول
+
+170
+00:15:35,920 --> 00:15:41,580
+constant على الأول و constant على من؟ على الثاني و
+
+171
+00:15:41,580 --> 00:15:46,620
+بعد برجع معلوماتي في calculus بيه بدي أجيب قداش 
+
+172
+00:15:46,620 --> 00:15:53,2
+
+201
+00:19:05,170 --> 00:19:11,370
+نشوف الآن كيف بدنا نجيب هذه هذي شو أصلها يا بنات؟
+
+202
+00:19:11,370 --> 00:19:21,630
+exponential E أس سالب T هذي شو أصلها؟ E أس اثنين T
+
+203
+00:19:21,630 --> 00:19:26,410
+طبعًا احنا
+
+204
+00:19:26,410 --> 00:19:29,970
+مطلوب نحفظ ولا بدنا إيش نحفظ المرة اللي فاتت
+
+205
+00:19:29,970 --> 00:19:35,280
+قلت لكم بتجيبوا الكتب معكم،اللي جابت كتابها جابته،
+
+206
+00:19:35,280 --> 00:19:39,820
+واللي ما جابتش أخذت احتياطاتي وجبت لكم الجدول
+
+207
+00:19:39,820 --> 00:19:47,620
+المصور صفحة 319 تمام؟ يلا وزعوا بحيث كل مقعد يكون
+
+208
+00:19:47,620 --> 00:19:53,080
+عليه ورقات جدول، يلا خذ يلا وزع الباقي، بسرعة
+
+209
+00:19:53,080 --> 00:19:58,300
+بسرعة يلا، من حد ما نوصل للشكل اللي عندنا هذا يبقى
+
+210
+00:19:58,300 --> 00:20:01,540
+capital Y of this اللي هو Laplace transform لل
+
+211
+00:20:01,540 --> 00:20:05,680
+solution يساوي الجزء اللي عندنا هذا، إذا بناء عليه
+
+212
+00:20:05,680 --> 00:20:12,940
+بروح بقول له solution of 
+
+213
+00:20:15,300 --> 00:20:22,860
+differential equation one is بتقول لي y الصغيرة as
+
+214
+00:20:22,860 --> 00:20:28,300
+a function of t يساوي، يبقى هذا ل plus transform
+
+215
+00:20:28,300 --> 00:20:34,500
+لهذا، هو الأصل تبعها، يبقى بده يساوي جداش هنا
+
+216
+00:20:34,500 --> 00:20:41,230
+طولتين يبقى هاي طولتين بخليها زي ما هي، باجي لمن؟
+
+217
+00:20:41,230 --> 00:20:46,030
+ل الواحد على S زائد واحد، كلكم افتحوا لي في
+
+218
+00:20:46,030 --> 00:20:49,010
+الكتاب صفحة الثلاثمية والتسعة عشر أو الورق اللي
+
+219
+00:20:49,010 --> 00:20:53,710
+وزعت لكم عليها، هذه سبكي من العمود اللي على الشمال
+
+220
+00:20:53,710 --> 00:20:59,210
+بتاخذ العمود اللي على اليمين، بروح بدور عندي على S
+
+221
+00:20:59,210 --> 00:21:05,430
+وراحنا على S زائد واحد، بطلع في النقطة رقم اثنين
+
+222
+00:21:05,430 --> 00:21:12,530
+مكتوب واحد على اس ناقص ايه بواحد، مظبوط؟ لكنها جداش
+
+223
+00:21:12,530 --> 00:21:17,250
+بالزائد تمام، يبقى هنا لما صارت بالزائد معناته هي
+
+224
+00:21:17,250 --> 00:21:27,050
+E أس سالب T يعني E أس سالب T يبقى هنا صار
+
+225
+00:21:27,050 --> 00:21:34,900
+ثلثين في E أس سالب، تبعدها، زائد ثلث اللي هو اللي
+
+226
+00:21:34,900 --> 00:21:40,300
+برا هاي ثلث اللي برا واحد على اس ناقص اثنين برضه
+
+227
+00:21:40,300 --> 00:21:46,060
+نفس النقطة، نقطة رقم اثنين واحد على اس ناقص ايه
+
+228
+00:21:46,060 --> 00:21:53,180
+اجبالها جداش E أس ET يبقى هذا ههه اللي هي مين اللي
+
+229
+00:21:53,180 --> 00:22:02,960
+هي الدالة وهذا لابلاس ترانسفورم اللي هي اللي هي
+
+230
+00:22:02,960 --> 00:22:02,980
+اللي هي اللي هي اللي هي اللي هي اللي هي اللي هي
+
+231
+00:22:02,980 --> 00:22:03,180
+اللي هي اللي هي اللي هي اللي هي اللي هي اللي هي
+
+232
+00:22:03,180 --> 00:22:03,260
+اللي هي اللي هي اللي هي اللي هي اللي هي اللي هي
+
+233
+00:22:03,260 --> 00:22:19,260
+اللي هي اللي 
+
+234
+00:22:19,260 --> 00:22:28,180
+هي، يبقى هذا الحل المطلوب يبقى
+
+235
+00:22:28,180 --> 00:22:33,580
+بدك
+
+236
+00:22:33,580 --> 00:22:38,040
+تشتق الحل هذا مرتين وتجي تعوض من حدود التكامل وهي
+
+237
+00:22:38,040 --> 00:22:42,280
+الجواب عندك زي ما كنا بنعمل قبل، طبعًا الشغل اللي
+
+238
+00:22:42,280 --> 00:22:46,100
+اشتغلته هو هذا السبب اللي خلاني اشتغله لإن ما قال
+
+239
+00:22:46,100 --> 00:22:51,080
+قال لي، صلفه سكت تمام؟ فاضطريت أنا، وقلت إن دي بدل
+
+240
+00:22:51,080 --> 00:22:55,200
+الحل اثنين، لكن لو قال لي من البداية use Laplace 
+
+241
+00:22:55,200 --> 00:23:00,820
+transform إذا automatic بدي اروح مباشرة على
+
+242
+00:23:00,820 --> 00:23:04,500
+Laplace transform اللي همام القطوة الثانية هذه
+
+243
+00:23:04,500 --> 00:23:10,200
+ماشي؟ حد بتحب تسأل أي سؤال قبل مواصلة الأمثلة؟
+
+244
+00:23:10,200 --> 00:23:13,420
+ماعندي، كل المحاضرة أمثلة؟ ما في هذا نظري، قلص
+
+245
+00:23:13,420 --> 00:23:19,610
+النظرية، هل بتحب تسأل أي سؤال؟ طبعًا أنا قلت لكم ال
+
+246
+00:23:19,610 --> 00:23:22,710
+derivative بتاعه بديش يا كنت أحفظه، طلع لي في آخر
+
+247
+00:23:22,710 --> 00:23:30,550
+سطر عندك آخر سطر بتاعك مكتوب عندك هنا اللي هو اللي
+
+248
+00:23:30,550 --> 00:23:36,730
+على الشمال عندك F to the derivative N F وفوقها N
+
+249
+00:23:36,730 --> 00:23:41,460
+بين قوسين as a function of T اللي جبالها سطر طويل
+
+250
+00:23:41,460 --> 00:23:46,960
+هذا اليومين لبلاس ترانسفورم للمشتقة قانونية لـ F
+
+251
+00:23:46,960 --> 00:23:50,980
+شايفينه اللي قتلنا ساعة قبل شوية، كتبناه على 
+
+252
+00:23:50,980 --> 00:23:56,440
+اللوح، آخر سطر تحت S أس N capital F of S اللي
+
+253
+00:23:56,440 --> 00:24:00,400
+احنا ما بنقول عليها capital Y of S اللي بعدها S
+
+254
+00:24:00,400 --> 00:24:04,480
+أس N ناقص واحد F of Zero ناقص ناقص لغاية آخر term
+
+255
+00:24:04,480 --> 00:24:10,590
+F of N ناقص واحد عند من عند Zero، كل F حط في مكانها
+
+256
+00:24:10,590 --> 00:24:15,310
+Y بنكون A، نفس الكلام اللي كتبناه هنا على اللوح قبل 
+
+257
+00:24:15,310 --> 00:24:21,630
+قليل تمام؟ كل سؤال هيطلع الشكل مش دائمًا بدي يطلع
+
+258
+00:24:21,630 --> 00:24:25,950
+exponential زي هذه، بس سؤال يطلع exponential بقدر
+
+259
+00:24:25,950 --> 00:24:30,010
+الله يمكن يطلع الجواب T to the power N يمكن Sine
+
+260
+00:24:30,010 --> 00:24:35,880
+يمكن Cos يمكن Gauss يمكن Sine يمكن T في Cos أو تي
+
+261
+00:24:35,880 --> 00:24:40,120
+في Cos يمكن إلى أخرى، أي دالة من مجموعة الدوال ال
+
+262
+00:24:40,120 --> 00:24:44,360
+18 أو ال 19 اللي عندك هدول خلاص؟ والمرة اللي فاتت
+
+263
+00:24:44,360 --> 00:24:47,160
+ابتدينا وحسبنا لا plus لا transform والواحد طلع
+
+264
+00:24:47,160 --> 00:24:52,600
+قداش؟ وعد المسلمين، أول واحدة فوق جايها عندك في
+
+265
+00:24:52,600 --> 00:24:59,180
+الجدول، أول واحدة فوق تمام؟ طيب، نجي ناخذ المثال رقم 
+
+266
+00:24:59,180 --> 00:25:05,010
+اثنين، يبقى مثال رقم اثنين، لا نترككم تايهين نقول لكم 
+
+267
+00:25:05,010 --> 00:25:13,170
+use Laplace transform example example
+
+268
+00:25:13,170 --> 00:25:25,790
+use
+
+269
+00:25:25,790 --> 00:25:30,470
+Laplace transform
+
+270
+00:25:53,960 --> 00:26:03,840
+أول واحدة أو نمرة أ أو نمرة واحد اللي هو من Y 
+
+271
+00:26:03,840 --> 00:26:12,580
+double prime ناقص أربعة Y prime زائد أربعة Y تساوي
+
+272
+00:26:12,580 --> 00:26:20,780
+زيرو، والـ Y عند زيرو بده يساوي الواحد، والـ Y prime
+
+273
+00:26:20,780 --> 00:26:27,480
+عند زيرو كذلك تساوي كده؟ تساوي واحد، solution
+
+274
+00:26:31,500 --> 00:26:35,880
+يبقى بدي أخذ Laplace transform للطرفين، مش هشغل
+
+275
+00:26:35,880 --> 00:26:38,920
+الشغل التفصيلي هذا، لأ، هدخل Laplace على كل واحدة
+
+276
+00:26:38,920 --> 00:26:46,240
+فيهم دوري، يبقى بدي أجي أقول Laplace لـ Y double prime
+
+277
+00:26:46,240 --> 00:26:53,680
+ناقص أربعة في Laplace لـ Y prime زائد أربعة في 
+
+278
+00:26:53,680 --> 00:26:57,880
+Laplace لـ Y Laplace لـ Zero بالزينة
+
+279
+00:27:08,040 --> 00:27:18,680
+ناقص S في Y عند Zero ناقص Y عند Zero، هذا كله term
+
+280
+00:27:18,680 --> 00:27:23,420
+الأول، اللي بعده ناقص أربعة في
+
+281
+00:27:29,980 --> 00:27:40,100
+ناقص Y عند الـ zero زائد أربعة في مين في capital Y 
+
+282
+00:27:40,100 --> 00:27:41,120
+of S
+
+283
+00:27:54,030 --> 00:28:04,510
+يبقى ناقص S في واحد، و Y prime ناقص واحد، ناقص أربعة S
+
+284
+00:28:04,510 --> 00:28:12,630
+في capital Y of S ناقص في ناقص، بزائد أربعة في Y عند 
+
+285
+00:28:12,630 --> 00:28:17,310
+الـ zero اللي بقد إيش بواحد، خلاصنا من القوس هذا
+
+286
+00:28:17,310 --> 00:28:25,610
+زائد أربعة capital Y of S كله بده يساوي Zero، بعد
+
+287
+00:28:25,610 --> 00:28:30,710
+ذلك تذهب وتأخذ اللي فيهم capital Y of S مع بعضهم
+
+288
+00:28:30,710 --> 00:28:39,090
+بقوة سن واحد، يبقى S squared ناقص أربعة S زائد 
+
+289
+00:28:39,090 --> 00:28:49,460
+أربعة كله في capital Y of S ضايلة هنا ناقص S وعندك
+
+290
+00:28:49,460 --> 00:28:57,200
+هنا ناقص واحد وزائد أربعة بظهر زائد ثلاثة كله بده
+
+291
+00:28:57,200 --> 00:29:01,760
+يساوي مين؟ بده يساوي Zero هذه يا بنات، إيش بتعطينا
+
+292
+00:29:01,760 --> 00:29:10,240
+المثل هذا باعتبار S ناقص اثنين الكل تربيع، يبقى S
+
+293
+00:29:10,240 --> 00:29:17,870
+ناقص اثنين الكل تربيع، فاهمين؟ في capital Y of S
+
+294
+00:29:17,870 --> 00:29:21,630
+يساوي هذي هوديها على الجهة الثانية يبقى إيش
+
+295
+00:29:21,630 --> 00:29:29,750
+بيصير؟ S ناقص ثلاثة، بناء عليه صار Laplace للحل 
+
+296
+00:29:29,750 --> 00:29:38,050
+capital Y of S بده يساوي S ناقص ثلاثة على S ناقص 
+
+297
+00:29:38,050 --> 00:29:43,470
+اثنين لكل تربيع، الشكل اللي عندنا، إذا شو بدي أعمل
+
+298
+00:29:43,470 --> 00:29:49,090
+لهذه؟ بدي أعمل لها partial fractions، يبقى هذه
+
+299
+00:29:49,090 --> 00:29:56,990
+تساوي، S ولا لا؟ درجة البسط أقل من درجة المقام يبقى
+
+300
+00:29:56,990 --> 00:30:04,020
+احنا جاهزين، بس المقام من الدرجة الأولى ومكرر، إذا
+
+301
+00:30:04,020 --> 00:30:10,200
+بدي كرر باللي درسنا في calculus بيه، بقول S ناقص اثنين
+
+302
+00:30:10,200 --> 00:30:18,320
+زائد كسر ثاني S ناقص اثنين لكل تربيع، بالشكل اللي 
+
+303
+00:30:18,320 --> 00:30:24,100
+عنا هنا، هذا من الدرجة الأولى بقول A هذا كمان من 
+
+304
+00:30:24,100 --> 00:30:32,410
+الدرجة الأولى ومكرر بقول B، يبقى هكذا كنا بنعمل
+
+305
+00:30:32,410 --> 00:30:37,870
+فيه Calculus، B، الآن بدي أجي لمن؟ للمعادلة اللي
+
+306
+00:30:37,870 --> 00:30:44,010
+عندنا هذه كلها وبدي أضربها في من؟ في المقام اللي 
+
+307
+00:30:44,010 --> 00:30:48,590
+عندنا هذا، مشان ما يضل عندي كسور، بصير معادلة
+
+308
+00:30:48,590 --> 00:30:54,250
+عادية، بصير سهل علينا حل هذه المعادلة
+
+309
+00:31:07,880 --> 00:31:14,320
+طيب نجي نضرب وين؟ في المقام يبقى المعادلة دي بيصير
+
+310
+00:31:14,320 --> 00:31:24,080
+S ناقص ثلاثة تساوي، يبقى A في S ناقص اثنين زائد B
+
+311
+00:31:24,080 --> 00:31:31,520
+يبقى بطل يصير عندي كسور يبقى قدامي أكثر من طريق يا
+
+312
+00:31:31,520 --> 00:31:36,500
+بحط قيم لـ S من عندي زي المثال اللي قبل يا بفكه
+
+313
+00:31:36,500 --> 00:31:41,200
+بعمل إيش؟ مقارنة بين الطرفين، يبقى ذاكرنا كتاب
+
+314
+00:31:41,200 --> 00:31:45,380
+الطريقة الأولى، والآن سأذكركم بالطريقة الثانية
+
+315
+00:31:45,380 --> 00:31:52,900
+يبقى هذه يا بنات لو بدها تفكه يبقى AS-2AB
+
+316
+00:31:54,450 --> 00:32:00,070
+لو جيت الآن بالعربي بمقارنة المعاملات في الطرفين
+
+317
+00:32:00,070 --> 00:32:06,230
+هذا ال term كله ما له ما في فيه S وهذا هو الوحيد
+
+318
+00:32:06,230 --> 00:32:12,630
+اللي فيه S، يبقى بناء على هذا ال S المعامل تبع ال S
+
+319
+00:32:12,630 --> 00:32:17,890
+هنا جداش A المعامل تبع هنا اللي هو جداش بواحد، إذا
+
+320
+00:32:17,890 --> 00:32:25,000
+A تساوي واحد، الباقي الحد الخالي من S اللي هو ناقص
+
+321
+00:32:25,000 --> 00:32:30,820
+اثنين A زائد B، ده كله يعتبر مقدار ثابت، المقدار
+
+322
+00:32:30,820 --> 00:32:37,140
+الثابت جداش عندنا هنا سالب ثلاثة، باخذه بإشارته، الآن
+
+323
+00:32:37,140 --> 00:32:41,880
+A عندي بواحد يبقى المعادلة هذه لو شيلت ال A وحطيت 
+
+324
+00:32:41,880 --> 00:32:48,140
+مكانها واحد بصير ناقص اثنين في واحد زائد B يساوي
+
+325
+00:32:48,140 --> 00:32:54,960
+ناقص ثلاثة، إذا B تساوي قداش ناقص واحد، سالب اثنين
+
+326
+00:32:54,960 --> 00:32:57,840
+ودّيه على الجهة الثانية بيصير اثنين وسالب ثلاثة بضل
+
+327
+00:32:57,840 --> 00:33:05,220
+جداش سالب واحد، يبقى هي جبت له قيمة ثوابت A و B يبقى
+
+328
+00:33:05,220 --> 00:33:11,620
+بناء عليه أصبح capital Y of S بده يساوي بده أشيل
+
+329
+00:33:11,620 --> 00:33:18,610
+ال A وحط قيمته اللي هي بواحد، يبقى واحد على اس ناقص
+
+330
+00:33:18,610 --> 00:33:27,490
+اثنين، زائد B يبقى ناقص واحد على اس ناقص اثنين لكل
+
+331
+00:33:27,490 --> 00:33:37,230
+تربيع، يبقى هذا يعني Laplace يتغير الرجل للحل، لإن بده
+
+332
+00:33:37,230 --> 00:33:43,990
+يجيب الحل يبقى
+
+333
+00:33:43,990 --> 00:33:46,130
+بده يجيب الحل
+
+334
+00:33:51,510 --> 00:33:58,770
+of the initial value problem one is هذه بداية
+
+335
+00:33:58,770 --> 00:34:07,410
+المثال، سامحالي، one نمرة واحد، يجب أن أقول Y of T بدل
+
+336
+00:34:07,410 --> 00:34:13,150
+ساعة واحد على S ناقص اثنين، توسع جبنا عليه مين؟ E 
+
+337
+00:34:13,150 --> 00:34:18,770
+أس اثنين T، نجي
+
+338
+00:34:18,770 --> 00:34:24,570
+واحد على S ناقص اثنين الكل تربيع يعني بدنا ندور
+
+339
+00:34:24,570 --> 00:34:30,710
+على مين؟ الواحد على S ناقص الكل تربيع في العمود
+
+340
+00:34:30,710 --> 00:34:35,420
+اللي على اليمين، هذابنجي بطلع الأولى، لأ الثانية
+
+341
+00:34:35,420 --> 00:34:41,040
+الثالثة، الرابعة، الخامسة مش عارف وين أنزل، وصلنا
+
+342
+00:34:41,040 --> 00:34:48,940
+لجداش لرقم 11، طلعي لرقم 11 عندك إيش مكتوب عندي in 
+
+343
+00:34:48,940 --> 00:34:54,820
+factorial على s ناقص ال a to the power in minus 
+
+344
+00:34:54,820 --> 00:35:01,590
+one، هذه أقرب واحدة موجودة عندي، صحيح ولا لأ؟ اه بس
+
+345
+00:35:01,590 --> 00:35:06,090
+إيش أنت كاتب هنا؟ أنت كاتب واحد ما عنديش factorial
+
+346
+00:35:06,570 --> 00:35:11,250
+أقول لك لأ ما هو الواحد هو الواحد factorial صحيح
+
+347
+00:35:11,250 --> 00:35:17,230
+يعني كأنها جداش يا بنات اللي هي واحد على اس ناقص
+
+348
+00:35:17,230 --> 00:35:24,890
+اثنين ناقص واحد factorial على اس ناقص اثنين، اص
+
+349
+00:35:24,890 --> 00:35:30,260
+واحد زي واحد، يعني إنّي بجداش بواحد، أطلع يبقى هنا
+
+350
+00:35:30,260 --> 00:35:38,220
+رقم N factorial على S ناقص كله to the power N plus 
+
+351
+00:35:38,220 --> 00:35:44,680
+الـ one، يبقى بناء عليه هذا شو بدها تكون T to the 
+
+352
+00:35:44,680 --> 00:35:51,700
+power N، ال N عندي أنا بقد إيش؟ يبقى T فقط، مضبوط
+
+353
+00:35:51,700 --> 00:35:57,120
+فاهمين؟ في ال E أس ET الإشارة عندنا هنا بالنقص وفي 
+
+354
+00:35:57,120 --> 00:36:03,740
+الجدول عندنا هنا بالنقص يبقى E أس اثنين T بالضبط
+
+355
+00:36:03,740 --> 00:36:11,600
+تمامًا رقم 11، طلع فيها كويسبس إنّ عندك بقد إيش بواحد
+
+356
+00:36:11,600 --> 00:36:19,880
+صحيح وبعد يعني يا بنات أحيانًا أحيانًا بتلعش النتيجة 
+
+357
+00:36:19,880 --> 00:36:24,220
+هنا أو هنا بالنص زي مين زي ما هو موجود عندي في
+
+358
+00:36:24,220 --> 00:36:28,520
+الجدول، بد تحويرة بسيطة بقى تخليه في صورة الجدول
+
+359
+00:36:28,520 --> 00:36:32,280
+يبقى جداش تعملي هذه التحويرة ممكن تدربي في رقم 
+
+360
+00:36:32,280 --> 00:36:35,220
+وتجسمي على الرقم، أنا التحويرة البسيطة بس قلت
+
+361
+00:36:35,220 --> 00:36:40,690
+الواحد هو عبارة عن مين؟ عن واحد factorial تمام، يبقى
+
+362
+00:36:40,690 --> 00:36:45,670
+انتهى المثال اللي عندنا، بروح للمثال اللي بعده، بروح
+
+363
+00:36:45,670 --> 00:36:52,810
+للمثال رقم اثنين، مثال رقم اثنين بيقول لي Y to the
+
+364
+00:36:52,810 --> 00:36:58,130
+derivative IV يعني to the derivative four
+
+365
+00:36:58,130 --> 00:37:04,810
+بالاختصار to the derivative four ناقص Y يساوي Zero
+
+366
+00:37:05,440 --> 00:37:09,720
+وال condition اللي عندنا Y عند ال Zero بده يساوي
+
+367
+00:37:09,720 --> 00:37:14,260
+واحد، ال condition الثاني Y prime عند ال Zero بده
+
+368
+00:37:14,260 --> 00:37:19,480
+يساوي زيرو، ال condition الثالث Y double prime عند
+
+369
+00:37:19,480 --> 00:37:24,840
+ال Zero بده يساوي واحد، ال condition الرابع Y
+
+370
+00:37:24,840 --> 00:37:30,2
+
+401
+00:40:47,740 --> 00:40:52,520
+راحت وهذه بـ S يبقى زائد S
+
+402
+00:40:55,110 --> 00:41:00,550
+ماذا رأيك؟ أخلي capital Y of S لحالها يبقى هاي
+
+403
+00:41:00,550 --> 00:41:06,610
+capital Y of S يساوي هاذي في بينهم عامل مشترك يقول
+
+404
+00:41:06,610 --> 00:41:14,670
+S يبقى لو أخدت S عامل مشترك بظل S تربيع زائد واحد
+
+405
+00:41:15,780 --> 00:41:22,320
+على تحليل الفرق بين المربعين اللي هو S تربيع ناقص 
+
+406
+00:41:22,320 --> 00:41:29,110
+واحد في S تربيع زائد واحد أظن القوس هذا هو نفس
+
+407
+00:41:29,110 --> 00:41:34,770
+القوس هذا مع السلامة، إذا هذا السؤال يختلف عن
+
+408
+00:41:34,770 --> 00:41:40,610
+سابقه في إنه فيه صار عنده اختصارات بين البسط
+
+409
+00:41:40,610 --> 00:41:45,770
+والمقام، إذا في اختصارات يا بنات بنختصرها، ما فيش 
+
+410
+00:41:45,770 --> 00:41:50,790
+اختصارات يبقى كل شيء كما هو
+
+411
+00:41:53,550 --> 00:42:00,050
+طيب يبقى بناء عليه أصبح عندي capital Y of S بده
+
+412
+00:42:00,050 --> 00:42:07,430
+يساوي بقي عندي في البسط S والمقام قداش؟ S تربيع
+
+413
+00:42:07,430 --> 00:42:12,950
+ناقص واحد ليه كمان؟ فرق بين المربعين اللي هو عبارة
+
+414
+00:42:12,950 --> 00:42:19,860
+عن S ناقص واحد في S زائد واحد يبقى من الحلل دائما
+
+415
+00:42:19,860 --> 00:42:25,920
+أو أبدا إلى أبسط العوامل الأولية المقام من الدرجة
+
+416
+00:42:25,920 --> 00:42:30,760
+الثانية البسط من الدرجة الأولى يبقى جاهزين طيب هل 
+
+417
+00:42:30,760 --> 00:42:36,200
+ممكن يكون أو لو كان البسط من الدرجة الثالثة وشو بدي
+
+418
+00:42:36,200 --> 00:42:42,000
+أعمله؟ بنقسم جسمها مطولة ثم بنروح نعمل partially
+
+419
+00:42:42,000 --> 00:42:47,040
+fractions لكن هيك جاهز بقول constant على القوس
+
+420
+00:42:47,040 --> 00:42:54,260
+الأول زائد constant على القوس الثاني بدون أي مشاكل
+
+421
+00:42:54,920 --> 00:42:59,680
+بعد ذلك بضرب الطرفين في المقام اللي عندنا هذا، شو
+
+422
+00:42:59,680 --> 00:43:05,940
+بيصير عندنا؟ بيصير الـ S يساوي A في S زائد واحد 
+
+423
+00:43:05,940 --> 00:43:14,080
+زائد B في S ناقص الواحد فبجي بقوله هنا لو كانت الـ S
+
+424
+00:43:14,080 --> 00:43:20,080
+تساوي واحد، بده أحط قيم لـ S من عندي، بحيث أضيع أحد
+
+425
+00:43:20,080 --> 00:43:26,600
+المجهول ويبقى المجهول الثاني، لو كانت الـ S بواحد،
+
+426
+00:43:26,600 --> 00:43:32,700
+يبقى واحد بده يساوي إيه؟ واحد زائد واحد وهذا مع
+
+427
+00:43:32,700 --> 00:43:38,320
+السلامة اتنين A؟ يبقى بناء عليه الـ A هتساوي كده؟
+
+428
+00:43:38,320 --> 00:43:45,270
+نصف لو كانت الـ S بسالب واحد بطير A وبحصل على
+
+429
+00:43:45,270 --> 00:43:51,870
+مين؟ على B يبقى باجي بقوله لو كانت الـ S تساوي سالب
+
+430
+00:43:51,870 --> 00:43:58,130
+واحد يبقى بصير عندي سالب واحد يساوي هذا بطير وهنا
+
+431
+00:43:58,130 --> 00:44:03,980
+بظل عندي سالب اتنين B سالب واحد وسالب واحد يبقى
+
+432
+00:44:03,980 --> 00:44:10,780
+سالب اتنين B ومنها B تساوي كمان كده؟ هي كمان نصف
+
+433
+00:44:10,780 --> 00:44:16,700
+الشكل اللي عندنا إذا أصبح capital Y of S للـ
+
+434
+00:44:16,700 --> 00:44:24,350
+Laplace transform للحل بده يساوي هي نصف عندك واحد على
+
+435
+00:44:24,350 --> 00:44:33,630
+S ناقص واحد تمام؟ وهنا هي كمان بنصف واحد على S
+
+436
+00:44:33,630 --> 00:44:40,030
+زائد واحد تمام؟
+
+437
+00:44:40,030 --> 00:44:46,290
+طيب لو جيش جماعة تقولوله مرة و يعني؟ مش فاهم؟
+
+438
+00:44:47,540 --> 00:44:54,520
+منها ممكن أخلق كل واحد زي ما هو هذا بيقفع لي E أس T 
+
+439
+00:44:54,520 --> 00:45:01,450
+وهذا E أس T ناقص T تمام؟ بجيب أجمعهم مرة واحدة
+
+440
+00:45:01,450 --> 00:45:05,370
+يابنات هذا بدل الـ exponential والاسم هنا أفضل
+
+441
+00:45:05,370 --> 00:45:08,690
+حاجة لو كيف تبدأ بالـ exponential تقع على كل الحطب
+
+442
+00:45:08,690 --> 00:45:10,210
+بس أنا ما بديش دلوقت دلوقت دلوقت دلوقت دلوقت دلوقت
+
+443
+00:45:10,210 --> 00:45:12,730
+دلوقت دلوقت دلوقت دلوقت دلوقت دلوقت دلوقت دلوقت
+
+444
+00:45:12,730 --> 00:45:15,410
+دلوقت دلوقت دلوقت دلوقت دلوقت دلوقت دلوقت دلوقت
+
+445
+00:45:15,410 --> 00:45:23,870
+دلوقت دلوقت دلوقت دلوقت دلوقت دلوقت دلوقت دلوقت
+
+446
+00:45:23,870 --> 00:45:26,350
+دلوقت دلوقت دلوقت دلوقت دلوقت دلوقت دلوقت دلوقت
+
+447
+00:45:26,350 --> 00:45:31,870
+دلوقت دلوقت دلوقت طيب هذا الكلام يساوي نصف مهيئ
+
+448
+00:45:31,870 --> 00:45:39,270
+جزء ده واحد المقامات كـ S ناقص واحد بـ S زائد واحد
+
+449
+00:45:47,990 --> 00:45:54,450
+تمام؟ يبقى هذا نصف فيه ناقص واحد وزايد واحد مع
+
+450
+00:45:54,450 --> 00:46:01,150
+السلامة بيظل عندنا اتنين S وهذا الفرق بين المربعين
+
+451
+00:46:01,150 --> 00:46:05,190
+يبقى S تربيع ناقص واحد
+
+452
+00:46:08,140 --> 00:46:15,920
+مص مع اتنين مع السلامة يبقى بالضبط لـ S على S 
+
+453
+00:46:15,920 --> 00:46:17,800
+تربيع ناقص واحد
+
+454
+00:46:22,050 --> 00:46:26,470
+يبقى التنتين عندي ماشي، ما عنديش مشكلة، هذه وهذه
+
+455
+00:46:26,470 --> 00:46:30,850
+الاتنين صح، لكن أنا بفكر في تفكير آخر غير التفكير
+
+456
+00:46:30,850 --> 00:46:36,310
+المباشر، أي نعم، باجي الآن على الجدول وبطلع، طبعا
+
+457
+00:46:36,310 --> 00:46:41,460
+أنا تعمدت أعملها بالطريقة دي ليش؟ بده يخليك تروح
+
+458
+00:46:41,460 --> 00:46:46,380
+تجيبها من الجدول، يعني أنا عندي S على S تربيع مش
+
+459
+00:46:46,380 --> 00:46:51,160
+ناقص واحد، S تربيع ناقص A تربيع وبعد هيك الـ A 
+
+460
+00:46:51,160 --> 00:46:56,580
+بواحد، دي بجيب باجي بطلع على الـ S على S تربيع ناقص
+
+461
+00:46:56,580 --> 00:47:01,840
+واحد، اللي هو مين يا بناتي؟ دي رقم قداش؟ 8
+
+462
+00:47:01,840 --> 00:47:07,840
+ممتاز جدا 8 فيها عندي a على S تربيع ناقص a 
+
+463
+00:47:07,840 --> 00:47:14,200
+تربيع الـ a هنا عندي قداش؟ اللي هو بواحد تمام يبقى
+
+464
+00:47:14,200 --> 00:47:20,100
+هنا S على S تربيع ناقص واحد يبقى هذه قوس واحد في T
+
+465
+00:47:20,100 --> 00:47:25,480
+يعني قوس T تمام يبقى بناء عليه solution
+
+466
+00:47:32,530 --> 00:47:42,050
+Y of T بده يساوي قوس T لو 
+
+467
+00:47:42,050 --> 00:47:47,130
+من البداية ما سويتش هالحركة دي اللي عملتها جيت من
+
+468
+00:47:47,130 --> 00:47:53,550
+هنا قلت نصف ونصف خد نصف عمل أو شركة بضل الأول E أس T
+
+469
+00:47:53,550 --> 00:48:00,000
+زائد E أس ناقص T على الاتنين يبقى هادي قوس T يبقى
+
+470
+00:48:00,000 --> 00:48:03,540
+لو خلتيها زي ما قلتيلي E أس T و E أس ناقص T و
+
+471
+00:48:03,540 --> 00:48:07,220
+فيها نصف يبقى قوس T كتبتيها دغري يبقى عملت من الأول
+
+472
+00:48:07,220 --> 00:48:12,220
+دغري أو عملتها بالشكل هذا سيئا وأنا قلتلك تعمد
+
+473
+00:48:12,220 --> 00:48:16,200
+اكتبها وأواصلها للصيغة هذه عشان أخليك تتعلم
+
+474
+00:48:16,200 --> 00:48:20,280
+الصيغة الجديدة من الجدول غير الصيغة رقم 2 اللي 
+
+475
+00:48:20,280 --> 00:48:24,860
+اتعلمناها قبل ذلك تمام؟ أيوة
+
+476
+00:48:38,870 --> 00:48:44,030
+بعد ما اختصرنا يعني S على S تربيع ناقص واحد خلاص
+
+477
+00:48:44,030 --> 00:48:47,350
+يعني طلعتي Y of S بدل ما عملنا الـ partial 
+
+478
+00:48:47,350 --> 00:48:52,110
+fraction تقول تقدر بيمشي الحال ما عنديش مشكلة تمام؟
+
+479
+00:48:52,110 --> 00:48:55,570
+بس إن سميت حالي مش عارف، كويس؟ لأن وإنت في 
+
+480
+00:48:55,570 --> 00:48:59,170
+الامتحان بيجيش في بالك خلاص عندك تك تك بده يوصل
+
+481
+00:48:59,170 --> 00:49:02,850
+لتحليل ويطلع كل واحد هيكل في دماغك، تمام؟ لكن في
+
+482
+00:49:02,850 --> 00:49:06,570
+بعض عنده دقة نظر نفسه بيقولي اه لا هذه موجودة في
+
+483
+00:49:06,570 --> 00:49:09,510
+الجدول، إذا روحت جبتيها في الجدول الكلام صحي وما حدش 
+
+484
+00:49:09,510 --> 00:49:13,710
+اللي عندك أي اعتراض زي توسع وصلنا هنا وقلنا اكتبها
+
+485
+00:49:13,710 --> 00:49:16,310
+exponential وقلت لا بديش أكتبها الـ exponential روحت
+
+486
+00:49:16,310 --> 00:49:20,930
+جبت فكرة ثانية ووصلنا إلى مين؟ إلى نفس النتيجة هذه
+
+487
+00:49:20,930 --> 00:49:25,210
+والله هذه سيئة لكن لاحظتوا الآن احنا أخدنا ثلاثة
+
+488
+00:49:25,210 --> 00:49:31,310
+أمثلة الطرف اليمين كله zero طيب لو كان الطرف اليمين
+
+489
+00:49:31,310 --> 00:49:35,810
+ده اللي ثانية يعني يعني أخدنا ثلاثة أمثلة كله
+
+490
+00:49:35,810 --> 00:49:38,830
+homogeneous differential طيب لو كانت non
+
+491
+00:49:38,830 --> 00:49:46,550
+homogeneous عندما نقول إليك المثال التالي رقم 3 
+
+492
+00:50:10,080 --> 00:50:18,100
+يبقى مثال رقم 3 بيقول لي y double prime ناقص
+
+493
+00:50:18,100 --> 00:50:29,560
+اتنين y prime زائد اتنين y يساوي E أس ناقص T و y 
+
+494
+00:50:29,560 --> 00:50:35,180
+عند الـ zero بده يساوي zero و y prime عند الـ zero 
+
+495
+00:50:35,180 --> 00:50:38,700
+بده يساوي واحد
+
+496
+00:50:53,540 --> 00:51:01,010
+هنا بدنا نأخذ الـ Laplace transform للطرفين وعندك الـ Laplace
+
+497
+00:51:01,010 --> 00:51:04,470
+لـ E أس T بجيبها كمان من وين؟ من الجدول مش لسه
+
+498
+00:51:04,470 --> 00:51:08,350
+بضعوها أحسبها زي ما كنا نحسبها المرة الماضية يبقى 
+
+499
+00:51:08,350 --> 00:51:13,910
+باجي بقولك هي Laplace transform للـ Y double prime
+
+500
+00:51:13,910 --> 00:51:19,630
+ناقص اتنين Laplace transform للـ Y prime زائد اتنين
+
+501
+00:51:19,630 --> 00:51:25,810
+Laplace transform للـ Y بده يساوي Laplace transform للـ E
+
+502
+00:51:25,810 --> 00:51:32,720
+أس ناقص T يبقى Laplace transform للطرفين بعد هيك 
+
+503
+00:51:32,720 --> 00:51:38,200
+بروحي أطبق النظرية اللي أخذناها قبل قليل هذه عبارة
+
+504
+00:51:38,200 --> 00:51:48,660
+عن S2 في capital Y of S ناقص S في Y عند Zero ناقص
+
+505
+00:51:48,660 --> 00:51:53,820
+Y prime عند Zero خلصنا الـ term الأول نيجي للـ term
+
+506
+00:51:53,820 --> 00:52:01,020
+الثاني ناقص اتنين وافتح قوس S capital Y of S
+
+507
+00:52:01,020 --> 00:52:07,760
+ناقص Y عند الـ zero خلصنا الـ term الثاني بنجي للـ
+
+508
+00:52:07,760 --> 00:52:15,120
+term الثالث زائد اتنين اللي هو main capital Y of S
+
+509
+00:52:15,120 --> 00:52:19,620
+بالشكل اللي عندنا هذا بده يساوي أخذنا الـ Laplace
+
+510
+00:52:19,620 --> 00:52:23,480
+للطرف الشمال، بدنا الـ Laplace للطرف اليمين يبقى 
+
+511
+00:52:23,480 --> 00:52:28,360
+الطرف اليمين من الجدول واحد على قداش؟ واحد على S 
+
+512
+00:52:28,360 --> 00:52:36,740
+زائد واحد من الجدول عندك رقم 2، تمام؟ طيب،
+
+513
+00:52:36,740 --> 00:52:41,360
+الآن بدنا نيجي نعوض من الـ initial conditions في
+
+514
+00:52:41,360 --> 00:52:49,760
+هذه المعادلة يبقى S2 في capital Y of S ناقص S في Y 
+
+515
+00:52:49,760 --> 00:52:58,540
+عند 0 بقداش؟ بـ 0 ناقص Y prime of 0 اللي هو 1 ناقص 
+
+516
+00:52:58,540 --> 00:53:08,520
+2S capital Y of S ناقص في ناقص بزائد 2 في Y عند 0
+
+517
+00:53:08,520 --> 00:53:16,120
+اللي هو 0 زائد اتنين capital Y of S يساوي واحد على
+
+518
+00:53:16,120 --> 00:53:24,180
+S زائد الواحد بتاخذوا اللي فيهم capital Y of S مع
+
+519
+00:53:24,180 --> 00:53:31,400
+بعض يبقى بيصير عندنا S square ناقص اتنين S زائد
+
+520
+00:53:31,400 --> 00:53:38,190
+اتنين كله في capital Y of S هذا راح مع السلامة، ضل 
+
+521
+00:53:38,190 --> 00:53:43,550
+عندي هنا قداش؟ ناقص واحدة وهذا راح مع السلامة
+
+522
+00:53:43,550 --> 00:53:51,770
+الله يساهل عليه يبقى النتيجة واحد على S زائد واحد
+
+523
+00:53:51,770 --> 00:54:00,150
+زائد واحد مظبوط إيه؟ طيب، إيش رأيك هذه هيك؟ اللي 
+
+524
+00:54:00,150 --> 00:54:06,090
+هو مين؟ لو وحدتلها المقامات كله S زائد واحد، بيصير
+
+525
+00:54:06,090 --> 00:54:13,670
+واحد زائد S زائد واحد تمام؟ يعني مين؟ يعني S
+
+526
+00:54:13,670 --> 00:54:22,580
+زائد اتنين على S زائد واحد طيب أنا بدي capital Y
+
+527
+00:54:22,580 --> 00:54:32,580
+of S فبجي بقوله capital Y of S يساوي S زائد 2 على
+
+528
+00:54:32,580 --> 00:54:42,160
+S زائد 1 مقسوما على S تربيع ناقص 2 S زائد 2 سؤال
+
+529
+00:54:44,430 --> 00:54:49,450
+القوس هذا بتحلل؟ لا ما أقدرش أحلله بيخليه زي ما هو
+
+530
+00:54:49,450 --> 00:54:53,990
+ماشي خليه الله بيفرجها إن شاء الله بتفرج يبقى
+
+531
+00:54:53,990 --> 00:54:57,910
+باجي بقوله هذا الكلام بتروح أعمله إيه عشان partial 
+
+532
+00:54:57,910 --> 00:55:05,230
+fractions يبقى بقوله هذا الكسر وهذا الـ S زائد واحد
+
+533
+00:55:05,230 --> 00:55:12,030
+وهذا زائد وهذا الكسر الثاني S square ناقص اتنين S
+
+534
+00:55:12,030 --> 00:55:18,050
+زائد اتنين هذا من الدرجة الأولى يبقى بحطله constant
+
+535
+00:55:18,050 --> 00:55:24,490
+هذا من الدرجة الثانية ولا يمكن تحليله يعني ما أقدرش
+
+536
+00:55:24,490 --> 00:55:28,650
+أبسطه أكتر من هيك يبقى بده أحط الـ bus من الدرجة
+
+537
+00:55:28,650 --> 00:55:34,590
+الأولى أقل منه بمقدار واحد هذا من الدرجة الثانية
+
+538
+00:55:34,590 --> 00:55:40,550
+بحطله الدرجة الأولى يبقى Bs زائد C
+
+539
+00:55:42,870 --> 00:55:46,910
+بعد هيك بروح بضرب الطرفين في المقدار اللي عندنا
+
+540
+00:55:46,910 --> 00:55:56,630
+هنا تمام؟ بيصير المعادلة عندي S زائد 2 تساوي A في S
+
+541
+00:55:56,630 --> 00:56:08,470
+تربيع ناقص 2 S زائد 2 زائد الـ B في S زائد الـ C في 
+
+542
+00:56:08,470 --> 00:56:15,630
+من؟ في الـ S زائد الـ 1 هذا السؤال مش زي اللي قبل هذا
+
+543
+00:56:15,630 --> 00:56:20,790
+أُتقل شوية شكله تمام أُتقل والله أخاف مدام بنحل
+
+544
+00:56:20,790 --> 00:56:25,630
+ما عندناهاش مشكلة زيدي 2 يساوي بده أفك الأقواس
+
+545
+00:56:25,630 --> 00:56:33,610
+هذه لو فكتهاش بيصير عندي A S تربيع ناقص اتنين A في
+
+546
+00:56:33,610 --> 00:56:47,120
+S زيدي 2A زائد Bs تربيع زائد B في S زائد C
+
+547
+00:56:47,120 --> 00:56:49,680
+في S زائد C
+
+548
+00:56:52,210 --> 00:56:57,710
+هذا الكلام بده يساوي بدي أجمع تعين الـ S تربيع مع
+
+549
+00:56:57,710 --> 00:57:02,570
+بعض وتبعين الـ S مع بعض والـ constants مع بعض و
+
+550
+00:57:02,570 --> 00:57:07,070
+أشوف لوين بتوصلنا المعادلة هذه طلعيني هنا بقدر
+
+551
+00:57:07,070 --> 00:57:13,850
+أقول A زائد الـ B كله في الـ S تربيع يبقى خلصنا من
+
+552
+00:57:13,850 --> 00:57:20,140
+هذه ومن هذه بدي أدور على اللي فيهم S هذه واحدة وها
+
+553
+00:57:20,140 --> 00:57:28,440
+دي الثانية وها دي الثالثة يبقى زائد B زائد الـ C
+
+554
+00:57:28,440 --> 00:57:39,380
+ناقص 2A كله في S بلوا الثوابت عند هنا 2A وهنا C
+
+555
+00:57:39,380 --> 00:57:50,330
+زائد 2A زائد C كل هذا الكلام S زائد 2 يساوي هذا
+
+556
+00:57:50,330 --> 00:58:06,570
+المقدار طيب
+
+557
+00:58:06,570 --> 00:58:12,430
+نبدأ نقارن المعاملات في الطرفين يبقى بناء عليه 
+
+558
+00:58:12,820 --> 00:58:17,460
+الـ A زائد الـ B كم بتساوي يا بنات؟ Zero لأن 
+
+559
+00:58:17,460 --> 00:58:22,580
+ما عنديش S تربيع في الطرف الشمال بعدك B زائد C
+
+560
+00:58:22,580 --> 00:58:29,420
+بيزايد C ناقص اتنين A يساوي معامل الـ S هنا ليه؟
+
+561
+00:58:29,420 --> 00:58:35,640
+واحد المعادلة الثالثة اللي هو اتنين A زيدي الـ C
+
+562
+00:58:35,640 --> 00:58:43,100
+يبقى اتنين A زيدي الـ C بده يساوي كده؟ بده يساوي 
+
+563
+00:58:43,100 --> 00:58:52,760
+اتنين تمام؟ إذا هذه بتعطيني كده؟ إن B بده يساوي A
+
+564
+00:58:52,760 --> 00:58:58,940
+بس بالسالب يبقى 
+
+565
+00:58:58,940 --> 00:59:08,210
+الـ B تساوي مين؟ سالب A وهذه بتعطينا إن الـ C بده
+
+566
+00:59:08,210 --> 00:59:16,230
+يساوي اتنين ناقص اتنين A تمام؟ إذا بروح شو أعمل؟
+
+567
+00:59:16,230 --> 00:59:21,610
+أ
+
+601
+01:03:48,240 --> 01:03:53,480
+طلعوني كويس يبقى أصبح عندي capital Y of S بده
+
+602
+01:03:53,480 --> 01:04:01,960
+يساوي خمس في مين في واحد على S زائد واحد اللي
+
+603
+01:04:01,960 --> 01:04:08,640
+بعدها ناقص خمس فيه بدي أخد هذا لحاله يا بنات على
+
+604
+01:04:08,640 --> 01:04:14,540
+المقام والسبع لحالها على المقام يبقى باجي بقوله هنا
+
+605
+01:04:14,540 --> 01:04:23,500
+ناقص خمس في S ناقص واحد على S ناقص واحد لكل تربيع
+
+606
+01:04:23,500 --> 01:04:30,740
+زائد واحد يبقى أخدت ال term الأول على المقام ناقص
+
+607
+01:04:30,740 --> 01:04:39,200
+خمس مع ناقص سبعة بزايد اللي هو سبعة خمس يبقى زائد
+
+608
+01:04:39,200 --> 01:04:47,300
+سبعة على خمسة بضل عند مين؟ بضل عشان دي ال واحد على
+
+609
+01:04:47,300 --> 01:04:56,480
+S ناقص واحد لكل تربيع زائد واحد تمام؟
+
+610
+01:04:57,530 --> 01:05:03,430
+الهم نقدر نقول يا خلصنا يا شبه خلصنا يا المثلة طلع
+
+611
+01:05:03,430 --> 01:05:07,650
+مرة تانية يبقى السارة عندي بدل ما هو term هنا
+
+612
+01:05:07,650 --> 01:05:12,950
+خلتها تلات term خمس في المقدار اللي عندنا هذا ناقص
+
+613
+01:05:12,950 --> 01:05:15,550
+خمس في S ناقص واحد على S ناقص واحد في كل تربيع
+
+614
+01:05:15,550 --> 01:05:19,090
+زائد واحد زائد سبعة أخماس واحد على S ناقص واحد في
+
+615
+01:05:19,090 --> 01:05:25,530
+كل تربيع زائد واحد بنفتح الجدول و نبحث عن الاسم
+
+616
+01:05:25,530 --> 01:05:27,950
+اللي يسمى الاسم اللي يسمى الاسم اللي يسمى الاسم
+
+617
+01:05:27,950 --> 01:05:28,170
+اللي يسمى الاسم اللي يسمى الاسم اللي يسمى الاسم
+
+618
+01:05:28,170 --> 01:05:29,610
+اللي يسمى الاسم اللي يسمى الاسم اللي يسمى الاسم
+
+619
+01:05:29,610 --> 01:05:35,870
+اللي يسمى الاسم اللي يسمى الاسم اللي 
+
+620
+01:05:35,870 --> 01:05:38,830
+يسمى الاسم اللي يسمى الاسم اللي يسمى الاسم اللي
+
+621
+01:05:38,830 --> 01:05:38,930
+يسمى الاسم اللي يسمى الاسم اللي يسمى الاسم اللي
+
+622
+01:05:38,930 --> 01:05:38,990
+يسمى الاسم اللي يسمى الاسم اللي يسمى الاسم اللي
+
+623
+01:05:38,990 --> 01:05:43,910
+يسمى الاسم اللي يسمى الاسم اللي يسمى الاسم
+
+624
+01:05:53,570 --> 01:06:02,440
+ندور في الجدول على المقدار بين القوسين عشرة طيب
+
+625
+01:06:02,440 --> 01:06:07,260
+عشرة ل S ناقص ال A S ناقص ال A لكل تربيع زائد B
+
+626
+01:06:07,260 --> 01:06:13,800
+تربيع طبعا ال A يساوي ال B يساوي قدر؟ واحد طيب
+
+627
+01:06:13,800 --> 01:06:21,120
+جبنا إن عليه بيكون الجواب هو E أس T Cos T مظبوط
+
+628
+01:06:21,520 --> 01:06:30,220
+يبقى هنا E Ost Cos T هذا النقطة رقم عشرة من الجدول
+
+629
+01:06:30,220 --> 01:06:35,620
+اللي بين ايديكوا نجي للنقطة الأخيرة اللي هو الزائد
+
+630
+01:06:35,620 --> 01:06:41,850
+سبعة أخماس فيه طلع لفوق شوية الخطوة اللي قبلها أو
+
+631
+01:06:41,850 --> 01:06:46,690
+النقطة اللي قبلها اللي يمين رقم تسعة يبقى رقم تسعة
+
+632
+01:06:46,690 --> 01:06:51,430
+هي بي على S نقص الكل تربيع زائد بيه تربيع يبقى
+
+633
+01:06:51,430 --> 01:06:58,210
+ايه تساوي بيه كذلك تساوي كدهش واحد يبقى E of T Sin
+
+634
+01:06:58,210 --> 01:07:07,360
+T يبقى هنا في ال E of T في Sin T يبقى هذا الـ
+
+635
+01:07:07,360 --> 01:07:12,860
+solution للـ differential equation المواطع حد فيكم
+
+636
+01:07:12,860 --> 01:07:19,560
+بيحب يسأل أي سؤال هنا؟ ننتقل
+
+637
+01:07:19,560 --> 01:07:27,740
+إلى المثال اللي بعده بس بنجيبه بطريقة غير هذه يبقى
+
+638
+01:07:27,740 --> 01:07:36,070
+example هذا سؤال 25 من أسئلة الكتاب بقول find the
+
+639
+01:07:36,070 --> 01:07:43,550
+Laplace transform find the Laplace transform
+
+640
+01:07:43,550 --> 01:07:47,290
+Laplace
+
+641
+01:07:47,290 --> 01:07:55,870
+transform capital Y of S للابلاس لل Y of the
+
+642
+01:07:55,870 --> 01:08:02,410
+solution of
+
+643
+01:08:02,410 --> 01:08:04,150
+the initial value problem
+
+644
+01:08:10,700 --> 01:08:19,800
+Y double A prime زائد Y تساوي أحد أمرين ياما T لما
+
+645
+01:08:19,800 --> 01:08:26,900
+T محصورة بين الـ Zero و بين الواحد ياما Zero لما T
+
+646
+01:08:26,900 --> 01:08:33,660
+أكبر من أو تساوي الواحد و less than infinity و ال y
+
+647
+01:08:33,660 --> 01:08:40,120
+عند ال zero بده تساوي zero و كذلك ال y prime عند
+
+648
+01:08:40,120 --> 01:08:43,700
+ال zero بده يساوي جدار بده يساوي zero
+
+649
+01:08:59,030 --> 01:09:05,210
+هذا المثال يختلف عن سابقاته من الأمثلة في إن له
+
+650
+01:09:05,210 --> 01:09:11,070
+شكل معين يعني piecewise function تمام؟ المثلة أو
+
+651
+01:09:11,070 --> 01:09:15,830
+الـG of T اللي علي مين مجزئ إلى جزئين وليس جزئا
+
+652
+01:09:15,830 --> 01:09:21,610
+واحدا كما كان قبل قليل من كل بسيطة جزئين ولا تلاتة
+
+653
+01:09:21,610 --> 01:09:25,570
+ولا أربعة مادام ال function معرفة يبقى أنا مقيد
+
+654
+01:09:25,570 --> 01:09:29,520
+بهذا التعريفلأ بلاس ترانسفورم له تعريف يبقى أنا
+
+655
+01:09:29,520 --> 01:09:34,140
+مقيد كذلك لمين بهذا التعريف إذا أنا أخد لأ بلاس
+
+656
+01:09:34,140 --> 01:09:39,660
+ترانسفورم لمن؟ للطرفين بقوله كويس يبقى أنا بدي أخد
+
+657
+01:09:39,660 --> 01:09:46,440
+لأ بلاس ترانسفورم ل Y'' زائد لـ plus transform للـ
+
+658
+01:09:46,440 --> 01:09:53,260
+y بده يساوي ل plus transform لمن؟ للطرف اليمين لكن
+
+659
+01:09:53,260 --> 01:09:58,900
+الطرف اليمين هذا مجزق إلى جزئين من zero لواحد و من
+
+660
+01:09:58,900 --> 01:10:04,000
+واحد لغاية infinity الـ plus transform للدالة مش
+
+661
+01:10:04,000 --> 01:10:08,200
+بيبدأ من عندي ال zero لغاية infinity إذا إحنا
+
+662
+01:10:08,200 --> 01:10:13,560
+جزقنا لوين؟ إلى جزئين إذا بروح أحط التعريف
+
+663
+01:10:13,560 --> 01:10:20,660
+integration من zero لواحد لل E أُس ناقص ST في
+
+664
+01:10:20,660 --> 01:10:29,600
+الدالة، جداش الدالة؟ يبقى ده تي دي تي زي التكامل من
+
+665
+01:10:29,600 --> 01:10:36,000
+واحد لغاية infinity يبقى من واحد لغاية infinity
+
+666
+01:10:36,000 --> 01:10:41,920
+إلى ال E أقص ناقص ST وقيمة الدالة هنا جداش Zero
+
+667
+01:10:41,920 --> 01:10:47,480
+يبقى في Zero في دي تي إذا ال term هذا كله بروح
+
+668
+01:10:47,480 --> 01:10:53,320
+بجداش Zero مع السلامة غير مأسوف عليه يبقى بدنا نيجي
+
+669
+01:10:53,320 --> 01:10:58,060
+نطبق النظرية على الطرف الشمال اللي عندنا يبقى هادي
+
+670
+01:10:58,060 --> 01:11:06,200
+S Square في capital Y of S ناقص S في Y عند ال zero
+
+671
+01:11:06,200 --> 01:11:11,960
+ناقص Y prime عند ال zero طبقنا النظرية على ال term
+
+672
+01:11:11,960 --> 01:11:16,760
+الأول نطبق النظرية على ال term التاني يبقى زائد
+
+673
+01:11:16,760 --> 01:11:23,220
+capital Y of S مرة واحدة هذا ما هوش improper
+
+674
+01:11:23,220 --> 01:11:26,520
+integral يعني improper integral واحد zero هناك
+
+675
+01:11:26,520 --> 01:11:29,920
+يبقى ده اللي عند مين ده اللي الترميك بديه كامل
+
+676
+01:11:29,920 --> 01:11:35,230
+integration by parts عادي جدالكن هذا بكمله بالجدول
+
+677
+01:11:35,230 --> 01:11:39,970
+أسهلي يبقى باجي بقوله في الهام الشيك باخد جزء
+
+678
+01:11:39,970 --> 01:11:47,010
+derivatives و جزء باخده من integrals تمام؟ ال
+
+679
+01:11:47,010 --> 01:11:56,120
+derivative T والintegral E أس ناقص ST مشتقتها بواحد
+
+680
+01:11:56,120 --> 01:12:02,100
+التكامل تبعها ب E أس ناقص T على مين على ناقص S
+
+681
+01:12:02,100 --> 01:12:08,080
+بنقسم على تفاضل الـ S إذا الـ S من الدرجة الأولى
+
+682
+01:12:08,080 --> 01:12:15,040
+نشتق كمان مرة يبقى Zero نكمل كمان مرة يبقى E أس
+
+683
+01:12:15,040 --> 01:12:22,340
+ناقص ST على ناقص S في ناقص S يبقى بزايد S ترابيع
+
+684
+01:12:22,960 --> 01:12:28,660
+هدى فى هدى بالموجب وهدى فى هدى بالسالب يبقى صارت
+
+685
+01:12:28,660 --> 01:12:33,800
+المثلة تبعتنا على الشكل التالي تطلعي لبناء يبقى
+
+686
+01:12:33,800 --> 01:12:44,000
+هنا بصير ناقص E أس ناقص ST على S كمان ناقص E أس
+
+687
+01:12:44,000 --> 01:12:51,250
+ناقص ST على مين على S تربيع والحكي هذا كله من عند
+
+688
+01:12:51,250 --> 01:12:56,370
+الـ zero لغاية كدهش لغاية الواحد طيب هذه و هذه
+
+689
+01:12:56,370 --> 01:13:04,930
+بقدر أخدها عام المشترك في شيء هنا ولا طرف .. هذا
+
+690
+01:13:04,930 --> 01:13:14,250
+هذا طيب باجي بقول اه هنا في T هنا T مظبوط و الباجي
+
+691
+01:13:14,250 --> 01:13:20,180
+كله سليم مئة بالمئة صحيح طيب بنعوض الآن بنجمع هدول
+
+692
+01:13:20,180 --> 01:13:25,960
+اتنين مع بعض يبقى بصير عندي S تربيع زائد واحد كله
+
+693
+01:13:25,960 --> 01:13:32,040
+في capital Y of S الآن Y عند Zero جلب Zero و Y
+
+694
+01:13:32,040 --> 01:13:37,970
+Prime عند Zero يبقى هذا بقير يبقى هنا كله ناقص Zero
+
+695
+01:13:37,970 --> 01:13:43,990
+يساوي بتعوض بحدود التكامل القيمة اللي فوق ناقص
+
+696
+01:13:43,990 --> 01:13:48,590
+القيمة اللي تحت يبقى المعوضة عن T بواحد بصير عندنا
+
+697
+01:13:48,590 --> 01:13:59,130
+ناقص E أس ناقص S على S عوضت بواحد هنا ناقص E أس
+
+698
+01:13:59,130 --> 01:14:07,470
+ناقص S على S تربيع نقص القيم اللي تحت نقص مع نقص
+
+699
+01:14:07,470 --> 01:14:16,790
+بصير الزائد Zero في رقم يبقى ب Zero وهذه زاد هنا
+
+700
+01:14:16,790 --> 01:14:24,010
+حطيت E وال Zero اللي هو واحد على S يبقى زائد واحد
+
+701
+01:14:24,010 --> 01:14:33,780
+على S واحد على S تربيع تمام طيب كويس يبقى بناء عليه
+
+702
+01:14:33,780 --> 01:14:40,020
+إيه الخاطر أجسم كله الآن على مين؟ على S تربيع زائد
+
+703
+01:14:40,020 --> 01:14:45,540
+واحد بيكون جيبنا لأ plus transform يبقى capital Y
+
+704
+01:14:45,540 --> 01:14:52,580
+of S بده يساوي اللي هو مين؟ E والله خد أخد الموجة
+
+705
+01:14:52,580 --> 01:14:56,530
+في الأول أسهل و أخلي السلم في اللي بعده يبقى هذه
+
+706
+01:14:56,530 --> 01:15:04,310
+واحد على S تربيع في S تربيع زائد واحد خلصنا منها
+
+707
+01:15:04,310 --> 01:15:13,050
+اللي بعدها ناقص EOS ناقص S على مين على S في S
+
+708
+01:15:13,050 --> 01:15:23,790
+تربيع زائد واحد ناقص IOS ناقص S عالمين على S تربيع
+
+709
+01:15:23,790 --> 01:15:30,950
+في S تربيع زائد واحد الشكل اللي عنها خلاص روحي
+
+710
+01:15:30,950 --> 01:15:33,670
+وخليها قال لي هو بس هاتي ليا place ال transform
+
+711
+01:15:33,670 --> 01:15:37,940
+للحل ما قاليش هات شكل الحلو اللي ما بده يجيش بشكل
+
+712
+01:15:37,940 --> 01:15:42,300
+الحل بيصير معقد لسه partial fraction ويطلع جزئين
+
+713
+01:15:42,300 --> 01:15:46,780
+وكمان جزئين وكمان جزئين كيف جزئين هدول تلاتة مش
+
+714
+01:15:46,780 --> 01:15:52,240
+جزئين كمان ويمكن يطلعوا أربعة كمان حسب الكثرة الله
+
+715
+01:15:52,240 --> 01:15:57,990
+أعلم إذا لحد هنا جبناله Laplace transform لو بدك
+
+716
+01:15:57,990 --> 01:16:03,670
+تجمعهم كلهم مع بعض وتوحدي المقامات وتوحدي براتك
+
+717
+01:16:03,670 --> 01:16:10,690
+والنتيجة على الشكل التالي اللي هو E أُس S ناقص S
+
+718
+01:16:10,690 --> 01:16:19,370
+ناقص واحد على S تربيع في مين؟ في S تربيع زائد واحد
+
+719
+01:16:19,370 --> 01:16:23,710
+كله في ال E أُس S بتعمل ايه؟ هو اللي ما تعملاش
+
+720
+01:16:23,710 --> 01:16:29,470
+ما تفرجش عندنا آخر مثال في هذا ال section يبقى
+
+721
+01:16:29,470 --> 01:16:35,170
+example يقول
+
+722
+01:16:35,170 --> 01:16:37,150
+solve the initial value problem
+
+723
+01:16:44,020 --> 01:16:52,100
+واي دابلي برايم ناقص ستة واي برايم زائد تسعة واي
+
+724
+01:16:52,100 --> 01:17:01,340
+بده يساوي ت تربيع E أس اتنين T والواي عند ال zero
+
+725
+01:17:01,340 --> 01:17:07,320
+بده يساوي اتنين والواي برايم عند ال zero بده يساوي
+
+726
+01:17:07,320 --> 01:17:08,260
+ستة
+
+727
+01:17:20,540 --> 01:17:26,460
+بناخد لبلاس ترانسفورم للطرفين يبقى بدي أخد لبلاس
+
+728
+01:17:26,460 --> 01:17:34,560
+ترانسفورم لل Y'' نقص ستة لبلاس ترانسفورم لل Y''
+
+729
+01:17:34,560 --> 01:17:41,740
+زائد تسعة لبلاس ترانسفورم لل Y بدي أساوي لبلاس
+
+730
+01:17:41,740 --> 01:17:47,640
+ترانسفورم لT تربيع في E أس اتنين T
+
+731
+01:17:50,680 --> 01:17:57,200
+طرف الشمال هنطبق عليه النظرية يبقى S2 في capital Y
+
+732
+01:17:57,200 --> 01:18:05,520
+of S ناقص S في Y عند Zero ناقص Y prime عند Zero
+
+733
+01:18:06,470 --> 01:18:13,930
+اللي بعده ناقص ستة وتفتح يقوس يبقى S في capital Y
+
+734
+01:18:13,930 --> 01:18:21,710
+of S ناقص Y عند ال zero خلصنا منه اللي بعده زائد
+
+735
+01:18:21,710 --> 01:18:29,450
+تسعة capital Y of S بده يساوي حد بعرفاش إلا أروح
+
+736
+01:18:29,450 --> 01:18:39,790
+أدور وين في الجدول T تربيع في A أُس اتنان
+
+737
+01:18:39,790 --> 01:18:45,560
+T اللي هي من ابنات 11 ممتاز جدا يبقى لو جيت في
+
+738
+01:18:45,560 --> 01:18:52,760
+العمود الأول اللي هو رقم 11 T to the power N E أس
+
+739
+01:18:52,760 --> 01:18:57,220
+A T و ال N positive احنا عندنا هايه اتنين و
+
+740
+01:18:57,220 --> 01:19:01,300
+الاتنين positive و ال A عندي كمان يبقى داشت بيه
+
+741
+01:19:01,300 --> 01:19:05,880
+الاتنين يبقى بدي أكتب النتيجة عند اليمين اتنين
+
+742
+01:19:05,880 --> 01:19:13,820
+factorial على S ناقص اتنين لكل كداشت يبقى هذه اللي
+
+743
+01:19:13,820 --> 01:19:20,820
+هي عبارة عن in factorial يعني اتنين factorial على
+
+744
+01:19:20,820 --> 01:19:27,460
+اللي هو ال S ناقص اتنين لكل تكيب الشكل اللي عندنا
+
+745
+01:19:27,460 --> 01:19:35,300
+يبقى هذه جيبتها من الجدول part 11 بالدرجة هطبق اللي
+
+746
+01:19:35,300 --> 01:19:38,180
+هو المعلومات اللي عندي في ال initial conditions
+
+747
+01:19:38,180 --> 01:19:42,840
+على المعادلة اللي عندها يبقى هذي بيصير S square
+
+748
+01:19:42,840 --> 01:19:52,620
+capital Y of S Y عند 0 ب 2 يبقى ناقص 2S Y prime
+
+749
+01:19:52,620 --> 01:19:55,460
+عند 0 يبقى ناقص 6
+
+750
+01:20:02,050 --> 01:20:10,510
+ناقص في ناقص بزايد ستة في واي عند ال zero اللي هو
+
+751
+01:20:10,510 --> 01:20:19,210
+بإثنين تمام Y عند Zero اللي هو ب 2 زائد 9 capital Y
+
+752
+01:20:19,210 --> 01:20:29,850
+of S بده تساوي 2 factorial على S ناقص 2 اللي هو
+
+753
+01:20:29,850 --> 01:20:31,570
+الكل تكيب
+
+754
+01:20:34,130 --> 01:20:42,850
+بنجمع العامل المشتركة يبقى S²-6S زائد
+
+755
+01:20:42,850 --> 01:20:52,600
+9 كله في capital Y of S بتضل عندك هنا جداش ناقص
+
+756
+01:20:52,600 --> 01:21:00,280
+إثنين S ناقص ستة وزائد اتناش بضل زائد ستة يبقى
+
+757
+01:21:00,280 --> 01:21:05,020
+زائد ستة يسوى الطرف اليمين اللي هو اتنين factorial
+
+758
+01:21:05,020 --> 01:21:13,220
+على S ناقص اتنين لكل تكيد طيب تمام تمام هذه بيصير
+
+759
+01:21:13,220 --> 01:21:20,620
+ايش بيصير capital Y of S مضروبة في أمين هذه بنات
+
+760
+01:21:20,620 --> 01:21:29,000
+اللي هو S ناقص تلاتة من كل تربيع يبقى في S ناقص
+
+761
+01:21:29,000 --> 01:21:35,050
+تلاتة من كل تربيع S ناقص ثلاثة الكل تاريبي هذه S
+
+762
+01:21:35,050 --> 01:21:42,750
+ناقص إثنين S ناقص إثنين مظبوط ما عنديش تلاتة نتأكد
+
+763
+01:21:42,750 --> 01:21:49,310
+منها لا يا بني أنا اتصلي E أس تلاتة T وليست إثنين
+
+764
+01:21:49,310 --> 01:21:58,480
+بدي أقول هذه E أس تلاتة T يبقى لما نجينا حسبناها
+
+765
+01:21:58,480 --> 01:22:07,440
+هنا بصير S ناقص تلاتة وهذه S ناقص تلاتة وهذه S
+
+766
+01:22:07,440 --> 01:22:14,900
+ناقص تلاتة والباقي كل شي زي ما هو يبقى بس اللي بين
+
+767
+01:22:14,900 --> 01:22:18,380
+قصين بصلي الله عبارة عن S ناقص إثنين وS ناقص تلاتة
+
+768
+01:22:18,940 --> 01:22:23,140
+يبقى هذا بده يساوي اللي هو من النجو الهادي على
+
+769
+01:22:23,140 --> 01:22:29,120
+الشجرة التانية ولو أخدنا ناقص إثنين عامل مشترك
+
+770
+01:22:29,420 --> 01:22:34,240
+بصير اس ناقص ثلاثة هذه لو نجلنا
+
+801
+01:25:43,230 --> 01:25:52,290
+رقم أحد عشر برضه يبقى T أس كام أس أربعة يبقى T أس
+
+802
+01:25:52,290 --> 01:25:59,870
+أربعة في E أس ثلاثة T E أس ثلاثة T لإن الـ A عندي 
+
+803
+01:25:59,870 --> 01:26:02,090
+بكام ثلاثة
+
+804
+01:26:03,980 --> 01:26:08,440
+خلاص يبقى هذا هو الحل التابع له يعني يا بنات
+
+805
+01:26:08,440 --> 01:26:13,430
+لما يطلع الشغل زي هيك يمكن ما تقدرش تجيبيها من
+
+806
+01:26:13,430 --> 01:26:17,350
+الجدران بدها فبركة بسيطة ضربنا فرق مجسمنا عليه
+
+807
+01:26:17,350 --> 01:26:21,890
+إذا صارت الـ A موجودة في الجدران قبل قليل كان عندي
+
+808
+01:26:21,890 --> 01:26:27,150
+S تربيع ناقص اثنين S زائد اثنين فحولت إلى S ناقص
+
+809
+01:26:27,150 --> 01:26:31,630
+اثنين S تربيع ناقص اثنين S زائد واحد زائد واحد
+
+810
+01:26:31,630 --> 01:26:34,790
+يبقى صارت S ناقص واحد الكل تربيع زائد واحد يعني
+
+811
+01:26:34,790 --> 01:26:38,550
+أحيانًا الفبركات الرياضية هذه هي اللي بتوديك لوين
+
+812
+01:26:38,710 --> 01:26:43,690
+لصيغة تابعة للجدول وبالتالي بتقدر تجيب الـ function
+
+813
+01:26:43,690 --> 01:26:49,070
+المناظرة لـ Laplace transform بدنا المسائل تابعة
+
+814
+01:26:49,070 --> 01:27:01,310
+exercises 6-2 exercises 6-2 المسائل من 1 لغاية 26
+
+815
+01:27:06,070 --> 01:27:11,350
+حاولي تحلي بقدر المكان تتدربي عليهم لإن المسائل
+
+816
+01:27:11,350 --> 01:27:18,710
+هدول ضروريات جداً لإنه لا يكاد يخلو امتحان نهائي
+
+817
+01:27:18,710 --> 01:27:25,570
+وأظنه لن يخلو من استخدام Laplace transform للحصول
+
+818
+01:27:25,570 --> 01:27:29,750
+على حل المعادلة التفاضلية أعطيكم العافية 
diff --git a/PL9fwy3NUQKwa8ZDfSFGn6H8xVFLzqmCZC/RDSrZpOLp38_raw.json b/PL9fwy3NUQKwa8ZDfSFGn6H8xVFLzqmCZC/RDSrZpOLp38_raw.json
new file mode 100644
index 0000000000000000000000000000000000000000..060def6d51a4869ce50b12f9b415f898a4272ede
--- /dev/null
+++ b/PL9fwy3NUQKwa8ZDfSFGn6H8xVFLzqmCZC/RDSrZpOLp38_raw.json
@@ -0,0 +1 @@
+{"segments": [{"id": 1, "seek": 2856, "start": 9.34, "end": 28.56, "text": "بسم الله الرحمن الرحيم المرة اللى فاتت بدأنا بتعريف لبلاس ترانسفورم وحسبنا لبلاس ترانسفورم مجموعة من الدوال اليوم ان شاء الله هنعطيكم مجموعة من الدوال و لبلاس ترانسفورم اللى موجودة قبالك في جدول", "tokens": [3555, 38251, 21984, 34892, 5016, 27842, 34892, 5016, 32640, 9673, 25720, 13672, 7578, 6156, 9307, 2655, 47525, 10721, 8315, 39894, 3615, 16572, 5172, 5296, 3555, 15040, 3794, 6055, 2288, 7649, 3794, 5172, 13063, 2304, 4032, 5016, 35457, 8315, 5296, 3555, 15040, 3794, 6055, 2288, 7649, 3794, 5172, 13063, 2304, 3714, 7435, 2304, 2407, 27884, 9154, 32748, 2407, 6027, 45595, 20498, 16472, 13412, 16606, 21984, 8032, 1863, 3615, 9566, 1829, 24793, 3714, 7435, 2304, 2407, 27884, 9154, 32748, 2407, 6027, 4032, 5296, 3555, 15040, 3794, 6055, 2288, 7649, 3794, 5172, 13063, 2304, 13672, 7578, 3714, 29245, 23328, 3660, 12174, 3555, 6027, 4117, 8978, 10874, 3215, 12610], "avg_logprob": -0.14843749761019112, "compression_ratio": 2.225, "no_speech_prob": 5.960464477539063e-08, "words": [{"start": 9.340000000000002, "end": 10.38, "word": "بسم", "probability": 0.5238037109375}, {"start": 10.38, "end": 10.62, "word": " الله", "probability": 0.9599609375}, {"start": 10.62, "end": 11.04, "word": " الرحمن", "probability": 0.96923828125}, {"start": 11.04, "end": 11.62, "word": " الرحيم", "probability": 0.99169921875}, {"start": 11.62, "end": 13.5, "word": " المرة", "probability": 0.837646484375}, {"start": 13.5, "end": 13.66, "word": " اللى", "probability": 0.671630859375}, {"start": 13.66, "end": 13.98, "word": " فاتت", "probability": 0.8502604166666666}, {"start": 13.98, "end": 14.56, "word": " بدأنا", "probability": 0.8181966145833334}, {"start": 14.56, "end": 15.2, "word": " بتعريف", "probability": 0.978759765625}, {"start": 15.2, "end": 15.72, "word": " لبلاس", "probability": 0.62628173828125}, {"start": 15.72, "end": 16.88, "word": " ترانسفورم", "probability": 0.8654436383928571}, {"start": 16.88, "end": 17.96, "word": " وحسبنا", "probability": 0.853515625}, {"start": 17.96, "end": 18.38, "word": " لبلاس", "probability": 0.9556884765625}, {"start": 18.38, "end": 19.32, "word": " ترانسفورم", "probability": 0.9919084821428571}, {"start": 19.32, "end": 20.12, "word": " مجموعة", "probability": 0.89716796875}, {"start": 20.12, "end": 20.64, "word": " من", "probability": 0.98681640625}, {"start": 20.64, "end": 21.56, "word": " الدوال", "probability": 0.8152669270833334}, {"start": 21.56, "end": 22.62, "word": " اليوم", "probability": 0.878662109375}, {"start": 22.62, "end": 22.8, "word": " ان", "probability": 0.7294921875}, {"start": 22.8, "end": 22.96, "word": " شاء", "probability": 0.95166015625}, {"start": 22.96, "end": 23.0, "word": " الله", "probability": 0.95361328125}, {"start": 23.0, "end": 23.68, "word": " هنعطيكم", "probability": 0.859130859375}, {"start": 23.68, "end": 24.16, "word": " مجموعة", "probability": 0.90947265625}, {"start": 24.16, "end": 24.34, "word": " من", "probability": 0.982421875}, {"start": 24.34, "end": 24.78, "word": " الدوال", "probability": 0.947265625}, {"start": 24.78, "end": 24.96, "word": " و", "probability": 0.61767578125}, {"start": 24.96, "end": 25.58, "word": " لبلاس", "probability": 0.92822265625}, {"start": 25.58, "end": 26.4, "word": " ترانسفورم", "probability": 0.9899553571428571}, {"start": 26.4, "end": 26.66, "word": " اللى", "probability": 0.763671875}, {"start": 26.66, "end": 27.3, "word": " موجودة", "probability": 0.8907470703125}, {"start": 27.3, "end": 27.82, "word": " قبالك", "probability": 0.83935546875}, {"start": 27.82, "end": 28.04, "word": " في", "probability": 0.90478515625}, {"start": 28.04, "end": 28.56, "word": " جدول", "probability": 0.9855143229166666}], "temperature": 1.0}, {"id": 2, "seek": 4602, "start": 39.96, "end": 46.02, "text": "موضوع اليوم موضوع solution of initial value problems", "tokens": [2304, 2407, 11242, 45367, 45595, 20498, 3714, 2407, 11242, 45367, 3827, 295, 5883, 2158, 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resolution ثم الآن بنحل نفس المعادلة ب Laplace transform بس Laplace transform", "tokens": [1829, 3555, 4587, 7578, 1975, 5016, 8315, 43242, 8315, 5883, 2158, 1154, 44945, 5016, 995, 12610, 8717, 29245, 3215, 21542, 1211, 23758, 6055, 3555, 3615, 9673, 3615, 18513, 37977, 4724, 995, 14851, 9778, 3215, 10943, 2369, 6742, 4088, 1975, 5016, 8315, 8978, 29739, 28259, 10632, 11331, 1211, 9957, 11296, 11331, 1211, 6225, 995, 16254, 30767, 2304, 7649, 38637, 2304, 39182, 29910, 23275, 11331, 1211, 9957, 11296, 20666, 383, 8669, 38637, 2304, 6024, 48506, 44945, 5016, 1211, 8717, 36178, 9673, 3615, 18513, 37977, 4724, 2369, 6742, 4088, 4724, 3794, 2369, 6742, 4088], "avg_logprob": -0.20329483128760173, "compression_ratio": 1.714975845410628, "no_speech_prob": 0.0, "words": [{"start": 46.35, "end": 46.83, "word": "يبقى", "probability": 0.672454833984375}, {"start": 46.83, "end": 47.13, "word": " احنا", "probability": 0.9329427083333334}, {"start": 47.13, "end": 47.49, "word": " عندنا", 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0.7317708333333334}, {"start": 79.66, "end": 80.1, "word": " لهم", "probability": 0.934326171875}, {"start": 80.1, "end": 81.3, "word": " ثوابت", "probability": 0.816162109375}, {"start": 81.3, "end": 81.44, "word": " و", "probability": 0.96044921875}, {"start": 81.44, "end": 81.92, "word": " ليست", "probability": 0.805419921875}, {"start": 81.92, "end": 82.24, "word": " أي", "probability": 0.479736328125}, {"start": 82.24, "end": 83.42, "word": " معاملة", "probability": 0.8572591145833334}], "temperature": 1.0}, {"id": 5, "seek": 10449, "start": 84.27, "end": 104.49, "text": "فبجي بقول في هذا ال section we shall use Laplace transform لنستخدم تحويلات لابلاس مشان الحل ال initial value problems مسائل القيم الحدية for linear differential equations للمعادلات الخطية with constant coefficients بمعاملات ثابتة ذات", "tokens": [5172, 3555, 7435, 1829, 4724, 39648, 8978, 23758, 2423, 3541, 321, 4393, 764, 2369, 6742, 4088, 5296, 1863, 14851, 9778, 40448, 6055, 5016, 2407, 26895, 9307, 5296, 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"word": " shall", "probability": 0.95458984375}, {"start": 86.61, "end": 86.91, "word": " use", "probability": 0.888671875}, {"start": 86.91, "end": 87.37, "word": " Laplace", "probability": 0.724853515625}, {"start": 87.37, "end": 88.21, "word": " transform", "probability": 0.6826171875}, {"start": 88.21, "end": 89.05, "word": " لنستخدم", "probability": 0.8177734375}, {"start": 89.05, "end": 89.81, "word": " تحويلات", "probability": 0.9421875}, {"start": 89.81, "end": 90.41, "word": " لابلاس", "probability": 0.6295166015625}, {"start": 90.41, "end": 90.75, "word": " مشان", "probability": 0.5272216796875}, {"start": 90.75, "end": 91.17, "word": " الحل", "probability": 0.948486328125}, {"start": 91.17, "end": 91.29, "word": " ال", "probability": 0.93994140625}, {"start": 91.29, "end": 92.39, "word": " initial", "probability": 0.818359375}, {"start": 92.39, "end": 93.37, "word": " value", "probability": 0.9482421875}, {"start": 93.37, "end": 94.13, "word": " problems", "probability": 0.80322265625}, {"start": 94.13, "end": 94.85, "word": " مسائل", "probability": 0.9132486979166666}, {"start": 94.85, "end": 95.31, "word": " القيم", "probability": 0.847900390625}, {"start": 95.31, "end": 96.13, "word": " الحدية", "probability": 0.8779296875}, {"start": 96.13, "end": 96.49, "word": " for", "probability": 0.91357421875}, {"start": 96.49, "end": 96.87, "word": " linear", "probability": 0.91943359375}, {"start": 96.87, "end": 97.41, "word": " differential", "probability": 0.8330078125}, {"start": 97.41, "end": 98.21, "word": " equations", "probability": 0.91796875}, {"start": 98.21, "end": 99.51, "word": " للمعادلات", "probability": 0.9423014322916666}, {"start": 99.51, "end": 100.31, "word": " الخطية", "probability": 0.9534505208333334}, {"start": 100.31, "end": 100.53, "word": " with", "probability": 0.92626953125}, {"start": 100.53, "end": 101.07, "word": " constant", "probability": 0.96240234375}, {"start": 101.07, "end": 101.89, "word": " coefficients", "probability": 0.9404296875}, {"start": 101.89, "end": 102.97, "word": " بمعاملات", "probability": 0.9778645833333334}, {"start": 102.97, "end": 104.07, "word": " ثابتة", "probability": 0.9774169921875}, {"start": 104.07, "end": 104.49, "word": " ذات", "probability": 0.67333984375}], "temperature": 1.0}, {"id": 6, "seek": 12934, "start": 105.94, "end": 129.34, "text": "يعني بدنا نترجم الكلام اللى قولناه قبل بصيغة أخرى that is we shall solve the differential equation a y double prime زيادة b y prime زيادة c y يساوي zero طبعا ال a و ال b و ال c constant لإن احنا جايلين with constant coefficients ما لها by Laplace transform بتحويلات Laplace", "tokens": [40228, 22653, 47525, 8315, 8717, 2655, 47341, 2304, 2423, 28820, 10943, 13672, 7578, 12174, 12610, 8315, 3224, 12174, 36150, 4724, 9381, 1829, 17082, 3660, 5551, 34740, 7578, 300, 307, 321, 4393, 5039, 264, 15756, 5367, 257, 288, 3834, 5835, 30767, 1829, 18513, 3660, 272, 288, 5835, 30767, 1829, 18513, 3660, 269, 288, 7251, 3794, 995, 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"word": " a", "probability": 0.85302734375}, {"start": 119.66, "end": 119.82, "word": " و", "probability": 0.56591796875}, {"start": 119.82, "end": 119.92, "word": " ال", "probability": 0.87890625}, {"start": 119.92, "end": 120.1, "word": " b", "probability": 0.97265625}, {"start": 120.1, "end": 120.24, "word": " و", "probability": 0.93994140625}, {"start": 120.24, "end": 120.38, "word": " ال", "probability": 0.96337890625}, {"start": 120.38, "end": 120.66, "word": " c", "probability": 0.98046875}, {"start": 120.66, "end": 121.5, "word": " constant", "probability": 0.6748046875}, {"start": 121.5, "end": 121.84, "word": " لإن", "probability": 0.8681640625}, {"start": 121.84, "end": 122.04, "word": " احنا", "probability": 0.7906087239583334}, {"start": 122.04, "end": 122.66, "word": " جايلين", "probability": 0.78399658203125}, {"start": 122.66, "end": 123.12, "word": " with", "probability": 0.86181640625}, {"start": 123.12, "end": 124.04, "word": " constant", "probability": 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نعطي نظرية تتحدث عن كيفية إيجاد لبلاس للمشتقة الأولى لبلاس للمشتقة الثانية", "tokens": [1863, 5016, 995, 12610, 8717, 5016, 1211, 9673, 3615, 18513, 1211, 9307, 13672, 7578, 39894, 30544, 15844, 25124, 28820, 13672, 7578, 12174, 3215, 10943, 8315, 29538, 4724, 995, 14851, 9778, 3215, 10943, 1975, 2407, 4724, 995, 14851, 9778, 3215, 10943, 16712, 5016, 2407, 26895, 9307, 5296, 3555, 15040, 3794, 44381, 1975, 5016, 8315, 9673, 25720, 13672, 7578, 6156, 9307, 3660, 5551, 9778, 3215, 8315, 5296, 3555, 15040, 3794, 24976, 3215, 2407, 6027, 4032, 19528, 8717, 47283, 3215, 5296, 3555, 15040, 3794, 5296, 19528, 8592, 2655, 4587, 9307, 3714, 19913, 3555, 2407, 9566, 5551, 9778, 3215, 8315, 5296, 3555, 15040, 3794, 24976, 3215, 2407, 6027, 18863, 18513, 10632, 4032, 8592, 38688, 8315, 9122, 33911, 44945, 32277, 2304, 3224, 47525, 8315, 8717, 1829, 7435, 1829, 6024, 48506, 8717, 3615, 9566, 1829, 8717, 19913, 2288, 10632, 6055, 2655, 24401, 12984, 18871, 9122, 33911, 10632, 11933, 1829, 7435, 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"word": " وشوفنا", "probability": 0.9344482421875}, {"start": 149.62, "end": 149.86, "word": " كيف", "probability": 0.9833984375}, {"start": 149.86, "end": 150.42, "word": " بناسمه", "probability": 0.6163330078125}, {"start": 150.42, "end": 150.78, "word": " بدنا", "probability": 0.818603515625}, {"start": 150.78, "end": 151.18, "word": " نيجي", "probability": 0.8682861328125}, {"start": 151.18, "end": 151.94, "word": " الآن", "probability": 0.649658203125}, {"start": 151.94, "end": 152.78, "word": " نعطي", "probability": 0.9530029296875}, {"start": 152.78, "end": 153.36, "word": " نظرية", "probability": 0.929931640625}, {"start": 153.36, "end": 154.06, "word": " تتحدث", "probability": 0.83203125}, {"start": 154.06, "end": 154.3, "word": " عن", "probability": 0.9833984375}, {"start": 154.3, "end": 155.0, "word": " كيفية", "probability": 0.984375}, {"start": 155.0, "end": 155.54, "word": " إيجاد", "probability": 0.9327392578125}, {"start": 155.54, "end": 156.3, "word": " لبلاس", 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24793, 764, 2369, 6742, 4088, 1365, 1365, 764, 2369, 6742, 4088], "avg_logprob": -0.5286458358168602, "compression_ratio": 1.308641975308642, "no_speech_prob": 0.0, "words": [{"start": 1501.67, "end": 1502.03, "word": "لا", "probability": 0.283935546875}, {"start": 1502.03, "end": 1502.89, "word": " نترككم", "probability": 0.55755615234375}, {"start": 1502.89, "end": 1503.65, "word": " تايهين", "probability": 0.61334228515625}, {"start": 1503.65, "end": 1504.69, "word": " نقول", "probability": 0.52490234375}, {"start": 1504.69, "end": 1505.01, "word": " لكم", "probability": 0.672119140625}, {"start": 1505.01, "end": 1505.27, "word": " use", "probability": 0.62255859375}, {"start": 1505.27, "end": 1506.15, "word": " Laplace", "probability": 0.709228515625}, {"start": 1506.15, "end": 1507.15, "word": " transform", "probability": 0.7744140625}, {"start": 1507.15, "end": 1509.65, "word": " example", "probability": 0.37939453125}, {"start": 1509.65, "end": 1513.17, "word": " example", "probability": 0.47705078125}, {"start": 1513.17, "end": 1525.79, "word": " use", "probability": 0.82568359375}, {"start": 1525.79, "end": 1527.83, "word": " Laplace", "probability": 0.908935546875}, {"start": 1527.83, "end": 1530.47, "word": " transform", "probability": 0.94287109375}], "temperature": 1.0}, {"id": 65, "seek": 155962, "start": 1553.96, "end": 1559.62, "text": "اول واحدة او نمرة ا او نمرة واحد", "tokens": [995, 12610, 36764, 24401, 3660, 1975, 2407, 8717, 2304, 25720, 1975, 1975, 2407, 8717, 2304, 25720, 36764, 24401], "avg_logprob": -0.39905428572704915, "compression_ratio": 1.2954545454545454, "no_speech_prob": 0.0, "words": [{"start": 1553.9599999999998, "end": 1555.12, "word": "اول", "probability": 0.39849853515625}, {"start": 1555.12, "end": 1555.86, "word": " واحدة", "probability": 0.7577311197916666}, {"start": 1555.86, "end": 1557.1, "word": " او", "probability": 0.822021484375}, {"start": 1557.1, "end": 1557.52, "word": " نمرة", "probability": 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{"start": 1568.94, "end": 1570.64, "word": " زائد", "probability": 0.86279296875}, {"start": 1570.64, "end": 1571.42, "word": " أربعة", "probability": 0.8904622395833334}, {"start": 1571.42, "end": 1571.82, "word": " y", "probability": 0.9306640625}, {"start": 1571.82, "end": 1572.58, "word": " تساوي", "probability": 0.9163818359375}, {"start": 1572.58, "end": 1573.34, "word": " زيرو", "probability": 0.6751302083333334}, {"start": 1573.34, "end": 1574.76, "word": " و", "probability": 0.50732421875}, {"start": 1574.76, "end": 1575.58, "word": " ال", "probability": 0.7548828125}, {"start": 1575.58, "end": 1576.06, "word": " y", "probability": 0.87353515625}, {"start": 1576.06, "end": 1576.46, "word": " عند", "probability": 0.98681640625}, {"start": 1576.46, "end": 1577.06, "word": " زيرو", "probability": 0.7431640625}, {"start": 1577.06, "end": 1577.44, "word": " بده", "probability": 0.703125}, {"start": 1577.44, "end": 1577.96, "word": " يساوي", "probability": 0.9603271484375}, 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" هذا", "probability": 0.7333984375}, {"start": 1597.06, "end": 1597.28, "word": " لأ", "probability": 0.84814453125}, {"start": 1597.28, "end": 1597.82, "word": " هدخل", "probability": 0.9525146484375}, {"start": 1597.82, "end": 1598.18, "word": " Laplace", "probability": 0.86962890625}, {"start": 1598.18, "end": 1598.36, "word": " على", "probability": 0.5673828125}, {"start": 1598.36, "end": 1598.56, "word": " كل", "probability": 0.96826171875}, {"start": 1598.56, "end": 1598.92, "word": " واحدة", "probability": 0.9646809895833334}, {"start": 1598.92, "end": 1599.22, "word": " فيهم", "probability": 0.91552734375}, {"start": 1599.22, "end": 1599.9, "word": " دوري", "probability": 0.9235026041666666}, {"start": 1599.9, "end": 1600.7, "word": " يبقى", "probability": 0.85150146484375}, {"start": 1600.7, "end": 1601.22, "word": " بداجي", "probability": 0.6023763020833334}, {"start": 1601.22, "end": 1601.76, "word": " اقول", "probability": 0.92626953125}, {"start": 1601.76, "end": 1604.0, 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5201.79, "word": " وبالتالي", "probability": 0.9150390625}, {"start": 5201.79, "end": 5202.61, "word": " بتقدر", "probability": 0.8395182291666666}, {"start": 5202.61, "end": 5202.89, "word": " تجيب", "probability": 0.8974609375}, {"start": 5202.89, "end": 5203.07, "word": " ال", "probability": 0.92431640625}, {"start": 5203.07, "end": 5203.69, "word": " function", "probability": 0.55419921875}, {"start": 5203.69, "end": 5204.73, "word": " المناضرة", "probability": 0.742919921875}, {"start": 5204.73, "end": 5205.09, "word": " لـ", "probability": 0.48895263671875}, {"start": 5205.09, "end": 5205.67, "word": " Laplace", "probability": 0.59033203125}, {"start": 5205.67, "end": 5206.85, "word": " transform", "probability": 0.61279296875}, {"start": 5206.85, "end": 5207.97, "word": " بدنا", "probability": 0.6212158203125}, {"start": 5207.97, "end": 5208.65, "word": " المسائل", "probability": 0.9296875}, {"start": 5208.65, "end": 5209.07, "word": " تابعة", "probability": 0.9200846354166666}, {"start": 5209.07, "end": 5209.83, "word": " exercises", "probability": 0.61376953125}, {"start": 5209.83, "end": 5210.41, "word": " 6", "probability": 0.78515625}, {"start": 5210.41, "end": 5211.13, "word": "-2", "probability": 0.6715087890625}, {"start": 5211.13, "end": 5212.57, "word": " exercises", "probability": 0.1453857421875}, {"start": 5212.57, "end": 5214.15, "word": " 6", "probability": 0.9052734375}, {"start": 5214.15, "end": 5214.89, "word": "-2", "probability": 0.959228515625}, {"start": 5214.89, "end": 5217.01, "word": " المسائل", "probability": 0.9678955078125}, {"start": 5217.01, "end": 5217.55, "word": " من", "probability": 0.982421875}, {"start": 5217.55, "end": 5218.37, "word": " 1", "probability": 0.8564453125}, {"start": 5218.37, "end": 5219.99, "word": " لغاية", "probability": 0.9698486328125}, {"start": 5219.99, "end": 5221.31, "word": " 26", "probability": 0.9736328125}], "temperature": 1.0}, {"id": 226, "seek": 524975, "start": 5226.07, "end": 5249.75, "text": "حاول تحلي بقدر المكان تتدربي عليهم لإن المسائل هدول ضروريات جدا لإنه لا يكاد يخلو امتحان نهائي وأظنه لن يخلو من استخدام Laplace transform للحصول على حل المعادلة التفاضلية اعطيكوا العافية", "tokens": [5016, 995, 12610, 6055, 5016, 20292, 4724, 28543, 2288, 9673, 41361, 6055, 2655, 3215, 2288, 21292, 25894, 16095, 5296, 28814, 1863, 9673, 3794, 16373, 1211, 8032, 3215, 12610, 48812, 2288, 13063, 1829, 9307, 10874, 28259, 5296, 28814, 1863, 3224, 20193, 7251, 4117, 18513, 7251, 9778, 1211, 2407, 1975, 2304, 2655, 5016, 7649, 8717, 3224, 16373, 1829, 36725, 19913, 1863, 3224, 5296, 1863, 7251, 9778, 1211, 2407, 9154, 44713, 9778, 3215, 10943, 2369, 6742, 4088, 24976, 5016, 9381, 12610, 15844, 11331, 1211, 9673, 3615, 18513, 37977, 16712, 5172, 46958, 1211, 10632, 1975, 3615, 9566, 1829, 4117, 14407, 18863, 31845, 10632], "avg_logprob": -0.15812500163912774, "compression_ratio": 1.6548223350253808, "no_speech_prob": 5.960464477539063e-08, "words": [{"start": 5226.07, "end": 5226.59, "word": "حاول", "probability": 0.95556640625}, {"start": 5226.59, "end": 5227.03, "word": " تحلي", "probability": 0.7747395833333334}, {"start": 5227.03, "end": 5227.55, "word": " بقدر", "probability": 0.98046875}, {"start": 5227.55, "end": 5228.07, "word": " المكان", "probability": 0.772216796875}, {"start": 5228.07, "end": 5228.83, "word": " تتدربي", "probability": 0.70849609375}, {"start": 5228.83, "end": 5229.53, "word": " عليهم", "probability": 0.981201171875}, {"start": 5229.53, "end": 5230.53, "word": " لإن", "probability": 0.8268229166666666}, {"start": 5230.53, "end": 5231.35, "word": " المسائل", "probability": 0.934814453125}, {"start": 5231.35, "end": 5231.95, "word": " هدول", "probability": 0.8134765625}, {"start": 5231.95, "end": 5234.01, "word": " ضروريات", "probability": 0.82939453125}, {"start": 5234.01, "end": 5234.57, "word": " جدا", "probability": 0.982177734375}, {"start": 5234.57, "end": 5235.61, "word": " لإنه", "probability": 0.7718505859375}, {"start": 5235.61, "end": 5235.81, "word": " لا", "probability": 0.89599609375}, {"start": 5235.81, "end": 5236.65, "word": " يكاد", "probability": 0.9552408854166666}, {"start": 5236.65, "end": 5237.19, "word": " يخلو", "probability": 0.932861328125}, {"start": 5237.19, "end": 5237.81, "word": " امتحان", "probability": 0.97294921875}, {"start": 5237.81, "end": 5238.71, "word": " نهائي", "probability": 0.9580078125}, {"start": 5238.71, "end": 5240.47, "word": " وأظنه", "probability": 0.75787353515625}, {"start": 5240.47, "end": 5241.03, "word": " لن", "probability": 0.95361328125}, {"start": 5241.03, "end": 5241.59, "word": " يخلو", "probability": 0.954833984375}, {"start": 5241.59, "end": 5241.81, "word": " من", "probability": 0.98095703125}, {"start": 5241.81, "end": 5242.41, "word": " استخدام", "probability": 0.9669189453125}, {"start": 5242.41, "end": 5243.03, "word": " Laplace", "probability": 0.69873046875}, {"start": 5243.03, "end": 5243.93, "word": " transform", "probability": 0.44580078125}, {"start": 5243.93, "end": 5245.57, "word": " للحصول", "probability": 0.9234619140625}, {"start": 5245.57, "end": 5245.89, "word": " على", "probability": 0.93017578125}, {"start": 5245.89, "end": 5246.41, "word": " حل", "probability": 0.986328125}, {"start": 5246.41, "end": 5247.67, "word": " المعادلة", "probability": 0.9857177734375}, {"start": 5247.67, "end": 5248.87, "word": " التفاضلية", "probability": 0.9455078125}, {"start": 5248.87, "end": 5249.47, "word": " اعطيكوا", "probability": 0.8004964192708334}, {"start": 5249.47, "end": 5249.75, "word": " العافية", "probability": 0.7708333333333334}], "temperature": 1.0}], "language": "ar", "language_probability": 1.0, "duration": 5250.357, "duration_after_vad": 5029.521593750007}
\ No newline at end of file
diff --git a/PL9fwy3NUQKwa8ZDfSFGn6H8xVFLzqmCZC/RDSrZpOLp38_raw.srt b/PL9fwy3NUQKwa8ZDfSFGn6H8xVFLzqmCZC/RDSrZpOLp38_raw.srt
new file mode 100644
index 0000000000000000000000000000000000000000..fb8d26724f8381e318ac4dca6dc6152eca6ea914
--- /dev/null
+++ b/PL9fwy3NUQKwa8ZDfSFGn6H8xVFLzqmCZC/RDSrZpOLp38_raw.srt
@@ -0,0 +1,3316 @@
+1
+00:00:09,340 --> 00:00:14,560
+بسم الله الرحمن الرحيم المرة اللى فاتت بدأنا
+
+2
+00:00:14,560 --> 00:00:19,320
+بتعريف لبلاس ترانسفورم وحسبنا لبلاس ترانسفورم
+
+3
+00:00:19,320 --> 00:00:24,160
+مجموعة من الدوال اليوم ان شاء الله هنعطيكم مجموعة
+
+4
+00:00:24,160 --> 00:00:28,040
+من الدوال و لبلاس ترانسفورم اللى موجودة قبالك في
+
+5
+00:00:28,040 --> 00:00:28,560
+جدول
+
+6
+00:00:39,960 --> 00:00:45,300
+موضوع اليوم موضوع solution of initial value
+
+7
+00:00:45,300 --> 00:00:48,770
+problemsيبقى احنا عندنا initial value problem
+
+8
+00:00:48,770 --> 00:00:54,230
+بنحاول نوجد الحل هذا تبع المعادلة باستخدام Laplace
+
+9
+00:00:54,230 --> 00:01:00,770
+transform احنا في البداية حلينها حل عادي زمان ثم
+
+10
+00:01:00,770 --> 00:01:05,730
+بعد ذلك حلينها بال C resolution ثم الآن بنحل نفس
+
+11
+00:01:05,730 --> 00:01:09,650
+المعادلة ب Laplace transform بس Laplace transform
+
+12
+00:01:09,880 --> 00:01:14,180
+فقط هنستخدمه للدوال with constant coefficient
+
+13
+00:01:14,180 --> 00:01:18,240
+للمعادلات التفاضلية و with constant coefficients
+
+14
+00:01:18,240 --> 00:01:23,420
+يبقى المعاملات كلهما لهم ثوابت و ليست أي معاملة
+
+15
+00:01:24,270 --> 00:01:27,370
+فبجي بقول في هذا ال section we shall use Laplace
+
+16
+00:01:27,370 --> 00:01:31,290
+transform لنستخدم تحويلات لابلاس مشان الحل ال
+
+17
+00:01:31,290 --> 00:01:36,490
+initial value problems مسائل القيم الحدية for
+
+18
+00:01:36,490 --> 00:01:40,310
+linear differential equations للمعادلات الخطية
+
+19
+00:01:40,310 --> 00:01:46,620
+with constant coefficients بمعاملات ثابتة ذاتيعني
+
+20
+00:01:46,620 --> 00:01:51,220
+بدنا نترجم الكلام اللى قولناه قبل بصيغة أخرى that
+
+21
+00:01:51,220 --> 00:01:54,580
+is we shall solve the differential equation a y
+
+22
+00:01:54,580 --> 00:01:58,720
+double prime زيادة b y prime زيادة c y يساوي zero
+
+23
+00:01:58,720 --> 00:02:02,660
+طبعا ال a و ال b و ال c constant لإن احنا جايلين
+
+24
+00:02:02,660 --> 00:02:07,020
+with constant coefficients ما لها by Laplace
+
+25
+00:02:07,020 --> 00:02:12,020
+transform بتحويلات Laplaceنحاول نحل المعادلات اللى
+
+26
+00:02:12,020 --> 00:02:15,580
+بتكون على الشكل اللى قدامنا هذه باستخدام او
+
+27
+00:02:15,580 --> 00:02:20,180
+باستخدام التحويلات لبلاس لكن احنا المرة اللى فاتة
+
+28
+00:02:20,180 --> 00:02:26,680
+أخدنا لبلاس للدوال ولم ناخد لبلاس للمشتقات مظبوط
+
+29
+00:02:26,680 --> 00:02:30,780
+أخدنا لبلاس للدوال العادية وشوفنا كيف بناسمه بدنا
+
+30
+00:02:30,780 --> 00:02:36,300
+نيجي الآن نعطي نظرية تتحدث عن كيفية إيجاد لبلاس
+
+31
+00:02:36,300 --> 00:02:40,000
+للمشتقة الأولى لبلاس للمشتقة الثانيةلابلاس
+
+32
+00:02:40,000 --> 00:02:43,800
+ترانسفورم للمشتقة ثالثة لابلاس ترانسفورم للمشتقة
+
+33
+00:02:43,800 --> 00:02:50,000
+أنونية يبقى النظرية بتقول لو كان لابلاس ال F prime
+
+34
+00:02:50,000 --> 00:02:54,460
+exist يبقى في هذه الحالة لكل ال S اللي أكبر من A
+
+35
+00:02:54,460 --> 00:03:00,960
+then لابلاس ترانسفورم لل F prime of T عمليا سيسوى
+
+36
+00:03:00,960 --> 00:03:06,220
+S في لابلاس ال F of T ناقص ال F of Zero أثناء
+
+37
+00:03:06,220 --> 00:03:09,900
+الكتابة واحنا بنحلممكن ما نكتبش الكلام اللي عندنا،
+
+38
+00:03:09,900 --> 00:03:14,940
+هنروح نكتب S في capital Y of S مين capital Y of S؟
+
+39
+00:03:14,940 --> 00:03:19,040
+هو لا plus لمين؟ للي F of T لإن احنا قولنا لا plus
+
+40
+00:03:19,040 --> 00:03:24,000
+للي F of T بقطعة دالة في S تمام؟ ولمّا كانت
+
+41
+00:03:24,000 --> 00:03:30,730
+المسألة بدلالة Y كلهافبروح بقول capital Y of S
+
+42
+00:03:30,730 --> 00:03:34,330
+ناقص F of zero اللي هي قيمة الدالة عند ال zero
+
+43
+00:03:34,330 --> 00:03:39,550
+يعني قيمة ال Y عند ال zero F هذي هذي لبالك مش F
+
+44
+00:03:39,550 --> 00:03:45,270
+هذي هه هذي هه ممكن أقولك هذي G of T مش هم
+
+45
+00:03:45,270 --> 00:03:50,030
+ماتلأخبطيش يبقى هذي G of T يبقى ال F of T تبعتنا
+
+46
+00:03:50,030 --> 00:03:57,950
+هذي هي Y تمام؟أذا بقول مرة تانية Laplace transform
+
+47
+00:03:57,950 --> 00:04:04,450
+لل F prime of T هو S في Laplace لل F of T نقص F of
+
+48
+00:04:04,450 --> 00:04:10,310
+Zero عمليا هكتب S في capital Y of S نقص Y of Zero
+
+49
+00:04:10,310 --> 00:04:13,310
+طبعا في الكتاب مكتوب هيكفى احنا بنكتب هذا الكتاب و
+
+50
+00:04:13,310 --> 00:04:16,730
+هذا الكتاب لكن عند الشغل العملي ممكن اكتب هذه
+
+51
+00:04:16,730 --> 00:04:20,370
+مباشرة و بديش اللي جابلها لإن انا شغلي بده أجيب
+
+52
+00:04:20,370 --> 00:04:28,220
+capital Y of SY of S هو Laplace تبع F of T يعني
+
+53
+00:04:28,220 --> 00:04:32,480
+أنا بس باعد كتابة المعادلة من جديد يعني بده اكتب
+
+54
+00:04:32,480 --> 00:04:37,240
+هذه دغري و اكتب مين اكتب هذه طيب هذا Laplace
+
+55
+00:04:37,240 --> 00:04:40,940
+للمشتقة الأولى تعالى اخدى Laplace للمشتقة الثانية
+
+56
+00:04:40,940 --> 00:04:46,460
+as a function of T يبقى الأولى بعدين بمين بS تانية
+
+57
+00:04:47,880 --> 00:04:52,140
+الثالثة استكايب الرابعة S أس أربعة وبتبدأ الأس
+
+58
+00:04:52,140 --> 00:04:57,180
+ينقص كل ten بنقص من الأس واحد طلعيلي هنا يبقى S
+
+59
+00:04:57,180 --> 00:05:02,800
+تربية في ال plus لل F of T كله بناقص بعده ناقص
+
+60
+00:05:02,800 --> 00:05:07,380
+الاستربية صارت هنا إيش S أجاني F of Zero بعدها
+
+61
+00:05:07,380 --> 00:05:13,590
+مشتقة ال F and Man and Zeroأو عملياً هقول S تربيع
+
+62
+00:05:13,590 --> 00:05:20,090
+في capital Y of S ناقص S في Y عند ال zero ناقص Y
+
+63
+00:05:20,090 --> 00:05:26,540
+prime عند ال zeroعليها بنروح نجيب لبلاس المشتقة
+
+64
+00:05:26,540 --> 00:05:31,160
+التالتة لبلاس المشتقة الرابعة in general بروح بقول
+
+65
+00:05:31,160 --> 00:05:36,880
+لبلاس للمشتقة النونية يبقى بده أبدأ S أُس N S أُس
+
+66
+00:05:36,880 --> 00:05:40,840
+N ناقص واحد S أُس N ناقص اتنين وضل نزل لغاية موصل
+
+67
+00:05:40,840 --> 00:05:47,260
+ل S و آخر term لا يوجد فيه S تمام مرة تانية يبقى
+
+68
+00:05:47,260 --> 00:05:52,340
+لبلاس للتفاضل رقم N عند T بده يساوي S أُس N في
+
+69
+00:05:52,340 --> 00:05:56,860
+لبلاس F of Tأو لسهولة N's that fold سأبدأ فيها دي
+
+70
+00:05:56,860 --> 00:06:03,000
+دوري يبقى S أس N في capital Y of S ناقص S أس N
+
+71
+00:06:03,000 --> 00:06:08,320
+ناقص واحد في Y and Zero وبعد هيك باب المشتقة
+
+72
+00:06:08,320 --> 00:06:11,740
+الأولى المشتقة دي يعني المشتقة بتطلع و S مالها
+
+73
+00:06:11,740 --> 00:06:16,020
+بتنزل عكس بعضهذه الأس تبعها بنزل وهذه المشتقة
+
+74
+00:06:16,020 --> 00:06:19,120
+تبعها بتطلع، مشتقة الأولى، المشتقة التانية،
+
+75
+00:06:19,120 --> 00:06:24,520
+التالتة، الرابعة إلى آخرها يبقى S أس N كابتال Y of
+
+76
+00:06:24,520 --> 00:06:30,440
+S ناقص S أس N ناقص واحد Y عند ال zero ناقص S أس N
+
+77
+00:06:30,440 --> 00:06:35,620
+ناقص اتنين Y prime عند ال zeroاللي بعدها يبقى S
+
+78
+00:06:35,620 --> 00:06:40,640
+أُس N ناقص ثلاثة و Y W Prime and Zero أظل ماشي
+
+79
+00:06:40,640 --> 00:06:45,720
+لغاية S Y to the derivative N ناقص اتنين and Zero
+
+80
+00:06:45,720 --> 00:06:50,580
+آخر term مافيش فيه S زي ماكان آخر term هنا كله
+
+81
+00:06:50,580 --> 00:06:54,900
+مافيش فيه S تمين في Y to the derivative N minus ال
+
+82
+00:06:54,900 --> 00:07:01,480
+one and Zero يعني آخر term هنا بيكون هو المشتقة
+
+83
+00:07:01,480 --> 00:07:07,290
+فلعينمشتقة تانية أخر ترم بيكون مين؟ مشتقة الأولى
+
+84
+00:07:07,290 --> 00:07:12,270
+يعني لو كانت المشتقة التالتة بيصير أخر ترم مشتقة
+
+85
+00:07:12,270 --> 00:07:18,510
+الثانية و هكذا تمام؟ طيب الآن بدنا نروح نشتغل عملي
+
+86
+00:07:18,510 --> 00:07:22,730
+يعني بنشوف كيف التطبيق العملي لصيغة اللي موجودة
+
+87
+00:07:22,730 --> 00:07:26,910
+هذه طيب السؤال قبل ما تبدأ هذه الصيغة بدنا نحفظها؟
+
+88
+00:07:27,050 --> 00:07:31,690
+لا بدناش يجيك تحفظيها تمام؟ هعطيك إياها في جدول
+
+89
+00:07:31,690 --> 00:07:36,850
+موجود الصيغة عندك هنا المهم بدي كيف أستخدمها بعد
+
+90
+00:07:36,850 --> 00:07:42,890
+قليل هقولكوا كيف بدنا نشتغل بالجدول هذا ال .. الآن
+
+91
+00:07:42,890 --> 00:07:47,890
+بدنا نيجي نحل مثال على هذا الكلام طيب قال لي حل
+
+92
+00:07:47,890 --> 00:07:53,620
+المعادلة التفاضلية ولم يتكلم كلمةسأخبرك ان انا
+
+93
+00:07:53,620 --> 00:08:02,160
+ممكن احل الطريقة القديمة باستخدام
+
+94
+00:08:02,160 --> 00:08:07,660
+لابلاس ترانسفورم لتحل الاختصار الاختصار الاختصار
+
+95
+00:08:07,660 --> 00:08:12,380
+الاختصار الاختصار الاختصار الاختصار الاختصار
+
+96
+00:08:12,380 --> 00:08:19,260
+الاختصار الاختصار الاختصار الاختصار الاختصار
+
+97
+00:08:19,260 --> 00:08:20,040
+الاختصار الاختصار الاختصار الاختصار الاختصار
+
+98
+00:08:20,040 --> 00:08:20,040
+الاختصار الاختصار الاختصار الاختصار الاختصار
+
+99
+00:08:20,040 --> 00:08:20,040
+الاختصار الاختصار الاختصار الاختصار الاختصار
+
+100
+00:08:20,040 --> 00:08:20,040
+الاختصار الاختصار الاختصار الاختصار الاختصار
+
+101
+00:08:20,040 --> 00:08:22,410
+الاختصار الاختصار الاختصار الاختصطريقتنا القديمة
+
+102
+00:08:22,410 --> 00:08:26,490
+وبالطريقة من؟ لجديدة لإنه ماقالليش قاللي solve the
+
+103
+00:08:26,490 --> 00:08:32,950
+following initial value problems بس تمام إذا أنا
+
+104
+00:08:32,950 --> 00:08:36,890
+لو أجالي السؤال بهذا الشكل لامتحان ليه الحرية أحل
+
+105
+00:08:36,890 --> 00:08:40,610
+بالطريقة اللي بديها يبقى أنا لو بده أحل بالطريقة
+
+106
+00:08:40,610 --> 00:08:50,700
+القديمة بقوله هيك solutionلت يتساوي E of RT be a
+
+107
+00:08:50,700 --> 00:09:01,180
+solution of equation one then the characteristic
+
+108
+00:09:01,180 --> 00:09:04,520
+equation is
+
+109
+00:09:06,610 --> 00:09:12,430
+أر تربية ناقص ار ناقص اتنين يساوي زيرو هذه لو جيت
+
+110
+00:09:12,430 --> 00:09:18,750
+احللها كحاصل ضرب قوسين ويساوي زيرو يبقى هنا ار هنا
+
+111
+00:09:18,750 --> 00:09:25,510
+ار هنا واحد هنا اتنين هنا ناقص هنا زائد هي ناقص ار
+
+112
+00:09:25,510 --> 00:09:30,630
+وناقص اتنين ار بضل ناقص ار هي في النص ومنها ار one
+
+113
+00:09:30,630 --> 00:09:37,770
+تساوي سالب واحدوR2 تساوي كده؟ تساوي اتنين، تمام؟
+
+114
+00:09:37,770 --> 00:09:45,350
+إذا صار إن الحل هو Y يساوي C1 في E أس ناقص T زائد
+
+115
+00:09:45,350 --> 00:09:53,610
+C2 في E أس اتنين Tيبقى هذا الحل اللى احنا اتعلمناه
+
+116
+00:09:53,610 --> 00:09:59,570
+قبل طبعا الحين مابديش الحل هذا بدي اروح لحل اخر
+
+117
+00:09:59,570 --> 00:10:02,990
+بواسط ال initial value problem او ب ال serious
+
+118
+00:10:02,990 --> 00:10:06,810
+solution بس ان كان بده serious solution بدي اعطيني
+
+119
+00:10:06,810 --> 00:10:10,710
+نقطة مظبوط هذا ماعطانيش نقطة يبقى in serious
+
+120
+00:10:10,710 --> 00:10:16,910
+solution طبعا ايه كويس يبقى بداجي ايش بداجي اقوله
+
+121
+00:10:16,910 --> 00:10:19,010
+هنا another solution
+
+122
+00:10:24,860 --> 00:10:30,200
+بناخد محل آخر يبقى ناخد Laplace transform للطرفين
+
+123
+00:10:30,200 --> 00:10:35,440
+يبقى بدي جيلك عندك هنا Laplace transform ل Y
+
+124
+00:10:35,440 --> 00:10:41,120
+double prime ناقص Y prime زائد اتنين Y بده يساوي
+
+125
+00:10:41,120 --> 00:10:48,040
+Laplace ل Zero تكامل
+
+126
+00:10:48,040 --> 00:10:53,380
+EOS ناقص T ضرب Zero في DT يبقى Zero كويس يبقى هذا
+
+127
+00:10:53,380 --> 00:10:58,460
+بده يساوي Zeroطيب هذا الان linear ل plus linear
+
+128
+00:10:58,460 --> 00:11:03,100
+function مظبوط اذا هذا شو بده يعطينا بده يعطينا ل
+
+129
+00:11:03,100 --> 00:11:10,480
+plus لل y double prime ناقص ل plus لل y prime زي
+
+130
+00:11:10,480 --> 00:11:16,080
+دي اتنين ل plus لل y كله بده يساوي مان؟ بده يساوي
+
+131
+00:11:16,080 --> 00:11:23,860
+زيرو ايش فيه؟ اه هذه ناقص المثلة خلاص يبقى هذه
+
+132
+00:11:23,860 --> 00:11:30,850
+ناقصتمام هنا كتبت اه وهنا نقص تمام يبقى كله بالشكل
+
+133
+00:11:30,850 --> 00:11:33,890
+اللي عنه هذا الان بدي اشيل ال plus لل y double
+
+134
+00:11:33,890 --> 00:11:39,530
+prime و احط القيمة بتبعته و اشيل ال plus لمن؟ لل y
+
+135
+00:11:39,530 --> 00:11:43,170
+prime و ال y و احط القيمة بتبعته من وين؟ من الكلام
+
+136
+00:11:43,170 --> 00:11:47,250
+اللي قعدنا عنه هذا بدي نمسك الأولى ال plus لل y
+
+137
+00:11:47,250 --> 00:11:52,610
+double prime يبقى هي عبارة عن s تربية في capital Y
+
+138
+00:11:52,610 --> 00:12:01,350
+of sناقص s في main في ال y عند ال zero ناقص y
+
+139
+00:12:01,350 --> 00:12:07,800
+prime عند ال zeroيبقى يخلصنا من الجزء الأول اللي
+
+140
+00:12:07,800 --> 00:12:13,520
+بعده هاي ناقص وبتفتح يقوس حتى ماتخلطيش بده يجي ال
+
+141
+00:12:13,520 --> 00:12:18,860
+Y prime هي موجودة عند أول واحدة يبقى هي S في
+
+142
+00:12:18,860 --> 00:12:28,430
+capital Y of S ناقص Y عند ال zeroوصلنا لبعدها نقص
+
+143
+00:12:28,430 --> 00:12:34,850
+اتنين capital Y of S كل هذا الكلام بده يساوي كده؟
+
+144
+00:12:34,850 --> 00:12:42,110
+بده يساوي Zeroاذا بدى اعرف بعد هيك ماهو شكل
+
+145
+00:12:42,110 --> 00:12:47,170
+capital Y of S بنقولك بسيطة، اذا خلينا نفك هذه
+
+146
+00:12:47,170 --> 00:12:54,310
+يبقى هذه S تربيع في capital Y of S ناقص S في Y عند
+
+147
+00:12:54,310 --> 00:12:59,910
+ال zero معطعة، بقدرش؟بواحد يبقى بداشي لو احط
+
+148
+00:12:59,910 --> 00:13:07,110
+مكانها واحد الان ناقص Y' عند ال zero بقداش بزيرو
+
+149
+00:13:07,110 --> 00:13:13,870
+مع السلامة خلصنا ال term الأول بداجي هذا ناقص S في
+
+150
+00:13:13,870 --> 00:13:20,170
+capital Y of S ناقص في ناقص بزائد Y عند ال zero
+
+151
+00:13:20,170 --> 00:13:28,230
+بقداش بواحداللي بعدها نقص اتنين capital Y of S بده
+
+152
+00:13:28,230 --> 00:13:34,530
+يساوي Zero طلعيلي ال term هذا و ال term هذا و ال
+
+153
+00:13:34,530 --> 00:13:40,050
+term هذافيهم capital Y of S، صحيح ولا لأ؟ إذا
+
+154
+00:13:40,050 --> 00:13:44,170
+بتاخدوا عامل مشترك من الكلشو، بيبقى لدي هنا، بيبقى
+
+155
+00:13:44,170 --> 00:13:53,390
+لدي S ترابيع، ناقص S، ناقصي 2، كله في capital Y of
+
+156
+00:13:53,390 --> 00:14:01,440
+Sهذه ناقص S في واحد بناقص S هذه Zero مع السلام
+
+157
+00:14:01,440 --> 00:14:06,540
+الله يسهل عليها هذه زائد واحد قلصت كله بده يساوي
+
+158
+00:14:06,540 --> 00:14:12,800
+كده؟ بده يساوي Zero اللي فيها capital Y of S بده
+
+159
+00:14:12,800 --> 00:14:17,720
+اخليها في شجة و الباقي وين؟ في شجة تانيةأنا بديش
+
+160
+00:14:17,720 --> 00:14:23,220
+هذه انا بدي capital Y of S فبروح بقوله capital Y
+
+161
+00:14:23,220 --> 00:14:32,360
+of S بدي سوى S ناقص واحد تقسيم S زائد واحد في مين
+
+162
+00:14:32,360 --> 00:14:41,580
+في S ناقص اتنين واضح ان اختصارات ماعنديش طيب كيف
+
+163
+00:14:41,580 --> 00:14:43,060
+بدي أسوي فيها هذه
+
+164
+00:14:45,990 --> 00:14:49,470
+بقول بسيطة جدا سمعنا بال partial fractions في
+
+165
+00:14:49,470 --> 00:14:55,250
+Calculus B كسور الجزئية اذا بروح بحلل هذا الكسر
+
+166
+00:14:55,250 --> 00:15:01,090
+الى مجموع كسرين او تلاتة او اربعة حسب طبيعة المثلة
+
+167
+00:15:01,090 --> 00:15:07,830
+بجيب اطلع انا عند المقام اللي هو قوسين وقوس التاني
+
+168
+00:15:07,830 --> 00:15:13,400
+يبقىDifferent coefficients، معاملات مختلفة، إذا
+
+169
+00:15:13,400 --> 00:15:18,080
+باجي بقوله هذا الكلام يساوية، هذا جوس، اللي هو
+
+170
+00:15:18,080 --> 00:15:24,060
+الـS زائد واحد، الجوس اللي هو زائد و هذا كسر و هذا
+
+171
+00:15:24,060 --> 00:15:30,980
+التانيبعد هيك باجي بقول كل واحد من المقامات مختلف
+
+172
+00:15:30,980 --> 00:15:35,920
+عن الثاني وكل واحد من الدرجة الأولى إذا بقول
+
+173
+00:15:35,920 --> 00:15:41,580
+constant على الأول و constant على من؟ على الثاني و
+
+174
+00:15:41,580 --> 00:15:46,620
+بعد براجع معلوماتي في calculus بيه بدي أجيب قداش
+
+175
+00:15:46,620 --> 00:15:53,280
+قيمة كل من a و b بعد بقول بتيجي على هذه المعادلة
+
+176
+00:15:53,280 --> 00:16:00,000
+كلهامش هانا بالسماء هذه، بدي أروح أضرب الطرفين في
+
+177
+00:16:00,000 --> 00:16:04,980
+المقام، يبقى لو روحت ضربت الطرفين في المقام هذه،
+
+178
+00:16:04,980 --> 00:16:10,930
+هتعطيني مين؟أس ناقص واحد اللي هو فوق ضربته هنا
+
+179
+00:16:10,930 --> 00:16:18,270
+هيختصر معاني هذه هتعطيني مين تساوي A في S ناقص
+
+180
+00:16:18,270 --> 00:16:28,010
+اتنين بدي هضرب هنا زائد B في S زائد واحد تمام؟
+
+181
+00:16:28,010 --> 00:16:32,250
+الحين بده اجيب A وB بيبقى اشتغل الشغل اللي بدكيا
+
+182
+00:16:32,250 --> 00:16:42,580
+فبجي بقول لو كانتS تساوي سالب واحدسالب واحد سالب
+
+183
+00:16:42,580 --> 00:16:48,700
+واحد يساوي سالب واحد و سالب واحد سالب تلاتة يبقى
+
+184
+00:16:48,700 --> 00:16:54,580
+سالب تلاتة ايه وهذه مع السلامة اذا ايه يا بنات
+
+185
+00:16:54,580 --> 00:17:01,760
+تساوي قداش تساوي تلتين بالموجة يبقى الايه هتساوي
+
+186
+00:17:01,760 --> 00:17:08,720
+تلتين تمام اتتمام طيب لو كانت ال S تساوي اتنين
+
+187
+00:17:10,470 --> 00:17:17,770
+اتنين ناقص واحد تساوي اتنين
+
+188
+00:17:17,770 --> 00:17:27,010
+واحد تلاتة بي يبقى تلاتة بي ومنها يبقى بي بدها
+
+189
+00:17:27,010 --> 00:17:32,510
+تساوي مضال هنا واحد و هنا تلاتة بي تساوي تلت
+
+190
+00:17:34,690 --> 00:17:41,850
+يبقى صرف مسألتي على الشكل التالي يبقى capital Y of
+
+191
+00:17:41,850 --> 00:17:51,270
+S يساوي ال A عندي بتلتين يبقى هاي تلتين على S زائد
+
+192
+00:17:51,270 --> 00:17:59,730
+واحد على S زائد واحد اللي بعده B بتلت يبقى زائد
+
+193
+00:17:59,730 --> 00:18:08,060
+تلت على S ناقص اتنينهذه مقادير ثابتة يعني بقدر
+
+194
+00:18:08,060 --> 00:18:15,620
+اقول هذا الكلام يساوي تلتين في جداش في واحد على
+
+195
+00:18:15,620 --> 00:18:25,020
+مين على اس زائد واحد تمام هنا زائد تلت في مين في
+
+196
+00:18:25,020 --> 00:18:32,640
+واحد على اس ناقص اتنين بالشكل اللي عندنا طيب
+
+197
+00:18:32,640 --> 00:18:39,940
+هو جالي هات الحلأنا جبت الأن لبلاس ترانسفورم للحل،
+
+198
+00:18:39,940 --> 00:18:44,060
+مظبوط؟ أنا بديش لبلاس ترانسفورم، أنا بدي الحل
+
+199
+00:18:44,060 --> 00:18:48,840
+itself لأن هنا فوق جيبنا حل، ولو أننا لسه ماجيبناش
+
+200
+00:18:48,840 --> 00:18:52,100
+ال initial continuous ممكن أروح هذه و أجيب C1 و C2
+
+201
+00:18:52,100 --> 00:18:56,400
+قداش تساوي، الحين هوريك قداش C1 يساوي 2 و بدك أنت
+
+202
+00:18:56,400 --> 00:19:00,500
+تروح تكمل الحل اللي فوق و تتبت أنه C1 هو الرقم
+
+203
+00:19:00,500 --> 00:19:05,170
+اللي بدي يطلع عنه هنا و C2 هو نفس الرقمبس خلينا
+
+204
+00:19:05,170 --> 00:19:11,370
+نشوف الان كيف بدنا نجيب هذه هذي شو أصلها يا بنات؟
+
+205
+00:19:11,370 --> 00:19:21,630
+exponential E أس سالب T هذي شو أصلها؟ E أس اتنين T
+
+206
+00:19:21,630 --> 00:19:26,410
+طبعا احنا
+
+207
+00:19:26,410 --> 00:19:29,970
+مطلوب نحفظ و لا بدنا اش نحفظ المرة اللي فاتت
+
+208
+00:19:29,970 --> 00:19:35,280
+قلتلكوا بتجيبوا الكتب معاكماللي جابت كتابها جابته،
+
+209
+00:19:35,280 --> 00:19:39,820
+واللي ما جابتش أخدت احتياطاتي وجبتلكوا الجدول
+
+210
+00:19:39,820 --> 00:19:47,620
+المصور صفحة 319 تمام؟ يلا وزعوا بحيث كل مقعد يكون
+
+211
+00:19:47,620 --> 00:19:53,080
+عليه ورقات جدول، يلا خد يلا وزع الباقى، بسرعة
+
+212
+00:19:53,080 --> 00:19:58,300
+بسرعة يلامن حد ما نوصل للشكل اللي عندنا هذا يبقى
+
+213
+00:19:58,300 --> 00:20:01,540
+capital Y of this اللي هو Laplace transform لل
+
+214
+00:20:01,540 --> 00:20:05,680
+solution يسوى الجزء اللي عندنا هذا إذا بناء عليه
+
+215
+00:20:05,680 --> 00:20:12,940
+بروح بقوله solution of
+
+216
+00:20:15,300 --> 00:20:22,860
+differential equation one is بتقولي لي y small as
+
+217
+00:20:22,860 --> 00:20:28,300
+a function of t يساوي يبقى هذا ل plus transform
+
+218
+00:20:28,300 --> 00:20:34,500
+لدى لهذا هو الأصل تبعها يبقى بده يساوي جداش هنا
+
+219
+00:20:34,500 --> 00:20:41,230
+طولتين يبقى هاي طولتين بخليها زي ما هيو باجي لمن؟
+
+220
+00:20:41,230 --> 00:20:46,030
+ل الواحد على S زائد واحد، كلكوا افتحوا لي في
+
+221
+00:20:46,030 --> 00:20:49,010
+الكتاب صفحه التلاتمية وتسعة عشر او الورق اللي
+
+222
+00:20:49,010 --> 00:20:53,710
+وزعنالكوا عليها هذه سبيكي من العمود اللي ع الشمال
+
+223
+00:20:53,710 --> 00:20:59,210
+بتاخد العمود اللي على اليمين بروح بدور عندي على S
+
+224
+00:20:59,210 --> 00:21:05,430
+وراحت على S زائد واحدبطلع في النقطة رقم اتنين
+
+225
+00:21:05,430 --> 00:21:12,530
+مكتوب واحد على اس ناقص ايه بواحد مظبوط لكنها دهاش
+
+226
+00:21:12,530 --> 00:21:17,250
+بالزائد تمام يبقى هنا لما صارت بالزائد معناته هي
+
+227
+00:21:17,250 --> 00:21:27,050
+اي أس سالب ا ت يعني اي أس سالب ت يبقى هنا صار
+
+228
+00:21:27,050 --> 00:21:34,900
+تلتين في اي أس سالب تبعدها زائد تلت اللي هو اللي
+
+229
+00:21:34,900 --> 00:21:40,300
+برا هاي تلت اللي برا واحد على اس ناقص اتنين برضه
+
+230
+00:21:40,300 --> 00:21:46,060
+نفس النقطة نقطة رقم اتنين واحد على اس ناقص ايه
+
+231
+00:21:46,060 --> 00:21:53,180
+اجبالها جداش E أس ETيبقى هذا ههه اللي هي مين اللي
+
+232
+00:21:53,180 --> 00:22:02,960
+هي الدالة و هذا لابلاس ترانسفورم اللي هي اللي هي
+
+233
+00:22:02,960 --> 00:22:02,960
+اللي هي اللي هي اللي هي اللي هي اللي هي اللي هي
+
+234
+00:22:02,960 --> 00:22:02,960
+اللي هي اللي هي اللي هي اللي هي اللي هي اللي هي
+
+235
+00:22:02,960 --> 00:22:02,960
+اللي هي اللي هي اللي هي اللي هي اللي هي اللي هي
+
+236
+00:22:02,960 --> 00:22:02,980
+اللي هي اللي هي اللي هي اللي هي اللي هي اللي هي
+
+237
+00:22:02,980 --> 00:22:02,980
+اللي هي اللي هي اللي هي اللي هي اللي هي اللي هي
+
+238
+00:22:02,980 --> 00:22:02,980
+اللي هي اللي هي اللي هي اللي هي اللي هي اللي هي
+
+239
+00:22:02,980 --> 00:22:03,180
+اللي هي اللي هي اللي هي اللي هي اللي هي اللي هي
+
+240
+00:22:03,180 --> 00:22:03,180
+اللي هي اللي هي اللي هي اللي هي اللي هي اللي هي
+
+241
+00:22:03,180 --> 00:22:03,180
+اللي هي اللي هي اللي هي اللي هي اللي هي اللي هي
+
+242
+00:22:03,180 --> 00:22:03,260
+اللي هي اللي هي اللي هي اللي هي اللي هي اللي هي
+
+243
+00:22:03,260 --> 00:22:19,260
+اللي هي اللي
+
+244
+00:22:19,260 --> 00:22:28,180
+هييبقى هذا الحل المطلوب يبقى
+
+245
+00:22:28,180 --> 00:22:33,580
+بدك
+
+246
+00:22:33,580 --> 00:22:38,040
+تشتق الحل هذا مرتين و تجي تعوض من حوض التكامل وهي
+
+247
+00:22:38,040 --> 00:22:42,280
+الجواب عندك زي ما كنا بنعمل قبل طبعا الشغل اللي
+
+248
+00:22:42,280 --> 00:22:46,100
+اشتغلته هو هذا السبب اللي خلاني اشتغله لإن ما جول
+
+249
+00:22:46,100 --> 00:22:51,080
+مجلش جلي صلفه سكتتمام؟ فاضطريت انا و قلت ان دي بدل
+
+250
+00:22:51,080 --> 00:22:55,200
+الحل اتنين لكن لو قاللي من البداية use Laplace
+
+251
+00:22:55,200 --> 00:23:00,820
+transform اذا automatic بدى اروح مباشرة على
+
+252
+00:23:00,820 --> 00:23:04,500
+Laplace transform اللي همام القطوة الثانية هذه
+
+253
+00:23:04,500 --> 00:23:10,200
+ماشي؟ حد بتحب تسأل اي سؤال قبل مواصل الأمثلة؟
+
+254
+00:23:10,200 --> 00:23:13,420
+ماعنديش كل المحاضرة أمثلة؟ مافيش هذا نظري، قلص
+
+255
+00:23:13,420 --> 00:23:19,610
+النظريهل بتحب تسأل اي سؤال؟ طبعا انا قولتلك ال
+
+256
+00:23:19,610 --> 00:23:22,710
+derivative بتاعه بديش يا كنت احفظيه طلعيلي في اخر
+
+257
+00:23:22,710 --> 00:23:30,550
+سطر عندك اخر سطر بتاعك مكتوب عندك هنا اللي هو اللي
+
+258
+00:23:30,550 --> 00:23:36,730
+على الشمال عندك F to the derivative N F و فوقها N
+
+259
+00:23:36,730 --> 00:23:41,460
+بين جسين as a function of Tاللي جبالها سطر طويل
+
+260
+00:23:41,460 --> 00:23:46,960
+هذا اليومين لبلاس ترانسفورم للمشتق قانونية لF
+
+261
+00:23:46,960 --> 00:23:50,980
+شايفينه اللي قُتول ساعة قبل شوية كتبناه على
+
+262
+00:23:50,980 --> 00:23:56,440
+اللواحي آخر سطر تحت S أُس N capital F of S اللي
+
+263
+00:23:56,440 --> 00:24:00,400
+احنا مايقولاش عليها capital Y of S اللي بعدها S
+
+264
+00:24:00,400 --> 00:24:04,480
+أُس N ناقص واحد F of Zero ناقص ناقص لغاية آخر term
+
+265
+00:24:04,480 --> 00:24:10,590
+F of N ناقص واحد عند من عند Zeroكل F حط في مكانها
+
+266
+00:24:10,590 --> 00:24:15,310
+Y بنكون A نفس الكلام اللي كتبناه هنا على اللوح قبل
+
+267
+00:24:15,310 --> 00:24:21,630
+قليل تمام؟ كل سؤال هيطلع الشكل مش دايما بدي يطلع
+
+268
+00:24:21,630 --> 00:24:25,950
+exponential زي هذه بس سؤال يطلع exponential بقدر
+
+269
+00:24:25,950 --> 00:24:30,010
+الله يمكن يطلع الجواب T to the power N يمكن Sine
+
+270
+00:24:30,010 --> 00:24:35,880
+يمكن Cos يمكن Gauss يمكن Sine يمكن T في Cosأو تي
+
+271
+00:24:35,880 --> 00:24:40,120
+في جوش يمكن إلى اخرى اي دالة من مجموعة الدوال ال
+
+272
+00:24:40,120 --> 00:24:44,360
+18 او ال 19 اللي عندك هدول خلاص؟ و المرة اللي فاتت
+
+273
+00:24:44,360 --> 00:24:47,160
+ابتدت و حسبنا لا plus لا transform ولا الواحد طلع
+
+274
+00:24:47,160 --> 00:24:52,600
+قداش وعد الاسلمين اول واحدة فوق جايها عندك في
+
+275
+00:24:52,600 --> 00:24:59,180
+الجدول اول واحدة فوق تمام؟ طيب نجي ناخد المثال رقم
+
+276
+00:24:59,180 --> 00:25:05,010
+اتنين يبقى مثال رقم اتنينلا نترككم تايهين نقول لكم
+
+277
+00:25:05,010 --> 00:25:13,170
+use Laplace transform example example
+
+278
+00:25:13,170 --> 00:25:25,790
+use
+
+279
+00:25:25,790 --> 00:25:30,470
+Laplace transform
+
+280
+00:25:53,960 --> 00:26:03,840
+اول واحدة او نمرة ا او نمرة واحداللي هو من y
+
+281
+00:26:03,840 --> 00:26:12,580
+double prime ناقص أربعة y prime زائد أربعة y تساوي
+
+282
+00:26:12,580 --> 00:26:20,780
+زيرو و ال y عند زيرو بده يساوي الواحد و ال y prime
+
+283
+00:26:20,780 --> 00:26:27,480
+عند زيرو كذلك تساوي كده؟ تساوي واحد solution
+
+284
+00:26:31,500 --> 00:26:35,880
+يبقى بدي اخد Laplace transform للطرفين مش هشغل
+
+285
+00:26:35,880 --> 00:26:38,920
+الشغل التفصيلي هذا لأ هدخل Laplace على كل واحدة
+
+286
+00:26:38,920 --> 00:26:46,240
+فيهم دوري يبقى بداجي اقول Laplace ل Y double prime
+
+287
+00:26:46,240 --> 00:26:53,680
+ناقص اربعة في Laplace ل Y prime زائد اربعة في
+
+288
+00:26:53,680 --> 00:26:57,880
+Laplace ل Y Laplace ل Zero بالزينة
+
+289
+00:27:08,040 --> 00:27:18,680
+نقص S في Y عند Zero ناقص Y عند Zero هذا كله term
+
+290
+00:27:18,680 --> 00:27:23,420
+الأول اللي بعده ناقص أربعة في
+
+291
+00:27:29,980 --> 00:27:40,100
+لاقص y عند الـ zero زائد أربعة في مين في capital Y
+
+292
+00:27:40,100 --> 00:27:41,120
+of S
+
+293
+00:27:54,030 --> 00:28:04,510
+يبقى ناقص S في واحد و Y prime ناقص واحدنقص اربعة S
+
+294
+00:28:04,510 --> 00:28:12,630
+في capital Y of S نقص في نقص بزائد اربعة في Y عند
+
+295
+00:28:12,630 --> 00:28:17,310
+ال zero اللي بقدرش ايه بواحد خلاصنا من القوس هذا
+
+296
+00:28:17,310 --> 00:28:25,610
+زائد اربعة capital Y of S كله بده يساوي Zeroبعد
+
+297
+00:28:25,610 --> 00:28:30,710
+ذلك تذهب و تأخذ اللي فيهم capital Y of S مع بعضهم
+
+298
+00:28:30,710 --> 00:28:39,090
+بقوة سن واحد يبقى S squared ماقص أربعة S زائد
+
+299
+00:28:39,090 --> 00:28:49,460
+أربعة كله في capital Y of Sضايلة هنا ناقص S وعندك
+
+300
+00:28:49,460 --> 00:28:57,200
+هنا ناقص واحد وزائد أربعة بظهر زائد تلاتة كله بده
+
+301
+00:28:57,200 --> 00:29:01,760
+يساوي مين؟ بده يساوي Zero هذه يا بناتيش بتعطينا
+
+302
+00:29:01,760 --> 00:29:10,240
+المثل هذا باعتبار S ناقص اتنين الكل تربية يبقى S
+
+303
+00:29:10,240 --> 00:29:17,870
+ناقص اتنين الكل تربيةفاهمين؟ في capital Y of S
+
+304
+00:29:17,870 --> 00:29:21,630
+يساوي هذي هوديها عليه الشجة التانية يبقى ايش
+
+305
+00:29:21,630 --> 00:29:29,750
+بيصير؟ S ناقص ثلاثة بناء عليه صار Laplace للحل
+
+306
+00:29:29,750 --> 00:29:38,050
+capital Y of S بده يساوي S ناقص ثلاثة على S ناقص
+
+307
+00:29:38,050 --> 00:29:43,470
+اتنين لكل ترابيع الشكل اللي عندناإذا شو بدي أعمل
+
+308
+00:29:43,470 --> 00:29:49,090
+لهذه؟ بدي أعمل لها partial fractions يبقى هذه
+
+309
+00:29:49,090 --> 00:29:56,990
+تساوى S ولا لا درجة البسط أقل من درجة المقام يبقى
+
+310
+00:29:56,990 --> 00:30:04,020
+احنا جاهزين بس المقام من الدرجة الأولى ومكرراذا
+
+311
+00:30:04,020 --> 00:30:10,200
+بدكر باللي درسنا في calculus بيه بقول S ناقص اتنين
+
+312
+00:30:10,200 --> 00:30:18,320
+زاد كسر تاني S ناقص اتنين لكل تربيع بالشكل اللي
+
+313
+00:30:18,320 --> 00:30:24,100
+عنا هنا هذا من الدرجة الأولى بقول A هذا كمان من
+
+314
+00:30:24,100 --> 00:30:32,410
+الدرجة الأولى و مكرر بقول Bيبقى هكذا، كنا بنعمل
+
+315
+00:30:32,410 --> 00:30:37,870
+فيه Calculus B الآن بدي أجي لمن؟ للمعادلة اللي
+
+316
+00:30:37,870 --> 00:30:44,010
+عندنا هذه كلها و بدي أضربها في من؟ في المقام اللي
+
+317
+00:30:44,010 --> 00:30:48,590
+عندنا هذا، مشان مايضلش عندي كسور، بصير معادلة
+
+318
+00:30:48,590 --> 00:30:54,250
+عادية، بصير سهل علينا حل هذه المعادلة
+
+319
+00:31:07,880 --> 00:31:14,320
+طيبنجي نضرب وين؟ في المقام يبقى المعادلة دي بيصير
+
+320
+00:31:14,320 --> 00:31:24,080
+S ناقص تلاتة تساوي يبقى A في S ناقص اتنين زائد B
+
+321
+00:31:24,080 --> 00:31:31,520
+يبقى بطل يصير عندي كسور يبقى قدامي اكتر من طريق يا
+
+322
+00:31:31,520 --> 00:31:36,500
+بحط قيم ل S من عندي زي المثال اللي قبل يا بفكه
+
+323
+00:31:36,500 --> 00:31:41,200
+بعمل ايه؟ مقارنة بين الطرفينيبقى ذاكرنا كتاب
+
+324
+00:31:41,200 --> 00:31:45,380
+الطريقة الأولى و الآن سأذكركم بالطريقة الثانية
+
+325
+00:31:45,380 --> 00:31:52,900
+يبقى هذه يا بنات لو بدها فكهة يبقى AS-2AB
+
+326
+00:31:54,450 --> 00:32:00,070
+لو جيت الان بالعربي بمقارنة المعاملات في الطرفين
+
+327
+00:32:00,070 --> 00:32:06,230
+هذا ال term كله ماله مافيش فيه S وهذا هو الوحيد
+
+328
+00:32:06,230 --> 00:32:12,630
+اللي فيه S يبقى بناء على هذا ال S المعامل تبع ال S
+
+329
+00:32:12,630 --> 00:32:17,890
+هنا جداش A المعامل تبع هنا اللي هو جداش بواحد إذا
+
+330
+00:32:17,890 --> 00:32:25,000
+A تساوي واحدالباقي الحد الخالي من S اللي هو ناقص
+
+331
+00:32:25,000 --> 00:32:30,820
+اتنين A زائد بيها ده كله يعتبر مقدار ثابت المقدار
+
+332
+00:32:30,820 --> 00:32:37,140
+الثابت جديش عندنا هنا سالب تلاتة باخده بإشارتهالان
+
+333
+00:32:37,140 --> 00:32:41,880
+a عندي بواحد يبقى المعادلة هذه لو شيلت ال a و حطيت
+
+334
+00:32:41,880 --> 00:32:48,140
+مكانها واحد بصير ناقص اتنين في واحد زائد بي يسوى
+
+335
+00:32:48,140 --> 00:32:54,960
+ناقص تلاتة اذا بي تسوى قداش ناقص واحدسالب اتنين
+
+336
+00:32:54,960 --> 00:32:57,840
+ودعه على الشجة التانية بصير اتنين وسالب تلاتة بضل
+
+337
+00:32:57,840 --> 00:33:05,220
+جداش سالب واحد يبقى هاي جبتله قيمة ثوابت A وB يبقى
+
+338
+00:33:05,220 --> 00:33:11,620
+بناء عليه أصبح capital Y of S بده يساوي بده اشيل
+
+339
+00:33:11,620 --> 00:33:18,610
+ال A وحط قيمته اللي هي بواحديبقى واحد على اس ناقص
+
+340
+00:33:18,610 --> 00:33:27,490
+اتنين زائد بيبقى ناقص واحد على اس ناقص اتنين لكل
+
+341
+00:33:27,490 --> 00:33:37,230
+تربيةيبقى هذا يعني لابلاس يتغير الرجل للحل لان بده
+
+342
+00:33:37,230 --> 00:33:43,990
+يجيب الحل يبقى
+
+343
+00:33:43,990 --> 00:33:46,130
+بده يجيب الحل
+
+344
+00:33:51,510 --> 00:33:58,770
+of the initial value problem one is هذه بداية
+
+345
+00:33:58,770 --> 00:34:07,410
+المثلة سامحالي one نمرة واحديجب ان اقول Y of T بدل
+
+346
+00:34:07,410 --> 00:34:13,150
+ساعة واحد على S ناقص اتنين توسع جيبنا عليه مين؟ E
+
+347
+00:34:13,150 --> 00:34:18,770
+أس اتنين T نجي
+
+348
+00:34:18,770 --> 00:34:24,570
+واحد على S ناقص اتنين الكل تربية يعني بدنا ندور
+
+349
+00:34:24,570 --> 00:34:30,710
+على مين؟ الواحد على S ناقص الكل تربية في العمود
+
+350
+00:34:30,710 --> 00:34:35,420
+اللي على اليمين هذابنجي بطلع الأولى لأتانية
+
+351
+00:34:35,420 --> 00:34:41,040
+التالتة الرابعة الخامسة مش عارف وين انزل وصلنا
+
+352
+00:34:41,040 --> 00:34:48,940
+لجداش لرقم 11 طلعي لرقم 11 عندك ايش مكتوب عندي in
+
+353
+00:34:48,940 --> 00:34:54,820
+factorial على s ناقص ال a to the power in minus
+
+354
+00:34:54,820 --> 00:35:01,590
+oneهذه أقرب واحدة موجودة عندى، صحيح ولا لأ؟ اه بس
+
+355
+00:35:01,590 --> 00:35:06,090
+ايش انت كاتب هنا؟ انت كاتب واحد ماعنديش factorial
+
+356
+00:35:06,570 --> 00:35:11,250
+أقول لك لأ ما هو الواحد هو الواحد factorial صحيح
+
+357
+00:35:11,250 --> 00:35:17,230
+يعني كأنها هداش يا بنات اللي هي واحد على اس ناقص
+
+358
+00:35:17,230 --> 00:35:24,890
+اتنين ناقص واحد factorial على اس ناقص اتنين اص
+
+359
+00:35:24,890 --> 00:35:30,260
+واحد زي واحد يعني اني بجداشبواحد اتطلع يبقى هنا
+
+360
+00:35:30,260 --> 00:35:38,220
+رقم N factorial على S ناقص كله to the power N plus
+
+361
+00:35:38,220 --> 00:35:44,680
+ال one يبقى بناء عليه هذا شو بدها تكون تي to the
+
+362
+00:35:44,680 --> 00:35:51,700
+power N ال N عندي انا بقدرش يبقى تي فقطمضبوط
+
+363
+00:35:51,700 --> 00:35:57,120
+فاهمين في ال E أس ET الإشارة عندنا هنا بالنقص وفي
+
+364
+00:35:57,120 --> 00:36:03,740
+الجدول عندنا هنا بالنقص يبقى E أس اتنين T بالضبط
+
+365
+00:36:03,740 --> 00:36:11,600
+تماما رقم 11 طلع فيها كويسبس ان عندك بقدرش بواحد
+
+366
+00:36:11,600 --> 00:36:19,880
+صحيح وبعد يعني يا بنات أحيانا أحيانا بتلعش النتيجة
+
+367
+00:36:19,880 --> 00:36:24,220
+هنا أو هنا بالنص زي مين زي ما هو موجود عندى في
+
+368
+00:36:24,220 --> 00:36:28,520
+الجدول بد تحويرة بسيطة بقى تخليه في صوت الجدول
+
+369
+00:36:28,520 --> 00:36:32,280
+يبقى جدا تعملي هذه التحويرة ممكن تدربي في رقم
+
+370
+00:36:32,280 --> 00:36:35,220
+وتجسمي على الرقم أنا التحويرة البسيطة بس قلت
+
+371
+00:36:35,220 --> 00:36:40,690
+الواحد هو عبارة عن مين؟عن واحد factorial تمام يبقى
+
+372
+00:36:40,690 --> 00:36:45,670
+انتهى المثال اللي عندنا بروح للمثال ان بعده بروح
+
+373
+00:36:45,670 --> 00:36:52,810
+للمثال رقم اتنين مثال رقم اتنين بيقول لي Y to the
+
+374
+00:36:52,810 --> 00:36:58,130
+derivative IV يعني to the derivative four
+
+375
+00:36:58,130 --> 00:37:04,810
+بالاختصار to the derivative four ناقص Y يسوى Zero
+
+376
+00:37:05,440 --> 00:37:09,720
+وال condition اللى عندنا y عند ال zero بده يساوي
+
+377
+00:37:09,720 --> 00:37:14,260
+واحد ال condition التانى y prime عند ال zero بده
+
+378
+00:37:14,260 --> 00:37:19,480
+يساوي زيرو ال condition التالت y double prime عند
+
+379
+00:37:19,480 --> 00:37:24,840
+ال zero بده يساوي واحد ال condition الرابع y
+
+380
+00:37:24,840 --> 00:37:30,220
+triple prime عند ال zero بده يساوي قداش بده يساوي
+
+381
+00:37:30,220 --> 00:37:30,940
+زيرو
+
+382
+00:37:33,980 --> 00:37:37,720
+بنحل المثال اللي بين ايديانها دي باستخدام Laplace
+
+383
+00:37:37,720 --> 00:37:43,060
+transform إذا بدروح أخد Laplace transform لمين؟
+
+384
+00:37:43,060 --> 00:37:50,620
+للطرفين يبقى باجي بقوله solution بدي Laplace
+
+385
+00:37:50,620 --> 00:37:54,660
+transform لل Y to the derivative 4
+
+386
+00:37:57,250 --> 00:38:04,450
+نقص لـ plus transform لمن؟ لل Y بده يساوي كدهش؟
+
+387
+00:38:04,450 --> 00:38:09,950
+بده يساوي زي ما الان بده اطبق النظرية اللي أخدناها
+
+388
+00:38:09,950 --> 00:38:14,190
+قبل قليل و اللي موجودة عندك في الجدول آخر سطر
+
+389
+00:38:15,740 --> 00:38:20,980
+المشتاق قانوني ان ان عندي بقدرش باربع يبقى ابدأ
+
+390
+00:38:20,980 --> 00:38:28,960
+اقول اس اص اربع يبقى هنا اس اص اربع فاهمين في
+
+391
+00:38:28,960 --> 00:38:38,020
+capital Y of S ناقص است كيب في ال Y and Zero ناقص
+
+392
+00:38:38,020 --> 00:38:45,920
+است ربيع في ال Y prime and Zeroناقص S في الـY W'
+
+393
+00:38:46,600 --> 00:38:53,620
+عند الـ0 ناقص المشتقة التالتة عند الـ0 يبقى هي
+
+394
+00:38:53,620 --> 00:38:58,700
+طبقت النظرية فقط على مين؟ على Y to the derivative
+
+395
+00:38:58,700 --> 00:39:06,720
+of 4 مشتقة الرابعة وصلنا لهذه فبجي بقوله ناقص Y of
+
+396
+00:39:06,720 --> 00:39:13,740
+S بده يساوي مين؟ بده يساوي 0الان بدي اجي أعوض في
+
+397
+00:39:13,740 --> 00:39:17,800
+هذه المعادلة من ال initial conditions اللي ماتا
+
+398
+00:39:17,800 --> 00:39:26,060
+عننا يبقى S أُس أربع شو رايك؟ مفيش غير هذه S؟ خدها
+
+399
+00:39:26,060 --> 00:39:34,960
+بالمرة دوري يبقى ناقص واحد كله في capital Y of Sهي
+
+400
+00:39:34,960 --> 00:39:38,560
+خلصت الأولى و الأخيرة بقى ال main اللى فى النص
+
+401
+00:39:38,560 --> 00:39:45,660
+يبقى ناقص s تكيب في y عند ال zero y عند ال zero
+
+402
+00:39:45,660 --> 00:39:51,280
+اللى بقداش اه بواحد يبقى s تكيب مضروبة فى واحد
+
+403
+00:39:51,280 --> 00:39:57,820
+ناقص s تربيع في y prime عند ال zero اللى بقداش اه
+
+404
+00:39:57,820 --> 00:40:04,610
+بزيرومضروبة في Zero اللي بعدها ناقص S في Y double
+
+405
+00:40:04,610 --> 00:40:10,610
+prime and Zero اللي مضروبة في واحد اللي بعدها ناقص
+
+406
+00:40:10,610 --> 00:40:15,630
+المشتقة التالتة اللي هو كل Zero يساوي جداش يساوي
+
+407
+00:40:15,630 --> 00:40:22,320
+Zeroتمام تمام، إذا هذه الرنادق بقدر أحللها كفرق
+
+408
+00:40:22,320 --> 00:40:31,100
+بين المربعين يبقى هذه S تربيع ناقص واحد في S تربيع
+
+409
+00:40:31,100 --> 00:40:40,100
+زائد واحد كله في capital Y of Sهذه سنقولها على
+
+410
+00:40:40,100 --> 00:40:47,740
+الشجة التانية يبقى S تكييب يبقى S تكييب هذي ب Zero
+
+411
+00:40:47,740 --> 00:40:52,520
+راحت وهذه ب S يبقى زائد S
+
+412
+00:40:55,110 --> 00:41:00,550
+ماذا رايك؟ اخلي capital Y of S لحالها يبقى هاي
+
+413
+00:41:00,550 --> 00:41:06,610
+capital Y of S يساوي هاذي في بينهم عامل مشترك يقول
+
+414
+00:41:06,610 --> 00:41:14,670
+S يبقى لو أخدت S عامل مشترك بظل S تربيع زائد واحد
+
+415
+00:41:15,780 --> 00:41:22,320
+على تحليل الفرق بين المربعين اللي هو S تربيع ناقص
+
+416
+00:41:22,320 --> 00:41:29,110
+واحد في S تربيع زائد واحدأظن القوس هذا هو نفس
+
+417
+00:41:29,110 --> 00:41:34,770
+القوس هذا مع السلامة، إذا هذا السؤال يختلف عن
+
+418
+00:41:34,770 --> 00:41:40,610
+سابقه في إنه فيه صار عنده اختصارات بين البسط
+
+419
+00:41:40,610 --> 00:41:45,770
+والمقام، إذا في اختصارات يا بنات بنختصرها، مافيش
+
+420
+00:41:45,770 --> 00:41:50,790
+اختصارات يبقى كل شيء كما هو
+
+421
+00:41:53,550 --> 00:42:00,050
+طيب يبقى بناء عليه أصبح عندي capital Y of S بده
+
+422
+00:42:00,050 --> 00:42:07,430
+يساوي بقي عندي في البصد S والمقام قداشر S تربيع
+
+423
+00:42:07,430 --> 00:42:12,950
+ناقص واحد ليه كمان فرق بين المربعين اللي هو عبارة
+
+424
+00:42:12,950 --> 00:42:19,860
+عن S ناقص واحد في S زائد واحديبقى من الحلل دائما
+
+425
+00:42:19,860 --> 00:42:25,920
+أو أبدا إلى أبسط العوامل الأولية المقام من الدرجة
+
+426
+00:42:25,920 --> 00:42:30,760
+الثانية البصد من الدرجة الأولى يبقى جاهزين طب هل
+
+427
+00:42:30,760 --> 00:42:36,200
+ممكن يكون أو لو كان البصد من الدرجة التالتة وش بدي
+
+428
+00:42:36,200 --> 00:42:42,000
+أعمله؟بنقسم جسمها مطولة ثم بنروح نعمل partially
+
+429
+00:42:42,000 --> 00:42:47,040
+fractions لكن هيك جاهز بقول constant على الجوس
+
+430
+00:42:47,040 --> 00:42:54,260
+الأول زائد constant على الجوس الثاني بدون أي مشاكل
+
+431
+00:42:54,920 --> 00:42:59,680
+بعد ذلك بادرب الطرفين في المقام اللي عندنا هذا، شو
+
+432
+00:42:59,680 --> 00:43:05,940
+بيصير عندنا؟ بيصير ال S يساوي A في S زائد واحد
+
+433
+00:43:05,940 --> 00:43:14,080
+زائد B في S ناقص الواحدفبجي بقوله هنا لو كانت ال S
+
+434
+00:43:14,080 --> 00:43:20,080
+تساوي واحد، بده أحط قيم ل S من عندي، بحيث أضيع أحد
+
+435
+00:43:20,080 --> 00:43:26,600
+المجهول ويبقى المجهول الثاني، لو كانت ال S بواحد،
+
+436
+00:43:26,600 --> 00:43:32,700
+يبقى واحد بده يساوي ايه؟ واحد زائد واحد و هذا مع
+
+437
+00:43:32,700 --> 00:43:38,320
+السلامة اتنين ايه؟ يبقى بناء عليه ال A هتساوي كده؟
+
+438
+00:43:38,320 --> 00:43:45,270
+نصالان لو كانت ال S بسالب واحد بطير ايه وبحصل على
+
+439
+00:43:45,270 --> 00:43:51,870
+مين؟ على B يبقى باجي بقوله لو كانت ال S تساوي سالب
+
+440
+00:43:51,870 --> 00:43:58,130
+واحد يبقى بصير عندي سالب واحد يساوي هذا بطير وهنا
+
+441
+00:43:58,130 --> 00:44:03,980
+بظل عندي سالب اتنين Bسالب واحد وسالب واحد يبقى
+
+442
+00:44:03,980 --> 00:44:10,780
+سالب اتنين بي ومنها بي تساوي كمان كدهش كمان نص
+
+443
+00:44:10,780 --> 00:44:16,700
+الشكل اللي عندنا اذا اصبح capital Y of this للا
+
+444
+00:44:16,700 --> 00:44:24,350
+plus transform للحل بده يساوي هاي نصوعندك واحد على
+
+445
+00:44:24,350 --> 00:44:33,630
+اس ناقص واحد تمام؟ وهنا بيه كمان بنص واحد على اس
+
+446
+00:44:33,630 --> 00:44:40,030
+زائد واحد تمام؟
+
+447
+00:44:40,030 --> 00:44:46,290
+طيب لو جيش جماعة تقولوله مرة و يعني؟ مش من فاهم؟
+
+448
+00:44:47,540 --> 00:44:54,520
+منها ممكن اخلق كل واحد زي ما هو هذا يقفع لي E قصتي
+
+449
+00:44:54,520 --> 00:45:01,450
+وهذا E قص ناقصتي تمام؟يجيب اجمعهم مرة واحدة
+
+450
+00:45:01,450 --> 00:45:05,370
+يابانين هذا بدلة ال exponential والاسم هنا افضل
+
+451
+00:45:05,370 --> 00:45:08,690
+حاجة لو كيف تبدأ بال exponential اقع على كل الحطب
+
+452
+00:45:08,690 --> 00:45:10,210
+بس انا مابديش دلوقت دلوقت دلوقت دلوقت دلوقت دلوقت
+
+453
+00:45:10,210 --> 00:45:12,730
+دلوقت دلوقت دلوقت دلوقت دلوقت دلوقت دلوقت دلوقت
+
+454
+00:45:12,730 --> 00:45:15,410
+دلوقت دلوقت دلوقت دلوقت دلوقت دلوقت دلوقت دلوقت
+
+455
+00:45:15,410 --> 00:45:23,870
+دلوقت دلوقت دلوقت دلوقت دلوقت دلوقت دلوقت دلوقت
+
+456
+00:45:23,870 --> 00:45:26,350
+دلوقت دلوقت دلوقت دلوقت دلوقت دلوقت دلوقت دلوقت
+
+457
+00:45:26,350 --> 00:45:31,870
+دلوقت دلوقت دلوقت دلطيب هذا الكلام يساوي نص مهيئ
+
+458
+00:45:31,870 --> 00:45:39,270
+جزء ده واحد المقامات ك S ناقص واحد بS زائد واحد
+
+459
+00:45:47,990 --> 00:45:54,450
+تمام؟ يبقى هذا نص فيه ناقص واحد وزايد واحد مع
+
+460
+00:45:54,450 --> 00:46:01,150
+السلامة بيظل عندنا اتنين S وهذا الفرق بين المربعين
+
+461
+00:46:01,150 --> 00:46:05,190
+يبقى S تربيع ناقص واحد
+
+462
+00:46:08,140 --> 00:46:15,920
+مص مع اتنين مع السلامة يبقى بالدقاج ل S على S
+
+463
+00:46:15,920 --> 00:46:17,800
+تربيع ناقص واحد
+
+464
+00:46:22,050 --> 00:46:26,470
+يبقى التنتين عندي ماشي، ماعنديش مشكلة، هذه وهذه
+
+465
+00:46:26,470 --> 00:46:30,850
+الاتنين صح، لكن انا هفكر في تفكير اخر غير التفكير
+
+466
+00:46:30,850 --> 00:46:36,310
+المباشر، اي نعم، باجي الآن على الجدول و بطلع، طبعا
+
+467
+00:46:36,310 --> 00:46:41,460
+انا اتعمدتهتعملها بالطريقة ده ليش؟ بده يخليك تروح
+
+468
+00:46:41,460 --> 00:46:46,380
+تجيبيها من الجدول، يعني انا عندي S على S تربية مش
+
+469
+00:46:46,380 --> 00:46:51,160
+ناقص واحد، S تربية ناقص A تربية و بعد هيك ال A
+
+470
+00:46:51,160 --> 00:46:56,580
+بواحد، دي بجباجي بتطلع على ال S على S تربية ناقص
+
+471
+00:46:56,580 --> 00:47:01,840
+واحد، اللي هو مين يا بناتي؟ دي رقم جديش؟تمانية
+
+472
+00:47:01,840 --> 00:47:07,840
+ممتاز جدا تمانية فيها عندي a على s تربية ناقص a
+
+473
+00:47:07,840 --> 00:47:14,200
+تربية ال a هنا عندى مقداش اللي هو بواحد تمام يبقى
+
+474
+00:47:14,200 --> 00:47:20,100
+هنا s على s تربية ناقص واحد يبقى هذه جوش واحد في T
+
+475
+00:47:20,100 --> 00:47:25,480
+يعني جوش T تمام يبقى بناء عليه solution
+
+476
+00:47:32,530 --> 00:47:42,050
+Y of T بده يساوي جوش T لو
+
+477
+00:47:42,050 --> 00:47:47,130
+من البداية ما سويتش هالحركة دي اللي عملتها جيت من
+
+478
+00:47:47,130 --> 00:47:53,550
+هنا قلت نص و نص خد نص عمل او شركة بضل الأول E أس T
+
+479
+00:47:53,550 --> 00:48:00,000
+زائد E أس ناقص T على الاتنين يبقى هادي جوش Tيبقى
+
+480
+00:48:00,000 --> 00:48:03,540
+لو خلتيها زي ما قلتيلي E was تي و E was ناقصتي و
+
+481
+00:48:03,540 --> 00:48:07,220
+فيها نص يبقى جوشتي كتبتيها دغري يبقى عملت من الأول
+
+482
+00:48:07,220 --> 00:48:12,220
+دغري أو عملتها بالشكل هذا سيئا و أنا قلتك اتعمد
+
+483
+00:48:12,220 --> 00:48:16,200
+اكتبها و اواصلها للصيغة هذه عشان اخليك تتعلم
+
+484
+00:48:16,200 --> 00:48:20,280
+الصيغة جديدة من الجدول غير الصيغة رقم اتنين اللي
+
+485
+00:48:20,280 --> 00:48:24,860
+اتعلمناها قبل ذلك تمام؟ ايوة
+
+486
+00:48:38,870 --> 00:48:44,030
+بعد ما اختصرنا يعني S على S تربية ناقص واحدخلاص
+
+487
+00:48:44,030 --> 00:48:47,350
+يعني اطلعتي Y of S بدل ما عملنا ال partial
+
+488
+00:48:47,350 --> 00:48:52,110
+friction تقول تقدر بيمشي الحال ماعندي مشكلة تمام؟
+
+489
+00:48:52,110 --> 00:48:55,570
+بس ان سميت حالي مش عارف، كويس؟ لإن وانت في
+
+490
+00:48:55,570 --> 00:48:59,170
+الامتحان بيجيش في بالك خلاص عندك تك تك بده يوصل
+
+491
+00:48:59,170 --> 00:49:02,850
+لتحليل ويطلع كل واحد، هيكل في دماغك، تمام؟ لكن في
+
+492
+00:49:02,850 --> 00:49:06,570
+بعض عنده دقة نظر نفسه بيقولي اه لا هذه موجودة في
+
+493
+00:49:06,570 --> 00:49:09,510
+الجدل، إذا روحت جبتيها في الجدل، الكلام صحي وماحدش
+
+494
+00:49:09,510 --> 00:49:13,710
+اللي عندك اي اعتراضزي توسع وصلنا هنا وقلنا اكتبها
+
+495
+00:49:13,710 --> 00:49:16,310
+exponential وقلت لا بديش اكتبها الاكسبونيون روحت
+
+496
+00:49:16,310 --> 00:49:20,930
+جبت فكرة تانية ووصلنا الى مين الى نفس النتيجة هذه
+
+497
+00:49:20,930 --> 00:49:25,210
+والله هذه سيئة لكن لاحظتوا الآن احنا أخدنا ثلاثة
+
+498
+00:49:25,210 --> 00:49:31,310
+أمثلة الطرف اليمين كله zero طب لو كان الطرف اليمين
+
+499
+00:49:31,310 --> 00:49:35,810
+ده اللي تانية يعني يعني أخدنا ثلاثة أمثلة كله
+
+500
+00:49:35,810 --> 00:49:38,830
+homogeneous differential طب لو كانت non
+
+501
+00:49:38,830 --> 00:49:46,550
+homogeneousعندما نقول إليك المثال التالي رقم تلاتة
+
+502
+00:50:10,080 --> 00:50:18,100
+يبقى مثال رقم تلاتة بيقول لي y double prime ناقص
+
+503
+00:50:18,100 --> 00:50:29,560
+اتنين y prime زائد اتنين y يساوي E أس ناقص T و y
+
+504
+00:50:29,560 --> 00:50:35,180
+عند ال zero بده يساوي zero و y prime عند ال zero
+
+505
+00:50:35,180 --> 00:50:38,700
+بده يساوي واحد
+
+506
+00:50:53,540 --> 00:51:01,010
+هنا بدنا ناخد الفلاس ترانسفورم للطرفينوعندك لبلاس
+
+507
+00:51:01,010 --> 00:51:04,470
+ال E أُس T بجيبها كمان منويا من الجدول مش لسه
+
+508
+00:51:04,470 --> 00:51:08,350
+بضعوها أحسبها زي ما كنا نحسبها المرة الماضية يبقى
+
+509
+00:51:08,350 --> 00:51:13,910
+باجي بقولك هاي لبلاس transform لل Y double prime
+
+510
+00:51:13,910 --> 00:51:19,630
+ناقص اتنين لبلاس transform لل Y prime زائد اتنين
+
+511
+00:51:19,630 --> 00:51:25,810
+لبلاس transform لل Y بده يسوي لبلاس transform لل E
+
+512
+00:51:25,810 --> 00:51:32,720
+أُس ناقص Tيبقى لها place transform للطرفين بعد هيك
+
+513
+00:51:32,720 --> 00:51:38,200
+بروح أطبق النظرية اللي أخدناها قبل قليل هذه عبارة
+
+514
+00:51:38,200 --> 00:51:48,660
+عن S2 في capital Y of S ناقص S في Y عند Zero ناقص
+
+515
+00:51:48,660 --> 00:51:53,820
+Y prime عند Zeroخلصنا ال term الأول نجي لل term
+
+516
+00:51:53,820 --> 00:52:01,020
+التاني ناقص اتنين و افتح يقوس S capital Y of S
+
+517
+00:52:01,020 --> 00:52:07,760
+ناقص Y عند ال zero خلصنا ال term التاني بنجي لل
+
+518
+00:52:07,760 --> 00:52:15,120
+term التالت زائد اتنين اللي هو main capital Y of S
+
+519
+00:52:15,120 --> 00:52:19,620
+بالشكل اللي عندنا هذا بده يساويأخدنا الـ plus
+
+520
+00:52:19,620 --> 00:52:23,480
+للطرف الشمال، بدنا الـ plus للطرف اليمين يبقى
+
+521
+00:52:23,480 --> 00:52:28,360
+الطرف اليمين من الجدول واحد ع جداش ابناد على S
+
+522
+00:52:28,360 --> 00:52:36,740
+زائد واحد من الجدول عندك رقم اتنين، تمام؟ طيب،
+
+523
+00:52:36,740 --> 00:52:41,360
+الان بدنا نيجي نعوض من ال initial conditions في
+
+524
+00:52:41,360 --> 00:52:49,760
+هذه المعادلةيبقى S2 في capital Y of S ناقص S في Y
+
+525
+00:52:49,760 --> 00:52:58,540
+عند 0 بقداش؟ ب0 ناقص Y prime of 0 اللي هو 1 ناقص
+
+526
+00:52:58,540 --> 00:53:08,520
+2S capital Y of S ناقص فناقص بزائد 2 في Y عند 0
+
+527
+00:53:08,520 --> 00:53:16,120
+اللي هو 0زائد اتنين capital Y of S يساوي واحد على
+
+528
+00:53:16,120 --> 00:53:24,180
+S زائد الواحد بتاخدوا اللي فيهم capital Y of S مع
+
+529
+00:53:24,180 --> 00:53:31,400
+بعض يبقاش بيصير عندنا S square ناقص اتنين S زائد
+
+530
+00:53:31,400 --> 00:53:38,190
+اتنينكله في capital Y of S هذا راح مع السلامة، ضال
+
+531
+00:53:38,190 --> 00:53:43,550
+عندي هنا قداش؟ ناقص واحدة و هذا راح مع السلامة
+
+532
+00:53:43,550 --> 00:53:51,770
+الله يساهل عليه يبقى النتيجة واحد على S زائد واحد
+
+533
+00:53:51,770 --> 00:54:00,150
+زائد واحد، مظبوط ايه؟طيب، إيش رأيك هذه هيك؟ اللي
+
+534
+00:54:00,150 --> 00:54:06,090
+هو مين؟ لو حدتلها المقامات كله S زائد واحد، بيصير
+
+535
+00:54:06,090 --> 00:54:13,670
+واحد زائد S زائد واحد، تمام؟ يعني مين؟ يعني S
+
+536
+00:54:13,670 --> 00:54:22,580
+زائدي اتنين على S زائد واحدطيب انا بدي capital Y
+
+537
+00:54:22,580 --> 00:54:32,580
+of S فبجي بقوله capital Y of S يساوي S زائد 2 على
+
+538
+00:54:32,580 --> 00:54:42,160
+S زائد 1 مقسوما على S تربيع ناقص 2 S زائد 2 سؤال
+
+539
+00:54:44,430 --> 00:54:49,450
+القوس هذا بتحلل؟ لأ ماقدرش أحلله بيخلّيه زي ما هو
+
+540
+00:54:49,450 --> 00:54:53,990
+ماشي خلّيه الله بيفرجها ان شاء الله بتفرج يبقى
+
+541
+00:54:53,990 --> 00:54:57,910
+باجي بقوله هذا الكلام بتروح أعمله ايه عشان partial
+
+542
+00:54:57,910 --> 00:55:05,230
+fractions يبقى بقوله هذا الكسر وهذا ال S زائد واحد
+
+543
+00:55:05,230 --> 00:55:12,030
+وهذا زائد وهذا الكسر التاني S square نقص اتنين S
+
+544
+00:55:12,030 --> 00:55:18,050
+زائد اتنينهذا من الدرجة الأولى يبقى بحطله constant
+
+545
+00:55:18,050 --> 00:55:24,490
+هذا من الدرجة الثانية ولا يمكن تحليله يعني ماقدرش
+
+546
+00:55:24,490 --> 00:55:28,650
+أبسطه أكتر من هيك يبقى بده أحط ال bus من الدرجة
+
+547
+00:55:28,650 --> 00:55:34,590
+الأولى أقل منه بمقدار واحد هذا من الدرجة الثانية
+
+548
+00:55:34,590 --> 00:55:40,550
+بحطله الدرجة الأولى يبقى بي اس زائد سي
+
+549
+00:55:42,870 --> 00:55:46,910
+بعد هيك بروح بضرب الطرفين في المقدار اللي عندنا
+
+550
+00:55:46,910 --> 00:55:56,630
+هنا تمام؟ بصير المعادلة عندي S زائد 2 تساوي A في S
+
+551
+00:55:56,630 --> 00:56:08,470
+تربيع نقص 2 S زائد 2 زائد ال B في S زائد ال C في
+
+552
+00:56:08,470 --> 00:56:15,630
+من؟ في ال S زائد ال 1هذا السؤال مش زي اللى قبل هذا
+
+553
+00:56:15,630 --> 00:56:20,790
+اتقال شوية شكله تمام اتقال والله اخاف مدام بنحل
+
+554
+00:56:20,790 --> 00:56:25,630
+ماعناهاش مشكلة زيدي اتنين يساوي بده افك الأقواس
+
+555
+00:56:25,630 --> 00:56:33,610
+هذه لو فكتهاش بصير عندي A S تربيع ناقص اتنين A في
+
+556
+00:56:33,610 --> 00:56:47,120
+S زيدي اتنين Aزاد بي اس تربيع زاد بي في اس زاد سي
+
+557
+00:56:47,120 --> 00:56:49,680
+في اس زاد سي
+
+558
+00:56:52,210 --> 00:56:57,710
+هذا الكلام بدى يساوي بدى أجمع تعين ال S تربيع مع
+
+559
+00:56:57,710 --> 00:57:02,570
+بعض وتبعين ال S مع بعض و ال constants مع بعض و
+
+560
+00:57:02,570 --> 00:57:07,070
+أشوف لوين بتوصلنا المعادلة هذه طالعيني هنا بقدر
+
+561
+00:57:07,070 --> 00:57:13,850
+أقول A زائد ال B كله في ال S تربيع يبقى خلصنا من
+
+562
+00:57:13,850 --> 00:57:20,140
+هذه و من هذه بدى أدور على اللي فيهم S هذه واحدةوها
+
+563
+00:57:20,140 --> 00:57:28,440
+دي التانية وها دي التالتة يبقى زائد B زائد ال C
+
+564
+00:57:28,440 --> 00:57:39,380
+نقص 2A كله في S بلوا الثوابت عند هنا 2A و هنا C
+
+565
+00:57:39,380 --> 00:57:50,330
+زائد 2A زائد Cكل هذا الكلام S زائد 2 يساوي هذا
+
+566
+00:57:50,330 --> 00:58:06,570
+المقدار طيب
+
+567
+00:58:06,570 --> 00:58:12,430
+نبدأ نقارن المعاملات في الطرفين يبقى بناء ان عليهم
+
+568
+00:58:12,820 --> 00:58:17,460
+الـ A زائد الـ B كم بتساوي يا بنات؟ Zero لإن
+
+569
+00:58:17,460 --> 00:58:22,580
+ماعنديش S تربية في الطرف الشمال بعدك B زائد C
+
+570
+00:58:22,580 --> 00:58:29,420
+بيزايد C ناقص اتنين A يساوي معامل الـ S هنا ليه؟
+
+571
+00:58:29,420 --> 00:58:35,640
+واحدالمعادلة التالتة اللي هو اتنين A زيدي ال C
+
+572
+00:58:35,640 --> 00:58:43,100
+يبقى اتنين A زيدي ال C بده يساوي كده؟ بده يساوي
+
+573
+00:58:43,100 --> 00:58:52,760
+اتنين تمام؟ اذا هذه بتعطيني كده؟ انه B بده يساوي A
+
+574
+00:58:52,760 --> 00:58:58,940
+بس بالسالب يبقى
+
+575
+00:58:58,940 --> 00:59:08,210
+ال Bتساوي مين سالب ايه وهذه بتعطينا ان ال C بده
+
+576
+00:59:08,210 --> 00:59:16,230
+يساوي اتنين ناقص اتنين ايه تمام؟ اذا هروح شو اعمل؟
+
+577
+00:59:16,230 --> 00:59:21,610
+اخد ليه اتنين هدول و اعوض في مين؟ في المعادلة اللي
+
+578
+00:59:21,610 --> 00:59:29,700
+في النصيبقى هنا ال B اللي هي بسالب A وال C اللي هو
+
+579
+00:59:29,700 --> 00:59:41,340
+بزايد 2 ناقص 2A وهنا عندك كمان ناقص 2A يساوي 1يبقى
+
+580
+00:59:41,340 --> 00:59:55,680
+هدول كام ايه؟ سالب خمسة ايه؟ سالب خمسة ايه؟ سالب
+
+581
+00:59:55,680 --> 01:00:04,160
+خمسة ايه؟ سالب خمسة ايه؟ سالب خمسة ايه؟خمس طيب لما
+
+582
+01:00:04,160 --> 01:00:11,180
+ال a يساوي خمس بيبقى داشر سالب خمس يبقى و ال b بده
+
+583
+01:00:11,180 --> 01:00:15,980
+يساوي من سالب خمس جبت ال a و ال b بيبقى المين
+
+584
+01:00:15,980 --> 01:00:23,260
+عندنا ال c يبقى ال c هيساوي اتنين ناقص اتنين في
+
+585
+01:00:23,260 --> 01:00:33,300
+خمس طبعا يبقى هذا الكلام يساوي اتنين ناقصخمسين
+
+586
+01:00:33,300 --> 01:00:40,960
+مظبوط؟ يبقى خمسين بدل كده؟ واحد صحيح و تلت أخمس،
+
+587
+01:00:40,960 --> 01:00:48,580
+مظبوط؟ يعني كده؟ سبعة أخمس؟تمن أخمس بتاكدي؟ طيب لو
+
+588
+01:00:48,580 --> 01:00:52,440
+وحدنا المقابلات بيصير عشرة ناقص اتنين بتمانى يبقى
+
+589
+01:00:52,440 --> 01:00:58,640
+فعلا تمن أخمس وليست سبع أخمس كما زعمت قبل قليل
+
+590
+01:00:58,640 --> 01:01:03,900
+تمام؟ إذا جيبنا ال A والB والC بيخلصنا يبقى
+
+591
+01:01:03,900 --> 01:01:09,910
+capital Y of S بده يساوييعني ال a plus transform
+
+592
+01:01:09,910 --> 01:01:14,150
+لدالة اللي هو انا بديه يساوي a على s زائد واحد ال
+
+593
+01:01:14,150 --> 01:01:23,800
+a بخمس يبقى هذا خمس على s زائد الواحداللي بعدها
+
+594
+01:01:23,800 --> 01:01:32,100
+بيب سالب خمس يبقى زائد سالب خمس في اس اللي بعدها
+
+595
+01:01:32,100 --> 01:01:39,760
+سيب تمان أحماس يبقى زائد تمانية على خمسة كله على
+
+596
+01:01:39,760 --> 01:01:48,820
+اس تربيع نقص اتنين اس زائد اتنين المسألة الآن
+
+597
+01:01:48,820 --> 01:01:56,340
+مسألة ترتيبية فقط لغيريبقى يا بنات لو أخدت هنا خمس
+
+598
+01:01:56,340 --> 01:02:04,500
+عامل مشترك ايش بيظل عندى؟ واحد على اس زائد واحدهنا
+
+599
+01:02:04,500 --> 01:02:13,320
+خط ناقص خمس عامل مشترك ايش بيظل عندى بيظل عندى S
+
+600
+01:02:13,320 --> 01:02:20,940
+ناقص تمانية على مين على اللي هو المقدار اللي عندنا
+
+601
+01:02:20,940 --> 01:02:27,040
+شو رايك هذا اللي عندنا بدي أسوى S تربيع ناقص اتنين
+
+602
+01:02:27,040 --> 01:02:38,820
+S زائد واحد زائد واحد ماشي الحالة؟طيب هذا الكلام
+
+603
+01:02:38,820 --> 01:02:46,280
+بده يساوي هذا الخمس في واحد على اس زائد واحد هذا
+
+604
+01:02:46,280 --> 01:02:52,360
+ماعناش مشكلة فيه وصلنا لناقص خمس
+
+605
+01:02:53,960 --> 01:02:59,960
+هذا لو جيته اعمل مثله مربع اس ناقص واحد لكل تربية
+
+606
+01:02:59,960 --> 01:03:07,400
+اذا بدي اخلي هنا اس ناقص واحد بيظل كده؟ ناقص سبعة
+
+607
+01:03:07,400 --> 01:03:15,200
+يعني هذا بيظل ناقص خمس في اس ناقص واحد ناقص سبعة
+
+608
+01:03:15,200 --> 01:03:21,420
+على اس ناقص واحد لكل تربية زائد واحد
+
+609
+01:03:24,490 --> 01:03:31,510
+تمام؟ طيب نيجي أرتب باقى المثلة، يفجأة بدنا نيجي
+
+610
+01:03:31,510 --> 01:03:36,790
+أرتب مسألتنا من جديد و نشوف لوين بدنا نوصل
+
+611
+01:03:48,240 --> 01:03:53,480
+طلعوني كويس يبقى أصبح عندي capital Y of S بده
+
+612
+01:03:53,480 --> 01:04:01,960
+يساوي خمس في مين في واحد على S زائد واحد اللي
+
+613
+01:04:01,960 --> 01:04:08,640
+بعدها ناقص خمس فيه بدي أخد هذا لحاله يا بنات على
+
+614
+01:04:08,640 --> 01:04:14,540
+المقام والسبع لحالها على المقاميبقى باجي بقوله هنا
+
+615
+01:04:14,540 --> 01:04:23,500
+ناقص خمس في S ناقص واحد على S ناقص واحد لكل تربيع
+
+616
+01:04:23,500 --> 01:04:30,740
+زائد واحد يبقى أخدت ال term الأول على المقامناقص
+
+617
+01:04:30,740 --> 01:04:39,200
+خمس مع ناقص سبعة بزايد اللي هو سبعة خمس يبقى زائد
+
+618
+01:04:39,200 --> 01:04:47,300
+سبعة على خمسة بضل عند مين؟ بضل عشان دي ال واحد على
+
+619
+01:04:47,300 --> 01:04:56,480
+اس ناقص واحد لكل تربيع زائد واحد تمام؟
+
+620
+01:04:57,530 --> 01:05:03,430
+الهم نقدر نقول يا خلصنايا شبه خلصنايا المثلة طلع
+
+621
+01:05:03,430 --> 01:05:07,650
+مرة تانية يبقى السارة عندي بدل ما هو term هنا
+
+622
+01:05:07,650 --> 01:05:12,950
+خلتها تلات term خمس في المقدار اللي عندنا هذا ناقص
+
+623
+01:05:12,950 --> 01:05:15,550
+خمس في S ناقص واحد على S ناقص واحد في كل تربية
+
+624
+01:05:15,550 --> 01:05:19,090
+زائد واحد زائد سبعة أخمس واحد على S ناقص واحد في
+
+625
+01:05:19,090 --> 01:05:25,530
+كل تربية زائد واحدبنفتح الجدول و نبحث عن الاسم
+
+626
+01:05:25,530 --> 01:05:27,950
+اللي يسمى الاسم اللي يسمى الاسم اللي يسمى الاسم
+
+627
+01:05:27,950 --> 01:05:28,170
+اللي يسمى الاسم اللي يسمى الاسم اللي يسمى الاسم
+
+628
+01:05:28,170 --> 01:05:29,610
+اللي يسمى الاسم اللي يسمى الاسم اللي يسمى الاسم
+
+629
+01:05:29,610 --> 01:05:35,870
+اللي يسمى الاسم اللي يسمى الاسم اللي
+
+630
+01:05:35,870 --> 01:05:38,830
+يسمى الاسم اللي يسمى الاسم اللي يسمى الاسم اللي
+
+631
+01:05:38,830 --> 01:05:38,830
+يسمى الاسم اللي يسمى الاسم اللي يسمى الاسم اللي
+
+632
+01:05:38,830 --> 01:05:38,930
+يسمى الاسم اللي يسمى الاسم اللي يسمى الاسم اللي
+
+633
+01:05:38,930 --> 01:05:38,990
+يسمى الاسم اللي يسمى الاسم اللي يسمى الاسم اللي
+
+634
+01:05:38,990 --> 01:05:43,910
+يسمى الاسم اللي يسمى الاسم اللي يسمى الاسم
+
+635
+01:05:53,570 --> 01:06:02,440
+اندور في الجدول على المقدار بين القاوسينعشرة طيب
+
+636
+01:06:02,440 --> 01:06:07,260
+عشرة ل S ناقص ال A S ناقص ال A لكل تربية زائد B
+
+637
+01:06:07,260 --> 01:06:13,800
+تربية طبعا ال A يساوي ال B يساوي قدر؟ واحد طيب
+
+638
+01:06:13,800 --> 01:06:21,120
+جبنا ان عليه بيكون الجواب هو E أس T Cos T مظبوط
+
+639
+01:06:21,520 --> 01:06:30,220
+يبقى هنا E Ost Cos T هذا النقطة رقم عشرة من الجدول
+
+640
+01:06:30,220 --> 01:06:35,620
+اللي بين ايداكوا نجي للنقطة الأخيرة اللي هو الزائد
+
+641
+01:06:35,620 --> 01:06:41,850
+سبعة أخماس فيهطلع لفوق شوية الخطوة اللى قبلها او
+
+642
+01:06:41,850 --> 01:06:46,690
+النقطة اللى قبلها اللى يمين رقم تسعة يبقى رقم تسعة
+
+643
+01:06:46,690 --> 01:06:51,430
+هي بي على اس نقص الكل تربية زائد بيه تربية يبقى
+
+644
+01:06:51,430 --> 01:06:58,210
+ايه تساوي بيه كذلك تساوي كدهش واحد يبقى E of T Sin
+
+645
+01:06:58,210 --> 01:07:07,360
+T يبقى هنا في ال E of T في Sin Tيبقى هذا الـ
+
+646
+01:07:07,360 --> 01:07:12,860
+solution للـ differential equation المواطع حد فيكم
+
+647
+01:07:12,860 --> 01:07:19,560
+بتحب تسأل أي سؤال هنا؟ ننتقل
+
+648
+01:07:19,560 --> 01:07:27,740
+إلى المثال اللي بعده بس بنجيبه بطريقة غير هذه يبقى
+
+649
+01:07:27,740 --> 01:07:36,070
+example هذا سؤال 25 من أسئلة الكتاببقول find the
+
+650
+01:07:36,070 --> 01:07:43,550
+Laplace transform find the Laplace transform
+
+651
+01:07:43,550 --> 01:07:47,290
+Laplace
+
+652
+01:07:47,290 --> 01:07:55,870
+transform capital Y of S للابلاس لل Y of the
+
+653
+01:07:55,870 --> 01:08:02,410
+solution of
+
+654
+01:08:02,410 --> 01:08:04,150
+the initial value problem
+
+655
+01:08:10,700 --> 01:08:19,800
+Y double A prime زائد Y تساوي أحد أمرين ياما T لما
+
+656
+01:08:19,800 --> 01:08:26,900
+T محصورة بين الـ Zero و بين الواحد ياما Zero لما T
+
+657
+01:08:26,900 --> 01:08:33,660
+أكبر من أو تساوي الواحد و less than infinityو ال y
+
+658
+01:08:33,660 --> 01:08:40,120
+عند ال zero بده تساوي zero و كذلك ال y prime عند
+
+659
+01:08:40,120 --> 01:08:43,700
+ال zero بده يساوي جدار بده يساوي zero
+
+660
+01:08:59,030 --> 01:09:05,210
+هذا المثال يختلف عن سابقاته من الأمثلة في إن له
+
+661
+01:09:05,210 --> 01:09:11,070
+شكل معين يعني piecewise function تمام؟ المثلة أو
+
+662
+01:09:11,070 --> 01:09:15,830
+الـG of T اللي علي مين مجزئ إلى جزئين وليس جزئا
+
+663
+01:09:15,830 --> 01:09:21,610
+واحدا كما كان قبل قليل من كل بسيطة جزئين ولا تلاتة
+
+664
+01:09:21,610 --> 01:09:25,570
+ولا أربعة مادام ال function معرفة يبقى أنا مقيد
+
+665
+01:09:25,570 --> 01:09:29,520
+بهذا التعريفلأ بلاس ترانسفورم له تعريف يبقى أنا
+
+666
+01:09:29,520 --> 01:09:34,140
+مقيد كذلك لمين بهذا التعريف اذا انا اخد لأ بلاس
+
+667
+01:09:34,140 --> 01:09:39,660
+ترانسفورم لمن؟ للطرفين بقوله كويس يبقى انا بدي اخد
+
+668
+01:09:39,660 --> 01:09:46,440
+لأ بلاس ترانسفورم ل Y''زائد لـ plus transform للـ
+
+669
+01:09:46,440 --> 01:09:53,260
+y بده يساوي ل plus transform لمن؟ للطرف اليمين لكن
+
+670
+01:09:53,260 --> 01:09:58,900
+الطرف اليمين هذا مجزق إلى جزين من zero لواحد و من
+
+671
+01:09:58,900 --> 01:10:04,000
+واحد لغاية infinityالـ plus transform للدالة مش
+
+672
+01:10:04,000 --> 01:10:08,200
+بيبدأ من عندي ال zero لغاية infinity إذا إحنا
+
+673
+01:10:08,200 --> 01:10:13,560
+جزقنا لوين؟ إلى جزئين إذا بروح أحط التعريف
+
+674
+01:10:13,560 --> 01:10:20,660
+integration من zero لواحد لل E أُس ناقص ST في
+
+675
+01:10:20,660 --> 01:10:29,600
+الدالة، جداش الدالة؟يبقى ده تي دي تي زي التكامل من
+
+676
+01:10:29,600 --> 01:10:36,000
+واحد لغاية infinity يبقى من واحد لغاية infinity
+
+677
+01:10:36,000 --> 01:10:41,920
+إلا ال E أقص ناقص ST وقيمة الدالة هنا جداش Zero
+
+678
+01:10:41,920 --> 01:10:47,480
+يبقى في Zero في دي تي إذا ال term هذا كله بروح
+
+679
+01:10:47,480 --> 01:10:53,320
+بجداش Zero مع السلامة غير مأسوف عليهيبقى بدنا نيجي
+
+680
+01:10:53,320 --> 01:10:58,060
+نطبق النظرية على الطرف الشمال اللي عندنا يبقى هادي
+
+681
+01:10:58,060 --> 01:11:06,200
+S Square في capital Y of S ناقص S في Y عند ال zero
+
+682
+01:11:06,200 --> 01:11:11,960
+ناقص Y prime عند ال zero طبقنا النظرية على ال term
+
+683
+01:11:11,960 --> 01:11:16,760
+الأول نطبق النظرية على ال term التاني يبقى زائد
+
+684
+01:11:16,760 --> 01:11:23,220
+capital Y of S مرة واحدةهذا ما هوش improper
+
+685
+01:11:23,220 --> 01:11:26,520
+integral يعني improper integral واحد zero هناك
+
+686
+01:11:26,520 --> 01:11:29,920
+يبقى ده اللي عند مين ده اللي الترميك بديه كامل
+
+687
+01:11:29,920 --> 01:11:35,230
+integration by parts عادي جدالكن هذا بكمله بالجدول
+
+688
+01:11:35,230 --> 01:11:39,970
+أسهلي يبقى باجي بقوله في الهام الشيك باخد جزء
+
+689
+01:11:39,970 --> 01:11:47,010
+derivatives و جزء باخده من integrals تمام؟ ال
+
+690
+01:11:47,010 --> 01:11:56,120
+derivative T والintegral E أس ناقص STمشتقتها بواحد
+
+691
+01:11:56,120 --> 01:12:02,100
+التكامل تبعها ب E أس ناقص T على مين على ناقص S
+
+692
+01:12:02,100 --> 01:12:08,080
+بنقسم على تفاضل الـ S إذا الـ S من الدرجة الأولى
+
+693
+01:12:08,080 --> 01:12:15,040
+نشتق كمان مرة يبقى Zero نكمل كمان مرة يبقى E أس
+
+694
+01:12:15,040 --> 01:12:22,340
+ناقص ST على ناقص S في ناقص S يبقى بزايد S ترابيع
+
+695
+01:12:22,960 --> 01:12:28,660
+هدى فى هدى بالموجب وهدى فى هدى بالسالب يبقى صارت
+
+696
+01:12:28,660 --> 01:12:33,800
+المثلة تبعتنا على الشكل التالي تطلعى لبناء يبقى
+
+697
+01:12:33,800 --> 01:12:44,000
+هنا بصير ناقص E أس ناقص ST على S كمان ناقص E أس
+
+698
+01:12:44,000 --> 01:12:51,250
+ناقص ST على مين على S تربيةوالحكي هذا كله من عند
+
+699
+01:12:51,250 --> 01:12:56,370
+الـ zero لغاية كدهش لغاية الواحد طيب هذه و هذه
+
+700
+01:12:56,370 --> 01:13:04,930
+بقدر أخدها عام المشترك في شيء هنا ولا طرف .. هذا
+
+701
+01:13:04,930 --> 01:13:14,250
+هذا طيب باجي بقول اه هنا في T هنا T مظبوط و الباجي
+
+702
+01:13:14,250 --> 01:13:20,180
+كله سليم مئة بالمئة صحيحطيب بنعوض الآن بنجمع هدول
+
+703
+01:13:20,180 --> 01:13:25,960
+اتنين مع بعض يبقى بصير عندي S تربيع زائد واحد كله
+
+704
+01:13:25,960 --> 01:13:32,040
+في capital Y of S الان Y عند Zero جلب Zero و Y
+
+705
+01:13:32,040 --> 01:13:37,970
+Prime عند Zero يبقى هذا بقيريبقى هنا كله ناقص Zero
+
+706
+01:13:37,970 --> 01:13:43,990
+يساوي بتعوض بحدود التكامل القيمة اللى فوق ناقص
+
+707
+01:13:43,990 --> 01:13:48,590
+القيمة اللى تحت يبقى المعوضة عن T بواحد بصير عندنا
+
+708
+01:13:48,590 --> 01:13:59,130
+ناقص E أس ناقص S على S عوضت بواحد هنا ناقص E أس
+
+709
+01:13:59,130 --> 01:14:07,470
+ناقص S على S تربيعنقص القيم اللي تحت نقص مع نقص
+
+710
+01:14:07,470 --> 01:14:16,790
+بصير الزائد Zero في رقم يبقى ب Zero وهذه زاد هنا
+
+711
+01:14:16,790 --> 01:14:24,010
+حطيت E وال Zero اللي هو واحد على S يبقى زائد واحد
+
+712
+01:14:24,010 --> 01:14:33,780
+على S واحد على S تربيع تمامطب كويس يبقى بناء عليه
+
+713
+01:14:33,780 --> 01:14:40,020
+إيه الخاطر أجسم كله الآن على مين؟ على S تربية زائد
+
+714
+01:14:40,020 --> 01:14:45,540
+واحد بيكون جيبنا لأ plus transform يبقى capital Y
+
+715
+01:14:45,540 --> 01:14:52,580
+of S بده يساوي اللي هو مين؟ E والله خد أاخد الموجة
+
+716
+01:14:52,580 --> 01:14:56,530
+في الأول أسهل و أخلي السلم في اللي بعدهيبقى هذه
+
+717
+01:14:56,530 --> 01:15:04,310
+واحد على S تربية في S تربية زائد واحد خلصنا منها
+
+718
+01:15:04,310 --> 01:15:13,050
+اللي بعدها ناقص EOS ناقص S على مين على S في S
+
+719
+01:15:13,050 --> 01:15:23,790
+تربيةزائد واحد ناقص IOS ناقص S عالمين على S تربيع
+
+720
+01:15:23,790 --> 01:15:30,950
+في S تربيع زائد واحد الشكل اللي عنها خلاص روحي
+
+721
+01:15:30,950 --> 01:15:33,670
+وخليها قال لي هو بس هاتي ليا place ال transform
+
+722
+01:15:33,670 --> 01:15:37,940
+للحل ماقلليش هات شكل الحلواللي ما بده يجيش بشكل
+
+723
+01:15:37,940 --> 01:15:42,300
+الحل بيصير معقد لسه partial fraction ويطلع جزئين
+
+724
+01:15:42,300 --> 01:15:46,780
+وكمان جزئين وكمان جزئين كيف جزئين هدول تلاتة مش
+
+725
+01:15:46,780 --> 01:15:52,240
+جزئين كمان ويمكن يطلعوا أربعة كمان حسب الكثرة الله
+
+726
+01:15:52,240 --> 01:15:57,990
+أعلم إذا لحد هنا جبناله Laplace transformلو بدك
+
+727
+01:15:57,990 --> 01:16:03,670
+تجمعهم كلهم مع بعض وتوحدي المقامات وتوحدي براتك
+
+728
+01:16:03,670 --> 01:16:10,690
+والنتيجة على الشكل التالي اللي هو E أُس S ناقص S
+
+729
+01:16:10,690 --> 01:16:19,370
+ناقص واحد على S تربيع في مين؟ في S تربيع زائد واحد
+
+730
+01:16:19,370 --> 01:16:23,710
+كله في ال E أُس S بتعمل ايه؟ هو اللي ماتعملاش
+
+731
+01:16:23,710 --> 01:16:29,470
+ماتفرجش عندنااخر مثال في هذا ال section يبقى
+
+732
+01:16:29,470 --> 01:16:35,170
+example يقول
+
+733
+01:16:35,170 --> 01:16:37,150
+solve the initial value problem
+
+734
+01:16:44,020 --> 01:16:52,100
+واي دابلي برايم ناقص ستة واي برايم زائد تسعة واي
+
+735
+01:16:52,100 --> 01:17:01,340
+بده يساوي ت تربيع E أس اتنين T والواي عند ال zero
+
+736
+01:17:01,340 --> 01:17:07,320
+بده يساوي اتنين والواي برايم عند ال zero بده يساوي
+
+737
+01:17:07,320 --> 01:17:08,260
+ستة
+
+738
+01:17:20,540 --> 01:17:26,460
+بناخد لبلاس ترانسفورم للطرفين يبقى بدي اخد لبلاس
+
+739
+01:17:26,460 --> 01:17:34,560
+ترانسفورم لل Y'' نقص ستة لبلاس ترانسفورم لل Y''
+
+740
+01:17:34,560 --> 01:17:41,740
+زائد تسعة لبلاس ترانسفورم لل Y بدي أساوي لبلاس
+
+741
+01:17:41,740 --> 01:17:47,640
+ترانسفورم لT تربيع في E أس اتنين T
+
+742
+01:17:50,680 --> 01:17:57,200
+طرف الشمال هنطبق عليه النظرية يبقى S2 في capital Y
+
+743
+01:17:57,200 --> 01:18:05,520
+of S ناقص S في Y عند Zero ناقص Y prime عند Zero
+
+744
+01:18:06,470 --> 01:18:13,930
+اللي بعده ناقص ستة وتفتح يقوس يبقى S في capital Y
+
+745
+01:18:13,930 --> 01:18:21,710
+of S ناقص Y عند ال zero خلصنا منه اللي بعده زائد
+
+746
+01:18:21,710 --> 01:18:29,450
+تسعة capital Y of S بده يساوي حد بعرفاش إلا أروح
+
+747
+01:18:29,450 --> 01:18:39,790
+أدور وين في الجدولT تربيع في A أُس اتنان
+
+748
+01:18:39,790 --> 01:18:45,560
+T اللي هي من ابنات 11 ممتاز جدايبقى لو جيت في
+
+749
+01:18:45,560 --> 01:18:52,760
+العمود الأول اللي هو رقم 11 T to the power N E أس
+
+750
+01:18:52,760 --> 01:18:57,220
+A T و ال N positive احنا عندنا هايه اتنين و
+
+751
+01:18:57,220 --> 01:19:01,300
+الاتنين positive و ال A عندي كمان يبقى داشت بيه
+
+752
+01:19:01,300 --> 01:19:05,880
+الاتنين يبقى بدي اكتب النتيجة عند اليمين اتنين
+
+753
+01:19:05,880 --> 01:19:13,820
+factorial على S ناقص اتنين لكل كداشتيبقى هذه اللي
+
+754
+01:19:13,820 --> 01:19:20,820
+هي عبارة عن in factorial يعني اتنين factorial على
+
+755
+01:19:20,820 --> 01:19:27,460
+اللي هو ال S ناقص اتنين لكل تكييب الشكل اللي عندنا
+
+756
+01:19:27,460 --> 01:19:35,300
+يبقى هذه جيبتها من الجدول part 11بالدرجة هطبق اللي
+
+757
+01:19:35,300 --> 01:19:38,180
+هو المعلومات اللي عندي في ال initial conditions
+
+758
+01:19:38,180 --> 01:19:42,840
+على المعادلة اللي عناها يبقى هذي بيصير S square
+
+759
+01:19:42,840 --> 01:19:52,620
+capital Y of S Y عند 0 ب 2 يبقى ناقص 2S Y prime
+
+760
+01:19:52,620 --> 01:19:55,460
+عند 0 يبقى ناقص 6
+
+761
+01:20:02,050 --> 01:20:10,510
+ناقص في ناقص بزايد ستة في واي عند ال zero اللي هو
+
+762
+01:20:10,510 --> 01:20:19,210
+باتنينتمام Y عند Zero اللي هو ب 2 زائد 9 capital Y
+
+763
+01:20:19,210 --> 01:20:29,850
+of S بده تساوي 2 factorial على S ناقص 2 اللي هو
+
+764
+01:20:29,850 --> 01:20:31,570
+الكل تكييب
+
+765
+01:20:34,130 --> 01:20:42,850
+بنجمع العامل المشتركة يبقى S²-6Sزاد
+
+766
+01:20:42,850 --> 01:20:52,600
+9 كله في capital Y of Sبتضل عندك هنا جداش ناقص
+
+767
+01:20:52,600 --> 01:21:00,280
+اتنين S ناقص ستة وزائد اتناش بضل زائد ستة يبقى
+
+768
+01:21:00,280 --> 01:21:05,020
+زائد ستة يسوى الطرف اليمين اللي هو اتنين factorial
+
+769
+01:21:05,020 --> 01:21:13,220
+على S ناقص اتنين لكل تكيدطيب تمام تمام هذه بيصير
+
+770
+01:21:13,220 --> 01:21:20,620
+ايش بيصير capital Y of S مضروبة في امين هذه بنات
+
+771
+01:21:20,620 --> 01:21:29,000
+اللي هو S ناقص تلاتة من كل تربيع يبقى في S ناقص
+
+772
+01:21:29,000 --> 01:21:35,050
+تلاتة من كل تربيعS ناقص ثلاثة الكل تاريبي هذه S
+
+773
+01:21:35,050 --> 01:21:42,750
+ناقص اتنين S ناقص اتنين مظبوط ماعنديش تلاتة نتأكد
+
+774
+01:21:42,750 --> 01:21:49,310
+منها لا يا بني انا اتصلي E أس تلاتة T وليست اتنين
+
+775
+01:21:49,310 --> 01:21:58,480
+بدي اقول هذه E أس تلاتة Tيبقى لما نجينا حسبناها
+
+776
+01:21:58,480 --> 01:22:07,440
+هنا بصير S ناقص تلاتة وهذه S ناقص تلاتة وهذه S
+
+777
+01:22:07,440 --> 01:22:14,900
+ناقص تلاتة والباقي كل شي زي ما هو يبقى بس اللي بين
+
+778
+01:22:14,900 --> 01:22:18,380
+قصين بصلى الله عبارة عن S ناقص اتنين وS ناقص تلاتة
+
+779
+01:22:18,940 --> 01:22:23,140
+يبقى هذا بده يساوي اللي هو من النجو الهادي على
+
+780
+01:22:23,140 --> 01:22:29,120
+الشجرة التانية و لو أخدنا ناقص اتنين عامل مشترك
+
+781
+01:22:29,420 --> 01:22:34,240
+بصير اس ناقص ثلاثة هذه لو نجلناها على الشجة
+
+782
+01:22:34,240 --> 01:22:40,180
+التانية و اه بيصير بدون ناقص اتنين فقط فاهمين اللي
+
+783
+01:22:40,180 --> 01:22:44,900
+هي اتنين اس ناقص ست اللي هو عكس هذه تماما و بظل
+
+784
+01:22:44,900 --> 01:22:50,620
+زائد ال term اللي عندنا هذا زائد اللي هو اتنين
+
+785
+01:22:50,620 --> 01:23:01,020
+factorial على مين على اس ناقص اتنينالكل تاكهيت كي
+
+786
+01:23:01,020 --> 01:23:05,260
+اثنين ناقص تلاتة صحيح اس ناقص تلاتة هو اس ناقص
+
+787
+01:23:05,260 --> 01:23:11,890
+تلاتةالروح نجسم الطرفين على main على S ناقص تلاتة
+
+788
+01:23:11,890 --> 01:23:19,010
+لكل تربية يبقى بيصير capital Y of S يساوي اتنين
+
+789
+01:23:19,010 --> 01:23:25,890
+على S ناقص تلاتة زائدي اتنين factorial على main
+
+790
+01:23:25,890 --> 01:23:30,390
+على S ناقص تلاتة to the power five
+
+791
+01:23:33,660 --> 01:23:41,080
+خلاص بدنا نجيبلها ل plus transfer بيكون خلصنا لكن
+
+792
+01:23:41,080 --> 01:23:45,420
+اطلعيلي لهذه السهل نجيبلها ل plus transfer طيب
+
+793
+01:23:45,420 --> 01:23:49,560
+تعالى نطلع لهذه السهل والله ما هوش سهل اذا انا
+
+794
+01:23:49,560 --> 01:23:54,240
+بتطلع في العمود الأخير طلعيلي في العمود الأخر
+
+795
+01:23:54,240 --> 01:23:58,280
+وشوفوا لمين أنسب حاجة لهذه الشغل
+
+796
+01:24:05,850 --> 01:24:14,570
+11 صحيح بس في فارق ان الرقم اللى عندي فوق الاصل
+
+797
+01:24:14,570 --> 01:24:19,950
+يكون كدهأربعة factorial تمام يبقى الأصل يكون عندي
+
+798
+01:24:19,950 --> 01:24:24,450
+أربعة factorial بقوله بسيطة يبقى هذه سهلة جدا إذا
+
+799
+01:24:24,450 --> 01:24:27,610
+أنا ب fabric المثل بحيث صير عندي بدل اتنين
+
+800
+01:24:27,610 --> 01:24:33,090
+factorial أربعة فاكتوريال اتنين صح ولا لأ يعني هذه
+
+801
+01:24:33,090 --> 01:24:40,250
+بقدر أقول تساوي اتنين في واحد على اس ناقص ثلاثة
+
+802
+01:24:40,520 --> 01:24:45,400
+زائد اتنين اللي هو اتنين factorial اتنين بدي اقرب
+
+803
+01:24:45,400 --> 01:24:50,880
+في اربعة factorial و اقسم على اربعة factorial
+
+804
+01:24:50,880 --> 01:24:55,520
+كأنني ضرب في قداش واحد صحي مستيقظش اللي ضربت فيه
+
+805
+01:24:55,520 --> 01:25:02,560
+روحت ايه قسمت عليه والمقام هذا له ال S ناقص ثلاثة
+
+806
+01:25:02,560 --> 01:25:08,140
+to the power خمسة بالشكل اللي عندنا هناطب الاربعة
+
+807
+01:25:08,140 --> 01:25:13,160
+factorial اللي اربعة في تلاتة و اتناش في اتنين و
+
+808
+01:25:13,160 --> 01:25:17,120
+اربعة و عشرين و عندي فوق يعني واحدة اتناش تمام
+
+809
+01:25:17,120 --> 01:25:27,640
+تمام تمام اذا صار the solution is y as a function
+
+810
+01:25:27,640 --> 01:25:34,950
+of t يساوي اتنين اظن هذه E واست تلاتة Tرقم اتنين
+
+811
+01:25:34,950 --> 01:25:43,230
+من الجدول زائد واحد على اتناش هذه كمان مش بصير من
+
+812
+01:25:43,230 --> 01:25:52,290
+رقم احداش برضه يبقى T أس كداش أس أربعة يبقى T أس
+
+813
+01:25:52,290 --> 01:25:59,870
+أربعة في E أس تلاتة T E أس تلاتة T لإن ال A عندي
+
+814
+01:25:59,870 --> 01:26:02,090
+بقداش اتلاتة
+
+815
+01:26:03,980 --> 01:26:08,440
+خلاص نا يبجى هذا هو الحل التابع له يعني يا بنات
+
+816
+01:26:08,440 --> 01:26:13,430
+لما يطلع الشغل زي هيكيمكن ما تقدرش تجيبيها من
+
+817
+01:26:13,430 --> 01:26:17,350
+الجدران بدها فبراكه بسيطه ضربنا فرقه مجسمنا عليه
+
+818
+01:26:17,350 --> 01:26:21,890
+إذا صارت أندي موجودة في الجدران قبل قليل كان عندي
+
+819
+01:26:21,890 --> 01:26:27,150
+S تربيه ناقص اتنين S زائد اتنين فحولت إلى S ناقص
+
+820
+01:26:27,150 --> 01:26:31,630
+اتنين S تربيه ناقص اتنين S زائد واحد زائد واحد
+
+821
+01:26:31,630 --> 01:26:34,790
+يبقى صارت S ناقص واحد لكل تربيه زائد واحد يعني
+
+822
+01:26:34,790 --> 01:26:38,550
+أحيان الفبراكات الرياضية هذه هي اللي بتوديك لوين
+
+823
+01:26:38,710 --> 01:26:43,690
+لصيغة تابعة الجدول وبالتالي بتقدر تجيب ال function
+
+824
+01:26:43,690 --> 01:26:49,070
+المناضرة لـ Laplace transform بدنا المسائل تابعة
+
+825
+01:26:49,070 --> 01:27:01,310
+exercises 6-2 exercises 6-2 المسائل من 1 لغاية 26
+
+826
+01:27:06,070 --> 01:27:11,350
+حاول تحلي بقدر المكان تتدربي عليهم لإن المسائل
+
+827
+01:27:11,350 --> 01:27:18,710
+هدول ضروريات جدا لإنه لا يكاد يخلو امتحان نهائي
+
+828
+01:27:18,710 --> 01:27:25,570
+وأظنه لن يخلو من استخدام Laplace transform للحصول
+
+829
+01:27:25,570 --> 01:27:29,750
+على حل المعادلة التفاضلية اعطيكوا العافية
+
diff --git a/PL9fwy3NUQKwa8ZDfSFGn6H8xVFLzqmCZC/VYRFN1d1OwA.srt b/PL9fwy3NUQKwa8ZDfSFGn6H8xVFLzqmCZC/VYRFN1d1OwA.srt
new file mode 100644
index 0000000000000000000000000000000000000000..d19c8f99c7c7e95254accc6a0cec976996667db7
--- /dev/null
+++ b/PL9fwy3NUQKwa8ZDfSFGn6H8xVFLzqmCZC/VYRFN1d1OwA.srt
@@ -0,0 +1,2467 @@
+1
+00:00:09,580 --> 00:00:15,870
+بسم الله الرحمن الرحيم، نذكر في الآخر نظرية قلناها 
+
+2
+00:00:15,870 --> 00:00:20,070
+المرة اللي فاتت، لأنّنا نبدأ دراستنا عليها اليوم على 
+
+3
+00:00:20,070 --> 00:00:26,090
+النظرية الماضية إن شاء الله تبارك وتعالى طبعًا
+
+4
+00:00:26,090 --> 00:00:29,450
+موضوعنا موضوع اللي هو الـ non-homogeneous
+
+5
+00:00:29,450 --> 00:00:33,030
+differential equation، بنحلها بطريقة الـ
+
+6
+00:00:33,030 --> 00:00:38,230
+undetermined coefficients، يعني المعاملات المجهولة
+
+7
+00:00:38,230 --> 00:00:43,270
+تمام؟ آخر نظرية قلناها المرة اللي فاتت أنّ لو عندي 
+
+8
+00:00:43,270 --> 00:00:49,910
+non-homogeneous differential equation مثل هذه مثلًا 
+
+9
+00:00:49,910 --> 00:00:53,510
+كويس، second order non-homogeneous differential
+
+10
+00:00:53,510 --> 00:00:58,420
+equation، يبقى الحل بتبعها بيكون على الشكل الآتي
+
+11
+00:00:58,420 --> 00:01:02,960
+بأخذ الـ homogeneous، بجيب الحلين تبعات الـ
+
+12
+00:01:02,960 --> 00:01:07,800
+homogeneous، يبقى Y1 و Y2، يبقى حل الـ homogeneous هي
+
+13
+00:01:07,800 --> 00:01:14,420
+C1Y1 زائد C2Y2، وبروح بأخذ الـ particular solution
+
+14
+00:01:14,420 --> 00:01:18,040
+الحل الخاص للـ non-homogeneous differential
+
+15
+00:01:18,040 --> 00:01:22,760
+equation، بجمع الاثنين مع بعض بيكون هذا هو الحل تبع
+
+16
+00:01:22,760 --> 00:01:26,100
+مين؟ تابع الـ Non-homogeneous differential equation
+
+17
+00:01:26,350 --> 00:01:30,650
+هذا ما أثبتناه المرة الماضية في نظرية رقم 2 من 
+
+18
+00:01:30,650 --> 00:01:36,370
+المرة الماضية، يعني كلامنا الآن هو تطبيق على نظرية
+
+19
+00:01:36,370 --> 00:01:41,970
+رقم 2، إحنا جايين لقصة الـ 8، طريقة الـ undetermined
+
+20
+00:01:41,970 --> 00:01:45,410
+coefficients، يعني كيف بدها تكون الطريقة هذه؟ بنقول
+
+21
+00:01:45,410 --> 00:01:51,230
+ما يأتي، بنستخدم هذه الطريقة إذا تحقق في المعادلة 
+
+22
+00:01:51,230 --> 00:01:58,240
+التفاضلية شرطين، الشرط الأول أن المعاملات كانت ثوابت 
+
+23
+00:01:58,240 --> 00:02:04,320
+الـ A والـ B والـ C ثوابت وليس دوال في T، الشرط الثاني 
+
+24
+00:02:04,320 --> 00:02:10,200
+لازم G of T تبقى على شكل معين، مش أيّ دالة يا الله 
+
+25
+00:02:11,000 --> 00:02:16,560
+يبقى g of t and the function g of t has a special 
+
+26
+00:02:16,560 --> 00:02:21,460
+form، شكل خاص كما هو مبين في الجدول، والآن بنوضح
+
+27
+00:02:21,460 --> 00:02:25,680
+الجدول، يبقى طريقة الـ undetermined coefficients 
+
+28
+00:02:25,680 --> 00:02:26,980
+بستخدمها في
+
+29
+00:02:29,940 --> 00:02:35,000
+في الحالة التالية، يعني إذا تحقق شرطين، الشرط الأول
+
+30
+00:02:35,000 --> 00:02:40,960
+أنّ المعاملات تبع Y'' وY' وY ثوابت، يعني الـ A والـ B
+
+31
+00:02:40,960 --> 00:02:45,840
+والـ C ثوابت، الشرط الثاني أن G of T بدها تبقى على شكل 
+
+32
+00:02:45,840 --> 00:02:51,840
+معين، سؤالنا هو: ما هو الشكل تبع g of t اللي بتطبق
+
+33
+00:02:51,840 --> 00:02:55,280
+عليه طريقة الـ undetermined coefficients اللي جاوب
+
+34
+00:02:55,280 --> 00:02:58,840
+على هذا السؤال هو الجدول اللي بين إيديكم هذا
+
+35
+00:02:58,840 --> 00:03:04,360
+الجدول يتلخص في إيه؟ لو كان g of t على أي شكل من 
+
+36
+00:03:04,360 --> 00:03:08,930
+الأشكال الثلاثة أو الأربعة أو الخمسة اللي هنا أنتم
+
+37
+00:03:08,930 --> 00:03:12,550
+شايفينهم ثلاثة، لكنّهم أكثر، يبقى بدي يكون شكل الـ
+
+38
+00:03:12,550 --> 00:03:16,550
+particular solution، Capital Y of T، بدي يكون على
+
+39
+00:03:16,550 --> 00:03:18,490
+الشكل اللي عندنا هذا
+
+40
+00:03:20,930 --> 00:03:26,430
+نبدأ بواحد، لو كانت G of T كثيرة حدود فقط، من درجة 
+
+41
+00:03:26,430 --> 00:03:30,010
+الأولى، من الثانية، الثالثة، الرابعة، جدّ ما يكون،
+
+42
+00:03:30,010 --> 00:03:34,930
+يبقى بدها يكون شكل الـ particular solution T to the
+
+43
+00:03:34,930 --> 00:03:41,590
+power S في كثيرة حدود مشابهة لمين؟ لكثيرة الحدود،
+
+44
+00:03:41,590 --> 00:03:45,470
+لأنّ المعاملات مختلفة، الـ polynomial من الدرجة
+
+45
+00:03:45,470 --> 00:03:48,970
+النونية، بدها تكون من درجة نونية لكيّ المعاملات ما هيش 
+
+46
+00:03:48,970 --> 00:03:54,030
+هيّ، لكن كلها مضروبة في مين؟ في T to the power of S
+
+47
+00:03:54,030 --> 00:04:00,950
+يا ترى الـ S هذه؟ هأجيب لكم عليها بعد قليل، تمام؟ الـ ...
+
+48
+00:04:00,950 --> 00:04:06,150
+نمرّة اثنين، لو كان Polynomial في Exponential، يعني 
+
+49
+00:04:06,150 --> 00:04:10,890
+Polynomial من الدرجة النونية في E أس Alpha T، يا 
+
+50
+00:04:10,890 --> 00:04:17,090
+بنات، مش Alpha N، Alpha T طبعًا، يبقى بدها يكون شكل الـ
+
+51
+00:04:17,090 --> 00:04:20,830
+particular solution T to the power S في Polynomial
+
+52
+00:04:20,830 --> 00:04:26,590
+من الدرجة النونية في E أس Alpha T، يعني هنا الـ
+
+53
+00:04:26,590 --> 00:04:29,050
+Polynomial من الدرجة النونية، بدها تكون هنا الـ 
+
+54
+00:04:29,050 --> 00:04:31,530
+Polynomial من الدرجة النونية، لكن المعاملات مالها 
+
+55
+00:04:31,530 --> 00:04:37,470
+مختلفة، في مين؟ في الـ exponential، E أس Alpha T، لأنّ
+
+56
+00:04:37,470 --> 00:04:43,020
+هذا بالضبط تمامًا، يبقى إيه كام حالة؟ حالتين، يبقى
+
+57
+00:04:43,020 --> 00:04:46,320
+بدنا نيجي للحالة الثالثة، الحالة الثالثة لو كانت
+
+58
+00:04:46,320 --> 00:04:52,560
+حاصل ضرب Polynomial في Exponential في Cosine فقط
+
+59
+00:04:52,560 --> 00:04:59,400
+أو Polynomial في Exponential في Sin فقط، أو 
+
+60
+00:04:59,400 --> 00:05:03,760
+Polynomial في Exponential في مجموعة الـ Sin والـ
+
+61
+00:05:03,760 --> 00:05:08,660
+Cosine، أو الفرق في ما بينهم، اتجمع وطرح وضرب وقسم
+
+62
+00:05:08,660 --> 00:05:15,220
+يعني بتاع الله، إصحوا يا بنات، لكل واحدة لحالهم، يا مجموعهم أو 
+
+63
+00:05:15,220 --> 00:05:19,640
+طرحهم، الاثنين، الزاوية هذه نفس الزاوية هذه، مش كل
+
+64
+00:05:19,640 --> 00:05:23,240
+واحدة زاوية شكل، إذا كانت كل واحدة زاوية شكل، إلا 
+
+65
+00:05:23,240 --> 00:05:28,120
+كلام ثاني، تمام؟ يبقى هذه كام حالة؟ رقم ثلاثة، ثلاث
+
+66
+00:05:28,120 --> 00:05:32,100
+حالة، يبقى الـ خمسة صاروا مش ثلاثة، تمام؟ زي ما
+
+67
+00:05:32,100 --> 00:05:36,640
+قلنا لكم قبل قليل، شو بدها تكون شكل الحل؟ افترض ما عنديش
+
+68
+00:05:36,640 --> 00:05:41,890
+إلاّ هذا اللي فوق، Polynomial في Exponential في Cosine
+
+69
+00:05:41,890 --> 00:05:47,510
+بدّك تكتب شكل الـ Y of T على الشكل التالي: T to the
+
+70
+00:05:47,510 --> 00:05:51,690
+power S، Polynomial من الدرجة النونية زي ما هي 
+
+71
+00:05:51,690 --> 00:05:56,450
+Polynomial من الدرجة النونية في Cosine زائد Polynomial 
+
+72
+00:05:56,450 --> 00:06:00,150
+أخرى من الدرجة النونية في Sine في الـ Exponential
+
+73
+00:06:00,150 --> 00:06:05,670
+يعني لو كانت Cosine لحالها، بدّك تكتب Cosine و Sine
+
+74
+00:06:06,220 --> 00:06:11,360
+ولو كانت Sine لحالها، بدّي أكتب بي كمان Cosine و Sin
+
+75
+00:06:11,360 --> 00:06:15,400
+ولو كان مجموعهم أو الفرق في بينهم، بدّي أكتب كمان
+
+76
+00:06:15,400 --> 00:06:18,420
+Cosine و Sin، وكل واحدة مضروبة في Polynomial في
+
+77
+00:06:18,420 --> 00:06:23,180
+الـ Exponential، دي ربّالك من الكلام هذا، طب 
+
+78
+00:06:23,180 --> 00:06:28,160
+افترض ما كانش عندي مثلًا Polynomial، عندي Exponential
+
+79
+00:06:28,160 --> 00:06:35,330
+في Cosine، برضه بدّي أكتب Constant 
+
+80
+00:06:35,330 --> 00:06:39,730
+في Cosine زائد Constant في Sine في الـ Exponential
+
+81
+00:06:39,730 --> 00:06:44,930
+وهكذا، فبفرض الـ Exponential ما عنديش، ما عنديش إلاّ
+
+82
+00:06:44,930 --> 00:06:48,650
+Polynomial في Cosine أو Sine، بكل بساطة بشيل الـ
+
+83
+00:06:48,650 --> 00:06:52,150
+Exponential اللي عندنا هنا، وهكذا، يعني هذه الحالة
+
+84
+00:06:52,150 --> 00:06:55,730
+الثالثة ممكن تتفرّع منها، بدل الحالة عشرة، مش أجد
+
+85
+00:06:55,730 --> 00:06:59,470
+الثلاثة، واحد غايب مش مشكلة، بيضلوا الاثنين الثانيين
+
+86
+00:06:59,470 --> 00:07:04,730
+تيجوا، وبدّي أكتب زيهم، وهكذا، واضح كلامي؟ طيّب، نجي 
+
+87
+00:07:04,730 --> 00:07:11,330
+ما هي قصة الـ S هذه؟ تعالوا نشوف، هذه هي المعادلة
+
+88
+00:07:11,330 --> 00:07:15,610
+الأصلية، أخذت الـ homogeneous differential equation، و
+
+89
+00:07:15,610 --> 00:07:21,630
+طلّعت حلّها C1Y1 زائد C2Y2 زائد C2Y2 
+
+90
+00:07:25,430 --> 00:07:30,790
+the non negative integer S، يبقى الـ S هذه عدد صحيح
+
+91
+00:07:30,790 --> 00:07:35,650
+موجب، قد يكون صفر، وقد يكون واحد، وقد يكون اثنين 
+
+92
+00:07:35,650 --> 00:07:41,840
+فقط لغير المعادلة اللي هي من الرتبة الثانية، مالها
+
+93
+00:07:41,840 --> 00:07:46,960
+بيقول it's the smallest integer، أصغر عدد صحيح، such
+
+94
+00:07:46,960 --> 00:07:52,020
+that، بحيث no term، ما فيش عندي ولا حدّ في الـ
+
+95
+00:07:52,020 --> 00:07:56,500
+particular solution، Capital Y of T، is a solution لـ
+
+96
+00:07:56,500 --> 00:08:00,580
+الـ homogeneous differential equation المناظرة، يعني 
+
+97
+00:08:00,580 --> 00:08:07,150
+إيش؟ يعني لما نكتب شكل الحل اللي عندي هذا، بدّه ما يكون
+
+98
+00:08:07,150 --> 00:08:13,550
+ولا Term فيه زي أي Term في حل الـ homogeneous، يعني 
+
+99
+00:08:13,550 --> 00:08:19,410
+إحنا عندنا حل الـ homogeneous اللي هو C1Y1 زائد C2Y2
+
+100
+00:08:19,410 --> 00:08:24,730
+كام Term؟ Termين، بدّي ما يكون ولا Term من الـ Termين هدول
+
+101
+00:08:24,730 --> 00:08:31,510
+يشبه أي Term من الـ Terms اللي موجودة عندي هذا، طيّب 
+
+102
+00:08:31,510 --> 00:08:37,740
+افترض كان في تشابه، هذه الـ Terms تبعات الحلّ
+
+103
+00:08:37,740 --> 00:08:43,460
+الـ homogeneous والـ non-homogeneous، إذا ما فيش Term يشبه أي 
+
+104
+00:08:43,460 --> 00:08:45,660
+Term، سبحان الله
+
+105
+00:08:46,870 --> 00:08:52,350
+من البداية قبل ما نشتغل، طب إذا لقيته Term هنا يشبه
+
+106
+00:08:52,350 --> 00:08:58,450
+Term هنا، Automatic بحط S بقد إيش؟ عندها هنا بواحد، و
+
+107
+00:08:58,450 --> 00:09:03,030
+بعدين بطلع، لما قلت حط S بواحد بصير هذه T أس N زائد
+
+108
+00:09:03,030 --> 00:09:07,450
+واحد، T أس N إلى A N T
+
+109
+00:09:15,100 --> 00:09:18,420
+هل هناك تشابه بين الطرفين أو لا؟ إذا لم يكن هناك
+
+110
+00:09:18,420 --> 00:09:22,340
+تشابه، فالله المؤمن القتال، يبقى S بواحد، إذا لا
+
+111
+00:09:22,340 --> 00:09:27,460
+يزال هناك تشابه، فأنا بحط S بقد إيش؟ باثنين، يعني اضرب
+
+112
+00:09:27,460 --> 00:09:32,950
+الحل اللي عندي في T تربيع، طبعًا من حدّ مجرّب، إيه؟
+
+113
+00:09:32,950 --> 00:09:37,350
+تربية، لا يمكن يتلاقي Term في الـ particular solution
+
+114
+00:09:37,350 --> 00:09:42,790
+يشبه أي Term في الحل الـ non-homogeneous
+
+115
+00:09:42,790 --> 00:09:49,050
+differential equation، ماشي يا بنات؟ يبقى من الآن
+
+116
+00:09:49,050 --> 00:09:53,790
+فصاعدًا، بدّي ألخّص الكلام اللي قلته مرّة ثانية عشان
+
+117
+00:09:53,790 --> 00:09:57,840
+اللي جايب التأخير، بنحل الـ Non-homogeneous
+
+118
+00:09:57,840 --> 00:10:01,940
+differential equation بالشكل هذا، اللي المعاملات
+
+119
+00:10:01,940 --> 00:10:07,160
+كلّها ثوابت، و G of T على أي شكل من الأشكال الثلاثة
+
+120
+00:10:07,160 --> 00:10:12,520
+اللي عندنا هذه، تمام؟ مش أنا حل ههه أول ما أبدأ
+
+121
+00:10:12,520 --> 00:10:16,600
+بطلع في المعادلة اللي عندي، المعاملات تبعت ثوابت
+
+122
+00:10:16,600 --> 00:10:20,700
+ماشي الحال؟ عن طريق G of T بدّي أطلع فيها أيّ شكل
+
+123
+00:10:20,700 --> 00:10:25,740
+من الأشكال هذه موجود، إذا بقدر أحل بالـ undetermined
+
+124
+00:10:25,740 --> 00:10:29,380
+coefficients، طيّب كيف بدّي أسوي؟ بدّي آخذ الـ
+
+125
+00:10:29,380 --> 00:10:32,040
+homogeneous differential equation اللي عندي هذا في
+
+126
+00:10:32,040 --> 00:10:36,870
+الأول، قبل المبدأ، وطلع الحل تبعها زي ما كنا بنحلّ في
+
+127
+00:10:36,870 --> 00:10:41,390
+الـ sections الماضية، repeated roots, unrepeated
+
+128
+00:10:41,390 --> 00:10:44,550
+roots, complex roots أو complex conjugate roots
+
+129
+00:10:44,550 --> 00:10:48,110
+تمام؟ جبنا الحلّ، بنبرّز وبنقول له قعد ع الشجرة لسه
+
+130
+00:10:48,110 --> 00:10:51,970
+بدّنا نرجع لك، بدّنا نيجي نجيّب شكل الـ particular
+
+131
+00:10:51,970 --> 00:10:57,030
+solution، شكل الـ particular solution بيعتمد على شكل
+
+132
+00:10:57,030 --> 00:11:01,450
+الـ G of T، بعدين بطلع في الـ G of T، لقيته 
+
+133
+00:11:01,450 --> 00:11:06,410
+Polynomial، بحط T أس S في Polynomial زيها، بس
+
+134
+00:11:06,410 --> 00:11:10,150
+الثوابت بتصير، ومش الثوابت اللي هناك، ثوابت جداد، 
+
+135
+00:11:10,150 --> 00:11:17,260
+تمام؟ وبعدين بطلع، هل كل Term هنا فيه شبه من أيّ
+
+136
+00:11:17,260 --> 00:11:21,060
+Term من حالة المعادلة هذه ولا لأ؟ إذا ما فيش تشابه
+
+137
+00:11:21,060 --> 00:11:25,920
+بقول له S بـ Zero وبالتالي بكون عندي هذا، اضطريت 
+
+138
+00:11:25,920 --> 00:11:31,970
+بالمرة، وبيضل هذا هو الحلّ، بالمثل هنا وهنا وهنا، بطيّر
+
+139
+00:11:31,970 --> 00:11:36,190
+الـ T to the power S، والباقي بيضلّ هو، العلم تمام؟
+
+140
+00:11:36,190 --> 00:11:40,950
+لقيته فيه تشابه، بقول استنى شويّة، حط S بواحد، يبقى
+
+141
+00:11:40,950 --> 00:11:45,710
+بيصير أنّ دي T أس واحد، يعني T، بتصير T مضروبة في الـ 
+
+142
+00:11:45,710 --> 00:11:51,010
+Polynomial هنا أو هنا أو هنا، وهنا، يبقى صار عندي
+
+143
+00:11:51,010 --> 00:11:55,090
+عدّة Terms، إن زاد واحد، وإن زاد واحد، وإن 
+
+144
+00:11:55,090 --> 00:12:01,190
+نقص واحد لغاية AN في T، وبعدين بطلع، هل أي 
+
+145
+00:12:01,190 --> 00:12:05,710
+Term عندي يشبه أي Term في حل الـ homogeneous ولا لا
+
+146
+00:12:06,300 --> 00:12:10,480
+إذا ما فيش تشابه خلاص تمام، يبقى S بواحد، إذا في 
+
+147
+00:12:10,480 --> 00:12:15,080
+تشابه بحط S باثنين، من الحدّ ما تحط S باثنين مش
+
+148
+00:12:15,080 --> 00:12:23,000
+هتلاقي ولا Term في اللي هنا يشبه أي Term من هنا، بعد
+
+149
+00:12:23,000 --> 00:12:27,800
+ذلك بيظلّ الـ routine، كيف بدنا نجد الثوابت؟ هذا ما 
+
+150
+00:12:27,800 --> 00:12:35,120
+سنعرفه لكم من خلال المسائل، يبقى يا بنات عمود في
+
+151
+00:12:35,120 --> 00:12:39,660
+قرية عندي أنّ أطلع لي S أول شيء، بدّك تحلّ الـ 
+
+152
+00:12:39,660 --> 00:12:45,000
+homogeneous هذه، بعد ذلك بدّك تطلع لي شكل الـ S، أنا
+
+153
+00:12:45,000 --> 00:12:48,480
+كمُصحّح، إذا جبت لي الـ S صحيح بوصّل عليه عشر درجات، بحط
+
+154
+00:12:48,480 --> 00:12:51,980
+لك سبعة على حال الـ homogeneous أو على قيمة S صحيح
+
+155
+00:12:51,980 --> 00:12:55,320
+بحطّ لك سبعة درجات، والثلاثة على الشغل الروتيني بس
+
+156
+00:12:55,320 --> 00:12:59,440
+اللي بيظلّ بعد ذلك، تمام؟ في حدا فيكم اللي إيه تسأل
+
+157
+00:12:59,440 --> 00:13:02,680
+في الكلام اللي قلته قبله؟ خلاص، ما عنديش نظرية، خلاص
+
+158
+00:13:02,680 --> 00:13:06,900
+بدّنا نش ننقش على مجموعة من الأمثلة، حدا فيكم بتسأل
+
+159
+00:13:06,900 --> 00:13:15,170
+إيه سؤال؟ آه، مش؟ الكلام اللي قلناه بدّنا ندخّله على 
+
+160
+00:13:15,170 --> 00:13:24,190
+أرض الواقع من خلال الأمثلة، أوّل مثال، examples، أوّل
+
+161
+00:13:24,190 --> 00:13:29,590
+مثال من هذه الأمثلة اللي هو سؤال 17 من الكتاب
+
+162
+00:13:29,590 --> 00:13:36,150
+بيقول Solve the initial value problem 
+
+163
+00:13:56,300 --> 00:13:57,700
+Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''
+
+164
+00:14:07,480 --> 00:14:11,140
+يبقى أقول أنّ أنا أوّل شغلة بدّي أعملها بدّي أحلّ الـ
+
+165
+00:14:11,140 --> 00:14:15,560
+homogeneous differential equation، لذلك بروح بقول 
+
+166
+00:14:15,560 --> 00:14:26,920
+Let Y تساوي E قصة RT، be the solution of the 
+
+167
+00:14:26,920 --> 00:14:33,380
+homogeneous differential equation
+
+168
+00:15:00
+
+216
+00:20:25,690 --> 00:20:30,510
+كده شو سافر خليها الخطوة دي بنخليها للاخر بعد ما
+
+217
+00:20:30,510 --> 00:20:38,620
+جيب الـ A و الـ B يبقى capital Y of T بدها تساوي اللي
+
+218
+00:20:38,620 --> 00:20:42,840
+عندنا اللي هو A T sine زائد B T sine اتنين دي كده
+
+219
+00:20:42,840 --> 00:20:48,800
+بده اجيبها كتالي بدروح اشتقها مرتين و اعوض في راسي
+
+220
+00:20:48,800 --> 00:20:55,260
+المسألة فبجيب اقوله هاي Y prime as a function of T
+
+221
+00:20:55,260 --> 00:21:00,440
+هذه يا بنات مشتقة حصل ضرب دلتين وهذه مشتقة حصل ضرب 
+
+222
+00:21:00,440 --> 00:21:12,730
+دالتين يبقى هذا بيصير a في sin 2t زائد 2at في cos 2t 
+
+223
+00:21:12,730 --> 00:21:18,290
+يبقى اللي كتبته هذا مشتقت من الدالة الأولى كحاصل
+
+224
+00:21:18,290 --> 00:21:32,680
+ضرب دالتين زائد b في cos 2t ناقص 2bt في sin 2t في
+
+225
+00:21:32,680 --> 00:21:37,600
+حاجة بقدر أجمعها مع بعض بقت لكلها لإن هنا a sine
+
+226
+00:21:37,600 --> 00:21:43,740
+وعندك هنا t في sine وبالتالي انسى الموضوع بدنا
+
+227
+00:21:43,740 --> 00:21:50,220
+نشتاق كمان مرة يبقى باجي بقوله y double prime as a
+
+228
+00:21:50,220 --> 00:21:55,300
+function of t يبقى هذا الكلام بده يساوي لنشتاق
+
+229
+00:21:55,300 --> 00:22:00,780
+يبقى 2a في cosine 2t
+
+230
+00:22:02,600 --> 00:22:10,100
+هذه المشتقة تحصل ضرب دالتين يبقى زائد 2a في
+
+231
+00:22:10,100 --> 00:22:21,160
+cosine 2t ناقص 4a t في sin 2t خلصنا
+
+232
+00:22:21,160 --> 00:22:26,800
+مشتقة أول two terms بدنا نيجي لمشتقة الـ two terms
+
+233
+00:22:26,800 --> 00:22:35,800
+الأخرى يبقى ناقص 2b في sin 2t نيجي هنا
+
+234
+00:22:35,800 --> 00:22:47,440
+ناقص 2b في sin 2t ناقص اللي هو 4b
+
+235
+00:22:47,440 --> 00:22:51,080
+t في cos 2t
+
+236
+00:22:55,900 --> 00:23:03,100
+هذه هي نفس هذه صحيح ولا لأ يبقى هذه تساوي 4
+
+237
+00:23:03,100 --> 00:23:05,800
+a cos 2t
+
+238
+00:23:10,480 --> 00:23:17,660
+هذول التنتين يبقى ناقص 4b sin 2t ناقص
+
+239
+00:23:17,660 --> 00:23:24,340
+4b sin 2t بقى اللي عندنا مين؟ هذه و
+
+240
+00:23:24,340 --> 00:23:30,560
+هذه مافيش بينهم أي شغلة يبقى ناقص 4a t sin
+
+241
+00:23:30,560 --> 00:23:39,520
+2t وهنا ناقص 4b t cos 2t
+
+242
+00:23:56,300 --> 00:24:01,700
+الآن بعد ما جبنا الـ particular solution المشتقة
+
+243
+00:24:01,700 --> 00:24:05,840
+الأولى للمشتقة الثانية بدي ارجع و اوض وين في 
+
+244
+00:24:05,840 --> 00:24:10,460
+المعادلة رقم start يبقى باجي بقوله substitute
+
+245
+00:24:19,610 --> 00:24:23,990
+ونحصل على Y double prime
+
+246
+00:24:29,420 --> 00:24:36,580
+يبقى 4a cos 2t
+
+247
+00:24:36,580 --> 00:24:40,280
+-4b 
+
+248
+00:24:40,280 --> 00:24:42,620
+sin 2t
+
+249
+00:24:53,690 --> 00:25:02,150
+ناقص 4b ناقص 4b t cos 2t هذا من 
+
+250
+00:25:02,150 --> 00:25:09,170
+هذا Y ضابر الفراية بدي 4 Y وين الـ Y هيها بنروح
+
+251
+00:25:09,170 --> 00:25:15,570
+اضرب هذه في مين؟ في 4 بالموجب يبقى زائد 4a
+
+252
+00:25:15,570 --> 00:25:26,350
+t sin 2t يبقى زائد 4a t sin 2t وهنا زائد
+
+253
+00:25:26,350 --> 00:25:35,810
+4b t cos 2t 2T كله بده يساوي
+
+254
+00:25:35,810 --> 00:25:38,930
+3
+
+255
+00:25:38,930 --> 00:25:46,430
+sin 2t تمام تعالوا نجمع و نشوف عندك هنا
+
+256
+00:25:46,430 --> 00:25:51,850
+4a t sin 2t بالموجب وهذه بالسلب مع
+
+257
+00:25:51,850 --> 00:25:58,120
+السلامة وهذه بالسالب وهذه بالموجب مع السلامة كمان
+
+258
+00:25:58,120 --> 00:26:04,500
+يبقى شو ضال عندي امانات؟ 4 a cos 2t
+
+259
+00:26:04,500 --> 00:26:11,980
+ناقص 4b sin 2t بدي اساوي 3 في sin
+
+260
+00:26:11,980 --> 00:26:18,770
+2t نعمل مقارنة بين الطرفين يعني بمقارنة
+
+261
+00:26:18,770 --> 00:26:23,990
+المعاملات في الطرفين بيصير معامل الـ cosine هنا هو
+
+262
+00:26:23,990 --> 00:26:28,170
+معامل الـ cosine هنا و معامل الـ sine هنا هو معامل
+
+263
+00:26:28,170 --> 00:26:33,210
+الـ sine هنا يبقى بيصير عندك 4 ايه؟ قداش sin
+
+264
+00:26:33,210 --> 00:26:38,230
+بنات؟ 0 ماعنديش cosine هنا يبقى اللي يطيّره كإنه
+
+265
+00:26:38,230 --> 00:26:44,270
+zero يبقى 4 A تساوي 0 ومنها A تساوي 0
+
+266
+00:26:44,270 --> 00:26:50,690
+و ناقص 4 B بده يساوي قداش 3 المعامل تبع الـ
+
+267
+00:26:50,690 --> 00:26:54,850
+sin هو نفس المعامل تبع الـ sin يبقى B بده يساوي
+
+268
+00:26:54,850 --> 00:27:01,280
+ناقص 3/4 إذا بناء عليه الـ particular solution
+
+269
+00:27:01,280 --> 00:27:08,040
+Y of T صار على الشكل التالي هيونا الـ A بـ 0
+
+270
+00:27:08,040 --> 00:27:13,500
+يبقى الـ term هذا الله سهل عليه الـ B بسالب 3/4
+
+271
+00:27:13,500 --> 00:27:22,020
+يبقى صار سالب 3/4 T في Cos 2T
+
+272
+00:27:23,000 --> 00:27:30,000
+يبقى start the general solution
+
+273
+00:27:30,000 --> 00:27:43,000
+of the differential equation start is Y تساوي c1y1
+
+274
+00:27:43,000 --> 00:27:52,510
+c2y2 زائد capital Y of T يبقى Y تساوي طبعا طلعنا
+
+275
+00:27:52,510 --> 00:28:02,250
+اللي كان مبروز اللي هو من اللي هو c1 cos 2t c2 sin
+
+276
+00:28:02,250 --> 00:28:10,730
+2t ناقص 3/4 t في cos 2t
+
+277
+00:28:13,080 --> 00:28:18,280
+لحد هنا انتهى حل المسألة لكن اشراح قال لي اعطاني
+
+278
+00:28:18,280 --> 00:28:23,320
+الناس الـ conditions يعني بدي اجيب منهم قداش قيمة
+
+279
+00:28:23,320 --> 00:28:29,380
+c1 و c2 إذا ماعطيني Y عند الـ 0 و Y prime عند الـ
+
+280
+00:28:29,380 --> 00:28:34,880
+0 يبقى بدروح اشتق عادي يبقى باجي بقوله Y prime
+
+281
+00:28:34,880 --> 00:28:35,680
+يساوي
+
+282
+00:28:39,300 --> 00:28:47,460
+-2C1Sin2T زائد اللي هو 2C2Cos2T
+
+283
+00:28:47,460 --> 00:28:56,900
+هذه حصل ضرب دالتين ناقص 3/4 Cos2T ناقص مع
+
+284
+00:28:56,900 --> 00:29:07,170
+ناقص بيصير زائد 3/2T في Sin2T تفاضل cos
+
+285
+00:29:07,170 --> 00:29:12,350
+بسلب sin مع سلب بصير موجب ضرب تفاضل بيساوي اللي هو
+
+286
+00:29:12,350 --> 00:29:17,630
+2 مع الـ 4 نضال 3/2T sin 2T
+
+287
+00:29:17,630 --> 00:29:21,850
+يبقى هاي المشتقة الآن نيجي الآن من الـ initial
+
+288
+00:29:21,850 --> 00:29:25,390
+conditions الـ initial condition الأولاني قال ان Y
+
+289
+00:29:25,390 --> 00:29:30,670
+عند الـ 0 بده يساوي 2 يبقى Y عند الـ 0 بده
+
+290
+00:29:30,670 --> 00:29:35,770
+يساوي 2 implies يبقى بده اشيل كل Y واحط مكانها
+
+291
+00:29:35,770 --> 00:29:42,650
+2 و اشيل كل T واحط مكانها 0 يبقى بصير عند هنا 2
+
+292
+00:29:42,650 --> 00:29:51,530
+تساوي C1 حط هذه بـ 0 مع السلامة حط هذه بـ 0 في 1
+
+293
+00:29:51,530 --> 00:30:00,240
+بـ 0 مع السلامة يبقى C1 يساوي كده؟ 2 جاهزينالانتشار
+
+294
+00:30:00,240 --> 00:30:01,300
+الانتشار الانتشار الانتشار الانتشار الانتشار
+
+295
+00:30:01,300 --> 00:30:02,340
+الانتشار الانتشار الانتشار الانتشار الانتشار
+
+296
+00:30:02,340 --> 00:30:04,900
+الانتشار الانتشار الانتشار الانتشار الانتشار
+
+297
+00:30:04,900 --> 00:30:07,440
+الانتشار الانتشار الانتشار الانتشار الانتشار
+
+298
+00:30:07,440 --> 00:30:08,900
+الانتشار الانتشار الانتشار الانتشار الانتشار
+
+299
+00:30:08,900 --> 00:30:14,680
+الانتشار الانتشار الانتشار الانتشار الانتشار
+
+300
+00:30:14,680 --> 00:30:24,100
+الانتشار الانتشار الانتشار الانتش زيرو بضل 2 سي
+
+301
+00:30:24,100 --> 00:30:31,740
+2 زيرو بضل ناقص 3/4 زيرو هذا مع السلامة 
+
+302
+00:30:31,740 --> 00:30:37,360
+تمام يبقى بنات هذا بده يعطيلك انه 2 C2
+
+303
+00:30:37,360 --> 00:30:41,680
+يساوي -3/4 بجيبها على الشجة هذا بيصير -
+
+304
+00:30:41,680 --> 00:30:48,800
+1 + 3/4 بضل جديد -1/4 يبقى -1/4
+
+305
+00:30:49,060 --> 00:30:57,020
+هذا بدي اعطيك ان c2 يساوي سالب 8 يبقى اصبح الـ
+
+306
+00:30:57,020 --> 00:31:03,460
+solution اللي عندي هذا على الشكل التالي Y تساوي c1
+
+307
+00:31:03,460 --> 00:31:12,920
+بـ 2 يبقى 2 cosine 2t c2 بسالب 8 يبقى سالب 8 
+
+308
+00:31:12,920 --> 00:31:26,990
+sin 2t ناقص 3/4 T cosine 2T يبقى هذا حل
+
+309
+00:31:26,990 --> 00:31:30,730
+الـ initial value problem اللي عندنا حد فيه كله
+
+310
+00:31:30,730 --> 00:31:37,770
+يتساول هنا يبقى كل سؤال بد بشكل بيعتمد على شكل G 
+
+311
+00:31:37,770 --> 00:31:38,850
+of T
+
+312
+00:32:09,620 --> 00:32:20,680
+مثال 2 سؤال
+
+313
+00:32:20,680 --> 00:32:32,100
+6 من الكتاب will you find the general solution
+
+314
+00:32:32,100 --> 00:32:34,800
+of
+
+315
+00:32:45,340 --> 00:32:53,100
+Y'Y'Y يساوي 2
+
+316
+00:33:09,650 --> 00:33:13,130
+التكتيك اللي اتبعناها في حل المثال الماضي بنتبعه
+
+317
+00:33:13,130 --> 00:33:18,850
+هنا مع الفرق ملاحظة شكل الـG of T نهيكة عن ان هذه
+
+318
+00:33:18,850 --> 00:33:24,990
+ماهياش initial value problem طب كويس يبقى بدي ابدأ
+
+319
+00:33:24,990 --> 00:33:32,870
+بنفس الطريقة بدي اقول له let Y تساوي E أس RT بـ A
+
+320
+00:33:32,870 --> 00:33:36,450
+solution of
+
+321
+00:34:05,310 --> 00:34:06,710
+Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''
+
+322
+00:34:06,940 --> 00:34:13,500
+يبقى R زائد 1 لكل تربيع يساوي 0 يبقى الـ R 
+
+323
+00:34:13,500 --> 00:34:23,680
+تساوي كدهش -1 يبقى هنا solution of
+
+324
+00:34:23,680 --> 00:34:34,640
+the homogeneous differential equation is Y تساوي C
+
+325
+00:34:34,640 --> 00:34:43,730
+1 C2 في T في أثناء قصة T و بين مروزها نقول طيحة
+
+326
+00:34:43,730 --> 00:34:50,970
+على شجرة و هذا حد أظن repeated roots اللي أخدناه
+
+327
+00:34:50,970 --> 00:34:55,110
+المرة الماضية بيقول C1 زي C2 في T في الـ
+
+328
+00:34:55,110 --> 00:34:58,990
+exponential اللي بتطلع عندنا الآن بعد هيك بدنا نجي
+
+329
+00:34:58,990 --> 00:35:02,610
+لمين للـ non homogeneous differential equation بدي 
+
+330
+00:35:02,610 --> 00:35:07,070
+أجيب الـ particular solution للـ non-homogeneous
+
+331
+00:35:07,070 --> 00:35:12,110
+differential equation فبروح بقوله the particular
+
+332
+00:35:12,110 --> 00:35:15,430
+solution
+
+333
+00:35:15,430 --> 00:35:27,800
+of equation star is capital Y of T بده يساوي بعدها
+
+334
+00:35:27,800 --> 00:35:34,040
+بطلع على شكل G of T فبعدها بقول T to the power S
+
+335
+00:35:34,040 --> 00:35:38,280
+فيه constant في الـ exponential يبقى polynomial من
+
+336
+00:35:38,280 --> 00:35:46,100
+الدرجة الصفرية يعني constant في E أس -T بالشكل
+
+337
+00:35:46,100 --> 00:35:54,330
+اللي عندنا بعد هكذا بروح أشوف ما هو شكل الـ S بأجي
+
+338
+00:35:54,330 --> 00:35:59,210
+بطلع constant فيه و -T أظن في عندي constant
+
+339
+00:35:59,210 --> 00:36:04,210
+فيه و -T له الـ term الأول صح؟ يبقى الـ S
+
+340
+00:36:04,210 --> 00:36:09,270
+بقداش؟ لو حطيت الـ S بـ 1 تنتهي المشكلة ولا بتظل
+
+341
+00:36:09,270 --> 00:36:14,270
+تزال القائمة تعالى نشوف حط الـ S بـ 1 بصير A T في
+
+342
+00:36:14,270 --> 00:36:20,530
+E أثناء قصة T باجي بقارن بلاقي زي هذا مصبوط يبقى S
+
+343
+00:36:20,530 --> 00:36:26,010
+تساوي 1 محلتش المشكلة يبقى S بقداش يبقى هنا هه
+
+344
+00:36:26,010 --> 00:36:33,120
+هيرالاس تساوي 2 طب لو حطيت S بـ 2 تنحل
+
+345
+00:36:33,120 --> 00:36:38,360
+المشكلة بصير A T تربيع في الـ exponential ماعنديش
+
+346
+00:36:38,360 --> 00:36:41,400
+constant في T تربيع في الـ exponential يبقى ايك
+
+347
+00:36:41,400 --> 00:36:47,520
+بتبقى مالها انحلت من المشكلة يبقى اصبح capital Y
+
+348
+00:36:47,520 --> 00:36:55,900
+of T تساوي A T تربيع في E أثناء قصتي الآن بروح نجيب
+
+349
+00:36:55,900 --> 00:37:03,940
+ما هو شكل الـ main شكل الـ a فبروح اشتق هذه مرتين إذا
+
+350
+00:37:03,940 --> 00:37:09,380
+لو روحت اشتقتها المرة الأولى بصير capital Y prime
+
+351
+00:37:09,380 --> 00:37:20,960
+of T بدي اساوي 2A T في E ناقص T ناقص A T تربيع في
+
+352
+00:37:20,960 --> 00:37:31,900
+E ناقص T أو يا بنات بقدر اقول 2A T ناقص A T تربيع 
+
+353
+00:37:31,900 --> 00:37:37,900
+كله في E ناقص T يعني أخد E ناقص T عامل مشترك
+
+354
+00:37:37,900 --> 00:37:44,920
+نجيب المشتقة تاني يبقى capital Y double prime of T
+
+355
+00:37:44,920 --> 00:37:50,520
+بدي اجيب الدل اللي هو يبقى دي مشتقة حاصل ضرب دالتين
+
+356
+00:37:50,520 --> 00:38:01,460
+يبقى 2A في E أس -T ناقص 2A T في E أس -T
+
+357
+00:38:01,460 --> 00:38:07,400
+تفضل الأس -1 والـ exponential كما هي خلصنا 
+
+358
+00:38:07,400 --> 00:38:12,220
+مشتقة أول term بدنا نيجي للـ term التاني يبقى ناقص
+
+359
+00:38:12,220 --> 00:38:23,400
+2a t في E أس -t زائد اللي هو A T تربيع في
+
+360
+00:38:23,400 --> 00:38:30,220
+E أس -t طلع لي هذه و هذه 2 زي بعض بدي أخدهم 
+
+361
+00:38:30,220 --> 00:38:34,500
+مع بعض و أخد الـ exponential برا عامل مشترك يبقى 
+
+362
+00:38:34,500 --> 00:38:44,220
+هذه بدأ تعطيني الشكل التالي 2A و هنا ناقص 4A T ناقص 
+
+363
+00:38:44,220 --> 00:38:51,900
+4A T و زائد A T تربيع كله في الـ exponential E أس
+
+364
+00:38:51,900 --> 00:38:57,500
+-T نمسك المعلومات اللي عندنا نرجع نعوض وين في 
+
+365
+00:38:57,500 --> 00:39:05,520
+المعادلة الى star يبقى باقي بقوله substitute in 
+
+366
+00:39:05,520 --> 00:39:08,500
+equation star
+
+367
+00:39:10,320 --> 00:39:15,500
+نحصل على ما يأتي Y double prime بدخل الـ
+
+368
+00:39:15,500 --> 00:39:19,980
+exponential من الكل برا يبقى ايش بيصير النمنات هاي
+
+369
+00:39:19,980 --> 00:39:28,580
+2A ناقص 4A T زائد A T تربيع خلصنا Y
+
+370
+00:39:28,580 --> 00:39:34,100
+double prime 2 بده اضربها في Y' هاي Y' هنا بده
+
+371
+00:39:34,100 --> 00:39:42,200
+اضربها في 2 بصير 4A T يبقى زائد 4A T
+
+372
+00:39:42,200 --> 00:39:50,830
+ناقص 2A T تربيع يبقى أي ضربت هذه وين؟ في 2
+
+373
+00:39:50,830 --> 00:39:59,350
+بعدها زائد Y وين Y هيها يبقى زائد A T تربيع يبقى
+
+374
+00:39:59,350 --> 00:40:07,530
+زائد A T تربيع كل هذا في E أس -T هذا الطرف 
+
+375
+00:40:07,530 --> 00:40:16,490
+الشمال بدي اساوي 2 E أس -T الآن بقدر اقسم
+
+376
+00:40:16,490 --> 00:40:20,550
+الطرفين على الـ exponential ان الـ exponential الرقم
+
+377
+00:40:20,550 --> 00:40:25,630
+اكبر من الـ 0 يبقى لو قسمت عليه بروح الـ term هذا 
+
+378
+00:40:25,630 --> 00:40:31,950
+مع الـ term هنا بعد هيك بده اجمع عند هنا 2A
+
+379
+00:40:31,950 --> 00:40:41,270
+مافيش غيرها يبقى هذه 2A ناقص 4A T زائد
+
+380
+00:40:41,270 --> 00:40:47,750
+4A T مع السلامة بضل عندي A T تربيع و A T تربيع
+
+381
+00:40:47,750 --> 00:40:54,250
+بـ 2A T تربيع و سالب 2A T تربيع يبقى مع
+
+382
+00:
+
+431
+00:47:08,060 --> 00:47:15,580
+اعيدها كمان مرة اتنين y w prime زائد ثلاثة y prime
+
+432
+00:47:15,580 --> 00:47:25,250
+زائد y يساوي ثلاثة sine T طبعا هتسأل واحدة فيكوا
+
+433
+00:47:25,250 --> 00:47:30,730
+إذا لم يكونوا واحدات أكثر أقول له مال فعلا، فتقول لي
+
+434
+00:47:30,730 --> 00:47:34,630
+طيب أرجعهم للأصل، فأقول له بقى تعالي نجمع، يبقى لو
+
+435
+00:47:34,630 --> 00:47:38,730
+جمعنا هذا بيصير اثنين الطرف الأيسر يساوي الطرف
+
+436
+00:47:38,730 --> 00:47:42,730
+الأيمن، صح ولا لا؟ لو قسمنا على اثنين بيصير الطرف
+
+437
+00:47:42,730 --> 00:47:45,610
+الأيسر يساوي نصف الطرف الأيمن، كأننا ضربنا الطرف
+
+438
+00:47:45,610 --> 00:47:50,850
+الأيمن في قداش، في نصف  نصف مقل وكنستن، هل يغير من
+
+439
+00:47:50,850 --> 00:47:56,220
+الشكل العام للحل؟ بيغير؟ لن يغير من الشكل العام،
+
+440
+00:47:56,220 --> 00:48:01,900
+يكون الأصل نقسم عليه وهكذا تمام؟ يبقى هذا لن يغير
+
+441
+00:48:01,900 --> 00:48:06,340
+في الشكل العام للحل على الإطلاق طب افرض كانوا
+
+442
+00:48:06,340 --> 00:48:11,090
+الثلاثة تيرمات والله أربعة، كل واحد شكله مش علاقة
+
+443
+00:48:11,090 --> 00:48:14,650
+بينهم بدل المعادلة هم يجب أن تكتب 3 أو 4 معادلة
+
+444
+00:48:14,650 --> 00:48:19,870
+حسب وضع المسألة طب تعالي نشوف كيف بدنا نكمل بعد
+
+445
+00:48:19,870 --> 00:48:25,510
+ذلك يبقى أنا قسمت مسألتي صارت لي مسألتين والآن 
+
+446
+00:48:25,510 --> 00:48:30,270
+بدنا نيجي للمسألتين مش واحدة تمام بدنا نيجي للمسألة
+
+447
+00:48:30,270 --> 00:48:34,930
+الأولى بدنا نجيب ال particular solution وهروح
+
+448
+00:48:34,930 --> 00:48:43,620
+أسميه Y1 of T هذه كمية المجدداش إذا بدي أكتب كمية
+
+449
+00:48:43,620 --> 00:48:44,320
+المجدداش المجدداش المجدداش المجدداش المجدداش
+
+450
+00:48:44,320 --> 00:48:47,620
+المجدداش المجدداش المجدداش المجدداش المجدداش
+
+451
+00:48:47,620 --> 00:48:50,300
+المجدداش المجدداش المجدداش المجدداش المجدداش
+
+452
+00:48:50,300 --> 00:48:50,380
+المجدداش المجدداش المجدداش المجدداش المجدداش
+
+453
+00:48:50,380 --> 00:48:51,740
+المجدداش المجدداش المجدداش المجدداش المجدداش
+
+454
+00:48:51,740 --> 00:48:56,180
+المجدداش المجدداش المجدداش المجدداش المجدداش
+
+455
+00:48:56,180 --> 00:49:03,000
+المجدداش المجدداش المجدداش المجدداش المجدداش المجد
+
+456
+00:49:03,520 --> 00:49:07,740
+يبقى هذه polynomial من الدرجة الثانية ولو أنه
+
+457
+00:49:07,740 --> 00:49:10,680
+ماعنديش إلا term واحد وهذول طيرات يبقى بدك
+
+458
+00:49:10,680 --> 00:49:15,840
+تكتبيها كاملة وقد ما يطلع ال constants هذول يطلع
+
+459
+00:49:15,840 --> 00:49:22,720
+طيب بدنا نيجي هذه بدي أسميها Y2 of T يبقى T to the
+
+460
+00:49:22,720 --> 00:49:29,600
+power S فيه مدهجة أشوف برضه بنفس الطريقة هذه
+
+461
+00:49:29,600 --> 00:49:33,700
+constant فيه sign بدي أقول constant فيه sign زائد
+
+462
+00:49:33,700 --> 00:49:40,100
+كونستانت في كوساين بحيث ولا كونستانت من هدول بيكون
+
+463
+00:49:40,100 --> 00:49:47,720
+موجود هناك إذا هنا باجي بقول هذه a sin t زائد b في
+
+464
+00:49:47,720 --> 00:49:53,400
+cos t ولا كونستانت من هنا هو نفس الكونستانت اللي
+
+465
+00:49:53,400 --> 00:49:58,260
+هنا الآن بتروح ادور على S هنا و S هنا كداش تساوي
+
+466
+00:49:58,260 --> 00:50:04,180
+باجي بطلع غطي هذه و باجي للمقدار بين القوسين في أي
+
+467
+00:50:04,180 --> 00:50:11,580
+تشابه بين هنا وهنا يبقى S بقداش Zero يبقى هنا S
+
+468
+00:50:11,580 --> 00:50:19,910
+تساوي Zero طب وهنا؟ بدهجة أشوف في تشابه ما بين هنا
+
+469
+00:50:19,910 --> 00:50:26,630
+وما بين هنا يبقى كمان S بزيرو يبقى هنا كمان S
+
+470
+00:50:26,630 --> 00:50:33,930
+بزيرو يبقى أصبح capital Y1 of T في الحالة الأولى
+
+471
+00:50:33,930 --> 00:50:44,050
+بده يساوي A0 T تربيع زائد A1T زائد A2 و capital Y2
+
+472
+00:50:44,050 --> 00:50:46,470
+of T بده يساوي من
+
+473
+00:51:15,510 --> 00:51:21,310
+Y1Y1Y1Y1Y1Y1Y1Y1Y1 بدنا y2 prime as a function of t
+
+474
+00:51:21,310 --> 00:51:30,690
+يبقى a cosine t ناقص b في sine t بدنا y2 double
+
+475
+00:51:30,690 --> 00:51:36,730
+prime as a function of t يبقى ناقص a في sine t
+
+476
+00:51:36,730 --> 00:51:45,160
+ناقص b في cosine من t اللي فوق سميناها star
+
+477
+00:51:45,160 --> 00:51:49,540
+المعادلة هذه يسميها 1 يا بناتي والمعادلة هذه
+
+478
+00:51:49,540 --> 00:51:55,460
+يسميها لمين اثنين يبقى هذول بتعوضهم في المعادلة
+
+479
+00:51:55,460 --> 00:52:00,320
+واحد واللي هناك بتعوضهم أين في المعادلة اثنين
+
+480
+00:52:00,320 --> 00:52:07,620
+يبقى بدنا نيجي نقول له صح باسم substitute in equation
+
+481
+00:52:07,620 --> 00:52:15,170
+one we get نجل ال equation و نقل 2y double prime
+
+482
+00:52:15,170 --> 00:52:19,830
+وين ال y double prime؟ ها يعني، نروح فيه كمان مين؟
+
+483
+00:52:19,830 --> 00:52:27,330
+اثنين، يبقى هذه أربعة هنا، خلصنا منها، قل زائد
+
+484
+00:52:27,330 --> 00:52:33,780
+ثلاثة y prime زائد ثلاثة y prime يبقى هذه الدروبة
+
+485
+00:52:33,780 --> 00:52:42,280
+في من؟ في ثلاثة يبقى زائد ستة a naught t زائد
+
+486
+00:52:42,280 --> 00:52:50,580
+ثلاثة a one هضربها في ثلاثة اللي بعدها زائد Y يبقى
+
+487
+00:52:50,580 --> 00:53:02,100
+Y اللي فوق يبقى زائد A0 T تربيع زائد A1 T زائد A2
+
+488
+00:53:02,100 --> 00:53:05,740
+كله بده يساوي مين ال T تربيع
+
+489
+00:53:07,820 --> 00:53:13,980
+نمسك الثانية بالمرة yw prime هيها زي ما هي والله
+
+490
+00:53:13,980 --> 00:53:17,520
+في اثنين هي لأ اثنين yw prime لقد ضربنا هذه في
+
+491
+00:53:17,520 --> 00:53:25,700
+اثنين يبقى هنا بالداجة وأقول لصابس تت يوت and
+
+492
+00:53:25,700 --> 00:53:32,700
+equation اثنين ويقل طبعا الشركة نخلص واحدة واحدة
+
+493
+00:53:32,700 --> 00:53:40,910
+نمسك هذه طويلة هنا أربعة a node وهي ثلاثة a one
+
+494
+00:53:40,910 --> 00:53:46,810
+هذول ال constants يبقى أربعة a node زائد ثلاثة a
+
+495
+00:53:46,810 --> 00:53:57,390
+one بنيا ستة a node تي يبقى زائد ستة a node زائد
+
+496
+00:53:57,390 --> 00:54:01,410
+اه استني في a two يا بناتي وهنا
+
+497
+00:54:03,510 --> 00:54:09,210
+زائد A2 اللي هو الثوابت زائد A2 هذه الثوابت
+
+498
+00:54:09,210 --> 00:54:15,310
+أخذناهم مع بعض هذه فيها T وهذه فيها T يبقى زائد
+
+499
+00:54:15,310 --> 00:54:27,230
+6A0 زائد A1 كله في T خلصنا منها زائد A0 T تربيع
+
+500
+00:54:27,230 --> 00:54:33,400
+كله بيساوي T تربيع بدنا نقارن المعاملات في الطرفين
+
+501
+00:54:35,590 --> 00:54:41,550
+يبقى ال a naught كده تساوي؟ يبقى a naught تساوي
+
+502
+00:54:41,550 --> 00:54:49,850
+واحد الآن ستة a naught زائد a one تساوي كده؟ Zero
+
+503
+00:54:49,850 --> 00:54:57,690
+a naught كده؟ واحد يبقى هذا يعطيك أن a one يساوي
+
+504
+00:54:57,690 --> 00:55:05,950
+كده؟ سالب ستة الآن أربعة a node زائد ثلاثة a one
+
+505
+00:55:05,950 --> 00:55:10,710
+زائد a two بده يساوي zero لأنه ماعنديش هنا
+
+506
+00:55:10,710 --> 00:55:17,550
+constant تمام المعلومات اللي حصلتها دي عليها هناها
+
+507
+00:55:17,550 --> 00:55:22,530
+بده نستخدمها في مين في المعادلة الثالثة يبقى a
+
+508
+00:55:22,530 --> 00:55:28,990
+node بواحد بضل أربعة وهندك a1 بناقص 6 يبقى ناقص 3
+
+509
+00:55:28,990 --> 00:55:40,990
+في 6 ب 18 زائد a2 يساوي 0 يبقى a2 يساوي a2 بده
+
+510
+00:55:40,990 --> 00:55:45,770
+يساوي هنا بيبقى ناقص 14 وديها على الشجرة الثانية
+
+511
+00:55:45,770 --> 00:55:54,680
+بصير 14 يبقى أصبح capital Y1 of 3 اللي فوق بده نشيل
+
+512
+00:55:54,680 --> 00:56:00,620
+ال a نقطة وحط بدل 1 يبقى بوضع ال T تربيع بده نشيل ال
+
+513
+00:56:00,620 --> 00:56:08,060
+a1 وحط مكانها ناقص 6T أو بده نشيل ال a2 وحط مكانها
+
+514
+00:56:08,060 --> 00:56:13,760
+قداش 14 اللي عملناه هنا بده نروح نكرر المعادلة
+
+515
+00:56:13,760 --> 00:56:19,310
+الثانية يبقى بدنا نيجي للمعادلة رقم اثنين لأن اثنين y w
+
+516
+00:56:19,310 --> 00:56:26,030
+prime يبقى هذه بتضربها في قداش؟ في اثنين يبقى سالب
+
+517
+00:56:26,030 --> 00:56:34,430
+اثنين a sine t سالب اثنين b cosine t ثلاثة في ال y
+
+518
+00:56:34,430 --> 00:56:41,040
+prime يبقى هذه بتضربها في ثلاثة زائد ثلاثةA cosine
+
+519
+00:56:41,040 --> 00:56:50,320
+of T ناقص ثلاثة B sine of T بعدها زائد Y Y هي فوق
+
+520
+00:56:50,320 --> 00:56:58,080
+يبقى زائد اللي هو مين A في sine of T زائد B في
+
+521
+00:56:58,080 --> 00:57:06,900
+cosine of T كله بده يساوي ثلاثة في sine of T نيجي
+
+522
+00:57:06,900 --> 00:57:13,380
+نشوف سالب اثنين ايه ال sign التي وايه ال sign
+
+523
+00:57:13,380 --> 00:57:21,840
+التي ما فيش غيرها يبقى هذه وهذه بضل ناقص ايه في ال
+
+524
+00:57:21,840 --> 00:57:33,250
+sine التي ناقص اثنين بي كوساين ال T وبي كوساين ال T و
+
+525
+00:57:33,250 --> 00:57:41,570
+بي كوساين ال T بضل ناقص بي في كوساين ال T يبقى هذه و
+
+526
+00:57:41,570 --> 00:57:48,790
+هذه راحة بضل عندك ثلاثة A كوساين ال T زائد ثلاثة A
+
+527
+00:57:48,790 --> 00:58:00,520
+كوساين ال T ناقص ثلاثة بي في ساين ال T بدي أجمع
+
+528
+00:58:00,520 --> 00:58:07,220
+اللي فيهم ساين مع بعض يبقى يا بنات هذه ناقص A و
+
+529
+00:58:07,220 --> 00:58:18,500
+ناقص ثلاثة بي كله في ساين ال T وزائد ثلاثة A ناقص B
+
+530
+00:58:18,500 --> 00:58:26,900
+في cos T بيكون ثلاثة sin T نعمل مقارنة ما بين
+
+531
+00:58:26,900 --> 00:58:39,380
+الطرفين يبقى ناقص B ناقص A ناقص A ناقص ثلاثة B في
+
+532
+00:58:39,380 --> 00:58:43,680
+sin T بيكون ثلاثة
+
+533
+00:58:44,360 --> 00:58:51,220
+اللي بعدها ثلاثة a ناقص ال b بده يساوي كداش Zero
+
+534
+00:58:51,220 --> 00:58:55,580
+لإن ما عنديش cosine على الشجرة الثانية معادلتين
+
+535
+00:58:55,580 --> 00:58:59,860
+بمجهولين بدي أحل المعادلتين هذول مع بعض وأشوف
+
+536
+00:58:59,860 --> 00:59:05,160
+كداش النتيجة أقول لو روحت ضربت المعادلة الأولى في
+
+537
+00:59:05,160 --> 00:59:13,780
+ثلاثة بصير ناقص ثلاثة a ناقص تسعة b بده يساوي تسعة
+
+538
+00:59:14,090 --> 00:59:20,990
+وهنا هذه خلتها زي ما هي ناقص B يساوي Zero وجيت
+
+539
+00:59:20,990 --> 00:59:26,910
+جمع بيروحوا هذول مع بعض يبقى هذا بيصير ناقص عشرة
+
+540
+00:59:26,910 --> 00:59:36,930
+B يساوي تسعة ومنها B يساوي ناقص تسعة على عشرة جبت ال B
+
+541
+00:59:36,930 --> 00:59:44,850
+بروح أجيب من ال A يبقى ال A بقدر أجيبها من هنا من
+
+542
+00:59:44,850 --> 00:59:54,190
+المعادلة هذه 3A بده يساوي B بده يساوي قداش ناقص 9
+
+543
+00:59:54,190 --> 01:00:01,750
+على 10 بدي ايه؟ بقسم كله على قداش على ثلاثة يبقى
+
+544
+01:00:01,750 --> 01:00:09,610
+ايه؟ بناقص ثلاثة على عشرة وهذه مين؟ هذه ال B اللي
+
+545
+01:00:09,610 --> 01:00:18,290
+عندنا إذاً إنصار capital Y2 of t بده يساوي ال a
+
+546
+01:00:18,290 --> 01:00:26,790
+عندي بناقص ثلاثة على عشرة في sin t وال b سالب
+
+547
+01:00:26,790 --> 01:00:37,670
+تسعة على عشرة سالب تسعة على عشرة ثمين في cos t طيب جبت
+
+548
+01:00:37,670 --> 01:00:43,890
+y واحد وجبت y اثنين مجموع اثنين بيكوّل لمين ال
+
+549
+01:00:43,890 --> 01:00:48,610
+particular solution يبقى بصير ال particular
+
+550
+01:00:48,610 --> 01:00:55,770
+solution capital Y of T يساوي Y one of T زائد Y
+
+551
+01:00:55,770 --> 01:01:06,100
+two of T ويساوي T تربيع ناقص ستة T زائد أربعة عشر ناقص
+
+552
+01:01:06,100 --> 01:01:13,640
+ثلاثة على عشرة sine T ناقص تسعة على عشرة cosine من
+
+553
+01:01:13,640 --> 01:01:23,220
+cosine T بدنا ال general solution يبقى باجي بقوله
+
+554
+01:01:23,220 --> 01:01:33,100
+the general solution of
+
+555
+01:01:34,090 --> 01:01:51,350
+Equation star is Y يساوي C1 Y1 C2 Y2 Y of T يبقى Y
+
+556
+01:01:51,350 --> 01:02:04,550
+يساوي C1 في E أس ناقص T C2 في E أس ناقص T على 2 زائد
+
+557
+01:02:04,550 --> 01:02:10,590
+ال particular solution يبقى زائد T تربيع ناقص ستة
+
+558
+01:02:10,590 --> 01:02:22,570
+T زائد أربعة عشر ناقص ثلاثة على عشرة sin T ناقص
+
+559
+01:02:22,570 --> 01:02:31,510
+تسعة على عشرة في cos T يبقى هذا ال general solution
+
+560
+01:02:31,510 --> 01:02:38,150
+تبع المعادلة اللي عندنا حد فيكوا ليه التساؤل؟
+
+561
+01:02:38,150 --> 01:02:41,770
+ابقى لاحظ أن حساب ال constant بزهج شوية فبدك تكون
+
+562
+01:02:41,770 --> 01:02:49,130
+patient تكون صبورة شوية مشان ما تخلطش و بشواجه
+
+563
+01:02:49,130 --> 01:02:50,270
+شوية براحة
+
+564
+01:02:56,180 --> 01:03:01,340
+ممكن يجيك سؤال في الامتحان بالشكل هذا وتضطري تقسم
+
+565
+01:03:01,340 --> 01:03:06,860
+المعادلة إلى معادلتين وممكن يجيك مباشرة حل
+
+566
+01:03:06,860 --> 01:03:12,400
+المعادلة لو سكتي وأنت حرة حل براحتك تمام وممكن
+
+567
+01:03:12,400 --> 01:03:16,960
+نعطيك سؤال ونقول لكثير ال particular solution و
+
+568
+01:03:16,960 --> 01:03:20,920
+don't evaluate the constants ما تحسبيش ال constants
+
+569
+01:03:20,920 --> 01:03:24,920
+كيف نعطيك مثال توضيحي على ذلك
+
+570
+01:03:36,060 --> 01:03:45,940
+سؤال الرابع determine a
+
+571
+01:03:45,940 --> 01:03:50,240
+suitable form
+
+572
+01:03:50,240 --> 01:03:57,300
+شكل مناسب for the particular solution
+
+573
+01:04:06,030 --> 01:04:22,070
+على المحلل المحدد Y of T of الاختصارات
+
+574
+01:04:22,070 --> 01:04:25,670
+التالية الاختصارات
+
+575
+01:04:25,670 --> 01:04:29,530
+التالية الاختصارات الاختصارات الاختصارات
+
+576
+01:04:29,530 --> 01:04:30,850
+الاختصارات الاختصارات الاختصارات الاختصارات
+
+577
+01:04:30,850 --> 01:04:33,430
+الاختصارات الاختصارات الاختصارات
+
+578
+01:04:35,340 --> 01:04:40,740
+the constants ما تحسبيش
+
+579
+01:04:40,740 --> 01:04:48,880
+الثوابت نمرا A سؤال عشرين من الكتاب يقول يو اي
+
+580
+01:04:48,880 --> 01:04:57,360
+دابلر prime زائد Y يساوي T في واحد زائد ساين T
+
+581
+01:05:30,140 --> 01:05:36,480
+سؤال مرة ثانية بيقول لي حدد لي شكل مناسب suitable
+
+582
+01:05:36,480 --> 01:05:41,780
+form لمين لل particular solution capital Y of T
+
+583
+01:05:41,780 --> 01:05:46,460
+لكل من المعادلة التفاضلية الثانية وقال لي don't
+
+584
+01:05:46,460 --> 01:05:49,660
+evaluate the consonants لو ما بدناش هيك نحاسب ال
+
+585
+01:05:49,660 --> 01:05:54,180
+consonants بنكتب لكادبين جوسينه بخط غامق حتى كل
+
+586
+01:05:54,180 --> 01:05:57,700
+واحد ما يروح يقعد يقعد يحاسبه لضيع الوقت فيها بيكون
+
+587
+01:05:57,700 --> 01:06:00,620
+السؤال مقصوص لخمس دقائق بدي كله عشر دقائق ولا ربع
+
+588
+01:06:00,620 --> 01:06:03,660
+ساعة مشان نجيب الكون وصلا لا احنا ما بدناش احنا ما بدناش
+
+589
+01:06:03,660 --> 01:06:07,560
+بتعرف تجيبي شكل ال particular solution ولا لأ
+
+590
+01:06:07,560 --> 01:06:12,240
+تمام أعطاني أول مثلة بالشكل اللي عندنا هذا بقوله
+
+591
+01:06:12,240 --> 01:06:15,900
+كويس هذه هي بالشكل هذا لكن احنا ما شفناش في المثال
+
+592
+01:06:15,900 --> 01:06:20,200
+واحد زي ال sign ال T لكن أنا بقدر أكتب هذه على
+
+593
+01:06:20,200 --> 01:06:26,890
+الشكل التالي T زي T في sign ال T يبقى فكيت الجوس
+
+594
+01:06:26,890 --> 01:06:33,030
+وبالتالي صار شكله ملوك يبقى أنا بدنا نيجي ناخد solution
+
+595
+01:06:33,030 --> 01:06:37,610
+بده نحل ال homogeneous في الأول يبقى باجي بقوله
+
+596
+01:06:37,610 --> 01:06:48,490
+let Y تساوي E أس RT ب solution of the differential
+
+597
+01:06:48,490 --> 01:06:59,540
+equation اللي هو YW prime زائد Y يساوي Zero then the
+
+598
+01:06:59,540 --> 01:07:08,900
+characteristic equation is R تربيع زائد واحد يساوي
+
+5
+
+646
+01:12:26,100 --> 01:12:31,140
+particular solution y of t بده يساوي الـ y one اللي 
+
+647
+01:12:31,140 --> 01:12:38,640
+هو الـ a not t زائد الـ a one الـ y two يبقى زائد b
+
+648
+01:12:38,640 --> 01:12:49,900
+not t تربيع زائد b one t في من في صينة t زائد d
+
+649
+01:12:49,900 --> 01:12:58,650
+not t تربيع زائد d one t في منفي cos T يبقى هذا ال
+
+650
+01:12:58,650 --> 01:13:03,990
+particular solution اللي بده إياه اللي بده إياه
+
+651
+01:13:03,990 --> 01:13:07,830
+تمام؟ يبقى أنت يا أنا من قصة من ال particular
+
+652
+01:13:07,830 --> 01:13:12,840
+solution لو قال لي هاتلي الـ general solution بدي
+
+653
+01:13:12,840 --> 01:13:17,000
+أروح أحسب الـ constants دول لكن لو قال لي don't
+
+654
+01:13:17,000 --> 01:13:20,420
+evaluate the constants و هاتلي الـ general solution
+
+655
+01:13:20,420 --> 01:13:24,360
+بجمعله بس هذا و هذاك و بقول له هاي الـ general
+
+656
+01:13:24,360 --> 01:13:28,420
+solution يعطيك العافية تمام؟ بس إن ما كتبليش
+
+657
+01:13:28,420 --> 01:13:32,520
+بنجوسين don't evaluate the constants بدك تروح
+
+658
+01:13:32,520 --> 01:13:38,120
+وتحسبيهم غصباً عنك طيب نيجي ناخد نمرة B من السؤال
+
+659
+01:13:44,780 --> 01:13:53,220
+يبقى نمرة B له سؤال 23 بيقول
+
+660
+01:13:53,220 --> 01:13:58,440
+ليه المعادلة اللي هو نفس السؤال اللي عندنا هذا
+
+661
+01:13:58,440 --> 01:14:03,740
+بديش أغير نص لإنه هذا A وهذا نمرة B مباشرة Y
+
+662
+01:14:03,740 --> 01:14:13,520
+double prime ناقص 4Y prime زائد 4Y بده يساوي 2T
+
+663
+01:14:13,520 --> 01:14:22,570
+تربيعأتنين T ترابيع زائد أربعة T E أس اتنين T
+
+664
+01:14:22,570 --> 01:14:33,530
+أربعة T E أس اتنين T زائد T Sin زائد T Sin اتنين T
+
+665
+01:14:33,530 --> 01:14:36,750
+هذه
+
+666
+01:14:36,750 --> 01:14:42,840
+سميها ليه الـ equation start يبقى هذا الـ equation
+
+667
+01:14:42,840 --> 01:14:47,480
+star نفس المطلوب اللي عندنا هذا بدنا نجيب شكل الـ
+
+668
+01:14:47,480 --> 01:14:52,700
+particular solution بدون ما نحسب man بدون ما نحسب
+
+669
+01:14:52,700 --> 01:14:57,760
+الـ constants بعدين بقوله كويس يبقى هاي الـ solution
+
+670
+01:14:57,760 --> 01:15:00,780
+بعدين
+
+671
+01:15:00,780 --> 01:15:12,970
+بقوله let Y تساوي E أُس RT بأي solution of the
+
+672
+01:15:12,970 --> 01:15:22,310
+differential equation اللي هي ماين YW ناقص أربعة Y
+
+673
+01:15:22,310 --> 01:15:28,670
+زائد أربعة Y تساوي Zero بدنا نجيب ال
+
+674
+01:15:28,670 --> 01:15:35,990
+characteristic equation then The characteristic
+
+675
+01:15:35,990 --> 01:15:46,450
+equation is R تربيع ناقص أربعة R زائد أربعة بده
+
+676
+01:15:46,450 --> 01:15:53,730
+يساوي Zero هذه تعني أن R ناقص اتنين لكل تربيع
+
+677
+01:15:53,730 --> 01:15:59,710
+يساوي Zero يبقى repeated rows R واحد بده يساوي R
+
+678
+01:15:59,710 --> 01:16:06,860
+اتنين بده يساوي قداش يبقى بناء عليه حل الهموجينس YC
+
+679
+01:16:06,860 --> 01:16:17,540
+C1 زائد C2T في E أوس 2T الآن بدنا نيجي لل
+
+680
+01:16:17,540 --> 01:16:21,830
+particular solution يبقى المعادلة هذه ما شاء الله
+
+681
+01:16:21,830 --> 01:16:26,670
+مدرجة تانية مدرجة الأولى في exponential مدرجة
+
+682
+01:16:26,670 --> 01:16:32,350
+الأولى في sine يعني لما للجدول كله راح ولا لا يبقى
+
+683
+01:16:32,350 --> 01:16:39,150
+لما .. يعني إجباري بدي أفصلها لقداش لتلت معادلات
+
+684
+01:16:39,150 --> 01:16:46,690
+مش تنتين يبقى بروح بقوله the differential equation
+
+685
+01:16:46,690 --> 01:16:56,240
+a star is written as يكتب على الشكل التالي الهيمين
+
+686
+01:16:56,240 --> 01:17:07,240
+yw ناقص اربعة y زائد اربعة y يساوي اتنين T تربيع و
+
+687
+01:17:07,240 --> 01:17:12,110
+بده اسمي هذه المعادلة رقم واحد بعد ذلك نعيدها كمان
+
+688
+01:17:12,110 --> 01:17:27,300
+مرة yw'-4y' زاد 4y يساوي 4t في e أقصى 2t هذه
+
+689
+01:17:27,300 --> 01:17:36,460
+المعادلة نسميها رقم 2 ونذهب إلى المعادلة YW'-4Y
+
+690
+01:17:36,460 --> 01:17:46,920
+'زائد 4Y يسامر طرف اليمين T في صين 2T ونسمي هذه
+
+691
+01:17:46,920 --> 01:17:53,410
+المعادلة رقم 3 بدي اجيب الـ particular solution لكل
+
+692
+01:17:53,410 --> 01:17:57,230
+معادلة من المعادلات الثلاث
+
+693
+01:18:19,720 --> 01:18:24,980
+أنا برجع للمعادلة الأولى وبدي اجيب الـ particular
+
+694
+01:18:24,980 --> 01:18:32,260
+solution فبروح بقوله capital Y1 of T بدي يساوي T
+
+695
+01:18:32,260 --> 01:18:38,300
+to the power S فيه هذي polynomial من الدرجة يبقى
+
+696
+01:18:38,300 --> 01:18:47,100
+بدروح اقوله a نقطة تربيع زائد a one T زائد a two
+
+697
+01:18:56,030 --> 01:19:01,490
+هل تشبه أي term من هنا لأ لأنه ماعنديش exponential
+
+698
+01:19:01,490 --> 01:19:05,150
+صحيح اللي بين قوسين من ضر يقولوا بس مضروبة في
+
+699
+01:19:05,150 --> 01:19:08,990
+exponential ماعنديش exponential على الإطلاق يبقى
+
+700
+01:19:08,990 --> 01:19:15,930
+هنا S بقداش يبقى هنا بصير S تساوي Zero يبقى أصبح
+
+701
+01:19:15,930 --> 01:19:22,850
+capital Y one of T بدي ساوي a not t تربيه زائد a
+
+702
+01:19:22,850 --> 01:19:30,170
+one t زائد a two تهيلة منها نيجي لهذه بدي capital
+
+703
+01:19:30,170 --> 01:19:37,390
+Y two of T T to the power S فيه طلعي لهذه
+
+704
+01:19:37,390 --> 01:19:42,130
+polynomial من الدرجة الأولى في الـ exponential إذا
+
+705
+01:19:42,130 --> 01:19:46,090
+بدي أكتبها polynomial من الدرجة الأولى في الـ
+
+706
+01:19:46,090 --> 01:19:50,510
+exponential بس بروحش أستخدم الرموز هذه بدي أجيب
+
+707
+01:19:50,510 --> 01:20:00,790
+غيرها يبقى بروح بقوله B0T زائد B1 كلها في E أس
+
+708
+01:20:00,790 --> 01:20:08,030
+اتنين T و بعد ذلك بقول استنى شوية تعالى نشوف قداش
+
+709
+01:20:08,030 --> 01:20:14,150
+اسم بغطي هذه و باجي فى المقدار بين القوسين و
+
+710
+01:20:14,150 --> 01:20:20,210
+بقارنه مع حل الـ homogenous differential equation
+
+711
+01:20:20,210 --> 01:20:24,830
+في constant فيه يوسع اتنين T و أنا عند هنا
+
+712
+01:20:24,830 --> 01:20:29,490
+constant فيه يوسع اتنين T يبقى فيه تشابه يبدأ أحط S
+
+713
+01:20:29,490 --> 01:20:37,070
+بقداش لو حطيت S بواحد بصير B not T تربيع تمام
+
+714
+01:20:37,070 --> 01:20:41,750
+ماعنديش الحمد لله تتربيع بس بيبقى B one T في ال
+
+715
+01:20:41,750 --> 01:20:47,610
+exponential موجود هنا يبقى S تساوي واحد لا تفيه
+
+716
+01:20:47,610 --> 01:20:53,770
+بالغرض وإنما S بقداش يبقى لو حطيت S تساوي اتنين
+
+717
+01:20:53,770 --> 01:20:58,970
+بضل تشابه عندي لأ اللاحظة لما كتبتلك الجدول في
+
+718
+01:20:58,970 --> 01:21:02,650
+بداية المعادلة قولتلك S يا Zero يا واحد يا اتنين
+
+719
+01:21:02,650 --> 01:21:08,190
+لا تزيد على ذلك في المعادلة من الرتبة الثانية لك
+
+720
+01:21:08,190 --> 01:21:11,650
+لو صارت تلتة و رابعة يمكن جيب تلاتة او اربعة او
+
+721
+01:21:11,650 --> 01:21:15,010
+خمسة كمان بس هذا موضوع الشابتر اللي جاي إن شاء
+
+722
+01:21:15,010 --> 01:21:19,450
+الله اللي هو شابتر أربعة تمام يبقى الـ S تساوي اتنين
+
+723
+01:21:19,450 --> 01:21:28,070
+إذا صار capital Y2 of T بده يساوي B0 T تكعيب
+
+724
+01:21:28,070 --> 01:21:39,110
+زائد B1 T تربيع في E أس اتنين T تمام طيب بدنا نيجي
+
+725
+01:21:39,110 --> 01:21:47,990
+لمين لسؤال رقم تلاتة بنذهب نجيب Y3 as a function of
+
+726
+01:21:47,990 --> 01:21:54,910
+T يبقى T to the power S في Polynomial
+
+727
+01:21:54,910 --> 01:21:59,830
+من الدرجة الأولى في Sine إذا بالزمن Polynomial من
+
+728
+01:21:59,830 --> 01:22:03,710
+الدرجة الأولى في Sine و Polynomial من الدرجة
+
+729
+01:22:03,710 --> 01:22:08,190
+الأولى في Cosine و Exponential ماله ماعنديش يبقى
+
+730
+01:22:08,190 --> 01:22:11,510
+بدنا نجي نكتب Polynomial من الدرجة الأولى في Sine
+
+731
+01:22:11,510 --> 01:22:14,770
+والرموز اللي استخدمتها الإيهات والبيهات انسوا
+
+732
+01:22:14,770 --> 01:22:19,160
+الموضوع و السيهات يلحقوهم لإن السيهات كتبناهم هنا
+
+733
+01:22:19,160 --> 01:22:24,440
+يبقى دي و إيه بناخد يبقى باجي بقول له هذه بقدر
+
+734
+01:22:24,440 --> 01:22:32,940
+أكتبها D نوت تي زائد D وان في صين اتنين تي زائد
+
+735
+01:22:32,940 --> 01:22:41,600
+E نوت تي زائد E وان كله في قصين اتنين تي
+
+736
+01:22:41,600 --> 01:22:47,760
+وهيقفلنا بعد هيك هاي القوس الكبير بدأ من هنا وقفل
+
+737
+01:22:47,760 --> 01:22:53,860
+هنا و الـ T تدبر S مضروبة في الكل بدنا نيجي نشوف الـ
+
+738
+01:22:53,860 --> 01:23:02,880
+S هل يوجد عندي constant في T في صيني 2T constant
+
+739
+01:23:02,880 --> 01:23:06,360
+ماعنديش الحمد لله الصيني ولا كتر يا ريح دماغك
+
+740
+01:23:06,360 --> 01:23:13,600
+بالمرة يبقى هنا S بقداش؟ 0 يبقى هنا الـ S بدها تساوي
+
+741
+01:23:13,600 --> 01:23:20,200
+0 يبقى بناء علي Y تلاتة as a function of T بده
+
+742
+01:23:20,200 --> 01:23:31,200
+يساوي D NOT T زائد D 1 كله في sin 2T زائد E NOT T
+
+743
+01:23:31,200 --> 01:23:37,240
+زائد E 1 في cos 2T
+
+744
+01:23:39,280 --> 01:23:44,600
+قال لي هات الـ particular solution يبقى باجي بقوله
+
+745
+01:23:44,600 --> 01:23:50,060
+the particular solution
+
+746
+01:23:50,060 --> 01:24:00,560
+of equation star is capital Y of T بده يسوي
+
+747
+01:24:00,560 --> 01:24:10,170
+capital Y1 of T capital Y2 of T زائد capital Y3 of
+
+748
+01:24:10,170 --> 01:24:19,350
+T يبقى capital Y of T يبقى يساوي الأولان هو A0 T
+
+749
+01:24:19,350 --> 01:24:31,950
+ترابيع زائد A1 T زائد A2 capital Y2 B0 T تكعيب B0
+
+750
+01:24:31,950 --> 01:24:46,300
+T تكعيب زائد B0 T ب1t تربيع ب1t تربيع في E أش اتنين
+
+751
+01:24:46,300 --> 01:24:56,820
+T E أش اتنين T زائد اللي بعده D نقدر T زائد D one
+
+752
+01:24:56,820 --> 01:25:00,100
+تمام في Sine اتنين T
+
+753
+01:25:12,300 --> 01:25:15,500
+يبقى هذا الـ particular solution
+
+754
+01:25:17,530 --> 01:25:21,590
+الآن لحد هيك انتهى الـ section بنات و إلى يكون
+
+755
+01:25:21,590 --> 01:25:30,290
+أرقام المسائل أكثر الـ sizes تلاتة ستة المسائل من
+
+756
+01:25:30,290 --> 01:25:41,060
+واحد لغاية تمنتاشر الـ even ومن تسعة عشر لغاية ستة
+
+757
+01:25:41,060 --> 01:25:50,480
+وعشرين part A فقط بدنا الـ odd يالا خليهم مرة
+
+758
+01:25:50,480 --> 01:25:57,400
+even ومرة odd الآن ضايل عندنا هو section تلاتة
+
+759
+01:25:57,400 --> 01:25:57,820
+سبعة 
diff --git a/PL9fwy3NUQKwa8ZDfSFGn6H8xVFLzqmCZC/VYRFN1d1OwA_raw.json b/PL9fwy3NUQKwa8ZDfSFGn6H8xVFLzqmCZC/VYRFN1d1OwA_raw.json
new file mode 100644
index 0000000000000000000000000000000000000000..5aadea78258054bccca88a43b7b42070ed94169e
--- /dev/null
+++ b/PL9fwy3NUQKwa8ZDfSFGn6H8xVFLzqmCZC/VYRFN1d1OwA_raw.json
@@ -0,0 +1 @@
+{"segments": [{"id": 1, "seek": 1178, "start": 9.58, "end": 11.78, "text": "بسم الله الرحمن الرحيم", "tokens": [3555, 38251, 21984, 34892, 5016, 27842, 34892, 5016, 32640], "avg_logprob": -0.09643554612994194, "compression_ratio": 1.0789473684210527, "no_speech_prob": 0.0, "words": [{"start": 9.580000000000002, "end": 10.56, "word": "بسم", "probability": 0.748291015625}, {"start": 10.56, "end": 10.8, "word": " الله", "probability": 0.96484375}, {"start": 10.8, "end": 11.2, "word": " الرحمن", "probability": 0.9264322916666666}, {"start": 11.2, "end": 11.78, "word": " الرحيم", "probability": 0.9930013020833334}], "temperature": 1.0}, {"id": 2, "seek": 3233, "start": 13.23, "end": 32.33, "text": "بنذكر بالاخر نظرية قولناها المرة اللي فاتة لإنه بنبدأ دراستنا عليها اليوم على النظرية الماضية ان شاء الله تبارك وتعالى طبعا موضوعنا موضوع اللي هو ال non homogeneous differential equation بنحلها بطريقة", "tokens": [3555, 1863, 8848, 37983, 20666, 47283, 2288, 8717, 19913, 2288, 10632, 12174, 12610, 8315, 11296, 9673, 25720, 13672, 1829, 6156, 9307, 3660, 5296, 28814, 1863, 3224, 44945, 44510, 10721, 11778, 23557, 14851, 8315, 25894, 11296, 45595, 20498, 15844, 28239, 19913, 2288, 10632, 9673, 46958, 10632, 16472, 13412, 16606, 21984, 6055, 3555, 9640, 4117, 34683, 3615, 6027, 7578, 23032, 3555, 3615, 995, 3714, 2407, 11242, 45367, 8315, 3714, 2407, 11242, 45367, 13672, 1829, 31439, 2423, 2107, 42632, 15756, 5367, 44945, 5016, 1211, 11296, 4724, 9566, 16572, 28671], "avg_logprob": -0.17465876847848125, "compression_ratio": 1.6105769230769231, "no_speech_prob": 0.0, "words": [{"start": 13.23, "end": 14.05, "word": "بنذكر", "probability": 0.70635986328125}, {"start": 14.05, "end": 14.91, "word": " بالاخر", "probability": 0.71484375}, {"start": 14.91, "end": 15.37, "word": " نظرية", "probability": 0.974609375}, {"start": 15.37, "end": 15.87, "word": " قولناها", "probability": 0.8243408203125}, {"start": 15.87, "end": 16.19, "word": " المرة", "probability": 0.8466796875}, {"start": 16.19, "end": 16.37, "word": " اللي", "probability": 0.6630859375}, {"start": 16.37, "end": 16.71, "word": " فاتة", "probability": 0.7408854166666666}, {"start": 16.71, "end": 16.99, "word": " لإنه", "probability": 0.634765625}, {"start": 16.99, "end": 17.63, "word": " بنبدأ", "probability": 0.7310384114583334}, {"start": 17.63, "end": 18.37, "word": " دراستنا", "probability": 0.96533203125}, {"start": 18.37, "end": 19.05, "word": " عليها", "probability": 0.9814453125}, {"start": 19.05, "end": 19.83, "word": " اليوم", "probability": 0.934326171875}, {"start": 19.83, "end": 20.07, "word": " على", "probability": 0.8994140625}, {"start": 20.07, "end": 20.91, "word": " النظرية", "probability": 0.9671630859375}, {"start": 20.91, "end": 22.35, "word": " الماضية", "probability": 0.994140625}, {"start": 22.35, "end": 22.87, "word": " ان", "probability": 0.58154296875}, {"start": 22.87, "end": 23.23, "word": " شاء", "probability": 0.951904296875}, {"start": 23.23, "end": 23.51, "word": " الله", "probability": 0.93212890625}, {"start": 23.51, "end": 24.03, "word": " تبارك", "probability": 0.8995361328125}, {"start": 24.03, "end": 24.71, "word": " وتعالى", "probability": 0.86932373046875}, {"start": 24.71, "end": 26.09, "word": " طبعا", "probability": 0.9281005859375}, {"start": 26.09, "end": 26.71, "word": " موضوعنا", "probability": 0.98046875}, {"start": 26.71, "end": 27.77, "word": " موضوع", "probability": 0.9302978515625}, {"start": 27.77, "end": 28.15, "word": " اللي", "probability": 0.938720703125}, {"start": 28.15, "end": 28.31, "word": " هو", "probability": 0.9775390625}, {"start": 28.31, "end": 28.47, "word": " ال", "probability": 0.51806640625}, {"start": 28.47, "end": 28.75, "word": " non", "probability": 0.6865234375}, {"start": 28.75, "end": 29.45, "word": " homogeneous", "probability": 0.54248046875}, {"start": 29.45, "end": 30.03, "word": " differential", "probability": 0.87744140625}, {"start": 30.03, "end": 30.69, "word": " equation", "probability": 0.97705078125}, {"start": 30.69, "end": 31.45, "word": " بنحلها", "probability": 0.9326171875}, {"start": 31.45, "end": 32.33, "word": " بطريقة", "probability": 0.9677734375}], "temperature": 1.0}, {"id": 3, "seek": 5409, "start": 32.65, "end": 54.09, "text": "الـ undetermined coefficients يعني المعاملات المجهولة تمام؟ آخر نظرية قلناها المرة اللي فاتت أنه لو عندي non-homogeneous differential equation مثل هذه مثلا كويس second order non-homogeneous differential equation", "tokens": [6027, 39184, 674, 35344, 2001, 31994, 37495, 22653, 9673, 3615, 10943, 1211, 9307, 9673, 7435, 3224, 12610, 3660, 46811, 10943, 22807, 19753, 34740, 8717, 19913, 2288, 10632, 12174, 1211, 8315, 11296, 9673, 25720, 13672, 1829, 6156, 9307, 2655, 14739, 3224, 45164, 18871, 16254, 2107, 12, 71, 298, 31112, 15756, 5367, 50113, 1211, 29538, 50113, 15040, 9122, 45865, 3794, 1150, 1668, 2107, 12, 71, 298, 31112, 15756, 5367], "avg_logprob": -0.22690716604976094, "compression_ratio": 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"probability": 0.9983723958333334}, {"start": 425.99, "end": 426.21, "word": " ال", "probability": 0.9375}, {"start": 426.21, "end": 426.63, "word": " S", "probability": 0.66455078125}, {"start": 426.63, "end": 427.27, "word": " هذه", "probability": 0.6591796875}, {"start": 427.27, "end": 428.09, "word": " تعالى", "probability": 0.8815104166666666}, {"start": 428.09, "end": 428.43, "word": " نشوف", "probability": 0.9964192708333334}], "temperature": 1.0}, {"id": 21, "seek": 44163, "start": 429.87, "end": 441.63, "text": "هذه هي المعادلة الأصلية اخذت ال homogenous differential equation و طلعت الحالتها c1y1 زائد c2y2 زائد c2y2", "tokens": [3224, 24192, 39896, 9673, 3615, 18513, 37977, 16247, 36520, 10632, 1975, 9778, 8848, 2655, 2423, 3655, 45519, 15756, 5367, 4032, 23032, 1211, 34268, 21542, 6027, 2655, 11296, 269, 16, 88, 16, 30767, 16373, 3215, 269, 17, 88, 17, 30767, 16373, 3215, 269, 17, 88, 17], "avg_logprob": -0.46637227029904077, "compression_ratio": 1.2063492063492063, 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"word": " T", "probability": 0.8369140625}, {"start": 569.28, "end": 570.42, "word": " تربيع", "probability": 0.803466796875}], "temperature": 1.0}, {"id": 28, "seek": 59492, "start": 570.71, "end": 594.93, "text": "طبعا من حد مجروف يتيه تربية لايمكن يتلاقي term في ال particular solution يشبه أي term في الحل ال non homogeneous differential equation ماشي يا بنات يبقى من الأن فصاعدا بدي ألخص الكلام اللي قلته مرة ثانية عشان اللي أجيبه التأخرات", "tokens": [9566, 3555, 3615, 995, 9154, 11331, 3215, 3714, 7435, 32887, 5172, 7251, 31371, 3224, 6055, 25513, 10632, 20193, 32640, 19452, 7251, 2655, 15040, 38436, 1433, 8978, 2423, 1729, 3827, 7251, 8592, 3555, 3224, 36632, 1433, 8978, 21542, 1211, 2423, 2107, 42632, 15756, 5367, 3714, 33599, 1829, 35186, 4724, 8315, 2655, 7251, 3555, 4587, 7578, 9154, 16247, 1863, 6156, 9381, 995, 22488, 995, 4724, 16254, 5551, 1211, 9778, 9381, 2423, 28820, 10943, 13672, 1829, 12174, 1211, 47395, 3714, 25720, 38637, 7649, 10632, 6225, 8592, 7649, 13672, 1829, 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{"start": 585.55, "end": 586.03, "word": " equation", "probability": 0.39990234375}, {"start": 586.03, "end": 586.75, "word": " ماشي", "probability": 0.6827799479166666}, {"start": 586.75, "end": 586.87, "word": " يا", "probability": 0.85986328125}, {"start": 586.87, "end": 587.29, "word": " بنات", "probability": 0.7394205729166666}, {"start": 587.29, "end": 588.13, "word": " يبقى", "probability": 0.9432373046875}, {"start": 588.13, "end": 588.29, "word": " من", "probability": 0.9638671875}, {"start": 588.29, "end": 589.05, "word": " الأن", "probability": 0.69873046875}, {"start": 589.05, "end": 590.23, "word": " فصاعدا", "probability": 0.90888671875}, {"start": 590.23, "end": 590.71, "word": " بدي", "probability": 0.3797607421875}, {"start": 590.71, "end": 591.21, "word": " ألخص", "probability": 0.91015625}, {"start": 591.21, "end": 591.69, "word": " الكلام", "probability": 0.9064127604166666}, {"start": 591.69, "end": 591.85, "word": " اللي", "probability": 0.904052734375}, {"start": 591.85, "end": 592.25, "word": " قلته", "probability": 0.953125}, {"start": 592.25, "end": 592.77, "word": " مرة", "probability": 0.97607421875}, {"start": 592.77, "end": 593.41, "word": " ثانية", "probability": 0.9915364583333334}, {"start": 593.41, "end": 593.79, "word": " عشان", "probability": 0.750732421875}, {"start": 593.79, "end": 593.95, "word": " اللي", "probability": 0.955810546875}, {"start": 593.95, "end": 594.35, "word": " أجيبه", "probability": 0.785009765625}, {"start": 594.35, "end": 594.93, "word": " التأخرات", "probability": 0.7705078125}], "temperature": 1.0}, {"id": 29, "seek": 61736, "start": 595.38, "end": 617.36, "text": "نحل الـ Non-homogeneous differential equation بالشكل هذا اللي المعاملات كلها ثوابت وG of T على أي شكل من الأشكال التلاتة اللي عندنا هذه تمام؟ مش أنا حل ههه أول ما ابدوا باطلع في المعادلة اللي عندى المعاملات تبعت ثوابت ماشي الحال", "tokens": [1863, 5016, 1211, 2423, 39184, 8774, 12, 71, 298, 31112, 15756, 5367, 20666, 8592, 28820, 23758, 13672, 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differential", "probability": 0.8359375}, {"start": 598.48, "end": 599.18, "word": " equation", "probability": 0.94970703125}, {"start": 599.18, "end": 599.86, "word": " بالشكل", "probability": 0.8865559895833334}, {"start": 599.86, "end": 600.36, "word": " هذا", "probability": 0.78857421875}, {"start": 600.36, "end": 601.0, "word": " اللي", "probability": 0.595458984375}, {"start": 601.0, "end": 601.94, "word": " المعاملات", "probability": 0.91083984375}, {"start": 601.94, "end": 602.52, "word": " كلها", "probability": 0.856201171875}, {"start": 602.52, "end": 603.16, "word": " ثوابت", "probability": 0.910888671875}, {"start": 603.16, "end": 603.72, "word": " وG", "probability": 0.552734375}, {"start": 603.72, "end": 604.06, "word": " of", "probability": 0.368408203125}, {"start": 604.06, "end": 604.38, "word": " T", "probability": 0.900390625}, {"start": 604.38, "end": 604.8, "word": " على", "probability": 0.8310546875}, {"start": 604.8, "end": 605.08, "word": " أي", "probability": 0.78466796875}, {"start": 605.08, "end": 605.54, "word": " شكل", "probability": 0.968017578125}, {"start": 605.54, "end": 605.76, "word": " من", "probability": 0.9775390625}, {"start": 605.76, "end": 606.48, "word": " الأشكال", "probability": 0.9613037109375}, {"start": 606.48, "end": 607.16, "word": " التلاتة", "probability": 0.8885498046875}, {"start": 607.16, "end": 607.28, "word": " اللي", "probability": 0.827880859375}, {"start": 607.28, "end": 607.64, "word": " عندنا", "probability": 0.972412109375}, {"start": 607.64, "end": 607.92, "word": " هذه", "probability": 0.505859375}, {"start": 607.92, "end": 609.7, "word": " تمام؟", "probability": 0.55615234375}, {"start": 609.7, "end": 610.24, "word": " مش", "probability": 0.9365234375}, {"start": 610.24, "end": 610.46, "word": " أنا", "probability": 0.5400390625}, {"start": 610.46, "end": 610.94, "word": " حل", "probability": 0.823486328125}, {"start": 610.94, "end": 611.5, "word": " ههه", "probability": 0.5812174479166666}, {"start": 611.5, "end": 612.1, "word": " أول", "probability": 0.6962890625}, {"start": 612.1, "end": 612.3, "word": " ما", "probability": 0.490478515625}, {"start": 612.3, "end": 612.52, "word": " ابدوا", "probability": 0.428955078125}, {"start": 612.52, "end": 613.1, "word": " باطلع", "probability": 0.74755859375}, {"start": 613.1, "end": 613.26, "word": " في", "probability": 0.90966796875}, {"start": 613.26, "end": 613.8, "word": " المعادلة", "probability": 0.8865966796875}, {"start": 613.8, "end": 614.14, "word": " اللي", "probability": 0.96923828125}, {"start": 614.14, "end": 614.26, "word": " عندى", "probability": 0.662109375}, {"start": 614.26, "end": 615.56, "word": " المعاملات", "probability": 0.92880859375}, {"start": 615.56, "end": 615.98, "word": " تبعت", "probability": 0.8577473958333334}, {"start": 615.98, "end": 616.6, "word": " ثوابت", "probability": 0.9312744140625}, {"start": 616.6, "end": 616.96, "word": " ماشي", "probability": 0.9034830729166666}, {"start": 616.96, "end": 617.36, "word": " الحال", "probability": 0.9384765625}], "temperature": 1.0}, {"id": 30, "seek": 63338, "start": 617.66, "end": 633.38, "text": "عن طريق جي وف تي بدي اتطلع فيها اي شكل من الأشكال هذه موجود اذا بقدر احل بال undetermined coefficients طيب كيف بدي اسوي؟ بدي اخد ال homogeneous differential equation اللي عندى هذا في الاول قبل المبدأ", "tokens": [3615, 1863, 23032, 16572, 4587, 10874, 1829, 4032, 5172, 6055, 1829, 4724, 16254, 1975, 2655, 9566, 1211, 3615, 8978, 11296, 1975, 1829, 13412, 28820, 9154, 16247, 8592, 4117, 6027, 29538, 3714, 29245, 23328, 1975, 15730, 4724, 28543, 2288, 1975, 5016, 1211, 20666, 674, 35344, 2001, 31994, 23032, 1829, 3555, 9122, 33911, 4724, 16254, 24525, 45865, 22807, 4724, 16254, 1975, 9778, 3215, 2423, 42632, 15756, 5367, 13672, 1829, 43242, 7578, 23758, 8978, 42963, 12610, 12174, 36150, 9673, 44510, 10721], "avg_logprob": -0.3878560111492495, "compression_ratio": 1.4549763033175356, "no_speech_prob": 0.0, "words": [{"start": 617.66, "end": 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"probability": 0.7294921875}, {"start": 621.96, "end": 623.22, "word": " موجود", "probability": 0.97216796875}, {"start": 623.22, "end": 623.82, "word": " اذا", "probability": 0.650634765625}, {"start": 623.82, "end": 624.4, "word": " بقدر", "probability": 0.9501953125}, {"start": 624.4, "end": 624.64, "word": " احل", "probability": 0.8426106770833334}, {"start": 624.64, "end": 624.8, "word": " بال", "probability": 0.94482421875}, {"start": 624.8, "end": 625.74, "word": " undetermined", "probability": 0.73876953125}, {"start": 625.74, "end": 626.54, "word": " coefficients", "probability": 0.85107421875}, {"start": 626.54, "end": 627.38, "word": " طيب", "probability": 0.8826497395833334}, {"start": 627.38, "end": 627.64, "word": " كيف", "probability": 0.6103515625}, {"start": 627.64, "end": 627.82, "word": " بدي", "probability": 0.76025390625}, {"start": 627.82, "end": 628.72, "word": " اسوي؟", "probability": 0.6739095052083334}, {"start": 628.72, "end": 628.94, "word": " بدي", "probability": 0.84326171875}, {"start": 628.94, "end": 629.28, "word": " اخد", "probability": 0.8346354166666666}, {"start": 629.28, "end": 629.38, "word": " ال", "probability": 0.966796875}, {"start": 629.38, "end": 629.9, "word": " homogeneous", "probability": 0.473876953125}, {"start": 629.9, "end": 630.62, "word": " differential", "probability": 0.85791015625}, {"start": 630.62, "end": 631.12, "word": " equation", "probability": 0.97705078125}, {"start": 631.12, "end": 631.28, "word": " اللي", "probability": 0.84326171875}, {"start": 631.28, "end": 631.64, "word": " عندى", "probability": 0.788330078125}, {"start": 631.64, "end": 631.88, "word": " هذا", "probability": 0.25927734375}, {"start": 631.88, "end": 632.04, "word": " في", "probability": 0.837890625}, {"start": 632.04, "end": 632.5, "word": " الاول", "probability": 0.752197265625}, {"start": 632.5, "end": 632.88, "word": " قبل", "probability": 0.939208984375}, {"start": 632.88, "end": 633.38, "word": " المبدأ", "probability": 0.9641927083333334}], "temperature": 1.0}, {"id": 31, "seek": 65477, "start": 633.55, "end": 654.77, "text": "و طلع الحل تبعها زي ما كنا بنحل في ال sections الماضية repeated roots, unrepeated roots, complex roots أو complex conjugate roots تمام؟ جيبنا الحل بنبرز و بنقول له قعد ع الشجة لسه بدنا نرجعلك بدنا نيجي نجيب شكل ال particular solution شكل ال particular solution", "tokens": [2407, 23032, 1211, 3615, 21542, 1211, 6055, 3555, 3615, 11296, 30767, 1829, 19446, 9122, 8315, 44945, 5016, 1211, 8978, 2423, 10863, 9673, 46958, 10632, 10477, 10669, 11, 20584, 494, 770, 10669, 11, 3997, 10669, 34051, 3997, 45064, 10669, 46811, 10943, 22807, 10874, 1829, 3555, 8315, 21542, 1211, 44945, 26890, 11622, 4032, 44945, 39648, 46740, 12174, 22488, 6225, 25124, 7435, 3660, 5296, 3794, 3224, 47525, 8315, 8717, 47341, 3615, 23275, 47525, 8315, 8717, 1829, 7435, 1829, 8717, 7435, 1829, 3555, 13412, 28820, 2423, 1729, 3827, 13412, 28820, 2423, 1729, 3827], "avg_logprob": 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ناقص", "probability": 0.9947509765625}, {"start": 2304.74, "end": 2305.38, "word": " t", "probability": 0.81884765625}, {"start": 2305.38, "end": 2306.56, "word": " طلعيلي", "probability": 0.84404296875}, {"start": 2306.56, "end": 2306.86, "word": " هذه", "probability": 0.464599609375}, {"start": 2306.86, "end": 2307.02, "word": " و", "probability": 0.68701171875}, {"start": 2307.02, "end": 2307.3, "word": " هذه", "probability": 0.89892578125}, {"start": 2307.3, "end": 2307.8, "word": " اتنين", "probability": 0.930419921875}, {"start": 2307.8, "end": 2308.14, "word": " زي", "probability": 0.97119140625}, {"start": 2308.14, "end": 2308.64, "word": " بعض", "probability": 0.99365234375}], "temperature": 1.0}, {"id": 101, "seek": 233271, "start": 2309.26, "end": 2332.72, "text": "بدي أخدهم مع بعض و أخد ال exponential برا عامل مشترك يبقى هذه بدأ تعطيني الشكل التالي 2A و هنا ناقص 4AT ناقص 4AT و زائد AT تربيع كله في ال exponential E أس ناقص T", "tokens": [3555, 16254, 5551, 9778, 3215, 16095, 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بده يسوى A0 T تربيه زائد A1T زائد A2 و capital Y2 of T بده يسوى من", "tokens": [41185, 6055, 8592, 16758, 3224, 19446, 49374, 34105, 4032, 19446, 49374, 34105, 7251, 3555, 4587, 7578, 9122, 2304, 7649, 318, 4724, 11622, 13546, 2407, 7251, 3555, 4587, 7578, 34105, 9122, 2304, 7649, 318, 4724, 11622, 13546, 2407, 7251, 3555, 4587, 7578, 5551, 9381, 49628, 4238, 398, 16, 295, 314, 8978, 21542, 6027, 3660, 16247, 12610, 7578, 47525, 3224, 7251, 3794, 2407, 7578, 316, 15, 314, 6055, 2288, 21292, 3224, 30767, 16373, 3215, 316, 16, 51, 30767, 16373, 3215, 316, 17, 4032, 4238, 398, 17, 295, 314, 47525, 3224, 7251, 3794, 2407, 7578, 9154], "avg_logprob": -0.18783244458918877, "compression_ratio": 1.75, "no_speech_prob": 0.0, "words": [{"start": 3017.11, "end": 3017.49, "word": "في", "probability": 0.5029296875}, {"start": 3017.49, "end": 3018.71, "word": " تشابه", "probability": 0.9815673828125}, {"start": 3018.71, "end": 3018.97, "word": " ما", "probability": 0.58984375}, {"start": 3018.97, 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" كمان", "probability": 0.9912109375}, {"start": 3025.97, "end": 3026.63, "word": " S", "probability": 0.953125}, {"start": 3026.63, "end": 3027.45, "word": " بزيرو", "probability": 0.9849853515625}, {"start": 3027.45, "end": 3028.19, "word": " يبقى", "probability": 0.978759765625}, {"start": 3028.19, "end": 3028.95, "word": " أصبح", "probability": 0.8912760416666666}, {"start": 3028.95, "end": 3030.11, "word": " capital", "probability": 0.57421875}, {"start": 3030.11, "end": 3031.15, "word": " Y1", "probability": 0.802001953125}, {"start": 3031.15, "end": 3031.91, "word": " of", "probability": 0.908203125}, {"start": 3031.91, "end": 3032.43, "word": " T", "probability": 0.908203125}, {"start": 3032.43, "end": 3032.93, "word": " في", "probability": 0.85205078125}, {"start": 3032.93, "end": 3033.51, "word": " الحالة", "probability": 0.9835611979166666}, {"start": 3033.51, "end": 3033.93, "word": " الأولى", "probability": 0.9777018229166666}, {"start": 3033.93, "end": 3034.17, "word": " بده", "probability": 0.3028564453125}, {"start": 3034.17, "end": 3034.71, "word": " يسوى", "probability": 0.78826904296875}, {"start": 3034.71, "end": 3035.77, "word": " A0", "probability": 0.645263671875}, {"start": 3035.77, "end": 3036.21, "word": " T", "probability": 0.57470703125}, {"start": 3036.21, "end": 3036.91, "word": " تربيه", "probability": 0.65283203125}, {"start": 3036.91, "end": 3037.87, "word": " زائد", "probability": 0.8693033854166666}, {"start": 3037.87, "end": 3039.57, "word": " A1T", "probability": 0.8356119791666666}, {"start": 3039.57, "end": 3040.49, "word": " زائد", "probability": 0.9606119791666666}, {"start": 3040.49, "end": 3041.29, "word": " A2", "probability": 0.99462890625}, {"start": 3041.29, "end": 3042.03, "word": " و", "probability": 0.92822265625}, {"start": 3042.03, "end": 3042.63, "word": " capital", "probability": 0.69580078125}, {"start": 3042.63, "end": 3044.05, "word": " Y2", "probability": 0.9921875}, {"start": 3044.05, "end": 3044.63, "word": " of", "probability": 0.9716796875}, {"start": 3044.63, "end": 3045.17, "word": " T", "probability": 0.98681640625}, {"start": 3045.17, "end": 3045.85, "word": " بده", "probability": 0.965087890625}, {"start": 3045.85, "end": 3046.29, "word": " يسوى", "probability": 0.901611328125}, {"start": 3046.29, "end": 3046.47, "word": " من", "probability": 0.51220703125}], "temperature": 1.0}, {"id": 131, "seek": 307691, "start": 3075.51, "end": 3076.91, "text": "Y1Y1Y1Y1Y1Y1Y1Y1Y1", "tokens": [56, 16, 56, 16, 56, 16, 56, 16, 56, 16, 56, 16, 56, 16, 56, 16, 56, 16], "avg_logprob": -0.4374999968629134, "compression_ratio": 1.5, "no_speech_prob": 0.0, "words": [{"start": 3075.5099999999998, "end": 3076.91, "word": "Y1Y1Y1Y1Y1Y1Y1Y1Y1", "probability": 0.8337809244791666}], "temperature": 1.0}, {"id": 132, "seek": 310181, "start": 3077.05, "end": 3101.81, "text": "بدنا y2 prime as a function of t يبقى a cosine t ناقص b في sine t بدنا y2 double prime as a function of t يبقى ناقص a في sine t ناقص b في cosine من t", "tokens": [44510, 8315, 288, 17, 5835, 382, 257, 2445, 295, 256, 7251, 3555, 4587, 7578, 257, 23565, 256, 8717, 995, 4587, 9381, 272, 8978, 18609, 256, 47525, 8315, 288, 17, 3834, 5835, 382, 257, 2445, 295, 256, 7251, 3555, 4587, 7578, 8717, 995, 4587, 9381, 257, 8978, 18609, 256, 8717, 995, 4587, 9381, 272, 8978, 23565, 9154, 256], "avg_logprob": -0.17793641727546167, "compression_ratio": 1.7289719626168225, "no_speech_prob": 0.0, "words": [{"start": 3077.05, "end": 3077.91, "word": "بدنا", "probability": 0.536224365234375}, {"start": 3077.91, "end": 3079.03, "word": " y2", "probability": 0.6796875}, {"start": 3079.03, "end": 3079.71, "word": " prime", "probability": 0.55517578125}, {"start": 3079.71, "end": 3080.05, "word": " as", "probability": 0.951171875}, {"start": 3080.05, "end": 3080.33, "word": " a", "probability": 0.8603515625}, {"start": 3080.33, "end": 3080.83, "word": " function", "probability": 0.97412109375}, {"start": 3080.83, "end": 3081.13, "word": " of", "probability": 0.98388671875}, {"start": 3081.13, "end": 3081.31, "word": " t", "probability": 0.74462890625}, {"start": 3081.31, "end": 3081.85, "word": " يبقى", "probability": 0.9227294921875}, {"start": 3081.85, "end": 3082.27, "word": " a", "probability": 0.81494140625}, {"start": 3082.27, "end": 3083.11, "word": " cosine", "probability": 0.61669921875}, {"start": 3083.11, "end": 3083.81, "word": " t", "probability": 0.67919921875}, {"start": 3083.81, "end": 3085.05, "word": " ناقص", "probability": 0.8212890625}, {"start": 3085.05, "end": 3085.45, "word": " b", "probability": 0.8232421875}, {"start": 3085.45, "end": 3085.75, "word": " في", "probability": 0.92724609375}, {"start": 3085.75, "end": 3086.93, "word": " sine", "probability": 0.45849609375}, {"start": 3086.93, "end": 3087.47, "word": " t", "probability": 0.455078125}, {"start": 3087.47, "end": 3088.91, "word": " بدنا", "probability": 0.932373046875}, {"start": 3088.91, "end": 3090.19, "word": " y2", "probability": 0.970703125}, {"start": 3090.19, "end": 3090.69, "word": " double", "probability": 0.484619140625}, {"start": 3090.69, "end": 3091.47, "word": " prime", "probability": 0.8857421875}, {"start": 3091.47, "end": 3091.89, "word": " as", "probability": 0.982421875}, {"start": 3091.89, "end": 3092.21, "word": " a", "probability": 0.97119140625}, {"start": 3092.21, "end": 3092.61, "word": " function", "probability": 0.9765625}, {"start": 3092.61, "end": 3093.05, "word": " of", "probability": 0.98095703125}, {"start": 3093.05, "end": 3093.31, "word": " t", "probability": 0.9716796875}, {"start": 3093.31, "end": 3094.21, "word": " يبقى", "probability": 0.98046875}, {"start": 3094.21, "end": 3094.89, "word": " ناقص", "probability": 0.9954833984375}, {"start": 3094.89, "end": 3095.29, "word": " a", "probability": 0.986328125}, {"start": 3095.29, "end": 3095.49, "word": " في", "probability": 0.97900390625}, {"start": 3095.49, "end": 3096.09, "word": " sine", "probability": 0.787109375}, {"start": 3096.09, "end": 3096.73, "word": " t", "probability": 0.95263671875}, {"start": 3096.73, "end": 3098.09, "word": " ناقص", "probability": 0.985595703125}, {"start": 3098.09, "end": 3098.63, "word": " b", "probability": 0.98046875}, {"start": 3098.63, "end": 3099.21, "word": " في", "probability": 0.9716796875}, {"start": 3099.21, "end": 3100.29, "word": " cosine", "probability": 0.94970703125}, {"start": 3100.29, "end": 3100.87, "word": " من", "probability": 0.95947265625}, {"start": 3100.87, "end": 3101.81, "word": " t", "probability": 0.572265625}], "temperature": 1.0}, {"id": 133, "seek": 312988, "start": 3103.46, "end": 3129.88, "text": "اللي فوق سميناها star المعادلة هذي يسميها 1 يا بناتي والمعادلة هذي يسميها لمين اتنين يبقى هدول بتدعوضهم في المعادلة واحد واللي هناك بتدعوضهم اين في المعادلة اتنين يبقى بداجي اقوله صح باسم substitute in equation one we get", "tokens": [6027, 20292, 6156, 30543, 8608, 2304, 1829, 8315, 11296, 3543, 9673, 3615, 18513, 37977, 8032, 8848, 1829, 7251, 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اتنين هي لأ اتنين yw prime لقد اضرب هذه في اتنين يبقى هنا بالداجة و اقول لصابس تت يوت and equation اتنين ويقل طبعا الشركة نخلص واحدة واحدة نمسك هذه", "tokens": [1863, 2304, 3794, 4117, 16712, 7649, 10632, 20666, 2304, 25720, 288, 86, 5835, 39896, 11296, 30767, 1829, 19446, 39896, 16070, 43761, 8978, 1975, 2655, 1863, 9957, 39896, 5296, 10721, 1975, 2655, 1863, 9957, 288, 86, 5835, 5296, 28543, 1975, 11242, 25513, 29538, 8978, 1975, 2655, 1863, 9957, 7251, 3555, 4587, 7578, 34105, 20666, 3215, 26108, 3660, 4032, 1975, 39648, 5296, 9381, 16758, 3794, 6055, 2655, 7251, 35473, 293, 5367, 1975, 2655, 1863, 9957, 4032, 1829, 4587, 1211, 23032, 3555, 3615, 995, 25124, 31747, 3660, 8717, 9778, 1211, 9381, 36764, 24401, 3660, 36764, 24401, 3660, 8717, 2304, 3794, 4117, 29538], "avg_logprob": -0.31281248688697816, "compression_ratio": 1.6567164179104477, "no_speech_prob": 0.0, "words": [{"start": 3187.82, "end": 3188.38, "word": "نمسك", "probability": 0.7972412109375}, {"start": 3188.38, "end": 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3763.65, "word": " تكون", "probability": 0.809326171875}, {"start": 3763.65, "end": 3764.41, "word": " صبورة", "probability": 0.8291015625}, {"start": 3764.41, "end": 3764.97, "word": " شوية", "probability": 0.96875}, {"start": 3764.97, "end": 3765.79, "word": " مشان", "probability": 0.79052734375}, {"start": 3765.79, "end": 3766.69, "word": " ماتخلطش", "probability": 0.7102864583333334}, {"start": 3766.69, "end": 3767.39, "word": " و", "probability": 0.83740234375}, {"start": 3767.39, "end": 3769.13, "word": " بشواجه", "probability": 0.692041015625}, {"start": 3769.13, "end": 3769.65, "word": " شوية", "probability": 0.88134765625}, {"start": 3769.65, "end": 3770.27, "word": " براحة", "probability": 0.8369140625}], "temperature": 1.0}, {"id": 161, "seek": 380492, "start": 3776.18, "end": 3804.92, "text": "ممكن يجيك سؤال في الامتحان بالشكل هذا و تضطري تقسم المعادلة إلى معادلتين و ممكن يجيك مباشرة حل المعادلة لو نسكت و انت حرة حل براحتك تمام و ممكن نعطيك سؤال و نقول كثير ال particular solution و don't evaluate the constants ماتحسبيش ال constants كيف نعطيك مثال توضيحي على ذلك", "tokens": [2304, 43020, 7251, 7435, 1829, 4117, 8608, 33604, 6027, 8978, 2423, 10943, 2655, 5016, 7649, 20666, 8592, 28820, 23758, 4032, 6055, 11242, 9566, 16572, 6055, 4587, 38251, 9673, 3615, 18513, 37977, 30731, 20449, 18513, 1211, 2655, 9957, 4032, 3714, 43020, 7251, 7435, 1829, 4117, 3714, 3555, 33599, 25720, 11331, 1211, 9673, 3615, 18513, 37977, 45164, 8717, 3794, 4117, 2655, 4032, 16472, 2655, 11331, 25720, 11331, 1211, 4724, 23557, 33753, 4117, 46811, 10943, 4032, 3714, 43020, 8717, 3615, 9566, 1829, 4117, 8608, 33604, 6027, 4032, 8717, 39648, 9122, 12984, 13546, 2423, 1729, 3827, 4032, 500, 380, 13059, 264, 35870, 3714, 9307, 5016, 35457, 1829, 8592, 2423, 35870, 9122, 33911, 8717, 3615, 9566, 1829, 4117, 50113, 6027, 33427, 11242, 1829, 5016, 1829, 15844, 29910, 23275], "avg_logprob": -0.17691531645194178, "compression_ratio": 1.7609561752988048, "no_speech_prob": 0.0, "words": [{"start": 3776.18, "end": 3776.68, "word": "ممكن", "probability": 0.75146484375}, {"start": 3776.68, "end": 3777.14, "word": " يجيك", "probability": 0.9024658203125}, {"start": 3777.14, "end": 3777.62, "word": " سؤال", "probability": 0.91650390625}, {"start": 3777.62, "end": 3777.74, "word": " في", "probability": 0.88232421875}, {"start": 3777.74, "end": 3778.54, "word": " الامتحان", "probability": 0.93525390625}, {"start": 3778.54, "end": 3779.84, "word": " بالشكل", "probability": 0.8230794270833334}, {"start": 3779.84, "end": 3780.18, "word": " هذا", "probability": 0.94384765625}, {"start": 3780.18, "end": 3780.36, "word": " و", "probability": 0.6240234375}, {"start": 3780.36, "end": 3780.8, "word": " تضطري", "probability": 0.709228515625}, {"start": 3780.8, "end": 3781.34, "word": " تقسم", "probability": 0.7766927083333334}, {"start": 3781.34, "end": 3782.14, "word": " المعادلة", "probability": 0.980224609375}, {"start": 3782.14, "end": 3782.58, "word": " إلى", "probability": 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{"start": 3789.6, "end": 3789.9, "word": " حل", "probability": 0.911376953125}, {"start": 3789.9, "end": 3790.64, "word": " براحتك", "probability": 0.9493408203125}, {"start": 3790.64, "end": 3791.34, "word": " تمام", "probability": 0.766357421875}, {"start": 3791.34, "end": 3791.96, "word": " و", "probability": 0.410888671875}, {"start": 3791.96, "end": 3792.4, "word": " ممكن", "probability": 0.96435546875}, {"start": 3792.4, "end": 3792.96, "word": " نعطيك", "probability": 0.98193359375}, {"start": 3792.96, "end": 3793.58, "word": " سؤال", "probability": 0.98779296875}, {"start": 3793.58, "end": 3793.72, "word": " و", "probability": 0.57421875}, {"start": 3793.72, "end": 3793.9, "word": " نقول", "probability": 0.929443359375}, {"start": 3793.9, "end": 3794.54, "word": " كثير", "probability": 0.60986328125}, {"start": 3794.54, "end": 3794.72, "word": " ال", "probability": 0.34619140625}, {"start": 3794.72, "end": 3795.22, "word": " particular", "probability": 0.66259765625}, {"start": 3795.22, "end": 3796.16, "word": " solution", "probability": 0.81640625}, {"start": 3796.16, "end": 3796.96, "word": " و", "probability": 0.908203125}, {"start": 3796.96, "end": 3797.42, "word": " don't", "probability": 0.89306640625}, {"start": 3797.42, "end": 3797.94, "word": " evaluate", "probability": 0.88916015625}, {"start": 3797.94, "end": 3798.28, "word": " the", "probability": 0.86376953125}, {"start": 3798.28, "end": 3798.86, "word": " constants", "probability": 0.86474609375}, {"start": 3798.86, "end": 3799.92, "word": " ماتحسبيش", "probability": 0.76318359375}, {"start": 3799.92, "end": 3800.5, "word": " ال", "probability": 0.9677734375}, {"start": 3800.5, "end": 3800.92, "word": " constants", "probability": 0.9267578125}, {"start": 3800.92, "end": 3801.36, "word": " كيف", "probability": 0.94677734375}, {"start": 3801.36, "end": 3801.82, "word": " نعطيك", "probability": 0.94365234375}, {"start": 3801.82, "end": 3802.46, "word": " مثال", "probability": 0.8193359375}, {"start": 3802.46, "end": 3803.84, "word": " توضيحي", "probability": 0.87138671875}, {"start": 3803.84, "end": 3804.14, "word": " على", "probability": 0.833984375}, {"start": 3804.14, "end": 3804.92, "word": " ذلك", "probability": 0.990478515625}], "temperature": 1.0}, {"id": 162, "seek": 383730, "start": 3816.06, "end": 3837.3, "text": "سؤال الرابع determine a suitable form شكل مناسب for the particular solution", "tokens": [3794, 33604, 6027, 34892, 16758, 3615, 6997, 257, 12873, 1254, 13412, 28820, 3714, 8315, 35457, 337, 264, 1729, 3827], "avg_logprob": -0.21972655951976777, "compression_ratio": 1.0, "no_speech_prob": 0.0, "words": [{"start": 3816.06, "end": 3816.62, "word": "سؤال", "probability": 0.7304280598958334}, {"start": 3816.62, "end": 3817.34, "word": " الرابع", "probability": 0.98388671875}, {"start": 3817.34, "end": 3820.2, "word": " determine", "probability": 0.377685546875}, {"start": 3820.2, "end": 3825.94, "word": " a", "probability": 0.427978515625}, {"start": 3825.94, "end": 3826.54, "word": " suitable", "probability": 0.978515625}, {"start": 3826.54, "end": 3830.24, "word": " form", "probability": 0.94140625}, {"start": 3830.24, "end": 3832.46, "word": " شكل", "probability": 0.87548828125}, {"start": 3832.46, "end": 3833.44, "word": " مناسب", "probability": 0.9510091145833334}, {"start": 3833.44, "end": 3835.48, "word": " for", "probability": 0.96484375}, {"start": 3835.48, "end": 3835.68, "word": " the", "probability": 0.90283203125}, {"start": 3835.68, "end": 3836.22, "word": " particular", "probability": 0.91943359375}, {"start": 3836.22, "end": 3837.3, "word": " solution", "probability": 0.95947265625}], "temperature": 1.0}, {"id": 163, "seek": 387343, "start": 3846.03, "end": 3873.43, "text": "على المحلل المحدد Y of T of الاختصارات التالية الاختصارات التالية الاختصارات الاختصارات الاختصارات الاختصارات الاختصارات الاختصارات الاختصارات الاختصارات الاختصارات الاختصارات الاختصارات الاختصارات الاختصارات الاختصارات", "tokens": [3615, 23942, 9673, 5016, 1211, 1211, 9673, 24401, 3215, 398, 295, 314, 295, 2423, 47283, 2655, 9381, 9640, 9307, 16712, 6027, 10632, 2423, 47283, 2655, 9381, 9640, 9307, 16712, 6027, 10632, 2423, 47283, 2655, 9381, 9640, 9307, 2423, 47283, 2655, 9381, 9640, 9307, 2423, 47283, 2655, 9381, 9640, 9307, 2423, 47283, 2655, 9381, 9640, 9307, 2423, 47283, 2655, 9381, 9640, 9307, 2423, 47283, 2655, 9381, 9640, 9307, 2423, 47283, 2655, 9381, 9640, 9307, 2423, 47283, 2655, 9381, 9640, 9307, 2423, 47283, 2655, 9381, 9640, 9307, 2423, 47283, 2655, 9381, 9640, 9307, 2423, 47283, 2655, 9381, 9640, 9307, 2423, 47283, 2655, 9381, 9640, 9307, 2423, 47283, 2655, 9381, 9640, 9307, 2423, 47283, 2655, 9381, 9640, 9307], "avg_logprob": -0.27074352163693, "compression_ratio": 5.746478873239437, "no_speech_prob": 0.0, "words": [{"start": 3846.03, "end": 3846.41, "word": "على", "probability": 0.3060302734375}, {"start": 3846.41, "end": 3847.35, "word": " المحلل", "probability": 0.355621337890625}, {"start": 3847.35, "end": 3847.71, "word": " المحدد", "probability": 0.5615234375}, {"start": 3847.71, "end": 3850.25, "word": " Y", "probability": 0.419921875}, {"start": 3850.25, "end": 3851.31, "word": " of", "probability": 0.375732421875}, {"start": 3851.31, "end": 3851.93, "word": " T", "probability": 0.88818359375}, {"start": 3851.93, "end": 3854.21, "word": " of", "probability": 0.2958984375}, {"start": 3854.21, "end": 3862.07, "word": " الاختصارات", "probability": 0.6907552083333334}, {"start": 3862.07, "end": 3862.07, "word": " التالية", "probability": 0.62939453125}, {"start": 3862.07, "end": 3865.67, "word": " الاختصارات", "probability": 0.8434855143229166}, {"start": 3865.67, "end": 3866.79, "word": " التالية", "probability": 0.7887369791666666}, {"start": 3866.79, "end": 3867.59, "word": " الاختصارات", "probability": 0.77978515625}, {"start": 3867.59, "end": 3869.43, "word": " الاختصارات", "probability": 0.8583170572916666}, {"start": 3869.43, "end": 3869.53, "word": " الاختصارات", "probability": 0.8851725260416666}, {"start": 3869.53, "end": 3869.67, "word": " الاختصارات", "probability": 0.9043782552083334}, {"start": 3869.67, "end": 3870.41, "word": " الاختصارات", "probability": 0.9270833333333334}, {"start": 3870.41, "end": 3870.47, "word": " الاختصارات", "probability": 0.9522298177083334}, {"start": 3870.47, "end": 3870.85, "word": " الاختصارات", "probability": 0.9674479166666666}, {"start": 3870.85, "end": 3870.85, "word": " الاختصارات", "probability": 0.9765625}, {"start": 3870.85, "end": 3870.85, "word": " الاختصارات", "probability": 0.9820149739583334}, {"start": 3870.85, "end": 3870.85, "word": " الاختصارات", "probability": 0.9850260416666666}, {"start": 3870.85, "end": 3870.85, "word": " الاختصارات", "probability": 0.986328125}, {"start": 3870.85, "end": 3870.85, "word": " الاختصارات", "probability": 0.9877115885416666}, {"start": 3870.85, "end": 3870.85, "word": " الاختصارات", "probability": 0.9883626302083334}, {"start": 3870.85, "end": 3873.43, "word": " الاختصارات", "probability": 0.9890950520833334}], "temperature": 1.0}, {"id": 164, "seek": 389736, "start": 3875.34, "end": 3897.36, "text": "the constants تحسبيش الثوابت نمرا A سؤال عشرين من الكتاب يقول يو اي دابلر prime زائد Y يساوي T في واحد زائد صينة T", "tokens": [3322, 35870, 6055, 5016, 35457, 1829, 8592, 6024, 104, 14407, 3555, 2655, 8717, 2304, 23557, 316, 8608, 33604, 6027, 6225, 46309, 9957, 9154, 33251, 2655, 16758, 7251, 39648, 7251, 2407, 1975, 1829, 11778, 16758, 1211, 2288, 5835, 30767, 16373, 3215, 398, 7251, 3794, 995, 45865, 314, 8978, 36764, 24401, 30767, 16373, 3215, 20328, 9957, 3660, 314], "avg_logprob": -0.3511513157894737, "compression_ratio": 1.2602739726027397, "no_speech_prob": 0.0, "words": [{"start": 3875.34, "end": 3875.62, "word": "the", "probability": 0.07940673828125}, {"start": 3875.62, "end": 3876.74, "word": " constants", "probability": 0.7490234375}, {"start": 3876.74, "end": 3880.74, "word": " تحسبيش", "probability": 0.8142578125}, {"start": 3880.74, "end": 3882.14, "word": " الثوابت", "probability": 0.839453125}, {"start": 3882.14, "end": 3883.58, "word": " نمرا", "probability": 0.4397786458333333}, {"start": 3883.58, "end": 3884.18, "word": " A", "probability": 0.51416015625}, {"start": 3884.18, "end": 3885.72, "word": " سؤال", "probability": 0.8953450520833334}, {"start": 3885.72, "end": 3886.36, "word": " عشرين", "probability": 0.9095052083333334}, {"start": 3886.36, "end": 3886.6, "word": " من", "probability": 0.96826171875}, {"start": 3886.6, "end": 3887.2, "word": " الكتاب", "probability": 0.9830729166666666}, {"start": 3887.2, "end": 3888.34, "word": " يقول", "probability": 0.751708984375}, {"start": 3888.34, "end": 3888.62, "word": " يو", "probability": 0.35516357421875}, {"start": 3888.62, "end": 3888.88, "word": " اي", "probability": 0.5975341796875}, {"start": 3888.88, "end": 3889.48, "word": " دابلر", "probability": 0.65924072265625}, {"start": 3889.48, "end": 3889.98, "word": " prime", "probability": 0.3779296875}, {"start": 3889.98, "end": 3891.46, "word": " زائد", "probability": 0.8440755208333334}, {"start": 3891.46, "end": 3892.0, "word": " Y", "probability": 0.55615234375}, {"start": 3892.0, "end": 3893.28, "word": " يساوي", "probability": 0.8995361328125}, {"start": 3893.28, "end": 3893.78, "word": " T", "probability": 0.87060546875}, {"start": 3893.78, "end": 3894.48, "word": " في", "probability": 0.9296875}, {"start": 3894.48, "end": 3895.34, "word": " واحد", "probability": 0.932373046875}, {"start": 3895.34, "end": 3896.46, "word": " زائد", "probability": 0.96142578125}, {"start": 3896.46, "end": 3897.18, "word": " صينة", "probability": 0.573974609375}, {"start": 3897.18, "end": 3897.36, "word": " T", "probability": 0.923828125}], "temperature": 1.0}, {"id": 165, "seek": 395692, "start": 3930.14, "end": 3956.92, "text": "سؤال مرة تانية بيقوللي حددلي شكل مناسب suitable form لمين لل particular solution capital Y of T لكل من المعادلة التفاضلية تانية وقاللي don't evaluate the consonants لو بدناش هيك تحاسب ال consonants بنكتب لكادبين جوسينه بخط غامج حتى كل واحد مش تروح تقعد تقعد تحاسبه لضيع الوقت فيها", "tokens": [3794, 33604, 6027, 3714, 25720, 6055, 7649, 10632, 4724, 1829, 39648, 20292, 11331, 3215, 3215, 20292, 13412, 28820, 3714, 8315, 35457, 12873, 1254, 32767, 9957, 24976, 1729, 3827, 4238, 398, 295, 314, 5296, 28820, 9154, 9673, 3615, 18513, 37977, 16712, 5172, 46958, 1211, 10632, 6055, 7649, 10632, 4032, 4587, 6027, 20292, 500, 380, 13059, 264, 30843, 1719, 45164, 47525, 8315, 8592, 39896, 4117, 6055, 5016, 32277, 3555, 2423, 30843, 1719, 44945, 4117, 2655, 3555, 5296, 4117, 18513, 3555, 9957, 10874, 41779, 9957, 3224, 4724, 9778, 9566, 32771, 10943, 7435, 11331, 49975, 28242, 36764, 24401, 37893, 6055, 32887, 5016, 6055, 4587, 22488, 6055, 4587, 22488, 6055, 5016, 32277, 3555, 3224, 5296, 11242, 40228, 2423, 30543, 2655, 8978, 11296], "avg_logprob": -0.24748410372915913, "compression_ratio": 1.599264705882353, "no_speech_prob": 0.0, "words": 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1.0}, {"id": 184, "seek": 438864, "start": 4375.35, "end": 4388.65, "text": "في cos T يبقى هذا ال particular solution اللي بده إياه اللي بده إياه تمام؟ يبقى انت يا أنا من قصة من ال particular solution", "tokens": [41185, 3792, 314, 7251, 3555, 4587, 7578, 23758, 2423, 1729, 3827, 13672, 1829, 47525, 3224, 11933, 25528, 3224, 13672, 1829, 47525, 3224, 11933, 25528, 3224, 46811, 10943, 22807, 7251, 3555, 4587, 7578, 16472, 2655, 35186, 41850, 9154, 12174, 9381, 3660, 9154, 2423, 1729, 3827], "avg_logprob": -0.3493055502573649, "compression_ratio": 1.5294117647058822, "no_speech_prob": 0.0, "words": [{"start": 4375.35, "end": 4375.63, "word": "في", "probability": 0.25439453125}, {"start": 4375.63, "end": 4376.21, "word": " cos", "probability": 0.3984375}, {"start": 4376.21, "end": 4377.11, "word": " T", "probability": 0.1884765625}, {"start": 4377.11, "end": 4378.09, "word": " يبقى", "probability": 0.9176025390625}, {"start": 4378.09, "end": 4378.47, "word": " هذا", "probability": 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"probability": 0.533203125}, {"start": 4385.67, "end": 4385.81, "word": " يا", "probability": 0.3232421875}, {"start": 4385.81, "end": 4385.95, "word": " أنا", "probability": 0.72607421875}, {"start": 4385.95, "end": 4386.11, "word": " من", "probability": 0.479248046875}, {"start": 4386.11, "end": 4386.55, "word": " قصة", "probability": 0.9283854166666666}, {"start": 4386.55, "end": 4386.71, "word": " من", "probability": 0.43212890625}, {"start": 4386.71, "end": 4387.27, "word": " ال", "probability": 0.791015625}, {"start": 4387.27, "end": 4387.83, "word": " particular", "probability": 0.875}, {"start": 4387.83, "end": 4388.65, "word": " solution", "probability": 0.96240234375}], "temperature": 1.0}, {"id": 185, "seek": 441812, "start": 4388.98, "end": 4418.12, "text": "لو قال لي هاتلي ال general solution بدي أروح أحسب ال constants دول لكن لو قال لي don't evaluate the constants و هاتلي ال general solution بجمعله بس هذا و هذاك و بقول له هاي ال general solution يعطيك العافية تمام؟ بس إن 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" يساوي", "probability": 0.65753173828125}, {"start": 5055.51, "end": 5056.97, "word": " الأولان", "probability": 0.8828125}, {"start": 5056.97, "end": 5057.37, "word": " هو", "probability": 0.1392822265625}, {"start": 5057.37, "end": 5058.63, "word": " A0", "probability": 0.4368896484375}, {"start": 5058.63, "end": 5059.35, "word": " T", "probability": 0.6298828125}, {"start": 5059.35, "end": 5060.15, "word": " ترابيع", "probability": 0.6937255859375}, {"start": 5060.15, "end": 5061.25, "word": " زائد", "probability": 0.7006022135416666}, {"start": 5061.25, "end": 5062.17, "word": " A1", "probability": 0.918701171875}, {"start": 5062.17, "end": 5062.71, "word": " T", "probability": 0.352294921875}, {"start": 5062.71, "end": 5063.85, "word": " زائد", "probability": 0.9508463541666666}, {"start": 5063.85, "end": 5064.99, "word": " A2", "probability": 0.9873046875}, {"start": 5064.99, "end": 5066.29, "word": " capital", "probability": 0.59765625}, {"start": 5066.29, "end": 5067.57, "word": " Y2", "probability": 0.97900390625}, {"start": 5067.57, "end": 5068.79, "word": " B0", "probability": 0.4820556640625}, {"start": 5068.79, "end": 5069.15, "word": " T", "probability": 0.9072265625}, {"start": 5069.15, "end": 5070.15, "word": " تكييب", "probability": 0.91796875}, {"start": 5070.15, "end": 5071.95, "word": " B0", "probability": 0.83740234375}, {"start": 5071.95, "end": 5072.43, "word": " T", "probability": 0.79345703125}, {"start": 5072.43, "end": 5073.37, "word": " تكييب", "probability": 0.9923828125}, {"start": 5073.37, "end": 5074.19, "word": " زائد", "probability": 0.9622395833333334}, {"start": 5074.19, "end": 5075.77, "word": " B0", "probability": 0.98974609375}, {"start": 5075.77, "end": 5076.73, "word": " T", "probability": 0.92919921875}], "temperature": 1.0}, {"id": 212, "seek": 510010, "start": 5078.48, "end": 5100.1, "text": "ب1t تربيع ب1t تربيع في E أش اتنين T E أش اتنين T زائد اللي بعده D نقدر T زائد D one تمام في Sine اتنين T", "tokens": [3555, 16, 83, 6055, 2288, 21292, 3615, 4724, 16, 83, 6055, 2288, 21292, 3615, 8978, 462, 5551, 8592, 1975, 2655, 1863, 9957, 314, 462, 5551, 8592, 1975, 2655, 1863, 9957, 314, 30767, 16373, 3215, 13672, 1829, 39182, 3224, 413, 8717, 28543, 2288, 314, 30767, 16373, 3215, 413, 472, 46811, 10943, 8978, 318, 533, 1975, 2655, 1863, 9957, 314], "avg_logprob": -0.380561435626725, "compression_ratio": 1.5092592592592593, "no_speech_prob": 0.0, "words": [{"start": 5078.4800000000005, "end": 5079.88, "word": "ب1t", "probability": 0.2471923828125}, {"start": 5079.88, "end": 5081.06, "word": " تربيع", "probability": 0.564453125}, {"start": 5081.06, "end": 5082.66, "word": " ب1t", "probability": 0.6075032552083334}, {"start": 5082.66, "end": 5083.56, "word": " تربيع", "probability": 0.92041015625}, {"start": 5083.56, "end": 5084.22, "word": " في", "probability": 0.65625}, {"start": 5084.22, "end": 5084.74, "word": " E", "probability": 0.2315673828125}, {"start": 5084.74, "end": 5085.48, "word": " أش", "probability": 0.636962890625}, {"start": 5085.48, "end": 5086.3, "word": " اتنين", "probability": 0.8546142578125}, {"start": 5086.3, "end": 5086.8, "word": " T", "probability": 0.83935546875}, {"start": 5086.8, "end": 5088.04, "word": " E", "probability": 0.75048828125}, {"start": 5088.04, "end": 5088.62, "word": " أش", "probability": 0.905029296875}, {"start": 5088.62, "end": 5089.42, "word": " اتنين", "probability": 0.9747314453125}, {"start": 5089.42, "end": 5089.72, "word": " T", "probability": 0.94775390625}, {"start": 5089.72, "end": 5090.36, "word": " زائد", "probability": 0.82666015625}, {"start": 5090.36, "end": 5091.1, "word": " اللي", "probability": 0.804931640625}, {"start": 5091.1, "end": 5091.62, "word": " بعده", "probability": 0.854736328125}, {"start": 5091.62, "end": 5092.02, "word": " D", "probability": 0.5390625}, {"start": 5092.02, "end": 5093.18, "word": " نقدر", "probability": 0.60302734375}, {"start": 5093.18, "end": 5094.7, "word": " T", "probability": 0.4111328125}, {"start": 5094.7, "end": 5095.64, "word": " زائد", "probability": 0.9716796875}, {"start": 5095.64, "end": 5096.16, "word": " D", "probability": 0.9580078125}, {"start": 5096.16, "end": 5096.82, "word": " one", "probability": 0.25244140625}, {"start": 5096.82, "end": 5097.96, "word": " تمام", "probability": 0.5760498046875}, {"start": 5097.96, "end": 5098.22, "word": " في", "probability": 0.73193359375}, {"start": 5098.22, "end": 5098.74, "word": " Sine", "probability": 0.57183837890625}, {"start": 5098.74, "end": 5099.52, "word": " اتنين", "probability": 0.9581298828125}, {"start": 5099.52, "end": 5100.1, "word": " T", "probability": 0.9794921875}], "temperature": 1.0}, {"id": 213, "seek": 511550, "start": 5112.3, "end": 5115.5, "text": "يبقى هذا ال particular solution", "tokens": [1829, 3555, 4587, 7578, 23758, 2423, 644, 14646, 3827], "avg_logprob": -0.643359375, "compression_ratio": 0.8163265306122449, "no_speech_prob": 0.0, "words": [{"start": 5112.3, "end": 5113.46, "word": "يبقى", "probability": 0.69970703125}, {"start": 5113.46, "end": 5113.7, "word": " هذا", "probability": 0.86474609375}, {"start": 5113.7, "end": 5113.86, "word": " ال", "probability": 0.68115234375}, {"start": 5113.86, "end": 5114.44, "word": " particular", "probability": 0.43450927734375}, {"start": 5114.44, "end": 5115.5, "word": " solution", "probability": 0.9462890625}], "temperature": 1.0}, {"id": 214, "seek": 513383, "start": 5117.53, "end": 5133.83, "text": "الان لحد هيك انتهى ال section ابنات و الى يكون ارقام المسائل اكثر ال sizes تلاتة ستة المسائل من واحد لغاية تمنتاشر ال even", "tokens": [6027, 7649, 5296, 24401, 39896, 4117, 16472, 47395, 7578, 2423, 3541, 1975, 3555, 1863, 9307, 4032, 2423, 7578, 7251, 30544, 1975, 2288, 4587, 10943, 9673, 3794, 16373, 1211, 1975, 4117, 49115, 2423, 11602, 6055, 1211, 9307, 3660, 8608, 2655, 3660, 9673, 3794, 16373, 1211, 9154, 36764, 24401, 5296, 17082, 995, 10632, 46811, 29399, 33599, 2288, 2423, 754], "avg_logprob": -0.27559267549679195, "compression_ratio": 1.5185185185185186, "no_speech_prob": 0.0, "words": [{"start": 5117.53, "end": 5118.03, "word": "الان", "probability": 0.747802734375}, {"start": 5118.03, "end": 5118.49, "word": " لحد", "probability": 0.672119140625}, {"start": 5118.49, "end": 5118.81, "word": " هيك", "probability": 0.5750732421875}, {"start": 5118.81, "end": 5119.25, "word": " انتهى", "probability": 0.9405924479166666}, {"start": 5119.25, "end": 5119.39, "word": " ال", "probability": 0.445068359375}, {"start": 5119.39, "end": 5119.61, "word": " section", "probability": 0.6962890625}, {"start": 5119.61, "end": 5120.35, "word": " ابنات", "probability": 0.49041748046875}, {"start": 5120.35, "end": 5120.95, "word": " و", "probability": 0.498779296875}, {"start": 5120.95, "end": 5121.21, "word": " الى", "probability": 0.54376220703125}, {"start": 5121.21, "end": 5121.59, "word": " يكون", "probability": 0.92822265625}, {"start": 5121.59, "end": 5122.43, "word": " ارقام", "probability": 0.904541015625}, {"start": 5122.43, "end": 5123.63, "word": " المسائل", "probability": 0.94921875}, {"start": 5123.63, "end": 5125.05, "word": " اكثر", "probability": 0.6988118489583334}, {"start": 5125.05, "end": 5125.23, "word": " ال", "probability": 0.77734375}, {"start": 5125.23, "end": 5125.83, "word": " sizes", "probability": 0.90673828125}, {"start": 5125.83, "end": 5127.63, "word": " تلاتة", "probability": 0.84619140625}, {"start": 5127.63, "end": 5128.49, "word": " ستة", "probability": 0.8395182291666666}, {"start": 5128.49, "end": 5130.07, "word": " المسائل", "probability": 0.97412109375}, {"start": 5130.07, "end": 5130.29, "word": " من", "probability": 0.97021484375}, {"start": 5130.29, "end": 5130.93, "word": " واحد", "probability": 0.97607421875}, {"start": 5130.93, "end": 5131.49, "word": " لغاية", "probability": 0.974609375}, {"start": 5131.49, "end": 5132.87, "word": " تمنتاشر", "probability": 0.80523681640625}, {"start": 5132.87, "end": 5133.15, "word": " ال", "probability": 0.78515625}, {"start": 5133.15, "end": 5133.83, "word": " even", "probability": 0.91064453125}], "temperature": 1.0}, {"id": 215, "seek": 515782, "start": 5135.72, "end": 5157.82, "text": "ومن تسعة عشر لغاية ستة وعشرين part ايه فقط بدنا ال odd يالا خليهم مرة even ومرة odd الان ضايل عندنا هو section تلاتة سبعة", "tokens": [2407, 27842, 6055, 3794, 27884, 6225, 46309, 5296, 17082, 995, 10632, 8608, 2655, 3660, 4032, 3615, 46309, 9957, 644, 1975, 1829, 3224, 6156, 47432, 47525, 8315, 2423, 7401, 7251, 6027, 995, 16490, 20292, 16095, 3714, 25720, 754, 4032, 2304, 25720, 7401, 2423, 7649, 48812, 995, 26895, 43242, 8315, 31439, 3541, 6055, 1211, 9307, 3660, 8608, 3555, 27884], "avg_logprob": -0.27532327997273415, "compression_ratio": 1.3971631205673758, "no_speech_prob": 0.0, "words": [{"start": 5135.72, "end": 5136.6, "word": "ومن", "probability": 0.6064453125}, {"start": 5136.6, "end": 5138.3, "word": " تسعة", "probability": 0.6599934895833334}, {"start": 5138.3, "end": 5139.0, "word": " عشر", "probability": 0.626953125}, {"start": 5139.0, "end": 5140.34, "word": " لغاية", "probability": 0.9794921875}, {"start": 5140.34, "end": 5141.06, "word": " ستة", "probability": 0.9723307291666666}, {"start": 5141.06, "end": 5142.18, "word": " وعشرين", "probability": 0.89697265625}, {"start": 5142.18, "end": 5143.82, "word": " part", "probability": 0.7841796875}, {"start": 5143.82, "end": 5145.1, "word": " ايه", "probability": 0.6241861979166666}, {"start": 5145.1, "end": 5145.94, "word": " فقط", "probability": 0.97412109375}, {"start": 5145.94, "end": 5146.76, "word": " بدنا", "probability": 0.9189453125}, {"start": 5146.76, "end": 5147.12, "word": " ال", "probability": 0.89208984375}, {"start": 5147.12, "end": 5147.7, "word": " odd", "probability": 0.7119140625}, {"start": 5147.7, "end": 5149.72, "word": " يالا", "probability": 0.7156575520833334}, {"start": 5149.72, "end": 5150.14, "word": " خليهم", "probability": 0.8611653645833334}, {"start": 5150.14, "end": 5150.48, "word": " مرة", "probability": 0.936767578125}, {"start": 5150.48, "end": 5150.94, "word": " even", "probability": 0.92626953125}, {"start": 5150.94, "end": 5152.14, "word": " ومرة", "probability": 0.827880859375}, {"start": 5152.14, "end": 5152.84, "word": " odd", "probability": 0.935546875}, {"start": 5152.84, "end": 5155.0, "word": " الان", "probability": 0.6820068359375}, {"start": 5155.0, "end": 5155.34, "word": " ضايل", "probability": 0.5275472005208334}, {"start": 5155.34, "end": 5155.66, "word": " عندنا", "probability": 0.885986328125}, {"start": 5155.66, "end": 5156.08, "word": " هو", "probability": 0.1549072265625}, {"start": 5156.08, "end": 5156.78, "word": " section", "probability": 0.80712890625}, {"start": 5156.78, "end": 5157.4, "word": " تلاتة", "probability": 0.9349365234375}, {"start": 5157.4, "end": 5157.82, "word": " سبعة", "probability": 0.9191080729166666}], "temperature": 1.0}], "language": "ar", "language_probability": 1.0, "duration": 5158.406, "duration_after_vad": 4897.927843750002}
\ No newline at end of file
diff --git a/PL9fwy3NUQKwa8ZDfSFGn6H8xVFLzqmCZC/XSq4pVrKvY4.srt b/PL9fwy3NUQKwa8ZDfSFGn6H8xVFLzqmCZC/XSq4pVrKvY4.srt
new file mode 100644
index 0000000000000000000000000000000000000000..f3585e9daa1f57260b38bbbd10007bf4fea672b6
--- /dev/null
+++ b/PL9fwy3NUQKwa8ZDfSFGn6H8xVFLzqmCZC/XSq4pVrKvY4.srt
@@ -0,0 +1,2814 @@
+1
+00:00:00,000 --> 00:00:02,560
+موسيقى
+
+2
+00:00:10,560 --> 00:00:15,380
+المرة اللي فاتت ابتدأنا في section ثلاثة واحد اللي
+
+3
+00:00:15,380 --> 00:00:19,420
+هو second order homogeneous linear differential
+
+4
+00:00:19,420 --> 00:00:23,040
+equations شرحنا هذه النقطة جيبنا المعادلة 
+
+5
+00:00:23,040 --> 00:00:26,700
+التفاضلية من الرتبة الثانية و constant
+
+6
+00:00:26,700 --> 00:00:30,940
+coefficients جيبنا ال auxiliary equation أو ال
+
+7
+00:00:30,940 --> 00:00:35,280
+characteristic equation أعطينا على ذلك مجموعة من
+
+8
+00:00:35,280 --> 00:00:41,720
+الأمثلة ولا يزال هناك أمثلة المثال رقم ثلاثة بيقول 
+
+9
+00:00:41,720 --> 00:00:44,960
+solve the initial value problem أربعة y double
+
+10
+00:00:44,960 --> 00:00:49,300
+prime ناقص y يساوي صفر y عند صفر تساوي اثنين و y
+
+11
+00:00:49,300 --> 00:00:54,720
+prime عند صفر تساوي بيتا قال لي ومن ثم هاتلي شكل
+
+12
+00:00:54,720 --> 00:01:00,640
+البيتا بحيث أن الحل بده يقول الأصفر لما t بده 
+
+13
+00:01:00,640 --> 00:01:05,110
+تروح لوين؟ للما لا نهاية إذا مطلوبين في المثال
+
+14
+00:01:05,110 --> 00:01:08,130
+المطلوب الأول يجب أن نحل ال initial value problem
+
+15
+00:01:08,130 --> 00:01:13,530
+والمطلوب الثاني يجب أن نجده قيمة beta لما t تذهب
+
+16
+00:01:13,530 --> 00:01:19,230
+للما لا نهاية ويكون الحل مساويا للصفر إذا نمشي بنفس
+
+17
+00:01:19,230 --> 00:01:24,390
+التكتيك اللي اتبعناه المرة الماضية في المحاضرة
+
+18
+00:01:24,390 --> 00:01:30,480
+الماضية كانت تالية أبدأ أقول له let Y تساوي e أس rt
+
+19
+00:01:30,480 --> 00:01:45,840
+بي a solution to the given differential equation
+
+20
+00:01:45,840 --> 00:01:50,900
+يبقى بناء عليها بقول له the characteristic
+
+21
+00:01:50,900 --> 00:02:00,480
+equation is 4R تربيع ناقص واحد يساوي كده ايش؟ zero
+
+22
+00:02:00,480 --> 00:02:11,320
+ومنها R تربيع تساوي ربع يبقى R تساوي زائد أو ناقص
+
+23
+00:02:11,320 --> 00:02:18,280
+نصف يبقى صارت الجذور عندي two real different roots
+
+24
+00:02:18,280 --> 00:02:24,880
+اللي هو مين؟ قيمتين حقيقيتين ومختلفتين يبقى بناء
+
+25
+00:02:24,880 --> 00:02:28,040
+عليه شكل ال general solution
+
+26
+00:02:35,880 --> 00:02:47,320
+Given differential equation as يبقى Y تساوي C1 e
+
+27
+00:02:47,320 --> 00:02:56,660
+أس سالب نصف t يعني t على 2 زائد C2 e أس نصف t بالشكل
+
+28
+00:02:56,660 --> 00:03:01,700
+اللي عندنا هذا هذا شكل الحل لكن راح أعطانا mainly
+
+29
+00:03:01,700 --> 00:03:07,720
+two initial conditions يبقى لو روحنا اشتقينا الحل
+
+30
+00:03:07,720 --> 00:03:15,560
+لأن هذا بيصير y' يساوي ناقص نصف C1 e أس ناقص t
+
+31
+00:03:15,560 --> 00:03:25,980
+على اثنين زائد نصف C2 e أس t على اثنين بناء عليه
+
+32
+00:03:25,980 --> 00:03:28,740
+بدأ نيجي على ال initial conditions اللي عندنا الآن
+
+33
+00:03:28,740 --> 00:03:35,320
+عندنا y عند ال zero بده يساوي 2 هذا معناه أن ال y
+
+34
+00:03:35,320 --> 00:03:44,420
+هذه 2 تساوي C1 وبيصير e of 0 اللي هو بواحد زائد C2 
+
+35
+00:03:44,420 --> 00:03:49,820
+e of 0 اللي هو بواحد ال condition الثاني y prime
+
+36
+00:03:50,920 --> 00:03:56,540
+عند 0 بده يساوي قد ايش؟ بيتا هذا الكلام بده
+
+37
+00:03:56,540 --> 00:04:04,940
+يعطينا ايه؟ بده يعطينا أنه بيتا بدها تساوي بده آجي
+
+38
+00:04:04,940 --> 00:04:11,080
+على الهدو هات مكانها دي اللي بيصير ناقص نصف C1 يبقى
+
+39
+00:04:11,080 --> 00:04:21,760
+ناقص نصف C1 وهناك زائد نصف C2 نحن بالنساس نحاول
+
+40
+00:04:21,760 --> 00:04:26,260
+نتخلص من أحد المجاهيل ونحصل على المجهول الثاني
+
+41
+00:04:26,260 --> 00:04:30,900
+بروح للمعادلة الأولى بيخليها زي ما هي اثنين تساوي
+
+42
+00:04:30,900 --> 00:04:38,740
+C1 زائد C2 المعادلة الثانية اثنين بيتا بدها تساوي 
+
+43
+00:04:38,740 --> 00:04:45,890
+ناقص C1 زائد C2 لو جمعنا هدول بيروحوا مع بعض يبقى
+
+44
+00:04:45,890 --> 00:04:54,470
+بناء عليه هذا حاطينه أن 2C2 بدها تساوي 2 زائد 2
+
+45
+00:04:54,470 --> 00:05:02,870
+بيتا لو قسمنا الكل على 2 بيصير C2 بدها تساوي 1
+
+46
+00:05:02,870 --> 00:05:10,140
+زائد بيتا نرجع نجيب C1 يبقى بنروح نعوض في المعادلة
+
+47
+00:05:10,140 --> 00:05:17,000
+الأولى يبقى اثنين بدها تساوي C1 بدنا اياها زائد 1
+
+48
+00:05:17,000 --> 00:05:24,600
+زائد بيتا إذا بناء عليه C1 بدها تساوي ننقل هذه على 
+
+49
+00:05:24,600 --> 00:05:31,260
+الجهة الثانية يبقى لدي جداش واحد ناقص بيتا يبقى
+
+50
+00:05:31,260 --> 00:05:35,420
+أصبح الحل تبع ال initial value problem the
+
+51
+00:05:35,420 --> 00:05:47,710
+solution of the initial value problem is Y تساوي Y
+
+52
+00:05:47,710 --> 00:05:52,950
+تساوي C1 بدي أشيل وأكتب بداله من الواحد ناقص بيتا
+
+53
+00:05:52,950 --> 00:06:00,850
+واحد ناقص بيتا في e أس ناقص t على اثنين C2 واحد
+
+54
+00:06:00,850 --> 00:06:08,550
+زائد بيتا يبقى هنا كمان واحد زائد بيتا في e أس t على اثنين
+
+55
+00:06:08,550 --> 00:06:14,310
+يبقى هذا شكل الحل تبع ال initial value
+
+56
+00:06:14,310 --> 00:06:19,590
+problem وبالتالي هذا هو المطلوب الأول في المسألة
+
+57
+00:06:19,590 --> 00:06:24,080
+solve the initial value problem حلناها المطلوب 
+
+58
+00:06:24,080 --> 00:06:31,560
+الثاني يقول find beta بحيث الحل هذا بده يقترب من
+
+59
+00:06:31,560 --> 00:06:35,580
+الصفر أو بده يقول إلى الصفر لما t بده تروح لوين؟
+
+60
+00:06:35,580 --> 00:06:41,660
+للمالا نهاية يعني هاخد ال limit للطرفين لما t بده
+
+61
+00:06:41,660 --> 00:06:45,580
+تروح للمالا نهاية وأسويه بقد ايش؟ بالصفر وأشوف شو
+
+62
+00:06:45,580 --> 00:06:52,840
+بيعطينا إذا بدي آخد limit لل y لما t بدها تروح
+
+63
+00:06:52,840 --> 00:06:57,700
+للما لا نهاية هو عبارة عن limit لما t بدها تروح
+
+64
+00:06:57,700 --> 00:07:04,080
+للما لا نهاية للواحد ناقص بيتا في e أس ناقص t على
+
+65
+00:07:04,080 --> 00:07:11,680
+اثنين زائد واحد زائد بيتا في e أس t على اثنين وكل
+
+66
+00:07:11,680 --> 00:07:16,400
+هذا الكلام بده يساوي قد ايش؟ يا بنات بده يساوي zero
+
+67
+00:07:22,610 --> 00:07:29,090
+بنزل تحت ناقص بيتا عدد على ما لا نهاية يبقى ناقص بيتا
+
+68
+00:07:29,090 --> 00:07:32,150
+نهاية يبقى ناقص بيتا عدد على ما لا نهاية يبقى ناقص
+
+69
+00:07:32,150 --> 00:07:32,550
+بيتا عدد على ما لا نهاية يبقى ناقص بيتا عدد على ما لا
+
+70
+00:07:32,550 --> 00:07:34,730
+نهاية يبقى ناقص بيتا عدد على ما لا نهاية يبقى ناقص
+
+71
+00:07:34,730 --> 00:07:38,170
+بيتا عدد على ما لا نهاية يبقى ناقص بيتا عدد على ما لا
+
+72
+00:07:38,170 --> 00:07:42,690
+نهاية يبقى ناقص بيتا عدد على ما لا نهاية يبقى ناقص
+
+73
+00:07:42,690 --> 00:07:43,630
+بيتا عدد على ما لا نهاية يب
+
+74
+00:07:47,590 --> 00:07:54,490
+معقول هذا الكلام؟ طيب سؤال هذا الكلام ما جاش ممكن 
+
+75
+00:07:54,490 --> 00:08:00,750
+يساوي zero هذا لا يمكن أن يساوي zero في يوم من
+
+76
+00:08:00,750 --> 00:08:04,550
+الأيام دائما وأبدا greater than zero يبقى اللي 
+
+77
+00:08:04,550 --> 00:08:08,470
+بدي أخلي هذا المقدار zero اللي هو المعامل صحيح ولا 
+
+78
+00:08:08,470 --> 00:08:15,290
+لا لواحد زائد بيتا يبقى بأجي بقوله since بما أن e
+
+79
+00:08:15,290 --> 00:08:22,380
+أس t على اثنين greater than zero we have أن الواحد
+
+80
+00:08:22,380 --> 00:08:26,880
+زائد بيتا هي اللي بدها تساوي zero يبقى بناء علينا
+
+81
+00:08:26,880 --> 00:08:31,800
+البيتا جداش بدها تساوي يبقى لو كانت بيتا تساوي
+
+82
+00:08:31,800 --> 00:08:35,700
+سالب واحد في ال initial condition اللي احنا حاطينه
+
+83
+00:08:35,700 --> 00:08:41,320
+هذا لكان الحل بده يروح فعلا ل zero لما t بده تروح
+
+84
+00:08:41,320 --> 00:08:48,700
+لوين؟ للما لا نهاية حد فيكوا لاقي تساوي هنا يا بنات؟ هي
+
+85
+00:08:48,700 --> 00:08:54,100
+أي تساؤل؟ طب لاحظوا أن احنا أخذنا خمسة أمثلة و
+
+86
+00:08:54,100 --> 00:08:58,200
+كلهم على نفس النمط تقريبا طبعا بتتخلف المسألة إلى 
+
+87
+00:08:58,200 --> 00:09:03,000
+أخرى لكن كله بنفس المفهوم طب بدنا نعطي مثال آخر
+
+88
+00:09:03,000 --> 00:09:07,700
+بس بطريقة غير شكل كيف؟ بدنا نعطيكوا الحل ونقول 
+
+89
+00:09:07,700 --> 00:09:11,960
+بدنا المسألة الأساسية يبقى مثال رقم أربعة
+
+90
+00:09:39,890 --> 00:09:44,510
+الحل العام بتاعها هو 
+
+91
+00:09:45,920 --> 00:09:55,840
+Y تساوي C1 في e أس 2t زائد C2 في e أس ناقص
+
+92
+00:09:55,840 --> 00:10:00,760
+3t واعتبري لهذه المعادلة اللي هي رقم واحد
+
+93
+00:10:10,370 --> 00:10:14,130
+بنرجع لسؤالنا مرة ثانية بيقول هات لي المعادلة
+
+94
+00:10:14,130 --> 00:10:19,390
+التفاضلية اللي الحل العام تبعها على الشكل Y يساوي 
+
+95
+00:10:19,390 --> 00:10:27,070
+C1 في e أس 2t زائد C2 في e أس سالب 3
+
+96
+00:10:27,070 --> 00:10:32,450
+t بيقوله كويس يبقى هذا حل عام للمعادلة لنعرف ما هي 
+
+97
+00:10:32,450 --> 00:10:37,170
+المعادلة التفاضلية اللي هذا الحل تبعها بالشكل
+
+98
+00:10:37,170 --> 00:10:38,470
+العام كيف نسويه؟ بنهاية
+
+99
+00:10:48,460 --> 00:10:55,330
+ممتاز يعني هذه معادلة من أي رتبة؟ ثانية لأن عندي
+
+100
+00:10:55,330 --> 00:11:00,670
+مجموعة ثوابت كويس يبقى هذه من الرتبة الثانية يبقى
+
+101
+00:11:00,670 --> 00:11:08,670
+أنا لو قدرت أجيب C1 و C2 بنقدر ايش؟ عشان نجيب الشكل
+
+102
+00:11:08,670 --> 00:11:14,650
+العام للمعادلة مشان أجيب C1 و C2 بدي معادلتين وبدي 
+
+103
+00:11:14,650 --> 00:11:18,110
+المشتقة الأولى تكون موجودة والمشتقة الثانية تكون 
+
+104
+00:11:18,110 --> 00:11:22,210
+موجودة صحيح ولا لا؟ إذا بتروح أجيب المشتقة الأولى
+
+105
+00:11:22,210 --> 00:11:27,970
+والمشتقة الثانية واستغلهم في إيجاد قيمتين ثابتين C1
+
+106
+00:11:27,970 --> 00:11:33,430
+و C2 وبالتالي بأجيب شكل المعادلة التفاضلية لذلك شو
+
+107
+00:11:33,430 --> 00:11:39,830
+بدي أعمل؟ بتروح تشتق مرتين وبعد هيك نشتغل شغلنا 
+
+108
+00:11:39,830 --> 00:11:43,670
+إذا لو جيت هنا يا بنات قلت y prime yourself؟
+
+109
+00:11:48,370 --> 00:11:55,320
+2C1e2t-3C2e-3t يبقى هاي جبت المشتقة الأولى لكن
+
+110
+00:11:55,320 --> 00:11:58,800
+معادلة منها الرتبة الثانية يعني بيلزمني كمان main 
+
+111
+00:11:58,800 --> 00:12:05,440
+مشتقة ثانية إذا لو روحت جبت ال y double prime يبقى هذه
+
+112
+00:12:05,440 --> 00:12:12,960
+بدها تساوي أربعة C1 e أس 2t زائد تسعة C
+
+113
+00:12:12,960 --> 00:12:21,750
+2 e أس سالب 3t تمام طيب ايش رأيك؟ هدول بدي 
+
+114
+00:12:21,750 --> 00:12:29,490
+أضيع أحد المجاهيل يعني بدي أضيع C1 أو C2 شو نعمل؟ 
+
+115
+00:12:29,490 --> 00:12:34,890
+ممكن نقرب المعادلة الأولى في سالب 2 ونجمعها مع 
+
+116
+00:12:34,890 --> 00:12:38,890
+مين؟ مع المعادلة التالية وبالتالي بكون ضيعنا أحد
+
+117
+00:12:38,890 --> 00:12:44,990
+المجاهيل وبنجيب المجهول الثاني إذا لو جيت للمعادلة
+
+118
+00:12:44,990 --> 00:12:50,370
+الاثنين هدول مع بعض بدي أضرب المعادلة الأولى في 
+
+119
+00:12:50,370 --> 00:12:57,330
+سالب اثنين يبقى بيصير عندي سالب اثنين y يساوي سالب
+
+120
+00:12:57,330 --> 00:13:07,190
+اثنين C1 e أس 2t سالب اثنين C2 e أس سالب 3
+
+121
+00:13:07,190 --> 00:13:15,390
+t المعادلة الثانية بدي أخليها زي ما هي y' يساوي 2C1e
+
+122
+00:13:15,390 --> 00:13:21,550
+-2t-3C2e
+
+123
+00:13:21,550 --> 00:13:28,010
+-3t يبقى ضربت المعادلة الأولى في سالب اثنين
+
+124
+00:13:28,010 --> 00:13:32,810
+والمعادلة الثانية خليتها كما هي شوفت لحظة ترمي 
+
+125
+00:13:32,810 --> 00:13:38,350
+الاثنين هدول الاثنين are the same يبقى عند الجمع 
+
+126
+00:13:38,350 --> 00:13:45,410
+مع السلامة يبقى بيصير عندنا y prime ناقص اثنين y 
+
+127
+00:13:45,410 --> 00:13:54,550
+يساوي نجمع هدول بيصير ناقص خمسة C2 e أس ناقص
+
+128
+00:13:54,550 --> 00:14:02,350
+3 من هذه المعادلة بقدر أجيب له C2 تمام يبقى 
+
+129
+00:14:02,350 --> 00:14:07,510
+بقدر أجيب C2 اللي عندنا هذه مشان أجيب C2 شو رأيك
+
+130
+00:14:07,510 --> 00:14:13,340
+أضرب الطرفين في e أس 3t يبقى لو ضربنا الطرفين في
+
+131
+00:14:13,340 --> 00:14:20,320
+e أس 3t أو في ناقص e أس 3t بدي أضرب هذه 
+
+132
+00:14:20,320 --> 00:14:28,700
+كلها المعادلة في ناقص e أس سالب 3t مش هنخليها
+
+133
+00:14:28,700 --> 00:14:34,400
+C2 بالموجب بيقبلش بيصير عندنا بيصير خمسة C2 هذا 
+
+134
+00:14:34,400 --> 00:14:38,980
+الطرف اليمين لأنه أنا ضربتها في ايش؟ في سالب يبقى 
+
+135
+00:14:38,980 --> 00:14:42,900
+بيصير موجب e أس 3e مع e أس ناقص 3e بيصير
+
+136
+00:14:42,900 --> 00:14:48,340
+e أس صفر في C2 في C2 خلصنا من الطرف اليمين الطرف 
+
+137
+00:14:48,340 --> 00:14:53,680
+الشمال بدنا نضربه ونقوله فقداش؟ فناقص يبقى بيصير
+
+138
+00:14:54,300 --> 00:15:00,960
+هذه بالموجب وهذه بالسالب على طول الخط يبقى بيصير
+
+139
+00:15:00,960 --> 00:15:09,880
+عندي جداش يساوي 2y ناقص y prime 2y ناقص y prime
+
+140
+00:15:09,880 --> 00:15:16,910
+وكل هذا الكلام مضروب في e أس 3t أظن نقسم على خمسة
+
+141
+00:15:16,910 --> 00:15:24,510
+يكون جبنا C2 يفضل لو قسمنا على خمسة بيصير C2 يساوي
+
+142
+00:15:24,510 --> 00:15:32,070
+خمس في مين؟ في 2y ناقص y prime في e أس 3t
+
+143
+00:15:40,830 --> 00:15:47,470
+لو جيت على المعادلة الأولى مثلا يبقى بيصير عندنا 
+
+144
+00:15:47,470 --> 00:15:55,030
+substitute in
+
+145
+00:15:55,030 --> 00:16:02,310
+equation one we get نحصل على ما يأتي هاي y على
+
+146
+00:16:02,310 --> 00:16:12,370
+الجهة اليسار تساوي C1 بيبقى C1e2t
+
+147
+00:16:12,370 --> 00:16:22,970
+C2 زائد اللي هو مين؟ خمس في اثنين y ناقص y prime في 
+
+148
+00:16:22,970 --> 00:16:28,010
+مين؟ في e أس سالب 3t مع e و زائد 3t مع
+
+149
+00:16:28,010 --> 00:16:34,210
+السلامة يبقى اتخلصنا منها طيب بدي أجيب هذه اين؟ 
+
+150
+00:16:34,210 --> 00:16:39,570
+على الجهة الثانية بيصير عندي مين؟ C1 e أس 2
+
+151
+00:16:39,570 --> 00:16:44,750
+t زي ما هو هذه بدي اجي يا بنات بإشارة سالبة يبقى 
+
+152
+00:16:44,750 --> 00:16:53,450
+بيصير عندي y سالب اثنين y ناقص y prime كلها على
+
+153
+00:16:53,450 --> 00:17:00,350
+كده ايش؟ على خمسة أو لو وحدنا المقامات كلها على خمسة
+
+154
+00:17:00,350 --> 00:17:10,160
+بيصير خمسة y ناقص اثنين y زائد y prime y ويساوي اللي 
+
+155
+00:17:10,160 --> 00:17:17,100
+هو 3y زائد y prime كل على جداش على خمسة طيب 
+
+156
+00:17:17,100 --> 00:17:22,460
+احنا بدنا C1 يبقى الـ C1 بدي اضرب الكل في e أس ناقص 
+
+157
+00:17:22,460 --> 00:17:30,140
+2t يبقى خمس في 3y زائد y prime في e أس
+
+158
+00:17:30,140 --> 00:17:38,930
+ناقص 2t يبقى جبت C1 و C2 ارجع اعوض في المعادلة
+
+159
+00:17:38,930 --> 00:17:45,590
+الأولى والثانية نرجع نكبح اللينا
+
+160
+00:17:50,480 --> 00:17:55,420
+لو عوضت في المعادلة بنفع؟ ما بنفعش بيصير مقدرة سواء 
+
+161
+00:17:55,420 --> 00:17:58,840
+مقدرة وبتظهرش المشتقة الثانية أنا بدي المشتقة
+
+162
+00:17:58,840 --> 00:18:02,180
+الثانية إذا المعلومات اللي جبتها من المعادلة 
+
+163
+00:18:02,180 --> 00:18:05,520
+الأولى والثانية بتروح تعوض بها وين؟ في المعادلة
+
+164
+00:18:05,520 --> 00:18:09,230
+الجاتة بتستنى اللي هي من المعادلة رقم؟ 3 
+
+165
+00:18:09,230 --> 00:18:14,350
+إذا بدي أشيل C1 و C2 من المعادلة رقم 3 بكون 
+
+166
+00:18:14,350 --> 00:18:20,870
+حصلت على المطلوب يبقى بناء عليه بدي يصير عندنا
+
+167
+00:18:20,870 --> 00:18:30,670
+مين؟ بدها تساوي أربعة في C1 وين C1 هيو يبقى أربعة
+
+168
+00:18:30,670 --> 00:18:38,690
+على خمسة في 3y زائد y prime في e أس ناقص 2
+
+169
+00:18:38,690 --> 00:18:42,990
+t مع e أس 
+
+216
+00:23:23,370 --> 00:23:24,030
+وعشرين
+
+217
+00:23:59,940 --> 00:24:03,520
+الواحد اللي خلصت أعمل أراضي الأشكال
+
+218
+00:24:13,750 --> 00:24:18,870
+وهي آخر سطر لازال موجود طيب
+
+219
+00:24:18,870 --> 00:24:24,370
+ننتقل الآن للـ section الجديد أو الـ level section 3
+
+220
+00:24:24,370 --> 00:24:25,370
+-2
+
+221
+00:24:45,620 --> 00:24:50,460
+يبقى section ثلاثة اثنين قولوا fundamental
+
+222
+00:24:50,460 --> 00:24:55,360
+solutions
+
+223
+00:24:55,360 --> 00:25:06,500
+مجموعة الحلول الأساسية of the linear homogeneous
+
+224
+00:25:06,500 --> 00:25:11,980
+differential equations
+
+225
+00:25:17,740 --> 00:25:24,180
+بنعرف شغلة جديدة ما كناش بنعرفها قبل هيك بقول let
+
+226
+00:25:24,180 --> 00:25:34,160
+الـ P and الـ Q be continuous functions be
+
+227
+00:25:34,160 --> 00:25:46,720
+continuous functions دوال متصلة on an interval
+
+228
+00:25:49,730 --> 00:25:57,630
+ثم لأي عملية فاي ثم لأي 
+
+229
+00:25:57,630 --> 00:26:10,170
+عملية فاي هذا مرتفع مرتفع 
+
+230
+00:26:10,170 --> 00:26:14,030
+مرتفع مرتفع
+
+231
+00:26:22,830 --> 00:26:34,950
+the differential operator
+
+232
+00:26:34,950 --> 00:26:49,390
+المؤثر التفاضلي الـ by the equation بالمعادلة اللي
+
+233
+00:26:49,390 --> 00:27:01,750
+هي من L of Phi بده يساوي Phi double prime زائد P of
+
+234
+00:27:01,750 --> 00:27:10,710
+T أو زائد P في الـ Phi prime زائد Q في الـ Phi
+
+235
+00:27:17,970 --> 00:27:24,270
+the value of 
+
+236
+00:27:24,270 --> 00:27:30,730
+L of I at
+
+237
+00:27:30,730 --> 00:27:39,870
+any point T اللي موجودة في الـ interval I
+
+238
+00:27:42,590 --> 00:27:52,910
+بروح بقول L of Phi of T بدي يساوي Phi double prime of T
+
+239
+00:27:52,910 --> 00:28:03,270
+زائد P of T في Phi prime of T زائد Q of T في Phi
+
+240
+00:28:03,270 --> 00:28:04,650
+of T
+
+241
+00:28:09,620 --> 00:28:11,200
+ماذا يحصل؟
+
+242
+00:28:36,950 --> 00:28:41,730
+كلمة differential operator مؤثر تفاضلي لم نسمع
+
+243
+00:28:41,730 --> 00:28:46,490
+بهذه التسمية من قبل لا في calculus a ولا b ولا c
+
+244
+00:28:46,490 --> 00:28:51,990
+لكن هذا احنا سمعنا به في المعادلة التفاضلية أنا ما
+
+245
+00:28:51,990 --> 00:28:58,030
+بهمني الاسم بهمني الجسم بهمني ما هو الشكل المؤثر
+
+246
+00:28:58,030 --> 00:29:04,470
+التفاضلي ولماذا سمي بهذا الاسم؟ يبقى العنوان اللي
+
+247
+00:29:04,470 --> 00:29:07,590
+احنا رافعينه الـ fundamental solutions مجموعة
+
+248
+00:29:07,590 --> 00:29:11,850
+الحلول الأساسية of the linear homogeneous differential
+
+249
+00:29:11,850 --> 00:29:17,190
+equations للمعادلة التفاضلية الخطية المتجانسة هذا
+
+250
+00:29:17,190 --> 00:29:20,930
+موضوع هذا الـ section طبعا لما أقول fundamental
+
+251
+00:29:20,930 --> 00:29:24,810
+solution مجموعة الحلول الأساسية كأنه بداية الـ general
+
+252
+00:29:24,810 --> 00:29:30,850
+solution تمام الـ general الحل العام الذي يحتوي كل 
+
+253
+00:29:30,850 --> 00:29:35,450
+الحلول الأخرى فلما أقول هذه مجموعة الحلول الأساسية
+
+254
+00:29:35,450 --> 00:29:41,780
+بأي حل آخر بيكون منضوي تحت هذه الحلول نبدأ المهد
+
+255
+00:29:41,780 --> 00:29:45,840
+لهذا الكلام بالتعريف التالي ثم بنظرية التعريف 
+
+256
+00:29:45,840 --> 00:29:50,640
+بيقول افترض أني عندي دالتين P and Q الدالتين
+
+257
+00:29:50,640 --> 00:29:56,180
+دوال متصلة على فترة ما واللتكن هذه الفترة I open
+
+258
+00:29:56,180 --> 00:30:01,040
+closed half open ما عنديش مشكلة تمام جالي for any 
+
+259
+00:30:01,040 --> 00:30:06,180
+function phi لأي function phi that is twice
+
+260
+00:30:06,180 --> 00:30:10,420
+differentiable عن فترة I يعني لو عندي function phi
+
+261
+00:30:10,420 --> 00:30:16,200
+قابلة للاشتقاق مرتين على هذه الفترة لو زيادة أكثر
+
+262
+00:30:16,200 --> 00:30:19,960
+ما فيش مشكلة المهم على الأقل بيبقى قابلة للاشتقاق
+
+263
+00:30:19,960 --> 00:30:23,020
+مرتين على المشتقة الأولى exist والمشتقة الثانية
+
+264
+00:30:23,020 --> 00:30:29,160
+exist على نفس الفترة هذه بنعرف المؤثر التفاضلي اللي
+
+265
+00:30:29,160 --> 00:30:35,900
+حددنا له الرمز L by the equation بالمعادلة التالية L
+
+266
+00:30:35,900 --> 00:30:41,960
+of Phi شو معناه رياضيا، شو معناه عمليا، المشتقة
+
+267
+00:30:41,960 --> 00:30:46,200
+الثانية للدالة Phi زائد الـ function P اللي
+
+268
+00:30:46,200 --> 00:30:51,780
+فوق مضروبة في مشتقة الـ Phi زائد الـ همين الدالة Q
+
+269
+00:30:51,780 --> 00:30:57,120
+اللي فوق مضروبة في Phi itself لاحظوا الاشتقاق من
+
+270
+00:30:57,120 --> 00:31:03,640
+الرتبة الثانية يبقى من هنا سميناه مؤثر تفاضلي لأن
+
+271
+00:31:03,640 --> 00:31:09,340
+المشتقات موجودة من هنا سميناه مؤثر تفاضلي، شو
+
+272
+00:31:09,340 --> 00:31:14,440
+بيعمل؟ هو عبارة عن مجموعة المشتقة الثانية لـ Phi
+
+273
+00:31:14,440 --> 00:31:18,900
+زي P of T المعطاة في مشتقة الـ Phi زي Q of T
+
+274
+00:31:18,900 --> 00:31:23,650
+المعطاة في Phi يعني لو جينا نقارن بينه وبين
+
+275
+00:31:23,650 --> 00:31:28,970
+المعادلة التفاضلية من الرتبة الثانية مش هيها برضه
+
+276
+00:31:28,970 --> 00:31:33,150
+كنا بنقول y double prime زي p of t في y prime زي q
+
+277
+00:31:33,150 --> 00:31:40,210
+of t في y بده يساوي zero صحيح ولا لا؟ تمام تمام لو
+
+278
+00:31:40,210 --> 00:31:44,790
+المؤثر التفاضلي بدي أحسبه عند أي نقطة موجودة في الـ
+
+279
+00:31:44,790 --> 00:31:49,830
+interval فاي بقول ممتاز ده بنخليه يؤثر على الـ
+
+280
+00:31:49,830 --> 00:31:55,410
+variable اللي هو T يبقى بيصير عند مين الـPhi of T
+
+281
+00:31:55,410 --> 00:31:59,310
+هو عبارة عن Phi double prime of T زائد P of T في
+
+282
+00:31:59,310 --> 00:32:04,470
+الـPhi Prime of T زائد Q of T في الـPhi خلي
+
+283
+00:32:04,470 --> 00:32:10,000
+المعلومة هذه عندك وتعالى ناخد النظرية التالية و
+
+284
+00:32:10,000 --> 00:32:14,060
+بدنا نحاول نقرأ بعد ذلك النظرية ونفهم ما هو 
+
+285
+00:32:14,060 --> 00:32:19,640
+المقصود منها يبقى بنا نيجي لأن النظرية بتقول ما
+
+286
+00:32:19,640 --> 00:32:26,500
+يأتي consider the
+
+287
+00:32:26,500 --> 00:32:32,080
+initial value problem مين هي الـ initial value
+
+288
+00:32:32,080 --> 00:32:40,740
+problem؟ Y double prime زائد P of T في Y prime زائد Q of
+
+289
+00:32:40,740 --> 00:32:49,580
+T في الـ Y بده يساوي G of T وفي نفس الوقت Y عند الـ T
+
+290
+00:32:49,580 --> 00:32:57,100
+node بده يساوي Y node Y prime عند الـ T node بده
+
+291
+00:32:57,100 --> 00:33:11,240
+يساوي Y prime node where حيث الـ P والـ q و الـ gene
+
+292
+00:33:11,240 --> 00:33:21,200
+our continuous functions are continuous functions
+
+293
+00:33:21,200 --> 00:33:30,600
+on an interval I
+
+294
+00:33:30,600 --> 00:33:38,640
+على اللي هو الفترة اللي عندنا I وهذا يحتوي على نقطة
+
+295
+00:33:38,640 --> 00:33:43,120
+T0 وهذا يحتوي
+
+296
+00:33:43,120 --> 00:33:47,320
+على
+
+297
+00:33:47,320 --> 00:33:52,020
+نقطة T0
+
+298
+00:33:52,020 --> 00:33:55,500
+هناك
+
+299
+00:33:55,500 --> 00:34:00,920
+قيمة محددة هناك 
+
+300
+00:34:00,920 --> 00:34:03,080
+قيمة محددة
+
+301
+00:34:06,230 --> 00:34:13,970
+one solution there exactly
+
+302
+00:34:13,970 --> 00:34:28,230
+one solution y تساوي five of t five of t of
+
+303
+00:34:28,230 --> 00:34:41,010
+this problem of this initial value problem and the
+
+304
+00:34:41,010 --> 00:34:50,450
+solution exists on
+
+305
+00:34:50,450 --> 00:34:55,930
+the interval I
+
+306
+00:35:37,010 --> 00:35:41,410
+نرجع لنص النظرية اللي احنا كتبناها مرة ثانية بدنا
+
+307
+00:35:41,410 --> 00:35:45,850
+نقرأ ثانية وبعدين هطلع عليكم مجموعة من الأسئلة 
+
+308
+00:35:45,850 --> 00:35:50,490
+دققوا معايا جالي اعتبر الـ initial value problem
+
+309
+00:35:50,490 --> 00:35:54,470
+أعطاني معادلة مرتبة ثانية زي ما أنتم شايفين وحطلي
+
+310
+00:35:54,470 --> 00:35:59,310
+عليها two initial conditions بعدها قال لي حيث الـ P
+
+311
+00:35:59,310 --> 00:36:02,430
+والـ Q والـ G اللي هو الرمز اللي بنكرره دائما
+
+312
+00:36:02,430 --> 00:36:06,110
+كانت هو الـ functions على الـ interval I وقال لي الـ
+
+313
+00:36:06,110 --> 00:36:10,210
+interval I بتحتوي نقطة من T node يبقى T node هي
+
+314
+00:36:10,210 --> 00:36:14,890
+نقطة موجودة في الـ interval I اللي عندنا في الـ
+
+315
+00:36:14,890 --> 00:36:19,770
+interval I يبقى T node موجودة داخل الـ interval قال
+
+316
+00:36:19,770 --> 00:36:25,050
+لي then there is exactly يبقى دي كلها تعتبر معلومات
+
+317
+00:36:25,260 --> 00:36:30,920
+إذا قال لي هناك حل
+
+318
+00:36:30,920 --> 00:36:38,500
+واحد فقط يوجد على
+
+319
+00:36:38,500 --> 00:36:41,380
+الفترة اللي عندنا اللي هي I
+
+320
+00:36:45,190 --> 00:36:49,570
+initial value problem احنا لما كان معنا الشروط
+
+321
+00:36:49,570 --> 00:36:53,850
+كنا بنجيب الـ general solution اللي ممكن يكون مئة
+
+322
+00:36:53,850 --> 00:36:57,290
+solution ولا ألف solution ولا مليون solution حسب
+
+323
+00:36:57,290 --> 00:37:01,790
+ما نغير الـ constants مظبوط لكن لما كنا نعود بالـ
+
+324
+00:37:01,790 --> 00:37:05,790
+initial conditions كنا بنجيب اللي حل واحد بضل عندي
+
+325
+00:37:05,790 --> 00:37:09,910
+C1 و C2 يبقى بيصير عندي there is a unique solution
+
+326
+00:37:09,910 --> 00:37:15,890
+حل وحيد فقط ما فيش غيره النظرية بتقول هذا الـ 
+
+327
+00:37:15,890 --> 00:37:20,290
+initial condition موجود عندك وهذول الدوال الـ P و
+
+328
+00:37:20,290 --> 00:37:23,310
+الـ Q والـ G continuous function على الـ interval I
+
+329
+00:37:23,310 --> 00:37:28,650
+والـ interval I بتحتوي على النقطة T0 جلد أن there
+
+330
+00:37:28,650 --> 00:37:34,330
+exist يوجد exactly one solution وهذا معرف على نفس
+
+331
+00:37:34,330 --> 00:37:39,030
+الفترة اللي هي I يعني كأن الـ domain تبع هذا الحل
+
+332
+00:37:39,030 --> 00:37:44,040
+هو نفس الفترة اللي هي عملناها I مين تقولي ماذا فهمتِ
+
+333
+00:37:44,040 --> 00:37:50,300
+من نص النظرية؟ تفضلي، نتعرض عليكِ في الأول ياخدعك،
+
+334
+00:37:50,300 --> 00:37:53,420
+تفضلي،
+
+335
+00:37:53,420 --> 00:37:58,500
+ممتاز،
+
+336
+00:37:58,500 --> 00:38:04,040
+إجابة إيجابيتين، أعطتنا مفهوم، المفهوم الواحد إن أي
+
+337
+00:38:04,040 --> 00:38:10,310
+problem لها حل، كلامها جيد، ممتاز جدا الإجابة
+
+338
+00:38:10,310 --> 00:38:14,690
+الثانية أن هذا الحل يكون وحيدا، واي الناس بيقول
+
+339
+00:38:14,690 --> 00:38:18,530
+there is exactly، بالضبط يوجد one صلى الله عليه
+
+340
+00:38:18,530 --> 00:38:23,870
+وسلامه ما وجدتش اتنين، هذا أعطتني مفهومين من خلال نص
+
+341
+00:38:23,870 --> 00:38:28,070
+النظرية، كلامها سليم مائة بالمائة، في مفهوم كمان
+
+342
+00:38:28,070 --> 00:38:33,670
+ثالث ممكن نفهم يا بنات؟ على الحل نفسه، اه مين اللي
+
+343
+00:38:33,670 --> 00:38:37,330
+بتحكي اللي بتقول هذا الحل فترة؟ اه أنتِ؟ واسمك أنتِ؟
+
+344
+00:38:38,290 --> 00:38:43,850
+هدوء أبو شويش بتتكمل لأخدعه ما فات، يعني عندما
+
+345
+00:38:43,850 --> 00:38:49,950
+تستدرك عليها ما فات بتقول إن هذا الحل الوحيد يتحقق
+
+346
+00:38:49,950 --> 00:38:54,810
+عالمين على نفس الفترة I اللي دوالي الثلاثة الـ P و
+
+347
+00:38:54,810 --> 00:38:58,650
+الـ Q والـ جي كنتني واص عليها، كلام سليم، هذه
+
+348
+00:38:58,650 --> 00:39:04,900
+المفهوم تبع النظرية يبقى في عندي حل، وحل وحيد، و
+
+349
+00:39:04,900 --> 00:39:09,740
+الحل معرف على نفس الفترة اللي همين اللي الدول
+
+350
+00:39:09,740 --> 00:39:14,720
+الثلاثة هذه معرفة عليها، كلام مظبوط، يبقى هي اللي
+
+351
+00:39:14,720 --> 00:39:17,960
+بتقوله نظري، أكثر من هيك ما بينه، يعني النظري بتقول
+
+352
+00:39:17,960 --> 00:39:22,970
+في عندك حل، والحل هذا وحيد ما فيش غيره والحل بيكون
+
+353
+00:39:22,970 --> 00:39:25,770
+معرف على نفس الفترة اللي دوالها دي بيكون عليها
+
+354
+00:39:25,770 --> 00:39:33,210
+دوال متصلة يبقى باللخص ما قالته الأخت دعاء والأخت
+
+355
+00:39:33,210 --> 00:39:44,770
+الثانية في التالي يبقى بدي أقول this theorem says
+
+356
+00:39:44,770 --> 00:39:46,110
+three things
+
+357
+00:39:51,250 --> 00:39:57,950
+هذه بتقول ثلاثة أشياء نمرة واحد the initial value 
+
+358
+00:39:57,950 --> 00:40:05,270
+problem has a solution في حل الـ initial value
+
+359
+00:40:05,270 --> 00:40:16,170
+problem اثنين the initial value problem has only
+
+360
+00:40:16,170 --> 00:40:27,880
+one solution ما فيش إلا حل واحد فقط لغيره ثلاثة the
+
+361
+00:40:27,880 --> 00:40:32,920
+solution phi
+
+362
+00:40:32,920 --> 00:40:43,160
+of T is defined معرف on the interval
+
+363
+00:40:49,740 --> 00:40:59,040
+على الفترة I where the coefficient
+
+364
+00:40:59,040 --> 00:41:04,320
+coefficients
+
+365
+00:41:04,320 --> 00:41:13,940
+اللي هو الـ P والـ Q and الـ G are continuous
+
+366
+00:41:19,130 --> 00:41:28,190
+continuous and the solution and solution
+
+367
+00:41:28,190 --> 00:41:32,670
+is
+
+368
+00:41:32,670 --> 00:41:47,310
+at least على الأقل a twice differentiable function
+
+369
+00:41:54,770 --> 00:41:59,530
+نعطي بعض الأمثلة على هذه المفاهيم
+
+370
+00:42:20,500 --> 00:42:31,920
+المثال الأول example بيقول
+
+371
+00:42:31,920 --> 00:42:37,900
+يُحدد determine the
+
+372
+00:42:37,900 --> 00:42:39,340
+longest interval
+
+373
+00:42:52,900 --> 00:43:04,020
+the initial value problem have
+
+374
+00:43:04,020 --> 00:43:07,360
+a
+
+375
+00:43:07,360 --> 00:43:11,220
+unique twice
+
+376
+00:43:11,220 --> 00:43:12,880
+differentiable solution
+
+377
+00:43:39,000 --> 00:43:45,140
+don't attempt to
+
+378
+00:43:45,140 --> 00:43:46,280
+find the solution
+
+379
+00:44:00,370 --> 00:44:09,210
+عشرة من الكتاب طبعا y double prime زائد cosine t في الـ y
+
+380
+00:44:09,210 --> 00:44:22,760
+prime زائد y في الـ absolute value لـ t زائد ثلاثة لن 
+
+381
+00:44:22,760 --> 00:44:30,080
+absolute value لـ T في الـ Y بده يساوي Zero والـ Y
+
+382
+00:44:30,080 --> 00:44:37,960
+عند اثنين بده يساوي ثلاثة والـ Y prime عند اثنين
+
+383
+00:44:37,960 --> 00:44:40,760
+بده يساوي مان بده يساوي واحد
+
+384
+00:44:58,310 --> 00:45:02,690
+يبقى النظرية السابقة قبل قليل لما أعطاني معادلة
+
+385
+00:45:02,690 --> 00:45:06,290
+فاضلة من رتبة ثانية نحط عليها two initial conditions
+
+386
+00:45:06,290 --> 00:45:12,010
+والمعاملات كانت دوال متصلة على فترة واللتكن هذه
+
+387
+00:45:12,010 --> 00:45:19,050
+الفترة I قال there exists exactly يوجد حل وحيد لهذه
+
+388
+00:45:19,050 --> 00:45:25,850
+المعادلة والحل هذا موجود على نفس الفترة اللي هي
+
+389
+00:45:25,850 --> 00:45:30,310
+اللي عندنا I السؤال اللي عندنا هنا شبه بيقول بيقول
+
+390
+00:45:30,310 --> 00:45:35,480
+هات لي أكبر فترة بحيث أن الـ initial value problem
+
+391
+00:45:35,480 --> 00:45:39,980
+has a unique twice differentiable solution يعني
+
+392
+00:45:39,980 --> 00:45:45,800
+عندها حل قابل للاشتقاق مرتين عليها وياك تحاول توجد
+
+393
+00:45:45,800 --> 00:45:49,520
+هذا الحل يعني أنا مش طالب الحل تبع المعادلة أنا
+
+394
+00:45:49,520 --> 00:45:54,900
+طالب الفترة بس اللي الحل عليها بيكون معرف صحيح حل
+
+395
+00:45:54,900 --> 00:46:00,880
+واحد وقابل للاشتقاق مرتين على هذه الفترة بقول لك كويس
+
+396
+00:46:01,320 --> 00:46:05,180
+إذا أنا بدي آجي أطبق النظرية بدي أدور على 
+
+397
+00:46:05,180 --> 00:46:09,840
+المعاملات وين المعاملات اللي عندي cosine T وثلاثة 
+
+398
+00:46:09,840 --> 00:46:14,460
+لانتهينا Zero ريحني تمام يبقى هذه constant
+
+399
+00:46:14,460 --> 00:46:18,080
+function الـ constant function بتعتبريها متصلة على
+
+400
+00:46:18,080 --> 00:46:23,320
+أي فترة على أي فترة بدك إياها إذا أنا لو جيت للـ 
+
+401
+00:46:23,320 --> 00
+
+431
+00:49:26,660 --> 00:49:34,580
+الاثنين and the functions
+
+432
+00:49:34,580 --> 00:49:44,460
+هي cosine الـ T and تلاتة لين absolute value لـ T
+
+433
+00:49:44,460 --> 00:49:51,240
+are continuous يبقى هذه الفترة اللي هو إيه عشان
+
+434
+00:49:51,240 --> 00:49:52,180
+بده إياها
+
+435
+00:49:55,110 --> 00:50:00,390
+اللي طبعًا ما تحلش المعادلة أو أصح تحاول تحل
+
+436
+00:50:00,390 --> 00:50:05,310
+المعادلة يعني مش تروح تضيع وقتك بالبلاش لذلك لو
+
+437
+00:50:05,310 --> 00:50:10,170
+جاكي سؤال يا بنات في الامتحان بقرأ السؤال جيدًا قبل
+
+438
+00:50:10,170 --> 00:50:15,050
+ما أمسك الجلم و أبدأ حل و بحدد ما هو المطلوب من
+
+439
+00:50:15,050 --> 00:50:18,730
+السؤال إذا حددت ما هو المطلوب من السؤال بسجل وقت
+
+440
+00:50:18,730 --> 00:50:22,090
+كويس ما حددت بسيطة أمسك الجلم و أنا مش عارف وين
+
+441
+00:50:22,090 --> 00:50:30,430
+رايح، حطيب نمرة V من نفس السؤال بيقول
+
+442
+00:50:30,430 --> 00:50:39,730
+لي X ناقص اثنين YW prime
+
+443
+00:50:42,260 --> 00:50:54,200
+y prime زائد x ناقص اثنين ثاني الـ x ثاني الـ x كل
+
+444
+00:50:54,200 --> 00:51:01,020
+هذا في y بده يساوي zero و ال initial conditions y
+
+445
+00:51:01,020 --> 00:51:06,580
+عندي التلاتة بده يساوي واحد و y prime عندي التلاتة
+
+446
+00:51:06,580 --> 00:51:10,460
+بده يساوي قداش؟ بده يساوي اثنين
+
+447
+00:51:16,650 --> 00:51:22,570
+يبقى نفس السؤال قال لي هات لي أطول فترة بحيث تدلّق
+
+448
+00:51:22,570 --> 00:51:26,170
+قابلة اشتقاق بحيث الحل تبعد الـ function يكون قابل
+
+449
+00:51:26,170 --> 00:51:30,690
+الاشتقاق مرتين على نفس الفترة يعني أنا بدأ أطبّق له
+
+450
+00:51:30,690 --> 00:51:34,870
+النظرية اللي قبلها بقليل بقوله كويس هذا السؤال
+
+451
+00:51:34,870 --> 00:51:39,900
+بيختلف عن سابقه، سابقه كان المعامل تبع y double
+
+452
+00:51:39,900 --> 00:51:45,660
+prime واحد صحيح روحنا باعتبار كأنه جاسمين وجاهزين
+
+453
+00:51:45,660 --> 00:51:50,300
+هذه لا المعامل x ناقص اثنين إذا أنا بدأ اروح أجسم
+
+454
+00:51:50,300 --> 00:51:55,380
+على مين؟ على x ناقص اثنين إذا لو جسمت الطرفين على x
+
+455
+00:51:55,380 --> 00:52:01,000
+ناقص اثنين بيصير y double prime زائد واحد على x
+
+456
+00:52:01,000 --> 00:52:06,800
+ناقص اثنين في الـ y prime زائد تان الـ x في y
+
+457
+00:52:09,790 --> 00:52:18,990
+أصبح الـ P of X هي واحد على X ناقص اثنين as in الـ
+
+458
+00:52:18,990 --> 00:52:23,530
+discontinuity بيحصل وين؟ عند اثنين يعني هذه
+
+459
+00:52:23,530 --> 00:52:29,870
+continuous على كل real line مع هذا الاثنين يبقى
+
+460
+00:52:29,870 --> 00:52:32,970
+هذه is continuous
+
+461
+00:52:34,510 --> 00:52:45,190
+for all x التي لا تساوي اثنين for all x التي لا
+
+462
+00:52:45,190 --> 00:52:48,950
+تساوي اثنين for all x التي لا تساوي اثنين for all
+
+463
+00:52:48,950 --> 00:52:57,390
+x التي لا تساوي اثنين for all x التي لا تساوي
+
+464
+00:52:57,390 --> 00:53:04,150
+اثنين، باية على اثنين و تلاتة باية على اثنين و خمسة
+
+465
+00:53:04,150 --> 00:53:09,190
+باية على اثنين طبعًا كله زائد أو ناقص كله زائد أو
+
+466
+00:53:09,190 --> 00:53:15,410
+ناقص اللي هو تلاتة باية على اثنين زائد أو ناقص
+
+467
+00:53:15,410 --> 00:53:21,710
+كذلك خمسة باية على اثنين وإلى ما شاء الله طب
+
+468
+00:53:21,710 --> 00:53:27,220
+تعالوا خليني على الـ real line هيك نشوف شغلنا كويس، لو
+
+469
+00:53:27,220 --> 00:53:33,100
+جيت قلت هذا الـ real لاين هي الـ zero بعد الـ zero
+
+470
+00:53:33,100 --> 00:53:38,400
+بيجيني واحد بعد الواحد بيجيني مين؟ اثنين بعد اثنين
+
+471
+00:53:38,400 --> 00:53:41,860
+بيجيني مين؟ بيجيني تلاتة
+
+472
+00:53:44,300 --> 00:53:48,980
+وبعد تلاتة أربعة خمسة إلى آخره مش هذا موضوعنا،
+
+473
+00:53:48,980 --> 00:53:53,420
+موضوعنا أن الـ discontinuity هذا حصل عند اثنين،
+
+474
+00:53:53,420 --> 00:53:58,760
+يعني عند اثنين هذا في discontinuity لمن؟ للدالة
+
+475
+00:53:58,760 --> 00:54:03,220
+الأولى، الدالة الثانية الـ discontinuity عند الـ بايع
+
+476
+00:54:03,220 --> 00:54:07,920
+ثاني البايع قداش يا بنات؟ تلاتة صحيحه وأربعة عشر من مية
+
+477
+00:54:07,920 --> 00:54:12,220
+على اثنين يعني أكثر من واحد ونصف بحاجة بسيطة يعني
+
+478
+00:54:12,220 --> 00:54:18,060
+في discontinuity هنا تقريبًا يبقى هذه اللي هي الـ by
+
+479
+00:54:18,060 --> 00:54:22,960
+على اثنين في ان اللي بدأ ليه تلاتة by على اثنين
+
+480
+00:54:23,250 --> 00:54:27,370
+يعني واحدة باية على اثنين لحوالي واحد ونصف،
+
+481
+00:54:27,370 --> 00:54:36,010
+مظبوط؟ واحد ونصف في تلاتة باربعة ونصف، مش هيك؟
+
+482
+00:54:36,010 --> 00:54:41,310
+يبقى تلاتة باية على اثنين بدها تجيكي هنا، هذه هنا
+
+483
+00:54:41,310 --> 00:54:46,190
+بدها تجيكي أربعة وهنا بدها تجيكي ليه؟ تلاتة باية
+
+484
+00:54:46,190 --> 00:54:51,450
+على مين؟ على الاثنين مرة ثانية
+
+485
+00:54:55,670 --> 00:55:00,870
+يبقى هذه الثلاثة باعي على اثنين في discontinuity
+
+486
+00:55:00,870 --> 00:55:06,850
+كمان، وية عندها، طب احنا جالي هات للـ longest interval
+
+487
+00:55:06,850 --> 00:55:10,750
+بقولوا استنى شوية برجع للـ initial condition الـ
+
+488
+00:55:10,750 --> 00:55:14,790
+initial condition محسوب وين؟ عندي التلاتة إذا
+
+489
+00:55:14,790 --> 00:55:20,710
+التلاتة موجود داخل الفترة المفتوحة من اثنين لتلاتة
+
+490
+00:55:20,710 --> 00:55:25,970
+pi على اثنين الفترة اللي عندنا هذه ها هاج هذه اللي
+
+491
+00:55:25,970 --> 00:55:29,750
+الفترة اللي تحتوي على الـ initial condition، مسكت من
+
+492
+00:55:29,750 --> 00:55:31,990
+عند الـ discontinuity اللي بعده إلى الـ
+
+493
+00:55:31,990 --> 00:55:35,170
+discontinuity اللي بعده، يبقى الفترة في ما بينهم
+
+494
+00:55:35,170 --> 00:55:40,510
+كلًا الدالتين أو جميع الدوال على هذه الفترة هي دوال
+
+495
+00:55:40,510 --> 00:55:49,430
+متصلة يبقى باجي بقول له the longest interval
+
+496
+00:55:49,430 --> 00:55:55,690
+interval interval
+
+497
+00:55:59,330 --> 00:56:09,210
+that contains اللي هو تلاتة is من اثنين لغاية
+
+498
+00:56:09,210 --> 00:56:16,650
+تلاتة by على اثنين and the
+
+499
+00:56:16,650 --> 00:56:29,240
+functions are continuous on it جميع الدوال اللي هو
+
+500
+00:56:29,240 --> 00:56:37,180
+بالتالي الـ solution عليها بيكون صحيحة and the
+
+501
+00:56:37,180 --> 00:56:40,880
+functions are continuous or infinite and the
+
+502
+00:56:40,880 --> 00:56:42,580
+solution
+
+503
+00:56:44,090 --> 00:56:50,490
+exist و الحل عليها بيكون مانو؟ بيكون متحقق أو موجود
+
+504
+00:56:50,490 --> 00:56:55,230
+يبقى مثل هذا النوع من المسائل بس بده الفترة و
+
+505
+00:56:55,230 --> 00:56:59,450
+جابوها المدرسين لكوا في أعمال الفصل بيجيبوها كثير
+
+506
+00:56:59,450 --> 00:57:03,630
+هات للفترة اللي الحل عليها بيكون صحيح، يكبر، يكبر
+
+507
+00:57:03,630 --> 00:57:08,790
+أكثر من هيك، د مابدناش من هذا النوع من المسائل
+
+508
+00:57:27,030 --> 00:57:32,570
+فضلي أنا أنا أنا أنا أنا أنا أنا أنا أنا
+
+509
+00:57:37,700 --> 00:57:41,740
+احنا حددنا الدالة الأولى وأن الـ discontinuity
+
+510
+00:57:41,740 --> 00:57:46,000
+تبعها يبقى باقي بكون تبقى continuous جينا على
+
+511
+00:57:46,000 --> 00:57:50,500
+الدالة الثانية حددت الـ discontinuity تبعها يبقى
+
+512
+00:57:50,500 --> 00:57:54,740
+بروح على الـ initial condition جال لي why عندي
+
+513
+00:57:54,740 --> 00:58:01,030
+التلاتة، يبقى الحل بدّه يكون وين؟ عندها T تساوي تلاتة
+
+514
+00:58:01,030 --> 00:58:05,010
+وعندها X يساوي تلاتة، باجي بدور على التلاتة
+
+515
+00:58:05,010 --> 00:58:08,890
+موجودة في أي من الفترات اللي بتبقى continuous
+
+516
+00:58:08,890 --> 00:58:13,950
+عليها، طبعًا هنا كم فترة عندها يا بنات؟ اثنين،
+
+517
+00:58:13,950 --> 00:58:17,870
+تلاتة، عشرة، مية، مليون، جد ما بدك، إلى أن يرسل
+
+518
+00:58:17,870 --> 00:58:21,330
+الله الأرض وامن عليها، بس أنا ما بديش أكل، بدي
+
+519
+00:58:21,330 --> 00:58:26,030
+الفترة التي تحتوي على الرقم تلاتة، على X يساوي
+
+520
+00:58:26,030 --> 00:58:31,070
+تلاتة، باجي بطلع، بلاقي تلاتة هذه اللي جالها الـ
+
+521
+00:58:31,070 --> 00:58:34,070
+discontinuity عند اثنين والثانية الـ discontinuity
+
+522
+00:58:34,070 --> 00:58:38,870
+عند تلاتة باية على اثنين، مظبوط؟ يعني تها لو جيت
+
+523
+00:58:38,870 --> 00:58:44,950
+أرسمها لك، راسم، بقول لك هيهذه الدالة الأولى كانت عند
+
+524
+00:58:44,950 --> 00:58:50,250
+اثنين، عند اثنين مفتوحة بعدها continuous وقبلها
+
+525
+00:58:50,250 --> 00:58:55,870
+continuous على طول، جينا للثانية عند الـ by على
+
+526
+00:58:55,870 --> 00:59:00,910
+اثنين، قبل اثنين ما ليش علاقة فيها، جينا بعد اثنين
+
+527
+00:59:00,910 --> 00:59:07,010
+لجينا تلاتة هي التلاتة اللي احنا بنحسب عندها، تمام؟
+
+528
+00:59:07,010 --> 00:59:10,590
+جينا اللي بعد اللي هو تلاتة باية على اثنين، يبقى
+
+529
+00:59:10,590 --> 00:59:14,610
+هذه تلاتة باية على اثنين في discontinuity عندها
+
+530
+00:59:14,610 --> 00:59:19,470
+يبقى بيصير بعدها ولسه خمسة باية على اثنين بدنا
+
+531
+00:59:19,470 --> 00:59:22,130
+نوقف عنده وسبعة باية على اثنين بدنا... كله بدنا
+
+532
+00:59:22,130 --> 00:59:26,270
+نوقف عنده، وهنا لما نيجي لباية على اثنين، باية على
+
+533
+00:59:26,270 --> 00:59:30,780
+اثنين اجت قبل اثنين، يبقى هذه اللي همّ باية على
+
+534
+00:59:30,780 --> 00:59:35,660
+اثنين، إذا هذه تبقى continuous على الفترة اللي
+
+535
+00:59:35,660 --> 00:59:40,300
+عندنا هذه، تمام؟ إذا أين المنطقة المشتركة بين
+
+536
+00:59:40,300 --> 00:59:45,180
+الفترتين والتي تحتوي على الرقم تلاتة، بلاقي إلا
+
+537
+00:59:45,180 --> 00:59:50,950
+الفترة اللي عندنا هذه، هذه المنطقة المشتركة ما بين
+
+538
+00:59:50,950 --> 00:59:54,410
+الـ continuity للدالة الأولى والـ continuity للدالة
+
+539
+00:59:54,410 --> 00:59:57,630
+الثانية يعني بدّها الفترة اللي two functions
+
+540
+00:59:57,630 --> 01:00:01,410
+continuous عليها وبتجمل هذه الفترة على الرقم
+
+541
+01:00:01,410 --> 01:00:04,750
+تلاتة اللي حسبنا الـ initial conditions عندهم، ماشي
+
+542
+01:00:04,750 --> 01:00:13,610
+طيب بننتقل الآن إلى نظرية جديدة كذلك، يبقى theorem
+
+543
+01:00:18,050 --> 01:00:23,150
+قعد الكتاب بيسميها اللي هو main بيسميها الـ
+
+544
+01:00:23,150 --> 01:00:33,530
+principle of superposition، الـ principle of
+
+545
+01:00:33,530 --> 01:00:37,090
+superposition
+
+546
+01:00:37,090 --> 01:00:42,470
+قاعدة
+
+547
+01:00:42,470 --> 01:00:46,730
+التطابق، بيقول
+
+548
+01:00:46,730 --> 01:00:55,920
+الـ FY1 and Y2 are
+
+549
+01:00:55,920 --> 01:01:00,200
+two
+
+550
+01:01:00,200 --> 01:01:05,840
+solutions
+
+551
+01:01:05,840 --> 01:01:22,570
+of the differential equation L of Y بده يساوي L of
+
+552
+01:01:22,570 --> 01:01:29,750
+Y بده يساوي YW prime زي P of T في الـ Y prime زي Q
+
+553
+01:01:29,750 --> 01:01:35,510
+of T في الـ Y بده يساوي Zero واعتبريه لهذه المعادلة
+
+554
+01:01:35,510 --> 01:01:45,930
+رقم واحد then Y يساوي C واحد Y واحد زي C اثنين Y
+
+555
+01:01:45,930 --> 01:01:52,880
+اثنين is also
+
+556
+01:01:52,880 --> 01:01:59,180
+a solution for
+
+557
+01:01:59,180 --> 01:02:07,040
+any values
+
+558
+01:02:07,040 --> 01:02:12,420
+of the constants
+
+559
+01:02:14,010 --> 01:02:28,090
+والعنوان هي الواقع C1 وC2 أخد هذه الملاحظة إذا C1
+
+560
+01:02:28,090 --> 01:02:34,490
+تساوي 0 أو C2 تساوي 0
+
+561
+01:02:38,810 --> 01:02:44,910
+C2Y2 or C1Y1
+
+562
+01:02:44,910 --> 01:02:58,650
+is a solution is a solution for the same
+
+563
+01:02:58,650 --> 01:03:03,710
+differential equation one
+
+564
+01:03:35,270 --> 01:03:39,970
+بنشوف ليش سمّنها قاعدة التطابق principle of
+
+565
+01:03:39,970 --> 01:03:45,650
+superposition قل لو كان عندي y1 و y2 عبارة عن حلين
+
+566
+01:03:45,650 --> 01:03:51,190
+للمعادلة التفاضلية اللي قدامنا هذه، ثم كونستانت في
+
+567
+01:03:51,190 --> 01:03:57,190
+الحل الأول زائد كونستانت في الحل الثاني is also is
+
+568
+01:03:57,190 --> 01:04:02,530
+a solution for any values of the constant c1 and
+
+569
+01:04:02,530 --> 01:04:08,430
+c2 يبقى احنا عندنا حلين، من الحلين بدي أجيب كمان حل
+
+570
+01:04:09,820 --> 01:04:13,860
+يتطابق مع حل المعادلة التفاضلية، يعني بدّه يكون كذلك
+
+571
+01:04:13,860 --> 01:04:19,420
+هو حل المعادلة التفاضلية اللي عندنا هذه، شوفوا يا
+
+572
+01:04:19,420 --> 01:04:24,520
+بنات بقول الملاحظة لو كان C1 يساوي 0، لو شلنا C1
+
+573
+01:04:24,520 --> 01:04:30,870
+وحطينا بدل C0 ايش بيظل؟ بيصير الشكل الحل Y تساوي
+
+574
+01:04:30,870 --> 01:04:37,230
+C2Y2، لإن أنا هنا ما حطّتش أي conditions على C1 وC2
+
+575
+01:04:37,230 --> 01:04:42,170
+أنه جالس لإنّي to real constant يبقى أي ثوابت لا تنق
+
+576
+01:04:42,170 --> 01:04:46,880
+صفر ولا غير الصفر، طب افرض C2 كمان في Zero بيصير Y
+
+577
+01:04:46,880 --> 01:04:51,280
+تساوي Zero هو عبارة عن حل مين للمعادلة التفاضلي؟
+
+578
+01:04:51,280 --> 01:04:55,740
+Zero ومشتقة Zero بـ Zero ومشتقة Zero بـ Zero
+
+579
+01:04:55,740 --> 01:05:01,420
+ومجموعهم يساوي قداش؟ يساوي Zero، يبقى هنا لو كان أحد
+
+580
+01:05:01,420 --> 01:05:07,260
+الثوابت أو كلاهما كمان Zero، يبقى اللي بيظل بيكون هو
+
+581
+01:05:07,260 --> 01:05:12,720
+مين؟ حل المعادلة، فلو كان c1 بـ zero بيظل أن c2 y2 هو
+
+582
+01:05:12,720 --> 01:05:18,160
+حل المعادلة التفاضلية، وكذلك لو كان c2 هو zero بيظل
+
+583
+01:05:18,160 --> 01:05:23,840
+أن c1 y1 هو عبارة عن حل مين للمعادلة التفاضلية، إذا
+
+584
+01:05:23,840 --> 01:05:28,660
+يا بنات أنا لو قدرت أجيب حلين للمعادلة التفاضلية
+
+585
+01:05:28,660 --> 01:05:34,760
+بقدر أجيب حل ثالث للمعادلة التفاضلية باستخدام مين؟
+
+586
+01:05:35,080 --> 01:05:39,540
+الحلين، ما هو الحل الثالث؟ كونستانت في الحل الأول و
+
+587
+01:05:39,540 --> 01:05:43,200
+كونستانت في الحل الثاني وبجمع الاثنين بيعطيني حل
+
+588
+01:05:43,200 --> 01:05:47,620
+جديد للمعادلة التفاضلية، طبعًا واحدة هتسأل وتقول
+
+589
+01:05:47,620 --> 01:05:53,580
+تقدر تبرهن هذا الكلام؟ أقول لها بنقدر والبرهان very
+
+590
+01:05:53,580 --> 01:05:57,260
+easy مش صعب يعني، يبقى هذا الـ proof
+
+591
+01:06:01,420 --> 01:06:05,960
+بيقول ليش؟ لو كان Y1 هو حل المعادلة هذه، يبقى
+
+592
+01:06:05,960 --> 01:06:14,200
+هيحققها، صحيح ولا لأ؟ يبقى بادي بقول، الآن Y1 is a
+
+593
+01:06:14,200 --> 01:06:24,600
+solution ماذا سنجد من هذا الوضع؟ أن الـ L of Y1 يساوي
+
+594
+01:06:24,600 --> 01:06:34,120
+Y1 double prime زائد P of T في Y1 prime زائد Q of
+
+595
+01:06:34,120 --> 01:06:37,080
+T في Y1 يزيد
+
+596
+01:06:39,680 --> 01:06:49,860
+طيب الآن Y2 is a solution بده يعطينا أن الـ L of Y2
+
+597
+01:06:49,860 --> 01:06:58,020
+بده يساوي Y2 double prime زاد P of T في الـ Y2
+
+598
+01:06:58,020 --> 01:07:05,260
+prime زاد الـ Q of T في الـ Y2 بده يساوي Zero كذلك
+
+599
+01:07:07,760 --> 01:07:13,500
+هذه المعقدات حتى الآن جالي Y1 وY2 هم حلّوا
+
+600
+01:07:13,500 --> 01:07:18,320
+المعادلة التفاضلية، شو بدّي أثبت؟ بدّي أثبت أن هذا
+
+601
+01:07:18,320 --> 01:07:25,460
+ماله؟ حل آخر للمعادلة التفاضلية بقوله إذا لو جدت
+
+602
+01:07:25,460 --> 01:07:33,760
+أثبت أن الـ L وC1 Y1 زي C2 Y2 يساوي Zero بتم
+
+603
+01:07:33,760 --> 01:07:42,360
+المطلوب، لو قلت أثبت أن c1y1 زاد c2y2 بدّه يستوي 0
+
+604
+01:07:42,360 --> 01:07:46,920
+بيصير هذا هو عبارة عن حل مين للمعادلة التفاضلية
+
+605
+01:07:46,920 --> 01:07:52,380
+بقول لها
+
+646
+01:13:53,140 --> 01:14:03,860
+y one prime y two prime - ماقص y one prime y two is called
+
+647
+01:14:03,860 --> 01:14:09,560
+is
+
+648
+01:14:09,560 --> 01:14:13,480
+called the Wronskian
+
+649
+01:14:31,640 --> 01:14:35,280
+و بالروح نكتب
+
+650
+01:15:01,370 --> 01:15:14,390
+هنا سنكتب الشكل التالي و هو W of Y1 وY2 وY2 prime وY2 prime
+
+651
+01:15:14,390 --> 01:15:17,790
+وY2 prime
+
+652
+01:15:17,790 --> 01:15:21,950
+وY2 prime
+
+653
+01:15:21,950 --> 01:15:28,610
+وY2 prime وY2 prime وY2 prime وY2 prime وY2 prime وY2 prime وY2 prime وY2 prime وY2 prime وY2 prime وY2 prime وY2 prime
+
+654
+01:15:28,610 --> 01:15:28,670
+وY2 prime وY2 prime وY2 prime وY2 prime وY2 prime وY2 prime وY2 prime وY2 prime وY2 prime وY2 prime وY2 prime وY2 prime
+
+655
+01:15:28,670 --> 01:15:28,710
+وY2 prime وY2 prime وY2 prime وY2 prime وY2 prime وY2 prime وY2 prime وY2 prime وY2 prime وY2 prime وY2 prime وY2 prime
+
+656
+01:15:28,710 --> 01:15:28,750
+وY2 prime وY2 prime وY2 prime وY2 prime وY2 prime وY2 prime وY2 prime وY2 prime وY2 prime وY2 prime وY2 prime وY2 prime
+
+657
+01:15:28,750 --> 01:15:55,390
+وY2 prime وY2 prime وY2 prime وY2 prime as a determinant كمحدد ها
+
+658
+01:15:55,390 --> 01:15:59,190
+دي البركة هنا والله بقول اللي عندي y واحد و y اتنين
+
+659
+01:15:59,190 --> 01:16:01,970
+are two solutions لل homogenous differential
+
+660
+01:16:01,970 --> 01:16:06,950
+equation اللي عندنا إذا فينا function جديدة الحل
+
+661
+01:16:06,950 --> 01:16:12,210
+الأول في مشتقة الحل الثاني ناقص مشتقة الحل الأول
+
+662
+01:16:12,210 --> 01:16:16,930
+في الحل الثاني بيعطينا function جديدة بسميها ال
+
+663
+01:16:16,930 --> 01:16:21,590
+Wronskian ال w silent يا بنات منطقش ال w يبقى
+
+664
+01:16:21,590 --> 01:16:26,310
+بسميها ال Wronskian of ال y one و ال y two and we
+
+665
+01:16:26,310 --> 01:16:32,650
+write بنروح نكتب القيمة العددية لمين للWronskian
+
+666
+01:16:32,650 --> 01:16:38,970
+حدّده الرمز W as a function of T أو W ل Y1 وY2 as
+
+667
+01:16:38,970 --> 01:16:46,150
+a function of T وهو عبارة عن المحدد الثانائي Y1 صف
+
+668
+01:16:46,150 --> 01:16:53,380
+الأول تبع Y1 وY2 صف التاني مشتقة Y1 ومشتقة Y2وكنا
+
+669
+01:16:53,380 --> 01:16:57,140
+زمان بنفك المحددات نقول حاصل ضرب عناصر القطر
+
+670
+01:16:57,140 --> 01:17:03,800
+الرئيسي ناقص حاصل ضرب عناصر القطر الثانوي يبقى لو
+
+671
+01:17:03,800 --> 01:17:11,360
+جيت حاصل ضرب عناصر القطر الرئيسي يبقى Y1Y2'
+
+672
+01:17:12,000 --> 01:17:21,180
+ناقص حاصل ضرب عناصر القطر الثانوي يبقى Y1'Y2 بهذا
+
+673
+01:17:21,180 --> 01:17:26,200
+الشكل يبقى من ال alpha ساعدا إذا بدى أحسب ال Wronskian
+
+674
+01:17:26,200 --> 01:17:30,580
+كله ال two solutions بحط الحل الأول حل التاني
+
+675
+01:17:30,580 --> 01:17:35,080
+مشتقة الأول مشتقة التاني باخد المحدد بفك المحدد
+
+676
+01:17:35,080 --> 01:17:38,640
+القيمة اللى بتطلع بتكون هي ال Wronskian كله ال main
+
+677
+01:17:38,640 --> 01:17:43,040
+ال two solutions للمعادلة التفاضلية اللى عندنا
+
+678
+01:17:43,040 --> 01:17:47,100
+نعطيكي مثال توضيح بسيط يبقى example
+
+679
+01:17:55,860 --> 01:18:07,160
+Find the Wronskian for
+
+680
+01:18:07,160 --> 01:18:15,780
+the functions T وT E of T
+
+681
+01:18:18,570 --> 01:18:23,150
+عرف جداش ومستقل لمين الانتقالات الموجودة في
+
+682
+01:18:23,150 --> 01:18:24,610
+الانتقالات الموجودة في الانتقالات الموجودة في
+
+683
+01:18:24,610 --> 01:18:28,770
+الانتقالات
+
+684
+01:18:28,770 --> 01:18:31,450
+الموجودة في الانتقالات الموجودة في الانتقالات
+
+685
+01:18:31,450 --> 01:18:33,610
+الموجودة في الانتقالات الموجودة في الانتقالات
+
+686
+01:18:33,610 --> 01:18:36,090
+الموجودة في الانتقالات الموجودة في الانتقالات
+
+687
+01:18:36,090 --> 01:18:36,110
+الموجودة في الانتقالات الموجودة في الانتقالات
+
+688
+01:18:36,110 --> 01:18:36,170
+الموجودة في الانتقالات الموجودة في الانتقالات
+
+689
+01:18:36,170 --> 01:18:41,710
+الموجودة في الانتقالات الموجودة في الانت
+
+690
+01:18:42,420 --> 01:18:49,160
+بواحد هذه مشتقة حاصن ضرب دالتين يبقى الأولى في
+
+691
+01:18:49,160 --> 01:18:54,880
+مشتقة الدالة الثانية زائد دالة ثانية في مشتقة
+
+692
+01:18:54,880 --> 01:19:01,800
+الأولى يبقى T EOS T بالشكل اللى عندناالرح نحسب هذا
+
+693
+01:19:01,800 --> 01:19:08,460
+المحدد يبجى بدنفكه حاصل ضرب عناصر قطر رئيسي ماقص
+
+694
+01:19:08,460 --> 01:19:12,660
+حاصل ضرب عناصر قطر الثانوي حاصل ضرب عناصر قطر
+
+695
+01:19:12,660 --> 01:19:19,820
+الرئيسي يبجى T في E of T زائد T تربية في E of T
+
+696
+01:19:20,440 --> 01:19:26,760
+ضربنا الـ T في كل من الترميل الاتنين هدول ناقص
+
+697
+01:19:26,760 --> 01:19:33,900
+حاصل ضرب عناصر القطر الثانوي ناقص T في E أُس T أظن
+
+698
+01:19:33,900 --> 01:19:40,600
+هذا وهذا مع السلامة يبقى النتيجة T تربيع في E أُس
+
+699
+01:19:40,600 --> 01:19:46,920
+T هي ال function اللي احنا قلنا عليها اللي خارجي
+
+700
+01:19:46,920 --> 01:19:51,490
+طرح لمين يبقى اتنين لتو functions هدول يبقى هذا
+
+701
+01:19:51,490 --> 01:19:57,330
+رونسكين لمين لتو functions وهكذا اي دالتين حطيهم
+
+702
+01:19:57,330 --> 01:20:02,310
+حط مستقبتهم هات المحدد اثناء لهم بيعطيكي قيمة
+
+703
+01:20:02,310 --> 01:20:08,770
+رونسكين لهم كمان نظرية اخرى في محاضرة اليوم يبقى
+
+704
+01:20:08,770 --> 01:20:14,350
+theorem we
+
+705
+01:20:14,350 --> 01:20:15,410
+suppose that
+
+706
+01:20:23,070 --> 01:20:34,130
+الـ Y1 و Y2 هما اتجارات
+
+707
+01:20:34,130 --> 01:20:42,590
+دفعية
+
+708
+01:20:45,220 --> 01:20:57,420
+of the differential equation L of Y تساوي Y double
+
+709
+01:20:57,420 --> 01:21:07,020
+prime زائد P of T في ال Y prime زائد ل Q of T في
+
+710
+01:21:07,020 --> 01:21:14,420
+ال Y بده يساوي Zero سميلي هذه المعادلة رقم واحد and
+
+711
+01:21:14,420 --> 01:21:21,280
+that الورنسكين
+
+712
+01:21:21,280 --> 01:21:31,420
+عند ال T نوت بده يساوي Y1 عند ال T نوت في Y2 prime
+
+713
+01:21:31,930 --> 01:21:39,530
+عند الـ T node ناقص Y1 prime عند ال T node في Y2
+
+714
+01:21:39,530 --> 01:21:49,990
+عند ال T node لا يسوى Zero with مع ال initial
+
+715
+01:21:49,990 --> 01:21:59,150
+conditions او with اللي
+
+716
+01:21:59,150 --> 01:22:09,380
+هولا يساوي zero و ال Y عند ال T node يساوي Y node
+
+717
+01:22:09,380 --> 01:22:17,840
+و Y
+
+718
+01:22:17,840 --> 01:22:27,140
+prime عند ال T node يساوي Y node prime او Y عند ال
+
+719
+01:22:27,140 --> 01:22:34,670
+T nodeو I عند ال T نوت و I prime عند ال T نوت أبو
+
+720
+01:22:34,670 --> 01:22:40,990
+دي ساوي و I prime دوري لكن أبو دي ساوي و I prime
+
+721
+01:22:40,990 --> 01:22:49,950
+نوت دوري و هاد يسميها لإتنين هاد المعادلة ساميها
+
+722
+01:22:49,950 --> 01:22:53,290
+معادلة اتنين
+
+723
+01:22:56,870 --> 01:23:08,750
+ثم هناك اختيار ثم هناك اختيار من
+
+724
+01:23:08,750 --> 01:23:19,570
+الْمَصَادِر C1
+
+725
+01:23:19,570 --> 01:23:22,670
+وC2
+
+726
+01:23:22,670 --> 01:23:24,110
+لذلك
+
+727
+01:23:27,920 --> 01:23:37,940
+بحيث ان y تساوي c واحد y واحد زائد c اتنين y اتنين
+
+728
+01:23:37,940 --> 01:23:44,820
+satisfied satisfied
+
+729
+01:23:44,820 --> 01:23:47,880
+the
+
+730
+01:23:47,880 --> 01:23:53,880
+differential equation
+
+731
+01:23:53,880 --> 01:23:55,840
+when
+
+732
+01:23:57,520 --> 01:24:09,520
+and the given initial conditions
+
+733
+01:24:09,520 --> 01:24:12,740
+اتنى
+
+734
+01:27:05,040 --> 01:27:10,440
+نظرية بتقول ما ياتي افترض ان Y1 و Y2 عبارة عن حليل
+
+735
+01:27:10,440 --> 01:27:15,780
+المعادلة التفاضلية اللى عندنا هذه and that و ال
+
+736
+01:27:15,780 --> 01:27:20,710
+Wronskian كان عندهم كان لا يساوي zeroوطني two
+
+737
+01:27:20,710 --> 01:27:26,510
+initial conditions كذلك طبعا الWronskian can win عند
+
+738
+01:27:26,510 --> 01:27:30,910
+نقطة محددة عند T node مش حيالها عند نقطة واحدة
+
+739
+01:27:30,910 --> 01:27:35,190
+الWronskian can هذا لا يساوي zero قال لي إن حدث ذلك
+
+740
+01:27:35,190 --> 01:27:43,710
+يبقى هلاقي two constants C1 وC2 بحيث أن هذا يكون
+
+741
+01:27:43,710 --> 01:27:49,950
+حل للمعادلة التفاضليةو كذلك and the given initial
+
+742
+01:27:49,950 --> 01:27:54,650
+conditions و كذلك أن يحل المعادلة التفاضلية بهذه
+
+743
+01:27:54,650 --> 01:28:00,150
+الشروط المتاع أو اختصارا يحقق ال initial value
+
+744
+01:28:00,150 --> 01:28:06,410
+problem المتاع اللي عندنا مرة تانية لو كان Y1 و Y2
+
+745
+01:28:06,410 --> 01:28:14,500
+حلل المعادلة التفاضلية بدي اضمن ان هدول بيخلوا لي
+
+746
+01:28:14,500 --> 01:28:20,100
+وجود c1 و c2 بحتي يكون هذا حل شو اللى بده يضمنلي؟
+
+747
+01:28:20,100 --> 01:28:25,780
+بده يضمنلي ان الWronskian هذا لا يساوي zero لكن لو
+
+748
+01:28:25,780 --> 01:28:31,120
+طلع الWronskian يساوي zero بضمنش وجود حلين يبقى هنا
+
+749
+01:28:31,120 --> 01:28:35,780
+بضمن وجود حالين إذا كان الغنوز كان عنده نقطة ماله
+
+750
+01:28:35,780 --> 01:28:39,980
+لا يساوي منها نقطة هي النقطة تبع ال condition
+
+751
+01:28:39,980 --> 01:28:45,920
+الاتنين هدول إن حدث ذلك يبقى بضمن وجود هذا الحل و
+
+752
+01:28:45,920 --> 01:28:51,420
+بضمن وجود حل ال initial value problem واضح كلامي
+
+753
+01:28:51,920 --> 01:28:55,380
+طيب الكلام اللي بنقوله هذا بنروح نحطه على أرض
+
+754
+01:28:55,380 --> 01:29:00,300
+الواقع عمليا بيقول السؤال بنقطتين قال يهاتل
+
+755
+01:29:00,300 --> 01:29:04,680
+الWronskian تبع الحلين تبع المعادلة هذه طب نفترض
+
+756
+01:29:04,680 --> 01:29:10,180
+جيبنا and ومن ثم أكتب لل general solution يبقى أنا
+
+757
+01:29:10,180 --> 01:29:14,840
+بدروح أجيب الWronskian و أشوف هل فعلا يساوي zero
+
+758
+01:29:14,840 --> 01:29:20,700
+والله لا يساوي 0 اتنين جالي هاتلي كمان حل ال
+
+759
+01:29:20,700 --> 01:29:26,140
+initial value problem ب two conditions اللي عندنا
+
+760
+01:29:26,140 --> 01:29:30,460
+هنا بالضبط زي النظرية بقوله بسيطة اذا انا بدي ارجع
+
+761
+01:29:30,460 --> 01:29:34,240
+للحل زي ما كنا بنحل وين في ال section اللي فات
+
+762
+01:29:34,240 --> 01:29:38,700
+بطلع المعادلة معادلة من الرتبة الثانية بمعاملات
+
+763
+01:29:38,700 --> 01:29:49,000
+ثابتة يبقى بداجي اقوله let y تساوي e أس RT ب إيه
+
+764
+01:29:49,000 --> 01:29:58,300
+solution of المعادلة التفاضلية y w prime زائد خمسة
+
+765
+01:29:58,300 --> 01:30:04,060
+y prime زائد ستة y يساوي zero سميلي هذه المعادلة
+
+766
+01:30:04,060 --> 01:30:09,020
+ليهما رقم واحد يبقى then
+
+767
+01:30:16,580 --> 01:30:26,880
+R تربيع زائد خمسة R زائد ستة يساوي زيرو هذه
+
+768
+01:30:26,880 --> 01:30:33,840
+المعادلة بقدر احللها كتالي جسين بده يساوي زيرو هذه
+
+769
+01:30:33,840 --> 01:30:41,460
+R وهذه R وهذه اتنين في تلاتة وهذه زائد وهذه زائد
+
+770
+01:30:41,460 --> 01:30:52,540
+بناء عليها R1 هيسوي سالب اتنين وR2 سالب تلاتة اذا
+
+771
+01:30:52,540 --> 01:30:58,380
+صار هذا general solution
+
+772
+01:31:05,170 --> 01:31:13,010
+C1E-2T C2E-3T
+
+773
+01:31:15,400 --> 01:31:21,660
+يبقى هذا الحل يا بناتي الهواي واحد وهذا الحل ماين
+
+774
+01:31:21,660 --> 01:31:28,220
+الهواي اتنين، مظبوط ولا لا؟ يعني اصلا عندي Y واحد
+
+775
+01:31:28,220 --> 01:31:36,270
+E أس ناقص اتنين T وY اتنين E أس ناقص تلاتة T طب
+
+776
+01:31:36,270 --> 01:31:40,950
+نرجع و نكتب له ال general solution كتبنا ال
+
+777
+01:31:40,950 --> 01:31:45,110
+general solution سبقنا احنا الاصل نجيب له ال
+
+778
+01:31:45,110 --> 01:31:48,030
+general solution قبل و بعد نكتب بعد هيك نكتب له ال
+
+779
+01:31:48,030 --> 01:31:51,810
+general solution مش مشكلة اذا بتروح اجيب له ال
+
+780
+01:31:51,810 --> 01:31:57,230
+general solution نسكم تبع الحل الأول E أص ناقص
+
+781
+01:31:57,230 --> 01:32:04,720
+اتنين T و E أص ناقص تلاتة T بجهة المحدد بحط الحل
+
+782
+01:32:04,720 --> 01:32:13,800
+الأول وهذا الحل الثاني اشتغل ناقص اتنين اي اس ناقص
+
+783
+01:32:13,800 --> 01:32:19,780
+اتنين تي و هنا ناقص تلاتة اي اس ناقص تلاتة تي و
+
+784
+01:32:19,780 --> 01:32:20,980
+يساوي
+
+785
+01:32:23,370 --> 01:32:26,910
+يبقى ال Wronskian as a function of T يساوي
+
+786
+01:32:26,910 --> 01:32:34,050
+بالدحال حاصل باربع ناصر القطر الرئيسي لناقص تلاتة
+
+787
+01:32:34,050 --> 01:32:42,030
+E أس ناقص خمسة T ناقص مع ناقص بصير الزائد اتنين E
+
+788
+01:32:42,030 --> 01:32:49,350
+أس ناقص خمسة T يبقى الجواب يبقى القداش ناقص E أس
+
+789
+01:32:49,350 --> 01:32:55,900
+ناقص خمسة T يبقى زي ما انتوا شايفين الورسكين ماله
+
+790
+01:32:55,900 --> 01:33:01,920
+لا يساوي zero مدام لا يساوي zero إذا ال general
+
+791
+01:33:01,920 --> 01:33:08,440
+solution اللي بده ي exist وهذا هو شكله يعني بعد ما
+
+792
+01:33:08,440 --> 01:33:13,050
+أجيب له الورسكين بقوله إذاهذا هو ال general
+
+793
+01:33:13,050 --> 01:33:25,050
+solution C1E-2T C2E-3T لحل المطلوب طيب خلصنا
+
+794
+01:33:25,050 --> 01:33:28,610
+المطلوب الأول كتبنا له general solution و جيبناه
+
+795
+01:33:28,610 --> 01:33:33,850
+ورا اسكين جالي و من ثم حل ال initial value problem
+
+796
+01:33:33,850 --> 01:33:38,390
+اللي عندنا هذه يبقى بدنا نيجي لل initial value
+
+797
+01:33:38,390 --> 01:33:43,130
+problem ال initial value problem ماعطيني شكل ال y
+
+798
+01:33:43,130 --> 01:33:48,510
+عند ال zero شكل ال y prime y موجودة إذا بالزمن مين
+
+799
+01:33:48,510 --> 01:33:58,990
+إذا مرة تانية y تساوي c1 في e أس ناقص اتنين t c2
+
+800
+01:33:58,990 --> 01:34:05,850
+في e أس ناقص تلاتة t الآن ال y عند ال zero يسوى
+
+801
+01:34:05,850 --> 01:34:13,450
+zero أظن Y عند Zero بده يساوي Zero implies هذا Zero
+
+802
+01:34:13,450 --> 01:34:21,570
+بده يساوي EO Zero بواحد يبقى C1 EO Zero بواحد يبقى
+
+803
+01:34:21,570 --> 01:34:26,770
+زائد C2 بدي اشتقها دي يا بناتي يبقى ال y prime
+
+804
+01:34:26,770 --> 01:34:33,810
+يساوي ناقص اتنين c واحد e اص ناقص اتنين ناقص تلاتة
+
+805
+01:34:33,810 --> 01:34:40,170
+c اتنين e اص ناقص تلاتة t ال initial condition
+
+806
+01:34:40,170 --> 01:34:45,090
+التاني اللي هو y prime عند zero بدي يساوي واحد Y'
+
+807
+01:34:45,810 --> 01:34:52,330
+عند الـ zero بده يساوي واحد implies Y' بواحد يساوي
+
+808
+01:34:52,330 --> 01:34:57,210
+هشيل هذه و احط مكانها zero بصير هذا بواحد بناقص
+
+809
+01:34:57,210 --> 01:35:05,010
+اتنين C1 ناقص تلاتة C2 شو رايكوا بدأجي المعادلة
+
+810
+01:35:05,010 --> 01:35:10,410
+الأولى واضغبها في اتنين يبقى zero بساوي اتنين C
+
+811
+01:35:10,410 --> 01:35:15,370
+واحد زائد اتنين C اتنين المعادلة الثانية بدي
+
+812
+01:35:15,370 --> 01:35:21,360
+انزلها زي ما هي ناقص اتنين C واحد ماقص تلاتة C
+
+813
+01:35:21,360 --> 01:35:26,200
+اتنين و نجمع هذول بروحوا مع السلامة الواحد زي ال
+
+814
+01:35:26,200 --> 01:35:32,300
+zero اللي هو واحد يساوي الناقص C اتنين يبقى C
+
+815
+01:35:32,300 --> 01:35:38,960
+اتنين يساوي قداش ناقص واحد إذا لو كان C اتنين ناقص
+
+816
+01:35:38,960 --> 01:35:45,660
+واحد C واحد بده يساوي واحد و C واحد بده يساوي واحد
+
+817
+01:35:45,660 --> 01:35:48,520
+يبقى أصبح the solution
+
+818
+01:35:53,830 --> 01:36:04,940
+والقضايا الاصلاحية هي واي تساوي وين الحل اللى حصلنا
+
+819
+01:36:04,940 --> 01:36:10,400
+عليه هى فوق
\ No newline at end of file
diff --git a/PL9fwy3NUQKwa8ZDfSFGn6H8xVFLzqmCZC/XSq4pVrKvY4_postprocess.srt b/PL9fwy3NUQKwa8ZDfSFGn6H8xVFLzqmCZC/XSq4pVrKvY4_postprocess.srt
new file mode 100644
index 0000000000000000000000000000000000000000..f30c7c1ebb2440286a33edf4632026c6d9b4b72c
--- /dev/null
+++ b/PL9fwy3NUQKwa8ZDfSFGn6H8xVFLzqmCZC/XSq4pVrKvY4_postprocess.srt
@@ -0,0 +1,3296 @@
+1
+00:00:00,000 --> 00:00:02,560
+موسيقى
+
+2
+00:00:10,560 --> 00:00:15,380
+المرة اللى فاتت ابتدأنا في section تلاتة واحد اللى
+
+3
+00:00:15,380 --> 00:00:19,420
+هو second order homogeneous linear differential
+
+4
+00:00:19,420 --> 00:00:23,040
+equations شرحنا هذه النقطة جيبنا المعادلة
+
+5
+00:00:23,040 --> 00:00:26,700
+التفاضلية من الرتبة الثانية وال constant
+
+6
+00:00:26,700 --> 00:00:30,940
+coefficients جيبنا ال auxiliary equation او ال
+
+7
+00:00:30,940 --> 00:00:35,280
+characteristic equation اعطينا على ذلك مجموعة من
+
+8
+00:00:35,280 --> 00:00:41,720
+الأمثلة ولا يزال هناك مثالاتالمثال رقم تلاتة بيقول
+
+9
+00:00:41,720 --> 00:00:44,960
+solve the initial value problem اربعة y double
+
+10
+00:00:44,960 --> 00:00:49,300
+prime ناقص y يساوي زيرو y عند زيرو تساوي اتنين و y
+
+11
+00:00:49,300 --> 00:00:54,720
+prime عند زيرو تساوي بيتا قال لي و من ثم هاتلي شكل
+
+12
+00:00:54,720 --> 00:01:00,640
+البيتا بحيث ان الحل بده يقول الاصفر لما تي بده
+
+13
+00:01:00,640 --> 00:01:05,110
+تروح لوينللماء لانهاء اذا مطلوبين في المثال
+
+14
+00:01:05,110 --> 00:01:08,130
+المطلوب الاول يجب ان نحل ال initial value problem
+
+15
+00:01:08,130 --> 00:01:13,530
+والمطلوب الثاني يجب ان نجده قيمة beta لما T تذهب
+
+16
+00:01:13,530 --> 00:01:19,230
+للماء لانهاء ويكون الحل مساويا للصفر اذا نمشي بنفس
+
+17
+00:01:19,230 --> 00:01:24,390
+التكتيك اللى اتبعناه المرة الماضية في المحاضرة
+
+18
+00:01:24,390 --> 00:01:30,480
+الماضية كانت تاليةبدأ أقول له let Y تسوى E أُس RT
+
+19
+00:01:30,480 --> 00:01:45,840
+بي A solution to the given differential equation
+
+20
+00:01:45,840 --> 00:01:50,900
+يبقى بناء عليها بقول له the characteristic
+
+21
+00:01:50,900 --> 00:02:00,480
+equation is4R تربيع ناقص واحد يسوي كده اش؟ Zero
+
+22
+00:02:00,480 --> 00:02:11,320
+ومنها R تربيع تساوي ربع يبقى R تساوي زائد او ناقص
+
+23
+00:02:11,320 --> 00:02:18,280
+نصيبقى صارت الجذور عندي two real different truths
+
+24
+00:02:18,280 --> 00:02:24,880
+اللي هو مين؟ قيمتين حقيقيتين ومختلفتين يبقى بناء
+
+25
+00:02:24,880 --> 00:02:28,040
+عليه شكل ال general solution
+
+26
+00:02:35,880 --> 00:02:47,320
+Given differential equation as يبقى Y تساوي C1 A
+
+27
+00:02:47,320 --> 00:02:56,660
+أس سالب نص T يعني T على 2 زائد C2 A أس نص T بالشكل
+
+28
+00:02:56,660 --> 00:03:01,700
+اللي عندنا هذاهذا شكل الحل لكن راح اعطانا mainly
+
+29
+00:03:01,700 --> 00:03:07,720
+two initial conditions يبقى لو روحنا اشتقنا الحل
+
+30
+00:03:07,720 --> 00:03:15,560
+لأن هذا بيصير Y' يساوي ناقص مصي one E أس ناقص T
+
+31
+00:03:15,560 --> 00:03:25,980
+على اتنين زائد مصي two E أس T على اتنينبناء عليه
+
+32
+00:03:25,980 --> 00:03:28,740
+بدأ نيجي على ال initial conditions اللي عندنا الان
+
+33
+00:03:28,740 --> 00:03:35,320
+عندنا y عند ال zero بده يساوي 2 هذا معناه ان ال y
+
+34
+00:03:35,320 --> 00:03:44,420
+هذه 2 تساوي c1 و بيصير e of 0 اللي هو بواحد زاد c2
+
+35
+00:03:44,420 --> 00:03:49,820
+e of 0 اللي هو بواحد ال condition التاني y prime
+
+36
+00:03:50,920 --> 00:03:56,540
+عين دي ال zero بده يساوي قداش beta هذا الكلام بده
+
+37
+00:03:56,540 --> 00:04:04,940
+يعطينا ايه بده يعطينا انه beta بدها تساوي بده اجي
+
+38
+00:04:04,940 --> 00:04:11,080
+على ال هدوحات مكانة دي اللي بيصير ناقص نص C1 يبقى
+
+39
+00:04:11,080 --> 00:04:21,760
+ناقص نص C1 و هناك زائد نص C2نحن بالنساس نحاول
+
+40
+00:04:21,760 --> 00:04:26,260
+نتخلص من أحد المجاهل و نحصل على المجهول التاني
+
+41
+00:04:26,260 --> 00:04:30,900
+بروح المعادلة الأولى بيخليها زي ما هي اتنين تساوي
+
+42
+00:04:30,900 --> 00:04:38,740
+C1 زائد C2 المعادلة التانية اتنين بيتا بدرساوي
+
+43
+00:04:38,740 --> 00:04:45,890
+ناقص C1 زائد C2 لو جمعنا هدول بروحوا مع بعضيبقى
+
+44
+00:04:45,890 --> 00:04:54,470
+بناء عليه هذا حياطناه انه 2C2 بده يساوي 2 زائد 2
+
+45
+00:04:54,470 --> 00:05:02,870
+Beta لو جسمنا كله على 2 بصير C2 بده يساوي من 1
+
+46
+00:05:02,870 --> 00:05:10,140
+زائد Betaنرجع نجيب C1 يبقى بناروح نعوض في المعادلة
+
+47
+00:05:10,140 --> 00:05:17,000
+الأولى يبقى اتنين بالدرساوي C1 بدناياها زائد واحد
+
+48
+00:05:17,000 --> 00:05:24,600
+زائد betaإذا بناء عليه C1 يبدو ساوي ننقل هذه على
+
+49
+00:05:24,600 --> 00:05:31,260
+الشجة التانية يبقى لدي جداش واحد ماقص بيتا يبقى
+
+50
+00:05:31,260 --> 00:05:35,420
+أصبح الحل تبع ال initial value problem the
+
+51
+00:05:35,420 --> 00:05:47,710
+solution of the initial value problem is Y تساويY
+
+52
+00:05:47,710 --> 00:05:52,950
+تساوي C1 بدا أشيل و أكتب بباله من الواحد ناقص Beta
+
+53
+00:05:52,950 --> 00:06:00,850
+واحد ناقص Beta في E أس ناقص T على اتنين C2 واحد
+
+54
+00:06:00,850 --> 00:06:08,550
+زائد Betaيبقى هنا كمان واحد زائد beta في E أس two
+
+55
+00:06:08,550 --> 00:06:14,310
+على اتنين يبقى هذا شكل الحل تبع ال initial value
+
+56
+00:06:14,310 --> 00:06:19,590
+problem وبالتالي هذا هو المطموب الأول في المسألة
+
+57
+00:06:19,590 --> 00:06:24,080
+solve the initial value problem حلناهاالمطلوب
+
+58
+00:06:24,080 --> 00:06:31,560
+التاني يقول find beta بحيث الحل هذا بده يقترب من
+
+59
+00:06:31,560 --> 00:06:35,580
+الصفر او بده يقول الى الصفر لما ت بده تقول لوين
+
+60
+00:06:35,580 --> 00:06:41,660
+للمال انهي، يعني هاخد ال limit للطرفين لما ت بده
+
+61
+00:06:41,660 --> 00:06:45,580
+تروح للمال انهي و أسويه بقداش بالصفر و أشوف شو
+
+62
+00:06:45,580 --> 00:06:52,840
+بيعطيناأذا بدي أخد limit لل Y لما T بدها تروح
+
+63
+00:06:52,840 --> 00:06:57,700
+للماء لنهاية هو عبارة عن limit لما T بدها تروح
+
+64
+00:06:57,700 --> 00:07:04,080
+للماء لنهاية للواحد ناقص Beta في E أس ناقص T على
+
+65
+00:07:04,080 --> 00:07:11,680
+اتنين زائد واحد زائد Beta في E أس T على اتنين وكل
+
+66
+00:07:11,680 --> 00:07:16,400
+هذا الكلام بده يسوى جداش يا بنات بده يسوى Zero
+
+67
+00:07:22,610 --> 00:07:29,090
+بنزل تحت نقص بيتا عدد على مالة نهاية يبقى نقص بيتا
+
+68
+00:07:29,090 --> 00:07:32,150
+نهاية يبقى نقص بيتا عدد على مالة نهاية يبقى نقص
+
+69
+00:07:32,150 --> 00:07:32,550
+بيتا عدد على مالة نهاية يبقى نقص بيتا عدد على مالة
+
+70
+00:07:32,550 --> 00:07:34,730
+نهاية يبقى نقص بيتا عدد على مالة نهاية يبقى نقص
+
+71
+00:07:34,730 --> 00:07:38,170
+بيتا عدد على مالة نهاية يبقى نقص بيتا عدد على مالة
+
+72
+00:07:38,170 --> 00:07:42,690
+نهاية يبقى نقص بيتا عدد على مالة نهاية يبقى نقص
+
+73
+00:07:42,690 --> 00:07:43,630
+بيتا عدد على مالة نهاية يب
+
+74
+00:07:47,590 --> 00:07:54,490
+معقول هذا الكلام؟ طيب سؤال هذا الكلام ماجتش ممكن
+
+75
+00:07:54,490 --> 00:08:00,750
+يساوي zeroهذا لا يمكن أن يساوي zero في يوم من
+
+76
+00:08:00,750 --> 00:08:04,550
+الأيام دائما و أبدا greater than zero يبقى اللي
+
+77
+00:08:04,550 --> 00:08:08,470
+بدي أخلي هذا المقدار zero اللي هو المعامل صحيح ولا
+
+78
+00:08:08,470 --> 00:08:15,290
+لا لواحد زائد beta يبقى باجي بقوله sense بما أن E
+
+79
+00:08:15,290 --> 00:08:22,380
+أس T على اتنين greater than zero we haveإن الواحد
+
+80
+00:08:22,380 --> 00:08:26,880
+زائد بيتا هي اللي بدها تساوي Zero يبقى بناء علينا
+
+81
+00:08:26,880 --> 00:08:31,800
+البيتا جداش بدها تساوي يبقى لو كانت بيتا تساوي
+
+82
+00:08:31,800 --> 00:08:35,700
+سالب واحد في ال initial condition اللي احنا حاطينه
+
+83
+00:08:35,700 --> 00:08:41,320
+هذا لكان الحل بده يروح فعلا ل Zero لما تي بده تروح
+
+84
+00:08:41,320 --> 00:08:48,700
+لوين؟ لما لا نهاية حد فيكوا لاقي تساوي هنا بنات؟هي
+
+85
+00:08:48,700 --> 00:08:54,100
+اي تساؤل؟ طب لاحظوا ان احنا أخدنا خمسة أمثلة و
+
+86
+00:08:54,100 --> 00:08:58,200
+كلهم على نفس النمط تقريبا، طبعا تخلف المسألة إلى
+
+87
+00:08:58,200 --> 00:09:03,000
+أخرى، لكن كله بنفس المفهوم طب بدنا نعطي مثال آخر
+
+88
+00:09:03,000 --> 00:09:07,700
+بس بطريقة غير شكل، كيف؟ بدنا نعطيكوا الحل و نقول
+
+89
+00:09:07,700 --> 00:09:11,960
+بدنا المسألة الأساسية، يبقى مثال رقم أربعة
+
+90
+00:09:39,890 --> 00:09:44,510
+الحل العام بتاعها هو
+
+91
+00:09:45,920 --> 00:09:55,840
+Y تساوي C1 في E أس اتنين T زاد C2 في E أس ناقص
+
+92
+00:09:55,840 --> 00:10:00,760
+تلاتة T واعتبري لهذه المعادلة اللي هي رقم واحد
+
+93
+00:10:10,370 --> 00:10:14,130
+بنرجع لسؤالنا مرة تانية بيقول يهاتل المعادلة
+
+94
+00:10:14,130 --> 00:10:19,390
+التفاضلية اللي الحل العام تبعها على الشكل Y يسوى
+
+95
+00:10:19,390 --> 00:10:27,070
+C1 في E أس اتنين T زائد C2 في E أس تلاتة سلب تلاتة
+
+96
+00:10:27,070 --> 00:10:32,450
+T بيقوله كويس يبجى هذا حل عام للمعادلة لنعرف ما هي
+
+97
+00:10:32,450 --> 00:10:37,170
+المعادلة التفاضلية اللي هذا الحل تبعها بالشكل
+
+98
+00:10:37,170 --> 00:10:38,470
+العام كيف نسويه بنها
+
+99
+00:10:48,460 --> 00:10:55,330
+ممتاز، يعني هذه معدلة من أي رتبة؟تانية لأنه عندي
+
+100
+00:10:55,330 --> 00:11:00,670
+مجموحة الليل كويس يبقى هذه من الرتبية التانية يبقى
+
+101
+00:11:00,670 --> 00:11:08,670
+انا لو قدرت اجيب C1 وC2 بنقدر ايه؟ عشان نجيب الشكل
+
+102
+00:11:08,670 --> 00:11:14,650
+العام للمعادلة مشان اجيب C1 وC2 بدى معادلتين وبدى
+
+103
+00:11:14,650 --> 00:11:18,110
+المشتقة الأولى تكون موجودة والمشتقة التانية تكون
+
+104
+00:11:18,110 --> 00:11:22,210
+موجودة صحيح ولا لا؟إذا بتروح أجيب المشتقة الأولى
+
+105
+00:11:22,210 --> 00:11:27,970
+والمشتقة الثانية واستغلهم في إيجاد قيمتين ثابت C1
+
+106
+00:11:27,970 --> 00:11:33,430
+وC2 وبالتالي بجيب شكل المعادلة التفاضلية لذلك شو
+
+107
+00:11:33,430 --> 00:11:39,830
+بدى أعمل؟ بتروح أشتق مرتين وبعد هيك نشتغل شغلنا،
+
+108
+00:11:39,830 --> 00:11:43,670
+إذا لو جيت هنا بنات قولت why prime yourself؟
+
+109
+00:11:48,370 --> 00:11:55,320
+2C1E2T-3C2E-3Tيبقى هاي جبت المشتقة الأولى لكن
+
+110
+00:11:55,320 --> 00:11:58,800
+معادلة منها الرتبة الثانية يعني بلزمني كمان main
+
+111
+00:11:58,800 --> 00:12:05,440
+مشتقة ثانية إذا لو روحت جبت ال yw prime يبقى هذه
+
+112
+00:12:05,440 --> 00:12:12,960
+بدها تساوي أربعة C one E أس اتنين T زائد تسعة C
+
+113
+00:12:12,960 --> 00:12:21,750
+two E أس سالب تلاتة Tتمام طب ايش رأيك؟ هدول بد
+
+114
+00:12:21,750 --> 00:12:29,490
+أضيع أحد المجاهيل، يعني بد أضيع C1 أو C2، شو نعمل؟
+
+115
+00:12:29,490 --> 00:12:34,890
+ممكن نقرب المعادلة الأولى في سالب 2 و نجمعها مع
+
+116
+00:12:34,890 --> 00:12:38,890
+مين؟ مع المعادلة التالية و بالتالي بكون ضيعنا أحد
+
+117
+00:12:38,890 --> 00:12:44,990
+المجاهيلوبنجيب المجهول الثاني إذا لو جيت للمعادلة
+
+118
+00:12:44,990 --> 00:12:50,370
+الاتنين هدول مع بعض بدي أضرب المعادلة الأولى في
+
+119
+00:12:50,370 --> 00:12:57,330
+سلب اتنين يبقى بصير عندي سلب اتنين Y يسوى سلب
+
+120
+00:12:57,330 --> 00:13:07,190
+اتنين C1 E أس اتنين T سلب اتنين C2 E أس سلب تلاتة
+
+121
+00:13:07,190 --> 00:13:15,390
+Tالمعادلة الثانية بده خليها زي ما هي Y' يساوي 2C1E
+
+122
+00:13:15,390 --> 00:13:21,550
+-2T-3C2E
+
+123
+00:13:21,550 --> 00:13:28,010
+-3T يبقى ضربت المعادلة الأولى في سلب اتنين
+
+124
+00:13:28,010 --> 00:13:32,810
+والمعادلة الثانية خلتها كما هي شوفت لحظة ترمي
+
+125
+00:13:32,810 --> 00:13:38,350
+الاتنين هدولالاتنين are the same يبقى عند الجامع
+
+126
+00:13:38,350 --> 00:13:45,410
+مع السلامة يبقى بصير عندنا y prime ناقص اتنين y
+
+127
+00:13:45,410 --> 00:13:54,550
+يساوي نجمع هدول بصير ناقص خمسة c اتنين e أس ناقص
+
+128
+00:13:54,550 --> 00:14:02,350
+تلاتةمن هذه المعادلة بقدر أجيب له C2 تمام يبقى
+
+129
+00:14:02,350 --> 00:14:07,510
+بقدر أجيب C2 اللي عندنا هذه مشان أجيب C2 شو رايك
+
+130
+00:14:07,510 --> 00:14:13,340
+أضرب الطرفين في E أسطلات Tيبقى لو ضربنا الطرفين في
+
+131
+00:14:13,340 --> 00:14:20,320
+E أس تلاتة T أو في ناقص E أس تلاتة T، بدي أضرب هذه
+
+132
+00:14:20,320 --> 00:14:28,700
+كلها المعادلة في ناقص E أس ناقص تلاتة Tمش هنخلّيها
+
+133
+00:14:28,700 --> 00:14:34,400
+C2 بالموجة بيقبلش بيصير عندنا بيصير خمسة C2 هذا
+
+134
+00:14:34,400 --> 00:14:38,980
+الطرف اليمين لأنه انا ضربها فياش؟ في سالب يبقى
+
+135
+00:14:38,980 --> 00:14:42,900
+بيصير موجة E Os ثلاثة E مع E Os ناقص ثلاثة E بيصير
+
+136
+00:14:42,900 --> 00:14:48,340
+E Os Zero في C2 في C2 خلّصنا من الطرف اليمين الطرف
+
+137
+00:14:48,340 --> 00:14:53,680
+الشمال بدنا نضربه و نقولنا فقداش فناقص يبقى بيصير
+
+138
+00:14:54,300 --> 00:15:00,960
+هذه بالموجب وهذه بالسلب على طول الخط يبقى بصير
+
+139
+00:15:00,960 --> 00:15:09,880
+عندى جداش يساوي 2Y ناقص Y prime 2Y ناقص Y prime
+
+140
+00:15:09,880 --> 00:15:16,910
+وكل هذا الكلام مضروب في EOS 3Dأظن نقسم على خمسة
+
+141
+00:15:16,910 --> 00:15:24,510
+يكون جيبنا C2 يفقه لو قسمنا على خمسة بصير C2 يساوي
+
+142
+00:15:24,510 --> 00:15:32,070
+خمس فمين فتنين Y ناقص Y prime في E أس تلاتة T
+
+143
+00:15:40,830 --> 00:15:47,470
+لو جيت على المعادلة الأولى مثلا يبقى بصير عندنا
+
+144
+00:15:47,470 --> 00:15:55,030
+substitute in
+
+145
+00:15:55,030 --> 00:16:02,310
+equation one we getنحصل على ما ياتي هاي Y على
+
+146
+00:16:02,310 --> 00:16:12,370
+الشجة الشمال تساوي C1 بيبقى C1E2T
+
+147
+00:16:12,370 --> 00:16:22,970
+C2 زائد اللي هو مين خمس في اتنين Y ناقص Y primeفى
+
+148
+00:16:22,970 --> 00:16:28,010
+مين؟ فى E أس ناقص ثلاثة T مع E وزايد ثلاثة T مع
+
+149
+00:16:28,010 --> 00:16:34,210
+السلامة يبقى اتخلصنا منها طيب بدي اجيب هذه اين؟
+
+150
+00:16:34,210 --> 00:16:39,570
+على الشجة التانية بصير عندي مين؟ C واحد E أس اتنين
+
+151
+00:16:39,570 --> 00:16:44,750
+T زي ما هو هذه بدي اتيجي يا بنات بإشارة سالم يبقى
+
+152
+00:16:44,750 --> 00:16:53,450
+بصير عندي Yسالب اتنين y ناقص y prime كلها على
+
+153
+00:16:53,450 --> 00:17:00,350
+كدهش؟ على خمسة او لو وحدنا المقامات كلها على خمسة
+
+154
+00:17:00,350 --> 00:17:10,160
+بصير خمسة y ناقص اتنين y زائد y prime y وساوياللي
+
+155
+00:17:10,160 --> 00:17:17,100
+هو تلاتة Y زائد Y Prime كله على جداش على خمسة طب
+
+156
+00:17:17,100 --> 00:17:22,460
+احنا بدنا C1 يبقى الـC1 بدي اضغط كله في E أس ناقص
+
+157
+00:17:22,460 --> 00:17:30,140
+اتنين T يبقى خمس في تلاتة Y زائد Y Prime في E أس
+
+158
+00:17:30,140 --> 00:17:38,930
+ناقص اتنين Tيبقى جبت C1 و C2 ارجع اعوض في المعادلة
+
+159
+00:17:38,930 --> 00:17:45,590
+الأولى و التانية نرجع نكبح اللينا
+
+160
+00:17:50,480 --> 00:17:55,420
+لو عوضت في المعادلة، بنفع؟ بنفعش، بصير مقدرة سواء
+
+161
+00:17:55,420 --> 00:17:58,840
+مقدرة و بتظهرش المشتقة الثانية، أنا بدي المشتقة
+
+162
+00:17:58,840 --> 00:18:02,180
+الثانية، إذا المعلومات اللي جبتها من المعادلة
+
+163
+00:18:02,180 --> 00:18:05,520
+الأولى والثانية بتروح عوض بها وين؟ في المعادلة
+
+164
+00:18:05,520 --> 00:18:09,230
+الجاتة بتستنى، اللي هي من المعادلة الرقم؟تلاتة،
+
+165
+00:18:09,230 --> 00:18:14,350
+إذا بدي أشيل C1 وC2 من المعادلة، رقم تلاتة بكون
+
+166
+00:18:14,350 --> 00:18:20,870
+حصلت على المطلوب يبقى بناء عليه، بدي يصير عندنا
+
+167
+00:18:20,870 --> 00:18:30,670
+مين؟بدا تساوي أربعة في C1 وين C1 هيو يبقى أربعة
+
+168
+00:18:30,670 --> 00:18:38,690
+على خمسة في تلاتة Y زائد Y prime في إيوس نقص اتنين
+
+169
+00:18:38,690 --> 00:18:42,990
+T مع إيوس اتنين T مع السلام الله يسهل عليهم
+
+170
+00:19:01,520 --> 00:19:06,380
+يبقى ماضلش عندي exponential functions مش ضايل عندي
+
+171
+00:19:06,380 --> 00:19:10,990
+الا المعادلة التفاضلية بس بدي أعيد ترتيبهايبقى لو
+
+172
+00:19:10,990 --> 00:19:16,090
+ضربت كله في خمسة، شو بيصير عندي؟ خمسة y double
+
+173
+00:19:16,090 --> 00:19:24,190
+prime يسوى اتماشر y زائد اربعة y prime زائد
+
+174
+00:19:24,190 --> 00:19:34,680
+تمانتاشر y ناقص تسعة y primeطب نجمع خمسة y w prime
+
+175
+00:19:34,680 --> 00:19:39,720
+يساوي عندي اتلاشر y وعندي تمانتاشر بصير كدهش
+
+176
+00:19:39,720 --> 00:19:48,960
+تلاتين y عندي اربع y prime وناقصها بيبقى ناقص خمسة
+
+177
+00:19:48,960 --> 00:19:55,690
+y primeتمام؟ طيب شو رايك نقسم كله على خمسة؟ يبقى
+
+178
+00:19:55,690 --> 00:20:01,130
+لو قسمنا على خمسة هذه بتعطينا ما يأتي Y double
+
+179
+00:20:01,130 --> 00:20:09,730
+prime بدأت ساوي ستة Y ناقص Y primeبنعملها معادلة
+
+180
+00:20:09,730 --> 00:20:19,990
+صفرية بيصير yw prime زائد y prime مقص 6y تساوي 0
+
+181
+00:20:19,990 --> 00:20:24,250
+أليست homogeneous differential equation with
+
+182
+00:20:24,250 --> 00:20:29,310
+constant coefficients؟ مظبوط يبقى هي المعادلة
+
+183
+00:20:29,310 --> 00:20:34,770
+التفاضلية اللي الحل تبعها كان على الشكل اللي عندنا
+
+184
+00:20:34,770 --> 00:20:38,550
+هذا اللي أعطاناهذه المعاملة التفاضية لو روحتها و
+
+185
+00:20:38,550 --> 00:20:42,290
+حلتيها من جديد فبتطلع عندك main الحل اللى عندناها
+
+186
+00:20:42,290 --> 00:20:46,210
+حاطط في الكتاب عندك بيجي اربع اسهلة او خمس اسهلة
+
+187
+00:20:46,210 --> 00:20:52,030
+منها الموديل هذا احدهم كويس يبقى الباقي بنعمله
+
+188
+00:20:52,030 --> 00:20:56,270
+بنفس التكتيك و نفس الطريقةالمعادلة بيطالي بدي
+
+189
+00:20:56,270 --> 00:21:00,810
+أشتقها مرتين أحل المعادلة مع بعض أعود في المعادلة
+
+190
+00:21:00,810 --> 00:21:05,070
+التالتة عشان أجيب الكون أصلا C1 وC2 بالتالي بكون
+
+191
+00:21:05,070 --> 00:21:11,210
+حصلت على الحل كيف
+
+192
+00:21:11,210 --> 00:21:15,290
+ما تسوي جيبي لتحلي المعادلة مع بعض و أجيب C1 وC2
+
+193
+00:21:15,290 --> 00:21:21,370
+بأي طريقة شئتي كيف؟ مش لازم نجيبهم و نحصل على
+
+194
+00:21:21,370 --> 00:21:21,910
+المعادلة
+
+195
+00:21:27,500 --> 00:21:38,240
+تعالى اقولى بس شو الفكرة ايش الفكرة اللى عندي ال
+
+196
+00:21:38,240 --> 00:21:46,780
+characteristic
+
+197
+00:21:46,780 --> 00:21:54,590
+equationوجهة نمر أخرى، وجهة بس هذه تميل إلى الحفظ
+
+198
+00:21:54,590 --> 00:22:00,610
+وليس إلى الفهم، صح؟ فهم، فهمك كويس أنا تماما، كلام
+
+199
+00:22:00,610 --> 00:22:04,290
+اللي بتقوله زميلتك صحية، بتقول أنا عند اللي هو قار
+
+200
+00:22:04,290 --> 00:22:07,670
+واحد وقار اثنان، بنقول هو الله كلامك صحيبدها
+
+201
+00:22:07,670 --> 00:22:12,610
+ترجعها إلى أصلها، يعني هذا بدها تقول إذا أنا عندي
+
+202
+00:22:12,610 --> 00:22:19,210
+جوس اسمه R نقص اتنين وعندي جوس اسمه R زائد تلاتة،
+
+203
+00:22:19,210 --> 00:22:23,250
+هدول مضروبات في بعضهم يساوي Zeroلش؟ لأن الحالين
+
+204
+00:22:23,250 --> 00:22:28,010
+are real and different، هي فاهم أن الحالين من خلال
+
+205
+00:22:28,010 --> 00:22:30,890
+ال two roots له اتنين are real and different، فبدت
+
+206
+00:22:30,890 --> 00:22:34,250
+تعمل العملية العكسية، برضه كلامها صحيح، مافي
+
+207
+00:22:34,250 --> 00:22:37,950
+إشكالية، كلامها مظلوم، وهي تعتبر another method
+
+208
+00:22:37,950 --> 00:22:41,770
+for the solution سواء هذين، والله هذين الاتنين
+
+209
+00:22:41,770 --> 00:22:46,070
+بوصلوا لنفس النتيجة، على أي حال، في فصل الماضي، في
+
+210
+00:22:46,070 --> 00:22:50,630
+انتحار أعمال الفصل الأول، جابولهم سؤال على هذه
+
+211
+00:22:50,630 --> 00:22:51,210
+النقطة
+
+212
+00:22:58,980 --> 00:23:03,140
+لحد هنا يكون انتهى ال section و لا يكون أرقام
+
+213
+00:23:03,140 --> 00:23:09,490
+المسائلعشان اكتبها هنا اكسر
+
+214
+00:23:09,490 --> 00:23:14,910
+سايزز ثلاثة
+
+215
+00:23:14,910 --> 00:23:23,370
+واحد المسائل من واحد لغاية تمانتاش وكذلك سؤال واحد
+
+216
+00:23:23,370 --> 00:23:24,030
+وعشرين
+
+217
+00:23:59,940 --> 00:24:03,520
+الواحد اللي خلصت أعمل أراضي الأشكال
+
+218
+00:24:13,750 --> 00:24:18,870
+وهي اخر سطر لازال موجود طيب
+
+219
+00:24:18,870 --> 00:24:24,370
+ننتقل الان لل section الجديد أو ال level section 3
+
+220
+00:24:24,370 --> 00:24:25,370
+-2
+
+221
+00:24:45,620 --> 00:24:50,460
+يبقى section تلاتة اتنين قلول fundamental
+
+222
+00:24:50,460 --> 00:24:55,360
+solutions
+
+223
+00:24:55,360 --> 00:25:06,500
+مجموعة الحلول الأساسية of linear homogeneous
+
+224
+00:25:06,500 --> 00:25:11,980
+differential equations
+
+225
+00:25:17,740 --> 00:25:24,180
+بنعرف شغلة جديدة ماكناش بنعرفها قبل هيك بقول let
+
+226
+00:25:24,180 --> 00:25:34,160
+ال P and ل Q بيه continuous functions بيه
+
+227
+00:25:34,160 --> 00:25:46,720
+continuous functions دوال متاصلة on an interval
+
+228
+00:25:49,730 --> 00:25:57,630
+ثم لأي عملية فاي ثم لأي
+
+229
+00:25:57,630 --> 00:26:10,170
+عملية فاي هذا مرتفع مرتفع
+
+230
+00:26:10,170 --> 00:26:14,030
+مرتفع مرتفع
+
+231
+00:26:22,830 --> 00:26:34,950
+the differential operator
+
+232
+00:26:34,950 --> 00:26:49,390
+المؤثر التفاضلي ال by theQuestion بالمعادلة اللي
+
+233
+00:26:49,390 --> 00:27:01,750
+هي من L of Phi بده ساوي Phi double prime زائد P of
+
+234
+00:27:01,750 --> 00:27:10,710
+T او زائد P في ال Phi prime زائد Q في ال Phi
+
+235
+00:27:17,970 --> 00:27:24,270
+the value of
+
+236
+00:27:24,270 --> 00:27:30,730
+L of I at
+
+237
+00:27:30,730 --> 00:27:39,870
+any point T اللي موجودة في ال interval I
+
+238
+00:27:42,590 --> 00:27:52,910
+بروح بقول L of Phi of T بدي ساوي Phi W prime of T
+
+239
+00:27:52,910 --> 00:28:03,270
+زائد P of T في Phi prime of T زائد Q of T في Phi
+
+240
+00:28:03,270 --> 00:28:04,650
+of T
+
+241
+00:28:09,620 --> 00:28:11,200
+ماذا بيحصل؟
+
+242
+00:28:36,950 --> 00:28:41,730
+كلمة differential operator مؤثر تفاضلي لم نسمع
+
+243
+00:28:41,730 --> 00:28:46,490
+بهذه التسمية من قبل لا في calculus a ولا b ولا c
+
+244
+00:28:46,490 --> 00:28:51,990
+لكن هذا احنا سمعنا به في المعادلة التفاضلية انا ما
+
+245
+00:28:51,990 --> 00:28:58,030
+بهمن الاسم بهمن الجسم بهمن ما هو الشكل المؤثر
+
+246
+00:28:58,030 --> 00:29:04,470
+التفاضلي ولماذا سمي بهذا الاسميبقى العنوان اللي
+
+247
+00:29:04,470 --> 00:29:07,590
+احنا رافعينه ال fundamental solutions مجموعة
+
+248
+00:29:07,590 --> 00:29:11,850
+الحلول الأساسية of linear homogeneous differential
+
+249
+00:29:11,850 --> 00:29:17,190
+equations للمعادلة التفاضلية الخطية المتجانسة هذا
+
+250
+00:29:17,190 --> 00:29:20,930
+موضوع هذا ال sectionطبعا لما اقول fundamental
+
+251
+00:29:20,930 --> 00:29:24,810
+solution مجموعة الحلول الأساسية كأنه بد ال general
+
+252
+00:29:24,810 --> 00:29:30,850
+solution تمام ال general الحل العام اللذي يحتوي كل
+
+253
+00:29:30,850 --> 00:29:35,450
+الحلول الأخرى فلما اقول هذه مجموعة الحلول الأساسية
+
+254
+00:29:35,450 --> 00:29:41,780
+بأي حل أخر بيكون منضوي تحت هذه الحلولنبدأ المهد
+
+255
+00:29:41,780 --> 00:29:45,840
+لهذا الكلام بالتعريف التالي ثم بنظرية التعريف
+
+256
+00:29:45,840 --> 00:29:50,640
+بيقول افترض اني عندي دوال تنتين P and Q التنتين
+
+257
+00:29:50,640 --> 00:29:56,180
+دوال متصلة على فترة ما والتكن الفترة هادى I open
+
+258
+00:29:56,180 --> 00:30:01,040
+closed half open ماعنديش مشكلةتمام جالي for any
+
+259
+00:30:01,040 --> 00:30:06,180
+function phi لأي function phi that is twice
+
+260
+00:30:06,180 --> 00:30:10,420
+differentiable عن فترة I يعني لو عندي function phi
+
+261
+00:30:10,420 --> 00:30:16,200
+قابلة للاشتقاء مرتين على هذه الفترة لو زيادة أكتر
+
+262
+00:30:16,200 --> 00:30:19,960
+مافيش مشكلة المهم على الأقل بيبقى قابلة للاشتقاء
+
+263
+00:30:19,960 --> 00:30:23,020
+مرتين على المشتقى الأولى exist والمشتقى الثانية
+
+264
+00:30:23,020 --> 00:30:29,160
+exist على نفس الفترة هذهبنعرف المؤثر التفاضلي اللي
+
+265
+00:30:29,160 --> 00:30:35,900
+حدّيله الرمز L by the equation بالمعادلة A تالية L
+
+266
+00:30:35,900 --> 00:30:41,960
+of Phi شو معناه رياضيا، شو معناه عمليا، المشتقة
+
+267
+00:30:41,960 --> 00:30:46,200
+الثانية اللي الدالة Phi زائد ال function P اللي
+
+268
+00:30:46,200 --> 00:30:51,780
+فوق مضروبة في مشتقة ال Phi زائد ال همين الدالة Q
+
+269
+00:30:51,780 --> 00:30:57,120
+اللي فوق مضروبة في Phi itselfلاحظوا الاشتقاق من
+
+270
+00:30:57,120 --> 00:31:03,640
+الرتبة الثانية يبقى من هنا سميته مؤثر تفاضلي لأن
+
+271
+00:31:03,640 --> 00:31:09,340
+المشتقات موجودة من هنا سمناه مؤثر تفاضلي، شو
+
+272
+00:31:09,340 --> 00:31:14,440
+بيعمل؟ هو عبارة عن مجموعة المشتقة الثانية لـ Phi
+
+273
+00:31:14,440 --> 00:31:18,900
+زي P of T المعطاة في مشتقة الـ Phi زي Q of T
+
+274
+00:31:18,900 --> 00:31:23,650
+المعطاة في Phiيعني لو جينا نقارن بينه وبين
+
+275
+00:31:23,650 --> 00:31:28,970
+المعادلة التفابلية من الرتبة الثانية مش هيها برضه
+
+276
+00:31:28,970 --> 00:31:33,150
+كنا بقول y double prime زي p of t في y prime زي q
+
+277
+00:31:33,150 --> 00:31:40,210
+of t في y بده يساوي zero صحيح ولا لا؟ تمام تماملو
+
+278
+00:31:40,210 --> 00:31:44,790
+المؤثر التفاضلي بدي احسبه عند اي نقطة موجودة في ال
+
+279
+00:31:44,790 --> 00:31:49,830
+interval فاي بقول ممتاز ده بنخليه يؤثر على ال
+
+280
+00:31:49,830 --> 00:31:55,410
+variable اللي هو T يبقى بصير عند مين الـPhi of T
+
+281
+00:31:55,410 --> 00:31:59,310
+هو عبارة عن فايدة بالـPrime of T زاد P of T في
+
+282
+00:31:59,310 --> 00:32:04,470
+الـPhi Prime of T زاد Q of T في الـPhi خلي
+
+283
+00:32:04,470 --> 00:32:10,000
+المعلومة هذه عندك و تعالى ناخد النظرية التاليةو
+
+284
+00:32:10,000 --> 00:32:14,060
+بدنا نحاول نقرأ بعد ذلك النظرية و نفهم ما هو
+
+285
+00:32:14,060 --> 00:32:19,640
+المقصود منها يبقى بنا نيجي لأن النظرية بتقول ما
+
+286
+00:32:19,640 --> 00:32:26,500
+يأتي consider the
+
+287
+00:32:26,500 --> 00:32:32,080
+initial value problem مين هي ال initial value
+
+288
+00:32:32,080 --> 00:32:40,740
+problem؟ YW prime زائد P of T في Y primeزائد Q of
+
+289
+00:32:40,740 --> 00:32:49,580
+T في ال Y بده ساوي G of T وفي نفس الوقت Y عند ال T
+
+290
+00:32:49,580 --> 00:32:57,100
+node بده ساوي Y node Y prime عند ال T node بده
+
+291
+00:32:57,100 --> 00:33:11,240
+ساوي Y prime node where حيث ال Pوالـ q و ال gene
+
+292
+00:33:11,240 --> 00:33:21,200
+our continuous functions are continuous functions
+
+293
+00:33:21,200 --> 00:33:30,600
+on an interval I
+
+294
+00:33:30,600 --> 00:33:38,640
+على اللي هو الفترة اللي عندنا Iوهذا يحتوي على نقطة
+
+295
+00:33:38,640 --> 00:33:43,120
+T0 وهذا يحتوي
+
+296
+00:33:43,120 --> 00:33:47,320
+على
+
+297
+00:33:47,320 --> 00:33:52,020
+نقطة T0
+
+298
+00:33:52,020 --> 00:33:55,500
+هناك
+
+299
+00:33:55,500 --> 00:34:00,920
+حلوة محددة هناك
+
+300
+00:34:00,920 --> 00:34:03,080
+حلوة محددة
+
+301
+00:34:06,230 --> 00:34:13,970
+one solution there exactly
+
+302
+00:34:13,970 --> 00:34:28,230
+one solution y تساوي five of t five of t of
+
+303
+00:34:28,230 --> 00:34:41,010
+this problem of this initial value problemand the
+
+304
+00:34:41,010 --> 00:34:50,450
+solution exists on
+
+305
+00:34:50,450 --> 00:34:55,930
+the interval I
+
+306
+00:35:37,010 --> 00:35:41,410
+نرجع لنص النظرية اللى احنا كتبينها مرة تانية بدنا
+
+307
+00:35:41,410 --> 00:35:45,850
+نقرأ تانية و بعدين هطلع عليكم مجموعة من الأسئلة
+
+308
+00:35:45,850 --> 00:35:50,490
+دججوا معايا جالي اعتبر ال initial value problem
+
+309
+00:35:50,490 --> 00:35:54,470
+اعطاني معادلة مرتبة تانية زى ما انت شايفين و حطلي
+
+310
+00:35:54,470 --> 00:35:59,310
+عليها two initial conditionsبعدها قال لي حيث ال P
+
+311
+00:35:59,310 --> 00:36:02,430
+و ال Q و ال G اللي هو الأسطوان اللي بنكررها دايما
+
+312
+00:36:02,430 --> 00:36:06,110
+كنت هو ال functions على ال interval I و قال لي ال
+
+313
+00:36:06,110 --> 00:36:10,210
+interval I بتحتوي نقطة من T node يبقى T node هي
+
+314
+00:36:10,210 --> 00:36:14,890
+نقطة موجودة في ال interval I اللي عندنا في ال
+
+315
+00:36:14,890 --> 00:36:19,770
+interval I يبقى T node موجودة داخل ال interval قال
+
+316
+00:36:19,770 --> 00:36:25,050
+لي then there is exactly يبقى دي كلها تعتبر ماطيان
+
+317
+00:36:25,260 --> 00:36:30,920
+إذا قال لي هناك حل
+
+318
+00:36:30,920 --> 00:36:38,500
+واحد فقط يوجد على
+
+319
+00:36:38,500 --> 00:36:41,380
+الفترة اللي عندنا الهيمين I
+
+320
+00:36:45,190 --> 00:36:49,570
+initial value problem احنا لما كان معنا الشروط
+
+321
+00:36:49,570 --> 00:36:53,850
+بجينا نجيب ال general solution اللي ممكن يكون مئة
+
+322
+00:36:53,850 --> 00:36:57,290
+solution ولا الف solution ولا مليون solution حسب
+
+323
+00:36:57,290 --> 00:37:01,790
+ما نغير ال constants مظبوط لكن لما كنا نعود بال
+
+324
+00:37:01,790 --> 00:37:05,790
+initial conditions بلاجيش اللي حل واحد بضلش عندي
+
+325
+00:37:05,790 --> 00:37:09,910
+C1 وC2 يبقى بصير عندي there is a unique solution
+
+326
+00:37:09,910 --> 00:37:15,890
+حل وحيد فقط مافيش غيره النظرية بتقولهذا الـ
+
+327
+00:37:15,890 --> 00:37:20,290
+initial condition موجود عندك و هدول الدوال ال P و
+
+328
+00:37:20,290 --> 00:37:23,310
+ال Q و ال G continuous function على ال interval I
+
+329
+00:37:23,310 --> 00:37:28,650
+و ال interval I بتحتوي على النقطة T0 جلد ان there
+
+330
+00:37:28,650 --> 00:37:34,330
+exist يوجد exactly one solution و هذا معرف على نفس
+
+331
+00:37:34,330 --> 00:37:39,030
+الفترة اللي هي I يعني كأن ال domain تبع هذا الحل
+
+332
+00:37:39,030 --> 00:37:44,040
+هو نفس الفترة اللي هي عملنا Iمين تقولي ماذا فهمت
+
+333
+00:37:44,040 --> 00:37:50,300
+من نص النظرية؟ تفضلي، نتعرض عليك في الأول ياخدعك،
+
+334
+00:37:50,300 --> 00:37:53,420
+تفضلي،
+
+335
+00:37:53,420 --> 00:37:58,500
+ممتاز،
+
+336
+00:37:58,500 --> 00:38:04,040
+أجابة إيجابتين، أعطتنا مفهوم، المفهوم الواحد إن أي
+
+337
+00:38:04,040 --> 00:38:10,310
+problem لها حل، كلامها جيد، ممتاز جداالإجابة
+
+338
+00:38:10,310 --> 00:38:14,690
+الثانية أن هذا الحل يكون وحيدا و اي الناس بيقول
+
+339
+00:38:14,690 --> 00:38:18,530
+there is exactly، بالضبط يوجد one صلى الله عليه
+
+340
+00:38:18,530 --> 00:38:23,870
+وما جدتش اتنين، هذا أعطتني مفهومين من خلال نص
+
+341
+00:38:23,870 --> 00:38:28,070
+النظرية، كلامها سليم مائة بالمائة، في مفهوم كمان
+
+342
+00:38:28,070 --> 00:38:33,670
+تالت ممكن نفهم يا بنات؟ على الحل نفسه، اه مين اللي
+
+343
+00:38:33,670 --> 00:38:37,330
+بتحكي اللي بتقول هذا الحل فترة؟ اه انت؟ واسمك انت؟
+
+344
+00:38:38,290 --> 00:38:43,850
+هدوء أبو شويش بتتكمل لأخدعه ما فات، يعني عندما
+
+345
+00:38:43,850 --> 00:38:49,950
+تستدرك عليها ما فات بتقول إن هذا الحل الوحيد يتحقق
+
+346
+00:38:49,950 --> 00:38:54,810
+عالمين على نفس الفترة I اللي دوالي التلاتة ال P و
+
+347
+00:38:54,810 --> 00:38:58,650
+ال Q و الجي كنتني واص عليها، كلام سليم، هذه
+
+348
+00:38:58,650 --> 00:39:04,900
+المفهوم تبع النظريةيبقى في عندي حل، و الحل وحيد، و
+
+349
+00:39:04,900 --> 00:39:09,740
+الحل معرف على نفس الفترة الليومين اللي الدول
+
+350
+00:39:09,740 --> 00:39:14,720
+التلاتة هذه معرفة عليها، كلام مظبوط، يبقى هاي اللي
+
+351
+00:39:14,720 --> 00:39:17,960
+بتقوله نظري، أكتر من هيك مابينه، يعني النظري بتقول
+
+352
+00:39:17,960 --> 00:39:22,970
+في عندك حل، و الحل هذا وحيد مافيش غيرهوالحل بيكون
+
+353
+00:39:22,970 --> 00:39:25,770
+معرف على نفس الفترة اللي دوالها دي بيكون عليها
+
+354
+00:39:25,770 --> 00:39:33,210
+دوال متاصلة يبقى باللخص ما قالته الأخ دعاء والأخت
+
+355
+00:39:33,210 --> 00:39:44,770
+الثانية في التالي يبقى بدي بقول this theorem say
+
+356
+00:39:44,770 --> 00:39:46,110
+three things
+
+357
+00:39:51,250 --> 00:39:57,950
+هذه بتقول ثلاثة أشياء نمر واحد the initial value
+
+358
+00:39:57,950 --> 00:40:05,270
+problem has a solution في حل ال initial value
+
+359
+00:40:05,270 --> 00:40:16,170
+problem اتنين the initial value problem has only
+
+360
+00:40:16,170 --> 00:40:27,880
+one solutionمافيش إلا حل واحد فقط لغيره تلاتة the
+
+361
+00:40:27,880 --> 00:40:32,920
+solution phi
+
+362
+00:40:32,920 --> 00:40:43,160
+of T is defined معرف on the interval
+
+363
+00:40:49,740 --> 00:40:59,040
+على الفترة I wear the coefficient
+
+364
+00:40:59,040 --> 00:41:04,320
+coefficients
+
+365
+00:41:04,320 --> 00:41:13,940
+اللي هو ال P و ال Q and ال G are continuous
+
+366
+00:41:19,130 --> 00:41:28,190
+continuous and the solution and solution
+
+367
+00:41:28,190 --> 00:41:32,670
+is
+
+368
+00:41:32,670 --> 00:41:47,310
+at least على الأقل a twice differentiable function
+
+369
+00:41:54,770 --> 00:41:59,530
+نعطي بعض الأمثلة على هذه المفاهيم
+
+370
+00:42:20,500 --> 00:42:31,920
+المثال الأول example بيقول
+
+371
+00:42:31,920 --> 00:42:37,900
+ي determine the
+
+372
+00:42:37,900 --> 00:42:39,340
+longest interval
+
+373
+00:42:52,900 --> 00:43:04,020
+The initial value problem have
+
+374
+00:43:04,020 --> 00:43:07,360
+a
+
+375
+00:43:07,360 --> 00:43:11,220
+unique twice
+
+376
+00:43:11,220 --> 00:43:12,880
+differentiable solution
+
+377
+00:43:39,000 --> 00:43:45,140
+don't attempt to
+
+378
+00:43:45,140 --> 00:43:46,280
+find the solution
+
+379
+00:44:00,370 --> 00:44:09,210
+عشرة من الكتاب طبعا yw prime زائد cosine t في ال y
+
+380
+00:44:09,210 --> 00:44:22,760
+prime زائد y في ال absolute value ل tزائد تلاتة لن
+
+381
+00:44:22,760 --> 00:44:30,080
+absolute value ل T في ال Y بده يساوي Zero و ال Y
+
+382
+00:44:30,080 --> 00:44:37,960
+عند اتنين بده يساوي تلاتة و ال Y prime عند اتنين
+
+383
+00:44:37,960 --> 00:44:40,760
+بده يساوي مان بده يساوي واحد
+
+384
+00:44:58,310 --> 00:45:02,690
+يبقى النظرية السابقة لقبل قليل لما أعطاني معادلة
+
+385
+00:45:02,690 --> 00:45:06,290
+فاضولة من رتبة نوحط عليها two initial conditions
+
+386
+00:45:06,290 --> 00:45:12,010
+والمعاملات كانت دوال متصلة على فترة والتكن هذه
+
+387
+00:45:12,010 --> 00:45:19,050
+الفترة Iقال there exists exactly يوجد حل وحيب لهذه
+
+388
+00:45:19,050 --> 00:45:25,850
+المعادلة و الحل هذا موجود على نفس الفترة الامين
+
+389
+00:45:25,850 --> 00:45:30,310
+اللي عنده I السؤال اللي عندنا هنا شبه قول قول
+
+390
+00:45:30,310 --> 00:45:35,480
+هاتلي أكبر فترةبحيث ان ال initial value problem
+
+391
+00:45:35,480 --> 00:45:39,980
+has a unique twice differentiable solution يعني
+
+392
+00:45:39,980 --> 00:45:45,800
+عندها حل قابل الاشتقاق مرتين عليها وياك تحاول توجد
+
+393
+00:45:45,800 --> 00:45:49,520
+هذا الحل يعني انا مش طالب الحل تبع المعادل انا
+
+394
+00:45:49,520 --> 00:45:54,900
+طالب الفترة بس اللي الحل عليها بيكون معله صحيح حل
+
+395
+00:45:54,900 --> 00:46:00,880
+واحد وقابل اشتقاق مرتين على هذه الفترة بقولك كويس
+
+396
+00:46:01,320 --> 00:46:05,180
+اذا انا بدي اجي اطبق النظرية بدي ادور على
+
+397
+00:46:05,180 --> 00:46:09,840
+المعاملات وين المعاملة اللي عندى cosine T و تلاتة
+
+398
+00:46:09,840 --> 00:46:14,460
+لانتهينا Zero ريحني تمام يبقى هذه constant
+
+399
+00:46:14,460 --> 00:46:18,080
+function ال constant function بتعتبريها متصلة على
+
+400
+00:46:18,080 --> 00:46:23,320
+اي فترة على اي فترة بدك ايها اذا انا لو جيت لل
+
+401
+00:46:23,320 --> 00:46:31,040
+cosine Tفي النقطة الـ cosine تبع الـ function أو
+
+402
+00:46:31,040 --> 00:46:35,700
+الـ cosine T ماهياش معرف عليها يعني لما رسمنا
+
+403
+00:46:35,700 --> 00:46:40,260
+cosine ويتس undefined هذه يا بنات اذا ماذا ذاكرين
+
+404
+00:46:40,260 --> 00:46:45,440
+رسمتها لـin absolute value لـT فكانت بالشكل هذا
+
+405
+00:46:45,440 --> 00:46:51,440
+هيكومن هنا نفس القصة وهي تجينا هكذا هذا اللي هو
+
+406
+00:46:51,440 --> 00:46:58,620
+واحد وهذا هنا ياش سالب واحد وهذا T وهذا Y هذا لين
+
+407
+00:46:58,620 --> 00:47:03,840
+اللي هو absolute value اللتي الرسمتين مع بعض وهذا
+
+408
+00:47:03,840 --> 00:47:07,860
+النقطة اللي هي من ال zero يبقى تلاتة لين absolute
+
+409
+00:47:07,860 --> 00:47:13,680
+value اللتي معرفة لكل real line مع هذا ال zero
+
+410
+00:47:13,680 --> 00:47:22,040
+يبقى هذهas continuous for all
+
+411
+00:47:25,430 --> 00:47:31,250
+مظبوط؟ إذا وين المنطقة المشتركة ما بين الدلتين
+
+412
+00:47:31,250 --> 00:47:35,230
+اللي بيكونوا التنتين عليهم continuous يبقى باجي
+
+413
+00:47:35,230 --> 00:47:44,990
+بقوله هنا the functions are continuous دوال متصلة
+
+414
+00:47:44,990 --> 00:47:52,490
+on الفترة من سالب infinity ل zero and zero و
+
+415
+00:47:52,490 --> 00:47:59,950
+infinityيبقى صار عندى كام فترة ممتاز جدا يعنى انا
+
+416
+00:47:59,950 --> 00:48:04,720
+لو جيت قولت هذا ال real line وهذا ال zeroيبقى
+
+417
+00:48:04,720 --> 00:48:10,880
+الدوال معرفة عن الفترة اليامين والفترة الشمال، ايش
+
+418
+00:48:10,880 --> 00:48:15,280
+بيقول هو قال هاتل ال longest interval، برجع لمين؟
+
+419
+00:48:15,280 --> 00:48:19,300
+لل initial conditions، مين ال initial conditions؟
+
+420
+00:48:19,300 --> 00:48:23,880
+قال لي Y عندي اتنين و Y prime عندي اتنين، اتنين
+
+421
+00:48:23,880 --> 00:48:26,600
+هادي موجودة في الفترة اللي عالمية و الفترة اللي ع
+
+422
+00:48:26,600 --> 00:48:30,450
+الشماليبقى اللي على الشمال هذي الله سهل عليها مش
+
+423
+00:48:30,450 --> 00:48:36,370
+لازمالي يبقى اتنين بتجيني وين هنا هاي واحد وهي هنا
+
+424
+00:48:36,370 --> 00:48:42,350
+اتنين اللي ال initial conditions محسبات عندها يعني
+
+425
+00:48:42,350 --> 00:48:48,690
+الحل بدي يكون صحيح وين عند هذه النقطة exist على
+
+426
+00:48:48,690 --> 00:48:53,270
+نفس الفترة اللتي تحتوي من اللي هو الاتنين اللي
+
+427
+00:48:53,270 --> 00:49:03,500
+عندنا فبجي بقوله اذاthe solution exists
+
+428
+00:49:03,500 --> 00:49:06,600
+on
+
+429
+00:49:06,600 --> 00:49:17,500
+the interval على الفترة من zero و infinity that
+
+430
+00:49:17,500 --> 00:49:26,660
+هذه الفترة contains الأولى اتنينيبقى بتحتوي على
+
+431
+00:49:26,660 --> 00:49:34,580
+الاتنين and the functions
+
+432
+00:49:34,580 --> 00:49:44,460
+الهي cosine ال T and تلاتة لين absolute value ل T
+
+433
+00:49:44,460 --> 00:49:51,240
+are continuous يبقى هذه الفترة اللي هو إيه عشان
+
+434
+00:49:51,240 --> 00:49:52,180
+بده إياها
+
+435
+00:49:55,110 --> 00:50:00,390
+اللي طبعا ما تحلش المعادلة او اصحى تحاول تحل
+
+436
+00:50:00,390 --> 00:50:05,310
+المعادلة يعني مش تروح تضيع وقتك بالبلاش لذلك لو
+
+437
+00:50:05,310 --> 00:50:10,170
+جاكي سؤال يا بنات في الامتحان بقرأ السؤال جيدا قبل
+
+438
+00:50:10,170 --> 00:50:15,050
+ما امسك الجلم و ابدأ حل و بحدد ما هو المطلوب من
+
+439
+00:50:15,050 --> 00:50:18,730
+السؤال اذا حددت ما هو المطلوب من السؤال بستجل وقت
+
+440
+00:50:18,730 --> 00:50:22,090
+كويس ما احددت بسيطة امسك الجلم و انا مش عارف وين
+
+441
+00:50:22,090 --> 00:50:30,430
+رايحطيب نمرى V من نفس السؤال بيقول
+
+442
+00:50:30,430 --> 00:50:39,730
+لي X ناقص اتنين YW prime
+
+443
+00:50:42,260 --> 00:50:54,200
+y prime زائد x ناقص اتنين تاني ال x تاني ال x كل
+
+444
+00:50:54,200 --> 00:51:01,020
+هدا في y بده يساوي zero و ال initial conditions y
+
+445
+00:51:01,020 --> 00:51:06,580
+عندى التلاتة بده يساوي واحد و y prime عندى التلاتة
+
+446
+00:51:06,580 --> 00:51:10,460
+بده يساوي قداش بده يساوي لاتنين
+
+447
+00:51:16,650 --> 00:51:22,570
+يبقى نفس السؤال قال لي هات لي أطول فترة بحيث تدلق
+
+448
+00:51:22,570 --> 00:51:26,170
+قابل اشتقاق بحيث الحل تبعد ال function يكون قابل
+
+449
+00:51:26,170 --> 00:51:30,690
+اشتقاق مرتين على نفس الفترة يعني أنا بدأ أطبق له
+
+450
+00:51:30,690 --> 00:51:34,870
+النظرية اللي قبلها قليل بقوله كويس هذا السؤال
+
+451
+00:51:34,870 --> 00:51:39,900
+بيختلف عن سابقهسابقه كان المعامل تبع y double
+
+452
+00:51:39,900 --> 00:51:45,660
+prime واحد صحيح روحنا باعتبار كأنه جاسمين وجاهزين
+
+453
+00:51:45,660 --> 00:51:50,300
+هذه لأ المعامل x ناقص اتنين اذا انا بدأ اروح اجسم
+
+454
+00:51:50,300 --> 00:51:55,380
+على مين على x ناقص اتنين اذا لو جسمت الطرفين على x
+
+455
+00:51:55,380 --> 00:52:01,000
+ناقص اتنين بصير y double prime زائد واحد على x
+
+456
+00:52:01,000 --> 00:52:06,800
+ناقص اتنين في ال y prime زائد تان ال x في y
+
+457
+00:52:09,790 --> 00:52:18,990
+أصبح ال P of X هي واحد على X ناقص اتنين as in ال
+
+458
+00:52:18,990 --> 00:52:23,530
+discontinuity بيحصل وين؟ عند اتنين يعني هذه
+
+459
+00:52:23,530 --> 00:52:29,870
+continuous على كل real line مع هذا الاتنين يبقى
+
+460
+00:52:29,870 --> 00:52:32,970
+هذه is continuous
+
+461
+00:52:34,510 --> 00:52:45,190
+for all x التي لا تساوي اتنين for all x التي لا
+
+462
+00:52:45,190 --> 00:52:48,950
+تساوي اتنين for all x التي لا تساوي اتنين for all
+
+463
+00:52:48,950 --> 00:52:57,390
+x التي لا تساوي اتنين for all x التي لا تساوي
+
+464
+00:52:57,390 --> 00:53:04,150
+اتنينباية على اتنين و تلاتة باية على اتنين و خمسة
+
+465
+00:53:04,150 --> 00:53:09,190
+باية على اتنين طبعا كله زائد او ناقص كله زائد او
+
+466
+00:53:09,190 --> 00:53:15,410
+ناقص اللي هو تلاتة باية على اتنين زائد او ناقص
+
+467
+00:53:15,410 --> 00:53:21,710
+كذلك خمسة باية على اتنين و الى ما شاء الله طب
+
+468
+00:53:21,710 --> 00:53:27,220
+تعالوا خليني على ال real line هك نشوف شغلنا كويسلو
+
+469
+00:53:27,220 --> 00:53:33,100
+جيت قلت هذا الريال لاي هي ال zero بعد ال zero
+
+470
+00:53:33,100 --> 00:53:38,400
+بجيني واحد بعد ال واحد بجيني مين اتنين بعد اتنين
+
+471
+00:53:38,400 --> 00:53:41,860
+بجيني مين بجيني تلاتة
+
+472
+00:53:44,300 --> 00:53:48,980
+و بعد تلاتة اربعة خمسة الى اخره مش هذا موضوعنا،
+
+473
+00:53:48,980 --> 00:53:53,420
+موضوعنا ان ال discontinuity هذا حصل عند اتنين،
+
+474
+00:53:53,420 --> 00:53:58,760
+يعني عند اتنين هذا في discontinuity لمن؟ للدالة
+
+475
+00:53:58,760 --> 00:54:03,220
+الأولىالدالة التانية ال discontinuity عند ال بايع
+
+476
+00:54:03,220 --> 00:54:07,920
+تاني البايع قداشة بنات تلاتة صحيحه اربعتاشر من مية
+
+477
+00:54:07,920 --> 00:54:12,220
+على اتنين يعني اكتر من واحد و نص بحاجة بسيطة يعني
+
+478
+00:54:12,220 --> 00:54:18,060
+في discontinuity هنا تقريبا يبقى هذه اللي هي ال by
+
+479
+00:54:18,060 --> 00:54:22,960
+على اتنين في ان اللي بدأ ليه تلاتة by على اتنين
+
+480
+00:54:23,250 --> 00:54:27,370
+يعني واحدة باية على اتنين لحوالي واحدة و نص،
+
+481
+00:54:27,370 --> 00:54:36,010
+مظبوط؟ واحدة و نص في تلاتة باربعة و نص، مش هيك؟
+
+482
+00:54:36,010 --> 00:54:41,310
+يبقى تلاتة باية على اتنين بدها تجيكي هنا هذه هنا
+
+483
+00:54:41,310 --> 00:54:46,190
+بدها تجيكي اربعة و هنا بدها تجيكي ليه تلاتة باية
+
+484
+00:54:46,190 --> 00:54:51,450
+على مين؟ على الاتنين مرة تانية
+
+485
+00:54:55,670 --> 00:55:00,870
+يبقى هذه الثلاثة باعي على اتنين في discontinuity
+
+486
+00:55:00,870 --> 00:55:06,850
+كمانوية عندهاطب احنا جالي هات لل longest interval
+
+487
+00:55:06,850 --> 00:55:10,750
+بقولوا استنى شوية برجع لل initial condition ال
+
+488
+00:55:10,750 --> 00:55:14,790
+initial condition محسب وين؟ عندى التلاتة اذا
+
+489
+00:55:14,790 --> 00:55:20,710
+التلاتة موجود داخل الفترة المفتوحة من اتنين لتلاتة
+
+490
+00:55:20,710 --> 00:55:25,970
+pi على اتنين الفترة اللى عندنا هذه ها هاج هذه اللى
+
+491
+00:55:25,970 --> 00:55:29,750
+الفترة اللى تحتوي على ال initial conditionمسكت من
+
+492
+00:55:29,750 --> 00:55:31,990
+عند ال discontinuity اللي بعده إلى ال
+
+493
+00:55:31,990 --> 00:55:35,170
+discontinuity اللي بعده يبقى الفترة في ما بينهم
+
+494
+00:55:35,170 --> 00:55:40,510
+كلا الدالتين أو جميع الدوال على هذه الفترة هي دوال
+
+495
+00:55:40,510 --> 00:55:49,430
+متاصلة يبقى باجي بيقول له the longest interval
+
+496
+00:55:49,430 --> 00:55:55,690
+interval interval
+
+497
+00:55:59,330 --> 00:56:09,210
+that contains اللي هو تلاتة is من اتنين لغاية
+
+498
+00:56:09,210 --> 00:56:16,650
+تلاتة by على اتنين and the
+
+499
+00:56:16,650 --> 00:56:29,240
+functions are continuous on itجميع الدوال اللي هو
+
+500
+00:56:29,240 --> 00:56:37,180
+بالتالي ال solution عليها بيكون صحية and the
+
+501
+00:56:37,180 --> 00:56:40,880
+functions are continuous or infinite and the
+
+502
+00:56:40,880 --> 00:56:42,580
+solution
+
+503
+00:56:44,090 --> 00:56:50,490
+exist و الحل عليها بيكون مانو بيكون متحقق أو موجود
+
+504
+00:56:50,490 --> 00:56:55,230
+يبقى مثل هذا النوع من المسائل بس بده الفترة و
+
+505
+00:56:55,230 --> 00:56:59,450
+جابوها المدرسين لكوا في أعمال الفصل بيجيبوها كتير
+
+506
+00:56:59,450 --> 00:57:03,630
+هات للفترة اللي الحل عليها بيكون صحيح يكبر يكبر
+
+507
+00:57:03,630 --> 00:57:08,790
+أكتر من هيكد مابدناش من هذا النوع من المسائل
+
+508
+00:57:27,030 --> 00:57:32,570
+فضلي انا انا انا انا انا انا انا انا انا
+
+509
+00:57:37,700 --> 00:57:41,740
+أحنا حددنا الدالة الأولى وان ال discontinuity
+
+510
+00:57:41,740 --> 00:57:46,000
+تبعها يبقى باقي بكون تبقى continuous جينا على
+
+511
+00:57:46,000 --> 00:57:50,500
+الدالة التانية حددت ال discontinuity تبعها يبقى
+
+512
+00:57:50,500 --> 00:57:54,740
+بروح على ال initial condition جال لي why عندي
+
+513
+00:57:54,740 --> 00:58:01,030
+التلاتةيبقى الحل بدى يكون وين عندها T تساوي تلاتة
+
+514
+00:58:01,030 --> 00:58:05,010
+و عندها X يساوي تلاتة، باجي بدور على التلاتة
+
+515
+00:58:05,010 --> 00:58:08,890
+موجودة في أي من الفترات اللى بتبقى continuous
+
+516
+00:58:08,890 --> 00:58:13,950
+عليها، طبعا هنا كام فترة عندها يا بنات؟تنتين،
+
+517
+00:58:13,950 --> 00:58:17,870
+تلاتة، عشرة، مية، مليون، جد ما بدك، إلي أن يرسل
+
+518
+00:58:17,870 --> 00:58:21,330
+الله الأرض وامن عليها، بس أنا مابديش ياكل، بدي
+
+519
+00:58:21,330 --> 00:58:26,030
+الفترة التي تحتوي على الرقم تلاتة، على X يسوى
+
+520
+00:58:26,030 --> 00:58:31,070
+تلاتة، باجي بطلع، بلاقي تلاتة هذه اللي جالة ال
+
+521
+00:58:31,070 --> 00:58:34,070
+discontinuity عند اتنين والتانية ال discontinuity
+
+522
+00:58:34,070 --> 00:58:38,870
+عند تلاتة بقى على اتنين، مظبوط؟ يعني تها لو جيت
+
+523
+00:58:38,870 --> 00:58:44,950
+أرسمها لك راسم بقولك هيهذه الدالة الأولى كانت عند
+
+524
+00:58:44,950 --> 00:58:50,250
+اتنين عند اتنين مفتوحة بعدها continuous و قبلها
+
+525
+00:58:50,250 --> 00:58:55,870
+continuous على طول جينا للتانية عند ال by على
+
+526
+00:58:55,870 --> 00:59:00,910
+اتنين قبل اتنين ماليش علاقة فيها جينا بعد اتنين
+
+527
+00:59:00,910 --> 00:59:07,010
+لجينا تلاتة هي التلاتة اللي احنا بنحسب عندهاتمام؟
+
+528
+00:59:07,010 --> 00:59:10,590
+جينا اللى بعد اللى هو تلاتة باية على اتنين يبقى
+
+529
+00:59:10,590 --> 00:59:14,610
+هذه تلاتة باية على اتنين في discontinuity عندها
+
+530
+00:59:14,610 --> 00:59:19,470
+يبقى بيصير بعدها و لسه خمسة باية على اتنين بدنا
+
+531
+00:59:19,470 --> 00:59:22,130
+نوقف عنده و سبعة باية على اتنين بدنا .. كله بدنا
+
+532
+00:59:22,130 --> 00:59:26,270
+نوقف عنده وهنا لما نيجي لباية على اتنين، باية على
+
+533
+00:59:26,270 --> 00:59:30,780
+اتنين اجت قبل اتنين، يبقى هذه اللي همينباية على
+
+534
+00:59:30,780 --> 00:59:35,660
+اتنين، إذا هذه تبقى continuous على الفترة اللي
+
+535
+00:59:35,660 --> 00:59:40,300
+عندنا هذه، تمام؟ إذا أين المنطقة المشتركة بين
+
+536
+00:59:40,300 --> 00:59:45,180
+الفترتين والتي تحتوي على الرقم تلاتة، بلاجيش إلا
+
+537
+00:59:45,180 --> 00:59:50,950
+الفترة اللي عندنا هذههذه المنطقة المشتركة ما بين
+
+538
+00:59:50,950 --> 00:59:54,410
+ال continuity للدالة الأولى و ال continuity للدالة
+
+539
+00:59:54,410 --> 00:59:57,630
+التانية يعني بد الفترة اللى two functions
+
+540
+00:59:57,630 --> 01:00:01,410
+continuous عليها و بتجتمل هذه الفترة على الرقم
+
+541
+01:00:01,410 --> 01:00:04,750
+تلاتة اللى حسبنا ال initial conditions عندهم ماشي
+
+542
+01:00:04,750 --> 01:00:13,610
+طيب بننتقل الآن إلى نظرية جديدة كذلك يبقى theorem
+
+543
+01:00:18,050 --> 01:00:23,150
+قعد الكتاب بيسميها اللي هو main بيسميها ال
+
+544
+01:00:23,150 --> 01:00:33,530
+principle of superposition ال principle of
+
+545
+01:00:33,530 --> 01:00:37,090
+superposition
+
+546
+01:00:37,090 --> 01:00:42,470
+قاعدة
+
+547
+01:00:42,470 --> 01:00:46,730
+التطابق بيقول
+
+548
+01:00:46,730 --> 01:00:55,920
+ال FY1 and Y2 are
+
+549
+01:00:55,920 --> 01:01:00,200
+two
+
+550
+01:01:00,200 --> 01:01:05,840
+solutions
+
+551
+01:01:05,840 --> 01:01:22,570
+of the differential equation L of Yبدي يساوي L of
+
+552
+01:01:22,570 --> 01:01:29,750
+Y بدي يساوي Y W prime زي P of T في ال Y prime زي Q
+
+553
+01:01:29,750 --> 01:01:35,510
+of T في ال Y بدي يساوي Zero واعتبريه لهذه المعادلة
+
+554
+01:01:35,510 --> 01:01:45,930
+رقم واحد then Y يساوي C واحد Y واحد زي C اتنين Y
+
+555
+01:01:45,930 --> 01:01:52,880
+اتنينis also
+
+556
+01:01:52,880 --> 01:01:59,180
+a solution for
+
+557
+01:01:59,180 --> 01:02:07,040
+any values
+
+558
+01:02:07,040 --> 01:02:12,420
+of the constants
+
+559
+01:02:14,010 --> 01:02:28,090
+والعنوان هي الواقع C1 وC2 اخد هذه الملاحظة اذا C1
+
+560
+01:02:28,090 --> 01:02:34,490
+تساوي 0 او C2 تساوي 0
+
+561
+01:02:38,810 --> 01:02:44,910
+C2Y2 or C1Y1
+
+562
+01:02:44,910 --> 01:02:58,650
+is a solution is a solution for the same
+
+563
+01:02:58,650 --> 01:03:03,710
+differential equation one
+
+564
+01:03:35,270 --> 01:03:39,970
+بنشوف ليش سمنها قاعدة التطابق principle of
+
+565
+01:03:39,970 --> 01:03:45,650
+superpositionقل لو كان عندي y1 و y2 عبارة عن حلين
+
+566
+01:03:45,650 --> 01:03:51,190
+للمعادلة التفاضلية اللى قدامنا هذه ثم كونستانت في
+
+567
+01:03:51,190 --> 01:03:57,190
+الحل الأول زائد كونستانت في الحل الثاني is also is
+
+568
+01:03:57,190 --> 01:04:02,530
+a solution for any values of the constant c1 and
+
+569
+01:04:02,530 --> 01:04:08,430
+c2 يبقى احنا عندنا حلين من الحلين بدي أجيب كمان حل
+
+570
+01:04:09,820 --> 01:04:13,860
+يتطابق مع حل المعادلة التفاضلية يعني بدي يكون كذلك
+
+571
+01:04:13,860 --> 01:04:19,420
+هو حل المعادلة التفاضلية اللي عندنا هذه شوفوا يا
+
+572
+01:04:19,420 --> 01:04:24,520
+بنات بقول الملاحظة لو كان C1 يساوي 0 لو شيلنا C1
+
+573
+01:04:24,520 --> 01:04:30,870
+وحطينا بدل C0 ايش بيظل؟بصير الشكل الحل Y تساوي
+
+574
+01:04:30,870 --> 01:04:37,230
+C2Y2 لإن انا هنا ماحطتش اي conditions على C1 وC2
+
+575
+01:04:37,230 --> 01:04:42,170
+انه جالس لاني to real constant يبقى اي ثواب تلانق
+
+576
+01:04:42,170 --> 01:04:46,880
+صفر ولا غير الصفرطب افرض C2 كمان في Zero يصير Y
+
+577
+01:04:46,880 --> 01:04:51,280
+تساوي Zero هو عبارة عن حل مين للمعادلة التفضلي
+
+578
+01:04:51,280 --> 01:04:55,740
+Zero ومشتقت Zero ب Zero ومشتقت Zero ب Zero
+
+579
+01:04:55,740 --> 01:05:01,420
+ومجموعهم يسوى قداش يسوى Zero يبقى هنا لو كان أحد
+
+580
+01:05:01,420 --> 01:05:07,260
+السوابط أو كلاهما كمان Zeroيبقى اللي بظل بيكون هو
+
+581
+01:05:07,260 --> 01:05:12,720
+مين حل المعادلة فلو كان c1 ب zero بظل ان c2 y2 هو
+
+582
+01:05:12,720 --> 01:05:18,160
+حل المعادلة التفاضلية وكذلك لو كان c2 هو zero بظل
+
+583
+01:05:18,160 --> 01:05:23,840
+ان c1 y1 هو عبارة عن حل مين للمعادلة التفاضلية اذا
+
+584
+01:05:23,840 --> 01:05:28,660
+يا بنات انا لو جدرت اجيب حلين للمعادلة التفاضلية
+
+585
+01:05:28,660 --> 01:05:34,760
+بقدر اجيب حل ثالث للمعادلة التفاضلية باستخدام مين
+
+586
+01:05:35,080 --> 01:05:39,540
+الحلين ما هو الحل الثالث constant في الحل الأول و
+
+587
+01:05:39,540 --> 01:05:43,200
+constant في الحل الثاني و بجمع الاتنين بيعطيني حل
+
+588
+01:05:43,200 --> 01:05:47,620
+جديد للمعادلة التفاضلية طبعا واحدة هتسأل و تقول
+
+589
+01:05:47,620 --> 01:05:53,580
+تقدر تبرهن هذا الكلام؟ اقولها بنقدر و البرهن very
+
+590
+01:05:53,580 --> 01:05:57,260
+easy مش صعب يعني يبقى هذا ال proof
+
+591
+01:06:01,420 --> 01:06:05,960
+بقول ليش؟ لو كان Y1 هو حل المعادلة هذه، يبقى
+
+592
+01:06:05,960 --> 01:06:14,200
+هيحققها، صحيح ولا لأ؟ يبقى بادي بقول، الآن Y1 is a
+
+593
+01:06:14,200 --> 01:06:24,600
+solutionماذا سنجد من هذا الوضع ان ال L of Y1 يساوي
+
+594
+01:06:24,600 --> 01:06:34,120
+Y1 double prime زائد P of T في Y1 prime زائد Q of
+
+595
+01:06:34,120 --> 01:06:37,080
+T في Y1 يزيد
+
+596
+01:06:39,680 --> 01:06:49,860
+طيب الان Y2 is a solution بده يعطينا ان ال L of Y2
+
+597
+01:06:49,860 --> 01:06:58,020
+بده يساوي Y2 double prime زاد P of T في ال Y2
+
+598
+01:06:58,020 --> 01:07:05,260
+prime زاد ال Q of T في ال Y2 بده يساوي Zero كذلك
+
+599
+01:07:07,760 --> 01:07:13,500
+هذه المعقيدات حتى الآن جالي Y1 وY2 هم حللوا
+
+600
+01:07:13,500 --> 01:07:18,320
+المعادلة التفاضلية شو بدي اثبت؟ بدي اثبت ان هذا
+
+601
+01:07:18,320 --> 01:07:25,460
+ماله حل اخر للمعادلة التفاضلية بقوله اذا لو جدت
+
+602
+01:07:25,460 --> 01:07:33,760
+اثبت ان ال L وC1 Y1 زي C2 Y2 يساوي Zero بتم
+
+603
+01:07:33,760 --> 01:07:42,360
+المطلوبلو قلت اثبت ان c1y1 زاد c2y2 بده يستوي 0
+
+604
+01:07:42,360 --> 01:07:46,920
+بصير هذا هو عبارة عن حل ميم للمعادلة التفاضلية
+
+605
+01:07:46,920 --> 01:07:52,380
+بقولها نرجع لل L of y مين اجا مكانها
+
+606
+01:07:57,520 --> 01:08:04,120
+هذا بيصير c1y1 زي c2y2
+
+607
+01:08:04,120 --> 01:08:13,480
+كله double prime زي p of t في ال y prime اللي هو
+
+608
+01:08:13,480 --> 01:08:18,920
+c1y1 زي c2y2
+
+609
+01:08:18,920 --> 01:08:30,650
+كله primeزائد لـ Q of T في C1Y1 زائد C2Y2
+
+610
+01:08:32,770 --> 01:08:39,490
+لو طلع هذا المجموع يساوي zero إذا بصير هذا فعلا
+
+611
+01:08:39,490 --> 01:08:45,010
+عبارة عن حل مين للمعادلة التفاضلية اللي عندنا يبقى
+
+612
+01:08:45,010 --> 01:08:54,710
+صار عندنا المسألة كالتالي هذا ال LR C1Y1 زائد C2Y2
+
+613
+01:08:54,710 --> 01:08:59,030
+يساوي هذه الدالة بدنا نشتقها كم مرة
+
+614
+01:09:06,100 --> 01:09:15,080
+زاد c2 في y2 double prime يبقى ده c1 في y1 double
+
+615
+01:09:15,080 --> 01:09:22,960
+prime زاد c2 في y2 double primeيبقى انتهينا من ال
+
+616
+01:09:22,960 --> 01:09:27,300
+term الأول بدنا نيجي لل term التاني برضه معناته
+
+617
+01:09:27,300 --> 01:09:33,580
+مشتقة Y1 و مشتقة Y2 و بدي أضربها في Pt أدخلها على
+
+618
+01:09:33,580 --> 01:09:44,600
+كل واحدة فيهم يبقى بصير عندنا زائد P of T في C1 في
+
+619
+01:09:44,600 --> 01:09:55,870
+ال Y1 prime زائد P of Tفي c2 في ال y2 prime يبقى
+
+620
+01:09:55,870 --> 01:10:01,610
+خلاصنا من ال term هذا بل هذا بنفس الطريقة يبقى
+
+621
+01:10:01,610 --> 01:10:15,310
+زائد اللي هو q of t في c1 y1 زائد ل q of t في c2
+
+622
+01:10:15,310 --> 01:10:23,650
+y2يبقى هذا الكلام بتنسى واطلعلي في هذه و هذه او
+
+623
+01:10:23,650 --> 01:10:32,690
+هذه فيهم C1 عامل مشترك صح يبقى هاي C1 و هذا بضل
+
+624
+01:10:32,690 --> 01:10:42,750
+عندما يأتي ها Y1 W prime زائد P of T في Y1 A prime
+
+625
+01:10:43,230 --> 01:10:51,790
+زائد ال Q of T في ال Y1 اللي بظل Term اللي عندنا
+
+626
+01:10:51,790 --> 01:10:56,530
+هذا و Term اللي عندنا هذا و Term اللي عندنا هذا
+
+627
+01:10:56,530 --> 01:11:04,950
+بدأ أخد C2 عامل مشترك بظل Y2 W prime زائد P of T
+
+628
+01:11:04,950 --> 01:11:14,140
+في ال Y2 prime زائد Q of T في ال Y2الـ Y2 هذا
+
+629
+01:11:14,140 --> 01:11:21,240
+الكلام بده يساوي C1V طلعيلي هنا هذا بقداشي بناتي
+
+630
+01:11:21,240 --> 01:11:29,120
+هو الجوس الأول صح ولا لأ يبقى هذا بده يساوي C1V0
+
+631
+01:11:29,120 --> 01:11:39,130
+زي C2 اللي هو التانييبقى هذا C2 في 0 هو يسوي 0
+
+632
+01:11:39,130 --> 01:11:45,250
+زائد 0 يبقى يسوي قداش Zero يبقى الآن شو تفسيره
+
+633
+01:11:45,250 --> 01:11:50,070
+لهذا الكلام احنا ابتدأنا من بال function هذه طلع
+
+634
+01:11:50,070 --> 01:11:54,150
+تأثير ال L عليها يبدو يسوي Zero معناته هذا عبارة
+
+635
+01:11:54,150 --> 01:12:00,090
+عن mainعبارة عن حل المعادلة التفاضلية يبقى this
+
+636
+01:12:00,090 --> 01:12:11,390
+means that هذا يعني ان y سوى c1y1 زي c2y2 is a
+
+637
+01:12:11,390 --> 01:12:22,150
+solution of the differential equation
+
+638
+01:12:22,150 --> 01:12:23,470
+one
+
+639
+01:12:45,600 --> 01:12:49,080
+طيب نعطي تعريف جديد definition
+
+640
+01:13:01,260 --> 01:13:09,020
+تعريف يقول ما يأتي if y1
+
+641
+01:13:09,020 --> 01:13:17,020
+and y2 are solutions
+
+642
+01:13:22,030 --> 01:13:29,170
+of the homogeneous differential
+
+643
+01:13:29,170 --> 01:13:34,290
+equation
+
+644
+01:13:34,290 --> 01:13:42,670
+y double prime زائد P of T في ال Y prime زائد Q of
+
+645
+01:13:42,670 --> 01:13:53,140
+T في ال Yبدر ساوي زيرو then the function ادالة y
+
+646
+01:13:53,140 --> 01:14:03,860
+one y two prime ماقص y one prime y two is called
+
+647
+01:14:03,860 --> 01:14:09,560
+is
+
+648
+01:14:09,560 --> 01:14:13,480
+called the run skin
+
+649
+01:14:31,640 --> 01:14:35,280
+و بالروح نكتب
+
+650
+01:15:01,370 --> 01:15:14,390
+هنا سنكتب الشكل التالي و هو W of Y1 وY2 وY2 وY2
+
+651
+01:15:14,390 --> 01:15:17,790
+وY2
+
+652
+01:15:17,790 --> 01:15:21,950
+وY2
+
+653
+01:15:21,950 --> 01:15:28,610
+وY2 وY2 وY2 وY2 وY2 وY2 وY2 وY2 وY2 وY2 وY2 وY2
+
+654
+01:15:28,610 --> 01:15:28,670
+وY2 وY2 وY2 وY2 وY2 وY2 وY2 وY2 وY2 وY2 وY2 وY2
+
+655
+01:15:28,670 --> 01:15:28,710
+وY2 وY2 وY2 وY2 وY2 وY2 وY2 وY2 وY2 وY2 وY2 وY2
+
+656
+01:15:28,710 --> 01:15:28,750
+وY2 وY2 وY2 وY2 وY2 وY2 وY2 وY2 وY2 وY2 وY2 وY2
+
+657
+01:15:28,750 --> 01:15:55,390
+وY2 وY2 وY2 وYas a determinant كمحدد ها
+
+658
+01:15:55,390 --> 01:15:59,190
+دي البركة هنا واللهبقول اللي عندي y واحد و y اتنين
+
+659
+01:15:59,190 --> 01:16:01,970
+are two solutions لل homogenous differential
+
+660
+01:16:01,970 --> 01:16:06,950
+equation اللي عندنا إذا فينا function جديدة الحل
+
+661
+01:16:06,950 --> 01:16:12,210
+الأول في مشتقة الحل الثاني ناقص مشتقة الحل الأول
+
+662
+01:16:12,210 --> 01:16:16,930
+في الحل الثاني بيعطينا function جديدة بسميها ال
+
+663
+01:16:16,930 --> 01:16:21,590
+runescan ال w silent يا بنات منطقش ال w يبقى
+
+664
+01:16:21,590 --> 01:16:26,310
+بسميها ال runescan of ال y one و ال y two and we
+
+665
+01:16:26,310 --> 01:16:32,650
+writeبنروح نكتب القيمة العددية لمين لرونس كندا
+
+666
+01:16:32,650 --> 01:16:38,970
+حدّله الرمز W as a function of T أو W ل Y1 وY2 as
+
+667
+01:16:38,970 --> 01:16:46,150
+a function of T وهو عبارة عن المحدد الثانائي Y1 صف
+
+668
+01:16:46,150 --> 01:16:53,380
+الأول تبع Y1 وY2 صف التاني مشتقة Y1 ومشتقة Y2وكنا
+
+669
+01:16:53,380 --> 01:16:57,140
+زمان بنفك المحددات نقول حاصل ضرب عناصر القطر
+
+670
+01:16:57,140 --> 01:17:03,800
+الرئيسي ناقص حاصل ضرب عناصر القطر الثانوي يبقى لو
+
+671
+01:17:03,800 --> 01:17:11,360
+جيت حاصل ضرب عناصر القطر الرئيسي يبقى Y1Y2'
+
+672
+01:17:12,000 --> 01:17:21,180
+ناقص حاصل ضرب عناصر القطر الثانوي يبقى Y1'Y2 بهذا
+
+673
+01:17:21,180 --> 01:17:26,200
+الشكليبقى من ال alpha ساعدا إذا بدى أحسب ال owners
+
+674
+01:17:26,200 --> 01:17:30,580
+كله ال two solutions بحط الحل الأول حل التاني
+
+675
+01:17:30,580 --> 01:17:35,080
+مشتقة الأول مشتقة التاني باخد المحدد بفك المحدد
+
+676
+01:17:35,080 --> 01:17:38,640
+القيمة اللى بتطلع بتكون هي ال owners كله ال main
+
+677
+01:17:38,640 --> 01:17:43,040
+ال two solutions للمعادلة التفاضلية اللى عندنا
+
+678
+01:17:43,040 --> 01:17:47,100
+نعطيكي مثال توضيح بسيط يبقى example
+
+679
+01:17:55,860 --> 01:18:07,160
+Find the run skin for
+
+680
+01:18:07,160 --> 01:18:15,780
+the functions T وT E of T
+
+681
+01:18:18,570 --> 01:18:23,150
+عرف جداش ومستقل لمين الانتقالات الموجودة في
+
+682
+01:18:23,150 --> 01:18:24,610
+الانتقالات الموجودة في الانتقالات الموجودة في
+
+683
+01:18:24,610 --> 01:18:28,770
+الانتقالات
+
+684
+01:18:28,770 --> 01:18:31,450
+الموجودة في الانتقالات الموجودة في الانتقالات
+
+685
+01:18:31,450 --> 01:18:33,610
+الموجودة في الانتقالات الموجودة في الانتقالات
+
+686
+01:18:33,610 --> 01:18:36,090
+الموجودة في الانتقالات الموجودة في الانتقالات
+
+687
+01:18:36,090 --> 01:18:36,110
+الموجودة في الانتقالات الموجودة في الانتقالات
+
+688
+01:18:36,110 --> 01:18:36,170
+الموجودة في الانتقالات الموجودة في الانتقالات
+
+689
+01:18:36,170 --> 01:18:41,710
+الموجودة في الانتقالات الموجودة في الانت
+
+690
+01:18:42,420 --> 01:18:49,160
+بواحد هذه مشتقة حاصن ضرب دالتين يبقى الأولى في
+
+691
+01:18:49,160 --> 01:18:54,880
+مشتقة الدالة الثانية زائد دالة ثانية في مشتقة
+
+692
+01:18:54,880 --> 01:19:01,800
+الأولى يبقى T EOS T بالشكل اللى عندناالرح نحسب هذا
+
+693
+01:19:01,800 --> 01:19:08,460
+المحدد يبجى بدنفكه حاصل ضرب عناصر قطر رئيسي ماقص
+
+694
+01:19:08,460 --> 01:19:12,660
+حاصل ضرب عناصر قطر الثانوي حاصل ضرب عناصر قطر
+
+695
+01:19:12,660 --> 01:19:19,820
+الرئيسي يبجى T في E of T زائد T تربية في E of T
+
+696
+01:19:20,440 --> 01:19:26,760
+ضربنا الـ T في كل من الترميل الاتنين هدول ناقص
+
+697
+01:19:26,760 --> 01:19:33,900
+حاصل ضرب عناصر القطر الثانوي ناقص T في E أُس T أظن
+
+698
+01:19:33,900 --> 01:19:40,600
+هذا وهذا مع السلامة يبقى النتيجة T تربيع في E أُس
+
+699
+01:19:40,600 --> 01:19:46,920
+T هي ال function اللي احنا قلنا عليها اللي خارجي
+
+700
+01:19:46,920 --> 01:19:51,490
+طرح لمينيبقى اتنين لتو functions هدول يبقى هذا
+
+701
+01:19:51,490 --> 01:19:57,330
+رونسكين لمين لتو functions وهكذا اي دالتين حطيهم
+
+702
+01:19:57,330 --> 01:20:02,310
+حط مستقبتهم هات المحدد اثناء لهم بيعطيكي قيمة
+
+703
+01:20:02,310 --> 01:20:08,770
+رونسكين لهم كمان نظرية اخرى في محاضرة اليوم يبقى
+
+704
+01:20:08,770 --> 01:20:14,350
+theorem we
+
+705
+01:20:14,350 --> 01:20:15,410
+suppose that
+
+706
+01:20:23,070 --> 01:20:34,130
+الـ Y1 و Y2 هما اتجارات
+
+707
+01:20:34,130 --> 01:20:42,590
+دفعية
+
+708
+01:20:45,220 --> 01:20:57,420
+of the differential equation L of Y تساوي Y double
+
+709
+01:20:57,420 --> 01:21:07,020
+prime زائد P of T في ال Y prime زائد ل Q of T في
+
+710
+01:21:07,020 --> 01:21:14,420
+ال Y بده يساوي Zero سميلي هذه المعادلة رقم واحدand
+
+711
+01:21:14,420 --> 01:21:21,280
+that الورنسكين
+
+712
+01:21:21,280 --> 01:21:31,420
+عند ال T نوت بده يساوي Y1 عند ال T نوت في Y2 prime
+
+713
+01:21:31,930 --> 01:21:39,530
+عند الـ T node ناقص Y1 prime عند ال T node في Y2
+
+714
+01:21:39,530 --> 01:21:49,990
+عند ال T node لا يسوى Zero with مع ال initial
+
+715
+01:21:49,990 --> 01:21:59,150
+conditions او with اللي
+
+716
+01:21:59,150 --> 01:22:09,380
+هولا يساوي zero و ال Y عند ال T node يساوي Y node
+
+717
+01:22:09,380 --> 01:22:17,840
+و Y
+
+718
+01:22:17,840 --> 01:22:27,140
+prime عند ال T node يساوي Y node prime او Y عند ال
+
+719
+01:22:27,140 --> 01:22:34,670
+T nodeو I عند ال T نوت و I prime عند ال T نوت أبو
+
+720
+01:22:34,670 --> 01:22:40,990
+دي ساوي و I prime دوري لكن أبو دي ساوي و I prime
+
+721
+01:22:40,990 --> 01:22:49,950
+نوت دوري و هاد يسميها لإتنين هاد المعادلة ساميها
+
+722
+01:22:49,950 --> 01:22:53,290
+معادلة اتنين
+
+723
+01:22:56,870 --> 01:23:08,750
+ثم هناك اختيار ثم هناك اختيار من
+
+724
+01:23:08,750 --> 01:23:19,570
+المصادر C1
+
+725
+01:23:19,570 --> 01:23:22,670
+وC2
+
+726
+01:23:22,670 --> 01:23:24,110
+لذلك
+
+727
+01:23:27,920 --> 01:23:37,940
+بحيث ان y تساوي c واحد y واحد زائد c اتنين y اتنين
+
+728
+01:23:37,940 --> 01:23:44,820
+satisfied satisfied
+
+729
+01:23:44,820 --> 01:23:47,880
+the
+
+730
+01:23:47,880 --> 01:23:53,880
+differential equation
+
+731
+01:23:53,880 --> 01:23:55,840
+when
+
+732
+01:23:57,520 --> 01:24:09,520
+and the given initial conditions
+
+733
+01:24:09,520 --> 01:24:12,740
+اتنى
+
+734
+01:27:05,040 --> 01:27:10,440
+نظرية بتقول ما ياتي افترض ان Y1 و Y2 عبارة عن حليل
+
+735
+01:27:10,440 --> 01:27:15,780
+المعادلة التفاضلية اللى عندنا هذه and that و ال
+
+736
+01:27:15,780 --> 01:27:20,710
+warrants كان عندهم كان لا يساوي zeroوطني two
+
+737
+01:27:20,710 --> 01:27:26,510
+initial conditions كذلك طبعا الwoners can win عند
+
+738
+01:27:26,510 --> 01:27:30,910
+نقطة محددة عند T node مش حيالها عند نقطة واحدة
+
+739
+01:27:30,910 --> 01:27:35,190
+الwoners can هذا لا يساوي zero قال لي إن حدث ذلك
+
+740
+01:27:35,190 --> 01:27:43,710
+يبقى هلاقي two constants C1 وC2 بحيث أن هذا يكون
+
+741
+01:27:43,710 --> 01:27:49,950
+حل للمعادلة التفاضليةو كذلك and the given initial
+
+742
+01:27:49,950 --> 01:27:54,650
+conditions و كذلك أن يحل المعادلة التفاضلية بهذه
+
+743
+01:27:54,650 --> 01:28:00,150
+الشروط المتاع أو اختصارا يحقق ال initial value
+
+744
+01:28:00,150 --> 01:28:06,410
+problem المتاع اللي عندنا مرة تانية لو كان Y1 و Y2
+
+745
+01:28:06,410 --> 01:28:14,500
+حلل المعادلة التفاضليةبدى اضمن ان هدول بيخلوا لي
+
+746
+01:28:14,500 --> 01:28:20,100
+وجود c1 و c2 بحتي يكون هذا حل شو اللى بده يضمنلي؟
+
+747
+01:28:20,100 --> 01:28:25,780
+بده يضمنلي ان الoneskin هذا لا يساوي zero لكن لو
+
+748
+01:28:25,780 --> 01:28:31,120
+طلع الoneskin يساوي zero بضمنش وجود حلينيبقى هنا
+
+749
+01:28:31,120 --> 01:28:35,780
+بضمن وجود حالين إذا كان الغنوز كان عنده نقطة ماله
+
+750
+01:28:35,780 --> 01:28:39,980
+لا يساوي منها نقطة هي النقطة تبع ال condition
+
+751
+01:28:39,980 --> 01:28:45,920
+الاتنين هدول إن حدث ذلك يبقى بضمن وجود هذا الحل و
+
+752
+01:28:45,920 --> 01:28:51,420
+بضمن وجود حل ال initial value problem واضح كلامي
+
+753
+01:28:51,920 --> 01:28:55,380
+طيب الكلام اللي بنقوله هذا بنروح نحطه على أرض
+
+754
+01:28:55,380 --> 01:29:00,300
+الواقع عمليا بيقول السؤال بنقطتين قال يهاتل
+
+755
+01:29:00,300 --> 01:29:04,680
+الوانوزكن تبع الحلين تبع المعادلة هذه طب نفترض
+
+756
+01:29:04,680 --> 01:29:10,180
+جيبنا and ومن ثم أكتب لل general solution يبقى أنا
+
+757
+01:29:10,180 --> 01:29:14,840
+بدروح أجيب الوانوزكن و أشوف هل فعلا يساوي zero
+
+758
+01:29:14,840 --> 01:29:20,700
+والله لا يساوي0 اتنين جالي هاتلي كمان حل ال
+
+759
+01:29:20,700 --> 01:29:26,140
+initial value problem ب two conditions اللي عندنا
+
+760
+01:29:26,140 --> 01:29:30,460
+هنا بالضبط زي النظرية بقوله بسيطة اذا انا بدي ارجع
+
+761
+01:29:30,460 --> 01:29:34,240
+للحل زي ما كنا بنحل وين في ال section اللي فات
+
+762
+01:29:34,240 --> 01:29:38,700
+بطلع المعادلة معادلة من الرتبة الثانية بمعاملات
+
+763
+01:29:38,700 --> 01:29:49,000
+ثابتة يبقى بداجي اقوله lety تساوي e أس RT ب إيه
+
+764
+01:29:49,000 --> 01:29:58,300
+solution of المعادلة التفاضية y w prime زائد خمسة
+
+765
+01:29:58,300 --> 01:30:04,060
+y prime زائد ستة y يساوي zero سميلي هذه المعادلة
+
+766
+01:30:04,060 --> 01:30:09,020
+ليهما رقم واحد يبقى then
+
+767
+01:30:16,580 --> 01:30:26,880
+R تربيع زائد خمسة R زائد ستة يساوي زيرو هذه
+
+768
+01:30:26,880 --> 01:30:33,840
+المعادلة بقدر احللها كتالي جسين بده يساوي زيرو هذه
+
+769
+01:30:33,840 --> 01:30:41,460
+R وهذه Rوهذه اتنين في تلاتة وهذه زائد وهذه زايد
+
+770
+01:30:41,460 --> 01:30:52,540
+بناء عليها R1 هيسوي سالب اتنين وR2 سالب تلاتة اذا
+
+771
+01:30:52,540 --> 01:30:58,380
+صار هذا general solution
+
+772
+01:31:05,170 --> 01:31:13,010
+C1E-2T C2E-3T
+
+773
+01:31:15,400 --> 01:31:21,660
+يبقى هذا الحل يا بناتي الهواي واحد وهذا الحل ماين
+
+774
+01:31:21,660 --> 01:31:28,220
+الهواي اتنين، مظبوط ولا لا؟ يعني اصلا عندي Y واحد
+
+775
+01:31:28,220 --> 01:31:36,270
+E أس ناقص اتنين T وY اتنين E أس ناقص تلاتة Tطب
+
+776
+01:31:36,270 --> 01:31:40,950
+نرجع و نكتب له ال general solution كتبنا ال
+
+777
+01:31:40,950 --> 01:31:45,110
+general solution سبقنا احنا الاصل نجيب له ال
+
+778
+01:31:45,110 --> 01:31:48,030
+general solution قبل و بعد نكتب بعد هيك نكتب له ال
+
+779
+01:31:48,030 --> 01:31:51,810
+general solution مش مشكلة اذا بتروح اجيب له ال
+
+780
+01:31:51,810 --> 01:31:57,230
+general solution نسكم تبع الحل الأول E أص ناقص
+
+781
+01:31:57,230 --> 01:32:04,720
+اتنين T و E أص ناقص تلاتة T بجهة المحددبحط الحل
+
+782
+01:32:04,720 --> 01:32:13,800
+الأول وهذا الحل الثاني اشتغل ناقص اتنين اي اس ناقص
+
+783
+01:32:13,800 --> 01:32:19,780
+اتنين تي و هنا ناقص تلاتة اي اس ناقص تلاتة تي و
+
+784
+01:32:19,780 --> 01:32:20,980
+يساوي
+
+785
+01:32:23,370 --> 01:32:26,910
+يبقى ال wellness can as a function of T يساوي
+
+786
+01:32:26,910 --> 01:32:34,050
+بالدحال حاصل باربع ناصر القطر الرئيسي لناقص تلاتة
+
+787
+01:32:34,050 --> 01:32:42,030
+E أس ناقص خمسة T ناقص مع ناقص بصير الزائد اتنين E
+
+788
+01:32:42,030 --> 01:32:49,350
+أس ناقص خمسة T يبقى الجواب يبقى القداش ناقص E أس
+
+789
+01:32:49,350 --> 01:32:55,900
+ناقص خمسة Tيبقى زي ما انتوا شايفين الورسكين ماله
+
+790
+01:32:55,900 --> 01:33:01,920
+لا يساوي zero مدام لا يساوي zero إذا ال general
+
+791
+01:33:01,920 --> 01:33:08,440
+solution اللي بده ي exist وهذا هو شكله يعني بعد ما
+
+792
+01:33:08,440 --> 01:33:13,050
+أجيب له الورسكين بقوله إذاهذا هو ال general
+
+793
+01:33:13,050 --> 01:33:25,050
+solution C1E-2T C2E-3T لحل المطلوب طيب خلصنا
+
+794
+01:33:25,050 --> 01:33:28,610
+المطلوب الأول كتبنا له general solution و جيبناه
+
+795
+01:33:28,610 --> 01:33:33,850
+ورا اسكين جالي و من ثم حل ال initial value problem
+
+796
+01:33:33,850 --> 01:33:38,390
+اللي عندنا هذه يبقى بدنا نيجي لل initial value
+
+797
+01:33:38,390 --> 01:33:43,130
+problemالـ initial value problem ماعطيني شكل ال y
+
+798
+01:33:43,130 --> 01:33:48,510
+عند ال zero شكل ال y prime y موجودة إذا بالزمن مين
+
+799
+01:33:48,510 --> 01:33:58,990
+إذا مرة تانية y تساوي c1 في e أس ناقص اتنين t c2
+
+800
+01:33:58,990 --> 01:34:05,850
+في e أس ناقص تلاتة t الآن ال y عند ال zero يسوى
+
+801
+01:34:05,850 --> 01:34:13,450
+zero أظنY عند Zero بده يساوي Zero implies هذا Zero
+
+802
+01:34:13,450 --> 01:34:21,570
+بده يساوي EO Zero بواحد يبقى C1 EO Zero بواحد يبقى
+
+803
+01:34:21,570 --> 01:34:26,770
+زائد C2بدي اشتقها دي يا بناتي يبقى ال y prime
+
+804
+01:34:26,770 --> 01:34:33,810
+يساوي ناقص اتنين c واحد e اص ناقص اتنين ناقص تلاتة
+
+805
+01:34:33,810 --> 01:34:40,170
+c اتنين e اص ناقص تلاتة t ال initial condition
+
+806
+01:34:40,170 --> 01:34:45,090
+التاني اللي هو y prime عند zero بدي يساوي واحدY'
+
+807
+01:34:45,810 --> 01:34:52,330
+عند الـ zero بده يساوي واحد implies Y' بواحد يساوي
+
+808
+01:34:52,330 --> 01:34:57,210
+هشيل هذه و احط مكانها zero بصير هذا بواحد بناقص
+
+809
+01:34:57,210 --> 01:35:05,010
+اتنين C1 ناقص تلاتة C2شو رايكوا بدأجي المعادلة
+
+810
+01:35:05,010 --> 01:35:10,410
+الأولى واضغبها في اتنين يبقى zero بساوي اتنين C
+
+811
+01:35:10,410 --> 01:35:15,370
+واحد زائد اتنين C اتنين المعادلة الثانية بدي
+
+812
+01:35:15,370 --> 01:35:21,360
+انزلها زي ما هي ناقص اتنين C واحدماقص تلاتة C
+
+813
+01:35:21,360 --> 01:35:26,200
+اتنين و نجمع هذول بروحوا مع السلامة الواحد زي ال
+
+814
+01:35:26,200 --> 01:35:32,300
+zero اللي هو واحد يساوي الناقص C اتنين يبقى C
+
+815
+01:35:32,300 --> 01:35:38,960
+اتنين يساوي قداش ناقص واحد إذا لو كان C اتنين ناقص
+
+816
+01:35:38,960 --> 01:35:45,660
+واحد C واحد بده يساوي واحد و C واحد بده يساوي واحد
+
+817
+01:35:45,660 --> 01:35:48,520
+يبقى أصبح the solution
+
+818
+01:35:53,830 --> 01:36:04,940
+والقضايا الاصلاحية هي واي تساويوين الحل اللى حصلنا
+
+819
+01:36:04,940 --> 01:36:10,400
+عليه هى فوق هشيل c واحد و احط مكانه واحد يبقى
+
+820
+01:36:10,400 --> 01:36:18,140
+بيصير E أس ناقص اتنين T ناقص E أس ناقص تلاتة T
+
+821
+01:36:18,140 --> 01:36:22,640
+يبقى هى الشكل اللى ال solution لمين لل initial
+
+822
+01:36:22,640 --> 01:36:29,680
+value problem لحد هنا stopيعطيكوا العافية لسه
+
+823
+01:36:29,680 --> 01:36:34,940
+لازلنا في نفس ال section ولما ننتهي بعد للمرة
+
+824
+01:36:34,940 --> 01:36:36,960
+القادمة ان شاء الله
+
diff --git a/PL9fwy3NUQKwa8ZDfSFGn6H8xVFLzqmCZC/XSq4pVrKvY4_raw.json b/PL9fwy3NUQKwa8ZDfSFGn6H8xVFLzqmCZC/XSq4pVrKvY4_raw.json
new file mode 100644
index 0000000000000000000000000000000000000000..21f77d952050a125c5bdc224af17ce7e6ad227a7
--- /dev/null
+++ b/PL9fwy3NUQKwa8ZDfSFGn6H8xVFLzqmCZC/XSq4pVrKvY4_raw.json
@@ -0,0 +1 @@
+{"segments": [{"id": 1, "seek": 256, "start": 0.0, "end": 2.56, "text": "موسيقى", "tokens": [2304, 41779, 1829, 4587, 7578], "avg_logprob": -0.21679687003294626, "compression_ratio": 0.5714285714285714, "no_speech_prob": 0.004974365234375, "words": [{"start": 0.0, "end": 2.56, "word": "موسيقى", "probability": 0.793505859375}], "temperature": 1.0}, {"id": 2, "seek": 3942, "start": 10.56, "end": 39.42, "text": "المرة اللى فاتت ابتدأنا في section تلاتة واحد اللى هو second order homogeneous linear differential equations شرحنا هذه النقطة جيبنا المعادلة التفاضلية من الرتبة الثانية وال constant coefficients جيبنا ال auxiliary equation او ال characteristic equation اعطينا على ذلك مجموعة من الأمثلة ولا يزال هناك مثالات", "tokens": [45340, 25720, 13672, 7578, 6156, 9307, 2655, 48127, 2655, 3215, 10721, 8315, 8978, 3541, 6055, 1211, 9307, 3660, 36764, 24401, 13672, 7578, 31439, 1150, 1668, 42632, 8213, 15756, 11787, 13412, 2288, 5016, 8315, 29538, 28239, 47432, 3660, 10874, 1829, 3555, 8315, 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{"start": 122.42, "end": 123.04, "word": " R", "probability": 0.876953125}, {"start": 123.04, "end": 124.28, "word": " تربيع", "probability": 0.970703125}, {"start": 124.28, "end": 126.56, "word": " تساوي", "probability": 0.7882080078125}, {"start": 126.56, "end": 127.14, "word": " ربع", "probability": 0.9147135416666666}, {"start": 127.14, "end": 128.36, "word": " يبقى", "probability": 0.9595947265625}, {"start": 128.36, "end": 128.7, "word": " R", "probability": 0.93115234375}, {"start": 128.7, "end": 129.44, "word": " تساوي", "probability": 0.9669189453125}, {"start": 129.44, "end": 130.26, "word": " زائد", "probability": 0.888671875}, {"start": 130.26, "end": 130.56, "word": " او", "probability": 0.881591796875}, {"start": 130.56, "end": 131.32, "word": " ناقص", "probability": 0.99462890625}, {"start": 131.32, "end": 131.74, "word": " نص", "probability": 0.980224609375}], "temperature": 1.0}, {"id": 7, "seek": 14804, "start": 133.16, "end": 148.04, "text": "يبقى صارت الجذور عندي two real different truths اللي هو مين؟ قيمتين حقيقيتين ومختلفتين يبقى بناء عليه شكل ال general solution", "tokens": [1829, 3555, 4587, 7578, 20328, 9640, 2655, 25724, 8848, 13063, 18871, 16254, 732, 957, 819, 30079, 13672, 1829, 31439, 3714, 9957, 22807, 12174, 32640, 2655, 9957, 11331, 38436, 4587, 36081, 9957, 4032, 2304, 46456, 46538, 2655, 9957, 7251, 3555, 4587, 7578, 44945, 16606, 47356, 13412, 28820, 2423, 2674, 3827], "avg_logprob": -0.16234375655651093, "compression_ratio": 1.304054054054054, "no_speech_prob": 0.0, "words": [{"start": 133.16, "end": 133.98, "word": "يبقى", "probability": 0.876220703125}, {"start": 133.98, "end": 134.64, "word": " صارت", "probability": 0.7825520833333334}, {"start": 134.64, "end": 135.08, "word": " الجذور", "probability": 0.9700520833333334}, {"start": 135.08, "end": 135.46, "word": " عندي", "probability": 0.87646484375}, {"start": 135.46, "end": 135.98, "word": " two", "probability": 0.65771484375}, {"start": 135.98, "end": 136.86, "word": " 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"probability": 0.948486328125}, {"start": 145.96, "end": 146.22, "word": " ال", "probability": 0.95849609375}, {"start": 146.22, "end": 146.7, "word": " general", "probability": 0.78271484375}, {"start": 146.7, "end": 148.04, "word": " solution", "probability": 0.95166015625}], "temperature": 1.0}, {"id": 8, "seek": 17766, "start": 155.88, "end": 177.66, "text": "Given differential equation as يبقى Y تساوي C1 A أس سالب نص T يعني T على 2 زائد C2 A أس نص T بالشكل اللي عندنا هذا", "tokens": [38, 5709, 15756, 5367, 382, 7251, 3555, 4587, 7578, 398, 6055, 3794, 995, 45865, 383, 16, 316, 5551, 3794, 8608, 6027, 3555, 8717, 9381, 314, 37495, 22653, 314, 15844, 568, 30767, 16373, 3215, 383, 17, 316, 5551, 3794, 8717, 9381, 314, 20666, 8592, 28820, 13672, 1829, 43242, 8315, 23758], "avg_logprob": -0.26453125894069673, "compression_ratio": 1.1714285714285715, "no_speech_prob": 0.0, "words": [{"start": 155.88, "end": 157.07999999999998, "word": "Given", "probability": 0.486236572265625}, {"start": 157.07999999999998, "end": 158.28, "word": " differential", "probability": 0.658203125}, {"start": 158.28, "end": 160.14, "word": " equation", "probability": 0.9345703125}, {"start": 160.14, "end": 161.3, "word": " as", "probability": 0.6318359375}, {"start": 161.3, "end": 162.9, "word": " يبقى", "probability": 0.81787109375}, {"start": 162.9, "end": 163.34, "word": " Y", "probability": 0.5751953125}, {"start": 163.34, "end": 164.86, "word": " تساوي", "probability": 0.70819091796875}, {"start": 164.86, "end": 166.36, "word": " C1", "probability": 0.83544921875}, {"start": 166.36, "end": 167.32, "word": " A", "probability": 0.22021484375}, {"start": 167.32, "end": 167.92, "word": " أس", "probability": 0.56494140625}, {"start": 167.92, "end": 168.72, "word": " سالب", "probability": 0.8154296875}, {"start": 168.72, "end": 169.24, "word": " نص", "probability": 0.99365234375}, {"start": 169.24, "end": 169.66, "word": " T", "probability": 0.9541015625}, {"start": 169.66, "end": 170.12, "word": " يعني", "probability": 0.80615234375}, {"start": 170.12, "end": 170.44, "word": " T", "probability": 0.9248046875}, {"start": 170.44, "end": 170.74, "word": " على", "probability": 0.705078125}, {"start": 170.74, "end": 171.18, "word": " 2", "probability": 0.61279296875}, {"start": 171.18, "end": 172.3, "word": " زائد", "probability": 0.8483072916666666}, {"start": 172.3, "end": 173.46, "word": " C2", "probability": 0.918701171875}, {"start": 173.46, "end": 174.4, "word": " A", "probability": 0.77978515625}, {"start": 174.4, "end": 174.96, "word": " أس", "probability": 0.9794921875}, {"start": 174.96, "end": 175.72, "word": " نص", "probability": 0.990234375}, {"start": 175.72, "end": 176.06, "word": " T", "probability": 0.986328125}, {"start": 176.06, "end": 176.66, "word": " بالشكل", "probability": 0.8981119791666666}, {"start": 176.66, "end": 176.8, "word": " اللي", "probability": 0.974609375}, {"start": 176.8, "end": 177.26, "word": " عندنا", "probability": 0.96435546875}, {"start": 177.26, "end": 177.66, "word": " هذا", "probability": 0.62841796875}], "temperature": 1.0}, {"id": 9, "seek": 20328, "start": 178.74, "end": 203.28, "text": "هذا شكل الحل لكن راح اعطانا mainly two initial conditions يبقى لو روحنا اشتقنا الحل لأن هذا بيصير Y' يساوي ناقص مصي one E أس ناقص T على اتنين زائد مصي two E أس T على اتنين", "tokens": [3224, 15730, 13412, 28820, 21542, 1211, 44381, 12602, 39319, 1975, 3615, 9566, 7649, 995, 8704, 732, 5883, 4487, 7251, 3555, 4587, 7578, 45164, 12602, 2407, 5016, 8315, 1975, 8592, 2655, 4587, 8315, 21542, 1211, 5296, 33456, 23758, 4724, 1829, 9381, 13546, 398, 6, 7251, 3794, 995, 45865, 8717, 995, 4587, 9381, 3714, 9381, 1829, 472, 462, 5551, 3794, 8717, 995, 4587, 9381, 314, 15844, 1975, 2655, 1863, 9957, 30767, 16373, 3215, 3714, 9381, 1829, 732, 462, 5551, 3794, 314, 15844, 1975, 2655, 1863, 9957], "avg_logprob": -0.23180146988700417, "compression_ratio": 1.5141242937853108, "no_speech_prob": 0.0, "words": [{"start": 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"temperature": 1.0}, {"id": 10, "seek": 22982, "start": 204.86, "end": 229.82, "text": "بناء عليه بدأ نيجي على ال initial conditions اللي عندنا الان عندنا y عند ال zero بده يساوي 2 هذا معناه ان ال y هذه 2 تساوي c1 و بيصير e of 0 اللي هو بواحد زاد c2 e of 0 اللي هو بواحد ال condition التاني y prime", "tokens": [3555, 1863, 16606, 47356, 47525, 10721, 8717, 1829, 7435, 1829, 15844, 2423, 5883, 4487, 13672, 1829, 43242, 8315, 2423, 7649, 43242, 8315, 288, 43242, 2423, 4018, 47525, 3224, 7251, 3794, 995, 45865, 568, 23758, 20449, 8315, 3224, 16472, 2423, 288, 29538, 568, 6055, 3794, 995, 45865, 269, 16, 4032, 4724, 1829, 9381, 13546, 308, 295, 1958, 13672, 1829, 31439, 4724, 14407, 24401, 30767, 18513, 269, 17, 308, 295, 1958, 13672, 1829, 31439, 4724, 14407, 24401, 2423, 4188, 16712, 7649, 1829, 288, 5835], "avg_logprob": -0.3354668566979558, "compression_ratio": 1.7297297297297298, "no_speech_prob": 0.0, "words": [{"start": 204.86, "end": 205.42, "word": "بناء", "probability": 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"probability": 0.619140625}, {"start": 216.4, "end": 217.26, "word": " تساوي", "probability": 0.911376953125}, {"start": 217.26, "end": 217.94, "word": " c1", "probability": 0.697265625}, {"start": 217.94, "end": 218.1, "word": " و", "probability": 0.488525390625}, {"start": 218.1, "end": 218.46, "word": " بيصير", "probability": 0.7352294921875}, {"start": 218.46, "end": 218.94, "word": " e", "probability": 0.63623046875}, {"start": 218.94, "end": 219.42, "word": " of", "probability": 0.1663818359375}, {"start": 219.42, "end": 220.1, "word": " 0", "probability": 0.458984375}, {"start": 220.1, "end": 220.34, "word": " اللي", "probability": 0.84814453125}, {"start": 220.34, "end": 220.46, "word": " هو", "probability": 0.96630859375}, {"start": 220.46, "end": 221.06, "word": " بواحد", "probability": 0.6492513020833334}, {"start": 221.06, "end": 223.38, "word": " زاد", "probability": 0.777099609375}, {"start": 223.38, "end": 224.42, "word": " c2", "probability": 0.9091796875}, {"start": 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{"start": 910.82, "end": 911.28, "word": " هذا", "probability": 0.9560546875}, {"start": 911.28, "end": 911.92, "word": " الكلام", "probability": 0.9098307291666666}, {"start": 911.92, "end": 912.7, "word": " مضروب", "probability": 0.9420166015625}, {"start": 912.7, "end": 913.0, "word": " في", "probability": 0.8046875}, {"start": 913.0, "end": 913.64, "word": " EOS", "probability": 0.44482421875}, {"start": 913.64, "end": 914.5, "word": " 3D", "probability": 0.507568359375}], "temperature": 1.0}, {"id": 41, "seek": 93207, "start": 915.37, "end": 932.07, "text": "أظن نقسم على خمسة يكون جيبنا C2 يفقه لو قسمنا على خمسة بصير C2 يساوي خمس فمين فتنين Y ناقص Y prime في E أس تلاتة T", "tokens": [10721, 19913, 1863, 8717, 4587, 38251, 15844, 16490, 2304, 3794, 3660, 7251, 30544, 10874, 1829, 3555, 8315, 383, 17, 7251, 5172, 4587, 3224, 45164, 12174, 38251, 8315, 15844, 16490, 2304, 3794, 3660, 4724, 9381, 13546, 383, 17, 7251, 3794, 995, 45865, 16490, 2304, 3794, 6156, 2304, 9957, 6156, 2655, 1863, 9957, 398, 8717, 995, 4587, 9381, 398, 5835, 8978, 462, 5551, 3794, 6055, 1211, 9307, 3660, 314], "avg_logprob": -0.23161764464834156, "compression_ratio": 1.3597122302158273, "no_speech_prob": 0.0, "words": [{"start": 915.37, "end": 915.79, "word": "أظن", "probability": 0.7102457682291666}, {"start": 915.79, "end": 916.13, "word": " نقسم", "probability": 0.9033203125}, {"start": 916.13, "end": 916.31, "word": " على", "probability": 0.84716796875}, {"start": 916.31, "end": 916.91, "word": " خمسة", "probability": 0.9351806640625}, {"start": 916.91, "end": 917.57, "word": " يكون", "probability": 0.623046875}, {"start": 917.57, "end": 917.97, "word": " جيبنا", "probability": 0.92041015625}, {"start": 917.97, "end": 918.65, "word": " C2", "probability": 0.6927490234375}, {"start": 918.65, "end": 919.41, "word": " يفقه", "probability": 0.618560791015625}, {"start": 919.41, "end": 919.61, "word": " لو", "probability": 0.93505859375}, {"start": 919.61, "end": 920.35, "word": " قسمنا", "probability": 0.9417317708333334}, {"start": 920.35, "end": 920.71, "word": " على", "probability": 0.91259765625}, {"start": 920.71, "end": 921.53, "word": " خمسة", "probability": 0.98974609375}, {"start": 921.53, "end": 922.07, "word": " بصير", "probability": 0.7120768229166666}, {"start": 922.07, "end": 923.25, "word": " C2", "probability": 0.965576171875}, {"start": 923.25, "end": 924.51, "word": " يساوي", "probability": 0.74688720703125}, {"start": 924.51, "end": 925.49, "word": " خمس", "probability": 0.9444986979166666}, {"start": 925.49, "end": 926.41, "word": " فمين", "probability": 0.7450358072916666}, {"start": 926.41, "end": 927.51, "word": " فتنين", "probability": 0.8519287109375}, {"start": 927.51, "end": 927.95, "word": " Y", "probability": 0.68505859375}, {"start": 927.95, "end": 928.71, "word": " ناقص", "probability": 0.964111328125}, {"start": 928.71, "end": 929.07, "word": " Y", "probability": 0.8212890625}, {"start": 929.07, "end": 929.67, "word": " prime", "probability": 0.29931640625}, {"start": 929.67, "end": 930.13, "word": " في", "probability": 0.84130859375}, {"start": 930.13, "end": 930.61, "word": " E", "probability": 0.8388671875}, {"start": 930.61, "end": 931.09, "word": " أس", "probability": 0.5592041015625}, {"start": 931.09, "end": 931.87, "word": " تلاتة", "probability": 0.882080078125}, {"start": 931.87, "end": 932.07, "word": " T", "probability": 0.794921875}], "temperature": 1.0}, {"id": 42, "seek": 95855, "start": 940.83, "end": 958.55, "text": "لو جيت على المعادلة الأولى مثلا يبقى بصير عندنا substitute in equation one we get", "tokens": [1211, 2407, 10874, 36081, 15844, 9673, 3615, 18513, 37977, 16247, 12610, 7578, 50113, 15040, 7251, 3555, 4587, 7578, 4724, 9381, 13546, 43242, 8315, 15802, 294, 5367, 472, 321, 483], "avg_logprob": -0.2632812440395355, "compression_ratio": 1.1009174311926606, "no_speech_prob": 0.0, "words": [{"start": 940.83, "end": 942.23, "word": "لو", "probability": 0.4155731201171875}, {"start": 942.23, "end": 942.53, "word": " جيت", "probability": 0.785400390625}, {"start": 942.53, "end": 942.73, "word": " على", "probability": 0.7353515625}, {"start": 942.73, "end": 943.43, "word": " المعادلة", "probability": 0.914306640625}, {"start": 943.43, "end": 944.17, "word": " الأولى", "probability": 0.9736328125}, {"start": 944.17, "end": 945.03, "word": " مثلا", "probability": 0.923583984375}, {"start": 945.03, "end": 945.99, "word": " يبقى", "probability": 0.937255859375}, {"start": 945.99, "end": 946.55, "word": " بصير", "probability": 0.95751953125}, {"start": 946.55, "end": 947.47, "word": " عندنا", "probability": 0.804443359375}, {"start": 947.47, "end": 948.71, "word": " substitute", "probability": 0.5830078125}, {"start": 948.71, "end": 955.03, "word": " in", "probability": 0.7890625}, {"start": 955.03, "end": 956.57, "word": " equation", "probability": 0.955078125}, {"start": 956.57, "end": 957.61, "word": " one", "probability": 0.580078125}, {"start": 957.61, "end": 958.05, "word": " we", "probability": 0.86279296875}, {"start": 958.05, "end": 958.55, "word": " get", "probability": 0.64453125}], "temperature": 1.0}, {"id": 43, "seek": 98207, "start": 959.41, "end": 982.07, "text": "نحصل على ما ياتي هاي Y على الشجة الشمال تساوي C1 بيبقى C1E2T C2 زائد اللي هو مين خمس في اتنين Y ناقص Y prime", "tokens": [1863, 5016, 36520, 15844, 19446, 7251, 9307, 1829, 8032, 47302, 398, 15844, 25124, 7435, 3660, 25124, 2304, 6027, 6055, 3794, 995, 45865, 383, 16, 4724, 1829, 3555, 4587, 7578, 383, 16, 36, 17, 51, 383, 17, 30767, 16373, 3215, 13672, 1829, 31439, 3714, 9957, 16490, 2304, 3794, 8978, 1975, 2655, 1863, 9957, 398, 8717, 995, 4587, 9381, 398, 5835], "avg_logprob": -0.2945312390724818, "compression_ratio": 1.2773722627737227, "no_speech_prob": 0.0, "words": [{"start": 959.41, "end": 960.07, "word": "نحصل", "probability": 0.8016764322916666}, {"start": 960.07, "end": 960.35, "word": " على", "probability": 0.9052734375}, {"start": 960.35, "end": 960.63, "word": " ما", "probability": 0.7666015625}, {"start": 960.63, "end": 961.17, "word": " ياتي", "probability": 0.7417805989583334}, {"start": 961.17, "end": 961.67, "word": " هاي", "probability": 0.454864501953125}, {"start": 961.67, "end": 962.01, "word": " Y", "probability": 0.6552734375}, {"start": 962.01, "end": 962.31, "word": " على", "probability": 0.658203125}, {"start": 962.31, "end": 962.85, "word": " الشجة", "probability": 0.90087890625}, {"start": 962.85, "end": 963.47, "word": " الشمال", "probability": 0.9767252604166666}, {"start": 963.47, "end": 964.21, "word": " تساوي", "probability": 0.892333984375}, {"start": 964.21, "end": 966.51, "word": " C1", "probability": 0.7177734375}, {"start": 966.51, "end": 968.55, "word": " بيبقى", "probability": 0.73447265625}, {"start": 968.55, "end": 972.37, "word": " C1E2T", "probability": 0.645654296875}, {"start": 972.37, "end": 974.23, "word": " C2", "probability": 0.8837890625}, {"start": 974.23, "end": 975.47, "word": " زائد", "probability": 0.7692057291666666}, {"start": 975.47, "end": 975.97, "word": " اللي", "probability": 0.620361328125}, {"start": 975.97, "end": 976.19, "word": " هو", "probability": 0.9384765625}, {"start": 976.19, "end": 976.49, "word": " مين", "probability": 0.803955078125}, {"start": 976.49, "end": 977.47, "word": " خمس", "probability": 0.81982421875}, {"start": 977.47, "end": 978.05, "word": " في", "probability": 0.7666015625}, {"start": 978.05, "end": 978.89, "word": " اتنين", "probability": 0.916748046875}, {"start": 978.89, "end": 979.51, "word": " Y", "probability": 0.93603515625}, {"start": 979.51, "end": 980.79, "word": " ناقص", "probability": 0.971435546875}, {"start": 980.79, "end": 981.23, "word": " Y", "probability": 0.84521484375}, {"start": 981.23, "end": 982.07, "word": " prime", "probability": 0.36962890625}], "temperature": 1.0}, {"id": 44, "seek": 100649, "start": 982.65, "end": 1006.49, "text": "فى مين؟ فى E أس ناقص ثلاثة T مع E وزايد ثلاثة T مع السلامة يبقى اتخلصنا منها طيب بدي اجيب هذه اين؟ على الشجة التانية بصير عندي مين؟ C واحد E أس اتنين T زي ما هو هذه بدي اتيجي يا بنات بإشارة سالم يبقى بصير عندي Y", "tokens": [5172, 7578, 3714, 9957, 22807, 6156, 7578, 462, 5551, 3794, 8717, 995, 4587, 9381, 38637, 1211, 5718, 104, 3660, 314, 20449, 462, 4032, 11622, 995, 25708, 38637, 1211, 5718, 104, 3660, 314, 20449, 21136, 37440, 3660, 7251, 3555, 4587, 7578, 1975, 2655, 9778, 1211, 9381, 8315, 9154, 11296, 23032, 1829, 3555, 4724, 16254, 1975, 7435, 1829, 3555, 29538, 1975, 9957, 22807, 15844, 25124, 7435, 3660, 16712, 7649, 10632, 4724, 9381, 13546, 18871, 16254, 3714, 9957, 22807, 383, 36764, 24401, 462, 5551, 3794, 1975, 2655, 1863, 9957, 314, 30767, 1829, 19446, 31439, 29538, 4724, 16254, 1975, 31371, 7435, 1829, 35186, 4724, 8315, 2655, 4724, 28814, 8592, 9640, 3660, 8608, 45340, 7251, 3555, 4587, 7578, 4724, 9381, 13546, 18871, 16254, 398], "avg_logprob": -0.27213540598750113, "compression_ratio": 1.8391959798994975, "no_speech_prob": 0.0, "words": [{"start": 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T", "probability": 0.9130859375}, {"start": 987.75, "end": 988.01, "word": " مع", "probability": 0.904296875}, {"start": 988.01, "end": 988.91, "word": " السلامة", "probability": 0.9290364583333334}, {"start": 988.91, "end": 989.57, "word": " يبقى", "probability": 0.921630859375}, {"start": 989.57, "end": 990.31, "word": " اتخلصنا", "probability": 0.8828125}, {"start": 990.31, "end": 991.11, "word": " منها", "probability": 0.991455078125}, {"start": 991.11, "end": 992.47, "word": " طيب", "probability": 0.75439453125}, {"start": 992.47, "end": 992.75, "word": " بدي", "probability": 0.55035400390625}, {"start": 992.75, "end": 993.11, "word": " اجيب", "probability": 0.8631591796875}, {"start": 993.11, "end": 993.39, "word": " هذه", "probability": 0.55419921875}, {"start": 993.39, "end": 994.21, "word": " اين؟", "probability": 0.66162109375}, {"start": 994.21, "end": 994.43, "word": " على", "probability": 0.65185546875}, {"start": 994.43, "end": 995.03, "word": " الشجة", "probability": 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1000.47, "end": 1000.69, "word": " هو", "probability": 0.97509765625}, {"start": 1000.69, "end": 1001.45, "word": " هذه", "probability": 0.73486328125}, {"start": 1001.45, "end": 1001.69, "word": " بدي", "probability": 0.684814453125}, {"start": 1001.69, "end": 1002.05, "word": " اتيجي", "probability": 0.711669921875}, {"start": 1002.05, "end": 1002.17, "word": " يا", "probability": 0.58447265625}, {"start": 1002.17, "end": 1002.55, "word": " بنات", "probability": 0.9182942708333334}, {"start": 1002.55, "end": 1003.35, "word": " بإشارة", "probability": 0.96865234375}, {"start": 1003.35, "end": 1003.91, "word": " سالم", "probability": 0.685791015625}, {"start": 1003.91, "end": 1004.75, "word": " يبقى", "probability": 0.97021484375}, {"start": 1004.75, "end": 1005.19, "word": " بصير", "probability": 0.9775390625}, {"start": 1005.19, "end": 1005.75, "word": " عندي", "probability": 0.949951171875}, {"start": 1005.75, "end": 1006.49, "word": " Y", "probability": 0.95263671875}], "temperature": 1.0}, {"id": 45, "seek": 102915, "start": 1006.79, "end": 1029.15, "text": "سالب اتنين y ناقص y prime كلها على كدهش؟ على خمسة او لو وحدنا المقامات كلها على خمسة بصير خمسة y ناقص اتنين y زائد y prime y وساوي", "tokens": [3794, 6027, 3555, 1975, 2655, 1863, 9957, 288, 8717, 995, 4587, 9381, 288, 5835, 28242, 11296, 15844, 9122, 3215, 3224, 8592, 22807, 15844, 16490, 2304, 3794, 3660, 1975, 2407, 45164, 4032, 24401, 8315, 9673, 4587, 10943, 9307, 28242, 11296, 15844, 16490, 2304, 3794, 3660, 4724, 9381, 13546, 16490, 2304, 3794, 3660, 288, 8717, 995, 4587, 9381, 1975, 2655, 1863, 9957, 288, 30767, 16373, 3215, 288, 5835, 288, 46952, 995, 45865], "avg_logprob": -0.16494278127038983, "compression_ratio": 1.6363636363636365, "no_speech_prob": 5.960464477539063e-08, "words": [{"start": 1006.79, "end": 1008.07, "word": "سالب", "probability": 0.6383260091145834}, {"start": 1008.07, "end": 1009.55, "word": " اتنين", "probability": 0.906494140625}, {"start": 1009.55, "end": 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1738.03, "word": " المؤثر", "probability": 0.9886067708333334}, {"start": 1738.03, "end": 1739.59, "word": " التفاضلي", "probability": 0.9732666015625}, {"start": 1739.59, "end": 1740.35, "word": " ولماذا", "probability": 0.855224609375}, {"start": 1740.35, "end": 1740.97, "word": " سمي", "probability": 0.7859700520833334}, {"start": 1740.97, "end": 1742.17, "word": " بهذا", "probability": 0.9375}, {"start": 1742.17, "end": 1742.85, "word": " الاسم", "probability": 0.8797200520833334}], "temperature": 1.0}, {"id": 75, "seek": 175861, "start": 1743.51, "end": 1758.61, "text": "يبقى العنوان اللي احنا رافعينه ال fundamental solutions مجموعة الحلول الأساسية of linear homogeneous differential equations للمعادلة التفاضلية الخطية المتجانسة هذا موضوع هذا ال section", "tokens": [1829, 3555, 4587, 7578, 18863, 1863, 2407, 7649, 13672, 1829, 1975, 5016, 8315, 12602, 31845, 3615, 9957, 3224, 2423, 8088, 6547, 3714, 7435, 2304, 2407, 27884, 21542, 1211, 12610, 16247, 3794, 32277, 10632, 295, 8213, 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1746.85, "end": 1747.59, "word": " مجموعة", "probability": 0.91435546875}, {"start": 1747.59, "end": 1748.17, "word": " الحلول", "probability": 0.9851888020833334}, {"start": 1748.17, "end": 1749.39, "word": " الأساسية", "probability": 0.94970703125}, {"start": 1749.39, "end": 1750.05, "word": " of", "probability": 0.84765625}, {"start": 1750.05, "end": 1750.51, "word": " linear", "probability": 0.93701171875}, {"start": 1750.51, "end": 1751.17, "word": " homogeneous", "probability": 0.6708984375}, {"start": 1751.17, "end": 1751.85, "word": " differential", "probability": 0.84326171875}, {"start": 1751.85, "end": 1752.63, "word": " equations", "probability": 0.89501953125}, {"start": 1752.63, "end": 1753.67, "word": " للمعادلة", "probability": 0.9171875}, {"start": 1753.67, "end": 1754.47, "word": " التفاضلية", "probability": 0.90107421875}, {"start": 1754.47, "end": 1755.23, "word": " الخطية", "probability": 0.9134114583333334}, {"start": 1755.23, "end": 1756.91, "word": " المتجانسة", 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"word": " الحلول", "probability": 0.990234375}, {"start": 1762.37, "end": 1762.85, "word": " الأساسية", "probability": 0.9656982421875}, {"start": 1762.85, "end": 1763.57, "word": " كأنه", "probability": 0.8899739583333334}, {"start": 1763.57, "end": 1763.91, "word": " بد", "probability": 0.7529296875}, {"start": 1763.91, "end": 1764.23, "word": " ال", "probability": 0.85498046875}, {"start": 1764.23, "end": 1764.81, "word": " general", "probability": 0.8994140625}, {"start": 1764.81, "end": 1766.13, "word": " solution", "probability": 0.97509765625}, {"start": 1766.13, "end": 1767.21, "word": " تمام", "probability": 0.860107421875}, {"start": 1767.21, "end": 1767.77, "word": " ال", "probability": 0.61328125}, {"start": 1767.77, "end": 1768.09, "word": " general", "probability": 0.87060546875}, {"start": 1768.09, "end": 1768.63, "word": " الحل", "probability": 0.781494140625}, {"start": 1768.63, "end": 1769.05, "word": " العام", "probability": 0.977294921875}, {"start": 1769.05, "end": 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"probability": 0.959228515625}, {"start": 2357.96, "end": 2358.16, "word": " في", "probability": 0.58056640625}, {"start": 2358.16, "end": 2358.66, "word": " عندك", "probability": 0.97802734375}, {"start": 2358.66, "end": 2359.5, "word": " حل،", "probability": 0.9435221354166666}, {"start": 2359.5, "end": 2359.58, "word": " و", "probability": 0.958984375}, {"start": 2359.58, "end": 2359.96, "word": " الحل", "probability": 0.98193359375}, {"start": 2359.96, "end": 2360.18, "word": " هذا", "probability": 0.7578125}, {"start": 2360.18, "end": 2360.66, "word": " وحيد", "probability": 0.95556640625}, {"start": 2360.66, "end": 2361.22, "word": " مافيش", "probability": 0.7417805989583334}, {"start": 2361.22, "end": 2361.68, "word": " غيره", "probability": 0.9962565104166666}], "temperature": 1.0}, {"id": 98, "seek": 238611, "start": 2361.91, "end": 2386.11, "text": "والحل بيكون معرف على نفس الفترة اللي دوالها دي بيكون عليها دوال متاصلة يبقى باللخص ما قالته الأخ دعاء والأخت الثانية في التالي 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"probability": 0.93212890625}, {"start": 2412.75, "end": 2416.17, "word": " only", "probability": 0.595703125}, {"start": 2416.17, "end": 2418.69, "word": " one", "probability": 0.9541015625}, {"start": 2418.69, "end": 2419.97, "word": " solution", "probability": 0.95556640625}], "temperature": 1.0}, {"id": 100, "seek": 244316, "start": 2421.22, "end": 2443.16, "text": "مافيش إلا حل واحد فقط لغيره تلاتة the solution phi of T is defined معرف on the interval", "tokens": [15042, 41185, 8592, 11933, 15040, 11331, 1211, 36764, 24401, 6156, 47432, 5296, 17082, 13546, 3224, 6055, 1211, 9307, 3660, 264, 3827, 13107, 295, 314, 307, 7642, 20449, 28480, 322, 264, 15035], "avg_logprob": -0.354980462230742, "compression_ratio": 1.063063063063063, "no_speech_prob": 0.0, "words": [{"start": 2421.22, "end": 2422.14, "word": "مافيش", "probability": 0.6230875651041666}, {"start": 2422.14, "end": 2422.4, "word": " إلا", "probability": 0.708984375}, {"start": 2422.4, "end": 2422.96, "word": " حل", 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"probability": 0.9638671875}], "temperature": 1.0}, {"id": 103, "seek": 251953, "start": 2514.77, "end": 2519.53, "text": "نعطي بعض الأمثلة على هذه المفاهيم", "tokens": [1863, 3615, 9566, 1829, 45030, 11242, 16247, 2304, 12984, 37977, 15844, 29538, 9673, 5172, 40294, 32640], "avg_logprob": -0.19255514705882354, "compression_ratio": 0.953125, "no_speech_prob": 0.0, "words": [{"start": 2514.77, "end": 2516.09, "word": "نعطي", "probability": 0.688385009765625}, {"start": 2516.09, "end": 2516.37, "word": " بعض", "probability": 0.832763671875}, {"start": 2516.37, "end": 2517.07, "word": " الأمثلة", "probability": 0.9849853515625}, {"start": 2517.07, "end": 2517.69, "word": " على", "probability": 0.8984375}, {"start": 2517.69, "end": 2518.25, "word": " هذه", "probability": 0.970703125}, {"start": 2518.25, "end": 2519.53, "word": " المفاهيم", "probability": 0.9874267578125}], "temperature": 1.0}, {"id": 104, "seek": 255934, "start": 2540.5, "end": 2559.34, "text": "المثال الأول example بيقول ي determine the longest interval", "tokens": [45340, 12984, 6027, 16247, 12610, 1365, 4724, 1829, 39648, 7251, 6997, 264, 15438, 15035], "avg_logprob": -0.294531246026357, "compression_ratio": 1.0, "no_speech_prob": 0.0, "words": [{"start": 2540.5, "end": 2541.12, "word": "المثال", "probability": 0.8919270833333334}, {"start": 2541.12, "end": 2541.56, "word": " الأول", "probability": 0.830810546875}, {"start": 2541.56, "end": 2543.1, "word": " example", "probability": 0.336181640625}, {"start": 2543.1, "end": 2551.92, "word": " بيقول", "probability": 0.8352864583333334}, {"start": 2551.92, "end": 2552.08, "word": " ي", "probability": 0.52880859375}, {"start": 2552.08, "end": 2552.88, "word": " determine", "probability": 0.90771484375}, {"start": 2552.88, "end": 2557.9, "word": " the", "probability": 0.865234375}, {"start": 2557.9, "end": 2558.34, "word": " longest", "probability": 0.97119140625}, {"start": 2558.34, "end": 2559.34, "word": " interval", "probability": 0.962890625}], "temperature": 1.0}, {"id": 105, "seek": 259288, "start": 2572.9, "end": 2592.88, "text": "The initial value problem have a unique twice differentiable solution", "tokens": [2278, 5883, 2158, 1154, 362, 257, 3845, 6091, 819, 9364, 3827], "avg_logprob": -0.4208984424670537, "compression_ratio": 1.0298507462686568, "no_speech_prob": 0.0, "words": [{"start": 2572.9, "end": 2573.4, "word": "The", "probability": 0.05157470703125}, {"start": 2573.4, "end": 2575.26, "word": " initial", "probability": 0.9111328125}, {"start": 2575.26, "end": 2575.8, "word": " value", "probability": 0.9580078125}, {"start": 2575.8, "end": 2576.54, "word": " problem", "probability": 0.8212890625}, {"start": 2576.54, "end": 2584.02, "word": " have", "probability": 0.447021484375}, {"start": 2584.02, "end": 2587.36, "word": " a", "probability": 0.8623046875}, {"start": 2587.36, "end": 2588.04, "word": " unique", "probability": 0.82421875}, {"start": 2588.04, "end": 2591.22, "word": " twice", "probability": 0.8466796875}, {"start": 2591.22, "end": 2591.92, "word": " differentiable", "probability": 0.921142578125}, {"start": 2591.92, "end": 2592.88, "word": " solution", "probability": 0.951171875}], "temperature": 1.0}, {"id": 106, "seek": 262628, "start": 2619.0, "end": 2626.28, "text": "don't attempt to find the solution", "tokens": [13966, 380, 5217, 281, 915, 264, 3827], "avg_logprob": -0.4311523549258709, "compression_ratio": 0.8095238095238095, "no_speech_prob": 0.0, "words": [{"start": 2619.0, "end": 2620.4, "word": "don't", "probability": 0.5726318359375}, {"start": 2620.4, "end": 2621.8, "word": " attempt", "probability": 0.5205078125}, {"start": 2621.8, "end": 2625.14, "word": " to", "probability": 0.7822265625}, {"start": 2625.14, "end": 2625.52, "word": " find", "probability": 0.9326171875}, {"start": 2625.52, "end": 2625.76, "word": " the", "probability": 0.64453125}, {"start": 2625.76, "end": 2626.28, "word": " solution", "probability": 0.97265625}], "temperature": 1.0}, {"id": 107, "seek": 265869, "start": 2640.37, "end": 2658.69, "text": "عشرة من الكتاب طبعا yw prime زائد cosine t في ال y prime زائد y في ال absolute value ل t", "tokens": [3615, 8592, 25720, 9154, 33251, 2655, 16758, 23032, 3555, 3615, 995, 288, 86, 5835, 30767, 16373, 3215, 23565, 256, 8978, 2423, 288, 5835, 30767, 16373, 3215, 288, 8978, 2423, 8236, 2158, 5296, 256], "avg_logprob": -0.45588235206463756, "compression_ratio": 1.2222222222222223, "no_speech_prob": 0.0, "words": [{"start": 2640.37, "end": 2641.77, "word": "عشرة", "probability": 0.6171875}, {"start": 2641.77, "end": 2641.99, "word": " من", "probability": 0.83447265625}, {"start": 2641.99, "end": 2642.77, "word": " الكتاب", "probability": 0.9420572916666666}, {"start": 2642.77, "end": 2643.35, "word": " طبعا", "probability": 0.7552947998046875}, {"start": 2643.35, "end": 2645.01, "word": " yw", "probability": 0.5152587890625}, {"start": 2645.01, "end": 2645.71, "word": " prime", "probability": 0.533203125}, {"start": 2645.71, "end": 2647.07, "word": " زائد", "probability": 0.65673828125}, {"start": 2647.07, "end": 2647.65, "word": " cosine", "probability": 0.537109375}, {"start": 2647.65, "end": 2648.47, "word": " t", "probability": 0.435791015625}, {"start": 2648.47, "end": 2648.71, "word": " في", "probability": 0.861328125}, {"start": 2648.71, "end": 2648.89, "word": " ال", "probability": 0.5458984375}, {"start": 2648.89, "end": 2649.21, "word": " y", "probability": 0.736328125}, {"start": 2649.21, "end": 2650.05, "word": " prime", "probability": 0.771484375}, {"start": 2650.05, "end": 2652.37, "word": " زائد", "probability": 0.9459635416666666}, {"start": 2652.37, "end": 2653.97, "word": " y", "probability": 0.8798828125}, {"start": 2653.97, "end": 2655.01, "word": " في", "probability": 0.8759765625}, {"start": 2655.01, "end": 2655.15, "word": " ال", "probability": 0.415283203125}, {"start": 2655.15, "end": 2656.07, "word": " absolute", "probability": 0.59228515625}, {"start": 2656.07, "end": 2657.87, "word": " value", "probability": 0.9765625}, {"start": 2657.87, "end": 2658.35, "word": " ل", "probability": 0.84765625}, {"start": 2658.35, "end": 2658.69, "word": " t", "probability": 0.42626953125}], "temperature": 1.0}, {"id": 108, "seek": 268076, "start": 2659.68, "end": 2680.76, "text": "زائد تلاتة لن absolute value ل T في ال Y بده يساوي Zero و ال Y عند اتنين بده يساوي تلاتة و ال Y prime عند اتنين بده يساوي مان بده يساوي واحد", "tokens": [11622, 16373, 3215, 6055, 1211, 9307, 3660, 5296, 1863, 8236, 2158, 5296, 314, 8978, 2423, 398, 47525, 3224, 7251, 3794, 995, 45865, 17182, 4032, 2423, 398, 43242, 1975, 2655, 1863, 9957, 47525, 3224, 7251, 3794, 995, 45865, 6055, 1211, 9307, 3660, 4032, 2423, 398, 5835, 43242, 1975, 2655, 1863, 9957, 47525, 3224, 7251, 3794, 995, 45865, 3714, 7649, 47525, 3224, 7251, 3794, 995, 45865, 36764, 24401], "avg_logprob": -0.24813432657896584, "compression_ratio": 1.7619047619047619, "no_speech_prob": 4.76837158203125e-07, "words": [{"start": 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Zero", "probability": 0.420654296875}, {"start": 2668.44, "end": 2669.42, "word": " و", "probability": 0.505859375}, {"start": 2669.42, "end": 2669.68, "word": " ال", "probability": 0.52685546875}, {"start": 2669.68, "end": 2670.08, "word": " Y", "probability": 0.97705078125}, {"start": 2670.08, "end": 2671.22, "word": " عند", "probability": 0.849609375}, {"start": 2671.22, "end": 2672.02, "word": " اتنين", "probability": 0.8038330078125}, {"start": 2672.02, "end": 2672.52, "word": " بده", "probability": 0.9716796875}, {"start": 2672.52, "end": 2673.14, "word": " يساوي", "probability": 0.9884033203125}, {"start": 2673.14, "end": 2674.26, "word": " تلاتة", "probability": 0.97314453125}, {"start": 2674.26, "end": 2675.02, "word": " و", "probability": 0.869140625}, {"start": 2675.02, "end": 2675.18, "word": " ال", "probability": 0.90625}, {"start": 2675.18, "end": 2675.48, "word": " Y", "probability": 0.9775390625}, {"start": 2675.48, "end": 2676.3, "word": " prime", "probability": 0.447265625}, {"start": 2676.3, "end": 2677.08, "word": " عند", "probability": 0.947265625}, {"start": 2677.08, "end": 2677.96, "word": " اتنين", "probability": 0.9886474609375}, {"start": 2677.96, "end": 2678.56, "word": " بده", "probability": 0.98974609375}, {"start": 2678.56, "end": 2678.96, "word": " يساوي", "probability": 0.9871826171875}, {"start": 2678.96, "end": 2679.36, "word": " مان", "probability": 0.5040283203125}, {"start": 2679.36, "end": 2680.04, "word": " بده", "probability": 0.936767578125}, {"start": 2680.04, "end": 2680.4, "word": " يساوي", "probability": 0.9893798828125}, {"start": 2680.4, "end": 2680.76, "word": " واحد", "probability": 0.968505859375}], "temperature": 1.0}, {"id": 109, "seek": 271347, "start": 2698.31, "end": 2713.47, "text": "يبقى النظرية السابقة لقبل قليل لما أعطاني معادلة فاضولة من رتبة نوحط عليها two initial conditions والمعاملات كانت دوال متصلة على فترة والتكن هذه الفترة I", "tokens": [1829, 3555, 4587, 7578, 28239, 19913, 2288, 10632, 21136, 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"probability": 0.70166015625}, {"start": 2701.89, "end": 2702.25, "word": " أعطاني", "probability": 0.711328125}, {"start": 2702.25, "end": 2702.69, "word": " معادلة", "probability": 0.9801432291666666}, {"start": 2702.69, "end": 2703.35, "word": " فاضولة", "probability": 0.8043212890625}, {"start": 2703.35, "end": 2703.47, "word": " من", "probability": 0.98828125}, {"start": 2703.47, "end": 2703.91, "word": " رتبة", "probability": 0.9117838541666666}, {"start": 2703.91, "end": 2704.53, "word": " نوحط", "probability": 0.6131591796875}, {"start": 2704.53, "end": 2704.89, "word": " عليها", "probability": 0.975830078125}, {"start": 2704.89, "end": 2705.07, "word": " two", "probability": 0.78076171875}, {"start": 2705.07, "end": 2705.61, "word": " initial", "probability": 0.87841796875}, {"start": 2705.61, "end": 2706.29, "word": " conditions", "probability": 0.95556640625}, {"start": 2706.29, "end": 2707.35, "word": " والمعاملات", "probability": 0.9109700520833334}, {"start": 2707.35, "end": 2708.57, "word": " كانت", "probability": 0.9443359375}, {"start": 2708.57, "end": 2709.37, "word": " دوال", "probability": 0.8505859375}, {"start": 2709.37, "end": 2710.15, "word": " متصلة", "probability": 0.87841796875}, {"start": 2710.15, "end": 2710.43, "word": " على", "probability": 0.92529296875}, {"start": 2710.43, "end": 2711.07, "word": " فترة", "probability": 0.9908854166666666}, {"start": 2711.07, "end": 2711.69, "word": " والتكن", "probability": 0.5931396484375}, {"start": 2711.69, "end": 2712.01, "word": " هذه", "probability": 0.8701171875}, {"start": 2712.01, "end": 2712.91, "word": " الفترة", "probability": 0.9847005208333334}, {"start": 2712.91, "end": 2713.47, "word": " I", "probability": 0.8427734375}], "temperature": 1.0}, {"id": 110, "seek": 273245, "start": 2713.95, "end": 2732.45, "text": "قال there exists exactly يوجد حل وحيب لهذه المعادلة و الحل هذا موجود على نفس الفترة الامين اللي عنده I السؤال اللي عندنا هنا شبه قول قول هاتلي أكبر فترة", "tokens": [4587, 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"probability": 0.97900390625}, {"start": 2717.19, "end": 2718.03, "word": " وحيب", "probability": 0.792236328125}, {"start": 2718.03, "end": 2719.05, "word": " لهذه", "probability": 0.952392578125}, {"start": 2719.05, "end": 2719.93, "word": " المعادلة", "probability": 0.9813232421875}, {"start": 2719.93, "end": 2720.49, "word": " و", "probability": 0.381103515625}, {"start": 2720.49, "end": 2721.01, "word": " الحل", "probability": 0.916259765625}, {"start": 2721.01, "end": 2721.51, "word": " هذا", "probability": 0.92724609375}, {"start": 2721.51, "end": 2722.59, "word": " موجود", "probability": 0.9908854166666666}, {"start": 2722.59, "end": 2722.97, "word": " على", "probability": 0.943359375}, {"start": 2722.97, "end": 2723.51, "word": " نفس", "probability": 0.997314453125}, {"start": 2723.51, "end": 2724.71, "word": " الفترة", "probability": 0.9905598958333334}, {"start": 2724.71, "end": 2725.85, "word": " الامين", "probability": 0.4333089192708333}, {"start": 2725.85, "end": 2726.21, "word": " اللي", "probability": 0.515380859375}, {"start": 2726.21, "end": 2726.83, "word": " عنده", "probability": 0.2611083984375}, {"start": 2726.83, "end": 2727.05, "word": " I", "probability": 0.81201171875}, {"start": 2727.05, "end": 2728.23, "word": " السؤال", "probability": 0.9811197916666666}, {"start": 2728.23, "end": 2728.41, "word": " اللي", "probability": 0.953369140625}, {"start": 2728.41, "end": 2728.69, "word": " عندنا", "probability": 0.690673828125}, {"start": 2728.69, "end": 2728.87, "word": " هنا", "probability": 0.931640625}, {"start": 2728.87, "end": 2729.21, "word": " شبه", "probability": 0.5987955729166666}, {"start": 2729.21, "end": 2729.91, "word": " قول", "probability": 0.58056640625}, {"start": 2729.91, "end": 2730.31, "word": " قول", "probability": 0.58935546875}, {"start": 2730.31, "end": 2730.79, "word": " هاتلي", "probability": 0.623779296875}, {"start": 2730.79, "end": 2731.71, "word": " أكبر", "probability": 0.9075520833333334}, {"start": 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{"start": 3899.58, "end": 3899.92, "word": " هنا", "probability": 0.97607421875}, {"start": 3899.92, "end": 3900.22, "word": " لو", "probability": 0.9423828125}, {"start": 3900.22, "end": 3900.8, "word": " كان", "probability": 0.98291015625}, {"start": 3900.8, "end": 3901.42, "word": " أحد", "probability": 0.785888671875}, {"start": 3901.42, "end": 3902.54, "word": " السوابط", "probability": 0.9068603515625}, {"start": 3902.54, "end": 3903.04, "word": " أو", "probability": 0.87939453125}, {"start": 3903.04, "end": 3904.14, "word": " كلاهما", "probability": 0.7850341796875}, {"start": 3904.14, "end": 3904.72, "word": " كمان", "probability": 0.9903971354166666}, {"start": 3904.72, "end": 3905.2, "word": " Zero", "probability": 0.9501953125}], "temperature": 1.0}, {"id": 159, "seek": 393476, "start": 3905.5, "end": 3934.76, "text": "يبقى اللي بظل بيكون هو مين حل المعادلة فلو كان c1 ب zero بظل ان c2 y2 هو حل المعادلة التفاضلية وكذلك لو كان c2 هو zero بظل ان c1 y1 هو عبارة عن حل مين للمعادلة التفاضلية اذا يا بنات انا لو جدرت اجيب حلين للمعادلة التفاضلية بقدر اجيب حل ثالث للمعادلة التفاضلية باستخدام مين", "tokens": [1829, 3555, 4587, 7578, 13672, 1829, 4724, 19913, 1211, 4724, 1829, 30544, 31439, 3714, 9957, 11331, 1211, 9673, 3615, 18513, 37977, 6156, 1211, 2407, 25961, 269, 16, 4724, 4018, 4724, 19913, 1211, 16472, 269, 17, 288, 17, 31439, 11331, 1211, 9673, 3615, 18513, 37977, 16712, 5172, 46958, 1211, 10632, 4032, 4117, 8848, 23275, 45164, 25961, 269, 17, 31439, 4018, 4724, 19913, 1211, 16472, 269, 16, 288, 16, 31439, 6225, 3555, 9640, 3660, 18871, 11331, 1211, 3714, 9957, 5296, 19528, 3615, 18513, 37977, 16712, 5172, 46958, 1211, 10632, 1975, 15730, 35186, 4724, 8315, 2655, 1975, 8315, 45164, 10874, 3215, 43500, 1975, 7435, 1829, 3555, 11331, 1211, 9957, 5296, 19528, 3615, 18513, 37977, 16712, 5172, 46958, 1211, 10632, 4724, 28543, 2288, 1975, 7435, 1829, 3555, 11331, 1211, 38637, 6027, 12984, 5296, 19528, 3615, 18513, 37977, 16712, 5172, 46958, 1211, 10632, 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3921.16, "end": 3921.48, "word": " حل", "probability": 0.988525390625}, {"start": 3921.48, "end": 3921.88, "word": " مين", "probability": 0.962890625}, {"start": 3921.88, "end": 3922.88, "word": " للمعادلة", "probability": 0.94794921875}, {"start": 3922.88, "end": 3923.54, "word": " التفاضلية", "probability": 0.97509765625}, {"start": 3923.54, "end": 3923.84, "word": " اذا", "probability": 0.63671875}, {"start": 3923.84, "end": 3924.04, "word": " يا", "probability": 0.98095703125}, {"start": 3924.04, "end": 3924.48, "word": " بنات", "probability": 0.8984375}, {"start": 3924.48, "end": 3924.94, "word": " انا", "probability": 0.92724609375}, {"start": 3924.94, "end": 3925.74, "word": " لو", "probability": 0.97802734375}, {"start": 3925.74, "end": 3926.26, "word": " جدرت", "probability": 0.9376627604166666}, {"start": 3926.26, "end": 3926.76, "word": " اجيب", "probability": 0.953125}, {"start": 3926.76, "end": 3927.26, "word": " حلين", "probability": 0.8292643229166666}, {"start": 3927.26, "end": 3927.88, "word": " للمعادلة", "probability": 0.9396484375}, {"start": 3927.88, "end": 3928.66, "word": " التفاضلية", "probability": 0.975}, {"start": 3928.66, "end": 3929.22, "word": " بقدر", "probability": 0.9850260416666666}, {"start": 3929.22, "end": 3929.96, "word": " اجيب", "probability": 0.968017578125}, {"start": 3929.96, "end": 3930.68, "word": " حل", "probability": 0.977294921875}, {"start": 3930.68, "end": 3932.02, "word": " ثالث", "probability": 0.9812825520833334}, {"start": 3932.02, "end": 3932.92, "word": " للمعادلة", "probability": 0.97041015625}, {"start": 3932.92, "end": 3933.6, "word": " التفاضلية", "probability": 0.978125}, {"start": 3933.6, "end": 3934.4, "word": " باستخدام", "probability": 0.9811197916666666}, {"start": 3934.4, "end": 3934.76, "word": " مين", "probability": 0.958251953125}], "temperature": 1.0}, {"id": 160, "seek": 395726, "start": 3935.08, "end": 3957.26, "text": "الحلين ما هو الحل الثالث constant في الحل الأول و constant في الحل الثاني و بجمع الاتنين بيعطيني حل جديد للمعادلة التفاضلية طبعا واحدة هتسأل و تقول تقدر تبرهن هذا الكلام؟ اقولها بنقدر و البرهن very easy مش صعب يعني يبقى هذا ال proof", "tokens": [6027, 5016, 1211, 9957, 19446, 31439, 21542, 1211, 6024, 104, 6027, 12984, 5754, 8978, 21542, 1211, 16247, 12610, 4032, 5754, 8978, 21542, 1211, 6024, 104, 7649, 1829, 4032, 4724, 7435, 2304, 3615, 2423, 9307, 1863, 9957, 4724, 40228, 9566, 1829, 22653, 11331, 1211, 10874, 16254, 3215, 5296, 19528, 3615, 18513, 37977, 16712, 5172, 46958, 1211, 10632, 23032, 3555, 3615, 995, 36764, 24401, 3660, 8032, 2655, 3794, 10721, 1211, 4032, 6055, 39648, 6055, 28543, 2288, 6055, 26890, 3224, 1863, 23758, 2423, 28820, 10943, 22807, 1975, 39648, 11296, 44945, 28543, 2288, 4032, 2423, 26890, 3224, 1863, 588, 1858, 37893, 20328, 3615, 3555, 37495, 22653, 7251, 3555, 4587, 7578, 23758, 2423, 8177], "avg_logprob": -0.18196022740819237, "compression_ratio": 1.8148148148148149, "no_speech_prob": 1.1920928955078125e-07, "words": 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"probability": 0.81396484375}, {"start": 3953.58, "end": 3954.16, "word": " easy", "probability": 0.96875}, {"start": 3954.16, "end": 3954.44, "word": " مش", "probability": 0.94775390625}, {"start": 3954.44, "end": 3955.2, "word": " صعب", "probability": 0.805908203125}, {"start": 3955.2, "end": 3955.48, "word": " يعني", "probability": 0.78662109375}, {"start": 3955.48, "end": 3956.3, "word": " يبقى", "probability": 0.90966796875}, {"start": 3956.3, "end": 3956.68, "word": " هذا", "probability": 0.96826171875}, {"start": 3956.68, "end": 3956.84, "word": " ال", "probability": 0.93310546875}, {"start": 3956.84, "end": 3957.26, "word": " proof", "probability": 0.90283203125}], "temperature": 1.0}, {"id": 161, "seek": 397518, "start": 3961.42, "end": 3975.18, "text": "بقول ليش؟ لو كان Y1 هو حل المعادلة هذه، يبقى هيحققها، صحيح ولا لأ؟ يبقى بادي بقول، الآن Y1 is a solution", "tokens": [3555, 39648, 32239, 8592, 22807, 45164, 25961, 398, 16, 31439, 11331, 1211, 9673, 3615, 18513, 37977, 29538, 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3965.08, "end": 3965.56, "word": " هذه،", "probability": 0.617919921875}, {"start": 3965.56, "end": 3965.96, "word": " يبقى", "probability": 0.9395751953125}, {"start": 3965.96, "end": 3967.38, "word": " هيحققها،", "probability": 0.8794759114583334}, {"start": 3967.38, "end": 3967.76, "word": " صحيح", "probability": 0.986083984375}, {"start": 3967.76, "end": 3967.9, "word": " ولا", "probability": 0.91064453125}, {"start": 3967.9, "end": 3968.72, "word": " لأ؟", "probability": 0.78173828125}, {"start": 3968.72, "end": 3969.16, "word": " يبقى", "probability": 0.9737548828125}, {"start": 3969.16, "end": 3969.48, "word": " بادي", "probability": 0.5049641927083334}, {"start": 3969.48, "end": 3970.14, "word": " بقول،", "probability": 0.79638671875}, {"start": 3970.14, "end": 3970.9, "word": " الآن", "probability": 0.6929931640625}, {"start": 3970.9, "end": 3972.52, "word": " Y1", "probability": 0.957275390625}, {"start": 3972.52, "end": 3973.42, "word": " is", "probability": 0.892578125}, 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3995.86, "end": 3997.08, "word": " يزيد", "probability": 0.559326171875}], "temperature": 1.0}, {"id": 163, "seek": 402526, "start": 3999.68, "end": 4025.26, "text": "طيب الان Y2 is a solution بده يعطينا ان ال L of Y2 بده يساوي Y2 double prime زاد P of T في ال Y2 prime زاد ال Q of T في ال Y2 بده يساوي Zero كذلك", "tokens": [9566, 1829, 3555, 2423, 7649, 398, 17, 307, 257, 3827, 47525, 3224, 37495, 9566, 1829, 8315, 16472, 2423, 441, 295, 398, 17, 47525, 3224, 7251, 3794, 995, 45865, 398, 17, 3834, 5835, 30767, 18513, 430, 295, 314, 8978, 2423, 398, 17, 5835, 30767, 18513, 2423, 1249, 295, 314, 8978, 2423, 398, 17, 47525, 3224, 7251, 3794, 995, 45865, 17182, 9122, 8848, 23275], "avg_logprob": -0.24293155424178592, "compression_ratio": 1.467153284671533, "no_speech_prob": 0.0, "words": [{"start": 3999.68, "end": 4000.26, "word": "طيب", "probability": 0.66278076171875}, {"start": 4000.26, "end": 4001.08, "word": " الان", "probability": 0.716796875}, {"start": 4001.08, "end": 4002.74, 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"هذه المعقيدات حتى الآن جالي Y1 وY2 هم حللوا المعادلة التفاضلية شو بدي اثبت؟ بدي اثبت ان هذا ماله حل اخر للمعادلة التفاضلية بقوله اذا لو جدت اثبت ان ال L وC1 Y1 زي C2 Y2 يساوي Zero بتم المطلوب", "tokens": [3224, 24192, 9673, 3615, 4587, 25708, 9307, 11331, 49975, 6024, 48506, 10874, 6027, 1829, 398, 16, 4032, 56, 17, 8032, 2304, 11331, 1211, 1211, 14407, 9673, 3615, 18513, 37977, 16712, 5172, 46958, 1211, 10632, 13412, 2407, 4724, 16254, 1975, 12984, 3555, 2655, 22807, 4724, 16254, 1975, 12984, 3555, 2655, 16472, 23758, 3714, 6027, 3224, 11331, 1211, 1975, 34740, 5296, 19528, 3615, 18513, 37977, 16712, 5172, 46958, 1211, 10632, 4724, 39648, 3224, 1975, 15730, 45164, 10874, 3215, 2655, 1975, 12984, 3555, 2655, 16472, 2423, 441, 4032, 34, 16, 398, 16, 30767, 1829, 383, 17, 398, 17, 7251, 3794, 995, 45865, 17182, 4724, 39237, 9673, 9566, 1211, 37746], "avg_logprob": -0.2374415865568357, "compression_ratio": 1.7621621621621621, "no_speech_prob": 2.384185791015625e-07, "words": [{"start": 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0.751708984375}, {"start": 4035.12, "end": 4035.38, "word": " بدي", "probability": 0.765869140625}, {"start": 4035.38, "end": 4036.58, "word": " اثبت؟", "probability": 0.766748046875}, {"start": 4036.58, "end": 4036.96, "word": " بدي", "probability": 0.89453125}, {"start": 4036.96, "end": 4037.5, "word": " اثبت", "probability": 0.955322265625}, {"start": 4037.5, "end": 4037.84, "word": " ان", "probability": 0.86328125}, {"start": 4037.84, "end": 4038.32, "word": " هذا", "probability": 0.78515625}, {"start": 4038.32, "end": 4039.0, "word": " ماله", "probability": 0.77587890625}, {"start": 4039.0, "end": 4040.04, "word": " حل", "probability": 0.984130859375}, {"start": 4040.04, "end": 4040.74, "word": " اخر", "probability": 0.782470703125}, {"start": 4040.74, "end": 4041.46, "word": " للمعادلة", "probability": 0.96748046875}, {"start": 4041.46, "end": 4042.4, "word": " التفاضلية", "probability": 0.96171875}, {"start": 4042.4, "end": 4043.58, "word": " بقوله", "probability": 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{"start": 4052.3, "end": 4053.08, "word": " يساوي", "probability": 0.7725830078125}, {"start": 4053.08, "end": 4053.36, "word": " Zero", "probability": 0.384033203125}, {"start": 4053.36, "end": 4053.76, "word": " بتم", "probability": 0.48248291015625}, {"start": 4053.76, "end": 4054.38, "word": " المطلوب", "probability": 0.9439697265625}], "temperature": 1.0}, {"id": 165, "seek": 407238, "start": 4056.16, "end": 4072.38, "text": "لو قلت اثبت ان c1y1 زاد c2y2 بده يستوي 0 بصير هذا هو عبارة عن حل ميم للمعادلة التفاضلية بقولها نرجع لل L of y مين اجا مكانها", "tokens": [1211, 2407, 12174, 1211, 2655, 1975, 12984, 3555, 2655, 16472, 269, 16, 88, 16, 30767, 18513, 269, 17, 88, 17, 47525, 3224, 7251, 14851, 45865, 1958, 4724, 9381, 13546, 23758, 31439, 6225, 3555, 9640, 3660, 18871, 11331, 1211, 3714, 32640, 5296, 19528, 3615, 18513, 37977, 16712, 5172, 46958, 1211, 10632, 4724, 39648, 11296, 8717, 47341, 3615, 24976, 441, 295, 288, 3714, 9957, 1975, 7435, 995, 3714, 41361, 11296], 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بصير", "probability": 0.8946940104166666}, {"start": 4062.78, "end": 4063.08, "word": " هذا", "probability": 0.833984375}, {"start": 4063.08, "end": 4063.38, "word": " هو", "probability": 0.97216796875}, {"start": 4063.38, "end": 4063.74, "word": " عبارة", "probability": 0.7728271484375}, {"start": 4063.74, "end": 4063.92, "word": " عن", "probability": 0.97802734375}, {"start": 4063.92, "end": 4064.26, "word": " حل", "probability": 0.939453125}, {"start": 4064.26, "end": 4064.72, "word": " ميم", "probability": 0.803466796875}, {"start": 4064.72, "end": 4065.86, "word": " للمعادلة", "probability": 0.825390625}, {"start": 4065.86, "end": 4066.92, "word": " التفاضلية", "probability": 0.88486328125}, {"start": 4066.92, "end": 4068.18, "word": " بقولها", "probability": 0.7757161458333334}, {"start": 4068.18, "end": 4069.34, "word": " نرجع", "probability": 0.9778645833333334}, {"start": 4069.34, "end": 4069.66, "word": " لل", "probability": 0.783203125}, {"start": 4069.66, "end": 4070.12, 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"end": 4110.65, "text": "زائد لـ Q of T في C1Y1 زائد C2Y2", "tokens": [11622, 16373, 3215, 5296, 39184, 1249, 295, 314, 8978, 383, 16, 56, 16, 30767, 16373, 3215, 383, 17, 56, 17], "avg_logprob": -0.23158482142857142, "compression_ratio": 0.9361702127659575, "no_speech_prob": 0.0, "words": [{"start": 4101.21, "end": 4102.45, "word": "زائد", "probability": 0.67333984375}, {"start": 4102.45, "end": 4103.37, "word": " لـ", "probability": 0.4879150390625}, {"start": 4103.37, "end": 4103.77, "word": " Q", "probability": 0.4580078125}, {"start": 4103.77, "end": 4104.41, "word": " of", "probability": 0.75390625}, {"start": 4104.41, "end": 4104.97, "word": " T", "probability": 0.94091796875}, {"start": 4104.97, "end": 4105.45, "word": " في", "probability": 0.91552734375}, {"start": 4105.45, "end": 4107.85, "word": " C1Y1", "probability": 0.8154296875}, {"start": 4107.85, "end": 4108.53, "word": " زائد", "probability": 0.7841796875}, {"start": 4108.53, "end": 4110.65, "word": " C2Y2", 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t في c1 y1 زائد ل q of t في c2 y2", "tokens": [41185, 269, 17, 8978, 2423, 288, 17, 5835, 7251, 3555, 4587, 7578, 16490, 1211, 33546, 8315, 9154, 2423, 1433, 23758, 4724, 1211, 23758, 44945, 36178, 41950, 16572, 28671, 7251, 3555, 4587, 7578, 30767, 16373, 3215, 13672, 1829, 31439, 9505, 295, 256, 8978, 269, 16, 288, 16, 30767, 16373, 3215, 5296, 9505, 295, 256, 8978, 269, 17, 288, 17], "avg_logprob": -0.1731991474911318, "compression_ratio": 1.4198473282442747, "no_speech_prob": 0.0, "words": [{"start": 4190.25, "end": 4190.49, "word": "في", "probability": 0.187255859375}, {"start": 4190.49, "end": 4191.99, "word": " c2", "probability": 0.64501953125}, {"start": 4191.99, "end": 4192.67, "word": " في", "probability": 0.87890625}, {"start": 4192.67, "end": 4192.91, "word": " ال", "probability": 0.5185546875}, {"start": 4192.91, "end": 4194.11, "word": " y2", "probability": 0.81103515625}, {"start": 4194.11, "end": 4194.81, "word": " prime", "probability": 0.62060546875}, {"start": 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ضرب عناصر القطر الثانوي يبقى لو جيت حاصل ضرب عناصر القطر الرئيسي يبقى Y1Y2' ناقص حاصل ضرب عناصر القطر الثانوي يبقى Y1'Y2 بهذا الشكل", "tokens": [2407, 4117, 8315, 30767, 2304, 7649, 44945, 5172, 4117, 9673, 24401, 3215, 9307, 8717, 39648, 11331, 33546, 1211, 48812, 25513, 18871, 33546, 2288, 25062, 9566, 2288, 34892, 19986, 1829, 3794, 1829, 8717, 995, 4587, 9381, 11331, 33546, 1211, 48812, 25513, 18871, 33546, 2288, 25062, 9566, 2288, 6024, 104, 7649, 45865, 7251, 3555, 4587, 7578, 45164, 10874, 36081, 11331, 33546, 1211, 48812, 25513, 18871, 33546, 2288, 25062, 9566, 2288, 34892, 19986, 1829, 3794, 1829, 7251, 3555, 4587, 7578, 398, 16, 56, 17, 6, 8717, 995, 4587, 9381, 11331, 33546, 1211, 48812, 25513, 18871, 33546, 2288, 25062, 9566, 2288, 6024, 104, 7649, 45865, 7251, 3555, 4587, 7578, 398, 16, 6, 56, 17, 4724, 3224, 15730, 25124, 28820], "avg_logprob": -0.10930765323854726, "compression_ratio": 2.4685314685314683, "no_speech_prob": 1.7881393432617188e-07, "words": [{"start": 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193, "seek": 481541, "start": 4788.01, "end": 4815.41, "text": "يبقى اتنين لتو functions هدول يبقى هذا رونسكين لمين لتو functions وهكذا اي دالتين حطيهم حط مستقبتهم هات المحدد اثناء لهم بيعطيكي قيمة رونسكين لهم كمان نظرية اخرى في محاضرة اليوم يبقى theorem we suppose that", "tokens": [1829, 3555, 4587, 7578, 1975, 2655, 1863, 9957, 5296, 2655, 2407, 6828, 8032, 3215, 12610, 7251, 3555, 4587, 7578, 23758, 12602, 11536, 3794, 4117, 9957, 32767, 9957, 5296, 2655, 2407, 6828, 37037, 4117, 15730, 1975, 1829, 11778, 6027, 2655, 9957, 11331, 9566, 1829, 16095, 11331, 9566, 3714, 14851, 4587, 3555, 2655, 16095, 8032, 9307, 9673, 24401, 3215, 1975, 12984, 1863, 16606, 5296, 16095, 4724, 40228, 9566, 1829, 4117, 1829, 12174, 32640, 3660, 12602, 11536, 3794, 4117, 9957, 5296, 16095, 9122, 2304, 7649, 8717, 19913, 2288, 10632, 1975, 34740, 7578, 8978, 3714, 5016, 46958, 25720, 45595, 20498, 7251, 3555, 4587, 7578, 20904, 321, 7297, 300], "avg_logprob": -0.27127977098737444, "compression_ratio": 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4867.8, "end": 4868.72, "word": " بده", "probability": 0.608154296875}, {"start": 4868.72, "end": 4869.24, "word": " يساوي", "probability": 0.90283203125}, {"start": 4869.24, "end": 4869.66, "word": " Zero", "probability": 0.60400390625}, {"start": 4869.66, "end": 4870.54, "word": " سميلي", "probability": 0.8414306640625}, {"start": 4870.54, "end": 4870.98, "word": " هذه", "probability": 0.78369140625}, {"start": 4870.98, "end": 4871.64, "word": " المعادلة", "probability": 0.978271484375}, {"start": 4871.64, "end": 4872.34, "word": " رقم", "probability": 0.9842122395833334}, {"start": 4872.34, "end": 4873.06, "word": " واحد", "probability": 0.89013671875}], "temperature": 1.0}, {"id": 196, "seek": 489142, "start": 4873.9, "end": 4891.42, "text": "and that الورنسكين عند ال T نوت بده يساوي Y1 عند ال T نوت في Y2 prime", "tokens": [474, 300, 2423, 13063, 1863, 3794, 4117, 9957, 43242, 2423, 314, 8717, 35473, 47525, 3224, 7251, 3794, 995, 45865, 398, 16, 43242, 2423, 314, 8717, 35473, 8978, 398, 17, 5835], "avg_logprob": -0.485131029159792, "compression_ratio": 1.1954022988505748, "no_speech_prob": 0.0, "words": [{"start": 4873.9, "end": 4874.42, "word": "and", "probability": 0.07513427734375}, {"start": 4874.42, "end": 4875.1, "word": " that", "probability": 0.88818359375}, {"start": 4875.1, "end": 4881.28, "word": " الورنسكين", "probability": 0.8153483072916666}, {"start": 4881.28, "end": 4881.94, "word": " عند", "probability": 0.45751953125}, {"start": 4881.94, "end": 4882.22, "word": " ال", "probability": 0.51171875}, {"start": 4882.22, "end": 4882.46, "word": " T", "probability": 0.465087890625}, {"start": 4882.46, "end": 4883.04, "word": " نوت", "probability": 0.5228271484375}, {"start": 4883.04, "end": 4884.92, "word": " بده", "probability": 0.459564208984375}, {"start": 4884.92, "end": 4885.56, "word": " يساوي", "probability": 0.851806640625}, {"start": 4885.56, "end": 4887.2, "word": " Y1", "probability": 0.668212890625}, {"start": 4887.2, "end": 4888.36, "word": " عند", "probability": 0.75439453125}, {"start": 4888.36, "end": 4888.7, "word": " ال", "probability": 0.75390625}, {"start": 4888.7, "end": 4888.92, "word": " T", "probability": 0.97314453125}, {"start": 4888.92, "end": 4889.4, "word": " نوت", "probability": 0.973388671875}, {"start": 4889.4, "end": 4889.76, "word": " في", "probability": 0.7978515625}, {"start": 4889.76, "end": 4890.66, "word": " Y2", "probability": 0.9287109375}, {"start": 4890.66, "end": 4891.42, "word": " prime", "probability": 0.2288818359375}], "temperature": 1.0}, {"id": 197, "seek": 491949, "start": 4891.93, "end": 4919.49, "text": "عند الـ T node ناقص Y1 prime عند ال T node في Y2 عند ال T node لا يسوى Zero with مع ال initial conditions او with اللي هو", "tokens": [3615, 41260, 2423, 39184, 314, 9984, 8717, 995, 4587, 9381, 398, 16, 5835, 43242, 2423, 314, 9984, 8978, 398, 17, 43242, 2423, 314, 9984, 20193, 7251, 3794, 2407, 7578, 17182, 365, 20449, 2423, 5883, 4487, 1975, 2407, 365, 13672, 1829, 31439], 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4909.49, "end": 4909.99, "word": " initial", "probability": 0.84619140625}, {"start": 4909.99, "end": 4911.31, "word": " conditions", "probability": 0.8623046875}, {"start": 4911.31, "end": 4912.71, "word": " او", "probability": 0.6641845703125}, {"start": 4912.71, "end": 4913.51, "word": " with", "probability": 0.9130859375}, {"start": 4913.51, "end": 4919.15, "word": " اللي", "probability": 0.957763671875}, {"start": 4919.15, "end": 4919.49, "word": " هو", "probability": 0.98828125}], "temperature": 1.0}, {"id": 198, "seek": 494800, "start": 4920.82, "end": 4948.0, "text": "لا يساوي zero و ال Y عند ال T node يساوي Y node و Y prime عند ال T node يساوي Y node prime او Y عند ال T node", "tokens": [15040, 7251, 3794, 995, 45865, 4018, 4032, 2423, 398, 43242, 2423, 314, 9984, 7251, 3794, 995, 45865, 398, 9984, 4032, 398, 5835, 43242, 2423, 314, 9984, 7251, 3794, 995, 45865, 398, 9984, 5835, 1975, 2407, 398, 43242, 2423, 314, 9984], "avg_logprob": -0.3170731591015327, "compression_ratio": 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لكن", "probability": 0.27978515625}, {"start": 4957.77, "end": 4959.47, "word": " أبو", "probability": 0.8247884114583334}, {"start": 4959.47, "end": 4959.53, "word": " دي", "probability": 0.9873046875}, {"start": 4959.53, "end": 4959.97, "word": " ساوي", "probability": 0.9366861979166666}, {"start": 4959.97, "end": 4960.19, "word": " و", "probability": 0.96484375}, {"start": 4960.19, "end": 4960.43, "word": " I", "probability": 0.95947265625}, {"start": 4960.43, "end": 4960.99, "word": " prime", "probability": 0.85302734375}, {"start": 4960.99, "end": 4961.57, "word": " نوت", "probability": 0.864990234375}, {"start": 4961.57, "end": 4963.43, "word": " دوري", "probability": 0.9532877604166666}, {"start": 4963.43, "end": 4964.71, "word": " و", "probability": 0.78466796875}, {"start": 4964.71, "end": 4965.01, "word": " هاد", "probability": 0.5396728515625}, {"start": 4965.01, "end": 4965.69, "word": " يسميها", "probability": 0.958251953125}, {"start": 4965.69, "end": 4966.49, "word": " لإتنين", "probability": 0.772021484375}, {"start": 4966.49, "end": 4968.21, "word": " هاد", "probability": 0.880615234375}, {"start": 4968.21, "end": 4968.99, "word": " المعادلة", "probability": 0.9903564453125}, {"start": 4968.99, "end": 4969.95, "word": " ساميها", "probability": 0.818115234375}, {"start": 4969.95, "end": 4972.13, "word": " معادلة", "probability": 0.986328125}, {"start": 4972.13, "end": 4973.29, "word": " اتنين", "probability": 0.85791015625}], "temperature": 1.0}, {"id": 200, "seek": 500410, "start": 4976.87, "end": 5004.11, "text": "ثم هناك اختيار ثم هناك اختيار من المصادر C1 وC2 لذلك", "tokens": [12984, 2304, 34105, 4117, 1975, 9778, 31371, 9640, 38637, 2304, 34105, 4117, 1975, 9778, 31371, 9640, 9154, 9673, 9381, 18513, 2288, 383, 16, 4032, 34, 17, 5296, 8848, 23275], "avg_logprob": -0.4989583075046539, "compression_ratio": 1.267605633802817, "no_speech_prob": 0.0, "words": [{"start": 4976.87, "end": 4977.23, "word": "ثم", "probability": 0.59539794921875}, 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satisfied the differential equation when", "tokens": [49628, 1829, 12984, 16472, 288, 6055, 3794, 995, 45865, 269, 36764, 24401, 288, 36764, 24401, 30767, 16373, 3215, 269, 1975, 2655, 1863, 9957, 288, 1975, 2655, 1863, 9957, 11239, 11239, 264, 15756, 5367, 562], "avg_logprob": -0.3214285595076425, "compression_ratio": 1.3009708737864079, "no_speech_prob": 0.0, "words": [{"start": 5007.92, "end": 5008.8, "word": "بحيث", "probability": 0.8756510416666666}, {"start": 5008.8, "end": 5009.28, "word": " ان", "probability": 0.70068359375}, {"start": 5009.28, "end": 5011.14, "word": " y", "probability": 0.374267578125}, {"start": 5011.14, "end": 5012.92, "word": " تساوي", "probability": 0.6152191162109375}, {"start": 5012.92, "end": 5013.26, "word": " c", "probability": 0.6435546875}, {"start": 5013.26, "end": 5013.8, "word": " واحد", "probability": 0.603271484375}, {"start": 5013.8, "end": 5014.08, "word": " y", "probability": 0.43896484375}, {"start": 5014.08, "end": 5014.66, "word": " 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202, "seek": 505274, "start": 5037.52, "end": 5052.74, "text": "and the given initial conditions اتنى", "tokens": [474, 264, 2212, 5883, 4487, 1975, 2655, 1863, 7578], "avg_logprob": -0.24355469048023223, "compression_ratio": 0.8541666666666666, "no_speech_prob": 0.0, "words": [{"start": 5037.52, "end": 5038.4, "word": "and", "probability": 0.474365234375}, {"start": 5038.4, "end": 5039.92, "word": " the", "probability": 0.8876953125}, {"start": 5039.92, "end": 5041.64, "word": " given", "probability": 0.89453125}, {"start": 5041.64, "end": 5044.32, "word": " initial", "probability": 0.94775390625}, {"start": 5044.32, "end": 5049.52, "word": " conditions", "probability": 0.861328125}, {"start": 5049.52, "end": 5052.74, "word": " اتنى", "probability": 0.7664794921875}], "temperature": 1.0}, {"id": 203, "seek": 523893, "start": 5225.04, "end": 5238.94, "text": "نظرية بتقول ما ياتي افترض ان Y1 و Y2 عبارة عن حليل المعادلة التفاضلية اللى عندنا هذه and that و ال warrants كان عندهم كان لا يساوي zero", "tokens": [1863, 19913, 2288, 10632, 39894, 39648, 19446, 7251, 9307, 1829, 1975, 5172, 2655, 43042, 16472, 398, 16, 4032, 398, 17, 6225, 3555, 9640, 3660, 18871, 11331, 20292, 1211, 9673, 3615, 18513, 37977, 16712, 5172, 46958, 1211, 10632, 13672, 7578, 43242, 8315, 29538, 293, 300, 4032, 2423, 1516, 10968, 25961, 43242, 16095, 25961, 20193, 7251, 3794, 995, 45865, 4018], "avg_logprob": -0.2707891989562471, "compression_ratio": 1.3836477987421383, "no_speech_prob": 0.0, "words": [{"start": 5225.04, "end": 5225.52, "word": "نظرية", "probability": 0.77880859375}, {"start": 5225.52, "end": 5225.9, "word": " بتقول", "probability": 0.826171875}, {"start": 5225.9, "end": 5226.08, "word": " ما", "probability": 0.8583984375}, {"start": 5226.08, "end": 5226.58, "word": " ياتي", "probability": 0.6175130208333334}, {"start": 5226.58, "end": 5227.84, "word": " افترض", "probability": 0.903564453125}, {"start": 5227.84, "end": 5228.08, "word": " ان", "probability": 0.65966796875}, {"start": 5228.08, "end": 5228.68, "word": " Y1", "probability": 0.62890625}, {"start": 5228.68, "end": 5228.86, "word": " و", "probability": 0.8681640625}, {"start": 5228.86, "end": 5229.32, "word": " Y2", "probability": 0.76708984375}, {"start": 5229.32, "end": 5229.8, "word": " عبارة", "probability": 0.9140625}, {"start": 5229.8, "end": 5229.94, "word": " عن", "probability": 0.91748046875}, {"start": 5229.94, "end": 5230.44, "word": " حليل", "probability": 0.7733561197916666}, {"start": 5230.44, "end": 5231.08, "word": " المعادلة", "probability": 0.9188232421875}, {"start": 5231.08, "end": 5232.16, "word": " التفاضلية", "probability": 0.91513671875}, {"start": 5232.16, "end": 5232.64, "word": " اللى", "probability": 0.7822265625}, {"start": 5232.64, "end": 5233.0, "word": " عندنا", "probability": 0.988037109375}, {"start": 5233.0, "end": 5233.34, "word": " هذه", "probability": 0.384765625}, {"start": 5233.34, "end": 5234.7, "word": " and", "probability": 0.591796875}, {"start": 5234.7, "end": 5235.16, "word": " that", "probability": 0.9013671875}, {"start": 5235.16, "end": 5235.62, "word": " و", "probability": 0.6357421875}, {"start": 5235.62, "end": 5235.78, "word": " ال", "probability": 0.86669921875}, {"start": 5235.78, "end": 5236.28, "word": " warrants", "probability": 0.38299560546875}, {"start": 5236.28, "end": 5236.52, "word": " كان", "probability": 0.875}, {"start": 5236.52, "end": 5237.04, "word": " عندهم", "probability": 0.97216796875}, {"start": 5237.04, "end": 5237.48, "word": " كان", "probability": 0.87646484375}, {"start": 5237.48, "end": 5237.78, "word": " لا", "probability": 0.82373046875}, {"start": 5237.78, "end": 5238.54, "word": " يساوي", "probability": 0.888916015625}, {"start": 5238.54, "end": 5238.94, "word": " zero", "probability": 0.51513671875}], "temperature": 1.0}, {"id": 204, "seek": 526619, "start": 5239.67, "end": 5266.19, "text": "وطني two initial conditions كذلك طبعا الwoners can win عند نقطة محددة عند T node مش حيالها عند نقطة واحدة الwoners can هذا لا يساوي zero قال لي إن حدث ذلك يبقى هلاقي two constants C1 وC2 بحيث أن هذا يكون حل للمعادلة التفاضلية", "tokens": [2407, 9566, 22653, 732, 5883, 4487, 9122, 8848, 23275, 23032, 3555, 3615, 995, 2423, 14693, 433, 393, 1942, 43242, 8717, 47432, 3660, 3714, 24401, 41891, 43242, 314, 9984, 37893, 11331, 1829, 6027, 11296, 43242, 8717, 47432, 3660, 36764, 24401, 3660, 2423, 14693, 433, 393, 23758, 20193, 7251, 3794, 995, 45865, 4018, 50239, 32239, 36145, 11331, 3215, 12984, 29910, 23275, 7251, 3555, 4587, 7578, 8032, 15040, 38436, 732, 35870, 383, 16, 4032, 34, 17, 4724, 5016, 1829, 12984, 14739, 23758, 7251, 30544, 11331, 1211, 5296, 19528, 3615, 18513, 37977, 16712, 5172, 46958, 1211, 10632], "avg_logprob": -0.28291222960390944, "compression_ratio": 1.5429864253393666, "no_speech_prob": 0.0, "words": [{"start": 5239.67, "end": 5240.35, "word": "وطني", "probability": 0.5016276041666666}, {"start": 5240.35, "end": 5240.71, "word": " two", "probability": 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"probability": 0.56591796875}, {"start": 5248.65, "end": 5248.97, "word": " node", "probability": 0.4296875}, {"start": 5248.97, "end": 5249.25, "word": " مش", "probability": 0.73583984375}, {"start": 5249.25, "end": 5249.73, "word": " حيالها", "probability": 0.8193359375}, {"start": 5249.73, "end": 5249.91, "word": " عند", "probability": 0.74560546875}, {"start": 5249.91, "end": 5250.35, "word": " نقطة", "probability": 0.9456380208333334}, {"start": 5250.35, "end": 5250.91, "word": " واحدة", "probability": 0.99169921875}, {"start": 5250.91, "end": 5251.97, "word": " الwoners", "probability": 0.783203125}, {"start": 5251.97, "end": 5252.15, "word": " can", "probability": 0.8662109375}, {"start": 5252.15, "end": 5252.35, "word": " هذا", "probability": 0.225830078125}, {"start": 5252.35, "end": 5252.51, "word": " لا", "probability": 0.48583984375}, {"start": 5252.51, "end": 5252.93, "word": " يساوي", "probability": 0.779296875}, {"start": 5252.93, "end": 5253.21, "word": " zero", 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conditions", "probability": 0.87646484375}, {"start": 5270.97, "end": 5271.45, "word": " و", "probability": 0.77490234375}, {"start": 5271.45, "end": 5271.91, "word": " كذلك", "probability": 0.8465169270833334}, {"start": 5271.91, "end": 5272.15, "word": " أن", "probability": 0.337646484375}, {"start": 5272.15, "end": 5272.67, "word": " يحل", "probability": 0.9593098958333334}, {"start": 5272.67, "end": 5273.27, "word": " المعادلة", "probability": 0.9158935546875}, {"start": 5273.27, "end": 5274.09, "word": " التفاضلية", "probability": 0.9302734375}, {"start": 5274.09, "end": 5274.65, "word": " بهذه", "probability": 0.88134765625}, {"start": 5274.65, "end": 5275.35, "word": " الشروط", "probability": 0.9537760416666666}, {"start": 5275.35, "end": 5276.21, "word": " المتاع", "probability": 0.5101725260416666}, {"start": 5276.21, "end": 5276.91, "word": " أو", "probability": 0.74365234375}, {"start": 5276.91, "end": 5277.87, "word": " اختصارا", "probability": 0.9328125}, {"start": 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5778.14, "end": 5779.16, "word": " يبقى", "probability": 0.979248046875}, {"start": 5779.16, "end": 5779.38, "word": " هى", "probability": 0.869873046875}, {"start": 5779.38, "end": 5779.96, "word": " الشكل", "probability": 0.92822265625}, {"start": 5779.96, "end": 5780.18, "word": " اللى", "probability": 0.922119140625}, {"start": 5780.18, "end": 5780.32, "word": " ال", "probability": 0.77294921875}, {"start": 5780.32, "end": 5780.76, "word": " solution", "probability": 0.96240234375}, {"start": 5780.76, "end": 5781.38, "word": " لمين", "probability": 0.6932779947916666}, {"start": 5781.38, "end": 5781.96, "word": " لل", "probability": 0.6044921875}, {"start": 5781.96, "end": 5782.64, "word": " initial", "probability": 0.84814453125}, {"start": 5782.64, "end": 5783.6, "word": " value", "probability": 0.98095703125}, {"start": 5783.6, "end": 5784.94, "word": " problem", "probability": 0.450439453125}, {"start": 5784.94, "end": 5786.3, "word": " لحد", "probability": 0.93017578125}, {"start": 5786.3, "end": 5786.58, "word": " هنا", "probability": 0.892578125}, {"start": 5786.58, "end": 5787.04, "word": " stop", "probability": 0.7978515625}], "temperature": 1.0}, {"id": 228, "seek": 579696, "start": 5787.5, "end": 5796.96, "text": "يعطيكوا العافية لسه لازلنا في نفس ال section ولما ننتهي بعد للمرة القادمة ان شاء الله", "tokens": [40228, 9566, 1829, 4117, 14407, 18863, 31845, 10632, 5296, 3794, 3224, 5296, 31377, 1211, 8315, 8978, 8717, 36178, 2423, 3541, 35525, 15042, 8717, 29399, 3224, 1829, 39182, 5296, 19528, 25720, 25062, 18513, 46007, 16472, 13412, 16606, 21984], "avg_logprob": -0.1237664407021121, "compression_ratio": 1.2869565217391303, "no_speech_prob": 2.8014183044433594e-06, "words": [{"start": 5787.5, "end": 5788.18, "word": "يعطيكوا", "probability": 0.84169921875}, {"start": 5788.18, "end": 5788.9, "word": " العافية", "probability": 0.8938802083333334}, {"start": 5788.9, "end": 5789.68, "word": " لسه", "probability": 0.8142903645833334}, {"start": 5789.68, "end": 5790.46, "word": " لازلنا", "probability": 0.94091796875}, {"start": 5790.46, "end": 5790.68, "word": " في", "probability": 0.76123046875}, {"start": 5790.68, "end": 5790.98, "word": " نفس", "probability": 0.9951171875}, {"start": 5790.98, "end": 5791.16, "word": " ال", "probability": 0.96484375}, {"start": 5791.16, "end": 5791.56, "word": " section", "probability": 0.8857421875}, {"start": 5791.56, "end": 5792.42, "word": " ولما", "probability": 0.64892578125}, {"start": 5792.42, "end": 5793.4, "word": " ننتهي", "probability": 0.9569091796875}, {"start": 5793.4, "end": 5793.86, "word": " بعد", "probability": 0.9052734375}, {"start": 5793.86, "end": 5794.94, "word": " للمرة", "probability": 0.9637044270833334}, {"start": 5794.94, "end": 5795.78, "word": " القادمة", "probability": 0.9905598958333334}, {"start": 5795.78, "end": 5796.22, "word": " ان", "probability": 0.84033203125}, {"start": 5796.22, "end": 5796.66, "word": " شاء", "probability": 0.985107421875}, {"start": 5796.66, "end": 5796.96, "word": " الله", "probability": 0.94873046875}], "temperature": 1.0}], "language": "ar", "language_probability": 1.0, "duration": 5797.651, "duration_after_vad": 5245.366593750032}
\ No newline at end of file
diff --git a/PL9fwy3NUQKwa8ZDfSFGn6H8xVFLzqmCZC/_NMCQUdH1C8.srt b/PL9fwy3NUQKwa8ZDfSFGn6H8xVFLzqmCZC/_NMCQUdH1C8.srt
new file mode 100644
index 0000000000000000000000000000000000000000..b4b338c6a749383d0cde2040cda57768143bc5cd
--- /dev/null
+++ b/PL9fwy3NUQKwa8ZDfSFGn6H8xVFLzqmCZC/_NMCQUdH1C8.srt
@@ -0,0 +1,2469 @@
+1
+00:00:09,860 --> 00:00:14,730
+بسم الله الرحمن الرحيم، المرة الفاتة بدأنا في حل
+
+2
+00:00:14,730 --> 00:00:18,510
+non homogeneous differential equation التي على 
+
+3
+00:00:18,510 --> 00:00:22,810
+الشكل الذي عندنا هذا *، استخدمنا المرة الفاتة 
+
+4
+00:00:22,810 --> 00:00:26,910
+طريقة الـ undetermined coefficients، طريقة المعاملات 
+
+5
+00:00:26,910 --> 00:00:32,390
+المجهولة، وقلنا اشترطنا شرطين، الشرط الأول لازم يكون 
+
+6
+00:00:32,390 --> 00:00:37,810
+المعاملات هذه ثوابت، الشرط الثاني لازم  G(t) تبقى
+
+7
+00:00:37,810 --> 00:00:42,320
+على شكل polynomial أو polynomial في exponential أو
+
+8
+00:00:42,320 --> 00:00:45,820
+polynomial في exponential في sin أو cos أو
+
+9
+00:00:45,820 --> 00:00:51,160
+مجموعهما أو الفرق فيما بينهما، اليوم إن شاء الله 
+
+10
+00:00:51,160 --> 00:00:54,900
+نأخذ طريقة جديدة اسمها طريقة الـ variation of
+
+11
+00:00:55,030 --> 00:01:02,470
+Parameters، تغيير الوسيطات، يعني في عندنا متغيرات
+
+12
+00:01:02,470 --> 00:01:06,530
+بدنا نستبدلها، وفي عندنا أشياء بدنا نستبدلها بأشياء 
+
+13
+00:01:06,530 --> 00:01:11,520
+أخرى، هذه المقصود بالـ variation of parameters، اثنان 
+
+14
+00:01:11,520 --> 00:01:17,020
+المعاملات ليست ثوابت، والله ما هي ثوابت، ممكن 
+
+15
+00:01:17,020 --> 00:01:21,360
+يكونوا هذه ثوابت، وممكن ما يكونوش ثوابت، ما أفرقش 
+
+16
+00:01:21,360 --> 00:01:27,670
+عندنا اثنان، الـ G(t) ياخذ على أي شكل بدك، سواء 
+
+17
+00:01:27,670 --> 00:01:31,190
+كان polynomial، exponential، مش polynomial، دوال 
+
+18
+00:01:31,190 --> 00:01:35,570
+مثلثية، في الـ bus، في المقام، في مش عارف إيه، أي 
+
+19
+00:01:35,570 --> 00:01:39,310
+functions، ما عنديش قيود على الـ functions مش زي
+
+20
+00:01:39,310 --> 00:01:42,950
+طريقة الـ undetermined coefficients ما عنديش قيود
+
+21
+00:01:42,950 --> 00:01:47,250
+بالمرة تتلخص هذه الطريقة باختصار يا بنات في الشكل
+
+22
+00:01:47,250 --> 00:01:50,340
+التالي، باروح بجيب الـ homogeneous differential
+
+23
+00:01:50,340 --> 00:01:54,820
+equation زي المرة الماضية وبجيب الحل تبع الـ 
+
+24
+00:01:54,820 --> 00:02:02,330
+homogeneous وبكون الحل عندي على الشكل هذا، بعد هيك 
+
+25
+00:02:02,330 --> 00:02:07,250
+مشان أجيب الـ particular solution تبع المعادلة بجعل 
+
+26
+00:02:07,250 --> 00:02:15,310
+ثوابت c1 و c2 بستبدلهم بدوال أخرى، وتكون u1 و u2
+
+27
+00:02:15,310 --> 00:02:19,490
+يعني بصير الـ particular solution ده اللي جديد أي 
+
+28
+00:02:19,490 --> 00:02:25,750
+u1 مضروبة في الحل الأول اللي جيبناه y1 وزائد u2
+
+29
+00:02:25,750 --> 00:02:30,760
+مضروبة في الحل الثاني اللي هو y2، إذا باختصار بنقول
+
+30
+00:02:30,760 --> 00:02:34,920
+ما يأتي، اعتبر المعادلة التفاضلية الخطية مرتبة 
+
+31
+00:02:34,920 --> 00:02:39,880
+ثانية بالشكل هذا، المعامل تبع y double prime لازم 
+
+32
+00:02:39,880 --> 00:02:44,400
+يكون واحد صحيح، يعني لو ما كانش بدنا نروح إياه نجسم 
+
+33
+00:02:44,400 --> 00:02:47,240
+على الدالة الموجودة في الـ y double prime بحيث 
+
+34
+00:02:47,240 --> 00:02:53,120
+أضمن دائما وأبدا أن شكل المعامل تبع y double 
+
+35
+00:02:53,120 --> 00:02:54,180
+prime هو واحد
+
+36
+00:03:07,860 --> 00:03:12,060
+الآن نفترض y1 و y2 لـ linearly independent 
+
+37
+00:03:12,060 --> 00:03:15,300
+solutions للـ homogeneous differential equation
+
+38
+00:03:15,300 --> 00:03:18,460
+يبقى صار الحل العام تبع الـ homogeneous
+
+39
+00:03:18,460 --> 00:03:22,810
+differential equation على الشكل الذي عندنا هذا، بقول
+
+40
+00:03:22,810 --> 00:03:27,010
+to find a particular solution، مش هنجيب الحل الخاص
+
+41
+00:03:27,010 --> 00:03:32,210
+للمعادلة بطريقة الـ variation of parameters بتغيير
+
+42
+00:03:32,210 --> 00:03:37,970
+الوسيطات، we replace the constants، نستبدل replace
+
+43
+00:03:37,970 --> 00:03:45,380
+يعني نستبدل الثوابت C1 و C2 بـ two functions U1 as 
+
+44
+00:03:45,380 --> 00:03:49,720
+a function of t و U2 as a function of t، يعني بدي 
+
+45
+00:03:49,720 --> 00:03:57,480
+أشيل C1 وأحط مكانها U1، وأشيل C2 وأحط مكانها U2
+
+46
+00:03:57,480 --> 00:04:02,800
+ليه بيطلع عندي؟ بدي أسمع من الـ particular solution
+
+47
+00:04:02,800 --> 00:04:09,430
+السؤال هو كيف بيجيب الـ U1 و U2؟ بنجي على الحل الذي 
+
+48
+00:04:09,430 --> 00:04:14,150
+صار عندي، الـ Y = c1y1 + c2y2 
+
+49
+00:04:14,150 --> 00:04:20,610
+نشتق مرة ونشتق اثنين ونرجع نعوض
+
+50
+00:04:20,610 --> 00:04:25,080
+في المعادلة الأصلية اللي هو *، أو نجمعه ونطرحه ون 
+
+51
+00:04:25,080 --> 00:04:29,560
+نجسمه ونختصره ونشتريه لغاية ما نوصل لمين؟ لغاية 
+
+52
+00:04:29,560 --> 00:04:32,740
+ما نوصل لـ U1 و U2، يعني قصة طويلة، بدنا على الأقل 
+
+53
+00:04:32,740 --> 00:04:36,840
+مصارعة عشان نخلص الشغل، هذه أنسى الموضوع بهمن 
+
+54
+00:04:36,840 --> 00:04:40,180
+تعرفيه الشكل الـ U1 as a function of t هو
+
+55
+00:04:40,180 --> 00:04:46,500
+عبارة عن سالب تكامل الحل الثاني، إحنا بدنا U1 
+
+56
+00:04:46,500 --> 00:04:53,810
+يبقى بأخذ تكامل الحل الثاني الـ Y2 مضروب في الـ G(t) 
+
+57
+00:04:53,810 --> 00:04:58,890
+مقسوم على الورونسكين تبع الـ two solutions Y1 
+
+58
+00:04:58,890 --> 00:05:05,410
+و Y2، بالمثل U2 هي تكامل Y1، يعني كأنه
+
+59
+00:05:05,410 --> 00:05:09,850
+عكس U1، معاها Y2، U2 معاها مين؟ Y1 
+
+60
+00:05:09,850 --> 00:05:14,650
+يبقى بدون إشارة سالب في الـ U1، في إشارة سالب في
+
+61
+00:05:14,650 --> 00:05:18,120
+الـ U2، ما عنديش إشارة سالب، يبقى الـ U2 as a
+
+62
+00:05:18,120 --> 00:05:22,040
+function of t هي تكامل Y1(t) في G(t) على
+
+63
+00:05:22,040 --> 00:05:27,280
+الورونسكين تبع الـ Y1 و Y2 as a function of t، يبقى هذا
+
+64
+00:05:27,280 --> 00:05:31,080
+الورونسكين as a function of t، وهذا الورونسكين as a 
+
+65
+00:05:31,080 --> 00:05:39,530
+function of t، حصلت على U1 و U2، بضرب Y1 في U1، Y2 في U2 و 
+
+66
+00:05:39,530 --> 00:05:43,810
+بجمع الاثنين بيعطوني الحل الخاص، بدي الـ general
+
+67
+00:05:43,810 --> 00:05:49,690
+solution بجمع الحل الخاص الذي حصلت عليه مع الحل
+
+68
+00:05:49,690 --> 00:05:53,890
+العام تبع الـ homogeneous، اثنان مع بعض، تبقى النظرية
+
+69
+00:05:53,890 --> 00:05:58,490
+التي اخذناها المرة قبل الماضية، وكنا بنحل عليها
+
+70
+00:05:58,490 --> 00:06:01,950
+المرة الماضية، بنجيب حل الـ homogeneous والـ
+
+71
+00:06:01,950 --> 00:06:04,890
+particular solution تبع الـ non homogeneous بنجمع
+
+72
+00:06:04,890 --> 00:06:07,850
+الاثنين بيعطينا الـ general solution تبع المعادلة
+
+73
+00:06:07,850 --> 00:06:14,530
+الأصلية، فهمت الطريقة؟ بعيد كمان مرة علشان اللي
+
+74
+00:06:14,530 --> 00:06:19,130
+وصلنا متأخرات، بيعطينا المعادلة ذلك، وجوجل هات الـ 
+
+75
+00:06:19,130 --> 00:06:22,880
+general solution، بروح بأخذ الـ homogeneous تبعته 
+
+76
+00:06:22,880 --> 00:06:26,940
+المعادلة هذه بحلها بأي طريقة من الطرق التي سبقت 
+
+77
+00:06:26,940 --> 00:06:30,680
+دراستها في الـ sections الماضية من section 1 لغاية 
+
+78
+00:06:30,680 --> 00:06:37,320
+section 5، حلناها وجيبنا Y1 و Y2، إذا جبنا حل الـ
+
+79
+00:06:37,320 --> 00:06:40,600
+homogeneous differential equation، بدنا نجيب
+
+80
+00:06:40,600 --> 00:06:45,260
+particular solution للمعادلة *، بفرض أن الـ 
+
+81
+00:06:45,260 --> 00:06:49,340
+particular solution على الصيغة التي هي هذه بس
+
+82
+00:06:49,340 --> 00:06:54,780
+بشيل c1 بحط بدله function u1 وبشيل c2
+
+83
+00:06:54,780 --> 00:06:58,340
+بحط بدله function u2، فبصير الشكل الـ 
+
+84
+00:06:58,340 --> 00:07:02,320
+particular solution على الشكل الذي أمامنا هذا، مين 
+
+85
+00:07:02,320 --> 00:07:07,020
+هي u1؟ u1 هي سالب تكامل y2 مضروبة
+
+86
+00:07:07,020 --> 00:07:10,740
+في G(t) على الورونسكين تبع الـ y1 والـ y2
+
+87
+00:07:10,740 --> 00:07:17,020
+as a function of t، والـ u2 هي عبارة عن تكامل Y1 
+
+88
+00:07:17,020 --> 00:07:21,300
+(t) في الـ G(t) على الورونسكين تبع الـ Y1 و Y2 as 
+
+89
+00:07:21,300 --> 00:07:26,540
+a function of t، جبت الـ U1 وجبت الـ U2، وروح بعوض
+
+90
+00:07:26,540 --> 00:07:32,280
+في هذه بكون جبت شكل الحل الخاص، بجمع الذي هو الحل 
+
+91
+00:07:32,280 --> 00:07:36,340
+الخاص مع الحل العام تبع الـ homogeneous الاثنين مع بعض
+
+92
+00:07:36,340 --> 00:07:39,840
+بجمع الحل المعادلة الأصلية
+
+93
+00:07:52,050 --> 00:08:00,390
+المثال الأول بيقول هاتلي الـ general solution 
+
+94
+00:08:08,120 --> 00:08:13,180
+سؤال الأول بيقول له سؤال 10 من الكتاب بيقول find 
+
+95
+00:08:13,180 --> 00:08:16,820
+the 
+
+96
+00:08:16,820 --> 00:08:27,100
+general solution 
+
+97
+00:08:27,100 --> 00:08:35,720
+of the differential equation of the differential 
+
+98
+00:08:35,720 --> 00:08:49,650
+equation للمعادلة التفاضلية يساوي
+
+99
+00:08:49,650 --> 00:08:57,370
+e<sup>t</sup> على 1 + t<sup>2</sup>، وهذه المعادلة الأصلية
+
+100
+00:09:07,290 --> 00:09:12,590
+الـ tactic الذي اتبع في حالة الجزء النظري في حالة
+
+101
+00:09:12,590 --> 00:09:14,710
+الـ variation of parameters هو الـ tactic الذي
+
+102
+00:09:14,710 --> 00:09:18,870
+نتبعه الآن عند حل المثال، يبقى بدنا نأخذ الـ 
+
+103
+00:09:18,870 --> 00:09:22,170
+homogeneous differential equation ونروح من هنا لو
+
+104
+00:09:22,170 --> 00:09:25,770
+جئنا للـ homogeneous بنلاقي المعاملات، إذا نزل
+
+105
+00:09:25,770 --> 00:09:33,630
+sections الماضية بروح بقول له let y = e<sup>rt</sup> be 
+
+106
+00:09:33,630 --> 00:09:38,990
+a solution of the
+
+107
+00:09:47,640 --> 00:09:58,580
+بناء عليه then the characteristic equation is r
+
+108
+00:09:58,580 --> 00:10:05,680
+تربيع ناقص اثنين r زائد واحد تساوي كده؟ تساوي صفر
+
+109
+00:10:05,680 --> 00:10:10,880
+هذه يا بنات لو حللناها r ناقص واحد في r ناقص واحد 
+
+110
+00:10:10,880 --> 00:10:17,780
+لكل تربيع تساوي صفر، ومنها r1 تساوي r2 
+
+111
+00:10:17,780 --> 00:10:27,230
+تساوي كده؟ واحد صحيح، يبقى صار الحل أن yc = 
+
+112
+00:10:27,230 --> 00:10:38,370
+c1 + c2t في e<sup>t</sup>، أو أن شئتنا فقلنا c1 e<sup>t</sup> 
+
+113
+00:10:38,370 --> 00:10:47,440
+زائد c2t في e<sup>t</sup>، يبقى الحل الأول y1 هو e<sup>t</sup> و
+
+114
+00:10:47,440 --> 00:10:56,100
+الحل الثاني هو te<sup>t</sup>، بعد ذلك بروز هذا سنرجع له 
+
+115
+00:10:56,100 --> 00:11:00,960
+تمام، يبقى نروح نجيب الـ particular solution للـ 
+
+116
+00:11:00,960 --> 00:11:06,810
+equation، المعامل هنا واحد صحيح، يبقى إحنا جاهزين 
+
+117
+00:11:06,810 --> 00:11:10,190
+معناه مش مشكلة، إن شاء الله يكون اثنين ثلاثة أربعة 
+
+118
+00:11:10,190 --> 00:11:12,750
+بيكتب اسمي على هذا الرقم الذي هو الـ constant
+
+119
+00:11:12,750 --> 00:11:18,310
+اشتراطنا بيكون واحد صحيح، تمام، يبقى بأجي بقول the
+
+120
+00:11:18,310 --> 00:11:27,890
+particular solution of the
+
+121
+00:11:41,500 --> 00:11:52,620
+U1 يبقى U1(t) في e<sup>t</sup> وشيل c2 واكتب بدلا U2 
+
+122
+00:11:52,620 --> 00:12:00,550
+(t) في t في e<sup>t</sup>، جاب المحسب الـ U1 والـ U2 بالزمن 
+
+123
+00:12:00,550 --> 00:12:06,970
+الورونسكين، تمام، يبقى بده أروح أجيب له الورونسكين تبع
+
+124
+00:12:06,970 --> 00:12:12,990
+الحل الأول والحل الثاني as a function of t، الحل 
+
+125
+00:12:12,990 --> 00:12:20,330
+الأول هو e<sup>t</sup> والحل الثاني هو t في e<sup>t</sup>، نشتق 
+
+126
+00:12:20,330 --> 00:12:27,500
+هذا بـ e<sup>t</sup>، نشتق هذا بمشتقة حاصل ضرب دالتين، يبقى 
+
+127
+00:12:27,500 --> 00:12:33,860
+مشتقة الأولى في الثانية زائد الأولى في مشتقة مين 
+
+128
+00:12:33,860 --> 00:12:41,500
+الدالة الثانية، انفك المحدد بالضرب التبادلي يبقى
+
+129
+00:12:41,500 --> 00:12:49,820
+هنا بصير e<sup>2t</sup> زائد t في e<sup>2t</sup>، هذا
+
+130
+00:12:49,820 --> 00:12:55,790
+حاصل ضرب عناصر القطر الرئيسي نقص حاصل ضرب عناصر
+
+131
+00:12:55,790 --> 00:13:03,510
+القطر الثانوي يبقى ناقص t في e<sup>2t</sup>، هذا و 
+
+132
+00:13:03,510 --> 00:13:09,910
+هذا في كم؟ في صفر، هذا الكلام يساوي كم؟ الذي عمرها 
+
+133
+00:13:09,910 --> 00:13:15,470
+ما حتساوي صفر، ليش؟ لأن الـ Exponential دائما وأبدا
+
+134
+00:13:15,470 --> 00:13:19,650
+أكبر من مين؟ من الـ صفر، إذا الحل الذي بيطلع عنهم 
+
+135
+00:13:19,650 --> 00:13:24,430
+يبنى linearly independent solution وبالتالي
+
+136
+00:13:24,430 --> 00:13:28,170
+بيكونوا لـ Fundamental Set of Solutions أو الـ
+
+137
+00:13:28,170 --> 00:13:31,210
+General Solution لمين؟ للـ Homogeneous
+
+138
+00:13:31,210 --> 00:13:35,580
+Differential Equation، على أي حال أن هذا الآن بتروح 
+
+139
+00:13:35,580 --> 00:13:42,160
+تحسب له U1 و U2، يبقى بدي U1 as a function of t
+
+140
+00:13:42,160 --> 00:13:50,400
+الذي هو ناقص تكامل Y2(t) في G(t) على
+
+141
+00:13:50,400 --> 00:13:58,120
+الورونسكين as a function of t dt، يبقى هذه سالب 
+
+142
+00:13:58,120 --> 00:14:05,650
+وهذه تكامل، بتداجر الـ Y2، Y2 هو te<sup>t</sup>، يبقى
+
+143
+00:14:05,650 --> 00:14:13,130
+هذه te<sup>t</sup> في G(t)، وين G(t) هيها فوق 
+
+144
+00:14:13,130 --> 00:14:21,630
+يبقى هذا بيصير e<sup>t</sup> وبتنزل تحت واحد 
+
+145
+00:14:21,630 --> 00:14:28,070
+زائد t<sup>2</sup>، بيّلت تحت مين عندي؟ الورونسكين، الورونسكين 
+
+146
+00:14:28,070 --> 00:14:36,520
+جداش؟ e<sup>2t</sup>، كله في dt، يبقى لو ضربت هذه في 
+
+147
+00:14:36,520 --> 00:14:42,880
+هذه يا بنات بصير جداش e<sup>2t</sup> مع e<sup>2t</sup>
+
+148
+00:14:42,880 --> 00:14:48,420
+التي بتاعت مع السلامة، يبقى هذا الكلام يساوي الناقص
+
+149
+00:14:48,420 --> 00:14:54,280
+تكامل t على 1 + t<sup>2</sup> dt
+
+150
+00:14:57,690 --> 00:15:06,050
+أظن البسط فاضل المقام، كيف؟ بده اثنين يعني بتمان 
+
+151
+00:15:06,050 --> 00:15:12,510
+وعاد اثنين بشانيك بكلامنا صحيح بروح نضرب في نصف هيك 
+
+152
+00:15:12,510 --> 00:15:23,250
+صار البسط فاضل المقام، يساوي ناقص نصف ln (1 +
+
+153
+00:15:23,250 --> 00:15:27,890
+t<sup>2</sup>) بدون absolute value لأنها قيمة موجبة t، لو
+
+154
+00:15:27,890 --> 00:15:31,890
+حتى لو كان سالبة بالتربيع بصير موجبة زائد واحد يبقى 
+
+155
+00:15:31,890 --> 00:15:36,750
+هذه positive quantity على طول الخط، بس كنا كاملنا 
+
+156
+00:15:36,750 --> 00:15:42,170
+بنقول زائد constant، خلّيني أكتب الـ constant هذا، يبقى
+
+157
+00:15:42,170 --> 00:15:49,310
+زائد c1، وتعالي نتفهم على الـ c1 هذا كده إيش ممكن 
+
+158
+00:15:49,310 --> 00:15:56,470
+نأخده؟ خلي الـ C1، ما بديش آخده صفر، خده خمسة، مثلاً،
+
+159
+00:15:56,470 --> 00:16:01,610
+لو جدل أنا أخذت خمسة، إيش الذي بيحصل؟ بصير عندي
+
+160
+00:16:01,610 --> 00:16:08,670
+هذا المقدار زائد c1، لما أجي أضربه ههه فاهمين؟
+
+161
+00:16:08,670 --> 00:16:14,110
+هذا الذي هو U1، يبقى U1 بدي أجي أضربها وين؟ وين
+
+162
+00:16:14,110 --> 00:16:21,130
+راح الـ U1 هي؟ بدي أضربها هنا، بصير رقم في e<sup>t</sup> يعني
+
+163
+00:16:21,130 --> 00:16:27,610
+بصير تكرار وبالتالي بصير تشابه مع مين؟ مع الحل هذا
+
+164
+00:16:27,610 --> 00:16:31,830
+يبجي مشان أتخلص من الأشياء هذه دائما وأبدا مش في
+
+165
+00:16:31,830 --> 00:16:38,850
+السؤال هذا، في كل المسائل الذي بأخذ c1 بـ 0، طيب
+
+166
+00:16:38,850 --> 00:16:47,090
+الحين هشيرلها، طيب بداخل U2، Y1(t) يساوي تكامل
+
+167
+00:16:47,090 --> 00:16:55,730
+Y1(t) في G(t) على الورونسكين (t)، كله بالنسبة 
+
+168
+00:16:55,730 --> 00:17:02,160
+إلى dt، ويساوي تكامل، الـ Y1 يا بناتي الذي هو مين؟ e
+
+169
+00:17:02,160 --> 00:17:10,060
+<sup>t</sup> والـ G(t) ليه e<sup>t</sup> على 1 + t<sup>2</sup> 
+
+170
+00:17:10,060 --> 00:17:17,680
+والورونسكين الذي هو e<sup>2t</sup> في
+
+216
+00:23:27,070 --> 00:23:35,170
+سالب واحد والـ μ يساوي واحد إذا صار YC بدي يساوي
+
+217
+00:23:35,170 --> 00:23:43,550
+E أس λ T λ بواحد يبقى E أس T λ بسالب 
+
+218
+00:23:43,550 --> 00:23:47,570
+واحد E أس ناقص T تمام فاهمين؟
+
+219
+00:23:57,710 --> 00:24:05,170
+يبقى هذا حل الـ homogeneous differential equation
+
+220
+00:24:05,900 --> 00:24:09,580
+ماذا ترى؟ خلّيني أحسب الورونسكين بالمرة قبل ما 
+
+221
+00:24:09,580 --> 00:24:14,040
+أجيب الـ particular solution حتى تظل المسألة ماشية
+
+222
+00:24:14,040 --> 00:24:19,440
+معانا بطريقة سلسة يبقى بدي أجيب الورونسكين as a
+
+223
+00:24:19,440 --> 00:24:26,920
+function of T الحل الأول هو E أس ناقص T في cos T
+
+224
+00:24:26,920 --> 00:24:35,620
+الحل الثاني هو E أس سالب T في sin T بنشتق الدالة
+
+225
+00:24:35,620 --> 00:24:42,720
+الأولى حاصل ضرب دالتين يبقى مشتقة الأولى زي ما هي
+
+226
+00:24:42,720 --> 00:24:50,160
+في مشتقة الثانية من بسالب واحد في cos T بعد ذلك الـ
+
+227
+00:24:50,160 --> 00:24:55,880
+E نقص T كما هي في مشتقة الـ cos E بسالبSin يبقى
+
+228
+00:24:55,880 --> 00:25:03,060
+السالب E أس سالب T في Sin T الدالة الثانية بنفس
+
+229
+00:25:03,060 --> 00:25:11,180
+الطريقة يبقى ناقص E أس ناقص T في Sin T زائد E أس
+
+230
+00:25:11,180 --> 00:25:20,460
+ناقص T في Cos T طبعا نجي نطلع قداش قيمة هذا المحدد
+
+231
+00:25:20,460 --> 00:25:25,160
+ويوسف حاصل ضرب عناصر القطر الرئيسي ناقص حاصل ضرب 
+
+232
+00:25:25,160 --> 00:25:33,460
+عناصر القطر الثانوي يبقى هدف هدف تطلع بقداش بسالب
+
+233
+00:25:33,460 --> 00:25:41,540
+أو سالب اثنين T سالب أو سالب اثنين T في Sin T في 
+
+234
+00:25:41,540 --> 00:25:44,100
+Cos T في Sin 
+
+235
+00:25:49,640 --> 00:25:56,600
+يبقى زائد E أسالب اثنين T في cos T زائد E أس سلب
+
+236
+00:25:56,600 --> 00:26:05,560
+اثنين T فمين فيه cosine تربيع T هذا الرئيسي ناقص
+
+237
+00:26:05,560 --> 00:26:12,340
+ثانوي مع ناقص بصير إيه؟ زائد يبقى زائد E أس نقص
+
+238
+00:26:12,340 --> 00:26:21,340
+اثنين T sine T cosine T تمام؟ هدى في هدى، بعد ذلك 
+
+239
+00:26:21,340 --> 00:26:29,920
+هدى كمان زائد إيه أس ناقص اثنين T في sign تربيع T
+
+240
+00:26:29,920 --> 00:26:34,960
+شراي كمانات هدى و هدى مع السلامة، واحدة موجبة و
+
+241
+00:26:34,960 --> 00:26:40,900
+واحدة سالبة هذه تساوي بياخد E أس ناقص اثنين عامل
+
+242
+00:26:40,900 --> 00:26:48,080
+مشترك T بضالك cosine تربيعي زائد sine تربيعي له
+
+243
+00:26:48,080 --> 00:26:56,680
+مقداش يبقى الجواب E أس ناقص اثنين T وهذا لا يمكن أن 
+
+244
+00:26:56,680 --> 00:26:57,500
+يساوي
+
+245
+00:27:03,100 --> 00:27:07,320
+يبقى الكلام اللي كتبته هذا معله هو الـ general
+
+246
+00:27:07,320 --> 00:27:12,020
+solution للـ homogeneous differential equation بدنا 
+
+247
+00:27:12,020 --> 00:27:18,180
+نروح نجيب الـ particular solution لمين؟ للمعادلة
+
+248
+00:27:18,180 --> 00:27:20,480
+الأصلية
+
+249
+00:27:35,300 --> 00:27:39,420
+المعادلة الأصلية وين؟ لأن هدري سمنها star ففاجي 
+
+250
+00:27:39,420 --> 00:27:46,780
+بقولهم the particular solution
+
+251
+00:27:46,780 --> 00:27:51,020
+of equation
+
+252
+00:27:56,560 --> 00:28:07,900
+Y of T يبقى 
+
+253
+00:28:07,900 --> 00:28:18,700
+U1 of T في E السالب T في Cos T
+
+254
+00:28:46,270 --> 00:28:55,690
+Y2Y2Y2Y2Y2Y2Y2Y2Y2Y2Y2Y2Y2Y2Y2 يبقى 
+
+255
+00:28:55,690 --> 00:29:03,470
+E أسالب T في صينة T الـ G of T طلع المعاملة واحد
+
+256
+00:29:03,470 --> 00:29:11,690
+يبقى احنا جاهزين يبقى اثنين E أسالب T اثنين E
+
+257
+00:29:11,690 --> 00:29:20,060
+أسالب T في تان تربيع T كله علامين على الرمز كان 
+
+258
+00:29:20,060 --> 00:29:31,120
+طالعنا E والسالب اثنين T DT ويساوي سالب تكامل أظن
+
+259
+00:29:31,120 --> 00:29:37,720
+هذه مع هذه مع هذه الله يسهل عليهم غير ما سوف عليهم
+
+260
+00:29:37,720 --> 00:29:43,200
+بضل عندي سالب تكامل تان تربيع يا بنات اللي همين
+
+261
+00:29:43,520 --> 00:29:53,960
+اللي هي sin تربيع T على cos تربيع T في sin T في DT
+
+262
+00:29:53,960 --> 00:30:00,660
+يبقى هذا الكلام بده يساوي تكامل اش رايك بده أكتب
+
+263
+00:30:00,660 --> 00:30:07,360
+الـ sin تربيع بدلالة الـ cos تربيع يبقى واحد ناقص
+
+264
+00:30:07,360 --> 00:30:17,050
+cos تربيع T ماشي ماذا تقولون في اثنين نسيناها برا
+
+265
+00:30:17,050 --> 00:30:24,090
+آه في اثنين أي اثنين ماشي الحال وهذا اثنين برا و
+
+266
+00:30:24,090 --> 00:30:29,010
+هنا cosine تربيع الـ T بتقولون اللي نسيت الشرف
+
+267
+00:30:29,010 --> 00:30:36,490
+الناقص ما نستهاش طلع هنا ناقص sin t dt بدي أكتبها D
+
+268
+00:30:36,490 --> 00:30:42,620
+cosine هو مشتقة الـ cosine في قداش سالب ساين يبقى 
+
+269
+00:30:42,620 --> 00:30:49,180
+السالب ساين ت دي ت ودي أقول دي كوساين ت يبقى هذه
+
+270
+00:30:49,180 --> 00:30:57,820
+دي لكساين ت يعني مشتقة كساين ت لو ناقص ساين ت دي ت
+
+271
+00:30:57,820 --> 00:31:03,580
+يبقى شلت إشارة السالب مع الـ ساين ت مع الـ دي ت وكتبت
+
+272
+00:31:03,580 --> 00:31:08,340
+بدالها دي كوساين طب عملت هيك ليش تعالى أقولك ليش
+
+273
+00:31:08,340 --> 00:31:13,600
+عملت هيك يبقى هذا الكلام يساوي اللي هو الاثنين 
+
+274
+00:31:13,600 --> 00:31:21,600
+اللي برا وهي تكامل واحد على cosine تربيع الـ T وهنا 
+
+275
+00:31:21,600 --> 00:31:29,800
+ناقص واحد كله في دي cosine T يعني كأنه إيش احنا يا 
+
+276
+00:31:29,800 --> 00:31:36,410
+بنات؟ بنكمل واحد على X تربيع ناقص واحد DX يعني تبري
+
+277
+00:31:36,410 --> 00:31:42,230
+Cos T كأنها كلها X تمام؟ يبقى نتيجة التكامل بدها
+
+278
+00:31:42,230 --> 00:31:47,990
+تكون على الشكل التالي أي اثنين فيه قداش تكامل واحد 
+
+279
+00:31:47,990 --> 00:31:52,520
+على X تربيع؟ سالب واحد على X إذا هذا بتبقى الجدران
+
+280
+00:31:52,520 --> 00:32:01,100
+سالب واحد على cosine T يبقى سالب واحد على cosine T
+
+281
+00:32:01,100 --> 00:32:10,940
+ناقص cosine T يبقى ناقص cosine T و C1 ده ما بنشيلها
+
+282
+00:32:10,940 --> 00:32:17,580
+يبقى هنا زائد C1 وهنا بنقول take C1 تساوي Zero
+
+283
+00:32:18,650 --> 00:32:25,930
+تمام؟ يبقى هذا لو أخدت بـ 0 يصير U1 as a function
+
+284
+00:32:25,930 --> 00:32:33,870
+of T هي عبارة عن مين؟ عن ناقص اثنين على cos T 
+
+285
+00:32:33,870 --> 00:32:43,310
+وناقص اثنين cos T في حد يقول لي تسأل قبل ما أفوت
+
+286
+00:32:43,310 --> 00:32:48,390
+مش فاهمة تكامل مش فاهمة نقطة تسألني في أي تسأل؟
+
+287
+00:32:51,480 --> 00:33:01,370
+نعود الآن لـ U2 of T يبدو يسوي تكامل Y1 of T في G
+
+288
+00:33:01,370 --> 00:33:06,490
+of T على الورونسكين as a function of T دي T يسوي
+
+289
+00:33:06,490 --> 00:33:15,550
+تكامل Y1 اللي همين E أس ناقص T Cos T يبقى E أس
+
+290
+00:33:15,550 --> 00:33:26,150
+ناقص T في Cos T الـ G of T اللي هي اثنين E أس ناقص T
+
+291
+00:33:26,150 --> 00:33:36,030
+في تان تربيع T كله على الورونسكين E أس ناقص 2T يبقى 
+
+292
+00:33:36,030 --> 00:33:44,550
+هذا بنختصر بصير بصير تكامل و أي اثنين برا و بيضل cos
+
+293
+00:33:44,550 --> 00:33:50,170
+T فقط لا غير و تان تربيع
+
+294
+00:33:59,960 --> 00:34:05,200
+يساوي اثنين تكامل أظن في اختصار بين cosine و
+
+295
+00:34:05,200 --> 00:34:12,560
+cosine تربيع يبقى بضال عندي sin تربيع t فقط على
+
+296
+00:34:12,560 --> 00:34:22,010
+cosine t dt طيب هذه اللي بقدر أكتبها على الشكل 
+
+297
+00:34:22,010 --> 00:34:28,710
+التالي اثنين تكامل sin
+
+298
+00:34:28,710 --> 00:34:34,710
+تربيع يبقى واحد ناقص cosine تربيع يبقى واحد ناقص
+
+299
+00:34:34,710 --> 00:34:42,410
+cosine تربيع الـ T كله على cosine T DT ويساوي اثنين 
+
+300
+00:34:42,410 --> 00:34:51,290
+تكامل واحد على cosine بس يبقى sec الـ T و هنا ناقص
+
+301
+00:34:51,290 --> 00:34:56,710
+cosine تربيع على cosine بيبقى الـ cosine T واحدة 
+
+302
+00:34:56,710 --> 00:35:11,570
+كلها دي T يساوي اثنين يبقى 
+
+303
+00:35:11,570 --> 00:35:21,170
+اثنين ln absolute value لـ sec T زائد tan T وهنا
+
+304
+00:35:21,170 --> 00:35:30,450
+ناقص C2 وتكامل الـ cosine بـ sin T وزائد constant C2
+
+305
+00:35:30,450 --> 00:35:41,290
+وبنقول هنا take code C2 يساوي 0 يبقى صارة إن U2 as
+
+306
+00:35:41,290 --> 00:35:47,390
+a function of T هو عبارة عن اثنين ln absolute 
+
+307
+00:35:47,390 --> 00:35:58,030
+value لـ sec T زائد tan T ناقص اثنين sin T إذا بقدر 
+
+308
+00:35:58,030 --> 00:36:03,610
+أجيب شكل الـ particular solution تمام
+
+309
+00:36:12,370 --> 00:36:19,870
+بقول له the particular solution
+
+310
+00:36:19,870 --> 00:36:25,750
+of equation
+
+311
+00:36:25,750 --> 00:36:35,850
+star is capital Y of T بده يساوي U واحد في الـ Y
+
+312
+00:36:35,850 --> 00:36:44,380
+one زائد U اثنين في الـ Y two إذا capital Y of T بده 
+
+313
+00:36:44,380 --> 00:36:52,620
+يسمى وين الـ U1؟ هاد الـ U1، هاد إيه؟ اللي كتبناها
+
+314
+00:36:52,620 --> 00:36:57,560
+على الشكل هذا، هاد الـ U1، هاد بنا نضربها في 
+
+315
+00:36:57,560 --> 00:37:05,760
+مين وبالاتبدأ إن أنا أضربها في الـ Y1 هذي ههه مظبوط 
+
+316
+00:37:05,760 --> 00:37:10,160
+مش هذي الـ Y1 يعني كأنها ههه خاني أختصرها لك بعدين
+
+317
+00:37:10,160 --> 00:37:18,640
+مش مشكلة يبقى بداجي أقول E أس ناقص T في Cos T في 
+
+318
+00:37:19,480 --> 00:37:24,140
+الـ U1 اللي هو اثنين أو سالب اثنين على كوساين ت
+
+319
+00:37:24,140 --> 00:37:33,840
+سالب اثنين على كوساين T سالب اثنين كوساين T زي الـ
+
+320
+00:37:33,840 --> 00:37:41,600
+Y2 اللي هو E أس ناقص T في ساين T فاللي طلعناها 
+
+321
+00:37:41,600 --> 00:37:50,220
+تحت هذه اللي هو اثنين ln absolute value لمن لـ sec T
+
+322
+00:37:50,220 --> 00:37:59,980
+زائد tan T و هنا ناقص اثنين صيني T بالشكل اللي 
+
+323
+00:37:59,980 --> 00:38:06,780
+عندنا هذا الآن بدنا نجيب الـ general solution بعد
+
+324
+00:38:06,780 --> 00:38:13,310
+ما جبنا شكل main شكل الـ particular solution بس 
+
+325
+00:38:13,310 --> 00:38:18,670
+خلينا نشوف يا ترى فيها اختصارات والله ما فيهاش
+
+326
+00:38:18,670 --> 00:38:25,960
+اختصارات لو جمعناها يعني هنا بيصير والله يمكن يكون
+
+327
+00:38:25,960 --> 00:38:30,240
+فيها اختصارات تعالى نشوف كده بده تساوي هذه المناطب
+
+328
+00:38:30,240 --> 00:38:37,560
+بيصير عندي ناقص اثنين و E أس سالب T و الـ cosine مع 
+
+329
+00:38:37,560 --> 00:38:44,980
+الـ cosine بتروح و هنا سالب اثنين E أس ناقص T في
+
+330
+00:38:44,980 --> 00:38:53,620
+cosine تربيع T تمام خلاصنا منها هدى زائد اثنين E أس
+
+331
+00:38:53,620 --> 00:39:01,000
+ناقص T في صين الـ T في الـ absolute value لـ شك الـ T
+
+332
+00:39:01,000 --> 00:39:11,980
+زائد tan T ناقص اثنين E أس ناقص T في صين تربيع الـ 
+
+333
+00:39:11,980 --> 00:39:19,520
+T والله كويس طليلي في هدى هو هدى بقدر أخد سالب 
+
+334
+00:39:19,520 --> 00:39:25,420
+اثنين عامل مشترك إيش بيضل عندي؟ بيضل sin تربيع
+
+335
+00:39:25,420 --> 00:39:30,920
+زائد cos تربيع اللي بيبقى داشر يعني هذا بيصير سالب 
+
+336
+00:39:30,920 --> 00:39:37,480
+اثنين E أس ناقص T سالب اثنين E أس ناقص T وبيضلش
+
+337
+00:39:37,480 --> 00:39:45,220
+الامن اللي فالمص هذا يبقى زائد اثنين E أس ناقص T في
+
+338
+00:39:45,220 --> 00:39:47,580
+sin T فلن
+
+339
+00:39:53,890 --> 00:39:59,510
+ممتاز طيب إيش رايك هذه و هذه نفس هذه يبقى سالب
+
+340
+00:39:59,510 --> 00:40:07,170
+أربعة يبقى النتيجة سالب أربعة E أس ناقص T زائد
+
+341
+00:40:07,170 --> 00:40:17,230
+اثنين E أس ناقص T في صين T في ln sec T زائد tan T
+
+342
+00:40:18,270 --> 00:40:28,510
+إذا أنا باجي بقول له the general solution of the
+
+343
+00:40:28,510 --> 00:40:39,210
+differential equation star is y يساوي YC هيه عند هنا
+
+344
+00:40:39,210 --> 00:40:51,800
+تحت يبقى C1 E أس ناقص T في Cos T زائد C2 E أس ناقص T
+
+345
+00:40:51,800 --> 00:41:01,740
+في Sin T ناقص أربعة E أس ناقص T زائد اثنين E أس ناقص 
+
+346
+00:41:01,740 --> 00:41:14,180
+T في Sin T في ln absolute value sec T زائد tan T في 
+
+347
+00:41:14,180 --> 00:41:16,020
+أي تساول هنا يا بنادي
+
+348
+00:41:54,370 --> 00:42:06,930
+كمان مثال مثال
+
+349
+00:42:06,930 --> 00:42:11,830
+ثلاثة سؤال
+
+350
+00:42:11,830 --> 00:42:20,650
+من الكتاب بيقول fy1 بده يساوي T تربيع and 
+
+351
+00:42:22,110 --> 00:42:35,630
+Y2 بدي يساوي T تربيع ln T are two linearly
+
+352
+00:42:35,630 --> 00:42:40,290
+independent solutions
+
+353
+00:42:40,290 --> 00:42:43,650
+of
+
+354
+00:42:43,650 --> 00:42:48,330
+the homogeneous
+
+355
+00:42:53,180 --> 00:43:01,600
+Differential Equation لـ T تربيع Y double prime
+
+356
+00:43:01,600 --> 00:43:11,160
+ناقص ثلاثة T Y prime زائد أربعة Y تساوي Zero
+
+357
+00:43:11,160 --> 00:43:16,720
+وسميلي هذه المعادلة رقم واحد Find a particular 
+
+358
+00:43:16,720 --> 00:43:17,940
+solution
+
+359
+00:43:30,160 --> 00:43:36,840
+تبحث عن حلول معينة مختلفة للإيقاع
+
+360
+00:43:42,000 --> 00:43:49,520
+Equation للمعادلة التفاضلية T تربيع Y double prime
+
+361
+00:43:49,520 --> 00:43:53,140
+ناقص
+
+362
+00:43:53,140 --> 00:44:08,600
+ثلاثة T Y prime زائد أربعة Y تساوي T تربيع ln T و
+
+363
+00:44:08,600 --> 00:44:18,120
+الـ T greater than zero و هذه المعادلة رقم اثنين
+
+364
+00:44:36,850 --> 00:44:43,230
+يبقى هذا السؤال يختلف عن سابقينه في أمر واحد فقط 
+
+365
+00:44:43,230 --> 00:44:48,090
+شو الأمر هذا؟ أن المعادلة اللي معانا للمعاملات
+
+366
+00:44:48,090 --> 00:44:53,290
+تبعها مالها ماهي ثوابت واحنا أخدنا إذا المعادلة
+
+367
+00:44:53,290 --> 00:45:00,010
+ماهي ثوابت لازم يعطيني أحد الحلول وأن أروح أجيب
+
+368
+00:45:00,010 --> 00:45:05,000
+الحل الآخر بطريقة reduction of order مظبوط؟ لكن
+
+369
+00:45:05,000 --> 00:45:09,920
+الحمد لله ريحني وقال لي خد هدول الحلين هيهم معك 
+
+370
+00:45:09,920 --> 00:45:14,500
+يبقى ريحني من طريقة مين الـ reduction of order
+
+371
+00:45:14,500 --> 00:45:19,880
+وبالتالي قال لي لو كانوا هدول اثنين T تربيع و T
+
+372
+00:45:19,880 --> 00:45:24,000
+تربيع ln T هم حلين للـ homogeneous differential
+
+373
+00:45:24,000 --> 00:45:29,660
+equation بدي شكل الحل الخاص لمين للمعادلة اللي 
+
+374
+00:45:29,660 --> 00:45:35,610
+عندنا هذه بقول لك كويس يعني هو ريحني وبالتالي قال 
+
+375
+00:45:35,610 --> 00:45:40,450
+اثنين linearly independent إذا المعادلة الأولى
+
+376
+00:45:40,450 --> 00:45:51,450
+واحد حلها بجيبه في سطر يبقى فبجيبه هنا solution of
+
+377
+00:45:51,450 --> 00:46:00,330
+equation
+
+378
+00:46:00,330 --> 00:46:13,050
+one المعادلة الأولى هو YC بده يساوي C1 في من؟ في T
+
+379
+00:46:13,050 --> 00:46:22,230
+تربيع زائد C2 في T تربيع في ln T مش هيك؟ وين راح 
+
+380
+00:46:22,230 --> 00:46:30,040
+تقع ln T؟ ln الـ T تمام تمام يبقى هذا لو طلب الـ
+
+381
+00:46:30,040 --> 00:46:34,020
+general solution برجعله مطلبش بلاش لكن هو طلب فقط
+
+382
+00:46:34,020 --> 00:46:39,180
+من الـ particular solution للمعادلة رقم اثنين بقوله
+
+383
+00:46:39,180 --> 00:46:42,880
+بسيطة يبقى بدي أشيل c واحد و أحط مكانه function y
+
+384
+00:46:42,880 --> 00:46:48,220
+واحد و U واحد و أشيل U اثنين و أحط بدله function U
+
+385
+00:46:48,220 --> 00:46:52,740
+اثنين لكن مع الفرق بدرو حسب الورونسكين تبعهم من
+
+386
+00:46:52,740 --> 00:46:57,920
+البداية قبل ما أجيب الحل اللي أنا بدي إياه يبقى لو 
+
+387
+00:46:57,920
+
+431
+00:51:43,390 --> 00:51:55,890
+يبقى هذا الكلام يساوي سالب طول لنت لكل تقييم أو 
+
+432
+00:51:55,890 --> 00:52:01,530
+لنت كيب T لو كتبتيه لنت كيب T ما عنا مشكلة وبنروح 
+
+433
+00:52:01,530 --> 00:52:08,810
+ونقول زائد constant C1 وهنا بنقول تاك C1 بده يساوي 
+
+434
+00:52:08,810 --> 00:52:17,050
+Zero تمام يبقى هذا بده يعطيلك انه مين إن ال U1 بده 
+
+435
+00:52:17,050 --> 00:52:25,080
+يساوي سالب طول لنت لكل تكيب بنروح نجيب له مان اللي 
+
+436
+00:52:25,080 --> 00:52:32,860
+هو U2 يبقى U2 as a function of T بيساوي تكامل Y1 
+
+437
+00:52:32,860 --> 00:52:38,720
+of T في G of T على الرونسكين as a function of T dt
+
+438
+00:52:40,640 --> 00:52:46,260
+يبقى هذا الكلام بده يسوي تكامل Y1 اللي هو T تربيع
+
+439
+00:52:46,260 --> 00:52:52,900
+فقط لغير يبقى T تربيع و ال G of T اللي طلعت عندنا
+
+440
+00:52:52,900 --> 00:53:00,080
+اللي هي لن T و الرنس كان اللي هو قداش كان T تكيب
+
+441
+00:53:00,080 --> 00:53:10,790
+DT يبقى صار تكامل للن T على ت دي ت أو تكامل ل لن ت
+
+442
+00:53:10,790 --> 00:53:19,610
+مشتقة لن ت عظيم نضيف للأس واحد و بنجسم على الأسر
+
+443
+00:53:19,610 --> 00:53:24,950
+يعني لن ت لكل تربيع على اتنين يعني النص
+
+444
+00:53:27,170 --> 00:53:37,710
+لنتي الكل تربيع زائد كونستان C2 و بناخد C2 بقداش B0
+
+445
+00:53:37,710 --> 00:53:47,610
+يبقى أصبح U2 بده يساوي من اللي هو نص لنتي الكل
+
+446
+00:53:47,610 --> 00:53:53,880
+تربيع إذا بقدر أجيب له شكل ال particular solution
+
+447
+00:53:53,880 --> 00:54:03,720
+يبقى capital Y of T بديه 7 وين capital Y؟ U1 في T 
+
+448
+00:54:03,720 --> 00:54:09,660
+تربية وين ال U1؟ هذي ال U1 بدي أضربها في قداش في T
+
+449
+00:54:09,660 --> 00:54:18,970
+تربية يبقى سالب تلت T تربيع سالب تلت T تربيع تي
+
+450
+00:54:18,970 --> 00:54:31,730
+تربيع في لين تيل كل تكيب اللي بعده زائد مصر في من؟
+
+451
+00:54:31,730 --> 00:54:42,190
+في .. where راحت؟ الكلمة بتلعب في T تربيع في
+
+452
+00:54:42,190 --> 00:54:49,310
+ال لن T كل تكعيب مظبوط لإن وعندي ال لن T وعندي ال لن
+
+453
+00:54:49,310 --> 00:54:55,610
+T تربيع يبقى بيصير سالب تلت زائد نص بيبقى الجداش
+
+454
+00:54:55,610 --> 00:54:57,970
+زائد سادس 
+
+455
+00:55:05,890 --> 00:55:11,210
+هذا البرتكيرال سوليوشن اللي بده لو قاللي هاتلي ال
+
+456
+00:55:11,210 --> 00:55:17,010
+general solution بروح بجمعله هذا مع من مع اللي فوق
+
+457
+00:55:17,010 --> 00:55:20,010
+بجيب لمين ال general solution
+
+458
+00:55:25,200 --> 00:55:46,880
+بنتهي هذا الفيديو وانتهي 
+
+459
+00:55:46,880 --> 00:55:47,600
+هذا الفيديو
+
+460
+00:55:52,960 --> 00:55:57,080
+هل تحب تسأل اي سؤال هنا يا بنان؟ يبقى هذا السؤال
+
+461
+00:55:57,080 --> 00:56:02,820
+يختلف عن سابقاها بإن المعاملات ما هي اجتماعات
+
+462
+00:56:02,820 --> 00:56:08,360
+وإنما دوال في T كان بإمكاني أصي هذه السؤال بصيغة 
+
+463
+00:56:08,360 --> 00:56:17,880
+أخرى أقول لك سؤال كتالي if Y1 يسوى T تربيع is a
+
+464
+00:56:17,880 --> 00:56:22,210
+solution لل differential equation هذه؟ هتيلي الحل 
+
+465
+00:56:22,210 --> 00:56:26,970
+الثاني تمام؟ يبقى مقدميش إلا ال reduction of order
+
+466
+00:56:26,970 --> 00:56:31,910
+إجباري في شغلها ليش المعاملات ما هيش ثوابت يبقى 
+
+467
+00:56:31,910 --> 00:56:34,870
+بروح بجيب ال reduction of order و بجيب الحل التاني
+
+468
+00:56:34,870 --> 00:56:40,090
+لازم يطلع الحل التاني على الشكل هنا تمام؟ وبالتالي
+
+469
+00:56:40,090 --> 00:56:43,530
+جيبتله الحل اللي فوق و بعدين بروح بجيبله particle
+
+470
+00:56:43,530 --> 00:56:47,610
+of solution اللي جيبناه اللي عندنا هنا وكتير بيجي
+
+471
+00:56:47,610 --> 00:56:52,430
+في الامتحانات زيك لكن إن غلطة في الحل التاني غلطة
+
+472
+00:56:52,430 --> 00:56:58,790
+في الحل الكلي بيصير مظبوط أو كان بممكن اقولك بس إن
+
+473
+00:56:58,790 --> 00:57:01,730
+قلتك تأكديلي إن هذا حل تاني بتروح تعوضلي في
+
+474
+00:57:01,730 --> 00:57:05,530
+المعادرة لكن قلتك use reduction of order to find
+
+475
+00:57:05,530 --> 00:57:09,670
+أو to show that the second solution is كذا ومن ثم 
+
+476
+00:57:09,670 --> 00:57:12,270
+هتي ال solution يبقى بدك استخدم ال reduction of
+
+477
+00:57:12,270 --> 00:57:19,850
+order و بعدين تروح لمين هل بتسأل أي سؤال؟ 
+
+478
+00:57:44,440 --> 00:57:49,420
+طبعا بنتح ناك خلصنا لحد هنا الامتحان لكن أحيانا
+
+479
+00:57:49,420 --> 00:57:53,320
+بنجيب مسائل على غير ما اتعودنا في المحاضرات
+
+480
+00:57:53,320 --> 00:57:58,480
+الماضية كيف؟ يعني بيجيش السؤال مباشر بيقولك حل 
+
+481
+00:57:58,480 --> 00:58:01,880
+المسألة دي باستخدام التعويضة الفلانية و بروح 
+
+482
+00:58:01,880 --> 00:58:05,080
+بيعطينا التعويضة معينة و أنا بدأ أستخدم التعويضة
+
+483
+00:58:05,080 --> 00:58:10,140
+هذه في حل المسألة كيف المسألة يمكن تطلع first
+
+484
+00:58:10,140 --> 00:58:14,310
+order ويمكن تطلع second order و انطلعت first order
+
+485
+00:58:14,310 --> 00:58:18,810
+يمكن exact يمكن homogeneous يمكن separable يمكن 
+
+486
+00:58:18,810 --> 00:58:23,090
+linear يمكن Bernoulli يمكن أشوف المعادل المناسب و
+
+487
+00:58:23,090 --> 00:58:30,210
+أروح احلبها يمكن تبقى المثل second order يمكن يطلع
+
+488
+00:58:30,210 --> 00:58:33,790
+question with y missing question with d missing
+
+489
+00:58:34,060 --> 00:58:37,040
+يمكن يطلع لـ non-homogeneous differential
+
+490
+00:58:37,040 --> 00:58:40,240
+equation، variation of parameters أو undetermined
+
+491
+00:58:40,240 --> 00:58:43,840
+coefficients يبقى أنا بدي أشوف المناسب اللي عندي و 
+
+492
+00:58:43,840 --> 00:58:48,320
+أروح أحل المثلة بالطريقة التي تناسبها 
+
+493
+00:58:52,610 --> 00:58:57,490
+الاسئلة و بدى أجيبهم لكم الامتحانات السابقة مشان
+
+494
+00:58:57,490 --> 00:59:01,850
+نعرف كيف بدى نشتغل هالشغل هادى يبقى احنا مسائل
+
+495
+00:59:01,850 --> 00:59:09,920
+عامة الآن على شبطر اتنين و شبطرتلاتة كويس يبقى هنا
+
+496
+00:59:09,920 --> 00:59:14,440
+exercises
+
+497
+00:59:14,440 --> 00:59:28,660
+أو examples on using باستخدام substitution استخدام 
+
+498
+00:59:28,660 --> 00:59:37,230
+التعويد substitution to solve thedifferential
+
+499
+00:59:37,230 --> 00:59:42,470
+equation أول
+
+500
+00:59:42,470 --> 00:59:52,490
+سؤال جبناه في امتحان سنة الألفين بيقول use the 
+
+501
+00:59:52,490 --> 00:59:55,890
+substitution
+
+502
+00:59:55,890 --> 01:00:08,230
+استخدم التعويضة U تساوي E أس Y to solve the
+
+503
+01:00:08,230 --> 01:00:18,870
+differential equation المعادلة التفاضلية X Y ناقص 
+
+504
+01:00:18,870 --> 01:00:24,270
+X تكيب في E أس ناقص Y يساوي 2
+
+505
+01:01:01,570 --> 01:01:04,850
+واضح إنه السؤال تبعناه the first order 
+
+506
+01:01:04,850 --> 01:01:08,470
+differential equation وليس second order بقول
+
+507
+01:01:08,470 --> 01:01:12,670
+يستخدم التعويضة U تساوي E اص Y to solve the 
+
+508
+01:01:12,670 --> 01:01:17,150
+differential equation سؤالي هو هل في في مثلة كلها
+
+509
+01:01:17,150 --> 01:01:24,310
+E اص Y؟ لأ في عندي ايش؟ E اص سالب Y اذا ممكن اتخلص 
+
+510
+01:01:24,310 --> 01:01:28,690
+من E اص سالب Y و أحول مثلة كلها بدلالة مين؟ يبقى
+
+511
+01:01:28,690 --> 01:01:33,570
+بروح أضرب كله في مين؟ في الـ E أُس Y المعادلة يبقى
+
+512
+01:01:33,570 --> 01:01:39,870
+باجي بقوله solution بدي أضرب كله في E أُس Y إيش
+
+513
+01:01:39,870 --> 01:01:46,410
+بصير يا بنات؟ X في E أُس Y في الـY' ناقص X تكيب 
+
+514
+01:01:46,410 --> 01:01:54,210
+تساوي 2E أُس Y تمام؟ يبقى بطل يصير عندي E أُس ناقص
+
+515
+01:01:54,210 --> 01:02:04,860
+Y كله بدلالة E أُس Y هذه الـ U تساوي U² بدي أشتق
+
+516
+01:02:04,860 --> 01:02:13,620
+يبقى دي U على دي X يبقى هنا دي U على دي X يعني منه
+
+517
+01:02:13,620 --> 01:02:19,820
+U' تساوي اشتقاق هذه بالنسبة إلى X يبقى مشتقة الـ 
+
+518
+01:02:19,820 --> 01:02:25,120
+exponential بالـ exponential itself في المشتقة 
+
+519
+01:02:25,120 --> 01:02:29,760
+تبعتها المعلومات اللي حصلت عليها بدي اعوضها في
+
+520
+01:02:29,760 --> 01:02:37,420
+المعادلة هذه اطلعيلي هذه جداش ب U prime يبقى ثارة
+
+521
+01:02:37,420 --> 01:02:45,440
+X في ال U prime ناقص X تكيب يساوي اتنين U
+
+522
+01:02:48,250 --> 01:02:51,550
+طيب شو رايك اكتبها على الشكل التالي
+
+523
+01:03:00,250 --> 01:03:05,270
+مش رايك أجسم على مين؟ على X يبقى لو جسمت على X
+
+524
+01:03:05,270 --> 01:03:15,090
+بصير U' ناقص اتنين على X هذه كلها في ال U ناقص
+
+525
+01:03:15,090 --> 01:03:20,310
+اتنين على X في ال U بده يساوي X تربيع مش رايكوا 
+
+526
+01:03:20,310 --> 01:03:26,170
+فيها هذه؟ لين؟ يبقى خلاص صارت زي أول ماخدنا في 
+
+527
+01:03:26,170 --> 01:03:33,700
+الشاب طريق اتنين يبقى هذه linear first order
+
+528
+01:03:33,700 --> 01:03:41,750
+differential equation كذا كنا بنحل ال linear من هنا 
+
+529
+01:03:41,750 --> 01:03:48,470
+نقول ميو اف اكس يساوي اي اث ناقص اتنين تكامل واحد 
+
+530
+01:03:48,470 --> 01:03:55,410
+على اكس مالها دي اكس يبقى اي اث ناقص اتنين لن
+
+531
+01:03:55,410 --> 01:04:01,170
+absolute في الاكس اللي مش حرطش عندي بقول له اه يبقى 
+
+532
+01:04:01,170 --> 01:04:06,410
+هذه absolute value ل X أُس ناقص اتنين يعني واحد على 
+
+533
+01:04:06,410 --> 01:04:10,710
+X تربيع كمية مربعة لإن تربيع حطيت ال absolute و لا
+
+534
+01:04:10,710 --> 01:04:17,150
+شيلتي سيان يبقى صار هذا الميو of X بدي أخد الميو
+
+535
+01:04:17,150 --> 01:04:21,730
+of X و روح شو عمله بدي أضربه في المعادلة اللي عندنا
+
+536
+01:04:21,730 --> 01:04:25,880
+هذه يبقى ايش بيصير المعادلة هذه على الشكل التالي
+
+537
+01:04:25,880 --> 01:04:31,860
+واحد على X تربيع U prime ناقص بدي اضرب في واحدة
+
+538
+01:04:31,860 --> 01:04:38,200
+اللي يبقى ناقص اتنين على X تكيب في ال U بدي ساوي
+
+539
+01:04:38,200 --> 01:04:45,620
+قداش بدي ساوي واحد أو بمعنى آخر هذه واحد على X
+
+540
+01:04:45,620 --> 01:04:52,590
+تربيع في ال U كله prime بيساوي قداش إن كامل الطرفين
+
+541
+01:04:52,590 --> 01:04:59,810
+يبقى بصير واحد على X تربيع في ال U واحد على X
+
+542
+01:04:59,810 --> 01:05:06,390
+تربيع في ال U بدي شوي X زائد constant C
+
+543
+01:05:08,500 --> 01:05:15,040
+مضرب كله في من؟ في ال X تربيع يبقى بصير ال U مين 
+
+544
+01:05:15,040 --> 01:05:24,040
+هي ال U هذه؟ E أوس Y يبقى E أوس Y يساوي X تكيب
+
+545
+01:05:24,040 --> 01:05:31,640
+زائد C X تربيع تمام؟ احنا بدنا E أوس Y ولا بدنا Y
+
+546
+01:05:31,640 --> 01:05:41,770
+الحل؟ نأخد لن للطرفين إذا ال Y بدها تساوي لن اللي 
+
+547
+01:05:41,770 --> 01:05:51,590
+هو X تكيب زائد C X تربيع هذا هو الحل اللي عندنا
+
+548
+01:05:51,590 --> 01:05:56,010
+خلاص نعطيكم
+
+549
+01:05:56,010 --> 01:05:57,010
+مثال آخر
+
+550
+01:06:00,310 --> 01:06:05,590
+مثال سنة تسعة وتسعين هذا سنة اللي جابلها يبقى هذا
+
+551
+01:06:05,590 --> 01:06:12,250
+اتنين سنة التلات تسعات انتخابات عربية بقول ي solve
+
+552
+01:06:12,250 --> 01:06:20,750
+the differential equation حل المعادلة التفاضلية y
+
+553
+01:06:20,750 --> 01:06:42,700
+في y double prime ناقص y prime تربيع يستخدم
+
+554
+01:06:42,700 --> 01:06:53,680
+تعويض
+
+555
+01:06:54,340 --> 01:07:03,680
+V تساوي لن ال Y طب
+
+556
+01:07:03,680 --> 01:07:08,300
+لو ماعطانيش التعويضة هذه وجه بقى طالع في المثل
+
+557
+01:07:08,300 --> 01:07:12,760
+الأول واهلة ايش ممكن تقولي عن المثل اللي فوق هذه
+
+558
+01:07:12,760 --> 01:07:21,510
+question with with ايش T missing T مفقودة يبقى تروح
+
+559
+01:07:21,510 --> 01:07:25,890
+احلها على equation والـ T مسك لكن كونه وطني تعويضة 
+
+560
+01:07:25,890 --> 01:07:32,130
+بدأ أضطر استخدمين هذه التعويضة طيب التعويضة هذه 
+
+561
+01:07:32,130 --> 01:07:39,730
+ممكن أكتبها بشكل آخر احنا عندنا مين ال V يسوى اللي 
+
+562
+01:07:39,730 --> 01:07:47,110
+لنا ال Y إذا لو رفعت اتنين كأس للعدد E بصير هنا ال 
+
+563
+01:07:47,110 --> 01:07:50,410
+Y تساوي E أس V
+
+564
+01:07:55,180 --> 01:08:02,800
+طب ايش رأيكوا بدي أشتقها؟ بدي أشتقها بالنسبة لمن؟
+
+565
+01:08:02,800 --> 01:08:08,280
+ل T أو كانت في X أو اتبعها في X بدي أشتقها بالنسبة 
+
+566
+01:08:08,280 --> 01:08:14,900
+ل X بالنسبة ل T ما عنا مشكلة يبقى بداجي اقول دي Y
+
+567
+01:08:14,900 --> 01:08:22,230
+by دي T اللي هو Y prime يجب أن يكون مشتقة الـ EOSV 
+
+568
+01:08:22,230 --> 01:08:30,150
+بالـ EOSV السلفين في الـ V' طيب إذا بدى أروح أجيب
+
+569
+01:08:30,150 --> 01:08:37,750
+المشتقة الثانية يبقى هذه مشتقة حاصل ضب دلتين يبقى 
+
+570
+01:08:37,750 --> 01:08:47,350
+EOSV في مشتقة الدلة الثانية VW' زائد ال V' زي ما هي
+
+571
+01:08:47,350 --> 01:08:56,690
+في مشتقة ال EOSV ب EOSV في ال V' يبقى صارة المشتقة
+
+572
+01:08:56,690 --> 01:09:07,570
+اللي عندي VW' زائد V' لكل تربيع كله في EOSV
+
+573
+01:09:10,030 --> 01:09:14,850
+بناخد هذه المعلومات ونعوضها في المعادلة اللي عندنا
+
+574
+01:09:14,850 --> 01:09:20,610
+هنا هذي سميها للمعادلة star نجي نقول هنا
+
+575
+01:09:20,610 --> 01:09:26,570
+substitute and
+
+576
+01:09:26,570 --> 01:09:31,090
+equation star we get
+
+577
+01:09:33,740 --> 01:09:40,120
+الـ Y هشيلها و اكتب بدلها مين؟ E Os V يبقى E Os V
+
+578
+01:09:40,120 --> 01:09:50,340
+الـ Y W Prime هيه يبقى بصير عندي E Os 2 V في مين؟
+
+579
+01:09:50,340 --> 01:09:57,260
+في الـ V W Prime نقص V Prime لكل تربيه هي خلصنا 
+
+580
+01:09:57,260 --> 01:10:05,350
+منها الان ال Y' و Y' يجب أن أربعها لأنها تربيه
+
+581
+01:10:16,490 --> 01:10:23,510
+في الاصل منها بدها تساوي Y تربيع ل E أس اتنين V
+
+582
+01:10:23,510 --> 01:10:31,750
+يبقى E أس اتنين V لإن ال Y هو ميعطينيها بقداش V
+
+583
+01:10:31,750 --> 01:10:38,270
+طيب ايش رايكوا أبسط المعادلة كلها من أولها لآخرها
+
+584
+01:10:38,270 --> 01:10:44,950
+نقسم عالميا على E أس اتنين V لأن هو رقم أكبر من 
+
+585
+01:10:44,950 --> 01:10:45,270
+Zero
+
+586
+01:10:57,780 --> 01:11:05,200
+طيب يبقى آلة المسألة الشكل التالي بعد القسمة
+
+587
+01:11:07,130 --> 01:11:14,350
+زائد v prime تربيع ناقص v prime تربيع بده يسوى 
+
+588
+01:11:14,350 --> 01:11:22,010
+قداش v اظن هذه وهذه مع السلامة تمام يبقى آلة
+
+589
+01:11:22,010 --> 01:11:29,430
+المسألة الى v double prime ناقص v تسوى zero
+
+590
+01:11:31,650 --> 01:11:35,950
+هوموجينياس differential equation من ال second
+
+591
+01:11:35,950 --> 01:11:42,010
+order كيف بنحلها يعني
+
+592
+01:11:42,010 --> 01:11:44,870
+بدنا نروح نجيب ال characteristic equation ممتاز 
+
+593
+01:11:44,870 --> 01:11:49,030
+جدا يبقى بدنا نروح نحلها بواسطة ال characteristic
+
+594
+01:11:49,030 --> 01:11:59,120
+equation يبقى باجي بقوله let V تساوي E أس RT ب
+
+595
+01:11:59,120 --> 01:12:02,200
+Solution
+
+596
+01:12:02,200 --> 01:12:08,500
+then the characteristic 
+
+597
+01:12:08,500 --> 01:12:20,140
+equation is R تربيع ناقص واحد يساوي Zero يبقى هاد 
+
+598
+01:12:20,140 --> 01:12:28,180
+ايش؟ R تساوي زائد أو ناقص مين واحد يبقى معنا هذا
+
+599
+01:12:28,180 --> 01:12:39,760
+الكلام إن V بتصير عندنا
+
+600
+01:12:39,760 --> 01:12:47,720
+ال V of T as a function of T هي عبارة عن C1 EOS T
+
+601
+01:12:47,720 --> 01:12:58,910
+C2 EOS ناقص T مظبوط؟ لكن V of T مين هي؟ لن ال Y إذا
+
+602
+01:12:58,910 --> 01:13:05,070
+لن ال Y هي اللي بتسوي هذا الكلام هذا بدي أعطيكي إن 
+
+603
+01:13:05,070
+
+646
+01:18:30,900 --> 01:18:36,940
+من الرتبة الثانية إلى مين؟ إلى الرتبة الأولى
+
+647
+01:18:36,940 --> 01:18:43,260
+يبقى صارت مسألة بسيطة جدا يبقى ده W prime ناقص
+
+648
+01:18:43,260 --> 01:18:50,580
+واحد على X W بدي أساوي قداش؟ بساوي Zero تمام؟ يعني
+
+649
+01:18:50,580 --> 01:18:59,240
+بصير عندك W prime على W بدي أساوي قداش؟ واحد على X
+
+650
+01:18:59,240 --> 01:19:07,820
+نكامل؟ يبقى لو كاملنا بصير ln الـW  فما في داعي لل
+
+651
+01:19:07,820 --> 01:19:13,660
+absolute value لأنها بالموجب تمام؟ بده يساوي كمان
+
+652
+01:19:13,660 --> 01:19:19,900
+ln ال X ولا داعي لأن ال X greater than zero زائد
+
+653
+01:19:19,900 --> 01:19:26,140
+constant C طيب إيش رأيك ال constant C؟ لو كتبت ln
+
+654
+01:19:26,140 --> 01:19:31,720
+C، بيمشي الحال؟ ما فيش مشكلة أوك و lnC زي ما بدك طب
+
+655
+01:19:31,720 --> 01:19:36,540
+ليش سويت هيك؟ هذا اللي بدنا نجاوب عليه نجاوب عليه
+
+656
+01:19:36,540 --> 01:19:45,840
+بصير المسألة lnW يساوي lnXC ln زائد ln بقدر أشبهها
+
+657
+01:19:45,840 --> 01:19:49,640
+بالـln وبقدر أطيّر اللنات وبالتالي لازم يطلع عندي
+
+658
+01:19:49,640 --> 01:19:55,940
+ln ولا exponential يبقى هذه ln و ln بقدر أرفع
+
+659
+01:19:55,940 --> 01:20:04,940
+اتنين قوى للعدد إيه يبقى W بدها تساوي X في C مضبوط
+
+660
+01:20:04,940 --> 01:20:12,850
+طيب نيجي هنا نقول هذه ال W بقداش يا بنات؟ Y'-Y يبقى
+
+661
+01:20:12,850 --> 01:20:27,010
+Y'-Y يساوي 6 إيش الشكل المعادلة هذه إيش
+
+662
+01:20:27,010 --> 01:20:33,130
+اسمها Linear مظبوط يبقى Linear إحنا حلينا المسألة
+
+663
+01:20:33,130 --> 01:20:37,990
+الأولانية تكامل عادي جدا طلعت لمعادلة جديدة Linear
+
+664
+01:20:37,990 --> 01:20:45,990
+First Order يبقى هذه linear first order
+
+665
+01:20:45,990 --> 01:20:54,690
+differential equation تمام يعني إيش اللي حصل؟ أجيب
+
+666
+01:20:54,690 --> 01:21:01,630
+طريقتين من الطرق بسؤال واحد، أعوض هذه قادتني إلى
+
+667
+01:21:01,630 --> 01:21:06,190
+separable equation ال W في شجرة و ال X في شجرة يبعد
+
+668
+01:21:06,190 --> 01:21:10,420
+ال separable equation واسيبربوا قادتنا إلى من؟
+
+669
+01:21:10,420 --> 01:21:15,060
+إلى ال linear من هنا أجت أهمية من؟ أهمية السؤال
+
+670
+01:21:15,060 --> 01:21:18,640
+يعني السؤال اللي ممكن أختار مش ببلاش يعطيك لأ أنا
+
+671
+01:21:18,640 --> 01:21:22,960
+قاصد ومتعمد أجيبك طريقتين أو معادلتين من اللي
+
+672
+01:21:22,960 --> 01:21:28,520
+اتعلمتي تحليهم مشان نيجي نحلهم هنا بسؤال يعني بيستاهل
+
+673
+01:21:28,520 --> 01:21:33,980
+يكون سؤال امتحان مضبوط طيب كويس يبقى بنحلها بال
+
+674
+01:21:33,980 --> 01:21:40,220
+linear بسيطة جدا هذه جاهزة كويس يبقى باجي بقول لمين؟
+
+675
+01:21:40,220 --> 01:21:47,920
+U of X دو يساوي E أس ناقص تكامل DX ما عنديش المعامل
+
+676
+01:21:47,920 --> 01:21:55,140
+سالب واحد يبقى يساوي E أس ناقص X بدي أروح أضرب
+
+677
+01:21:55,140 --> 01:22:01,500
+المعادلة اللي فوق هذه في E أس ناقص X بصير E أس ناقص
+
+678
+01:22:01,500 --> 01:22:10,280
+X في Y prime ناقص E أس ناقص X في Y يساوي CX في E أس
+
+679
+01:22:10,280 --> 01:22:19,440
+ناقص X أو بمعنى آخر هذه الآن E أس ناقص X في Y الكل
+
+680
+01:22:19,440 --> 01:22:29,280
+prime يساوي CX E أس ناقص AX انكملي يبقى E أس ناقص X
+
+681
+01:22:29,280 --> 01:22:40,100
+في Y يساوي تكامل CX في E أس ناقص X في DX تكامل هذه
+
+682
+01:22:40,100 --> 01:22:47,720
+بيعطيني تكامل هذا هذا CX أيوة كيف نكامل هذا؟ كيف؟
+
+683
+01:22:47,720 --> 01:22:52,180
+by parts عادي جدا وعلى الجدول كمان مش لسه بدي U و D لأ
+
+684
+01:22:52,180 --> 01:22:57,170
+لأ جاهزين إذا باجي بقوله على الجدول بقول له هنا
+
+685
+01:22:57,170 --> 01:23:03,270
+derivatives وهنا بدي أجيب له integrals إيش ال
+
+686
+01:23:03,270 --> 01:23:08,170
+derivatives بدي أخد له CX و ال integrals بدي أخد له
+
+687
+01:23:08,170 --> 01:23:17,040
+E-x تفاضل هذه بقداش؟ بـC تكامل E أس ناقص E أس ناقص X
+
+688
+01:23:17,040 --> 01:23:22,140
+يعني E أس ناقص X على ناقص واحد يعني ناقص E أس ناقص X
+
+689
+01:23:22,140 --> 01:23:29,740
+تفضل الـC بقدرش بـ0 تكامل E أس ناقص X E أس ناقص X
+
+690
+01:23:29,740 --> 01:23:36,340
+إشارة موجب وإشارة موجب إشارة سالب يبقى النتيجة إشارة
+
+691
+01:23:36,340 --> 01:23:45,660
+E أس ناقص X في الـY بدها تساوي ناقص CX E ناقص X ناقص
+
+692
+01:23:45,660 --> 01:23:52,860
+C E ناقص X زائد constant من C1 تبع التكامل ما 
+
+693
+01:23:52,860 --> 01:23:56,900
+ننساهوش هذا لأن إحنا عند المشتق الثاني معناته عندي
+
+694
+01:23:56,900 --> 01:24:03,370
+two constants طيب نضرب فيه و E أس X هذه مش هنتخلص
+
+695
+01:24:03,370 --> 01:24:10,970
+منها نحصل على Y يبقى Y حتساوي سالب CX وهنا سالب C
+
+696
+01:24:10,970 --> 01:24:20,910
+وهنا زائد C1 E أس X يبقى هذا شكل الحل اللي عندنا
+
+697
+01:24:20,910 --> 01:24:23,350
+تبع من؟ تبع المسألة
+
+698
+01:24:36,050 --> 01:24:42,170
+طيب في سؤال جبته أنا في امتحان لطلبة طلبات في ال
+
+699
+01:24:42,170 --> 01:24:50,810
+2005 بيقول ما يأتي هذا قداش؟ تلاتة هذا أربعة وهذا 
+
+700
+01:24:50,810 --> 01:25:00,150
+في ال 2005 بيقول use the substitution use the
+
+701
+01:25:00,150 --> 01:25:02,150
+substitution
+
+702
+01:25:06,490 --> 01:25:20,290
+U يساوي Y ناقص X تساوي الـ differential equation
+
+703
+01:25:20,290 --> 01:25:35,690
+لتحل المعادلة التفاضلية Dy بDX يساوي Sine تربيع Y
+
+704
+01:25:35,690 --> 01:25:51,330
+ناقص X يبقى
+
+705
+01:25:51,330 --> 01:25:58,130
+أنا بدي أجيب للتعويض اللي أعطاه لي جالي ليه يساوي Y
+
+706
+01:25:58,130 --> 01:26:03,350
+ناقص X كنت أستخدم هذه التعويضة في حل المعادلة اللي
+
+707
+01:26:03,350 --> 01:26:09,310
+عندنا إحنا نتدرج نقول إن Sine تربيع Y أو Sine
+
+708
+01:26:09,310 --> 01:26:14,150
+تربيع X ونقول إيش؟ Sine تربيع Y ناقص X إذا بدي أروح
+
+709
+01:26:14,150 --> 01:26:17,710
+أشيل Y ناقص X وأحط مكانها U يبقى هاي شيلناها وحطينا
+
+710
+01:26:17,710 --> 01:26:22,770
+بدلها مين؟ حطينا بدلها U يبقى يا بنات لو جيت
+
+711
+01:26:22,770 --> 01:26:31,170
+قلت بدي ال U' ال U' يعني مين؟ ال dU على dX نكتبها
+
+712
+01:26:31,170 --> 01:26:36,170
+بالتفصيل، بلاش تقولها يعني بدي أشتق الدالة كلها
+
+713
+01:26:36,170 --> 01:26:46,250
+بالنسبة إلى X يبقى DY على DX ومشتقة ال X بقدرش بـ 1
+
+714
+01:26:47,000 --> 01:26:54,500
+يبقى بناء على اليسار عندنا dU على dX زائد
+
+715
+01:26:54,500 --> 01:27:00,180
+واحد بدها تساوي dY على dX إذا بدي أجيب
+
+716
+01:27:00,180 --> 01:27:05,240
+المقاس اللي بتبعثيه أشيل dY على dX وأكتب
+
+717
+01:27:05,240 --> 01:27:10,920
+بدلها dY على dX زائد واحد يبقى هنا إيش بصير؟
+
+718
+01:27:10,920 --> 01:27:18,730
+ال dY على dX اللي هي dY على dX زائد واحد
+
+719
+01:27:18,730 --> 01:27:28,770
+يساوي من؟ يساوي ال Sine تربيع ال U تمام تمام يبقى
+
+720
+01:27:28,770 --> 01:27:37,030
+بدل مكان المتغير Y و X صار المتغير U و X تمام يبقى
+
+721
+01:27:37,030 --> 01:27:46,110
+هذه بصير main اللي هو dU على dX يساوي Sine تربيع
+
+722
+01:27:46,110 --> 01:27:55,580
+ال U ناقص واحد كويس؟ طب إيش رأيك لو جيت قلت لك هذه
+
+723
+01:27:55,580 --> 01:28:05,010
+تساوي ناقص واحد ناقص Sine تربيع ال U، بنفع؟ طب اللي
+
+724
+01:28:05,010 --> 01:28:10,690
+بين قوسين هي مين؟ قوسين تربيع ال U يبقى صار عندنا
+
+725
+01:28:10,690 --> 01:28:19,750
+مين؟ اللي هو dU على dX يساوي ناقص قوسين تربيع ال U
+
+726
+01:28:19,750 --> 01:28:25,240
+شو رأيك نفصل المتغيرات؟ يبقى صارت separation of
+
+727
+01:28:25,240 --> 01:28:35,280
+variable صار dU على Cosine تربيع ال U يساوي ناقص DX
+
+728
+01:28:35,280 --> 01:28:41,700
+فقط لغير أو أنشئنا فقلنا واحد على Cosine تربيع ال
+
+729
+01:28:41,700 --> 01:28:51,780
+U منين؟ Sine تربيع ال U dU سالب DX نكامل الطرفين
+
+730
+01:28:52,940 --> 01:29:00,020
+قداش؟ نكامل Sine بيه U dU بتان ال U يبقى تان
+
+731
+01:29:00,020 --> 01:29:09,160
+ال U يساوي ناقص X زائد constant C طب أنا مين؟ بدي
+
+732
+01:29:09,160 --> 01:29:16,330
+تان ال U بدي ال U يبقى بناء عليه ال U ها دي بدها
+
+733
+01:29:16,330 --> 01:29:23,670
+تساوي Tan inverse ل C ناقص X
+
+734
+01:29:27,310 --> 01:29:33,210
+مظبوط إيه؟ يعني ناخد تان انفرس للطرفين باجي بقول U
+
+735
+01:29:33,210 --> 01:29:40,910
+هي عبارة عن مين؟ Y ناقص X يبقى صار عندي Y ناقص X
+
+736
+01:29:40,910 --> 01:29:48,970
+يساوي Tan inverse ل C ناقص ال X ونودي ال X على الشجرة
+
+737
+01:29:48,970 --> 01:29:54,190
+التانية يبقى حصلنا على الحل تبع المسألة يبقى هذا
+
+738
+01:29:54,190 --> 01:30:06,180
+يعطينا إن Y تساوي X زائد Tan inverse لمن؟ ل C ناقص
+
+739
+01:30:06,180 --> 01:30:12,960
+X الشكل اللي عندنا هذا هو الحل تبع المعادلة L عن N
+
+740
+01:30:15,420 --> 01:30:19,620
+يبقى هي عندك بدل السؤال أربعة أسئلة وكلها تعويضات
+
+741
+01:30:19,620 --> 01:30:23,800
+وكلها مسائل امتحانات يعني لو جيبنالكم سؤال في
+
+742
+01:30:23,800 --> 01:30:28,560
+الامتحان القادم إن شاء الله يكون هي ضربناكي على
+
+743
+01:30:28,560 --> 01:30:35,240
+مين؟ على أمثلة على هذا الموضوع طبعا حد في كل هذه
+
+744
+01:30:35,240 --> 01:30:40,730
+التساؤلات المرة القادمة إن شاء الله يوم الأربعاء بنبدأ 
+
+745
+01:30:40,730 --> 01:30:44,690
+chapter أربعة يوم الأربعاء بنبدأ chapter أربعة إن
+
+746
+01:30:44,690 --> 01:30:49,130
+شاء الله chapter أربعة هو تعميم ل chapter تلاتة
+
+747
+01:30:49,130 --> 01:30:52,570
+يعني بيبقى ال second order بيشوف third order
+
+748
+01:30:52,570 --> 01:30:56,090
+fourth order and nth order تمام؟
diff --git a/PL9fwy3NUQKwa8ZDfSFGn6H8xVFLzqmCZC/_NMCQUdH1C8_postprocess.srt b/PL9fwy3NUQKwa8ZDfSFGn6H8xVFLzqmCZC/_NMCQUdH1C8_postprocess.srt
new file mode 100644
index 0000000000000000000000000000000000000000..7b14edb1143443d9503dc7d7b8ba811d981dbb21
--- /dev/null
+++ b/PL9fwy3NUQKwa8ZDfSFGn6H8xVFLzqmCZC/_NMCQUdH1C8_postprocess.srt
@@ -0,0 +1,2992 @@
+1
+00:00:09,860 --> 00:00:14,730
+بسم الله الرحمن الرحيمالمرة الفاتة بدأنا في حلال
+
+2
+00:00:14,730 --> 00:00:18,510
+non homogeneous differential equation اللى على
+
+3
+00:00:18,510 --> 00:00:22,810
+الشكل اللى عندنا هذا star استخدمنا المرة الفاتة
+
+4
+00:00:22,810 --> 00:00:26,910
+طريقة ال undetermined coefficients طريقة المعاملات
+
+5
+00:00:26,910 --> 00:00:32,390
+المجهولة وقلنا اشترطنا شرطين الشرط الأول لازم يكون
+
+6
+00:00:32,390 --> 00:00:37,810
+المعاملات هدول ثوابت الشرط التانى لازم GOT تبقى
+
+7
+00:00:37,810 --> 00:00:42,320
+على شكل polynomialأو polynomial في exponential أو
+
+8
+00:00:42,320 --> 00:00:45,820
+polynomial في exponential في sin أو cos أو
+
+9
+00:00:45,820 --> 00:00:51,160
+مجموعهما أو الفرق في ما بينهما اليوم ان شاء الله
+
+10
+00:00:51,160 --> 00:00:54,900
+ناخد طريقة جديدة اسمها طريقة ال variation of
+
+11
+00:00:55,030 --> 00:01:02,470
+Parameters تغيير الوسيطات يعني في عندنا متغيرات
+
+12
+00:01:02,470 --> 00:01:06,530
+بدنا نستبدلها وفي عندنا شغلات بدنا نستبدلها بشغلات
+
+13
+00:01:06,530 --> 00:01:11,520
+أخرى، هاي المقصود بال variation of parametersإتنان
+
+14
+00:01:11,520 --> 00:01:17,020
+المعاملات ليست ثوابت و الله ماهياش ثوابت ممكن
+
+15
+00:01:17,020 --> 00:01:21,360
+يكونوا هدول ثوابت و ممكن مايكونوش ثوابت مستفرقش
+
+16
+00:01:21,360 --> 00:01:27,670
+عندنا إتنان ال G of T ياخد على أي شكل بدكياسواء
+
+17
+00:01:27,670 --> 00:01:31,190
+كان polynomial، exponential، مش polynomial، دوال
+
+18
+00:01:31,190 --> 00:01:35,570
+مثلثية، في ال bus، في المقام، في مش عارف ايه، اي
+
+19
+00:01:35,570 --> 00:01:39,310
+functions ماعنديش قيود على ال functions مش زي
+
+20
+00:01:39,310 --> 00:01:42,950
+طريقة ال undetermined coefficients ماعنديش قيود
+
+21
+00:01:42,950 --> 00:01:47,250
+بالمرة تتلخص هذه الطريقة باختصار يا بنات في الشكل
+
+22
+00:01:47,250 --> 00:01:50,340
+التاليباروح بجيب ال homogeneous differential
+
+23
+00:01:50,340 --> 00:01:54,820
+equation زي المرة الماضية و بجيب main الحل تبع ال
+
+24
+00:01:54,820 --> 00:02:02,330
+homogeneous و بكون الحل عندي على الشكل هذابعد هيك
+
+25
+00:02:02,330 --> 00:02:07,250
+مشان أجيب ال particular solution تبع المعادلة بجعل
+
+26
+00:02:07,250 --> 00:02:15,310
+ثوابت c1 و c2 بستبدلهم بدوال أخرى و التكون u1 و u2
+
+27
+00:02:15,310 --> 00:02:19,490
+يعني بصير ال particular solution ده اللي جديد اي
+
+28
+00:02:19,490 --> 00:02:25,750
+u1 مضروبة في الحل الأول اللي جيبناه y1 وزائد u2
+
+29
+00:02:25,750 --> 00:02:30,760
+مضروبة في الحل الثاني اللي هو u8إذا باختصار بنقول
+
+30
+00:02:30,760 --> 00:02:34,920
+ما يأتي اعتبر المعادلة التفاضلية الخطية مرتبة
+
+31
+00:02:34,920 --> 00:02:39,880
+ثانية بالشكل هذا المعامل تبع y double prime لازم
+
+32
+00:02:39,880 --> 00:02:44,400
+يكون واحد صحيح يعني لو ماكانش بدنا نروح إياه نجسم
+
+33
+00:02:44,400 --> 00:02:47,240
+على الدالة اللي موجودة في ال y double prime بحيث
+
+34
+00:02:47,240 --> 00:02:53,120
+أضمن دائما و أبدا أن شكل المعامل تبع y double
+
+35
+00:02:53,120 --> 00:02:54,180
+prime هو مام
+
+36
+00:03:07,860 --> 00:03:12,060
+الان نفترض مواعي واحد و اتنين لـnearly independent
+
+37
+00:03:12,060 --> 00:03:15,300
+solutions للـ homogeneous differential equation
+
+38
+00:03:15,300 --> 00:03:18,460
+يبقى صار الحل العام تبع الـ homogeneous
+
+39
+00:03:18,460 --> 00:03:22,810
+differential equation على الشكل اللى عندنا هذابقول
+
+40
+00:03:22,810 --> 00:03:27,010
+to find a particular solution مش هنتجيب الحل الخاص
+
+41
+00:03:27,010 --> 00:03:32,210
+للمعادلة بطريقة ال variation of parameters بتغيير
+
+42
+00:03:32,210 --> 00:03:37,970
+الوسيطات we replace the constants نستبدل replace
+
+43
+00:03:37,970 --> 00:03:45,380
+يعني نستبدلالثوابت C1 و C2 by two functions U1 as
+
+44
+00:03:45,380 --> 00:03:49,720
+a function of T و U2 as a function of T يعني بدي
+
+45
+00:03:49,720 --> 00:03:57,480
+أشيل C1 و أحط مكانها U1 و أشيل C2 و أحط مكانها U2
+
+46
+00:03:57,480 --> 00:04:02,800
+ليه بيطلع عندي بدي أسمع من ال particular solution
+
+47
+00:04:02,800 --> 00:04:09,430
+السؤال هو كيف بيجيب ال U1 و U2بنجي على الحل اللي
+
+48
+00:04:09,430 --> 00:04:14,150
+صار عندي ال بطاقر هو يساوي يواحد و يواحد زي ديو
+
+49
+00:04:14,150 --> 00:04:20,610
+اتنين و يتنام نشتاق مرة و نشتاق اتنين و نرجع نعوض
+
+50
+00:04:20,610 --> 00:04:25,080
+في المعادلة الأصلية اللي هو starأو نجمعه و نطرحه و
+
+51
+00:04:25,080 --> 00:04:29,560
+نجسمه و نختصره و نشتريه لغاية ما نوصل لمين لغاية
+
+52
+00:04:29,560 --> 00:04:32,740
+ما نوصل ان يوين يعني قصة طويلة بدنا على الأقل
+
+53
+00:04:32,740 --> 00:04:36,840
+مصارعة عشان نخلص الشغل هذه انسى الموضوع بهمن
+
+54
+00:04:36,840 --> 00:04:40,180
+تعرفيه الشكل ال يواحد as a function of the هو
+
+55
+00:04:40,180 --> 00:04:46,500
+عبارة عن سالب تكامل الحل الثاني احنا بدنا يواحد
+
+56
+00:04:46,500 --> 00:04:53,810
+يبقى باخد تكامل الحل الثاني ال Y2مضروب في الـ G of
+
+57
+00:04:53,810 --> 00:04:58,890
+T مقسم على الورلسكين تبع ال two solutions U Y واحد
+
+58
+00:04:58,890 --> 00:05:05,410
+وY اتنين بالمثل U اتنين هي تكامل Y واحد يعني كأنه
+
+59
+00:05:05,410 --> 00:05:09,850
+عكس U واحد معاها Y اتنين U اتنين معاها مين؟ Y واحد
+
+60
+00:05:09,850 --> 00:05:14,650
+يبقى بدون إشارة سالب في ال U one في إشارة سالب في
+
+61
+00:05:14,650 --> 00:05:18,120
+ال U two ماعنديش إشارة سالبيبقى ال U2 as a
+
+62
+00:05:18,120 --> 00:05:22,040
+function of T هي تكامل Y1 of T في G of T على
+
+63
+00:05:22,040 --> 00:05:27,280
+رونسكين تبع ال Y1 وY2 as a function of T يبقى هذا
+
+64
+00:05:27,280 --> 00:05:31,080
+ال رونسكين as a function of T وهذا ال رونسكين as a
+
+65
+00:05:31,080 --> 00:05:39,530
+function of T حصلت على U1 وU2 بضرب Y1 U1 Y2في U2 و
+
+66
+00:05:39,530 --> 00:05:43,810
+بجمع الاتنين بيعطوني الحل الخاص بدي ال general
+
+67
+00:05:43,810 --> 00:05:49,690
+solution بجمع الحل الخاص اللي حصلت عليه مع الحل
+
+68
+00:05:49,690 --> 00:05:53,890
+العام تبع ال homogeneous اتنين مع بعض تبقى النظرية
+
+69
+00:05:53,890 --> 00:05:58,490
+اللي خدناها المرة قبل الماضية و كنا بنحل عليها
+
+70
+00:05:58,490 --> 00:06:01,950
+المرة الماضيةبنجيب حل ال homogeneous و ال
+
+71
+00:06:01,950 --> 00:06:04,890
+particular solution تبع ال non homogeneous بنجمع
+
+72
+00:06:04,890 --> 00:06:07,850
+الاتنين بيعطينا ال general solution تبع المعادلة
+
+73
+00:06:07,850 --> 00:06:14,530
+الاصلية فهمت الطريقة بعيد كمان مرة علشان اللي
+
+74
+00:06:14,530 --> 00:06:19,130
+وصلنا متأخرات بيعطينا المعادلة ذلك و جوجل هات ال
+
+75
+00:06:19,130 --> 00:06:22,880
+general solutionبروح باخد ال homogeneous تبعتله
+
+76
+00:06:22,880 --> 00:06:26,940
+المعادلة هذه بحلها بأي طريقة من الطرق التي سبقت
+
+77
+00:06:26,940 --> 00:06:30,680
+دراستها في ال sections الماضية من section 1 لغاية
+
+78
+00:06:30,680 --> 00:06:37,320
+section 5 حلناها و جيبنا Y1 و Y2 إذا جبنا حل ال
+
+79
+00:06:37,320 --> 00:06:40,600
+homogeneous differential equation بدنا نجيب
+
+80
+00:06:40,600 --> 00:06:45,260
+particular solution للمعادلة starبفرض ان ال
+
+81
+00:06:45,260 --> 00:06:49,340
+particular solution على الصيغة اللى انها دى بس
+
+82
+00:06:49,340 --> 00:06:54,780
+بشيل c1 بحط بدله functionيو واحد و بشيل c اتنين
+
+83
+00:06:54,780 --> 00:06:58,340
+بحط بدل ال function يو اتنين فبصير الشكل ال
+
+84
+00:06:58,340 --> 00:07:02,320
+particular solution على الشكل اللي قدامنا هذا مين
+
+85
+00:07:02,320 --> 00:07:07,020
+هي يو واحد؟ يو واحد هي سالب تكامل y اتنين مضروبة
+
+86
+00:07:07,020 --> 00:07:10,740
+في g of t على الرنس كين تبع ال y واحد و ال y اتنين
+
+87
+00:07:10,740 --> 00:07:17,020
+as a function of t واليو اتنين هي عبارة عن تكاملY1
+
+88
+00:07:17,020 --> 00:07:21,300
+of T في الـ G of T على الرونسكين تبع ال Y1 وY2 as
+
+89
+00:07:21,300 --> 00:07:26,540
+a function of T جبت ال U1 و جبت ال U2 و روح بعوض
+
+90
+00:07:26,540 --> 00:07:32,280
+في هذه بكون جبت شكل الحل الخاص بجمع اللي هو الحل
+
+91
+00:07:32,280 --> 00:07:36,340
+الخاص مع الحل العام تبع الهموجوذ الأثنين مع بعض
+
+92
+00:07:36,340 --> 00:07:39,840
+بجمع الحل المعادلة الأصلية
+
+93
+00:07:52,050 --> 00:08:00,390
+المثال الأول بيقول هاتلي لل general solution
+
+94
+00:08:08,120 --> 00:08:13,180
+سؤال الأول بيقول له سؤال عشرة من الكتاب بيقول find
+
+95
+00:08:13,180 --> 00:08:16,820
+the
+
+96
+00:08:16,820 --> 00:08:27,100
+general solution
+
+97
+00:08:27,100 --> 00:08:35,720
+of the differential equation of the differential
+
+98
+00:08:35,720 --> 00:08:49,650
+equationللمعادلة التفاضلية يساوي
+
+99
+00:08:49,650 --> 00:08:57,370
+E of T على 1 زائد T تربيع وهذه المعادلة الأصلية
+
+100
+00:09:07,290 --> 00:09:12,590
+ال tactic اللى اتبع في حالة الجزء النظري في حالة
+
+101
+00:09:12,590 --> 00:09:14,710
+ال variation of parameters هو ال tactic اللى
+
+102
+00:09:14,710 --> 00:09:18,870
+بنتبعه الآن عند حل المثلةيبقى بدنا ناخد ال
+
+103
+00:09:18,870 --> 00:09:22,170
+homogenous differential equation ونروح من هنا لو
+
+104
+00:09:22,170 --> 00:09:25,770
+جينا لل homogenous بنلاقي المعاملات اذا نزل
+
+105
+00:09:25,770 --> 00:09:33,630
+سيكشنرز الماضية بروح بقوله let Y تساوي E أُس RT be
+
+106
+00:09:33,630 --> 00:09:38,990
+a solution of the
+
+107
+00:09:47,640 --> 00:09:58,580
+بناء عليه then the characteristic equation isR
+
+108
+00:09:58,580 --> 00:10:05,680
+تربيع ناقص اتنين R زائد واحد تساوي كده؟ تساوي Zero
+
+109
+00:10:05,680 --> 00:10:10,880
+هذه يا بنات لو حللناها R ناقص واحد في R ناقص واحد
+
+110
+00:10:10,880 --> 00:10:17,780
+لكل تربيع تساوي Zero ومنها R واحد تساوي R اتنين
+
+111
+00:10:17,780 --> 00:10:27,230
+تساوي كده؟واحد صحيح يبقى صار الحل ان YC بدر ساوي
+
+112
+00:10:27,230 --> 00:10:38,370
+C1 زائد C2T في E أس T او ان شيتنا فقولنا C1 E أس T
+
+113
+00:10:38,370 --> 00:10:47,440
+زائد C1T في E أس Tيبقى الحل الأول Y1 هو POST و
+
+114
+00:10:47,440 --> 00:10:56,100
+الحل الثاني هو T EOST بعد ذلك بروز هذا سنرجع له
+
+115
+00:10:56,100 --> 00:11:00,960
+تمام يبقى نروح نجيب ال particular solution لل
+
+116
+00:11:00,960 --> 00:11:06,810
+equationالمعامل هنا واحد صحيح يبقى احنا جاهزين
+
+117
+00:11:06,810 --> 00:11:10,190
+ماعناه مش مشكلة ان شاء الله يكون اتنين تلاتة اربعة
+
+118
+00:11:10,190 --> 00:11:12,750
+بيكتب اسمي على هذا الرقم اللي هو ال constant
+
+119
+00:11:12,750 --> 00:11:18,310
+اشتراطنا بيكون واحد صحيح تمام يبقى باجي بقول the
+
+120
+00:11:18,310 --> 00:11:27,890
+particular solution of the
+
+121
+00:11:41,500 --> 00:11:52,620
+U1 يبقى U1 of T في E of T وشيل C2 و اكتب بدلا U2
+
+122
+00:11:52,620 --> 00:12:00,550
+of T في T في E of Tجاب المحسب الـU1 و الـU2 بالزمن
+
+123
+00:12:00,550 --> 00:12:06,970
+الرونسكين تمام يبقى بده أروح أجيب له الرونسكين تبع
+
+124
+00:12:06,970 --> 00:12:12,990
+الحل الأول و الحل التاني as a function of T الحل
+
+125
+00:12:12,990 --> 00:12:20,330
+الأول هو E و S T و الحل التاني هو T في U S T نشتق
+
+126
+00:12:20,330 --> 00:12:27,500
+هذا ب E و S T نشتق هذا بمشتقة حاصل ضربدالتين يبقى
+
+127
+00:12:27,500 --> 00:12:33,860
+مشتقة الأولى فى التانية زائد الأولى فى مشتقة مين
+
+128
+00:12:33,860 --> 00:12:41,500
+الدالة ا الثانية انفك المحدد بالضرب التبادلى يبقى
+
+129
+00:12:41,500 --> 00:12:49,820
+هنا بصير E أس اتنين T زائد T فى E أس اتنين T هذا
+
+130
+00:12:49,820 --> 00:12:55,790
+حاصل ضرب عناصر القطر الرئيسىنقص حاصل ضرب عناصر
+
+131
+00:12:55,790 --> 00:13:03,510
+القطر الثانوي يبقى ناقص T في E أس اتنين T هذا و
+
+132
+00:13:03,510 --> 00:13:09,910
+هذا في كم؟ في Zero هذا الكلام يساوي كم؟ اللي عمرها
+
+133
+00:13:09,910 --> 00:13:15,470
+ماحتساوي Zeroليش؟ لأن الـ Exponential دائما و أبدا
+
+134
+00:13:15,470 --> 00:13:19,650
+أكبر من مين من الـ Zero إذا الحل اللي بيطلع عنهم
+
+135
+00:13:19,650 --> 00:13:24,430
+يبنى Linearly Independent Solution وبالتالي
+
+136
+00:13:24,430 --> 00:13:28,170
+بيكونوا لـ Fundamental Set of Solutions أو الـ
+
+137
+00:13:28,170 --> 00:13:31,210
+General Solution لمين؟ للـ Homogeneous
+
+138
+00:13:31,210 --> 00:13:35,580
+Differential Equationعلى اي حال ان هذا الان بتروح
+
+139
+00:13:35,580 --> 00:13:42,160
+احسب له U1 و U2 يبقى بدي U1 as a function of T
+
+140
+00:13:42,160 --> 00:13:50,400
+اللي هو ناقص تكامل Y2 of T في G of T على
+
+141
+00:13:50,400 --> 00:13:58,120
+الوانوسكين as a function of T DT يبقى هاي سالب
+
+142
+00:13:58,120 --> 00:14:05,650
+وهاي تكاملبتداجر ال Y2 Y2 هو من T في E أُس T يبقى
+
+143
+00:14:05,650 --> 00:14:13,130
+هاي T في E أُس T في G of T وين G of T هيها فوق
+
+144
+00:14:13,130 --> 00:14:21,630
+يبقى هذا بيصير من بيصير E أُس T و بتنزل تحت واحد
+
+145
+00:14:21,630 --> 00:14:28,070
+زائد T تربيعبيل تحت مين عندى؟ ايرونيسكن ايرونيسكن
+
+146
+00:14:28,070 --> 00:14:36,520
+جداش؟ E أس اتنين T كله في DTيبقى لو ضربت هدى فى
+
+147
+00:14:36,520 --> 00:14:42,880
+هدى يا بنات بصير جداش اؤس اتنين T مع اؤس اتنين T
+
+148
+00:14:42,880 --> 00:14:48,420
+اللى بتاعت مع السلامة يبقى هذا الكلام يساوي الناقص
+
+149
+00:14:48,420 --> 00:14:54,280
+تكامل T على واحد زائد T ترابيع DT
+
+150
+00:14:57,690 --> 00:15:06,050
+أظن البسطة فاضل المقام كيف؟ بدا اتنين يعني بتمان
+
+151
+00:15:06,050 --> 00:15:12,510
+وعاد اتنين بشانيك بكلامنا صحيح بروح نضرب في نص هيك
+
+152
+00:15:12,510 --> 00:15:23,250
+صار البسطة فاضل المقاميساوي ناقص نص لإن واحد زائد
+
+153
+00:15:23,250 --> 00:15:27,890
+T تربية بدون absolute value لإنها قيمة موجبة T لو
+
+154
+00:15:27,890 --> 00:15:31,890
+حتى لو كان سلبة بالربعة بصير موجبة زائد واحد يبقى
+
+155
+00:15:31,890 --> 00:15:36,750
+هذه positive quantity على طول الخط بس كنا كاملنا
+
+156
+00:15:36,750 --> 00:15:42,170
+بنقول زائد constantخليني اكتب ال constant هذا يبقى
+
+157
+00:15:42,170 --> 00:15:49,310
+زائد c1 و تعالوا نتفهم على ال c1 هذا كده ايش ممكن
+
+158
+00:15:49,310 --> 00:15:56,470
+ناخده؟خلّي الـ C1 بدّيش أخده سفر، خديه خمسة، مثلا،
+
+159
+00:15:56,470 --> 00:16:01,610
+لو جدل أنا أخدت خمسة، إيش اللي بيحصل؟ بصير عندي
+
+160
+00:16:01,610 --> 00:16:08,670
+هذا المقدار زائد C1، لما أجي أضربه، ههه، فاهمين؟
+
+161
+00:16:08,670 --> 00:16:14,110
+هذا اللي هو U1، يبقى U1 بدي أجي أضربها وين؟ وين
+
+162
+00:16:14,110 --> 00:16:21,130
+راح الـ U1 هي؟ بدي أضربها هنابصير رقم في UST يعني
+
+163
+00:16:21,130 --> 00:16:27,610
+بصير تكرار وبالتالي بصير تشابه مع مين مع الحل هذا
+
+164
+00:16:27,610 --> 00:16:31,830
+يبجي مشان أتخلص من الاشياء هذه دائما و أبدا مش في
+
+165
+00:16:31,830 --> 00:16:38,850
+السؤال هذا في كل المساوي اللي باخد C1 ب 0 طيب
+
+166
+00:16:38,850 --> 00:16:47,090
+الحين هشيرلها طيب بداخل ال U2Y1 of T يساوي تكامل
+
+167
+00:16:47,090 --> 00:16:55,730
+Y1 of T في G of T على الورنسكين of T كله بالنسبة
+
+168
+00:16:55,730 --> 00:17:02,160
+الى DT ويساوي تكاملالـ Y1 يا بناتي اللي هو مين؟ E
+
+169
+00:17:02,160 --> 00:17:10,060
+أُس T والـ G of T ليه E أُس T على واحد زائد T
+
+170
+00:17:10,060 --> 00:17:17,680
+تربية والرنسكين اللي هو E أُس اتنين T في D T صارت
+
+171
+00:17:17,680 --> 00:17:25,560
+المسألة تكامل واحد على واحد زائد T تربية DT بدنا
+
+172
+00:17:25,560 --> 00:17:30,380
+نكامل هذا، جديش؟تان انفرستي ممتاز يبقى هذه جاهزة
+
+173
+00:17:30,380 --> 00:17:35,160
+لا بدأش لشغل اليمين ولا الشمال يبقى هذه تان
+
+174
+00:17:35,160 --> 00:17:44,120
+انفرستي زاد كونستانتاني C2 يبقى زي ما حد C1 ب zero
+
+175
+00:17:44,120 --> 00:17:52,940
+C2 بقدرش ب zero يبقى باجي بقول تاك ودينا C1 بده
+
+176
+00:17:52,940 --> 00:17:56,200
+يساوي C2 بده يساوي zero
+
+177
+00:18:18,160 --> 00:18:24,700
+أذا لما أخدنا كل واحد بـ0 بيصير U1 ناقص نص لإن
+
+178
+00:18:24,700 --> 00:18:30,520
+واحد زائد T تربيع و بيصير U2 تان inverse T إذا
+
+179
+00:18:30,520 --> 00:18:34,880
+بقدر أجيب شكل ال particular solution يبقى باجي
+
+180
+00:18:34,880 --> 00:18:41,540
+بقوله the particular solution
+
+181
+00:18:47,280 --> 00:18:52,640
+يبقى كتابنا ال particular solution هى يبقى بدى
+
+182
+00:18:52,640 --> 00:19:02,500
+اشيل UN هى وجهه يقول ناقص نص Eost في لن يبقى ناقص
+
+183
+00:19:02,500 --> 00:19:16,090
+نص Eost في لننقص E أُس T وراحت هنا نقص نص وهنا E
+
+184
+00:19:16,090 --> 00:19:25,450
+أُس T في ال N اللي هي واحد زائد ت تربيع الآن يقول
+
+185
+00:19:25,450 --> 00:19:33,550
+تان انفرس في من؟ في T في E أُس T يبقى T في E أُس T
+
+186
+00:19:33,550 --> 00:19:40,590
+في تان انفرس Tاختصارات مافيش بيقولش بيظل زي ما هو
+
+187
+00:19:40,590 --> 00:19:50,910
+فبروح بقول هنا the general solution of the
+
+188
+00:19:50,910 --> 00:20:01,080
+differentialEquation star is y يساوي yc زائد
+
+189
+00:20:01,080 --> 00:20:08,260
+capital y of t إذا بيصير ال y يساوي c1
+
+190
+00:20:13,720 --> 00:20:21,320
+بنضيف عليها particular solution نقص نص Eost لإن
+
+191
+00:20:21,320 --> 00:20:29,820
+واحد زائد T تربيع Eost
+
+192
+00:20:33,390 --> 00:20:38,810
+يبقى هذا هو ال general solution لل equation star
+
+193
+00:20:38,810 --> 00:20:44,430
+اللي عندك فيه أي تساوي لبنات التكتيك اللي عملناها
+
+194
+00:20:44,430 --> 00:20:49,590
+تتبعيها عندك كل مسألة بضل عليك بس تكاملي مشان تجيب
+
+195
+00:20:49,590 --> 00:20:55,190
+اللي و واحد و اتنين و باقى الشغل كله روتيني ناخد
+
+196
+00:20:55,190 --> 00:21:00,970
+كمان مثال مثال
+
+197
+00:21:00,970 --> 00:21:13,230
+اتنينFind the general solution of differential
+
+198
+00:21:13,230 --> 00:21:16,390
+equation YW'
+
+199
+00:21:21,030 --> 00:21:32,430
+زائد اتنين Y بدي ساوي اتنين E أس ناقص T تان ترابيع
+
+200
+00:21:32,430 --> 00:21:40,230
+ال T و دستار سؤال مش موجود في الكتاب سؤال خارجي
+
+201
+00:21:40,230 --> 00:21:44,890
+نفس
+
+202
+00:21:44,890 --> 00:21:48,600
+ال tactic اللي ابتدينا به هناك هنبتدي به هنايبقى
+
+203
+00:21:48,600 --> 00:21:59,500
+بداجي اقول له let y تساوي E أس RT بيه solution of
+
+204
+00:21:59,500 --> 00:22:08,380
+the equation y w prime اتنين y prime زائد اتنين y
+
+205
+00:22:08,380 --> 00:22:09,820
+يساوي زيرو
+
+206
+00:22:13,630 --> 00:22:23,490
+The characteristic equation is R تربيع زائد اتنين
+
+207
+00:22:23,490 --> 00:22:29,350
+R زائد اتنين تساوي Zero أظن لا يمكن تحليل هذه
+
+208
+00:22:29,350 --> 00:22:34,900
+المعادلة، مظبوط؟ يبقى بروح نحلها كيف؟بالقانون
+
+209
+00:22:34,900 --> 00:22:42,300
+العام يبقى R تساوي ناقص باء زيد أو ناقص الجدري
+
+210
+00:22:42,300 --> 00:22:48,500
+التربيعي لباء تربيع ناقص أربعة ألف اللي هي بواحد
+
+211
+00:22:48,500 --> 00:22:55,500
+جيم اللي هي باتنين كله على اتنين ألف اتنين في واحد
+
+212
+00:22:56,090 --> 00:23:04,330
+تمام يبقى هذه نقص اتنين زاد او نقص اربع نقص تمانية
+
+213
+00:23:04,330 --> 00:23:11,910
+بظهر سالب اربعة تحت الجدر يعني بتطلع باتنين I كله
+
+214
+00:23:11,910 --> 00:23:18,630
+على قداش على اتنين يبقى ناقص واحد زاد او ناقص I
+
+215
+00:23:18,630 --> 00:23:27,070
+يبقى لان ده بقداش و ميوبواحد يبقى هنا لاندا تساوي
+
+216
+00:23:27,070 --> 00:23:35,170
+سالب واحد وال ميو يساوي واحد إذا صار YC بدي يساوي
+
+217
+00:23:35,170 --> 00:23:43,550
+E أس لاندا T لاندا بواحد يبقى E أس T لاندا بسالب
+
+218
+00:23:43,550 --> 00:23:47,570
+واحد E أس ناقص T تمام فاهمين؟
+
+219
+00:23:57,710 --> 00:24:05,170
+يبقى هذا حل الـ homogeneous differential equation
+
+220
+00:24:05,900 --> 00:24:09,580
+ماذا ترى؟ خلّيني أحسب الورونسكين بالمرة قبل ما
+
+221
+00:24:09,580 --> 00:24:14,040
+أجيب ال particular solution حتى تظل المسألة ماشية
+
+222
+00:24:14,040 --> 00:24:19,440
+معانا بطريقة سلسة يبقى بدي أجيب الورونسكين as a
+
+223
+00:24:19,440 --> 00:24:26,920
+function of T الحل الأول هو E أس ناقص T في cos T
+
+224
+00:24:26,920 --> 00:24:35,620
+الحل التاني هو E أس سالب T في sin Tبنشتق الدالة
+
+225
+00:24:35,620 --> 00:24:42,720
+الأولى حاصل ضرب دالتين يبقى مشتقة الأولى زي ما هي
+
+226
+00:24:42,720 --> 00:24:50,160
+في مشتقة الأسلوب من بسالب واحد في cos T بعد ذلك ال
+
+227
+00:24:50,160 --> 00:24:55,880
+EOS نقص T كما هي في مشتقة ال cos E بسالبSin يبقى
+
+228
+00:24:55,880 --> 00:25:03,060
+السالب E أس سالب T في Sin T الدالة تانية بنفس
+
+229
+00:25:03,060 --> 00:25:11,180
+الطريقة يبقى ناقص E أس ناقص T في Sin T زيد E أس
+
+230
+00:25:11,180 --> 00:25:20,460
+ناقص T في Cos Tطبعا نجي نطلع قداش قيمة هذا المحدد
+
+231
+00:25:20,460 --> 00:25:25,160
+ويوسف حاصل ضرب عناصر القطر الرئيسي ناقص حاصل ضرب
+
+232
+00:25:25,160 --> 00:25:33,460
+عناصر القطر الثانوي يبقى هدف هدف تطلع بقداش بسالب
+
+233
+00:25:33,460 --> 00:25:41,540
+او سالب اتنين T سالب او سالب اتنين T في Sin T في
+
+234
+00:25:41,540 --> 00:25:44,100
+Cos T في Sin
+
+235
+00:25:49,640 --> 00:25:56,600
+يبقى زائد a أساليب اتنين T في cos Tزائد E أس سلب
+
+236
+00:25:56,600 --> 00:26:05,560
+اتنين T فمين فيه cosine تربيع T هذا الرئيسي نقص
+
+237
+00:26:05,560 --> 00:26:12,340
+ثانوي مع نقص بصير ايه؟ زائد يبقى زائد E أس نقص
+
+238
+00:26:12,340 --> 00:26:21,340
+اتنين T sine T cosine Tتمام؟ هدى فى هدى، بعد ذلك
+
+239
+00:26:21,340 --> 00:26:29,920
+هدى كمان زائد إيه أس ناقص اتنين T في sign تاربيع T
+
+240
+00:26:29,920 --> 00:26:34,960
+شراي كمانات هدى و هدى مع السلامة، واحدة موجبة و
+
+241
+00:26:34,960 --> 00:26:40,900
+واحدة سالبةهذه تساوي بيداخد EOS ناقص اتنين عامل
+
+242
+00:26:40,900 --> 00:26:48,080
+مشترك T بضالك cosine تربيتي زائد sine تربيتي له
+
+243
+00:26:48,080 --> 00:26:56,680
+مقداش يبقى الجواب EOS ناقص اتنين T وهذا لا يمكن ان
+
+244
+00:26:56,680 --> 00:26:57,500
+يساوي
+
+245
+00:27:03,100 --> 00:27:07,320
+يبقى الكلام اللى كتبته هذا معله هو ال general
+
+246
+00:27:07,320 --> 00:27:12,020
+solution لل homogenous differential equation بدنا
+
+247
+00:27:12,020 --> 00:27:18,180
+نروح نجيب ال particular solution لمين؟ للمعادلة
+
+248
+00:27:18,180 --> 00:27:20,480
+الأصلية
+
+249
+00:27:35,300 --> 00:27:39,420
+المعادلة الأصلية وين؟ لأن هدري سمنها star ففاجي
+
+250
+00:27:39,420 --> 00:27:46,780
+بقولهم the particular solution
+
+251
+00:27:46,780 --> 00:27:51,020
+of equation
+
+252
+00:27:56,560 --> 00:28:07,900
+Y of T يبقى
+
+253
+00:28:07,900 --> 00:28:18,700
+U1 of T في E السالب T في Cos T
+
+254
+00:28:46,270 --> 00:28:55,690
+Y2Y2Y2Y2Y2Y2Y2Y2Y2Y2Y2Y2Y2Y2Y2 يبقى
+
+255
+00:28:55,690 --> 00:29:03,470
+E أسالب T في صينة T الـ G of T طلع المعاملة واحد
+
+256
+00:29:03,470 --> 00:29:11,690
+يبقى احنا جاهزين يبقى اتنين E أسالب T اتنين E
+
+257
+00:29:11,690 --> 00:29:20,060
+أسالب T في تان ترابيع Tكله علامين على الرمز كان
+
+258
+00:29:20,060 --> 00:29:31,120
+طالعنا E والسالب اتنين T DT ويساوي سالب تكامل اظن
+
+259
+00:29:31,120 --> 00:29:37,720
+هذه مع هذه مع هذه الله يسهل عليهم غير ما سوف عليهم
+
+260
+00:29:37,720 --> 00:29:43,200
+بضل عند اي سالب تكامل تان تربية يا بنات اللي همين
+
+261
+00:29:43,520 --> 00:29:53,960
+اللي هي sin تربيع T على cos تربيع T في sin T في DT
+
+262
+00:29:53,960 --> 00:30:00,660
+يبقى هذا الكلام بده يساوي تكامل اش رايك بده اكتب
+
+263
+00:30:00,660 --> 00:30:07,360
+ال sin تربيع بدلالة ال cos تربيع يبقى واحد ناقص
+
+264
+00:30:07,360 --> 00:30:17,050
+cos تربيع T ماشيماذا تقولون في اتنين نسيناها برا
+
+265
+00:30:17,050 --> 00:30:24,090
+اه في اتنين اي اتنين ماشي الحال و هذا اتنين برا و
+
+266
+00:30:24,090 --> 00:30:29,010
+هنا cosine تربيع ال T بتقولون اللي نسيت الشرف
+
+267
+00:30:29,010 --> 00:30:36,490
+النقص مانستهاش طلع هنا ناقص sin t dt بدي اكتبها D
+
+268
+00:30:36,490 --> 00:30:42,620
+cosine هو مش شقة ال cosine في قداشسالب ساين يبقى
+
+269
+00:30:42,620 --> 00:30:49,180
+السالب ساين ت دي ت ودي اقول دي كوساين ت يبقى هذه
+
+270
+00:30:49,180 --> 00:30:57,820
+دي لكساين ت يعني مشتقت كساين ت لو ناقص ساين ت دي ت
+
+271
+00:30:57,820 --> 00:31:03,580
+يبقى شلت إشارة السالب مع الساين ت مع ال دي ت وكتبت
+
+272
+00:31:03,580 --> 00:31:08,340
+بدالها دي كساينطب عملت هيك ليش تعالى أقولك ليش
+
+273
+00:31:08,340 --> 00:31:13,600
+عملت هيك يبقى هذا الكلام يساوي اللي هو الاتنين
+
+274
+00:31:13,600 --> 00:31:21,600
+اللي برا وهي تكامل واحد على cosine تربيع ال T وهنا
+
+275
+00:31:21,600 --> 00:31:29,800
+ناقص واحد كله في دي cosine T يعني كأنه ايش احنا يا
+
+276
+00:31:29,800 --> 00:31:36,410
+بنات؟بنكمل واحد على X تربية ناقص واحد DX يعني تبري
+
+277
+00:31:36,410 --> 00:31:42,230
+Cos T كأنها كلها X تمام؟ يبقى نتيجة التكمل بدها
+
+278
+00:31:42,230 --> 00:31:47,990
+تكون على الشكل التالي اي اتنين فيه جداش تكمل واحد
+
+279
+00:31:47,990 --> 00:31:52,520
+على X تربية؟سالب واحد على X إذا هذا بتبقى الجدران
+
+280
+00:31:52,520 --> 00:32:01,100
+سالب واحد على cosine T يبقى سالب واحد على cosine T
+
+281
+00:32:01,100 --> 00:32:10,940
+ناقص cosine T يبقى ناقص cosine T وC1 ده مابناشيها
+
+282
+00:32:10,940 --> 00:32:17,580
+يبقى هنا زائد C1 وهنا بنقول take C1 تساوي Zero
+
+283
+00:32:18,650 --> 00:32:25,930
+تمام؟ يبقى هذا لو أخدت بـ0 يصير U1 as a function
+
+284
+00:32:25,930 --> 00:32:33,870
+of T هي عبارة عن مين؟ عن ناقص اتنين على cos T
+
+285
+00:32:33,870 --> 00:32:43,310
+وناقص اتنين cos T في حد يقول لي تسأل قبل ما افوت
+
+286
+00:32:43,310 --> 00:32:48,390
+مش فاهمة تكامل مش فاهمة نقطة تسألني في اي تسأل؟
+
+287
+00:32:51,480 --> 00:33:01,370
+نعود الان لـ U2 of Tيبدو يسوي تكامل Y1 of T في G
+
+288
+00:33:01,370 --> 00:33:06,490
+of T على الرونسكين as a function of T دي T يسوي
+
+289
+00:33:06,490 --> 00:33:15,550
+تكامل Y1 اللي همين E أس ناقص T Cos T يبقى E أس
+
+290
+00:33:15,550 --> 00:33:26,150
+ناقص T في Cos T الـ G of T اللي هي اتنينEos ناقص T
+
+291
+00:33:26,150 --> 00:33:36,030
+في تان تربيع T كله على الرونسكين Eos ناقص 2T يبقى
+
+292
+00:33:36,030 --> 00:33:44,550
+هذا بنتش بصير بصير تكامل و اي اتنين برا و بيضل cos
+
+293
+00:33:44,550 --> 00:33:50,170
+T فقط لا غير و تان تربيع
+
+294
+00:33:59,960 --> 00:34:05,200
+يساوي اتنين تكامل اظن في اختصار بين cosine و
+
+295
+00:34:05,200 --> 00:34:12,560
+cosine تربية يبقى بضال عندي sin تربية t فقط على
+
+296
+00:34:12,560 --> 00:34:22,010
+cosine t dtطيب هذه اللي بقدر اكتبها على الشكل
+
+297
+00:34:22,010 --> 00:34:28,710
+التالي اتنين تكامل sin
+
+298
+00:34:28,710 --> 00:34:34,710
+تربيع يبقى واحد ناقص cosine تربيع يبقى واحد ناقص
+
+299
+00:34:34,710 --> 00:34:42,410
+cosine تربيع ال T كله على cosine T DT ويسوى اتنين
+
+300
+00:34:42,410 --> 00:34:51,290
+تكامل واحد على cosineبسك يبقى سك ال T و هنا ناقص
+
+301
+00:34:51,290 --> 00:34:56,710
+cosine تربيه على cosine بيبقى ال cosine T واحدة
+
+302
+00:34:56,710 --> 00:35:11,570
+كلها دي Tيساوي اتنين يبقى
+
+303
+00:35:11,570 --> 00:35:21,170
+اتنين لان absolute value لسك T زائد تاني Tوهنا
+
+304
+00:35:21,170 --> 00:35:30,450
+ناقص C2 وتكامل ال cosine بsin 80 وزائد constant C2
+
+305
+00:35:30,450 --> 00:35:41,290
+وبنقول هنا take code C2يساوي 0 يبقى صارة ان U2 as
+
+306
+00:35:41,290 --> 00:35:47,390
+a function of T هو عبارة عن اتنين لان absolute
+
+307
+00:35:47,390 --> 00:35:58,030
+value لسك T زائد تاني T نقص اتنين sin T اذا بقدر
+
+308
+00:35:58,030 --> 00:36:03,610
+اجيب شكل ال particular solution تمام
+
+309
+00:36:12,370 --> 00:36:19,870
+بقول له the particular solution
+
+310
+00:36:19,870 --> 00:36:25,750
+of equation
+
+311
+00:36:25,750 --> 00:36:35,850
+star is capital Y of T بده يساوي U واحد في ال Y
+
+312
+00:36:35,850 --> 00:36:44,380
+one زائد U اتنين في ال Y twoاذا capital Y of T بده
+
+313
+00:36:44,380 --> 00:36:52,620
+يسمى وين ال U1؟ هاد ال U1، هاد ايه؟ اللي كتبناها
+
+314
+00:36:52,620 --> 00:36:57,560
+على الشكل هذا، هاد ال U1، هاد بنا نضربها في
+
+315
+00:36:57,560 --> 00:37:05,760
+مينوبالاتبدا ان انا اضربها في ال Y1 هذي ههه مظبوط
+
+316
+00:37:05,760 --> 00:37:10,160
+مش هذي ال Y1 يعني كأنها ههه خاني اختصرها لك بعدين
+
+317
+00:37:10,160 --> 00:37:18,640
+مش مشكلة يبقى بداجي اقول E أس ناقص T في Cos T في
+
+318
+00:37:19,480 --> 00:37:24,140
+الـ U1 اللي هو اتنين او سالب اتنين على كوساين ت
+
+319
+00:37:24,140 --> 00:37:33,840
+سالب اتنين على كوساين T سالب اتنين كوساين T زي ال
+
+320
+00:37:33,840 --> 00:37:41,600
+Y2 اللي هو E أُس ناقص T في ساين T فاللي طلعناها
+
+321
+00:37:41,600 --> 00:37:50,220
+تحت هذهاللي هو اتنين لين absolute value لمن ل سك T
+
+322
+00:37:50,220 --> 00:37:59,980
+زائد تاني T و هنا ناقص اتنين صيني T بالشكل اللي
+
+323
+00:37:59,980 --> 00:38:06,780
+عندنا هذا الان بدنا نجيب ال general solution بعد
+
+324
+00:38:06,780 --> 00:38:13,310
+ما جيبنا شكل mainشكل ال particular solution بس
+
+325
+00:38:13,310 --> 00:38:18,670
+خلينا نشوف يا ترى فيها اختصارات والله مافيهاش
+
+326
+00:38:18,670 --> 00:38:25,960
+اختصارات لو جمعناهايعني هنا بيصير والله يمكن يكون
+
+327
+00:38:25,960 --> 00:38:30,240
+فيها اختصارات تعالى نشوف كده بده تساوي هذه المناطب
+
+328
+00:38:30,240 --> 00:38:37,560
+بيصير عندى ناقص اتنين و E أس سالب T و ال cosine مع
+
+329
+00:38:37,560 --> 00:38:44,980
+ال cosine بتروح و هنا سالب اتنين E أس ناقص T في
+
+330
+00:38:44,980 --> 00:38:53,620
+cosine تربيع T تمام خلاصنا منهاهدي زائد اتنين EOS
+
+331
+00:38:53,620 --> 00:39:01,000
+ناقص T في صين ال T في ال absolute value لشك ال T
+
+332
+00:39:01,000 --> 00:39:11,980
+زائد تاني T ناقص اتنين EOS ناقص T في صين تربيع ال
+
+333
+00:39:11,980 --> 00:39:19,520
+T والله كويس طليلي في هدي هو هديبقدر اخد سالب
+
+334
+00:39:19,520 --> 00:39:25,420
+اتنين عامل مشترك ايش بيضل عندى؟ بيضل sin تربية
+
+335
+00:39:25,420 --> 00:39:30,920
+زائد cos تربية اللى بيبقى داشر يعنى هذا بيصير سالب
+
+336
+00:39:30,920 --> 00:39:37,480
+اتنين Eos ناقص T سالب اتنين Eos ناقص T وبيضلش
+
+337
+00:39:37,480 --> 00:39:45,220
+الامن اللى فالمص هذا يبقى زائد اتنين Eos ناقص T في
+
+338
+00:39:45,220 --> 00:39:47,580
+sin T فلن
+
+339
+00:39:53,890 --> 00:39:59,510
+ممتاز طيب إيش راحك هذه و هذه نفس هذه يبقى سالب
+
+340
+00:39:59,510 --> 00:40:07,170
+أربعة يبقى النتيجة سالب أربعة يوس ناقص T زائد
+
+341
+00:40:07,170 --> 00:40:17,230
+اتنين يوس ناقص T في صينة T في لن سكتي زائد تانتي
+
+342
+00:40:18,270 --> 00:40:28,510
+اذا انا باجي بقول له the general solution of the
+
+343
+00:40:28,510 --> 00:40:39,210
+differential equation star is y سوى yc هيه عند هنا
+
+344
+00:40:39,210 --> 00:40:51,800
+تحتيبقى C1 EOS ناقص T في Cos T زائد C2 EOS ناقص T
+
+345
+00:40:51,800 --> 00:41:01,740
+في Sin T ناقص أربعة EOS ناقص T زائد اتنين EOS ناقص
+
+346
+00:41:01,740 --> 00:41:14,180
+T في Sin T في لن absolute valueسك T زائد تاني T في
+
+347
+00:41:14,180 --> 00:41:16,020
+اي تساول هنا يا بنادى
+
+348
+00:41:54,370 --> 00:42:06,930
+كمان مثال مثال
+
+349
+00:42:06,930 --> 00:42:11,830
+تلاتة سؤال
+
+350
+00:42:11,830 --> 00:42:20,650
+من الكتاب بيقول fy1 بده يساوي T تربيع and
+
+351
+00:42:22,110 --> 00:42:35,630
+Y2 بدي ساوي T تربيع لينية T are two linearly
+
+352
+00:42:35,630 --> 00:42:40,290
+independent solutions
+
+353
+00:42:40,290 --> 00:42:43,650
+of
+
+354
+00:42:43,650 --> 00:42:48,330
+the homogeneous
+
+355
+00:42:53,180 --> 00:43:01,600
+Differential Equation لـ T تربيع Y double prime
+
+356
+00:43:01,600 --> 00:43:11,160
+ناقص ثلاثة T Y prime زائد أربعة Y تساوي Zero
+
+357
+00:43:11,160 --> 00:43:16,720
+وسميلي هذه المعادلة رقم واحد Find a particular
+
+358
+00:43:16,720 --> 00:43:17,940
+solution
+
+359
+00:43:30,160 --> 00:43:36,840
+تبحث عن حلول معينة مختلفة للإيقاع
+
+360
+00:43:42,000 --> 00:43:49,520
+Equation للمعادلة التفاضلية T تربيع Y double prime
+
+361
+00:43:49,520 --> 00:43:53,140
+ناقص
+
+362
+00:43:53,140 --> 00:44:08,600
+تلاتة T Y prime زائد أربعة Y تساوي T تربيع لن Tو
+
+363
+00:44:08,600 --> 00:44:18,120
+ال T greater than zero و هذه المعادلة رقم اتنين
+
+364
+00:44:36,850 --> 00:44:43,230
+يبقى هذا السؤال يختلف عن سابقينه في أمر واحد فقط
+
+365
+00:44:43,230 --> 00:44:48,090
+شو الأمر هذا؟ ان المعادلة اللى ماتاها للمعاملات
+
+366
+00:44:48,090 --> 00:44:53,290
+تبعتها مالها ماهياش ثوابت واحنا أخدنا إذا المعادلة
+
+367
+00:44:53,290 --> 00:45:00,010
+ماهياش ثوابت لازم يعطيني أحد الحلول واني أروح أجيب
+
+368
+00:45:00,010 --> 00:45:05,000
+الحل الأخر بطريقة reduction of order مظبوط؟لكن
+
+369
+00:45:05,000 --> 00:45:09,920
+الحمد لله ريحني وقال لي خد هدول الحالين هيهم معاك
+
+370
+00:45:09,920 --> 00:45:14,500
+يبقى ريحني من طريقة مين ال reduction of order
+
+371
+00:45:14,500 --> 00:45:19,880
+وبالتالي قال لي لو كانوا هدول اتنين T تربيع وT
+
+372
+00:45:19,880 --> 00:45:24,000
+تربيع لان T هم حالين لل homogeneous differential
+
+373
+00:45:24,000 --> 00:45:29,660
+equation بدي شكل الحل الخاص لمين للمعادلة اللي
+
+374
+00:45:29,660 --> 00:45:35,610
+عندنا هذه بقول لك كويس يعني هو ريحنيوبالتالي قال
+
+375
+00:45:35,610 --> 00:45:40,450
+اتنين linearly independent اذا المعادلة الأولى
+
+376
+00:45:40,450 --> 00:45:51,450
+واحد حلها بجيبه في سطر يبقى فبجيبه هنا solution of
+
+377
+00:45:51,450 --> 00:46:00,330
+equation
+
+378
+00:46:00,330 --> 00:46:13,050
+oneالمعادلة الأولى هو YC بده يساوي C1 في من؟ في T
+
+379
+00:46:13,050 --> 00:46:22,230
+تربيع زائد C2 في T تربيع في لن T مش هيك؟ وين راح
+
+380
+00:46:22,230 --> 00:46:30,040
+تقع لن T؟ لن ال T تمام تماميبقى هذا لو طلب ال
+
+381
+00:46:30,040 --> 00:46:34,020
+general solution برجعله مطلبش بلاش لكن هو طلب فقط
+
+382
+00:46:34,020 --> 00:46:39,180
+من ال particular solution للمعادلة رقم اتنين بقوله
+
+383
+00:46:39,180 --> 00:46:42,880
+بسيطة يبقى بدي أشيل c واحد و أحط مكانه function y
+
+384
+00:46:42,880 --> 00:46:48,220
+واحد و u واحد و أشيل u اتنين و أحط بدله function u
+
+385
+00:46:48,220 --> 00:46:52,740
+اتنين لكن مع الفرق بدرو حسب الرونسكين تبعهم من
+
+386
+00:46:52,740 --> 00:46:57,920
+البداية قبل ما أجيب الحل اللي انا بديهايبقى لو
+
+387
+00:46:57,920 --> 00:47:03,560
+روحت أخدت رونسكين as a function of T الحل الأول T
+
+388
+00:47:03,560 --> 00:47:10,780
+تربيع والحل التاني T تربيع فلن T مشتقة الأول اتنين
+
+389
+00:47:10,780 --> 00:47:19,660
+T التاني حاصل ضرب دالتين يبقى اتنين T لن T زائد T
+
+390
+00:47:19,660 --> 00:47:26,930
+تربيع فلن T مشتقة لن T ليبقى داشر مع T تربيعبتظل
+
+391
+00:47:26,930 --> 00:47:32,710
+بس T واحدة يبقى هاي T بده افكر المحدد اللي عندنا
+
+392
+00:47:32,710 --> 00:47:42,790
+هذا يبقى بصير اتنين T تكعيب لان ال T زائد T تكعيب
+
+393
+00:47:42,790 --> 00:47:50,750
+ناقص اتنين T تكعيبلأن ال T أظن هذه وهذه مع السلامة
+
+394
+00:47:50,750 --> 00:47:58,530
+بظل الجواب T تكيب وهذا لا يساوي Zero ليش؟ لأن T
+
+395
+00:47:58,530 --> 00:48:03,690
+أكبر من Zero هو مطالوين في المسألة إذا جبت له
+
+396
+00:48:03,690 --> 00:48:06,810
+رونسكين وطلع طلع طلع طلع طلع طلع طلع طلع طلع طلع
+
+397
+00:48:06,810 --> 00:48:07,990
+طلع طلع طلع طلع طلع طلع طلع طلع طلع طلع طلع طلع
+
+398
+00:48:07,990 --> 00:48:08,850
+طلع طلع طلع طلع طلع طلع طلع طلع طلع طلع طلع طلع
+
+399
+00:48:08,850 --> 00:48:15,110
+طلع طلع طلع طلع طلع طلع
+
+400
+00:48:23,600 --> 00:48:32,780
+Equation اتنين is non
+
+401
+00:48:32,780 --> 00:48:39,620
+homogeneousيبقى Y of T يبقى يساوي يبقى يساوي يبقى
+
+402
+00:48:39,620 --> 00:48:45,160
+يساوي يبقى يبقى يبقى يبقى يبقى يبقى يبقى يبقى يبقى
+
+403
+00:48:45,160 --> 00:48:49,900
+يبقى يبقى
+
+404
+00:48:49,900 --> 00:48:52,400
+يبقى يبقى يبقى يبقى يبقى يبقى يبقى يبقى يبقى يبقى
+
+405
+00:48:52,400 --> 00:48:52,420
+يبقى يبقى يبقى يبقى يبقى يبقى يبقى يبقى يبقى يبقى
+
+406
+00:48:52,420 --> 00:49:01,420
+يبقى يبقى يبقى يبقى يبقى يبقى يبقى
+
+407
+00:49:01,420 --> 00:49:06,690
+يالمعادلة هذه اشترقنا من؟ لازم يكون المعامل واحد
+
+408
+00:49:06,690 --> 00:49:10,370
+صحيح يبقى اول خطوة بدي اعمله بدي اجسم المعادلة
+
+409
+00:49:10,370 --> 00:49:16,470
+كلها على مين T تربيع يبقى باجي بقوله قبل ما اكتب
+
+410
+00:49:16,470 --> 00:49:27,750
+where باجي بقوله the differential equation two is
+
+411
+00:49:27,750 --> 00:49:29,050
+written
+
+412
+00:49:30,810 --> 00:49:37,710
+نقسم على T تربيع بصير يو عندي Y double prime ناقص
+
+413
+00:49:37,710 --> 00:49:47,590
+تلاتة على T في ال Y prime زائد أربعة على T تربيع
+
+414
+00:49:47,590 --> 00:49:55,610
+في ال Y كله بده يساوي من لن T فقط لا غيرالحين بقدر
+
+415
+00:49:55,610 --> 00:49:59,550
+أجيبله بسهولة بدون أخطاء، لو ما قسمتيش بصي شغلك
+
+416
+00:49:59,550 --> 00:50:05,130
+غلط، عادي لبالك، شكل ال G of T تغير، G of T كان T
+
+417
+00:50:05,130 --> 00:50:10,850
+تربية لن T، بس هنا صار لن T واحدة، تمام؟يبقى باجي
+
+418
+00:50:10,850 --> 00:50:18,370
+بقوله ال U1 as a function of T ناقص تكامل Y2 of T
+
+419
+00:50:18,370 --> 00:50:24,330
+في ال G of T على الرنسكين as a function of T DT
+
+420
+00:50:24,330 --> 00:50:31,430
+يبقى سالب تكامل ال Y2 اللي عندنا اللي هي main لت
+
+421
+00:50:31,430 --> 00:50:40,320
+تربيع للنت يبقى هاي ت تربيع وهذا للنت تمامالـ G of
+
+422
+00:50:40,320 --> 00:50:45,260
+T اللي يجهد يا بنات ليه جديدة مش العتيقة يعني
+
+423
+00:50:45,260 --> 00:50:51,280
+المعادلة الصحيحة مش عادية يبقى اللي يمين لن ت كل
+
+424
+00:50:51,280 --> 00:50:56,000
+هذا الكلام على الرونسكين اللي هو طالع في قديش ت
+
+425
+00:50:56,000 --> 00:51:06,040
+تكيب ت تكيب كله دي ت يبقى صارة المسألة تكامل لن ت
+
+426
+00:51:06,040 --> 00:51:15,250
+الكل تربيععلى T D T تمام؟ يبقى هذا الكلام بده
+
+427
+00:51:15,250 --> 00:51:22,750
+يساوي تكامل LN T لكل تربيع مشتقة LN T بنفع هيك؟
+
+428
+00:51:22,750 --> 00:51:28,370
+لإن مشتقة LN T بجداش بواحدة على T D T إذا واحدة
+
+429
+00:51:28,370 --> 00:51:33,210
+على T D T بدي أقول مشتقة LN T يعني في سالب بس برا
+
+430
+00:51:33,210 --> 00:51:35,950
+هي السالب وهي السالب
+
+431
+00:51:43,390 --> 00:51:55,890
+يبقى هذا الكلام يساوي سالب طول لنت لنت لكل تقييمأو
+
+432
+00:51:55,890 --> 00:52:01,530
+لنت كيب T لو كتبتيه لنت كيب T ماعنا مشكلة وبنروح
+
+433
+00:52:01,530 --> 00:52:08,810
+ونقول زائد constant C1 وهنا بنقول تاك C1 بده يساوي
+
+434
+00:52:08,810 --> 00:52:17,050
+Zero تمام يبقى هذا بده يعطيلك انه مين ان ال U1 بده
+
+435
+00:52:17,050 --> 00:52:25,080
+يساوي سالب طول لنت لكل تكيببنروح نجيب له مان اللي
+
+436
+00:52:25,080 --> 00:52:32,860
+هو U2 يبقى U2 as a function of T بيساوي تكامل Y1
+
+437
+00:52:32,860 --> 00:52:38,720
+of T في G of T على الرونسكين as a function of T dt
+
+438
+00:52:40,640 --> 00:52:46,260
+يبقى هذا الكلام بده يسوي تكامل Y1 اللي هو T تربيع
+
+439
+00:52:46,260 --> 00:52:52,900
+فقط لغير يبقى T تربيع و ال G of T اللي طلعت عندنا
+
+440
+00:52:52,900 --> 00:53:00,080
+اللي هي لن T و الرنس كان اللي هو قداش كان T تكيب
+
+441
+00:53:00,080 --> 00:53:10,790
+DT يبقى صار تكامل للن Tعلى ت دي ت أو تكامل ل لن ت
+
+442
+00:53:10,790 --> 00:53:19,610
+مشتقة لن ت عظيم نضيف لل أس واحد و بنجسم على الأسر
+
+443
+00:53:19,610 --> 00:53:24,950
+يعني لن ت لكل تربية على اتنين يعني النص
+
+444
+00:53:27,170 --> 00:53:37,710
+لنتي الكل تربيع زائد كونستان C2 وبناخد C2 بقداش B0
+
+445
+00:53:37,710 --> 00:53:47,610
+يبقى أصبح U2 بده يساوي من اللي هو نص لنتي الكل
+
+446
+00:53:47,610 --> 00:53:53,880
+تربيعإذا بقدر أجيب له شكل ال particular solution
+
+447
+00:53:53,880 --> 00:54:03,720
+يبقى capital Y of T بديه 7 وين capital Y؟ U1 في T
+
+448
+00:54:03,720 --> 00:54:09,660
+تربية وين ال U1؟ هذي ال U1 بدي أضربها في قداش في T
+
+449
+00:54:09,660 --> 00:54:18,970
+تربية يبقى سالب تلت T تربية سالب تلت T تربيةتي
+
+450
+00:54:18,970 --> 00:54:31,730
+تربيع في لين تيل كل تكيب اللي بعده زائد مصر في من؟
+
+451
+00:54:31,730 --> 00:54:42,190
+في .. where راحت؟الكلمة بتلعب في T تربيع في
+
+452
+00:54:42,190 --> 00:54:49,310
+ال N T كل تكعيب مظبوط لإن وعندي ال N T وعندي ال N
+
+453
+00:54:49,310 --> 00:54:55,610
+T تربيع يبقى بيصير سالب تلت زائد نص بيبقى الجداش
+
+454
+00:54:55,610 --> 00:54:57,970
+زائد سادس
+
+455
+00:55:05,890 --> 00:55:11,210
+هذا البرتكيرال سوليوشن اللي بده لو قاللي هاتلي ال
+
+456
+00:55:11,210 --> 00:55:17,010
+general solution بروح بجمعله هذا مع من مع اللي فوق
+
+457
+00:55:17,010 --> 00:55:20,010
+بجيب لمين ال general solution
+
+458
+00:55:25,200 --> 00:55:46,880
+بنتهي هذا الفيديو وانتهي
+
+459
+00:55:46,880 --> 00:55:47,600
+هذا الفيديو
+
+460
+00:55:52,960 --> 00:55:57,080
+هل تحب تسأل اي سؤال هنا يا بنان؟ يبقى هذا السؤال
+
+461
+00:55:57,080 --> 00:56:02,820
+يختلف عن سابقاها بإن المعاملات ما هي اجتماعات
+
+462
+00:56:02,820 --> 00:56:08,360
+وانما دوال في T كان بإمكاني أصي هذه السؤال بصيغة
+
+463
+00:56:08,360 --> 00:56:17,880
+أخرى أقول لك سؤال كتالي if Y1 يسوى T تربيع is a
+
+464
+00:56:17,880 --> 00:56:22,210
+solution لل differential equation هذه؟هتيلي الحل
+
+465
+00:56:22,210 --> 00:56:26,970
+الثاني تمام؟ يبقى مقدميش إلا ال reduction of order
+
+466
+00:56:26,970 --> 00:56:31,910
+إجباري في شغلها ليش المعاملات ما هيش ثوابت يبقى
+
+467
+00:56:31,910 --> 00:56:34,870
+بروح بجيب ال reduction of order و بجيب الحل التاني
+
+468
+00:56:34,870 --> 00:56:40,090
+لازم يطلع الحل التاني على الشكل هنا تمام؟ وبالتالي
+
+469
+00:56:40,090 --> 00:56:43,530
+جيبتله الحل اللي فوق و بعدين بروح بجيبله particle
+
+470
+00:56:43,530 --> 00:56:47,610
+of solution اللي جيبناه اللي عندنا هناوكتير بيجي
+
+471
+00:56:47,610 --> 00:56:52,430
+في الامتحانات زيك لكن ان غلطة في الحل التاني غلطة
+
+472
+00:56:52,430 --> 00:56:58,790
+في الحل الكلي بيصير مظبوط او كان بممكن اقولك بس ان
+
+473
+00:56:58,790 --> 00:57:01,730
+قلتك تأكديلي ان هذا حل تاني بتروح تعوضلي في
+
+474
+00:57:01,730 --> 00:57:05,530
+المعادرة لكن قلتك use reduction of order to find
+
+475
+00:57:05,530 --> 00:57:09,670
+او to show that the second solution is كذا ومن ثم
+
+476
+00:57:09,670 --> 00:57:12,270
+هتي ال solution يبقى بدك استخدم ال reduction of
+
+477
+00:57:12,270 --> 00:57:19,850
+order و بعدين تروح لمينهل بتسأل أي سؤال؟
+
+478
+00:57:44,440 --> 00:57:49,420
+طبعا بنتح ناك خلصنا لحد هنا الامتحان لكن أحيانا
+
+479
+00:57:49,420 --> 00:57:53,320
+بنجيب مسائل على غير ما اتعودنا في المحاضرات
+
+480
+00:57:53,320 --> 00:57:58,480
+الماضية كيف؟ يعني بيجيش السؤال مباشر بيقولك حل
+
+481
+00:57:58,480 --> 00:58:01,880
+المسألة دي باستخدام التعويضة الفلانية و بروح
+
+482
+00:58:01,880 --> 00:58:05,080
+بيعطينا التعويضة معينة و أنا بدأ أستخدم التعويضة
+
+483
+00:58:05,080 --> 00:58:10,140
+هذه في حل المسألة كيف المسألة يمكن تطلع first
+
+484
+00:58:10,140 --> 00:58:14,310
+order ويمكن تطلع second orderوانطلعت first order
+
+485
+00:58:14,310 --> 00:58:18,810
+يمكن exact يمكن homogeneous يمكن separable يمكن
+
+486
+00:58:18,810 --> 00:58:23,090
+linear يمكن Bernoulli يمكن اشوف المعادل المناسب و
+
+487
+00:58:23,090 --> 00:58:30,210
+اروح احلبها يمكن تبقى المثل second order يمكن يطلع
+
+488
+00:58:30,210 --> 00:58:33,790
+question with y missing question with d missing
+
+489
+00:58:34,060 --> 00:58:37,040
+يمكن يطلع لـ non-homogeneous differential
+
+490
+00:58:37,040 --> 00:58:40,240
+equation، variation of parameters أو undetermined
+
+491
+00:58:40,240 --> 00:58:43,840
+coefficients يبقى أنا بدي أشوف المناسب اللي عندي و
+
+492
+00:58:43,840 --> 00:58:48,320
+أروح أحل المثلة بالطريقة التي تناسبها
+
+493
+00:58:52,610 --> 00:58:57,490
+الاسئلة و بدى أجيبهم لكم الامتحانات السابقة مشان
+
+494
+00:58:57,490 --> 00:59:01,850
+نعرف كيف بدى نشتغل هالشغل هادى يبقى احنا مسائل
+
+495
+00:59:01,850 --> 00:59:09,920
+عامة الآن على شبطر اتنين و شبطرتلاتة كويس يبقى هنا
+
+496
+00:59:09,920 --> 00:59:14,440
+exercises
+
+497
+00:59:14,440 --> 00:59:28,660
+او examples on using باستخدام substitution استخدام
+
+498
+00:59:28,660 --> 00:59:37,230
+التعويد substitution to solve thedifferential
+
+499
+00:59:37,230 --> 00:59:42,470
+equation أول
+
+500
+00:59:42,470 --> 00:59:52,490
+سؤال جبناه في امتحان سنة الألفين بيقول use the
+
+501
+00:59:52,490 --> 00:59:55,890
+substitution
+
+502
+00:59:55,890 --> 01:00:08,230
+استخدم التعويضةU تساوي E أس Y تsolve the
+
+503
+01:00:08,230 --> 01:00:18,870
+differential equation المعادلة التفاضلية X Y ناقص
+
+504
+01:00:18,870 --> 01:00:24,270
+X تكيب في E أس ناقص Y يساوي 2
+
+505
+01:01:01,570 --> 01:01:04,850
+واضح انه السؤال تبعناه the first order
+
+506
+01:01:04,850 --> 01:01:08,470
+differential equation وليس second order بقول
+
+507
+01:01:08,470 --> 01:01:12,670
+يستخدم التعويضة U تساوي E اص Y to solve the
+
+508
+01:01:12,670 --> 01:01:17,150
+differential equation سؤالي هو هل في في مثلة كلها
+
+509
+01:01:17,150 --> 01:01:24,310
+E اص Y؟ لأ في عندي ايش؟ E اص سالب Y اذا ممكن اتخلص
+
+510
+01:01:24,310 --> 01:01:28,690
+من E اص سالب Y و احول مثلة كلها بدلالة مين؟يبقى
+
+511
+01:01:28,690 --> 01:01:33,570
+بروح أضرب كله في مين؟ في الـ E أُس Y المعادلة يبقى
+
+512
+01:01:33,570 --> 01:01:39,870
+باجي بقوله solution بدي أضرب كله في E أُس Y إيش
+
+513
+01:01:39,870 --> 01:01:46,410
+بصير يا بنات؟ X في E أُس Y في الـY' ناقص X تكيب
+
+514
+01:01:46,410 --> 01:01:54,210
+تساوي 2E أُس Y تمام؟ يبقى بطل يصير عندي E أُس ناقص
+
+515
+01:01:54,210 --> 01:02:04,860
+Y كله بدللة E أُس Yهذه الـ U تساوي U² بدي أشتق
+
+516
+01:02:04,860 --> 01:02:13,620
+يبقى دي U على دي X يبقى هنا دي U على دي X يعني منه
+
+517
+01:02:13,620 --> 01:02:19,820
+U' تساوي اشتقاق هذه بالنسبة إلى X يبقى مشتقة الـ
+
+518
+01:02:19,820 --> 01:02:25,120
+exponential بالـ exponential itself في المشتقة
+
+519
+01:02:25,120 --> 01:02:29,760
+تبعتهاالمعلومات اللى حصلت عليها بدي اعوضها في
+
+520
+01:02:29,760 --> 01:02:37,420
+المعادلة هذه اطلعيلي هذه جداش ب U prime يبقى ثارة
+
+521
+01:02:37,420 --> 01:02:45,440
+X في ال U prime ناقص X تكيب يساوي اتنين U
+
+522
+01:02:48,250 --> 01:02:51,550
+طيب شو رايك اكتبها على الشكل التالي
+
+523
+01:03:00,250 --> 01:03:05,270
+مش رايك اجسم على مين؟ على X يبقى لو جسمت على X
+
+524
+01:03:05,270 --> 01:03:15,090
+بصير U' ناقص اتنين على X هذه كلها في ال U ناقص
+
+525
+01:03:15,090 --> 01:03:20,310
+اتنين على X في ال U بده يساوي X تربية مش رايكوا
+
+526
+01:03:20,310 --> 01:03:26,170
+فيها هذه؟ لين؟ يبقى خلاص صارت زي أول ماخدنا في
+
+527
+01:03:26,170 --> 01:03:33,700
+الشاب طريق اتنينيبقى هذه linear first order
+
+528
+01:03:33,700 --> 01:03:41,750
+differential equation كذا كنا بنحل ال linearمن هنا
+
+529
+01:03:41,750 --> 01:03:48,470
+نقول ميو اف اكس يساوي اي اث ناقص اتنين تكامل واحد
+
+530
+01:03:48,470 --> 01:03:55,410
+على اكس مالها دي اكس يبقى اي اث ناقص اتنين لن
+
+531
+01:03:55,410 --> 01:04:01,170
+absolute في الاكس اللي مش حرطش عنديبقول له اه يبقى
+
+532
+01:04:01,170 --> 01:04:06,410
+هذه absolute value ل X اص ناقص اتنين يعني واحد على
+
+533
+01:04:06,410 --> 01:04:10,710
+X تربية كمية مربعة لإن تربية حطيت ال absolute و لا
+
+534
+01:04:10,710 --> 01:04:17,150
+شيلتي سيان يبقى صار هذا الميو of X بدي اخد الميو
+
+535
+01:04:17,150 --> 01:04:21,730
+of X وروح شو عمله بدي اضربه في المعادلة اللي عندنا
+
+536
+01:04:21,730 --> 01:04:25,880
+هذهيبقى ايش بيصير المعادلة هذه على الشكل التالي
+
+537
+01:04:25,880 --> 01:04:31,860
+واحد على اكس تربية U prime ناقص بدي اضرب في واحدة
+
+538
+01:04:31,860 --> 01:04:38,200
+اللي يبقى ناقص اتنين على اكس تكيب في ال U بدي ساوي
+
+539
+01:04:38,200 --> 01:04:45,620
+قداش بدي ساوي واحد او بمعنى اخر هذه واحد على اكس
+
+540
+01:04:45,620 --> 01:04:52,590
+تربية في ال U كله prime بيساوي قداشإن كامل الطرفين
+
+541
+01:04:52,590 --> 01:04:59,810
+يبقى بصير واحد على X تربية في ال U واحد على X
+
+542
+01:04:59,810 --> 01:05:06,390
+تربية في ال U بدي شوي X زائد constant C
+
+543
+01:05:08,500 --> 01:05:15,040
+مضرب كله في من؟ في ال X تربيع يبقى بصير ال U مين
+
+544
+01:05:15,040 --> 01:05:24,040
+هي ال U هذه؟ E أوس Y يبقى E أوس Y يساوي X تكيب
+
+545
+01:05:24,040 --> 01:05:31,640
+زائد C X تربيع تمام؟ احنا بدنا E أوس Y ولا بدنا Y
+
+546
+01:05:31,640 --> 01:05:41,770
+الحل؟ناخد لن للطرفين إذا ال Y بدها تساوي لن اللي
+
+547
+01:05:41,770 --> 01:05:51,590
+هو X تكيب زائد C X تربيع هذا هو الحل اللي عندنا
+
+548
+01:05:51,590 --> 01:05:56,010
+خلاص نعطيكم
+
+549
+01:05:56,010 --> 01:05:57,010
+مثال آخر
+
+550
+01:06:00,310 --> 01:06:05,590
+مثال سنة تسعة وتسعين هذا سنة اللي جابلها يبقى هذا
+
+551
+01:06:05,590 --> 01:06:12,250
+اتنين سنة التلات تسعات انتخابات عربية بقول ي solve
+
+552
+01:06:12,250 --> 01:06:20,750
+the differential equation حل المعادلة التفاضلية y
+
+553
+01:06:20,750 --> 01:06:42,700
+في y double prime ناقص y primeترابيع يستخدم
+
+554
+01:06:42,700 --> 01:06:53,680
+تعويض
+
+555
+01:06:54,340 --> 01:07:03,680
+V تساوي لن ال Y طب
+
+556
+01:07:03,680 --> 01:07:08,300
+لو ماعطانيش التعويضة هذه وجه بقى طالع في المثل
+
+557
+01:07:08,300 --> 01:07:12,760
+الأول واهلة ايش ممكن تقولي عن المثل اللي فوق هذه
+
+558
+01:07:12,760 --> 01:07:21,510
+question with with ايش T missing T مفقودةيبقى تروح
+
+559
+01:07:21,510 --> 01:07:25,890
+أحلها على equation والـT مسك لكن كونه وطني تعويضة
+
+560
+01:07:25,890 --> 01:07:32,130
+بدأ أضطر استخدمين هذه التعويضة طيب التعويضة هذه
+
+561
+01:07:32,130 --> 01:07:39,730
+ممكن أكتبها بشكل آخر احنا عندنا مين ال V يسوى اللي
+
+562
+01:07:39,730 --> 01:07:47,110
+لنا ال Y إذا لو رفعت اتنين كأس للعدد E بصير هنا ال
+
+563
+01:07:47,110 --> 01:07:50,410
+Y تساوي E أس V
+
+564
+01:07:55,180 --> 01:08:02,800
+طب ايش رأيكوا بدي اشتقها؟ بدي اشتقها بالنسبة لمن؟
+
+565
+01:08:02,800 --> 01:08:08,280
+ل T او كانت في X او اتبعها في X بدي اشتقها بالنسبة
+
+566
+01:08:08,280 --> 01:08:14,900
+ل X بالنسبة ل T ماعنا مشكلة يبقى بداجي اقول دي Y
+
+567
+01:08:14,900 --> 01:08:22,230
+by دي T اللي هو Y primeيجب أن يكون مشتقة الـ EOSV
+
+568
+01:08:22,230 --> 01:08:30,150
+بالـ EOSV السلفين في الـ Y' طيب إذا بدى أروح أجيب
+
+569
+01:08:30,150 --> 01:08:37,750
+المشتقة الثانية يبقى هذه مشتقة حاصل ضب دلتين يبقى
+
+570
+01:08:37,750 --> 01:08:47,350
+EOSV في مشتقة الدلة الثانية VW'زائد ال V' زي ما هي
+
+571
+01:08:47,350 --> 01:08:56,690
+في مشتقة ال EOSV ب EOSV في ال V' يبقى صارة المشتقة
+
+572
+01:08:56,690 --> 01:09:07,570
+اللي عندي VW' زائد V' لكل تربيع كله في EOSV
+
+573
+01:09:10,030 --> 01:09:14,850
+بناخد هذه المعلومات ونعوضها في المعادلة اللي عندنا
+
+574
+01:09:14,850 --> 01:09:20,610
+هنا هذي سميها للمعادلة star نجي نقول هنا
+
+575
+01:09:20,610 --> 01:09:26,570
+substitute and
+
+576
+01:09:26,570 --> 01:09:31,090
+equation star we get
+
+577
+01:09:33,740 --> 01:09:40,120
+الـ Y هشيلها و اكتب بدلها مين؟ E Os V يبقى E Os V
+
+578
+01:09:40,120 --> 01:09:50,340
+الـ Y W Prime هيه يبقى بصير عندي E Os 2 V في مين؟
+
+579
+01:09:50,340 --> 01:09:57,260
+في الـ V W Prime نقص V Prime لكل تربيه هي خلصنا
+
+580
+01:09:57,260 --> 01:10:05,350
+منهاالان ال Y' وY' يجب أن أربعها لأنها تربية
+
+581
+01:10:16,490 --> 01:10:23,510
+في الاصلة منها بدها تساوي Y تربيع ل E أس اتنين V
+
+582
+01:10:23,510 --> 01:10:31,750
+يبقى E أس اتنين V لإن ال Y هو ميعطينيها بقداش V
+
+583
+01:10:31,750 --> 01:10:38,270
+طيب إيش رايكوا أبسط المعادلة كلها من أولها لآخرها
+
+584
+01:10:38,270 --> 01:10:44,950
+نقسم عالميا على E أس اتنين V لأن هو رقم أكبر من
+
+585
+01:10:44,950 --> 01:10:45,270
+Zero
+
+586
+01:10:57,780 --> 01:11:05,200
+طيب يبقى آلة المسألة الشكل التالي بعد القسمة
+
+587
+01:11:07,130 --> 01:11:14,350
+زائد v prime تاربيع ناقص v prime تاربيع بده يسوى
+
+588
+01:11:14,350 --> 01:11:22,010
+قداش v اظن هذه وهذه مع السلامة تمام يبقى آلة
+
+589
+01:11:22,010 --> 01:11:29,430
+المسألة الى v double prime ناقص v تسوى zero
+
+590
+01:11:31,650 --> 01:11:35,950
+هوموجينياس differential equation من ال second
+
+591
+01:11:35,950 --> 01:11:42,010
+order كيف بنحلها يعني
+
+592
+01:11:42,010 --> 01:11:44,870
+بدنا نروح نجيب ال characteristic equation ممتاز
+
+593
+01:11:44,870 --> 01:11:49,030
+جدا يبقى بدنا نروح نحلها بواسطة ال characteristic
+
+594
+01:11:49,030 --> 01:11:59,120
+equation يبقى باجي بقوله letV تساوي E أس RT ب
+
+595
+01:11:59,120 --> 01:12:02,200
+Solution
+
+596
+01:12:02,200 --> 01:12:08,500
+then the characteristic
+
+597
+01:12:08,500 --> 01:12:20,140
+equation is R ترابيع ناقص واحد يساوي Zero يبقى هاد
+
+598
+01:12:20,140 --> 01:12:28,180
+ايش؟R تساوي زائد او ناقص مين واحد يبقى معنا هذا
+
+599
+01:12:28,180 --> 01:12:39,760
+الكلام ان V بتصير عندنا
+
+600
+01:12:39,760 --> 01:12:47,720
+ال V of T as a function of T هي عبارة عن C1 EOS T
+
+601
+01:12:47,720 --> 01:12:58,910
+C2 EOS ناقص Tمظبوط؟ لكن V of T مين هي؟ لن ال Y إذا
+
+602
+01:12:58,910 --> 01:13:05,070
+لن ال Y هي اللي بتسوي هذا الكلام هذا بدي أعطيكي ان
+
+603
+01:13:05,070 --> 01:13:14,910
+لن ال Y يسوى C1 E Os T C2 E Os ناقص T لن ال Y بقدر
+
+604
+01:13:14,910 --> 01:13:15,850
+أتخلص منها
+
+605
+01:13:19,280 --> 01:13:25,020
+ناخد الترفع كله كأسل العدد A يبقى ماجي بقوله
+
+606
+01:13:25,020 --> 01:13:30,120
+solution of
+
+607
+01:13:30,120 --> 01:13:37,120
+equationY تساوي
+
+608
+01:13:37,120 --> 01:13:48,940
+E أس C واحد E أس T زائد C اتنين E أس سالب T بالشكل
+
+609
+01:13:48,940 --> 01:13:57,200
+اللي عندنا طيب هذه كمان فكرة غير الفكرة الأولى
+
+610
+01:13:57,630 --> 01:14:02,330
+الأولى كانت على ال first order وهذه كانت على
+
+611
+01:14:02,330 --> 01:14:05,790
+second order
+
+612
+01:14:19,520 --> 01:14:26,760
+برضه سنة تسعة و تسعين الأولاني كان في شهر أربع
+
+613
+01:14:26,760 --> 01:14:32,880
+يعني انا الفصل وهذه في نهاية الفصل في شهر ستة
+
+614
+01:14:32,880 --> 01:14:41,000
+السؤال التالت برضه سنة تسعة و تسعين final بيقول
+
+615
+01:14:41,000 --> 01:14:49,560
+use the substitution useThe Substitution
+
+616
+01:14:49,560 --> 01:14:59,300
+تخدم التعويضة الـ W يساوي Y تربية ناقص Y ليه أكبر
+
+617
+01:14:59,300 --> 01:15:11,820
+من Zero to solve the differential equation لحل
+
+618
+01:15:11,820 --> 01:15:23,840
+المعادلة التفاضليةYW' ناقص واحد على X زائد واحد في
+
+619
+01:15:23,840 --> 01:15:32,040
+Y' زائد واحد على X في Y يساوي Zero وال X greater
+
+620
+01:15:32,040 --> 01:15:39,880
+than Zero شكل
+
+621
+01:15:39,880 --> 01:15:45,440
+التعويضة بختلف عن التعويتين السابقاتلأن هذا بيجمع
+
+622
+01:15:45,440 --> 01:16:06,080
+ما بين الواعي ومشتقتها نرجع
+
+623
+01:16:06,080 --> 01:16:11,160
+لسؤالنا مرة تانية شوف السؤال ايش بيقول وكيف بدنا
+
+624
+01:16:11,160 --> 01:16:18,330
+نبدأ نحلالسؤال بيقول استخدم التعويضة W يساوي
+
+625
+01:16:18,330 --> 01:16:22,750
+المشتقة الأولى ل Y ناقص ال Y وهذه المشتقة دائما و
+
+626
+01:16:22,750 --> 01:16:27,570
+أبدا أكبر من ال zero عشان اتحل المعادلة التفاضلية
+
+627
+01:16:27,570 --> 01:16:31,350
+اللى قدامنا هذه وزي ما انت شايف المعادلة من الرتبة
+
+628
+01:16:31,350 --> 01:16:36,810
+الثانية ممتاز جال استخدم التعويضة إذا بتروح استخدم
+
+629
+01:16:36,810 --> 01:16:41,590
+له مين التعويضة اللى جال عليه هذهأحنا عندنا w
+
+630
+01:16:41,590 --> 01:16:48,330
+يساوي y prime ناقص y هلحين عندنا بنات اتدالة
+
+631
+01:16:48,330 --> 01:16:52,090
+بدلالة y و t ولا x و t
+
+632
+01:16:55,450 --> 01:17:00,930
+يعني T أجاب بدالها من؟ بدالها X ممتاز جدا يبقى Y'
+
+633
+01:17:01,350 --> 01:17:07,870
+هذه هي عبارة عن dy على dx تمام؟ اذا انا لو جيت
+
+634
+01:17:07,870 --> 01:17:15,930
+اشتقت هذه بالنسبة ل X بحصل على W' صح ولا لا؟ W'
+
+635
+01:17:16,610 --> 01:17:23,330
+يسوى مشتقة الأولى بYW' ناقص مشتقة الثانية اللي هي
+
+636
+01:17:23,330 --> 01:17:29,720
+من؟Y prime طب كويس تعالى نشوف المعادلة تبعتنا هذه
+
+637
+01:17:29,720 --> 01:17:36,380
+شكلها هذه يا بنات معادلتنا YW prime ناقص واحد على
+
+638
+01:17:36,380 --> 01:17:45,160
+X Y prime ناقص Y prime زائد واحد على X في ال Y كله
+
+639
+01:17:45,160 --> 01:17:50,460
+بده يساوي مين بده يساوي Zero تمامإذاً هذه بقدر
+
+640
+01:17:50,460 --> 01:17:57,480
+أقول yw prime ناقص y prime الأولى و التالتى مع بعض
+
+641
+01:17:57,480 --> 01:18:02,700
+هذه و هذه بقدر أاخد منهم واحد على x عامل مشترك
+
+642
+01:18:02,700 --> 01:18:08,640
+يبقى لو أخد سلب واحد على x عامل مشترك بظل y prime
+
+643
+01:18:08,640 --> 01:18:16,240
+ناقص y ساوي زير تمامهيه والله هذه كويسة العملية
+
+644
+01:18:16,240 --> 01:18:23,340
+اللى عملتها برضه أفدتني صار هدمين w prime و هدمين
+
+645
+01:18:23,340 --> 01:18:30,900
+w موطن اذا المعادلة هذه عملنا لها reduction of
+
+646
+01:18:30,900 --> 01:18:36,940
+order من الرتبة الثانيةالى مين؟ الى الرتبة الأولى
+
+647
+01:18:36,940 --> 01:18:43,260
+يبقى صارت مسألة بسيطة جدا يبقى ده W prime ناقص
+
+648
+01:18:43,260 --> 01:18:50,580
+واحد على X W بدي ساوي قداش؟ بساوي Zero تمام؟ يعني
+
+649
+01:18:50,580 --> 01:18:59,240
+بصير عندك W prime على W بدي ساوي قداش؟ واحد على X
+
+650
+01:18:59,240 --> 01:19:07,820
+مكامل؟ يبقى لو كاملنابصير لن الـW فش داعي لل
+
+651
+01:19:07,820 --> 01:19:13,660
+absolute value لأنها بالموجة تمام؟ بده يساوي كمان
+
+652
+01:19:13,660 --> 01:19:19,900
+لن ال X ولا داعي لأن ال X greater than zero زائد
+
+653
+01:19:19,900 --> 01:19:26,140
+constant C طيب إيش رأيك ال constant C؟ لو كتبت لن
+
+654
+01:19:26,140 --> 01:19:31,720
+C، بيمشي الحال؟ماش اشكالية اوكك و LNC زي ما بدك طب
+
+655
+01:19:31,720 --> 01:19:36,540
+ليش سويت هيك هذا اللي بدنا نجاوب عليه نجاوب عليه
+
+656
+01:19:36,540 --> 01:19:45,840
+بصير المسألة LNW يساوي LNXCلن زاد لن بقدر اشبهها
+
+657
+01:19:45,840 --> 01:19:49,640
+باللن و بقدر اطيّر اللنات وبالتالي لابد اطلع عندى
+
+658
+01:19:49,640 --> 01:19:55,940
+لن ولا exponential يبقى هذه لن و لن بقدر ارفع
+
+659
+01:19:55,940 --> 01:20:04,940
+اتنين كاس للعدد ايه يبقى w بدى يسوى x في c مصبوط
+
+660
+01:20:04,940 --> 01:20:12,850
+طيب نجي هنا نقول هذه ال w بقداش يا بناتY'-Y يبقى
+
+661
+01:20:12,850 --> 01:20:27,010
+Y'-Y يساوي 6 إيه الشكل المعادل هذه إيش
+
+662
+01:20:27,010 --> 01:20:33,130
+اسمها Linear مظبوط يبقى Linear إحنا حلنا المثلة
+
+663
+01:20:33,130 --> 01:20:37,990
+الأولانية تكامل عادي جدا طلعت لمعادلة جديدة Linear
+
+664
+01:20:37,990 --> 01:20:45,990
+First Orderيبقى هذه linear first order
+
+665
+01:20:45,990 --> 01:20:54,690
+differential equation تمام يعني ايش اللي حصل اجيب
+
+666
+01:20:54,690 --> 01:21:01,630
+طريقتين من الطرق بسؤال واحد تعوض هذه قادتني الى
+
+667
+01:21:01,630 --> 01:21:06,190
+separable equation ال W في شجة و ال X في شجة يبعد
+
+668
+01:21:06,190 --> 01:21:10,420
+ال separable equationواسيبربوا القادتنا إلى من؟
+
+669
+01:21:10,420 --> 01:21:15,060
+إلى ال linear من هنا أجت أهمية من؟ أهمية السؤال
+
+670
+01:21:15,060 --> 01:21:18,640
+يعني السؤال اللي ممكن اختار مش ببلاش يعطيك لأ انا
+
+671
+01:21:18,640 --> 01:21:22,960
+قاصد و متعمد اجيبك طريقتين او معادلتين من اللي
+
+672
+01:21:22,960 --> 01:21:28,520
+اتعلمتي حلهم مشان نيجي نحلهم هنا بسؤال يعني بستاهل
+
+673
+01:21:28,520 --> 01:21:33,980
+يكون سؤال امتحانمظبوط طيب كويس يبقى بنحلها بال
+
+674
+01:21:33,980 --> 01:21:40,220
+linear بسيطة جدا هذه جاهزة كويس يبقى باجي بقول لم
+
+675
+01:21:40,220 --> 01:21:47,920
+U of X دو ساوي E أص ناقص تكامل DX ماعنديش المعامل
+
+676
+01:21:47,920 --> 01:21:55,140
+سالب واحد يبقى يساوي E أص ناقص X بدي أروح أضرب
+
+677
+01:21:55,140 --> 01:22:01,500
+المعادلة اللي فوق هذه في E أص ناقص Xبصير EOS ناقص
+
+678
+01:22:01,500 --> 01:22:10,280
+X في Y prime ناقص EOS ناقص X في Y يساوي CX في EOS
+
+679
+01:22:10,280 --> 01:22:19,440
+ناقص X او بمعنى اخر هذه الان EOS ناقص X في Y الكلة
+
+680
+01:22:19,440 --> 01:22:29,280
+prime يساوي CX EOS ناقص AX انكمليبقى E أص ناقص X
+
+681
+01:22:29,280 --> 01:22:40,100
+في Y يسوى تكامل CX في E أص ناقص X في DX تكامل هذه
+
+682
+01:22:40,100 --> 01:22:47,720
+بيعطيني تكامل هذا هذا CX ايوة كيف نكامل هذا؟ كيف؟
+
+683
+01:22:47,720 --> 01:22:52,180
+bypass عادي جدا وع الجدول كمان مش لسه بدي U وD لأ
+
+684
+01:22:52,180 --> 01:22:57,170
+لأ جاهزين اذا باجي بقوله على الجدولبقول له هنا
+
+685
+01:22:57,170 --> 01:23:03,270
+derivatives و هنا بده اجيب له integrals ايه ال
+
+686
+01:23:03,270 --> 01:23:08,170
+derivatives بده اخدله cx و ال integrals بده اخدله
+
+687
+01:23:08,170 --> 01:23:17,040
+e-x تفاضل هذه بقداش؟بـC تكامل هدف ناقص EOS ناقص X
+
+688
+01:23:17,040 --> 01:23:22,140
+يعني EOS ناقص X على ناقص واحد يعني ناقص EOS ناقص X
+
+689
+01:23:22,140 --> 01:23:29,740
+تفضل الـC بقدرش بـ0 تكامل هدف EOS ناقص X هدف هدف
+
+690
+01:23:29,740 --> 01:23:36,340
+إشارة موجب وهدف هدف إشارة سالب يبقى النتيجة أثارة
+
+691
+01:23:36,340 --> 01:23:45,660
+EOS ناقص X في الـYبدى يساوي ناقص CX E ناقص X ناقص
+
+692
+01:23:45,660 --> 01:23:52,860
+C E ناقص X زائد constant من C1 تبع التكامل ما
+
+693
+01:23:52,860 --> 01:23:56,900
+ننساهوش هذا لإن احنا عند المشتق الثاني معناته اندي
+
+694
+01:23:56,900 --> 01:24:03,370
+two constantsطيب نضرب فيه وص إكس هذي مش هنتخلص
+
+695
+01:24:03,370 --> 01:24:10,970
+منها نحصل على Y يبقى Y هتساوي سالب CX وهنا سالب C
+
+696
+01:24:10,970 --> 01:24:20,910
+وهنا زائد C1 E وص X يبقى هذا شكل الحل اللي عندنا
+
+697
+01:24:20,910 --> 01:24:23,350
+تبع من؟ تبع المثلة
+
+698
+01:24:36,050 --> 01:24:42,170
+طيب في سؤال جبته انا في امتحان لطلبه طلبات في ال
+
+699
+01:24:42,170 --> 01:24:50,810
+2005 بيقول ما يأتي هذا قداش تلاتة هذا اربعة و هذا
+
+700
+01:24:50,810 --> 01:25:00,150
+في ال 2005 بيقول use the substitution use the
+
+701
+01:25:00,150 --> 01:25:02,150
+substitution
+
+702
+01:25:06,490 --> 01:25:20,290
+U يساوي Y ناقص X تسالف الـ differential equation
+
+703
+01:25:20,290 --> 01:25:35,690
+لتحل المعادلة التفاضلية Dy بDX يساوي Sine تربيعY
+
+704
+01:25:35,690 --> 01:25:51,330
+ناقص X يبقى
+
+705
+01:25:51,330 --> 01:25:58,130
+أنا بدأجي للتعويض اللي اعطاه هالي جالي ليه تساوي Y
+
+706
+01:25:58,130 --> 01:26:03,350
+ناقص X كنت استخدم هذه التعويضة في حل المعادلة اللي
+
+707
+01:26:03,350 --> 01:26:09,310
+عندناأحنا تدارج أن نقول أن صين تربيع Y أو صين
+
+708
+01:26:09,310 --> 01:26:14,150
+تربيع X ونقول أيش صين تربيع Y ناقص X إذا بدي أروح
+
+709
+01:26:14,150 --> 01:26:17,710
+أشيل Y ناقص X و أحط مكانها U يبقى هاي شيلناها و
+
+710
+01:26:17,710 --> 01:26:22,770
+حطينا بدلها مين؟ حطينا بدلها U يبقى يا بنات لو جيت
+
+711
+01:26:22,770 --> 01:26:31,170
+قلت بدي ال U' ال U' يعني مين؟ ال U على D نكتبها
+
+712
+01:26:31,170 --> 01:26:36,170
+بالتفصيل، بلاش تقولهايعني بدي اشتق الدالة كلها
+
+713
+01:26:36,170 --> 01:26:46,250
+بالنسبة الى X يبقى DY على DX ومشتقة ال X بقدرش ب 1
+
+714
+01:26:47,000 --> 01:26:54,500
+يبقى بناء على اليسار عندنا دي يو على دي إكس زائد
+
+715
+01:26:54,500 --> 01:27:00,180
+واحد بدي أسوأ من دي واي على دي إكس إذا بدي أجيل
+
+716
+01:27:00,180 --> 01:27:05,240
+المقاس اللي بتبعتي أشيل دي واي على دي إكس و أكتب
+
+717
+01:27:05,240 --> 01:27:10,920
+بدلها دي وي على دي إكس زائد واحد يبقى هنا إيش بصير
+
+718
+01:27:10,920 --> 01:27:18,730
+الدي واي على دي إكس اللي هي دي يوعلى dx زائد واحد
+
+719
+01:27:18,730 --> 01:27:28,770
+يساوي من؟ يساوي ال sign تربيع ال Uتمام تمام يبقى
+
+720
+01:27:28,770 --> 01:27:37,030
+بدل مكان المتغير y و x صار المتغير u و x تمام يبقى
+
+721
+01:27:37,030 --> 01:27:46,110
+هذه بيصير main اللي هو du على dx يساوي sin تاربيع
+
+722
+01:27:46,110 --> 01:27:55,580
+ال u ناقص واحدكويس؟ طب إيش رايك لو جيت قولتلك هذه
+
+723
+01:27:55,580 --> 01:28:05,010
+تساوي ناقص واحد ناقص ساينتر بي اليوم، بنفع؟طب اللي
+
+724
+01:28:05,010 --> 01:28:10,690
+بين قوسين هي مين؟ قوسين تربية اليوم يبقى صار عندنا
+
+725
+01:28:10,690 --> 01:28:19,750
+مين؟ اللي هو du على dx يسوى ناقص قوسين تربية اليوم
+
+726
+01:28:19,750 --> 01:28:25,240
+شو رأيك نفصل المتغيرات؟يبقى صارت separation of
+
+727
+01:28:25,240 --> 01:28:35,280
+variable صار DU على cosine تربيع ال U يسوى ناقص DX
+
+728
+01:28:35,280 --> 01:28:41,700
+فقط لغير او انشئتنا فقلنا واحد على cosine تربيع ال
+
+729
+01:28:41,700 --> 01:28:51,780
+U منين؟ six تربيع ال U DU سالب DX انكمل الطرفين
+
+730
+01:28:52,940 --> 01:29:00,020
+قداش تكمل sector بيه U دي U بتاني ال U يبقى تاني
+
+731
+01:29:00,020 --> 01:29:09,160
+ال U يسوى ناقص X زائد constant C طب انا مين؟ بديش
+
+732
+01:29:09,160 --> 01:29:16,330
+تاني ال U بدي ال Uيبقى بناء عليه ال U ها دي بدها
+
+733
+01:29:16,330 --> 01:29:23,670
+تساوي tan inverse ل C ناقص X
+
+734
+01:29:27,310 --> 01:29:33,210
+مظبوط ايه؟ يعني احد تان انفرس للطرفين باجي بقول U
+
+735
+01:29:33,210 --> 01:29:40,910
+هي عبارة عن مين؟ Y ناقص X يبقى صار عندي Y ناقص X
+
+736
+01:29:40,910 --> 01:29:48,970
+يساوي تان انفرس ل C ناقص ال X ود ال X على الشجرة
+
+737
+01:29:48,970 --> 01:29:54,190
+التانية يبقى حصلنا على الحل تبع المثلة يبقى هذا
+
+738
+01:29:54,190 --> 01:30:06,180
+يعطينا ان Yتساوي X زائد tan inverse لمن؟ ل C ناقص
+
+739
+01:30:06,180 --> 01:30:12,960
+X الشكل اللي عندنا هذا هو الحل تبع المعادلة L عن N
+
+740
+01:30:15,420 --> 01:30:19,620
+يبقى هي عندك بدل السؤال أربعة أسئلة وكلها تعويضات
+
+741
+01:30:19,620 --> 01:30:23,800
+وكلها مسائل امتحانات يعني لو جيبنالكم سؤال في
+
+742
+01:30:23,800 --> 01:30:28,560
+الامتحان القادم الله سمحه الله يكون هي ضربناكي على
+
+743
+01:30:28,560 --> 01:30:35,240
+مين على أمثلة على هذا الموضوع طبعا حد في كل هذه
+
+744
+01:30:35,240 --> 01:30:40,730
+التساؤلالمرة القادمة ان شاء الله يوم الأربعة بنبدأ
+
+745
+01:30:40,730 --> 01:30:44,690
+chapter أربعة يوم الأربعة بنبدأ chapter أربعة ان
+
+746
+01:30:44,690 --> 01:30:49,130
+شاء الله chapter أربعة هو تعميم ل chapter تلاتة
+
+747
+01:30:49,130 --> 01:30:52,570
+يعني بيبقى ال second order بيشوف third order
+
+748
+01:30:52,570 --> 01:30:56,090
+fourth order and nth order تمام؟
+
diff --git a/PL9fwy3NUQKwa8ZDfSFGn6H8xVFLzqmCZC/_NMCQUdH1C8_raw.json b/PL9fwy3NUQKwa8ZDfSFGn6H8xVFLzqmCZC/_NMCQUdH1C8_raw.json
new file mode 100644
index 0000000000000000000000000000000000000000..df3e17d9ca604d1a630af4d36fa64cd3a279292a
--- /dev/null
+++ b/PL9fwy3NUQKwa8ZDfSFGn6H8xVFLzqmCZC/_NMCQUdH1C8_raw.json
@@ -0,0 +1 @@
+{"segments": [{"id": 1, "seek": 1198, "start": 9.86, "end": 11.98, "text": "بسم الله الرحمن الرحيم", "tokens": [3555, 38251, 21984, 34892, 5016, 27842, 34892, 5016, 32640], "avg_logprob": -0.07368164286017417, "compression_ratio": 1.0789473684210527, "no_speech_prob": 0.0, "words": [{"start": 9.86, "end": 10.82, "word": "بسم", "probability": 0.792724609375}, {"start": 10.82, "end": 11.02, "word": " الله", "probability": 0.9697265625}, {"start": 11.02, "end": 11.46, "word": " الرحمن", "probability": 0.9454752604166666}, {"start": 11.46, "end": 11.98, "word": " الرحيم", "probability": 0.9947916666666666}], "temperature": 1.0}, {"id": 2, "seek": 3890, "start": 12.79, "end": 38.91, "text": "المرة الفاتة بدأنا في حلال non homogeneous differential equation اللى على الشكل اللى عندنا هذا star استخدمنا المرة الفاتة طريقة ال undetermined coefficients طريقة المعاملات المجهولة وقلنا اشترطنا شرطين الشرط الأول لازم يكون المعاملات هدول ثوابت الشرط التانى لازم GOT تبقى على شكل polynomial", "tokens": 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هذا", "probability": 0.6904296875}, {"start": 20.03, "end": 20.69, "word": " star", "probability": 0.270751953125}, {"start": 20.69, "end": 22.03, "word": " استخدمنا", "probability": 0.9140625}, {"start": 22.03, "end": 22.31, "word": " المرة", "probability": 0.9638671875}, {"start": 22.31, "end": 22.81, "word": " الفاتة", "probability": 0.9371744791666666}, {"start": 22.81, "end": 23.37, "word": " طريقة", "probability": 0.9900716145833334}, {"start": 23.37, "end": 23.61, "word": " ال", "probability": 0.94775390625}, {"start": 23.61, "end": 24.59, "word": " undetermined", "probability": 0.7893880208333334}, {"start": 24.59, "end": 25.33, "word": " coefficients", "probability": 0.88134765625}, {"start": 25.33, "end": 25.95, "word": " طريقة", "probability": 0.95849609375}, {"start": 25.95, "end": 26.91, "word": " المعاملات", "probability": 0.99326171875}, {"start": 26.91, "end": 28.09, "word": " المجهولة", "probability": 0.9912109375}, {"start": 28.09, "end": 28.89, "word": " وقلنا", 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عندي على الشكل هذا", "tokens": [3555, 9640, 2407, 5016, 4724, 7435, 1829, 3555, 2423, 42632, 15756, 5367, 30767, 1829, 9673, 25720, 9673, 46958, 10632, 4032, 4724, 7435, 1829, 3555, 2135, 21542, 1211, 6055, 3555, 3615, 2423, 42632, 4032, 4724, 30544, 21542, 1211, 18871, 16254, 15844, 25124, 28820, 23758], "avg_logprob": -0.2634943127632141, "compression_ratio": 1.4264705882352942, "no_speech_prob": 0.0, "words": [{"start": 108.32, "end": 108.82, "word": "باروح", "probability": 0.482086181640625}, {"start": 108.82, "end": 109.18, "word": " بجيب", "probability": 0.9158935546875}, {"start": 109.18, "end": 109.28, "word": " ال", "probability": 0.9189453125}, {"start": 109.28, "end": 109.78, "word": " homogeneous", "probability": 0.360107421875}, {"start": 109.78, "end": 110.34, "word": " differential", "probability": 0.771484375}, {"start": 110.34, "end": 110.94, "word": " equation", "probability": 0.54052734375}, {"start": 110.94, "end": 111.28, "word": " زي", "probability": 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لـnearly independent solutions للـ homogeneous differential equation يبقى صار الحل العام تبع الـ homogeneous differential equation على الشكل اللى عندنا هذا", "tokens": [6027, 7649, 8717, 5172, 2655, 43042, 3714, 14407, 3615, 1829, 36764, 24401, 4032, 1975, 2655, 1863, 9957, 5296, 39184, 716, 289, 356, 6695, 6547, 24976, 39184, 42632, 15756, 5367, 7251, 3555, 4587, 7578, 20328, 9640, 21542, 1211, 18863, 10943, 6055, 3555, 3615, 2423, 39184, 42632, 15756, 5367, 15844, 25124, 28820, 13672, 7578, 43242, 8315, 23758], "avg_logprob": -0.4550781154206821, "compression_ratio": 1.5058823529411764, "no_speech_prob": 5.960464477539063e-08, "words": [{"start": 187.85999999999999, "end": 188.82, "word": "الان", "probability": 0.146759033203125}, {"start": 188.82, "end": 189.78, "word": " نفترض", "probability": 0.74456787109375}, {"start": 189.78, "end": 190.12, "word": " مواعي", "probability": 0.6364288330078125}, {"start": 190.12, "end": 190.44, "word": " واحد", "probability": 0.58074951171875}, 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"بقول to find a particular solution مش هنتجيب الحل الخاص للمعادلة بطريقة ال variation of parameters بتغيير الوسيطات we replace the constants نستبدل replace يعني نستبدل", "tokens": [3555, 39648, 281, 915, 257, 1729, 3827, 37893, 8032, 29399, 7435, 1829, 3555, 21542, 1211, 33962, 33546, 5296, 19528, 3615, 18513, 37977, 4724, 9566, 16572, 28671, 2423, 12990, 295, 9834, 39894, 17082, 1829, 13546, 2423, 41779, 1829, 9566, 9307, 321, 7406, 264, 35870, 8717, 14851, 44510, 1211, 7406, 37495, 22653, 8717, 14851, 44510, 1211], "avg_logprob": -0.1741477213122628, "compression_ratio": 1.346820809248555, "no_speech_prob": 0.0, "words": [{"start": 202.23, "end": 202.81, "word": "بقول", "probability": 0.5250244140625}, {"start": 202.81, "end": 203.05, "word": " to", "probability": 0.1697998046875}, {"start": 203.05, "end": 203.43, "word": " find", "probability": 0.9228515625}, {"start": 203.43, "end": 203.67, "word": " a", "probability": 0.94775390625}, {"start": 203.67, "end": 204.19, "word": " 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2114.39, "word": " value", "probability": 0.98876953125}, {"start": 2114.39, "end": 2115.31, "word": " لسك", "probability": 0.8250325520833334}, {"start": 2115.31, "end": 2116.17, "word": " T", "probability": 0.319091796875}, {"start": 2116.17, "end": 2118.33, "word": " زائد", "probability": 0.7047526041666666}, {"start": 2118.33, "end": 2119.57, "word": " تاني", "probability": 0.869140625}, {"start": 2119.57, "end": 2119.83, "word": " T", "probability": 0.56396484375}], "temperature": 1.0}, {"id": 93, "seek": 213555, "start": 2120.39, "end": 2135.55, "text": "وهنا ناقص C2 وتكامل ال cosine بsin 80 وزائد constant C2 وبنقول هنا take code C2", "tokens": [2407, 3224, 8315, 8717, 995, 4587, 9381, 383, 17, 34683, 4117, 10943, 1211, 2423, 23565, 4724, 19767, 4688, 4032, 11622, 16373, 3215, 5754, 383, 17, 46599, 1863, 39648, 34105, 747, 3089, 383, 17], "avg_logprob": -0.36443016108344584, "compression_ratio": 1.1111111111111112, "no_speech_prob": 0.0, "words": [{"start": 2120.39, "end": 2121.17, "word": "وهنا", "probability": 0.5655110677083334}, {"start": 2121.17, "end": 2122.07, "word": " ناقص", "probability": 0.74609375}, {"start": 2122.07, "end": 2122.87, "word": " C2", "probability": 0.6903076171875}, {"start": 2122.87, "end": 2123.91, "word": " وتكامل", "probability": 0.8448486328125}, {"start": 2123.91, "end": 2124.11, "word": " ال", "probability": 0.72998046875}, {"start": 2124.11, "end": 2124.85, "word": " cosine", "probability": 0.61376953125}, {"start": 2124.85, "end": 2126.41, "word": " بsin", "probability": 0.6351318359375}, {"start": 2126.41, "end": 2127.31, "word": " 80", "probability": 0.260009765625}, {"start": 2127.31, "end": 2128.67, "word": " وزائد", "probability": 0.72998046875}, {"start": 2128.67, "end": 2129.25, "word": " constant", "probability": 0.56787109375}, {"start": 2129.25, "end": 2130.45, "word": " C2", "probability": 0.9736328125}, {"start": 2130.45, "end": 2131.69, "word": " وبنقول", "probability": 0.81298828125}, {"start": 2131.69, "end": 2132.45, "word": " هنا", "probability": 0.822265625}, {"start": 2132.45, "end": 2133.31, "word": " take", "probability": 0.5703125}, {"start": 2133.31, "end": 2134.09, "word": " code", "probability": 0.400634765625}, {"start": 2134.09, "end": 2135.55, "word": " C2", "probability": 0.969970703125}], "temperature": 1.0}, {"id": 94, "seek": 216361, "start": 2135.93, "end": 2163.61, "text": "يساوي 0 يبقى صارة ان U2 as a function of T هو عبارة عن اتنين لان absolute value لسك T زائد تاني T نقص اتنين sin T اذا بقدر اجيب شكل ال particular solution تمام", "tokens": [1829, 3794, 995, 45865, 1958, 7251, 3555, 4587, 7578, 20328, 9640, 3660, 16472, 624, 17, 382, 257, 2445, 295, 314, 31439, 6225, 3555, 9640, 3660, 18871, 1975, 2655, 1863, 9957, 5296, 7649, 8236, 2158, 5296, 3794, 4117, 314, 30767, 16373, 3215, 6055, 7649, 1829, 314, 8717, 4587, 9381, 1975, 2655, 1863, 9957, 3343, 314, 1975, 15730, 4724, 28543, 2288, 1975, 7435, 1829, 3555, 13412, 28820, 2423, 1729, 3827, 46811, 10943], 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T", "probability": 0.8828125}, {"start": 2143.13, "end": 2143.93, "word": " هو", "probability": 0.89990234375}, {"start": 2143.93, "end": 2144.57, "word": " عبارة", "probability": 0.79754638671875}, {"start": 2144.57, "end": 2144.93, "word": " عن", "probability": 0.9814453125}, {"start": 2144.93, "end": 2145.83, "word": " اتنين", "probability": 0.84979248046875}, {"start": 2145.83, "end": 2146.93, "word": " لان", "probability": 0.334625244140625}, {"start": 2146.93, "end": 2147.39, "word": " absolute", "probability": 0.7578125}, {"start": 2147.39, "end": 2148.49, "word": " value", "probability": 0.99169921875}, {"start": 2148.49, "end": 2149.61, "word": " لسك", "probability": 0.7008463541666666}, {"start": 2149.61, "end": 2150.31, "word": " T", "probability": 0.378662109375}, {"start": 2150.31, "end": 2151.69, "word": " زائد", "probability": 0.8326822916666666}, {"start": 2151.69, "end": 2152.41, "word": " تاني", "probability": 0.8546549479166666}, {"start": 2152.41, "end": 2152.73, 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"word": " تمام", "probability": 0.896728515625}], "temperature": 1.0}, {"id": 95, "seek": 219985, "start": 2172.37, "end": 2199.85, "text": "بقول له the particular solution of equation star is capital Y of T بده يساوي U واحد في ال Y one زائد U اتنين في ال Y two", "tokens": [3555, 39648, 46740, 264, 1729, 3827, 295, 5367, 3543, 307, 4238, 398, 295, 314, 47525, 3224, 7251, 3794, 995, 45865, 624, 36764, 24401, 8978, 2423, 398, 472, 30767, 16373, 3215, 624, 1975, 2655, 1863, 9957, 8978, 2423, 398, 732], "avg_logprob": -0.198046875, "compression_ratio": 1.1923076923076923, "no_speech_prob": 0.0, "words": [{"start": 2172.37, "end": 2172.95, "word": "بقول", "probability": 0.8583984375}, {"start": 2172.95, "end": 2173.27, "word": " له", "probability": 0.52978515625}, {"start": 2173.27, "end": 2174.11, "word": " the", "probability": 0.60205078125}, {"start": 2174.11, "end": 2176.41, "word": " particular", "probability": 0.87353515625}, {"start": 2176.41, "end": 2179.87, "word": " solution", 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"text": "اذا capital Y of T بده يسمى وين ال U1؟ هاد ال U1، هاد ايه؟ اللي كتبناها على الشكل هذا، هاد ال U1، هاد بنا نضربها في مينوبالات", "tokens": [45636, 995, 4238, 398, 295, 314, 47525, 3224, 7251, 38251, 7578, 4032, 9957, 2423, 624, 16, 22807, 8032, 18513, 2423, 624, 16, 12399, 8032, 18513, 1975, 1829, 3224, 22807, 13672, 1829, 9122, 2655, 3555, 8315, 11296, 15844, 25124, 28820, 23758, 12399, 8032, 18513, 2423, 624, 16, 12399, 8032, 18513, 4724, 8315, 8717, 11242, 25513, 11296, 8978, 3714, 9957, 37746, 6027, 9307], "avg_logprob": -0.3767640999247951, "compression_ratio": 1.4609929078014185, "no_speech_prob": 0.0, "words": [{"start": 2200.46, "end": 2200.9, "word": "اذا", "probability": 0.519683837890625}, {"start": 2200.9, "end": 2201.5, "word": " capital", "probability": 0.4638671875}, {"start": 2201.5, "end": 2202.72, "word": " Y", "probability": 0.869140625}, {"start": 2202.72, "end": 2203.34, "word": " of", "probability": 0.822265625}, {"start": 2203.34, "end": 2203.82, "word": " T", "probability": 0.88623046875}, {"start": 2203.82, "end": 2204.38, "word": " بده", "probability": 0.50537109375}, {"start": 2204.38, "end": 2204.74, "word": " يسمى", "probability": 0.6241048177083334}, {"start": 2204.74, "end": 2205.7, "word": " وين", "probability": 0.61077880859375}, {"start": 2205.7, "end": 2205.86, "word": " ال", "probability": 0.990234375}, {"start": 2205.86, "end": 2207.52, "word": " U1؟", "probability": 0.5375162760416666}, {"start": 2207.52, "end": 2208.18, "word": " هاد", "probability": 0.4102783203125}, {"start": 2208.18, "end": 2208.38, "word": " ال", "probability": 0.92041015625}, {"start": 2208.38, "end": 2209.88, "word": " U1،", "probability": 0.77490234375}, {"start": 2209.88, "end": 2210.4, "word": " هاد", "probability": 0.81494140625}, {"start": 2210.4, "end": 2211.38, "word": " ايه؟", "probability": 0.7520751953125}, {"start": 2211.38, "end": 2211.66, "word": " اللي", "probability": 0.932861328125}, {"start": 2211.66, "end": 2212.62, "word": " كتبناها", "probability": 0.98896484375}, {"start": 2212.62, "end": 2213.02, "word": " على", "probability": 0.91357421875}, {"start": 2213.02, "end": 2213.54, "word": " الشكل", "probability": 0.983154296875}, {"start": 2213.54, "end": 2213.9, "word": " هذا،", "probability": 0.65478515625}, {"start": 2213.9, "end": 2214.18, "word": " هاد", "probability": 0.95361328125}, {"start": 2214.18, "end": 2214.3, "word": " ال", "probability": 0.96826171875}, {"start": 2214.3, "end": 2216.18, "word": " U1،", "probability": 0.8400065104166666}, {"start": 2216.18, "end": 2216.56, "word": " هاد", "probability": 0.927734375}, {"start": 2216.56, "end": 2216.82, "word": " بنا", "probability": 0.41064453125}, {"start": 2216.82, "end": 2217.38, "word": " نضربها", "probability": 0.9388427734375}, {"start": 2217.38, "end": 2217.56, "word": " في", "probability": 0.95654296875}, {"start": 2217.56, "end": 2218.44, "word": " مينوبالات", "probability": 0.62764892578125}], "temperature": 1.0}, {"id": 97, "seek": 223864, "start": 2219.5, "end": 2238.64, "text": "بدا ان انا اضربها في ال Y1 هذي ههه مظبوط مش هذي ال Y1 يعني كأنها ههه خاني اختصرها لك بعدين مش مشكلة يبقى بداجي اقول E أس ناقص T في Cos T في", "tokens": [3555, 28259, 16472, 1975, 8315, 1975, 11242, 25513, 11296, 8978, 2423, 398, 16, 8032, 8848, 1829, 8032, 3224, 3224, 3714, 19913, 3555, 2407, 9566, 37893, 8032, 8848, 1829, 2423, 398, 16, 37495, 22653, 9122, 33456, 11296, 8032, 3224, 3224, 16490, 7649, 1829, 1975, 46456, 9381, 2288, 11296, 5296, 4117, 39182, 9957, 37893, 37893, 28820, 3660, 7251, 3555, 4587, 7578, 47525, 26108, 1829, 1975, 39648, 462, 5551, 3794, 8717, 995, 4587, 9381, 314, 8978, 15855, 314, 8978], "avg_logprob": -0.3112824566952594, "compression_ratio": 1.5359477124183007, "no_speech_prob": 0.0, "words": [{"start": 2219.5, "end": 2220.02, "word": "بدا", "probability": 0.608154296875}, {"start": 2220.02, "end": 2220.2, "word": " ان", "probability": 0.4521484375}, {"start": 2220.2, "end": 2220.54, "word": " انا", 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linearly independent اذا المعادلة الأولى واحد حلها بجيبه في سطر يبقى فبجيبه هنا solution of equation one", "tokens": [37746, 6027, 2655, 6027, 1829, 50239, 1975, 2655, 1863, 9957, 43586, 6695, 1975, 15730, 9673, 3615, 18513, 37977, 16247, 12610, 7578, 36764, 24401, 11331, 1211, 11296, 4724, 7435, 1829, 3555, 3224, 8978, 8608, 9566, 2288, 7251, 3555, 4587, 7578, 6156, 3555, 7435, 1829, 3555, 3224, 34105, 3827, 295, 5367, 472], "avg_logprob": -0.2699142285421783, "compression_ratio": 1.289655172413793, "no_speech_prob": 0.0, "words": [{"start": 2734.19, "end": 2735.27, "word": "وبالتالي", "probability": 0.90615234375}, {"start": 2735.27, "end": 2735.61, "word": " قال", "probability": 0.52294921875}, {"start": 2735.61, "end": 2736.07, "word": " اتنين", "probability": 0.572601318359375}, {"start": 2736.07, "end": 2736.27, "word": " linearly", "probability": 0.385009765625}, {"start": 2736.27, "end": 2737.65, "word": " independent", "probability": 0.92041015625}, {"start": 2737.65, "end": 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0.59326171875}, {"start": 5439.11, "end": 5439.39, "word": " شاء", "probability": 0.967041015625}, {"start": 5439.39, "end": 5439.57, "word": " الله", "probability": 0.9677734375}, {"start": 5439.57, "end": 5439.79, "word": " يوم", "probability": 0.921875}, {"start": 5439.79, "end": 5440.03, "word": " الأربعة", "probability": 0.85107421875}, {"start": 5440.03, "end": 5440.73, "word": " بنبدأ", "probability": 0.794921875}, {"start": 5440.73, "end": 5441.33, "word": " chapter", "probability": 0.7001953125}, {"start": 5441.33, "end": 5442.13, "word": " أربعة", "probability": 0.6944986979166666}, {"start": 5442.13, "end": 5442.73, "word": " يوم", "probability": 0.56781005859375}, {"start": 5442.73, "end": 5443.37, "word": " الأربعة", "probability": 0.9659830729166666}, {"start": 5443.37, "end": 5443.79, "word": " بنبدأ", "probability": 0.8240559895833334}, {"start": 5443.79, "end": 5444.11, "word": " chapter", "probability": 0.94287109375}, {"start": 5444.11, "end": 5444.53, "word": " أربعة", "probability": 0.9404296875}, {"start": 5444.53, "end": 5444.69, "word": " ان", "probability": 0.353515625}, {"start": 5444.69, "end": 5444.87, "word": " شاء", "probability": 0.992431640625}, {"start": 5444.87, "end": 5445.05, "word": " الله", "probability": 0.9609375}, {"start": 5445.05, "end": 5445.83, "word": " chapter", "probability": 0.7197265625}, {"start": 5445.83, "end": 5446.39, "word": " أربعة", "probability": 0.9378255208333334}, {"start": 5446.39, "end": 5446.69, "word": " هو", "probability": 0.9267578125}, {"start": 5446.69, "end": 5447.67, "word": " تعميم", "probability": 0.95703125}, {"start": 5447.67, "end": 5447.89, "word": " ل", "probability": 0.9033203125}, {"start": 5447.89, "end": 5448.29, "word": " chapter", "probability": 0.89794921875}, {"start": 5448.29, "end": 5449.13, "word": " تلاتة", "probability": 0.8868408203125}, {"start": 5449.13, "end": 5449.87, "word": " يعني", "probability": 0.837890625}, {"start": 5449.87, "end": 5450.25, "word": " بيبقى", 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\ No newline at end of file
diff --git a/PL9fwy3NUQKwa8ZDfSFGn6H8xVFLzqmCZC/_NMCQUdH1C8_raw.srt b/PL9fwy3NUQKwa8ZDfSFGn6H8xVFLzqmCZC/_NMCQUdH1C8_raw.srt
new file mode 100644
index 0000000000000000000000000000000000000000..7e2bf7d3451bf1244b60568dea75d34876bf0edd
--- /dev/null
+++ b/PL9fwy3NUQKwa8ZDfSFGn6H8xVFLzqmCZC/_NMCQUdH1C8_raw.srt
@@ -0,0 +1,3004 @@
+1
+00:00:09,860 --> 00:00:14,730
+بسم الله الرحمن الرحيمالمرة الفاتة بدأنا في حلال
+
+2
+00:00:14,730 --> 00:00:18,510
+non homogeneous differential equation اللى على
+
+3
+00:00:18,510 --> 00:00:22,810
+الشكل اللى عندنا هذا star استخدمنا المرة الفاتة
+
+4
+00:00:22,810 --> 00:00:26,910
+طريقة ال undetermined coefficients طريقة المعاملات
+
+5
+00:00:26,910 --> 00:00:32,390
+المجهولة وقلنا اشترطنا شرطين الشرط الأول لازم يكون
+
+6
+00:00:32,390 --> 00:00:37,810
+المعاملات هدول ثوابت الشرط التانى لازم GOT تبقى
+
+7
+00:00:37,810 --> 00:00:42,320
+على شكل polynomialأو polynomial في exponential أو
+
+8
+00:00:42,320 --> 00:00:45,820
+polynomial في exponential في sin أو cos أو
+
+9
+00:00:45,820 --> 00:00:51,160
+مجموعهما أو الفرق في ما بينهما اليوم ان شاء الله
+
+10
+00:00:51,160 --> 00:00:54,900
+ناخد طريقة جديدة اسمها طريقة ال variation of
+
+11
+00:00:55,030 --> 00:01:02,470
+Parameters تغيير الوسيطات يعني في عندنا متغيرات
+
+12
+00:01:02,470 --> 00:01:06,530
+بدنا نستبدلها وفي عندنا شغلات بدنا نستبدلها بشغلات
+
+13
+00:01:06,530 --> 00:01:11,520
+أخرى، هاي المقصود بال variation of parametersإتنان
+
+14
+00:01:11,520 --> 00:01:17,020
+المعاملات ليست ثوابت و الله ماهياش ثوابت ممكن
+
+15
+00:01:17,020 --> 00:01:21,360
+يكونوا هدول ثوابت و ممكن مايكونوش ثوابت مستفرقش
+
+16
+00:01:21,360 --> 00:01:27,670
+عندنا إتنان ال G of T ياخد على أي شكل بدكياسواء
+
+17
+00:01:27,670 --> 00:01:31,190
+كان polynomial، exponential، مش polynomial، دوال
+
+18
+00:01:31,190 --> 00:01:35,570
+مثلثية، في ال bus، في المقام، في مش عارف ايه، اي
+
+19
+00:01:35,570 --> 00:01:39,310
+functions ماعنديش قيود على ال functions مش زي
+
+20
+00:01:39,310 --> 00:01:42,950
+طريقة ال undetermined coefficients ماعنديش قيود
+
+21
+00:01:42,950 --> 00:01:47,250
+بالمرة تتلخص هذه الطريقة باختصار يا بنات في الشكل
+
+22
+00:01:47,250 --> 00:01:50,340
+التاليباروح بجيب ال homogeneous differential
+
+23
+00:01:50,340 --> 00:01:54,820
+equation زي المرة الماضية و بجيب main الحل تبع ال
+
+24
+00:01:54,820 --> 00:02:02,330
+homogeneous و بكون الحل عندي على الشكل هذابعد هيك
+
+25
+00:02:02,330 --> 00:02:07,250
+مشان أجيب ال particular solution تبع المعادلة بجعل
+
+26
+00:02:07,250 --> 00:02:15,310
+ثوابت c1 و c2 بستبدلهم بدوال أخرى و التكون u1 و u2
+
+27
+00:02:15,310 --> 00:02:19,490
+يعني بصير ال particular solution ده اللي جديد اي
+
+28
+00:02:19,490 --> 00:02:25,750
+u1 مضروبة في الحل الأول اللي جيبناه y1 وزائد u2
+
+29
+00:02:25,750 --> 00:02:30,760
+مضروبة في الحل الثاني اللي هو u8إذا باختصار بنقول
+
+30
+00:02:30,760 --> 00:02:34,920
+ما يأتي اعتبر المعادلة التفاضلية الخطية مرتبة
+
+31
+00:02:34,920 --> 00:02:39,880
+ثانية بالشكل هذا المعامل تبع y double prime لازم
+
+32
+00:02:39,880 --> 00:02:44,400
+يكون واحد صحيح يعني لو ماكانش بدنا نروح إياه نجسم
+
+33
+00:02:44,400 --> 00:02:47,240
+على الدالة اللي موجودة في ال y double prime بحيث
+
+34
+00:02:47,240 --> 00:02:53,120
+أضمن دائما و أبدا أن شكل المعامل تبع y double
+
+35
+00:02:53,120 --> 00:02:54,180
+prime هو مام
+
+36
+00:03:07,860 --> 00:03:12,060
+الان نفترض مواعي واحد و اتنين لـnearly independent
+
+37
+00:03:12,060 --> 00:03:15,300
+solutions للـ homogeneous differential equation
+
+38
+00:03:15,300 --> 00:03:18,460
+يبقى صار الحل العام تبع الـ homogeneous
+
+39
+00:03:18,460 --> 00:03:22,810
+differential equation على الشكل اللى عندنا هذابقول
+
+40
+00:03:22,810 --> 00:03:27,010
+to find a particular solution مش هنتجيب الحل الخاص
+
+41
+00:03:27,010 --> 00:03:32,210
+للمعادلة بطريقة ال variation of parameters بتغيير
+
+42
+00:03:32,210 --> 00:03:37,970
+الوسيطات we replace the constants نستبدل replace
+
+43
+00:03:37,970 --> 00:03:45,380
+يعني نستبدلالثوابت C1 و C2 by two functions U1 as
+
+44
+00:03:45,380 --> 00:03:49,720
+a function of T و U2 as a function of T يعني بدي
+
+45
+00:03:49,720 --> 00:03:57,480
+أشيل C1 و أحط مكانها U1 و أشيل C2 و أحط مكانها U2
+
+46
+00:03:57,480 --> 00:04:02,800
+ليه بيطلع عندي بدي أسمع من ال particular solution
+
+47
+00:04:02,800 --> 00:04:09,430
+السؤال هو كيف بيجيب ال U1 و U2بنجي على الحل اللي
+
+48
+00:04:09,430 --> 00:04:14,150
+صار عندي ال بطاقر هو يساوي يواحد و يواحد زي ديو
+
+49
+00:04:14,150 --> 00:04:20,610
+اتنين و يتنام نشتاق مرة و نشتاق اتنين و نرجع نعوض
+
+50
+00:04:20,610 --> 00:04:25,080
+في المعادلة الأصلية اللي هو starأو نجمعه و نطرحه و
+
+51
+00:04:25,080 --> 00:04:29,560
+نجسمه و نختصره و نشتريه لغاية ما نوصل لمين لغاية
+
+52
+00:04:29,560 --> 00:04:32,740
+ما نوصل ان يوين يعني قصة طويلة بدنا على الأقل
+
+53
+00:04:32,740 --> 00:04:36,840
+مصارعة عشان نخلص الشغل هذه انسى الموضوع بهمن
+
+54
+00:04:36,840 --> 00:04:40,180
+تعرفيه الشكل ال يواحد as a function of the هو
+
+55
+00:04:40,180 --> 00:04:46,500
+عبارة عن سالب تكامل الحل الثاني احنا بدنا يواحد
+
+56
+00:04:46,500 --> 00:04:53,810
+يبقى باخد تكامل الحل الثاني ال Y2مضروب في الـ G of
+
+57
+00:04:53,810 --> 00:04:58,890
+T مقسم على الورلسكين تبع ال two solutions U Y واحد
+
+58
+00:04:58,890 --> 00:05:05,410
+وY اتنين بالمثل U اتنين هي تكامل Y واحد يعني كأنه
+
+59
+00:05:05,410 --> 00:05:09,850
+عكس U واحد معاها Y اتنين U اتنين معاها مين؟ Y واحد
+
+60
+00:05:09,850 --> 00:05:14,650
+يبقى بدون إشارة سالب في ال U one في إشارة سالب في
+
+61
+00:05:14,650 --> 00:05:18,120
+ال U two ماعنديش إشارة سالبيبقى ال U2 as a
+
+62
+00:05:18,120 --> 00:05:22,040
+function of T هي تكامل Y1 of T في G of T على
+
+63
+00:05:22,040 --> 00:05:27,280
+رونسكين تبع ال Y1 وY2 as a function of T يبقى هذا
+
+64
+00:05:27,280 --> 00:05:31,080
+ال رونسكين as a function of T وهذا ال رونسكين as a
+
+65
+00:05:31,080 --> 00:05:39,530
+function of T حصلت على U1 وU2 بضرب Y1 U1 Y2في U2 و
+
+66
+00:05:39,530 --> 00:05:43,810
+بجمع الاتنين بيعطوني الحل الخاص بدي ال general
+
+67
+00:05:43,810 --> 00:05:49,690
+solution بجمع الحل الخاص اللي حصلت عليه مع الحل
+
+68
+00:05:49,690 --> 00:05:53,890
+العام تبع ال homogeneous اتنين مع بعض تبقى النظرية
+
+69
+00:05:53,890 --> 00:05:58,490
+اللي خدناها المرة قبل الماضية و كنا بنحل عليها
+
+70
+00:05:58,490 --> 00:06:01,950
+المرة الماضيةبنجيب حل ال homogeneous و ال
+
+71
+00:06:01,950 --> 00:06:04,890
+particular solution تبع ال non homogeneous بنجمع
+
+72
+00:06:04,890 --> 00:06:07,850
+الاتنين بيعطينا ال general solution تبع المعادلة
+
+73
+00:06:07,850 --> 00:06:14,530
+الاصلية فهمت الطريقة بعيد كمان مرة علشان اللي
+
+74
+00:06:14,530 --> 00:06:19,130
+وصلنا متأخرات بيعطينا المعادلة ذلك و جوجل هات ال
+
+75
+00:06:19,130 --> 00:06:22,880
+general solutionبروح باخد ال homogeneous تبعتله
+
+76
+00:06:22,880 --> 00:06:26,940
+المعادلة هذه بحلها بأي طريقة من الطرق التي سبقت
+
+77
+00:06:26,940 --> 00:06:30,680
+دراستها في ال sections الماضية من section 1 لغاية
+
+78
+00:06:30,680 --> 00:06:37,320
+section 5 حلناها و جيبنا Y1 و Y2 إذا جبنا حل ال
+
+79
+00:06:37,320 --> 00:06:40,600
+homogeneous differential equation بدنا نجيب
+
+80
+00:06:40,600 --> 00:06:45,260
+particular solution للمعادلة starبفرض ان ال
+
+81
+00:06:45,260 --> 00:06:49,340
+particular solution على الصيغة اللى انها دى بس
+
+82
+00:06:49,340 --> 00:06:54,780
+بشيل c1 بحط بدله functionيو واحد و بشيل c اتنين
+
+83
+00:06:54,780 --> 00:06:58,340
+بحط بدل ال function يو اتنين فبصير الشكل ال
+
+84
+00:06:58,340 --> 00:07:02,320
+particular solution على الشكل اللي قدامنا هذا مين
+
+85
+00:07:02,320 --> 00:07:07,020
+هي يو واحد؟ يو واحد هي سالب تكامل y اتنين مضروبة
+
+86
+00:07:07,020 --> 00:07:10,740
+في g of t على الرنس كين تبع ال y واحد و ال y اتنين
+
+87
+00:07:10,740 --> 00:07:17,020
+as a function of t واليو اتنين هي عبارة عن تكاملY1
+
+88
+00:07:17,020 --> 00:07:21,300
+of T في الـ G of T على الرونسكين تبع ال Y1 وY2 as
+
+89
+00:07:21,300 --> 00:07:26,540
+a function of T جبت ال U1 و جبت ال U2 و روح بعوض
+
+90
+00:07:26,540 --> 00:07:32,280
+في هذه بكون جبت شكل الحل الخاص بجمع اللي هو الحل
+
+91
+00:07:32,280 --> 00:07:36,340
+الخاص مع الحل العام تبع الهموجوذ الأثنين مع بعض
+
+92
+00:07:36,340 --> 00:07:39,840
+بجمع الحل المعادلة الأصلية
+
+93
+00:07:52,050 --> 00:08:00,390
+المثال الأول بيقول هاتلي لل general solution
+
+94
+00:08:08,120 --> 00:08:13,180
+سؤال الأول بيقول له سؤال عشرة من الكتاب بيقول find
+
+95
+00:08:13,180 --> 00:08:16,820
+the
+
+96
+00:08:16,820 --> 00:08:27,100
+general solution
+
+97
+00:08:27,100 --> 00:08:35,720
+of the differential equation of the differential
+
+98
+00:08:35,720 --> 00:08:49,650
+equationللمعادلة التفاضلية يساوي
+
+99
+00:08:49,650 --> 00:08:57,370
+E of T على 1 زائد T تربيع وهذه المعادلة الأصلية
+
+100
+00:09:07,290 --> 00:09:12,590
+ال tactic اللى اتبع في حالة الجزء النظري في حالة
+
+101
+00:09:12,590 --> 00:09:14,710
+ال variation of parameters هو ال tactic اللى
+
+102
+00:09:14,710 --> 00:09:18,870
+بنتبعه الآن عند حل المثلةيبقى بدنا ناخد ال
+
+103
+00:09:18,870 --> 00:09:22,170
+homogenous differential equation ونروح من هنا لو
+
+104
+00:09:22,170 --> 00:09:25,770
+جينا لل homogenous بنلاقي المعاملات اذا نزل
+
+105
+00:09:25,770 --> 00:09:33,630
+سيكشنرز الماضية بروح بقوله let Y تساوي E أُس RT be
+
+106
+00:09:33,630 --> 00:09:38,990
+a solution of the
+
+107
+00:09:47,640 --> 00:09:58,580
+بناء عليه then the characteristic equation isR
+
+108
+00:09:58,580 --> 00:10:05,680
+تربيع ناقص اتنين R زائد واحد تساوي كده؟ تساوي Zero
+
+109
+00:10:05,680 --> 00:10:10,880
+هذه يا بنات لو حللناها R ناقص واحد في R ناقص واحد
+
+110
+00:10:10,880 --> 00:10:17,780
+لكل تربيع تساوي Zero ومنها R واحد تساوي R اتنين
+
+111
+00:10:17,780 --> 00:10:27,230
+تساوي كده؟واحد صحيح يبقى صار الحل ان YC بدر ساوي
+
+112
+00:10:27,230 --> 00:10:38,370
+C1 زائد C2T في E أس T او ان شيتنا فقولنا C1 E أس T
+
+113
+00:10:38,370 --> 00:10:47,440
+زائد C1T في E أس Tيبقى الحل الأول Y1 هو POST و
+
+114
+00:10:47,440 --> 00:10:56,100
+الحل الثاني هو T EOST بعد ذلك بروز هذا سنرجع له
+
+115
+00:10:56,100 --> 00:11:00,960
+تمام يبقى نروح نجيب ال particular solution لل
+
+116
+00:11:00,960 --> 00:11:06,810
+equationالمعامل هنا واحد صحيح يبقى احنا جاهزين
+
+117
+00:11:06,810 --> 00:11:10,190
+ماعناه مش مشكلة ان شاء الله يكون اتنين تلاتة اربعة
+
+118
+00:11:10,190 --> 00:11:12,750
+بيكتب اسمي على هذا الرقم اللي هو ال constant
+
+119
+00:11:12,750 --> 00:11:18,310
+اشتراطنا بيكون واحد صحيح تمام يبقى باجي بقول the
+
+120
+00:11:18,310 --> 00:11:27,890
+particular solution of the
+
+121
+00:11:41,500 --> 00:11:52,620
+U1 يبقى U1 of T في E of T وشيل C2 و اكتب بدلا U2
+
+122
+00:11:52,620 --> 00:12:00,550
+of T في T في E of Tجاب المحسب الـU1 و الـU2 بالزمن
+
+123
+00:12:00,550 --> 00:12:06,970
+الرونسكين تمام يبقى بده أروح أجيب له الرونسكين تبع
+
+124
+00:12:06,970 --> 00:12:12,990
+الحل الأول و الحل التاني as a function of T الحل
+
+125
+00:12:12,990 --> 00:12:20,330
+الأول هو E و S T و الحل التاني هو T في U S T نشتق
+
+126
+00:12:20,330 --> 00:12:27,500
+هذا ب E و S T نشتق هذا بمشتقة حاصل ضربدالتين يبقى
+
+127
+00:12:27,500 --> 00:12:33,860
+مشتقة الأولى فى التانية زائد الأولى فى مشتقة مين
+
+128
+00:12:33,860 --> 00:12:41,500
+الدالة ا الثانية انفك المحدد بالضرب التبادلى يبقى
+
+129
+00:12:41,500 --> 00:12:49,820
+هنا بصير E أس اتنين T زائد T فى E أس اتنين T هذا
+
+130
+00:12:49,820 --> 00:12:55,790
+حاصل ضرب عناصر القطر الرئيسىنقص حاصل ضرب عناصر
+
+131
+00:12:55,790 --> 00:13:03,510
+القطر الثانوي يبقى ناقص T في E أس اتنين T هذا و
+
+132
+00:13:03,510 --> 00:13:09,910
+هذا في كم؟ في Zero هذا الكلام يساوي كم؟ اللي عمرها
+
+133
+00:13:09,910 --> 00:13:15,470
+ماحتساوي Zeroليش؟ لأن الـ Exponential دائما و أبدا
+
+134
+00:13:15,470 --> 00:13:19,650
+أكبر من مين من الـ Zero إذا الحل اللي بيطلع عنهم
+
+135
+00:13:19,650 --> 00:13:24,430
+يبنى Linearly Independent Solution وبالتالي
+
+136
+00:13:24,430 --> 00:13:28,170
+بيكونوا لـ Fundamental Set of Solutions أو الـ
+
+137
+00:13:28,170 --> 00:13:31,210
+General Solution لمين؟ للـ Homogeneous
+
+138
+00:13:31,210 --> 00:13:35,580
+Differential Equationعلى اي حال ان هذا الان بتروح
+
+139
+00:13:35,580 --> 00:13:42,160
+احسب له U1 و U2 يبقى بدي U1 as a function of T
+
+140
+00:13:42,160 --> 00:13:50,400
+اللي هو ناقص تكامل Y2 of T في G of T على
+
+141
+00:13:50,400 --> 00:13:58,120
+الوانوسكين as a function of T DT يبقى هاي سالب
+
+142
+00:13:58,120 --> 00:14:05,650
+وهاي تكاملبتداجر ال Y2 Y2 هو من T في E أُس T يبقى
+
+143
+00:14:05,650 --> 00:14:13,130
+هاي T في E أُس T في G of T وين G of T هيها فوق
+
+144
+00:14:13,130 --> 00:14:21,630
+يبقى هذا بيصير من بيصير E أُس T و بتنزل تحت واحد
+
+145
+00:14:21,630 --> 00:14:28,070
+زائد T تربيعبيل تحت مين عندى؟ ايرونيسكن ايرونيسكن
+
+146
+00:14:28,070 --> 00:14:36,520
+جداش؟ E أس اتنين T كله في DTيبقى لو ضربت هدى فى
+
+147
+00:14:36,520 --> 00:14:42,880
+هدى يا بنات بصير جداش اؤس اتنين T مع اؤس اتنين T
+
+148
+00:14:42,880 --> 00:14:48,420
+اللى بتاعت مع السلامة يبقى هذا الكلام يساوي الناقص
+
+149
+00:14:48,420 --> 00:14:54,280
+تكامل T على واحد زائد T ترابيع DT
+
+150
+00:14:57,690 --> 00:15:06,050
+أظن البسطة فاضل المقام كيف؟ بدا اتنين يعني بتمان
+
+151
+00:15:06,050 --> 00:15:12,510
+وعاد اتنين بشانيك بكلامنا صحيح بروح نضرب في نص هيك
+
+152
+00:15:12,510 --> 00:15:23,250
+صار البسطة فاضل المقاميساوي ناقص نص لإن واحد زائد
+
+153
+00:15:23,250 --> 00:15:27,890
+T تربية بدون absolute value لإنها قيمة موجبة T لو
+
+154
+00:15:27,890 --> 00:15:31,890
+حتى لو كان سلبة بالربعة بصير موجبة زائد واحد يبقى
+
+155
+00:15:31,890 --> 00:15:36,750
+هذه positive quantity على طول الخط بس كنا كاملنا
+
+156
+00:15:36,750 --> 00:15:42,170
+بنقول زائد constantخليني اكتب ال constant هذا يبقى
+
+157
+00:15:42,170 --> 00:15:49,310
+زائد c1 و تعالوا نتفهم على ال c1 هذا كده ايش ممكن
+
+158
+00:15:49,310 --> 00:15:56,470
+ناخده؟خلّي الـ C1 بدّيش أخده سفر، خديه خمسة، مثلا،
+
+159
+00:15:56,470 --> 00:16:01,610
+لو جدل أنا أخدت خمسة، إيش اللي بيحصل؟ بصير عندي
+
+160
+00:16:01,610 --> 00:16:08,670
+هذا المقدار زائد C1، لما أجي أضربه، ههه، فاهمين؟
+
+161
+00:16:08,670 --> 00:16:14,110
+هذا اللي هو U1، يبقى U1 بدي أجي أضربها وين؟ وين
+
+162
+00:16:14,110 --> 00:16:21,130
+راح الـ U1 هي؟ بدي أضربها هنابصير رقم في UST يعني
+
+163
+00:16:21,130 --> 00:16:27,610
+بصير تكرار وبالتالي بصير تشابه مع مين مع الحل هذا
+
+164
+00:16:27,610 --> 00:16:31,830
+يبجي مشان أتخلص من الاشياء هذه دائما و أبدا مش في
+
+165
+00:16:31,830 --> 00:16:38,850
+السؤال هذا في كل المساوي اللي باخد C1 ب 0 طيب
+
+166
+00:16:38,850 --> 00:16:47,090
+الحين هشيرلها طيب بداخل ال U2Y1 of T يساوي تكامل
+
+167
+00:16:47,090 --> 00:16:55,730
+Y1 of T في G of T على الورنسكين of T كله بالنسبة
+
+168
+00:16:55,730 --> 00:17:02,160
+الى DT ويساوي تكاملالـ Y1 يا بناتي اللي هو مين؟ E
+
+169
+00:17:02,160 --> 00:17:10,060
+أُس T والـ G of T ليه E أُس T على واحد زائد T
+
+170
+00:17:10,060 --> 00:17:17,680
+تربية والرنسكين اللي هو E أُس اتنين T في D T صارت
+
+171
+00:17:17,680 --> 00:17:25,560
+المسألة تكامل واحد على واحد زائد T تربية DT بدنا
+
+172
+00:17:25,560 --> 00:17:30,380
+نكامل هذا، جديش؟تان انفرستي ممتاز يبقى هذه جاهزة
+
+173
+00:17:30,380 --> 00:17:35,160
+لا بدأش لشغل اليمين ولا الشمال يبقى هذه تان
+
+174
+00:17:35,160 --> 00:17:44,120
+انفرستي زاد كونستانتاني C2 يبقى زي ما حد C1 ب zero
+
+175
+00:17:44,120 --> 00:17:52,940
+C2 بقدرش ب zero يبقى باجي بقول تاك ودينا C1 بده
+
+176
+00:17:52,940 --> 00:17:56,200
+يساوي C2 بده يساوي zero
+
+177
+00:18:18,160 --> 00:18:24,700
+أذا لما أخدنا كل واحد بـ0 بيصير U1 ناقص نص لإن
+
+178
+00:18:24,700 --> 00:18:30,520
+واحد زائد T تربيع و بيصير U2 تان inverse T إذا
+
+179
+00:18:30,520 --> 00:18:34,880
+بقدر أجيب شكل ال particular solution يبقى باجي
+
+180
+00:18:34,880 --> 00:18:41,540
+بقوله the particular solution
+
+181
+00:18:47,280 --> 00:18:52,640
+يبقى كتابنا ال particular solution هى يبقى بدى
+
+182
+00:18:52,640 --> 00:19:02,500
+اشيل UN هى وجهه يقول ناقص نص Eost في لن يبقى ناقص
+
+183
+00:19:02,500 --> 00:19:16,090
+نص Eost في لننقص E أُس T وراحت هنا نقص نص وهنا E
+
+184
+00:19:16,090 --> 00:19:25,450
+أُس T في ال N اللي هي واحد زائد ت تربيع الآن يقول
+
+185
+00:19:25,450 --> 00:19:33,550
+تان انفرس في من؟ في T في E أُس T يبقى T في E أُس T
+
+186
+00:19:33,550 --> 00:19:40,590
+في تان انفرس Tاختصارات مافيش بيقولش بيظل زي ما هو
+
+187
+00:19:40,590 --> 00:19:50,910
+فبروح بقول هنا the general solution of the
+
+188
+00:19:50,910 --> 00:20:01,080
+differentialEquation star is y يساوي yc زائد
+
+189
+00:20:01,080 --> 00:20:08,260
+capital y of t إذا بيصير ال y يساوي c1
+
+190
+00:20:13,720 --> 00:20:21,320
+بنضيف عليها particular solution نقص نص Eost لإن
+
+191
+00:20:21,320 --> 00:20:29,820
+واحد زائد T تربيع Eost
+
+192
+00:20:33,390 --> 00:20:38,810
+يبقى هذا هو ال general solution لل equation star
+
+193
+00:20:38,810 --> 00:20:44,430
+اللي عندك فيه أي تساوي لبنات التكتيك اللي عملناها
+
+194
+00:20:44,430 --> 00:20:49,590
+تتبعيها عندك كل مسألة بضل عليك بس تكاملي مشان تجيب
+
+195
+00:20:49,590 --> 00:20:55,190
+اللي و واحد و اتنين و باقى الشغل كله روتيني ناخد
+
+196
+00:20:55,190 --> 00:21:00,970
+كمان مثال مثال
+
+197
+00:21:00,970 --> 00:21:13,230
+اتنينFind the general solution of differential
+
+198
+00:21:13,230 --> 00:21:16,390
+equation YW'
+
+199
+00:21:21,030 --> 00:21:32,430
+زائد اتنين Y بدي ساوي اتنين E أس ناقص T تان ترابيع
+
+200
+00:21:32,430 --> 00:21:40,230
+ال T و دستار سؤال مش موجود في الكتاب سؤال خارجي
+
+201
+00:21:40,230 --> 00:21:44,890
+نفس
+
+202
+00:21:44,890 --> 00:21:48,600
+ال tactic اللي ابتدينا به هناك هنبتدي به هنايبقى
+
+203
+00:21:48,600 --> 00:21:59,500
+بداجي اقول له let y تساوي E أس RT بيه solution of
+
+204
+00:21:59,500 --> 00:22:08,380
+the equation y w prime اتنين y prime زائد اتنين y
+
+205
+00:22:08,380 --> 00:22:09,820
+يساوي زيرو
+
+206
+00:22:13,630 --> 00:22:23,490
+The characteristic equation is R تربيع زائد اتنين
+
+207
+00:22:23,490 --> 00:22:29,350
+R زائد اتنين تساوي Zero أظن لا يمكن تحليل هذه
+
+208
+00:22:29,350 --> 00:22:34,900
+المعادلة، مظبوط؟ يبقى بروح نحلها كيف؟بالقانون
+
+209
+00:22:34,900 --> 00:22:42,300
+العام يبقى R تساوي ناقص باء زيد أو ناقص الجدري
+
+210
+00:22:42,300 --> 00:22:48,500
+التربيعي لباء تربيع ناقص أربعة ألف اللي هي بواحد
+
+211
+00:22:48,500 --> 00:22:55,500
+جيم اللي هي باتنين كله على اتنين ألف اتنين في واحد
+
+212
+00:22:56,090 --> 00:23:04,330
+تمام يبقى هذه نقص اتنين زاد او نقص اربع نقص تمانية
+
+213
+00:23:04,330 --> 00:23:11,910
+بظهر سالب اربعة تحت الجدر يعني بتطلع باتنين I كله
+
+214
+00:23:11,910 --> 00:23:18,630
+على قداش على اتنين يبقى ناقص واحد زاد او ناقص I
+
+215
+00:23:18,630 --> 00:23:27,070
+يبقى لان ده بقداش و ميوبواحد يبقى هنا لاندا تساوي
+
+216
+00:23:27,070 --> 00:23:35,170
+سالب واحد وال ميو يساوي واحد إذا صار YC بدي يساوي
+
+217
+00:23:35,170 --> 00:23:43,550
+E أس لاندا T لاندا بواحد يبقى E أس T لاندا بسالب
+
+218
+00:23:43,550 --> 00:23:47,570
+واحد E أس ناقص T تمام فاهمين؟
+
+219
+00:23:57,710 --> 00:24:05,170
+يبقى هذا حل الـ homogeneous differential equation
+
+220
+00:24:05,900 --> 00:24:09,580
+ماذا ترى؟ خلّيني أحسب الورونسكين بالمرة قبل ما
+
+221
+00:24:09,580 --> 00:24:14,040
+أجيب ال particular solution حتى تظل المسألة ماشية
+
+222
+00:24:14,040 --> 00:24:19,440
+معانا بطريقة سلسة يبقى بدي أجيب الورونسكين as a
+
+223
+00:24:19,440 --> 00:24:26,920
+function of T الحل الأول هو E أس ناقص T في cos T
+
+224
+00:24:26,920 --> 00:24:35,620
+الحل التاني هو E أس سالب T في sin Tبنشتق الدالة
+
+225
+00:24:35,620 --> 00:24:42,720
+الأولى حاصل ضرب دالتين يبقى مشتقة الأولى زي ما هي
+
+226
+00:24:42,720 --> 00:24:50,160
+في مشتقة الأسلوب من بسالب واحد في cos T بعد ذلك ال
+
+227
+00:24:50,160 --> 00:24:55,880
+EOS نقص T كما هي في مشتقة ال cos E بسالبSin يبقى
+
+228
+00:24:55,880 --> 00:25:03,060
+السالب E أس سالب T في Sin T الدالة تانية بنفس
+
+229
+00:25:03,060 --> 00:25:11,180
+الطريقة يبقى ناقص E أس ناقص T في Sin T زيد E أس
+
+230
+00:25:11,180 --> 00:25:20,460
+ناقص T في Cos Tطبعا نجي نطلع قداش قيمة هذا المحدد
+
+231
+00:25:20,460 --> 00:25:25,160
+ويوسف حاصل ضرب عناصر القطر الرئيسي ناقص حاصل ضرب
+
+232
+00:25:25,160 --> 00:25:33,460
+عناصر القطر الثانوي يبقى هدف هدف تطلع بقداش بسالب
+
+233
+00:25:33,460 --> 00:25:41,540
+او سالب اتنين T سالب او سالب اتنين T في Sin T في
+
+234
+00:25:41,540 --> 00:25:44,100
+Cos T في Sin
+
+235
+00:25:49,640 --> 00:25:56,600
+يبقى زائد a أساليب اتنين T في cos Tزائد E أس سلب
+
+236
+00:25:56,600 --> 00:26:05,560
+اتنين T فمين فيه cosine تربيع T هذا الرئيسي نقص
+
+237
+00:26:05,560 --> 00:26:12,340
+ثانوي مع نقص بصير ايه؟ زائد يبقى زائد E أس نقص
+
+238
+00:26:12,340 --> 00:26:21,340
+اتنين T sine T cosine Tتمام؟ هدى فى هدى، بعد ذلك
+
+239
+00:26:21,340 --> 00:26:29,920
+هدى كمان زائد إيه أس ناقص اتنين T في sign تاربيع T
+
+240
+00:26:29,920 --> 00:26:34,960
+شراي كمانات هدى و هدى مع السلامة، واحدة موجبة و
+
+241
+00:26:34,960 --> 00:26:40,900
+واحدة سالبةهذه تساوي بيداخد EOS ناقص اتنين عامل
+
+242
+00:26:40,900 --> 00:26:48,080
+مشترك T بضالك cosine تربيتي زائد sine تربيتي له
+
+243
+00:26:48,080 --> 00:26:56,680
+مقداش يبقى الجواب EOS ناقص اتنين T وهذا لا يمكن ان
+
+244
+00:26:56,680 --> 00:26:57,500
+يساوي
+
+245
+00:27:03,100 --> 00:27:07,320
+يبقى الكلام اللى كتبته هذا معله هو ال general
+
+246
+00:27:07,320 --> 00:27:12,020
+solution لل homogenous differential equation بدنا
+
+247
+00:27:12,020 --> 00:27:18,180
+نروح نجيب ال particular solution لمين؟ للمعادلة
+
+248
+00:27:18,180 --> 00:27:20,480
+الأصلية
+
+249
+00:27:35,300 --> 00:27:39,420
+المعادلة الأصلية وين؟ لأن هدري سمنها star ففاجي
+
+250
+00:27:39,420 --> 00:27:46,780
+بقولهم the particular solution
+
+251
+00:27:46,780 --> 00:27:51,020
+of equation
+
+252
+00:27:56,560 --> 00:28:07,900
+Y of T يبقى
+
+253
+00:28:07,900 --> 00:28:18,700
+U1 of T في E السالب T في Cos T
+
+254
+00:28:46,270 --> 00:28:55,690
+Y2Y2Y2Y2Y2Y2Y2Y2Y2Y2Y2Y2Y2Y2Y2 يبقى
+
+255
+00:28:55,690 --> 00:29:03,470
+E أسالب T في صينة T الـ G of T طلع المعاملة واحد
+
+256
+00:29:03,470 --> 00:29:11,690
+يبقى احنا جاهزين يبقى اتنين E أسالب T اتنين E
+
+257
+00:29:11,690 --> 00:29:20,060
+أسالب T في تان ترابيع Tكله علامين على الرمز كان
+
+258
+00:29:20,060 --> 00:29:31,120
+طالعنا E والسالب اتنين T DT ويساوي سالب تكامل اظن
+
+259
+00:29:31,120 --> 00:29:37,720
+هذه مع هذه مع هذه الله يسهل عليهم غير ما سوف عليهم
+
+260
+00:29:37,720 --> 00:29:43,200
+بضل عند اي سالب تكامل تان تربية يا بنات اللي همين
+
+261
+00:29:43,520 --> 00:29:53,960
+اللي هي sin تربيع T على cos تربيع T في sin T في DT
+
+262
+00:29:53,960 --> 00:30:00,660
+يبقى هذا الكلام بده يساوي تكامل اش رايك بده اكتب
+
+263
+00:30:00,660 --> 00:30:07,360
+ال sin تربيع بدلالة ال cos تربيع يبقى واحد ناقص
+
+264
+00:30:07,360 --> 00:30:17,050
+cos تربيع T ماشيماذا تقولون في اتنين نسيناها برا
+
+265
+00:30:17,050 --> 00:30:24,090
+اه في اتنين اي اتنين ماشي الحال و هذا اتنين برا و
+
+266
+00:30:24,090 --> 00:30:29,010
+هنا cosine تربيع ال T بتقولون اللي نسيت الشرف
+
+267
+00:30:29,010 --> 00:30:36,490
+النقص مانستهاش طلع هنا ناقص sin t dt بدي اكتبها D
+
+268
+00:30:36,490 --> 00:30:42,620
+cosine هو مش شقة ال cosine في قداشسالب ساين يبقى
+
+269
+00:30:42,620 --> 00:30:49,180
+السالب ساين ت دي ت ودي اقول دي كوساين ت يبقى هذه
+
+270
+00:30:49,180 --> 00:30:57,820
+دي لكساين ت يعني مشتقت كساين ت لو ناقص ساين ت دي ت
+
+271
+00:30:57,820 --> 00:31:03,580
+يبقى شلت إشارة السالب مع الساين ت مع ال دي ت وكتبت
+
+272
+00:31:03,580 --> 00:31:08,340
+بدالها دي كساينطب عملت هيك ليش تعالى أقولك ليش
+
+273
+00:31:08,340 --> 00:31:13,600
+عملت هيك يبقى هذا الكلام يساوي اللي هو الاتنين
+
+274
+00:31:13,600 --> 00:31:21,600
+اللي برا وهي تكامل واحد على cosine تربيع ال T وهنا
+
+275
+00:31:21,600 --> 00:31:29,800
+ناقص واحد كله في دي cosine T يعني كأنه ايش احنا يا
+
+276
+00:31:29,800 --> 00:31:36,410
+بنات؟بنكمل واحد على X تربية ناقص واحد DX يعني تبري
+
+277
+00:31:36,410 --> 00:31:42,230
+Cos T كأنها كلها X تمام؟ يبقى نتيجة التكمل بدها
+
+278
+00:31:42,230 --> 00:31:47,990
+تكون على الشكل التالي اي اتنين فيه جداش تكمل واحد
+
+279
+00:31:47,990 --> 00:31:52,520
+على X تربية؟سالب واحد على X إذا هذا بتبقى الجدران
+
+280
+00:31:52,520 --> 00:32:01,100
+سالب واحد على cosine T يبقى سالب واحد على cosine T
+
+281
+00:32:01,100 --> 00:32:10,940
+ناقص cosine T يبقى ناقص cosine T وC1 ده مابناشيها
+
+282
+00:32:10,940 --> 00:32:17,580
+يبقى هنا زائد C1 وهنا بنقول take C1 تساوي Zero
+
+283
+00:32:18,650 --> 00:32:25,930
+تمام؟ يبقى هذا لو أخدت بـ0 يصير U1 as a function
+
+284
+00:32:25,930 --> 00:32:33,870
+of T هي عبارة عن مين؟ عن ناقص اتنين على cos T
+
+285
+00:32:33,870 --> 00:32:43,310
+وناقص اتنين cos T في حد يقول لي تسأل قبل ما افوت
+
+286
+00:32:43,310 --> 00:32:48,390
+مش فاهمة تكامل مش فاهمة نقطة تسألني في اي تسأل؟
+
+287
+00:32:51,480 --> 00:33:01,370
+نعود الان لـ U2 of Tيبدو يسوي تكامل Y1 of T في G
+
+288
+00:33:01,370 --> 00:33:06,490
+of T على الرونسكين as a function of T دي T يسوي
+
+289
+00:33:06,490 --> 00:33:15,550
+تكامل Y1 اللي همين E أس ناقص T Cos T يبقى E أس
+
+290
+00:33:15,550 --> 00:33:26,150
+ناقص T في Cos T الـ G of T اللي هي اتنينEos ناقص T
+
+291
+00:33:26,150 --> 00:33:36,030
+في تان تربيع T كله على الرونسكين Eos ناقص 2T يبقى
+
+292
+00:33:36,030 --> 00:33:44,550
+هذا بنتش بصير بصير تكامل و اي اتنين برا و بيضل cos
+
+293
+00:33:44,550 --> 00:33:50,170
+T فقط لا غير و تان تربيع
+
+294
+00:33:59,960 --> 00:34:05,200
+يساوي اتنين تكامل اظن في اختصار بين cosine و
+
+295
+00:34:05,200 --> 00:34:12,560
+cosine تربية يبقى بضال عندي sin تربية t فقط على
+
+296
+00:34:12,560 --> 00:34:22,010
+cosine t dtطيب هذه اللي بقدر اكتبها على الشكل
+
+297
+00:34:22,010 --> 00:34:28,710
+التالي اتنين تكامل sin
+
+298
+00:34:28,710 --> 00:34:34,710
+تربيع يبقى واحد ناقص cosine تربيع يبقى واحد ناقص
+
+299
+00:34:34,710 --> 00:34:42,410
+cosine تربيع ال T كله على cosine T DT ويسوى اتنين
+
+300
+00:34:42,410 --> 00:34:51,290
+تكامل واحد على cosineبسك يبقى سك ال T و هنا ناقص
+
+301
+00:34:51,290 --> 00:34:56,710
+cosine تربيه على cosine بيبقى ال cosine T واحدة
+
+302
+00:34:56,710 --> 00:35:11,570
+كلها دي Tيساوي اتنين يبقى
+
+303
+00:35:11,570 --> 00:35:21,170
+اتنين لان absolute value لسك T زائد تاني Tوهنا
+
+304
+00:35:21,170 --> 00:35:30,450
+ناقص C2 وتكامل ال cosine بsin 80 وزائد constant C2
+
+305
+00:35:30,450 --> 00:35:41,290
+وبنقول هنا take code C2يساوي 0 يبقى صارة ان U2 as
+
+306
+00:35:41,290 --> 00:35:47,390
+a function of T هو عبارة عن اتنين لان absolute
+
+307
+00:35:47,390 --> 00:35:58,030
+value لسك T زائد تاني T نقص اتنين sin T اذا بقدر
+
+308
+00:35:58,030 --> 00:36:03,610
+اجيب شكل ال particular solution تمام
+
+309
+00:36:12,370 --> 00:36:19,870
+بقول له the particular solution
+
+310
+00:36:19,870 --> 00:36:25,750
+of equation
+
+311
+00:36:25,750 --> 00:36:35,850
+star is capital Y of T بده يساوي U واحد في ال Y
+
+312
+00:36:35,850 --> 00:36:44,380
+one زائد U اتنين في ال Y twoاذا capital Y of T بده
+
+313
+00:36:44,380 --> 00:36:52,620
+يسمى وين ال U1؟ هاد ال U1، هاد ايه؟ اللي كتبناها
+
+314
+00:36:52,620 --> 00:36:57,560
+على الشكل هذا، هاد ال U1، هاد بنا نضربها في
+
+315
+00:36:57,560 --> 00:37:05,760
+مينوبالاتبدا ان انا اضربها في ال Y1 هذي ههه مظبوط
+
+316
+00:37:05,760 --> 00:37:10,160
+مش هذي ال Y1 يعني كأنها ههه خاني اختصرها لك بعدين
+
+317
+00:37:10,160 --> 00:37:18,640
+مش مشكلة يبقى بداجي اقول E أس ناقص T في Cos T في
+
+318
+00:37:19,480 --> 00:37:24,140
+الـ U1 اللي هو اتنين او سالب اتنين على كوساين ت
+
+319
+00:37:24,140 --> 00:37:33,840
+سالب اتنين على كوساين T سالب اتنين كوساين T زي ال
+
+320
+00:37:33,840 --> 00:37:41,600
+Y2 اللي هو E أُس ناقص T في ساين T فاللي طلعناها
+
+321
+00:37:41,600 --> 00:37:50,220
+تحت هذهاللي هو اتنين لين absolute value لمن ل سك T
+
+322
+00:37:50,220 --> 00:37:59,980
+زائد تاني T و هنا ناقص اتنين صيني T بالشكل اللي
+
+323
+00:37:59,980 --> 00:38:06,780
+عندنا هذا الان بدنا نجيب ال general solution بعد
+
+324
+00:38:06,780 --> 00:38:13,310
+ما جيبنا شكل mainشكل ال particular solution بس
+
+325
+00:38:13,310 --> 00:38:18,670
+خلينا نشوف يا ترى فيها اختصارات والله مافيهاش
+
+326
+00:38:18,670 --> 00:38:25,960
+اختصارات لو جمعناهايعني هنا بيصير والله يمكن يكون
+
+327
+00:38:25,960 --> 00:38:30,240
+فيها اختصارات تعالى نشوف كده بده تساوي هذه المناطب
+
+328
+00:38:30,240 --> 00:38:37,560
+بيصير عندى ناقص اتنين و E أس سالب T و ال cosine مع
+
+329
+00:38:37,560 --> 00:38:44,980
+ال cosine بتروح و هنا سالب اتنين E أس ناقص T في
+
+330
+00:38:44,980 --> 00:38:53,620
+cosine تربيع T تمام خلاصنا منهاهدي زائد اتنين EOS
+
+331
+00:38:53,620 --> 00:39:01,000
+ناقص T في صين ال T في ال absolute value لشك ال T
+
+332
+00:39:01,000 --> 00:39:11,980
+زائد تاني T ناقص اتنين EOS ناقص T في صين تربيع ال
+
+333
+00:39:11,980 --> 00:39:19,520
+T والله كويس طليلي في هدي هو هديبقدر اخد سالب
+
+334
+00:39:19,520 --> 00:39:25,420
+اتنين عامل مشترك ايش بيضل عندى؟ بيضل sin تربية
+
+335
+00:39:25,420 --> 00:39:30,920
+زائد cos تربية اللى بيبقى داشر يعنى هذا بيصير سالب
+
+336
+00:39:30,920 --> 00:39:37,480
+اتنين Eos ناقص T سالب اتنين Eos ناقص T وبيضلش
+
+337
+00:39:37,480 --> 00:39:45,220
+الامن اللى فالمص هذا يبقى زائد اتنين Eos ناقص T في
+
+338
+00:39:45,220 --> 00:39:47,580
+sin T فلن
+
+339
+00:39:53,890 --> 00:39:59,510
+ممتاز طيب إيش راحك هذه و هذه نفس هذه يبقى سالب
+
+340
+00:39:59,510 --> 00:40:07,170
+أربعة يبقى النتيجة سالب أربعة يوس ناقص T زائد
+
+341
+00:40:07,170 --> 00:40:17,230
+اتنين يوس ناقص T في صينة T في لن سكتي زائد تانتي
+
+342
+00:40:18,270 --> 00:40:28,510
+اذا انا باجي بقول له the general solution of the
+
+343
+00:40:28,510 --> 00:40:39,210
+differential equation star is y سوى yc هيه عند هنا
+
+344
+00:40:39,210 --> 00:40:51,800
+تحتيبقى C1 EOS ناقص T في Cos T زائد C2 EOS ناقص T
+
+345
+00:40:51,800 --> 00:41:01,740
+في Sin T ناقص أربعة EOS ناقص T زائد اتنين EOS ناقص
+
+346
+00:41:01,740 --> 00:41:14,180
+T في Sin T في لن absolute valueسك T زائد تاني T في
+
+347
+00:41:14,180 --> 00:41:16,020
+اي تساول هنا يا بنادى
+
+348
+00:41:54,370 --> 00:42:06,930
+كمان مثال مثال
+
+349
+00:42:06,930 --> 00:42:11,830
+تلاتة سؤال
+
+350
+00:42:11,830 --> 00:42:20,650
+من الكتاب بيقول fy1 بده يساوي T تربيع and
+
+351
+00:42:22,110 --> 00:42:35,630
+Y2 بدي ساوي T تربيع لينية T are two linearly
+
+352
+00:42:35,630 --> 00:42:40,290
+independent solutions
+
+353
+00:42:40,290 --> 00:42:43,650
+of
+
+354
+00:42:43,650 --> 00:42:48,330
+the homogeneous
+
+355
+00:42:53,180 --> 00:43:01,600
+Differential Equation لـ T تربيع Y double prime
+
+356
+00:43:01,600 --> 00:43:11,160
+ناقص ثلاثة T Y prime زائد أربعة Y تساوي Zero
+
+357
+00:43:11,160 --> 00:43:16,720
+وسميلي هذه المعادلة رقم واحد Find a particular
+
+358
+00:43:16,720 --> 00:43:17,940
+solution
+
+359
+00:43:30,160 --> 00:43:36,840
+تبحث عن حلول معينة مختلفة للإيقاع
+
+360
+00:43:42,000 --> 00:43:49,520
+Equation للمعادلة التفاضلية T تربيع Y double prime
+
+361
+00:43:49,520 --> 00:43:53,140
+ناقص
+
+362
+00:43:53,140 --> 00:44:08,600
+تلاتة T Y prime زائد أربعة Y تساوي T تربيع لن Tو
+
+363
+00:44:08,600 --> 00:44:18,120
+ال T greater than zero و هذه المعادلة رقم اتنين
+
+364
+00:44:36,850 --> 00:44:43,230
+يبقى هذا السؤال يختلف عن سابقينه في أمر واحد فقط
+
+365
+00:44:43,230 --> 00:44:48,090
+شو الأمر هذا؟ ان المعادلة اللى ماتاها للمعاملات
+
+366
+00:44:48,090 --> 00:44:53,290
+تبعتها مالها ماهياش ثوابت واحنا أخدنا إذا المعادلة
+
+367
+00:44:53,290 --> 00:45:00,010
+ماهياش ثوابت لازم يعطيني أحد الحلول واني أروح أجيب
+
+368
+00:45:00,010 --> 00:45:05,000
+الحل الأخر بطريقة reduction of order مظبوط؟لكن
+
+369
+00:45:05,000 --> 00:45:09,920
+الحمد لله ريحني وقال لي خد هدول الحالين هيهم معاك
+
+370
+00:45:09,920 --> 00:45:14,500
+يبقى ريحني من طريقة مين ال reduction of order
+
+371
+00:45:14,500 --> 00:45:19,880
+وبالتالي قال لي لو كانوا هدول اتنين T تربيع وT
+
+372
+00:45:19,880 --> 00:45:24,000
+تربيع لان T هم حالين لل homogeneous differential
+
+373
+00:45:24,000 --> 00:45:29,660
+equation بدي شكل الحل الخاص لمين للمعادلة اللي
+
+374
+00:45:29,660 --> 00:45:35,610
+عندنا هذه بقول لك كويس يعني هو ريحنيوبالتالي قال
+
+375
+00:45:35,610 --> 00:45:40,450
+اتنين linearly independent اذا المعادلة الأولى
+
+376
+00:45:40,450 --> 00:45:51,450
+واحد حلها بجيبه في سطر يبقى فبجيبه هنا solution of
+
+377
+00:45:51,450 --> 00:46:00,330
+equation
+
+378
+00:46:00,330 --> 00:46:13,050
+oneالمعادلة الأولى هو YC بده يساوي C1 في من؟ في T
+
+379
+00:46:13,050 --> 00:46:22,230
+تربيع زائد C2 في T تربيع في لن T مش هيك؟ وين راح
+
+380
+00:46:22,230 --> 00:46:30,040
+تقع لن T؟ لن ال T تمام تماميبقى هذا لو طلب ال
+
+381
+00:46:30,040 --> 00:46:34,020
+general solution برجعله مطلبش بلاش لكن هو طلب فقط
+
+382
+00:46:34,020 --> 00:46:39,180
+من ال particular solution للمعادلة رقم اتنين بقوله
+
+383
+00:46:39,180 --> 00:46:42,880
+بسيطة يبقى بدي أشيل c واحد و أحط مكانه function y
+
+384
+00:46:42,880 --> 00:46:48,220
+واحد و u واحد و أشيل u اتنين و أحط بدله function u
+
+385
+00:46:48,220 --> 00:46:52,740
+اتنين لكن مع الفرق بدرو حسب الرونسكين تبعهم من
+
+386
+00:46:52,740 --> 00:46:57,920
+البداية قبل ما أجيب الحل اللي انا بديهايبقى لو
+
+387
+00:46:57,920 --> 00:47:03,560
+روحت أخدت رونسكين as a function of T الحل الأول T
+
+388
+00:47:03,560 --> 00:47:10,780
+تربيع والحل التاني T تربيع فلن T مشتقة الأول اتنين
+
+389
+00:47:10,780 --> 00:47:19,660
+T التاني حاصل ضرب دالتين يبقى اتنين T لن T زائد T
+
+390
+00:47:19,660 --> 00:47:26,930
+تربيع فلن T مشتقة لن T ليبقى داشر مع T تربيعبتظل
+
+391
+00:47:26,930 --> 00:47:32,710
+بس T واحدة يبقى هاي T بده افكر المحدد اللي عندنا
+
+392
+00:47:32,710 --> 00:47:42,790
+هذا يبقى بصير اتنين T تكعيب لان ال T زائد T تكعيب
+
+393
+00:47:42,790 --> 00:47:50,750
+ناقص اتنين T تكعيبلأن ال T أظن هذه وهذه مع السلامة
+
+394
+00:47:50,750 --> 00:47:58,530
+بظل الجواب T تكيب وهذا لا يساوي Zero ليش؟ لأن T
+
+395
+00:47:58,530 --> 00:48:03,690
+أكبر من Zero هو مطالوين في المسألة إذا جبت له
+
+396
+00:48:03,690 --> 00:48:06,810
+رونسكين وطلع طلع طلع طلع طلع طلع طلع طلع طلع طلع
+
+397
+00:48:06,810 --> 00:48:07,990
+طلع طلع طلع طلع طلع طلع طلع طلع طلع طلع طلع طلع
+
+398
+00:48:07,990 --> 00:48:08,850
+طلع طلع طلع طلع طلع طلع طلع طلع طلع طلع طلع طلع
+
+399
+00:48:08,850 --> 00:48:08,850
+طلع طلع طلع طلع طلع طلع طلع طلع طلع طلع طلع طلع
+
+400
+00:48:08,850 --> 00:48:15,110
+طلع طلع طلع طلع طلع طلع
+
+401
+00:48:15,110 --> 00:48:15,110
+ط
+
+402
+00:48:23,600 --> 00:48:32,780
+Equation اتنين is non
+
+403
+00:48:32,780 --> 00:48:39,620
+homogeneousيبقى Y of T يبقى يساوي يبقى يساوي يبقى
+
+404
+00:48:39,620 --> 00:48:45,160
+يساوي يبقى يبقى يبقى يبقى يبقى يبقى يبقى يبقى يبقى
+
+405
+00:48:45,160 --> 00:48:49,900
+يبقى يبقى
+
+406
+00:48:49,900 --> 00:48:52,400
+يبقى يبقى يبقى يبقى يبقى يبقى يبقى يبقى يبقى يبقى
+
+407
+00:48:52,400 --> 00:48:52,420
+يبقى يبقى يبقى يبقى يبقى يبقى يبقى يبقى يبقى يبقى
+
+408
+00:48:52,420 --> 00:48:52,420
+يبقى يبقى يبقى يبقى يبقى يبقى يبقى يبقى يبقى يبقى
+
+409
+00:48:52,420 --> 00:49:01,420
+يبقى يبقى يبقى يبقى يبقى يبقى يبقى
+
+410
+00:49:01,420 --> 00:49:06,690
+يالمعادلة هذه اشترقنا من؟ لازم يكون المعامل واحد
+
+411
+00:49:06,690 --> 00:49:10,370
+صحيح يبقى اول خطوة بدي اعمله بدي اجسم المعادلة
+
+412
+00:49:10,370 --> 00:49:16,470
+كلها على مين T تربيع يبقى باجي بقوله قبل ما اكتب
+
+413
+00:49:16,470 --> 00:49:27,750
+where باجي بقوله the differential equation two is
+
+414
+00:49:27,750 --> 00:49:29,050
+written
+
+415
+00:49:30,810 --> 00:49:37,710
+نقسم على T تربيع بصير يو عندي Y double prime ناقص
+
+416
+00:49:37,710 --> 00:49:47,590
+تلاتة على T في ال Y prime زائد أربعة على T تربيع
+
+417
+00:49:47,590 --> 00:49:55,610
+في ال Y كله بده يساوي من لن T فقط لا غيرالحين بقدر
+
+418
+00:49:55,610 --> 00:49:59,550
+أجيبله بسهولة بدون أخطاء، لو ما قسمتيش بصي شغلك
+
+419
+00:49:59,550 --> 00:50:05,130
+غلط، عادي لبالك، شكل ال G of T تغير، G of T كان T
+
+420
+00:50:05,130 --> 00:50:10,850
+تربية لن T، بس هنا صار لن T واحدة، تمام؟يبقى باجي
+
+421
+00:50:10,850 --> 00:50:18,370
+بقوله ال U1 as a function of T ناقص تكامل Y2 of T
+
+422
+00:50:18,370 --> 00:50:24,330
+في ال G of T على الرنسكين as a function of T DT
+
+423
+00:50:24,330 --> 00:50:31,430
+يبقى سالب تكامل ال Y2 اللي عندنا اللي هي main لت
+
+424
+00:50:31,430 --> 00:50:40,320
+تربيع للنت يبقى هاي ت تربيع وهذا للنت تمامالـ G of
+
+425
+00:50:40,320 --> 00:50:45,260
+T اللي يجهد يا بنات ليه جديدة مش العتيقة يعني
+
+426
+00:50:45,260 --> 00:50:51,280
+المعادلة الصحيحة مش عادية يبقى اللي يمين لن ت كل
+
+427
+00:50:51,280 --> 00:50:56,000
+هذا الكلام على الرونسكين اللي هو طالع في قديش ت
+
+428
+00:50:56,000 --> 00:51:06,040
+تكيب ت تكيب كله دي ت يبقى صارة المسألة تكامل لن ت
+
+429
+00:51:06,040 --> 00:51:15,250
+الكل تربيععلى T D T تمام؟ يبقى هذا الكلام بده
+
+430
+00:51:15,250 --> 00:51:22,750
+يساوي تكامل LN T لكل تربيع مشتقة LN T بنفع هيك؟
+
+431
+00:51:22,750 --> 00:51:28,370
+لإن مشتقة LN T بجداش بواحدة على T D T إذا واحدة
+
+432
+00:51:28,370 --> 00:51:33,210
+على T D T بدي أقول مشتقة LN T يعني في سالب بس برا
+
+433
+00:51:33,210 --> 00:51:35,950
+هي السالب وهي السالب
+
+434
+00:51:43,390 --> 00:51:55,890
+يبقى هذا الكلام يساوي سالب طول لنت لنت لكل تقييمأو
+
+435
+00:51:55,890 --> 00:52:01,530
+لنت كيب T لو كتبتيه لنت كيب T ماعنا مشكلة وبنروح
+
+436
+00:52:01,530 --> 00:52:08,810
+ونقول زائد constant C1 وهنا بنقول تاك C1 بده يساوي
+
+437
+00:52:08,810 --> 00:52:17,050
+Zero تمام يبقى هذا بده يعطيلك انه مين ان ال U1 بده
+
+438
+00:52:17,050 --> 00:52:25,080
+يساوي سالب طول لنت لكل تكيببنروح نجيب له مان اللي
+
+439
+00:52:25,080 --> 00:52:32,860
+هو U2 يبقى U2 as a function of T بيساوي تكامل Y1
+
+440
+00:52:32,860 --> 00:52:38,720
+of T في G of T على الرونسكين as a function of T dt
+
+441
+00:52:40,640 --> 00:52:46,260
+يبقى هذا الكلام بده يسوي تكامل Y1 اللي هو T تربيع
+
+442
+00:52:46,260 --> 00:52:52,900
+فقط لغير يبقى T تربيع و ال G of T اللي طلعت عندنا
+
+443
+00:52:52,900 --> 00:53:00,080
+اللي هي لن T و الرنس كان اللي هو قداش كان T تكيب
+
+444
+00:53:00,080 --> 00:53:10,790
+DT يبقى صار تكامل للن Tعلى ت دي ت أو تكامل ل لن ت
+
+445
+00:53:10,790 --> 00:53:19,610
+مشتقة لن ت عظيم نضيف لل أس واحد و بنجسم على الأسر
+
+446
+00:53:19,610 --> 00:53:24,950
+يعني لن ت لكل تربية على اتنين يعني النص
+
+447
+00:53:27,170 --> 00:53:37,710
+لنتي الكل تربيع زائد كونستان C2 وبناخد C2 بقداش B0
+
+448
+00:53:37,710 --> 00:53:47,610
+يبقى أصبح U2 بده يساوي من اللي هو نص لنتي الكل
+
+449
+00:53:47,610 --> 00:53:53,880
+تربيعإذا بقدر أجيب له شكل ال particular solution
+
+450
+00:53:53,880 --> 00:54:03,720
+يبقى capital Y of T بديه 7 وين capital Y؟ U1 في T
+
+451
+00:54:03,720 --> 00:54:09,660
+تربية وين ال U1؟ هذي ال U1 بدي أضربها في قداش في T
+
+452
+00:54:09,660 --> 00:54:18,970
+تربية يبقى سالب تلت T تربية سالب تلت T تربيةتي
+
+453
+00:54:18,970 --> 00:54:31,730
+تربيع في لين تيل كل تكيب اللي بعده زائد مصر في من؟
+
+454
+00:54:31,730 --> 00:54:42,190
+في .. where راحت؟الكلمة بتلعب في T تربيع في
+
+455
+00:54:42,190 --> 00:54:49,310
+ال N T كل تكعيب مظبوط لإن وعندي ال N T وعندي ال N
+
+456
+00:54:49,310 --> 00:54:55,610
+T تربيع يبقى بيصير سالب تلت زائد نص بيبقى الجداش
+
+457
+00:54:55,610 --> 00:54:57,970
+زائد سادس
+
+458
+00:55:05,890 --> 00:55:11,210
+هذا البرتكيرال سوليوشن اللي بده لو قاللي هاتلي ال
+
+459
+00:55:11,210 --> 00:55:17,010
+general solution بروح بجمعله هذا مع من مع اللي فوق
+
+460
+00:55:17,010 --> 00:55:20,010
+بجيب لمين ال general solution
+
+461
+00:55:25,200 --> 00:55:46,880
+بنتهي هذا الفيديو وانتهي
+
+462
+00:55:46,880 --> 00:55:47,600
+هذا الفيديو
+
+463
+00:55:52,960 --> 00:55:57,080
+هل تحب تسأل اي سؤال هنا يا بنان؟ يبقى هذا السؤال
+
+464
+00:55:57,080 --> 00:56:02,820
+يختلف عن سابقاها بإن المعاملات ما هي اجتماعات
+
+465
+00:56:02,820 --> 00:56:08,360
+وانما دوال في T كان بإمكاني أصي هذه السؤال بصيغة
+
+466
+00:56:08,360 --> 00:56:17,880
+أخرى أقول لك سؤال كتالي if Y1 يسوى T تربيع is a
+
+467
+00:56:17,880 --> 00:56:22,210
+solution لل differential equation هذه؟هتيلي الحل
+
+468
+00:56:22,210 --> 00:56:26,970
+الثاني تمام؟ يبقى مقدميش إلا ال reduction of order
+
+469
+00:56:26,970 --> 00:56:31,910
+إجباري في شغلها ليش المعاملات ما هيش ثوابت يبقى
+
+470
+00:56:31,910 --> 00:56:34,870
+بروح بجيب ال reduction of order و بجيب الحل التاني
+
+471
+00:56:34,870 --> 00:56:40,090
+لازم يطلع الحل التاني على الشكل هنا تمام؟ وبالتالي
+
+472
+00:56:40,090 --> 00:56:43,530
+جيبتله الحل اللي فوق و بعدين بروح بجيبله particle
+
+473
+00:56:43,530 --> 00:56:47,610
+of solution اللي جيبناه اللي عندنا هناوكتير بيجي
+
+474
+00:56:47,610 --> 00:56:52,430
+في الامتحانات زيك لكن ان غلطة في الحل التاني غلطة
+
+475
+00:56:52,430 --> 00:56:58,790
+في الحل الكلي بيصير مظبوط او كان بممكن اقولك بس ان
+
+476
+00:56:58,790 --> 00:57:01,730
+قلتك تأكديلي ان هذا حل تاني بتروح تعوضلي في
+
+477
+00:57:01,730 --> 00:57:05,530
+المعادرة لكن قلتك use reduction of order to find
+
+478
+00:57:05,530 --> 00:57:09,670
+او to show that the second solution is كذا ومن ثم
+
+479
+00:57:09,670 --> 00:57:12,270
+هتي ال solution يبقى بدك استخدم ال reduction of
+
+480
+00:57:12,270 --> 00:57:19,850
+order و بعدين تروح لمينهل بتسأل أي سؤال؟
+
+481
+00:57:44,440 --> 00:57:49,420
+طبعا بنتح ناك خلصنا لحد هنا الامتحان لكن أحيانا
+
+482
+00:57:49,420 --> 00:57:53,320
+بنجيب مسائل على غير ما اتعودنا في المحاضرات
+
+483
+00:57:53,320 --> 00:57:58,480
+الماضية كيف؟ يعني بيجيش السؤال مباشر بيقولك حل
+
+484
+00:57:58,480 --> 00:58:01,880
+المسألة دي باستخدام التعويضة الفلانية و بروح
+
+485
+00:58:01,880 --> 00:58:05,080
+بيعطينا التعويضة معينة و أنا بدأ أستخدم التعويضة
+
+486
+00:58:05,080 --> 00:58:10,140
+هذه في حل المسألة كيف المسألة يمكن تطلع first
+
+487
+00:58:10,140 --> 00:58:14,310
+order ويمكن تطلع second orderوانطلعت first order
+
+488
+00:58:14,310 --> 00:58:18,810
+يمكن exact يمكن homogeneous يمكن separable يمكن
+
+489
+00:58:18,810 --> 00:58:23,090
+linear يمكن Bernoulli يمكن اشوف المعادل المناسب و
+
+490
+00:58:23,090 --> 00:58:30,210
+اروح احلبها يمكن تبقى المثل second order يمكن يطلع
+
+491
+00:58:30,210 --> 00:58:33,790
+question with y missing question with d missing
+
+492
+00:58:34,060 --> 00:58:37,040
+يمكن يطلع لـ non-homogeneous differential
+
+493
+00:58:37,040 --> 00:58:40,240
+equation، variation of parameters أو undetermined
+
+494
+00:58:40,240 --> 00:58:43,840
+coefficients يبقى أنا بدي أشوف المناسب اللي عندي و
+
+495
+00:58:43,840 --> 00:58:48,320
+أروح أحل المثلة بالطريقة التي تناسبها
+
+496
+00:58:52,610 --> 00:58:57,490
+الاسئلة و بدى أجيبهم لكم الامتحانات السابقة مشان
+
+497
+00:58:57,490 --> 00:59:01,850
+نعرف كيف بدى نشتغل هالشغل هادى يبقى احنا مسائل
+
+498
+00:59:01,850 --> 00:59:09,920
+عامة الآن على شبطر اتنين و شبطرتلاتة كويس يبقى هنا
+
+499
+00:59:09,920 --> 00:59:14,440
+exercises
+
+500
+00:59:14,440 --> 00:59:28,660
+او examples on using باستخدام substitution استخدام
+
+501
+00:59:28,660 --> 00:59:37,230
+التعويد substitution to solve thedifferential
+
+502
+00:59:37,230 --> 00:59:42,470
+equation أول
+
+503
+00:59:42,470 --> 00:59:52,490
+سؤال جبناه في امتحان سنة الألفين بيقول use the
+
+504
+00:59:52,490 --> 00:59:55,890
+substitution
+
+505
+00:59:55,890 --> 01:00:08,230
+استخدم التعويضةU تساوي E أس Y تsolve the
+
+506
+01:00:08,230 --> 01:00:18,870
+differential equation المعادلة التفاضلية X Y ناقص
+
+507
+01:00:18,870 --> 01:00:24,270
+X تكيب في E أس ناقص Y يساوي 2
+
+508
+01:01:01,570 --> 01:01:04,850
+واضح انه السؤال تبعناه the first order
+
+509
+01:01:04,850 --> 01:01:08,470
+differential equation وليس second order بقول
+
+510
+01:01:08,470 --> 01:01:12,670
+يستخدم التعويضة U تساوي E اص Y to solve the
+
+511
+01:01:12,670 --> 01:01:17,150
+differential equation سؤالي هو هل في في مثلة كلها
+
+512
+01:01:17,150 --> 01:01:24,310
+E اص Y؟ لأ في عندي ايش؟ E اص سالب Y اذا ممكن اتخلص
+
+513
+01:01:24,310 --> 01:01:28,690
+من E اص سالب Y و احول مثلة كلها بدلالة مين؟يبقى
+
+514
+01:01:28,690 --> 01:01:33,570
+بروح أضرب كله في مين؟ في الـ E أُس Y المعادلة يبقى
+
+515
+01:01:33,570 --> 01:01:39,870
+باجي بقوله solution بدي أضرب كله في E أُس Y إيش
+
+516
+01:01:39,870 --> 01:01:46,410
+بصير يا بنات؟ X في E أُس Y في الـY' ناقص X تكيب
+
+517
+01:01:46,410 --> 01:01:54,210
+تساوي 2E أُس Y تمام؟ يبقى بطل يصير عندي E أُس ناقص
+
+518
+01:01:54,210 --> 01:02:04,860
+Y كله بدللة E أُس Yهذه الـ U تساوي U² بدي أشتق
+
+519
+01:02:04,860 --> 01:02:13,620
+يبقى دي U على دي X يبقى هنا دي U على دي X يعني منه
+
+520
+01:02:13,620 --> 01:02:19,820
+U' تساوي اشتقاق هذه بالنسبة إلى X يبقى مشتقة الـ
+
+521
+01:02:19,820 --> 01:02:25,120
+exponential بالـ exponential itself في المشتقة
+
+522
+01:02:25,120 --> 01:02:29,760
+تبعتهاالمعلومات اللى حصلت عليها بدي اعوضها في
+
+523
+01:02:29,760 --> 01:02:37,420
+المعادلة هذه اطلعيلي هذه جداش ب U prime يبقى ثارة
+
+524
+01:02:37,420 --> 01:02:45,440
+X في ال U prime ناقص X تكيب يساوي اتنين U
+
+525
+01:02:48,250 --> 01:02:51,550
+طيب شو رايك اكتبها على الشكل التالي
+
+526
+01:03:00,250 --> 01:03:05,270
+مش رايك اجسم على مين؟ على X يبقى لو جسمت على X
+
+527
+01:03:05,270 --> 01:03:15,090
+بصير U' ناقص اتنين على X هذه كلها في ال U ناقص
+
+528
+01:03:15,090 --> 01:03:20,310
+اتنين على X في ال U بده يساوي X تربية مش رايكوا
+
+529
+01:03:20,310 --> 01:03:26,170
+فيها هذه؟ لين؟ يبقى خلاص صارت زي أول ماخدنا في
+
+530
+01:03:26,170 --> 01:03:33,700
+الشاب طريق اتنينيبقى هذه linear first order
+
+531
+01:03:33,700 --> 01:03:41,750
+differential equation كذا كنا بنحل ال linearمن هنا
+
+532
+01:03:41,750 --> 01:03:48,470
+نقول ميو اف اكس يساوي اي اث ناقص اتنين تكامل واحد
+
+533
+01:03:48,470 --> 01:03:55,410
+على اكس مالها دي اكس يبقى اي اث ناقص اتنين لن
+
+534
+01:03:55,410 --> 01:04:01,170
+absolute في الاكس اللي مش حرطش عنديبقول له اه يبقى
+
+535
+01:04:01,170 --> 01:04:06,410
+هذه absolute value ل X اص ناقص اتنين يعني واحد على
+
+536
+01:04:06,410 --> 01:04:10,710
+X تربية كمية مربعة لإن تربية حطيت ال absolute و لا
+
+537
+01:04:10,710 --> 01:04:17,150
+شيلتي سيان يبقى صار هذا الميو of X بدي اخد الميو
+
+538
+01:04:17,150 --> 01:04:21,730
+of X وروح شو عمله بدي اضربه في المعادلة اللي عندنا
+
+539
+01:04:21,730 --> 01:04:25,880
+هذهيبقى ايش بيصير المعادلة هذه على الشكل التالي
+
+540
+01:04:25,880 --> 01:04:31,860
+واحد على اكس تربية U prime ناقص بدي اضرب في واحدة
+
+541
+01:04:31,860 --> 01:04:38,200
+اللي يبقى ناقص اتنين على اكس تكيب في ال U بدي ساوي
+
+542
+01:04:38,200 --> 01:04:45,620
+قداش بدي ساوي واحد او بمعنى اخر هذه واحد على اكس
+
+543
+01:04:45,620 --> 01:04:52,590
+تربية في ال U كله prime بيساوي قداشإن كامل الطرفين
+
+544
+01:04:52,590 --> 01:04:59,810
+يبقى بصير واحد على X تربية في ال U واحد على X
+
+545
+01:04:59,810 --> 01:05:06,390
+تربية في ال U بدي شوي X زائد constant C
+
+546
+01:05:08,500 --> 01:05:15,040
+مضرب كله في من؟ في ال X تربيع يبقى بصير ال U مين
+
+547
+01:05:15,040 --> 01:05:24,040
+هي ال U هذه؟ E أوس Y يبقى E أوس Y يساوي X تكيب
+
+548
+01:05:24,040 --> 01:05:31,640
+زائد C X تربيع تمام؟ احنا بدنا E أوس Y ولا بدنا Y
+
+549
+01:05:31,640 --> 01:05:41,770
+الحل؟ناخد لن للطرفين إذا ال Y بدها تساوي لن اللي
+
+550
+01:05:41,770 --> 01:05:51,590
+هو X تكيب زائد C X تربيع هذا هو الحل اللي عندنا
+
+551
+01:05:51,590 --> 01:05:56,010
+خلاص نعطيكم
+
+552
+01:05:56,010 --> 01:05:57,010
+مثال آخر
+
+553
+01:06:00,310 --> 01:06:05,590
+مثال سنة تسعة وتسعين هذا سنة اللي جابلها يبقى هذا
+
+554
+01:06:05,590 --> 01:06:12,250
+اتنين سنة التلات تسعات انتخابات عربية بقول ي solve
+
+555
+01:06:12,250 --> 01:06:20,750
+the differential equation حل المعادلة التفاضلية y
+
+556
+01:06:20,750 --> 01:06:42,700
+في y double prime ناقص y primeترابيع يستخدم
+
+557
+01:06:42,700 --> 01:06:53,680
+تعويض
+
+558
+01:06:54,340 --> 01:07:03,680
+V تساوي لن ال Y طب
+
+559
+01:07:03,680 --> 01:07:08,300
+لو ماعطانيش التعويضة هذه وجه بقى طالع في المثل
+
+560
+01:07:08,300 --> 01:07:12,760
+الأول واهلة ايش ممكن تقولي عن المثل اللي فوق هذه
+
+561
+01:07:12,760 --> 01:07:21,510
+question with with ايش T missing T مفقودةيبقى تروح
+
+562
+01:07:21,510 --> 01:07:25,890
+أحلها على equation والـT مسك لكن كونه وطني تعويضة
+
+563
+01:07:25,890 --> 01:07:32,130
+بدأ أضطر استخدمين هذه التعويضة طيب التعويضة هذه
+
+564
+01:07:32,130 --> 01:07:39,730
+ممكن أكتبها بشكل آخر احنا عندنا مين ال V يسوى اللي
+
+565
+01:07:39,730 --> 01:07:47,110
+لنا ال Y إذا لو رفعت اتنين كأس للعدد E بصير هنا ال
+
+566
+01:07:47,110 --> 01:07:50,410
+Y تساوي E أس V
+
+567
+01:07:55,180 --> 01:08:02,800
+طب ايش رأيكوا بدي اشتقها؟ بدي اشتقها بالنسبة لمن؟
+
+568
+01:08:02,800 --> 01:08:08,280
+ل T او كانت في X او اتبعها في X بدي اشتقها بالنسبة
+
+569
+01:08:08,280 --> 01:08:14,900
+ل X بالنسبة ل T ماعنا مشكلة يبقى بداجي اقول دي Y
+
+570
+01:08:14,900 --> 01:08:22,230
+by دي T اللي هو Y primeيجب أن يكون مشتقة الـ EOSV
+
+571
+01:08:22,230 --> 01:08:30,150
+بالـ EOSV السلفين في الـ Y' طيب إذا بدى أروح أجيب
+
+572
+01:08:30,150 --> 01:08:37,750
+المشتقة الثانية يبقى هذه مشتقة حاصل ضب دلتين يبقى
+
+573
+01:08:37,750 --> 01:08:47,350
+EOSV في مشتقة الدلة الثانية VW'زائد ال V' زي ما هي
+
+574
+01:08:47,350 --> 01:08:56,690
+في مشتقة ال EOSV ب EOSV في ال V' يبقى صارة المشتقة
+
+575
+01:08:56,690 --> 01:09:07,570
+اللي عندي VW' زائد V' لكل تربيع كله في EOSV
+
+576
+01:09:10,030 --> 01:09:14,850
+بناخد هذه المعلومات ونعوضها في المعادلة اللي عندنا
+
+577
+01:09:14,850 --> 01:09:20,610
+هنا هذي سميها للمعادلة star نجي نقول هنا
+
+578
+01:09:20,610 --> 01:09:26,570
+substitute and
+
+579
+01:09:26,570 --> 01:09:31,090
+equation star we get
+
+580
+01:09:33,740 --> 01:09:40,120
+الـ Y هشيلها و اكتب بدلها مين؟ E Os V يبقى E Os V
+
+581
+01:09:40,120 --> 01:09:50,340
+الـ Y W Prime هيه يبقى بصير عندي E Os 2 V في مين؟
+
+582
+01:09:50,340 --> 01:09:57,260
+في الـ V W Prime نقص V Prime لكل تربيه هي خلصنا
+
+583
+01:09:57,260 --> 01:10:05,350
+منهاالان ال Y' وY' يجب أن أربعها لأنها تربية
+
+584
+01:10:16,490 --> 01:10:23,510
+في الاصلة منها بدها تساوي Y تربيع ل E أس اتنين V
+
+585
+01:10:23,510 --> 01:10:31,750
+يبقى E أس اتنين V لإن ال Y هو ميعطينيها بقداش V
+
+586
+01:10:31,750 --> 01:10:38,270
+طيب إيش رايكوا أبسط المعادلة كلها من أولها لآخرها
+
+587
+01:10:38,270 --> 01:10:44,950
+نقسم عالميا على E أس اتنين V لأن هو رقم أكبر من
+
+588
+01:10:44,950 --> 01:10:45,270
+Zero
+
+589
+01:10:57,780 --> 01:11:05,200
+طيب يبقى آلة المسألة الشكل التالي بعد القسمة
+
+590
+01:11:07,130 --> 01:11:14,350
+زائد v prime تاربيع ناقص v prime تاربيع بده يسوى
+
+591
+01:11:14,350 --> 01:11:22,010
+قداش v اظن هذه وهذه مع السلامة تمام يبقى آلة
+
+592
+01:11:22,010 --> 01:11:29,430
+المسألة الى v double prime ناقص v تسوى zero
+
+593
+01:11:31,650 --> 01:11:35,950
+هوموجينياس differential equation من ال second
+
+594
+01:11:35,950 --> 01:11:42,010
+order كيف بنحلها يعني
+
+595
+01:11:42,010 --> 01:11:44,870
+بدنا نروح نجيب ال characteristic equation ممتاز
+
+596
+01:11:44,870 --> 01:11:49,030
+جدا يبقى بدنا نروح نحلها بواسطة ال characteristic
+
+597
+01:11:49,030 --> 01:11:59,120
+equation يبقى باجي بقوله letV تساوي E أس RT ب
+
+598
+01:11:59,120 --> 01:12:02,200
+Solution
+
+599
+01:12:02,200 --> 01:12:08,500
+then the characteristic
+
+600
+01:12:08,500 --> 01:12:20,140
+equation is R ترابيع ناقص واحد يساوي Zero يبقى هاد
+
+601
+01:12:20,140 --> 01:12:28,180
+ايش؟R تساوي زائد او ناقص مين واحد يبقى معنا هذا
+
+602
+01:12:28,180 --> 01:12:39,760
+الكلام ان V بتصير عندنا
+
+603
+01:12:39,760 --> 01:12:47,720
+ال V of T as a function of T هي عبارة عن C1 EOS T
+
+604
+01:12:47,720 --> 01:12:58,910
+C2 EOS ناقص Tمظبوط؟ لكن V of T مين هي؟ لن ال Y إذا
+
+605
+01:12:58,910 --> 01:13:05,070
+لن ال Y هي اللي بتسوي هذا الكلام هذا بدي أعطيكي ان
+
+606
+01:13:05,070 --> 01:13:14,910
+لن ال Y يسوى C1 E Os T C2 E Os ناقص T لن ال Y بقدر
+
+607
+01:13:14,910 --> 01:13:15,850
+أتخلص منها
+
+608
+01:13:19,280 --> 01:13:25,020
+ناخد الترفع كله كأسل العدد A يبقى ماجي بقوله
+
+609
+01:13:25,020 --> 01:13:30,120
+solution of
+
+610
+01:13:30,120 --> 01:13:37,120
+equationY تساوي
+
+611
+01:13:37,120 --> 01:13:48,940
+E أس C واحد E أس T زائد C اتنين E أس سالب T بالشكل
+
+612
+01:13:48,940 --> 01:13:57,200
+اللي عندنا طيب هذه كمان فكرة غير الفكرة الأولى
+
+613
+01:13:57,630 --> 01:14:02,330
+الأولى كانت على ال first order وهذه كانت على
+
+614
+01:14:02,330 --> 01:14:05,790
+second order
+
+615
+01:14:19,520 --> 01:14:26,760
+برضه سنة تسعة و تسعين الأولاني كان في شهر أربع
+
+616
+01:14:26,760 --> 01:14:32,880
+يعني انا الفصل وهذه في نهاية الفصل في شهر ستة
+
+617
+01:14:32,880 --> 01:14:41,000
+السؤال التالت برضه سنة تسعة و تسعين final بيقول
+
+618
+01:14:41,000 --> 01:14:49,560
+use the substitution useThe Substitution
+
+619
+01:14:49,560 --> 01:14:59,300
+تخدم التعويضة الـ W يساوي Y تربية ناقص Y ليه أكبر
+
+620
+01:14:59,300 --> 01:15:11,820
+من Zero to solve the differential equation لحل
+
+621
+01:15:11,820 --> 01:15:23,840
+المعادلة التفاضليةYW' ناقص واحد على X زائد واحد في
+
+622
+01:15:23,840 --> 01:15:32,040
+Y' زائد واحد على X في Y يساوي Zero وال X greater
+
+623
+01:15:32,040 --> 01:15:39,880
+than Zero شكل
+
+624
+01:15:39,880 --> 01:15:45,440
+التعويضة بختلف عن التعويتين السابقاتلأن هذا بيجمع
+
+625
+01:15:45,440 --> 01:16:06,080
+ما بين الواعي ومشتقتها نرجع
+
+626
+01:16:06,080 --> 01:16:11,160
+لسؤالنا مرة تانية شوف السؤال ايش بيقول وكيف بدنا
+
+627
+01:16:11,160 --> 01:16:18,330
+نبدأ نحلالسؤال بيقول استخدم التعويضة W يساوي
+
+628
+01:16:18,330 --> 01:16:22,750
+المشتقة الأولى ل Y ناقص ال Y وهذه المشتقة دائما و
+
+629
+01:16:22,750 --> 01:16:27,570
+أبدا أكبر من ال zero عشان اتحل المعادلة التفاضلية
+
+630
+01:16:27,570 --> 01:16:31,350
+اللى قدامنا هذه وزي ما انت شايف المعادلة من الرتبة
+
+631
+01:16:31,350 --> 01:16:36,810
+الثانية ممتاز جال استخدم التعويضة إذا بتروح استخدم
+
+632
+01:16:36,810 --> 01:16:41,590
+له مين التعويضة اللى جال عليه هذهأحنا عندنا w
+
+633
+01:16:41,590 --> 01:16:48,330
+يساوي y prime ناقص y هلحين عندنا بنات اتدالة
+
+634
+01:16:48,330 --> 01:16:52,090
+بدلالة y و t ولا x و t
+
+635
+01:16:55,450 --> 01:17:00,930
+يعني T أجاب بدالها من؟ بدالها X ممتاز جدا يبقى Y'
+
+636
+01:17:01,350 --> 01:17:07,870
+هذه هي عبارة عن dy على dx تمام؟ اذا انا لو جيت
+
+637
+01:17:07,870 --> 01:17:15,930
+اشتقت هذه بالنسبة ل X بحصل على W' صح ولا لا؟ W'
+
+638
+01:17:16,610 --> 01:17:23,330
+يسوى مشتقة الأولى بYW' ناقص مشتقة الثانية اللي هي
+
+639
+01:17:23,330 --> 01:17:29,720
+من؟Y prime طب كويس تعالى نشوف المعادلة تبعتنا هذه
+
+640
+01:17:29,720 --> 01:17:36,380
+شكلها هذه يا بنات معادلتنا YW prime ناقص واحد على
+
+641
+01:17:36,380 --> 01:17:45,160
+X Y prime ناقص Y prime زائد واحد على X في ال Y كله
+
+642
+01:17:45,160 --> 01:17:50,460
+بده يساوي مين بده يساوي Zero تمامإذاً هذه بقدر
+
+643
+01:17:50,460 --> 01:17:57,480
+أقول yw prime ناقص y prime الأولى و التالتى مع بعض
+
+644
+01:17:57,480 --> 01:18:02,700
+هذه و هذه بقدر أاخد منهم واحد على x عامل مشترك
+
+645
+01:18:02,700 --> 01:18:08,640
+يبقى لو أخد سلب واحد على x عامل مشترك بظل y prime
+
+646
+01:18:08,640 --> 01:18:16,240
+ناقص y ساوي زير تمامهيه والله هذه كويسة العملية
+
+647
+01:18:16,240 --> 01:18:23,340
+اللى عملتها برضه أفدتني صار هدمين w prime و هدمين
+
+648
+01:18:23,340 --> 01:18:30,900
+w موطن اذا المعادلة هذه عملنا لها reduction of
+
+649
+01:18:30,900 --> 01:18:36,940
+order من الرتبة الثانيةالى مين؟ الى الرتبة الأولى
+
+650
+01:18:36,940 --> 01:18:43,260
+يبقى صارت مسألة بسيطة جدا يبقى ده W prime ناقص
+
+651
+01:18:43,260 --> 01:18:50,580
+واحد على X W بدي ساوي قداش؟ بساوي Zero تمام؟ يعني
+
+652
+01:18:50,580 --> 01:18:59,240
+بصير عندك W prime على W بدي ساوي قداش؟ واحد على X
+
+653
+01:18:59,240 --> 01:19:07,820
+مكامل؟ يبقى لو كاملنابصير لن الـW فش داعي لل
+
+654
+01:19:07,820 --> 01:19:13,660
+absolute value لأنها بالموجة تمام؟ بده يساوي كمان
+
+655
+01:19:13,660 --> 01:19:19,900
+لن ال X ولا داعي لأن ال X greater than zero زائد
+
+656
+01:19:19,900 --> 01:19:26,140
+constant C طيب إيش رأيك ال constant C؟ لو كتبت لن
+
+657
+01:19:26,140 --> 01:19:31,720
+C، بيمشي الحال؟ماش اشكالية اوكك و LNC زي ما بدك طب
+
+658
+01:19:31,720 --> 01:19:36,540
+ليش سويت هيك هذا اللي بدنا نجاوب عليه نجاوب عليه
+
+659
+01:19:36,540 --> 01:19:45,840
+بصير المسألة LNW يساوي LNXCلن زاد لن بقدر اشبهها
+
+660
+01:19:45,840 --> 01:19:49,640
+باللن و بقدر اطيّر اللنات وبالتالي لابد اطلع عندى
+
+661
+01:19:49,640 --> 01:19:55,940
+لن ولا exponential يبقى هذه لن و لن بقدر ارفع
+
+662
+01:19:55,940 --> 01:20:04,940
+اتنين كاس للعدد ايه يبقى w بدى يسوى x في c مصبوط
+
+663
+01:20:04,940 --> 01:20:12,850
+طيب نجي هنا نقول هذه ال w بقداش يا بناتY'-Y يبقى
+
+664
+01:20:12,850 --> 01:20:27,010
+Y'-Y يساوي 6 إيه الشكل المعادل هذه إيش
+
+665
+01:20:27,010 --> 01:20:33,130
+اسمها Linear مظبوط يبقى Linear إحنا حلنا المثلة
+
+666
+01:20:33,130 --> 01:20:37,990
+الأولانية تكامل عادي جدا طلعت لمعادلة جديدة Linear
+
+667
+01:20:37,990 --> 01:20:45,990
+First Orderيبقى هذه linear first order
+
+668
+01:20:45,990 --> 01:20:54,690
+differential equation تمام يعني ايش اللي حصل اجيب
+
+669
+01:20:54,690 --> 01:21:01,630
+طريقتين من الطرق بسؤال واحد تعوض هذه قادتني الى
+
+670
+01:21:01,630 --> 01:21:06,190
+separable equation ال W في شجة و ال X في شجة يبعد
+
+671
+01:21:06,190 --> 01:21:10,420
+ال separable equationواسيبربوا القادتنا إلى من؟
+
+672
+01:21:10,420 --> 01:21:15,060
+إلى ال linear من هنا أجت أهمية من؟ أهمية السؤال
+
+673
+01:21:15,060 --> 01:21:18,640
+يعني السؤال اللي ممكن اختار مش ببلاش يعطيك لأ انا
+
+674
+01:21:18,640 --> 01:21:22,960
+قاصد و متعمد اجيبك طريقتين او معادلتين من اللي
+
+675
+01:21:22,960 --> 01:21:28,520
+اتعلمتي حلهم مشان نيجي نحلهم هنا بسؤال يعني بستاهل
+
+676
+01:21:28,520 --> 01:21:33,980
+يكون سؤال امتحانمظبوط طيب كويس يبقى بنحلها بال
+
+677
+01:21:33,980 --> 01:21:40,220
+linear بسيطة جدا هذه جاهزة كويس يبقى باجي بقول لم
+
+678
+01:21:40,220 --> 01:21:47,920
+U of X دو ساوي E أص ناقص تكامل DX ماعنديش المعامل
+
+679
+01:21:47,920 --> 01:21:55,140
+سالب واحد يبقى يساوي E أص ناقص X بدي أروح أضرب
+
+680
+01:21:55,140 --> 01:22:01,500
+المعادلة اللي فوق هذه في E أص ناقص Xبصير EOS ناقص
+
+681
+01:22:01,500 --> 01:22:10,280
+X في Y prime ناقص EOS ناقص X في Y يساوي CX في EOS
+
+682
+01:22:10,280 --> 01:22:19,440
+ناقص X او بمعنى اخر هذه الان EOS ناقص X في Y الكلة
+
+683
+01:22:19,440 --> 01:22:29,280
+prime يساوي CX EOS ناقص AX انكمليبقى E أص ناقص X
+
+684
+01:22:29,280 --> 01:22:40,100
+في Y يسوى تكامل CX في E أص ناقص X في DX تكامل هذه
+
+685
+01:22:40,100 --> 01:22:47,720
+بيعطيني تكامل هذا هذا CX ايوة كيف نكامل هذا؟ كيف؟
+
+686
+01:22:47,720 --> 01:22:52,180
+bypass عادي جدا وع الجدول كمان مش لسه بدي U وD لأ
+
+687
+01:22:52,180 --> 01:22:57,170
+لأ جاهزين اذا باجي بقوله على الجدولبقول له هنا
+
+688
+01:22:57,170 --> 01:23:03,270
+derivatives و هنا بده اجيب له integrals ايه ال
+
+689
+01:23:03,270 --> 01:23:08,170
+derivatives بده اخدله cx و ال integrals بده اخدله
+
+690
+01:23:08,170 --> 01:23:17,040
+e-x تفاضل هذه بقداش؟بـC تكامل هدف ناقص EOS ناقص X
+
+691
+01:23:17,040 --> 01:23:22,140
+يعني EOS ناقص X على ناقص واحد يعني ناقص EOS ناقص X
+
+692
+01:23:22,140 --> 01:23:29,740
+تفضل الـC بقدرش بـ0 تكامل هدف EOS ناقص X هدف هدف
+
+693
+01:23:29,740 --> 01:23:36,340
+إشارة موجب وهدف هدف إشارة سالب يبقى النتيجة أثارة
+
+694
+01:23:36,340 --> 01:23:45,660
+EOS ناقص X في الـYبدى يساوي ناقص CX E ناقص X ناقص
+
+695
+01:23:45,660 --> 01:23:52,860
+C E ناقص X زائد constant من C1 تبع التكامل ما
+
+696
+01:23:52,860 --> 01:23:56,900
+ننساهوش هذا لإن احنا عند المشتق الثاني معناته اندي
+
+697
+01:23:56,900 --> 01:24:03,370
+two constantsطيب نضرب فيه وص إكس هذي مش هنتخلص
+
+698
+01:24:03,370 --> 01:24:10,970
+منها نحصل على Y يبقى Y هتساوي سالب CX وهنا سالب C
+
+699
+01:24:10,970 --> 01:24:20,910
+وهنا زائد C1 E وص X يبقى هذا شكل الحل اللي عندنا
+
+700
+01:24:20,910 --> 01:24:23,350
+تبع من؟ تبع المثلة
+
+701
+01:24:36,050 --> 01:24:42,170
+طيب في سؤال جبته انا في امتحان لطلبه طلبات في ال
+
+702
+01:24:42,170 --> 01:24:50,810
+2005 بيقول ما يأتي هذا قداش تلاتة هذا اربعة و هذا
+
+703
+01:24:50,810 --> 01:25:00,150
+في ال 2005 بيقول use the substitution use the
+
+704
+01:25:00,150 --> 01:25:02,150
+substitution
+
+705
+01:25:06,490 --> 01:25:20,290
+U يساوي Y ناقص X تسالف الـ differential equation
+
+706
+01:25:20,290 --> 01:25:35,690
+لتحل المعادلة التفاضلية Dy بDX يساوي Sine تربيعY
+
+707
+01:25:35,690 --> 01:25:51,330
+ناقص X يبقى
+
+708
+01:25:51,330 --> 01:25:58,130
+أنا بدأجي للتعويض اللي اعطاه هالي جالي ليه تساوي Y
+
+709
+01:25:58,130 --> 01:26:03,350
+ناقص X كنت استخدم هذه التعويضة في حل المعادلة اللي
+
+710
+01:26:03,350 --> 01:26:09,310
+عندناأحنا تدارج أن نقول أن صين تربيع Y أو صين
+
+711
+01:26:09,310 --> 01:26:14,150
+تربيع X ونقول أيش صين تربيع Y ناقص X إذا بدي أروح
+
+712
+01:26:14,150 --> 01:26:17,710
+أشيل Y ناقص X و أحط مكانها U يبقى هاي شيلناها و
+
+713
+01:26:17,710 --> 01:26:22,770
+حطينا بدلها مين؟ حطينا بدلها U يبقى يا بنات لو جيت
+
+714
+01:26:22,770 --> 01:26:31,170
+قلت بدي ال U' ال U' يعني مين؟ ال U على D نكتبها
+
+715
+01:26:31,170 --> 01:26:36,170
+بالتفصيل، بلاش تقولهايعني بدي اشتق الدالة كلها
+
+716
+01:26:36,170 --> 01:26:46,250
+بالنسبة الى X يبقى DY على DX ومشتقة ال X بقدرش ب 1
+
+717
+01:26:47,000 --> 01:26:54,500
+يبقى بناء على اليسار عندنا دي يو على دي إكس زائد
+
+718
+01:26:54,500 --> 01:27:00,180
+واحد بدي أسوأ من دي واي على دي إكس إذا بدي أجيل
+
+719
+01:27:00,180 --> 01:27:05,240
+المقاس اللي بتبعتي أشيل دي واي على دي إكس و أكتب
+
+720
+01:27:05,240 --> 01:27:10,920
+بدلها دي وي على دي إكس زائد واحد يبقى هنا إيش بصير
+
+721
+01:27:10,920 --> 01:27:18,730
+الدي واي على دي إكس اللي هي دي يوعلى dx زائد واحد
+
+722
+01:27:18,730 --> 01:27:28,770
+يساوي من؟ يساوي ال sign تربيع ال Uتمام تمام يبقى
+
+723
+01:27:28,770 --> 01:27:37,030
+بدل مكان المتغير y و x صار المتغير u و x تمام يبقى
+
+724
+01:27:37,030 --> 01:27:46,110
+هذه بيصير main اللي هو du على dx يساوي sin تاربيع
+
+725
+01:27:46,110 --> 01:27:55,580
+ال u ناقص واحدكويس؟ طب إيش رايك لو جيت قولتلك هذه
+
+726
+01:27:55,580 --> 01:28:05,010
+تساوي ناقص واحد ناقص ساينتر بي اليوم، بنفع؟طب اللي
+
+727
+01:28:05,010 --> 01:28:10,690
+بين قوسين هي مين؟ قوسين تربية اليوم يبقى صار عندنا
+
+728
+01:28:10,690 --> 01:28:19,750
+مين؟ اللي هو du على dx يسوى ناقص قوسين تربية اليوم
+
+729
+01:28:19,750 --> 01:28:25,240
+شو رأيك نفصل المتغيرات؟يبقى صارت separation of
+
+730
+01:28:25,240 --> 01:28:35,280
+variable صار DU على cosine تربيع ال U يسوى ناقص DX
+
+731
+01:28:35,280 --> 01:28:41,700
+فقط لغير او انشئتنا فقلنا واحد على cosine تربيع ال
+
+732
+01:28:41,700 --> 01:28:51,780
+U منين؟ six تربيع ال U DU سالب DX انكمل الطرفين
+
+733
+01:28:52,940 --> 01:29:00,020
+قداش تكمل sector بيه U دي U بتاني ال U يبقى تاني
+
+734
+01:29:00,020 --> 01:29:09,160
+ال U يسوى ناقص X زائد constant C طب انا مين؟ بديش
+
+735
+01:29:09,160 --> 01:29:16,330
+تاني ال U بدي ال Uيبقى بناء عليه ال U ها دي بدها
+
+736
+01:29:16,330 --> 01:29:23,670
+تساوي tan inverse ل C ناقص X
+
+737
+01:29:27,310 --> 01:29:33,210
+مظبوط ايه؟ يعني احد تان انفرس للطرفين باجي بقول U
+
+738
+01:29:33,210 --> 01:29:40,910
+هي عبارة عن مين؟ Y ناقص X يبقى صار عندي Y ناقص X
+
+739
+01:29:40,910 --> 01:29:48,970
+يساوي تان انفرس ل C ناقص ال X ود ال X على الشجرة
+
+740
+01:29:48,970 --> 01:29:54,190
+التانية يبقى حصلنا على الحل تبع المثلة يبقى هذا
+
+741
+01:29:54,190 --> 01:30:06,180
+يعطينا ان Yتساوي X زائد tan inverse لمن؟ ل C ناقص
+
+742
+01:30:06,180 --> 01:30:12,960
+X الشكل اللي عندنا هذا هو الحل تبع المعادلة L عن N
+
+743
+01:30:15,420 --> 01:30:19,620
+يبقى هي عندك بدل السؤال أربعة أسئلة وكلها تعويضات
+
+744
+01:30:19,620 --> 01:30:23,800
+وكلها مسائل امتحانات يعني لو جيبنالكم سؤال في
+
+745
+01:30:23,800 --> 01:30:28,560
+الامتحان القادم الله سمحه الله يكون هي ضربناكي على
+
+746
+01:30:28,560 --> 01:30:35,240
+مين على أمثلة على هذا الموضوع طبعا حد في كل هذه
+
+747
+01:30:35,240 --> 01:30:40,730
+التساؤلالمرة القادمة ان شاء الله يوم الأربعة بنبدأ
+
+748
+01:30:40,730 --> 01:30:44,690
+chapter أربعة يوم الأربعة بنبدأ chapter أربعة ان
+
+749
+01:30:44,690 --> 01:30:49,130
+شاء الله chapter أربعة هو تعميم ل chapter تلاتة
+
+750
+01:30:49,130 --> 01:30:52,570
+يعني بيبقى ال second order بيشوف third order
+
+751
+01:30:52,570 --> 01:30:56,090
+fourth order and nth order تمام؟
+
diff --git a/PL9fwy3NUQKwa8ZDfSFGn6H8xVFLzqmCZC/aLofgEh8GKI.srt b/PL9fwy3NUQKwa8ZDfSFGn6H8xVFLzqmCZC/aLofgEh8GKI.srt
new file mode 100644
index 0000000000000000000000000000000000000000..bb9a8ccda14496937565950a9ae4d8011d222f18
--- /dev/null
+++ b/PL9fwy3NUQKwa8ZDfSFGn6H8xVFLzqmCZC/aLofgEh8GKI.srt
@@ -0,0 +1,2628 @@
+1
+00:00:00,000 --> 00:00:02,580
+موسيقى
+
+2
+00:00:10,460 --> 00:00:14,980
+بسم الله الرحمن الرحيم كنا نتحدث المرة الماضية عن
+
+3
+00:00:14,980 --> 00:00:19,400
+الطريقة الأولى لحل اللي هو الـ homogeneous
+
+4
+00:00:19,400 --> 00:00:22,440
+differential equation with constant coefficients
+
+5
+00:00:22,440 --> 00:00:28,420
+وكانت اللي هو طريقة الحل 
+
+6
+00:00:28,420 --> 00:00:34,040
+المعادلة المتجانسة عن طريق اللي هو فرض Y تساوي E
+
+7
+00:00:34,040 --> 00:00:40,470
+أس RT وكنا نطلع عندنا عدد احتمالات/احتمال الحلول 
+
+8
+00:00:40,470 --> 00:00:45,490
+تكون أو لما نجيب الـ characteristic equation احتمال
+
+9
+00:00:45,490 --> 00:00:50,470
+الجذور كلها تبقى حقيقية ومختلفة احتمال تبقى
+
+10
+00:00:50,470 --> 00:00:56,330
+complex احتمال تبقى repeated real ممكن تبقى 
+
+11
+00:00:56,330 --> 00:01:01,170
+repeated complex على كل هذه الحالات اخذنا على ذلك
+
+12
+00:01:01,170 --> 00:01:06,270
+ثلاثة أمثلة والآن نكمل الأمثلة على نفس الموضوع
+
+13
+00:01:06,270 --> 00:01:10,070
+يبقى السؤال لو المثال رقم اثنين بيقول show that
+
+14
+00:01:10,070 --> 00:01:14,090
+the general solution of the differential equation Y
+
+15
+00:01:14,090 --> 00:01:18,470
+to the derivative of 4 لما نحط الرقم بين قوسين تعني 
+
+16
+00:01:18,470 --> 00:01:22,130
+المشتقة بدون أقوى C يعني أس يبقى Y to the 
+
+17
+00:01:22,130 --> 00:01:25,330
+derivative of 4 minus Y يساوي Zero can be written
+
+18
+00:01:25,330 --> 00:01:31,370
+as يمكن أن نكتب هذا الحل على صيغة C1 Cos T زائد C2
+
+19
+00:01:31,370 --> 00:01:37,690
+Sin T زائد C3 Cosh T زائد C4 Sinh T مدام بقول
+
+20
+00:01:37,690 --> 00:01:41,350
+احتمال الحل يكون على الشكل هذا يمكن لما نحل ما 
+
+21
+00:01:41,350 --> 00:01:46,450
+يطلعش هذا الشكل إذا طلع طيب إذا ما طلعش أنا بدي 
+
+22
+00:01:46,450 --> 00:01:51,510
+أحول المسألة بحيث فعلا تصير في الشكل اللي عندنا
+
+23
+00:01:51,510 --> 00:01:54,890
+هذا هذا المطلوب الأول بعدين قال لي solve the 
+
+24
+00:01:54,890 --> 00:01:58,170
+initial value problem نفس المثال اللي عندنا بس حط 
+
+25
+00:01:58,170 --> 00:02:03,590
+عليه الشروط الأربعة اللي من خلالها بقدر أجيب قيمة 
+
+26
+00:02:03,590 --> 00:02:08,910
+الثوابت اللي موجودة عندنا إذا نيجي للحل مع المطلوب
+
+27
+00:02:08,910 --> 00:02:15,910
+الأول اللي هو نمرة A أفترض أن الحل اللي عندي على 
+
+28
+00:02:15,910 --> 00:02:21,190
+الصيغة هو Y تساوي E أس RT وجيب الـ characteristic
+
+29
+00:02:21,190 --> 00:02:27,330
+equation المناظرة لهذه المعادلة بيجي أقول له let Y
+
+30
+00:02:27,330 --> 00:02:33,230
+تساوي E أس RT be a solution 
+
+31
+00:02:40,410 --> 00:02:47,190
+بعد ذلك الاختصار 
+
+32
+00:02:47,190 --> 00:02:55,440
+الوحيد هو اللي هو R أس أربعة ناقص واحد يساوي Zero
+
+33
+00:02:55,440 --> 00:03:01,980
+هذه ممكن أحللها كفرق بين المربعين يبقى لو حللناها 
+
+34
+00:03:01,980 --> 00:03:07,340
+كفرق بين المربعين بصير R تربيع ناقص واحد في R
+
+35
+00:03:07,340 --> 00:03:13,440
+تربيع زائد واحد يساوي Zero هذه كمان ممكن أحللها
+
+36
+00:03:13,440 --> 00:03:20,280
+كفرق بين المربعين يبقى بصير R تربيع زائد واحد هذه 
+
+37
+00:03:20,280 --> 00:03:25,500
+فرق بين مربعين R ناقص واحد في R زائد واحد يساوي
+
+38
+00:03:25,500 --> 00:03:31,780
+Zero يعني هذه معناته ما لها لا يوجد لها تحليل
+
+39
+00:03:31,780 --> 00:03:38,460
+وبالتالي الـ R هتبقى Complex يبقى هذا معناته أن R 
+
+40
+00:03:38,460 --> 00:03:47,380
+واحد واثنين اللي هو بده يساوي زائد أو ناقص I و R
+
+41
+00:03:47,380 --> 00:03:53,860
+ثلاثة بده يساوي واحد و R أربعة بده يساوي ناقص 
+
+42
+00:03:53,860 --> 00:03:59,040
+واحد إذا صار شكل الحل على الشكل التالي YC
+
+43
+00:04:23,450 --> 00:04:27,830
+بدي أقارن بين الحل اللي عندي والحل اللي هو قاله
+
+44
+00:04:28,310 --> 00:04:32,110
+بلاحظ هذول الاثنين هما نفس هذول الاثنين ما عندنا مشكلة
+
+45
+00:04:32,110 --> 00:04:38,150
+فيهم تمام C1 cos T C2 sin T نفس الشيء لكن الخلاف 
+
+46
+00:04:38,150 --> 00:04:42,470
+وين؟ خلاف ما بين هذول الاثنين هنا معطيين بدالة Cosh و Sinh
+
+47
+00:04:42,470 --> 00:04:47,070
+هنا معطيين بدالة الـ exponential E أس T و E أس ناقص
+
+48
+00:04:47,070 --> 00:04:52,820
+T لو راجعنا بالذاكرة إلى الـ formula من صيغة Euler بقى 
+
+49
+00:04:52,820 --> 00:05:01,340
+نقول E أس IT يساوي Cos T زائد I Sin T مظبوط
+
+50
+00:05:01,340 --> 00:05:09,420
+و E أس -IT يساوي Cos T ناقص I Sin T تمام
+
+51
+00:05:09,420 --> 00:05:14,440
+يبقى بنحاول نستخدم اللي هو اللي عندنا هنا أو 
+
+52
+00:05:14,440 --> 00:05:20,080
+نستخدم تعريف الـ Cosh و الـ Sinh إذا كنتوا بتذكروا ابعتوا 
+
+53
+00:05:20,080 --> 00:05:23,740
+خاصية اللي درسوا معايا Calculus بيه أن لو جمعت 
+
+54
+00:05:23,740 --> 00:05:29,900
+الـ Cosh زائد الـ Sinh بيعطيني E أس T ولو طرحت الـ Cosh
+
+55
+00:05:29,900 --> 00:05:36,480
+ناقص الـ Sinh بيعطيني مين؟ E أس -T بنذكركوا تذكير
+
+56
+00:05:36,480 --> 00:05:45,320
+اللي ليس إلا بيجي نقول Cosh T زائد Sinh T طبعا
+
+57
+00:05:45,320 --> 00:05:53,320
+بتشوفوا قدرش هذا يساوي الـ Cosh هي E أس T زائد E أس -
+
+58
+00:05:53,320 --> 00:06:01,280
+T على اثنين هذه Cosh الـ Sinh كانت E أس T ناقص E أس -
+
+59
+00:06:01,280 --> 00:06:09,150
+T على اثنين لو جمعنا كله على اثنين يبقى المقام هذا
+
+60
+00:06:09,150 --> 00:06:12,950
+هو نفس المقام هذا، إذا بضل الاثنين بدي أجمعهم،
+
+61
+00:06:12,950 --> 00:06:18,510
+هتروح هذه وهذه مع بعض، بضل اثنين E أس T اللي هو من
+
+62
+00:06:18,510 --> 00:06:27,330
+E أس T بنفس الطريقة Similarly اللي 
+
+63
+00:06:27,330 --> 00:06:35,960
+هو Cosh T ناقص Sinh T كل هذا الكلام بدي اسمه
+
+64
+00:06:35,960 --> 00:06:42,930
+مين؟ E أس -T تمام؟ إذا بدي أجي على الحل اللي 
+
+65
+00:06:42,930 --> 00:06:49,210
+عندنا ده اللي بدي اسميه star ونعوض فيه يعني بدي
+
+66
+00:06:49,210 --> 00:06:55,350
+أشيل E أس T اللي عندي هذه وأكتب بدالها Cosh زائد
+
+67
+00:06:55,350 --> 00:07:00,030
+Sinh وأشيل E أس -T وأكتب بدالها Cosh ناقص 
+
+68
+00:07:00,030 --> 00:07:04,330
+Sinh يبقى من بعدها بدي أجي أقول له substitute
+
+69
+00:07:13,970 --> 00:07:23,350
+نحصل على ما يأتي YC اللي هو طالبه C1 Cos T C2
+
+70
+00:07:23,350 --> 00:07:31,910
+Sin T C3 مضروبة في E أس T اللي هي main مش C3 كي واحد
+
+71
+00:07:31,910 --> 00:07:38,370
+سميناها كي واحد هي عندي في E أس T اللي هي Cosh T 
+
+72
+00:07:38,370 --> 00:07:51,090
+زائد Sinh T زائد ك اثنين في Cosh T ناقص Sinh T
+
+73
+00:07:53,490 --> 00:08:03,370
+هذا الكلام يساوي C1 cos T C2 sin T زائد  الـ Cosh اللي
+
+74
+00:08:03,370 --> 00:08:08,230
+فيها Cosh وهذه فيها Cosh إذا ممكن أخذ منهم Cosh عامل
+
+75
+00:08:08,230 --> 00:08:18,150
+مشترك بصير عندي K1 زائد K2 في Cosh T نجي لهذه مضروبة 
+
+76
+00:08:18,150 --> 00:08:24,190
+في K1 وهذه مضروبة في K2 يبقى K1 ناقص
+
+77
+00:08:24,190 --> 00:08:33,650
+K2 في Sinh T هذا الكلام يساوي C1 في Cos T
+
+78
+00:08:33,650 --> 00:08:39,850
+C2 في Sin T طالعي لهذه K1 زي K2 هذا
+
+79
+00:08:39,850 --> 00:08:48,700
+مُقدار ثابت إذن ممكن نسميه C3 يبقى زائد C3 في Cosh 
+
+80
+00:08:48,700 --> 00:08:58,040
+T زائد C4 في Sinh T يبقى شلت هذا حطيت بدله C3
+
+81
+00:08:58,040 --> 00:09:03,260
+وشلت هذا حطيت بدله C4 أظن هي الصيغة اللي طلبها
+
+82
+00:09:03,260 --> 00:09:10,570
+هذه خلصنا يبقى حطينا له الحل على الصيغة اللي هو
+
+83
+00:09:10,570 --> 00:09:15,350
+بده إياه وبالتالي انتهينا من المطلوب الأول من 
+
+84
+00:09:15,350 --> 00:09:22,490
+المسألة، المطلوب الثاني نمرة B كيف؟ لما طلعتش 
+
+85
+00:09:22,490 --> 00:09:27,070
+الصيغة؟ لازم إنك بدها تطلع هذه الصيغة، ليش؟ لأن 
+
+86
+00:09:27,070 --> 00:09:30,430
+الـ exponential أصلا بدلالة الـ Cosh والـ Sinh وهو
+
+87
+00:09:30,430 --> 00:09:34,990
+أعطاني السؤال بدي إياها بدلالة الـ Cosh و الـ Sinh تمام؟
+
+88
+00:09:34,990 --> 00:09:38,930
+يبقى فيش مجال، مدام شيلت الـ exponential هذي والـ
+
+89
+00:09:38,930 --> 00:09:42,770
+exponential هذي لازم تنكتب بدلالة الـ Cosh والـ Sinh، 
+
+90
+00:09:42,770 --> 00:09:46,530
+فكيف بدها تطلع؟ لأ أنت من الأول اول ما شفت
+
+91
+00:09:46,530 --> 00:09:48,030
+السؤال قلت إذا طلعت 
+
+92
+00:09:50,860 --> 00:09:54,020
+معناها لأ مش في حالة ثانية، في شغل عندنا بتبقى
+
+93
+00:09:54,020 --> 00:09:58,260
+غلط طيب؟ لكن الـ كون هو طلعنا على شغلنا صح وهو
+
+94
+00:09:58,260 --> 00:10:03,680
+المطلوب جبناه طيب نيجي للمطلوب الثاني جالي solve the
+
+95
+00:10:03,680 --> 00:10:08,660
+initial value problem يبقى بدنا نجي لهذه المعادلة 
+
+96
+00:10:08,660 --> 00:10:11,920
+اللي عندنا أصلا homogeneous هي نفس المعادلة اللي
+
+97
+00:10:11,920 --> 00:10:16,880
+فوق بس حطينا عليها الـ initial conditions جابلي
+
+98
+00:10:16,880 --> 00:10:21,720
+الـ Y بدون اشتقاق مشتقة الأولى الثانية الثالثة وكل
+
+99
+00:10:21,720 --> 00:10:26,420
+وين عند الـ zero إذا بدأنا نجي للمثال اللي عندنا ها
+
+100
+00:10:26,420 --> 00:10:31,980
+وده نشتقه مرة واثنين وثلاثة ونعوض بالقيم constants
+
+101
+00:10:31,980 --> 00:10:38,340
+اللي عندنا هنا يبقى بالدرجة الأولى عندي هنا للـ YC prime Y 
+
+102
+00:10:38,340 --> 00:10:48,080
+prime بتفضل الـ Cosine بسالب C1 sin T زائد C2 في Cosine T
+
+103
+00:10:48,080 --> 00:10:53,520
+طبعا بتفضل الـ Cosh بالـ Sinh وبتفضل الـ Sinh بـ Cosh بدون
+
+104
+00:10:53,520 --> 00:10:57,580
+negative sign ما عنديش إشارة سالب زي الـ Sin والـ 
+
+105
+00:10:57,580 --> 00:11:07,490
+Cosine زائد C3 في Sinh T زائد C4 في Cosh T بعد
+
+106
+00:11:07,490 --> 00:11:16,430
+هيك بدنا YC double prime نشتغل كمان مرة يبقى ناقص C1 cos T
+
+107
+00:11:16,430 --> 00:11:30,170
+ناقص C2 sin T زائد C3 في Cosh T زائد C4 في Sinh T 
+
+108
+00:11:30,170 --> 00:11:35,670
+هذا المشتقة الثانية بالمثل بدنا نروح نجيب المشتقة
+
+109
+00:11:35,670 --> 00:11:47,540
+الثالثة يبقى بصير C1 في sin T ناقص C2 في cos T زائد
+
+110
+00:11:47,540 --> 00:11:51,080
+C3 في Sinh T 
+
+111
+00:11:59,970 --> 00:12:03,470
+يبقى جبنا المشتقات الثلاثة اللي عندنا هذا بدي 
+
+112
+00:12:03,470 --> 00:12:07,270
+أرجع للـ initial conditions اللي عندنا للـ initial
+
+113
+00:12:07,270 --> 00:12:12,410
+conditions الأولاني بيقول لي Y عند الـ zero بده 
+
+114
+00:12:12,410 --> 00:12:19,410
+تساوي zero وين الـ Y هيها؟ يبقى هي Y بـ zero تساوي
+
+115
+00:12:19,630 --> 00:12:26,370
+بدأت أشيل كل T وأضع مكانها Zero فالليلة Cos Zero 
+
+116
+00:12:26,370 --> 00:12:34,010
+بواحد في C1 بـ C1  ندى Sin Zero مع السلامة Cosh Zero
+
+117
+00:12:34,010 --> 00:12:41,520
+كذلك بواحد يبقى زائد C3 Sinh Zero بـ Zero نجي 
+
+118
+00:12:41,520 --> 00:12:47,420
+الـ condition الثاني جالي Y prime عند Zero كذلك بده
+
+119
+00:12:47,420 --> 00:12:52,700
+يساوي Zero وين Y prime هي يبقى هذه Zero Cos Zero ب
+
+120
+00:12:52,700 --> 00:12:58,740
+واحد يبقى بـ C2 Sinh Zero بـ Zero مع السلامة 
+
+121
+00:12:58,740 --> 00:13:05,220
+Cosh Zero بواحد يبقى زائد C4 نجي للـ condition
+
+122
+00:13:05,220 --> 00:13:09,020
+الثالث الـ condition الثالث بيقول لي Y double prime عند 0
+
+123
+00:13:09,020 --> 00:13:18,140
+بـ 1 Y double prime عند 0 بده يساوي 1 implies أن الـ 1 هي 
+
+124
+00:13:18,140 --> 00:13:24,760
+الـ Y double prime تمام بدنا نعوض عن T بـ 0 يبقى ايش بيصير 
+
+125
+00:13:24,760 --> 00:13:33,540
+عندي هنا سالب C1 Sin Zero مع السلامة زائد C3
+
+126
+00:13:33,540 --> 00:13:39,200
+والثاني مع السلامة نيجي للـ condition الرابع جالي Y 
+
+127
+00:13:39,200 --> 00:13:44,240
+triple prime عند Zero بده يساوي الواحد employees
+
+128
+00:13:44,240 --> 00:13:48,640
+واحد بده أعوض في المشتقة الثالثة يبقى Sin Zero بضل 
+
+129
+00:13:48,640 --> 00:13:59,900
+ناقص C2 Cos Zero ناقص C2 و Sin Zero زائد C4 يبقى زائد C4
+
+130
+00:13:59,900 --> 00:14:06,380
+يطلعولي للمعادلة الأولى والثالثة بدي أجمع هذول 
+
+131
+00:14:06,380 --> 00:14:13,160
+هذول الاثنين لو جمعتهم مع بعض بصير سالب
+
+132
+00:14:13,160 --> 00:14:18,780
+C1 مع C1 بيبقى 2C3
+
+133
+00:14:18,780 --> 00:14:21,740
+بيبقى واحد
+
+134
+00:14:22,610 --> 00:14:28,690
+تمام أجمع Zero زائد واحد هيبقى واحد سالب C1 مع الموجب ب
+
+135
+00:14:28,690 --> 00:14:36,590
+C1 بضل اثنين C3 يساوي واحد ومنها C3 بده يساوي نصف
+
+136
+00:14:36,590 --> 00:14:44,650
+طيب لما C3 يساوي نصف C1 بيبقى كده بسالب نصف و C1
+
+137
+00:14:44,650 --> 00:14:51,040
+يساوي سالب نصف بده  أجمع المعادلة الثانية مع 
+
+138
+00:14:51,040 --> 00:14:58,080
+المعادلة الرابعة أجمع Zero زائد واحد بده يعطيكي واحد 
+
+139
+00:14:58,080 --> 00:15:08,060
+بده يساوي نجمع C2 مع C2 يبقى بيضل 2C4 يبقى 2C4
+
+140
+00:15:08,060 --> 00:15:17,060
+ومنها C4 يساوي قداش نصف لما C4 بده يساوي نصف يبقى C2
+
+141
+00:15:17,060 --> 00:15:25,520
+بسالب نصف و C2 يساوي سالب نصف إذا نقدر نجيبه بالشكل 
+
+142
+00:15:25,520 --> 00:15:32,360
+العام لحل الـ initial value problem يبقى الحل صار
+
+143
+00:15:32,360 --> 00:15:39,530
+YC يساوي يبدا يجي لـ C1 C1 طلع عندنا بسالب نصف يبقى 
+
+144
+00:15:39,530 --> 00:15:48,690
+ناقص نصف cos T و C2 طلع عندنا بسالب نصف كذلك يبقى 
+
+145
+00:15:48,690 --> 00:15:58,070
+ناقص نصف في sin T و C3 طلع بنصف يبقى زائد نصف اللي هو 
+
+146
+00:15:58,070 --> 00:16:06,680
+Cosh T و C4 يبقى
+
+147
+00:16:06,680 --> 00:16:14,100
+زائد نصف في Sinh T يبقى ده حل الـ initial value
+
+148
+00:16:14,100 --> 00:16:15,680
+problem اللي عندنا
+
+149
+00:16:29,090 --> 00:16:31,930
+طبعا المرة اللي فاتت ما حلناش الـ initial value 
+
+150
+00:16:31,930 --> 00:16:37,390
+problem وما أعطانا ولا سؤال بهذه الطريقة هي بقى نعمل
+
+151
+00:16:37,390 --> 00:16:43,720
+فيه تحويرة مشان نطلع شكل الجواب نَعْطيكم كمان مثال
+
+152
+00:16:43,720 --> 00:16:50,100
+على نفس الموضوع برضه بيختلف نوعا ما وحلناش 
+
+153
+00:16:50,100 --> 00:16:56,860
+زيّه من قبل يبقى بنيجي للمثال رقم ثلاثة سؤال واحد
+
+154
+00:16:56,860 --> 00:17:04,320
+وعشرين من الكتاب بيقول solve the differential
+
+155
+00:17:04,320 --> 00:17:09,800
+equation حل المعادلة التفاضلية Y to the 
+
+156
+00:17:09,800 --> 00:17:16,870
+derivative 8 زائد 2 Y to the derivative 4
+
+157
+00:17:16,870 --> 00:17:36,930
+زائد 16 Y بده يساوي قداش؟ بده يساوي زيرو المرة
+
+158
+00:17:36,930 --> 00:17:42,700
+اللي فاتت كده بتذكروا قلنا فيه عندنا real
+
+159
+00:17:42,700 --> 00:17:46,960
+and unequal roots وخلصنا منها واخدنا عليها أمثلة
+
+160
+00:17:46,960 --> 00:17:51,140
+بعدها قلنا complex roots واخدنا عليها أحيانا real
+
+161
+00:17:51,140 --> 00:17:54,800
+وأحيانا complex جينا للـ repeated roots قلنا ممكن
+
+162
+00:17:54,800 --> 00:17:59,200
+تبقى repeated وreal أو ممكن تبقى repeated و
+
+163
+00:17:59,200 --> 00:18:03,580
+complex repeated و complex ما شوفناش ولا مثال حتى
+
+164
+00:18:03,580 --> 00:18:10,040
+اللحظة تمام؟ لكن هي واجية يبقى هذا repeated complex 
+
+165
+00:18:10,040 --> 00:18:15,320
+conjugate roots نشوف كيف نتعامل معه يبقى بنفس 
+
+166
+00:18:15,320 --> 00:18:18,760
+التكتيك اللي بدأنا به بالمثال اللي قبل هبدأ في حاجة
+
+167
+00:18:18,760 --> 00:18:29,160
+أقول له هنا let Y تساوي E أس RT be a solution of 
+
+168
+00:18:29,160 --> 00:18:35,460
+equation one سميّنا لها D1 then the
+
+169
+00:18:39,250 --> 00:18:48,830
+Equation is R أس 8 زائد 2 R أس 4
+
+170
+00:18:48,830 --> 00:18:55,950
+زائد 16 يساوي Zero أظن أن هذه لو جيتها حللتها
+
+171
+00:18:55,950 --> 00:19:00,770
+بيصير عندي ايش بيصير عندي R أس 4
+
+172
+00:19:
+
+216
+00:23:51,380 --> 00:23:57,460
+دورات كاملة لا تؤثر على القيمة على الإطلاق يعني يا
+
+217
+00:23:57,460 --> 00:24:06,200
+بنات هذه بيصير E أُس I π  زائد 2M π  و ال M
+
+218
+00:24:06,200 --> 00:24:11,380
+تساوى 0 و 1 و 2 و 3 و زي ما بدك إلى
+
+219
+00:24:11,380 --> 00:24:17,020
+مال نهاية كلها بتعطيني نفس القيمة طيب كويس هذا
+
+220
+00:24:17,020 --> 00:24:23,490
+مين؟ هذا كله قيمة من؟ سالب واحد كتبته على شكل
+
+221
+00:24:23,490 --> 00:24:27,730
+complex number بهذا الشكل طيب احنا بدنا سالب واحد
+
+222
+00:24:27,730 --> 00:24:33,730
+الأس الرابع يبقى بده أجيب له سالب واحد الأس الرابع يبقى لو
+
+223
+00:24:33,730 --> 00:24:40,730
+قلت سالب واحد الأس الرابع هيساوي E أُس I π زائد
+
+224
+00:24:40,730 --> 00:24:50,080
+2M π  كل هذا الأس الرابع هذا أس مركب يعني بنضرب
+
+225
+00:24:50,080 --> 00:24:58,240
+الأسس في بعضها ضرب يبقى هذه بدها تساوي E أُس I في ال
+
+226
+00:24:58,240 --> 00:25:09,220
+π على 4 زائد M π على 2 بنفع؟ اه طيب
+
+227
+00:25:09,220 --> 00:25:17,030
+ممتاز جدا طيب هذه بتجيب لي كم جذر بتجيب لي مال 
+
+228
+00:25:17,030 --> 00:25:23,930
+نهاية من الجذور M 0 1 2 3 4 5 أساسي زي ما بدك بس
+
+229
+00:25:23,930 --> 00:25:28,390
+أنا ما بديش مال نهاية مكفيني من أربعة جذور يعني هذا
+
+230
+00:25:28,390 --> 00:25:32,230
+بتنفع للأربعة جذور وبتنفع للتلت جذور وبتنفع للست
+
+231
+00:25:32,230 --> 00:25:37,350
+جذور وبتنفع للمية جذر قد ما عندك أسس بتقدر تشتغل
+
+232
+00:25:37,350 --> 00:25:42,140
+اللي بدك إياه يعني يبقى هذا بنات من الآن فصاعدا سالب واحد
+
+233
+00:25:42,140 --> 00:25:46,700
+أس أي أس بدّه يساوي الـ exponential وحطّ الأس اللي
+
+234
+00:25:46,700 --> 00:25:49,680
+بدّك إيّاه هاي حطينا الأس اللي بدنا إياه اللي هو
+
+235
+00:25:49,680 --> 00:25:53,360
+موجود عندنا صار الشكل اللي عندنا على الشكل هذي بدّه
+
+236
+00:25:53,360 --> 00:26:00,660
+أحطّ M بـ 0 بجيب الجذرين المترافقين الأولين بحطّ M
+
+237
+00:26:00,660 --> 00:26:04,920
+بـ 1 بـ 2 بـ 3 بجيب الأربعة جذور اللي أنا
+
+238
+00:26:04,920 --> 00:26:13,210
+بدّي إيّاه يبقى هنا بدّي أقعد آخذ M تساوي 0 1 و
+
+239
+00:26:13,210 --> 00:26:18,990
+2 و 3 أيه الـ 4 و الباقي مش لازم ليه طيب
+
+240
+00:26:18,990 --> 00:26:27,470
+لو أخذت M بـ 0 M بـ 0 يبقى يصير عندي E أُس I 
+
+241
+00:26:27,470 --> 00:26:36,220
+π على 4 مظبوط؟ طيب لو أخذت M بـ 1 يبقى بيصير I
+
+242
+00:26:36,220 --> 00:26:43,600
+π على 4 زائد π على 2 يبقى إذا أخذت M
+
+243
+00:26:43,600 --> 00:26:49,460
+بـ 1 بيصير π على 2 بيصير ربع و نص بيصير تلت
+
+244
+00:26:49,460 --> 00:27:00,020
+ربع يبقى هذه لـ E أُس I تلت ربع π طيب بدّه ياخذ M بـ
+
+245
+00:27:00,020 --> 00:27:06,340
+2 يبقى لو أخذنا M بـ 2 بتروح مع 2 بيصير π زائد π
+
+246
+00:27:06,340 --> 00:27:12,060
+على 4 يعني كم؟ 1 و ربع π يعني 5 π على
+
+247
+00:27:12,060 --> 00:27:20,280
+4 يبقى E أُس I 5 π على 4 خلصنا 2
+
+248
+00:27:20,280 --> 00:27:25,480
+بروح نحطّ مين؟ 3 يبقى بيصير 3 على 2 و
+
+249
+00:27:25,480 --> 00:27:35,440
+كم؟ يبقى E أُس I يبقى E أُس I يبقى E أُس I يبقى
+
+250
+00:27:35,440 --> 00:27:38,740
+E أُس I يبقى E أُس I يبقى E أُس I يبقى E أُس I
+
+251
+00:27:38,740 --> 00:27:39,320
+يبقى E أُس I يبقى E أُس I يبقى E أُس I يبقى E
+
+252
+00:27:39,320 --> 00:27:39,940
+أُس I يبقى E أُس I يبقى E أُس I يبقى E أُس I
+
+253
+00:27:39,940 --> 00:27:41,400
+يبقى E أُس I يبقى E أُس I يبقى E أُس I يبقى E
+
+254
+00:27:41,400 --> 00:27:44,060
+أُس I يبقى E أُس I يبقى E أُس I يبقى E أُس I
+
+255
+00:27:44,060 --> 00:27:49,800
+يبقى E أُس I يبقى 
+
+256
+00:27:54,240 --> 00:28:04,320
+Four roots are هنا جذري 2 في المقدار هذا يبقى
+
+257
+00:28:04,320 --> 00:28:10,580
+جذري 2 بدّه يضرب في كل واحدة من هذول مظبوط يبقى
+
+258
+00:28:10,580 --> 00:28:19,240
+هاي جذر 2 في E أُس I π على 4 جذر 2 في E أُس I
+
+259
+00:28:19,240 --> 00:28:27,120
+3 π على 4 جذر 2 في E أُس I 5 π على
+
+260
+00:28:27,120 --> 00:28:33,900
+4 جذر 2 في E أُس I 7 π على 4
+
+261
+00:28:36,470 --> 00:28:42,690
+طيب كويس بدّي أجيب كل واحدة من الـ exponential بدلالة
+
+262
+00:28:42,690 --> 00:28:46,870
+λ و μ مش احنا الحال بقينا نقول λ
+
+263
+00:28:46,870 --> 00:28:53,190
+زائد I μ و الثانية λ ناقص I μ إذا بدّي أجيب
+
+264
+00:28:53,190 --> 00:28:57,990
+الجذور بهذه الشكلة كيف؟ بدّي أرجع أكتب هذه بدلالة
+
+265
+00:28:57,990 --> 00:29:01,820
+القاعدة اللي عندي يعني بدّي أكتبها الحل اللي هو ال
+
+266
+00:29:01,820 --> 00:29:09,260
+cos π على 4 زائد I sin π على 4 يبقى هاي جذري
+
+267
+00:29:09,260 --> 00:29:18,880
+2 في اللي هو مين cos π على 4 زائد I sin π
+
+268
+00:29:18,880 --> 00:29:26,660
+على 4 هذا الأولاني الثاني و جذر 2 في cosine
+
+269
+00:29:26,660 --> 00:29:34,740
+3 π على 4 زائد I sine 3 π على 4
+
+270
+00:29:35,300 --> 00:29:45,760
+واللي بعده جذر 2 في cos 5 π على 4 زائد i sin 5 π
+
+271
+00:29:45,760 --> 00:29:56,400
+على 4 و الأخير جذر 2 في cos 7 π على 4 زائد i sin
+
+272
+00:29:56,400 --> 00:30:00,960
+7 π على 4 بالشكل اللي عندنا
+
+273
+00:30:25,670 --> 00:30:29,610
+فحصوا معي كمان مرة بدّي أعطيكم نص في الـ soufflé 
+
+274
+00:30:29,610 --> 00:30:35,290
+لأنه بدنا نكمل بدنا نبني عليه و نكمل طبعا هذه
+
+275
+00:30:35,290 --> 00:30:38,510
+فرضنا الحل على الشكل هذا طلعت الـ characteristic
+
+276
+00:30:38,510 --> 00:30:44,050
+equation بالشكل هذا أخذت جوز منهم أخذت الجذر الرابع
+
+277
+00:30:44,050 --> 00:30:48,670
+اللي اقترحنا صار له جذر 2 في سالب 1 الأس الرابع
+
+278
+00:30:48,670 --> 00:30:54,150
+بدّي أعرف قداش الجذور تبعت السالب واحد الأربعة جذور
+
+279
+00:30:54,150 --> 00:30:59,070
+فجيت جبت له سالب واحد سالب واحد بـ 0 في I كوساين
+
+280
+00:30:59,070 --> 00:31:03,490
+180 بسالب 1 ساين 180 بـ 0 إذا
+
+281
+00:31:03,490 --> 00:31:08,420
+الـ term هذا كتبته على الشكل هذا طبقا لصيغة Euler
+
+282
+00:31:08,420 --> 00:31:15,200
+يبقى هذا E أُس -I π الزوايا هذول لو ضفت لهم دورات كاملة
+
+283
+00:31:15,200 --> 00:31:19,900
+ما عندي مشكلة لا تتغير القيمة يعني هذا اللي بيعتبره
+
+284
+00:31:19,900 --> 00:31:25,560
+periodic functions دوال دورية إذا الـ -1 أُس
+
+285
+00:31:25,560 --> 00:31:29,880
+الرابع إذا الـ -1 هو الـ cosine π زائد 2M 
+
+286
+00:31:29,880 --> 00:31:34,440
+π و الـ M 0 1 و 2 و 3 و 4 و
+
+287
+00:31:34,440 --> 00:31:38,120
+5 إلى ما شاء الله و هنا الـ sine π زائد 2
+
+288
+00:31:38,120 --> 00:31:41,880
+M π اللي بقدر اكتبه E أُس I π زائد 2M π
+
+289
+00:31:41,880 --> 00:31:46,520
+و هذه قيم الـ M أنا ما بدي سالب واحد و أنا ما بدي سالب
+
+290
+00:31:46,520 --> 00:31:50,560
+واحد أُس الـ 4 فقلت سالب واحد أُس الـ 4 إذا بدّه يساوي الـ
+
+291
+00:31:50,560 --> 00:31:55,140
+exponential كلّها أُس الـ 4 هذا الأس مركب يبقى بضرب
+
+292
+00:31:55,140 --> 00:31:59,900
+الأسوس في بعضها ضرب يبقى لما نضرب الأسوس في بعضها
+
+293
+00:31:59,900 --> 00:32:06,220
+بيصير π على 4 و هذه M π على 2 لأنّه على
+
+294
+00:32:06,220 --> 00:32:10,080
+4 بتختصر بيصير M π على 2 بالشكل اللي
+
+295
+00:32:10,080 --> 00:32:16,450
+عندنا هذا ماشي تمام بدّه نجيب الـ 4 جذور مرة واحدة
+
+296
+00:32:16,450 --> 00:32:20,130
+بمرة ثانية 3 بمرة ثانية
+
+297
+00:32:29,740 --> 00:32:34,240
+هنا حطيت الـ M بـ 1 π على 4 زائد π على
+
+298
+00:32:34,240 --> 00:32:38,960
+2 اللي هو تلت ربع π حطيت الـ M بـ 2 بيصير
+
+299
+00:32:38,960 --> 00:32:41,940
+مع 2 بتروح بيضلّ π على 4 زائد π يعني
+
+300
+00:32:41,940 --> 00:32:46,720
+1 و ربع π يعني 5 على 4 π حطيتها
+
+301
+00:32:46,720 --> 00:32:50,100
+بـ 3 3 على 2 يعني 1 و نص π و ربع
+
+302
+00:32:50,100 --> 00:32:55,010
+بـ 2 اللي ربع يعني 7 π على 4 الآن بدأ
+
+303
+00:32:55,010 --> 00:32:58,590
+أكتب هذه بالصيغة Euler بدلالة الـ cosine و الـ sine
+
+304
+00:32:58,590 --> 00:33:03,710
+فروحنا كتبناها كل واحدة من الجذور الأربعة بدلالة
+
+305
+00:33:03,710 --> 00:33:08,230
+الـ cosine و الـ sine بعد ما دخلنا جذر 2 اللي خليناه
+
+306
+00:33:08,230 --> 00:33:11,610
+و رانا في الأول يبقى شكل الـ roots على الشكل اللي
+
+307
+00:33:11,610 --> 00:33:17,650
+عندنا هذا الآن جتا 45 1 على جذر 2
+
+308
+00:33:17,650 --> 00:33:22,690
+وجيب الـ 45 1 على جذر 2 يبقى شكل الـ
+
+309
+00:33:22,690 --> 00:33:28,950
+root صار بالشكل هذا هاي جذر 2 في 1 على جذر
+
+310
+00:33:28,950 --> 00:33:36,410
+2 زائد I على جذر 2 هذا الأول الثاني جذر
+
+311
+00:33:36,410 --> 00:33:43,390
+2 فيه هنا جت الـ 135 π على الـ 4 135 
+
+312
+00:33:43,390 --> 00:33:47,130
+315 بـ 135 في الـ 4 الثانية الـ cosine سالب
+
+313
+00:33:47,130 --> 00:33:51,790
+يبقى و cosine π على 4 بإشارات سالب يعني
+
+314
+00:33:51,790 --> 00:34:00,310
+سالب 1 على جذر 2 زائد I على جذر 2 ليش؟
+
+315
+00:34:00,310 --> 00:34:04,570
+لأن جيب الـ 45 بيساوي جيب الـ 135 و
+
+316
+00:34:04,570 --> 00:34:09,350
+30 في الربع الثاني الجيب بيكون بإشارة من موجب
+
+317
+00:34:09,350 --> 00:34:14,050
+نيجي للي بعدها جذر
+
+318
+00:34:14,050 --> 00:34:21,340
+2 فيه بنجي هنا cosine 5 π على 4 5 و
+
+319
+00:34:21,340 --> 00:34:26,380
+40 في 5 اللي هو بـ 225 يعني
+
+320
+00:34:26,380 --> 00:34:31,600
+في الربع الثالث يبقى الـ cosine بالثالث لازم يطلع
+
+321
+00:34:31,600 --> 00:34:38,220
+هذا المرافق لواحد فيهم يبقى بيصير هنا سالب 1
+
+322
+00:34:38,220 --> 00:34:43,800
+على جذر 2 و
+
+323
+00:34:43,800 --> 00:34:49,840
+الـ sign كمان هذي في الربع الثالث كمان بإشارة سالب
+
+324
+00:34:50,030 --> 00:34:57,790
+يبقى ناقص I على 2 يبقى ناقص I على جذر 2
+
+325
+00:34:57,790 --> 00:35:03,490
+بالشكل هذا هيطلعي هذا و هذا هما المترافقين صحيح ولا
+
+326
+00:35:03,490 --> 00:35:08,950
+لا؟ طيب تقدروا بدون مرجع للحسابات تقولوا لي قداش اللي
+
+327
+00:35:08,950 --> 00:35:16,270
+ضايل هذا؟ اللي هو المرافق لهذا اللي هو 1 على جذر
+
+328
+00:35:16,270 --> 00:35:22,870
+2 ناقص I على من؟ على جذر 2 بتدخل جذر 2
+
+329
+00:35:22,870 --> 00:35:30,830
+جوا يبقى ده ايش بيصير 1 زائد I ناقص 1 زائد I
+
+330
+00:35:30,830 --> 00:35:40,400
+و ناقص 1 ناقص I و 1 ناقص I طلعوا لي في 2 هدول
+
+331
+00:35:40,400 --> 00:35:47,020
+هدول مترافقين مع بعض صحيح ولا لا؟ و هدول 2
+
+332
+00:35:47,020 --> 00:35:54,240
+كمان مترافقين مع بعض يبقى conjugate يبقى هذه
+
+333
+00:35:54,240 --> 00:36:02,430
+الجذور المترافقة طيب هدول كم جذر يا بنات؟ 4 جذور،
+
+334
+00:36:02,430 --> 00:36:07,770
+لسه في 4 زيهم، مظبوط؟ لأن احنا أخذنا هنا جزء
+
+335
+00:36:07,770 --> 00:36:12,230
+واحد فقط، و لسه كمان بقى الجذور بيبقى في 4
+
+336
+00:36:12,230 --> 00:36:18,890
+جذور زيهم، يبقى الجذور complex and repeated تمام؟
+
+337
+00:36:18,890 --> 00:36:23,770
+يبقى بدّه نعرف ما هو شكل الحل في هذه الحالة، يبقى
+
+338
+00:36:23,770 --> 00:36:32,640
+باجي بقول له Y<sub>C</sub>  to 7 نمسك الأولاني هنا هنا λ
+
+339
+00:36:32,640 --> 00:36:41,680
+بقدّاش بـ 1 و μ بـ 1 يبقى بالداجي أقول له C<sub>1</sub> زي
+
+340
+00:36:41,680 --> 00:36:45,760
+اه طبعا قبلها هيبقى نكتب λ λ يا بنات هنا اللي
+
+341
+00:36:45,760 --> 00:36:52,020
+هي مين E أُس λ اللي هي بـ 1 يبقى E أُس t في
+
+342
+00:36:52,020 --> 00:37:03,170
+مين في C<sub>1</sub> زي C<sub>2</sub> في t في Cos t زائد C<sub>3</sub> زائد C
+
+343
+00:37:03,170 --> 00:37:12,370
+<sub>4</sub> t في Sin الـ t هذول كم حل؟ كم واحد هذول
+
+344
+00:37:12,370 --> 00:37:17,330
+كم؟ لسه بتكتبي كمان؟ هذول 4 حلول يعني جبنا
+
+345
+00:37:17,330 --> 00:37:22,520
+الحل المقابل له فكتبنا على الشكل هذا متذكرين لما
+
+346
+00:37:22,520 --> 00:37:28,000
+كنا real و ده بقى نقول C<sub>1</sub> زي C<sub>2</sub> t E أُس t هنا جان
+
+347
+00:37:28,000 --> 00:37:33,740
+الـ cosine و الـ sine يبقى هنا complex و مكرر خلصنا
+
+348
+00:37:33,740 --> 00:37:38,610
+تبعت الـ E أُس t بدنا نجيب تبعت مين؟ الـ E أُس سالب
+
+349
+00:37:38,610 --> 00:37:44,810
+يعني احنا خلصنا هذا و هذا يبقى
+
+350
+00:37:44,810 --> 00:37:53,730
+زائد E أُس -t اللي هي λ خدنا C<sub>5</sub>
+
+351
+00:37:53,730 --> 00:37:56,390
+زائد C<sub>6</sub> t
+
+352
+00:38:10,310 --> 00:38:15,530
+كتابتها يبقى هاي
+
+353
+00:38:15,530 --> 00:38:19,790
+بيصير حل الـ homogenous differential equation من
+
+354
+00:38:19,790 --> 00:38:26,130
+الرتبة الثامنة complex و مكرر زي ما أنتم شايفينه
+
+355
+00:38:27,540 --> 00:38:32,740
+حد بتحب تسأل أي سؤال؟ أنتِ هنا احنا مسترشدين بناء على
+
+356
+00:38:32,740 --> 00:38:37,340
+هذا طيب
+
+357
+00:38:37,340 --> 00:38:43,220
+وصلنا للـ exercises يبقى بدّي للـ exercises 4
+
+358
+00:38:43,220 --> 00:38:54,470
+2 المسائل من 1 أو من 11 لغاية 24 القدّ و
+
+359
+00:38:54,470 --> 00:39:01,990
+المسائل من 29 لغاية 35 و من
+
+360
+00:39:01,990 --> 00:39:05,630
+الحجم كمان سؤال 38
+
+361
+00:39:25,470 --> 00:39:28,450
+لحد هنا أوقف بالنسبة للـ homogeneous differential
+
+362
+00:39:28,450 --> 00:39:32,170
+equation بدنا نروح للـ non-homogeneous
+
+363
+00:39:32,170 --> 00:39:36,710
+differential equation و اليوم نأخذ أول طريقة فقط
+
+364
+00:39:36,710 --> 00:39:40,750
+اللي هو طريقة الـ undetermined coefficients يبقى
+
+365
+00:39:40,750 --> 00:39:49,050
+بنيجي لـ section 4-3 اللي هو the method of
+
+366
+00:39:49,050 --> 00:39:54,570
+undetermined 
+
+367
+00:39:54,570 --> 00:39:54,930
+coefficients
+
+368
+00:40:00,570 --> 00:40:06,510
+نفس الطريقة اللي أخذناها للـ second order نأخذها للـ
+
+369
+00:40:06,510 --> 00:40:15,330
+ninth order يبقى consider the differential
+
+370
+00:40:15,330 --> 00:40:24,430
+equation y to the derivative n مضروبة في الـ a<sub>0</sub> زائد
+
+371
+00:40:24,430 --> 00:40:30,510
+a<sub>1</sub> y to the derivative n ناقص الـ 1 زائد و نظلّ
+
+372
+00:40:30,510 --> 00:40:37,450
+ماشيين لغاية ما نوصل للـ a<sub>n-1</sub> y'
+
+373
+00:40:37,450 --> 00:40:44,090
+زائد الـ a<sub>n</sub> y بدّه يساوي الـ g(t) و سمّي المعادلة
+
+374
+00:40:44,090 --> 00:40:49,610
+هذه رقم 1 The
+
+375
+00:40:49,610 --> 00:40:51,810
+solution
+
+376
+00:40:53,610 --> 00:41:07,790
+of the differential equation one is Y تساوي Y<sub>C</sub>
+
+377
+00:41:07,790 --> 00:41:20,850
+زائد Y(t) حيث Y<sub>C</sub> is the solution
+
+378
+00:41:24,830 --> 00:41:32,030
+هذه هي حلقة الإيقاع
+
+379
+00:41:32,030 --> 00:41:35,150
+الـ homogeneous
+
+380
+00:41:35,150 --> 00:41:36,310
+الـ homogeneous الـ homogeneous الـ homogeneous
+
+381
+00:41:36,310 --> 00:41:38,110
+الـ homogeneous الـ homogeneous الـ homogeneous
+
+382
+
+431
+00:53:07,530 --> 00:53:11,110
+في الحل اللي هو YC حل ال homogenous differential
+
+432
+00:53:11,110 --> 00:53:14,730
+equation أظن ما جيبناها شيء جديد هو هو اللي تبقى
+
+433
+00:53:14,730 --> 00:53:19,570
+second order بس عمّمناه زي ما أنتم شايفين طيب
+
+434
+00:53:19,570 --> 00:53:22,610
+بدنا نبدأ طب حد رفيقكم تسأل أسئلة جابي المدخل في
+
+435
+00:53:22,610 --> 00:53:26,470
+الأمثلة ايش 
+
+436
+00:53:26,470 --> 00:53:40,780
+طيبيبقى أول
+
+437
+00:53:40,780 --> 00:53:46,840
+شغلة نبدأ فيها هي حل الهوموجينيس يبقى باجي بقوله
+
+438
+00:53:46,840 --> 00:53:57,020
+let Y تساوي E أس RT be a solution of the
+
+439
+00:54:10,310 --> 00:54:18,070
+يبقى باجي بقول ذي characteristic equation of
+
+440
+00:54:18,070 --> 00:54:26,470
+the equation اتنين is R تكعيب زائد أربعة R تساوي كدهاش
+
+441
+00:54:26,470 --> 00:54:32,850
+Zero ومنها R في R تربيع زائد أربعة بيساوي كدهاش
+
+442
+00:54:32,850 --> 00:54:40,830
+Zero يبقى ال R تساوي Zero R واحد وR اثنين و تلاتة 
+
+443
+00:54:40,830 --> 00:54:49,360
+بده يساوي زائد أو ناقص اثنين I لأنها كمية تخيلية يبقى
+
+444
+00:54:49,360 --> 00:54:57,960
+هذا بدي أعطيك شكل ال Y C بديه يساوي C واحد في E أس
+
+445
+00:54:57,960 --> 00:55:04,760
+Zero بواحد مع السلامة هذي بده يصير الزاد لمدة
+
+446
+00:55:04,760 --> 00:55:11,370
+ما عنديش ما عنديش إلا ميويبقى هنا بجي بقوله c3 cos
+
+447
+00:55:11,370 --> 00:55:20,930
+2t c4 sin 2t و ببرزها لإني بدي أرجعلها بعد قليل
+
+448
+00:55:20,930 --> 00:55:25,310
+الآن بدنا نجي نجيب الـ particular solution
+
+449
+00:55:25,310 --> 00:55:33,130
+للمعادلة رقم واحد فبجي بقوله هنا capital Y of T
+
+450
+00:55:33,130 --> 00:55:40,020
+بده يساوي نجي بطلع Polynomial من الدرجة الأولى يبقى
+
+451
+00:55:40,020 --> 00:55:44,900
+باكتب له T to the power S وبحف بينه same
+
+452
+00:55:44,900 --> 00:55:50,000
+polynomial من الدرجة الأولى اللي هو A naught T
+
+453
+00:55:50,000 --> 00:55:56,560
+زائد ال A1 وبقول له استنى شوية هك وتعالى نشوف قداش
+
+454
+00:55:56,560 --> 00:56:02,400
+قيمة Sبغطي هذا term واجب أخطلع للمقدار بين القوسين
+
+455
+00:56:02,400 --> 00:56:10,800
+هل أي term هنا يشبه أي term من الترمات هدول هذا
+
+456
+00:56:10,800 --> 00:56:15,500
+constant وهذا constant يبقى فيه تشابه إذا بدى أحط
+
+457
+00:56:15,500 --> 00:56:22,640
+s بقدرش؟ بواحد لو حطيت s بواحد هذه تدخل جوا بصير
+
+458
+00:56:22,640 --> 00:56:30,630
+a0t تربيع زائد a1tفى تشابه بين هدول معاهي term هنا
+
+459
+00:56:30,630 --> 00:56:35,830
+لأ يبقى اللي بتحل الاشكالية فقط S تساوي واحد يبقى
+
+460
+00:56:35,830 --> 00:56:42,350
+باجي بقوله here ال S تساوي واحد يبقى هدف بده
+
+461
+00:56:42,350 --> 00:56:49,810
+يعطيني انه capital Y of T هو عبارة عن a node T
+
+462
+00:56:49,810 --> 00:56:59,750
+تربيع زائد a one Tتمام؟ الآن بدي اروح اطلع قداش
+
+463
+00:56:59,750 --> 00:57:05,070
+قيمة اللي هو ال a node و ال a1 و قاعد هيك بنرجع
+
+464
+00:57:05,070 --> 00:57:09,690
+لمين لل general solution اذا لازم اللي اشتقها كام
+
+465
+00:57:09,690 --> 00:57:17,330
+مرة؟ ثلاث مرات اذا بدي اروح اجيبله y prime of t ب2
+
+466
+00:57:17,330 --> 00:57:27,090
+a node t زائد a1بالزملة YOTWP
+
+467
+00:57:27,090 --> 00:57:35,570
+نشتق كمان مرة باتنين نوت هذه مع السلامة وهذه مشتقة
+
+468
+00:57:35,570 --> 00:57:40,690
+ال a1 بدنا المشتقة من الثانية يبقى جيبنا
+
+469
+00:57:40,690 --> 00:57:44,970
+المشتقة الثانية خلصنا منها بس بدنا نروح نجيب من
+
+470
+00:57:44,970 --> 00:57:51,920
+المشتقة الثالثة يبقى هذا بدي يعطيك ان المشتقة
+
+471
+00:57:51,920 --> 00:57:57,960
+الثالثة يكبتل Y triple A prime of T بدي يسوى قداش
+
+472
+00:57:57,960 --> 00:58:03,760
+Zero لأن اثنين مقدار ثابت وال a node مقدار ثابت نرجع
+
+473
+00:58:03,760 --> 00:58:08,520
+نعوض وين في المعادلة اللي هي رقم واحد اللي عندنا
+
+474
+00:58:08,520 --> 00:58:20,160
+يبقى باجي بقوله هنا substitute in equation one وجت
+
+475
+00:58:20,160 --> 00:58:23,760
+يبقى بدنا نرجع لل equation one
+
+476
+00:58:45,930 --> 00:58:51,650
+يبقى y triple prime ب Zero يبقى هي ال Zero راح و
+
+477
+00:58:51,650 --> 00:58:57,590
+عندك أربعة في y prime وين y prime هي يبقى بصير
+
+478
+00:58:57,590 --> 00:59:06,910
+ثمانية a node t زائد ثمانية a node t زائد أربعة a
+
+479
+00:59:06,910 --> 00:59:07,230
+one
+
+480
+00:59:17,860 --> 00:59:21,000
+نعمل مقارنة ما بين الطرفين نعمل مقارنة ما بين
+
+481
+00:59:21,000 --> 00:59:23,800
+الطرفين نعمل مقارنة ما بين الطرفين يبقى ثمانية a
+
+482
+00:59:23,800 --> 00:59:29,040
+note بده يسوى قداش أمانات واحد هذا بده يعطيك ان a
+
+483
+00:59:29,040 --> 00:59:34,900
+note يسوى قداش ثمان اللي بعدها أربعة a one بده
+
+484
+00:59:34,900 --> 00:59:41,060
+يسوى من زيرو يبقى ال a one بده يساوي من زيرو يبقى
+
+485
+00:59:41,060 --> 00:59:47,860
+صار شكل ال Y of T على الشكل التاليبرجع لل Y of T
+
+486
+00:59:47,860 --> 00:59:52,720
+اللي عندنا اللي همين ال Y of T هايه يبقى هنا S
+
+487
+00:59:52,720 --> 00:59:56,100
+بواحد صار بالشكل اللي عندنا هذا بدي أشيل A نوع ده
+
+488
+00:59:56,100 --> 01:00:00,980
+و أحط مكانه ثمان و هذا ب Zero مع السلامة يبقى صار
+
+489
+01:00:00,980 --> 01:00:08,330
+ثمان T تربيع يبقى هنا ثمان T تربيع يبقى بناء عليه Y
+
+490
+01:00:08,330 --> 01:00:14,030
+تساوي YC زائد capital Y of T Y الساوية YC اللي
+
+491
+01:00:14,030 --> 01:00:25,130
+برزناها فوق يبقى C1 زائد C3 C2 Cos T زائد C3 في
+
+492
+01:00:25,130 --> 01:00:25,890
+ال sign
+
+493
+01:00:34,120 --> 01:00:43,570
+بنضيف عليهم capital Y of T بثمان T تربيعطيب حتى
+
+494
+01:00:43,570 --> 01:00:47,450
+الآن ما استخدمتش ال initial conditions يبقى بدي
+
+495
+01:00:47,450 --> 01:00:51,610
+أري على ال initial conditions اللي أنا بدي أشتق
+
+496
+01:00:51,610 --> 01:00:58,850
+مرتين يبقى باجي بقوله y' يساوي هذا مع السلامة
+
+497
+01:00:58,850 --> 01:01:08,900
+وتفضل cos بسالب 2C2 في sin 2Tوزائد اثنين C تلاتة
+
+498
+01:01:08,900 --> 01:01:20,760
+كوسين اثنين T وزائد أربعة T وين الخطأ؟ why C؟ اه C
+
+499
+01:01:20,760 --> 01:01:26,920
+اثنين يعني هذه بنفسها هو C اثنين وهذه C تلاتة C
+
+500
+01:01:26,920 --> 01:01:34,660
+اثنين وC تلاتة ماشي يبقى هنا c1 زي c2 زي c3 مظبوط
+
+501
+01:01:34,660 --> 01:01:39,340
+هي يبقى اشتقينا و الاشتقاق صحيح ما فيش فيه أي مشكلة
+
+502
+01:01:39,340 --> 01:01:45,480
+تمام طيب بدنا نجيب yw prime يساوي نشتق هذه كمان
+
+503
+01:01:45,480 --> 01:01:53,340
+مرة يبقى ناقص أربعة c2 كوسين اثنين t ناقص أربعة c
+
+504
+01:01:53,340 --> 01:02:00,830
+تلاتة ساين اثنين t زائد رابع على ال condition
+
+505
+01:02:00,830 --> 01:02:04,030
+الأولاني
+
+506
+01:02:04,030 --> 01:02:08,510
+يجب أن يكون y عند ال Zero يسوى 0 y عند ال Zero
+
+507
+01:02:08,510 --> 01:02:13,130
+يسوى 0 يبقى
+
+508
+01:02:13,130 --> 01:02:20,610
+هدى c1 كوسين صفر بواحد زائد c2 هدى بزيرو مع السلامة
+
+509
+01:02:20,610 --> 01:02:25,800
+و هدى بزيرو مع السلامة كله يسوى كده؟ الـ Condition
+
+510
+01:02:25,800 --> 01:02:31,860
+الثاني y' عند 0 يكون سوى 0 ومن هنا نجي لهذه بـ 0
+
+511
+01:02:31,860 --> 01:02:39,940
+بصير هذا كوسين صفر بواحد يبقى هنا اثنين C تلاتة
+
+512
+01:02:39,940 --> 01:02:46,080
+وهذا بـ 0 بصير يكون سوى كده؟ يكون سوى 0 الـ
+
+513
+01:02:46,080 --> 01:02:52,310
+Condition الثالث y'' عند 0 أظن يكون سوى 1مظبوط
+
+514
+01:02:52,310 --> 01:03:00,830
+يبقى هذا بده يعطيك YW Prime هايها اللي هو ناقص 4C2
+
+515
+01:03:00,830 --> 01:03:06,810
+و هذا مع السلامة و هذا زائد أربعة بده يساوي مين؟
+
+516
+01:03:06,810 --> 01:03:11,770
+بده يساوي Zero من هذه أمانات بقدر أقول إذا C3
+
+517
+01:03:11,770 --> 01:03:20,610
+تساوي Zero تمام؟ نجي من هنا بقدر أجيب له كمان C2
+
+518
+01:03:20,610 --> 01:03:31,730
+يبقى هذا معناه انه ايش الواحد؟ اه بتساوي واحد صحيح
+
+519
+01:03:31,730 --> 01:03:37,070
+حقه يبقى هذه تساوي واحد مظبوط يبقى هدى معناه هذا
+
+520
+01:03:37,070 --> 01:03:46,480
+معناه انه سالب أربعة C اثنين يساوي تلت ربعربع بيجي
+
+521
+01:03:46,480 --> 01:03:50,980
+بالسلبان واحد بيظل تلت ربع يبقى هذا بدي أعطيك
+
+522
+01:03:50,980 --> 01:04:01,400
+انه C2 بده يساوي سالب تلاتة على ستاشر لما C2 بده
+
+523
+01:04:01,400 --> 01:04:06,760
+يساوي سالب تلاتة على ستاشر إذا C1 بتلاتة على ستاشر
+
+524
+01:04:06,760 --> 01:04:15,020
+و C3 بده يساوي تلاتة على ستاشر وين الواحد؟
+
+525
+01:04:19,430 --> 01:04:28,510
+سي تلاتة خليكي معايا الحين هذا سي اثنين بتلاتة
+
+526
+01:04:28,510 --> 01:04:32,830
+على ستاشر و سي اثنين بسالب تلاتة على ستاشر بدي
+
+527
+01:04:32,830 --> 01:04:37,690
+أعوض الآن سي اثنين بسالب تلاتة على ستاشر أنجليها
+
+528
+01:04:37,690 --> 01:04:44,190
+على الشجة الثانية بصير اه C1 يسوي 3 ع 16 اه C1 هذي
+
+529
+01:04:44,190 --> 01:04:49,170
+C1 ب 3 ع 16 مظبوط إذا بدي بيصير شكل المعادلة شكل
+
+530
+01:04:49,170 --> 01:04:57,910
+الحل على الشكل التالي Y يسوي C1 اللي هي 3 ع 16 و C2
+
+531
+01:04:57,910 --> 01:05:09,130
+هو ناقص 3 على 16 في cos 2t و C3 بزيرو و بطير ال
+
+532
+01:05:09,130 --> 01:05:17,010
+term هذا و بظل بس 8T تربيع يبقى هذا الشكل الحل تبع
+
+533
+01:05:17,010 --> 01:05:19,630
+ال initial value problem
+
+534
+01:05:41,520 --> 01:05:51,580
+المثال الثاني مثال
+
+535
+01:05:51,580 --> 01:05:57,940
+اثنين find
+
+536
+01:05:57,940 --> 01:06:00,520
+the general solution of the differential equation
+
+537
+01:06:10,110 --> 01:06:14,750
+of the differential equation اللي هو y to the
+
+538
+01:06:14,750 --> 01:06:23,930
+derivative 4 ناقص y بده يساوي تلاتة T زائد cosine
+
+539
+01:06:23,930 --> 01:06:32,750
+ال T وسميه لهذا المعادلة رقم 1 نفس الطريقة اللي
+
+540
+01:06:32,750 --> 01:06:41,010
+بدأنا فيها solution يبقى بالدرجة أقوله letY تساوي
+
+541
+01:06:41,010 --> 01:06:51,350
+E أس RT be a solution of Y to the derivative 4 ناقص
+
+542
+01:06:51,350 --> 01:06:57,250
+Y يساوي Zero هذا بدي يعطيك ان ال characteristic
+
+543
+01:06:57,250 --> 01:07:05,970
+equation is R أربعة ناقص واحد يساوي Zero إذا صارت
+
+544
+01:07:05,970 --> 01:07:11,950
+R تربيع ناقص واحد في R تربيع زائد واحد يساوي Zero
+
+545
+01:07:11,950 --> 01:07:19,050
+يبقى R ناقص واحد في R زائد واحد فرق بين المربعين
+
+546
+01:07:19,050 --> 01:07:26,930
+يساوي Zero يبقى R تساوي واحد وR تساوي سالب واحد
+
+547
+01:07:26,930 --> 01:07:33,610
+هذه R واحد هذه R اثنين وهذه R تلاتة وأربعة اللي هو
+
+548
+01:07:33,610 --> 01:07:39,110
+بده يساوي زائد أو ناقص I يبقى صار حل ال homogenous
+
+549
+01:07:39,110 --> 01:07:49,850
+YC بده يساوي C1 E أس T C2 E أس ناقص T زائد C تلاتة
+
+550
+01:07:49,850 --> 01:08:00,210
+cosine T زائد C أربعة في ساين T كويس بالدالي لشكل
+
+551
+01:08:00,210 --> 01:08:06,530
+G of T بنعمل من الدرجة الأولى الزائد كوسين وليست
+
+552
+01:08:06,530 --> 01:08:11,390
+مضروبة درجة إذا بنرجع لطريقتنا الميان اللي عتيجة
+
+553
+01:08:11,390 --> 01:08:18,330
+أني أجزء المعادلة إلى معادلتين فبجي بقوله ذا
+
+554
+01:08:18,770 --> 01:08:27,150
+differential equation one is written as وروح
+
+555
+01:08:27,150 --> 01:08:33,570
+بكتبها y to the derivative four ناقص y يسوي تلاتة
+
+556
+01:08:33,570 --> 01:08:40,790
+T الثانية y to the derivative four ناقص y يسوي cos
+
+557
+01:08:40,790 --> 01:08:50,450
+T بدنا نيجي لهذه capital Y one of TY1 of T بيبقى
+
+558
+01:08:50,450 --> 01:08:51,390
+Y1 of T بيبقى Y1 of T بيبقى Y1 of T بيبقى Y1 of T
+
+559
+01:08:51,390 --> 01:08:52,210
+بيبقى Y1 of T بيبقى Y1 of T بيبقى Y1 of T بيبقى Y1
+
+560
+01:08:52,210 --> 01:08:54,570
+of T بيبقى Y1 of T بيبقى Y1 of T بيبقى Y1 of T
+
+561
+01:08:54,570 --> 01:08:54,790
+بيبقى Y1 of T بيبقى Y1 of T بيبقى Y1 of T
+
+562
+01:08:54,790 --> 01:08:54,850
+بيبقى Y1 of T بيبقى Y1 of T بيبقى Y1 of T
+
+563
+01:08:54,850 --> 01:08:56,990
+بيبقى Y1 of T بيبقى Y1 of T بيبقى Y1 of T بيبقى Y1
+
+564
+01:08:56,990 --> 01:09:11,650
+of T بيبقى Y1 of T بيبقى Y1
+
+565
+01:09:11,650 --> 01:09:19,050
+of T بيبقلأ يبقى باجي بقوله here ال S تساوي 0 إذا
+
+566
+01:09:19,050 --> 01:09:27,030
+صار capital Y1 of T بدي يساوي a naught T زائد a واحد
+
+567
+01:09:27,030 --> 01:09:36,390
+بالمرة نخلصه يالا هاتي لي Y1 prime a naught وال Y1
+
+568
+01:09:36,390 --> 01:09:47,630
+double prime ب 0و Y1'' بزيرو و Y4'' بدو يساوي زيرو
+
+569
+01:09:47,630 --> 01:09:56,310
+نعود في المعادلة يبقى هاي زيرو ناقص Y ناقص Y هيها
+
+570
+01:09:56,310 --> 01:10:07,650
+يبقى ناقص A0 T ناقص A1 بدو يساوي تلاتة T ومنها ناقص
+
+571
+01:10:07,650 --> 01:10:15,260
+a0 بده يسوى تلاتة يبقى a0 بده يساوي كده؟ سالب تلاتة
+
+572
+01:10:15,260 --> 01:10:21,620
+و سالب a1 بده يساوي Zero يبقى ال a1 بده يساوي Zero
+
+573
+01:10:21,620 --> 01:10:30,640
+يبقى أصبح Y1 as a function of T بده يساوي عندك ال
+
+574
+01:10:30,640 --> 01:10:39,450
+a0 بسالب تلاتة يبقى هاي سالب تلاتة T فقط ما غير نجي
+
+575
+01:10:39,450 --> 01:10:48,170
+للتانية هادي بدنا نجيب Y2 Y2 as a function of T
+
+576
+01:10:48,170 --> 01:10:55,510
+هادي T to the power S في هنا اللي هو polynomial من
+
+577
+01:10:55,510 --> 01:11:01,970
+درجة الصفر يعني A cosine T زائد B في sine T
+
+578
+01:11:05,830 --> 01:11:10,790
+المعامل هو واحد صحيح يعني دالة من الدرجة الصفرية
+
+579
+01:11:10,790 --> 01:11:15,990
+فقلنا كونوسين في كوسين زي كونوسين في من في ساين نجي
+
+580
+01:11:15,990 --> 01:11:21,070
+المقدار بين القوسين في تشابه مع أي term هنا اه في
+
+581
+01:11:21,070 --> 01:11:26,570
+تشابه هذا بيشبه هذا و هذا بيشبه هذا يبقى بدي احط
+
+582
+01:11:26,570 --> 01:11:33,760
+اس بقداش بواحد لو حطيت اس بواحد بصير AT cos T ما فيش
+
+583
+01:11:33,760 --> 01:11:38,540
+زيها و BT sin T كمان ما فيش زيها يبقى ال S عندي
+
+584
+01:11:38,540 --> 01:11:44,240
+هنا بيبقى دا شر بواحد يبقى باجي بقوله here ال S
+
+585
+01:11:44,240 --> 01:11:50,940
+تساوي واحد يبقى بناء عليه سار كابتل Y2 of T بيبقى
+
+586
+01:11:50,940 --> 01:12:01,730
+ساوي AT cos T زائد BT في sin T نشتق أربع مرات و
+
+587
+01:12:01,730 --> 01:12:09,170
+نعود في الدالة اللي فوق يبقى يبقى y2 prime يبقى a
+
+588
+01:12:09,170 --> 01:12:17,670
+cosine of t ناقص a t في sine of t نشتق هذه يبقى
+
+589
+01:12:17,670 --> 01:12:26,980
+زائد b في sine of t زائد بي تي في كوسين التين كل
+
+590
+01:12:26,980 --> 01:12:32,920
+واحدة فيهم مشتقت حاصل ضرب دالتين فرعان واضع
+
+591
+01:12:32,920 --> 01:12:38,900
+اختصارات ما فيش يبقى بظل كل شيء زي ما هو لأن هذي
+
+592
+01:12:38,900 --> 01:12:45,600
+كوسين هناك تي في كوسين ولا واحد زي الثانية Y2W'
+
+593
+01:12:46,280 --> 01:12:57,780
+يبقى سالب A في ساين T و سالب A في ساين T و سالب A
+
+594
+01:12:57,780 --> 01:13:07,720
+T في كوسينة T مشتقة الأولى هي بإشارة سالب وهذه
+
+595
+01:13:07,720 --> 01:13:14,320
+حصل ضرب داليتين تبقى سالب a sin t و سالب a t تفضل
+
+596
+01:13:14,320 --> 01:13:19,810
+sin ب cos خلصنا أول two terms بداجي لمين؟ لـ two
+
+597
+01:13:19,810 --> 01:13:29,390
+terms الثانية يبقى زائد بي في
+
+646
+01:20:41,400 --> 01:20:47,960
+بيقول لك determine a
+
+647
+01:20:47,960 --> 01:20:51,680
+suitable form
+
+648
+01:20:51,680 --> 01:21:03,860
+شكل مناسب for the particular solution
+
+649
+01:21:09,480 --> 01:21:20,800
+و Y of T وبعد ذلك don't evaluate the constants
+
+650
+01:21:20,800 --> 01:21:25,580
+بدل ما 
+
+651
+01:21:25,580 --> 01:21:31,940
+تحسبون الثوابت، ولو جاب لك سؤال في الامتحان يمكن
+
+652
+01:21:31,940 --> 01:21:35,960
+نجيبه زي هيك، لسمح الله نقول لك ما تحسبوش قيم حتى
+
+653
+01:21:35,960 --> 01:21:40,140
+ما تضيعيش وقتك وأنت بتشتقه وتجمعه، وغالبًا في اللي
+
+654
+01:21:40,140 --> 01:21:44,400
+لازم يغلّقه، يبقى أنت بس بدّي شكل الحل الخاص، والله
+
+655
+01:21:44,400 --> 01:21:48,740
+يعطيك العافية، بتطلع هيك مكتوب عادي دائمًا، أما ده في
+
+656
+01:21:48,740 --> 01:21:54,260
+الامتحانات السابقة بنحطها بخط غامق وبننقصّن حتى عشر
+
+657
+01:21:54,260 --> 01:22:03,730
+الكل يشوفها، نمرّة ايه؟ سؤال 18 من الكتاب بيقول لي Y 
+
+658
+01:22:03,730 --> 01:22:13,030
+to the derivative 4 زائد 2 Y triple prime زائد
+
+659
+01:22:13,030 --> 01:22:22,100
+2 Y double prime بده يساوي 3 E<sup>st</sup> زائد
+
+660
+01:22:22,100 --> 01:22:34,380
+2 T E<sup>-T</sup> زائد E<sup>-T</sup> في sin T  و
+
+661
+01:22:34,380 --> 01:22:36,600
+المعادلة رقم 1
+
+662
+01:23:06,020 --> 01:23:08,820
+ماذا تسأل؟
+
+663
+01:23:14,220 --> 01:23:18,580
+جمعناهم يا أختي، وين؟ هي جبنا Y<sub>1</sub>، هي Y<sub>3</sub>
+
+664
+01:23:18,580 --> 01:23:24,540
+Y<sub>2</sub>، Y<sub>4</sub>، و هي Y<sub>2</sub>، 
+
+665
+01:23:24,540 --> 01:23:25,860
+جمعناهم
+
+666
+01:23:55,980 --> 01:24:00,560
+طيب السؤال هذا بيقول لك يجي بس شكل الـ particular
+
+667
+01:24:00,560 --> 01:24:05,640
+solution لكن شكل الـ particular solution بيعتمد على 
+
+668
+01:24:05,640 --> 01:24:08,880
+حل الـ homogeneous، إذا بروح حل الـ homogeneous في
+
+669
+01:24:08,880 --> 01:24:17,300
+الأول قبل كل شيء، يبقى باجي بقوله solution let
+
+670
+01:24:17,990 --> 01:24:27,030
+Y تساوي E<sup>rt</sup> بإيه؟ solution of the differential
+
+671
+01:24:27,030 --> 01:24:33,570
+equation Y to the derivative 4 زائد 2 Y triple
+
+672
+01:24:33,570 --> 01:24:40,670
+prime زائد 2 Y prime كله بده يساوي 0، يبقى
+
+673
+01:24:40,670 --> 01:24:48,250
+then the characteristic equation is المعادلة
+
+674
+01:24:48,250 --> 01:24:54,830
+ المميزة لهذه المعادلة، r<sup>4</sup> زائد 2 r<sup>3</sup>
+
+675
+01:24:54,830 --> 01:25:00,610
+تكعيب زائد 2 r<sup>2</sup> يساوي قد ايش؟ 0، يبقى بناء
+
+676
+01:25:00,610 --> 01:25:05,830
+عليها، لو أخدت r<sup>2</sup> عامل مشترك، بظل عندي r<sup>2</sup>
+
+677
+01:25:05,830 --> 01:25:11,730
+زائد 2 r زائد 2 يساوي 0، من هذه المعادلة
+
+678
+01:25:11,730 --> 01:25:16,850
+بقدر أقول إذا r<sub>1</sub> بدها تساوي r<sub>2</sub> بدها تساوي
+
+679
+01:25:16,850 --> 01:25:22,490
+قد ايش؟ 0، جذور حقيقية ومكررة كل واحد منهم يساوي
+
+680
+01:25:22,490 --> 01:25:30,750
+0، هذه لا يمكن تحليلها، يبقى r<sub>3</sub> و r<sub>4</sub> هو
+
+681
+01:25:30,750 --> 01:25:36,650
+عبارة عن حلّها بالقانون، ناقص 2 زائد وناقص الجذر
+
+682
+01:25:36,650 --> 01:25:43,130
+التربيعي لـ b تربيع ناقص 4 a c اللي هو
+
+683
+01:25:43,130 --> 01:25:50,930
+بواحد، و c بـ 2، كله على قد ايش؟ على 2، ويساوي
+
+684
+01:25:50,930 --> 01:25:55,520
+سالب 2 زائد وناقص 2 في 4 في 8 بده
+
+685
+01:25:55,520 --> 01:26:00,940
+أشيل الـ 4، وضل سالب 4 تحت الجذر، يبقى زائد أو
+
+686
+01:26:00,940 --> 01:26:06,960
+ناقص 2 i على الـ 2 اللي هو يساوي سالب 1 زائد
+
+687
+01:26:06,960 --> 01:26:12,740
+أو ناقص مين؟ i، يبقى صار عندنا لأن لأن ده بسالب 1
+
+688
+01:26:12,980 --> 01:26:22,820
+و b بـ قد ايش؟ بـ 1، يبقى صار y<sub>c</sub> بدها تساوي c<sub>1</sub> زائد
+
+689
+01:26:22,820 --> 01:26:29,660
+c<sub>2</sub> في t في E<sup>0</sup>، E<sup>0</sup> اللي بـ قد ايش؟ بـ 1
+
+690
+01:26:29,660 --> 01:26:31,260
+زائد
+
+691
+01:26:34,040 --> 01:26:44,800
+يبقى E<sup>-T</sup> في c<sub>3</sub> cos T زائد c<sub>4</sub> sin
+
+692
+01:26:44,800 --> 01:26:49,980
+T، يبقى هذا حلّ الـ y<sub>c</sub>
+
+693
+01:26:50,860 --> 01:26:55,420
+بنروح نجيب الـ particular solution للمعادلة اللي 
+
+694
+01:26:55,420 --> 01:27:00,420
+عندنا اللي هي رقم 1 اللي تحت، هذه المعادلة بطلع 
+
+695
+01:27:00,420 --> 01:27:06,020
+3 تيرمات، الحمد لله ولا واحد زي التلاتة هذه 
+
+696
+01:27:06,020 --> 01:27:08,980
+polynomial في exponential، هذه الـ sin في اللي كل 
+
+697
+01:27:08,980 --> 01:27:13,520
+إيدينا انحطرت، أجزاء المعادلة اللي عندي لك، معادلة
+
+698
+01:27:13,520 --> 01:27:20,240
+لثلاث معادلات، يبقى باجي بقوله the differential
+
+699
+01:27:20,240 --> 01:27:30,720
+equation one is written as Y to the derivative 
+
+700
+01:27:30,720 --> 01:27:36,360
+four زائد 2 triple prime زائد 2 Y double
+
+701
+01:27:36,360 --> 01:27:44,380
+prime يساوي 3 E<sup>st</sup> نفس المعادلة، زائد 2 
+
+702
+01:27:44,380 --> 01:27:45,780
+triple prime
+
+703
+01:27:54,320 --> 01:28:00,220
+نفس المعادلة Y to the derivative of four زائد
+
+704
+01:28:00,220 --> 01:28:05,640
+2 Y triple prime زائد 2 Y double prime
+
+705
+01:28:05,640 --> 01:28:11,360
+يساوي الterm الآخر E<sup>-T</sup> في sin T
+
+706
+01:28:21,570 --> 01:28:28,090
+طيب، يبقى بدنا نجيب Y<sub>1</sub>(t)، هذي polynomial 
+
+707
+01:28:28,090 --> 01:28:34,210
+exponential، يبقى t<sup>s</sup> في ايه؟ في الـ E
+
+708
+01:28:34,210 --> 01:28:43,250
+of t، طبعًا في زيها، يبقى هنا الـ s بـ -t، يبقى هنا الـ
+
+709
+01:28:43,250 --> 01:28:49,850
+s يبقى 0، يبقى هنا الـ s تساوي 0، يبقى صار
+
+710
+01:28:49,850 --> 01:28:55,970
+Y<sub>1</sub>(t) يساوي A E<sup>t</sup> خلصنا من هذه، نيجي
+
+711
+01:28:55,970 --> 01:29:04,110
+لهذه Y<sub>2</sub>(t)، t<sup>s</sup>، هذه polynomial من
+
+712
+01:29:04,110 --> 01:29:10,250
+الدرجة الأولى، يبقى a<sub>0</sub> t زائد a<sub>1</sub> فيه، و
+
+713
+01:29:10,250 --> 01:29:14,110
+E<sup>-t</sup> في t<sup>s</sup>، بتسيب كمان t<sup>s</sup>
+
+714
+01:29:19,400 --> 01:29:22,220
+الـ exponential موجودة بس مضروبة في مين؟ في الـ
+
+715
+01:29:22,220 --> 01:29:27,200
+sine أو الـ cosine؟ ما عنديش، يبقى هنا كمان s بـ 0
+
+716
+01:29:27,200 --> 01:29:34,520
+يبقى الـ s تساوي 0، يبقى Y<sub>2</sub>(t) يساوي a
+
+717
+01:29:34,520 --> 01:29:43,000
+<sub>0</sub> t زائد a<sub>1</sub> في الـ E<sup>-T</sup> نيجي لبعدها، Y<sub>3</sub>
+
+718
+01:29:43,000 --> 01:29:48,110
+as a function of T، t<sup>s</sup>، فيه هذا
+
+719
+01:29:48,110 --> 01:29:54,350
+exponential في الـ Sin، يبقى هنا سمينا a بـ قد ايش أقول 
+
+720
+01:29:54,350 --> 01:29:59,130
+بي، يبقى b
+
+721
+01:29:59,130 --> 01:30:10,340
+في cos T زائد في sin T في الـ a و E<sup>-T</sup>، تعال
+
+722
+01:30:10,340 --> 01:30:16,620
+نشوف هل هذا في تشابه، constant في الـ exponential
+
+723
+01:30:16,620 --> 01:30:20,640
+و الثاني
+
+724
+01:30:20,640 --> 01:30:27,520
+كمان في زيّه، لكن لو حطينا الـ s بواحد، بيتغير تمامًا
+
+725
+01:30:27,520 --> 01:30:35,000
+يبقى باجي بقوله here، الـ s تساوي 1، يبقى صار
+
+726
+01:30:35,000 --> 01:30:40,360
+Y<sub>3</sub> as a function of T هو عبارة عن
+
+727
+01:30:40,360 --> 01:30:49,920
+مين؟ عن t في الـ E<sup>-T</sup> في b cos T زائد d في
+
+728
+01:30:49,920 --> 01:30:56,580
+sin T، بناء عليه شهر الـ Y(t) اللي بدّوا
+
+729
+01:30:56,580 --> 01:31:02,830
+إيّاها، y<sub>1</sub> زائد y<sub>2</sub> زائد y<sub>3</sub>
+
+730
+01:31:02,830 --> 01:31:10,050
+و اللي هي بدها تساوي A في الـ E<sup>t</sup> زائد a<sub>0</sub> t 
+
+731
+01:31:10,050 --> 01:31:19,490
+زائد a<sub>1</sub> في الـ E<sup>-T</sup> زائد t في الـ E<sup> </sup>
+
+732
+01:31:19,490 --> 01:31:28,640
+<sup>-T</sup> في الـ b cos t زائد d في sin t، و هذا
+
+733
+01:31:28,640 --> 01:31:36,440
+هو المطلوب من المسألة، خلاص 
+
+734
+01:31:36,440 --> 01:31:40,360
+قالت احسبش الثوابت، يبقى خلاص لحد هنا، الله يعطينا 
+
+735
+01:31:40,360 --> 01:31:46,020
+عافية، بس بدّه شكل الحل الخاص، و هذا كان نمرّة a من
+
+736
+01:31:46,020 --> 01:31:53,400
+المثلة، بدنا نروح لنمرّة b، نمرّة بسؤال من خارج الكتاب
+
+737
+01:31:53,400 --> 01:32:02,300
+بيقول لك ما يأتي بـ Y to the derivative 4 زائد Y
+
+738
+01:32:02,300 --> 01:32:10,900
+triple prime بدّه يساوي 1 - T تربيع في E<sup> </sup>
+
+739
+01:32:10,900 --> 01:32:11,880
+<sup>-T</sup>
+
+740
+01:32:16,940 --> 01:32:23,280
+يبقى بنا بس الـ particular solution لحلّ اللي عندنا
+
+741
+01:32:23,280 --> 01:32:28,540
+فقط، لغته، يبقى باجي بقوله نفس الـ tactic اللي كنا
+
+742
+01:32:28,540 --> 01:32:39,520
+بنتبعه قبل قليل، let y تساوي E<sup>rt</sup> be a solution
+
+743
+01:32:39,520 --> 01:32:44,960
+of the differential equation، Y to the derivative of
+
+744
+01:32:44,960 --> 01:32:53,080
+4 زائد المشتقة الثالثة، يبقى
+
+745
+01:32:53,080 --> 01:33:02,990
+بناءً عليه، the characteristic equation is r<sup>4</sup>
+
+746
+01:33:02,990 --> 01:33:09,810
+زائد r<sup>3</sup> يساوي 0، أو إن شئت قولنا r
+
+747
+01:33:09,810 --> 01:33:18,320
+<sup>3</sup> في r زائد 1 بتساوي من 0، يبقى r<sub>1</sub> يبقى r<sub>2</sub>
+
+748
+01:33:18,320 --> 01:33:23,760
+يبقى r<sub>3</sub> يبقى r<sub>4</sub> يبقى r<sub>4</sub> يبقى r<sub>2</sub> يبقى r<sub>2</sub> يبقى r<sub>3</sub>
+
+749
+01:33:23,760 --> 01:33:23,940
+يبقى r<sub>4</sub> يبقى r<sub>4</sub> يبقى r<sub>2</sub> يبقى r<sub>4</sub> يبقى r<sub>4</sub> يبقى r<sub>4</sub>
+
+750
+01:33:23,940 --> 01:33:28,800
+يبقى r<sub>4</sub> يبقى r<sub>4</sub> يبقى r<sub>4</sub> يبقى r<sub>4</sub> يبقى r<sub>4</sub> يبقى r<sub>4</sub>
+
+751
+01:33:28,800 --> 01:33:31,500
+يبقى r<sub>4</sub> يبقى r<sub>4</sub> يبقى r<sub>4</sub> يبقى r<sub>4</sub> يبقى r<sub>4</sub> يبقى r<sub>4</sub>
+
+752
+01:33:31,500 --> 01:33:32,340
+يبقى r<sub>4</sub> يبقى r<sub>4</sub> يبقى r<sub>4</sub> يبقى r<sub>4</sub> يبقى r<sub>4</sub> يبقى r<sub>4</sub>
+
+753
+01:33:32,340 --> 01:33:43,880
+يبقى r<sub>4</sub> يبقى r<sub>4</sub> يبقى r<sub>4</sub> يبقى r<sub>4</sub> يبقى r<sub>4</sub>
+
+754
+01:33:43,880 --> 01:33:48,580
+يبقى الآن بدنا نجي لمين؟ لـ Non homogeneous
+
+755
+01:33:48,580 --> 01:33:53,640
+differential equation المعادلة اللي عندنا، واضح إنه
+
+756
+01:33:53,640 --> 01:33:58,060
+تيرمين هذا الـ constant لحاله، ومجموعة مع دالة ثانية
+
+757
+01:33:58,060 --> 01:34:02,900
+مختلفة تمامًا عن الدالة هذه، إذا بنحجز المعادلة إلى
+
+758
+01:34:02,900 --> 01:34:08,900
+معادلتين، فباجي بقول له، لو سميت هذه المعادلة رقم 1
+
+759
+01:34:08,900 --> 01:34:16,440
+بروحي بقول له that differential equation one is
+
+760
+01:34:16,440 --> 01:34:25,720
+written as بكتبها على الشكل التالي، Y to the
+
+761
+01:34:25,720 --> 01:34:31,780
+derivative four زائد Y triple prime بدّها تساوي قد ايش؟
+
+762
+01:34:31,780 --> 01:34:36,540
+1، المعادلة الثانية نفسها، Y to the derivative
+
+763
+01:34:36,540 --> 01:34:43,160
+four زائد Y triple prime بدّها تساوي إنّه - t تربيع
+
+764
+01:34:43,570 --> 01:34:53,010
+في E<sup>-t</sup>، نجي هنا شكلنا بدنا نجيب Y<sub>1</sub>(t)
+
+765
+01:34:57,790 --> 01:35:05,530
+يبقى t<sup>s</sup>، هذه كونستانت بكتبها كونستانت فقط 
+
+766
+01:35:05,530 --> 01:35:10,950
+لا غير بالشكل اللي عندنا هنا، أبنجي نشوف c في t<sup> </sup>
+
+767
+01:35:10,950 --> 01:35:17,170
+<sup>s</sup> كونستانت موجودة، بحط s بـ قد ايش؟ بـ 1،
+
+768
+01:35:17,170 --> 01:35:27,860
+بيصير a t موجودة، a t تربيع موجودة، يبقى s 
+
+769
+01:35:27,860 --> 01:35:36,020
+بـ 3، يبقى هنا s تساوي 3، يبقى صار Y<sub> </sub>
+
+770
+01:35:36,020 --> 01:35:43,180
+<sub>1</sub>(t) a t<sup>3</sup>، شوفت ايش الفرق بين هذا 
+
+771
+01:35:43,180 --> 01:35:47,800
+السؤال و الأسئلة السابقة، يبقى هنا s طلعت بـ 3
+
+772
+01:35:47,800 --> 01:35:52,910
+لا بـ 0 ولا بـ 1، طيب نيجي للتانية هذه، يبقى باجي 
+
+773
+01:35:52,910 --> 01:35:59,350
+لـ Y<sub>2</sub>(t)، t<sup>s</sup>، هذي polynomial
+
+774
+01:35:59,350 --> 01:36:04,350
+من الدرجة الثانية، في من الـ exponential، إذا باجي
+
+775
+01:36:04,350 --> 01:36:15,030
+أقول له a<sub>0</sub> t تربيع، a<sub>1</sub> t، a<sub>2</sub> في E<sup>-t</sup>، بدّي أشوف
+
+776
+01:36:15,030 --> 01:36:19,790
+الـ s بـ قد ايش بعد ما تكون كونستانت في exponential هي 
+
+777
+01:36:19,790 --> 01:36:20,710
+موجودة
+
+778
+01:36:23,620 --> 01:36:29,020
+لو حطيت t بـ 1، بيصير t<sup>3</sup> في الـ exponential مش
+
+779
+01:36:29,020 --> 01:36:34,340
+موجودة، t تربيع في الـ exponential مش موجودة، t في
+
+780
+01:36:34,340 --> 01:36:36,240
+الـ exponential مش موجودة
+
+781
+01:36:39,070 --> 01:36:46,230
+يبقى هنا الـ s تساوي 1، يبقى من هنا عليه أصبح
+
+782
+01:36:46,230 --> 01:36:55,650
+Y<sub>2</sub>(t) يساوي a<sub>0</sub> t<sup>3</sup> زائد a<sub>1</sub> t تربيع
+
+783
+01:36:55,650 --> 01:37:03,380
+زائد a<sub>2</sub> t في الـ E<sup>-t</sup>، يبقى بناء عليه أحصر إن 
+
+784
+01:37:03,380 --> 01:37:12,860
+Y(t) هو y<sub>1</sub> زائد y<sub>2</sub>، y<sub>1</sub> اللي 
+
+785
+01:37:12,860 --> 01:37:22,100
+هو a t<sup>3</sup> زائد y<sub>2</sub> اللي هو a<sub>0</sub> t<sup>3</sup>
+
+786
+01:37:22,100 --> 01:37:27,460
+زائد a<sub>1</sub> t تربيع زائد
+
+787
+01:37:29,010 --> 01:37:37,050
+a<sub>1</sub> t تربيع زائد a<sub>2</sub> t كله في الـ exponential E<sup> </sup>
+
+788
+01:37:37,050 --> 01:37:38,430
+<sup>-T</sup>
+
+789
+01:37:48,900 --> 01:37:55,100
+سالب معناها هذا سالب، لما بدّي أجي أحسب هيك مقادير الـ 
+
+790
+01:37:55,100 --> 01:37:59,840
+constants بتجي معانا، يعني لما بدّي أجي هيك الـ a<sub> </sub>
+
+791
+01:37:59,840 --> 01:38:04,960
+<sub>0</sub> و الـ a<sub>1</sub> و الـ a<sub>2</sub> بتدخل معانا من المعادلة، يعني
+
+792
+01:38:04,960 --> 01:38:13,540
+بيصير ايش؟ بيصير a<sub>1</sub> بدّها تساوي ناقص 1 و الـ a<sub>0</sub> بـ
+
+793
+01:38:13,540 --> 01:38:18,400
+0 و الـ a<sub>2</sub> بـ 0 و هكذا، تمام؟
+
+794
+01:38:20,240 --> 01:38:25,700
+طيب، المرة الجاية إن شاء الله بنكمل يعني المحاضرة
+
+795
+01:38:25,700 --> 01:38:31,700
+القادمة يوم الأربعاء إن شاء الله تعالى بنطلع..
+
+796
+01:38:31,700 --> 01:38:37,340
+بنكمل الـ section اللي ضايل، و بنعطيكم أرقام
+
+797
+01:38:37,340 --> 01:38:39,620
+المسائل على الـ two sections
diff --git a/PL9fwy3NUQKwa8ZDfSFGn6H8xVFLzqmCZC/aLofgEh8GKI_postprocess.srt b/PL9fwy3NUQKwa8ZDfSFGn6H8xVFLzqmCZC/aLofgEh8GKI_postprocess.srt
new file mode 100644
index 0000000000000000000000000000000000000000..91b764c0762e65c09d0676757c291ba2f0bc2790
--- /dev/null
+++ b/PL9fwy3NUQKwa8ZDfSFGn6H8xVFLzqmCZC/aLofgEh8GKI_postprocess.srt
@@ -0,0 +1,3188 @@
+1
+00:00:00,000 --> 00:00:02,580
+موسيقى
+
+2
+00:00:10,460 --> 00:00:14,980
+بسم الله الرحمن الرحيم كنا بتحدث المرة الماضية عن
+
+3
+00:00:14,980 --> 00:00:19,400
+الطريقة الأولى لحل اللي هو ال homogeneous
+
+4
+00:00:19,400 --> 00:00:22,440
+differential equation with constant coefficients
+
+5
+00:00:22,440 --> 00:00:28,420
+وكانت اللي هو طريقة الحل
+
+6
+00:00:28,420 --> 00:00:34,040
+المعادلة المتجانسة عن طريق اللي هو فرض Y تساوي E
+
+7
+00:00:34,040 --> 00:00:40,470
+أس RT وكنا بطلع عندنا أدت احتمالاتاحتمال الحلول
+
+8
+00:00:40,470 --> 00:00:45,490
+تكون او لما نجيب ال characteristic equation احتمال
+
+9
+00:00:45,490 --> 00:00:50,470
+الجذور كلها تبقى حقيقية و مختلفة احتمال تبقى
+
+10
+00:00:50,470 --> 00:00:56,330
+complex احتمال تبقى repeated realممكن تبقى
+
+11
+00:00:56,330 --> 00:01:01,170
+repeated complex على كده الأمرين واخدنا على ذلك
+
+12
+00:01:01,170 --> 00:01:06,270
+ثلاثة أمثلة والأن بنكمل الأمثلة على نفس الموضوع
+
+13
+00:01:06,270 --> 00:01:10,070
+يبقى السؤال لو المثال رقم اثنين بيقول show that
+
+14
+00:01:10,070 --> 00:01:14,090
+the general solution of the differential equationY
+
+15
+00:01:14,090 --> 00:01:18,470
+to the derivative of 4 لما حط الرقم بين جثين تعني
+
+16
+00:01:18,470 --> 00:01:22,130
+المشتقة بدون أقوى C يعني أس يبقى Y to the
+
+17
+00:01:22,130 --> 00:01:25,330
+derivative of 4 minus Y يساوي Zero can be written
+
+18
+00:01:25,330 --> 00:01:31,370
+as يمكن أن نكتب هذا الحل على صيغة C1 Cos T زائد C2
+
+19
+00:01:31,370 --> 00:01:37,690
+Sin T زائد C3 Gosh T زائد C4 Sin T مدام بقول
+
+20
+00:01:37,690 --> 00:01:41,350
+احتمال الحل يكون على الشكل هذا يمكن لما نحل ما
+
+21
+00:01:41,350 --> 00:01:46,450
+يطلعشالشكل هذا اذا طلع كنبة اذا ما طلعش مانتا بدي
+
+22
+00:01:46,450 --> 00:01:51,510
+احول المسألة بحيث فعلا تصير في الشكل اللي عندنا
+
+23
+00:01:51,510 --> 00:01:54,890
+هذا هذا المطلوب الأول بعدين قال لي solve ال
+
+24
+00:01:54,890 --> 00:01:58,170
+initial value problem نفس المثل اللي عندنا بس حط
+
+25
+00:01:58,170 --> 00:02:03,590
+عليه الشروط الأربعة اللي من خلالها بقدر أجيب قيمة
+
+26
+00:02:03,590 --> 00:02:08,910
+الثوابت اللي موجودة عندنا اذا نيجي الحل مع المطلوب
+
+27
+00:02:08,910 --> 00:02:15,910
+الأول اللي هو نمرة Aأفترض أن الحل اللي عندي على
+
+28
+00:02:15,910 --> 00:02:21,190
+الصيغة هو Y تساوي E أُس RT وجيب ال characteristic
+
+29
+00:02:21,190 --> 00:02:27,330
+equation المناظرة لهذه المعادلة بيجي أقول له let Y
+
+30
+00:02:27,330 --> 00:02:33,230
+تساوي E أُس RT بيه solution
+
+31
+00:02:40,410 --> 00:02:47,190
+بعد ذلك الاختصار
+
+32
+00:02:47,190 --> 00:02:55,440
+الوحيد هواللي هو R أس أربعة ناقص واحد يساوي Zero
+
+33
+00:02:55,440 --> 00:03:01,980
+هذه ممكن أحللها كفرق بين المربعين يبقى لو حللناها
+
+34
+00:03:01,980 --> 00:03:07,340
+كفرق بين المربعين بصير R تربيع ناقص واحد في R
+
+35
+00:03:07,340 --> 00:03:13,440
+تربيع زائد واحد يساوي Zero هذه كمان ممكن أحللها
+
+36
+00:03:13,440 --> 00:03:20,280
+كفرق بين المربعينيبقى بالصير R تربيع زائد واحد هذه
+
+37
+00:03:20,280 --> 00:03:25,500
+فرق بين المربعين R ناقص واحد في R زائد واحد يساوي
+
+38
+00:03:25,500 --> 00:03:31,780
+Zero يعني هذه معناته ما لها لا يوجد لها تحليل
+
+39
+00:03:31,780 --> 00:03:38,460
+وبالتالي ال R هتبقى Complex يبقى هذا معناته ان R
+
+40
+00:03:38,460 --> 00:03:47,380
+واحد و اتنيناللي هو بده ساوي زائد او ناقص I وR
+
+41
+00:03:47,380 --> 00:03:53,860
+تلاتة بده ساوي واحد وR اربعة بده ساوي مين ناقص
+
+42
+00:03:53,860 --> 00:03:59,040
+واحد اذا صار شكل الحل على الشكل التالي YC
+
+43
+00:04:23,450 --> 00:04:27,830
+بدي اقارن بين الحل اللي عندي و الحل اللي هو قاله
+
+44
+00:04:28,310 --> 00:04:32,110
+بلاحظ اتنين هذول هما نفس اتنين هذول ماعناش مشكلة
+
+45
+00:04:32,110 --> 00:04:38,150
+فيهم تمام C1 cos T C2 sin T نفس الشيء لكن الخلاف
+
+46
+00:04:38,150 --> 00:04:42,470
+وين؟ خلاف ما بين اتنين هنا معطنية بدالة جوش وسنش
+
+47
+00:04:42,470 --> 00:04:47,070
+هنا معطنية بدالة ال exponential E أس T وE أس ناقص
+
+48
+00:04:47,070 --> 00:04:52,820
+T لو راجعنا بالذاكرة إلى الغراءمن صيغة Euler بقى
+
+49
+00:04:52,820 --> 00:05:01,340
+نقول E أُس I T يكو ساين T زائد I ساين T مظبوط
+
+50
+00:05:01,340 --> 00:05:09,420
+اتنين E أس ناقص I T لكو ساين T ناقص I ساين T تمام
+
+51
+00:05:09,420 --> 00:05:14,440
+يبقى بنحاول نستخدم اللي هو اللي عندنا هنا او
+
+52
+00:05:14,440 --> 00:05:20,080
+نستخدم تعريف الجوش والسنجإذا كنتوا بتدركوا ابيتكوا
+
+53
+00:05:20,080 --> 00:05:23,740
+خاصية اللي درسوا معايا Calculus بيه ان لو جمعت
+
+54
+00:05:23,740 --> 00:05:29,900
+القوش زائد السنش بيعطيني E أس T ولو طرحت القوش
+
+55
+00:05:29,900 --> 00:05:36,480
+ناقص السنش بيعطيني مين E أس ناقص T بنذكركوا تذكير
+
+56
+00:05:36,480 --> 00:05:45,320
+اللي ليس إلا بجينا نقول قوش T زائد سنش T طبعا
+
+57
+00:05:45,320 --> 00:05:53,320
+بتشوفوا قدرش هذا يساويالجوش هي EOS T زائد EOS ناقص
+
+58
+00:05:53,320 --> 00:06:01,280
+T على اتنين هذه جوش السنج كانت EOS T ناقص EOS ناقص
+
+59
+00:06:01,280 --> 00:06:09,150
+T على اتنين لو جمعنا كله على اتنينيبقى المقام هذا
+
+60
+00:06:09,150 --> 00:06:12,950
+هو نفس المقام هذا، إذا بضلي الأربعة بدي أجمعهم،
+
+61
+00:06:12,950 --> 00:06:18,510
+هتروح هذه و هذه مع بعض، بضلي اتنين Eost اللي هو من
+
+62
+00:06:18,510 --> 00:06:27,330
+Eost بنفس الطريقة Similarly اللي
+
+63
+00:06:27,330 --> 00:06:35,960
+هو Gauche ال T ناقصالـ T كل هذا الكلام بدي اسمه
+
+64
+00:06:35,960 --> 00:06:42,930
+مين؟ E أس ناقص Tتمام؟ إذا بدي أجي على الحل اللي
+
+65
+00:06:42,930 --> 00:06:49,210
+عندنا ده اللي بدي أسميه star وانعوض فيه يعني بدي
+
+66
+00:06:49,210 --> 00:06:55,350
+أشيل E أُس T اللي عندي هذه و أكتب بدالها gosh زائد
+
+67
+00:06:55,350 --> 00:07:00,030
+cinch و أشيل E أُس ناقص T و أكتب بدالها gosh ناقص
+
+68
+00:07:00,030 --> 00:07:04,330
+cinch يبقى منان عليه بدي أجي أقول له service
+
+69
+00:07:13,970 --> 00:07:23,350
+نحصل على ما يأتي اله YC اللي هو طالبه C1 Cos T C2
+
+70
+00:07:23,350 --> 00:07:31,910
+Sin T C3 مضروبة في Eost اللي هي main مش C3 كي واحد
+
+71
+00:07:31,910 --> 00:07:38,370
+سمنها كي واحد هي عندي في Eost اللي هي gaucheال T
+
+72
+00:07:38,370 --> 00:07:51,090
+زائد سنش ال T زائد كتنين في جوش ال T ناقص سنش ال T
+
+73
+00:07:53,490 --> 00:08:03,370
+هذا الكلام يساوي C1 cos T C2 sin T زاد الطلاق لهذه
+
+74
+00:08:03,370 --> 00:08:08,230
+فيها جوش وهذه فيها جوش إذا ممكن أخذ منهم جوش عمل
+
+75
+00:08:08,230 --> 00:08:18,150
+مشترك بصير عندي K1 زاد K2 في جوش Tنجي لهذه مضروبة
+
+76
+00:08:18,150 --> 00:08:24,190
+في K واحد وهذه مضروبة في K اتنين يبقى K واحد ناقص
+
+77
+00:08:24,190 --> 00:08:33,650
+K اتنين في سنش T هذا الكلام يساوي C واحد في Cos T
+
+78
+00:08:33,650 --> 00:08:39,850
+C اتنين في Sin T طالعي لهذه K واحد زي K اتنين هذا
+
+79
+00:08:39,850 --> 00:08:48,700
+مقتار ثابتإذن اقتصادي ساميه C3 يبقى زائد C3 في قوش
+
+80
+00:08:48,700 --> 00:08:58,040
+ال T زائد C4 في سنش ال T يبقى شلت هذا حطيت بدله C3
+
+81
+00:08:58,040 --> 00:09:03,260
+و شلت هذا حطيت بدله C4 أظن هي الصيغة اللي طلبها
+
+82
+00:09:03,260 --> 00:09:10,570
+هذهخلصنا يبقى حطنا له الحل على الصيغة اللي هو
+
+83
+00:09:10,570 --> 00:09:15,350
+بدهياه وبالتالي انتهينا من المطلوب الأول من
+
+84
+00:09:15,350 --> 00:09:22,490
+المسألة، المطلوب التاني نمر بيهكيف؟ لما طلعتش
+
+85
+00:09:22,490 --> 00:09:27,070
+الصيغة؟ رصب ان عنك بدها تطلع هذه الصيغة، ليش؟ لإن
+
+86
+00:09:27,070 --> 00:09:30,430
+ال exponential أصلا بدلالة الجوش والسنش، و هو
+
+87
+00:09:30,430 --> 00:09:34,990
+أطاني السؤال، بديها بدلالة الجوش والسنش، تمام؟
+
+88
+00:09:34,990 --> 00:09:38,930
+يبقى فيش مكانية، مدام شيلت ال exponential هذي و ال
+
+89
+00:09:38,930 --> 00:09:42,770
+exponential هذي، لازم تنكتب بدلالة الجوش والسنش،
+
+90
+00:09:42,770 --> 00:09:46,530
+فكيف بداش تطلع؟ لأ انت من الأول، اول ما شرفت
+
+91
+00:09:46,530 --> 00:09:48,030
+السؤال، قلت إذا طلعت
+
+92
+00:09:50,860 --> 00:09:54,020
+معناته لأ مش في حالة تانية، في شغل عندنا بتبقى
+
+93
+00:09:54,020 --> 00:09:58,260
+غلط، طيب؟ لكن الكون هو طلعتنا على شغلنا صح وهو
+
+94
+00:09:58,260 --> 00:10:03,680
+المطلوب جيبناهطيب نجي المطلوب التاني جالي solve ال
+
+95
+00:10:03,680 --> 00:10:08,660
+initial value problem يبقى بدنا نجي هذه المعادلة
+
+96
+00:10:08,660 --> 00:10:11,920
+اللي عندنا أصلا homogeneous هي نفس المعادلة اللي
+
+97
+00:10:11,920 --> 00:10:16,880
+فوق بس حق عليها main ال initial conditions جابلي
+
+98
+00:10:16,880 --> 00:10:21,720
+الدلة بدون اشتقاق مشتقة الأولى التانية التالتة وكل
+
+99
+00:10:21,720 --> 00:10:26,420
+وين عندي ال zero إذا بدأ أجي للمثل اللي عنديها ها
+
+100
+00:10:26,420 --> 00:10:31,980
+وده اشتقها مرة و اتنينو تلاتة و اعوض بال constants
+
+101
+00:10:31,980 --> 00:10:38,340
+اللي عندنا هنايبقى بالدرجة عندي هنا لل Y C Prime Y
+
+102
+00:10:38,340 --> 00:10:48,080
+سواء تفضل cosine بسلب C1 sin T زائد C2 في cosine T
+
+103
+00:10:48,080 --> 00:10:53,520
+طبعا تفضل الجوش بالسنش و تفضل السنش بمان بجوش بدون
+
+104
+00:10:53,520 --> 00:10:57,580
+negative sign ماعنديش إشارة سلب زي ال sign و ال
+
+105
+00:10:57,580 --> 00:11:07,490
+cosine زائد C3 في سنش Tزائد C أربعة في جوش Tبعد
+
+106
+00:11:07,490 --> 00:11:16,430
+هيك بدي YCW' نشتغل كمان مرة يبقى ناقص C1 cos T
+
+107
+00:11:16,430 --> 00:11:30,170
+ناقص C2 sin T زائد C3 في قوش T زائد C4 في سنش T
+
+108
+00:11:30,170 --> 00:11:35,670
+هذا المشتقة الثانية بالمثل بدنا نروح نجيب المشتقة
+
+109
+00:11:35,670 --> 00:11:47,540
+التالتةيبقى بصير C1 في sin T نقص C2 في cos T زائد
+
+110
+00:11:47,540 --> 00:11:51,080
+C3 في sin T
+
+111
+00:11:59,970 --> 00:12:03,470
+يبقى جيبنا المشتقات التلاتة اللي عندنا هذا بدي
+
+112
+00:12:03,470 --> 00:12:07,270
+أرجع لل initial conditions اللي عندنا لل initial
+
+113
+00:12:07,270 --> 00:12:12,410
+conditions الأولاني بيقول لي Y عند ال zero بده
+
+114
+00:12:12,410 --> 00:12:19,410
+تساوي zero وين ال Y هيها؟ يبقى هي Y ب zero تساوي
+
+115
+00:12:19,630 --> 00:12:26,370
+بدأت أشيل كل T و أضع مكانها Zero فالليلة Cos Zero
+
+116
+00:12:26,370 --> 00:12:34,010
+بواحد في C1 بC1 ندى Sin Zero مع السلامة Gosh Zero
+
+117
+00:12:34,010 --> 00:12:41,520
+كذلك بواحديبقى زائد C تلاتة سينشة Zero ب Zero نجي
+
+118
+00:12:41,520 --> 00:12:47,420
+ال condition التاني جالي Y Prime عند Zero كذلك بده
+
+119
+00:12:47,420 --> 00:12:52,700
+يسوي Zero وين Y Prime هي يبقى هذه Zero قصان صفر ب
+
+120
+00:12:52,700 --> 00:12:58,740
+واحد يبقى ب C اتنين سينشة Zero ب Zero مع السلامة
+
+121
+00:12:58,740 --> 00:13:05,220
+جوش Zero ب واحد يبقى زائد C أربعنجي ال condition
+
+122
+00:13:05,220 --> 00:13:09,020
+التالت ال condition التالت بيقولي yw prime عند 0
+
+123
+00:13:09,020 --> 00:13:18,140
+ب1 yw prime عند 0 بده يساوي 1 implies ان ال 1 هي
+
+124
+00:13:18,140 --> 00:13:24,760
+ال yw prime تمام بدنا نعوض عن tb0يبقى ايش بيصير
+
+125
+00:13:24,760 --> 00:13:33,540
+عندي هنا سالب C1 هدب Zero مع السلامة زائد C3
+
+126
+00:13:33,540 --> 00:13:39,200
+والتاني مع السلامة نيجي ال condition التالت جالي Y
+
+127
+00:13:39,200 --> 00:13:44,240
+triple prime عند Zero بده يساوي الواحدemployees
+
+128
+00:13:44,240 --> 00:13:48,640
+واحد بده اعوض في المشتقة التالتة يبقى هدف zero بضل
+
+129
+00:13:48,640 --> 00:13:59,900
+ناقص c2 ناقص c2 وهدف zero زائد c4 يبقى زائد c4
+
+130
+00:13:59,900 --> 00:14:06,380
+اطلعولي للمعادلة الأولى والتالتة بده اجمع الاتنين
+
+131
+00:14:06,380 --> 00:14:13,160
+هدول مع بعضهذول اتنين لو جمعتهم مع بعض بقير سالب
+
+132
+00:14:13,160 --> 00:14:18,780
+C1 مع C1 بيبقى 2C3
+
+133
+00:14:18,780 --> 00:14:21,740
+بيبقى واحد
+
+134
+00:14:22,610 --> 00:14:28,690
+تمام اجمع zero زاد واحد هيب واحد سالب C1 معموجة ب
+
+135
+00:14:28,690 --> 00:14:36,590
+C1 بظل اتنين C3 يساوي واحد ومنها C3 بده يساوي نص
+
+136
+00:14:36,590 --> 00:14:44,650
+طب لما C3 يساوي نص C1 بيبقى كدهش بسالب نص و C1
+
+137
+00:14:44,650 --> 00:14:51,040
+يساوي سالب نص بدهش اجمع المعادلة التانيةمع
+
+138
+00:14:51,040 --> 00:14:58,080
+المعادلة من الرابع اجمع ZERO واحد بده يعطيكي واحد
+
+139
+00:14:58,080 --> 00:15:08,060
+بده يساوي نجمع C2 مع C2 يبقى بيضلي 2C4 يبقى 2C4
+
+140
+00:15:08,060 --> 00:15:17,060
+ومنها C4 يسوى قداش نص لما C4 بده يسوى نص يبقى C2
+
+141
+00:15:17,060 --> 00:15:25,520
+بسالب نصوC2 يساوي سالب نص إذا نقدر نجيه بالشكل
+
+142
+00:15:25,520 --> 00:15:32,360
+العام لحل ال initial value problem يبقى الحل صار
+
+143
+00:15:32,360 --> 00:15:39,530
+YC يساويبدا يجي الى C1 C1 طلع عندنا بناقص نص يبقى
+
+144
+00:15:39,530 --> 00:15:48,690
+ناقص نص cos T وC2 طلع عندنا بناقص نص كذلك يبقى
+
+145
+00:15:48,690 --> 00:15:58,070
+ناقص نص في sin T وC3 طلع بنص يبقى زائد نص اللي هو
+
+146
+00:15:58,070 --> 00:16:06,680
+cos Tو C4 يبقى
+
+147
+00:16:06,680 --> 00:16:14,100
+زائد نص في سن شتتي يبقى ده حل ال initial value
+
+148
+00:16:14,100 --> 00:16:15,680
+problem اللي عندنا
+
+149
+00:16:29,090 --> 00:16:31,930
+طبعا المرة اللى فاتت ماحلناش ال national value
+
+150
+00:16:31,930 --> 00:16:37,390
+problem وماعطناش ولا سؤال بهذه الطريقة هي بقى نعمل
+
+151
+00:16:37,390 --> 00:16:43,720
+فيه تحويرة مشان نطلع شكل الجوابنعطيكم كمان مثال
+
+152
+00:16:43,720 --> 00:16:50,100
+على نفس الموضوع برضه يختلف حما و نوعا و ماحلناش
+
+153
+00:16:50,100 --> 00:16:56,860
+زيه من قبل يبقى بنجي للمثال الرقم تلاتة لسؤال واحد
+
+154
+00:16:56,860 --> 00:17:04,320
+و عشرين من الكتاب بيقول solve the differential
+
+155
+00:17:04,320 --> 00:17:09,800
+equation حل المعادلة التفاضلية why to the
+
+156
+00:17:09,800 --> 00:17:16,870
+derivative eightزائد ات واي to the derivative four
+
+157
+00:17:16,870 --> 00:17:36,930
+زائد ست عشر واي بده يساوي قداش بده يساوي زي المرة
+
+158
+00:17:36,930 --> 00:17:42,700
+اللي باتت كده بتذكروا قلنافيه عنده والحاجة real
+
+159
+00:17:42,700 --> 00:17:46,960
+and unequal roots وخلصنا منها واخدنا عليها أمثلة
+
+160
+00:17:46,960 --> 00:17:51,140
+بعدها قولنا complex roots واخدنا عليها أحيانا real
+
+161
+00:17:51,140 --> 00:17:54,800
+و أحيانا complex جينا لل repeated roots قولنا ممكن
+
+162
+00:17:54,800 --> 00:17:59,200
+تبقى repeated و real أو ممكن تبقى repeated و
+
+163
+00:17:59,200 --> 00:18:03,580
+complex repeated و complex ماشوفناش ولا مثال حتى
+
+164
+00:18:03,580 --> 00:18:10,040
+اللحظة تمام؟ لكن هي و جاييبقى هذا repeated complex
+
+165
+00:18:10,040 --> 00:18:15,320
+conjugate roots نشوف كيف نتعامل معاه يبقى بنفس
+
+166
+00:18:15,320 --> 00:18:18,760
+التكتيكة اللي بدأت بالمثال اللي جابله هبدأ في حاجة
+
+167
+00:18:18,760 --> 00:18:29,160
+أقوله هنا let Y تساوي E أُس RTBA solution of
+
+168
+00:18:29,160 --> 00:18:35,460
+equation one سمي لها D one then the
+
+169
+00:18:39,250 --> 00:18:48,830
+Equation is R أس تمانية زائد تمانية R أس أربعة
+
+170
+00:18:48,830 --> 00:18:55,950
+زائد ستاشر يساوي زيرو أظن أن هذه لو جيتها حللتها
+
+171
+00:18:55,950 --> 00:19:00,770
+بيصير عندي ايش بيصير عندي R أس أربعة
+
+172
+00:19:06,570 --> 00:19:11,850
+أربعة كل هذا الكلام بده يساوي Zero يعني الجوس
+
+173
+00:19:11,850 --> 00:19:17,870
+الأول هو من نفس الجوس التاني يعني اللي هأعمل للجوس
+
+174
+00:19:17,870 --> 00:19:21,430
+الأول بدي أعمل للجوس التاني يعني أصلا الجذور مالها
+
+175
+00:19:21,430 --> 00:19:28,010
+مكررة طيب بدي أخد واحد من الجواس يبقى أرقص أربعة
+
+176
+00:19:28,010 --> 00:19:32,510
+بده يساوي قداش أظن لما ناخد الجذر التربيهي أبصي
+
+177
+00:19:32,510 --> 00:19:41,250
+كمية حيوليةطيب طلع معايا كويس يبقى ال R تساوي ناقص
+
+178
+00:19:41,250 --> 00:19:51,230
+أربع أس رابع يعني كأنها أربع أس رابع في ناقص واحد
+
+179
+00:19:51,230 --> 00:19:58,410
+أس رابع، مصبوط؟ طيب أربع أس رابع عبارة عن جذري
+
+180
+00:19:58,410 --> 00:20:05,770
+اتنينلأن أس ربع يعني أس نص لكل أس نص أربع أس نص
+
+181
+00:20:05,770 --> 00:20:12,150
+باتنين أس نص يعني جذر اتنين يبقى آلة إلى جذر اتنين
+
+182
+00:20:12,150 --> 00:20:20,170
+في سالب واحد أس مين أس ربع هذه قيمة R طيب تعالى
+
+183
+00:20:20,170 --> 00:20:26,720
+هدول كام جذر بدهم يطلعوا هنا؟أربعة جذور لان هذه
+
+184
+00:20:26,720 --> 00:20:31,560
+معدلة من درجة رابع اربعة جذور وكمان مكررة يبقى بدى
+
+185
+00:20:31,560 --> 00:20:36,440
+كمان اربعة جذور اخرى اذا جبنا الأربعة جذور هذه
+
+186
+00:20:36,440 --> 00:20:40,820
+بصير الشغل روتينيا بصير complex conjugated
+
+187
+00:20:40,820 --> 00:20:50,520
+repeatedكمبليكس ومكررة ومترافقة يبقى أنا بدأ أجيب
+
+188
+00:20:50,520 --> 00:20:56,980
+الجذور التخيلية للسالب واحد الأربعة جذور هذي قداش
+
+189
+00:20:56,980 --> 00:21:01,200
+شوفوا هالطريقة اللي بنحسبه بهالجذور وبدك تعتمديها
+
+190
+00:21:01,200 --> 00:21:06,000
+بعد هيك لأي سؤال آخر بنفس الطريقة في بعض الأسئلة
+
+191
+00:21:06,000 --> 00:21:10,690
+في التمرين لازالت على نفس الموضوعطيب يا ماناتى،
+
+192
+00:21:10,690 --> 00:21:18,030
+الان لو جيتلى الرقم ناقص واحد، أليس هو ناقص واحد
+
+193
+00:21:18,030 --> 00:21:25,010
+زائد zero في I؟ Zero اللي هو في I، I ب zero زائد
+
+194
+00:21:25,010 --> 00:21:28,950
+ناقص واحد هو ناقص واحد، ماساويتش شيء، كويب؟ طيب،
+
+195
+00:21:28,950 --> 00:21:33,710
+بدي أكتب دلالة ال cosine و ال sine، قداش cosine
+
+196
+00:21:33,710 --> 00:21:39,900
+مية و تمانين يا بنات؟اذا بدى اقول هذا cosine 180
+
+197
+00:21:39,900 --> 00:21:47,860
+فقداش صين المية و تمانين Zero يبقى
+
+198
+00:21:47,860 --> 00:21:57,200
+زائد I في صين المية و تمانينسمعته بصيغة Euler اللي
+
+199
+00:21:57,200 --> 00:22:02,800
+هي E أس I ثيتا يساوي cosine ثيتا زائد I sine ثيتا
+
+200
+00:22:02,800 --> 00:22:12,340
+تمام يبقى طبقا لصيغة Euler هذه E أس I باي يعني اي
+
+201
+00:22:12,340 --> 00:22:19,100
+باي انذاكر ابقى E أس I ثيتا يساوي cosine ثيتا زائد
+
+202
+00:22:19,100 --> 00:22:29,160
+I sine ثيتاوE أس سالب I ثيتا يساوي Cos θ ناقص I
+
+203
+00:22:29,160 --> 00:22:37,000
+sin ثيتا هذه هي هذه بس بختلفوا عن بعضهذا يكون اقص
+
+204
+00:22:37,000 --> 00:22:42,280
+اي في سالب ثيتا يعني ال cosine لسالب ثيتا ال
+
+205
+00:22:42,280 --> 00:22:46,620
+cosine even يبقى هي ال cosine ثيتا اي ال sine
+
+206
+00:22:46,620 --> 00:22:51,020
+لسالب ثيتا ال sine قد يبقى سالب بطلع برا يبقى سالة
+
+207
+00:22:51,020 --> 00:22:55,690
+ال cosine ثيتا ناقص اي في ال sine ثيتاخلّي هذه
+
+208
+00:22:55,690 --> 00:22:59,450
+المعلومتين عندك و الأن هذي احنا بنشتغل عليهم يبقى
+
+209
+00:22:59,450 --> 00:23:09,030
+اذا cosine باي زائد I sin باي هي E أس I باي طيب
+
+210
+00:23:09,030 --> 00:23:13,210
+ايش رأيك الزاوية اللي عندها دي لو ضفت لها دورات
+
+211
+00:23:13,210 --> 00:23:19,550
+كاملة اتنين باي اربعة باي ستة باي هل تتأثرلأ طب
+
+212
+00:23:19,550 --> 00:23:24,090
+بدى اضافلها وشوف يمكن الله يحلها شوية يبقى صار
+
+213
+00:23:24,090 --> 00:23:33,530
+السلب عندى واحد هو cosine باي زائد اتنين M باي و
+
+214
+00:23:33,530 --> 00:23:37,750
+ال M بتاخد واحد و اتنين و تلاتة الى ما شاء الله
+
+215
+00:23:37,750 --> 00:23:51,380
+زائد I sine اللي هو مين باي زائد اتنين M بامن M by
+
+216
+00:23:51,380 --> 00:23:57,460
+دورات كاملة لا تؤثر على القيمة على الإطلاق يعني يا
+
+217
+00:23:57,460 --> 00:24:06,200
+بنات هذه بيصير E أُس I باي زائد اتنين M by و ال M
+
+218
+00:24:06,200 --> 00:24:11,380
+تسوى Zero و واحد و اتنين و تلاتة و زي ما بدك إلى
+
+219
+00:24:11,380 --> 00:24:17,020
+مال نهاية كلها بتعطيني نفس القيمة طيب كويس هذا
+
+220
+00:24:17,020 --> 00:24:23,490
+مين؟هذا كله قيمة من؟ سالب واحد كتبته على شكل
+
+221
+00:24:23,490 --> 00:24:27,730
+complex number بهذا الشكل طيب احنا بدنا سالب واحد
+
+222
+00:24:27,730 --> 00:24:33,730
+قص جداش يبقى بده اجيبله سالب واحد قص رابع يبقى لو
+
+223
+00:24:33,730 --> 00:24:40,730
+قلت سالب واحد قص رابع هيساوي E قص I في باي زائد
+
+224
+00:24:40,730 --> 00:24:50,080
+اتنين M باي كل هذا قص رابعهذا أس مركب يعني بنضرب
+
+225
+00:24:50,080 --> 00:24:58,240
+الأسس في بعضها ضرب يبقى هذه بدأت ساوي E أس I في ال
+
+226
+00:24:58,240 --> 00:25:09,220
+πاي على أربع زائد M باي على اتنين بنفع؟ اه طيب
+
+227
+00:25:09,220 --> 00:25:17,030
+ممتاز جدا طيب هذه بتجيب لي كام جذربتجيبلي مالة
+
+228
+00:25:17,030 --> 00:25:23,930
+نهاية من الجذور M0 1 2 3 4 5 اساسي زي ما بدك بس
+
+229
+00:25:23,930 --> 00:25:28,390
+انا مابديش مالة نهاية مكفن من اربعة جذور يعني هذا
+
+230
+00:25:28,390 --> 00:25:32,230
+بتنفع للاربعة جذور وبتنفع للتلت جذور وبتنفع للست
+
+231
+00:25:32,230 --> 00:25:37,350
+جذور وبتنفع للمية جدر قد ما عندك أسس بتقدر تشتغل
+
+232
+00:25:37,350 --> 00:25:42,140
+اللي بدكي يعنييبقى هذا بنات من الآن فصلة سالب واحد
+
+233
+00:25:42,140 --> 00:25:46,700
+أس أي أس بده يساوي ال exponential وحط الأس اللي
+
+234
+00:25:46,700 --> 00:25:49,680
+بدك إياه هاي حطينا الأس اللي بدنا إياه اللي هو
+
+235
+00:25:49,680 --> 00:25:53,360
+موجود عندنا سار الشكل اللي عندنا على الشكل هذي بده
+
+236
+00:25:53,360 --> 00:26:00,660
+أحط MB0 بجيب الجذرين المترافقين الأولين بحط M
+
+237
+00:26:00,660 --> 00:26:04,920
+بواحد B تنين بتلاتة بجيب الأربعة الجذور اللي أنا
+
+238
+00:26:04,920 --> 00:26:13,210
+بدي إياهايبقى هنا بدى اقعد اخد M تساوي Zero واحد و
+
+239
+00:26:13,210 --> 00:26:18,990
+اتنين و تلتة ايه الاربع و الباقي مش لازم ليه طيب
+
+240
+00:26:18,990 --> 00:26:27,470
+لو اخدت M بي Zero م بي Zero يبقاش مصير عندي E أس I
+
+241
+00:26:27,470 --> 00:26:36,220
+Pi على أربع مظلوم؟طيب لو أخدت M بواحد يبقى بيصير I
+
+242
+00:26:36,220 --> 00:26:43,600
+باي على أربع زائد باي على اتنين يبقى اذا أخدت M
+
+243
+00:26:43,600 --> 00:26:49,460
+بواحد بيصير باي على اتنين بيصير ربع و نص بقدرش تلت
+
+244
+00:26:49,460 --> 00:27:00,020
+ربع يبقى هذه ل E أس I تلت ربع بايطيب بده ياخد M ب
+
+245
+00:27:00,020 --> 00:27:06,340
+2 يبقى لو أخدنا M ب 2 بتروح مع 2 بصير باي زائد باي
+
+246
+00:27:06,340 --> 00:27:12,060
+على أربع يعني كم؟ واحد و ربع باي يعني خمسة باي على
+
+247
+00:27:12,060 --> 00:27:20,280
+أربع يبقى E أس I خمسة باي على أربع خلصنا اتنين
+
+248
+00:27:20,280 --> 00:27:25,480
+بروح نحط مين؟ تلاتة يبقى بصير تلاتة على اتنين و
+
+249
+00:27:25,480 --> 00:27:35,440
+كم؟يبقى اي اس اي يبقى اي اس اي يبقى اي اس اي يبقى
+
+250
+00:27:35,440 --> 00:27:38,740
+اي اس اي يبقى اي اس اي يبقى اي اس اي يبقى اي اس اي
+
+251
+00:27:38,740 --> 00:27:39,320
+يبقى اي اس اي يبقى اي اس اي يبقى اي اس اي يبقى اي
+
+252
+00:27:39,320 --> 00:27:39,940
+اس اي يبقى اي اس اي يبقى اي اس اي يبقى اي اس اي
+
+253
+00:27:39,940 --> 00:27:41,400
+يبقى اي اس اي يبقى اي اس اي يبقى اي اس اي يبقى اي
+
+254
+00:27:41,400 --> 00:27:44,060
+اس اي يبقى اي اس اي يبقى اي اس اي يبقى اي اس اي
+
+255
+00:27:44,060 --> 00:27:49,800
+يبقى اي اس اي يبقى
+
+256
+00:27:54,240 --> 00:28:04,320
+Four roots are هنا جذري اتنين في المقدار هذا يبقى
+
+257
+00:28:04,320 --> 00:28:10,580
+جذري اتنين بده يضرب في كل واحدة من هذولمظبوط يبقى
+
+258
+00:28:10,580 --> 00:28:19,240
+هاي جذر 2 في E أس I باية على أربعة جذر 2 في E أس I
+
+259
+00:28:19,240 --> 00:28:27,120
+تلاتة باية على أربعة جذر 2 في E أس I خمسة باية على
+
+260
+00:28:27,120 --> 00:28:33,900
+أربعة جذر 2 في E أس I سبعة باية على أربعة
+
+261
+00:28:36,470 --> 00:28:42,690
+طب كويس بدي أجيب كل واحدة من ال exponential بدلالة
+
+262
+00:28:42,690 --> 00:28:46,870
+lambda والي ميو مش احنا الحال بقيا نقول lambda
+
+263
+00:28:46,870 --> 00:28:53,190
+زائد I ميو والتانية lambda ناقص I ميو إذا بدي أجيب
+
+264
+00:28:53,190 --> 00:28:57,990
+الجذور بهذه الشكلة كيف؟ بدي أرجع أكتب هذه بدلالة
+
+265
+00:28:57,990 --> 00:29:01,820
+القاعدة اللي عندييعني بدي اكتبها الحل اللي هو ال
+
+266
+00:29:01,820 --> 00:29:09,260
+cos pi على 4 زائد I sin pi على 4 يبقى هاي جذيري
+
+267
+00:29:09,260 --> 00:29:18,880
+اتنين في اللي هو مين cos pi على 4 زائد I sin pi
+
+268
+00:29:18,880 --> 00:29:26,660
+على 4هذا الأولاني التاني و جذر اتنين في cosine
+
+269
+00:29:26,660 --> 00:29:34,740
+تلاتة pi على اربعة زائد I sine تلاتة pi على اربعة
+
+270
+00:29:35,300 --> 00:29:45,760
+واللي بعده جذري 2 في cos 5pi على 4 زائد i sin 5pi
+
+271
+00:29:45,760 --> 00:29:56,400
+على 4 والاخير جذري 2 في cos 7pi على 4 زائد i sin
+
+272
+00:29:56,400 --> 00:30:00,960
+7pi على 4 بالشكل اللي عندنا
+
+273
+00:30:25,670 --> 00:30:29,610
+فاحصوا معايا كمان مرة بدي أعطيكم نص في الـ soufflé
+
+274
+00:30:29,610 --> 00:30:35,290
+لإنه بدنا نكمل بدنا نبني عليه و نكمل طبعا هذه
+
+275
+00:30:35,290 --> 00:30:38,510
+فرضنا الحل على الشكل هذا طلعت ال characteristic
+
+276
+00:30:38,510 --> 00:30:44,050
+equation بالشكل هذاأخذت جوز منهم أخذت الجدر الرابع
+
+277
+00:30:44,050 --> 00:30:48,670
+اللي اقترفين صار له جدر اتنين في سالب واحد أس ربع
+
+278
+00:30:48,670 --> 00:30:54,150
+بدي اعرف قداش الجذور تبعت السالب واحد الأربعة جذور
+
+279
+00:30:54,150 --> 00:30:59,070
+فجيت جوز له سالب واحد سالب واحد زيرو في I كوصين
+
+280
+00:30:59,070 --> 00:31:03,490
+مية و تمانين بسالب واحد سين مية و تمانين بزيرو اذا
+
+281
+00:31:03,490 --> 00:31:08,420
+ال term هذا كتبته على الشكل هذاطبقا لصيغة Euler
+
+282
+00:31:08,420 --> 00:31:15,200
+يبقى هذا E-I-Y الزوايا هدول لو ضفتلهم دورات كاملة
+
+283
+00:31:15,200 --> 00:31:19,900
+ماعندي مشكلة لا تتغير القيمةيعني هذا اللي بيعتبره
+
+284
+00:31:19,900 --> 00:31:25,560
+periodic functions دوال دورية اذا الناقص واحد اص
+
+285
+00:31:25,560 --> 00:31:29,880
+ربع اذا الناقص واحد هو ال cosine باي زائد اتنين M
+
+286
+00:31:29,880 --> 00:31:34,440
+باي و ال M Zero واحد و اتنين و تلاتة و اربعة و
+
+287
+00:31:34,440 --> 00:31:38,120
+خمسة الى ما شاء الله و هنا ال sine باي زائد اتنين
+
+288
+00:31:38,120 --> 00:31:41,880
+M باي اللي بقدر اكتبه E اص I باي زائد اتنين M باي
+
+289
+00:31:41,880 --> 00:31:46,520
+و هذه قيم ال Mأنا مابدي سالب واحد وانا مابدي سالب
+
+290
+00:31:46,520 --> 00:31:50,560
+واحد أس ربع فقولت سالب واحد أس ربع إذا بدي يسوى ال
+
+291
+00:31:50,560 --> 00:31:55,140
+exponential كلها أس ربع هذا الأس مركب يبقى بضرب
+
+292
+00:31:55,140 --> 00:31:59,900
+الأسوس في بعضها ضرب يبقى لما نقضه بالأسوس في بعضها
+
+293
+00:31:59,900 --> 00:32:06,220
+بيصير باي على أربعة وهذه م باي على اتنين لأنه على
+
+294
+00:32:06,220 --> 00:32:10,080
+أربعة تختصر بيصير م باي على اتنين بالشكل اللي
+
+295
+00:32:10,080 --> 00:32:16,450
+عندنا هذاماشي تمام بده نجيب الاربعة جذور مرة واحد
+
+296
+00:32:16,450 --> 00:32:20,130
+بمرة أخرى تلاتة بمرة أخرى
+
+297
+00:32:29,740 --> 00:32:34,240
+هنا حطيت ال M بواحد باي على أربع زائد باي على
+
+298
+00:32:34,240 --> 00:32:38,960
+اتنين اللي هو تلت تربع باي حطيت ال M باتنين بيصير
+
+299
+00:32:38,960 --> 00:32:41,940
+مع اتنين بتروح بيضال باي على أربع زائد باي يعني
+
+300
+00:32:41,940 --> 00:32:46,720
+واحد و ربع باي يعني خمسة على أربع باي حطيتها
+
+301
+00:32:46,720 --> 00:32:50,100
+بتلاتة تلاتة على اتنين يعني واحد و نص باي وربع
+
+302
+00:32:50,100 --> 00:32:55,010
+باتنين اللي ربع يعني سبعة باي على أربعالان بدأ
+
+303
+00:32:55,010 --> 00:32:58,590
+اكتب هذه بالصيغة Euler بدلالة ال cosine والصين
+
+304
+00:32:58,590 --> 00:33:03,710
+فروحنا كتبناها كل واحدة من الجذور الأربعة بدلالة
+
+305
+00:33:03,710 --> 00:33:08,230
+ال cosine والصين بعد ما دخلنا جذر اتنين اللي خلناه
+
+306
+00:33:08,230 --> 00:33:11,610
+ورانا في الأول يبقى صلة ال roots على الشكل اللي
+
+307
+00:33:11,610 --> 00:33:17,650
+عندنا هذا الان جتا خمسة واربعينواحد على جذر اتنين
+
+308
+00:33:17,650 --> 00:33:22,690
+وجيب الخمسة واربعين واحد على جذر اتنين يبقى شكل ال
+
+309
+00:33:22,690 --> 00:33:28,950
+road صار بالشكل هذا هاي جذر اتنين في واحد على جذر
+
+310
+00:33:28,950 --> 00:33:36,410
+اتنين زائد I على جذر اتنين هذا الأول التاني جذر
+
+311
+00:33:36,410 --> 00:33:43,390
+اتنين فيههنا جت ال 135 بي على الرابعة خمسة واروية
+
+312
+00:33:43,390 --> 00:33:47,130
+تلاتة بمية خمسة في الرابعة التانية ال cosine سالب
+
+313
+00:33:47,130 --> 00:33:51,790
+يبقى و cosine بي على الرابعة بيشارات سالب يعني
+
+314
+00:33:51,790 --> 00:34:00,310
+سالبوحد على جذر اتنين زائد I على جذر اتنين ليش؟
+
+315
+00:34:00,310 --> 00:34:04,570
+لان جيب الخمسة و رمعين بيساوي جيب المية و خمسة و
+
+316
+00:34:04,570 --> 00:34:09,350
+تلاتين في الربع الثاني الجيب بيكون بإشارة من موجب
+
+317
+00:34:09,350 --> 00:34:14,050
+نيجي للي بعدها جذر
+
+318
+00:34:14,050 --> 00:34:21,340
+اتنين فيبنجي هنا cosine خمسة باي على أربع خمسة و
+
+319
+00:34:21,340 --> 00:34:26,380
+أربعين في خمسة اللي هو بمتين و خمسة و عشرين يعني
+
+320
+00:34:26,380 --> 00:34:31,600
+في الرابع التالت يبقى ال cosine بالثالث لازم يطلع
+
+321
+00:34:31,600 --> 00:34:38,220
+هذا المرافق لواحد فيهميبقاش بيصير هنا سالب واحد
+
+322
+00:34:38,220 --> 00:34:43,800
+على جذر اتنين و
+
+323
+00:34:43,800 --> 00:34:49,840
+ال sign كمان هذي في الرابع التالت كمان بإشارة سالب
+
+324
+00:34:50,030 --> 00:34:57,790
+يبقى ناقص I على اتنين يبقى ناقص I على جدر اتنين
+
+325
+00:34:57,790 --> 00:35:03,490
+بالشكل هذا هطلعي هذا و هذا هما المترافقين صحيح ولا
+
+326
+00:35:03,490 --> 00:35:08,950
+لا؟ طب تقدروا بدون مرجع للحسابات تقولولي قداش اللي
+
+327
+00:35:08,950 --> 00:35:16,270
+ضايل هذا؟اللي هو المراتق لهذا اللي هو واحد على جدر
+
+328
+00:35:16,270 --> 00:35:22,870
+اتنين ناقص I على من؟ على جدر اتنين بتدخل جدر اتنين
+
+329
+00:35:22,870 --> 00:35:30,830
+جوا يبقى ده اش بصير واحد زائد I ناقص واحد زائد I
+
+330
+00:35:30,830 --> 00:35:40,400
+وناقص واحد ناقص I وواحد ناقص Iطلعيلي في اتنين هدول
+
+331
+00:35:40,400 --> 00:35:47,020
+هدول مترافقين مع بعض صحيح ولا لا؟ و هدول اتنين
+
+332
+00:35:47,020 --> 00:35:54,240
+كمان مترافقين مع بعض يبقى conjugate يبقى هذه
+
+333
+00:35:54,240 --> 00:36:02,430
+الجذور المترافقة طيب هدول كم جذر ابنات؟أربعة جذور،
+
+334
+00:36:02,430 --> 00:36:07,770
+لسه في أربعة زيهم، مظبوط؟ لإن احنا أخدنا هنا جزء
+
+335
+00:36:07,770 --> 00:36:12,230
+واحد فقط، و لسه كمان بقى الجذور بيبقى في أربعة
+
+336
+00:36:12,230 --> 00:36:18,890
+جذور زيهم، يبقى الجذور complex and repeated تمام؟
+
+337
+00:36:18,890 --> 00:36:23,770
+يبقى بده نعرف ما هو شكل الحل في هذه الحالة، يبقى
+
+338
+00:36:23,770 --> 00:36:32,640
+باجي بقوله YC to 7نمسك الأولاني هنا هنا Lambda
+
+339
+00:36:32,640 --> 00:36:41,680
+بقداش بواحد و ميو بواحد يبقى بالداجي اقوله C1 زي
+
+340
+00:36:41,680 --> 00:36:45,760
+اه طبعا قبل هيبقى نكتب Lambda Lambda بنات هنا اللي
+
+341
+00:36:45,760 --> 00:36:52,020
+هي مين E أس Lambda اللي هي بواحد يبقى E أس T في
+
+342
+00:36:52,020 --> 00:37:03,170
+مين في C1 زي C2 في T في Cos Tزائد C ثلاثة زائد C
+
+343
+00:37:03,170 --> 00:37:12,370
+أربعة T في sign ال T هذول كام حل؟ كام واحد هذول
+
+344
+00:37:12,370 --> 00:37:17,330
+كتم؟ لسه بتكتب كمان؟ هذول أربعة حلول يعني جيبنا
+
+345
+00:37:17,330 --> 00:37:22,520
+الحلو المقرر تبعه فكتبنا على الشكل هنامتذكرين لما
+
+346
+00:37:22,520 --> 00:37:28,000
+كنا real و ده بقى نقول C1 زي C2 T E و S T هنا جان
+
+347
+00:37:28,000 --> 00:37:33,740
+ال cosine و ال sine يبقى هنا complex و مكرر خلصنا
+
+348
+00:37:33,740 --> 00:37:38,610
+تبعت ال E و S T بدنا نجيب تبعت مين؟الـ E أُس سالق
+
+349
+00:37:38,610 --> 00:37:44,810
+يعني احنا خلصنا هذا وهذا يبقى
+
+350
+00:37:44,810 --> 00:37:53,730
+زائد E أُس ناقص T اللي هي Lambda خدنا ستة C خمسة
+
+351
+00:37:53,730 --> 00:37:56,390
+زائد C ستة T
+
+352
+00:38:10,310 --> 00:38:15,530
+كتابتها يبقى هاي
+
+353
+00:38:15,530 --> 00:38:19,790
+بصير حل ال homogenous differential equation من
+
+354
+00:38:19,790 --> 00:38:26,130
+الرتبة الثامنة complex و مكرر زي ما انتوا شايفينه
+
+355
+00:38:27,540 --> 00:38:32,740
+حد بتحب تسأل اي سؤال؟ انت هنا احنا مستقشن بناء على
+
+356
+00:38:32,740 --> 00:38:37,340
+هذا طيب
+
+357
+00:38:37,340 --> 00:38:43,220
+وصلنا لل exercises يبقى بدالي لل exercises اربعة
+
+358
+00:38:43,220 --> 00:38:54,470
+اتنين المسائل من واحد او من 11 لغاية 24القد و
+
+359
+00:38:54,470 --> 00:39:01,990
+المسائل من تسعة و عشرين لغاية خمسة و تلتين و من
+
+360
+00:39:01,990 --> 00:39:05,630
+الحجهم كمان سؤال تمانية و تلتين
+
+361
+00:39:25,470 --> 00:39:28,450
+لحد هنا أوقف بالنسبة للـ homogeneous differential
+
+362
+00:39:28,450 --> 00:39:32,170
+equation بدنا نروح للـ non-homogeneous
+
+363
+00:39:32,170 --> 00:39:36,710
+differential equation و اليوم ناخد أول طريقة فقط
+
+364
+00:39:36,710 --> 00:39:40,750
+اللي هو طريقة الـ undetermined coefficients يبقى
+
+365
+00:39:40,750 --> 00:39:49,050
+بنيجي ل section 4-3 اللي هو the method of
+
+366
+00:39:49,050 --> 00:39:54,570
+undetermined
+
+367
+00:39:54,570 --> 00:39:54,930
+coefficients
+
+368
+00:40:00,570 --> 00:40:06,510
+نفس الطريقة اللي أخدناها لل second order ناخدها لل
+
+369
+00:40:06,510 --> 00:40:15,330
+ninth order يبقى consider the differential
+
+370
+00:40:15,330 --> 00:40:24,430
+equation y to the derivative n مضروبة في ال a0زائد
+
+371
+00:40:24,430 --> 00:40:30,510
+a1 y to the derivative n minus ال 1 زائد ونظل
+
+372
+00:40:30,510 --> 00:40:37,450
+ماشيين لغاية ما نوصل لل a n minus ال 1 y a prime
+
+373
+00:40:37,450 --> 00:40:44,090
+زائد ال a n y بده يساوي ال g of t وسميلي المعادلة
+
+374
+00:40:44,090 --> 00:40:49,610
+هذه رقم 1 The
+
+375
+00:40:49,610 --> 00:40:51,810
+solution
+
+376
+00:40:53,610 --> 00:41:07,790
+of the differential equation one is Y تساوي YC
+
+377
+00:41:07,790 --> 00:41:20,850
+زائد capital Y of T where حيث YC is the solution
+
+378
+00:41:24,830 --> 00:41:32,030
+هذه هي الحلقة للإيقاع
+
+379
+00:41:32,030 --> 00:41:35,150
+الهوموجينيوز
+
+380
+00:41:35,150 --> 00:41:36,310
+الهوموجينيوز الهوموجينيوز الهوموجينيوز
+
+381
+00:41:36,310 --> 00:41:38,110
+الهوموجينيوز الهوموجينيوز الهوموجينيوز
+
+382
+00:41:38,110 --> 00:41:40,570
+الهوموجينيوز الهوموجينيوز الهوموجينيوز
+
+383
+00:41:40,570 --> 00:41:40,650
+الهوموجينيوز الهوموجينيوز الهوموجينيوز
+
+384
+00:41:40,650 --> 00:41:41,050
+الهوموجينيوز الهوموجينيوز الهوموجينيوز
+
+385
+00:41:41,050 --> 00:41:41,070
+الهوموجينيوز الهوموجينيوز الهوموجينيوز
+
+386
+00:41:41,070 --> 00:41:45,510
+الهوموجينيوز الهوموجينيوز الهوموجينيوز
+
+387
+00:41:45,510 --> 00:41:49,750
+الهوموجينيوز الهوموجين
+
+388
+00:41:50,270 --> 00:41:58,690
+زائد زائد a n minus ال one في ال y prime زائد a n
+
+389
+00:41:58,690 --> 00:42:07,950
+في ال y بده ساوي مين zero and capital Y of T is a
+
+390
+00:42:07,950 --> 00:42:16,850
+particular solution is a particular solution هو
+
+391
+00:42:16,850 --> 00:42:31,150
+الحل الخاصof the differential equation one we
+
+392
+00:42:31,150 --> 00:42:41,470
+use the method of undetermined coefficients
+
+393
+00:42:41,470 --> 00:42:45,850
+undetermined
+
+394
+00:42:45,850 --> 00:42:47,910
+coefficients
+
+395
+00:43:17,810 --> 00:43:21,570
+الشكل الخاص according
+
+396
+00:43:25,620 --> 00:43:31,240
+to the following table
+
+397
+00:50:22,480 --> 00:50:28,220
+نرجع لموضوع الـ Undetermined coefficients طبعا لما
+
+398
+00:50:28,220 --> 00:50:32,540
+قرأت هذا الكلام وجدته لم يختلف شيئا عن ال second
+
+399
+00:50:32,540 --> 00:50:36,920
+order differential equations مظبوط فبجباجي بقول
+
+400
+00:50:36,920 --> 00:50:39,720
+method of undetermined coefficients طريقة
+
+401
+00:50:39,720 --> 00:50:43,760
+المعاملات المجهولة المعادلة في صيغتها العامة اللي
+
+402
+00:50:43,760 --> 00:50:48,060
+هو ال non-homogeneous بالشكل اللي عندنا هذاالـ
+
+403
+00:50:48,060 --> 00:50:52,820
+solution تبع ال equation one هو عبارة عن جزءين حل
+
+404
+00:50:52,820 --> 00:50:56,920
+ال homogeneous ذات حل خاص لل non homogeneous نجمع
+
+405
+00:50:56,920 --> 00:51:01,900
+الاتنين بيعطيني الحل ال general solution لل non
+
+406
+00:51:01,900 --> 00:51:05,580
+homogeneous differential equation يبقى YC هو حل ال
+
+407
+00:51:05,580 --> 00:51:09,420
+homogeneous differential equation اللي عندنا وYT
+
+408
+00:51:09,420 --> 00:51:14,040
+هو الحل الخاص للمعادلة الأساسية اللي هي واحد بس
+
+409
+00:51:14,040 --> 00:51:18,530
+بشرطلما نستخدم الـ Undetermined coefficients بد
+
+410
+00:51:18,530 --> 00:51:23,450
+المعاملات دول ثوابت زي ما انت شايفينهم بدها G of T
+
+411
+00:51:23,450 --> 00:51:29,490
+تبقى على شكل معين يبقى has a particular form G of
+
+412
+00:51:29,490 --> 00:51:32,930
+T بدت تبقى على شكل خاص according to the following
+
+413
+00:51:32,930 --> 00:51:37,830
+table طبقا للجدول التالف لو كانت ال G of T
+
+414
+00:51:37,830 --> 00:51:41,550
+polynomial يبقى بدي أقوله T to the power S في
+
+415
+00:51:41,550 --> 00:51:46,040
+polynomial مناضرة لألو كان polynomial في
+
+416
+00:51:46,040 --> 00:51:49,400
+exponential يكبر T to the power S polynomial في
+
+417
+00:51:49,400 --> 00:51:53,440
+exponential لو كان polynomial في exponential في
+
+418
+00:51:53,440 --> 00:52:01,320
+cosine BT أو sin BT أو مجموعهما أو الفرق فيما
+
+419
+00:52:01,320 --> 00:52:05,600
+بينهما على كل الأربعة أمور بدي اكتب T to the power
+
+420
+00:52:05,600 --> 00:52:11,260
+S polynomial من الدرجة رقم M في ال cosineزاد
+
+421
+00:52:11,260 --> 00:52:15,600
+polynomial تانية من الدرجة m في ال sign وكل هذا
+
+422
+00:52:15,600 --> 00:52:20,920
+مضروب في main في ال exponential دلت قصة ال S هذه
+
+423
+00:52:20,920 --> 00:52:25,160
+جداش يمكن zero تطلع يمكن واحد يمكن اتنين يمكن
+
+424
+00:52:25,160 --> 00:52:28,500
+تلاتة يمكن اربعة يمكن خمسة في second order
+
+425
+00:52:28,500 --> 00:52:32,200
+برينجوليا zero وواحد واتنين بس واحدة من التلات قيم
+
+426
+00:52:32,550 --> 00:52:41,110
+لكن في ال order from 1,2,0,1,2,3,4,5,10 لغاية ال N
+
+427
+00:52:41,110 --> 00:52:49,410
+يبقى ال S هو أصغر رقم موجب صحيح بحيث انه ماعنديش
+
+428
+00:52:49,410 --> 00:52:55,890
+ولا term في ال YT بده يساوي term in YC يبقى
+
+429
+00:52:55,890 --> 00:53:00,990
+differs يختلف from every term in the solution YC
+
+430
+00:53:01,270 --> 00:53:07,530
+بدي كل term في capital YT يختلف عن اي term موجود
+
+431
+00:53:07,530 --> 00:53:11,110
+في الحل اللي هو YC حل ال homogenous differential
+
+432
+00:53:11,110 --> 00:53:14,730
+equation أظن ماجيبناها شي جديد هو هو اللي تبقى
+
+433
+00:53:14,730 --> 00:53:19,570
+second order بس عمّمناه زي ما أنتوا شايفين طيب
+
+434
+00:53:19,570 --> 00:53:22,610
+بدنا نبدأ طب حد رفيكوا تسأل أسئلة جابي المدخل في
+
+435
+00:53:22,610 --> 00:53:26,470
+الأمثلة ايش
+
+436
+00:53:26,470 --> 00:53:40,780
+طيبيبقى اول
+
+437
+00:53:40,780 --> 00:53:46,840
+شغلة نبدأ فيها هي حل الهوموجينيس يبقى باجي بقوله
+
+438
+00:53:46,840 --> 00:53:57,020
+let Y تساوي E أس RT BA solution of the
+
+439
+00:54:10,310 --> 00:54:18,070
+يبقى باجي بقول ذي characteristic equationof
+
+440
+00:54:18,070 --> 00:54:26,470
+equation اتنين is R تكيب زائد اربعة R تساوي كدهاش
+
+441
+00:54:26,470 --> 00:54:32,850
+Zero ومنها R في R تربيع زائد اربعة بيساوي كدهاش
+
+442
+00:54:32,850 --> 00:54:40,830
+Zero يبقى ال R تساوي Zero R واحد وR اتنين و تلاتة
+
+443
+00:54:40,830 --> 00:54:49,360
+بده يساوي زائد او ناقص اتنين Iانه كمية تخيلية يبقى
+
+444
+00:54:49,360 --> 00:54:57,960
+هذا بدي اعطيك شكل ال Y C بديه ساوى C واحد في E أس
+
+445
+00:54:57,960 --> 00:55:04,760
+Zero بواحد مع السلامة هذي بده يصير الزاد لمدة
+
+446
+00:55:04,760 --> 00:55:11,370
+ماعنديش ماعنديش الا ميويبقى هنا بجي بقوله c3 cos
+
+447
+00:55:11,370 --> 00:55:20,930
+2t c4 sin 2t و ببروزها لإني بدي أرجعلها بعد قليل
+
+448
+00:55:20,930 --> 00:55:25,310
+الان بدنا نجي نجيب main ال particular solution
+
+449
+00:55:25,310 --> 00:55:33,130
+للمعادلة رقم واحد فبجي بقوله هنا capital Y of T
+
+450
+00:55:33,130 --> 00:55:40,020
+بده يساوي نجي بطلعPolynomial من الدرجة الأولى يبقى
+
+451
+00:55:40,020 --> 00:55:44,900
+باكتب له T to the power S وبحف بينه same
+
+452
+00:55:44,900 --> 00:55:50,000
+polynomial من الدرجة الأولى اللي هو A naught T
+
+453
+00:55:50,000 --> 00:55:56,560
+زائد ال A1 وبقول له استنى شوية هك وتعالى نشوف قداش
+
+454
+00:55:56,560 --> 00:56:02,400
+قيمة Sبغطي هذا term واجب اخطلع للمقدار بين القوسين
+
+455
+00:56:02,400 --> 00:56:10,800
+هل اي term هنا يشبه اي term من الترمات هدول هذا
+
+456
+00:56:10,800 --> 00:56:15,500
+constant وهذا constant يبقى فيه تشابه إذا بدى أحط
+
+457
+00:56:15,500 --> 00:56:22,640
+s بقدرش؟ بواحد لو حطيت s بواحد هذه تدخل جوا بصير
+
+458
+00:56:22,640 --> 00:56:30,630
+a0t تربية زائد a1tفى تشابه بين هدول معاهى term هنا
+
+459
+00:56:30,630 --> 00:56:35,830
+لأ يبقى اللى بتحل الاشكالية فقط S تساوي واحد يبقى
+
+460
+00:56:35,830 --> 00:56:42,350
+باجى بقوله here ال S تساوي واحد يبقى هدف بده
+
+461
+00:56:42,350 --> 00:56:49,810
+يعطينى انه capital Y of T هو عبارة عن a node T
+
+462
+00:56:49,810 --> 00:56:59,750
+تربية زائد a one Tتمام؟ الان بدى اروح اطلع قداش
+
+463
+00:56:59,750 --> 00:57:05,070
+قيمة اللى هو ال a node و ال a1 و قاعد هيك بنرجع
+
+464
+00:57:05,070 --> 00:57:09,690
+لمين لل general solution اذا لازم اللى اشتقها كام
+
+465
+00:57:09,690 --> 00:57:17,330
+مرة؟ ثلاث مرات اذا بدى اروح اجيبله y prime of t ب2
+
+466
+00:57:17,330 --> 00:57:27,090
+a node t زائد a1بالزملة YOTWP
+
+467
+00:57:27,090 --> 00:57:35,570
+نشتق كمان مرة باتنين نوت هذه مع السلامة وهذه مشتقة
+
+468
+00:57:35,570 --> 00:57:40,690
+التاب واحد بدنا المشتقة من التانية يبقى جيبنا
+
+469
+00:57:40,690 --> 00:57:44,970
+المشتقة الثانية خلصنا منها بس بدنا نروح نجيب من
+
+470
+00:57:44,970 --> 00:57:51,920
+المشتقة التالتة يبقىهذا بدى يعطيك ان المشتقة
+
+471
+00:57:51,920 --> 00:57:57,960
+التالتة يكبتل Y triple A prime of T بدى يسوى قداش
+
+472
+00:57:57,960 --> 00:58:03,760
+Zero لان اتنين مقدار ثابت والاينود مقدار ثابت نرجع
+
+473
+00:58:03,760 --> 00:58:08,520
+نعوض وين في المعادلة اللى هي رقم واحد اللى عندنا
+
+474
+00:58:08,520 --> 00:58:20,160
+يبقى باجي بقوله هنا substitute in equation oneو جت
+
+475
+00:58:20,160 --> 00:58:23,760
+يبقى بيدنا نرجع لل equation one
+
+476
+00:58:45,930 --> 00:58:51,650
+يبقى y triple prime ب zero يبقى هي ال zero راح و
+
+477
+00:58:51,650 --> 00:58:57,590
+عندك اربعة في y prime وين y prime هي يبقى بصير
+
+478
+00:58:57,590 --> 00:59:06,910
+تمانية a node t زائد تمانية a node t زائد اربعة a
+
+479
+00:59:06,910 --> 00:59:07,230
+one
+
+480
+00:59:17,860 --> 00:59:21,000
+نعمل مقارنة ما بين الطرفين نعمل مقارنة ما بين
+
+481
+00:59:21,000 --> 00:59:23,800
+الطرفين نعمل مقارنة ما بين الطرفينيبقى تمانية a
+
+482
+00:59:23,800 --> 00:59:29,040
+note بده يسوى قداش امانات واحد هذا بده يعطيك ان a
+
+483
+00:59:29,040 --> 00:59:34,900
+note يسوى قداش تمان اللي بعدها اربعة a one بده
+
+484
+00:59:34,900 --> 00:59:41,060
+يسوى من زيرو يبقى ال a one بده يسوى من زيرو يبقى
+
+485
+00:59:41,060 --> 00:59:47,860
+صار شكل ال Y of T على الشكل التاليبرجع لل Y of T
+
+486
+00:59:47,860 --> 00:59:52,720
+اللى عندنا اللى همين ال Y of T هايه يبقى هنا S
+
+487
+00:59:52,720 --> 00:59:56,100
+بواحد صار بالشكل اللى عندنا هذا بدي اشيل A نوع ده
+
+488
+00:59:56,100 --> 01:00:00,980
+و أحط مكانها تمون و هذا ب Zero مع السلامة يبقى صار
+
+489
+01:00:00,980 --> 01:00:08,330
+تمون T تاربيعيبقى هنا تمن T تربية يبقى بناء عليه Y
+
+490
+01:00:08,330 --> 01:00:14,030
+تساوي YC زائد capital Y of T Y الساوية YC اللي
+
+491
+01:00:14,030 --> 01:00:25,130
+بروزناها فوق يبقى C1 زائد C3 C2 Cos T زائد C3 في
+
+492
+01:00:25,130 --> 01:00:25,890
+ال sign
+
+493
+01:00:34,120 --> 01:00:43,570
+بنضيف عليهم capital Y of T بكتوم ت تربيعطيب حتى
+
+494
+01:00:43,570 --> 01:00:47,450
+الآن ما استخدمتش ال initial conditions يبقى بدي
+
+495
+01:00:47,450 --> 01:00:51,610
+اري على ال initial conditions اللي انا بدي اشتق
+
+496
+01:00:51,610 --> 01:00:58,850
+مرتين يبقى باجي بقوله y' يساوي هذا مع السلامة
+
+497
+01:00:58,850 --> 01:01:08,900
+وتفضل cos بسالب 2C2 في sin 2Tوزائد اتنين C تلاتة
+
+498
+01:01:08,900 --> 01:01:20,760
+كوصين اتنين T وزائد رابعة T وين الخطأ؟ why C؟ اه C
+
+499
+01:01:20,760 --> 01:01:26,920
+اتنين يعني هذه بنفسها هو C اتنين وهذه C تلاتة C
+
+500
+01:01:26,920 --> 01:01:34,660
+اتنين وC تلاتة ماشييبقى هنا c1 زي c2 زي c3 مظبوط
+
+501
+01:01:34,660 --> 01:01:39,340
+هي يبقى اشتقانا و الاشتقاق صحيح مافيش فيه اي مشكلة
+
+502
+01:01:39,340 --> 01:01:45,480
+تمام طيب بدنا نجيب yw prime يساوي نشتق هذه كمان
+
+503
+01:01:45,480 --> 01:01:53,340
+مرة يبقى ناقص اربعة c2 كوصين اتنين t ناقص اربعة c
+
+504
+01:01:53,340 --> 01:02:00,830
+تلاتة صين اتنين t زائد رابطعلى ال condition
+
+505
+01:02:00,830 --> 01:02:04,030
+الأولاني
+
+506
+01:02:04,030 --> 01:02:08,510
+يجب ان يكون y عند ال zero يسوى 0 y عند ال zero
+
+507
+01:02:08,510 --> 01:02:13,130
+يسوى 0 يبقى
+
+508
+01:02:13,130 --> 01:02:20,610
+هدى c1 كسين صفر بواحد زايد c2 هدى بزيره مع السلامة
+
+509
+01:02:20,610 --> 01:02:25,800
+و هدى بزيره مع السلامة كله يسوى كده؟الـ Condition
+
+510
+01:02:25,800 --> 01:02:31,860
+التاني y' عند 0 يكون سوى 0 ومن هنا نجي لهذه بـ 0
+
+511
+01:02:31,860 --> 01:02:39,940
+بقير هذا كوصين صفر بواحد يبقى هنا اتنين C ثلاثة
+
+512
+01:02:39,940 --> 01:02:46,080
+وهذا بـ 0 بقير يكون سوى كده؟ يكون سوى 0 الـ
+
+513
+01:02:46,080 --> 01:02:52,310
+Condition التالت y'' عند 0 أظن يكون سوى 1مظبوط
+
+514
+01:02:52,310 --> 01:03:00,830
+يبقى هذا بده يعطيك YW Prime هايها اللي هو ناقص 4C2
+
+515
+01:03:00,830 --> 01:03:06,810
+و هذا مع السلامة و هذا زائد رابع بده يساوي مين؟
+
+516
+01:03:06,810 --> 01:03:11,770
+بده يساوي Zero من هذه أمانات بقدر أقول إذا C3
+
+517
+01:03:11,770 --> 01:03:20,610
+تساوي Zeroتمام؟ نجي من هنا بقدر أجيبله كمان C2
+
+518
+01:03:20,610 --> 01:03:31,730
+يبقى هذا معناه انه ايش الواحد؟ اه بتسوي واحد صحيح
+
+519
+01:03:31,730 --> 01:03:37,070
+حقه يبقى هذه تسوي واحد مظبوطيبقى هدى معناه هذا
+
+520
+01:03:37,070 --> 01:03:46,480
+معناه انه سالب اربعة C اتنين يساوي تلت ربعربع بيجي
+
+521
+01:03:46,480 --> 01:03:50,980
+بالسلبان واحد بيظل تلات تربع يبقى هذا بدي اعطيك
+
+522
+01:03:50,980 --> 01:04:01,400
+انه C2 بده يساوي سالب تلاتة على ستاش لما C2 بده
+
+523
+01:04:01,400 --> 01:04:06,760
+يساوي سالب تلاتة على ستاش اذا C1 بتلاتة على ستاش
+
+524
+01:04:06,760 --> 01:04:15,020
+وC3 بده يساوي تلاتة على ستاش وين الواحد؟
+
+525
+01:04:19,430 --> 01:04:28,510
+سي تلاتة خليكي معايا هالحين هذا سي اتنين ابتلاتة
+
+526
+01:04:28,510 --> 01:04:32,830
+على عربي و سي اتنين ابسالب تلاتة على ستاشر بدي
+
+527
+01:04:32,830 --> 01:04:37,690
+اعوض الان سي اتنين ابسالب تلاتة على ستاشر انجليه
+
+528
+01:04:37,690 --> 01:04:44,190
+على الشجة التانيةبصير اه C1 يسوي 3 ع 16 اه C1 هذي
+
+529
+01:04:44,190 --> 01:04:49,170
+C1 ب 3 ع 16 مظبوط اذا بدي بيصير شكل المعادلة شكل
+
+530
+01:04:49,170 --> 01:04:57,910
+الحل على الشكل التالي Y يسوي C1 اللي هي 3 ع 16و C2
+
+531
+01:04:57,910 --> 01:05:09,130
+هو ناقص 3 على 16 في cos 2t و C3 بزير و بطير ال
+
+532
+01:05:09,130 --> 01:05:17,010
+term هذا و بظل بس 8T تربيع يبقى هذا الشكل الحل تبع
+
+533
+01:05:17,010 --> 01:05:19,630
+ال initial value problem
+
+534
+01:05:41,520 --> 01:05:51,580
+المثال الثاني مثال
+
+535
+01:05:51,580 --> 01:05:57,940
+اتنين find
+
+536
+01:05:57,940 --> 01:06:00,520
+the general solution of the differential equation
+
+537
+01:06:10,110 --> 01:06:14,750
+of the differential equation الي هو y to the
+
+538
+01:06:14,750 --> 01:06:23,930
+derivative 4 ناقص y بده يساوي تلاتة T زائد cosine
+
+539
+01:06:23,930 --> 01:06:32,750
+ال T وسميه لهذا المعادلة رقم 1 نفس الطريقة اللي
+
+540
+01:06:32,750 --> 01:06:41,010
+بدأنا فيها solution يبقى بالدهجة أقوله letY تساوي
+
+541
+01:06:41,010 --> 01:06:51,350
+E أس RT با solution of Y to the derivative 4 ناقص
+
+542
+01:06:51,350 --> 01:06:57,250
+Y يساوي Zero هذا بدي أعطيك ان ال characteristic
+
+543
+01:06:57,250 --> 01:07:05,970
+equation is R أربعة ناقص واحد يساوي Zero إذا صارت
+
+544
+01:07:05,970 --> 01:07:11,950
+R ترابيع ناقص واحدفى R تربيه زياد واحد يساوي Zero
+
+545
+01:07:11,950 --> 01:07:19,050
+يبقى R ناقص واحد فى R زاد واحد فرق بين المربعين
+
+546
+01:07:19,050 --> 01:07:26,930
+يساوي Zero يبقى R تساوي واحد وR تساوي سالب واحد
+
+547
+01:07:26,930 --> 01:07:33,610
+هذه R واحد هذه R اتنين وهذه R تلاتة واربعةاللي هو
+
+548
+01:07:33,610 --> 01:07:39,110
+بدر سوى زائد او ناقص I يبقى صار حل ال homogenous
+
+549
+01:07:39,110 --> 01:07:49,850
+YC بدر سوى C1 E أس T C2 E أس ناقص T زائد C تلاتة
+
+550
+01:07:49,850 --> 01:08:00,210
+cosine T زائد C أربعة في صينة T كويس بالدالي لشكل
+
+551
+01:08:00,210 --> 01:08:06,530
+G of Tبنعمل من الدرجة الأولى الزائد كوصين وليست
+
+552
+01:08:06,530 --> 01:08:11,390
+مضروبة درجة إذا بنرجع لطريقتنا الميان اللي عتيجة
+
+553
+01:08:11,390 --> 01:08:18,330
+أني أجزء المعادلة إلى معادلتين فبجي بقوله ذا
+
+554
+01:08:18,770 --> 01:08:27,150
+differential equation one is written as وروح
+
+555
+01:08:27,150 --> 01:08:33,570
+بكتبها y to the derivative four ناقص y يسوي تلاتة
+
+556
+01:08:33,570 --> 01:08:40,790
+T التانية y to the derivative four ناقص y يسوي cos
+
+557
+01:08:40,790 --> 01:08:50,450
+T بدنا نيجي لهذه capital Y one of TY1 of T بيبقى
+
+558
+01:08:50,450 --> 01:08:51,390
+Y1 of T بيبقى Y1 of T بيبقى Y1 of T بيبقى Y1 of T
+
+559
+01:08:51,390 --> 01:08:52,210
+بيبقى Y1 of T بيبقى Y1 of T بيبقى Y1 of T بيبقى Y1
+
+560
+01:08:52,210 --> 01:08:54,570
+of T بيبقى Y1 of T بيبقى Y1 of T بيبقى Y1 of T
+
+561
+01:08:54,570 --> 01:08:54,790
+بيبقى Y1 of T بيبقى Y1 of T بيبقى Y1 of T بيبقى Y1
+
+562
+01:08:54,790 --> 01:08:54,850
+of T بيبقى Y1 of T بيبقى Y1 of T بيبقى Y1 of T
+
+563
+01:08:54,850 --> 01:08:56,990
+بيبقى Y1 of T بيبقى Y1 of T بيبقى Y1 of T بيبقى Y1
+
+564
+01:08:56,990 --> 01:09:11,650
+of T بيبقى Y1 of T بيبقى Y1
+
+565
+01:09:11,650 --> 01:09:19,050
+of T بيبقلأ يبقى باجي بقوله here ال S تساوي 0 إذا
+
+566
+01:09:19,050 --> 01:09:27,030
+صار capital Y1 of T بدي ساوي a naught T زائد a عنه
+
+567
+01:09:27,030 --> 01:09:36,390
+بالمرة نخلصه يالا هاتي لي Y1 prime a naught وال Y1
+
+568
+01:09:36,390 --> 01:09:47,630
+double prime ب0وY1'' بزيرو وY4'' بدو ساوي زيرو
+
+569
+01:09:47,630 --> 01:09:56,310
+نعود في المعادلة يبقى هاي زيرو ناقص Y ناقص Y هيها
+
+570
+01:09:56,310 --> 01:10:07,650
+يبقى ناقص A0 T ناقص A1 بدو ساوي تلاتة Tو منها ناقص
+
+571
+01:10:07,650 --> 01:10:15,260
+a0 بده يسوى تلاتةيبقى a0 بده يساوي كده؟ سالب تلاتة
+
+572
+01:10:15,260 --> 01:10:21,620
+و سالب a1 بده يساوي Zero يبقى ال a1 بده يساوي Zero
+
+573
+01:10:21,620 --> 01:10:30,640
+يبقى أصبح Y1 as a function of T بده يساوي عندك ال
+
+574
+01:10:30,640 --> 01:10:39,450
+a0 بسالب تلاتة يبقى هاي سالب تلاتة T فقط ما غيرنجي
+
+575
+01:10:39,450 --> 01:10:48,170
+للتانية هادي بدنا نجيب Y2 Y2 as a function of T
+
+576
+01:10:48,170 --> 01:10:55,510
+هادي T to the power S في هنا اللي هو polynomial من
+
+577
+01:10:55,510 --> 01:11:01,970
+ضرر الصفر يعني A cosine T زائد B في sine T
+
+578
+01:11:05,830 --> 01:11:10,790
+المعامل هو واحد صحيح يعني دالة من الدرجة الصفرية
+
+579
+01:11:10,790 --> 01:11:15,990
+فقلنا كونوسين في كوسين زي كونوسين في من في صين نجي
+
+580
+01:11:15,990 --> 01:11:21,070
+المقدار بين القوسين في تشابه مع اي term هنا اه في
+
+581
+01:11:21,070 --> 01:11:26,570
+تشابه هذا بيشبه هذا و هذا بيشبه هذا يبقى بدي احط
+
+582
+01:11:26,570 --> 01:11:33,760
+اس بقداش بواحد لو حطيت اس بواحدبصير AT cos T مافيش
+
+583
+01:11:33,760 --> 01:11:38,540
+زيها و BT sin T كمان مافيش زيها يبقى ال S عيندي
+
+584
+01:11:38,540 --> 01:11:44,240
+هنا بيبقى داشر بواحد يبقى باجي بقوله here ال S
+
+585
+01:11:44,240 --> 01:11:50,940
+تساوي واحد يبقى بناء عليه سار كابتل Y2 of T بيبقى
+
+586
+01:11:50,940 --> 01:12:01,730
+ساوي AT cos T زائد BT في sin Tنشتق أربع مرات و
+
+587
+01:12:01,730 --> 01:12:09,170
+نعود في الدالة اللى فوق يبقى يبقى y2 prime يبقى a
+
+588
+01:12:09,170 --> 01:12:17,670
+cosine of t ناقص a t في sine of t نشتق هذه يبقى
+
+589
+01:12:17,670 --> 01:12:26,980
+زائد b في sine of tزائد بي تي في كوصين التين كل
+
+590
+01:12:26,980 --> 01:12:32,920
+واحدة فيهم مشتقت حاصل ضرب دالتين فرعان واضع
+
+591
+01:12:32,920 --> 01:12:38,900
+اختصارات مافيش يبقى بظل كل شي زي ما هو لإن هذي
+
+592
+01:12:38,900 --> 01:12:45,600
+كوصين هناك تي في كوصين ولا واحد زي التانيةY2W'
+
+593
+01:12:46,280 --> 01:12:57,780
+يبقى سالب A في صينة T و سالب A في صينة T و سالب A
+
+594
+01:12:57,780 --> 01:13:07,720
+T في قصينة Tمشتقة الأولى هي بإشارة سالب وهذه
+
+595
+01:13:07,720 --> 01:13:14,320
+حصل ضرب داليتين تبقى سالب a sin t و سالب a t تفضل
+
+596
+01:13:14,320 --> 01:13:19,810
+sin ب cos خلصنا أول two terms بداجي لمين؟لـ two
+
+597
+01:13:19,810 --> 01:13:29,390
+terms التانية يبقى زائد بي في cosine ت زائد بي في
+
+598
+01:13:29,390 --> 01:13:39,390
+cosine ت ناقص بي ت في sine ت يبقى اشتقنهم طلع هذه
+
+599
+01:13:39,390 --> 01:13:47,690
+هي هذه مظبوط يبقى هذه بيصير ناقص اتنين ا في sine t
+
+600
+01:13:48,250 --> 01:13:59,070
+وهذه هي هذه يبقى ازايد 2B في cos T بيبقى عندى ناقص
+
+601
+01:13:59,070 --> 01:14:08,150
+AT في cos T وناقص BT في sin T بدنا نروح نجيب
+
+602
+01:14:08,150 --> 01:14:15,760
+المشتقة الثالثةيساوى نشتق كمان مرة يبقى هاي ناقص
+
+603
+01:14:15,760 --> 01:14:23,120
+اتنين a cosine of t ناقص اتنين b في sine of t
+
+604
+01:14:23,120 --> 01:14:27,260
+خلصنا اول two terms بنانيجى لل two terms اللي
+
+605
+01:14:27,260 --> 01:14:33,750
+بعتهم كل واحدة فيهم مشتقت حصل ضربدالتين يبقى مشتقة
+
+606
+01:14:33,750 --> 01:14:45,010
+الأولى بناقص a cos t زائد at في sin t وناقص b في
+
+607
+01:14:45,010 --> 01:14:58,420
+sin t وناقص bt في cos tانجمعهم يبقى هنا بصير ناقص
+
+608
+01:14:58,420 --> 01:15:09,520
+ثلاثة A في Cos T و هنا ناقص ثلاثة B في Sin T و
+
+609
+01:15:09,520 --> 01:15:20,040
+زائد A T في Sin T و ناقص B T في Cos T
+
+610
+01:15:22,110 --> 01:15:29,650
+انجيب المشتقة الرابعة يالا اخر مشتقة يبقى Y اتنين
+
+611
+01:15:29,650 --> 01:15:42,260
+المشتقة الرابعة بده يساوي تلاتةتلاتة a sin t ناقص
+
+612
+01:15:42,260 --> 01:15:52,840
+تلاتة b في cos t زائد a في sin t زائد a في sin t
+
+613
+01:15:52,840 --> 01:16:06,210
+زائد at في cos t ناقص b في cos t زائد btفى الـ
+
+614
+01:16:06,210 --> 01:16:30,050
+sign 80 نجمعهم
+
+615
+01:16:30,740 --> 01:16:39,720
+يبقى صارت المشتقة الرابعة as a function of T و7
+
+616
+01:16:39,720 --> 01:16:46,460
+قلين تلاتة A sin وكمان A sin يبقى أربعة A sin يبقى
+
+617
+01:16:46,460 --> 01:16:56,170
+أربعة A sin T ناقص أربعة B في cos Tمظبوط لاخص
+
+618
+01:16:56,170 --> 01:17:01,290
+اربعة بي في cosine of T ضال عندي زائد AT في cosine
+
+619
+01:17:01,290 --> 01:17:10,650
+of T زائد AT في cosine of T وعندك زائد BT في sine
+
+620
+01:17:10,650 --> 01:17:18,950
+of T زائد BT في sine of T اللي هو بنرجع العموض في
+
+621
+01:17:18,950 --> 01:17:23,530
+المعادل اللي فوق تمام يبقى بدي Y
+
+622
+01:17:29,300 --> 01:17:36,970
+واللي بيه عندك كمان قداش ناقص Yهذه المرحلة تتساوي
+
+623
+01:17:36,970 --> 01:17:40,490
+بالكوصينة
+
+624
+01:17:40,490 --> 01:17:51,250
+T وY تنزلها زي ما هي 4A في كوصينة T نقص 4B في
+
+625
+01:17:51,250 --> 01:17:52,790
+كوصينة T
+
+626
+01:17:56,820 --> 01:18:04,280
+زي ال B T في صينة T ناقص Y وين ال Y هايها بده
+
+627
+01:18:04,280 --> 01:18:11,380
+اضربها بإشارة سالب يبقى ايش بصير أبناء سالب A T
+
+628
+01:18:11,380 --> 01:18:19,500
+Cos T سالب B T في صينة Tيبقى هدول التنتيج الملهوم
+
+629
+01:18:19,500 --> 01:18:25,320
+مع السلامة يبقى صار عند مين؟ y to the derivative
+
+630
+01:18:25,320 --> 01:18:36,800
+for ناقص y يسوى 4a sin t ناقص 4b cos t كله سيسوى
+
+631
+01:18:36,800 --> 01:18:46,860
+cos t اللي على اليمين هذا سيسوى cos tتمام نقد
+
+632
+01:18:46,860 --> 01:18:52,820
+مقارنة ما بين الطرفين يبقى أربعة A تساوي Zero
+
+633
+01:18:52,820 --> 01:19:02,080
+ومنها A تساوي Zero وعندك سالب أربعة B تساوي معامل
+
+634
+01:19:02,080 --> 01:19:10,910
+الكوصين بواحد يبقى B تساوي سالب رابعيبقى بناء عليه
+
+635
+01:19:10,910 --> 01:19:19,050
+أصبح Y2 as a function of T بده يساوي ال A قولنا
+
+636
+01:19:19,050 --> 01:19:24,910
+مقدش B0 يبقى طاري ال term الأول وال B بسالب رابع
+
+637
+01:19:24,910 --> 01:19:32,450
+في T في صيني T مظلوم يبقى هاي جيبنا Y2
+
+638
+01:19:34,590 --> 01:19:44,170
+Y يبقى Y يسوى YC يبقى Y يسوى
+
+639
+01:19:44,170 --> 01:19:51,690
+Y يسوى Y يسوى Y يسوى Y يسوى Y
+
+640
+01:19:51,690 --> 01:20:04,780
+يسوىزائد C3 Cos T C4 Sin T زائد Y1 هيو جبناه يبقى
+
+641
+01:20:04,780 --> 01:20:07,560
+ناقص تلاتة T
+
+642
+01:20:12,180 --> 01:20:20,880
+Y2 ناقص رابع T في صينة T هذا هو ال general
+
+643
+01:20:20,880 --> 01:20:25,380
+solution لمين للمعادلة الأساسية اللي عندنا اللي هو
+
+644
+01:20:25,380 --> 01:20:32,580
+رقم 2 طيب
+
+645
+01:20:32,580 --> 01:20:38,520
+نبطل نحسب constants يبقى بنعطيك المثال رقم 3
+
+646
+01:20:41,400 --> 01:20:47,960
+بيقول ي determine a
+
+647
+01:20:47,960 --> 01:20:51,680
+suitable form
+
+648
+01:20:51,680 --> 01:21:03,860
+شكل مناسب for the particular solution
+
+649
+01:21:09,480 --> 01:21:20,800
+و Y of T و بعد ذلك don't evaluate the constants
+
+650
+01:21:20,800 --> 01:21:25,580
+بدلاش
+
+651
+01:21:25,580 --> 01:21:31,940
+تحسبون الثوابتولو جيبنا لك سؤال في الامتحان يمكن
+
+652
+01:21:31,940 --> 01:21:35,960
+نجيبه زي هيك لسمح الله نقولك ما تحاسبوش قنوص حتى
+
+653
+01:21:35,960 --> 01:21:40,140
+ماضيعيش وقتك وانت بتشتقه وتجمعه وغالبيا في اللي
+
+654
+01:21:40,140 --> 01:21:44,400
+لازم يغلقه يبقى أنت بس بدي شكل الحل الخاص و الله
+
+655
+01:21:44,400 --> 01:21:48,740
+يعطيك العافية بتطلع هال مكتوب عادي دائما اما ده في
+
+656
+01:21:48,740 --> 01:21:54,260
+الامتحانات السابقة بنحطها بخط غامق وبينقصين حتى عش
+
+657
+01:21:54,260 --> 01:22:03,730
+الكل يشوفها نمرأ ايه؟سؤال 18 من الكتاب بيقول لي Y
+
+658
+01:22:03,730 --> 01:22:13,030
+to the derivative 4 زائد اتنين Y triple prime زائد
+
+659
+01:22:13,030 --> 01:22:22,100
+اتنين Y double prime بده يساوي تلاتة Eostزائد
+
+660
+01:22:22,100 --> 01:22:34,380
+اتنين T E أس ناقص T زائد E أس ناقص T في sign ات ود
+
+661
+01:22:34,380 --> 01:22:36,600
+المعادلة رقم واحد
+
+662
+01:23:06,020 --> 01:23:08,820
+ماذا تسأل؟
+
+663
+01:23:14,220 --> 01:23:18,580
+جمعناهم يا أختي، وين؟ هاي جبنا واي واحد، هاي واسلب
+
+664
+01:23:18,580 --> 01:23:24,540
+تلاتة، واي اتنين، واسلب رابع، وهاي واي اتنين،
+
+665
+01:23:24,540 --> 01:23:25,860
+جمعناهم
+
+666
+01:23:55,980 --> 01:24:00,560
+طيب السؤال هذا بيقول ياتي بس شكل ال particular
+
+667
+01:24:00,560 --> 01:24:05,640
+solution لكن شكل ال particular solution بيعتمد على
+
+668
+01:24:05,640 --> 01:24:08,880
+حل ال homogeneous إذا بروح حل ال homogeneous في
+
+669
+01:24:08,880 --> 01:24:17,300
+الأول قبل كل شيء يبقى باجي بقوله solution let
+
+670
+01:24:17,990 --> 01:24:27,030
+Y تساوي E أس RT بإيه؟ Solution of the differential
+
+671
+01:24:27,030 --> 01:24:33,570
+equation Y to the derivative 4 زائد اتنين Y triple
+
+672
+01:24:33,570 --> 01:24:40,670
+primeزي دي اتنين W prime كله بده يسوي Zero يبقى
+
+673
+01:24:40,670 --> 01:24:48,250
+then the characteristic equation is المعادلة
+
+674
+01:24:48,250 --> 01:24:54,830
+المميزة لهذه المعادلة يار أس أربعة زي دي اتنين R
+
+675
+01:24:54,830 --> 01:25:00,610
+تكيب زي دي اتنين R تربيع يسوي قداش Zero يبقى بناء
+
+676
+01:25:00,610 --> 01:25:05,830
+علي لو أخدت R تربيع عامل مشتركبظل عندي R تربيه
+
+677
+01:25:05,830 --> 01:25:11,730
+زايد اتنين R زايد اتنين يساوي Zero من هذه المعادلة
+
+678
+01:25:11,730 --> 01:25:16,850
+بقدر اقول اذا R واحد بدي يساوي R اتنين بدي يساوي
+
+679
+01:25:16,850 --> 01:25:22,490
+قداش Zero جذور حقيقية و مقررة كل واحد يوم يساوي
+
+680
+01:25:22,490 --> 01:25:30,750
+Zero هذه لا يمكن تحليلهايبقى R ثلاثة واربعة هو
+
+681
+01:25:30,750 --> 01:25:36,650
+عبارة عن حلها بالقانون ناقص اتنين زائد وناقص الجدر
+
+682
+01:25:36,650 --> 01:25:43,130
+التربية الى با تربية ناقص اربعة ألف جيم اللي هو
+
+683
+01:25:43,130 --> 01:25:50,930
+بواحد وجيم باتنين كله على جداش على اتنين ويساوي
+
+684
+01:25:50,930 --> 01:25:55,520
+سالب اتنين زائدة وناقصأتنين في أربعة في تمانية بده
+
+685
+01:25:55,520 --> 01:26:00,940
+اشيل مقاربة وضل سالب أربعة تحت الجدر يبقى زائد او
+
+686
+01:26:00,940 --> 01:26:06,960
+ناقص اتنين I عال اتنين اللي هو ساوي سالب واحد زائد
+
+687
+01:26:06,960 --> 01:26:12,740
+او ناقص مين I يبقى سارة عند لان لان ده بسالب واحد
+
+688
+01:26:12,980 --> 01:26:22,820
+والى ميو بجداش بواحد يبجى صار yc بده يساوي c1 زائد
+
+689
+01:26:22,820 --> 01:26:29,660
+c2 في t في e of zero e of zero اللى بجداش بواحد
+
+690
+01:26:29,660 --> 01:26:31,260
+زائد
+
+691
+01:26:34,040 --> 01:26:44,800
+يبقى E أُس ناقص T في C تلاتة Cos T زاد C أربع Sin
+
+692
+01:26:44,800 --> 01:26:49,980
+T يبقى هذا حل الـ YC
+
+693
+01:26:50,860 --> 01:26:55,420
+بنروح نجيب ال particular solution للمعادلة اللي
+
+694
+01:26:55,420 --> 01:27:00,420
+عندنا اللي هي رقم واحد اللي تحت هذه المعادلة باطلع
+
+695
+01:27:00,420 --> 01:27:06,020
+تلت يرمته الحمد لله ولا واحد زي التل هذه
+
+696
+01:27:06,020 --> 01:27:08,980
+polynomial في exponential هذه ال sign في اللي كل
+
+697
+01:27:08,980 --> 01:27:13,520
+إيدي انحطر أجزء المعادلة اللي عندي لكم معادلة
+
+698
+01:27:13,520 --> 01:27:20,240
+لثلاث معادلات يبقى باجي بقوله ذاDifferential
+
+699
+01:27:20,240 --> 01:27:30,720
+equation one is written as Y to the derivative
+
+700
+01:27:30,720 --> 01:27:36,360
+four زائد اتنين triple prime زائد اتنين Y double
+
+701
+01:27:36,360 --> 01:27:44,380
+prime يسوى تلاتة Eost نفس المعادلة زائد اتنين
+
+702
+01:27:44,380 --> 01:27:45,780
+triple prime
+
+703
+01:27:54,320 --> 01:28:00,220
+نفس المعادلة y to the derivative of four زائد
+
+704
+01:28:00,220 --> 01:28:05,640
+اتنين y triple prime زائد اتنين y double prime
+
+705
+01:28:05,640 --> 01:28:11,360
+يساوي الterm الاخر e اصناق ال T في sin T
+
+706
+01:28:21,570 --> 01:28:28,090
+طيب يبقى بدنا نجيب capital Y1 of T هذي polynomial
+
+707
+01:28:28,090 --> 01:28:34,210
+exponential يبقى T to the power S في ايه؟ في ال E
+
+708
+01:28:34,210 --> 01:28:43,250
+of T طبعا في زيهايبقى هنا ال S ناقص T يبقى هنا ال
+
+709
+01:28:43,250 --> 01:28:49,850
+S يبقى Zero يبقى هنا ال S تساوي Zero يبقى صار
+
+710
+01:28:49,850 --> 01:28:55,970
+Capital Y one of T يساوي F E of T خلصنا من هذه نجي
+
+711
+01:28:55,970 --> 01:29:04,110
+لهذه Y two of T T to the power S هذه polynomial من
+
+712
+01:29:04,110 --> 01:29:10,250
+الدرجة الأولىيبقى a naught t زائد a one فيه و
+
+713
+01:29:10,250 --> 01:29:14,110
+اصناع تاستي تسيبيه كمان T to the power s
+
+714
+01:29:19,400 --> 01:29:22,220
+الـ exponential موجودة بس مضوبة في مين؟ في الـ
+
+715
+01:29:22,220 --> 01:29:27,200
+sine أو الـ cosine؟ ماعنديش يبقى هنا كمان S بـ 0
+
+716
+01:29:27,200 --> 01:29:34,520
+يبقى الـ S تساوي 0 يبقى capital Y2 of T يساوي A
+
+717
+01:29:34,520 --> 01:29:43,000
+not T زائد A1 في الـ E أُس ناقص T نيجي لبعدها Y3
+
+718
+01:29:43,000 --> 01:29:48,110
+as a function of T T to the power S فيههذا
+
+719
+01:29:48,110 --> 01:29:54,350
+exponential في الـSin يبقى هنا سمينا A بقدرش أقول
+
+720
+01:29:54,350 --> 01:29:59,130
+بي يبقى بي
+
+721
+01:29:59,130 --> 01:30:10,340
+في cos T زي دي في sin T في الـA واس ناقص Tتعالى
+
+722
+01:30:10,340 --> 01:30:16,620
+نشوف هل هذا في تشابه constant P في ال exponential
+
+723
+01:30:16,620 --> 01:30:20,640
+والتانى
+
+724
+01:30:20,640 --> 01:30:27,520
+كمان في زيه لكن لو حطينا ال S بواحد يتغير تماما
+
+725
+01:30:27,520 --> 01:30:35,000
+يبقى باجي بقوله hereالـ S تساوي واحد يبقى صار
+
+726
+01:30:35,000 --> 01:30:40,360
+capital Y تلاتة as a function of T هو عبارة عن
+
+727
+01:30:40,360 --> 01:30:49,920
+مين؟ عن T في الـ EOS ناقص T في B Cos T زائد D في
+
+728
+01:30:49,920 --> 01:30:56,580
+Sin T بناء عليه شهر ال capital Y of T اللي بدّوا
+
+729
+01:30:56,580 --> 01:31:02,830
+إياهايو اي واحد زائد واي اتنين زائد واي تلاتة
+
+730
+01:31:02,830 --> 01:31:10,050
+واللي هي بدها تساوي A في ال E أس T زائد A not T
+
+731
+01:31:10,050 --> 01:31:19,490
+زائد A one في ال E أس ناقص T زائد T في ال E أس
+
+732
+01:31:19,490 --> 01:31:28,640
+ناقص T في ال B cosine Tزائد دي في sign ال T وهذا
+
+733
+01:31:28,640 --> 01:31:36,440
+هو المطلوب من المسألة خلاص
+
+734
+01:31:36,440 --> 01:31:40,360
+قالت تحسبش الثوابط يبقى خلاص لحد هنا الله يعطينا
+
+735
+01:31:40,360 --> 01:31:46,020
+عافية بس بده شكل الحل الخاص وهذا كان نمرة A من
+
+736
+01:31:46,020 --> 01:31:53,400
+المثلة بدنا نروح لنمرة Bنمر بسؤال من خارج الكتاب
+
+737
+01:31:53,400 --> 01:32:02,300
+بيقول ما يأتي ب Y to the derivative 4 زائد Y
+
+738
+01:32:02,300 --> 01:32:10,900
+triple prime بده يساوي واحد ناقص T تربيع في E أس
+
+739
+01:32:10,900 --> 01:32:11,880
+ناقص T
+
+740
+01:32:16,940 --> 01:32:23,280
+يبقى بنا بس ال particular solution لحل اللي عندنا
+
+741
+01:32:23,280 --> 01:32:28,540
+فقط لغته يبقى بداجي أقوله نفس ال tactic اللي كنا
+
+742
+01:32:28,540 --> 01:32:39,520
+بنتبعه قبل قليل let y تسوى E أُس RT be a solution
+
+743
+01:32:39,520 --> 01:32:44,960
+of the differential equationY to the derivative of
+
+744
+01:32:44,960 --> 01:32:53,080
+4 زائد المشتقة التالتة يبقى
+
+745
+01:32:53,080 --> 01:33:02,990
+بناء العلياThe characteristic equation is R أربعة
+
+746
+01:33:02,990 --> 01:33:09,810
+زائد R تكييب يساوي Zero او ان شئتولنا فاقولنا R
+
+747
+01:33:09,810 --> 01:33:18,320
+تكييب في R زائد واحد بتساوي من Zeroيبقى R1 يبقى R2
+
+748
+01:33:18,320 --> 01:33:23,760
+يبقى R3 يبقى R4 يبقى R4 يبقى R2 يبقى R2 يبقى R3
+
+749
+01:33:23,760 --> 01:33:23,940
+يبقى R4 يبقى R4 يبقى R2 يبقى R4 يبقى R4 يبقى R4
+
+750
+01:33:23,940 --> 01:33:28,800
+يبقى R4 يبقى R4 يبقى R4 يبقى R4 يبقى R4 يبقى R4
+
+751
+01:33:28,800 --> 01:33:31,500
+يبقى R4 يبقى R4 يبقى R4 يبقى R4 يبقى R4 يبقى R4
+
+752
+01:33:31,500 --> 01:33:32,340
+يبقى R4 يبقى R4 يبقى R4 يبقى R4 يبقى R4 يبقى R4
+
+753
+01:33:32,340 --> 01:33:43,880
+يبقى R4 يبقى R4 يبقى R4 يبقى R4 يبقى R4
+
+754
+01:33:43,880 --> 01:33:48,580
+يبالان بدنا نجي لمين لـNon homogeneous
+
+755
+01:33:48,580 --> 01:33:53,640
+differential equation المعادلة اللى عندنا واضح انه
+
+756
+01:33:53,640 --> 01:33:58,060
+تيرمين هذا ال constant لحاله ومجموعة مع دالة تانية
+
+757
+01:33:58,060 --> 01:34:02,900
+مختلفة تماما عن الدالة هذه إذا حجز المعادلة إلى
+
+758
+01:34:02,900 --> 01:34:08,900
+معادلتين فباجي بقول لو سميت هذه المعادلة رقم واحد
+
+759
+01:34:08,900 --> 01:34:16,440
+بروح بقول له that differential equationone is
+
+760
+01:34:16,440 --> 01:34:25,720
+written as بكتبها على الشكل التالي y to the
+
+761
+01:34:25,720 --> 01:34:31,780
+derivative four زائد y triple prime بدي ساوي قداش
+
+762
+01:34:31,780 --> 01:34:36,540
+واحد المعادلة التانية نفسها y to the derivative
+
+763
+01:34:36,540 --> 01:34:43,160
+four زائد y triple prime بدي ساوي انها قصتي تربية
+
+764
+01:34:43,570 --> 01:34:53,010
+يصنع قصتي نجي هنا شكلنا بدنا نجيب capital Y1 of T
+
+765
+01:34:57,790 --> 01:35:05,530
+يبقى T to the power S هذه كنستان بكتبها كنستان فقط
+
+766
+01:35:05,530 --> 01:35:10,950
+لا غير بالشكل اللي عندنا هنا ابنجي نشوف C بيكمن T
+
+767
+01:35:10,950 --> 01:35:17,170
+to the power S كنستان موجود بيحط S بقدرش؟ بواحد
+
+768
+01:35:17,170 --> 01:35:27,860
+بيصير AT موجودة اقص باتنين AT تربية موجودةيبقى S
+
+769
+01:35:27,860 --> 01:35:36,020
+بي تلاتة يبقى هنا S تساوي تلاتة يبقى صار capital Y
+
+770
+01:35:36,020 --> 01:35:43,180
+of one of T A T تكعيب شوفت ايش الفرق بين هذا
+
+771
+01:35:43,180 --> 01:35:47,800
+السؤال و الأسئلة السابقة يبقى هنا S طلعت بي تلاتة
+
+772
+01:35:47,800 --> 01:35:52,910
+لا ب Zero ولا بواحد طيب نجي للتانية هذهيبقى بداجي
+
+773
+01:35:52,910 --> 01:35:59,350
+ل capital Y2 of T T to the power S هذي polynomial
+
+774
+01:35:59,350 --> 01:36:04,350
+من الدرجة الثانية في من ال exponential اذا بداجي
+
+775
+01:36:04,350 --> 01:36:15,030
+اقول له A0 T تربيع A1 T A2 في E و اثناق T بدى اشوف
+
+776
+01:36:15,030 --> 01:36:19,790
+ال S بقداش بعد ما تكون أسطن في exponential هي
+
+777
+01:36:19,790 --> 01:36:20,710
+موجود
+
+778
+01:36:23,620 --> 01:36:29,020
+لو حطيت T بواحد بيصير T تكيب في ال exponential مش
+
+779
+01:36:29,020 --> 01:36:34,340
+موجودة، T تربية في ال exponential مش موجودة، T في
+
+780
+01:36:34,340 --> 01:36:36,240
+ال exponential مش موجودة
+
+781
+01:36:39,070 --> 01:36:46,230
+يبقى هنا ال S تساوي واحد يبقى من هنا عليه أصبح
+
+782
+01:36:46,230 --> 01:36:55,650
+capital Y2 of T يساوي A نط T تكيب زائد A1T تربيع
+
+783
+01:36:55,650 --> 01:37:03,380
+زائد A2T في ال A أس ناقص Tيبقى بناء علي احصار ان
+
+784
+01:37:03,380 --> 01:37:12,860
+كابتنال Y of T هو Y واحد زائد Y اتنين Y واحد اللي
+
+785
+01:37:12,860 --> 01:37:22,100
+هو A T تكييب زائد Y اتنين اللي هو A نوت T تكييب
+
+786
+01:37:22,100 --> 01:37:27,460
+زائد A one T تربيع زائد
+
+787
+01:37:29,010 --> 01:37:37,050
+A1t تربيه الزائد A2t كله في ال exponential E أس
+
+788
+01:37:37,050 --> 01:37:38,430
+ناقص T
+
+789
+01:37:48,900 --> 01:37:55,100
+سالب معناه هذا سالب لما بدى اتي احسب كده مقادير ال
+
+790
+01:37:55,100 --> 01:37:59,840
+constants تيجي معانا يعني لما بدى اتيم كده ال a
+
+791
+01:37:59,840 --> 01:38:04,960
+node و ال a1 و ال a2 تدخل معانا من السلبة يعني
+
+792
+01:38:04,960 --> 01:38:13,540
+بصير ايش بصير a1 بده ساوي ناقص واحد و ال a node ب
+
+793
+01:38:13,540 --> 01:38:18,400
+zero و ال a2 ب zero و هكذا تمام؟
+
+794
+01:38:20,240 --> 01:38:25,700
+طيب المرة جاية ان شاء الله بنكمل يعني المحاضرة
+
+795
+01:38:25,700 --> 01:38:31,700
+القادمة يوم الأربعاء ان شاء الله تعالى بنطلع ..
+
+796
+01:38:31,700 --> 01:38:37,340
+بنكمل ال section اللي ضايل و بنعطيكوا أرقام
+
+797
+01:38:37,340 --> 01:38:39,620
+المسائل على ال two sections
+
diff --git a/PL9fwy3NUQKwa8ZDfSFGn6H8xVFLzqmCZC/aLofgEh8GKI_raw.json b/PL9fwy3NUQKwa8ZDfSFGn6H8xVFLzqmCZC/aLofgEh8GKI_raw.json
new file mode 100644
index 0000000000000000000000000000000000000000..65e754c748c2f5320494839eda7d61b70d3567f0
--- /dev/null
+++ b/PL9fwy3NUQKwa8ZDfSFGn6H8xVFLzqmCZC/aLofgEh8GKI_raw.json
@@ -0,0 +1 @@
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"probability": 0.62841796875}, {"start": 42.03, "end": 42.51, "word": " نجيب", "probability": 0.9827880859375}, {"start": 42.51, "end": 42.77, "word": " ال", "probability": 0.93994140625}, {"start": 42.77, "end": 43.43, "word": " characteristic", "probability": 0.63330078125}, {"start": 43.43, "end": 44.37, "word": " equation", "probability": 0.93798828125}, {"start": 44.37, "end": 45.49, "word": " احتمال", "probability": 0.948974609375}, {"start": 45.49, "end": 45.97, "word": " الجذور", "probability": 0.96630859375}, {"start": 45.97, "end": 46.41, "word": " كلها", "probability": 0.963134765625}, {"start": 46.41, "end": 46.83, "word": " تبقى", "probability": 0.92236328125}, {"start": 46.83, "end": 47.61, "word": " حقيقية", "probability": 0.9886474609375}, {"start": 47.61, "end": 47.81, "word": " و", "probability": 0.98583984375}, {"start": 47.81, "end": 48.77, "word": " مختلفة", "probability": 0.902099609375}, {"start": 48.77, "end": 49.55, "word": " احتمال", "probability": 0.927490234375}, {"start": 49.55, "end": 50.47, "word": " تبقى", "probability": 0.9866943359375}, {"start": 50.47, "end": 51.67, "word": " complex", "probability": 0.93212890625}, {"start": 51.67, "end": 52.61, "word": " احتمال", "probability": 0.971923828125}, {"start": 52.61, "end": 53.33, "word": " تبقى", "probability": 0.9918212890625}, {"start": 53.33, "end": 54.17, "word": " repeated", "probability": 0.95947265625}, {"start": 54.17, "end": 55.09, "word": " real", "probability": 0.55615234375}], "temperature": 1.0}, {"id": 4, "seek": 7333, "start": 55.45, "end": 73.33, "text": "ممكن تبقى repeated complex على كده الأمرين واخدنا على ذلك ثلاثة أمثلة والأن بنكمل الأمثلة على نفس الموضوع يبقى السؤال لو المثال رقم اثنين بيقول show that the general solution of the differential equation", "tokens": [2304, 43020, 6055, 3555, 4587, 7578, 10477, 3997, 15844, 9122, 3215, 3224, 16247, 29973, 9957, 4032, 47283, 3215, 8315, 15844, 29910, 23275, 38637, 1211, 5718, 104, 3660, 5551, 2304, 12984, 37977, 4032, 6027, 33456, 44945, 24793, 1211, 16247, 2304, 12984, 37977, 15844, 8717, 36178, 9673, 2407, 11242, 45367, 7251, 3555, 4587, 7578, 21136, 33604, 6027, 45164, 9673, 12984, 6027, 12602, 4587, 2304, 1975, 12984, 1863, 9957, 4724, 1829, 39648, 855, 300, 264, 2674, 3827, 295, 264, 15756, 5367], "avg_logprob": -0.2333860785900792, "compression_ratio": 1.5049019607843137, "no_speech_prob": 0.0, "words": [{"start": 55.45, "end": 55.91, "word": "ممكن", "probability": 0.4884033203125}, {"start": 55.91, "end": 56.33, "word": " تبقى", "probability": 0.81243896484375}, {"start": 56.33, "end": 56.91, "word": " repeated", "probability": 0.57470703125}, {"start": 56.91, "end": 58.17, "word": " complex", "probability": 0.83349609375}, {"start": 58.17, "end": 58.53, "word": " على", "probability": 0.67333984375}, {"start": 58.53, "end": 58.97, "word": " كده", "probability": 0.6271158854166666}, {"start": 58.97, "end": 59.55, "word": " الأمرين", "probability": 0.9376627604166666}, {"start": 59.55, "end": 60.49, "word": " واخدنا", "probability": 0.684326171875}, {"start": 60.49, "end": 60.69, "word": " على", "probability": 0.82275390625}, {"start": 60.69, "end": 61.17, "word": " ذلك", "probability": 0.98583984375}, {"start": 61.17, "end": 62.11, "word": " ثلاثة", "probability": 0.9607421875}, {"start": 62.11, "end": 62.79, "word": " أمثلة", "probability": 0.9478759765625}, {"start": 62.79, "end": 63.53, "word": " والأن", "probability": 0.5069986979166666}, {"start": 63.53, "end": 64.11, "word": " بنكمل", "probability": 0.8076985677083334}, {"start": 64.11, "end": 64.61, "word": " الأمثلة", "probability": 0.9786376953125}, {"start": 64.61, "end": 64.87, "word": " على", "probability": 0.9072265625}, {"start": 64.87, "end": 65.29, "word": " نفس", "probability": 0.994384765625}, {"start": 65.29, "end": 66.27, "word": " الموضوع", "probability": 0.9896240234375}, {"start": 66.27, "end": 67.19, "word": " يبقى", "probability": 0.966796875}, {"start": 67.19, "end": 67.59, "word": " 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76.11, "end": 76.45, "word": " حط", "probability": 0.64892578125}, {"start": 76.45, "end": 76.91, "word": " الرقم", "probability": 0.96923828125}, {"start": 76.91, "end": 77.19, "word": " بين", "probability": 0.951171875}, {"start": 77.19, "end": 77.75, "word": " جثين", "probability": 0.7438151041666666}, {"start": 77.75, "end": 78.47, "word": " تعني", "probability": 0.6092529296875}, {"start": 78.47, "end": 79.11, "word": " المشتقة", "probability": 0.81982421875}, {"start": 79.11, "end": 79.47, "word": " بدون", "probability": 0.84228515625}, {"start": 79.47, "end": 79.93, "word": " أقوى", "probability": 0.735107421875}, {"start": 79.93, "end": 80.05, "word": " C", "probability": 0.49658203125}, {"start": 80.05, "end": 80.35, "word": " يعني", "probability": 0.936279296875}, {"start": 80.35, "end": 80.81, "word": " أس", "probability": 0.6502685546875}, {"start": 80.81, "end": 81.61, "word": " يبقى", "probability": 0.9517822265625}, {"start": 81.61, "end": 81.83, "word": " Y", 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85.81, "word": " as", "probability": 0.9560546875}, {"start": 85.81, "end": 86.49, "word": " يمكن", "probability": 0.935791015625}, {"start": 86.49, "end": 86.67, "word": " أن", "probability": 0.72998046875}, {"start": 86.67, "end": 87.07, "word": " نكتب", "probability": 0.9371337890625}, {"start": 87.07, "end": 87.27, "word": " هذا", "probability": 0.93603515625}, {"start": 87.27, "end": 87.61, "word": " الحل", "probability": 0.98095703125}, {"start": 87.61, "end": 87.85, "word": " على", "probability": 0.94189453125}, {"start": 87.85, "end": 88.73, "word": " صيغة", "probability": 0.9053955078125}, {"start": 88.73, "end": 89.39, "word": " C1", "probability": 0.71630859375}, {"start": 89.39, "end": 89.77, "word": " Cos", "probability": 0.3251953125}, {"start": 89.77, "end": 90.31, "word": " T", "probability": 0.7138671875}, {"start": 90.31, "end": 90.73, "word": " زائد", "probability": 0.5380045572916666}, {"start": 90.73, "end": 91.37, "word": " C2", "probability": 0.973388671875}, {"start": 91.37, "end": 91.79, "word": " Sin", "probability": 0.90673828125}, {"start": 91.79, "end": 92.21, "word": " T", "probability": 0.95849609375}, {"start": 92.21, "end": 92.97, "word": " زائد", "probability": 0.9376627604166666}, {"start": 92.97, "end": 93.59, "word": " C3", "probability": 0.947509765625}, {"start": 93.59, "end": 94.01, "word": " Gosh", "probability": 0.23565673828125}, {"start": 94.01, "end": 94.19, "word": " T", "probability": 0.95849609375}, {"start": 94.19, "end": 94.53, "word": " زائد", "probability": 0.900390625}, {"start": 94.53, "end": 95.37, "word": " C4", "probability": 0.99365234375}, {"start": 95.37, "end": 95.93, "word": " Sin", "probability": 0.734375}, {"start": 95.93, "end": 96.41, "word": " T", "probability": 0.95166015625}, {"start": 96.41, "end": 97.33, "word": " مدام", "probability": 0.6826171875}, {"start": 97.33, "end": 97.69, "word": " بقول", "probability": 0.867919921875}, {"start": 97.69, "end": 98.47, "word": " احتمال", "probability": 0.8511962890625}, {"start": 98.47, "end": 98.99, "word": " الحل", "probability": 0.988037109375}, {"start": 98.99, "end": 99.35, "word": " يكون", "probability": 0.98095703125}, {"start": 99.35, "end": 99.53, "word": " على", "probability": 0.94384765625}, {"start": 99.53, "end": 99.93, "word": " الشكل", "probability": 0.95361328125}, {"start": 99.93, "end": 100.15, "word": " هذا", "probability": 0.87841796875}, {"start": 100.15, "end": 100.53, "word": " يمكن", "probability": 0.964599609375}, {"start": 100.53, "end": 100.81, "word": " لما", "probability": 0.7186279296875}, {"start": 100.81, "end": 101.21, "word": " نحل", "probability": 0.8955078125}, {"start": 101.21, "end": 101.35, "word": " ما", "probability": 0.43994140625}, {"start": 101.35, "end": 102.03, "word": " يطلعش", "probability": 0.91748046875}], "temperature": 1.0}, {"id": 6, "seek": 13105, "start": 102.35, "end": 131.05, "text": "الشكل هذا اذا طلع كنبة اذا ما طلعش مانتا بدي احول المسألة بحيث فعلا تصير في الشكل اللي عندنا هذا هذا المطلوب الأول بعدين قال لي solve ال initial value problem نفس المثل اللي عندنا بس حط عليه الشروط الأربعة اللي من خلالها بقدر أجيب قيمة الثوابت اللي موجودة عندنا اذا نيجي الحل مع المطلوب الأول اللي هو نمرة A", "tokens": [6027, 8592, 28820, 23758, 1975, 15730, 23032, 1211, 3615, 9122, 1863, 49401, 1975, 15730, 19446, 23032, 1211, 3615, 8592, 3714, 7649, 2655, 995, 4724, 16254, 1975, 5016, 12610, 9673, 3794, 10721, 37977, 4724, 5016, 1829, 12984, 6156, 3615, 15040, 6055, 9381, 13546, 8978, 25124, 28820, 13672, 1829, 43242, 8315, 23758, 23758, 9673, 9566, 1211, 37746, 16247, 12610, 39182, 9957, 50239, 32239, 5039, 2423, 5883, 2158, 1154, 8717, 36178, 9673, 12984, 1211, 13672, 1829, 43242, 8315, 4724, 3794, 11331, 9566, 47356, 25124, 32887, 9566, 16247, 25513, 27884, 13672, 1829, 9154, 16490, 1211, 6027, 11296, 4724, 28543, 2288, 5551, 7435, 1829, 3555, 12174, 32640, 3660, 6024, 104, 14407, 3555, 2655, 13672, 1829, 3714, 29245, 23328, 3660, 43242, 8315, 1975, 15730, 8717, 1829, 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" Zero", "probability": 0.5625}, {"start": 760.6, "end": 761.52, "word": " نجي", "probability": 0.7325846354166666}, {"start": 761.52, "end": 761.62, "word": " ال", "probability": 0.90966796875}, {"start": 761.62, "end": 762.08, "word": " condition", "probability": 0.830078125}, {"start": 762.08, "end": 762.86, "word": " التاني", "probability": 0.935546875}, {"start": 762.86, "end": 763.32, "word": " جالي", "probability": 0.6352945963541666}, {"start": 763.32, "end": 763.9, "word": " Y", "probability": 0.7900390625}, {"start": 763.9, "end": 764.74, "word": " Prime", "probability": 0.339599609375}, {"start": 764.74, "end": 765.26, "word": " عند", "probability": 0.98095703125}, {"start": 765.26, "end": 765.86, "word": " Zero", "probability": 0.87939453125}, {"start": 765.86, "end": 766.94, "word": " كذلك", "probability": 0.9737955729166666}, {"start": 766.94, "end": 767.42, "word": " بده", "probability": 0.679443359375}, {"start": 767.42, "end": 767.76, "word": " يسوي", "probability": 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equation و اليوم ناخد أول طريقة فقط اللي هو طريقة الـ undetermined coefficients يبقى بنيجي ل section 4-3 اللي هو the method of undetermined coefficients", "tokens": [1211, 24401, 34105, 5551, 30543, 5172, 20666, 1863, 35457, 3660, 24976, 39184, 42632, 15756, 5367, 47525, 8315, 8717, 32887, 5016, 24976, 39184, 2107, 12, 71, 298, 31112, 15756, 5367, 4032, 45595, 20498, 8717, 47283, 3215, 5551, 12610, 23032, 16572, 28671, 6156, 47432, 13672, 1829, 31439, 23032, 16572, 28671, 2423, 39184, 674, 35344, 2001, 31994, 7251, 3555, 4587, 7578, 44945, 1829, 7435, 1829, 5296, 3541, 1017, 12, 18, 13672, 1829, 31439, 264, 3170, 295, 674, 35344, 2001, 31994], "avg_logprob": -0.3373397539059321, "compression_ratio": 1.68, "no_speech_prob": 0.0, "words": [{"start": 2365.47, "end": 2365.97, "word": "لحد", "probability": 0.6116943359375}, {"start": 2365.97, "end": 2366.23, "word": " هنا", "probability": 0.7421875}, {"start": 2366.23, "end": 2366.63, "word": " أوقف", "probability": 0.4813435872395833}, 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" رقم", "probability": 0.9733072916666666}, {"start": 2445.09, "end": 2445.91, "word": " 1", "probability": 0.576171875}, {"start": 2445.91, "end": 2449.61, "word": " The", "probability": 0.232421875}, {"start": 2449.61, "end": 2451.81, "word": " solution", "probability": 0.8740234375}], "temperature": 1.0}, {"id": 106, "seek": 248085, "start": 2453.61, "end": 2480.85, "text": "of the differential equation one is Y تساوي YC زائد capital Y of T where حيث YC is the solution", "tokens": [2670, 264, 15756, 5367, 472, 307, 398, 6055, 3794, 995, 45865, 398, 34, 30767, 16373, 3215, 4238, 398, 295, 314, 689, 11331, 1829, 12984, 398, 34, 307, 264, 3827], "avg_logprob": -0.3481770733992259, "compression_ratio": 1.019047619047619, "no_speech_prob": 0.0, "words": [{"start": 2453.61, "end": 2454.25, "word": "of", "probability": 0.097900390625}, {"start": 2454.25, "end": 2455.47, "word": " the", "probability": 0.85107421875}, {"start": 2455.47, "end": 2457.17, "word": " differential", "probability": 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هو الحل الخاص للمعادلة الأساسية اللي هي واحد بس بشرط", "tokens": [6027, 39184, 3827, 6055, 3555, 3615, 2423, 5367, 472, 31439, 6225, 3555, 9640, 3660, 18871, 10874, 11622, 38207, 9957, 11331, 1211, 2423, 42632, 29910, 9307, 11331, 1211, 16490, 33546, 24976, 2107, 42632, 8717, 7435, 2304, 3615, 2423, 9307, 1863, 9957, 4724, 40228, 9566, 1829, 22653, 21542, 1211, 2423, 2674, 3827, 24976, 2107, 42632, 15756, 5367, 7251, 3555, 4587, 7578, 398, 34, 31439, 11331, 1211, 2423, 42632, 15756, 5367, 13672, 1829, 43242, 8315, 4032, 56, 51, 31439, 21542, 1211, 33962, 33546, 5296, 19528, 3615, 18513, 37977, 16247, 3794, 32277, 10632, 13672, 1829, 39896, 36764, 24401, 4724, 3794, 4724, 46309, 9566], "avg_logprob": -0.22968750223517417, "compression_ratio": 1.8652173913043477, "no_speech_prob": 0.0, "words": [{"start": 3047.62, "end": 3048.06, "word": "الـ", "probability": 0.22174072265625}, {"start": 3048.06, "end": 3048.56, "word": " solution", "probability": 0.446533203125}, {"start": 3048.56, 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"end": 3054.36, "word": " حل", "probability": 0.982666015625}, {"start": 3054.36, "end": 3054.86, "word": " خاص", "probability": 0.98046875}, {"start": 3054.86, "end": 3055.04, "word": " لل", "probability": 0.85693359375}, {"start": 3055.04, "end": 3055.28, "word": " non", "probability": 0.78173828125}, {"start": 3055.28, "end": 3055.86, "word": " homogeneous", "probability": 0.78955078125}, {"start": 3055.86, "end": 3056.92, "word": " نجمع", "probability": 0.78997802734375}, {"start": 3056.92, "end": 3057.46, "word": " الاتنين", "probability": 0.7642822265625}, {"start": 3057.46, "end": 3058.14, "word": " بيعطيني", "probability": 0.6568359375}, {"start": 3058.14, "end": 3058.88, "word": " الحل", "probability": 0.9599609375}, {"start": 3058.88, "end": 3059.4, "word": " ال", "probability": 0.8837890625}, {"start": 3059.4, "end": 3059.8, "word": " general", "probability": 0.79443359375}, {"start": 3059.8, "end": 3060.44, "word": " solution", "probability": 0.97216796875}, {"start": 3060.44, "end": 3060.66, "word": " لل", "probability": 0.88720703125}, {"start": 3060.66, "end": 3061.9, "word": " non", "probability": 0.78564453125}, {"start": 3061.9, "end": 3062.36, "word": " homogeneous", "probability": 0.90283203125}, {"start": 3062.36, "end": 3062.86, "word": " differential", "probability": 0.951171875}, {"start": 3062.86, "end": 3063.38, "word": " equation", "probability": 0.97119140625}, {"start": 3063.38, "end": 3064.3, "word": " يبقى", "probability": 0.968017578125}, {"start": 3064.3, "end": 3064.8, "word": " YC", "probability": 0.5732421875}, {"start": 3064.8, "end": 3065.06, "word": " هو", "probability": 0.95166015625}, {"start": 3065.06, "end": 3065.46, "word": " حل", "probability": 0.939697265625}, {"start": 3065.46, "end": 3065.58, "word": " ال", "probability": 0.990234375}, {"start": 3065.58, "end": 3066.06, "word": " homogeneous", "probability": 0.83251953125}, {"start": 3066.06, "end": 3066.68, "word": " differential", "probability": 0.9521484375}, {"start": 3066.68, "end": 3067.2, "word": " equation", "probability": 0.99072265625}, {"start": 3067.2, "end": 3067.38, "word": " اللي", "probability": 0.72314453125}, {"start": 3067.38, "end": 3067.78, "word": " عندنا", "probability": 0.98974609375}, {"start": 3067.78, "end": 3069.42, "word": " وYT", "probability": 0.8271484375}, {"start": 3069.42, "end": 3069.64, "word": " هو", "probability": 0.94580078125}, {"start": 3069.64, "end": 3070.12, "word": " الحل", "probability": 0.981201171875}, {"start": 3070.12, "end": 3070.64, "word": " الخاص", "probability": 0.9912109375}, {"start": 3070.64, "end": 3071.4, "word": " للمعادلة", "probability": 0.893359375}, {"start": 3071.4, "end": 3072.4, "word": " الأساسية", "probability": 0.973388671875}, {"start": 3072.4, "end": 3072.98, "word": " اللي", "probability": 0.8525390625}, {"start": 3072.98, "end": 3073.16, "word": " هي", "probability": 0.849609375}, {"start": 3073.16, "end": 3073.58, "word": " واحد", "probability": 0.889404296875}, {"start": 3073.58, "end": 3074.04, "word": " بس", "probability": 0.8173828125}, {"start": 3074.04, "end": 3074.82, "word": " بشرط", "probability": 0.8694661458333334}], "temperature": 1.0}, {"id": 114, "seek": 310375, "start": 3074.89, "end": 3103.75, "text": "لما نستخدم الـ Undetermined coefficients بد المعاملات دول ثوابت زي ما انت شايفينهم بدها G of T تبقى على شكل معين يبقى has a particular form G of T بدت تبقى على شكل خاص according to the following table طبقا للجدول التالف لو كانت ال G of T polynomial يبقى بدي أقوله T to the power S في polynomial مناضرة لأ", "tokens": [1211, 15042, 8717, 14851, 9778, 40448, 2423, 39184, 2719, 35344, 2001, 31994, 47525, 9673, 3615, 10943, 1211, 9307, 11778, 12610, 38637, 14407, 3555, 2655, 30767, 1829, 19446, 16472, 2655, 13412, 995, 33911, 9957, 16095, 47525, 11296, 460, 295, 314, 6055, 3555, 4587, 7578, 15844, 13412, 28820, 20449, 9957, 7251, 3555, 4587, 7578, 575, 257, 1729, 1254, 460, 295, 314, 47525, 2655, 6055, 3555, 4587, 7578, 15844, 13412, 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"probability": 0.8759765625}, {"start": 3084.33, "end": 3085.03, "word": " شكل", "probability": 0.981201171875}, {"start": 3085.03, "end": 3085.77, "word": " معين", "probability": 0.925537109375}, {"start": 3085.77, "end": 3086.73, "word": " يبقى", "probability": 0.970703125}, {"start": 3086.73, "end": 3087.05, "word": " has", "probability": 0.5390625}, {"start": 3087.05, "end": 3087.35, "word": " a", "probability": 0.9794921875}, {"start": 3087.35, "end": 3088.03, "word": " particular", "probability": 0.92724609375}, {"start": 3088.03, "end": 3088.75, "word": " form", "probability": 0.95263671875}, {"start": 3088.75, "end": 3089.25, "word": " G", "probability": 0.416015625}, {"start": 3089.25, "end": 3089.49, "word": " of", "probability": 0.962890625}, {"start": 3089.49, "end": 3089.65, "word": " T", "probability": 0.9873046875}, {"start": 3089.65, "end": 3090.01, "word": " بدت", "probability": 0.5390625}, {"start": 3090.01, "end": 3090.47, "word": " تبقى", "probability": 0.9814453125}, {"start": 3090.47, "end": 3090.73, "word": " على", "probability": 0.9521484375}, {"start": 3090.73, "end": 3091.19, "word": " شكل", "probability": 0.984130859375}, {"start": 3091.19, "end": 3091.63, "word": " خاص", "probability": 0.9853515625}, {"start": 3091.63, "end": 3092.11, "word": " according", "probability": 0.9404296875}, {"start": 3092.11, "end": 3092.43, "word": " to", "probability": 0.97998046875}, {"start": 3092.43, "end": 3092.59, "word": " the", "probability": 0.90966796875}, {"start": 3092.59, "end": 3092.93, "word": " following", "probability": 0.7109375}, {"start": 3092.93, "end": 3093.51, "word": " table", "probability": 0.90087890625}, {"start": 3093.51, "end": 3094.37, "word": " طبقا", "probability": 0.833740234375}, {"start": 3094.37, "end": 3095.01, "word": " للجدول", "probability": 0.94091796875}, {"start": 3095.01, "end": 3095.77, "word": " التالف", "probability": 0.8595377604166666}, {"start": 3095.77, "end": 3096.45, "word": " لو", "probability": 0.892578125}, {"start": 3096.45, "end": 3097.11, "word": " كانت", "probability": 0.9853515625}, {"start": 3097.11, "end": 3097.35, "word": " ال", "probability": 0.77197265625}, {"start": 3097.35, "end": 3097.45, "word": " G", "probability": 0.484375}, {"start": 3097.45, "end": 3097.67, "word": " of", "probability": 0.966796875}, {"start": 3097.67, "end": 3097.83, "word": " T", "probability": 0.98828125}, {"start": 3097.83, "end": 3098.69, "word": " polynomial", "probability": 0.30615234375}, {"start": 3098.69, "end": 3099.17, "word": " يبقى", "probability": 0.7884521484375}, {"start": 3099.17, "end": 3099.39, "word": " بدي", "probability": 0.5418701171875}, {"start": 3099.39, "end": 3099.91, "word": " أقوله", "probability": 0.6842447916666666}, {"start": 3099.91, "end": 3100.21, "word": " T", "probability": 0.83056640625}, {"start": 3100.21, "end": 3100.45, "word": " to", "probability": 0.810546875}, {"start": 3100.45, "end": 3100.67, "word": " the", "probability": 0.9208984375}, {"start": 3100.67, "end": 3100.95, "word": " power", "probability": 0.83740234375}, {"start": 3100.95, "end": 3101.29, "word": " S", "probability": 0.61376953125}, {"start": 3101.29, "end": 3101.55, "word": " في", "probability": 0.9072265625}, {"start": 3101.55, "end": 3102.29, "word": " polynomial", "probability": 0.64404296875}, {"start": 3102.29, "end": 3103.33, "word": " مناضرة", "probability": 0.78759765625}, {"start": 3103.33, "end": 3103.75, "word": " لأ", "probability": 0.80810546875}], "temperature": 1.0}, {"id": 115, "seek": 313030, "start": 3104.32, "end": 3130.3, "text": "لو كان polynomial في exponential يكبر T to the power S polynomial في exponential لو كان polynomial في exponential في cosine BT أو sin BT أو مجموعهما أو الفرق فيما بينهما على كل الأربعة أمور بدي اكتب T to the power S polynomial من الدرجة رقم M في ال cosine", "tokens": [1211, 2407, 25961, 26110, 8978, 21510, 7251, 4117, 3555, 2288, 314, 281, 264, 1347, 318, 26110, 8978, 21510, 45164, 25961, 26110, 8978, 21510, 8978, 23565, 31144, 34051, 3343, 31144, 34051, 3714, 7435, 2304, 45367, 3224, 15042, 34051, 27188, 2288, 4587, 8978, 15042, 49374, 3224, 15042, 15844, 28242, 16247, 25513, 27884, 5551, 2304, 13063, 4724, 16254, 1975, 4117, 2655, 3555, 314, 281, 264, 1347, 318, 26110, 9154, 32748, 47341, 3660, 12602, 4587, 2304, 376, 8978, 2423, 23565], "avg_logprob": -0.21408279917456888, "compression_ratio": 1.89010989010989, "no_speech_prob": 0.0, "words": [{"start": 3104.32, "end": 3104.8, "word": "لو", "probability": 0.77099609375}, {"start": 3104.8, "end": 3105.08, "word": " كان", "probability": 0.98046875}, {"start": 3105.08, "end": 3105.7, "word": " polynomial", "probability": 0.9091796875}, {"start": 3105.7, "end": 3106.04, "word": " في", "probability": 0.95947265625}, {"start": 3106.04, "end": 3106.78, "word": " exponential", "probability": 0.603515625}, {"start": 3106.78, "end": 3107.24, "word": " يكبر", "probability": 0.62213134765625}, {"start": 3107.24, "end": 3107.44, "word": " T", "probability": 0.50390625}, {"start": 3107.44, "end": 3107.6, "word": " to", "probability": 0.194580078125}, {"start": 3107.6, "end": 3107.84, "word": " the", "probability": 0.91943359375}, {"start": 3107.84, "end": 3108.1, "word": " power", "probability": 0.80419921875}, {"start": 3108.1, "end": 3108.38, "word": " S", "probability": 0.67724609375}, {"start": 3108.38, "end": 3109.08, "word": " polynomial", "probability": 0.830078125}, {"start": 3109.08, "end": 3109.4, "word": " في", "probability": 0.94970703125}, {"start": 3109.4, "end": 3110.04, "word": " exponential", "probability": 0.92333984375}, {"start": 3110.04, "end": 3111.08, "word": " لو", "probability": 0.71240234375}, {"start": 3111.08, "end": 3111.44, "word": " كان", "probability": 0.9912109375}, {"start": 3111.44, "end": 3112.06, "word": " polynomial", "probability": 0.962890625}, {"start": 3112.06, "end": 3112.34, "word": " في", "probability": 0.9619140625}, {"start": 3112.34, "end": 3113.04, "word": " exponential", "probability": 0.9306640625}, {"start": 3113.04, "end": 3113.44, "word": " في", "probability": 0.97265625}, {"start": 3113.44, "end": 3114.3, "word": " cosine", "probability": 0.67138671875}, {"start": 3114.3, "end": 3115.08, "word": " BT", "probability": 0.492431640625}, {"start": 3115.08, "end": 3115.9, "word": " أو", "probability": 0.7197265625}, {"start": 3115.9, "end": 3116.76, "word": " sin", "probability": 0.394775390625}, {"start": 3116.76, "end": 3117.48, "word": " BT", "probability": 0.88330078125}, {"start": 3117.48, "end": 3118.06, "word": " أو", "probability": 0.81884765625}, {"start": 3118.06, "end": 3119.48, "word": " مجموعهما", "probability": 0.8245442708333334}, {"start": 3119.48, "end": 3120.12, "word": " أو", "probability": 0.82470703125}, {"start": 3120.12, "end": 3120.84, "word": " الفرق", "probability": 0.9619140625}, {"start": 3120.84, "end": 3121.32, "word": " فيما", "probability": 0.702392578125}, {"start": 3121.32, "end": 3121.9, "word": " 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{"start": 3459.39, "end": 3460.19, "word": " يبقى", "probability": 0.9639892578125}, {"start": 3460.19, "end": 3460.69, "word": " جيبنا", "probability": 0.8958740234375}, {"start": 3460.69, "end": 3461.53, "word": " المشتقة", "probability": 0.9700927734375}, {"start": 3461.53, "end": 3462.23, "word": " الثانية", "probability": 0.905029296875}, {"start": 3462.23, "end": 3463.19, "word": " خلصنا", "probability": 0.989990234375}, {"start": 3463.19, "end": 3463.51, "word": " منها", "probability": 0.994140625}, {"start": 3463.51, "end": 3463.79, "word": " بس", "probability": 0.9677734375}, {"start": 3463.79, "end": 3464.09, "word": " بدنا", "probability": 0.973388671875}, {"start": 3464.09, "end": 3464.31, "word": " نروح", "probability": 0.9357096354166666}, {"start": 3464.31, "end": 3464.63, "word": " نجيب", "probability": 0.9752197265625}, {"start": 3464.63, "end": 3464.97, "word": " من", "probability": 0.94091796875}, {"start": 3464.97, "end": 3466.39, "word": " المشتقة", "probability": 0.8970947265625}, {"start": 3466.39, "end": 3467.57, "word": " التالتة", "probability": 0.9539794921875}, {"start": 3467.57, "end": 3468.77, "word": " يبقى", "probability": 0.9857177734375}], "temperature": 1.0}, {"id": 129, "seek": 349758, "start": 3469.02, "end": 3497.58, "text": "هذا بدى يعطيك ان المشتقة التالتة يكبتل Y triple A prime of T بدى يسوى قداش Zero لان اتنين مقدار ثابت والاينود مقدار ثابت نرجع نعوض وين في المعادلة اللى هي رقم واحد اللى عندنا يبقى باجي بقوله هنا substitute in equation one", "tokens": [3224, 15730, 47525, 7578, 37495, 9566, 1829, 4117, 16472, 9673, 8592, 2655, 28671, 16712, 6027, 2655, 3660, 7251, 4117, 3555, 2655, 1211, 398, 15508, 316, 5835, 295, 314, 47525, 7578, 7251, 3794, 2407, 7578, 12174, 3215, 33599, 17182, 5296, 7649, 1975, 2655, 1863, 9957, 3714, 28543, 9640, 38637, 16758, 2655, 16070, 995, 9957, 23328, 3714, 28543, 9640, 38637, 16758, 2655, 8717, 47341, 3615, 8717, 3615, 2407, 11242, 4032, 9957, 8978, 9673, 3615, 18513, 37977, 13672, 7578, 39896, 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" واحد", "probability": 0.949951171875}, {"start": 3487.62, "end": 3488.02, "word": " اللى", "probability": 0.96044921875}, {"start": 3488.02, "end": 3488.52, "word": " عندنا", "probability": 0.88037109375}, {"start": 3488.52, "end": 3489.14, "word": " يبقى", "probability": 0.83685302734375}, {"start": 3489.14, "end": 3489.52, "word": " باجي", "probability": 0.6748046875}, {"start": 3489.52, "end": 3490.1, "word": " بقوله", "probability": 0.83642578125}, {"start": 3490.1, "end": 3490.6, "word": " هنا", "probability": 0.908203125}, {"start": 3490.6, "end": 3493.6, "word": " substitute", "probability": 0.4869181315104167}, {"start": 3493.6, "end": 3495.0, "word": " in", "probability": 0.45947265625}, {"start": 3495.0, "end": 3496.38, "word": " equation", "probability": 0.966796875}, {"start": 3496.38, "end": 3497.58, "word": " one", "probability": 0.7392578125}], "temperature": 1.0}, {"id": 130, "seek": 350376, "start": 3498.02, "end": 3503.76, "text": "و جت يبقى بيدنا نرجع لل equation one", "tokens": [2407, 10874, 2655, 7251, 3555, 4587, 7578, 4724, 25708, 8315, 8717, 47341, 3615, 24976, 5367, 472], "avg_logprob": -0.5202205882352942, "compression_ratio": 0.9, "no_speech_prob": 0.0, "words": [{"start": 3498.02, "end": 3498.48, "word": "و", "probability": 0.35986328125}, {"start": 3498.48, "end": 3500.16, "word": " جت", "probability": 0.29022216796875}, {"start": 3500.16, "end": 3501.62, "word": " يبقى", "probability": 0.67828369140625}, {"start": 3501.62, "end": 3501.94, "word": " بيدنا", "probability": 0.580322265625}, {"start": 3501.94, "end": 3502.38, "word": " نرجع", "probability": 0.9679361979166666}, {"start": 3502.38, "end": 3502.6, "word": " لل", "probability": 0.69580078125}, {"start": 3502.6, "end": 3503.2, "word": " equation", "probability": 0.8916015625}, {"start": 3503.2, "end": 3503.76, "word": " one", "probability": 0.65478515625}], "temperature": 1.0}, {"id": 131, "seek": 354723, "start": 3525.93, "end": 3547.23, "text": "يبقى y triple prime ب zero يبقى هي ال zero راح و عندك اربعة في y prime وين y prime هي يبقى بصير تمانية a node t زائد تمانية a node t زائد اربعة a one", "tokens": [1829, 3555, 4587, 7578, 288, 15508, 5835, 4724, 4018, 7251, 3555, 4587, 7578, 39896, 2423, 4018, 12602, 39319, 4032, 43242, 4117, 1975, 25513, 27884, 8978, 288, 5835, 4032, 9957, 288, 5835, 39896, 7251, 3555, 4587, 7578, 4724, 9381, 13546, 46811, 7649, 10632, 257, 9984, 256, 30767, 16373, 3215, 46811, 7649, 10632, 257, 9984, 256, 30767, 16373, 3215, 1975, 25513, 27884, 257, 472], "avg_logprob": -0.36706349395570304, "compression_ratio": 1.5925925925925926, "no_speech_prob": 0.0, "words": [{"start": 3525.9300000000003, "end": 3527.13, "word": "يبقى", "probability": 0.69744873046875}, {"start": 3527.13, "end": 3527.21, "word": " y", "probability": 0.08172607421875}, {"start": 3527.21, "end": 3527.53, "word": " triple", "probability": 0.343017578125}, {"start": 3527.53, "end": 3528.09, "word": " prime", "probability": 0.86181640625}, {"start": 3528.09, 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3534.43, "word": " prime", "probability": 0.7587890625}, {"start": 3534.43, "end": 3534.79, "word": " وين", "probability": 0.774169921875}, {"start": 3534.79, "end": 3535.07, "word": " y", "probability": 0.6376953125}, {"start": 3535.07, "end": 3535.79, "word": " prime", "probability": 0.88232421875}, {"start": 3535.79, "end": 3536.43, "word": " هي", "probability": 0.84033203125}, {"start": 3536.43, "end": 3537.23, "word": " يبقى", "probability": 0.8909912109375}, {"start": 3537.23, "end": 3537.59, "word": " بصير", "probability": 0.8733723958333334}, {"start": 3537.59, "end": 3538.39, "word": " تمانية", "probability": 0.797607421875}, {"start": 3538.39, "end": 3538.97, "word": " a", "probability": 0.79638671875}, {"start": 3538.97, "end": 3539.69, "word": " node", "probability": 0.402099609375}, {"start": 3539.69, "end": 3540.27, "word": " t", "probability": 0.5654296875}, {"start": 3540.27, "end": 3541.45, "word": " زائد", "probability": 0.8118489583333334}, {"start": 3541.45, "end": 3542.53, "word": " تمانية", "probability": 0.8917643229166666}, {"start": 3542.53, "end": 3543.21, "word": " a", "probability": 0.98681640625}, {"start": 3543.21, "end": 3543.95, "word": " node", "probability": 0.92919921875}, {"start": 3543.95, "end": 3544.67, "word": " t", "probability": 0.78466796875}, {"start": 3544.67, "end": 3545.57, "word": " زائد", "probability": 0.9539388020833334}, {"start": 3545.57, "end": 3546.47, "word": " اربعة", "probability": 0.88720703125}, {"start": 3546.47, "end": 3546.91, "word": " a", "probability": 0.962890625}, {"start": 3546.91, "end": 3547.23, "word": " one", "probability": 0.64501953125}], "temperature": 1.0}, {"id": 132, "seek": 356102, "start": 3557.86, "end": 3561.02, "text": "نعمل مقارنة ما بين الطرفين نعمل مقارنة ما بين الطرفين نعمل مقارنة ما بين الطرفين", "tokens": [1863, 25957, 1211, 3714, 4587, 9640, 1863, 3660, 19446, 49374, 41950, 28480, 9957, 8717, 25957, 1211, 3714, 4587, 9640, 1863, 3660, 19446, 49374, 41950, 28480, 9957, 8717, 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4075.89, "word": " T", "probability": 0.8916015625}, {"start": 4075.89, "end": 4077.63, "word": " كويس", "probability": 0.7195638020833334}, {"start": 4077.63, "end": 4079.09, "word": " بالدالي", "probability": 0.63201904296875}, {"start": 4079.09, "end": 4080.21, "word": " لشكل", "probability": 0.8553059895833334}, {"start": 4080.21, "end": 4080.67, "word": " G", "probability": 0.658203125}, {"start": 4080.67, "end": 4081.07, "word": " of", "probability": 0.296630859375}, {"start": 4081.07, "end": 4081.41, "word": " T", "probability": 0.98291015625}], "temperature": 1.0}, {"id": 154, "seek": 409833, "start": 4082.13, "end": 4098.33, "text": "بنعمل من الدرجة الأولى الزائد كوصين وليست مضروبة درجة إذا بنرجع لطريقتنا الميان اللي عتيجة أني أجزء المعادلة إلى معادلتين فبجي بقوله ذا", "tokens": [3555, 1863, 25957, 1211, 9154, 32748, 47341, 3660, 16247, 12610, 7578, 6024, 110, 16373, 3215, 9122, 2407, 9381, 9957, 4032, 20292, 14851, 3714, 11242, 32887, 49401, 11778, 47341, 3660, 11933, 15730, 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حصل ضرب داليتين تبقى سالب a sin t و سالب a t تفضل sin ب cos خلصنا أول two terms بداجي لمين؟", "tokens": [2304, 8592, 2655, 28671, 16247, 12610, 7578, 39896, 4724, 28814, 8592, 9640, 3660, 8608, 6027, 3555, 37037, 24192, 11331, 36520, 48812, 25513, 11778, 6027, 36081, 9957, 6055, 3555, 4587, 7578, 8608, 6027, 3555, 257, 3343, 256, 4032, 8608, 6027, 3555, 257, 256, 6055, 5172, 11242, 1211, 3343, 4724, 3792, 16490, 1211, 9381, 8315, 5551, 12610, 732, 2115, 47525, 26108, 1829, 32767, 9957, 22807], "avg_logprob": -0.35913086822256446, "compression_ratio": 1.408450704225352, "no_speech_prob": 0.0, "words": [{"start": 4381.14, "end": 4382.0, "word": "مشتقة", "probability": 0.66357421875}, {"start": 4382.0, "end": 4382.58, "word": " الأولى", "probability": 0.91259765625}, {"start": 4382.58, "end": 4382.86, "word": " هي", "probability": 0.72900390625}, {"start": 4382.86, "end": 4383.98, "word": " بإشارة", "probability": 0.80126953125}, {"start": 4383.98, "end": 4384.7, "word": " سالب", 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4400.33, "word": " terms", "probability": 0.75341796875}, {"start": 4400.33, "end": 4401.03, "word": " التانية", "probability": 0.86962890625}, {"start": 4401.03, "end": 4402.11, "word": " يبقى", "probability": 0.925048828125}, {"start": 4402.11, "end": 4402.91, "word": " زائد", "probability": 0.6247965494791666}, {"start": 4402.91, "end": 4404.09, "word": " بي", "probability": 0.5721435546875}, {"start": 4404.09, "end": 4404.93, "word": " في", "probability": 0.9443359375}, {"start": 4404.93, "end": 4406.29, "word": " cosine", "probability": 0.355224609375}, {"start": 4406.29, "end": 4406.85, "word": " ت", "probability": 0.2880859375}, {"start": 4406.85, "end": 4408.29, "word": " زائد", "probability": 0.9016927083333334}, {"start": 4408.29, "end": 4408.97, "word": " بي", "probability": 0.97900390625}, {"start": 4408.97, "end": 4409.39, "word": " في", "probability": 0.9775390625}, {"start": 4409.39, "end": 4410.47, "word": " cosine", "probability": 0.90673828125}, {"start": 4410.47, 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4420.15, "word": " هذه", "probability": 0.96044921875}, {"start": 4420.15, "end": 4421.43, "word": " مظبوط", "probability": 0.86533203125}, {"start": 4421.43, "end": 4422.35, "word": " يبقى", "probability": 0.9490966796875}, {"start": 4422.35, "end": 4422.67, "word": " هذه", "probability": 0.7607421875}, {"start": 4422.67, "end": 4423.45, "word": " بيصير", "probability": 0.77105712890625}, {"start": 4423.45, "end": 4424.49, "word": " ناقص", "probability": 0.977294921875}, {"start": 4424.49, "end": 4425.45, "word": " اتنين", "probability": 0.92578125}, {"start": 4425.45, "end": 4425.97, "word": " ا", "probability": 0.8662109375}, {"start": 4425.97, "end": 4426.33, "word": " في", "probability": 0.91357421875}, {"start": 4426.33, "end": 4427.25, "word": " sine", "probability": 0.81884765625}, {"start": 4427.25, "end": 4427.69, "word": " t", "probability": 0.427490234375}], "temperature": 1.0}, {"id": 169, "seek": 445059, "start": 4428.25, "end": 4450.59, "text": "وهذه هي هذه يبقى ازايد 2B في cos T بيبقى عندى ناقص AT في cos T وناقص BT في sin T بدنا نروح نجيب المشتقة الثالثة", "tokens": [2407, 3224, 24192, 39896, 29538, 7251, 3555, 4587, 7578, 1975, 11622, 995, 25708, 568, 33, 8978, 3792, 314, 4724, 1829, 3555, 4587, 7578, 43242, 7578, 8717, 995, 4587, 9381, 8872, 8978, 3792, 314, 4032, 8315, 4587, 9381, 31144, 8978, 3343, 314, 47525, 8315, 8717, 32887, 5016, 8717, 7435, 1829, 3555, 9673, 8592, 2655, 28671, 6024, 104, 6027, 12984, 3660], "avg_logprob": -0.27604168057441714, "compression_ratio": 1.4206349206349207, "no_speech_prob": 0.0, "words": [{"start": 4428.25, "end": 4429.29, "word": "وهذه", "probability": 0.5481770833333334}, {"start": 4429.29, "end": 4429.83, "word": " هي", "probability": 0.4873046875}, {"start": 4429.83, "end": 4430.47, "word": " هذه", "probability": 0.78564453125}, {"start": 4430.47, "end": 4431.63, "word": " يبقى", "probability": 0.9190673828125}, {"start": 4431.63, "end": 4432.39, "word": " ازايد", "probability": 0.5986785888671875}, {"start": 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معانا", "probability": 0.9845377604166666}, {"start": 5883.62, "end": 5884.06, "word": " من", "probability": 0.96728515625}, {"start": 5884.06, "end": 5884.7, "word": " السلبة", "probability": 0.5410970052083334}, {"start": 5884.7, "end": 5884.96, "word": " يعني", "probability": 0.8857421875}, {"start": 5884.96, "end": 5885.24, "word": " بصير", "probability": 0.7740885416666666}, {"start": 5885.24, "end": 5885.64, "word": " ايش", "probability": 0.9261067708333334}, {"start": 5885.64, "end": 5886.46, "word": " بصير", "probability": 0.8785807291666666}, {"start": 5886.46, "end": 5887.58, "word": " a1", "probability": 0.9560546875}, {"start": 5887.58, "end": 5888.62, "word": " بده", "probability": 0.5335693359375}, {"start": 5888.62, "end": 5889.22, "word": " ساوي", "probability": 0.7900390625}, {"start": 5889.22, "end": 5890.38, "word": " ناقص", "probability": 0.95947265625}, {"start": 5890.38, "end": 5891.4, "word": " واحد", "probability": 0.960693359375}, {"start": 5891.4, "end": 5892.46, "word": " و", "probability": 0.409912109375}, {"start": 5892.46, "end": 5892.7, "word": " ال", "probability": 0.96533203125}, {"start": 5892.7, "end": 5892.94, "word": " a", "probability": 0.97900390625}, {"start": 5892.94, "end": 5893.34, "word": " node", "probability": 0.85986328125}, {"start": 5893.34, "end": 5893.54, "word": " ب", "probability": 0.67578125}, {"start": 5893.54, "end": 5893.82, "word": " zero", "probability": 0.380859375}, {"start": 5893.82, "end": 5894.02, "word": " و", "probability": 0.83349609375}, {"start": 5894.02, "end": 5894.14, "word": " ال", "probability": 0.93994140625}, {"start": 5894.14, "end": 5894.68, "word": " a2", "probability": 0.955810546875}, {"start": 5894.68, "end": 5895.36, "word": " ب", "probability": 0.89892578125}, {"start": 5895.36, "end": 5895.74, "word": " zero", "probability": 0.8544921875}, {"start": 5895.74, "end": 5895.98, "word": " و", "probability": 0.7646484375}, {"start": 5895.98, "end": 5896.7, "word": " هكذا", 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5900.72, "word": "طيب", "probability": 0.9337565104166666}, {"start": 5900.72, "end": 5901.14, "word": " المرة", "probability": 0.9228515625}, {"start": 5901.14, "end": 5901.52, "word": " جاية", "probability": 0.5779622395833334}, {"start": 5901.52, "end": 5901.62, "word": " ان", "probability": 0.7294921875}, {"start": 5901.62, "end": 5901.94, "word": " شاء", "probability": 0.95166015625}, {"start": 5901.94, "end": 5902.04, "word": " الله", "probability": 0.96337890625}, {"start": 5902.04, "end": 5903.08, "word": " بنكمل", "probability": 0.9752604166666666}, {"start": 5903.08, "end": 5904.76, "word": " يعني", "probability": 0.5670166015625}, {"start": 5904.76, "end": 5905.7, "word": " المحاضرة", "probability": 0.9891357421875}, {"start": 5905.7, "end": 5906.64, "word": " القادمة", "probability": 0.9900716145833334}, {"start": 5906.64, "end": 5906.94, "word": " يوم", "probability": 0.974365234375}, {"start": 5906.94, "end": 5908.16, "word": " الأربعاء", "probability": 0.8382568359375}, {"start": 5908.16, "end": 5908.4, "word": " ان", "probability": 0.673828125}, {"start": 5908.4, "end": 5908.7, "word": " شاء", "probability": 0.981689453125}, {"start": 5908.7, "end": 5908.98, "word": " الله", "probability": 0.95263671875}, {"start": 5908.98, "end": 5909.88, "word": " تعالى", "probability": 0.9244791666666666}, {"start": 5909.88, "end": 5911.52, "word": " بنطلع", "probability": 0.8572998046875}, {"start": 5911.52, "end": 5911.7, "word": " ..", "probability": 0.71533203125}, {"start": 5911.7, "end": 5912.86, "word": " بنكمل", "probability": 0.8865559895833334}, {"start": 5912.86, "end": 5913.04, "word": " ال", "probability": 0.9228515625}, {"start": 5913.04, "end": 5913.52, "word": " section", "probability": 0.69921875}, {"start": 5913.52, "end": 5913.82, "word": " اللي", "probability": 0.960693359375}, {"start": 5913.82, "end": 5914.4, "word": " ضايل", "probability": 0.8984375}, {"start": 5914.4, "end": 5915.52, "word": " و", "probability": 0.9228515625}, {"start": 5915.52, "end": 5916.88, "word": " بنعطيكوا", "probability": 0.9051106770833334}, {"start": 5916.88, "end": 5917.34, "word": " أرقام", "probability": 0.9732666015625}, {"start": 5917.34, "end": 5918.04, "word": " المسائل", "probability": 0.9259033203125}, {"start": 5918.04, "end": 5918.3, "word": " على", "probability": 0.9033203125}, {"start": 5918.3, "end": 5918.48, "word": " ال", "probability": 0.96728515625}, {"start": 5918.48, "end": 5918.74, "word": " two", "probability": 0.9345703125}, {"start": 5918.74, "end": 5919.62, "word": " sections", "probability": 0.91455078125}], "temperature": 1.0}], "language": "ar", "language_probability": 1.0, "duration": 5920.949, "duration_after_vad": 5238.194718750032}
\ No newline at end of file
diff --git a/PL9fwy3NUQKwa8ZDfSFGn6H8xVFLzqmCZC/aLofgEh8GKI_raw.srt b/PL9fwy3NUQKwa8ZDfSFGn6H8xVFLzqmCZC/aLofgEh8GKI_raw.srt
new file mode 100644
index 0000000000000000000000000000000000000000..3270a8687c60866ad72a964d5cfcf82ce436bd5c
--- /dev/null
+++ b/PL9fwy3NUQKwa8ZDfSFGn6H8xVFLzqmCZC/aLofgEh8GKI_raw.srt
@@ -0,0 +1,3192 @@
+1
+00:00:00,000 --> 00:00:02,580
+موسيقى
+
+2
+00:00:10,460 --> 00:00:14,980
+بسم الله الرحمن الرحيم كنا بتحدث المرة الماضية عن
+
+3
+00:00:14,980 --> 00:00:19,400
+الطريقة الأولى لحل اللي هو ال homogeneous
+
+4
+00:00:19,400 --> 00:00:22,440
+differential equation with constant coefficients
+
+5
+00:00:22,440 --> 00:00:28,420
+وكانت اللي هو طريقة الحل
+
+6
+00:00:28,420 --> 00:00:34,040
+المعادلة المتجانسة عن طريق اللي هو فرض Y تساوي E
+
+7
+00:00:34,040 --> 00:00:40,470
+أس RT وكنا بطلع عندنا أدت احتمالاتاحتمال الحلول
+
+8
+00:00:40,470 --> 00:00:45,490
+تكون او لما نجيب ال characteristic equation احتمال
+
+9
+00:00:45,490 --> 00:00:50,470
+الجذور كلها تبقى حقيقية و مختلفة احتمال تبقى
+
+10
+00:00:50,470 --> 00:00:56,330
+complex احتمال تبقى repeated realممكن تبقى
+
+11
+00:00:56,330 --> 00:01:01,170
+repeated complex على كده الأمرين واخدنا على ذلك
+
+12
+00:01:01,170 --> 00:01:06,270
+ثلاثة أمثلة والأن بنكمل الأمثلة على نفس الموضوع
+
+13
+00:01:06,270 --> 00:01:10,070
+يبقى السؤال لو المثال رقم اثنين بيقول show that
+
+14
+00:01:10,070 --> 00:01:14,090
+the general solution of the differential equationY
+
+15
+00:01:14,090 --> 00:01:18,470
+to the derivative of 4 لما حط الرقم بين جثين تعني
+
+16
+00:01:18,470 --> 00:01:22,130
+المشتقة بدون أقوى C يعني أس يبقى Y to the
+
+17
+00:01:22,130 --> 00:01:25,330
+derivative of 4 minus Y يساوي Zero can be written
+
+18
+00:01:25,330 --> 00:01:31,370
+as يمكن أن نكتب هذا الحل على صيغة C1 Cos T زائد C2
+
+19
+00:01:31,370 --> 00:01:37,690
+Sin T زائد C3 Gosh T زائد C4 Sin T مدام بقول
+
+20
+00:01:37,690 --> 00:01:41,350
+احتمال الحل يكون على الشكل هذا يمكن لما نحل ما
+
+21
+00:01:41,350 --> 00:01:46,450
+يطلعشالشكل هذا اذا طلع كنبة اذا ما طلعش مانتا بدي
+
+22
+00:01:46,450 --> 00:01:51,510
+احول المسألة بحيث فعلا تصير في الشكل اللي عندنا
+
+23
+00:01:51,510 --> 00:01:54,890
+هذا هذا المطلوب الأول بعدين قال لي solve ال
+
+24
+00:01:54,890 --> 00:01:58,170
+initial value problem نفس المثل اللي عندنا بس حط
+
+25
+00:01:58,170 --> 00:02:03,590
+عليه الشروط الأربعة اللي من خلالها بقدر أجيب قيمة
+
+26
+00:02:03,590 --> 00:02:08,910
+الثوابت اللي موجودة عندنا اذا نيجي الحل مع المطلوب
+
+27
+00:02:08,910 --> 00:02:15,910
+الأول اللي هو نمرة Aأفترض أن الحل اللي عندي على
+
+28
+00:02:15,910 --> 00:02:21,190
+الصيغة هو Y تساوي E أُس RT وجيب ال characteristic
+
+29
+00:02:21,190 --> 00:02:27,330
+equation المناظرة لهذه المعادلة بيجي أقول له let Y
+
+30
+00:02:27,330 --> 00:02:33,230
+تساوي E أُس RT بيه solution
+
+31
+00:02:40,410 --> 00:02:47,190
+بعد ذلك الاختصار
+
+32
+00:02:47,190 --> 00:02:55,440
+الوحيد هواللي هو R أس أربعة ناقص واحد يساوي Zero
+
+33
+00:02:55,440 --> 00:03:01,980
+هذه ممكن أحللها كفرق بين المربعين يبقى لو حللناها
+
+34
+00:03:01,980 --> 00:03:07,340
+كفرق بين المربعين بصير R تربيع ناقص واحد في R
+
+35
+00:03:07,340 --> 00:03:13,440
+تربيع زائد واحد يساوي Zero هذه كمان ممكن أحللها
+
+36
+00:03:13,440 --> 00:03:20,280
+كفرق بين المربعينيبقى بالصير R تربيع زائد واحد هذه
+
+37
+00:03:20,280 --> 00:03:25,500
+فرق بين المربعين R ناقص واحد في R زائد واحد يساوي
+
+38
+00:03:25,500 --> 00:03:31,780
+Zero يعني هذه معناته ما لها لا يوجد لها تحليل
+
+39
+00:03:31,780 --> 00:03:38,460
+وبالتالي ال R هتبقى Complex يبقى هذا معناته ان R
+
+40
+00:03:38,460 --> 00:03:47,380
+واحد و اتنيناللي هو بده ساوي زائد او ناقص I وR
+
+41
+00:03:47,380 --> 00:03:53,860
+تلاتة بده ساوي واحد وR اربعة بده ساوي مين ناقص
+
+42
+00:03:53,860 --> 00:03:59,040
+واحد اذا صار شكل الحل على الشكل التالي YC
+
+43
+00:04:23,450 --> 00:04:27,830
+بدي اقارن بين الحل اللي عندي و الحل اللي هو قاله
+
+44
+00:04:28,310 --> 00:04:32,110
+بلاحظ اتنين هذول هما نفس اتنين هذول ماعناش مشكلة
+
+45
+00:04:32,110 --> 00:04:38,150
+فيهم تمام C1 cos T C2 sin T نفس الشيء لكن الخلاف
+
+46
+00:04:38,150 --> 00:04:42,470
+وين؟ خلاف ما بين اتنين هنا معطنية بدالة جوش وسنش
+
+47
+00:04:42,470 --> 00:04:47,070
+هنا معطنية بدالة ال exponential E أس T وE أس ناقص
+
+48
+00:04:47,070 --> 00:04:52,820
+T لو راجعنا بالذاكرة إلى الغراءمن صيغة Euler بقى
+
+49
+00:04:52,820 --> 00:05:01,340
+نقول E أُس I T يكو ساين T زائد I ساين T مظبوط
+
+50
+00:05:01,340 --> 00:05:09,420
+اتنين E أس ناقص I T لكو ساين T ناقص I ساين T تمام
+
+51
+00:05:09,420 --> 00:05:14,440
+يبقى بنحاول نستخدم اللي هو اللي عندنا هنا او
+
+52
+00:05:14,440 --> 00:05:20,080
+نستخدم تعريف الجوش والسنجإذا كنتوا بتدركوا ابيتكوا
+
+53
+00:05:20,080 --> 00:05:23,740
+خاصية اللي درسوا معايا Calculus بيه ان لو جمعت
+
+54
+00:05:23,740 --> 00:05:29,900
+القوش زائد السنش بيعطيني E أس T ولو طرحت القوش
+
+55
+00:05:29,900 --> 00:05:36,480
+ناقص السنش بيعطيني مين E أس ناقص T بنذكركوا تذكير
+
+56
+00:05:36,480 --> 00:05:45,320
+اللي ليس إلا بجينا نقول قوش T زائد سنش T طبعا
+
+57
+00:05:45,320 --> 00:05:53,320
+بتشوفوا قدرش هذا يساويالجوش هي EOS T زائد EOS ناقص
+
+58
+00:05:53,320 --> 00:06:01,280
+T على اتنين هذه جوش السنج كانت EOS T ناقص EOS ناقص
+
+59
+00:06:01,280 --> 00:06:09,150
+T على اتنين لو جمعنا كله على اتنينيبقى المقام هذا
+
+60
+00:06:09,150 --> 00:06:12,950
+هو نفس المقام هذا، إذا بضلي الأربعة بدي أجمعهم،
+
+61
+00:06:12,950 --> 00:06:18,510
+هتروح هذه و هذه مع بعض، بضلي اتنين Eost اللي هو من
+
+62
+00:06:18,510 --> 00:06:27,330
+Eost بنفس الطريقة Similarly اللي
+
+63
+00:06:27,330 --> 00:06:35,960
+هو Gauche ال T ناقصالـ T كل هذا الكلام بدي اسمه
+
+64
+00:06:35,960 --> 00:06:42,930
+مين؟ E أس ناقص Tتمام؟ إذا بدي أجي على الحل اللي
+
+65
+00:06:42,930 --> 00:06:49,210
+عندنا ده اللي بدي أسميه star وانعوض فيه يعني بدي
+
+66
+00:06:49,210 --> 00:06:55,350
+أشيل E أُس T اللي عندي هذه و أكتب بدالها gosh زائد
+
+67
+00:06:55,350 --> 00:07:00,030
+cinch و أشيل E أُس ناقص T و أكتب بدالها gosh ناقص
+
+68
+00:07:00,030 --> 00:07:04,330
+cinch يبقى منان عليه بدي أجي أقول له service
+
+69
+00:07:13,970 --> 00:07:23,350
+نحصل على ما يأتي اله YC اللي هو طالبه C1 Cos T C2
+
+70
+00:07:23,350 --> 00:07:31,910
+Sin T C3 مضروبة في Eost اللي هي main مش C3 كي واحد
+
+71
+00:07:31,910 --> 00:07:38,370
+سمنها كي واحد هي عندي في Eost اللي هي gaucheال T
+
+72
+00:07:38,370 --> 00:07:51,090
+زائد سنش ال T زائد كتنين في جوش ال T ناقص سنش ال T
+
+73
+00:07:53,490 --> 00:08:03,370
+هذا الكلام يساوي C1 cos T C2 sin T زاد الطلاق لهذه
+
+74
+00:08:03,370 --> 00:08:08,230
+فيها جوش وهذه فيها جوش إذا ممكن أخذ منهم جوش عمل
+
+75
+00:08:08,230 --> 00:08:18,150
+مشترك بصير عندي K1 زاد K2 في جوش Tنجي لهذه مضروبة
+
+76
+00:08:18,150 --> 00:08:24,190
+في K واحد وهذه مضروبة في K اتنين يبقى K واحد ناقص
+
+77
+00:08:24,190 --> 00:08:33,650
+K اتنين في سنش T هذا الكلام يساوي C واحد في Cos T
+
+78
+00:08:33,650 --> 00:08:39,850
+C اتنين في Sin T طالعي لهذه K واحد زي K اتنين هذا
+
+79
+00:08:39,850 --> 00:08:48,700
+مقتار ثابتإذن اقتصادي ساميه C3 يبقى زائد C3 في قوش
+
+80
+00:08:48,700 --> 00:08:58,040
+ال T زائد C4 في سنش ال T يبقى شلت هذا حطيت بدله C3
+
+81
+00:08:58,040 --> 00:09:03,260
+و شلت هذا حطيت بدله C4 أظن هي الصيغة اللي طلبها
+
+82
+00:09:03,260 --> 00:09:10,570
+هذهخلصنا يبقى حطنا له الحل على الصيغة اللي هو
+
+83
+00:09:10,570 --> 00:09:15,350
+بدهياه وبالتالي انتهينا من المطلوب الأول من
+
+84
+00:09:15,350 --> 00:09:22,490
+المسألة، المطلوب التاني نمر بيهكيف؟ لما طلعتش
+
+85
+00:09:22,490 --> 00:09:27,070
+الصيغة؟ رصب ان عنك بدها تطلع هذه الصيغة، ليش؟ لإن
+
+86
+00:09:27,070 --> 00:09:30,430
+ال exponential أصلا بدلالة الجوش والسنش، و هو
+
+87
+00:09:30,430 --> 00:09:34,990
+أطاني السؤال، بديها بدلالة الجوش والسنش، تمام؟
+
+88
+00:09:34,990 --> 00:09:38,930
+يبقى فيش مكانية، مدام شيلت ال exponential هذي و ال
+
+89
+00:09:38,930 --> 00:09:42,770
+exponential هذي، لازم تنكتب بدلالة الجوش والسنش،
+
+90
+00:09:42,770 --> 00:09:46,530
+فكيف بداش تطلع؟ لأ انت من الأول، اول ما شرفت
+
+91
+00:09:46,530 --> 00:09:48,030
+السؤال، قلت إذا طلعت
+
+92
+00:09:50,860 --> 00:09:54,020
+معناته لأ مش في حالة تانية، في شغل عندنا بتبقى
+
+93
+00:09:54,020 --> 00:09:58,260
+غلط، طيب؟ لكن الكون هو طلعتنا على شغلنا صح وهو
+
+94
+00:09:58,260 --> 00:10:03,680
+المطلوب جيبناهطيب نجي المطلوب التاني جالي solve ال
+
+95
+00:10:03,680 --> 00:10:08,660
+initial value problem يبقى بدنا نجي هذه المعادلة
+
+96
+00:10:08,660 --> 00:10:11,920
+اللي عندنا أصلا homogeneous هي نفس المعادلة اللي
+
+97
+00:10:11,920 --> 00:10:16,880
+فوق بس حق عليها main ال initial conditions جابلي
+
+98
+00:10:16,880 --> 00:10:21,720
+الدلة بدون اشتقاق مشتقة الأولى التانية التالتة وكل
+
+99
+00:10:21,720 --> 00:10:26,420
+وين عندي ال zero إذا بدأ أجي للمثل اللي عنديها ها
+
+100
+00:10:26,420 --> 00:10:31,980
+وده اشتقها مرة و اتنينو تلاتة و اعوض بال constants
+
+101
+00:10:31,980 --> 00:10:38,340
+اللي عندنا هنايبقى بالدرجة عندي هنا لل Y C Prime Y
+
+102
+00:10:38,340 --> 00:10:48,080
+سواء تفضل cosine بسلب C1 sin T زائد C2 في cosine T
+
+103
+00:10:48,080 --> 00:10:53,520
+طبعا تفضل الجوش بالسنش و تفضل السنش بمان بجوش بدون
+
+104
+00:10:53,520 --> 00:10:57,580
+negative sign ماعنديش إشارة سلب زي ال sign و ال
+
+105
+00:10:57,580 --> 00:11:07,490
+cosine زائد C3 في سنش Tزائد C أربعة في جوش Tبعد
+
+106
+00:11:07,490 --> 00:11:16,430
+هيك بدي YCW' نشتغل كمان مرة يبقى ناقص C1 cos T
+
+107
+00:11:16,430 --> 00:11:30,170
+ناقص C2 sin T زائد C3 في قوش T زائد C4 في سنش T
+
+108
+00:11:30,170 --> 00:11:35,670
+هذا المشتقة الثانية بالمثل بدنا نروح نجيب المشتقة
+
+109
+00:11:35,670 --> 00:11:47,540
+التالتةيبقى بصير C1 في sin T نقص C2 في cos T زائد
+
+110
+00:11:47,540 --> 00:11:51,080
+C3 في sin T
+
+111
+00:11:59,970 --> 00:12:03,470
+يبقى جيبنا المشتقات التلاتة اللي عندنا هذا بدي
+
+112
+00:12:03,470 --> 00:12:07,270
+أرجع لل initial conditions اللي عندنا لل initial
+
+113
+00:12:07,270 --> 00:12:12,410
+conditions الأولاني بيقول لي Y عند ال zero بده
+
+114
+00:12:12,410 --> 00:12:19,410
+تساوي zero وين ال Y هيها؟ يبقى هي Y ب zero تساوي
+
+115
+00:12:19,630 --> 00:12:26,370
+بدأت أشيل كل T و أضع مكانها Zero فالليلة Cos Zero
+
+116
+00:12:26,370 --> 00:12:34,010
+بواحد في C1 بC1 ندى Sin Zero مع السلامة Gosh Zero
+
+117
+00:12:34,010 --> 00:12:41,520
+كذلك بواحديبقى زائد C تلاتة سينشة Zero ب Zero نجي
+
+118
+00:12:41,520 --> 00:12:47,420
+ال condition التاني جالي Y Prime عند Zero كذلك بده
+
+119
+00:12:47,420 --> 00:12:52,700
+يسوي Zero وين Y Prime هي يبقى هذه Zero قصان صفر ب
+
+120
+00:12:52,700 --> 00:12:58,740
+واحد يبقى ب C اتنين سينشة Zero ب Zero مع السلامة
+
+121
+00:12:58,740 --> 00:13:05,220
+جوش Zero ب واحد يبقى زائد C أربعنجي ال condition
+
+122
+00:13:05,220 --> 00:13:09,020
+التالت ال condition التالت بيقولي yw prime عند 0
+
+123
+00:13:09,020 --> 00:13:18,140
+ب1 yw prime عند 0 بده يساوي 1 implies ان ال 1 هي
+
+124
+00:13:18,140 --> 00:13:24,760
+ال yw prime تمام بدنا نعوض عن tb0يبقى ايش بيصير
+
+125
+00:13:24,760 --> 00:13:33,540
+عندي هنا سالب C1 هدب Zero مع السلامة زائد C3
+
+126
+00:13:33,540 --> 00:13:39,200
+والتاني مع السلامة نيجي ال condition التالت جالي Y
+
+127
+00:13:39,200 --> 00:13:44,240
+triple prime عند Zero بده يساوي الواحدemployees
+
+128
+00:13:44,240 --> 00:13:48,640
+واحد بده اعوض في المشتقة التالتة يبقى هدف zero بضل
+
+129
+00:13:48,640 --> 00:13:59,900
+ناقص c2 ناقص c2 وهدف zero زائد c4 يبقى زائد c4
+
+130
+00:13:59,900 --> 00:14:06,380
+اطلعولي للمعادلة الأولى والتالتة بده اجمع الاتنين
+
+131
+00:14:06,380 --> 00:14:13,160
+هدول مع بعضهذول اتنين لو جمعتهم مع بعض بقير سالب
+
+132
+00:14:13,160 --> 00:14:18,780
+C1 مع C1 بيبقى 2C3
+
+133
+00:14:18,780 --> 00:14:21,740
+بيبقى واحد
+
+134
+00:14:22,610 --> 00:14:28,690
+تمام اجمع zero زاد واحد هيب واحد سالب C1 معموجة ب
+
+135
+00:14:28,690 --> 00:14:36,590
+C1 بظل اتنين C3 يساوي واحد ومنها C3 بده يساوي نص
+
+136
+00:14:36,590 --> 00:14:44,650
+طب لما C3 يساوي نص C1 بيبقى كدهش بسالب نص و C1
+
+137
+00:14:44,650 --> 00:14:51,040
+يساوي سالب نص بدهش اجمع المعادلة التانيةمع
+
+138
+00:14:51,040 --> 00:14:58,080
+المعادلة من الرابع اجمع ZERO واحد بده يعطيكي واحد
+
+139
+00:14:58,080 --> 00:15:08,060
+بده يساوي نجمع C2 مع C2 يبقى بيضلي 2C4 يبقى 2C4
+
+140
+00:15:08,060 --> 00:15:17,060
+ومنها C4 يسوى قداش نص لما C4 بده يسوى نص يبقى C2
+
+141
+00:15:17,060 --> 00:15:25,520
+بسالب نصوC2 يساوي سالب نص إذا نقدر نجيه بالشكل
+
+142
+00:15:25,520 --> 00:15:32,360
+العام لحل ال initial value problem يبقى الحل صار
+
+143
+00:15:32,360 --> 00:15:39,530
+YC يساويبدا يجي الى C1 C1 طلع عندنا بناقص نص يبقى
+
+144
+00:15:39,530 --> 00:15:48,690
+ناقص نص cos T وC2 طلع عندنا بناقص نص كذلك يبقى
+
+145
+00:15:48,690 --> 00:15:58,070
+ناقص نص في sin T وC3 طلع بنص يبقى زائد نص اللي هو
+
+146
+00:15:58,070 --> 00:16:06,680
+cos Tو C4 يبقى
+
+147
+00:16:06,680 --> 00:16:14,100
+زائد نص في سن شتتي يبقى ده حل ال initial value
+
+148
+00:16:14,100 --> 00:16:15,680
+problem اللي عندنا
+
+149
+00:16:29,090 --> 00:16:31,930
+طبعا المرة اللى فاتت ماحلناش ال national value
+
+150
+00:16:31,930 --> 00:16:37,390
+problem وماعطناش ولا سؤال بهذه الطريقة هي بقى نعمل
+
+151
+00:16:37,390 --> 00:16:43,720
+فيه تحويرة مشان نطلع شكل الجوابنعطيكم كمان مثال
+
+152
+00:16:43,720 --> 00:16:50,100
+على نفس الموضوع برضه يختلف حما و نوعا و ماحلناش
+
+153
+00:16:50,100 --> 00:16:56,860
+زيه من قبل يبقى بنجي للمثال الرقم تلاتة لسؤال واحد
+
+154
+00:16:56,860 --> 00:17:04,320
+و عشرين من الكتاب بيقول solve the differential
+
+155
+00:17:04,320 --> 00:17:09,800
+equation حل المعادلة التفاضلية why to the
+
+156
+00:17:09,800 --> 00:17:16,870
+derivative eightزائد ات واي to the derivative four
+
+157
+00:17:16,870 --> 00:17:36,930
+زائد ست عشر واي بده يساوي قداش بده يساوي زي المرة
+
+158
+00:17:36,930 --> 00:17:42,700
+اللي باتت كده بتذكروا قلنافيه عنده والحاجة real
+
+159
+00:17:42,700 --> 00:17:46,960
+and unequal roots وخلصنا منها واخدنا عليها أمثلة
+
+160
+00:17:46,960 --> 00:17:51,140
+بعدها قولنا complex roots واخدنا عليها أحيانا real
+
+161
+00:17:51,140 --> 00:17:54,800
+و أحيانا complex جينا لل repeated roots قولنا ممكن
+
+162
+00:17:54,800 --> 00:17:59,200
+تبقى repeated و real أو ممكن تبقى repeated و
+
+163
+00:17:59,200 --> 00:18:03,580
+complex repeated و complex ماشوفناش ولا مثال حتى
+
+164
+00:18:03,580 --> 00:18:10,040
+اللحظة تمام؟ لكن هي و جاييبقى هذا repeated complex
+
+165
+00:18:10,040 --> 00:18:15,320
+conjugate roots نشوف كيف نتعامل معاه يبقى بنفس
+
+166
+00:18:15,320 --> 00:18:18,760
+التكتيكة اللي بدأت بالمثال اللي جابله هبدأ في حاجة
+
+167
+00:18:18,760 --> 00:18:29,160
+أقوله هنا let Y تساوي E أُس RTBA solution of
+
+168
+00:18:29,160 --> 00:18:35,460
+equation one سمي لها D one then the
+
+169
+00:18:39,250 --> 00:18:48,830
+Equation is R أس تمانية زائد تمانية R أس أربعة
+
+170
+00:18:48,830 --> 00:18:55,950
+زائد ستاشر يساوي زيرو أظن أن هذه لو جيتها حللتها
+
+171
+00:18:55,950 --> 00:19:00,770
+بيصير عندي ايش بيصير عندي R أس أربعة
+
+172
+00:19:06,570 --> 00:19:11,850
+أربعة كل هذا الكلام بده يساوي Zero يعني الجوس
+
+173
+00:19:11,850 --> 00:19:17,870
+الأول هو من نفس الجوس التاني يعني اللي هأعمل للجوس
+
+174
+00:19:17,870 --> 00:19:21,430
+الأول بدي أعمل للجوس التاني يعني أصلا الجذور مالها
+
+175
+00:19:21,430 --> 00:19:28,010
+مكررة طيب بدي أخد واحد من الجواس يبقى أرقص أربعة
+
+176
+00:19:28,010 --> 00:19:32,510
+بده يساوي قداش أظن لما ناخد الجذر التربيهي أبصي
+
+177
+00:19:32,510 --> 00:19:41,250
+كمية حيوليةطيب طلع معايا كويس يبقى ال R تساوي ناقص
+
+178
+00:19:41,250 --> 00:19:51,230
+أربع أس رابع يعني كأنها أربع أس رابع في ناقص واحد
+
+179
+00:19:51,230 --> 00:19:58,410
+أس رابع، مصبوط؟ طيب أربع أس رابع عبارة عن جذري
+
+180
+00:19:58,410 --> 00:20:05,770
+اتنينلأن أس ربع يعني أس نص لكل أس نص أربع أس نص
+
+181
+00:20:05,770 --> 00:20:12,150
+باتنين أس نص يعني جذر اتنين يبقى آلة إلى جذر اتنين
+
+182
+00:20:12,150 --> 00:20:20,170
+في سالب واحد أس مين أس ربع هذه قيمة R طيب تعالى
+
+183
+00:20:20,170 --> 00:20:26,720
+هدول كام جذر بدهم يطلعوا هنا؟أربعة جذور لان هذه
+
+184
+00:20:26,720 --> 00:20:31,560
+معدلة من درجة رابع اربعة جذور وكمان مكررة يبقى بدى
+
+185
+00:20:31,560 --> 00:20:36,440
+كمان اربعة جذور اخرى اذا جبنا الأربعة جذور هذه
+
+186
+00:20:36,440 --> 00:20:40,820
+بصير الشغل روتينيا بصير complex conjugated
+
+187
+00:20:40,820 --> 00:20:50,520
+repeatedكمبليكس ومكررة ومترافقة يبقى أنا بدأ أجيب
+
+188
+00:20:50,520 --> 00:20:56,980
+الجذور التخيلية للسالب واحد الأربعة جذور هذي قداش
+
+189
+00:20:56,980 --> 00:21:01,200
+شوفوا هالطريقة اللي بنحسبه بهالجذور وبدك تعتمديها
+
+190
+00:21:01,200 --> 00:21:06,000
+بعد هيك لأي سؤال آخر بنفس الطريقة في بعض الأسئلة
+
+191
+00:21:06,000 --> 00:21:10,690
+في التمرين لازالت على نفس الموضوعطيب يا ماناتى،
+
+192
+00:21:10,690 --> 00:21:18,030
+الان لو جيتلى الرقم ناقص واحد، أليس هو ناقص واحد
+
+193
+00:21:18,030 --> 00:21:25,010
+زائد zero في I؟ Zero اللي هو في I، I ب zero زائد
+
+194
+00:21:25,010 --> 00:21:28,950
+ناقص واحد هو ناقص واحد، ماساويتش شيء، كويب؟ طيب،
+
+195
+00:21:28,950 --> 00:21:33,710
+بدي أكتب دلالة ال cosine و ال sine، قداش cosine
+
+196
+00:21:33,710 --> 00:21:39,900
+مية و تمانين يا بنات؟اذا بدى اقول هذا cosine 180
+
+197
+00:21:39,900 --> 00:21:47,860
+فقداش صين المية و تمانين Zero يبقى
+
+198
+00:21:47,860 --> 00:21:57,200
+زائد I في صين المية و تمانينسمعته بصيغة Euler اللي
+
+199
+00:21:57,200 --> 00:22:02,800
+هي E أس I ثيتا يساوي cosine ثيتا زائد I sine ثيتا
+
+200
+00:22:02,800 --> 00:22:12,340
+تمام يبقى طبقا لصيغة Euler هذه E أس I باي يعني اي
+
+201
+00:22:12,340 --> 00:22:19,100
+باي انذاكر ابقى E أس I ثيتا يساوي cosine ثيتا زائد
+
+202
+00:22:19,100 --> 00:22:29,160
+I sine ثيتاوE أس سالب I ثيتا يساوي Cos θ ناقص I
+
+203
+00:22:29,160 --> 00:22:37,000
+sin ثيتا هذه هي هذه بس بختلفوا عن بعضهذا يكون اقص
+
+204
+00:22:37,000 --> 00:22:42,280
+اي في سالب ثيتا يعني ال cosine لسالب ثيتا ال
+
+205
+00:22:42,280 --> 00:22:46,620
+cosine even يبقى هي ال cosine ثيتا اي ال sine
+
+206
+00:22:46,620 --> 00:22:51,020
+لسالب ثيتا ال sine قد يبقى سالب بطلع برا يبقى سالة
+
+207
+00:22:51,020 --> 00:22:55,690
+ال cosine ثيتا ناقص اي في ال sine ثيتاخلّي هذه
+
+208
+00:22:55,690 --> 00:22:59,450
+المعلومتين عندك و الأن هذي احنا بنشتغل عليهم يبقى
+
+209
+00:22:59,450 --> 00:23:09,030
+اذا cosine باي زائد I sin باي هي E أس I باي طيب
+
+210
+00:23:09,030 --> 00:23:13,210
+ايش رأيك الزاوية اللي عندها دي لو ضفت لها دورات
+
+211
+00:23:13,210 --> 00:23:19,550
+كاملة اتنين باي اربعة باي ستة باي هل تتأثرلأ طب
+
+212
+00:23:19,550 --> 00:23:24,090
+بدى اضافلها وشوف يمكن الله يحلها شوية يبقى صار
+
+213
+00:23:24,090 --> 00:23:33,530
+السلب عندى واحد هو cosine باي زائد اتنين M باي و
+
+214
+00:23:33,530 --> 00:23:37,750
+ال M بتاخد واحد و اتنين و تلاتة الى ما شاء الله
+
+215
+00:23:37,750 --> 00:23:51,380
+زائد I sine اللي هو مين باي زائد اتنين M بامن M by
+
+216
+00:23:51,380 --> 00:23:57,460
+دورات كاملة لا تؤثر على القيمة على الإطلاق يعني يا
+
+217
+00:23:57,460 --> 00:24:06,200
+بنات هذه بيصير E أُس I باي زائد اتنين M by و ال M
+
+218
+00:24:06,200 --> 00:24:11,380
+تسوى Zero و واحد و اتنين و تلاتة و زي ما بدك إلى
+
+219
+00:24:11,380 --> 00:24:17,020
+مال نهاية كلها بتعطيني نفس القيمة طيب كويس هذا
+
+220
+00:24:17,020 --> 00:24:23,490
+مين؟هذا كله قيمة من؟ سالب واحد كتبته على شكل
+
+221
+00:24:23,490 --> 00:24:27,730
+complex number بهذا الشكل طيب احنا بدنا سالب واحد
+
+222
+00:24:27,730 --> 00:24:33,730
+قص جداش يبقى بده اجيبله سالب واحد قص رابع يبقى لو
+
+223
+00:24:33,730 --> 00:24:40,730
+قلت سالب واحد قص رابع هيساوي E قص I في باي زائد
+
+224
+00:24:40,730 --> 00:24:50,080
+اتنين M باي كل هذا قص رابعهذا أس مركب يعني بنضرب
+
+225
+00:24:50,080 --> 00:24:58,240
+الأسس في بعضها ضرب يبقى هذه بدأت ساوي E أس I في ال
+
+226
+00:24:58,240 --> 00:25:09,220
+πاي على أربع زائد M باي على اتنين بنفع؟ اه طيب
+
+227
+00:25:09,220 --> 00:25:17,030
+ممتاز جدا طيب هذه بتجيب لي كام جذربتجيبلي مالة
+
+228
+00:25:17,030 --> 00:25:23,930
+نهاية من الجذور M0 1 2 3 4 5 اساسي زي ما بدك بس
+
+229
+00:25:23,930 --> 00:25:28,390
+انا مابديش مالة نهاية مكفن من اربعة جذور يعني هذا
+
+230
+00:25:28,390 --> 00:25:32,230
+بتنفع للاربعة جذور وبتنفع للتلت جذور وبتنفع للست
+
+231
+00:25:32,230 --> 00:25:37,350
+جذور وبتنفع للمية جدر قد ما عندك أسس بتقدر تشتغل
+
+232
+00:25:37,350 --> 00:25:42,140
+اللي بدكي يعنييبقى هذا بنات من الآن فصلة سالب واحد
+
+233
+00:25:42,140 --> 00:25:46,700
+أس أي أس بده يساوي ال exponential وحط الأس اللي
+
+234
+00:25:46,700 --> 00:25:49,680
+بدك إياه هاي حطينا الأس اللي بدنا إياه اللي هو
+
+235
+00:25:49,680 --> 00:25:53,360
+موجود عندنا سار الشكل اللي عندنا على الشكل هذي بده
+
+236
+00:25:53,360 --> 00:26:00,660
+أحط MB0 بجيب الجذرين المترافقين الأولين بحط M
+
+237
+00:26:00,660 --> 00:26:04,920
+بواحد B تنين بتلاتة بجيب الأربعة الجذور اللي أنا
+
+238
+00:26:04,920 --> 00:26:13,210
+بدي إياهايبقى هنا بدى اقعد اخد M تساوي Zero واحد و
+
+239
+00:26:13,210 --> 00:26:18,990
+اتنين و تلتة ايه الاربع و الباقي مش لازم ليه طيب
+
+240
+00:26:18,990 --> 00:26:27,470
+لو اخدت M بي Zero م بي Zero يبقاش مصير عندي E أس I
+
+241
+00:26:27,470 --> 00:26:36,220
+Pi على أربع مظلوم؟طيب لو أخدت M بواحد يبقى بيصير I
+
+242
+00:26:36,220 --> 00:26:43,600
+باي على أربع زائد باي على اتنين يبقى اذا أخدت M
+
+243
+00:26:43,600 --> 00:26:49,460
+بواحد بيصير باي على اتنين بيصير ربع و نص بقدرش تلت
+
+244
+00:26:49,460 --> 00:27:00,020
+ربع يبقى هذه ل E أس I تلت ربع بايطيب بده ياخد M ب
+
+245
+00:27:00,020 --> 00:27:06,340
+2 يبقى لو أخدنا M ب 2 بتروح مع 2 بصير باي زائد باي
+
+246
+00:27:06,340 --> 00:27:12,060
+على أربع يعني كم؟ واحد و ربع باي يعني خمسة باي على
+
+247
+00:27:12,060 --> 00:27:20,280
+أربع يبقى E أس I خمسة باي على أربع خلصنا اتنين
+
+248
+00:27:20,280 --> 00:27:25,480
+بروح نحط مين؟ تلاتة يبقى بصير تلاتة على اتنين و
+
+249
+00:27:25,480 --> 00:27:35,440
+كم؟يبقى اي اس اي يبقى اي اس اي يبقى اي اس اي يبقى
+
+250
+00:27:35,440 --> 00:27:38,740
+اي اس اي يبقى اي اس اي يبقى اي اس اي يبقى اي اس اي
+
+251
+00:27:38,740 --> 00:27:39,320
+يبقى اي اس اي يبقى اي اس اي يبقى اي اس اي يبقى اي
+
+252
+00:27:39,320 --> 00:27:39,940
+اس اي يبقى اي اس اي يبقى اي اس اي يبقى اي اس اي
+
+253
+00:27:39,940 --> 00:27:41,400
+يبقى اي اس اي يبقى اي اس اي يبقى اي اس اي يبقى اي
+
+254
+00:27:41,400 --> 00:27:44,060
+اس اي يبقى اي اس اي يبقى اي اس اي يبقى اي اس اي
+
+255
+00:27:44,060 --> 00:27:49,800
+يبقى اي اس اي يبقى
+
+256
+00:27:54,240 --> 00:28:04,320
+Four roots are هنا جذري اتنين في المقدار هذا يبقى
+
+257
+00:28:04,320 --> 00:28:10,580
+جذري اتنين بده يضرب في كل واحدة من هذولمظبوط يبقى
+
+258
+00:28:10,580 --> 00:28:19,240
+هاي جذر 2 في E أس I باية على أربعة جذر 2 في E أس I
+
+259
+00:28:19,240 --> 00:28:27,120
+تلاتة باية على أربعة جذر 2 في E أس I خمسة باية على
+
+260
+00:28:27,120 --> 00:28:33,900
+أربعة جذر 2 في E أس I سبعة باية على أربعة
+
+261
+00:28:36,470 --> 00:28:42,690
+طب كويس بدي أجيب كل واحدة من ال exponential بدلالة
+
+262
+00:28:42,690 --> 00:28:46,870
+lambda والي ميو مش احنا الحال بقيا نقول lambda
+
+263
+00:28:46,870 --> 00:28:53,190
+زائد I ميو والتانية lambda ناقص I ميو إذا بدي أجيب
+
+264
+00:28:53,190 --> 00:28:57,990
+الجذور بهذه الشكلة كيف؟ بدي أرجع أكتب هذه بدلالة
+
+265
+00:28:57,990 --> 00:29:01,820
+القاعدة اللي عندييعني بدي اكتبها الحل اللي هو ال
+
+266
+00:29:01,820 --> 00:29:09,260
+cos pi على 4 زائد I sin pi على 4 يبقى هاي جذيري
+
+267
+00:29:09,260 --> 00:29:18,880
+اتنين في اللي هو مين cos pi على 4 زائد I sin pi
+
+268
+00:29:18,880 --> 00:29:26,660
+على 4هذا الأولاني التاني و جذر اتنين في cosine
+
+269
+00:29:26,660 --> 00:29:34,740
+تلاتة pi على اربعة زائد I sine تلاتة pi على اربعة
+
+270
+00:29:35,300 --> 00:29:45,760
+واللي بعده جذري 2 في cos 5pi على 4 زائد i sin 5pi
+
+271
+00:29:45,760 --> 00:29:56,400
+على 4 والاخير جذري 2 في cos 7pi على 4 زائد i sin
+
+272
+00:29:56,400 --> 00:30:00,960
+7pi على 4 بالشكل اللي عندنا
+
+273
+00:30:25,670 --> 00:30:29,610
+فاحصوا معايا كمان مرة بدي أعطيكم نص في الـ soufflé
+
+274
+00:30:29,610 --> 00:30:35,290
+لإنه بدنا نكمل بدنا نبني عليه و نكمل طبعا هذه
+
+275
+00:30:35,290 --> 00:30:38,510
+فرضنا الحل على الشكل هذا طلعت ال characteristic
+
+276
+00:30:38,510 --> 00:30:44,050
+equation بالشكل هذاأخذت جوز منهم أخذت الجدر الرابع
+
+277
+00:30:44,050 --> 00:30:48,670
+اللي اقترفين صار له جدر اتنين في سالب واحد أس ربع
+
+278
+00:30:48,670 --> 00:30:54,150
+بدي اعرف قداش الجذور تبعت السالب واحد الأربعة جذور
+
+279
+00:30:54,150 --> 00:30:59,070
+فجيت جوز له سالب واحد سالب واحد زيرو في I كوصين
+
+280
+00:30:59,070 --> 00:31:03,490
+مية و تمانين بسالب واحد سين مية و تمانين بزيرو اذا
+
+281
+00:31:03,490 --> 00:31:08,420
+ال term هذا كتبته على الشكل هذاطبقا لصيغة Euler
+
+282
+00:31:08,420 --> 00:31:15,200
+يبقى هذا E-I-Y الزوايا هدول لو ضفتلهم دورات كاملة
+
+283
+00:31:15,200 --> 00:31:19,900
+ماعندي مشكلة لا تتغير القيمةيعني هذا اللي بيعتبره
+
+284
+00:31:19,900 --> 00:31:25,560
+periodic functions دوال دورية اذا الناقص واحد اص
+
+285
+00:31:25,560 --> 00:31:29,880
+ربع اذا الناقص واحد هو ال cosine باي زائد اتنين M
+
+286
+00:31:29,880 --> 00:31:34,440
+باي و ال M Zero واحد و اتنين و تلاتة و اربعة و
+
+287
+00:31:34,440 --> 00:31:38,120
+خمسة الى ما شاء الله و هنا ال sine باي زائد اتنين
+
+288
+00:31:38,120 --> 00:31:41,880
+M باي اللي بقدر اكتبه E اص I باي زائد اتنين M باي
+
+289
+00:31:41,880 --> 00:31:46,520
+و هذه قيم ال Mأنا مابدي سالب واحد وانا مابدي سالب
+
+290
+00:31:46,520 --> 00:31:50,560
+واحد أس ربع فقولت سالب واحد أس ربع إذا بدي يسوى ال
+
+291
+00:31:50,560 --> 00:31:55,140
+exponential كلها أس ربع هذا الأس مركب يبقى بضرب
+
+292
+00:31:55,140 --> 00:31:59,900
+الأسوس في بعضها ضرب يبقى لما نقضه بالأسوس في بعضها
+
+293
+00:31:59,900 --> 00:32:06,220
+بيصير باي على أربعة وهذه م باي على اتنين لأنه على
+
+294
+00:32:06,220 --> 00:32:10,080
+أربعة تختصر بيصير م باي على اتنين بالشكل اللي
+
+295
+00:32:10,080 --> 00:32:16,450
+عندنا هذاماشي تمام بده نجيب الاربعة جذور مرة واحد
+
+296
+00:32:16,450 --> 00:32:20,130
+بمرة أخرى تلاتة بمرة أخرى
+
+297
+00:32:29,740 --> 00:32:34,240
+هنا حطيت ال M بواحد باي على أربع زائد باي على
+
+298
+00:32:34,240 --> 00:32:38,960
+اتنين اللي هو تلت تربع باي حطيت ال M باتنين بيصير
+
+299
+00:32:38,960 --> 00:32:41,940
+مع اتنين بتروح بيضال باي على أربع زائد باي يعني
+
+300
+00:32:41,940 --> 00:32:46,720
+واحد و ربع باي يعني خمسة على أربع باي حطيتها
+
+301
+00:32:46,720 --> 00:32:50,100
+بتلاتة تلاتة على اتنين يعني واحد و نص باي وربع
+
+302
+00:32:50,100 --> 00:32:55,010
+باتنين اللي ربع يعني سبعة باي على أربعالان بدأ
+
+303
+00:32:55,010 --> 00:32:58,590
+اكتب هذه بالصيغة Euler بدلالة ال cosine والصين
+
+304
+00:32:58,590 --> 00:33:03,710
+فروحنا كتبناها كل واحدة من الجذور الأربعة بدلالة
+
+305
+00:33:03,710 --> 00:33:08,230
+ال cosine والصين بعد ما دخلنا جذر اتنين اللي خلناه
+
+306
+00:33:08,230 --> 00:33:11,610
+ورانا في الأول يبقى صلة ال roots على الشكل اللي
+
+307
+00:33:11,610 --> 00:33:17,650
+عندنا هذا الان جتا خمسة واربعينواحد على جذر اتنين
+
+308
+00:33:17,650 --> 00:33:22,690
+وجيب الخمسة واربعين واحد على جذر اتنين يبقى شكل ال
+
+309
+00:33:22,690 --> 00:33:28,950
+road صار بالشكل هذا هاي جذر اتنين في واحد على جذر
+
+310
+00:33:28,950 --> 00:33:36,410
+اتنين زائد I على جذر اتنين هذا الأول التاني جذر
+
+311
+00:33:36,410 --> 00:33:43,390
+اتنين فيههنا جت ال 135 بي على الرابعة خمسة واروية
+
+312
+00:33:43,390 --> 00:33:47,130
+تلاتة بمية خمسة في الرابعة التانية ال cosine سالب
+
+313
+00:33:47,130 --> 00:33:51,790
+يبقى و cosine بي على الرابعة بيشارات سالب يعني
+
+314
+00:33:51,790 --> 00:34:00,310
+سالبوحد على جذر اتنين زائد I على جذر اتنين ليش؟
+
+315
+00:34:00,310 --> 00:34:04,570
+لان جيب الخمسة و رمعين بيساوي جيب المية و خمسة و
+
+316
+00:34:04,570 --> 00:34:09,350
+تلاتين في الربع الثاني الجيب بيكون بإشارة من موجب
+
+317
+00:34:09,350 --> 00:34:14,050
+نيجي للي بعدها جذر
+
+318
+00:34:14,050 --> 00:34:21,340
+اتنين فيبنجي هنا cosine خمسة باي على أربع خمسة و
+
+319
+00:34:21,340 --> 00:34:26,380
+أربعين في خمسة اللي هو بمتين و خمسة و عشرين يعني
+
+320
+00:34:26,380 --> 00:34:31,600
+في الرابع التالت يبقى ال cosine بالثالث لازم يطلع
+
+321
+00:34:31,600 --> 00:34:38,220
+هذا المرافق لواحد فيهميبقاش بيصير هنا سالب واحد
+
+322
+00:34:38,220 --> 00:34:43,800
+على جذر اتنين و
+
+323
+00:34:43,800 --> 00:34:49,840
+ال sign كمان هذي في الرابع التالت كمان بإشارة سالب
+
+324
+00:34:50,030 --> 00:34:57,790
+يبقى ناقص I على اتنين يبقى ناقص I على جدر اتنين
+
+325
+00:34:57,790 --> 00:35:03,490
+بالشكل هذا هطلعي هذا و هذا هما المترافقين صحيح ولا
+
+326
+00:35:03,490 --> 00:35:08,950
+لا؟ طب تقدروا بدون مرجع للحسابات تقولولي قداش اللي
+
+327
+00:35:08,950 --> 00:35:16,270
+ضايل هذا؟اللي هو المراتق لهذا اللي هو واحد على جدر
+
+328
+00:35:16,270 --> 00:35:22,870
+اتنين ناقص I على من؟ على جدر اتنين بتدخل جدر اتنين
+
+329
+00:35:22,870 --> 00:35:30,830
+جوا يبقى ده اش بصير واحد زائد I ناقص واحد زائد I
+
+330
+00:35:30,830 --> 00:35:40,400
+وناقص واحد ناقص I وواحد ناقص Iطلعيلي في اتنين هدول
+
+331
+00:35:40,400 --> 00:35:47,020
+هدول مترافقين مع بعض صحيح ولا لا؟ و هدول اتنين
+
+332
+00:35:47,020 --> 00:35:54,240
+كمان مترافقين مع بعض يبقى conjugate يبقى هذه
+
+333
+00:35:54,240 --> 00:36:02,430
+الجذور المترافقة طيب هدول كم جذر ابنات؟أربعة جذور،
+
+334
+00:36:02,430 --> 00:36:07,770
+لسه في أربعة زيهم، مظبوط؟ لإن احنا أخدنا هنا جزء
+
+335
+00:36:07,770 --> 00:36:12,230
+واحد فقط، و لسه كمان بقى الجذور بيبقى في أربعة
+
+336
+00:36:12,230 --> 00:36:18,890
+جذور زيهم، يبقى الجذور complex and repeated تمام؟
+
+337
+00:36:18,890 --> 00:36:23,770
+يبقى بده نعرف ما هو شكل الحل في هذه الحالة، يبقى
+
+338
+00:36:23,770 --> 00:36:32,640
+باجي بقوله YC to 7نمسك الأولاني هنا هنا Lambda
+
+339
+00:36:32,640 --> 00:36:41,680
+بقداش بواحد و ميو بواحد يبقى بالداجي اقوله C1 زي
+
+340
+00:36:41,680 --> 00:36:45,760
+اه طبعا قبل هيبقى نكتب Lambda Lambda بنات هنا اللي
+
+341
+00:36:45,760 --> 00:36:52,020
+هي مين E أس Lambda اللي هي بواحد يبقى E أس T في
+
+342
+00:36:52,020 --> 00:37:03,170
+مين في C1 زي C2 في T في Cos Tزائد C ثلاثة زائد C
+
+343
+00:37:03,170 --> 00:37:12,370
+أربعة T في sign ال T هذول كام حل؟ كام واحد هذول
+
+344
+00:37:12,370 --> 00:37:17,330
+كتم؟ لسه بتكتب كمان؟ هذول أربعة حلول يعني جيبنا
+
+345
+00:37:17,330 --> 00:37:22,520
+الحلو المقرر تبعه فكتبنا على الشكل هنامتذكرين لما
+
+346
+00:37:22,520 --> 00:37:28,000
+كنا real و ده بقى نقول C1 زي C2 T E و S T هنا جان
+
+347
+00:37:28,000 --> 00:37:33,740
+ال cosine و ال sine يبقى هنا complex و مكرر خلصنا
+
+348
+00:37:33,740 --> 00:37:38,610
+تبعت ال E و S T بدنا نجيب تبعت مين؟الـ E أُس سالق
+
+349
+00:37:38,610 --> 00:37:44,810
+يعني احنا خلصنا هذا وهذا يبقى
+
+350
+00:37:44,810 --> 00:37:53,730
+زائد E أُس ناقص T اللي هي Lambda خدنا ستة C خمسة
+
+351
+00:37:53,730 --> 00:37:56,390
+زائد C ستة T
+
+352
+00:38:10,310 --> 00:38:15,530
+كتابتها يبقى هاي
+
+353
+00:38:15,530 --> 00:38:19,790
+بصير حل ال homogenous differential equation من
+
+354
+00:38:19,790 --> 00:38:26,130
+الرتبة الثامنة complex و مكرر زي ما انتوا شايفينه
+
+355
+00:38:27,540 --> 00:38:32,740
+حد بتحب تسأل اي سؤال؟ انت هنا احنا مستقشن بناء على
+
+356
+00:38:32,740 --> 00:38:37,340
+هذا طيب
+
+357
+00:38:37,340 --> 00:38:43,220
+وصلنا لل exercises يبقى بدالي لل exercises اربعة
+
+358
+00:38:43,220 --> 00:38:54,470
+اتنين المسائل من واحد او من 11 لغاية 24القد و
+
+359
+00:38:54,470 --> 00:39:01,990
+المسائل من تسعة و عشرين لغاية خمسة و تلتين و من
+
+360
+00:39:01,990 --> 00:39:05,630
+الحجهم كمان سؤال تمانية و تلتين
+
+361
+00:39:25,470 --> 00:39:28,450
+لحد هنا أوقف بالنسبة للـ homogeneous differential
+
+362
+00:39:28,450 --> 00:39:32,170
+equation بدنا نروح للـ non-homogeneous
+
+363
+00:39:32,170 --> 00:39:36,710
+differential equation و اليوم ناخد أول طريقة فقط
+
+364
+00:39:36,710 --> 00:39:40,750
+اللي هو طريقة الـ undetermined coefficients يبقى
+
+365
+00:39:40,750 --> 00:39:49,050
+بنيجي ل section 4-3 اللي هو the method of
+
+366
+00:39:49,050 --> 00:39:54,570
+undetermined
+
+367
+00:39:54,570 --> 00:39:54,930
+coefficients
+
+368
+00:40:00,570 --> 00:40:06,510
+نفس الطريقة اللي أخدناها لل second order ناخدها لل
+
+369
+00:40:06,510 --> 00:40:15,330
+ninth order يبقى consider the differential
+
+370
+00:40:15,330 --> 00:40:24,430
+equation y to the derivative n مضروبة في ال a0زائد
+
+371
+00:40:24,430 --> 00:40:30,510
+a1 y to the derivative n minus ال 1 زائد ونظل
+
+372
+00:40:30,510 --> 00:40:37,450
+ماشيين لغاية ما نوصل لل a n minus ال 1 y a prime
+
+373
+00:40:37,450 --> 00:40:44,090
+زائد ال a n y بده يساوي ال g of t وسميلي المعادلة
+
+374
+00:40:44,090 --> 00:40:49,610
+هذه رقم 1 The
+
+375
+00:40:49,610 --> 00:40:51,810
+solution
+
+376
+00:40:53,610 --> 00:41:07,790
+of the differential equation one is Y تساوي YC
+
+377
+00:41:07,790 --> 00:41:20,850
+زائد capital Y of T where حيث YC is the solution
+
+378
+00:41:24,830 --> 00:41:32,030
+هذه هي الحلقة للإيقاع
+
+379
+00:41:32,030 --> 00:41:35,150
+الهوموجينيوز
+
+380
+00:41:35,150 --> 00:41:36,310
+الهوموجينيوز الهوموجينيوز الهوموجينيوز
+
+381
+00:41:36,310 --> 00:41:38,110
+الهوموجينيوز الهوموجينيوز الهوموجينيوز
+
+382
+00:41:38,110 --> 00:41:40,570
+الهوموجينيوز الهوموجينيوز الهوموجينيوز
+
+383
+00:41:40,570 --> 00:41:40,650
+الهوموجينيوز الهوموجينيوز الهوموجينيوز
+
+384
+00:41:40,650 --> 00:41:41,050
+الهوموجينيوز الهوموجينيوز الهوموجينيوز
+
+385
+00:41:41,050 --> 00:41:41,050
+الهوموجينيوز الهوموجينيوز الهوموجينيوز
+
+386
+00:41:41,050 --> 00:41:41,070
+الهوموجينيوز الهوموجينيوز الهوموجينيوز
+
+387
+00:41:41,070 --> 00:41:45,510
+الهوموجينيوز الهوموجينيوز الهوموجينيوز
+
+388
+00:41:45,510 --> 00:41:49,750
+الهوموجينيوز الهوموجين
+
+389
+00:41:50,270 --> 00:41:58,690
+زائد زائد a n minus ال one في ال y prime زائد a n
+
+390
+00:41:58,690 --> 00:42:07,950
+في ال y بده ساوي مين zero and capital Y of T is a
+
+391
+00:42:07,950 --> 00:42:16,850
+particular solution is a particular solution هو
+
+392
+00:42:16,850 --> 00:42:31,150
+الحل الخاصof the differential equation one we
+
+393
+00:42:31,150 --> 00:42:41,470
+use the method of undetermined coefficients
+
+394
+00:42:41,470 --> 00:42:45,850
+undetermined
+
+395
+00:42:45,850 --> 00:42:47,910
+coefficients
+
+396
+00:43:17,810 --> 00:43:21,570
+الشكل الخاص according
+
+397
+00:43:25,620 --> 00:43:31,240
+to the following table
+
+398
+00:50:22,480 --> 00:50:28,220
+نرجع لموضوع الـ Undetermined coefficients طبعا لما
+
+399
+00:50:28,220 --> 00:50:32,540
+قرأت هذا الكلام وجدته لم يختلف شيئا عن ال second
+
+400
+00:50:32,540 --> 00:50:36,920
+order differential equations مظبوط فبجباجي بقول
+
+401
+00:50:36,920 --> 00:50:39,720
+method of undetermined coefficients طريقة
+
+402
+00:50:39,720 --> 00:50:43,760
+المعاملات المجهولة المعادلة في صيغتها العامة اللي
+
+403
+00:50:43,760 --> 00:50:48,060
+هو ال non-homogeneous بالشكل اللي عندنا هذاالـ
+
+404
+00:50:48,060 --> 00:50:52,820
+solution تبع ال equation one هو عبارة عن جزءين حل
+
+405
+00:50:52,820 --> 00:50:56,920
+ال homogeneous ذات حل خاص لل non homogeneous نجمع
+
+406
+00:50:56,920 --> 00:51:01,900
+الاتنين بيعطيني الحل ال general solution لل non
+
+407
+00:51:01,900 --> 00:51:05,580
+homogeneous differential equation يبقى YC هو حل ال
+
+408
+00:51:05,580 --> 00:51:09,420
+homogeneous differential equation اللي عندنا وYT
+
+409
+00:51:09,420 --> 00:51:14,040
+هو الحل الخاص للمعادلة الأساسية اللي هي واحد بس
+
+410
+00:51:14,040 --> 00:51:18,530
+بشرطلما نستخدم الـ Undetermined coefficients بد
+
+411
+00:51:18,530 --> 00:51:23,450
+المعاملات دول ثوابت زي ما انت شايفينهم بدها G of T
+
+412
+00:51:23,450 --> 00:51:29,490
+تبقى على شكل معين يبقى has a particular form G of
+
+413
+00:51:29,490 --> 00:51:32,930
+T بدت تبقى على شكل خاص according to the following
+
+414
+00:51:32,930 --> 00:51:37,830
+table طبقا للجدول التالف لو كانت ال G of T
+
+415
+00:51:37,830 --> 00:51:41,550
+polynomial يبقى بدي أقوله T to the power S في
+
+416
+00:51:41,550 --> 00:51:46,040
+polynomial مناضرة لألو كان polynomial في
+
+417
+00:51:46,040 --> 00:51:49,400
+exponential يكبر T to the power S polynomial في
+
+418
+00:51:49,400 --> 00:51:53,440
+exponential لو كان polynomial في exponential في
+
+419
+00:51:53,440 --> 00:52:01,320
+cosine BT أو sin BT أو مجموعهما أو الفرق فيما
+
+420
+00:52:01,320 --> 00:52:05,600
+بينهما على كل الأربعة أمور بدي اكتب T to the power
+
+421
+00:52:05,600 --> 00:52:11,260
+S polynomial من الدرجة رقم M في ال cosineزاد
+
+422
+00:52:11,260 --> 00:52:15,600
+polynomial تانية من الدرجة m في ال sign وكل هذا
+
+423
+00:52:15,600 --> 00:52:20,920
+مضروب في main في ال exponential دلت قصة ال S هذه
+
+424
+00:52:20,920 --> 00:52:25,160
+جداش يمكن zero تطلع يمكن واحد يمكن اتنين يمكن
+
+425
+00:52:25,160 --> 00:52:28,500
+تلاتة يمكن اربعة يمكن خمسة في second order
+
+426
+00:52:28,500 --> 00:52:32,200
+برينجوليا zero وواحد واتنين بس واحدة من التلات قيم
+
+427
+00:52:32,550 --> 00:52:41,110
+لكن في ال order from 1,2,0,1,2,3,4,5,10 لغاية ال N
+
+428
+00:52:41,110 --> 00:52:49,410
+يبقى ال S هو أصغر رقم موجب صحيح بحيث انه ماعنديش
+
+429
+00:52:49,410 --> 00:52:55,890
+ولا term في ال YT بده يساوي term in YC يبقى
+
+430
+00:52:55,890 --> 00:53:00,990
+differs يختلف from every term in the solution YC
+
+431
+00:53:01,270 --> 00:53:07,530
+بدي كل term في capital YT يختلف عن اي term موجود
+
+432
+00:53:07,530 --> 00:53:11,110
+في الحل اللي هو YC حل ال homogenous differential
+
+433
+00:53:11,110 --> 00:53:14,730
+equation أظن ماجيبناها شي جديد هو هو اللي تبقى
+
+434
+00:53:14,730 --> 00:53:19,570
+second order بس عمّمناه زي ما أنتوا شايفين طيب
+
+435
+00:53:19,570 --> 00:53:22,610
+بدنا نبدأ طب حد رفيكوا تسأل أسئلة جابي المدخل في
+
+436
+00:53:22,610 --> 00:53:26,470
+الأمثلة ايش
+
+437
+00:53:26,470 --> 00:53:40,780
+طيبيبقى اول
+
+438
+00:53:40,780 --> 00:53:46,840
+شغلة نبدأ فيها هي حل الهوموجينيس يبقى باجي بقوله
+
+439
+00:53:46,840 --> 00:53:57,020
+let Y تساوي E أس RT BA solution of the
+
+440
+00:54:10,310 --> 00:54:18,070
+يبقى باجي بقول ذي characteristic equationof
+
+441
+00:54:18,070 --> 00:54:26,470
+equation اتنين is R تكيب زائد اربعة R تساوي كدهاش
+
+442
+00:54:26,470 --> 00:54:32,850
+Zero ومنها R في R تربيع زائد اربعة بيساوي كدهاش
+
+443
+00:54:32,850 --> 00:54:40,830
+Zero يبقى ال R تساوي Zero R واحد وR اتنين و تلاتة
+
+444
+00:54:40,830 --> 00:54:49,360
+بده يساوي زائد او ناقص اتنين Iانه كمية تخيلية يبقى
+
+445
+00:54:49,360 --> 00:54:57,960
+هذا بدي اعطيك شكل ال Y C بديه ساوى C واحد في E أس
+
+446
+00:54:57,960 --> 00:55:04,760
+Zero بواحد مع السلامة هذي بده يصير الزاد لمدة
+
+447
+00:55:04,760 --> 00:55:11,370
+ماعنديش ماعنديش الا ميويبقى هنا بجي بقوله c3 cos
+
+448
+00:55:11,370 --> 00:55:20,930
+2t c4 sin 2t و ببروزها لإني بدي أرجعلها بعد قليل
+
+449
+00:55:20,930 --> 00:55:25,310
+الان بدنا نجي نجيب main ال particular solution
+
+450
+00:55:25,310 --> 00:55:33,130
+للمعادلة رقم واحد فبجي بقوله هنا capital Y of T
+
+451
+00:55:33,130 --> 00:55:40,020
+بده يساوي نجي بطلعPolynomial من الدرجة الأولى يبقى
+
+452
+00:55:40,020 --> 00:55:44,900
+باكتب له T to the power S وبحف بينه same
+
+453
+00:55:44,900 --> 00:55:50,000
+polynomial من الدرجة الأولى اللي هو A naught T
+
+454
+00:55:50,000 --> 00:55:56,560
+زائد ال A1 وبقول له استنى شوية هك وتعالى نشوف قداش
+
+455
+00:55:56,560 --> 00:56:02,400
+قيمة Sبغطي هذا term واجب اخطلع للمقدار بين القوسين
+
+456
+00:56:02,400 --> 00:56:10,800
+هل اي term هنا يشبه اي term من الترمات هدول هذا
+
+457
+00:56:10,800 --> 00:56:15,500
+constant وهذا constant يبقى فيه تشابه إذا بدى أحط
+
+458
+00:56:15,500 --> 00:56:22,640
+s بقدرش؟ بواحد لو حطيت s بواحد هذه تدخل جوا بصير
+
+459
+00:56:22,640 --> 00:56:30,630
+a0t تربية زائد a1tفى تشابه بين هدول معاهى term هنا
+
+460
+00:56:30,630 --> 00:56:35,830
+لأ يبقى اللى بتحل الاشكالية فقط S تساوي واحد يبقى
+
+461
+00:56:35,830 --> 00:56:42,350
+باجى بقوله here ال S تساوي واحد يبقى هدف بده
+
+462
+00:56:42,350 --> 00:56:49,810
+يعطينى انه capital Y of T هو عبارة عن a node T
+
+463
+00:56:49,810 --> 00:56:59,750
+تربية زائد a one Tتمام؟ الان بدى اروح اطلع قداش
+
+464
+00:56:59,750 --> 00:57:05,070
+قيمة اللى هو ال a node و ال a1 و قاعد هيك بنرجع
+
+465
+00:57:05,070 --> 00:57:09,690
+لمين لل general solution اذا لازم اللى اشتقها كام
+
+466
+00:57:09,690 --> 00:57:17,330
+مرة؟ ثلاث مرات اذا بدى اروح اجيبله y prime of t ب2
+
+467
+00:57:17,330 --> 00:57:27,090
+a node t زائد a1بالزملة YOTWP
+
+468
+00:57:27,090 --> 00:57:35,570
+نشتق كمان مرة باتنين نوت هذه مع السلامة وهذه مشتقة
+
+469
+00:57:35,570 --> 00:57:40,690
+التاب واحد بدنا المشتقة من التانية يبقى جيبنا
+
+470
+00:57:40,690 --> 00:57:44,970
+المشتقة الثانية خلصنا منها بس بدنا نروح نجيب من
+
+471
+00:57:44,970 --> 00:57:51,920
+المشتقة التالتة يبقىهذا بدى يعطيك ان المشتقة
+
+472
+00:57:51,920 --> 00:57:57,960
+التالتة يكبتل Y triple A prime of T بدى يسوى قداش
+
+473
+00:57:57,960 --> 00:58:03,760
+Zero لان اتنين مقدار ثابت والاينود مقدار ثابت نرجع
+
+474
+00:58:03,760 --> 00:58:08,520
+نعوض وين في المعادلة اللى هي رقم واحد اللى عندنا
+
+475
+00:58:08,520 --> 00:58:20,160
+يبقى باجي بقوله هنا substitute in equation oneو جت
+
+476
+00:58:20,160 --> 00:58:23,760
+يبقى بيدنا نرجع لل equation one
+
+477
+00:58:45,930 --> 00:58:51,650
+يبقى y triple prime ب zero يبقى هي ال zero راح و
+
+478
+00:58:51,650 --> 00:58:57,590
+عندك اربعة في y prime وين y prime هي يبقى بصير
+
+479
+00:58:57,590 --> 00:59:06,910
+تمانية a node t زائد تمانية a node t زائد اربعة a
+
+480
+00:59:06,910 --> 00:59:07,230
+one
+
+481
+00:59:17,860 --> 00:59:21,000
+نعمل مقارنة ما بين الطرفين نعمل مقارنة ما بين
+
+482
+00:59:21,000 --> 00:59:23,800
+الطرفين نعمل مقارنة ما بين الطرفينيبقى تمانية a
+
+483
+00:59:23,800 --> 00:59:29,040
+note بده يسوى قداش امانات واحد هذا بده يعطيك ان a
+
+484
+00:59:29,040 --> 00:59:34,900
+note يسوى قداش تمان اللي بعدها اربعة a one بده
+
+485
+00:59:34,900 --> 00:59:41,060
+يسوى من زيرو يبقى ال a one بده يسوى من زيرو يبقى
+
+486
+00:59:41,060 --> 00:59:47,860
+صار شكل ال Y of T على الشكل التاليبرجع لل Y of T
+
+487
+00:59:47,860 --> 00:59:52,720
+اللى عندنا اللى همين ال Y of T هايه يبقى هنا S
+
+488
+00:59:52,720 --> 00:59:56,100
+بواحد صار بالشكل اللى عندنا هذا بدي اشيل A نوع ده
+
+489
+00:59:56,100 --> 01:00:00,980
+و أحط مكانها تمون و هذا ب Zero مع السلامة يبقى صار
+
+490
+01:00:00,980 --> 01:00:08,330
+تمون T تاربيعيبقى هنا تمن T تربية يبقى بناء عليه Y
+
+491
+01:00:08,330 --> 01:00:14,030
+تساوي YC زائد capital Y of T Y الساوية YC اللي
+
+492
+01:00:14,030 --> 01:00:25,130
+بروزناها فوق يبقى C1 زائد C3 C2 Cos T زائد C3 في
+
+493
+01:00:25,130 --> 01:00:25,890
+ال sign
+
+494
+01:00:34,120 --> 01:00:43,570
+بنضيف عليهم capital Y of T بكتوم ت تربيعطيب حتى
+
+495
+01:00:43,570 --> 01:00:47,450
+الآن ما استخدمتش ال initial conditions يبقى بدي
+
+496
+01:00:47,450 --> 01:00:51,610
+اري على ال initial conditions اللي انا بدي اشتق
+
+497
+01:00:51,610 --> 01:00:58,850
+مرتين يبقى باجي بقوله y' يساوي هذا مع السلامة
+
+498
+01:00:58,850 --> 01:01:08,900
+وتفضل cos بسالب 2C2 في sin 2Tوزائد اتنين C تلاتة
+
+499
+01:01:08,900 --> 01:01:20,760
+كوصين اتنين T وزائد رابعة T وين الخطأ؟ why C؟ اه C
+
+500
+01:01:20,760 --> 01:01:26,920
+اتنين يعني هذه بنفسها هو C اتنين وهذه C تلاتة C
+
+501
+01:01:26,920 --> 01:01:34,660
+اتنين وC تلاتة ماشييبقى هنا c1 زي c2 زي c3 مظبوط
+
+502
+01:01:34,660 --> 01:01:39,340
+هي يبقى اشتقانا و الاشتقاق صحيح مافيش فيه اي مشكلة
+
+503
+01:01:39,340 --> 01:01:45,480
+تمام طيب بدنا نجيب yw prime يساوي نشتق هذه كمان
+
+504
+01:01:45,480 --> 01:01:53,340
+مرة يبقى ناقص اربعة c2 كوصين اتنين t ناقص اربعة c
+
+505
+01:01:53,340 --> 01:02:00,830
+تلاتة صين اتنين t زائد رابطعلى ال condition
+
+506
+01:02:00,830 --> 01:02:04,030
+الأولاني
+
+507
+01:02:04,030 --> 01:02:08,510
+يجب ان يكون y عند ال zero يسوى 0 y عند ال zero
+
+508
+01:02:08,510 --> 01:02:13,130
+يسوى 0 يبقى
+
+509
+01:02:13,130 --> 01:02:20,610
+هدى c1 كسين صفر بواحد زايد c2 هدى بزيره مع السلامة
+
+510
+01:02:20,610 --> 01:02:25,800
+و هدى بزيره مع السلامة كله يسوى كده؟الـ Condition
+
+511
+01:02:25,800 --> 01:02:31,860
+التاني y' عند 0 يكون سوى 0 ومن هنا نجي لهذه بـ 0
+
+512
+01:02:31,860 --> 01:02:39,940
+بقير هذا كوصين صفر بواحد يبقى هنا اتنين C ثلاثة
+
+513
+01:02:39,940 --> 01:02:46,080
+وهذا بـ 0 بقير يكون سوى كده؟ يكون سوى 0 الـ
+
+514
+01:02:46,080 --> 01:02:52,310
+Condition التالت y'' عند 0 أظن يكون سوى 1مظبوط
+
+515
+01:02:52,310 --> 01:03:00,830
+يبقى هذا بده يعطيك YW Prime هايها اللي هو ناقص 4C2
+
+516
+01:03:00,830 --> 01:03:06,810
+و هذا مع السلامة و هذا زائد رابع بده يساوي مين؟
+
+517
+01:03:06,810 --> 01:03:11,770
+بده يساوي Zero من هذه أمانات بقدر أقول إذا C3
+
+518
+01:03:11,770 --> 01:03:20,610
+تساوي Zeroتمام؟ نجي من هنا بقدر أجيبله كمان C2
+
+519
+01:03:20,610 --> 01:03:31,730
+يبقى هذا معناه انه ايش الواحد؟ اه بتسوي واحد صحيح
+
+520
+01:03:31,730 --> 01:03:37,070
+حقه يبقى هذه تسوي واحد مظبوطيبقى هدى معناه هذا
+
+521
+01:03:37,070 --> 01:03:46,480
+معناه انه سالب اربعة C اتنين يساوي تلت ربعربع بيجي
+
+522
+01:03:46,480 --> 01:03:50,980
+بالسلبان واحد بيظل تلات تربع يبقى هذا بدي اعطيك
+
+523
+01:03:50,980 --> 01:04:01,400
+انه C2 بده يساوي سالب تلاتة على ستاش لما C2 بده
+
+524
+01:04:01,400 --> 01:04:06,760
+يساوي سالب تلاتة على ستاش اذا C1 بتلاتة على ستاش
+
+525
+01:04:06,760 --> 01:04:15,020
+وC3 بده يساوي تلاتة على ستاش وين الواحد؟
+
+526
+01:04:19,430 --> 01:04:28,510
+سي تلاتة خليكي معايا هالحين هذا سي اتنين ابتلاتة
+
+527
+01:04:28,510 --> 01:04:32,830
+على عربي و سي اتنين ابسالب تلاتة على ستاشر بدي
+
+528
+01:04:32,830 --> 01:04:37,690
+اعوض الان سي اتنين ابسالب تلاتة على ستاشر انجليه
+
+529
+01:04:37,690 --> 01:04:44,190
+على الشجة التانيةبصير اه C1 يسوي 3 ع 16 اه C1 هذي
+
+530
+01:04:44,190 --> 01:04:49,170
+C1 ب 3 ع 16 مظبوط اذا بدي بيصير شكل المعادلة شكل
+
+531
+01:04:49,170 --> 01:04:57,910
+الحل على الشكل التالي Y يسوي C1 اللي هي 3 ع 16و C2
+
+532
+01:04:57,910 --> 01:05:09,130
+هو ناقص 3 على 16 في cos 2t و C3 بزير و بطير ال
+
+533
+01:05:09,130 --> 01:05:17,010
+term هذا و بظل بس 8T تربيع يبقى هذا الشكل الحل تبع
+
+534
+01:05:17,010 --> 01:05:19,630
+ال initial value problem
+
+535
+01:05:41,520 --> 01:05:51,580
+المثال الثاني مثال
+
+536
+01:05:51,580 --> 01:05:57,940
+اتنين find
+
+537
+01:05:57,940 --> 01:06:00,520
+the general solution of the differential equation
+
+538
+01:06:10,110 --> 01:06:14,750
+of the differential equation الي هو y to the
+
+539
+01:06:14,750 --> 01:06:23,930
+derivative 4 ناقص y بده يساوي تلاتة T زائد cosine
+
+540
+01:06:23,930 --> 01:06:32,750
+ال T وسميه لهذا المعادلة رقم 1 نفس الطريقة اللي
+
+541
+01:06:32,750 --> 01:06:41,010
+بدأنا فيها solution يبقى بالدهجة أقوله letY تساوي
+
+542
+01:06:41,010 --> 01:06:51,350
+E أس RT با solution of Y to the derivative 4 ناقص
+
+543
+01:06:51,350 --> 01:06:57,250
+Y يساوي Zero هذا بدي أعطيك ان ال characteristic
+
+544
+01:06:57,250 --> 01:07:05,970
+equation is R أربعة ناقص واحد يساوي Zero إذا صارت
+
+545
+01:07:05,970 --> 01:07:11,950
+R ترابيع ناقص واحدفى R تربيه زياد واحد يساوي Zero
+
+546
+01:07:11,950 --> 01:07:19,050
+يبقى R ناقص واحد فى R زاد واحد فرق بين المربعين
+
+547
+01:07:19,050 --> 01:07:26,930
+يساوي Zero يبقى R تساوي واحد وR تساوي سالب واحد
+
+548
+01:07:26,930 --> 01:07:33,610
+هذه R واحد هذه R اتنين وهذه R تلاتة واربعةاللي هو
+
+549
+01:07:33,610 --> 01:07:39,110
+بدر سوى زائد او ناقص I يبقى صار حل ال homogenous
+
+550
+01:07:39,110 --> 01:07:49,850
+YC بدر سوى C1 E أس T C2 E أس ناقص T زائد C تلاتة
+
+551
+01:07:49,850 --> 01:08:00,210
+cosine T زائد C أربعة في صينة T كويس بالدالي لشكل
+
+552
+01:08:00,210 --> 01:08:06,530
+G of Tبنعمل من الدرجة الأولى الزائد كوصين وليست
+
+553
+01:08:06,530 --> 01:08:11,390
+مضروبة درجة إذا بنرجع لطريقتنا الميان اللي عتيجة
+
+554
+01:08:11,390 --> 01:08:18,330
+أني أجزء المعادلة إلى معادلتين فبجي بقوله ذا
+
+555
+01:08:18,770 --> 01:08:27,150
+differential equation one is written as وروح
+
+556
+01:08:27,150 --> 01:08:33,570
+بكتبها y to the derivative four ناقص y يسوي تلاتة
+
+557
+01:08:33,570 --> 01:08:40,790
+T التانية y to the derivative four ناقص y يسوي cos
+
+558
+01:08:40,790 --> 01:08:50,450
+T بدنا نيجي لهذه capital Y one of TY1 of T بيبقى
+
+559
+01:08:50,450 --> 01:08:51,390
+Y1 of T بيبقى Y1 of T بيبقى Y1 of T بيبقى Y1 of T
+
+560
+01:08:51,390 --> 01:08:52,210
+بيبقى Y1 of T بيبقى Y1 of T بيبقى Y1 of T بيبقى Y1
+
+561
+01:08:52,210 --> 01:08:54,570
+of T بيبقى Y1 of T بيبقى Y1 of T بيبقى Y1 of T
+
+562
+01:08:54,570 --> 01:08:54,790
+بيبقى Y1 of T بيبقى Y1 of T بيبقى Y1 of T بيبقى Y1
+
+563
+01:08:54,790 --> 01:08:54,850
+of T بيبقى Y1 of T بيبقى Y1 of T بيبقى Y1 of T
+
+564
+01:08:54,850 --> 01:08:56,990
+بيبقى Y1 of T بيبقى Y1 of T بيبقى Y1 of T بيبقى Y1
+
+565
+01:08:56,990 --> 01:09:11,650
+of T بيبقى Y1 of T بيبقى Y1
+
+566
+01:09:11,650 --> 01:09:19,050
+of T بيبقلأ يبقى باجي بقوله here ال S تساوي 0 إذا
+
+567
+01:09:19,050 --> 01:09:27,030
+صار capital Y1 of T بدي ساوي a naught T زائد a عنه
+
+568
+01:09:27,030 --> 01:09:36,390
+بالمرة نخلصه يالا هاتي لي Y1 prime a naught وال Y1
+
+569
+01:09:36,390 --> 01:09:47,630
+double prime ب0وY1'' بزيرو وY4'' بدو ساوي زيرو
+
+570
+01:09:47,630 --> 01:09:56,310
+نعود في المعادلة يبقى هاي زيرو ناقص Y ناقص Y هيها
+
+571
+01:09:56,310 --> 01:10:07,650
+يبقى ناقص A0 T ناقص A1 بدو ساوي تلاتة Tو منها ناقص
+
+572
+01:10:07,650 --> 01:10:15,260
+a0 بده يسوى تلاتةيبقى a0 بده يساوي كده؟ سالب تلاتة
+
+573
+01:10:15,260 --> 01:10:21,620
+و سالب a1 بده يساوي Zero يبقى ال a1 بده يساوي Zero
+
+574
+01:10:21,620 --> 01:10:30,640
+يبقى أصبح Y1 as a function of T بده يساوي عندك ال
+
+575
+01:10:30,640 --> 01:10:39,450
+a0 بسالب تلاتة يبقى هاي سالب تلاتة T فقط ما غيرنجي
+
+576
+01:10:39,450 --> 01:10:48,170
+للتانية هادي بدنا نجيب Y2 Y2 as a function of T
+
+577
+01:10:48,170 --> 01:10:55,510
+هادي T to the power S في هنا اللي هو polynomial من
+
+578
+01:10:55,510 --> 01:11:01,970
+ضرر الصفر يعني A cosine T زائد B في sine T
+
+579
+01:11:05,830 --> 01:11:10,790
+المعامل هو واحد صحيح يعني دالة من الدرجة الصفرية
+
+580
+01:11:10,790 --> 01:11:15,990
+فقلنا كونوسين في كوسين زي كونوسين في من في صين نجي
+
+581
+01:11:15,990 --> 01:11:21,070
+المقدار بين القوسين في تشابه مع اي term هنا اه في
+
+582
+01:11:21,070 --> 01:11:26,570
+تشابه هذا بيشبه هذا و هذا بيشبه هذا يبقى بدي احط
+
+583
+01:11:26,570 --> 01:11:33,760
+اس بقداش بواحد لو حطيت اس بواحدبصير AT cos T مافيش
+
+584
+01:11:33,760 --> 01:11:38,540
+زيها و BT sin T كمان مافيش زيها يبقى ال S عيندي
+
+585
+01:11:38,540 --> 01:11:44,240
+هنا بيبقى داشر بواحد يبقى باجي بقوله here ال S
+
+586
+01:11:44,240 --> 01:11:50,940
+تساوي واحد يبقى بناء عليه سار كابتل Y2 of T بيبقى
+
+587
+01:11:50,940 --> 01:12:01,730
+ساوي AT cos T زائد BT في sin Tنشتق أربع مرات و
+
+588
+01:12:01,730 --> 01:12:09,170
+نعود في الدالة اللى فوق يبقى يبقى y2 prime يبقى a
+
+589
+01:12:09,170 --> 01:12:17,670
+cosine of t ناقص a t في sine of t نشتق هذه يبقى
+
+590
+01:12:17,670 --> 01:12:26,980
+زائد b في sine of tزائد بي تي في كوصين التين كل
+
+591
+01:12:26,980 --> 01:12:32,920
+واحدة فيهم مشتقت حاصل ضرب دالتين فرعان واضع
+
+592
+01:12:32,920 --> 01:12:38,900
+اختصارات مافيش يبقى بظل كل شي زي ما هو لإن هذي
+
+593
+01:12:38,900 --> 01:12:45,600
+كوصين هناك تي في كوصين ولا واحد زي التانيةY2W'
+
+594
+01:12:46,280 --> 01:12:57,780
+يبقى سالب A في صينة T و سالب A في صينة T و سالب A
+
+595
+01:12:57,780 --> 01:13:07,720
+T في قصينة Tمشتقة الأولى هي بإشارة سالب وهذه
+
+596
+01:13:07,720 --> 01:13:14,320
+حصل ضرب داليتين تبقى سالب a sin t و سالب a t تفضل
+
+597
+01:13:14,320 --> 01:13:19,810
+sin ب cos خلصنا أول two terms بداجي لمين؟لـ two
+
+598
+01:13:19,810 --> 01:13:29,390
+terms التانية يبقى زائد بي في cosine ت زائد بي في
+
+599
+01:13:29,390 --> 01:13:39,390
+cosine ت ناقص بي ت في sine ت يبقى اشتقنهم طلع هذه
+
+600
+01:13:39,390 --> 01:13:47,690
+هي هذه مظبوط يبقى هذه بيصير ناقص اتنين ا في sine t
+
+601
+01:13:48,250 --> 01:13:59,070
+وهذه هي هذه يبقى ازايد 2B في cos T بيبقى عندى ناقص
+
+602
+01:13:59,070 --> 01:14:08,150
+AT في cos T وناقص BT في sin T بدنا نروح نجيب
+
+603
+01:14:08,150 --> 01:14:15,760
+المشتقة الثالثةيساوى نشتق كمان مرة يبقى هاي ناقص
+
+604
+01:14:15,760 --> 01:14:23,120
+اتنين a cosine of t ناقص اتنين b في sine of t
+
+605
+01:14:23,120 --> 01:14:27,260
+خلصنا اول two terms بنانيجى لل two terms اللي
+
+606
+01:14:27,260 --> 01:14:33,750
+بعتهم كل واحدة فيهم مشتقت حصل ضربدالتين يبقى مشتقة
+
+607
+01:14:33,750 --> 01:14:45,010
+الأولى بناقص a cos t زائد at في sin t وناقص b في
+
+608
+01:14:45,010 --> 01:14:58,420
+sin t وناقص bt في cos tانجمعهم يبقى هنا بصير ناقص
+
+609
+01:14:58,420 --> 01:15:09,520
+ثلاثة A في Cos T و هنا ناقص ثلاثة B في Sin T و
+
+610
+01:15:09,520 --> 01:15:20,040
+زائد A T في Sin T و ناقص B T في Cos T
+
+611
+01:15:22,110 --> 01:15:29,650
+انجيب المشتقة الرابعة يالا اخر مشتقة يبقى Y اتنين
+
+612
+01:15:29,650 --> 01:15:42,260
+المشتقة الرابعة بده يساوي تلاتةتلاتة a sin t ناقص
+
+613
+01:15:42,260 --> 01:15:52,840
+تلاتة b في cos t زائد a في sin t زائد a في sin t
+
+614
+01:15:52,840 --> 01:16:06,210
+زائد at في cos t ناقص b في cos t زائد btفى الـ
+
+615
+01:16:06,210 --> 01:16:30,050
+sign 80 نجمعهم
+
+616
+01:16:30,740 --> 01:16:39,720
+يبقى صارت المشتقة الرابعة as a function of T و7
+
+617
+01:16:39,720 --> 01:16:46,460
+قلين تلاتة A sin وكمان A sin يبقى أربعة A sin يبقى
+
+618
+01:16:46,460 --> 01:16:56,170
+أربعة A sin T ناقص أربعة B في cos Tمظبوط لاخص
+
+619
+01:16:56,170 --> 01:17:01,290
+اربعة بي في cosine of T ضال عندي زائد AT في cosine
+
+620
+01:17:01,290 --> 01:17:10,650
+of T زائد AT في cosine of T وعندك زائد BT في sine
+
+621
+01:17:10,650 --> 01:17:18,950
+of T زائد BT في sine of T اللي هو بنرجع العموض في
+
+622
+01:17:18,950 --> 01:17:23,530
+المعادل اللي فوق تمام يبقى بدي Y
+
+623
+01:17:29,300 --> 01:17:36,970
+واللي بيه عندك كمان قداش ناقص Yهذه المرحلة تتساوي
+
+624
+01:17:36,970 --> 01:17:40,490
+بالكوصينة
+
+625
+01:17:40,490 --> 01:17:51,250
+T وY تنزلها زي ما هي 4A في كوصينة T نقص 4B في
+
+626
+01:17:51,250 --> 01:17:52,790
+كوصينة T
+
+627
+01:17:56,820 --> 01:18:04,280
+زي ال B T في صينة T ناقص Y وين ال Y هايها بده
+
+628
+01:18:04,280 --> 01:18:11,380
+اضربها بإشارة سالب يبقى ايش بصير أبناء سالب A T
+
+629
+01:18:11,380 --> 01:18:19,500
+Cos T سالب B T في صينة Tيبقى هدول التنتيج الملهوم
+
+630
+01:18:19,500 --> 01:18:25,320
+مع السلامة يبقى صار عند مين؟ y to the derivative
+
+631
+01:18:25,320 --> 01:18:36,800
+for ناقص y يسوى 4a sin t ناقص 4b cos t كله سيسوى
+
+632
+01:18:36,800 --> 01:18:46,860
+cos t اللي على اليمين هذا سيسوى cos tتمام نقد
+
+633
+01:18:46,860 --> 01:18:52,820
+مقارنة ما بين الطرفين يبقى أربعة A تساوي Zero
+
+634
+01:18:52,820 --> 01:19:02,080
+ومنها A تساوي Zero وعندك سالب أربعة B تساوي معامل
+
+635
+01:19:02,080 --> 01:19:10,910
+الكوصين بواحد يبقى B تساوي سالب رابعيبقى بناء عليه
+
+636
+01:19:10,910 --> 01:19:19,050
+أصبح Y2 as a function of T بده يساوي ال A قولنا
+
+637
+01:19:19,050 --> 01:19:24,910
+مقدش B0 يبقى طاري ال term الأول وال B بسالب رابع
+
+638
+01:19:24,910 --> 01:19:32,450
+في T في صيني T مظلوم يبقى هاي جيبنا Y2
+
+639
+01:19:34,590 --> 01:19:44,170
+Y يبقى Y يسوى YC يبقى Y يسوى
+
+640
+01:19:44,170 --> 01:19:51,690
+Y يسوى Y يسوى Y يسوى Y يسوى Y
+
+641
+01:19:51,690 --> 01:20:04,780
+يسوىزائد C3 Cos T C4 Sin T زائد Y1 هيو جبناه يبقى
+
+642
+01:20:04,780 --> 01:20:07,560
+ناقص تلاتة T
+
+643
+01:20:12,180 --> 01:20:20,880
+Y2 ناقص رابع T في صينة T هذا هو ال general
+
+644
+01:20:20,880 --> 01:20:25,380
+solution لمين للمعادلة الأساسية اللي عندنا اللي هو
+
+645
+01:20:25,380 --> 01:20:32,580
+رقم 2 طيب
+
+646
+01:20:32,580 --> 01:20:38,520
+نبطل نحسب constants يبقى بنعطيك المثال رقم 3
+
+647
+01:20:41,400 --> 01:20:47,960
+بيقول ي determine a
+
+648
+01:20:47,960 --> 01:20:51,680
+suitable form
+
+649
+01:20:51,680 --> 01:21:03,860
+شكل مناسب for the particular solution
+
+650
+01:21:09,480 --> 01:21:20,800
+و Y of T و بعد ذلك don't evaluate the constants
+
+651
+01:21:20,800 --> 01:21:25,580
+بدلاش
+
+652
+01:21:25,580 --> 01:21:31,940
+تحسبون الثوابتولو جيبنا لك سؤال في الامتحان يمكن
+
+653
+01:21:31,940 --> 01:21:35,960
+نجيبه زي هيك لسمح الله نقولك ما تحاسبوش قنوص حتى
+
+654
+01:21:35,960 --> 01:21:40,140
+ماضيعيش وقتك وانت بتشتقه وتجمعه وغالبيا في اللي
+
+655
+01:21:40,140 --> 01:21:44,400
+لازم يغلقه يبقى أنت بس بدي شكل الحل الخاص و الله
+
+656
+01:21:44,400 --> 01:21:48,740
+يعطيك العافية بتطلع هال مكتوب عادي دائما اما ده في
+
+657
+01:21:48,740 --> 01:21:54,260
+الامتحانات السابقة بنحطها بخط غامق وبينقصين حتى عش
+
+658
+01:21:54,260 --> 01:22:03,730
+الكل يشوفها نمرأ ايه؟سؤال 18 من الكتاب بيقول لي Y
+
+659
+01:22:03,730 --> 01:22:13,030
+to the derivative 4 زائد اتنين Y triple prime زائد
+
+660
+01:22:13,030 --> 01:22:22,100
+اتنين Y double prime بده يساوي تلاتة Eostزائد
+
+661
+01:22:22,100 --> 01:22:34,380
+اتنين T E أس ناقص T زائد E أس ناقص T في sign ات ود
+
+662
+01:22:34,380 --> 01:22:36,600
+المعادلة رقم واحد
+
+663
+01:23:06,020 --> 01:23:08,820
+ماذا تسأل؟
+
+664
+01:23:14,220 --> 01:23:18,580
+جمعناهم يا أختي، وين؟ هاي جبنا واي واحد، هاي واسلب
+
+665
+01:23:18,580 --> 01:23:24,540
+تلاتة، واي اتنين، واسلب رابع، وهاي واي اتنين،
+
+666
+01:23:24,540 --> 01:23:25,860
+جمعناهم
+
+667
+01:23:55,980 --> 01:24:00,560
+طيب السؤال هذا بيقول ياتي بس شكل ال particular
+
+668
+01:24:00,560 --> 01:24:05,640
+solution لكن شكل ال particular solution بيعتمد على
+
+669
+01:24:05,640 --> 01:24:08,880
+حل ال homogeneous إذا بروح حل ال homogeneous في
+
+670
+01:24:08,880 --> 01:24:17,300
+الأول قبل كل شيء يبقى باجي بقوله solution let
+
+671
+01:24:17,990 --> 01:24:27,030
+Y تساوي E أس RT بإيه؟ Solution of the differential
+
+672
+01:24:27,030 --> 01:24:33,570
+equation Y to the derivative 4 زائد اتنين Y triple
+
+673
+01:24:33,570 --> 01:24:40,670
+primeزي دي اتنين W prime كله بده يسوي Zero يبقى
+
+674
+01:24:40,670 --> 01:24:48,250
+then the characteristic equation is المعادلة
+
+675
+01:24:48,250 --> 01:24:54,830
+المميزة لهذه المعادلة يار أس أربعة زي دي اتنين R
+
+676
+01:24:54,830 --> 01:25:00,610
+تكيب زي دي اتنين R تربيع يسوي قداش Zero يبقى بناء
+
+677
+01:25:00,610 --> 01:25:05,830
+علي لو أخدت R تربيع عامل مشتركبظل عندي R تربيه
+
+678
+01:25:05,830 --> 01:25:11,730
+زايد اتنين R زايد اتنين يساوي Zero من هذه المعادلة
+
+679
+01:25:11,730 --> 01:25:16,850
+بقدر اقول اذا R واحد بدي يساوي R اتنين بدي يساوي
+
+680
+01:25:16,850 --> 01:25:22,490
+قداش Zero جذور حقيقية و مقررة كل واحد يوم يساوي
+
+681
+01:25:22,490 --> 01:25:30,750
+Zero هذه لا يمكن تحليلهايبقى R ثلاثة واربعة هو
+
+682
+01:25:30,750 --> 01:25:36,650
+عبارة عن حلها بالقانون ناقص اتنين زائد وناقص الجدر
+
+683
+01:25:36,650 --> 01:25:43,130
+التربية الى با تربية ناقص اربعة ألف جيم اللي هو
+
+684
+01:25:43,130 --> 01:25:50,930
+بواحد وجيم باتنين كله على جداش على اتنين ويساوي
+
+685
+01:25:50,930 --> 01:25:55,520
+سالب اتنين زائدة وناقصأتنين في أربعة في تمانية بده
+
+686
+01:25:55,520 --> 01:26:00,940
+اشيل مقاربة وضل سالب أربعة تحت الجدر يبقى زائد او
+
+687
+01:26:00,940 --> 01:26:06,960
+ناقص اتنين I عال اتنين اللي هو ساوي سالب واحد زائد
+
+688
+01:26:06,960 --> 01:26:12,740
+او ناقص مين I يبقى سارة عند لان لان ده بسالب واحد
+
+689
+01:26:12,980 --> 01:26:22,820
+والى ميو بجداش بواحد يبجى صار yc بده يساوي c1 زائد
+
+690
+01:26:22,820 --> 01:26:29,660
+c2 في t في e of zero e of zero اللى بجداش بواحد
+
+691
+01:26:29,660 --> 01:26:31,260
+زائد
+
+692
+01:26:34,040 --> 01:26:44,800
+يبقى E أُس ناقص T في C تلاتة Cos T زاد C أربع Sin
+
+693
+01:26:44,800 --> 01:26:49,980
+T يبقى هذا حل الـ YC
+
+694
+01:26:50,860 --> 01:26:55,420
+بنروح نجيب ال particular solution للمعادلة اللي
+
+695
+01:26:55,420 --> 01:27:00,420
+عندنا اللي هي رقم واحد اللي تحت هذه المعادلة باطلع
+
+696
+01:27:00,420 --> 01:27:06,020
+تلت يرمته الحمد لله ولا واحد زي التل هذه
+
+697
+01:27:06,020 --> 01:27:08,980
+polynomial في exponential هذه ال sign في اللي كل
+
+698
+01:27:08,980 --> 01:27:13,520
+إيدي انحطر أجزء المعادلة اللي عندي لكم معادلة
+
+699
+01:27:13,520 --> 01:27:20,240
+لثلاث معادلات يبقى باجي بقوله ذاDifferential
+
+700
+01:27:20,240 --> 01:27:30,720
+equation one is written as Y to the derivative
+
+701
+01:27:30,720 --> 01:27:36,360
+four زائد اتنين triple prime زائد اتنين Y double
+
+702
+01:27:36,360 --> 01:27:44,380
+prime يسوى تلاتة Eost نفس المعادلة زائد اتنين
+
+703
+01:27:44,380 --> 01:27:45,780
+triple prime
+
+704
+01:27:54,320 --> 01:28:00,220
+نفس المعادلة y to the derivative of four زائد
+
+705
+01:28:00,220 --> 01:28:05,640
+اتنين y triple prime زائد اتنين y double prime
+
+706
+01:28:05,640 --> 01:28:11,360
+يساوي الterm الاخر e اصناق ال T في sin T
+
+707
+01:28:21,570 --> 01:28:28,090
+طيب يبقى بدنا نجيب capital Y1 of T هذي polynomial
+
+708
+01:28:28,090 --> 01:28:34,210
+exponential يبقى T to the power S في ايه؟ في ال E
+
+709
+01:28:34,210 --> 01:28:43,250
+of T طبعا في زيهايبقى هنا ال S ناقص T يبقى هنا ال
+
+710
+01:28:43,250 --> 01:28:49,850
+S يبقى Zero يبقى هنا ال S تساوي Zero يبقى صار
+
+711
+01:28:49,850 --> 01:28:55,970
+Capital Y one of T يساوي F E of T خلصنا من هذه نجي
+
+712
+01:28:55,970 --> 01:29:04,110
+لهذه Y two of T T to the power S هذه polynomial من
+
+713
+01:29:04,110 --> 01:29:10,250
+الدرجة الأولىيبقى a naught t زائد a one فيه و
+
+714
+01:29:10,250 --> 01:29:14,110
+اصناع تاستي تسيبيه كمان T to the power s
+
+715
+01:29:19,400 --> 01:29:22,220
+الـ exponential موجودة بس مضوبة في مين؟ في الـ
+
+716
+01:29:22,220 --> 01:29:27,200
+sine أو الـ cosine؟ ماعنديش يبقى هنا كمان S بـ 0
+
+717
+01:29:27,200 --> 01:29:34,520
+يبقى الـ S تساوي 0 يبقى capital Y2 of T يساوي A
+
+718
+01:29:34,520 --> 01:29:43,000
+not T زائد A1 في الـ E أُس ناقص T نيجي لبعدها Y3
+
+719
+01:29:43,000 --> 01:29:48,110
+as a function of T T to the power S فيههذا
+
+720
+01:29:48,110 --> 01:29:54,350
+exponential في الـSin يبقى هنا سمينا A بقدرش أقول
+
+721
+01:29:54,350 --> 01:29:59,130
+بي يبقى بي
+
+722
+01:29:59,130 --> 01:30:10,340
+في cos T زي دي في sin T في الـA واس ناقص Tتعالى
+
+723
+01:30:10,340 --> 01:30:16,620
+نشوف هل هذا في تشابه constant P في ال exponential
+
+724
+01:30:16,620 --> 01:30:20,640
+والتانى
+
+725
+01:30:20,640 --> 01:30:27,520
+كمان في زيه لكن لو حطينا ال S بواحد يتغير تماما
+
+726
+01:30:27,520 --> 01:30:35,000
+يبقى باجي بقوله hereالـ S تساوي واحد يبقى صار
+
+727
+01:30:35,000 --> 01:30:40,360
+capital Y تلاتة as a function of T هو عبارة عن
+
+728
+01:30:40,360 --> 01:30:49,920
+مين؟ عن T في الـ EOS ناقص T في B Cos T زائد D في
+
+729
+01:30:49,920 --> 01:30:56,580
+Sin T بناء عليه شهر ال capital Y of T اللي بدّوا
+
+730
+01:30:56,580 --> 01:31:02,830
+إياهايو اي واحد زائد واي اتنين زائد واي تلاتة
+
+731
+01:31:02,830 --> 01:31:10,050
+واللي هي بدها تساوي A في ال E أس T زائد A not T
+
+732
+01:31:10,050 --> 01:31:19,490
+زائد A one في ال E أس ناقص T زائد T في ال E أس
+
+733
+01:31:19,490 --> 01:31:28,640
+ناقص T في ال B cosine Tزائد دي في sign ال T وهذا
+
+734
+01:31:28,640 --> 01:31:36,440
+هو المطلوب من المسألة خلاص
+
+735
+01:31:36,440 --> 01:31:40,360
+قالت تحسبش الثوابط يبقى خلاص لحد هنا الله يعطينا
+
+736
+01:31:40,360 --> 01:31:46,020
+عافية بس بده شكل الحل الخاص وهذا كان نمرة A من
+
+737
+01:31:46,020 --> 01:31:53,400
+المثلة بدنا نروح لنمرة Bنمر بسؤال من خارج الكتاب
+
+738
+01:31:53,400 --> 01:32:02,300
+بيقول ما يأتي ب Y to the derivative 4 زائد Y
+
+739
+01:32:02,300 --> 01:32:10,900
+triple prime بده يساوي واحد ناقص T تربيع في E أس
+
+740
+01:32:10,900 --> 01:32:11,880
+ناقص T
+
+741
+01:32:16,940 --> 01:32:23,280
+يبقى بنا بس ال particular solution لحل اللي عندنا
+
+742
+01:32:23,280 --> 01:32:28,540
+فقط لغته يبقى بداجي أقوله نفس ال tactic اللي كنا
+
+743
+01:32:28,540 --> 01:32:39,520
+بنتبعه قبل قليل let y تسوى E أُس RT be a solution
+
+744
+01:32:39,520 --> 01:32:44,960
+of the differential equationY to the derivative of
+
+745
+01:32:44,960 --> 01:32:53,080
+4 زائد المشتقة التالتة يبقى
+
+746
+01:32:53,080 --> 01:33:02,990
+بناء العلياThe characteristic equation is R أربعة
+
+747
+01:33:02,990 --> 01:33:09,810
+زائد R تكييب يساوي Zero او ان شئتولنا فاقولنا R
+
+748
+01:33:09,810 --> 01:33:18,320
+تكييب في R زائد واحد بتساوي من Zeroيبقى R1 يبقى R2
+
+749
+01:33:18,320 --> 01:33:23,760
+يبقى R3 يبقى R4 يبقى R4 يبقى R2 يبقى R2 يبقى R3
+
+750
+01:33:23,760 --> 01:33:23,940
+يبقى R4 يبقى R4 يبقى R2 يبقى R4 يبقى R4 يبقى R4
+
+751
+01:33:23,940 --> 01:33:28,800
+يبقى R4 يبقى R4 يبقى R4 يبقى R4 يبقى R4 يبقى R4
+
+752
+01:33:28,800 --> 01:33:31,500
+يبقى R4 يبقى R4 يبقى R4 يبقى R4 يبقى R4 يبقى R4
+
+753
+01:33:31,500 --> 01:33:32,340
+يبقى R4 يبقى R4 يبقى R4 يبقى R4 يبقى R4 يبقى R4
+
+754
+01:33:32,340 --> 01:33:43,880
+يبقى R4 يبقى R4 يبقى R4 يبقى R4 يبقى R4
+
+755
+01:33:43,880 --> 01:33:48,580
+يبالان بدنا نجي لمين لـNon homogeneous
+
+756
+01:33:48,580 --> 01:33:53,640
+differential equation المعادلة اللى عندنا واضح انه
+
+757
+01:33:53,640 --> 01:33:58,060
+تيرمين هذا ال constant لحاله ومجموعة مع دالة تانية
+
+758
+01:33:58,060 --> 01:34:02,900
+مختلفة تماما عن الدالة هذه إذا حجز المعادلة إلى
+
+759
+01:34:02,900 --> 01:34:08,900
+معادلتين فباجي بقول لو سميت هذه المعادلة رقم واحد
+
+760
+01:34:08,900 --> 01:34:16,440
+بروح بقول له that differential equationone is
+
+761
+01:34:16,440 --> 01:34:25,720
+written as بكتبها على الشكل التالي y to the
+
+762
+01:34:25,720 --> 01:34:31,780
+derivative four زائد y triple prime بدي ساوي قداش
+
+763
+01:34:31,780 --> 01:34:36,540
+واحد المعادلة التانية نفسها y to the derivative
+
+764
+01:34:36,540 --> 01:34:43,160
+four زائد y triple prime بدي ساوي انها قصتي تربية
+
+765
+01:34:43,570 --> 01:34:53,010
+يصنع قصتي نجي هنا شكلنا بدنا نجيب capital Y1 of T
+
+766
+01:34:57,790 --> 01:35:05,530
+يبقى T to the power S هذه كنستان بكتبها كنستان فقط
+
+767
+01:35:05,530 --> 01:35:10,950
+لا غير بالشكل اللي عندنا هنا ابنجي نشوف C بيكمن T
+
+768
+01:35:10,950 --> 01:35:17,170
+to the power S كنستان موجود بيحط S بقدرش؟ بواحد
+
+769
+01:35:17,170 --> 01:35:27,860
+بيصير AT موجودة اقص باتنين AT تربية موجودةيبقى S
+
+770
+01:35:27,860 --> 01:35:36,020
+بي تلاتة يبقى هنا S تساوي تلاتة يبقى صار capital Y
+
+771
+01:35:36,020 --> 01:35:43,180
+of one of T A T تكعيب شوفت ايش الفرق بين هذا
+
+772
+01:35:43,180 --> 01:35:47,800
+السؤال و الأسئلة السابقة يبقى هنا S طلعت بي تلاتة
+
+773
+01:35:47,800 --> 01:35:52,910
+لا ب Zero ولا بواحد طيب نجي للتانية هذهيبقى بداجي
+
+774
+01:35:52,910 --> 01:35:59,350
+ل capital Y2 of T T to the power S هذي polynomial
+
+775
+01:35:59,350 --> 01:36:04,350
+من الدرجة الثانية في من ال exponential اذا بداجي
+
+776
+01:36:04,350 --> 01:36:15,030
+اقول له A0 T تربيع A1 T A2 في E و اثناق T بدى اشوف
+
+777
+01:36:15,030 --> 01:36:19,790
+ال S بقداش بعد ما تكون أسطن في exponential هي
+
+778
+01:36:19,790 --> 01:36:20,710
+موجود
+
+779
+01:36:23,620 --> 01:36:29,020
+لو حطيت T بواحد بيصير T تكيب في ال exponential مش
+
+780
+01:36:29,020 --> 01:36:34,340
+موجودة، T تربية في ال exponential مش موجودة، T في
+
+781
+01:36:34,340 --> 01:36:36,240
+ال exponential مش موجودة
+
+782
+01:36:39,070 --> 01:36:46,230
+يبقى هنا ال S تساوي واحد يبقى من هنا عليه أصبح
+
+783
+01:36:46,230 --> 01:36:55,650
+capital Y2 of T يساوي A نط T تكيب زائد A1T تربيع
+
+784
+01:36:55,650 --> 01:37:03,380
+زائد A2T في ال A أس ناقص Tيبقى بناء علي احصار ان
+
+785
+01:37:03,380 --> 01:37:12,860
+كابتنال Y of T هو Y واحد زائد Y اتنين Y واحد اللي
+
+786
+01:37:12,860 --> 01:37:22,100
+هو A T تكييب زائد Y اتنين اللي هو A نوت T تكييب
+
+787
+01:37:22,100 --> 01:37:27,460
+زائد A one T تربيع زائد
+
+788
+01:37:29,010 --> 01:37:37,050
+A1t تربيه الزائد A2t كله في ال exponential E أس
+
+789
+01:37:37,050 --> 01:37:38,430
+ناقص T
+
+790
+01:37:48,900 --> 01:37:55,100
+سالب معناه هذا سالب لما بدى اتي احسب كده مقادير ال
+
+791
+01:37:55,100 --> 01:37:59,840
+constants تيجي معانا يعني لما بدى اتيم كده ال a
+
+792
+01:37:59,840 --> 01:38:04,960
+node و ال a1 و ال a2 تدخل معانا من السلبة يعني
+
+793
+01:38:04,960 --> 01:38:13,540
+بصير ايش بصير a1 بده ساوي ناقص واحد و ال a node ب
+
+794
+01:38:13,540 --> 01:38:18,400
+zero و ال a2 ب zero و هكذا تمام؟
+
+795
+01:38:20,240 --> 01:38:25,700
+طيب المرة جاية ان شاء الله بنكمل يعني المحاضرة
+
+796
+01:38:25,700 --> 01:38:31,700
+القادمة يوم الأربعاء ان شاء الله تعالى بنطلع ..
+
+797
+01:38:31,700 --> 01:38:37,340
+بنكمل ال section اللي ضايل و بنعطيكوا أرقام
+
+798
+01:38:37,340 --> 01:38:39,620
+المسائل على ال two sections
+
diff --git a/PL9fwy3NUQKwa8ZDfSFGn6H8xVFLzqmCZC/dANTZFG0kHA.srt b/PL9fwy3NUQKwa8ZDfSFGn6H8xVFLzqmCZC/dANTZFG0kHA.srt
new file mode 100644
index 0000000000000000000000000000000000000000..bab8f0d19dd8b44f4a2a2ffac6d4aa8f24ee7bca
--- /dev/null
+++ b/PL9fwy3NUQKwa8ZDfSFGn6H8xVFLzqmCZC/dANTZFG0kHA.srt
@@ -0,0 +1,2542 @@
+1
+00:00:17,140 --> 00:00:21,380
+الكتاب المقرر هو Elementary Differential Equations
+
+2
+00:00:21,380 --> 00:00:25,620
+and Boundary Value Problems الطبعة هي الطبعة 
+
+3
+00:00:25,620 --> 00:00:34,110
+الثامنة المؤلفان William Boyce and Richard C. DiPrima
+
+4
+00:00:34,110 --> 00:00:38,190
+chapters المقررة من هذا الكتاب ابتداء من section 1
+
+5
+00:00:38,190 --> 00:00:46,430
+وحتى section 6 يبقى ستة Sections سندرسها خلال هذا
+
+6
+00:00:46,430 --> 00:00:52,540
+الفصل إن شاء الله تبارك وتعالى المراجع لهذا الكتاب 
+
+7
+00:00:52,540 --> 00:00:56,600
+لو رحت المكتب أي كتاب في المعادلة التفاضلية 
+
+8
+00:00:56,600 --> 00:01:00,320
+الموجود في المكتب عندنا والحمد لله فيها بدأ الكتاب 
+
+9
+00:01:00,320 --> 00:01:06,160
+عشرة لمؤلفين مختلفين كله ممكن اه ممكن يكون مرجع
+
+10
+00:01:06,160 --> 00:01:12,600
+معاكي ترجعي له وقت ما شئتي نجي ل chapter one يبقى 
+
+11
+00:01:12,600 --> 00:01:17,080
+نجي لأول Chapter اللي هو Chapter 1
+
+12
+00:01:26,790 --> 00:01:34,990
+Introduction introduction يعني مقدمة في هذه 
+
+13
+00:01:34,990 --> 00:01:41,430
+المقدمة سنعطي بعض المفاهيم الأساسية يعني ماذا 
+
+14
+00:01:41,430 --> 00:01:48,540
+معنى معادلة تفاضلية ما معنى معادلة تفاضلية عادية ما 
+
+15
+00:01:48,540 --> 00:01:52,760
+معنى رتبة المعادلة التفاضلية طبعا احنا لدرجة في
+
+16
+00:01:52,760 --> 00:01:58,300
+دماغنا قبل ذلك درجة المعادلة هذه درجة المعادلة
+
+17
+00:01:58,300 --> 00:02:01,820
+العادية من الدرجة الثانية الثالثة لأ احنا فيه
+
+18
+00:02:01,820 --> 00:02:06,880
+عندنا هنا رتبة المعادلة التفاضلية والرتبة تعتمد
+
+19
+00:02:06,880 --> 00:02:11,040
+على المشتقة الأولى والمشتقة الثانية والمشتقة
+
+20
+00:02:11,040 --> 00:02:16,570
+الثالثة أو الرابعة أو النونية التي تظهر في المعادلة
+
+21
+00:02:16,570 --> 00:02:21,830
+التفاضلية يبقى هذا مثلا ما نسميه برتبة المعادلة 
+
+22
+00:02:21,830 --> 00:02:28,910
+التفاضلية وهذا ما سنعرفه بعد قليل هنعرف كمان ما هو
+
+23
+00:02:28,910 --> 00:02:34,150
+Solution للمعادلة التفاضلية ما هو حل المعادلة
+
+24
+00:02:34,150 --> 00:02:42,110
+التفاضلية ما هو الحل العام للمعادلة التفاضلية ما هي 
+
+25
+00:02:42,110 --> 00:02:47,750
+ال initial value problems يعني معادلة تفاضلية و
+
+26
+00:02:47,750 --> 00:02:52,310
+عليها شروط بنسميها الشروط الابتدائية أو ال initial
+
+27
+00:02:52,310 --> 00:02:57,530
+Conditions فإن وجدت معادلة تفاضلية بشروط عليها
+
+28
+00:02:57,530 --> 00:03:02,480
+بنسميها Initial Value Problems أما عن أنواع
+
+29
+00:03:02,480 --> 00:03:07,280
+المعادلات فهذا ما سنتعرض له في ال Chapters بعد ذلك 
+
+30
+00:03:07,280 --> 00:03:10,640
+يعني بديش أقوله في ال introduction و أروح أعيده
+
+31
+00:03:10,640 --> 00:03:15,700
+مرة ثانية لأ بنخليه كل واحد في موقعه بنعرف شو يعني
+
+32
+00:03:15,700 --> 00:03:19,660
+Linear Differential Equation ما هي Non-Linear
+
+33
+00:03:19,660 --> 00:03:23,120
+Differential Equations أنواع ال Linear Differential
+
+34
+00:03:23,120 --> 00:03:27,600
+Equations إلى آخره يبقى هذا مثلا اتعرض له في حينه
+
+35
+00:03:27,600 --> 00:03:31,920
+يبقى زي ما تشوفين في ال Introduction مكتوب عندكم
+
+36
+00:03:31,920 --> 00:03:35,280
+في الكتابة على شكل Three Sections احنا ال Three
+
+37
+00:03:35,280 --> 00:03:39,220
+Sections يمكن نجمعهم لك بس في صفحتين لأن هذه
+
+38
+00:03:39,220 --> 00:03:44,000
+مقدمات بس بدنا الطالب يعرفها حتى نقدر نشتغل في من؟ 
+
+39
+00:03:44,000 --> 00:03:47,780
+في ال Sections اللي بعديها إن شاء الله تبارك
+
+40
+00:03:47,780 --> 00:03:58,440
+وتعالى بنجي بعد هيك ل Chapter 2 اللي
+
+41
+00:03:58,440 --> 00:04:07,980
+هو First Order Differential Equations
+
+42
+00:04:11,130 --> 00:04:14,710
+كلمة Differential خلال المساق هذا كله يجب أن 
+
+43
+00:04:14,710 --> 00:04:22,950
+اختصرها إلى Diff. Eqs. هختصرها إلى Eqs. يبقى 
+
+44
+00:04:22,950 --> 00:04:27,090
+هذه اختصار كلمة Differential Equations
+
+45
+00:04:29,310 --> 00:04:34,070
+الـ First Order يعني المعادلة التفاضلية من الرتبة
+
+46
+00:04:34,070 --> 00:04:40,050
+الأولى هذه هندرس فيها مجموعة من المعادلات اللي
+
+47
+00:04:40,050 --> 00:04:43,610
+كلهم من الرتبة الأولى حاجة اسمها ال Linear
+
+48
+00:04:43,610 --> 00:04:49,120
+Differential Equations المعادلة التفاضلية الخطية 
+
+49
+00:04:49,120 --> 00:04:54,120
+حاجة اسمها Separable Equations يعني المعادلات اللي
+
+50
+00:04:54,120 --> 00:04:59,200
+فيها بدنا نفصل المتغيرات ال Exact Equations
+
+51
+00:04:59,200 --> 00:05:02,700
+المعادلات التامة ال Homogeneous Equations
+
+52
+00:05:02,700 --> 00:05:08,340
+المعادلات المتجانسة يبقى خلال هذا ال Chapter بدنا
+
+53
+00:05:08,340 --> 00:05:17,970
+ندرس ما يأتي ال Linear Equations المعادلات الخطية 
+
+54
+00:05:17,970 --> 00:05:24,350
+Separable Equations
+
+55
+00:05:24,350 --> 00:05:29,030
+Separable
+
+56
+00:05:29,030 --> 00:05:33,650
+جاء من كلمة Separate منفصل يبقى Separable
+
+57
+00:05:33,650 --> 00:05:38,730
+Equations هي المعادلات اللي نقدر نفصل فيها متغيرات
+
+58
+00:05:38,730 --> 00:05:42,930
+في شجرة والمتغير الآخر في الشجرة الثانية يعني بيكون
+
+59
+00:05:42,930 --> 00:05:48,890
+فيها متغيرين بنفس أحدهم في ناحية والمتغير الآخر في
+
+60
+00:05:48,890 --> 00:05:53,110
+ناحية أخرى يبقى هذا اللي بنسميها Separable
+
+61
+00:05:53,110 --> 00:06:00,130
+Equations فينا حاجة اسمها ال Exact Equations
+
+62
+00:06:00,130 --> 00:06:08,510
+and Integrating Factors
+
+63
+00:06:14,930 --> 00:06:19,410
+Exact Equations يعني المعادلات التامة Integrating
+
+64
+00:06:19,410 --> 00:06:25,750
+Factors عوامل التكامل يعني المعادلة قد تكون Exact
+
+65
+00:06:25,750 --> 00:06:31,730
+ويمكن أن نحتاج مقال نيجي نحسبها مالجهاش Exact نضرب 
+
+66
+00:06:31,730 --> 00:06:37,230
+في دالة ما هذه الدالة بتحولها إلى Exact Equation
+
+67
+00:06:37,230 --> 00:06:43,490
+هذه الدالة بنسميها ايش اللي هو عامل التكامل من هذه
+
+68
+00:06:43,490 --> 00:06:48,090
+المعادلة كيف عامل التكامل هذا بدنا نحصل عليه هذا ما
+
+69
+00:06:48,090 --> 00:06:53,790
+سنشير إليه في حينه إن شاء الله تبارك وتعالى يبقى 
+
+70
+00:06:53,790 --> 00:06:57,410
+النوع الثالث هو ال Exact Equations and Integrating
+
+71
+00:06:57,410 --> 00:07:03,230
+Factors عندنا كمان حاجة اسمه ال Homogeneous
+
+72
+00:07:03,230 --> 00:07:11,630
+Differential Equations المعادلات المتجانسة 
+
+73
+00:07:13,800 --> 00:07:19,320
+يبقى هذه الأربعة أنواع من المعادلات التي سنتدرسها
+
+74
+00:07:19,320 --> 00:07:24,540
+في ال Chapter الثاني و ال First Order Differential
+
+75
+00:07:24,540 --> 00:07:29,140
+Equation في حد قابلنا يا بنات معادلات ليست على أي
+
+76
+00:07:29,140 --> 00:07:35,240
+نوع من الأربعة الأربعة يعني ليست Linear ليست
+
+77
+00:07:35,240 --> 00:07:41,380
+Separable ليست Exact ليست Homogeneous لكن يمكن 
+
+78
+00:07:41,820 --> 00:07:48,220
+تحويل هذه المعادلة بطريقة ما إلى أي نوع من الأنواع
+
+79
+00:07:48,220 --> 00:07:52,960
+الأربعة فمثلا في حالة ال Linear Equations باجي على
+
+80
+00:07:52,960 --> 00:07:57,700
+المعادلة بلاقيها ماهياش Linear لكن لو عملت شغل هيك 
+
+81
+00:07:57,700 --> 00:08:03,180
+تتحول إلى Linear وهذه الشغلة بنسميها حد من الذكراه
+
+82
+00:08:03,180 --> 00:08:08,920
+يا شبنات اللي درسوا قبل ذلك طب احنا بنسميها Bernoulli
+
+83
+00:08:08,920 --> 00:08:14,470
+Equation معادلة بيرنولي يمكن تحويلها إلى معادلة
+
+84
+00:08:14,470 --> 00:08:18,450
+خطية إلى Linear Differential Equation Separable
+
+85
+00:08:18,450 --> 00:08:22,350
+Equation يمكن معادلة ما تلاقيهاش Separable لكن
+
+86
+00:08:22,350 --> 00:08:27,730
+بتعويضها ما بسيطة يمكن تحويلها إلى Separable
+
+87
+00:08:27,730 --> 00:08:32,390
+Equation ال Exact Equation يمكن ما تجباش Exact لكن
+
+88
+00:08:32,390 --> 00:08:38,460
+نضربها في عامل التكامل يحويلها إلى مين؟ المعادلة
+
+89
+00:08:38,460 --> 00:08:50,440
+الـ Homogeneous هي المعادلة
+
+90
+00:08:50,440 --> 00:08:56,270
+التي لا تظهر Homogeneous وبالتالي الـ Homogeneous
+
+91
+00:08:56,270 --> 00:09:00,750
+Differential ممكن بعملية ما تبقاش Homogeneous لكن
+
+92
+00:09:00,750 --> 00:09:04,350
+نحولها إلى مين؟ إلى Homogeneous Differential
+
+93
+00:09:04,350 --> 00:09:09,250
+Equations هنشوف كيف هنحل المعادلة ده المعادلات هذه
+
+94
+00:09:09,250 --> 00:09:13,350
+لما قلت لك First Order يعني لا تظهر في المعادلة إلا
+
+95
+00:09:13,350 --> 00:09:19,000
+المشتقة الأولى يبقى لو كملتها بحصل على حل المعادلة
+
+96
+00:09:19,000 --> 00:09:24,960
+تكامل عادي جدا يعني كل سؤال من مسائل المعادلة التفاضلية
+
+97
+00:09:24,960 --> 00:09:31,200
+بده تكامل ومن هنا قلت لك المادة تحتاج أساسا لمين
+
+98
+00:09:31,200 --> 00:09:37,940
+لتكامل بتجي ما عدا عند ال Exact Equations هذه في 
+
+99
+00:09:37,940 --> 00:09:41,260
+حاجة أخدناها في Calculus C طبعا بعضكم ماخدتش 
+
+100
+00:09:41,260 --> 00:09:45,880
+Calculus C مظبوط؟ فيه ماخدش العدد اشوف ارفعي ده
+
+101
+00:09:45,880 --> 00:09:51,140
+ماخدش كال كلصى يعني الرابع ماعناهاش مشكلة اللي 
+
+102
+00:09:51,140 --> 00:09:55,780
+ماأخدناهوش بكال كلصى هاطولك خلال خمس دقائق يعني 
+
+103
+00:09:55,780 --> 00:09:59,320
+اللي أخدت كال كلصى و اللي ماأخدت بصيره سِيان خمس
+
+104
+00:09:59,320 --> 00:10:04,000
+دقائق بس بفهمك الشيء اللي مطلوب من كال كلصى هو
+
+105
+00:10:04,000 --> 00:10:09,070
+الاشتقاق الجزئي Partial Differentiation اللي هو
+
+106
+00:10:09,070 --> 00:10:13,750
+التفاضل الجزئي باعطيكي إياه في خمس دقائق و بالتالي
+
+107
+00:10:13,750 --> 00:10:17,590
+ماعندناش إشكالية أما يقولوا كده ماخدتيش C بتقدريش 
+
+108
+00:10:17,590 --> 00:10:22,690
+تاخدي معاكش؟ لأ بتقدري تاخدي و بدون أي مشكلة مافي
+
+109
+00:10:22,690 --> 00:10:27,670
+مشكلة في هذه العالم غير هيك مش هيلزمنا الاشتقاق
+
+110
+00:10:27,670 --> 00:10:31,750
+الجزئي طيلة دراستنا بس بلزمنا في ال Section هذا
+
+111
+00:10:31,750 --> 00:10:36,470
+اللي هو ال Exact Equations and Integrating Factors 
+
+112
+00:10:36,470 --> 00:10:43,670
+فقط لا غير يبقى هذا كل ما سيدرس في Main في ال
+
+113
+00:10:43,670 --> 00:10:48,670
+First Order Linear Differential Equations بنجي ل
+
+114
+00:10:48,670 --> 00:10:57,810
+Chapter تلاتة اللي هو Second Order Differential 
+
+115
+00:10:57,810 --> 00:11:04,510
+Equations المعادلة
+
+116
+00:11:04,510 --> 00:11:11,010
+التفاضلية من الرتبة الثانية يعني هيظهر عندنا زي ما 
+
+117
+00:11:11,010 --> 00:11:14,310
+ظهر في ال Chapter الماضي المشتقة الأولى هيظهر هنا
+
+118
+00:11:14,310 --> 00:11:18,210
+عندنا مين؟ المشتقة الثانية والأولى، بيصيروا
+
+119
+00:11:18,210 --> 00:11:22,610
+الاثنتين مالهم بيظهروا في المثال وربما ما تظهرش إلا
+
+120
+00:11:22,610 --> 00:11:26,690
+المشتقة الثانية فقط، على أي حال الأولى أو الثانية
+
+121
+00:11:26,690 --> 00:11:30,770
+معناها، المشكلة احنا بناخد ال General Form الشكل
+
+122
+00:11:30,770 --> 00:11:35,830
+العام وبالتالي الباقي بيكون شيء تخصيصي من الشيء 
+
+123
+00:11:35,830 --> 00:11:40,130
+العام يبقى Second Order Differential Equations
+
+124
+00:11:40,130 --> 00:11:44,970
+هنجسم المعادلة إلى جزئين المعادلة التفاضلية من
+
+125
+00:11:44,970 --> 00:11:45,950
+الرتبة الثانية
+
+126
+00:11:50,420 --> 00:11:57,300
+المعادلة التفاضلية هي المعادلة
+
+127
+00:11:57,300 --> 00:12:00,820
+التفاضلية هي المعادلة التفاضلية هي المعادلة
+
+128
+00:12:00,820 --> 00:12:02,680
+التفاضلية هي المعادلة التفاضلية هي المعادلة
+
+129
+00:12:02,680 --> 00:12:04,100
+التفاضلية هي المعادلة التفاضلية هي المعادلة
+
+130
+00:12:04,100 --> 00:12:04,220
+التفاضلية هي المعادلة التفاضلية هي المعادلة
+
+131
+00:12:04,220 --> 00:12:05,340
+التفاضلية هي المعادلة التفاضلية هي المعادلة
+
+132
+00:12:05,340 --> 00:12:07,600
+التفاضلية هي المعادلة التفاضلية هي المعادلة
+
+133
+00:12:07,600 --> 00:12:09,650
+التفاضلية هي المعادلة هذه بنسميها Homogeneous 
+
+134
+00:12:09,650 --> 00:12:13,250
+Differential Equation الـ Non-Homogeneous
+
+135
+00:12:13,250 --> 00:12:15,970
+Differential Equation المعادلة بالكتابة الكاملة و
+
+136
+00:12:15,970 --> 00:12:20,990
+الطرف اليمين بيكونش Zero بيكون Function ثاني يبقى 
+
+137
+00:12:20,990 --> 00:12:24,950
+هذا ال Non-Homogeneous Differential Equation يبقى
+
+138
+00:12:24,950 --> 00:12:32,150
+هنبدأ أول شغلة بمين؟ بال Homogeneous Differential
+
+139
+00:12:32,150 --> 00:12:37,370
+Equation كويس
+
+140
+00:12:40,180 --> 00:12:43,500
+طبعا ال Homogeneous Differential Equation بتكون من 
+
+141
+00:12:43,500 --> 00:12:50,360
+الرتبة الثانية الرتبة الثانية أي معادلة من الرتبة
+
+142
+00:12:50,360 --> 00:12:58,100
+الثانية هنفترض إليها حل ما حل معين الحل المعين هذا
+
+143
+00:12:58,100 --> 00:13:03,030
+بده يقودنا إلى معادلة من الدرجة الثانية معادلة
+
+144
+00:13:03,030 --> 00:13:06,030
+عادية زي بقى التانية عدادية زي طبعة الصف الثامن
+
+145
+00:13:06,030 --> 00:13:10,950
+والتاسع من الدرجة الثانية بنروح نحل المعادلة اللي 
+
+146
+00:13:10,950 --> 00:13:15,230
+عندنا هذه معادلة من الدرجة الثانية ممكن نحلها
+
+147
+00:13:15,230 --> 00:13:21,870
+بالتحليل أو بالجذر القانون اللي هو ناقص ب زائد أو 
+
+148
+00:13:21,870 --> 00:13:24,890
+ناقص الجذر التربيعي اللي ب تربيع ناقص أربعة أ ج
+
+149
+00:13:24,890 --> 00:13:29,310
+على اثنين أ بهذه أو هذه بنحل معادلة الدرجة
+
+150
+00:13:29,310 --> 00:13:32,870
+الثانية ما دام معادلة من طريق الثانية يبقى إليها
+
+151
+00:13:32,870 --> 00:13:37,890
+حلّين الحلّين هذول يا بنات ممكن يكونوا اثنين are
+
+152
+00:13:37,890 --> 00:13:44,270
+Real and Different تمام؟ يبقى Real and Different
+
+153
+00:13:44,270 --> 00:13:49,370
+يعني حلّين حقيقيين ومختلفين ولا واحد زي الثاني
+
+154
+00:13:49,370 --> 00:13:57,230
+تمام؟ ممكن يكون الحلّين حقيقيين ومُتكررين زي بعض حلّان
+
+155
+00:13:57,230 --> 00:14:02,790
+مُطبقين اثنين زي بعض تماما الحالة الثالثة ممكن
+
+156
+00:14:02,790 --> 00:14:07,330
+اثنين يكونوا are Complex Conjugate يعني حلّين
+
+157
+00:14:07,330 --> 00:14:15,010
+كميتين مركبتين أو كميتين تخيليتين واثنين مترافقة
+
+158
+00:14:15,010 --> 00:14:20,950
+Conjugate يعني مترافقة يبقى هنيجي لحاجة اسمها
+
+159
+00:14:20,950 --> 00:14:27,070
+المعادلة المميزة للمعادلة التفاضلية يبقى هذه
+
+160
+00:14:27,070 --> 00:14:30,810
+بنسميها ال Characteristic Equation ال
+
+161
+00:14:30,810 --> 00:14:42,150
+Characteristic Equation
+
+162
+00:14:42,150 --> 00:14:47,510
+هي معادلة من الدرجة الثانية مش من الرتبة يعني انتقل
+
+163
+00:14:47,510 --> 00:14:53,180
+من الرتبة إلى مين إلى درجة نتيجة للحل اللي فرضناه
+
+164
+00:14:53,180 --> 00:14:57,600
+لمين؟ للمعادلة التفاضلية طب الحل بيكون على شكل
+
+165
+00:14:57,600 --> 00:15:03,440
+Exponential Function يعني كيف الـ Homogeneous هذه؟
+
+166
+00:15:03,440 --> 00:15:09,040
+يعني زي ما نقول Y'' + P(t) في Y'
+
+167
+00:15:09,040 --> 00:15:15,020
++ Q(t) في Y بده يساوي Zero الطرف
+
+168
+00:15:15,020 --> 00:15:18,280
+اليمين بيكون يساوي Zero هذه هي الـ Homogeneous
+
+169
+00:15:18,280 --> 00:15:25,840
+Differential Equation المعادلة على الشكل هذا لو كان
+
+170
+00:15:25,840 --> 00:15:34,660
+كل من P(t) و Q(t) Constant ثابت يبقى الحل اللي 
+
+171
+00:15:34,660 --> 00:15:41,100
+عندنا هنا بيكون على الشكل Y = e<sup>rt</sup> 
+
+172
+00:15:41,100 --> 00:15:46,000
+Exponential Function أصلا الـ Exponential اللي
+
+173
+00:15:46,000 --> 00:15:50,490
+بنعرف ان الفضل ههبط و لا لأ طبعا R هو مقدار عددي 
+
+174
+00:15:50,490 --> 00:15:54,650
+اثنين تلاتة أربعة نص تلاتة أربعة جد ما يكون و T هو
+
+175
+00:15:54,650 --> 00:15:58,530
+ال Parameter أو المتغير ال Variable يبقى أظن لو
+
+176
+00:15:58,530 --> 00:16:04,230
+بدنا نشتق الاشتقاق الأول بيصير ايش؟ R e<sup>rt</sup> لو 
+
+177
+00:16:04,230 --> 00:16:10,540
+نشتقها كمان مرة بيصير R<sup>2</sup> e<sup>rt</sup> تمام؟ وبالتالي
+
+178
+00:16:10,540 --> 00:16:16,640
+المعادلة هذا نتيجة لهذا الحل بتتحول إلى معادلة من
+
+179
+00:16:16,640 --> 00:16:26,320
+الدرجة الثانية على الصيغة R<sup>2</sup> + aR + b 
+
+180
+00:16:26,320 --> 00:16:32,080
+= Zero يبقى هذه معادلة عادية من الدرجة الثانية
+
+181
+00:16:32,080 --> 00:16:39,690
+هذه لما نيجي نحلها سيظهر عندي أحد ثلاثة أمور
+
+216
+00:19:54,920 --> 00:19:59,960
+للمعادلات اللي العوامل عندهم هذه ما هي ثوابت
+
+217
+00:19:59,960 --> 00:20:04,960
+وإنما متغيرات بعد هيك بروح لل homogeneous
+
+218
+00:20:04,960 --> 00:20:08,460
+differential equations بدينا بال homogeneous
+
+219
+00:20:08,460 --> 00:20:12,240
+differential equations ابنجي لمين ل non
+
+220
+00:20:12,240 --> 00:20:21,040
+homogeneous non homogeneous differential equations
+
+221
+00:20:21,040 --> 00:20:25,960
+لازلنا داخل الـ section أو الـ chapter رقم تلاتة فيها
+
+222
+00:20:25,960 --> 00:20:30,880
+نبنات طريقة ثانية للحل الطريقة الأولى بسميها ال
+
+223
+00:20:30,880 --> 00:20:35,000
+undetermined coefficients والطريقة الثانية بسميها
+
+224
+00:20:35,000 --> 00:20:41,420
+الـ variation of parameters يبقى الطريقة الأولى في
+
+225
+00:20:41,420 --> 00:20:47,700
+هذه الحالة اسمها طريقة الـ undetermined
+
+226
+00:20:47,700 --> 00:20:51,180
+coefficients
+
+227
+00:20:56,330 --> 00:21:03,170
+والطريقة الثانية اسمها طريقة الـ variation of
+
+228
+00:21:03,170 --> 00:21:19,330
+parameters يبقى
+
+229
+00:21:19,330 --> 00:21:23,850
+نرجع مرة ثانية نذكر
+
+230
+00:21:23,850 --> 00:21:28,050
+تذكرة المعادلة الـ second order سأقسمها إلى قسمين
+
+231
+00:21:28,050 --> 00:21:32,790
+القسم الأول هو الـ homogeneous والقسم الثاني هو
+
+232
+00:21:32,790 --> 00:21:36,430
+الـ non homogeneous differential equation في حالة
+
+233
+00:21:36,430 --> 00:21:40,150
+الـ homogeneous differential equation إذا كانت
+
+234
+00:21:40,150 --> 00:21:44,950
+المعاملات هذه ثوابت سأفترض الحل على صيغة Y تساوي
+
+235
+00:21:44,950 --> 00:21:51,730
+e^rt نتيجة لذلك ستظهر معادلة بالشكل اللي عندنا
+
+236
+00:21:51,730 --> 00:21:56,360
+هذا معادلة من الدرجة الثانية بضعوها حلها بيطلع عندي
+
+237
+00:21:56,360 --> 00:22:01,960
+تلات حالات اللي هو real and different roots, real
+
+238
+00:22:01,960 --> 00:22:06,300
+repeated roots اللي هو complex conjugate roots
+
+239
+00:22:06,300 --> 00:22:11,240
+يبقى طالع جذور المعادلة هذه واحد من الأمور التلاتة
+
+240
+00:22:11,240 --> 00:22:16,700
+نتيجة لذلك بيصير حل المعادلة التفاضلية على شكل
+
+241
+00:22:16,700 --> 00:22:21,280
+ما كل واحدة من التلاتة لها شكل بيختلف عن الشكل
+
+242
+00:22:21,280 --> 00:22:27,050
+الآخر سنعرف اللي هي أشكال في حينه إن شاء الله تبارك
+
+243
+00:22:27,050 --> 00:22:33,950
+وتعالوا بعد هيك جينا من الـ repeated roots هذه ولو
+
+244
+00:22:33,950 --> 00:22:40,090
+كان المعاملات هدول ليست ثوابت وإنما دوال في T
+
+245
+00:22:40,090 --> 00:22:45,190
+sin T cos T T تربيع T ناقص 1 T تربيع زائد
+
+246
+00:22:45,190 --> 00:22:49,510
+2 T زائد 3 الآخرين يعني أي function من ال
+
+247
+00:22:49,510 --> 00:22:53,830
+functions اللي مرت علينا يبقى في هذه الحالة أول
+
+248
+00:22:53,830 --> 00:22:59,750
+طريقة طريقة reduction of order ننتقل الآن لل non
+
+249
+00:22:59,750 --> 00:23:03,230
+homogeneous differential equations إذا ولّا
+
+250
+00:23:03,230 --> 00:23:07,750
+المعادلات ثوابت بستخدم طريقة الـ undetermined
+
+251
+00:23:07,750 --> 00:23:13,770
+coefficients طريقة المعاملات المجهولة إذا ولّا
+
+252
+00:23:13,770 --> 00:23:20,170
+المعاملات هدول متغيرات لك الخيار بين أن تستخدم الـ
+
+253
+00:23:20,170 --> 00:23:23,670
+undetermined coefficients أو نستخدم طريقة الـ
+
+254
+00:23:23,670 --> 00:23:28,950
+variation of parameters طبعا فرق شاسع بين الطريقتين
+
+255
+00:23:28,950 --> 00:23:34,630
+الطريقة الأولى تعتمد على أمرين أن المعاملات ثوابت
+
+256
+00:23:34,630 --> 00:23:38,990
+والدالة هذه ليست صفر وإنما بتكون على شكل معين
+
+257
+00:23:38,990 --> 00:23:43,450
+polynomial في exponential polynomial في
+
+258
+00:23:43,450 --> 00:23:47,850
+exponential في دالة مثلثية sin أو cos أو
+
+259
+00:23:47,850 --> 00:23:52,330
+مجموعهما أو الفرق فيما بينهما طريقة الـ variation of
+
+260
+00:23:52,330 --> 00:23:56,150
+parameters بهمهاش هدول ثوابت والله مش ثوابت ثوابت
+
+261
+00:23:56,150 --> 00:24:00,990
+ماشي الحال مش ثوابت ماشي الحال ما عندها مشكلة اتنين
+
+262
+00:24:00,990 --> 00:24:05,010
+الدالة لاعلمين ايش ما يكون شكلها هيكون ما عندهاش مشكلة
+
+263
+00:24:05,010 --> 00:24:09,410
+كذلك يبقى هذه الطرق المختلفة لحل المعادلة
+
+264
+00:24:09,410 --> 00:24:14,870
+التفاضلية تلاتة reduction of order, undetermined 
+
+265
+00:24:14,870 --> 00:24:19,990
+coefficients, variation of parameters يبقى هذه هي
+
+266
+00:24:19,990 --> 00:24:24,310
+الطرق الثلاث لحل المعادلة التفاضلية اللي احنا
+
+267
+00:24:24,310 --> 00:24:28,770
+درسناها في chapter 3 ابنجي ل chapter 4
+
+268
+00:24:45,440 --> 00:24:50,780
+chapter أربعة يا بنات بدنا نعمم chapter تلاتة يعني chapter
+
+269
+00:24:50,780 --> 00:24:55,950
+أربعة هو تعميم ل chapter تلاتة ليه؟ بناخد المعادلة من
+
+270
+00:24:55,950 --> 00:24:59,010
+الرتبة الثالثة من الرتبة الرابعة من الخامسة من
+
+271
+00:24:59,010 --> 00:25:04,190
+الرتبة النونية in general يبقى هذه اسمها higher
+
+272
+00:25:04,190 --> 00:25:08,490
+order differential equations المعادلة التفاضلية من
+
+273
+00:25:08,490 --> 00:25:13,910
+الرتب العليا يعني أكثر من اثنين أربعة فما فوق
+
+274
+00:25:13,910 --> 00:25:23,150
+ف chapter أربعة chapter أربعة اسمه higher order
+
+275
+00:25:27,510 --> 00:25:32,910
+order differential equations
+
+276
+00:25:32,910 --> 00:25:35,970
+هذا
+
+277
+00:25:35,970 --> 00:25:40,950
+لن نأتي فيه بجديد نفس التكتيك اللي اتبع في chapter 3
+
+278
+00:25:40,950 --> 00:25:46,830
+هنتبعه مين في chapter 4 يبقى هنقسمه إلى homogeneous
+
+279
+00:26:01,710 --> 00:26:06,450
+نفس هذا الـ characteristic equation اللي على الشكل
+
+280
+00:26:06,450 --> 00:26:10,170
+اللي عندنا هذا هذا هيك هتصير معادلة بس بيصير من
+
+281
+00:26:10,170 --> 00:26:17,950
+الرتبة النونية تمام يبقى هذه هناخد بالنا برضه الـ
+
+282
+00:26:17,950 --> 00:26:24,690
+characteristic equation ونروح نحللها ونشوف ما هو
+
+283
+00:26:24,690 --> 00:26:29,690
+شكل الجذور في الحالات المختلفة بنيجي لل non
+
+284
+00:26:29,690 --> 00:26:34,230
+homogeneous هنستخدم لها نفس الكلام اللي استخدمناه
+
+285
+00:26:34,230 --> 00:26:39,210
+هنا اللي هو الـ undetermined
+
+286
+00:26:39,210 --> 00:26:41,050
+coefficients
+
+287
+00:26:44,270 --> 00:26:51,370
+undetermined coefficients والطريقة الثانية التي
+
+288
+00:26:51,370 --> 00:27:06,370
+هي variation of parameters يبقى
+
+289
+00:27:06,370 --> 00:27:11,790
+هذا مين لل higher order لهمين لل chapter رقم أربعة
+
+290
+00:27:12,060 --> 00:27:18,200
+يبقى chapter رقم أربعة هو تعميم ل chapter رقم تلاتة مافي
+
+291
+00:27:18,200 --> 00:27:22,860
+معلومة جديدة إن نفس الفكر بتاعة اللي هو chapter رقم تلاتة
+
+292
+00:27:22,860 --> 00:27:27,870
+بس اه بنعمل بدل ما تحلّي هنا معادلة من الدرجة
+
+293
+00:27:27,870 --> 00:27:31,170
+الثانية بيصير تحلي معادلة من الدرجة الثالثة أو
+
+294
+00:27:31,170 --> 00:27:34,930
+الدرجة الرابعة أو الدرجة الخامسة أو السادسة أو ما
+
+295
+00:27:34,930 --> 00:27:40,570
+إلى ذلك هذا ومن هنا صار تعميم لهذه الحالة هيطلع
+
+296
+00:27:40,570 --> 00:27:43,850
+نفس الطرق الثلاث اللي هي reduction of order أو
+
+297
+00:27:43,850 --> 00:27:46,610
+variation of parameters أو undetermined
+
+298
+00:27:46,610 --> 00:27:48,570
+coefficients نفس الطرق
+
+299
+00:27:51,210 --> 00:27:54,230
+يبقى هذا اللي هنشوفه إن شاء الله وتبارك وتعالى
+
+300
+00:27:54,230 --> 00:28:06,210
+في chapter 4 ابنجي ل chapter 5 chapter
+
+301
+00:28:06,210 --> 00:28:14,490
+5 ابنجي لحاجة اسمها series solution of
+
+302
+00:28:14,490 --> 00:28:19,770
+the second order
+
+303
+00:28:22,640 --> 00:28:29,060
+differential equations أول
+
+304
+00:28:29,060 --> 00:28:34,300
+section في هذا الـ chapter بيذكرك بمين بالمتسلسلات
+
+305
+00:28:34,300 --> 00:28:40,580
+الـ power series, Taylor series, Maclaurin series والـ
+
+306
+00:28:40,580 --> 00:28:45,180
+convergence تبعهم يبقى أول section كأنه Calculus B
+
+307
+00:28:45,180 --> 00:28:49,600
+جزء من Calculus B مش كتير يعني بعض المعلومات
+
+308
+00:28:49,600 --> 00:28:54,660
+البسيطة التي تستخدم بعد ذلك مش لسه بدنا نروح كيف
+
+309
+00:28:54,660 --> 00:28:59,080
+نجيب الـ Taylor أو الـ Maclaurin series لدالة تمام عند
+
+310
+00:28:59,080 --> 00:29:03,270
+نقطة معينة لأ لأ لأ هذا كلام انتهى خطيب الـ
+
+311
+00:29:03,270 --> 00:29:09,190
+Calculus بيهم للتذكير بهذه المفاهيم لأن بعضها
+
+312
+00:29:09,190 --> 00:29:14,650
+سيلزم في الـ sections القادمة بهمنا كيف نحل
+
+313
+00:29:14,650 --> 00:29:20,290
+المعادلة من الرتبة الثانية باستخدام المتسلسلات
+
+314
+00:29:23,380 --> 00:29:27,780
+بس مش هنعتمد على الـ series كتير يعني مش تفهموا إنّه
+
+315
+00:29:27,780 --> 00:29:30,800
+بدنا نبدأ chapter الـ series اللي هو من أول لأخر
+
+316
+00:29:30,800 --> 00:29:35,480
+chapter عشرة كان ولا لا؟ اه لا لا لا معلومات بسيطة
+
+317
+00:29:35,480 --> 00:29:39,380
+ثم بنشوف كيف بنحل المعادلة الثانية باستخدام
+
+318
+00:29:39,670 --> 00:29:46,250
+المتسلسلات هذا بيشغل حوالي خمسة sections من
+
+319
+00:29:46,250 --> 00:29:51,350
+الـ chapter تقريبا تمام ابنجي لآخر chapter اللي هو
+
+320
+00:29:51,350 --> 00:29:58,810
+chapter ستة chapter ستة
+
+321
+00:29:58,810 --> 00:30:03,930
+حاجة اسمها Laplace transforms
+
+322
+00:30:16,140 --> 00:30:22,860
+تحويلات Laplace تحويلات
+
+323
+00:30:22,860 --> 00:30:30,060
+Laplace بنلجأ لها أو نستخدمها لتسهيل المسائل
+
+324
+00:30:30,060 --> 00:30:35,800
+المختلفة يعني أحيانا صعب نتعامل مع دالة مباشرة
+
+325
+00:30:35,800 --> 00:30:41,700
+بنجيب دالة مكافئة لها بتحويل معين أو بيصير إن
+
+326
+00:30:41,700 --> 00:30:45,620
+اتعامل مع الدالة الجديدة التي تكافئ الدالة
+
+327
+00:30:45,620 --> 00:30:49,420
+المعلومة هذه الأمور بنسميها تحويلات اللي هو
+
+328
+00:30:49,420 --> 00:30:56,240
+Laplace transform يعني سنعطيها تعريف ثم نستخدم هذا
+
+329
+00:30:56,240 --> 00:31:02,620
+التعريف لإيجاد Laplace transform لدوال مختلفة ثم
+
+330
+00:31:02,620 --> 00:31:07,760
+بعد ذلك نستخدم Laplace transform لحل المعادلات
+
+331
+00:31:07,760 --> 00:31:14,070
+التفاضلية طبعا يبقى أول شغلة نعطي تعريف للابلاس
+
+332
+00:31:14,070 --> 00:31:18,610
+transform والتعريف هذا يعتمد على الـ improper
+
+333
+00:31:18,610 --> 00:31:26,230
+integrals يعني هو تكامل من صفر لما لا نهاية لـ
+
+334
+00:31:26,230 --> 00:31:31,690
+e^-st مضروب في الـ function اللي بدنا نوجد لها
+
+335
+00:31:31,690 --> 00:31:36,620
+Laplace transform بدنا نكامل حصل ضرب هذا وطلع
+
+336
+00:31:36,620 --> 00:31:40,980
+القيمة القيمة اللي بتطلع بيكون هو تكامل هي قيمة
+
+337
+00:31:40,980 --> 00:31:47,000
+Laplace transform للدالة المعطاة مثلا لو بدي
+
+338
+00:31:47,000 --> 00:31:55,040
+Laplace transform للدالة f of t بقول هو تكامل من
+
+339
+00:31:55,040 --> 00:32:03,990
+zero لـ infinity للـ e أس ناقص st للـ f of t dt يبقى
+
+340
+00:32:03,990 --> 00:32:10,650
+هذا تعريف لـ Laplace transform لدالة ما لـ Laplace
+
+341
+00:32:10,650 --> 00:32:14,970
+transform للدالة f of t والتكامل من zero لـ
+
+342
+00:32:14,970 --> 00:32:23,540
+infinity للـ e أس ناقص st للـ f of t dt هتطلع دالة
+
+343
+00:32:23,540 --> 00:32:31,000
+بدلالة المتغير s وبالتالي هروح نسميها بدل f of
+
+344
+00:32:31,000 --> 00:32:37,920
+t هنقول capital F of s تمام؟ يبقى هتطلع
+
+345
+00:32:37,920 --> 00:32:43,900
+function في s هذه الـ function تكافئ عمليا الدالة
+
+346
+00:32:43,900 --> 00:32:49,710
+الأصلية لـ f of t لأن مين ما كانت تكون تمام يبقى هذا
+
+347
+00:32:49,710 --> 00:32:53,810
+تعريف لابلاس ترانسفورم الـ section الأول هنجيب لابلاس
+
+348
+00:32:53,810 --> 00:33:00,390
+ترانسفورم لدوال متعددة بعدين بنعطيكوا جدول موجود
+
+349
+00:33:00,390 --> 00:33:04,310
+بالكتابة وبنجيبهلكوا في الامتحان لو شفتوا أي ورقة
+
+350
+00:33:04,310 --> 00:33:08,070
+امتحان نهائي لمادة المعادلات التفاضلية بتلاقي معاها
+
+351
+00:33:08,070 --> 00:33:14,910
+جدول الجدول هذا لابلاس ترانسفورم
+
+352
+00:33:14,910 --> 00:33:23,180
+لمن لهذه الدوال كل بكل موجود معك يبقى هذا
+
+353
+00:33:23,180 --> 00:33:26,480
+بالنسبة لي الـ section اللي بعد هيك كيف بدنا نستخدم
+
+354
+00:33:26,480 --> 00:33:33,080
+Laplace transform لحل المعادلات المختلفة طبعا
+
+355
+00:33:33,080 --> 00:33:37,180
+سنعطي بعض النظريات اللي بتحدد Laplace transform
+
+356
+00:33:37,180 --> 00:33:41,480
+للمشتقة الأولى شو شكله Laplace transform للمشتقة
+
+357
+00:33:41,480 --> 00:33:45,780
+الثانية شو شكله Laplace transform للمشتقة النونية
+
+358
+00:33:45,780 --> 00:33:50,380
+in general شو شكله وبرضه الصيغة هذه هتكون موجودة
+
+359
+00:33:50,380 --> 00:33:56,100
+عندك وين في الجدول إن شاء الله تبارك وتعالى يبقى
+
+360
+00:33:56,100 --> 00:34:04,980
+هذا إجمالا ما سندرسه في هذا الـ chapter في هذا المساق
+
+361
+00:34:04,980 --> 00:34:11,100
+أو هذا المقرر خلال هذا الفصل طيب حد بتسأل أي سؤال
+
+362
+00:34:11,100 --> 00:34:16,840
+قبل أن ندخل فيه بس الـ introduction اللي هي شبه
+
+363
+00:34:16,840 --> 00:34:20,500
+المساهمة الـ introduction اللي هو بتكلم بس عن
+
+364
+00:34:20,500 --> 00:34:25,480
+المقدمة المعادلات التفاضلية حد بتحب تسأل أي سؤال
+
+365
+00:34:25,480 --> 00:34:31,320
+لأن العدد شبه تكامل الحضور يعني الحضور تلاتة وتلاتة
+
+366
+00:34:31,320 --> 00:34:39,100
+ستة ثمانية أربعة عشر تسعة عشر تلاتة وعشرين سبعة
+
+367
+00:34:39,100 --> 00:34:44,160
+وعشرين تلاتين اثنين وتلاتين خمسة وتلاتين ثمانية
+
+368
+00:34:44,160 --> 00:34:50,440
+وتلاتين اثنين وأربعين شبه تكامل حسب التسجيل حد
+
+369
+00:34:50,440 --> 00:34:58,640
+بتسأل أي سؤال ايش طيب يبقى الآن بنبدأ في مين في
+
+370
+00:34:58,640 --> 00:35:03,220
+المقدمة تبع المعادلات التفاضلية
+
+371
+00:36:50,930 --> 00:36:55,370
+الدالة المجهولة اسمها
+
+372
+00:36:57,730 --> 00:37:01,970
+هي تسمى كتابة مقارنة
+
+373
+00:37:20,390 --> 00:37:26,330
+يبقى an equation المعادلة contains تحتوي أو تشتمل
+
+374
+00:37:26,330 --> 00:37:31,430
+one or more derivatives يعني فيها المشتقة الأولى
+
+375
+00:37:31,430 --> 00:37:35,870
+أو الثانية أو أكثر الثالثة أو الرابعة أو ما إلى
+
+376
+00:37:35,870 --> 00:37:42,490
+ذلك of a non function لدالة مجهولة is called a
+
+377
+00:37:42,490 --> 00:37:47,470
+differential equation for example نعطي مثال لو روحنا
+
+378
+00:37:47,470 --> 00:37:56,030
+نقول y double prime زائد مثلا 5 y prime زائد
+
+379
+00:37:56,030 --> 00:38:06,150
+6 y تساوي صفر مثلا is a differential أو تساوي t
+
+380
+00:38:06,150 --> 00:38:10,970
+مثلا is a differential equation
+
+381
+00:38:20,940 --> 00:38:26,800
+يبقى مرة ثانية an equation contains المعادلة اللي
+
+382
+00:38:26,800 --> 00:38:32,980
+تحتوي أو تجتمل على مشتقة أولى أو أكثر مشتقة ثانية
+
+383
+00:38:32,980 --> 00:38:39,060
+أو ثالثة أو رابعة أو خامسة أو الأخرى لمجهول ده اللي
+
+384
+00:38:39,060 --> 00:38:43,260
+مجهول is called a differential equation طلع لي في
+
+385
+00:38:43,260 --> 00:38:47,100
+المعادلة اللي عندنا هذه هل احنا عارفين شكل الـ y
+
+386
+00:38:48,530 --> 00:38:53,310
+عارفين y تساوي ايش يعني بدلالاتنا؟ نعرفش يبقى y
+
+387
+00:38:53,310 --> 00:38:57,930
+دالة مجهولة احنا بدنا نبحث عليها اللي بدنا نبحث
+
+388
+00:38:57,930 --> 00:39:01,130
+ما هو الشكل الـ y الشكل الـ y بكون هو الصليوشن
+
+389
+00:39:01,130 --> 00:39:06,040
+اللي مين للمعادلة التفاضلية اللي عندنا يبقى دالة
+
+390
+00:39:06,040 --> 00:39:10,600
+مجهولة إذا ظهرت بهذا الشكل على سبيل المثال بقول
+
+391
+00:39:10,600 --> 00:39:15,140
+هذه معادلة تفاضلية يبقى المعادلة التفاضلية هي تظهر
+
+392
+00:39:15,140 --> 00:39:18,760
+المشتق الأول أو الثاني أو الثالث أو الرابع أو أو
+
+393
+00:39:18,760 --> 00:39:24,680
+الآخرين بنسميها معادلة تفاضلية المعادلات التفاضلية
+
+394
+00:39:24,680 --> 00:39:30,540
+نوعان النوع الأول هي معادلة تفاضلية عادية وهي
+
+395
+00:39:30,540 --> 00:39:34,100
+موضوع دراستنا خلال هذا الفصل
+
+396
+00:39:42,240 --> 00:39:46,880
+هذه المعادلة تظهر فيها المشتقات العادية اللي
+
+3
+
+431
+00:44:21,980 --> 00:44:25,320
+المعادلة التفاضلية يبقى أنا عندي function في
+
+432
+00:44:25,320 --> 00:44:30,720
+متغير واحد فقط قلنا with respect to a single
+
+433
+00:44:37,150 --> 00:44:41,790
+بتصير المشتقات مشتقات عادية وبالتالي المعادلة
+
+434
+00:44:41,790 --> 00:44:45,390
+التفاضلية اللي عندنا بيكون معادلة تفاضلية عادية
+
+435
+00:44:45,390 --> 00:44:51,510
+بنقول عليها معادلة تفاضلية عادية زي إيش مثلا لو قلت
+
+436
+00:44:51,510 --> 00:44:56,110
+y prime زائد ثلاثة y يساوي E أس تي معادلة ظهرت فيها
+
+437
+00:44:56,110 --> 00:45:02,910
+باسمين المشتقة الأولى يبقى one derivative يبقى
+
+438
+00:45:02,910 --> 00:45:08,570
+معادلة تفاضلية من الرتبة الأولى الآن لو كانت
+
+439
+00:45:08,570 --> 00:45:11,850
+المعادلة بالشكل اللي عندنا هذا يبقى ظاهرة المشتقة
+
+440
+00:45:11,850 --> 00:45:18,790
+الأولى والمشتقة الثانية يبقى هذا one or more أكثر
+
+441
+00:45:18,790 --> 00:45:23,790
+من مين من المشتقة والمشتقات العادية يبقى في هذه
+
+442
+00:45:23,790 --> 00:45:29,510
+الحالة بقول هذه معادلة تفاضلية عادية حد بيسأل أي
+
+443
+00:45:29,510 --> 00:45:36,330
+سؤال هنا؟ آه طيب بدنا نروح لحاجة اسمها اللي هو حل
+
+444
+00:45:36,330 --> 00:45:44,010
+أو رتبة المعادلة التفاضلية definition the
+
+445
+00:45:44,010 --> 00:45:48,970
+order of 
+
+446
+00:45:48,970 --> 00:45:59,610
+a differential equation رتبة المعادلة التفاضلية is
+
+447
+00:46:00,160 --> 00:46:17,280
+the order of the
+
+448
+00:46:17,280 --> 00:46:28,000
+highest derivative in
+
+449
+00:46:28,000 --> 00:46:28,840
+the equation
+
+450
+00:46:37,320 --> 00:46:47,680
+على سبيل المثال الـ differential equation
+
+451
+00:46:47,680 --> 00:46:58,560
+الـ differential equation d تكعيب y على d t تكعيب
+
+452
+00:46:58,560 --> 00:47:10,630
+ناقص اثنين dy على dt أس أربعة زائد y
+
+453
+00:47:10,630 --> 00:47:19,230
+تساوي t لأن t is of the
+
+454
+00:47:42,920 --> 00:47:52,060
+رتبة المعادلة التفاضلية رتبة المعادلة التفاضلية هي
+
+455
+00:47:52,060 --> 00:47:58,860
+رتبة أعلى 
+
+456
+00:47:58,860 --> 00:48:04,810
+معامل تفاضلي يظهر في المعادلة in the equation يبقى
+
+457
+00:48:04,810 --> 00:48:08,550
+أنا باجي على المعادلة التفاضلية وبشوف مين أعلى
+
+458
+00:48:08,550 --> 00:48:13,630
+مشتقة موجودة فيها أعلى مشتقة موجودة فيها بتكون هي
+
+459
+00:48:13,630 --> 00:48:19,050
+رتبة مين المعادلة التفاضلية بنعطي مثال توضيحي for
+
+460
+00:48:19,050 --> 00:48:23,630
+example the differential equation d تكعيب y
+
+461
+00:48:23,630 --> 00:48:30,790
+على dt تكعيب نقص اثنين dy على dt أس أربعة زائد y
+
+462
+00:48:30,790 --> 00:48:37,410
+تساوى t لأن t is of بدنا نعرف قداش ال order تبعها يا 
+
+463
+00:48:37,410 --> 00:48:43,890
+ترى هل هو ثلاثة والله قداش والله أربعة مش أربعة
+
+464
+00:48:43,890 --> 00:48:48,750
+يعني إذا 
+
+465
+00:48:48,750 --> 00:48:53,550
+القضية خلافية بين الفقهاء البعض بيقولوا ثلاثة و
+
+466
+00:48:53,550 --> 00:48:57,650
+البعض بيقولوا أربعة أنا بسألك شو اسم ممكن أتعرف
+
+467
+00:48:57,650 --> 00:49:04,610
+عليكي بتسامي بتسامي النجار تعتقد، طبعا هذه أول
+
+468
+00:49:04,610 --> 00:49:09,630
+محاضرة، وبالتالي تعتقد، مش بيقول، تعتقد أن
+
+469
+00:49:09,630 --> 00:49:14,930
+المعادلة هذه من رتبة رقم أربعة، وأنا أسأل هل 
+
+470
+00:49:14,930 --> 00:49:18,290
+الأربعة هذه مشتقة ولا أس؟
+
+471
+00:49:21,070 --> 00:49:26,710
+ممتاز جدا بس طبعا شايفة يبقى بتقول أس للمشتقة بقول
+
+472
+00:49:26,710 --> 00:49:31,950
+كلامها صحيح لكن أرجع للتعريف هل أنا قلت أس
+
+473
+00:49:31,950 --> 00:49:37,950
+المشتقة ولا المشتقة نفسها وما قلت أس المشتقة صحيح
+
+474
+00:49:37,950 --> 00:49:41,610
+ولا لا نرجع للتعريف the order of the differential
+
+475
+00:49:41,610 --> 00:49:45,970
+equation is the order of the highest derivative
+
+476
+00:49:45,970 --> 00:49:53,860
+يبقى هو رتبة أعلى ولم أقول هي أس مام؟ يبقى أربعة
+
+477
+00:49:53,860 --> 00:49:59,200
+هذا الرقم أربعة ماله خطأ ولا صح؟ خطأ بل very wrong
+
+478
+00:49:59,200 --> 00:50:04,240
+نشكرها على سؤالها إنها قالت هذه أربعة لأن الكل 
+
+479
+00:50:04,240 --> 00:50:08,480
+بفهم الآخرين إن الرتبة ليست أربعة وإنما
+
+480
+00:50:08,480 --> 00:50:14,770
+الرتبة ثلاثة، لأن ثلاثة هي أعلى مشتقة موجودة في هذه
+
+481
+00:50:14,770 --> 00:50:19,110
+الوضع، مش أربعة، لو قضيت أربعة بمليون، بتظل هي من
+
+482
+00:50:19,110 --> 00:50:24,410
+رتبة الثالثة، ليش؟ إن أربعة أس وليست مشتقة، واحنا
+
+483
+00:50:24,410 --> 00:50:29,950
+بيقول ال order هو رتبة المشتقة، يعني المشتقة
+
+484
+00:50:29,950 --> 00:50:33,630
+الأولى ولا الثانية ولا الثالثة ولا الرابعة، تمام؟
+
+485
+00:50:33,730 --> 00:50:38,690
+يبقى أربعة ليست مشتقة و للمشتقة الرقم ثلاثة كان 
+
+486
+00:50:38,690 --> 00:50:45,710
+بإمكاني مكتوبهاش زي هيك اهو هاكتب d تكعيب y على dt تكعيب
+
+487
+00:50:45,710 --> 00:50:54,760
+ناقص اثنين dy على dt أس أربعة زائد y تساوي t لين t إذا
+
+488
+00:50:54,760 --> 00:50:58,720
+هذه والله هذه أعلى المشتقة الموجودة عندها من
+
+489
+00:50:58,720 --> 00:51:05,180
+المشتقة التالية إذا هذه is of the third order من
+
+490
+00:51:05,180 --> 00:51:12,380
+الرتبة الثالثة وليست الرابعة ابقى is of the third
+
+491
+00:51:12,380 --> 00:51:16,440
+order تمام؟
+
+492
+00:51:16,680 --> 00:51:22,740
+يبقى جبتها والله بدل المرة مرتين في سؤال بخيارات
+
+493
+00:51:22,740 --> 00:51:27,780
+متعددة بحط شغلة زيك طبعا بحطلها كمان واحدة وبقول
+
+494
+00:51:27,780 --> 00:51:31,280
+of the nth order of the third order of the zero
+
+495
+00:51:31,280 --> 00:51:35,300
+order of the fourth order وحطيلي خط تحت الإجابة 
+
+496
+00:51:35,300 --> 01:00:40,260
+الصحية يعني جبتها قبل ذلك بدل المرة مرتين يوم أن
+
+497
+01:00:40,260 --> 01:00:45,900
+درست المادة سابقا يبقى بتروح بتروحي وين بتشوفي أعلى
+
+498
+01:00:45,900 --> 01:00:50,120
+معامل تفاضل، يعني كان بيمكن يتحيل عليك بطريقة
+
+499
+01:00:50,120 --> 01:00:56,360
+ثانية ويقول لك هذه تربيع، بصير هذا مثلا هاك تربيع،
+
+500
+01:00:56,360 --> 01:01:02,880
+وهذه أربعة، إنّي أتمنّى وأحط لك اثنين، ثلاثة، أربعة،
+
+501
+01:01:02,880 --> 01:01:07,900
+ستة، ثلاثة مثلا، وحطيلي اللي تقطحت اللي جابتها
+
+502
+01:01:07,900 --> 01:01:11,890
+الصحية يبقى الإجابة الصحية قداش؟ هادية، رغم أنّي
+
+503
+01:01:11,890 --> 01:01:16,890
+غيرتها، لكن ضالة is of the third order من الرتبة
+
+504
+01:01:16,890 --> 01:01:21,450
+الثالثة، لكن إذا بتكلم عن الدرجة، بقول الدرجة 
+
+505
+01:01:21,450 --> 01:01:26,070
+الرابعة مش موافق كدرجة كرتبة لأ إذا احنا ما لنا
+
+506
+01:01:26,070 --> 01:01:30,630
+علاقة بالدرجة وإنما لنا علاقة بالرتبة الدرجة هذا
+
+507
+01:01:30,630 --> 01:01:35,530
+للصف الثامن والتاسع تمام يبقى هنا هقول من الرتبة
+
+508
+01:01:35,530 --> 01:01:42,190
+الثالثة تمام هذا بالنسبة لرتبة المعادلة التفاضلية
+
+509
+01:01:42,190 --> 01:01:47,290
+بدنا نيجي لحل المعادلة التفاضلية يبقى كمان
+
+510
+01:01:47,290 --> 01:01:47,990
+definition
+
+511
+01:01:55,140 --> 01:02:05,560
+The solution of a differential equation حل 
+
+512
+01:02:05,560 --> 01:02:11,380
+المعادلة التفاضلية is a function
+
+513
+01:02:16,120 --> 01:02:29,040
+معرفة defined on an interval معرفة على فترة ما on
+
+514
+01:02:29,040 --> 01:02:40,840
+an interval i مثلا and satisfy and
+
+515
+01:02:40,840 --> 01:02:44,460
+satisfy the differential equation
+
+516
+01:02:48,930 --> 01:02:58,910
+وتحقق المعادلة التفاضلية for example كمثال على ذلك
+
+517
+01:02:58,910 --> 01:03:12,790
+for example y تساوي e أس 2t is a solution is a
+
+518
+01:03:12,790 --> 01:03:16,550
+solution of the
+
+519
+01:03:25,960 --> 01:03:30,940
+y'' نقص اثنين y تساوي صفر
+
+520
+01:03:56,900 --> 01:04:02,440
+مرة ثانية حل المعادلة التفاضلية the solution of a
+
+521
+01:04:02,440 --> 01:04:07,060
+differential equation هو عبارة عن دالة دالة معرفة
+
+522
+01:04:07,060 --> 01:04:13,320
+على فترة محددة والتكن i وفي نفس الوقت تحقق من
+
+523
+01:04:13,320 --> 01:04:17,140
+المعادلة التفاضلية يعني إيه؟ يعني لو عوضتها في
+
+524
+01:04:17,140 --> 01:04:21,200
+المعادلة التفاضلية بدها إيش؟ بدها تتحقق يعني
+
+525
+01:04:21,200 --> 01:04:25,770
+تخلي الطرف اليمين زي الطرف اللي على الشمال مثلا
+
+526
+01:04:25,770 --> 01:04:39,310
+يبقى الدالة y تساوي e أس اثنين t هي
+
+527
+01:04:39,310 --> 01:04:41,290
+حل هذه المعرفة
+
+528
+01:04:50,280 --> 01:04:54,280
+على كل الـ real line الـ exponential function 
+
+529
+01:04:54,280 --> 01:04:57,280
+ 
+530
+01:04:57,280 --> 01:05:04,660
+ 
+
+531
+01:05:04,660 --> 01:05:15,140
+
+532
+01:05:17,120 --> 01:05:21,540
+وقدّمنا فيه امتحانًا ونجحنا بجدارة يعني طب هذه بدنا 
+
+533
+01:05:21,540 --> 01:05:26,240
+نشوف كيف حالة هذه لو جات اشتقها قداش بتكون مشتقتها 
+
+534
+01:05:26,240 --> 01:05:33,010
+اثنين e أس اثنين t يبقى بده يشيل هذه ويكتب اثنين e
+
+535
+01:05:33,010 --> 01:05:37,910
+أس اثنين t نقص اثنين e أس اثنين t قداش يبقى 
+
+536
+01:05:37,910 --> 01:05:43,110
+الجواب صفر زي الطرف اليمين إذا فعلا هذه حل طب
+
+537
+01:05:43,110 --> 01:05:47,090
+عشان واحدة تقول لك كيف جبت هذه كيف جبت هو شغلنا 
+
+538
+01:05:47,090 --> 01:05:52,370
+بداية من المرة القادمة و لنهاية المقرر كل شغلنا
+
+539
+01:05:52,370 --> 01:05:58,790
+إيجاد الحلول للمعادلات التفاضلية نعطيكي مثال آخر
+
+540
+01:05:59,280 --> 01:06:06,420
+يبقى example show
+
+541
+01:06:06,420 --> 01:06:10,060
+that
+
+542
+01:06:10,060 --> 01:06:21,260
+y تساوي t e أس t is a solution is
+
+543
+01:06:21,260 --> 01:06:30,990
+a solution of the differentialEquation هي عبارة عن 
+
+544
+01:06:30,990 --> 01:06:38,930
+حل المعادلة التفاضلية y double prime نقص اثنين y prime 
+
+545
+01:06:38,930 --> 01:06:48,930
+زائد y تساوي صفر on the interval على الفترة من
+
+546
+01:06:48,930 --> 01:06:51,510
+سالب infinity ل infinity
+
+547
+01:07:03,070 --> 01:07:08,350
+يبقى حل المعادلة التفاضلية هو عن دالة معرفة على
+
+548
+01:07:08,350 --> 01:07:14,250
+فترة وتحقق المعادلة الحمد لله قال يبين لي إن هذا 
+
+549
+01:07:14,250 --> 01:07:20,430
+هو حل للمعادلة التفاضلية على الفترة السؤال هو قداش 
+
+550
+01:07:20,430 --> 01:07:28,410
+domain t في e أس t بمعنى آخر هل توجد نقطة الدالة
+
+551
+01:07:28,410 --> 01:07:33,780
+هذه ماهياش معرفة عندها؟ لأ كله من سالب حتى عند صفر 
+
+552
+01:07:33,780 --> 01:07:37,400
+عند صفر بتطلع صفر في e of صفر اللي هو بواحد
+
+553
+01:07:37,400 --> 01:07:45,640
+يبقى صفر معرفة يبقى باجي بقول له ال y تساوي t في e
+
+554
+01:07:45,640 --> 01:07:54,580
+of t is defined معرفة for all t اللي موجودة في ال
+
+555
+01:07:54,580 --> 01:07:59,850
+interval من سالب infinity إلى infinite يبقى الدلل
+
+556
+01:07:59,850 --> 01:08:04,510
+يا طهالي هي معرفة عليها كل الفضل لكن هي حل والله 
+
+557
+01:08:04,510 --> 01:08:09,270
+مش حل لسه أنا مش عارف تمام؟ يبقى بهذه فيها المشتقة
+
+558
+01:08:09,270 --> 01:08:12,570
+الأولى والثانية إذا بدي أروح أجيب المشتقة الأولى
+
+559
+01:08:12,570 --> 01:08:18,630
+والمشتقة الثانية يبقى لما أقول له y تساوي t e أس t
+
+560
+01:08:18,630 --> 01:08:24,210
+بدي أروح أجيب له المشتقة الأولى هذه يا بنات تعتبر
+
+561
+01:08:24,210 --> 01:08:30,140
+دالة وهذه دالة إذا مشتقة حاصل ضرب الأولى في مشتقة
+
+562
+01:08:30,140 --> 01:08:35,120
+الثانية زائد الثانية في مشتقة الأولى يبقى الأولى
+
+563
+01:08:35,120 --> 01:08:39,100
+اللي هي t مشتقة ال exponential بال exponential
+
+564
+01:08:39,100 --> 01:08:45,720
+أس t زائد الدالة الثانية في مشتقة الأولى اللي هي
+
+565
+01:08:45,720 --> 01:08:51,360
+بواحد هذه المشتقة الأولى بدنا نروح نجيب المشتقة 
+
+566
+01:08:51,360 --> 01:08:58,300
+الثانية يبقى بدي واي ضعف لقايم بدنا نروح نشتق هذه 
+
+567
+01:08:58,300 --> 01:09:04,180
+الجزء الأول برضه مشتقة حاصل ضرب دالتين الأولى في
+
+568
+01:09:04,180 --> 01:09:09,140
+مشتقة الدالة الثانية زائد الدالة الثانية في مشتقة
+
+569
+01:09:09,140 --> 01:09:15,730
+الأولى نجي للي بعدها زائد مشتقة ال e أس t بال e أس t
+
+570
+01:09:15,730 --> 01:09:25,870
+itself يبقى الجواب t e أس t زائد 2 e أس t الآن نمسك
+
+571
+01:09:25,870 --> 01:09:29,690
+المعلومات اللي حصلنا عليها ونرجع نعوض في المعادلة 
+
+572
+01:09:29,690 --> 01:09:35,770
+اللي فوق يبقى بدأ خدّاله الآن y double prime نقص 2 y 
+
+573
+01:09:35,770 --> 01:09:42,150
+prime زائد y إن شاء الله الناتج يساوي الصفر بيكون
+
+574
+01:09:42,150 --> 01:09:51,470
+هذا هو عن حل يبقى هذا الكلام يبقى يساوي يبقى يبقى
+
+575
+01:09:51,470 --> 01:09:59,670
+يبقى يبقى يبقى يبقى يبقى يبقى يبقى يبقى يبقى يبقى
+
+576
+01:09:59,670 --> 01:09:59,910
+ يبقى يبقى يبقى يبقى يبقى يبقى يبقى يبقى يبقى يبقى
+
+577
+01:09:59,910 --> 01:10:01,330
+يبقى يبقى يبقى يبقى يبقى يبقى يبقى يبقى يبقى يبقى
+
+578
+01:10:01,330 --> 01:10:07,940
+يبقى يبقى يبقى يبقى يبقى t e أس t زائد e أس t
+
+579
+01:10:07,940 --> 01:10:14,200
+شيلنا y prime وحطينا منين قيمتها قال لي زائد y
+
+580
+01:10:14,200 --> 01:10:21,380
+وين y اللي هي طالب الأصل يبقى زائد t e أس t بدي
+
+581
+01:10:21,380 --> 01:10:26,300
+أشوف كده إيش بيطلع هدول يبقى هذا الكلام يساعد هذه
+
+582
+01:10:26,300 --> 01:10:34,260
+هي هذه صحيح ولا لأ يبقى اثنين t e و أس t زائدي
+
+583
+01:10:34,260 --> 01:10:41,700
+اثنين e و أس t بده أفكّ الجثّ هذا نقص اثنين t e و
+
+584
+01:10:41,700 --> 01:10:49,920
+أس t نقص اثنين e و أس t طلعي ليه؟ هذه وهذه
+
+585
+01:10:49,920 --> 01:10:56,180
+بإشارتين مختلفتين صحيح ولا لأ؟ يبقى عند الجامع
+
+586
+01:10:56,180 --> 01:11:03,810
+بيثلاشه هذه وهذه نفس القصة بإشارتين يبقى المجموع
+
+587
+01:11:03,810 --> 01:11:08,410
+الكل قداش بيطلع صفر اللي هو الطرف اليمين من
+
+588
+01:11:08,410 --> 01:11:14,030
+المعادلة اللي عندنا هذه يبقى أثبت له y'' نقص 2y' زائد y
+
+589
+01:11:14,030 --> 01:11:19,630
+كله يساوي مين صفر يبقى فعلا هذه حل المعادلة على
+
+590
+01:11:19,630 --> 01:11:26,390
+الفترة من سالب infinity إلى infinity y تساوي t في ال
+
+591
+01:11:26,390 --> 01:11:35,970
+e أس t is a solution of y double prime نقص اثنين
+
+592
+01:11:35,970 --> 01:11:43,230
+y prime زائد y يساوي صفر on ال interval من سالب
+
+593
+01:11:43,230 --> 01:11:46,310
+infinity إلى infinity
+
+594
+01:12:14,540 --> 01:12:20,580
+not ملاحظة بسيطة المعادلة التفاضلية يا ابنتي ممكن ما 
+
+595
+01:12:20,580 --> 01:12:24,860
+يكونش لحل واحد وبس ممكن حلّان ممكن ثلاثة ممكن ما لا
+
+596
+01:12:24,860 --> 01:12:29,280
+نهاية من الحلول يعني ليس بالضرورة أن يكون حلًّا
+
+597
+01:12:29,280 --> 01:12:33,060
+واحدا فقط يبقى باجي بقول له the differential
+
+598
+01:12:33,060 --> 01:12:39,460
+equation may
+
+599
+01:12:39,460 --> 01:12:40,400
+have
+
+600
+01:12:44,530 --> 01:12:58,790
+more than more than one solution ممكن يكون لها 
+
+601
+01:12:58,790 --> 01:13:05,930
+أكثر من حلّ حلّين ثلاثة أربعة جد ما يكون نعطي
+
+602
+01:13:05,930 --> 01:13:10,670
+definition the set of all solutions
+
+603
+01:13:13,400 --> 01:13:20,780
+of all solutions of
+
+604
+01:13:20,780 --> 01:13:25,960
+a given differential 
+
+605
+01:13:25,960 --> 01:13:34,320
+equation لمعادلة تفاضلية مُعطَى is called نروح
+
+606
+01:13:34,320 --> 01:13:39,300
+نسمّيها general solution نسمّيها
+
+607
+01:13:40,370 --> 01:13:51,090
+general solution of differential 
+
+608
+01:13:51,090 --> 01:13:
+
+646
+01:09:19,730 --> 01:09:32,930
+لمشتقتها at a single value عند قيمة واحدة  of the 
+
+647
+01:09:32,930 --> 01:09:36,050
+independent
+
+648
+01:09:42,060 --> 01:09:53,300
+variable عند قيمة واحدة للمتغير المستقل then the
+
+649
+01:09:53,300 --> 01:10:08,580
+differential equation is called بنسميها an initial
+
+650
+01:10:36,550 --> 01:10:49,270
+والقوانين المعروفة والقيم المعطاة تسمى بـInitial
+
+651
+01:10:49,270 --> 01:10:58,570
+Conditions يبقى
+
+652
+01:10:58,570 --> 01:11:05,450
+الشروط الابتدائية على
+
+653
+01:11:05,450 --> 01:11:05,890
+سبيل المثال
+
+654
+01:11:14,770 --> 01:11:19,470
+على سبيل المثال الاختصارات
+
+655
+01:11:19,470 --> 01:11:23,950
+الاختصارات الاختصارات الاختصارات الاختصارات
+
+656
+01:11:23,950 --> 01:11:25,370
+الاختصارات الاختصارات الاختصارات الاختصارات
+
+657
+01:11:25,370 --> 01:11:25,450
+الاختصارات الاختصارات الاختصارات الاختصارات
+
+658
+01:11:25,450 --> 01:11:32,810
+الاختصارات الاختصارات
+
+659
+01:11:32,810 --> 01:11:34,710
+الاختصارات الاختصارات الاختصارات الاختصارات
+
+660
+01:11:34,710 --> 01:11:34,750
+الاختصارات الاختصارات الاختصارات الاختصارات
+
+661
+01:11:34,750 --> 01:11:35,210
+الاختصارات الاختصارات الاختصارات الاختصارات
+
+662
+01:11:35,210 --> 01:11:39,050
+الاختصارات الاختصارات الاختصارات الاختصارات
+
+663
+01:11:39,050 --> 01:11:42,070
+الاختصارات
+
+664
+01:11:44,410 --> 01:11:54,230
+و الـ y عند الـ y على 2 ساوي سلبي 2 و الـ y عند الـ y
+
+665
+01:11:54,230 --> 01:12:04,530
+على 2 ساوي 1 من الـ value problems
+
+666
+01:12:46,080 --> 01:12:50,860
+بنرجع لهذا التعريف مرة ثانية وبعد ذلك نروح نحطه
+
+667
+01:12:50,860 --> 01:12:55,860
+على أرض الواقع بقول if we are given values إذا
+
+668
+01:12:55,860 --> 01:13:02,080
+أعطينا قيم of the unknown function لدالة المجهولة
+
+669
+01:13:02,080 --> 01:13:06,440
+and its derivative ومشتقاتها أعطينا قيم لدالة
+
+670
+01:13:06,440 --> 01:13:12,500
+المجهولة ومشتقات الدالة المجهولة وين؟At a single
+
+671
+01:13:12,500 --> 01:13:18,860
+value عند قيمة محددة أو قيمة معينة واحدة فقط لمين
+
+672
+01:13:18,860 --> 01:13:23,760
+للـ independent variable للمتغير المستقل لما أقول Y
+
+673
+01:13:23,760 --> 01:13:27,780
+ده اللي في T يا بناتي يبقى Y هو المتغير التابع و T
+
+674
+01:13:27,780 --> 01:13:34,380
+هو المتغير المستقل يعني إيه ده؟ وحصلنا على قيم لها
+
+675
+01:13:34,380 --> 01:13:41,160
+نتيجة ليعطاها قيمة محددة للمتغير المستقل عطينا قيم
+
+676
+01:13:41,160 --> 01:13:46,700
+لـY ومشتقاتها نتيجة ليعطاها قيمة للمتغير المستقل
+
+677
+01:13:50,120 --> 01:13:55,320
+بقول عليها initial value problem يعني مسألة القيم
+
+678
+01:13:55,320 --> 01:14:02,460
+الابتدائية تمام وهختصرها IVP مش very important person
+
+679
+01:14:02,460 --> 01:14:06,740
+VIP تبع الشخصية لأ لأ لأ initial value problem
+
+680
+01:14:06,740 --> 01:14:11,620
+الحرف الأول initial الحرف الثاني V اللي هو ال
+
+681
+01:14:11,620 --> 01:14:15,980
+value الحرف الثالث P جاية من كلمة مين problem يبقى
+
+682
+01:14:15,980 --> 01:14:22,620
+كلمة initial value problem هاختصرها إلى IVP طب
+
+683
+01:14:22,620 --> 01:14:26,380
+الشروط اللي حطيناها هذه بسميها initial conditions
+
+684
+01:14:26,380 --> 01:14:31,640
+الشروط الابتدائية and the given values والقيم اللي
+
+685
+01:14:31,640 --> 01:14:35,700
+أعطيناها هذه are called the initial conditions
+
+686
+01:14:35,700 --> 01:14:40,120
+نعطي الآن مثال على الكلام اللي احنا جايلينه هنا
+
+687
+01:14:40,560 --> 01:14:44,840
+مثلًا الـ differential equations طلّي لهذه من أي
+
+688
+01:14:44,840 --> 01:14:51,160
+رتبة من الرتبة الأولى تمام أعطينا أن قيمة y عند ال
+
+689
+01:14:51,160 --> 01:14:55,000
+zero يساوي كده؟ خمسة يبقى ما عندش إلا condition واحد
+
+690
+01:14:55,000 --> 01:15:00,400
+جدّيش عندك رتب جدّيش بتعطي conditions الرتبة الأولى
+
+691
+01:15:00,400 --> 01:15:03,480
+بتعطي condition واحد الرتبة الثانية بدك تعطي two
+
+692
+01:15:03,480 --> 01:15:06,740
+conditions الرتبة الثالثة three conditions وهكذا
+
+693
+01:15:06,740 --> 01:15:12,080
+يعني إذا عند الرتبة الثالثة بدي أعطي condition لـ y
+
+694
+01:15:12,080 --> 01:15:19,390
+ولـ y prime ولـ y double prime بتعطي قيم لهم هذه
+
+695
+01:15:19,390 --> 01:15:24,090
+المعادلة من الرتبة الأولى رغم أن الرتبة الأولى ليست
+
+696
+01:15:24,090 --> 01:15:29,250
+موجودة فهيش يقول why عند بي على اتنين بده تساوي
+
+697
+01:15:29,250 --> 01:15:33,530
+قدّاش سالب اتنين why prime عند بي على اتنين بده
+
+698
+01:15:33,530 --> 01:15:38,990
+تساوي قدّاش واحد يبقى حطيت شرطين لاحظي عند نفس ال
+
+699
+01:15:38,990 --> 01:15:43,970
+independent variable يبقى هنا تيب بي على اتنين وهنا 
+
+700
+01:15:43,970 --> 01:15:47,550
+مش هذا عندها نقطة وهذا عندها نقطة ثانية يعني
+
+701
+01:15:47,550 --> 01:15:50,590
+عندها قيمة للمتغير المسؤول عنها؟ لأ عندها نفس
+
+702
+01:15:50,590 --> 01:15:56,250
+القيمة روحنا قلنا هنا وهنا at a single value عند
+
+703
+01:15:56,250 --> 01:15:59,590
+قيمة واحدة يبقى الباية على اتنين هذه اللي كانت
+
+704
+01:15:59,590 --> 01:16:03,690
+single value في التعريف للـ independent variable
+
+705
+01:16:04,010 --> 01:16:10,290
+للمتغير المستقل أعطتني قيمة لـ Y وأعطتني قيمة لـ Y'
+
+706
+01:16:11,170 --> 01:16:15,190
+زي ما أنت شايفة يبقى إذا عندي معادلة بالشرط أو
+
+707
+01:16:15,190 --> 01:16:19,790
+معادلة بشرطين أو معادلة بثلاثة شروط أو بأربعة شروط
+
+708
+01:16:19,790 --> 01:16:26,710
+بسمي هذه initial value problem طيب
+
+709
+01:16:26,710 --> 01:16:30,910
+ليش الـ initial value problem؟ لو ما أعطانيش ال
+
+710
+01:16:30,910 --> 01:16:37,210
+condition هذا بيطلع عندي الجواب هه بثابت، إذا
+
+711
+01:16:37,210 --> 01:16:40,590
+المعادلة من الرتبة الأولى، بثابتين، لأنه بدنا
+
+712
+01:16:40,590 --> 01:16:44,790
+نكامل، ونتيجة التكامل بيجي لي ثابت مظبوط أو لا؟
+
+713
+01:16:44,790 --> 01:16:49,270
+بثابتين إذا من الرتبة الثانية، بثلاثة أو بثلاثة
+
+714
+01:16:49,270 --> 01:16:52,830
+ثوابت من الرتبة اللي هو الثالثة وهكذا الـ initial
+
+715
+01:16:52,830 --> 01:16:57,810
+conditions منها من خلالها بجيب قدّاش مقدار اللي هو
+
+716
+01:16:57,810 --> 01:17:02,290
+المقدار الثابت أو قدّاش قيمة المقدار الثابت اللي
+
+717
+01:17:02,290 --> 01:17:07,030
+موجود عندنا حد بتحب تسأل أي تسأل في كل ما سمعته
+
+718
+01:17:07,030 --> 01:17:12,050
+اليوم في هذه المحاضرة تسأل أسئلة زي مسألة أخذنا قبل
+
+719
+01:17:12,050 --> 01:17:15,330
+شوية وأجبناها تفضلي لأن معادلة تفاضلية ما ينفعش
+
+720
+01:17:15,330 --> 01:17:19,690
+تكون Zero Order ما ينفعش تكون Zero Order ما ينفعش
+
+721
+01:17:19,690 --> 01:17:21,610
+تكون Zero Order ما ينفعش تكون Zero Order ما ينفعش
+
+722
+01:17:21,610 --> 01:17:21,930
+تكون Zero Order ما ينفعش تكون Zero Order ما ينفعش
+
+723
+01:17:21,930 --> 01:17:22,350
+تكون Zero Order ما ينفعش تكون Zero Order ما ينفعش
+
+724
+01:17:22,350 --> 01:17:23,330
+تكون Zero Order ما ينفعش تكون Zero Order ما ينفعش
+
+725
+01:17:23,330 --> 01:17:25,590
+تكون Zero Order ما ينفعش تكون Zero Order ما ينفعش
+
+726
+01:17:25,590 --> 01:17:27,130
+تكون Zero Order ما ينفعش تكون Zero Order ما ينفعش
+
+727
+01:17:27,130 --> 01:17:27,170
+تكون Zero Order ما ينفعش تكون Zero Order ما ينفعش
+
+728
+01:17:27,170 --> 01:17:30,610
+تكون Zero Order ما ينفعش تكون Zero Order ما ينفعش
+
+729
+01:17:30,610 --> 01:17:31,450
+تكون Zero Order ما ينفعش تكون Zero Order ما ينفعش
+
+730
+01:17:31,450 --> 01:17:39,430
+تكون Zero Order ما ينفعش تكون Zero 
+
+731
+01:17:39,450 --> 01:17:43,070
+قلنا أول ما بدأنا المعادلة التفاضلية هي معادلة
+
+732
+01:17:43,070 --> 01:17:48,770
+يظهر فيها one or more يعني لازم على الأقل تظهر
+
+733
+01:17:48,770 --> 01:17:53,410
+مين؟ المشتقة الأولى حتى أقول من الرتبة .. من جهة
+
+734
+01:17:53,410 --> 01:17:56,090
+الرتبة الأولى، الثانية، الثالثة، الرابعة، بنفع
+
+735
+01:17:56,090 --> 01:18:00,610
+أقول من الرتبة رقم ناقص تلاتة؟ كيف رتبة ناقص
+
+736
+01:18:00,610 --> 01:18:06,370
+تلاتة؟ هي في تفاضل بننزل نزول؟ طيب حالتك تلاقي سؤال
+
+737
+01:18:06,370 --> 01:18:13,040
+ثاني؟ خلاص يبقى إن شاء الله يوم الاثنين بدنا نبدأ
+
+738
+01:18:13,040 --> 01:18:16,480
+يا بنات في الـ first order differential equation
+
+739
+01:18:16,480 --> 01:18:22,680
+ياريت تحضري لي أول section أو أول two sections من
+
+740
+01:18:22,680 --> 01:18:26,860
+chapter اتنين اللي هو تبدأ بالـ linear واللي بعده
+
+741
+01:18:26,860 --> 01:18:29,780
+ماشي إن شاء الله وتعالى يعطيكم العافية
diff --git a/PL9fwy3NUQKwa8ZDfSFGn6H8xVFLzqmCZC/dANTZFG0kHA_postprocess.srt b/PL9fwy3NUQKwa8ZDfSFGn6H8xVFLzqmCZC/dANTZFG0kHA_postprocess.srt
new file mode 100644
index 0000000000000000000000000000000000000000..1152bf80be17522a1ad6532edb6922a4d1498d28
--- /dev/null
+++ b/PL9fwy3NUQKwa8ZDfSFGn6H8xVFLzqmCZC/dANTZFG0kHA_postprocess.srt
@@ -0,0 +1,2964 @@
+1
+00:00:17,140 --> 00:00:21,380
+الكتاب المقرر هو elementary differential equations
+
+2
+00:00:21,380 --> 00:00:25,620
+and boundary value problems الطبعة هي الطبعة
+
+3
+00:00:25,620 --> 00:00:34,110
+الثامنةالمؤلفان William Boyce and Richard Brima ال
+
+4
+00:00:34,110 --> 00:00:38,190
+chapters المقررة من هذا الكتاب ابتداء من section 1
+
+5
+00:00:38,190 --> 00:00:46,430
+وحتى section 6 يبقى ستة كاشن سندرسها خلال هذا
+
+6
+00:00:46,430 --> 00:00:52,540
+الفصل ان شاء الله تبارك وتعالىالمراجع لهذا الكتاب
+
+7
+00:00:52,540 --> 00:00:56,600
+لو روحت المكتب اي كتاب في المعادلة التفاضلي
+
+8
+00:00:56,600 --> 00:01:00,320
+الموجود في المكتب عندنا والحمد لله فيها بدأ الكتاب
+
+9
+00:01:00,320 --> 00:01:06,160
+عشرة لمؤلفين مختلفين كله ممكن اه ممكن يكون مرجع
+
+10
+00:01:06,160 --> 00:01:12,600
+معاكي ترجعيله وقت ما شئتي نجي ل chapter one يبقى
+
+11
+00:01:12,600 --> 00:01:17,080
+نجي لأول chapter اللي هو chapter one
+
+12
+00:01:26,790 --> 00:01:34,990
+introduction introduction يعني مقدمة في هذه
+
+13
+00:01:34,990 --> 00:01:41,430
+المقدمة سنعطي بعض المفاهيم الأساسية يعني ذلك ما
+
+14
+00:01:41,430 --> 00:01:48,540
+معنى معادلة تفاضلية ما معنى معادلة تفاضلية عاديةما
+
+15
+00:01:48,540 --> 00:01:52,760
+معنى رتبة المعادلة التفاضلية طبعا احنا لدرجة في
+
+16
+00:01:52,760 --> 00:01:58,300
+دماغنا قبل ذلك درجة المعادلة هذه درجة المعادلة
+
+17
+00:01:58,300 --> 00:02:01,820
+العادية من الدرجة التانية التالتة لأ احنا فيه
+
+18
+00:02:01,820 --> 00:02:06,880
+عندنا هنا رتبة المعادلة التفاضلية والرتبة تعتمد
+
+19
+00:02:06,880 --> 00:02:11,040
+على المشتقة الأولى والمشتقة التانية والمشتقة
+
+20
+00:02:11,040 --> 00:02:16,570
+التالتة او الرابعة او النونيةالتي تظهر في المعادلة
+
+21
+00:02:16,570 --> 00:02:21,830
+التفاضلية يبقى هذا مثلا ما نسميه برتبة المعادلة
+
+22
+00:02:21,830 --> 00:02:28,910
+التفاضلية وهذا ما سنعرفه بعد قليل هنعرف كمان ما هو
+
+23
+00:02:28,910 --> 00:02:34,150
+solution للمعادلة التفاضلية ما هو حل المعادلة
+
+24
+00:02:34,150 --> 00:02:42,110
+التفاضلية ما هو الحل العام للمعادلة التفاضليةما هي
+
+25
+00:02:42,110 --> 00:02:47,750
+ال initial value problems يعني معادلة تفاضلية و
+
+26
+00:02:47,750 --> 00:02:52,310
+عليها شروط بنسميها الشروط الابتدائية او ال initial
+
+27
+00:02:52,310 --> 00:02:57,530
+conditions فإن وجدت معادلة تفاضلية بشروط عليها
+
+28
+00:02:57,530 --> 00:03:02,480
+بنسميها initial value problemsأما عن أنواع
+
+29
+00:03:02,480 --> 00:03:07,280
+المعادلات فهذا ما سنتعرض له في ال chapters بعد ذلك
+
+30
+00:03:07,280 --> 00:03:10,640
+يعني بديش أقوله في ال introduction و أروح أعيده
+
+31
+00:03:10,640 --> 00:03:15,700
+مرة ثانية لأ بنخليه كل واحد في موقعه بنعرف شو يعني
+
+32
+00:03:15,700 --> 00:03:19,660
+linear differential equation ما هي non-linear
+
+33
+00:03:19,660 --> 00:03:23,120
+differential equationsأنواع ال linear differential
+
+34
+00:03:23,120 --> 00:03:27,600
+equations إلى آخرى يبقى هذا مثلا اتعرض له في حينه
+
+35
+00:03:27,600 --> 00:03:31,920
+يبقى زي ما تشوفين في ال introduction مكتوب عندكم
+
+36
+00:03:31,920 --> 00:03:35,280
+في الكتابة على شكل three sections احنا ال three
+
+37
+00:03:35,280 --> 00:03:39,220
+sections يمكن نجمعهم لك بس في صفحتين لأن هذي
+
+38
+00:03:39,220 --> 00:03:44,000
+مقدمات بس بدنا الطالب يعرفها حتى نقدر نشتغل في من؟
+
+39
+00:03:44,000 --> 00:03:47,780
+في ال sections اللي بعديها ان شاء الله تبارك
+
+40
+00:03:47,780 --> 00:03:58,440
+وتعالىبنجي بعد هيك ل chapter 2 اللي
+
+41
+00:03:58,440 --> 00:04:07,980
+هو first order differential equations
+
+42
+00:04:11,130 --> 00:04:14,710
+كلمة differential خلال المساق هذا كله يجب ان
+
+43
+00:04:14,710 --> 00:04:22,950
+اختصرها الى DIFF Equations هختصرها الى EQNS يبقى
+
+44
+00:04:22,950 --> 00:04:27,090
+هذه اختصار كلمة differential equations
+
+45
+00:04:29,310 --> 00:04:34,070
+الـ first order يعني المعادلة التفاضلية من الرتبة
+
+46
+00:04:34,070 --> 00:04:40,050
+الأولى هذه هندرس فيها مجموعة من المعادلات اللي
+
+47
+00:04:40,050 --> 00:04:43,610
+كلهم من الرتبة الأولى حاجة اسمها ال linear
+
+48
+00:04:43,610 --> 00:04:49,120
+differential equationsالمعادلة التفاضلية الخطية
+
+49
+00:04:49,120 --> 00:04:54,120
+حاجة اسمها separable equations يعني المعادلات اللى
+
+50
+00:04:54,120 --> 00:04:59,200
+فيها بدنا نفصل المتغيرات ال exact equations
+
+51
+00:04:59,200 --> 00:05:02,700
+المعادلات التامة ال homogeneous equations
+
+52
+00:05:02,700 --> 00:05:08,340
+المعادلات المتجانسة يبقى خلال هذا ال chapter بدنا
+
+53
+00:05:08,340 --> 00:05:17,970
+ندرس ما يأتي ال linear equationsالمعادلات الخطية
+
+54
+00:05:17,970 --> 00:05:24,350
+separable equations
+
+55
+00:05:24,350 --> 00:05:29,030
+separable
+
+56
+00:05:29,030 --> 00:05:33,650
+جاء من كلمة separate منفصل يبقى separable
+
+57
+00:05:33,650 --> 00:05:38,730
+equations هي المعادلات اللي نقدر نفصل فيها متغيرات
+
+58
+00:05:38,730 --> 00:05:42,930
+في شجةوالمتغير الآخر في الشجرة التانية يعني بيكون
+
+59
+00:05:42,930 --> 00:05:48,890
+فيها متغيرين بنفس أحدهم في ناحية والمتغير الآخر في
+
+60
+00:05:48,890 --> 00:05:53,110
+ناحية أخرى يبقى هذا اللي بنسميها separable
+
+61
+00:05:53,110 --> 00:06:00,130
+equations فينا حاجة اسمها ال exact equations
+
+62
+00:06:00,130 --> 00:06:08,510
+and integrating factors
+
+63
+00:06:14,930 --> 00:06:19,410
+exact equations يعني المعادلات التامة integrating
+
+64
+00:06:19,410 --> 00:06:25,750
+factors عوامل التكامل يعني المعادلة قد تكون exact
+
+65
+00:06:25,750 --> 00:06:31,730
+ويمكن ان نحتاج مقال نيجي نحسبها مالجهاش exact نضرب
+
+66
+00:06:31,730 --> 00:06:37,230
+في دالة ما هذه الدالة بتحولها الى exact equation
+
+67
+00:06:37,230 --> 00:06:43,490
+هذه الدالة بنسميها اش اللي هو عامل التكامل من لهذه
+
+68
+00:06:43,490 --> 00:06:48,090
+المعادلةكيف عمل التكمل هذا بدنا نحصل عليه هذا ما
+
+69
+00:06:48,090 --> 00:06:53,790
+سنشير إليه في حينه ان شاء الله تبارك وتعالى يبقى
+
+70
+00:06:53,790 --> 00:06:57,410
+النوع الثالث هو ال exact equations and integrating
+
+71
+00:06:57,410 --> 00:07:03,230
+factors عندنا كمان حاجة اسمة ال homogeneous
+
+72
+00:07:03,230 --> 00:07:11,630
+different equations المعادلات المتجانسة
+
+73
+00:07:13,800 --> 00:07:19,320
+يبقى هذه الأربعة أنواع من المعادلات التي سنتدرسها
+
+74
+00:07:19,320 --> 00:07:24,540
+في الشابتر الثاني و ال first order differential
+
+75
+00:07:24,540 --> 00:07:29,140
+equation في حد قابلنا يا بنات معادلات ليست على أي
+
+76
+00:07:29,140 --> 00:07:35,240
+نوع من الأربعة الأربعة يعني ليست linear ليست
+
+77
+00:07:35,240 --> 00:07:41,380
+separable ليست exact ليست homogeneous لكن يمكن
+
+78
+00:07:41,820 --> 00:07:48,220
+تحويل هذه المعادلة بطريقة ما إلى أي نوع من الأنواع
+
+79
+00:07:48,220 --> 00:07:52,960
+الأربعة فمثلا في حالة ال linear equations باجي على
+
+80
+00:07:52,960 --> 00:07:57,700
+المعادلة بلاقيها ماهياش linear لكن لو عملت شغل هيك
+
+81
+00:07:57,700 --> 00:08:03,180
+تتحول إلى linear وهذه الشغلة بنسميها حد من الذكراه
+
+82
+00:08:03,180 --> 00:08:08,920
+يا شبنات اللي درسوا قبل ذلك طب احنا بنسميها Bernol
+
+83
+00:08:08,920 --> 00:08:14,470
+equationمعادلة بيرنولي يمكن تحويلها إلى معادلة
+
+84
+00:08:14,470 --> 00:08:18,450
+خطية إلى linear differential equation separable
+
+85
+00:08:18,450 --> 00:08:22,350
+equation يمكن معادلة ما تلاقيهاش separable لكن
+
+86
+00:08:22,350 --> 00:08:27,730
+بتعويضها ما بسيطة يمكن تحويلها إلى separable
+
+87
+00:08:27,730 --> 00:08:32,390
+equation ال exact equation يمكن ما تجباش exact لكن
+
+88
+00:08:32,390 --> 00:08:38,460
+نضربها في عامل التكمل يحويلها إلى مين؟المعادلة
+
+89
+00:08:38,460 --> 00:08:50,440
+الهوموجينية هي المعادلة
+
+90
+00:08:50,440 --> 00:08:56,270
+التي لا تظهر هموجينياوبالتالي الـ homogeneous
+
+91
+00:08:56,270 --> 00:09:00,750
+differential ممكن بعملية ما تبقاش homogeneous لكن
+
+92
+00:09:00,750 --> 00:09:04,350
+نحولها إلى مين؟ إلى homogeneous differential
+
+93
+00:09:04,350 --> 00:09:09,250
+equations هنشوف كيف هنحل المعادلة ده المعادلات هذه
+
+94
+00:09:09,250 --> 00:09:13,350
+لما قلتلك first order يعني لا تظهر في المعادلة إلا
+
+95
+00:09:13,350 --> 00:09:19,000
+المشتقة الأولىيبقى لو كملتها بحصل على حل المعادلة
+
+96
+00:09:19,000 --> 00:09:24,960
+تكامل عادي جدا يعني كل سؤال من مسائل المعادلة تادي
+
+97
+00:09:24,960 --> 00:09:31,200
+بده تكامل ومن هنا قلتك المادة تحتاج أساسا لمين
+
+98
+00:09:31,200 --> 00:09:37,940
+لتكامل بتجي ما عدا عند ال exact equations هذه في
+
+99
+00:09:37,940 --> 00:09:41,260
+حاجة أخدناها في calculus C طبعا بعضكم ماخدتش
+
+100
+00:09:41,260 --> 00:09:45,880
+calculus C مظبوط؟فيه مقداش العدد اشوف ارفعى ده
+
+101
+00:09:45,880 --> 00:09:51,140
+مقداش كال كلصى يعني الرابع ماعناهاش مشكلة اللي
+
+102
+00:09:51,140 --> 00:09:55,780
+مااخدناهوش بكال كلصى هاطولك خلال خمس دقائق يعني
+
+103
+00:09:55,780 --> 00:09:59,320
+اللي اخدت كال كلصى و اللي مااخدت بصيره سيان خمس
+
+104
+00:09:59,320 --> 00:10:04,000
+دقائق بس بفهمك الشيء اللي مطلوب من كال كلصى هو
+
+105
+00:10:04,000 --> 00:10:09,070
+الاشتقاق الجزءىpartial differentiation اللي هو
+
+106
+00:10:09,070 --> 00:10:13,750
+التفاضل الجزء ايه باعطيكيها في خمس دقائق و بتالي
+
+107
+00:10:13,750 --> 00:10:17,590
+ماعناش إشكالية أما يقولوا كده ماخدتيش C بتقدريش
+
+108
+00:10:17,590 --> 00:10:22,690
+تاخده معاكش؟ لأ بتقدري تاخدي و بدون أي مشكلة مافي
+
+109
+00:10:22,690 --> 00:10:27,670
+مشكلة في هذه العالمغير هيك مش هيلزمنا الاشتقاق
+
+110
+00:10:27,670 --> 00:10:31,750
+الجزئي طيلي دراستنا بس بلزمنا في ال section هذا
+
+111
+00:10:31,750 --> 00:10:36,470
+اللي هو ال exact equations and integrating factors
+
+112
+00:10:36,470 --> 00:10:43,670
+فقط لا غير يبقى هذا كل ما سيدرس في main في ال
+
+113
+00:10:43,670 --> 00:10:48,670
+first order linear differential equations بنجي ل
+
+114
+00:10:48,670 --> 00:10:57,810
+charter تلاتة اللي هو secondorder differential
+
+115
+00:10:57,810 --> 00:11:04,510
+equations المعادلة
+
+116
+00:11:04,510 --> 00:11:11,010
+التفاضلية من الرتبة الثانية يعني هيظهر عندنافزي ما
+
+117
+00:11:11,010 --> 00:11:14,310
+ظهر في ال chapter الماضي المشتقة الأولى هيظهر هنا
+
+118
+00:11:14,310 --> 00:11:18,210
+عندنا مين؟ المشتقة الثانية والأولى، بيصيروا
+
+119
+00:11:18,210 --> 00:11:22,610
+التنتين مالهم بيظهروا في المثال وربما ماتظهرش الا
+
+120
+00:11:22,610 --> 00:11:26,690
+المشتقة الثانية فقط، على أي حال الأولى أو الثانية
+
+121
+00:11:26,690 --> 00:11:30,770
+معناها، المشكلة احنا بناخد ال general formالشكل
+
+122
+00:11:30,770 --> 00:11:35,830
+العام وبالتالي الباقي بيكون شيء تخصيصي من الشيء
+
+123
+00:11:35,830 --> 00:11:40,130
+العام يبقى second order differential equations
+
+124
+00:11:40,130 --> 00:11:44,970
+هنجسم المعادلة إلى جزئين المعادلة التفاضلية من
+
+125
+00:11:44,970 --> 00:11:45,950
+الرتبة الثانية
+
+126
+00:11:50,420 --> 00:11:57,300
+المعادلة التفاضلية هي المعادلة
+
+127
+00:11:57,300 --> 00:12:00,820
+التفاضلية هي المعادلة التفاضلية هي المعادلة
+
+128
+00:12:00,820 --> 00:12:02,680
+التفاضلية هي المعادلة التفاضلية هي المعادلة
+
+129
+00:12:02,680 --> 00:12:04,100
+التفاضلية هي المعادلة التفاضلية هي المعادلة
+
+130
+00:12:04,100 --> 00:12:04,220
+التفاضلية هي المعادلة التفاضلية هي المعادلة
+
+131
+00:12:04,220 --> 00:12:05,340
+التفاضلية هي المعادلة التفاضلية هي المعادلة
+
+132
+00:12:05,340 --> 00:12:07,600
+التفاضلية هي المعادلة التفاضلية هي المعادلة
+
+133
+00:12:07,600 --> 00:12:09,650
+التفاضلية هي المعادلةهذه بنسميها homogeneous
+
+134
+00:12:09,650 --> 00:12:13,250
+differential equation الـ non homogeneous
+
+135
+00:12:13,250 --> 00:12:15,970
+differential equation المعادلة بالكتابة الكاملة و
+
+136
+00:12:15,970 --> 00:12:20,990
+الطرف اليمين بيكونش zero بيكون function تاني يبقى
+
+137
+00:12:20,990 --> 00:12:24,950
+هذا ال non homogeneous differential equation يبقى
+
+138
+00:12:24,950 --> 00:12:32,150
+هنبدأ أول شغلة بمين؟ بال homogeneous differential
+
+139
+00:12:32,150 --> 00:12:37,370
+equation كويس
+
+140
+00:12:40,180 --> 00:12:43,500
+طبعا ال homogenous differential equation بتكون من
+
+141
+00:12:43,500 --> 00:12:50,360
+الرتبة الثانية الرتبة الثانية أي معادلة من الرتبة
+
+142
+00:12:50,360 --> 00:12:58,100
+الثانية هنفترض إليها حل ما حل معين الحل المعين هذا
+
+143
+00:12:58,100 --> 00:13:03,030
+بده يقودنا إلى معادلة من الدرجة الثانيةمعادلة
+
+144
+00:13:03,030 --> 00:13:06,030
+عادية زي بقى التانية عدادية زي طبعة الصف التامن
+
+145
+00:13:06,030 --> 00:13:10,950
+والتاسع من الدرجة الثانية بنروح نحل المعادلة اللي
+
+146
+00:13:10,950 --> 00:13:15,230
+عندنا هذه معادلة من الدرجة الثانية ممكن نحلها
+
+147
+00:13:15,230 --> 00:13:21,870
+بالتحليل او بالجذر القانون اللي هو ناقص با زاد او
+
+148
+00:13:21,870 --> 00:13:24,890
+ناقص الجذر التربية اللي با التربية ناقص اربعة الف
+
+149
+00:13:24,890 --> 00:13:29,310
+جيمة على اتنين الف بهذه او هذه بنحل معادلة الدرجة
+
+150
+00:13:29,310 --> 00:13:32,870
+الثانيةما دام مؤادرة من طريق التاني يبقى إليها
+
+151
+00:13:32,870 --> 00:13:37,890
+حالين الحالين هدول يا بنات ممكن يكونوا اتنين are
+
+152
+00:13:37,890 --> 00:13:44,270
+real and different تمام؟ يبقى real and different
+
+153
+00:13:44,270 --> 00:13:49,370
+يعني حالين حقيقين ومختلفين ولا واحد زي التاني
+
+154
+00:13:49,370 --> 00:13:57,230
+تمام؟ ممكن يكون الحالين حقيقين ومكرتنين زي بعضحلان
+
+155
+00:13:57,230 --> 00:14:02,790
+ممطبقان اتنين زي بعض تماما الحالة التالتة ممكن
+
+156
+00:14:02,790 --> 00:14:07,330
+اتنين يكونوا are complex conjugate يعني حلين
+
+157
+00:14:07,330 --> 00:14:15,010
+كميتين مركبتين او كميتين تخيليتين و اتنين مترافقة
+
+158
+00:14:15,010 --> 00:14:20,950
+conjugate يعني مترافقةيبقى هانيجي لحاجة اسمة
+
+159
+00:14:20,950 --> 00:14:27,070
+المعادلة المميزة للمعادلة التفاضلية يبقى هذه
+
+160
+00:14:27,070 --> 00:14:30,810
+بنسميها ال characteristic equation ال
+
+161
+00:14:30,810 --> 00:14:42,150
+characteristic equation
+
+162
+00:14:42,150 --> 00:14:47,510
+هي معادلة من الدرجة الثانيةمش من الرثب يعني انتقل
+
+163
+00:14:47,510 --> 00:14:53,180
+من الرثب الى مين الى درجة نتيجةللحل اللي فرضناه
+
+164
+00:14:53,180 --> 00:14:57,600
+لمين؟ للمعادلة التفاضية طب الحل بيكون على شكل
+
+165
+00:14:57,600 --> 00:15:03,440
+exponential function يعني كيف ال homogeneous هذه؟
+
+166
+00:15:03,440 --> 00:15:09,040
+يعني زي ما نقول y double prime زائد p of t في ال y
+
+167
+00:15:09,040 --> 00:15:15,020
+prime زائد ل q of t في ال y بده يساوي zero الطرف
+
+168
+00:15:15,020 --> 00:15:18,280
+اليمين بيكون يساوي zero هذه هي ال homogeneous
+
+169
+00:15:18,280 --> 00:15:25,840
+differential equationالمعادلة على الشكل هذا لو كان
+
+170
+00:15:25,840 --> 00:15:34,660
+كل من Pt و Q of T constant ثابت يبقى الحل اللي
+
+171
+00:15:34,660 --> 00:15:41,100
+عندنا هنا بيكون على الشكل Y تساوي E أُس RT
+
+172
+00:15:41,100 --> 00:15:46,000
+exponential function أصلا ال exponential اللي
+
+173
+00:15:46,000 --> 00:15:50,490
+بنعرف ان الفضل ههبط و لا لأطبعاً R هو مقدار عددي
+
+174
+00:15:50,490 --> 00:15:54,650
+اتنين تلاتة اربعة نص تلاتة اربعة جد ما يكون و T هو
+
+175
+00:15:54,650 --> 00:15:58,530
+ال parameter أو المتغير ال variable يبقى اظن لو
+
+176
+00:15:58,530 --> 00:16:04,230
+بدنا نشتق الاشتقاق الاول بيصير ايش؟ R في US RT لو
+
+177
+00:16:04,230 --> 00:16:10,540
+نشتقها كمان مرة بيصير R تربية US RT تمام؟وبالتالي
+
+178
+00:16:10,540 --> 00:16:16,640
+المعادلة هذا نتيجة لهذا الحل بتتحول إلى معادلة من
+
+179
+00:16:16,640 --> 00:16:26,320
+الدرجة الثانية على الصيغة R تربية زائد A R زائد B
+
+180
+00:16:26,320 --> 00:16:32,080
+تساوي Zero يبقى هذه معادلة عادية من الدرجة الثانية
+
+181
+00:16:32,080 --> 00:16:39,690
+هذه لما نيجي نحلها سيظهر عندي أحد ثلاثة أموراللي
+
+182
+00:16:39,690 --> 00:16:51,250
+همين real and different roots يبقى
+
+183
+00:16:51,250 --> 00:17:00,690
+جذور حقيقية ومختلفة الأمر الثاني real and equal
+
+184
+00:17:00,690 --> 00:17:04,850
+roots الأمر
+
+185
+00:17:04,850 --> 00:17:06,890
+الثالث complex
+
+186
+00:17:10,110 --> 00:17:16,170
+conjugate roots يبقى
+
+187
+00:17:16,170 --> 00:17:21,870
+هذه الاحتمالات الثلاثة والتي لا رابع عليها يبقى
+
+188
+00:17:21,870 --> 00:17:28,290
+المعادلة هذه لما نقاش أحلها بيطلع عندنا أحد الأمور
+
+189
+00:17:28,290 --> 00:17:33,330
+التلاتة هذا يا بنات حلناها في الصف التامن والتاسع
+
+190
+00:17:33,330 --> 00:17:36,990
+بقينا حل عاديهذه المعادلة بدأت تقول إنها ليست لدي
+
+191
+00:17:36,990 --> 00:17:41,950
+حل لأنها ليست موجودة في الزمان لكن لما درسنا
+
+192
+00:17:41,950 --> 00:17:46,270
+الكميات التخيولية أو ال complex numbers الأعداد
+
+193
+00:17:46,270 --> 00:17:51,710
+المركبة صارنا بنقدر نحلها وبالتالي بصير عندنا ثلاث
+
+194
+00:17:51,710 --> 00:17:56,070
+حالات زي ما انتوا شايفينها في كل حالة من الحالات
+
+195
+00:17:56,070 --> 00:18:01,390
+الثلاث بصير المعادلة التفاضلية هذه لها صورة معينة
+
+196
+00:18:01,390 --> 00:18:06,270
+لميمللحل يبقى بنعرف صورة الحل في الحالة الأولى
+
+197
+00:18:06,270 --> 00:18:09,830
+صورة الحل في الحالة التانية صورة الحل في الحالة
+
+198
+00:18:09,830 --> 00:18:13,890
+الثالثة ثالثة وبالتالي عرفنا حل ال homogeneous
+
+199
+00:18:13,890 --> 00:18:20,270
+differential equations تمام هذا قلنا لو كانت
+
+200
+00:18:20,270 --> 00:18:27,650
+constants تمام طب لو ماكانوش constantsلو هذا حصل
+
+201
+00:18:27,650 --> 00:18:33,190
+انه مش constants والحلول كانت real and equal
+
+202
+00:18:33,190 --> 00:18:39,290
+repeated roots بنسميها الحلول المكررة بند real and
+
+203
+00:18:39,290 --> 00:18:45,050
+equal بنختصرها بعض الكتب إلى repeated roots
+
+204
+00:18:45,050 --> 00:18:53,070
+repeated أو real and equal سيان هذه الكلمة بدأ
+
+205
+00:18:53,070 --> 00:18:58,980
+real and equal كويس؟نفترض أنها كانت معين للحلول
+
+206
+00:18:58,980 --> 00:19:02,380
+repeated ذاك المعادلة على الشكل اللي فوق، هذول ما
+
+207
+00:19:02,380 --> 00:19:07,940
+هو مشكله الصندوق عادي، في أن طريقة للحل اسمها
+
+208
+00:19:07,940 --> 00:19:15,120
+طريقة reduction of orders، يبقى في أن حاجة اسمها
+
+209
+00:19:15,120 --> 00:19:20,640
+طريقة reduction of
+
+210
+00:19:20,640 --> 00:19:22,200
+orders
+
+211
+00:19:30,360 --> 00:19:36,200
+طريقة اختزال الرتبة بطريقة ما بنحط عوضة معينة
+
+212
+00:19:36,200 --> 00:19:40,720
+بننزل رتبة المعادلة من الدرجة الثانية إلى الدرجة
+
+213
+00:19:40,720 --> 00:19:45,400
+الأولى بنحل المعادلة حصلت تظهر عندنا المشتق الأولى
+
+214
+00:19:45,400 --> 00:19:49,500
+كمان مرة بنروح بنكابل كمان مرة وبالتالي بنجيب من
+
+215
+00:19:49,500 --> 00:19:54,920
+الحل يبقى ظهرت عندنا طريقة reduction of earnings
+
+216
+00:19:54,920 --> 00:19:59,960
+لمنللمعادلات اللي العوامل عندهم هذه ما هي استوابط
+
+217
+00:19:59,960 --> 00:20:04,960
+وانما متغيرات بعد هيك بروح لل homogeneous
+
+218
+00:20:04,960 --> 00:20:08,460
+differential equations بدينا بال homogeneous
+
+219
+00:20:08,460 --> 00:20:12,240
+differential equations ابنجي لمين ل non
+
+220
+00:20:12,240 --> 00:20:21,040
+homogeneous non homogeneous differential equations
+
+221
+00:20:21,040 --> 00:20:25,960
+لازلنا داخل ال section أو ال chapter رقم تلاتةفيها
+
+222
+00:20:25,960 --> 00:20:30,880
+نبنات طريقة تاني للحل الطريقة الأولى بسميها ال
+
+223
+00:20:30,880 --> 00:20:35,000
+undetermined coefficients و الطريقة التانية بسميها
+
+224
+00:20:35,000 --> 00:20:41,420
+ال variation of parameters يبقى الطريقة الأولى في
+
+225
+00:20:41,420 --> 00:20:47,700
+هذه الحالة اسمها طريقة ال undetermined
+
+226
+00:20:47,700 --> 00:20:51,180
+coefficients
+
+227
+00:20:56,330 --> 00:21:03,170
+والطريقة الثانية اسمها طريقة ال variation of
+
+228
+00:21:03,170 --> 00:21:19,330
+parameters يبقى
+
+229
+00:21:19,330 --> 00:21:23,850
+نرجع مرة تانية نذكر
+
+230
+00:21:23,850 --> 00:21:28,050
+تذكرةالمعادلة الـ second order سأقسمها إلى قسمين
+
+231
+00:21:28,050 --> 00:21:32,790
+القسم الأول هو الـ homogeneous و القسم التاني هو
+
+232
+00:21:32,790 --> 00:21:36,430
+الـ non homogeneous differential equation في حالة
+
+233
+00:21:36,430 --> 00:21:40,150
+الـ homogeneous differential equation إذا كانت
+
+234
+00:21:40,150 --> 00:21:44,950
+المعاملات هذه ثوابت سأفترض الحل على صيغة Y تساوي
+
+235
+00:21:44,950 --> 00:21:51,730
+EOSRT نتيجة لذلك ستظهر معادلة بالشكل اللي عندنا
+
+236
+00:21:51,730 --> 00:21:56,360
+هذا معادلة من الدرجة التانيةبضعوها حلها بيطلع عندي
+
+237
+00:21:56,360 --> 00:22:01,960
+تلات حالات اللي هو real and different roots, real
+
+238
+00:22:01,960 --> 00:22:06,300
+repeated roots اللي هو complex conjugate roots
+
+239
+00:22:06,300 --> 00:22:11,240
+يبقى طالع جذور المعادلة هذه واحد من الأمور التلاتة
+
+240
+00:22:11,240 --> 00:22:16,700
+نتيجة لذلك بيصير حل المعادلة لأن التفاضلية على شكل
+
+241
+00:22:16,700 --> 00:22:21,280
+ما كل واحدة من التلاتة لها شكل بيختلف عن الشكل
+
+242
+00:22:21,280 --> 00:22:27,050
+الآخرسنعرف اللي هي اشكال في حينه ان شاء الله تبارك
+
+243
+00:22:27,050 --> 00:22:33,950
+وتعالى بعد هيك جينا من ال repeated roots هذه و لو
+
+244
+00:22:33,950 --> 00:22:40,090
+كان المعاملات هدول ليست ثوابت و انما دوال في T
+
+245
+00:22:40,090 --> 00:22:45,190
+sine T cosine T T تربية T نقص واحد T تربية زائد
+
+246
+00:22:45,190 --> 00:22:49,510
+اتنين T زائد تلاتة الاخرين يعني اي function من ال
+
+247
+00:22:49,510 --> 00:22:53,830
+functions اللي مرت علينايبقى في هذه الحالة أول
+
+248
+00:22:53,830 --> 00:22:59,750
+طريقة طريقة reduction of orders ننتقل الآن لل non
+
+249
+00:22:59,750 --> 00:23:03,230
+homogeneous differential equations إذا ولّا
+
+250
+00:23:03,230 --> 00:23:07,750
+المعادلات ثوابت بستخدم طريقة ال undetermined
+
+251
+00:23:07,750 --> 00:23:13,770
+coefficients طريقة المعاملات المجهولة إذا ولّا
+
+252
+00:23:13,770 --> 00:23:20,170
+المعاملات هدول متغيراتلك الخيار بين ان تستخدم ال
+
+253
+00:23:20,170 --> 00:23:23,670
+undetermined coefficients او نستخدم طريقة ال
+
+254
+00:23:23,670 --> 00:23:28,950
+variation of parameters طبعا فرق شاسة بينه طريقتين
+
+255
+00:23:28,950 --> 00:23:34,630
+طريقة الاولى تعتمد على امرين ان المعاملات ثوابت
+
+256
+00:23:34,630 --> 00:23:38,990
+والدالة هذه ليست صفر وانما بتكون على شكل معين
+
+257
+00:23:38,990 --> 00:23:43,450
+polynomial polynomial في exponential polynomial في
+
+258
+00:23:43,450 --> 00:23:47,850
+exponential في دالة متلاتية signأو كوصين أو
+
+259
+00:23:47,850 --> 00:23:52,330
+مجموعهما أو الفرق فيما بينهم طريقة ال variation of
+
+260
+00:23:52,330 --> 00:23:56,150
+parameters بهمهاش هدول ثوابت والله مش ثوابت ثوابت
+
+261
+00:23:56,150 --> 00:24:00,990
+ماشي الحال مش ثوابت ماشي الحال ماعندها مشكلة اتنين
+
+262
+00:24:00,990 --> 00:24:05,010
+الدالة لاعلمين ايش مايكون شكل هيكون ماعندهاش مشكلة
+
+263
+00:24:05,010 --> 00:24:09,410
+كذلك يبقى هذه الطرق المختلفة لحل المعادلة
+
+264
+00:24:09,410 --> 00:24:14,870
+التفاضلية تلاتةreduction of order, entertainment
+
+265
+00:24:14,870 --> 00:24:19,990
+coefficients, variation of parameters يبقى هذه هي
+
+266
+00:24:19,990 --> 00:24:24,310
+الطرق الثلاث لحل المعادلة التفاضلية اللي احنا
+
+267
+00:24:24,310 --> 00:24:28,770
+درسها في chapter 3 ابناجي ل chapter 4
+
+268
+00:24:45,440 --> 00:24:50,780
+شبتر اربع يا بنات بدنا نعمم شبتر تلاتة يعني شبتر
+
+269
+00:24:50,780 --> 00:24:55,950
+اربع هو تعميم لشبتر تلاتة ليه؟بناخد المعادلة من
+
+270
+00:24:55,950 --> 00:24:59,010
+الرتبة التالتة من الرتبة الرابعة من الخمسة من
+
+271
+00:24:59,010 --> 00:25:04,190
+الرتبة النونية in general يبقى هذه اسمها higher
+
+272
+00:25:04,190 --> 00:25:08,490
+order differential equations المعادلة التفاضلية من
+
+273
+00:25:08,490 --> 00:25:13,910
+الرتب العليا يعني اكتر من اتنين اربعة فما فوق
+
+274
+00:25:13,910 --> 00:25:23,150
+فشبتر اربعة شبتر اربعة اسمه higher order
+
+275
+00:25:27,510 --> 00:25:32,910
+order differential equations
+
+276
+00:25:32,910 --> 00:25:35,970
+هذا
+
+277
+00:25:35,970 --> 00:25:40,950
+لن نأتي فيه بجديد نفس التكتيك اللى اتبع في شبطر 3
+
+278
+00:25:40,950 --> 00:25:46,830
+هنتبعه مين في شبطر 4 يبقى هنقسمه الى homogeneous
+
+279
+00:26:01,710 --> 00:26:06,450
+نفس هذا الـ characteristic equation اللي على الشكل
+
+280
+00:26:06,450 --> 00:26:10,170
+اللي عندنا هدا هدا هيك هتصير معادلة بس بيصير من
+
+281
+00:26:10,170 --> 00:26:17,950
+الرتبة النونية تماميبقى هذه هناخد بالها برضه ال
+
+282
+00:26:17,950 --> 00:26:24,690
+characteristic equation ونروح نحللها ونشوف ما هو
+
+283
+00:26:24,690 --> 00:26:29,690
+شكل الجذور في الحالات المختلفة بنيجي لل non
+
+284
+00:26:29,690 --> 00:26:34,230
+homogeneous هنستخدم لها نفس الكلام اللي استخدمنا
+
+285
+00:26:34,230 --> 00:26:39,210
+هنا اللي هو ال undetermined
+
+286
+00:26:39,210 --> 00:26:41,050
+coefficients
+
+287
+00:26:44,270 --> 00:26:51,370
+undetermined coefficients و الطريقة الثانية التي
+
+288
+00:26:51,370 --> 00:27:06,370
+هي variation of parameters يبقى
+
+289
+00:27:06,370 --> 00:27:11,790
+هذا مين لل higher order لهمين المل شبط الرقم أربعة
+
+290
+00:27:12,060 --> 00:27:18,200
+يبقى شبط الرقم اربع هو تعميم لشبط الرقم تلاتة مافي
+
+291
+00:27:18,200 --> 00:27:22,860
+معلومة ان نفس الفكر تبعت اللي هو شبط الرقم تلاتة
+
+292
+00:27:22,860 --> 00:27:27,870
+بس اه بنعملبدل ما تحلي هنا معادلة من الدرجة
+
+293
+00:27:27,870 --> 00:27:31,170
+الثانية بصير تحلي معادلة من الدرجة التالتة او
+
+294
+00:27:31,170 --> 00:27:34,930
+الدرجة الرابعة او الدرجة الخامسة او السادسة او ما
+
+295
+00:27:34,930 --> 00:27:40,570
+إلى ذلك هذا و من هنا صار تعميم لهذه الحالة هيطلع
+
+296
+00:27:40,570 --> 00:27:43,850
+نفس الطرق الثلاثة اللي هي reduction of order او
+
+297
+00:27:43,850 --> 00:27:46,610
+variation of parameters او undetermined
+
+298
+00:27:46,610 --> 00:27:48,570
+coefficients نفس الطرق
+
+299
+00:27:51,210 --> 00:27:54,230
+يبقى هذا اللى هنشوفه ان شاء الله و تبارك و تعالى
+
+300
+00:27:54,230 --> 00:28:06,210
+في شبتر 4 ابنجي لشبتر 5 شبتر
+
+301
+00:28:06,210 --> 00:28:14,490
+5 ابنجي لحاجة اسمها series solution of
+
+302
+00:28:14,490 --> 00:28:19,770
+the second order
+
+303
+00:28:22,640 --> 00:28:29,060
+differential equations اول
+
+304
+00:28:29,060 --> 00:28:34,300
+section في هذا ال chapter بيذكرك بمين بالمتسلسلات
+
+305
+00:28:34,300 --> 00:28:40,580
+ال power series ,tyler series, mclaren seriesو ال
+
+306
+00:28:40,580 --> 00:28:45,180
+convergence تبعهم يبقى أول section كأنه calculus B
+
+307
+00:28:45,180 --> 00:28:49,600
+جزء من calculus B مش كتير يعني بعض المعلومات
+
+308
+00:28:49,600 --> 00:28:54,660
+البسيطة التي تستخدم بعد ذلك مش لسه بدنا نروح كيف
+
+309
+00:28:54,660 --> 00:28:59,080
+نجيب ال Tylor أو ال macron series لدالة تمام عند
+
+310
+00:28:59,080 --> 00:29:03,270
+نقطة تماملأ لأ لأ لأ هذا كلام انتهى خطيب ال
+
+311
+00:29:03,270 --> 00:29:09,190
+calculus بيهم للتذكير بهذه المفاهيم لأن بعضها
+
+312
+00:29:09,190 --> 00:29:14,650
+سيلزم في ال sections القادمة بهمنا كيف نحل
+
+313
+00:29:14,650 --> 00:29:20,290
+المعادلة من الرتبة الثانية باستخدام المتسلسلات
+
+314
+00:29:23,380 --> 00:29:27,780
+بس مش هنعتمد على ال series كتير يعني مش تفهموا انه
+
+315
+00:29:27,780 --> 00:29:30,800
+بدنا نبدأ chapter ال series اللي هو من أول لأخر
+
+316
+00:29:30,800 --> 00:29:35,480
+chapter عشرة كان ولا لا؟ اه لا لا لا معلومات بسيطة
+
+317
+00:29:35,480 --> 00:29:39,380
+ثم بنشوف كيف بنحل المعادلة تانية بالاستخدام
+
+318
+00:29:39,670 --> 00:29:46,250
+المتسلسلات هذا بيشغل حوالي خمسة sections من
+
+319
+00:29:46,250 --> 00:29:51,350
+الشابتر تقريبا تمام ابنجي لآخر chapter اللي هو
+
+320
+00:29:51,350 --> 00:29:58,810
+chapter ستة chapter ستة
+
+321
+00:29:58,810 --> 00:30:03,930
+حاجة اسمها Laplace transforms
+
+322
+00:30:16,140 --> 00:30:22,860
+تحويلات Laplace تحويلات
+
+323
+00:30:22,860 --> 00:30:30,060
+Laplace بنلجأ لها أو نستخدمها لتسهيل المسائل
+
+324
+00:30:30,060 --> 00:30:35,800
+المختلفة يعني أحيانا صعب نتعامل مع دالة مباشرة
+
+325
+00:30:35,800 --> 00:30:41,700
+بنجيب دالة مكافئة لهابتحويلة المعينة أو بصير ان
+
+326
+00:30:41,700 --> 00:30:45,620
+اتعامل مع الدالة الجديدة التي تكافئ الدالة
+
+327
+00:30:45,620 --> 00:30:49,420
+المعلومة هذه الأمور بنسميها تحويلات اللي هو
+
+328
+00:30:49,420 --> 00:30:56,240
+Laplace transform يعني سنعطيها تعريف ثم نستخدم هذا
+
+329
+00:30:56,240 --> 00:31:02,620
+التعريف لإيجاد Laplace transform لدوال مختلفة ثم
+
+330
+00:31:02,620 --> 00:31:07,760
+بعد ذلك نستخدم Laplace transform لحل المعادلات
+
+331
+00:31:07,760 --> 00:31:14,070
+التفاضليةطبعا يبقى أول شغلة نعطي تعريف للابلاس
+
+332
+00:31:14,070 --> 00:31:18,610
+ترانسفورم والتعريف هذا يعتمد على الـ improper
+
+333
+00:31:18,610 --> 00:31:26,230
+integrals يعني هو تكامل من صفر لما لا نهاية ل
+
+334
+00:31:26,230 --> 00:31:31,690
+EOSST مضروب في ال function اللى بدنا نوجد لها
+
+335
+00:31:31,690 --> 00:31:36,620
+لابلاس ترانسفورم بدنا نكامل حصل الدرب هذاوانطلع
+
+336
+00:31:36,620 --> 00:31:40,980
+القيمة القيمة اللى بتطلع بيكون هو تكامل هي قيمة
+
+337
+00:31:40,980 --> 00:31:47,000
+Laplace transform للدالة المطيانة مثلا لو بدي
+
+338
+00:31:47,000 --> 00:31:55,040
+Laplace transform للدالة f of t بقول هو تكامل من
+
+339
+00:31:55,040 --> 00:32:03,990
+zero ل infinity لل E أس ناقص ST لل F of T DTيبقى
+
+340
+00:32:03,990 --> 00:32:10,650
+هذا تعريف لـ plus transform لدالة ما ل plus
+
+341
+00:32:10,650 --> 00:32:14,970
+transform لدالة f of t و integration من zero ل
+
+342
+00:32:14,970 --> 00:32:23,540
+infinity لل E أث ناقص ST لل F of T DTهتطلع دلة
+
+343
+00:32:23,540 --> 00:32:31,000
+بدلالة المتغير S وبالتالي هروح نسميها بدل plus F
+
+344
+00:32:31,000 --> 00:32:37,920
+of T هنقول capital F of S تمام؟ يبقى هتطلع
+
+345
+00:32:37,920 --> 00:32:43,900
+function في S هذه ال function تكافئ عامليا الدلال
+
+346
+00:32:43,900 --> 00:32:49,710
+الأصلي ل F of T لأن مين ما كانت تكونتمام يبقى هذا
+
+347
+00:32:49,710 --> 00:32:53,810
+تعريف لبلاس ترانسفورم ال section الأول هنجيب لبلاس
+
+348
+00:32:53,810 --> 00:33:00,390
+ترانسفورم لدوال متعددة بعدين بنعطيكوا جدول موجود
+
+349
+00:33:00,390 --> 00:33:04,310
+بالكتابة و بنجيبهلكوا في الامتحانلو شفتوا اي ورقة
+
+350
+00:33:04,310 --> 00:33:08,070
+امتحان نهائي لمادة المعالج التفاضلية بتلاقي معاها
+
+351
+00:33:08,070 --> 00:33:14,910
+جدول الجدول هذا لبلاس ترنسفورم
+
+352
+00:33:14,910 --> 00:33:23,180
+لمن لهذه الدوال كل بكل موجود معاكييبقى هذا
+
+353
+00:33:23,180 --> 00:33:26,480
+بالنسبالي ال sectional بعد هيك كيف بدنا نستخدم
+
+354
+00:33:26,480 --> 00:33:33,080
+Laplace transform لحل المعادلات المختلفة طبعا
+
+355
+00:33:33,080 --> 00:33:37,180
+سنعطي بعض نظريات اللي بتحدد Laplace transform
+
+356
+00:33:37,180 --> 00:33:41,480
+للمشتقة الأولى شو شكله Laplace transform للمشتقة
+
+357
+00:33:41,480 --> 00:33:45,780
+الثانية شو شكله Laplace transform للمشتقة النونية
+
+358
+00:33:45,780 --> 00:33:50,380
+in general شو شكله وبرضه الصيغة هذه هتكون موجودة
+
+359
+00:33:50,380 --> 00:33:56,100
+عندك وينفي الجدول ان شاء الله تبارك وتعالى يبقى
+
+360
+00:33:56,100 --> 00:34:04,980
+هذا اجمالا ما سندرسه في هذا الشبطة في هذا المساق
+
+361
+00:34:04,980 --> 00:34:11,100
+او هذا المقرر خلال هذا الفصلطيب حد بتسأل أي سؤال
+
+362
+00:34:11,100 --> 00:34:16,840
+قبل أن ندخل فيه بس ال introduction اللي هي شبه
+
+363
+00:34:16,840 --> 00:34:20,500
+المساحنة ال introduction اللي هو بتكلم بس عن
+
+364
+00:34:20,500 --> 00:34:25,480
+المقدمة المعادلات التفاضلية حد بتحب تسأل أي سؤال
+
+365
+00:34:25,480 --> 00:34:31,320
+لأن العدد شبه تكامل الآنيعني الحضور تلاتة و تلاتة
+
+366
+00:34:31,320 --> 00:34:39,100
+ستة تمانية أفماش ستاش تسعة تاش تلاتة و عشرين سبعة
+
+367
+00:34:39,100 --> 00:34:44,160
+و عشرين تلاتين اتنين و تلاتين خمسة و تلاتين تمانية
+
+368
+00:34:44,160 --> 00:34:50,440
+و تلاتين اتنين و اربعين شبه تكامل حسب التسجيل حد
+
+369
+00:34:50,440 --> 00:34:58,640
+بتسأل اي سؤال ايش طيب يبقى الآن بنبدأ في مينفي
+
+370
+00:34:58,640 --> 00:35:03,220
+المقدمة تبع المعادلات التفاضلية
+
+371
+00:36:50,930 --> 00:36:55,370
+الدالة المجهولة اسمها
+
+372
+00:36:57,730 --> 00:37:01,970
+هي تسمى كتابة مقارنة
+
+373
+00:37:20,390 --> 00:37:26,330
+يبقى an equation المعادلة contains تحتوي أو تشتمل
+
+374
+00:37:26,330 --> 00:37:31,430
+one or more derivatives يعني فيها المشتقة الأولى
+
+375
+00:37:31,430 --> 00:37:35,870
+او التانية او اكثر التالتة او الرابعة او ما إلى
+
+376
+00:37:35,870 --> 00:37:42,490
+ذلك of a non function لدالة مجهولة is called a
+
+377
+00:37:42,490 --> 00:37:47,470
+differential equation for example نعطي مثال لو روح
+
+378
+00:37:47,470 --> 00:37:56,030
+نقولنا whyبابلي prime زائد مثلا خمسة y prime زائد
+
+379
+00:37:56,030 --> 00:38:06,150
+ستة y تساوي زيرو مثلا is a differential او تساوي T
+
+380
+00:38:06,150 --> 00:38:10,970
+مثلا is a differential equation
+
+381
+00:38:20,940 --> 00:38:26,800
+يبقى مرة تانية an equation contains المعادلة اللى
+
+382
+00:38:26,800 --> 00:38:32,980
+تحتوي أو تجتمل على مشتقة أولى او اكثر مشتقة تانية
+
+383
+00:38:32,980 --> 00:38:39,060
+او تالتة او رابعة او خمسة او الاخرى لمجهول ده اللى
+
+384
+00:38:39,060 --> 00:38:43,260
+مجهول is called a differential equation طلعلي في
+
+385
+00:38:43,260 --> 00:38:47,100
+المعادلة اللى عندنا هذه هل احنا عارفين شكل ال Y
+
+386
+00:38:48,530 --> 00:38:53,310
+عارفين why تسوي ايش يعني بدلالتي؟ نعرفش يبقى why
+
+387
+00:38:53,310 --> 00:38:57,930
+دالة مجهولة احنا بدنا نبحث عليها اللي بدنا نبحث
+
+388
+00:38:57,930 --> 00:39:01,130
+ماهو الشكل ال why الشكل ال why بكون هو الصليوش
+
+389
+00:39:01,130 --> 00:39:06,040
+اللي مين للمعادلة التفاضلية اللي عندنايبقى دالة
+
+390
+00:39:06,040 --> 00:39:10,600
+مجهولة إذا ظهرت بهذا الشكل على سبيل المثال بقول
+
+391
+00:39:10,600 --> 00:39:15,140
+هذه معادلة تفاضلية يبقى المعادلة التفاضلية هي تظهر
+
+392
+00:39:15,140 --> 00:39:18,760
+المشتق الأول أو التاني أو التالت أو الرابع أو أو
+
+393
+00:39:18,760 --> 00:39:24,680
+الاخرين بنسميها معادلة تفاضلية المعادلات التفاضلية
+
+394
+00:39:24,680 --> 00:39:30,540
+نوعان النوع الأول هي معادلة تفاضلية عادية وهي
+
+395
+00:39:30,540 --> 00:39:34,100
+موضوع دراستنا خلال هذا الفصل
+
+396
+00:39:42,240 --> 00:39:46,880
+هذه المعادلة تظهر فيها المشتقات العادية اللي
+
+397
+00:39:46,880 --> 00:39:52,280
+اتعلمناها في calculus a وb لكن النوع الثاني اللي
+
+398
+00:39:52,280 --> 00:39:57,100
+هي معادلة التفاضلية الجزئية partial differential
+
+399
+00:39:57,100 --> 00:39:59,880
+equations هذه تبعت calculus E وهذه مالناش علاقة
+
+400
+00:39:59,880 --> 00:40:04,030
+فيهاتمام يبقى احنا موضوعنا موضوع ال ordinary
+
+401
+00:40:04,030 --> 00:40:09,770
+differential equations هنعطيها تعريف كذلك يبقى
+
+402
+00:40:09,770 --> 00:40:15,330
+definition اخر if
+
+403
+00:40:15,330 --> 00:40:20,670
+the differential equation if the differential
+
+404
+00:40:20,670 --> 00:40:30,470
+equation اذا كانت المعادلة التفاضلية containsتشتمل
+
+405
+00:40:30,470 --> 00:40:38,590
+only فقط ordinary derivatives
+
+406
+00:40:38,590 --> 00:40:44,990
+مشتقات عادية زي اللي اتعلمناها ordinary
+
+407
+00:40:44,990 --> 00:40:53,730
+derivatives with respect with
+
+408
+00:40:53,730 --> 00:40:56,550
+respect to a single
+
+409
+00:41:11,320 --> 00:41:23,780
+independent independent variable then
+
+410
+00:41:23,780 --> 00:41:36,370
+it isثم يقول انها
+
+411
+00:41:36,370 --> 00:41:44,510
+عادية عادية
+
+412
+00:41:44,510 --> 00:41:48,510
+عادية
+
+413
+00:41:48,510 --> 00:41:50,150
+عادية عادية عادية عادية عادية
+
+414
+00:42:04,290 --> 00:42:09,790
+كمثال على ذلك Y
+
+415
+00:42:09,790 --> 00:42:20,950
+prime زائد تلاتة Y يساوي E أساسي T و Y double
+
+416
+00:42:20,950 --> 00:42:33,700
+primeنقص y' زائد 6y يسوى 0 are ordinary
+
+417
+00:42:33,700 --> 00:42:37,920
+differential
+
+418
+00:42:37,920 --> 00:42:41,260
+equations
+
+419
+00:42:58,300 --> 00:43:03,200
+يبقى مرة ثانية بنرجع لهذا التعريف يبقى عرفنا
+
+420
+00:43:03,200 --> 00:43:06,560
+التعريف الأول هو تعريف المعادلة التفاضلية in
+
+421
+00:43:06,560 --> 00:43:11,910
+generalمعادلة التفاضولية العادية
+
+422
+00:43:38,690 --> 00:43:43,990
+أو إذا كانت الدالة في متغيرين أو في تلاتة بيصير
+
+423
+00:43:43,990 --> 00:43:48,230
+اشتقاق جزءي وبالتالي بيسميها معادلة تفاضلية جزية
+
+424
+00:43:48,230 --> 00:43:52,430
+لكن إذا كانت ال function دالة في متغير واحد زي ما
+
+425
+00:43:52,430 --> 00:43:57,430
+كنا نقول في الكلقل الصحيو يتساوي F of X يبقى Y
+
+426
+00:43:57,430 --> 00:44:01,850
+دالة في X فقط X هو المتغير المستقل ال independent
+
+427
+00:44:01,850 --> 00:44:06,300
+وY هو المتغير التابعاللي هو dependent variable
+
+428
+00:44:06,300 --> 00:44:12,380
+تمام؟ لكن لو كانت Y تسوى F of X و T يبقى صارت دالة
+
+429
+00:44:12,380 --> 00:44:17,900
+في مين؟ فاش عندي اشتقاق قعدت بيصير اشتقاق جزئي و
+
+430
+00:44:17,900 --> 00:44:21,980
+هذا خارج نطاق دراستنا مالناهش علاقة فيه فيه
+
+431
+00:44:21,980 --> 00:44:25,320
+المعادلة التفاصيلية يبقى انا عندي function في
+
+432
+00:44:25,320 --> 00:44:30,720
+متغير واحد فقط قلنا with respect to a single
+
+433
+00:44:37,150 --> 00:44:41,790
+بتصير المشتقات مشتقات عادية وبالتالي المعادلة
+
+434
+00:44:41,790 --> 00:44:45,390
+التفاضلية اللي عندنا بيكون معادلة تفاضلية عادية
+
+435
+00:44:45,390 --> 00:44:51,510
+بنقول عليها معادلة تفاضلية عاديةزي ايش مثلا لو قلت
+
+436
+00:44:51,510 --> 00:44:56,110
+y prime زائد تلاتة y يسوي E أستي معادلة ظهرت فيها
+
+437
+00:44:56,110 --> 00:45:02,910
+باسمين المشتقاء الأولى يبقى one derivative يبقى
+
+438
+00:45:02,910 --> 00:45:08,570
+معادلة تفاضلية من الرتبة الأولىالان لو كانت
+
+439
+00:45:08,570 --> 00:45:11,850
+المعادلة بالشكل اللي عندنا هذا يبقى ظاهرة المشتقة
+
+440
+00:45:11,850 --> 00:45:18,790
+الأولى والمشتقة الثانية يبقى هذا one or more اكثر
+
+441
+00:45:18,790 --> 00:45:23,790
+من مين من المشتقة والمشتقات عادية يبقى في هذه
+
+442
+00:45:23,790 --> 00:45:29,510
+الحالة بقول هذه معادلة تفاضلية عادية حد بتسأل اي
+
+443
+00:45:29,510 --> 00:45:36,330
+سؤال هنا؟أه طيب بدنا نروح لحاجة اسمها اللي هو حل
+
+444
+00:45:36,330 --> 00:45:44,010
+أو رتبة المعادلة التفاضلية definition the
+
+445
+00:45:44,010 --> 00:45:48,970
+order of
+
+446
+00:45:48,970 --> 00:45:59,610
+a differential equation رتبة المعادلة التفاضلية is
+
+447
+00:46:00,160 --> 00:46:17,280
+the order of the
+
+448
+00:46:17,280 --> 00:46:28,000
+highest derivative in
+
+449
+00:46:28,000 --> 00:46:28,840
+the equation
+
+450
+00:46:37,320 --> 00:46:47,680
+على سبيل المثال الـ differential equation
+
+451
+00:46:47,680 --> 00:46:58,560
+الـ differential equation T في D تكييب Y على D T
+
+452
+00:46:58,560 --> 00:47:10,630
+تكييب ناقص اتنيندي واي على دي ت أربع زائد واي
+
+453
+00:47:10,630 --> 00:47:19,230
+تساوي ت لإن ت is of the
+
+454
+00:47:42,920 --> 00:47:52,060
+رتبة المعادلة التفاضلية رتبة المعادلة التفاضلية هي
+
+455
+00:47:52,060 --> 00:47:58,860
+رتبة أعلى
+
+456
+00:47:58,860 --> 00:48:04,810
+معامل تفاضلي يظهر في المعادلة in the equationيبقى
+
+457
+00:48:04,810 --> 00:48:08,550
+أنا باجي على المعادلة التفاضلية وبشوف مين أعلى
+
+458
+00:48:08,550 --> 00:48:13,630
+مشتقة موجودة فيها أعلى مشتقة موجودة فيها بتكون هي
+
+459
+00:48:13,630 --> 00:48:19,050
+رتبة مين المعادلة التفاضلية بنعطي مثال توضيحه for
+
+460
+00:48:19,050 --> 00:48:23,630
+example the differential equation T في D تكيب Y
+
+461
+00:48:23,630 --> 00:48:30,790
+على DT تكيب نقص اتنين DY على DT أس أربع زائد Y
+
+462
+00:48:30,790 --> 00:48:37,410
+تسوى T لان T is ofبدنا نعرف جداش ال order تبعها يا
+
+463
+00:48:37,410 --> 00:48:43,890
+ترى هل هو تلاتة و الله جداش و الله اربعة مش اربعة
+
+464
+00:48:43,890 --> 00:48:48,750
+يعني اذا
+
+465
+00:48:48,750 --> 00:48:53,550
+القضية خلافية بين الفقهات البعض بيقولوا تلاتة و
+
+466
+00:48:53,550 --> 00:48:57,650
+البعض بيقولوا اربعة انا بسألك شو اسم ممكن اتعرف
+
+467
+00:48:57,650 --> 00:49:04,610
+عليكي باتسامابتسام النجار تعتقد، طبعا هذه أول
+
+468
+00:49:04,610 --> 00:49:09,630
+محاضرة، وبالتالي تعتقد، مش بيقول، تعتقد أن
+
+469
+00:49:09,630 --> 00:49:14,930
+المعادلة هذه من رتبة رقم أربعة، وأنا أسأل هل
+
+470
+00:49:14,930 --> 00:49:18,290
+الأربعة هذه مشتقة ولا أس؟
+
+471
+00:49:21,070 --> 00:49:26,710
+ممتاز جدا بس طبعا شاية يبقى بتقول أُس للمشتقة بقول
+
+472
+00:49:26,710 --> 00:49:31,950
+كلامها صحيح لكن أرجع للتعريف هل أنا قلت أُس
+
+473
+00:49:31,950 --> 00:49:37,950
+المشتقة ولا المشتقة نفسها وماقلتش أُس المشتقة صحيح
+
+474
+00:49:37,950 --> 00:49:41,610
+ولا لا نرجع للتعريف the order of the differential
+
+475
+00:49:41,610 --> 00:49:45,970
+equation is the order of the highest derivative
+
+476
+00:49:45,970 --> 00:49:53,860
+يبقى هو رتبة أعلى ولم أقول هي أُستمام؟ يبقى أربعة
+
+477
+00:49:53,860 --> 00:49:59,200
+هذا الرقم أربعة ماله خطأ ولا صح؟ خطأ بل very wrong
+
+478
+00:49:59,200 --> 00:50:04,240
+نشكرها على سؤالها إنها قالت هذه أربعة لأن النبات
+
+479
+00:50:04,240 --> 00:50:08,480
+الكل بفهم الآخرين إن الرتبة ليست أربعة وإنما
+
+480
+00:50:08,480 --> 00:50:14,770
+الرتبةتلاتة، لأن تلاتة هي أعلى مشتقة موجودة في هذه
+
+481
+00:50:14,770 --> 00:50:19,110
+الوضع، مش أربعة، لو قضيت أربعة بمليون، بتظل هي من
+
+482
+00:50:19,110 --> 00:50:24,410
+رتبة التالتة، ليش؟ ان أربعة أس وليست مشتقة، واحنا
+
+483
+00:50:24,410 --> 00:50:29,950
+بيقول ال order هو رتبة المشتقة، يعني المشتقة
+
+484
+00:50:29,950 --> 00:50:33,630
+الأولى ولا التانية ولا التالتة ولا الرابع، تمام؟
+
+485
+00:50:33,730 --> 00:50:38,690
+يبقى أربعة ليست مشتقة و للمشتقة الرقم تلاتة كان
+
+486
+00:50:38,690 --> 00:50:45,710
+بإمكاني مكتوبهاش زي هيك اهو هاكتب T Y triple prime
+
+487
+00:50:45,710 --> 00:50:54,760
+نقص اتنين Y prime أس اربعةزائد Y تساوي T لين T إذا
+
+488
+00:50:54,760 --> 00:50:58,720
+هذه والله هذه أعلى المشتقة الموجودة عندها من
+
+489
+00:50:58,720 --> 00:51:05,180
+المشتقة التالية إذا هذه is of the third order من
+
+490
+00:51:05,180 --> 00:51:12,380
+الرتبة الثالثة وليست الرابعة ابقى is of the third
+
+491
+00:51:12,380 --> 00:51:16,440
+order تمام؟
+
+492
+00:51:16,680 --> 00:51:22,740
+يبقى جبتها والله بدل المرة مرتين في سؤال بخيارات
+
+493
+00:51:22,740 --> 00:51:27,780
+متعددة بحط شغلة زيك طبعا بحطلها كمان واحدة و بقول
+
+494
+00:51:27,780 --> 00:51:31,280
+of the nth order of the third order of the zero
+
+495
+00:51:31,280 --> 00:51:35,300
+order of the fourth order وحطيلي خط تحت الإجابة
+
+496
+00:51:35,300 --> 00:51:40,260
+الصحية يعني جبتها قبل ذلك بدل المرة مرتين يوم أن
+
+497
+00:51:40,260 --> 00:51:45,900
+درست المادة سابقايبقى بك تربي تروحي وين تشوفي أعلى
+
+498
+00:51:45,900 --> 00:51:50,120
+معامل تفاضل، يعني كان بيمكن يتحيل عليك بطريقة
+
+499
+00:51:50,120 --> 00:51:56,360
+تانية ويقولك هذه تربيع، بصير هذا مثلا هاك تربيع،
+
+500
+00:51:56,360 --> 00:52:02,880
+وهذه أربعة، اني أتمن واحطلك اتنين، تلاتة، أربعة،
+
+501
+00:52:02,880 --> 00:52:07,900
+ستة، تلاتة مثلا، وحطيلي اللي تقطحت اللي جابها
+
+502
+00:52:07,900 --> 00:52:11,890
+الصحيةيبقى الإجابة صحية قداش؟ هادية، رغم أني
+
+503
+00:52:11,890 --> 00:52:16,890
+غيرتها، لكن ضالة is of the third order من الرتبة
+
+504
+00:52:16,890 --> 00:52:21,450
+أثنية، لكن إذا بتكلم عن الدرجة، بقول الدرجة
+
+505
+00:52:21,450 --> 00:52:26,070
+الرابعةمش موافق كدرجة كرتبة لأ إذا احنا مالاش
+
+506
+00:52:26,070 --> 00:52:30,630
+علاقة بالدرجة وإنما إلنا علاقة بالرتبة الدرجة هذا
+
+507
+00:52:30,630 --> 00:52:35,530
+للصف التامن والتاسع تمام يبقى هنا هقول من الرتبة
+
+508
+00:52:35,530 --> 00:52:42,190
+الثالثة تمام هذا بالنسبة لرتبة المعادلة التفاضلية
+
+509
+00:52:42,190 --> 00:52:47,290
+بدنا نيجي لحل المعادلة التفاضلية يبقى كمان
+
+510
+00:52:47,290 --> 00:52:47,990
+definition
+
+511
+00:52:55,140 --> 00:53:05,560
+The solution of a differential equation حل
+
+512
+00:53:05,560 --> 00:53:11,380
+المعادلة التفاضلية is a function
+
+513
+00:53:16,120 --> 00:53:29,040
+معرفة defined on an interval معرفة على فترة ما on
+
+514
+00:53:29,040 --> 00:53:40,840
+an interval I مثلا and satisfy and
+
+515
+00:53:40,840 --> 00:53:44,460
+satisfy the differential equation
+
+516
+00:53:48,930 --> 00:53:58,910
+وتحقق المعادلة التفاضلية for example كمثال على ذلك
+
+517
+00:53:58,910 --> 00:54:12,790
+for example Y تساوي E أقصى 2T is a solution is a
+
+518
+00:54:12,790 --> 00:54:16,550
+solution of the
+
+519
+00:54:25,960 --> 00:54:30,940
+نقص اتنين Y تساوي زيرو
+
+520
+00:54:56,900 --> 00:55:02,440
+مرة تانية حل المعادلة التفاضلية the solution of a
+
+521
+00:55:02,440 --> 00:55:07,060
+differential equation هو عبارة عن دالة دالة معرفة
+
+522
+00:55:07,060 --> 00:55:13,320
+على فترة محددة والتكن I وفي نفس الوقت تحقق من
+
+523
+00:55:13,320 --> 00:55:17,140
+المعادلة التفاضلية يعني ايه؟ يعني لو اوطفها في
+
+524
+00:55:17,140 --> 00:55:21,200
+المعادلة التفاضلية بدها ايش؟ بدها اتحققها يعني
+
+525
+00:55:21,200 --> 00:55:25,770
+تخلي الطرف اليمين زي الطرف اللي على الشمالمثلا
+
+526
+00:55:25,770 --> 00:55:39,310
+يبقى الدالة Y تساوي E أس اتنين T هي
+
+527
+00:55:39,310 --> 00:55:41,290
+حل هذه المعرفة
+
+528
+00:55:50,280 --> 00:55:54,280
+على كل الـ real line الـ exponential function EO6
+
+529
+00:55:54,280 --> 00:55:57,280
+EO6 EO6 EO6 EO6 EO6 EO6 EO6 EO6 EO6 EO6 EO6 EO6
+
+530
+00:55:57,280 --> 00:56:04,660
+EO6 EO6 EO6 EO6 EO6 EO6 EO6 EO6 EO6
+
+531
+00:56:04,660 --> 00:56:15,140
+EO6 EO6
+
+532
+00:56:17,120 --> 00:56:21,540
+وقدمنا فيه امتحانة ونجحنا بجدارة يعني طب هذه بدنا
+
+533
+00:56:21,540 --> 00:56:26,240
+نشوف كيف حالة هذه لو جات اشتقها قداش بتكون مشتقتها
+
+534
+00:56:26,240 --> 00:56:33,010
+اثنان E أس اثنان Tيبقى بده يشيل هذه ويكتب لتنين E
+
+535
+00:56:33,010 --> 00:56:37,910
+أس اتنين T ناقص اتنين E أس اتنين T مقدش يبقى
+
+536
+00:56:37,910 --> 00:56:43,110
+الجواب Zero زي الطرف اليمين إذا فعلا هذه حل طب
+
+537
+00:56:43,110 --> 00:56:47,090
+عشان واحدة تقولك كيف جبت هذه كيف جبت هو شغلنا
+
+538
+00:56:47,090 --> 00:56:52,370
+بداية من المرة القادمة و لنهاية المقرر كل شغلنا
+
+539
+00:56:52,370 --> 00:56:58,790
+إيجاد الحلول للمعادلات التفضلية نعطيكي مثال آخر
+
+540
+00:56:59,280 --> 00:57:06,420
+يبقى example show
+
+541
+00:57:06,420 --> 00:57:10,060
+that
+
+542
+00:57:10,060 --> 00:57:21,260
+y تساوي T E أس T is a solution is
+
+543
+00:57:21,260 --> 00:57:30,990
+a solution of the differentialEquation هي عبارة عن
+
+544
+00:57:30,990 --> 00:57:38,930
+حل المعادلة التفاضلية y w prime نقص اتنين y prime
+
+545
+00:57:38,930 --> 00:57:48,930
+زائد y تساوي زيرو on the interval على الفترة من
+
+546
+00:57:48,930 --> 00:57:51,510
+سالب infinity ل infinity
+
+547
+00:58:03,070 --> 00:58:08,350
+يبقى حل المعادلة التفاضلية هو عن دالة معرفة على
+
+548
+00:58:08,350 --> 00:58:14,250
+فترة وتحقق المعادلة الحمد لله قال يبين لي إن هذا
+
+549
+00:58:14,250 --> 00:58:20,430
+هو حل للمعادلة التفاضلية على الفترة السؤال هو جداش
+
+550
+00:58:20,430 --> 00:58:28,410
+domain T في E أس T بمعنى أخر هل توجد نقطة الدالة
+
+551
+00:58:28,410 --> 00:58:33,780
+هذه ماهياش معرفة عندها؟لأ كله من سالب حتى عند Zero
+
+552
+00:58:33,780 --> 00:58:37,400
+عند Zero بتطلع Zero في E of Zero اللي هو بواحد
+
+553
+00:58:37,400 --> 00:58:45,640
+يبقى Zero معرفة يبقى باجي بقوله ال Y تساوي T في E
+
+554
+00:58:45,640 --> 00:58:54,580
+of T is defined معرفة for all T اللي موجودة في ال
+
+555
+00:58:54,580 --> 00:58:59,850
+interval من سالب Infinity إلى Infiniteيبقى الدلل
+
+556
+00:58:59,850 --> 00:59:04,510
+يا طهالي هي معرفة عليها كل الفضل لكن هي حل والله
+
+557
+00:59:04,510 --> 00:59:09,270
+مش حل لسه انا مش عارف تمام؟ يبقى بهذه فيها المشتقة
+
+558
+00:59:09,270 --> 00:59:12,570
+الأولى والثانية إذا بدي أروح أجيب المشتقة الأولى
+
+559
+00:59:12,570 --> 00:59:18,630
+والمشتقة الثانية يبقى لما أقول له Y تسوى T E Os T
+
+560
+00:59:18,630 --> 00:59:24,210
+بدي أروح أجيب له المشتقة الأولى هذه يا بنات تعتبر
+
+561
+00:59:24,210 --> 00:59:30,140
+دلل وهذه دلل إذا مشتقة حاصل ضربالأولى في مشتقة
+
+562
+00:59:30,140 --> 00:59:35,120
+الثانية زائد الثانية في مشتقة الأولى يبقى الأولى
+
+563
+00:59:35,120 --> 00:59:39,100
+اللى هى T مشتقة ال exponential بال exponential
+
+564
+00:59:39,100 --> 00:59:45,720
+اتسل زائد الدالة التانية في مشتقة الأولى اللى هى
+
+565
+00:59:45,720 --> 00:59:51,360
+بواحدهذه المشتقة الأولى بدنا نروح نجيب المشتقة
+
+566
+00:59:51,360 --> 00:59:58,300
+الثانية يبقى بد واي ضعف لقايم بدنا نروح نشتق هذه
+
+567
+00:59:58,300 --> 01:00:04,180
+الجزء الأول برضه مشتقة حاصل ضرب دالتين الأولى في
+
+568
+01:00:04,180 --> 01:00:09,140
+مشتقة الدالة التانية زائد الدالة التانية في مشتقة
+
+569
+01:00:09,140 --> 01:00:15,730
+الأولى نجي للي بعدها زائدمشتقة ال Eost بال Eost
+
+570
+01:00:15,730 --> 01:00:25,870
+itself يبقى الجواب T Eost زائد 2 Eost الان نمسك
+
+571
+01:00:25,870 --> 01:00:29,690
+المعلومات اللى حصلنا عليها و نرجع نعود في المعادل
+
+572
+01:00:29,690 --> 01:00:35,770
+اللى فوق يبقى بدأ خدله الان Y double prime نقص 2 Y
+
+573
+01:00:35,770 --> 01:00:42,150
+prime زائد Yإن طلب الله الناتج يساوي الصفر بيكون
+
+574
+01:00:42,150 --> 01:00:51,470
+هذا هو عن حل يبقى هذا الكلام يبقى يساوي يبقى يبقى
+
+575
+01:00:51,470 --> 01:00:59,670
+يبقى يبقى يبقى يبقى يبقى يبقى يبقى يبقى يبقى يبقى
+
+576
+01:00:59,670 --> 01:00:59,910
+يبقى يبقى يبقى يبقى يبقى يبقى يبقى يبقى يبقى يبقى
+
+577
+01:00:59,910 --> 01:01:01,330
+يبقى يبقى يبقى يبقى يبقى يبقى يبقى يبقى يبقى يبقى
+
+578
+01:01:01,330 --> 01:01:07,940
+يبقى يبقى يبقى يبقى ييبقى T E Os T زائد E Os T
+
+579
+01:01:07,940 --> 01:01:14,200
+شيلنا Y Prime و حطينا منين قيمتها قال لي زائد Y
+
+580
+01:01:14,200 --> 01:01:21,380
+وين Y اللي هي طالب الأصل يبقى زائد T E Os T بدي
+
+581
+01:01:21,380 --> 01:01:26,300
+أشوف كده إيش بيطلع هدول يبقى هذا الكلام يساعد هذه
+
+582
+01:01:26,300 --> 01:01:34,260
+هي هذه صحيح ولا لأيبقى اتنين T E و أس T زائدي
+
+583
+01:01:34,260 --> 01:01:41,700
+اتنين E و أس T بده افك الجث هذا ناقص اتنين T E و
+
+584
+01:01:41,700 --> 01:01:49,920
+أس T ناقص اتنين E و أس T طلعي ليه؟ هذه و هذه
+
+585
+01:01:49,920 --> 01:01:56,180
+بإشارتين مختلفتين صحيح ولا لأ؟ يبقى عند الجامع
+
+586
+01:01:56,180 --> 01:02:03,810
+بيثلاشههذه و هذه نفس القصة بإشارتين يبقى المجموع
+
+587
+01:02:03,810 --> 01:02:08,410
+الكل قداش بطلع Zero اللي هو الطرف اليمين من
+
+588
+01:02:08,410 --> 01:02:14,030
+المعادلة اللي عندنا هذه يبقى أثبت له Y''-2Y''زاد Y
+
+589
+01:02:14,030 --> 01:02:19,630
+كله يساوي مين Zero يبقى فعلا هذه حل المعادلة على
+
+590
+01:02:19,630 --> 01:02:26,390
+الفترة من سلب Infinity إلى InfinityY تساوي T في ال
+
+591
+01:02:26,390 --> 01:02:35,970
+E أس T is a solution of Y double A prime نقص اتنين
+
+592
+01:02:35,970 --> 01:02:43,230
+Y prime زائد Y يساوي Zero on ال interval من سالب
+
+593
+01:02:43,230 --> 01:02:46,310
+Infinity إلى Infinity
+
+594
+01:03:14,540 --> 01:03:20,580
+not ملاحظة بسيطة المعادلة تفضل يا ابنت ممكن ما
+
+595
+01:03:20,580 --> 01:03:24,860
+يكونش لحل واحد و بس ممكن حلان ممكن تلان ممكن ما لا
+
+596
+01:03:24,860 --> 01:03:29,280
+نهاية من الحلول يعني ليس بالضرورة أن يكون حلا
+
+597
+01:03:29,280 --> 01:03:33,060
+واحدا فقط يبقى باجي بقوله the differential
+
+598
+01:03:33,060 --> 01:03:39,460
+equation may
+
+599
+01:03:39,460 --> 01:03:40,400
+have
+
+600
+01:03:44,530 --> 01:03:58,790
+more than more than one solution ممكن يكون لها
+
+601
+01:03:58,790 --> 01:04:05,930
+أكتر من حل حلين تلاتة أربعة جد ما يكون نعطي
+
+602
+01:04:05,930 --> 01:04:10,670
+definition the set of all solutions
+
+603
+01:04:13,400 --> 01:04:20,780
+of all solutions of
+
+604
+01:04:20,780 --> 01:04:25,960
+a given differential
+
+605
+01:04:25,960 --> 01:04:34,320
+equation لدالة تفاضلية مُعطَى is called نروح
+
+606
+01:04:34,320 --> 01:04:39,300
+نسميها general solution نسميها
+
+607
+01:04:40,370 --> 01:04:51,090
+general solution of differential
+
+608
+01:04:51,090 --> 01:04:57,930
+equation of the
+
+609
+01:04:57,930 --> 01:05:07,490
+differential equation for example كمثال
+
+610
+01:05:07,490 --> 01:05:08,230
+لذلك
+
+611
+01:05:28,520 --> 01:05:44,650
+Y'-2Y يساوي 0Y تساوي C يقص اتنين T و C is any
+
+612
+01:05:44,650 --> 01:05:49,490
+positive
+
+613
+01:05:49,490 --> 01:05:52,690
+real number
+
+614
+01:06:22,810 --> 01:06:29,050
+المعادلة التفاضية ممكن يكون لها أكثر من حل، حلين،
+
+615
+01:06:29,050 --> 01:06:33,350
+تلاتة، أربعة، ما لنهاجة، ما يكون معنا مشكلةنقطة
+
+616
+01:06:33,350 --> 01:06:37,850
+تعريف بقول the set of all solutions يبقى لو جمعنا
+
+617
+01:06:37,850 --> 01:06:44,450
+كل الحلول للمعادلة التفاضلية وحطناهم في set معينة
+
+618
+01:06:44,450 --> 01:06:48,510
+بسمي ال set هذه هي ال general solution حل العام
+
+619
+01:06:48,510 --> 01:06:54,150
+للمعادلة التفاضلية الذي يجتمل على كل حل من حلول
+
+620
+01:06:54,150 --> 01:06:58,770
+المعادلة يبقى بسميه the general solution of the
+
+621
+01:06:58,770 --> 01:07:02,730
+differential equationعلى سبيل المثال المعادلة هذه
+
+622
+01:07:02,730 --> 01:07:08,250
+توس اخدناها قبل قليل صحيح؟ وقلنا ايش الحل تبعها؟ E
+
+623
+01:07:08,250 --> 01:07:13,810
+اوس اتنين T لكن لو رحت قلت انا في عندي Y يساوي C E
+
+624
+01:07:13,810 --> 01:07:17,250
+اوس اتنين يقولوا C is any positive real number
+
+625
+01:07:17,250 --> 01:07:21,060
+احنا في الحل اللي اعطيناه كانت C انا بجداشبواحد
+
+626
+01:07:21,060 --> 01:07:27,540
+حطيها خمسة ونشوف هل بتحققها ولا لأ لو كانت خمسة
+
+627
+01:07:27,540 --> 01:07:33,240
+يبقاش بالصير خمسة في E أوس اتنين T بده اشتقها وشقة
+
+628
+01:07:33,240 --> 01:07:37,980
+E أوس اتنين T باتنين E أوس اتنين في خمسة بعشرة E
+
+629
+01:07:37,980 --> 01:07:44,960
+أوس اتنين Tيبقى هي عشرة E أوس اتنين T نقص اتنين في
+
+630
+01:07:44,960 --> 01:07:48,260
+خمسة E أوس اتنين يبقى عشرة E أوس اتنين يبقى
+
+631
+01:07:48,260 --> 01:07:51,720
+المجموع يسوي قداشي زرع ان شاء الله تاخديها بواحد
+
+632
+01:07:51,720 --> 01:07:57,140
+عالمية مش عشرة .. مش خمسة واحد عالمية حطي اي رقم
+
+633
+01:07:57,140 --> 01:08:01,840
+موجة بيجي في بني ان شاء الله تحطي جدر اتنينيبقى
+
+634
+01:08:01,840 --> 01:08:06,800
+حاطي اي رقم موجب ييجي في بالك بيطلع عندك حال يبقى
+
+635
+01:08:06,800 --> 01:08:08,840
+كم حالة عندي اللي هو المعادلة التفاضلية اللي بيصير
+
+636
+01:08:08,840 --> 01:08:14,690
+هذهما لنهاية من الحلول، تمام؟ كل غيريسي، كل واحد،
+
+637
+01:08:14,690 --> 01:08:19,150
+مثلا اللي قعدت هنا حوالي الآن، صار بيجي ما يقرب من
+
+638
+01:08:19,150 --> 01:08:23,550
+خمسين، كل واحدة تحط حل، بيطلع عندها حل، كل واحدة
+
+639
+01:08:23,550 --> 01:08:28,010
+مختلفة عن أخر، كل واحد يحقق المعادلة التفاضلية،
+
+640
+01:08:28,010 --> 01:08:32,490
+إذا المعادلة التفاضلية يمكن أن يكون لها مجموعة من
+
+641
+01:08:32,490 --> 01:08:38,470
+الحلول وليس حلا واحدة نعطي آخر تعريف في هذه
+
+642
+01:08:38,470 --> 01:08:49,360
+المقدمةdefinition if we are given values if we are
+
+643
+01:08:49,360 --> 01:08:57,000
+given values اذا اعطينا قيم of the unknown
+
+644
+01:08:57,000 --> 01:09:07,140
+function of the unknown function للدلة المجهولة
+
+645
+01:09:07,140 --> 01:09:19,730
+andits derivatives and its derivatives وعطينا حلول
+
+646
+01:09:19,730 --> 01:09:32,930
+لمشتقتها at a single value عند قيمة واحدة of the
+
+647
+01:09:32,930 --> 01:09:36,050
+independent
+
+648
+01:09:42,060 --> 01:09:53,300
+variable عند قيمة واحدة للمتغير المستقل then the
+
+649
+01:09:53,300 --> 01:10:08,580
+differential equation is called بنسميها an initial
+
+650
+01:10:36,550 --> 01:10:49,270
+والقيم المعطاهاالقوانين المعروفة تسمى بـInitial
+
+651
+01:10:49,270 --> 01:10:58,570
+Conditions يبقى
+
+652
+01:10:58,570 --> 01:11:05,450
+الشروط الابتدائية على
+
+653
+01:11:05,450 --> 01:11:05,890
+سبيل المثال
+
+654
+01:11:14,770 --> 01:11:19,470
+على سبيل المثال الاختصارات
+
+655
+01:11:19,470 --> 01:11:23,950
+الاختصارات الاختصارات الاختصارات الاختصارات
+
+656
+01:11:23,950 --> 01:11:25,370
+الاختصارات الاختصارات الاختصارات الاختصارات
+
+657
+01:11:25,370 --> 01:11:25,450
+الاختصارات الاختصارات الاختصارات الاختصارات
+
+658
+01:11:25,450 --> 01:11:32,810
+الاختصارات الاختصارات
+
+659
+01:11:32,810 --> 01:11:34,710
+الاختصارات الاختصارات الاختصارات الاختصارات
+
+660
+01:11:34,710 --> 01:11:34,750
+الاختصارات الاختصارات الاختصارات الاختصارات
+
+661
+01:11:34,750 --> 01:11:35,210
+الاختصارات الاختصارات الاختصارات الاختصارات
+
+662
+01:11:35,210 --> 01:11:39,050
+الاختصارات الاختصارات الاختصارات الاختصارات
+
+663
+01:11:39,050 --> 01:11:42,070
+الاختصارات
+
+664
+01:11:44,410 --> 01:11:54,230
+و ال y عند ال y على 2 ساوي سلبي 2 و ال y عند ال y
+
+665
+01:11:54,230 --> 01:12:04,530
+على 2 ساوي واحد من ال value problems
+
+666
+01:12:46,080 --> 01:12:50,860
+بنرجع لهذا التعريف مرة ثانية وبعد ذلك نروح نحطه
+
+667
+01:12:50,860 --> 01:12:55,860
+على أرض الواقع بقول if we are given values إذا
+
+668
+01:12:55,860 --> 01:13:02,080
+أعطينا قيم of the unknown function لدالة المجهولة
+
+669
+01:13:02,080 --> 01:13:06,440
+and its derivative ومشتقات أعطينا قيم لدالة
+
+670
+01:13:06,440 --> 01:13:12,500
+المجهولة ومشتقات الدالة المجهولة وين؟At a single
+
+671
+01:13:12,500 --> 01:13:18,860
+value عند قيمة محددة او قيمة معينة واحدة فقط لمين
+
+672
+01:13:18,860 --> 01:13:23,760
+لل independent variable للمتغير المستقل لما اقول Y
+
+673
+01:13:23,760 --> 01:13:27,780
+ده اللي في T يا بناتي يبقى Y هو المتغير التابع و T
+
+674
+01:13:27,780 --> 01:13:34,380
+هو المتغير المستقل يعني ايه ده؟وحصلنا على قيم لها
+
+675
+01:13:34,380 --> 01:13:41,160
+نتيجة ليعطاها قيمة محددة للمتغير المستقل عطينا قيم
+
+676
+01:13:41,160 --> 01:13:46,700
+لـY مشتقتاتها نتيجة ليعطاها قيمة للمتغير المستقل
+
+677
+01:13:50,120 --> 01:13:55,320
+بقول عليها initial value problem يعني مسألة القيم
+
+678
+01:13:55,320 --> 01:14:02,460
+الحدية تمام و هختصرها IVP مش very important person
+
+679
+01:14:02,460 --> 01:14:06,740
+VIP تبع الشخصية لأ لأ لأ initial value problem
+
+680
+01:14:06,740 --> 01:14:11,620
+الحرف الأول initial الحرف التاني V اللي هو ال
+
+681
+01:14:11,620 --> 01:14:15,980
+value الحرف التالت P جاية من كلمة مين problemيبقى
+
+682
+01:14:15,980 --> 01:14:22,620
+كلمة initial value problem هاختصرها إلى IVP طب
+
+683
+01:14:22,620 --> 01:14:26,380
+الشروط اللي حطيناها هذه بسميها initial conditions
+
+684
+01:14:26,380 --> 01:14:31,640
+الشروط الابتدائية and the given values والقيم اللي
+
+685
+01:14:31,640 --> 01:14:35,700
+اعطيناها هذه are called the initial conditions
+
+686
+01:14:35,700 --> 01:14:40,120
+نعطي الآن مثال على الكلام اللي احنا جايلينه هنا
+
+687
+01:14:40,560 --> 01:14:44,840
+مثلًا الـ differential equations طلّي لهذه من أي
+
+688
+01:14:44,840 --> 01:14:51,160
+رتبةمن الرتبة الأولى تمام اعطينا ان قيمة y عند ال
+
+689
+01:14:51,160 --> 01:14:55,000
+zero يسوى كده؟ خمس يبقى ماعندش الا condition واحد
+
+690
+01:14:55,000 --> 01:15:00,400
+جديش عندك رتب جديش بتعطي conditions الرتبة الأولى
+
+691
+01:15:00,400 --> 01:15:03,480
+بتعطي condition واحد الرتبة الثانية بدك تعطي two
+
+692
+01:15:03,480 --> 01:15:06,740
+conditions الرتبة التالتة three conditions و هكذا
+
+693
+01:15:06,740 --> 01:15:12,080
+يعني اذا عند الرتبة التالتة بدي اعطي condition ل y
+
+694
+01:15:12,080 --> 01:15:19,390
+و ل y prime و ل y w primeبتعطي قيم لهم دولهذه
+
+695
+01:15:19,390 --> 01:15:24,090
+المعادلة من الرتبة أسنى رغم أن الرتبة الأولى ليست
+
+696
+01:15:24,090 --> 01:15:29,250
+موجودة فهيش يقول why عند بي على اتنين بده تسوى
+
+697
+01:15:29,250 --> 01:15:33,530
+قداش سالب اتنين why prime عند بي على اتنين بده
+
+698
+01:15:33,530 --> 01:15:38,990
+تسوى قداش واحد يبقى حطيت شرطين لاحظى عند نفس ال
+
+699
+01:15:38,990 --> 01:15:43,970
+independent variable يبقى هنا تيب بي على اتنين و
+
+700
+01:15:43,970 --> 01:15:47,550
+هنا مش هذا عنده نقطة و هذا عنده نقطة تانيةيعني
+
+701
+01:15:47,550 --> 01:15:50,590
+عنده قيمة للمتغير المسؤول عنها؟ لأ عندها نفس
+
+702
+01:15:50,590 --> 01:15:56,250
+القيمة روحنا قولنا هنا و هنا at a single value عند
+
+703
+01:15:56,250 --> 01:15:59,590
+قيمة واحدة يبقى الباية على اتنين هذه اللي كانت
+
+704
+01:15:59,590 --> 01:16:03,690
+single value في التعريف لل independent variable
+
+705
+01:16:04,010 --> 01:16:10,290
+للمتغير المستقل اعطتني قيمة ل Y و اعطتني قيمة ل Y'
+
+706
+01:16:11,170 --> 01:16:15,190
+زي ما انت شايفه يبقى اذا عندي معادلة بالشرط او
+
+707
+01:16:15,190 --> 01:16:19,790
+معادلة بشرطين او معادلة بثلاثة شروط او باربعة شروط
+
+708
+01:16:19,790 --> 01:16:26,710
+بسمي هذه initial value problem طيب
+
+709
+01:16:26,710 --> 01:16:30,910
+ليش ال initial value problem؟لو ماعطنيش ال
+
+710
+01:16:30,910 --> 01:16:37,210
+condition هذا بيطلع عندي الجواب هه بثابت، اذا
+
+711
+01:16:37,210 --> 01:16:40,590
+المعادلة من الرتبة الأولى، بثابتين، لأنه بدنا
+
+712
+01:16:40,590 --> 01:16:44,790
+نكامل، ونتيجة التكامل بجيني ثابتمظبوط او لا؟
+
+713
+01:16:44,790 --> 01:16:49,270
+بثابتان اذا من الرتبة الثانية، بثلاث او بثلاثة
+
+714
+01:16:49,270 --> 01:16:52,830
+ثوابت من الرتبة اللي هو التالتة و هكذا ال initial
+
+715
+01:16:52,830 --> 01:16:57,810
+conditions منها من خلالها بجيب قداش مقدار اللي هو
+
+716
+01:16:57,810 --> 01:17:02,290
+المقدار الثابت أو قداش قيمة المقدار الثابت اللي
+
+717
+01:17:02,290 --> 01:17:07,030
+موجود عندنا حد بتحب تسأل اي تسأل في كل ما سمعته
+
+718
+01:17:07,030 --> 01:17:12,050
+اليوم في هذه المحاضرة تسأل اسأله زي مسألة أخنا قبل
+
+719
+01:17:12,050 --> 01:17:15,330
+شوية و اجبناها اتفضليلأن معادلة تفاضية ماينفعش
+
+720
+01:17:15,330 --> 01:17:19,690
+تكون Zero Order ماينفعش تكون Zero Order ماينفعش
+
+721
+01:17:19,690 --> 01:17:21,610
+تكون Zero Order ماينفعش تكون Zero Order ماينفعش
+
+722
+01:17:21,610 --> 01:17:21,930
+تكون Zero Order ماينفعش تكون Zero Order ماينفعش
+
+723
+01:17:21,930 --> 01:17:22,350
+تكون Zero Order ماينفعش تكون Zero Order ماينفعش
+
+724
+01:17:22,350 --> 01:17:23,330
+تكون Zero Order ماينفعش تكون Zero Order ماينفعش
+
+725
+01:17:23,330 --> 01:17:25,590
+تكون Zero Order ماينفعش تكون Zero Order ماينفعش
+
+726
+01:17:25,590 --> 01:17:27,130
+تكون Zero Order ماينفعش تكون Zero Order ماينفعش
+
+727
+01:17:27,130 --> 01:17:27,170
+تكون Zero Order ماينفعش تكون Zero Order ماينفعش
+
+728
+01:17:27,170 --> 01:17:30,610
+تكون Zero Order ماينفعش تكون Zero Order ماينفعش
+
+729
+01:17:30,610 --> 01:17:31,450
+تكون Zero Order ماينفعش تكون Zero Order ماينفعش
+
+730
+01:17:31,450 --> 01:17:39,430
+تكون Zero Order ماينفعش تكون Zero
+
+731
+01:17:39,450 --> 01:17:43,070
+قلنا أول ما بدأنا المعادلة التفاضلية هي معادلة
+
+732
+01:17:43,070 --> 01:17:48,770
+يظهر فيها one or more يعني لازم على الأقل تظهر
+
+733
+01:17:48,770 --> 01:17:53,410
+مين؟ المشتقة الأولى حتى أقول من الرتبة .. من جهة
+
+734
+01:17:53,410 --> 01:17:56,090
+الرتبة الأولى، التانية، التالتة، الرابعة، بنفع
+
+735
+01:17:56,090 --> 01:18:00,610
+أقول من الرتبة رقم ناقص تلاتة؟ كيف رتبة ناقص
+
+736
+01:18:00,610 --> 01:18:06,370
+تلاتة؟ هي في تفاضل بنزل نزول؟ طيب حالتك تلاقي سؤال
+
+737
+01:18:06,370 --> 01:18:13,040
+تاني؟خلاص يبقى ان شاء الله يوم الأثنين بدنا نبدأ
+
+738
+01:18:13,040 --> 01:18:16,480
+يا بنات في ال first order differential equation
+
+739
+01:18:16,480 --> 01:18:22,680
+ياريت اتحضريلي اول section او اول two sections من
+
+740
+01:18:22,680 --> 01:18:26,860
+chapter اتنين اللي هو تبدأ بال linear و اللي بعده
+
+741
+01:18:26,860 --> 01:18:29,780
+ماشي ان شاء الله و تعالى يعطيكوا العافية
+
diff --git a/PL9fwy3NUQKwa8ZDfSFGn6H8xVFLzqmCZC/dANTZFG0kHA_raw.json b/PL9fwy3NUQKwa8ZDfSFGn6H8xVFLzqmCZC/dANTZFG0kHA_raw.json
new file mode 100644
index 0000000000000000000000000000000000000000..e3c6cdf4573ec2d6f93839f8e16e0742d8e80de4
--- /dev/null
+++ b/PL9fwy3NUQKwa8ZDfSFGn6H8xVFLzqmCZC/dANTZFG0kHA_raw.json
@@ -0,0 +1 @@
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"probability": 0.95166015625}, {"start": 1054.09, "end": 1054.55, "word": " عادي", "probability": 0.8551432291666666}], "temperature": 1.0}, {"id": 44, "seek": 108184, "start": 1055.11, "end": 1081.85, "text": "هذه المعادلة بدأت تقول إنها ليست لدي حل لأنها ليست موجودة في الزمان لكن لما درسنا الكميات التخيولية أو ال complex numbers الأعداد المركبة صارنا بنقدر نحلها وبالتالي بصير عندنا ثلاث حالات زي ما انتوا شايفينها في كل حالة من الحالات الثلاث بصير المعادلة التفاضلية هذه لها صورة معينة لميم", "tokens": [3224, 24192, 9673, 3615, 18513, 37977, 47525, 10721, 2655, 6055, 39648, 36145, 11296, 32239, 14851, 5296, 16254, 11331, 1211, 5296, 33456, 11296, 32239, 14851, 3714, 29245, 23328, 3660, 8978, 6024, 110, 2304, 7649, 44381, 5296, 15042, 11778, 2288, 3794, 8315, 33251, 2304, 1829, 9307, 16712, 9778, 1829, 12610, 10632, 34051, 2423, 3997, 3547, 16247, 22488, 18513, 9673, 31747, 49401, 20328, 9640, 8315, 44945, 28543, 2288, 8717, 5016, 1211, 11296, 46599, 6027, 2655, 6027, 1829, 4724, 9381, 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{"start": 1056.89, "end": 1056.99, "word": " لدي", "probability": 0.6551513671875}, {"start": 1056.99, "end": 1057.49, "word": " حل", "probability": 0.922119140625}, {"start": 1057.49, "end": 1058.67, "word": " لأنها", "probability": 0.2719319661458333}, {"start": 1058.67, "end": 1059.03, "word": " ليست", "probability": 0.78125}, {"start": 1059.03, "end": 1059.49, "word": " موجودة", "probability": 0.7674560546875}, {"start": 1059.49, "end": 1059.69, "word": " في", "probability": 0.3935546875}, {"start": 1059.69, "end": 1060.15, "word": " الزمان", "probability": 0.8310546875}, {"start": 1060.15, "end": 1061.13, "word": " لكن", "probability": 0.415283203125}, {"start": 1061.13, "end": 1061.47, "word": " لما", "probability": 0.7012939453125}, {"start": 1061.47, "end": 1061.95, "word": " درسنا", "probability": 0.885498046875}, {"start": 1061.95, "end": 1062.55, "word": " الكميات", "probability": 0.80352783203125}, {"start": 1062.55, "end": 1063.45, "word": " التخيولية", "probability": 0.8173828125}, {"start": 1063.45, "end": 1063.61, "word": " أو", "probability": 0.65087890625}, {"start": 1063.61, "end": 1063.77, "word": " ال", "probability": 0.52685546875}, {"start": 1063.77, "end": 1064.33, "word": " complex", "probability": 0.53955078125}, {"start": 1064.33, "end": 1065.27, "word": " numbers", "probability": 0.66064453125}, {"start": 1065.27, "end": 1066.27, "word": " الأعداد", "probability": 0.7073974609375}, {"start": 1066.27, "end": 1066.97, "word": " المركبة", "probability": 0.85791015625}, {"start": 1066.97, "end": 1067.39, "word": " صارنا", "probability": 0.4803059895833333}, {"start": 1067.39, "end": 1068.11, "word": " بنقدر", "probability": 0.7738444010416666}, {"start": 1068.11, "end": 1069.07, "word": " نحلها", "probability": 0.8289794921875}, {"start": 1069.07, "end": 1069.85, "word": " وبالتالي", "probability": 0.95107421875}, {"start": 1069.85, "end": 1070.47, "word": " بصير", "probability": 0.7493489583333334}, {"start": 1070.47, "end": 1070.99, "word": " عندنا", "probability": 0.894775390625}, {"start": 1070.99, "end": 1071.71, "word": " ثلاث", "probability": 0.9090576171875}, {"start": 1071.71, "end": 1072.41, "word": " حالات", "probability": 0.9737955729166666}, {"start": 1072.41, "end": 1072.77, "word": " زي", "probability": 0.840087890625}, {"start": 1072.77, "end": 1072.85, "word": " ما", "probability": 0.970703125}, {"start": 1072.85, "end": 1073.03, "word": " انتوا", "probability": 0.7386067708333334}, {"start": 1073.03, "end": 1073.93, "word": " شايفينها", "probability": 0.87890625}, {"start": 1073.93, "end": 1074.13, "word": " في", "probability": 0.8486328125}, {"start": 1074.13, "end": 1074.79, "word": " كل", "probability": 0.97802734375}, {"start": 1074.79, "end": 1075.29, "word": " حالة", "probability": 0.9952799479166666}, {"start": 1075.29, "end": 1075.45, "word": " من", "probability": 0.9931640625}, {"start": 1075.45, "end": 1076.07, "word": " الحالات", "probability": 0.7960611979166666}, {"start": 1076.07, "end": 1076.73, "word": " الثلاث", "probability": 0.96328125}, {"start": 1076.73, "end": 1077.53, "word": " بصير", "probability": 0.9352213541666666}, {"start": 1077.53, "end": 1078.19, "word": " المعادلة", "probability": 0.991943359375}, {"start": 1078.19, "end": 1079.13, "word": " التفاضلية", "probability": 0.89287109375}, {"start": 1079.13, "end": 1079.53, "word": " هذه", "probability": 0.68505859375}, {"start": 1079.53, "end": 1080.11, "word": " لها", "probability": 0.965087890625}, {"start": 1080.11, "end": 1080.79, "word": " صورة", "probability": 0.9959309895833334}, {"start": 1080.79, "end": 1081.39, "word": " معينة", "probability": 0.9777018229166666}, {"start": 1081.39, "end": 1081.85, "word": " لميم", "probability": 0.591064453125}], "temperature": 1.0}, {"id": 45, "seek": 110429, "start": 1082.11, "end": 1104.29, "text": "للحل يبقى بنعرف صورة الحل في الحالة الأولى صورة الحل في الحالة التانية صورة الحل في الحالة الثالثة ثالثة وبالتالي عرفنا حل ال homogeneous differential equations تمام هذا قلنا لو كانت constants تمام طب لو ماكانوش constants", "tokens": [1211, 1211, 5016, 1211, 7251, 3555, 4587, 7578, 44945, 3615, 28480, 20328, 13063, 3660, 21542, 1211, 8978, 21542, 6027, 3660, 16247, 12610, 7578, 20328, 13063, 3660, 21542, 1211, 8978, 21542, 6027, 3660, 16712, 7649, 10632, 20328, 13063, 3660, 21542, 1211, 8978, 21542, 6027, 3660, 6024, 104, 6027, 12984, 3660, 38637, 6027, 12984, 3660, 46599, 6027, 2655, 6027, 1829, 6225, 28480, 8315, 11331, 1211, 2423, 42632, 15756, 11787, 46811, 10943, 23758, 12174, 1211, 8315, 45164, 25961, 2655, 35870, 46811, 10943, 23032, 3555, 45164, 19446, 41361, 2407, 8592, 35870], "avg_logprob": -0.14994673651050439, "compression_ratio": 1.9777777777777779, "no_speech_prob": 0.0, "words": [{"start": 1082.11, "end": 1083.25, "word": "للحل", "probability": 0.72845458984375}, {"start": 1083.25, "end": 1084.11, "word": " يبقى", "probability": 0.9298095703125}, {"start": 1084.11, "end": 1084.55, "word": " بنعرف", "probability": 0.91552734375}, {"start": 1084.55, "end": 1084.87, "word": " صورة", "probability": 0.9142252604166666}, {"start": 1084.87, "end": 1085.25, "word": " الحل", "probability": 0.963623046875}, {"start": 1085.25, "end": 1085.41, "word": " في", "probability": 0.84228515625}, {"start": 1085.41, "end": 1085.83, "word": " الحالة", "probability": 0.9044596354166666}, {"start": 1085.83, "end": 1086.27, "word": " الأولى", "probability": 0.9581705729166666}, {"start": 1086.27, "end": 1086.89, "word": " صورة", "probability": 0.8486328125}, {"start": 1086.89, "end": 1087.29, "word": " الحل", "probability": 0.9775390625}, {"start": 1087.29, "end": 1087.43, "word": " في", "probability": 0.955078125}, {"start": 1087.43, "end": 1087.83, "word": " الحالة", "probability": 0.9744466145833334}, {"start": 1087.83, "end": 1088.25, "word": " التانية", "probability": 0.8912760416666666}, {"start": 1088.25, "end": 1088.85, "word": " صورة", "probability": 0.9689127604166666}, {"start": 1088.85, "end": 1089.23, "word": " الحل", "probability": 0.9697265625}, {"start": 1089.23, "end": 1089.37, "word": " في", "probability": 0.95751953125}, {"start": 1089.37, "end": 1089.83, "word": " الحالة", "probability": 0.9879557291666666}, {"start": 1089.83, "end": 1090.45, "word": " الثالثة", "probability": 0.9265625}, {"start": 1090.45, "end": 1091.13, "word": " ثالثة", "probability": 0.82391357421875}, {"start": 1091.13, "end": 1091.97, "word": " وبالتالي", "probability": 0.91708984375}, {"start": 1091.97, "end": 1092.47, "word": " عرفنا", "probability": 0.9783528645833334}, {"start": 1092.47, "end": 1093.05, "word": " حل", "probability": 0.957275390625}, {"start": 1093.05, "end": 1093.19, "word": " ال", "probability": 0.9892578125}, {"start": 1093.19, "end": 1093.89, "word": " homogeneous", "probability": 0.50390625}, {"start": 1093.89, "end": 1095.03, "word": " differential", "probability": 0.853515625}, {"start": 1095.03, "end": 1096.95, "word": " equations", "probability": 0.78271484375}, {"start": 1096.95, "end": 1097.89, "word": " تمام", "probability": 0.80810546875}, {"start": 1097.89, "end": 1098.77, "word": " هذا", "probability": 0.6357421875}, {"start": 1098.77, "end": 1099.23, "word": " قلنا", "probability": 0.68603515625}, {"start": 1099.23, "end": 1099.49, "word": " لو", "probability": 0.97314453125}, {"start": 1099.49, "end": 1100.27, "word": " كانت", "probability": 0.98779296875}, {"start": 1100.27, "end": 1100.95, "word": " constants", "probability": 0.7626953125}, {"start": 1100.95, "end": 1102.31, "word": " تمام", "probability": 0.8291015625}, {"start": 1102.31, "end": 1102.89, "word": " طب", "probability": 0.732421875}, {"start": 1102.89, "end": 1103.11, "word": " لو", "probability": 0.97021484375}, {"start": 1103.11, "end": 1103.71, "word": " ماكانوش", "probability": 0.7913818359375}, {"start": 1103.71, "end": 1104.29, "word": " constants", "probability": 0.96337890625}], "temperature": 1.0}, {"id": 46, "seek": 113534, "start": 1105.95, "end": 1135.35, "text": "لو هذا حصل انه مش constants والحلول كانت real and equal repeated roots بنسميها الحلول المكررة بند real and equal بنختصرها بعض الكتب إلى repeated roots repeated أو real and equal سيان هذه الكلمة بدأ real and equal كويس؟", "tokens": [1211, 2407, 23758, 11331, 36520, 16472, 3224, 37893, 35870, 16070, 5016, 1211, 12610, 25961, 2655, 957, 293, 2681, 10477, 10669, 44945, 38251, 1829, 11296, 21542, 1211, 12610, 9673, 37983, 25720, 4724, 41260, 957, 293, 2681, 44945, 46456, 9381, 2288, 11296, 45030, 11242, 33251, 2655, 3555, 30731, 10477, 10669, 10477, 34051, 957, 293, 2681, 8608, 1829, 7649, 29538, 33251, 19528, 3660, 47525, 10721, 957, 293, 2681, 9122, 45865, 3794, 22807], "avg_logprob": -0.2439732185431889, "compression_ratio": 1.7542857142857142, "no_speech_prob": 0.0, "words": [{"start": 1105.95, "end": 1106.35, "word": "لو", "probability": 0.80615234375}, {"start": 1106.35, "end": 1106.81, "word": " هذا", "probability": 0.7724609375}, {"start": 1106.81, "end": 1107.65, "word": " حصل", "probability": 0.849853515625}, {"start": 1107.65, "end": 1108.35, "word": " انه", "probability": 0.76318359375}, {"start": 1108.35, "end": 1108.51, "word": " مش", "probability": 0.80859375}, {"start": 1108.51, "end": 1109.25, "word": " constants", "probability": 0.496826171875}, {"start": 1109.25, "end": 1110.67, "word": " والحلول", "probability": 0.84844970703125}, {"start": 1110.67, "end": 1111.31, "word": " كانت", "probability": 0.948486328125}, {"start": 1111.31, "end": 1111.55, "word": " real", "probability": 0.873046875}, {"start": 1111.55, "end": 1112.25, "word": " and", "probability": 0.9404296875}, {"start": 1112.25, "end": 1113.19, "word": " equal", "probability": 0.8740234375}, {"start": 1113.19, "end": 1114.53, "word": " repeated", "probability": 0.73876953125}, {"start": 1114.53, "end": 1115.23, "word": " roots", "probability": 0.77294921875}, {"start": 1115.23, "end": 1115.85, "word": " بنسميها", "probability": 0.8123779296875}, {"start": 1115.85, "end": 1116.65, "word": " الحلول", "probability": 0.99169921875}, {"start": 1116.65, "end": 1117.69, "word": " المكررة", "probability": 0.9490559895833334}, {"start": 1117.69, "end": 1118.43, "word": " بند", "probability": 0.2779541015625}, {"start": 1118.43, "end": 1118.79, "word": " real", "probability": 0.91552734375}, {"start": 1118.79, "end": 1119.29, "word": " and", "probability": 0.955078125}, {"start": 1119.29, "end": 1119.73, "word": " equal", "probability": 0.904296875}, {"start": 1119.73, "end": 1121.07, "word": " بنختصرها", "probability": 0.90224609375}, {"start": 1121.07, "end": 1121.45, "word": " بعض", "probability": 0.6357421875}, {"start": 1121.45, "end": 1121.75, "word": " الكتب", "probability": 0.97705078125}, {"start": 1121.75, "end": 1122.43, "word": " إلى", "probability": 0.1988525390625}, {"start": 1122.43, "end": 1123.41, "word": " repeated", "probability": 0.96435546875}, {"start": 1123.41, "end": 1125.05, "word": " roots", "probability": 0.8798828125}, {"start": 1125.05, "end": 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يبقى هذه هي الطرق الثلاث لحل المعادلة التفاضلية اللي احنا درسها في chapter 3 ابناجي ل chapter 4", "tokens": [265, 40335, 295, 1668, 11, 12393, 31994, 11, 12990, 295, 9834, 7251, 3555, 4587, 7578, 29538, 39896, 41950, 2288, 4587, 6024, 104, 1211, 5718, 104, 5296, 5016, 1211, 9673, 3615, 18513, 37977, 16712, 5172, 46958, 1211, 10632, 13672, 1829, 1975, 5016, 8315, 11778, 2288, 3794, 11296, 8978, 7187, 805, 48127, 1863, 26108, 1829, 5296, 7187, 1017], "avg_logprob": -0.23725329574785733, "compression_ratio": 1.3630952380952381, "no_speech_prob": 0.0, "words": [{"start": 1452.31, "end": 1452.97, "word": "reduction", "probability": 0.489227294921875}, {"start": 1452.97, "end": 1453.27, "word": " of", "probability": 0.9658203125}, {"start": 1453.27, "end": 1453.79, "word": " order,", "probability": 0.91064453125}, {"start": 1454.23, "end": 1454.87, "word": " entertainment", "probability": 0.423828125}, {"start": 1454.87, "end": 1455.91, "word": " coefficients,", "probability": 0.5654296875}, 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اتنين اربعة فما فوق فشبتر اربعة شبتر اربعة اسمه higher order differential equations", "tokens": [3555, 1863, 47283, 3215, 9673, 3615, 18513, 37977, 9154, 34892, 2655, 49401, 16712, 6027, 2655, 3660, 9154, 34892, 2655, 49401, 34892, 16758, 27884, 9154, 33962, 2304, 3794, 3660, 9154, 34892, 2655, 49401, 28239, 11536, 10632, 294, 2674, 7251, 3555, 4587, 7578, 29538, 24525, 2304, 11296, 2946, 1668, 15756, 11787, 9673, 3615, 18513, 37977, 16712, 5172, 46958, 1211, 10632, 9154, 34892, 2655, 3555, 18863, 20292, 995, 37495, 22653, 1975, 4117, 2655, 2288, 9154, 1975, 2655, 1863, 9957, 1975, 25513, 27884, 6156, 15042, 6156, 30543, 6156, 8592, 3555, 2655, 2288, 1975, 25513, 27884, 13412, 3555, 2655, 2288, 1975, 25513, 27884, 24525, 2304, 3224, 2946, 1668, 15756, 11787], "avg_logprob": -0.17216981581921847, "compression_ratio": 2.1776649746192893, "no_speech_prob": 0.0, "words": [{"start": 1494.33, "end": 1494.81, "word": "بناخد", "probability": 0.611480712890625}, {"start": 1494.81, "end": 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1543.41, "end": 1544.19, "word": " يبقى", "probability": 0.909912109375}, {"start": 1544.19, "end": 1545.61, "word": " هنقسمه", "probability": 0.9529296875}, {"start": 1545.61, "end": 1546.21, "word": " الى", "probability": 0.718994140625}, {"start": 1546.21, "end": 1546.83, "word": " homogeneous", "probability": 0.89990234375}], "temperature": 1.0}, {"id": 62, "seek": 157345, "start": 1561.71, "end": 1573.45, "text": "نفس هذا الـ characteristic equation اللي على الشكل اللي عندنا هدا هدا هيك هتصير معادلة بس بيصير من الرتبة النونية تمام", "tokens": [1863, 36178, 23758, 2423, 39184, 16282, 5367, 13672, 1829, 15844, 25124, 28820, 13672, 1829, 43242, 8315, 8032, 28259, 8032, 28259, 39896, 4117, 8032, 2655, 9381, 13546, 20449, 18513, 37977, 4724, 3794, 4724, 1829, 9381, 13546, 9154, 34892, 2655, 49401, 28239, 11536, 10632, 46811, 10943], "avg_logprob": -0.3543402804268731, "compression_ratio": 1.4370370370370371, "no_speech_prob": 0.0, "words": [{"start": 1561.71, "end": 1562.63, "word": 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ترانسفورم والتعريف هذا يعتمد على الـ improper integrals يعني هو تكامل من صفر لما لا نهاية ل EOSST مضروب في ال function اللى بدنا نوجد لها لابلاس ترانسفورم بدنا نكامل حصل الدرب هذا", "tokens": [9566, 3555, 3615, 995, 7251, 3555, 4587, 7578, 5551, 12610, 13412, 17082, 37977, 8717, 3615, 9566, 1829, 37279, 16572, 5172, 5296, 15040, 3555, 15040, 3794, 6055, 2288, 7649, 3794, 5172, 13063, 2304, 16070, 2655, 3615, 16572, 5172, 23758, 7251, 34268, 2304, 3215, 15844, 2423, 39184, 40651, 3572, 1124, 37495, 22653, 31439, 6055, 4117, 10943, 1211, 9154, 20328, 5172, 2288, 5296, 15042, 20193, 8717, 11296, 10632, 5296, 462, 4367, 6840, 3714, 11242, 32887, 3555, 8978, 2423, 2445, 13672, 7578, 47525, 8315, 8717, 29245, 3215, 5296, 11296, 5296, 16758, 15040, 3794, 6055, 2288, 7649, 3794, 5172, 13063, 2304, 47525, 8315, 8717, 4117, 10943, 1211, 11331, 36520, 32748, 25513, 23758], "avg_logprob": -0.3356481536670967, "compression_ratio": 1.6079295154185023, "no_speech_prob": 0.0, "words": [{"start": 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[41185, 9673, 28543, 46007, 6055, 3555, 3615, 9673, 3615, 18513, 1211, 9307, 16712, 5172, 46958, 1211, 10632], "avg_logprob": -0.19292534473869535, "compression_ratio": 1.0666666666666667, "no_speech_prob": 4.76837158203125e-07, "words": [{"start": 2098.1, "end": 2098.64, "word": "في", "probability": 0.323486328125}, {"start": 2098.64, "end": 2099.7, "word": " المقدمة", "probability": 0.9427083333333334}, {"start": 2099.7, "end": 2100.0, "word": " تبع", "probability": 0.73291015625}, {"start": 2100.0, "end": 2101.18, "word": " المعادلات", "probability": 0.93466796875}, {"start": 2101.18, "end": 2103.22, "word": " التفاضلية", "probability": 0.90693359375}], "temperature": 1.0}, {"id": 86, "seek": 221537, "start": 2210.93, "end": 2215.37, "text": "الدالة المجهولة اسمها", "tokens": [6027, 3215, 6027, 3660, 9673, 7435, 3224, 12610, 3660, 24525, 2304, 11296], "avg_logprob": -0.49939903846153844, "compression_ratio": 1.0, "no_speech_prob": 0.0, "words": [{"start": 2210.93, "end": 2212.33, "word": "الدالة", "probability": 0.6435394287109375}, {"start": 2212.33, "end": 2213.73, "word": " المجهولة", "probability": 0.959765625}, {"start": 2213.73, "end": 2215.37, "word": " اسمها", "probability": 0.66864013671875}], "temperature": 1.0}, {"id": 87, "seek": 222196, "start": 2217.73, "end": 2221.97, "text": "هي تسمى كتابة مقارنة", "tokens": [3224, 1829, 6055, 38251, 7578, 9122, 2655, 16758, 3660, 3714, 4587, 9640, 1863, 3660], "avg_logprob": -0.7604166587193807, "compression_ratio": 0.8604651162790697, "no_speech_prob": 0.0, "words": [{"start": 2217.73, "end": 2218.21, "word": "هي", "probability": 0.2838134765625}, {"start": 2218.21, "end": 2218.85, "word": " تسمى", "probability": 0.6256510416666666}, {"start": 2218.85, "end": 2220.61, "word": " كتابة", "probability": 0.6181488037109375}, {"start": 2220.61, "end": 2221.97, "word": " مقارنة", "probability": 0.58748779296875}], "temperature": 1.0}, {"id": 88, "seek": 226859, "start": 2240.39, "end": 2268.59, "text": "يبقى an equation المعادلة contains تحتوي أو تشتمل one or more derivatives يعني فيها المشتقة الأولى او التانية او اكثر التالتة او الرابعة او ما إلى ذلك of a non function لدالة مجهولة is called a differential equation for example نعطي مثال لو روح نقولنا why", "tokens": [1829, 3555, 4587, 7578, 364, 5367, 9673, 3615, 18513, 37977, 8306, 6055, 33753, 45865, 34051, 6055, 8592, 39237, 1211, 472, 420, 544, 33733, 37495, 22653, 8978, 11296, 9673, 8592, 2655, 28671, 16247, 12610, 7578, 1975, 2407, 16712, 7649, 10632, 1975, 2407, 1975, 4117, 49115, 16712, 6027, 2655, 3660, 1975, 2407, 34892, 16758, 27884, 1975, 2407, 19446, 30731, 29910, 23275, 295, 257, 2107, 2445, 5296, 3215, 6027, 3660, 3714, 7435, 3224, 12610, 3660, 307, 1219, 257, 15756, 5367, 337, 1365, 8717, 3615, 9566, 1829, 50113, 6027, 45164, 12602, 2407, 5016, 8717, 39648, 8315, 983], "avg_logprob": -0.18118351475989564, "compression_ratio": 1.5267489711934157, "no_speech_prob": 0.0, "words": [{"start": 2240.39, "end": 2240.93, "word": 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differential او تساوي T مثلا is a differential equation", "tokens": [3555, 16758, 20292, 5835, 30767, 16373, 3215, 50113, 15040, 16490, 2304, 3794, 3660, 288, 5835, 30767, 16373, 3215, 8608, 2655, 3660, 288, 6055, 3794, 995, 45865, 30767, 13546, 2407, 50113, 15040, 307, 257, 15756, 1975, 2407, 6055, 3794, 995, 45865, 314, 50113, 15040, 307, 257, 15756, 5367], "avg_logprob": -0.26318359064559144, "compression_ratio": 1.4912280701754386, "no_speech_prob": 0.0, "words": [{"start": 2269.35, "end": 2270.13, "word": "بابلي", "probability": 0.2746988932291667}, {"start": 2270.13, "end": 2270.73, "word": " prime", "probability": 0.24560546875}, {"start": 2270.73, "end": 2272.01, "word": " زائد", "probability": 0.6537272135416666}, {"start": 2272.01, "end": 2272.59, "word": " مثلا", "probability": 0.926513671875}, {"start": 2272.59, "end": 2273.75, "word": " خمسة", "probability": 0.9539794921875}, {"start": 2273.75, "end": 2274.27, "word": " y", "probability": 0.6435546875}, {"start": 2274.27, 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"end": 2286.15, "word": " T", "probability": 0.7236328125}, {"start": 2286.15, "end": 2286.71, "word": " مثلا", "probability": 0.98193359375}, {"start": 2286.71, "end": 2287.61, "word": " is", "probability": 0.90234375}, {"start": 2287.61, "end": 2288.33, "word": " a", "probability": 0.98779296875}, {"start": 2288.33, "end": 2289.57, "word": " differential", "probability": 0.8564453125}, {"start": 2289.57, "end": 2290.97, "word": " equation", "probability": 0.98388671875}], "temperature": 1.0}, {"id": 90, "seek": 232710, "start": 2300.94, "end": 2327.1, "text": "يبقى مرة تانية an equation contains المعادلة اللى تحتوي أو تجتمل على مشتقة أولى او اكثر مشتقة تانية او تالتة او رابعة او خمسة او الاخرى لمجهول ده اللى مجهول is called a differential equation طلعلي في المعادلة اللى عندنا هذه هل احنا عارفين شكل ال Y", "tokens": [1829, 3555, 4587, 7578, 3714, 25720, 6055, 7649, 10632, 364, 5367, 8306, 9673, 3615, 18513, 37977, 13672, 7578, 6055, 33753, 45865, 34051, 6055, 7435, 39237, 1211, 15844, 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"probability": 0.91455078125}, {"start": 2821.28, "end": 2822.32, "word": " اتنين", "probability": 0.9163818359375}], "temperature": 1.0}, {"id": 110, "seek": 283923, "start": 2822.75, "end": 2839.23, "text": "دي واي على دي ت أربع زائد واي تساوي ت لإن ت is of the", "tokens": [16254, 4032, 47302, 15844, 11778, 1829, 6055, 5551, 25513, 3615, 30767, 16373, 3215, 4032, 47302, 6055, 3794, 995, 45865, 6055, 5296, 28814, 1863, 6055, 307, 295, 264], "avg_logprob": -0.4400111490062305, "compression_ratio": 1.0897435897435896, "no_speech_prob": 0.0, "words": [{"start": 2822.75, "end": 2823.27, "word": "دي", "probability": 0.06512451171875}, {"start": 2823.27, "end": 2823.97, "word": " واي", "probability": 0.638671875}, {"start": 2823.97, "end": 2824.97, "word": " على", "probability": 0.34716796875}, {"start": 2824.97, "end": 2825.59, "word": " دي", "probability": 0.895751953125}, {"start": 2825.59, "end": 2825.95, "word": " ت", "probability": 0.52685546875}, {"start": 2825.95, "end": 2827.39, 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4705.04, "word": " هو", "probability": 0.54736328125}, {"start": 4705.04, "end": 4705.34, "word": " تبدأ", "probability": 0.91943359375}, {"start": 4705.34, "end": 4705.54, "word": " بال", "probability": 0.9619140625}, {"start": 4705.54, "end": 4705.9, "word": " linear", "probability": 0.76416015625}, {"start": 4705.9, "end": 4706.1, "word": " و", "probability": 0.6298828125}, {"start": 4706.1, "end": 4706.24, "word": " اللي", "probability": 0.910888671875}, {"start": 4706.24, "end": 4706.86, "word": " بعده", "probability": 0.868896484375}, {"start": 4706.86, "end": 4707.92, "word": " ماشي", "probability": 0.8209635416666666}, {"start": 4707.92, "end": 4708.32, "word": " ان", "probability": 0.59716796875}, {"start": 4708.32, "end": 4708.52, "word": " شاء", "probability": 0.984619140625}, {"start": 4708.52, "end": 4708.7, "word": " الله", "probability": 0.96875}, {"start": 4708.7, "end": 4708.88, "word": " و", "probability": 0.467529296875}, {"start": 4708.88, "end": 4709.0, "word": " 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\ No newline at end of file
diff --git a/PL9fwy3NUQKwa8ZDfSFGn6H8xVFLzqmCZC/dANTZFG0kHA_raw.srt b/PL9fwy3NUQKwa8ZDfSFGn6H8xVFLzqmCZC/dANTZFG0kHA_raw.srt
new file mode 100644
index 0000000000000000000000000000000000000000..5fc505d9da93db6b6757f70d594d97e000a2ff57
--- /dev/null
+++ b/PL9fwy3NUQKwa8ZDfSFGn6H8xVFLzqmCZC/dANTZFG0kHA_raw.srt
@@ -0,0 +1,2996 @@
+1
+00:00:17,140 --> 00:00:21,380
+الكتاب المقرر هو elementary differential equations
+
+2
+00:00:21,380 --> 00:00:25,620
+and boundary value problems الطبعة هي الطبعة
+
+3
+00:00:25,620 --> 00:00:34,110
+الثامنةالمؤلفان William Boyce and Richard Brima ال
+
+4
+00:00:34,110 --> 00:00:38,190
+chapters المقررة من هذا الكتاب ابتداء من section 1
+
+5
+00:00:38,190 --> 00:00:46,430
+وحتى section 6 يبقى ستة كاشن سندرسها خلال هذا
+
+6
+00:00:46,430 --> 00:00:52,540
+الفصل ان شاء الله تبارك وتعالىالمراجع لهذا الكتاب
+
+7
+00:00:52,540 --> 00:00:56,600
+لو روحت المكتب اي كتاب في المعادلة التفاضلي
+
+8
+00:00:56,600 --> 00:01:00,320
+الموجود في المكتب عندنا والحمد لله فيها بدأ الكتاب
+
+9
+00:01:00,320 --> 00:01:06,160
+عشرة لمؤلفين مختلفين كله ممكن اه ممكن يكون مرجع
+
+10
+00:01:06,160 --> 00:01:12,600
+معاكي ترجعيله وقت ما شئتي نجي ل chapter one يبقى
+
+11
+00:01:12,600 --> 00:01:17,080
+نجي لأول chapter اللي هو chapter one
+
+12
+00:01:26,790 --> 00:01:34,990
+introduction introduction يعني مقدمة في هذه
+
+13
+00:01:34,990 --> 00:01:41,430
+المقدمة سنعطي بعض المفاهيم الأساسية يعني ذلك ما
+
+14
+00:01:41,430 --> 00:01:48,540
+معنى معادلة تفاضلية ما معنى معادلة تفاضلية عاديةما
+
+15
+00:01:48,540 --> 00:01:52,760
+معنى رتبة المعادلة التفاضلية طبعا احنا لدرجة في
+
+16
+00:01:52,760 --> 00:01:58,300
+دماغنا قبل ذلك درجة المعادلة هذه درجة المعادلة
+
+17
+00:01:58,300 --> 00:02:01,820
+العادية من الدرجة التانية التالتة لأ احنا فيه
+
+18
+00:02:01,820 --> 00:02:06,880
+عندنا هنا رتبة المعادلة التفاضلية والرتبة تعتمد
+
+19
+00:02:06,880 --> 00:02:11,040
+على المشتقة الأولى والمشتقة التانية والمشتقة
+
+20
+00:02:11,040 --> 00:02:16,570
+التالتة او الرابعة او النونيةالتي تظهر في المعادلة
+
+21
+00:02:16,570 --> 00:02:21,830
+التفاضلية يبقى هذا مثلا ما نسميه برتبة المعادلة
+
+22
+00:02:21,830 --> 00:02:28,910
+التفاضلية وهذا ما سنعرفه بعد قليل هنعرف كمان ما هو
+
+23
+00:02:28,910 --> 00:02:34,150
+solution للمعادلة التفاضلية ما هو حل المعادلة
+
+24
+00:02:34,150 --> 00:02:42,110
+التفاضلية ما هو الحل العام للمعادلة التفاضليةما هي
+
+25
+00:02:42,110 --> 00:02:47,750
+ال initial value problems يعني معادلة تفاضلية و
+
+26
+00:02:47,750 --> 00:02:52,310
+عليها شروط بنسميها الشروط الابتدائية او ال initial
+
+27
+00:02:52,310 --> 00:02:57,530
+conditions فإن وجدت معادلة تفاضلية بشروط عليها
+
+28
+00:02:57,530 --> 00:03:02,480
+بنسميها initial value problemsأما عن أنواع
+
+29
+00:03:02,480 --> 00:03:07,280
+المعادلات فهذا ما سنتعرض له في ال chapters بعد ذلك
+
+30
+00:03:07,280 --> 00:03:10,640
+يعني بديش أقوله في ال introduction و أروح أعيده
+
+31
+00:03:10,640 --> 00:03:15,700
+مرة ثانية لأ بنخليه كل واحد في موقعه بنعرف شو يعني
+
+32
+00:03:15,700 --> 00:03:19,660
+linear differential equation ما هي non-linear
+
+33
+00:03:19,660 --> 00:03:23,120
+differential equationsأنواع ال linear differential
+
+34
+00:03:23,120 --> 00:03:27,600
+equations إلى آخرى يبقى هذا مثلا اتعرض له في حينه
+
+35
+00:03:27,600 --> 00:03:31,920
+يبقى زي ما تشوفين في ال introduction مكتوب عندكم
+
+36
+00:03:31,920 --> 00:03:35,280
+في الكتابة على شكل three sections احنا ال three
+
+37
+00:03:35,280 --> 00:03:39,220
+sections يمكن نجمعهم لك بس في صفحتين لأن هذي
+
+38
+00:03:39,220 --> 00:03:44,000
+مقدمات بس بدنا الطالب يعرفها حتى نقدر نشتغل في من؟
+
+39
+00:03:44,000 --> 00:03:47,780
+في ال sections اللي بعديها ان شاء الله تبارك
+
+40
+00:03:47,780 --> 00:03:58,440
+وتعالىبنجي بعد هيك ل chapter 2 اللي
+
+41
+00:03:58,440 --> 00:04:07,980
+هو first order differential equations
+
+42
+00:04:11,130 --> 00:04:14,710
+كلمة differential خلال المساق هذا كله يجب ان
+
+43
+00:04:14,710 --> 00:04:22,950
+اختصرها الى DIFF Equations هختصرها الى EQNS يبقى
+
+44
+00:04:22,950 --> 00:04:27,090
+هذه اختصار كلمة differential equations
+
+45
+00:04:29,310 --> 00:04:34,070
+الـ first order يعني المعادلة التفاضلية من الرتبة
+
+46
+00:04:34,070 --> 00:04:40,050
+الأولى هذه هندرس فيها مجموعة من المعادلات اللي
+
+47
+00:04:40,050 --> 00:04:43,610
+كلهم من الرتبة الأولى حاجة اسمها ال linear
+
+48
+00:04:43,610 --> 00:04:49,120
+differential equationsالمعادلة التفاضلية الخطية
+
+49
+00:04:49,120 --> 00:04:54,120
+حاجة اسمها separable equations يعني المعادلات اللى
+
+50
+00:04:54,120 --> 00:04:59,200
+فيها بدنا نفصل المتغيرات ال exact equations
+
+51
+00:04:59,200 --> 00:05:02,700
+المعادلات التامة ال homogeneous equations
+
+52
+00:05:02,700 --> 00:05:08,340
+المعادلات المتجانسة يبقى خلال هذا ال chapter بدنا
+
+53
+00:05:08,340 --> 00:05:17,970
+ندرس ما يأتي ال linear equationsالمعادلات الخطية
+
+54
+00:05:17,970 --> 00:05:24,350
+separable equations
+
+55
+00:05:24,350 --> 00:05:29,030
+separable
+
+56
+00:05:29,030 --> 00:05:33,650
+جاء من كلمة separate منفصل يبقى separable
+
+57
+00:05:33,650 --> 00:05:38,730
+equations هي المعادلات اللي نقدر نفصل فيها متغيرات
+
+58
+00:05:38,730 --> 00:05:42,930
+في شجةوالمتغير الآخر في الشجرة التانية يعني بيكون
+
+59
+00:05:42,930 --> 00:05:48,890
+فيها متغيرين بنفس أحدهم في ناحية والمتغير الآخر في
+
+60
+00:05:48,890 --> 00:05:53,110
+ناحية أخرى يبقى هذا اللي بنسميها separable
+
+61
+00:05:53,110 --> 00:06:00,130
+equations فينا حاجة اسمها ال exact equations
+
+62
+00:06:00,130 --> 00:06:08,510
+and integrating factors
+
+63
+00:06:14,930 --> 00:06:19,410
+exact equations يعني المعادلات التامة integrating
+
+64
+00:06:19,410 --> 00:06:25,750
+factors عوامل التكامل يعني المعادلة قد تكون exact
+
+65
+00:06:25,750 --> 00:06:31,730
+ويمكن ان نحتاج مقال نيجي نحسبها مالجهاش exact نضرب
+
+66
+00:06:31,730 --> 00:06:37,230
+في دالة ما هذه الدالة بتحولها الى exact equation
+
+67
+00:06:37,230 --> 00:06:43,490
+هذه الدالة بنسميها اش اللي هو عامل التكامل من لهذه
+
+68
+00:06:43,490 --> 00:06:48,090
+المعادلةكيف عمل التكمل هذا بدنا نحصل عليه هذا ما
+
+69
+00:06:48,090 --> 00:06:53,790
+سنشير إليه في حينه ان شاء الله تبارك وتعالى يبقى
+
+70
+00:06:53,790 --> 00:06:57,410
+النوع الثالث هو ال exact equations and integrating
+
+71
+00:06:57,410 --> 00:07:03,230
+factors عندنا كمان حاجة اسمة ال homogeneous
+
+72
+00:07:03,230 --> 00:07:11,630
+different equations المعادلات المتجانسة
+
+73
+00:07:13,800 --> 00:07:19,320
+يبقى هذه الأربعة أنواع من المعادلات التي سنتدرسها
+
+74
+00:07:19,320 --> 00:07:24,540
+في الشابتر الثاني و ال first order differential
+
+75
+00:07:24,540 --> 00:07:29,140
+equation في حد قابلنا يا بنات معادلات ليست على أي
+
+76
+00:07:29,140 --> 00:07:35,240
+نوع من الأربعة الأربعة يعني ليست linear ليست
+
+77
+00:07:35,240 --> 00:07:41,380
+separable ليست exact ليست homogeneous لكن يمكن
+
+78
+00:07:41,820 --> 00:07:48,220
+تحويل هذه المعادلة بطريقة ما إلى أي نوع من الأنواع
+
+79
+00:07:48,220 --> 00:07:52,960
+الأربعة فمثلا في حالة ال linear equations باجي على
+
+80
+00:07:52,960 --> 00:07:57,700
+المعادلة بلاقيها ماهياش linear لكن لو عملت شغل هيك
+
+81
+00:07:57,700 --> 00:08:03,180
+تتحول إلى linear وهذه الشغلة بنسميها حد من الذكراه
+
+82
+00:08:03,180 --> 00:08:08,920
+يا شبنات اللي درسوا قبل ذلك طب احنا بنسميها Bernol
+
+83
+00:08:08,920 --> 00:08:14,470
+equationمعادلة بيرنولي يمكن تحويلها إلى معادلة
+
+84
+00:08:14,470 --> 00:08:18,450
+خطية إلى linear differential equation separable
+
+85
+00:08:18,450 --> 00:08:22,350
+equation يمكن معادلة ما تلاقيهاش separable لكن
+
+86
+00:08:22,350 --> 00:08:27,730
+بتعويضها ما بسيطة يمكن تحويلها إلى separable
+
+87
+00:08:27,730 --> 00:08:32,390
+equation ال exact equation يمكن ما تجباش exact لكن
+
+88
+00:08:32,390 --> 00:08:38,460
+نضربها في عامل التكمل يحويلها إلى مين؟المعادلة
+
+89
+00:08:38,460 --> 00:08:50,440
+الهوموجينية هي المعادلة
+
+90
+00:08:50,440 --> 00:08:56,270
+التي لا تظهر هموجينياوبالتالي الـ homogeneous
+
+91
+00:08:56,270 --> 00:09:00,750
+differential ممكن بعملية ما تبقاش homogeneous لكن
+
+92
+00:09:00,750 --> 00:09:04,350
+نحولها إلى مين؟ إلى homogeneous differential
+
+93
+00:09:04,350 --> 00:09:09,250
+equations هنشوف كيف هنحل المعادلة ده المعادلات هذه
+
+94
+00:09:09,250 --> 00:09:13,350
+لما قلتلك first order يعني لا تظهر في المعادلة إلا
+
+95
+00:09:13,350 --> 00:09:19,000
+المشتقة الأولىيبقى لو كملتها بحصل على حل المعادلة
+
+96
+00:09:19,000 --> 00:09:24,960
+تكامل عادي جدا يعني كل سؤال من مسائل المعادلة تادي
+
+97
+00:09:24,960 --> 00:09:31,200
+بده تكامل ومن هنا قلتك المادة تحتاج أساسا لمين
+
+98
+00:09:31,200 --> 00:09:37,940
+لتكامل بتجي ما عدا عند ال exact equations هذه في
+
+99
+00:09:37,940 --> 00:09:41,260
+حاجة أخدناها في calculus C طبعا بعضكم ماخدتش
+
+100
+00:09:41,260 --> 00:09:45,880
+calculus C مظبوط؟فيه مقداش العدد اشوف ارفعى ده
+
+101
+00:09:45,880 --> 00:09:51,140
+مقداش كال كلصى يعني الرابع ماعناهاش مشكلة اللي
+
+102
+00:09:51,140 --> 00:09:55,780
+مااخدناهوش بكال كلصى هاطولك خلال خمس دقائق يعني
+
+103
+00:09:55,780 --> 00:09:59,320
+اللي اخدت كال كلصى و اللي مااخدت بصيره سيان خمس
+
+104
+00:09:59,320 --> 00:10:04,000
+دقائق بس بفهمك الشيء اللي مطلوب من كال كلصى هو
+
+105
+00:10:04,000 --> 00:10:09,070
+الاشتقاق الجزءىpartial differentiation اللي هو
+
+106
+00:10:09,070 --> 00:10:13,750
+التفاضل الجزء ايه باعطيكيها في خمس دقائق و بتالي
+
+107
+00:10:13,750 --> 00:10:17,590
+ماعناش إشكالية أما يقولوا كده ماخدتيش C بتقدريش
+
+108
+00:10:17,590 --> 00:10:22,690
+تاخده معاكش؟ لأ بتقدري تاخدي و بدون أي مشكلة مافي
+
+109
+00:10:22,690 --> 00:10:27,670
+مشكلة في هذه العالمغير هيك مش هيلزمنا الاشتقاق
+
+110
+00:10:27,670 --> 00:10:31,750
+الجزئي طيلي دراستنا بس بلزمنا في ال section هذا
+
+111
+00:10:31,750 --> 00:10:36,470
+اللي هو ال exact equations and integrating factors
+
+112
+00:10:36,470 --> 00:10:43,670
+فقط لا غير يبقى هذا كل ما سيدرس في main في ال
+
+113
+00:10:43,670 --> 00:10:48,670
+first order linear differential equations بنجي ل
+
+114
+00:10:48,670 --> 00:10:57,810
+charter تلاتة اللي هو secondorder differential
+
+115
+00:10:57,810 --> 00:11:04,510
+equations المعادلة
+
+116
+00:11:04,510 --> 00:11:11,010
+التفاضلية من الرتبة الثانية يعني هيظهر عندنافزي ما
+
+117
+00:11:11,010 --> 00:11:14,310
+ظهر في ال chapter الماضي المشتقة الأولى هيظهر هنا
+
+118
+00:11:14,310 --> 00:11:18,210
+عندنا مين؟ المشتقة الثانية والأولى، بيصيروا
+
+119
+00:11:18,210 --> 00:11:22,610
+التنتين مالهم بيظهروا في المثال وربما ماتظهرش الا
+
+120
+00:11:22,610 --> 00:11:26,690
+المشتقة الثانية فقط، على أي حال الأولى أو الثانية
+
+121
+00:11:26,690 --> 00:11:30,770
+معناها، المشكلة احنا بناخد ال general formالشكل
+
+122
+00:11:30,770 --> 00:11:35,830
+العام وبالتالي الباقي بيكون شيء تخصيصي من الشيء
+
+123
+00:11:35,830 --> 00:11:40,130
+العام يبقى second order differential equations
+
+124
+00:11:40,130 --> 00:11:44,970
+هنجسم المعادلة إلى جزئين المعادلة التفاضلية من
+
+125
+00:11:44,970 --> 00:11:45,950
+الرتبة الثانية
+
+126
+00:11:50,420 --> 00:11:57,300
+المعادلة التفاضلية هي المعادلة
+
+127
+00:11:57,300 --> 00:12:00,820
+التفاضلية هي المعادلة التفاضلية هي المعادلة
+
+128
+00:12:00,820 --> 00:12:02,680
+التفاضلية هي المعادلة التفاضلية هي المعادلة
+
+129
+00:12:02,680 --> 00:12:04,100
+التفاضلية هي المعادلة التفاضلية هي المعادلة
+
+130
+00:12:04,100 --> 00:12:04,220
+التفاضلية هي المعادلة التفاضلية هي المعادلة
+
+131
+00:12:04,220 --> 00:12:04,220
+التفاضلية هي المعادلة التفاضلية هي المعادلة
+
+132
+00:12:04,220 --> 00:12:04,220
+التفاضلية هي المعادلة التفاضلية هي المعادلة
+
+133
+00:12:04,220 --> 00:12:04,220
+التفاضلية هي المعادلة التفاضلية هي المعادلة
+
+134
+00:12:04,220 --> 00:12:04,220
+التفاضلية هي المعادلة التفاضلية هي المعادلة
+
+135
+00:12:04,220 --> 00:12:05,340
+التفاضلية هي المعادلة التفاضلية هي المعادلة
+
+136
+00:12:05,340 --> 00:12:07,600
+التفاضلية هي المعادلة التفاضلية هي المعادلة
+
+137
+00:12:07,600 --> 00:12:09,650
+التفاضلية هي المعادلةهذه بنسميها homogeneous
+
+138
+00:12:09,650 --> 00:12:13,250
+differential equation الـ non homogeneous
+
+139
+00:12:13,250 --> 00:12:15,970
+differential equation المعادلة بالكتابة الكاملة و
+
+140
+00:12:15,970 --> 00:12:20,990
+الطرف اليمين بيكونش zero بيكون function تاني يبقى
+
+141
+00:12:20,990 --> 00:12:24,950
+هذا ال non homogeneous differential equation يبقى
+
+142
+00:12:24,950 --> 00:12:32,150
+هنبدأ أول شغلة بمين؟ بال homogeneous differential
+
+143
+00:12:32,150 --> 00:12:37,370
+equation كويس
+
+144
+00:12:40,180 --> 00:12:43,500
+طبعا ال homogenous differential equation بتكون من
+
+145
+00:12:43,500 --> 00:12:50,360
+الرتبة الثانية الرتبة الثانية أي معادلة من الرتبة
+
+146
+00:12:50,360 --> 00:12:58,100
+الثانية هنفترض إليها حل ما حل معين الحل المعين هذا
+
+147
+00:12:58,100 --> 00:13:03,030
+بده يقودنا إلى معادلة من الدرجة الثانيةمعادلة
+
+148
+00:13:03,030 --> 00:13:06,030
+عادية زي بقى التانية عدادية زي طبعة الصف التامن
+
+149
+00:13:06,030 --> 00:13:10,950
+والتاسع من الدرجة الثانية بنروح نحل المعادلة اللي
+
+150
+00:13:10,950 --> 00:13:15,230
+عندنا هذه معادلة من الدرجة الثانية ممكن نحلها
+
+151
+00:13:15,230 --> 00:13:21,870
+بالتحليل او بالجذر القانون اللي هو ناقص با زاد او
+
+152
+00:13:21,870 --> 00:13:24,890
+ناقص الجذر التربية اللي با التربية ناقص اربعة الف
+
+153
+00:13:24,890 --> 00:13:29,310
+جيمة على اتنين الف بهذه او هذه بنحل معادلة الدرجة
+
+154
+00:13:29,310 --> 00:13:32,870
+الثانيةما دام مؤادرة من طريق التاني يبقى إليها
+
+155
+00:13:32,870 --> 00:13:37,890
+حالين الحالين هدول يا بنات ممكن يكونوا اتنين are
+
+156
+00:13:37,890 --> 00:13:44,270
+real and different تمام؟ يبقى real and different
+
+157
+00:13:44,270 --> 00:13:49,370
+يعني حالين حقيقين ومختلفين ولا واحد زي التاني
+
+158
+00:13:49,370 --> 00:13:57,230
+تمام؟ ممكن يكون الحالين حقيقين ومكرتنين زي بعضحلان
+
+159
+00:13:57,230 --> 00:14:02,790
+ممطبقان اتنين زي بعض تماما الحالة التالتة ممكن
+
+160
+00:14:02,790 --> 00:14:07,330
+اتنين يكونوا are complex conjugate يعني حلين
+
+161
+00:14:07,330 --> 00:14:15,010
+كميتين مركبتين او كميتين تخيليتين و اتنين مترافقة
+
+162
+00:14:15,010 --> 00:14:20,950
+conjugate يعني مترافقةيبقى هانيجي لحاجة اسمة
+
+163
+00:14:20,950 --> 00:14:27,070
+المعادلة المميزة للمعادلة التفاضلية يبقى هذه
+
+164
+00:14:27,070 --> 00:14:30,810
+بنسميها ال characteristic equation ال
+
+165
+00:14:30,810 --> 00:14:42,150
+characteristic equation
+
+166
+00:14:42,150 --> 00:14:47,510
+هي معادلة من الدرجة الثانيةمش من الرثب يعني انتقل
+
+167
+00:14:47,510 --> 00:14:53,180
+من الرثب الى مين الى درجة نتيجةللحل اللي فرضناه
+
+168
+00:14:53,180 --> 00:14:57,600
+لمين؟ للمعادلة التفاضية طب الحل بيكون على شكل
+
+169
+00:14:57,600 --> 00:15:03,440
+exponential function يعني كيف ال homogeneous هذه؟
+
+170
+00:15:03,440 --> 00:15:09,040
+يعني زي ما نقول y double prime زائد p of t في ال y
+
+171
+00:15:09,040 --> 00:15:15,020
+prime زائد ل q of t في ال y بده يساوي zero الطرف
+
+172
+00:15:15,020 --> 00:15:18,280
+اليمين بيكون يساوي zero هذه هي ال homogeneous
+
+173
+00:15:18,280 --> 00:15:25,840
+differential equationالمعادلة على الشكل هذا لو كان
+
+174
+00:15:25,840 --> 00:15:34,660
+كل من Pt و Q of T constant ثابت يبقى الحل اللي
+
+175
+00:15:34,660 --> 00:15:41,100
+عندنا هنا بيكون على الشكل Y تساوي E أُس RT
+
+176
+00:15:41,100 --> 00:15:46,000
+exponential function أصلا ال exponential اللي
+
+177
+00:15:46,000 --> 00:15:50,490
+بنعرف ان الفضل ههبط و لا لأطبعاً R هو مقدار عددي
+
+178
+00:15:50,490 --> 00:15:54,650
+اتنين تلاتة اربعة نص تلاتة اربعة جد ما يكون و T هو
+
+179
+00:15:54,650 --> 00:15:58,530
+ال parameter أو المتغير ال variable يبقى اظن لو
+
+180
+00:15:58,530 --> 00:16:04,230
+بدنا نشتق الاشتقاق الاول بيصير ايش؟ R في US RT لو
+
+181
+00:16:04,230 --> 00:16:10,540
+نشتقها كمان مرة بيصير R تربية US RT تمام؟وبالتالي
+
+182
+00:16:10,540 --> 00:16:16,640
+المعادلة هذا نتيجة لهذا الحل بتتحول إلى معادلة من
+
+183
+00:16:16,640 --> 00:16:26,320
+الدرجة الثانية على الصيغة R تربية زائد A R زائد B
+
+184
+00:16:26,320 --> 00:16:32,080
+تساوي Zero يبقى هذه معادلة عادية من الدرجة الثانية
+
+185
+00:16:32,080 --> 00:16:39,690
+هذه لما نيجي نحلها سيظهر عندي أحد ثلاثة أموراللي
+
+186
+00:16:39,690 --> 00:16:51,250
+همين real and different roots يبقى
+
+187
+00:16:51,250 --> 00:17:00,690
+جذور حقيقية ومختلفة الأمر الثاني real and equal
+
+188
+00:17:00,690 --> 00:17:04,850
+roots الأمر
+
+189
+00:17:04,850 --> 00:17:06,890
+الثالث complex
+
+190
+00:17:10,110 --> 00:17:16,170
+conjugate roots يبقى
+
+191
+00:17:16,170 --> 00:17:21,870
+هذه الاحتمالات الثلاثة والتي لا رابع عليها يبقى
+
+192
+00:17:21,870 --> 00:17:28,290
+المعادلة هذه لما نقاش أحلها بيطلع عندنا أحد الأمور
+
+193
+00:17:28,290 --> 00:17:33,330
+التلاتة هذا يا بنات حلناها في الصف التامن والتاسع
+
+194
+00:17:33,330 --> 00:17:36,990
+بقينا حل عاديهذه المعادلة بدأت تقول إنها ليست لدي
+
+195
+00:17:36,990 --> 00:17:41,950
+حل لأنها ليست موجودة في الزمان لكن لما درسنا
+
+196
+00:17:41,950 --> 00:17:46,270
+الكميات التخيولية أو ال complex numbers الأعداد
+
+197
+00:17:46,270 --> 00:17:51,710
+المركبة صارنا بنقدر نحلها وبالتالي بصير عندنا ثلاث
+
+198
+00:17:51,710 --> 00:17:56,070
+حالات زي ما انتوا شايفينها في كل حالة من الحالات
+
+199
+00:17:56,070 --> 00:18:01,390
+الثلاث بصير المعادلة التفاضلية هذه لها صورة معينة
+
+200
+00:18:01,390 --> 00:18:06,270
+لميمللحل يبقى بنعرف صورة الحل في الحالة الأولى
+
+201
+00:18:06,270 --> 00:18:09,830
+صورة الحل في الحالة التانية صورة الحل في الحالة
+
+202
+00:18:09,830 --> 00:18:13,890
+الثالثة ثالثة وبالتالي عرفنا حل ال homogeneous
+
+203
+00:18:13,890 --> 00:18:20,270
+differential equations تمام هذا قلنا لو كانت
+
+204
+00:18:20,270 --> 00:18:27,650
+constants تمام طب لو ماكانوش constantsلو هذا حصل
+
+205
+00:18:27,650 --> 00:18:33,190
+انه مش constants والحلول كانت real and equal
+
+206
+00:18:33,190 --> 00:18:39,290
+repeated roots بنسميها الحلول المكررة بند real and
+
+207
+00:18:39,290 --> 00:18:45,050
+equal بنختصرها بعض الكتب إلى repeated roots
+
+208
+00:18:45,050 --> 00:18:53,070
+repeated أو real and equal سيان هذه الكلمة بدأ
+
+209
+00:18:53,070 --> 00:18:58,980
+real and equal كويس؟نفترض أنها كانت معين للحلول
+
+210
+00:18:58,980 --> 00:19:02,380
+repeated ذاك المعادلة على الشكل اللي فوق، هذول ما
+
+211
+00:19:02,380 --> 00:19:07,940
+هو مشكله الصندوق عادي، في أن طريقة للحل اسمها
+
+212
+00:19:07,940 --> 00:19:15,120
+طريقة reduction of orders، يبقى في أن حاجة اسمها
+
+213
+00:19:15,120 --> 00:19:20,640
+طريقة reduction of
+
+214
+00:19:20,640 --> 00:19:22,200
+orders
+
+215
+00:19:30,360 --> 00:19:36,200
+طريقة اختزال الرتبة بطريقة ما بنحط عوضة معينة
+
+216
+00:19:36,200 --> 00:19:40,720
+بننزل رتبة المعادلة من الدرجة الثانية إلى الدرجة
+
+217
+00:19:40,720 --> 00:19:45,400
+الأولى بنحل المعادلة حصلت تظهر عندنا المشتق الأولى
+
+218
+00:19:45,400 --> 00:19:49,500
+كمان مرة بنروح بنكابل كمان مرة وبالتالي بنجيب من
+
+219
+00:19:49,500 --> 00:19:54,920
+الحل يبقى ظهرت عندنا طريقة reduction of earnings
+
+220
+00:19:54,920 --> 00:19:59,960
+لمنللمعادلات اللي العوامل عندهم هذه ما هي استوابط
+
+221
+00:19:59,960 --> 00:20:04,960
+وانما متغيرات بعد هيك بروح لل homogeneous
+
+222
+00:20:04,960 --> 00:20:08,460
+differential equations بدينا بال homogeneous
+
+223
+00:20:08,460 --> 00:20:12,240
+differential equations ابنجي لمين ل non
+
+224
+00:20:12,240 --> 00:20:21,040
+homogeneous non homogeneous differential equations
+
+225
+00:20:21,040 --> 00:20:25,960
+لازلنا داخل ال section أو ال chapter رقم تلاتةفيها
+
+226
+00:20:25,960 --> 00:20:30,880
+نبنات طريقة تاني للحل الطريقة الأولى بسميها ال
+
+227
+00:20:30,880 --> 00:20:35,000
+undetermined coefficients و الطريقة التانية بسميها
+
+228
+00:20:35,000 --> 00:20:41,420
+ال variation of parameters يبقى الطريقة الأولى في
+
+229
+00:20:41,420 --> 00:20:47,700
+هذه الحالة اسمها طريقة ال undetermined
+
+230
+00:20:47,700 --> 00:20:51,180
+coefficients
+
+231
+00:20:56,330 --> 00:21:03,170
+والطريقة الثانية اسمها طريقة ال variation of
+
+232
+00:21:03,170 --> 00:21:19,330
+parameters يبقى
+
+233
+00:21:19,330 --> 00:21:23,850
+نرجع مرة تانية نذكر
+
+234
+00:21:23,850 --> 00:21:28,050
+تذكرةالمعادلة الـ second order سأقسمها إلى قسمين
+
+235
+00:21:28,050 --> 00:21:32,790
+القسم الأول هو الـ homogeneous و القسم التاني هو
+
+236
+00:21:32,790 --> 00:21:36,430
+الـ non homogeneous differential equation في حالة
+
+237
+00:21:36,430 --> 00:21:40,150
+الـ homogeneous differential equation إذا كانت
+
+238
+00:21:40,150 --> 00:21:44,950
+المعاملات هذه ثوابت سأفترض الحل على صيغة Y تساوي
+
+239
+00:21:44,950 --> 00:21:51,730
+EOSRT نتيجة لذلك ستظهر معادلة بالشكل اللي عندنا
+
+240
+00:21:51,730 --> 00:21:56,360
+هذا معادلة من الدرجة التانيةبضعوها حلها بيطلع عندي
+
+241
+00:21:56,360 --> 00:22:01,960
+تلات حالات اللي هو real and different roots, real
+
+242
+00:22:01,960 --> 00:22:06,300
+repeated roots اللي هو complex conjugate roots
+
+243
+00:22:06,300 --> 00:22:11,240
+يبقى طالع جذور المعادلة هذه واحد من الأمور التلاتة
+
+244
+00:22:11,240 --> 00:22:16,700
+نتيجة لذلك بيصير حل المعادلة لأن التفاضلية على شكل
+
+245
+00:22:16,700 --> 00:22:21,280
+ما كل واحدة من التلاتة لها شكل بيختلف عن الشكل
+
+246
+00:22:21,280 --> 00:22:27,050
+الآخرسنعرف اللي هي اشكال في حينه ان شاء الله تبارك
+
+247
+00:22:27,050 --> 00:22:33,950
+وتعالى بعد هيك جينا من ال repeated roots هذه و لو
+
+248
+00:22:33,950 --> 00:22:40,090
+كان المعاملات هدول ليست ثوابت و انما دوال في T
+
+249
+00:22:40,090 --> 00:22:45,190
+sine T cosine T T تربية T نقص واحد T تربية زائد
+
+250
+00:22:45,190 --> 00:22:49,510
+اتنين T زائد تلاتة الاخرين يعني اي function من ال
+
+251
+00:22:49,510 --> 00:22:53,830
+functions اللي مرت علينايبقى في هذه الحالة أول
+
+252
+00:22:53,830 --> 00:22:59,750
+طريقة طريقة reduction of orders ننتقل الآن لل non
+
+253
+00:22:59,750 --> 00:23:03,230
+homogeneous differential equations إذا ولّا
+
+254
+00:23:03,230 --> 00:23:07,750
+المعادلات ثوابت بستخدم طريقة ال undetermined
+
+255
+00:23:07,750 --> 00:23:13,770
+coefficients طريقة المعاملات المجهولة إذا ولّا
+
+256
+00:23:13,770 --> 00:23:20,170
+المعاملات هدول متغيراتلك الخيار بين ان تستخدم ال
+
+257
+00:23:20,170 --> 00:23:23,670
+undetermined coefficients او نستخدم طريقة ال
+
+258
+00:23:23,670 --> 00:23:28,950
+variation of parameters طبعا فرق شاسة بينه طريقتين
+
+259
+00:23:28,950 --> 00:23:34,630
+طريقة الاولى تعتمد على امرين ان المعاملات ثوابت
+
+260
+00:23:34,630 --> 00:23:38,990
+والدالة هذه ليست صفر وانما بتكون على شكل معين
+
+261
+00:23:38,990 --> 00:23:43,450
+polynomial polynomial في exponential polynomial في
+
+262
+00:23:43,450 --> 00:23:47,850
+exponential في دالة متلاتية signأو كوصين أو
+
+263
+00:23:47,850 --> 00:23:52,330
+مجموعهما أو الفرق فيما بينهم طريقة ال variation of
+
+264
+00:23:52,330 --> 00:23:56,150
+parameters بهمهاش هدول ثوابت والله مش ثوابت ثوابت
+
+265
+00:23:56,150 --> 00:24:00,990
+ماشي الحال مش ثوابت ماشي الحال ماعندها مشكلة اتنين
+
+266
+00:24:00,990 --> 00:24:05,010
+الدالة لاعلمين ايش مايكون شكل هيكون ماعندهاش مشكلة
+
+267
+00:24:05,010 --> 00:24:09,410
+كذلك يبقى هذه الطرق المختلفة لحل المعادلة
+
+268
+00:24:09,410 --> 00:24:14,870
+التفاضلية تلاتةreduction of order, entertainment
+
+269
+00:24:14,870 --> 00:24:19,990
+coefficients, variation of parameters يبقى هذه هي
+
+270
+00:24:19,990 --> 00:24:24,310
+الطرق الثلاث لحل المعادلة التفاضلية اللي احنا
+
+271
+00:24:24,310 --> 00:24:28,770
+درسها في chapter 3 ابناجي ل chapter 4
+
+272
+00:24:45,440 --> 00:24:50,780
+شبتر اربع يا بنات بدنا نعمم شبتر تلاتة يعني شبتر
+
+273
+00:24:50,780 --> 00:24:55,950
+اربع هو تعميم لشبتر تلاتة ليه؟بناخد المعادلة من
+
+274
+00:24:55,950 --> 00:24:59,010
+الرتبة التالتة من الرتبة الرابعة من الخمسة من
+
+275
+00:24:59,010 --> 00:25:04,190
+الرتبة النونية in general يبقى هذه اسمها higher
+
+276
+00:25:04,190 --> 00:25:08,490
+order differential equations المعادلة التفاضلية من
+
+277
+00:25:08,490 --> 00:25:13,910
+الرتب العليا يعني اكتر من اتنين اربعة فما فوق
+
+278
+00:25:13,910 --> 00:25:23,150
+فشبتر اربعة شبتر اربعة اسمه higher order
+
+279
+00:25:23,150 --> 00:25:23,150
+differential equations
+
+280
+00:25:27,510 --> 00:25:32,910
+order differential equations
+
+281
+00:25:32,910 --> 00:25:35,970
+هذا
+
+282
+00:25:35,970 --> 00:25:40,950
+لن نأتي فيه بجديد نفس التكتيك اللى اتبع في شبطر 3
+
+283
+00:25:40,950 --> 00:25:46,830
+هنتبعه مين في شبطر 4 يبقى هنقسمه الى homogeneous
+
+284
+00:26:01,710 --> 00:26:06,450
+نفس هذا الـ characteristic equation اللي على الشكل
+
+285
+00:26:06,450 --> 00:26:10,170
+اللي عندنا هدا هدا هيك هتصير معادلة بس بيصير من
+
+286
+00:26:10,170 --> 00:26:17,950
+الرتبة النونية تماميبقى هذه هناخد بالها برضه ال
+
+287
+00:26:17,950 --> 00:26:24,690
+characteristic equation ونروح نحللها ونشوف ما هو
+
+288
+00:26:24,690 --> 00:26:29,690
+شكل الجذور في الحالات المختلفة بنيجي لل non
+
+289
+00:26:29,690 --> 00:26:34,230
+homogeneous هنستخدم لها نفس الكلام اللي استخدمنا
+
+290
+00:26:34,230 --> 00:26:39,210
+هنا اللي هو ال undetermined
+
+291
+00:26:39,210 --> 00:26:41,050
+coefficients
+
+292
+00:26:44,270 --> 00:26:51,370
+undetermined coefficients و الطريقة الثانية التي
+
+293
+00:26:51,370 --> 00:27:06,370
+هي variation of parameters يبقى
+
+294
+00:27:06,370 --> 00:27:11,790
+هذا مين لل higher order لهمين المل شبط الرقم أربعة
+
+295
+00:27:12,060 --> 00:27:18,200
+يبقى شبط الرقم اربع هو تعميم لشبط الرقم تلاتة مافي
+
+296
+00:27:18,200 --> 00:27:22,860
+معلومة ان نفس الفكر تبعت اللي هو شبط الرقم تلاتة
+
+297
+00:27:22,860 --> 00:27:27,870
+بس اه بنعملبدل ما تحلي هنا معادلة من الدرجة
+
+298
+00:27:27,870 --> 00:27:31,170
+الثانية بصير تحلي معادلة من الدرجة التالتة او
+
+299
+00:27:31,170 --> 00:27:34,930
+الدرجة الرابعة او الدرجة الخامسة او السادسة او ما
+
+300
+00:27:34,930 --> 00:27:40,570
+إلى ذلك هذا و من هنا صار تعميم لهذه الحالة هيطلع
+
+301
+00:27:40,570 --> 00:27:43,850
+نفس الطرق الثلاثة اللي هي reduction of order او
+
+302
+00:27:43,850 --> 00:27:46,610
+variation of parameters او undetermined
+
+303
+00:27:46,610 --> 00:27:48,570
+coefficients نفس الطرق
+
+304
+00:27:51,210 --> 00:27:54,230
+يبقى هذا اللى هنشوفه ان شاء الله و تبارك و تعالى
+
+305
+00:27:54,230 --> 00:28:06,210
+في شبتر 4 ابنجي لشبتر 5 شبتر
+
+306
+00:28:06,210 --> 00:28:14,490
+5 ابنجي لحاجة اسمها series solution of
+
+307
+00:28:14,490 --> 00:28:19,770
+the second order
+
+308
+00:28:22,640 --> 00:28:29,060
+differential equations اول
+
+309
+00:28:29,060 --> 00:28:34,300
+section في هذا ال chapter بيذكرك بمين بالمتسلسلات
+
+310
+00:28:34,300 --> 00:28:40,580
+ال power series ,tyler series, mclaren seriesو ال
+
+311
+00:28:40,580 --> 00:28:45,180
+convergence تبعهم يبقى أول section كأنه calculus B
+
+312
+00:28:45,180 --> 00:28:49,600
+جزء من calculus B مش كتير يعني بعض المعلومات
+
+313
+00:28:49,600 --> 00:28:54,660
+البسيطة التي تستخدم بعد ذلك مش لسه بدنا نروح كيف
+
+314
+00:28:54,660 --> 00:28:59,080
+نجيب ال Tylor أو ال macron series لدالة تمام عند
+
+315
+00:28:59,080 --> 00:29:03,270
+نقطة تماملأ لأ لأ لأ هذا كلام انتهى خطيب ال
+
+316
+00:29:03,270 --> 00:29:09,190
+calculus بيهم للتذكير بهذه المفاهيم لأن بعضها
+
+317
+00:29:09,190 --> 00:29:14,650
+سيلزم في ال sections القادمة بهمنا كيف نحل
+
+318
+00:29:14,650 --> 00:29:20,290
+المعادلة من الرتبة الثانية باستخدام المتسلسلات
+
+319
+00:29:23,380 --> 00:29:27,780
+بس مش هنعتمد على ال series كتير يعني مش تفهموا انه
+
+320
+00:29:27,780 --> 00:29:30,800
+بدنا نبدأ chapter ال series اللي هو من أول لأخر
+
+321
+00:29:30,800 --> 00:29:35,480
+chapter عشرة كان ولا لا؟ اه لا لا لا معلومات بسيطة
+
+322
+00:29:35,480 --> 00:29:39,380
+ثم بنشوف كيف بنحل المعادلة تانية بالاستخدام
+
+323
+00:29:39,670 --> 00:29:46,250
+المتسلسلات هذا بيشغل حوالي خمسة sections من
+
+324
+00:29:46,250 --> 00:29:51,350
+الشابتر تقريبا تمام ابنجي لآخر chapter اللي هو
+
+325
+00:29:51,350 --> 00:29:58,810
+chapter ستة chapter ستة
+
+326
+00:29:58,810 --> 00:30:03,930
+حاجة اسمها Laplace transforms
+
+327
+00:30:16,140 --> 00:30:22,860
+تحويلات Laplace تحويلات
+
+328
+00:30:22,860 --> 00:30:30,060
+Laplace بنلجأ لها أو نستخدمها لتسهيل المسائل
+
+329
+00:30:30,060 --> 00:30:35,800
+المختلفة يعني أحيانا صعب نتعامل مع دالة مباشرة
+
+330
+00:30:35,800 --> 00:30:41,700
+بنجيب دالة مكافئة لهابتحويلة المعينة أو بصير ان
+
+331
+00:30:41,700 --> 00:30:45,620
+اتعامل مع الدالة الجديدة التي تكافئ الدالة
+
+332
+00:30:45,620 --> 00:30:49,420
+المعلومة هذه الأمور بنسميها تحويلات اللي هو
+
+333
+00:30:49,420 --> 00:30:56,240
+Laplace transform يعني سنعطيها تعريف ثم نستخدم هذا
+
+334
+00:30:56,240 --> 00:31:02,620
+التعريف لإيجاد Laplace transform لدوال مختلفة ثم
+
+335
+00:31:02,620 --> 00:31:07,760
+بعد ذلك نستخدم Laplace transform لحل المعادلات
+
+336
+00:31:07,760 --> 00:31:14,070
+التفاضليةطبعا يبقى أول شغلة نعطي تعريف للابلاس
+
+337
+00:31:14,070 --> 00:31:18,610
+ترانسفورم والتعريف هذا يعتمد على الـ improper
+
+338
+00:31:18,610 --> 00:31:26,230
+integrals يعني هو تكامل من صفر لما لا نهاية ل
+
+339
+00:31:26,230 --> 00:31:31,690
+EOSST مضروب في ال function اللى بدنا نوجد لها
+
+340
+00:31:31,690 --> 00:31:36,620
+لابلاس ترانسفورم بدنا نكامل حصل الدرب هذاوانطلع
+
+341
+00:31:36,620 --> 00:31:40,980
+القيمة القيمة اللى بتطلع بيكون هو تكامل هي قيمة
+
+342
+00:31:40,980 --> 00:31:47,000
+Laplace transform للدالة المطيانة مثلا لو بدي
+
+343
+00:31:47,000 --> 00:31:55,040
+Laplace transform للدالة f of t بقول هو تكامل من
+
+344
+00:31:55,040 --> 00:32:03,990
+zero ل infinity لل E أس ناقص ST لل F of T DTيبقى
+
+345
+00:32:03,990 --> 00:32:10,650
+هذا تعريف لـ plus transform لدالة ما ل plus
+
+346
+00:32:10,650 --> 00:32:14,970
+transform لدالة f of t و integration من zero ل
+
+347
+00:32:14,970 --> 00:32:23,540
+infinity لل E أث ناقص ST لل F of T DTهتطلع دلة
+
+348
+00:32:23,540 --> 00:32:31,000
+بدلالة المتغير S وبالتالي هروح نسميها بدل plus F
+
+349
+00:32:31,000 --> 00:32:37,920
+of T هنقول capital F of S تمام؟ يبقى هتطلع
+
+350
+00:32:37,920 --> 00:32:43,900
+function في S هذه ال function تكافئ عامليا الدلال
+
+351
+00:32:43,900 --> 00:32:49,710
+الأصلي ل F of T لأن مين ما كانت تكونتمام يبقى هذا
+
+352
+00:32:49,710 --> 00:32:53,810
+تعريف لبلاس ترانسفورم ال section الأول هنجيب لبلاس
+
+353
+00:32:53,810 --> 00:33:00,390
+ترانسفورم لدوال متعددة بعدين بنعطيكوا جدول موجود
+
+354
+00:33:00,390 --> 00:33:04,310
+بالكتابة و بنجيبهلكوا في الامتحانلو شفتوا اي ورقة
+
+355
+00:33:04,310 --> 00:33:08,070
+امتحان نهائي لمادة المعالج التفاضلية بتلاقي معاها
+
+356
+00:33:08,070 --> 00:33:14,910
+جدول الجدول هذا لبلاس ترنسفورم
+
+357
+00:33:14,910 --> 00:33:23,180
+لمن لهذه الدوال كل بكل موجود معاكييبقى هذا
+
+358
+00:33:23,180 --> 00:33:26,480
+بالنسبالي ال sectional بعد هيك كيف بدنا نستخدم
+
+359
+00:33:26,480 --> 00:33:33,080
+Laplace transform لحل المعادلات المختلفة طبعا
+
+360
+00:33:33,080 --> 00:33:37,180
+سنعطي بعض نظريات اللي بتحدد Laplace transform
+
+361
+00:33:37,180 --> 00:33:41,480
+للمشتقة الأولى شو شكله Laplace transform للمشتقة
+
+362
+00:33:41,480 --> 00:33:45,780
+الثانية شو شكله Laplace transform للمشتقة النونية
+
+363
+00:33:45,780 --> 00:33:50,380
+in general شو شكله وبرضه الصيغة هذه هتكون موجودة
+
+364
+00:33:50,380 --> 00:33:56,100
+عندك وينفي الجدول ان شاء الله تبارك وتعالى يبقى
+
+365
+00:33:56,100 --> 00:34:04,980
+هذا اجمالا ما سندرسه في هذا الشبطة في هذا المساق
+
+366
+00:34:04,980 --> 00:34:11,100
+او هذا المقرر خلال هذا الفصلطيب حد بتسأل أي سؤال
+
+367
+00:34:11,100 --> 00:34:16,840
+قبل أن ندخل فيه بس ال introduction اللي هي شبه
+
+368
+00:34:16,840 --> 00:34:20,500
+المساحنة ال introduction اللي هو بتكلم بس عن
+
+369
+00:34:20,500 --> 00:34:25,480
+المقدمة المعادلات التفاضلية حد بتحب تسأل أي سؤال
+
+370
+00:34:25,480 --> 00:34:31,320
+لأن العدد شبه تكامل الآنيعني الحضور تلاتة و تلاتة
+
+371
+00:34:31,320 --> 00:34:39,100
+ستة تمانية أفماش ستاش تسعة تاش تلاتة و عشرين سبعة
+
+372
+00:34:39,100 --> 00:34:44,160
+و عشرين تلاتين اتنين و تلاتين خمسة و تلاتين تمانية
+
+373
+00:34:44,160 --> 00:34:50,440
+و تلاتين اتنين و اربعين شبه تكامل حسب التسجيل حد
+
+374
+00:34:50,440 --> 00:34:58,640
+بتسأل اي سؤال ايش طيب يبقى الآن بنبدأ في مينفي
+
+375
+00:34:58,640 --> 00:35:03,220
+المقدمة تبع المعادلات التفاضلية
+
+376
+00:36:50,930 --> 00:36:55,370
+الدالة المجهولة اسمها
+
+377
+00:36:57,730 --> 00:37:01,970
+هي تسمى كتابة مقارنة
+
+378
+00:37:20,390 --> 00:37:26,330
+يبقى an equation المعادلة contains تحتوي أو تشتمل
+
+379
+00:37:26,330 --> 00:37:31,430
+one or more derivatives يعني فيها المشتقة الأولى
+
+380
+00:37:31,430 --> 00:37:35,870
+او التانية او اكثر التالتة او الرابعة او ما إلى
+
+381
+00:37:35,870 --> 00:37:42,490
+ذلك of a non function لدالة مجهولة is called a
+
+382
+00:37:42,490 --> 00:37:47,470
+differential equation for example نعطي مثال لو روح
+
+383
+00:37:47,470 --> 00:37:56,030
+نقولنا whyبابلي prime زائد مثلا خمسة y prime زائد
+
+384
+00:37:56,030 --> 00:38:06,150
+ستة y تساوي زيرو مثلا is a differential او تساوي T
+
+385
+00:38:06,150 --> 00:38:10,970
+مثلا is a differential equation
+
+386
+00:38:20,940 --> 00:38:26,800
+يبقى مرة تانية an equation contains المعادلة اللى
+
+387
+00:38:26,800 --> 00:38:32,980
+تحتوي أو تجتمل على مشتقة أولى او اكثر مشتقة تانية
+
+388
+00:38:32,980 --> 00:38:39,060
+او تالتة او رابعة او خمسة او الاخرى لمجهول ده اللى
+
+389
+00:38:39,060 --> 00:38:43,260
+مجهول is called a differential equation طلعلي في
+
+390
+00:38:43,260 --> 00:38:47,100
+المعادلة اللى عندنا هذه هل احنا عارفين شكل ال Y
+
+391
+00:38:48,530 --> 00:38:53,310
+عارفين why تسوي ايش يعني بدلالتي؟ نعرفش يبقى why
+
+392
+00:38:53,310 --> 00:38:57,930
+دالة مجهولة احنا بدنا نبحث عليها اللي بدنا نبحث
+
+393
+00:38:57,930 --> 00:39:01,130
+ماهو الشكل ال why الشكل ال why بكون هو الصليوش
+
+394
+00:39:01,130 --> 00:39:06,040
+اللي مين للمعادلة التفاضلية اللي عندنايبقى دالة
+
+395
+00:39:06,040 --> 00:39:10,600
+مجهولة إذا ظهرت بهذا الشكل على سبيل المثال بقول
+
+396
+00:39:10,600 --> 00:39:15,140
+هذه معادلة تفاضلية يبقى المعادلة التفاضلية هي تظهر
+
+397
+00:39:15,140 --> 00:39:18,760
+المشتق الأول أو التاني أو التالت أو الرابع أو أو
+
+398
+00:39:18,760 --> 00:39:24,680
+الاخرين بنسميها معادلة تفاضلية المعادلات التفاضلية
+
+399
+00:39:24,680 --> 00:39:30,540
+نوعان النوع الأول هي معادلة تفاضلية عادية وهي
+
+400
+00:39:30,540 --> 00:39:34,100
+موضوع دراستنا خلال هذا الفصل
+
+401
+00:39:42,240 --> 00:39:46,880
+هذه المعادلة تظهر فيها المشتقات العادية اللي
+
+402
+00:39:46,880 --> 00:39:52,280
+اتعلمناها في calculus a وb لكن النوع الثاني اللي
+
+403
+00:39:52,280 --> 00:39:57,100
+هي معادلة التفاضلية الجزئية partial differential
+
+404
+00:39:57,100 --> 00:39:59,880
+equations هذه تبعت calculus E وهذه مالناش علاقة
+
+405
+00:39:59,880 --> 00:40:04,030
+فيهاتمام يبقى احنا موضوعنا موضوع ال ordinary
+
+406
+00:40:04,030 --> 00:40:09,770
+differential equations هنعطيها تعريف كذلك يبقى
+
+407
+00:40:09,770 --> 00:40:15,330
+definition اخر if
+
+408
+00:40:15,330 --> 00:40:20,670
+the differential equation if the differential
+
+409
+00:40:20,670 --> 00:40:30,470
+equation اذا كانت المعادلة التفاضلية containsتشتمل
+
+410
+00:40:30,470 --> 00:40:38,590
+only فقط ordinary derivatives
+
+411
+00:40:38,590 --> 00:40:44,990
+مشتقات عادية زي اللي اتعلمناها ordinary
+
+412
+00:40:44,990 --> 00:40:53,730
+derivatives with respect with
+
+413
+00:40:53,730 --> 00:40:56,550
+respect to a single
+
+414
+00:41:11,320 --> 00:41:23,780
+independent independent variable then
+
+415
+00:41:23,780 --> 00:41:36,370
+it isثم يقول انها
+
+416
+00:41:36,370 --> 00:41:44,510
+عادية عادية
+
+417
+00:41:44,510 --> 00:41:48,510
+عادية
+
+418
+00:41:48,510 --> 00:41:50,150
+عادية عادية عادية عادية عادية
+
+419
+00:42:04,290 --> 00:42:09,790
+كمثال على ذلك Y
+
+420
+00:42:09,790 --> 00:42:20,950
+prime زائد تلاتة Y يساوي E أساسي T و Y double
+
+421
+00:42:20,950 --> 00:42:33,700
+primeنقص y' زائد 6y يسوى 0 are ordinary
+
+422
+00:42:33,700 --> 00:42:37,920
+differential
+
+423
+00:42:37,920 --> 00:42:41,260
+equations
+
+424
+00:42:58,300 --> 00:43:03,200
+يبقى مرة ثانية بنرجع لهذا التعريف يبقى عرفنا
+
+425
+00:43:03,200 --> 00:43:06,560
+التعريف الأول هو تعريف المعادلة التفاضلية in
+
+426
+00:43:06,560 --> 00:43:11,910
+generalمعادلة التفاضولية العادية
+
+427
+00:43:38,690 --> 00:43:43,990
+أو إذا كانت الدالة في متغيرين أو في تلاتة بيصير
+
+428
+00:43:43,990 --> 00:43:48,230
+اشتقاق جزءي وبالتالي بيسميها معادلة تفاضلية جزية
+
+429
+00:43:48,230 --> 00:43:52,430
+لكن إذا كانت ال function دالة في متغير واحد زي ما
+
+430
+00:43:52,430 --> 00:43:57,430
+كنا نقول في الكلقل الصحيو يتساوي F of X يبقى Y
+
+431
+00:43:57,430 --> 00:44:01,850
+دالة في X فقط X هو المتغير المستقل ال independent
+
+432
+00:44:01,850 --> 00:44:06,300
+وY هو المتغير التابعاللي هو dependent variable
+
+433
+00:44:06,300 --> 00:44:12,380
+تمام؟ لكن لو كانت Y تسوى F of X و T يبقى صارت دالة
+
+434
+00:44:12,380 --> 00:44:17,900
+في مين؟ فاش عندي اشتقاق قعدت بيصير اشتقاق جزئي و
+
+435
+00:44:17,900 --> 00:44:21,980
+هذا خارج نطاق دراستنا مالناهش علاقة فيه فيه
+
+436
+00:44:21,980 --> 00:44:25,320
+المعادلة التفاصيلية يبقى انا عندي function في
+
+437
+00:44:25,320 --> 00:44:30,720
+متغير واحد فقط قلنا with respect to a single
+
+438
+00:44:37,150 --> 00:44:41,790
+بتصير المشتقات مشتقات عادية وبالتالي المعادلة
+
+439
+00:44:41,790 --> 00:44:45,390
+التفاضلية اللي عندنا بيكون معادلة تفاضلية عادية
+
+440
+00:44:45,390 --> 00:44:51,510
+بنقول عليها معادلة تفاضلية عاديةزي ايش مثلا لو قلت
+
+441
+00:44:51,510 --> 00:44:56,110
+y prime زائد تلاتة y يسوي E أستي معادلة ظهرت فيها
+
+442
+00:44:56,110 --> 00:45:02,910
+باسمين المشتقاء الأولى يبقى one derivative يبقى
+
+443
+00:45:02,910 --> 00:45:08,570
+معادلة تفاضلية من الرتبة الأولىالان لو كانت
+
+444
+00:45:08,570 --> 00:45:11,850
+المعادلة بالشكل اللي عندنا هذا يبقى ظاهرة المشتقة
+
+445
+00:45:11,850 --> 00:45:18,790
+الأولى والمشتقة الثانية يبقى هذا one or more اكثر
+
+446
+00:45:18,790 --> 00:45:23,790
+من مين من المشتقة والمشتقات عادية يبقى في هذه
+
+447
+00:45:23,790 --> 00:45:29,510
+الحالة بقول هذه معادلة تفاضلية عادية حد بتسأل اي
+
+448
+00:45:29,510 --> 00:45:36,330
+سؤال هنا؟أه طيب بدنا نروح لحاجة اسمها اللي هو حل
+
+449
+00:45:36,330 --> 00:45:44,010
+أو رتبة المعادلة التفاضلية definition the
+
+450
+00:45:44,010 --> 00:45:48,970
+order of
+
+451
+00:45:48,970 --> 00:45:59,610
+a differential equation رتبة المعادلة التفاضلية is
+
+452
+00:46:00,160 --> 00:46:17,280
+the order of the
+
+453
+00:46:17,280 --> 00:46:28,000
+highest derivative in
+
+454
+00:46:28,000 --> 00:46:28,840
+the equation
+
+455
+00:46:37,320 --> 00:46:47,680
+على سبيل المثال الـ differential equation
+
+456
+00:46:47,680 --> 00:46:58,560
+الـ differential equation T في D تكييب Y على D T
+
+457
+00:46:58,560 --> 00:47:10,630
+تكييب ناقص اتنيندي واي على دي ت أربع زائد واي
+
+458
+00:47:10,630 --> 00:47:19,230
+تساوي ت لإن ت is of the
+
+459
+00:47:42,920 --> 00:47:52,060
+رتبة المعادلة التفاضلية رتبة المعادلة التفاضلية هي
+
+460
+00:47:52,060 --> 00:47:58,860
+رتبة أعلى
+
+461
+00:47:58,860 --> 00:48:04,810
+معامل تفاضلي يظهر في المعادلة in the equationيبقى
+
+462
+00:48:04,810 --> 00:48:08,550
+أنا باجي على المعادلة التفاضلية وبشوف مين أعلى
+
+463
+00:48:08,550 --> 00:48:13,630
+مشتقة موجودة فيها أعلى مشتقة موجودة فيها بتكون هي
+
+464
+00:48:13,630 --> 00:48:19,050
+رتبة مين المعادلة التفاضلية بنعطي مثال توضيحه for
+
+465
+00:48:19,050 --> 00:48:23,630
+example the differential equation T في D تكيب Y
+
+466
+00:48:23,630 --> 00:48:30,790
+على DT تكيب نقص اتنين DY على DT أس أربع زائد Y
+
+467
+00:48:30,790 --> 00:48:37,410
+تسوى T لان T is ofبدنا نعرف جداش ال order تبعها يا
+
+468
+00:48:37,410 --> 00:48:43,890
+ترى هل هو تلاتة و الله جداش و الله اربعة مش اربعة
+
+469
+00:48:43,890 --> 00:48:48,750
+يعني اذا
+
+470
+00:48:48,750 --> 00:48:53,550
+القضية خلافية بين الفقهات البعض بيقولوا تلاتة و
+
+471
+00:48:53,550 --> 00:48:57,650
+البعض بيقولوا اربعة انا بسألك شو اسم ممكن اتعرف
+
+472
+00:48:57,650 --> 00:49:04,610
+عليكي باتسامابتسام النجار تعتقد، طبعا هذه أول
+
+473
+00:49:04,610 --> 00:49:09,630
+محاضرة، وبالتالي تعتقد، مش بيقول، تعتقد أن
+
+474
+00:49:09,630 --> 00:49:14,930
+المعادلة هذه من رتبة رقم أربعة، وأنا أسأل هل
+
+475
+00:49:14,930 --> 00:49:18,290
+الأربعة هذه مشتقة ولا أس؟
+
+476
+00:49:21,070 --> 00:49:26,710
+ممتاز جدا بس طبعا شاية يبقى بتقول أُس للمشتقة بقول
+
+477
+00:49:26,710 --> 00:49:31,950
+كلامها صحيح لكن أرجع للتعريف هل أنا قلت أُس
+
+478
+00:49:31,950 --> 00:49:37,950
+المشتقة ولا المشتقة نفسها وماقلتش أُس المشتقة صحيح
+
+479
+00:49:37,950 --> 00:49:41,610
+ولا لا نرجع للتعريف the order of the differential
+
+480
+00:49:41,610 --> 00:49:45,970
+equation is the order of the highest derivative
+
+481
+00:49:45,970 --> 00:49:53,860
+يبقى هو رتبة أعلى ولم أقول هي أُستمام؟ يبقى أربعة
+
+482
+00:49:53,860 --> 00:49:59,200
+هذا الرقم أربعة ماله خطأ ولا صح؟ خطأ بل very wrong
+
+483
+00:49:59,200 --> 00:50:04,240
+نشكرها على سؤالها إنها قالت هذه أربعة لأن النبات
+
+484
+00:50:04,240 --> 00:50:08,480
+الكل بفهم الآخرين إن الرتبة ليست أربعة وإنما
+
+485
+00:50:08,480 --> 00:50:14,770
+الرتبةتلاتة، لأن تلاتة هي أعلى مشتقة موجودة في هذه
+
+486
+00:50:14,770 --> 00:50:19,110
+الوضع، مش أربعة، لو قضيت أربعة بمليون، بتظل هي من
+
+487
+00:50:19,110 --> 00:50:24,410
+رتبة التالتة، ليش؟ ان أربعة أس وليست مشتقة، واحنا
+
+488
+00:50:24,410 --> 00:50:29,950
+بيقول ال order هو رتبة المشتقة، يعني المشتقة
+
+489
+00:50:29,950 --> 00:50:33,630
+الأولى ولا التانية ولا التالتة ولا الرابع، تمام؟
+
+490
+00:50:33,730 --> 00:50:38,690
+يبقى أربعة ليست مشتقة و للمشتقة الرقم تلاتة كان
+
+491
+00:50:38,690 --> 00:50:45,710
+بإمكاني مكتوبهاش زي هيك اهو هاكتب T Y triple prime
+
+492
+00:50:45,710 --> 00:50:54,760
+نقص اتنين Y prime أس اربعةزائد Y تساوي T لين T إذا
+
+493
+00:50:54,760 --> 00:50:58,720
+هذه والله هذه أعلى المشتقة الموجودة عندها من
+
+494
+00:50:58,720 --> 00:51:05,180
+المشتقة التالية إذا هذه is of the third order من
+
+495
+00:51:05,180 --> 00:51:12,380
+الرتبة الثالثة وليست الرابعة ابقى is of the third
+
+496
+00:51:12,380 --> 00:51:16,440
+order تمام؟
+
+497
+00:51:16,680 --> 00:51:22,740
+يبقى جبتها والله بدل المرة مرتين في سؤال بخيارات
+
+498
+00:51:22,740 --> 00:51:27,780
+متعددة بحط شغلة زيك طبعا بحطلها كمان واحدة و بقول
+
+499
+00:51:27,780 --> 00:51:31,280
+of the nth order of the third order of the zero
+
+500
+00:51:31,280 --> 00:51:35,300
+order of the fourth order وحطيلي خط تحت الإجابة
+
+501
+00:51:35,300 --> 00:51:40,260
+الصحية يعني جبتها قبل ذلك بدل المرة مرتين يوم أن
+
+502
+00:51:40,260 --> 00:51:45,900
+درست المادة سابقايبقى بك تربي تروحي وين تشوفي أعلى
+
+503
+00:51:45,900 --> 00:51:50,120
+معامل تفاضل، يعني كان بيمكن يتحيل عليك بطريقة
+
+504
+00:51:50,120 --> 00:51:56,360
+تانية ويقولك هذه تربيع، بصير هذا مثلا هاك تربيع،
+
+505
+00:51:56,360 --> 00:52:02,880
+وهذه أربعة، اني أتمن واحطلك اتنين، تلاتة، أربعة،
+
+506
+00:52:02,880 --> 00:52:07,900
+ستة، تلاتة مثلا، وحطيلي اللي تقطحت اللي جابها
+
+507
+00:52:07,900 --> 00:52:11,890
+الصحيةيبقى الإجابة صحية قداش؟ هادية، رغم أني
+
+508
+00:52:11,890 --> 00:52:16,890
+غيرتها، لكن ضالة is of the third order من الرتبة
+
+509
+00:52:16,890 --> 00:52:21,450
+أثنية، لكن إذا بتكلم عن الدرجة، بقول الدرجة
+
+510
+00:52:21,450 --> 00:52:26,070
+الرابعةمش موافق كدرجة كرتبة لأ إذا احنا مالاش
+
+511
+00:52:26,070 --> 00:52:30,630
+علاقة بالدرجة وإنما إلنا علاقة بالرتبة الدرجة هذا
+
+512
+00:52:30,630 --> 00:52:35,530
+للصف التامن والتاسع تمام يبقى هنا هقول من الرتبة
+
+513
+00:52:35,530 --> 00:52:42,190
+الثالثة تمام هذا بالنسبة لرتبة المعادلة التفاضلية
+
+514
+00:52:42,190 --> 00:52:47,290
+بدنا نيجي لحل المعادلة التفاضلية يبقى كمان
+
+515
+00:52:47,290 --> 00:52:47,990
+definition
+
+516
+00:52:55,140 --> 00:53:05,560
+The solution of a differential equation حل
+
+517
+00:53:05,560 --> 00:53:11,380
+المعادلة التفاضلية is a function
+
+518
+00:53:16,120 --> 00:53:29,040
+معرفة defined on an interval معرفة على فترة ما on
+
+519
+00:53:29,040 --> 00:53:40,840
+an interval I مثلا and satisfy and
+
+520
+00:53:40,840 --> 00:53:44,460
+satisfy the differential equation
+
+521
+00:53:48,930 --> 00:53:58,910
+وتحقق المعادلة التفاضلية for example كمثال على ذلك
+
+522
+00:53:58,910 --> 00:54:12,790
+for example Y تساوي E أقصى 2T is a solution is a
+
+523
+00:54:12,790 --> 00:54:16,550
+solution of the
+
+524
+00:54:25,960 --> 00:54:30,940
+نقص اتنين Y تساوي زيرو
+
+525
+00:54:56,900 --> 00:55:02,440
+مرة تانية حل المعادلة التفاضلية the solution of a
+
+526
+00:55:02,440 --> 00:55:07,060
+differential equation هو عبارة عن دالة دالة معرفة
+
+527
+00:55:07,060 --> 00:55:13,320
+على فترة محددة والتكن I وفي نفس الوقت تحقق من
+
+528
+00:55:13,320 --> 00:55:17,140
+المعادلة التفاضلية يعني ايه؟ يعني لو اوطفها في
+
+529
+00:55:17,140 --> 00:55:21,200
+المعادلة التفاضلية بدها ايش؟ بدها اتحققها يعني
+
+530
+00:55:21,200 --> 00:55:25,770
+تخلي الطرف اليمين زي الطرف اللي على الشمالمثلا
+
+531
+00:55:25,770 --> 00:55:39,310
+يبقى الدالة Y تساوي E أس اتنين T هي
+
+532
+00:55:39,310 --> 00:55:41,290
+حل هذه المعرفة
+
+533
+00:55:50,280 --> 00:55:54,280
+على كل الـ real line الـ exponential function EO6
+
+534
+00:55:54,280 --> 00:55:57,280
+EO6 EO6 EO6 EO6 EO6 EO6 EO6 EO6 EO6 EO6 EO6 EO6
+
+535
+00:55:57,280 --> 00:56:04,660
+EO6 EO6 EO6 EO6 EO6 EO6 EO6 EO6 EO6
+
+536
+00:56:04,660 --> 00:56:15,140
+EO6 EO6
+
+537
+00:56:17,120 --> 00:56:21,540
+وقدمنا فيه امتحانة ونجحنا بجدارة يعني طب هذه بدنا
+
+538
+00:56:21,540 --> 00:56:26,240
+نشوف كيف حالة هذه لو جات اشتقها قداش بتكون مشتقتها
+
+539
+00:56:26,240 --> 00:56:33,010
+اثنان E أس اثنان Tيبقى بده يشيل هذه ويكتب لتنين E
+
+540
+00:56:33,010 --> 00:56:37,910
+أس اتنين T ناقص اتنين E أس اتنين T مقدش يبقى
+
+541
+00:56:37,910 --> 00:56:43,110
+الجواب Zero زي الطرف اليمين إذا فعلا هذه حل طب
+
+542
+00:56:43,110 --> 00:56:47,090
+عشان واحدة تقولك كيف جبت هذه كيف جبت هو شغلنا
+
+543
+00:56:47,090 --> 00:56:52,370
+بداية من المرة القادمة و لنهاية المقرر كل شغلنا
+
+544
+00:56:52,370 --> 00:56:58,790
+إيجاد الحلول للمعادلات التفضلية نعطيكي مثال آخر
+
+545
+00:56:59,280 --> 00:57:06,420
+يبقى example show
+
+546
+00:57:06,420 --> 00:57:10,060
+that
+
+547
+00:57:10,060 --> 00:57:21,260
+y تساوي T E أس T is a solution is
+
+548
+00:57:21,260 --> 00:57:30,990
+a solution of the differentialEquation هي عبارة عن
+
+549
+00:57:30,990 --> 00:57:38,930
+حل المعادلة التفاضلية y w prime نقص اتنين y prime
+
+550
+00:57:38,930 --> 00:57:48,930
+زائد y تساوي زيرو on the interval على الفترة من
+
+551
+00:57:48,930 --> 00:57:51,510
+سالب infinity ل infinity
+
+552
+00:58:03,070 --> 00:58:08,350
+يبقى حل المعادلة التفاضلية هو عن دالة معرفة على
+
+553
+00:58:08,350 --> 00:58:14,250
+فترة وتحقق المعادلة الحمد لله قال يبين لي إن هذا
+
+554
+00:58:14,250 --> 00:58:20,430
+هو حل للمعادلة التفاضلية على الفترة السؤال هو جداش
+
+555
+00:58:20,430 --> 00:58:28,410
+domain T في E أس T بمعنى أخر هل توجد نقطة الدالة
+
+556
+00:58:28,410 --> 00:58:33,780
+هذه ماهياش معرفة عندها؟لأ كله من سالب حتى عند Zero
+
+557
+00:58:33,780 --> 00:58:37,400
+عند Zero بتطلع Zero في E of Zero اللي هو بواحد
+
+558
+00:58:37,400 --> 00:58:45,640
+يبقى Zero معرفة يبقى باجي بقوله ال Y تساوي T في E
+
+559
+00:58:45,640 --> 00:58:54,580
+of T is defined معرفة for all T اللي موجودة في ال
+
+560
+00:58:54,580 --> 00:58:59,850
+interval من سالب Infinity إلى Infiniteيبقى الدلل
+
+561
+00:58:59,850 --> 00:59:04,510
+يا طهالي هي معرفة عليها كل الفضل لكن هي حل والله
+
+562
+00:59:04,510 --> 00:59:09,270
+مش حل لسه انا مش عارف تمام؟ يبقى بهذه فيها المشتقة
+
+563
+00:59:09,270 --> 00:59:12,570
+الأولى والثانية إذا بدي أروح أجيب المشتقة الأولى
+
+564
+00:59:12,570 --> 00:59:18,630
+والمشتقة الثانية يبقى لما أقول له Y تسوى T E Os T
+
+565
+00:59:18,630 --> 00:59:24,210
+بدي أروح أجيب له المشتقة الأولى هذه يا بنات تعتبر
+
+566
+00:59:24,210 --> 00:59:30,140
+دلل وهذه دلل إذا مشتقة حاصل ضربالأولى في مشتقة
+
+567
+00:59:30,140 --> 00:59:35,120
+الثانية زائد الثانية في مشتقة الأولى يبقى الأولى
+
+568
+00:59:35,120 --> 00:59:39,100
+اللى هى T مشتقة ال exponential بال exponential
+
+569
+00:59:39,100 --> 00:59:45,720
+اتسل زائد الدالة التانية في مشتقة الأولى اللى هى
+
+570
+00:59:45,720 --> 00:59:51,360
+بواحدهذه المشتقة الأولى بدنا نروح نجيب المشتقة
+
+571
+00:59:51,360 --> 00:59:58,300
+الثانية يبقى بد واي ضعف لقايم بدنا نروح نشتق هذه
+
+572
+00:59:58,300 --> 01:00:04,180
+الجزء الأول برضه مشتقة حاصل ضرب دالتين الأولى في
+
+573
+01:00:04,180 --> 01:00:09,140
+مشتقة الدالة التانية زائد الدالة التانية في مشتقة
+
+574
+01:00:09,140 --> 01:00:15,730
+الأولى نجي للي بعدها زائدمشتقة ال Eost بال Eost
+
+575
+01:00:15,730 --> 01:00:25,870
+itself يبقى الجواب T Eost زائد 2 Eost الان نمسك
+
+576
+01:00:25,870 --> 01:00:29,690
+المعلومات اللى حصلنا عليها و نرجع نعود في المعادل
+
+577
+01:00:29,690 --> 01:00:35,770
+اللى فوق يبقى بدأ خدله الان Y double prime نقص 2 Y
+
+578
+01:00:35,770 --> 01:00:42,150
+prime زائد Yإن طلب الله الناتج يساوي الصفر بيكون
+
+579
+01:00:42,150 --> 01:00:51,470
+هذا هو عن حل يبقى هذا الكلام يبقى يساوي يبقى يبقى
+
+580
+01:00:51,470 --> 01:00:59,670
+يبقى يبقى يبقى يبقى يبقى يبقى يبقى يبقى يبقى يبقى
+
+581
+01:00:59,670 --> 01:00:59,910
+يبقى يبقى يبقى يبقى يبقى يبقى يبقى يبقى يبقى يبقى
+
+582
+01:00:59,910 --> 01:01:01,330
+يبقى يبقى يبقى يبقى يبقى يبقى يبقى يبقى يبقى يبقى
+
+583
+01:01:01,330 --> 01:01:01,330
+يبقى يبقى يبقى يبقى يبقى يبقى يبقى يبقى يبقى يبقى
+
+584
+01:01:01,330 --> 01:01:07,940
+يبقى يبقى يبقى يبقى ييبقى T E Os T زائد E Os T
+
+585
+01:01:07,940 --> 01:01:14,200
+شيلنا Y Prime و حطينا منين قيمتها قال لي زائد Y
+
+586
+01:01:14,200 --> 01:01:21,380
+وين Y اللي هي طالب الأصل يبقى زائد T E Os T بدي
+
+587
+01:01:21,380 --> 01:01:26,300
+أشوف كده إيش بيطلع هدول يبقى هذا الكلام يساعد هذه
+
+588
+01:01:26,300 --> 01:01:34,260
+هي هذه صحيح ولا لأيبقى اتنين T E و أس T زائدي
+
+589
+01:01:34,260 --> 01:01:41,700
+اتنين E و أس T بده افك الجث هذا ناقص اتنين T E و
+
+590
+01:01:41,700 --> 01:01:49,920
+أس T ناقص اتنين E و أس T طلعي ليه؟ هذه و هذه
+
+591
+01:01:49,920 --> 01:01:56,180
+بإشارتين مختلفتين صحيح ولا لأ؟ يبقى عند الجامع
+
+592
+01:01:56,180 --> 01:02:03,810
+بيثلاشههذه و هذه نفس القصة بإشارتين يبقى المجموع
+
+593
+01:02:03,810 --> 01:02:08,410
+الكل قداش بطلع Zero اللي هو الطرف اليمين من
+
+594
+01:02:08,410 --> 01:02:14,030
+المعادلة اللي عندنا هذه يبقى أثبت له Y''-2Y''زاد Y
+
+595
+01:02:14,030 --> 01:02:19,630
+كله يساوي مين Zero يبقى فعلا هذه حل المعادلة على
+
+596
+01:02:19,630 --> 01:02:26,390
+الفترة من سلب Infinity إلى InfinityY تساوي T في ال
+
+597
+01:02:26,390 --> 01:02:35,970
+E أس T is a solution of Y double A prime نقص اتنين
+
+598
+01:02:35,970 --> 01:02:43,230
+Y prime زائد Y يساوي Zero on ال interval من سالب
+
+599
+01:02:43,230 --> 01:02:46,310
+Infinity إلى Infinity
+
+600
+01:03:14,540 --> 01:03:20,580
+not ملاحظة بسيطة المعادلة تفضل يا ابنت ممكن ما
+
+601
+01:03:20,580 --> 01:03:24,860
+يكونش لحل واحد و بس ممكن حلان ممكن تلان ممكن ما لا
+
+602
+01:03:24,860 --> 01:03:29,280
+نهاية من الحلول يعني ليس بالضرورة أن يكون حلا
+
+603
+01:03:29,280 --> 01:03:33,060
+واحدا فقط يبقى باجي بقوله the differential
+
+604
+01:03:33,060 --> 01:03:39,460
+equation may
+
+605
+01:03:39,460 --> 01:03:40,400
+have
+
+606
+01:03:44,530 --> 01:03:58,790
+more than more than one solution ممكن يكون لها
+
+607
+01:03:58,790 --> 01:04:05,930
+أكتر من حل حلين تلاتة أربعة جد ما يكون نعطي
+
+608
+01:04:05,930 --> 01:04:10,670
+definition the set of all solutions
+
+609
+01:04:13,400 --> 01:04:20,780
+of all solutions of
+
+610
+01:04:20,780 --> 01:04:25,960
+a given differential
+
+611
+01:04:25,960 --> 01:04:34,320
+equation لدالة تفاضلية مُعطَى is called نروح
+
+612
+01:04:34,320 --> 01:04:39,300
+نسميها general solution نسميها
+
+613
+01:04:40,370 --> 01:04:51,090
+general solution of differential
+
+614
+01:04:51,090 --> 01:04:57,930
+equation of the
+
+615
+01:04:57,930 --> 01:05:07,490
+differential equation for example كمثال
+
+616
+01:05:07,490 --> 01:05:08,230
+لذلك
+
+617
+01:05:28,520 --> 01:05:44,650
+Y'-2Y يساوي 0Y تساوي C يقص اتنين T و C is any
+
+618
+01:05:44,650 --> 01:05:49,490
+positive
+
+619
+01:05:49,490 --> 01:05:52,690
+real number
+
+620
+01:06:22,810 --> 01:06:29,050
+المعادلة التفاضية ممكن يكون لها أكثر من حل، حلين،
+
+621
+01:06:29,050 --> 01:06:33,350
+تلاتة، أربعة، ما لنهاجة، ما يكون معنا مشكلةنقطة
+
+622
+01:06:33,350 --> 01:06:37,850
+تعريف بقول the set of all solutions يبقى لو جمعنا
+
+623
+01:06:37,850 --> 01:06:44,450
+كل الحلول للمعادلة التفاضلية وحطناهم في set معينة
+
+624
+01:06:44,450 --> 01:06:48,510
+بسمي ال set هذه هي ال general solution حل العام
+
+625
+01:06:48,510 --> 01:06:54,150
+للمعادلة التفاضلية الذي يجتمل على كل حل من حلول
+
+626
+01:06:54,150 --> 01:06:58,770
+المعادلة يبقى بسميه the general solution of the
+
+627
+01:06:58,770 --> 01:07:02,730
+differential equationعلى سبيل المثال المعادلة هذه
+
+628
+01:07:02,730 --> 01:07:08,250
+توس اخدناها قبل قليل صحيح؟ وقلنا ايش الحل تبعها؟ E
+
+629
+01:07:08,250 --> 01:07:13,810
+اوس اتنين T لكن لو رحت قلت انا في عندي Y يساوي C E
+
+630
+01:07:13,810 --> 01:07:17,250
+اوس اتنين يقولوا C is any positive real number
+
+631
+01:07:17,250 --> 01:07:21,060
+احنا في الحل اللي اعطيناه كانت C انا بجداشبواحد
+
+632
+01:07:21,060 --> 01:07:27,540
+حطيها خمسة ونشوف هل بتحققها ولا لأ لو كانت خمسة
+
+633
+01:07:27,540 --> 01:07:33,240
+يبقاش بالصير خمسة في E أوس اتنين T بده اشتقها وشقة
+
+634
+01:07:33,240 --> 01:07:37,980
+E أوس اتنين T باتنين E أوس اتنين في خمسة بعشرة E
+
+635
+01:07:37,980 --> 01:07:44,960
+أوس اتنين Tيبقى هي عشرة E أوس اتنين T نقص اتنين في
+
+636
+01:07:44,960 --> 01:07:48,260
+خمسة E أوس اتنين يبقى عشرة E أوس اتنين يبقى
+
+637
+01:07:48,260 --> 01:07:51,720
+المجموع يسوي قداشي زرع ان شاء الله تاخديها بواحد
+
+638
+01:07:51,720 --> 01:07:57,140
+عالمية مش عشرة .. مش خمسة واحد عالمية حطي اي رقم
+
+639
+01:07:57,140 --> 01:08:01,840
+موجة بيجي في بني ان شاء الله تحطي جدر اتنينيبقى
+
+640
+01:08:01,840 --> 01:08:06,800
+حاطي اي رقم موجب ييجي في بالك بيطلع عندك حال يبقى
+
+641
+01:08:06,800 --> 01:08:08,840
+كم حالة عندي اللي هو المعادلة التفاضلية اللي بيصير
+
+642
+01:08:08,840 --> 01:08:14,690
+هذهما لنهاية من الحلول، تمام؟ كل غيريسي، كل واحد،
+
+643
+01:08:14,690 --> 01:08:19,150
+مثلا اللي قعدت هنا حوالي الآن، صار بيجي ما يقرب من
+
+644
+01:08:19,150 --> 01:08:23,550
+خمسين، كل واحدة تحط حل، بيطلع عندها حل، كل واحدة
+
+645
+01:08:23,550 --> 01:08:28,010
+مختلفة عن أخر، كل واحد يحقق المعادلة التفاضلية،
+
+646
+01:08:28,010 --> 01:08:32,490
+إذا المعادلة التفاضلية يمكن أن يكون لها مجموعة من
+
+647
+01:08:32,490 --> 01:08:38,470
+الحلول وليس حلا واحدة نعطي آخر تعريف في هذه
+
+648
+01:08:38,470 --> 01:08:49,360
+المقدمةdefinition if we are given values if we are
+
+649
+01:08:49,360 --> 01:08:57,000
+given values اذا اعطينا قيم of the unknown
+
+650
+01:08:57,000 --> 01:09:07,140
+function of the unknown function للدلة المجهولة
+
+651
+01:09:07,140 --> 01:09:19,730
+andits derivatives and its derivatives وعطينا حلول
+
+652
+01:09:19,730 --> 01:09:32,930
+لمشتقتها at a single value عند قيمة واحدة of the
+
+653
+01:09:32,930 --> 01:09:36,050
+independent
+
+654
+01:09:42,060 --> 01:09:53,300
+variable عند قيمة واحدة للمتغير المستقل then the
+
+655
+01:09:53,300 --> 01:10:08,580
+differential equation is called بنسميها an initial
+
+656
+01:10:36,550 --> 01:10:49,270
+والقيم المعطاهاالقوانين المعروفة تسمى بـInitial
+
+657
+01:10:49,270 --> 01:10:58,570
+Conditions يبقى
+
+658
+01:10:58,570 --> 01:11:05,450
+الشروط الابتدائية على
+
+659
+01:11:05,450 --> 01:11:05,890
+سبيل المثال
+
+660
+01:11:14,770 --> 01:11:19,470
+على سبيل المثال الاختصارات
+
+661
+01:11:19,470 --> 01:11:23,950
+الاختصارات الاختصارات الاختصارات الاختصارات
+
+662
+01:11:23,950 --> 01:11:25,370
+الاختصارات الاختصارات الاختصارات الاختصارات
+
+663
+01:11:25,370 --> 01:11:25,370
+الاختصارات الاختصارات الاختصارات الاختصارات
+
+664
+01:11:25,370 --> 01:11:25,450
+الاختصارات الاختصارات الاختصارات الاختصارات
+
+665
+01:11:25,450 --> 01:11:32,810
+الاختصارات الاختصارات
+
+666
+01:11:32,810 --> 01:11:34,710
+الاختصارات الاختصارات الاختصارات الاختصارات
+
+667
+01:11:34,710 --> 01:11:34,750
+الاختصارات الاختصارات الاختصارات الاختصارات
+
+668
+01:11:34,750 --> 01:11:35,210
+الاختصارات الاختصارات الاختصارات الاختصارات
+
+669
+01:11:35,210 --> 01:11:39,050
+الاختصارات الاختصارات الاختصارات الاختصارات
+
+670
+01:11:39,050 --> 01:11:42,070
+الاختصارات
+
+671
+01:11:44,410 --> 01:11:54,230
+و ال y عند ال y على 2 ساوي سلبي 2 و ال y عند ال y
+
+672
+01:11:54,230 --> 01:12:04,530
+على 2 ساوي واحد من ال value problems
+
+673
+01:12:46,080 --> 01:12:50,860
+بنرجع لهذا التعريف مرة ثانية وبعد ذلك نروح نحطه
+
+674
+01:12:50,860 --> 01:12:55,860
+على أرض الواقع بقول if we are given values إذا
+
+675
+01:12:55,860 --> 01:13:02,080
+أعطينا قيم of the unknown function لدالة المجهولة
+
+676
+01:13:02,080 --> 01:13:06,440
+and its derivative ومشتقات أعطينا قيم لدالة
+
+677
+01:13:06,440 --> 01:13:12,500
+المجهولة ومشتقات الدالة المجهولة وين؟At a single
+
+678
+01:13:12,500 --> 01:13:18,860
+value عند قيمة محددة او قيمة معينة واحدة فقط لمين
+
+679
+01:13:18,860 --> 01:13:23,760
+لل independent variable للمتغير المستقل لما اقول Y
+
+680
+01:13:23,760 --> 01:13:27,780
+ده اللي في T يا بناتي يبقى Y هو المتغير التابع و T
+
+681
+01:13:27,780 --> 01:13:34,380
+هو المتغير المستقل يعني ايه ده؟وحصلنا على قيم لها
+
+682
+01:13:34,380 --> 01:13:41,160
+نتيجة ليعطاها قيمة محددة للمتغير المستقل عطينا قيم
+
+683
+01:13:41,160 --> 01:13:46,700
+لـY مشتقتاتها نتيجة ليعطاها قيمة للمتغير المستقل
+
+684
+01:13:50,120 --> 01:13:55,320
+بقول عليها initial value problem يعني مسألة القيم
+
+685
+01:13:55,320 --> 01:14:02,460
+الحدية تمام و هختصرها IVP مش very important person
+
+686
+01:14:02,460 --> 01:14:06,740
+VIP تبع الشخصية لأ لأ لأ initial value problem
+
+687
+01:14:06,740 --> 01:14:11,620
+الحرف الأول initial الحرف التاني V اللي هو ال
+
+688
+01:14:11,620 --> 01:14:15,980
+value الحرف التالت P جاية من كلمة مين problemيبقى
+
+689
+01:14:15,980 --> 01:14:22,620
+كلمة initial value problem هاختصرها إلى IVP طب
+
+690
+01:14:22,620 --> 01:14:26,380
+الشروط اللي حطيناها هذه بسميها initial conditions
+
+691
+01:14:26,380 --> 01:14:31,640
+الشروط الابتدائية and the given values والقيم اللي
+
+692
+01:14:31,640 --> 01:14:35,700
+اعطيناها هذه are called the initial conditions
+
+693
+01:14:35,700 --> 01:14:40,120
+نعطي الآن مثال على الكلام اللي احنا جايلينه هنا
+
+694
+01:14:40,560 --> 01:14:44,840
+مثلًا الـ differential equations طلّي لهذه من أي
+
+695
+01:14:44,840 --> 01:14:51,160
+رتبةمن الرتبة الأولى تمام اعطينا ان قيمة y عند ال
+
+696
+01:14:51,160 --> 01:14:55,000
+zero يسوى كده؟ خمس يبقى ماعندش الا condition واحد
+
+697
+01:14:55,000 --> 01:15:00,400
+جديش عندك رتب جديش بتعطي conditions الرتبة الأولى
+
+698
+01:15:00,400 --> 01:15:03,480
+بتعطي condition واحد الرتبة الثانية بدك تعطي two
+
+699
+01:15:03,480 --> 01:15:06,740
+conditions الرتبة التالتة three conditions و هكذا
+
+700
+01:15:06,740 --> 01:15:12,080
+يعني اذا عند الرتبة التالتة بدي اعطي condition ل y
+
+701
+01:15:12,080 --> 01:15:19,390
+و ل y prime و ل y w primeبتعطي قيم لهم دولهذه
+
+702
+01:15:19,390 --> 01:15:24,090
+المعادلة من الرتبة أسنى رغم أن الرتبة الأولى ليست
+
+703
+01:15:24,090 --> 01:15:29,250
+موجودة فهيش يقول why عند بي على اتنين بده تسوى
+
+704
+01:15:29,250 --> 01:15:33,530
+قداش سالب اتنين why prime عند بي على اتنين بده
+
+705
+01:15:33,530 --> 01:15:38,990
+تسوى قداش واحد يبقى حطيت شرطين لاحظى عند نفس ال
+
+706
+01:15:38,990 --> 01:15:43,970
+independent variable يبقى هنا تيب بي على اتنين و
+
+707
+01:15:43,970 --> 01:15:47,550
+هنا مش هذا عنده نقطة و هذا عنده نقطة تانيةيعني
+
+708
+01:15:47,550 --> 01:15:50,590
+عنده قيمة للمتغير المسؤول عنها؟ لأ عندها نفس
+
+709
+01:15:50,590 --> 01:15:56,250
+القيمة روحنا قولنا هنا و هنا at a single value عند
+
+710
+01:15:56,250 --> 01:15:59,590
+قيمة واحدة يبقى الباية على اتنين هذه اللي كانت
+
+711
+01:15:59,590 --> 01:16:03,690
+single value في التعريف لل independent variable
+
+712
+01:16:04,010 --> 01:16:10,290
+للمتغير المستقل اعطتني قيمة ل Y و اعطتني قيمة ل Y'
+
+713
+01:16:11,170 --> 01:16:15,190
+زي ما انت شايفه يبقى اذا عندي معادلة بالشرط او
+
+714
+01:16:15,190 --> 01:16:19,790
+معادلة بشرطين او معادلة بثلاثة شروط او باربعة شروط
+
+715
+01:16:19,790 --> 01:16:26,710
+بسمي هذه initial value problem طيب
+
+716
+01:16:26,710 --> 01:16:30,910
+ليش ال initial value problem؟لو ماعطنيش ال
+
+717
+01:16:30,910 --> 01:16:37,210
+condition هذا بيطلع عندي الجواب هه بثابت، اذا
+
+718
+01:16:37,210 --> 01:16:40,590
+المعادلة من الرتبة الأولى، بثابتين، لأنه بدنا
+
+719
+01:16:40,590 --> 01:16:44,790
+نكامل، ونتيجة التكامل بجيني ثابتمظبوط او لا؟
+
+720
+01:16:44,790 --> 01:16:49,270
+بثابتان اذا من الرتبة الثانية، بثلاث او بثلاثة
+
+721
+01:16:49,270 --> 01:16:52,830
+ثوابت من الرتبة اللي هو التالتة و هكذا ال initial
+
+722
+01:16:52,830 --> 01:16:57,810
+conditions منها من خلالها بجيب قداش مقدار اللي هو
+
+723
+01:16:57,810 --> 01:17:02,290
+المقدار الثابت أو قداش قيمة المقدار الثابت اللي
+
+724
+01:17:02,290 --> 01:17:07,030
+موجود عندنا حد بتحب تسأل اي تسأل في كل ما سمعته
+
+725
+01:17:07,030 --> 01:17:12,050
+اليوم في هذه المحاضرة تسأل اسأله زي مسألة أخنا قبل
+
+726
+01:17:12,050 --> 01:17:15,330
+شوية و اجبناها اتفضليلأن معادلة تفاضية ماينفعش
+
+727
+01:17:15,330 --> 01:17:19,690
+تكون Zero Order ماينفعش تكون Zero Order ماينفعش
+
+728
+01:17:19,690 --> 01:17:21,610
+تكون Zero Order ماينفعش تكون Zero Order ماينفعش
+
+729
+01:17:21,610 --> 01:17:21,610
+تكون Zero Order ماينفعش تكون Zero Order ماينفعش
+
+730
+01:17:21,610 --> 01:17:21,930
+تكون Zero Order ماينفعش تكون Zero Order ماينفعش
+
+731
+01:17:21,930 --> 01:17:22,350
+تكون Zero Order ماينفعش تكون Zero Order ماينفعش
+
+732
+01:17:22,350 --> 01:17:23,330
+تكون Zero Order ماينفعش تكون Zero Order ماينفعش
+
+733
+01:17:23,330 --> 01:17:25,590
+تكون Zero Order ماينفعش تكون Zero Order ماينفعش
+
+734
+01:17:25,590 --> 01:17:27,130
+تكون Zero Order ماينفعش تكون Zero Order ماينفعش
+
+735
+01:17:27,130 --> 01:17:27,170
+تكون Zero Order ماينفعش تكون Zero Order ماينفعش
+
+736
+01:17:27,170 --> 01:17:30,610
+تكون Zero Order ماينفعش تكون Zero Order ماينفعش
+
+737
+01:17:30,610 --> 01:17:31,450
+تكون Zero Order ماينفعش تكون Zero Order ماينفعش
+
+738
+01:17:31,450 --> 01:17:39,430
+تكون Zero Order ماينفعش تكون Zero
+
+739
+01:17:39,450 --> 01:17:43,070
+قلنا أول ما بدأنا المعادلة التفاضلية هي معادلة
+
+740
+01:17:43,070 --> 01:17:48,770
+يظهر فيها one or more يعني لازم على الأقل تظهر
+
+741
+01:17:48,770 --> 01:17:53,410
+مين؟ المشتقة الأولى حتى أقول من الرتبة .. من جهة
+
+742
+01:17:53,410 --> 01:17:56,090
+الرتبة الأولى، التانية، التالتة، الرابعة، بنفع
+
+743
+01:17:56,090 --> 01:18:00,610
+أقول من الرتبة رقم ناقص تلاتة؟ كيف رتبة ناقص
+
+744
+01:18:00,610 --> 01:18:06,370
+تلاتة؟ هي في تفاضل بنزل نزول؟ طيب حالتك تلاقي سؤال
+
+745
+01:18:06,370 --> 01:18:13,040
+تاني؟خلاص يبقى ان شاء الله يوم الأثنين بدنا نبدأ
+
+746
+01:18:13,040 --> 01:18:16,480
+يا بنات في ال first order differential equation
+
+747
+01:18:16,480 --> 01:18:22,680
+ياريت اتحضريلي اول section او اول two sections من
+
+748
+01:18:22,680 --> 01:18:26,860
+chapter اتنين اللي هو تبدأ بال linear و اللي بعده
+
+749
+01:18:26,860 --> 01:18:29,780
+ماشي ان شاء الله و تعالى يعطيكوا العافية
+
diff --git a/PL9fwy3NUQKwa8ZDfSFGn6H8xVFLzqmCZC/e5F8lf-FFH0_postprocess.srt b/PL9fwy3NUQKwa8ZDfSFGn6H8xVFLzqmCZC/e5F8lf-FFH0_postprocess.srt
new file mode 100644
index 0000000000000000000000000000000000000000..f8793db29a5aed8235f55cc2806276ca8db05b1b
--- /dev/null
+++ b/PL9fwy3NUQKwa8ZDfSFGn6H8xVFLzqmCZC/e5F8lf-FFH0_postprocess.srt
@@ -0,0 +1,3332 @@
+1
+00:00:12,160 --> 00:00:15,740
+المره اللي فات بدينا في section 2-6 ال exact
+
+2
+00:00:15,740 --> 00:00:21,680
+equations and integrating factors وبدينا فقط بال
+
+3
+00:00:21,680 --> 00:00:26,180
+exact equations وعرفنا شرط ال exactness كالتالي
+
+4
+00:00:29,810 --> 00:00:38,750
+مكتوب معاك اذا m of x y dx زي ال n of x y dy تساوي
+
+5
+00:00:38,750 --> 00:00:47,950
+zero is exact if and only ifاللي هو ال partial m
+
+6
+00:00:47,950 --> 00:00:55,530
+by partial y بده يساوي partial n by partial x هذه
+
+7
+00:00:55,530 --> 00:00:59,890
+عبارة عن نظرية وبرهنها وقلنا هذه بتسهلي عملية
+
+8
+00:00:59,890 --> 00:01:04,650
+اثبات ان ال function هذه exact واخدنا على ذلك
+
+9
+00:01:04,650 --> 00:01:10,990
+مثالا واحدا الان بنروح ناخد المثال لرقم اتنين يبقى
+
+10
+00:01:10,990 --> 00:01:19,390
+example twoExample 2 بيقول
+
+11
+00:01:19,390 --> 00:01:27,990
+Solve the differential equation حل المعادلة
+
+12
+00:01:27,990 --> 00:01:36,890
+التفاضلية المعادلة موطعة للشكل التالف Y في E أس XY
+
+13
+00:01:38,310 --> 00:01:47,910
+فى cosine اتنين X ناقص اتنين E أُس XY فى sine
+
+14
+00:01:47,910 --> 00:02:00,230
+اتنين X زائد اتنين X كل هذا الكلام فى DX زائد X فى
+
+15
+00:02:00,230 --> 00:02:05,810
+E أُس XY فى cosine اتنين X
+
+16
+00:02:26,140 --> 00:02:32,800
+هذه المعادلة هي المعادلة رقم 1يبقى انا بدى ابحث في
+
+17
+00:02:32,800 --> 00:02:37,280
+البداية هل هذه المعادلة exact والله ماهياش exact
+
+18
+00:02:37,280 --> 00:02:41,680
+باجي لشرط ال exactness اللى مواطة فوق يبقى بدى
+
+19
+00:02:41,680 --> 00:02:49,900
+ابحث عن partial M by partial Y يساوي مرة الإفادة
+
+20
+00:02:49,900 --> 00:02:53,800
+يقولنا يا بنات إذا احنا بنفضل بالنسبة إلى Y يبقى
+
+21
+00:02:53,800 --> 00:03:00,020
+بنعتبر ال X كونستنطل ومقدار ثابتبنجي لهذه يبقى
+
+22
+00:03:00,020 --> 00:03:07,020
+cosine X هذه مقدار ثابت عند هنا Y وعندي E أس XY
+
+23
+00:03:07,020 --> 00:03:14,070
+يبقى دول حاصن ضرب دالتين إذا دول هستخدم مشتقتحاصل
+
+24
+00:03:14,070 --> 00:03:17,850
+ضارب دلتين دل الأولى في مشتقة الثانية زي ده
+
+25
+00:03:17,850 --> 00:03:22,370
+الثانية في مشتقة الأولى يبقى لو جت اشتق الأولى
+
+26
+00:03:22,370 --> 00:03:27,130
+بالنسبة له يبقى مشتقة هذه بقداش واحد صحيح بصير
+
+27
+00:03:27,130 --> 00:03:34,730
+عندي E أس XY في Cos 2X Cos 2X لأنه مقدار ثابت
+
+28
+00:03:34,730 --> 00:03:40,360
+مالوش دعوة زائدهذا الـ Y اللي برا يجب أن تكون الـ
+
+29
+00:03:40,360 --> 00:03:44,900
+Exponential الـ Exponential مشتقتة بنفسها ضرب
+
+30
+00:03:44,900 --> 00:03:49,480
+مشتقت الـ Os تبعها الـ Os بيشتقوا بالنسبة لـ Y
+
+31
+00:03:49,480 --> 00:03:54,820
+مشتقوا بالنسبة لـ Y اللي هو بمين؟ ب X يبقى زائد Y
+
+32
+00:03:54,820 --> 00:03:55,720
+في X
+
+33
+00:04:13,620 --> 00:04:20,690
+يبقى ناقص اتنين X في E أس XY في كوصين اتنين Xفى
+
+34
+00:04:20,690 --> 00:04:27,050
+الـ sine اتنين X ومشتقة هدى بقداش ب Zero تمام لإن
+
+35
+00:04:27,050 --> 00:04:31,050
+احنا نشتق بالنسبة الى Y بعد اكه بدنا نروح نشتق
+
+36
+00:04:31,050 --> 00:04:35,910
+الجزء الثانى هذا بالاسم لمين الى X يبقى بدى
+
+37
+00:04:35,910 --> 00:04:42,690
+partial N by partial X يساوي بجى لادالة هدى طلعلي
+
+38
+00:04:42,690 --> 00:04:48,200
+ال term الأول هدى فيها Xو هذه فيها X و هذه فيها X
+
+39
+00:04:48,200 --> 00:04:53,200
+يعني مشتق اتحاصل ضرب تلات دوال نذكر ال calculus
+
+40
+00:04:53,200 --> 00:04:57,960
+ايه؟ بشتق الأولة و بثبت التنتين التانية بعدين بشتق
+
+41
+00:04:57,960 --> 00:05:01,000
+اللي في النص و بثبت اللي قبل هو اللي بعدها بعدين
+
+42
+00:05:01,000 --> 00:05:05,020
+بشتق الأخيرة و بثبت التنتين اللي قبل يكون خلصنا
+
+43
+00:05:05,020 --> 00:05:10,930
+اشتقاهيبقى بداجي أشتق هذه كالتالي مشتقة الأولى
+
+44
+00:05:10,930 --> 00:05:20,470
+بتروح بضل قداش عندي E أس XY في Cos 2X بعد هيك زائد
+
+45
+00:05:20,470 --> 00:05:26,010
+Xفى هذه بدى اشتقها بالنسبة ل X هي عبارة عن مين Y
+
+46
+00:05:26,010 --> 00:05:34,490
+في E أُس XY في Cos 2X هيك اشتقت الأولى والتانية
+
+47
+00:05:34,490 --> 00:05:40,330
+يبقى زائد ولا بيصير مشتقة ال cosine بسالب صين يبقى
+
+48
+00:05:40,330 --> 00:05:42,830
+سالب 2X
+
+49
+00:05:59,140 --> 00:06:03,700
+تعالى نقارن بين كل ترم من الترمات التلاتة
+
+50
+00:06:07,200 --> 00:06:13,960
+الترم التاني هو نفسه الترم التالت هو نفسه تمام
+
+51
+00:06:13,960 --> 00:06:17,900
+التمام يبقى القمتين صاروا بالهم زي بعض يبقى
+
+52
+00:06:17,900 --> 00:06:24,040
+بنستنتج من التنتين هذول انه partial M by partial Y
+
+53
+00:06:24,040 --> 00:06:30,580
+يسوى partial N by partial X هذا ايش بده يعطينا بده
+
+54
+00:06:30,580 --> 00:06:35,020
+يعطينا ان ذا differential
+
+55
+00:06:41,530 --> 00:06:51,330
+مدام exact يبقى there exist a function إبصي of x و
+
+56
+00:06:51,330 --> 00:06:57,850
+y بدها تساوي constant c such that بيحيث لنا
+
+57
+00:07:08,170 --> 00:07:22,190
+Y في E أس X Y Y في E أس X Y في Cos 2X ناقص 2 E أس
+
+58
+00:07:22,190 --> 00:07:32,390
+XY في Sin 2Xزائد اتنين X وطفابل الابسعي بالنسبة
+
+59
+00:07:32,390 --> 00:07:40,130
+الى Y يسوى ال term الأخير X E أس XY فيه cosine
+
+60
+00:07:40,130 --> 00:07:48,230
+اتنين X ناقص تلاتة مرة
+
+61
+00:07:48,230 --> 00:07:53,230
+تانية المرة اللي فاتتة أعرفنا ال exact equation
+
+62
+00:07:53,700 --> 00:07:59,220
+قلنا ال differential equation ال M DX زاد ال M DY
+
+63
+00:07:59,220 --> 00:08:04,640
+بقول عنها exact إذا جدرت لاجي function ψ of XY
+
+64
+00:08:04,640 --> 00:08:09,800
+تسوي constant بحيث مشتقة ال ψ بالنسبة لX بده يسوى
+
+65
+00:08:09,800 --> 00:08:14,970
+ال M و مشتقة ال ψ بالنسبة لY بده يسوى 100بدي يساوي
+
+66
+00:08:14,970 --> 00:08:23,370
+ال N تمام؟ يعني هذه كلها N و هذه كلها مرة واحدة هي
+
+67
+00:08:23,370 --> 00:08:30,530
+عبارة عن مين؟ عبارة عن M طيب كويس، الآن بضوحة كامل
+
+68
+00:08:30,530 --> 00:08:36,750
+إحداهما بنكمل أسهل فيهما فالعيلي هذه بدنا نكملها
+
+69
+00:08:36,750 --> 00:08:41,990
+بالنسبة لمين؟ ال X آه هذه حصل ضرب دلتين و بدنا
+
+70
+00:08:41,990 --> 00:08:47,180
+نكملهاأيه ال exponential في ال cosine بدي أرجع ال
+
+71
+00:08:47,180 --> 00:08:52,020
+integration by parts و بدها مرتين نكملها وبعد
+
+72
+00:08:52,020 --> 00:08:57,100
+مرتين بطلع main راسي المثلة قصة طويلة هذه وهذه
+
+73
+00:08:57,100 --> 00:09:01,700
+زيها بنفس الطريقة إذا التكامل هذه بالنسبة ل X
+
+74
+00:09:01,700 --> 00:09:06,900
+difficult شوية فيها نوع من الصعوبة نجي لهذه بدي
+
+75
+00:09:06,900 --> 00:09:11,120
+أكملها بالنسبة ل Y هذا constant هذا constant هذا
+
+76
+00:09:11,120 --> 00:09:15,830
+constantيبقى تكمل من الـ exponential المثال تبع
+
+77
+00:09:15,830 --> 00:09:19,910
+المرة اللي فترة اتكملنا لبساى بالنسبة الى X المرة
+
+78
+00:09:19,910 --> 00:09:24,550
+هذه بنا نتكمل لبساى بالنسبة اله أسهل ليه كتير يبقى
+
+79
+00:09:24,550 --> 00:09:31,750
+لو جه تكمل هذه باجي بقوله يبقى ابساى of XY يساوي
+
+80
+00:09:31,750 --> 00:09:36,570
+يبقى من التكامل هذه ابناط بالنسبة لمن؟ ل Y ال X
+
+81
+00:09:36,570 --> 00:09:41,130
+ثابت و ال cosine ثابتوالـ exponential تكاملها كما
+
+82
+00:09:41,130 --> 00:09:46,890
+هو مقسما على تفاضل المشتقة إذا كانت من الدرجة
+
+83
+00:09:46,890 --> 00:09:51,470
+الأولى طبعا من الدرجة الأولى بالنسبة ل Y ال X
+
+84
+00:09:51,470 --> 00:09:56,350
+يعتبر مقدار ثابت يبقى بنقسمعليه؟ لأنه بنكمل
+
+85
+00:09:56,350 --> 00:10:04,370
+بالنسبة الى Y يبقى X في E وال 6Y مقسم على X في Cos
+
+86
+00:10:04,370 --> 00:10:14,230
+2X ماقص 3Y زائد مقدار ثابت احنا بنكمل بالنسبة لمن؟
+
+87
+00:10:14,230 --> 00:10:20,930
+يبقى المقدار ثابت بدلالة من؟بدأ اه دلالة X لان X
+
+88
+00:10:20,930 --> 00:10:27,950
+يعتبر ثابت بالنسبة ل Y يفجأ زائد F of X بعد هيك
+
+89
+00:10:27,950 --> 00:10:34,450
+بدنا نروح نفضل هدي بالنسبة ل X و نسويها بمين بتدل
+
+90
+00:10:34,450 --> 00:10:39,530
+اللي عندنا هدي يفجأ بدأ أخد partial F of Psi by
+
+91
+00:10:39,530 --> 00:10:44,090
+partial X بدأ افضل هدي بالنسبة ل X طبعا بتروح هدي
+
+92
+00:10:44,090 --> 00:10:48,650
+مع هديبروح الله يسهل عليهم بظل عند e أوس x y في
+
+93
+00:10:48,650 --> 00:10:54,250
+cosine اتنين x لما نفاضلها بالنسبة ل x إذا المشتقت
+
+94
+00:10:54,250 --> 00:10:59,550
+حاصل ضرب داليتين y في e أوس x y
+
+95
+00:11:14,900 --> 00:11:19,760
+مشتقت هذه بالنسبة لل X بقداش؟ بـ0 مع السلام الله
+
+96
+00:11:19,760 --> 00:11:28,480
+يسهل عليها بضال عندي زائد F prime of Xالان عندي
+
+97
+00:11:28,480 --> 00:11:32,140
+partial of y على partial of x وعندي partial of y
+
+98
+00:11:32,140 --> 00:11:36,640
+على partial of x بده ساوي القيمتين البعض يبقى لو
+
+99
+00:11:36,640 --> 00:11:41,180
+جينا ساوينا القيمتين البعض بده يكون عند مين؟ y في
+
+100
+00:11:41,180 --> 00:11:51,080
+e أس x y في cos 2x نقص 2 e أس x y في sin 2x زائد f
+
+101
+00:11:51,080 --> 00:11:57,340
+prime of x بده يساوي المقدار اللي عنده هناكY E أس
+
+102
+00:11:57,340 --> 00:12:13,520
+XY في Cos 2X ناقص 2 E أس XY في Sin 2X زائد 2X
+
+103
+00:12:13,520 --> 00:12:16,540
+تعالى
+
+104
+00:12:16,540 --> 00:12:21,200
+نشوفأظن ال term هذا هو ال term هذا بالضبط تماما
+
+105
+00:12:21,200 --> 00:12:26,000
+يبقى لو جيبناه عنده بروح هذا هو ال term هذا بالضبط
+
+106
+00:12:26,000 --> 00:12:33,840
+تماما بضلش عندي إلا ال f prime of x يسوى قداش 2x
+
+107
+00:12:33,840 --> 00:12:39,360
+يبقى هذا بده يعطينا أن ال f of x بدنا نكامل هذا يا
+
+108
+00:12:39,360 --> 00:12:49,680
+بناتيبقى تكامل 2X DX يساوي X تربية زائد كونستانت
+
+109
+00:12:49,680 --> 00:12:57,420
+C1 يبقى باجي بقوله the solution of
+
+110
+00:12:57,420 --> 00:13:04,920
+the differential equation 1 is
+
+111
+00:13:13,930 --> 00:13:25,530
+يبقى اليمين EOS XY في Cos 2X ناقص تلاتة Y
+
+112
+00:13:28,630 --> 00:13:40,150
+زاد C1 يبقى C1 يساوي C1 مرة واحدة ورايا دماغك يبقى
+
+113
+00:13:40,150 --> 00:13:42,670
+هذا هو حل المثل
+
+114
+00:13:45,350 --> 00:13:49,170
+يبقى هذا هو المثال الثاني على الـ exact equation
+
+115
+00:13:49,170 --> 00:13:54,190
+ممكن يجي السؤال بغير الصيغة الأولى وغير الصيغة
+
+116
+00:13:54,190 --> 00:13:59,530
+التانية وفي نفس الوقت على ال exact كيف كالتالي
+
+117
+00:13:59,530 --> 00:14:07,590
+خديلك السؤال example 3 بقول find the value of the
+
+118
+00:14:07,590 --> 00:14:20,640
+constant B find the valueof the constant B هتيه
+
+119
+00:14:20,640 --> 00:14:27,620
+لمقدار الثابت B such that
+
+120
+00:14:27,620 --> 00:14:39,480
+the differential equation اللي هي مين؟ X Y تربية
+
+121
+00:14:39,480 --> 00:14:55,060
+زائدب X تربيع Y كله في DX زائد X تكييب زائد Y في X
+
+122
+00:14:55,060 --> 00:15:01,360
+تربيع DY بده يسوي ال zero is exact
+
+123
+00:15:36,090 --> 00:15:42,790
+سؤال مرة تانية السؤال بيقول لي هاتلي قيمة الثابت B
+
+124
+00:15:42,790 --> 00:15:46,750
+بحيث أن ال differential equation اللي قدامنا هذه
+
+125
+00:15:46,750 --> 00:15:51,040
+is exactيبقى هو ميعطيني ان ال differential
+
+126
+00:15:51,040 --> 00:15:55,500
+equation exact صحيح ولا لأ اذا الشرط partial m by
+
+127
+00:15:55,500 --> 00:16:01,720
+partial y بده يساوي partial n by partial x مظبوط
+
+128
+00:16:01,720 --> 00:16:08,280
+يبقى باجي بقوله since بما ان the differential
+
+129
+00:16:08,280 --> 00:16:20,000
+equation is exact we haveاللي همين partial M by
+
+130
+00:16:20,000 --> 00:16:27,060
+partial Y يسوى partial N by partial X إذا انت عالى
+
+131
+00:16:27,060 --> 00:16:31,560
+نفضل الجزء الأول بالنسبة إلى Y والجزء التالى
+
+132
+00:16:31,560 --> 00:16:38,040
+بالنسبة إلى Xيبقى partial M by partial Y هو تفضل
+
+133
+00:16:38,040 --> 00:16:45,020
+الجزء الأول يبقى 2XY ال X مقدر ثابت وال Y تربية
+
+134
+00:16:45,020 --> 00:16:52,660
+مشتقتها 2Y هذا بالنسبة إلى Y بطير ال Y يبقى زائد ب
+
+135
+00:16:52,660 --> 00:16:57,930
+X تربيةيبدو يسوى partial in by partial x يبقى فضل
+
+136
+00:16:57,930 --> 00:17:04,290
+هذا من نسبة اله x يبقى اللي هو قداش تلاتة x تربية
+
+137
+00:17:04,290 --> 00:17:13,830
+زيدي اتنين y xطب اتطلعيل هنا هذا 2YX يساوي من 2YX
+
+138
+00:17:13,830 --> 00:17:19,090
+لو راحت عندها بتروح يبقى بس تنتج من هذا الكلام ان
+
+139
+00:17:19,090 --> 00:17:26,710
+ال B X تربيع بده يساوي تلاتة X تربيع ممكن نقسم كله
+
+140
+00:17:26,710 --> 00:17:33,560
+على X تربيع يبقى النتيجة كده؟ B تساوي تلاتةلو
+
+141
+00:17:33,560 --> 00:17:38,980
+شيلنا بي اللى عندنا هذه و بحطنا مكانها تلاتة و
+
+142
+00:17:38,980 --> 00:17:42,800
+روحنا بحثنا هل هذه ال function او هل هذه ال
+
+143
+00:17:42,800 --> 00:17:45,880
+equation exact ولا ماهياش exact من اللى جيها
+
+144
+00:17:45,880 --> 00:17:52,220
+automatic هي عبارة عن exact equation طيب عنوان تبع
+
+145
+00:17:52,220 --> 00:17:56,340
+هذا section اللى كنا رافعينه اتنين ستة كانexact
+
+146
+00:17:56,340 --> 00:18:01,240
+equations and integrating factors حتى الآن لم
+
+147
+00:18:01,240 --> 00:18:05,980
+نتكلم عن مين؟ عن ال integrating factors يبقى بدنا
+
+148
+00:18:05,980 --> 00:18:10,730
+نتكلم عن ال integrating factorsبنعطي تعريف لل
+
+149
+00:18:10,730 --> 00:18:16,270
+integrating factor وبعد هيك نحاول نوجد شكل ال
+
+150
+00:18:16,270 --> 00:18:22,150
+integrating factor لبعض لل equations وبعد هيك ناخد
+
+151
+00:18:22,150 --> 00:18:27,450
+أمثلة عليه يبقى بدنا نيجي للشطرة الثانية من هذا ال
+
+152
+00:18:27,450 --> 00:18:33,310
+section اللي هو integrating factors
+
+153
+00:18:35,520 --> 00:18:41,440
+عوامل التكامل بنعطي تعريف لعامل التكامل يبقى
+
+154
+00:18:41,440 --> 00:18:45,940
+definition بقول
+
+155
+00:18:45,940 --> 00:18:53,460
+if the differential equation if the differential
+
+156
+00:18:53,460 --> 00:19:07,850
+equation اللي هو M of X وYDX زائد N of XY DY تساوي
+
+157
+00:19:07,850 --> 00:19:15,050
+Zero وسميها لهذه المعادلة رقم واحد is not exact is
+
+158
+00:19:15,050 --> 00:19:24,430
+not exact but the differential equation but the
+
+159
+00:19:24,430 --> 00:19:33,250
+differentialequation ولكن المعادلة التفاضلية لميو
+
+160
+00:19:33,250 --> 00:19:46,510
+of x y في m of x y في dx زائد لميو of x y لميو of
+
+161
+00:19:46,510 --> 00:20:01,170
+x y في n of x y dy تساوي 0is exact is exact then
+
+162
+00:20:01,170 --> 00:20:13,750
+ومن ثم لميو of x y is called an integrating factor
+
+163
+00:20:13,750 --> 00:20:20,330
+an integrating factor
+
+164
+00:20:20,330 --> 00:20:27,940
+عامل تكامل forاستخدام البرنامج الوطني differential
+
+165
+00:20:27,940 --> 00:20:32,460
+equation
+
+166
+00:20:32,460 --> 00:20:33,920
+one
+
+167
+00:21:02,870 --> 00:21:09,750
+نعود للتعريف مرة ثانية التعريف بيقول ما يأتي if
+
+168
+00:21:09,750 --> 00:21:13,430
+the differential equation اللي هو ال mdx زايد ال n
+
+169
+00:21:13,430 --> 00:21:17,770
+dy بالساوية zero is not exact يعني روحنا حسبنا
+
+170
+00:21:17,770 --> 00:21:21,170
+تفاضة ال m بالنسبة ال y و تفاضة ال n بالنسبة ال x
+
+171
+00:21:21,170 --> 00:21:25,510
+لجينا هم are not equalبسوش بعض يبقى في هذه الحالة
+
+172
+00:21:25,510 --> 00:21:27,390
+تبقى ال differential equation اللي عندنا معاها
+
+173
+00:21:27,390 --> 00:21:32,830
+ماهياش exact يبقى في هذه الحالة بيقول هذا not
+
+174
+00:21:32,830 --> 00:21:35,470
+exact بقضى differential equation روحنا على
+
+175
+00:21:35,470 --> 00:21:39,890
+المعادلة هذه وضربناها في دالة أخرى الدالة الأخرى
+
+176
+00:21:39,890 --> 00:21:46,390
+اسمتها Mu of XY يبقى صوت Mu of XY في M و Mu of XY
+
+177
+00:21:46,390 --> 00:21:52,800
+في N هذي Dy هذي X كله بدل ساوي Zeroجيت أخد partial
+
+178
+00:21:52,800 --> 00:21:56,580
+ال term هذا كله by partial y و partial ال term هذا
+
+179
+00:21:56,580 --> 00:22:01,280
+كله by partial x لجيت اتنين are equal يبقى
+
+180
+00:22:01,280 --> 00:22:06,420
+المعادلة الجديدة هداش بالصير exact ان حدث ذلك يبقى
+
+181
+00:22:06,420 --> 00:22:11,360
+الدالة mu of x y بقول هي عامل تكامل للمعادلة
+
+182
+00:22:11,360 --> 00:22:17,400
+التفاضلية اللي هو رقم 1 السؤال هو من وين بدنا
+
+183
+00:22:17,400 --> 00:22:22,390
+نجيبه عامل التكامل؟طبعا له طرق للحسابات ممكن نعطيك
+
+184
+00:22:22,390 --> 00:22:27,210
+المثلة و نقولك بينيه لإن هذه الدالة عامل تكامل و
+
+185
+00:22:27,210 --> 00:22:32,970
+ممكن نطلب منك إيجاد عامل تكامل ثم حل المعادلة
+
+186
+00:22:32,970 --> 00:22:38,790
+التفاضلية لذلك حاطط عندك في التمرينبدل السؤال يمكن
+
+187
+00:22:38,790 --> 00:22:44,070
+تلاتة هناخد بعض الأسئلة هذه و نحلها و نبيّلك كيف
+
+188
+00:22:44,070 --> 00:22:50,050
+بنحسب عامل التكامل و من ثم بدنا نروح إياه نستخدمه
+
+189
+00:22:50,050 --> 00:22:54,550
+فعندك سؤال تلاتة و عشرين فهعطلك العنوان التالي
+
+190
+00:22:54,550 --> 00:22:58,970
+some integrating
+
+191
+00:22:58,970 --> 00:23:02,770
+factors
+
+192
+00:23:10,210 --> 00:23:18,370
+سؤال 23 من الكتاب بيقول show that
+
+193
+00:23:18,370 --> 00:23:27,830
+if partial m by partial x ناقص partial m by
+
+194
+00:23:27,830 --> 00:23:41,670
+partial y على m يساوي q of y whereحيث الـ Q و الـ
+
+195
+00:23:41,670 --> 00:23:54,910
+Q is a function of Y only فقط في Y فقط then the
+
+196
+00:23:54,910 --> 00:24:08,000
+differential equation M DX زائد N DY تساوي Zerohas
+
+197
+00:24:08,000 --> 00:24:12,420
+an
+
+198
+00:24:12,420 --> 00:24:18,240
+integrating factor
+
+199
+00:24:18,240 --> 00:24:24,840
+in
+
+200
+00:24:24,840 --> 00:24:30,620
+the
+
+201
+00:24:30,620 --> 00:24:42,190
+form في الشكل التالياللي هو الـ Mu of Y بديساوي E
+
+202
+00:24:42,190 --> 00:24:57,110
+أُس تكامل لـ Q of Y في Dy لـ Q of Y في Dy كويس
+
+203
+00:24:57,110 --> 00:25:03,440
+نرجع مرة تانيةهذا محطوط على شكل سؤال في الكتاب
+
+204
+00:25:03,440 --> 00:25:09,740
+وفيه كمان سؤال تاني بعده مباشرة هنعطيكيه بعد قليل
+
+205
+00:25:09,740 --> 00:25:10,380
+كذلك
+
+206
+00:25:16,450 --> 00:25:21,190
+صحيح و لذلك سمنها عامل اتكامل يعني هو بيقول هيك
+
+207
+00:25:21,190 --> 00:25:26,550
+يعني احنا عامل المعادلة الأصلية is not exact لكن
+
+208
+00:25:26,550 --> 00:25:30,410
+لو ضربناها في الميو هذه بيصير المعادلة exact
+
+209
+00:25:30,410 --> 00:25:34,950
+وبالتالي بنحلها زي ما كنا نحل المسائل قبل قليل
+
+210
+00:25:34,950 --> 00:25:38,910
+يعني انا اللي عند المعادلة not exact بدي أحولها
+
+211
+00:25:38,910 --> 00:25:45,210
+إلى exact ثم أقوم بحلها زي ما كنت بحل قبل قليلفي
+
+212
+00:25:45,210 --> 00:25:49,750
+نيجي جالي some integrating factors بعض عوامل
+
+213
+00:25:49,750 --> 00:25:56,110
+التكامل هذه المثلة فيها عامل لحالة واحدة فقط بيقول
+
+214
+00:25:56,110 --> 00:26:00,570
+يبينلي ان تفاضل N بالنسبة ل X نقص تفاضل N بالنسبة
+
+215
+00:26:00,570 --> 00:26:05,770
+ل Y على M لو كان يساوي Q of Y يعني ده اللي فيه،
+
+216
+00:26:05,770 --> 00:26:11,110
+بمعنى أخرإن الدالة الأصلية عندها دي ماكنتش exact
+
+217
+00:26:11,110 --> 00:26:15,010
+بدليل إن partial n على partial x و partial z
+
+218
+00:26:15,010 --> 00:26:19,170
+بيسووش بعض لإن لو سووا بعض لجيت الفرق منهم عاش
+
+219
+00:26:19,170 --> 00:26:23,510
+Zero تمام يبقى هدول بيسووش بعض يعني المعادلة not
+
+220
+00:26:23,510 --> 00:26:29,670
+exact إذا لو طرحت الأثنين من بعض و جسمت على M لجيت
+
+221
+00:26:29,670 --> 00:26:35,720
+الناتج function في Y فقطحتى لو كانت كونستانت
+
+222
+00:26:35,720 --> 00:26:40,660
+باعتبارها function في y يبقى where q is a function
+
+223
+00:26:40,660 --> 00:26:44,780
+of y only then the differential equation اللي
+
+224
+00:26:44,780 --> 00:26:48,220
+عندها هذا has an integrating factor in the form
+
+225
+00:26:48,560 --> 00:26:57,880
+يبقى الشكل عامل التكامل دلّة في Y فقط وشكل U of Y
+
+226
+00:26:57,880 --> 00:27:03,520
+يساوي A والتكامل Q of Y دي Y يعني تكامل كل النتيجة
+
+227
+00:27:03,520 --> 00:27:08,490
+اللي عندنا هذه النتيجة تبقى بس دلّة في Yيبقى بقى
+
+228
+00:27:08,490 --> 00:27:12,050
+كاملة بكون حصلت على مين على عمل التكامل بضرب
+
+229
+00:27:12,050 --> 00:27:16,510
+المعادلة الأصلية فيه بكون حصلنا على exact equation
+
+230
+00:27:16,510 --> 00:27:21,550
+بحلها كما كنت بحل من قبل طب بس من وين جبته هذا بدك
+
+231
+00:27:21,550 --> 00:27:26,910
+تثبته مش هيك صح ولا لا يبقى هنا بقى أجي بقوله ال
+
+232
+00:27:26,910 --> 00:27:29,030
+proof أو ال solution
+
+233
+00:27:32,620 --> 00:27:38,380
+بدي أثبت أن هذا التكامل عليه كـ exponential هو
+
+234
+00:27:38,380 --> 00:27:42,880
+عبارة عن ال integrating factor لمن؟ للدالة اللي
+
+235
+00:27:42,880 --> 00:27:46,180
+عندنا هذه او لل equation اللي يبقى بالدرجة أقوله
+
+236
+00:27:46,180 --> 00:27:58,940
+let mu of y be an integrating factor
+
+237
+00:28:02,280 --> 00:28:13,940
+of the differential equation اللي هو ال M DX زائد
+
+238
+00:28:13,940 --> 00:28:22,540
+ال N DY بده يساوي زير زي ما انت شايفه فرضه انه
+
+239
+00:28:22,540 --> 00:28:26,260
+دالة في Y شو شكله انا مش عارف يبقى يبدأ بحث اللي
+
+240
+00:28:26,260 --> 00:28:34,020
+انا عن شكل الدالة لـ Mu of Y يبقى thenبدي اضربها
+
+241
+00:28:34,020 --> 00:28:44,420
+في الميو يبقى الميو في ال M في DX زائد الميو في ال
+
+242
+00:28:44,420 --> 00:28:49,860
+N في DY بده سوى Zero is Exact
+
+243
+00:28:52,920 --> 00:28:57,760
+صحيح؟ طبقا للتعريف يبقى درابط في الـ Mu صارت
+
+244
+00:28:57,760 --> 00:29:02,760
+الدالة هذه exact إذا تفاضل هذه بالنسبة إلى Y بيسوي
+
+245
+00:29:02,760 --> 00:29:07,360
+تفاضل هذه بالنسبة إلى X يبقى هذا شو بدا تعطينا؟
+
+246
+00:29:07,360 --> 00:29:16,000
+بدا تعطينا إن partial by partial Y لـ Mu في M يسوى
+
+247
+00:29:16,000 --> 00:29:20,780
+partial by partial X لـ Mu في M
+
+248
+00:29:23,440 --> 00:29:30,640
+إذا نادق كل واحدة فيها مشتقة حاصل ضرب دالتين يبقى
+
+249
+00:29:30,640 --> 00:29:37,720
+الدالة الأولى في مشتقة الدالة الثانية زائد الدالة
+
+250
+00:29:37,720 --> 00:29:44,480
+الثانية في مشتقة الدالة الأولى هذا الطرف الشمال
+
+251
+00:29:44,480 --> 00:29:48,280
+الطرف اليمين يساوي لميو
+
+252
+00:30:11,980 --> 00:30:17,780
+سؤال هدفيكوا بتقدر تقولي قداش هذه القيمة عدديا يا
+
+253
+00:30:17,780 --> 00:30:18,340
+مانات؟
+
+254
+00:30:21,910 --> 00:30:27,850
+زيرو صحيح لإن ميو فانكشن في Y إذا مشتقتها بالنسبة
+
+255
+00:30:27,850 --> 00:30:35,930
+ل X هي تساوي زيرو إذا هذه تساوي زيرو because إن
+
+256
+00:30:35,930 --> 00:30:44,100
+الميو is a function of Y onlyتمام يبقى ال term
+
+257
+00:30:44,100 --> 00:30:48,700
+الأخير هذا ماله؟ الله ساهل عليه مع السلامة طيب
+
+258
+00:30:48,700 --> 00:30:55,580
+نيجي لل term هذا هذا مشتقة ميو جزئيا بالنسبة لمين؟
+
+259
+00:30:55,580 --> 00:31:00,530
+بالنسبة ال why صحيح ولا لأ؟لكن انا فارض ان الـ mu
+
+260
+00:31:00,530 --> 00:31:05,650
+function في y فقط يبقى هذا اشتقاق كله ولا اشتقاق
+
+261
+00:31:05,650 --> 00:31:13,210
+جزء يبقى اشتقاق كله اذا هذه بتصير كالتالي الـmu في
+
+262
+00:31:13,210 --> 00:31:21,890
+partial m by partial y زائد m في d mu على dy بده
+
+263
+00:31:21,890 --> 00:31:27,810
+يساوي الـmu في partial n على partial x
+
+264
+00:31:30,300 --> 00:31:34,400
+طب ايش رايك؟ بدي اخلي هذه في الشجة و بدي اجيب هذه
+
+265
+00:31:34,400 --> 00:31:38,240
+على الشجة التانية يبقى لو جبتها على الشجة التانية
+
+266
+00:31:38,240 --> 00:31:44,220
+بقدر اخد لميو منهم عامل مشترك يبقى لو جبتها بصير
+
+267
+00:31:44,220 --> 00:31:49,420
+على الشجة التانية هذه هالميو عامل مشترك بظل عندي
+
+268
+00:31:49,420 --> 00:31:56,140
+partial n by partial x ناقص partial m by partial y
+
+269
+00:31:56,760 --> 00:32:03,580
+جبت هذه عند هذه، ضالت هذه لحالها يبقى تساوي M في D
+
+270
+00:32:03,580 --> 00:32:06,140
+Mu على Dy
+
+271
+00:32:08,630 --> 00:32:14,690
+طب كويس ايش رايك؟ هذه بتصير على الشكل التالي بيدا
+
+272
+00:32:14,690 --> 00:32:22,990
+جسم على M ضرب م على M في م يبقاش بصير عندي هنا هذه
+
+273
+00:32:22,990 --> 00:32:30,050
+بتصير partial N by partial X ناقص partial M by
+
+274
+00:32:30,050 --> 00:32:39,060
+partial Y كله على Mبدو اسم في دي واي بالمرة يساوي
+
+275
+00:32:39,060 --> 00:32:51,620
+دي ميو على الميو مصبوط طيب هوصلنا لشوية طيب انكامل
+
+276
+00:32:51,620 --> 00:32:56,680
+الطرفين او قبل انكامل هذه اش احنا فرضينها في نص
+
+277
+00:32:56,680 --> 00:33:04,320
+المثلةمش هي عبارة عن ال EQ وين راحت؟ مش هذه هي ال
+
+278
+00:33:04,320 --> 00:33:08,960
+EQ صح ولا لأ؟ إذا بدي أشيلها و أكتب بدلها ال EQ
+
+279
+00:33:08,960 --> 00:33:22,440
+هذا معناته إن ال EQ of Y في DY بدي ساوي DMU على
+
+280
+00:33:22,440 --> 00:33:32,400
+الميو بدي أكمل الطرفينيبقى تكامل لـ Q of Y دي Y
+
+281
+00:33:32,400 --> 00:33:44,920
+بدرساوي لان absolute value للي ميو زائد كونستانسي
+
+282
+00:33:44,920 --> 00:33:50,380
+صح ممكن اخد كونستانسي اي قيمة للسهولة بقدر اخده ب
+
+283
+00:33:50,380 --> 00:34:03,270
+zero يبقى هنا تكc تساوي زيرو نحصلتكامل لـ q of y
+
+284
+00:34:03,270 --> 00:34:10,030
+dy يسوى لـ absolute value لـ mu أنا مابديش
+
+285
+00:34:10,030 --> 00:34:15,230
+absolute value لـ mu بدي الـ mu itself يبقى الـ mu
+
+286
+00:34:15,230 --> 00:34:22,930
+أو absolute value لـ mu بدي سوى E أُس تكامل لـ q
+
+287
+00:34:22,930 --> 00:34:29,660
+of y dyأمر ال X بونينش اللي باخد قيمة سالبة؟ لأ
+
+288
+00:34:29,660 --> 00:34:33,300
+يبقى ال absolute value لا معنى لها يبقى بدون
+
+289
+00:34:33,300 --> 00:34:40,780
+absolute value يبقى صارت لم U of Y يسوى E أس تكامل
+
+290
+00:34:40,780 --> 00:34:47,420
+EQ of Y DY أظن و هو المطلوب؟مش هي اللي بدنا نثبته؟
+
+291
+00:34:47,420 --> 00:34:51,620
+هي جيبناها قيمة الـ mu of y هي ال exponential a
+
+292
+00:34:51,620 --> 00:34:57,580
+مرفوعة للأس تكامل q of y dy حد فيكوا اللي هي تساول
+
+293
+00:34:57,580 --> 00:35:05,560
+هنا؟ هيا اتفضلي ليش حولنا ايش؟
+
+294
+00:35:05,560 --> 00:35:12,180
+هذه؟ هذه اللي قال الـ mu function في مين؟في why؟
+
+295
+00:35:12,180 --> 00:35:15,400
+إذا لما تبقى الدالة في متغير واحد اشتقاق جزء،
+
+296
+00:35:15,400 --> 00:35:20,480
+والله اشتقاق كل اشتقاق الجزء إذا كانت الدالة في
+
+297
+00:35:20,480 --> 00:35:24,300
+متغيرين أو أكثر، بس إذا متغير واحد يبقى اشتقاق كله
+
+298
+00:35:24,300 --> 00:35:29,300
+وليس اشتقاقا جزئيا، مش شاكرا بحياتي؟ هدأ ولا لا؟
+
+299
+00:35:29,300 --> 00:35:35,200
+اه مانسيتش يعني انامظبوط؟ واضحة؟ طيب كويس يبقى الـ
+
+300
+00:35:35,200 --> 00:35:40,240
+Mu of Y بيساوي ال exponential E of QY Dy في اي
+
+301
+00:35:40,240 --> 00:35:46,220
+تساوي تاني يا بناان؟ اسأل واتخافوش حتى لو كان
+
+302
+00:35:46,220 --> 00:35:50,500
+السؤال غلط، تسأل اليوم غلط، مكرا بتسأل ايه صح؟ حب
+
+303
+00:35:50,500 --> 00:35:55,770
+تسأل تاني؟ طيب انا اللي باسأل، لازم تكونش تسألأنا
+
+304
+00:35:55,770 --> 00:36:01,670
+هحط السؤال التاني وخليكوا تروحوا تثبتوا أنتوا بنفس
+
+305
+00:36:01,670 --> 00:36:12,390
+الطريقة اللي أثبتنا فيها السؤال هذا دكتور
+
+306
+00:36:12,390 --> 00:36:15,530
+هل بتعمل اجتماعات اجتماعات اللي هتستخدمها انهم
+
+307
+00:36:15,530 --> 00:36:22,830
+يعملوا بيانات نشاط؟ اه كدهلأ دي مرة واحد بيكتبش دي
+
+308
+00:36:22,830 --> 00:36:27,530
+جداش قيمته top or b في ال equation بس في ال
+
+309
+00:36:27,530 --> 00:36:31,690
+equation exact و بدك تتأكد انها exact ولا لأ هذا
+
+310
+00:36:31,690 --> 00:36:34,170
+هو لو ما طلعتش exact معناته ال integrating factor
+
+311
+00:36:34,170 --> 00:36:39,970
+تبعت غلط او اشتقاق غلط واحد من الاتنين تمام نجي
+
+312
+00:36:39,970 --> 00:36:44,050
+للسؤال الثاني او ال integrating factor التاني اللي
+
+313
+00:36:44,050 --> 00:36:48,550
+محطوط عندكوا على السؤال اللي بعد اعتقد 24يبقى
+
+314
+00:36:48,550 --> 00:36:55,030
+الانتجاريك فترة تانية بيقول if ال partial m by
+
+315
+00:36:55,030 --> 00:37:02,450
+partial y ناقص partial n by partial x على n بده
+
+316
+00:37:02,450 --> 00:37:13,390
+يساوي f of x where حيث ال f of x is a function
+
+317
+00:37:31,130 --> 00:37:38,010
+عامل التكامل of the differential equation of the
+
+318
+00:37:38,010 --> 00:37:48,470
+differential equation MDXزائد ال N Dy تساوي Zero
+
+319
+00:37:48,470 --> 00:38:01,030
+is لـ Mu of X بدي ساوي E أسطى كامل F of X DX وهذه
+
+320
+00:38:01,030 --> 00:38:09,530
+الكبانات بدك تروح تتبتيها و تشيك عليه كيف؟ بنفس ال
+
+321
+00:38:09,530 --> 00:38:14,260
+tactic اللي مشينا فيهبس بدل هذه partial mu by
+
+322
+00:38:14,260 --> 00:38:17,740
+partial y بيصير عندك partial mu by partial x هذه
+
+323
+00:38:17,740 --> 00:38:21,680
+بتتحول الاشتقاء الكامل وهذه بيصير في zero يامو
+
+324
+00:38:21,680 --> 00:38:26,800
+بيطلع معاك نتيجة دوري تمام؟ طيب هذا بالنسبة لمين
+
+325
+00:38:26,800 --> 00:38:30,720
+ال integrating factor التاني السؤال هو كيف بدنا
+
+326
+00:38:30,720 --> 00:38:35,000
+نميز مبادئ ال integrating factor هذا وال
+
+327
+00:38:35,000 --> 00:38:41,630
+integrating factor الثاني هذامظبوط احنا هنتلخبط
+
+328
+00:38:41,630 --> 00:38:46,430
+نجسم على M و لا نجسم على N هذا بيكون جسم على M و
+
+329
+00:38:46,430 --> 00:38:50,530
+لا نجسم على N الفارق بينهم ان هذا N و هذا N هذا
+
+330
+00:38:50,530 --> 00:38:53,830
+سالب و هذا موجب و هذا كموجب و هذا سالب نقلب الغضب
+
+331
+00:38:53,830 --> 00:39:00,290
+تمام بكل بساطة طلعيه هنا كويس تيجي لبعد السالب شو
+
+332
+00:39:00,290 --> 00:39:05,470
+اسمه partial M على partial Y ال M هذه بتصير في
+
+333
+00:39:05,470 --> 00:39:11,200
+المقاموالدلة بدأت تطلع function في main في y بلّع
+
+334
+00:39:11,200 --> 00:39:15,380
+هنا هي السلم partial in على partial x يبقى سمن على
+
+335
+00:39:15,380 --> 00:39:19,640
+main و الناتج function في المتغير اللي تحتها
+
+336
+00:39:19,640 --> 00:39:24,650
+وبالتالي بصير مش إمكانية للخطأ تمامايبقى بأطلع على
+
+337
+00:39:24,650 --> 00:39:28,750
+تبع الشرط اللي مكتوب بالسالق partial n يبقى بدي
+
+338
+00:39:28,750 --> 00:39:34,210
+أجسم على n والنتج بدي تطلع دالة في x partial m على
+
+339
+00:39:34,210 --> 00:39:40,250
+partial y بدي أجسم على m والنتج بدي تطلع دالة في y
+
+340
+00:39:40,250 --> 00:39:44,910
+طبعا الان بدنا ناخد أمثلة على ال integrating
+
+341
+00:39:44,910 --> 00:39:52,070
+factors أول مثل بيقول ما ياتي
+
+342
+00:39:58,250 --> 00:40:04,290
+example one find
+
+343
+00:40:04,290 --> 00:40:08,690
+the
+
+344
+00:40:08,690 --> 00:40:15,170
+integrating factor
+
+345
+00:40:15,170 --> 00:40:25,890
+بدنا نعمل التكامل and solve the following
+
+346
+00:40:30,930 --> 00:40:39,790
+differential equations نمر ا دي
+
+347
+00:40:39,790 --> 00:40:53,350
+اكس زائد X على Y ماقص sign ال Y كلها في دي Y بدأت
+
+348
+00:40:53,350 --> 00:41:05,350
+ساوي Zero وال Ygreater than zero سمي
+
+349
+00:41:05,350 --> 00:41:11,070
+المعادلة رقم واحد يبقى
+
+350
+00:41:11,070 --> 00:41:19,450
+بدالي لل solution هذا سؤال 27 من الكتابة هنا سؤال
+
+351
+00:41:19,450 --> 00:41:25,380
+مرة تانيةبقول هاتلي عاملة تكمن للمعادلة اللي عندنا
+
+352
+00:41:25,380 --> 00:41:30,880
+هذه، اتنين حل هذه المعادلة كذلك، بنقوله والله
+
+353
+00:41:30,880 --> 00:41:36,000
+كويس، الأول نتأكد هل هي exact، والله ماهياش exact،
+
+354
+00:41:36,000 --> 00:41:40,780
+مش هروح أدرب دوري ولا أحسب دوري، يبقى هذه عندنا M،
+
+355
+00:41:40,780 --> 00:41:46,160
+ابجداش يا بنات؟يبقى هذا بدي اعطيك partial M على
+
+356
+00:41:46,160 --> 00:41:51,800
+partial Y بدي ساوي قداش Zero بدنا partial N على
+
+357
+00:41:51,800 --> 00:41:59,960
+partial X مشتقة هذه بقداش1 على Y في غيرها ومشتقتها
+
+358
+00:41:59,960 --> 00:42:05,500
+دي مهيب Zero تمام يبقى هذا بدي اعطيلك انه partial
+
+359
+00:42:05,500 --> 00:42:12,140
+M على partial Y لا يساوي partial N على partial X
+
+360
+00:42:12,140 --> 00:42:20,420
+هذا بدي اعطيلك انه لا differential equation one is
+
+361
+00:42:20,420 --> 00:42:22,040
+not exact
+
+362
+00:42:25,340 --> 00:42:29,360
+بقى هذا بيعطيه ان المعادلة هذه ماهياش exact إذا
+
+363
+00:42:29,360 --> 00:42:34,440
+بدى أروح أدور على function ال function هذه تخليها
+
+364
+00:42:34,440 --> 00:42:40,340
+لي exact بقوله والله كويسكيف بنسويه؟ بنقول تعالى
+
+365
+00:42:40,340 --> 00:42:44,100
+نشوف ال integrating factors اللى عندنا انا عندي
+
+366
+00:42:44,100 --> 00:42:48,320
+partial M على partial Y يساوي Zero partial N على
+
+367
+00:42:48,320 --> 00:42:54,060
+partial X يساوي واحد على Y اذا كيف ماعمل الفرق
+
+368
+00:42:54,060 --> 00:42:59,060
+الفرق بينهم واحد على Y اما بالموجب او بالسالم صحيح
+
+369
+00:42:59,060 --> 00:43:02,940
+ولا لا؟لو جسمت على واحد بيطلع واحد على Y اللي هو
+
+370
+00:43:02,940 --> 00:43:08,780
+function في Y only يبقى أفضل شغل أروح أخده من
+
+371
+00:43:08,780 --> 00:43:17,870
+partial NPartial N على Partial X ناقص Partial M
+
+372
+00:43:17,870 --> 00:43:24,650
+على Partial Y على M وشوفوا كده إيش تساوي Partial N
+
+373
+00:43:24,650 --> 00:43:30,050
+على Partial X بواحد على Y Partial M على Partial Y
+
+374
+00:43:30,050 --> 00:43:36,050
+ب Zero نقسم على M اللي هو بواحد يسوى واحد على Y ل
+
+375
+00:43:36,050 --> 00:43:41,680
+function of Y onlyأمام
+
+376
+00:44:06,710 --> 00:44:11,730
+أذا حسبنا تفاضل N بالنسبة ل X نقص تفاضل N بالنسبة
+
+377
+00:44:11,730 --> 00:44:16,030
+ل Y على Y لجناح function في Y only يبقى عامل
+
+378
+00:44:16,030 --> 00:44:19,290
+التكامل هيكون function في Y
+
+379
+00:44:24,910 --> 00:44:30,970
+ايه استكامل ل Q of Y دي Y طبعا مين ل Q of Y هذه
+
+380
+00:44:30,970 --> 00:44:36,890
+كلها ل Q of Y هذه كلها اللي كنا مزلها في السؤال ل
+
+381
+00:44:36,890 --> 00:44:40,610
+Q of Y يبقى هذا بده ساوي
+
+382
+00:44:45,730 --> 00:44:53,490
+يبقى الجواب E أسلن absolute value ل Y لكن Y أكبر
+
+383
+00:44:53,490 --> 00:44:57,630
+من Zero يبقى لا داعي لمين للاbsolute ماعطيني Y
+
+384
+00:44:57,630 --> 00:45:02,730
+أكبر من Zero إذن النتيجة تسوى كده؟ Y يبقى ال
+
+385
+00:45:02,730 --> 00:45:07,960
+integrating factor هو Yبعد هيك بدنا نضرب المعادلة
+
+386
+00:45:07,960 --> 00:45:12,560
+واحد كلها في ال integrating factor اللي هو Y يبقى
+
+387
+00:45:12,560 --> 00:45:18,000
+باجي بقوله multiply equation
+
+388
+00:45:18,390 --> 00:45:29,290
+one by y we get نحصل على المعادلة بيصير y في dx
+
+389
+00:45:29,290 --> 00:45:38,930
+زائد تعالى نجي للتانى هنا نضرب في y بيصير x ناقص y
+
+390
+00:45:40,080 --> 00:45:47,340
+فى الـSin الـY كله دى Y بدى يساوي كده؟ بدى يساوي
+
+391
+00:45:47,340 --> 00:45:51,640
+Zero تعالى نبحث هل هى Exact ولا لا إذا ماطلعتش
+
+392
+00:45:51,640 --> 00:45:56,120
+Exact يبقى فينا شغل غلط فى الحسابات بدنا نروح
+
+393
+00:45:56,120 --> 00:46:03,160
+نراجع من الحسابات إذا بدى أخد تفاضل ال M بالنسبة
+
+394
+00:46:03,160 --> 00:46:10,850
+إلى Y كده يا بنات؟ هى هى كده؟بتاخد تفاضل ال N
+
+395
+00:46:10,850 --> 00:46:16,290
+بالنسبة إلى X يبقى تفاضل هذا يسمي ال X اللي بقدرش
+
+396
+00:46:16,290 --> 00:46:21,290
+واحد وهذه كلها ب Zero يبقى هذا بدي أخد تفاضل N
+
+397
+00:46:21,290 --> 00:46:27,310
+بالنسبة إلى Y يسوي تفاضل ال N بالنسبة إلى X سميلي
+
+398
+00:46:27,310 --> 00:46:32,230
+هذه المعادلة اتنين يا بنات يبقى هذا بدي أعطيلك ان
+
+399
+00:46:32,230 --> 00:46:42,430
+ذاDifferential equation 2 is exact المعادلة
+
+400
+00:46:42,430 --> 00:46:48,770
+2 هي نفس المعادلة 1 بس بعد ما ضربناها في Y يعني هي
+
+401
+00:46:48,770 --> 00:46:53,370
+نفس المعادلة يعني هذه تكافئ المعادلة أصلا و لا لو
+
+402
+00:46:53,370 --> 00:46:56,750
+قسمناها على Y فتطلع المعادلة اللي فوق يبقى هذه
+
+403
+00:46:56,750 --> 00:47:03,320
+تكافئ هذه تماماطيب مادام exact يبقى هذا بده يعطيك
+
+404
+00:47:03,320 --> 00:47:10,240
+there exists a function psi of x y يساوي constant
+
+405
+00:47:10,240 --> 00:47:18,890
+c such that بحيث أنPartial Epsilon by Partial X
+
+406
+00:47:18,890 --> 00:47:24,490
+يسوى ال term الأول من المعادلة الجديدة اللي هو Y و
+
+407
+00:47:24,490 --> 00:47:32,290
+Partial Epsilon by Partial Y يسوى X ناقص Y في Sine
+
+408
+00:47:32,290 --> 00:47:32,710
+Y
+
+409
+00:47:37,050 --> 00:47:41,570
+يبقى يابا كامل هذا بالنسبة ل X يابا كامل هذا
+
+410
+00:47:41,570 --> 00:47:46,910
+بالنسبة ل Y يبقى
+
+411
+00:47:46,910 --> 00:47:51,260
+هذا بالنسبة ل X أسهل لأنها تعتبر مقدار ثابتإذا لو
+
+412
+00:47:51,260 --> 00:47:56,780
+جيت كاملت هد يا بنات بصير إب ساي of X Y يساوي
+
+413
+00:47:56,780 --> 00:48:01,520
+مقدار ثابت مالكش دعوة أنا بكمل بالنسبة ل X يبقى
+
+414
+00:48:01,520 --> 00:48:07,450
+Quadro of X و بقول زائد function of manof Y لأن
+
+415
+00:48:07,450 --> 00:48:13,250
+التكمل كان بالنسبة لمين ال X طيب نشتق هذه يبقى
+
+416
+00:48:13,250 --> 00:48:20,950
+partial of Psi by partial Y يساوي هذا X وهنا زائد
+
+417
+00:48:20,950 --> 00:48:28,210
+F prime of Y من التنتين هذول مع بعض شو بستنتج
+
+418
+00:48:28,210 --> 00:48:38,590
+بستنتج ان X زائد F prime of Yيسوي x ناقص y في sign
+
+419
+00:48:38,590 --> 00:48:47,450
+ال y يبقى ال f prime of y ناقص y في sign ال y بدنا
+
+420
+00:48:47,450 --> 00:48:54,090
+نكمل ايوة يبقى يا بنات بدي اخد هنا derivatives و
+
+421
+00:48:54,090 --> 00:49:00,610
+بدي اخد هنا integral زي calculus b بدي احط هنا y و
+
+422
+00:49:00,610 --> 00:49:09,190
+هنا ناقص sign ال yمشتقة هدف كده؟ واحد مشتقة تكامل
+
+423
+00:49:09,190 --> 00:49:14,790
+ال sign ب سالب cosine مع السالب بصير cosine ال Y
+
+424
+00:49:14,790 --> 00:49:21,210
+مشتقة ال واحد ب zero تكامل ال cosine بال sign ال Y
+
+425
+00:49:21,210 --> 00:49:28,390
+هدف هدف موجب وهدف هدف سالب إذا بناء عليه أصبح ال F
+
+426
+00:49:28,390 --> 00:49:42,230
+of Y يساويy في cos y ناقص sin y زائد constant
+
+427
+00:49:42,230 --> 00:49:52,640
+وليكن c1 يبقى بالي بقول له the solution ofوإن الـ
+
+428
+00:49:52,640 --> 00:50:05,020
+differential equation one is إبسايد of XY يساوي
+
+429
+00:50:05,020 --> 00:50:18,100
+هيها Y في Xالـ F of Y يبقى زائد ها Y في Cos Y ناقص
+
+430
+00:50:18,100 --> 00:50:27,220
+Sin Y وهذا كله بيساوي من Constant Cيبقى هنا انا
+
+431
+00:50:27,220 --> 00:50:34,220
+انا انا انا انا انا
+
+432
+00:50:34,220 --> 00:50:34,320
+انا انا انا انا انا انا انا انا انا انا انا انا
+
+433
+00:50:34,320 --> 00:50:34,400
+انا انا انا انا انا انا انا انا انا انا انا انا
+
+434
+00:50:34,400 --> 00:50:38,400
+انا انا انا انا انا انا
+
+435
+00:50:38,400 --> 00:50:38,460
+انا انا انا انا انا انا انا انا انا انا انا انا
+
+436
+00:50:38,460 --> 00:50:44,220
+انا انا
+
+437
+00:51:11,060 --> 00:51:22,360
+يبقى نمره بيه بيقوللي x y نقص زائد y تربيع كله في
+
+438
+00:51:22,360 --> 00:51:36,100
+dx زائد x زائد 2y ناقص واحد في dy بده ساوي زيه
+
+439
+00:51:36,100 --> 00:51:45,730
+وسميها للمعنى الرقم واحدنحل هذه المعادلة ناخد
+
+440
+00:51:45,730 --> 00:51:53,430
+تفاضل ال N بالنسبة ل Y
+
+441
+00:51:53,430 --> 00:52:03,130
+ب X زائد 2Y ناخد تفاضل ال N بالنسبة ل X
+
+442
+00:52:10,130 --> 00:52:17,290
+واضح ان اتنين ليسوا بعض يبقى هذا بدي اعطيك تفاضل
+
+443
+00:52:17,290 --> 00:52:25,230
+ال M بالنسبة الى Y لا يسوى تفاضل ال N بالنسبة الى
+
+444
+00:52:25,230 --> 00:52:28,950
+X هذا بدي اعطيك ان ال
+
+445
+00:52:34,270 --> 00:52:40,670
+is not exact ماهياش exact يبقى الواحد يدور على
+
+446
+00:52:40,670 --> 00:52:45,670
+مين؟ على ال integrating factor بقوله والله كويس
+
+447
+00:52:45,670 --> 00:52:49,270
+تعالى ندور على ال integrating factor partially and
+
+448
+00:52:49,270 --> 00:52:53,990
+by partially واناقص partially يبقى هذا ناقص هذا اه
+
+449
+00:52:53,990 --> 00:53:00,170
+هو هذا ولا لا صح؟ والله كويس فرصة طيبة يبقى لو جيت
+
+450
+00:53:00,170 --> 00:53:07,940
+قلتهنا تفاضل ال M بالنسبة إلى Y ناقص تفاضل ال N
+
+451
+00:53:07,940 --> 00:53:12,820
+بالنسبة ل X بده يسموه عالمياً وبده النتج يطلع
+
+452
+00:53:12,820 --> 00:53:17,640
+function في X only يبقى partial M على partial Y
+
+453
+00:53:17,640 --> 00:53:22,860
+اللي هو X زائد 2Y تفاضل ال N بالنسبة ل X اللي هو
+
+454
+00:53:22,860 --> 00:53:30,240
+واحد على ان ال X زائد 2Y ناقص واحد كله بيساوي
+
+455
+00:53:30,240 --> 00:53:37,250
+كدهاش؟اكس زي اتنين
+
+456
+00:53:37,250 --> 00:53:41,170
+واحد نقلها كل هذا بيساوي كده اش واحد يا عمي الكونص
+
+457
+00:53:41,170 --> 00:53:46,550
+ده ماراه تعتبريه function في المتغير اللي عندك هذا
+
+458
+00:53:46,550 --> 00:53:54,800
+هنا يبقى هذا باعتبره function of x onlyيبقى صار ال
+
+459
+00:53:54,800 --> 00:54:02,220
+integrating factor ميو of X يبقى يستكامل
+
+460
+00:54:02,220 --> 00:54:08,340
+واحد في DX يبقى الجواب قداش U6 يبقى ال integrating
+
+461
+00:54:08,340 --> 00:54:13,620
+factor هو مين هو U6 إذا بدي أجي للمعادلة اللي عندي
+
+462
+00:54:13,620 --> 00:54:19,600
+هذه فوق و أضربها كلها في مين في U6 يبقى باجي بقوله
+
+463
+00:54:19,600 --> 00:54:20,600
+multiply
+
+464
+00:54:23,250 --> 00:54:34,970
+equation one by u6 we get بضربيني في u6 بصير x y
+
+465
+00:54:34,970 --> 00:54:48,770
+u6 زائد y تربيع في u6 في dx زائداكس EOS6 زائدي
+
+466
+00:54:48,770 --> 00:54:57,690
+اتنين Y EOS6 ناقص EOS6 كله في DY بده يساوي كده؟
+
+467
+00:54:57,690 --> 00:54:59,650
+بده يساوي Zero
+
+468
+00:55:24,950 --> 00:55:28,810
+طيب هذه المعادلة التفاظلية أصبحت على الشكل اللي
+
+469
+00:55:28,810 --> 00:55:32,030
+انا هذا يبقى هذه المعادلة اللي بدي أسميها المعادلة
+
+470
+00:55:32,030 --> 00:55:37,650
+رقم اتنينإذا بدى أبحث هل هذه exact والله ماهياش
+
+471
+00:55:37,650 --> 00:55:44,490
+exact إذا بدى أخد تفاضل ال M بالنسبة إلى Y يبقى
+
+472
+00:55:44,490 --> 00:55:49,270
+بدى أشتق هذه كلها بالنسبة إلى Y واضح له ال X E
+
+473
+00:55:49,270 --> 00:56:00,790
+وال6 X E وال6 خلصنا من A A زائة X E وال6 زائد 2
+
+474
+00:56:04,400 --> 00:56:11,740
+بعد ذلك ياخد تفاضل ال N بالنسبة إلى X يبقى هذا
+
+475
+00:56:11,740 --> 00:56:18,700
+حاصل ضرب دالتين يبقى الدالة الأولى في مشتقة ال X
+
+476
+00:56:18,700 --> 00:56:24,360
+بال X بال X يتصل زائد الدالة التانية E وال 6 في
+
+477
+00:56:24,360 --> 00:56:32,480
+مشتقة ال X يبقى دلاش بواحدإتنين Y في مشتقة ال EOSX
+
+478
+00:56:32,480 --> 00:56:38,580
+بال EOSX itself ناقص مشتقة ال EOSX بال EOSX
+
+479
+00:56:38,580 --> 00:56:43,980
+فالليلي هذه و هذه الله يسهل عليهم غير مأسوف عليهم
+
+480
+00:56:43,980 --> 00:56:50,960
+يبقى هذا الكلام جداش بده يساوي بده يساوي X في EOSX
+
+481
+00:56:50,960 --> 00:57:00,280
+زائد اتنين Y EOSXطلع هنا و هناك بتلاقي القمتين نفس
+
+482
+00:57:00,280 --> 00:57:06,380
+الشيء معناة ال termين هدول بيسووا بعض تفاضل ال M
+
+483
+00:57:06,380 --> 00:57:13,140
+بالنسبة إلى Y يسوى تفاضل ال N بالنسبة إلى X هذا
+
+484
+00:57:13,140 --> 00:57:19,200
+بدي يعطينا ان ال differential equation اتنين
+
+485
+00:57:19,200 --> 00:57:27,970
+سمناها اتنين as exactيبقى هذا بدي يعطينا ان هناك
+
+486
+00:57:27,970 --> 00:57:38,830
+مفهوم إبسائي of x y such that بحيث ان partial
+
+487
+00:57:38,830 --> 00:57:46,590
+إبسائيعلى partial x يساوي تفاضل إبصاي بالنسبة إلى
+
+488
+00:57:46,590 --> 00:57:58,630
+x اللي هو main x y u6 زائد y تربية ال u6 و partial
+
+489
+00:57:58,630 --> 00:58:02,570
+إبصاي by partial y ال term التاني
+
+490
+00:58:13,640 --> 00:58:20,780
+السؤال هو أيه ما أسهل أن نكمل الدالة الأولى
+
+491
+00:58:20,780 --> 00:58:26,580
+بالنسبة ل X و الله الدالة التانية بالنسبة ل Y؟تعني
+
+492
+00:58:26,580 --> 00:58:31,260
+بالنسبة ل Y أسهل كتير لأن الأولى حاصل ضرب دالتين
+
+493
+00:58:31,260 --> 00:58:34,860
+وبدنا نكملها هضطر للجدول وقص integration by parts
+
+494
+00:58:34,860 --> 00:58:41,780
+لكن هذه أبدا هذه دوري إذا لو جيت كملت هذه بالنسبة
+
+495
+00:58:41,780 --> 00:58:49,680
+إلى Y يبقى if Psi of X وY تساوي بدي أكملها بالنسبة
+
+496
+00:58:49,680 --> 00:58:58,800
+ل Y X في E وال 6 مقدار ثابت فبنضربه في Yزائد اتنين
+
+497
+00:58:58,800 --> 00:59:06,060
+y تكمل اكسبونين يبقى
+
+498
+00:59:06,060 --> 00:59:11,740
+Y تربية على اتنين تروح مع اتنين يبقى Y تربية في U6
+
+499
+00:59:11,740 --> 00:59:20,420
+ناقص U6 في Y زائد constant له function في مين؟بعد
+
+500
+00:59:20,420 --> 00:59:26,280
+ذلك نفضل هذه الدالة بالنسبة ل X و نسويها بالمين
+
+501
+00:59:26,280 --> 00:59:31,360
+بالدالة التانية يبقى بداجي اخد partial of psi by
+
+502
+00:59:31,360 --> 00:59:36,380
+partial X يساوي هذه مستقلة حصل ضر دالتين وال Y
+
+503
+00:59:36,380 --> 00:59:46,160
+مقدار ثابت يبقى EO6 في Y زائد الهمين X EO6 في Y
+
+504
+00:59:47,050 --> 00:59:52,090
+اللي بعدها بده اشتقها بالنسبة ل X يبقى Y تربية في
+
+505
+00:59:52,090 --> 01:00:01,090
+US X اللي بعدها ناقص US X في Y زائد F prime of X
+
+506
+01:00:01,730 --> 01:00:08,150
+يبقى EO6 في Y و سالب EO6 في Y مع السلامة يبقى آلة
+
+507
+01:00:08,150 --> 01:00:14,550
+المسألة إلى partial of Psi by partial X يسوى X EO6
+
+508
+01:00:14,550 --> 01:00:23,390
+في Y زائد Y تربية في EO6 زائد F prime of Xبنسوي ال
+
+509
+01:00:23,390 --> 01:00:27,590
+term اللى عندنا هذا بال term اللى عندنا هذا بنحصل
+
+510
+01:00:27,590 --> 01:00:34,790
+على إيش على إنه ال X في ال EOSX في ال Y زائد Y
+
+511
+01:00:34,790 --> 01:00:44,050
+تربية في ال EOSX زائد F prime of X يساوي XY EOSX
+
+512
+01:00:44,050 --> 01:00:55,400
+زائد Y تربية EOSXY تربية U6 مع Y تربية U6 XE و 6Y
+
+513
+01:00:55,400 --> 01:01:02,440
+في XE و 6Y مع السلامة يبقى قالة الى F prime of X
+
+514
+01:01:02,440 --> 01:01:09,960
+يسوى قداش Zero معناه هذا الكلام ان ال F of X بدى
+
+515
+01:01:09,960 --> 01:01:16,480
+يسوى constant C1 لذلك بروح بقوله the solution
+
+516
+01:01:18,550 --> 01:01:29,570
+of the differential equation one is epsilon of x,y
+
+517
+01:01:29,570 --> 01:01:37,160
+يساوي وده ال epsilon اللي حصلنا عليها هييبقى
+
+518
+01:01:37,160 --> 01:01:49,740
+اليمين X US X في ال Y زائد Y تربيع في US X ناقص US
+
+519
+01:01:49,740 --> 01:01:57,420
+XY وهذا المقدار ثابت يبقى هذا كله بيسوي مقدار ثابت
+
+520
+01:01:57,420 --> 01:01:59,540
+بالشكل اللي عندنا هذا
+
+521
+01:02:09,310 --> 01:02:15,070
+لخاطر اعطيكم كمان مثال اللي هو برضه سؤال من الكتاب
+
+522
+01:02:37,670 --> 01:02:50,590
+example 2 هذا
+
+523
+01:02:50,590 --> 01:02:57,430
+سؤال تلاتين من الكتاب بيقول solve the differential
+
+524
+01:02:57,430 --> 01:03:04,090
+equation اللي
+
+525
+01:03:04,090 --> 01:03:18,640
+هو أربعةx تكيب على y تربيع زائد تلاتة على y كل هذا
+
+526
+01:03:18,640 --> 01:03:32,520
+الكلام في dx في dx زائد تلاتة في x على y تربيع
+
+527
+01:03:32,520 --> 01:03:49,970
+زائدأربعة Y كل هذا الكلام في DY يساوي Zero يبقى
+
+528
+01:03:49,970 --> 01:03:55,210
+عندي مثل هذا السؤال تلاتين بالكتاب بيقولي بدنا نحل
+
+529
+01:03:55,210 --> 01:04:01,310
+المثلة هذه بقوله بسيطةيبقى زي ما تشاهدين فيها قصور
+
+530
+01:04:01,310 --> 01:04:05,190
+فيش في البصط وفي المقام يبقى انا لو خليته كله في
+
+531
+01:04:05,190 --> 01:04:10,930
+البصط بصير سلي في الحسابات وخاصة عند الاشتقاء يبقى
+
+532
+01:04:10,930 --> 01:04:15,270
+كل حاجة في المقام بيطلعها في البصط وبالتالي الأس
+
+533
+01:04:15,270 --> 01:04:21,750
+تبعها بيصير بإشارة مخالفة أو بإشارة سالف يبقى هنا
+
+534
+01:04:21,750 --> 01:04:28,660
+solutionالمعادلة هذه هكتبها على الشكل التالي اربعة
+
+535
+01:04:28,660 --> 01:04:39,760
+X تكييب Y اصناقس اتنين زائد تلاتة Y اصناقس واحد
+
+536
+01:04:39,760 --> 01:04:49,620
+هذا كله في من كله في DX زائدتلاتة اكس واي اثناء
+
+537
+01:04:49,620 --> 01:04:55,740
+اقصى اتنين زائد اربعة واي دي واي زائد اربعة واي دي
+
+538
+01:04:55,740 --> 01:04:58,680
+واي زائد اربعة واي دي واي زائد اربعة واي دي واي
+
+539
+01:05:15,960 --> 01:05:21,900
+طيب بنبحث هل المثل هذه exact ولا ماهياش exact يبقى
+
+540
+01:05:21,900 --> 01:05:24,580
+تفاضل ال M بالنسبة إلى Y
+
+541
+01:05:34,530 --> 01:05:40,270
+تفاضل M بالنسبة إلى Y أربعة X تكييب مقدار ثابت
+
+542
+01:05:40,270 --> 01:05:47,010
+تفاضل Y ناقص اتنين بناقص اتنين في أربعة بناقص
+
+543
+01:05:47,010 --> 01:05:56,350
+تمانية X تكييب Y ناقص تلاتةوهذه يا بنات ناقص تلاتة
+
+544
+01:05:56,350 --> 01:06:02,830
+Y أس ناقص اتنين هاي خلصنا تفاضلها بالنسبة إلى Y
+
+545
+01:06:02,830 --> 01:06:11,870
+بنانيجي تفاضل ال N بالنسبة إلى X تلاتة Y أس ناقص
+
+546
+01:06:11,870 --> 01:06:19,320
+اتنين وهذه بقدراش Zero الله سهل عليهاطيب طلع في
+
+547
+01:06:19,320 --> 01:06:24,460
+هدول المعادلات اللي عندنا بقول والله شكلهم بسووش
+
+548
+01:06:24,460 --> 01:06:30,220
+بعض صحيح يبقى هذا بدي اعطيك main انه تفاضل ال N
+
+549
+01:06:30,220 --> 01:06:36,120
+بالنسبة الى Y لا يسوى تفاضل ال N بالنسبة الى main
+
+550
+01:06:36,120 --> 01:06:42,380
+ال X يبقى هذا بدي اعطيك انه the differential
+
+551
+01:06:42,980 --> 01:06:55,080
+Equation one is not exact إذن بدنا ندور على ال
+
+552
+01:06:55,080 --> 01:07:01,290
+integrating factorأجرب أطرح جيل و أجسم على مين
+
+553
+01:07:30,250 --> 01:07:34,790
+يبقى انا اغمق عينيه واخدت عن جنه واشوف شو اللي بده
+
+554
+01:07:34,790 --> 01:07:41,630
+يصير you serve partial m by partial y هيها تمام زي
+
+555
+01:07:41,630 --> 01:07:50,010
+ما هي ناقص تمانية x تكيب y اص ناقص تلاتة ناقص
+
+556
+01:07:50,010 --> 01:07:53,150
+تلاتة y اص ناقص اتنين
+
+557
+01:07:58,580 --> 01:08:11,260
+نقص تلاتة Y أس ناقص اتنين يبقى
+
+558
+01:08:11,260 --> 01:08:15,580
+تلاتة X Y أس ناقص اتنين
+
+559
+01:08:21,920 --> 01:08:27,560
+كويس؟ باجي بقول لأ على n اه مظبوط و هذه ناقص لها
+
+560
+01:08:27,560 --> 01:08:33,280
+صحيح كويس يعني هذه ايش بيصير؟ بيصير يا بنات ناقص
+
+561
+01:08:33,280 --> 01:08:43,740
+تمانية x تكيبواي أس ناقص تلاتة ناقص ستة واي أس
+
+562
+01:08:43,740 --> 01:08:53,020
+ناقص اتنين على تلاتة X واي أس ناقص اتنين زائد أربع
+
+563
+01:08:53,020 --> 01:08:57,540
+Y طيب،
+
+564
+01:08:57,540 --> 01:09:01,310
+إيش رايك؟ في عمل مشترك في ال busخلّيني أطلّر
+
+565
+01:09:01,310 --> 01:09:10,010
+الناقص عام المشترك و 2 عام المشترك و Y أس ناقص 2
+
+566
+01:09:10,010 --> 01:09:20,210
+عام المشترك صحيح؟ بيضل كده؟ بيضل 4 X تكيب 4 X تكيب
+
+567
+01:09:20,210 --> 01:09:31,190
+Y أس ناقص 1 و هنا زائد 3 فقط لغير صحيح؟طيب نيجي
+
+568
+01:09:31,190 --> 01:09:39,030
+على المقام المقام ممكن اخد ايش Y بيصير Y اصلاق
+
+569
+01:09:39,030 --> 01:09:46,670
+اصلاق بدي اخد Y السالب واحد يبقى Y السالب واحد
+
+570
+01:09:46,670 --> 01:09:55,650
+عامل مشترك بضل ان انا قداش بضل تلاتة Xتلاتة اكس
+
+571
+01:09:55,650 --> 01:10:02,850
+واي والسالب واحد زائد
+
+572
+01:10:02,850 --> 01:10:07,070
+اربع
+
+573
+01:10:07,070 --> 01:10:14,430
+واي تربيع لو تضرب فيها تصير هذه في شغلة في بصة
+
+574
+01:10:14,430 --> 01:10:23,320
+المقام في شغلة مشتركةلأ يبقى هذه ما زبطتش معاك
+
+575
+01:10:23,320 --> 01:10:27,900
+يبقى أنا تصرفت بعقليتك انت في الامتحان و
+
+576
+01:10:27,900 --> 01:10:30,700
+الغالبيتنا يحكوا مش دقيق في النظر في الامتحان
+
+577
+01:10:30,700 --> 01:10:36,060
+مربوك يبقى هذه ما زبطتش صحيح ولا لا؟ ايوة بدي
+
+578
+01:10:36,060 --> 01:10:40,780
+اقلبها بدي اقلبها و اشوف ايش اللي بصير يبقى لو
+
+579
+01:10:40,780 --> 01:10:45,240
+قلبت هي ايش اللي بصير؟ بصير كالتالي يبقى هذه
+
+580
+01:10:45,240 --> 01:10:50,890
+ماجيبتش نتيجة يا بناتبدي اخد تفاضل ال M بالنسبة
+
+581
+01:10:50,890 --> 01:10:58,470
+الى X ناقص تفاضل ال M بالنسبة الى Y كله مقسوما على
+
+582
+01:10:58,470 --> 01:11:02,910
+Mأنا قدر أجيب عليك صح من الأول بس مابديش مابدي
+
+583
+01:11:02,910 --> 01:11:06,530
+أفكر بعدين كأن مشاربة ككتيرة اللي بقى سهلة مش سهلة
+
+584
+01:11:06,530 --> 01:11:10,650
+زي اللي قبل يبقى تفاضل ال N بالنسبة ل X اللي هي
+
+585
+01:11:10,650 --> 01:11:16,310
+تلاتة Y اص ناقص اتنين تفاضل ال N بالنسبة ل Y
+
+586
+01:11:16,310 --> 01:11:22,910
+الناقص بيصير كله زائد يبقى زائد تمانية X تكييب Y
+
+587
+01:11:22,910 --> 01:11:32,350
+اص ناقص اتنين زائد Y اص ناقص تلاتةY اص ناقص تلاتة
+
+588
+01:11:32,350 --> 01:11:40,450
+زائد تلاتة Y اص ناقص اتنين كل هذا الكلام على مين؟
+
+589
+01:11:40,450 --> 01:11:49,830
+على M ال M وين ال M؟ اللي هو اربع X تكيب وراه اربع
+
+590
+01:11:49,830 --> 01:11:56,970
+X تكيب Y اص ناقص اتنين زائد تلاتة Y اص ناقص واحد
+
+591
+01:11:58,700 --> 01:12:06,920
+طيب هذه تلاتة و تلاتة ستة يا بنات يبقى هاي
+
+592
+01:12:06,920 --> 01:12:14,220
+تمانية x تكيب y اص ناقص تلاتة زاد ستة y اص ناقص
+
+593
+01:12:14,220 --> 01:12:23,060
+اتنين على اربع x تكيب y اص ناقص اتنين زاد تلاتة y
+
+594
+01:12:23,060 --> 01:12:29,530
+اص ناقص واحد y الساوييبقى الاتنين عامل مشترك و Y
+
+595
+01:12:29,530 --> 01:12:34,750
+نقص اتنين نفس المعامل اللي كان هناك بيشارت سالب
+
+596
+01:12:34,750 --> 01:12:44,370
+تمام بضل قديش عندي اربع X تكييب و Y سالب واحدY أس
+
+597
+01:12:44,370 --> 01:12:53,670
+سالب واحد زائد تلاتة فقط لغير على المقام Y أس ناقص
+
+598
+01:12:53,670 --> 01:13:00,050
+واحد عام المشترك بضل أربع X تكييب Y أس ناقص واحد
+
+599
+01:13:10,880 --> 01:13:20,420
+يبقى النتيجة تساوي 2y-1 يبقى 2 على y يبقى function
+
+600
+01:13:20,420 --> 01:13:26,880
+of y
+
+601
+01:13:26,880 --> 01:13:27,520
+only
+
+602
+01:13:33,490 --> 01:13:42,510
+بصير عند الـ Mu of Y يبقى E أستكامل اتنين على Y Dy
+
+603
+01:13:43,490 --> 01:13:59,710
+يبقى E أس اتنين لن absolute value ل Y
+
+604
+01:13:59,710 --> 01:14:00,530
+تربيع
+
+605
+01:14:07,050 --> 01:14:12,530
+تمام تمام اذا صار عامل التكمل هو Y تربيع بالدرجة
+
+606
+01:14:12,530 --> 01:14:15,670
+على المعادلة الأصلية اللى عندنا هدى وضربها في مين
+
+607
+01:14:15,670 --> 01:14:23,190
+في Y تربيع يبقى multiply equation
+
+608
+01:14:23,190 --> 01:14:33,450
+one by Y تربيع we get نضرب في Y تربيع اش بيصير
+
+609
+01:14:33,450 --> 01:14:43,330
+عندنااربع اكس تكييب فقط زائد تلاتة Y اص ناقص واحد
+
+610
+01:14:43,330 --> 01:14:50,270
+كله في DX زائد تلاتة X ك
+
+611
+01:14:55,410 --> 01:15:01,830
+أربعة اكس تكيب في Y تربية بتروح تلاتة Y تربية في Y
+
+612
+01:15:01,830 --> 01:15:09,950
+بتبقى تلاتة Y بس تلاتة Y صحيح وهنا تلاتة X بتروح
+
+613
+01:15:09,950 --> 01:15:17,910
+ال Y وهنا زائد أربعة Y تكيب دي Y بدرسياوي Zero
+
+614
+01:15:17,910 --> 01:15:24,720
+طلعيلي هناهذا بدي اعطيكي partial M by partial Y
+
+615
+01:15:24,720 --> 01:15:30,020
+يساوي التفاضل هذا بالنسبة لـY البلجاني بقدرش تلاتة
+
+616
+01:15:30,020 --> 01:15:35,100
+و التفاضل هذا بالنسبة لـX بقدرش تلاتة كذلك يبقى
+
+617
+01:15:35,100 --> 01:15:41,480
+يساوي التفاضل الـN بالنسبة لـX هذا بدي اعطيكي the
+
+618
+01:15:41,480 --> 01:15:48,860
+differential equation is exact
+
+619
+01:15:52,270 --> 01:16:00,270
+هذا سوف يعطيك there exists a function psi of x و y
+
+620
+01:16:00,270 --> 01:16:04,090
+سواء يكون أصلاً c such that
+
+621
+01:16:06,850 --> 01:16:14,010
+بارشال إبصاي على بارشال X يساوي أربع X تكييب زائد
+
+622
+01:16:14,010 --> 01:16:20,890
+تلاتة Y و بارشال إبصاي على بارشال Y يساوي تلاتة X
+
+623
+01:16:20,890 --> 01:16:28,460
+زائد أربع Y تكييبأظن انكمل هذا بالنسبة ل X سهل
+
+624
+01:16:28,460 --> 01:16:33,320
+وانكمل هذا بالنسبة ل Y سهل يبقى اي واحدة بتصدر
+
+625
+01:16:33,320 --> 01:16:40,760
+يبقى لو جيت قولتلك بـPsi of X وY سوى يبقى كامل
+
+626
+01:16:40,760 --> 01:16:45,780
+بالنسبة لمن ال X يبقى باضيف لل أس واحد وبقسم على
+
+627
+01:16:45,780 --> 01:16:50,940
+الأس الجديد بتروح الأربعة مع الأربعة وهنا زائد
+
+628
+01:16:50,940 --> 01:16:59,550
+تلاتة Y Xزائد f of y يبقى هذا بيدي اعطيك partial
+
+629
+01:16:59,550 --> 01:17:05,710
+psi by partial y يساوي نفضل بالنسبة ل y يبقى هذه
+
+630
+01:17:05,710 --> 01:17:14,270
+مع السلامة و بظل بس تلاتة x زائد f prime of y
+
+631
+01:17:18,110 --> 01:17:25,610
+من هدول اتنين مع بعض بس تنتج انه f prime of y بده
+
+632
+01:17:25,610 --> 01:17:32,550
+يساوي كده اش اربع y تكيب يبقى هذا بده يعطيكي ان ال
+
+633
+01:17:32,550 --> 01:17:40,170
+f of y y اص اربع زائد constant c1 يبقى باجي بقوله
+
+634
+01:17:40,170 --> 01:17:45,290
+solution is
+
+635
+01:17:45,290 --> 01:17:56,390
+epsilonx of x of y يساوي x أُص أربعة x أُص أربعة
+
+636
+01:17:56,390 --> 01:18:05,670
+زائد تلاتة x y ال f of y اللي هي في قداش f y أُص
+
+637
+01:18:05,670 --> 01:18:11,670
+أربعة كل هذا الكلام يساوي constant c بالشكل اللي
+
+638
+01:18:11,670 --> 01:18:12,910
+عندنا هذا
+
+639
+01:18:16,830 --> 01:18:17,890
+هي اي تساؤل
+
+640
+01:18:44,090 --> 01:18:50,890
+طيب بدنا أسهل على التمرين يبقى exercises أكتبهم لك
+
+641
+01:18:50,890 --> 01:18:58,790
+هنا exercises اتنين ستة المسائل التالية من واحد
+
+642
+01:18:58,790 --> 01:19:09,850
+للاتناشر القدر ومن تلتاش لستاش تلتاش لستاش ومن
+
+643
+01:19:09,850 --> 01:19:11,970
+تمنتاش لتلتا وعشرين
+
+644
+01:19:15,430 --> 01:19:21,810
+طبعا سؤال 23 قرهناه الكتاب قبل شوية على اللوح
+
+645
+01:19:25,630 --> 01:19:29,630
+الان في انا تمارين عامة يا بنات على هذا الشبطر ككل
+
+646
+01:19:29,630 --> 01:19:35,710
+انتهى الشبطر لكن احنا ما انتهيناش في عندك تمارين
+
+647
+01:19:35,710 --> 01:19:40,670
+عامة على هذا الشبطر خلال هذه التمارين العامة
+
+648
+01:19:40,670 --> 01:19:45,160
+المجموعة الاولى مباشرة على كل ما درسناهلكن حطلي
+
+649
+01:19:45,160 --> 01:19:51,440
+كمان تلت شغلات جديدة تقولوا كلها الى linear او
+
+650
+01:19:51,440 --> 01:19:55,900
+exact او homogeneous او ما الى ذلك فى عندنا معادلة
+
+651
+01:19:55,900 --> 01:19:59,540
+اسمها معادلة tricate equation
+
+652
+01:20:02,170 --> 01:20:10,350
+هذا حطه في الكتاب يبقى exercises page صفحة اللي هو
+
+653
+01:20:10,350 --> 01:20:15,690
+مية و واحد و تلاتين لغاية مية و تلاتة و تلاتين
+
+654
+01:20:15,690 --> 01:20:21,290
+اللي هي التمارين العام على هذا الشبطر حط فيها سؤال
+
+655
+01:20:21,290 --> 01:20:31,150
+تلاتة و تلاتين اللي هو ركاتي ركاتي
+
+656
+01:20:32,000 --> 01:20:41,980
+Equation ايه شركة equation هنا it is an equation
+
+657
+01:20:41,980 --> 01:20:45,780
+in
+
+658
+01:20:45,780 --> 01:20:50,520
+the form الشكل
+
+659
+01:20:50,520 --> 01:21:02,090
+التاليDY على DT يساوي Q1 of T زائد Q2 of T في ال Y
+
+660
+01:21:02,090 --> 01:21:10,290
+زائد Q3 of T في من في ال Y تربيع وهذه سميها
+
+661
+01:21:10,290 --> 01:21:12,410
+للمعادلة رقم 1
+
+662
+01:21:47,480 --> 01:21:52,940
+طيب لو أنا أطلع في المعادلة هذه بقول لم يسبق لنا
+
+663
+01:21:52,940 --> 01:21:58,260
+أن رأينا في هذا الشبطر معادلة زي هيك دالة في T،
+
+664
+01:21:58,260 --> 01:22:02,260
+دالة في T في Y، دالة في T في من؟ في ال Y تربية،
+
+665
+01:22:02,260 --> 01:22:07,560
+لكن لو شيلت هذه قلت اه والله هذه مرة عالية، هذه
+
+666
+01:22:07,560 --> 01:22:13,480
+Bernoulli equation صح ولا لا؟لو شيلت هذه بقول اه
+
+667
+01:22:13,480 --> 01:22:17,160
+والله هذه ال linear equation لكن لا اخلها لبرنولا
+
+668
+01:22:17,160 --> 01:22:22,580
+على شجة ولا اخلها لمين linear على شجة اذا بدنا
+
+669
+01:22:22,580 --> 01:22:28,220
+نشوف كيف بدنا نحل المعادلة هذه من هذا القبيل فهو
+
+670
+01:22:28,220 --> 01:22:31,340
+بيعطيني دائما من المسائل من هذا القبيل بيعطيني حل
+
+671
+01:22:31,340 --> 01:22:36,940
+خاص و بطلب مني إيجاد ال general solution فبقول
+
+672
+01:22:36,940 --> 01:22:51,220
+الآن ما يأتيY1 هو عبارة
+
+673
+01:22:51,220 --> 01:22:58,740
+عن حل خاص particular solution of the differential
+
+674
+01:22:58,740 --> 01:23:07,300
+equation one then the general solution
+
+675
+01:23:10,400 --> 01:23:19,580
+general solution the general solution of the
+
+676
+01:23:19,580 --> 01:23:31,860
+differential equation one is y تسوى y one زائد
+
+677
+01:23:31,860 --> 01:23:37,640
+واحد على v of t where
+
+678
+01:23:39,860 --> 01:23:53,600
+حيث الـ V of T is a function that we
+
+679
+01:23:53,600 --> 01:24:01,100
+can find it as
+
+680
+01:24:01,100 --> 01:24:01,580
+follows
+
+681
+01:24:19,950 --> 01:24:24,690
+مرة تانية Recate equation هي معادلة على الشكل اللي
+
+682
+01:24:24,690 --> 01:24:30,870
+قدامنا هذا تمام الآن بدنا نبحث عن الحل العام لهذه
+
+683
+01:24:30,870 --> 01:24:36,030
+المعادلة مشان نوجد الحل العام لازم يعطيني حل خاص
+
+684
+01:24:36,030 --> 01:24:40,670
+لها ومن خلال الحل الخاص بقدر أروح أجيب الحل العام
+
+685
+01:24:40,670 --> 01:24:46,310
+لهذه المعادلة فبقول fy1 أيضا حل خاص للمعادلة اللي
+
+686
+01:24:46,310 --> 01:24:53,080
+عندنا هذهثم حل العاملة المعادلة رقم واحد هو Y
+
+687
+01:24:53,080 --> 01:25:00,120
+يساوي Y1 زائد واحد على V of Tمن هي ال V of T هي
+
+688
+01:25:00,120 --> 01:25:04,780
+عبارة عن ال .. بدنا نحاول نوجي ده كتل يعني أنا
+
+689
+01:25:04,780 --> 01:25:11,120
+لازم أروح أعرف ما هو شكل ال V of T بقوله كويس احنا
+
+690
+01:25:11,120 --> 01:25:23,500
+الآن since Y1 is a solution of equation 1 we have
+
+691
+01:25:24,830 --> 01:25:29,530
+مدام هذا الحل إذا هيحقق المعادلة صحيح ولا لا يبقاش
+
+692
+01:25:29,530 --> 01:25:41,170
+بيصير dy1 على dt بده يساوي q1 of t زيدي q2 of t في
+
+693
+01:25:41,170 --> 01:25:51,670
+ال y1 زيدي q3 of t في ال y1 تربيت
+
+694
+01:25:51,670 --> 01:26:04,950
+طيب كويس بنرجح احناالـ Y بيكون Y1 زائد 1 على V of
+
+695
+01:26:04,950 --> 01:26:11,470
+T هذا يعطينا حل عام لمين للمعادلة اللي قلنا عنها
+
+696
+01:26:11,470 --> 01:26:17,210
+إذا تعالى نشتق هذه ونشوف ايش بتعطينا يبقى لو جينا
+
+697
+01:26:17,210 --> 01:26:22,650
+اشتقناها باجي بقول يبقى DY على DT بيكون
+
+698
+01:26:25,330 --> 01:26:33,770
+على DT ناقص واحد على V تربيع في DV على DT تربيع
+
+699
+01:26:33,770 --> 01:26:40,170
+يعني واحد على V مش تقطع واحد على V تربيع في DV على
+
+700
+01:26:40,170 --> 01:26:44,970
+DT الان بدأ امسك المعلومات اللي عندي وارجع اعوض
+
+701
+01:26:44,970 --> 01:26:50,550
+وين في المعادلة رقم واحد يبقى باجي بقوله هنا ال
+
+702
+01:26:50,550 --> 01:27:02,000
+Sabes تتيوت انquestion one we get نحصل علامات بدي
+
+703
+01:27:02,000 --> 01:27:06,720
+اشيل dy على dt واحط قيمة هذه اللي هو الطرف الشمال
+
+704
+01:27:06,720 --> 01:27:17,520
+يبقى dy على dt شو بصير اللي هو dy one على dt ناقص
+
+705
+01:27:17,520 --> 01:27:25,350
+واحد على v تربيع في dv على dtبدي أسوأ الطرف اليمين
+
+706
+01:27:25,350 --> 01:27:35,870
+Q1 of T خليك زي ما انت زائد Q2 of T في مين في Y
+
+707
+01:27:35,870 --> 01:27:41,790
+بدي أشيل ال Y و أحط قيمتها هي اللي هو Y1 زائد 1
+
+708
+01:27:41,790 --> 01:27:50,800
+على Vيبقى هذه Y1 زائد واحد على V اختصارا بدل ما
+
+709
+01:27:50,800 --> 01:27:57,760
+اقول V of T افهم انها V of T يبقى شيلنا Y وحطينا
+
+710
+01:27:57,760 --> 01:28:00,940
+وابدالها Y1 زائد واحد على V
+
+711
+01:28:13,240 --> 01:28:20,710
+يبقى أصبحت المسألة على الشكل التاليطلع يا بناتي شو
+
+712
+01:28:20,710 --> 01:28:30,890
+بده يصير ده يصير عندي dy1 على dt ناقص واحد على v
+
+713
+01:28:30,890 --> 01:28:38,470
+تربيع ناقص واحد على v تربيع في ال dv على dt يساوي
+
+714
+01:28:38,470 --> 01:28:44,930
+ها بده افك الأقواس اللي عندنا هذه يبقى q1 of t
+
+715
+01:28:44,930 --> 01:28:57,080
+زائدQ2 of T في الـ Y1 Q2 of T في الـ Y1 زائد Q2 of
+
+716
+01:28:57,080 --> 01:29:07,100
+T في 1 على V أو رايحة خلاص Q2 of T على V مباشرة
+
+717
+01:29:07,100 --> 01:29:18,500
+لسهولة Q2 زائد Q3 of Tبدا فكها ده يا بنات بصير Y
+
+718
+01:29:18,500 --> 01:29:27,380
+واحد تربيع زائد Q three of T اتنين حاصل ضرب
+
+719
+01:29:27,380 --> 01:29:34,600
+الكيميتين يبقى هاي الاتنين في Y one على V في Y one
+
+720
+01:29:34,600 --> 01:29:37,440
+على V زائد
+
+721
+01:29:47,690 --> 01:30:00,860
+وهذا الكلام يساوي Q1 of T زائد Q2 of T في Y1زائد ل
+
+722
+01:30:00,860 --> 01:30:07,900
+Q3 of T في ال Y1 تربيع يبقى خلاص ال term هذا و ال
+
+723
+01:30:07,900 --> 01:30:12,900
+term هذا و ال term هذا هذا في واحد على V و هذا في
+
+724
+01:30:12,900 --> 01:30:19,800
+واحد على V إذا بقدر أخد واحد على V عامل مشترك بظل
+
+725
+01:30:19,800 --> 01:30:31,680
+ل Q2 of T زائد 2 ل Q3 of T في ال Y1خلصنا منهم زائد
+
+726
+01:30:31,680 --> 01:30:38,580
+Q3 of T على main على V تربية ايش رايكوا هذه يا
+
+727
+01:30:38,580 --> 01:30:50,100
+بنات؟ مش هي Dy1 على Dt صح؟ هي Dy1 وراها تاي Dy1
+
+728
+01:30:50,100 --> 01:30:57,990
+على Dt هذه اه صح؟ سكت الناس هو، مظبوط؟يبقى هذه هي
+
+729
+01:30:57,990 --> 01:31:03,690
+هذه يبقى لو جبتها عندها كلها هتروح مع هذه ايش بظل
+
+730
+01:31:03,690 --> 01:31:11,790
+عندى ناقص واحد على V تربيع في DV على DT بدي ساوي
+
+731
+01:31:11,790 --> 01:31:23,210
+واحد على V في Q2 of T زادى 2 Q3 of T في Y1 زائدEQ
+
+732
+01:31:23,210 --> 01:31:30,270
+ثلاثة of T على V تربيع طيب ايش رايك؟ بدى اضعه كله
+
+733
+01:31:30,270 --> 01:31:39,950
+في سالب V تربيع دي ماشي بضل عند هنا DV على DT بده
+
+734
+01:31:39,950 --> 01:31:49,310
+يساوي سالب EQ اتنين of T زائد اتنين EQ تلاتة of T
+
+735
+01:31:49,720 --> 01:31:59,900
+فى ال Y1 هذا كله فى ال V تمام هنا ضربنا فى سالب V
+
+736
+01:31:59,900 --> 01:32:07,180
+تربيع يبقى سالب Q ثلاثة of V طب بدى أجيب هذا على
+
+737
+01:32:07,180 --> 01:32:16,000
+الشجة التانية DV على DT زائد Q ثلاثة of T زائد
+
+738
+01:32:16,000 --> 01:32:22,930
+اتنينى Q ثلاثة of T فى ال Y1فى ال V يساوي الناقص Q
+
+739
+01:32:22,930 --> 01:32:32,170
+ثلاثة of T مرة علينا قبل هك دالة زي هك V prime
+
+740
+01:32:32,170 --> 01:32:39,230
+زائد P of T في Y بتساوي G of T اللي همين Linear
+
+741
+01:32:39,230 --> 01:32:42,570
+يبقى حولت مثلا America equation إلى Linear
+
+742
+01:32:42,570 --> 01:32:52,260
+equation بهذه الطريقة يبقى هنا Linearfirst order
+
+743
+01:32:52,260 --> 01:33:06,220
+differential equation that can be solved as before
+
+744
+01:33:06,220 --> 01:33:15,940
+يبقى بقدر أحلها زي قبلto get عشان نحصل على V of T
+
+745
+01:33:15,940 --> 01:33:21,480
+وبالتالي بتجبر خلصت ايه؟ خلصت مسألتنا طب نعطيكوا
+
+746
+01:33:21,480 --> 01:33:27,780
+مثال توضيحي فيانكوا سؤالين في الكتاب، فده يعطيكوا
+
+747
+01:33:27,780 --> 01:33:31,600
+أحدهما، والتاني بصير عليكوا حلو
+
+748
+01:33:42,630 --> 01:33:50,230
+السؤال بيقول ما يأتي example
+
+749
+01:33:50,230 --> 01:33:55,690
+if
+
+750
+01:33:55,690 --> 01:34:06,610
+y1 of t بدى يسوى واحد على T وT greater than zero
+
+751
+01:34:06,610 --> 01:34:11,170
+is a power
+
+752
+01:34:32,600 --> 01:34:42,610
+Y' تساوي سالب واحد على T ترابيعسالب واحد عالى T في
+
+753
+01:34:42,610 --> 01:34:54,670
+ال Y زائد Y تربيع سمها للمعادلة هذه find its
+
+754
+01:34:54,670 --> 01:34:59,670
+general solution
+
+755
+01:35:19,410 --> 01:35:23,690
+سؤال مرة تانية بيحطيني y واحد سواء واحد على t و ال
+
+756
+01:35:23,690 --> 01:35:27,730
+t greater than zero هي عبارة عن حل خاص للمعادلة
+
+757
+01:35:27,730 --> 01:35:31,810
+اللي عندنا هذه فجهة ال general solution بتطلع في
+
+758
+01:35:31,810 --> 01:35:36,190
+المعادلة هذه y prime سلب واحد على t يعني function
+
+759
+01:35:36,190 --> 01:35:40,530
+في t function في t في y function t اللي هو
+
+760
+01:35:40,530 --> 01:35:46,910
+constant في y تكيب يبقى هدري ك equation يبقى هنا
+
+761
+01:35:46,910 --> 01:35:57,780
+equationone is ricati equation اذا بقول له the
+
+762
+01:35:57,780 --> 01:36:10,620
+general solution is y يسوى y one زائد واحد على v
+
+763
+01:36:10,620 --> 01:36:18,100
+of t و لسه ال v of t بدنا نعرف ما هو شكلهامشان هيك
+
+764
+01:36:18,100 --> 01:36:22,680
+باجي أقول هو يعطيني واحد على T عبارة عن حل إذا
+
+765
+01:36:22,680 --> 01:36:27,040
+الواحد على T يحقق مين؟ يحقق المعادل اللي عندنا
+
+766
+01:36:27,040 --> 01:36:38,620
+since بما أن هو واحد واحد على T is a solution of
+
+767
+01:36:38,620 --> 01:36:46,120
+the differential equation when we have
+
+768
+01:36:49,940 --> 01:36:57,460
+يبقى مشتقته مقداش يا بنات دي
+
+769
+01:36:57,460 --> 01:37:03,400
+مقداش؟ مستخدم سالب واحد على T تربية صحيح ولا لا؟
+
+770
+01:37:03,400 --> 01:37:08,960
+لكن احنا مدام هيك شوراك نشتق هذه وقلصنا صح؟ مش
+
+771
+01:37:08,960 --> 01:37:23,770
+هحسن ليه؟ ويه هذا؟ اللي هو ال D Yعلى دي تي ناقص
+
+772
+01:37:23,770 --> 01:37:32,370
+واحد على V تربية في ال DV على دي تي هذا بدي يعطيكي
+
+773
+01:37:32,370 --> 01:37:40,860
+ما يأتيبنجي للـ dy1 على dt بدي الـ dy1 او هذه بدها
+
+774
+01:37:40,860 --> 01:37:45,240
+تساوي نشتاق الطرف اليمين كله دي dy على dt صارت
+
+775
+01:37:45,240 --> 01:37:51,560
+بالشكل ان هذا تمام يبقى بدي امسك هذه dy1 جداش
+
+776
+01:37:51,560 --> 01:37:59,460
+مشتاقتها سالب واحد على T تربية سالب واحد على V
+
+777
+01:37:59,460 --> 01:38:02,940
+تربية في الـDV على DT
+
+778
+01:38:06,170 --> 01:38:15,550
+سالب واحد على T تربيع سالب واحد على T في Y جداش ال
+
+779
+01:38:15,550 --> 01:38:21,990
+Y بY1 زاد واحد على V يبقى Y1 اللي هيبقى جداش يا
+
+780
+01:38:21,990 --> 01:38:22,510
+بنات
+
+781
+01:38:38,400 --> 01:38:44,090
+طيب اظن لو اجت هادي عند هادي مع السلامةبصير أن
+
+782
+01:38:44,090 --> 01:38:52,090
+سالب واحد على V تربيع في DV على DT بيساوي سالب
+
+783
+01:38:52,090 --> 01:39:00,330
+واحد على T ويونب واحد على T زائد واحد على V زائد
+
+784
+01:39:00,330 --> 01:39:09,240
+واحد على T زائد واحد على V الكل تربيعنفك التربية
+
+785
+01:39:09,240 --> 01:39:14,820
+لأنها دي يا بنات بصير سالب واحد على V تربية في ال
+
+786
+01:39:14,820 --> 01:39:22,760
+DV على DT بسالب واحد على T تربيةيبقى سالب واحد على
+
+787
+01:39:22,760 --> 01:39:32,480
+T تربية سالب واحد على T في V زائد واحد على T تربية
+
+788
+01:39:32,480 --> 01:39:42,760
+زائد اتنين على T في V زائد واحد على V تربية طلعيلي
+
+789
+01:39:42,760 --> 01:39:48,560
+هنا واحد على T تربية وسالب واحد على T تربية مع
+
+790
+01:39:48,560 --> 01:39:49,500
+السلامة
+
+791
+01:40:01,860 --> 01:40:09,820
+يبقى اش بصير عامة هنا بصير سالب واحد على V تربية
+
+792
+01:40:09,820 --> 01:40:19,820
+سالب واحد على V تربية في ال DV على DT بالدرساويدى
+
+793
+01:40:19,820 --> 01:40:25,240
+V على دى T بدّى سامع راح اتهدي مع هادي اطلعيه
+
+794
+01:40:25,240 --> 01:40:34,080
+لهادي واطلعيه لهادي ها بيضل واحد على TVيبقى زائد
+
+795
+01:40:34,080 --> 01:40:42,980
+واحد على T في V هنا زائد واحد على V تربية اضربيني
+
+796
+01:40:42,980 --> 01:40:51,860
+الطريقين كله في سلب V تربية بظل عندي DV على DT لما
+
+797
+01:40:51,860 --> 01:40:58,300
+نضرب في سلب V تربية بظل سالب واحد على T في ال V
+
+798
+01:40:58,300 --> 01:41:04,950
+زائد جداش يا بنات زائد واحديبقى هذا كله يسوى هكذا
+
+799
+01:41:04,950 --> 01:41:12,870
+DV على DT يسوى، تمام؟ يعني اذا صارت هذه DV على DT
+
+800
+01:41:12,870 --> 01:41:21,630
+زائد واحد على T في الـV ستسوى كم؟ سالب واحد، أه،
+
+801
+01:41:21,630 --> 01:41:28,070
+هذه سالب واحد، مظبوط، هذه سالب واحد، ستسوى سالب
+
+802
+01:41:28,070 --> 01:41:34,340
+واحد، ايش رأيك في المعادلة هذه؟لينير صح ولا لأ
+
+803
+01:41:34,340 --> 01:41:46,400
+يبقى هذه linear first order differential equation
+
+804
+01:41:46,400 --> 01:41:55,570
+بدنا نحلها يبقى بدنا ل mu of TE أُس تكامل واحد على
+
+805
+01:41:55,570 --> 01:42:03,990
+T DT ب E LN T اذا انجلي T أكبر من Zero يبقى E أس
+
+806
+01:42:03,990 --> 01:42:10,650
+LN T يبقى يساوي قداش T يبقى بدنا نضرب المعادلة هذه
+
+807
+01:42:10,650 --> 01:42:21,310
+كلها في T بصير T في DV على DT زائد V يساوي سالب T
+
+808
+01:42:23,040 --> 01:42:29,460
+يبقى بناء عليه هذا عبارة عن T في V كل prime بسالب
+
+809
+01:42:29,460 --> 01:42:36,660
+T انكمل الطرفين يبقى T في V يسوى سالب T تربيه على
+
+810
+01:42:36,660 --> 01:42:44,680
+اتنين زائد constant Cنقسم كله على T يبقى V of T
+
+811
+01:42:44,680 --> 01:42:51,120
+اللي احنا جاعدين بندور عليها بده يساوي سالب T على
+
+812
+01:42:51,120 --> 01:43:01,460
+2 سالب T على 2 زائد C على T او ان شيتنا فاقلناكله
+
+813
+01:43:01,460 --> 01:43:09,020
+على اتنين T بتنين C كله
+
+814
+01:43:09,020 --> 01:43:12,040
+اتنين T على اتنين بتنين T على اتنين T على اتنين T
+
+815
+01:43:12,040 --> 01:43:12,200
+على اتنين T على اتنين T على اتنين T على اتنين T
+
+816
+01:43:12,200 --> 01:43:16,340
+على اتنين T على اتنين T على اتنين T على اتنين T
+
+817
+01:43:16,340 --> 01:43:17,840
+على اتنين T على اتنين T على اتنين T على اتنين T
+
+818
+01:43:17,840 --> 01:43:18,460
+على اتنين T على اتنين T على اتنين T على اتنين T
+
+819
+01:43:18,460 --> 01:43:18,860
+على اتنين T على اتنين T على اتنين T على اتنين T
+
+820
+01:43:18,860 --> 01:43:19,140
+على اتنين T على اتنين T على اتنين T على اتنين T
+
+821
+01:43:19,140 --> 01:43:25,720
+على اتنين T على اتنين T على اتنهذا يعني V of T
+
+822
+01:43:25,720 --> 01:43:31,520
+وليس V of T بدي ال general solution يبقى ذا
+
+823
+01:43:31,520 --> 01:43:35,700
+general solution
+
+824
+01:43:35,700 --> 01:43:48,140
+Y يسوى Y one زائد واحد على V of T يبقى Y يسوى Y
+
+825
+01:43:48,140 --> 01:43:58,250
+one الوطنية واحد على Tزائد واحد على V of T تنين C
+
+826
+01:43:58,250 --> 01:44:07,650
+ناقص T تربيع على اتنين T او تقدر تقول Y تساوي واحد
+
+827
+01:44:07,650 --> 01:44:17,590
+على T زائد اتنين T على اتنين C ناقص T تربيع هذا ال
+
+828
+01:44:17,590 --> 01:44:20,990
+general solution تبع المعادلة
+
+829
+01:44:23,910 --> 01:44:29,450
+طيب لازلنا في نفس التمرين العامة و لسه عندنا
+
+830
+01:44:29,450 --> 01:44:34,090
+موضوعين في نفس التمرين العامة حاجة نسميها T
+
+831
+01:44:34,090 --> 01:44:38,850
+missing او Y missing بيكون في المعادلة يا اما
+
+832
+01:44:38,850 --> 01:44:43,490
+بشوفش T بالمرة يا اما بشوفش Y المرة القادمة ان شاء
+
+833
+01:44:43,490 --> 01:44:49,750
+الله بنشوف كيف ننحل هذا النوع من المسائل
+
diff --git a/PL9fwy3NUQKwa8ZDfSFGn6H8xVFLzqmCZC/e5F8lf-FFH0_raw.json b/PL9fwy3NUQKwa8ZDfSFGn6H8xVFLzqmCZC/e5F8lf-FFH0_raw.json
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index 0000000000000000000000000000000000000000..5b55e24a474f5f7eb42e79e6c63f8b5ea5885bb1
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@@ -0,0 +1 @@
+{"segments": [{"id": 1, "seek": 2618, "start": 12.16, "end": 26.18, "text": "المره اللي فات بدينا في section 2-6 ال exact equations and integrating factors وبدينا فقط بال exact equations وعرفنا شرط ال exactness كالتالي", "tokens": [6027, 29973, 3224, 13672, 1829, 6156, 9307, 47525, 1829, 8315, 8978, 3541, 568, 12, 21, 2423, 1900, 11787, 293, 26889, 6771, 46599, 16254, 8315, 6156, 47432, 20666, 1900, 11787, 4032, 3615, 28480, 8315, 13412, 2288, 9566, 2423, 1900, 1287, 9122, 6027, 2655, 6027, 1829], "avg_logprob": -0.4253472354676988, "compression_ratio": 1.391304347826087, "no_speech_prob": 0.0, "words": [{"start": 12.159999999999998, "end": 13.12, "word": "المره", "probability": 0.2647705078125}, {"start": 13.12, "end": 13.22, "word": " اللي", "probability": 0.406005859375}, {"start": 13.22, "end": 13.38, "word": " فات", "probability": 0.690185546875}, {"start": 13.38, "end": 13.82, "word": " بدينا", "probability": 0.7522786458333334}, {"start": 13.82, "end": 14.0, "word": " في", "probability": 0.79833984375}, {"start": 14.0, "end": 14.32, "word": " section", "probability": 0.59228515625}, {"start": 14.32, "end": 14.68, "word": " 2", "probability": 0.34619140625}, {"start": 14.68, "end": 15.16, "word": "-6", "probability": 0.613525390625}, {"start": 15.16, "end": 15.36, "word": " ال", "probability": 0.256103515625}, {"start": 15.36, "end": 15.74, "word": " exact", "probability": 0.265625}, {"start": 15.74, "end": 16.8, "word": " equations", "probability": 0.84033203125}, {"start": 16.8, "end": 17.76, "word": " and", "probability": 0.88818359375}, {"start": 17.76, "end": 18.64, "word": " integrating", "probability": 0.9384765625}, {"start": 18.64, "end": 19.52, "word": " factors", "probability": 0.96337890625}, {"start": 19.52, "end": 20.62, "word": " وبدينا", "probability": 0.7060546875}, {"start": 20.62, "end": 21.38, "word": " فقط", "probability": 0.983642578125}, {"start": 21.38, "end": 21.68, "word": " بال", "probability": 0.98046875}, {"start": 21.68, 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"word": " فى", "probability": 0.951416015625}, {"start": 107.27, "end": 107.91, "word": " sine", "probability": 0.373779296875}, {"start": 107.91, "end": 109.13, "word": " اتنين", "probability": 0.9794921875}, {"start": 109.13, "end": 109.87, "word": " X", "probability": 0.99169921875}, {"start": 109.87, "end": 111.57, "word": " زائد", "probability": 0.8738606770833334}, {"start": 111.57, "end": 112.41, "word": " اتنين", "probability": 0.9866943359375}, {"start": 112.41, "end": 113.03, "word": " X", "probability": 0.99462890625}, {"start": 113.03, "end": 113.61, "word": " كل", "probability": 0.876953125}, {"start": 113.61, "end": 114.01, "word": " هذا", "probability": 0.92333984375}, {"start": 114.01, "end": 114.81, "word": " الكلام", "probability": 0.9552408854166666}, {"start": 114.81, "end": 115.33, "word": " فى", "probability": 0.91796875}, {"start": 115.33, "end": 115.99, "word": " DX", "probability": 0.8330078125}, {"start": 115.99, "end": 118.33, "word": " زائد", "probability": 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"compression_ratio": 1.1020408163265305, "no_speech_prob": 0.0, "words": [{"start": 146.14000000000001, "end": 147.3, "word": "هذه", "probability": 0.182891845703125}, {"start": 147.3, "end": 147.92, "word": " المعادلة", "probability": 0.874267578125}, {"start": 147.92, "end": 148.0, "word": " هي", "probability": 0.1845703125}, {"start": 148.0, "end": 148.76, "word": " المعادلة", "probability": 0.84832763671875}, {"start": 148.76, "end": 149.3, "word": " رقم", "probability": 0.8606770833333334}, {"start": 149.3, "end": 149.64, "word": " 1", "probability": 0.4150390625}], "temperature": 1.0}, {"id": 7, "seek": 17768, "start": 151.28, "end": 177.68, "text": "يبقى انا بدى ابحث في البداية هل هذه المعادلة exact والله ماهياش exact باجي لشرط ال exactness اللى مواطة فوق يبقى بدى ابحث عن partial M by partial Y يساوي مرة الإفادة يقولنا يا بنات إذا احنا بنفضل بالنسبة إلى Y يبقى بنعتبر ال X كونستنطل ومقدار ثابت", "tokens": [1829, 3555, 4587, 7578, 1975, 8315, 47525, 7578, 48127, 5016, 12984, 8978, 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"probability": 0.6943359375}, {"start": 768.58, "end": 769.68, "word": " كونستانت", "probability": 0.677978515625}, {"start": 769.68, "end": 770.62, "word": " C1", "probability": 0.82861328125}, {"start": 770.62, "end": 771.52, "word": " يبقى", "probability": 0.9173583984375}, {"start": 771.52, "end": 771.88, "word": " باجي", "probability": 0.579833984375}, {"start": 771.88, "end": 772.66, "word": " بقوله", "probability": 0.6995442708333334}, {"start": 772.66, "end": 773.26, "word": " the", "probability": 0.2322998046875}, {"start": 773.26, "end": 774.34, "word": " solution", "probability": 0.94921875}, {"start": 774.34, "end": 777.42, "word": " of", "probability": 0.95654296875}, {"start": 777.42, "end": 778.68, "word": " the", "probability": 0.69189453125}, {"start": 778.68, "end": 780.5, "word": " differential", "probability": 0.89697265625}, {"start": 780.5, "end": 782.64, "word": " equation", "probability": 0.97607421875}, {"start": 782.64, "end": 783.78, "word": " 1", "probability": 0.464599609375}, {"start": 783.78, "end": 784.92, "word": " is", "probability": 0.8681640625}], "temperature": 1.0}, {"id": 34, "seek": 80553, "start": 793.93, "end": 805.53, "text": "يبقى اليمين EOS XY في Cos 2X ناقص تلاتة Y", "tokens": [1829, 3555, 4587, 7578, 2423, 32640, 9957, 462, 4367, 48826, 8978, 15855, 568, 55, 8717, 995, 4587, 9381, 6055, 1211, 9307, 3660, 398], "avg_logprob": -0.5276692931850752, "compression_ratio": 0.8857142857142857, "no_speech_prob": 0.0, "words": [{"start": 793.9300000000001, "end": 795.33, "word": "يبقى", "probability": 0.63140869140625}, {"start": 795.33, "end": 795.99, "word": " اليمين", "probability": 0.7718098958333334}, {"start": 795.99, "end": 797.23, "word": " EOS", "probability": 0.38525390625}, {"start": 797.23, "end": 798.23, "word": " XY", "probability": 0.474853515625}, {"start": 798.23, "end": 799.37, "word": " في", "probability": 0.427490234375}, {"start": 799.37, "end": 800.23, "word": " Cos", "probability": 0.272705078125}, {"start": 800.23, "end": 802.13, "word": " 2X", "probability": 0.779541015625}, {"start": 802.13, "end": 803.93, "word": " ناقص", "probability": 0.75799560546875}, {"start": 803.93, "end": 805.03, "word": " تلاتة", "probability": 0.8446044921875}, {"start": 805.03, "end": 805.53, "word": " Y", "probability": 0.91650390625}], "temperature": 1.0}, {"id": 35, "seek": 82267, "start": 808.63, "end": 822.67, "text": "زاد C1 يبقى C1 يساوي C1 مرة واحدة ورايا دماغك يبقى هذا هو حل المثل", "tokens": [11622, 18513, 383, 16, 7251, 3555, 4587, 7578, 383, 16, 7251, 3794, 995, 45865, 383, 16, 3714, 25720, 36764, 24401, 3660, 4032, 23557, 25528, 11778, 2304, 5718, 118, 4117, 7251, 3555, 4587, 7578, 23758, 31439, 11331, 1211, 9673, 12984, 1211], "avg_logprob": -0.45960365272149806, "compression_ratio": 1.2727272727272727, "no_speech_prob": 6.556510925292969e-07, "words": [{"start": 808.63, "end": 810.03, "word": "زاد", "probability": 0.263580322265625}, {"start": 810.03, "end": 810.77, "word": " C1", "probability": 0.61328125}, {"start": 810.77, "end": 813.55, "word": " يبقى", "probability": 0.571746826171875}, {"start": 813.55, "end": 813.87, "word": " C1", "probability": 0.4498291015625}, {"start": 813.87, "end": 815.41, "word": " يساوي", "probability": 0.6013336181640625}, {"start": 815.41, "end": 816.13, "word": " C1", "probability": 0.5068359375}, {"start": 816.13, "end": 816.55, "word": " مرة", "probability": 0.757080078125}, {"start": 816.55, "end": 816.89, "word": " واحدة", "probability": 0.96923828125}, {"start": 816.89, "end": 817.21, "word": " ورايا", "probability": 0.8753255208333334}, {"start": 817.21, "end": 817.91, "word": " دماغك", "probability": 0.92138671875}, {"start": 817.91, "end": 820.15, "word": " يبقى", "probability": 0.674041748046875}, {"start": 820.15, "end": 820.57, "word": " هذا", "probability": 0.22607421875}, {"start": 820.57, "end": 821.05, "word": " هو", "probability": 0.734375}, {"start": 821.05, "end": 821.61, "word": " حل", "probability": 0.91748046875}, {"start": 821.61, "end": 822.67, "word": " المثل", "probability": 0.8111979166666666}], "temperature": 1.0}, {"id": 36, "seek": 85283, "start": 825.35, "end": 852.83, "text": "يبقى هذا هو المثال الثاني على الـ exact equation ممكن يجي السؤال بغير الصيغة الأولى وغير الصيغة التانية وفي نفس الوقت على ال exact كيف كالتالي خديلك السؤال example 3 بقول find the value of the constant B find the value", "tokens": [1829, 3555, 4587, 7578, 23758, 31439, 9673, 12984, 6027, 6024, 104, 7649, 1829, 15844, 2423, 39184, 1900, 5367, 3714, 43020, 7251, 7435, 1829, 21136, 33604, 6027, 4724, 17082, 13546, 31767, 1829, 17082, 3660, 16247, 12610, 7578, 4032, 17082, 13546, 31767, 1829, 17082, 3660, 16712, 7649, 10632, 4032, 41185, 8717, 36178, 2423, 30543, 2655, 15844, 2423, 1900, 9122, 33911, 9122, 6027, 2655, 6027, 1829, 16490, 16254, 23275, 21136, 33604, 6027, 1365, 805, 4724, 39648, 915, 264, 2158, 295, 264, 5754, 363, 915, 264, 2158], "avg_logprob": -0.17206100676031338, "compression_ratio": 1.6683417085427135, "no_speech_prob": 0.0, "words": [{"start": 825.35, "end": 825.81, "word": "يبقى", "probability": 0.740234375}, {"start": 825.81, "end": 826.11, "word": " هذا", "probability": 0.91650390625}, {"start": 826.11, "end": 826.39, "word": " هو", "probability": 0.9443359375}, {"start": 826.39, "end": 826.87, "word": " المثال", "probability": 0.97314453125}, {"start": 826.87, "end": 827.37, "word": " الثاني", "probability": 0.9256591796875}, {"start": 827.37, "end": 827.65, "word": " على", "probability": 0.83642578125}, {"start": 827.65, "end": 827.81, "word": " الـ", "probability": 0.57666015625}, {"start": 827.81, "end": 828.25, "word": " exact", "probability": 0.5693359375}, {"start": 828.25, "end": 829.17, "word": " equation", "probability": 0.97900390625}, {"start": 829.17, "end": 830.35, "word": " ممكن", "probability": 0.949951171875}, {"start": 830.35, "end": 831.13, "word": " يجي", "probability": 0.8396809895833334}, {"start": 831.13, "end": 831.73, "word": " السؤال", "probability": 0.9576822916666666}, {"start": 831.73, "end": 832.31, "word": " بغير", "probability": 0.8597005208333334}, {"start": 832.31, "end": 832.89, "word": " الصيغة", "probability": 0.977783203125}, {"start": 832.89, "end": 833.35, "word": " الأولى", "probability": 0.9773763020833334}, {"start": 833.35, "end": 833.69, "word": " وغير", "probability": 0.83056640625}, {"start": 833.69, "end": 834.19, "word": " الصيغة", "probability": 0.9849853515625}, {"start": 834.19, "end": 834.67, "word": " التانية", "probability": 0.9440104166666666}, {"start": 834.67, "end": 835.35, "word": " وفي", "probability": 0.873779296875}, {"start": 835.35, "end": 835.61, "word": " نفس", "probability": 0.998291015625}, {"start": 835.61, "end": 836.09, "word": " الوقت", "probability": 0.98681640625}, {"start": 836.09, "end": 836.57, "word": " على", "probability": 0.8974609375}, {"start": 836.57, "end": 837.25, "word": " ال", "probability": 0.96533203125}, {"start": 837.25, "end": 837.87, "word": " exact", "probability": 0.62109375}, {"start": 837.87, "end": 838.71, "word": " كيف", "probability": 0.75927734375}, {"start": 838.71, "end": 839.53, "word": " كالتالي", "probability": 0.80322265625}, {"start": 839.53, "end": 840.51, "word": " خديلك", "probability": 0.5489095052083334}, {"start": 840.51, "end": 841.35, "word": " السؤال", "probability": 0.89013671875}, {"start": 841.35, "end": 842.41, "word": " example", "probability": 0.83251953125}, {"start": 842.41, "end": 843.27, "word": " 3", "probability": 0.6015625}, {"start": 843.27, "end": 846.25, "word": " بقول", "probability": 0.791748046875}, {"start": 846.25, "end": 846.57, "word": " find", "probability": 0.88232421875}, {"start": 846.57, "end": 846.77, "word": " the", "probability": 0.892578125}, {"start": 846.77, "end": 847.15, "word": " value", "probability": 0.97900390625}, {"start": 847.15, "end": 847.39, "word": " of", "probability": 0.982421875}, {"start": 847.39, "end": 847.59, "word": " the", "probability": 0.86328125}, {"start": 847.59, "end": 848.35, "word": " constant", "probability": 0.95166015625}, {"start": 848.35, "end": 848.85, "word": " B", "probability": 0.444580078125}, {"start": 848.85, "end": 850.05, "word": " find", "probability": 0.8837890625}, {"start": 850.05, "end": 851.17, "word": " the", "probability": 0.9091796875}, {"start": 851.17, "end": 852.83, "word": " value", "probability": 0.982421875}], "temperature": 1.0}, {"id": 37, "seek": 88102, "start": 853.62, "end": 881.02, "text": "of the constant B هتيه لمقدار الثابت B such that the differential equation اللي هي مين؟ X Y تربية زائد", "tokens": [2670, 264, 5754, 363, 8032, 31371, 3224, 32767, 28543, 9640, 6024, 104, 16758, 2655, 363, 1270, 300, 264, 15756, 5367, 2423, 20292, 39896, 3714, 9957, 22807, 1783, 398, 6055, 25513, 10632, 30767, 16373, 3215], "avg_logprob": -0.37343750510896956, "compression_ratio": 1.096, "no_speech_prob": 0.0, "words": [{"start": 853.62, "end": 854.38, "word": "of", "probability": 0.487548828125}, {"start": 854.38, "end": 855.6, "word": " the", "probability": 0.84814453125}, {"start": 855.6, "end": 857.48, "word": " constant", "probability": 0.95263671875}, {"start": 857.48, "end": 859.28, "word": " B", "probability": 0.3896484375}, {"start": 859.28, "end": 860.64, "word": " هتيه", "probability": 0.48388671875}, {"start": 860.64, "end": 861.26, "word": " لمقدار", "probability": 0.92431640625}, {"start": 861.26, "end": 861.88, "word": " الثابت", "probability": 0.8818359375}, {"start": 861.88, "end": 862.42, "word": " B", "probability": 0.8232421875}, {"start": 862.42, "end": 863.76, "word": " such", "probability": 0.7548828125}, {"start": 863.76, "end": 867.62, "word": " that", "probability": 0.95263671875}, {"start": 867.62, "end": 869.12, "word": " the", "probability": 0.61376953125}, {"start": 869.12, "end": 871.26, "word": " differential", "probability": 0.87890625}, {"start": 871.26, "end": 874.04, "word": " equation", "probability": 0.98291015625}, {"start": 874.04, "end": 875.9, "word": " اللي", "probability": 0.340576171875}, {"start": 875.9, "end": 876.14, "word": " هي", "probability": 0.86572265625}, {"start": 876.14, "end": 877.12, "word": " مين؟", "probability": 0.615966796875}, {"start": 877.12, "end": 877.64, "word": " X", "probability": 0.348876953125}, {"start": 877.64, "end": 878.72, "word": " Y", "probability": 0.60986328125}, {"start": 878.72, "end": 879.48, "word": " تربية", "probability": 0.79541015625}, {"start": 879.48, "end": 881.02, "word": " زائد", "probability": 0.8776041666666666}], "temperature": 1.0}, {"id": 38, "seek": 90136, "start": 881.5, "end": 901.36, "text": "ب X تربيع Y كله في DX زائد X تكييب زائد Y في X تربيع DY بده يسوي ال zero is exact", "tokens": [3555, 1783, 6055, 2288, 21292, 3615, 398, 28242, 3224, 8978, 48817, 30767, 16373, 3215, 1783, 6055, 4117, 1829, 1829, 3555, 30767, 16373, 3215, 398, 8978, 1783, 6055, 2288, 21292, 3615, 48427, 47525, 3224, 7251, 3794, 45865, 2423, 4018, 307, 1900], "avg_logprob": -0.27553354821554044, "compression_ratio": 1.21, "no_speech_prob": 1.7881393432617188e-07, "words": [{"start": 881.5, "end": 881.88, "word": "ب", "probability": 0.323974609375}, {"start": 881.88, "end": 882.94, "word": " X", "probability": 0.2470703125}, {"start": 882.94, "end": 883.66, "word": " تربيع", "probability": 0.79949951171875}, {"start": 883.66, "end": 884.08, "word": " Y", "probability": 0.9833984375}, {"start": 884.08, "end": 885.58, "word": " كله", "probability": 0.892822265625}, {"start": 885.58, "end": 885.8, "word": " في", "probability": 0.91845703125}, {"start": 885.8, "end": 886.28, "word": " DX", "probability": 0.798828125}, {"start": 886.28, "end": 888.08, "word": " زائد", "probability": 0.7888997395833334}, {"start": 888.08, "end": 889.94, "word": " X", "probability": 0.8134765625}, {"start": 889.94, "end": 890.98, "word": " تكييب", "probability": 0.855517578125}, {"start": 890.98, "end": 893.08, "word": " زائد", "probability": 0.8982747395833334}, {"start": 893.08, "end": 894.18, "word": " Y", "probability": 0.974609375}, {"start": 894.18, "end": 894.66, "word": " في", "probability": 0.7783203125}, {"start": 894.66, "end": 895.06, "word": " X", "probability": 0.9814453125}, {"start": 895.06, "end": 895.86, "word": " تربيع", "probability": 0.94873046875}, {"start": 895.86, "end": 896.88, "word": " DY", "probability": 0.658203125}, {"start": 896.88, "end": 897.52, "word": " بده", "probability": 0.565185546875}, {"start": 897.52, "end": 897.94, "word": " يسوي", "probability": 0.7144368489583334}, {"start": 897.94, "end": 898.1, "word": " ال", "probability": 0.83154296875}, {"start": 898.1, "end": 898.48, "word": " zero", "probability": 0.2491455078125}, {"start": 898.48, "end": 899.84, "word": " is", "probability": 0.859375}, {"start": 899.84, "end": 901.36, "word": " exact", "probability": 0.9208984375}], "temperature": 1.0}, {"id": 39, "seek": 94821, "start": 936.09, "end": 948.21, "text": "سؤال مرة تانية السؤال بيقول لي هاتلي قيمة الثابت B بحيث أن ال differential equation اللي قدامنا هذه is exact", "tokens": [3794, 33604, 6027, 3714, 25720, 6055, 7649, 10632, 21136, 33604, 6027, 4724, 1829, 39648, 32239, 8032, 9307, 20292, 12174, 32640, 3660, 6024, 104, 16758, 2655, 363, 4724, 5016, 1829, 12984, 14739, 2423, 15756, 5367, 13672, 1829, 12174, 3215, 10943, 8315, 29538, 307, 1900], "avg_logprob": -0.2835582318631085, "compression_ratio": 1.3, "no_speech_prob": 0.0, "words": [{"start": 936.09, "end": 936.99, "word": "سؤال", "probability": 0.85302734375}, {"start": 936.99, "end": 937.27, "word": " مرة", "probability": 0.8642578125}, {"start": 937.27, "end": 937.69, "word": " تانية", "probability": 0.9078776041666666}, {"start": 937.69, "end": 939.43, "word": " السؤال", "probability": 0.7931315104166666}, {"start": 939.43, "end": 939.83, "word": " بيقول", "probability": 0.7523600260416666}, {"start": 939.83, "end": 940.13, "word": " لي", "probability": 0.1802978515625}, {"start": 940.13, "end": 941.17, "word": " هاتلي", "probability": 0.6034342447916666}, {"start": 941.17, "end": 941.65, "word": " قيمة", "probability": 0.98779296875}, {"start": 941.65, "end": 942.39, "word": " الثابت", "probability": 0.8587646484375}, {"start": 942.39, "end": 942.79, "word": " B", "probability": 0.397216796875}, {"start": 942.79, "end": 943.93, "word": " بحيث", "probability": 0.971923828125}, {"start": 943.93, "end": 944.23, "word": " أن", "probability": 0.293701171875}, {"start": 944.23, "end": 944.43, "word": " ال", "probability": 0.83056640625}, {"start": 944.43, "end": 944.85, "word": " differential", "probability": 0.583984375}, {"start": 944.85, "end": 945.59, "word": " equation", "probability": 0.98583984375}, {"start": 945.59, "end": 945.79, "word": " اللي", "probability": 0.86767578125}, {"start": 945.79, "end": 946.37, "word": " قدامنا", "probability": 0.9703369140625}, {"start": 946.37, "end": 946.75, "word": " هذه", "probability": 0.3701171875}, {"start": 946.75, "end": 947.35, "word": " is", "probability": 0.6923828125}, {"start": 947.35, "end": 948.21, "word": " exact", "probability": 0.90673828125}], "temperature": 1.0}, {"id": 40, "seek": 97488, "start": 948.58, "end": 974.88, "text": "يبقى هو ميعطيني ان ال differential equation exact صحيح ولا لأ اذا الشرط partial m by partial y بده يساوي partial n by partial x مظبوط يبقى باجي بقوله since بما ان the differential equation is exact we have", "tokens": [1829, 3555, 4587, 7578, 31439, 3714, 40228, 9566, 9957, 1829, 16472, 2423, 15756, 5367, 1900, 20328, 5016, 1829, 5016, 49429, 5296, 10721, 1975, 15730, 25124, 2288, 9566, 14641, 275, 538, 14641, 288, 47525, 3224, 7251, 3794, 995, 45865, 14641, 297, 538, 14641, 2031, 3714, 19913, 3555, 2407, 9566, 7251, 3555, 4587, 7578, 4724, 26108, 1829, 4724, 39648, 3224, 1670, 4724, 15042, 16472, 264, 15756, 5367, 307, 1900, 321, 362], "avg_logprob": -0.2917410569531577, "compression_ratio": 1.5083798882681565, "no_speech_prob": 0.0, "words": [{"start": 948.58, 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عبارة عن حل خاص particular solution of the differential equation one then the general solution", "tokens": [56, 16, 31439, 6225, 3555, 9640, 3660, 18871, 11331, 1211, 16490, 33546, 1729, 3827, 295, 264, 15756, 5367, 472, 550, 264, 2674, 3827], "avg_logprob": -0.4589843762417634, "compression_ratio": 1.0857142857142856, "no_speech_prob": 5.960464477539063e-08, "words": [{"start": 4960.64, "end": 4961.74, "word": "Y1", "probability": 0.6075439453125}, {"start": 4961.74, "end": 4962.58, "word": " هو", "probability": 0.449951171875}, {"start": 4962.58, "end": 4971.22, "word": " عبارة", "probability": 0.77215576171875}, {"start": 4971.22, "end": 4971.48, "word": " عن", "probability": 0.99462890625}, {"start": 4971.48, "end": 4971.86, "word": " حل", "probability": 0.80224609375}, {"start": 4971.86, "end": 4972.52, "word": " خاص", "probability": 0.98193359375}, {"start": 4972.52, "end": 4973.68, "word": " particular", "probability": 0.1497802734375}, {"start": 4973.68, "end": 4974.76, "word": " solution", "probability": 0.95751953125}, {"start": 4974.76, "end": 4975.86, "word": " of", "probability": 0.86328125}, {"start": 4975.86, "end": 4977.06, "word": " the", "probability": 0.439453125}, {"start": 4977.06, "end": 4978.74, "word": " differential", "probability": 0.8828125}, {"start": 4978.74, "end": 4980.62, "word": " equation", "probability": 0.98291015625}, {"start": 4980.62, "end": 4981.3, "word": " one", "probability": 0.29736328125}, {"start": 4981.3, "end": 4983.84, "word": " then", "probability": 0.401611328125}, {"start": 4983.84, "end": 4985.58, "word": " the", "probability": 0.5576171875}, {"start": 4985.58, "end": 4986.16, "word": " general", "probability": 0.90625}, {"start": 4986.16, "end": 4987.3, "word": " solution", "probability": 0.96044921875}], "temperature": 1.0}, {"id": 206, "seek": 501764, "start": 4990.4, "end": 5017.64, "text": "general solution the general solution of the differential equation one is y تسوى y one زائد واحد على v of t where", "tokens": [1766, 2790, 3827, 264, 2674, 3827, 295, 264, 15756, 5367, 472, 307, 288, 6055, 3794, 2407, 7578, 288, 472, 30767, 16373, 3215, 36764, 24401, 15844, 371, 295, 256, 689], "avg_logprob": -0.3257812559604645, "compression_ratio": 1.2427184466019416, "no_speech_prob": 1.7881393432617188e-07, "words": [{"start": 4990.400000000001, "end": 4991.8, "word": "general", "probability": 0.545196533203125}, {"start": 4991.8, "end": 4993.2, "word": " solution", "probability": 0.93212890625}, {"start": 4993.2, "end": 4994.92, "word": " the", "probability": 0.1324462890625}, {"start": 4994.92, "end": 4995.42, "word": " general", "probability": 0.89013671875}, {"start": 4995.42, "end": 4996.6, "word": " solution", "probability": 0.970703125}, {"start": 4996.6, "end": 4997.98, "word": " of", "probability": 0.94970703125}, {"start": 4997.98, "end": 4999.58, "word": " the", "probability": 0.68359375}, {"start": 4999.58, "end": 5001.48, "word": " differential", "probability": 0.87548828125}, {"start": 5001.48, "end": 5003.62, "word": " equation", "probability": 0.97705078125}, {"start": 5003.62, "end": 5004.24, "word": " one", "probability": 0.74072265625}, {"start": 5004.24, "end": 5006.5, "word": " is", "probability": 0.91552734375}, {"start": 5006.5, "end": 5008.82, "word": " y", "probability": 0.6123046875}, {"start": 5008.82, "end": 5009.94, "word": " تسوى", "probability": 0.58447265625}, {"start": 5009.94, "end": 5010.32, "word": " y", "probability": 0.9130859375}, {"start": 5010.32, "end": 5010.84, "word": " one", "probability": 0.56884765625}, {"start": 5010.84, "end": 5011.86, "word": " زائد", "probability": 0.9415690104166666}, {"start": 5011.86, "end": 5012.66, "word": " واحد", "probability": 0.985107421875}, {"start": 5012.66, "end": 5013.72, "word": " على", "probability": 0.70556640625}, {"start": 5013.72, "end": 5014.32, "word": " v", "probability": 0.60107421875}, {"start": 5014.32, "end": 5015.0, "word": " of", "probability": 0.95166015625}, {"start": 5015.0, "end": 5015.54, "word": " t", "probability": 0.78369140625}, {"start": 5015.54, "end": 5017.64, "word": " where", "probability": 0.8759765625}], "temperature": 1.0}, {"id": 207, "seek": 504158, "start": 5019.86, "end": 5041.58, "text": "حيث الـ V of T is a function that we can find it as follows", "tokens": [5016, 1829, 12984, 2423, 39184, 691, 295, 314, 307, 257, 2445, 300, 321, 393, 915, 309, 382, 10002], "avg_logprob": -0.2623355137674432, "compression_ratio": 0.8904109589041096, "no_speech_prob": 0.0, "words": [{"start": 5019.86, "end": 5020.62, "word": "حيث", "probability": 0.7513020833333334}, {"start": 5020.62, "end": 5022.34, "word": " الـ", "probability": 0.783203125}, {"start": 5022.34, "end": 5022.54, "word": " V", "probability": 0.33544921875}, {"start": 5022.54, "end": 5023.04, "word": " of", "probability": 0.6826171875}, {"start": 5023.04, "end": 5023.52, "word": " T", "probability": 0.97900390625}, {"start": 5023.52, "end": 5025.3, "word": " is", "probability": 0.57470703125}, {"start": 5025.3, "end": 5026.54, "word": " a", "probability": 0.982421875}, {"start": 5026.54, "end": 5027.76, "word": " function", "probability": 0.974609375}, {"start": 5027.76, "end": 5029.68, "word": " that", "probability": 0.83935546875}, {"start": 5029.68, "end": 5033.6, "word": " we", "probability": 0.91748046875}, {"start": 5033.6, "end": 5035.2, "word": " can", "probability": 0.96533203125}, {"start": 5035.2, "end": 5037.04, "word": " find", "probability": 0.75146484375}, {"start": 5037.04, "end": 5037.74, "word": " it", "probability": 0.90234375}, {"start": 5037.74, "end": 5041.1, "word": " as", "probability": 0.97705078125}, {"start": 5041.1, "end": 5041.58, "word": " follows", "probability": 0.51806640625}], "temperature": 1.0}, {"id": 208, "seek": 508697, "start": 5059.95, "end": 5086.97, "text": "مرة تانية Recate equation هي معادلة على الشكل اللي قدامنا هذا تمام الآن بدنا نبحث عن الحل العام لهذه المعادلة مشان نوجد الحل العام لازم يعطيني حل خاص لها ومن خلال الحل الخاص بقدر أروح أجيب الحل العام لهذه المعادلة فبقول fy1 أيضا حل خاص للمعادلة اللي عندنا هذه", "tokens": [2304, 25720, 6055, 7649, 10632, 9647, 473, 5367, 39896, 20449, 18513, 37977, 15844, 25124, 28820, 13672, 1829, 12174, 3215, 10943, 8315, 23758, 46811, 10943, 6024, 48506, 47525, 8315, 8717, 49628, 12984, 18871, 21542, 1211, 18863, 10943, 46740, 24192, 9673, 3615, 18513, 37977, 37893, 7649, 8717, 29245, 3215, 21542, 1211, 18863, 10943, 5296, 31377, 2304, 7251, 3615, 9566, 9957, 1829, 11331, 1211, 16490, 33546, 5296, 11296, 4032, 27842, 16490, 1211, 6027, 21542, 1211, 33962, 33546, 4724, 28543, 2288, 5551, 32887, 5016, 5551, 7435, 1829, 3555, 21542, 1211, 18863, 10943, 46740, 24192, 9673, 3615, 18513, 37977, 6156, 3555, 39648, 38777, 16, 36632, 11242, 995, 11331, 1211, 16490, 33546, 5296, 19528, 3615, 18513, 37977, 13672, 1829, 43242, 8315, 29538], "avg_logprob": -0.20753205688590678, "compression_ratio": 2.013333333333333, "no_speech_prob": 5.960464477539062e-07, "words": 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"seek": 512350, "start": 5098.44, "end": 5123.5, "text": "من هي ال V of T هي عبارة عن ال .. بدنا نحاول نوجي ده كتل يعني أنا لازم أروح أعرف ما هو شكل ال V of T بقوله كويس احنا الآن since Y1 is a solution of equation 1 we have", "tokens": [27842, 39896, 2423, 691, 295, 314, 39896, 6225, 3555, 9640, 3660, 18871, 2423, 4386, 47525, 8315, 8717, 5016, 995, 12610, 8717, 29245, 1829, 11778, 3224, 9122, 2655, 1211, 37495, 22653, 41850, 5296, 31377, 2304, 5551, 32887, 5016, 5551, 3615, 28480, 19446, 31439, 13412, 28820, 2423, 691, 295, 314, 4724, 39648, 3224, 9122, 45865, 3794, 1975, 5016, 8315, 6024, 48506, 1670, 398, 16, 307, 257, 3827, 295, 5367, 502, 321, 362], "avg_logprob": -0.22348151660301316, "compression_ratio": 1.3977272727272727, "no_speech_prob": 5.960464477539062e-07, "words": [{"start": 5098.44, "end": 5098.88, "word": "من", "probability": 0.38720703125}, {"start": 5098.88, "end": 5099.14, "word": " هي", "probability": 0.8232421875}, {"start": 5099.14, "end": 5099.28, "word": " 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36764, 24401, 15844, 691, 295, 314, 7251, 3555, 4587, 7578, 398, 7251, 3794, 2407, 7578, 398, 472, 2423, 2407, 9566, 1863, 10632, 36764, 24401, 15844, 314], "avg_logprob": -0.32192460412070867, "compression_ratio": 1.5606060606060606, "no_speech_prob": 1.1920928955078125e-07, "words": [{"start": 6203.28, "end": 6203.68, "word": "هذا", "probability": 0.613525390625}, {"start": 6203.68, "end": 6203.98, "word": " يعني", "probability": 0.800537109375}, {"start": 6203.98, "end": 6204.6, "word": " V", "probability": 0.60107421875}, {"start": 6204.6, "end": 6205.36, "word": " of", "probability": 0.6474609375}, {"start": 6205.36, "end": 6205.72, "word": " T", "probability": 0.97265625}, {"start": 6205.72, "end": 6206.54, "word": " وليس", "probability": 0.50360107421875}, {"start": 6206.54, "end": 6207.04, "word": " V", "probability": 0.54345703125}, {"start": 6207.04, "end": 6207.28, "word": " of", "probability": 0.779296875}, {"start": 6207.28, "end": 6207.4, "word": " T", "probability": 0.96630859375}, {"start": 6207.4, "end": 6207.7, "word": " بدي", "probability": 0.47454833984375}, {"start": 6207.7, "end": 6207.9, "word": " ال", "probability": 0.62353515625}, {"start": 6207.9, "end": 6208.22, "word": " general", "probability": 0.27783203125}, {"start": 6208.22, "end": 6209.26, "word": " solution", "probability": 0.97119140625}, {"start": 6209.26, "end": 6210.58, "word": " يبقى", "probability": 0.8724365234375}, {"start": 6210.58, "end": 6211.52, "word": " ذا", "probability": 0.309356689453125}, {"start": 6211.52, "end": 6212.58, "word": " general", "probability": 0.7041015625}, {"start": 6212.58, "end": 6215.7, "word": " solution", "probability": 0.96337890625}, {"start": 6215.7, "end": 6217.96, "word": " Y", "probability": 0.6689453125}, {"start": 6217.96, "end": 6219.08, "word": " يسوى", "probability": 0.7197265625}, {"start": 6219.08, "end": 6219.52, "word": " Y", "probability": 0.91748046875}, {"start": 6219.52, "end": 6220.02, "word": " one", "probability": 0.1605224609375}, {"start": 6220.02, "end": 6221.2, "word": " زائد", "probability": 0.9246419270833334}, {"start": 6221.2, "end": 6221.98, "word": " واحد", "probability": 0.968994140625}, {"start": 6221.98, "end": 6222.96, "word": " على", "probability": 0.84716796875}, {"start": 6222.96, "end": 6223.36, "word": " V", "probability": 0.982421875}, {"start": 6223.36, "end": 6223.96, "word": " of", "probability": 0.97607421875}, {"start": 6223.96, "end": 6224.24, "word": " T", "probability": 0.99072265625}, {"start": 6224.24, "end": 6225.78, "word": " يبقى", "probability": 0.9744873046875}, {"start": 6225.78, "end": 6226.52, "word": " Y", "probability": 0.96923828125}, {"start": 6226.52, "end": 6227.5, "word": " يسوى", "probability": 0.93505859375}, {"start": 6227.5, "end": 6228.14, "word": " Y", "probability": 0.953125}, {"start": 6228.14, "end": 6228.64, "word": " one", "probability": 0.94140625}, {"start": 6228.64, "end": 6229.88, "word": " الوطنية", "probability": 0.865087890625}, {"start": 6229.88, "end": 6230.42, "word": " واحد", "probability": 0.9072265625}, {"start": 6230.42, "end": 6230.78, "word": " على", "probability": 0.7021484375}, {"start": 6230.78, "end": 6231.16, "word": " T", "probability": 0.84375}], "temperature": 1.0}, {"id": 254, "seek": 626099, "start": 6232.37, "end": 6260.99, "text": "زائد واحد على V of T تنين C ناقص T تربيع على اتنين T او تقدر تقول Y تساوي واحد على T زائد اتنين T على اتنين C ناقص T تربيع هذا ال general solution تبع المعادلة", "tokens": [11622, 16373, 3215, 36764, 24401, 15844, 691, 295, 314, 6055, 1863, 9957, 383, 8717, 995, 4587, 9381, 314, 6055, 2288, 21292, 3615, 15844, 1975, 2655, 1863, 9957, 314, 1975, 2407, 6055, 28543, 2288, 6055, 39648, 398, 6055, 3794, 995, 45865, 36764, 24401, 15844, 314, 30767, 16373, 3215, 1975, 2655, 1863, 9957, 314, 15844, 1975, 2655, 1863, 9957, 383, 8717, 995, 4587, 9381, 314, 6055, 2288, 21292, 3615, 23758, 2423, 2674, 3827, 6055, 3555, 3615, 9673, 3615, 18513, 37977], "avg_logprob": -0.18947784508330912, "compression_ratio": 1.6887417218543046, "no_speech_prob": 1.430511474609375e-06, "words": [{"start": 6232.37, "end": 6233.55, "word": "زائد", "probability": 0.5792643229166666}, {"start": 6233.55, "end": 6235.01, "word": " واحد", "probability": 0.906494140625}, {"start": 6235.01, "end": 6235.61, "word": " على", "probability": 0.640625}, {"start": 6235.61, "end": 6236.01, "word": " V", "probability": 0.72705078125}, {"start": 6236.01, "end": 6236.43, "word": " of", "probability": 0.83056640625}, {"start": 6236.43, "end": 6236.83, "word": " T", "probability": 0.95654296875}, {"start": 6236.83, "end": 6237.75, "word": " تنين", "probability": 0.5641276041666666}, {"start": 6237.75, "end": 6238.25, "word": " C", "probability": 0.68359375}, {"start": 6238.25, "end": 6239.37, "word": " ناقص", "probability": 0.931396484375}, {"start": 6239.37, "end": 6239.57, "word": " T", "probability": 0.9267578125}, {"start": 6239.57, "end": 6240.27, "word": " تربيع", "probability": 0.773193359375}, {"start": 6240.27, "end": 6240.65, "word": " على", "probability": 0.888671875}, {"start": 6240.65, "end": 6241.61, "word": " اتنين", "probability": 0.8468017578125}, {"start": 6241.61, "end": 6242.09, "word": " T", "probability": 0.96337890625}, {"start": 6242.09, "end": 6243.15, "word": " او", "probability": 0.837646484375}, {"start": 6243.15, "end": 6243.97, "word": " تقدر", "probability": 0.8665364583333334}, {"start": 6243.97, "end": 6244.41, "word": " تقول", "probability": 0.982177734375}, {"start": 6244.41, "end": 6245.51, "word": " Y", "probability": 0.2127685546875}, {"start": 6245.51, "end": 6246.45, "word": " تساوي", "probability": 0.9393310546875}, {"start": 6246.45, "end": 6247.65, "word": " واحد", "probability": 0.97509765625}, {"start": 6247.65, "end": 6248.23, "word": " على", "probability": 0.73974609375}, {"start": 6248.23, "end": 6248.75, "word": " T", "probability": 0.9375}, {"start": 6248.75, "end": 6250.25, "word": " زائد", "probability": 0.95166015625}, {"start": 6250.25, "end": 6251.61, "word": " اتنين", "probability": 0.9796142578125}, {"start": 6251.61, "end": 6252.17, "word": " T", "probability": 0.99267578125}, {"start": 6252.17, "end": 6253.05, "word": " على", "probability": 0.85205078125}, {"start": 6253.05, "end": 6253.83, "word": " اتنين", "probability": 0.9688720703125}, {"start": 6253.83, "end": 6254.35, "word": " C", "probability": 0.99365234375}, {"start": 6254.35, "end": 6255.61, "word": " ناقص", "probability": 0.9853515625}, {"start": 6255.61, "end": 6255.83, "word": " T", "probability": 0.98291015625}, {"start": 6255.83, "end": 6256.57, "word": " تربيع", "probability": 0.955322265625}, {"start": 6256.57, "end": 6257.31, "word": " هذا", "probability": 0.861328125}, {"start": 6257.31, "end": 6257.59, "word": " ال", "probability": 0.8515625}, {"start": 6257.59, "end": 6257.93, "word": " general", "probability": 0.49169921875}, {"start": 6257.93, "end": 6258.63, "word": " solution", "probability": 0.97509765625}, {"start": 6258.63, "end": 6258.99, "word": " تبع", "probability": 0.9189453125}, {"start": 6258.99, "end": 6260.99, "word": " المعادلة", "probability": 0.838623046875}], "temperature": 1.0}, {"id": 255, "seek": 628975, "start": 6263.91, "end": 6289.75, "text": "طيب لازلنا في نفس التمرين العامة و لسه عندنا موضوعين في نفس التمرين العامة حاجة نسميها T missing او Y missing بيكون في المعادلة يا اما بشوفش T بالمرة يا اما بشوفش Y المرة القادمة ان شاء الله بنشوف كيف ننحل هذا النوع من المسائل", "tokens": [9566, 1829, 3555, 5296, 31377, 1211, 8315, 8978, 8717, 36178, 16712, 29973, 9957, 18863, 10943, 3660, 4032, 5296, 3794, 3224, 43242, 8315, 3714, 2407, 11242, 45367, 9957, 8978, 8717, 36178, 16712, 29973, 9957, 18863, 10943, 3660, 11331, 26108, 3660, 8717, 38251, 1829, 11296, 314, 5361, 1975, 2407, 398, 5361, 4724, 1829, 30544, 8978, 9673, 3615, 18513, 37977, 35186, 1975, 15042, 4724, 8592, 38688, 8592, 314, 20666, 2304, 25720, 35186, 1975, 15042, 4724, 8592, 38688, 8592, 398, 9673, 25720, 25062, 18513, 46007, 16472, 13412, 16606, 21984, 44945, 8592, 38688, 9122, 33911, 8717, 1863, 5016, 1211, 23758, 28239, 45367, 9154, 9673, 3794, 16373, 1211], "avg_logprob": -0.11756674656011526, "compression_ratio": 1.9306930693069306, "no_speech_prob": 3.814697265625e-06, "words": [{"start": 6263.91, "end": 6265.03, "word": "طيب", "probability": 0.5851236979166666}, {"start": 6265.03, "end": 6266.09, "word": " لازلنا", "probability": 0.8905029296875}, {"start": 6266.09, "end": 6266.33, "word": " في", "probability": 0.8515625}, {"start": 6266.33, "end": 6266.63, "word": " نفس", "probability": 0.96044921875}, {"start": 6266.63, "end": 6267.33, "word": " التمرين", "probability": 0.91259765625}, {"start": 6267.33, "end": 6268.05, "word": " العامة", "probability": 0.756103515625}, {"start": 6268.05, "end": 6268.59, "word": " و", "probability": 0.6171875}, {"start": 6268.59, "end": 6268.99, "word": " لسه", "probability": 0.91943359375}, {"start": 6268.99, "end": 6269.45, "word": " عندنا", "probability": 0.921630859375}, {"start": 6269.45, "end": 6270.61, "word": " موضوعين", "probability": 0.9904296875}, {"start": 6270.61, "end": 6270.81, "word": " في", "probability": 0.9443359375}, {"start": 6270.81, "end": 6271.09, "word": " نفس", "probability": 0.96435546875}, {"start": 6271.09, "end": 6271.81, "word": " التمرين", "probability": 0.9923502604166666}, {"start": 6271.81, "end": 6272.55, "word": " العامة", "probability": 0.990234375}, {"start": 6272.55, "end": 6273.37, "word": " حاجة", "probability": 0.8846028645833334}, {"start": 6273.37, "end": 6273.87, "word": " نسميها", "probability": 0.8970947265625}, {"start": 6273.87, "end": 6274.09, "word": " T", "probability": 0.62109375}, {"start": 6274.09, "end": 6274.67, "word": " missing", "probability": 0.8759765625}, {"start": 6274.67, "end": 6275.55, "word": " او", "probability": 0.857421875}, {"start": 6275.55, "end": 6275.83, "word": " Y", "probability": 0.8818359375}, {"start": 6275.83, "end": 6276.39, "word": " missing", "probability": 0.93017578125}, {"start": 6276.39, "end": 6276.95, "word": " بيكون", "probability": 0.8525390625}, {"start": 6276.95, "end": 6277.23, "word": " في", "probability": 0.85205078125}, {"start": 6277.23, "end": 6278.05, "word": " المعادلة", "probability": 0.990966796875}, {"start": 6278.05, "end": 6278.67, "word": " يا", "probability": 0.6552734375}, {"start": 6278.67, "end": 6278.85, "word": " اما", "probability": 0.906982421875}, {"start": 6278.85, "end": 6279.45, "word": " بشوفش", "probability": 0.8724365234375}, {"start": 6279.45, "end": 6279.71, "word": " T", "probability": 0.91455078125}, {"start": 6279.71, "end": 6280.25, "word": " بالمرة", "probability": 0.8665364583333334}, {"start": 6280.25, "end": 6280.47, "word": " يا", "probability": 0.80810546875}, {"start": 6280.47, "end": 6280.59, "word": " اما", "probability": 0.965576171875}, {"start": 6280.59, "end": 6281.23, "word": " بشوفش", "probability": 0.975341796875}, {"start": 6281.23, "end": 6281.65, "word": " Y", "probability": 0.984375}, {"start": 6281.65, "end": 6282.47, "word": " المرة", "probability": 0.864990234375}, {"start": 6282.47, "end": 6283.03, "word": " القادمة", "probability": 0.9840494791666666}, {"start": 6283.03, "end": 6283.25, "word": " ان", "probability": 0.869140625}, {"start": 6283.25, "end": 6283.49, "word": " شاء", "probability": 0.966064453125}, {"start": 6283.49, "end": 6283.63, "word": " الله", "probability": 0.962890625}, {"start": 6283.63, "end": 6284.57, "word": " بنشوف", "probability": 0.900390625}, {"start": 6284.57, "end": 6284.89, "word": " كيف", "probability": 0.980712890625}, {"start": 6284.89, "end": 6285.69, "word": " ننحل", "probability": 0.8922119140625}, {"start": 6285.69, "end": 6286.51, "word": " هذا", "probability": 0.93896484375}, {"start": 6286.51, "end": 6287.13, "word": " النوع", "probability": 0.979248046875}, {"start": 6287.13, "end": 6287.91, "word": " من", "probability": 0.9892578125}, {"start": 6287.91, "end": 6289.75, "word": " المسائل", "probability": 0.960693359375}], "temperature": 1.0}], "language": "ar", "language_probability": 1.0, "duration": 6290.5875, "duration_after_vad": 5862.952218750037}
\ No newline at end of file
diff --git a/PL9fwy3NUQKwa8ZDfSFGn6H8xVFLzqmCZC/e5F8lf-FFH0_raw.srt b/PL9fwy3NUQKwa8ZDfSFGn6H8xVFLzqmCZC/e5F8lf-FFH0_raw.srt
new file mode 100644
index 0000000000000000000000000000000000000000..0c1b3c2e2f70ea11f72a40f5cd8371deb3885a58
--- /dev/null
+++ b/PL9fwy3NUQKwa8ZDfSFGn6H8xVFLzqmCZC/e5F8lf-FFH0_raw.srt
@@ -0,0 +1,3336 @@
+1
+00:00:12,160 --> 00:00:15,740
+المره اللي فات بدينا في section 2-6 ال exact
+
+2
+00:00:15,740 --> 00:00:21,680
+equations and integrating factors وبدينا فقط بال
+
+3
+00:00:21,680 --> 00:00:26,180
+exact equations وعرفنا شرط ال exactness كالتالي
+
+4
+00:00:29,810 --> 00:00:38,750
+مكتوب معاك اذا m of x y dx زي ال n of x y dy تساوي
+
+5
+00:00:38,750 --> 00:00:47,950
+zero is exact if and only ifاللي هو ال partial m
+
+6
+00:00:47,950 --> 00:00:55,530
+by partial y بده يساوي partial n by partial x هذه
+
+7
+00:00:55,530 --> 00:00:59,890
+عبارة عن نظرية وبرهنها وقلنا هذه بتسهلي عملية
+
+8
+00:00:59,890 --> 00:01:04,650
+اثبات ان ال function هذه exact واخدنا على ذلك
+
+9
+00:01:04,650 --> 00:01:10,990
+مثالا واحدا الان بنروح ناخد المثال لرقم اتنين يبقى
+
+10
+00:01:10,990 --> 00:01:19,390
+example twoExample 2 بيقول
+
+11
+00:01:19,390 --> 00:01:27,990
+Solve the differential equation حل المعادلة
+
+12
+00:01:27,990 --> 00:01:36,890
+التفاضلية المعادلة موطعة للشكل التالف Y في E أس XY
+
+13
+00:01:38,310 --> 00:01:47,910
+فى cosine اتنين X ناقص اتنين E أُس XY فى sine
+
+14
+00:01:47,910 --> 00:02:00,230
+اتنين X زائد اتنين X كل هذا الكلام فى DX زائد X فى
+
+15
+00:02:00,230 --> 00:02:05,810
+E أُس XY فى cosine اتنين X
+
+16
+00:02:26,140 --> 00:02:32,800
+هذه المعادلة هي المعادلة رقم 1يبقى انا بدى ابحث في
+
+17
+00:02:32,800 --> 00:02:37,280
+البداية هل هذه المعادلة exact والله ماهياش exact
+
+18
+00:02:37,280 --> 00:02:41,680
+باجي لشرط ال exactness اللى مواطة فوق يبقى بدى
+
+19
+00:02:41,680 --> 00:02:49,900
+ابحث عن partial M by partial Y يساوي مرة الإفادة
+
+20
+00:02:49,900 --> 00:02:53,800
+يقولنا يا بنات إذا احنا بنفضل بالنسبة إلى Y يبقى
+
+21
+00:02:53,800 --> 00:03:00,020
+بنعتبر ال X كونستنطل ومقدار ثابتبنجي لهذه يبقى
+
+22
+00:03:00,020 --> 00:03:07,020
+cosine X هذه مقدار ثابت عند هنا Y وعندي E أس XY
+
+23
+00:03:07,020 --> 00:03:14,070
+يبقى دول حاصن ضرب دالتين إذا دول هستخدم مشتقتحاصل
+
+24
+00:03:14,070 --> 00:03:17,850
+ضارب دلتين دل الأولى في مشتقة الثانية زي ده
+
+25
+00:03:17,850 --> 00:03:22,370
+الثانية في مشتقة الأولى يبقى لو جت اشتق الأولى
+
+26
+00:03:22,370 --> 00:03:27,130
+بالنسبة له يبقى مشتقة هذه بقداش واحد صحيح بصير
+
+27
+00:03:27,130 --> 00:03:34,730
+عندي E أس XY في Cos 2X Cos 2X لأنه مقدار ثابت
+
+28
+00:03:34,730 --> 00:03:40,360
+مالوش دعوة زائدهذا الـ Y اللي برا يجب أن تكون الـ
+
+29
+00:03:40,360 --> 00:03:44,900
+Exponential الـ Exponential مشتقتة بنفسها ضرب
+
+30
+00:03:44,900 --> 00:03:49,480
+مشتقت الـ Os تبعها الـ Os بيشتقوا بالنسبة لـ Y
+
+31
+00:03:49,480 --> 00:03:54,820
+مشتقوا بالنسبة لـ Y اللي هو بمين؟ ب X يبقى زائد Y
+
+32
+00:03:54,820 --> 00:03:55,720
+في X
+
+33
+00:04:13,620 --> 00:04:20,690
+يبقى ناقص اتنين X في E أس XY في كوصين اتنين Xفى
+
+34
+00:04:20,690 --> 00:04:27,050
+الـ sine اتنين X ومشتقة هدى بقداش ب Zero تمام لإن
+
+35
+00:04:27,050 --> 00:04:31,050
+احنا نشتق بالنسبة الى Y بعد اكه بدنا نروح نشتق
+
+36
+00:04:31,050 --> 00:04:35,910
+الجزء الثانى هذا بالاسم لمين الى X يبقى بدى
+
+37
+00:04:35,910 --> 00:04:42,690
+partial N by partial X يساوي بجى لادالة هدى طلعلي
+
+38
+00:04:42,690 --> 00:04:48,200
+ال term الأول هدى فيها Xو هذه فيها X و هذه فيها X
+
+39
+00:04:48,200 --> 00:04:53,200
+يعني مشتق اتحاصل ضرب تلات دوال نذكر ال calculus
+
+40
+00:04:53,200 --> 00:04:57,960
+ايه؟ بشتق الأولة و بثبت التنتين التانية بعدين بشتق
+
+41
+00:04:57,960 --> 00:05:01,000
+اللي في النص و بثبت اللي قبل هو اللي بعدها بعدين
+
+42
+00:05:01,000 --> 00:05:05,020
+بشتق الأخيرة و بثبت التنتين اللي قبل يكون خلصنا
+
+43
+00:05:05,020 --> 00:05:10,930
+اشتقاهيبقى بداجي أشتق هذه كالتالي مشتقة الأولى
+
+44
+00:05:10,930 --> 00:05:20,470
+بتروح بضل قداش عندي E أس XY في Cos 2X بعد هيك زائد
+
+45
+00:05:20,470 --> 00:05:26,010
+Xفى هذه بدى اشتقها بالنسبة ل X هي عبارة عن مين Y
+
+46
+00:05:26,010 --> 00:05:34,490
+في E أُس XY في Cos 2X هيك اشتقت الأولى والتانية
+
+47
+00:05:34,490 --> 00:05:40,330
+يبقى زائد ولا بيصير مشتقة ال cosine بسالب صين يبقى
+
+48
+00:05:40,330 --> 00:05:42,830
+سالب 2X
+
+49
+00:05:59,140 --> 00:06:03,700
+تعالى نقارن بين كل ترم من الترمات التلاتة
+
+50
+00:06:07,200 --> 00:06:13,960
+الترم التاني هو نفسه الترم التالت هو نفسه تمام
+
+51
+00:06:13,960 --> 00:06:17,900
+التمام يبقى القمتين صاروا بالهم زي بعض يبقى
+
+52
+00:06:17,900 --> 00:06:24,040
+بنستنتج من التنتين هذول انه partial M by partial Y
+
+53
+00:06:24,040 --> 00:06:30,580
+يسوى partial N by partial X هذا ايش بده يعطينا بده
+
+54
+00:06:30,580 --> 00:06:35,020
+يعطينا ان ذا differential
+
+55
+00:06:41,530 --> 00:06:51,330
+مدام exact يبقى there exist a function إبصي of x و
+
+56
+00:06:51,330 --> 00:06:57,850
+y بدها تساوي constant c such that بيحيث لنا
+
+57
+00:07:08,170 --> 00:07:22,190
+Y في E أس X Y Y في E أس X Y في Cos 2X ناقص 2 E أس
+
+58
+00:07:22,190 --> 00:07:32,390
+XY في Sin 2Xزائد اتنين X وطفابل الابسعي بالنسبة
+
+59
+00:07:32,390 --> 00:07:40,130
+الى Y يسوى ال term الأخير X E أس XY فيه cosine
+
+60
+00:07:40,130 --> 00:07:48,230
+اتنين X ناقص تلاتة مرة
+
+61
+00:07:48,230 --> 00:07:53,230
+تانية المرة اللي فاتتة أعرفنا ال exact equation
+
+62
+00:07:53,700 --> 00:07:59,220
+قلنا ال differential equation ال M DX زاد ال M DY
+
+63
+00:07:59,220 --> 00:08:04,640
+بقول عنها exact إذا جدرت لاجي function ψ of XY
+
+64
+00:08:04,640 --> 00:08:09,800
+تسوي constant بحيث مشتقة ال ψ بالنسبة لX بده يسوى
+
+65
+00:08:09,800 --> 00:08:14,970
+ال M و مشتقة ال ψ بالنسبة لY بده يسوى 100بدي يساوي
+
+66
+00:08:14,970 --> 00:08:23,370
+ال N تمام؟ يعني هذه كلها N و هذه كلها مرة واحدة هي
+
+67
+00:08:23,370 --> 00:08:30,530
+عبارة عن مين؟ عبارة عن M طيب كويس، الآن بضوحة كامل
+
+68
+00:08:30,530 --> 00:08:36,750
+إحداهما بنكمل أسهل فيهما فالعيلي هذه بدنا نكملها
+
+69
+00:08:36,750 --> 00:08:41,990
+بالنسبة لمين؟ ال X آه هذه حصل ضرب دلتين و بدنا
+
+70
+00:08:41,990 --> 00:08:47,180
+نكملهاأيه ال exponential في ال cosine بدي أرجع ال
+
+71
+00:08:47,180 --> 00:08:52,020
+integration by parts و بدها مرتين نكملها وبعد
+
+72
+00:08:52,020 --> 00:08:57,100
+مرتين بطلع main راسي المثلة قصة طويلة هذه وهذه
+
+73
+00:08:57,100 --> 00:09:01,700
+زيها بنفس الطريقة إذا التكامل هذه بالنسبة ل X
+
+74
+00:09:01,700 --> 00:09:06,900
+difficult شوية فيها نوع من الصعوبة نجي لهذه بدي
+
+75
+00:09:06,900 --> 00:09:11,120
+أكملها بالنسبة ل Y هذا constant هذا constant هذا
+
+76
+00:09:11,120 --> 00:09:15,830
+constantيبقى تكمل من الـ exponential المثال تبع
+
+77
+00:09:15,830 --> 00:09:19,910
+المرة اللي فترة اتكملنا لبساى بالنسبة الى X المرة
+
+78
+00:09:19,910 --> 00:09:24,550
+هذه بنا نتكمل لبساى بالنسبة اله أسهل ليه كتير يبقى
+
+79
+00:09:24,550 --> 00:09:31,750
+لو جه تكمل هذه باجي بقوله يبقى ابساى of XY يساوي
+
+80
+00:09:31,750 --> 00:09:36,570
+يبقى من التكامل هذه ابناط بالنسبة لمن؟ ل Y ال X
+
+81
+00:09:36,570 --> 00:09:41,130
+ثابت و ال cosine ثابتوالـ exponential تكاملها كما
+
+82
+00:09:41,130 --> 00:09:46,890
+هو مقسما على تفاضل المشتقة إذا كانت من الدرجة
+
+83
+00:09:46,890 --> 00:09:51,470
+الأولى طبعا من الدرجة الأولى بالنسبة ل Y ال X
+
+84
+00:09:51,470 --> 00:09:56,350
+يعتبر مقدار ثابت يبقى بنقسمعليه؟ لأنه بنكمل
+
+85
+00:09:56,350 --> 00:10:04,370
+بالنسبة الى Y يبقى X في E وال 6Y مقسم على X في Cos
+
+86
+00:10:04,370 --> 00:10:14,230
+2X ماقص 3Y زائد مقدار ثابت احنا بنكمل بالنسبة لمن؟
+
+87
+00:10:14,230 --> 00:10:20,930
+يبقى المقدار ثابت بدلالة من؟بدأ اه دلالة X لان X
+
+88
+00:10:20,930 --> 00:10:27,950
+يعتبر ثابت بالنسبة ل Y يفجأ زائد F of X بعد هيك
+
+89
+00:10:27,950 --> 00:10:34,450
+بدنا نروح نفضل هدي بالنسبة ل X و نسويها بمين بتدل
+
+90
+00:10:34,450 --> 00:10:39,530
+اللي عندنا هدي يفجأ بدأ أخد partial F of Psi by
+
+91
+00:10:39,530 --> 00:10:44,090
+partial X بدأ افضل هدي بالنسبة ل X طبعا بتروح هدي
+
+92
+00:10:44,090 --> 00:10:48,650
+مع هديبروح الله يسهل عليهم بظل عند e أوس x y في
+
+93
+00:10:48,650 --> 00:10:54,250
+cosine اتنين x لما نفاضلها بالنسبة ل x إذا المشتقت
+
+94
+00:10:54,250 --> 00:10:59,550
+حاصل ضرب داليتين y في e أوس x y
+
+95
+00:11:14,900 --> 00:11:19,760
+مشتقت هذه بالنسبة لل X بقداش؟ بـ0 مع السلام الله
+
+96
+00:11:19,760 --> 00:11:28,480
+يسهل عليها بضال عندي زائد F prime of Xالان عندي
+
+97
+00:11:28,480 --> 00:11:32,140
+partial of y على partial of x وعندي partial of y
+
+98
+00:11:32,140 --> 00:11:36,640
+على partial of x بده ساوي القيمتين البعض يبقى لو
+
+99
+00:11:36,640 --> 00:11:41,180
+جينا ساوينا القيمتين البعض بده يكون عند مين؟ y في
+
+100
+00:11:41,180 --> 00:11:51,080
+e أس x y في cos 2x نقص 2 e أس x y في sin 2x زائد f
+
+101
+00:11:51,080 --> 00:11:57,340
+prime of x بده يساوي المقدار اللي عنده هناكY E أس
+
+102
+00:11:57,340 --> 00:12:13,520
+XY في Cos 2X ناقص 2 E أس XY في Sin 2X زائد 2X
+
+103
+00:12:13,520 --> 00:12:16,540
+تعالى
+
+104
+00:12:16,540 --> 00:12:21,200
+نشوفأظن ال term هذا هو ال term هذا بالضبط تماما
+
+105
+00:12:21,200 --> 00:12:26,000
+يبقى لو جيبناه عنده بروح هذا هو ال term هذا بالضبط
+
+106
+00:12:26,000 --> 00:12:33,840
+تماما بضلش عندي إلا ال f prime of x يسوى قداش 2x
+
+107
+00:12:33,840 --> 00:12:39,360
+يبقى هذا بده يعطينا أن ال f of x بدنا نكامل هذا يا
+
+108
+00:12:39,360 --> 00:12:49,680
+بناتيبقى تكامل 2X DX يساوي X تربية زائد كونستانت
+
+109
+00:12:49,680 --> 00:12:57,420
+C1 يبقى باجي بقوله the solution of
+
+110
+00:12:57,420 --> 00:13:04,920
+the differential equation 1 is
+
+111
+00:13:13,930 --> 00:13:25,530
+يبقى اليمين EOS XY في Cos 2X ناقص تلاتة Y
+
+112
+00:13:28,630 --> 00:13:40,150
+زاد C1 يبقى C1 يساوي C1 مرة واحدة ورايا دماغك يبقى
+
+113
+00:13:40,150 --> 00:13:42,670
+هذا هو حل المثل
+
+114
+00:13:45,350 --> 00:13:49,170
+يبقى هذا هو المثال الثاني على الـ exact equation
+
+115
+00:13:49,170 --> 00:13:54,190
+ممكن يجي السؤال بغير الصيغة الأولى وغير الصيغة
+
+116
+00:13:54,190 --> 00:13:59,530
+التانية وفي نفس الوقت على ال exact كيف كالتالي
+
+117
+00:13:59,530 --> 00:14:07,590
+خديلك السؤال example 3 بقول find the value of the
+
+118
+00:14:07,590 --> 00:14:20,640
+constant B find the valueof the constant B هتيه
+
+119
+00:14:20,640 --> 00:14:27,620
+لمقدار الثابت B such that
+
+120
+00:14:27,620 --> 00:14:39,480
+the differential equation اللي هي مين؟ X Y تربية
+
+121
+00:14:39,480 --> 00:14:55,060
+زائدب X تربيع Y كله في DX زائد X تكييب زائد Y في X
+
+122
+00:14:55,060 --> 00:15:01,360
+تربيع DY بده يسوي ال zero is exact
+
+123
+00:15:36,090 --> 00:15:42,790
+سؤال مرة تانية السؤال بيقول لي هاتلي قيمة الثابت B
+
+124
+00:15:42,790 --> 00:15:46,750
+بحيث أن ال differential equation اللي قدامنا هذه
+
+125
+00:15:46,750 --> 00:15:51,040
+is exactيبقى هو ميعطيني ان ال differential
+
+126
+00:15:51,040 --> 00:15:55,500
+equation exact صحيح ولا لأ اذا الشرط partial m by
+
+127
+00:15:55,500 --> 00:16:01,720
+partial y بده يساوي partial n by partial x مظبوط
+
+128
+00:16:01,720 --> 00:16:08,280
+يبقى باجي بقوله since بما ان the differential
+
+129
+00:16:08,280 --> 00:16:20,000
+equation is exact we haveاللي همين partial M by
+
+130
+00:16:20,000 --> 00:16:27,060
+partial Y يسوى partial N by partial X إذا انت عالى
+
+131
+00:16:27,060 --> 00:16:31,560
+نفضل الجزء الأول بالنسبة إلى Y والجزء التالى
+
+132
+00:16:31,560 --> 00:16:38,040
+بالنسبة إلى Xيبقى partial M by partial Y هو تفضل
+
+133
+00:16:38,040 --> 00:16:45,020
+الجزء الأول يبقى 2XY ال X مقدر ثابت وال Y تربية
+
+134
+00:16:45,020 --> 00:16:52,660
+مشتقتها 2Y هذا بالنسبة إلى Y بطير ال Y يبقى زائد ب
+
+135
+00:16:52,660 --> 00:16:57,930
+X تربيةيبدو يسوى partial in by partial x يبقى فضل
+
+136
+00:16:57,930 --> 00:17:04,290
+هذا من نسبة اله x يبقى اللي هو قداش تلاتة x تربية
+
+137
+00:17:04,290 --> 00:17:13,830
+زيدي اتنين y xطب اتطلعيل هنا هذا 2YX يساوي من 2YX
+
+138
+00:17:13,830 --> 00:17:19,090
+لو راحت عندها بتروح يبقى بس تنتج من هذا الكلام ان
+
+139
+00:17:19,090 --> 00:17:26,710
+ال B X تربيع بده يساوي تلاتة X تربيع ممكن نقسم كله
+
+140
+00:17:26,710 --> 00:17:33,560
+على X تربيع يبقى النتيجة كده؟ B تساوي تلاتةلو
+
+141
+00:17:33,560 --> 00:17:38,980
+شيلنا بي اللى عندنا هذه و بحطنا مكانها تلاتة و
+
+142
+00:17:38,980 --> 00:17:42,800
+روحنا بحثنا هل هذه ال function او هل هذه ال
+
+143
+00:17:42,800 --> 00:17:45,880
+equation exact ولا ماهياش exact من اللى جيها
+
+144
+00:17:45,880 --> 00:17:52,220
+automatic هي عبارة عن exact equation طيب عنوان تبع
+
+145
+00:17:52,220 --> 00:17:56,340
+هذا section اللى كنا رافعينه اتنين ستة كانexact
+
+146
+00:17:56,340 --> 00:18:01,240
+equations and integrating factors حتى الآن لم
+
+147
+00:18:01,240 --> 00:18:05,980
+نتكلم عن مين؟ عن ال integrating factors يبقى بدنا
+
+148
+00:18:05,980 --> 00:18:10,730
+نتكلم عن ال integrating factorsبنعطي تعريف لل
+
+149
+00:18:10,730 --> 00:18:16,270
+integrating factor وبعد هيك نحاول نوجد شكل ال
+
+150
+00:18:16,270 --> 00:18:22,150
+integrating factor لبعض لل equations وبعد هيك ناخد
+
+151
+00:18:22,150 --> 00:18:27,450
+أمثلة عليه يبقى بدنا نيجي للشطرة الثانية من هذا ال
+
+152
+00:18:27,450 --> 00:18:33,310
+section اللي هو integrating factors
+
+153
+00:18:35,520 --> 00:18:41,440
+عوامل التكامل بنعطي تعريف لعامل التكامل يبقى
+
+154
+00:18:41,440 --> 00:18:45,940
+definition بقول
+
+155
+00:18:45,940 --> 00:18:53,460
+if the differential equation if the differential
+
+156
+00:18:53,460 --> 00:19:07,850
+equation اللي هو M of X وYDX زائد N of XY DY تساوي
+
+157
+00:19:07,850 --> 00:19:15,050
+Zero وسميها لهذه المعادلة رقم واحد is not exact is
+
+158
+00:19:15,050 --> 00:19:24,430
+not exact but the differential equation but the
+
+159
+00:19:24,430 --> 00:19:33,250
+differentialequation ولكن المعادلة التفاضلية لميو
+
+160
+00:19:33,250 --> 00:19:46,510
+of x y في m of x y في dx زائد لميو of x y لميو of
+
+161
+00:19:46,510 --> 00:20:01,170
+x y في n of x y dy تساوي 0is exact is exact then
+
+162
+00:20:01,170 --> 00:20:13,750
+ومن ثم لميو of x y is called an integrating factor
+
+163
+00:20:13,750 --> 00:20:20,330
+an integrating factor
+
+164
+00:20:20,330 --> 00:20:27,940
+عامل تكامل forاستخدام البرنامج الوطني differential
+
+165
+00:20:27,940 --> 00:20:32,460
+equation
+
+166
+00:20:32,460 --> 00:20:33,920
+one
+
+167
+00:21:02,870 --> 00:21:09,750
+نعود للتعريف مرة ثانية التعريف بيقول ما يأتي if
+
+168
+00:21:09,750 --> 00:21:13,430
+the differential equation اللي هو ال mdx زايد ال n
+
+169
+00:21:13,430 --> 00:21:17,770
+dy بالساوية zero is not exact يعني روحنا حسبنا
+
+170
+00:21:17,770 --> 00:21:21,170
+تفاضة ال m بالنسبة ال y و تفاضة ال n بالنسبة ال x
+
+171
+00:21:21,170 --> 00:21:25,510
+لجينا هم are not equalبسوش بعض يبقى في هذه الحالة
+
+172
+00:21:25,510 --> 00:21:27,390
+تبقى ال differential equation اللي عندنا معاها
+
+173
+00:21:27,390 --> 00:21:32,830
+ماهياش exact يبقى في هذه الحالة بيقول هذا not
+
+174
+00:21:32,830 --> 00:21:35,470
+exact بقضى differential equation روحنا على
+
+175
+00:21:35,470 --> 00:21:39,890
+المعادلة هذه وضربناها في دالة أخرى الدالة الأخرى
+
+176
+00:21:39,890 --> 00:21:46,390
+اسمتها Mu of XY يبقى صوت Mu of XY في M و Mu of XY
+
+177
+00:21:46,390 --> 00:21:52,800
+في N هذي Dy هذي X كله بدل ساوي Zeroجيت أخد partial
+
+178
+00:21:52,800 --> 00:21:56,580
+ال term هذا كله by partial y و partial ال term هذا
+
+179
+00:21:56,580 --> 00:22:01,280
+كله by partial x لجيت اتنين are equal يبقى
+
+180
+00:22:01,280 --> 00:22:06,420
+المعادلة الجديدة هداش بالصير exact ان حدث ذلك يبقى
+
+181
+00:22:06,420 --> 00:22:11,360
+الدالة mu of x y بقول هي عامل تكامل للمعادلة
+
+182
+00:22:11,360 --> 00:22:17,400
+التفاضلية اللي هو رقم 1 السؤال هو من وين بدنا
+
+183
+00:22:17,400 --> 00:22:22,390
+نجيبه عامل التكامل؟طبعا له طرق للحسابات ممكن نعطيك
+
+184
+00:22:22,390 --> 00:22:27,210
+المثلة و نقولك بينيه لإن هذه الدالة عامل تكامل و
+
+185
+00:22:27,210 --> 00:22:32,970
+ممكن نطلب منك إيجاد عامل تكامل ثم حل المعادلة
+
+186
+00:22:32,970 --> 00:22:38,790
+التفاضلية لذلك حاطط عندك في التمرينبدل السؤال يمكن
+
+187
+00:22:38,790 --> 00:22:44,070
+تلاتة هناخد بعض الأسئلة هذه و نحلها و نبيّلك كيف
+
+188
+00:22:44,070 --> 00:22:50,050
+بنحسب عامل التكامل و من ثم بدنا نروح إياه نستخدمه
+
+189
+00:22:50,050 --> 00:22:54,550
+فعندك سؤال تلاتة و عشرين فهعطلك العنوان التالي
+
+190
+00:22:54,550 --> 00:22:58,970
+some integrating
+
+191
+00:22:58,970 --> 00:23:02,770
+factors
+
+192
+00:23:10,210 --> 00:23:18,370
+سؤال 23 من الكتاب بيقول show that
+
+193
+00:23:18,370 --> 00:23:27,830
+if partial m by partial x ناقص partial m by
+
+194
+00:23:27,830 --> 00:23:41,670
+partial y على m يساوي q of y whereحيث الـ Q و الـ
+
+195
+00:23:41,670 --> 00:23:54,910
+Q is a function of Y only فقط في Y فقط then the
+
+196
+00:23:54,910 --> 00:24:08,000
+differential equation M DX زائد N DY تساوي Zerohas
+
+197
+00:24:08,000 --> 00:24:12,420
+an
+
+198
+00:24:12,420 --> 00:24:18,240
+integrating factor
+
+199
+00:24:18,240 --> 00:24:24,840
+in
+
+200
+00:24:24,840 --> 00:24:30,620
+the
+
+201
+00:24:30,620 --> 00:24:42,190
+form في الشكل التالياللي هو الـ Mu of Y بديساوي E
+
+202
+00:24:42,190 --> 00:24:57,110
+أُس تكامل لـ Q of Y في Dy لـ Q of Y في Dy كويس
+
+203
+00:24:57,110 --> 00:25:03,440
+نرجع مرة تانيةهذا محطوط على شكل سؤال في الكتاب
+
+204
+00:25:03,440 --> 00:25:09,740
+وفيه كمان سؤال تاني بعده مباشرة هنعطيكيه بعد قليل
+
+205
+00:25:09,740 --> 00:25:10,380
+كذلك
+
+206
+00:25:16,450 --> 00:25:21,190
+صحيح و لذلك سمنها عامل اتكامل يعني هو بيقول هيك
+
+207
+00:25:21,190 --> 00:25:26,550
+يعني احنا عامل المعادلة الأصلية is not exact لكن
+
+208
+00:25:26,550 --> 00:25:30,410
+لو ضربناها في الميو هذه بيصير المعادلة exact
+
+209
+00:25:30,410 --> 00:25:34,950
+وبالتالي بنحلها زي ما كنا نحل المسائل قبل قليل
+
+210
+00:25:34,950 --> 00:25:38,910
+يعني انا اللي عند المعادلة not exact بدي أحولها
+
+211
+00:25:38,910 --> 00:25:45,210
+إلى exact ثم أقوم بحلها زي ما كنت بحل قبل قليلفي
+
+212
+00:25:45,210 --> 00:25:49,750
+نيجي جالي some integrating factors بعض عوامل
+
+213
+00:25:49,750 --> 00:25:56,110
+التكامل هذه المثلة فيها عامل لحالة واحدة فقط بيقول
+
+214
+00:25:56,110 --> 00:26:00,570
+يبينلي ان تفاضل N بالنسبة ل X نقص تفاضل N بالنسبة
+
+215
+00:26:00,570 --> 00:26:05,770
+ل Y على M لو كان يساوي Q of Y يعني ده اللي فيه،
+
+216
+00:26:05,770 --> 00:26:11,110
+بمعنى أخرإن الدالة الأصلية عندها دي ماكنتش exact
+
+217
+00:26:11,110 --> 00:26:15,010
+بدليل إن partial n على partial x و partial z
+
+218
+00:26:15,010 --> 00:26:19,170
+بيسووش بعض لإن لو سووا بعض لجيت الفرق منهم عاش
+
+219
+00:26:19,170 --> 00:26:23,510
+Zero تمام يبقى هدول بيسووش بعض يعني المعادلة not
+
+220
+00:26:23,510 --> 00:26:29,670
+exact إذا لو طرحت الأثنين من بعض و جسمت على M لجيت
+
+221
+00:26:29,670 --> 00:26:35,720
+الناتج function في Y فقطحتى لو كانت كونستانت
+
+222
+00:26:35,720 --> 00:26:40,660
+باعتبارها function في y يبقى where q is a function
+
+223
+00:26:40,660 --> 00:26:44,780
+of y only then the differential equation اللي
+
+224
+00:26:44,780 --> 00:26:48,220
+عندها هذا has an integrating factor in the form
+
+225
+00:26:48,560 --> 00:26:57,880
+يبقى الشكل عامل التكامل دلّة في Y فقط وشكل U of Y
+
+226
+00:26:57,880 --> 00:27:03,520
+يساوي A والتكامل Q of Y دي Y يعني تكامل كل النتيجة
+
+227
+00:27:03,520 --> 00:27:08,490
+اللي عندنا هذه النتيجة تبقى بس دلّة في Yيبقى بقى
+
+228
+00:27:08,490 --> 00:27:12,050
+كاملة بكون حصلت على مين على عمل التكامل بضرب
+
+229
+00:27:12,050 --> 00:27:16,510
+المعادلة الأصلية فيه بكون حصلنا على exact equation
+
+230
+00:27:16,510 --> 00:27:21,550
+بحلها كما كنت بحل من قبل طب بس من وين جبته هذا بدك
+
+231
+00:27:21,550 --> 00:27:26,910
+تثبته مش هيك صح ولا لا يبقى هنا بقى أجي بقوله ال
+
+232
+00:27:26,910 --> 00:27:29,030
+proof أو ال solution
+
+233
+00:27:32,620 --> 00:27:38,380
+بدي أثبت أن هذا التكامل عليه كـ exponential هو
+
+234
+00:27:38,380 --> 00:27:42,880
+عبارة عن ال integrating factor لمن؟ للدالة اللي
+
+235
+00:27:42,880 --> 00:27:46,180
+عندنا هذه او لل equation اللي يبقى بالدرجة أقوله
+
+236
+00:27:46,180 --> 00:27:58,940
+let mu of y be an integrating factor
+
+237
+00:28:02,280 --> 00:28:13,940
+of the differential equation اللي هو ال M DX زائد
+
+238
+00:28:13,940 --> 00:28:22,540
+ال N DY بده يساوي زير زي ما انت شايفه فرضه انه
+
+239
+00:28:22,540 --> 00:28:26,260
+دالة في Y شو شكله انا مش عارف يبقى يبدأ بحث اللي
+
+240
+00:28:26,260 --> 00:28:34,020
+انا عن شكل الدالة لـ Mu of Y يبقى thenبدي اضربها
+
+241
+00:28:34,020 --> 00:28:44,420
+في الميو يبقى الميو في ال M في DX زائد الميو في ال
+
+242
+00:28:44,420 --> 00:28:49,860
+N في DY بده سوى Zero is Exact
+
+243
+00:28:52,920 --> 00:28:57,760
+صحيح؟ طبقا للتعريف يبقى درابط في الـ Mu صارت
+
+244
+00:28:57,760 --> 00:29:02,760
+الدالة هذه exact إذا تفاضل هذه بالنسبة إلى Y بيسوي
+
+245
+00:29:02,760 --> 00:29:07,360
+تفاضل هذه بالنسبة إلى X يبقى هذا شو بدا تعطينا؟
+
+246
+00:29:07,360 --> 00:29:16,000
+بدا تعطينا إن partial by partial Y لـ Mu في M يسوى
+
+247
+00:29:16,000 --> 00:29:20,780
+partial by partial X لـ Mu في M
+
+248
+00:29:23,440 --> 00:29:30,640
+إذا نادق كل واحدة فيها مشتقة حاصل ضرب دالتين يبقى
+
+249
+00:29:30,640 --> 00:29:37,720
+الدالة الأولى في مشتقة الدالة الثانية زائد الدالة
+
+250
+00:29:37,720 --> 00:29:44,480
+الثانية في مشتقة الدالة الأولى هذا الطرف الشمال
+
+251
+00:29:44,480 --> 00:29:48,280
+الطرف اليمين يساوي لميو
+
+252
+00:30:11,980 --> 00:30:17,780
+سؤال هدفيكوا بتقدر تقولي قداش هذه القيمة عدديا يا
+
+253
+00:30:17,780 --> 00:30:18,340
+مانات؟
+
+254
+00:30:21,910 --> 00:30:27,850
+زيرو صحيح لإن ميو فانكشن في Y إذا مشتقتها بالنسبة
+
+255
+00:30:27,850 --> 00:30:35,930
+ل X هي تساوي زيرو إذا هذه تساوي زيرو because إن
+
+256
+00:30:35,930 --> 00:30:44,100
+الميو is a function of Y onlyتمام يبقى ال term
+
+257
+00:30:44,100 --> 00:30:48,700
+الأخير هذا ماله؟ الله ساهل عليه مع السلامة طيب
+
+258
+00:30:48,700 --> 00:30:55,580
+نيجي لل term هذا هذا مشتقة ميو جزئيا بالنسبة لمين؟
+
+259
+00:30:55,580 --> 00:31:00,530
+بالنسبة ال why صحيح ولا لأ؟لكن انا فارض ان الـ mu
+
+260
+00:31:00,530 --> 00:31:05,650
+function في y فقط يبقى هذا اشتقاق كله ولا اشتقاق
+
+261
+00:31:05,650 --> 00:31:13,210
+جزء يبقى اشتقاق كله اذا هذه بتصير كالتالي الـmu في
+
+262
+00:31:13,210 --> 00:31:21,890
+partial m by partial y زائد m في d mu على dy بده
+
+263
+00:31:21,890 --> 00:31:27,810
+يساوي الـmu في partial n على partial x
+
+264
+00:31:30,300 --> 00:31:34,400
+طب ايش رايك؟ بدي اخلي هذه في الشجة و بدي اجيب هذه
+
+265
+00:31:34,400 --> 00:31:38,240
+على الشجة التانية يبقى لو جبتها على الشجة التانية
+
+266
+00:31:38,240 --> 00:31:44,220
+بقدر اخد لميو منهم عامل مشترك يبقى لو جبتها بصير
+
+267
+00:31:44,220 --> 00:31:49,420
+على الشجة التانية هذه هالميو عامل مشترك بظل عندي
+
+268
+00:31:49,420 --> 00:31:56,140
+partial n by partial x ناقص partial m by partial y
+
+269
+00:31:56,760 --> 00:32:03,580
+جبت هذه عند هذه، ضالت هذه لحالها يبقى تساوي M في D
+
+270
+00:32:03,580 --> 00:32:06,140
+Mu على Dy
+
+271
+00:32:08,630 --> 00:32:14,690
+طب كويس ايش رايك؟ هذه بتصير على الشكل التالي بيدا
+
+272
+00:32:14,690 --> 00:32:22,990
+جسم على M ضرب م على M في م يبقاش بصير عندي هنا هذه
+
+273
+00:32:22,990 --> 00:32:30,050
+بتصير partial N by partial X ناقص partial M by
+
+274
+00:32:30,050 --> 00:32:39,060
+partial Y كله على Mبدو اسم في دي واي بالمرة يساوي
+
+275
+00:32:39,060 --> 00:32:51,620
+دي ميو على الميو مصبوط طيب هوصلنا لشوية طيب انكامل
+
+276
+00:32:51,620 --> 00:32:56,680
+الطرفين او قبل انكامل هذه اش احنا فرضينها في نص
+
+277
+00:32:56,680 --> 00:33:04,320
+المثلةمش هي عبارة عن ال EQ وين راحت؟ مش هذه هي ال
+
+278
+00:33:04,320 --> 00:33:08,960
+EQ صح ولا لأ؟ إذا بدي أشيلها و أكتب بدلها ال EQ
+
+279
+00:33:08,960 --> 00:33:22,440
+هذا معناته إن ال EQ of Y في DY بدي ساوي DMU على
+
+280
+00:33:22,440 --> 00:33:32,400
+الميو بدي أكمل الطرفينيبقى تكامل لـ Q of Y دي Y
+
+281
+00:33:32,400 --> 00:33:44,920
+بدرساوي لان absolute value للي ميو زائد كونستانسي
+
+282
+00:33:44,920 --> 00:33:50,380
+صح ممكن اخد كونستانسي اي قيمة للسهولة بقدر اخده ب
+
+283
+00:33:50,380 --> 00:34:03,270
+zero يبقى هنا تكc تساوي زيرو نحصلتكامل لـ q of y
+
+284
+00:34:03,270 --> 00:34:10,030
+dy يسوى لـ absolute value لـ mu أنا مابديش
+
+285
+00:34:10,030 --> 00:34:15,230
+absolute value لـ mu بدي الـ mu itself يبقى الـ mu
+
+286
+00:34:15,230 --> 00:34:22,930
+أو absolute value لـ mu بدي سوى E أُس تكامل لـ q
+
+287
+00:34:22,930 --> 00:34:29,660
+of y dyأمر ال X بونينش اللي باخد قيمة سالبة؟ لأ
+
+288
+00:34:29,660 --> 00:34:33,300
+يبقى ال absolute value لا معنى لها يبقى بدون
+
+289
+00:34:33,300 --> 00:34:40,780
+absolute value يبقى صارت لم U of Y يسوى E أس تكامل
+
+290
+00:34:40,780 --> 00:34:47,420
+EQ of Y DY أظن و هو المطلوب؟مش هي اللي بدنا نثبته؟
+
+291
+00:34:47,420 --> 00:34:51,620
+هي جيبناها قيمة الـ mu of y هي ال exponential a
+
+292
+00:34:51,620 --> 00:34:57,580
+مرفوعة للأس تكامل q of y dy حد فيكوا اللي هي تساول
+
+293
+00:34:57,580 --> 00:35:05,560
+هنا؟ هيا اتفضلي ليش حولنا ايش؟
+
+294
+00:35:05,560 --> 00:35:12,180
+هذه؟ هذه اللي قال الـ mu function في مين؟في why؟
+
+295
+00:35:12,180 --> 00:35:15,400
+إذا لما تبقى الدالة في متغير واحد اشتقاق جزء،
+
+296
+00:35:15,400 --> 00:35:20,480
+والله اشتقاق كل اشتقاق الجزء إذا كانت الدالة في
+
+297
+00:35:20,480 --> 00:35:24,300
+متغيرين أو أكثر، بس إذا متغير واحد يبقى اشتقاق كله
+
+298
+00:35:24,300 --> 00:35:29,300
+وليس اشتقاقا جزئيا، مش شاكرا بحياتي؟ هدأ ولا لا؟
+
+299
+00:35:29,300 --> 00:35:35,200
+اه مانسيتش يعني انامظبوط؟ واضحة؟ طيب كويس يبقى الـ
+
+300
+00:35:35,200 --> 00:35:40,240
+Mu of Y بيساوي ال exponential E of QY Dy في اي
+
+301
+00:35:40,240 --> 00:35:46,220
+تساوي تاني يا بناان؟ اسأل واتخافوش حتى لو كان
+
+302
+00:35:46,220 --> 00:35:50,500
+السؤال غلط، تسأل اليوم غلط، مكرا بتسأل ايه صح؟ حب
+
+303
+00:35:50,500 --> 00:35:55,770
+تسأل تاني؟ طيب انا اللي باسأل، لازم تكونش تسألأنا
+
+304
+00:35:55,770 --> 00:36:01,670
+هحط السؤال التاني وخليكوا تروحوا تثبتوا أنتوا بنفس
+
+305
+00:36:01,670 --> 00:36:12,390
+الطريقة اللي أثبتنا فيها السؤال هذا دكتور
+
+306
+00:36:12,390 --> 00:36:15,530
+هل بتعمل اجتماعات اجتماعات اللي هتستخدمها انهم
+
+307
+00:36:15,530 --> 00:36:22,830
+يعملوا بيانات نشاط؟ اه كدهلأ دي مرة واحد بيكتبش دي
+
+308
+00:36:22,830 --> 00:36:27,530
+جداش قيمته top or b في ال equation بس في ال
+
+309
+00:36:27,530 --> 00:36:31,690
+equation exact و بدك تتأكد انها exact ولا لأ هذا
+
+310
+00:36:31,690 --> 00:36:34,170
+هو لو ما طلعتش exact معناته ال integrating factor
+
+311
+00:36:34,170 --> 00:36:39,970
+تبعت غلط او اشتقاق غلط واحد من الاتنين تمام نجي
+
+312
+00:36:39,970 --> 00:36:44,050
+للسؤال الثاني او ال integrating factor التاني اللي
+
+313
+00:36:44,050 --> 00:36:48,550
+محطوط عندكوا على السؤال اللي بعد اعتقد 24يبقى
+
+314
+00:36:48,550 --> 00:36:55,030
+الانتجاريك فترة تانية بيقول if ال partial m by
+
+315
+00:36:55,030 --> 00:37:02,450
+partial y ناقص partial n by partial x على n بده
+
+316
+00:37:02,450 --> 00:37:13,390
+يساوي f of x where حيث ال f of x is a function
+
+317
+00:37:31,130 --> 00:37:38,010
+عامل التكامل of the differential equation of the
+
+318
+00:37:38,010 --> 00:37:48,470
+differential equation MDXزائد ال N Dy تساوي Zero
+
+319
+00:37:48,470 --> 00:38:01,030
+is لـ Mu of X بدي ساوي E أسطى كامل F of X DX وهذه
+
+320
+00:38:01,030 --> 00:38:09,530
+الكبانات بدك تروح تتبتيها و تشيك عليه كيف؟ بنفس ال
+
+321
+00:38:09,530 --> 00:38:14,260
+tactic اللي مشينا فيهبس بدل هذه partial mu by
+
+322
+00:38:14,260 --> 00:38:17,740
+partial y بيصير عندك partial mu by partial x هذه
+
+323
+00:38:17,740 --> 00:38:21,680
+بتتحول الاشتقاء الكامل وهذه بيصير في zero يامو
+
+324
+00:38:21,680 --> 00:38:26,800
+بيطلع معاك نتيجة دوري تمام؟ طيب هذا بالنسبة لمين
+
+325
+00:38:26,800 --> 00:38:30,720
+ال integrating factor التاني السؤال هو كيف بدنا
+
+326
+00:38:30,720 --> 00:38:35,000
+نميز مبادئ ال integrating factor هذا وال
+
+327
+00:38:35,000 --> 00:38:41,630
+integrating factor الثاني هذامظبوط احنا هنتلخبط
+
+328
+00:38:41,630 --> 00:38:46,430
+نجسم على M و لا نجسم على N هذا بيكون جسم على M و
+
+329
+00:38:46,430 --> 00:38:50,530
+لا نجسم على N الفارق بينهم ان هذا N و هذا N هذا
+
+330
+00:38:50,530 --> 00:38:53,830
+سالب و هذا موجب و هذا كموجب و هذا سالب نقلب الغضب
+
+331
+00:38:53,830 --> 00:39:00,290
+تمام بكل بساطة طلعيه هنا كويس تيجي لبعد السالب شو
+
+332
+00:39:00,290 --> 00:39:05,470
+اسمه partial M على partial Y ال M هذه بتصير في
+
+333
+00:39:05,470 --> 00:39:11,200
+المقاموالدلة بدأت تطلع function في main في y بلّع
+
+334
+00:39:11,200 --> 00:39:15,380
+هنا هي السلم partial in على partial x يبقى سمن على
+
+335
+00:39:15,380 --> 00:39:19,640
+main و الناتج function في المتغير اللي تحتها
+
+336
+00:39:19,640 --> 00:39:24,650
+وبالتالي بصير مش إمكانية للخطأ تمامايبقى بأطلع على
+
+337
+00:39:24,650 --> 00:39:28,750
+تبع الشرط اللي مكتوب بالسالق partial n يبقى بدي
+
+338
+00:39:28,750 --> 00:39:34,210
+أجسم على n والنتج بدي تطلع دالة في x partial m على
+
+339
+00:39:34,210 --> 00:39:40,250
+partial y بدي أجسم على m والنتج بدي تطلع دالة في y
+
+340
+00:39:40,250 --> 00:39:44,910
+طبعا الان بدنا ناخد أمثلة على ال integrating
+
+341
+00:39:44,910 --> 00:39:52,070
+factors أول مثل بيقول ما ياتي
+
+342
+00:39:58,250 --> 00:40:04,290
+example one find
+
+343
+00:40:04,290 --> 00:40:08,690
+the
+
+344
+00:40:08,690 --> 00:40:15,170
+integrating factor
+
+345
+00:40:15,170 --> 00:40:25,890
+بدنا نعمل التكامل and solve the following
+
+346
+00:40:30,930 --> 00:40:39,790
+differential equations نمر ا دي
+
+347
+00:40:39,790 --> 00:40:53,350
+اكس زائد X على Y ماقص sign ال Y كلها في دي Y بدأت
+
+348
+00:40:53,350 --> 00:41:05,350
+ساوي Zero وال Ygreater than zero سمي
+
+349
+00:41:05,350 --> 00:41:11,070
+المعادلة رقم واحد يبقى
+
+350
+00:41:11,070 --> 00:41:19,450
+بدالي لل solution هذا سؤال 27 من الكتابة هنا سؤال
+
+351
+00:41:19,450 --> 00:41:25,380
+مرة تانيةبقول هاتلي عاملة تكمن للمعادلة اللي عندنا
+
+352
+00:41:25,380 --> 00:41:30,880
+هذه، اتنين حل هذه المعادلة كذلك، بنقوله والله
+
+353
+00:41:30,880 --> 00:41:36,000
+كويس، الأول نتأكد هل هي exact، والله ماهياش exact،
+
+354
+00:41:36,000 --> 00:41:40,780
+مش هروح أدرب دوري ولا أحسب دوري، يبقى هذه عندنا M،
+
+355
+00:41:40,780 --> 00:41:46,160
+ابجداش يا بنات؟يبقى هذا بدي اعطيك partial M على
+
+356
+00:41:46,160 --> 00:41:51,800
+partial Y بدي ساوي قداش Zero بدنا partial N على
+
+357
+00:41:51,800 --> 00:41:59,960
+partial X مشتقة هذه بقداش1 على Y في غيرها ومشتقتها
+
+358
+00:41:59,960 --> 00:42:05,500
+دي مهيب Zero تمام يبقى هذا بدي اعطيلك انه partial
+
+359
+00:42:05,500 --> 00:42:12,140
+M على partial Y لا يساوي partial N على partial X
+
+360
+00:42:12,140 --> 00:42:20,420
+هذا بدي اعطيلك انه لا differential equation one is
+
+361
+00:42:20,420 --> 00:42:22,040
+not exact
+
+362
+00:42:25,340 --> 00:42:29,360
+بقى هذا بيعطيه ان المعادلة هذه ماهياش exact إذا
+
+363
+00:42:29,360 --> 00:42:34,440
+بدى أروح أدور على function ال function هذه تخليها
+
+364
+00:42:34,440 --> 00:42:40,340
+لي exact بقوله والله كويسكيف بنسويه؟ بنقول تعالى
+
+365
+00:42:40,340 --> 00:42:44,100
+نشوف ال integrating factors اللى عندنا انا عندي
+
+366
+00:42:44,100 --> 00:42:48,320
+partial M على partial Y يساوي Zero partial N على
+
+367
+00:42:48,320 --> 00:42:54,060
+partial X يساوي واحد على Y اذا كيف ماعمل الفرق
+
+368
+00:42:54,060 --> 00:42:59,060
+الفرق بينهم واحد على Y اما بالموجب او بالسالم صحيح
+
+369
+00:42:59,060 --> 00:43:02,940
+ولا لا؟لو جسمت على واحد بيطلع واحد على Y اللي هو
+
+370
+00:43:02,940 --> 00:43:08,780
+function في Y only يبقى أفضل شغل أروح أخده من
+
+371
+00:43:08,780 --> 00:43:17,870
+partial NPartial N على Partial X ناقص Partial M
+
+372
+00:43:17,870 --> 00:43:24,650
+على Partial Y على M وشوفوا كده إيش تساوي Partial N
+
+373
+00:43:24,650 --> 00:43:30,050
+على Partial X بواحد على Y Partial M على Partial Y
+
+374
+00:43:30,050 --> 00:43:36,050
+ب Zero نقسم على M اللي هو بواحد يسوى واحد على Y ل
+
+375
+00:43:36,050 --> 00:43:41,680
+function of Y onlyأمام
+
+376
+00:44:06,710 --> 00:44:11,730
+أذا حسبنا تفاضل N بالنسبة ل X نقص تفاضل N بالنسبة
+
+377
+00:44:11,730 --> 00:44:16,030
+ل Y على Y لجناح function في Y only يبقى عامل
+
+378
+00:44:16,030 --> 00:44:19,290
+التكامل هيكون function في Y
+
+379
+00:44:24,910 --> 00:44:30,970
+ايه استكامل ل Q of Y دي Y طبعا مين ل Q of Y هذه
+
+380
+00:44:30,970 --> 00:44:36,890
+كلها ل Q of Y هذه كلها اللي كنا مزلها في السؤال ل
+
+381
+00:44:36,890 --> 00:44:40,610
+Q of Y يبقى هذا بده ساوي
+
+382
+00:44:45,730 --> 00:44:53,490
+يبقى الجواب E أسلن absolute value ل Y لكن Y أكبر
+
+383
+00:44:53,490 --> 00:44:57,630
+من Zero يبقى لا داعي لمين للاbsolute ماعطيني Y
+
+384
+00:44:57,630 --> 00:45:02,730
+أكبر من Zero إذن النتيجة تسوى كده؟ Y يبقى ال
+
+385
+00:45:02,730 --> 00:45:07,960
+integrating factor هو Yبعد هيك بدنا نضرب المعادلة
+
+386
+00:45:07,960 --> 00:45:12,560
+واحد كلها في ال integrating factor اللي هو Y يبقى
+
+387
+00:45:12,560 --> 00:45:18,000
+باجي بقوله multiply equation
+
+388
+00:45:18,390 --> 00:45:29,290
+one by y we get نحصل على المعادلة بيصير y في dx
+
+389
+00:45:29,290 --> 00:45:38,930
+زائد تعالى نجي للتانى هنا نضرب في y بيصير x ناقص y
+
+390
+00:45:40,080 --> 00:45:47,340
+فى الـSin الـY كله دى Y بدى يساوي كده؟ بدى يساوي
+
+391
+00:45:47,340 --> 00:45:51,640
+Zero تعالى نبحث هل هى Exact ولا لا إذا ماطلعتش
+
+392
+00:45:51,640 --> 00:45:56,120
+Exact يبقى فينا شغل غلط فى الحسابات بدنا نروح
+
+393
+00:45:56,120 --> 00:46:03,160
+نراجع من الحسابات إذا بدى أخد تفاضل ال M بالنسبة
+
+394
+00:46:03,160 --> 00:46:10,850
+إلى Y كده يا بنات؟ هى هى كده؟بتاخد تفاضل ال N
+
+395
+00:46:10,850 --> 00:46:16,290
+بالنسبة إلى X يبقى تفاضل هذا يسمي ال X اللي بقدرش
+
+396
+00:46:16,290 --> 00:46:21,290
+واحد وهذه كلها ب Zero يبقى هذا بدي أخد تفاضل N
+
+397
+00:46:21,290 --> 00:46:27,310
+بالنسبة إلى Y يسوي تفاضل ال N بالنسبة إلى X سميلي
+
+398
+00:46:27,310 --> 00:46:32,230
+هذه المعادلة اتنين يا بنات يبقى هذا بدي أعطيلك ان
+
+399
+00:46:32,230 --> 00:46:42,430
+ذاDifferential equation 2 is exact المعادلة
+
+400
+00:46:42,430 --> 00:46:48,770
+2 هي نفس المعادلة 1 بس بعد ما ضربناها في Y يعني هي
+
+401
+00:46:48,770 --> 00:46:53,370
+نفس المعادلة يعني هذه تكافئ المعادلة أصلا و لا لو
+
+402
+00:46:53,370 --> 00:46:56,750
+قسمناها على Y فتطلع المعادلة اللي فوق يبقى هذه
+
+403
+00:46:56,750 --> 00:47:03,320
+تكافئ هذه تماماطيب مادام exact يبقى هذا بده يعطيك
+
+404
+00:47:03,320 --> 00:47:10,240
+there exists a function psi of x y يساوي constant
+
+405
+00:47:10,240 --> 00:47:18,890
+c such that بحيث أنPartial Epsilon by Partial X
+
+406
+00:47:18,890 --> 00:47:24,490
+يسوى ال term الأول من المعادلة الجديدة اللي هو Y و
+
+407
+00:47:24,490 --> 00:47:32,290
+Partial Epsilon by Partial Y يسوى X ناقص Y في Sine
+
+408
+00:47:32,290 --> 00:47:32,710
+Y
+
+409
+00:47:37,050 --> 00:47:41,570
+يبقى يابا كامل هذا بالنسبة ل X يابا كامل هذا
+
+410
+00:47:41,570 --> 00:47:46,910
+بالنسبة ل Y يبقى
+
+411
+00:47:46,910 --> 00:47:51,260
+هذا بالنسبة ل X أسهل لأنها تعتبر مقدار ثابتإذا لو
+
+412
+00:47:51,260 --> 00:47:56,780
+جيت كاملت هد يا بنات بصير إب ساي of X Y يساوي
+
+413
+00:47:56,780 --> 00:48:01,520
+مقدار ثابت مالكش دعوة أنا بكمل بالنسبة ل X يبقى
+
+414
+00:48:01,520 --> 00:48:07,450
+Quadro of X و بقول زائد function of manof Y لأن
+
+415
+00:48:07,450 --> 00:48:13,250
+التكمل كان بالنسبة لمين ال X طيب نشتق هذه يبقى
+
+416
+00:48:13,250 --> 00:48:20,950
+partial of Psi by partial Y يساوي هذا X وهنا زائد
+
+417
+00:48:20,950 --> 00:48:28,210
+F prime of Y من التنتين هذول مع بعض شو بستنتج
+
+418
+00:48:28,210 --> 00:48:38,590
+بستنتج ان X زائد F prime of Yيسوي x ناقص y في sign
+
+419
+00:48:38,590 --> 00:48:47,450
+ال y يبقى ال f prime of y ناقص y في sign ال y بدنا
+
+420
+00:48:47,450 --> 00:48:54,090
+نكمل ايوة يبقى يا بنات بدي اخد هنا derivatives و
+
+421
+00:48:54,090 --> 00:49:00,610
+بدي اخد هنا integral زي calculus b بدي احط هنا y و
+
+422
+00:49:00,610 --> 00:49:09,190
+هنا ناقص sign ال yمشتقة هدف كده؟ واحد مشتقة تكامل
+
+423
+00:49:09,190 --> 00:49:14,790
+ال sign ب سالب cosine مع السالب بصير cosine ال Y
+
+424
+00:49:14,790 --> 00:49:21,210
+مشتقة ال واحد ب zero تكامل ال cosine بال sign ال Y
+
+425
+00:49:21,210 --> 00:49:28,390
+هدف هدف موجب وهدف هدف سالب إذا بناء عليه أصبح ال F
+
+426
+00:49:28,390 --> 00:49:42,230
+of Y يساويy في cos y ناقص sin y زائد constant
+
+427
+00:49:42,230 --> 00:49:52,640
+وليكن c1 يبقى بالي بقول له the solution ofوإن الـ
+
+428
+00:49:52,640 --> 00:50:05,020
+differential equation one is إبسايد of XY يساوي
+
+429
+00:50:05,020 --> 00:50:18,100
+هيها Y في Xالـ F of Y يبقى زائد ها Y في Cos Y ناقص
+
+430
+00:50:18,100 --> 00:50:27,220
+Sin Y وهذا كله بيساوي من Constant Cيبقى هنا انا
+
+431
+00:50:27,220 --> 00:50:34,220
+انا انا انا انا انا
+
+432
+00:50:34,220 --> 00:50:34,320
+انا انا انا انا انا انا انا انا انا انا انا انا
+
+433
+00:50:34,320 --> 00:50:34,400
+انا انا انا انا انا انا انا انا انا انا انا انا
+
+434
+00:50:34,400 --> 00:50:38,400
+انا انا انا انا انا انا
+
+435
+00:50:38,400 --> 00:50:38,460
+انا انا انا انا انا انا انا انا انا انا انا انا
+
+436
+00:50:38,460 --> 00:50:44,220
+انا انا
+
+437
+00:51:11,060 --> 00:51:22,360
+يبقى نمره بيه بيقوللي x y نقص زائد y تربيع كله في
+
+438
+00:51:22,360 --> 00:51:36,100
+dx زائد x زائد 2y ناقص واحد في dy بده ساوي زيه
+
+439
+00:51:36,100 --> 00:51:45,730
+وسميها للمعنى الرقم واحدنحل هذه المعادلة ناخد
+
+440
+00:51:45,730 --> 00:51:53,430
+تفاضل ال N بالنسبة ل Y
+
+441
+00:51:53,430 --> 00:52:03,130
+ب X زائد 2Y ناخد تفاضل ال N بالنسبة ل X
+
+442
+00:52:10,130 --> 00:52:17,290
+واضح ان اتنين ليسوا بعض يبقى هذا بدي اعطيك تفاضل
+
+443
+00:52:17,290 --> 00:52:25,230
+ال M بالنسبة الى Y لا يسوى تفاضل ال N بالنسبة الى
+
+444
+00:52:25,230 --> 00:52:28,950
+X هذا بدي اعطيك ان ال
+
+445
+00:52:34,270 --> 00:52:40,670
+is not exact ماهياش exact يبقى الواحد يدور على
+
+446
+00:52:40,670 --> 00:52:45,670
+مين؟ على ال integrating factor بقوله والله كويس
+
+447
+00:52:45,670 --> 00:52:49,270
+تعالى ندور على ال integrating factor partially and
+
+448
+00:52:49,270 --> 00:52:53,990
+by partially واناقص partially يبقى هذا ناقص هذا اه
+
+449
+00:52:53,990 --> 00:53:00,170
+هو هذا ولا لا صح؟ والله كويس فرصة طيبة يبقى لو جيت
+
+450
+00:53:00,170 --> 00:53:07,940
+قلتهنا تفاضل ال M بالنسبة إلى Y ناقص تفاضل ال N
+
+451
+00:53:07,940 --> 00:53:12,820
+بالنسبة ل X بده يسموه عالمياً وبده النتج يطلع
+
+452
+00:53:12,820 --> 00:53:17,640
+function في X only يبقى partial M على partial Y
+
+453
+00:53:17,640 --> 00:53:22,860
+اللي هو X زائد 2Y تفاضل ال N بالنسبة ل X اللي هو
+
+454
+00:53:22,860 --> 00:53:30,240
+واحد على ان ال X زائد 2Y ناقص واحد كله بيساوي
+
+455
+00:53:30,240 --> 00:53:37,250
+كدهاش؟اكس زي اتنين
+
+456
+00:53:37,250 --> 00:53:41,170
+واحد نقلها كل هذا بيساوي كده اش واحد يا عمي الكونص
+
+457
+00:53:41,170 --> 00:53:46,550
+ده ماراه تعتبريه function في المتغير اللي عندك هذا
+
+458
+00:53:46,550 --> 00:53:54,800
+هنا يبقى هذا باعتبره function of x onlyيبقى صار ال
+
+459
+00:53:54,800 --> 00:54:02,220
+integrating factor ميو of X يبقى يستكامل
+
+460
+00:54:02,220 --> 00:54:08,340
+واحد في DX يبقى الجواب قداش U6 يبقى ال integrating
+
+461
+00:54:08,340 --> 00:54:13,620
+factor هو مين هو U6 إذا بدي أجي للمعادلة اللي عندي
+
+462
+00:54:13,620 --> 00:54:19,600
+هذه فوق و أضربها كلها في مين في U6 يبقى باجي بقوله
+
+463
+00:54:19,600 --> 00:54:20,600
+multiply
+
+464
+00:54:23,250 --> 00:54:34,970
+equation one by u6 we get بضربيني في u6 بصير x y
+
+465
+00:54:34,970 --> 00:54:48,770
+u6 زائد y تربيع في u6 في dx زائداكس EOS6 زائدي
+
+466
+00:54:48,770 --> 00:54:57,690
+اتنين Y EOS6 ناقص EOS6 كله في DY بده يساوي كده؟
+
+467
+00:54:57,690 --> 00:54:59,650
+بده يساوي Zero
+
+468
+00:55:24,950 --> 00:55:28,810
+طيب هذه المعادلة التفاظلية أصبحت على الشكل اللي
+
+469
+00:55:28,810 --> 00:55:32,030
+انا هذا يبقى هذه المعادلة اللي بدي أسميها المعادلة
+
+470
+00:55:32,030 --> 00:55:37,650
+رقم اتنينإذا بدى أبحث هل هذه exact والله ماهياش
+
+471
+00:55:37,650 --> 00:55:44,490
+exact إذا بدى أخد تفاضل ال M بالنسبة إلى Y يبقى
+
+472
+00:55:44,490 --> 00:55:49,270
+بدى أشتق هذه كلها بالنسبة إلى Y واضح له ال X E
+
+473
+00:55:49,270 --> 00:56:00,790
+وال6 X E وال6 خلصنا من A A زائة X E وال6 زائد 2
+
+474
+00:56:04,400 --> 00:56:11,740
+بعد ذلك ياخد تفاضل ال N بالنسبة إلى X يبقى هذا
+
+475
+00:56:11,740 --> 00:56:18,700
+حاصل ضرب دالتين يبقى الدالة الأولى في مشتقة ال X
+
+476
+00:56:18,700 --> 00:56:24,360
+بال X بال X يتصل زائد الدالة التانية E وال 6 في
+
+477
+00:56:24,360 --> 00:56:32,480
+مشتقة ال X يبقى دلاش بواحدإتنين Y في مشتقة ال EOSX
+
+478
+00:56:32,480 --> 00:56:38,580
+بال EOSX itself ناقص مشتقة ال EOSX بال EOSX
+
+479
+00:56:38,580 --> 00:56:43,980
+فالليلي هذه و هذه الله يسهل عليهم غير مأسوف عليهم
+
+480
+00:56:43,980 --> 00:56:50,960
+يبقى هذا الكلام جداش بده يساوي بده يساوي X في EOSX
+
+481
+00:56:50,960 --> 00:57:00,280
+زائد اتنين Y EOSXطلع هنا و هناك بتلاقي القمتين نفس
+
+482
+00:57:00,280 --> 00:57:06,380
+الشيء معناة ال termين هدول بيسووا بعض تفاضل ال M
+
+483
+00:57:06,380 --> 00:57:13,140
+بالنسبة إلى Y يسوى تفاضل ال N بالنسبة إلى X هذا
+
+484
+00:57:13,140 --> 00:57:19,200
+بدي يعطينا ان ال differential equation اتنين
+
+485
+00:57:19,200 --> 00:57:27,970
+سمناها اتنين as exactيبقى هذا بدي يعطينا ان هناك
+
+486
+00:57:27,970 --> 00:57:38,830
+مفهوم إبسائي of x y such that بحيث ان partial
+
+487
+00:57:38,830 --> 00:57:46,590
+إبسائيعلى partial x يساوي تفاضل إبصاي بالنسبة إلى
+
+488
+00:57:46,590 --> 00:57:58,630
+x اللي هو main x y u6 زائد y تربية ال u6 و partial
+
+489
+00:57:58,630 --> 00:58:02,570
+إبصاي by partial y ال term التاني
+
+490
+00:58:13,640 --> 00:58:20,780
+السؤال هو أيه ما أسهل أن نكمل الدالة الأولى
+
+491
+00:58:20,780 --> 00:58:26,580
+بالنسبة ل X و الله الدالة التانية بالنسبة ل Y؟تعني
+
+492
+00:58:26,580 --> 00:58:31,260
+بالنسبة ل Y أسهل كتير لأن الأولى حاصل ضرب دالتين
+
+493
+00:58:31,260 --> 00:58:34,860
+وبدنا نكملها هضطر للجدول وقص integration by parts
+
+494
+00:58:34,860 --> 00:58:41,780
+لكن هذه أبدا هذه دوري إذا لو جيت كملت هذه بالنسبة
+
+495
+00:58:41,780 --> 00:58:49,680
+إلى Y يبقى if Psi of X وY تساوي بدي أكملها بالنسبة
+
+496
+00:58:49,680 --> 00:58:58,800
+ل Y X في E وال 6 مقدار ثابت فبنضربه في Yزائد اتنين
+
+497
+00:58:58,800 --> 00:59:06,060
+y تكمل اكسبونين يبقى
+
+498
+00:59:06,060 --> 00:59:11,740
+Y تربية على اتنين تروح مع اتنين يبقى Y تربية في U6
+
+499
+00:59:11,740 --> 00:59:20,420
+ناقص U6 في Y زائد constant له function في مين؟بعد
+
+500
+00:59:20,420 --> 00:59:26,280
+ذلك نفضل هذه الدالة بالنسبة ل X و نسويها بالمين
+
+501
+00:59:26,280 --> 00:59:31,360
+بالدالة التانية يبقى بداجي اخد partial of psi by
+
+502
+00:59:31,360 --> 00:59:36,380
+partial X يساوي هذه مستقلة حصل ضر دالتين وال Y
+
+503
+00:59:36,380 --> 00:59:46,160
+مقدار ثابت يبقى EO6 في Y زائد الهمين X EO6 في Y
+
+504
+00:59:47,050 --> 00:59:52,090
+اللي بعدها بده اشتقها بالنسبة ل X يبقى Y تربية في
+
+505
+00:59:52,090 --> 01:00:01,090
+US X اللي بعدها ناقص US X في Y زائد F prime of X
+
+506
+01:00:01,730 --> 01:00:08,150
+يبقى EO6 في Y و سالب EO6 في Y مع السلامة يبقى آلة
+
+507
+01:00:08,150 --> 01:00:14,550
+المسألة إلى partial of Psi by partial X يسوى X EO6
+
+508
+01:00:14,550 --> 01:00:23,390
+في Y زائد Y تربية في EO6 زائد F prime of Xبنسوي ال
+
+509
+01:00:23,390 --> 01:00:27,590
+term اللى عندنا هذا بال term اللى عندنا هذا بنحصل
+
+510
+01:00:27,590 --> 01:00:34,790
+على إيش على إنه ال X في ال EOSX في ال Y زائد Y
+
+511
+01:00:34,790 --> 01:00:44,050
+تربية في ال EOSX زائد F prime of X يساوي XY EOSX
+
+512
+01:00:44,050 --> 01:00:55,400
+زائد Y تربية EOSXY تربية U6 مع Y تربية U6 XE و 6Y
+
+513
+01:00:55,400 --> 01:01:02,440
+في XE و 6Y مع السلامة يبقى قالة الى F prime of X
+
+514
+01:01:02,440 --> 01:01:09,960
+يسوى قداش Zero معناه هذا الكلام ان ال F of X بدى
+
+515
+01:01:09,960 --> 01:01:16,480
+يسوى constant C1 لذلك بروح بقوله the solution
+
+516
+01:01:18,550 --> 01:01:29,570
+of the differential equation one is epsilon of x,y
+
+517
+01:01:29,570 --> 01:01:37,160
+يساوي وده ال epsilon اللي حصلنا عليها هييبقى
+
+518
+01:01:37,160 --> 01:01:49,740
+اليمين X US X في ال Y زائد Y تربيع في US X ناقص US
+
+519
+01:01:49,740 --> 01:01:57,420
+XY وهذا المقدار ثابت يبقى هذا كله بيسوي مقدار ثابت
+
+520
+01:01:57,420 --> 01:01:59,540
+بالشكل اللي عندنا هذا
+
+521
+01:02:09,310 --> 01:02:15,070
+لخاطر اعطيكم كمان مثال اللي هو برضه سؤال من الكتاب
+
+522
+01:02:37,670 --> 01:02:50,590
+example 2 هذا
+
+523
+01:02:50,590 --> 01:02:57,430
+سؤال تلاتين من الكتاب بيقول solve the differential
+
+524
+01:02:57,430 --> 01:03:04,090
+equation اللي
+
+525
+01:03:04,090 --> 01:03:18,640
+هو أربعةx تكيب على y تربيع زائد تلاتة على y كل هذا
+
+526
+01:03:18,640 --> 01:03:32,520
+الكلام في dx في dx زائد تلاتة في x على y تربيع
+
+527
+01:03:32,520 --> 01:03:49,970
+زائدأربعة Y كل هذا الكلام في DY يساوي Zero يبقى
+
+528
+01:03:49,970 --> 01:03:55,210
+عندي مثل هذا السؤال تلاتين بالكتاب بيقولي بدنا نحل
+
+529
+01:03:55,210 --> 01:04:01,310
+المثلة هذه بقوله بسيطةيبقى زي ما تشاهدين فيها قصور
+
+530
+01:04:01,310 --> 01:04:05,190
+فيش في البصط وفي المقام يبقى انا لو خليته كله في
+
+531
+01:04:05,190 --> 01:04:10,930
+البصط بصير سلي في الحسابات وخاصة عند الاشتقاء يبقى
+
+532
+01:04:10,930 --> 01:04:15,270
+كل حاجة في المقام بيطلعها في البصط وبالتالي الأس
+
+533
+01:04:15,270 --> 01:04:21,750
+تبعها بيصير بإشارة مخالفة أو بإشارة سالف يبقى هنا
+
+534
+01:04:21,750 --> 01:04:28,660
+solutionالمعادلة هذه هكتبها على الشكل التالي اربعة
+
+535
+01:04:28,660 --> 01:04:39,760
+X تكييب Y اصناقس اتنين زائد تلاتة Y اصناقس واحد
+
+536
+01:04:39,760 --> 01:04:49,620
+هذا كله في من كله في DX زائدتلاتة اكس واي اثناء
+
+537
+01:04:49,620 --> 01:04:55,740
+اقصى اتنين زائد اربعة واي دي واي زائد اربعة واي دي
+
+538
+01:04:55,740 --> 01:04:58,680
+واي زائد اربعة واي دي واي زائد اربعة واي دي واي
+
+539
+01:05:15,960 --> 01:05:21,900
+طيب بنبحث هل المثل هذه exact ولا ماهياش exact يبقى
+
+540
+01:05:21,900 --> 01:05:24,580
+تفاضل ال M بالنسبة إلى Y
+
+541
+01:05:34,530 --> 01:05:40,270
+تفاضل M بالنسبة إلى Y أربعة X تكييب مقدار ثابت
+
+542
+01:05:40,270 --> 01:05:47,010
+تفاضل Y ناقص اتنين بناقص اتنين في أربعة بناقص
+
+543
+01:05:47,010 --> 01:05:56,350
+تمانية X تكييب Y ناقص تلاتةوهذه يا بنات ناقص تلاتة
+
+544
+01:05:56,350 --> 01:06:02,830
+Y أس ناقص اتنين هاي خلصنا تفاضلها بالنسبة إلى Y
+
+545
+01:06:02,830 --> 01:06:11,870
+بنانيجي تفاضل ال N بالنسبة إلى X تلاتة Y أس ناقص
+
+546
+01:06:11,870 --> 01:06:19,320
+اتنين وهذه بقدراش Zero الله سهل عليهاطيب طلع في
+
+547
+01:06:19,320 --> 01:06:24,460
+هدول المعادلات اللي عندنا بقول والله شكلهم بسووش
+
+548
+01:06:24,460 --> 01:06:30,220
+بعض صحيح يبقى هذا بدي اعطيك main انه تفاضل ال N
+
+549
+01:06:30,220 --> 01:06:36,120
+بالنسبة الى Y لا يسوى تفاضل ال N بالنسبة الى main
+
+550
+01:06:36,120 --> 01:06:42,380
+ال X يبقى هذا بدي اعطيك انه the differential
+
+551
+01:06:42,980 --> 01:06:55,080
+Equation one is not exact إذن بدنا ندور على ال
+
+552
+01:06:55,080 --> 01:07:01,290
+integrating factorأجرب أطرح جيل و أجسم على مين
+
+553
+01:07:30,250 --> 01:07:34,790
+يبقى انا اغمق عينيه واخدت عن جنه واشوف شو اللي بده
+
+554
+01:07:34,790 --> 01:07:41,630
+يصير you serve partial m by partial y هيها تمام زي
+
+555
+01:07:41,630 --> 01:07:50,010
+ما هي ناقص تمانية x تكيب y اص ناقص تلاتة ناقص
+
+556
+01:07:50,010 --> 01:07:53,150
+تلاتة y اص ناقص اتنين
+
+557
+01:07:58,580 --> 01:08:11,260
+نقص تلاتة Y أس ناقص اتنين يبقى
+
+558
+01:08:11,260 --> 01:08:15,580
+تلاتة X Y أس ناقص اتنين
+
+559
+01:08:21,920 --> 01:08:27,560
+كويس؟ باجي بقول لأ على n اه مظبوط و هذه ناقص لها
+
+560
+01:08:27,560 --> 01:08:33,280
+صحيح كويس يعني هذه ايش بيصير؟ بيصير يا بنات ناقص
+
+561
+01:08:33,280 --> 01:08:43,740
+تمانية x تكيبواي أس ناقص تلاتة ناقص ستة واي أس
+
+562
+01:08:43,740 --> 01:08:53,020
+ناقص اتنين على تلاتة X واي أس ناقص اتنين زائد أربع
+
+563
+01:08:53,020 --> 01:08:57,540
+Y طيب،
+
+564
+01:08:57,540 --> 01:09:01,310
+إيش رايك؟ في عمل مشترك في ال busخلّيني أطلّر
+
+565
+01:09:01,310 --> 01:09:10,010
+الناقص عام المشترك و 2 عام المشترك و Y أس ناقص 2
+
+566
+01:09:10,010 --> 01:09:20,210
+عام المشترك صحيح؟ بيضل كده؟ بيضل 4 X تكيب 4 X تكيب
+
+567
+01:09:20,210 --> 01:09:31,190
+Y أس ناقص 1 و هنا زائد 3 فقط لغير صحيح؟طيب نيجي
+
+568
+01:09:31,190 --> 01:09:39,030
+على المقام المقام ممكن اخد ايش Y بيصير Y اصلاق
+
+569
+01:09:39,030 --> 01:09:46,670
+اصلاق بدي اخد Y السالب واحد يبقى Y السالب واحد
+
+570
+01:09:46,670 --> 01:09:55,650
+عامل مشترك بضل ان انا قداش بضل تلاتة Xتلاتة اكس
+
+571
+01:09:55,650 --> 01:10:02,850
+واي والسالب واحد زائد
+
+572
+01:10:02,850 --> 01:10:07,070
+اربع
+
+573
+01:10:07,070 --> 01:10:14,430
+واي تربيع لو تضرب فيها تصير هذه في شغلة في بصة
+
+574
+01:10:14,430 --> 01:10:23,320
+المقام في شغلة مشتركةلأ يبقى هذه ما زبطتش معاك
+
+575
+01:10:23,320 --> 01:10:27,900
+يبقى أنا تصرفت بعقليتك انت في الامتحان و
+
+576
+01:10:27,900 --> 01:10:30,700
+الغالبيتنا يحكوا مش دقيق في النظر في الامتحان
+
+577
+01:10:30,700 --> 01:10:36,060
+مربوك يبقى هذه ما زبطتش صحيح ولا لا؟ ايوة بدي
+
+578
+01:10:36,060 --> 01:10:40,780
+اقلبها بدي اقلبها و اشوف ايش اللي بصير يبقى لو
+
+579
+01:10:40,780 --> 01:10:45,240
+قلبت هي ايش اللي بصير؟ بصير كالتالي يبقى هذه
+
+580
+01:10:45,240 --> 01:10:50,890
+ماجيبتش نتيجة يا بناتبدي اخد تفاضل ال M بالنسبة
+
+581
+01:10:50,890 --> 01:10:58,470
+الى X ناقص تفاضل ال M بالنسبة الى Y كله مقسوما على
+
+582
+01:10:58,470 --> 01:11:02,910
+Mأنا قدر أجيب عليك صح من الأول بس مابديش مابدي
+
+583
+01:11:02,910 --> 01:11:06,530
+أفكر بعدين كأن مشاربة ككتيرة اللي بقى سهلة مش سهلة
+
+584
+01:11:06,530 --> 01:11:10,650
+زي اللي قبل يبقى تفاضل ال N بالنسبة ل X اللي هي
+
+585
+01:11:10,650 --> 01:11:16,310
+تلاتة Y اص ناقص اتنين تفاضل ال N بالنسبة ل Y
+
+586
+01:11:16,310 --> 01:11:22,910
+الناقص بيصير كله زائد يبقى زائد تمانية X تكييب Y
+
+587
+01:11:22,910 --> 01:11:32,350
+اص ناقص اتنين زائد Y اص ناقص تلاتةY اص ناقص تلاتة
+
+588
+01:11:32,350 --> 01:11:40,450
+زائد تلاتة Y اص ناقص اتنين كل هذا الكلام على مين؟
+
+589
+01:11:40,450 --> 01:11:49,830
+على M ال M وين ال M؟ اللي هو اربع X تكيب وراه اربع
+
+590
+01:11:49,830 --> 01:11:56,970
+X تكيب Y اص ناقص اتنين زائد تلاتة Y اص ناقص واحد
+
+591
+01:11:58,700 --> 01:12:06,920
+طيب هذه تلاتة و تلاتة ستة يا بنات يبقى هاي
+
+592
+01:12:06,920 --> 01:12:14,220
+تمانية x تكيب y اص ناقص تلاتة زاد ستة y اص ناقص
+
+593
+01:12:14,220 --> 01:12:23,060
+اتنين على اربع x تكيب y اص ناقص اتنين زاد تلاتة y
+
+594
+01:12:23,060 --> 01:12:29,530
+اص ناقص واحد y الساوييبقى الاتنين عامل مشترك و Y
+
+595
+01:12:29,530 --> 01:12:34,750
+نقص اتنين نفس المعامل اللي كان هناك بيشارت سالب
+
+596
+01:12:34,750 --> 01:12:44,370
+تمام بضل قديش عندي اربع X تكييب و Y سالب واحدY أس
+
+597
+01:12:44,370 --> 01:12:53,670
+سالب واحد زائد تلاتة فقط لغير على المقام Y أس ناقص
+
+598
+01:12:53,670 --> 01:13:00,050
+واحد عام المشترك بضل أربع X تكييب Y أس ناقص واحد
+
+599
+01:13:10,880 --> 01:13:20,420
+يبقى النتيجة تساوي 2y-1 يبقى 2 على y يبقى function
+
+600
+01:13:20,420 --> 01:13:26,880
+of y
+
+601
+01:13:26,880 --> 01:13:27,520
+only
+
+602
+01:13:33,490 --> 01:13:42,510
+بصير عند الـ Mu of Y يبقى E أستكامل اتنين على Y Dy
+
+603
+01:13:43,490 --> 01:13:59,710
+يبقى E أس اتنين لن absolute value ل Y
+
+604
+01:13:59,710 --> 01:14:00,530
+تربيع
+
+605
+01:14:07,050 --> 01:14:12,530
+تمام تمام اذا صار عامل التكمل هو Y تربيع بالدرجة
+
+606
+01:14:12,530 --> 01:14:15,670
+على المعادلة الأصلية اللى عندنا هدى وضربها في مين
+
+607
+01:14:15,670 --> 01:14:23,190
+في Y تربيع يبقى multiply equation
+
+608
+01:14:23,190 --> 01:14:33,450
+one by Y تربيع we get نضرب في Y تربيع اش بيصير
+
+609
+01:14:33,450 --> 01:14:43,330
+عندنااربع اكس تكييب فقط زائد تلاتة Y اص ناقص واحد
+
+610
+01:14:43,330 --> 01:14:50,270
+كله في DX زائد تلاتة X ك
+
+611
+01:14:55,410 --> 01:15:01,830
+أربعة اكس تكيب في Y تربية بتروح تلاتة Y تربية في Y
+
+612
+01:15:01,830 --> 01:15:09,950
+بتبقى تلاتة Y بس تلاتة Y صحيح وهنا تلاتة X بتروح
+
+613
+01:15:09,950 --> 01:15:17,910
+ال Y وهنا زائد أربعة Y تكيب دي Y بدرسياوي Zero
+
+614
+01:15:17,910 --> 01:15:24,720
+طلعيلي هناهذا بدي اعطيكي partial M by partial Y
+
+615
+01:15:24,720 --> 01:15:30,020
+يساوي التفاضل هذا بالنسبة لـY البلجاني بقدرش تلاتة
+
+616
+01:15:30,020 --> 01:15:35,100
+و التفاضل هذا بالنسبة لـX بقدرش تلاتة كذلك يبقى
+
+617
+01:15:35,100 --> 01:15:41,480
+يساوي التفاضل الـN بالنسبة لـX هذا بدي اعطيكي the
+
+618
+01:15:41,480 --> 01:15:48,860
+differential equation is exact
+
+619
+01:15:52,270 --> 01:16:00,270
+هذا سوف يعطيك there exists a function psi of x و y
+
+620
+01:16:00,270 --> 01:16:04,090
+سواء يكون أصلاً c such that
+
+621
+01:16:06,850 --> 01:16:14,010
+بارشال إبصاي على بارشال X يساوي أربع X تكييب زائد
+
+622
+01:16:14,010 --> 01:16:20,890
+تلاتة Y و بارشال إبصاي على بارشال Y يساوي تلاتة X
+
+623
+01:16:20,890 --> 01:16:28,460
+زائد أربع Y تكييبأظن انكمل هذا بالنسبة ل X سهل
+
+624
+01:16:28,460 --> 01:16:33,320
+وانكمل هذا بالنسبة ل Y سهل يبقى اي واحدة بتصدر
+
+625
+01:16:33,320 --> 01:16:40,760
+يبقى لو جيت قولتلك بـPsi of X وY سوى يبقى كامل
+
+626
+01:16:40,760 --> 01:16:45,780
+بالنسبة لمن ال X يبقى باضيف لل أس واحد وبقسم على
+
+627
+01:16:45,780 --> 01:16:50,940
+الأس الجديد بتروح الأربعة مع الأربعة وهنا زائد
+
+628
+01:16:50,940 --> 01:16:59,550
+تلاتة Y Xزائد f of y يبقى هذا بيدي اعطيك partial
+
+629
+01:16:59,550 --> 01:17:05,710
+psi by partial y يساوي نفضل بالنسبة ل y يبقى هذه
+
+630
+01:17:05,710 --> 01:17:14,270
+مع السلامة و بظل بس تلاتة x زائد f prime of y
+
+631
+01:17:18,110 --> 01:17:25,610
+من هدول اتنين مع بعض بس تنتج انه f prime of y بده
+
+632
+01:17:25,610 --> 01:17:32,550
+يساوي كده اش اربع y تكيب يبقى هذا بده يعطيكي ان ال
+
+633
+01:17:32,550 --> 01:17:40,170
+f of y y اص اربع زائد constant c1 يبقى باجي بقوله
+
+634
+01:17:40,170 --> 01:17:45,290
+solution is
+
+635
+01:17:45,290 --> 01:17:56,390
+epsilonx of x of y يساوي x أُص أربعة x أُص أربعة
+
+636
+01:17:56,390 --> 01:18:05,670
+زائد تلاتة x y ال f of y اللي هي في قداش f y أُص
+
+637
+01:18:05,670 --> 01:18:11,670
+أربعة كل هذا الكلام يساوي constant c بالشكل اللي
+
+638
+01:18:11,670 --> 01:18:12,910
+عندنا هذا
+
+639
+01:18:16,830 --> 01:18:17,890
+هي اي تساؤل
+
+640
+01:18:44,090 --> 01:18:50,890
+طيب بدنا أسهل على التمرين يبقى exercises أكتبهم لك
+
+641
+01:18:50,890 --> 01:18:58,790
+هنا exercises اتنين ستة المسائل التالية من واحد
+
+642
+01:18:58,790 --> 01:19:09,850
+للاتناشر القدر ومن تلتاش لستاش تلتاش لستاش ومن
+
+643
+01:19:09,850 --> 01:19:11,970
+تمنتاش لتلتا وعشرين
+
+644
+01:19:15,430 --> 01:19:21,810
+طبعا سؤال 23 قرهناه الكتاب قبل شوية على اللوح
+
+645
+01:19:25,630 --> 01:19:29,630
+الان في انا تمارين عامة يا بنات على هذا الشبطر ككل
+
+646
+01:19:29,630 --> 01:19:35,710
+انتهى الشبطر لكن احنا ما انتهيناش في عندك تمارين
+
+647
+01:19:35,710 --> 01:19:40,670
+عامة على هذا الشبطر خلال هذه التمارين العامة
+
+648
+01:19:40,670 --> 01:19:45,160
+المجموعة الاولى مباشرة على كل ما درسناهلكن حطلي
+
+649
+01:19:45,160 --> 01:19:51,440
+كمان تلت شغلات جديدة تقولوا كلها الى linear او
+
+650
+01:19:51,440 --> 01:19:55,900
+exact او homogeneous او ما الى ذلك فى عندنا معادلة
+
+651
+01:19:55,900 --> 01:19:59,540
+اسمها معادلة tricate equation
+
+652
+01:20:02,170 --> 01:20:10,350
+هذا حطه في الكتاب يبقى exercises page صفحة اللي هو
+
+653
+01:20:10,350 --> 01:20:15,690
+مية و واحد و تلاتين لغاية مية و تلاتة و تلاتين
+
+654
+01:20:15,690 --> 01:20:21,290
+اللي هي التمارين العام على هذا الشبطر حط فيها سؤال
+
+655
+01:20:21,290 --> 01:20:31,150
+تلاتة و تلاتين اللي هو ركاتي ركاتي
+
+656
+01:20:32,000 --> 01:20:41,980
+Equation ايه شركة equation هنا it is an equation
+
+657
+01:20:41,980 --> 01:20:45,780
+in
+
+658
+01:20:45,780 --> 01:20:50,520
+the form الشكل
+
+659
+01:20:50,520 --> 01:21:02,090
+التاليDY على DT يساوي Q1 of T زائد Q2 of T في ال Y
+
+660
+01:21:02,090 --> 01:21:10,290
+زائد Q3 of T في من في ال Y تربيع وهذه سميها
+
+661
+01:21:10,290 --> 01:21:12,410
+للمعادلة رقم 1
+
+662
+01:21:47,480 --> 01:21:52,940
+طيب لو أنا أطلع في المعادلة هذه بقول لم يسبق لنا
+
+663
+01:21:52,940 --> 01:21:58,260
+أن رأينا في هذا الشبطر معادلة زي هيك دالة في T،
+
+664
+01:21:58,260 --> 01:22:02,260
+دالة في T في Y، دالة في T في من؟ في ال Y تربية،
+
+665
+01:22:02,260 --> 01:22:07,560
+لكن لو شيلت هذه قلت اه والله هذه مرة عالية، هذه
+
+666
+01:22:07,560 --> 01:22:13,480
+Bernoulli equation صح ولا لا؟لو شيلت هذه بقول اه
+
+667
+01:22:13,480 --> 01:22:17,160
+والله هذه ال linear equation لكن لا اخلها لبرنولا
+
+668
+01:22:17,160 --> 01:22:22,580
+على شجة ولا اخلها لمين linear على شجة اذا بدنا
+
+669
+01:22:22,580 --> 01:22:28,220
+نشوف كيف بدنا نحل المعادلة هذه من هذا القبيل فهو
+
+670
+01:22:28,220 --> 01:22:31,340
+بيعطيني دائما من المسائل من هذا القبيل بيعطيني حل
+
+671
+01:22:31,340 --> 01:22:36,940
+خاص و بطلب مني إيجاد ال general solution فبقول
+
+672
+01:22:36,940 --> 01:22:51,220
+الآن ما يأتيY1 هو عبارة
+
+673
+01:22:51,220 --> 01:22:58,740
+عن حل خاص particular solution of the differential
+
+674
+01:22:58,740 --> 01:23:07,300
+equation one then the general solution
+
+675
+01:23:10,400 --> 01:23:19,580
+general solution the general solution of the
+
+676
+01:23:19,580 --> 01:23:31,860
+differential equation one is y تسوى y one زائد
+
+677
+01:23:31,860 --> 01:23:37,640
+واحد على v of t where
+
+678
+01:23:39,860 --> 01:23:53,600
+حيث الـ V of T is a function that we
+
+679
+01:23:53,600 --> 01:24:01,100
+can find it as
+
+680
+01:24:01,100 --> 01:24:01,580
+follows
+
+681
+01:24:19,950 --> 01:24:24,690
+مرة تانية Recate equation هي معادلة على الشكل اللي
+
+682
+01:24:24,690 --> 01:24:30,870
+قدامنا هذا تمام الآن بدنا نبحث عن الحل العام لهذه
+
+683
+01:24:30,870 --> 01:24:36,030
+المعادلة مشان نوجد الحل العام لازم يعطيني حل خاص
+
+684
+01:24:36,030 --> 01:24:40,670
+لها ومن خلال الحل الخاص بقدر أروح أجيب الحل العام
+
+685
+01:24:40,670 --> 01:24:46,310
+لهذه المعادلة فبقول fy1 أيضا حل خاص للمعادلة اللي
+
+686
+01:24:46,310 --> 01:24:53,080
+عندنا هذهثم حل العاملة المعادلة رقم واحد هو Y
+
+687
+01:24:53,080 --> 01:25:00,120
+يساوي Y1 زائد واحد على V of Tمن هي ال V of T هي
+
+688
+01:25:00,120 --> 01:25:04,780
+عبارة عن ال .. بدنا نحاول نوجي ده كتل يعني أنا
+
+689
+01:25:04,780 --> 01:25:11,120
+لازم أروح أعرف ما هو شكل ال V of T بقوله كويس احنا
+
+690
+01:25:11,120 --> 01:25:23,500
+الآن since Y1 is a solution of equation 1 we have
+
+691
+01:25:24,830 --> 01:25:29,530
+مدام هذا الحل إذا هيحقق المعادلة صحيح ولا لا يبقاش
+
+692
+01:25:29,530 --> 01:25:41,170
+بيصير dy1 على dt بده يساوي q1 of t زيدي q2 of t في
+
+693
+01:25:41,170 --> 01:25:51,670
+ال y1 زيدي q3 of t في ال y1 تربيت
+
+694
+01:25:51,670 --> 01:26:04,950
+طيب كويس بنرجح احناالـ Y بيكون Y1 زائد 1 على V of
+
+695
+01:26:04,950 --> 01:26:11,470
+T هذا يعطينا حل عام لمين للمعادلة اللي قلنا عنها
+
+696
+01:26:11,470 --> 01:26:17,210
+إذا تعالى نشتق هذه ونشوف ايش بتعطينا يبقى لو جينا
+
+697
+01:26:17,210 --> 01:26:22,650
+اشتقناها باجي بقول يبقى DY على DT بيكون
+
+698
+01:26:25,330 --> 01:26:33,770
+على DT ناقص واحد على V تربيع في DV على DT تربيع
+
+699
+01:26:33,770 --> 01:26:40,170
+يعني واحد على V مش تقطع واحد على V تربيع في DV على
+
+700
+01:26:40,170 --> 01:26:44,970
+DT الان بدأ امسك المعلومات اللي عندي وارجع اعوض
+
+701
+01:26:44,970 --> 01:26:50,550
+وين في المعادلة رقم واحد يبقى باجي بقوله هنا ال
+
+702
+01:26:50,550 --> 01:27:02,000
+Sabes تتيوت انquestion one we get نحصل علامات بدي
+
+703
+01:27:02,000 --> 01:27:06,720
+اشيل dy على dt واحط قيمة هذه اللي هو الطرف الشمال
+
+704
+01:27:06,720 --> 01:27:17,520
+يبقى dy على dt شو بصير اللي هو dy one على dt ناقص
+
+705
+01:27:17,520 --> 01:27:25,350
+واحد على v تربيع في dv على dtبدي أسوأ الطرف اليمين
+
+706
+01:27:25,350 --> 01:27:35,870
+Q1 of T خليك زي ما انت زائد Q2 of T في مين في Y
+
+707
+01:27:35,870 --> 01:27:41,790
+بدي أشيل ال Y و أحط قيمتها هي اللي هو Y1 زائد 1
+
+708
+01:27:41,790 --> 01:27:50,800
+على Vيبقى هذه Y1 زائد واحد على V اختصارا بدل ما
+
+709
+01:27:50,800 --> 01:27:57,760
+اقول V of T افهم انها V of T يبقى شيلنا Y وحطينا
+
+710
+01:27:57,760 --> 01:28:00,940
+وابدالها Y1 زائد واحد على V
+
+711
+01:28:13,240 --> 01:28:20,710
+يبقى أصبحت المسألة على الشكل التاليطلع يا بناتي شو
+
+712
+01:28:20,710 --> 01:28:30,890
+بده يصير ده يصير عندي dy1 على dt ناقص واحد على v
+
+713
+01:28:30,890 --> 01:28:38,470
+تربيع ناقص واحد على v تربيع في ال dv على dt يساوي
+
+714
+01:28:38,470 --> 01:28:44,930
+ها بده افك الأقواس اللي عندنا هذه يبقى q1 of t
+
+715
+01:28:44,930 --> 01:28:57,080
+زائدQ2 of T في الـ Y1 Q2 of T في الـ Y1 زائد Q2 of
+
+716
+01:28:57,080 --> 01:29:07,100
+T في 1 على V أو رايحة خلاص Q2 of T على V مباشرة
+
+717
+01:29:07,100 --> 01:29:18,500
+لسهولة Q2 زائد Q3 of Tبدا فكها ده يا بنات بصير Y
+
+718
+01:29:18,500 --> 01:29:27,380
+واحد تربيع زائد Q three of T اتنين حاصل ضرب
+
+719
+01:29:27,380 --> 01:29:34,600
+الكيميتين يبقى هاي الاتنين في Y one على V في Y one
+
+720
+01:29:34,600 --> 01:29:37,440
+على V زائد
+
+721
+01:29:47,690 --> 01:30:00,860
+وهذا الكلام يساوي Q1 of T زائد Q2 of T في Y1زائد ل
+
+722
+01:30:00,860 --> 01:30:07,900
+Q3 of T في ال Y1 تربيع يبقى خلاص ال term هذا و ال
+
+723
+01:30:07,900 --> 01:30:12,900
+term هذا و ال term هذا هذا في واحد على V و هذا في
+
+724
+01:30:12,900 --> 01:30:19,800
+واحد على V إذا بقدر أخد واحد على V عامل مشترك بظل
+
+725
+01:30:19,800 --> 01:30:31,680
+ل Q2 of T زائد 2 ل Q3 of T في ال Y1خلصنا منهم زائد
+
+726
+01:30:31,680 --> 01:30:38,580
+Q3 of T على main على V تربية ايش رايكوا هذه يا
+
+727
+01:30:38,580 --> 01:30:50,100
+بنات؟ مش هي Dy1 على Dt صح؟ هي Dy1 وراها تاي Dy1
+
+728
+01:30:50,100 --> 01:30:57,990
+على Dt هذه اه صح؟ سكت الناس هو، مظبوط؟يبقى هذه هي
+
+729
+01:30:57,990 --> 01:31:03,690
+هذه يبقى لو جبتها عندها كلها هتروح مع هذه ايش بظل
+
+730
+01:31:03,690 --> 01:31:11,790
+عندى ناقص واحد على V تربيع في DV على DT بدي ساوي
+
+731
+01:31:11,790 --> 01:31:23,210
+واحد على V في Q2 of T زادى 2 Q3 of T في Y1 زائدEQ
+
+732
+01:31:23,210 --> 01:31:30,270
+ثلاثة of T على V تربيع طيب ايش رايك؟ بدى اضعه كله
+
+733
+01:31:30,270 --> 01:31:39,950
+في سالب V تربيع دي ماشي بضل عند هنا DV على DT بده
+
+734
+01:31:39,950 --> 01:31:49,310
+يساوي سالب EQ اتنين of T زائد اتنين EQ تلاتة of T
+
+735
+01:31:49,720 --> 01:31:59,900
+فى ال Y1 هذا كله فى ال V تمام هنا ضربنا فى سالب V
+
+736
+01:31:59,900 --> 01:32:07,180
+تربيع يبقى سالب Q ثلاثة of V طب بدى أجيب هذا على
+
+737
+01:32:07,180 --> 01:32:16,000
+الشجة التانية DV على DT زائد Q ثلاثة of T زائد
+
+738
+01:32:16,000 --> 01:32:22,930
+اتنينى Q ثلاثة of T فى ال Y1فى ال V يساوي الناقص Q
+
+739
+01:32:22,930 --> 01:32:32,170
+ثلاثة of T مرة علينا قبل هك دالة زي هك V prime
+
+740
+01:32:32,170 --> 01:32:39,230
+زائد P of T في Y بتساوي G of T اللي همين Linear
+
+741
+01:32:39,230 --> 01:32:42,570
+يبقى حولت مثلا America equation إلى Linear
+
+742
+01:32:42,570 --> 01:32:52,260
+equation بهذه الطريقة يبقى هنا Linearfirst order
+
+743
+01:32:52,260 --> 01:33:06,220
+differential equation that can be solved as before
+
+744
+01:33:06,220 --> 01:33:15,940
+يبقى بقدر أحلها زي قبلto get عشان نحصل على V of T
+
+745
+01:33:15,940 --> 01:33:21,480
+وبالتالي بتجبر خلصت ايه؟ خلصت مسألتنا طب نعطيكوا
+
+746
+01:33:21,480 --> 01:33:27,780
+مثال توضيحي فيانكوا سؤالين في الكتاب، فده يعطيكوا
+
+747
+01:33:27,780 --> 01:33:31,600
+أحدهما، والتاني بصير عليكوا حلو
+
+748
+01:33:42,630 --> 01:33:50,230
+السؤال بيقول ما يأتي example
+
+749
+01:33:50,230 --> 01:33:55,690
+if
+
+750
+01:33:55,690 --> 01:34:06,610
+y1 of t بدى يسوى واحد على T وT greater than zero
+
+751
+01:34:06,610 --> 01:34:11,170
+is a power
+
+752
+01:34:32,600 --> 01:34:42,610
+Y' تساوي سالب واحد على T ترابيعسالب واحد عالى T في
+
+753
+01:34:42,610 --> 01:34:54,670
+ال Y زائد Y تربيع سمها للمعادلة هذه find its
+
+754
+01:34:54,670 --> 01:34:59,670
+general solution
+
+755
+01:35:19,410 --> 01:35:23,690
+سؤال مرة تانية بيحطيني y واحد سواء واحد على t و ال
+
+756
+01:35:23,690 --> 01:35:27,730
+t greater than zero هي عبارة عن حل خاص للمعادلة
+
+757
+01:35:27,730 --> 01:35:31,810
+اللي عندنا هذه فجهة ال general solution بتطلع في
+
+758
+01:35:31,810 --> 01:35:36,190
+المعادلة هذه y prime سلب واحد على t يعني function
+
+759
+01:35:36,190 --> 01:35:40,530
+في t function في t في y function t اللي هو
+
+760
+01:35:40,530 --> 01:35:46,910
+constant في y تكيب يبقى هدري ك equation يبقى هنا
+
+761
+01:35:46,910 --> 01:35:57,780
+equationone is ricati equation اذا بقول له the
+
+762
+01:35:57,780 --> 01:36:10,620
+general solution is y يسوى y one زائد واحد على v
+
+763
+01:36:10,620 --> 01:36:18,100
+of t و لسه ال v of t بدنا نعرف ما هو شكلهامشان هيك
+
+764
+01:36:18,100 --> 01:36:22,680
+باجي أقول هو يعطيني واحد على T عبارة عن حل إذا
+
+765
+01:36:22,680 --> 01:36:27,040
+الواحد على T يحقق مين؟ يحقق المعادل اللي عندنا
+
+766
+01:36:27,040 --> 01:36:38,620
+since بما أن هو واحد واحد على T is a solution of
+
+767
+01:36:38,620 --> 01:36:46,120
+the differential equation when we have
+
+768
+01:36:49,940 --> 01:36:57,460
+يبقى مشتقته مقداش يا بنات دي
+
+769
+01:36:57,460 --> 01:37:03,400
+مقداش؟ مستخدم سالب واحد على T تربية صحيح ولا لا؟
+
+770
+01:37:03,400 --> 01:37:08,960
+لكن احنا مدام هيك شوراك نشتق هذه وقلصنا صح؟ مش
+
+771
+01:37:08,960 --> 01:37:23,770
+هحسن ليه؟ ويه هذا؟ اللي هو ال D Yعلى دي تي ناقص
+
+772
+01:37:23,770 --> 01:37:32,370
+واحد على V تربية في ال DV على دي تي هذا بدي يعطيكي
+
+773
+01:37:32,370 --> 01:37:40,860
+ما يأتيبنجي للـ dy1 على dt بدي الـ dy1 او هذه بدها
+
+774
+01:37:40,860 --> 01:37:45,240
+تساوي نشتاق الطرف اليمين كله دي dy على dt صارت
+
+775
+01:37:45,240 --> 01:37:51,560
+بالشكل ان هذا تمام يبقى بدي امسك هذه dy1 جداش
+
+776
+01:37:51,560 --> 01:37:59,460
+مشتاقتها سالب واحد على T تربية سالب واحد على V
+
+777
+01:37:59,460 --> 01:38:02,940
+تربية في الـDV على DT
+
+778
+01:38:06,170 --> 01:38:15,550
+سالب واحد على T تربيع سالب واحد على T في Y جداش ال
+
+779
+01:38:15,550 --> 01:38:21,990
+Y بY1 زاد واحد على V يبقى Y1 اللي هيبقى جداش يا
+
+780
+01:38:21,990 --> 01:38:22,510
+بنات
+
+781
+01:38:38,400 --> 01:38:44,090
+طيب اظن لو اجت هادي عند هادي مع السلامةبصير أن
+
+782
+01:38:44,090 --> 01:38:52,090
+سالب واحد على V تربيع في DV على DT بيساوي سالب
+
+783
+01:38:52,090 --> 01:39:00,330
+واحد على T ويونب واحد على T زائد واحد على V زائد
+
+784
+01:39:00,330 --> 01:39:09,240
+واحد على T زائد واحد على V الكل تربيعنفك التربية
+
+785
+01:39:09,240 --> 01:39:14,820
+لأنها دي يا بنات بصير سالب واحد على V تربية في ال
+
+786
+01:39:14,820 --> 01:39:22,760
+DV على DT بسالب واحد على T تربيةيبقى سالب واحد على
+
+787
+01:39:22,760 --> 01:39:32,480
+T تربية سالب واحد على T في V زائد واحد على T تربية
+
+788
+01:39:32,480 --> 01:39:42,760
+زائد اتنين على T في V زائد واحد على V تربية طلعيلي
+
+789
+01:39:42,760 --> 01:39:48,560
+هنا واحد على T تربية وسالب واحد على T تربية مع
+
+790
+01:39:48,560 --> 01:39:49,500
+السلامة
+
+791
+01:40:01,860 --> 01:40:09,820
+يبقى اش بصير عامة هنا بصير سالب واحد على V تربية
+
+792
+01:40:09,820 --> 01:40:19,820
+سالب واحد على V تربية في ال DV على DT بالدرساويدى
+
+793
+01:40:19,820 --> 01:40:25,240
+V على دى T بدّى سامع راح اتهدي مع هادي اطلعيه
+
+794
+01:40:25,240 --> 01:40:34,080
+لهادي واطلعيه لهادي ها بيضل واحد على TVيبقى زائد
+
+795
+01:40:34,080 --> 01:40:42,980
+واحد على T في V هنا زائد واحد على V تربية اضربيني
+
+796
+01:40:42,980 --> 01:40:51,860
+الطريقين كله في سلب V تربية بظل عندي DV على DT لما
+
+797
+01:40:51,860 --> 01:40:58,300
+نضرب في سلب V تربية بظل سالب واحد على T في ال V
+
+798
+01:40:58,300 --> 01:41:04,950
+زائد جداش يا بنات زائد واحديبقى هذا كله يسوى هكذا
+
+799
+01:41:04,950 --> 01:41:12,870
+DV على DT يسوى، تمام؟ يعني اذا صارت هذه DV على DT
+
+800
+01:41:12,870 --> 01:41:21,630
+زائد واحد على T في الـV ستسوى كم؟ سالب واحد، أه،
+
+801
+01:41:21,630 --> 01:41:28,070
+هذه سالب واحد، مظبوط، هذه سالب واحد، ستسوى سالب
+
+802
+01:41:28,070 --> 01:41:34,340
+واحد، ايش رأيك في المعادلة هذه؟لينير صح ولا لأ
+
+803
+01:41:34,340 --> 01:41:46,400
+يبقى هذه linear first order differential equation
+
+804
+01:41:46,400 --> 01:41:55,570
+بدنا نحلها يبقى بدنا ل mu of TE أُس تكامل واحد على
+
+805
+01:41:55,570 --> 01:42:03,990
+T DT ب E LN T اذا انجلي T أكبر من Zero يبقى E أس
+
+806
+01:42:03,990 --> 01:42:10,650
+LN T يبقى يساوي قداش T يبقى بدنا نضرب المعادلة هذه
+
+807
+01:42:10,650 --> 01:42:21,310
+كلها في T بصير T في DV على DT زائد V يساوي سالب T
+
+808
+01:42:23,040 --> 01:42:29,460
+يبقى بناء عليه هذا عبارة عن T في V كل prime بسالب
+
+809
+01:42:29,460 --> 01:42:36,660
+T انكمل الطرفين يبقى T في V يسوى سالب T تربيه على
+
+810
+01:42:36,660 --> 01:42:44,680
+اتنين زائد constant Cنقسم كله على T يبقى V of T
+
+811
+01:42:44,680 --> 01:42:51,120
+اللي احنا جاعدين بندور عليها بده يساوي سالب T على
+
+812
+01:42:51,120 --> 01:43:01,460
+2 سالب T على 2 زائد C على T او ان شيتنا فاقلناكله
+
+813
+01:43:01,460 --> 01:43:09,020
+على اتنين T بتنين C كله
+
+814
+01:43:09,020 --> 01:43:12,040
+اتنين T على اتنين بتنين T على اتنين T على اتنين T
+
+815
+01:43:12,040 --> 01:43:12,200
+على اتنين T على اتنين T على اتنين T على اتنين T
+
+816
+01:43:12,200 --> 01:43:16,340
+على اتنين T على اتنين T على اتنين T على اتنين T
+
+817
+01:43:16,340 --> 01:43:17,840
+على اتنين T على اتنين T على اتنين T على اتنين T
+
+818
+01:43:17,840 --> 01:43:18,460
+على اتنين T على اتنين T على اتنين T على اتنين T
+
+819
+01:43:18,460 --> 01:43:18,460
+على اتنين T على اتنين T على اتنين T على اتنين T
+
+820
+01:43:18,460 --> 01:43:18,860
+على اتنين T على اتنين T على اتنين T على اتنين T
+
+821
+01:43:18,860 --> 01:43:19,140
+على اتنين T على اتنين T على اتنين T على اتنين T
+
+822
+01:43:19,140 --> 01:43:25,720
+على اتنين T على اتنين T على اتنهذا يعني V of T
+
+823
+01:43:25,720 --> 01:43:31,520
+وليس V of T بدي ال general solution يبقى ذا
+
+824
+01:43:31,520 --> 01:43:35,700
+general solution
+
+825
+01:43:35,700 --> 01:43:48,140
+Y يسوى Y one زائد واحد على V of T يبقى Y يسوى Y
+
+826
+01:43:48,140 --> 01:43:58,250
+one الوطنية واحد على Tزائد واحد على V of T تنين C
+
+827
+01:43:58,250 --> 01:44:07,650
+ناقص T تربيع على اتنين T او تقدر تقول Y تساوي واحد
+
+828
+01:44:07,650 --> 01:44:17,590
+على T زائد اتنين T على اتنين C ناقص T تربيع هذا ال
+
+829
+01:44:17,590 --> 01:44:20,990
+general solution تبع المعادلة
+
+830
+01:44:23,910 --> 01:44:29,450
+طيب لازلنا في نفس التمرين العامة و لسه عندنا
+
+831
+01:44:29,450 --> 01:44:34,090
+موضوعين في نفس التمرين العامة حاجة نسميها T
+
+832
+01:44:34,090 --> 01:44:38,850
+missing او Y missing بيكون في المعادلة يا اما
+
+833
+01:44:38,850 --> 01:44:43,490
+بشوفش T بالمرة يا اما بشوفش Y المرة القادمة ان شاء
+
+834
+01:44:43,490 --> 01:44:49,750
+الله بنشوف كيف ننحل هذا النوع من المسائل
+
diff --git a/PL9fwy3NUQKwa8ZDfSFGn6H8xVFLzqmCZC/euAOHAsWFbk.srt b/PL9fwy3NUQKwa8ZDfSFGn6H8xVFLzqmCZC/euAOHAsWFbk.srt
new file mode 100644
index 0000000000000000000000000000000000000000..bffa355b43e400d238b918235795ecea0c4b5ddb
--- /dev/null
+++ b/PL9fwy3NUQKwa8ZDfSFGn6H8xVFLzqmCZC/euAOHAsWFbk.srt
@@ -0,0 +1,3299 @@
+1
+00:00:10,560 --> 00:00:14,900
+بسم الله الرحمن الرحيم، آخر حاجة كنا نتكلم فيها 
+
+2
+00:00:14,900 --> 00:00:18,760
+المرة اللي فاتت هي الـ homogeneous equations يعني
+
+3
+00:00:18,760 --> 00:00:24,500
+المعادلات المتجانسة، وقلنا كل معادلة تفاضلية من 
+
+4
+00:00:24,500 --> 00:00:30,120
+الرتبة الأولى بنقدر نكتبها بدلالة Y على X أو X على 
+
+5
+00:00:30,120 --> 00:00:35,160
+Y نسميها homogenous differential equation،  وأخدنا 
+
+6
+00:00:35,160 --> 00:00:41,540
+على ذلك مثال واحدة، وإلى يكون المثال الأخير يبقى 
+
+7
+00:00:41,540 --> 00:00:49,720
+نمرة B هو سؤال ستة وتلاتين من الكتاب بيقول X تربيع
+
+8
+00:00:49,720 --> 00:01:01,060
+زائد تلاتة XY زائد Y تربيع كله في DX ناقص X تربيع 
+
+9
+00:01:01,060 --> 00:01:07,850
+في DY بده يساوي كده؟ بده يساوي زيرو، وبنحل المعادلة
+
+10
+00:01:07,850 --> 00:01:11,930
+اللي عندنا، هذه المعادلة لسه بدأ ببحث هل هي
+
+11
+00:01:11,930 --> 00:01:15,230
+homogeneous ولا non homogeneous differential
+
+12
+00:01:15,230 --> 00:01:20,670
+equation، بقوله بسيطة هذه المعادلة لو جينا كتبناها 
+
+13
+00:01:20,670 --> 00:01:29,030
+بطريقة أخرى على الشكل التالي، يبقى لو روحت كتبتها x
+
+14
+00:01:29,030 --> 00:01:34,590
+تربيع dy، نجلنا هذه وين؟ على الشجة التانية بدها 
+
+15
+00:01:34,590 --> 00:01:41,730
+تساوي اللي هو x تربيع زائد تلاتة x y زائد تلاتة x 
+
+16
+00:01:41,730 --> 00:01:50,950
+y زائد y تربيع dx، بدي أروح أقسم الطرفين على x تربيع
+
+17
+00:01:50,950 --> 00:01:58,710
+على dx، يبقى المعادلة دي بيصير dy by dx يساوي x
+
+18
+00:01:58,710 --> 00:02:05,950
+square زائد تلاتة xy زائد y square كله على x
+
+19
+00:02:05,950 --> 00:02:11,780
+square، هذا يجب أن يساوي، يجب أن أوزع الـ dx على 
+
+20
+00:02:11,780 --> 00:02:16,660
+المقام يبقى x تربيع على x تربيع يبقى كم؟ بواحد
+
+21
+00:02:16,660 --> 00:02:23,180
+زائد تلاتة x على x تربيع يبقى x في المقام و y في 
+
+22
+00:02:23,180 --> 00:02:31,300
+الـ dx يبقى y على x، شكل أن هذا y تربيع على x تربيع
+
+23
+00:02:31,300 --> 00:02:37,660
+هي عبارة عن y على x لكل تربيع، يبقى زي ما أنتو
+
+24
+00:02:37,660 --> 00:02:41,720
+شايفين يا بنات، المعادلة صارت dy على dx constant
+
+25
+00:02:41,720 --> 00:02:46,500
+constant ثاني في y على x، y على x الكل تربيع، هذا
+
+26
+00:02:46,500 --> 00:02:51,280
+يعني أنه قدرنا نكتب المعادلة الأصلية اللي عندنا 
+
+27
+00:02:51,280 --> 00:02:56,700
+بدلالة الدالة اللي هو المتغير فيها يعتبر y على x
+
+28
+00:02:56,700 --> 00:03:00,580
+يبقى دي شو اسمها؟ homogenous differential equation
+
+29
+00:03:00,580 --> 00:03:08,120
+يبقى دي سميها اللي هي المعادلة رقم واحد، يبقى so the
+
+30
+00:03:08,120 --> 00:03:15,440
+differential equation one is homogeneous
+
+31
+00:03:17,670 --> 00:03:21,410
+ما دام homogeneous، يبقى الآن بدي أمشي بطريقة الحل
+
+32
+00:03:21,410 --> 00:03:26,350
+تبع المثال الأخير في المحاضرة الماضية، فبجي بقول
+
+33
+00:03:26,350 --> 00:03:33,210
+put V تساوي Y على X، هذا بدي يعطينا أن Y بدي يساوي 
+
+34
+00:03:33,210 --> 00:03:41,370
+XV، لو جينا اشتقينا هيبقى DY على DX بدي يساوي V زائد 
+
+35
+00:03:41,370 --> 00:03:47,380
+X في DV على DX، الآن بدي أجي إلى المعادلة اللي هندى
+
+36
+00:03:47,380 --> 00:03:52,260
+بدي أشيل dy على dx وأحط قيمتها بدلالة الـ variable 
+
+37
+00:03:52,260 --> 00:03:58,220
+الجديد اللي هو v، يبقى المعادلة هدي وتصبح على الشكل
+
+38
+00:03:58,220 --> 00:04:06,400
+التالي، V زائد X في dv على dx يساوي الطرف اليمين
+
+39
+00:04:06,400 --> 00:04:14,800
+واحد زائد تلاتة v زائد v تربيع، بدي أكتب المعادلة
+
+40
+00:04:14,800 --> 00:04:21,100
+هذه على الشكل التالي، X في D V على DX يساوي الـ V
+
+41
+00:04:21,100 --> 00:04:27,160
+هيبقى نفسي، بضيف سالب V للطرفين، يبقى هذه مع السلامة
+
+42
+00:04:27,160 --> 00:04:35,680
+وهذه بظل واحد زائد اتنين V زائد V تربيع، أو ممكن 
+
+43
+00:04:35,680 --> 00:04:42,220
+أكتب على الشكل التالي، الـ X في DV على DX يساوي V
+
+44
+00:04:42,220 --> 00:04:54,740
+زائد واحد لكل تربيع، طيب بنحاول نفصل المتغيرات يبقى
+
+45
+00:04:54,740 --> 00:05:01,180
+بناء عليه هاد بيصير DV على V زائد واحد لكل تربيع
+
+46
+00:05:01,180 --> 00:05:08,560
+يساوي DX على X، يبقى هاد صارت separable equation
+
+47
+00:05:08,560 --> 00:05:14,120
+يبقى فصل ده منهم المتغيرات، يبقى هاد separable
+
+48
+00:05:14,120 --> 00:05:16,080
+equation
+
+49
+00:05:17,240 --> 00:05:24,240
+مش هنحل المعادلة هذي، بروح بكامل الطرفين، يبقى تكامل
+
+50
+00:05:24,240 --> 00:05:27,800
+الطرف الشمال، حد فيك بتعرف تقولي شو تكامل هذا 
+
+51
+00:05:27,800 --> 00:05:35,680
+المقدار هذا، V 
+
+52
+00:05:35,680 --> 00:05:41,040
+زائد واحد لكل تربيع، مش V تربيع زائد واحد، V زي
+
+53
+00:05:41,040 --> 00:05:42,780
+تكامل واحد على X تربيع
+
+54
+00:05:46,990 --> 00:05:51,130
+قداش تكامل وحدة الـ X تربيع؟
+
+55
+00:05:53,610 --> 00:05:56,850
+بس واحدة واحدة تحكي، احنا سئلنا اللغة اللي .. شو
+
+56
+00:05:56,850 --> 00:06:03,070
+اسمك أنتِ؟ براء، براءت من الله ورسوله إلى الذين 
+
+57
+00:06:03,070 --> 00:06:08,190
+عهدتم من المشركين، عارفة صورتاش هذي؟ التوبة، التوبة
+
+58
+00:06:08,190 --> 00:06:11,190
+يبقى مشان إن تتوب عليك من الكلمتين اللي قلتيهم في
+
+59
+00:06:11,190 --> 00:06:15,820
+الأول، بالنجداش تكامل واحد عليك تربيع؟ سائل بواحد
+
+60
+00:06:15,820 --> 00:06:20,060
+على X، ممتاز جدا، هذه كمان اللي بينجو سين من الدرجة
+
+61
+00:06:20,060 --> 00:06:24,400
+الأولى، ومعامل V هو الواحد الصحيح، يبقى تكامله سالب
+
+62
+00:06:24,400 --> 00:06:30,380
+واحد على V زائد واحد، يبقى بالتكامل بصير هذه سالب 
+
+63
+00:06:30,380 --> 00:06:35,700
+واحد على V زائد واحدة، تكامل الطرف الشمال، الطرف
+
+64
+00:06:35,700 --> 00:06:41,280
+اليمين، Ln absolute value لـ X زائد constant C
+
+65
+00:06:41,280 --> 00:06:49,040
+وليكن على سبيل المثال C1، طيب ممكن نضرب الطرفين في 
+
+66
+00:06:49,040 --> 00:06:53,680
+إشارة سالب، يبقى لو ضربنا في إشارة سالب بصير واحد 
+
+67
+00:06:53,680 --> 00:07:01,200
+على V زائد واحد يساوي Ln absolute value لـ X بإشارة
+
+68
+00:07:01,200 --> 00:07:11,080
+سالب، سالب C1، الآن ممكن سالب C1 أحطها بمين؟ بـ C مرة 
+
+69
+00:07:11,080 --> 00:07:16,780
+واحدة، يبقى هذا الكلام بدي أعطيك إنه واحد على شو
+
+70
+00:07:16,780 --> 00:07:23,320
+رأيك V، هذه مش هي عبارة عن Y على X زائد واحد يساوي 
+
+71
+00:07:23,320 --> 00:07:31,020
+سالب Ln absolute value لـ X زائد C، والـ C يساوي سالب
+
+72
+00:07:31,020 --> 00:07:37,780
+C1، طيب هذه يا بنات ممكن أوحد المقامات لـ X وجمع
+
+73
+00:07:37,780 --> 00:07:45,540
+بيصير X على Y زائد X زائد Ln absolute value لـ X
+
+74
+00:07:45,540 --> 00:07:50,900
+بدل سواء قداش Constancy، يبقى هذا الـ solution تبع
+
+75
+00:07:50,900 --> 00:07:56,570
+المعادلة اللي عندنا، عليك بنتهي هذا الـ section، أنا
+
+76
+00:07:56,570 --> 00:08:02,890
+بروحي ناخد المسائل التالتة، يبقى exercises اتنين
+
+77
+00:08:02,890 --> 00:08:12,070
+اتنين، المسائل من واحد إلى ثمانية الـ odd ومن تسعة 
+
+78
+00:08:12,070 --> 00:08:19,230
+إلى عشرين برضه الـ odd بس بدنا ناخد part
+
+79
+00:08:24,480 --> 00:08:31,860
+ثلاثة مطاليب بيكفين، A وC، وبعدها من واحد وثلاثين 
+
+80
+00:08:31,860 --> 00:08:37,300
+لغاية ثمانية وثلاثين كذلك الـ odd
+
+81
+00:09:11,810 --> 00:09:16,470
+بنجي لـ section اتنين ثلاثة، وبنقول الله سهل عليك ما
+
+82
+00:09:16,470 --> 00:09:21,790
+انتش لازم منه، وبنروح على section اتنين أربعة، وزيه
+
+83
+00:09:21,790 --> 00:09:26,630
+لكن بدنا نروح على أسئلة section اتنين أربعة هتطلع
+
+84
+00:09:26,630 --> 00:09:33,630
+موضوعين داخل الـ exercises، كويسة؟ بقى هدول اتنين
+
+85
+00:09:33,630 --> 00:09:38,550
+مهمين فبدنا نروح حتى واحد مهم والتاني يعنيفبدنا 
+
+86
+00:09:38,550 --> 00:09:45,450
+نروح ناخد النقطتين هدول، فباجي بيقوله in the
+
+87
+00:09:45,450 --> 00:09:48,530
+exercises 
+
+88
+00:09:48,530 --> 00:09:57,770
+of section اتنين أربعة، there is two subjects
+
+89
+00:10:05,690 --> 00:10:11,430
+يبقى فيها موضوعين، الموضوع الأول الـ very important 
+
+90
+00:10:11,430 --> 00:10:19,930
+الـ Bernoulli equation، معادلة بيرنولي، والموضوع 
+
+91
+00:10:19,930 --> 00:10:26,170
+الثاني الـ discontinuous
+
+92
+00:10:26,170 --> 00:10:29,110
+coefficients
+
+93
+00:10:35,560 --> 00:10:41,200
+بنبدأ بالموضوع الأول، بيرنالي 
+
+94
+00:10:41,200 --> 00:10:44,700
+equation
+
+95
+00:11:06,700 --> 00:11:10,960
+سيكشن اتنين أربعة كاتب الفرق بين الـ linear والـ 
+
+96
+00:11:10,960 --> 00:11:15,340
+non-linear differential equations، احنا المرة اللي
+
+97
+00:11:15,340 --> 00:11:18,860
+فاتت قولنا لكم ما هو شكل الـ linear first order
+
+98
+00:11:18,860 --> 00:11:22,540
+differential equation، قولنا لكم y prime زي الـ P of
+
+99
+00:11:22,540 --> 00:11:28,500
+T في Y بده يساوي G of T، أي معادلة على غير هذا الشكل
+
+100
+00:11:28,500 --> 00:11:32,860
+تعتبر إيه؟ non-linear differential equation، وبشرط
+
+101
+00:11:32,860 --> 00:11:34,240
+أن الـ P of T 
+
+102
+00:11:47,070 --> 00:11:53,050
+المعامل P of T وG of T ممكن ما يكونوش دوال متصلة
+
+103
+00:11:53,080 --> 00:11:56,780
+طبعا هنقيم مثال على الـ Discontinuous coefficients
+
+104
+00:11:56,780 --> 00:12:02,380
+وكيف هنحل هذا النوع من المسائل، وبردولي هي non
+
+105
+00:12:02,380 --> 00:12:07,260
+homogeneous differential equation، بس بنحولها إلى 
+
+106
+00:12:07,260 --> 00:12:11,620
+من إلى homogeneous أو إلى linear differential
+
+107
+00:12:11,620 --> 00:12:15,200
+equation، يعني الـ non linear differential equation
+
+108
+00:12:15,200 --> 00:12:20,110
+بنحولها إلى linear differential equation، بدنا نعرف 
+
+109
+00:12:20,110 --> 00:12:25,210
+ما هو الشكل العام لها، وبعد هيك كيف بدنا نحل هذا
+
+110
+00:12:25,210 --> 00:12:32,050
+النوع من المسائل، فبجي بقول له ده differential
+
+111
+00:12:32,050 --> 00:12:40,170
+equation لـ Y prime زائد P of T في الـ Y
+
+112
+00:12:57,010 --> 00:13:03,790
+يبقى هذه معادلة ماهياش معادلة خطية، لكن في بعض
+
+113
+00:13:03,790 --> 00:13:09,010
+الحالات الخاصة ممكن تكون هذه المعادلة معادلة خطية،
+
+114
+00:13:09,010 --> 00:13:14,950
+شو الحالات الخاصة؟ فبجي بقوله لو كانت الـ n تساوي 
+
+115
+00:13:14,950 --> 00:13:28,650
+zero، يبقى then the above equation as Y' زائد P of T
+
+116
+00:13:28,650 --> 00:13:35,290
+في الـ Y بيساوي G of T في Y أس 0، Y أس 0 في قداش؟
+
+117
+00:13:35,290 --> 00:13:39,770
+بواحد، يبقى صلة المواد على شكل .. مين هي هذه؟ هذه
+
+118
+00:13:39,770 --> 00:13:43,270
+الـ linear اللي كنا بنحل فيها المرة اللي فاتت، يبقى 
+
+119
+00:13:43,270 --> 00:13:52,890
+هذه linear، الآن لو كانت كذلك الـ N تساوي واحد، يبقى
+
+120
+00:13:52,890 --> 00:13:58,790
+the above equation is Y prime زائد P of T في الـ Y
+
+121
+00:13:58,790 --> 00:14:07,220
+بدي يساوي G of T في Y أس واحد، يبقى بـ Y، ممكن أعيد
+
+122
+00:14:07,220 --> 00:14:13,860
+كتابة المعادلة هذه على الشكل التالي، y prime زائد
+
+123
+00:14:13,860 --> 00:14:17,880
+بصير
+
+124
+00:14:17,880 --> 00:14:27,200
+P of T ناقص G of T كله في الـ Y، يبقى
+
+125
+00:14:27,200 --> 00:14:31,560
+صارت Y prime زائد function في Y، يبقى صارت G of T 
+
+126
+00:14:33,160 --> 00:14:39,160
+يبقى هذه كذلك linear differential equation، يبقى 
+
+127
+00:14:39,160 --> 00:14:43,760
+هذا ما عندناش علاقة فيها، إذا مشان تبقى المعادلة على
+
+128
+00:14:43,760 --> 00:14:50,740
+هذا الشكل ممنوع تكون لا بزيرو ولا بواحد، تمام؟ وهي 
+
+129
+00:14:50,740 --> 00:14:56,020
+هذه اللي بدنا نبدأ نشتغلها ونحلها، فبعدين بقوله
+
+130
+00:15:00,640 --> 00:15:03,560
+إن N لا تساوي واحد
+
+131
+00:15:08,300 --> 00:15:19,700
+السؤال هو Y' زائد P of T في Y بده يساوي G of T في Y
+
+132
+00:15:19,700 --> 00:15:27,700
+to the derivative N، ومسميه للمعادلة Head Star is a 
+
+133
+00:15:27,700 --> 00:15:32,720
+nonlinear
+
+134
+00:15:32,720 --> 00:15:34,980
+differential equation
+
+135
+00:15:53,240 --> 00:16:00,160
+ممكن نحولها to a linear 
+
+136
+00:16:08,790 --> 00:16:16,190
+order differential equation، ممكن نحولها إلى معادلة
+
+137
+00:16:16,190 --> 00:16:26,230
+خطية من الرتبة الأولى as follow، كتالي، شوفوا
+
+138
+00:16:26,230 --> 00:16:27,450
+كيف هنحولها يا بنات؟
+
+139
+00:16:31,350 --> 00:16:36,510
+بدي أعمل خطوتين بس، بكون حولتها الى linear، الخطوة 
+
+140
+00:16:36,510 --> 00:16:42,370
+الأولى الآن بدي بتطلع على Y هذه المضربة في مين؟ في
+
+141
+00:16:42,370 --> 00:16:49,130
+G of T، بضرب المعادلة هذه في Y مرفوع لنفس الأس هذا بس
+
+142
+00:16:49,130 --> 00:16:58,790
+بإشارة سالب، يبقى الخطوة الأولى بقوله multiply both
+
+143
+00:16:58,790 --> 00:17:00,710
+sides
+
+144
+00:17:02,720 --> 00:17:14,680
+of equation star by y to the minus n we get، يصير
+
+145
+00:17:14,680 --> 00:17:21,140
+المعادلة على الشكل التالي، y to the minus n في y
+
+146
+00:17:21,140 --> 00:17:32,200
+prime، P of T في الـ Y to the power واحد ناقص N يساوي 
+
+147
+00:17:32,200 --> 00:17:42,080
+الـ G of T مرة
+
+148
+00:17:42,080 --> 00:17:42,480
+ثانية
+
+149
+00:17:51,920 --> 00:17:57,020
+الخطوة الأولى هي أن أضرب المعادلة star في main في
+
+150
+00:17:57,020 --> 00:18:01,960
+y to the minus n، يعني بدي أضربها في نفس الـ term
+
+151
+00:18:01,960 --> 00:18:07,820
+لأن هذا بس بإشارة سالب الاسترة، يبقى بيصير عندك y to 
+
+152
+00:18:07,820 --> 00:18:13,640
+the minus n في الـ y prime، هيها الآن هذي Y أس واحد
+
+153
+00:18:13,640 --> 00:18:20,100
+بيجيها y to the minus n بيصير y to the واحد minus
+
+154
+00:18:20,100 --> 00:18:24,200
+الـ n، والـ P of T كما هي، الطرف اليمين بيصير Y أس 
+
+155
+00:18:24,200 --> 00:18:30,360
+zero، بواحد اللي ما فضلش عندي إلا G of T، انتهينا من 
+
+156
+00:18:30,360 --> 00:18:35,420
+الخطوة الأولى، بدنا نجي للخطوة الثانية، هذا بناهات 
+
+157
+00:18:35,420 --> 00:18:40,380
+الـ term اللي عندنا هذا بناخده ع شجة وبنروح وبـ
+
+158
+00:18:40,380 --> 00:18:47,460
+نحطه بمتغير جديد، يبقى باجي بقول الـ pot حطنا V
+
+159
+00:18:47,460 --> 00:18:54,720
+تساوي Y to the one minus M، وبعد هيك اشتق، يبقى لو
+
+160
+00:18:54,720 --> 00:19:02,260
+اشتقينا بصير عندي V' يساوي الأس في Y مرفوعة لنفس
+
+161
+00:19:02,260 --> 00:19:09,080
+الأس مطروح من واحد في مشتقة الـ Y itself، اليمين Y' 
+
+162
+00:19:10,350 --> 00:19:16,050
+مش ذاكرين لما كنا نقول مشتقة جوس مرفوع لأس، الأس في 
+
+163
+00:19:16,050 --> 00:19:19,630
+الجوس مرفوعة لنفس الأس مطروح من واحد فيه مشتقة
+
+164
+00:19:19,630 --> 00:19:24,630
+مداخل جوس، احنا ما اشتقناش بالنسبة لـ Y، نشتق بالنسبة لـ X
+
+165
+00:19:24,630 --> 00:19:28,310
+لو كنا بنشتق بالنسبة لـ Y اللي قلنا على طول خط واحد
+
+166
+00:19:28,310 --> 00:19:33,810
+ناقص Y و Y أس ناقص N وسكتنا، لكن كنا بنشتق بالنسبة
+
+167
+00:19:33,810 --> 00:19:39,250
+لـ X، بقول الأس واحد ناقص N في y مرفوعة لنفس الأس
+
+168
+00:19:39,250 --> 00:19:43,950
+مطروح من هو، يبقى Y أس ناقص N في مشتقة الـ y itself 
+
+169
+00:19:43,950 --> 00:19:50,310
+اللي هي Y prime، تمام؟ طيب بطلع هنا الـ term
+
+170
+00:19:50,310 --> 00:19:55,780
+اللي أنها ده هيه، بس فيش في واحد ناقص N، واحد ناقص N
+
+171
+00:19:55,780 --> 00:20:01,700
+هذا رقم مظبوط، يبقى بنقدر نقسم عليه، يبقى بيصير واحد 
+
+172
+00:20:01,700 --> 00:20:08,560
+على واحد ناقص N في الـ V' يساوي Y أس ناقص N في الـ 
+
+173
+00:20:08,560 --> 00:20:14,730
+Y'، إذا بنجي ناخد المعلومة هذه اللي
+
+216
+00:24:22,940 --> 00:24:27,200
+خلّيها على الشجرة إذا هذه ههه هي برنامج بس مش
+
+217
+00:24:27,200 --> 00:24:32,220
+مرتبة بدنا نروح نعيد ترتيبها إذا لو روحنا نعيدها 
+
+218
+00:24:32,220 --> 00:24:36,940
+ترتيبها بنقدر نكتبها على الشكل التالي فبجي بقوله
+
+219
+00:24:36,940 --> 00:24:37,200
+لا
+
+220
+00:24:41,910 --> 00:24:52,930
+T تربيع DY على DT ناقص T في Y بده يساوي Y تربيع
+
+221
+00:24:55,350 --> 00:25:00,950
+ناقص Y تربيع موافقين يبقى ناقص Y تربيع كويس صحيين
+
+222
+00:25:00,950 --> 00:25:06,510
+تمام طيب بعد هيك بدنا نروح نقسم على T تربيع أو نضرب 
+
+223
+00:25:06,510 --> 00:25:11,030
+الطرفين في واحد على T تربيع وهذا ممكن لأن T
+
+224
+00:25:11,030 --> 00:25:14,730
+greater than zero لا يمكن أن تساوي ال zero يبقى
+
+225
+00:25:14,730 --> 00:25:21,130
+بيصير المعادلة على الشكل التالي Dy على Dt ناقص واحد
+
+226
+00:25:21,130 --> 00:25:29,130
+على T في ال Y يساوي ناقص واحد على T تربيع في ال Y
+
+227
+00:25:29,130 --> 00:25:34,070
+تربيع واضح أن المعادلة على الشكل اللي عندنا تمام
+
+228
+00:25:34,070 --> 00:25:39,470
+يبقى هذه Bernoulli equation يبقى هذه اللي هي من
+
+229
+00:25:39,470 --> 00:25:47,410
+Bernoulli equation يبقى هذه معادلة Bernoulli طبعا
+
+230
+00:25:47,410 --> 00:25:55,950
+زي ما تشوفين non linear هذه non linear يبقى إيش
+
+231
+00:25:55,950 --> 00:26:00,790
+بدنا نعمل لها بدنا نروح نحولها إلى linear first order
+
+232
+00:26:00,790 --> 00:26:05,050
+differential equation يبقى بنضرب الطرفين في مين في
+
+233
+00:26:05,050 --> 00:26:11,810
+Y أس ناقص اثنين هذه Y هذه بس بأس مخالف للأس تبعها
+
+234
+00:26:11,810 --> 00:26:15,030
+يبقى بجي بقوله هنا multiply
+
+235
+00:26:23,290 --> 00:26:28,930
+بتصير المعادلة على الشكل التالي y-2
+
+236
+00:26:36,950 --> 00:26:42,410
+هنا Y تجيني Y أصل ناقص اثنين بيصير Y أصل ناقص واحد
+
+237
+00:26:42,410 --> 00:26:51,030
+يبقى في Y أصل ناقص واحد يساوي ناقص واحد على T تربيع
+
+238
+00:26:51,750 --> 00:26:56,430
+بعد ذلك بنروح بنعمل التعويض اللي قلنا عليها فوق هي
+
+239
+00:26:56,430 --> 00:27:02,470
+في الخطوة هان بنعملها لمن؟ لدالة جديدة يبقى بنروح بقول له 
+
+240
+00:27:02,470 --> 00:27:14,340
+put V تساوي من Y أس سالب واحد نشتقها يبقى V' يساوي 
+
+241
+00:27:14,340 --> 00:27:24,040
+سالب Y أس سالب اثنين في مين؟ في Y' كويس يبقى صار عندي
+
+242
+00:27:24,040 --> 00:27:33,200
+ناقص V' بده يساوي Y أس minus 2 في Y' اللي هو مين؟
+
+243
+00:27:33,200 --> 00:27:37,660
+ال term اللي عندنا هذا يبقى بتصبح المعادلة على
+
+244
+00:27:37,660 --> 00:27:47,220
+الشكل التالي هذه سالب V prime وهنا سالب واحد على T
+
+245
+00:27:47,220 --> 00:27:55,020
+في V بده يساوي سالب واحد على T تربيع لو ضربنا
+
+246
+00:27:55,020 --> 00:28:01,230
+المعادلة كلها في سالب واحد يبقى ما بصير المعادلة يبقى
+
+247
+00:28:01,230 --> 00:28:09,210
+V' زائد واحد على T في ال V بده يساوي قد إيش واحد
+
+248
+00:28:09,210 --> 00:28:14,910
+على T تربيع المعادلة هذه يا بنات شو صارت؟ Linear
+
+249
+00:28:15,340 --> 00:28:20,020
+يبقى حولنا المعادلة من non linear first order
+
+250
+00:28:20,020 --> 00:28:25,440
+differential equation إلى ال linear first order
+
+251
+00:28:25,440 --> 00:28:30,760
+differential equation وبالتالي بدنا نروح نحل
+
+252
+00:28:30,760 --> 00:28:35,260
+المعادلة هذه زي ما كنا بنحل المرة الماضية في
+
+253
+00:28:35,260 --> 00:28:36,260
+section 2
+
+254
+00:28:39,450 --> 00:28:47,310
+بعد ذلك بنراجع ال section نتأكد
+
+255
+00:28:47,310 --> 00:28:51,850
+إن هذا المعامل هو واحد صحيح، الحمد لله جاهز، يبقى
+
+256
+00:28:51,850 --> 00:28:57,200
+بدنا نروح نجيب عامل التكامل اللي هو الـMRT فبعدين
+
+257
+00:28:57,200 --> 00:29:03,760
+بقوله لـ Mu of T بدي يساوي E أُس تكامل، إنتبهي به P 
+
+258
+00:29:03,760 --> 00:29:11,860
+of T DT E أُس تكامل P of T هو المعامل تبع ال V اللي
+
+259
+00:29:11,860 --> 00:29:21,040
+عندنا، اللي هو 1 على T يبقى 1 على T DT E أُس لن T 
+
+260
+00:29:21,040 --> 00:29:27,400
+بقول إيش بس ال value إن T greater than 0 موجبة ما عندناش
+
+261
+00:29:27,400 --> 00:29:33,620
+مشكلة يبقى هذا الكلام بدنا نكتب قد إيش بعد ذلك هذه
+
+262
+00:29:33,620 --> 00:29:37,820
+المعادلة اللي صارت linear يا بنات سامحها للمعادلة
+
+263
+00:29:37,820 --> 00:29:44,240
+اسمها قبلها ما سميناهاش يبقى سامحها للمعادلة star
+
+264
+00:29:44,240 --> 00:29:52,140
+يبقى باجي بقوله multiply equation
+
+265
+00:29:59,110 --> 00:30:09,800
+نحصل على ما يأتي يبقى بصير T في ال V Prime زائد V 
+
+266
+00:30:09,800 --> 00:30:17,920
+بده يساوي واحد على T فقط ل V تمام؟ هذه بدنا نعيد 
+
+267
+00:30:17,920 --> 00:30:24,160
+صياغتها مرة ثانية هذه يا بنات باجي بقول هي عبارة عن T
+
+268
+00:30:24,160 --> 00:30:31,270
+عامل التكامل في ال V الكل Prime لو جيت اشتقيت يدك حصل
+
+269
+00:30:31,270 --> 00:30:36,730
+ضرب دالتين بتعطيك هذا بالضبط تماما يبقى بده يساوي 
+
+270
+00:30:36,730 --> 00:30:44,850
+مين؟ واحد على T يبقى لو روحنا كاملنا بصير T في ال
+
+271
+00:30:44,850 --> 00:30:53,870
+V بده يساوي تكامل واحد على T DT زائد constant C1
+
+272
+00:30:53,870 --> 00:30:54,790
+مثلا
+
+273
+00:30:56,980 --> 00:31:07,040
+يبقى بصير T في ال V يساوي لن T زائد constant C1
+
+274
+00:31:10,190 --> 00:31:20,070
+بنقسم كله على T يبقى لو قسمنا على T بصير V تساوي لن
+
+275
+00:31:20,070 --> 00:31:25,530
+T والله خلّيها زائد C وخلاصنا زي ما هي لن T زائد
+
+276
+00:31:25,530 --> 00:31:31,550
+C خليها C زي ما هي مقسمة على مين؟ مقسمة كلها على
+
+277
+00:31:31,550 --> 00:31:39,660
+T إحنا قد إيش فرضنا V هنا؟ Y أصل ناقص واحد يعني هذا
+
+278
+00:31:39,660 --> 00:31:45,980
+كله بده يساوي Y أصل ناقص واحد يعني معنى هذا الكلام
+
+279
+00:31:45,980 --> 00:31:55,200
+أن واحد على Y يساوي ln T زائد C على مين؟ على T طب
+
+280
+00:31:55,200 --> 00:32:00,500
+أنا ما بدي واحد على Y بدي Y أصل يبقى بنقلب المعادلة
+
+281
+00:32:00,500 --> 00:32:07,920
+يبقى بصير الحل عندنا Y يساوي T على لن T زائد
+
+282
+00:32:07,920 --> 00:32:13,240
+constant C هذا هو حل المعادلة التفاضلية اللي عندنا
+
+283
+00:32:13,240 --> 00:32:17,960
+يبقى المعادلة كانت non-linear حولناها إلى linear
+
+284
+00:32:17,960 --> 00:32:24,840
+روحنا حلينا المعادلة اللي عندنا هذه بناخد كمان مثال
+
+285
+00:32:24,840 --> 00:32:27,720
+example 2
+
+286
+00:32:36,550 --> 00:32:48,470
+solve the initial value problem اللي هي من dy على dt
+
+287
+00:32:48,470 --> 00:32:59,190
+زائد y يساوي واحد على y أصل نص وال y عند ال zero 
+
+288
+00:32:59,190 --> 00:33:02,770
+بده يساوي قد إيش؟ بده يساوي أربعة
+
+289
+00:33:39,280 --> 00:33:43,340
+بنرجع لسؤالنا مرة ثانية هذه معادلة زي اللي قبل
+
+290
+00:33:43,340 --> 00:33:46,860
+بصراحة حطينا عليها شرطة المرة اللي فاتت قلنا لو
+
+291
+00:33:46,860 --> 00:33:49,860
+المعادلة حطينا عليها شرطة بنسميها initial value
+
+292
+00:33:49,860 --> 00:33:56,260
+problem طيب بنعيد كتابة المعادلة مرة ثانية يبقى
+
+293
+00:33:56,260 --> 00:34:03,360
+المعادلة هي عبارة عن y prime زائد y يساوي y أس ناقص
+
+294
+00:34:03,360 --> 00:34:09,780
+نص طلعناها فوق، ممتاز جدا، يعني يا بنات 
+
+295
+00:34:09,780 --> 00:34:16,160
+الأس اللي هنا ده، ليس بالضرورة أن يكون عدد صحيح
+
+296
+00:34:16,670 --> 00:34:20,070
+في المثال أو لما حطينا المعادلة الصينينة اللي كانت
+
+297
+00:34:20,070 --> 00:34:25,070
+ال star قلنا why to the power n ولم أقول إن ال n
+
+298
+00:34:25,070 --> 00:34:29,850
+is an integer يعني Integer ماشي كسري ماشي ما عندنا
+
+299
+00:34:29,850 --> 00:34:34,690
+مشكلة في هذه الحالة يبقى ما يكون يكون الأس ما عندنا
+
+300
+00:34:34,690 --> 00:34:39,590
+مشكلة المهم يكون real number طبعا طيب صارت بالشكل
+
+301
+00:34:39,590 --> 00:34:43,960
+اللي عندنا هذا إذا هذه هي مين؟ معادلة مين؟ معادلة
+
+302
+00:34:43,960 --> 00:34:48,820
+Bernoulli على طول الخط جاهزة مشان هيك لو هذه
+
+303
+00:34:48,820 --> 00:34:53,780
+بنقوله Bernoulli question دغري يبقى هذه Bernoulli
+
+304
+00:34:53,780 --> 00:34:59,610
+question يبقى معادلة Bernoulli مشان هيك بنروح بنضرب 
+
+305
+00:34:59,610 --> 00:35:05,870
+الطرفين في مين؟ في Y أصل نص بالموجب يبقى بجي بقوله
+
+306
+00:35:05,870 --> 00:35:15,070
+بصير Y أصل نص في Y prime زائد Y أصل ثلاثة على اثنين 
+
+307
+00:35:15,070 --> 00:35:20,930
+بده يساوي قد إيش؟ بده يساوي واحد طبعا يبقى صبت
+
+308
+00:35:20,930 --> 00:35:24,810
+المعادلة على الشكل اللي عندنا هنا بعد هيك بدنا نجي
+
+309
+00:35:24,810 --> 00:35:29,690
+ال term هذا كله ونحطه بمين؟ ب variable جديد اللي 
+
+310
+00:35:29,690 --> 00:35:37,990
+هو V يبقى لو جيت حطيت ال V تساوي Y أس ثلاثة على اثنين بدنا
+
+311
+00:35:37,990 --> 00:35:47,980
+نشتقها يبقى ال V prime يساوي ثلاثة على اثنين Y أس قد إيش؟ واحد 
+
+312
+00:35:47,980 --> 00:35:53,560
+ونص يعني بنطرح منها واحد بضال نص في مين؟ في ال Y
+
+313
+00:35:53,560 --> 00:35:57,940
+prime طب أنا ما بدي ثلاثة على اثنين بدي أشوف خلصتها
+
+314
+00:35:57,940 --> 00:36:01,920
+ثلاثة على اثنين يبقى بعض الورد برافو في قد إيش؟ في
+
+315
+00:36:01,920 --> 00:36:09,320
+طلعتين يبقى هي تلتين V Prime يساوي Y أصل نص في ال Y 
+
+316
+00:36:09,320 --> 00:36:14,340
+Prime يبقى Y أصل نص في ال Y Prime هي طلعت ليه؟ تلتين
+
+317
+00:36:14,340 --> 00:36:21,300
+V Prime يبقى صارت تلتين V Prime زائد هذا عطينا 
+
+318
+00:36:21,300 --> 00:36:28,610
+بكبير V يساوي واحد لو ضربنا كله في ثلاثة على اثنين
+
+319
+00:36:28,610 --> 00:36:35,130
+مش هنخلي معامل V' هو واحد صحيح يبقى بصير عندنا V' 
+
+320
+00:36:35,890 --> 00:36:42,450
+زائد ثلاثة على اثنين V يساوي قد إيش؟ ثلاثة على اثنين،
+
+321
+00:36:42,450 --> 00:36:46,630
+إيش رأيك في المعادلة هذه؟ Linear يبقى صارت
+
+322
+00:36:46,630 --> 00:36:50,670
+المعادلة هذه Linear first order differential
+
+323
+00:36:50,670 --> 00:36:55,510
+equation يبقى بدنا نحلها زي ما كنا بنحل قبلها بنبدأ 
+
+324
+00:36:55,510 --> 00:37:01,350
+بالضرورة أن نحضر له مين؟ ال Mu of T E أُس تكامل
+
+325
+00:37:01,350 --> 00:37:06,270
+قد إيش ال P of T هنا يا بنات؟ كل نص اللي هو ثلاثة 
+
+326
+00:37:06,270 --> 00:37:13,450
+على اثنين فبجي بقوله تكامل ثلاثة على اثنين DT يبقى
+
+327
+00:37:13,450 --> 00:37:19,630
+E أُس ثلاثة على اثنين كله في مين؟ في T يعني كأنه 
+
+328
+00:37:19,630 --> 00:37:27,160
+تماماً E أُس ثلاثة T على اثنين بنجي للمعادلة اللي هان 
+
+329
+00:37:27,160 --> 00:37:31,880
+هذه وبنضربها كلها في مين؟ في ال integrating factor
+
+330
+00:37:31,880 --> 00:37:36,620
+يبقى باجي بقول سميلي هذه اللي سميناها linear هذه
+
+331
+00:37:36,620 --> 00:37:42,840
+سميها اللي هي ال star يبقى باجي بقول multiply
+
+332
+00:37:42,840 --> 00:37:46,820
+equation
+
+333
+00:37:47,460 --> 00:37:53,860
+star بـ integrating factor E أس ثلاثة T على 
+
+334
+00:37:53,860 --> 00:37:59,320
+اثنين we get E 
+
+335
+00:37:59,320 --> 00:38:07,820
+أس ثلاثة على اثنين T في ال V prime زائد ثلاثة على
+
+336
+00:38:07,820 --> 00:38:15,060
+اثنين E أس ثلاثة T على الاثنين V بده يساوي ثلاثة
+
+337
+00:38:15,060 --> 00:38:22,060
+على اثنين E أس ثلاثة على اثنين E أس ثلاثة T على 
+
+338
+00:38:22,060 --> 00:38:29,420
+الاثنين هذا بدي يعطينا ما رأيك في الأولى هذه؟ أليست 
+
+339
+00:38:29,420 --> 00:38:38,440
+هي عامل التكامل مضروب في V الكل prime؟ اه لو جيت
+
+340
+00:38:38,440 --> 00:38:42,340
+اشتقيت هذه automatic حصل ضرب دالتين بتعطيك هذا 
+
+341
+00:38:42,340 --> 00:38:46,580
+المشتق حرفيا لو ما طلعتش معناته عامل التكامل اللي
+
+342
+00:38:46,580 --> 00:38:53,540
+حسبتيه خاطئ طيب هذا الكلام بده يساوي قد إيش؟ ثلاثة على 
+
+343
+00:38:53,540 --> 00:38:59,640
+اثنين E أُس ثلاثة T على مين؟ على الاثنين طب بدنا
+
+344
+00:38:59,640 --> 00:39:04,860
+نكامل الطرفين يبقى by integration
+
+345
+00:39:36,260 --> 00:39:41,100
+بدنا نكامل بصير طب إحنا بدنا V لحالها ما بدناش E 
+
+346
+00:39:41,100 --> 00:39:46,040
+أس سالب يبقى بنروح بنضرب الطرفين في E سالب ثلاثة على
+
+347
+00:39:46,040 --> 00:39:52,500
+اثنين T يبقى معنى هذا الكلام V تساوي طب V أصلاً 
+
+348
+00:39:52,500 --> 00:39:59,660
+قد إيش إحنا كاتبينها؟ Y أصل ثلاثة على اثنين يبقى Y أصل
+
+349
+00:39:59,660 --> 00:40:08,260
+ثلاثة على اثنين تساوي واحد زائد C في E أُس ناقص ثلاثة T على من؟ على الاثنين طب إحنا عندما ال
+
+350
+00:40:08,260 --> 00:40:13,380
+condition Y under zero تساوي أربعة الآن y عند ال
+
+351
+00:40:13,380 --> 00:40:20,740
+zero تساوي أربعة implies بدنا نشيل ال y هذه ونحط
+
+352
+00:40:20,740 --> 00:40:25,900
+مكانها قد إيش؟ أربعة أصل ثلاثة على اثنين يساوي واحد
+
+353
+00:40:25,900 --> 00:40:33,620
+زائد c E أصل zero هذه قد إيش؟ واحد تمام هذه 
+
+354
+00:40:33,620 --> 00:40:43,650
+الـ بنات تعني الجذر التربيعي لأربعة تكعيب أربعة
+
+355
+00:40:43,650 --> 00:40:48,850
+تكعيب في قد إيش؟ أربعة في أربعة بـ ستة عشر في أربعة
+
+356
+00:40:48,850 --> 00:40:53,330
+بـ أربعة وستين تحت الجذر يبقى بقد إيش؟ بثمانية هذا
+
+357
+00:40:53,330 --> 00:40:59,250
+معناه إن ثمانية تساوي واحد زائد C يبقى C تساوي
+
+358
+00:41:05,930 --> 00:41:16,370
+قد إيش؟ سبعة يبقى أصبح عندنا هنا the solution is 
+
+359
+00:41:16,370 --> 00:41:25,730
+Y أس ثلاثة على اثنين يساوي واحد زائد سبعة E أُس ناقص
+
+360
+00:41:25,730 --> 00:41:33,960
+ثلاثة T على اثنين فأنا بقدر أجيب Y مرة واحدة يبقى
+
+361
+00:41:33,960 --> 00:41:40,880
+باجي بقوله يبقى Y يساوي يعني بدنا ناخد هذا أس ثلثين
+
+362
+00:41:40,880 --> 00:41:48,500
+بدنا نساوي اليمين أس ثلثين يبقى واحد زائد سبعة E
+
+363
+00:41:48,500 --> 00:41:56,400
+أس سالب ثلاثة T على اثنين كله أس ثلثين هذا هو الحل
+
+364
+00:41:56,400 --> 00:41:59,020
+تبع المعادلة التفاضلية 
+
+365
+00:42:01,560 --> 00:42:07,000
+طيب عليك انتهينا من Bernoulli question للأسف
+
+366
+00:42:07,000 --> 00:42:12,160
+الشديد في الكتاب ما تيني بس 4 أسئلة ومش كتير أنا 
+
+367
+00:42:12,160 --> 00:42:18,840
+هأعطيكوا أسئلة بالإضافة لأسئلة الكتاب يبقى نروح
+
+368
+00:42:18,840 --> 00:42:22,980
+نُعطيـكوا الأسئلة التالية ك exercises
+
+370
+00:42:45,450 --> 00:42:51,830
+يبقى exercises solve
+
+371
+00:42:51,830 --> 00:42:56,330
+the
+
+372
+00:42:56,330 --> 00:43:01,990
+following
+
+373
+00:43:01,990 --> 00:43:07,150
+differential equations
+
+374
+00:43:07,150 --> 00:43:18,780
+السؤال الأول Y' ناقص Y يساوي E أُس T في ال Y تربيع
+
+375
+00:43:18,780 --> 00:43:30,360
+سؤال الثاني T في ال Y' ناقص واحد زائد T كله في ال
+
+376
+00:43:30,360 --> 00:43:37,120
+Y بده يساوي T في ال Y تربيع و T greater than zero
+
+377
+00:43:37,120 --> 00:43:48,670
+سؤال الثالث بيقول اثنين T في ال Y prime زائد
+
+378
+00:43:48,670 --> 00:43:58,210
+Y يساوي اثنين T تربيع على Y تكعيب وال Y عند الواحد 
+
+379
+00:43:58,210 --> 00:44:05,150
+بده يساوي قد إيش؟ اثنين و T greater than zero السؤال
+
+380
+00:44:05,150 --> 00:44:15,030
+الرابع وما أدرك ما السؤال الرابع بيقول Y' ناقص واحد
+
+381
+00:44:15,030 --> 00:44:25,190
+على واحد زائد T كله في ال Y بده يساوي واحد
+
+382
+00:44:25,190 --> 00:44:37,220
+زائد T في E أُس T في ال Y السؤال الخامس لو 
+
+383
+00:44:37,220 --> 00:44:45,960
+exercises 2 أربعة المسائل من 28
+
+384
+00:44:45,960 --> 00:44:48,460
+لغاية 30
+
+385
+00:45:11,660 --> 00:45:17,160
+مرة ثانية طبعا المسائل الأربعة الأولى من خارج 
+
+386
+00:45:17,160 --> 00:45:22,200
+الكتاب بيقول لحل المسائل التالية هو يعطيني
+
+431
+00:49:40,860 --> 00:49:47,840
+differential equation is اللي هو مين y prime زائد 
+
+432
+00:49:47,840 --> 00:49:55,280
+اثنين y تساوي قداش في الفترة هذه قيمة g of t واحد
+
+433
+00:49:55,280 --> 00:50:00,880
+صحيح as in linear وهنا continuous  وcontinuous
+
+434
+00:50:00,880 --> 00:50:05,840
+ماعندي مشكلة وأنا فقط حاصر نفسي على الفترة من zero
+
+435
+00:50:05,840 --> 00:50:12,250
+لغاية واحد يبقى هذه صارت linear مدام linear إذا بروح
+
+436
+00:50:12,250 --> 00:50:20,910
+أجيب ال mu of T مباشرة يساوي E أس تكامل اثنين DT
+
+437
+00:50:20,910 --> 00:50:28,310
+يبقى E أس اثنين T يبقى هذا صار من ال mu of T شو
+
+438
+00:50:28,310 --> 00:50:35,160
+بعمل؟ بضرب المعادلة فيه يبقى بيصير E أس اثنين T في
+
+439
+00:50:35,160 --> 00:50:41,660
+ال Y Prime اثنين E أس اثنين T في ال Y يساوي E أس
+
+440
+00:50:41,660 --> 00:50:47,480
+اثنين T تمام؟ يبقى صارت المعادلة على الشكل اللي
+
+441
+00:50:47,480 --> 00:50:54,460
+قدامنا هذا تماما طيب الآن هذه جاهزة وخالصة يعني 
+
+442
+00:50:54,460 --> 00:51:01,000
+بقدر أكتبها على الشكل هذا عامل التكامل وهذا Y كله
+
+443
+00:51:01,000 --> 00:51:09,310
+prime يساوي E أش اثنين T إن كامل الطرفين يبقى بيصير
+
+444
+00:51:09,310 --> 00:51:16,250
+عندنا E أس اثنين T في ال Y يساوي E أس اثنين T على
+
+445
+00:51:16,250 --> 00:51:23,970
+اثنين زائد constant C أو بمعنى آخر بقدر أقول أن ال
+
+446
+00:51:23,970 --> 00:51:38,520
+Y تساوي نصف زائد C على E أس اثنين T أو نصف زائد C في
+
+447
+00:51:38,520 --> 00:51:44,220
+E أس ناقص اثنين T طيب تعالوا نطلع نعطيني ال initial
+
+448
+00:51:44,220 --> 00:51:48,420
+condition ال initial condition قال لي Y عند Zero
+
+449
+00:51:48,420 --> 00:51:51,900
+يساوي Zero إذا احنا في الفترة هذه والله في الفترة 
+
+450
+00:51:51,900 --> 00:51:57,840
+الأولى Y عند Zero يبقى Zero عند الفترة الأولى يبقى 
+
+451
+00:51:57,840 --> 00:52:03,220
+باجي بقوله الآن أنا عندي initial condition y عندي 
+
+452
+00:52:03,220 --> 00:52:06,860
+ال zero يساوي zero بنفع أستخدم ال condition هذا 
+
+453
+00:52:06,860 --> 00:52:12,840
+لفترة ثانية لا يبعثك الله بنقدرش يبقى y عندي ال 
+
+454
+00:52:12,840 --> 00:52:18,120
+zero بده يساوي قداش بده يساوي zero implies هي ال
+
+455
+00:52:18,120 --> 00:52:25,820
+zero بده يساوي نصف زائد c في e أس zero اللي هو قداش
+
+456
+00:52:26,190 --> 00:52:32,170
+بواحد يبقى بناء على اليسار C يساوي كده؟ سالب نصف
+
+457
+00:52:32,170 --> 00:52:38,050
+يبقى أصبح ال solution على الشكل التالي Y يساوي
+
+458
+00:52:38,050 --> 00:52:48,210
+النصف ناقص نصف E أس ناقص اثنين T والـ T محصورة ما
+
+459
+00:52:48,210 --> 00:52:52,850
+بين ال zero و ما بين الواحد هذا شكل الحل على
+
+460
+00:52:52,850 --> 00:52:59,550
+الفترة T الأولى بنروح لوين؟ للفترة الثانية يبقى
+
+461
+00:52:59,550 --> 00:53:10,550
+باجي بقوله if T greater than one then the
+
+462
+00:53:10,550 --> 00:53:18,090
+differential equation as نرجع للمعادلة الأصلية y
+
+463
+00:53:18,090 --> 00:53:25,190
+prime زائد اثنين y تساوي g of t بعد الواحد قداش g
+
+464
+00:53:25,190 --> 00:53:32,870
+of t يبقى هذه بدها تساوي zero يبقى هذه linear كذلك 
+
+465
+00:53:32,870 --> 00:53:35,810
+بس مش هلال دي على الحلطة رابعة الطريقة اثنين لأ
+
+466
+00:53:35,810 --> 00:53:38,950
+بحلها فقط وواحدة ومش محتاج ل integrating factor 
+
+467
+00:53:38,950 --> 00:53:44,690
+ولا غيره فبقى بقول له هذا بتعطينا أن y' يساوي ناقص
+
+468
+00:53:44,690 --> 00:53:53,230
+اثنين y أو أن شئتم فقولوا y' على y يساوي ناقص اثنين
+
+469
+00:53:53,230 --> 00:54:01,920
+أظن بقدر أكملها هذه صح؟ يبقى شو تكملها؟ قداش؟ لن 
+
+470
+00:54:01,920 --> 00:54:09,400
+absolute value لل Y بدها تساوي تكامل هذي اللي بناقص
+
+471
+00:54:09,400 --> 00:54:16,840
+اثنين T زائد constant وليكن C1 طب أنا مابديش لن
+
+472
+00:54:16,840 --> 00:54:22,130
+لبس اللي بدي ال Y itself يبقى باجي بقوله هذا يعني 
+
+473
+00:54:22,130 --> 00:54:28,970
+أنه absolute value ل Y بدها تساوي E أس ناقص اثنين T 
+
+474
+00:54:28,970 --> 00:54:36,790
+زائد C1 طيب سؤال هذا exponential عمره بياخد قيمة
+
+475
+00:54:36,790 --> 00:54:41,390
+سلبية؟ يبقى لا داعي لل absolute value لأن ال 
+
+476
+00:54:41,390 --> 00:54:45,070
+absolute value احتمال أن تبقى سالبة ولا موجبة لكن
+
+477
+00:54:45,070 --> 00:54:48,610
+لما انضمنت أنها موجبة يبقى لها معنى لل absolute
+
+478
+00:54:48,610 --> 00:54:53,070
+value إذا منشيل ال absolute value بروح نقول أن
+
+479
+00:54:53,070 --> 00:55:00,290
+الحل Y بدها تساوي E أس ناقص اثنين T في E أس C one
+
+480
+00:55:22,590 --> 00:55:28,730
+يبقى كأن الحل أصبح على الشكل التالي 
+
+481
+00:55:44,560 --> 00:55:50,680
+Y تساوي أحد أمرين الأمر الأول اللي بروزنا نصف ناقص
+
+482
+00:55:50,680 --> 00:55:57,900
+نصف في E أس ناقص اثنين T نصف ناقص نصف في E أس ناقص 
+
+483
+00:55:57,900 --> 00:56:03,520
+اثنين T وT أكبر من أو يساوي Zero أقل من أو يساوي
+
+484
+00:56:03,520 --> 00:56:03,940
+الواحد
+
+485
+00:56:15,060 --> 00:56:23,320
+طب إيش رأيكوا بقدر أجيب ال c احنا 
+
+486
+00:56:23,320 --> 00:56:28,240
+شروطنا بتبقى continuous دائما وابدا بدي أخلي الحل
+
+487
+00:56:28,240 --> 00:56:32,960
+هذا continuous مشان الحل هذا continuous برجع
+
+488
+00:56:32,960 --> 00:56:37,400
+لتعريف ال continuous function زمان قلنا أن بتبقى 
+
+489
+00:56:37,400 --> 00:56:41,080
+الدالة بتبقى continuous عند نقطة النقطة مين عندنا
+
+490
+00:56:41,080 --> 00:56:47,330
+هنا واحد إذا كان قيمة الدالة عند الواحد يساوي نهاية
+
+491
+00:56:47,330 --> 00:56:50,750
+الدالة عند الواحد مش هيك أخذها في الكلقوا لصغير
+
+492
+00:56:50,750 --> 00:56:54,430
+يبقى باقي أن أقول limit ال F of X لما ال X بدأت
+
+493
+00:56:54,430 --> 00:57:00,610
+تروح ال X node يساوي ال F of X node itself يبقى
+
+494
+00:57:00,610 --> 00:57:06,990
+باجي بقول هنا ال Y is continuous
+
+495
+00:57:08,070 --> 00:57:15,070
+at x يساوي واحد يعني مش الدلال أصلي الحل تبعها بدي
+
+496
+00:57:15,070 --> 00:57:21,870
+يكون continuous عند x يساوي واحد if ال limit لل y 
+
+497
+00:57:21,870 --> 00:57:27,090
+لما ال y بدها تروح للواحد من جهة اليمين بدي يساوي
+
+498
+00:57:27,090 --> 00:57:33,590
+قيمة y عند الواحد طب واحد هتقولي طب ليش من جهة
+
+499
+00:57:33,590 --> 00:57:37,310
+الشمال؟ لأ، هتقولك من جهة الشمال ما هي لازم تساوي
+
+500
+00:57:37,310 --> 00:57:40,250
+ليه الجهة اليمين، عشان تبقى قيمة، it doesn't
+
+501
+00:57:40,250 --> 00:57:44,930
+exist. اثنين، لابد أقولك واحد من جهة الشمال هتعطيك
+
+502
+00:57:44,930 --> 00:57:48,710
+نفس قيمة الدالة اللي هي المعطلة و اتقالي ماعنديش
+
+503
+00:57:48,710 --> 00:57:53,740
+مشكلة، ماساويش شيء، يعني بيصير تكرار ممل فيبتعلي
+
+504
+00:57:53,740 --> 00:57:58,540
+نأخذ ال limit اللي عندنا هنا يبقى هذا ال limit لما 
+
+505
+00:57:58,540 --> 00:58:05,740
+Y بدها تروح للواحد من جهة اليمين الآن أنا عند هذا 
+
+506
+00:58:05,740 --> 00:58:11,080
+ال real line وهذا عند الواحد وهذا عند ال zero أنا 
+
+507
+00:58:11,080 --> 00:58:15,300
+رايح للواحد من جهة يد اليمين يعني احنا قبل
+
+508
+00:58:15,300 --> 00:58:20,550
+الواحد ولا بعد الواحد أنا رايح للواحد من جهة E
+
+509
+00:58:20,550 --> 00:58:24,970
+اليمين يبقى احنا بعد الواحد والله قابل الواحد بعد 
+
+510
+00:58:24,970 --> 00:58:31,030
+الواحد قيمة الدالة كده؟ C في E أس ناقص اثنين C 
+
+511
+00:58:31,030 --> 00:58:38,350
+يبقى C في E أس ناقص اثنين T بده يساوي Y عند الواحد
+
+512
+00:58:38,350 --> 00:58:42,730
+قيمة الدالة عند الواحد لما T تساوي واحد هاي قيمة
+
+513
+00:58:42,730 --> 00:58:49,600
+الدالة صح ولا لا؟ يبقى بيصير تساوي النصف ناقص نصف في 
+
+514
+00:58:49,600 --> 00:58:56,060
+E أس ناقص اثنين في واحد في E أس ناقص اثنين طيب العوض
+
+515
+00:58:56,060 --> 00:59:02,180
+تعود مباشر يبقى C في E أس ناقص اثنين يساوي النصف
+
+516
+00:59:02,180 --> 00:59:08,100
+ناقص نصف في E أس ناقص اثنين هذه معادلة مجهول فيها بس
+
+517
+00:59:08,100 --> 00:59:13,770
+مين؟ يبقى بدي أضرب كله في اي تربية بكون جيب من C
+
+518
+00:59:13,770 --> 00:59:22,470
+يبقى هذا بدي يعطينا أن C يساوي نصف اي تربية ناقص نصف
+
+519
+00:59:22,470 --> 00:59:29,590
+يعني نصف في اي تربية ناقص واحد يبقى أصبح the 
+
+520
+00:59:29,590 --> 00:59:30,610
+solution
+
+521
+00:59:34,280 --> 00:59:43,180
+of the initial value of problem is y تساوي الجزئين 
+
+522
+00:59:43,180 --> 00:59:51,300
+الجزء الأول نصف ناقص نصف E أس ناقص اثنين T الجزء
+
+523
+00:59:51,300 --> 00:59:56,320
+الأول اللي جبناه فوق الآن بدي أشيل C وأحط قيمتها
+
+524
+00:59:56,320 --> 01:00:01,720
+يبقى هنا نصف في E تربية ناقص واحد
+
+525
+01:00:19,690 --> 01:00:24,750
+طبعا أبسط من السؤال هذا أسهل شوية كمان
+
+526
+01:00:47,970 --> 01:00:53,990
+بدنا نجي ل section 2 5 ونقول الله يسهل عليك بروح
+
+527
+01:00:53,990 --> 01:00:58,950
+ل section 2 6 اللي هو مين اللي هو exact
+
+528
+01:01:01,540 --> 01:01:10,780
+equations and integrating factors
+
+529
+01:01:10,780 --> 01:01:16,320
+المعادلة
+
+530
+01:01:16,320 --> 01:01:19,140
+تمام وعوامل التكامل
+
+531
+01:01:27,690 --> 01:01:32,150
+هذا ال section يا بنات هو ال section الوحيد اللي
+
+532
+01:01:32,150 --> 01:01:36,950
+لازمنا فيه من calculus C اللي قلتلكوا أول محاضرة
+
+533
+01:01:36,950 --> 01:01:42,110
+خشيت عليكم نأخذها في خمس دقائق أو أقل طيب قبل ما 
+
+534
+01:01:42,110 --> 01:01:47,810
+نبدأ بدنا نقول شو بدنا من calculus C احنا في 
+
+535
+01:01:47,810 --> 01:01:52,250
+calculus A وB كله بيجينا نأخذ الدالة Y function في
+
+536
+01:01:52,250 --> 01:01:58,960
+متغير واحد مصغور؟ طب لو صارت function في متغيرين أو 
+
+537
+01:01:58,960 --> 01:02:03,800
+ثلاثة كيف بدنا نشتق؟ بقول اشتقاق في هذه الحالة
+
+538
+01:02:03,800 --> 01:02:09,820
+يكون اشتقاقا جزئيا يبقى إذا كانت الدالة وعي في
+
+539
+01:02:09,820 --> 01:02:15,120
+متغير واحد بقول اشتقاق كله لكن إذا دالة في متغيرين
+
+540
+01:02:15,120 --> 01:02:20,680
+أو ثلاثة أو أربعة أو خمسة بقول اشتقاق جزئي تمام؟
+
+541
+01:02:20,680 --> 01:02:27,070
+نعطيكوا توضيح لو جينا تقول لك f ال y تساوي
+
+542
+01:02:27,070 --> 01:02:34,430
+function في x و z يبقى خالتها y ده اللي في مين فيه 
+
+543
+01:02:34,430 --> 01:02:44,130
+متغيرين مثلا روح تقول لك x تربيع z تكعيب زائدها
+
+544
+01:02:44,130 --> 01:02:51,110
+ثلاثة x z تربيع ناقص واحد then
+
+545
+01:02:54,020 --> 01:02:59,020
+افترض إذا اشتقها بالنسبة إلى x فابقى أقول اشتقاق 
+
+546
+01:02:59,020 --> 01:03:05,280
+جزئي بقول partial y by partial x شكل أنا بقى لما
+
+547
+01:03:05,280 --> 01:03:11,320
+كنت أقول dy على dx بقول partial y by partial x
+
+548
+01:03:11,320 --> 01:03:15,000
+يبقى اشتقاق جزئي من حد ما يشوف الرمز هذا يبقى
+
+549
+01:03:15,000 --> 01:03:20,040
+اشتقاق جزئي لما اشتقها بنات بالنسبة ل x بعتبر كل 
+
+550
+01:03:20,040 --> 01:03:26,810
+المتغيرات الأخرى ثوابت طبعا يبقى بدي يكون عندي هنا
+
+551
+01:03:26,810 --> 01:03:32,810
+z ثابت بشتق باسمين وثابت بظل زي ما هو يبقى أديش
+
+552
+01:03:32,810 --> 01:03:37,350
+مشتقة ال X تربيع ب 2XZ
+
+553
+01:03:37,350 --> 01:03:46,290
+كعيب زي ثلاثة Z تربيع وسالب واحد مشتقة بزيرو and
+
+554
+01:03:46,290 --> 01:03:53,660
+لو بدي partial Y by partial Z يبقى بذا تثابت، ده 
+
+555
+01:03:53,660 --> 01:03:59,280
+اشتق بالنسبة لمن؟ يبقى ال X يبقى ال X تربيع هذي
+
+556
+01:03:59,280 --> 01:04:03,960
+ثابتة، يبقى بقوله ال X تربيع زي ما أنتِ زدت كي
+
+557
+01:04:03,960 --> 01:04:11,400
+بيصير ثلاثة زد تربيع وصلنا زاد زاد، ثلاثة X مالكش
+
+558
+01:04:11,400 --> 01:04:18,210
+دعوة الـ z تربيع ما فقدش بـ 2z ومشتقة السلب 1 بـ 0
+
+559
+01:04:18,210 --> 01:04:26,910
+يبقى صارت 3x تربيع z تربيع زائد 6xz بالمثل لو بدي
+
+560
+01:04:26,910 --> 01:04:32,970
+أكامل، لو بدي أكامل بالنسبة إلى x، بعتبر الـ z هذه
+
+561
+01:04:32,970 --> 01:04:38,890
+ثابتة وهذه ثابتة وبكمل بس الـ 3 و2x لو بدها كامل
+
+562
+01:04:38,890 --> 01:04:42,950
+بالنسبة الى z يبقى ثلاثة x تربيع ثابتة وبضال and
+
+563
+01:04:42,950 --> 01:04:48,870
+main زد تكعيب على ثلاثة تكاملها وده ستة x ثابتة و
+
+564
+01:04:48,870 --> 01:04:54,630
+بضال z تربيع على main على اثنين وهكذا صعب هذي؟
+
+565
+01:04:54,630 --> 01:04:59,590
+هذا اللي بدنا منك الكلسي كله اللي شفتيه أكثر من 
+
+566
+01:04:59,590 --> 01:05:06,740
+هيك بدنا ماشي؟ بس في عندي كمان شغلة لو أنا عندي 
+
+567
+01:05:06,740 --> 01:05:12,900
+دالة في متغيرين وبدي أجيب مشتقتها اشتقاقا كاملا
+
+568
+01:05:12,900 --> 01:05:21,480
+يعني لو كانت في هي ال function في x و y وبدي أجيب
+
+569
+01:05:21,480 --> 01:05:28,580
+الاشتقاق الكل لها هذه النقطة الأولى اللي بدنا ياها
+
+570
+01:05:28,580 --> 01:05:34,380
+وهذه النقطة الثانية يبقى يا بنات بدي دي فاي
+
+571
+01:05:34,380 --> 01:05:41,020
+الاشتقاق الكلي لفاي بروح بقول هذا عبارة عن partial
+
+572
+01:05:41,020 --> 01:05:48,080
+fi على partial x في dx زائد partial fi على partial
+
+573
+01:05:48,080 --> 01:05:50,020
+y في dy
+
+574
+01:05:52,120 --> 01:05:58,140
+في دالة فيه متغيرين بدي أجيب الاشتقاق الكل بالنسبة
+
+575
+01:05:58,140 --> 01:06:03,640
+لفي فبقول دي في هي partial في على partial x في دي
+
+576
+01:06:03,640 --> 01:06:09,840
+x زي partial في على partial y في دي y تمام؟ أكثر
+
+577
+01:06:09,840 --> 01:06:13,810
+من هيك بدناش ولا حاجة والآن الكلام اللي بقوله لكوا
+
+578
+01:06:13,810 --> 01:06:19,750
+هنبدأ نطبقه على أرض الواقع بس قبل بدنا نشوف شو شكل
+
+579
+01:06:19,750 --> 01:06:23,590
+ال exact equation أو ما هو تعريف ال exact equation
+
+580
+01:06:23,590 --> 01:06:29,750
+وبعد هيك بدنا نشوف كيف بدنا نحل هذه المعادلة يبقى
+
+581
+01:06:29,750 --> 01:06:34,850
+هذه المقدمة منات اللي وعدناكوا فيها من خمس دقائق
+
+582
+01:06:34,850 --> 01:06:42,490
+اللي هتلزمنا فقط لغيره يبقى بدنا نيجي لمين لل exact
+
+583
+01:06:42,490 --> 01:06:52,930
+equations يبقى 
+
+584
+01:06:52,930 --> 01:06:57,630
+هذا النقطة الأولى نمرا واحد اللي هي exact
+
+585
+01:06:57,630 --> 01:07:02,910
+equations طبعا ال section فيه نقطتين ال exact
+
+586
+01:07:02,910 --> 01:07:06,350
+equations وال integrating factors ال integrating
+
+587
+01:07:06,350 --> 01:07:10,370
+factors حال جائلها لما تكون المعادلة ماهياش exact
+
+588
+01:07:10,370 --> 01:07:15,810
+وربما سنعرفه خلال هذه المحاضرة وربما في المحاضرة
+
+589
+01:07:15,810 --> 01:07:20,810
+القادمة تمام يبقى من هنا ال exact equations the
+
+590
+01:07:20,810 --> 01:07:25,190
+first order
+
+591
+01:07:27,690 --> 01:07:37,950
+Differential equation y prime يساوي f of x و y can
+
+592
+01:07:37,950 --> 01:07:47,090
+be written as ممكن نكتب على الشكل التالي 
+
+593
+01:07:49,540 --> 01:08:01,660
+by dx يساوي سالب M في ال XY على N في ال XY زي
+
+594
+01:08:01,660 --> 01:08:08,760
+المرة اللي فاتت بالظبط this is possible هذا الكلام
+
+595
+01:08:08,760 --> 01:08:11,780
+ممكن for example
+
+596
+01:08:35,680 --> 01:08:42,520
+تاك تاك تاك تاك
+
+597
+01:08:42,520 --> 01:08:44,880
+تاك تاك تاك تاك تاك تاك تاك تاك تاك تاك تاك تاك
+
+598
+01:08:45,510 --> 01:08:56,770
+differential equation is written as
+
+599
+01:08:56,770 --> 01:09:07,290
+أكتبها على الشكل التالي اللي هو m of x y dx زائد n 
+
+600
+01:09:07,290 --> 01:09:14,190
+of x y dy بدها تساوي من؟ بدها تساوي
+
+601
+01:09:41,040 --> 01:09:45,000
+كويس نرجع لموضوعنا لسه أنا ما عرفتش ال exact
+
+646
+01:14:45,570 --> 01:14:49,710
+بدي أشير إلى ملاحظة بسيطة الآن ال differential
+
+647
+01:14:49,710 --> 01:14:55,150
+equation بقول عنها exact يعني لو كانت exact لازم
+
+648
+01:14:55,150 --> 01:14:55,730
+ألاقي 
+
+649
+01:15:07,970 --> 01:15:15,090
+طيب كويس طلعيني بس هنا احنا دي فاي لو كان فانكشن 
+
+650
+01:15:15,090 --> 01:15:20,140
+في x و y يبقى دي فاي بده يساوي هذا ال term أيش هنا
+
+651
+01:15:20,140 --> 01:15:25,220
+احنا قلنا دي إبصاي بده يساوي ال term هذا اللي لنا
+
+652
+01:15:25,220 --> 01:15:31,320
+صحيح ولا لا يبقى لحد هنا انتهى التعريف لكن أنا 
+
+653
+01:15:31,320 --> 01:15:37,320
+بقدر أقوله إيه دي إبصاي of x و y هذه معلومة جانبية
+
+654
+01:15:37,320 --> 01:15:41,960
+آه لسه ما وصلناش النظرية بقدر أقول هي partial إبصاي
+
+655
+01:15:41,960 --> 01:15:47,440
+على partial x في ال dx زائد partial إبصاي على 
+
+656
+01:15:47,440 --> 01:15:53,600
+partial y في ال dy يبقى كأنه هذه عبارة عن مين يا
+
+657
+01:15:53,600 --> 01:16:01,800
+بناتي ال M وهذه كأنها عبارة عن مين عبارة عن ال N
+
+658
+01:16:01,800 --> 01:16:07,960
+بالضبط تمامًا كويس هايه لو قلت هنا إبصاي بصير هنا
+
+659
+01:16:07,960 --> 01:16:13,880
+إبصاي هنا إبصاي هنا إبصاي بالضبط تمامًا يبقى هذه
+
+660
+01:16:13,880 --> 01:16:23,540
+جيبناها من وين؟ هذا من كالكولاس C هذي من كالكولاس
+
+661
+01:16:23,540 --> 01:16:30,980
+C هذي من كالكولاس C طيب سيبينا من المعلومة هذه و
+
+662
+01:16:30,980 --> 01:16:37,480
+بدي أسأل السؤال التالي هل سهل أن أجيب ندور على ال
+
+663
+01:16:37,480 --> 01:16:44,620
+function of xi of x و y و نوجدها هيك مش سهل لكن في
+
+664
+01:16:44,620 --> 01:16:50,800
+نظرية هذه النظرية بتسهل عملية إيجاد هذه الدالة نجي 
+
+665
+01:16:50,800 --> 01:16:55,940
+للنظرية نشوف شو بتقول هذه النظرية يبقى ال theorem
+
+666
+01:16:55,940 --> 01:17:01,640
+بيقول
+
+667
+01:17:01,640 --> 01:17:12,620
+ليلة ال M و ال N و ال partial M على partial Y and
+
+668
+01:17:13,870 --> 01:17:21,650
+الـ Partial N على Partial X بـ Continuous
+
+669
+01:17:21,650 --> 01:17:24,710
+Functions
+
+670
+01:17:24,710 --> 01:17:32,550
+يبقى دوال متصلة in a region
+
+671
+01:17:58,450 --> 01:18:01,710
+معادلة التفاضلية M
+
+672
+01:18:12,300 --> 01:18:13,700
+YYYYYYYYYY
+
+673
+01:19:08,350 --> 01:19:14,710
+بنرجع لنظرية ثانية بيقول إيش؟ افترض أن عندي M و N
+
+674
+01:19:14,710 --> 01:19:20,170
+و تفاضل M بالنسبة ل Y تفاضل ال N بالنسبة ل X عبارة 
+
+675
+01:19:20,170 --> 01:19:24,810
+عن continuous functions على المستطيل اللي عندنا،
+
+676
+01:19:24,810 --> 01:19:28,810
+كويس؟ اللي هو X محصورة من Alpha إلى Beta وY محصورة
+
+677
+01:19:28,810 --> 01:19:32,550
+من جامعة إلى جامعة قيم يعني هنا القيمتين وهذه
+
+678
+01:19:32,550 --> 01:19:36,950
+القيمتين يعني على شكل مستطيل بعد ذلك الـ
+
+679
+01:19:36,950 --> 01:19:40,930
+differential equation اللي عند هذه الأساسية بقول
+
+680
+01:19:40,930 --> 01:19:46,530
+عنها exact إذا كان تفاضل ال N بالنسبة إلى Y يساوي 
+
+681
+01:19:46,530 --> 01:19:51,830
+تفاضل ال N بالنسبة إلى X إذا صارت قصتي سهلة بقدر
+
+682
+01:19:51,830 --> 01:19:55,490
+أحكم على مين على المعادلة اللي عندي هل هي exact
+
+683
+01:19:55,490 --> 01:20:02,480
+بسهولة و أجتشلو جيت هنا فاضلت ال M بالنسبة E ل Y
+
+684
+01:20:02,480 --> 01:20:06,680
+طبعًا هي مضروبة في DX بدها فاضلها بالنسبة ل Y و جيت
+
+685
+01:20:06,680 --> 01:20:10,480
+فاضلت هذه بالنسبة ل X اللي هي مضروبة في Y بدي يكون
+
+686
+01:20:10,480 --> 01:20:14,920
+اتنين مالهم are equal إن كانوا equal بتبقى هذه إيش
+
+687
+01:20:14,920 --> 01:20:21,080
+exact لكن قال لي في المثلة if and only if يعني هذه
+
+688
+01:20:21,080 --> 01:20:26,600
+في اتجاهين لو كانت exact إذا الشرط هذا صحيح و العكس
+
+689
+01:20:26,600 --> 01:20:31,100
+لو كان الشرط صحيح يبقى المعادلة التفاضلية المعطلة
+
+690
+01:20:31,100 --> 01:20:37,280
+بتكون مالها exactly بدنا نبرهن هذه النظرية أحد
+
+691
+01:20:37,280 --> 01:20:42,760
+الاتجاهات very easy الثاني شوي لكن بنقدر عليه 
+
+692
+01:20:42,760 --> 01:20:45,120
+يبقى باجي بقول prove
+
+693
+01:20:52,760 --> 01:20:58,880
+كون F اندول F يبقى بتدمش البرهان في اتجاهين بدي 
+
+694
+01:20:58,880 --> 01:21:03,220
+أفترض واحد صحيح و أروح أثبت مين و بعد هيك أمشي
+
+695
+01:21:03,220 --> 01:21:08,160
+العملية العكسية مش هيك أخذتو في مبادئ رياضية صح 
+
+696
+01:21:08,160 --> 01:21:12,240
+ولا لا طب احنا أخذنا في مبادئ رياضية ثلاث طرق
+
+697
+01:21:12,240 --> 01:21:21,770
+للبراهين Direct Pro برهان مباشر و إيش كمان؟ و بعد
+
+698
+01:21:21,770 --> 01:21:29,130
+ال direct إيش فيه كمان؟ contrapositive يعني
+
+699
+01:21:29,130 --> 01:21:33,710
+اتجاهها بدي أعطيني اتجاه الثاني بأخذ معاكوس أو ال
+
+700
+01:21:33,710 --> 01:21:36,870
+negation لذا الطرف بدي أعطيني ال negation للطرف
+
+701
+01:21:36,870 --> 01:21:41,370
+الثاني أو ال contradiction بقول أثبت كذا بقول 
+
+702
+01:21:41,370 --> 01:21:46,260
+أفترض مش هيك ذا قدني إلى تناقض يبقى أفراني غلط
+
+703
+01:21:46,260 --> 01:21:49,840
+وعكس و هو الصح مش هي الطرق الطرق الطرق اللي
+
+704
+01:21:49,840 --> 01:21:53,720
+اتعلمتها من بدأ اللي درسوا مبادئ رياضية لكن اللي
+
+705
+01:21:53,720 --> 01:21:57,700
+خلصوا بس سنة أولى لسه ما أخذوش مبادئ هذا لطلبة 
+
+706
+01:21:57,700 --> 01:22:02,140
+العلوم والترابية بس طلبة الهندسة مالهمش الشغلة
+
+707
+01:22:02,140 --> 01:22:06,570
+تمام طيب ما علينا أنا بس مجرد معلومة بقولها اللي
+
+708
+01:22:06,570 --> 01:22:10,430
+بيحب يستفيد منها يستفيد منها احنا الآن بدنا نمشي
+
+709
+01:22:10,430 --> 01:22:14,210
+direct flow بدنا نمسك طرفه و نوصل لهوين للطرف
+
+710
+01:22:14,210 --> 01:22:22,210
+الثاني فبجي بقول assume افترض that سميلي هذه
+
+711
+01:22:22,210 --> 01:22:26,550
+المعادلة اللي هي رقم واحد assume that the
+
+712
+01:22:26,550 --> 01:22:32,950
+differential equation one is exact
+
+713
+01:22:37,250 --> 01:22:42,370
+اللي هو مين؟ المطلوب الأول هذي exact if and only
+
+714
+01:22:42,370 --> 01:22:47,950
+if هذيك بفضل أفرض هذي انها exact يبقى شو بدي أثبت؟
+
+715
+01:22:47,950 --> 01:22:52,650
+بدي أثبت هذي صح ولا لأ؟ يبقى مدام فرضت أن المعادلة
+
+716
+01:22:52,650 --> 01:22:57,430
+هذي exact بدي أحاول أثبت اللي عندنا هذي طبعًا؟
+
+717
+01:22:57,430 --> 01:23:05,500
+بقوله then أو هذي exact then there exist حسب
+
+718
+01:23:05,500 --> 01:23:10,260
+التعريف هي التعريف لسه فوق ممكن نمسحه there exist
+
+719
+01:23:10,260 --> 01:23:19,860
+a function psi of x و y تساوي constant c such that
+
+720
+01:23:19,860 --> 01:23:25,420
+بحيث أن بحيث
+
+721
+01:23:25,420 --> 01:23:31,770
+أن دي psi يساوي كذا such that الدى ابساى
+
+722
+01:23:34,990 --> 01:23:44,950
+الدي اب ساي بده يساوي اللي هو M DX زائد ال N في DY
+
+723
+01:23:44,950 --> 01:23:49,430
+بده اختصار فبدل ما أقول M of X و Y يبقى بده أقول M
+
+724
+01:23:49,430 --> 01:23:54,030
+دوري و N of X و Y يبقى أنه معروف ضمن أن M are
+
+725
+01:23:54,030 --> 01:24:01,850
+functions of X and Y طيب الآن برجع لمين لكالكلسي
+
+726
+01:24:01,850 --> 01:24:10,300
+but و لكن دي إبصي يساوي partial إبصي على partial x
+
+727
+01:24:10,300 --> 01:24:17,400
+في dx زائد partial إبصي على partial y في dy هذا من
+
+728
+01:24:17,400 --> 01:24:24,810
+كل قلصية طيب هذه هي هذه يبقى شو بس تنتج أن المعامل
+
+729
+01:24:24,810 --> 01:24:28,190
+اللي مضروب في DX بدي يساوي نفس المعامل و المعامل 
+
+730
+01:24:28,190 --> 01:24:32,850
+اللي مضروب في Y بدي يساوي نفس المعامل يبقى ال M
+
+731
+01:24:32,850 --> 01:24:42,690
+تساوي partial A بSi على partial X and ال N تساوي 
+
+732
+01:24:42,690 --> 01:24:45,870
+partial A بSi على partial Y
+
+733
+01:24:50,130 --> 01:24:56,110
+احنا نريد أن نثبت أن تفاضل M بالنسبة ل Y يساوي
+
+734
+01:24:56,110 --> 01:25:01,440
+تفاضل N بالنسبة ل M طب أنا M هيها عندي سنة موجودة بدي 
+
+735
+01:25:01,440 --> 01:25:07,540
+أروح أفاضلها بالنسبة لمن؟ إلى Y فبروح بقوله اللي هو
+
+736
+01:25:07,540 --> 01:25:15,220
+تفاضل ال M بالنسبة إلى Y يساوي بدي أروح أفاضل هذي
+
+737
+01:25:15,220 --> 01:25:21,940
+بالنسبة إلى Y يبقى تفاضل بالنسبة إلى Y ل M مين ال
+
+738
+01:25:21,940 --> 01:25:27,480
+M اللي partial of Psi by partial X يعني يا بنات
+
+739
+01:25:27,480 --> 01:25:36,240
+كأنه بدي أجيب المشتقة الثانية لإبصاي طب كويس ها دي 
+
+740
+01:25:36,240 --> 01:25:43,180
+هها اللي هي partial square إبصاي على partial y
+
+741
+01:25:43,180 --> 01:25:48,060
+partial x سؤال
+
+742
+01:25:49,440 --> 01:25:55,000
+بقدر أبدل ال X مكان ال Y و ال Y مكان ال X اللي 
+
+743
+01:25:55,000 --> 01:25:59,760
+درسه Calculus C بنقدر؟ بنقدر في حالة واحدة لو كانت 
+
+744
+01:25:59,760 --> 01:26:05,940
+الدالة دالة متصلة لو كانت متصلة بنقدر نبدل
+
+745
+01:26:05,940 --> 01:26:10,480
+without problems بس لو ما كانتش متصلة يبقى الشغل هذا
+
+746
+01:26:10,480 --> 01:26:17,540
+غلط طيب تعالوا نرجع لهنا بقولي هدول are continuous
+
+747
+01:26:17,540 --> 01:26:23,240
+صحيح ولا لأ؟ يبقى بقدر أبدل و أنا مرتاح ما عنديش 
+
+748
+01:26:23,240 --> 01:26:28,260
+مشكلة يبقى هذا الكلام بقدر أقول يساوي partial
+
+749
+01:26:28,260 --> 01:26:37,450
+square على partial x partial y because of the
+
+750
+01:26:37,450 --> 01:26:40,490
+continuity
+
+751
+01:26:40,490 --> 01:26:47,790
+بسبب الاتصال طيب هذا الكلام يساوي بدي أعيده مرة 
+
+752
+01:26:47,790 --> 01:26:52,070
+ثانية partial على partial x خليكي برا ببقى اللي
+
+753
+01:26:52,070 --> 01:26:57,980
+عندي partial fy على partial y فال partial of y على 
+
+754
+01:26:57,980 --> 01:27:04,360
+partial of y يعني أنه يبقى 
+
+755
+01:27:04,360 --> 01:27:10,120
+partial n على partial x أظن و هو المطلوب يبقى هاي
+
+756
+01:27:10,120 --> 01:27:13,460
+يثبتنا أن partial M على partial Y يساوي 100 partial
+
+757
+01:27:13,460 --> 01:27:16,540
+N على partial X هذا هو الاثبات السهل لهذا الجزء
+
+758
+01:27:16,540 --> 01:27:22,400
+السهل هذا بدي يعطينا أن partial M على partial Y
+
+759
+01:27:22,400 --> 01:27:31,320
+يساوي partial N على partial X هذا الاتجاه الأول نجي
+
+760
+01:27:31,320 --> 01:27:35,040
+للاتجاه الثاني الاتجاه الثاني بنروح نقول 
+
+761
+01:27:35,040 --> 01:27:45,210
+conversely العكس بدي افترض أن هذا الصحيح و بناء عليه 
+
+762
+01:27:45,210 --> 01:27:51,210
+أثبت أن المعادلة هذه مالها exact يعني إذا وجدت لاجي
+
+763
+01:27:51,210 --> 01:27:55,450
+function بيساوي و فيكساوي و يساوي يكون أصلًا تحققها
+
+764
+01:27:55,450 --> 01:27:59,530
+بيصير كلامي صح وبالتالي بيكون برهنة النظرية تمامًا
+
+765
+01:27:59,700 --> 01:28:08,000
+يبقى باجي بقوله assume افترض أن ال partial m by
+
+766
+01:28:08,000 --> 01:28:19,480
+partial y يساوي partial n by partial x وبالتالي
+
+767
+01:28:19,480 --> 01:28:24,800
+بنحاول نثبت أن المعادلة هذه مالها معادلة exact
+
+768
+01:28:24,800 --> 01:28:31,480
+بقوله كويس مشان هيك بروح افترض في عندي دالة من عندي 
+
+769
+01:28:31,480 --> 01:28:42,020
+بروح بقوله let phi of x y be a function such that
+
+770
+01:28:42,020 --> 01:28:53,660
+بحيث أن ال m تساوي partial phi على partial x بروح
+
+771
+01:28:53,660 --> 01:28:59,800
+من عندي، بختار دالة، بحيث الدالة هذه مشتقتها
+
+772
+01:28:59,800 --> 01:29:06,950
+بالنسبة ل X، بدي يعطينا مين؟ ال M تبعت مين؟ تبعت
+
+773
+01:29:06,950 --> 01:29:10,750
+المعادلة التفاضلية لأن اللي بدي أثبت إن ما لها 
+
+774
+01:29:10,750 --> 01:29:17,950
+exact يبقى أنا جبت ال M بدلالة مين بدلالة ال five
+
+775
+01:29:17,950 --> 01:29:23,330
+مظبوط ولا لأ؟ بدي أروح أجيب ال N بدلالة ال five
+
+776
+01:29:23,330 --> 01:29:38,760
+يبقى هنا بقوله الآن want to find N in terms of Phi
+
+777
+01:29:38,760 --> 01:29:45,800
+طبعًا مش Phi هذا اللي فيها الخاوية Phi of XY يعني
+
+778
+01:29:45,800 --> 01:29:50,680
+يعني بنروح أجيب ال N بدلالة ال term اللي عندنا هنا
+
+779
+01:29:50,680 --> 01:29:56,260
+بقوله والله كويس نبدأ بهذه أنا عندي المعلومة هذه
+
+780
+01:29:57,430 --> 01:30:02,150
+ماذا رأيكم؟ بتروح أفاضلها بالنسبة إلى Y لأنه 
+
+781
+01:30:02,150 --> 01:30:07,170
+ما عطني condition بدي أستفيد منه يبقى باجي بقوله
+
+782
+01:30:07,170 --> 01:30:15,850
+الآن partial M by partial Y تساوي partial على 
+
+783
+01:30:15,850 --> 01:30:22,850
+partial Y ل M من ال M؟ partial في على partial اكس
+
+784
+01:30:22,850 --> 01:30:32,270
+يبقى partial في على partial اكس يعني هذه بقدر أقول
+
+785
+01:30:32,270 --> 01:30:40,830
+partial square في by partial y partial x الآن ال M
+
+786
+01:30:40,830 --> 01:30:45,840
+هذه اتفاقنا يا بنات انها مالها continuous يبقى بقدر
+
+787
+01:30:45,840 --> 01:30:51,400
+أبدل هذه صحيح؟ يعني هذا الكلام بدي يساوي partial
+
+788
+01:30:51,400 --> 01:31:01,020
+على partial X ل partial Phi على partial Y يبقى هذا
+
+789
+01:31:01,020 --> 01:31:04,780
+because of
+
+790
+01:31:04,780 --> 01:31:09,140
+the continuity
+
+791
+01:31:13,550 --> 01:31:23,170
+الحين هذه but و لكن partial m على partial y يساوي 
+
+792
+01:31:23,170 --> 01:31:28,270
+partial n على partial x صحيح ولا لأ؟ هذا موضع هيئة
+
+793
+01:31:29,080 --> 01:31:33,420
+طب partial M على partial Y جيبته هيك يبقى هدول
+
+794
+01:31:33,420 --> 01:31:40,120
+بيساووا بعض يبقى هذا بدي يعطينا انه مهم ان partial
+
+795
+01:31:40,120 --> 01:31:47,480
+على partial X ل partial Phi على partial Y يساوي 
+
+796
+01:31:47,480 --> 01:31:57,020
+partial N على partial X طب إيش رأيك؟ بدي أنقل هذه
+
+797
+01:31:57,020 --> 01:32:04,150
+على الشكة الثانية إيش بيصير؟ بيصير partial N على 
+
+798
+01:32:04,150 --> 01:32:10,310
+partial X ناقص partial على partial X ل partial Phi
+
+799
+01:32:10,310 --> 01:32:18,830
+على partial Y يساوي قداش Zero أليس هذا معناه اشتقاق
+
+800
+01:32:18,830 --> 01:32:26,210
+الجزئين بالنسبة ل X؟ مشتقة المجموع الجبري لدالتين
+
+801
+01:32:26,210 --> 01:32:31,930
+يساوي المجموع الجبري لمشتقتيهما يعني هذا بقدر أكتبه 
+
+802
+01:32:31,930 --> 01:32:39,530
+على الشكل التالي partial على partial X لل N ناقص
+
+803
+01:32:39,530 --> 01:32:47,700
+partial Phi على partial Y يساوي Zero لو تدخلها تصير 
+
+804
+01:32:47,700 --> 01:32:52,200
+مشتقة الأولى ناقص مشتقة الثانية، ما ساويتش شيء، أنا
+
+805
+01:32:52,200 --> 01:32:58,240
+بدي أسألكم السؤال التالي، الحين لو جات لي دالة
+
+806
+01:32:58,240 --> 01:33:04,440
+و فاضلتها بالنسبة لما تغير و طلعت تفاضلها يساوي صفر، إيش 
+
+807
+01:33:04,440 --> 01:33:10,590
+معناها؟ الدالة هذه ثابتة يعني هذه الدالة ثابتة 
+
+808
+01:33:10,590 --> 01:33:16,390
+بالنسبة لمين؟ ل X يعني هذه الدالة ليست function في X
+
+809
+01:33:16,390 --> 01:33:23,150
+و إنما مقدار ثابت يبقى هذه function في Y ليش؟ لأن
+
+810
+01:33:23,150 --> 01:33:28,170
+ثابت عندي من أن عندي متغيرين إذا عند X بعتبر Y
+
+811
+01:33:28,170 --> 01:33:33,590
+ثابت صح ولا لأ؟ لأن ده اللي في المتغيرين يبقى هذا 
+
+812
+01:33:33,590 --> 01:33:44,360
+معناه أن الآن ناقص partial phi على partial y is a
+
+813
+01:33:44,360 --> 01:33:52,860
+function of y only يعني ما هيش function في x لأن
+
+814
+01:33:52,860 --> 01:33:59,580
+تفاضلها بالنسبة ل x يساوي zero يبقى هذا اللي بينغسيه 
+
+815
+01:33:59,580 --> 01:34:04,060
+لما فاضلته بالنسبة ل X طالع Zero معناته الدالة بين
+
+816
+01:34:04,060 --> 01:34:12,100
+القوسين ليست function في X يبقى function في Y يبقى
+
+817
+01:34:12,100 --> 01:34:24,080
+بناء عليه LN ناقص partial Fi على partial Y يبقى F
+
+818
+01:34:24,080 --> 01:34:28,430
+of Y يعني ده لا في why فقط 
+
+819
+01:34:39,030 --> 01:34:43,970
+طيب ما دام دالة في Y بدي أجيب ال N
+
+861
+01:39:26,280 --> 01:39:34,540
+الاختصاص
+
+862
+01:39:37,490 --> 01:39:44,090
+أنا عنده الآن شرط ال exactness المعادلة Mdx + N Dy
+
+863
+01:39:44,090 --> 01:39:49,290
+بيساوي 0 is exact إذا كان تفاضل M بالنسبة إلى Y
+
+864
+01:39:49,290 --> 01:39:56,150
+إذا كان تفاضل M بالنسبة إلى Y يساوي تفاضل N بالنسبة 
+
+865
+01:39:56,150 --> 01:39:57,950
+إلى X
+
+866
+01:40:00,170 --> 01:40:05,890
+هيبقى البرهان بيحصل في اتجاهين، افترض
+
+867
+01:40:05,890 --> 01:40:10,450
+أن المعادلة الأصلية اللي عندنا هذه is exact معناته
+
+868
+01:40:10,450 --> 01:40:14,050
+لازم ألاقي function ψ of x و y بيبقى تساوي
+
+869
+01:40:14,050 --> 01:40:22,290
+constant بحيث أن d ψ هي M dx زائد N dy لكن من
+
+870
+01:40:22,290 --> 01:40:26,950
+كالكولاس، ال d ψ هي تفاضل ψ بالنسبة لـ x dx زي تفاضل
+
+871
+01:40:26,950 --> 01:40:33,380
+ψ بالنسبة لـ y. أقارن بين المعادلتين، بجيب ال M بدلالة
+
+872
+01:40:33,380 --> 01:40:36,560
+الإبصاى و بجيب ال N بدلالة الإبصاى
+
+873
+01:40:40,640 --> 01:40:44,400
+أنا أو بدي أوصل ال condition اللي هو partial M على
+
+874
+01:40:44,400 --> 01:40:47,540
+partial Y سواء partial. هذا اللي بدي أوصله، بقوله
+
+875
+01:40:47,540 --> 01:40:53,020
+كويس، احنا عندنا M مطلوب تفاضلها بالنسبة إلى Y، إذا
+
+876
+01:40:53,020 --> 01:40:57,120
+حاجة فاضلها دي بالنسبة لما M إلى Y يبقى بيصير
+
+877
+01:40:57,120 --> 01:41:01,020
+partial M على partial Y سواء partial على partial Y
+
+878
+01:41:01,020 --> 01:41:05,480
+لـ partial Y على partial X. هذه تعتبر المشتقة
+
+879
+01:41:05,480 --> 01:41:11,640
+الثانية. بدي أبدل الـ X و الـ Y مكان بعض لإن دالة
+
+880
+01:41:11,640 --> 01:41:16,060
+continuous معتنية في نص النظرية، يفجأة هذا الكلام
+
+881
+01:41:16,060 --> 01:41:20,160
+بده يساوي، بعد ما بدلت بده أرجعها مرة تانية، أخد ال
+
+882
+01:41:20,160 --> 01:41:23,200
+partial على partial X برا و ده ال partial يبصيا
+
+883
+01:41:23,200 --> 01:41:26,500
+على partial Y. ال partial يبصيا على partial Y هيه ب
+
+884
+01:41:26,500 --> 01:41:30,560
+N. يفجأة بدي أشيل و أكتب بدله N. يفجأة بديت partial M
+
+885
+01:41:30,560 --> 01:41:34,640
+على partial Y، وصلت إلى مين؟ partial N على partial X
+
+886
+01:41:34,640 --> 01:41:39,080
+وهو المطلوب الأول. المطلوب التاني بدنا نمشي في
+
+887
+01:41:39,080 --> 01:41:43,520
+الاتجاه المعاكس، فقلنا conversely, assume that 
+
+888
+01:41:43,520 --> 01:41:49,140
+افترضنا ال condition هذا موجود الآن بدنا نحاول
+
+889
+01:41:49,140 --> 01:41:53,820
+نثبت أن الدالة اللي عندنا هذه مالها exact. تعريف ال
+
+890
+01:41:53,820 --> 01:41:58,360
+exact هذي بقول عن exact إذا قدرت ألاقي function ψ
+
+891
+01:41:58,360 --> 01:42:01,780
+of x و y بده يساوي constant بحيث partial ψ على
+
+892
+01:42:01,780 --> 01:42:05,720
+partial x بده يساوي ال M و partial ψ على partial y
+
+893
+01:42:05,720 --> 01:42:10,720
+بده يساوي ال N أو d ψ بده يساوي المعادلة اللي
+
+894
+01:42:10,720 --> 01:42:16,930
+عندنا هذي. بقوله بسيطة، فترضنا هذى. فرقت من عندي دالة
+
+895
+01:42:16,930 --> 01:42:22,530
+بحيث ال M يساوي مشتقة هذه الدالة بالنسبة لمن؟ ال X
+
+896
+01:42:22,530 --> 01:42:28,710
+يبقى أنا فرقت عند ال M بدلالة مشتقة دالة Φ بذهب
+
+897
+01:42:28,710 --> 01:42:35,950
+هشوف ما هو شكل ال N بالنسبة لمن؟ نسبة ال Φ، بقولك
+
+898
+01:42:35,950 --> 01:42:40,070
+كويس، أنت عندك المعلومة هذه، بدي تساوي partial N على
+
+899
+01:42:40,070 --> 01:42:44,350
+partial X. خدت المعلومة هذه. أنا شيلت ال M و حطيت
+
+900
+01:42:44,350 --> 01:42:48,230
+قيمتها بالفرض اللي أنا فرضه، صارت المعادلة بالشكل
+
+901
+01:42:48,230 --> 01:42:53,910
+هذا، عملت Champion XY بسبب ال continuity صار عند
+
+902
+01:42:53,910 --> 01:43:00,590
+مين؟ partial M على A. هذا الشرط الأساسي. هذا معناه أن
+
+903
+01:43:00,590 --> 01:43:05,220
+القيمة اللي حصلت عليها هنا بدأت تساوي partial N على
+
+904
+01:43:05,220 --> 01:43:09,420
+partial X. وديت هذه على الشجة التانية و أخدت partial
+
+905
+01:43:09,420 --> 01:43:15,240
+على partial X لمشتقة ما بينها القوسين، طلعته إيش؟
+
+906
+01:43:15,240 --> 01:43:19,780
+برا. طب طلع هذا قد إيش؟ يساوي Zero، معناته هذه
+
+907
+01:43:19,780 --> 01:43:24,660
+constant function بالنسبة لمين؟ ال X. طب لما يكون
+
+908
+01:43:24,660 --> 01:43:28,400
+عندي ال constant function بالنسبة ل X يبقى هذه ال
+
+909
+01:43:28,400 --> 01:43:33,440
+constant function بتكون دالة في Y. يبقى روحت قلت هذه
+
+910
+01:43:33,440 --> 01:43:37,500
+هي عبارة عن دلة في مين؟ في y. نجلت هذه على الشكل
+
+911
+01:43:37,500 --> 01:43:42,760
+التاني، وبالتالي جبت ال N بدلالة Φ على الشكل اللي
+
+912
+01:43:42,760 --> 01:43:46,780
+عندنا هذا. بعد ذلك، روحت مسكت المعادلة هذه وعوّضت
+
+913
+01:43:46,780 --> 01:43:52,050
+فيها، امشي امشي، وصلت لحد هنا، باجي بقول هذه المكان
+
+914
+01:43:52,050 --> 01:43:56,950
+كلها مشتقة ال Φ و هذه بقدر أكتبها على الشكل التالي
+
+915
+01:43:56,950 --> 01:44:02,790
+اللي عندنا، مشتقة و مشتقة، أخدت المشتقة الكلية لهم
+
+916
+01:44:02,790 --> 01:44:06,750
+اللي بقى إن جثمين، بده يسميها إبصاى و هذه المعادلة
+
+917
+01:44:06,750 --> 01:44:10,750
+أصلاً تساوي zero، فسميتها ب zero. حل المعادلة هذه
+
+918
+01:44:10,750 --> 01:44:14,630
+بالتكامل اللي بقى بالتكامل بتعطي الميان constant c
+
+919
+01:44:14,630 --> 01:44:18,430
+بقى إبصاى و بيكسوي يساوي constant c. هذا معناته أن
+
+920
+01:44:18,430 --> 01:44:23,070
+المعادلة هذه مالها exact differential equation
+
+921
+01:44:23,070 --> 01:44:29,230
+تمام؟ طب الآن بدنا بس شوية أمثلة على هذا الموضوع.
+
+922
+01:44:29,230 --> 01:44:35,530
+حدا فيكم بيتسأل أي سؤال هنا؟ آه في البرهان في أي
+
+923
+01:44:35,530 --> 01:44:39,770
+نقطة مش فاهمينه، مش واضح إيه و أخري في أي تساؤل؟ 
+
+924
+01:44:39,770 --> 01:44:46,130
+ندخل للأمثلة. التكتيك اللي طبعنا هنا بنا نتابعه بنا
+
+925
+01:44:46,130 --> 01:44:50,910
+نفاضل و نكامل كمان الآن زي ما هتشوفي في الأسئلة
+
+926
+01:44:50,910 --> 01:44:54,790
+example
+
+927
+01:44:54,790 --> 01:45:02,490
+one, solve
+
+928
+01:45:02,490 --> 01:45:13,690
+the differential equation اللي هو 2xy تربيع
+
+929
+01:45:13,690 --> 01:45:30,350
+2xy تربيع زائد 2y زائد اللي هو 2x تربيع y زائد 
+
+930
+01:45:30,350 --> 01:45:38,110
+2x في ال y prime بده يساوي مين؟ Zero. و هذه المعادلة
+
+931
+01:45:38,110 --> 01:45:44,980
+نحلها و خلصنا. مكافئة طيب بدي أحطها على ال standard
+
+932
+01:45:44,980 --> 01:45:50,560
+form اللي عندنا هذا بنات عشان أقدر أشتغل بدي دالة
+
+933
+01:45:50,560 --> 01:45:54,880
+مضروبة في dx و دالة تانية مضروبة في dy، بجي بقوله
+
+934
+01:45:54,880 --> 01:46:00,580
+هذه أصلاً y prime هي عبارة عن مين؟ عبارة عن dy على 
+
+935
+01:46:00,580 --> 01:46:05,440
+dx. صحيح ولا لأ؟ يبقى معنا هذا الكلام بدي أضرب كله
+
+936
+01:46:05,440 --> 01:46:16,850
+في dx، يبقى هنا solution. السؤال هو 2 x y 
+
+937
+01:46:16,850 --> 01:46:25,050
+تربيع زائد 2y dx زائد 2x تربيع 
+
+938
+01:46:25,050 --> 01:46:34,410
+y زائد 2x dy بده يساوي 0. الآن هذه 
+
+939
+01:46:34,410 --> 01:46:39,330
+إيش تعتبر M؟ و هذه شو تعتبر N؟
+
+940
+01:46:41,640 --> 01:46:46,820
+طبعاً تفاضل ال M بالنسبة إلى Y
+
+941
+01:46:59,430 --> 01:47:06,530
+تفاضله بالنسبة لـ Y يساوي كم؟ 4XY 
+
+942
+01:47:06,530 --> 01:47:12,810
+بالنسبة لـ X يساوي
+
+943
+01:47:12,810 --> 01:47:19,550
+كم؟ 4XY زائد 2. تفاضل بالنسبة ال X  X تربيع
+
+944
+01:47:19,550 --> 01:47:23,790
+تفاضل بـ 2X مع 2 بيصير 4XY. Y تفاضلها
+
+945
+01:47:23,790 --> 01:47:29,330
+بـ 2، طلعت نفس النتيجة مظبوط. يبقى هذا الكلام بده
+
+946
+01:47:29,330 --> 01:47:34,430
+يعطينا تفاضل ال M بالنسبة لـ Y يساوي تفاضل ال N
+
+947
+01:47:34,430 --> 01:47:40,630
+بالنسبة لـ X. هذا معناه هذا اللي هي المعادلة 1
+
+948
+01:47:40,630 --> 01:47:46,870
+أحدث الشكل اللي عندنا هنا differential equation
+
+949
+01:47:46,870 --> 01:47:55,390
+when is exact. هذا بده يعطينا there exist a 
+
+950
+01:47:55,390 --> 01:48:05,130
+function ψ of x y such that بحيث أن partial ψ
+
+951
+01:48:05,130 --> 01:48:15,400
+على partial x يساوي ال M، من ال M هيها. يساوي ال M
+
+952
+01:48:15,400 --> 01:48:24,620
+يساوي ال N يساوي ال Y يساوي ال Y يساوي ال Y يساوي
+
+953
+01:48:24,620 --> 01:48:29,700
+ال Y يساوي
+
+954
+01:48:29,700 --> 01:48:33,260
+ال M
+
+955
+01:48:33,260 --> 01:48:36,160
+يساوي ال M يساوي ال Y يساوي ال M يساوي ال Y يساوي
+
+956
+01:48:36,160 --> 01:48:36,220
+ال Y يساوي ال M يساوي ال Y يساوي ال M يساوي ال Y
+
+957
+01:48:36,220 --> 01:48:36,960
+يساوي ال M يساوي ال Y يساوي ال M يساوي ال Y يساوي
+
+958
+01:48:36,960 --> 01:48:37,000
+ال M يساوي ال M يساوي ال Y يساوي ال M يساوي ال M
+
+959
+01:48:37,000 --> 01:48:37,060
+يساوي ال M يساوي ال M يساوي ال M يساوي ال M يساوي
+
+960
+01:48:37,060 --> 01:48:39,720
+يساوي ال M يساوي ال M يساوي ال M يساوي. بصراحة أنا مش
+
+961
+01:48:39,720 --> 01:48:43,880
+عارف شكلها، لكن عارف مشتقتها، إذا بقدر أكملها،
+
+962
+01:48:43,880 --> 01:48:49,120
+يبقى بنات هذه لو بده أكملها، بده يكملها بالنسبة لمن؟
+
+963
+01:48:49,120 --> 01:48:54,420
+لـ X، تكاملها بالنسبة لـ X، هذي السهل. و هذه السهل، لو بده
+
+964
+01:48:54,420 --> 01:48:58,600
+يكمل هذه، تكاملها بالنسبة لـ وايها، هذه السهل، يبقى
+
+965
+01:48:58,600 --> 01:49:04,000
+أي واحدة فيهم بتصدق، بس اللحظة الثابتة التكامل،
+
+966
+01:49:04,000 --> 01:49:06,680
+يبقى الآن بقوله by integration
+
+967
+01:49:09,560 --> 01:49:14,920
+بدي اروح أكمل، يبقى بيصير عندك، بدي أكمل هذه يا بنات
+
+968
+01:49:14,920 --> 01:49:25,580
+بدي أكمل بالنسبة لمن؟ لـ X، يبقى هذه لـ X إيش بيصير؟ X
+
+969
+01:49:25,580 --> 01:49:32,480
+تربيع على 2، بتروح 2 مع 2 بيظل X تربيع Y
+
+970
+01:49:32,480 --> 01:49:37,980
+تربيع زائد 2Y. بدي أكملها بالنسبة لـ X، هذا كله يعتبر
+
+971
+01:49:37,980 --> 01:49:46,450
+مقدار ثابت يبقى بيصير 2y في x زائد constant مش
+
+972
+01:49:46,450 --> 01:49:52,070
+ال constant العادي رقم، ال constant function في عكس
+
+973
+01:49:52,070 --> 01:49:55,270
+الدالة اللي كملت بالنسبة لكسي، يبقى function في
+
+974
+01:49:55,270 --> 01:50:03,470
+مين؟ في y. يبقى زائد function of y. الآن بدي أجيب قد إيش
+
+975
+01:50:03,470 --> 01:50:09,390
+قيمة F of Y، مشان هيك بدي اروح أشتق هذه الدالة بالنسبة
+
+976
+01:50:09,390 --> 01:50:17,390
+لمين؟ لـ Y. يبقى هذا بدي يعطينا partial Epsilon على
+
+977
+01:50:17,390 --> 01:50:22,530
+partial Y يساوي بالفعل هذه بالنسبة لـ Y يا بنات، يبقى
+
+978
+01:50:22,530 --> 01:50:33,830
+2 X تربيع Y يبقى 2 X تربيع Y. يبقى 2 X
+
+979
+01:50:33,830 --> 01:50:41,350
+يبقى زائد 2X زائد F prime of Y
+
+980
+01:50:44,380 --> 01:50:51,720
+صح ولا لا؟ صح. يكوا كمان مرة، احنا قلنا بنلاقي
+
+981
+01:50:51,720 --> 01:50:56,780
+function ψ of x y بحيث أنه تفاضل ψ بالنسبة لـ x
+
+982
+01:50:56,780 --> 01:51:02,720
+يساوي ال M. تفاضل ψ بالنسبة لـ y يساوي ال N. روحت على
+
+983
+01:51:02,720 --> 01:51:08,140
+هذه، كملتها بالنسبة لـ x، حصلت على الدالة هذه. طب بدي
+
+984
+01:51:08,140 --> 01:51:12,760
+أشتقها، روحت اشتقتها. طب ما هي مشتقتها هي اللي فوق؟
+
+985
+01:51:20,620 --> 01:51:27,720
+بستنتج أن 2X تربيع Y زائد 2X يساوي 
+
+986
+01:51:27,720 --> 01:51:33,800
+2X تربيع Y زائد 2X زائد F prime of Y
+
+987
+01:51:34,600 --> 01:51:39,360
+أصلاً لو جبت هذا عند هذا بيروح، و لو جبت هذا عند هذا
+
+988
+01:51:39,360 --> 01:51:45,220
+بيروح. هذا بده يعطينا أن F prime of y بده يساوي قد إيش؟
+
+989
+01:51:45,220 --> 01:51:50,800
+هذا الحين function في مين؟ في متغير واحد، صح ولا لأ؟
+
+990
+01:51:50,800 --> 01:51:59,280
+يبقى هذا معناه أن F of y بده يساوي قد إيش؟ c1. يبقى
+
+991
+01:51:59,280 --> 01:52:03,180
+بيروح بقوله ها the solution
+
+992
+01:52:21,280 --> 01:52:27,220
+كل هذا الكلام بده يساوي C
+
+993
+01:52:29,710 --> 01:52:33,970
+لأن قلنا there exists a function of ψ of x و y
+
+994
+01:52:33,970 --> 01:52:44,290
+حط لي تساوي C2 يلا هذه تساوي C2. طيب إيش رأيك؟ بدي 
+
+995
+01:52:44,290 --> 01:52:46,190
+أجيب C1 and C2؟
+
+996
+01:53:06,110 --> 01:53:12,870
+هذا هو حل المعادلة التفاضلية.
+
+997
+01:53:14,840 --> 01:53:16,620
+لسه لازمنا في نفس ال section. 
diff --git a/PL9fwy3NUQKwa8ZDfSFGn6H8xVFLzqmCZC/euAOHAsWFbk_postprocess.srt b/PL9fwy3NUQKwa8ZDfSFGn6H8xVFLzqmCZC/euAOHAsWFbk_postprocess.srt
new file mode 100644
index 0000000000000000000000000000000000000000..6e5c9354fb240e7200730381f02519151ea4a953
--- /dev/null
+++ b/PL9fwy3NUQKwa8ZDfSFGn6H8xVFLzqmCZC/euAOHAsWFbk_postprocess.srt
@@ -0,0 +1,3988 @@
+1
+00:00:10,560 --> 00:00:14,900
+بسم الله الرحمن الرحيمأخر حاجة كنا نتكلم فيها
+
+2
+00:00:14,900 --> 00:00:18,760
+المرة اللي فاتت هي ال homogenous equations يعني
+
+3
+00:00:18,760 --> 00:00:24,500
+المعادلات المتجانسة و قولنا كل معادلة تفاضلية من
+
+4
+00:00:24,500 --> 00:00:30,120
+الرتبة الأولى بنقدر نكتبها بدلالة Y على X أو X على
+
+5
+00:00:30,120 --> 00:00:35,160
+Y نسميها homogenous differential equation و أخدنا
+
+6
+00:00:35,160 --> 00:00:41,540
+على ذلك مثال واحدة وإلى يكون المثال الأخير يبقى
+
+7
+00:00:41,540 --> 00:00:49,720
+نمرة Bهو سؤال ستة وتلاتين من الكتاب بيقول X تربية
+
+8
+00:00:49,720 --> 00:01:01,060
+زائد تلاتة XY زائد Y تربية كله في DX ناقص X تربية
+
+9
+00:01:01,060 --> 00:01:07,850
+في DY بده يساوي كده؟ بده يساوي زي وايبنحل المعادلة
+
+10
+00:01:07,850 --> 00:01:11,930
+اللي عندنا هذه المعادلة لسه بدأ ببحث هل هي
+
+11
+00:01:11,930 --> 00:01:15,230
+homogeneous ولا non homogeneous differential
+
+12
+00:01:15,230 --> 00:01:20,670
+equation بقوله بسيطة هذه المعادلة لو جينا كتبناها
+
+13
+00:01:20,670 --> 00:01:29,030
+بطريقة أخرى على الشكل التالييبقى لو روحت كتبتها x
+
+14
+00:01:29,030 --> 00:01:34,590
+تربيع dy نجلنا هذه وين؟ على الشجة التانية بدها
+
+15
+00:01:34,590 --> 00:01:41,730
+تساوي اللي هو x تربيع زائد تلاتة x y زائد تلاتة x
+
+16
+00:01:41,730 --> 00:01:50,950
+y زائد y تربيع dxبادروح أجسم الطرفين على x تربيع
+
+17
+00:01:50,950 --> 00:01:58,710
+على dx يبقى المعادلة دي بيصير dy by dx يسوى x
+
+18
+00:01:58,710 --> 00:02:05,950
+square زائد تلاتة xy زائد y square كله على x
+
+19
+00:02:05,950 --> 00:02:11,780
+squareهذا يجب ان يساوي يجب ان اوزع ال bus على
+
+20
+00:02:11,780 --> 00:02:16,660
+المقام يبقى x تربيه على x تربيه يبقى كم؟ بواحد
+
+21
+00:02:16,660 --> 00:02:23,180
+زائد تلاتة x على x تربيه يبقى x في المقام و y في
+
+22
+00:02:23,180 --> 00:02:31,300
+ال bus يبقى y على x شكل ان هذا y تربيه على x تربيه
+
+23
+00:02:31,300 --> 00:02:37,660
+هي عبارة عن y على x لكل تربيهيبقى زي ما انتوا
+
+24
+00:02:37,660 --> 00:02:41,720
+شايفين يا بنات المعادلة صارت dy على dx constant
+
+25
+00:02:41,720 --> 00:02:46,500
+constant تاني في y على x y على x الكل تربية هذا
+
+26
+00:02:46,500 --> 00:02:51,280
+يعني انه قدرنا نكتب المعادلة الأصلي اللي عندنا
+
+27
+00:02:51,280 --> 00:02:56,700
+بدلال الدالة اللي هو المتغير فيها يعتبر y على x
+
+28
+00:02:56,700 --> 00:03:00,580
+يبقى دي شو اسمها homogeneous differential equation
+
+29
+00:03:00,580 --> 00:03:08,120
+يبقى دي سميها اللي هي المعادلة رقم واحديبقى so the
+
+30
+00:03:08,120 --> 00:03:15,440
+differential equation one is homogeneous
+
+31
+00:03:17,670 --> 00:03:21,410
+ما دام homogeneous يبقى الأن بدي أمشي بطريقة الحل
+
+32
+00:03:21,410 --> 00:03:26,350
+تبع المثال الأخير في المحاضرة الماضية فبجي بقول
+
+33
+00:03:26,350 --> 00:03:33,210
+put V تساوي Y على X هذا بدي يعطينا ان Y بدي يساوي
+
+34
+00:03:33,210 --> 00:03:41,370
+XV لو جينا اشتقنا هيبقى DY على DX بدي يساوي V زائد
+
+35
+00:03:41,370 --> 00:03:47,380
+X في DV على DXالان بدي اجي الى المعادلة اللى هندى
+
+36
+00:03:47,380 --> 00:03:52,260
+بدي اشيل dy على dx واحط قمةها بدللة ال variable
+
+37
+00:03:52,260 --> 00:03:58,220
+الجديد اللى هو v يبقى المعادلة هدى وتصبح على الشكل
+
+38
+00:03:58,220 --> 00:04:06,400
+التالي v زائد x في dv على dx يساوي الطرف اليمين
+
+39
+00:04:06,400 --> 00:04:14,800
+واحد زائد تلاتة v زائد v تربيعبدي اكتب المعادلة
+
+40
+00:04:14,800 --> 00:04:21,100
+هذه على الشكل التالي X في D V على DX يساوي ال V
+
+41
+00:04:21,100 --> 00:04:27,160
+هبقى نفسي بضيف سالب V للطرفين يبقى هذه مع السلامة
+
+42
+00:04:27,160 --> 00:04:35,680
+وهذه بظل واحد زائد اتنين Vزائد V تربيع أو ممكن
+
+43
+00:04:35,680 --> 00:04:42,220
+اكتب على الشكل التالي ال X في DV على DX يسوى V
+
+44
+00:04:42,220 --> 00:04:54,740
+زائد واحد لكل تربيعطيب بنحاول نفصل المتغيرات يبقى
+
+45
+00:04:54,740 --> 00:05:01,180
+بناء عليه هاد بيصير DV على V زائد واحد لكل تربيع
+
+46
+00:05:01,180 --> 00:05:08,560
+يسوى DX على X يبقى هاد صارت separable equation
+
+47
+00:05:08,560 --> 00:05:14,120
+يبقى فصل ده منهم المتغيرات يبقى هاد separable
+
+48
+00:05:14,120 --> 00:05:16,080
+equation
+
+49
+00:05:17,240 --> 00:05:24,240
+مش هنحل المعادلة هذي بروح بكامل الطرفين يبقى تكامل
+
+50
+00:05:24,240 --> 00:05:27,800
+الطرف الشمال حد فيك بتعرف تقولي شو تكامل هذا
+
+51
+00:05:27,800 --> 00:05:35,680
+المقدار هذا V
+
+52
+00:05:35,680 --> 00:05:41,040
+زائد واحد لكل تربية مش V تربية زائد واحد V زي
+
+53
+00:05:41,040 --> 00:05:42,780
+تكامل واحد على X تربية
+
+54
+00:05:46,990 --> 00:05:51,130
+قداش تكامل وحدة ال X تربية؟
+
+55
+00:05:53,610 --> 00:05:56,850
+بس واحدة واحدة تحكي احنا سئلنا اللغة اللي .. شو
+
+56
+00:05:56,850 --> 00:06:03,070
+اسمك انتي؟ براء براءت من الله ورسوله الى الذين
+
+57
+00:06:03,070 --> 00:06:08,190
+عهدتم من المشركين عارفة صورتاش هذي؟ التوبة التوبة
+
+58
+00:06:08,190 --> 00:06:11,190
+يبقى مشان ان توب عليك من الكلمتين اللي قلتيهم في
+
+59
+00:06:11,190 --> 00:06:15,820
+الأول بالنجداش تكامل واحد عليك استربياسائل بواحد
+
+60
+00:06:15,820 --> 00:06:20,060
+على X ممتاز جدا هذه كمان اللي بينجو سين من الدرجة
+
+61
+00:06:20,060 --> 00:06:24,400
+الأولى ومعامل V هو الواحد الصحيح يبقى تكاملة سالب
+
+62
+00:06:24,400 --> 00:06:30,380
+واحد على V زائد واحد يبقى بالتكامل بصير هذه سالب
+
+63
+00:06:30,380 --> 00:06:35,700
+واحد على V زائد واحدة تكمل الطرف الشمال الطرف
+
+64
+00:06:35,700 --> 00:06:41,280
+اليمين Lin absolute value ل X زائد constant C
+
+65
+00:06:41,280 --> 00:06:49,040
+وليكن على سبيل المثال C1طيب ممكن نضرب الطرفين في
+
+66
+00:06:49,040 --> 00:06:53,680
+إشارة سالب يبقى لو ضربنا في إشارة سالب بصير واحد
+
+67
+00:06:53,680 --> 00:07:01,200
+على V زائد واحد يسوى لن absolute value ل X بإشارة
+
+68
+00:07:01,200 --> 00:07:11,080
+سالب سالب C1الان ممكن سالب C1 احطها بمين ب C مرة
+
+69
+00:07:11,080 --> 00:07:16,780
+واحدة يبقى هذا الكلام بدي اعطيك انه واحد على شو
+
+70
+00:07:16,780 --> 00:07:23,320
+رايك V هذه مش هي عبارة عن Y على X زائد واحد يساوي
+
+71
+00:07:23,320 --> 00:07:31,020
+سالب لل absolute value لك زائد C والC يساوي سالب
+
+72
+00:07:31,020 --> 00:07:37,780
+C1طيب هذه يا بنات ممكن اوحد المقامات ل X وجمع
+
+73
+00:07:37,780 --> 00:07:45,540
+بيصير X على Y زائد X زائد Lin absolute value ل X
+
+74
+00:07:45,540 --> 00:07:50,900
+بدل سواء قداش Constancy يبقى هذا ال solution تبع
+
+75
+00:07:50,900 --> 00:07:56,570
+المعادلة اللي عندناعليك بنتهي هذا ال section انا
+
+76
+00:07:56,570 --> 00:08:02,890
+بروح ناخد المسائل التالت يبقى exercises اتنين
+
+77
+00:08:02,890 --> 00:08:12,070
+اتنين المسائل من واحد الى تمانية ال odd ومن تسعة
+
+78
+00:08:12,070 --> 00:08:19,230
+الى عشرين برضه ال odd بس بدنا ناخد part
+
+79
+00:08:24,480 --> 00:08:31,860
+تلات مطاليب بيكفين A وC و بعدها من واحد و تلاتين
+
+80
+00:08:31,860 --> 00:08:37,300
+لغاية تمانية و تلاتين كذلك الاد
+
+81
+00:09:11,810 --> 00:09:16,470
+بنجي ل section اتنين تلاتة وبنقول الله سهل عليك ما
+
+82
+00:09:16,470 --> 00:09:21,790
+انتش لازم منه وبنروح على section اتنين اربع وزيه
+
+83
+00:09:21,790 --> 00:09:26,630
+لكن بدنا نروح على اسئلة section اتنين اربع هتطلع
+
+84
+00:09:26,630 --> 00:09:33,630
+موضوعين داخل ال exercises كويسة؟ بقى هدول اتنين
+
+85
+00:09:33,630 --> 00:09:38,550
+مهمين فبدنا نروح حتى واحد مهم و التاني يعنيفبدنا
+
+86
+00:09:38,550 --> 00:09:45,450
+نروح ناخد النقطتين هدول فباجي بيقوله in the
+
+87
+00:09:45,450 --> 00:09:48,530
+exercises
+
+88
+00:09:48,530 --> 00:09:57,770
+of section اتنين اربعة there is two subjects
+
+89
+00:10:05,690 --> 00:10:11,430
+يبقى فيها موضوعين الموضوع الأول اله very important
+
+90
+00:10:11,430 --> 00:10:19,930
+اله Bernoulli equation معادلة بيرنولي والموضوع
+
+91
+00:10:19,930 --> 00:10:26,170
+الثاني اله discontinuous
+
+92
+00:10:26,170 --> 00:10:29,110
+coefficients
+
+93
+00:10:35,560 --> 00:10:41,200
+بنبدأ بالموضوع الأول بيرنالي
+
+94
+00:10:41,200 --> 00:10:44,700
+equation
+
+95
+00:11:06,700 --> 00:11:10,960
+سيكشن اتنين اربعة كاتب الفرق بين ال linear و ال
+
+96
+00:11:10,960 --> 00:11:15,340
+non-linear differential equations احنا المرة اللي
+
+97
+00:11:15,340 --> 00:11:18,860
+فات قولنا لكم ما هو شكل ال linear first order
+
+98
+00:11:18,860 --> 00:11:22,540
+differential equation قولنا لكم y prime زي ال P of
+
+99
+00:11:22,540 --> 00:11:28,500
+T في Y بده يسوى G of T اي معادلة على غير هذا الشكل
+
+100
+00:11:28,500 --> 00:11:32,860
+تعتبر ايه؟ non-linear differential equation وبشرط
+
+101
+00:11:32,860 --> 00:11:34,240
+ان ال P of T
+
+102
+00:11:47,070 --> 00:11:53,050
+المعاملة P of T وG of T ممكن مايكونوش دوال متصلة
+
+103
+00:11:53,080 --> 00:11:56,780
+طبعا هنقيم مثال على الـ Discontinuous coefficients
+
+104
+00:11:56,780 --> 00:12:02,380
+وكيف هنحل هذا النوع من المسائل وبردولي هي non
+
+105
+00:12:02,380 --> 00:12:07,260
+homogeneous differential equation بس بنحولها إلى
+
+106
+00:12:07,260 --> 00:12:11,620
+من إلى homogeneous أو إلى linear differential
+
+107
+00:12:11,620 --> 00:12:15,200
+equation يعني ال non linear differential equation
+
+108
+00:12:15,200 --> 00:12:20,110
+بنحولها إلى linear differential equationبدنا نعرف
+
+109
+00:12:20,110 --> 00:12:25,210
+ما هو الشكل العام لها وبعد هيك كيف بدنا نحل هذا
+
+110
+00:12:25,210 --> 00:12:32,050
+النوع من المسائل فبجي بقول له ده differential
+
+111
+00:12:32,050 --> 00:12:40,170
+equation ل Y prime زائد P of T في ال Y
+
+112
+00:12:57,010 --> 00:13:03,790
+يبقى هذه معادلة ماهياش معادلة خطيةلكن في بعض
+
+113
+00:13:03,790 --> 00:13:09,010
+الحالات الخاصة ممكن تكون هذه المعادلة معادلة خطية،
+
+114
+00:13:09,010 --> 00:13:14,950
+شو الحالات الخاصة؟ فبجي بقوله لو كانت ال in تساوي
+
+115
+00:13:14,950 --> 00:13:28,650
+zero يبقى then the above equation asY'زايد P of T
+
+116
+00:13:28,650 --> 00:13:35,290
+في ال Y بيساوي G of T في Y أُس 0 Y أُس 0 في قداش؟
+
+117
+00:13:35,290 --> 00:13:39,770
+بواحد يبقى صلة المواد على شكل .. مين هي هذه؟ هذه
+
+118
+00:13:39,770 --> 00:13:43,270
+ال linear اللي كنا بنحل فيها المرة اللي فاتت يبقى
+
+119
+00:13:43,270 --> 00:13:52,890
+هذه linearالان لو كانت كذلك ال N تساوي واحد يبقى
+
+120
+00:13:52,890 --> 00:13:58,790
+the above equation is Y prime زائد P of T في ال Y
+
+121
+00:13:58,790 --> 00:14:07,220
+بدي ساوي ال G of T في Y أس واحد يبقى بYممكن اعيد
+
+122
+00:14:07,220 --> 00:14:13,860
+كتابة المعادلة هذه على الشكل التالي y prime زائد
+
+123
+00:14:13,860 --> 00:14:17,880
+بصير
+
+124
+00:14:17,880 --> 00:14:27,200
+p of t ناقص g of t كله في ال y يبقى
+
+125
+00:14:27,200 --> 00:14:31,560
+صارة y prime زائد function في y يبقى صارة g of t
+
+126
+00:14:33,160 --> 00:14:39,160
+يبقى هذه كذلك linear differential equation يبقى
+
+127
+00:14:39,160 --> 00:14:43,760
+هذا ماعناش علاقة فيها إذا مشان تبقى المعادلة على
+
+128
+00:14:43,760 --> 00:14:50,740
+هذا الشكل ممنوع تكون لا بزيرو ولا بواحد تمام؟ وهي
+
+129
+00:14:50,740 --> 00:14:56,020
+هذه اللي بدنا نبدأ نشتغلها ونحلها فبعدين بقوله
+
+130
+00:15:00,640 --> 00:15:03,560
+إن لا تساوي واحد
+
+131
+00:15:08,300 --> 00:15:19,700
+السؤال هو Y' زائد P of T في Y بده يسوى G of T في Y
+
+132
+00:15:19,700 --> 00:15:27,700
+to the derivative N ومسميه للمعادل Head Star is a
+
+133
+00:15:27,700 --> 00:15:32,720
+nonlinear
+
+134
+00:15:32,720 --> 00:15:34,980
+differential equation
+
+135
+00:15:53,240 --> 00:16:00,160
+ممكن نحوّلها to a linear
+
+136
+00:16:08,790 --> 00:16:16,190
+order differential equation ممكن نحولها إلى معادلة
+
+137
+00:16:16,190 --> 00:16:26,230
+خطية من الرتبة الأولى as follow كتالي شوفوا
+
+138
+00:16:26,230 --> 00:16:27,450
+كيف هنحولها يا بنات
+
+139
+00:16:31,350 --> 00:16:36,510
+بدي اعمل خطوطين بس بكون حولتها الى linear الخطوة
+
+140
+00:16:36,510 --> 00:16:42,370
+الاولى الان بدي بتطلع على Y هذه المضربة في من في
+
+141
+00:16:42,370 --> 00:16:49,130
+GRT بضرب المعادلة هذه في Y مرفوع لنفس الأس هذا بس
+
+142
+00:16:49,130 --> 00:16:58,790
+بإشارة سالب يبقى الخطوة الاولى بقوله multiply both
+
+143
+00:16:58,790 --> 00:17:00,710
+sides
+
+144
+00:17:02,720 --> 00:17:14,680
+of equation star by y to the minus n we get يصير
+
+145
+00:17:14,680 --> 00:17:21,140
+المعادلة على الشكل التالي y to the minus n في y
+
+146
+00:17:21,140 --> 00:17:32,200
+primeP of T في ال Y to the power واحد ناقص N يساوي
+
+147
+00:17:32,200 --> 00:17:42,080
+ال G of T مرة
+
+148
+00:17:42,080 --> 00:17:42,480
+تانية
+
+149
+00:17:51,920 --> 00:17:57,020
+الخطوة الأولى هي أن أضرب المعادلة star في main في
+
+150
+00:17:57,020 --> 00:18:01,960
+y to the minus n يعني بدي أضربها في نفس ال term
+
+151
+00:18:01,960 --> 00:18:07,820
+لأن هذا بس بإشارة سالب الأسترةيبقى بيصير عندك y to
+
+152
+00:18:07,820 --> 00:18:13,640
+the minus n في ال y prime هيها الآن هذي y أس واحد
+
+153
+00:18:13,640 --> 00:18:20,100
+بيجيها y to the minus n بيصير y to the واحد minus
+
+154
+00:18:20,100 --> 00:18:24,200
+ال n و ال P of T كما هي الطرف اليمين بيصير y أس
+
+155
+00:18:24,200 --> 00:18:30,360
+zeroبواحد اللي مافضلش عندي إلا G of T انتهينا من
+
+156
+00:18:30,360 --> 00:18:35,420
+الخطوة الأولى بدنا نجي للخطوة التانية هذا بناهات
+
+157
+00:18:35,420 --> 00:18:40,380
+ال term اللي عندنا هذا بناخده ع شجة و بنروح و
+
+158
+00:18:40,380 --> 00:18:47,460
+بنحطه بمتغير جديد يبقى باجي بقول ال pot حطنا V
+
+159
+00:18:47,460 --> 00:18:54,720
+تساوي Y to the one minus Mو بعد هيك اشتق يبقى لو
+
+160
+00:18:54,720 --> 00:19:02,260
+اشتقنا بصير عندي V' يساوي الأس في Y مرفوعة لنفس
+
+161
+00:19:02,260 --> 00:19:09,080
+الأس مطروح من واحد في مشتقة ال Y itself اليمين Y'
+
+162
+00:19:10,350 --> 00:19:16,050
+مش ذاكرين لما كنا نقول مشتقة جوس مرفوع لأس الأس في
+
+163
+00:19:16,050 --> 00:19:19,630
+الجوس مرفوع لنفس الأس ماتروح من واحد فيه مشتقة
+
+164
+00:19:19,630 --> 00:19:24,630
+مداخل جوس احنا ماشتقش بالنسبة ل Y نشتق بالنسبة ل X
+
+165
+00:19:24,630 --> 00:19:28,310
+لو كنا بنشتق بالنسبة ل Y اللي قلنا على طول خط واحد
+
+166
+00:19:28,310 --> 00:19:33,810
+ناقص Y و Y أس ناقص N و سكتنا لكن كنا بنشتق بالنسبة
+
+167
+00:19:33,810 --> 00:19:39,250
+ل X بقول الأس واحد ناقص Nفي y مرفوعة لنفس الأس
+
+168
+00:19:39,250 --> 00:19:43,950
+مطروح من هو يبقى y أس ناقص in في مشتقة ال y itself
+
+169
+00:19:43,950 --> 00:19:50,310
+اللي هي main ل y prime تمام؟ طيب بطلع هنا ال term
+
+170
+00:19:50,310 --> 00:19:55,780
+اللي أنها ده هيهبس فيش في واحد ناقص N واحد ناقص N
+
+171
+00:19:55,780 --> 00:20:01,700
+هذا رقم مظبوط يبقى بنقدر نجسم عليه يبقى بيصير واحد
+
+172
+00:20:01,700 --> 00:20:08,560
+على واحد ناقص N في ال V' يساوي Y أس ناقص N في ال
+
+173
+00:20:08,560 --> 00:20:14,730
+Y'إذا بنجي ناخد المعلومة هذه اللي اشتغلناها هنا و
+
+174
+00:20:14,730 --> 00:20:18,770
+نجي نعوّبه بقوايا في المعادلة اللي عندنا يبقى هذا
+
+175
+00:20:18,770 --> 00:20:26,310
+ال term بشيله كله واحد ناقص N في ال V prime زائد P
+
+176
+00:20:26,310 --> 00:20:34,070
+of T هذا سميته V بده يساوي من G of Tهذا الرقم
+
+177
+00:20:34,070 --> 00:20:38,170
+مكتوب على شكل كسر ممكن اتخلص من الكسر لو ضربت
+
+178
+00:20:38,170 --> 00:20:44,110
+الطرفين كله في مين؟ في 1 ناقص N يبقى المعادلة هذه
+
+179
+00:20:44,110 --> 00:20:54,310
+V' زائد 1 ناقص N في P of T في V بيستوي 1 ناقص N في
+
+180
+00:20:54,310 --> 00:21:02,150
+G of Tالان المقدار بين القوسين هذا رقم بغير شكل
+
+181
+00:21:02,150 --> 00:21:06,610
+المعادلة المعادلة هذه صارت Linear ولا لا؟ يبقى
+
+182
+00:21:06,610 --> 00:21:10,770
+المعادلة الأصلية ان الـ Star تحولت إلى Linear
+
+183
+00:21:10,770 --> 00:21:14,930
+First Order Differential Equation يبقى هذه صارت
+
+184
+00:21:14,930 --> 00:21:25,390
+Linear First Order Differential Equation ذات
+
+185
+00:21:26,940 --> 00:21:37,100
+can be solved ممكن الحلها as before كما كنا بنحلها
+
+186
+00:21:37,100 --> 00:21:44,060
+قبل ذلك في section اتنين واحد sold as before in
+
+187
+00:21:44,060 --> 00:21:53,460
+section اتنين واحد اه طب احنا الأن خدنا اربع شغلات
+
+188
+00:21:55,080 --> 00:21:59,140
+أربع شغلات المرة اللي فاتت واليوم الشغل الأول ال
+
+189
+00:21:59,140 --> 00:22:02,140
+linear first order differential equation الشغل
+
+190
+00:22:02,140 --> 00:22:07,640
+التاني non linear و حولتها إلى linear يبقى شغل تام
+
+191
+00:22:07,640 --> 00:22:12,380
+التالتة separable equations الرابعة ال homogeneous
+
+192
+00:22:12,380 --> 00:22:16,580
+differential equation اللي حولناها ل separable
+
+193
+00:22:16,580 --> 00:22:22,710
+differential equations تمام؟ و لسه ما نشوفتمام؟
+
+194
+00:22:22,710 --> 00:22:29,090
+يبقى هذه صارت Linear بقدر أحلها كما كان من قبل حد
+
+195
+00:22:29,090 --> 00:22:34,010
+فيكوا يقولها أي تساؤل هنا في الجزء النظري علما أنه
+
+196
+00:22:34,010 --> 00:22:38,070
+لما ندى نشتغل عمل الآن أمثلة هنمشي بنفس ال tactic
+
+197
+00:22:38,070 --> 00:22:42,610
+اللى اتبعنا هنا نفس ال tactic هذا بضبط مش هنغيره
+
+198
+00:22:42,610 --> 00:22:46,730
+هو هو بعينه يعني اللى اشتغلنا النظري هروح نشتغله
+
+199
+00:22:46,730 --> 00:22:50,890
+عمل الآن حد فيكوا يقولها أي تساؤل؟
+
+200
+00:22:52,020 --> 00:22:58,400
+ندخل الى الأمثلة يبقى
+
+201
+00:22:58,400 --> 00:23:10,920
+المثال الأول يبقى example one solve
+
+202
+00:23:10,920 --> 00:23:12,360
+the differential equation
+
+203
+00:23:18,170 --> 00:23:21,390
+حل المعادلة التفاضلية
+
+204
+00:23:48,790 --> 00:23:54,610
+طيب هل هذه المثلة هي linear first order
+
+205
+00:23:54,610 --> 00:23:58,310
+differential equation؟ لكن هذه الشكل هي شكل بردوني
+
+206
+00:23:58,310 --> 00:24:05,090
+بس مش مرتبةأحنا بنقول هذه المعادلة y prime زائد P
+
+207
+00:24:05,090 --> 00:24:08,670
+of P of P of P of P of P of P of P of P of P of P
+
+208
+00:24:08,670 --> 00:24:09,630
+of P of P of P of P of P of P of P of P of P of P
+
+209
+00:24:09,630 --> 00:24:10,950
+of P of P of P of P of P of P of P of P of P of P
+
+210
+00:24:10,950 --> 00:24:14,310
+of P of P of P of P of P of P of P of P of P of P
+
+211
+00:24:14,310 --> 00:24:14,670
+of P of P of P of P of P of P of P of P of P of P
+
+212
+00:24:14,670 --> 00:24:14,790
+of P of P of P of P of P of P of P of P of P of P
+
+213
+00:24:14,790 --> 00:24:14,870
+of P of P of P of P of P of P of P of P of P of P
+
+214
+00:24:14,870 --> 00:24:16,230
+of P of P of P of P of P of P of P of P of P of P
+
+215
+00:24:16,230 --> 00:24:22,940
+of P of P of P of Pوالواجهة و التربية و التكييف
+
+216
+00:24:22,940 --> 00:24:27,200
+خلّيها على الشجرة إذا هذه ههه هي برنامج بس مش
+
+217
+00:24:27,200 --> 00:24:32,220
+مرتبة بدنا نروح نعيد ترتيبها إذا لو روحنا نعيدنا
+
+218
+00:24:32,220 --> 00:24:36,940
+ترتيبها بنقدر نكتبها على الشكل التالي فبجي بقوله
+
+219
+00:24:36,940 --> 00:24:37,200
+لا
+
+220
+00:24:41,910 --> 00:24:52,930
+T تربيع DY على DT ناقص T في Y بده يساوي Y تربيع
+
+221
+00:24:55,350 --> 00:25:00,950
+ناقص Y تربيه موافقين يبقى ناقص Y تربيه كويس صحيين
+
+222
+00:25:00,950 --> 00:25:06,510
+تمام طيب بعد هيك بدرح اجسم على T تربيه او اضرب
+
+223
+00:25:06,510 --> 00:25:11,030
+الطرفين في واحد على T تربيه وهذا ممكن لان T
+
+224
+00:25:11,030 --> 00:25:14,730
+greater than zero لا يمكن ان تسوى ال zero يبقى
+
+225
+00:25:14,730 --> 00:25:21,130
+بيصير المعادلة على الشكل التالي Dy على Dtناقص واحد
+
+226
+00:25:21,130 --> 00:25:29,130
+على T في ال Y يسوى ناقص واحد على T تربيع في ال Y
+
+227
+00:25:29,130 --> 00:25:34,070
+تربيع واضح ان المعادلة على الشكل اللي عندنا تمام
+
+228
+00:25:34,070 --> 00:25:39,470
+يبقى هذه Bernoulli equation يبقى هذه اللي هي من
+
+229
+00:25:39,470 --> 00:25:47,410
+Bernoulli equation يبقى هذه معادلة Bernoulliطبعا
+
+230
+00:25:47,410 --> 00:25:55,950
+زي ما تشايفين non linear هدى non linear يبقى اش
+
+231
+00:25:55,950 --> 00:26:00,790
+بدى اعمل الها بدروح احولها الى linear first order
+
+232
+00:26:00,790 --> 00:26:05,050
+differential equation يبقى بنضرب الطرفين في مين في
+
+233
+00:26:05,050 --> 00:26:11,810
+Y أس ناقصي اتنين ها Y هدى بس بأس مخالف للأس تبعها
+
+234
+00:26:11,810 --> 00:26:15,030
+يبقى بجي بقوله هنا multiply
+
+235
+00:26:23,290 --> 00:26:28,930
+بتصير المعادلة على الشكل التالي y-2
+
+236
+00:26:36,950 --> 00:26:42,410
+هنا Y يجيني Y اص ناقص اتنين بيصير Y اص ناقص واحد
+
+237
+00:26:42,410 --> 00:26:51,030
+يبقى في Y اص ناقص واحد يساوي ناقص واحد على T تربيع
+
+238
+00:26:51,750 --> 00:26:56,430
+بعد ذلك بروح نعمل التعويض اللي قلنا عليها فوق هي
+
+239
+00:26:56,430 --> 00:27:02,470
+في الامش هنعملها لمن؟ لدلة جديدة يبقى بروح بقول له
+
+240
+00:27:02,470 --> 00:27:14,340
+put V تسوى من Y أسالب واحدنشتقها يبقى V' يساوي
+
+241
+00:27:14,340 --> 00:27:24,040
+سالب Y أساليب 2 في ماين؟ في Y' كويس يبقى صار عندي
+
+242
+00:27:24,040 --> 00:27:33,200
+ناقص V' بده يساوي Y أس minus 2 في Y' اللي هو ماين؟
+
+243
+00:27:33,200 --> 00:27:37,660
+ال term اللي عندنا هذايبقى بتصبح المعادلة على
+
+244
+00:27:37,660 --> 00:27:47,220
+الشكل التالي هذه سالب V prime وهنا سالب واحد على T
+
+245
+00:27:47,220 --> 00:27:55,020
+في V بده يساوي سالب واحد على T تربيع لو ضربنا
+
+246
+00:27:55,020 --> 00:28:01,230
+المعادلة كلها في سالب واحديبقاش بصير المعادلة يبقى
+
+247
+00:28:01,230 --> 00:28:09,210
+V' زائد واحد على T في ال V بدي الساوي قداش واحد
+
+248
+00:28:09,210 --> 00:28:14,910
+على T تربيع المعادلة هذه يا بنات شو صارت؟ Linear
+
+249
+00:28:15,340 --> 00:28:20,020
+يبقى حولنا المعادلة من non linear first order
+
+250
+00:28:20,020 --> 00:28:25,440
+differential equation إلى ال linear first order
+
+251
+00:28:25,440 --> 00:28:30,760
+differential equation وبالتالي بدنا نروح نحل
+
+252
+00:28:30,760 --> 00:28:35,260
+المعادلة هذه زي ما كنا بنحل المرة الماضية في
+
+253
+00:28:35,260 --> 00:28:36,260
+section 2
+
+254
+00:28:39,450 --> 00:28:47,310
+بعد ذلك نراجع ال section نتأكد
+
+255
+00:28:47,310 --> 00:28:51,850
+إن هذا المعامل هو واحد صحيح، الحمد لله جاهز، يبقى
+
+256
+00:28:51,850 --> 00:28:57,200
+بدنا نروح نجيب عامل التكامل اللي هو الـMRTفبعدين
+
+257
+00:28:57,200 --> 00:29:03,760
+بقوله لـ Mu of T بدي يسوي E أستكامل، ان ذاكر به P
+
+258
+00:29:03,760 --> 00:29:11,860
+of T DT E أستكامل P of T هو المعامل تبع ال V اللي
+
+259
+00:29:11,860 --> 00:29:21,040
+عندنا، اللي هو 1 على Tيبقى 1 على T DT E أسلن T
+
+260
+00:29:21,040 --> 00:29:27,400
+بقول شبس ال value ان T greater than 0 موجبة ماعناش
+
+261
+00:29:27,400 --> 00:29:33,620
+مشكلة يبقى هذا الكلام بدي أقين قداشبعد ذلك هذه
+
+262
+00:29:33,620 --> 00:29:37,820
+المعادلة اللي صارت linear أبنات سامحها للمعادلة
+
+263
+00:29:37,820 --> 00:29:44,240
+اسم قبلها ما سامناش يبقى سامحها للمعادلة أس تار
+
+264
+00:29:44,240 --> 00:29:52,140
+يبقى باجي بقوله multiply question
+
+265
+00:29:59,110 --> 00:30:09,800
+نحصل على ما يأتييبقى مصير T في ال V Prime زائد V
+
+266
+00:30:09,800 --> 00:30:17,920
+بده ساوي واحد على T فقط ل V تمام؟ هذه بده اعيد
+
+267
+00:30:17,920 --> 00:30:24,160
+صياغتها مرة تانية هذه بنات باجي بقول هي عبارة عن T
+
+268
+00:30:24,160 --> 00:30:31,270
+عامل التكامل في ال V لكل Primeلو جت اشتقت يدك حصل
+
+269
+00:30:31,270 --> 00:30:36,730
+ضرب دلتين بتعطيك هذا بالضبط تماما يبقى بده تساوي
+
+270
+00:30:36,730 --> 00:30:44,850
+مين؟ واحد على T يبقى لو روحنا كاملنا بصير T في ال
+
+271
+00:30:44,850 --> 00:30:53,870
+V بده يساوي تكامل واحد على T DT زائد constant C1
+
+272
+00:30:53,870 --> 00:30:54,790
+مثلا
+
+273
+00:30:56,980 --> 00:31:07,040
+يبقى بصير T في ال V يساوي لمة T زائد constant C1
+
+274
+00:31:10,190 --> 00:31:20,070
+نقسم كله على T يبقى لو جسمنا على T بصير V تساوي لن
+
+275
+00:31:20,070 --> 00:31:25,530
+T و الله خلّيها زائد C و خلاصنا زي ما هي لن T زائد
+
+276
+00:31:25,530 --> 00:31:31,550
+C خلّيها C زي ما هي مقسمة على مين؟ مقسمة كلها على
+
+277
+00:31:31,550 --> 00:31:39,660
+T احنا جداش فرضين V هناY أوص ناقص واحد يعني هذا
+
+278
+00:31:39,660 --> 00:31:45,980
+كله بد يساوي Y أوص ناقص واحد يعني معنى هذا الكلام
+
+279
+00:31:45,980 --> 00:31:55,200
+ان واحد على Y يساوي ln T زائد C على مين على T طب
+
+280
+00:31:55,200 --> 00:32:00,500
+انا مابدي واحد على Y بدي Y اتصل يبقى بنجلبالمعادلة
+
+281
+00:32:00,500 --> 00:32:07,920
+يبقى بصير الحل عندنا Y يساوي T على لن T زائد
+
+282
+00:32:07,920 --> 00:32:13,240
+constant C هذا هو حل المعادلة التفاضلية اللي عندنا
+
+283
+00:32:13,240 --> 00:32:17,960
+يبقى المعادلة كانت non-linear حولناها إلى linear
+
+284
+00:32:17,960 --> 00:32:24,840
+روحنا حلينا المعادلة اللي عندنا هذه ناخد كمان مثال
+
+285
+00:32:24,840 --> 00:32:27,720
+example 2
+
+286
+00:32:36,550 --> 00:32:48,470
+solve the initial value problem الهي من dy على dt
+
+287
+00:32:48,470 --> 00:32:59,190
+زائد y يساوي واحد على y أص نص و ال y عند ال zero
+
+288
+00:32:59,190 --> 00:33:02,770
+بده يساوي كده اش بده يساوي أربع
+
+289
+00:33:39,280 --> 00:33:43,340
+نرجع لسؤالنا مرة تانية هذه معادلة زي اللي قبل
+
+290
+00:33:43,340 --> 00:33:46,860
+بصراحة حط عليها شرق المرة اللي فات قلنا لو
+
+291
+00:33:46,860 --> 00:33:49,860
+المعادلة حط عليها شرق بنسميها initial value
+
+292
+00:33:49,860 --> 00:33:56,260
+problem طيب بنعيد كتابة المعادلة مرة تانية يبقى
+
+293
+00:33:56,260 --> 00:34:03,360
+المعادلة هي عبارة عن y prime زائد y يسوى y أس ناقص
+
+294
+00:34:03,360 --> 00:34:09,780
+نصمصبوح؟ طلعناها فوق، ممتاز جدا، يعني يا بنات
+
+295
+00:34:09,780 --> 00:34:16,160
+القسط اللي هنا ده، ليس بالضرورة أن يكون عددا صحيحا
+
+296
+00:34:16,670 --> 00:34:20,070
+فى المثال او لما نحطينا المعادلة الصينية اللى كانت
+
+297
+00:34:20,070 --> 00:34:25,070
+ال star قولنا why to the power n ولم اقول ان ال n
+
+298
+00:34:25,070 --> 00:34:29,850
+is an integer يعني انتجر ماشي كسري ماشي ماعنا
+
+299
+00:34:29,850 --> 00:34:34,690
+مشكلة في هذه الحالة يبقاش ما يكون يكون الأس ماعنا
+
+300
+00:34:34,690 --> 00:34:39,590
+مشكلة المهم يكون real number طبعا طيب صارت بالشكل
+
+301
+00:34:39,590 --> 00:34:43,960
+اللى عندنا هذا إذا هذه هي مين معادلة مين؟معادلة
+
+302
+00:34:43,960 --> 00:34:48,820
+Bernoulli على طول الخط جاهزة مشان هيك لو هدى
+
+303
+00:34:48,820 --> 00:34:53,780
+بنقوله Bernoulli question دغري يبقى هدى Bernoulli
+
+304
+00:34:53,780 --> 00:34:59,610
+questionيبقى معادلة Bernoulli مشان هيك بروح بضرب
+
+305
+00:34:59,610 --> 00:35:05,870
+الطرفين في مين في Y أص نص بالموجة يبقى بجي بقوله
+
+306
+00:35:05,870 --> 00:35:15,070
+بصير Y أص نص في Y prime زائد Y أص تلاتة على اتنين
+
+307
+00:35:15,070 --> 00:35:20,930
+بده يساوي قداش؟ بده يساوي واحدطبعا يبقى صبت
+
+308
+00:35:20,930 --> 00:35:24,810
+المعادلة على الشكل اللي عندنا هنا بعد هيك بدي أجي
+
+309
+00:35:24,810 --> 00:35:29,690
+ال term هذا كله و أحطه بمين ب variable جديد اللي
+
+310
+00:35:29,690 --> 00:35:37,990
+هو V يبقى لو جيت حطيت ال V تسوي Y أس 3 على 2 بدي
+
+311
+00:35:37,990 --> 00:35:47,980
+أشتقها يبقى ال V prime يسوي 3 على 2 Y أس كده؟و احد
+
+312
+00:35:47,980 --> 00:35:53,560
+و نص بدأ اطلع منها واحد بضال نص في من؟ في ال Y
+
+313
+00:35:53,560 --> 00:35:57,940
+prime طب انا بديش تلاتة على اتنين بديش اشوف خلجتها
+
+314
+00:35:57,940 --> 00:36:01,920
+تلاتة على اتنين يبقى بعض الورد برافين في جداش في
+
+315
+00:36:01,920 --> 00:36:09,320
+طلتينيبقى هاي تلتين V Prime يساوي Y أص نص في ال Y
+
+316
+00:36:09,320 --> 00:36:14,340
+Prime يبقى Y أص نص في ال Y Prime هي طلعت ليه تلتين
+
+317
+00:36:14,340 --> 00:36:21,300
+V Prime يبقى صارت تلتين V Prime زاد هذا عطيته
+
+318
+00:36:21,300 --> 00:36:28,610
+بكبير V يساوي واحدلو ضربت كله في تلاتة على اتنين
+
+319
+00:36:28,610 --> 00:36:35,130
+مش هنخلي معامل V' هو واحد صحيح يبقى بصير عندنا V'
+
+320
+00:36:35,890 --> 00:36:42,450
+زي تلاتة على اتنين V يساوي كباش تلاتة على اتنين،
+
+321
+00:36:42,450 --> 00:36:46,630
+إيش رأيك في المعادلة هذه؟ linear يبقى صرعة
+
+322
+00:36:46,630 --> 00:36:50,670
+المعادلة هذه linear first order differential
+
+323
+00:36:50,670 --> 00:36:55,510
+equation يبقى بده حلها زي ما كنت بحل قبليبدأ
+
+324
+00:36:55,510 --> 00:37:01,350
+بالضرورة أن أحضر له مين؟ الـ Mu of T E أُس تكامل
+
+325
+00:37:01,350 --> 00:37:06,270
+جداش الـ P of T هنا بنات؟ كل نص أنت اللي هو تلاتة
+
+326
+00:37:06,270 --> 00:37:13,450
+على اتنين فبجي بقوله تكامل تلاتة على اتنين DT يبقى
+
+327
+00:37:13,450 --> 00:37:19,630
+E أُس تلاتة على اتنين كله في مين؟ في T يعني كأنه
+
+328
+00:37:19,630 --> 00:37:27,160
+تماما E أُس تلاتة T على اتنينبجي للمعادلة اللي هان
+
+329
+00:37:27,160 --> 00:37:31,880
+هذه وبضربها كلها في مين؟ في ال integrating factor
+
+330
+00:37:31,880 --> 00:37:36,620
+يبقى باجي بقول سميلي هذه اللي سمناها linear هذه
+
+331
+00:37:36,620 --> 00:37:42,840
+سميها اللي هي ال star يبقى باجي بقول multiply
+
+332
+00:37:42,840 --> 00:37:46,820
+equation
+
+333
+00:37:47,460 --> 00:37:53,860
+أس تار باي ال integrating factor E أس تلاتة T على
+
+334
+00:37:53,860 --> 00:37:59,320
+اتنين we get E
+
+335
+00:37:59,320 --> 00:38:07,820
+أس تلاتة على اتنين T في ال V prime زائد تلاتة على
+
+336
+00:38:07,820 --> 00:38:15,060
+اتنين E أس تلاتة T على الاتنين Vبدي يساوي تلاتة
+
+337
+00:38:15,060 --> 00:38:22,060
+على اتنين E أس تلاتة على اتنين E أس تلاتة T على
+
+338
+00:38:22,060 --> 00:38:29,420
+الاتنين هذا بدي يعطيناما رأيك في الأولى هذه؟ أليست
+
+339
+00:38:29,420 --> 00:38:38,440
+هي عامل التكامل مضروب في V الكل prime؟ اه لو جتش
+
+340
+00:38:38,440 --> 00:38:42,340
+تقيتي هذه automatic حصل ضرب دلتين بتعطيك هذا
+
+341
+00:38:42,340 --> 00:38:46,580
+المشتق حرفيا لو ما طلعتش معناته عامل التكامل اللي
+
+342
+00:38:46,580 --> 00:38:53,540
+حسبتيه خاطأطيب هذا الكلام بده يساوي كده؟ تلاتة على
+
+343
+00:38:53,540 --> 00:38:59,640
+اثنين اقص تلاتة T على مين؟ على الاتنين طب بدنا
+
+344
+00:38:59,640 --> 00:39:04,860
+نكامل الطرفين يبقى by integration
+
+345
+00:39:36,260 --> 00:39:41,100
+بدنا نكامل بصيرطب احنا بدنا V لحالها، مابدناش E
+
+346
+00:39:41,100 --> 00:39:46,040
+أسالب يبقى بروح بضرب الطرفين في E سالب تلاتة على
+
+347
+00:39:46,040 --> 00:39:52,500
+اتنين T يبقى معنى هذا الكلام V تساوي طب V أصلا
+
+348
+00:39:52,500 --> 00:39:59,660
+قداشة احنا كاتبينها؟Y أز تلاتة على اتنين يبقى Y أز
+
+349
+00:39:59,660 --> 00:40:08,260
+تلاتة على اتنين تساوي واحد زائد C في E أصناق أز
+
+350
+00:40:08,260 --> 00:40:13,380
+تلاتة T على من؟ على الاتنين طب احنا عندما ال
+
+351
+00:40:13,380 --> 00:40:20,740
+condition Y under zero تساوياربع الان y عند ال
+
+352
+00:40:20,740 --> 00:40:25,900
+zero تساوي اربع implies بده اشيل ال y هذه و احط
+
+353
+00:40:25,900 --> 00:40:33,620
+مكانها جدوش اربع اص تلاتة على اتنين يساوي واحد
+
+354
+00:40:33,620 --> 00:40:43,650
+زائد c ايه اص zero ديه جدوش اك واحد تمامهذه
+
+355
+00:40:43,650 --> 00:40:48,850
+الأبنات تعني الجذري التربيعي لأربعة تكعيب اربعة
+
+356
+00:40:48,850 --> 00:40:53,330
+تكعيب في قداش؟ اربعة في اربعة بستاش في اربعة
+
+357
+00:40:53,330 --> 00:40:59,250
+باربعة وستين تحت الجذري يبقى بقداش؟ بتمانيةهذا
+
+358
+00:40:59,250 --> 00:41:05,930
+معناه انه تمانية تساوي واحد زائد C يبقى C تساوي
+
+359
+00:41:05,930 --> 00:41:16,370
+قداشر سبعة يبقى اصبح عندنا هنا the solution is
+
+360
+00:41:16,370 --> 00:41:25,730
+Y أس ثلاثة على اتنين يساوي واحد زائد سبعة E أصناع
+
+361
+00:41:25,730 --> 00:41:33,960
+أس ثلاثة T على اتنينفانا بقدر اجيب Yمرة واحدة يبقى
+
+362
+00:41:33,960 --> 00:41:40,880
+باجي بقوله يبقى Y يساوي يعني بدي أخد هذا أسطولتين
+
+363
+00:41:40,880 --> 00:41:48,500
+بدي أساوي اليمين أسطولتين يبقى واحد زائد سبعة E
+
+364
+00:41:48,500 --> 00:41:56,400
+أسالب تلاتة T على اتنين كله أسطولتين هذا هو الحل
+
+365
+00:41:56,400 --> 00:41:59,020
+تبع المعادلة التفاضلي
+
+366
+00:42:01,560 --> 00:42:07,000
+طيب عليك انتهينا من Bernoulli question للأسف
+
+367
+00:42:07,000 --> 00:42:12,160
+الشديد في الكتاب ماتيني بس 4 أسئلة ومش كتير انا
+
+368
+00:42:12,160 --> 00:42:18,840
+هعطيكوا أسئلة بالاضافة لأسئلتي الكتاب يبقى نروح
+
+369
+00:42:18,840 --> 00:42:22,980
+نعطيكوا الأسئلة التالية ك exercises
+
+370
+00:42:45,450 --> 00:42:51,830
+يبقى exercises solve
+
+371
+00:42:51,830 --> 00:42:56,330
+the
+
+372
+00:42:56,330 --> 00:43:01,990
+following
+
+373
+00:43:01,990 --> 00:43:07,150
+differential equations
+
+374
+00:43:07,150 --> 00:43:18,780
+السؤال الأولY' ناقص Y يسوي E أُس T في ال Y تربيع
+
+375
+00:43:18,780 --> 00:43:30,360
+سؤال التاني T في ال Y' ناقص واحد زائد T كله في ال
+
+376
+00:43:30,360 --> 00:43:37,120
+Y بده يسوي T في ال Y تربيع وT greater than zero
+
+377
+00:43:37,120 --> 00:43:48,670
+سؤال التالتبقول اتنين T في ال Y prime زائد
+
+378
+00:43:48,670 --> 00:43:58,210
+Y يساوي اتنين T تربيع على Y تكيب وال Y عند الواحد
+
+379
+00:43:58,210 --> 00:44:05,150
+بده يساوي جداش اتنين وT greater than zero السؤال
+
+380
+00:44:05,150 --> 00:44:15,030
+الرابعوما أدرك ما السؤال الرابع بيقول Y' ماقص واحد
+
+381
+00:44:15,030 --> 00:44:25,190
+على واحد زائد T كله في تاني ال Y بده يساوي واحد
+
+382
+00:44:25,190 --> 00:44:37,220
+زائد T في E أس T في سكة ال Y السؤال الخامسالو
+
+383
+00:44:37,220 --> 00:44:45,960
+exercises اتنين اربعة المسائل من تمانية و عشرين
+
+384
+00:44:45,960 --> 00:44:48,460
+لغاية تلاتين
+
+385
+00:45:11,660 --> 00:45:17,160
+مرة تانية طبعا المسائل الأربعة الأولى من خارج
+
+386
+00:45:17,160 --> 00:45:22,200
+الكتاب بيقول لحل المسائل التالية هو يعطاني أربعة
+
+387
+00:45:22,200 --> 00:45:27,240
+مسائل لكتاب بدنا منه تلت مسائل تمانية و عشرين تسعة
+
+388
+00:45:27,240 --> 00:45:32,480
+و عشرين تلتين اللي هو من section اتنين اربعة بيكون
+
+389
+00:45:32,480 --> 00:45:36,220
+غطينا موضوع Bernoulli اللي هو النقطة الأولى من ال
+
+390
+00:45:36,220 --> 00:45:41,230
+exercise اللي وعدناكوا فيهابالمنا ان النقطة
+
+391
+00:45:41,230 --> 00:45:45,290
+الثانية دي discontinuous coefficients المعاملات
+
+392
+00:45:45,290 --> 00:45:55,470
+غيرت المتاصلة يبقى بدنا نيجي للنقطة الثانية يبقى
+
+393
+00:45:55,470 --> 00:46:00,430
+النقطة الثانية اللي هي discontinuous
+
+394
+00:46:01,640 --> 00:46:06,000
+موجود عندك في الكتاب بهذا الاسم وهذا اللي هو
+
+395
+00:46:06,000 --> 00:46:12,300
+العنوان discontinuous coefficients في ال exercises
+
+396
+00:46:12,300 --> 00:46:19,160
+تبعات section 2 أربعة عندك مثال ايه عندك سؤالين
+
+397
+00:46:19,160 --> 00:46:23,910
+فقط في الكتابأحنا بنحل واحد و انت بتروح تحلي
+
+398
+00:46:23,910 --> 00:46:32,950
+الثاني يبقى نعطي example اللي هو سؤال 32 من الكتاب
+
+399
+00:46:32,950 --> 00:46:40,550
+و بضل عليك السؤال 33 solve the initial value
+
+400
+00:46:40,550 --> 00:46:48,100
+problemاللي هو main y prime زيدي اتنين y بده يساوي
+
+401
+00:46:48,100 --> 00:46:55,280
+ال g of t و ال y عند ال zero بده يساوي zero where
+
+402
+00:46:57,770 --> 00:47:04,610
+الـ G of T تساوي أحد أمرين الأمر الأول ممكن تكون
+
+403
+00:47:04,610 --> 00:47:10,490
+واحد لما T محصورة بين Zero و واحد أو ممكن تكون
+
+404
+00:47:10,490 --> 00:47:15,290
+Zero لما T تبقاش أكبر من الواحد
+
+405
+00:47:20,330 --> 00:47:25,770
+سؤال شفوي من تعريف الـ G of T continuous ولا
+
+406
+00:47:25,770 --> 00:47:33,170
+discontinuous عند الواحد؟يبقى من 0 ل 1 قيمتها واحد
+
+407
+00:47:33,170 --> 00:47:38,670
+عند اللي هو بعد الواحد بتنزل بصير قيمتها جديش Zero
+
+408
+00:47:38,670 --> 00:47:42,610
+يبقى من Zero ل واحد تبقى خط مستقيم تنزل مرة واحدة
+
+409
+00:47:42,610 --> 00:47:47,070
+وبتمشي بعد ذلك وفق فيه discontinuity وين عند
+
+410
+00:47:47,070 --> 00:47:55,950
+الواحد يبقى باجي بقوله solution ال G of T is
+
+411
+00:47:55,950 --> 00:47:59,270
+discontinuous
+
+412
+00:48:00,560 --> 00:48:08,520
+أت T تساوي واحد يعنيها بس مجرد اللي هو رسم للتوضيح
+
+413
+00:48:08,520 --> 00:48:13,200
+لكن مالوش داعي بالحل لو جينا و قولنا هذا T و قولنا
+
+414
+00:48:13,200 --> 00:48:18,760
+هذا Y من عند ال zero لغاية الواحد الدالة بالشكل
+
+415
+00:48:18,760 --> 00:48:25,740
+اللي عندنا هذا وهي مغلقة وهنا مغلقةوبتيجي نازلة
+
+416
+00:48:25,740 --> 00:48:31,000
+تحت على الواحد تماما بالشكل هذا من هنا بيصير
+
+417
+00:48:31,000 --> 00:48:36,520
+مفتوحة وبيظل ماشية لوين إلى ما لا نهاية بالشكل
+
+418
+00:48:36,520 --> 00:48:41,580
+اللي عندها طبعا هذا القيمة اللي هي واحد تمام يبقى
+
+419
+00:48:41,580 --> 00:48:46,420
+هذا الشكل هون في discontinuity وين عند الواحد يعني
+
+420
+00:48:46,420 --> 00:48:51,590
+jump discontinuity قفزتمن الواحد إلى الصفر مش قفزت
+
+421
+00:48:51,590 --> 00:48:55,490
+إلى أعلى قفزت إلى أسفل يبقى ال G of T is
+
+422
+00:48:55,490 --> 00:49:00,610
+discontinuous at T تساوي واحد طب كيف نحلها ان احنا
+
+423
+00:49:00,610 --> 00:49:05,430
+عندنا شرط أساسي مشان نحل ال linear phase ان تبقى
+
+424
+00:49:05,430 --> 00:49:10,090
+ال G of T والP of T are continuous function من
+
+425
+00:49:10,090 --> 00:49:15,250
+جملة بسيط بجسم مسئلتي إلى مسئلتين باخد الفترة
+
+426
+00:49:15,250 --> 00:49:19,110
+الأولى من Zero لواحد و باخد الفترة التانيةبعد
+
+427
+00:49:19,110 --> 00:49:23,310
+الواحدة وبالتالي بيطلع حلين وبعدها كنشوف نقدر
+
+428
+00:49:23,310 --> 00:49:27,430
+ندخلهم حل واحد و الله شو المشكلة طيب على أي حال
+
+429
+00:49:27,430 --> 00:49:34,830
+بداجي اقوله if T أكبر من أو تساوي ال zero أقل من
+
+430
+00:49:34,830 --> 00:49:37,650
+تساوي واحد then
+
+431
+00:49:40,860 --> 00:49:47,840
+differential equation is اللي هو مين y prime زائد
+
+432
+00:49:47,840 --> 00:49:55,280
+اتنين y تساوي قداش في الفترة هذه قيمة g of t واحد
+
+433
+00:49:55,280 --> 00:50:00,880
+صحيح as in linear وهنا continuous وcontinuous
+
+434
+00:50:00,880 --> 00:50:05,840
+ماعندي مشكلة وانا فقط حاصر نفسي على الفترة من zero
+
+435
+00:50:05,840 --> 00:50:12,250
+لغاية واحد يبقى هذه صارت linearمدام لينر اذا بروح
+
+436
+00:50:12,250 --> 00:50:20,910
+اجيب ال mu of T مباشرة يساوي E أس تكامل اتنين DT
+
+437
+00:50:20,910 --> 00:50:28,310
+يبقى E أس اتنين T يبقى هذا صار من ال mu of D شو
+
+438
+00:50:28,310 --> 00:50:35,160
+بعمل؟ بضرب المعادلة فيهيبقى بيصير E أس اتنين T في
+
+439
+00:50:35,160 --> 00:50:41,660
+ال Y Prime اتنين E أس اتنين T في ال Y يسوى E أس
+
+440
+00:50:41,660 --> 00:50:47,480
+اتنين T تمام؟ يبقى صارت المعادلة على الشكل اللي
+
+441
+00:50:47,480 --> 00:50:54,460
+قدامنا هذا تماما طيب الآن هذه جاهزة وخالصة يعني
+
+442
+00:50:54,460 --> 00:51:01,000
+بقدر اكتبها على الشكل هذا عامل التكاملوهذا Y كله
+
+443
+00:51:01,000 --> 00:51:09,310
+prime يساوي E أش اتنين Tإن كامل الطرفين يبقى بيصير
+
+444
+00:51:09,310 --> 00:51:16,250
+عندنا E أس اتنين T في ال Y يسوى E أس اتنين T على
+
+445
+00:51:16,250 --> 00:51:23,970
+اتنين زائد constant C أو بمعنى آخر بقدر اقول ان ال
+
+446
+00:51:23,970 --> 00:51:38,520
+Y تساوي نص زائد C على E أس اتنين Tأو نص زائد C في
+
+447
+00:51:38,520 --> 00:51:44,220
+EOS ناقص اتنين T طيب تعالوا نطلع نعطيني ال initial
+
+448
+00:51:44,220 --> 00:51:48,420
+condition ال initial condition قال لي Y عند Zero
+
+449
+00:51:48,420 --> 00:51:51,900
+يساوي Zero إذا احنا في الفترة هذه والله في الفترة
+
+450
+00:51:51,900 --> 00:51:57,840
+الأولى Y عند Zero يبقى Zero عند الفترة الأولىيبقى
+
+451
+00:51:57,840 --> 00:52:03,220
+باجي بقوله الان انا عندي initial condition y عندي
+
+452
+00:52:03,220 --> 00:52:06,860
+ال zero يساوي zero بنفع استخدم ال condition هذا
+
+453
+00:52:06,860 --> 00:52:12,840
+لفترة تانية لا يبعتلك الله بنقدرش يبقى y عندي ال
+
+454
+00:52:12,840 --> 00:52:18,120
+zero بده يساوي جداش بده يساوي zero implies هي ال
+
+455
+00:52:18,120 --> 00:52:25,820
+zero بده يساوي نص زائد c في e أس zero اللي هو جداش
+
+456
+00:52:26,190 --> 00:52:32,170
+بواحد يبقى بناء على اليسار C يساوي كده؟ سالب نص
+
+457
+00:52:32,170 --> 00:52:38,050
+يبقى أصبح ال solution على الشكل التالي Y يساوي
+
+458
+00:52:38,050 --> 00:52:48,210
+النص ناقص نص E أس ناقص اتنين T و ال T محصورة ما
+
+459
+00:52:48,210 --> 00:52:52,850
+بين ال zero و ما بين ال واحد هذا شكل الحل على
+
+460
+00:52:52,850 --> 00:52:59,550
+الفترة T الأولىبنروح لوين؟ للفترة الثانية يبقى
+
+461
+00:52:59,550 --> 00:53:10,550
+باجي بقوله if T greater than one then the
+
+462
+00:53:10,550 --> 00:53:18,090
+differentialEquation as نرجع للمعادلة الاصلية y
+
+463
+00:53:18,090 --> 00:53:25,190
+prime زائد اتنين y تساوي g of t بعد الواحد قداش g
+
+464
+00:53:25,190 --> 00:53:32,870
+of t يبقى هذه بدها تساوي zero يبقى هذه linear كذلك
+
+465
+00:53:32,870 --> 00:53:35,810
+بس مش هلال دي على الحلطة رابعة الطريقة اتنين لأ
+
+466
+00:53:35,810 --> 00:53:38,950
+بحلها فقط و واحدة و مش محتاج ل integrating factor
+
+467
+00:53:38,950 --> 00:53:44,690
+ولا غيرهفبقى بقول له هذا بتعطينا ان y' يسوى ناقص
+
+468
+00:53:44,690 --> 00:53:53,230
+اتنين y او ان شئتم فقولوا y' على y يسوى ناقص اتنين
+
+469
+00:53:53,230 --> 00:54:01,920
+اظن بقدر اكملها هذه صح؟ يبقى شو تكملها؟ قداش؟لن
+
+470
+00:54:01,920 --> 00:54:09,400
+absolute value لل Y بد يساوي تكامل هذي اللي بناقص
+
+471
+00:54:09,400 --> 00:54:16,840
+اتنين T زائد constant وليكن C1 طب انا مابديش لن
+
+472
+00:54:16,840 --> 00:54:22,130
+لبس اللي بد ال Y itselfيبقى باجي بقوله هذا يعني
+
+473
+00:54:22,130 --> 00:54:28,970
+انه absolute value ل Y بده يساوي E اص ناقص اتنين T
+
+474
+00:54:28,970 --> 00:54:36,790
+زائد C1 طيب سؤال هذا exponential عمره بياخد قيمة
+
+475
+00:54:36,790 --> 00:54:41,390
+سالبة؟يبقى لا داعي لل absolute value لأن ال
+
+476
+00:54:41,390 --> 00:54:45,070
+absolute value احتمال ان تبقى سلبى ولا موجبة لكن
+
+477
+00:54:45,070 --> 00:54:48,610
+لما انضمنت انها موجبة يبقى لها معنى لل absolute
+
+478
+00:54:48,610 --> 00:54:53,070
+value إذا منشيل ال absolute value بروح نقول ان
+
+479
+00:54:53,070 --> 00:55:00,290
+الحل Y بدر يسوى E أص ناقص اتنين T في E أص C one
+
+480
+00:55:22,590 --> 00:55:28,730
+يبقى كأن الحل أصبح على الشكل التالي
+
+481
+00:55:44,560 --> 00:55:50,680
+Y تساوي احد امرين الامر الاول اللي بروزنا نص ناقص
+
+482
+00:55:50,680 --> 00:55:57,900
+نص في E أس ناقص اتنين T نص ناقص نص في E أس ناقص
+
+483
+00:55:57,900 --> 00:56:03,520
+اتنين T وT اكبر من أو يساوي Zero اقل من أو يساوي
+
+484
+00:56:03,520 --> 00:56:03,940
+الواحد
+
+485
+00:56:15,060 --> 00:56:23,320
+طب ايش رايكوا بقدر اجيب ال c احنا
+
+486
+00:56:23,320 --> 00:56:28,240
+شروطنا بتبقى continuous دايما وابدا بدي اخلي الحل
+
+487
+00:56:28,240 --> 00:56:32,960
+هذا continuous مشان الحل هذا continuous برجع
+
+488
+00:56:32,960 --> 00:56:37,400
+لتعريف ال continuous function زمان قلنا ان بتبقى
+
+489
+00:56:37,400 --> 00:56:41,080
+الدلة بتبقى continuous عند نقطة النقطة مين عندنا
+
+490
+00:56:41,080 --> 00:56:47,330
+هنا واحدإذا كان قيمة الدالة عند الواحد يساوي نهاية
+
+491
+00:56:47,330 --> 00:56:50,750
+الدالة عند الواحد مش هيك أخدها في الكلقوا لصغير
+
+492
+00:56:50,750 --> 00:56:54,430
+يبقى باقى أن أقول limit ال F of X لما ال X بدأ
+
+493
+00:56:54,430 --> 00:57:00,610
+تروح ال X node يساوي ال F of X node itself يبقى
+
+494
+00:57:00,610 --> 00:57:06,990
+باجي بقول هنا ال Y is continuous
+
+495
+00:57:08,070 --> 00:57:15,070
+at x يساوي واحد يعني مش الدلال أصلي الحل تبعها بدي
+
+496
+00:57:15,070 --> 00:57:21,870
+يكون continuous عند x يساوي واحد if ال limit لل y
+
+497
+00:57:21,870 --> 00:57:27,090
+لما ال y بدها تروح لل واحد من جهة اليمين بدي يساوي
+
+498
+00:57:27,090 --> 00:57:33,590
+قيمة y عند الواحدطب واحد هتقولي طب ليش من جهة
+
+499
+00:57:33,590 --> 00:57:37,310
+الشمال؟ لأ، هتقولك من جهة الشمال ما هي لازم تساوي
+
+500
+00:57:37,310 --> 00:57:40,250
+ليه الجهة اليمين، عشان تبقى قليمة، it doesn't
+
+501
+00:57:40,250 --> 00:57:44,930
+exist. اتنين، لابد أقولك واحد من جهة الشمال هتعطيك
+
+502
+00:57:44,930 --> 00:57:48,710
+نفس قيمة الدالة اللي هي المعطلة و اتقالي ماعنديش
+
+503
+00:57:48,710 --> 00:57:53,740
+مشكلة، ماساويش شيء، يعني بيصير تكرار مملفيبتعلي
+
+504
+00:57:53,740 --> 00:57:58,540
+ناخد ال limit اللي عندنا هنا يبقى هذا ال limit لما
+
+505
+00:57:58,540 --> 00:58:05,740
+Y بدها تروح للواحد من جهة اليامين الان انا عند هذا
+
+506
+00:58:05,740 --> 00:58:11,080
+ال real line وهذا عند الواحد وهذا عند ال zero انا
+
+507
+00:58:11,080 --> 00:58:15,300
+رايح للواحد من جهة ايد اليامين يعني احنا قبل
+
+508
+00:58:15,300 --> 00:58:20,550
+الواحد و لا بعد الواحدأنا رايح للواحد من جهة E
+
+509
+00:58:20,550 --> 00:58:24,970
+اليامين يبقى احنا بعد الواحد والله قابل الواحد بعد
+
+510
+00:58:24,970 --> 00:58:31,030
+الواحد قيمة الدالة كده؟ C في E اص ناقص اتنين C
+
+511
+00:58:31,030 --> 00:58:38,350
+يبقى C في E اص ناقص اتنين T بده يساوي Y عند الواحد
+
+512
+00:58:38,350 --> 00:58:42,730
+قيمة الدالة عند الواحد لما T تساوي واحد هاي قيمة
+
+513
+00:58:42,730 --> 00:58:49,600
+الدالة صح ولا لا؟ يبقى بصير تساوي المصناقص نص في
+
+514
+00:58:49,600 --> 00:58:56,060
+EOS ناقص اتنين في واحد في EOS ناقص اتنين طيب العوض
+
+515
+00:58:56,060 --> 00:59:02,180
+تعود مباشر يبقى C في EOS ناقص اتنين يساوي النص
+
+516
+00:59:02,180 --> 00:59:08,100
+ناقص نص في EOS ناقص اتنين هذه معادلة مجهول فيها بس
+
+517
+00:59:08,100 --> 00:59:13,770
+مين؟يبقى بدي اضرب كله في اي تربية بكون جيب من C
+
+518
+00:59:13,770 --> 00:59:22,470
+يبقى هذا بدي يعطينا ان C يساوي نص اي تربية ناقص نص
+
+519
+00:59:22,470 --> 00:59:29,590
+يعني نص في اي تربية ناقص واحد يبقى أصبح the
+
+520
+00:59:29,590 --> 00:59:30,610
+solution
+
+521
+00:59:34,280 --> 00:59:43,180
+of the nation value of problem is y تساوي الجزءين
+
+522
+00:59:43,180 --> 00:59:51,300
+الجزء الأول نص ناقص نص E أس ناقص اتنين T الجزء
+
+523
+00:59:51,300 --> 00:59:56,320
+الأول اللي جيبناه فوق الان بدي أشيل C و أحط قيمتها
+
+524
+00:59:56,320 --> 01:00:01,720
+يبقى هنا نص في E تربية ناقص واحد
+
+525
+01:00:19,690 --> 01:00:24,750
+طبعا أبسط من السؤال هذا أسهل شوية كمان
+
+526
+01:00:47,970 --> 01:00:53,990
+بدنا نجي ل section 2 5 و نقول الله يسهل عليك بروح
+
+527
+01:00:53,990 --> 01:00:58,950
+ل section 2 6 اللي هو مين اللي هو exact
+
+528
+01:01:01,540 --> 01:01:10,780
+equations and integrating factors
+
+529
+01:01:10,780 --> 01:01:16,320
+المعادلة
+
+530
+01:01:16,320 --> 01:01:19,140
+تم وعوامل التكامل
+
+531
+01:01:27,690 --> 01:01:32,150
+هذا ال section يا بنات هو ال section الوحيد اللي
+
+532
+01:01:32,150 --> 01:01:36,950
+لازمنا فيه من calculus C اللي قلتلكوا أول محاضرة
+
+533
+01:01:36,950 --> 01:01:42,110
+خشيت عليكم ناخدها في خمس دقاج أو أقل طيب قبل ما
+
+534
+01:01:42,110 --> 01:01:47,810
+نبدأ بدنا نقول شو بدنا من calculus C احنا في
+
+535
+01:01:47,810 --> 01:01:52,250
+calculus A وB كله بجينا ناخد الدالة Y function في
+
+536
+01:01:52,250 --> 01:01:58,960
+متغير واحدمصغور؟ طب لو صارت function في متغيرين أو
+
+537
+01:01:58,960 --> 01:02:03,800
+تلاتة كيف بدنا نشتق؟ بقول اشتقاق في هذه الحالة
+
+538
+01:02:03,800 --> 01:02:09,820
+يكون اشتقاقا جزئيا يبقى إذا كانت الدالة وعي في
+
+539
+01:02:09,820 --> 01:02:15,120
+متغير واحد بقول اشتقاق كله لكن إذا دالة في متغيرين
+
+540
+01:02:15,120 --> 01:02:20,680
+أو تلاتة أو أربعة أو خمسة بقول اشتقاق جزئي تمام؟
+
+541
+01:02:20,680 --> 01:02:27,070
+نعطيكوا توضيحلو جيها تقولش لك f ال y تساوي
+
+542
+01:02:27,070 --> 01:02:34,430
+function في x و z يبقى خالتها y ده اللي في مين فيه
+
+543
+01:02:34,430 --> 01:02:44,130
+متغيرين مثلا روح تقولش لك x تربيع z تكيب زائدها
+
+544
+01:02:44,130 --> 01:02:51,110
+تلاتة x z تربيع ناقص واحد then
+
+545
+01:02:54,020 --> 01:02:59,020
+افترض اذا اشتقها بالنسبة الى x فابقى اقول اشتقاق
+
+546
+01:02:59,020 --> 01:03:05,280
+جزي بقول partial y by partial x شكل انا بقى لما
+
+547
+01:03:05,280 --> 01:03:11,320
+كنت اقول dy على dx بقول partial y by partial x
+
+548
+01:03:11,320 --> 01:03:15,000
+يبقى اشتقاق جزي من حد ما يشوف الرمز هذا يبقى
+
+549
+01:03:15,000 --> 01:03:20,040
+اشتقاق جزي لما اشتقها بنات بالنسبة ل x بعتبر كل
+
+550
+01:03:20,040 --> 01:03:26,810
+المتغيرات الأخرى ثوابتطبعا يبقى بدى يكون عندى هنا
+
+551
+01:03:26,810 --> 01:03:32,810
+z ثابت بشتق باسمين و ثابت بظل زى ما هو يبقى أداش
+
+552
+01:03:32,810 --> 01:03:37,350
+مشتقة ال X تربيع ب2XZ
+
+553
+01:03:37,350 --> 01:03:46,290
+كعيب زى تلاتة Z تربيع و سالب واحد مشتقة بزيرو and
+
+554
+01:03:46,290 --> 01:03:53,660
+لو بدى partial Y by partial Zيبقى بذا تثابت، ده
+
+555
+01:03:53,660 --> 01:03:59,280
+اشتق بالنسبة لمن؟ يبقى ال X يبقى ال X تربية هذي
+
+556
+01:03:59,280 --> 01:04:03,960
+ثابتة، يبقى بقوله ال X تربية زي ما انتي زدت كي
+
+557
+01:04:03,960 --> 01:04:11,400
+بصير تلاتة زد تربية وصلنا زاد زاد، تلاتة X مالكيش
+
+558
+01:04:11,400 --> 01:04:18,210
+دعوةالـ z تربية مافقداش بـ 2z ومشتقة السلب 1 بـ 0
+
+559
+01:04:18,210 --> 01:04:26,910
+يبقى صارت 3x تربية z تربية زائد 6xz بالمثل لو بدي
+
+560
+01:04:26,910 --> 01:04:32,970
+أكامل، لو بدي أكامل بالنسبة إلى x، بعتبر الـ z هذه
+
+561
+01:04:32,970 --> 01:04:38,890
+ثابتة وهذه ثابتة و بكمل بس الـ 3 و2xلو بدها كامل
+
+562
+01:04:38,890 --> 01:04:42,950
+بالنسبة الى z يبقى تلاتة x تربية ثابتة و بضال and
+
+563
+01:04:42,950 --> 01:04:48,870
+main زد تكييب على تلاتة تكاملة وده ستة x ثابتة و
+
+564
+01:04:48,870 --> 01:04:54,630
+بضال z تربية على main على اتنين و هكذا صعب هذي؟
+
+565
+01:04:54,630 --> 01:04:59,590
+هذا اللي بدنا منك الكلسي كله اللي شفتيه اكتر من
+
+566
+01:04:59,590 --> 01:05:06,740
+هيك بدناشماشي؟ بس في عندي كمان شغلة لو أنا عندى
+
+567
+01:05:06,740 --> 01:05:12,900
+دالة فى متغيرين وبدى اجيب مشتقتها اشتقاقا كاملا
+
+568
+01:05:12,900 --> 01:05:21,480
+يعنى لو كانت في هي ال function فى x و y وبدى اجيب
+
+569
+01:05:21,480 --> 01:05:28,580
+الاشتقاق الكل لهاهذه النقطة الأولى اللى بدنا ياها
+
+570
+01:05:28,580 --> 01:05:34,380
+وهذه النقطة التانية يبقى يا بنات بدي دي فاي
+
+571
+01:05:34,380 --> 01:05:41,020
+الاشتقاق الكلى لفاي بروح بقول هذا عبارة عن partial
+
+572
+01:05:41,020 --> 01:05:48,080
+fi على partial x في dx زائد partial fi على partial
+
+573
+01:05:48,080 --> 01:05:50,020
+y في dy
+
+574
+01:05:52,120 --> 01:05:58,140
+في دالة فيه متغيرين بدي أجيب الاشتقاق الكل بالنسبة
+
+575
+01:05:58,140 --> 01:06:03,640
+لفي فبقول دي في هي partial في على partial x في دي
+
+576
+01:06:03,640 --> 01:06:09,840
+x زي partial في على partial y في دي y تمام؟ أكتر
+
+577
+01:06:09,840 --> 01:06:13,810
+من هيك بدناش ولا حاجةوالان الكلام اللى بقوله لكوا
+
+578
+01:06:13,810 --> 01:06:19,750
+هنبدأ نطبقه على أرض الواقع بس قبل بدنا نشوف شو شكل
+
+579
+01:06:19,750 --> 01:06:23,590
+ال exact equation او ماهو تعريف ال exact equation
+
+580
+01:06:23,590 --> 01:06:29,750
+و بعد هيك بدنا نشوف كيف بدنا نحل هذه المعادلة يبقى
+
+581
+01:06:29,750 --> 01:06:34,850
+هذه المقدمة منات اللى وعدناكوا فيها من خمس دقائق
+
+582
+01:06:34,850 --> 01:06:42,490
+اللى هتلزمنا فقط لغيريبقى بدنا نيجي لمين لل exact
+
+583
+01:06:42,490 --> 01:06:52,930
+equations يبقى
+
+584
+01:06:52,930 --> 01:06:57,630
+هذا النقطة الأولى نمرا واحد اللي هي exact
+
+585
+01:06:57,630 --> 01:07:02,910
+equationsطبعا ال section فيه نقطتين ال exact
+
+586
+01:07:02,910 --> 01:07:06,350
+equations و ال integrating factors ال integrating
+
+587
+01:07:06,350 --> 01:07:10,370
+factors حال جائلها لما تكون المعادلة ماهياش exact
+
+588
+01:07:10,370 --> 01:07:15,810
+و ربما سنعرفه خلال هذه المحاضرة و ربما في المحاضرة
+
+589
+01:07:15,810 --> 01:07:20,810
+القادمة تمام يبقى من هنا ال exact equations the
+
+590
+01:07:20,810 --> 01:07:25,190
+first order
+
+591
+01:07:27,690 --> 01:07:37,950
+Differential equation y prime يساوي f of x و y can
+
+592
+01:07:37,950 --> 01:07:47,090
+be written as ممكن نكتب على الشكل التالي
+
+593
+01:07:49,540 --> 01:08:01,660
+by dx يساوي سالب M في ال XY على N في ال XY زي
+
+594
+01:08:01,660 --> 01:08:08,760
+المرة اللي فاتت بالظبط this is possible هذا الكلام
+
+595
+01:08:08,760 --> 01:08:11,780
+ممكن for example
+
+596
+01:08:35,680 --> 01:08:42,520
+تاك تاك تاك تاك
+
+597
+01:08:42,520 --> 01:08:44,880
+تاك تاك تاك تاك تاك تاك تاك تاك تاك تاك تاك تاك
+
+598
+01:08:45,510 --> 01:08:56,770
+differential equation is written as
+
+599
+01:08:56,770 --> 01:09:07,290
+اكتبها على الشكل التالي اللي هو m of x y dx زائد n
+
+600
+01:09:07,290 --> 01:09:14,190
+of x y dy بده يساوي من؟ بده يساوي
+
+601
+01:09:41,040 --> 01:09:45,000
+كويس نرجع لموضوعنا لسه أنا ماعرفتش ال exact
+
+602
+01:09:45,000 --> 01:09:49,040
+equation ولا اتكلمتش كل اللي عملته حطيت ال
+
+603
+01:09:49,040 --> 01:09:53,410
+function في صيغة اخرىالان ال first order
+
+604
+01:09:53,410 --> 01:09:57,610
+differential equation y' يساوي function في x و y
+
+605
+01:09:57,610 --> 01:10:02,570
+can be written as ممكن اكتبه على الشكل التالي dy
+
+606
+01:10:02,570 --> 01:10:07,850
+على dx بده يساوي ناقص m of x و y على n of x و y
+
+607
+01:10:07,850 --> 01:10:12,590
+السؤال هو هل هذا ممكن ولا غير ممكن الإجابة ممكن
+
+608
+01:10:12,590 --> 01:10:20,390
+كيف ممكن اخلي n of x و y هذه بواحد كدهش بضلسالب M
+
+609
+01:10:20,390 --> 01:10:24,970
+of X يبقى سالب M of X وY هي ال F of X وY صحيح ولا
+
+610
+01:10:24,970 --> 01:10:28,610
+لأ؟ يبقى ال F of X وY هي سالب M of X وY وبالتالي
+
+611
+01:10:28,610 --> 01:10:33,230
+ماعندي مشكلة يعني هذا أبسط الشغل الممكن يعني بقدر
+
+612
+01:10:33,230 --> 01:10:36,690
+اكتبها فعلا والدليل على ذلك ممكن اكتبها بالشكل هذا
+
+613
+01:10:36,690 --> 01:10:42,510
+إذا صار الكلام هذا ممكن طيب لو جيت ضرب ضرب تبادل
+
+614
+01:10:42,510 --> 01:10:50,340
+ايش بصير؟ بصير N of X وY في Dyيساوي سالب M of X Y
+
+615
+01:10:50,340 --> 01:10:54,620
+في DX هتيها على الشجرة تانية لو جيبناها على الشجرة
+
+616
+01:10:54,620 --> 01:10:59,820
+تانية بصير M of X Y DX زاد N of X Y DY بيبقى يساوي
+
+617
+01:10:59,820 --> 01:11:05,120
+من؟ Zero المعادلة ها دي يا بنات بقول عنها exact لو
+
+618
+01:11:05,120 --> 01:11:12,540
+جدرت ألاجي function Epsi of X Y تساوي مقدارا ثابتا
+
+619
+01:11:12,820 --> 01:11:17,600
+بعيطة أن مشتقة هذه الدالة بالنسبة ل X بتعطين ال M
+
+620
+01:11:17,600 --> 01:11:25,520
+ومشتقتها بالنسبة ل Y بتعطين ال M يبقى نكتب لك هذا
+
+621
+01:11:25,520 --> 01:11:30,140
+التعريف يبقى هذا ال definition تبع ال exact
+
+622
+01:11:30,140 --> 01:11:34,820
+function بقول differential equation
+
+623
+01:11:41,200 --> 01:11:51,940
+اللي هو M of XY DX زائد N of XY DY تساوي Zero وبدي
+
+624
+01:11:51,940 --> 01:12:00,220
+أسميها المعادلة رقم واحد is said
+
+625
+01:12:00,220 --> 01:12:16,950
+to be exact بقول عنها معادلة تامةإذا كان هناك
+
+626
+01:12:16,950 --> 01:12:30,030
+مفهوم بـ Psi of X و Y فهو Psi of X Y Psi of X Y
+
+627
+01:12:30,030 --> 01:12:33,910
+Psi of X Y
+
+628
+01:12:37,850 --> 01:12:52,230
+بحيث ان such that d psi of x of y يساوي ال m of x
+
+629
+01:12:52,230 --> 01:13:03,170
+of y dx زائد ال n of x of y dy وهذه اللي هي بدأت
+
+630
+01:13:03,170 --> 01:13:04,710
+ساوي zero
+
+631
+01:13:20,580 --> 01:13:25,080
+بنرجع الآن للتعريف اللي احنا كاتبينه هذا المر عليه
+
+632
+01:13:25,080 --> 01:13:30,680
+مرة ثانية احنا هنا المعادلة اللي عندنا ها دي ها ها
+
+633
+01:13:30,680 --> 01:13:34,690
+وصلنا الي كتابتها على الشكل اللي عندنا هذايبقى
+
+634
+01:13:34,690 --> 01:13:40,550
+المعادلة هذه بقدر اقول ان هذه exact اذا تحقق الشرط
+
+635
+01:13:40,550 --> 01:13:44,910
+التالي يبقى المعادلة اللي عندها هذه قماحة بقول
+
+636
+01:13:44,910 --> 01:13:50,410
+عنها exact اذا جدرت لاجي function بدي اسميها
+
+637
+01:13:50,410 --> 01:13:57,350
+epsilon of x y بحيث ان دي epsilon طبعا ال epsilon
+
+638
+01:13:57,350 --> 01:14:02,890
+of x y سوياشمقدار ثابت Constant C بحيث ان دي Epsi
+
+639
+01:14:02,890 --> 01:14:09,890
+of XY يعني مشتقتها بدها تساوي من المعادلة اللي
+
+640
+01:14:09,890 --> 01:14:14,430
+عندنا هذه وهذه طبيعي تساوي كده؟ تساوي Zero
+
+641
+01:14:18,200 --> 01:14:23,300
+مش كتير ولا لا؟ اه يعني كيف بتلاقيها ال function
+
+642
+01:14:23,300 --> 01:14:27,400
+هذه عملية شاقة، اذا بيتروح ادور، كل واحد هتقعد
+
+643
+01:14:27,400 --> 01:14:32,460
+يدور من جهته، يمكن تلاقيها و يمكن مالاجيهاش، تمام؟
+
+644
+01:14:32,460 --> 01:14:38,970
+لكن في نظرية هذه، النظرية بتسهلعملية إيجاد الإبسع
+
+645
+01:14:38,970 --> 01:14:45,570
+I of X وY وهذا ما سنعرفه بعد قليل لكن قبل أن نعرفه
+
+646
+01:14:45,570 --> 01:14:49,710
+بدي أشير إلى ملاحظة بسيطة الآن ال differential
+
+647
+01:14:49,710 --> 01:14:55,150
+equation بقول عنها exact يعني لو كانت exact لازم
+
+648
+01:14:55,150 --> 01:14:55,730
+ألاقي
+
+649
+01:15:07,970 --> 01:15:15,090
+طيب كويس طلعيني بس هنا احنا دي فاي لو كان فانكشن
+
+650
+01:15:15,090 --> 01:15:20,140
+في x و y يبقى دي فاي بده يسوي هذا ال termأيش هنا
+
+651
+01:15:20,140 --> 01:15:25,220
+احنا قلنا دي إبصاي بده يسوى ال term هذا اللي لنا
+
+652
+01:15:25,220 --> 01:15:31,320
+صحيح ولا لا يبقى لحد هنا انتهى التعريف لكن انا
+
+653
+01:15:31,320 --> 01:15:37,320
+بقدر اقوله ايه دي إبصاي of x و y هذه معلومة جانبية
+
+654
+01:15:37,320 --> 01:15:41,960
+اه لسه ماوصلناش النظرية بقدر اقول هي partial إبصاي
+
+655
+01:15:41,960 --> 01:15:47,440
+على partial x في ال dx زائد partial إبصاي على
+
+656
+01:15:47,440 --> 01:15:53,600
+partial yفي ال BY يبقى كأنه هذه عبارة عن مين يا
+
+657
+01:15:53,600 --> 01:16:01,800
+بناتي ال M وهذه كأنها عبارة عن مين عبارة عن ال N
+
+658
+01:16:01,800 --> 01:16:07,960
+بالضبط تماما كويس هايه لو قلت هنا إبصاي بصير هنا
+
+659
+01:16:07,960 --> 01:16:13,880
+إبصاي هنا إبصاي هنا إبصاي بالضبط تماما يبقى هذه
+
+660
+01:16:13,880 --> 01:16:23,540
+جيبناها من وينهذا من كالكولاس C هذي من كالكولاس
+
+661
+01:16:23,540 --> 01:16:30,980
+C هذي من كالكولاس C طيب سيبينا من المعلومة هذه و
+
+662
+01:16:30,980 --> 01:16:37,480
+بدى أسأل السؤال التالي هل سهل ان جيب ندور على ال
+
+663
+01:16:37,480 --> 01:16:44,620
+function of xi of x و y و نوجدها هيك مش سهللكن في
+
+664
+01:16:44,620 --> 01:16:50,800
+نظرية هذه النظرية بتسهل عملية إيجاد هذه الدلة نجي
+
+665
+01:16:50,800 --> 01:16:55,940
+للنظرية نشوف شو بتقول هذه النظرية يبقى ال theorem
+
+666
+01:16:55,940 --> 01:17:01,640
+بيقول
+
+667
+01:17:01,640 --> 01:17:12,620
+ليلة ال M و ال N و ال partial M على partial Y and
+
+668
+01:17:13,870 --> 01:17:21,650
+الـ Partial N على Partial X بـ Continuous
+
+669
+01:17:21,650 --> 01:17:24,710
+Functions
+
+670
+01:17:24,710 --> 01:17:32,550
+يبقى دوال متصلة in a region
+
+671
+01:17:58,450 --> 01:18:01,710
+معادلة التفاضلية M
+
+672
+01:18:12,300 --> 01:18:13,700
+YYYYYYYYYY
+
+673
+01:19:08,350 --> 01:19:14,710
+بنرجع لنظرية تانية بيقول ايش؟ افترض ان عندي M و N
+
+674
+01:19:14,710 --> 01:19:20,170
+و تفاضل M بالنسبة ل Y تفاضل ال N بالنسبة ل X عبارة
+
+675
+01:19:20,170 --> 01:19:24,810
+عن continuous functions على المستطيل اللي عندنا،
+
+676
+01:19:24,810 --> 01:19:28,810
+كويس؟ اللي هو X محصورة من Alpha إلى Beta وY محصورة
+
+677
+01:19:28,810 --> 01:19:32,550
+من جامعة إلى جامعة قيم يعني هنا القيمتين وهذه
+
+678
+01:19:32,550 --> 01:19:36,950
+القيمتين يعني على شكل مستاطيلبعد ذلك الـ
+
+679
+01:19:36,950 --> 01:19:40,930
+differential equation اللي عند هذه الأساسية بقول
+
+680
+01:19:40,930 --> 01:19:46,530
+عنها exact إذا كان تفاضل ال N بالنسبة إلى Y يساوي
+
+681
+01:19:46,530 --> 01:19:51,830
+تفاضل ال N بالنسبة إلى X إذا صرت قصتي سهلة بقدر
+
+682
+01:19:51,830 --> 01:19:55,490
+أحكم على مين على المعادلة اللي عندي هل هي exact
+
+683
+01:19:55,490 --> 01:20:02,480
+بسهولة و أجتشلو جيت هنا فاضلت ال M بالنسبة E ل Y
+
+684
+01:20:02,480 --> 01:20:06,680
+طبعا هي مضروبة في DX بدها فاضلها بالنسبة ل Y و جيت
+
+685
+01:20:06,680 --> 01:20:10,480
+فاضلت هذه بالنسبة ل X اللي هي مضروبة في Y بدي يكون
+
+686
+01:20:10,480 --> 01:20:14,920
+اتنين مالهم are equal ان كانوا equal بتبقى هذه إيش
+
+687
+01:20:14,920 --> 01:20:21,080
+exact لكن قال لي في المثلة if and only if يعني هذه
+
+688
+01:20:21,080 --> 01:20:26,600
+في اتجاهين لو كانت exact إذا الشرط هذا صحيحوالعكس
+
+689
+01:20:26,600 --> 01:20:31,100
+لو كان الشرط صحيح يبقى المعادلة التفاضلية المعطلة
+
+690
+01:20:31,100 --> 01:20:37,280
+بتكون مالها exactly بدنا نبرهن هذه النظرية أحد
+
+691
+01:20:37,280 --> 01:20:42,760
+الاتجاهات very easy التاني شنك شوية لكن بنقدر عليه
+
+692
+01:20:42,760 --> 01:20:45,120
+يبقى باجي بقول prove
+
+693
+01:20:52,760 --> 01:20:58,880
+كون F اندول F يبقى بتدمش البرهان في اتجاهين بدي
+
+694
+01:20:58,880 --> 01:21:03,220
+افترض واحد صحيح و اروح اثبت مين و بعد هيك امشي
+
+695
+01:21:03,220 --> 01:21:08,160
+العملية العكسية مش هيك أخدتوا في مبادئ رياضية صح
+
+696
+01:21:08,160 --> 01:21:12,240
+ولا لا طب احنا أخدنا في مبادئ رياضية ثلاث طرق
+
+697
+01:21:12,240 --> 01:21:21,770
+للبراهين Direct Pro برهان مباشر و إيش كمان؟و بعد
+
+698
+01:21:21,770 --> 01:21:29,130
+ال direct ايش فيه كمان؟ contrapositive يعني
+
+699
+01:21:29,130 --> 01:21:33,710
+اتجاهها بدي اعطيني اتجاه التاني باخد معاكوس او ال
+
+700
+01:21:33,710 --> 01:21:36,870
+negation لذا الطرف بدي اعطيني ال negation للطرف
+
+701
+01:21:36,870 --> 01:21:41,370
+التاني او ال contradiction بقول اثبت كذا بقول
+
+702
+01:21:41,370 --> 01:21:46,260
+افترض مش هيكاذا قدني الى تناقض يبقى افراني غلط
+
+703
+01:21:46,260 --> 01:21:49,840
+وعكس و هو الصح مش هي الطرق الطرق الطرق اللى
+
+704
+01:21:49,840 --> 01:21:53,720
+اتعلمتها من بدأ اللى درسوا مبادئ رياضية لكن اللى
+
+705
+01:21:53,720 --> 01:21:57,700
+خلصوا بس سنة أولى لسه ماخدوش مبادر هذا لطلبة
+
+706
+01:21:57,700 --> 01:22:02,140
+العلوم والترابية بس طلبة الهندسة مالهمش الشغلة
+
+707
+01:22:02,140 --> 01:22:06,570
+تمام طيب ما عليناأنا بس مجرد معلومة بقولها اللي
+
+708
+01:22:06,570 --> 01:22:10,430
+بحب يستفيد منها يستفيد منها احنا الان بدنا نمشي
+
+709
+01:22:10,430 --> 01:22:14,210
+direct flow بدنا نمسك طرفه و نوصل لهوين للطرف
+
+710
+01:22:14,210 --> 01:22:22,210
+الثاني فبجي بقول assume افترض that سميلي هذه
+
+711
+01:22:22,210 --> 01:22:26,550
+المعادلة اللي هي رقم واحد assume that the
+
+712
+01:22:26,550 --> 01:22:32,950
+differential equation one is exact
+
+713
+01:22:37,250 --> 01:22:42,370
+اللي هو مين؟ المطلوب الأول هذي exact if and only
+
+714
+01:22:42,370 --> 01:22:47,950
+if هذيك بفضل أفرض هذي انها exact يبقى شو بدى أثبت؟
+
+715
+01:22:47,950 --> 01:22:52,650
+بدى أثبت هذي صح ولا لأ؟ يبقى مدام فرقت ان المعادلة
+
+716
+01:22:52,650 --> 01:22:57,430
+هذي exact بدى أحاول أثبت اللي عندنا هذي طبعا؟
+
+717
+01:22:57,430 --> 01:23:05,500
+بقوله thenأو هذي exact then there exist حسب
+
+718
+01:23:05,500 --> 01:23:10,260
+التعريف هي التعريف لسه فوق ممكن نمسحه there exist
+
+719
+01:23:10,260 --> 01:23:19,860
+a function psi of x و y تسوي constant c such that
+
+720
+01:23:19,860 --> 01:23:25,420
+بحيث أن بحيث
+
+721
+01:23:25,420 --> 01:23:31,770
+أن دي psi يسوي كذا such thatالدى ابساى
+
+722
+01:23:34,990 --> 01:23:44,950
+الدي اب ساي بده ساوي اللي هو M DX زائد ال N في DY
+
+723
+01:23:44,950 --> 01:23:49,430
+بده اختصار فبدل ما اقول M of X و Y يبقى بده اقول M
+
+724
+01:23:49,430 --> 01:23:54,030
+دوري و N of X و Y يبقى انه معروف ضمن ان M are
+
+725
+01:23:54,030 --> 01:24:01,850
+functions of X and Y طيب الان برجع لمين لكالكلسي
+
+726
+01:24:01,850 --> 01:24:10,300
+butولكن دي إبصي يساوي partial إبصي على partial x
+
+727
+01:24:10,300 --> 01:24:17,400
+في dx زائد partial إبصي على partial y في dy هذا من
+
+728
+01:24:17,400 --> 01:24:24,810
+كل قلصيةطيب هذه هي هذه يبقى شو بس تنتج ان المعامل
+
+729
+01:24:24,810 --> 01:24:28,190
+اللي مضروب في DX بدي يسوي نفس المعامل والمعامل
+
+730
+01:24:28,190 --> 01:24:32,850
+اللي مضروب في Y بدي يسوي نفس المعامل يبقى ال M
+
+731
+01:24:32,850 --> 01:24:42,690
+تساوي partial A بSi على partial X and ال N تساوي
+
+732
+01:24:42,690 --> 01:24:45,870
+partial A بSi على partial Y
+
+733
+01:24:50,130 --> 01:24:56,110
+أحنا نريد أن نثبت أن تفاضل M بالنسبة ل Y يسوى
+
+734
+01:24:56,110 --> 01:25:01,440
+تفاضل N بالنسبة ل Mطب انا M هيها عندي سنة موجة بدي
+
+735
+01:25:01,440 --> 01:25:07,540
+روح افاضلها بالنسبة لمن؟ الى Y فبروح بقوله اللي هو
+
+736
+01:25:07,540 --> 01:25:15,220
+تفاضل ال M بالنسبة الى Y يساوي بدي روح افاضل هدى
+
+737
+01:25:15,220 --> 01:25:21,940
+بالنسبة الى Y يبقى تفاضل بالنسبة الى Y ل M مين ال
+
+738
+01:25:21,940 --> 01:25:27,480
+M اللي partial of Psi by partial Xيعني يا بنات
+
+739
+01:25:27,480 --> 01:25:36,240
+كأنه بدي أجيب المشتقة الثانية لإبصاي طب كويس ها دي
+
+740
+01:25:36,240 --> 01:25:43,180
+هها اللي هي partial square إبصاي على partial y
+
+741
+01:25:43,180 --> 01:25:48,060
+partial x سؤال
+
+742
+01:25:49,440 --> 01:25:55,000
+بقدر ابدل ال X مكان ال Y و ال Y مكان ال X اللي
+
+743
+01:25:55,000 --> 01:25:59,760
+درسه Calculus C بنقدر؟ بنقدر في حالة واحدة لو كانت
+
+744
+01:25:59,760 --> 01:26:05,940
+الدالة دالة متاصلة لو كانت متاصلة بنقدر نبدل
+
+745
+01:26:05,940 --> 01:26:10,480
+without problemsبس لو ماكنتش متصل يبقى الشغل هذا
+
+746
+01:26:10,480 --> 01:26:17,540
+غلط طيب تعالوا نرجع لهنش بقولي هدول are continuous
+
+747
+01:26:17,540 --> 01:26:23,240
+صحيح ولا لأ يبقى بقدر أبدل وانا مرتاح ماعنديش
+
+748
+01:26:23,240 --> 01:26:28,260
+مشكلة يبقى هذا الكلام بقدر أقول يساوي partial
+
+749
+01:26:28,260 --> 01:26:37,450
+squareعلى partial x partial y because of the
+
+750
+01:26:37,450 --> 01:26:40,490
+continuity
+
+751
+01:26:40,490 --> 01:26:47,790
+بسبب الاتصال طيب هذا الكلام يساوي بدي أعيده مرة
+
+752
+01:26:47,790 --> 01:26:52,070
+تانية partial على partial x خليكي برا ببقى اللي
+
+753
+01:26:52,070 --> 01:26:57,980
+عندي partial fy على partial yفال partial of y على
+
+754
+01:26:57,980 --> 01:27:04,360
+partial of y يعني أنه يبقى
+
+755
+01:27:04,360 --> 01:27:10,120
+partial n على partial x أظن و هو المطلوبيبقى هاي
+
+756
+01:27:10,120 --> 01:27:13,460
+يثبتنا ان partial M على partial Y يسوى 100 partial
+
+757
+01:27:13,460 --> 01:27:16,540
+N على partial X هذا هو الاثبات السهل لهذا الجزء
+
+758
+01:27:16,540 --> 01:27:22,400
+السهل هذا بده يعطينا ان partial M على partial Y
+
+759
+01:27:22,400 --> 01:27:31,320
+يسوى partial N على partial X هذا الاتجاه الأول نجي
+
+760
+01:27:31,320 --> 01:27:35,040
+للاتجاه الثاني الاتجاه الثاني بنروح نقول
+
+761
+01:27:35,040 --> 01:27:45,210
+conversely العكسبدي افترض ان هذا الصحيح وبناء عليه
+
+762
+01:27:45,210 --> 01:27:51,210
+اثبت ان المعادلة هذه مالها exact يعني اذا جدت لاجي
+
+763
+01:27:51,210 --> 01:27:55,450
+function بيساوي و فيكساوي و يساوي يكون اصلا تحققها
+
+764
+01:27:55,450 --> 01:27:59,530
+بيصير كلامي صح وبالتالي بيكون برهنة النظرية تماما
+
+765
+01:27:59,700 --> 01:28:08,000
+يبقى باجي بقوله assume افترض ان ال partial m by
+
+766
+01:28:08,000 --> 01:28:19,480
+partial y يساوي partial n by partial x وبالتالي
+
+767
+01:28:19,480 --> 01:28:24,800
+بنحاول نثبت ان المعادلة هذه مالها معادلة exact
+
+768
+01:28:24,800 --> 01:28:31,480
+بقوله كويسمشان هيك بروح افترض في عندي دالة من عندي
+
+769
+01:28:31,480 --> 01:28:42,020
+بروح بقوله let phi of x y be a function such that
+
+770
+01:28:42,020 --> 01:28:53,660
+بحيث ان ال m تساوي partial phi على partial xبروح
+
+771
+01:28:53,660 --> 01:28:59,800
+من عندى، بختار دالة، بحيث الدالة هذه مشتقتها
+
+772
+01:28:59,800 --> 01:29:06,950
+بالنسبة ل X، بدي يعطينا مين؟ ال M تبعت مين؟تبعت
+
+773
+01:29:06,950 --> 01:29:10,750
+المعادلة التفاضلية لأن اللي بدى أثبت إن ما لها
+
+774
+01:29:10,750 --> 01:29:17,950
+exact يبجى أنا جبت ال M بدلالة مين بدلالة ال five
+
+775
+01:29:17,950 --> 01:29:23,330
+مظبوط ولا لأ بدى أروح أجيب ال N بدلالة ال five
+
+776
+01:29:23,330 --> 01:29:38,760
+يبجى هنا بقوله الآن wantto find N in terms of Phi
+
+777
+01:29:38,760 --> 01:29:45,800
+طبعا مش Phi هذا اللي فيها الخاوية Phi of XY يعني
+
+778
+01:29:45,800 --> 01:29:50,680
+يعني بنروح أجيب ال N بدلالة ال term اللي عندنا هنا
+
+779
+01:29:50,680 --> 01:29:56,260
+بقوله والله كويس نبدأ بهذه أنا عندي المعلومة هذه
+
+780
+01:29:57,430 --> 01:30:02,150
+ماذا رايكوا؟ بتروح أفاضلها بالنسبة إلى Y لأنه
+
+781
+01:30:02,150 --> 01:30:07,170
+ماعطيني condition بدي أستفيد منه يبقى باجي بقوله
+
+782
+01:30:07,170 --> 01:30:15,850
+الان partial M by partial Y تساوي partial على
+
+783
+01:30:15,850 --> 01:30:22,850
+partial Y ل M من ال M؟بارشال في على بارشال اكس
+
+784
+01:30:22,850 --> 01:30:32,270
+يبقى بارشال في على بارشال اكس يعني هذه بقدر اقول
+
+785
+01:30:32,270 --> 01:30:40,830
+partial square في by partial y partial x الان ال M
+
+786
+01:30:40,830 --> 01:30:45,840
+هذه اتفاقنا يا بنات انها مالهاcontinuous يبقى بقدر
+
+787
+01:30:45,840 --> 01:30:51,400
+أبدل هذه صحيح؟ يعني هذا الكلام بده يسوي partial
+
+788
+01:30:51,400 --> 01:31:01,020
+على partial X ل partial Phi على partial Y يبقى هذا
+
+789
+01:31:01,020 --> 01:31:04,780
+because of
+
+790
+01:31:04,780 --> 01:31:09,140
+the continuity
+
+791
+01:31:13,550 --> 01:31:23,170
+الحين هذه but و لكن partial m على partial y يسوى
+
+792
+01:31:23,170 --> 01:31:28,270
+partial n على partial x صحيح ولا لأ؟ هذا موطع هيئة
+
+793
+01:31:29,080 --> 01:31:33,420
+طب partial M على partial Y جيبته هيك يبقى هدول
+
+794
+01:31:33,420 --> 01:31:40,120
+بيسووا بعض يبقى هذا بده يعطينا انه مهم انه partial
+
+795
+01:31:40,120 --> 01:31:47,480
+على partial X ل partial Phi على partial Y يسوى
+
+796
+01:31:47,480 --> 01:31:57,020
+partial N على partial X طب إيش رأيك؟ بدي أنقل هذه
+
+797
+01:31:57,020 --> 01:32:04,150
+على الشكات تانيةأيش بيصير؟ بيصير partial N على
+
+798
+01:32:04,150 --> 01:32:10,310
+partial X ماقص partial على partial X لpartial Phi
+
+799
+01:32:10,310 --> 01:32:18,830
+على partial Y سوى قداش Zero أليس هذا معناه اشتقاق
+
+800
+01:32:18,830 --> 01:32:26,210
+الجزئين بالنسبة ل X؟مشتقة المجموع الجبري لدالتين
+
+801
+01:32:26,210 --> 01:32:31,930
+يساوي المجموع الجبري لمشتقتيهم يعني هذا بقدر اكتبه
+
+802
+01:32:31,930 --> 01:32:39,530
+على الشكل التالي partial على partial X لل N ناقص
+
+803
+01:32:39,530 --> 01:32:47,700
+partial Phi على partial Y سوى Zلو تدخلها تصير
+
+804
+01:32:47,700 --> 01:32:52,200
+مشتقة الأولى ناقص مشتقة التانى، ماساويتش شيء، انا
+
+805
+01:32:52,200 --> 01:32:58,240
+بدي اسألكوا السؤال التالى، الحين لو جاتلي دالة
+
+806
+01:32:58,240 --> 01:33:04,440
+وفضلتها بالنسبة لما تغير وطلعت تفضل يساوي صفر، ايش
+
+807
+01:33:04,440 --> 01:33:10,590
+معناها؟الدالة هذه ثابتة يعني هذه الدالة ثابتة
+
+808
+01:33:10,590 --> 01:33:16,390
+بنسبة لمين ل X يعني هذه الدالة ليست function في X
+
+809
+01:33:16,390 --> 01:33:23,150
+وإنما مقدار ثابت يبقى هذه function في Y ليش؟ لأن
+
+810
+01:33:23,150 --> 01:33:28,170
+ثابت عندي من أن عندي متغيرين إذا عند X بعتبر Y
+
+811
+01:33:28,170 --> 01:33:33,590
+ثابت صح ولا لأ؟ لأن ده اللي في المتغيرين يبقى هذا
+
+812
+01:33:33,590 --> 01:33:44,360
+معناهإن الان ناقص partial phi على partial y is a
+
+813
+01:33:44,360 --> 01:33:52,860
+function of y only يعني ماهياش function في x لأن
+
+814
+01:33:52,860 --> 01:33:59,580
+تفاضلها بالنسبة ل x يسوى zeroيبقى هذا اللي بينغسيه
+
+815
+01:33:59,580 --> 01:34:04,060
+لما فضلته بالنسبة ل X طالع Zero معناته الدالة بين
+
+816
+01:34:04,060 --> 01:34:12,100
+القوسين ليست function في X يبقى function في Y يبقى
+
+817
+01:34:12,100 --> 01:34:24,080
+بناء عليه LN ناقص partial Fi على partial Y يبقى F
+
+818
+01:34:24,080 --> 01:34:28,430
+of Yيعني ده لا في why فقط
+
+819
+01:34:39,030 --> 01:34:43,970
+طيب مادام دالة في Y بدي اجيب ال N لان احنا مش بجي
+
+820
+01:34:43,970 --> 01:34:49,170
+نقول بدي اجيب ال N بدلالة مين بدلالة في هي اللي
+
+821
+01:34:49,170 --> 01:34:53,670
+انا بدور عليه يبجي هي وصلت لها انجلي هذه ع الشجة
+
+822
+01:34:53,670 --> 01:35:01,390
+التانية بصير عندنا ال N تساوي partial في على
+
+823
+01:35:01,390 --> 01:35:10,130
+partial Y زائد ال F of Yبصبوب؟ طيب نرجع للمعادلة
+
+824
+01:35:10,130 --> 01:35:14,950
+العصرية اللى بدي أثبت انها exact انا بدي أثبت انها
+
+825
+01:35:14,950 --> 01:35:21,110
+exact باجي بقوله الان هى احنا فرضنا وين ما عندكوا
+
+826
+01:35:21,110 --> 01:35:26,170
+ال verse لهيه فرضنا هذا بصبوب؟ اذا بدي أثبت ان
+
+827
+01:35:26,170 --> 01:35:32,510
+المعادلة هذه مالها is exact يبقى باجي بقوله ال M
+
+828
+01:35:32,510 --> 01:35:41,020
+DXزائد ال n dy بده يساوي ال m يا بنات اللي فرضناها
+
+829
+01:35:41,020 --> 01:35:46,720
+وراحت هي partial phi على partial x يبقى هذه
+
+830
+01:35:46,720 --> 01:35:56,160
+partial phi على partial x في dx زائد ال n هي فوق
+
+831
+01:35:56,160 --> 01:36:05,400
+partial phi على partial y زائدالـ f of y كله في
+
+832
+01:36:05,400 --> 01:36:15,300
+الـ dy بده يساوي zero كله هذا طيب طلعيلي هنا هذا
+
+833
+01:36:15,300 --> 01:36:21,440
+الكلام يساوي بده افك هذي واخدهم مع بعض يبقى شبسيط
+
+834
+01:36:21,440 --> 01:36:27,240
+عندي partial phi على partial x في dx زي partial
+
+835
+01:36:27,240 --> 01:36:38,930
+phi على partial y في dyزائد f of y في dy طيب
+
+836
+01:36:38,930 --> 01:36:46,910
+تعالى أخد هذه أليست هذه هي الاشتقاق الكل لفاي يعني
+
+837
+01:36:46,910 --> 01:36:55,370
+هذه هي d fi of x و y بصبوط زي ما عملنا بتاعة
+
+838
+01:36:55,370 --> 01:37:04,250
+الإبصاي طيب هذه يا بناتبدي اكتبها على الشكل التالي
+
+839
+01:37:04,250 --> 01:37:12,350
+if one of d if one of y
+
+840
+01:37:21,470 --> 01:37:33,460
+لما كنا نقول كو صين ال X DX، أليست مشتقة صين X؟هذه
+
+841
+01:37:33,460 --> 01:37:39,280
+هي هذه انا عندي f of y ورا ال f of y dy بدي اقول
+
+842
+01:37:39,280 --> 01:37:44,420
+مشتق الدالة تانية اسمها f one of one مظبوط بدل ما
+
+843
+01:37:44,420 --> 01:37:49,840
+كنت اقول cosine x dx هي ال d sine ال x يبقى نفس
+
+844
+01:37:49,840 --> 01:37:55,240
+القصة d fy طب ليه شويت هيك بقولك اه لإن هذه مشتقة
+
+845
+01:37:55,240 --> 01:37:59,660
+كلية و هذه مشتقة كلية بقدر اخدها مشتقة كلية واحدة
+
+846
+01:37:59,660 --> 01:38:11,090
+يبقى هذه كإنها dلـ fi of x و y زائد f1 of y صحيح؟
+
+847
+01:38:11,090 --> 01:38:16,410
+هذه الـ function جديدة كلها بده سميها تسمية جديدة
+
+848
+01:38:23,510 --> 01:38:27,830
+هذه شيلت المقدار بين القوصات وسميتها بصي تسمية
+
+849
+01:38:27,830 --> 01:38:34,270
+جديدة كل هذا بيسوي كده؟ بيسوي Zero يبقى هذا كله
+
+850
+01:38:34,270 --> 01:38:40,590
+بيسوي Zero لو كملت الدالة هذه كده بتعطينا؟ هذا
+
+851
+01:38:40,590 --> 01:38:51,700
+بيعطيك انه Psi of X Y يسوى C وC is constantيبقى
+
+852
+01:38:51,700 --> 01:38:56,020
+صرة المعنى ال exact ولا لا مش شايف تعريف ال exact
+
+853
+01:38:56,020 --> 01:39:01,900
+يبقى
+
+854
+01:39:01,900 --> 01:39:13,440
+thisهذا يعني ان الاختصار الاختصار الاختصار
+
+855
+01:39:13,440 --> 01:39:15,720
+الاختصار الاختصار الاختصار الاختصار الاختصار
+
+856
+01:39:15,720 --> 01:39:18,620
+الاختصار الاختصار الاختصار الاختصار الاختصار
+
+857
+01:39:18,620 --> 01:39:19,940
+الاختصار الاختصار الاختصار الاختصار الاختصار
+
+858
+01:39:19,940 --> 01:39:23,200
+الاختصار الاختصار الاختصار الاختصار الاختصار
+
+859
+01:39:23,200 --> 01:39:23,260
+الاختصار الاختصار الاختصار الاختصار الاختصار
+
+860
+01:39:23,260 --> 01:39:26,280
+الاختصار الاختصار الاختصار الاختصار الاختصار
+
+861
+01:39:26,280 --> 01:39:34,540
+الاختص
+
+862
+01:39:37,490 --> 01:39:44,090
+أنا عنده الآن شرط ال exactness المعادلة Mdx Zn Dy
+
+863
+01:39:44,090 --> 01:39:49,290
+بيساوي 0 is exact إذا كان تفاضل M بالنسبة إلى Y
+
+864
+01:39:49,290 --> 01:39:56,150
+إذا كان تفاضل M بالنسبة إلى Y سوى تفاضل N بالنسبة
+
+865
+01:39:56,150 --> 01:39:57,950
+إلى X
+
+866
+01:40:00,170 --> 01:40:05,890
+هيبقى البرهان بيحصل في اتجاهين افترض
+
+867
+01:40:05,890 --> 01:40:10,450
+ان المعادلة الاصلية اللى عندنا هذه is exact معناته
+
+868
+01:40:10,450 --> 01:40:14,050
+لازم الاقي function ψ of x و y بيبقى تساوي
+
+869
+01:40:14,050 --> 01:40:22,290
+constant بحيث ان d ψ هي mx زائد ال n dy لكن من
+
+870
+01:40:22,290 --> 01:40:26,950
+كالكولاسي ال d ψ هي تفضل ψ بالنسبة ل x dx زي تفضل
+
+871
+01:40:26,950 --> 01:40:33,380
+ψ بالنسبة ل yأقارن بين المعادلتين بجيب ال M بدلالة
+
+872
+01:40:33,380 --> 01:40:36,560
+الإبصاى و بجيب ال N بدلالة الإبصاى
+
+873
+01:40:40,640 --> 01:40:44,400
+أنا او بدي أوصل ال condition اللي هو partial M على
+
+874
+01:40:44,400 --> 01:40:47,540
+partial Y سواء partial هذا اللي بدي أوصله بقوله
+
+875
+01:40:47,540 --> 01:40:53,020
+كويس احنا عندنا M مطلوب تفاضلها بالنسبة إلى Y إذا
+
+876
+01:40:53,020 --> 01:40:57,120
+حاجة فاضلها دي بالنسبة لما M إلى Y يبقى بصير
+
+877
+01:40:57,120 --> 01:41:01,020
+partial M على partial Y سواء partial على partial Y
+
+878
+01:41:01,020 --> 01:41:05,480
+ل partial Y على partial X هذه تعتبر المشتقة
+
+879
+01:41:05,480 --> 01:41:11,640
+الثانيةبدي أبدل الـ X و الـ Y مكان البعض لإن دالة
+
+880
+01:41:11,640 --> 01:41:16,060
+continuous معتنية في نص النظرية يفجأة هذا الكلام
+
+881
+01:41:16,060 --> 01:41:20,160
+بده يساوي بعد ما بدلت بده أرجعها مرة تانية أخد ال
+
+882
+01:41:20,160 --> 01:41:23,200
+partial على partial X برا و ده ال partial يبصيا
+
+883
+01:41:23,200 --> 01:41:26,500
+على partial Y ال partial يبصيا على partial Y هيه ب
+
+884
+01:41:26,500 --> 01:41:30,560
+N يفجأة بدي أشيل وكتب بدله N يفجأة بديت partial M
+
+885
+01:41:30,560 --> 01:41:34,640
+على partial Y وصلت إلى مين partial Nعلى partial X
+
+886
+01:41:34,640 --> 01:41:39,080
+وهو المطلوب الأول المطلوب التاني بدنا نمشي في
+
+887
+01:41:39,080 --> 01:41:43,520
+الاتجاه المعاكس فقلنا conversely assume that
+
+888
+01:41:43,520 --> 01:41:49,140
+افترضنا ال condition هذا موجود الآن بدنا نحاول
+
+889
+01:41:49,140 --> 01:41:53,820
+نثبت أن الدالة اللي عندنا هذه مالها exactتعريف ال
+
+890
+01:41:53,820 --> 01:41:58,360
+exact هذي بقول عن exact إذا جدرت لاجي function ψ
+
+891
+01:41:58,360 --> 01:42:01,780
+of x و y بده يساوي constant بحيث partial ψ على
+
+892
+01:42:01,780 --> 01:42:05,720
+partial x بده يساوي ال m و partial ψ على partial y
+
+893
+01:42:05,720 --> 01:42:10,720
+بده يساوي ال minimum أو d ψ بده يساوي المعادل اللي
+
+894
+01:42:10,720 --> 01:42:16,930
+عندنا هذي بقوله بسيطة فترضنا هذافرقت من عندى دالة
+
+895
+01:42:16,930 --> 01:42:22,530
+بحيث ال M يسوى مشتقة هذه الدالة بالنسبة لمن ال X
+
+896
+01:42:22,530 --> 01:42:28,710
+يبجى انا فرقت عند ال M بدلالة مشتقة دالة Phi بذهب
+
+897
+01:42:28,710 --> 01:42:35,950
+هشوف ما هو شكل ال N بالنسبة لمن نسبة ال Phi بقولك
+
+898
+01:42:35,950 --> 01:42:40,070
+كويس انت عندك المعلومة هذه بدى تسوى partial N على
+
+899
+01:42:40,070 --> 01:42:44,350
+partial X خدت المعلومة هذهأنا شيلت ال M و حطيت
+
+900
+01:42:44,350 --> 01:42:48,230
+قيمتها بالفرض اللي انا فرضه صارت المعاملة بالشكل
+
+901
+01:42:48,230 --> 01:42:53,910
+هذا عملت Champion XY بسبب ال continuity صار عند
+
+902
+01:42:53,910 --> 01:43:00,590
+مين partial M على A هذا الشرط الأساسي هذا معناه أن
+
+903
+01:43:00,590 --> 01:43:05,220
+القيمة اللي حصلت عليها هنا بدأت سوى partial Nعلى
+
+904
+01:43:05,220 --> 01:43:09,420
+partial X وديت هذه على الشجة التانية واخدت partial
+
+905
+01:43:09,420 --> 01:43:15,240
+على partial X لمشتقة ما بينها القوسين طلعته ايش؟
+
+906
+01:43:15,240 --> 01:43:19,780
+برا طب طلع هذا مقداش؟ يساوي Zero معناته هذه
+
+907
+01:43:19,780 --> 01:43:24,660
+constant function بالنسبة لمين؟ ال X طب لما يكون
+
+908
+01:43:24,660 --> 01:43:28,400
+عندي ال constant function بالنسبة ل X يبقى هذه ال
+
+909
+01:43:28,400 --> 01:43:33,440
+constant function بتكون دالة في Yيبقى روحت قلت هذه
+
+910
+01:43:33,440 --> 01:43:37,500
+هي عبارة عن دلة في مين في why نجلت هذه على الشكل
+
+911
+01:43:37,500 --> 01:43:42,760
+التاني وبالتالي جبت ال N بدلالة Phi على الشكل اللي
+
+912
+01:43:42,760 --> 01:43:46,780
+عندنا هذا بعد ذلك روحت مسكت المعادلة هذه وعوّط
+
+913
+01:43:46,780 --> 01:43:52,050
+فيها امشي امشي وصلت لحد هناباجي بقول هذه المكان
+
+914
+01:43:52,050 --> 01:43:56,950
+كلصي مشتقة الفي و هذه بقدر اكتبها على الشكل التالي
+
+915
+01:43:56,950 --> 01:44:02,790
+اللي عندنا مشتقة و مشتقة أخدت المشتقة الكلية لهم
+
+916
+01:44:02,790 --> 01:44:06,750
+اللي بقى ان جثمين بده يسميها ابصي و هذه المعادلة
+
+917
+01:44:06,750 --> 01:44:10,750
+أصلا تساوي zero فسميتها ب zero حل المعادلة هذه
+
+918
+01:44:10,750 --> 01:44:14,630
+بالتكامل اللي بقى بالتكامل بتعطي الميان constant c
+
+919
+01:44:14,630 --> 01:44:18,430
+بقى ابصي و بيكسوي يساوي constant c هذا معناته ان
+
+920
+01:44:18,430 --> 01:44:23,070
+المعادلة هذه مالهاexact differential equation
+
+921
+01:44:23,070 --> 01:44:29,230
+تمام؟ طب الآن بدنا بس شوية أمثلة على هذا الموضوع
+
+922
+01:44:29,230 --> 01:44:35,530
+حدا فيكم بتسأل أي سؤال هنا؟ أه في البرهان في أي
+
+923
+01:44:35,530 --> 01:44:39,770
+نقطة مش فاهمينه مش واضح ايه واخري في أي تساؤل؟
+
+924
+01:44:39,770 --> 01:44:46,130
+ندخل للأمثلةالتكتيك اللى طبعنا هنا بنا نتابعه بنا
+
+925
+01:44:46,130 --> 01:44:50,910
+نفاضل و نكامل كمان الآن زى ما هتشوفى فى الأسئلة
+
+926
+01:44:50,910 --> 01:44:54,790
+example
+
+927
+01:44:54,790 --> 01:45:02,490
+one solve
+
+928
+01:45:02,490 --> 01:45:13,690
+the differential equation اللى هو اتنين2xy تربيع
+
+929
+01:45:13,690 --> 01:45:30,350
+2xy تربيع زائدي 2y زائد اللي هو 2x تربيع y زائد
+
+930
+01:45:30,350 --> 01:45:38,110
+2x في ال y prime بده يساوي مين؟ Zero وهذه المعادلة
+
+931
+01:45:38,110 --> 01:45:44,980
+نحلهاوخلصنا مكافئة طيب بدي أحطها على ال standard
+
+932
+01:45:44,980 --> 01:45:50,560
+form اللي عندنا هذا بنات عشان أقدر أشتغل بدي دالة
+
+933
+01:45:50,560 --> 01:45:54,880
+مضروبة في dx ودالة تانية مضروبة في dy بجي بقوله
+
+934
+01:45:54,880 --> 01:46:00,580
+هذه أصلا y prime هي عبارة عن مين عبارة عن dy على
+
+935
+01:46:00,580 --> 01:46:05,440
+dx صحيح ولا لأ يبقى معنا هذا الكلام بدي أضرب كله
+
+936
+01:46:05,440 --> 01:46:16,850
+في dx يبقى هنا solutionالسؤال هو اتنين اكس واي
+
+937
+01:46:16,850 --> 01:46:25,050
+ترابية زائد اتنين واي دي اكس زائد اتنين اكس ترابية
+
+938
+01:46:25,050 --> 01:46:34,410
+واي زائد اتنين اكس دي واي بده يساوي زين الان هذه
+
+939
+01:46:34,410 --> 01:46:39,330
+ايش تعتبر M وهذه شو تعتبر N
+
+940
+01:46:41,640 --> 01:46:46,820
+طبعا تفاضل ال M بالنسبة الى Y
+
+941
+01:46:59,430 --> 01:47:06,530
+تفاضله بالنسبة ل Y يسوى كم؟ 2 تفاضله
+
+942
+01:47:06,530 --> 01:47:12,810
+بالنسبة ل X يسوى
+
+943
+01:47:12,810 --> 01:47:19,550
+كم؟أربعة XY زائدي اتنين تفاضل بالنسبة ال X X تربية
+
+944
+01:47:19,550 --> 01:47:23,790
+تفاضل باتنين X مع اتنين بيصير أربعة XY Y تفاضلها
+
+945
+01:47:23,790 --> 01:47:29,330
+باتنين طلعت نفسي النتيجة مظبوط يبقى هذا الكلام بده
+
+946
+01:47:29,330 --> 01:47:34,430
+يعطينا تفاضل ال M بالنسبة ال Y يسوى تفاضل ال N
+
+947
+01:47:34,430 --> 01:47:40,630
+بالنسبة ال X هذا معناه هذا اللي هي المعادلة واحد
+
+948
+01:47:40,630 --> 01:47:46,870
+أحدث الشكل اللي عندنا هناdifferential equation
+
+949
+01:47:46,870 --> 01:47:55,390
+when is exact هذا بده يعطينا there exist a
+
+950
+01:47:55,390 --> 01:48:05,130
+function psi of x y such that بحيث ان partial psi
+
+951
+01:48:05,130 --> 01:48:15,400
+على partial x يساوي ال m من ال m هيهايساوي ال M
+
+952
+01:48:15,400 --> 01:48:24,620
+يساوي ال N يساوي ال Y يساوي ال Y يساوي ال Y يساوي
+
+953
+01:48:24,620 --> 01:48:29,700
+ال Y يساوي
+
+954
+01:48:29,700 --> 01:48:33,260
+ال M
+
+955
+01:48:33,260 --> 01:48:36,160
+يساوي ال M يساوي ال Y يساوي ال M يساوي ال Y يساوي
+
+956
+01:48:36,160 --> 01:48:36,220
+ال Y يساوي ال M يساوي ال Y يساوي ال M يساوي ال Y
+
+957
+01:48:36,220 --> 01:48:36,960
+يساوي ال M يساوي ال Y يساوي ال M يساوي ال Y يساوي
+
+958
+01:48:36,960 --> 01:48:37,000
+ال M يساوي ال M يساوي ال Y يساوي ال M يساوي ال M
+
+959
+01:48:37,000 --> 01:48:37,060
+يساوي ال M يساوي ال M يساوي ال M يساوي ال M يساوي
+
+960
+01:48:37,060 --> 01:48:39,720
+يساوي ال M يساوي ال M يساوي ال M يسبصراحة أنا مش
+
+961
+01:48:39,720 --> 01:48:43,880
+عارف شكلها، لكن عارف مشتقتها، إذا بقدر أكملها،
+
+962
+01:48:43,880 --> 01:48:49,120
+يبقى بنات هذه لو بده أكملها، بده أكملها بنسبة لمن؟
+
+963
+01:48:49,120 --> 01:48:54,420
+ل X، تكاملها باسم X، هذي السهل وهذه السهل، لو بده
+
+964
+01:48:54,420 --> 01:48:58,600
+أكمل هذه، تكاملها بالنسبة لوايها، هذه السهل، يبقى
+
+965
+01:48:58,600 --> 01:49:04,000
+أي واحدة فيهم بتصد، بس اللحظة الثابتة التكامل،
+
+966
+01:49:04,000 --> 01:49:06,680
+يبقى الآن بقوله by integration
+
+967
+01:49:09,560 --> 01:49:14,920
+بدا اروح اكمل يبقى بصير عندك بدا اكمل هذه يا بنات
+
+968
+01:49:14,920 --> 01:49:25,580
+بدا اكمل بالنسبة لمن ل X يبقى هذه ل X ايش بصير X
+
+969
+01:49:25,580 --> 01:49:32,480
+تربيع على 2 بتروح اتنين مع اتنين بظل X تربيع Y
+
+970
+01:49:32,480 --> 01:49:37,980
+تربيع زاد 2Y بدا اكملها بالنسبة ل X هذا كله يعتبر
+
+971
+01:49:37,980 --> 01:49:46,450
+مقدارثابت يبقى بصير اتنين y في x زائد constant مش
+
+972
+01:49:46,450 --> 01:49:52,070
+ال constant العادي رقم ال constant function في عكس
+
+973
+01:49:52,070 --> 01:49:55,270
+الدالة اللي اكملت بالنسبة لكسي يبقى function في
+
+974
+01:49:55,270 --> 01:50:03,470
+مين في y يبقى زائد function of yالان بدى اجيب قداش
+
+975
+01:50:03,470 --> 01:50:09,390
+قيمة F of Y مشان هيك بدروح اشتق هذه الدالة بالنسبة
+
+976
+01:50:09,390 --> 01:50:17,390
+لمن؟ ل Y يبقى هذا بدى يعطينا partial Epsilon على
+
+977
+01:50:17,390 --> 01:50:22,530
+partial Y يسوى بالفعل هذه بالنسبة ل Y يا بنات يبقى
+
+978
+01:50:22,530 --> 01:50:33,830
+2 X تربيه Yيبقى اتنين اكس تربيع Y يبقى اتنين اكس
+
+979
+01:50:33,830 --> 01:50:41,350
+يبقى زائد اتنين اكس زائد F prime of Y
+
+980
+01:50:44,380 --> 01:50:51,720
+صح ولا لا؟ صحيكوا كمان مرة احنا قلنا بنلاقي
+
+981
+01:50:51,720 --> 01:50:56,780
+function ψ of x y بحيث انه تفاضل ψ بالنسبة ل x
+
+982
+01:50:56,780 --> 01:51:02,720
+يساوي ال M تفاضل ψ بالنسبة ل y يساوي ال N روحت على
+
+983
+01:51:02,720 --> 01:51:08,140
+هذه كملتها بالنسبة ل x حصلت على الدالة هذه طب بدي
+
+984
+01:51:08,140 --> 01:51:12,760
+اشتقها روحت اشتقتها طب ما هي ماشتقتها هي اللي فوق؟
+
+985
+01:51:20,620 --> 01:51:27,720
+بستنتج ان اتنين اكس تربية Y زائد اتنين X يساوي
+
+986
+01:51:27,720 --> 01:51:33,800
+اتنين اكس تربية Y زائد اتنين X زائد F prime of Y
+
+987
+01:51:34,600 --> 01:51:39,360
+أصلا لو جبت هذا عند هذا بروح و لو جبت هذا عند هذا
+
+988
+01:51:39,360 --> 01:51:45,220
+بروح هذا بده يعطينا انه f prime of y بده يسوي قداش
+
+989
+01:51:45,220 --> 01:51:50,800
+هذا الحين function في مين في متغير واحد صح ولا لأ
+
+990
+01:51:50,800 --> 01:51:59,280
+يبقى هذا معناه انه f of y بده يسوي قداش c1 يبقى
+
+991
+01:51:59,280 --> 01:52:03,180
+بروح بقوله ها the solution
+
+992
+01:52:21,280 --> 01:52:27,220
+كل هذا الكلام بده يساوي C
+
+993
+01:52:29,710 --> 01:52:33,970
+لأن قلنا there exists a function of psi of x و y
+
+994
+01:52:33,970 --> 01:52:44,290
+حطيلي تساوي C2 يالا هذه تساوي C2 طيب إيش رايك؟ بدي
+
+995
+01:52:44,290 --> 01:52:46,190
+أجيب C1 and C2
+
+996
+01:53:06,110 --> 01:53:12,870
+هذا هو حل المعادلة التفاضلية
+
+997
+01:53:14,840 --> 01:53:16,620
+لسة لازمنا في نفس ال section
+
diff --git a/PL9fwy3NUQKwa8ZDfSFGn6H8xVFLzqmCZC/euAOHAsWFbk_raw.json b/PL9fwy3NUQKwa8ZDfSFGn6H8xVFLzqmCZC/euAOHAsWFbk_raw.json
new file mode 100644
index 0000000000000000000000000000000000000000..721ee13e78b48a97ab4cc2b4442e3135fe99fbd6
--- /dev/null
+++ b/PL9fwy3NUQKwa8ZDfSFGn6H8xVFLzqmCZC/euAOHAsWFbk_raw.json
@@ -0,0 +1 @@
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713.08, "end": 738.96, "text": "طبعا هنقيم مثال على الـ Discontinuous coefficients وكيف هنحل هذا النوع من المسائل وبردولي هي non homogeneous differential equation بس بنحولها إلى من إلى homogeneous أو إلى linear differential equation يعني ال non linear differential equation بنحولها إلى linear differential equation", "tokens": [9566, 3555, 3615, 995, 8032, 1863, 4587, 32640, 50113, 6027, 15844, 2423, 39184, 4208, 9000, 259, 12549, 31994, 4032, 4117, 33911, 8032, 1863, 5016, 1211, 23758, 28239, 45367, 9154, 9673, 3794, 16373, 1211, 4032, 26890, 3215, 12610, 1829, 39896, 2107, 42632, 15756, 5367, 4724, 3794, 44945, 5016, 12610, 11296, 30731, 9154, 30731, 42632, 34051, 30731, 8213, 15756, 5367, 37495, 22653, 2423, 2107, 8213, 15756, 5367, 44945, 5016, 12610, 11296, 30731, 8213, 15756, 5367], "avg_logprob": -0.2856841196079512, "compression_ratio": 1.855721393034826, "no_speech_prob": 0.0, "words": [{"start": 713.08, "end": 713.48, "word": "طبعا", "probability": 0.787139892578125}, {"start": 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إلى", "probability": 0.94921875}, {"start": 736.84, "end": 737.3, "word": " linear", "probability": 0.9326171875}, {"start": 737.3, "end": 738.12, "word": " differential", "probability": 0.89892578125}, {"start": 738.12, "end": 738.96, "word": " equation", "probability": 0.982421875}], "temperature": 1.0}, {"id": 31, "seek": 76017, "start": 739.29, "end": 760.17, "text": "بدنا نعرف ما هو الشكل العام لها وبعد هيك كيف بدنا نحل هذا النوع من المسائل فبجي بقول له ده differential equation ل Y prime زائد P of T في ال Y", "tokens": [3555, 3215, 8315, 8717, 3615, 28480, 19446, 31439, 25124, 28820, 18863, 10943, 5296, 11296, 46599, 22488, 39896, 4117, 9122, 33911, 47525, 8315, 8717, 5016, 1211, 23758, 28239, 45367, 9154, 9673, 3794, 16373, 1211, 6156, 3555, 7435, 1829, 4724, 39648, 46740, 11778, 3224, 15756, 5367, 5296, 398, 5835, 30767, 16373, 3215, 430, 295, 314, 8978, 2423, 398], "avg_logprob": -0.2886513199722558, "compression_ratio": 1.361963190184049, "no_speech_prob": 0.0, "words": 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{"start": 959.26, "end": 960.16, "word": " linear", "probability": 0.9169921875}], "temperature": 1.0}, {"id": 41, "seek": 98745, "start": 968.79, "end": 987.45, "text": "order differential equation ممكن نحولها إلى معادلة خطية من الرتبة الأولى as follow كتالي شوفوا كيف هنحولها يا بنات", "tokens": [4687, 15756, 5367, 3714, 43020, 8717, 5016, 12610, 11296, 30731, 20449, 18513, 37977, 16490, 9566, 10632, 9154, 34892, 2655, 49401, 16247, 12610, 7578, 382, 1524, 9122, 2655, 6027, 1829, 13412, 38688, 14407, 9122, 33911, 8032, 1863, 5016, 12610, 11296, 35186, 4724, 8315, 2655], "avg_logprob": -0.24946733564138412, "compression_ratio": 1.2642857142857142, "no_speech_prob": 0.0, "words": [{"start": 968.7900000000001, "end": 970.19, "word": "order", "probability": 0.335693359375}, {"start": 970.19, "end": 971.59, "word": " differential", "probability": 0.8427734375}, {"start": 971.59, "end": 973.63, "word": " equation", "probability": 0.96484375}, {"start": 973.63, "end": 975.01, "word": " ممكن", "probability": 0.7822265625}, {"start": 975.01, "end": 975.61, "word": " نحولها", "probability": 0.6905517578125}, {"start": 975.61, "end": 975.77, "word": " إلى", "probability": 0.615234375}, {"start": 975.77, "end": 976.19, "word": " معادلة", "probability": 0.9178059895833334}, {"start": 976.19, "end": 976.87, "word": " خطية", "probability": 0.8125}, {"start": 976.87, "end": 977.33, "word": " من", "probability": 0.982421875}, {"start": 977.33, "end": 978.13, "word": " الرتبة", "probability": 0.814453125}, {"start": 978.13, "end": 978.89, "word": " الأولى", "probability": 0.9723307291666666}, {"start": 978.89, "end": 979.67, "word": " as", "probability": 0.79443359375}, {"start": 979.67, "end": 980.49, "word": " follow", "probability": 0.388671875}, {"start": 980.49, "end": 982.47, "word": " كتالي", "probability": 0.871337890625}, {"start": 982.47, "end": 986.23, "word": " شوفوا", "probability": 0.9256184895833334}, {"start": 986.23, "end": 986.41, "word": " كيف", "probability": 0.971923828125}, {"start": 986.41, "end": 986.99, "word": " هنحولها", "probability": 0.8466796875}, {"start": 986.99, "end": 987.19, "word": " يا", "probability": 0.335693359375}, {"start": 987.19, "end": 987.45, "word": " بنات", "probability": 0.8050130208333334}], "temperature": 1.0}, {"id": 42, "seek": 102071, "start": 991.35, "end": 1020.71, "text": "بدي اعمل خطوطين بس بكون حولتها الى linear الخطوة الاولى الان بدي بتطلع على Y هذه المضربة في من في GRT بضرب المعادلة هذه في Y مرفوع لنفس الأس هذا بس بإشارة سالب يبقى الخطوة الاولى بقوله multiply both sides", "tokens": [3555, 16254, 1975, 25957, 1211, 16490, 9566, 2407, 9566, 9957, 4724, 3794, 4724, 30544, 11331, 12610, 2655, 11296, 2423, 7578, 8213, 33962, 9566, 2407, 3660, 42963, 12610, 7578, 2423, 7649, 4724, 16254, 39894, 9566, 1211, 3615, 15844, 398, 29538, 9673, 11242, 25513, 3660, 8978, 9154, 8978, 10903, 51, 4724, 11242, 25513, 9673, 3615, 18513, 37977, 29538, 8978, 398, 3714, 28480, 45367, 5296, 1863, 36178, 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0.6031494140625}, {"start": 1003.51, "end": 1004.79, "word": " بضرب", "probability": 0.8460286458333334}, {"start": 1004.79, "end": 1005.61, "word": " المعادلة", "probability": 0.9783935546875}, {"start": 1005.61, "end": 1006.15, "word": " هذه", "probability": 0.94140625}, {"start": 1006.15, "end": 1006.55, "word": " في", "probability": 0.95849609375}, {"start": 1006.55, "end": 1006.91, "word": " Y", "probability": 0.96826171875}, {"start": 1006.91, "end": 1007.57, "word": " مرفوع", "probability": 0.8673502604166666}, {"start": 1007.57, "end": 1008.09, "word": " لنفس", "probability": 0.9625651041666666}, {"start": 1008.09, "end": 1008.63, "word": " الأس", "probability": 0.60302734375}, {"start": 1008.63, "end": 1008.91, "word": " هذا", "probability": 0.7080078125}, {"start": 1008.91, "end": 1009.13, "word": " بس", "probability": 0.919189453125}, {"start": 1009.13, "end": 1009.95, "word": " بإشارة", "probability": 0.94658203125}, {"start": 1009.95, "end": 1010.99, "word": " سالب", "probability": 0.7687174479166666}, {"start": 1010.99, "end": 1011.77, "word": " يبقى", "probability": 0.94189453125}, {"start": 1011.77, "end": 1012.33, "word": " الخطوة", "probability": 0.9813232421875}, {"start": 1012.33, "end": 1013.01, "word": " الاولى", "probability": 0.97705078125}, {"start": 1013.01, "end": 1013.73, "word": " بقوله", "probability": 0.869140625}, {"start": 1013.73, "end": 1014.81, "word": " multiply", "probability": 0.87890625}, {"start": 1014.81, "end": 1018.79, "word": " both", "probability": 0.93017578125}, {"start": 1018.79, "end": 1020.71, "word": " sides", "probability": 0.92626953125}], "temperature": 1.0}, {"id": 43, "seek": 104196, "start": 1022.72, "end": 1041.96, "text": "of equation star by y to the minus n we get يصير المعادلة على الشكل التالي y to the minus n في y prime", "tokens": [2670, 5367, 3543, 538, 288, 281, 264, 3175, 297, 321, 483, 7251, 9381, 13546, 9673, 3615, 18513, 37977, 15844, 25124, 28820, 16712, 6027, 1829, 288, 281, 264, 3175, 297, 8978, 288, 5835], "avg_logprob": -0.29545454545454547, "compression_ratio": 1.2149532710280373, "no_speech_prob": 0.0, "words": [{"start": 1022.72, "end": 1023.34, "word": "of", "probability": 0.081298828125}, {"start": 1023.34, "end": 1025.22, "word": " equation", "probability": 0.92529296875}, {"start": 1025.22, "end": 1027.02, "word": " star", "probability": 0.59130859375}, {"start": 1027.02, "end": 1028.7, "word": " by", "probability": 0.87451171875}, {"start": 1028.7, "end": 1029.98, "word": " y", "probability": 0.818359375}, {"start": 1029.98, "end": 1030.3, "word": " to", "probability": 0.80859375}, {"start": 1030.3, "end": 1030.54, "word": " the", "probability": 0.92236328125}, {"start": 1030.54, "end": 1030.94, "word": " minus", "probability": 0.943359375}, {"start": 1030.94, "end": 1031.7, "word": " n", "probability": 0.85986328125}, {"start": 1031.7, "end": 1032.82, "word": " we", "probability": 0.7509765625}, {"start": 1032.82, "end": 1033.52, "word": " get", "probability": 0.94091796875}, {"start": 1033.52, "end": 1034.68, "word": " يصير", "probability": 0.6577962239583334}, {"start": 1034.68, "end": 1035.24, "word": " المعادلة", "probability": 0.91943359375}, {"start": 1035.24, "end": 1035.46, "word": " على", "probability": 0.89892578125}, {"start": 1035.46, "end": 1035.96, "word": " الشكل", "probability": 0.912109375}, {"start": 1035.96, "end": 1036.74, "word": " التالي", "probability": 0.8894856770833334}, {"start": 1036.74, "end": 1038.34, "word": " y", "probability": 0.65625}, {"start": 1038.34, "end": 1038.66, "word": " to", "probability": 0.93212890625}, {"start": 1038.66, "end": 1038.92, "word": " the", "probability": 0.9296875}, {"start": 1038.92, "end": 1039.32, "word": " minus", "probability": 0.982421875}, {"start": 1039.32, "end": 1040.0, "word": " n", "probability": 0.89697265625}, {"start": 1040.0, "end": 1040.64, "word": " في", "probability": 0.87646484375}, {"start": 1040.64, "end": 1041.14, "word": " y", "probability": 0.41357421875}, {"start": 1041.14, "end": 1041.96, "word": " prime", "probability": 0.59375}], "temperature": 1.0}, {"id": 44, "seek": 106248, "start": 1044.02, "end": 1062.48, "text": "P of T في ال Y to the power واحد ناقص N يساوي ال G of T مرة تانية", "tokens": [47, 295, 314, 8978, 2423, 398, 281, 264, 1347, 36764, 24401, 8717, 995, 4587, 9381, 426, 7251, 3794, 995, 45865, 2423, 460, 295, 314, 3714, 25720, 6055, 7649, 10632], "avg_logprob": -0.2154947931567828, "compression_ratio": 1.0574712643678161, "no_speech_prob": 0.0, "words": [{"start": 1044.02, "end": 1044.3, "word": "P", "probability": 0.36669921875}, {"start": 1044.3, "end": 1045.24, "word": " of", "probability": 0.1678466796875}, {"start": 1045.24, "end": 1045.7, "word": " T", "probability": 0.93359375}, {"start": 1045.7, "end": 1046.22, "word": " في", "probability": 0.74755859375}, {"start": 1046.22, "end": 1046.44, "word": " ال", "probability": 0.413818359375}, {"start": 1046.44, "end": 1046.78, "word": " Y", "probability": 0.46240234375}, {"start": 1046.78, "end": 1047.06, "word": " to", "probability": 0.87890625}, {"start": 1047.06, "end": 1047.46, "word": " the", "probability": 0.8974609375}, {"start": 1047.46, "end": 1048.32, "word": " power", "probability": 0.78369140625}, {"start": 1048.32, "end": 1049.14, "word": " واحد", "probability": 0.7384033203125}, {"start": 1049.14, "end": 1050.04, "word": " ناقص", "probability": 0.9794921875}, {"start": 1050.04, "end": 1050.58, "word": " N", "probability": 0.908203125}, {"start": 1050.58, "end": 1052.2, "word": " يساوي", "probability": 0.8779296875}, {"start": 1052.2, "end": 1052.94, "word": " ال", "probability": 0.72607421875}, {"start": 1052.94, "end": 1053.3, "word": " G", "probability": 0.81396484375}, {"start": 1053.3, "end": 1054.14, "word": " of", "probability": 0.93994140625}, {"start": 1054.14, "end": 1054.54, "word": " T", "probability": 0.99072265625}, {"start": 1054.54, "end": 1062.08, "word": " مرة", "probability": 0.935546875}, {"start": 1062.08, "end": 1062.48, "word": " تانية", "probability": 0.9619140625}], "temperature": 1.0}, {"id": 45, "seek": 108540, "start": 1071.92, "end": 1085.4, "text": "الخطوة الأولى هي أن أضرب المعادلة star في main في y to the minus n يعني بدي أضربها في نفس ال term لأن هذا بس بإشارة سالب الأسترة", "tokens": [6027, 9778, 9566, 2407, 3660, 16247, 12610, 7578, 39896, 14739, 5551, 11242, 25513, 9673, 3615, 18513, 37977, 3543, 8978, 2135, 8978, 288, 281, 264, 3175, 297, 37495, 22653, 4724, 16254, 5551, 11242, 25513, 11296, 8978, 8717, 36178, 2423, 1433, 5296, 33456, 23758, 4724, 3794, 4724, 28814, 8592, 9640, 3660, 8608, 6027, 3555, 16247, 14851, 25720], "avg_logprob": -0.41434151785714285, "compression_ratio": 1.3666666666666667, "no_speech_prob": 0.0, "words": [{"start": 1071.92, "end": 1072.76, "word": "الخطوة", "probability": 0.705029296875}, {"start": 1072.76, "end": 1073.16, "word": " الأولى", "probability": 0.87744140625}, {"start": 1073.16, "end": 1073.42, "word": " هي", "probability": 0.546875}, {"start": 1073.42, "end": 1073.76, "word": " أن", "probability": 0.33056640625}, {"start": 1073.76, "end": 1074.1, "word": " أضرب", "probability": 0.514404296875}, {"start": 1074.1, "end": 1074.94, "word": " المعادلة", "probability": 0.88427734375}, {"start": 1074.94, "end": 1075.58, "word": " star", "probability": 0.261474609375}, {"start": 1075.58, "end": 1076.1, "word": " في", "probability": 0.84375}, {"start": 1076.1, "end": 1076.54, "word": " main", "probability": 0.183349609375}, {"start": 1076.54, "end": 1077.02, "word": " في", "probability": 0.6123046875}, {"start": 1077.02, "end": 1077.42, "word": " y", "probability": 0.806640625}, {"start": 1077.42, "end": 1077.76, "word": " to", "probability": 0.2489013671875}, {"start": 1077.76, "end": 1078.02, "word": " the", "probability": 0.91455078125}, {"start": 1078.02, "end": 1078.54, "word": " minus", "probability": 0.87548828125}, {"start": 1078.54, "end": 1079.22, "word": " n", "probability": 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{"start": 1674.42, "end": 1675.02, "word": " ضربنا", "probability": 0.9871419270833334}, {"start": 1675.02, "end": 1675.72, "word": " المعادلة", "probability": 0.9901123046875}, {"start": 1675.72, "end": 1676.28, "word": " كلها", "probability": 0.99072265625}, {"start": 1676.28, "end": 1676.52, "word": " في", "probability": 0.97021484375}, {"start": 1676.52, "end": 1677.18, "word": " سالب", "probability": 0.96728515625}, {"start": 1677.18, "end": 1677.64, "word": " واحد", "probability": 0.978515625}], "temperature": 1.0}, {"id": 72, "seek": 169491, "start": 1678.05, "end": 1694.91, "text": "يبقاش بصير المعادلة يبقى V' زائد واحد على T في ال V بدي الساوي قداش واحد على T تربيع المعادلة هذه يا بنات شو صارت؟ Linear", "tokens": [1829, 3555, 4587, 33599, 4724, 9381, 13546, 9673, 3615, 18513, 37977, 7251, 3555, 4587, 7578, 691, 6, 30767, 16373, 3215, 36764, 24401, 15844, 314, 8978, 2423, 691, 4724, 16254, 21136, 995, 45865, 12174, 3215, 33599, 36764, 24401, 15844, 314, 6055, 2288, 21292, 3615, 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"text": "فيبتعلي ناخد ال limit اللي عندنا هنا يبقى هذا ال limit لما Y بدها تروح للواحد من جهة اليامين الان انا عند هذا ال real line وهذا عند الواحد وهذا عند ال zero انا رايح للواحد من جهة ايد اليامين يعني احنا قبل الواحد و لا بعد الواحد", "tokens": [5172, 1829, 3555, 2655, 3615, 20292, 8717, 47283, 3215, 2423, 4948, 13672, 1829, 43242, 8315, 34105, 7251, 3555, 4587, 7578, 23758, 2423, 4948, 5296, 15042, 398, 47525, 11296, 6055, 32887, 5016, 24976, 14407, 24401, 9154, 10874, 3224, 3660, 45595, 10943, 9957, 2423, 7649, 1975, 8315, 43242, 23758, 2423, 957, 1622, 37037, 15730, 43242, 2423, 14407, 24401, 37037, 15730, 43242, 2423, 4018, 1975, 8315, 12602, 47302, 5016, 24976, 14407, 24401, 9154, 10874, 3224, 3660, 1975, 25708, 45595, 10943, 9957, 37495, 22653, 1975, 5016, 8315, 12174, 36150, 2423, 14407, 24401, 4032, 20193, 39182, 2423, 14407, 24401], "avg_logprob": -0.1584703947368421, "compression_ratio": 2.0869565217391304, "no_speech_prob": 2.384185791015625e-07, "words": [{"start": 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3555, 3615, 995, 2423, 3541, 8978, 3224, 8717, 47432, 2655, 9957, 2423, 1900, 11787, 4032, 2423, 26889, 6771, 2423, 26889, 6771, 11331, 6027, 10874, 16373, 1211, 11296, 5296, 15042, 6055, 30544, 9673, 3615, 18513, 37977, 19446, 3224, 1829, 33599, 1900, 4032, 12602, 3555, 15042, 8608, 1863, 3615, 28480, 3224, 16490, 1211, 6027, 29538, 9673, 5016, 46958, 25720, 4032, 12602, 3555, 15042, 8978, 9673, 5016, 46958, 25720, 25062, 18513, 46007, 46811, 10943, 7251, 3555, 4587, 7578, 9154, 34105, 2423, 1900, 11787, 264, 700, 1668], "avg_logprob": -0.1709558781455545, "compression_ratio": 1.7609756097560976, "no_speech_prob": 5.960464477539063e-08, "words": [{"start": 4020.03, "end": 4020.45, "word": "طبعا", "probability": 0.767822265625}, {"start": 4020.45, "end": 4020.55, "word": " ال", "probability": 0.6396484375}, {"start": 4020.55, "end": 4020.87, "word": " section", "probability": 0.7392578125}, {"start": 4020.87, "end": 4021.17, "word": " فيه", "probability": 0.90380859375}, {"start": 4021.17, "end": 4021.89, "word": " نقطتين", "probability": 0.97119140625}, {"start": 4021.89, "end": 4022.53, "word": " ال", "probability": 0.8203125}, {"start": 4022.53, "end": 4022.91, "word": " exact", "probability": 0.60009765625}, {"start": 4022.91, "end": 4023.55, "word": " equations", "probability": 0.81494140625}, {"start": 4023.55, "end": 4023.75, "word": " و", "probability": 0.5849609375}, {"start": 4023.75, "end": 4023.85, "word": " ال", "probability": 0.85009765625}, {"start": 4023.85, "end": 4024.47, "word": " integrating", "probability": 0.91650390625}, {"start": 4024.47, "end": 4025.31, "word": " factors", "probability": 0.96240234375}, {"start": 4025.31, "end": 4025.83, "word": " ال", "probability": 0.80908203125}, {"start": 4025.83, "end": 4026.35, "word": " integrating", "probability": 0.8876953125}, {"start": 4026.35, "end": 4027.05, "word": " factors", "probability": 0.95263671875}, {"start": 4027.05, "end": 4027.49, "word": " حال", "probability": 0.845703125}, {"start": 4027.49, "end": 4027.93, "word": " جائلها", "probability": 0.759765625}, {"start": 4027.93, "end": 4028.15, "word": " لما", "probability": 0.890625}, {"start": 4028.15, "end": 4028.45, "word": " تكون", "probability": 0.982421875}, {"start": 4028.45, "end": 4028.95, "word": " المعادلة", "probability": 0.9866943359375}, {"start": 4028.95, "end": 4029.67, "word": " ماهياش", "probability": 0.853515625}, {"start": 4029.67, "end": 4030.37, "word": " exact", "probability": 0.8583984375}, {"start": 4030.37, "end": 4030.93, "word": " و", "probability": 0.9736328125}, {"start": 4030.93, "end": 4031.35, "word": " ربما", "probability": 0.8956705729166666}, {"start": 4031.35, "end": 4032.15, "word": " سنعرفه", "probability": 0.94765625}, {"start": 4032.15, "end": 4032.71, "word": " خلال", "probability": 0.98876953125}, {"start": 4032.71, "end": 4033.17, "word": " هذه", "probability": 0.982421875}, {"start": 4033.17, "end": 4034.29, "word": " المحاضرة", "probability": 0.9896240234375}, {"start": 4034.29, "end": 4034.51, "word": " و", "probability": 0.9619140625}, {"start": 4034.51, "end": 4034.93, "word": " ربما", "probability": 0.9625651041666666}, {"start": 4034.93, "end": 4035.15, "word": " في", "probability": 0.92822265625}, {"start": 4035.15, "end": 4035.81, "word": " المحاضرة", "probability": 0.9957275390625}, {"start": 4035.81, "end": 4036.65, "word": " القادمة", "probability": 0.99267578125}, {"start": 4036.65, "end": 4037.73, "word": " تمام", "probability": 0.81787109375}, {"start": 4037.73, "end": 4038.41, "word": " يبقى", "probability": 0.8939208984375}, {"start": 4038.41, "end": 4038.57, "word": " من", "probability": 0.25537109375}, {"start": 4038.57, "end": 4038.67, "word": " هنا", "probability": 0.400634765625}, {"start": 4038.67, "end": 4038.79, "word": " ال", "probability": 0.86376953125}, {"start": 4038.79, "end": 4039.19, "word": " exact", "probability": 0.97802734375}, {"start": 4039.19, "end": 4040.01, "word": " equations", "probability": 0.92236328125}, {"start": 4040.01, "end": 4040.81, "word": " the", "probability": 0.2413330078125}, {"start": 4040.81, "end": 4042.63, "word": " first", "probability": 0.85888671875}, {"start": 4042.63, "end": 4045.19, "word": " order", "probability": 0.96240234375}], "temperature": 1.0}, {"id": 169, "seek": 406709, "start": 4047.69, "end": 4067.09, "text": "Differential equation y prime يساوي f of x و y can be written as ممكن نكتب على الشكل التالي", "tokens": [35, 15790, 831, 5367, 288, 5835, 7251, 3794, 995, 45865, 283, 295, 2031, 4032, 288, 393, 312, 3720, 382, 3714, 43020, 8717, 4117, 2655, 3555, 15844, 25124, 28820, 16712, 6027, 1829], "avg_logprob": -0.38818358443677425, "compression_ratio": 1.0625, "no_speech_prob": 0.0, "words": [{"start": 4047.6899999999996, "end": 4049.0899999999997, "word": "Differential", "probability": 0.4482218424479167}, {"start": 4049.0899999999997, "end": 4050.49, "word": " equation", "probability": 0.712890625}, {"start": 4050.49, "end": 4052.13, "word": " y", "probability": 0.474609375}, {"start": 4052.13, "end": 4052.95, "word": " prime", "probability": 0.34912109375}, {"start": 4052.95, "end": 4054.23, "word": " يساوي", "probability": 0.799072265625}, {"start": 4054.23, "end": 4054.85, "word": " f", "probability": 0.67138671875}, {"start": 4054.85, "end": 4055.69, "word": " of", "probability": 0.8505859375}, {"start": 4055.69, "end": 4056.15, "word": " x", "probability": 0.95703125}, {"start": 4056.15, "end": 4056.39, "word": " و", "probability": 0.69970703125}, {"start": 4056.39, "end": 4056.79, "word": " y", "probability": 0.74169921875}, {"start": 4056.79, "end": 4057.95, "word": " can", "probability": 0.72412109375}, {"start": 4057.95, "end": 4060.13, "word": " be", "probability": 0.94091796875}, {"start": 4060.13, "end": 4061.97, "word": " written", "probability": 0.9130859375}, {"start": 4061.97, "end": 4063.59, "word": " as", "probability": 0.9521484375}, {"start": 4063.59, "end": 4064.65, "word": " ممكن", "probability": 0.636474609375}, {"start": 4064.65, "end": 4065.41, "word": " نكتب", "probability": 0.9022216796875}, {"start": 4065.41, "end": 4065.69, "word": " على", "probability": 0.325439453125}, {"start": 4065.69, "end": 4066.31, "word": " الشكل", "probability": 0.949462890625}, {"start": 4066.31, "end": 4067.09, "word": " التالي", "probability": 0.8943684895833334}], "temperature": 1.0}, {"id": 170, "seek": 409178, "start": 4069.54, "end": 4091.78, "text": "by dx يساوي سالب M في ال XY على N في ال XY زي المرة اللي فاتت بالظبط this is possible هذا الكلام ممكن for example", "tokens": [2322, 30017, 7251, 3794, 995, 45865, 8608, 6027, 3555, 376, 8978, 2423, 48826, 15844, 426, 8978, 2423, 48826, 30767, 1829, 9673, 25720, 13672, 1829, 6156, 9307, 2655, 20666, 19913, 3555, 9566, 341, 307, 1944, 23758, 2423, 28820, 10943, 3714, 43020, 337, 1365], "avg_logprob": -0.21638808555381242, "compression_ratio": 1.2651515151515151, "no_speech_prob": 1.1920928955078125e-07, "words": [{"start": 4069.54, "end": 4070.02, "word": "by", "probability": 0.1116943359375}, {"start": 4070.02, "end": 4070.9, "word": " dx", "probability": 0.732421875}, {"start": 4070.9, "end": 4072.28, "word": " يساوي", "probability": 0.75506591796875}, {"start": 4072.28, "end": 4073.74, "word": " سالب", "probability": 0.7372233072916666}, {"start": 4073.74, "end": 4074.66, "word": " M", "probability": 0.362548828125}, {"start": 4074.66, "end": 4075.56, "word": " في", "probability": 0.7548828125}, {"start": 4075.56, "end": 4075.74, "word": " ال", "probability": 0.63232421875}, {"start": 4075.74, "end": 4076.32, "word": " XY", "probability": 0.314453125}, {"start": 4076.32, "end": 4077.64, "word": " على", "probability": 0.72021484375}, {"start": 4077.64, "end": 4078.36, "word": " N", "probability": 0.9404296875}, {"start": 4078.36, "end": 4079.06, "word": " في", "probability": 0.982421875}, {"start": 4079.06, "end": 4079.34, "word": " ال", "probability": 0.916015625}, {"start": 4079.34, "end": 4080.6, "word": " XY", "probability": 0.9228515625}, {"start": 4080.6, "end": 4081.66, "word": " زي", "probability": 0.8662109375}, {"start": 4081.66, "end": 4081.98, "word": " المرة", "probability": 0.984130859375}, {"start": 4081.98, "end": 4082.14, "word": " اللي", "probability": 0.843994140625}, {"start": 4082.14, "end": 4082.48, "word": " فاتت", "probability": 0.94189453125}, {"start": 4082.48, "end": 4083.24, "word": " بالظبط", "probability": 0.9808349609375}, {"start": 4083.24, "end": 4084.1, "word": " this", "probability": 0.52392578125}, {"start": 4084.1, "end": 4084.6, "word": " is", "probability": 0.96435546875}, {"start": 4084.6, "end": 4086.1, "word": " possible", "probability": 0.96875}, {"start": 4086.1, "end": 4087.88, "word": " هذا", "probability": 0.90478515625}, {"start": 4087.88, "end": 4088.76, "word": " الكلام", "probability": 0.9755859375}, {"start": 4088.76, "end": 4090.04, "word": " ممكن", "probability": 0.986083984375}, {"start": 4090.04, "end": 4091.04, "word": " for", "probability": 0.87060546875}, {"start": 4091.04, "end": 4091.78, "word": " example", "probability": 0.97607421875}], "temperature": 1.0}, {"id": 171, "seek": 412488, "start": 4115.68, "end": 4124.88, "text": "تاك تاك تاك تاك تاك تاك تاك تاك تاك تاك تاك تاك تاك تاك تاك تاك", "tokens": [2655, 995, 4117, 6055, 995, 4117, 6055, 995, 4117, 6055, 995, 4117, 6055, 995, 4117, 6055, 995, 4117, 6055, 995, 4117, 6055, 995, 4117, 6055, 995, 4117, 6055, 995, 4117, 6055, 995, 4117, 6055, 995, 4117, 6055, 995, 4117, 6055, 995, 4117, 6055, 995, 4117, 6055, 995, 4117], "avg_logprob": -0.2694515208808743, "compression_ratio": 5.842105263157895, "no_speech_prob": 0.0, "words": [{"start": 4115.68, "end": 4117.08, "word": "تاك", "probability": 0.4762166341145833}, {"start": 4117.08, "end": 4118.48, "word": " تاك", "probability": 0.5682373046875}, {"start": 4118.48, "end": 4119.26, "word": " تاك", "probability": 0.7859700520833334}, {"start": 4119.26, "end": 4122.52, "word": " تاك", "probability": 0.9054361979166666}, {"start": 4122.52, "end": 4123.06, "word": " تاك", "probability": 0.9305013020833334}, {"start": 4123.06, "end": 4123.42, "word": " تاك", "probability": 0.9381510416666666}, {"start": 4123.42, "end": 4123.68, "word": " تاك", "probability": 0.9441731770833334}, {"start": 4123.68, "end": 4124.8, "word": " تاك", "probability": 0.9493815104166666}, {"start": 4124.8, "end": 4124.8, "word": " تاك", "probability": 0.9537760416666666}, {"start": 4124.8, "end": 4124.8, "word": " تاك", "probability": 0.9588216145833334}, {"start": 4124.8, "end": 4124.8, "word": " تاك", "probability": 0.9630533854166666}, {"start": 4124.8, "end": 4124.8, "word": " تاك", "probability": 0.96728515625}, {"start": 4124.8, "end": 4124.8, "word": " تاك", "probability": 0.9703776041666666}, {"start": 4124.8, "end": 4124.8, "word": " تاك", "probability": 0.9728190104166666}, {"start": 4124.8, "end": 4124.8, "word": " تاك", "probability": 0.9744466145833334}, {"start": 4124.8, "end": 4124.88, "word": " تاك", "probability": 0.9755859375}], "temperature": 1.0}, {"id": 172, "seek": 415418, "start": 4125.51, "end": 4154.19, "text": "differential equation is written as اكتبها على الشكل التالي اللي هو m of x y dx زائد n of x y dy بده يساوي من؟ بده يساوي", "tokens": [67, 15790, 831, 5367, 307, 3720, 382, 1975, 4117, 2655, 3555, 11296, 15844, 25124, 28820, 16712, 6027, 1829, 13672, 1829, 31439, 275, 295, 2031, 288, 30017, 30767, 16373, 3215, 297, 295, 2031, 288, 14584, 47525, 3224, 7251, 3794, 995, 45865, 9154, 22807, 47525, 3224, 7251, 3794, 995, 45865], "avg_logprob": -0.3450255004727111, "compression_ratio": 1.3203125, "no_speech_prob": 0.0, "words": [{"start": 4125.51, "end": 4127.13, "word": "differential", "probability": 0.4370829264322917}, {"start": 4127.13, "end": 4129.23, "word": " equation", "probability": 0.953125}, {"start": 4129.23, "end": 4130.57, "word": " is", "probability": 0.837890625}, {"start": 4130.57, "end": 4131.15, "word": " written", "probability": 0.890625}, {"start": 4131.15, "end": 4136.77, "word": " as", "probability": 0.966796875}, {"start": 4136.77, "end": 4137.87, "word": " اكتبها", "probability": 0.7356201171875}, {"start": 4137.87, "end": 4138.05, "word": " على", "probability": 0.84326171875}, {"start": 4138.05, "end": 4138.55, "word": " الشكل", "probability": 0.95849609375}, {"start": 4138.55, "end": 4139.25, "word": " التالي", "probability": 0.9842122395833334}, {"start": 4139.25, "end": 4140.15, "word": " اللي", "probability": 0.6395263671875}, {"start": 4140.15, "end": 4140.35, "word": " هو", "probability": 0.470458984375}, {"start": 4140.35, "end": 4140.89, "word": " m", "probability": 0.426513671875}, {"start": 4140.89, "end": 4142.59, "word": " of", "probability": 0.7763671875}, {"start": 4142.59, "end": 4143.25, "word": " x", "probability": 0.896484375}, {"start": 4143.25, "end": 4144.57, "word": " y", "probability": 0.62109375}, {"start": 4144.57, "end": 4145.43, "word": " dx", "probability": 0.8369140625}, {"start": 4145.43, "end": 4146.73, "word": " زائد", "probability": 0.77587890625}, {"start": 4146.73, "end": 4147.29, "word": " n", "probability": 0.83984375}, {"start": 4147.29, "end": 4148.31, "word": " of", "probability": 0.9501953125}, {"start": 4148.31, "end": 4148.79, "word": " x", "probability": 0.97705078125}, {"start": 4148.79, "end": 4149.53, "word": " y", "probability": 0.9052734375}, {"start": 4149.53, "end": 4150.53, "word": " dy", "probability": 0.95361328125}, {"start": 4150.53, "end": 4151.67, "word": " بده", "probability": 0.693115234375}, {"start": 4151.67, "end": 4152.15, "word": " يساوي", "probability": 0.926513671875}, {"start": 4152.15, "end": 4152.99, "word": " من؟", "probability": 0.3599853515625}, {"start": 4152.99, "end": 4153.35, "word": " بده", "probability": 0.891845703125}, {"start": 4153.35, "end": 4154.19, "word": " يساوي", "probability": 0.9866943359375}], "temperature": 1.0}, {"id": 173, "seek": 419112, "start": 4181.04, "end": 4191.12, "text": "كويس نرجع لموضوعنا لسه أنا ماعرفتش ال exact equation ولا اتكلمتش كل اللي عملته حطيت ال function في صيغة اخرى", "tokens": [4117, 45865, 3794, 8717, 47341, 3615, 32767, 2407, 11242, 45367, 8315, 5296, 3794, 3224, 41850, 19446, 3615, 28480, 2655, 8592, 2423, 1900, 5367, 49429, 1975, 2655, 4117, 19528, 2655, 8592, 28242, 13672, 1829, 6225, 42213, 47395, 11331, 9566, 36081, 2423, 2445, 8978, 20328, 1829, 17082, 3660, 1975, 34740, 7578], "avg_logprob": -0.21843750536441803, "compression_ratio": 1.2846715328467153, "no_speech_prob": 0.0, "words": [{"start": 4181.040000000001, "end": 4182.02, "word": "كويس", "probability": 0.5487467447916666}, {"start": 4182.02, "end": 4183.0, "word": " نرجع", "probability": 0.6866861979166666}, {"start": 4183.0, "end": 4183.6, "word": " لموضوعنا", "probability": 0.813427734375}, {"start": 4183.6, "end": 4183.92, "word": " لسه", "probability": 0.8544921875}, {"start": 4183.92, "end": 4184.06, "word": " أنا", "probability": 0.21533203125}, {"start": 4184.06, "end": 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عندنا هذه وهذه طبيعي تساوي كده؟ تساوي Zero", "tokens": [2304, 28543, 9640, 38637, 16758, 2655, 8574, 394, 383, 4724, 5016, 1829, 12984, 16472, 11778, 1829, 9970, 7691, 295, 48826, 37495, 22653, 37893, 2655, 38149, 11296, 47525, 11296, 6055, 3794, 995, 45865, 9154, 9673, 3615, 18513, 37977, 13672, 1829, 43242, 8315, 29538, 37037, 24192, 23032, 21292, 3615, 1829, 6055, 3794, 995, 45865, 9122, 3215, 3224, 22807, 6055, 3794, 995, 45865, 17182], "avg_logprob": -0.29385080068342145, "compression_ratio": 1.3933333333333333, "no_speech_prob": 5.960464477539063e-08, "words": [{"start": 4438.63, "end": 4439.49, "word": "مقدار", "probability": 0.6643473307291666}, {"start": 4439.49, "end": 4439.99, "word": " ثابت", "probability": 0.9832356770833334}, {"start": 4439.99, "end": 4440.77, "word": " Constant", "probability": 0.5843505859375}, {"start": 4440.77, "end": 4441.03, "word": " C", "probability": 0.64990234375}, {"start": 4441.03, "end": 4441.85, "word": " بحيث", "probability": 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ببقى", "probability": 0.72216796875}, {"start": 5211.95, "end": 5212.07, "word": " اللي", "probability": 0.973876953125}, {"start": 5212.07, "end": 5212.39, "word": " عندي", "probability": 0.711181640625}, {"start": 5212.39, "end": 5212.97, "word": " partial", "probability": 0.970703125}, {"start": 5212.97, "end": 5213.53, "word": " fy", "probability": 0.1619873046875}, {"start": 5213.53, "end": 5214.17, "word": " على", "probability": 0.6591796875}, {"start": 5214.17, "end": 5215.07, "word": " partial", "probability": 0.96044921875}, {"start": 5215.07, "end": 5215.75, "word": " y", "probability": 0.99267578125}], "temperature": 1.0}, {"id": 214, "seek": 522896, "start": 5216.58, "end": 5228.96, "text": "فال partial of y على partial of y يعني أنه يبقى partial n على partial x أظن و هو المطلوب", "tokens": [5172, 6027, 14641, 295, 288, 15844, 14641, 295, 288, 37495, 22653, 14739, 3224, 7251, 3555, 4587, 7578, 14641, 297, 15844, 14641, 2031, 5551, 19913, 1863, 4032, 31439, 9673, 9566, 1211, 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"word": " يبقى", "probability": 0.6798095703125}, {"start": 5224.36, "end": 5224.88, "word": " partial", "probability": 0.321044921875}, {"start": 5224.88, "end": 5225.76, "word": " n", "probability": 0.256103515625}, {"start": 5225.76, "end": 5226.6, "word": " على", "probability": 0.7001953125}, {"start": 5226.6, "end": 5227.16, "word": " partial", "probability": 0.91064453125}, {"start": 5227.16, "end": 5227.64, "word": " x", "probability": 0.8525390625}, {"start": 5227.64, "end": 5228.02, "word": " أظن", "probability": 0.6375732421875}, {"start": 5228.02, "end": 5228.12, "word": " و", "probability": 0.3818359375}, {"start": 5228.12, "end": 5228.26, "word": " هو", "probability": 0.9638671875}, {"start": 5228.26, "end": 5228.96, "word": " المطلوب", "probability": 0.983642578125}], "temperature": 1.0}, {"id": 215, "seek": 525904, "start": 5229.56, "end": 5259.04, "text": "يبقى هاي يثبتنا ان partial M على partial Y يسوى 100 partial N على partial X هذا هو الاثبات السهل لهذا الجزء السهل هذا بده يعطينا ان partial M على partial Y يسوى partial N على partial X هذا الاتجاه الأول نجي للاتجاه الثاني الاتجاه الثاني بنروح نقول conversely العكس", "tokens": [1829, 3555, 4587, 7578, 8032, 47302, 7251, 12984, 3555, 2655, 8315, 16472, 14641, 376, 15844, 14641, 398, 7251, 3794, 2407, 7578, 2319, 14641, 426, 15844, 14641, 1783, 23758, 31439, 2423, 5718, 104, 3555, 9307, 21136, 3224, 1211, 46740, 15730, 25724, 11622, 38207, 21136, 3224, 1211, 23758, 47525, 3224, 37495, 9566, 1829, 8315, 16472, 14641, 376, 15844, 14641, 398, 7251, 3794, 2407, 7578, 14641, 426, 15844, 14641, 1783, 23758, 2423, 9307, 7435, 40294, 16247, 12610, 8717, 7435, 1829, 24976, 9307, 7435, 40294, 6024, 104, 7649, 1829, 2423, 9307, 7435, 40294, 6024, 104, 7649, 1829, 44945, 32887, 5016, 8717, 39648, 2615, 736, 18863, 4117, 3794], "avg_logprob": -0.18674879148602486, "compression_ratio": 2.126984126984127, "no_speech_prob": 1.1920928955078125e-07, "words": [{"start": 5229.56, "end": 5229.98, "word": "يبقى", "probability": 0.80279541015625}, {"start": 5229.98, "end": 5230.12, "word": " هاي", "probability": 0.30145263671875}, {"start": 5230.12, "end": 5230.62, "word": " يثبتنا", "probability": 0.8923828125}, {"start": 5230.62, "end": 5230.76, "word": " ان", "probability": 0.73486328125}, {"start": 5230.76, "end": 5231.02, "word": " partial", "probability": 0.50927734375}, {"start": 5231.02, "end": 5231.3, "word": " M", "probability": 0.58935546875}, {"start": 5231.3, "end": 5231.46, "word": " على", "probability": 0.62548828125}, {"start": 5231.46, "end": 5231.86, "word": " partial", "probability": 0.90576171875}, {"start": 5231.86, "end": 5232.12, "word": " Y", "probability": 0.9609375}, {"start": 5232.12, "end": 5232.44, "word": " يسوى", "probability": 0.7413330078125}, {"start": 5232.44, "end": 5232.8, "word": " 100", "probability": 0.66064453125}, {"start": 5232.8, "end": 5233.46, "word": " partial", "probability": 0.65185546875}, {"start": 5233.46, "end": 5233.88, "word": " N", "probability": 0.900390625}, {"start": 5233.88, "end": 5234.06, "word": " على", "probability": 0.8056640625}, {"start": 5234.06, "end": 5234.3, "word": " partial", "probability": 0.94677734375}, {"start": 5234.3, "end": 5234.4, "word": " X", "probability": 0.80126953125}, {"start": 5234.4, "end": 5234.66, "word": " هذا", "probability": 0.619140625}, {"start": 5234.66, "end": 5234.84, "word": " هو", "probability": 0.84375}, {"start": 5234.84, "end": 5235.38, "word": " الاثبات", "probability": 0.84638671875}, {"start": 5235.38, "end": 5235.9, "word": " السهل", "probability": 0.9638671875}, {"start": 5235.9, "end": 5236.18, "word": " لهذا", "probability": 0.735107421875}, {"start": 5236.18, "end": 5236.54, "word": " الجزء", "probability": 0.9781901041666666}, {"start": 5236.54, "end": 5237.16, "word": " السهل", "probability": 0.98779296875}, {"start": 5237.16, "end": 5238.02, "word": " هذا", "probability": 0.8134765625}, {"start": 5238.02, "end": 5238.42, "word": " بده", "probability": 0.4881591796875}, {"start": 5238.42, "end": 5239.1, "word": " يعطينا", "probability": 0.92236328125}, {"start": 5239.1, "end": 5239.68, "word": " ان", "probability": 0.8701171875}, {"start": 5239.68, "end": 5240.28, "word": " partial", "probability": 0.8837890625}, {"start": 5240.28, "end": 5240.94, "word": " M", "probability": 0.98681640625}, {"start": 5240.94, "end": 5241.28, "word": " على", "probability": 0.82373046875}, {"start": 5241.28, "end": 5241.84, "word": " partial", "probability": 0.91748046875}, {"start": 5241.84, "end": 5242.4, "word": " Y", "probability": 0.9921875}, {"start": 5242.4, "end": 5243.3, "word": " يسوى", "probability": 0.912109375}, {"start": 5243.3, "end": 5243.94, "word": " partial", "probability": 0.9189453125}, {"start": 5243.94, "end": 5244.76, "word": " N", "probability": 0.958984375}, {"start": 5244.76, "end": 5245.7, "word": " على", "probability": 0.8544921875}, {"start": 5245.7, "end": 5246.76, "word": " partial", "probability": 0.95458984375}, {"start": 5246.76, "end": 5247.58, "word": " X", "probability": 0.98974609375}, {"start": 5247.58, "end": 5248.32, "word": " هذا", "probability": 0.89892578125}, {"start": 5248.32, "end": 5249.12, "word": " الاتجاه", "probability": 0.808349609375}, {"start": 5249.12, "end": 5250.14, "word": " الأول", "probability": 0.92041015625}, {"start": 5250.14, "end": 5251.32, "word": " نجي", "probability": 0.8714192708333334}, {"start": 5251.32, "end": 5252.12, "word": " للاتجاه", "probability": 0.88525390625}, {"start": 5252.12, "end": 5252.8, "word": " الثاني", "probability": 0.96923828125}, {"start": 5252.8, "end": 5253.7, "word": " الاتجاه", "probability": 0.88525390625}, {"start": 5253.7, "end": 5254.16, "word": " الثاني", "probability": 0.9744873046875}, {"start": 5254.16, "end": 5254.56, "word": " بنروح", "probability": 0.83447265625}, {"start": 5254.56, "end": 5255.04, "word": " نقول", "probability": 0.76025390625}, {"start": 5255.04, "end": 5257.8, "word": " conversely", "probability": 0.88330078125}, {"start": 5257.8, "end": 5259.04, "word": " العكس", "probability": 0.9637044270833334}], "temperature": 1.0}, {"id": 216, "seek": 527953, "start": 5260.19, "end": 5279.53, "text": "بدي افترض ان هذا الصحيح وبناء عليه اثبت ان المعادلة هذه مالها exact يعني اذا جدت لاجي function بيساوي و فيكساوي و يساوي يكون اصلا تحققها بيصير كلامي صح وبالتالي بيكون برهنة النظرية تماما", "tokens": [3555, 16254, 1975, 5172, 2655, 43042, 16472, 23758, 31767, 5016, 1829, 5016, 46599, 1863, 16606, 47356, 1975, 12984, 3555, 2655, 16472, 9673, 3615, 18513, 37977, 29538, 3714, 6027, 11296, 1900, 37495, 22653, 1975, 15730, 10874, 3215, 2655, 5296, 26108, 1829, 2445, 4724, 1829, 3794, 995, 45865, 4032, 8978, 4117, 3794, 995, 45865, 4032, 7251, 3794, 995, 45865, 7251, 30544, 1975, 9381, 15040, 6055, 5016, 4587, 4587, 11296, 4724, 1829, 9381, 13546, 28242, 10943, 1829, 20328, 5016, 46599, 6027, 2655, 6027, 1829, 4724, 1829, 30544, 4724, 2288, 3224, 1863, 3660, 28239, 19913, 2288, 10632, 46811, 10943, 995], "avg_logprob": -0.27094073148117853, "compression_ratio": 1.6548223350253808, "no_speech_prob": 5.960464477539063e-08, "words": [{"start": 5260.19, "end": 5260.65, "word": "بدي", "probability": 0.4326171875}, {"start": 5260.65, "end": 5261.35, "word": " افترض", "probability": 0.8997802734375}, {"start": 5261.35, "end": 5261.79, "word": " ان", "probability": 0.83056640625}, {"start": 5261.79, "end": 5262.31, "word": " هذا", "probability": 0.69140625}, {"start": 5262.31, "end": 5263.59, "word": " الصحيح", "probability": 0.8917236328125}, {"start": 5263.59, "end": 5264.55, "word": " وبناء", "probability": 0.7965494791666666}, {"start": 5264.55, "end": 5265.21, "word": " عليه", "probability": 0.912109375}, {"start": 5265.21, "end": 5266.09, "word": " اثبت", "probability": 0.914794921875}, {"start": 5266.09, "end": 5266.33, "word": " ان", "probability": 0.92236328125}, {"start": 5266.33, "end": 5266.99, "word": " المعادلة", "probability": 0.9749755859375}, {"start": 5266.99, "end": 5267.29, "word": " هذه", "probability": 0.65283203125}, {"start": 5267.29, "end": 5267.83, "word": " مالها", "probability": 0.8486328125}, {"start": 5267.83, "end": 5269.23, "word": " exact", "probability": 0.5029296875}, {"start": 5269.23, "end": 5269.73, "word": " يعني", "probability": 0.794189453125}, {"start": 5269.73, "end": 5270.09, "word": " اذا", "probability": 0.88720703125}, {"start": 5270.09, "end": 5270.65, "word": " جدت", "probability": 0.8455403645833334}, {"start": 5270.65, "end": 5271.21, "word": " لاجي", "probability": 0.8308919270833334}, {"start": 5271.21, "end": 5272.19, "word": " function", "probability": 0.955078125}, {"start": 5272.19, "end": 5273.15, "word": " بيساوي", "probability": 0.399755859375}, {"start": 5273.15, "end": 5273.25, "word": " و", "probability": 0.5166015625}, {"start": 5273.25, "end": 5273.73, "word": " فيكساوي", "probability": 0.65087890625}, {"start": 5273.73, "end": 5273.85, "word": " و", "probability": 0.74853515625}, {"start": 5273.85, "end": 5274.11, "word": " يساوي", "probability": 0.8865966796875}, {"start": 5274.11, "end": 5274.35, "word": " يكون", "probability": 0.812255859375}, {"start": 5274.35, "end": 5274.63, "word": " اصلا", "probability": 0.6816813151041666}, {"start": 5274.63, "end": 5275.45, "word": " تحققها", "probability": 0.959765625}, {"start": 5275.45, "end": 5275.73, "word": " بيصير", "probability": 0.71600341796875}, {"start": 5275.73, "end": 5276.25, "word": " كلامي", "probability": 0.9593098958333334}, {"start": 5276.25, "end": 5276.59, "word": " صح", "probability": 0.99609375}, {"start": 5276.59, "end": 5277.33, "word": " وبالتالي", "probability": 0.91591796875}, {"start": 5277.33, "end": 5277.61, "word": " بيكون", "probability": 0.8868815104166666}, {"start": 5277.61, "end": 5278.19, "word": " برهنة", "probability": 0.747607421875}, {"start": 5278.19, "end": 5278.83, "word": " النظرية", "probability": 0.9564208984375}, {"start": 5278.83, "end": 5279.53, "word": " تماما", "probability": 0.9923502604166666}], "temperature": 1.0}, {"id": 217, "seek": 530616, "start": 5279.7, "end": 5306.16, "text": "يبقى باجي بقوله assume افترض ان ال partial m by partial y يساوي partial n by partial x وبالتالي بنحاول نثبت ان المعادلة هذه مالها معادلة exact بقوله كويس", "tokens": [1829, 3555, 4587, 7578, 4724, 26108, 1829, 4724, 39648, 3224, 6552, 1975, 5172, 2655, 43042, 16472, 2423, 14641, 275, 538, 14641, 288, 7251, 3794, 995, 45865, 14641, 297, 538, 14641, 2031, 46599, 6027, 2655, 6027, 1829, 44945, 5016, 995, 12610, 8717, 12984, 3555, 2655, 16472, 9673, 3615, 18513, 37977, 29538, 19446, 1211, 11296, 20449, 18513, 37977, 1900, 4724, 39648, 3224, 9122, 45865, 3794], "avg_logprob": -0.15930175152607262, "compression_ratio": 1.54, "no_speech_prob": 0.0, "words": [{"start": 5279.7, "end": 5280.4, "word": "يبقى", "probability": 0.872802734375}, {"start": 5280.4, "end": 5280.8, "word": " باجي", "probability": 0.6980794270833334}, {"start": 5280.8, "end": 5281.5, "word": " بقوله", "probability": 0.8388671875}, {"start": 5281.5, "end": 5282.54, "word": " assume", "probability": 0.4638671875}, {"start": 5282.54, "end": 5284.82, "word": " افترض", "probability": 0.8370361328125}, {"start": 5284.82, "end": 5285.6, "word": " ان", "probability": 0.91259765625}, {"start": 5285.6, "end": 5285.86, "word": " ال", "probability": 0.88671875}, {"start": 5285.86, "end": 5286.46, "word": " partial", "probability": 0.65966796875}, {"start": 5286.46, "end": 5287.32, "word": " m", "probability": 0.477294921875}, {"start": 5287.32, "end": 5288.0, "word": " by", "probability": 0.85009765625}, {"start": 5288.0, "end": 5288.66, "word": " partial", "probability": 0.95166015625}, {"start": 5288.66, "end": 5289.2, "word": " y", "probability": 0.9638671875}, {"start": 5289.2, "end": 5290.4, "word": " يساوي", "probability": 0.8629150390625}, {"start": 5290.4, "end": 5291.16, "word": " partial", "probability": 0.92578125}, {"start": 5291.16, "end": 5291.98, "word": " n", "probability": 0.88916015625}, {"start": 5291.98, "end": 5292.84, "word": " by", "probability": 0.978515625}, {"start": 5292.84, "end": 5293.52, "word": " partial", "probability": 0.94970703125}, {"start": 5293.52, "end": 5294.46, "word": " x", "probability": 0.97119140625}, {"start": 5294.46, "end": 5299.48, "word": " وبالتالي", "probability": 0.9287109375}, {"start": 5299.48, "end": 5300.14, "word": " بنحاول", "probability": 0.88818359375}, {"start": 5300.14, "end": 5300.66, "word": " نثبت", "probability": 0.9915771484375}, {"start": 5300.66, "end": 5300.92, "word": " ان", "probability": 0.77197265625}, {"start": 5300.92, "end": 5301.54, "word": " المعادلة", "probability": 0.9798583984375}, {"start": 5301.54, "end": 5301.86, "word": " هذه", "probability": 0.7685546875}, {"start": 5301.86, "end": 5302.32, "word": " مالها", "probability": 0.751953125}, {"start": 5302.32, "end": 5303.72, "word": " معادلة", "probability": 0.97705078125}, {"start": 5303.72, "end": 5304.8, "word": " exact", "probability": 0.90625}, {"start": 5304.8, "end": 5305.7, "word": " بقوله", "probability": 0.8932291666666666}, {"start": 5305.7, "end": 5306.16, "word": " كويس", "probability": 0.9835611979166666}], "temperature": 1.0}, {"id": 218, "seek": 533092, "start": 5307.2, "end": 5330.92, "text": "مشان هيك بروح افترض في عندي دالة من عندي بروح بقوله let phi of x y be a function such that بحيث ان ال m تساوي partial phi على partial x", "tokens": [2304, 8592, 7649, 39896, 4117, 4724, 32887, 5016, 1975, 5172, 2655, 43042, 8978, 18871, 16254, 11778, 6027, 3660, 9154, 18871, 16254, 4724, 32887, 5016, 4724, 39648, 3224, 718, 13107, 295, 2031, 288, 312, 257, 2445, 1270, 300, 4724, 5016, 1829, 12984, 16472, 2423, 275, 6055, 3794, 995, 45865, 14641, 13107, 15844, 14641, 2031], "avg_logprob": -0.21122685819864273, "compression_ratio": 1.3150684931506849, "no_speech_prob": 0.0, "words": [{"start": 5307.2, "end": 5307.74, "word": "مشان", "probability": 0.6984049479166666}, {"start": 5307.74, "end": 5308.14, "word": " هيك", "probability": 0.8154296875}, {"start": 5308.14, "end": 5308.48, "word": " بروح", "probability": 0.6055501302083334}, {"start": 5308.48, "end": 5309.28, "word": " افترض", "probability": 0.9129638671875}, {"start": 5309.28, "end": 5309.76, "word": " في", "probability": 0.7646484375}, {"start": 5309.76, "end": 5310.24, "word": " عندي", "probability": 0.897216796875}, {"start": 5310.24, "end": 5310.76, "word": " دالة", "probability": 0.97900390625}, {"start": 5310.76, "end": 5310.94, "word": " من", "probability": 0.97021484375}, {"start": 5310.94, "end": 5311.48, "word": " عندي", "probability": 0.9404296875}, {"start": 5311.48, "end": 5312.54, "word": " بروح", "probability": 0.97509765625}, {"start": 5312.54, "end": 5313.26, "word": " بقوله", "probability": 0.8810221354166666}, {"start": 5313.26, "end": 5313.9, "word": " let", "probability": 0.685546875}, {"start": 5313.9, "end": 5315.22, "word": " phi", "probability": 0.364501953125}, {"start": 5315.22, "end": 5315.92, "word": " of", "probability": 0.8291015625}, {"start": 5315.92, "end": 5316.46, "word": " x", "probability": 0.75341796875}, {"start": 5316.46, "end": 5317.16, "word": " y", "probability": 0.49462890625}, {"start": 5317.16, "end": 5318.08, "word": " be", "probability": 0.79345703125}, {"start": 5318.08, "end": 5319.18, "word": " a", "probability": 0.98046875}, {"start": 5319.18, "end": 5320.16, "word": " function", "probability": 0.9794921875}, {"start": 5320.16, "end": 5321.38, "word": " such", "probability": 0.96923828125}, {"start": 5321.38, "end": 5322.02, "word": " that", "probability": 0.9560546875}, {"start": 5322.02, "end": 5324.02, "word": " بحيث", "probability": 0.9798583984375}, {"start": 5324.02, "end": 5324.44, "word": " ان", "probability": 0.5537109375}, {"start": 5324.44, "end": 5325.62, "word": " ال", "probability": 0.92626953125}, {"start": 5325.62, "end": 5326.44, "word": " m", "probability": 0.419921875}, {"start": 5326.44, "end": 5327.68, "word": " تساوي", "probability": 0.8492431640625}, {"start": 5327.68, "end": 5328.3, "word": " partial", "probability": 0.912109375}, {"start": 5328.3, "end": 5329.22, "word": " phi", "probability": 0.830078125}, {"start": 5329.22, "end": 5329.9, "word": " على", "probability": 0.54052734375}, {"start": 5329.9, "end": 5330.4, "word": " partial", "probability": 0.9541015625}, {"start": 5330.4, "end": 5330.92, "word": " x", "probability": 0.9931640625}], "temperature": 1.0}, {"id": 219, "seek": 534586, "start": 5333.16, "end": 5345.86, "text": "بروح من عندى، بختار دالة، بحيث الدالة هذه مشتقتها بالنسبة ل X، بدي يعطينا مين؟ ال M تبعت مين؟", "tokens": [3555, 32887, 5016, 9154, 43242, 7578, 12399, 4724, 46456, 9640, 11778, 6027, 3660, 12399, 4724, 5016, 1829, 12984, 32748, 6027, 3660, 29538, 37893, 2655, 38149, 11296, 20666, 1863, 35457, 3660, 5296, 1783, 12399, 4724, 16254, 37495, 9566, 1829, 8315, 3714, 9957, 22807, 2423, 376, 6055, 3555, 34268, 3714, 9957, 22807], "avg_logprob": -0.2241115213609209, 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"seek": 594286, "start": 5931.32, "end": 5942.86, "text": "يبقى صرة المعنى ال exact ولا لا مش شايف تعريف ال exact يبقى this", "tokens": [1829, 3555, 4587, 7578, 20328, 25720, 9673, 3615, 1863, 7578, 2423, 1900, 49429, 20193, 37893, 13412, 995, 33911, 37279, 16572, 5172, 2423, 1900, 7251, 3555, 4587, 7578, 341], "avg_logprob": -0.3157327627313548, "compression_ratio": 1.188235294117647, "no_speech_prob": 0.0, "words": [{"start": 5931.32, "end": 5931.7, "word": "يبقى", "probability": 0.8251953125}, {"start": 5931.7, "end": 5932.08, "word": " صرة", "probability": 0.43988037109375}, {"start": 5932.08, "end": 5932.48, "word": " المعنى", "probability": 0.8153076171875}, {"start": 5932.48, "end": 5932.6, "word": " ال", "probability": 0.60791015625}, {"start": 5932.6, "end": 5933.04, "word": " exact", "probability": 0.487548828125}, {"start": 5933.04, "end": 5933.34, "word": " ولا", "probability": 0.83984375}, {"start": 5933.34, "end": 5933.76, "word": " لا", "probability": 0.669921875}, 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نفاضل", "probability": 0.857177734375}, {"start": 6286.79, "end": 6286.93, "word": " و", "probability": 0.97265625}, {"start": 6286.93, "end": 6287.53, "word": " نكامل", "probability": 0.901611328125}, {"start": 6287.53, "end": 6287.97, "word": " كمان", "probability": 0.9404296875}, {"start": 6287.97, "end": 6288.41, "word": " الآن", "probability": 0.6168212890625}, {"start": 6288.41, "end": 6288.67, "word": " زى", "probability": 0.957763671875}, {"start": 6288.67, "end": 6288.73, "word": " ما", "probability": 0.83154296875}, {"start": 6288.73, "end": 6289.39, "word": " هتشوفى", "probability": 0.88037109375}, {"start": 6289.39, "end": 6290.03, "word": " فى", "probability": 0.819580078125}, {"start": 6290.03, "end": 6290.91, "word": " الأسئلة", "probability": 0.974853515625}, {"start": 6290.91, "end": 6294.79, "word": " example", "probability": 0.19189453125}, {"start": 6294.79, "end": 6297.53, "word": " one", "probability": 0.6318359375}, {"start": 6297.53, "end": 6302.49, "word": " solve", "probability": 0.857421875}, {"start": 6302.49, "end": 6304.51, "word": " the", "probability": 0.8388671875}, {"start": 6304.51, "end": 6306.27, "word": " differential", "probability": 0.89453125}, {"start": 6306.27, "end": 6308.33, "word": " equation", "probability": 0.98095703125}, {"start": 6308.33, "end": 6310.43, "word": " اللى", "probability": 0.953125}, {"start": 6310.43, "end": 6310.53, "word": " هو", "probability": 0.75634765625}, {"start": 6310.53, "end": 6311.19, "word": " اتنين", "probability": 0.9351806640625}], "temperature": 1.0}, {"id": 260, "seek": 634009, "start": 6311.47, "end": 6340.09, "text": "2xy تربيع 2xy تربيع زائدي 2y زائد اللي هو 2x تربيع y زائد 2x في ال y prime بده يساوي مين؟ Zero وهذه المعادلة نحلها", "tokens": [17, 12876, 6055, 2288, 21292, 3615, 568, 12876, 6055, 2288, 21292, 3615, 30767, 16373, 16254, 568, 88, 30767, 16373, 3215, 13672, 1829, 31439, 568, 87, 6055, 2288, 21292, 3615, 288, 30767, 16373, 3215, 568, 87, 8978, 2423, 288, 5835, 47525, 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"end": 6669.1, "word": " اشتقها", "probability": 0.8892578125}, {"start": 6669.1, "end": 6669.8, "word": " روحت", "probability": 0.87841796875}, {"start": 6669.8, "end": 6670.72, "word": " اشتقتها", "probability": 0.9330078125}, {"start": 6670.72, "end": 6670.9, "word": " طب", "probability": 0.856201171875}, {"start": 6670.9, "end": 6670.98, "word": " ما", "probability": 0.52880859375}, {"start": 6670.98, "end": 6671.06, "word": " هي", "probability": 0.9208984375}, {"start": 6671.06, "end": 6671.68, "word": " ماشتقتها", "probability": 0.8240234375}, {"start": 6671.68, "end": 6671.84, "word": " هي", "probability": 0.80810546875}, {"start": 6671.84, "end": 6672.02, "word": " اللي", "probability": 0.933349609375}, {"start": 6672.02, "end": 6672.76, "word": " فوق؟", "probability": 0.9630533854166666}], "temperature": 1.0}, {"id": 274, "seek": 669380, "start": 6680.62, "end": 6693.8, "text": "بستنتج ان اتنين اكس تربية Y زائد اتنين X يساوي اتنين اكس تربية Y زائد اتنين X زائد F prime of Y", "tokens": [3555, 14851, 29399, 7435, 16472, 1975, 2655, 1863, 9957, 1975, 4117, 3794, 6055, 25513, 10632, 398, 30767, 16373, 3215, 1975, 2655, 1863, 9957, 1783, 7251, 3794, 995, 45865, 1975, 2655, 1863, 9957, 1975, 4117, 3794, 6055, 25513, 10632, 398, 30767, 16373, 3215, 1975, 2655, 1863, 9957, 1783, 30767, 16373, 3215, 479, 5835, 295, 398], "avg_logprob": -0.20568182360042225, "compression_ratio": 1.7727272727272727, "no_speech_prob": 5.960464477539063e-08, "words": [{"start": 6680.62, "end": 6681.68, "word": "بستنتج", "probability": 0.600372314453125}, {"start": 6681.68, "end": 6682.1, "word": " ان", "probability": 0.39404296875}, {"start": 6682.1, "end": 6683.54, "word": " اتنين", "probability": 0.83203125}, {"start": 6683.54, "end": 6684.1, "word": " اكس", "probability": 0.7854817708333334}, {"start": 6684.1, "end": 6684.66, "word": " تربية", "probability": 0.8653971354166666}, {"start": 6684.66, "end": 6685.08, "word": " Y", "probability": 0.57421875}, {"start": 6685.08, "end": 6685.66, "word": " زائد", "probability": 0.6892903645833334}, {"start": 6685.66, "end": 6686.32, "word": " اتنين", "probability": 0.9705810546875}, {"start": 6686.32, "end": 6686.74, "word": " X", "probability": 0.8212890625}, {"start": 6686.74, "end": 6687.72, "word": " يساوي", "probability": 0.8453369140625}, {"start": 6687.72, "end": 6688.38, "word": " اتنين", "probability": 0.9635009765625}, {"start": 6688.38, "end": 6688.8, "word": " اكس", "probability": 0.8787434895833334}, {"start": 6688.8, "end": 6689.28, "word": " تربية", "probability": 0.9637044270833334}, {"start": 6689.28, "end": 6689.6, "word": " Y", "probability": 0.9814453125}, {"start": 6689.6, "end": 6690.1, "word": " زائد", "probability": 0.9554036458333334}, {"start": 6690.1, "end": 6690.78, "word": " اتنين", "probability": 0.98681640625}, {"start": 6690.78, "end": 6691.26, "word": " X", "probability": 0.990234375}, {"start": 6691.26, "end": 6691.88, "word": " زائد", "probability": 0.9508463541666666}, {"start": 6691.88, "end": 6692.36, "word": " F", "probability": 0.91552734375}, {"start": 6692.36, "end": 6693.18, "word": " prime", "probability": 0.328369140625}, {"start": 6693.18, "end": 6693.52, "word": " of", "probability": 0.6669921875}, {"start": 6693.52, "end": 6693.8, "word": " Y", "probability": 0.9794921875}], "temperature": 1.0}, {"id": 275, "seek": 672318, "start": 6694.6, "end": 6723.18, "text": "أصلا لو جبت هذا عند هذا بروح و لو جبت هذا عند هذا بروح هذا بده يعطينا انه f prime of y بده يسوي قداش هذا الحين function في مين في متغير واحد صح ولا لأ يبقى هذا معناه انه f of y بده يسوي قداش c1 يبقى بروح بقوله ها the solution", "tokens": [10721, 9381, 15040, 45164, 10874, 3555, 2655, 23758, 43242, 23758, 4724, 32887, 5016, 4032, 45164, 10874, 3555, 2655, 23758, 43242, 23758, 4724, 32887, 5016, 23758, 47525, 3224, 37495, 9566, 1829, 8315, 16472, 3224, 283, 5835, 295, 288, 47525, 3224, 7251, 3794, 45865, 12174, 3215, 33599, 23758, 21542, 9957, 2445, 8978, 3714, 9957, 8978, 44650, 17082, 13546, 36764, 24401, 20328, 5016, 49429, 5296, 10721, 7251, 3555, 4587, 7578, 23758, 20449, 8315, 3224, 16472, 3224, 283, 295, 288, 47525, 3224, 7251, 3794, 45865, 12174, 3215, 33599, 269, 16, 7251, 3555, 4587, 7578, 4724, 32887, 5016, 4724, 39648, 3224, 8032, 995, 264, 3827], "avg_logprob": -0.2086943033898231, "compression_ratio": 1.946524064171123, "no_speech_prob": 6.657838821411133e-05, "words": [{"start": 6694.6, "end": 6695.22, "word": "أصلا", "probability": 0.6330973307291666}, {"start": 6695.22, "end": 6695.44, "word": " لو", "probability": 0.482177734375}, {"start": 6695.44, "end": 6695.88, "word": " جبت", "probability": 0.8167317708333334}, {"start": 6695.88, "end": 6696.28, "word": " هذا", "probability": 0.7109375}, {"start": 6696.28, "end": 6696.62, "word": " عند", "probability": 0.92578125}, {"start": 6696.62, "end": 6696.98, "word": " هذا", "probability": 0.91943359375}, {"start": 6696.98, "end": 6697.58, "word": " بروح", "probability": 0.84912109375}, {"start": 6697.58, "end": 6697.96, "word": " و", "probability": 0.5263671875}, {"start": 6697.96, "end": 6698.18, "word": " لو", "probability": 0.90869140625}, {"start": 6698.18, "end": 6698.54, "word": " جبت", "probability": 0.9833984375}, {"start": 6698.54, "end": 6698.8, "word": " هذا", "probability": 0.953125}, {"start": 6698.8, "end": 6699.04, "word": " عند", "probability": 0.96435546875}, {"start": 6699.04, "end": 6699.36, "word": " هذا", "probability": 0.97265625}, {"start": 6699.36, "end": 6700.06, "word": " بروح", "probability": 0.9884440104166666}, {"start": 6700.06, "end": 6700.66, "word": " هذا", "probability": 0.8193359375}, {"start": 6700.66, "end": 6701.08, "word": " بده", "probability": 0.50830078125}, {"start": 6701.08, "end": 6701.58, "word": " يعطينا", "probability": 0.934814453125}, {"start": 6701.58, "end": 6702.04, "word": " انه", "probability": 0.5179443359375}, {"start": 6702.04, "end": 6702.42, "word": " f", "probability": 0.619140625}, {"start": 6702.42, "end": 6703.12, "word": " prime", "probability": 0.58154296875}, {"start": 6703.12, "end": 6703.66, "word": " of", "probability": 0.94140625}, {"start": 6703.66, "end": 6703.98, "word": " y", "probability": 0.79150390625}, {"start": 6703.98, "end": 6704.26, "word": " بده", "probability": 0.828857421875}, {"start": 6704.26, "end": 6704.48, "word": " يسوي", "probability": 0.7649739583333334}, {"start": 6704.48, "end": 6705.22, "word": " قداش", "probability": 0.8077799479166666}, {"start": 6705.22, "end": 6706.3, "word": " هذا", "probability": 0.492919921875}, {"start": 6706.3, "end": 6706.64, "word": " الحين", "probability": 0.876953125}, {"start": 6706.64, "end": 6707.16, "word": " function", "probability": 0.7421875}, {"start": 6707.16, "end": 6707.5, "word": " في", "probability": 0.8466796875}, {"start": 6707.5, "end": 6707.7, "word": " مين", "probability": 0.771484375}, {"start": 6707.7, "end": 6707.86, "word": " في", "probability": 0.56982421875}, {"start": 6707.86, "end": 6708.8, "word": " متغير", "probability": 0.96923828125}, {"start": 6708.8, "end": 6709.6, "word": " واحد", "probability": 0.990234375}, {"start": 6709.6, "end": 6710.18, "word": " صح", "probability": 0.904296875}, {"start": 6710.18, "end": 6710.4, "word": " ولا", "probability": 0.97265625}, {"start": 6710.4, "end": 6710.8, "word": " لأ", "probability": 0.753173828125}, {"start": 6710.8, "end": 6711.56, "word": " يبقى", "probability": 0.9171142578125}, {"start": 6711.56, "end": 6711.96, "word": " هذا", "probability": 0.982421875}, {"start": 6711.96, "end": 6712.82, "word": " معناه", "probability": 0.9820963541666666}, {"start": 6712.82, "end": 6713.76, "word": " انه", "probability": 0.879150390625}, {"start": 6713.76, "end": 6714.16, "word": " f", "probability": 0.8115234375}, {"start": 6714.16, "end": 6714.86, "word": " of", "probability": 0.9462890625}, {"start": 6714.86, "end": 6715.4, "word": " y", "probability": 0.9619140625}, {"start": 6715.4, "end": 6715.86, "word": " بده", "probability": 0.870849609375}, {"start": 6715.86, "end": 6716.1, "word": " يسوي", "probability": 0.9205729166666666}, {"start": 6716.1, "end": 6716.92, "word": " قداش", "probability": 0.982421875}, {"start": 6716.92, "end": 6718.44, "word": " c1", "probability": 0.741943359375}, {"start": 6718.44, "end": 6719.28, "word": " يبقى", "probability": 0.97119140625}, {"start": 6719.28, "end": 6719.74, "word": " بروح", "probability": 0.9788411458333334}, {"start": 6719.74, "end": 6720.92, "word": " بقوله", "probability": 0.8426106770833334}, {"start": 6720.92, "end": 6721.6, "word": " ها", "probability": 0.468017578125}, {"start": 6721.6, "end": 6722.04, "word": " the", "probability": 0.5986328125}, {"start": 6722.04, "end": 6723.18, "word": " solution", "probability": 0.958984375}], "temperature": 1.0}, {"id": 276, "seek": 674722, "start": 6741.28, "end": 6747.22, "text": "كل هذا الكلام بده يساوي C", "tokens": [28820, 23758, 2423, 28820, 10943, 47525, 3224, 7251, 3794, 995, 45865, 383], "avg_logprob": -0.4122596245545607, "compression_ratio": 0.88, "no_speech_prob": 1.7881393432617188e-07, "words": [{"start": 6741.280000000001, "end": 6742.68, "word": "كل", "probability": 0.3076171875}, {"start": 6742.68, "end": 6744.08, "word": " هذا", "probability": 0.79833984375}, {"start": 6744.08, "end": 6744.9, "word": " الكلام", "probability": 0.8645833333333334}, {"start": 6744.9, "end": 6745.74, "word": " بده", "probability": 0.471038818359375}, {"start": 6745.74, "end": 6746.64, "word": " يساوي", "probability": 0.96630859375}, {"start": 6746.64, "end": 6747.22, "word": " C", "probability": 0.46826171875}], "temperature": 1.0}, {"id": 277, "seek": 676619, "start": 6749.71, "end": 6766.19, "text": "لأن قلنا there exists a function of psi of x و y حطيلي تساوي C2 يالا هذه تساوي C2 طيب إيش رايك؟ بدي أجيب C1 and C2", "tokens": [1211, 33456, 12174, 1211, 8315, 456, 8198, 257, 2445, 295, 20304, 295, 2031, 4032, 288, 11331, 9566, 1829, 20292, 6055, 3794, 995, 45865, 383, 17, 7251, 6027, 995, 29538, 6055, 3794, 995, 45865, 383, 17, 23032, 1829, 3555, 11933, 1829, 8592, 12602, 47302, 4117, 22807, 4724, 16254, 5551, 7435, 1829, 3555, 383, 16, 293, 383, 17], "avg_logprob": -0.3758223767866168, "compression_ratio": 1.1911764705882353, "no_speech_prob": 0.0, "words": [{"start": 6749.71, "end": 6750.03, "word": "لأن", "probability": 0.3616943359375}, {"start": 6750.03, "end": 6750.39, "word": " قلنا", "probability": 0.7228190104166666}, {"start": 6750.39, "end": 6750.61, "word": " there", "probability": 0.1650390625}, {"start": 6750.61, "end": 6751.05, "word": " exists", "probability": 0.5185546875}, {"start": 6751.05, "end": 6751.23, "word": " a", "probability": 0.9384765625}, {"start": 6751.23, "end": 6751.61, "word": " function", "probability": 0.95849609375}, {"start": 6751.61, "end": 6751.85, "word": " of", "probability": 0.1995849609375}, {"start": 6751.85, "end": 6752.25, "word": " psi", "probability": 0.271484375}, {"start": 6752.25, "end": 6752.81, "word": " of", "probability": 0.93408203125}, {"start": 6752.81, "end": 6753.35, "word": " x", "probability": 0.77880859375}, {"start": 6753.35, "end": 6753.63, "word": " و", "probability": 0.5849609375}, {"start": 6753.63, "end": 6753.97, "word": " y", "probability": 0.78759765625}, {"start": 6753.97, "end": 6755.11, "word": " حطيلي", "probability": 0.59661865234375}, {"start": 6755.11, "end": 6756.01, "word": " تساوي", "probability": 0.9522705078125}, {"start": 6756.01, "end": 6757.73, "word": " C2", "probability": 0.68359375}, {"start": 6757.73, "end": 6759.41, "word": " يالا", "probability": 0.584716796875}, {"start": 6759.41, "end": 6759.81, "word": " هذه", "probability": 0.66943359375}, {"start": 6759.81, "end": 6760.79, "word": " تساوي", "probability": 0.9820556640625}, {"start": 6760.79, "end": 6762.11, "word": " C2", "probability": 0.97119140625}, {"start": 6762.11, "end": 6763.33, "word": " طيب", "probability": 0.7515462239583334}, {"start": 6763.33, "end": 6763.53, "word": " إيش", "probability": 0.779052734375}, {"start": 6763.53, "end": 6764.07, "word": " رايك؟", "probability": 0.81988525390625}, {"start": 6764.07, "end": 6764.29, "word": " بدي", "probability": 0.647705078125}, {"start": 6764.29, "end": 6764.61, "word": " أجيب", "probability": 0.9539794921875}, {"start": 6764.61, "end": 6765.21, "word": " C1", "probability": 0.971923828125}, {"start": 6765.21, "end": 6765.51, "word": " and", "probability": 0.490234375}, {"start": 6765.51, "end": 6766.19, "word": " C2", "probability": 0.993408203125}], "temperature": 1.0}, {"id": 278, "seek": 679287, "start": 6786.11, "end": 6792.87, "text": "هذا هو حل المعادلة التفاضلية", "tokens": [3224, 15730, 31439, 11331, 1211, 9673, 3615, 18513, 37977, 16712, 5172, 46958, 1211, 10632], "avg_logprob": -0.227734378973643, "compression_ratio": 0.896551724137931, "no_speech_prob": 0.0, "words": [{"start": 6786.110000000001, "end": 6787.51, "word": "هذا", "probability": 0.47674560546875}, {"start": 6787.51, "end": 6788.91, "word": " هو", "probability": 0.61328125}, {"start": 6788.91, "end": 6789.45, "word": " حل", "probability": 0.933837890625}, {"start": 6789.45, "end": 6791.05, "word": " المعادلة", "probability": 0.9718017578125}, {"start": 6791.05, "end": 6792.87, "word": " التفاضلية", "probability": 0.9154296875}], "temperature": 1.0}, {"id": 279, "seek": 679662, "start": 6794.84, "end": 6796.62, "text": "لسة لازمنا في نفس ال section", "tokens": [1211, 3794, 3660, 5296, 31377, 2304, 8315, 8978, 8717, 36178, 2423, 3541], "avg_logprob": -0.49909857603219837, "compression_ratio": 0.8, "no_speech_prob": 0.0, "words": [{"start": 6794.84, "end": 6795.32, "word": "لسة", "probability": 0.5263671875}, {"start": 6795.32, "end": 6795.76, "word": " لازمنا", "probability": 0.74554443359375}, {"start": 6795.76, "end": 6795.9, "word": " في", "probability": 0.8037109375}, {"start": 6795.9, "end": 6796.18, "word": " نفس", "probability": 0.558349609375}, {"start": 6796.18, "end": 6796.3, "word": " ال", "probability": 0.8291015625}, {"start": 6796.3, "end": 6796.62, "word": " section", "probability": 0.9111328125}], "temperature": 1.0}], "language": "ar", "language_probability": 1.0, "duration": 6797.363, "duration_after_vad": 6393.794093750035}
\ No newline at end of file
diff --git a/PL9fwy3NUQKwa8ZDfSFGn6H8xVFLzqmCZC/gssK8gZjcqI.srt b/PL9fwy3NUQKwa8ZDfSFGn6H8xVFLzqmCZC/gssK8gZjcqI.srt
new file mode 100644
index 0000000000000000000000000000000000000000..0cc62c3de7320c0131f7cd0344a06d43ac9ac4d8
--- /dev/null
+++ b/PL9fwy3NUQKwa8ZDfSFGn6H8xVFLzqmCZC/gssK8gZjcqI.srt
@@ -0,0 +1,2712 @@
+1
+00:00:09,600 --> 00:00:15,940
+بسم الله الرحمن الرحيم المرة الماضية دخلنا في حل
+
+2
+00:00:15,940 --> 00:00:19,480
+الـ non homogeneous differential equation واخذنا
+
+3
+00:00:19,480 --> 00:00:23,260
+الطريقة الأولى وهى طريقة الـ undetermined
+
+4
+00:00:23,260 --> 00:00:28,440
+coefficients وظهر علينا طريقة الـ variation of 
+
+5
+00:00:28,440 --> 00:00:32,700
+parameters اللي رفعناها فوق إن شاء الله هذه
+
+6
+00:00:32,700 --> 00:00:37,180
+الطريقة نفس الفكرة تابعة الـ second order لما نحلها
+
+7
+00:00:37,180 --> 00:00:40,880
+بالـ variation of parameters بنحل بطريقة الـ
+
+8
+00:00:40,880 --> 00:00:46,070
+variation of parameters إذا كانت المعاملات ثوابت أو
+
+9
+00:00:46,070 --> 00:00:52,490
+غير ثوابت بيهمنيش شكل g of t يكون أي شكل مش مقصور
+
+10
+00:00:52,490 --> 00:00:55,130
+زي الـ undetermined coefficients لازم يكون
+
+11
+00:00:55,130 --> 00:00:59,090
+المعاملات ثوابت و g of t تكون بشكل معين حسب جدولنا 
+
+12
+00:00:59,090 --> 00:01:02,430
+اللي عملنا له و g of t تكون أيش ما يكون شكلها
+
+13
+00:01:02,430 --> 00:01:06,070
+فبقول يعتبر اللي هو الـ nth order linear
+
+14
+00:01:06,070 --> 00:01:09,910
+differential equation بالشكل اللي قدامنا هذا لحظة
+
+15
+00:01:19,460 --> 00:01:23,860
+المعاملات هي هي متغيرات وقد تكون ثوابت بتفرقش لأن
+
+16
+00:01:23,860 --> 00:01:29,800
+ثوابت بتكون متغيرات المهم نعرف أن حل نقول assume
+
+17
+00:01:29,800 --> 00:01:34,280
+that we know a fundamental set of solutions Y1 وY2
+
+18
+00:01:34,280 --> 00:01:38,240
+وYN لمين؟ للـ homogeneous differential equation اللي
+
+19
+00:01:38,240 --> 00:01:42,240
+متساوي قد إيش؟ صفر يعني إذا عندي non homogeneous بدي
+
+20
+00:01:42,240 --> 00:01:45,120
+أجزئها لجزئين سواء كان بالـ undetermined
+
+21
+00:01:45,120 --> 00:01:48,860
+coefficients أو بالـ variation of parameter علي
+
+22
+00:01:48,860 --> 00:01:53,220
+الشكلتين بدي أخد الـ homogeneous وأطلع الحل تبع الـ
+
+23
+00:01:53,220 --> 00:01:56,440
+homogeneous differential equation وبعد ذلك بروح
+
+24
+00:01:56,440 --> 00:02:01,520
+لمين؟ للـ non homogeneous differential equation خلاص
+
+25
+00:02:01,520 --> 00:02:06,500
+الأمر نفس الفكرة تبع الـ undetermined بس هناك بنروح
+
+26
+00:02:06,500 --> 00:02:10,160
+عشان بنجيب particular solution وبيكون جبنا حل الـ
+
+27
+00:02:10,160 --> 00:02:13,820
+homogenous بنجمع الاثنين بنطلع من الـ general
+
+28
+00:02:13,820 --> 00:02:17,220
+solution هنا بنفس الطريقة بدي أروح أجيب الـ
+
+29
+00:02:17,220 --> 00:02:20,660
+particular solution للـ non homogeneous differential
+
+30
+00:02:20,660 --> 00:02:24,200
+equation أجمعه مع حل الـ homogenous differential
+
+31
+00:02:24,200 --> 00:02:27,980
+equation بيعطينا من الـ general solution للـ
+
+32
+00:02:27,980 --> 00:02:29,660
+differential equation كلها
+
+33
+00:02:33,120 --> 00:02:37,220
+الحل الهوموجيني يسمى الـ  homogeneous يسمى
+
+34
+00:02:37,220 --> 00:02:43,280
+الهوموجيني يسمى الهوموجيني يسمى الهوموجيني يسمى
+
+35
+00:02:43,280 --> 00:02:43,620
+الهوموجيني يسمى الهوموجيني يسمى الهوموجيني يسمى
+
+36
+00:02:43,620 --> 00:02:45,260
+الهوموجيني يسمى الهوموجيني يسمى الهوموجيني يسمى
+
+37
+00:02:45,260 --> 00:02:46,100
+الهوموجيني يسمى الهوموجيني يسمى الهوموجيني يسمى
+
+38
+00:02:46,100 --> 00:02:46,580
+الهوموجيني يسمى الهوموجيني يسمى الهوموجيني يسمى
+
+39
+00:02:46,580 --> 00:02:47,100
+الهوموجيني يسمى الهوموجيني يسمى الهوموجيني يسمى
+
+40
+00:02:47,100 --> 00:02:47,500
+الهوموجيني يسمى الهوموجيني يسمى الهوموجيني يسمى
+
+41
+00:02:47,500 --> 00:02:54,580
+الهوموجيني يسمى التغيير في الوسيطة to find a 
+
+42
+00:02:54,580 --> 00:02:59,000
+particular solution يبقى هذه بنستخدمها لإيجاد حل
+
+43
+00:02:59,000 --> 00:03:03,380
+خاص زي بناتي الجدول في الـ undetermined بنستخدمه
+
+44
+00:03:03,380 --> 00:03:06,760
+لإيجاد حل خاص وبعد هيك بنجيب الـ general solution
+
+45
+00:03:08,020 --> 00:03:13,000
+يبقى هذه الطريقة تتلخص بدي أشيل c1 و c2 و c3 لغاية
+
+46
+00:03:13,000 --> 00:03:20,320
+cn وأحط مكانهم functions u1 و u2 و u3 و un هيهم
+
+47
+00:03:20,320 --> 00:03:23,640
+بالشكل اللي هذا بحيث أن الـ particular solution
+
+48
+00:03:23,640 --> 00:03:28,100
+بيصير على الشكل اللي عندنا هذا u1 y1 زائد u2 y2
+
+49
+00:03:28,100 --> 00:03:34,460
+زائد u3 y3 زائد un اللي هو yn طب بدنا نجيب شكل كل
+
+50
+00:03:34,460 --> 00:03:39,760
+واحدة من الـ uiهات هذه فبقول له where الـ um as a 
+
+51
+00:03:39,760 --> 00:03:45,640
+function of T هي integration للـ g of T اللي هي هذه
+
+52
+00:03:45,640 --> 00:03:52,820
+مضروبة في الـ wronskian m of T على الـ wronskian of T أول شيء
+
+53
+00:03:52,820 --> 00:03:56,140
+الـ wronskian of T هذا الـ wronskian تبع الحلول اللي هو Y1
+
+54
+00:03:56,140 --> 00:04:03,020
+وY2 وY3 تمام؟ الآن مين الـ wronskian m؟ هو نفس الـ wronskian
+
+55
+00:04:03,020 --> 00:04:09,860
+هذا هه بس بدي أشيل الصف رقم m وأكتب بدل العمود
+
+56
+00:04:09,860 --> 00:04:17,670
+000001 يعني إيش؟ يعني لو كنت بدي u1 of T لأن احنا
+
+57
+00:04:17,670 --> 00:04:21,770
+لدينا u1 و u2 لغاية un باجي على الـ wronskian  الآن و
+
+58
+00:04:21,770 --> 00:04:26,430
+بشيل العمود الأول وبكتب دالة 0001 وباجي الأعمدة
+
+59
+00:04:26,430 --> 00:04:30,810
+أزاي ما هي وبفك المحدد وبجيب قيمته تمام؟ يبقى
+
+60
+00:04:30,810 --> 00:04:33,970
+جيبنا قيمة المحدد هذا، جيبنا قيمة المحدد هذا، نضرب 
+
+61
+00:04:33,970 --> 00:04:38,030
+في g of t ونروح نكامل بكون حصلنا على مين؟ على u1 طب
+
+62
+00:04:38,030 --> 00:04:45,720
+بدي u2 u2 of T بأجي w of T كما هي أو wronskian 2 of T
+
+63
+00:04:45,720 --> 00:04:49,720
+كيف؟ بسيب العمود الأول زي ما هو العمود العتيق مش
+
+64
+00:04:49,720 --> 00:04:53,880
+الجديد وباجي على العمود رقم اثنين بشيله كله بحط وب
+
+65
+00:04:53,880 --> 00:04:58,860
+بدله 0001 والأعمدة اللي بعده تبقى كما هي وهكذا
+
+66
+00:04:59,710 --> 00:05:02,850
+للـ wronskian ثلاثة أو wronskian أربعة أو wronskian خمسة
+
+67
+00:05:02,850 --> 00:05:06,650
+إلى آخره لغاية ما نخلص كل الـ uiهات اللي عندنا إذا
+
+68
+00:05:06,650 --> 00:05:09,190
+جبناهم بيقول خلاص جبنا الـ particular solution 
+
+69
+00:05:09,190 --> 00:05:14,410
+تمام يبقى باجي بقول له الـ um of T هو integration للـ 
+
+70
+00:05:14,410 --> 00:05:21,290
+g of T في الـ wronskian m of T على الـ w of T dt والـ m بدأ
+
+71
+00:05:21,290 --> 00:05:25,110
+يساوي واحد واثنين لغاية مين؟ لغاية الـ n يعني بدي
+
+72
+00:05:25,110 --> 00:05:30,130
+أجيب كل الـ uiهات فـ wronskian m is the determinant هو
+
+73
+00:05:30,130 --> 00:05:36,070
+عبارة عن المحدد يبقى بنقول ما يأتي الآن بدنا نحاول
+
+74
+00:05:36,070 --> 00:05:39,710
+نجيب الـ uiهات اللي عندنا دي واحد واثنين وثلاثة و
+
+75
+00:05:39,710 --> 00:05:46,560
+لغاية um بنحط الصورة العامة um of T هي عبارة عن
+
+76
+00:05:46,560 --> 00:05:51,140
+integration للـ g of T في الـ wronskian m as a
+
+77
+00:05:51,140 --> 00:05:55,600
+function of T على الـ wronskian of T كله بالنسبة لـ dt
+
+78
+00:05:55,600 --> 00:06:02,380
+مين هي الـ g of T؟ هي تبع المعادلة هذه ما غيرناش المعادلة 
+
+79
+00:06:02,380 --> 00:06:07,260
+الـ wronskian هذا هو تبع الحلول y1 وy2 لغاية yn
+
+80
+00:06:07,760 --> 00:06:12,080
+الـ wronskian m of T هو الـ wronskian اللي تحت هذا بس بعد
+
+81
+00:06:12,080 --> 00:06:17,040
+ما أغير كل عمود يعني إذا عندي بدي u واحد بغير
+
+82
+00:06:17,040 --> 00:06:21,720
+العمود الأول بكون عندي w واحد عندي u اثنين يبقى
+
+83
+00:06:21,720 --> 00:06:27,120
+هنا w اثنين of T باجي على العمود الثاني بغيره بحط
+
+84
+00:06:27,120 --> 00:06:33,740
+بداله 0001 وكده لغاية ما أوصل لمين؟ للـ un اللي
+
+85
+00:06:33,740 --> 00:06:38,410
+عندنا الـ un ها هي عبارة عن الـ g of T في 
+
+86
+00:06:38,410 --> 00:06:42,250
+الـ wronskian m of T مقسمة على الـ wronskian of T كله
+
+87
+00:06:42,250 --> 00:06:46,430
+بالنسبة لـ dt والـ m بتاخد 1 و2 لغاية الـ n يعني
+
+88
+00:06:46,430 --> 00:06:53,320
+بدي أجيب كل الـ uiهات مرة واحدة يبقى هي جبنا له الـ m
+
+89
+00:06:53,320 --> 00:06:58,660
+الـ wronskian m هو هو المحدد اللي بنحصل عليه من الـ w
+
+90
+00:06:58,660 --> 00:07:05,740
+of T باستبدال العمود رقم m بالعمود 0001 في بعض
+
+91
+00:07:05,740 --> 00:07:10,380
+الملاحظات لازم ندققها كويس واحنا بنشتغل تذكروا
+
+92
+00:07:10,380 --> 00:07:13,520
+في حالة الـ variation of parameters في حالة second
+
+93
+00:07:13,520 --> 00:07:18,800
+order اشترطنا أن المعامل تبع y double prime يكون واحد
+
+94
+00:07:19,220 --> 00:07:23,540
+هنا المعامل تبع y to the derivative n يكون واحد 
+
+95
+00:07:23,540 --> 00:07:29,820
+يبقى كتابنا هذا must be one يبقى المعامل تبع الـ y
+
+96
+00:07:29,820 --> 00:07:33,580
+to the derivative n لازم يكون واحد صحيح ليش؟ لأن
+
+97
+00:07:33,580 --> 00:07:38,970
+هذا لو ما كانش واحد صحيح يبقى بيكون ده لا ورقم بدنا
+
+98
+00:07:38,970 --> 00:07:43,810
+نقسم عليه حتى نضمن أن الجديدة هذه هي g of t مش
+
+99
+00:07:43,810 --> 00:07:48,010
+العتيقة يعني g of t هذه بنحصل عليه لما يكون المعامل
+
+100
+00:07:48,010 --> 00:07:52,550
+هنا main واحد صحيح يبقى بدك تعمل الخطوة هذه قبل كل
+
+101
+00:07:52,550 --> 00:07:56,730
+شيء أو تتأكد منها اثنين بيقول يا wronskian هذا بقدر
+
+102
+00:07:56,730 --> 00:08:01,680
+أحسبه بطريقة قابلة طريقة إيه؟ بالطريقة الـ second order 
+
+103
+00:08:01,680 --> 00:08:06,040
+بس احنا هنا للـ nth order يبقى باجي بقول wronskian
+
+104
+00:08:06,040 --> 00:08:11,120
+هو عبارة عن e أس تكامل p1 of T dt الـ
+
+105
+00:08:11,120 --> 00:08:16,000
+p1 هو مين؟ هو معامل y to the derivative n
+
+106
+00:08:16,000 --> 00:08:21,040
+ناقص الـ 1 طلع هي y n اللي بعدها يمين معامل هذا
+
+107
+00:08:21,040 --> 00:08:26,320
+يبقى لو كان في شغل هنا بدك تجسم عليها واللي بيطلع
+
+108
+00:08:26,320 --> 00:08:30,160
+بيكون هو p1 of T وبعضكم في الامتحان اللي فات 
+
+109
+00:08:30,160 --> 00:08:34,420
+ما جسموش وخلوا عليه وبالتالي طالع سؤالهم غلط لازم
+
+110
+00:08:34,420 --> 00:08:38,960
+إيش؟ المعامل هذا يكون واحد صحيح وكتبناها معكم قبل
+
+111
+00:08:38,960 --> 00:08:41,840
+ذلك في الـ second order لازم يكون المعامل هو main
+
+112
+00:08:41,840 --> 00:08:46,980
+واحد صحيح يبقى هذا كل ما يتعلق بقضية الـ variation
+
+113
+00:08:46,980 --> 00:08:52,150
+of parameters يعني حلنا الـ homogeneous بواسطة الـ 
+
+114
+00:08:52,150 --> 00:08:53,150
+Variation of Parameters
+
+115
+00:09:02,380 --> 00:09:06,860
+يبقى بدي أشيل الـ constants في مين؟ في الحل اللي هو 
+
+116
+00:09:06,860 --> 00:09:11,380
+y يساوي c1 y1 زائد c2 y2 زائد cnyn بدي أشيل الـ c هات 
+
+117
+00:09:11,380 --> 00:09:16,760
+هذه وأستبدلها بدوال u1 و u2 و u3 لغاية un طب بدي
+
+118
+00:09:16,760 --> 00:09:20,840
+أجيب عرف الشكل هم بيقول لك اه في أن علاقة العلاقة
+
+119
+00:09:20,840 --> 00:09:25,910
+هذه بتجيب لك أي ui منها غير العلاقة مين هي؟ um of T
+
+120
+00:09:25,910 --> 00:09:30,110
+بدي أسوي تكامل g of T في الـ wronskian m of T على
+
+121
+00:09:30,110 --> 00:09:35,270
+الـ wronskian of T كله بالنسبة لـ dt الـ wronskian m of T هو
+
+122
+00:09:35,270 --> 00:09:39,470
+عبارة عن الـ wronskian of T بعد ما أشيل إذا بدي u 1
+
+123
+00:09:39,470 --> 00:09:45,170
+بشيل العمود الأول وبحط بداله 0001 إذا wronskian 2
+
+124
+00:09:45,170 --> 00:09:48,030
+بأخلي العمود الأول زي ما هو بروح على العمود الثاني
+
+125
+00:09:48,030 --> 00:09:52,510
+بشيله وبحط بداله 0001 وهكذا تبقى بكون جبت الـ u 
+
+126
+00:09:52,510 --> 00:09:56,360
+هات بضربها في الـ yiهات اللي عندي بجمع بكون جبته الـ
+
+127
+00:09:56,360 --> 00:09:59,800
+particular solution للـ non homogeneous
+
+128
+00:09:59,800 --> 00:10:03,040
+differential equation بجمع مع حل الـ homogeneous
+
+129
+00:10:03,040 --> 00:10:06,900
+بيعطيني الـ general solution للـ non homogeneous
+
+130
+00:10:06,900 --> 00:10:11,020
+differential equation واضح كلامي إيه؟ حد فيكم بيحب
+
+131
+00:10:11,020 --> 00:10:14,020
+يسأل أي سؤال؟ خلاصنا الـ part النظري خلاصنا منه حد
+
+132
+00:10:14,020 --> 00:10:17,700
+بيحب يسأل أي سؤال؟ طب الكلام اللي سمعته بنروح
+
+133
+00:10:17,700 --> 00:10:22,800
+نطبقه على أرض الواقع مثال أو أول مثال بقول you 
+
+134
+00:10:22,800 --> 00:10:25,720
+find the general solution of the differential
+
+135
+00:10:25,720 --> 00:10:29,860
+equation y triple prime زائد y prime تساوي 6t
+
+136
+00:10:29,860 --> 00:10:35,000
+و t محصورة من سالب باي على اثنين إلى مين؟ إلى باي
+
+137
+00:10:35,000 --> 00:10:39,790
+على اثنين يعني حصرناها في فترة الدالة الـ 6 تبدأ تبقى
+
+138
+00:10:39,790 --> 00:10:43,210
+continuous على هذه الفترة تعرف أن عند البيعة 2
+
+139
+00:10:43,210 --> 00:10:47,450
+والسالب بيعة 2 الـ 6 is undefined زي الـ tan عند
+
+140
+00:10:47,450 --> 00:10:52,070
+البيعة 2 وسالب بيعة 2 ثلاثة بيعة 2 سالب ثلاثة بيعة 2
+
+141
+00:10:52,070 --> 00:10:56,090
+خمسة بيعة 2 سالب كل ما تبقى الدالة ماهي معرفة
+
+142
+00:10:56,090 --> 00:10:59,490
+يبقى أنا حصرناها في فترة معرفة عليها يعني الدالة
+
+143
+00:10:59,490 --> 00:11:05,350
+continuous على هذه الفترة طيب بدنا نيجي نحل يبقى
+
+144
+00:11:05,350 --> 00:11:10,650
+أول خطوة بتروح تجيب مين؟ حل الـ homogeneous صدر و حل
+
+145
+00:11:10,650 --> 00:11:14,550
+المعادلة رقم اثنين المعادلة اللي عندي من الدرجة
+
+146
+00:11:14,550 --> 00:11:18,470
+الثالثة يبقى نفس الـ tactic اللي اتبعناها في حالة 
+
+147
+00:11:18,470 --> 00:11:21,110
+الـ undetermined coefficients الجزء الأول هو الجزء
+
+148
+00:11:21,110 --> 00:11:28,690
+الأول هناك لا تغيير عليه فباجي بقول له solution let
+
+149
+00:11:29,360 --> 00:11:40,160
+y تساوي e أس rt بـ a solution of المعادلة التفاضلية
+
+150
+00:11:40,160 --> 00:11:44,920
+y triple prime زائد y prime تساوي zero
+
+151
+00:11:57,640 --> 00:12:02,580
+ممكن ناخد r عامل مشترك بيظل r تربيع زائد واحد 
+
+152
+00:12:02,580 --> 00:12:10,830
+يساوي zero يبقى r1 بده يساوي 0 و r2 و r3 بده يساوي
+
+153
+00:12:10,830 --> 00:12:19,670
+زائد أو ناقص كده i يبقى yc بده يساوي c1 في e أس 
+
+154
+00:12:19,670 --> 00:12:30,810
+zero يبقى بـ c1 زائد c2 cos t زائد c3 في sin t الشكل
+
+155
+00:12:30,810 --> 00:12:33,740
+اللي عندنا هنا هذا هو حل الـ homogeneous
+
+156
+00:12:33,740 --> 00:12:38,490
+differential equation بدنا نيجي ندور على particular
+
+157
+00:12:38,490 --> 00:12:44,670
+solution لحال مين؟ لحال اللي هو non homogeneous
+
+158
+00:12:44,670 --> 00:12:50,250
+differential equation بطريقة مين؟ بطريقة الـ 
+
+159
+00:12:50,250 --> 00:12:54,310
+variation of parameters ليش بطريقة الـ variation of
+
+160
+00:12:54,310 --> 00:12:59,890
+parameters؟ لأن الجزء اللي على اليمين له
+
+161
+00:12:59,890 --> 00:13:04,430
+polynomial وله polynomial fixed exponential والا
+
+162
+00:13:04,430 --> 00:13:08,450
+polynomial approximation في ساين أو كوساين سك واحدة
+
+163
+00:13:08,450 --> 00:13:13,250
+على كوساين مش كوساين تربيع واحدة على كوساين إذا اختلفت عن
+
+164
+00:13:13,250 --> 00:13:17,110
+الـ undetermined coefficients وطبعا جيبت لك وده سؤال
+
+165
+00:13:17,110 --> 00:13:21,430
+في الخيارات خليتها واحدة على cosine وقول لك بنحل بها
+
+166
+00:13:21,430 --> 00:13:25,090
+بطريقة إيش؟ الـ undetermined ولا الـ variation ولا الـ 
+
+167
+00:13:25,090 --> 00:13:27,830
+reduction ولا ولا بها الطرق ولا بطريقة من هذه
+
+168
+00:13:27,830 --> 00:13:31,390
+الطررق واختري الإجابة الصحيحة والإجابة الصحيحة هي طريقة
+
+169
+00:13:31,390 --> 00:13:36,130
+مين؟ الـ variation of parameters طيب تتلخص الـ 
+
+170
+00:13:36,130 --> 00:13:40,450
+variation of parameters إني بدي أشيل الـ c1 و c2 و c3 
+
+171
+00:13:40,450 --> 00:13:48,190
+وحط بدالها u1 و u2 و u3 بس قبل لا أحط ولا أشيل بدي
+
+172
+00:13:48,190 --> 00:13:52,990
+أحسب قد إيش الـ wronskian لكل واحدة من هدول لإني بدي
+
+173
+00:13:52,990 --> 00:13:58,570
+
+216
+00:18:37,010 --> 00:18:43,710
+ها بدك تبالغ و هذا ال run skin one as a function
+
+217
+00:18:43,710 --> 00:18:50,190
+of T على run skin of T dT بده يساوي تكامل ال G اللي 
+
+218
+00:18:50,190 --> 00:18:56,750
+هي سك T ال run skin one مقسومة بواحد صحيح يبقى هي
+
+219
+00:18:56,750 --> 00:19:03,400
+مضروبة في واحد على مين؟ على واحد كله dT يبقى بدنا 
+
+220
+00:19:03,400 --> 00:19:09,280
+نكامل مين يا فنان؟ بس سك T نعرف نكملها من كل plus
+
+221
+00:19:09,280 --> 00:19:14,220
+بيه؟ كدهش؟ 
+
+222
+00:19:14,220 --> 00:19:22,380
+لن سك زائد تان يبقى وتساوي لن absolute value لسك
+
+223
+00:19:22,380 --> 00:19:29,140
+T زائد تان T زائد constant K1 اللي هو تبع
+
+224
+00:19:29,140 --> 00:19:35,740
+التكامل طبعا بعد شوية هحط K1 ب 0 هنقولكم ليش بس 
+
+225
+00:19:35,740 --> 00:19:41,420
+يصبرونا علينا شوية بدنا نروح نجيب ال U2 يبقى بدنا 
+
+226
+00:19:41,420 --> 00:19:46,140
+نروح نجيب ال U2 as a function of T
+
+227
+00:19:52,080 --> 00:19:56,680
+يبقى بالداجي لل U2 as a function of T integration
+
+228
+00:19:56,680 --> 00:20:04,140
+لل G of T للورنسكين 2 of T على رونسكين of T كله في
+
+229
+00:20:04,140 --> 00:20:09,200
+dT يبقى هذا الكلام integration ل سك ال T في
+
+230
+00:20:09,200 --> 00:20:15,960
+الرونسكين 2 الرونسكين 2 هو طوله كده؟ ناقص cos T 
+
+231
+00:20:15,960 --> 00:20:23,380
+يبقى ناقص cos T على رونسكين T اللي هو كده؟ واحد
+
+232
+00:20:23,380 --> 00:20:28,520
+صحيح طب السك هذه مش هي مقلوب ال cos يعني بضرب 
+
+233
+00:20:28,520 --> 00:20:36,310
+السالب واحد يبقى هذه تساوي سالب تكامل dT يبقى سالب
+
+234
+00:20:36,310 --> 00:20:44,750
+T زائد constant K2 بعد هيك بدي أجيب ال U3 as a 
+
+235
+00:20:44,750 --> 00:20:51,650
+function of T تكامل لل GT في رونسكن 3 of T على
+
+236
+00:20:51,650 --> 00:20:58,830
+رونسكن RT كله dT يبقى هذا الكلام بدي يساوي تكامل ل
+
+237
+00:20:58,830 --> 00:21:03,850
+سك التى فالرونس كنيه ثري اللي هو سالب صين التى
+
+238
+00:21:03,850 --> 00:21:12,530
+سالب صين التى على ال one dt أو ان شيتنا فقولنا 
+
+239
+00:21:12,530 --> 00:21:20,210
+ناقص صين التى على القصين اللي واحد على قصين التى
+
+240
+00:21:20,210 --> 00:21:25,550
+ديتى السؤال هو هل الباص تفاضل المطار؟ يبقى اليوم
+
+241
+00:21:25,550 --> 00:21:31,790
+قداشر لن absolute value للمقام يبقى لن absolute
+
+242
+00:21:31,790 --> 00:21:34,490
+value لكوسايد ايش رأيكم؟ مالعيش خاطر احط ال
+
+243
+00:21:34,490 --> 00:21:42,010
+absolute لنفع لإن تي ون موجودة في الربع الرابع 
+
+244
+00:21:42,010 --> 00:21:45,890
+والربع الأول في الربع الرابع الكوسايد موجب وفي
+
+245
+00:21:45,890 --> 00:21:49,770
+الربع الأول موجب على الشك تاني يبقى حطة الأبسلويت 
+
+246
+00:21:49,770 --> 00:21:57,990
+والنشلتة بتفرقش عنها يبقى لن كوصين ال T زائد K3
+
+247
+00:21:57,990 --> 00:22:09,890
+الآن بدي أقوله take خدلي K1 يساوي K2 يساوي K3 يساوي
+
+248
+00:22:09,890 --> 00:22:20,210
+Zero طبعا في تسأل ليش أخدتهم ب Zero مش هذا سؤال؟ حد
+
+249
+00:22:20,210 --> 00:22:26,390
+بتقدر تعطيني جواب يا بنات؟ ليش أخدت الكهات هدول
+
+250
+00:22:26,390 --> 00:22:27,610
+بأصفار؟
+
+251
+00:22:31,150 --> 00:22:35,990
+هي اذكركم و تعالوا بال undetermined coefficient و 
+
+252
+00:22:35,990 --> 00:22:40,150
+نرجع تاني لما كنا نكتب ال particular solution
+
+253
+00:22:40,150 --> 00:22:43,810
+بجينا نقول T to the power S في الحل اللي عندنا هنا
+
+254
+00:22:43,810 --> 00:22:49,370
+ال S هذه بتعتمد هل أي جزء في الحل يشبه أي جزء من 
+
+255
+00:22:49,370 --> 00:22:53,230
+ال homogeneous ولا لأ؟ مظبوط ولا لأ؟ طب أنا لو خلت
+
+256
+00:22:53,230 --> 00:22:57,350
+هذا ال key هات هدى كواحد و كتنين و كتر محطتهاش بقى
+
+257
+00:22:57,350 --> 00:23:04,610
+أصفار لما أجيب ال particular solution y1 ضرب u1 صح
+
+258
+00:23:04,610 --> 00:23:11,330
+ولا لأ؟ يبقى بصير هنا هذه مضروبة في y2 وهذه مضروبة 
+
+259
+00:23:11,330 --> 00:23:15,670
+في y2 بصير y2 مكرر مضروبة في كل أسطن يبقى فيه
+
+260
+00:23:15,670 --> 00:23:19,670
+تشابه بينه و بين الأصلي ولا لأ؟ إذا لما أحط بيزيرو 
+
+261
+00:23:19,670 --> 00:23:23,470
+بكون ماعنديش تشابه بالمرة متخلصة من الشغل هذه
+
+262
+00:23:24,000 --> 00:23:27,920
+بقولها كمان مرة اللي كانت مش متابعة معانا الصح سه
+
+263
+00:23:27,920 --> 00:23:34,300
+معانا كويس ليش حطيت الكهات هدول كله بأصفار مرة
+
+264
+00:23:34,300 --> 00:23:39,840
+واحدة لإن لو خليته زي ما هو بأي كونستان آخر غير
+
+265
+00:23:39,840 --> 00:23:45,260
+الصفر تمام لما بده أجيب ال particular solution ايش
+
+266
+00:23:45,260 --> 00:23:57,780
+بنقول C1 هنا حطيته ب 1 في 1 هنا C2 U2 سالب T زائد K2 
+
+267
+00:23:57,780 --> 00:24:04,060
+لما ضبها في ال cosine بيصير constant في cosine زائد 
+
+268
+00:24:04,060 --> 00:24:09,040
+اللي هو T أو سالب T في ال cosine constant في ال
+
+269
+00:24:09,040 --> 00:24:14,030
+cosine مش هي هذه يبقى التشابه قائم صحيح ولا لأ؟ 
+
+270
+00:24:14,030 --> 00:24:17,650
+يبقى لما حط الكهات بأصفار كل التشابه ده بيكون
+
+271
+00:24:17,650 --> 00:24:24,530
+اتخلص منه و يبقى مش السؤال ده بس كل سؤال بعدين مثل
+
+272
+00:24:24,530 --> 00:24:31,020
+حط الكهات هدول كلهم بأصفار يبقى بناء عليه هذا بده
+
+273
+00:24:31,020 --> 00:24:37,360
+يعطيك ان U1 as a function of T اللي حصلنا عليه
+
+274
+00:24:37,360 --> 00:24:44,120
+اللي هو LEN absolute value ل 6T زائد 10T
+
+275
+00:25:10,340 --> 00:25:13,940
+هذا هو حل الـ homogeneous ولا الـ non-homogeneous
+
+276
+00:25:15,730 --> 00:25:20,930
+الـ non homogeneous يبقى هذا اللي هو U واحد Y واحد
+
+277
+00:25:20,930 --> 00:25:28,330
+زائد U اتنين Y اتنين زائد U تلاتة Y تلاتة طيب ال U
+
+278
+00:25:28,330 --> 00:25:29,870
+واحد عندي هنا مجداش 
+
+279
+00:25:36,620 --> 00:25:41,880
+وين ال U واحد؟ يبقى ها يها بدها ضربها في جداش في 
+
+280
+00:25:41,880 --> 00:25:46,680
+واحد إذا بتنزل زي ما هي يبقى هادا لين absolute
+
+281
+00:25:46,680 --> 00:25:57,750
+value ل 6T زائد تاني T بعد ذلك U2Y2 وين Y2 هي Cos T
+
+282
+00:25:57,750 --> 00:26:07,110
+بدي أضرب في من؟ في سالب T يبقى سالب T Cos T بعد 
+
+283
+00:26:07,110 --> 00:26:13,690
+ذلك C3 بدي أضرب مكان هي U3 يبقى بدي أضرب Sin T في 
+
+284
+00:26:13,690 --> 00:26:20,390
+U3 يبقى زائد Sin T في Lin Cos T
+
+285
+00:26:23,360 --> 00:26:27,340
+جبت له ال particular solution ايش ضال عليك؟ قال 
+
+286
+00:26:27,340 --> 00:26:29,760
+لي هاتل ال general solution لل non homogeneous
+
+287
+00:26:29,760 --> 00:26:34,420
+differential equation بروح بقول له the general 
+
+288
+00:26:34,420 --> 00:26:37,480
+solution
+
+289
+00:26:37,480 --> 00:26:52,240
+of equation 1 is Y تساوي YC زائد capital Y of T
+
+290
+00:26:52,240 --> 00:27:00,280
+يساوي YC هي عندنا بنزله زي ما هو يبقى C1 زائد C2 
+
+291
+00:27:00,280 --> 00:27:08,260
+في cos T C3 في sin T capital Y of T هي كله عندي 
+
+292
+00:27:08,260 --> 00:27:17,600
+يبقى زائد لين absolute value لسك ال T زائد تاني ال
+
+293
+00:27:17,600 --> 00:27:27,420
+T زائد sign ال T في ال N لكوصين ال T ناقص T في
+
+294
+00:27:27,420 --> 00:27:34,220
+كوصين ال T يبقى هذا هو الحل المطلوب حد فيكم بتحب
+
+295
+00:27:34,220 --> 00:27:40,020
+تسأل أي سؤال هنا؟ اه طويل شوية لكن برضه فكرته
+
+296
+00:27:40,020 --> 00:27:40,840
+جميلة جدا
+
+297
+00:27:54,450 --> 00:28:05,070
+نعطي مثال اخته 
+
+298
+00:28:05,070 --> 00:28:08,850
+شباب 
+
+299
+00:28:08,850 --> 00:28:14,330
+تسأل السؤال التالي بتقول لو كان g of t مثلا cosine 
+
+300
+00:28:14,330 --> 00:28:18,530
+of t بنفع حل بال variation of parameter و بال
+
+301
+00:28:18,530 --> 00:28:22,150
+undetermined coefficients بشرط المعامل ثلاث ثوابت
+
+302
+00:28:22,150 --> 00:28:27,070
+اه و الله بنفع بالطريقتين لو حلتي بال variation of 
+
+303
+00:28:27,070 --> 00:28:30,250
+parameter و بال undetermined coefficients اتنين صح
+
+304
+00:28:30,250 --> 00:28:34,610
+ماعنديش مشكلة ليش؟ لأن هذا اتفق حسب الجدول اللي
+
+305
+00:28:34,610 --> 00:28:37,670
+موجود في حالة ال undetermined coefficients و اتفق
+
+306
+00:28:37,670 --> 00:28:39,890
+معانا في حالة ال variation of parameter ما عندنا 
+
+307
+00:28:39,890 --> 00:28:46,560
+مشكلة في هذه الحالة تمام؟ بني للمثال رقم اتنين مثال
+
+308
+00:28:46,560 --> 00:28:54,460
+رقم اتنين بقول ما يأتي بقول given that إذا اعطيت
+
+309
+00:28:54,460 --> 00:29:06,360
+أن ال X و X تربيع and واحد على X are solutions are
+
+310
+00:29:06,360 --> 00:29:10,660
+solutions of
+
+311
+00:29:19,110 --> 00:29:27,890
+Homogeneous Differential Equation Corresponding To 
+
+312
+00:29:40,560 --> 00:29:43,020
+المناظرة للمعادلة
+
+313
+00:30:14,040 --> 00:30:15,440
+Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''
+
+314
+00:30:19,760 --> 00:30:21,560
+a particular solution
+
+315
+00:31:04,720 --> 00:31:10,580
+سؤال مرة ثانية بقول لو كان هدول ثلاثة حلول لل
+
+316
+00:31:10,580 --> 00:31:14,440
+homogeneous differential equation المناظرة cross
+
+317
+00:31:14,440 --> 00:31:19,380
+bonding to المناظرة لمين؟ للمعادلة دي يعني كأن 
+
+318
+00:31:19,380 --> 00:31:24,420
+المعادلة دي بس بدي أسويها بقداش؟ بالصفر تمام يعني 
+
+319
+00:31:24,420 --> 00:31:29,560
+هذه المعادلة الأصلية وحل ال homogeneous معطيني إياها مش
+
+320
+00:31:29,560 --> 00:31:33,320
+لسه بدوروا أدور عليه لأ جاي الحلول X و X تربيعه
+
+321
+00:31:33,320 --> 00:31:38,040
+مين؟ واحد على X قال لي إذا كان الأمر كذلك determine
+
+322
+00:31:38,040 --> 00:31:43,740
+a particular solution بقوله اه احنا مشان نجيب ال
+
+323
+00:31:43,740 --> 00:31:48,580
+general solution بدي هدول التلاتة يكونوا linearly 
+
+324
+00:31:48,580 --> 00:31:53,440
+independent أو هدول بيكونوا ال fundamental set of
+
+325
+00:31:53,440 --> 00:31:57,000
+solutions مش حيال الله حلول ومشي واجري صحيح ولا 
+
+326
+00:31:57,000 --> 00:32:00,120
+لأ؟ لأن ال fundamental set of solutions هم اللي
+
+327
+00:32:00,120 --> 00:32:03,160
+بيجيبوا ال general solution لل homogeneous 
+
+328
+00:32:03,160 --> 00:32:08,200
+differential equation يبقى أول شغلة بيختبر هل هدول
+
+329
+00:32:08,200 --> 00:32:12,340
+linearly independent ولا لأ؟ أو هل هدول بيكونوا ال
+
+330
+00:32:12,340 --> 00:32:17,150
+fundamental set of solution أم لا؟ واضح كلامي؟ يبقى
+
+331
+00:32:17,150 --> 00:32:22,970
+بتروح أخد ايش المحدد تبع التلاتة هدول يبقى باجي 
+
+332
+00:32:22,970 --> 00:32:27,350
+بقوله وطبعا المحدد ده ده هيفيدني في الحل بعد ذلك
+
+333
+00:32:27,350 --> 00:32:31,370
+مش يعني بداود و بروح .. لأ بنستفيد منه، إذا بتروح
+
+334
+00:32:31,370 --> 00:32:36,550
+أخد الwareness gain of X مش of T لإن المثل المكتوب
+
+335
+00:32:36,550 --> 00:32:39,850
+عندي كله بدلالة main X اللي هو ال independent
+
+336
+00:32:39,850 --> 00:32:45,500
+variable يبقى باجي بقوله الحل الأول اللي هو X والحل 
+
+337
+00:32:45,500 --> 00:32:50,360
+الثاني X تربيع والثاني واحد على X تحب تخلي واحد
+
+338
+00:32:50,360 --> 00:32:56,620
+على X وأنا أكتب X أس سالب واحد X أس سالب واحد ما عندناش
+
+339
+00:32:56,620 --> 00:33:03,960
+مشكلة تمام بده نشتق يبقى واحد اتنين X سالب X أس 
+
+340
+00:33:03,960 --> 00:33:13,410
+سالب اتنين الصفة التالت ZERO اتنين اتنين X أس سالب
+
+341
+00:33:13,410 --> 00:33:18,850
+تلاتة وهي المحدد بدي أفكر محدد باستخدام عناصر 
+
+342
+00:33:18,850 --> 00:33:24,250
+العمود الأول لشانه فيه صفر أو عناصر الصف التالت
+
+343
+00:33:24,250 --> 00:33:28,790
+سيان هيك و الله هيك كله بيعطيني نفس النتيجة يبقى
+
+344
+00:33:28,790 --> 00:33:34,430
+هاد يا بنات X فيه بدي أشطب صفه و عموده بيصير 
+
+345
+00:33:34,430 --> 00:33:42,910
+جداش هنا أربع X أس ناقص اتنين يبقى هنا أربع X 
+
+346
+00:33:42,910 --> 00:33:49,230
+أس ناقص اتنين هذا الرئيسي ناقص مع ناقص بيصير زائد
+
+347
+00:33:49,230 --> 00:33:55,130
+اتنين X أس ناقص اتنين زائد اتنين X أس ناقص
+
+348
+00:33:55,130 --> 00:34:02,250
+اتنين يساوي لسه كمان الحد اللي بعده بإشارته سالب 
+
+349
+00:34:02,250 --> 00:34:08,960
+حسب قعدة الإشارات يبقى سالب واحد فيه بدي أجوب أشطب
+
+350
+00:34:08,960 --> 00:34:16,060
+صفه و عموده يبقى بصير هذا فهذا باتنين X أس سالب
+
+351
+00:34:16,060 --> 00:34:19,020
+واحد يبقى اتنين 
+
+352
+00:34:27,980 --> 00:34:34,460
+ناقص اتنين X أس ناقص واحد ناقص اتنين X أس 
+
+353
+00:34:34,460 --> 00:34:38,940
+ناقص واحد نقص اتنين X أس ناقص واحد نقص اتنين
+
+354
+00:34:38,940 --> 00:34:39,600
+اكس أس ناقص واحد نقص اتنين اكس أس ناقص واحد نقص
+
+355
+00:34:39,600 --> 00:34:45,740
+ناقص واحد نقص اتنين اكس أس ناقص واحد نقص اتنين
+
+356
+00:34:45,740 --> 00:34:49,580
+اكس أس ناقص واحد نقص اتنين اكس أس ناقص واحد نقص
+
+357
+00:34:49,580 --> 00:34:59,500
+اتنين زي 2x-1 يعني جداش 6 على x 6x-1 يعني 6 على x
+
+358
+00:34:59,500 --> 00:35:04,030
+هل هذا الكلب يساوي zero في يوم من الأيام؟ طبعا لأ
+
+359
+00:35:04,030 --> 00:35:09,510
+لأنه اشترط في المثل ان x greater than 0 يبقى هذا
+
+360
+00:35:09,510 --> 00:35:17,430
+لا يمكن أن يساوي 0 مدام لا يساوي 0 سا اللي هو ال x
+
+361
+00:35:17,430 --> 00:35:23,450
+و ال x تربيع and ال 1 على x are linearly
+
+362
+00:35:23,450 --> 00:35:30,010
+independent يعني يتكونوا لمين؟ ال general solution 
+
+363
+00:35:30,010 --> 00:35:36,590
+تبع من؟ تبع ال homogeneous يعني هنا صار عندنا YC 
+
+364
+00:35:36,590 --> 00:35:46,800
+بدي يساوي C1 X C2 X تربيع C3 X أس ناقص واحديبقى
+
+365
+00:35:46,800 --> 00:35:51,440
+هذا حل مين؟ حل ال homogenous differential equation 
+
+366
+00:35:51,440 --> 00:35:56,320
+بدنا نيجي ل ال non homogenous ال runnerskin موجود
+
+367
+00:35:56,320 --> 00:35:59,080
+يبدأ يجيب ال runnerskin one و ال runnerskin two و
+
+368
+00:35:59,080 --> 00:36:03,860
+ال runnerskin three بس بدأ يطلع اه استرنا شوية طلع
+
+369
+00:36:03,860 --> 00:36:08,430
+في المعامل هنا قداش؟ X تكعيب ممنوع يظل هذا 
+
+370
+00:36:08,430 --> 00:36:13,030
+X تكعيب إذا بروح أجسم طرفين المعادلة كله عالميا 
+
+371
+00:36:13,030 --> 00:36:19,450
+على X تكعيب فباجي بقوله هنا the differential 
+
+372
+00:36:19,450 --> 00:36:28,910
+equation one is written as بروح أكتبه على الشكل 
+
+373
+00:36:28,910 --> 00:36:34,190
+الجديد يبقى y triple prime زي ما هو بتخلي المعاملة
+
+374
+00:36:34,190 --> 00:36:39,970
+تبعها واحد صحيحة زائد واحد على x في ال y double
+
+375
+00:36:39,970 --> 00:36:48,710
+prime اللي بعدها ناقص اتنين على x تربيع في ال y 
+
+376
+00:36:48,710 --> 00:36:55,130
+prime جسمناها على x تكعيب زائد اتنين على x تكعيب
+
+377
+00:36:55,130 --> 00:37:02,770
+كله في ال y يساوي كده يا بنات؟ يساوي من X يبقى هذه
+
+378
+00:37:02,770 --> 00:37:06,970
+المعادلة اللي صارت هنا يبقى صارت هذه يا بنات هي
+
+379
+00:37:06,970 --> 00:37:13,630
+هذه G of T مش اللي عندنا هذه G of T لأن المعامل 
+
+380
+00:37:13,630 --> 00:37:18,150
+هنا ماهوش واحد صحيح يبقى بيصير بالشكل اللي عندنا 
+
+381
+00:37:19,130 --> 00:37:25,030
+بقدر أجيب من الرونس كين وان as a function of T
+
+382
+00:37:25,030 --> 00:37:32,930
+تكامل لل G of T ل .. لأ بدنا نجيب الرونس كين وان
+
+383
+00:37
+
+431
+00:42:19,700 --> 00:42:24,440
+يبقى بدي أروح أجيب له الـ main اللي هو U1 as a
+
+432
+00:42:24,440 --> 00:42:33,480
+function of X يا بنات مش of T كله X كله X كله X
+
+433
+00:42:33,480 --> 00:42:39,180
+ما عنديش الـ T المثلة كلها بدلالة من؟ صح هي كلها بدلالة
+
+434
+00:42:39,180 --> 00:42:44,600
+من؟ بدلالة الـ X يبقى U1 as a function of X تكامل
+
+435
+00:42:44,600 --> 00:42:52,760
+الـ G of X في الـ Wronskian 1 of X على الـ Wronskian of
+
+436
+00:42:52,760 --> 00:42:59,480
+X كله as a function of X يساوي تكامل الـ G of X
+
+437
+00:42:59,480 --> 00:43:05,500
+اللي بيجي ده صار إن 2X مش 4X تربيع يبقى
+
+438
+00:43:05,500 --> 00:43:09,420
+هنا 2X هي نزلناها زي ما هي
+
+439
+00:43:13,370 --> 00:43:20,370
+سالب 3 يبقى سالب 3 على الـ Wronskian حسبناه
+
+440
+00:43:20,370 --> 00:43:28,390
+قبل شوية فكان جداش 6 على X يبقى هذا 6 على 
+
+441
+00:43:28,390 --> 00:43:35,420
+X كله في DX أما الـ 6 مع 6 مع السلامة و الـ X بتطلع
+
+442
+00:43:35,420 --> 00:43:46,620
+فوق بيبقى سالب تكامل X تربيع DX 2 في 3 ب 6 مع 6
+
+443
+00:43:46,620 --> 00:43:51,960
+الـ X تطلع فوق بيصير X تربيع و السالب برا يبقى هنا
+
+444
+00:43:51,960 --> 00:44:01,900
+سالب X تكعيب على 3 زائد K1 بعد ذلك بنروح نجيب الـ U2
+
+445
+00:44:01,900 --> 00:44:09,760
+integration للـ G of T لمين؟ للـ Wronskian 2 of T على 
+
+446
+00:44:09,760 --> 00:44:16,860
+الـ Wronskian of T كله في DT يساوي تكامل للـ 2X في
+
+447
+00:44:16,860 --> 00:44:24,410
+Wronskian 2 Wronskian 2 لم يبقى داش ب 2 على X يبقى هذا
+
+448
+00:44:24,410 --> 00:44:33,990
+2 على X كله على 6 على X DX يساوي أظن
+
+449
+00:44:33,990 --> 00:44:38,390
+إن الـ X هذه مع الـ X هذه مع السلامة بيطيروا و بيظل
+
+450
+00:44:38,390 --> 00:44:44,350
+عندي 2 في 2 ب 4 يعني 4 على 6 يبقى
+
+451
+00:44:44,350 --> 00:44:52,270
+4 على 6 تكامل للـ X DX هذه يا بنات بتروح مع هذه
+
+452
+00:44:52,270 --> 00:44:56,090
+مضروب 2 في 2 اللي هو ب 4 6 خليك برا
+
+453
+00:44:56,090 --> 00:44:59,330
+مضروب 1 على X بتنقل بالـ X فوت بيصير بالشكل اللي
+
+454
+00:44:59,330 --> 00:45:05,550
+عندنا هذا يبقى هذه كأنها 2/3 في X تربيع على
+
+455
+00:45:05,550 --> 00:45:15,930
+2 زائد constant K2 يعني 1/3 X تربيع زائد K2
+
+456
+00:45:18,070 --> 00:45:25,090
+بالمثل بنروح نجيب U3 يبقى هي تكامل طبعا كله Xاتي
+
+457
+00:45:25,090 --> 00:45:33,150
+يا بنات مش T كله بدلالة الـ X هذا كله بدلالة الـ X احنا
+
+458
+00:45:33,150 --> 00:45:37,950
+معالجة معانا هذه الـ T لأ هذه مظبوط كتبنا صح ده بس
+
+459
+00:45:37,950 --> 00:45:44,330
+هذه و كله بدلالة X مظبوط طيب يبقى هذه الـ g of x في 
+
+460
+00:45:44,330 --> 00:45:48,990
+الـ Wronskian 3 of x على الـ Wronskian as a function
+
+461
+00:45:48,990 --> 00:45:55,750
+of x dx يبقى تكامل للـ 2X فيه الـ Wronskian 3
+
+462
+00:45:55,750 --> 00:46:02,930
+of x كله بيبقى داش ب X تربيع يبقى ب X تربيع لمين؟
+
+463
+00:46:02,930 --> 00:46:11,600
+لـ 6 على X كله بالنسبة إلى DX 2 على 6 جداش
+
+464
+00:46:11,600 --> 00:46:19,540
+بطول تكامل هذه تطلع فوق بيصير جداش أبناء X أص 4
+
+465
+00:46:19,540 --> 00:46:24,880
+X تكعيب و تجيب و تكمل تصير X أص 4 DX يبقى هذه
+
+466
+00:46:24,880 --> 00:46:33,600
+1/3 و هذه X أص 5 على 5 زائد constant K3 يعني
+
+467
+00:46:33,600 --> 00:46:42,850
+1/15 X أص 5 زائد constant K3 الآن نقول
+
+468
+00:46:42,850 --> 00:46:51,910
+له take خذ لي K1 يساوي K2 يساوي K3 يساوي Zero وعرفته
+
+469
+00:46:51,910 --> 00:46:59,530
+ليش مظبوط يبقى بدي أروح أجيب له Capital Y of T اللي
+
+470
+00:46:59,530 --> 00:47:11,490
+هو U1 و Y1 زائد U2 و Y2 زائد U3 و Y3 و Y7 الآن نجي إلى 
+
+471
+00:47:11,490 --> 00:47:17,590
+الـ U1 الـ U1 مااني قاعد أبدأ عشان ناقص 1/3 X تكعيب
+
+472
+00:47:17,590 --> 00:47:26,750
+يبقى ناقص 1/3 X تكعيب فمين؟ في Y1 اللي هو X اللي
+
+473
+00:47:26,750 --> 00:47:35,870
+بعده بنجي لـ U2 الـ U2 لـ 1/3 X تربيع زائد 1/3 X
+
+474
+00:47:35,870 --> 00:47:44,010
+تربيع في من؟ في X تربيع بنجي لـ بعده U3 يبقى زائد
+
+475
+00:47:44,010 --> 00:47:51,250
+1/15 X أس 5 في X أس -1 ايش
+
+476
+00:47:51,250 --> 00:47:57,120
+رأيك؟ هذه هي هذه بيشارة مخالفة صح؟ يبقى يجرّوا
+
+477
+00:47:57,120 --> 00:48:01,640
+الـ فاتحة أنا روحهم على السلامة بضل إن أقدرش 1
+
+478
+00:48:01,640 --> 00:48:07,380
+على 15 X أس 4 هذا الـ particular solution
+
+479
+00:48:07,380 --> 00:48:11,480
+للـ differential equation 1 إذا بقدر أجيب له من
+
+480
+00:48:11,480 --> 00:48:17,680
+الـ general solution فبروح بقول له هنا the general
+
+481
+00:48:17,680 --> 00:48:31,160
+solution of the equation 1 is Y تساوي YC زائد 
+
+482
+00:48:31,160 --> 00:48:42,360
+Capital Y of T YC هي فوق تمام اللي هو C كيف؟
+
+483
+00:48:42,360 --> 00:48:47,280
+بس طالب الـ particular خلاص والله نايحنا يبقى خلاص
+
+484
+00:48:47,280 --> 00:48:51,680
+بروحي هذا والله يعطيك العافية خلاص هذا مسامحي نفيد
+
+485
+00:48:54,290 --> 00:48:56,990
+خلاص من النياط دي على جد المقبض زي ما دي بناكوس
+
+486
+00:48:56,990 --> 00:49:00,190
+في الامتحان don't evaluate اللي كنت أصلاً تبقى حاطة
+
+487
+00:49:00,190 --> 00:49:02,590
+تاريخ بين جوسينة بخاط غامج و اللي جات بعض الناس
+
+488
+00:49:02,590 --> 00:49:06,230
+لسه بتروح تحسب لي في الـ constant أصلاً بتضيع وقت هالبلاش
+
+489
+00:49:06,230 --> 00:49:11,950
+طب أنا مش طالب و تشتغلي ليش طيب
+
+490
+00:49:24,680 --> 00:49:29,480
+في عندكوا في الكتاب مجموعة من المسائل و كتب لك جي
+
+491
+00:49:29,480 --> 00:49:33,360
+و F T بدلالة جي و F T مخلية مش معطيكي قيمة إلها
+
+492
+00:49:33,360 --> 00:49:37,980
+و قال لك حلي بتقدر تكملها هذه؟ مش هتقدر تكملها،
+
+493
+00:49:37,980 --> 00:49:42,980
+بدنا نعطيكوا مثال منهم و نوريكوا كيف بنحل هذا النوع
+
+494
+00:49:42,980 --> 00:49:47,860
+من الأسئلة حد لاقي تساؤل هنا قبل ما نتقل إلى
+
+495
+00:49:47,860 --> 00:49:52,920
+المثال الثالث؟ حد فيكوا لاقي تساؤل هنا؟
+
+496
+00:50:12,000 --> 00:50:22,160
+مثال رقم 3 رقم 3 رقم 3 رقم 3
+
+497
+00:50:22,160 --> 00:50:28,840
+رقم 3 رقم 3 رقم 3 رقم 3 رقم
+
+498
+00:50:28,840 --> 00:50:30,680
+3 رقم 3 رقم 3 رقم 3 رقم 3 رقم
+
+499
+00:50:30,680 --> 00:50:30,720
+3 رقم 3 رقم 3 رقم 3 رقم 3 رقم
+
+500
+00:50:30,720 --> 00:50:37,940
+3 رقم 3 رقم 3
+
+501
+00:50:37,940 --> 00:50:39,280
+رقم ت
+
+502
+00:50:48,610 --> 00:51:00,190
+محتملة على التكاملات of a particular solution
+
+503
+00:51:00,190 --> 00:51:07,650
+of a particular solution of the
+
+504
+00:51:14,160 --> 00:51:21,380
+مشتقة ثالثة لـ Y ناقص المشتقة الثانية لـ Y زائد
+
+505
+00:51:21,380 --> 00:51:28,500
+المشتقة الأولى لـ Y ناقص Y بدون مشتقة يساوي G of T
+
+506
+00:51:28,500 --> 00:51:31,580
+و هذا المعادلة رقم واحد
+
+507
+00:51:54,450 --> 00:52:00,530
+Find a formula هات لي صيغة محتملة على التكاملات تبع
+
+508
+00:52:00,530 --> 00:52:03,310
+الـ particular solution للـ differential equation
+
+509
+00:52:03,310 --> 00:52:06,710
+اللي عندنا يعني فعلاً ما أعطاني معادلة تفاضلية و بذا
+
+510
+00:52:06,710 --> 00:52:11,570
+شكل لكن الطرف اليمين كاتب و كدالة أنا مش عارفة g
+
+511
+00:52:11,570 --> 00:52:15,030
+of t مين ما تكون تكون مش بعطيني زي السؤال بيجاب له
+
+512
+00:52:15,030 --> 00:52:18,950
+ده اللي بقعد نضربه و نختصره و نكامله إذا هذا هضل
+
+513
+00:52:18,950 --> 00:52:23,570
+بدلالة مين بدلالة التكامل التكتيك اللي اتبع في
+
+514
+00:52:23,570 --> 00:52:26,670
+المثالين اللي قبل له هو نفس التكتيك هذا اللهم إلا
+
+515
+00:52:26,670 --> 00:52:31,050
+بقدرش أكامل فبضل التكامل موجود و انفي المسألة كما
+
+516
+00:52:31,050 --> 00:52:35,830
+هو إذا أنا بدي أبدأ في حل الـ homogeneous ثم الـ non
+
+517
+00:52:35,830 --> 00:52:44,950
+homogeneous يبقى باجي بقول له solution let
+
+518
+00:52:44,950 --> 00:52:58,880
+y تساوي e أس RTBA solution of the Equation للمعادلة
+
+519
+00:52:58,880 --> 00:53:04,580
+Y triple prime ناقص Y double prime زائد Y prime
+
+520
+00:53:04,580 --> 00:53:11,000
+ناقص Y يساوي 0 هو الـ homogeneous يبقى then the
+
+521
+00:53:11,000 --> 00:53:21,020
+characteristic equation is R تكعيب ناقص R تربيع
+
+522
+00:53:21,020 --> 00:53:27,790
+زائد R ناقص 1 يساوي 0 الغلطة اللي كنت أشوفها من
+
+523
+00:53:27,790 --> 00:53:33,290
+بعضكوا في الامتحان و تكتب لي هذه R اه و هذه غلطة
+
+524
+00:53:33,290 --> 00:53:37,210
+فاحشة كبيرة جداً من الكبائر بالنسبة لنا في الامتحان
+
+525
+00:53:37,210 --> 00:53:42,660
+طيب نيجي نحل المعادلة اللي عندنا هذه طلع لي في هدول
+
+526
+00:53:42,660 --> 00:53:47,640
+2 ممكن آخذ منهم R تربيع عامل مشترك إذا لو
+
+527
+00:53:47,640 --> 00:53:52,000
+اخدت R تربيع عامل مشترك بيظل كده؟ R ناقص 1
+
+528
+00:53:52,000 --> 00:53:58,200
+و عندي ضايل هناك R ناقص 1 يساوي Zero إذا أنا ممكن
+
+529
+00:53:58,200 --> 00:54:04,940
+آخذ من الطرفين R ناقص 1 عامل مشترك بيضل من الجزء
+
+530
+00:54:04,940 --> 00:54:10,860
+الأول قداش R تربيع بيضل من الجزء الثاني قداش 1
+
+531
+00:54:10,860 --> 00:54:16,400
+صحيح يبقى زائد 1 يساوي zero من هذه المعادلة
+
+532
+00:54:16,400 --> 00:54:23,160
+بقدر أقول إن R1 يساوي 1 و R2 و R3 يبدو يساوي
+
+533
+00:54:23,160 --> 00:54:29,360
+الـ زائد أو ناقص إذا أصبح حل الـ homogeneous هو YC
+
+534
+00:54:29,360 --> 00:54:38,040
+يساوي C1 e أس 1 في T يبقى e أس T هدول Complex يبقى
+
+535
+00:54:38,040 --> 00:54:45,500
+زائد C2 Cos T زائد C3 في Sin T
+
+536
+00:54:50,080 --> 00:54:55,140
+يبقى هذا حل مين اللي هو اللي هو مجازف طبعاً هو جالي
+
+537
+00:54:55,140 --> 00:54:58,480
+formula محتوية على الـ integral للـ particular
+
+538
+00:54:58,480 --> 00:55:02,700
+solution بده شكل الـ particular solution كويس الـ
+
+539
+00:55:02,700 --> 00:55:07,700
+particular solution يبقى بده اشيل C1 و C2 و C3 و أحط
+
+540
+00:55:07,700 --> 00:55:14,000
+بدلهم مين U1 و U2 و U3 بس قبل بدك تحسب الـ Wronskian
+
+541
+00:55:14,000 --> 00:55:20,770
+للحلول الثلاثة هذه و بعد هيك الله بيفرجها يبقى بناء
+
+542
+00:55:20,770 --> 00:55:26,070
+عليها لو جبت اخدت الـ Wronskian as a function of T
+
+543
+00:55:26,070 --> 00:55:32,930
+يبقى باجي بقول له هذا الحل الأول E أس T و الحل
+
+544
+00:55:32,930 --> 00:55:39,280
+الثاني Cosine T و الحل الثالث Sin T بدي اشتق
+
+545
+00:55:39,280 --> 00:55:44,000
+المشتقة الأولى الـ exponential كما هي هذه ناقص Sin
+
+546
+00:55:44,000 --> 00:55:50,020
+T هذه Cosine T بدي اشتق كمان مرة يبقى الـ
+
+547
+00:55:50,020 --> 00:55:56,120
+exponential كما هي و هذه ناقص Cosine T و هذه ناقص
+
+548
+00:55:56,120 --> 00:56:03,260
+Sin T و هي المحدد بدي أحسب قداش قيمة هذا المحدد
+
+549
+00:56:03,260 --> 00:56:04,960
+و يساوي
+
+550
+00:56:07,510 --> 00:56:12,410
+ممكن بلغة المحادثة بالخاص آخذ E أس T عامل مشترك من
+
+551
+00:56:12,410 --> 00:56:16,890
+العمود الأول بيصبح 1 1 1 هو هأكتب المحادثة
+
+552
+00:56:16,890 --> 00:56:21,530
+يعني قصة طويلة و شيء لكن أنا بدي أفك دغري باستخدام
+
+553
+00:56:21,530 --> 00:56:25,670
+العمود الأول باستخدام الصف الأول بأي حاجة ماشية
+
+554
+00:56:25,670 --> 00:56:31,690
+على خليني أفك باستخدام العمود الأول يبقى هذا بدي
+
+555
+00:56:31,690 --> 00:56:38,920
+يساوي E أس T فيه يبقى بتروح أشتق بصفه و عموده يبقى يا
+
+556
+00:56:38,920 --> 00:56:44,680
+يا بنات كده؟ Sin تربيع زائد Cosine تربيع يبقى هذه
+
+557
+00:56:44,680 --> 00:56:51,960
+الـ Sin تربيع T زائد Cosine تربيع T انتهينا منها
+
+558
+00:56:51,960 --> 00:56:57,300
+يهودة هذه حسب قاعدة الإشارات وجب الله سالب كده؟
+
+559
+00:56:57,810 --> 00:57:06,030
+يبقى هاي ناقص E of T فيه بتروح اشتق بصفه و عموده
+
+560
+00:57:06,030 --> 00:57:16,890
+بيصير سالب Sin Cos و موجب Sin Cos يبقى سالب Sin T
+
+561
+00:57:16,890 --> 00:57:27,730
+Cos T زائد Sin T Cos T خلصنا منها و ضل الـ Term
+
+562
+00:57:27,730 --> 00:57:34,310
+الثالث حسب قاعدة الإشارات E أس T فين يبقى بنشتق
+
+563
+00:57:34,310 --> 00:57:40,450
+بصفه و عموده بيصير Cosine تربيع زائد Sine تربيع
+
+564
+00:57:40,450 --> 00:57:48,990
+يبقى Cosine تربيع T زائد Sine تربيع T و يسافر أظن
+
+565
+00:57:48,990 --> 00:57:53,160
+إن هذه راحت في الـ Zero يا بنات طيب بيضل هذه قداش
+
+566
+00:57:53,160 --> 00:58:00,240
+1 لـ E أس T و هنا 1 في E أس T يبقى الجواب كله
+
+567
+00:58:00,240 --> 00:58:07,560
+2 E أس T واضح ما له لا يساوي Zero إذا الحلول اللي
+
+568
+00:58:07,560 --> 00:58:11,720
+جبناها دول منهم بيكونوا لي الـ fundamental set of
+
+569
+00:58:11,720 --> 00:58:18,960
+solutions أو linearly independent يبقى هنا الـ E
+
+570
+00:58:18,960 --> 00:58:22,420
+أس T E أس T E أس T E أس T E أس T E أس T E
+
+571
+00:58:22,420 --> 00:58:23,440
+أس T E أس T E أس T E أس T E أس T E أس T
+
+572
+00:58:23,440 --> 00:58:27,400
+أس T E أس T E أس T E أس T E أس T E أس T
+
+573
+00:58:27,400 --> 00:58:28,500
+أس T E أس T E أس T E أس T E أس T E أس T
+
+574
+00:58:28,500 --> 00:58:28,700
+أس T E أس T E أس T E أس T E أس T E أس T
+
+575
+00:58:28,700 --> 00:58:31,850
+أس T E أس T E أس T E أس T E أس T ما دام
+
+576
+00:58:31,850 --> 00:58:36,850
+linearly independent هذا بدي يعطينا إنه حل الـ
+
+577
+00:58:36,850 --> 00:58:41,370
+homogeneous هو ما احنا كتبناه صحيح فوق خلاص و هذا
+
+578
+00:58:41,370 --> 00:58:44,890
+مش لازمني بس كويس إن تأكدنا إنهم linearly
+
+579
+00:58:44,890 --> 00:58:49,520
+independent و جبنا ايه؟ اللي هو الـ Wronskian بتجيب الـ
+
+580
+00:58:49,520 --> 00:58:54,040
+Wronskian 1 و Wronskian 2 و Wronskian 3 يبقى بتجيب الـ
+
+581
+00:58:54,040 --> 00:58:59,040
+Wronskian 1 as a function of t بس قبلها بتروح تتأكد
+
+582
+00:58:59,040 --> 00:59:04,420
+المعامل هنا قداش يبقى احنا جاهزين يبقى هذا الكلام
+
+583
+00:59:04,420 --> 00:59:10,060
+ها بدنا نجيب الـ Wronskian 1 الـ Wronskian 1 هو المحدد
+
+584
+00:59:10,060 --> 00:59:13,600
+اللي هو 001
+
+585
+00:59:31,110 --> 00:59:37,330
+يبقى العمودين 2 زي مهمة بدنا نفك هذه المحددات
+
+586
+00:59:37,330 --> 00:59:44,670
+باستخدام العمود الأول يبقى 1 فيه أشتق بصفه عموده
+
+587
+00:59:44,670 --> 00:59:50,990
+يبقى Sin تربيع زائد Cos تربيع يبقى Sin تربيع T
+
+588
+00:59:50,990 --> 00:59:56,880
+زائد Cos تربيع T كله يساوي قداش الـ 1 بدنا نيجي لـ
+
+589
+00:59:56,880 --> 01:00:03,060
+Wronskian 2 as a function of T يبقى على العمود الأول
+
+590
+01:00:03,060 --> 01:00:11,840
+E أس T E أس T E أس T العمود الثاني 001 العمود الثالث هو
+
+591
+01:00:11,840 --> 01:00:21,860
+Sin T و Cos T و - Sin T بالشكل اللي عندنا بتفكر المحدد
+
+592
+01:00:21,860 --> 01:00:27,240
+باستخدام عناصر العمود الثانية حسب قاعدة الإشارات
+
+593
+01:00:28,040 --> 01:00:35,100
+سلبية يبقى هذا الكلام سالب 1 فيه أشتق بصفه عموده
+
+594
+01:00:35,100 --> 01:00:41,260
+بيصير E of T Cosine ناقص E of T Sin يبقى E of T
+
+595
+01:00:41,260 --> 01:00:50,440
+Cosine T ناقص E of T في Sin T يعني هذه كأنها Sin T
+
+596
+01:00:50,440 --> 01:00:57,950
+ناقص Cosine T كله في الـ exponential E of T بالمرة
+
+597
+01:00:57
+
+646
+01:06:36,610 --> 01:06:45,210
+من T node لغاية T لمين لـ sign الـ S ناقص cosine الـ
+
+647
+01:06:45,210 --> 01:06:49,910
+S كله في GS في DS
+
+648
+01:06:58,000 --> 01:07:03,200
+إحنا بدنا بس إيش الـ particle of solution الصيغة
+
+649
+01:07:03,200 --> 01:07:15,320
+تبعت الـمجتمل على التكامل طيب
+
+650
+01:07:15,320 --> 01:07:24,330
+بدنا نيجي لـ U3 of T U3 of T يساوي تكامل من T node
+
+651
+01:07:24,330 --> 01:07:32,030
+لغاية T للـ G of S في الـ Wronskian 3 as a function of 
+
+652
+01:07:32,030 --> 01:07:40,210
+S على الـ Wronskian as a function of SDS ويساوي تكامل من
+
+653
+01:07:40,210 --> 01:07:45,710
+T نوت لـ T للـ G of S نحن نذهب إلى الـ Roneskini 3
+
+654
+01:07:45,710 --> 01:07:52,170
+الـ Roneskini 3 هو السالب عندنا يبقى نكتبه بالسالب
+
+655
+01:07:55,340 --> 01:08:08,880
+و cos sin T سالب sin T سالب cos T كله طبعًا S sin S
+
+656
+01:08:08,880 --> 01:08:19,800
+و cos S و E Os S كله على الإتنين E Os S في الـ DS
+
+657
+01:08:21,060 --> 01:08:29,140
+كله في الـ DS تمام طيب نص برا والـ EOS S مع الـ EOS S
+
+658
+01:08:29,140 --> 01:08:36,800
+مع السلامة يبقى بيصير إن الـ main يساوي نص تكامل من
+
+659
+01:08:36,800 --> 01:08:46,080
+T node إلى T لـ ناقص sign الـ S ناقص cosine الـ S كل
+
+660
+01:08:46,080 --> 01:08:49,620
+هذا في من؟ هذا W1
+
+661
+01:08:53,420 --> 01:09:04,420
+يبقى هذا كله في main في g of s كله في ds طيب ويبدو
+
+662
+01:09:04,420 --> 01:09:08,700
+الـ particular solution يبقى الـ particular solution
+
+663
+01:09:08,700 --> 01:09:21,280
+capital Y of T يبقى U1Y1 زي U2Y2 زي U3Y3 يبقى
+
+664
+01:09:21,280 --> 01:09:28,220
+capital Y of T بده يساوي الـ Y1 اللي هي كده إيش؟ E
+
+665
+01:09:28,220 --> 01:09:36,120
+of T يبقى هذه الـ E of T والـ Y1 اللي هي وسطها طب
+
+666
+01:09:36,120 --> 01:09:43,240
+الـ U1 الـ U1 اللي هي النص في التكامل يبقى هذا النص
+
+667
+01:09:43,240 --> 01:09:49,720
+برا يا بنات وهي تكامل من T node إلى T وجوا قداش فيه
+
+668
+01:09:49,720 --> 01:09:58,560
+أنا E أس ناقص S GS يبقى E أس ناقص S G of S في DS
+
+669
+01:09:59,780 --> 01:10:06,140
+بنيجي للي بعده زائد اللي هو cosine الـ T زائد
+
+670
+01:10:06,140 --> 01:10:13,660
+cosine الـ T الـ U2 اللي هو برضه نص يبقى يا نص خليك
+
+671
+01:10:13,660 --> 01:10:21,550
+برا هذا النص وهي تكامل لشانه مقدار ثابت من T ناد
+
+672
+01:10:21,550 --> 01:10:29,650
+إلى T لمين لـ sin الـ S ناقص كوسين الـ S لـ sin الـ S
+
+673
+01:10:29,650 --> 01:10:37,270
+ناقص كوسين الـ S كله أظن في E و S ولا فيش H في G 
+
+674
+01:10:37,270 --> 01:10:45,770
+of S في G of S كله في DS نيجي لـ U تلاتة U تلاتة
+
+675
+01:10:45,770 --> 01:10:53,260
+عندك sin الـ T يبقى Z هي sin الـ T و U تلاتة أيها
+
+676
+01:10:53,260 --> 01:11:00,840
+عندي هي النص برا وهي تكامل من T node إلى T لـ ناقص
+
+677
+01:11:00,840 --> 01:11:09,880
+sin الـ S ناقص cosine الـ S كله في قداش في G of S
+
+678
+01:11:09,880 --> 01:11:17,360
+في DS تمام؟
+
+679
+01:11:18,740 --> 01:11:24,800
+طيب إيش رايكوا أنا شايف فيه نص برا ونص ونص ناخد
+
+680
+01:11:24,800 --> 01:11:31,540
+وبرا من الكل تمام يبقى هذا نص برا الآن يا بناتي
+
+681
+01:11:31,540 --> 01:11:37,620
+الجو المتغير هو مين S واللي برا مين T يبقى كأنه
+
+682
+01:11:37,620 --> 01:11:42,020
+مقدار ثابت بالنسبة له صحيح ولا لا؟ ما لوش داعي في
+
+683
+01:11:42,020 --> 01:11:46,600
+دي S يبقى خليته برا التكامل والله جوا التكامل سَيّان
+
+684
+01:11:46,780 --> 01:11:51,000
+إذا بدي أكتبه جوا التكامل بيضغط أضربه بيصير جوا E
+
+685
+01:11:51,000 --> 01:11:56,200
+أس T في E أس ناقص S يعني E أس T ناقص الـ S لإنه
+
+686
+01:11:56,200 --> 01:12:01,860
+عندها الضرب تجمع الأسس يبقى بيصير إن هذا هي تكامل
+
+687
+01:12:01,860 --> 01:12:11,390
+من T نوت لغاية T للـ E أس T ناقص الـ S في الـ G of S
+
+688
+01:12:11,390 --> 01:12:17,790
+في الـ DS خلصنا الـ term الأول يبقى هنا هذا جوز كبير
+
+689
+01:12:17,790 --> 01:12:24,180
+جاب له وبعده نص مشانه نص نص نص أخذته من الكلونج 
+
+690
+01:12:24,180 --> 01:12:30,700
+للتكامل هذا يبقى زائد تكامل من T node إلى T هذه
+
+691
+01:12:30,700 --> 01:12:34,240
+بنفس الطريقة الـ cosine T تعتبر مقدار ثابت بقدر
+
+692
+01:12:34,240 --> 01:12:45,780
+أدخلها جوا بيصير عندي cos T في sin S ناقص cos T في
+
+693
+01:12:45,780 --> 01:12:56,190
+cos S كل هذا الكلام في G of S في D S تمام اللي بعده
+
+694
+01:12:56,190 --> 01:13:02,350
+بنفس الطريقة زائد نص خدناها برا يبقى تكامل من T
+
+695
+01:13:02,350 --> 01:13:09,230
+node إلى T بدي أدخل جوا دي بيصير ناقص sine T في
+
+696
+01:13:09,230 --> 01:13:19,230
+sine الـ S ناقص sine T في cosine الـ S وكل هذا في G
+
+697
+01:13:19,230 --> 01:13:21,710
+of S في الـ DS
+
+698
+01:13:30,130 --> 01:13:37,990
+خطوة الأخيرة في عويل مشتركة بدي أخدهم يبقى بيصير Y
+
+699
+01:13:37,990 --> 01:13:50,190
+of T يساوي نص تكامل تكامل تكامل تكامل تكامل تكامل
+
+700
+01:13:50,190 --> 01:13:53,270
+تكامل
+
+701
+01:13:53,270 --> 01:14:01,140
+تكامل بتطلعي لي جيوب اس دي اس جيوب اس دي اس جيوب اس
+
+702
+01:14:01,140 --> 01:14:05,700
+دي اس يبقى بدأ أخدها من الكل كمان عامل مشترك إيش
+
+703
+01:14:05,700 --> 01:14:13,800
+بيظل عندي هنا بس E أس T ناقص الـ S تمام؟ وهي فتحت
+
+704
+01:14:13,800 --> 01:14:17,880
+Guess مشان في الآخرة ضروبة كلها في جيوب اس هذي إيش
+
+705
+01:14:17,880 --> 01:14:29,490
+بيصير؟ بيصير الزائد cosine T في sine الـ S نقص cos T
+
+706
+01:14:29,490 --> 01:14:40,330
+في sin S نقص sin T
+
+707
+01:14:40,330 --> 01:14:48,450
+في cos S وهيجفلنا الجوز كله وهذا G of S وهذا DS
+
+708
+01:15:01,400 --> 01:15:09,800
+الخطوة الأخيرة يساوي نص تكامل من T node إلى T للـ E
+
+709
+01:15:09,800 --> 01:15:11,720
+أس T ناقص الـ S
+
+710
+01:15:15,240 --> 01:15:23,540
+هذه sin cos وهذه sin cos لو أخذت منهم ناقص عامل
+
+711
+01:15:23,540 --> 01:15:29,080
+مشترك إيش بيصير عندنا؟ هذه ناقص بيصير عندنا هذه
+
+712
+01:15:29,080 --> 01:15:36,400
+بالموجب وهذه بالسالم بيصير عندنا sin T cos S زائد
+
+713
+01:15:36,400 --> 01:15:47,120
+cos T في sin S أليست هذه هي sin t ناقص الـ S؟ هذه
+
+714
+01:15:47,120 --> 01:15:54,360
+اللي بدي أفكها sin t cos S ناقص cos T في sin S
+
+715
+01:15:54,360 --> 01:15:58,580
+هيها ولا لا؟ يبقى تخلص من التنتين اللي تحتهم خط
+
+716
+01:15:58,580 --> 01:16:05,590
+تالي هدول اللي تحتهم خط معوج يبقى بدي أخد كمان
+
+717
+01:16:05,590 --> 01:16:12,010
+ناقص عامل مشترك بيخلي التنتين بالزائد بيصير كساء
+
+718
+01:16:12,010 --> 01:16:18,950
+وين هما استنى شوية بالراديو الخطأ مردود هي cosine t
+
+719
+01:16:18,950 --> 01:16:23,830
+في sin s ناقص cosine اه هذه cosine s صحّيلي هذه بس
+
+720
+01:16:23,830 --> 01:16:29,590
+يا بنات cosine s تمام هذه بس نزلناها بالخطّة هيك
+
+721
+01:16:29,590 --> 01:16:33,550
+التانية sin مظبوط التانية مش فيها مشكلة وهذه مش
+
+722
+01:16:33,550 --> 01:16:37,010
+فيها مشكلة طيب هدول اللي تنتقل أما أخدت منهم ناقص
+
+723
+01:16:37,010 --> 01:16:41,790
+عامل بيصير cosine cosine زائد sin sin اللي هو
+
+724
+01:16:41,790 --> 01:16:49,770
+cosine منين؟ كوسين الفرق يبقى كوسين T ناقص الـ S
+
+725
+01:16:49,770 --> 01:16:55,270
+يبقى يخلصنا الأربع ترمات اللي بين قوسين وهي قفلنا
+
+726
+01:16:55,270 --> 01:17:04,160
+القوس كله وهي عندك G of S وهذا الـ D of S يبقى
+
+727
+01:17:04,160 --> 01:17:08,820
+خلينا الـ particular solution بدل الاتنين بدل
+
+728
+01:17:08,820 --> 01:17:14,100
+التكامل لإن الـ G of T أنا ما أعرفش قداش عنا يبقى هذا
+
+729
+01:17:14,100 --> 01:17:23,180
+أحد برضه أسئلة الكتاب اللي موجودة حد
+
+730
+01:17:23,180 --> 01:17:30,120
+بتحب تسأل أي سؤال هنا نمسح
+
+731
+01:17:30,120 --> 01:17:31,060
+الشجرة هذه
+
+732
+01:17:47,080 --> 01:17:52,500
+بدنا نراجع كلامنا صغير يا مانات على حكاية مين بس
+
+733
+01:17:52,500 --> 01:17:55,800
+قبل ما نراجع بدنا نعطيكوا أرقام مثال الـ section
+
+734
+01:17:55,800 --> 01:18:00,840
+اللي فات والـ section هذا الـ section اللي فات كان
+
+735
+01:18:00,840 --> 01:18:11,430
+exercises أربعة ثلاثة اللي هو من واحد لسبعتاشر ألكود و
+
+736
+01:18:11,430 --> 01:18:20,410
+exercises أربع أربع المسائل من واحد لغاية أربعة
+
+737
+01:18:20,410 --> 01:18:30,310
+عشر وبرضه ألكود وبناخد عليها كمان سؤال ترفع بدنا 
+
+738
+01:18:30,310 --> 01:18:37,790
+نيجي لـ section الآن خمسة واحد الـ power series
+
+739
+01:18:40,730 --> 01:18:44,110
+عارف أنا والله مش ذاكر وعارف وعارف كدهش بياخد
+
+740
+01:18:44,110 --> 01:18:48,610
+وكدهش بدي أعطي بدي أعطي كلمتين صغير مراجعة لبعض
+
+741
+01:18:48,610 --> 01:18:55,410
+الأشياء مش كلها كمان التي درست في calculus B يبقى
+
+742
+01:18:55,410 --> 01:19:00,150
+أول section يا بنات هو مراجعة وما لوش دخل بالموضوع
+
+743
+01:19:00,150 --> 01:19:05,010
+موضوعنا طيلة هذا الـ chapter هو الـ series solution
+
+744
+01:19:05,010 --> 01:19:09,890
+لـ second order differential equation يعني إذا بدي
+
+745
+01:19:09,890 --> 01:19:13,270
+أبدأ بالعنوان الرئيسي اللي قبل هذا اللي هو chapter
+
+746
+01:19:13,270 --> 01:19:23,210
+5 series solutions of
+
+747
+01:19:23,210 --> 01:19:27,130
+second order
+
+748
+01:19:28,950 --> 01:19:34,270
+Differential equation هذا هو العنوان الرئيسي للشكل
+
+749
+01:19:34,270 --> 01:19:39,890
+كله لكن أول section هو الـ power series الـ power
+
+750
+01:19:39,890 --> 01:19:45,770
+series منها أحد شكلين الشكل الأول اللي هو summation
+
+751
+01:19:45,770 --> 01:19:51,190
+من n equal zero to infinity للـ a n في الـ x ناقص الـ
+
+752
+01:19:51,190 --> 01:19:56,890
+x not to the power n لو حطيتها بالشكل الطويل يبقى
+
+753
+01:19:56,890 --> 01:20:02,670
+بداجي أشيل الـ N وأحط مكانها Zero بيصير A node في
+
+754
+01:20:02,670 --> 01:20:07,630
+الـ X ناقص الـ X node الـ Zero اللي هو بواحد زائد A1
+
+755
+01:20:07,630 --> 01:20:12,490
+في الـ X ناقص الـ X node زائد A2 في الـ X ناقص الـ X
+
+756
+01:20:12,490 --> 01:20:18,070
+node لكل تربيع زائد وانظر ما أشيل لغاية الحد ينوني A
+
+757
+01:20:18,070 --> 01:20:21,290
+N X ناقص الـ X node to the power N
+
+758
+01:20:25,840 --> 01:20:31,180
+هذا هو الشكل الأول الـ X node بنسميه المركز تبع الـ
+
+759
+01:20:31,180 --> 01:20:34,840
+power series
+
+760
+01:20:34,840 --> 01:20:39,200
+ممكن يكون الـ center هذي عند نقطة الأصل يعني لو
+
+761
+01:20:39,200 --> 01:20:46,930
+كانت الـ X node يساوي 0 الـ X node بده يساوي 0 يبقى
+
+762
+01:20:46,930 --> 01:20:50,450
+الـ summation بده يصير بالشكل هذا من عندي الـ 0 لـ
+
+763
+01:20:50,450 --> 01:20:56,510
+infinity للـ A N للـ X to the power N فقط يبقى X
+
+764
+01:20:56,510 --> 01:20:59,830
+node X node X node كلها هتطير من الـ series اللي
+
+765
+01:20:59,830 --> 01:21:08,790
+عندنا ويصبح شكلها A node زائد A1 X A2 X تربيع زائد
+
+766
+01:21:08,790 --> 01:21:14,440
+A N X to the power N زائد الآخرين يبقى هذا هو شكل
+
+767
+01:21:14,440 --> 01:21:20,740
+الـ power series in general طيب أنا عندي الـ power
+
+768
+01:21:20,740 --> 01:21:24,180
+series وبدي أشوفها converge ولا diverge شو
+
+769
+01:21:24,180 --> 01:21:26,720
+الاختبارات اللي كنا بنستخدمها في الـ calculus
+
+770
+01:21:26,720 --> 01:21:31,660
+نستخدمهم
+
+771
+01:21:31,660 --> 01:21:41,180
+للـ power series؟ الراتيو والانثروت بس فقط لغير يبقى
+
+772
+01:21:41,180 --> 01:21:49,380
+to test the convergence of
+
+773
+01:21:49,980 --> 01:22:01,260
+the power series we use بنروح نستخدم the ratio
+
+774
+01:22:01,260 --> 01:22:09,300
+test or the Enthrotest
+
+775
+01:22:13,400 --> 01:22:16,740
+يبقى يا بستخدم الـ ratio يا الـ in through الـ test
+
+776
+01:22:16,740 --> 01:22:21,500
+هدول اختبارين فقط اللي كنا بواسطتهم نختبر الـ power
+
+777
+01:22:21,500 --> 01:22:26,280
+series هل هي converge ولا diverse طيب الـ power
+
+778
+01:22:26,280 --> 01:22:29,940
+series هدي converge على طول ولا ممكن تكون عند
+
+779
+01:22:29,940 --> 01:22:35,700
+فترة وممكن تكون عند نقطة أي power series اللي أحد
+
+780
+01:22:35,700 --> 01:22:42,250
+الاحتمالات الثلاثة التالية convergence of the power
+
+781
+01:22:42,250 --> 01:22:47,930
+series
+
+782
+01:22:47,930 --> 01:22:52,850
+هدي اللي فاجأ بناته أو هدي أي واحدة منهم نفس
+
+783
+01:22:52,850 --> 01:23:02,670
+الكلام هدي ممكن تكون converge only at x node and
+
+784
+01:23:02,670 --> 01:23:12,500
+diverge elsewhere في أي مكان آخر Diverge كيف يعني؟
+
+785
+01:23:12,500 --> 01:23:19,000
+لو كان هذا الـ real line وهذه النقطة X0 ممكن عند
+
+786
+01:23:19,000 --> 01:23:25,140
+هذه النقطة تبقى converge لكن بعدها Diverge وقبلها
+
+787
+01:23:25,140 --> 01:23:31,240
+Diverge طب قداش الـ radius of convergence في هذه
+
+788
+01:23:31,240 --> 01:23:37,480
+الحالة الـ radius بتقول الله الـ convergence عنده
+
+789
+01:23:37,480 --> 01:23:40,940
+نقطة طول الفترة وبدأ جسمه على اثنين قداش طول
+
+790
+01:23:40,940 --> 01:23:45,180
+النقطة؟ Zero Zero يبقى الـ radius يكون ساوي Zero
+
+791
+01:23:45,180 --> 01:23:54,500
+يبقى هنا في هذه الحالة The radius of convergence
+
+792
+01:23:54,500 --> 01:23:59,100
+is احنا بقى هنسميه capital R واحنا بقى هنقوله
+
+793
+01:23:59,100 --> 01:24:05,080
+كتابنا هنا بيسميه الـ route ساوي Zero النقطة الثانية
+
+794
+01:24:05,080 --> 01:24:12,640
+يبقى
+
+795
+01:24:12,640 --> 01:24:18,440
+فترة
+
+796
+01:24:18,440 --> 01:24:22,080
+التقارب من ولا ولا اين سالب infinity لـ infinity
+
+797
+01:24:22,080 --> 01:24:29,280
+يبقى هذا يعطينا the interval of
+
+798
+01:24:40,030 --> 01:24:41,430
+الراديوس
+
+799
+01:24:43,910 --> 01:24:56,010
+radius of convergence as R يبقى
+
+800
+01:24:56,010 --> 01:25:00,930
+R تساوي infinity يعني يا بنات لو كان هذا هو الـ
+
+801
+01:25:00,930 --> 01:25:06,750
+real line يبقى الـ series converge على كل الفترة
+
+802
+01:25:06,750 --> 01:25:10,690
+بالاستثناء وهذا النقطة اللي هي من هنا الـ zero وهذا
+
+803
+01:25:10,690 --> 01:25:15,620
+يبقى الملئ و diverge ما عنديش بالمرة وبالتالي نص الـ
+
+804
+01:25:15,620 --> 01:25:19,360
+real line هو نصف القطر من صفر لما لا نهاية الطول
+
+805
+01:25:19,360 --> 01:25:24,000
+هذا بقداش؟ بما لا نهاية طيب النقطة الثالثة
+
+806
+01:25:24,000 --> 01:25:33,720
+والأخيرة اللي هو the series converge on الفترة
+
+807
+01:25:33,720 --> 01:25:36,300
+المفتوحة من A إلى B
+
+808
+01:25:39,740 --> 01:25:44,940
+بس على الفترة دي يعني لو جيت قلت هذا الـ real line
+
+809
+01:25:44,940 --> 01:25:50,460
+وهذا النقطة A وهذا النقطة B هنا في النص Converge
+
+810
+01:25:50,460 --> 01:25:59,640
+وهكذا Diverge وقبلها A Diverge كذلك طب عندي الـ A و
+
+811
+01:25:59,640 --> 01:26:00,180
+الـ B
+
+812
+01:26:02,900 --> 01:26:16,400
+وقد تكون converge وقد تكون diverge
+
+813
+01:26:16,400 --> 01:26:31,110
+الـ X أقل من A والـ X أكبر من B بأجي بيقول الـ X يساوي
+
+814
+01:26:31,110 --> 01:26:42,350
+بـ A الـ X يساوي بـ B الـ Series may converge or
+
+815
+01:26:42,350 --> 01:26:48,970
+may diverge يعني عند النقطة A والـ B الـ Series
+
+816
+01:26:48,970 --> 01:26:53,510
+ممكن تكون converge أو ممكن تكون diverge
diff --git a/PL9fwy3NUQKwa8ZDfSFGn6H8xVFLzqmCZC/gssK8gZjcqI_postprocess.srt b/PL9fwy3NUQKwa8ZDfSFGn6H8xVFLzqmCZC/gssK8gZjcqI_postprocess.srt
new file mode 100644
index 0000000000000000000000000000000000000000..7ad9a8c66dbff3aedc0e70b8cd47067cd07ca99b
--- /dev/null
+++ b/PL9fwy3NUQKwa8ZDfSFGn6H8xVFLzqmCZC/gssK8gZjcqI_postprocess.srt
@@ -0,0 +1,3264 @@
+1
+00:00:09,600 --> 00:00:15,940
+بسم الله الرحمن الرحيم المرة الماضية دخلنا في حل
+
+2
+00:00:15,940 --> 00:00:19,480
+ال non homogeneous differential equationواخدنا
+
+3
+00:00:19,480 --> 00:00:23,260
+الطريقة الأولى وهى طريقة ال undetermined
+
+4
+00:00:23,260 --> 00:00:28,440
+coefficients وظهر علينا طريقة ال variation of
+
+5
+00:00:28,440 --> 00:00:32,700
+parameters اللى رفعناها فوق ان شاء الله هذه
+
+6
+00:00:32,700 --> 00:00:37,180
+الطريقة نفس الفكرة تابعة ال second order لما نحلها
+
+7
+00:00:37,180 --> 00:00:40,880
+بال variation of parameters بنحل بطريقة ال
+
+8
+00:00:40,880 --> 00:00:46,070
+variation of parameters إذا كانتالمعاملات ثوابت او
+
+9
+00:00:46,070 --> 00:00:52,490
+غير ثوابت بيهمنيش شكل g of t يكون اي شكل مش مقصور
+
+10
+00:00:52,490 --> 00:00:55,130
+زي ال undetermined coefficients لازم يكون
+
+11
+00:00:55,130 --> 00:00:59,090
+المعاملات ثوابت و g of t تكون بشكل معين حسب جده
+
+12
+00:00:59,090 --> 00:01:02,430
+اللي عملنا له و g of t تكون ايش ما يكون شكلها
+
+13
+00:01:02,430 --> 00:01:06,070
+فبقول يعتبر اللي هو ال inf order linear
+
+14
+00:01:06,070 --> 00:01:09,910
+differential equation بالشكل اللي قدامنا هذا لحظة
+
+15
+00:01:19,460 --> 00:01:23,860
+المعاملات هي هى متغيرات وقد تكون ثوائي بتفريقش لأن
+
+16
+00:01:23,860 --> 00:01:29,800
+ثوائي بتكون متغيرات المهم نعرف ان حل نقول assume
+
+17
+00:01:29,800 --> 00:01:34,280
+that we know a fundamental set of solutions Y1 وY2
+
+18
+00:01:34,280 --> 00:01:38,240
+وYN لمينللـ homogeneous differential equation اللي
+
+19
+00:01:38,240 --> 00:01:42,240
+متساوي قداش صفر يعني إذا عندي non homogeneous بدي
+
+20
+00:01:42,240 --> 00:01:45,120
+أجزئها لجزئين سواء كان بال undetermined
+
+21
+00:01:45,120 --> 00:01:48,860
+coefficients أو بال variation أو parameter علي
+
+22
+00:01:48,860 --> 00:01:53,220
+الشكتين بدي أخد ال homogeneous و أطلع الحل تبع ال
+
+23
+00:01:53,220 --> 00:01:56,440
+homogeneous differential equation وبعد ذلك بروح
+
+24
+00:01:56,440 --> 00:02:01,520
+لمين لل non homogeneous differential equationخلاص
+
+25
+00:02:01,520 --> 00:02:06,500
+الأمر نفس الفكرة تبع ال undetermined بس هناك بنروح
+
+26
+00:02:06,500 --> 00:02:10,160
+عشان بنجيب particular solution و بيكون جيبنا حل ال
+
+27
+00:02:10,160 --> 00:02:13,820
+homogenous بنجمع الاتنين بنطلع من ال general
+
+28
+00:02:13,820 --> 00:02:17,220
+solution هنا بنفس الطريقة بدي أروح أجيب ال
+
+29
+00:02:17,220 --> 00:02:20,660
+particular solution لل non homogenous differential
+
+30
+00:02:20,660 --> 00:02:24,200
+equation أجمعه محل ال homogenous differential
+
+31
+00:02:24,200 --> 00:02:27,980
+equation بيعطينا من ال general solution لل
+
+32
+00:02:27,980 --> 00:02:29,660
+differential equation كلها
+
+33
+00:02:33,120 --> 00:02:37,220
+الحل الهوموجيني يسمى الـE2 الهوموجيني يسمى
+
+34
+00:02:37,220 --> 00:02:43,280
+الهوموجيني يسمى الهوموجيني يسمى الهوموجيني يسمى
+
+35
+00:02:43,280 --> 00:02:43,620
+الهوموجيني يسمى الهوموجيني يسمى الهوموجيني يسمى
+
+36
+00:02:43,620 --> 00:02:45,260
+الهوموجيني يسمى الهوموجيني يسمى الهوموجيني يسمى
+
+37
+00:02:45,260 --> 00:02:46,100
+الهوموجيني يسمى الهوموجيني يسمى الهوموجيني يسمى
+
+38
+00:02:46,100 --> 00:02:46,580
+الهوموجيني يسمى الهوموجيني يسمى الهوموجيني يسمى
+
+39
+00:02:46,580 --> 00:02:47,100
+الهوموجيني يسمى الهوموجيني يسمى الهوموجيني يسمى
+
+40
+00:02:47,100 --> 00:02:47,500
+الهوموجيني يسمى الهوموجيني يسمى الهوموجيني يسمى
+
+41
+00:02:47,500 --> 00:02:54,580
+الهوموجيني يسمى التغيير الوسيطة to find a
+
+42
+00:02:54,580 --> 00:02:59,000
+particular solution يبقى هذه بنستخدمها لإيجاد حل
+
+43
+00:02:59,000 --> 00:03:03,380
+خاص زي بناتي الجدول في ال undetermined بنستخدمه
+
+44
+00:03:03,380 --> 00:03:06,760
+لإيجاد حل خاص وبعد هيك بنجيب ال general solution
+
+45
+00:03:08,020 --> 00:03:13,000
+يبقى هذه الطريقة تتلخص بدي أشيل c1 و c2 و c3 لغاية
+
+46
+00:03:13,000 --> 00:03:20,320
+cin و أحط مكانهم functions u1 و u2 و u3 و un هيهم
+
+47
+00:03:20,320 --> 00:03:23,640
+بالشكل اللي هذا بحيث ان ال particular solution
+
+48
+00:03:23,640 --> 00:03:28,100
+بصير على الشكل اللي عندنا هذا u1 y1 زائد u2 y2
+
+49
+00:03:28,100 --> 00:03:34,460
+زائد u u زائد u n اللي هو yn طب بدنا نجيب شكل كل
+
+50
+00:03:34,460 --> 00:03:39,760
+واحدة من اليهات هذهفبقول له where ال U M as a
+
+51
+00:03:39,760 --> 00:03:45,640
+function of T هي integration لل G of Tاللي هي هذه
+
+52
+00:03:45,640 --> 00:03:52,820
+مضربة في الرنسكين M of T على الرنسكين of T اول شيء
+
+53
+00:03:52,820 --> 00:03:56,140
+الرنسكين of T هذا الرنسكين تبع الحلول اللي هو Y1
+
+54
+00:03:56,140 --> 00:04:03,020
+وY2 وY3 تمام؟ الآن مين الرنسكين M؟ هو نفس الرنسكين
+
+55
+00:04:03,020 --> 00:04:09,860
+هذا هه بس بدي اشيل الصف رقم M و اكتب بدل العمود
+
+56
+00:04:09,860 --> 00:04:17,670
+000001يعني إيش؟ يعني لو كنت بدي U1 of T لإن احنا
+
+57
+00:04:17,670 --> 00:04:21,770
+لدينا U1 و U2 لغاية UN باجي على رونسكينالاندا و
+
+58
+00:04:21,770 --> 00:04:26,430
+بشيل العمود الأول و بكتب داله 0001 و باجي الأعمدة
+
+59
+00:04:26,430 --> 00:04:30,810
+أزاي ما هي و بفك المحدد و بجيب قيمته تمام؟ يبقى
+
+60
+00:04:30,810 --> 00:04:33,970
+جيبنا قيمة المحدد هذا، جيبنا قيمة المحدد هذا، نضغط
+
+61
+00:04:33,970 --> 00:04:38,030
+في جيب و نروح كامل، بكون حصلنا على مين؟ على U1 طب
+
+62
+00:04:38,030 --> 00:04:45,720
+بدي U2U2 of T بأجي D of T كما هي او رنسكين 2 of T
+
+63
+00:04:45,720 --> 00:04:49,720
+كيف بسيب العمود الأول زي ما هو العمود العتيق مش
+
+64
+00:04:49,720 --> 00:04:53,880
+الجديد و بجي على العمود رقم اتنين بشيله كله بحق و
+
+65
+00:04:53,880 --> 00:04:58,860
+بدله 0001 و الأعمد اللي بعده تبقى كما هي و هكذا
+
+66
+00:04:59,710 --> 00:05:02,850
+للرونسكين ثلاثة أو رونسكين أربعة أو رونسكين خمسة
+
+67
+00:05:02,850 --> 00:05:06,650
+إلى آخره لغاية ما نخلص كل اليهات اللي عندنا إذا
+
+68
+00:05:06,650 --> 00:05:09,190
+جيبناهم بيقول خلاص جيبنا ال particle a solution
+
+69
+00:05:09,190 --> 00:05:14,410
+تمام يبقى باجي بقوله ال U M of T هو integration لل
+
+70
+00:05:14,410 --> 00:05:21,290
+G of T لرونسكين M of T على W of T DTوالـ M بدأ
+
+71
+00:05:21,290 --> 00:05:25,110
+يساوي واحد واثنين لغاية مين لغاية ال N يعني بدي
+
+72
+00:05:25,110 --> 00:05:30,130
+أجيب كل اليهات فبلونوسكين M is the determinant هو
+
+73
+00:05:30,130 --> 00:05:36,070
+عبارة عن المحدد يبقى بنقول ما ياتي الآن بدنا نحاول
+
+74
+00:05:36,070 --> 00:05:39,710
+نجيب اليهات اللي عندنا دي واحد و اتنين و تلاتة و
+
+75
+00:05:39,710 --> 00:05:46,560
+لغاية U Mبنحط الصورة العامة U M of T هي عبارة عن
+
+76
+00:05:46,560 --> 00:05:51,140
+integration للـ G of T في الرونسكين M as a
+
+77
+00:05:51,140 --> 00:05:55,600
+function of T على الرونسكين of T كله بالنسبة لـ DT
+
+78
+00:05:55,600 --> 00:06:02,380
+مين هي الـ G of T هي تبع اتنين هذه مغيرناش اتنين
+
+79
+00:06:02,380 --> 00:06:07,260
+الرونسكين هذا هو تبع الحلول Y1 وY2 لغاية YN
+
+80
+00:06:07,760 --> 00:06:12,080
+الرونسكين M of T هو الرونسكين اللى تحت هذا بس بعد
+
+81
+00:06:12,080 --> 00:06:17,040
+ما اغير كل عمود يعني اذا عندى بدي U واحد بغير
+
+82
+00:06:17,040 --> 00:06:21,720
+العمود الاول بكون عندى W واحد عندى U اثنين يبقى
+
+83
+00:06:21,720 --> 00:06:27,120
+هنا W اثنين of T باجى على العمود التانى بغيره بحط
+
+84
+00:06:27,120 --> 00:06:33,740
+بداله 0001 وكده لغاية ما اوصل لمن لل U N اللى
+
+85
+00:06:33,740 --> 00:06:38,410
+عندنا ال U Nهها هي عبارة عن الـ G of T فى
+
+86
+00:06:38,410 --> 00:06:42,250
+الرونسكين M of T مقسمة على الرونسكين of T كله
+
+87
+00:06:42,250 --> 00:06:46,430
+بالنسبة لـ DT والـ M بتاخد 1 و 2 لغاية ال N يعني
+
+88
+00:06:46,430 --> 00:06:53,320
+بدي أجيب كل اليهات مرة واحدةيبقى هاي جيبناله ال M
+
+89
+00:06:53,320 --> 00:06:58,660
+الرونسكين M هيو هو المحدد اللي بنحصل عليه من ال W
+
+90
+00:06:58,660 --> 00:07:05,740
+of T باستبدال العمود رقم M بالعمود 0001 فيقنع بعض
+
+91
+00:07:05,740 --> 00:07:10,380
+الملاحظات لازم ندقيقها كويس و احنا بنشتغل تذكروا
+
+92
+00:07:10,380 --> 00:07:13,520
+في حالة ال variation of parameters في حالة second
+
+93
+00:07:13,520 --> 00:07:18,800
+order اشترطنا ان المعامل تبع Y W prime يكون جداش
+
+94
+00:07:19,220 --> 00:07:23,540
+هنا المعامل تبع y to the derivative n يكون جديهش
+
+95
+00:07:23,540 --> 00:07:29,820
+يبقى كتابنا هذا must be one يبقى المعامل تبع ال y
+
+96
+00:07:29,820 --> 00:07:33,580
+to the derivative n لازم يكون واحد صحيح ليش؟ لأن
+
+97
+00:07:33,580 --> 00:07:38,970
+هذا لو ماكانش واحد صحيحيبقى بيكون ده لا ورقم بدنا
+
+98
+00:07:38,970 --> 00:07:43,810
+نقسم عليه حتى نضمن أنه الجديدة هذه هي G of T مش
+
+99
+00:07:43,810 --> 00:07:48,010
+العتيقة يعني G of T هذي بحصل عليه لما يكون المعامل
+
+100
+00:07:48,010 --> 00:07:52,550
+هنا main واحد صحيح يبقى بدك تعمل القطوة هذي قبل كل
+
+101
+00:07:52,550 --> 00:07:56,730
+شيء أو تتأكد منها اتنين بيقول يا رونسكين هذا بقدر
+
+102
+00:07:56,730 --> 00:08:01,680
+أحسمه بطريقة قابلطريقة ايه بالكلمة ال second order
+
+103
+00:08:01,680 --> 00:08:06,040
+بس احنا هنا لل nth order يبقى باجي بقول رونس كين
+
+104
+00:08:06,040 --> 00:08:11,120
+هو عبارة عن كرسان فيه وصناعة استكامل P1 of T DT ال
+
+105
+00:08:11,120 --> 00:08:16,000
+P1 هو مين؟ هو المعامل ال Y to the derivative N
+
+106
+00:08:16,000 --> 00:08:21,040
+minus ال 1 طلع هي Y N اللي بعدها يمين معاملة هذا
+
+107
+00:08:21,040 --> 00:08:26,320
+يبقى لو كان في شغل هنا بدك تجسم عليهاواللي بيطلع
+
+108
+00:08:26,320 --> 00:08:30,160
+بيكون هو P1 of T و بعضكوا في الامتحان اللي فات
+
+109
+00:08:30,160 --> 00:08:34,420
+ماجسموش وخلوا عليه وبالتالي طالع سؤالهم غلط لازم
+
+110
+00:08:34,420 --> 00:08:38,960
+ايش المعامل هذا يكون واحد صحيح وكتبناها معاكم قبل
+
+111
+00:08:38,960 --> 00:08:41,840
+ذلك في ال second order لازم يكون المعامل هو main
+
+112
+00:08:41,840 --> 00:08:46,980
+واحد صحيح يبقى هذا كل ما يتعلق بقضية ال variation
+
+113
+00:08:46,980 --> 00:08:52,150
+of parameters يعني حلالنهوموجينس بواسطة الـ
+
+114
+00:08:52,150 --> 00:08:53,150
+Variation of Parameters
+
+115
+00:09:02,380 --> 00:09:06,860
+يبقى بدي أشيل ال constants في مين في الحل اللي هو
+
+116
+00:09:06,860 --> 00:09:11,380
+y يساوي c1 y1 زي c2 y2 زي cnyn بدي أشيل ال c هات
+
+117
+00:09:11,380 --> 00:09:16,760
+هذي و أستبدلها بدوال u1 و u2 و u3 لغاية u1 طب بدي
+
+118
+00:09:16,760 --> 00:09:20,840
+أجيب عرف الشكل هم بقول لك اه في ان علاقة العلاقة
+
+119
+00:09:20,840 --> 00:09:25,910
+هذي بتجيبلك أي و منهم غير العلاقة مين هيU M of T
+
+120
+00:09:25,910 --> 00:09:30,110
+بدي سوي تكامل G of T فى الورونسكن M of T على
+
+121
+00:09:30,110 --> 00:09:35,270
+الرونسكن of T كله بالنسبة لدى T الرونسكن M of T هو
+
+122
+00:09:35,270 --> 00:09:39,470
+عبارة عن الرونسكن of T بعد ما اشيل اذا بدي U 1
+
+123
+00:09:39,470 --> 00:09:45,170
+بشيل العمود الأول و بحط بداله 0001 اذا رونسكن 2
+
+124
+00:09:45,170 --> 00:09:48,030
+بخل العمود الأول زى ما هو بروح على العمود التانى
+
+125
+00:09:48,030 --> 00:09:52,510
+بشيله و بحط بداله 0001 و هكذا تبقى بكون جبت ال U
+
+126
+00:09:52,510 --> 00:09:56,360
+هاتبضربها في الوايات اللى عندي بجمع بكون جبته ال
+
+127
+00:09:56,360 --> 00:09:59,800
+particular solution لل non homogeneous
+
+128
+00:09:59,800 --> 00:10:03,040
+differential equation بجمع محل ال homogeneous
+
+129
+00:10:03,040 --> 00:10:06,900
+بيعطيني ال general solution لل non homogeneous
+
+130
+00:10:06,900 --> 00:10:11,020
+differential equation واضح كلام ايه؟حد فيكم بتحب
+
+131
+00:10:11,020 --> 00:10:14,020
+تسأل اي سؤال؟ خلاصنا ال user نظري، خلاصنا منه، حد
+
+132
+00:10:14,020 --> 00:10:17,700
+بتحب تسأل اي سؤال؟ طب الكلام اللي سمعته بنروح
+
+133
+00:10:17,700 --> 00:10:22,800
+انطبقه على أرض الواقع مثال او اول مثال بقول you
+
+134
+00:10:22,800 --> 00:10:25,720
+find the general solution of the differential
+
+135
+00:10:25,720 --> 00:10:29,860
+equation Y triple A prime زي ال Y prime تساوي 6T
+
+136
+00:10:29,860 --> 00:10:35,000
+وT محصرة من سالف باي على اتنين إلى مين؟ إلى باي
+
+137
+00:10:35,000 --> 00:10:39,790
+على اتنينيعني حصرها في فترة الدالة الـ6 تبدأ تبقى
+
+138
+00:10:39,790 --> 00:10:43,210
+continuous على هذه الفترة تعرف ان عند البيعة 2
+
+139
+00:10:43,210 --> 00:10:47,450
+والسلب بيعة 2 الـ6 is undefined زي التان عند
+
+140
+00:10:47,450 --> 00:10:52,070
+البيعة 2 وسلب بيعة 2 تلاتة بيعة 2 سلب تلاتة بيعة 2
+
+141
+00:10:52,070 --> 00:10:56,090
+خمسة بيعة 2 سلب كل ما تبقى الدالة ماهياش معرفة
+
+142
+00:10:56,090 --> 00:10:59,490
+يبقى أنا حصرتها في فترة معرفة عليه يعني الدالة
+
+143
+00:10:59,490 --> 00:11:05,350
+continuous على هذهالفترة طيب بدنا نيجي نحل يبقى
+
+144
+00:11:05,350 --> 00:11:10,650
+أول خطوة بتروح اجيب مين حل ال homogenous صدر و حل
+
+145
+00:11:10,650 --> 00:11:14,550
+المعادلة رقم اتنين المعادلة اللي عندي من الدرجة
+
+146
+00:11:14,550 --> 00:11:18,470
+الثالثة يبقى نفس ال tactic اللي اتبعناها في حالة
+
+147
+00:11:18,470 --> 00:11:21,110
+ال undetermined coefficients الجزء الأول هو الجزء
+
+148
+00:11:21,110 --> 00:11:28,690
+الأول هناك لا تغيير عليه فبجي بقوله solution let
+
+149
+00:11:29,360 --> 00:11:40,160
+Y تساوي E أس RT ب A solution of المعادلة التفاضلية
+
+150
+00:11:40,160 --> 00:11:44,920
+Y triple prime زائد Y prime تساوي Zero
+
+151
+00:11:57,640 --> 00:12:02,580
+ممكن ناخد ر عامل مشترك بيظل ر تربيع زائد واحد
+
+152
+00:12:02,580 --> 00:12:10,830
+يساوي زيرويبقى R1 بده يساوي 0 وR2 و3 بده يساوي
+
+153
+00:12:10,830 --> 00:12:19,670
+زائد او نقص كده اش I يبقى Y C بده يساوي C1 في E أس
+
+154
+00:12:19,670 --> 00:12:30,810
+Zero يبقى بC1 زائد C2 Cos T زائد C3 في Sin T الشكل
+
+155
+00:12:30,810 --> 00:12:33,740
+اللي عندنا هناهذا هو حلل الـ Homogeneous
+
+156
+00:12:33,740 --> 00:12:38,490
+differential equationبدنا نيجي ندور على particular
+
+157
+00:12:38,490 --> 00:12:44,670
+solution لحال مين لحال اللي هو non homogeneous
+
+158
+00:12:44,670 --> 00:12:50,250
+differential equation بطريقة مين؟ بطريقة ال
+
+159
+00:12:50,250 --> 00:12:54,310
+variation of parameters ليش بطريقة ال variation of
+
+160
+00:12:54,310 --> 00:12:59,890
+parameters؟ لإن الجزء اللي على اليمين له
+
+161
+00:12:59,890 --> 00:13:04,430
+polynomial و له polynomial fixed exponentialوالا
+
+162
+00:13:04,430 --> 00:13:08,450
+polynomial approximation في صين او كوسين سك واحدة
+
+163
+00:13:08,450 --> 00:13:13,250
+ع كوسين مش كوسين يبصرة واحدة ع كوسين اذا اختلفت عن
+
+164
+00:13:13,250 --> 00:13:17,110
+ال undetermined coefficientsوطبعا جيبتلك وده سؤال
+
+165
+00:13:17,110 --> 00:13:21,430
+في الخيارات خليتها واحدة على cosine وقولك بنحل بها
+
+166
+00:13:21,430 --> 00:13:25,090
+بطريقة ايش ال undetermined ولا ال variation ولا ال
+
+167
+00:13:25,090 --> 00:13:27,830
+reduction ولا ولا بها الطرق ولا بطريقة من هذه
+
+168
+00:13:27,830 --> 00:13:31,390
+الطرق واختري الإجابة صحية والإجابة الصحية هي طريقة
+
+169
+00:13:31,390 --> 00:13:36,130
+مين ال variation of parameters طيب تتلخص ال
+
+170
+00:13:36,130 --> 00:13:40,450
+variation of parameters اني بدي اشيل ال C1 وC2 وC3
+
+171
+00:13:40,450 --> 00:13:48,190
+وحط بدالها U1 وU2 وU3بس قبل لا أحط ولا أشيل بدي
+
+172
+00:13:48,190 --> 00:13:52,990
+أحسب قداش الронسكن لكل واحدة من هدول لإنه بدي
+
+173
+00:13:52,990 --> 00:13:58,570
+أستخدمها في الحل إذا لو جيت للرونسكن as a function
+
+174
+00:13:58,570 --> 00:14:03,310
+of T و كتبت المحدد الحل الأول هنا قداش يا بنات؟
+
+175
+00:14:06,430 --> 00:14:13,230
+يبقى الحل الأول واحد و الحل التاني cos t و الحل
+
+176
+00:14:13,230 --> 00:14:23,010
+التالت sin t بدشتق يبقى zero سالب sin t cos t دشتق
+
+177
+00:14:23,010 --> 00:14:30,390
+كمان مرة يبقى zero ناقص cos t ناقص sin t وهيجفلنا
+
+178
+00:14:30,390 --> 00:14:35,490
+المحددبدي احسب جداش قيمة المحدد يبقى بدافك
+
+179
+00:14:35,490 --> 00:14:41,710
+وباستخدام عناصرالعمود الأول أسل لإن واحد في المحد
+
+180
+00:14:41,710 --> 00:14:45,110
+الأصغر مناظره و بعدين Zero Zero خلاص مع السلامة
+
+181
+00:14:45,110 --> 00:14:48,450
+مافيش داعي الاكتفته بيصير Zero دُغري يبقى هذا
+
+182
+00:14:48,450 --> 00:14:54,030
+الكلام بده يساوي هاي الواحد فيه خشط بصفه عمودة
+
+183
+00:14:54,030 --> 00:14:58,350
+بصيرها حاصل ضرب عناصر غطر رئيسي اللي هي جداش صين
+
+184
+00:14:58,350 --> 00:15:02,770
+تربيتي ناقص حاصل ضرب عناصر غطر التاني المعناقس
+
+185
+00:15:02,770 --> 00:15:09,270
+بيصير زاد وصين تربيتي اللي هي كلها جداشممتاز يبقى
+
+186
+00:15:09,270 --> 00:15:13,030
+رونسكين of T طالع بواحه صحيحة يسهل الحسابات تاني
+
+187
+00:15:13,030 --> 00:15:19,490
+الان بالداجة لرونسكين one of T يساويهيبقى اش بدى
+
+188
+00:15:19,490 --> 00:15:24,870
+اعمل داجي على العمود الاول بدى اشيله و احط بداله
+
+189
+00:15:24,870 --> 00:15:32,090
+001 زي ما حكينا تمام؟ بداجي الان لهدول العمودين
+
+190
+00:15:32,090 --> 00:15:37,990
+بنزلهم زي ما هم بندوا نتغير يبقى هي cosine ت و هي
+
+191
+00:15:37,990 --> 00:15:46,620
+ناقص sine ت و هي ناقص cosine tوهنا هي sin T وهنا
+
+192
+00:15:46,620 --> 00:15:54,510
+cos T ونقص sin Tتمام شايف بده فك المحدد باستخدام
+
+193
+00:15:54,510 --> 00:15:59,710
+عناصر العمود لوله انه أسهل صفر في محدده بصفر مع
+
+194
+00:15:59,710 --> 00:16:03,830
+السلامة صفر محدده بصفر ضال واحد حسب قاعة الإشارة
+
+195
+00:16:03,830 --> 00:16:09,450
+شرطه موجة بقى يبقى هذا الكلام بده يساوي واحد فيه
+
+196
+00:16:09,450 --> 00:16:14,390
+يبقى بدنشته بصفه وعمضه بصير cosine تربية
+
+197
+00:16:30,250 --> 00:16:34,170
+بالدرجة عاملة العمود الأول اللي كان بتخليه زي ما
+
+198
+00:16:34,170 --> 00:16:40,970
+هويبقى هذا واحد Zero Zero العمود الثاني بدي أشيله
+
+199
+00:16:40,970 --> 00:16:46,630
+و أكتب بدله Zero Zero واحد العمود الثالث يبقى كما
+
+200
+00:16:46,630 --> 00:16:55,750
+هو يبقى Sin T Cosin T ناقص Sin T وهذا المحددبارضه
+
+201
+00:16:55,750 --> 00:17:00,570
+بدى احاول افكه باستخدام عناصر العمود الاول يبقى
+
+202
+00:17:00,570 --> 00:17:06,910
+هذا الكلام بدى يسوى واحد فيه اشق بصفه وعموده بصير
+
+203
+00:17:06,910 --> 00:17:14,390
+ال zero ناقص cosine ت يبقى zero ناقص cosine ت يبقى
+
+204
+00:17:14,390 --> 00:17:15,710
+الجواب جداش
+
+205
+00:17:22,810 --> 00:17:27,210
+العمود الأول زي ما هو يا بنات مش هغيره العمود
+
+206
+00:17:27,210 --> 00:17:34,940
+التاني برضه بده نزله زي ما هو زي ما كاننقص sin T
+
+207
+00:17:34,940 --> 00:17:43,620
+نقص cos T العمود التالت هو اللي بدي أغيره 001 يبقى
+
+208
+00:17:43,620 --> 00:17:47,640
+هذا الكلام يساوي هذا الواحد بدي أفكه باستخدام
+
+209
+00:17:47,640 --> 00:17:53,340
+عنوصر العمود الأول أشط بيصفه وعموده بصير السالب
+
+210
+00:17:53,340 --> 00:18:01,680
+sin Tزائد زيرو يبقى سالب صين ال T زائد زيرو يساوي
+
+211
+00:18:01,680 --> 00:18:07,620
+سالب صين ال T يبقى جيبنا هدول يبقى قصتنا الحين
+
+212
+00:18:07,620 --> 00:18:13,300
+بصير سهلة يبقى بدي أجيب له ال U1 و ال U2 و ال U3
+
+213
+00:18:13,300 --> 00:18:17,480
+بس اتنى شوية أطلع في المعامل المعامل واحد صحيح
+
+214
+00:18:17,480 --> 00:18:24,540
+يبقى احنا جاهزين تمام يبقى بالفعل 6T هذه هي G of T
+
+215
+00:18:28,350 --> 00:18:37,010
+الـ U1 as a function of Tيبقى هذا تكامل ل G of T
+
+216
+00:18:37,010 --> 00:18:43,710
+ها بدك تبالك و هذا ال run skin one as a function
+
+217
+00:18:43,710 --> 00:18:50,190
+of T على run skin of T DT بده يسوى تكامل ال G اللي
+
+218
+00:18:50,190 --> 00:18:56,750
+هي سك T ال run skin one مقدش بواحد صحيح يبقى هي
+
+219
+00:18:56,750 --> 00:19:03,400
+مضروبة في واحد على مين على واحد كله DTيبقى بدى
+
+220
+00:19:03,400 --> 00:19:09,280
+تكمل مين يا فنان؟ بس سك تي نعرف نكملها من كل plus
+
+221
+00:19:09,280 --> 00:19:14,220
+بيه؟ كدهش؟
+
+222
+00:19:14,220 --> 00:19:22,380
+لن سك زائد تان يبقى وتساوي لن absolute value لسك
+
+223
+00:19:22,380 --> 00:19:29,140
+تي زائد تان تي زائد constant K one اللي هو تبع
+
+224
+00:19:29,140 --> 00:19:35,740
+التكاملطبعا بعد شوية هحط k1b0 هنقولكوا ليش بس
+
+225
+00:19:35,740 --> 00:19:41,420
+يصبروا علينا شوية بدنا نروح نجيب ال U2 يبقى بدنا
+
+226
+00:19:41,420 --> 00:19:46,140
+نروح نجيب ال U2 as a function of T
+
+227
+00:19:52,080 --> 00:19:56,680
+يبقى بالداجي لل U2 as a function of T integration
+
+228
+00:19:56,680 --> 00:20:04,140
+لل G of T للورنسكين 2 of T على رونسكين of T كله في
+
+229
+00:20:04,140 --> 00:20:09,200
+DTيبقى هذا الكلام integration ل سك ال T في
+
+230
+00:20:09,200 --> 00:20:15,960
+الرونسكين 2 الرونسكين 2 هو طوله كده؟ ناقص cos T
+
+231
+00:20:15,960 --> 00:20:23,380
+يبقى ناقص cos T على رونسكين T اللي هو كده؟ واحد
+
+232
+00:20:23,380 --> 00:20:28,520
+صحيح طب السك هذه مش هي مقلوب ال cos يعني بضلب
+
+233
+00:20:28,520 --> 00:20:36,310
+السالب واحد يبقى هذه تساوي سالب تكامل DTيبقى سالب
+
+234
+00:20:36,310 --> 00:20:44,750
+T زائد constant K2 بعد هيك بدي أجيب ال U3 as a
+
+235
+00:20:44,750 --> 00:20:51,650
+function of T تكامل لل GT في رونسكن 3 of T على
+
+236
+00:20:51,650 --> 00:20:58,830
+رونسكن RT كله DTيبقى هذا الكلام بدي يسوي تكامل ل
+
+237
+00:20:58,830 --> 00:21:03,850
+سك التى فالرونس كنيه ثري اللى هو سالب صين التى
+
+238
+00:21:03,850 --> 00:21:12,530
+سالب صين التى على ال one dt او ان شيتنا فقولنا
+
+239
+00:21:12,530 --> 00:21:20,210
+ناقص صين التى على القصين اللى واحد على قصين التى
+
+240
+00:21:20,210 --> 00:21:25,550
+ديتى السؤال هو هل الباص تفاضل المطار؟يبقى اليوم
+
+241
+00:21:25,550 --> 00:21:31,790
+قداشر لن absolute value للمقام يبقى لن absolute
+
+242
+00:21:31,790 --> 00:21:34,490
+value لكوسايد ايش رأيكم؟ مالعيش خاطر احط ال
+
+243
+00:21:34,490 --> 00:21:42,010
+absolute لنفع لإن تي ون موجودة في الربع الرابع
+
+244
+00:21:42,010 --> 00:21:45,890
+والربع الأول في الربع الرابع الكوسايد موجب وفي
+
+245
+00:21:45,890 --> 00:21:49,770
+الربع الأول موجب على الشك تانييبقى حطة الأبسلويت
+
+246
+00:21:49,770 --> 00:21:57,990
+والنشلتة بتفرقش عنها يبقى لن كوصين ال T زائد K3
+
+247
+00:21:57,990 --> 00:22:09,890
+الآن بدي أقوله take خدلي K1 يسوى K2 يسوى K3 يسوى
+
+248
+00:22:09,890 --> 00:22:20,210
+Zero طبعا في تسأل ليش أخدتهم ب Zeroمش هذا سؤال؟ حد
+
+249
+00:22:20,210 --> 00:22:26,390
+بتقدر تعطيني جواب يا بنات؟ ليش أخدت الكهات هدول
+
+250
+00:22:26,390 --> 00:22:27,610
+بأصفار؟
+
+251
+00:22:31,150 --> 00:22:35,990
+هي اذكركم و تعالوا بال undetermined coefficient و
+
+252
+00:22:35,990 --> 00:22:40,150
+نرجع تاني لما كنا نكتب ال particular solution
+
+253
+00:22:40,150 --> 00:22:43,810
+بجينا نقول T to the power S فى الحل اللى عندنا هنا
+
+254
+00:22:43,810 --> 00:22:49,370
+ال S هدى بتعتمد هل اى جزء فى الحل يشبه اى جزء من
+
+255
+00:22:49,370 --> 00:22:53,230
+ال homogeneous ولا لأ مظبوط ولا لأ طب انا لو خلت
+
+256
+00:22:53,230 --> 00:22:57,350
+هذا ال key هات هدى كواحد و كتنين و كتر محطتهاش بقى
+
+257
+00:22:57,350 --> 00:23:04,610
+أصفرلما أجيب ال particular solution y1 ضرب u1 صح
+
+258
+00:23:04,610 --> 00:23:11,330
+ولا لأ؟ يبقى بصير هنا هذه مضروبة في y2 وهذه مضروبة
+
+259
+00:23:11,330 --> 00:23:15,670
+في y2 بصير y2 مكرر مضروبة في كل أسطن يبقى فيه
+
+260
+00:23:15,670 --> 00:23:19,670
+تشابه بينه و بين الأصلي ولا لأ؟ إذا لما أحط بيزيرو
+
+261
+00:23:19,670 --> 00:23:23,470
+بكون ماعنديش تشابه بالمرة متخلصة من الشغل هذه
+
+262
+00:23:24,000 --> 00:23:27,920
+بقولها كمان مرة اللى كانت مش متابعة معانا الصح سه
+
+263
+00:23:27,920 --> 00:23:34,300
+معانا كويس ليش حطيت الكهات هدول كله بأصفر مرة
+
+264
+00:23:34,300 --> 00:23:39,840
+واحدة لإن لو خليته زي ما هو بأي كونستان أخر غير
+
+265
+00:23:39,840 --> 00:23:45,260
+الصفر تمام لما بده أجيب ال particular solution إيش
+
+266
+00:23:45,260 --> 00:23:57,780
+بنقول C1 هنا حطيته ب1 في 1هنا C2 U2 سالب T زيد K2
+
+267
+00:23:57,780 --> 00:24:04,060
+لما ضبها في ال cosine بيصير constant في cosine زاد
+
+268
+00:24:04,060 --> 00:24:09,040
+اللي هو T أو سالب T في ال cosine constant في ال
+
+269
+00:24:09,040 --> 00:24:14,030
+cosine مش هى هذه يبقى التشابه قائمصحيح ولا لأ؟
+
+270
+00:24:14,030 --> 00:24:17,650
+يبقى لما حط الكهات بأصفار كل التشابه ده بيكون
+
+271
+00:24:17,650 --> 00:24:24,530
+اتخلص منه و يبقى مش السؤال ده بس كل سؤال بعدين مثل
+
+272
+00:24:24,530 --> 00:24:31,020
+حط الكهات هدول كلهم بأصفاريبقى بناء عليه هذا بده
+
+273
+00:24:31,020 --> 00:24:37,360
+يعطيك ان U1 as a function of T اللي حصلنا عليه
+
+274
+00:24:37,360 --> 00:24:44,120
+اللي هو LEN absolute value ل 6T زائد 10T
+
+275
+00:25:10,340 --> 00:25:13,940
+هذا هو حل الـ homogeneous ولا الـ non-homogeneous
+
+276
+00:25:15,730 --> 00:25:20,930
+الـ non homogeneous يبقى هذا اللي هو U واحد Y واحد
+
+277
+00:25:20,930 --> 00:25:28,330
+زائد U اتنين Y اتنين زائد U تلاتة Y تلاتة طيب ال U
+
+278
+00:25:28,330 --> 00:25:29,870
+واحد عندي هنا مجداش
+
+279
+00:25:36,620 --> 00:25:41,880
+وين ال U واحد؟ يبقى هايها بدها ضربها في جداش في
+
+280
+00:25:41,880 --> 00:25:46,680
+واحد إذا بتنزل زي ما هي يبقى هادا لين absolute
+
+281
+00:25:46,680 --> 00:25:57,750
+value ل 6T زائد تاني Tبعد ذلك U2Y2 وين Y2 هي Cos T
+
+282
+00:25:57,750 --> 00:26:07,110
+بدي أضرب في من؟ في سالب T يبقى سالب T Cos T بعد
+
+283
+00:26:07,110 --> 00:26:13,690
+ذلك C3 بدي أضرب مكان هي U3 يبقى بدي أضرب Sin T في
+
+284
+00:26:13,690 --> 00:26:20,390
+U3 يبقى زائد Sin T في Lin Cos T
+
+285
+00:26:23,360 --> 00:26:27,340
+جبت له ال particular solution، ايش ضال عليك؟ قال
+
+286
+00:26:27,340 --> 00:26:29,760
+لي هاتل ال general solution لل non homogeneous
+
+287
+00:26:29,760 --> 00:26:34,420
+differential equation بروح بقول له the general
+
+288
+00:26:34,420 --> 00:26:37,480
+solution
+
+289
+00:26:37,480 --> 00:26:52,240
+of equation 1 isY تساوي YC زائد capital Y of T
+
+290
+00:26:52,240 --> 00:27:00,280
+يساوي YC هي عندنا بنزله زي ما هو يبقى C1 زائد C2
+
+291
+00:27:00,280 --> 00:27:08,260
+في cos T C3 في sin T capital Y of T هي كله عندي
+
+292
+00:27:08,260 --> 00:27:17,600
+يبقى زائد لين absolute valueلسك ال T زائد تاني ال
+
+293
+00:27:17,600 --> 00:27:27,420
+T زائد sign ال T في ال N لكوصين ال T ناقص T في
+
+294
+00:27:27,420 --> 00:27:34,220
+كوصين ال T يبقى هذا هو الحل المطلوب حد فيكم بتحب
+
+295
+00:27:34,220 --> 00:27:40,020
+تسأل أي سؤال هنا؟ اه طويل شوية لكن برضه فكرته
+
+296
+00:27:40,020 --> 00:27:40,840
+جميلة جدا
+
+297
+00:27:54,450 --> 00:28:05,070
+نعطي مثال اخته
+
+298
+00:28:05,070 --> 00:28:08,850
+شباب
+
+299
+00:28:08,850 --> 00:28:14,330
+تسأل السؤال التالي بتقول لو كان g of t مثلا cosine
+
+300
+00:28:14,330 --> 00:28:18,530
+of tبنفع حل بال variation of parameter و بال
+
+301
+00:28:18,530 --> 00:28:22,150
+undetermined coefficients بشرط المعامل ثلاث ثوابت
+
+302
+00:28:22,150 --> 00:28:27,070
+اه و الله بنفع بالطريقتين لو حلتي بال variation of
+
+303
+00:28:27,070 --> 00:28:30,250
+parameter و بال undetermined coefficients اتنين صح
+
+304
+00:28:30,250 --> 00:28:34,610
+ماعنديش مشكلة ليش؟ لأن هذا اتفق حسب الجدول اللى
+
+305
+00:28:34,610 --> 00:28:37,670
+موجود في حالة ال undetermined coefficients و اتفق
+
+306
+00:28:37,670 --> 00:28:39,890
+معانا في حالة ال variation of parameter ماعنا
+
+307
+00:28:39,890 --> 00:28:46,560
+مشكلة في هذه الحالة تمام؟بنى للمثال رقم اتنين مثال
+
+308
+00:28:46,560 --> 00:28:54,460
+رقم اتنين بقول ما يأتي بقول given that اذا اعطيت
+
+309
+00:28:54,460 --> 00:29:06,360
+ان ال X و X تربيع and واحد على X are solutions are
+
+310
+00:29:06,360 --> 00:29:10,660
+solutions of
+
+311
+00:29:19,110 --> 00:29:27,890
+Homogeneous Differential Equation Corresponding To
+
+312
+00:29:40,560 --> 00:29:43,020
+المناظرة للمعادلة
+
+313
+00:30:14,040 --> 00:30:15,440
+Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''
+
+314
+00:30:19,760 --> 00:30:21,560
+a particular solution
+
+315
+00:31:04,720 --> 00:31:10,580
+سؤال مرة ثانية بقول لو كان هدول ثلاثة حلول لل
+
+316
+00:31:10,580 --> 00:31:14,440
+homogeneous differential equation المناظرة cross
+
+317
+00:31:14,440 --> 00:31:19,380
+bonding to المناظرة لمين؟ للمعادلة دي يعني كأن
+
+318
+00:31:19,380 --> 00:31:24,420
+المعادلة دي بس بدي أسويها بقداش بالسفر تمام يعني
+
+319
+00:31:24,420 --> 00:31:29,560
+هذه المعادلة الأصلية وحل ال homogeneous معطنية مش
+
+320
+00:31:29,560 --> 00:31:33,320
+لسه بيدوروا أدور عليه لأ جاي الحلول X و X تربيعه
+
+321
+00:31:33,320 --> 00:31:38,040
+مين؟واحد على X قال لي اذا كان الأمر كذلك determine
+
+322
+00:31:38,040 --> 00:31:43,740
+a particular solution بقوله اه احنا مشان نجيب ال
+
+323
+00:31:43,740 --> 00:31:48,580
+general solution بدي هدول التلاتة يكونوا linearly
+
+324
+00:31:48,580 --> 00:31:53,440
+independentأو هدول بيكونوا ال fundamental set of
+
+325
+00:31:53,440 --> 00:31:57,000
+solutions مش حيال الله حلول ومشي واجري صحيح ولا
+
+326
+00:31:57,000 --> 00:32:00,120
+لأ؟ لأن ال fundamental set of solutions هم اللي
+
+327
+00:32:00,120 --> 00:32:03,160
+بيجيبوا ال general solution لل homogeneous
+
+328
+00:32:03,160 --> 00:32:08,200
+differential equation يبقى أول شغلة بيختبر هل هدول
+
+329
+00:32:08,200 --> 00:32:12,340
+linearly independent ولا لأ؟ أو هل هدول بيكونوا ال
+
+330
+00:32:12,340 --> 00:32:17,150
+fundamental set of solution ام لا؟ واضح كلامي؟يبقى
+
+331
+00:32:17,150 --> 00:32:22,970
+بتروح اخد ايش المحدد تبع التلاتة هدول يبقى باجي
+
+332
+00:32:22,970 --> 00:32:27,350
+بقوله وطبعا المحدد ده ده هيفيدني في الحل بعد ذلك
+
+333
+00:32:27,350 --> 00:32:31,370
+مش يعني بداود و بروح .. لأ بنستفيد منه، اذا بتروح
+
+334
+00:32:31,370 --> 00:32:36,550
+اخد الwareness gain of X مش of T لإن المثل المكتوب
+
+335
+00:32:36,550 --> 00:32:39,850
+عندي كله بدلالة main X اللي هو ال independent
+
+336
+00:32:39,850 --> 00:32:45,500
+variableيبقى باجي بقوله الحل الأول اللي هو X والحل
+
+337
+00:32:45,500 --> 00:32:50,360
+الثاني X تربيه والثاني واحد على X تحب تخلي واحد
+
+338
+00:32:50,360 --> 00:32:56,620
+على X وانا اكتب X أثناق واحد X أثناق واحد ماعناش
+
+339
+00:32:56,620 --> 00:33:03,960
+مشكلة تمام بده نشتق يبقى واحد اتنين X سالب X أثناق
+
+340
+00:33:03,960 --> 00:33:13,410
+اتنينالصفة التالت ZERO اتنين اتنين X اصلاق اص
+
+341
+00:33:13,410 --> 00:33:18,850
+تلاتة وهي المحددبدي افكر محدد باستخدام عناصر
+
+342
+00:33:18,850 --> 00:33:24,250
+العمود الاول لشانه فيه صفر او عناصر الصف التالت
+
+343
+00:33:24,250 --> 00:33:28,790
+سيان هيك و الله هيك كله بيعطيني نفس النتيجة يبقى
+
+344
+00:33:28,790 --> 00:33:34,430
+هاد يا بنات X فيه بدي اشطب صفها و عمودها بيصير
+
+345
+00:33:34,430 --> 00:33:42,910
+جداش هنااربع اكس اص ناقص اتنين يبقى هنا اربع اكس
+
+346
+00:33:42,910 --> 00:33:49,230
+اص ناقص اتنين هذا الرئيسي ناقص مع ناقص بيصير زائد
+
+347
+00:33:49,230 --> 00:33:55,130
+اتنين اكس اص ناقص اتنين زائد اتنين اكس اص ناقص
+
+348
+00:33:55,130 --> 00:34:02,250
+اتنين يساء لسه كمان الحد اللي بعده بإشارتهاش سالب
+
+349
+00:34:02,250 --> 00:34:08,960
+حسب قعدة الإشاراتيبقى سالب واحد فيه بدي أجوب أشطب
+
+350
+00:34:08,960 --> 00:34:16,060
+صفه و عموده يبقى بصير هذا فهذا باتنين X أُس سالب
+
+351
+00:34:16,060 --> 00:34:19,020
+واحد يبقى اتنين
+
+352
+00:34:27,980 --> 00:34:34,460
+نقص اتنين اكس واس ناقص واحد ناقص اتنين اكس واس
+
+353
+00:34:34,460 --> 00:34:38,940
+ناقص واحد نقص اتنين اكس واس ناقص واحد نقص اتنين
+
+354
+00:34:38,940 --> 00:34:39,600
+اكس واس ناقص واحد نقص اتنين اكس واس ناقص واحد نقص
+
+355
+00:34:39,600 --> 00:34:45,740
+ناقص واحد نقص اتنين اكس واس ناقص واحد نقص اتنين
+
+356
+00:34:45,740 --> 00:34:49,580
+اكس واس ناقص واحد نقص اتنين اكس واس ناقص واحد نقص
+
+357
+00:34:49,580 --> 00:34:59,500
+اتنينزي 2x-1 يعني جداش 6 على x 6x-1 يعني 6 على x
+
+358
+00:34:59,500 --> 00:35:04,030
+هل هذا الكلب يسوي zero في يوم من الأيام؟طبعا لأ
+
+359
+00:35:04,030 --> 00:35:09,510
+لأنه اشترط في المثل ان x greater than 0 يبقى هذا
+
+360
+00:35:09,510 --> 00:35:17,430
+لا يمكن أن يساوي 0 مدام لا يساوي 0 سا اللي هو ال x
+
+361
+00:35:17,430 --> 00:35:23,450
+و ال x تربية and ال 1 على x are linearly
+
+362
+00:35:23,450 --> 00:35:30,010
+independentيعني يتكوّنوا لمين؟ ال general solution
+
+363
+00:35:30,010 --> 00:35:36,590
+تبع من؟ تبع ال homogeneous يعني هنا صار عندنا YC
+
+364
+00:35:36,590 --> 00:35:46,800
+بدي يساوي C1 X C2 X تربيهة C3 X أُص ناقص واحديبقى
+
+365
+00:35:46,800 --> 00:35:51,440
+هذا حل مين؟ حل ال homogenous differential equation
+
+366
+00:35:51,440 --> 00:35:56,320
+بدنا نيجي ل ال non homogenous ال runnerskin موجود
+
+367
+00:35:56,320 --> 00:35:59,080
+يبدأ يجيب ال runnerskin one و ال runnerskin two و
+
+368
+00:35:59,080 --> 00:36:03,860
+ال runnerskin three بس بدأ يطلع اه استرنا شوية طلع
+
+369
+00:36:03,860 --> 00:36:08,430
+في المعامل هنا قداشاكستاكيبك ممنوع يظل هذا
+
+370
+00:36:08,430 --> 00:36:13,030
+اكستاكيب اذا بروح اجسم طرفين المعادلة كله عالميا
+
+371
+00:36:13,030 --> 00:36:19,450
+على اكستاكيب فباجي بقوله هنا the differential
+
+372
+00:36:19,450 --> 00:36:28,910
+equation one is written as بروح اكتبه على الشكل
+
+373
+00:36:28,910 --> 00:36:34,190
+الجديديبقى y triple prime زي ما هو بتخلي المعاملة
+
+374
+00:36:34,190 --> 00:36:39,970
+تبعها واحد صحية زائد واحد على x في ال y double
+
+375
+00:36:39,970 --> 00:36:48,710
+prime اللي بعدها ناقص اتنين على x تربيع في ال y
+
+376
+00:36:48,710 --> 00:36:55,130
+prime جسمناها على x تكييف زائد اتنين على x تكييف
+
+377
+00:36:55,130 --> 00:37:02,770
+كله في ال yيساوي كده يا بنات؟ يساوي من X يبقى هذه
+
+378
+00:37:02,770 --> 00:37:06,970
+المعادلة اللي صارت هنا يبقى صارت هذه يا بنات هي
+
+379
+00:37:06,970 --> 00:37:13,630
+هذه G of T مش اللي عندنا هذه G of T لأن المعامل
+
+380
+00:37:13,630 --> 00:37:18,150
+هنا ماهوش واحد صحيح يبقى بيصير بالشكل اللي عندنا
+
+381
+00:37:19,130 --> 00:37:25,030
+بقدر اجيب من الرونس كين وان as a function of T
+
+382
+00:37:25,030 --> 00:37:32,930
+تكامل لل G of T ل .. لأ بدنا نجيب الرونس كين وان
+
+383
+00:37:32,930 --> 00:37:39,130
+احنا في الأول قبله الرونس كين وان of T يبقى يساوي
+
+384
+00:37:39,130 --> 00:37:43,530
+العمول الأولبدالي على المحدد اللي عندي و اشيله و
+
+385
+00:37:43,530 --> 00:37:49,570
+اكتب بداله 001 يبقى 001
+
+386
+00:37:50,020 --> 00:37:57,320
+اللي بعده X تربيع اتنين X اتنين اللي بعده X أسالب
+
+387
+00:37:57,320 --> 00:38:04,020
+واحد سالب X أسالب اتنين اتنين X أسالب تلاتة بدي
+
+388
+00:38:04,020 --> 00:38:09,860
+افكر محدد بالاستخدام عناصر العمود الأول يبقى يساوي
+
+389
+00:38:09,860 --> 00:38:17,350
+واحد فيهوشط بصفه و عموده بصير هنا اربعة اكس اثناق
+
+390
+00:38:17,350 --> 00:38:26,310
+اثنين يبقى اربعة اكس اثناق اثنين بصير
+
+391
+00:38:26,310 --> 00:38:33,350
+سالب واحد يبقى هنا بصير عندى هذا كله بجداشف سالب
+
+392
+00:38:33,350 --> 00:38:40,830
+واحد وهنا سالب اتنينسالف اتنين يبقى الجواب كده؟
+
+393
+00:38:40,830 --> 00:38:47,130
+سالف تلاتة كونستر بعد ذلك بروح أجيب الرونسكين 2 as
+
+394
+00:38:47,130 --> 00:38:53,870
+a function of T برجع العمود الأول كما كان X واحد
+
+395
+00:38:53,870 --> 00:39:00,660
+زيرو العمود التاني Zero Zero واحدالثالث كما هو
+
+396
+00:39:00,660 --> 00:39:05,760
+يبقى x أوص ناقص واحد ناقص x أوص ناقص اتنين x أوص
+
+397
+00:39:05,760 --> 00:39:12,280
+ناقص تلاتة و يساوي بدا افكس المحدد باستخدام عناصر
+
+398
+00:39:12,280 --> 00:39:17,560
+العمودي الثاني لان هو اللي فيه الصفات يبقى حسب
+
+399
+00:39:17,560 --> 00:39:23,800
+قاعة الإشارات هذا إشارته ايه؟سالبة يبقى سالب واحد
+
+400
+00:39:23,800 --> 00:39:30,220
+وبدنا نروح نشطه بصفه و عموده بيضل لإن هنا قداش
+
+401
+00:39:30,220 --> 00:39:36,680
+اللي هو سالب X والسالب واحد يبقى سالب X والسالب
+
+402
+00:39:36,680 --> 00:39:43,280
+واحد هي عندنا الرئيسي ناقص X والسالب واحد ناقص X
+
+403
+00:39:43,280 --> 00:39:50,890
+والسالبواحد يبقى ناقص في ناقص بزايد وبضال عند هنا
+
+404
+00:39:50,890 --> 00:39:56,590
+اتنين على اكس اتنين اكس قص ناقص واحد يبقى اتنين
+
+405
+00:39:56,590 --> 00:40:02,270
+على اكس استاذ ليش الواحد ثالث؟ اللي هنيط منهم هذا
+
+406
+00:40:02,270 --> 00:40:06,910
+سمعت وقعت شرط المحددات في الثانوي لما كنت تفكر
+
+407
+00:40:06,910 --> 00:40:12,250
+محدد ثلاثيزائد، ناقص، زائد، ناقص، زائد، ناقص،
+
+408
+00:40:12,250 --> 00:40:18,230
+زائد، ناقص، زائد،
+
+409
+00:40:18,230 --> 00:40:22,270
+ناقص،
+
+410
+00:40:22,270 --> 00:40:25,510
+زائد، ناقص، زائد، ناقص، زائد، ناقص، زائد، ناقص،
+
+411
+00:40:25,510 --> 00:40:29,850
+زائد، ناقص، زائد، ناقص، زائد، ناقص، زائد، ناقص،
+
+412
+00:40:29,850 --> 00:40:29,890
+زائد، ناقص، زائد، ناقص، زائد، ناقص، زائد، ناقص،
+
+413
+00:40:29,890 --> 00:40:34,470
+زائد، ناقص، زائد، ناقص، زائد، ناقص، زائد، ناقصيبقى
+
+414
+00:40:34,470 --> 00:40:39,130
+حسب قعة الإشارات، الإشارة تبعت معلها بالسالب، يبقى
+
+415
+00:40:39,130 --> 00:40:44,820
+هذه العنصر اللي احنا بنحل بواسطتهيبقى حسب قاعدة
+
+416
+00:40:44,820 --> 00:40:49,280
+الإشارات إشارته مين؟ سالب يبقى الواحد هذا إشارته
+
+417
+00:40:49,280 --> 00:40:55,020
+سالب حسب قاعدة الإشارات قشط بصفه عموده بصير ناقص
+
+418
+00:40:55,020 --> 00:40:59,760
+إكسوس ناقص واحد ناقص إكسوس ناقص واحد يعني اتنين
+
+419
+00:40:59,760 --> 00:41:05,220
+إكسوس ناقص واحد يعني اتنين على إكس هذا الرونسكين
+
+420
+00:41:05,220 --> 00:41:05,900
+اتنين
+
+421
+00:41:10,810 --> 00:41:16,830
+العمود الأول زي ما هو مش هنغيره و العمود الثاني
+
+422
+00:41:16,830 --> 00:41:22,770
+كمان مش هنغيره بناروح للعمود التالت و نشيله و نحط
+
+423
+00:41:22,770 --> 00:41:25,330
+بداله 001
+
+424
+00:41:27,400 --> 00:41:35,200
+عناصر العمود الثالث باستخدام
+
+425
+00:41:35,200 --> 00:41:37,160
+المحدد
+
+426
+00:41:39,070 --> 00:41:46,590
+موجب يبقى أي واحد فيه اشط بصفه و عموده بصيلي اتنين
+
+427
+00:41:46,590 --> 00:41:54,630
+اكس تربيع ناقص اكس تربيع يبقى الجواب كده اكس تربيع
+
+428
+00:41:54,630 --> 00:41:59,970
+فقط لغير يبقى جنب ترونسكني التلاتة يبقى الان سهل
+
+429
+00:41:59,970 --> 00:42:07,500
+علي اجيب من اليهات التلاتة عندى يبقى بدنا نروحنجيب
+
+430
+00:42:07,500 --> 00:42:14,980
+U1 و U2 و U3 باستخدام التكامل
+
+431
+00:42:19,700 --> 00:42:24,440
+يبقى بدى أروح أجيب له main اللي هو U1 as a
+
+432
+00:42:24,440 --> 00:42:33,480
+function of X يا بنات مش of T كله X كله X كله X
+
+433
+00:42:33,480 --> 00:42:39,180
+ماعنديش T المثلة كلها بدلالة من؟ صح هي كلها بدلالة
+
+434
+00:42:39,180 --> 00:42:44,600
+من؟ بدلالة ال X يبقى U1 as a function of X تكامل
+
+435
+00:42:44,600 --> 00:42:52,760
+ال G of Xفى ال run skin 1 of X على ال run skin of
+
+436
+00:42:52,760 --> 00:42:59,480
+X كله as a function of X يساوي تكامل ال G of X
+
+437
+00:42:59,480 --> 00:43:05,500
+اللي يجى ده صارت ان اتنين X مش اربعة X تربية يبقى
+
+438
+00:43:05,500 --> 00:43:09,420
+هنا اتنين X هى نزلناها زى ما هي
+
+439
+00:43:13,370 --> 00:43:20,370
+سالب تلاتة يبقى سالب تلاتة على الرونسكين حسبناه
+
+440
+00:43:20,370 --> 00:43:28,390
+قبل شوية فكان جديش ستة على اكس يبقى هذا ستة على
+
+441
+00:43:28,390 --> 00:43:35,420
+اكس كله في DXأما 6 مع 6 مع السلامة و ال X بتطلع
+
+442
+00:43:35,420 --> 00:43:46,620
+فوق بيبقى سالب تكامل X تربيع DX 2 في 3 بال 6 مع 6
+
+443
+00:43:46,620 --> 00:43:51,960
+ال X تطلع فوق بيصير X تربيع والسالب برا يبقى هنا
+
+444
+00:43:51,960 --> 00:44:01,900
+سالب X تكيب على 3 زائد K1بعد ذلك بناروح نجيب ال U2
+
+445
+00:44:01,900 --> 00:44:09,760
+integration لل G of T لمين؟ للرونسكين 2 of T على
+
+446
+00:44:09,760 --> 00:44:16,860
+ال رونسكين of T كله في DT يسوى تكامل لل 2X في
+
+447
+00:44:16,860 --> 00:44:24,410
+رونسكين 2 رونسكين 2 لم يبقى داش ب2 على Xيبقى هذا
+
+448
+00:44:24,410 --> 00:44:33,990
+اتنين على اكس كله على ستة على اكس دي اكس يساوي اظن
+
+449
+00:44:33,990 --> 00:44:38,390
+ان ال X هذه مع ال X هذه مع السلامة بيطير و بيظل
+
+450
+00:44:38,390 --> 00:44:44,350
+عندى اتنين في اتنين باربع يعني اربع على ستة يبقى
+
+451
+00:44:44,350 --> 00:44:52,270
+اربع على ستة تكامل لل X DXهذه البنات بتروح مع هذه
+
+452
+00:44:52,270 --> 00:44:56,090
+مضال اتنين في اتنين اللي هو باربع ستة خليك برا
+
+453
+00:44:56,090 --> 00:44:59,330
+مضال واحد على X بتنقل بال X فوت بيصير بالشكل اللي
+
+454
+00:44:59,330 --> 00:45:05,550
+عندنا هذا يبقى هذه كأنها تلتين في X تربيع على
+
+455
+00:45:05,550 --> 00:45:15,930
+اتنين زائد constant K2 يعني تلت X تربيع زائد K2
+
+456
+00:45:18,070 --> 00:45:25,090
+بالمثل بناروح نجيب U3 يبقى هى تكاهة طبعا كله Xاتي
+
+457
+00:45:25,090 --> 00:45:33,150
+بنات مش T كله بدلالة ال X هذا كله بدلالة ال X احنا
+
+458
+00:45:33,150 --> 00:45:37,950
+معالجة معانا هدى ال T لأ هدى مظبوط اكتبنا صح ده بس
+
+459
+00:45:37,950 --> 00:45:44,330
+هدى و كله بدالة X مظبوططيب يبقى هذه الـ g of x في
+
+460
+00:45:44,330 --> 00:45:48,990
+الورنسكين three of x على الورنسكين as a function
+
+461
+00:45:48,990 --> 00:45:55,750
+of x dx يبقى تكامل للإتنين x فيه الورنسكين three
+
+462
+00:45:55,750 --> 00:46:02,930
+of x كله بيبقى داش بx تربيع يبقى بx تربيع لمين؟
+
+463
+00:46:02,930 --> 00:46:11,600
+لستة على x كله بالنسبة إلى dxأتنين على ستة بجداش
+
+464
+00:46:11,600 --> 00:46:19,540
+بطول تكامل هذي تطلع فوق بصير جداش أبناء X أص أربعة
+
+465
+00:46:19,540 --> 00:46:24,880
+X تكيب و تجيب و تكمل تصير X أص أربعة DX يبقى هذي
+
+466
+00:46:24,880 --> 00:46:33,600
+تلت و هذي X أص خمسة على خمسة زائد constant K3 يعني
+
+467
+00:46:33,600 --> 00:46:42,850
+واحد على خمستاشر X أص خمسةزائد كنستان K3 الان نقول
+
+468
+00:46:42,850 --> 00:46:51,910
+له take خدلي K1 يسوى K2 يسوى K3 يسوى Zero وعرفته
+
+469
+00:46:51,910 --> 00:46:59,530
+ليش مصبوط يبقى بده أروح أجيبله capital Y of Tاللي
+
+470
+00:46:59,530 --> 00:47:11,490
+هو U1 وY1 زائد U2 وY2 زائد U3 وY3 وY7 الآن نجي الى
+
+471
+00:47:11,490 --> 00:47:17,590
+ال U1 ال U1 ماني قاعد ابدأ عشان ناقص تلت X تكيب
+
+472
+00:47:17,590 --> 00:47:26,750
+يبقى ناقص تلت X تكيب فمين؟ في Y1 اللي هو X اللي
+
+473
+00:47:26,750 --> 00:47:35,870
+بعدهبنجي لـ U2 الـ U2 لتلت X تربية زائد تلت X
+
+474
+00:47:35,870 --> 00:47:44,010
+تربية في من؟ في X تربية نجي لبعده U3 يبقى زائد
+
+475
+00:47:44,010 --> 00:47:51,250
+واحد على خمستاشر X أس خمسة في X أس ناقص واحد ايش
+
+476
+00:47:51,250 --> 00:47:57,120
+رأيك؟ هذي هي هذي بيشارة مخالفة صح؟يبقى يجروا
+
+477
+00:47:57,120 --> 00:48:01,640
+الفاتحة انا روحهم على السلامة بضل ان اقدرش واحد
+
+478
+00:48:01,640 --> 00:48:07,380
+على خمستاشر X أُس أربعة هذا ال particular solution
+
+479
+00:48:07,380 --> 00:48:11,480
+لل differential equation one اذا بقدر اجيب له من
+
+480
+00:48:11,480 --> 00:48:17,680
+ال general solution فبروح بقول له هنا the general
+
+481
+00:48:17,680 --> 00:48:31,160
+solution of the equationone is Y تساوي YC زائد
+
+482
+00:48:31,160 --> 00:48:42,360
+capital Y of T YC هي فوق تمام اللي هو C كيف؟
+
+483
+00:48:42,360 --> 00:48:47,280
+بس طالب ال particular خلاص والله نايحنا يبقى خلاص
+
+484
+00:48:47,280 --> 00:48:51,680
+بروزي هذا والله يعطيك العافية خلاص هذا مسامحي نفيد
+
+485
+00:48:54,290 --> 00:48:56,990
+خلاص من الناياط دي على جد المقبض زي ما دي بناكوس
+
+486
+00:48:56,990 --> 00:49:00,190
+في الامتحان don't evaluate اللي كنت أصلا تبقى حاطة
+
+487
+00:49:00,190 --> 00:49:02,590
+تاريخ بين جوسينة بخاط غامج و اللي جات بعض الناس
+
+488
+00:49:02,590 --> 00:49:06,230
+لسه بتروح تحسبلي في الكون أصلا بتضيع وقت هالبلاش
+
+489
+00:49:06,230 --> 00:49:11,950
+طب أنا مش طالب و تشتغلي ليش طيب
+
+490
+00:49:24,680 --> 00:49:29,480
+في عندكوا في الكتاب مجموعة من المسائل وكتبليك جي
+
+491
+00:49:29,480 --> 00:49:33,360
+وف ت بدلالة جي وف ت مخلية مش ميعطيكي قيمة إلها
+
+492
+00:49:33,360 --> 00:49:37,980
+وقالليك حلي بتقدر تكمليها هذه؟ مش هتقدر تكمليها،
+
+493
+00:49:37,980 --> 00:49:42,980
+بدنا نعطيكوا مثال منهم ونوريكوا كيف بنحل هذا النوع
+
+494
+00:49:42,980 --> 00:49:47,860
+من الأسئلة حد لاقي تساول هنا قبل ما نتقل إلى
+
+495
+00:49:47,860 --> 00:49:52,920
+المثال الثالث؟ حد فيكوا لاقي تساول هنا؟
+
+496
+00:50:12,000 --> 00:50:22,160
+مثال رقم تلاتة رقم تلاتة رقم تلاتة رقم تلاتة
+
+497
+00:50:22,160 --> 00:50:28,840
+رقم تلاتة رقم تلاتة رقم تلاتة رقم تلاتة رقم
+
+498
+00:50:28,840 --> 00:50:30,680
+تلاتة رقم تلاتة رقم تلاتة رقم تلاتة رقم تلاتة رقم
+
+499
+00:50:30,680 --> 00:50:30,720
+تلاتة رقم تلاتة رقم تلاتة رقم تلاتة رقم تلاتة رقم
+
+500
+00:50:30,720 --> 00:50:37,940
+تلاتة رقم تلاتة رقم تلاتة
+
+501
+00:50:37,940 --> 00:50:39,280
+رقم ت
+
+502
+00:50:48,610 --> 00:51:00,190
+مجتمل على التكاملات of a particular solution
+
+503
+00:51:00,190 --> 00:51:07,650
+of a particular solution of the
+
+504
+00:51:14,160 --> 00:51:21,380
+مشتقة تالتة ل Y ناقص المشتقة الثانية ل Y زائد
+
+505
+00:51:21,380 --> 00:51:28,500
+المشتقة الأولى ل Y ناقص Y بدون مشتقة يساوي G of T
+
+506
+00:51:28,500 --> 00:51:31,580
+وهذا المعادلة رقم واحد
+
+507
+00:51:54,450 --> 00:52:00,530
+Find a formula هاتل صيغة مجتملة على التكاملات تبع
+
+508
+00:52:00,530 --> 00:52:03,310
+ال particular solution لل differential equation
+
+509
+00:52:03,310 --> 00:52:06,710
+اللي عندنايعني فعلا ماعطيني معادلة تفاضلي و بذا
+
+510
+00:52:06,710 --> 00:52:11,570
+شكل لكن الطرف اليمين كاتب و كدالة انا مش عارفة g
+
+511
+00:52:11,570 --> 00:52:15,030
+of t مين ما تكون تكون مش بعطيني زي السؤال يجابله
+
+512
+00:52:15,030 --> 00:52:18,950
+ده اللي بقعد نضربه و نختصره و نكامله إذا هذا هضل
+
+513
+00:52:18,950 --> 00:52:23,570
+بدلالة مين بدلالة التكامل التكتيك اللي اتبع في
+
+514
+00:52:23,570 --> 00:52:26,670
+المثالين اللي جابله هو نفس التكتيك هذا اللهم إلا
+
+515
+00:52:26,670 --> 00:52:31,050
+بقدرش أكامل فبضل التكامل موجود وانفي المسألة كما
+
+516
+00:52:31,050 --> 00:52:35,830
+هو إذا أنا بدي أبدأ في حل ال homogeneous ثم ال non
+
+517
+00:52:35,830 --> 00:52:44,950
+homogeneous يبقى باجي بقوله solution let
+
+518
+00:52:44,950 --> 00:52:58,880
+y تساوي e أس RTBA solution of theEquation للمعادلة
+
+519
+00:52:58,880 --> 00:53:04,580
+Y triple prime ناقص Y double prime زائد Y prime
+
+520
+00:53:04,580 --> 00:53:11,000
+ناقص Y يسوى 0 هو ال homogenous يبقى then the
+
+521
+00:53:11,000 --> 00:53:21,020
+characteristic equation is R تكييف ناقص R تربيع
+
+522
+00:53:21,020 --> 00:53:27,790
+زائد R ناقص 1 يسوى 0الغلطة اللى كنت اشوفها من
+
+523
+00:53:27,790 --> 00:53:33,290
+بعضكوا في الامتحان و تكتبلي هذه R اه و هذه غلطة
+
+524
+00:53:33,290 --> 00:53:37,210
+فاحشة كبيرة جدا من الكبائر بالنسبة لنا في الامتحان
+
+525
+00:53:37,210 --> 00:53:42,660
+طيب نيجي نحل المعادلة اللى عندنا هذهطلعيلي في هدول
+
+526
+00:53:42,660 --> 00:53:47,640
+اتنين ممكن اخد منهم R تربية عام المشترك اذا لو
+
+527
+00:53:47,640 --> 00:53:52,000
+اخدت R تربية عام المشترك بيظل كده؟ R ناقص واحد
+
+528
+00:53:52,000 --> 00:53:58,200
+وعندي ضايل هناك R ناقص واحد يساوي Zeroإذا أنا ممكن
+
+529
+00:53:58,200 --> 00:54:04,940
+أخد من الطرفين R ناقص واحد عامل مشترك مضل من الجزء
+
+530
+00:54:04,940 --> 00:54:10,860
+الأول قداش R تربيع مضل من الجزء الثاني قداش واحد
+
+531
+00:54:10,860 --> 00:54:16,400
+صحيح يبقى زائد واحد يساوي zero من هذه المعادلة
+
+532
+00:54:16,400 --> 00:54:23,160
+بقدر أقول ان R واحد يساوي واحدوR2 وR3 يبدو يساوي
+
+533
+00:54:23,160 --> 00:54:29,360
+الزائد او ناقص اذا اصبح حل ال homogeneous هو YC
+
+534
+00:54:29,360 --> 00:54:38,040
+يساوي C1A أس 1 في T يبقى A أس T هدول Complex يبقى
+
+535
+00:54:38,040 --> 00:54:45,500
+زائد C2 Cos T زائد C3 في Sin T
+
+536
+00:54:50,080 --> 00:54:55,140
+يبقى هذا حل مين اللي هو اللي هو مجازف طبعا هو جالي
+
+537
+00:54:55,140 --> 00:54:58,480
+formula محتوية على ال integral لل particular
+
+538
+00:54:58,480 --> 00:55:02,700
+solution بده شكل ال particular solution كويس ال
+
+539
+00:55:02,700 --> 00:55:07,700
+particular solution يبقى بده شيل C1 وC2 وC3 وحق
+
+540
+00:55:07,700 --> 00:55:14,000
+بدلها مين U1 وU2 وU3 بس قبل بدك تحسب ال runnerskin
+
+541
+00:55:14,000 --> 00:55:20,770
+للحلول التلاتة هذهو بعد هيك الله بيفرجها يبقى بناء
+
+542
+00:55:20,770 --> 00:55:26,070
+عليها لو جبت أخدت ال رونسكين as a function of T
+
+543
+00:55:26,070 --> 00:55:32,930
+يبقى باجي بقوله هذا الحل الأول E was T و الحل
+
+544
+00:55:32,930 --> 00:55:39,280
+التاني cosine T و الحل التالت sin Tبدي اشتق
+
+545
+00:55:39,280 --> 00:55:44,000
+المشتقة الاولى ال exponential كما هي هذه ناقص sin
+
+546
+00:55:44,000 --> 00:55:50,020
+t هذه cosine t بدي اشتق كمان مرة يبقى ال
+
+547
+00:55:50,020 --> 00:55:56,120
+exponential كما هي وهذه ناقص cosine t وهذه ناقص
+
+548
+00:55:56,120 --> 00:56:03,260
+sin t وهي المحدد بدي احسب قداش قيمة هذا المحدد
+
+549
+00:56:03,260 --> 00:56:04,960
+ويساوي
+
+550
+00:56:07,510 --> 00:56:12,410
+ممكن بلغة المحادثة بالخاص اخد Eost عامل مشترك من
+
+551
+00:56:12,410 --> 00:56:16,890
+العمود الأول يصبح واحد واحد واحد هو هكتب المحادثة
+
+552
+00:56:16,890 --> 00:56:21,530
+يعني قصة طويلة وشيء لكن انا بده افك دغري باستخدام
+
+553
+00:56:21,530 --> 00:56:25,670
+العمود الأول باستخدام الصف الأول بأي حاجة ماشية
+
+554
+00:56:25,670 --> 00:56:31,690
+على خليني افك باستخدام العمود الأول يبقى هذا بده
+
+555
+00:56:31,690 --> 00:56:38,920
+يساوي Eost فيهيبقى بتروح أشته بصفه و عموده يبقى يا
+
+556
+00:56:38,920 --> 00:56:44,680
+بنات كده؟ sin تربيه زائد cosine تربيه يبقى هذه
+
+557
+00:56:44,680 --> 00:56:51,960
+الـsin تربيه T زائد cosine تربيه T انتهينا منها
+
+558
+00:56:51,960 --> 00:56:57,300
+يهودة هذه حسب قاعدة الإشارات وجب الله سالب كده؟
+
+559
+00:56:57,810 --> 00:57:06,030
+يبقى هاي ناقص E of T فيه بتروح عشته بصفه و عموده
+
+560
+00:57:06,030 --> 00:57:16,890
+بصير سالب sin cos وموجب sin cos يبقى سالب sin T
+
+561
+00:57:16,890 --> 00:57:27,730
+cos T زائد sin T cos Tخلصنا منها وضل ال term
+
+562
+00:57:27,730 --> 00:57:34,310
+التالت حسب قاعدة الإشارات AOST فين يبقى بننشته
+
+563
+00:57:34,310 --> 00:57:40,450
+بصفه و عموده بصير cosine تربيه زائد sine تربيه
+
+564
+00:57:40,450 --> 00:57:48,990
+يبقى cosine تربيه T زائد sine تربيه T ويسافر اظن
+
+565
+00:57:48,990 --> 00:57:53,160
+ان هذه راحة في ال zero يا بناتطيب بضل هذه قداش
+
+566
+00:57:53,160 --> 00:58:00,240
+واحد ل Eost و هنا واحد في Eost يبقى الجواب كله
+
+567
+00:58:00,240 --> 00:58:07,560
+اتنين Eost واضح ماله لا يساوي Zero إذا الحلول اللي
+
+568
+00:58:07,560 --> 00:58:11,720
+جيبناها دول منهمبكونولي ال fundamental set of
+
+569
+00:58:11,720 --> 00:58:18,960
+solutions أو linearly independent يبقى هنا الـ E
+
+570
+00:58:18,960 --> 00:58:22,420
+أُس T E أُس T E أُس T E أُس T E أُس T E أُس T E
+
+571
+00:58:22,420 --> 00:58:23,440
+أُس T E أُس T E أُس T E أُس T E أُس T E أُس T E
+
+572
+00:58:23,440 --> 00:58:27,400
+أُس T E أُس T E أُس T E أُس T E أُس T E أُس T E
+
+573
+00:58:27,400 --> 00:58:28,500
+أُس T E أُس T E أُس T E أُس T E أُس T E أُس T E
+
+574
+00:58:28,500 --> 00:58:28,700
+أُس T E أُس T E أُس T E أُس T E أُس T E أُس T E
+
+575
+00:58:28,700 --> 00:58:31,850
+أُس T E أُس T E أُس T E أُس T E أُس Tما دام
+
+576
+00:58:31,850 --> 00:58:36,850
+linearly independent هذا بدي يعطينا انه حل ال
+
+577
+00:58:36,850 --> 00:58:41,370
+homogeneous هو ما احنا كتبناه صحيح فوق خلاص و هذا
+
+578
+00:58:41,370 --> 00:58:44,890
+مش لازمني بس كويس ان اتأكدنا انهم linearly
+
+579
+00:58:44,890 --> 00:58:49,520
+independent و جيبنا ايه؟ اللي هو الرونسكينبتجيب ال
+
+580
+00:58:49,520 --> 00:58:54,040
+runskin1 و runskin2 و runskin3 يبقى بتجيب ال
+
+581
+00:58:54,040 --> 00:58:59,040
+runskin1 as a function of t بس قبلها بتروح اتكد
+
+582
+00:58:59,040 --> 00:59:04,420
+المعامل هنا قداش يبقى احنا جاهزين يبقى هذا الكلام
+
+583
+00:59:04,420 --> 00:59:10,060
+ها بدنا نجيب ال runskin1 ال runskin1 هو المحدد
+
+584
+00:59:10,060 --> 00:59:13,600
+اللي هو 001
+
+585
+00:59:31,110 --> 00:59:37,330
+يبقى العمودين اتنين زي مهمة بدنا نفك هذه المحددات
+
+586
+00:59:37,330 --> 00:59:44,670
+باستخدامالعمود الأول يبقى واحد فيه اشط بصفه عموده
+
+587
+00:59:44,670 --> 00:59:50,990
+يبقى sin تربيه زائد cos تربيه يبقى sin تربيه T
+
+588
+00:59:50,990 --> 00:59:56,880
+زائد cos تربيه T كله يساوي جداشالواحد بدنا نيجر
+
+589
+00:59:56,880 --> 01:00:03,060
+رونسكين 2 as a function of T يبقى على العمود الأول
+
+590
+01:00:03,060 --> 01:00:11,840
+Eost Eost Eost العمود التاني 001 العمود التالت هو
+
+591
+01:00:11,840 --> 01:00:21,860
+sin T وcos T و- sin T بالشكل اللي عندنابتفكر محدد
+
+592
+01:00:21,860 --> 01:00:27,240
+باستخدام عناصر العمود الثانية حسب قاعدة الإشارات
+
+593
+01:00:28,040 --> 01:00:35,100
+سالبة يبقى هذا الكلام سالب واحد فيه اشط بصفه عموده
+
+594
+01:00:35,100 --> 01:00:41,260
+بيصير E of T cosine ناقص E of T sin يبقى E of T
+
+595
+01:00:41,260 --> 01:00:50,440
+cosine T ناقص E of T في sin T يعني هذه كأنها sin T
+
+596
+01:00:50,440 --> 01:00:57,950
+ناقص cosine T كله في ال exponential E of Tبالمرة
+
+597
+01:00:57,950 --> 01:01:04,090
+نجيب الرانس كيني 3 as a function of T العمود الأول
+
+598
+01:01:04,090 --> 01:01:11,510
+كما هو بدون تغيير العمود الثاني كما هو برضه زيه
+
+599
+01:01:11,510 --> 01:01:18,230
+بدون تغيير و هنا ناقص cosine of T والعمود التالت
+
+600
+01:01:18,230 --> 01:01:24,370
+اللي هو 001بدا فك المحدد باستخدام عناصر العمود
+
+601
+01:01:24,370 --> 01:01:30,670
+الثالث يبقى هذا الكلام يساوي حسب قاعة الإشارات
+
+602
+01:01:30,670 --> 01:01:39,230
+شرطه بالموجب يبقى في شطاب نصفه وعموده يبقى سالب
+
+603
+01:01:39,230 --> 01:01:49,550
+sin T في Eost وسالب cosine يبقى سالب Eost في sin T
+
+604
+01:02:06,540 --> 01:02:12,380
+خلصنا من الرونسكينز التلاتة اذا بقدر اجيب ال U1 و
+
+605
+01:02:12,380 --> 01:02:20,030
+U2 و U3 بدي اجيب ال U1 as a function of Tيبقى
+
+606
+01:02:20,030 --> 01:02:26,630
+تكامل جي او ت في رونسكين one او ت على رونسكين او ت
+
+607
+01:02:26,630 --> 01:02:33,810
+دي ت طيب ايش رايكوا بدل ما كل مرة احط كونصان هو
+
+608
+01:02:33,810 --> 01:02:38,390
+ايش رايكوا يخليه تكامل محدود وبالتالي يتخلص من جزء
+
+609
+01:02:38,390 --> 01:02:44,130
+ال رونسكين هذه تمام كيف يخليه تكامل محدود بقولك من
+
+610
+01:02:44,130 --> 01:02:51,260
+عندي ال T ناد لغاية ال Tمن الـ T node أي نقطة
+
+611
+01:02:51,260 --> 01:02:56,220
+موجودة على الهدى الدوال عليها continuous المعاملات
+
+612
+01:02:56,220 --> 01:02:59,640
+الدوال اللي عندي بما فيهم جيوبتي continuous على
+
+613
+01:02:59,640 --> 01:03:04,360
+الفترة من T node لغاية T node نقطة ثابتة تمام؟
+
+614
+01:03:04,360 --> 01:03:08,820
+وعند أي نقطة الدوال هذه متفق علينا تكون معرفة
+
+615
+01:03:08,820 --> 01:03:12,760
+عندها أو continuous عندنا ماشي العالم؟وبالتالي ما
+
+616
+01:03:12,760 --> 01:03:15,920
+كامل بقولش زي ال constant لا K واحد ولا K اتنين
+
+617
+01:03:15,920 --> 01:03:21,620
+ولا K تلاتة بمشي لها طيب بدها تسأل هو ده كمان سؤال
+
+618
+01:03:21,620 --> 01:03:26,320
+لو سويتك بده تقولي طب استنى شوية انت كاتب من T
+
+619
+01:03:26,320 --> 01:03:30,880
+node ل T قولتله صح قال يعني حدود التكامل T طب
+
+620
+01:03:30,880 --> 01:03:36,050
+المتغير اللي جهوه T بنفع؟عندما أقول يا كامل يجب أن
+
+621
+01:03:36,050 --> 01:03:41,510
+أشيل T و أضع مكانها T فالكلام ليس صحيح يبقى لو
+
+622
+01:03:41,510 --> 01:03:50,590
+روحت تغيرت ال T هذي و قلت هك GS WS و هنا WS و هنا
+
+623
+01:03:50,590 --> 01:03:57,990
+DSيبقى لما نكام نبتطلع دالة بدلالة S لما عوض بحدود
+
+624
+01:03:57,990 --> 01:04:02,950
+التكمل هذا الرقم و هذا T بصير كلها بدلالة T يبقى
+
+625
+01:04:02,950 --> 01:04:07,130
+ماقناششي مظبوط و اتريحنا من خلجة ال constant هذا
+
+626
+01:04:07,130 --> 01:04:11,440
+اللي بزهجنا كل مرة طلع و تقوم بالصفةمظبوط؟ طيب
+
+627
+01:04:11,440 --> 01:04:18,920
+كويس، إذا بده يصير هذا تكامل من T node إلى T للـG
+
+628
+01:04:18,920 --> 01:04:26,200
+of S كما هي ون هي وقدام اللي هي بواحد، يبقى في
+
+629
+01:04:26,200 --> 01:04:32,680
+واحد على مين؟ على الـW، وين الـW؟هذا الـ W له
+
+630
+01:04:32,680 --> 01:04:42,200
+اتنين EOS يبقى اتنين EOS S كله في DS يعني يا نص
+
+631
+01:04:42,200 --> 01:04:49,200
+خليك برا مالكش دعوة وهي تكامل من T node إلى T للـ
+
+632
+01:04:49,200 --> 01:04:58,800
+GRS على EOS S أو الـ EOS ناقص Sيالا خلّيني أطلعها
+
+633
+01:04:58,800 --> 01:05:01,700
+فوق و بلاشي نخلّي عندنا إيش في المقامات و إيش في
+
+634
+01:05:01,700 --> 01:05:05,400
+ال bus يبقى هذي لو طلعتها فوق إيش بصير يا بنات
+
+635
+01:05:05,400 --> 01:05:16,460
+بصير E أس ناقص S في ال G of S في ال D أس طيب هات
+
+636
+01:05:16,460 --> 01:05:23,340
+لل U2 باجي بقوله U2 as a function of T تكاملمن T
+
+637
+01:05:23,340 --> 01:05:30,880
+node ل T لل G of S لل one skin two as a function
+
+638
+01:05:30,880 --> 01:05:38,240
+of S على one skin of S كله بالنسبة الى DS يسوى
+
+639
+01:05:38,240 --> 01:05:47,300
+تكامل من عند T node لغاية T G of S خليك زي ما انت
+
+640
+01:05:48,390 --> 01:05:53,410
+ماعناش مشكلة معاك ابني جامين لغنس كنتو اللي هو
+
+641
+01:05:53,410 --> 01:06:00,370
+عنهانة يبقى بقدر أقوله sign s ناقص cosine s في E
+
+642
+01:06:00,370 --> 01:06:12,950
+أُس S يبقى أي قوس sign ال Sماقس cosine ال S كله E
+
+643
+01:06:12,950 --> 01:06:21,050
+أُس S على مين؟ على اتنين E أُس S كله بالنسبة إلى
+
+644
+01:06:21,050 --> 01:06:29,610
+DS تمام؟ يبقى هذا الكلام يشاويتختصر هذه مع هذه مع
+
+645
+01:06:29,610 --> 01:06:36,610
+السلامة والنص شرفنا برا يبقى هذا الكلام نص تكامل
+
+646
+01:06:36,610 --> 01:06:45,210
+من T node لغاية T لمين ل sign ال S ناقص cosine ال
+
+647
+01:06:45,210 --> 01:06:49,910
+S كله في GS في DS
+
+648
+01:06:58,000 --> 01:07:03,200
+أحنا بدنا بس ايش ال particle of solution الصيغة
+
+649
+01:07:03,200 --> 01:07:15,320
+تبعت المجتمل على التكامل طيب
+
+650
+01:07:15,320 --> 01:07:24,330
+بدنا نيجي لأ ل U3 of T U3 of Tيسوي تكامل من T node
+
+651
+01:07:24,330 --> 01:07:32,030
+لغاية T للـ G of S في الرونسكين 3 as a function of
+
+652
+01:07:32,030 --> 01:07:40,210
+S على الرونسكين as a function of SDS ويسوي تكاملمن
+
+653
+01:07:40,210 --> 01:07:45,710
+T نوت ل T للـ G of S نحن نذهب إلى الـ Roneskini 3
+
+654
+01:07:45,710 --> 01:07:52,170
+الـ Roneskini 3 هو السالب عندنا يبقى نكتبه بالسالب
+
+655
+01:07:55,340 --> 01:08:08,880
+و cos sin T سالب sin T سالب cos T كله طبعا S sin S
+
+656
+01:08:08,880 --> 01:08:19,800
+و cos S و E Os S كله على الإتنين E Os S في ال DS
+
+657
+01:08:21,060 --> 01:08:29,140
+كله في ال DS تمام طيب نص برا وال EOS S مع ال EOS S
+
+658
+01:08:29,140 --> 01:08:36,800
+مع السلامة يبقى بصير ان ال main يساوي نص تكامل من
+
+659
+01:08:36,800 --> 01:08:46,080
+T node إلى T لناقص sign ال S ناقص cosine ال S كل
+
+660
+01:08:46,080 --> 01:08:49,620
+هذا في من؟ هذا W1
+
+661
+01:08:53,420 --> 01:09:04,420
+يبقى هذا كله في main في g of s كله في ds طيب ويبدو
+
+662
+01:09:04,420 --> 01:09:08,700
+ال particular solution يبقى ال particular solution
+
+663
+01:09:08,700 --> 01:09:21,280
+capital Y of T يبقى U1Y1 زي U2Y2 زي U3Y3يبقى
+
+664
+01:09:21,280 --> 01:09:28,220
+capital Y of T بده يساوي ال Y1 اللي هي كده ايش? E
+
+665
+01:09:28,220 --> 01:09:36,120
+of T يبقى هذه ال E of T و ال Y1 اللي هي وسطها طب
+
+666
+01:09:36,120 --> 01:09:43,240
+ال U1 ال U1 اللي هي النص في التكامل يبقى هذا النص
+
+667
+01:09:43,240 --> 01:09:49,720
+برا يا بناتوهي تكمل من T node إلى T وجوا قداش فيه
+
+668
+01:09:49,720 --> 01:09:58,560
+انا E أص ناقص S GS يبقى E أص ناقص S G of S في DS
+
+669
+01:09:59,780 --> 01:10:06,140
+بنجي اللي بعده زائد اللي هو cosine ال T زائد
+
+670
+01:10:06,140 --> 01:10:13,660
+cosine ال T ال U2 اللي هو برضه نص يبقى يا نص خليك
+
+671
+01:10:13,660 --> 01:10:21,550
+برا هذا النص وهي تكامللشانه مقدار ثابت من T ناد
+
+672
+01:10:21,550 --> 01:10:29,650
+إلى T لمين لصين ال S ناقص كوصين ال S لصين ال S
+
+673
+01:10:29,650 --> 01:10:37,270
+ناقص كوصين ال S كله اظن في E و S و لا فيش H في G
+
+674
+01:10:37,270 --> 01:10:45,770
+of S في G of S كله في DS نجي ل U تلاتة U تلاتة
+
+675
+01:10:45,770 --> 01:10:53,260
+عندك بصين ال Tيبقى Z هي sign ال T و U تلاتة أيها
+
+676
+01:10:53,260 --> 01:11:00,840
+عندي هي النص برا وهي تكامل من T node إلى T لناقص
+
+677
+01:11:00,840 --> 01:11:09,880
+sign ال S ناقص cosine ال S كله في قداش في G of S
+
+678
+01:11:09,880 --> 01:11:17,360
+في DS تمام؟
+
+679
+01:11:18,740 --> 01:11:24,800
+طيب ايش رايكوا انا شايف فيه نص برا و نص و نص ناخد
+
+680
+01:11:24,800 --> 01:11:31,540
+ورا من الكل تمام يبقى هذا نص برا الان يا بناتي
+
+681
+01:11:31,540 --> 01:11:37,620
+الجو المتغير هو مين S و اللي برا مين T يبقى كأنه
+
+682
+01:11:37,620 --> 01:11:42,020
+مقدار ثابت بالنسبة له صحيح ولا لا؟ مالوش داعي في
+
+683
+01:11:42,020 --> 01:11:46,600
+دي S يبقى خليته برا التكامل والله جوا التكامل سيان
+
+684
+01:11:46,780 --> 01:11:51,000
+أذا بدي اكتبه جوا التكامل بيضغط اضربه بصير جوا E
+
+685
+01:11:51,000 --> 01:11:56,200
+أس T في E أس ناقص S يعني E أس T ناقص ال S لإنه
+
+686
+01:11:56,200 --> 01:12:01,860
+عندها الضرب تجمع الأسس يبقى بصير أن هذا هي تكامل
+
+687
+01:12:01,860 --> 01:12:11,390
+من T نوت لغاية Tلل E أس T ناقص ال S في ال G of S
+
+688
+01:12:11,390 --> 01:12:17,790
+في ال DS خلصنا ال term الأول يبقى هنا هذا جوس كبير
+
+689
+01:12:17,790 --> 01:12:24,180
+جابله وبعده نص مشانه نص نص نص أخدته من الكلونجي
+
+690
+01:12:24,180 --> 01:12:30,700
+للتكامل هذا يبقى زائد تكامل من T node إلى T هذه
+
+691
+01:12:30,700 --> 01:12:34,240
+بنفس الطريقة ال cosine T تعتبر مقدار ثابت بقدر
+
+692
+01:12:34,240 --> 01:12:45,780
+ادخلها جوابصير عندي cos T في sin S ناقص cos T في
+
+693
+01:12:45,780 --> 01:12:56,190
+cos S كل هذا الكلام في G of S في D Sتمام اللي بعده
+
+694
+01:12:56,190 --> 01:13:02,350
+بنفس الطريقة زائد نص خدناها برا يبقى تكامل من T
+
+695
+01:13:02,350 --> 01:13:09,230
+node إلى T بدي أدخل جوا دي بيصير ناقص sine T في
+
+696
+01:13:09,230 --> 01:13:19,230
+sine ال S ناقص sine T في cosine ال S وكل هذا في G
+
+697
+01:13:19,230 --> 01:13:21,710
+of S في ال DS
+
+698
+01:13:30,130 --> 01:13:37,990
+خطوة الأخيرة في عويل مشتركة بدي أخدهم يبقى بصير Y
+
+699
+01:13:37,990 --> 01:13:50,190
+of T يساوي نصتكامل تكامل تكامل تكامل تكامل تكامل
+
+700
+01:13:50,190 --> 01:13:53,270
+تكامل
+
+701
+01:13:53,270 --> 01:14:01,140
+تكاملبتطلعي لي جيوب اس دي اس جيوب اس دي اس جيوب اس
+
+702
+01:14:01,140 --> 01:14:05,700
+دي اس يبقى بدأ أخدها من الكل كمان عامل مشترك ايش
+
+703
+01:14:05,700 --> 01:14:13,800
+بيظل عندي هنا بس E أس T ناقص ال S تمام؟ وهي فتحت
+
+704
+01:14:13,800 --> 01:14:17,880
+Guess مشان في الآخرة ضروبة كلها في جيوب اس هذي ايش
+
+705
+01:14:17,880 --> 01:14:29,490
+بيصير؟ بيصير الزاد cosine T في sine ال Sنقص cos T
+
+706
+01:14:29,490 --> 01:14:40,330
+في sin S نقص sin T
+
+707
+01:14:40,330 --> 01:14:48,450
+في cos S وهيجفلنا الجوز كله وهذا G of S وهذا DS
+
+708
+01:15:01,400 --> 01:15:09,800
+الخطوة الأخيرة يساوي نص تكامل من T node إلى T لل E
+
+709
+01:15:09,800 --> 01:15:11,720
+أس T ناقص ال S
+
+710
+01:15:15,240 --> 01:15:23,540
+هذه sin cos وهذه sin cos لو أخذت منهم ناقص عامل
+
+711
+01:15:23,540 --> 01:15:29,080
+مشترك ايش بيصير عندنا؟ هذه ناقص بيصير عندنا هذه
+
+712
+01:15:29,080 --> 01:15:36,400
+بالموجب وهذه بالسالم بيصير عندنا sin T cos S زاد
+
+713
+01:15:36,400 --> 01:15:47,120
+cos T في sin Sأليست هذه هي sin t ناقص ال S؟ هذه
+
+714
+01:15:47,120 --> 01:15:54,360
+اللي بدي أفكها sin t cos S ناقص cos T في sin S
+
+715
+01:15:54,360 --> 01:15:58,580
+هيها ولا لا؟ يبقى تخلص من التنتين اللي تحتهم خط
+
+716
+01:15:58,580 --> 01:16:05,590
+تالي هدول اللي تحتهم خطمعروج يبقى بدي أخد كمان
+
+717
+01:16:05,590 --> 01:16:12,010
+ناقص عامل مشترك بشيره التنتين بالزائد بصير كساء
+
+718
+01:16:12,010 --> 01:16:18,950
+وين همااستنى شوية بالراديو الخطأ مردود هى cosine t
+
+719
+01:16:18,950 --> 01:16:23,830
+فى sin s ناقص cosine اه هذه cosine s صحيلي هذه بس
+
+720
+01:16:23,830 --> 01:16:29,590
+يا بنات cosine s تمام هذه بس نزلناها بالخطة هيك
+
+721
+01:16:29,590 --> 01:16:33,550
+التانية sin مظبوط التانية مش فيها مشكلة وهذه مش
+
+722
+01:16:33,550 --> 01:16:37,010
+فيها مشكلة طيب هدول اللى تنتقل اما اخدت منهم ناقص
+
+723
+01:16:37,010 --> 01:16:41,790
+عامل بصير cosine cosine زائد sin sin اللى هو
+
+724
+01:16:41,790 --> 01:16:49,770
+cosine منين؟كو صين الفرق يبقى كو صين T ناقص ال S
+
+725
+01:16:49,770 --> 01:16:55,270
+يبقى يخلصنا الأربع ترمات اللي بين قوسين وهي قفلنا
+
+726
+01:16:55,270 --> 01:17:04,160
+القوس كله وهي عندك G of S وهذا ال D of Sيبقى
+
+727
+01:17:04,160 --> 01:17:08,820
+خلّينا ال particular solution بدلة الاتمين بدلة
+
+728
+01:17:08,820 --> 01:17:14,100
+التكمل لإن ال G of T أنا ماعرفاش قداش عنا يبقى هذا
+
+729
+01:17:14,100 --> 01:17:23,180
+أحد برضه أسئلة الكتاب اللي موجودة حد
+
+730
+01:17:23,180 --> 01:17:30,120
+بتحب تسأل أي سؤال هنا نمسح
+
+731
+01:17:30,120 --> 01:17:31,060
+الشجرة هذه
+
+732
+01:17:47,080 --> 01:17:52,500
+بدنا نراجع كلامتنا صغير يا مانات على حكاية مين بس
+
+733
+01:17:52,500 --> 01:17:55,800
+قبل ما نراجع بدنا نعطيكوا أرقام مثال ال section
+
+734
+01:17:55,800 --> 01:18:00,840
+اللي فات و ال section هذا ال section اللي فات كان
+
+735
+01:18:00,840 --> 01:18:11,430
+exercises أربعة ثلاثة اللي هو من واحد لسبتاشالقد و
+
+736
+01:18:11,430 --> 01:18:20,410
+exercises اربع اربع المسائل من واحد لغاية اربعة
+
+737
+01:18:20,410 --> 01:18:30,310
+عشر و برضه القد و بناخد عليها كمان سؤال ترفع بدنا
+
+738
+01:18:30,310 --> 01:18:37,790
+نيجي ل section الان خمسة واحد ال power series
+
+739
+01:18:40,730 --> 01:18:44,110
+عارف انا والله مش ذاكر وعارف وعارف كدهش بياخد
+
+740
+01:18:44,110 --> 01:18:48,610
+وكدهش بدي اعطي بدي اعطي كلمتين صغير مراجعة لبعض
+
+741
+01:18:48,610 --> 01:18:55,410
+الأشياء مش كلها كمان التي درست في calculus B يبقى
+
+742
+01:18:55,410 --> 01:19:00,150
+أول section يا بنات هو مراجعة ومالوش دخل بالموضوع
+
+743
+01:19:00,150 --> 01:19:05,010
+موضوعنا طيلة هذا ال chapter هو ال series solution
+
+744
+01:19:05,010 --> 01:19:09,890
+ل second order differential equationيعني إذا بدي
+
+745
+01:19:09,890 --> 01:19:13,270
+أبدأ بالعنوان الرئيسي اللي قبل هذا اللي هو chapter
+
+746
+01:19:13,270 --> 01:19:23,210
+5 series solutions of
+
+747
+01:19:23,210 --> 01:19:27,130
+second order
+
+748
+01:19:28,950 --> 01:19:34,270
+Differential equation هذا هو العنوان الرئيسي للشكل
+
+749
+01:19:34,270 --> 01:19:39,890
+كله لكن أول section هو ال power series ال power
+
+750
+01:19:39,890 --> 01:19:45,770
+series منها أحد شكلين الشكل الأول ال هو summation
+
+751
+01:19:45,770 --> 01:19:51,190
+من n equal zero to infinity لل a n في ال x ناقص ال
+
+752
+01:19:51,190 --> 01:19:56,890
+x not to the power nلو حطيتها بالشكل الطويل يبقى
+
+753
+01:19:56,890 --> 01:20:02,670
+بداجي أشيل ال N و أحط مكانها Zero بصير A node في
+
+754
+01:20:02,670 --> 01:20:07,630
+ال X ناقص ال X node ال Zero اللي هو بواحد زائد A1
+
+755
+01:20:07,630 --> 01:20:12,490
+في ال X ناقص ال X node زائد A2 في ال X ناقص ال X
+
+756
+01:20:12,490 --> 01:20:18,070
+node لكل تربيع زائد وانظر ماشيل لغاية الحد ينوني A
+
+757
+01:20:18,070 --> 01:20:21,290
+N X ناقص ال X node to the power N
+
+758
+01:20:25,840 --> 01:20:31,180
+هذا هو الشكل الأول ال X node بنسميه المركز تبع ال
+
+759
+01:20:31,180 --> 01:20:34,840
+power series
+
+760
+01:20:34,840 --> 01:20:39,200
+ممكن يكون ال center هذي عند نقطة الأصل يعني لو
+
+761
+01:20:39,200 --> 01:20:46,930
+كانت ال X node يساوي 0الـ X node بده يساوي 0 يبقى
+
+762
+01:20:46,930 --> 01:20:50,450
+ال summation بده يصير بالشكل هذا من عندي ال 0 ل
+
+763
+01:20:50,450 --> 01:20:56,510
+infinity لل A N لل X to the power N فقط يبقى X
+
+764
+01:20:56,510 --> 01:20:59,830
+node X node X node كلها هبطير من ال series اللي
+
+765
+01:20:59,830 --> 01:21:08,790
+عندنا ويصبح شكلها A node زائد A1 X A2 X تربيع زائد
+
+766
+01:21:08,790 --> 01:21:14,440
+A N X to the power N زائد الاخرينيبقى هذا هو شكل
+
+767
+01:21:14,440 --> 01:21:20,740
+ال power series in general طيب انا عندي ال power
+
+768
+01:21:20,740 --> 01:21:24,180
+series و بدى أشوفها converge و لا diverge شو
+
+769
+01:21:24,180 --> 01:21:26,720
+الاختبارات اللي كنا بنستخدمها في ال calculus
+
+770
+01:21:26,720 --> 01:21:31,660
+نستخدمهم
+
+771
+01:21:31,660 --> 01:21:41,180
+لل power series؟الراتيو والانثروت بس فقط لغير يبقى
+
+772
+01:21:41,180 --> 01:21:49,380
+to test the convergence of
+
+773
+01:21:49,980 --> 01:22:01,260
+the power series we use بنروح نستخدم the ratio
+
+774
+01:22:01,260 --> 01:22:09,300
+test or the Enthrotest
+
+775
+01:22:13,400 --> 01:22:16,740
+يبقى يا بستخدم ال ratio يا ال in through ال test
+
+776
+01:22:16,740 --> 01:22:21,500
+هدول اختبارا فقط اللى كنا بواسطتهم نختبر ال power
+
+777
+01:22:21,500 --> 01:22:26,280
+series هل هى converge و لا diverse طيب ال power
+
+778
+01:22:26,280 --> 01:22:29,940
+series هدى converge على طول و لا ممكن تكون عند
+
+779
+01:22:29,940 --> 01:22:35,700
+فترة و ممكن تكون عند نقطة اى power series اللى احد
+
+780
+01:22:35,700 --> 01:22:42,250
+الاحتمالات الثلاثة التاليةconvergence of the power
+
+781
+01:22:42,250 --> 01:22:47,930
+series
+
+782
+01:22:47,930 --> 01:22:52,850
+هدى اللى فاجأ بناته او هدى اي واحدة منهم نفس
+
+783
+01:22:52,850 --> 01:23:02,670
+الكلام هدى ممكن تكون converge only at x node and
+
+784
+01:23:02,670 --> 01:23:12,500
+diverge elsewhereفي أي مكان آخر Diverge كيف يعني؟
+
+785
+01:23:12,500 --> 01:23:19,000
+لو كان هذا ال real line وهذه النقطة X0 ممكن عند
+
+786
+01:23:19,000 --> 01:23:25,140
+هذه النقطة تبقى converge لكن بعدها Diverge و قبلها
+
+787
+01:23:25,140 --> 01:23:31,240
+Diverge طب قداش ال radius of convergence في هذه
+
+788
+01:23:31,240 --> 01:23:37,480
+الحالة ال radiusتقول الله الـ convergence عنده
+
+789
+01:23:37,480 --> 01:23:40,940
+نقطة طول الفترة وبدأ جسمه على اتنين، قداش طول
+
+790
+01:23:40,940 --> 01:23:45,180
+النقطة؟ Zero Zero يبقى ال radius يكون ساوي Zero
+
+791
+01:23:45,180 --> 01:23:54,500
+يبقى هنا في هذه الحالة The radius of convergence
+
+792
+01:23:54,500 --> 01:23:59,100
+is احنا بقى هنسميه capital R و احنا بقى هنقوله
+
+793
+01:23:59,100 --> 01:24:05,080
+كتابنا هنا بسميه ال route ساوي Zeroالنقطة الثانية
+
+794
+01:24:05,080 --> 01:24:12,640
+يبقى
+
+795
+01:24:12,640 --> 01:24:18,440
+فترة
+
+796
+01:24:18,440 --> 01:24:22,080
+التقارب من و لا و اين نسالب infinity ل infinity
+
+797
+01:24:22,080 --> 01:24:29,280
+يبقى هذا يعطينا the interval of
+
+798
+01:24:40,030 --> 01:24:41,430
+الراديوس
+
+799
+01:24:43,910 --> 01:24:56,010
+radius of convergence as R يبقى
+
+800
+01:24:56,010 --> 01:25:00,930
+R تساوي infinity يعني يا بنات لو كان هذا هو ال
+
+801
+01:25:00,930 --> 01:25:06,750
+real line يبقى ال series converge على كل الفترة
+
+802
+01:25:06,750 --> 01:25:10,690
+بالاستثناء وهذا النقطة اللي هي من هنا ال zero وهذا
+
+803
+01:25:10,690 --> 01:25:15,620
+يبقى الملئ و diverge ماعنديش بالمرةوبالتالي نص الـ
+
+804
+01:25:15,620 --> 01:25:19,360
+real line هو نصف القطر، من صفر لما لا نهاية، الطول
+
+805
+01:25:19,360 --> 01:25:24,000
+هذا بقداش؟ بما لا نهاية طيب النقطة الثالثة
+
+806
+01:25:24,000 --> 01:25:33,720
+والاخيرة اللي هو the series converge on الفترة
+
+807
+01:25:33,720 --> 01:25:36,300
+المفتوحة من A إلى B
+
+808
+01:25:39,740 --> 01:25:44,940
+بس على الفترة دي يعني لو جيت قولت هذا ال real line
+
+809
+01:25:44,940 --> 01:25:50,460
+وهذا النقطة A وهذا النقطة B هنا في النص Converge
+
+810
+01:25:50,460 --> 01:25:59,640
+وهك Diverge وقبلها A Diverge كذلك طب عندي ال A و
+
+811
+01:25:59,640 --> 01:26:00,180
+ال B
+
+812
+01:26:02,900 --> 01:26:16,400
+و قد تكون converge و قد تكون diverge
+
+813
+01:26:16,400 --> 01:26:31,110
+الـ X أقل من A و X أكبر من B باجي بيقولالـ X يساوي
+
+814
+01:26:31,110 --> 01:26:42,350
+بـ A الـ X يساوي بـ B الـ Series may converge or
+
+815
+01:26:42,350 --> 01:26:48,970
+may diverge يعني عند النقطة A و الـ B الـ Series
+
+816
+01:26:48,970 --> 01:26:53,510
+ممكن تكون converge أو ممكن تكون diverge
+
diff --git a/PL9fwy3NUQKwa8ZDfSFGn6H8xVFLzqmCZC/gssK8gZjcqI_raw.srt b/PL9fwy3NUQKwa8ZDfSFGn6H8xVFLzqmCZC/gssK8gZjcqI_raw.srt
new file mode 100644
index 0000000000000000000000000000000000000000..3f766dbabc0f2136b8399728b8b8ec3cbeb1c5c9
--- /dev/null
+++ b/PL9fwy3NUQKwa8ZDfSFGn6H8xVFLzqmCZC/gssK8gZjcqI_raw.srt
@@ -0,0 +1,3288 @@
+1
+00:00:09,600 --> 00:00:15,940
+بسم الله الرحمن الرحيم المرة الماضية دخلنا في حل
+
+2
+00:00:15,940 --> 00:00:19,480
+ال non homogeneous differential equationواخدنا
+
+3
+00:00:19,480 --> 00:00:23,260
+الطريقة الأولى وهى طريقة ال undetermined
+
+4
+00:00:23,260 --> 00:00:28,440
+coefficients وظهر علينا طريقة ال variation of
+
+5
+00:00:28,440 --> 00:00:32,700
+parameters اللى رفعناها فوق ان شاء الله هذه
+
+6
+00:00:32,700 --> 00:00:37,180
+الطريقة نفس الفكرة تابعة ال second order لما نحلها
+
+7
+00:00:37,180 --> 00:00:40,880
+بال variation of parameters بنحل بطريقة ال
+
+8
+00:00:40,880 --> 00:00:46,070
+variation of parameters إذا كانتالمعاملات ثوابت او
+
+9
+00:00:46,070 --> 00:00:52,490
+غير ثوابت بيهمنيش شكل g of t يكون اي شكل مش مقصور
+
+10
+00:00:52,490 --> 00:00:55,130
+زي ال undetermined coefficients لازم يكون
+
+11
+00:00:55,130 --> 00:00:59,090
+المعاملات ثوابت و g of t تكون بشكل معين حسب جده
+
+12
+00:00:59,090 --> 00:01:02,430
+اللي عملنا له و g of t تكون ايش ما يكون شكلها
+
+13
+00:01:02,430 --> 00:01:06,070
+فبقول يعتبر اللي هو ال inf order linear
+
+14
+00:01:06,070 --> 00:01:09,910
+differential equation بالشكل اللي قدامنا هذا لحظة
+
+15
+00:01:19,460 --> 00:01:23,860
+المعاملات هي هى متغيرات وقد تكون ثوائي بتفريقش لأن
+
+16
+00:01:23,860 --> 00:01:29,800
+ثوائي بتكون متغيرات المهم نعرف ان حل نقول assume
+
+17
+00:01:29,800 --> 00:01:34,280
+that we know a fundamental set of solutions Y1 وY2
+
+18
+00:01:34,280 --> 00:01:38,240
+وYN لمينللـ homogeneous differential equation اللي
+
+19
+00:01:38,240 --> 00:01:42,240
+متساوي قداش صفر يعني إذا عندي non homogeneous بدي
+
+20
+00:01:42,240 --> 00:01:45,120
+أجزئها لجزئين سواء كان بال undetermined
+
+21
+00:01:45,120 --> 00:01:48,860
+coefficients أو بال variation أو parameter علي
+
+22
+00:01:48,860 --> 00:01:53,220
+الشكتين بدي أخد ال homogeneous و أطلع الحل تبع ال
+
+23
+00:01:53,220 --> 00:01:56,440
+homogeneous differential equation وبعد ذلك بروح
+
+24
+00:01:56,440 --> 00:02:01,520
+لمين لل non homogeneous differential equationخلاص
+
+25
+00:02:01,520 --> 00:02:06,500
+الأمر نفس الفكرة تبع ال undetermined بس هناك بنروح
+
+26
+00:02:06,500 --> 00:02:10,160
+عشان بنجيب particular solution و بيكون جيبنا حل ال
+
+27
+00:02:10,160 --> 00:02:13,820
+homogenous بنجمع الاتنين بنطلع من ال general
+
+28
+00:02:13,820 --> 00:02:17,220
+solution هنا بنفس الطريقة بدي أروح أجيب ال
+
+29
+00:02:17,220 --> 00:02:20,660
+particular solution لل non homogenous differential
+
+30
+00:02:20,660 --> 00:02:24,200
+equation أجمعه محل ال homogenous differential
+
+31
+00:02:24,200 --> 00:02:27,980
+equation بيعطينا من ال general solution لل
+
+32
+00:02:27,980 --> 00:02:29,660
+differential equation كلها
+
+33
+00:02:33,120 --> 00:02:37,220
+الحل الهوموجيني يسمى الـE2 الهوموجيني يسمى
+
+34
+00:02:37,220 --> 00:02:43,280
+الهوموجيني يسمى الهوموجيني يسمى الهوموجيني يسمى
+
+35
+00:02:43,280 --> 00:02:43,620
+الهوموجيني يسمى الهوموجيني يسمى الهوموجيني يسمى
+
+36
+00:02:43,620 --> 00:02:45,260
+الهوموجيني يسمى الهوموجيني يسمى الهوموجيني يسمى
+
+37
+00:02:45,260 --> 00:02:46,100
+الهوموجيني يسمى الهوموجيني يسمى الهوموجيني يسمى
+
+38
+00:02:46,100 --> 00:02:46,580
+الهوموجيني يسمى الهوموجيني يسمى الهوموجيني يسمى
+
+39
+00:02:46,580 --> 00:02:47,100
+الهوموجيني يسمى الهوموجيني يسمى الهوموجيني يسمى
+
+40
+00:02:47,100 --> 00:02:47,500
+الهوموجيني يسمى الهوموجيني يسمى الهوموجيني يسمى
+
+41
+00:02:47,500 --> 00:02:54,580
+الهوموجيني يسمى التغيير الوسيطة to find a
+
+42
+00:02:54,580 --> 00:02:59,000
+particular solution يبقى هذه بنستخدمها لإيجاد حل
+
+43
+00:02:59,000 --> 00:03:03,380
+خاص زي بناتي الجدول في ال undetermined بنستخدمه
+
+44
+00:03:03,380 --> 00:03:06,760
+لإيجاد حل خاص وبعد هيك بنجيب ال general solution
+
+45
+00:03:08,020 --> 00:03:13,000
+يبقى هذه الطريقة تتلخص بدي أشيل c1 و c2 و c3 لغاية
+
+46
+00:03:13,000 --> 00:03:20,320
+cin و أحط مكانهم functions u1 و u2 و u3 و un هيهم
+
+47
+00:03:20,320 --> 00:03:23,640
+بالشكل اللي هذا بحيث ان ال particular solution
+
+48
+00:03:23,640 --> 00:03:28,100
+بصير على الشكل اللي عندنا هذا u1 y1 زائد u2 y2
+
+49
+00:03:28,100 --> 00:03:34,460
+زائد u u زائد u n اللي هو yn طب بدنا نجيب شكل كل
+
+50
+00:03:34,460 --> 00:03:39,760
+واحدة من اليهات هذهفبقول له where ال U M as a
+
+51
+00:03:39,760 --> 00:03:45,640
+function of T هي integration لل G of Tاللي هي هذه
+
+52
+00:03:45,640 --> 00:03:52,820
+مضربة في الرنسكين M of T على الرنسكين of T اول شيء
+
+53
+00:03:52,820 --> 00:03:56,140
+الرنسكين of T هذا الرنسكين تبع الحلول اللي هو Y1
+
+54
+00:03:56,140 --> 00:04:03,020
+وY2 وY3 تمام؟ الآن مين الرنسكين M؟ هو نفس الرنسكين
+
+55
+00:04:03,020 --> 00:04:09,860
+هذا هه بس بدي اشيل الصف رقم M و اكتب بدل العمود
+
+56
+00:04:09,860 --> 00:04:17,670
+000001يعني إيش؟ يعني لو كنت بدي U1 of T لإن احنا
+
+57
+00:04:17,670 --> 00:04:21,770
+لدينا U1 و U2 لغاية UN باجي على رونسكينالاندا و
+
+58
+00:04:21,770 --> 00:04:26,430
+بشيل العمود الأول و بكتب داله 0001 و باجي الأعمدة
+
+59
+00:04:26,430 --> 00:04:30,810
+أزاي ما هي و بفك المحدد و بجيب قيمته تمام؟ يبقى
+
+60
+00:04:30,810 --> 00:04:33,970
+جيبنا قيمة المحدد هذا، جيبنا قيمة المحدد هذا، نضغط
+
+61
+00:04:33,970 --> 00:04:38,030
+في جيب و نروح كامل، بكون حصلنا على مين؟ على U1 طب
+
+62
+00:04:38,030 --> 00:04:45,720
+بدي U2U2 of T بأجي D of T كما هي او رنسكين 2 of T
+
+63
+00:04:45,720 --> 00:04:49,720
+كيف بسيب العمود الأول زي ما هو العمود العتيق مش
+
+64
+00:04:49,720 --> 00:04:53,880
+الجديد و بجي على العمود رقم اتنين بشيله كله بحق و
+
+65
+00:04:53,880 --> 00:04:58,860
+بدله 0001 و الأعمد اللي بعده تبقى كما هي و هكذا
+
+66
+00:04:59,710 --> 00:05:02,850
+للرونسكين ثلاثة أو رونسكين أربعة أو رونسكين خمسة
+
+67
+00:05:02,850 --> 00:05:06,650
+إلى آخره لغاية ما نخلص كل اليهات اللي عندنا إذا
+
+68
+00:05:06,650 --> 00:05:09,190
+جيبناهم بيقول خلاص جيبنا ال particle a solution
+
+69
+00:05:09,190 --> 00:05:14,410
+تمام يبقى باجي بقوله ال U M of T هو integration لل
+
+70
+00:05:14,410 --> 00:05:21,290
+G of T لرونسكين M of T على W of T DTوالـ M بدأ
+
+71
+00:05:21,290 --> 00:05:25,110
+يساوي واحد واثنين لغاية مين لغاية ال N يعني بدي
+
+72
+00:05:25,110 --> 00:05:30,130
+أجيب كل اليهات فبلونوسكين M is the determinant هو
+
+73
+00:05:30,130 --> 00:05:36,070
+عبارة عن المحدد يبقى بنقول ما ياتي الآن بدنا نحاول
+
+74
+00:05:36,070 --> 00:05:39,710
+نجيب اليهات اللي عندنا دي واحد و اتنين و تلاتة و
+
+75
+00:05:39,710 --> 00:05:46,560
+لغاية U Mبنحط الصورة العامة U M of T هي عبارة عن
+
+76
+00:05:46,560 --> 00:05:51,140
+integration للـ G of T في الرونسكين M as a
+
+77
+00:05:51,140 --> 00:05:55,600
+function of T على الرونسكين of T كله بالنسبة لـ DT
+
+78
+00:05:55,600 --> 00:06:02,380
+مين هي الـ G of T هي تبع اتنين هذه مغيرناش اتنين
+
+79
+00:06:02,380 --> 00:06:07,260
+الرونسكين هذا هو تبع الحلول Y1 وY2 لغاية YN
+
+80
+00:06:07,760 --> 00:06:12,080
+الرونسكين M of T هو الرونسكين اللى تحت هذا بس بعد
+
+81
+00:06:12,080 --> 00:06:17,040
+ما اغير كل عمود يعني اذا عندى بدي U واحد بغير
+
+82
+00:06:17,040 --> 00:06:21,720
+العمود الاول بكون عندى W واحد عندى U اثنين يبقى
+
+83
+00:06:21,720 --> 00:06:27,120
+هنا W اثنين of T باجى على العمود التانى بغيره بحط
+
+84
+00:06:27,120 --> 00:06:33,740
+بداله 0001 وكده لغاية ما اوصل لمن لل U N اللى
+
+85
+00:06:33,740 --> 00:06:38,410
+عندنا ال U Nهها هي عبارة عن الـ G of T فى
+
+86
+00:06:38,410 --> 00:06:42,250
+الرونسكين M of T مقسمة على الرونسكين of T كله
+
+87
+00:06:42,250 --> 00:06:46,430
+بالنسبة لـ DT والـ M بتاخد 1 و 2 لغاية ال N يعني
+
+88
+00:06:46,430 --> 00:06:53,320
+بدي أجيب كل اليهات مرة واحدةيبقى هاي جيبناله ال M
+
+89
+00:06:53,320 --> 00:06:58,660
+الرونسكين M هيو هو المحدد اللي بنحصل عليه من ال W
+
+90
+00:06:58,660 --> 00:07:05,740
+of T باستبدال العمود رقم M بالعمود 0001 فيقنع بعض
+
+91
+00:07:05,740 --> 00:07:10,380
+الملاحظات لازم ندقيقها كويس و احنا بنشتغل تذكروا
+
+92
+00:07:10,380 --> 00:07:13,520
+في حالة ال variation of parameters في حالة second
+
+93
+00:07:13,520 --> 00:07:18,800
+order اشترطنا ان المعامل تبع Y W prime يكون جداش
+
+94
+00:07:19,220 --> 00:07:23,540
+هنا المعامل تبع y to the derivative n يكون جديهش
+
+95
+00:07:23,540 --> 00:07:29,820
+يبقى كتابنا هذا must be one يبقى المعامل تبع ال y
+
+96
+00:07:29,820 --> 00:07:33,580
+to the derivative n لازم يكون واحد صحيح ليش؟ لأن
+
+97
+00:07:33,580 --> 00:07:38,970
+هذا لو ماكانش واحد صحيحيبقى بيكون ده لا ورقم بدنا
+
+98
+00:07:38,970 --> 00:07:43,810
+نقسم عليه حتى نضمن أنه الجديدة هذه هي G of T مش
+
+99
+00:07:43,810 --> 00:07:48,010
+العتيقة يعني G of T هذي بحصل عليه لما يكون المعامل
+
+100
+00:07:48,010 --> 00:07:52,550
+هنا main واحد صحيح يبقى بدك تعمل القطوة هذي قبل كل
+
+101
+00:07:52,550 --> 00:07:56,730
+شيء أو تتأكد منها اتنين بيقول يا رونسكين هذا بقدر
+
+102
+00:07:56,730 --> 00:08:01,680
+أحسمه بطريقة قابلطريقة ايه بالكلمة ال second order
+
+103
+00:08:01,680 --> 00:08:06,040
+بس احنا هنا لل nth order يبقى باجي بقول رونس كين
+
+104
+00:08:06,040 --> 00:08:11,120
+هو عبارة عن كرسان فيه وصناعة استكامل P1 of T DT ال
+
+105
+00:08:11,120 --> 00:08:16,000
+P1 هو مين؟ هو المعامل ال Y to the derivative N
+
+106
+00:08:16,000 --> 00:08:21,040
+minus ال 1 طلع هي Y N اللي بعدها يمين معاملة هذا
+
+107
+00:08:21,040 --> 00:08:26,320
+يبقى لو كان في شغل هنا بدك تجسم عليهاواللي بيطلع
+
+108
+00:08:26,320 --> 00:08:30,160
+بيكون هو P1 of T و بعضكوا في الامتحان اللي فات
+
+109
+00:08:30,160 --> 00:08:34,420
+ماجسموش وخلوا عليه وبالتالي طالع سؤالهم غلط لازم
+
+110
+00:08:34,420 --> 00:08:38,960
+ايش المعامل هذا يكون واحد صحيح وكتبناها معاكم قبل
+
+111
+00:08:38,960 --> 00:08:41,840
+ذلك في ال second order لازم يكون المعامل هو main
+
+112
+00:08:41,840 --> 00:08:46,980
+واحد صحيح يبقى هذا كل ما يتعلق بقضية ال variation
+
+113
+00:08:46,980 --> 00:08:52,150
+of parameters يعني حلالنهوموجينس بواسطة الـ
+
+114
+00:08:52,150 --> 00:08:53,150
+Variation of Parameters
+
+115
+00:09:02,380 --> 00:09:06,860
+يبقى بدي أشيل ال constants في مين في الحل اللي هو
+
+116
+00:09:06,860 --> 00:09:11,380
+y يساوي c1 y1 زي c2 y2 زي cnyn بدي أشيل ال c هات
+
+117
+00:09:11,380 --> 00:09:16,760
+هذي و أستبدلها بدوال u1 و u2 و u3 لغاية u1 طب بدي
+
+118
+00:09:16,760 --> 00:09:20,840
+أجيب عرف الشكل هم بقول لك اه في ان علاقة العلاقة
+
+119
+00:09:20,840 --> 00:09:25,910
+هذي بتجيبلك أي و منهم غير العلاقة مين هيU M of T
+
+120
+00:09:25,910 --> 00:09:30,110
+بدي سوي تكامل G of T فى الورونسكن M of T على
+
+121
+00:09:30,110 --> 00:09:35,270
+الرونسكن of T كله بالنسبة لدى T الرونسكن M of T هو
+
+122
+00:09:35,270 --> 00:09:39,470
+عبارة عن الرونسكن of T بعد ما اشيل اذا بدي U 1
+
+123
+00:09:39,470 --> 00:09:45,170
+بشيل العمود الأول و بحط بداله 0001 اذا رونسكن 2
+
+124
+00:09:45,170 --> 00:09:48,030
+بخل العمود الأول زى ما هو بروح على العمود التانى
+
+125
+00:09:48,030 --> 00:09:52,510
+بشيله و بحط بداله 0001 و هكذا تبقى بكون جبت ال U
+
+126
+00:09:52,510 --> 00:09:56,360
+هاتبضربها في الوايات اللى عندي بجمع بكون جبته ال
+
+127
+00:09:56,360 --> 00:09:59,800
+particular solution لل non homogeneous
+
+128
+00:09:59,800 --> 00:10:03,040
+differential equation بجمع محل ال homogeneous
+
+129
+00:10:03,040 --> 00:10:06,900
+بيعطيني ال general solution لل non homogeneous
+
+130
+00:10:06,900 --> 00:10:11,020
+differential equation واضح كلام ايه؟حد فيكم بتحب
+
+131
+00:10:11,020 --> 00:10:14,020
+تسأل اي سؤال؟ خلاصنا ال user نظري، خلاصنا منه، حد
+
+132
+00:10:14,020 --> 00:10:17,700
+بتحب تسأل اي سؤال؟ طب الكلام اللي سمعته بنروح
+
+133
+00:10:17,700 --> 00:10:22,800
+انطبقه على أرض الواقع مثال او اول مثال بقول you
+
+134
+00:10:22,800 --> 00:10:25,720
+find the general solution of the differential
+
+135
+00:10:25,720 --> 00:10:29,860
+equation Y triple A prime زي ال Y prime تساوي 6T
+
+136
+00:10:29,860 --> 00:10:35,000
+وT محصرة من سالف باي على اتنين إلى مين؟ إلى باي
+
+137
+00:10:35,000 --> 00:10:39,790
+على اتنينيعني حصرها في فترة الدالة الـ6 تبدأ تبقى
+
+138
+00:10:39,790 --> 00:10:43,210
+continuous على هذه الفترة تعرف ان عند البيعة 2
+
+139
+00:10:43,210 --> 00:10:47,450
+والسلب بيعة 2 الـ6 is undefined زي التان عند
+
+140
+00:10:47,450 --> 00:10:52,070
+البيعة 2 وسلب بيعة 2 تلاتة بيعة 2 سلب تلاتة بيعة 2
+
+141
+00:10:52,070 --> 00:10:56,090
+خمسة بيعة 2 سلب كل ما تبقى الدالة ماهياش معرفة
+
+142
+00:10:56,090 --> 00:10:59,490
+يبقى أنا حصرتها في فترة معرفة عليه يعني الدالة
+
+143
+00:10:59,490 --> 00:11:05,350
+continuous على هذهالفترة طيب بدنا نيجي نحل يبقى
+
+144
+00:11:05,350 --> 00:11:10,650
+أول خطوة بتروح اجيب مين حل ال homogenous صدر و حل
+
+145
+00:11:10,650 --> 00:11:14,550
+المعادلة رقم اتنين المعادلة اللي عندي من الدرجة
+
+146
+00:11:14,550 --> 00:11:18,470
+الثالثة يبقى نفس ال tactic اللي اتبعناها في حالة
+
+147
+00:11:18,470 --> 00:11:21,110
+ال undetermined coefficients الجزء الأول هو الجزء
+
+148
+00:11:21,110 --> 00:11:28,690
+الأول هناك لا تغيير عليه فبجي بقوله solution let
+
+149
+00:11:29,360 --> 00:11:40,160
+Y تساوي E أس RT ب A solution of المعادلة التفاضلية
+
+150
+00:11:40,160 --> 00:11:44,920
+Y triple prime زائد Y prime تساوي Zero
+
+151
+00:11:57,640 --> 00:12:02,580
+ممكن ناخد ر عامل مشترك بيظل ر تربيع زائد واحد
+
+152
+00:12:02,580 --> 00:12:10,830
+يساوي زيرويبقى R1 بده يساوي 0 وR2 و3 بده يساوي
+
+153
+00:12:10,830 --> 00:12:19,670
+زائد او نقص كده اش I يبقى Y C بده يساوي C1 في E أس
+
+154
+00:12:19,670 --> 00:12:30,810
+Zero يبقى بC1 زائد C2 Cos T زائد C3 في Sin T الشكل
+
+155
+00:12:30,810 --> 00:12:33,740
+اللي عندنا هناهذا هو حلل الـ Homogeneous
+
+156
+00:12:33,740 --> 00:12:38,490
+differential equationبدنا نيجي ندور على particular
+
+157
+00:12:38,490 --> 00:12:44,670
+solution لحال مين لحال اللي هو non homogeneous
+
+158
+00:12:44,670 --> 00:12:50,250
+differential equation بطريقة مين؟ بطريقة ال
+
+159
+00:12:50,250 --> 00:12:54,310
+variation of parameters ليش بطريقة ال variation of
+
+160
+00:12:54,310 --> 00:12:59,890
+parameters؟ لإن الجزء اللي على اليمين له
+
+161
+00:12:59,890 --> 00:13:04,430
+polynomial و له polynomial fixed exponentialوالا
+
+162
+00:13:04,430 --> 00:13:08,450
+polynomial approximation في صين او كوسين سك واحدة
+
+163
+00:13:08,450 --> 00:13:13,250
+ع كوسين مش كوسين يبصرة واحدة ع كوسين اذا اختلفت عن
+
+164
+00:13:13,250 --> 00:13:17,110
+ال undetermined coefficientsوطبعا جيبتلك وده سؤال
+
+165
+00:13:17,110 --> 00:13:21,430
+في الخيارات خليتها واحدة على cosine وقولك بنحل بها
+
+166
+00:13:21,430 --> 00:13:25,090
+بطريقة ايش ال undetermined ولا ال variation ولا ال
+
+167
+00:13:25,090 --> 00:13:27,830
+reduction ولا ولا بها الطرق ولا بطريقة من هذه
+
+168
+00:13:27,830 --> 00:13:31,390
+الطرق واختري الإجابة صحية والإجابة الصحية هي طريقة
+
+169
+00:13:31,390 --> 00:13:36,130
+مين ال variation of parameters طيب تتلخص ال
+
+170
+00:13:36,130 --> 00:13:40,450
+variation of parameters اني بدي اشيل ال C1 وC2 وC3
+
+171
+00:13:40,450 --> 00:13:48,190
+وحط بدالها U1 وU2 وU3بس قبل لا أحط ولا أشيل بدي
+
+172
+00:13:48,190 --> 00:13:52,990
+أحسب قداش الронسكن لكل واحدة من هدول لإنه بدي
+
+173
+00:13:52,990 --> 00:13:58,570
+أستخدمها في الحل إذا لو جيت للرونسكن as a function
+
+174
+00:13:58,570 --> 00:14:03,310
+of T و كتبت المحدد الحل الأول هنا قداش يا بنات؟
+
+175
+00:14:06,430 --> 00:14:13,230
+يبقى الحل الأول واحد و الحل التاني cos t و الحل
+
+176
+00:14:13,230 --> 00:14:23,010
+التالت sin t بدشتق يبقى zero سالب sin t cos t دشتق
+
+177
+00:14:23,010 --> 00:14:30,390
+كمان مرة يبقى zero ناقص cos t ناقص sin t وهيجفلنا
+
+178
+00:14:30,390 --> 00:14:35,490
+المحددبدي احسب جداش قيمة المحدد يبقى بدافك
+
+179
+00:14:35,490 --> 00:14:41,710
+وباستخدام عناصرالعمود الأول أسل لإن واحد في المحد
+
+180
+00:14:41,710 --> 00:14:45,110
+الأصغر مناظره و بعدين Zero Zero خلاص مع السلامة
+
+181
+00:14:45,110 --> 00:14:48,450
+مافيش داعي الاكتفته بيصير Zero دُغري يبقى هذا
+
+182
+00:14:48,450 --> 00:14:54,030
+الكلام بده يساوي هاي الواحد فيه خشط بصفه عمودة
+
+183
+00:14:54,030 --> 00:14:58,350
+بصيرها حاصل ضرب عناصر غطر رئيسي اللي هي جداش صين
+
+184
+00:14:58,350 --> 00:15:02,770
+تربيتي ناقص حاصل ضرب عناصر غطر التاني المعناقس
+
+185
+00:15:02,770 --> 00:15:09,270
+بيصير زاد وصين تربيتي اللي هي كلها جداشممتاز يبقى
+
+186
+00:15:09,270 --> 00:15:13,030
+رونسكين of T طالع بواحه صحيحة يسهل الحسابات تاني
+
+187
+00:15:13,030 --> 00:15:19,490
+الان بالداجة لرونسكين one of T يساويهيبقى اش بدى
+
+188
+00:15:19,490 --> 00:15:24,870
+اعمل داجي على العمود الاول بدى اشيله و احط بداله
+
+189
+00:15:24,870 --> 00:15:32,090
+001 زي ما حكينا تمام؟ بداجي الان لهدول العمودين
+
+190
+00:15:32,090 --> 00:15:37,990
+بنزلهم زي ما هم بندوا نتغير يبقى هي cosine ت و هي
+
+191
+00:15:37,990 --> 00:15:46,620
+ناقص sine ت و هي ناقص cosine tوهنا هي sin T وهنا
+
+192
+00:15:46,620 --> 00:15:54,510
+cos T ونقص sin Tتمام شايف بده فك المحدد باستخدام
+
+193
+00:15:54,510 --> 00:15:59,710
+عناصر العمود لوله انه أسهل صفر في محدده بصفر مع
+
+194
+00:15:59,710 --> 00:16:03,830
+السلامة صفر محدده بصفر ضال واحد حسب قاعة الإشارة
+
+195
+00:16:03,830 --> 00:16:09,450
+شرطه موجة بقى يبقى هذا الكلام بده يساوي واحد فيه
+
+196
+00:16:09,450 --> 00:16:14,390
+يبقى بدنشته بصفه وعمضه بصير cosine تربية
+
+197
+00:16:30,250 --> 00:16:34,170
+بالدرجة عاملة العمود الأول اللي كان بتخليه زي ما
+
+198
+00:16:34,170 --> 00:16:40,970
+هويبقى هذا واحد Zero Zero العمود الثاني بدي أشيله
+
+199
+00:16:40,970 --> 00:16:46,630
+و أكتب بدله Zero Zero واحد العمود الثالث يبقى كما
+
+200
+00:16:46,630 --> 00:16:55,750
+هو يبقى Sin T Cosin T ناقص Sin T وهذا المحددبارضه
+
+201
+00:16:55,750 --> 00:17:00,570
+بدى احاول افكه باستخدام عناصر العمود الاول يبقى
+
+202
+00:17:00,570 --> 00:17:06,910
+هذا الكلام بدى يسوى واحد فيه اشق بصفه وعموده بصير
+
+203
+00:17:06,910 --> 00:17:14,390
+ال zero ناقص cosine ت يبقى zero ناقص cosine ت يبقى
+
+204
+00:17:14,390 --> 00:17:15,710
+الجواب جداش
+
+205
+00:17:22,810 --> 00:17:27,210
+العمود الأول زي ما هو يا بنات مش هغيره العمود
+
+206
+00:17:27,210 --> 00:17:34,940
+التاني برضه بده نزله زي ما هو زي ما كاننقص sin T
+
+207
+00:17:34,940 --> 00:17:43,620
+نقص cos T العمود التالت هو اللي بدي أغيره 001 يبقى
+
+208
+00:17:43,620 --> 00:17:47,640
+هذا الكلام يساوي هذا الواحد بدي أفكه باستخدام
+
+209
+00:17:47,640 --> 00:17:53,340
+عنوصر العمود الأول أشط بيصفه وعموده بصير السالب
+
+210
+00:17:53,340 --> 00:18:01,680
+sin Tزائد زيرو يبقى سالب صين ال T زائد زيرو يساوي
+
+211
+00:18:01,680 --> 00:18:07,620
+سالب صين ال T يبقى جيبنا هدول يبقى قصتنا الحين
+
+212
+00:18:07,620 --> 00:18:13,300
+بصير سهلة يبقى بدي أجيب له ال U1 و ال U2 و ال U3
+
+213
+00:18:13,300 --> 00:18:17,480
+بس اتنى شوية أطلع في المعامل المعامل واحد صحيح
+
+214
+00:18:17,480 --> 00:18:24,540
+يبقى احنا جاهزين تمام يبقى بالفعل 6T هذه هي G of T
+
+215
+00:18:28,350 --> 00:18:37,010
+الـ U1 as a function of Tيبقى هذا تكامل ل G of T
+
+216
+00:18:37,010 --> 00:18:43,710
+ها بدك تبالك و هذا ال run skin one as a function
+
+217
+00:18:43,710 --> 00:18:50,190
+of T على run skin of T DT بده يسوى تكامل ال G اللي
+
+218
+00:18:50,190 --> 00:18:56,750
+هي سك T ال run skin one مقدش بواحد صحيح يبقى هي
+
+219
+00:18:56,750 --> 00:19:03,400
+مضروبة في واحد على مين على واحد كله DTيبقى بدى
+
+220
+00:19:03,400 --> 00:19:09,280
+تكمل مين يا فنان؟ بس سك تي نعرف نكملها من كل plus
+
+221
+00:19:09,280 --> 00:19:14,220
+بيه؟ كدهش؟
+
+222
+00:19:14,220 --> 00:19:22,380
+لن سك زائد تان يبقى وتساوي لن absolute value لسك
+
+223
+00:19:22,380 --> 00:19:29,140
+تي زائد تان تي زائد constant K one اللي هو تبع
+
+224
+00:19:29,140 --> 00:19:35,740
+التكاملطبعا بعد شوية هحط k1b0 هنقولكوا ليش بس
+
+225
+00:19:35,740 --> 00:19:41,420
+يصبروا علينا شوية بدنا نروح نجيب ال U2 يبقى بدنا
+
+226
+00:19:41,420 --> 00:19:46,140
+نروح نجيب ال U2 as a function of T
+
+227
+00:19:52,080 --> 00:19:56,680
+يبقى بالداجي لل U2 as a function of T integration
+
+228
+00:19:56,680 --> 00:20:04,140
+لل G of T للورنسكين 2 of T على رونسكين of T كله في
+
+229
+00:20:04,140 --> 00:20:09,200
+DTيبقى هذا الكلام integration ل سك ال T في
+
+230
+00:20:09,200 --> 00:20:15,960
+الرونسكين 2 الرونسكين 2 هو طوله كده؟ ناقص cos T
+
+231
+00:20:15,960 --> 00:20:23,380
+يبقى ناقص cos T على رونسكين T اللي هو كده؟ واحد
+
+232
+00:20:23,380 --> 00:20:28,520
+صحيح طب السك هذه مش هي مقلوب ال cos يعني بضلب
+
+233
+00:20:28,520 --> 00:20:36,310
+السالب واحد يبقى هذه تساوي سالب تكامل DTيبقى سالب
+
+234
+00:20:36,310 --> 00:20:44,750
+T زائد constant K2 بعد هيك بدي أجيب ال U3 as a
+
+235
+00:20:44,750 --> 00:20:51,650
+function of T تكامل لل GT في رونسكن 3 of T على
+
+236
+00:20:51,650 --> 00:20:58,830
+رونسكن RT كله DTيبقى هذا الكلام بدي يسوي تكامل ل
+
+237
+00:20:58,830 --> 00:21:03,850
+سك التى فالرونس كنيه ثري اللى هو سالب صين التى
+
+238
+00:21:03,850 --> 00:21:12,530
+سالب صين التى على ال one dt او ان شيتنا فقولنا
+
+239
+00:21:12,530 --> 00:21:20,210
+ناقص صين التى على القصين اللى واحد على قصين التى
+
+240
+00:21:20,210 --> 00:21:25,550
+ديتى السؤال هو هل الباص تفاضل المطار؟يبقى اليوم
+
+241
+00:21:25,550 --> 00:21:31,790
+قداشر لن absolute value للمقام يبقى لن absolute
+
+242
+00:21:31,790 --> 00:21:34,490
+value لكوسايد ايش رأيكم؟ مالعيش خاطر احط ال
+
+243
+00:21:34,490 --> 00:21:42,010
+absolute لنفع لإن تي ون موجودة في الربع الرابع
+
+244
+00:21:42,010 --> 00:21:45,890
+والربع الأول في الربع الرابع الكوسايد موجب وفي
+
+245
+00:21:45,890 --> 00:21:49,770
+الربع الأول موجب على الشك تانييبقى حطة الأبسلويت
+
+246
+00:21:49,770 --> 00:21:57,990
+والنشلتة بتفرقش عنها يبقى لن كوصين ال T زائد K3
+
+247
+00:21:57,990 --> 00:22:09,890
+الآن بدي أقوله take خدلي K1 يسوى K2 يسوى K3 يسوى
+
+248
+00:22:09,890 --> 00:22:20,210
+Zero طبعا في تسأل ليش أخدتهم ب Zeroمش هذا سؤال؟ حد
+
+249
+00:22:20,210 --> 00:22:26,390
+بتقدر تعطيني جواب يا بنات؟ ليش أخدت الكهات هدول
+
+250
+00:22:26,390 --> 00:22:27,610
+بأصفار؟
+
+251
+00:22:31,150 --> 00:22:35,990
+هي اذكركم و تعالوا بال undetermined coefficient و
+
+252
+00:22:35,990 --> 00:22:40,150
+نرجع تاني لما كنا نكتب ال particular solution
+
+253
+00:22:40,150 --> 00:22:43,810
+بجينا نقول T to the power S فى الحل اللى عندنا هنا
+
+254
+00:22:43,810 --> 00:22:49,370
+ال S هدى بتعتمد هل اى جزء فى الحل يشبه اى جزء من
+
+255
+00:22:49,370 --> 00:22:53,230
+ال homogeneous ولا لأ مظبوط ولا لأ طب انا لو خلت
+
+256
+00:22:53,230 --> 00:22:57,350
+هذا ال key هات هدى كواحد و كتنين و كتر محطتهاش بقى
+
+257
+00:22:57,350 --> 00:23:04,610
+أصفرلما أجيب ال particular solution y1 ضرب u1 صح
+
+258
+00:23:04,610 --> 00:23:11,330
+ولا لأ؟ يبقى بصير هنا هذه مضروبة في y2 وهذه مضروبة
+
+259
+00:23:11,330 --> 00:23:15,670
+في y2 بصير y2 مكرر مضروبة في كل أسطن يبقى فيه
+
+260
+00:23:15,670 --> 00:23:19,670
+تشابه بينه و بين الأصلي ولا لأ؟ إذا لما أحط بيزيرو
+
+261
+00:23:19,670 --> 00:23:23,470
+بكون ماعنديش تشابه بالمرة متخلصة من الشغل هذه
+
+262
+00:23:24,000 --> 00:23:27,920
+بقولها كمان مرة اللى كانت مش متابعة معانا الصح سه
+
+263
+00:23:27,920 --> 00:23:34,300
+معانا كويس ليش حطيت الكهات هدول كله بأصفر مرة
+
+264
+00:23:34,300 --> 00:23:39,840
+واحدة لإن لو خليته زي ما هو بأي كونستان أخر غير
+
+265
+00:23:39,840 --> 00:23:45,260
+الصفر تمام لما بده أجيب ال particular solution إيش
+
+266
+00:23:45,260 --> 00:23:57,780
+بنقول C1 هنا حطيته ب1 في 1هنا C2 U2 سالب T زيد K2
+
+267
+00:23:57,780 --> 00:24:04,060
+لما ضبها في ال cosine بيصير constant في cosine زاد
+
+268
+00:24:04,060 --> 00:24:09,040
+اللي هو T أو سالب T في ال cosine constant في ال
+
+269
+00:24:09,040 --> 00:24:14,030
+cosine مش هى هذه يبقى التشابه قائمصحيح ولا لأ؟
+
+270
+00:24:14,030 --> 00:24:17,650
+يبقى لما حط الكهات بأصفار كل التشابه ده بيكون
+
+271
+00:24:17,650 --> 00:24:24,530
+اتخلص منه و يبقى مش السؤال ده بس كل سؤال بعدين مثل
+
+272
+00:24:24,530 --> 00:24:31,020
+حط الكهات هدول كلهم بأصفاريبقى بناء عليه هذا بده
+
+273
+00:24:31,020 --> 00:24:37,360
+يعطيك ان U1 as a function of T اللي حصلنا عليه
+
+274
+00:24:37,360 --> 00:24:44,120
+اللي هو LEN absolute value ل 6T زائد 10T
+
+275
+00:25:10,340 --> 00:25:13,940
+هذا هو حل الـ homogeneous ولا الـ non-homogeneous
+
+276
+00:25:15,730 --> 00:25:20,930
+الـ non homogeneous يبقى هذا اللي هو U واحد Y واحد
+
+277
+00:25:20,930 --> 00:25:28,330
+زائد U اتنين Y اتنين زائد U تلاتة Y تلاتة طيب ال U
+
+278
+00:25:28,330 --> 00:25:29,870
+واحد عندي هنا مجداش
+
+279
+00:25:36,620 --> 00:25:41,880
+وين ال U واحد؟ يبقى هايها بدها ضربها في جداش في
+
+280
+00:25:41,880 --> 00:25:46,680
+واحد إذا بتنزل زي ما هي يبقى هادا لين absolute
+
+281
+00:25:46,680 --> 00:25:57,750
+value ل 6T زائد تاني Tبعد ذلك U2Y2 وين Y2 هي Cos T
+
+282
+00:25:57,750 --> 00:26:07,110
+بدي أضرب في من؟ في سالب T يبقى سالب T Cos T بعد
+
+283
+00:26:07,110 --> 00:26:13,690
+ذلك C3 بدي أضرب مكان هي U3 يبقى بدي أضرب Sin T في
+
+284
+00:26:13,690 --> 00:26:20,390
+U3 يبقى زائد Sin T في Lin Cos T
+
+285
+00:26:23,360 --> 00:26:27,340
+جبت له ال particular solution، ايش ضال عليك؟ قال
+
+286
+00:26:27,340 --> 00:26:29,760
+لي هاتل ال general solution لل non homogeneous
+
+287
+00:26:29,760 --> 00:26:34,420
+differential equation بروح بقول له the general
+
+288
+00:26:34,420 --> 00:26:37,480
+solution
+
+289
+00:26:37,480 --> 00:26:52,240
+of equation 1 isY تساوي YC زائد capital Y of T
+
+290
+00:26:52,240 --> 00:27:00,280
+يساوي YC هي عندنا بنزله زي ما هو يبقى C1 زائد C2
+
+291
+00:27:00,280 --> 00:27:08,260
+في cos T C3 في sin T capital Y of T هي كله عندي
+
+292
+00:27:08,260 --> 00:27:17,600
+يبقى زائد لين absolute valueلسك ال T زائد تاني ال
+
+293
+00:27:17,600 --> 00:27:27,420
+T زائد sign ال T في ال N لكوصين ال T ناقص T في
+
+294
+00:27:27,420 --> 00:27:34,220
+كوصين ال T يبقى هذا هو الحل المطلوب حد فيكم بتحب
+
+295
+00:27:34,220 --> 00:27:40,020
+تسأل أي سؤال هنا؟ اه طويل شوية لكن برضه فكرته
+
+296
+00:27:40,020 --> 00:27:40,840
+جميلة جدا
+
+297
+00:27:54,450 --> 00:28:05,070
+نعطي مثال اخته
+
+298
+00:28:05,070 --> 00:28:08,850
+شباب
+
+299
+00:28:08,850 --> 00:28:14,330
+تسأل السؤال التالي بتقول لو كان g of t مثلا cosine
+
+300
+00:28:14,330 --> 00:28:18,530
+of tبنفع حل بال variation of parameter و بال
+
+301
+00:28:18,530 --> 00:28:22,150
+undetermined coefficients بشرط المعامل ثلاث ثوابت
+
+302
+00:28:22,150 --> 00:28:27,070
+اه و الله بنفع بالطريقتين لو حلتي بال variation of
+
+303
+00:28:27,070 --> 00:28:30,250
+parameter و بال undetermined coefficients اتنين صح
+
+304
+00:28:30,250 --> 00:28:34,610
+ماعنديش مشكلة ليش؟ لأن هذا اتفق حسب الجدول اللى
+
+305
+00:28:34,610 --> 00:28:37,670
+موجود في حالة ال undetermined coefficients و اتفق
+
+306
+00:28:37,670 --> 00:28:39,890
+معانا في حالة ال variation of parameter ماعنا
+
+307
+00:28:39,890 --> 00:28:46,560
+مشكلة في هذه الحالة تمام؟بنى للمثال رقم اتنين مثال
+
+308
+00:28:46,560 --> 00:28:54,460
+رقم اتنين بقول ما يأتي بقول given that اذا اعطيت
+
+309
+00:28:54,460 --> 00:29:06,360
+ان ال X و X تربيع and واحد على X are solutions are
+
+310
+00:29:06,360 --> 00:29:10,660
+solutions of
+
+311
+00:29:19,110 --> 00:29:27,890
+Homogeneous Differential Equation Corresponding To
+
+312
+00:29:40,560 --> 00:29:43,020
+المناظرة للمعادلة
+
+313
+00:30:14,040 --> 00:30:15,440
+Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''Y''
+
+314
+00:30:19,760 --> 00:30:21,560
+a particular solution
+
+315
+00:31:04,720 --> 00:31:10,580
+سؤال مرة ثانية بقول لو كان هدول ثلاثة حلول لل
+
+316
+00:31:10,580 --> 00:31:14,440
+homogeneous differential equation المناظرة cross
+
+317
+00:31:14,440 --> 00:31:19,380
+bonding to المناظرة لمين؟ للمعادلة دي يعني كأن
+
+318
+00:31:19,380 --> 00:31:24,420
+المعادلة دي بس بدي أسويها بقداش بالسفر تمام يعني
+
+319
+00:31:24,420 --> 00:31:29,560
+هذه المعادلة الأصلية وحل ال homogeneous معطنية مش
+
+320
+00:31:29,560 --> 00:31:33,320
+لسه بيدوروا أدور عليه لأ جاي الحلول X و X تربيعه
+
+321
+00:31:33,320 --> 00:31:38,040
+مين؟واحد على X قال لي اذا كان الأمر كذلك determine
+
+322
+00:31:38,040 --> 00:31:43,740
+a particular solution بقوله اه احنا مشان نجيب ال
+
+323
+00:31:43,740 --> 00:31:48,580
+general solution بدي هدول التلاتة يكونوا linearly
+
+324
+00:31:48,580 --> 00:31:53,440
+independentأو هدول بيكونوا ال fundamental set of
+
+325
+00:31:53,440 --> 00:31:57,000
+solutions مش حيال الله حلول ومشي واجري صحيح ولا
+
+326
+00:31:57,000 --> 00:32:00,120
+لأ؟ لأن ال fundamental set of solutions هم اللي
+
+327
+00:32:00,120 --> 00:32:03,160
+بيجيبوا ال general solution لل homogeneous
+
+328
+00:32:03,160 --> 00:32:08,200
+differential equation يبقى أول شغلة بيختبر هل هدول
+
+329
+00:32:08,200 --> 00:32:12,340
+linearly independent ولا لأ؟ أو هل هدول بيكونوا ال
+
+330
+00:32:12,340 --> 00:32:17,150
+fundamental set of solution ام لا؟ واضح كلامي؟يبقى
+
+331
+00:32:17,150 --> 00:32:22,970
+بتروح اخد ايش المحدد تبع التلاتة هدول يبقى باجي
+
+332
+00:32:22,970 --> 00:32:27,350
+بقوله وطبعا المحدد ده ده هيفيدني في الحل بعد ذلك
+
+333
+00:32:27,350 --> 00:32:31,370
+مش يعني بداود و بروح .. لأ بنستفيد منه، اذا بتروح
+
+334
+00:32:31,370 --> 00:32:36,550
+اخد الwareness gain of X مش of T لإن المثل المكتوب
+
+335
+00:32:36,550 --> 00:32:39,850
+عندي كله بدلالة main X اللي هو ال independent
+
+336
+00:32:39,850 --> 00:32:45,500
+variableيبقى باجي بقوله الحل الأول اللي هو X والحل
+
+337
+00:32:45,500 --> 00:32:50,360
+الثاني X تربيه والثاني واحد على X تحب تخلي واحد
+
+338
+00:32:50,360 --> 00:32:56,620
+على X وانا اكتب X أثناق واحد X أثناق واحد ماعناش
+
+339
+00:32:56,620 --> 00:33:03,960
+مشكلة تمام بده نشتق يبقى واحد اتنين X سالب X أثناق
+
+340
+00:33:03,960 --> 00:33:13,410
+اتنينالصفة التالت ZERO اتنين اتنين X اصلاق اص
+
+341
+00:33:13,410 --> 00:33:18,850
+تلاتة وهي المحددبدي افكر محدد باستخدام عناصر
+
+342
+00:33:18,850 --> 00:33:24,250
+العمود الاول لشانه فيه صفر او عناصر الصف التالت
+
+343
+00:33:24,250 --> 00:33:28,790
+سيان هيك و الله هيك كله بيعطيني نفس النتيجة يبقى
+
+344
+00:33:28,790 --> 00:33:34,430
+هاد يا بنات X فيه بدي اشطب صفها و عمودها بيصير
+
+345
+00:33:34,430 --> 00:33:42,910
+جداش هنااربع اكس اص ناقص اتنين يبقى هنا اربع اكس
+
+346
+00:33:42,910 --> 00:33:49,230
+اص ناقص اتنين هذا الرئيسي ناقص مع ناقص بيصير زائد
+
+347
+00:33:49,230 --> 00:33:55,130
+اتنين اكس اص ناقص اتنين زائد اتنين اكس اص ناقص
+
+348
+00:33:55,130 --> 00:34:02,250
+اتنين يساء لسه كمان الحد اللي بعده بإشارتهاش سالب
+
+349
+00:34:02,250 --> 00:34:08,960
+حسب قعدة الإشاراتيبقى سالب واحد فيه بدي أجوب أشطب
+
+350
+00:34:08,960 --> 00:34:16,060
+صفه و عموده يبقى بصير هذا فهذا باتنين X أُس سالب
+
+351
+00:34:16,060 --> 00:34:19,020
+واحد يبقى اتنين
+
+352
+00:34:27,980 --> 00:34:34,460
+نقص اتنين اكس واس ناقص واحد ناقص اتنين اكس واس
+
+353
+00:34:34,460 --> 00:34:38,940
+ناقص واحد نقص اتنين اكس واس ناقص واحد نقص اتنين
+
+354
+00:34:38,940 --> 00:34:39,600
+اكس واس ناقص واحد نقص اتنين اكس واس ناقص واحد نقص
+
+355
+00:34:39,600 --> 00:34:39,600
+اتنين اكس واس ناقص واحد نقص اتنين اكس واس ناقص
+
+356
+00:34:39,600 --> 00:34:39,600
+واحد نقص اتنين اكس واس ناقص واحد نقص اتنين اكس واس
+
+357
+00:34:39,600 --> 00:34:45,740
+ناقص واحد نقص اتنين اكس واس ناقص واحد نقص اتنين
+
+358
+00:34:45,740 --> 00:34:49,580
+اكس واس ناقص واحد نقص اتنين اكس واس ناقص واحد نقص
+
+359
+00:34:49,580 --> 00:34:59,500
+اتنينزي 2x-1 يعني جداش 6 على x 6x-1 يعني 6 على x
+
+360
+00:34:59,500 --> 00:35:04,030
+هل هذا الكلب يسوي zero في يوم من الأيام؟طبعا لأ
+
+361
+00:35:04,030 --> 00:35:09,510
+لأنه اشترط في المثل ان x greater than 0 يبقى هذا
+
+362
+00:35:09,510 --> 00:35:17,430
+لا يمكن أن يساوي 0 مدام لا يساوي 0 سا اللي هو ال x
+
+363
+00:35:17,430 --> 00:35:23,450
+و ال x تربية and ال 1 على x are linearly
+
+364
+00:35:23,450 --> 00:35:30,010
+independentيعني يتكوّنوا لمين؟ ال general solution
+
+365
+00:35:30,010 --> 00:35:36,590
+تبع من؟ تبع ال homogeneous يعني هنا صار عندنا YC
+
+366
+00:35:36,590 --> 00:35:46,800
+بدي يساوي C1 X C2 X تربيهة C3 X أُص ناقص واحديبقى
+
+367
+00:35:46,800 --> 00:35:51,440
+هذا حل مين؟ حل ال homogenous differential equation
+
+368
+00:35:51,440 --> 00:35:56,320
+بدنا نيجي ل ال non homogenous ال runnerskin موجود
+
+369
+00:35:56,320 --> 00:35:59,080
+يبدأ يجيب ال runnerskin one و ال runnerskin two و
+
+370
+00:35:59,080 --> 00:36:03,860
+ال runnerskin three بس بدأ يطلع اه استرنا شوية طلع
+
+371
+00:36:03,860 --> 00:36:08,430
+في المعامل هنا قداشاكستاكيبك ممنوع يظل هذا
+
+372
+00:36:08,430 --> 00:36:13,030
+اكستاكيب اذا بروح اجسم طرفين المعادلة كله عالميا
+
+373
+00:36:13,030 --> 00:36:19,450
+على اكستاكيب فباجي بقوله هنا the differential
+
+374
+00:36:19,450 --> 00:36:28,910
+equation one is written as بروح اكتبه على الشكل
+
+375
+00:36:28,910 --> 00:36:34,190
+الجديديبقى y triple prime زي ما هو بتخلي المعاملة
+
+376
+00:36:34,190 --> 00:36:39,970
+تبعها واحد صحية زائد واحد على x في ال y double
+
+377
+00:36:39,970 --> 00:36:48,710
+prime اللي بعدها ناقص اتنين على x تربيع في ال y
+
+378
+00:36:48,710 --> 00:36:55,130
+prime جسمناها على x تكييف زائد اتنين على x تكييف
+
+379
+00:36:55,130 --> 00:37:02,770
+كله في ال yيساوي كده يا بنات؟ يساوي من X يبقى هذه
+
+380
+00:37:02,770 --> 00:37:06,970
+المعادلة اللي صارت هنا يبقى صارت هذه يا بنات هي
+
+381
+00:37:06,970 --> 00:37:13,630
+هذه G of T مش اللي عندنا هذه G of T لأن المعامل
+
+382
+00:37:13,630 --> 00:37:18,150
+هنا ماهوش واحد صحيح يبقى بيصير بالشكل اللي عندنا
+
+383
+00:37:19,130 --> 00:37:25,030
+بقدر اجيب من الرونس كين وان as a function of T
+
+384
+00:37:25,030 --> 00:37:32,930
+تكامل لل G of T ل .. لأ بدنا نجيب الرونس كين وان
+
+385
+00:37:32,930 --> 00:37:39,130
+احنا في الأول قبله الرونس كين وان of T يبقى يساوي
+
+386
+00:37:39,130 --> 00:37:43,530
+العمول الأولبدالي على المحدد اللي عندي و اشيله و
+
+387
+00:37:43,530 --> 00:37:49,570
+اكتب بداله 001 يبقى 001
+
+388
+00:37:50,020 --> 00:37:57,320
+اللي بعده X تربيع اتنين X اتنين اللي بعده X أسالب
+
+389
+00:37:57,320 --> 00:38:04,020
+واحد سالب X أسالب اتنين اتنين X أسالب تلاتة بدي
+
+390
+00:38:04,020 --> 00:38:09,860
+افكر محدد بالاستخدام عناصر العمود الأول يبقى يساوي
+
+391
+00:38:09,860 --> 00:38:17,350
+واحد فيهوشط بصفه و عموده بصير هنا اربعة اكس اثناق
+
+392
+00:38:17,350 --> 00:38:26,310
+اثنين يبقى اربعة اكس اثناق اثنين بصير
+
+393
+00:38:26,310 --> 00:38:33,350
+سالب واحد يبقى هنا بصير عندى هذا كله بجداشف سالب
+
+394
+00:38:33,350 --> 00:38:40,830
+واحد وهنا سالب اتنينسالف اتنين يبقى الجواب كده؟
+
+395
+00:38:40,830 --> 00:38:47,130
+سالف تلاتة كونستر بعد ذلك بروح أجيب الرونسكين 2 as
+
+396
+00:38:47,130 --> 00:38:53,870
+a function of T برجع العمود الأول كما كان X واحد
+
+397
+00:38:53,870 --> 00:39:00,660
+زيرو العمود التاني Zero Zero واحدالثالث كما هو
+
+398
+00:39:00,660 --> 00:39:05,760
+يبقى x أوص ناقص واحد ناقص x أوص ناقص اتنين x أوص
+
+399
+00:39:05,760 --> 00:39:12,280
+ناقص تلاتة و يساوي بدا افكس المحدد باستخدام عناصر
+
+400
+00:39:12,280 --> 00:39:17,560
+العمودي الثاني لان هو اللي فيه الصفات يبقى حسب
+
+401
+00:39:17,560 --> 00:39:23,800
+قاعة الإشارات هذا إشارته ايه؟سالبة يبقى سالب واحد
+
+402
+00:39:23,800 --> 00:39:30,220
+وبدنا نروح نشطه بصفه و عموده بيضل لإن هنا قداش
+
+403
+00:39:30,220 --> 00:39:36,680
+اللي هو سالب X والسالب واحد يبقى سالب X والسالب
+
+404
+00:39:36,680 --> 00:39:43,280
+واحد هي عندنا الرئيسي ناقص X والسالب واحد ناقص X
+
+405
+00:39:43,280 --> 00:39:50,890
+والسالبواحد يبقى ناقص في ناقص بزايد وبضال عند هنا
+
+406
+00:39:50,890 --> 00:39:56,590
+اتنين على اكس اتنين اكس قص ناقص واحد يبقى اتنين
+
+407
+00:39:56,590 --> 00:40:02,270
+على اكس استاذ ليش الواحد ثالث؟ اللي هنيط منهم هذا
+
+408
+00:40:02,270 --> 00:40:06,910
+سمعت وقعت شرط المحددات في الثانوي لما كنت تفكر
+
+409
+00:40:06,910 --> 00:40:12,250
+محدد ثلاثيزائد، ناقص، زائد، ناقص، زائد، ناقص،
+
+410
+00:40:12,250 --> 00:40:18,230
+زائد، ناقص، زائد،
+
+411
+00:40:18,230 --> 00:40:22,270
+ناقص،
+
+412
+00:40:22,270 --> 00:40:25,510
+زائد، ناقص، زائد، ناقص، زائد، ناقص، زائد، ناقص،
+
+413
+00:40:25,510 --> 00:40:29,850
+زائد، ناقص، زائد، ناقص، زائد، ناقص، زائد، ناقص،
+
+414
+00:40:29,850 --> 00:40:29,850
+زائد، ناقص، زائد، ناقص، زائد، ناقص، زائد، ناقص،
+
+415
+00:40:29,850 --> 00:40:29,890
+زائد، ناقص، زائد، ناقص، زائد، ناقص، زائد، ناقص،
+
+416
+00:40:29,890 --> 00:40:34,470
+زائد، ناقص، زائد، ناقص، زائد، ناقص، زائد، ناقصيبقى
+
+417
+00:40:34,470 --> 00:40:39,130
+حسب قعة الإشارات، الإشارة تبعت معلها بالسالب، يبقى
+
+418
+00:40:39,130 --> 00:40:44,820
+هذه العنصر اللي احنا بنحل بواسطتهيبقى حسب قاعدة
+
+419
+00:40:44,820 --> 00:40:49,280
+الإشارات إشارته مين؟ سالب يبقى الواحد هذا إشارته
+
+420
+00:40:49,280 --> 00:40:55,020
+سالب حسب قاعدة الإشارات قشط بصفه عموده بصير ناقص
+
+421
+00:40:55,020 --> 00:40:59,760
+إكسوس ناقص واحد ناقص إكسوس ناقص واحد يعني اتنين
+
+422
+00:40:59,760 --> 00:41:05,220
+إكسوس ناقص واحد يعني اتنين على إكس هذا الرونسكين
+
+423
+00:41:05,220 --> 00:41:05,900
+اتنين
+
+424
+00:41:10,810 --> 00:41:16,830
+العمود الأول زي ما هو مش هنغيره و العمود الثاني
+
+425
+00:41:16,830 --> 00:41:22,770
+كمان مش هنغيره بناروح للعمود التالت و نشيله و نحط
+
+426
+00:41:22,770 --> 00:41:25,330
+بداله 001
+
+427
+00:41:27,400 --> 00:41:35,200
+عناصر العمود الثالث باستخدام
+
+428
+00:41:35,200 --> 00:41:37,160
+المحدد
+
+429
+00:41:39,070 --> 00:41:46,590
+موجب يبقى أي واحد فيه اشط بصفه و عموده بصيلي اتنين
+
+430
+00:41:46,590 --> 00:41:54,630
+اكس تربيع ناقص اكس تربيع يبقى الجواب كده اكس تربيع
+
+431
+00:41:54,630 --> 00:41:59,970
+فقط لغير يبقى جنب ترونسكني التلاتة يبقى الان سهل
+
+432
+00:41:59,970 --> 00:42:07,500
+علي اجيب من اليهات التلاتة عندى يبقى بدنا نروحنجيب
+
+433
+00:42:07,500 --> 00:42:14,980
+U1 و U2 و U3 باستخدام التكامل
+
+434
+00:42:19,700 --> 00:42:24,440
+يبقى بدى أروح أجيب له main اللي هو U1 as a
+
+435
+00:42:24,440 --> 00:42:33,480
+function of X يا بنات مش of T كله X كله X كله X
+
+436
+00:42:33,480 --> 00:42:39,180
+ماعنديش T المثلة كلها بدلالة من؟ صح هي كلها بدلالة
+
+437
+00:42:39,180 --> 00:42:44,600
+من؟ بدلالة ال X يبقى U1 as a function of X تكامل
+
+438
+00:42:44,600 --> 00:42:52,760
+ال G of Xفى ال run skin 1 of X على ال run skin of
+
+439
+00:42:52,760 --> 00:42:59,480
+X كله as a function of X يساوي تكامل ال G of X
+
+440
+00:42:59,480 --> 00:43:05,500
+اللي يجى ده صارت ان اتنين X مش اربعة X تربية يبقى
+
+441
+00:43:05,500 --> 00:43:09,420
+هنا اتنين X هى نزلناها زى ما هي
+
+442
+00:43:13,370 --> 00:43:20,370
+سالب تلاتة يبقى سالب تلاتة على الرونسكين حسبناه
+
+443
+00:43:20,370 --> 00:43:28,390
+قبل شوية فكان جديش ستة على اكس يبقى هذا ستة على
+
+444
+00:43:28,390 --> 00:43:35,420
+اكس كله في DXأما 6 مع 6 مع السلامة و ال X بتطلع
+
+445
+00:43:35,420 --> 00:43:46,620
+فوق بيبقى سالب تكامل X تربيع DX 2 في 3 بال 6 مع 6
+
+446
+00:43:46,620 --> 00:43:51,960
+ال X تطلع فوق بيصير X تربيع والسالب برا يبقى هنا
+
+447
+00:43:51,960 --> 00:44:01,900
+سالب X تكيب على 3 زائد K1بعد ذلك بناروح نجيب ال U2
+
+448
+00:44:01,900 --> 00:44:09,760
+integration لل G of T لمين؟ للرونسكين 2 of T على
+
+449
+00:44:09,760 --> 00:44:16,860
+ال رونسكين of T كله في DT يسوى تكامل لل 2X في
+
+450
+00:44:16,860 --> 00:44:24,410
+رونسكين 2 رونسكين 2 لم يبقى داش ب2 على Xيبقى هذا
+
+451
+00:44:24,410 --> 00:44:33,990
+اتنين على اكس كله على ستة على اكس دي اكس يساوي اظن
+
+452
+00:44:33,990 --> 00:44:38,390
+ان ال X هذه مع ال X هذه مع السلامة بيطير و بيظل
+
+453
+00:44:38,390 --> 00:44:44,350
+عندى اتنين في اتنين باربع يعني اربع على ستة يبقى
+
+454
+00:44:44,350 --> 00:44:52,270
+اربع على ستة تكامل لل X DXهذه البنات بتروح مع هذه
+
+455
+00:44:52,270 --> 00:44:56,090
+مضال اتنين في اتنين اللي هو باربع ستة خليك برا
+
+456
+00:44:56,090 --> 00:44:59,330
+مضال واحد على X بتنقل بال X فوت بيصير بالشكل اللي
+
+457
+00:44:59,330 --> 00:45:05,550
+عندنا هذا يبقى هذه كأنها تلتين في X تربيع على
+
+458
+00:45:05,550 --> 00:45:15,930
+اتنين زائد constant K2 يعني تلت X تربيع زائد K2
+
+459
+00:45:18,070 --> 00:45:25,090
+بالمثل بناروح نجيب U3 يبقى هى تكاهة طبعا كله Xاتي
+
+460
+00:45:25,090 --> 00:45:33,150
+بنات مش T كله بدلالة ال X هذا كله بدلالة ال X احنا
+
+461
+00:45:33,150 --> 00:45:37,950
+معالجة معانا هدى ال T لأ هدى مظبوط اكتبنا صح ده بس
+
+462
+00:45:37,950 --> 00:45:44,330
+هدى و كله بدالة X مظبوططيب يبقى هذه الـ g of x في
+
+463
+00:45:44,330 --> 00:45:48,990
+الورنسكين three of x على الورنسكين as a function
+
+464
+00:45:48,990 --> 00:45:55,750
+of x dx يبقى تكامل للإتنين x فيه الورنسكين three
+
+465
+00:45:55,750 --> 00:46:02,930
+of x كله بيبقى داش بx تربيع يبقى بx تربيع لمين؟
+
+466
+00:46:02,930 --> 00:46:11,600
+لستة على x كله بالنسبة إلى dxأتنين على ستة بجداش
+
+467
+00:46:11,600 --> 00:46:19,540
+بطول تكامل هذي تطلع فوق بصير جداش أبناء X أص أربعة
+
+468
+00:46:19,540 --> 00:46:24,880
+X تكيب و تجيب و تكمل تصير X أص أربعة DX يبقى هذي
+
+469
+00:46:24,880 --> 00:46:33,600
+تلت و هذي X أص خمسة على خمسة زائد constant K3 يعني
+
+470
+00:46:33,600 --> 00:46:42,850
+واحد على خمستاشر X أص خمسةزائد كنستان K3 الان نقول
+
+471
+00:46:42,850 --> 00:46:51,910
+له take خدلي K1 يسوى K2 يسوى K3 يسوى Zero وعرفته
+
+472
+00:46:51,910 --> 00:46:59,530
+ليش مصبوط يبقى بده أروح أجيبله capital Y of Tاللي
+
+473
+00:46:59,530 --> 00:47:11,490
+هو U1 وY1 زائد U2 وY2 زائد U3 وY3 وY7 الآن نجي الى
+
+474
+00:47:11,490 --> 00:47:17,590
+ال U1 ال U1 ماني قاعد ابدأ عشان ناقص تلت X تكيب
+
+475
+00:47:17,590 --> 00:47:26,750
+يبقى ناقص تلت X تكيب فمين؟ في Y1 اللي هو X اللي
+
+476
+00:47:26,750 --> 00:47:35,870
+بعدهبنجي لـ U2 الـ U2 لتلت X تربية زائد تلت X
+
+477
+00:47:35,870 --> 00:47:44,010
+تربية في من؟ في X تربية نجي لبعده U3 يبقى زائد
+
+478
+00:47:44,010 --> 00:47:51,250
+واحد على خمستاشر X أس خمسة في X أس ناقص واحد ايش
+
+479
+00:47:51,250 --> 00:47:57,120
+رأيك؟ هذي هي هذي بيشارة مخالفة صح؟يبقى يجروا
+
+480
+00:47:57,120 --> 00:48:01,640
+الفاتحة انا روحهم على السلامة بضل ان اقدرش واحد
+
+481
+00:48:01,640 --> 00:48:07,380
+على خمستاشر X أُس أربعة هذا ال particular solution
+
+482
+00:48:07,380 --> 00:48:11,480
+لل differential equation one اذا بقدر اجيب له من
+
+483
+00:48:11,480 --> 00:48:17,680
+ال general solution فبروح بقول له هنا the general
+
+484
+00:48:17,680 --> 00:48:31,160
+solution of the equationone is Y تساوي YC زائد
+
+485
+00:48:31,160 --> 00:48:42,360
+capital Y of T YC هي فوق تمام اللي هو C كيف؟
+
+486
+00:48:42,360 --> 00:48:47,280
+بس طالب ال particular خلاص والله نايحنا يبقى خلاص
+
+487
+00:48:47,280 --> 00:48:51,680
+بروزي هذا والله يعطيك العافية خلاص هذا مسامحي نفيد
+
+488
+00:48:54,290 --> 00:48:56,990
+خلاص من الناياط دي على جد المقبض زي ما دي بناكوس
+
+489
+00:48:56,990 --> 00:49:00,190
+في الامتحان don't evaluate اللي كنت أصلا تبقى حاطة
+
+490
+00:49:00,190 --> 00:49:02,590
+تاريخ بين جوسينة بخاط غامج و اللي جات بعض الناس
+
+491
+00:49:02,590 --> 00:49:06,230
+لسه بتروح تحسبلي في الكون أصلا بتضيع وقت هالبلاش
+
+492
+00:49:06,230 --> 00:49:11,950
+طب أنا مش طالب و تشتغلي ليش طيب
+
+493
+00:49:24,680 --> 00:49:29,480
+في عندكوا في الكتاب مجموعة من المسائل وكتبليك جي
+
+494
+00:49:29,480 --> 00:49:33,360
+وف ت بدلالة جي وف ت مخلية مش ميعطيكي قيمة إلها
+
+495
+00:49:33,360 --> 00:49:37,980
+وقالليك حلي بتقدر تكمليها هذه؟ مش هتقدر تكمليها،
+
+496
+00:49:37,980 --> 00:49:42,980
+بدنا نعطيكوا مثال منهم ونوريكوا كيف بنحل هذا النوع
+
+497
+00:49:42,980 --> 00:49:47,860
+من الأسئلة حد لاقي تساول هنا قبل ما نتقل إلى
+
+498
+00:49:47,860 --> 00:49:52,920
+المثال الثالث؟ حد فيكوا لاقي تساول هنا؟
+
+499
+00:50:12,000 --> 00:50:22,160
+مثال رقم تلاتة رقم تلاتة رقم تلاتة رقم تلاتة
+
+500
+00:50:22,160 --> 00:50:28,840
+رقم تلاتة رقم تلاتة رقم تلاتة رقم تلاتة رقم
+
+501
+00:50:28,840 --> 00:50:30,680
+تلاتة رقم تلاتة رقم تلاتة رقم تلاتة رقم تلاتة رقم
+
+502
+00:50:30,680 --> 00:50:30,680
+تلاتة رقم تلاتة رقم تلاتة رقم تلاتة رقم تلاتة رقم
+
+503
+00:50:30,680 --> 00:50:30,680
+تلاتة رقم تلاتة رقم تلاتة رقم تلاتة رقم تلاتة رقم
+
+504
+00:50:30,680 --> 00:50:30,720
+تلاتة رقم تلاتة رقم تلاتة رقم تلاتة رقم تلاتة رقم
+
+505
+00:50:30,720 --> 00:50:37,940
+تلاتة رقم تلاتة رقم تلاتة
+
+506
+00:50:37,940 --> 00:50:39,280
+رقم ت
+
+507
+00:50:48,610 --> 00:51:00,190
+مجتمل على التكاملات of a particular solution
+
+508
+00:51:00,190 --> 00:51:07,650
+of a particular solution of the
+
+509
+00:51:14,160 --> 00:51:21,380
+مشتقة تالتة ل Y ناقص المشتقة الثانية ل Y زائد
+
+510
+00:51:21,380 --> 00:51:28,500
+المشتقة الأولى ل Y ناقص Y بدون مشتقة يساوي G of T
+
+511
+00:51:28,500 --> 00:51:31,580
+وهذا المعادلة رقم واحد
+
+512
+00:51:54,450 --> 00:52:00,530
+Find a formula هاتل صيغة مجتملة على التكاملات تبع
+
+513
+00:52:00,530 --> 00:52:03,310
+ال particular solution لل differential equation
+
+514
+00:52:03,310 --> 00:52:06,710
+اللي عندنايعني فعلا ماعطيني معادلة تفاضلي و بذا
+
+515
+00:52:06,710 --> 00:52:11,570
+شكل لكن الطرف اليمين كاتب و كدالة انا مش عارفة g
+
+516
+00:52:11,570 --> 00:52:15,030
+of t مين ما تكون تكون مش بعطيني زي السؤال يجابله
+
+517
+00:52:15,030 --> 00:52:18,950
+ده اللي بقعد نضربه و نختصره و نكامله إذا هذا هضل
+
+518
+00:52:18,950 --> 00:52:23,570
+بدلالة مين بدلالة التكامل التكتيك اللي اتبع في
+
+519
+00:52:23,570 --> 00:52:26,670
+المثالين اللي جابله هو نفس التكتيك هذا اللهم إلا
+
+520
+00:52:26,670 --> 00:52:31,050
+بقدرش أكامل فبضل التكامل موجود وانفي المسألة كما
+
+521
+00:52:31,050 --> 00:52:35,830
+هو إذا أنا بدي أبدأ في حل ال homogeneous ثم ال non
+
+522
+00:52:35,830 --> 00:52:44,950
+homogeneous يبقى باجي بقوله solution let
+
+523
+00:52:44,950 --> 00:52:58,880
+y تساوي e أس RTBA solution of theEquation للمعادلة
+
+524
+00:52:58,880 --> 00:53:04,580
+Y triple prime ناقص Y double prime زائد Y prime
+
+525
+00:53:04,580 --> 00:53:11,000
+ناقص Y يسوى 0 هو ال homogenous يبقى then the
+
+526
+00:53:11,000 --> 00:53:21,020
+characteristic equation is R تكييف ناقص R تربيع
+
+527
+00:53:21,020 --> 00:53:27,790
+زائد R ناقص 1 يسوى 0الغلطة اللى كنت اشوفها من
+
+528
+00:53:27,790 --> 00:53:33,290
+بعضكوا في الامتحان و تكتبلي هذه R اه و هذه غلطة
+
+529
+00:53:33,290 --> 00:53:37,210
+فاحشة كبيرة جدا من الكبائر بالنسبة لنا في الامتحان
+
+530
+00:53:37,210 --> 00:53:42,660
+طيب نيجي نحل المعادلة اللى عندنا هذهطلعيلي في هدول
+
+531
+00:53:42,660 --> 00:53:47,640
+اتنين ممكن اخد منهم R تربية عام المشترك اذا لو
+
+532
+00:53:47,640 --> 00:53:52,000
+اخدت R تربية عام المشترك بيظل كده؟ R ناقص واحد
+
+533
+00:53:52,000 --> 00:53:58,200
+وعندي ضايل هناك R ناقص واحد يساوي Zeroإذا أنا ممكن
+
+534
+00:53:58,200 --> 00:54:04,940
+أخد من الطرفين R ناقص واحد عامل مشترك مضل من الجزء
+
+535
+00:54:04,940 --> 00:54:10,860
+الأول قداش R تربيع مضل من الجزء الثاني قداش واحد
+
+536
+00:54:10,860 --> 00:54:16,400
+صحيح يبقى زائد واحد يساوي zero من هذه المعادلة
+
+537
+00:54:16,400 --> 00:54:23,160
+بقدر أقول ان R واحد يساوي واحدوR2 وR3 يبدو يساوي
+
+538
+00:54:23,160 --> 00:54:29,360
+الزائد او ناقص اذا اصبح حل ال homogeneous هو YC
+
+539
+00:54:29,360 --> 00:54:38,040
+يساوي C1A أس 1 في T يبقى A أس T هدول Complex يبقى
+
+540
+00:54:38,040 --> 00:54:45,500
+زائد C2 Cos T زائد C3 في Sin T
+
+541
+00:54:50,080 --> 00:54:55,140
+يبقى هذا حل مين اللي هو اللي هو مجازف طبعا هو جالي
+
+542
+00:54:55,140 --> 00:54:58,480
+formula محتوية على ال integral لل particular
+
+543
+00:54:58,480 --> 00:55:02,700
+solution بده شكل ال particular solution كويس ال
+
+544
+00:55:02,700 --> 00:55:07,700
+particular solution يبقى بده شيل C1 وC2 وC3 وحق
+
+545
+00:55:07,700 --> 00:55:14,000
+بدلها مين U1 وU2 وU3 بس قبل بدك تحسب ال runnerskin
+
+546
+00:55:14,000 --> 00:55:20,770
+للحلول التلاتة هذهو بعد هيك الله بيفرجها يبقى بناء
+
+547
+00:55:20,770 --> 00:55:26,070
+عليها لو جبت أخدت ال رونسكين as a function of T
+
+548
+00:55:26,070 --> 00:55:32,930
+يبقى باجي بقوله هذا الحل الأول E was T و الحل
+
+549
+00:55:32,930 --> 00:55:39,280
+التاني cosine T و الحل التالت sin Tبدي اشتق
+
+550
+00:55:39,280 --> 00:55:44,000
+المشتقة الاولى ال exponential كما هي هذه ناقص sin
+
+551
+00:55:44,000 --> 00:55:50,020
+t هذه cosine t بدي اشتق كمان مرة يبقى ال
+
+552
+00:55:50,020 --> 00:55:56,120
+exponential كما هي وهذه ناقص cosine t وهذه ناقص
+
+553
+00:55:56,120 --> 00:56:03,260
+sin t وهي المحدد بدي احسب قداش قيمة هذا المحدد
+
+554
+00:56:03,260 --> 00:56:04,960
+ويساوي
+
+555
+00:56:07,510 --> 00:56:12,410
+ممكن بلغة المحادثة بالخاص اخد Eost عامل مشترك من
+
+556
+00:56:12,410 --> 00:56:16,890
+العمود الأول يصبح واحد واحد واحد هو هكتب المحادثة
+
+557
+00:56:16,890 --> 00:56:21,530
+يعني قصة طويلة وشيء لكن انا بده افك دغري باستخدام
+
+558
+00:56:21,530 --> 00:56:25,670
+العمود الأول باستخدام الصف الأول بأي حاجة ماشية
+
+559
+00:56:25,670 --> 00:56:31,690
+على خليني افك باستخدام العمود الأول يبقى هذا بده
+
+560
+00:56:31,690 --> 00:56:38,920
+يساوي Eost فيهيبقى بتروح أشته بصفه و عموده يبقى يا
+
+561
+00:56:38,920 --> 00:56:44,680
+بنات كده؟ sin تربيه زائد cosine تربيه يبقى هذه
+
+562
+00:56:44,680 --> 00:56:51,960
+الـsin تربيه T زائد cosine تربيه T انتهينا منها
+
+563
+00:56:51,960 --> 00:56:57,300
+يهودة هذه حسب قاعدة الإشارات وجب الله سالب كده؟
+
+564
+00:56:57,810 --> 00:57:06,030
+يبقى هاي ناقص E of T فيه بتروح عشته بصفه و عموده
+
+565
+00:57:06,030 --> 00:57:16,890
+بصير سالب sin cos وموجب sin cos يبقى سالب sin T
+
+566
+00:57:16,890 --> 00:57:27,730
+cos T زائد sin T cos Tخلصنا منها وضل ال term
+
+567
+00:57:27,730 --> 00:57:34,310
+التالت حسب قاعدة الإشارات AOST فين يبقى بننشته
+
+568
+00:57:34,310 --> 00:57:40,450
+بصفه و عموده بصير cosine تربيه زائد sine تربيه
+
+569
+00:57:40,450 --> 00:57:48,990
+يبقى cosine تربيه T زائد sine تربيه T ويسافر اظن
+
+570
+00:57:48,990 --> 00:57:53,160
+ان هذه راحة في ال zero يا بناتطيب بضل هذه قداش
+
+571
+00:57:53,160 --> 00:58:00,240
+واحد ل Eost و هنا واحد في Eost يبقى الجواب كله
+
+572
+00:58:00,240 --> 00:58:07,560
+اتنين Eost واضح ماله لا يساوي Zero إذا الحلول اللي
+
+573
+00:58:07,560 --> 00:58:11,720
+جيبناها دول منهمبكونولي ال fundamental set of
+
+574
+00:58:11,720 --> 00:58:18,960
+solutions أو linearly independent يبقى هنا الـ E
+
+575
+00:58:18,960 --> 00:58:22,420
+أُس T E أُس T E أُس T E أُس T E أُس T E أُس T E
+
+576
+00:58:22,420 --> 00:58:23,440
+أُس T E أُس T E أُس T E أُس T E أُس T E أُس T E
+
+577
+00:58:23,440 --> 00:58:27,400
+أُس T E أُس T E أُس T E أُس T E أُس T E أُس T E
+
+578
+00:58:27,400 --> 00:58:28,500
+أُس T E أُس T E أُس T E أُس T E أُس T E أُس T E
+
+579
+00:58:28,500 --> 00:58:28,700
+أُس T E أُس T E أُس T E أُس T E أُس T E أُس T E
+
+580
+00:58:28,700 --> 00:58:28,700
+أُس T E أُس T E أُس T E أُس T E أُس T E أُس T E
+
+581
+00:58:28,700 --> 00:58:31,850
+أُس T E أُس T E أُس T E أُس T E أُس Tما دام
+
+582
+00:58:31,850 --> 00:58:36,850
+linearly independent هذا بدي يعطينا انه حل ال
+
+583
+00:58:36,850 --> 00:58:41,370
+homogeneous هو ما احنا كتبناه صحيح فوق خلاص و هذا
+
+584
+00:58:41,370 --> 00:58:44,890
+مش لازمني بس كويس ان اتأكدنا انهم linearly
+
+585
+00:58:44,890 --> 00:58:49,520
+independent و جيبنا ايه؟ اللي هو الرونسكينبتجيب ال
+
+586
+00:58:49,520 --> 00:58:54,040
+runskin1 و runskin2 و runskin3 يبقى بتجيب ال
+
+587
+00:58:54,040 --> 00:58:59,040
+runskin1 as a function of t بس قبلها بتروح اتكد
+
+588
+00:58:59,040 --> 00:59:04,420
+المعامل هنا قداش يبقى احنا جاهزين يبقى هذا الكلام
+
+589
+00:59:04,420 --> 00:59:10,060
+ها بدنا نجيب ال runskin1 ال runskin1 هو المحدد
+
+590
+00:59:10,060 --> 00:59:13,600
+اللي هو 001
+
+591
+00:59:31,110 --> 00:59:37,330
+يبقى العمودين اتنين زي مهمة بدنا نفك هذه المحددات
+
+592
+00:59:37,330 --> 00:59:44,670
+باستخدامالعمود الأول يبقى واحد فيه اشط بصفه عموده
+
+593
+00:59:44,670 --> 00:59:50,990
+يبقى sin تربيه زائد cos تربيه يبقى sin تربيه T
+
+594
+00:59:50,990 --> 00:59:56,880
+زائد cos تربيه T كله يساوي جداشالواحد بدنا نيجر
+
+595
+00:59:56,880 --> 01:00:03,060
+رونسكين 2 as a function of T يبقى على العمود الأول
+
+596
+01:00:03,060 --> 01:00:11,840
+Eost Eost Eost العمود التاني 001 العمود التالت هو
+
+597
+01:00:11,840 --> 01:00:21,860
+sin T وcos T و- sin T بالشكل اللي عندنابتفكر محدد
+
+598
+01:00:21,860 --> 01:00:27,240
+باستخدام عناصر العمود الثانية حسب قاعدة الإشارات
+
+599
+01:00:28,040 --> 01:00:35,100
+سالبة يبقى هذا الكلام سالب واحد فيه اشط بصفه عموده
+
+600
+01:00:35,100 --> 01:00:41,260
+بيصير E of T cosine ناقص E of T sin يبقى E of T
+
+601
+01:00:41,260 --> 01:00:50,440
+cosine T ناقص E of T في sin T يعني هذه كأنها sin T
+
+602
+01:00:50,440 --> 01:00:57,950
+ناقص cosine T كله في ال exponential E of Tبالمرة
+
+603
+01:00:57,950 --> 01:01:04,090
+نجيب الرانس كيني 3 as a function of T العمود الأول
+
+604
+01:01:04,090 --> 01:01:11,510
+كما هو بدون تغيير العمود الثاني كما هو برضه زيه
+
+605
+01:01:11,510 --> 01:01:18,230
+بدون تغيير و هنا ناقص cosine of T والعمود التالت
+
+606
+01:01:18,230 --> 01:01:24,370
+اللي هو 001بدا فك المحدد باستخدام عناصر العمود
+
+607
+01:01:24,370 --> 01:01:30,670
+الثالث يبقى هذا الكلام يساوي حسب قاعة الإشارات
+
+608
+01:01:30,670 --> 01:01:39,230
+شرطه بالموجب يبقى في شطاب نصفه وعموده يبقى سالب
+
+609
+01:01:39,230 --> 01:01:49,550
+sin T في Eost وسالب cosine يبقى سالب Eost في sin T
+
+610
+01:02:06,540 --> 01:02:12,380
+خلصنا من الرونسكينز التلاتة اذا بقدر اجيب ال U1 و
+
+611
+01:02:12,380 --> 01:02:20,030
+U2 و U3 بدي اجيب ال U1 as a function of Tيبقى
+
+612
+01:02:20,030 --> 01:02:26,630
+تكامل جي او ت في رونسكين one او ت على رونسكين او ت
+
+613
+01:02:26,630 --> 01:02:33,810
+دي ت طيب ايش رايكوا بدل ما كل مرة احط كونصان هو
+
+614
+01:02:33,810 --> 01:02:38,390
+ايش رايكوا يخليه تكامل محدود وبالتالي يتخلص من جزء
+
+615
+01:02:38,390 --> 01:02:44,130
+ال رونسكين هذه تمام كيف يخليه تكامل محدود بقولك من
+
+616
+01:02:44,130 --> 01:02:51,260
+عندي ال T ناد لغاية ال Tمن الـ T node أي نقطة
+
+617
+01:02:51,260 --> 01:02:56,220
+موجودة على الهدى الدوال عليها continuous المعاملات
+
+618
+01:02:56,220 --> 01:02:59,640
+الدوال اللي عندي بما فيهم جيوبتي continuous على
+
+619
+01:02:59,640 --> 01:03:04,360
+الفترة من T node لغاية T node نقطة ثابتة تمام؟
+
+620
+01:03:04,360 --> 01:03:08,820
+وعند أي نقطة الدوال هذه متفق علينا تكون معرفة
+
+621
+01:03:08,820 --> 01:03:12,760
+عندها أو continuous عندنا ماشي العالم؟وبالتالي ما
+
+622
+01:03:12,760 --> 01:03:15,920
+كامل بقولش زي ال constant لا K واحد ولا K اتنين
+
+623
+01:03:15,920 --> 01:03:21,620
+ولا K تلاتة بمشي لها طيب بدها تسأل هو ده كمان سؤال
+
+624
+01:03:21,620 --> 01:03:26,320
+لو سويتك بده تقولي طب استنى شوية انت كاتب من T
+
+625
+01:03:26,320 --> 01:03:30,880
+node ل T قولتله صح قال يعني حدود التكامل T طب
+
+626
+01:03:30,880 --> 01:03:36,050
+المتغير اللي جهوه T بنفع؟عندما أقول يا كامل يجب أن
+
+627
+01:03:36,050 --> 01:03:41,510
+أشيل T و أضع مكانها T فالكلام ليس صحيح يبقى لو
+
+628
+01:03:41,510 --> 01:03:50,590
+روحت تغيرت ال T هذي و قلت هك GS WS و هنا WS و هنا
+
+629
+01:03:50,590 --> 01:03:57,990
+DSيبقى لما نكام نبتطلع دالة بدلالة S لما عوض بحدود
+
+630
+01:03:57,990 --> 01:04:02,950
+التكمل هذا الرقم و هذا T بصير كلها بدلالة T يبقى
+
+631
+01:04:02,950 --> 01:04:07,130
+ماقناششي مظبوط و اتريحنا من خلجة ال constant هذا
+
+632
+01:04:07,130 --> 01:04:11,440
+اللي بزهجنا كل مرة طلع و تقوم بالصفةمظبوط؟ طيب
+
+633
+01:04:11,440 --> 01:04:18,920
+كويس، إذا بده يصير هذا تكامل من T node إلى T للـG
+
+634
+01:04:18,920 --> 01:04:26,200
+of S كما هي ون هي وقدام اللي هي بواحد، يبقى في
+
+635
+01:04:26,200 --> 01:04:32,680
+واحد على مين؟ على الـW، وين الـW؟هذا الـ W له
+
+636
+01:04:32,680 --> 01:04:42,200
+اتنين EOS يبقى اتنين EOS S كله في DS يعني يا نص
+
+637
+01:04:42,200 --> 01:04:49,200
+خليك برا مالكش دعوة وهي تكامل من T node إلى T للـ
+
+638
+01:04:49,200 --> 01:04:58,800
+GRS على EOS S أو الـ EOS ناقص Sيالا خلّيني أطلعها
+
+639
+01:04:58,800 --> 01:05:01,700
+فوق و بلاشي نخلّي عندنا إيش في المقامات و إيش في
+
+640
+01:05:01,700 --> 01:05:05,400
+ال bus يبقى هذي لو طلعتها فوق إيش بصير يا بنات
+
+641
+01:05:05,400 --> 01:05:16,460
+بصير E أس ناقص S في ال G of S في ال D أس طيب هات
+
+642
+01:05:16,460 --> 01:05:23,340
+لل U2 باجي بقوله U2 as a function of T تكاملمن T
+
+643
+01:05:23,340 --> 01:05:30,880
+node ل T لل G of S لل one skin two as a function
+
+644
+01:05:30,880 --> 01:05:38,240
+of S على one skin of S كله بالنسبة الى DS يسوى
+
+645
+01:05:38,240 --> 01:05:47,300
+تكامل من عند T node لغاية T G of S خليك زي ما انت
+
+646
+01:05:48,390 --> 01:05:53,410
+ماعناش مشكلة معاك ابني جامين لغنس كنتو اللي هو
+
+647
+01:05:53,410 --> 01:06:00,370
+عنهانة يبقى بقدر أقوله sign s ناقص cosine s في E
+
+648
+01:06:00,370 --> 01:06:12,950
+أُس S يبقى أي قوس sign ال Sماقس cosine ال S كله E
+
+649
+01:06:12,950 --> 01:06:21,050
+أُس S على مين؟ على اتنين E أُس S كله بالنسبة إلى
+
+650
+01:06:21,050 --> 01:06:29,610
+DS تمام؟ يبقى هذا الكلام يشاويتختصر هذه مع هذه مع
+
+651
+01:06:29,610 --> 01:06:36,610
+السلامة والنص شرفنا برا يبقى هذا الكلام نص تكامل
+
+652
+01:06:36,610 --> 01:06:45,210
+من T node لغاية T لمين ل sign ال S ناقص cosine ال
+
+653
+01:06:45,210 --> 01:06:49,910
+S كله في GS في DS
+
+654
+01:06:58,000 --> 01:07:03,200
+أحنا بدنا بس ايش ال particle of solution الصيغة
+
+655
+01:07:03,200 --> 01:07:15,320
+تبعت المجتمل على التكامل طيب
+
+656
+01:07:15,320 --> 01:07:24,330
+بدنا نيجي لأ ل U3 of T U3 of Tيسوي تكامل من T node
+
+657
+01:07:24,330 --> 01:07:32,030
+لغاية T للـ G of S في الرونسكين 3 as a function of
+
+658
+01:07:32,030 --> 01:07:40,210
+S على الرونسكين as a function of SDS ويسوي تكاملمن
+
+659
+01:07:40,210 --> 01:07:45,710
+T نوت ل T للـ G of S نحن نذهب إلى الـ Roneskini 3
+
+660
+01:07:45,710 --> 01:07:52,170
+الـ Roneskini 3 هو السالب عندنا يبقى نكتبه بالسالب
+
+661
+01:07:55,340 --> 01:08:08,880
+و cos sin T سالب sin T سالب cos T كله طبعا S sin S
+
+662
+01:08:08,880 --> 01:08:19,800
+و cos S و E Os S كله على الإتنين E Os S في ال DS
+
+663
+01:08:21,060 --> 01:08:29,140
+كله في ال DS تمام طيب نص برا وال EOS S مع ال EOS S
+
+664
+01:08:29,140 --> 01:08:36,800
+مع السلامة يبقى بصير ان ال main يساوي نص تكامل من
+
+665
+01:08:36,800 --> 01:08:46,080
+T node إلى T لناقص sign ال S ناقص cosine ال S كل
+
+666
+01:08:46,080 --> 01:08:49,620
+هذا في من؟ هذا W1
+
+667
+01:08:53,420 --> 01:09:04,420
+يبقى هذا كله في main في g of s كله في ds طيب ويبدو
+
+668
+01:09:04,420 --> 01:09:08,700
+ال particular solution يبقى ال particular solution
+
+669
+01:09:08,700 --> 01:09:21,280
+capital Y of T يبقى U1Y1 زي U2Y2 زي U3Y3يبقى
+
+670
+01:09:21,280 --> 01:09:28,220
+capital Y of T بده يساوي ال Y1 اللي هي كده ايش? E
+
+671
+01:09:28,220 --> 01:09:36,120
+of T يبقى هذه ال E of T و ال Y1 اللي هي وسطها طب
+
+672
+01:09:36,120 --> 01:09:43,240
+ال U1 ال U1 اللي هي النص في التكامل يبقى هذا النص
+
+673
+01:09:43,240 --> 01:09:49,720
+برا يا بناتوهي تكمل من T node إلى T وجوا قداش فيه
+
+674
+01:09:49,720 --> 01:09:58,560
+انا E أص ناقص S GS يبقى E أص ناقص S G of S في DS
+
+675
+01:09:59,780 --> 01:10:06,140
+بنجي اللي بعده زائد اللي هو cosine ال T زائد
+
+676
+01:10:06,140 --> 01:10:13,660
+cosine ال T ال U2 اللي هو برضه نص يبقى يا نص خليك
+
+677
+01:10:13,660 --> 01:10:21,550
+برا هذا النص وهي تكامللشانه مقدار ثابت من T ناد
+
+678
+01:10:21,550 --> 01:10:29,650
+إلى T لمين لصين ال S ناقص كوصين ال S لصين ال S
+
+679
+01:10:29,650 --> 01:10:37,270
+ناقص كوصين ال S كله اظن في E و S و لا فيش H في G
+
+680
+01:10:37,270 --> 01:10:45,770
+of S في G of S كله في DS نجي ل U تلاتة U تلاتة
+
+681
+01:10:45,770 --> 01:10:53,260
+عندك بصين ال Tيبقى Z هي sign ال T و U تلاتة أيها
+
+682
+01:10:53,260 --> 01:11:00,840
+عندي هي النص برا وهي تكامل من T node إلى T لناقص
+
+683
+01:11:00,840 --> 01:11:09,880
+sign ال S ناقص cosine ال S كله في قداش في G of S
+
+684
+01:11:09,880 --> 01:11:17,360
+في DS تمام؟
+
+685
+01:11:18,740 --> 01:11:24,800
+طيب ايش رايكوا انا شايف فيه نص برا و نص و نص ناخد
+
+686
+01:11:24,800 --> 01:11:31,540
+ورا من الكل تمام يبقى هذا نص برا الان يا بناتي
+
+687
+01:11:31,540 --> 01:11:37,620
+الجو المتغير هو مين S و اللي برا مين T يبقى كأنه
+
+688
+01:11:37,620 --> 01:11:42,020
+مقدار ثابت بالنسبة له صحيح ولا لا؟ مالوش داعي في
+
+689
+01:11:42,020 --> 01:11:46,600
+دي S يبقى خليته برا التكامل والله جوا التكامل سيان
+
+690
+01:11:46,780 --> 01:11:51,000
+أذا بدي اكتبه جوا التكامل بيضغط اضربه بصير جوا E
+
+691
+01:11:51,000 --> 01:11:56,200
+أس T في E أس ناقص S يعني E أس T ناقص ال S لإنه
+
+692
+01:11:56,200 --> 01:12:01,860
+عندها الضرب تجمع الأسس يبقى بصير أن هذا هي تكامل
+
+693
+01:12:01,860 --> 01:12:11,390
+من T نوت لغاية Tلل E أس T ناقص ال S في ال G of S
+
+694
+01:12:11,390 --> 01:12:17,790
+في ال DS خلصنا ال term الأول يبقى هنا هذا جوس كبير
+
+695
+01:12:17,790 --> 01:12:24,180
+جابله وبعده نص مشانه نص نص نص أخدته من الكلونجي
+
+696
+01:12:24,180 --> 01:12:30,700
+للتكامل هذا يبقى زائد تكامل من T node إلى T هذه
+
+697
+01:12:30,700 --> 01:12:34,240
+بنفس الطريقة ال cosine T تعتبر مقدار ثابت بقدر
+
+698
+01:12:34,240 --> 01:12:45,780
+ادخلها جوابصير عندي cos T في sin S ناقص cos T في
+
+699
+01:12:45,780 --> 01:12:56,190
+cos S كل هذا الكلام في G of S في D Sتمام اللي بعده
+
+700
+01:12:56,190 --> 01:13:02,350
+بنفس الطريقة زائد نص خدناها برا يبقى تكامل من T
+
+701
+01:13:02,350 --> 01:13:09,230
+node إلى T بدي أدخل جوا دي بيصير ناقص sine T في
+
+702
+01:13:09,230 --> 01:13:19,230
+sine ال S ناقص sine T في cosine ال S وكل هذا في G
+
+703
+01:13:19,230 --> 01:13:21,710
+of S في ال DS
+
+704
+01:13:30,130 --> 01:13:37,990
+خطوة الأخيرة في عويل مشتركة بدي أخدهم يبقى بصير Y
+
+705
+01:13:37,990 --> 01:13:50,190
+of T يساوي نصتكامل تكامل تكامل تكامل تكامل تكامل
+
+706
+01:13:50,190 --> 01:13:53,270
+تكامل
+
+707
+01:13:53,270 --> 01:14:01,140
+تكاملبتطلعي لي جيوب اس دي اس جيوب اس دي اس جيوب اس
+
+708
+01:14:01,140 --> 01:14:05,700
+دي اس يبقى بدأ أخدها من الكل كمان عامل مشترك ايش
+
+709
+01:14:05,700 --> 01:14:13,800
+بيظل عندي هنا بس E أس T ناقص ال S تمام؟ وهي فتحت
+
+710
+01:14:13,800 --> 01:14:17,880
+Guess مشان في الآخرة ضروبة كلها في جيوب اس هذي ايش
+
+711
+01:14:17,880 --> 01:14:29,490
+بيصير؟ بيصير الزاد cosine T في sine ال Sنقص cos T
+
+712
+01:14:29,490 --> 01:14:40,330
+في sin S نقص sin T
+
+713
+01:14:40,330 --> 01:14:48,450
+في cos S وهيجفلنا الجوز كله وهذا G of S وهذا DS
+
+714
+01:15:01,400 --> 01:15:09,800
+الخطوة الأخيرة يساوي نص تكامل من T node إلى T لل E
+
+715
+01:15:09,800 --> 01:15:11,720
+أس T ناقص ال S
+
+716
+01:15:15,240 --> 01:15:23,540
+هذه sin cos وهذه sin cos لو أخذت منهم ناقص عامل
+
+717
+01:15:23,540 --> 01:15:29,080
+مشترك ايش بيصير عندنا؟ هذه ناقص بيصير عندنا هذه
+
+718
+01:15:29,080 --> 01:15:36,400
+بالموجب وهذه بالسالم بيصير عندنا sin T cos S زاد
+
+719
+01:15:36,400 --> 01:15:47,120
+cos T في sin Sأليست هذه هي sin t ناقص ال S؟ هذه
+
+720
+01:15:47,120 --> 01:15:54,360
+اللي بدي أفكها sin t cos S ناقص cos T في sin S
+
+721
+01:15:54,360 --> 01:15:58,580
+هيها ولا لا؟ يبقى تخلص من التنتين اللي تحتهم خط
+
+722
+01:15:58,580 --> 01:16:05,590
+تالي هدول اللي تحتهم خطمعروج يبقى بدي أخد كمان
+
+723
+01:16:05,590 --> 01:16:12,010
+ناقص عامل مشترك بشيره التنتين بالزائد بصير كساء
+
+724
+01:16:12,010 --> 01:16:18,950
+وين همااستنى شوية بالراديو الخطأ مردود هى cosine t
+
+725
+01:16:18,950 --> 01:16:23,830
+فى sin s ناقص cosine اه هذه cosine s صحيلي هذه بس
+
+726
+01:16:23,830 --> 01:16:29,590
+يا بنات cosine s تمام هذه بس نزلناها بالخطة هيك
+
+727
+01:16:29,590 --> 01:16:33,550
+التانية sin مظبوط التانية مش فيها مشكلة وهذه مش
+
+728
+01:16:33,550 --> 01:16:37,010
+فيها مشكلة طيب هدول اللى تنتقل اما اخدت منهم ناقص
+
+729
+01:16:37,010 --> 01:16:41,790
+عامل بصير cosine cosine زائد sin sin اللى هو
+
+730
+01:16:41,790 --> 01:16:49,770
+cosine منين؟كو صين الفرق يبقى كو صين T ناقص ال S
+
+731
+01:16:49,770 --> 01:16:55,270
+يبقى يخلصنا الأربع ترمات اللي بين قوسين وهي قفلنا
+
+732
+01:16:55,270 --> 01:17:04,160
+القوس كله وهي عندك G of S وهذا ال D of Sيبقى
+
+733
+01:17:04,160 --> 01:17:08,820
+خلّينا ال particular solution بدلة الاتمين بدلة
+
+734
+01:17:08,820 --> 01:17:14,100
+التكمل لإن ال G of T أنا ماعرفاش قداش عنا يبقى هذا
+
+735
+01:17:14,100 --> 01:17:23,180
+أحد برضه أسئلة الكتاب اللي موجودة حد
+
+736
+01:17:23,180 --> 01:17:30,120
+بتحب تسأل أي سؤال هنا نمسح
+
+737
+01:17:30,120 --> 01:17:31,060
+الشجرة هذه
+
+738
+01:17:47,080 --> 01:17:52,500
+بدنا نراجع كلامتنا صغير يا مانات على حكاية مين بس
+
+739
+01:17:52,500 --> 01:17:55,800
+قبل ما نراجع بدنا نعطيكوا أرقام مثال ال section
+
+740
+01:17:55,800 --> 01:18:00,840
+اللي فات و ال section هذا ال section اللي فات كان
+
+741
+01:18:00,840 --> 01:18:11,430
+exercises أربعة ثلاثة اللي هو من واحد لسبتاشالقد و
+
+742
+01:18:11,430 --> 01:18:20,410
+exercises اربع اربع المسائل من واحد لغاية اربعة
+
+743
+01:18:20,410 --> 01:18:30,310
+عشر و برضه القد و بناخد عليها كمان سؤال ترفع بدنا
+
+744
+01:18:30,310 --> 01:18:37,790
+نيجي ل section الان خمسة واحد ال power series
+
+745
+01:18:40,730 --> 01:18:44,110
+عارف انا والله مش ذاكر وعارف وعارف كدهش بياخد
+
+746
+01:18:44,110 --> 01:18:48,610
+وكدهش بدي اعطي بدي اعطي كلمتين صغير مراجعة لبعض
+
+747
+01:18:48,610 --> 01:18:55,410
+الأشياء مش كلها كمان التي درست في calculus B يبقى
+
+748
+01:18:55,410 --> 01:19:00,150
+أول section يا بنات هو مراجعة ومالوش دخل بالموضوع
+
+749
+01:19:00,150 --> 01:19:05,010
+موضوعنا طيلة هذا ال chapter هو ال series solution
+
+750
+01:19:05,010 --> 01:19:09,890
+ل second order differential equationيعني إذا بدي
+
+751
+01:19:09,890 --> 01:19:13,270
+أبدأ بالعنوان الرئيسي اللي قبل هذا اللي هو chapter
+
+752
+01:19:13,270 --> 01:19:23,210
+5 series solutions of
+
+753
+01:19:23,210 --> 01:19:27,130
+second order
+
+754
+01:19:28,950 --> 01:19:34,270
+Differential equation هذا هو العنوان الرئيسي للشكل
+
+755
+01:19:34,270 --> 01:19:39,890
+كله لكن أول section هو ال power series ال power
+
+756
+01:19:39,890 --> 01:19:45,770
+series منها أحد شكلين الشكل الأول ال هو summation
+
+757
+01:19:45,770 --> 01:19:51,190
+من n equal zero to infinity لل a n في ال x ناقص ال
+
+758
+01:19:51,190 --> 01:19:56,890
+x not to the power nلو حطيتها بالشكل الطويل يبقى
+
+759
+01:19:56,890 --> 01:20:02,670
+بداجي أشيل ال N و أحط مكانها Zero بصير A node في
+
+760
+01:20:02,670 --> 01:20:07,630
+ال X ناقص ال X node ال Zero اللي هو بواحد زائد A1
+
+761
+01:20:07,630 --> 01:20:12,490
+في ال X ناقص ال X node زائد A2 في ال X ناقص ال X
+
+762
+01:20:12,490 --> 01:20:18,070
+node لكل تربيع زائد وانظر ماشيل لغاية الحد ينوني A
+
+763
+01:20:18,070 --> 01:20:21,290
+N X ناقص ال X node to the power N
+
+764
+01:20:25,840 --> 01:20:31,180
+هذا هو الشكل الأول ال X node بنسميه المركز تبع ال
+
+765
+01:20:31,180 --> 01:20:34,840
+power series
+
+766
+01:20:34,840 --> 01:20:39,200
+ممكن يكون ال center هذي عند نقطة الأصل يعني لو
+
+767
+01:20:39,200 --> 01:20:46,930
+كانت ال X node يساوي 0الـ X node بده يساوي 0 يبقى
+
+768
+01:20:46,930 --> 01:20:50,450
+ال summation بده يصير بالشكل هذا من عندي ال 0 ل
+
+769
+01:20:50,450 --> 01:20:56,510
+infinity لل A N لل X to the power N فقط يبقى X
+
+770
+01:20:56,510 --> 01:20:59,830
+node X node X node كلها هبطير من ال series اللي
+
+771
+01:20:59,830 --> 01:21:08,790
+عندنا ويصبح شكلها A node زائد A1 X A2 X تربيع زائد
+
+772
+01:21:08,790 --> 01:21:14,440
+A N X to the power N زائد الاخرينيبقى هذا هو شكل
+
+773
+01:21:14,440 --> 01:21:20,740
+ال power series in general طيب انا عندي ال power
+
+774
+01:21:20,740 --> 01:21:24,180
+series و بدى أشوفها converge و لا diverge شو
+
+775
+01:21:24,180 --> 01:21:26,720
+الاختبارات اللي كنا بنستخدمها في ال calculus
+
+776
+01:21:26,720 --> 01:21:31,660
+نستخدمهم
+
+777
+01:21:31,660 --> 01:21:41,180
+لل power series؟الراتيو والانثروت بس فقط لغير يبقى
+
+778
+01:21:41,180 --> 01:21:49,380
+to test the convergence of
+
+779
+01:21:49,980 --> 01:22:01,260
+the power series we use بنروح نستخدم the ratio
+
+780
+01:22:01,260 --> 01:22:09,300
+test or the Enthrotest
+
+781
+01:22:13,400 --> 01:22:16,740
+يبقى يا بستخدم ال ratio يا ال in through ال test
+
+782
+01:22:16,740 --> 01:22:21,500
+هدول اختبارا فقط اللى كنا بواسطتهم نختبر ال power
+
+783
+01:22:21,500 --> 01:22:26,280
+series هل هى converge و لا diverse طيب ال power
+
+784
+01:22:26,280 --> 01:22:29,940
+series هدى converge على طول و لا ممكن تكون عند
+
+785
+01:22:29,940 --> 01:22:35,700
+فترة و ممكن تكون عند نقطة اى power series اللى احد
+
+786
+01:22:35,700 --> 01:22:42,250
+الاحتمالات الثلاثة التاليةconvergence of the power
+
+787
+01:22:42,250 --> 01:22:47,930
+series
+
+788
+01:22:47,930 --> 01:22:52,850
+هدى اللى فاجأ بناته او هدى اي واحدة منهم نفس
+
+789
+01:22:52,850 --> 01:23:02,670
+الكلام هدى ممكن تكون converge only at x node and
+
+790
+01:23:02,670 --> 01:23:12,500
+diverge elsewhereفي أي مكان آخر Diverge كيف يعني؟
+
+791
+01:23:12,500 --> 01:23:19,000
+لو كان هذا ال real line وهذه النقطة X0 ممكن عند
+
+792
+01:23:19,000 --> 01:23:25,140
+هذه النقطة تبقى converge لكن بعدها Diverge و قبلها
+
+793
+01:23:25,140 --> 01:23:31,240
+Diverge طب قداش ال radius of convergence في هذه
+
+794
+01:23:31,240 --> 01:23:37,480
+الحالة ال radiusتقول الله الـ convergence عنده
+
+795
+01:23:37,480 --> 01:23:40,940
+نقطة طول الفترة وبدأ جسمه على اتنين، قداش طول
+
+796
+01:23:40,940 --> 01:23:45,180
+النقطة؟ Zero Zero يبقى ال radius يكون ساوي Zero
+
+797
+01:23:45,180 --> 01:23:54,500
+يبقى هنا في هذه الحالة The radius of convergence
+
+798
+01:23:54,500 --> 01:23:59,100
+is احنا بقى هنسميه capital R و احنا بقى هنقوله
+
+799
+01:23:59,100 --> 01:24:05,080
+كتابنا هنا بسميه ال route ساوي Zeroالنقطة الثانية
+
+800
+01:24:05,080 --> 01:24:12,640
+يبقى
+
+801
+01:24:12,640 --> 01:24:18,440
+فترة
+
+802
+01:24:18,440 --> 01:24:22,080
+التقارب من و لا و اين نسالب infinity ل infinity
+
+803
+01:24:22,080 --> 01:24:29,280
+يبقى هذا يعطينا the interval of
+
+804
+01:24:40,030 --> 01:24:41,430
+الراديوس
+
+805
+01:24:43,910 --> 01:24:56,010
+radius of convergence as R يبقى
+
+806
+01:24:56,010 --> 01:25:00,930
+R تساوي infinity يعني يا بنات لو كان هذا هو ال
+
+807
+01:25:00,930 --> 01:25:06,750
+real line يبقى ال series converge على كل الفترة
+
+808
+01:25:06,750 --> 01:25:10,690
+بالاستثناء وهذا النقطة اللي هي من هنا ال zero وهذا
+
+809
+01:25:10,690 --> 01:25:15,620
+يبقى الملئ و diverge ماعنديش بالمرةوبالتالي نص الـ
+
+810
+01:25:15,620 --> 01:25:19,360
+real line هو نصف القطر، من صفر لما لا نهاية، الطول
+
+811
+01:25:19,360 --> 01:25:24,000
+هذا بقداش؟ بما لا نهاية طيب النقطة الثالثة
+
+812
+01:25:24,000 --> 01:25:33,720
+والاخيرة اللي هو the series converge on الفترة
+
+813
+01:25:33,720 --> 01:25:36,300
+المفتوحة من A إلى B
+
+814
+01:25:39,740 --> 01:25:44,940
+بس على الفترة دي يعني لو جيت قولت هذا ال real line
+
+815
+01:25:44,940 --> 01:25:50,460
+وهذا النقطة A وهذا النقطة B هنا في النص Converge
+
+816
+01:25:50,460 --> 01:25:59,640
+وهك Diverge وقبلها A Diverge كذلك طب عندي ال A و
+
+817
+01:25:59,640 --> 01:26:00,180
+ال B
+
+818
+01:26:02,900 --> 01:26:16,400
+و قد تكون converge و قد تكون diverge
+
+819
+01:26:16,400 --> 01:26:31,110
+الـ X أقل من A و X أكبر من B باجي بيقولالـ X يساوي
+
+820
+01:26:31,110 --> 01:26:42,350
+بـ A الـ X يساوي بـ B الـ Series may converge or
+
+821
+01:26:42,350 --> 01:26:48,970
+may diverge يعني عند النقطة A و الـ B الـ Series
+
+822
+01:26:48,970 --> 01:26:53,510
+ممكن تكون converge أو ممكن تكون diverge
+
diff --git a/PL9fwy3NUQKwa8ZDfSFGn6H8xVFLzqmCZC/nOggX_oRaAA.srt b/PL9fwy3NUQKwa8ZDfSFGn6H8xVFLzqmCZC/nOggX_oRaAA.srt
new file mode 100644
index 0000000000000000000000000000000000000000..f74f3e98146ac09930ced6a26eeb0361c2679d61
--- /dev/null
+++ b/PL9fwy3NUQKwa8ZDfSFGn6H8xVFLzqmCZC/nOggX_oRaAA.srt
@@ -0,0 +1,2806 @@
+1
+00:00:00,000 --> 00:00:02,960
+أهلا و أهلا يا عزيزي و أهلا و أهلا يا عزيزي و أهلا 
+
+2
+00:00:02,960 --> 00:00:14,280
+و أهلا يا عزيزي و
+
+3
+00:00:14,280 --> 00:00:14,920
+أهلا و أهلا و أهلا و أهلا و أهلا و أهلا و أهلا و
+
+4
+00:00:14,920 --> 00:00:15,020
+أهلا و أهلا و أهلا و أهلا و أهلا و أهلا و أهلا و
+
+5
+00:00:15,020 --> 00:00:15,860
+أهلا و أهلا و أهلا و أهلا و أهلا و أهلا و أهلا و
+
+6
+00:00:15,860 --> 00:00:17,800
+أهلا و أهلا و أهلا و أهلا و أهلا و أهلا و أهلا و
+
+7
+00:00:17,800 --> 00:00:20,300
+أهلا و أهلا و أهلا و أهلا و أهلا و أهلا و أهلا و
+
+8
+00:00:20,300 --> 00:00:26,820
+أهلا و أهلا و أهلا و
+
+9
+00:00:26,820 --> 00:00:33,020
+السؤال يقول إذا رميت  إنها موضوعة فإنه يجيب عمليات
+
+10
+00:00:33,020 --> 00:00:36,480
+لازم يتولدوا و يتولدوا و يتولدوا و يتولدوا و
+
+11
+00:00:36,480 --> 00:00:38,600
+يتولدوا و يتولدوا و يتولدوا و يتولدوا و يتولدوا و
+
+12
+00:00:38,600 --> 00:00:39,600
+يتولدوا و يتولدوا و يتولدوا و يتولدوا و يتولدوا و
+
+13
+00:00:39,600 --> 00:00:39,740
+يتولدوا و يتولدوا و يتولدوا و يتولدوا و يتولدوا و
+
+14
+00:00:39,740 --> 00:00:40,280
+يتولدوا و يتولدوا و يتولدوا و يتولدوا و يتولدوا و
+
+15
+00:00:40,280 --> 00:00:42,440
+يتولدوا و يتولدوا و يتولدوا و يتولدوا و يتولدوا و
+
+16
+00:00:42,440 --> 00:00:47,180
+يتولدوا و يتولدوا و يتولدوا 
+
+17
+00:00:58,350 --> 00:01:08,270
+والشيء الوحيد لـ P or X دلوقت لو قلنا P or X اللي
+
+18
+00:01:08,270 --> 00:01:13,890
+يجب أن تكسب يعني أقصد من X لما أقصد لأنها دلوقت
+
+19
+00:01:13,890 --> 00:01:20,720
+هذه المثلة حددنا إلى حصل عشان أنا أعرف أنا أنا أعرف 
+
+20
+00:01:20,720 --> 00:01:25,700
+أنا أعرف أنا أعرف أنا أعرف أنا أعرف أنا أعرف
+
+21
+00:01:29,830 --> 00:01:36,170
+هذا الكلام لو كانت تساوي Zero هذا الكلام ما بيحصل
+
+22
+00:01:36,170 --> 00:01:43,110
+إلا إذا كانت الـ kicks يساوي واحد and الـ kicks 
+
+23
+00:01:43,110 --> 00:01:51,290
+يساوي ثلاثة  من مدونة أو Singular Points
+
+24
+00:01:54,400 --> 00:01:57,940
+النقاط الشاملة و النقاط النهائية اللي لدينا 
+
+25
+00:01:57,940 --> 00:02:02,260
+المعاملة الانتقالية هي النقاط اللي بتجعل المعاملة
+
+26
+00:02:02,260 --> 00:02:06,320
+تقع واحدة من الحاجة تساوي زيرو ما بنشتغلها لكل
+
+27
+00:02:06,320 --> 00:02:11,500
+نقطة نتجاهل نقاط اشتُهرت من قبلها يعني الـ singular
+
+28
+00:02:11,500 --> 00:02:18,470
+points و الـ ordinary points ordinary points يرجى
+
+29
+00:02:18,470 --> 00:02:22,870
+مادام هدول هم الـ singular points هدول بدي يعطيك أن
+
+30
+00:02:22,870 --> 00:02:28,730
+الـ X لها تساوي أربعة و الـ X لها تساوي أربعة and
+
+31
+00:02:28,730 --> 00:02:38,290
+الـ X لها تساوي Zero are ordinary points ordinary
+
+32
+00:02:38,290 --> 00:02:41,150
+points
+
+33
+00:02:43,470 --> 00:02:48,530
+تمام؟ بدنا نصيب الأكبر تعالى نيجي نتنا نجيب كل ده
+
+34
+00:02:48,530 --> 00:02:54,150
+نجيب يومنا تمام؟ السجن لا يكون في النقطة سالب
+
+35
+00:02:54,150 --> 00:02:59,350
+واحد و نقطة و ثلاث يجب أن نجيب سالب واحد يجب 
+
+36
+00:02:59,350 --> 00:03:06,870
+أن نجيب أي نقطة في سالب واحد ماذا نحن نحن نحن نحن 
+
+37
+00:03:06,870 --> 00:03:08,570
+نحن نحن نحن نحن نحن نحن نحن نحن نحن نحن نحن نحن
+
+38
+00:03:08,570 --> 00:03:11,610
+نحن نحن نحن نحن نحن نحن نحن نحن نحن نحن نحن نحن
+
+39
+00:03:11,610 --> 00:03:12,950
+نحن نحن نحن نحن نحن نحن نحن نحن نحن نحن نحن نحن
+
+40
+00:03:12,950 --> 00:03:14,290
+نحن نحن نحن نحن نحن نحن نحن نحن نحن نحن نحن نحن
+
+41
+00:03:14,290 --> 00:03:22,830
+نحن نحن نحن نحن نحن نحن نحن نحن 
+
+42
+00:03:22,830 --> 00:03:28,370
+نحن
+
+43
+00:03:28,370 --> 00:03:32,610
+إذا الـ singular point هي النقطة سالب واحد و
+
+44
+00:03:32,610 --> 00:03:39,670
+ثلاثة يبقى هذه النقطة هي الـ singular point و
+
+45
+00:03:39,670 --> 00:03:46,570
+الثلاثة كمان  اللي يمينها هي الـ singular point تمام 
+
+46
+00:03:46,570 --> 00:03:53,950
+تمام الآن قل لي هدول و قل لي هو مين أصغر lower bound
+
+47
+00:03:53,950 --> 00:03:57,810
+of radius of convergence لأن أنا بدي أروح أشوف
+
+48
+00:03:57,810 --> 00:04:01,910
+radius of convergence لأن هو ياخد أصغر فيلم يقول 
+
+49
+00:04:01,910 --> 00:04:07,790
+هو أصغر التقارب المطلوب ليجي عند النقطة الأولى عند
+
+50
+00:04:07,790 --> 00:04:09,690
+x⁻⁴
+
+51
+00:04:15,230 --> 00:04:19,490
+شوف إيش اللي بده يصير و أنا الاربعة هايم يعني ما
+
+52
+00:04:19,490 --> 00:04:23,230
+بده أشوف كده المسافة ما بده الاربعة مش سالب واحد
+
+53
+00:04:23,230 --> 00:04:27,910
+و أشوف كده المسافة بين الأربعة و ثلاثة صغيرة يوم 
+
+54
+00:04:27,910 --> 00:04:32,870
+بتكون يا مين الـ radius of convergence المطلوب
+
+55
+00:04:32,870 --> 00:04:38,600
+اللي يعمل الجمال اللي بنقوله الآن عند نقطة x تساوي
+
+56
+00:04:38,600 --> 00:04:43,780
+أربعة راح بده تساوي أربعة اللي هي النقطة اللي
+
+57
+00:04:43,780 --> 00:04:51,120
+عندنا ما تستخدمي الـ singular ماقص واحد و يساوي قدره
+
+58
+00:04:51,120 --> 00:04:57,620
+خمسة تدريجيا نأخذ روح اثنين بتساوي أربعة ماقص ثلاثة 
+
+59
+00:04:57,620 --> 00:05:02,620
+يساوي قدره واحد يبقى نصف قطر اتقال بالمطبق ودين
+
+60
+00:05:02,620 --> 00:05:07,300
+واحد اللي قالي احنا اللي هو الفرح أصغر واحد منهم
+
+61
+00:05:07,300 --> 00:05:18,210
+يبقى هنا بجي بيقولوا اثنين Lower down of the 
+
+62
+00:05:18,210 --> 00:05:24,810
+radius of convergence
+
+63
+00:05:24,810 --> 00:05:35,060
+is not zero يبقى رمضان سنة واحد هو رمضان لا ميل دا
+
+64
+00:05:35,060 --> 00:05:40,800
+رديوس أو كل فيها جامعة إذا الـ serious solution هذه
+
+65
+00:05:40,800 --> 00:05:51,840
+يجب أن أقول له الـ serious solution الموجودة
+
+66
+00:05:52,620 --> 00:05:59,200
+Summation من M equal 0 to infinity من A M في X نقص 
+
+67
+00:05:59,200 --> 00:06:02,480
+X نقص X نقص X نقص X نقص X نقص X نقص X نقص X نقص X
+
+68
+00:06:02,480 --> 00:06:04,280
+نقص X نقص X نقص X نقص X نقص X نقص X نقص X نقص X
+
+69
+00:06:04,280 --> 00:06:07,240
+نقص X نقص X نقص X نقص X نقص X نقص X نقص X نقص X
+
+70
+00:06:07,240 --> 00:06:07,680
+نقص X نقص X نقص X نقص X نقص X نقص X نقص X نقص X
+
+71
+00:06:07,680 --> 00:06:08,580
+نقص X نقص X نقص X نقص X نقص X نقص X نقص X نقص X
+
+72
+00:06:08,580 --> 00:06:17,620
+نقص X نقص X نقص X 
+
+73
+00:06:17,620 --> 00:06:29,150
+نقول لي يست عالم أقل for absolute value من X مع 
+
+74
+00:06:29,150 --> 00:06:34,450
+أصحابها أقل من الواحد اللي اعتمدناه لوله صغير كل
+
+75
+00:06:34,450 --> 00:06:42,170
+الدنيا الجهد عند النقطة x0 تساوي 4 لو جينا الآن عند 
+
+76
+00:06:42,170 --> 00:06:46,770
+النقطة x0 تساوي 4 
+
+77
+00:06:52,440 --> 00:06:59,200
+يبقى روح ون يساوي، اه هذه فيها سبب لأن هو دائما و 
+
+78
+00:06:59,200 --> 00:07:04,120
+أبدا أكبر من يزيل النسخوتر، تعني مثلا إذا كنت قاطب
+
+79
+00:07:04,120 --> 00:07:08,320
+بير، اللي هتسيبه تباركها أفضل دائما و أبدا في كل
+
+80
+00:07:08,320 --> 00:07:08,740
+مالها
+
+81
+00:07:15,890 --> 00:07:21,910
+النقطة اللي هي ناقص أربعة وإن ناقص أربعة هيها منها
+
+82
+00:07:21,910 --> 00:07:29,350
+إذا ناقص أربعة ناقص ناقص واحد يرجع ناقص ناقص واحد
+
+83
+00:07:46,040 --> 00:07:49,960
+النقطة الثانية كم؟ تلاتة 
+
+84
+00:08:06,810 --> 00:08:24,310
+radius of conveyor belts is راتب سبكتر تلتة سبكتر
+
+85
+00:08:28,090 --> 00:08:32,030
+this is your solution for summation from n equals
+
+86
+00:08:32,030 --> 00:08:38,950
+zero to infinity of b into x plus 4 to the power
+
+87
+00:08:38,950 --> 00:08:39,430
+of n
+
+88
+00:08:44,340 --> 00:08:53,880
+بتكون في الـ at least على الأقل for absolute value
+
+89
+00:08:53,880 --> 00:09:00,880
+للـ X زائد أربعة أقل من 2 أقل من 3 لتطلع لها هذا
+
+90
+00:09:00,880 --> 00:09:05,320
+بالنسبة للنقطة الثانية بالنسبة للنقطة الثانية X0 
+
+91
+00:09:05,320 --> 00:09:06,420
+يساوي 0 
+
+92
+00:09:24,800 --> 00:09:30,920
+النقطة الأولى هي نقص واحد، نقص نقص واحد هي نقص
+
+93
+00:09:30,920 --> 00:09:32,480
+واحد
+
+94
+00:09:40,360 --> 00:09:45,000
+بساوي كتير؟ absolutely بساوي تلاتة ليه تلاتة؟ من 
+
+95
+00:09:45,000 --> 00:09:54,740
+الاتنين هدول فبروح بقول دي lower bound for the
+
+96
+00:09:54,740 --> 00:10:01,840
+radius of convergence
+
+97
+00:10:01,840 --> 00:10:13,990
+is رقم ساوي واحد الآن بروح بقوله ده series solution
+
+98
+00:10:13,990 --> 00:10:23,790
+لو سمحت نبتدي equal zero to infinity لسي ان في ال 
+
+99
+00:10:23,790 --> 00:10:30,110
+X ماقس الـ zero يعني قدر يعني X to the power N
+
+100
+00:10:30,110 --> 00:10:42,570
+converge أفضل من أفضل من أفضل من أفضل من أفضل من
+
+101
+00:10:42,570 --> 00:10:47,310
+أفضل من أفضل من أفضل من أفضل من أفضل من أفضل من
+
+102
+00:10:47,310 --> 00:10:48,510
+أفضل من أفضل من أفضل من أفضل من أفضل من أفضل من 
+
+103
+00:10:48,510 --> 00:10:55,390
+أفضل من أفضل من أفضل من أفضل معناه نهاية لما يعمل 
+
+104
+00:10:55,390 --> 00:10:59,070
+كل واحدة من تنتيجة قرية مانا نهاية يبقى أي واحدة
+
+105
+00:10:59,070 --> 00:11:04,430
+فيهم يبقى converge على كل real line لكنها بناء
+
+106
+00:11:04,430 --> 00:11:10,210
+converge على فترة فقط ماغية يبقى هذا بالنسبة للمثال
+
+107
+00:11:10,210 --> 00:11:17,560
+رقم اللي هو الـ 10 بمجرد المثال رقم 3 يرجع البرنامج
+
+108
+00:11:17,560 --> 00:11:22,280
+إلى هذا رقم ثلاثة نفس المطلوب هذا ليس حاجة تغيره
+
+109
+00:11:22,280 --> 00:11:26,460
+يرجع البرنامج إلى هذا الرقم تغيرته بشكل معادل أن
+
+110
+00:11:26,460 --> 00:11:38,520
+هو واحد زائد X ترمية في ال YW5 زائد اثنين XY5 زائد
+
+111
+00:11:42,320 --> 00:11:48,760
+يساوي زيرو و الـ X نوض يساوي زيرو و الـ X نوض التالية
+
+112
+00:11:48,760 --> 00:11:50,680
+يساوي معك اسمه 
+
+113
+00:11:58,940 --> 00:12:03,880
+المثال السابق قبل قليل محور أن الـ singular quiz
+
+114
+00:12:03,880 --> 00:12:09,540
+كانت تنتمي هي واحدة كانت سالب واحد و ثانية  داشر
+
+115
+00:12:09,540 --> 00:12:14,920
+و ثانية تلاتة لكن هنا في سؤال تعالى تشوف مشكلته 
+
+116
+00:12:14,920 --> 00:12:18,240
+يبقى إيش مزاج يقوله solution 
+
+117
+00:12:20,590 --> 00:12:29,050
+الـ P of X يساوي واحد زاوية X تجارية بزيرو
+
+118
+00:12:29,050 --> 00:12:35,950
+معناه هذا الكلام أن X بدا يساوي زاوية أو نقطة I 
+
+119
+00:12:35,950 --> 00:12:44,150
+ممتاز جدا يتجسس من مقطة تحيولية اللي مجبر أكتبها
+
+120
+00:12:44,150 --> 00:12:44,570
+عبر
+
+121
+00:12:47,730 --> 00:12:55,110
+زائد أو ناقص أيه أنت عارف لأنه العدد المركب يكتب 
+
+122
+00:12:55,110 --> 00:13:00,690
+كمجموعة two terms جزء الحقيقة و جزء التخيلي الحقيقية 
+
+123
+00:13:00,690 --> 00:13:05,970
+ما راحش اللي معناه P0 فبروح بطب و على صيغة زيرو 
+
+124
+00:13:05,970 --> 00:13:13,100
+زائد أو ناقص أيه جمهور كان مفهوم وحدة زيرو زائد أيه 
+
+125
+00:13:13,100 --> 00:13:20,580
+و ثانية زيرو نقطة اتنين مش نقطة واحدة تمام الآن
+
+126
+00:13:20,580 --> 00:13:24,920
+نبدأ نشتغل نفس الشغل اللي اشتغلناه بس على كل نقطة
+
+127
+00:13:24,920 --> 00:13:29,300
+من النقطتين اللي اتنين من دولة بس قبل ذلك من الكتب 
+
+128
+00:13:29,300 --> 00:13:32,520
+الكتب وراه عرف الـ complex  أعرفش اللي دراسوا الـ 
+
+129
+00:13:32,520 --> 00:13:36,680
+complex علتيه اللي ما دراسوهش اللي عرفوهاش لذلك لو 
+
+130
+00:13:36,680 --> 00:13:43,120
+أفضل مسافة بين نقطتين في الـ complex play يرجع من
+
+131
+00:13:43,120 --> 00:13:47,100
+هنا نقطة ملاحظة و بعدين نستخدمها في الشبكة فبعدين
+
+132
+00:13:47,100 --> 00:13:56,520
+يقولون أن الـ distance between play
+
+133
+00:13:56,520 --> 00:14:07,650
+points المرزق دواعي يساوي x واحد زي الـ IY واحد and 
+
+134
+00:14:07,650 --> 00:14:16,970
+زد اثنين و زد اثنين يبدا يساوي x اثنين زي الـ IY 
+
+135
+00:14:16,970 --> 00:14:25,570
+اثنين in the complex complex
+
+136
+00:14:25,570 --> 00:14:28,490
+اثنين
+
+137
+00:14:35,340 --> 00:14:42,840
+بديها رمز Z واحد مقص Z اثنين absolute value هذه 
+
+138
+00:14:42,840 --> 00:14:49,520
+عبارة عن الجدرين التربيعي X واحد مقص X اثنين لكل 
+
+139
+00:14:49,520 --> 00:14:56,400
+تربيع زي Y واحد مقص Y اثنين لكل تربيع تقريبا كانت 
+
+140
+00:14:56,400 --> 00:15:02,840
+مشروع كونه عندك في الكتابة لكن عليها اسئلة 
+
+141
+00:15:20,410 --> 00:15:25,970
+قبل ما أكمل أن أقولها المقولة هذه مش قولها صح ولا
+
+142
+00:15:25,970 --> 00:15:33,750
+لأ any real number is a complex number صح ولا لأ و
+
+143
+00:15:33,750 --> 00:15:39,350
+بعدين نيجي العملية العكسية any complex number is a
+
+144
+00:15:39,350 --> 00:15:45,210
+real number ليس صح وليس غلق ولا كله غلق ولا كله صح
+
+145
+00:15:47,360 --> 00:15:51,360
+القانع real number is a complex number صح ولا لأ
+
+146
+00:15:51,360 --> 00:15:58,780
+؟ خطأ؟ اه ممتازة أنك بيقول بتقول هذا أن القانع 
+
+147
+00:15:58,780 --> 00:16:03,680
+الـ real number is a complex number هذا خطأ نجي نشوف 
+
+148
+00:16:03,680 --> 00:16:08,300
+قد إيش هو صح ولا خطأ خلاه هنا كويسة لو جاي تقولتك
+
+149
+00:16:08,300 --> 00:16:14,760
+التلاتة مثلا التلاتة هي لأ ولا لأ اللي اكتفه هذا
+
+150
+00:16:14,760 --> 00:16:15,120
+أصلا
+
+151
+00:16:19,330 --> 00:16:27,950
+مصحيح ولا لأ؟ مصحيح ولا لأ؟ مصحيح 
+
+152
+00:16:27,950 --> 00:16:40,470
+ولا لأ؟ مصحيح
+
+153
+00:16:40,470 --> 00:16:45,690
+ولا لأ؟ مصحيح ولا لأ؟ مصحيح ولا لأ؟ مصحيح ولا لأ؟
+
+154
+00:16:45,690 --> 00:16:50,530
+مصحيح ولا لأ؟ العكس ما هوش صحيح نهائي أبدا ولا عملك 
+
+155
+00:16:50,530 --> 00:16:56,930
+تجد complex number واحد يساوي real number إلا إذا
+
+156
+00:16:56,930 --> 00:17:02,950
+كان صفر غير لاشي بعد كامة يعني لو كان زيرو
+
+157
+00:17:02,950 --> 00:17:08,390
+فـ complex number هو زيرو زي زيرو في I صحيح أن هو
+
+158
+00:17:08,390 --> 00:17:11,990
+اللي بيسيوره بالنظر الانجليزي، لكن غير ذلك بعد
+
+159
+00:17:11,990 --> 00:17:17,190
+التغور، مش ممكنية أبدا، تمام؟ قال بس ودمرت علومه
+
+160
+00:17:17,190 --> 00:17:21,970
+أمشية ده زهنلها بالحلم، لكن كانت علومه جيدة
+
+161
+00:17:21,970 --> 00:17:27,250
+للدكتور يعرفها، طيب، نرجع الآن للموضوع الصغير سؤال 
+
+162
+00:17:27,250 --> 00:17:32,630
+اللي بيقول لي بيجيب جداش الـ radius of all virgins
+
+163
+00:17:32,630 --> 00:17:36,390
+لما يتي المعادلة الطابقة الاربونية اللي عندنا هذه 
+
+164
+00:17:36,390 --> 00:17:42,630
+الحلطة بجهها الحل كـ series صحية عليه بقولك ميسيا 
+
+165
+00:17:42,630 --> 00:17:45,890
+احنا طلعنا المفقودين تاخدوا الـ utility quotients
+
+166
+00:17:45,890 --> 00:17:49,350
+و تم نقطة الأولي النقطة الأولى جالسة x not equal to
+
+167
+00:17:49,350 --> 00:17:50,270
+zero
+
+168
+00:18:06,230 --> 00:18:22,710
+زيرو زائد زيرو في I زيرو 
+
+169
+00:18:22,710 --> 00:18:32,090
+زائد I الـ X تساوي I يعني سريعا وزاهم I بالشكل
+
+170
+00:18:32,090 --> 00:18:37,450
+العامل لها لأن هذه اللي صار X واحد و Y واحد و هذه 
+
+171
+00:18:37,450 --> 00:18:42,990
+صارت X اثنين و Y اثنين و واحد صحيح مظبوط فالمفروض أن 
+
+172
+00:18:42,990 --> 00:18:48,150
+هذه القادة تقدر أجيب جداش الفرق بين النقطتين اللي
+
+173
+00:18:48,150 --> 00:18:54,080
+هو نصف متر التقارب يبقى مثلا أقوله يبقى O1 يبقى
+
+174
+00:18:54,080 --> 00:19:02,960
+بيساوي الجدرين الترميه ليه X1-X2 يبقى كتير زيرو 
+
+175
+00:19:02,960 --> 00:19:11,120
+ناقص Zero لكل ترمية Y1 ناقص Y2 كدهش Y1؟ زيرو Y2
+
+176
+00:19:11,120 --> 00:19:20,440
+لو واحد لكل ترمية يب
+
+216
+00:24:25,210 --> 00:24:34,630
+خمسة عِلمَين على الفرق تحدث في هذا ال section أنّ هي
+
+217
+00:24:34,630 --> 00:24:42,110
+كل قران في المثال يبقى فيه ال exercises خمسة
+
+218
+00:24:42,110 --> 00:25:03,860
+الادامالوسائل من واحد لغاية ثمانية انتقل
+
+219
+00:25:03,860 --> 00:25:10,560
+الآن إلى section خلال يديني وهو section خمسة أرض
+
+220
+00:25:13,060 --> 00:25:20,380
+طبعًا الامتحان اللي هيُولد يوم أربع عشر تمامية أو
+
+221
+00:25:20,380 --> 00:25:25,400
+أربع عشر تمامية أولاً سبتشن
+
+222
+00:25:25,400 --> 00:25:34,200
+خمسة أربع نومين regular singular
+
+223
+00:25:34,200 --> 00:25:34,940
+points
+
+224
+00:25:50,360 --> 00:25:56,820
+كلمة regular اشتدت علينا ريجولر معناها مُضطردة مثلًا
+
+225
+00:25:56,820 --> 00:26:01,280
+لما آسف حقًا إذا ال singular point يعني ال
+
+226
+00:26:01,280 --> 00:26:04,580
+singular point اللي أنا عرفته قبل دي أما ال
+
+227
+00:26:04,580 --> 00:26:09,080
+singular point يعني قد تكون regular وقد تكون 
+
+228
+00:26:09,080 --> 00:26:14,190
+irregular بنشوف كيف بدّنا نميّز ما بين irregular
+
+229
+00:26:14,190 --> 00:26:18,950
+singular point و irregular singular point يعني
+
+230
+00:26:18,950 --> 00:26:24,530
+بميّز رجل ومش هنعمل هذا التمييز بدّنا نميّز بين
+
+231
+00:26:24,530 --> 00:26:30,570
+معاملات المعادلة التفاضلية النظيفة للثاني ال P 
+
+232
+00:26:30,570 --> 00:26:35,510
+وال Q وال R هذول بدّنا نعمل تمييز في بينهم هل هما 
+
+233
+00:26:35,510 --> 00:26:40,310
+polynomial كبيرات حدود مهمة ولا عادية؟ يعني
+
+234
+00:26:40,310 --> 00:26:44,990
+exponential، ده اللغة التجارية، ده اللغة العلمية،
+
+235
+00:26:44,990 --> 00:26:48,610
+أي .. أي شغلة تانية المهم ال polynomial اللي هو 
+
+236
+00:26:48,610 --> 00:26:53,530
+شغل حاله وباقي الدوات اللي هو شغل حاله، لأنها تحفظ
+
+237
+00:26:53,530 --> 00:27:00,950
+السماء و شوف كيف هتتعامل مع المسألتين يبقى الرقم
+
+238
+00:27:00,950 --> 00:27:05,870
+الأولى بالتناقص لو ماكانوش polynomial ماكانوش
+
+239
+00:27:05,870 --> 00:27:16,050
+كثيرات كلهم يبقى F ال P وال U and ال R معاملات 
+
+240
+00:27:16,050 --> 00:27:24,950
+الثلاثة of the differential equation للمعادلة
+
+241
+00:27:24,950 --> 00:27:32,130
+التفاضلية كابتن P of X في ال YW إطارِ كابتن Q of X 
+
+242
+00:27:32,130 --> 00:27:37,470
+في ال Y إطارِ كابتن R of X في ال Y تساوي Zero
+
+243
+00:27:37,470 --> 00:27:46,390
+وسمينا المعادلة هذه رقم واحد a general function
+
+244
+00:27:47,060 --> 00:27:52,400
+يبقى درّال عامة يعني إيش مقصود هي؟ يعني ما
+
+245
+00:27:52,400 --> 00:28:03,620
+polynomials لإن ماهياش كثيرات حدود then the x node
+
+246
+00:28:03,620 --> 00:28:13,040
+is regular singular regular
+
+247
+00:28:13,040 --> 00:28:14,800
+singular point
+
+248
+00:28:27,280 --> 00:28:35,900
+singular شرق الأول and both
+
+249
+00:28:35,900 --> 00:28:39,440
+of
+
+250
+00:28:39,440 --> 00:28:49,700
+x ناقص ال x نقطة very cute of x على ال key of x
+
+251
+00:28:49,700 --> 00:29:02,080
+and ال x أقصى ال X نقطة كل درجية بال A of X على ال
+
+252
+00:29:02,080 --> 00:29:12,340
+P of X على ال P of X بتجارب معنى R-Analytic R
+
+253
+00:29:12,340 --> 00:29:18,180
+-Analytic of X نقطة
+
+254
+00:29:27,320 --> 00:29:48,560
+F X-X0 Q of X على P of X على P of X and X-X0 ترمية
+
+255
+00:29:48,560 --> 00:30:00,500
+R of X على كتر P of X مانو مانو نهاب Convergent
+
+256
+00:30:00,500 --> 00:30:10,320
+هاب Convergent تايجر سيريز
+
+257
+00:30:10,320 --> 00:30:14,100
+سيريز
+
+258
+00:30:14,100 --> 00:30:18,760
+about اكسلون
+
+259
+00:30:18,760 --> 00:30:21,840
+نمر
+
+260
+00:30:21,840 --> 00:30:22,380
+اتنين
+
+261
+00:30:28,170 --> 00:30:47,370
+أ بيكيوك اندر ار and capital R are polynomials are
+
+262
+00:30:47,370 --> 00:31:01,740
+polynomials in equation one and f وإذا كان limit
+
+263
+00:31:01,740 --> 00:31:10,780
+لما ال x بدها تروح إلى x non لمن؟
+
+264
+00:31:10,780 --> 00:31:20,000
+لل x ناقص x non إلى q of x على captain p of x
+
+265
+00:31:22,610 --> 00:31:33,310
+خلاص يا عزيزي فهذه is Phi9 and
+
+266
+00:31:33,310 --> 00:31:43,510
+limit x to o from x0 to x minus x0 is full ترهيب
+
+267
+00:31:43,510 --> 00:31:51,870
+just R of x على capital E of x is Phi9
+
+268
+00:31:53,470 --> 00:32:01,390
+إذا كانت خامسة ثم اتصالها
+
+269
+00:32:01,390 --> 00:32:04,550
+إلى
+
+270
+00:32:04,550 --> 00:32:05,030
+موقع محدد
+
+271
+00:32:47,580 --> 00:32:57,440
+definition any singular point any singular point
+
+272
+00:32:57,440 --> 00:33:10,680
+of equation one that is not regular
+
+273
+00:33:15,530 --> 00:33:20,650
+is called an
+
+274
+00:33:20,650 --> 00:33:27,750
+irregular singular
+
+275
+00:33:27,750 --> 00:33:28,410
+point
+
+276
+00:33:51,070 --> 00:34:03,170
+Definition Declaration Declaration
+
+277
+00:34:13,550 --> 00:34:24,090
+all the singular points all the
+
+278
+00:34:24,090 --> 00:34:29,590
+singular points and
+
+279
+00:34:29,590 --> 00:34:30,810
+determining it up
+
+280
+00:34:48,710 --> 00:34:58,650
+H1H1 is a regular or irregular
+
+281
+00:35:09,020 --> 00:35:16,500
+وأرْخَم ثانية في الخط والواحد ناقص ثانية كل ثانية
+
+282
+00:35:16,500 --> 00:35:31,960
+واحد W' زائد X واحد ناقص X كله في Y' زائد واحد زائد
+
+283
+00:35:31,960 --> 00:35:37,000
+X كله في الواحد ندر ساوي Zero
+
+284
+00:36:01,170 --> 00:36:09,170
+الكلام اللي احنا كتبناه اليوم بارعة ثانية
+
+285
+00:36:10,680 --> 00:36:17,180
+هذه كتيرة حدود وماهياش كتيرة حدود إذا كتيرة حدود
+
+286
+00:36:17,180 --> 00:36:22,800
+تلها كلام وإذا ماهياش كتيرة حدود تلها كلام ذات طيب
+
+287
+00:36:22,800 --> 00:36:27,880
+نيجي الآن لتعريف على التقارير اللي عجبني على الشكلة
+
+288
+00:36:27,880 --> 00:36:32,320
+اللي عنها هذه أقول لو كده بيقول if you will are a
+
+289
+00:36:32,320 --> 00:36:37,080
+general function دي ربط يعني إيش؟  مبقى monogamous
+
+290
+00:36:37,080 --> 00:36:42,160
+فبسؤال كده كله ضروري، مايكونوش كورنوميا ضروري، ممكن
+
+291
+00:36:42,160 --> 00:36:45,440
+واحدة تكون كورنوميا لو كانت ثانية وثانية ثانية،
+
+292
+00:36:45,440 --> 00:36:52,260
+ممكن، عادل، بس أنّهم الثلاثة مع بعض ملموط، مايكونوش
+
+293
+00:36:52,260 --> 00:36:54,460
+كورنوميا، لو كانوا ثانية وثانية كورنوميا، لو
+
+294
+00:36:54,460 --> 00:36:59,300
+كانوا ثانية، ممكن، ممكن، ممكن، ممكن، ممكن، ممكن لكن
+
+295
+00:36:59,300 --> 00:37:04,360
+إن كانوا ثلاثة ممش غير نقلين فهناك مشكلة في هذه
+
+296
+00:37:04,360 --> 00:37:12,100
+المقصود ال general function إذا كانت 
+
+297
+00:37:12,100 --> 00:37:17,810
+هذه النقطة singular و تحقق شخصان آخرين الشرب
+
+298
+00:37:17,810 --> 00:37:22,910
+الأولاني خذ x مارفا سيكس ماوري ليس Angular I
+
+299
+00:37:22,910 --> 00:37:28,250
+وضربناها في ال Q على P يعني كانوا خليها معامل Y
+
+300
+00:37:28,250 --> 00:37:33,350
+بقرر في الجدير واقعة زي الجرسام للمعادلة كله على P
+
+301
+00:37:33,350 --> 00:37:37,490
+فكل ال Q على P لو خذت نفسي بالدرمال يعني الدرمال
+
+302
+00:37:37,490 --> 00:37:41,870
+الأول التيرم الثاني كان ال x-x اذا كنت تبقى اربع
+
+303
+00:37:41,870 --> 00:37:47,490
+فيكس على P of x اذا كنت تبقى اربع فيكس على P of x
+
+304
+00:37:47,490 --> 00:37:53,590
+اذا كنت تبقى اربع فيكس على P of x اذا كنت تبقى
+
+305
+00:37:53,590 --> 00:37:55,430
+اربع فيكس على P of x اذا كنت تبقى اربع فيكس على P
+
+306
+00:37:55,430 --> 00:37:56,670
+of x اذا كنت تبقى اربع فيكس على P of x اذا كنت
+
+307
+00:37:56,670 --> 00:37:56,750
+تبقى اربع فيكس على P of x اذا كنت تبقى اربع فيكس
+
+308
+00:37:56,750 --> 00:37:58,650
+على P of x اذا كنت تبقى اربع فيكس على P of x اذا
+
+309
+00:37:58,650 --> 00:38:03,990
+كنت تبقى اربع فيكس على P of x اذا كنت تبقى اربع
+
+310
+00:38:03,990 --> 00:38:08,600
+فيكس على P of x اذا كنت تبقى اربع فيكس الكلام
+
+311
+00:38:08,600 --> 00:38:13,920
+الجنسيّة are regular، لكن إذا ذهبوا هذا ال plan
+
+312
+00:38:13,920 --> 00:38:18,420
+يتبعهم ال conversion  تقيلوا سينتها من المين عند
+
+313
+00:38:18,420 --> 00:38:22,700
+الموقع اللي علانه، يبقى هذا لو كان ال plan فيه
+
+314
+00:38:22,700 --> 00:38:28,100
+ثلاثة general functions، أكثر من كل نوم يعني بنبقى
+
+315
+00:38:28,100 --> 00:38:31,920
+الشرط الأولى اللي بيبقى زي J Singular بس الشرط 
+
+316
+00:38:31,920 --> 00:38:36,840
+اللي اتيه ثانية مستبدلة منين بال limits فقط بغير 
+
+317
+00:38:36,840 --> 00:38:43,120
+يعني لو كل الثلاثة بالكثيرات حدودي لبندياش لأو لأو
+
+318
+00:38:43,120 --> 00:38:45,500
+لأو لأو لأو لأو لأو لأو لأو لأو لأو لأو لأو لأو
+
+319
+00:38:45,500 --> 00:38:46,300
+لأو لأو لأو لأو لأو لأو لأو لأو لأو لأو لأو لأو
+
+320
+00:38:46,300 --> 00:38:47,780
+لأو لأو لأو لأو لأو لأو لأو لأو لأو لأو لأو لأو
+
+321
+00:38:48,090 --> 00:38:54,330
+الثلاثة لولا لما تروح ال X لولا التالية لما تروح ال X
+
+322
+00:38:54,330 --> 00:38:58,470
+لولا التالية لما تروح ال X لولا التالية لما تروح ال
+
+323
+00:38:58,470 --> 00:38:59,610
+X لولا التالية لما تروح ال X لولا التالية لما تروح
+
+324
+00:38:59,610 --> 00:39:03,110
+تروح ال X لولا التالية لما تروح ال X لولا التالية
+
+325
+00:39:03,110 --> 00:39:07,330
+لما تروح ال X لولا التالية لما تروح ال X لولا
+
+326
+00:39:07,330 --> 00:39:13,330
+التاليّة لما تروح ال X لولا التالية
+
+327
+00:39:13,330 --> 00:39:19,150
+التاليّة لما تروح ال X لولا التالية لما تروح ال X يبقى
+
+328
+00:39:19,150 --> 00:39:23,790
+اتنين هذول ما قلّقوش finite يبقى أكثر بقول عنها معها
+
+329
+00:39:23,790 --> 00:39:30,990
+regular singular point أو
+
+330
+00:39:30,990 --> 00:39:34,510
+لو اثنين هذول ما قلّقوش
+
+331
+00:39:37,020 --> 00:39:40,600
+يبدأ النقطة اللي عندي بسميها يعني irregular
+
+332
+00:39:40,600 --> 00:39:49,360
+singular points يعني
+
+333
+00:39:49,360 --> 00:39:53,480
+لم يتحقق هذين الاثنين يبدأ بسميها عشان irregular
+
+334
+00:39:53,480 --> 00:40:00,920
+singular points يعني نقطة غير أو نقطة شابه غير طيب
+
+335
+00:40:00,920 --> 00:40:05,500
+هل بيود أنّ انت عندنا سؤال سؤال يقول ما يعني بيقول
+
+336
+00:40:05,500 --> 00:40:10,080
+لي أنّ هذول ما اتحققوش في النقطة الارجيالية، طيب
+
+337
+00:40:10,080 --> 00:40:15,160
+سؤال أنا جيت على هذا الدنيا، بتقول أنّ أنا جيت هنا،
+
+338
+00:40:15,160 --> 00:40:21,290
+أنا اللي اتفرج ورحت للثانية و رجيتها الله أنا لدي
+
+339
+00:40:21,290 --> 00:40:28,350
+فانشغلت لأنّ أنا أنا أنا أنا أنا أنا أنا أنا
+
+340
+00:40:28,350 --> 00:40:30,210
+أنا أنا أنا أنا أنا أنا أنا أنا أنا أنا أنا
+
+341
+00:40:30,210 --> 00:40:31,230
+أنا أنا أنا أنا أنا أنا أنا أنا أنا أنا أنا
+
+342
+00:40:31,230 --> 00:40:33,850
+أنا أنا أنا أنا أنا أنا أنا أنا أنا أنا أنا
+
+343
+00:40:33,850 --> 00:40:38,170
+أنا أنا أنا أنا أنا أنا أنا أنا أنا أنا أنا
+
+344
+00:40:38,170 --> 00:40:44,290
+أنا أنا أنا أنا أنا أنا
+
+345
+00:40:44,290 --> 00:40:48,860
+أنا لكن لو قلت لولا أنا لك بروح ببحث مين تنتقل لو
+
+346
+00:40:48,860 --> 00:40:53,760
+قلت لولا لا أنا لك أنا مش ببحث مين أنا بتنتقل طيب
+
+347
+00:40:53,760 --> 00:40:58,380
+السؤال الثاني ضروري أتركه يعني مابدأوش أدور فيه؟
+
+348
+00:40:58,380 --> 00:41:03,680
+ليس ضروري أي ورقة يوم يحطش بروح تدور أفضل ماتجي
+
+349
+00:41:03,680 --> 00:41:10,060
+تمثل هدف لو ذكرت تمثل هدف five nine بروح أدور عليها
+
+350
+00:41:10,060 --> 00:41:17,460
+five nine لو كانت هذه in finite يعني سمعي
+
+351
+00:41:17,460 --> 00:41:21,380
+بالإنفينيتي أو قولي بالإنفينيتي بروح أدور على ثاني
+
+352
+00:41:21,380 --> 00:41:25,200
+أولاده وأقرر يقولوا برايا مين وبرايا خارجه هذا
+
+353
+00:41:25,200 --> 00:41:31,560
+ما سنراه من خلال الأمثلة تعدى خالية فعلًا عندي سؤال
+
+354
+00:41:31,560 --> 00:41:35,340
+بدي أسأله إذا بدأت بالمعنى أسأله قبل أنّ أنت في
+
+355
+00:41:35,340 --> 00:41:40,480
+الأمثلة النقرة لزي دورة طويلة قراري ده المنورة
+
+356
+00:41:40,480 --> 00:41:48,820
+التجارية لكي نأخذ الدنيا التجارية قراري ده المنورة
+
+357
+00:41:48,820 --> 00:41:55,980
+التجارية لكي نأخذ الدنيا التجارية قراري ده المنورة
+
+358
+00:41:55,980 --> 00:42:01,360
+التجارية أشتغل الساعة في النتائج اللي قبلك وليه 
+
+359
+00:42:01,360 --> 00:42:04,320
+نفسك وانت تبقى على ال single point فأنا قاعد اللي 
+
+360
+00:42:04,320 --> 00:42:07,820
+هو complex اللي بيهرمليش complex وضعية اللي ما
+
+361
+00:42:07,820 --> 00:42:11,400
+تطلع تطلع اللي بأخذ ال limit وال limited to the
+
+362
+00:42:11,400 --> 00:42:15,200
+finite بيخبر الله أنّ أخبر هل هي complex أو لعدة 
+
+363
+00:42:15,200 --> 00:42:18,420
+اللي بيأخذ عنده ال limit هل هو complex ولا limited
+
+364
+00:42:19,970 --> 00:42:24,890
+طبعًا زي ما يفضلكم هاكم دورية أهل الوسام وفريق أهل 
+
+365
+00:42:24,890 --> 00:42:28,750
+الوسام ماشي عطيكوا فعالة evaluation منهم في
+
+366
+00:42:28,750 --> 00:42:31,470
+ال architectural context ومن أخر سنة في المملكة
+
+367
+00:42:31,470 --> 00:42:34,350
+العربية السعودية بس كده بالمفهوم اللي إذا كده
+
+368
+00:42:34,350 --> 00:42:38,110
+المعنى يكفي بس المعاناة الأقلومية ثانية ومعاناة
+
+369
+00:42:38,110 --> 00:42:42,170
+ميلاد مافي واي واي واي واي واي واي واي واي واي واي
+
+370
+00:42:42,170 --> 00:42:42,250
+واي واي واي واي واي واي واي واي واي واي واي
+
+371
+00:42:42,250 --> 00:42:45,120
+واي واي واي واي واي واي واي واي واي world mark ..
+
+372
+00:42:45,120 --> 00:42:49,020
+أو .. أو .. أو .. أو .. أو .. أو .. أو .. أو .. أو
+
+373
+00:42:49,020 --> 00:42:49,620
+.. أو .. أو .. أو .. أو .. أو .. أو .. أو .. أو ..
+
+374
+00:42:49,620 --> 00:42:50,180
+أو .. أو .. أو .. أو .. أو .. أو .. أو .. أو .. أو
+
+375
+00:42:50,180 --> 00:42:55,040
+.. أو .. أو .. أو .. أو .. أو .. أو .. أو .. أو ..
+
+376
+00:42:55,040 --> 00:42:58,060
+أو .. أو .. أو .. أو .. أو .. أو .. أو .. أو .. أو
+
+377
+00:42:58,060 --> 00:42:58,560
+.. أو .. أو .. أو .. أو .. أو .. أو .. أو .. أو ..
+
+378
+00:42:58,560 --> 00:42:59,580
+أو .. أو .. أو .. أو .. أو .. أو .. أو .. أو .. أو
+
+379
+00:42:59,580 --> 00:43:00,500
+.. أو .. أو .. أو .. أو .. أو .. أو .. أو .. أو ..
+
+380
+00:43:00,500 --> 00:43:09,340
+أو .. أو .. أو .. أو .. أو
+
+381
+00:43:09,340 --> 00:43:13,500
+..
+
+382
+00:43:13,500 --> 00:43:18,290
+أو زي ما أشوف في الرقم يبقى مندي أشوف همين من 
+
+383
+00:43:18,290 --> 00:43:22,630
+المواقع هذه تبقى regular singular point ومين أ
+
+384
+00:43:22,630 --> 00:43:27,790
+regular singular point ورقمي أو مجلة يبقى السؤال 
+
+385
+00:43:27,790 --> 00:43:32,290
+بس مندي أجيب ال singular وأشوف هل هي regular ومع 
+
+386
+00:43:32,290 --> 00:43:39,300
+كرجل يعطينا المسألة دلوقت يبقى هذه ال P ومتها بأجيب
+
+387
+00:43:39,300 --> 00:43:44,980
+ال C ونغميرها Point إذا أنا لو لدى بلد ممكن واحد
+
+388
+00:43:44,980 --> 00:43:50,340
+ما ترستيكس تجيب تجيب تجيب تجيب تجيب تجيب تجيب تجيب
+
+389
+00:43:50,340 --> 00:44:04,460
+تجيب تجيب تجيب تجيب تجيب تجيب تجيب
+
+390
+00:44:08,450 --> 00:44:16,770
+ممكن وانت إيش أو سالب واحد لو كانت واحد تصيبها 
+
+391
+00:44:16,770 --> 00:44:22,450
+لزيرة لو كانت سالب واحد تصيبها لزيرة يبقى هذه بدها
+
+392
+00:44:22,450 --> 00:44:30,590
+تساوي زيرة only x يساوي سالب واحد and x يساوي
+
+393
+00:44:30,590 --> 00:44:31,410
+واحد
+
+394
+00:44:33,930 --> 00:44:38,090
+يبقى جفت ال singular point بقى يبقى كل عدد
+
+431
+00:47:31,590 --> 00:47:36,790
+ثانوية في واحد زائد اتش كله في وايّمين بساوية درجة
+
+432
+00:47:36,790 --> 00:47:45,690
+الآن نذهب نبحث كل مقفل أنّها ثاني مقفل ثاني بعد ما
+
+433
+00:47:45,690 --> 00:47:50,590
+كتبت المعادلة بالصيغة الجديدة وبالتالي نجيب جناش ال
+
+434
+00:47:50,590 --> 00:47:54,550
+Q على P ونجيب جناش ال R على P
+
+435
+00:48:02,320 --> 00:48:08,240
+إذا كنت تجيء للمقبض أولًا بتأخذ limit لما ال X تذهب
+
+436
+00:48:08,240 --> 00:48:17,080
+من واحد أو قبل أن تكون at X يساوي 1 لما 
+
+437
+00:48:17,080 --> 00:48:22,460
+تذهب من واحد لِساوي واحد
+
+438
+00:48:29,480 --> 00:48:39,400
+لمن؟ لمن Q of X على P of X يساوي limit لما ال X
+
+439
+00:48:39,400 --> 00:48:45,360
+تبدأ تروح لـ -1 لل X ذلك واحد فيه، ليه Q على P
+
+440
+00:48:45,360 --> 00:48:49,760
+جانزة، فيه من؟ هذه النتيجة ساعة ما اختصرنا
+
+441
+00:48:49,760 --> 00:48:59,420
+الحدود اللي مطلوبة، يبقى هذا X على واحد ناقص x
+
+442
+00:48:59,420 --> 00:49:07,600
+في واحد زائد x الكل تربيع طبعًا طبعًا طبعًا طبعًا طبعًا
+
+443
+00:49:07,600 --> 00:49:11,900
+طبعًا طبعًا طبعًا طبعًا طبعًا طبعًا طبعًا طبعًا طبعًا طبعًا
+
+444
+00:49:11,900 --> 00:49:12,960
+طبعًا طبعًا طبعًا طبعًا طبعًا طبعًا طبعًا طبعًا طبعًا طبعًا
+
+445
+00:49:12,960 --> 00:49:15,640
+طبعًا طبعًا طبعًا طبعًا طبعًا طبعًا طبعًا طبعًا طبعًا طبعًا
+
+446
+00:49:15,640 --> 00:49:19,440
+طبعًا طبعًا طبعًا طبعًا طبعًا طبعًا 
+
+447
+00:49:27,380 --> 00:49:32,680
+طبعًا علينا أن ندخل X ونذهب إلى أين؟ X سالب واحد
+
+448
+00:49:32,680 --> 00:49:37,800
+يبقى هذه سالب واحد على هذه نحط مكانها سالب واحد
+
+449
+00:49:37,800 --> 00:49:43,600
+عشان نشوف ايه اثنين؟ هذه سالب واحد تصير جداش سين
+
+450
+00:49:43,600 --> 00:49:48,980
+ويبقى النتيجة جداش سالب اثنين أكمل؟ نعم اثنين
+
+451
+00:49:48,980 --> 00:49:53,740
+خلاص اللي عم أدخل آخر مرة X فاي نايم يعني هذه هنا
+
+452
+00:49:53,740 --> 00:50:01,650
+فاي نايم يبقى بناء عليه رقم X يساوي واحد منها
+
+453
+00:50:01,650 --> 00:50:09,230
+regular singular point يبقى لنا الساعة Z point
+
+454
+00:50:09,230 --> 00:50:19,650
+اللي هو X يساوي سالب واحد is an irregular singular
+
+455
+00:50:19,650 --> 00:50:22,970
+point
+
+456
+00:50:22,970 --> 00:50:33,690
+بس لو طلعت finite بروح على مقطع ثاني نجيء إذا X
+
+457
+00:50:33,690 --> 00:50:41,010
+يساوي واحد يبقى مقطع ثاني يبقى نأخذ نفس ال limit
+
+458
+00:50:41,010 --> 00:50:49,170
+أي limit بس ال X ولدك واحد للواحد لمن؟ لل X ماقص 
+
+459
+00:50:49,170 --> 00:50:49,830
+واحد
+
+460
+00:50:52,650 --> 00:51:00,150
+على P of X على P of X على P of X على P of X على P 
+
+461
+00:51:00,150 --> 00:51:08,550
+of X على P of X على P of X على 
+
+462
+00:51:08,550 --> 00:51:13,330
+P of 
+
+463
+00:51:13,330 --> 00:51:17,630
+X حتى لو قلت تحتاج فايلة خلاص الديناميكية دي هي
+
+464
+00:51:17,630 --> 00:51:21,750
+حسنة إذا نحن انتقلنا إلى من لن نفقد دنيا السن
+
+465
+00:51:21,750 --> 00:51:25,610
+برنامج الأولى وانتقلنا إلى من لن نفقد دنيا يعني
+
+466
+00:51:25,610 --> 00:51:31,730
+في هذه ال level لما ال x بدأ تروح للواحد لل x ما تس
+
+467
+00:51:31,730 --> 00:51:38,320
+واحد فيهلكي واللي طلعناها فوق هي همت ريّراتش X
+
+468
+00:51:38,320 --> 00:51:46,160
+على واحد ناقص X تبين في واحد زائد X الكل تربيع يزيد
+
+469
+00:51:47,780 --> 00:51:53,060
+هذه X ماكس راحت هذه واحد ماكس نختار واحد من هذه
+
+470
+00:51:53,060 --> 00:51:55,980
+نختار واحد من هذه نختار واحد من هذه نختار واحد من
+
+471
+00:51:55,980 --> 00:52:02,460
+هذه نختار 
+
+472
+00:52:02,460 --> 00:52:06,520
+واحد من هذه نختار
+
+473
+00:52:06,520 --> 00:52:12,620
+واحد من هذه
+
+474
+00:52:13,280 --> 00:52:16,620
+من هنا بتأخذ شبكت سالي بعرف المشترك، ومن هنا
+
+475
+00:52:16,620 --> 00:52:23,260
+بتأخذ شبكت سالي بعرف المشترك، ومن هنا
+
+476
+00:52:23,260 --> 00:52:23,720
+بتأخذ شبكت سالي بعرف المشترك، ومن هنا بتأخذ شبكت
+
+477
+00:52:23,720 --> 00:52:26,340
+ومن هنا بتأخذ شبكت سالي بعرف المشترك، ومن هنا
+
+478
+00:52:26,340 --> 00:52:29,160
+بتأخذ شبكت سالي بعرف المشترك، ومن هنا بتأخذ شبكت
+
+479
+00:52:29,160 --> 00:52:34,440
+سالي بعرف المشترك، ومن هنا بتأخذ شبكت سالي بعرف
+
+480
+00:52:34,440 --> 00:52:39,150
+المشترك، ومن هنا بعلى واحد زي واحد تربيع أربعة
+
+481
+00:52:39,150 --> 00:52:43,370
+يبقى سنة وأربعة فاين اين وما ذاكن فاين أعيد فاين
+
+482
+00:52:43,370 --> 00:52:45,830
+أعيد فاين أعيد فاين أعيد فاين أعيد فاين أعيد فاين
+
+483
+00:52:45,830 --> 00:52:46,950
+أعيد فاين أعيد فاين أعيد فاين أعيد فاين أعيد فاين
+
+484
+00:52:46,950 --> 00:52:48,710
+أعيد فاين أعيد فاين أعيد فاين أعيد فاين أعيد فاين
+
+485
+00:52:48,710 --> 00:52:52,590
+أعيد فاين أعيد فاين أعيد فاين أعيد فاين أعيد فاين
+
+486
+00:52:52,590 --> 00:52:52,910
+أعيد فاين أعيد فاين أعيد فاين أعيد فاين أعيد فاين
+
+487
+00:52:52,910 --> 00:53:01,470
+أعيد فاين أعيد فاين أعيد فاين أعيد فاين أعيد فا
+
+488
+00:53:04,680 --> 00:53:09,960
+يبقى هذا الكلام متساوي ال limit لما ال X بيروح لل
+
+489
+00:53:09,960 --> 00:53:19,380
+واحد لل X ناقص واحد كل تربيع أنا في هجمة يبقى واحد
+
+490
+00:53:19,380 --> 00:53:25,940
+ناقص X كل تربيع في واحد زي ال X يبقى واحد أو هذه
+
+491
+00:53:25,940 --> 00:53:30,960
+دوري على واحد ناقص X كل ذا تربيع
+
+492
+00:53:33,690 --> 00:53:40,090
+زائد X واحد زائد X شرايف دي راديو غالب
+
+493
+00:53:46,280 --> 00:53:52,400
+بتروح يعني هذه كأنها مضبوط تمامًا limit لما ال x
+
+494
+00:53:52,400 --> 00:53:58,120
+تروح للواحد لـ X ناقص واحد كل تربيع على X ناقص واحد
+
+495
+00:53:58,120 --> 00:54:04,020
+كل تربيع في واحد زائد X بتروح هذه معناه دي بس ال
+
+496
+00:54:04,020 --> 00:54:10,280
+limit لما ال X تروح للواحد لما ال X لفوق ال
+
+497
+00:54:10,280 --> 00:54:16,560
+واحد نسميه ل 1 على 1 زائد X من شركة ده مصف ف
+
+498
+00:54:16,560 --> 00:54:23,200
+أي نايت كده لف يرجع ف أي نايت يرجع لإن على النقطة
+
+499
+00:54:23,200 --> 00:54:29,620
+لإن هذه الساعة ال X لساعة واحد is a regular
+
+500
+00:54:29,620 --> 00:54:32,360
+singular point
+
+501
+00:54:37,870 --> 00:54:41,970
+يعني كان نفس المثال يبقى بعض ال singular وبعض ال
+
+502
+00:54:41,970 --> 00:54:48,570
+regular وبعض ال irregular ممكن كلهم regular وممكن
+
+503
+00:54:48,570 --> 00:54:53,830
+كلهم irregular كذلك يعني كل احتمالات ويبدأ
+
+504
+00:54:53,830 --> 00:54:59,490
+كل مسألة علاقة طيب هذا هو المثال الأول لنروح للآخر
+
+505
+00:54:59,490 --> 00:55:01,070
+المثال الثاني
+
+506
+00:55:15,820 --> 00:55:26,480
+X تربيع زي 19 Y تربيع فعلاً ما تس ثلاثة سيكس Y فاي 
+
+507
+00:55:26,480 --> 00:55:35,400
+زي واحد ناقص X كله في الواحد يبقى وايّمين بساوي زيت
+
+508
+00:55:41,300 --> 00:55:48,380
+بدا البداية قمت باستخدام Q of X بإنسان X مبين
+
+509
+00:55:48,380 --> 00:55:59,540
+لاتصال وقمت باستخدام Q of X ما فس ثلاثة Xكبت ال R 
+
+510
+00:55:59,540 --> 00:56:04,880
+of X بالسنونين واحد ما فسكت، شو رأيت الدلالد
+
+511
+00:56:04,880 --> 00:56:13,480
+هالول؟ هالول نوميّانز، كده هالول R نوميّانز
+
+512
+00:56:14,210 --> 00:56:17,930
+لو كما رأيت في المقصد الحقيقي أنا أتاب عليها كده
+
+513
+00:56:17,930 --> 00:56:25,990
+الـ S يتزايد ال E of X يتزايد X أكبر زي 9 لو
+
+514
+00:56:25,990 --> 00:56:33,850
+سويتها من 0 تجهش المسئولة عندنا ال X أكبر يساوي 9 
+
+515
+00:56:33,850 --> 00:56:36,230
+لِجالكسي الجديد
+
+516
+00:56:55,450 --> 00:57:01,590
+السؤال اللي جبناه
+
+517
+00:57:01,590 --> 00:57:02,470
+هو الطعام
+
+518
+00:57:06,900 --> 00:57:10,180
+مدى هؤلاء البرولوجيين اللي قطعوا دي يرجعوا يدخلوا
+
+519
+00:57:10,180 --> 00:57:15,260
+في نفس التحقيق اللي اتبعته قبل قليل يرجعوا ثانيًا
+
+520
+00:57:15,260 --> 00:57:20,320
+ويقولوا هؤلاء اللي اكتشفوا يقولوا هؤلاء اللي لديهم
+
+521
+00:57:20,320 --> 00:57:29,340
+5 Singular Points يرجعوا
+
+522
+00:57:29,340 --> 00:57:31,500
+هؤلاء ثم Singular Points
+
+523
+00:57:37,730 --> 00:57:40,650
+نقسم؟ نقسم يارب
+
+524
+00:57:54,070 --> 00:58:05,330
+YWπ-3X عليه يبقى
+
+525
+00:58:05,330 --> 00:58:17,700
+X ناقص ثلاثة I زائد ثلاثة I في Y prime زائد واحد 
+
+526
+00:58:17,700 --> 00:58:26,640
+ناقص X على X ناقص ثلاثة I في X زائد ثلاثة I في Y كله
+
+527
+00:58:26,640 --> 00:58:31,920
+بيساوي Zero محتاج 
+
+528
+00:58:31,920 --> 00:58:35,420
+ليه؟ هذا الكلام 
+
+529
+00:58:37,750 --> 00:58:47,470
+x² زائد 9 على الساوية X ناقص 3i في X زائد 3i تعال
+
+530
+00:58:47,470 --> 00:58:52,630
+نشوف لو ضربت هدول في بعض فعلاً بتطلع هذا ولا لأ أنا
+
+531
+00:58:52,630 --> 00:58:56,310
+أخبرتك أن الفرق بينهم مربعين بس بكمية تخيلية بيبقى
+
+532
+00:58:56,310 --> 00:58:58,690
+وليس بكمية حقيقية
+
+533
+00:59:06,080 --> 00:59:12,980
+3XI ومن السالم 3XI براهم مع السلمة والهالي بها
+
+534
+00:59:12,980 --> 00:59:19,400
+نسالم ثلاثة من ثلاثة نسالم تسعة و I بالعالي نسالم
+
+535
+00:59:19,400 --> 00:59:24,860
+واحد نسالم ثالث نسالم عشر وجرم تسعة بالفور نسالم
+
+536
+00:59:24,860 --> 00:59:29,140
+تسعة وعشر وجرم تسعة بالفور نسالم تسعة وعشر وجرم
+
+537
+00:59:29,530 --> 00:59:33,790
+يعني يا بنات جاني يفكرني لو حللتك من أول من هنا و
+
+538
+00:59:33,790 --> 00:59:37,890
+قلت لك تساوي زي إذا ولا مذكرنيها تبقى طيبة وكده
+
+539
+00:59:37,890 --> 00:59:41,990
+معاكي أنّ أنا ما أحلل عليك فأنت ما تحلل على الله يبقى
+
+540
+00:59:41,990 --> 00:59:48,090
+الآن أنا بدادي أقول المقطة الأولى بيبقى بدادي أقول
+
+541
+00:59:48,090 --> 00:59:56,990
+أنّ اثنين X يساوي سن ثلاثة تروح تأخذ ال limit لما ال X
+
+542
+00:59:56,990 --> 01:00:05,310
+كذا طول بزائد ثلاثة I أنّ ال X ماقص ثلاثة I وزائد
+
+543
+01:00:05,310 --> 01:00:11,790
+ثلاثة I بالصغير وماقص ماقص ثلاثة I زائد ثلاثة I أنّ
+
+544
+01:00:11,790 --> 01:00:19,490
+ال Q of X على ال P of X يساوي ال limit لما ال X ذهب
+
+545
+01:00:19,490 --> 01:00:26,690
+لسالب ثلاثة I لما ال X ذهب لسالب ثلاثة I لكي وعلى
+
+546
+01:00:26,690 --> 01:00:34,790
+P لايه عيزة يبقى هي اللي هو سالب ثلاثة X مقسومة على
+
+547
+01:00:34,790 --> 01:00:44,070
+من على X مقسومة على I في X زائد ثلاثة I طبعًا، 
+
+548
+01:00:44,070 --> 01:00:48,750
+نروح هذا term مع ال term اللي عندها يرجعنا
+
+549
+01:00:48,750 --> 01:00:54,530
+بالمسألة إلى ال limit لما ال X بده يروح من ثالث 
+
+550
+01:00:54,530 --> 01:01:04,280
+ثلاثة R لثالث ثلاثة X على X ناقص ثلاثة R أول خطوة
+
+551
+01:01:04,280 --> 01:01:09,560
+في إيجاد ال limit هي التعويض المباشر يبقى هاي ماقص
+
+552
+01:01:09,560 --> 01:01:17,380
+ثلاثة برا والعكس بتروح نوير لسالب ثلاثة I على سالف 
+
+553
+01:01:17,380 --> 01:01:30,580
+ثلاثة I سالب ثلاثة I طيب هل تساوي تسعة I على سالف
+
+554
+01:01:30,580 --> 01:01:31,100
+I
+
+555
+01:01:35,440 --> 01:01:41,620
+I مع I وسنة مع سنة ونصف على ستة ونزلت ثلاثة على
+
+556
+01:01:41,620 --> 01:01:47,500
+اثنين تبقى صعب النتيجة ثلاثة على اثنين ثلاثة على
+
+557
+01:01:47,500 --> 01:01:49,820
+اثنين ماله أسبوع يناير
+
+558
+01:01:52,650 --> 01:01:57,030
+تسعة تسعة تسعة تسعة تسعة تسعة تسعة تسعة تسعة تسعة
+
+559
+01:01:57,030 --> 01:02:04,050
+تسعة تسعة تسعة تسعة تسعة تسعة تسعة تسعة تسعة تسعة
+
+560
+01:02:04,050 --> 01:02:06,050
+تسعة تسعة تسعة تسعة تسعة تسعة تسعة تسعة تسعة تسعة
+
+561
+01:02:06,050 --> 01:02:07,870
+تسعة تسعة تسعة تسعة تسعة تسعة تسعة تسعة تسعة تسعة
+
+562
+01:02:07,870 --> 01:02:11,770
+تسعة تسعة تسعة تسعة تسعة
+
+563
+01:02:11,770 --> 01:02:16,630
+تسعة تسعة تسعة تسعة تسعة تسعة تسعة تسعة
+
+564
+01:02:16,630 --> 01:02:21,950
+تسعة تس
+
+565
+01:02:22,000 --> 01:02:30,260
+أها لما ال X بدها تروح لوين لِسان ثلاثة I لوين من
+
+566
+01:02:30,260 --> 01:02:41,740
+ال X زي ثلاثة I من R و F على ال E و B القرآن
+
+567
+01:02:41,740 --> 01:02:48,240
+الترميز مظهر بحيث يبقى هذا الكلام بالسيابين limit
+
+568
+01:02:48,240 --> 01:02:56,670
+لما ال X بدها تروح بزائد ثلاثة I من X زائد ثلاثة I
+
+569
+01:02:56,670 --> 01:03:04,430
+لكل جميع ال R of X والواحد من R of X هي واحد ناقص
+
+570
+01:03:04,430 --> 01:03:13,210
+X واحد ناقص X كله مكسوما على X ناقص ثلاثة I ب X 
+
+571
+01:03:13,210 --> 01:03:21,140
+زائد ثلاثة I ويزداد طبعًا في اختصارات دورس هذا مع
+
+572
+01:03:21,140 --> 01:03:26,840
+من مع دورس اللي عنده هذا يبقى مصير ال limit لما 
+
+573
+01:03:26,840 --> 01:03:35,500
+ال X بدأ تقوه لثالث ثلاثة I لل X زائد ثلاثة I تمين
+
+574
+01:03:35,500 --> 01:03:47,060
+في واحد ناقص X على من على X ناقص ثلاثة I بتشيل كل
+
+575
+01:03:47,060 --> 01:03:53,040
+اسم حفظتها سالب ثلاثة يبقى
+
+576
+01:03:53,040 --> 01:04:02,220
+هذا الكلام Zero في واحد سالب ثلاثة I عالمي على
+
+577
+01:04:02,220 --> 01:04:06,700
+سالب ثلاثة I سالب ثلاثة يبقى نفسي قدام
+
+578
+01:04:12,020 --> 01:04:15,200
+Do you find that you turn your coin right before
+
+579
+01:04:15,200 --> 01:04:36,060
+you have it, or that you have a singular coin?
+
+580
+01:04:36,060 --> 01:04:44,370
+Do you really serve the coin? X يساوي ثانية ثلاثة I
+
+581
+01:04:44,370 --> 01:04:47,870
+هو مجلد عادي
+
+582
+01:05:00,900 --> 01:05:09,640
+عشان نعمل نقطة ثانية X بساعدة اش فأنا هاعد إذا 
+
+583
+01:05:09,640 --> 01:05:13,920
+روح نفسي لنقطة أولى يجب أنّ أنا أعمل limit لما
+
+584
+01:05:13,920 --> 01:05:18,080
+ال X بدأ تروح ليه ثلاثة أعلى
+
+585
+01:05:29,940 --> 01:05:36,700
+يبقى عند نقطة X0 يسبب ثلاثة I يبقى حتى X ناقص
+
+586
+01:05:36,700 --> 01:05:39,680
+ثلاثة I تميل
+
+587
+01:05:42,200 --> 01:05:48,400
+على من؟ على capital Q of X يبقى limit لما ال X
+
+588
+01:05:48,400 --> 01:05:55,940
+تبقى واحدة ثلاثة I لل X ناقص ثلاثة I من Q على P
+
+589
+01:05:55,940 --> 01:06:05,490
+وين راحت ال Q على P دي غالب؟ وثلاثة ثلاثة X ثالث
+
+590
+01:06:05,490 --> 01:06:14,870
+ثلاثة X على X ناقص ثلاثة I في X زائد ثلاثة I طبعًا 
+
+591
+01:06:14,870 --> 01:06:20,510
+هاني وهاني مع السلامة يقلق المسألة إلى ال limit
+
+592
+01:06:20,510 --> 01:06:30,130
+لما ال X تدخل في ثلاثة I لثالث ثلاثة X على X زائد
+
+593
+01:06:30,130 --> 01:06:34,450
+ثلاثة I النتيجة
+
+594
+01:06:35,750 --> 01:06:44,970
+ثالث ثلاثة في ثلاثة I على ثلاثة I زائد ثلاثة I
+
+595
+01:06:44,970 --> 01:06:52,210
+يبقى ناقص تسعة I على ستة I كمان ناقص ثلاثة على
+
+596
+01:06:52,210 --> 01:06:58,650
+اثنين يبقى هماله I9 وده الـ finite إذا بدنا نروح 
+
+597
+01:06:58,650 --> 01:07:04,750
+لمين؟ للشرق الأخير لإننا بدنا نروح لاخد limit لما
+
+598
+01:07:04,750 --> 01:07:11,830
+ال X بده نروح لثلاثة I لل X ما تس ثلاثة I والترمية
+
+599
+01:07:11,830 --> 01:07:19,850
+في A of X أنا كنت ال E of X هو يساوي limit لما ال X
+
+600
+01:07:19,850 --> 01:07:27,590
+يروح ليه ثلاثة I لل X ناقص ثلاثة I التقرير ليه ال
+
+601
+01:07:27,590 --> 01:07:35,450
+R أو ال R على E اللي عبارة عن الواحد ناقص X كله 
+
+602
+01:07:35,450 --> 01:07:45,950
+مقسومة على X-3i ب X زائد 3i لإن هذا الكلام يجب أنّ
+
+603
+01:07:45,950 --> 01:07:49,97
+
+646
+01:12:53,230 --> 01:12:54,070
+على P EO6 على P EO6 على P EO6 على P EO6 على P EO6
+
+647
+01:12:54,070 --> 01:12:56,730
+على P EO6 على P EO6 على P EO6 على P EO6 على P EO6
+
+648
+01:12:56,730 --> 01:12:56,810
+على P EO6 على P EO6 على P EO6 على P EO6 على P EO6
+
+649
+01:12:56,810 --> 01:13:01,750
+على P EO6 على Pmax to the power n على n factorial
+
+650
+01:13:01,750 --> 01:13:08,910
+to converge for
+
+651
+01:13:08,910 --> 01:13:13,290
+all x converge for all x
+
+652
+01:13:20,810 --> 01:13:24,850
+لأن نكون غير جادة، أي الاختبار اللي أخذناه هنا يا
+
+653
+01:13:24,850 --> 01:13:30,170
+بناتي؟ هو يبقى إيه؟ هو يبقى إيه؟ هو يبقى
+
+654
+01:13:30,170 --> 01:13:30,210
+إيه؟ هو يبقى إيه؟ هو يبقى إيه؟ هو يبقى إيه؟
+
+655
+01:13:30,210 --> 01:13:30,650
+هو يبقى إيه؟ هو يبقى إيه؟ هو يبقى إيه؟ هو
+
+656
+01:13:30,650 --> 01:13:31,550
+يبقى إيه؟ هو يبقى إيه؟ هو يبقى إيه؟ هو يبقى
+
+657
+01:13:31,550 --> 01:13:34,050
+إيه؟ هو يبقى إيه؟ هو يبقى إيه؟ هو يبقى إيه؟
+
+658
+01:13:34,050 --> 01:13:38,450
+هو يبقى إيه؟
+
+659
+01:13:38,450 --> 01:13:44,510
+هو
+
+660
+01:13:44,510 --> 01:13:44,950
+يبقى 
+
+661
+01:13:48,180 --> 01:13:56,140
+من R Cos X تربيع هذه على كثيرة حدود يمكن أن يبدأ
+
+662
+01:13:56,140 --> 01:14:02,560
+بـ X تربيع فيها فعلينا نفسنا نجد أيش كل علامة زيها
+
+663
+01:14:02,560 --> 01:14:09,880
+لأن R Cos X علينا 3 Cos X على X بـ 3 Cos
+
+664
+01:14:09,880 --> 01:14:19,280
+X على X تطلع كده 3 X D Cos X أصلاً Cos X ألا X
+
+665
+01:14:19,280 --> 01:14:24,400
+كنا بنحسبها في تاني روميكسون ولو ضربناها في كمان X
+
+666
+01:14:24,400 --> 01:14:30,000
+تطلع من السيرة ألا X تطلع من القارس يرجى هذه كمان
+
+667
+01:14:30,000 --> 01:14:36,360
+is analytic because
+
+668
+01:14:36,360 --> 01:14:39,380
+Cos X
+
+669
+01:14:50,370 --> 01:14:59,070
+انالتك تحطي هنا بنات and fix yourself easy وهذه
+
+670
+01:14:59,070 --> 01:15:05,890
+اللي هي الانالتك كمان At X يساوي زي روز الشمس
+
+671
+01:15:05,890 --> 01:15:10,150
+هذه الـ singular point اللي عندنا إذا أنت حققت مين
+
+672
+01:15:10,150 --> 01:15:13,990
+الـ condition دي الساعة اللي بيبقى كبرها دي مدة
+
+673
+01:15:13,990 --> 01:15:20,470
+singular singular point إذا At X يساوي زي روز
+
+674
+01:15:20,470 --> 01:15:20,750
+الشمس
+
+675
+01:15:29,750 --> 01:15:37,050
+بعدين سأذكركم بتوصيل الـ X وشو هو المفتوح تبعها
+
+676
+01:15:37,050 --> 01:15:44,910
+بالنسبالي أنا أختارهم ثم اتنين الـ N اللي هو
+
+677
+01:15:44,910 --> 01:15:49,550
+الـ 3 X توصيل X
+
+678
+01:15:56,980 --> 01:16:05,340
+لنقص واحد إذا power in x أُسي 2 M عالمين على
+
+679
+01:16:05,340 --> 01:16:14,250
+2 M تقريباً بالشكل الهام، طبعاً اللي بقدر أكتبها
+
+680
+01:16:14,250 --> 01:16:19,170
+على الشكل التالي summation من N equal 0 to
+
+681
+01:16:19,170 --> 01:16:28,590
+infinity لثالث واحد تدفع تن في 3 X أس 2 N
+
+682
+01:16:28,590 --> 01:16:34,990
+زائد 1 على 2 N factorial مش عارف كل عليها
+
+683
+01:16:34,990 --> 01:16:40,830
+أنها تبقى هادة تبقى هادة مضمونة برد من تلك
+
+684
+01:16:40,830 --> 01:16:45,570
+البرصدية، طبعاً تعبنا أن الصين والكوسين والزي
+
+685
+01:16:45,570 --> 01:16:50,270
+والساين والسيك والجوش وأن الـ X واقعد على X وكذلك
+
+686
+01:16:50,270 --> 01:16:55,330
+برد كلها آلي مجانا تتبع على شكل تاني ومجانا تتبع
+
+687
+01:16:55,330 --> 01:16:55,350
+على شكل تاني ومجانا تتبع على شكل تاني ومجانا
+
+688
+01:16:55,350 --> 01:16:57,810
+تتبع على شكل تاني ومجانا تتبع على شكل تاني
+
+689
+01:16:57,810 --> 01:16:59,070
+ومجانا تتبع على شكل تاني ومجانا تتبع على شكل
+
+690
+01:16:59,070 --> 01:17:01,950
+تاني ومجانا تتبع على شكل تاني ومجانا تتبع على
+
+691
+01:17:01,950 --> 01:17:10,630
+شكل تاني ومجانا تتبع على شكل تاني وVersion X E
+
+692
+01:17:10,630 --> 01:17:22,350
+أُس X Lenin X واحدة على X تالي Inverse X وحط عليهم
+
+693
+01:17:22,350 --> 01:17:26,970
+E أُس X Lenin X تالي Inverse X وLenin X تالي
+
+694
+01:17:26,970 --> 01:17:33,210
+Inverse X كلهم هم مقدرتهم على شكل تايلور أو مقدرين
+
+695
+01:17:33,210 --> 01:17:37,130
+Series at any point عند أي نقطة
+
+696
+01:17:42,810 --> 01:17:48,090
+هذا السؤال اللي بين إيدينها بيختلف عن السؤالين
+
+697
+01:17:48,090 --> 01:17:53,940
+السابقين بأن المعاملات معاها ماهياش Polynomial كانت 
+
+698
+01:17:53,940 --> 01:17:58,800
+general functions فكان عندك ليه الـ 6 و 3 cos x are
+
+699
+01:17:58,800 --> 01:18:03,140
+general functions يعني not polynomials لذلك سنلجأ
+
+700
+01:18:03,140 --> 01:18:07,660
+إلى الحالة الأولى اللي ابتدينا فيها فباجي بقول
+
+701
+01:18:07,660 --> 01:18:12,420
+طبعاً هذه لا يمكن أن تساوي zero إلا إذا كانت x ساوي
+
+702
+01:18:12,420 --> 01:18:16,180
+zero بـ x ساوي zero is the only singular point
+
+703
+01:18:16,180 --> 01:18:22,180
+لمين الـ differential equation اللي عندنا بنقسم كله
+
+704
+01:18:22,180 --> 01:18:26,320
+على X فصارت المعادلة على الشكل اللي عندنا هذا إذا
+
+705
+01:18:26,320 --> 01:18:30,220
+بدي أشوف كده قيمة X نقص الـ X node في Q of X على P
+
+706
+01:18:30,220 --> 01:18:35,340
+of X يبقى يساوي X في E of X على X نختصر بظهر E of
+
+707
+01:18:35,340 --> 01:18:38,600
+X هذي أنا لاتك لأن بقدر أكتبها على شكل Taylor
+
+708
+01:18:38,600 --> 01:18:42,940
+Series أو هي عبارة عن McLaurin Series عند X يساوي
+
+709
+01:18:43,180 --> 01:18:48,060
+زيرو وبالتالي صارت هذه انالتك الآن بدي أجي للـ X
+
+710
+01:18:48,060 --> 01:18:51,920
+نقص الـ X نوت تربيع R of X على P of X الـ X نوت
+
+711
+01:18:51,920 --> 01:18:55,480
+بـ زيرو يبقى بصير X تربيع هدي على هدي ليه 3
+
+712
+01:18:55,480 --> 01:19:00,980
+cosine X على X نختصر بصير 3 X cosine X هذا
+
+713
+01:19:00,980 --> 01:19:06,640
+انالتك ليش؟ لأن هذا مفكوك الـ cosine Maclaurin
+
+714
+01:19:06,640 --> 01:19:11,890
+series at X يساوي زيرو ضربنا في 3 X دخلنا الـ X
+
+715
+01:19:11,890 --> 01:19:16,890
+ديوة صار الأس بدل 2 N بصير 2 N زاد 1
+
+716
+01:19:16,890 --> 01:19:20,890
+وهي الـ 3 وهي الـ 1 أس N كما هو والمقام
+
+717
+01:19:20,890 --> 01:19:26,190
+بـ 2 N فاكتوريال إذا هذه كمان analytic function
+
+718
+01:19:26,190 --> 01:19:30,310
+إذا صار الـ term الأول والـ term التاني تنتين are two
+
+719
+01:19:30,310 --> 01:19:35,010
+analytic functions يبقى الـ x يساوي 0 is a regular
+
+720
+01:19:35,010 --> 01:19:41,330
+singular point طيب مش كل الدول اللي بتيجي بهذه
+
+721
+01:19:41,330 --> 01:19:44,710
+السهولة هذه غير هي regular و irregular بعضها بتبقى
+
+722
+01:19:44,710 --> 01:19:49,710
+إيه مسائل صعبة شوية لكن نطلع نقول لو عندي two
+
+723
+01:19:49,710 --> 01:19:53,130
+functions واتنتين كانوا analytic عند النقطة دي
+
+724
+01:19:53,130 --> 01:19:59,340
+يبقى مجموعهم الجبري يعني جمع أو طرح نقصد به أو حاصل
+
+725
+01:19:59,340 --> 01:20:04,260
+ضرب الـ two functions f في g أو خارج قسمة الاتنين
+
+726
+01:20:04,260 --> 01:20:09,940
+بشرط الـ g عند النقطة x node ممنوعة تساوي zero دي
+
+727
+01:20:09,940 --> 01:20:13,840
+ريبيلك الـ g of x node is not equal to zero لأن
+
+728
+01:20:13,840 --> 01:20:18,080
+هذا بيصير معناه is undefined ماهياش معرفة are
+
+729
+01:20:18,080 --> 01:20:21,920
+analytic and main عند الـ x node الآن هشوف كيف
+
+730
+01:20:21,920 --> 01:20:28,930
+نستخدم هذه الـ remark في حل السؤال التالي من أسئلة
+
+731
+01:20:28,930 --> 01:20:38,150
+الكتاب وهو المثال رقم 4 إذا المثال رقم 4 بيقول
+
+732
+01:20:38,150 --> 01:20:46,190
+للـ X في الـ sign الـ X في الـ Y double prime زائد
+
+733
+01:20:46,190 --> 01:20:54,240
+3 Y prime 3 Y prime زائد XY بده يساوي كده؟
+
+734
+01:20:54,240 --> 01:21:00,580
+بده يساوي 0 واضح هذه الـ Polynomial من الدرجة
+
+735
+01:21:00,580 --> 01:21:04,940
+الصفرية هذه الـ Polynomial من الدرجة الأولى لكن هذه
+
+736
+01:21:04,940 --> 01:21:09,160
+لـ sign X ليست Polynomial يبقى هذه general
+
+737
+01:21:09,160 --> 01:21:20,900
+function يبقى بجي بقوله P of X sin الـ X is not a
+
+738
+01:21:20,900 --> 01:21:25,360
+polynomial تمام
+
+739
+01:21:25,360 --> 01:21:32,700
+طيب بدأ أسألكوا السؤال التالي is it a series X
+
+740
+01:21:32,700 --> 01:21:37,400
+في sin الـ X زي X فيكون sin الـ X نعم Series لكنها
+
+741
+01:21:37,400 --> 01:21:41,410
+ليس بتنمية يعني مش بتوفر حد محدد بتظلها ماشية إلى
+
+742
+01:21:41,410 --> 01:21:45,490
+وين لغاية ما لا نهاية ولو ضربناها في X زي ما ضربنا
+
+743
+01:21:45,490 --> 01:21:50,110
+الـ cosine هنا في X يبقى بيظلها Series وليست
+
+744
+01:21:50,110 --> 01:21:55,330
+Polynomial مش كثيرة حدود وإنما بيظل متسلسلة إلى ما
+
+745
+01:21:55,330 --> 01:22:01,510
+لا نهاية طيب تمام الآن بدي أشوف ما هي النقاط التي
+
+746
+01:22:01,510 --> 01:22:09,910
+تجعل الـ P of X يساوي 0 يبقى باجي بقوله P of X بده
+
+747
+01:22:09,910 --> 01:22:21,970
+يساوي X sin X equal 0
+
+748
+01:22:21,970 --> 01:22:29,430
+at X يساوي بنشوف إيش النقاط اللي بتخلي هذه القيمتين
+
+749
+01:22:29,430 --> 01:22:35,970
+حاصل ضربهم يساوي Zero أظل لو كانت X يساوي Zero صح؟
+
+750
+01:22:35,970 --> 01:22:40,670
+بيصير هذه بـ Zero و الـ sign Zero بـ Zero Zero Zero
+
+751
+01:22:40,670 --> 01:22:49,260
+Zero خلصنا؟ في غيرهم يعني؟ زي مين؟ باي، 2 باي،
+
+752
+01:22:49,260 --> 01:22:57,500
+3 باي، 4 باي، 5 باي وزيهم بالسالب يبقى
+
+753
+01:22:57,500 --> 01:23:04,820
+الزائد أو ناقص in by الـ X بيساوي zero و الـ X
+
+754
+01:23:04,820 --> 01:23:11,780
+بيساوي زائد أو ناقص in by و الـ in is an integer و
+
+755
+01:23:11,780 --> 01:23:16,840
+الـ in يساوي 1 و 2 و 3 وإلى ما لا نهاية
+
+756
+01:23:18,050 --> 01:23:22,930
+يعني الحمد لله كم singular point عندنا؟ ما له
+
+757
+01:23:22,930 --> 01:23:26,290
+نهاية من الـ singular points وهذا ما أشرت إليه قبل
+
+758
+01:23:26,290 --> 01:23:29,510
+شوية في بداية المحاضرة قلت لك ممكن يكون عندي نقطة
+
+759
+01:23:29,510 --> 01:23:33,270
+واحدة singular point ممكن يكون عندي نقطتين ممكن
+
+760
+01:23:33,270 --> 01:23:37,410
+يكون 3 ممكن ما له نهاية من النقطة اللي على
+
+761
+01:23:37,410 --> 01:23:40,370
+البعض كنت أستغرب عندما قلت يمكن يكون عندي ما له
+
+762
+01:23:40,370 --> 01:23:44,990
+نهاية من الـ singular لكن هي جيبنالكم يتهطل عندي
+
+763
+01:23:44,990 --> 01:23:49,370
+ما له نهاية من مين؟ من الـ singular طيب ما علينا بدي
+
+764
+01:23:49,370 --> 01:23:54,110
+أشوف النقاط هدول regular و الله irregular نيجي
+
+765
+01:23:54,110 --> 01:23:58,550
+نقوله تعالى نشوف الآن المعادلة هذه بتروح أكتبها
+
+766
+01:23:58,550 --> 01:24:02,970
+على الشكل التالي يبقى هذه هي المعادلة رقم 1
+
+767
+01:24:02,970 --> 01:24:09,750
+فبروح بقوله that differential equation one is
+
+768
+01:24:09,750 --> 01:24:10,830
+written
+
+769
+01:24:17,500 --> 01:24:24,380
+زائد 3 على X في الـ sign الـ X في الـ Y prime
+
+770
+01:24:24,380 --> 01:24:32,220
+زائد X بتروح مع X مضال 1 على الـ sign الـ X فقط
+
+771
+01:24:32,220 --> 01:24:34,940
+في الـ Y بدها تساوي زيرو
+
+772
+01:24:38,450 --> 01:24:43,570
+نمسك النقطة الأولى لـ X يساوي Zero يبقى بده أجي
+
+773
+01:24:43,570 --> 01:24:50,070
+أقوله at X بده يساوي Zero أخد ليه بتابانات؟ لأ لأن
+
+774
+01:24:50,070 --> 01:24:53,110
+هدول ماهياش Polynomial صحيح تنتين Polynomial بس
+
+775
+01:24:53,110 --> 01:24:57,410
+التالتة لأ يبقى in general التلاتة غير متحقق أن
+
+776
+01:24:57,410 --> 01:25:02,290
+التلاتة Polynomial يبقى بده أروح للحالة الأولى و
+
+777
+01:25:02,290 --> 01:25:09,140
+ليست من الحالة الثانية يعني بدي أشوف هل الـ X ناقص X
+
+778
+01:25:09,140 --> 01:25:18,300
+node اللي هو Zero في الـ Q of X على الـ R of X هل
+
+779
+01:25:18,300 --> 01:25:23,020
+بقدر اكتفها على شكل Polynomial أم لا؟ هل Taylor
+
+780
+01:25:23,020 --> 01:25:28,940
+Series أم لا؟ يبقى هدي بصير X في ميم في الـ Q على X
+
+781
+01:25:28,940 --> 01:25:35,820
+اللي هي 3 على X sin الـ X يبقى في 3 على X
+
+782
+01:25:35,820 --> 01:25:43,220
+في sin الـ X الـ X مع الـ X يبقى النتيجة كده 3
+
+783
+01:25:43,220 --> 01:25:49,970
+على sin الـ X السؤال هو بتقدر تكتبها على شكل Taylor
+
+784
+01:25:49,970 --> 01:25:54,950
+series أم لا؟ تقول استنى شوية تعالى نطلع للـ remark
+
+785
+01:25:54,950 --> 01:25:58,410
+اللي إحنا كاتبينه فوق أيش بتقولي الـ remark لو
+
+786
+01:25:58,410 --> 01:26:02,890
+كانوا تنتين analytic يبقى المجموعة والضرب وخرج
+
+787
+01:26:02,890 --> 01:26:07,810
+القسمة are analytic باجي بس لنفسي هل الـ sign
+
+788
+01:26:07,810 --> 01:26:13,770
+analytic الإجابة نعم نجي هل الـ 3 analytic يعني
+
+789
+01:26:13,770 --> 01:26:18,390
+هل الـ constant بقدر اكتبه عليه شكل Series وتبقى
+
+790
+01:26:18,390 --> 01:26:25,270
+طبعاً لأ يبقى هذه بصير مالها is not analytic يبقى
+
+791
+01:26:25,270 --> 01:26:35,730
+هذه الـ function هذه بـ الساوي is not analytic السبب
+
+792
+01:26:35,730 --> 01:26:38,610
+أن الـ 3 ما هيش انتظر مين اللي بتحكي
+
+793
+01:26:52,810 --> 01:27:01,400
+3 X مضروبة في الـ cosine وهي حاطنلك على شكل
+
+794
+01:27:01,400 --> 01:27:06,240
+summation وهي الـ summation ودخلتها جوا صارت هذه
+
+795
+01:27:06,240 --> 01:27:10,080
+على شكل ماكلورين أو تايلور Series ولا لا عند النقطة X
+
+796
+01:27:10,080 --> 01:27:13,580
+ساوي Zero صحيح ولا لا؟ طب يلا كتبيلي 3 على
+
+797
+01:27:13,580 --> 01:27:16,520
+الشكل هذا نشوف مش هنشوف كلامك صح ولا لا تبعت
+
+798
+01:27:16,520 --> 01:27:20,360
+المقام موافق صحيح الـ X مظبوط لكن هل يتل.. يعني
+
+799
+01:27:20,360 --> 01:27:25,400
+cosecant X 3 cosecant X عمرك جيبتي تايلور ولا
+
+800
+01:27:25,400 --> 01:27:30,300
+ماكلورين للـ cosecant طب مهم عند Zero مش معرفة أصلاً
+
+801
+01:27:30,300 --> 01:27:34,620
+صحيحة ولا لا؟ طب إحنا الشرط الذاتي تبع المقام لازم
+
+802
+01:27:34,620 --> 01:27:38,020
+يكون معرف مش يقولنا لما يكون عندنا خارج قسم
+
+803
+01:27:38,020 --> 01:27:42,640
+التنتين بدي هذه ممنوعة تساوي Zero عند Zero و sin
+
+804
+01:27:42,640 --> 01:27:47,800
+Zero في جداش يعني أمورها ما تصير Analytic مظبوط ولا
+
+805
+01:27:47,800 --> 01:27:53,560
+لا؟ خلاصنا؟ جنات يهودة؟ والكلام نفسنا مهين طيب
+
+806
+01:27:53,560 --> 01:27:56,400
+يبقى هذه سرعة النقطة Analytic يبقى النقطة اللي
+
+807
+01:27:56,400 --> 01:27:57,020
+عندنا مالها
+
+808
+01:28:00,210 --> 01:28:08,550
+يبقى هنا سا اللي هو الـ X يساوي 0 is irregular
+
+809
+01:28:08,550 --> 01:28:14,610
+singular point
+
+810
+01:28:40,920 --> 01:28:51,700
+عشان نذهب إلى نقاط التانية X يساوي زائد أو ناقص في
+
+811
+01:28:51,700 --> 01:28:52,440
+Y
+
+812
+01:28:56,110 --> 01:29:03,470
+الـ X نقص الـ X نواة في الـ Q of X على capital P
+
+813
+01:29:03,470 --> 01:29:09,850
+of X يبقى بيصير X زائد أو نقص in by I بدي أخدهم
+
+814
+01:29:09,850 --> 01:29:16,490
+مرة واحدة والـ Q على P ليه 3 على X sin X يبقى
+
+815
+01:29:16,490 --> 01:29:24,190
+فيه 3 على X في sin X طيب
+
+816
+01:29:24,190 --> 01:29:32,640
+طالعيني لهذهبقدر أكتبها مثل 3 X في كوسايت
+
+817
+01:29:32,640 --> 01:29:36,860
+يبقى هذه analytic and zero ولا لا؟ analytic طيب
+
+818
+01:29:36,860 --> 01:29:43,090
+اللي فوق هذي Polynomial من أي درجة؟ بالدرجة الأولى
+
+819
+01:29:43,090 --> 01:29:47,330
+والثانية بتكتب على شكل
\ No newline at end of file
diff --git a/PL9fwy3NUQKwa8ZDfSFGn6H8xVFLzqmCZC/nOggX_oRaAA_postprocess.srt b/PL9fwy3NUQKwa8ZDfSFGn6H8xVFLzqmCZC/nOggX_oRaAA_postprocess.srt
new file mode 100644
index 0000000000000000000000000000000000000000..1f7779bad309fa56cb9eedb0b6e8979d0b2525ba
--- /dev/null
+++ b/PL9fwy3NUQKwa8ZDfSFGn6H8xVFLzqmCZC/nOggX_oRaAA_postprocess.srt
@@ -0,0 +1,3436 @@
+1
+00:00:00,000 --> 00:00:02,960
+أهلا و أهلا يا عزيزي و أهلا و أهلا يا عزيزي و أهلا
+
+2
+00:00:02,960 --> 00:00:14,280
+و أهلا يا عزيزي و
+
+3
+00:00:14,280 --> 00:00:14,920
+أهلا و أهلا و أهلا و أهلا و أهلا و أهلا و أهلا و
+
+4
+00:00:14,920 --> 00:00:15,020
+أهلا و أهلا و أهلا و أهلا و أهلا و أهلا و أهلا و
+
+5
+00:00:15,020 --> 00:00:15,860
+أهلا و أهلا و أهلا و أهلا و أهلا و أهلا و أهلا و
+
+6
+00:00:15,860 --> 00:00:17,800
+أهلا و أهلا و أهلا و أهلا و أهلا و أهلا و أهلا و
+
+7
+00:00:17,800 --> 00:00:20,300
+أهلا و أهلا و أهلا و أهلا و أهلا و أهلا و أهلا و
+
+8
+00:00:20,300 --> 00:00:26,820
+أهلا و أهلا و أهلا و
+
+9
+00:00:26,820 --> 00:00:33,020
+أهالسؤال يقول اذا ترمى انه موضوعه فانه يجيب عمليات
+
+10
+00:00:33,020 --> 00:00:36,480
+لازم يتولدوا و يتولدوا و يتولدوا و يتولدوا و
+
+11
+00:00:36,480 --> 00:00:38,600
+يتولدوا و يتولدوا و يتولدوا و يتولدوا و يتولدوا و
+
+12
+00:00:38,600 --> 00:00:39,600
+يتولدوا و يتولدوا و يتولدوا و يتولدوا و يتولدوا و
+
+13
+00:00:39,600 --> 00:00:39,740
+يتولدوا و يتولدوا و يتولدوا و يتولدوا و يتولدوا و
+
+14
+00:00:39,740 --> 00:00:40,280
+يتولدوا و يتولدوا و يتولدوا و يتولدوا و يتولدوا و
+
+15
+00:00:40,280 --> 00:00:42,440
+يتولدوا و يتولدوا و يتولدوا و يتولدوا و يتولدوا و
+
+16
+00:00:42,440 --> 00:00:47,180
+يتولدوا و يتولدوا و يتولدوا
+
+17
+00:00:58,350 --> 00:01:08,270
+والشيء الوحيد لـ P or X دلوقت لو قلنا P or X اللي
+
+18
+00:01:08,270 --> 00:01:13,890
+يجب ان تكسب يعني اقصد من X لما اقصد لانها دلوقت
+
+19
+00:01:13,890 --> 00:01:20,720
+هذه المثلة حددنا الى حصلعشان انا اعرف انا انا اعرف
+
+20
+00:01:20,720 --> 00:01:25,700
+انا اعرف انا اعرف انا اعرف انا اعرف انا اعرف
+
+21
+00:01:29,830 --> 00:01:36,170
+هذا الكلام لو كانت تساوي Zero هذا الكلام مابيحصل
+
+22
+00:01:36,170 --> 00:01:43,110
+إلا إذا كانت ال kicks يساوي ساوي واحد and ال kicks
+
+23
+00:01:43,110 --> 00:01:51,290
+يساوي ثلاث سنة من مدونة او Singular Points
+
+24
+00:01:54,400 --> 00:01:57,940
+النقاط الشاملة والنقاط الوانهاتي اللي لدينا
+
+25
+00:01:57,940 --> 00:02:02,260
+المعاملة انتقالية هي النقاط اللي بتجعل المعاملة
+
+26
+00:02:02,260 --> 00:02:06,320
+تقع واحدة من الحاجة تسوى زيرو مانيش تبنيها لكل
+
+27
+00:02:06,320 --> 00:02:11,500
+نقطة يتجاه نقاط اشتهرت من قبلها يعني ال singular
+
+28
+00:02:11,500 --> 00:02:18,470
+points و ال ordinary pointsordinary points يرجى
+
+29
+00:02:18,470 --> 00:02:22,870
+مادام هدول هم ال singular points هدى بدي يعطيك ان
+
+30
+00:02:22,870 --> 00:02:28,730
+ال X لها تساوي أربعة و X لها تساوي ساوي أربعة and
+
+31
+00:02:28,730 --> 00:02:38,290
+ال X لها تساوي Zero are ordinary points ordinary
+
+32
+00:02:38,290 --> 00:02:41,150
+points
+
+33
+00:02:43,470 --> 00:02:48,530
+تمام؟ بدنا نصاب الأكترار تعالى بنتنا نجيب كل ده
+
+34
+00:02:48,530 --> 00:02:54,150
+نجيب يومنا تمام؟ السجن لا يكون في النقطة السالي
+
+35
+00:02:54,150 --> 00:02:59,350
+واحد ونقطة واثر ثلاث يجب أن نجيب السالي واحد يجب
+
+36
+00:02:59,350 --> 00:03:06,870
+أن نجيب أي نقطة في السالي واحدماذا نحن نحن نحن نحن
+
+37
+00:03:06,870 --> 00:03:08,570
+نحن نحن نحن نحن نحن نحن نحن نحن نحن نحن نحن نحن
+
+38
+00:03:08,570 --> 00:03:11,610
+نحن نحن نحن نحن نحن نحن نحن نحن نحن نحن نحن نحن
+
+39
+00:03:11,610 --> 00:03:12,950
+نحن نحن نحن نحن نحن نحن نحن نحن نحن نحن نحن نحن
+
+40
+00:03:12,950 --> 00:03:14,290
+نحن نحن نحن نحن نحن نحن نحن نحن نحن نحن نحن نحن
+
+41
+00:03:14,290 --> 00:03:22,830
+نحن نحن نحن نحن نحن نحن نحن نحن
+
+42
+00:03:22,830 --> 00:03:28,370
+نحن
+
+43
+00:03:28,370 --> 00:03:32,610
+نحإذا ال singular point هي النقطة سنة واحدة و
+
+44
+00:03:32,610 --> 00:03:39,670
+ثلاثة يبقى هذه النقطة هي ال singular point و
+
+45
+00:03:39,670 --> 00:03:46,570
+الثلاثة كمان دالي يمينه هي ال singular point تمام
+
+46
+00:03:46,570 --> 00:03:53,950
+تمام الان قللي هدلي و قللي هو مينأصغر lower bound
+
+47
+00:03:53,950 --> 00:03:57,810
+of radius of convergence لان انا بدي اروح اشوف
+
+48
+00:03:57,810 --> 00:04:01,910
+radius of convergence لان هو ياخد صغير فيلم يقول
+
+49
+00:04:01,910 --> 00:04:07,790
+هو اصغر التقارب المطلوب ليجي عند النقطة الأولى عند
+
+50
+00:04:07,790 --> 00:04:09,690
+x⁻⁴
+
+51
+00:04:15,230 --> 00:04:19,490
+شوف ايش اللي بده يصير وانا الاربعة هايم يعني ما
+
+52
+00:04:19,490 --> 00:04:23,230
+بده اشوف كده المسافة ما بده الاربعة مش سالف واحد
+
+53
+00:04:23,230 --> 00:04:27,910
+واشوف كده المسافة بين الأربعة وثلاثة صغيرة يوم
+
+54
+00:04:27,910 --> 00:04:32,870
+بتكون يا مين ال radius of convergence المطلوب
+
+55
+00:04:32,870 --> 00:04:38,600
+اليعملالجمال اللي بنقوله الآن عند نقطة x تساوي
+
+56
+00:04:38,600 --> 00:04:43,780
+أربعة روات بده ساوية أربعة اللي هي النقطة اللي
+
+57
+00:04:43,780 --> 00:04:51,120
+عندنا ما تستخدمي ال singularماقص واحد ويساوي قدره
+
+58
+00:04:51,120 --> 00:04:57,620
+خمسة تدريجي ناخد روح اثنين بتساوي اربعة ماقص ثلاثة
+
+59
+00:04:57,620 --> 00:05:02,620
+يساوي قدره واحد يبقى نصف قطر اتقال بالمطبق ودين
+
+60
+00:05:02,620 --> 00:05:07,300
+واحد اللي قاللي احنا اللي هو الفرح اصغر واحد منهم
+
+61
+00:05:07,300 --> 00:05:18,210
+يبقى هنا باجي بيقولوا اثنينLower down of the
+
+62
+00:05:18,210 --> 00:05:24,810
+radius of convergence
+
+63
+00:05:24,810 --> 00:05:35,060
+is not zeroيبقى رمضان سنة واحد هو رمضان لا ميل دا
+
+64
+00:05:35,060 --> 00:05:40,800
+رديوس او كل فيها جامعه اذا ال serious solution هذه
+
+65
+00:05:40,800 --> 00:05:51,840
+يجب ان اقول له ال serious solution الموجودة
+
+66
+00:05:52,620 --> 00:05:59,200
+Summation من M equal 0 to infinity من A M في X نقص
+
+67
+00:05:59,200 --> 00:06:02,480
+X نقص X نقص X نقص X نقص X نقص X نقص X نقص X نقص X
+
+68
+00:06:02,480 --> 00:06:04,280
+نقص X نقص X نقص X نقص X نقص X نقص X نقص X نقص X
+
+69
+00:06:04,280 --> 00:06:07,240
+نقص X نقص X نقص X نقص X نقص X نقص X نقص X نقص X
+
+70
+00:06:07,240 --> 00:06:07,680
+نقص X نقص X نقص X نقص X نقص X نقص X نقص X نقص X
+
+71
+00:06:07,680 --> 00:06:08,580
+نقص X نقص X نقص X نقص X نقص X نقص X نقص X نقص X
+
+72
+00:06:08,580 --> 00:06:17,620
+نقص X نقص X نقص X
+
+73
+00:06:17,620 --> 00:06:29,150
+نقاللي يست عالم أقل for absolute value من X مع
+
+74
+00:06:29,150 --> 00:06:34,450
+أصحابها أقل من الواحد اللي اعتمدناه لوله صغير كل
+
+75
+00:06:34,450 --> 00:06:42,170
+الدنياالجهد عند النقطة x0 تساوي 4 لو جينا الان عند
+
+76
+00:06:42,170 --> 00:06:46,770
+النقطة x0 تساوي 4
+
+77
+00:06:52,440 --> 00:06:59,200
+يبقى روح ون يساوي، اه هذه فيها سبب لأن هو دائما و
+
+78
+00:06:59,200 --> 00:07:04,120
+أبدا أكبر من يزيل النسخوتر، تعني مثلا إذا كنت قاطب
+
+79
+00:07:04,120 --> 00:07:08,320
+بير، اللي هتسيبه تباركها أفضل دائما و أبدا في كل
+
+80
+00:07:08,320 --> 00:07:08,740
+مالها
+
+81
+00:07:15,890 --> 00:07:21,910
+النقطة اللي هي ناقص أربعة وإن ناقص أربعة هيها منها
+
+82
+00:07:21,910 --> 00:07:29,350
+إذا ناقص أربعة ناقص ناقص واحد يرجع ناقص ناقص واحد
+
+83
+00:07:46,040 --> 00:07:49,960
+النقطة التانية كم؟ تلاتة
+
+84
+00:08:06,810 --> 00:08:24,310
+radius of conveyor belts is راتب سبكتر تلتة سبكتر
+
+85
+00:08:28,090 --> 00:08:32,030
+this is your solution for summation from n equals
+
+86
+00:08:32,030 --> 00:08:38,950
+zero to infinity of b into x plus 4 to the power
+
+87
+00:08:38,950 --> 00:08:39,430
+of n
+
+88
+00:08:44,340 --> 00:08:53,880
+بتكون في ال at least على الأقل for absolute value
+
+89
+00:08:53,880 --> 00:09:00,880
+لل X زائد أربعة أقل من 2 أقل من 3 لتطلع لها هذا
+
+90
+00:09:00,880 --> 00:09:05,320
+بالنسبة للنقطة الثانية بالنسبة للنقطة الثانية X0
+
+91
+00:09:05,320 --> 00:09:06,420
+يساوي 0
+
+92
+00:09:24,800 --> 00:09:30,920
+النقطة الأولى هي نقص واحد، نقص نقص واحد هي نقص
+
+93
+00:09:30,920 --> 00:09:32,480
+واحد
+
+94
+00:09:40,360 --> 00:09:45,000
+بساوي كتير؟ absolutely بساوي تلاتة ليه تلاتة؟ من
+
+95
+00:09:45,000 --> 00:09:54,740
+الاتنين هدول فبروح بقول دي lower bound for the
+
+96
+00:09:54,740 --> 00:10:01,840
+radius of convergence
+
+97
+00:10:01,840 --> 00:10:13,990
+is رقم ساوي واحد الان بروح بقوله دهسيريز سوليوشن
+
+98
+00:10:13,990 --> 00:10:23,790
+لو سماشي نبتدن equal zero to infinity لسي ان في ال
+
+99
+00:10:23,790 --> 00:10:30,110
+X ماقس ال zero يعني قدر يعني X to the power N
+
+100
+00:10:30,110 --> 00:10:42,570
+convergeأفضل من أفضل من أفضل من أفضل من أفضل من
+
+101
+00:10:42,570 --> 00:10:47,310
+أفضل من أفضل من أفضل من أفضل من أفضل من أفضل من
+
+102
+00:10:47,310 --> 00:10:48,510
+أفضل من أفضل من أفضل من أفضل من أفضل من أفضل من
+
+103
+00:10:48,510 --> 00:10:55,390
+أفضل من أفضل من أفضل من أفضلمعناه نهاية لما يعمل
+
+104
+00:10:55,390 --> 00:10:59,070
+كل واحدة من تنتيجة قرية مانا نهاية يبقى اي واحدة
+
+105
+00:10:59,070 --> 00:11:04,430
+فيهم يبقى كوندرش علي كل real line لكنها بناء
+
+106
+00:11:04,430 --> 00:11:10,210
+كوندرش علي فترة فقط ماغية يبقى هذا بالنسبة للمثال
+
+107
+00:11:10,210 --> 00:11:17,560
+رقم اللي هو الـ 10 بمجرد المثال رقم 3يرجع البرنامج
+
+108
+00:11:17,560 --> 00:11:22,280
+إلى هذا رقم ثلاثة نفس المطلوب هذا ليس حاجة تغيره
+
+109
+00:11:22,280 --> 00:11:26,460
+يرجع البرنامج إلى هذا الرقم تغيرته بشكل معادل ان
+
+110
+00:11:26,460 --> 00:11:38,520
+هو واحد زائد X ترمية في ال YW5 زائد اتنين XY5 زائد
+
+111
+00:11:42,320 --> 00:11:48,760
+يساوي زيرو وال X نوض يساوي زيرو وال X نوض التالية
+
+112
+00:11:48,760 --> 00:11:50,680
+يساوي معاك اسمه
+
+113
+00:11:58,940 --> 00:12:03,880
+المثال السابق قبل قليل محور ان ال singular quiz
+
+114
+00:12:03,880 --> 00:12:09,540
+كانت تنتم هي واحدة كانت سالف واحد وتانية داشر
+
+115
+00:12:09,540 --> 00:12:14,920
+وتانية تلاتة لكن هنا في سؤال تعالى تشوف مشكلته
+
+116
+00:12:14,920 --> 00:12:18,240
+يبقى ايش مزاج يقوله solution
+
+117
+00:12:20,590 --> 00:12:29,050
+الـ P of X يساوي واحد زاوية X تجارية بزيرو
+
+118
+00:12:29,050 --> 00:12:35,950
+معناه هذا الكلام ان X بدأ ساوي زاوية او نقطة I
+
+119
+00:12:35,950 --> 00:12:44,150
+ممتاز جدا يتجسس من مقطة تحيولية اللي مجبر اكتبها
+
+120
+00:12:44,150 --> 00:12:44,570
+عبر
+
+121
+00:12:47,730 --> 00:12:55,110
+زائد او ناقص ايه انت عارف لانه العدد المركب يكتب
+
+122
+00:12:55,110 --> 00:13:00,690
+كمجموعة two terms جزء الحقيقه وجزء التفاير الحقيقه
+
+123
+00:13:00,690 --> 00:13:05,970
+مارهاش اللي معناته P0 فبروح بطب وعلى صيغة zero
+
+124
+00:13:05,970 --> 00:13:13,100
+زائد او ناقص ايه جمهور كان مفهوموحدة زيرو زائد ايه
+
+125
+00:13:13,100 --> 00:13:20,580
+واتانية زيرو نقطة اتنين مش نقطة واحدة تمام الان
+
+126
+00:13:20,580 --> 00:13:24,920
+نبدأ نشتغل نفس الشغل اللي اشتغلناه بس على كل نقطة
+
+127
+00:13:24,920 --> 00:13:29,300
+من النقطتين اللي اتنين من دولة بس قبل ذلك من الكتب
+
+128
+00:13:29,300 --> 00:13:32,520
+الكتب وراه عرف ال complex فاعرفش اللي دراسوا ال
+
+129
+00:13:32,520 --> 00:13:36,680
+complex علتيه اللي ما دراسوهش اللي عرفوهاشلذلك لو
+
+130
+00:13:36,680 --> 00:13:43,120
+افضل مسافة بين نقطتين في ال complex play يرجع من
+
+131
+00:13:43,120 --> 00:13:47,100
+هنا نقطة ملاحظة و بعدين نستخدمها في الشبكة فبعدين
+
+132
+00:13:47,100 --> 00:13:56,520
+يقولون انها distance between play
+
+133
+00:13:56,520 --> 00:14:07,650
+points المرزق دواعييساوي x واحد زي ال IY واحد and
+
+134
+00:14:07,650 --> 00:14:16,970
+زد اتنين and زد اتنين يبدأ يساوي x اتنين زي ال IY
+
+135
+00:14:16,970 --> 00:14:25,570
+اتنين in the complex complex
+
+136
+00:14:25,570 --> 00:14:28,490
+اتنين
+
+137
+00:14:35,340 --> 00:14:42,840
+بديها رمز Z واحد مقص Z اتنين absolute value هذه
+
+138
+00:14:42,840 --> 00:14:49,520
+عبارة عن الجدرين التربيعي X واحد مقص X اتنين لكل
+
+139
+00:14:49,520 --> 00:14:56,400
+تربيع زي Y واحد مقص Y اتنين لكل تربيع تقريبا كانت
+
+140
+00:14:56,400 --> 00:15:02,840
+مشروع كونه عندك في الكتابة لكن عليها اسئلة
+
+141
+00:15:20,410 --> 00:15:25,970
+قبل ما اكمل ان اقولها المقول هذه مش قولها صح ولا
+
+142
+00:15:25,970 --> 00:15:33,750
+لأ any real number is a complex number صح ولا لأ و
+
+143
+00:15:33,750 --> 00:15:39,350
+بعدين نجيب العملية العكسية any complex number is a
+
+144
+00:15:39,350 --> 00:15:45,210
+real number ليس صح وليس غلق ولا كله غلق ولا كله صح
+
+145
+00:15:47,360 --> 00:15:51,360
+القانع الريال number is a complex number صح ولا لأ
+
+146
+00:15:51,360 --> 00:15:58,780
+؟ خطأ ؟ اه ممتازة انك بيقول بتقول هدا ان القانع
+
+147
+00:15:58,780 --> 00:16:03,680
+الريال number is a complex number هذا خطأ نجي شوف
+
+148
+00:16:03,680 --> 00:16:08,300
+قد هو صح ولا خطأ خلّاوي هنا كويسة لو جاي تقولتك
+
+149
+00:16:08,300 --> 00:16:14,760
+التلاتة مثلا التلاتة هي لأ ولا لأ اللي اكتفه هذا
+
+150
+00:16:14,760 --> 00:16:15,120
+اصلا
+
+151
+00:16:19,330 --> 00:16:27,950
+مصحيح ولا لأ؟ مصحيح ولا لأ؟ مصحيح
+
+152
+00:16:27,950 --> 00:16:40,470
+ولا لأ؟ مصحيح
+
+153
+00:16:40,470 --> 00:16:45,690
+ولا لأ؟ مصحيح ولا لأ؟ مصحيح ولا لأ؟ مصحيح ولا لأ؟
+
+154
+00:16:45,690 --> 00:16:50,530
+مصحيح ولا لأ؟العكس ما هوش صحيح نهائي أبدا ولا عملك
+
+155
+00:16:50,530 --> 00:16:56,930
+تجد complex number واحد يسوى real number إلا إذا
+
+156
+00:16:56,930 --> 00:17:02,950
+كان صفر غير لاشي بعد كامة يعني لو كان zero
+
+157
+00:17:02,950 --> 00:17:08,390
+فcomplex number هو zero زي zero في Iصحيح ان هو
+
+158
+00:17:08,390 --> 00:17:11,990
+اللي بيسيوريه بالنظر الانجليزي، لكن غير ذلك بعد
+
+159
+00:17:11,990 --> 00:17:17,190
+التغور، مش ممكنية أبدًا، تمام؟ قال بس ودمرت علومة
+
+160
+00:17:17,190 --> 00:17:21,970
+أمشية ده زهنلها بالحلم، لكن كانت علومة جيدة
+
+161
+00:17:21,970 --> 00:17:27,250
+للدكتور يعرفها، طيب، نرجع الآن للموضوع الصغيرسؤال
+
+162
+00:17:27,250 --> 00:17:32,630
+اللي بيقولني بيجيب جداش ال radius of all virgins
+
+163
+00:17:32,630 --> 00:17:36,390
+لما يتى المعادلة الطابقة الاربونية اللى عندنا هذه
+
+164
+00:17:36,390 --> 00:17:42,630
+الحلطة بجهها الحل ك series صحية عليه بقولك ميسيا
+
+165
+00:17:42,630 --> 00:17:45,890
+احنا طلعنا المفقودين تاخدوا ال utility quotients
+
+166
+00:17:45,890 --> 00:17:49,350
+وتم نقطة الاولة النقطة الاولى جالسة x not equal to
+
+167
+00:17:49,350 --> 00:17:50,270
+zero
+
+168
+00:18:06,230 --> 00:18:22,710
+زيرو زائد زيرو في I زيرو
+
+169
+00:18:22,710 --> 00:18:32,090
+زائد Iالـ X تساوي I يعني سريعًا وزاهم I بالشكل
+
+170
+00:18:32,090 --> 00:18:37,450
+العامل لها لأن هذه اللي صار X واحد وY واحد وهذه
+
+171
+00:18:37,450 --> 00:18:42,990
+صارت X اتنين وY اتنين وواحد صحيح مظبوط فالمفروض ان
+
+172
+00:18:42,990 --> 00:18:48,150
+هذه القادة تقدر اجيب جداش الفرق بين النقطتين اللي
+
+173
+00:18:48,150 --> 00:18:54,080
+هو نصف متر التقارىيبقى مثلًا اقوله يبقى O1 يبقى
+
+174
+00:18:54,080 --> 00:19:02,960
+بيساوي الجدرين الترميه ليه X1-X2 يبقى كتير Zero
+
+175
+00:19:02,960 --> 00:19:11,120
+ناقص Zero لكل ترمية Y1 ناقص Y2 كدهش Y1؟ Zero Y2
+
+176
+00:19:11,120 --> 00:19:20,440
+لواحد لكل ترمية يبقى كتير ترمية يبقى كتير ترمية
+
+177
+00:19:20,440 --> 00:19:20,540
+يبقى كتير ترمية يبقى كتير ترمية يبقى كتير ترمية
+
+178
+00:19:20,540 --> 00:19:23,870
+يبقى كتير ترمية يبقىيساوي الجدرين التربية يليه
+
+179
+00:19:23,870 --> 00:19:29,030
+النقطة اللي عندنا هذه والنقطة التانية الصالحة مين؟
+
+180
+00:19:29,030 --> 00:19:36,910
+ناقص A يتغير إلى Zero ناقص Zero في كل تربية زائد
+
+181
+00:19:36,910 --> 00:19:45,830
+Zero زائد واحد في كل تربيةواحد نفسه يبدأ بلاء عليه
+
+182
+00:19:45,830 --> 00:19:50,290
+ال road is always lower than for the radius of
+
+183
+00:19:50,290 --> 00:20:04,290
+convergence يبقى the lower bound for the radius of
+
+184
+00:20:04,290 --> 00:20:07,030
+convergence
+
+185
+00:20:27,520 --> 00:20:35,780
+للـ X ناقصيجب ان نقفل لانه يجيزيه مرضو يقفلاش الـ
+
+186
+00:20:35,780 --> 00:20:44,000
+0 تغريد x to the power n convert at least على
+
+187
+00:20:44,000 --> 00:20:49,540
+الأقل for absolute value of x مقصد 0 أقل من ال
+
+188
+00:20:49,540 --> 00:20:51,800
+minimum أقل من الماحدة
+
+189
+00:20:58,400 --> 00:21:03,380
+خلصنا من قصة النقل يظهر التاني ماذا؟ يظهر سالف نص
+
+190
+00:21:03,380 --> 00:21:10,220
+يظهر سالف نص يظهر
+
+191
+00:21:10,220 --> 00:21:16,640
+سالف نص يظهر سالف نص يظهر سالف نص يظهر سالف نص
+
+192
+00:21:16,640 --> 00:21:21,960
+يظهر سالف نص يظهر سالف نص يظهر سالف نص يظهر سالف
+
+193
+00:21:21,960 --> 00:21:30,490
+نصوهذا Y و R نمسك النقطة التانية and النقطة التي
+
+194
+00:21:30,490 --> 00:21:37,970
+خلقناها ال X يساوي R يعني مين يعني؟ Zero زائد R
+
+195
+00:21:38,830 --> 00:21:44,710
+بتروح نجيب الراوان يساوي الجذري التربيعي ده x
+
+196
+00:21:44,710 --> 00:21:52,550
+واحدة هو ناقص نص ناقص x اتنية اللي هو ال zero لكل
+
+197
+00:21:52,550 --> 00:21:59,630
+تربيعزي واي واحد اللي هو zero مابس واي اتنين اللي
+
+198
+00:21:59,630 --> 00:22:06,310
+هو واحد لكل تربيع يساوي جدر التربيع طبعا هذا رابع
+
+199
+00:22:06,310 --> 00:22:12,910
+وهنا قدر واحد يعني واحد و رابع قدر خمسة على اربع
+
+200
+00:22:12,910 --> 00:22:20,950
+يعني جدر خمسة على اتنين انا بروح اجيب له اتنين
+
+201
+00:22:21,390 --> 00:22:33,890
+يساوي الجدرين الترابيعي الان نغير النقطة X يساوي
+
+202
+00:22:33,890 --> 00:22:36,010
+Zero نقص I
+
+203
+00:22:41,240 --> 00:22:46,160
+اللي هي عبارة عن زير و نقص عيال بيروم بده يساوي X
+
+204
+00:22:46,160 --> 00:22:52,240
+واحد اللي هو ناقص نص ناقص زير لكل تربيع
+
+205
+00:22:56,640 --> 00:23:03,700
+zero ناقص ناقص واحد زائد واحد في كل تربيع يبقى جدر
+
+206
+00:23:03,700 --> 00:23:08,800
+التربيع إلى اربعة زائد واحد يبقى جدر خمسة على
+
+207
+00:23:08,800 --> 00:23:14,580
+اتنين لاتنين سوا بعض يبقى بناء عليه بناء على هذا
+
+208
+00:23:14,580 --> 00:23:25,360
+الكلام يجب يقولوا the lower bound for the radius
+
+209
+00:23:31,930 --> 00:23:40,770
+convergence is قرار تساوي كده جدر خمسة علامة
+
+210
+00:23:58,730 --> 00:24:01,510
+نقص نقص نقص نقص نقص نقص نقص نقص نقص نقص نقص نقص
+
+211
+00:24:01,510 --> 00:24:02,470
+نقص نقص نقص نقص نقص نقص نقص نقص نقص نقص نقص نقص
+
+212
+00:24:02,470 --> 00:24:07,910
+نقص نقص نقص نقص نقص نقص نقص نقص نقص نقص نقص نقص
+
+213
+00:24:07,910 --> 00:24:07,970
+نقص نقص نقص نقص نقص نقص نقص نقص نقص نقص نقص نقص
+
+214
+00:24:07,970 --> 00:24:10,130
+نقص نقص نق
+
+215
+00:24:17,630 --> 00:24:25,210
+then it's the north على قلب الراب اللي بيقول جدر
+
+216
+00:24:25,210 --> 00:24:34,630
+خمسة عالمين على الفرق تحدث في هذا ال section ان هي
+
+217
+00:24:34,630 --> 00:24:42,110
+كل قران في المثال يبقى فيه ال exercises خمسة
+
+218
+00:24:42,110 --> 00:25:03,860
+الادامالوسائل من واحد لغاية تمانية انتفل
+
+219
+00:25:03,860 --> 00:25:10,560
+الان الى section خلال يديني وهو section خمسة أرض
+
+220
+00:25:13,060 --> 00:25:20,380
+طبعا الامتحان اللي هي يولد يوم اربع تاشر تمامية او
+
+221
+00:25:20,380 --> 00:25:25,400
+اربع تاشر تمامية اولا سبتشن
+
+222
+00:25:25,400 --> 00:25:34,200
+خمسة اربع نومين regular singular
+
+223
+00:25:34,200 --> 00:25:34,940
+points
+
+224
+00:25:50,360 --> 00:25:56,820
+كلمة regular اشتيدة علينا ريجولر معناها مضطرة مثلا
+
+225
+00:25:56,820 --> 00:26:01,280
+لما آسف حقيا اذا ال singular point يعني ال
+
+226
+00:26:01,280 --> 00:26:04,580
+singular point اللي انا عرفته قبل دي اما ال
+
+227
+00:26:04,580 --> 00:26:09,080
+singular point يعني قد تكون regular و قد تكون
+
+228
+00:26:09,080 --> 00:26:14,190
+irregularبنشوف كيف بدّى نميز ما بين irregular
+
+229
+00:26:14,190 --> 00:26:18,950
+singular point وirregular singular point يعني
+
+230
+00:26:18,950 --> 00:26:24,530
+بميّاش رجل ومش هنعمل هذا التمييز بدّى نميز بين
+
+231
+00:26:24,530 --> 00:26:30,570
+معاملات المعادلة التفاضلية النضوفة للثاني ال P
+
+232
+00:26:30,570 --> 00:26:35,510
+والQ والR هدول بدّى نعمل تمييز في بينهاهل هما
+
+233
+00:26:35,510 --> 00:26:40,310
+polynomial كبيرات حدود مهمة ولا عادية؟ يعني
+
+234
+00:26:40,310 --> 00:26:44,990
+exponential، ده اللغة التجاربية، ده اللغة العلمية،
+
+235
+00:26:44,990 --> 00:26:48,610
+اي .. اي شغلة تانية المهم ال polynomial اللي هو
+
+236
+00:26:48,610 --> 00:26:53,530
+شغل حاله وباقي الدوات اللي هو شغل حاله، لأنها تحفظ
+
+237
+00:26:53,530 --> 00:27:00,950
+السماءوشوف كيف هتتعامل مع المسألتين يبقى الرقم
+
+238
+00:27:00,950 --> 00:27:05,870
+الأولى بالتناقص لو ماكانوش polynomial ماكانوش
+
+239
+00:27:05,870 --> 00:27:16,050
+كتيرات كلهم يبقى F ال P و ال U and ال R معاملات
+
+240
+00:27:16,050 --> 00:27:24,950
+التلاتة of the differential equationللمعادلة
+
+241
+00:27:24,950 --> 00:27:32,130
+التقريب كابتن P of X في الـ YW إطاري كابتن Q of X
+
+242
+00:27:32,130 --> 00:27:37,470
+في الـ Y إطاري كابتن R of X في الـ Y تساوي Zero
+
+243
+00:27:37,470 --> 00:27:46,390
+وسمينا المعادلة هذه رقم واحد a general function
+
+244
+00:27:47,060 --> 00:27:52,400
+يبقى درّال عامة يعني إيش مقصود هي يعني ما
+
+245
+00:27:52,400 --> 00:28:03,620
+polynomials لإن ماهياش كثيرات حدود then the x node
+
+246
+00:28:03,620 --> 00:28:13,040
+is regular singular regular
+
+247
+00:28:13,040 --> 00:28:14,800
+singular point
+
+248
+00:28:27,280 --> 00:28:35,900
+singular شرق الأول and both
+
+249
+00:28:35,900 --> 00:28:39,440
+of
+
+250
+00:28:39,440 --> 00:28:49,700
+x ناقص ال x نقطة very cute of x على ال key of x
+
+251
+00:28:49,700 --> 00:29:02,080
+and ال xأقصى ال X نقطة كل درجية بال A of X على ال
+
+252
+00:29:02,080 --> 00:29:12,340
+P of X على ال P of X بتجارب معنى R-Analytic R
+
+253
+00:29:12,340 --> 00:29:18,180
+-Analytic of X نقطة
+
+254
+00:29:27,320 --> 00:29:48,560
+F X-X0 Q of X على P of X على P of X and X-X0 ترمية
+
+255
+00:29:48,560 --> 00:30:00,500
+R of X على كتر P of Xمانو مانو نهاب Convergent
+
+256
+00:30:00,500 --> 00:30:10,320
+هاب Convergent تايجر سيريز
+
+257
+00:30:10,320 --> 00:30:14,100
+سيريز
+
+258
+00:30:14,100 --> 00:30:18,760
+about اكسلون
+
+259
+00:30:18,760 --> 00:30:21,840
+نمر
+
+260
+00:30:21,840 --> 00:30:22,380
+اتنين
+
+261
+00:30:28,170 --> 00:30:47,370
+أ بيكيوك اندر ار and capital R are polynomials are
+
+262
+00:30:47,370 --> 00:31:01,740
+polynomials in equation oneand f وإذا كان limit
+
+263
+00:31:01,740 --> 00:31:10,780
+لما ال x بدها تروح إلى x non لمن؟
+
+264
+00:31:10,780 --> 00:31:20,000
+لل x ناقص x non إلى q of x على captain p of x
+
+265
+00:31:22,610 --> 00:31:33,310
+خلاص يا عزيزي فهذه is Phi9 and
+
+266
+00:31:33,310 --> 00:31:43,510
+limit x to o from x0 to x minus x0 is full ترهيب
+
+267
+00:31:43,510 --> 00:31:51,870
+just R of x على capital E of x is Phi9
+
+268
+00:31:53,470 --> 00:32:01,390
+إذا كانت خامسة ثم إتصالها
+
+269
+00:32:01,390 --> 00:32:04,550
+إلى
+
+270
+00:32:04,550 --> 00:32:05,030
+موقع محدد
+
+271
+00:32:47,580 --> 00:32:57,440
+definition any singular point any singular point
+
+272
+00:32:57,440 --> 00:33:10,680
+of equation one that is not regular
+
+273
+00:33:15,530 --> 00:33:20,650
+is called an
+
+274
+00:33:20,650 --> 00:33:27,750
+irregular singular
+
+275
+00:33:27,750 --> 00:33:28,410
+point
+
+276
+00:33:51,070 --> 00:34:03,170
+Definition Declaration Declaration
+
+277
+00:34:13,550 --> 00:34:24,090
+all the singular points all the
+
+278
+00:34:24,090 --> 00:34:29,590
+singular points and
+
+279
+00:34:29,590 --> 00:34:30,810
+determining it up
+
+280
+00:34:48,710 --> 00:34:58,650
+H1H1 is a regular or irregular
+
+281
+00:35:09,020 --> 00:35:16,500
+وارخم ثانية في الخط والواحد نقص تانية كل ثانية
+
+282
+00:35:16,500 --> 00:35:31,960
+واحد W' زائد X واحد نقص X كله في Y' زائد واحد زائد
+
+283
+00:35:31,960 --> 00:35:37,000
+X كله في الواحد ندر ساوي Zero
+
+284
+00:36:01,170 --> 00:36:09,170
+الكلام اللى احنا كتبهه اليوم بارعة ثانية
+
+285
+00:36:10,680 --> 00:36:17,180
+هذه كتيرة كلوم وماهياش كتيرة كلوم إذا كتيرة كلوم
+
+286
+00:36:17,180 --> 00:36:22,800
+تلها كلام وإذا ماهياش كتيرة كلوم تلها كلام ذات طيب
+
+287
+00:36:22,800 --> 00:36:27,880
+نيجي الآن لتعرف على التقارير اللي عجبني على الشكلة
+
+288
+00:36:27,880 --> 00:36:32,320
+اللي عنها هذه أقول لو كده بيقول if you will are a
+
+289
+00:36:32,320 --> 00:36:37,080
+general function دي ربط يعني ايش؟ مبقى monogamous
+
+290
+00:36:37,080 --> 00:36:42,160
+فبسؤال كدهكله ضرورى، مايكونوش كورنوميا ضرورى، ممكن
+
+291
+00:36:42,160 --> 00:36:45,440
+واحدة تكون كورنوميا لو كانت تانية و تانية ثانية،
+
+292
+00:36:45,440 --> 00:36:52,260
+ممكن، عادل، بس انهم التلاتة مع بعض ملموط، مايكونوش
+
+293
+00:36:52,260 --> 00:36:54,460
+كورنوميا، لو كانوا تانية و تانية كورنوميا، لو
+
+294
+00:36:54,460 --> 00:36:59,300
+كانوا تانية، ممكن، ممكن، ممكن، ممكن، ممكن، ممكنلكن
+
+295
+00:36:59,300 --> 00:37:04,360
+إن كانوا تلاتة ممش غير نقلين فهناك مشكلة في هذه
+
+296
+00:37:04,360 --> 00:37:12,100
+المقصود ال general function إذا كانت
+
+297
+00:37:12,100 --> 00:37:17,810
+هذه النقطة singular و تحقق شخصان آخرينالشرب
+
+298
+00:37:17,810 --> 00:37:22,910
+الأولاني تخد اكس مارفا سيكس ماوري ليس Angular I
+
+299
+00:37:22,910 --> 00:37:28,250
+وضربناها في ال Q على P يعني كانوا خليها معامل Y
+
+300
+00:37:28,250 --> 00:37:33,350
+بقرر في الجدير واقعت زي الجرسام للمعادرة كله على P
+
+301
+00:37:33,350 --> 00:37:37,490
+فكل ال Q على P لو خدت نفسي بالدرمال يعني الدرمال
+
+302
+00:37:37,490 --> 00:37:41,870
+الأولالتيرم التاني كان ال x-x اذا كنت تبقى اربع
+
+303
+00:37:41,870 --> 00:37:47,490
+فيكس على P of x اذا كنت تبقى اربع فيكس على P of x
+
+304
+00:37:47,490 --> 00:37:53,590
+اذا كنت تبقى اربع فيكس على P of x اذا كنت تبقى
+
+305
+00:37:53,590 --> 00:37:55,430
+اربع فيكس على P of x اذا كنت تبقى اربع فيكس على P
+
+306
+00:37:55,430 --> 00:37:56,670
+of x اذا كنت تبقى اربع فيكس على P of x اذا كنت
+
+307
+00:37:56,670 --> 00:37:56,750
+تبقى اربع فيكس على P of x اذا كنت تبقى اربع فيكس
+
+308
+00:37:56,750 --> 00:37:58,650
+على P of x اذا كنت تبقى اربع فيكس على P of x اذا
+
+309
+00:37:58,650 --> 00:38:03,990
+كنت تبقى اربع فيكس على P of x اذا كنت تبقى اربع
+
+310
+00:38:03,990 --> 00:38:08,600
+فيكس على P of x اذا كنت تبقى اربع فيكسالكلام
+
+311
+00:38:08,600 --> 00:38:13,920
+الجنسية are regular، لكن إذا ذهبوا هذا الplan
+
+312
+00:38:13,920 --> 00:38:18,420
+يتبعهم ال conversion تقيلوا سينتها من المين عند
+
+313
+00:38:18,420 --> 00:38:22,700
+الموقع اللي علانه، يبقى هذا لو كان ال plan فيه
+
+314
+00:38:22,700 --> 00:38:28,100
+تلاتة general functions، أكثر من كل نوم يعنيبنبقى
+
+315
+00:38:28,100 --> 00:38:31,920
+الشرط الأولى اللى بيبقى زى J Singular بس الشرط
+
+316
+00:38:31,920 --> 00:38:36,840
+اللى اتيه التانية مستبدله منين بال limits فقط بغير
+
+317
+00:38:36,840 --> 00:38:43,120
+يعني لو كل التلاتة بالكتيرات حدودي لبندياش لأو لأو
+
+318
+00:38:43,120 --> 00:38:45,500
+لأو لأو لأو لأو لأو لأو لأو لأو لأو لأو لأو لأو
+
+319
+00:38:45,500 --> 00:38:46,300
+لأو لأو لأو لأو لأو لأو لأو لأو لأو لأو لأو لأو
+
+320
+00:38:46,300 --> 00:38:47,780
+لأو لأو لأو لأو لأو لأو لأو لأو لأو لأو لأو لأو
+
+321
+00:38:48,090 --> 00:38:54,330
+لتالة لولا لما تروح ال X لولا لتالية لما تروح ال X
+
+322
+00:38:54,330 --> 00:38:58,470
+لولا لتالية لما تروح ال X لولا لتالية لما تروح ال
+
+323
+00:38:58,470 --> 00:38:59,610
+X لولا لتالية لما تروح ال X لولا لتالية لما تروح
+
+324
+00:38:59,610 --> 00:39:03,110
+تروح ال X لولا لتالية لما تروح ال X لولا لتالية
+
+325
+00:39:03,110 --> 00:39:07,330
+لما تروح ال X لولا لتالية لما تروح ال X لولا
+
+326
+00:39:07,330 --> 00:39:13,330
+لتالية لما تروح ال X لولا لتالية
+
+327
+00:39:13,330 --> 00:39:19,150
+لتالية لما تروح ال X لولا لتالية لما تروح ال Xيبقى
+
+328
+00:39:19,150 --> 00:39:23,790
+اتنين هدول مقلقوش finite يبقى اكثر بقول عنها معاها
+
+329
+00:39:23,790 --> 00:39:30,990
+regular singular point او
+
+330
+00:39:30,990 --> 00:39:34,510
+لو اتنين هدول مقلقوش
+
+331
+00:39:37,020 --> 00:39:40,600
+يبدأ النقطة اللي عندي بسميها يعني irregular
+
+332
+00:39:40,600 --> 00:39:49,360
+singular points يعني
+
+333
+00:39:49,360 --> 00:39:53,480
+لم يتحقق هذين الاثنين يبدأ بسميها عشان irregular
+
+334
+00:39:53,480 --> 00:40:00,920
+singular points يعني نقطة غير او نقطة شابه غير طيب
+
+335
+00:40:00,920 --> 00:40:05,500
+هل بيود ان انت عندنا سؤال سؤال يقول ما يعنيبيقول
+
+336
+00:40:05,500 --> 00:40:10,080
+لي ان هدول ما اتحققوش في النقطة الارجيالية، طيب
+
+337
+00:40:10,080 --> 00:40:15,160
+سؤال انا جيت على هذا الدنيا، بتقول ان انا جيت هنا،
+
+338
+00:40:15,160 --> 00:40:21,290
+انا اللي اتفرجورحت للثانية و رجيتها الله انا لدي
+
+339
+00:40:21,290 --> 00:40:28,350
+فانشغلت لان انا انا انا انا انا انا انا انا انا
+
+340
+00:40:28,350 --> 00:40:30,210
+انا انا انا انا انا انا انا انا انا انا انا انا
+
+341
+00:40:30,210 --> 00:40:31,230
+انا انا انا انا انا انا انا انا انا انا انا انا
+
+342
+00:40:31,230 --> 00:40:33,850
+انا انا انا انا انا انا انا انا انا انا انا انا
+
+343
+00:40:33,850 --> 00:40:38,170
+انا انا انا انا انا انا انا انا انا انا انا انا
+
+344
+00:40:38,170 --> 00:40:44,290
+انا انا انا انا انا انا
+
+345
+00:40:44,290 --> 00:40:48,860
+انالكن لو قلت لولا انا لك بروح ببحث مين تتنقل لو
+
+346
+00:40:48,860 --> 00:40:53,760
+قلت لولا لا انا لك انا مش ببحث مين انا بتتنقل طيب
+
+347
+00:40:53,760 --> 00:40:58,380
+السؤال التاني ضروري اتركيه يعني مابدأوش اتدور فيه؟
+
+348
+00:40:58,380 --> 00:41:03,680
+ليس ضروري اي ورقة يوم يحطش بروح تدور افضل ماتي
+
+349
+00:41:03,680 --> 00:41:10,060
+تمثل هدف لو ذكت تمثل هدف five nine بروح ادور عليها
+
+350
+00:41:10,060 --> 00:41:17,460
+five nineلو كانت هذه in finite يعني سمعي
+
+351
+00:41:17,460 --> 00:41:21,380
+بالإنفينيتي أو قولي بالإنفينيتي بروح أدور على تاني
+
+352
+00:41:21,380 --> 00:41:25,200
+أولاده و أقرر يقولوا برايا مين و برايا خارجه هذا
+
+353
+00:41:25,200 --> 00:41:31,560
+ما سنراه من خلال الأمثلة تعدى خالية فعلا عندي سؤال
+
+354
+00:41:31,560 --> 00:41:35,340
+بدي أسأله اذا بدأت بالمعنى أسأله قبل أن أنت في
+
+355
+00:41:35,340 --> 00:41:40,480
+الامثلةالنقرة لزي دورة طويلة قراري ده المنورة
+
+356
+00:41:40,480 --> 00:41:48,820
+التجارية لكي ناخد الدنيا التجارية قراري ده المنورة
+
+357
+00:41:48,820 --> 00:41:55,980
+التجارية لكي ناخد الدنيا التجارية قراري ده المنورة
+
+358
+00:41:55,980 --> 00:42:01,360
+التجاريةأشتغل الساعة في النتائج اللى قبلك وليه
+
+359
+00:42:01,360 --> 00:42:04,320
+نفسك وانت تبقى على ال single point فانا قاعد اللى
+
+360
+00:42:04,320 --> 00:42:07,820
+هو complex اللى بيهرمليش complex وضعيه اللى ما
+
+361
+00:42:07,820 --> 00:42:11,400
+تطلع تطلع اللى بأخد ال limit و ال limited to the
+
+362
+00:42:11,400 --> 00:42:15,200
+finite بيخبر الله أن أخبر هل هي complex او لعدة
+
+363
+00:42:15,200 --> 00:42:18,420
+اللى بيأخد عنده ال limit هل هو complex ولا limited
+
+364
+00:42:19,970 --> 00:42:24,890
+طبعا زي ما يفضلكم هاكم دورية أهل الوسام و فريق أهل
+
+365
+00:42:24,890 --> 00:42:28,750
+الوسام ماشي عطيكوا فعالة evaluation منهم في
+
+366
+00:42:28,750 --> 00:42:31,470
+الarchitectural context و من أخر سنة في المملكة
+
+367
+00:42:31,470 --> 00:42:34,350
+العربية السعودية بس كده بالمفهوم اللي اذا كده
+
+368
+00:42:34,350 --> 00:42:38,110
+المعناه يكفي بس المعاناة الأقلومية تانية و معاناة
+
+369
+00:42:38,110 --> 00:42:42,170
+ميلاد مافي واي واي واي واي واي واي واي واي واي واي
+
+370
+00:42:42,170 --> 00:42:42,250
+واي واي واي واي واي واي واي واي واي واي واي واي
+
+371
+00:42:42,250 --> 00:42:45,120
+واي واي واي واي واي واي واي واي وايworld mark ..
+
+372
+00:42:45,120 --> 00:42:49,020
+او .. او .. او .. او .. او .. او .. او .. او .. او
+
+373
+00:42:49,020 --> 00:42:49,620
+.. او .. او .. او .. او .. او .. او .. او .. او ..
+
+374
+00:42:49,620 --> 00:42:50,180
+او .. او .. او .. او .. او .. او .. او .. او .. او
+
+375
+00:42:50,180 --> 00:42:55,040
+.. او .. او .. او .. او .. او .. او .. او .. او ..
+
+376
+00:42:55,040 --> 00:42:58,060
+او .. او .. او .. او .. او .. او .. او .. او .. او
+
+377
+00:42:58,060 --> 00:42:58,560
+.. او .. او .. او .. او .. او .. او .. او .. او ..
+
+378
+00:42:58,560 --> 00:42:59,580
+او .. او .. او .. او .. او .. او .. او .. او .. او
+
+379
+00:42:59,580 --> 00:43:00,500
+.. او .. او .. او .. او .. او .. او .. او .. او ..
+
+380
+00:43:00,500 --> 00:43:09,340
+او .. او .. او .. او .. او
+
+381
+00:43:09,340 --> 00:43:13,500
+..
+
+382
+00:43:13,500 --> 00:43:18,290
+اوزي ما اشوف في الرقم يبقى مندي اشوف همين من
+
+383
+00:43:18,290 --> 00:43:22,630
+الموقعات هذه تبقى regular singular point ومين ا
+
+384
+00:43:22,630 --> 00:43:27,790
+regular singular point ورقمي او مجلة يبقى السؤال
+
+385
+00:43:27,790 --> 00:43:32,290
+بس مندي اجيب ال singular واشوف هل هي regular ومع
+
+386
+00:43:32,290 --> 00:43:39,300
+كرجل يعطينا المسألة دلوقتيبقى هذه الـP ومتها باجيب
+
+387
+00:43:39,300 --> 00:43:44,980
+الـC ونغميرها Point إذا أنا لو لدى بلد ممكن واحد
+
+388
+00:43:44,980 --> 00:43:50,340
+ماترستيكس تجيب تجيب تجيب تجيب تجيب تجيب تجيب تجيب
+
+389
+00:43:50,340 --> 00:44:04,460
+تجيب تجيب تجيب تجيب تجيب تجيب تجيب
+
+390
+00:44:08,450 --> 00:44:16,770
+ممكن و انت ايش او سالب واحد لو كانت واحد تصيبها
+
+391
+00:44:16,770 --> 00:44:22,450
+لزيره لو كانت سالب واحد تصيبها لزيره يبقى هذه بدها
+
+392
+00:44:22,450 --> 00:44:30,590
+تساوي زيره only اكس يساوي سالب واحد and اكس يساوي
+
+393
+00:44:30,590 --> 00:44:31,410
+واحد
+
+394
+00:44:33,930 --> 00:44:38,090
+يبقى جفت ال singular point بقى يبقى كل عدد دول
+
+395
+00:44:38,090 --> 00:44:43,270
+اللي عندي هتقول بأنهم polynomial كانت إيراد حدود
+
+396
+00:44:43,270 --> 00:44:49,270
+يبقى الآن ال P of X اللي واحد ماطس X تربيع لكل
+
+397
+00:44:49,270 --> 00:44:55,030
+تربيع و P of X اللي بدأت ساوي X لواحد
+
+398
+00:45:06,010 --> 00:45:16,710
+يبقى أسهل من نقطة الأولى ومن نقطة الثانية من خلال
+
+399
+00:45:16,710 --> 00:45:20,350
+المعاملات الخاصة بالإفريقيا وبيفرق والواحد
+
+400
+00:45:28,370 --> 00:45:32,570
+النقطة الأولى اللى تبقى موجودة في الجانب الثاني
+
+401
+00:45:34,610 --> 00:45:39,950
+بتروح أحصل النهاية الأولى وشوف هل هي قطع يدعى
+
+402
+00:45:39,950 --> 00:45:43,170
+واحدة واحدة واحدة واحدة واحدة واحدة واحدة واحدة
+
+403
+00:45:43,170 --> 00:45:43,390
+واحدة واحدة واحدة واحدة واحدة واحدة واحدة واحدة
+
+404
+00:45:43,390 --> 00:45:47,450
+واحدة واحدة واحدة واحدة واحدة واحدة واحدة واحدة
+
+405
+00:45:47,450 --> 00:45:49,850
+واحدة واحدة واحدة واحدة واحدة واحدة واحدة واحدة
+
+406
+00:45:49,850 --> 00:45:49,930
+واحدة واحدة واحدة واحدة واحدة واحدة واحدة واحدة
+
+407
+00:45:49,930 --> 00:45:53,630
+واحدة واحدة واحدة واحدة واحدة واحدة واحدة واحدة
+
+408
+00:45:53,630 --> 00:45:54,590
+واحدة واحدة واحدة واحدة واحدة واحدة واحدة واحدة
+
+409
+00:45:54,590 --> 00:45:57,370
+واحدة واحدة واحدة واحدة واحدة واحدة واحدة واحدة
+
+410
+00:45:57,370 --> 00:46:02,370
+واحدة
+
+411
+00:46:02,370 --> 00:46:04,030
+واحدة
+
+412
+00:46:12,000 --> 00:46:13,960
+الشكل التالي هو
+
+413
+00:46:20,240 --> 00:46:26,680
+-x في y' مجسم عالمهم على هذا المفضل عشان اتحللوا
+
+414
+00:46:26,680 --> 00:46:28,660
+بالمعرفة مافي حاجة ان اتحللوا بالمعرفة مافي حاجة
+
+415
+00:46:28,660 --> 00:46:29,420
+ان اتحللوا بالمعرفة مافي حاجة ان اتحللوا بالمعرفة
+
+416
+00:46:29,420 --> 00:46:29,520
+مافي حاجة ان اتحللوا بالمعرفة مافي حاجة ان اتحللوا
+
+417
+00:46:29,520 --> 00:46:29,760
+بالمعرفة مافي حاجة ان اتحللوا بالمعرفة مافي حاجة
+
+418
+00:46:29,760 --> 00:46:30,680
+ان اتحللوا بالمعرفة مافي حاجة ان اتحللوا بالمعرفة
+
+419
+00:46:30,680 --> 00:46:35,900
+مافي حاجة ان اتحللوا بالمعرفة مافي حاجة ان اتحللوا
+
+420
+00:46:35,900 --> 00:46:48,080
+بالمعرفة مافي حاجة ان اتحللوا بالمعرفة مافي حاجة
+
+421
+00:46:48,080 --> 00:46:48,820
+ان
+
+422
+00:46:57,610 --> 00:47:03,130
+أبقى مرتبط في مقاطع المقاطع يجب أن نختصر يجب أن
+
+423
+00:47:03,130 --> 00:47:04,050
+نختصر يجب أن نختصر يجب أن نختصر يجب أن نختصر يجب
+
+424
+00:47:04,050 --> 00:47:04,110
+أن نختصر يجب أن نختصر يجب أن نختصر يجب أن نختصر
+
+425
+00:47:04,110 --> 00:47:06,750
+يجب أن نختصر يجب أن نختصر يجب أن نختصر يجب أن
+
+426
+00:47:06,750 --> 00:47:08,930
+نختصر يجب أن نختصر يجب أن نختصر يجب أن نختصر يجب
+
+427
+00:47:08,930 --> 00:47:09,590
+أن نختصر يجب أن نختصر يجب أن نختصر يجب أن نختصر
+
+428
+00:47:09,590 --> 00:47:12,950
+يجب أن نختصر يجب أن نختصر يجب
+
+429
+00:47:12,950 --> 00:47:25,010
+أن نختصر يجب أن نختصر يجب أن نختصر يجب
+
+430
+00:47:25,010 --> 00:47:31,590
+أن نختصجنبها زائد واحد على واحد ماقص اكسج كل
+
+431
+00:47:31,590 --> 00:47:36,790
+ثانوية في واحد زائد اتش كله في وايمين بساوية درجة
+
+432
+00:47:36,790 --> 00:47:45,690
+الآن نذهب نبحث كل مقفل انها تاني مقفل تاني بعد ما
+
+433
+00:47:45,690 --> 00:47:50,590
+كتبت المعاملة بالصيغة الجديدة وبالتالي جيب جناش ال
+
+434
+00:47:50,590 --> 00:47:54,550
+Q على P وجيب جناش ال R على P
+
+435
+00:48:02,320 --> 00:48:08,240
+إذا كنت تجي للمقبض أولا بتاخد limit لما ال X تذهب
+
+436
+00:48:08,240 --> 00:48:17,080
+من واحد أو قبل أن تكون at X يساوي 1 لما
+
+437
+00:48:17,080 --> 00:48:22,460
+تذهب من واحد لساوي واحد
+
+438
+00:48:29,480 --> 00:48:39,400
+لمن؟ لمن Q of X على P of X يساوي limit لما ال X
+
+439
+00:48:39,400 --> 00:48:45,360
+بدأ تروح ل-1 لل X ذالك واحد فيه، ليه Q على P
+
+440
+00:48:45,360 --> 00:48:49,760
+جانزة، فيه مين؟ هذه النتيجة ساعة ما اختصرنا
+
+441
+00:48:49,760 --> 00:48:59,420
+الاقتصادات اللي مطلوبة، يبقى هذا Xعلى واحد ناقص x
+
+442
+00:48:59,420 --> 00:49:07,600
+في واحد زائد x الكل دبي طبعا طبعا طبعا طبعا طبعا
+
+443
+00:49:07,600 --> 00:49:11,900
+طبعا طبعا طبعا طبعا طبعا طبعا طبعا طبعا طبعا طبعا
+
+444
+00:49:11,900 --> 00:49:12,960
+طبعا طبعا طبعا طبعا طبعا طبعا طبعا طبعا طبعا طبعا
+
+445
+00:49:12,960 --> 00:49:15,640
+طبعا طبعا طبعا طبعا طبعا طبعا طبعا طبعا طبعا طبعا
+
+446
+00:49:15,640 --> 00:49:19,440
+طبعا طبعا طبعا طبعا طبعا طبعا
+
+447
+00:49:27,380 --> 00:49:32,680
+طبعا علينا أن ندخل X و نذهب إلى أين؟ X سالب واحد
+
+448
+00:49:32,680 --> 00:49:37,800
+يبقى هذي سالب واحد على هذي نحط مكانها سالب واحد
+
+449
+00:49:37,800 --> 00:49:43,600
+عشان الصين ايه اتنين؟ هذي سالب واحد تصير جداش سين
+
+450
+00:49:43,600 --> 00:49:48,980
+و يبقى النتيجة جداش سالب الفيليفي أكمل؟ نعم اتنين
+
+451
+00:49:48,980 --> 00:49:53,740
+خلاص اللي عم ادخل اخر مرة X فاي نايم يعني هذي هنا
+
+452
+00:49:53,740 --> 00:50:01,650
+فاي نايميبقى بناء عليه رقم X يساوي واحد منها
+
+453
+00:50:01,650 --> 00:50:09,230
+regular singular point يبقى لنا الساعة Z point
+
+454
+00:50:09,230 --> 00:50:19,650
+اللي هو X يساوي سالف واحد is an irregular singular
+
+455
+00:50:19,650 --> 00:50:22,970
+point
+
+456
+00:50:22,970 --> 00:50:33,690
+بس لو طلعت finiteبروح على مقطع تاني نيجي اذا X
+
+457
+00:50:33,690 --> 00:50:41,010
+يساوي واحد يبقى مقطع تاني يبقى بناخد نفس ال limit
+
+458
+00:50:41,010 --> 00:50:49,170
+اي limit بس ال X ولدك واحد للواحد لمن؟ لل X ماقص
+
+459
+00:50:49,170 --> 00:50:49,830
+واحد
+
+460
+00:50:52,650 --> 00:51:00,150
+على P of X على P of X على P of X على P of X على P
+
+461
+00:51:00,150 --> 00:51:08,550
+of X على P of X على P of X على
+
+462
+00:51:08,550 --> 00:51:13,330
+P of
+
+463
+00:51:13,330 --> 00:51:17,630
+Xحتى لو قلت تحتاج فايلة خلاص الديناميكالية دي هي
+
+464
+00:51:17,630 --> 00:51:21,750
+حسنة إذا احنا انتقلنا إلى مين لن نفقد دنيا السن
+
+465
+00:51:21,750 --> 00:51:25,610
+برنامج الأولى وانتقلنا إلى مين لن نفقد دنيا يعني
+
+466
+00:51:25,610 --> 00:51:31,730
+في هذه ال level لما ال x بدأ تروح للواحد لل x ماتس
+
+467
+00:51:31,730 --> 00:51:38,320
+واحد فيهلكي و اللي طلعناها فوق هي همت ريّراتش X
+
+468
+00:51:38,320 --> 00:51:46,160
+على واحد مائص X تبين في واحد زايد X الكل دربي يزاد
+
+469
+00:51:47,780 --> 00:51:53,060
+هذه x ماكس راحت هذه واحد ماكس نختار واحد من هذه
+
+470
+00:51:53,060 --> 00:51:55,980
+نختار واحد من هذه نختار واحد من هذه نختار واحد من
+
+471
+00:51:55,980 --> 00:52:02,460
+هذه نختار
+
+472
+00:52:02,460 --> 00:52:06,520
+واحد من هذه نختار
+
+473
+00:52:06,520 --> 00:52:12,620
+واحد من هذه
+
+474
+00:52:13,280 --> 00:52:16,620
+من هنا يابتخد شبكت سالي بعرف المشترك، ومن هنا
+
+475
+00:52:16,620 --> 00:52:23,260
+يابتخد شبكت سالي بعرف المشترك، ومن هنا
+
+476
+00:52:23,260 --> 00:52:23,720
+يابتخد شبكت سالي بعرف المشترك، ومن هنا يابتخد شبكت
+
+477
+00:52:23,720 --> 00:52:26,340
+ومن هنا يابتخد شبكت سالي بعرف المشترك، ومن هنا
+
+478
+00:52:26,340 --> 00:52:29,160
+يابتخد شبكت سالي بعرف المشترك، ومن هنا يابتخد شبكت
+
+479
+00:52:29,160 --> 00:52:34,440
+سالي بعرف المشترك، ومن هنا يابتخد شبكت سالي بعرف
+
+480
+00:52:34,440 --> 00:52:39,150
+المشترك، ومن هنا يابعلى واحد زي واحد تربيه اربع
+
+481
+00:52:39,150 --> 00:52:43,370
+يبقى سنة واربع فاين اين وما زاكن فاين اعيد فاين
+
+482
+00:52:43,370 --> 00:52:45,830
+اعيد فاين اعيد فاين اعيد فاين اعيد فاين اعيد فاين
+
+483
+00:52:45,830 --> 00:52:46,950
+اعيد فاين اعيد فاين اعيد فاين اعيد فاين اعيد فاين
+
+484
+00:52:46,950 --> 00:52:48,710
+اعيد فاين اعيد فاين اعيد فاين اعيد فاين اعيد فاين
+
+485
+00:52:48,710 --> 00:52:52,590
+اعيد فاين اعيد فاين اعيد فاين اعيد فاين اعيد فاين
+
+486
+00:52:52,590 --> 00:52:52,910
+اعيد فاين اعيد فاين اعيد فاين اعيد فاين اعيد فاين
+
+487
+00:52:52,910 --> 00:53:01,470
+اعيد فاين اعيد فاين اعيد فاين اعيد فاين اعيد فا
+
+488
+00:53:04,680 --> 00:53:09,960
+يبقى هذا الكلام متساوي ال limit لما ال X بيروح لل
+
+489
+00:53:09,960 --> 00:53:19,380
+واحد لل X ناقص واحد كل ربيع انا في هجم يبقى واحد
+
+490
+00:53:19,380 --> 00:53:25,940
+ناقص X كل ربيع في واحد زي ال X يبقى واحد او هذه
+
+491
+00:53:25,940 --> 00:53:30,960
+دوري على واحد ناقص X كل ذا ربيع
+
+492
+00:53:33,690 --> 00:53:40,090
+زائد اكس واحد زائد اكس شرايف دي راديو غالب
+
+493
+00:53:46,280 --> 00:53:52,400
+بتروح يعني هذه كأنها مضبوط تماما limit لما ال x
+
+494
+00:53:52,400 --> 00:53:58,120
+تروح للواحد لكس ناقص واحد كل تربيع على x ناقص واحد
+
+495
+00:53:58,120 --> 00:54:04,020
+كل تربيع في واحد ذاتكس بتروح هذه معناه دي بس ال
+
+496
+00:54:04,020 --> 00:54:10,280
+limit لما ال text تروح للواحدلما ال text لفوق ال
+
+497
+00:54:10,280 --> 00:54:16,560
+واحد نميه ل واحد على واحد زاد اكس من شركة ده مصف ف
+
+498
+00:54:16,560 --> 00:54:23,200
+اي نايت كده لف يرجع ف اي نايت يرجع لان على النقطة
+
+499
+00:54:23,200 --> 00:54:29,620
+لان هذه الساعة ال text لساعة واحد is a regular
+
+500
+00:54:29,620 --> 00:54:32,360
+singular point
+
+501
+00:54:37,870 --> 00:54:41,970
+يعني كان نفس المثال يبقى بعض ال singular و بعض ال
+
+502
+00:54:41,970 --> 00:54:48,570
+regular و بعض ال irregular ممكن كلهم regular و
+
+503
+00:54:48,570 --> 00:54:53,830
+ممكن كلهم irregular كذلك يعني كل احتمالات و يبدأ
+
+504
+00:54:53,830 --> 00:54:59,490
+كل مسألة علاقة طيب هذا هو المثال الأول لنروح الآخر
+
+505
+00:54:59,490 --> 00:55:01,070
+المثال التاني
+
+506
+00:55:15,820 --> 00:55:26,480
+X درمية زي 19 Y درمية فعلا ماتس تلاتة سيكس Y فاي
+
+507
+00:55:26,480 --> 00:55:35,400
+زي واحد ناقص X كله في الواحد يبقى ساومين بساوي زيت
+
+508
+00:55:41,300 --> 00:55:48,380
+بدا البداية قمت باستخدام Q of X بإنسان X مبين
+
+509
+00:55:48,380 --> 00:55:59,540
+لإتصال و قمت باستخدام Q of X مافس تلاتة Xكبت ال R
+
+510
+00:55:59,540 --> 00:56:04,880
+of X بالسنونين واحد ما فسكت، شو رأيت الدلالد
+
+511
+00:56:04,880 --> 00:56:13,480
+هالول؟ هالول نوميانز، كده هالول R نوميانز
+
+512
+00:56:14,210 --> 00:56:17,930
+لو كما رأيت في المقصد الحقيقي انا اتاب عليها كده
+
+513
+00:56:17,930 --> 00:56:25,990
+الـ S يتزايد ال E of X يتزايد X أكبر زي 9 لو
+
+514
+00:56:25,990 --> 00:56:33,850
+سويتها من 0 تجهش المسئولة عندنا ال X أكبر يسوى 9
+
+515
+00:56:33,850 --> 00:56:36,230
+للجالكسي الجدد
+
+516
+00:56:55,450 --> 00:57:01,590
+السؤال اللي جيبناه
+
+517
+00:57:01,590 --> 00:57:02,470
+هو الطعام
+
+518
+00:57:06,900 --> 00:57:10,180
+مدى هؤلاء البرولوجيين اللي قطعوا دي يرجعوا يدخلوا
+
+519
+00:57:10,180 --> 00:57:15,260
+في نفس التحكيك اللي اتبعته قبل قليل يرجعوا تانية
+
+520
+00:57:15,260 --> 00:57:20,320
+ويقولوا هؤلاء اللي اكتشفوا يقولوا هؤلاء اللي لديهم
+
+521
+00:57:20,320 --> 00:57:29,340
+5 Singular Points يرجعوا
+
+522
+00:57:29,340 --> 00:57:31,500
+هؤلاء ثم Singular Points
+
+523
+00:57:37,730 --> 00:57:40,650
+نقسم؟ نقسم يارب
+
+524
+00:57:54,070 --> 00:58:05,330
+YWπ-3X عليه يبقى
+
+525
+00:58:05,330 --> 00:58:17,700
+X ناقص تلاتة Iزائد تلاتة I في Y prime زائد واحد
+
+526
+00:58:17,700 --> 00:58:26,640
+نقص X على X نقص تلاتة I في X زائد تلاتة I في Y كله
+
+527
+00:58:26,640 --> 00:58:31,920
+بيساوي Zero محتاج
+
+528
+00:58:31,920 --> 00:58:35,420
+ليه؟ هذا الكلام
+
+529
+00:58:37,750 --> 00:58:47,470
+x² زائد 9 على الساوية x ناقص 3i في x زائد 3i تعالى
+
+530
+00:58:47,470 --> 00:58:52,630
+نشوف لو ضرفت هدول في بعض فعلا بتطلع هذا ولا لأ انا
+
+531
+00:58:52,630 --> 00:58:56,310
+اخبرتك ان الفرق بينهم مربعين بس بكمية تخيله بيبقى
+
+532
+00:58:56,310 --> 00:58:58,690
+وليس بكمية حقيقية
+
+533
+00:59:06,080 --> 00:59:12,980
+3XI ومن السالم 3XI براهم مع السلمة والهالي بها
+
+534
+00:59:12,980 --> 00:59:19,400
+نسالم تلاتة من تلاتة نسالم تسعة وI بالعالي نسالم
+
+535
+00:59:19,400 --> 00:59:24,860
+واحد نسالم ثالث نسالم عشر وجرم تسعة بالفور نسالم
+
+536
+00:59:24,860 --> 00:59:29,140
+تسعة وعشر وجرم تسعة بالفور نسالم تسعة وعشر وجرم
+
+537
+00:59:29,530 --> 00:59:33,790
+يعني يا بنات جاني يفكرني لو حللتك من أول من هنا و
+
+538
+00:59:33,790 --> 00:59:37,890
+قلتك تساوي زي اذا و لا مذكرنيها تبقى طيابة و كده
+
+539
+00:59:37,890 --> 00:59:41,990
+معاكي ان انا ماحلل عليك فانت ماحلل على الله يبقى
+
+540
+00:59:41,990 --> 00:59:48,090
+الان انا بدادي اقول المقطة الأولة بيبقى بدادي اقول
+
+541
+00:59:48,090 --> 00:59:56,990
+ان اتن اكس يسوى سن تلاتةروح تاخد ال limit لما ال x
+
+542
+00:59:56,990 --> 01:00:05,310
+كذا طول بزايد ثلاثة I ان ال x ماقص ثلاثة I وزايد
+
+543
+01:00:05,310 --> 01:00:11,790
+ثلاثة I بالصغير وماقص ماقص ثلاثة I زايد ثلاثة I ان
+
+544
+01:00:11,790 --> 01:00:19,490
+ال Q of X على ال P of Xيساوي ال limit لما ال x ذهب
+
+545
+01:00:19,490 --> 01:00:26,690
+يسالب تلاتة I لما ال x ذهب يسالب تلاتة I لكي و على
+
+546
+01:00:26,690 --> 01:00:34,790
+P لايه عيزة يبقى هي اللي هو سالب تلاتة X مقسمة على
+
+547
+01:00:34,790 --> 01:00:44,070
+مين على X مقسمة على I في X زائد تلاتة Iطبعاً ،
+
+548
+01:00:44,070 --> 01:00:48,750
+نروح هذا term مع ال term اللي عندها يرجعنا
+
+549
+01:00:48,750 --> 01:00:54,530
+بالمسألة إلى ال limit لما ال X بده يروح من ثالث
+
+550
+01:00:54,530 --> 01:01:04,280
+تلاتة R لثالث تلاتة X على X ناقص تلاتة Rأول خطوة
+
+551
+01:01:04,280 --> 01:01:09,560
+في إيجاد ال limit هي التعويض المباشر يبقى هاي ماقص
+
+552
+01:01:09,560 --> 01:01:17,380
+تلاتة برا والعكس بتروح نوير لسالف تلاتة I على سالف
+
+553
+01:01:17,380 --> 01:01:30,580
+تلاتة I سالف تلاتة I طيب هل تساوي تسعة I على سالف
+
+554
+01:01:30,580 --> 01:01:31,100
+I
+
+555
+01:01:35,440 --> 01:01:41,620
+I مع I و سنة مع سنة و نصف على ستة و نزلت تلاتة على
+
+556
+01:01:41,620 --> 01:01:47,500
+اتنين تبقى صعب النتيجة تلاتة على اتنين تلاتة على
+
+557
+01:01:47,500 --> 01:01:49,820
+اتنين ماله أسبوع يناير
+
+558
+01:01:52,650 --> 01:01:57,030
+تسعة تسعة تسعة تسعة تسعة تسعة تسعة تسعة تسعة تسعة
+
+559
+01:01:57,030 --> 01:02:04,050
+تسعة تسعة تسعة تسعة تسعة تسعة تسعة تسعة تسعة تسعة
+
+560
+01:02:04,050 --> 01:02:06,050
+تسعة تسعة تسعة تسعة تسعة تسعة تسعة تسعة تسعة تسعة
+
+561
+01:02:06,050 --> 01:02:07,870
+تسعة تسعة تسعة تسعة تسعة تسعة تسعة تسعة تسعة تسعة
+
+562
+01:02:07,870 --> 01:02:11,770
+تسعة تسعة تسعة تسعة تسعة
+
+563
+01:02:11,770 --> 01:02:16,630
+تسعة تسعة تسعة تسعة تسعة تسعة تسعة تسعة
+
+564
+01:02:16,630 --> 01:02:21,950
+تسعة تس
+
+565
+01:02:22,000 --> 01:02:30,260
+اها لما ال X بدها تروح لوين لسان التلاتة I لوين من
+
+566
+01:02:30,260 --> 01:02:41,740
+ال X زي التلاتة I من R و F على ال E و B القرآن
+
+567
+01:02:41,740 --> 01:02:48,240
+الترميز مظهر بحيث يبقى هذا الكلام بالسيابين limit
+
+568
+01:02:48,240 --> 01:02:56,670
+لما ال X بدها تروحبزالد تلاتة I من X زالد تلاتة I
+
+569
+01:02:56,670 --> 01:03:04,430
+لكل جميع ال R of X والواحد من R of X هي واحد ماقص
+
+570
+01:03:04,430 --> 01:03:13,210
+X واحد ماقص X كله مكسوما على X ماقص تلاتة I ب X
+
+571
+01:03:13,210 --> 01:03:21,140
+زالد تلاتة I ويزدادطبعاً في اختصارات دورس هذا مع
+
+572
+01:03:21,140 --> 01:03:26,840
+مين مع دورس اللي عنده هذا يبقى مصير ال limit لما
+
+573
+01:03:26,840 --> 01:03:35,500
+ال x بدأ تقوه لثالث تلاتة I لل x زائد تلاتة I تمين
+
+574
+01:03:35,500 --> 01:03:47,060
+في واحد ناقص x على مين على x ناقص تلاتة Iبتشيل كل
+
+575
+01:03:47,060 --> 01:03:53,040
+اسم حفظتها سالب ثلاثة يبقى
+
+576
+01:03:53,040 --> 01:04:02,220
+هذا الكلام Zero في واحد سالب ثلاثة I عالمي على
+
+577
+01:04:02,220 --> 01:04:06,700
+سالب ثلاثة I سالب ثلاثة يبقى نفسي قدام
+
+578
+01:04:12,020 --> 01:04:15,200
+هل you find that you turn your coin right before
+
+579
+01:04:15,200 --> 01:04:36,060
+you have it, or that you have a singular coin؟
+
+580
+01:04:36,060 --> 01:04:44,370
+هل you really serve the coin؟X يساوي ثانية ثلاثة I
+
+581
+01:04:44,370 --> 01:04:47,870
+هو مجلد عادى
+
+582
+01:05:00,900 --> 01:05:09,640
+عشان نعمل نقطة تانية اكس بساعدة اش فانا هاعد اذا
+
+583
+01:05:09,640 --> 01:05:13,920
+روح نفسي لنقطة اولى يجب ان انا اعمل limit لما
+
+584
+01:05:13,920 --> 01:05:18,080
+الاكس بدأ تروح ليه ثلاثة اعلى
+
+585
+01:05:29,940 --> 01:05:36,700
+يبقى عند نقطة x0 يسبب تلاتة I يبقى حتى x ناطس
+
+586
+01:05:36,700 --> 01:05:39,680
+تلاتة I تميل
+
+587
+01:05:42,200 --> 01:05:48,400
+على مين؟ على capital Q of X يبقى limit لما ال X
+
+588
+01:05:48,400 --> 01:05:55,940
+تبقى واحدة تلاتة I لل X ماقص تلاتة I من Q على P
+
+589
+01:05:55,940 --> 01:06:05,490
+وين راحت ال Q على P دي غالب؟ وثالث تلاتة Xثالث
+
+590
+01:06:05,490 --> 01:06:14,870
+تلاتة X على X مخص ثلاثة I في X زائد تلاتة I طبعا
+
+591
+01:06:14,870 --> 01:06:20,510
+هاني وهاني مع السلامة يقلق المسألة إلى ال limit
+
+592
+01:06:20,510 --> 01:06:30,130
+لما ال X تدخل في تلاتة I لثالث تلاتة X على X زائد
+
+593
+01:06:30,130 --> 01:06:34,450
+تلاتة I النتيجة
+
+594
+01:06:35,750 --> 01:06:44,970
+ثالث تلاتة في تلاتة I على تلاتة I زائد تلاتة I
+
+595
+01:06:44,970 --> 01:06:52,210
+يبقى ناقص تسعة I على ستة I كمان ناقص تلاتة على
+
+596
+01:06:52,210 --> 01:06:58,650
+اتنين يبقى هماله I9وده الـ finite إذا بدنا نروح
+
+597
+01:06:58,650 --> 01:07:04,750
+لمين؟ للشرق الأخير لإننا بدنا نروح لاخد limit لما
+
+598
+01:07:04,750 --> 01:07:11,830
+ال X بده نروح لتلاتة I لل X ماتس تلاتة I والترمية
+
+599
+01:07:11,830 --> 01:07:19,850
+في A of Xأنا كنت ال E of X هو يساوي limit لما ال X
+
+600
+01:07:19,850 --> 01:07:27,590
+يروح ليه تلاتة I لل X ناقص تلاتة I التقرير ليه ال
+
+601
+01:07:27,590 --> 01:07:35,450
+R أو ال R على E اللي عبارة عن الواحد ناقص Xكله
+
+602
+01:07:35,450 --> 01:07:45,950
+مقسومة على x-3i ت x زائد 3i لأن هذا الكلام يجب أن
+
+603
+01:07:45,950 --> 01:07:49,970
+يستوي ال limit لما ال x بدل واحد يكون تلاتة ايه
+
+604
+01:07:49,970 --> 01:07:55,470
+طبعا هناك اختصار بين المصدر والمقام افضل ان اجده
+
+605
+01:07:55,470 --> 01:08:02,190
+اكتر اكتر اكتر اكتر اكتر
+
+606
+01:08:02,190 --> 01:08:03,110
+اكتر
+
+607
+01:08:13,020 --> 01:08:17,240
+عندك تلاتة آي ناقص تلاتة آي مقدر
+
+608
+01:08:22,500 --> 01:08:30,500
+على ثلاثة I زي ثلاثة I هو يسمي الدرج Zero كذلك هذه
+
+609
+01:08:30,500 --> 01:08:38,400
+ملحقة و I might يبقى هنا ساعة HX يسوي ثلاثة I
+
+610
+01:08:38,400 --> 01:08:44,300
+ملحقة HX ريجيونات
+
+611
+01:08:54,560 --> 01:08:58,640
+طبعا هذه المثالة النقطتين اللي هي انت تنتهي من
+
+612
+01:08:58,640 --> 01:09:02,340
+regular singular point لكن السؤال اللي بيعملوه إيش
+
+613
+01:09:02,340 --> 01:09:06,960
+يطلع regular وإيش يطلع irregular singular point
+
+614
+01:09:06,960 --> 01:09:11,460
+لكن السؤالين اللي يسمون هدولالوعاملات كانوا
+
+615
+01:09:11,460 --> 01:09:17,660
+polynomial لكن الفرق بينهما أن النقط في حالة
+
+616
+01:09:17,660 --> 01:09:21,700
+الأولى كانوا real وإن النقط في الحالة التانية
+
+617
+01:09:21,700 --> 01:09:28,240
+كانوا complex يرجع هذه الفرق من real لـ real طيب
+
+618
+01:09:28,240 --> 01:09:33,500
+روحنا لمثال الثالث المثال
+
+619
+01:09:33,500 --> 01:09:43,440
+الثالث يقول بعندك الـ x والـ y بقية Pi زائد P plus
+
+620
+01:09:43,440 --> 01:09:51,920
+x والـ y بقية Pi زائد تلاتة قصية x بالـ y بتساوية
+
+621
+01:09:51,920 --> 01:09:52,500
+2
+
+622
+01:10:12,080 --> 01:10:18,180
+أولونهم يعني ليسوا كثيرات كلهم يبقى عيب ان ال Q of
+
+623
+01:10:18,180 --> 01:10:25,080
+X بقى ال E of X عند ال R of X يستخدم التلاتة
+
+624
+01:10:25,080 --> 01:10:30,000
+أوصاها ال X R Marks
+
+625
+01:10:34,260 --> 01:10:39,080
+درجة هذه تجد تحكي راتروني بهدولة كمان ال general
+
+626
+01:10:39,080 --> 01:10:43,360
+functions اللي موجودة في الحالة الأولى إن كانت
+
+627
+01:10:43,360 --> 01:10:47,800
+موجودة عندنا وده فهذه الحالة الموجودة هنا كنت أرجع
+
+628
+01:10:47,800 --> 01:10:51,500
+لمين للprfix
+
+629
+01:10:51,500 --> 01:10:58,620
+الprfix اللي يتسمى جديد يتسمى Zero الfix يتسمى
+
+630
+01:10:58,620 --> 01:11:04,570
+Zero هذه فقطاللي بيبقى only singular point مافيش
+
+631
+01:11:04,570 --> 01:11:13,370
+ريحة يبقى هذي is the only singular point
+
+632
+01:11:16,770 --> 01:11:20,330
+why؟ جيبنا ال singular point إذا بداني لل
+
+633
+01:11:20,330 --> 01:11:26,270
+completion الأول وشوف هل التقعي لأ لأ لأ لأ لأ لأ
+
+634
+01:11:26,270 --> 01:11:32,190
+لأ لأ لأ لأ لأ لأ لأ لأ لأ لأ لأ لأ
+
+635
+01:11:32,290 --> 01:11:36,590
+اليقول معانا لرقم واحد الشكل التالي the
+
+636
+01:11:36,590 --> 01:11:44,590
+differential equation is written as المفتوح بالشكل
+
+637
+01:11:44,590 --> 01:11:53,870
+التالي y w prime زائد e وال6 على x ال y prime زائد
+
+638
+01:11:53,870 --> 01:12:03,500
+ثلاث قصير x على xمنها في الـ y بدها الـ 7 من الـ z
+
+639
+01:12:03,500 --> 01:12:10,320
+لذلك إذا أخد ال x مقفل ال x0 بيكون limit of the
+
+640
+01:12:10,320 --> 01:12:17,700
+value of x مقفل ال x0 تمامًا في u of x على capital
+
+641
+01:12:17,700 --> 01:12:24,260
+P of x y و ساعة ال x0 بيدخل لقناع 0 لإن ال x0
+
+642
+01:12:24,260 --> 01:12:32,010
+بيبقى 0 لما نشتغل في دمية xيجي ال EO6 على P EO6
+
+643
+01:12:32,010 --> 01:12:38,990
+على X EO6 على P EO6 على X EO6
+
+644
+01:12:38,990 --> 01:12:52,730
+على P EO6 على X EO6 على P EO6
+
+645
+01:12:52,730 --> 01:12:53,230
+على P EO6 على P EO6 على P EO6 على P EO6 على P EO6
+
+646
+01:12:53,230 --> 01:12:54,070
+على P EO6 على P EO6 على P EO6 على P EO6 على P EO6
+
+647
+01:12:54,070 --> 01:12:56,730
+على P EO6 على P EO6 على P EO6 على P EO6 على P EO6
+
+648
+01:12:56,730 --> 01:12:56,810
+على P EO6 على P EO6 على P EO6 على P EO6 على P EO6
+
+649
+01:12:56,810 --> 01:13:01,750
+على P EO6 على Pmax to the power n على n factorial
+
+650
+01:13:01,750 --> 01:13:08,910
+to converge for
+
+651
+01:13:08,910 --> 01:13:13,290
+all x converge for all x
+
+652
+01:13:20,810 --> 01:13:24,850
+لأ نكون غير جادة ايه الاختبار اللي ساخدوا هنا يا
+
+653
+01:13:24,850 --> 01:13:30,170
+بناتي؟ الهو يبقى ايه؟ الهو يبقى ايه؟ الهو يبقى
+
+654
+01:13:30,170 --> 01:13:30,210
+ايه؟ الهو يبقى ايه؟ الهو يبقى ايه؟ الهو يبقى ايه؟
+
+655
+01:13:30,210 --> 01:13:30,650
+الهو يبقى ايه؟ الهو يبقى ايه؟ الهو يبقى ايه؟ الهو
+
+656
+01:13:30,650 --> 01:13:31,550
+يبقى ايه؟ الهو يبقى ايه؟ الهو يبقى ايه؟ الهو يبقى
+
+657
+01:13:31,550 --> 01:13:34,050
+ايه؟ الهو يبقى ايه؟ الهو يبقى ايه؟ الهو يبقى ايه؟
+
+658
+01:13:34,050 --> 01:13:38,450
+الهو يبقى ايه؟
+
+659
+01:13:38,450 --> 01:13:44,510
+الهو
+
+660
+01:13:44,510 --> 01:13:44,950
+يبقى ا
+
+661
+01:13:48,180 --> 01:13:56,140
+من R Cos X تربيع هذه على كتر تنفيه يمكن أن يبدأ
+
+662
+01:13:56,140 --> 01:14:02,560
+تسوي X تربيع فيه فعلينا نفسنا نجد ايش كل علامة زيه
+
+663
+01:14:02,560 --> 01:14:09,880
+لإن R Cos X علينا تلاتة Cos X علي X بجه تلاتة Cos
+
+664
+01:14:09,880 --> 01:14:19,280
+X علي X تطلع كده تلاتة X D Cos Xأصلاً Cos X ألا X
+
+665
+01:14:19,280 --> 01:14:24,400
+كنا بحسبها في تاني روميكسون و لو ضربناها من كمان X
+
+666
+01:14:24,400 --> 01:14:30,000
+تطلع من السيرة ألا X تطلع من القارس يرجى هذه كمان
+
+667
+01:14:30,000 --> 01:14:36,360
+is analytic because
+
+668
+01:14:36,360 --> 01:14:39,380
+Cos X
+
+669
+01:14:50,370 --> 01:14:59,070
+انالتك تحطي هنا بنات and fix yourself easyوهذه
+
+670
+01:14:59,070 --> 01:15:05,890
+اللي هي الانالتك كمان ات اكس يساوي زي روز الشمس
+
+671
+01:15:05,890 --> 01:15:10,150
+هذه ال singular point اللي عندنا إذا انت حقق مين
+
+672
+01:15:10,150 --> 01:15:13,990
+ال condition دي الساعة اللي بيبقى كبرا دي مده
+
+673
+01:15:13,990 --> 01:15:20,470
+singular singular point إذا ات أكس يساوي زي روز
+
+674
+01:15:20,470 --> 01:15:20,750
+الشمس
+
+675
+01:15:29,750 --> 01:15:37,050
+بعدين سأذكركم بالتوصيل ال X وش هو المفتوح تبعها
+
+676
+01:15:37,050 --> 01:15:44,910
+بالنسبالي انا اختارهم ثم اتنين الان اللي هو
+
+677
+01:15:44,910 --> 01:15:49,550
+التلاتة X توصيل X
+
+678
+01:15:56,980 --> 01:16:05,340
+لنقص واحد اذا power in x أُسي اتنين M عالمين على
+
+679
+01:16:05,340 --> 01:16:14,250
+اتنين M تقريبا بالشكل الهاملطبعا اللي بقدر أكتبها
+
+680
+01:16:14,250 --> 01:16:19,170
+على الشكل التالي summation من N equal 0 to
+
+681
+01:16:19,170 --> 01:16:28,590
+infinity لثالث واحد تدفع تن في تلاتة X أس اتنين N
+
+682
+01:16:28,590 --> 01:16:34,990
+زائد واحد على اتنين N factorial مش عارف كل عليها
+
+683
+01:16:34,990 --> 01:16:40,830
+انها تبقى هادة تبقى هادة مضمونة برادمن تلك
+
+684
+01:16:40,830 --> 01:16:45,570
+البرصدية طبعا اتعبنا ان الصين والكوسين والزي
+
+685
+01:16:45,570 --> 01:16:50,270
+والسكس والسيش والجوش وان الاكس واقعد على اكس وكذلك
+
+686
+01:16:50,270 --> 01:16:55,330
+برصد كلها آلي مجانا تتبع على شكل تاني ومجانا تتبع
+
+687
+01:16:55,330 --> 01:16:55,350
+على شكل اتاني ومجانا تتبع على شكل اتاني ومجانا
+
+688
+01:16:55,350 --> 01:16:57,810
+تتبع على شكل اتاني ومجانا تتبع على شكل اتاني
+
+689
+01:16:57,810 --> 01:16:59,070
+ومجانا تتبع على شكل اتاني ومجانا تتبع على شكل
+
+690
+01:16:59,070 --> 01:17:01,950
+اتاني ومجانا تتبع على شكل اتاني ومجانا تتبع على
+
+691
+01:17:01,950 --> 01:17:10,630
+شكل اتاني ومجانا تتبع على شكل اتاني وVersion X E
+
+692
+01:17:10,630 --> 01:17:22,350
+أُس X Lenin X واحدة على X تالي Inverse X وحط عليهم
+
+693
+01:17:22,350 --> 01:17:26,970
+E أُس X Lenin X تالي Inverse X وLenin X تالي
+
+694
+01:17:26,970 --> 01:17:33,210
+Inverse X كلهم هم مقدرتهم على شكل تايلون أو مقدرين
+
+695
+01:17:33,210 --> 01:17:37,130
+Series at any point عند أي نقطة
+
+696
+01:17:42,810 --> 01:17:48,090
+هذا السؤال اللي بين إيدينها بيختلف عن السؤالين
+
+697
+01:17:48,090 --> 01:17:53,940
+السابقين بإن المعاملات معاهاماهياش polynomial كانت
+
+698
+01:17:53,940 --> 01:17:58,800
+general functions فكان عندك ليه ال 6 و 3 cos x are
+
+699
+01:17:58,800 --> 01:18:03,140
+general functions يعني not polynomials لذلك سنلجأ
+
+700
+01:18:03,140 --> 01:18:07,660
+إلى الحالة الأولى اللى ابتدينا فيها فباجي بقول
+
+701
+01:18:07,660 --> 01:18:12,420
+طبعا هذه لا يمكن أن تساوي zero إلا إذا كانت x ساوي
+
+702
+01:18:12,420 --> 01:18:16,180
+zero بيه x ساوي zero is the only singular point
+
+703
+01:18:16,180 --> 01:18:22,180
+لمين ال differential equation اللى عندنابنقسم كله
+
+704
+01:18:22,180 --> 01:18:26,320
+على X فصارت المعادلة على الشكل اللي عندنا هذا إذا
+
+705
+01:18:26,320 --> 01:18:30,220
+بدي أشوف كده قيمة X نقص ال X node في Q of X على P
+
+706
+01:18:30,220 --> 01:18:35,340
+of X يبقى يساوي X في E of X على X نختصر بظهر E of
+
+707
+01:18:35,340 --> 01:18:38,600
+X هذي أنا لاتك لإن بقدر أكتبها على شكل Tyler
+
+708
+01:18:38,600 --> 01:18:42,940
+Series أو هي عبارة عن McLaurin Series عند X يساوي
+
+709
+01:18:43,180 --> 01:18:48,060
+زيرو وبالتالي صارت هذه انالتك الان بدي اجي لل X
+
+710
+01:18:48,060 --> 01:18:51,920
+نقص ال X نوت تربيع R of X على P of X ال X نوت
+
+711
+01:18:51,920 --> 01:18:55,480
+بزيرو يبقى بصير X تربيع هدي على هدي ليه تلاتة
+
+712
+01:18:55,480 --> 01:19:00,980
+cosine X على X نختصر بصير تلاتة X cosine X هذا
+
+713
+01:19:00,980 --> 01:19:06,640
+انالتك ليش؟ لأن هذا مفكوك ال cosine Maclaurin
+
+714
+01:19:06,640 --> 01:19:11,890
+series at X يساوي زيرودربنا في تلاتة X دخلنا ال X
+
+715
+01:19:11,890 --> 01:19:16,890
+ديوة صار الأس بدل اتنين N بصير اتنين N زاد واحد
+
+716
+01:19:16,890 --> 01:19:20,890
+وهي التلاتة وهي السلم واحد أس N كما هو والمقام
+
+717
+01:19:20,890 --> 01:19:26,190
+بتنين N فاكتوريال إذا هذه كمان analytic function
+
+718
+01:19:26,190 --> 01:19:30,310
+إذا صار ال term الأول والterm التاني تنتين are two
+
+719
+01:19:30,310 --> 01:19:35,010
+analytic functionsيبقى الـ x يساوي 0 is a regular
+
+720
+01:19:35,010 --> 01:19:41,330
+singular point طيب مش كل الدول اللي بتيجي بهذه
+
+721
+01:19:41,330 --> 01:19:44,710
+السهولة هذه غير هي regular و irregular بعضها بتبقى
+
+722
+01:19:44,710 --> 01:19:49,710
+ايه مسائل صعبة شوية لكن نطلع نقول لو عندي two
+
+723
+01:19:49,710 --> 01:19:53,130
+functions واتنتين كانوا analytic عند النقطة دي
+
+724
+01:19:53,130 --> 01:19:59,340
+يبقى مجموعهم الجابريين جمع أو طرح نقصد بهأو حاصل
+
+725
+01:19:59,340 --> 01:20:04,260
+ضرب الـ two functions f في g أو خارج قسم الاتنين
+
+726
+01:20:04,260 --> 01:20:09,940
+بشرط الـ g عند النقطة x node ممنوعة تساوي zero دي
+
+727
+01:20:09,940 --> 01:20:13,840
+ريبالك الـ g of x node is not equal to zero لأن
+
+728
+01:20:13,840 --> 01:20:18,080
+هذا بيصير معناه is undefined ماهياش معرفة are
+
+729
+01:20:18,080 --> 01:20:21,920
+analytic and main عند ال x node الآن هشوف كيف
+
+730
+01:20:21,920 --> 01:20:28,930
+نستخدم هذه ال remark في حلالسؤال التالي من أسئلة
+
+731
+01:20:28,930 --> 01:20:38,150
+الكتاب وهو المثال الرقم 4 إذا المثال الرقم 4 بيقول
+
+732
+01:20:38,150 --> 01:20:46,190
+لل X في ال sign ال X في ال Y double prime زائد
+
+733
+01:20:46,190 --> 01:20:54,240
+تلاتة Y prime تلاتة Y primeزائد XY بده يساوي كده؟
+
+734
+01:20:54,240 --> 01:21:00,580
+بده يساوي 0 واضح هذه ال polynomial من الدرجة
+
+735
+01:21:00,580 --> 01:21:04,940
+الصفرية هذه ال polynomial من الدرجة الأولى لكن هذه
+
+736
+01:21:04,940 --> 01:21:09,160
+لأ sign X ليست polynomial يبقى هذه general
+
+737
+01:21:09,160 --> 01:21:20,900
+function يبقى بجي بقوله P of Xسين ال X is not a
+
+738
+01:21:20,900 --> 01:21:25,360
+polynomial تمام
+
+739
+01:21:25,360 --> 01:21:32,700
+طيب بدأ أسألكوا السؤال التالي is it a series X
+
+740
+01:21:32,700 --> 01:21:37,400
+في سين ال X زي X فيكون سين ال X نعم series لكنها
+
+741
+01:21:37,400 --> 01:21:41,410
+ليس بتنمية يعني مش بتوفر حد محددبتظلها ماشية إلى
+
+742
+01:21:41,410 --> 01:21:45,490
+وين لغاية ما لا نهاية ولو ضربناها في X زي ما ضربنا
+
+743
+01:21:45,490 --> 01:21:50,110
+ال cosine هنا في X يبقى بيظلها Series وليست
+
+744
+01:21:50,110 --> 01:21:55,330
+Polynomial مش كثيرة حدود وإنما بيظل متسلسلة إلى ما
+
+745
+01:21:55,330 --> 01:22:01,510
+لا نهاية طيب تمام الآن بدي أشوف ما هي النقطالتي
+
+746
+01:22:01,510 --> 01:22:09,910
+تجعل ال P of X يساوي 0 يبقى باجي بقوله P of X بده
+
+747
+01:22:09,910 --> 01:22:21,970
+يساوي X sin X equal 0
+
+748
+01:22:21,970 --> 01:22:29,430
+at X يساويبنشوف إيش النقاط اللي بتخلي هذه القيمتين
+
+749
+01:22:29,430 --> 01:22:35,970
+حاصل ضربهم يساوي Zero أظل لو كانت X يساوي Zero صح؟
+
+750
+01:22:35,970 --> 01:22:40,670
+بيصير هذه ب Zero و ال sign Zero ب Zero Zero Zero
+
+751
+01:22:40,670 --> 01:22:49,260
+Zero خلصنا؟ في غيرهم يعني؟ زي مين؟باي، نين باي،
+
+752
+01:22:49,260 --> 01:22:57,500
+تلاتة باي، أربع باي، خمسة باي وزيهم بالسالم يبقى
+
+753
+01:22:57,500 --> 01:23:04,820
+الزائد أو ناقص in byال X بيساوي zero and ال X
+
+754
+01:23:04,820 --> 01:23:11,780
+بيساوي زائد او ناقص in by و ال in is an integer و
+
+755
+01:23:11,780 --> 01:23:16,840
+ال in يساوي واحد و اتنين و تلاتة و الى ما لا نهاية
+
+756
+01:23:18,050 --> 01:23:22,930
+يعني الحمد لله كام singular point عندنا؟ مالة
+
+757
+01:23:22,930 --> 01:23:26,290
+نهاية من ال singular points وهذا ما أشرت إليه قبل
+
+758
+01:23:26,290 --> 01:23:29,510
+شوية في بداية المحاضرة قلت لك ممكن يكون عندي نقطة
+
+759
+01:23:29,510 --> 01:23:33,270
+واحدة singular point ممكن يكون عندي نقطتين ممكن
+
+760
+01:23:33,270 --> 01:23:37,410
+يكون تلاتة ممكن مالة نهاية من النقطة اللي على
+
+761
+01:23:37,410 --> 01:23:40,370
+البعض كنت استغرب عندما قلت يمكن يكون عندي مالة
+
+762
+01:23:40,370 --> 01:23:44,990
+نهاية من ال singularلكن هاي جيبنالكم يتهطل عندي
+
+763
+01:23:44,990 --> 01:23:49,370
+مالة نهاية من مين من ال singular طيب ما علينا بدى
+
+764
+01:23:49,370 --> 01:23:54,110
+اشوف النقاط هدولة regular و الله irregular نيجي
+
+765
+01:23:54,110 --> 01:23:58,550
+نقوله تعالى نشوف الان المعادلة هذه بتروح اكتبها
+
+766
+01:23:58,550 --> 01:24:02,970
+على الشكل التالف يبقى هذه هي المعادلة رقم واحد
+
+767
+01:24:02,970 --> 01:24:09,750
+فبروح بقوله that differential equation one is
+
+768
+01:24:09,750 --> 01:24:10,830
+written
+
+769
+01:24:17,500 --> 01:24:24,380
+زائد تلاتة على x في ال sign ال x في ال y prime
+
+770
+01:24:24,380 --> 01:24:32,220
+زائد x بتروح مع x مضال واحد على ال sign ال x فقط
+
+771
+01:24:32,220 --> 01:24:34,940
+في ال y بدها تساوي زيرو
+
+772
+01:24:38,450 --> 01:24:43,570
+نمسك النقطة الأولى ل X يساوي Zero يبقى بده أجي
+
+773
+01:24:43,570 --> 01:24:50,070
+أقوله at X بده يساوي Zero أخد ليه بتابانات؟ لأ لإن
+
+774
+01:24:50,070 --> 01:24:53,110
+هدول ماهياش Polynomial صحيح تنتين Polynomial بس
+
+775
+01:24:53,110 --> 01:24:57,410
+التالتة لأ يبقى in general التلاتة غير متحقق ان
+
+776
+01:24:57,410 --> 01:25:02,290
+التلاتة Polynomial يبقى بده أروح للحالة الأولى و
+
+777
+01:25:02,290 --> 01:25:09,140
+ليست من الحالة الثانيةيعني بدى اشوف هل ال X ناقص X
+
+778
+01:25:09,140 --> 01:25:18,300
+node اللى هو Zero في ال Q of X على ال R of X هل
+
+779
+01:25:18,300 --> 01:25:23,020
+بقدر اكتفها على شكل polynomial ام لا هل تايلور
+
+780
+01:25:23,020 --> 01:25:28,940
+سيريز ام لا يبقى هدى بصير X في ميمفي ال Q على X
+
+781
+01:25:28,940 --> 01:25:35,820
+اللي هي تلاتة على X ساين ال X يبقى في تلاتة على X
+
+782
+01:25:35,820 --> 01:25:43,220
+في ساين ال X ال X مع ال X يبقى النتيجة كده تلاتة
+
+783
+01:25:43,220 --> 01:25:49,970
+على ساين ال X السؤال هوبتقدر تكتبها على شكل taylor
+
+784
+01:25:49,970 --> 01:25:54,950
+series ام لا تقول استنى شوية تعالى نطلع لل remark
+
+785
+01:25:54,950 --> 01:25:58,410
+اللى احنا كاتبينه فوق ايش بتقولي ال remark لو
+
+786
+01:25:58,410 --> 01:26:02,890
+كانوا تنتين analytic يبقى المجموعة والضرب وخرج
+
+787
+01:26:02,890 --> 01:26:07,810
+القسمة are analytic باجى بس لنفسى هل ال sign
+
+788
+01:26:07,810 --> 01:26:13,770
+analytic الاجابة نعم نجى هل التلاتة analyticيعني
+
+789
+01:26:13,770 --> 01:26:18,390
+هل ال constant بقدر اكتبه عليه شكل series و تبقى
+
+790
+01:26:18,390 --> 01:26:25,270
+طبعا لأ يبقى هذه بصير مالها is not analytic يبقى
+
+791
+01:26:25,270 --> 01:26:35,730
+هذه ال function هذه بالساوية is not analytic السبب
+
+792
+01:26:35,730 --> 01:26:38,610
+ان التلاتة ما هيش انتظر مين اللي بتحكي
+
+793
+01:26:52,810 --> 01:27:01,400
+ثلاثة X مضروبة في الـ cosineوهي حطنلك على شكل
+
+794
+01:27:01,400 --> 01:27:06,240
+summation وهي ال summation ودخلتها جوا صارت هذه
+
+795
+01:27:06,240 --> 01:27:10,080
+على شكل ماكلون أو تايلور سيريز ولا لا عند النقطة X
+
+796
+01:27:10,080 --> 01:27:13,580
+ساوي Zero صحيح ولا لا طب يلا كتبيلي تلاتة على
+
+797
+01:27:13,580 --> 01:27:16,520
+الشكل هذا نشوف مش هنشوف كلامك صح ولا لا تبعت
+
+798
+01:27:16,520 --> 01:27:20,360
+المقامة موافق صحيح ال X مظبوط لكن هل يتل .. يعني
+
+799
+01:27:20,360 --> 01:27:25,400
+cosecant X تلاتة cosecant X عمرك جيبتي تايلور ولا
+
+800
+01:27:25,400 --> 01:27:30,300
+ماكلون لل cosecantطب مهم عند Zero مش معرفة أصلا
+
+801
+01:27:30,300 --> 01:27:34,620
+صحيحة ولا لا؟ طب احنا الشرط الذاتي تبع المقام لازم
+
+802
+01:27:34,620 --> 01:27:38,020
+يكون معرف مش يقولنا لما يكون عندنا خارق قسم
+
+803
+01:27:38,020 --> 01:27:42,640
+التنتين بدي هذه ممنوعة تساوي Zero عند Zero وصين
+
+804
+01:27:42,640 --> 01:27:47,800
+Zero في جداش يعني أمورها ماتصير Analytic مظبوط ولا
+
+805
+01:27:47,800 --> 01:27:53,560
+لا؟ خلاصنا؟ جنات يهودة؟ والكلام نفسنا مهين طيب
+
+806
+01:27:53,560 --> 01:27:56,400
+يبقى هذه سرعة النقطة Analytic يبقى النقطة اللي
+
+807
+01:27:56,400 --> 01:27:57,020
+عندنا مالها
+
+808
+01:28:00,210 --> 01:28:08,550
+يبقى هنا سا اللي هو ال X يساوي 0 is irregular
+
+809
+01:28:08,550 --> 01:28:14,610
+singular point
+
+810
+01:28:40,920 --> 01:28:51,700
+عشان نذهب الى نقاط التانية X يساوي زائد او ناقص في
+
+811
+01:28:51,700 --> 01:28:52,440
+Y
+
+812
+01:28:56,110 --> 01:29:03,470
+الـ X نقص الـ X نواة في الـ Q of X على capital P
+
+813
+01:29:03,470 --> 01:29:09,850
+of X يبقى بيصير X زائد او نقص in by I بدي اخدهم
+
+814
+01:29:09,850 --> 01:29:16,490
+مرة واحدة والـ Q على P ليه تلاتة على X sin X يبقى
+
+815
+01:29:16,490 --> 01:29:24,190
+فيه تلاتة على X في sin X طيب
+
+816
+01:29:24,190 --> 01:29:32,640
+طالعيني لهذهبقدر اكتبها مثل تلات اكس في كوسايت
+
+817
+01:29:32,640 --> 01:29:36,860
+يبقى هذه analytic and zero ولا لا analytic طيب
+
+818
+01:29:36,860 --> 01:29:43,090
+اللي فوق هذي polynomial من أي درجةبالدرجة الأولى
+
+819
+01:29:43,090 --> 01:29:47,330
+والثانية بتكتب على شكل summation طبعا هتقول ايش
+
+820
+01:29:47,330 --> 01:29:53,310
+بعد حدين بتصير الدالة عندك zero صح ولا لأ اه بقوله
+
+821
+01:29:53,310 --> 01:29:57,030
+بكتب الحدين اللي عني و بكتب زائد zero في كذا زائد
+
+822
+01:29:57,030 --> 01:30:00,910
+zero في كذا كتبت على شكل ايه تايلور او مكلونن
+
+823
+01:30:00,910 --> 01:30:04,650
+سيريزيبقى معناته مافيش مشكلة عندى في هذه الحالة
+
+824
+01:30:04,650 --> 01:30:09,790
+يبقى لو كان عندك اى polynomial بس تبقى بدلالة X مش
+
+825
+01:30:09,790 --> 01:30:14,570
+مقدار ثابت يبقى لو كانت بدل اى .. دل .. اى
+
+826
+01:30:14,570 --> 01:30:18,290
+polynomial من الدرجة الاولى فساعدا بقدر اكتب عليها
+
+827
+01:30:18,290 --> 01:30:22,470
+شكل تلوريسي اللى بخلى باقى الكميات كلهم جدا باسفار
+
+828
+01:30:22,470 --> 01:30:29,870
+وبالتالي هذه is ana .. analytic
+
+829
+01:30:36,430 --> 01:30:40,370
+عن طريق البرامج الاخرى
+
+830
+01:30:43,840 --> 01:30:48,400
+ماشي الحال هذا ايش لو جيت اتعود اتعود مباشر عند ال
+
+831
+01:30:48,400 --> 01:30:51,800
+X node مايطلعش ب zero مظبوط ولا لا لكن احنا هنا
+
+832
+01:30:51,800 --> 01:30:56,280
+بنقول توس يعني ال cosine ال cosine عند ال zero
+
+833
+01:30:56,280 --> 01:31:00,340
+طلعت أنلتك ولا لا وبالتالي ال sine عند ال zero
+
+834
+01:31:00,340 --> 01:31:05,720
+أنلتك زيها صحيح ولا لا يبقى السبب اللي هنا كانت
+
+835
+01:31:05,720 --> 01:31:10,400
+تلاتة ماقدرتش اكتبهاماقدرش اشوفها على شكل مين
+
+836
+01:31:10,400 --> 01:31:14,660
+تايلور سيلز هنا هذه من الدرجة الأولى اذا بقدر
+
+837
+01:31:14,660 --> 01:31:20,400
+اكتبهاهذه بقدر اكتبها تماما ال sign زي ال cosine
+
+838
+01:31:20,400 --> 01:31:29,200
+بس بس الأسس فردية على ما اذكر ال sign كانت sign ال
+
+839
+01:31:29,200 --> 01:31:34,640
+x كانت هي summation من n equal zero to infinity
+
+840
+01:31:34,640 --> 01:31:39,400
+اناقص واحد to the power n ل x أس اتنين n زاد واحد
+
+841
+01:31:39,400 --> 01:31:47,800
+على اتنين nزائد واحد factorial هذا series لصين ال
+
+842
+01:31:47,800 --> 01:31:53,120
+X يعني تايلور سيريز عند X يساوي Zero وبالتالي
+
+843
+01:31:53,120 --> 01:31:57,840
+ماعنا مشكلة اذا بدنا نروح ل ال condition التاني
+
+844
+01:31:57,840 --> 01:32:06,000
+اللي هو X ناقص ال X node في R of X على capital P
+
+845
+01:32:06,000 --> 01:32:11,850
+of X وهذه تربيةيبقى هذا الكلام يبدو يسوي x زد او
+
+846
+01:32:11,850 --> 01:32:20,830
+ناقص in by الكل تربيع وين راحت المعادلة يبقى واحد
+
+847
+01:32:20,830 --> 01:32:26,190
+على ال sign ال x مش هيك يبقى هذا كله على ال sign
+
+848
+01:32:26,190 --> 01:32:30,810
+ال x هذه analytic عند ال zero وهذه كذلك analytic
+
+849
+01:32:30,810 --> 01:32:39,700
+عند ال zero يبقى هذه is analyticأت اكس يساوي زيرو
+
+850
+01:32:39,700 --> 01:32:44,060
+معناه هذا الكلام انه كل النقاط هالقول مالهم
+
+851
+01:32:44,060 --> 01:32:49,160
+regular singular point ماعدا main ماعدا اكس يساوي
+
+852
+01:32:49,160 --> 01:32:58,820
+زيرو so the points اللي هو ال X يساوي ز أو ناقص in
+
+853
+01:32:58,820 --> 01:33:06,670
+by و ال N تساوي واحد و اتنين و تلاتة areregular
+
+854
+01:33:06,670 --> 01:33:12,390
+singular points
+
+855
+01:33:12,390 --> 01:33:19,650
+لحد ذلك انتهى هذا ال section وإلى يكون أرقام
+
+856
+01:33:19,650 --> 01:33:29,590
+المسائل يبقى exercises خمسة أربعة المسائل من واحد
+
+857
+01:33:29,590 --> 01:33:33,890
+لغاية تمانتاش القدر
+
+858
+01:33:40,770 --> 01:33:45,910
+طيب عليك انتهى section 5 أربعة الآن section خمسة
+
+859
+01:33:45,910 --> 01:33:48,890
+خمسة المرة القادمة ان شاء الله
+
diff --git a/PL9fwy3NUQKwa8ZDfSFGn6H8xVFLzqmCZC/nOggX_oRaAA_raw.srt b/PL9fwy3NUQKwa8ZDfSFGn6H8xVFLzqmCZC/nOggX_oRaAA_raw.srt
new file mode 100644
index 0000000000000000000000000000000000000000..6e52b3722d189dde7d7de6f5d0a0fa4d48d30d67
--- /dev/null
+++ b/PL9fwy3NUQKwa8ZDfSFGn6H8xVFLzqmCZC/nOggX_oRaAA_raw.srt
@@ -0,0 +1,3532 @@
+1
+00:00:00,000 --> 00:00:02,960
+أهلا و أهلا يا عزيزي و أهلا و أهلا يا عزيزي و أهلا
+
+2
+00:00:02,960 --> 00:00:14,280
+و أهلا يا عزيزي و
+
+3
+00:00:14,280 --> 00:00:14,920
+أهلا و أهلا و أهلا و أهلا و أهلا و أهلا و أهلا و
+
+4
+00:00:14,920 --> 00:00:15,020
+أهلا و أهلا و أهلا و أهلا و أهلا و أهلا و أهلا و
+
+5
+00:00:15,020 --> 00:00:15,020
+أهلا و أهلا و أهلا و أهلا و أهلا و أهلا و أهلا و
+
+6
+00:00:15,020 --> 00:00:15,860
+أهلا و أهلا و أهلا و أهلا و أهلا و أهلا و أهلا و
+
+7
+00:00:15,860 --> 00:00:17,800
+أهلا و أهلا و أهلا و أهلا و أهلا و أهلا و أهلا و
+
+8
+00:00:17,800 --> 00:00:20,300
+أهلا و أهلا و أهلا و أهلا و أهلا و أهلا و أهلا و
+
+9
+00:00:20,300 --> 00:00:26,820
+أهلا و أهلا و أهلا و
+
+10
+00:00:26,820 --> 00:00:33,020
+أهالسؤال يقول اذا ترمى انه موضوعه فانه يجيب عمليات
+
+11
+00:00:33,020 --> 00:00:36,480
+لازم يتولدوا و يتولدوا و يتولدوا و يتولدوا و
+
+12
+00:00:36,480 --> 00:00:38,600
+يتولدوا و يتولدوا و يتولدوا و يتولدوا و يتولدوا و
+
+13
+00:00:38,600 --> 00:00:39,600
+يتولدوا و يتولدوا و يتولدوا و يتولدوا و يتولدوا و
+
+14
+00:00:39,600 --> 00:00:39,740
+يتولدوا و يتولدوا و يتولدوا و يتولدوا و يتولدوا و
+
+15
+00:00:39,740 --> 00:00:40,280
+يتولدوا و يتولدوا و يتولدوا و يتولدوا و يتولدوا و
+
+16
+00:00:40,280 --> 00:00:42,440
+يتولدوا و يتولدوا و يتولدوا و يتولدوا و يتولدوا و
+
+17
+00:00:42,440 --> 00:00:47,180
+يتولدوا و يتولدوا و يتولدوا
+
+18
+00:00:58,350 --> 00:01:08,270
+والشيء الوحيد لـ P or X دلوقت لو قلنا P or X اللي
+
+19
+00:01:08,270 --> 00:01:13,890
+يجب ان تكسب يعني اقصد من X لما اقصد لانها دلوقت
+
+20
+00:01:13,890 --> 00:01:20,720
+هذه المثلة حددنا الى حصلعشان انا اعرف انا انا اعرف
+
+21
+00:01:20,720 --> 00:01:25,700
+انا اعرف انا اعرف انا اعرف انا اعرف انا اعرف
+
+22
+00:01:29,830 --> 00:01:36,170
+هذا الكلام لو كانت تساوي Zero هذا الكلام مابيحصل
+
+23
+00:01:36,170 --> 00:01:43,110
+إلا إذا كانت ال kicks يساوي ساوي واحد and ال kicks
+
+24
+00:01:43,110 --> 00:01:51,290
+يساوي ثلاث سنة من مدونة او Singular Points
+
+25
+00:01:54,400 --> 00:01:57,940
+النقاط الشاملة والنقاط الوانهاتي اللي لدينا
+
+26
+00:01:57,940 --> 00:02:02,260
+المعاملة انتقالية هي النقاط اللي بتجعل المعاملة
+
+27
+00:02:02,260 --> 00:02:06,320
+تقع واحدة من الحاجة تسوى زيرو مانيش تبنيها لكل
+
+28
+00:02:06,320 --> 00:02:11,500
+نقطة يتجاه نقاط اشتهرت من قبلها يعني ال singular
+
+29
+00:02:11,500 --> 00:02:18,470
+points و ال ordinary pointsordinary points يرجى
+
+30
+00:02:18,470 --> 00:02:22,870
+مادام هدول هم ال singular points هدى بدي يعطيك ان
+
+31
+00:02:22,870 --> 00:02:28,730
+ال X لها تساوي أربعة و X لها تساوي ساوي أربعة and
+
+32
+00:02:28,730 --> 00:02:38,290
+ال X لها تساوي Zero are ordinary points ordinary
+
+33
+00:02:38,290 --> 00:02:41,150
+points
+
+34
+00:02:43,470 --> 00:02:48,530
+تمام؟ بدنا نصاب الأكترار تعالى بنتنا نجيب كل ده
+
+35
+00:02:48,530 --> 00:02:54,150
+نجيب يومنا تمام؟ السجن لا يكون في النقطة السالي
+
+36
+00:02:54,150 --> 00:02:59,350
+واحد ونقطة واثر ثلاث يجب أن نجيب السالي واحد يجب
+
+37
+00:02:59,350 --> 00:03:06,870
+أن نجيب أي نقطة في السالي واحدماذا نحن نحن نحن نحن
+
+38
+00:03:06,870 --> 00:03:08,570
+نحن نحن نحن نحن نحن نحن نحن نحن نحن نحن نحن نحن
+
+39
+00:03:08,570 --> 00:03:11,610
+نحن نحن نحن نحن نحن نحن نحن نحن نحن نحن نحن نحن
+
+40
+00:03:11,610 --> 00:03:12,950
+نحن نحن نحن نحن نحن نحن نحن نحن نحن نحن نحن نحن
+
+41
+00:03:12,950 --> 00:03:14,290
+نحن نحن نحن نحن نحن نحن نحن نحن نحن نحن نحن نحن
+
+42
+00:03:14,290 --> 00:03:14,290
+نحن نحن نحن نحن نحن نحن نحن نحن نحن نحن نحن نحن
+
+43
+00:03:14,290 --> 00:03:22,830
+نحن نحن نحن نحن نحن نحن نحن نحن
+
+44
+00:03:22,830 --> 00:03:28,370
+نحن
+
+45
+00:03:28,370 --> 00:03:32,610
+نحإذا ال singular point هي النقطة سنة واحدة و
+
+46
+00:03:32,610 --> 00:03:39,670
+ثلاثة يبقى هذه النقطة هي ال singular point و
+
+47
+00:03:39,670 --> 00:03:46,570
+الثلاثة كمان دالي يمينه هي ال singular point تمام
+
+48
+00:03:46,570 --> 00:03:53,950
+تمام الان قللي هدلي و قللي هو مينأصغر lower bound
+
+49
+00:03:53,950 --> 00:03:57,810
+of radius of convergence لان انا بدي اروح اشوف
+
+50
+00:03:57,810 --> 00:04:01,910
+radius of convergence لان هو ياخد صغير فيلم يقول
+
+51
+00:04:01,910 --> 00:04:07,790
+هو اصغر التقارب المطلوب ليجي عند النقطة الأولى عند
+
+52
+00:04:07,790 --> 00:04:09,690
+x⁻⁴
+
+53
+00:04:15,230 --> 00:04:19,490
+شوف ايش اللي بده يصير وانا الاربعة هايم يعني ما
+
+54
+00:04:19,490 --> 00:04:23,230
+بده اشوف كده المسافة ما بده الاربعة مش سالف واحد
+
+55
+00:04:23,230 --> 00:04:27,910
+واشوف كده المسافة بين الأربعة وثلاثة صغيرة يوم
+
+56
+00:04:27,910 --> 00:04:32,870
+بتكون يا مين ال radius of convergence المطلوب
+
+57
+00:04:32,870 --> 00:04:38,600
+اليعملالجمال اللي بنقوله الآن عند نقطة x تساوي
+
+58
+00:04:38,600 --> 00:04:43,780
+أربعة روات بده ساوية أربعة اللي هي النقطة اللي
+
+59
+00:04:43,780 --> 00:04:51,120
+عندنا ما تستخدمي ال singularماقص واحد ويساوي قدره
+
+60
+00:04:51,120 --> 00:04:57,620
+خمسة تدريجي ناخد روح اثنين بتساوي اربعة ماقص ثلاثة
+
+61
+00:04:57,620 --> 00:05:02,620
+يساوي قدره واحد يبقى نصف قطر اتقال بالمطبق ودين
+
+62
+00:05:02,620 --> 00:05:07,300
+واحد اللي قاللي احنا اللي هو الفرح اصغر واحد منهم
+
+63
+00:05:07,300 --> 00:05:18,210
+يبقى هنا باجي بيقولوا اثنينLower down of the
+
+64
+00:05:18,210 --> 00:05:24,810
+radius of convergence
+
+65
+00:05:24,810 --> 00:05:35,060
+is not zeroيبقى رمضان سنة واحد هو رمضان لا ميل دا
+
+66
+00:05:35,060 --> 00:05:40,800
+رديوس او كل فيها جامعه اذا ال serious solution هذه
+
+67
+00:05:40,800 --> 00:05:51,840
+يجب ان اقول له ال serious solution الموجودة
+
+68
+00:05:52,620 --> 00:05:59,200
+Summation من M equal 0 to infinity من A M في X نقص
+
+69
+00:05:59,200 --> 00:06:02,480
+X نقص X نقص X نقص X نقص X نقص X نقص X نقص X نقص X
+
+70
+00:06:02,480 --> 00:06:04,280
+نقص X نقص X نقص X نقص X نقص X نقص X نقص X نقص X
+
+71
+00:06:04,280 --> 00:06:07,240
+نقص X نقص X نقص X نقص X نقص X نقص X نقص X نقص X
+
+72
+00:06:07,240 --> 00:06:07,680
+نقص X نقص X نقص X نقص X نقص X نقص X نقص X نقص X
+
+73
+00:06:07,680 --> 00:06:08,580
+نقص X نقص X نقص X نقص X نقص X نقص X نقص X نقص X
+
+74
+00:06:08,580 --> 00:06:08,580
+نقص X نقص X نقص X نقص X نقص X نقص X نقص X نقص X
+
+75
+00:06:08,580 --> 00:06:17,620
+نقص X نقص X نقص X
+
+76
+00:06:17,620 --> 00:06:29,150
+نقاللي يست عالم أقل for absolute value من X مع
+
+77
+00:06:29,150 --> 00:06:34,450
+أصحابها أقل من الواحد اللي اعتمدناه لوله صغير كل
+
+78
+00:06:34,450 --> 00:06:42,170
+الدنياالجهد عند النقطة x0 تساوي 4 لو جينا الان عند
+
+79
+00:06:42,170 --> 00:06:46,770
+النقطة x0 تساوي 4
+
+80
+00:06:52,440 --> 00:06:59,200
+يبقى روح ون يساوي، اه هذه فيها سبب لأن هو دائما و
+
+81
+00:06:59,200 --> 00:07:04,120
+أبدا أكبر من يزيل النسخوتر، تعني مثلا إذا كنت قاطب
+
+82
+00:07:04,120 --> 00:07:08,320
+بير، اللي هتسيبه تباركها أفضل دائما و أبدا في كل
+
+83
+00:07:08,320 --> 00:07:08,740
+مالها
+
+84
+00:07:15,890 --> 00:07:21,910
+النقطة اللي هي ناقص أربعة وإن ناقص أربعة هيها منها
+
+85
+00:07:21,910 --> 00:07:29,350
+إذا ناقص أربعة ناقص ناقص واحد يرجع ناقص ناقص واحد
+
+86
+00:07:46,040 --> 00:07:49,960
+النقطة التانية كم؟ تلاتة
+
+87
+00:08:06,810 --> 00:08:24,310
+radius of conveyor belts is راتب سبكتر تلتة سبكتر
+
+88
+00:08:28,090 --> 00:08:32,030
+this is your solution for summation from n equals
+
+89
+00:08:32,030 --> 00:08:38,950
+zero to infinity of b into x plus 4 to the power
+
+90
+00:08:38,950 --> 00:08:39,430
+of n
+
+91
+00:08:44,340 --> 00:08:53,880
+بتكون في ال at least على الأقل for absolute value
+
+92
+00:08:53,880 --> 00:09:00,880
+لل X زائد أربعة أقل من 2 أقل من 3 لتطلع لها هذا
+
+93
+00:09:00,880 --> 00:09:05,320
+بالنسبة للنقطة الثانية بالنسبة للنقطة الثانية X0
+
+94
+00:09:05,320 --> 00:09:06,420
+يساوي 0
+
+95
+00:09:24,800 --> 00:09:30,920
+النقطة الأولى هي نقص واحد، نقص نقص واحد هي نقص
+
+96
+00:09:30,920 --> 00:09:32,480
+واحد
+
+97
+00:09:40,360 --> 00:09:45,000
+بساوي كتير؟ absolutely بساوي تلاتة ليه تلاتة؟ من
+
+98
+00:09:45,000 --> 00:09:54,740
+الاتنين هدول فبروح بقول دي lower bound for the
+
+99
+00:09:54,740 --> 00:10:01,840
+radius of convergence
+
+100
+00:10:01,840 --> 00:10:13,990
+is رقم ساوي واحد الان بروح بقوله دهسيريز سوليوشن
+
+101
+00:10:13,990 --> 00:10:23,790
+لو سماشي نبتدن equal zero to infinity لسي ان في ال
+
+102
+00:10:23,790 --> 00:10:30,110
+X ماقس ال zero يعني قدر يعني X to the power N
+
+103
+00:10:30,110 --> 00:10:42,570
+convergeأفضل من أفضل من أفضل من أفضل من أفضل من
+
+104
+00:10:42,570 --> 00:10:47,310
+أفضل من أفضل من أفضل من أفضل من أفضل من أفضل من
+
+105
+00:10:47,310 --> 00:10:47,310
+أفضل من أفضل من أفضل من أفضل من أفضل من أفضل من
+
+106
+00:10:47,310 --> 00:10:48,510
+أفضل من أفضل من أفضل من أفضل من أفضل من أفضل من
+
+107
+00:10:48,510 --> 00:10:48,510
+أفضل من أفضل من أفضل من أفضل من أفضل من أفضل من
+
+108
+00:10:48,510 --> 00:10:48,510
+أفضل من أفضل من أفضل من أفضل من أفضل من أفضل من
+
+109
+00:10:48,510 --> 00:10:48,510
+أفضل من أفضل من أفضل من أفضل من أفضل من أفضل من
+
+110
+00:10:48,510 --> 00:10:55,390
+أفضل من أفضل من أفضل من أفضلمعناه نهاية لما يعمل
+
+111
+00:10:55,390 --> 00:10:59,070
+كل واحدة من تنتيجة قرية مانا نهاية يبقى اي واحدة
+
+112
+00:10:59,070 --> 00:11:04,430
+فيهم يبقى كوندرش علي كل real line لكنها بناء
+
+113
+00:11:04,430 --> 00:11:10,210
+كوندرش علي فترة فقط ماغية يبقى هذا بالنسبة للمثال
+
+114
+00:11:10,210 --> 00:11:17,560
+رقم اللي هو الـ 10 بمجرد المثال رقم 3يرجع البرنامج
+
+115
+00:11:17,560 --> 00:11:22,280
+إلى هذا رقم ثلاثة نفس المطلوب هذا ليس حاجة تغيره
+
+116
+00:11:22,280 --> 00:11:26,460
+يرجع البرنامج إلى هذا الرقم تغيرته بشكل معادل ان
+
+117
+00:11:26,460 --> 00:11:38,520
+هو واحد زائد X ترمية في ال YW5 زائد اتنين XY5 زائد
+
+118
+00:11:42,320 --> 00:11:48,760
+يساوي زيرو وال X نوض يساوي زيرو وال X نوض التالية
+
+119
+00:11:48,760 --> 00:11:50,680
+يساوي معاك اسمه
+
+120
+00:11:58,940 --> 00:12:03,880
+المثال السابق قبل قليل محور ان ال singular quiz
+
+121
+00:12:03,880 --> 00:12:09,540
+كانت تنتم هي واحدة كانت سالف واحد وتانية داشر
+
+122
+00:12:09,540 --> 00:12:14,920
+وتانية تلاتة لكن هنا في سؤال تعالى تشوف مشكلته
+
+123
+00:12:14,920 --> 00:12:18,240
+يبقى ايش مزاج يقوله solution
+
+124
+00:12:20,590 --> 00:12:29,050
+الـ P of X يساوي واحد زاوية X تجارية بزيرو
+
+125
+00:12:29,050 --> 00:12:35,950
+معناه هذا الكلام ان X بدأ ساوي زاوية او نقطة I
+
+126
+00:12:35,950 --> 00:12:44,150
+ممتاز جدا يتجسس من مقطة تحيولية اللي مجبر اكتبها
+
+127
+00:12:44,150 --> 00:12:44,570
+عبر
+
+128
+00:12:47,730 --> 00:12:55,110
+زائد او ناقص ايه انت عارف لانه العدد المركب يكتب
+
+129
+00:12:55,110 --> 00:13:00,690
+كمجموعة two terms جزء الحقيقه وجزء التفاير الحقيقه
+
+130
+00:13:00,690 --> 00:13:05,970
+مارهاش اللي معناته P0 فبروح بطب وعلى صيغة zero
+
+131
+00:13:05,970 --> 00:13:13,100
+زائد او ناقص ايه جمهور كان مفهوموحدة زيرو زائد ايه
+
+132
+00:13:13,100 --> 00:13:20,580
+واتانية زيرو نقطة اتنين مش نقطة واحدة تمام الان
+
+133
+00:13:20,580 --> 00:13:24,920
+نبدأ نشتغل نفس الشغل اللي اشتغلناه بس على كل نقطة
+
+134
+00:13:24,920 --> 00:13:29,300
+من النقطتين اللي اتنين من دولة بس قبل ذلك من الكتب
+
+135
+00:13:29,300 --> 00:13:32,520
+الكتب وراه عرف ال complex فاعرفش اللي دراسوا ال
+
+136
+00:13:32,520 --> 00:13:36,680
+complex علتيه اللي ما دراسوهش اللي عرفوهاشلذلك لو
+
+137
+00:13:36,680 --> 00:13:43,120
+افضل مسافة بين نقطتين في ال complex play يرجع من
+
+138
+00:13:43,120 --> 00:13:47,100
+هنا نقطة ملاحظة و بعدين نستخدمها في الشبكة فبعدين
+
+139
+00:13:47,100 --> 00:13:56,520
+يقولون انها distance between play
+
+140
+00:13:56,520 --> 00:14:07,650
+points المرزق دواعييساوي x واحد زي ال IY واحد and
+
+141
+00:14:07,650 --> 00:14:16,970
+زد اتنين and زد اتنين يبدأ يساوي x اتنين زي ال IY
+
+142
+00:14:16,970 --> 00:14:25,570
+اتنين in the complex complex
+
+143
+00:14:25,570 --> 00:14:28,490
+اتنين
+
+144
+00:14:35,340 --> 00:14:42,840
+بديها رمز Z واحد مقص Z اتنين absolute value هذه
+
+145
+00:14:42,840 --> 00:14:49,520
+عبارة عن الجدرين التربيعي X واحد مقص X اتنين لكل
+
+146
+00:14:49,520 --> 00:14:56,400
+تربيع زي Y واحد مقص Y اتنين لكل تربيع تقريبا كانت
+
+147
+00:14:56,400 --> 00:15:02,840
+مشروع كونه عندك في الكتابة لكن عليها اسئلة
+
+148
+00:15:20,410 --> 00:15:25,970
+قبل ما اكمل ان اقولها المقول هذه مش قولها صح ولا
+
+149
+00:15:25,970 --> 00:15:33,750
+لأ any real number is a complex number صح ولا لأ و
+
+150
+00:15:33,750 --> 00:15:39,350
+بعدين نجيب العملية العكسية any complex number is a
+
+151
+00:15:39,350 --> 00:15:45,210
+real number ليس صح وليس غلق ولا كله غلق ولا كله صح
+
+152
+00:15:47,360 --> 00:15:51,360
+القانع الريال number is a complex number صح ولا لأ
+
+153
+00:15:51,360 --> 00:15:58,780
+؟ خطأ ؟ اه ممتازة انك بيقول بتقول هدا ان القانع
+
+154
+00:15:58,780 --> 00:16:03,680
+الريال number is a complex number هذا خطأ نجي شوف
+
+155
+00:16:03,680 --> 00:16:08,300
+قد هو صح ولا خطأ خلّاوي هنا كويسة لو جاي تقولتك
+
+156
+00:16:08,300 --> 00:16:14,760
+التلاتة مثلا التلاتة هي لأ ولا لأ اللي اكتفه هذا
+
+157
+00:16:14,760 --> 00:16:15,120
+اصلا
+
+158
+00:16:19,330 --> 00:16:27,950
+مصحيح ولا لأ؟ مصحيح ولا لأ؟ مصحيح
+
+159
+00:16:27,950 --> 00:16:40,470
+ولا لأ؟ مصحيح
+
+160
+00:16:40,470 --> 00:16:45,690
+ولا لأ؟ مصحيح ولا لأ؟ مصحيح ولا لأ؟ مصحيح ولا لأ؟
+
+161
+00:16:45,690 --> 00:16:50,530
+مصحيح ولا لأ؟العكس ما هوش صحيح نهائي أبدا ولا عملك
+
+162
+00:16:50,530 --> 00:16:56,930
+تجد complex number واحد يسوى real number إلا إذا
+
+163
+00:16:56,930 --> 00:17:02,950
+كان صفر غير لاشي بعد كامة يعني لو كان zero
+
+164
+00:17:02,950 --> 00:17:08,390
+فcomplex number هو zero زي zero في Iصحيح ان هو
+
+165
+00:17:08,390 --> 00:17:11,990
+اللي بيسيوريه بالنظر الانجليزي، لكن غير ذلك بعد
+
+166
+00:17:11,990 --> 00:17:17,190
+التغور، مش ممكنية أبدًا، تمام؟ قال بس ودمرت علومة
+
+167
+00:17:17,190 --> 00:17:21,970
+أمشية ده زهنلها بالحلم، لكن كانت علومة جيدة
+
+168
+00:17:21,970 --> 00:17:27,250
+للدكتور يعرفها، طيب، نرجع الآن للموضوع الصغيرسؤال
+
+169
+00:17:27,250 --> 00:17:32,630
+اللي بيقولني بيجيب جداش ال radius of all virgins
+
+170
+00:17:32,630 --> 00:17:36,390
+لما يتى المعادلة الطابقة الاربونية اللى عندنا هذه
+
+171
+00:17:36,390 --> 00:17:42,630
+الحلطة بجهها الحل ك series صحية عليه بقولك ميسيا
+
+172
+00:17:42,630 --> 00:17:45,890
+احنا طلعنا المفقودين تاخدوا ال utility quotients
+
+173
+00:17:45,890 --> 00:17:49,350
+وتم نقطة الاولة النقطة الاولى جالسة x not equal to
+
+174
+00:17:49,350 --> 00:17:50,270
+zero
+
+175
+00:18:06,230 --> 00:18:22,710
+زيرو زائد زيرو في I زيرو
+
+176
+00:18:22,710 --> 00:18:32,090
+زائد Iالـ X تساوي I يعني سريعًا وزاهم I بالشكل
+
+177
+00:18:32,090 --> 00:18:37,450
+العامل لها لأن هذه اللي صار X واحد وY واحد وهذه
+
+178
+00:18:37,450 --> 00:18:42,990
+صارت X اتنين وY اتنين وواحد صحيح مظبوط فالمفروض ان
+
+179
+00:18:42,990 --> 00:18:48,150
+هذه القادة تقدر اجيب جداش الفرق بين النقطتين اللي
+
+180
+00:18:48,150 --> 00:18:54,080
+هو نصف متر التقارىيبقى مثلًا اقوله يبقى O1 يبقى
+
+181
+00:18:54,080 --> 00:19:02,960
+بيساوي الجدرين الترميه ليه X1-X2 يبقى كتير Zero
+
+182
+00:19:02,960 --> 00:19:11,120
+ناقص Zero لكل ترمية Y1 ناقص Y2 كدهش Y1؟ Zero Y2
+
+183
+00:19:11,120 --> 00:19:20,440
+لواحد لكل ترمية يبقى كتير ترمية يبقى كتير ترمية
+
+184
+00:19:20,440 --> 00:19:20,540
+يبقى كتير ترمية يبقى كتير ترمية يبقى كتير ترمية
+
+185
+00:19:20,540 --> 00:19:20,540
+يبقى كتير ترمية يبقى كتير ترمية يبقى كتير ترمية
+
+186
+00:19:20,540 --> 00:19:20,540
+يبقى كتير ترمية يبقى كتير ترمية يبقى كتير ترمية
+
+187
+00:19:20,540 --> 00:19:23,870
+يبقى كتير ترمية يبقىيساوي الجدرين التربية يليه
+
+188
+00:19:23,870 --> 00:19:29,030
+النقطة اللي عندنا هذه والنقطة التانية الصالحة مين؟
+
+189
+00:19:29,030 --> 00:19:36,910
+ناقص A يتغير إلى Zero ناقص Zero في كل تربية زائد
+
+190
+00:19:36,910 --> 00:19:45,830
+Zero زائد واحد في كل تربيةواحد نفسه يبدأ بلاء عليه
+
+191
+00:19:45,830 --> 00:19:50,290
+ال road is always lower than for the radius of
+
+192
+00:19:50,290 --> 00:20:04,290
+convergence يبقى the lower bound for the radius of
+
+193
+00:20:04,290 --> 00:20:07,030
+convergence
+
+194
+00:20:27,520 --> 00:20:35,780
+للـ X ناقصيجب ان نقفل لانه يجيزيه مرضو يقفلاش الـ
+
+195
+00:20:35,780 --> 00:20:44,000
+0 تغريد x to the power n convert at least على
+
+196
+00:20:44,000 --> 00:20:49,540
+الأقل for absolute value of x مقصد 0 أقل من ال
+
+197
+00:20:49,540 --> 00:20:51,800
+minimum أقل من الماحدة
+
+198
+00:20:58,400 --> 00:21:03,380
+خلصنا من قصة النقل يظهر التاني ماذا؟ يظهر سالف نص
+
+199
+00:21:03,380 --> 00:21:10,220
+يظهر سالف نص يظهر
+
+200
+00:21:10,220 --> 00:21:16,640
+سالف نص يظهر سالف نص يظهر سالف نص يظهر سالف نص
+
+201
+00:21:16,640 --> 00:21:21,960
+يظهر سالف نص يظهر سالف نص يظهر سالف نص يظهر سالف
+
+202
+00:21:21,960 --> 00:21:30,490
+نصوهذا Y و R نمسك النقطة التانية and النقطة التي
+
+203
+00:21:30,490 --> 00:21:37,970
+خلقناها ال X يساوي R يعني مين يعني؟ Zero زائد R
+
+204
+00:21:38,830 --> 00:21:44,710
+بتروح نجيب الراوان يساوي الجذري التربيعي ده x
+
+205
+00:21:44,710 --> 00:21:52,550
+واحدة هو ناقص نص ناقص x اتنية اللي هو ال zero لكل
+
+206
+00:21:52,550 --> 00:21:59,630
+تربيعزي واي واحد اللي هو zero مابس واي اتنين اللي
+
+207
+00:21:59,630 --> 00:22:06,310
+هو واحد لكل تربيع يساوي جدر التربيع طبعا هذا رابع
+
+208
+00:22:06,310 --> 00:22:12,910
+وهنا قدر واحد يعني واحد و رابع قدر خمسة على اربع
+
+209
+00:22:12,910 --> 00:22:20,950
+يعني جدر خمسة على اتنين انا بروح اجيب له اتنين
+
+210
+00:22:21,390 --> 00:22:33,890
+يساوي الجدرين الترابيعي الان نغير النقطة X يساوي
+
+211
+00:22:33,890 --> 00:22:36,010
+Zero نقص I
+
+212
+00:22:41,240 --> 00:22:46,160
+اللي هي عبارة عن زير و نقص عيال بيروم بده يساوي X
+
+213
+00:22:46,160 --> 00:22:52,240
+واحد اللي هو ناقص نص ناقص زير لكل تربيع
+
+214
+00:22:56,640 --> 00:23:03,700
+zero ناقص ناقص واحد زائد واحد في كل تربيع يبقى جدر
+
+215
+00:23:03,700 --> 00:23:08,800
+التربيع إلى اربعة زائد واحد يبقى جدر خمسة على
+
+216
+00:23:08,800 --> 00:23:14,580
+اتنين لاتنين سوا بعض يبقى بناء عليه بناء على هذا
+
+217
+00:23:14,580 --> 00:23:25,360
+الكلام يجب يقولوا the lower bound for the radius
+
+218
+00:23:31,930 --> 00:23:40,770
+convergence is قرار تساوي كده جدر خمسة علامة
+
+219
+00:23:58,730 --> 00:24:01,510
+نقص نقص نقص نقص نقص نقص نقص نقص نقص نقص نقص نقص
+
+220
+00:24:01,510 --> 00:24:02,470
+نقص نقص نقص نقص نقص نقص نقص نقص نقص نقص نقص نقص
+
+221
+00:24:02,470 --> 00:24:07,910
+نقص نقص نقص نقص نقص نقص نقص نقص نقص نقص نقص نقص
+
+222
+00:24:07,910 --> 00:24:07,910
+نقص نقص نقص نقص نقص نقص نقص نقص نقص نقص نقص نقص
+
+223
+00:24:07,910 --> 00:24:07,910
+نقص نقص نقص نقص نقص نقص نقص نقص نقص نقص نقص نقص
+
+224
+00:24:07,910 --> 00:24:07,970
+نقص نقص نقص نقص نقص نقص نقص نقص نقص نقص نقص نقص
+
+225
+00:24:07,970 --> 00:24:10,130
+نقص نقص نق
+
+226
+00:24:17,630 --> 00:24:25,210
+then it's the north على قلب الراب اللي بيقول جدر
+
+227
+00:24:25,210 --> 00:24:34,630
+خمسة عالمين على الفرق تحدث في هذا ال section ان هي
+
+228
+00:24:34,630 --> 00:24:42,110
+كل قران في المثال يبقى فيه ال exercises خمسة
+
+229
+00:24:42,110 --> 00:25:03,860
+الادامالوسائل من واحد لغاية تمانية انتفل
+
+230
+00:25:03,860 --> 00:25:10,560
+الان الى section خلال يديني وهو section خمسة أرض
+
+231
+00:25:13,060 --> 00:25:20,380
+طبعا الامتحان اللي هي يولد يوم اربع تاشر تمامية او
+
+232
+00:25:20,380 --> 00:25:25,400
+اربع تاشر تمامية اولا سبتشن
+
+233
+00:25:25,400 --> 00:25:34,200
+خمسة اربع نومين regular singular
+
+234
+00:25:34,200 --> 00:25:34,940
+points
+
+235
+00:25:50,360 --> 00:25:56,820
+كلمة regular اشتيدة علينا ريجولر معناها مضطرة مثلا
+
+236
+00:25:56,820 --> 00:26:01,280
+لما آسف حقيا اذا ال singular point يعني ال
+
+237
+00:26:01,280 --> 00:26:04,580
+singular point اللي انا عرفته قبل دي اما ال
+
+238
+00:26:04,580 --> 00:26:09,080
+singular point يعني قد تكون regular و قد تكون
+
+239
+00:26:09,080 --> 00:26:14,190
+irregularبنشوف كيف بدّى نميز ما بين irregular
+
+240
+00:26:14,190 --> 00:26:18,950
+singular point وirregular singular point يعني
+
+241
+00:26:18,950 --> 00:26:24,530
+بميّاش رجل ومش هنعمل هذا التمييز بدّى نميز بين
+
+242
+00:26:24,530 --> 00:26:30,570
+معاملات المعادلة التفاضلية النضوفة للثاني ال P
+
+243
+00:26:30,570 --> 00:26:35,510
+والQ والR هدول بدّى نعمل تمييز في بينهاهل هما
+
+244
+00:26:35,510 --> 00:26:40,310
+polynomial كبيرات حدود مهمة ولا عادية؟ يعني
+
+245
+00:26:40,310 --> 00:26:44,990
+exponential، ده اللغة التجاربية، ده اللغة العلمية،
+
+246
+00:26:44,990 --> 00:26:48,610
+اي .. اي شغلة تانية المهم ال polynomial اللي هو
+
+247
+00:26:48,610 --> 00:26:53,530
+شغل حاله وباقي الدوات اللي هو شغل حاله، لأنها تحفظ
+
+248
+00:26:53,530 --> 00:27:00,950
+السماءوشوف كيف هتتعامل مع المسألتين يبقى الرقم
+
+249
+00:27:00,950 --> 00:27:05,870
+الأولى بالتناقص لو ماكانوش polynomial ماكانوش
+
+250
+00:27:05,870 --> 00:27:16,050
+كتيرات كلهم يبقى F ال P و ال U and ال R معاملات
+
+251
+00:27:16,050 --> 00:27:24,950
+التلاتة of the differential equationللمعادلة
+
+252
+00:27:24,950 --> 00:27:32,130
+التقريب كابتن P of X في الـ YW إطاري كابتن Q of X
+
+253
+00:27:32,130 --> 00:27:37,470
+في الـ Y إطاري كابتن R of X في الـ Y تساوي Zero
+
+254
+00:27:37,470 --> 00:27:46,390
+وسمينا المعادلة هذه رقم واحد a general function
+
+255
+00:27:47,060 --> 00:27:52,400
+يبقى درّال عامة يعني إيش مقصود هي يعني ما
+
+256
+00:27:52,400 --> 00:28:03,620
+polynomials لإن ماهياش كثيرات حدود then the x node
+
+257
+00:28:03,620 --> 00:28:13,040
+is regular singular regular
+
+258
+00:28:13,040 --> 00:28:14,800
+singular point
+
+259
+00:28:27,280 --> 00:28:35,900
+singular شرق الأول and both
+
+260
+00:28:35,900 --> 00:28:39,440
+of
+
+261
+00:28:39,440 --> 00:28:49,700
+x ناقص ال x نقطة very cute of x على ال key of x
+
+262
+00:28:49,700 --> 00:29:02,080
+and ال xأقصى ال X نقطة كل درجية بال A of X على ال
+
+263
+00:29:02,080 --> 00:29:12,340
+P of X على ال P of X بتجارب معنى R-Analytic R
+
+264
+00:29:12,340 --> 00:29:18,180
+-Analytic of X نقطة
+
+265
+00:29:27,320 --> 00:29:48,560
+F X-X0 Q of X على P of X على P of X and X-X0 ترمية
+
+266
+00:29:48,560 --> 00:30:00,500
+R of X على كتر P of Xمانو مانو نهاب Convergent
+
+267
+00:30:00,500 --> 00:30:10,320
+هاب Convergent تايجر سيريز
+
+268
+00:30:10,320 --> 00:30:14,100
+سيريز
+
+269
+00:30:14,100 --> 00:30:18,760
+about اكسلون
+
+270
+00:30:18,760 --> 00:30:21,840
+نمر
+
+271
+00:30:21,840 --> 00:30:22,380
+اتنين
+
+272
+00:30:28,170 --> 00:30:47,370
+أ بيكيوك اندر ار and capital R are polynomials are
+
+273
+00:30:47,370 --> 00:31:01,740
+polynomials in equation oneand f وإذا كان limit
+
+274
+00:31:01,740 --> 00:31:10,780
+لما ال x بدها تروح إلى x non لمن؟
+
+275
+00:31:10,780 --> 00:31:20,000
+لل x ناقص x non إلى q of x على captain p of x
+
+276
+00:31:22,610 --> 00:31:33,310
+خلاص يا عزيزي فهذه is Phi9 and
+
+277
+00:31:33,310 --> 00:31:43,510
+limit x to o from x0 to x minus x0 is full ترهيب
+
+278
+00:31:43,510 --> 00:31:51,870
+just R of x على capital E of x is Phi9
+
+279
+00:31:53,470 --> 00:32:01,390
+إذا كانت خامسة ثم إتصالها
+
+280
+00:32:01,390 --> 00:32:04,550
+إلى
+
+281
+00:32:04,550 --> 00:32:05,030
+موقع محدد
+
+282
+00:32:47,580 --> 00:32:57,440
+definition any singular point any singular point
+
+283
+00:32:57,440 --> 00:33:10,680
+of equation one that is not regular
+
+284
+00:33:15,530 --> 00:33:20,650
+is called an
+
+285
+00:33:20,650 --> 00:33:27,750
+irregular singular
+
+286
+00:33:27,750 --> 00:33:28,410
+point
+
+287
+00:33:51,070 --> 00:34:03,170
+Definition Declaration Declaration
+
+288
+00:34:13,550 --> 00:34:24,090
+all the singular points all the
+
+289
+00:34:24,090 --> 00:34:29,590
+singular points and
+
+290
+00:34:29,590 --> 00:34:30,810
+determining it up
+
+291
+00:34:48,710 --> 00:34:58,650
+H1H1 is a regular or irregular
+
+292
+00:35:09,020 --> 00:35:16,500
+وارخم ثانية في الخط والواحد نقص تانية كل ثانية
+
+293
+00:35:16,500 --> 00:35:31,960
+واحد W' زائد X واحد نقص X كله في Y' زائد واحد زائد
+
+294
+00:35:31,960 --> 00:35:37,000
+X كله في الواحد ندر ساوي Zero
+
+295
+00:36:01,170 --> 00:36:09,170
+الكلام اللى احنا كتبهه اليوم بارعة ثانية
+
+296
+00:36:10,680 --> 00:36:17,180
+هذه كتيرة كلوم وماهياش كتيرة كلوم إذا كتيرة كلوم
+
+297
+00:36:17,180 --> 00:36:22,800
+تلها كلام وإذا ماهياش كتيرة كلوم تلها كلام ذات طيب
+
+298
+00:36:22,800 --> 00:36:27,880
+نيجي الآن لتعرف على التقارير اللي عجبني على الشكلة
+
+299
+00:36:27,880 --> 00:36:32,320
+اللي عنها هذه أقول لو كده بيقول if you will are a
+
+300
+00:36:32,320 --> 00:36:37,080
+general function دي ربط يعني ايش؟ مبقى monogamous
+
+301
+00:36:37,080 --> 00:36:42,160
+فبسؤال كدهكله ضرورى، مايكونوش كورنوميا ضرورى، ممكن
+
+302
+00:36:42,160 --> 00:36:45,440
+واحدة تكون كورنوميا لو كانت تانية و تانية ثانية،
+
+303
+00:36:45,440 --> 00:36:52,260
+ممكن، عادل، بس انهم التلاتة مع بعض ملموط، مايكونوش
+
+304
+00:36:52,260 --> 00:36:54,460
+كورنوميا، لو كانوا تانية و تانية كورنوميا، لو
+
+305
+00:36:54,460 --> 00:36:59,300
+كانوا تانية، ممكن، ممكن، ممكن، ممكن، ممكن، ممكنلكن
+
+306
+00:36:59,300 --> 00:37:04,360
+إن كانوا تلاتة ممش غير نقلين فهناك مشكلة في هذه
+
+307
+00:37:04,360 --> 00:37:12,100
+المقصود ال general function إذا كانت
+
+308
+00:37:12,100 --> 00:37:17,810
+هذه النقطة singular و تحقق شخصان آخرينالشرب
+
+309
+00:37:17,810 --> 00:37:22,910
+الأولاني تخد اكس مارفا سيكس ماوري ليس Angular I
+
+310
+00:37:22,910 --> 00:37:28,250
+وضربناها في ال Q على P يعني كانوا خليها معامل Y
+
+311
+00:37:28,250 --> 00:37:33,350
+بقرر في الجدير واقعت زي الجرسام للمعادرة كله على P
+
+312
+00:37:33,350 --> 00:37:37,490
+فكل ال Q على P لو خدت نفسي بالدرمال يعني الدرمال
+
+313
+00:37:37,490 --> 00:37:41,870
+الأولالتيرم التاني كان ال x-x اذا كنت تبقى اربع
+
+314
+00:37:41,870 --> 00:37:47,490
+فيكس على P of x اذا كنت تبقى اربع فيكس على P of x
+
+315
+00:37:47,490 --> 00:37:53,590
+اذا كنت تبقى اربع فيكس على P of x اذا كنت تبقى
+
+316
+00:37:53,590 --> 00:37:55,430
+اربع فيكس على P of x اذا كنت تبقى اربع فيكس على P
+
+317
+00:37:55,430 --> 00:37:56,670
+of x اذا كنت تبقى اربع فيكس على P of x اذا كنت
+
+318
+00:37:56,670 --> 00:37:56,750
+تبقى اربع فيكس على P of x اذا كنت تبقى اربع فيكس
+
+319
+00:37:56,750 --> 00:37:58,650
+على P of x اذا كنت تبقى اربع فيكس على P of x اذا
+
+320
+00:37:58,650 --> 00:38:03,990
+كنت تبقى اربع فيكس على P of x اذا كنت تبقى اربع
+
+321
+00:38:03,990 --> 00:38:08,600
+فيكس على P of x اذا كنت تبقى اربع فيكسالكلام
+
+322
+00:38:08,600 --> 00:38:13,920
+الجنسية are regular، لكن إذا ذهبوا هذا الplan
+
+323
+00:38:13,920 --> 00:38:18,420
+يتبعهم ال conversion تقيلوا سينتها من المين عند
+
+324
+00:38:18,420 --> 00:38:22,700
+الموقع اللي علانه، يبقى هذا لو كان ال plan فيه
+
+325
+00:38:22,700 --> 00:38:28,100
+تلاتة general functions، أكثر من كل نوم يعنيبنبقى
+
+326
+00:38:28,100 --> 00:38:31,920
+الشرط الأولى اللى بيبقى زى J Singular بس الشرط
+
+327
+00:38:31,920 --> 00:38:36,840
+اللى اتيه التانية مستبدله منين بال limits فقط بغير
+
+328
+00:38:36,840 --> 00:38:43,120
+يعني لو كل التلاتة بالكتيرات حدودي لبندياش لأو لأو
+
+329
+00:38:43,120 --> 00:38:45,500
+لأو لأو لأو لأو لأو لأو لأو لأو لأو لأو لأو لأو
+
+330
+00:38:45,500 --> 00:38:46,300
+لأو لأو لأو لأو لأو لأو لأو لأو لأو لأو لأو لأو
+
+331
+00:38:46,300 --> 00:38:47,780
+لأو لأو لأو لأو لأو لأو لأو لأو لأو لأو لأو لأو
+
+332
+00:38:47,780 --> 00:38:47,780
+لأو لأو لأو لأو لأو لأو لأو لأو لأو لأو لأو لأو لأ
+
+333
+00:38:48,090 --> 00:38:54,330
+لتالة لولا لما تروح ال X لولا لتالية لما تروح ال X
+
+334
+00:38:54,330 --> 00:38:58,470
+لولا لتالية لما تروح ال X لولا لتالية لما تروح ال
+
+335
+00:38:58,470 --> 00:38:59,610
+X لولا لتالية لما تروح ال X لولا لتالية لما تروح
+
+336
+00:38:59,610 --> 00:38:59,610
+ال X لولا لتالية لما تروح ال X لولا لتالية لما
+
+337
+00:38:59,610 --> 00:39:03,110
+تروح ال X لولا لتالية لما تروح ال X لولا لتالية
+
+338
+00:39:03,110 --> 00:39:07,330
+لما تروح ال X لولا لتالية لما تروح ال X لولا
+
+339
+00:39:07,330 --> 00:39:13,330
+لتالية لما تروح ال X لولا لتالية
+
+340
+00:39:13,330 --> 00:39:13,330
+لما تروح ال X لولا لتالية لما تروح ال X لولا
+
+341
+00:39:13,330 --> 00:39:19,150
+لتالية لما تروح ال X لولا لتالية لما تروح ال Xيبقى
+
+342
+00:39:19,150 --> 00:39:23,790
+اتنين هدول مقلقوش finite يبقى اكثر بقول عنها معاها
+
+343
+00:39:23,790 --> 00:39:30,990
+regular singular point او
+
+344
+00:39:30,990 --> 00:39:34,510
+لو اتنين هدول مقلقوش
+
+345
+00:39:37,020 --> 00:39:40,600
+يبدأ النقطة اللي عندي بسميها يعني irregular
+
+346
+00:39:40,600 --> 00:39:49,360
+singular points يعني
+
+347
+00:39:49,360 --> 00:39:53,480
+لم يتحقق هذين الاثنين يبدأ بسميها عشان irregular
+
+348
+00:39:53,480 --> 00:40:00,920
+singular points يعني نقطة غير او نقطة شابه غير طيب
+
+349
+00:40:00,920 --> 00:40:05,500
+هل بيود ان انت عندنا سؤال سؤال يقول ما يعنيبيقول
+
+350
+00:40:05,500 --> 00:40:10,080
+لي ان هدول ما اتحققوش في النقطة الارجيالية، طيب
+
+351
+00:40:10,080 --> 00:40:15,160
+سؤال انا جيت على هذا الدنيا، بتقول ان انا جيت هنا،
+
+352
+00:40:15,160 --> 00:40:21,290
+انا اللي اتفرجورحت للثانية و رجيتها الله انا لدي
+
+353
+00:40:21,290 --> 00:40:28,350
+فانشغلت لان انا انا انا انا انا انا انا انا انا
+
+354
+00:40:28,350 --> 00:40:30,210
+انا انا انا انا انا انا انا انا انا انا انا انا
+
+355
+00:40:30,210 --> 00:40:31,230
+انا انا انا انا انا انا انا انا انا انا انا انا
+
+356
+00:40:31,230 --> 00:40:31,230
+انا انا انا انا انا انا انا انا انا انا انا انا
+
+357
+00:40:31,230 --> 00:40:33,850
+انا انا انا انا انا انا انا انا انا انا انا انا
+
+358
+00:40:33,850 --> 00:40:38,170
+انا انا انا انا انا انا انا انا انا انا انا انا
+
+359
+00:40:38,170 --> 00:40:38,170
+انا انا انا انا انا انا انا انا انا انا انا انا
+
+360
+00:40:38,170 --> 00:40:38,170
+انا انا انا انا انا انا انا انا انا انا انا انا
+
+361
+00:40:38,170 --> 00:40:44,290
+انا انا انا انا انا انا
+
+362
+00:40:44,290 --> 00:40:48,860
+انالكن لو قلت لولا انا لك بروح ببحث مين تتنقل لو
+
+363
+00:40:48,860 --> 00:40:53,760
+قلت لولا لا انا لك انا مش ببحث مين انا بتتنقل طيب
+
+364
+00:40:53,760 --> 00:40:58,380
+السؤال التاني ضروري اتركيه يعني مابدأوش اتدور فيه؟
+
+365
+00:40:58,380 --> 00:41:03,680
+ليس ضروري اي ورقة يوم يحطش بروح تدور افضل ماتي
+
+366
+00:41:03,680 --> 00:41:10,060
+تمثل هدف لو ذكت تمثل هدف five nine بروح ادور عليها
+
+367
+00:41:10,060 --> 00:41:17,460
+five nineلو كانت هذه in finite يعني سمعي
+
+368
+00:41:17,460 --> 00:41:21,380
+بالإنفينيتي أو قولي بالإنفينيتي بروح أدور على تاني
+
+369
+00:41:21,380 --> 00:41:25,200
+أولاده و أقرر يقولوا برايا مين و برايا خارجه هذا
+
+370
+00:41:25,200 --> 00:41:31,560
+ما سنراه من خلال الأمثلة تعدى خالية فعلا عندي سؤال
+
+371
+00:41:31,560 --> 00:41:35,340
+بدي أسأله اذا بدأت بالمعنى أسأله قبل أن أنت في
+
+372
+00:41:35,340 --> 00:41:40,480
+الامثلةالنقرة لزي دورة طويلة قراري ده المنورة
+
+373
+00:41:40,480 --> 00:41:48,820
+التجارية لكي ناخد الدنيا التجارية قراري ده المنورة
+
+374
+00:41:48,820 --> 00:41:55,980
+التجارية لكي ناخد الدنيا التجارية قراري ده المنورة
+
+375
+00:41:55,980 --> 00:42:01,360
+التجاريةأشتغل الساعة في النتائج اللى قبلك وليه
+
+376
+00:42:01,360 --> 00:42:04,320
+نفسك وانت تبقى على ال single point فانا قاعد اللى
+
+377
+00:42:04,320 --> 00:42:07,820
+هو complex اللى بيهرمليش complex وضعيه اللى ما
+
+378
+00:42:07,820 --> 00:42:11,400
+تطلع تطلع اللى بأخد ال limit و ال limited to the
+
+379
+00:42:11,400 --> 00:42:15,200
+finite بيخبر الله أن أخبر هل هي complex او لعدة
+
+380
+00:42:15,200 --> 00:42:18,420
+اللى بيأخد عنده ال limit هل هو complex ولا limited
+
+381
+00:42:19,970 --> 00:42:24,890
+طبعا زي ما يفضلكم هاكم دورية أهل الوسام و فريق أهل
+
+382
+00:42:24,890 --> 00:42:28,750
+الوسام ماشي عطيكوا فعالة evaluation منهم في
+
+383
+00:42:28,750 --> 00:42:31,470
+الarchitectural context و من أخر سنة في المملكة
+
+384
+00:42:31,470 --> 00:42:34,350
+العربية السعودية بس كده بالمفهوم اللي اذا كده
+
+385
+00:42:34,350 --> 00:42:38,110
+المعناه يكفي بس المعاناة الأقلومية تانية و معاناة
+
+386
+00:42:38,110 --> 00:42:42,170
+ميلاد مافي واي واي واي واي واي واي واي واي واي واي
+
+387
+00:42:42,170 --> 00:42:42,250
+واي واي واي واي واي واي واي واي واي واي واي واي
+
+388
+00:42:42,250 --> 00:42:45,120
+واي واي واي واي واي واي واي واي وايworld mark ..
+
+389
+00:42:45,120 --> 00:42:49,020
+او .. او .. او .. او .. او .. او .. او .. او .. او
+
+390
+00:42:49,020 --> 00:42:49,620
+.. او .. او .. او .. او .. او .. او .. او .. او ..
+
+391
+00:42:49,620 --> 00:42:50,180
+او .. او .. او .. او .. او .. او .. او .. او .. او
+
+392
+00:42:50,180 --> 00:42:55,040
+.. او .. او .. او .. او .. او .. او .. او .. او ..
+
+393
+00:42:55,040 --> 00:42:58,060
+او .. او .. او .. او .. او .. او .. او .. او .. او
+
+394
+00:42:58,060 --> 00:42:58,560
+.. او .. او .. او .. او .. او .. او .. او .. او ..
+
+395
+00:42:58,560 --> 00:42:59,580
+او .. او .. او .. او .. او .. او .. او .. او .. او
+
+396
+00:42:59,580 --> 00:43:00,500
+.. او .. او .. او .. او .. او .. او .. او .. او ..
+
+397
+00:43:00,500 --> 00:43:09,340
+او .. او .. او .. او .. او
+
+398
+00:43:09,340 --> 00:43:13,500
+..
+
+399
+00:43:13,500 --> 00:43:18,290
+اوزي ما اشوف في الرقم يبقى مندي اشوف همين من
+
+400
+00:43:18,290 --> 00:43:22,630
+الموقعات هذه تبقى regular singular point ومين ا
+
+401
+00:43:22,630 --> 00:43:27,790
+regular singular point ورقمي او مجلة يبقى السؤال
+
+402
+00:43:27,790 --> 00:43:32,290
+بس مندي اجيب ال singular واشوف هل هي regular ومع
+
+403
+00:43:32,290 --> 00:43:39,300
+كرجل يعطينا المسألة دلوقتيبقى هذه الـP ومتها باجيب
+
+404
+00:43:39,300 --> 00:43:44,980
+الـC ونغميرها Point إذا أنا لو لدى بلد ممكن واحد
+
+405
+00:43:44,980 --> 00:43:50,340
+ماترستيكس تجيب تجيب تجيب تجيب تجيب تجيب تجيب تجيب
+
+406
+00:43:50,340 --> 00:44:04,460
+تجيب تجيب تجيب تجيب تجيب تجيب تجيب
+
+407
+00:44:08,450 --> 00:44:16,770
+ممكن و انت ايش او سالب واحد لو كانت واحد تصيبها
+
+408
+00:44:16,770 --> 00:44:22,450
+لزيره لو كانت سالب واحد تصيبها لزيره يبقى هذه بدها
+
+409
+00:44:22,450 --> 00:44:30,590
+تساوي زيره only اكس يساوي سالب واحد and اكس يساوي
+
+410
+00:44:30,590 --> 00:44:31,410
+واحد
+
+411
+00:44:33,930 --> 00:44:38,090
+يبقى جفت ال singular point بقى يبقى كل عدد دول
+
+412
+00:44:38,090 --> 00:44:43,270
+اللي عندي هتقول بأنهم polynomial كانت إيراد حدود
+
+413
+00:44:43,270 --> 00:44:49,270
+يبقى الآن ال P of X اللي واحد ماطس X تربيع لكل
+
+414
+00:44:49,270 --> 00:44:55,030
+تربيع و P of X اللي بدأت ساوي X لواحد
+
+415
+00:45:06,010 --> 00:45:16,710
+يبقى أسهل من نقطة الأولى ومن نقطة الثانية من خلال
+
+416
+00:45:16,710 --> 00:45:20,350
+المعاملات الخاصة بالإفريقيا وبيفرق والواحد
+
+417
+00:45:28,370 --> 00:45:32,570
+النقطة الأولى اللى تبقى موجودة في الجانب الثاني
+
+418
+00:45:34,610 --> 00:45:39,950
+بتروح أحصل النهاية الأولى وشوف هل هي قطع يدعى
+
+419
+00:45:39,950 --> 00:45:43,170
+واحدة واحدة واحدة واحدة واحدة واحدة واحدة واحدة
+
+420
+00:45:43,170 --> 00:45:43,390
+واحدة واحدة واحدة واحدة واحدة واحدة واحدة واحدة
+
+421
+00:45:43,390 --> 00:45:47,450
+واحدة واحدة واحدة واحدة واحدة واحدة واحدة واحدة
+
+422
+00:45:47,450 --> 00:45:49,850
+واحدة واحدة واحدة واحدة واحدة واحدة واحدة واحدة
+
+423
+00:45:49,850 --> 00:45:49,930
+واحدة واحدة واحدة واحدة واحدة واحدة واحدة واحدة
+
+424
+00:45:49,930 --> 00:45:53,630
+واحدة واحدة واحدة واحدة واحدة واحدة واحدة واحدة
+
+425
+00:45:53,630 --> 00:45:54,590
+واحدة واحدة واحدة واحدة واحدة واحدة واحدة واحدة
+
+426
+00:45:54,590 --> 00:45:57,370
+واحدة واحدة واحدة واحدة واحدة واحدة واحدة واحدة
+
+427
+00:45:57,370 --> 00:46:02,370
+واحدة
+
+428
+00:46:02,370 --> 00:46:04,030
+واحدة
+
+429
+00:46:12,000 --> 00:46:13,960
+الشكل التالي هو
+
+430
+00:46:20,240 --> 00:46:26,680
+-x في y' مجسم عالمهم على هذا المفضل عشان اتحللوا
+
+431
+00:46:26,680 --> 00:46:28,660
+بالمعرفة مافي حاجة ان اتحللوا بالمعرفة مافي حاجة
+
+432
+00:46:28,660 --> 00:46:29,420
+ان اتحللوا بالمعرفة مافي حاجة ان اتحللوا بالمعرفة
+
+433
+00:46:29,420 --> 00:46:29,520
+مافي حاجة ان اتحللوا بالمعرفة مافي حاجة ان اتحللوا
+
+434
+00:46:29,520 --> 00:46:29,760
+بالمعرفة مافي حاجة ان اتحللوا بالمعرفة مافي حاجة
+
+435
+00:46:29,760 --> 00:46:30,680
+ان اتحللوا بالمعرفة مافي حاجة ان اتحللوا بالمعرفة
+
+436
+00:46:30,680 --> 00:46:35,900
+مافي حاجة ان اتحللوا بالمعرفة مافي حاجة ان اتحللوا
+
+437
+00:46:35,900 --> 00:46:48,080
+بالمعرفة مافي حاجة ان اتحللوا بالمعرفة مافي حاجة
+
+438
+00:46:48,080 --> 00:46:48,820
+ان
+
+439
+00:46:57,610 --> 00:47:03,130
+أبقى مرتبط في مقاطع المقاطع يجب أن نختصر يجب أن
+
+440
+00:47:03,130 --> 00:47:04,050
+نختصر يجب أن نختصر يجب أن نختصر يجب أن نختصر يجب
+
+441
+00:47:04,050 --> 00:47:04,110
+أن نختصر يجب أن نختصر يجب أن نختصر يجب أن نختصر
+
+442
+00:47:04,110 --> 00:47:06,750
+يجب أن نختصر يجب أن نختصر يجب أن نختصر يجب أن
+
+443
+00:47:06,750 --> 00:47:08,930
+نختصر يجب أن نختصر يجب أن نختصر يجب أن نختصر يجب
+
+444
+00:47:08,930 --> 00:47:09,590
+أن نختصر يجب أن نختصر يجب أن نختصر يجب أن نختصر
+
+445
+00:47:09,590 --> 00:47:12,950
+يجب أن نختصر يجب أن نختصر يجب
+
+446
+00:47:12,950 --> 00:47:25,010
+أن نختصر يجب أن نختصر يجب أن نختصر يجب
+
+447
+00:47:25,010 --> 00:47:31,590
+أن نختصجنبها زائد واحد على واحد ماقص اكسج كل
+
+448
+00:47:31,590 --> 00:47:36,790
+ثانوية في واحد زائد اتش كله في وايمين بساوية درجة
+
+449
+00:47:36,790 --> 00:47:45,690
+الآن نذهب نبحث كل مقفل انها تاني مقفل تاني بعد ما
+
+450
+00:47:45,690 --> 00:47:50,590
+كتبت المعاملة بالصيغة الجديدة وبالتالي جيب جناش ال
+
+451
+00:47:50,590 --> 00:47:54,550
+Q على P وجيب جناش ال R على P
+
+452
+00:48:02,320 --> 00:48:08,240
+إذا كنت تجي للمقبض أولا بتاخد limit لما ال X تذهب
+
+453
+00:48:08,240 --> 00:48:17,080
+من واحد أو قبل أن تكون at X يساوي 1 لما
+
+454
+00:48:17,080 --> 00:48:22,460
+تذهب من واحد لساوي واحد
+
+455
+00:48:29,480 --> 00:48:39,400
+لمن؟ لمن Q of X على P of X يساوي limit لما ال X
+
+456
+00:48:39,400 --> 00:48:45,360
+بدأ تروح ل-1 لل X ذالك واحد فيه، ليه Q على P
+
+457
+00:48:45,360 --> 00:48:49,760
+جانزة، فيه مين؟ هذه النتيجة ساعة ما اختصرنا
+
+458
+00:48:49,760 --> 00:48:59,420
+الاقتصادات اللي مطلوبة، يبقى هذا Xعلى واحد ناقص x
+
+459
+00:48:59,420 --> 00:49:07,600
+في واحد زائد x الكل دبي طبعا طبعا طبعا طبعا طبعا
+
+460
+00:49:07,600 --> 00:49:11,900
+طبعا طبعا طبعا طبعا طبعا طبعا طبعا طبعا طبعا طبعا
+
+461
+00:49:11,900 --> 00:49:12,960
+طبعا طبعا طبعا طبعا طبعا طبعا طبعا طبعا طبعا طبعا
+
+462
+00:49:12,960 --> 00:49:15,640
+طبعا طبعا طبعا طبعا طبعا طبعا طبعا طبعا طبعا طبعا
+
+463
+00:49:15,640 --> 00:49:19,440
+طبعا طبعا طبعا طبعا طبعا طبعا
+
+464
+00:49:27,380 --> 00:49:32,680
+طبعا علينا أن ندخل X و نذهب إلى أين؟ X سالب واحد
+
+465
+00:49:32,680 --> 00:49:37,800
+يبقى هذي سالب واحد على هذي نحط مكانها سالب واحد
+
+466
+00:49:37,800 --> 00:49:43,600
+عشان الصين ايه اتنين؟ هذي سالب واحد تصير جداش سين
+
+467
+00:49:43,600 --> 00:49:48,980
+و يبقى النتيجة جداش سالب الفيليفي أكمل؟ نعم اتنين
+
+468
+00:49:48,980 --> 00:49:53,740
+خلاص اللي عم ادخل اخر مرة X فاي نايم يعني هذي هنا
+
+469
+00:49:53,740 --> 00:50:01,650
+فاي نايميبقى بناء عليه رقم X يساوي واحد منها
+
+470
+00:50:01,650 --> 00:50:09,230
+regular singular point يبقى لنا الساعة Z point
+
+471
+00:50:09,230 --> 00:50:19,650
+اللي هو X يساوي سالف واحد is an irregular singular
+
+472
+00:50:19,650 --> 00:50:22,970
+point
+
+473
+00:50:22,970 --> 00:50:33,690
+بس لو طلعت finiteبروح على مقطع تاني نيجي اذا X
+
+474
+00:50:33,690 --> 00:50:41,010
+يساوي واحد يبقى مقطع تاني يبقى بناخد نفس ال limit
+
+475
+00:50:41,010 --> 00:50:49,170
+اي limit بس ال X ولدك واحد للواحد لمن؟ لل X ماقص
+
+476
+00:50:49,170 --> 00:50:49,830
+واحد
+
+477
+00:50:52,650 --> 00:51:00,150
+على P of X على P of X على P of X على P of X على P
+
+478
+00:51:00,150 --> 00:51:08,550
+of X على P of X على P of X على
+
+479
+00:51:08,550 --> 00:51:13,330
+P of
+
+480
+00:51:13,330 --> 00:51:17,630
+Xحتى لو قلت تحتاج فايلة خلاص الديناميكالية دي هي
+
+481
+00:51:17,630 --> 00:51:21,750
+حسنة إذا احنا انتقلنا إلى مين لن نفقد دنيا السن
+
+482
+00:51:21,750 --> 00:51:25,610
+برنامج الأولى وانتقلنا إلى مين لن نفقد دنيا يعني
+
+483
+00:51:25,610 --> 00:51:31,730
+في هذه ال level لما ال x بدأ تروح للواحد لل x ماتس
+
+484
+00:51:31,730 --> 00:51:38,320
+واحد فيهلكي و اللي طلعناها فوق هي همت ريّراتش X
+
+485
+00:51:38,320 --> 00:51:46,160
+على واحد مائص X تبين في واحد زايد X الكل دربي يزاد
+
+486
+00:51:47,780 --> 00:51:53,060
+هذه x ماكس راحت هذه واحد ماكس نختار واحد من هذه
+
+487
+00:51:53,060 --> 00:51:55,980
+نختار واحد من هذه نختار واحد من هذه نختار واحد من
+
+488
+00:51:55,980 --> 00:52:02,460
+هذه نختار
+
+489
+00:52:02,460 --> 00:52:06,520
+واحد من هذه نختار
+
+490
+00:52:06,520 --> 00:52:12,620
+واحد من هذه
+
+491
+00:52:13,280 --> 00:52:16,620
+من هنا يابتخد شبكت سالي بعرف المشترك، ومن هنا
+
+492
+00:52:16,620 --> 00:52:23,260
+يابتخد شبكت سالي بعرف المشترك، ومن هنا
+
+493
+00:52:23,260 --> 00:52:23,720
+يابتخد شبكت سالي بعرف المشترك، ومن هنا يابتخد شبكت
+
+494
+00:52:23,720 --> 00:52:23,720
+سالي بعرف المشترك، ومن هنا يابتخد شبكت سالي بعرف
+
+495
+00:52:23,720 --> 00:52:23,720
+المشترك، ومن هنا يابتخد شبكت سالي بعرف المشترك،
+
+496
+00:52:23,720 --> 00:52:26,340
+ومن هنا يابتخد شبكت سالي بعرف المشترك، ومن هنا
+
+497
+00:52:26,340 --> 00:52:29,160
+يابتخد شبكت سالي بعرف المشترك، ومن هنا يابتخد شبكت
+
+498
+00:52:29,160 --> 00:52:34,440
+سالي بعرف المشترك، ومن هنا يابتخد شبكت سالي بعرف
+
+499
+00:52:34,440 --> 00:52:39,150
+المشترك، ومن هنا يابعلى واحد زي واحد تربيه اربع
+
+500
+00:52:39,150 --> 00:52:43,370
+يبقى سنة واربع فاين اين وما زاكن فاين اعيد فاين
+
+501
+00:52:43,370 --> 00:52:45,830
+اعيد فاين اعيد فاين اعيد فاين اعيد فاين اعيد فاين
+
+502
+00:52:45,830 --> 00:52:46,950
+اعيد فاين اعيد فاين اعيد فاين اعيد فاين اعيد فاين
+
+503
+00:52:46,950 --> 00:52:48,710
+اعيد فاين اعيد فاين اعيد فاين اعيد فاين اعيد فاين
+
+504
+00:52:48,710 --> 00:52:52,590
+اعيد فاين اعيد فاين اعيد فاين اعيد فاين اعيد فاين
+
+505
+00:52:52,590 --> 00:52:52,910
+اعيد فاين اعيد فاين اعيد فاين اعيد فاين اعيد فاين
+
+506
+00:52:52,910 --> 00:53:01,470
+اعيد فاين اعيد فاين اعيد فاين اعيد فاين اعيد فا
+
+507
+00:53:04,680 --> 00:53:09,960
+يبقى هذا الكلام متساوي ال limit لما ال X بيروح لل
+
+508
+00:53:09,960 --> 00:53:19,380
+واحد لل X ناقص واحد كل ربيع انا في هجم يبقى واحد
+
+509
+00:53:19,380 --> 00:53:25,940
+ناقص X كل ربيع في واحد زي ال X يبقى واحد او هذه
+
+510
+00:53:25,940 --> 00:53:30,960
+دوري على واحد ناقص X كل ذا ربيع
+
+511
+00:53:33,690 --> 00:53:40,090
+زائد اكس واحد زائد اكس شرايف دي راديو غالب
+
+512
+00:53:46,280 --> 00:53:52,400
+بتروح يعني هذه كأنها مضبوط تماما limit لما ال x
+
+513
+00:53:52,400 --> 00:53:58,120
+تروح للواحد لكس ناقص واحد كل تربيع على x ناقص واحد
+
+514
+00:53:58,120 --> 00:54:04,020
+كل تربيع في واحد ذاتكس بتروح هذه معناه دي بس ال
+
+515
+00:54:04,020 --> 00:54:10,280
+limit لما ال text تروح للواحدلما ال text لفوق ال
+
+516
+00:54:10,280 --> 00:54:16,560
+واحد نميه ل واحد على واحد زاد اكس من شركة ده مصف ف
+
+517
+00:54:16,560 --> 00:54:23,200
+اي نايت كده لف يرجع ف اي نايت يرجع لان على النقطة
+
+518
+00:54:23,200 --> 00:54:29,620
+لان هذه الساعة ال text لساعة واحد is a regular
+
+519
+00:54:29,620 --> 00:54:32,360
+singular point
+
+520
+00:54:37,870 --> 00:54:41,970
+يعني كان نفس المثال يبقى بعض ال singular و بعض ال
+
+521
+00:54:41,970 --> 00:54:48,570
+regular و بعض ال irregular ممكن كلهم regular و
+
+522
+00:54:48,570 --> 00:54:53,830
+ممكن كلهم irregular كذلك يعني كل احتمالات و يبدأ
+
+523
+00:54:53,830 --> 00:54:59,490
+كل مسألة علاقة طيب هذا هو المثال الأول لنروح الآخر
+
+524
+00:54:59,490 --> 00:55:01,070
+المثال التاني
+
+525
+00:55:15,820 --> 00:55:26,480
+X درمية زي 19 Y درمية فعلا ماتس تلاتة سيكس Y فاي
+
+526
+00:55:26,480 --> 00:55:35,400
+زي واحد ناقص X كله في الواحد يبقى ساومين بساوي زيت
+
+527
+00:55:41,300 --> 00:55:48,380
+بدا البداية قمت باستخدام Q of X بإنسان X مبين
+
+528
+00:55:48,380 --> 00:55:59,540
+لإتصال و قمت باستخدام Q of X مافس تلاتة Xكبت ال R
+
+529
+00:55:59,540 --> 00:56:04,880
+of X بالسنونين واحد ما فسكت، شو رأيت الدلالد
+
+530
+00:56:04,880 --> 00:56:13,480
+هالول؟ هالول نوميانز، كده هالول R نوميانز
+
+531
+00:56:14,210 --> 00:56:17,930
+لو كما رأيت في المقصد الحقيقي انا اتاب عليها كده
+
+532
+00:56:17,930 --> 00:56:25,990
+الـ S يتزايد ال E of X يتزايد X أكبر زي 9 لو
+
+533
+00:56:25,990 --> 00:56:33,850
+سويتها من 0 تجهش المسئولة عندنا ال X أكبر يسوى 9
+
+534
+00:56:33,850 --> 00:56:36,230
+للجالكسي الجدد
+
+535
+00:56:55,450 --> 00:57:01,590
+السؤال اللي جيبناه
+
+536
+00:57:01,590 --> 00:57:02,470
+هو الطعام
+
+537
+00:57:06,900 --> 00:57:10,180
+مدى هؤلاء البرولوجيين اللي قطعوا دي يرجعوا يدخلوا
+
+538
+00:57:10,180 --> 00:57:15,260
+في نفس التحكيك اللي اتبعته قبل قليل يرجعوا تانية
+
+539
+00:57:15,260 --> 00:57:20,320
+ويقولوا هؤلاء اللي اكتشفوا يقولوا هؤلاء اللي لديهم
+
+540
+00:57:20,320 --> 00:57:29,340
+5 Singular Points يرجعوا
+
+541
+00:57:29,340 --> 00:57:31,500
+هؤلاء ثم Singular Points
+
+542
+00:57:37,730 --> 00:57:40,650
+نقسم؟ نقسم يارب
+
+543
+00:57:54,070 --> 00:58:05,330
+YWπ-3X عليه يبقى
+
+544
+00:58:05,330 --> 00:58:17,700
+X ناقص تلاتة Iزائد تلاتة I في Y prime زائد واحد
+
+545
+00:58:17,700 --> 00:58:26,640
+نقص X على X نقص تلاتة I في X زائد تلاتة I في Y كله
+
+546
+00:58:26,640 --> 00:58:31,920
+بيساوي Zero محتاج
+
+547
+00:58:31,920 --> 00:58:35,420
+ليه؟ هذا الكلام
+
+548
+00:58:37,750 --> 00:58:47,470
+x² زائد 9 على الساوية x ناقص 3i في x زائد 3i تعالى
+
+549
+00:58:47,470 --> 00:58:52,630
+نشوف لو ضرفت هدول في بعض فعلا بتطلع هذا ولا لأ انا
+
+550
+00:58:52,630 --> 00:58:56,310
+اخبرتك ان الفرق بينهم مربعين بس بكمية تخيله بيبقى
+
+551
+00:58:56,310 --> 00:58:58,690
+وليس بكمية حقيقية
+
+552
+00:59:06,080 --> 00:59:12,980
+3XI ومن السالم 3XI براهم مع السلمة والهالي بها
+
+553
+00:59:12,980 --> 00:59:19,400
+نسالم تلاتة من تلاتة نسالم تسعة وI بالعالي نسالم
+
+554
+00:59:19,400 --> 00:59:24,860
+واحد نسالم ثالث نسالم عشر وجرم تسعة بالفور نسالم
+
+555
+00:59:24,860 --> 00:59:29,140
+تسعة وعشر وجرم تسعة بالفور نسالم تسعة وعشر وجرم
+
+556
+00:59:29,530 --> 00:59:33,790
+يعني يا بنات جاني يفكرني لو حللتك من أول من هنا و
+
+557
+00:59:33,790 --> 00:59:37,890
+قلتك تساوي زي اذا و لا مذكرنيها تبقى طيابة و كده
+
+558
+00:59:37,890 --> 00:59:41,990
+معاكي ان انا ماحلل عليك فانت ماحلل على الله يبقى
+
+559
+00:59:41,990 --> 00:59:48,090
+الان انا بدادي اقول المقطة الأولة بيبقى بدادي اقول
+
+560
+00:59:48,090 --> 00:59:56,990
+ان اتن اكس يسوى سن تلاتةروح تاخد ال limit لما ال x
+
+561
+00:59:56,990 --> 01:00:05,310
+كذا طول بزايد ثلاثة I ان ال x ماقص ثلاثة I وزايد
+
+562
+01:00:05,310 --> 01:00:11,790
+ثلاثة I بالصغير وماقص ماقص ثلاثة I زايد ثلاثة I ان
+
+563
+01:00:11,790 --> 01:00:19,490
+ال Q of X على ال P of Xيساوي ال limit لما ال x ذهب
+
+564
+01:00:19,490 --> 01:00:26,690
+يسالب تلاتة I لما ال x ذهب يسالب تلاتة I لكي و على
+
+565
+01:00:26,690 --> 01:00:34,790
+P لايه عيزة يبقى هي اللي هو سالب تلاتة X مقسمة على
+
+566
+01:00:34,790 --> 01:00:44,070
+مين على X مقسمة على I في X زائد تلاتة Iطبعاً ،
+
+567
+01:00:44,070 --> 01:00:48,750
+نروح هذا term مع ال term اللي عندها يرجعنا
+
+568
+01:00:48,750 --> 01:00:54,530
+بالمسألة إلى ال limit لما ال X بده يروح من ثالث
+
+569
+01:00:54,530 --> 01:01:04,280
+تلاتة R لثالث تلاتة X على X ناقص تلاتة Rأول خطوة
+
+570
+01:01:04,280 --> 01:01:09,560
+في إيجاد ال limit هي التعويض المباشر يبقى هاي ماقص
+
+571
+01:01:09,560 --> 01:01:17,380
+تلاتة برا والعكس بتروح نوير لسالف تلاتة I على سالف
+
+572
+01:01:17,380 --> 01:01:30,580
+تلاتة I سالف تلاتة I طيب هل تساوي تسعة I على سالف
+
+573
+01:01:30,580 --> 01:01:31,100
+I
+
+574
+01:01:35,440 --> 01:01:41,620
+I مع I و سنة مع سنة و نصف على ستة و نزلت تلاتة على
+
+575
+01:01:41,620 --> 01:01:47,500
+اتنين تبقى صعب النتيجة تلاتة على اتنين تلاتة على
+
+576
+01:01:47,500 --> 01:01:49,820
+اتنين ماله أسبوع يناير
+
+577
+01:01:52,650 --> 01:01:57,030
+تسعة تسعة تسعة تسعة تسعة تسعة تسعة تسعة تسعة تسعة
+
+578
+01:01:57,030 --> 01:02:04,050
+تسعة تسعة تسعة تسعة تسعة تسعة تسعة تسعة تسعة تسعة
+
+579
+01:02:04,050 --> 01:02:04,050
+تسعة تسعة تسعة تسعة تسعة تسعة تسعة تسعة تسعة تسعة
+
+580
+01:02:04,050 --> 01:02:06,050
+تسعة تسعة تسعة تسعة تسعة تسعة تسعة تسعة تسعة تسعة
+
+581
+01:02:06,050 --> 01:02:07,870
+تسعة تسعة تسعة تسعة تسعة تسعة تسعة تسعة تسعة تسعة
+
+582
+01:02:07,870 --> 01:02:07,870
+تسعة تسعة تسعة تسعة تسعة تسعة تسعة تسعة تسعة تسعة
+
+583
+01:02:07,870 --> 01:02:11,770
+تسعة تسعة تسعة تسعة تسعة
+
+584
+01:02:11,770 --> 01:02:16,630
+تسعة تسعة تسعة تسعة تسعة تسعة تسعة تسعة
+
+585
+01:02:16,630 --> 01:02:21,950
+تسعة تس
+
+586
+01:02:22,000 --> 01:02:30,260
+اها لما ال X بدها تروح لوين لسان التلاتة I لوين من
+
+587
+01:02:30,260 --> 01:02:41,740
+ال X زي التلاتة I من R و F على ال E و B القرآن
+
+588
+01:02:41,740 --> 01:02:48,240
+الترميز مظهر بحيث يبقى هذا الكلام بالسيابين limit
+
+589
+01:02:48,240 --> 01:02:56,670
+لما ال X بدها تروحبزالد تلاتة I من X زالد تلاتة I
+
+590
+01:02:56,670 --> 01:03:04,430
+لكل جميع ال R of X والواحد من R of X هي واحد ماقص
+
+591
+01:03:04,430 --> 01:03:13,210
+X واحد ماقص X كله مكسوما على X ماقص تلاتة I ب X
+
+592
+01:03:13,210 --> 01:03:21,140
+زالد تلاتة I ويزدادطبعاً في اختصارات دورس هذا مع
+
+593
+01:03:21,140 --> 01:03:26,840
+مين مع دورس اللي عنده هذا يبقى مصير ال limit لما
+
+594
+01:03:26,840 --> 01:03:35,500
+ال x بدأ تقوه لثالث تلاتة I لل x زائد تلاتة I تمين
+
+595
+01:03:35,500 --> 01:03:47,060
+في واحد ناقص x على مين على x ناقص تلاتة Iبتشيل كل
+
+596
+01:03:47,060 --> 01:03:53,040
+اسم حفظتها سالب ثلاثة يبقى
+
+597
+01:03:53,040 --> 01:04:02,220
+هذا الكلام Zero في واحد سالب ثلاثة I عالمي على
+
+598
+01:04:02,220 --> 01:04:06,700
+سالب ثلاثة I سالب ثلاثة يبقى نفسي قدام
+
+599
+01:04:12,020 --> 01:04:15,200
+هل you find that you turn your coin right before
+
+600
+01:04:15,200 --> 01:04:36,060
+you have it, or that you have a singular coin؟
+
+601
+01:04:36,060 --> 01:04:44,370
+هل you really serve the coin؟X يساوي ثانية ثلاثة I
+
+602
+01:04:44,370 --> 01:04:47,870
+هو مجلد عادى
+
+603
+01:05:00,900 --> 01:05:09,640
+عشان نعمل نقطة تانية اكس بساعدة اش فانا هاعد اذا
+
+604
+01:05:09,640 --> 01:05:13,920
+روح نفسي لنقطة اولى يجب ان انا اعمل limit لما
+
+605
+01:05:13,920 --> 01:05:18,080
+الاكس بدأ تروح ليه ثلاثة اعلى
+
+606
+01:05:29,940 --> 01:05:36,700
+يبقى عند نقطة x0 يسبب تلاتة I يبقى حتى x ناطس
+
+607
+01:05:36,700 --> 01:05:39,680
+تلاتة I تميل
+
+608
+01:05:42,200 --> 01:05:48,400
+على مين؟ على capital Q of X يبقى limit لما ال X
+
+609
+01:05:48,400 --> 01:05:55,940
+تبقى واحدة تلاتة I لل X ماقص تلاتة I من Q على P
+
+610
+01:05:55,940 --> 01:06:05,490
+وين راحت ال Q على P دي غالب؟ وثالث تلاتة Xثالث
+
+611
+01:06:05,490 --> 01:06:14,870
+تلاتة X على X مخص ثلاثة I في X زائد تلاتة I طبعا
+
+612
+01:06:14,870 --> 01:06:20,510
+هاني وهاني مع السلامة يقلق المسألة إلى ال limit
+
+613
+01:06:20,510 --> 01:06:30,130
+لما ال X تدخل في تلاتة I لثالث تلاتة X على X زائد
+
+614
+01:06:30,130 --> 01:06:34,450
+تلاتة I النتيجة
+
+615
+01:06:35,750 --> 01:06:44,970
+ثالث تلاتة في تلاتة I على تلاتة I زائد تلاتة I
+
+616
+01:06:44,970 --> 01:06:52,210
+يبقى ناقص تسعة I على ستة I كمان ناقص تلاتة على
+
+617
+01:06:52,210 --> 01:06:58,650
+اتنين يبقى هماله I9وده الـ finite إذا بدنا نروح
+
+618
+01:06:58,650 --> 01:07:04,750
+لمين؟ للشرق الأخير لإننا بدنا نروح لاخد limit لما
+
+619
+01:07:04,750 --> 01:07:11,830
+ال X بده نروح لتلاتة I لل X ماتس تلاتة I والترمية
+
+620
+01:07:11,830 --> 01:07:19,850
+في A of Xأنا كنت ال E of X هو يساوي limit لما ال X
+
+621
+01:07:19,850 --> 01:07:27,590
+يروح ليه تلاتة I لل X ناقص تلاتة I التقرير ليه ال
+
+622
+01:07:27,590 --> 01:07:35,450
+R أو ال R على E اللي عبارة عن الواحد ناقص Xكله
+
+623
+01:07:35,450 --> 01:07:45,950
+مقسومة على x-3i ت x زائد 3i لأن هذا الكلام يجب أن
+
+624
+01:07:45,950 --> 01:07:49,970
+يستوي ال limit لما ال x بدل واحد يكون تلاتة ايه
+
+625
+01:07:49,970 --> 01:07:55,470
+طبعا هناك اختصار بين المصدر والمقام افضل ان اجده
+
+626
+01:07:55,470 --> 01:08:02,190
+اكتر اكتر اكتر اكتر اكتر
+
+627
+01:08:02,190 --> 01:08:03,110
+اكتر
+
+628
+01:08:13,020 --> 01:08:17,240
+عندك تلاتة آي ناقص تلاتة آي مقدر
+
+629
+01:08:22,500 --> 01:08:30,500
+على ثلاثة I زي ثلاثة I هو يسمي الدرج Zero كذلك هذه
+
+630
+01:08:30,500 --> 01:08:38,400
+ملحقة و I might يبقى هنا ساعة HX يسوي ثلاثة I
+
+631
+01:08:38,400 --> 01:08:44,300
+ملحقة HX ريجيونات
+
+632
+01:08:54,560 --> 01:08:58,640
+طبعا هذه المثالة النقطتين اللي هي انت تنتهي من
+
+633
+01:08:58,640 --> 01:09:02,340
+regular singular point لكن السؤال اللي بيعملوه إيش
+
+634
+01:09:02,340 --> 01:09:06,960
+يطلع regular وإيش يطلع irregular singular point
+
+635
+01:09:06,960 --> 01:09:11,460
+لكن السؤالين اللي يسمون هدولالوعاملات كانوا
+
+636
+01:09:11,460 --> 01:09:17,660
+polynomial لكن الفرق بينهما أن النقط في حالة
+
+637
+01:09:17,660 --> 01:09:21,700
+الأولى كانوا real وإن النقط في الحالة التانية
+
+638
+01:09:21,700 --> 01:09:28,240
+كانوا complex يرجع هذه الفرق من real لـ real طيب
+
+639
+01:09:28,240 --> 01:09:33,500
+روحنا لمثال الثالث المثال
+
+640
+01:09:33,500 --> 01:09:43,440
+الثالث يقول بعندك الـ x والـ y بقية Pi زائد P plus
+
+641
+01:09:43,440 --> 01:09:51,920
+x والـ y بقية Pi زائد تلاتة قصية x بالـ y بتساوية
+
+642
+01:09:51,920 --> 01:09:52,500
+2
+
+643
+01:10:12,080 --> 01:10:18,180
+أولونهم يعني ليسوا كثيرات كلهم يبقى عيب ان ال Q of
+
+644
+01:10:18,180 --> 01:10:25,080
+X بقى ال E of X عند ال R of X يستخدم التلاتة
+
+645
+01:10:25,080 --> 01:10:30,000
+أوصاها ال X R Marks
+
+646
+01:10:34,260 --> 01:10:39,080
+درجة هذه تجد تحكي راتروني بهدولة كمان ال general
+
+647
+01:10:39,080 --> 01:10:43,360
+functions اللي موجودة في الحالة الأولى إن كانت
+
+648
+01:10:43,360 --> 01:10:47,800
+موجودة عندنا وده فهذه الحالة الموجودة هنا كنت أرجع
+
+649
+01:10:47,800 --> 01:10:51,500
+لمين للprfix
+
+650
+01:10:51,500 --> 01:10:58,620
+الprfix اللي يتسمى جديد يتسمى Zero الfix يتسمى
+
+651
+01:10:58,620 --> 01:11:04,570
+Zero هذه فقطاللي بيبقى only singular point مافيش
+
+652
+01:11:04,570 --> 01:11:13,370
+ريحة يبقى هذي is the only singular point
+
+653
+01:11:16,770 --> 01:11:20,330
+why؟ جيبنا ال singular point إذا بداني لل
+
+654
+01:11:20,330 --> 01:11:26,270
+completion الأول وشوف هل التقعي لأ لأ لأ لأ لأ لأ
+
+655
+01:11:26,270 --> 01:11:32,190
+لأ لأ لأ لأ لأ لأ لأ لأ لأ لأ لأ لأ
+
+656
+01:11:32,290 --> 01:11:36,590
+اليقول معانا لرقم واحد الشكل التالي the
+
+657
+01:11:36,590 --> 01:11:44,590
+differential equation is written as المفتوح بالشكل
+
+658
+01:11:44,590 --> 01:11:53,870
+التالي y w prime زائد e وال6 على x ال y prime زائد
+
+659
+01:11:53,870 --> 01:12:03,500
+ثلاث قصير x على xمنها في الـ y بدها الـ 7 من الـ z
+
+660
+01:12:03,500 --> 01:12:10,320
+لذلك إذا أخد ال x مقفل ال x0 بيكون limit of the
+
+661
+01:12:10,320 --> 01:12:17,700
+value of x مقفل ال x0 تمامًا في u of x على capital
+
+662
+01:12:17,700 --> 01:12:24,260
+P of x y و ساعة ال x0 بيدخل لقناع 0 لإن ال x0
+
+663
+01:12:24,260 --> 01:12:32,010
+بيبقى 0 لما نشتغل في دمية xيجي ال EO6 على P EO6
+
+664
+01:12:32,010 --> 01:12:38,990
+على X EO6 على P EO6 على X EO6
+
+665
+01:12:38,990 --> 01:12:52,730
+على P EO6 على X EO6 على P EO6
+
+666
+01:12:52,730 --> 01:12:53,230
+على P EO6 على P EO6 على P EO6 على P EO6 على P EO6
+
+667
+01:12:53,230 --> 01:12:53,230
+على P EO6 على P EO6 على P EO6 على P EO6 على P EO6
+
+668
+01:12:53,230 --> 01:12:53,230
+على P EO6 على P EO6 على P EO6 على P EO6 على P EO6
+
+669
+01:12:53,230 --> 01:12:54,070
+على P EO6 على P EO6 على P EO6 على P EO6 على P EO6
+
+670
+01:12:54,070 --> 01:12:56,730
+على P EO6 على P EO6 على P EO6 على P EO6 على P EO6
+
+671
+01:12:56,730 --> 01:12:56,810
+على P EO6 على P EO6 على P EO6 على P EO6 على P EO6
+
+672
+01:12:56,810 --> 01:12:56,810
+على P EO6 على P EO6 على P EO6 على P EO6 على P EO6
+
+673
+01:12:56,810 --> 01:13:01,750
+على P EO6 على Pmax to the power n على n factorial
+
+674
+01:13:01,750 --> 01:13:08,910
+to converge for
+
+675
+01:13:08,910 --> 01:13:13,290
+all x converge for all x
+
+676
+01:13:20,810 --> 01:13:24,850
+لأ نكون غير جادة ايه الاختبار اللي ساخدوا هنا يا
+
+677
+01:13:24,850 --> 01:13:30,170
+بناتي؟ الهو يبقى ايه؟ الهو يبقى ايه؟ الهو يبقى
+
+678
+01:13:30,170 --> 01:13:30,210
+ايه؟ الهو يبقى ايه؟ الهو يبقى ايه؟ الهو يبقى ايه؟
+
+679
+01:13:30,210 --> 01:13:30,650
+الهو يبقى ايه؟ الهو يبقى ايه؟ الهو يبقى ايه؟ الهو
+
+680
+01:13:30,650 --> 01:13:31,550
+يبقى ايه؟ الهو يبقى ايه؟ الهو يبقى ايه؟ الهو يبقى
+
+681
+01:13:31,550 --> 01:13:34,050
+ايه؟ الهو يبقى ايه؟ الهو يبقى ايه؟ الهو يبقى ايه؟
+
+682
+01:13:34,050 --> 01:13:38,450
+الهو يبقى ايه؟
+
+683
+01:13:38,450 --> 01:13:44,510
+الهو
+
+684
+01:13:44,510 --> 01:13:44,950
+يبقى ا
+
+685
+01:13:48,180 --> 01:13:56,140
+من R Cos X تربيع هذه على كتر تنفيه يمكن أن يبدأ
+
+686
+01:13:56,140 --> 01:14:02,560
+تسوي X تربيع فيه فعلينا نفسنا نجد ايش كل علامة زيه
+
+687
+01:14:02,560 --> 01:14:09,880
+لإن R Cos X علينا تلاتة Cos X علي X بجه تلاتة Cos
+
+688
+01:14:09,880 --> 01:14:19,280
+X علي X تطلع كده تلاتة X D Cos Xأصلاً Cos X ألا X
+
+689
+01:14:19,280 --> 01:14:24,400
+كنا بحسبها في تاني روميكسون و لو ضربناها من كمان X
+
+690
+01:14:24,400 --> 01:14:30,000
+تطلع من السيرة ألا X تطلع من القارس يرجى هذه كمان
+
+691
+01:14:30,000 --> 01:14:36,360
+is analytic because
+
+692
+01:14:36,360 --> 01:14:39,380
+Cos X
+
+693
+01:14:50,370 --> 01:14:59,070
+انالتك تحطي هنا بنات and fix yourself easyوهذه
+
+694
+01:14:59,070 --> 01:15:05,890
+اللي هي الانالتك كمان ات اكس يساوي زي روز الشمس
+
+695
+01:15:05,890 --> 01:15:10,150
+هذه ال singular point اللي عندنا إذا انت حقق مين
+
+696
+01:15:10,150 --> 01:15:13,990
+ال condition دي الساعة اللي بيبقى كبرا دي مده
+
+697
+01:15:13,990 --> 01:15:20,470
+singular singular point إذا ات أكس يساوي زي روز
+
+698
+01:15:20,470 --> 01:15:20,750
+الشمس
+
+699
+01:15:29,750 --> 01:15:37,050
+بعدين سأذكركم بالتوصيل ال X وش هو المفتوح تبعها
+
+700
+01:15:37,050 --> 01:15:44,910
+بالنسبالي انا اختارهم ثم اتنين الان اللي هو
+
+701
+01:15:44,910 --> 01:15:49,550
+التلاتة X توصيل X
+
+702
+01:15:56,980 --> 01:16:05,340
+لنقص واحد اذا power in x أُسي اتنين M عالمين على
+
+703
+01:16:05,340 --> 01:16:14,250
+اتنين M تقريبا بالشكل الهاملطبعا اللي بقدر أكتبها
+
+704
+01:16:14,250 --> 01:16:19,170
+على الشكل التالي summation من N equal 0 to
+
+705
+01:16:19,170 --> 01:16:28,590
+infinity لثالث واحد تدفع تن في تلاتة X أس اتنين N
+
+706
+01:16:28,590 --> 01:16:34,990
+زائد واحد على اتنين N factorial مش عارف كل عليها
+
+707
+01:16:34,990 --> 01:16:40,830
+انها تبقى هادة تبقى هادة مضمونة برادمن تلك
+
+708
+01:16:40,830 --> 01:16:45,570
+البرصدية طبعا اتعبنا ان الصين والكوسين والزي
+
+709
+01:16:45,570 --> 01:16:50,270
+والسكس والسيش والجوش وان الاكس واقعد على اكس وكذلك
+
+710
+01:16:50,270 --> 01:16:55,330
+برصد كلها آلي مجانا تتبع على شكل تاني ومجانا تتبع
+
+711
+01:16:55,330 --> 01:16:55,350
+على شكل اتاني ومجانا تتبع على شكل اتاني ومجانا
+
+712
+01:16:55,350 --> 01:16:57,810
+تتبع على شكل اتاني ومجانا تتبع على شكل اتاني
+
+713
+01:16:57,810 --> 01:16:59,070
+ومجانا تتبع على شكل اتاني ومجانا تتبع على شكل
+
+714
+01:16:59,070 --> 01:17:01,950
+اتاني ومجانا تتبع على شكل اتاني ومجانا تتبع على
+
+715
+01:17:01,950 --> 01:17:10,630
+شكل اتاني ومجانا تتبع على شكل اتاني وVersion X E
+
+716
+01:17:10,630 --> 01:17:22,350
+أُس X Lenin X واحدة على X تالي Inverse X وحط عليهم
+
+717
+01:17:22,350 --> 01:17:26,970
+E أُس X Lenin X تالي Inverse X وLenin X تالي
+
+718
+01:17:26,970 --> 01:17:33,210
+Inverse X كلهم هم مقدرتهم على شكل تايلون أو مقدرين
+
+719
+01:17:33,210 --> 01:17:37,130
+Series at any point عند أي نقطة
+
+720
+01:17:42,810 --> 01:17:48,090
+هذا السؤال اللي بين إيدينها بيختلف عن السؤالين
+
+721
+01:17:48,090 --> 01:17:53,940
+السابقين بإن المعاملات معاهاماهياش polynomial كانت
+
+722
+01:17:53,940 --> 01:17:58,800
+general functions فكان عندك ليه ال 6 و 3 cos x are
+
+723
+01:17:58,800 --> 01:18:03,140
+general functions يعني not polynomials لذلك سنلجأ
+
+724
+01:18:03,140 --> 01:18:07,660
+إلى الحالة الأولى اللى ابتدينا فيها فباجي بقول
+
+725
+01:18:07,660 --> 01:18:12,420
+طبعا هذه لا يمكن أن تساوي zero إلا إذا كانت x ساوي
+
+726
+01:18:12,420 --> 01:18:16,180
+zero بيه x ساوي zero is the only singular point
+
+727
+01:18:16,180 --> 01:18:22,180
+لمين ال differential equation اللى عندنابنقسم كله
+
+728
+01:18:22,180 --> 01:18:26,320
+على X فصارت المعادلة على الشكل اللي عندنا هذا إذا
+
+729
+01:18:26,320 --> 01:18:30,220
+بدي أشوف كده قيمة X نقص ال X node في Q of X على P
+
+730
+01:18:30,220 --> 01:18:35,340
+of X يبقى يساوي X في E of X على X نختصر بظهر E of
+
+731
+01:18:35,340 --> 01:18:38,600
+X هذي أنا لاتك لإن بقدر أكتبها على شكل Tyler
+
+732
+01:18:38,600 --> 01:18:42,940
+Series أو هي عبارة عن McLaurin Series عند X يساوي
+
+733
+01:18:43,180 --> 01:18:48,060
+زيرو وبالتالي صارت هذه انالتك الان بدي اجي لل X
+
+734
+01:18:48,060 --> 01:18:51,920
+نقص ال X نوت تربيع R of X على P of X ال X نوت
+
+735
+01:18:51,920 --> 01:18:55,480
+بزيرو يبقى بصير X تربيع هدي على هدي ليه تلاتة
+
+736
+01:18:55,480 --> 01:19:00,980
+cosine X على X نختصر بصير تلاتة X cosine X هذا
+
+737
+01:19:00,980 --> 01:19:06,640
+انالتك ليش؟ لأن هذا مفكوك ال cosine Maclaurin
+
+738
+01:19:06,640 --> 01:19:11,890
+series at X يساوي زيرودربنا في تلاتة X دخلنا ال X
+
+739
+01:19:11,890 --> 01:19:16,890
+ديوة صار الأس بدل اتنين N بصير اتنين N زاد واحد
+
+740
+01:19:16,890 --> 01:19:20,890
+وهي التلاتة وهي السلم واحد أس N كما هو والمقام
+
+741
+01:19:20,890 --> 01:19:26,190
+بتنين N فاكتوريال إذا هذه كمان analytic function
+
+742
+01:19:26,190 --> 01:19:30,310
+إذا صار ال term الأول والterm التاني تنتين are two
+
+743
+01:19:30,310 --> 01:19:35,010
+analytic functionsيبقى الـ x يساوي 0 is a regular
+
+744
+01:19:35,010 --> 01:19:41,330
+singular point طيب مش كل الدول اللي بتيجي بهذه
+
+745
+01:19:41,330 --> 01:19:44,710
+السهولة هذه غير هي regular و irregular بعضها بتبقى
+
+746
+01:19:44,710 --> 01:19:49,710
+ايه مسائل صعبة شوية لكن نطلع نقول لو عندي two
+
+747
+01:19:49,710 --> 01:19:53,130
+functions واتنتين كانوا analytic عند النقطة دي
+
+748
+01:19:53,130 --> 01:19:59,340
+يبقى مجموعهم الجابريين جمع أو طرح نقصد بهأو حاصل
+
+749
+01:19:59,340 --> 01:20:04,260
+ضرب الـ two functions f في g أو خارج قسم الاتنين
+
+750
+01:20:04,260 --> 01:20:09,940
+بشرط الـ g عند النقطة x node ممنوعة تساوي zero دي
+
+751
+01:20:09,940 --> 01:20:13,840
+ريبالك الـ g of x node is not equal to zero لأن
+
+752
+01:20:13,840 --> 01:20:18,080
+هذا بيصير معناه is undefined ماهياش معرفة are
+
+753
+01:20:18,080 --> 01:20:21,920
+analytic and main عند ال x node الآن هشوف كيف
+
+754
+01:20:21,920 --> 01:20:28,930
+نستخدم هذه ال remark في حلالسؤال التالي من أسئلة
+
+755
+01:20:28,930 --> 01:20:38,150
+الكتاب وهو المثال الرقم 4 إذا المثال الرقم 4 بيقول
+
+756
+01:20:38,150 --> 01:20:46,190
+لل X في ال sign ال X في ال Y double prime زائد
+
+757
+01:20:46,190 --> 01:20:54,240
+تلاتة Y prime تلاتة Y primeزائد XY بده يساوي كده؟
+
+758
+01:20:54,240 --> 01:21:00,580
+بده يساوي 0 واضح هذه ال polynomial من الدرجة
+
+759
+01:21:00,580 --> 01:21:04,940
+الصفرية هذه ال polynomial من الدرجة الأولى لكن هذه
+
+760
+01:21:04,940 --> 01:21:09,160
+لأ sign X ليست polynomial يبقى هذه general
+
+761
+01:21:09,160 --> 01:21:20,900
+function يبقى بجي بقوله P of Xسين ال X is not a
+
+762
+01:21:20,900 --> 01:21:25,360
+polynomial تمام
+
+763
+01:21:25,360 --> 01:21:32,700
+طيب بدأ أسألكوا السؤال التالي is it a series X
+
+764
+01:21:32,700 --> 01:21:37,400
+في سين ال X زي X فيكون سين ال X نعم series لكنها
+
+765
+01:21:37,400 --> 01:21:41,410
+ليس بتنمية يعني مش بتوفر حد محددبتظلها ماشية إلى
+
+766
+01:21:41,410 --> 01:21:45,490
+وين لغاية ما لا نهاية ولو ضربناها في X زي ما ضربنا
+
+767
+01:21:45,490 --> 01:21:50,110
+ال cosine هنا في X يبقى بيظلها Series وليست
+
+768
+01:21:50,110 --> 01:21:55,330
+Polynomial مش كثيرة حدود وإنما بيظل متسلسلة إلى ما
+
+769
+01:21:55,330 --> 01:22:01,510
+لا نهاية طيب تمام الآن بدي أشوف ما هي النقطالتي
+
+770
+01:22:01,510 --> 01:22:09,910
+تجعل ال P of X يساوي 0 يبقى باجي بقوله P of X بده
+
+771
+01:22:09,910 --> 01:22:21,970
+يساوي X sin X equal 0
+
+772
+01:22:21,970 --> 01:22:29,430
+at X يساويبنشوف إيش النقاط اللي بتخلي هذه القيمتين
+
+773
+01:22:29,430 --> 01:22:35,970
+حاصل ضربهم يساوي Zero أظل لو كانت X يساوي Zero صح؟
+
+774
+01:22:35,970 --> 01:22:40,670
+بيصير هذه ب Zero و ال sign Zero ب Zero Zero Zero
+
+775
+01:22:40,670 --> 01:22:49,260
+Zero خلصنا؟ في غيرهم يعني؟ زي مين؟باي، نين باي،
+
+776
+01:22:49,260 --> 01:22:57,500
+تلاتة باي، أربع باي، خمسة باي وزيهم بالسالم يبقى
+
+777
+01:22:57,500 --> 01:23:04,820
+الزائد أو ناقص in byال X بيساوي zero and ال X
+
+778
+01:23:04,820 --> 01:23:11,780
+بيساوي زائد او ناقص in by و ال in is an integer و
+
+779
+01:23:11,780 --> 01:23:16,840
+ال in يساوي واحد و اتنين و تلاتة و الى ما لا نهاية
+
+780
+01:23:18,050 --> 01:23:22,930
+يعني الحمد لله كام singular point عندنا؟ مالة
+
+781
+01:23:22,930 --> 01:23:26,290
+نهاية من ال singular points وهذا ما أشرت إليه قبل
+
+782
+01:23:26,290 --> 01:23:29,510
+شوية في بداية المحاضرة قلت لك ممكن يكون عندي نقطة
+
+783
+01:23:29,510 --> 01:23:33,270
+واحدة singular point ممكن يكون عندي نقطتين ممكن
+
+784
+01:23:33,270 --> 01:23:37,410
+يكون تلاتة ممكن مالة نهاية من النقطة اللي على
+
+785
+01:23:37,410 --> 01:23:40,370
+البعض كنت استغرب عندما قلت يمكن يكون عندي مالة
+
+786
+01:23:40,370 --> 01:23:44,990
+نهاية من ال singularلكن هاي جيبنالكم يتهطل عندي
+
+787
+01:23:44,990 --> 01:23:49,370
+مالة نهاية من مين من ال singular طيب ما علينا بدى
+
+788
+01:23:49,370 --> 01:23:54,110
+اشوف النقاط هدولة regular و الله irregular نيجي
+
+789
+01:23:54,110 --> 01:23:58,550
+نقوله تعالى نشوف الان المعادلة هذه بتروح اكتبها
+
+790
+01:23:58,550 --> 01:24:02,970
+على الشكل التالف يبقى هذه هي المعادلة رقم واحد
+
+791
+01:24:02,970 --> 01:24:09,750
+فبروح بقوله that differential equation one is
+
+792
+01:24:09,750 --> 01:24:10,830
+written
+
+793
+01:24:17,500 --> 01:24:24,380
+زائد تلاتة على x في ال sign ال x في ال y prime
+
+794
+01:24:24,380 --> 01:24:32,220
+زائد x بتروح مع x مضال واحد على ال sign ال x فقط
+
+795
+01:24:32,220 --> 01:24:34,940
+في ال y بدها تساوي زيرو
+
+796
+01:24:38,450 --> 01:24:43,570
+نمسك النقطة الأولى ل X يساوي Zero يبقى بده أجي
+
+797
+01:24:43,570 --> 01:24:50,070
+أقوله at X بده يساوي Zero أخد ليه بتابانات؟ لأ لإن
+
+798
+01:24:50,070 --> 01:24:53,110
+هدول ماهياش Polynomial صحيح تنتين Polynomial بس
+
+799
+01:24:53,110 --> 01:24:57,410
+التالتة لأ يبقى in general التلاتة غير متحقق ان
+
+800
+01:24:57,410 --> 01:25:02,290
+التلاتة Polynomial يبقى بده أروح للحالة الأولى و
+
+801
+01:25:02,290 --> 01:25:09,140
+ليست من الحالة الثانيةيعني بدى اشوف هل ال X ناقص X
+
+802
+01:25:09,140 --> 01:25:18,300
+node اللى هو Zero في ال Q of X على ال R of X هل
+
+803
+01:25:18,300 --> 01:25:23,020
+بقدر اكتفها على شكل polynomial ام لا هل تايلور
+
+804
+01:25:23,020 --> 01:25:28,940
+سيريز ام لا يبقى هدى بصير X في ميمفي ال Q على X
+
+805
+01:25:28,940 --> 01:25:35,820
+اللي هي تلاتة على X ساين ال X يبقى في تلاتة على X
+
+806
+01:25:35,820 --> 01:25:43,220
+في ساين ال X ال X مع ال X يبقى النتيجة كده تلاتة
+
+807
+01:25:43,220 --> 01:25:49,970
+على ساين ال X السؤال هوبتقدر تكتبها على شكل taylor
+
+808
+01:25:49,970 --> 01:25:54,950
+series ام لا تقول استنى شوية تعالى نطلع لل remark
+
+809
+01:25:54,950 --> 01:25:58,410
+اللى احنا كاتبينه فوق ايش بتقولي ال remark لو
+
+810
+01:25:58,410 --> 01:26:02,890
+كانوا تنتين analytic يبقى المجموعة والضرب وخرج
+
+811
+01:26:02,890 --> 01:26:07,810
+القسمة are analytic باجى بس لنفسى هل ال sign
+
+812
+01:26:07,810 --> 01:26:13,770
+analytic الاجابة نعم نجى هل التلاتة analyticيعني
+
+813
+01:26:13,770 --> 01:26:18,390
+هل ال constant بقدر اكتبه عليه شكل series و تبقى
+
+814
+01:26:18,390 --> 01:26:25,270
+طبعا لأ يبقى هذه بصير مالها is not analytic يبقى
+
+815
+01:26:25,270 --> 01:26:35,730
+هذه ال function هذه بالساوية is not analytic السبب
+
+816
+01:26:35,730 --> 01:26:38,610
+ان التلاتة ما هيش انتظر مين اللي بتحكي
+
+817
+01:26:52,810 --> 01:27:01,400
+ثلاثة X مضروبة في الـ cosineوهي حطنلك على شكل
+
+818
+01:27:01,400 --> 01:27:06,240
+summation وهي ال summation ودخلتها جوا صارت هذه
+
+819
+01:27:06,240 --> 01:27:10,080
+على شكل ماكلون أو تايلور سيريز ولا لا عند النقطة X
+
+820
+01:27:10,080 --> 01:27:13,580
+ساوي Zero صحيح ولا لا طب يلا كتبيلي تلاتة على
+
+821
+01:27:13,580 --> 01:27:16,520
+الشكل هذا نشوف مش هنشوف كلامك صح ولا لا تبعت
+
+822
+01:27:16,520 --> 01:27:20,360
+المقامة موافق صحيح ال X مظبوط لكن هل يتل .. يعني
+
+823
+01:27:20,360 --> 01:27:25,400
+cosecant X تلاتة cosecant X عمرك جيبتي تايلور ولا
+
+824
+01:27:25,400 --> 01:27:30,300
+ماكلون لل cosecantطب مهم عند Zero مش معرفة أصلا
+
+825
+01:27:30,300 --> 01:27:34,620
+صحيحة ولا لا؟ طب احنا الشرط الذاتي تبع المقام لازم
+
+826
+01:27:34,620 --> 01:27:38,020
+يكون معرف مش يقولنا لما يكون عندنا خارق قسم
+
+827
+01:27:38,020 --> 01:27:42,640
+التنتين بدي هذه ممنوعة تساوي Zero عند Zero وصين
+
+828
+01:27:42,640 --> 01:27:47,800
+Zero في جداش يعني أمورها ماتصير Analytic مظبوط ولا
+
+829
+01:27:47,800 --> 01:27:53,560
+لا؟ خلاصنا؟ جنات يهودة؟ والكلام نفسنا مهين طيب
+
+830
+01:27:53,560 --> 01:27:56,400
+يبقى هذه سرعة النقطة Analytic يبقى النقطة اللي
+
+831
+01:27:56,400 --> 01:27:57,020
+عندنا مالها
+
+832
+01:28:00,210 --> 01:28:08,550
+يبقى هنا سا اللي هو ال X يساوي 0 is irregular
+
+833
+01:28:08,550 --> 01:28:14,610
+singular point
+
+834
+01:28:40,920 --> 01:28:51,700
+عشان نذهب الى نقاط التانية X يساوي زائد او ناقص في
+
+835
+01:28:51,700 --> 01:28:52,440
+Y
+
+836
+01:28:56,110 --> 01:29:03,470
+الـ X نقص الـ X نواة في الـ Q of X على capital P
+
+837
+01:29:03,470 --> 01:29:09,850
+of X يبقى بيصير X زائد او نقص in by I بدي اخدهم
+
+838
+01:29:09,850 --> 01:29:16,490
+مرة واحدة والـ Q على P ليه تلاتة على X sin X يبقى
+
+839
+01:29:16,490 --> 01:29:24,190
+فيه تلاتة على X في sin X طيب
+
+840
+01:29:24,190 --> 01:29:32,640
+طالعيني لهذهبقدر اكتبها مثل تلات اكس في كوسايت
+
+841
+01:29:32,640 --> 01:29:36,860
+يبقى هذه analytic and zero ولا لا analytic طيب
+
+842
+01:29:36,860 --> 01:29:43,090
+اللي فوق هذي polynomial من أي درجةبالدرجة الأولى
+
+843
+01:29:43,090 --> 01:29:47,330
+والثانية بتكتب على شكل summation طبعا هتقول ايش
+
+844
+01:29:47,330 --> 01:29:53,310
+بعد حدين بتصير الدالة عندك zero صح ولا لأ اه بقوله
+
+845
+01:29:53,310 --> 01:29:57,030
+بكتب الحدين اللي عني و بكتب زائد zero في كذا زائد
+
+846
+01:29:57,030 --> 01:30:00,910
+zero في كذا كتبت على شكل ايه تايلور او مكلونن
+
+847
+01:30:00,910 --> 01:30:04,650
+سيريزيبقى معناته مافيش مشكلة عندى في هذه الحالة
+
+848
+01:30:04,650 --> 01:30:09,790
+يبقى لو كان عندك اى polynomial بس تبقى بدلالة X مش
+
+849
+01:30:09,790 --> 01:30:14,570
+مقدار ثابت يبقى لو كانت بدل اى .. دل .. اى
+
+850
+01:30:14,570 --> 01:30:18,290
+polynomial من الدرجة الاولى فساعدا بقدر اكتب عليها
+
+851
+01:30:18,290 --> 01:30:22,470
+شكل تلوريسي اللى بخلى باقى الكميات كلهم جدا باسفار
+
+852
+01:30:22,470 --> 01:30:29,870
+وبالتالي هذه is ana .. analytic
+
+853
+01:30:36,430 --> 01:30:40,370
+عن طريق البرامج الاخرى
+
+854
+01:30:43,840 --> 01:30:48,400
+ماشي الحال هذا ايش لو جيت اتعود اتعود مباشر عند ال
+
+855
+01:30:48,400 --> 01:30:51,800
+X node مايطلعش ب zero مظبوط ولا لا لكن احنا هنا
+
+856
+01:30:51,800 --> 01:30:56,280
+بنقول توس يعني ال cosine ال cosine عند ال zero
+
+857
+01:30:56,280 --> 01:31:00,340
+طلعت أنلتك ولا لا وبالتالي ال sine عند ال zero
+
+858
+01:31:00,340 --> 01:31:05,720
+أنلتك زيها صحيح ولا لا يبقى السبب اللي هنا كانت
+
+859
+01:31:05,720 --> 01:31:10,400
+تلاتة ماقدرتش اكتبهاماقدرش اشوفها على شكل مين
+
+860
+01:31:10,400 --> 01:31:14,660
+تايلور سيلز هنا هذه من الدرجة الأولى اذا بقدر
+
+861
+01:31:14,660 --> 01:31:20,400
+اكتبهاهذه بقدر اكتبها تماما ال sign زي ال cosine
+
+862
+01:31:20,400 --> 01:31:29,200
+بس بس الأسس فردية على ما اذكر ال sign كانت sign ال
+
+863
+01:31:29,200 --> 01:31:34,640
+x كانت هي summation من n equal zero to infinity
+
+864
+01:31:34,640 --> 01:31:39,400
+اناقص واحد to the power n ل x أس اتنين n زاد واحد
+
+865
+01:31:39,400 --> 01:31:47,800
+على اتنين nزائد واحد factorial هذا series لصين ال
+
+866
+01:31:47,800 --> 01:31:53,120
+X يعني تايلور سيريز عند X يساوي Zero وبالتالي
+
+867
+01:31:53,120 --> 01:31:57,840
+ماعنا مشكلة اذا بدنا نروح ل ال condition التاني
+
+868
+01:31:57,840 --> 01:32:06,000
+اللي هو X ناقص ال X node في R of X على capital P
+
+869
+01:32:06,000 --> 01:32:11,850
+of X وهذه تربيةيبقى هذا الكلام يبدو يسوي x زد او
+
+870
+01:32:11,850 --> 01:32:20,830
+ناقص in by الكل تربيع وين راحت المعادلة يبقى واحد
+
+871
+01:32:20,830 --> 01:32:26,190
+على ال sign ال x مش هيك يبقى هذا كله على ال sign
+
+872
+01:32:26,190 --> 01:32:30,810
+ال x هذه analytic عند ال zero وهذه كذلك analytic
+
+873
+01:32:30,810 --> 01:32:39,700
+عند ال zero يبقى هذه is analyticأت اكس يساوي زيرو
+
+874
+01:32:39,700 --> 01:32:44,060
+معناه هذا الكلام انه كل النقاط هالقول مالهم
+
+875
+01:32:44,060 --> 01:32:49,160
+regular singular point ماعدا main ماعدا اكس يساوي
+
+876
+01:32:49,160 --> 01:32:58,820
+زيرو so the points اللي هو ال X يساوي ز أو ناقص in
+
+877
+01:32:58,820 --> 01:33:06,670
+by و ال N تساوي واحد و اتنين و تلاتة areregular
+
+878
+01:33:06,670 --> 01:33:12,390
+singular points
+
+879
+01:33:12,390 --> 01:33:19,650
+لحد ذلك انتهى هذا ال section وإلى يكون أرقام
+
+880
+01:33:19,650 --> 01:33:29,590
+المسائل يبقى exercises خمسة أربعة المسائل من واحد
+
+881
+01:33:29,590 --> 01:33:33,890
+لغاية تمانتاش القدر
+
+882
+01:33:40,770 --> 01:33:45,910
+طيب عليك انتهى section 5 أربعة الآن section خمسة
+
+883
+01:33:45,910 --> 01:33:48,890
+خمسة المرة القادمة ان شاء الله
+
diff --git a/PL9fwy3NUQKwa8ZDfSFGn6H8xVFLzqmCZC/pb7CBRBKnwY.srt b/PL9fwy3NUQKwa8ZDfSFGn6H8xVFLzqmCZC/pb7CBRBKnwY.srt
new file mode 100644
index 0000000000000000000000000000000000000000..4d752e22fdb0427c8944f9c0a1b0895ef59acc58
--- /dev/null
+++ b/PL9fwy3NUQKwa8ZDfSFGn6H8xVFLzqmCZC/pb7CBRBKnwY.srt
@@ -0,0 +1,2402 @@
+1
+00:00:09,280 --> 00:00:15,060
+بسم الله الرحمن الرحيم الآن بدنا نكمل ما ابتدأنا به
+
+2
+00:00:15,060 --> 00:00:19,280
+في الـ section المرة الماضية اللي هو section ثلاثة
+
+3
+00:00:19,280 --> 00:00:24,060
+اثنين طبعًا هذا الـ section في أكبر section مليان
+
+4
+00:00:24,060 --> 00:00:29,620
+بـ نظريات في كل الـ sections المقررة، أخذنا بعض النظريات
+
+5
+00:00:29,620 --> 00:00:33,040
+المرة الماضية وكان آخر حاجة خدنا تعريف الـ
+
+6
+00:00:33,040 --> 00:00:37,760
+Wronskian أو الـ  Wronskian اللي بنيجي نحط الحل الأول و
+
+7
+00:00:37,760 --> 00:00:40,980
+الحل الثاني ومشتقة الأول ومشتقة الثاني كمحدد
+
+8
+00:00:40,980 --> 00:00:45,680
+ثنائي ونجيب قيمة المحدد، هذا حاصل ضرب عناصر القطر
+
+9
+00:00:45,680 --> 00:00:52,240
+الرئيسي ناقص حاصل ضرب عناصر القطر الثاني نجي 
+
+10
+00:00:52,240 --> 00:00:57,010
+لنظرية اللي عندنا اليوم، بيقول لو كان Y1 وY2 هما
+
+11
+00:00:57,010 --> 00:01:01,090
+عبارة عن two solutions للـ differential equation
+
+12
+00:01:01,090 --> 00:01:03,950
+اللي قدامنا اللي هو homogeneous second order
+
+13
+00:01:03,950 --> 00:01:08,870
+differential equation، وإذا قدرنا نجد النقطة الـ T
+
+14
+00:01:08,870 --> 00:01:13,150
+node بحيث الـ Wronskian تبع الحلين تبع المعادلات
+
+15
+00:01:13,150 --> 00:01:19,730
+التفاضلية عندهم لا يساوي صفر، إن حدث ذلك يبقى the
+
+16
+00:01:19,730 --> 00:01:24,350
+family of solutions مجموعة الحلول اللي على الشكل
+
+17
+00:01:24,350 --> 00:01:31,030
+C1Y1 زائد C2Y2، C1 وC2 are arbitrary constants، يبقى 
+
+18
+00:01:31,030 --> 00:01:37,630
+ثوابت اختيارية، includes هذا الحل بيشتمل على كل
+
+19
+00:01:37,630 --> 00:01:43,030
+الحلين للمعادلة التفاضلية، طبعًا يا بنات هذا الآن
+
+20
+00:01:43,030 --> 00:01:47,130
+اللي الكلام اللي بنقوله بيربط الـ section 32 مع الـ section 
+
+21
+00:01:47,130 --> 00:01:52,080
+31، إحنا في 31 كنا بندور على fundamental set
+
+22
+00:01:52,080 --> 00:01:55,780
+of solutions ولا الـ Wronskian ولا حاجة، عندنا معادلة
+
+23
+00:01:55,780 --> 00:01:59,860
+بحلها، بجيب حلين، بدرّب الـ C1 في الأول، الـ C2 في
+
+24
+00:01:59,860 --> 00:02:04,760
+الثاني بقول هذا هو الـ general solution، الآن إحنا
+
+25
+00:02:04,760 --> 00:02:09,420
+بدنا نقول وقد إيش فعلًا الحل أو الـ general solution
+
+26
+00:02:09,420 --> 00:02:14,020
+exists، بنقول لما الـ Wronskian عند نقطة ما بده يساوي 
+
+27
+00:02:14,020 --> 00:02:19,690
+قد إيش؟ لا يساوي صفر، مرة ثانية بقول إن عندي معادلة
+
+28
+00:02:19,690 --> 00:02:25,950
+تفاضلية إلها حلين، الـ Wronskian تبع الحلّين عند نقطة ما
+
+29
+00:02:25,950 --> 00:02:33,310
+النقطة هذه موجودة في الفترة اللي الـ P والدالة 
+
+30
+00:02:33,310 --> 00:02:39,350
+Q continuous عليها، إن حدث ذلك يبقى مجموعة الحلول 
+
+31
+00:02:39,350 --> 00:02:46,610
+بتشتمل على أي حل آخر منهم للمعادلة، طب إحنا العنوان
+
+32
+00:02:46,610 --> 00:02:49,650
+اللي إحنا رافعينه لهذا الـ section، fundamental set of 
+
+33
+00:02:49,650 --> 00:02:53,770
+solutions، المرة اللي فاتت ما اتكلمناش ولا كلمة على
+
+34
+00:02:53,770 --> 00:02:56,250
+الـ fundamental set of solutions، كنا بنيجي ناخد
+
+35
+00:02:56,250 --> 00:03:00,790
+نظريات، لكن طلع هنا بيقول إيش؟ إذا ضمنت إن الـ Wronskian
+
+36
+00:03:00,790 --> 00:03:05,650
+كان عندها نقطة لا يساوي صفر يبقى هذا بيشتمل على 
+
+37
+00:03:05,650 --> 00:03:11,530
+أي حل آخر لمام للمعادلة التفاضلية، الملاحظة بتقول
+
+38
+00:03:11,530 --> 00:03:15,770
+إذا الـ Wronskian كان هذا لا يساوي صفر يبقى الحلين
+
+39
+00:03:15,770 --> 00:03:21,700
+الاثنين دول بيكونوا لي مجموعة الحلول الأساسية، العنوان
+
+40
+00:03:21,700 --> 00:03:24,540
+اللي إحنا كنا رافعينه للـ section تلاتة اثنين المرة
+
+41
+00:03:24,540 --> 00:03:28,020
+الماضية، مجموعة الحلول الأساسية للـ differential
+
+42
+00:03:28,020 --> 00:03:32,540
+equation،  اللي كنا سابقًا من سماه الـ general
+
+43
+00:03:32,540 --> 00:03:36,540
+solution، يبقى الـ general solution للمعادلة
+
+44
+00:03:36,540 --> 00:03:40,950
+التفاضلية أو الـ Fundamental Set of Solutions
+
+45
+00:03:40,950 --> 00:03:45,650
+للمعادلة التفاضلية، مجموعة الحلول الأساسية، اثنين
+
+46
+00:03:45,650 --> 00:03:51,950
+نفس المعنى، هذه الصيغة تشتمل على أي حل آخر للمعادلة
+
+47
+00:03:51,950 --> 00:03:58,570
+التفاضلية الخطية من الرتبة الثانية، يبقى هذه الصيغة 
+
+48
+00:03:58,570 --> 00:04:02,710
+constant في الحل الأول زائد constant ثاني في الحل 
+
+49
+00:04:02,710 --> 00:04:09,480
+الثاني، تمام؟ إحنا ما جيبناش deep لكن أصلنا للحلول
+
+50
+00:04:09,480 --> 00:04:14,600
+القديمة بحيث نضمن موجود ولا نعرف موجود وقت إذا 
+
+51
+00:04:14,600 --> 00:04:18,500
+الـ Wronskian عنده نقطة داخل الـ interval المعرض عليها
+
+52
+00:04:18,500 --> 00:04:22,200
+الـ coefficients، بدي يكون الـ Wronskian هذا معله لا
+
+53
+00:04:22,200 --> 00:04:28,220
+يساوي صفر، نعطي مثال طبعًا تقول اتأكدلي إن هدول حلول
+
+54
+00:04:28,220 --> 00:04:33,470
+المعادلة، استفادوا من الجهة دي طيب اتأكدنا، بقول لي
+
+55
+00:04:33,470 --> 00:04:37,010
+ومن ثم دين show that بيبين لي إن الاثنين هدول
+
+56
+00:04:37,010 --> 00:04:41,030
+بيكونوا لي الـ fundamental set of solutions، اتجاه
+
+57
+00:04:41,030 --> 00:04:44,290
+المفهوم الثاني يعني إيه بتبدي تعملي؟ بدي أجيب
+
+58
+00:04:44,290 --> 00:04:48,950
+الـ Wronskian هذا هو، أثبت إنه ماله؟ لا يساوي ذلك، إن 
+
+59
+00:04:48,950 --> 00:04:52,050
+حدث ذلك اتجاه جولي بيكونوا لي مجموعة الحلول الأساسية 
+
+60
+00:04:52,050 --> 00:04:56,710
+وبالتالي بديقول شكل الـ general solution للمعادلة
+
+61
+00:04:56,710 --> 00:05:00,750
+التفاضلية، وقال لي هو مثلًا أكتب شكل الـ general
+
+62
+00:05:00,750 --> 00:05:04,030
+solution، طبعًا شكل الـ general solution بيكون على
+
+63
+00:05:04,030 --> 00:05:08,510
+الشكل اللي عندنا هذا، إذا خليني نمشي خطوة بخطوة،
+
+64
+00:05:08,510 --> 00:05:13,070
+جالي يبين لي إن هدول حلول المعادلة التفاضلية، مش
+
+65
+00:05:13,070 --> 00:05:17,770
+هيكونوا حلّين حصلوا المعادلة التفاضلية، يبقى 
+
+66
+00:05:17,770 --> 00:05:25,630
+أنا عندي Y واحد، يستوي قدر T ثانية، لو اشتغلت على Y
+
+67
+00:05:25,630 --> 00:05:31,390
+واحد إسرائيل يستوي قدر T كمان، مرضي Y واحد وقفل 
+
+68
+00:05:31,390 --> 00:05:35,910
+إسرائيل يستوي قدر يستوي اثنين، بدّاك تعوض في 
+
+69
+00:05:35,910 --> 00:05:40,150
+المعادلة، يستوي قدر T ثانية، وY واحد مضابق
+
+70
+00:05:40,150 --> 00:05:41,030
+لإسرائيل
+ 
+71
+00:05:43,860 --> 00:05:50,020
+إذا طلع هذا الكلام يساوي صفر فهذا يكون حل مين
+
+72
+00:05:50,020 --> 00:05:52,100
+للمعادلة التفاضلية
+
+73
+00:06:02,130 --> 00:06:09,150
+اللي هو T تربيع، يبقى T تربيع تقصد من T تربيع، وزي
+
+74
+00:06:09,150 --> 00:06:16,310
+ما يساوي صفر، هنا قدامها why one زي ما يساوي T تربيع is
+
+75
+00:06:16,310 --> 00:06:27,810
+a solution of the differential equation، للمعادلة 
+
+76
+00:06:27,810 --> 00:06:34,100
+ال تفاضلية، الاثنين في تاريخ يعني وايد قدر للتاريخ،
+
+77
+00:06:34,100 --> 00:06:39,090
+خاطر من الاثنين وايد بيشاوى الـ independent، بيشاوى الـ independent، الآن
+
+78
+00:06:39,090 --> 00:06:47,610
+similarly، بنفس الطريقة اللي هو Y2 يستوي T أُصناف
+
+79
+00:06:47,610 --> 00:07:03,370
+واحد تمام؟ لأنه اشتقّوا مرة، Y2 يستوي T أُصناف
+
+80
+00:07:03,370 --> 00:07:11,580
+ثانية، الآن بالنسبة للمعادلة التفاضلية،  T تربيع، Y2، من
+
+81
+00:07:11,580 --> 00:07:14,960
+بعض الأفراد، مقصد 62 Y2 
+
+82
+00:07:18,920 --> 00:07:36,780
+يتجارى يساوي T تربيع Y2، ويتجارى
+
+83
+00:07:36,780 --> 00:07:42,080
+T تربيع 
+
+84
+00:07:42,080 --> 00:07:50,640
+Y2، ويتجارى T تربيع، Y2، ويتجارى يساوي صفر، يمكن أن 
+
+85
+00:07:50,640 --> 00:07:58,400
+يكون Y يستوي واحد، يستوي واحد، يستوي ثلاث، يستوي ثلاث، يستوي ثلاث 
+
+86
+00:07:58,400 --> 00:08:06,000
+يستوي ثلاث، يستوي ثلاث، يستوي ثلاث، يستوي ثلاث، يستوي ثلاث، يستوي ثلاث
+
+87
+00:08:06,000 --> 00:08:14,900
+يستوي ثلاث، يستوي ثلاث، يستوي ثلاث، يستوي ثلاث، يستوي ثلاث، يستوي ثلاث
+
+88
+00:08:14,900 --> 00:08:14,920
+يستوي ثلاث، يستوي ثلاث، يستوي ثلاث، يستوي ثلاث، يستوي ثلاث، يستوي ثلاث 
+
+89
+00:08:14,920 --> 00:08:14,940
+يستوي ثلاث، يستوي ثلاث، يستوي ثلاث، يستوي ثلاث، يستوي ثلاث، يستوي ثلاث
+
+90
+00:08:14,940 --> 00:08:15,000
+يستوي ثلاث، يستوي ثلاث، يستوي ثلاث، يستوي ثلاث، يستوي ثلاث، يستوي ثلاث 
+
+91
+00:08:15,000 --> 00:08:15,180
+يستوي ثلاث، يستوي ثلاث، يستوي ثلاث، يستوي ثلاث، يستوي ثلاث، يستوي ثلاث
+
+92
+00:08:15,180 --> 00:08:19,530
+يستدل اللي بيأدي إن الاثنين هدول بيكونوا لي المجموعة
+
+93
+00:08:19,530 --> 00:08:24,690
+للحلول الأساسية، مصطلح القضية إن الـ Wronskian تبعهم
+
+94
+00:08:24,690 --> 00:08:28,570
+عن طريقهم، عن طريقهم، عن طريقهم، عن طريقهم، عن طريقهم، عن
+
+95
+00:08:28,570 --> 00:08:28,590
+طريقهم، عن طريقهم، عن طريقهم، عن طريقهم، عن طريقهم، عن طريقهم
+
+96
+00:08:28,590 --> 00:08:28,730
+عن طريقهم، عن طريقهم، عن طريقهم، عن طريقهم، عن طريقهم، عن
+
+97
+00:08:28,730 --> 00:08:29,450
+طريقهم، عن طريقهم، عن طريقهم، عن طريقهم، عن طريقهم، عن طريقهم
+
+98
+00:08:29,450 --> 00:08:30,130
+عن طريقهم، عن طريقهم، عن طريقهم، عن طريقهم، عن طريقهم، عن
+
+99
+00:08:30,130 --> 00:08:34,010
+طريقهم، عن طريقهم، عن طريقهم، عن طريقهم، عن طريقهم، عن طريقهم
+
+100
+00:08:34,010 --> 00:08:42,430
+عن طريقهم، عن 
+
+101
+00:08:43,860 --> 00:08:50,240
+الحل الأول اللي عندنا، همين P ثانية، والحل الثاني P
+
+102
+00:08:50,240 --> 00:08:58,700
+أصناف الواحد، نجدت نجدت اثنين P سالف، P و سالف اثنين 
+
+103
+00:09:06,560 --> 00:09:12,780
+يعني دلوقت نفس البرنامج كان نموذج P solution P 
+
+104
+00:09:12,780 --> 00:09:17,380
+ثلاثية، وثلاثية وثالث واحد نجدت إن المتحدث 
+
+105
+00:09:17,380 --> 00:09:21,380
+الإسرائيلي حصل الحاجات عن كل الموضوع يقفل فيه هنا
+
+106
+00:09:21,380 --> 00:09:27,820
+بضرورة إن إن المتحدث حصل ضرب على نفسه، كرهيزي، حاصل
+
+107
+00:09:27,820 --> 00:09:31,880
+ضرب على نفسه، كرهيزي، حاصل ضرب على نفسه، كرهيزي
+
+108
+00:09:31,880 --> 00:09:33,020
+كرهيزي واحد
+
+109
+00:10:00,640 --> 00:10:02,040
+عاصفة ضرب، عاصفة ضرب، عاصفة ضرب، عاصفة ضرب، عاصفة ضرب
+
+110
+00:10:02,040 --> 00:10:11,080
+عاصفة، هذا الرقم غير الصفر، إذا ما يمكن أن 
+
+111
+00:10:11,080 --> 00:10:15,900
+يكون مرضي المطمئن زي تطلع نقص ثلاث D مثلًا، يمكن 
+
+112
+00:10:15,900 --> 00:10:20,380
+تطلع نقص ثلاث على D، تلميح يفش يطلع بـ D آخر وعلى الـ 
+
+113
+00:10:20,380 --> 00:10:22,760
+interval تحت الشرطين عليه 
+
+114
+00:10:26,530 --> 00:10:44,590
+طيب، مدام لا يساوي صفر، يفكر، الاثنين هدول بتقنوني، ماهي
+
+115
+00:10:57,720 --> 00:11:05,660
+solutions of the given differential equation
+
+116
+00:11:05,660 --> 00:11:13,100
+differential equation، جالي مدام الـ Wronskian الـ 
+
+117
+00:11:13,100 --> 00:11:16,540
+general solution للـ differential equation جدًا
+
+118
+00:11:16,540 --> 00:11:25,100
+العليه، بروح بكله، الـ general solution is 
+
+119
+00:11:26,240 --> 00:11:40,020
+Y تساوي C1Y1 زائد C2Y2 تساوي C1T تربيع زائد C2T سالب واحد 
+
+120
+00:11:40,020 --> 00:11:46,200
+ينقل هذا الجدران، صيوزي، للعاملة التفاضنية المعطاة 
+
+121
+00:12:07,110 --> 00:12:10,650
+الشباب أساسي اللي لازم يقولوا اسم، هذا معناه
+
+122
+00:12:23,890 --> 00:12:28,200
+اللي بتقوله، لو كان الرئيس انصار سفير يبقى.. هم
+
+123
+00:12:28,200 --> 00:12:31,240
+إحنا مش ضامنين هل هم فنضامن الـ solution ولا مش هم
+
+124
+00:12:31,240 --> 00:12:36,000
+بيطلعوا حلّين بس بضامن إنهم يجيبولي شكل حل العالم
+
+125
+00:12:36,000 --> 00:12:40,080
+طبعًا أعطيكم بعض أبطالين يتعاملوا مع بعضهم وعالم
+
+126
+00:12:40,080 --> 00:12:42,840
+كله مش عارف إنهم يتعاملوا مع بعضهم، اه يتعاملوا مع 
+
+127
+00:12:42,840 --> 00:12:43,220
+بعضهم
+
+128
+00:12:56,420 --> 00:13:01,100
+التسهيل اللي بتطبخوه يا بنات، لأن اكتبه على الشكل 
+
+129
+00:13:01,100 --> 00:13:06,540
+التالي، اكتبه
+
+130
+00:13:06,540 --> 00:13:15,120
+على الشكل التالي، مفهوم، إذا sometimes أحيانًا
+
+131
+00:13:15,120 --> 00:13:24,060
+sometimes it is difficult for us, it is difficult
+
+132
+00:13:56,810 --> 00:14:09,780
+Y1-Y2 of the differential equation، المعادلة 
+
+133
+00:14:09,780 --> 00:14:18,440
+التفاضلية، L of Y يستوي Y بقية، I، زائد P of Y بقية 
+
+134
+00:14:18,440 --> 00:14:26,200
+I، زائد Q of Y يستوي صفر، اللي هي بقية ساقين
+
+135
+00:14:26,200 --> 00:14:28,480
+المعادلة أقل واحد
+
+136
+00:14:30,870 --> 00:14:37,890
+لذلك if he ask،  بروحي نسأل السؤال in turn without an
+
+137
+00:14:37,890 --> 00:14:44,090
+essential equation، without that differential
+
+138
+00:14:44,090 --> 00:14:57,310
+equation، one always always has a fundamental 
+
+139
+00:15:03,770 --> 00:15:13,290
+هي أفضل إن ستة solutions لأي
+
+140
+00:15:13,290 --> 00:15:23,670
+علامة ستة؟ باسه لازم أكون متأكد عنها لأن ستة is
+
+141
+00:15:23,670 --> 00:15:26,690
+the following 
+
+142
+00:15:33,290 --> 00:15:36,930
+طبعًا هي بيقول ما.. ما يرام
+
+143
+00:15:50,970 --> 00:16:00,670
+هذا الـ برادر الصحي هو الـ N of Y، Y double prime U exp 
+
+144
+00:16:00,670 --> 00:16:07,130
+Y prime U exp Y is equal to 0، وخلّى الـ برادر اللي هو 
+
+145
+00:16:07,130 --> 00:16:08,910
+أخير واحد
+
+146
+00:16:13,250 --> 00:16:22,610
+and make P and Q continuous functions of continuous 
+
+147
+00:16:22,610 --> 00:16:30,850
+functions that one could consider on some open
+
+148
+00:16:30,850 --> 00:16:40,570
+interval، on some open interval R 
+
+149
+00:16:49,380 --> 00:17:02,020
+والثاني هو some plus some point in the interval R 
+
+150
+00:17:07,320 --> 00:17:13,800
+FYI، الوضع أكثر 
+
+151
+00:17:13,800 --> 00:17:24,540
+في الوضع، الوضع أكثر في الوضع، الوضع، الوضع، الوضع 
+
+152
+00:17:24,540 --> 00:17:26,360
+الوضع، الوضع، الوضع، الوضع، الوضع، الوضع، الوضع، الوضع
+
+153
+00:17:26,360 --> 00:17:26,660
+الوضع، الوضع، الوضع، الوضع، الوضع، الوضع، الوضع، الوضع
+
+154
+00:17:26,660 --> 00:17:26,900
+الوضع، الوضع، الوضع، الوضع، الوضع، الوضع، الوضع، الوضع
+
+155
+00:17:26,900 --> 00:17:29,240
+الوضع، الوضع، الوضع، الوضع، الوضع، الـ
+
+156
+00:17:34,220 --> 00:17:45,320
+هو أي واحد واثنين يساوي واحد واثنين يساوي
+
+157
+00:17:45,320 --> 00:17:53,160
+واحد واثنين يساوي واحد واثنين يساوي واحد واثنين
+
+158
+00:17:53,160 --> 00:17:56,640
+يساوي واحد واثنين يساوي واحد واثنين يساوي واحد 
+
+159
+00:18:00,890 --> 00:18:09,070
+مش عارف why واحد الـ.. why اللي.. اللي ما بتعش في
+
+160
+00:18:09,070 --> 00:18:14,090
+الواقع، أنا 
+
+161
+00:18:14,090 --> 00:18:20,390
+ما بتعش في الواقع، أنا ما بتعش في الواقع، أنا 
+
+162
+00:18:20,390 --> 00:18:22,550
+ما بتعش في الواقع 
+
+163
+00:18:32,010 --> 00:18:34,890
+ده.. ده.. ده.. ده..
+
+164
+00:19:24,740 --> 00:19:26,140
+مش عارف كده
+
+165
+00:19:51,720 --> 00:19:57,580
+ليه احترام لحن كبير؟ أو بعض السنة ولو.. أو لو نصف
+
+166
+00:19:57,580 --> 00:20:02,680
+سنة ماسباش زي.. ساوية زي.. ماشي بتحصل؟ هنا ك..
+
+167
+00:20:02,680 --> 00:20:06,980
+هنا صرفات أحيانًا، it is difficult to find an
+
+168
+00:20:06,980 --> 00:20:10,680
+underlying conceptual solution، يعني أحيانًا نصار 
+
+169
+00:20:10,680 --> 00:20:15,260
+أتولوجي مجموعة التفكير الأساسي على صورة واحد وواحد 
+
+170
+00:20:15,260 --> 00:20:21,860
+واثنين وخمسين وخمسين إلا عندنا، Sometimes the
+
+171
+00:20:21,860 --> 00:20:24,500
+definition of a fundamental system solution هو 
+
+172
+00:20:24,500 --> 00:20:28,120
+واحد هو كامل وعالي وطبعًا ويبقى كامل عندنا ويبقى
+
+173
+00:20:28,120 --> 00:20:31,740
+كامل على الشكل اللي عندنا، فأنت ده صح كامل يا عزيزي
+
+174
+00:20:31,740 --> 00:20:36,
+
+216
+00:25:05,200 --> 00:25:10,300
+عالمين عالم نظرية لغوية بيكون مجلد فعلي بقى تبسيط
+
+217
+00:25:10,300 --> 00:25:16,950
+فوق Solution specify يعني اللي ضارنتك من النظرية
+
+218
+00:25:16,950 --> 00:25:20,630
+اللي عندك هذه المعادلة يعني أنت ممكن تكون ممكن
+
+219
+00:25:20,630 --> 00:25:22,090
+تكون ممكن تكون ممكن تكون ممكن تكون ممكن تكون ممكن
+
+220
+00:25:22,090 --> 00:25:22,130
+تكون ممكن تكون ممكن تكون ممكن تكون ممكن تكون ممكن
+
+221
+00:25:22,130 --> 00:25:22,690
+تكون ممكن تكون ممكن تكون ممكن تكون ممكن تكون ممكن
+
+222
+00:25:22,690 --> 00:25:22,970
+تكون ممكن تكون ممكن تكون ممكن تكون ممكن تكون ممكن
+
+223
+00:25:22,970 --> 00:25:23,230
+تكون ممكن تكون ممكن تكون ممكن تكون ممكن تكون ممكن
+
+224
+00:25:23,230 --> 00:25:23,810
+تكون ممكن تكون ممكن تكون ممكن تكون ممكن تكون ممكن
+
+225
+00:25:23,810 --> 00:25:24,050
+تكون ممكن تكون ممكن تكون ممكن تكون ممكن تكون ممكن
+
+226
+00:25:24,050 --> 00:25:27,430
+تكون ممكن تكون ممكن تكون ممكن تكون ممكن تكون ممكن
+
+227
+00:25:27,430 --> 00:25:32,340
+تكون ممكن تكون ممكن عشان أجيب حالتين أطلع هذه
+
+228
+00:25:32,340 --> 00:25:37,740
+المعادلة بمعاملات مختلفة يعني تولدت تولدت واحد
+
+229
+00:25:37,740 --> 00:25:42,800
+صحيح وثالث اتنين يعني كله أصلا إذا بناء العلماني
+
+230
+00:25:42,800 --> 00:25:53,020
+بقوله let Y تساوي T بساطة في S solution of the
+
+231
+00:25:53,020 --> 00:25:57,740
+differential equation
+
+232
+00:25:58,980 --> 00:26:08,320
+one then three characteristic equation زي section
+
+233
+00:26:08,320 --> 00:26:14,860
+تلاتة واحدة بدا yes اليومين r تركيب سائر r ناقص
+
+234
+00:26:14,860 --> 00:26:21,400
+اتنين يساوي zero لو جئنا حللنا هذه المعادلة بصير
+
+235
+00:26:21,400 --> 00:26:24,380
+يحصل y ارد كورسين يساوي zero
+
+236
+00:26:47,020 --> 00:26:48,420
+Y1 Y2 Y3 Y4 Y5 Y6 Y7 Y8 Y9 Y10 Y11 Y12 Y13 Y12 Y13 Y14 Y14 Y15 Y15 Y15 Y15 Y15 Y15 Y15 Y15 Y15 Y15 Y15 Y15 Y15 Y15 Y15 Y15 Y15 Y15 Y15 Y15 Y15 Y15 Y15 Y15 Y15 Y15 Y15 Y15 Y15 Y15 Y15 Y15 Y15 Y15 Y15 Y15 Y15 Y15 Y15 Y15 Y15 Y15 Y15 Y15 Y15 Y15 Y15 Y15 Y15 Y15 Y15 Y15 Y15 Y15 Y15 Y15 Y15 Y15 Y15 Y15 Y15 Y15 Y15 Y15 Y15 Y15 Y15 Y15 Y15 Y15 Y15 Y15 Y15 Y15 Y15 Y15 Y15 Y15 Y15 Y15 Y15 Y15
+
+237
+00:26:49,220 --> 00:26:58,900
+and why in the end you say إيه هو اسم أخصك ده؟ طيب
+
+238
+00:26:58,900 --> 00:27:04,820
+إذا شوف هدول بيجيبولي general solution ولا لا
+
+239
+00:27:04,820 --> 00:27:09,040
+فبعدين بقولوا إذا أخذ ال wallets can have a
+
+240
+00:27:09,040 --> 00:27:13,140
+function of T فالحل الأول يستيقظ
+
+241
+00:27:17,680 --> 00:27:30,740
+E-E-E-E-E-E-E-E-E-E-E-E-E-E-E-E-E-E-E-E-E-E-E-E-E
+
+242
+00:27:30,740 --> 00:27:40,160
+-E-E-E-E
+
+243
+00:27:40,160 --> 00:27:50,880
+-E-E عمر هذه تساوي 0؟ لأ لأ لأ لأ لأ لأ لأ لأ لأ لأ
+
+244
+00:27:50,880 --> 00:27:50,920
+لأ لأ لأ لأ لأ لأ لأ لأ لأ لأ لأ لأ لأ لأ لأ لأ
+
+245
+00:27:50,920 --> 00:27:54,460
+لأ لأ لأ لأ لأ لأ لأ لأ لأ لأ لأ لأ لأ لأ لأ لأ
+
+246
+00:27:54,460 --> 00:27:55,420
+لأ لأ لأ لأ لأ لأ لأ لأ لأ لأ لأ لأ لأ لأ لأ لأ
+
+247
+00:27:55,420 --> 00:27:56,000
+لأ لأ لأ لأ لأ لأ لأ لأ لأ لأ لأ لأ لأ لأ لأ لأ
+
+248
+00:27:56,000 --> 00:27:57,440
+لأ لأ لأ لأ لأ لأ لأ لأ لأ لأ لأ لأ لأ لأ لأ لأ
+
+249
+00:27:57,440 --> 00:28:08,780
+لأ لأ لأ لأ لأ لأ لأ لأ لأ لأ لأ
+
+250
+00:28:08,780 --> 00:28:10,080
+لأ ل
+
+251
+00:28:14,670 --> 00:28:25,550
+-84 هي fundamental set
+
+252
+00:28:25,550 --> 00:28:30,710
+of solutions
+
+253
+00:28:30,710 --> 00:28:41,610
+of the differential equation 1 لأن هذول بكاملور هي
+
+254
+00:28:41,610 --> 00:28:48,130
+مجموعة حلول أساسية للمعادلة مين؟ للمعادلة واحدة،
+
+255
+00:28:48,130 --> 00:28:54,210
+مبتعدين ومبتعدين آخر مجموعة الحلول الأساسية
+
+256
+00:28:54,210 --> 00:29:00,260
+للمعادلة هذه اللي بيطبق عليهم هي النظرية اللي
+
+257
+00:29:00,260 --> 00:29:05,060
+عندنا، طب تعال نشوف هل النظرية اللي عندنا بتطبق
+
+258
+00:29:05,060 --> 00:29:08,680
+عليها هذا الكلب أو لا، إذا بتطبق فهذا هو الموضوع،
+
+259
+00:29:08,680 --> 00:29:13,840
+وما بتطبقش فيه، يبقى نتفكس فيه، فيه شغلة ثانية،
+
+260
+00:29:13,840 --> 00:29:18,370
+إيه الشغلة الثانية؟ عشان نشوف دول ونشوف نشر متانى
+
+261
+00:29:18,370 --> 00:29:24,150
+ونكسر متانى، فنشوف كل الشروط الأربع هذه محققة و
+
+262
+00:29:24,150 --> 00:29:32,030
+مدادة، بمجرد ما نقوله، يبقى Y واحد عند اللقطة اللي
+
+263
+00:29:32,030 --> 00:29:36,390
+يحصل هذه، واللقطة اللي يحصل هذه كم كيلو متساوم
+
+264
+00:29:36,390 --> 00:29:43,820
+جدا، Zero يبقى بدل أقول Y واحد عند الـ Zero هاي Y
+
+265
+00:29:43,820 --> 00:29:48,760
+واحد يبقى a on zero يساوي واحد إذا تحققت ال
+
+266
+00:29:48,760 --> 00:29:56,220
+condition الأول ماشي الحاجة واحد الـ Y واحد اتقرع
+
+267
+00:29:56,220 --> 00:29:57,620
+إيه تدري يساوي
+
+268
+00:30:00,540 --> 00:30:08,940
+يبقى هذا بدل يعطيك M Y 1 D Prime M Zero تساوي واحد
+
+269
+00:30:08,940 --> 00:30:14,140
+يبقى الـ condition الثاني هذا اتحقق لأ ما اتحقق
+
+270
+00:30:14,140 --> 00:30:20,020
+لغاية حتى لو لم يبقى اتحقق ويبقى فاشل فاشل الحلول
+
+271
+00:30:20,020 --> 00:30:24,660
+جميعا من مجموعة الحلول التي بتحقق اللغة اللي
+
+272
+00:30:24,660 --> 00:30:33,110
+عندناها طيب المرة لو جت أخد Y2 عند الـ 0 اللي بدها
+
+273
+00:30:33,110 --> 00:30:39,270
+تساوي a أو الـ 0 طبعا اللي بدالي إذا الفشل الـ
+
+274
+00:30:39,270 --> 00:30:46,010
+condition الثاني هذا صاحب واحد وليس Zero طيب و الـ
+
+275
+00:30:46,010 --> 00:30:56,220
+Y2 prime عند Y2 prime بدو يساوي إنه ناقص اتنين فيه
+
+276
+00:30:56,220 --> 00:31:01,540
+قص ناقص اتنين هذا بيجيب عليك إنه Y اتنين يفرق
+
+277
+00:31:01,540 --> 00:31:06,020
+عند الـ Zero بيجيب عليك إنه ناقص اتنين ناقص اتنين
+
+278
+00:31:06,020 --> 00:31:11,420
+يعني لا شرط هذا اتحقق ولا شرط هذا اتحقق ولا شرط
+
+279
+00:31:11,420 --> 00:31:17,300
+هذا اتطبق مش واحد يعني الشروط الأربعة عملها ما حققتش
+
+280
+00:31:17,300 --> 00:31:26,130
+اتنين يبقى من هذا الاتنين هذا بالنسبالي بيقولك إن الـ
+
+281
+00:31:26,130 --> 00:31:39,050
+Y واحد و Y اتنين are not satisfied with conditions
+
+282
+00:31:39,050 --> 00:31:44,350
+of
+
+283
+00:31:44,350 --> 00:31:46,870
+the theory
+
+284
+00:31:50,060 --> 00:31:55,680
+اللي بيقولوا تحققوش لشروط المعبارية الله أشفننا يا
+
+285
+00:31:55,680 --> 00:32:02,340
+أمالك يرزمتك ترزمت حالك
+
+286
+00:32:02,340 --> 00:32:17,180
+خدمة
+
+287
+00:32:17,180 --> 00:32:23,910
+كلمة فالحلول اللي احنا جبناهم هدول صحيح تعملولي
+
+288
+00:32:23,910 --> 00:32:28,710
+فضل ما يكونوا سلوك السبعة النظرية لكن حققوش الانش
+
+289
+00:32:28,710 --> 00:32:33,890
+السلوك السبعة النظرية سلوك وشروط عليك لذلك حتة دي
+
+290
+00:32:33,890 --> 00:32:40,750
+specified لأ أربعة الأصغر لأن هدول اللي بيحققوا
+
+291
+00:32:40,750 --> 00:32:44,870
+مشروع تبع النموية اللي عندنا هذه بتقولوا ماشي طبعا
+
+292
+00:32:44,870 --> 00:32:50,650
+بدي أفضل إن عندي حلول بدل الحلول هدول يعني هدول
+
+293
+00:32:50,650 --> 00:32:55,890
+الحلول مدني حلول مجموعة الحلول الكاسرسية إذا منهم
+
+294
+00:32:55,890 --> 00:33:01,950
+بدي أخلق شكل الحل اللي بيحقق مان اللي بيحقق النموية
+
+295
+00:33:01,950 --> 00:33:12,160
+اللي عندنا هذه فبجري أقوله هذا as long that الـ Y
+
+296
+00:33:12,160 --> 00:33:20,680
+كلفة بيساوي C1 بيبقى مستيقظ زي C2 بيبقى مستيقظ
+
+297
+00:33:25,470 --> 00:33:34,610
+يجب أن أحفظ الـ Y3 عند الـ 0 يجب أن أحفظ الـ Y3
+
+298
+00:33:34,610 --> 00:33:37,130
+عند الـ 0 يجب أن أحفظ الـ Y3 عند الـ 0 يجب أن أحفظ
+
+299
+00:33:37,130 --> 00:33:39,330
+الـ Y3 عند الـ 0 يجب أن أحفظ الـ Y3 عند الـ 0 يجب
+
+300
+00:33:39,330 --> 00:33:43,830
+أن أحفظ الـ Y3
+
+301
+00:33:43,830 --> 00:33:46,870
+عند الـ 0 يجب أن أحفظ الـ Y3 عند الـ 0 يجب أن أحفظ
+
+302
+00:33:46,870 --> 00:33:50,290
+الـ Y3 عند الـ 0 يجب أن أحفظ الـ Y3 عند الـ 0 يجب
+
+303
+00:33:50,290 --> 00:33:52,510
+أن أحفظ الـ Y3 عند الـ 0 يجب أن أحفظ الـ Y3 عند
+
+304
+00:33:52,510 --> 00:33:52,790
+Y3 عند الـ 0 يجب أن أحفظ الـ Y3 عند الـ 0
+
+305
+00:34:15,230 --> 00:34:19,830
+يجب أن أنا
+
+306
+00:34:19,830 --> 00:34:27,740
+أفرض عندي حالتين سميت الأول Y3 والثاني Y4 وكل واحد
+
+307
+00:34:27,740 --> 00:34:33,980
+فيهم اعتمد على الحالتين اللي قلع لهم هدول لأن هدول
+
+308
+00:34:33,980 --> 00:34:38,790
+قلعوا ليه ماني قلتلهم الانتسابية بس مش هاجي مجموعة
+
+309
+00:34:38,790 --> 00:34:43,450
+الحلول اللي بتحقق شروط النظرية، روحت أنا فرطني إن
+
+310
+00:34:43,450 --> 00:34:48,870
+عندي حلل بتحقق شروط النظرية، اتخذت شروط النظرية و
+
+311
+00:34:48,870 --> 00:34:54,470
+قلت أروح أدور أنتي عندي C1 وC2 وC3 وC4 ولا لا،
+
+312
+00:34:54,470 --> 00:34:59,730
+لأن أنا جيتهم بتخلص تمام 100% بيصير عندنا ضغوية
+
+313
+00:34:59,730 --> 00:35:04,690
+حققة تنقل لهم من هنا إلى الشمال بيقولوا كويس كده
+
+314
+00:35:04,690 --> 00:35:12,030
+بيقولوا واحد ينقل الـ C1 وC2 وC3 وC4 بتمسك
+
+315
+00:35:12,030 --> 00:35:20,530
+الأولى اللي بتاخد Y3 عند Zero Yourself Y3 عند Zero
+
+316
+00:35:20,530 --> 00:35:30,980
+واحد ينقش بتعطيك هنا Y1 بتساوي C1 زي C2 والبطء
+
+317
+00:35:30,980 --> 00:35:43,860
+بتتاجر لـ Y3' يبقى Y3' يبقى Y3'
+
+318
+00:35:43,860 --> 00:35:51,260
+يبقى Y3' يبقى Y3' يبقى Y3' يبقى Y3' يبقى Y3' بدي
+
+319
+00:35:51,260 --> 00:35:58,520
+أعطينا إن Y تلاتة prime عند 0 Y تلاتة prime عند 0
+
+320
+00:35:58,520 --> 00:36:09,920
+بيساوي 0 بيساوي C1 ناقص اتنين C2 تمام؟ يبقى أولاً
+
+321
+00:36:09,920 --> 00:36:16,080
+صار عندنا معادلتين هدول معادلتين هنا وجه الطرف
+
+322
+00:36:16,080 --> 00:36:25,910
+ثاني بتتنصر اتنين يساوي C واحد أو اتنين C واحد زائد
+
+323
+00:36:25,910 --> 00:36:33,790
+اتنين C اتنين هذه زي ما هي Zero يساوي C واحد نقص
+
+324
+00:36:33,790 --> 00:36:40,010
+اتنين C اتنين أجمعها هلأ مع السلامة تصير تلاتة C
+
+325
+00:36:40,010 --> 00:36:45,210
+واحد تبقى تساوي اتنين تبقى C واحد تبقى ساوي درجة
+
+326
+00:36:45,210 --> 00:36:52,870
+طول الـ T طيب تمام لو الـ C1 ساوي طول 2 يبقى إيش
+
+327
+00:36:52,870 --> 00:36:59,490
+بسيط عنك اتنين C2 وأتيها على الشكل الثاني فتبقى
+
+328
+00:36:59,490 --> 00:37:04,450
+ساوي طول 2 أنا بدي أعطيك اللي بسيط اتنين فساوية
+
+329
+00:37:04,450 --> 00:37:12,670
+قدامك طول يبقى هنا Zero Y تلاتة ثم ساعة والآن Y
+
+330
+00:37:12,670 --> 00:37:17,970
+تلاتة أول واحد Y تلاتة ثم فوق C1
+
+331
+00:37:32,650 --> 00:37:37,250
+يبقى هذا الحل اللي بيحقق الـ two conditions اللي
+
+332
+00:37:37,250 --> 00:37:41,730
+اتنين هدول و Y تلاتة احدة زي رقم واحد و Y تلاتة و 5
+
+333
+00:37:41,730 --> 00:37:42,970
+احدة زي رقم واحد و Y تلاتة و 5 احدة زي رقم واحد و Y
+
+334
+00:37:42,970 --> 00:37:43,030
+تلاتة و 5 احدة زي رقم واحد و Y تلاتة و 5 احدة زي رقم
+
+335
+00:37:43,030 --> 00:37:43,270
+واحد و Y تلاتة و 5 احدة زي رقم واحد و Y تلاتة و 5 احدة
+
+336
+00:37:43,270 --> 00:37:43,850
+و 5 احدة زي رقم واحد و Y تلاتة و 5 احدة زي رقم واحد
+
+337
+00:37:43,850 --> 00:37:45,100
+و Y تلاتة و 5 احدة زي رقم واحد و Y إيه اللي عملنا الـ
+
+338
+00:37:45,100 --> 00:37:51,820
+Y3 بنروح نعمله لمان؟ Y4 لجمالي بيقولوا احنا عندنا
+
+339
+00:37:51,820 --> 00:38:01,380
+Y4 تساوي C3 E أس D زائد C4 E أس ناقص اتنين D
+
+340
+00:38:01,380 --> 00:38:11,080
+لجمالي أنا عليه الـ Dragon والـ Y4 Prime بالمرة
+
+341
+00:38:11,610 --> 00:38:19,210
+بتساوي C تلاتة minus t نقص اتنين C أربعة minus
+
+342
+00:38:19,210 --> 00:38:29,270
+اتنين D الأمر بيكون Y أربعة عند Zero بتزاوي
+
+343
+00:38:29,270 --> 00:38:37,070
+بتساوي C تلاتة زائد C أربعة حسب الـ condition اللي
+
+344
+00:38:37,070 --> 00:38:42,700
+عيبنا هذا بتساوي اكتران بتساوي Zero الآن بالشكل
+
+345
+00:38:42,700 --> 00:38:48,680
+اللي Y prime أربعة and Zero لسبع إيه Y prime
+
+346
+00:38:48,680 --> 00:38:56,180
+أربعة and Zero إنها تعطينا C تلاتة ناقص اتنين C
+
+347
+00:38:56,180 --> 00:39:04,580
+أربعة بدو يساوي الـ condition كده واحد صحيح إيه؟
+
+348
+00:39:04,580 --> 00:39:09,830
+بدنا ندى لو دينا ضربنا في اتنين يبقى لو ضربنا في
+
+349
+00:39:09,830 --> 00:39:14,130
+اتنين المعادلة الأولى بصير اتنين C تلاتة زائد
+
+350
+00:39:14,130 --> 00:39:19,090
+اتنين C أربعة يساوي Zero وهذه بدي أخليها زي ما هي
+
+351
+00:39:19,090 --> 00:39:26,690
+C تلاتة ناقص اتنين C أربعة يساوي جدار واحد أكبر
+
+352
+00:39:26,690 --> 00:39:32,910
+بروح هذا يبقى تلاتة C تلاتة يساوي واحد يبقى C
+
+353
+00:39:32,910 --> 00:39:40,930
+تلاتة يساوي جدار تلت لما C3 يتساوى بالطول C4 يتساوى
+
+354
+00:39:40,930 --> 00:40:00,870
+بالطول C4 يتساوى بالطول C4 يتساوى بالطول C4
+
+355
+00:40:00,870 --> 00:40:04,070
+يتساوى
+
+356
+00:40:04,070 --> 00:40:05,390
+بالطول
+
+357
+00:40:09,010 --> 00:40:13,430
+هي هدول اللي اتجهتين اللي شبكوا بحق كل شبكة
+
+358
+00:40:13,430 --> 00:40:21,270
+النظرية متأكد؟ نعم نعم نعم متأكد أنا أتأكد كمان و
+
+359
+00:40:21,270 --> 00:40:26,610
+الله زي أنا أنا أنا أنا أنا أنا أنا أنا أنا أنا
+
+360
+00:40:26,610 --> 00:40:31,470
+أنا أنا أنا أنا أنا أنا أنا
+
+361
+00:40:35,790 --> 00:40:43,450
+مشتركة في الـ Y3 وين الـ Y3' هي؟ إذا الـ Y3' عندي هو
+
+362
+00:40:43,450 --> 00:40:46,390
+0، فمشتركة في الـ Y3
+
+363
+00:40:52,800 --> 00:40:58,020
+نقصت كثير، طبعا، عامل الـ development كثير، نقصت
+
+364
+00:40:58,020 --> 00:41:01,540
+كثير، easy way، ده مظبوط، ما يتعقب في الـ
+
+365
+00:41:01,540 --> 00:41:04,940
+professions، وبالبيت الهدف يتحفظ it to
+
+366
+00:41:04,940 --> 00:41:09,700
+professions، فتاني على سؤال إيش ملي، happy، you
+
+367
+00:41:09,700 --> 00:41:13,320
+can't even accept the solution specified by
+
+368
+00:41:18,280 --> 00:41:23,320
+هؤلاء اللي هم مجموعة الحلول الأساسي اللي بيحققوا
+
+369
+00:41:23,320 --> 00:41:34,620
+شروط النظرية يبقى لنا ساعة Y3 and Y4 for the
+
+370
+00:41:34,620 --> 00:41:40,480
+fundamental set
+
+371
+00:41:40,480 --> 00:41:42,840
+of
+
+372
+00:41:52,210 --> 00:42:01,170
+set of solutions that satisfy
+
+373
+00:42:01,170 --> 00:42:13,030
+.. that satisfy the above premise إن كانت هؤلاء
+
+374
+00:42:13,030 --> 00:42:17,290
+الأفكار اللي بيحصلون من النظرية أدنى
+
+375
+00:42:26,390 --> 00:42:29,830
+ناخد بعض الأسئلة من الأسئلة التي كنا نلاقيها قبلها
+
+376
+00:42:29,830 --> 00:42:34,510
+وبعض الأسئلة التي تتحركين فيها الفيديوهات التي
+
+377
+00:42:34,510 --> 00:42:38,590
+تتحركين فيها هذه المساحة وخلال استخدام الوطن اللي
+
+378
+00:42:38,590 --> 00:42:42,970
+تحينا منه نستخدم هذه الأسئلة جميعا
+
+379
+00:42:50,130 --> 00:43:08,590
+اللي هو رفع الطوابق اللي هو رفع
+
+380
+00:43:08,590 --> 00:43:08,910
+الطوابق اللي هو رفع الطوابق اللي هو رفع الطوابق
+
+381
+00:43:08,910 --> 00:43:12,950
+رفع الطوابق اللي هو رفع الطوابق
+
+431
+00:48:11,570 --> 00:48:15,810
+of linear differential equation
+
+432
+00:48:31,510 --> 00:48:46,430
+سؤال تسعة عشر يقول ما F ترانسكل تبع الـ F والـ D F
+
+433
+00:48:46,430 --> 00:48:50,190
+ترانسكل
+
+434
+00:48:50,190 --> 00:48:52,930
+F
+
+435
+00:49:00,030 --> 00:49:13,530
+I F وإذا كان الـ U يساوي اثنين F ناقص G الـ U يساوي
+
+436
+00:49:13,530 --> 00:49:24,010
+اثنين فموينة P فتر ساوي F زائد اثنين G فانا ونسكن
+
+437
+00:49:24,010 --> 00:49:29,090
+I فأنا و نسكن
+
+438
+00:49:35,820 --> 00:49:50,160
+لدينا مانستين اللي هو W تبع الـ U والـ V of U and الـ
+
+439
+00:49:50,160 --> 00:50:01,080
+V الـ U and الـ V in pairs of المانستين تبع الـ F و
+
+440
+00:50:01,080 --> 00:50:01,620
+الـ G
+
+441
+00:50:38,290 --> 00:50:44,610
+سؤال مرة ثانية يقول لو كان الـ W of F and G هو
+
+442
+00:50:44,610 --> 00:50:51,660
+رونسكين تبع الدالة F و G وإذا كان الـ U function هي
+
+443
+00:50:51,660 --> 00:50:57,240
+عبارة عن اثنين F ناقص D والـ P function LF زي
+
+444
+00:50:57,240 --> 00:51:02,900
+الاثنين كان هذا الـ Wronskian تبع U بدلالة
+
+445
+00:51:02,900 --> 00:51:08,380
+الـ Wronskian تبع من F و D فقولوا طيب تعالوا نجيب
+
+446
+00:51:08,380 --> 00:51:12,690
+الـ Wronskian تبع الـ F و D ونشوف شو شكله، يبقى أنا
+
+447
+00:51:12,690 --> 00:51:18,690
+لو جيت لـ Wronskian تبع الـ F والـ G بقول له هذه المحدد
+
+448
+00:51:18,690 --> 00:51:27,890
+هذه F هذه G هذه F' هذه G' بدنا نفكر محدد هذا معناه
+
+449
+00:51:27,890 --> 00:51:35,050
+يبقى F في G' ناقص F' في G
+
+450
+00:51:41,560 --> 00:51:46,800
+احنا بدنا مين؟ بدنا Wronskian تبع الـ U و الـ V يبقى
+
+451
+00:51:46,800 --> 00:51:53,220
+بدنا نأخذ Wronskian تبع الـ U و الـ V يبقى الـ U الـ V
+
+452
+00:51:53,220 --> 00:51:59,760
+الـ U prime الـ V prime مطلوب ايه؟ يبقى هذا الكلام
+
+453
+00:51:59,760 --> 00:52:06,760
+بده يساوي الـ U بده أشيله واحطه اثنين F ناقص 
+
+454
+00:52:06,760 --> 00:52:15,180
+الـ G، الـ V، للـ F زائد اثنين G، الـ V، لـ U'، المبدأ
+
+455
+00:52:15,180 --> 00:52:21,100
+اشتق هذا، يبقى مشتقة المجموعة الجبرية لدالتين يبقى
+
+456
+00:52:21,100 --> 00:52:30,760
+اثنين F' ناقص G'، مشتقة هذه لـ F' زائد اثنين G'
+
+457
+00:52:31,400 --> 00:52:41,030
+يساوي، يبدا أفكر محدد هذا يبقى هدف اللي يقينه 2F-G F
+
+458
+00:52:41,030 --> 00:52:47,690
+prime زي 2G prime أي حاصل ضرب عناصر القطر الرئيسي
+
+459
+00:52:47,690 --> 00:52:57,810
+ناقص حاصل ضرب عناصر القطر الثانوي F زي 2G في 2F
+
+460
+00:52:57,810 --> 00:53:06,590
+prime ناقص G prime، يبقى هذا قيمة مين المحدد؟ تعالوا 
+
+461
+00:53:06,590 --> 00:53:11,150
+نفك خلاص وسط، يعني أفك القيود ده للمكان الحالي بيها
+
+462
+00:53:11,150 --> 00:53:15,550
+ونشوف إلى أين بدنا نوصل، يبقى هذا يا بنات بدها
+
+463
+00:53:15,550 --> 00:53:27,230
+تساوي اثنين F F F Prime زائد اثنين F G Prime اثنين
+
+464
+00:53:27,230 --> 00:53:31,090
+F F F Prime اثنين F F G Prime
+
+466
+00:53:57,250 --> 00:54:04,850
+أنا ضربت اثنين هذول في البعض ناقص اثنين G G prime
+
+467
+00:54:05,840 --> 00:54:13,780
+خلصت الـ term الأول بدي أدربه اثنين F F prime بس
+
+468
+00:54:13,780 --> 00:54:23,540
+بشرط من سالب يبقى سالب اثنين F F prime هنا سالب F
+
+469
+00:54:23,540 --> 00:54:27,620
+في سالب G زائد F G prime
+
+470
+00:54:35,880 --> 00:54:48,600
+ناقص أربعة F prime G ناقص أربعة F prime G ناقص مع ناقص
+
+471
+00:54:48,600 --> 00:54:55,540
+بصير زائد اثنين G G prime يبقى زائد اثنين G G
+
+472
+00:54:55,540 --> 00:54:55,960
+prime
+
+473
+00:55:06,960 --> 00:55:18,260
+تعالى تطلعلي 4 F G Prime وعندك F G Prime بصير خمسة
+
+474
+00:55:18,260 --> 00:55:27,610
+F G Prime، هذه بالسالب وهذه بالسالب التنتين نفس
+
+475
+00:55:27,610 --> 00:55:36,290
+الشيء مظبوط يبقى ناقص خمسة F prime G شو رأيك نأخذ
+
+476
+00:55:36,290 --> 00:55:41,090
+خمسة عامل مشترك ونشوف لوين بدنا نوصل، يبقى لو جينا
+
+477
+00:55:41,090 --> 00:55:48,970
+خمسة عامل مشترك بظل F G prime ناقص
+
+478
+00:55:53,320 --> 00:55:56,640
+طلع في المقدار بين القوسين
+
+479
+00:55:58,970 --> 00:56:11,790
+FG'-F'G FG'
+
+480
+00:56:11,790 --> 00:56:18,370
+-F'G FG'
+
+481
+00:56:21,370 --> 00:56:28,740
+-F'G FG'-F'G FG'-F'G طيب بدنا منكم exercises ثلاثة
+
+482
+00:56:28,740 --> 00:56:35,980
+اثنين المسائل التالية، يبقى exercises ثلاثة اثنين
+
+483
+00:56:35,980 --> 00:56:46,000
+بدنا المسائل من واحد لغاية أربع عشرة، والأد ومن سبعة عشر
+
+484
+00:56:46,000 --> 00:56:53,140
+لغاية ستة وعشرين، يبقى
+
+485
+00:56:53,140 --> 00:56:54,360
+بدنا المسائل هذه
+
+486
+00:56:58,690 --> 00:57:06,610
+بنروح الآن لـ section اللي بعده مرتبط ارتباط وثيق
+
+487
+00:57:06,610 --> 00:57:10,950
+بالـ Wronskian تبعنا هذا بيعتمد عليه اعتماد كله
+
+488
+00:57:10,950 --> 00:57:20,410
+يبقى section 3 3 بتحدث عن الـ linear independence
+
+489
+00:57:20,410 --> 00:57:24,490
+linear
+
+490
+00:57:24,490 --> 00:57:41,530
+independence and the Wronskian نعطي
+
+491
+00:57:41,530 --> 00:57:46,290
+تعريف وبعد ذلك بناخد أمثلة definition two
+
+492
+00:57:46,290 --> 00:57:57,750
+functions two functions f of t and الـ g of t are
+
+493
+00:57:57,750 --> 00:58:06,310
+said to be linearly
+
+494
+00:58:06,310 --> 00:58:07,390
+dependent
+
+495
+00:58:17,220 --> 00:58:23,580
+سأختصر كلمة linearly dependent يا بنات إلى الـ LD من
+
+496
+00:58:23,580 --> 00:58:38,900
+الآن فصاعدًا on an interval I if
+
+497
+00:58:38,900 --> 00:58:48,630
+there exist if there exist two constants two
+
+498
+00:58:48,630 --> 00:58:55,510
+constants ثابتين كواحد
+
+499
+00:58:55,510 --> 00:59:08,830
+and كاثنين not both zero not both zero مش كلهم
+
+500
+00:59:08,830 --> 00:59:19,990
+أصفار such that such that بحيث أن كواحد في الـ F of T
+
+501
+00:59:19,990 --> 00:59:29,570
+زائد كاثنين في الـ G of T بده يساوي zero for all T
+
+502
+00:59:29,570 --> 00:59:39,910
+اللي موجودة في الـ interval I also وكذلك الـ F and
+
+503
+00:59:39,910 --> 00:59:45,790
+الـ G are called
+
+504
+00:59:49,870 --> 01:00:06,330
+Linearly Independent LPI
+
+505
+01:00:06,330 --> 01:00:15,370
+FK1
+
+506
+01:00:15,860 --> 01:00:23,100
+في الـ F of T زائد K اثنين في الـ G of T يساوي Zero
+
+507
+01:00:23,100 --> 01:00:32,200
+Then K واحد بده يساوي K اثنين بده يساوي Zero
+
+508
+01:00:32,200 --> 01:00:40,000
+Example
+
+509
+01:00:40,000 --> 01:00:40,420
+one
+
+510
+01:00:48,210 --> 01:00:56,330
+determine whether determine
+
+511
+01:00:56,330 --> 01:01:08,050
+whether the given pair of functions the given pair
+
+512
+01:01:08,050 --> 01:01:14,330
+of functions are
+
+513
+01:01:15,490 --> 01:01:26,090
+Linearly Independent or Linearly Dependent الـ
+
+514
+01:01:26,090 --> 01:01:37,310
+F of T يساوي E أس ثلاثة T والـ G of T يساوي A أس
+
+515
+01:01:37,310 --> 01:01:40,650
+ثلاثة في T ناقص الواحد
+
+516
+01:01:48,330 --> 01:01:52,650
+طيب بنجي لعنوان اللي احنا رافعينه linear
+
+517
+01:01:52,650 --> 01:01:59,510
+independence الاستقلال الخطي عند الـ Wronskian والـ
+
+518
+01:01:59,510 --> 01:02:04,370
+Wronskian يعني هنشوف شو علاقة الاستقلال الخطي و
+
+519
+01:02:04,370 --> 01:02:10,250
+الاعتماد الخطي كمان بالـ Wronskian بنجي للتعريف اللي
+
+520
+01:02:10,250 --> 01:02:16,500
+احنا كاتبينه، بقول لو عندي two functions دالتين هذول
+
+521
+01:02:16,500 --> 01:02:20,960
+اللي بقول عنهم linearly dependent يعني بيتمدوا على
+
+522
+01:02:20,960 --> 01:02:27,520
+بعض خطيًا، linearly dependent هاختصرها إلى LD،
+
+523
+01:02:27,520 --> 01:02:32,280
+linearly dependent على الفترة اللي عندنا هذه if
+
+524
+01:02:32,280 --> 01:02:36,680
+they exist يعني إذا جدرنا نلاقي هذا الـ E المجلوب
+
+525
+01:02:36,680 --> 01:02:42,570
+هنا there exist إذا وجدت
+
+526
+01:02:42,570 --> 01:02:48,710
+ثابتين K واحد أو K اثنين، نقبض الـ 0 مش كلهم أصفار
+
+527
+01:02:48,710 --> 01:02:53,790
+بحيث أن K واحد في F of T زائد الـ K اثنين في G of T
+
+528
+01:02:53,790 --> 01:02:58,010
+بيدوا يساوي 0 لكل T الموجودة في I
+
+529
+01:03:01,400 --> 01:03:06,600
+أنا عندي دالتين F و G وبدي أشوف هل الدالتين هدول
+
+530
+01:03:06,600 --> 01:03:13,340
+معتمدتين على بعض خطيًا والله مستقلتين عن بعض خطيًا
+
+531
+01:03:13,340 --> 01:03:20,280
+بقولي آه إذا بتقدر تلاقي ثوابت اثنين ليس بالضرورة
+
+532
+01:03:20,280 --> 01:03:24,660
+أنه .. مش ليس بالضرورة يعني لو كان فيهم واحد صفر
+
+533
+01:03:24,660 --> 01:03:28,640
+و ثاني لأ فاش مشكلة، وإذا اثنين لا يساوي صفر
+
+534
+01:03:28,640 --> 01:03:32,470
+برضه فاش مشكلة، بحيث لو ضربت كونوسونت في الدالة
+
+535
+01:03:32,470 --> 01:03:34,950
+الأولى وكونوسونت في الدالة الثانية وجمعتهم، ماذي
+
+536
+01:03:34,950 --> 01:03:40,490
+يكون الناتج؟ صفر طيب، شو معنى الـ linear
+
+537
+01:03:40,490 --> 01:03:46,630
+independence للاستقلال؟ الخاطئ بيقول also الـ F و الـ G
+
+538
+01:03:46,630 --> 01:03:51,610
+أركون linearly independent الدالتين هدول مستقلتين
+
+539
+01:03:51,610 --> 01:03:55,910
+على البعض خطيًا، يعني دولة ماهي محتاجة كل دولة
+
+540
+01:03:55,910 --> 01:04:00,010
+لحالها مالها linearly independent
+
+541
+01:04:11,240 --> 01:04:18,580
+إذا أنا مش هنفرق بين الأمرين هل الدالتين هدول
+
+542
+01:04:18,580 --> 01:04:24,960
+مستقلتين خطيًا ومعتمدتين على بعض خطيًا، بدي ادورلي
+
+543
+01:04:24,960 --> 01:04:28,820
+على ثوابت اثنين، اضرب ثابت في الأول وثابت الثاني و
+
+544
+01:04:28,820 --> 01:04:33,120
+أجمع والاقيهم يساوي قداش صفر بعد ما يطلع في صفر
+
+545
+01:04:33,120 --> 01:04:38,540
+باطل على الثوابت الثاني والله إذا ثوابت اثنين أصفار
+
+546
+01:04:38,540 --> 01:04:44,180
+يبقى هدول الدالتين linearly independent وأن كان
+
+547
+01:04:44,180 --> 01:04:48,980
+اثنين مهماش أصفار أو واحد صفر والتاني اللي لأ يبقى
+
+548
+01:04:48,980 --> 01:04:53,650
+linearly dependent واضحة الصورة، يبقى عرفنا شو
+
+549
+01:04:53,650 --> 01:04:57,110
+الفرق بين الـ linear dependence والـ linear
+
+550
+01:04:57,110 --> 01:05:01,910
+independence الناس اللي أخذوا الجبر الخطي نفس الكلام
+
+551
+01:05:01,910 --> 01:05:07,050
+اللي بياخدوه في الجبر الخطي حرفيًا ماغيرناش فيه ولا
+
+552
+01:05:07,050 --> 01:05:12,590
+حاجة، طيب بدنا ننقل هذا المثال على أرض الواقع ببعض
+
+553
+01:05:12,590 --> 01:05:16,510
+الأمثلة، Gallery determine whether the given pair of
+
+554
+01:05:16,510 --> 01:05:20,790
+functions حدد لمين من أزواج الدوال التي بتبقى
+
+555
+01:05:20,790 --> 01:05:25,030
+linearly independent ومين linearly dependent
+
+556
+01:05:50,220 --> 01:05:58,200
+هل تقدر تجيبنا تابع مضروبة في الدالة الأولى وثابت
+
+557
+01:05:58,200 --> 01:06:04,000
+ثاني مضروبة في الدالة الثانية ونجمع يطلع النتج
+
+558
+01:06:04,000 --> 01:06:11,360
+يساوي zero نقدر وبعد ذلك بظهر أشوف شو شكلهم، ها
+
+559
+01:06:11,360 --> 01:06:14,460
+تقدروا؟
+
+560
+01:06:14,460 --> 01:06:22,480
+طيب ايش رأيك؟ هنا بداجي أقول assume افترضوا there
+
+561
+01:06:22,480 --> 01:06:32,940
+exists c1 و c2 such that بحيث أن c1 في e أس ثلاثة
+
+562
+01:06:32,940 --> 01:06:39,380
+t زائد c2 في e أس ثلاثة t ناقص ثلاثة بده يساوي zero
+
+563
+01:06:42,410 --> 01:06:47,350
+يلا هدّ أنتو بيجي 48 طالب أو زدت واحدة صارت 49
+
+564
+01:06:47,350 --> 01:06:53,170
+بدنا نعرف قداش، ها كل واحدة تفكر تجيب ثوابت من
+
+565
+01:06:53,170 --> 01:06:58,070
+عندها تقولي ها دي لو أخذنا c1 بكذا و c2 بكذا بيطلع
+
+566
+01:06:58,070 --> 01:07:06,870
+إنها تجي صفر يلا شوف أرقام ثوابت أيوة
+
+567
+01:07:11,150 --> 01:07:17,030
+خلامك خالص، بتقولي أنا بدها آخذ c1 هذا بواحد وبدها
+
+568
+01:07:17,030 --> 01:07:23,650
+تاخذ c2 بـ e تكعيب بس بالسالب يعني سالب e تكعيب
+
+569
+01:07:23,650 --> 01:07:29,090
+تعالوا نشوف هذا كلامها صح ولا غلط، يبقى بالدرجة أقول
+
+570
+01:07:29,090 --> 01:07:43,400
+take c1 يساوي واحد و c2 يساوي سالب e تكعيب، ثم سوف
+
+571
+01:07:43,400 --> 01:07:49,060
+نشوف كلامه صح ولا لأ، سي واحد بواحد بقاش بظل E أس
+
+572
+01:07:49,060 --> 01:07:58,020
+ثلاثة T زي سي اثنين اللي هو ناقص E تكعيب، E أس ثلاثة
+
+573
+01:07:58,020 --> 01:08:06,740
+T ناقص ثلاثة، هو يساوي E أس ثلاثة T ناقص E تكعيب مع
+
+574
+01:08:06,740 --> 01:08:13,380
+هذه بتجمع بضال قداش E أس ثلاثة T، يبقى E أس ثلاثة T
+
+575
+01:08:13,380 --> 01:08:19,700
+وE ساوي قداش صفر، هذي احنا جيبنا ثوابت اثنين بحيث
+
+576
+01:08:19,700 --> 01:08:24,320
+ضربنا كل صنفة الأول وكل صنفة الثانية وجمعنا وقالوا
+
+577
+01:08:24,320 --> 01:08:28,420
+إنها تجيب E ساوي صفر، بداجي أطلع في الثوابت اللي
+
+578
+01:08:28,420 --> 01:08:34,020
+جيبتهم، هل هدول بأصفار؟ يبقى هدول الدالتين مالهم
+
+579
+01:08:34,340 --> 01:08:43,360
+linearly dependent، يبقى س اللي هو الـ E أس ثلاثة T
+
+580
+01:08:43,360 --> 01:08:50,480
+and الـ E أس ثلاثة T ناقص ثلاثة are linearly
+
+581
+01:08:50,480 --> 01:08:59,640
+dependent because اللي هو خليها مشان التعريفة بدل
+
+582
+01:08:59,640 --> 01:09:06,560
+C واحد قوليلي K واحد و K2 مشان نخلي رموزنا زي ما هي
+
+583
+01:09:06,560 --> 01:09:17,020
+K1 و K2 وهذه K1 وهذه K2 تمام؟ لإنها دندن because
+
+584
+01:09:17,020 --> 01:09:27,600
+K1 لا يساوي Zero و K2 لا يساوي Zero وكذلك، طيب خذيني
+
+585
+01:09:27,600 --> 01:09:31,260
+نمرة B نمرة B
+
+586
+01:09:34,650 --> 01:09:44,850
+لو أخذنا اللي هو الـ F of T بده يساوي T والـ G of T
+
+587
+01:09:44,850 --> 01:09:50,610
+بده يساوي يساوي T السالب واحد وT greater than
+
+588
+01:09:50,610 --> 01:09:51,330
+zero
+
+589
+01:09:59,070 --> 01:10:03,110
+قام من عندنا لو حطينا مثلًا الـ T أكبر من صفر و T
+
+590
+01:10:03,110 --> 01:10:08,710
+أقل من صفر، وتبناه مظلوم؟ تفكر في اللي بدك تفكر
+
+591
+01:10:08,710 --> 01:10:14,710
+فيه؟ حطيت قيودنا؟ بأي
+
+592
+01:10:14,710 --> 01:10:19,770
+طريقة تشير تهاتيل التوابل؟ احنا لسه في بداية
+
+593
+01:10:19,770 --> 01:10:24,070
+الطريق، فأول يعني بس احنا بدنا نثبت المفهوم عندكم
+
+594
+01:10:24,070 --> 01:10:28,520
+وبعدين بنطور أسئلتنا، يعني إنها تعتبر أسئلة بسيطة و
+
+595
+01:10:28,520 --> 01:10:35,100
+بعد ذلك نشوف كيف نثبت الشغل هذه، طيب ما طيني سؤال
+
+596
+01:10:35,100 --> 01:10:38,840
+ثاني قال الـ f of t بده يساوي t والـ g of t بده
+
+597
+01:10:38,840 --> 01:10:46,700
+يساوي t والسالب واحد، بدي بقول له هنا assume افترضي
+
+598
+01:10:46,700 --> 01:10:56,500
+there exist كواحد وكاثنين such that بحيث أن كواحد
+
+599
+01:10:56,500 --> 01:11:03,640
+T زائد كاثنين في T ناقص واحد بده يساوي zero بتروح
+
+600
+01:11:03,640 --> 01:11:10,360
+هدور على كواحد وكاثنين، شو رأيك نشتق المعادلة هذه؟
+
+601
+01:11:10,360 --> 01:11:15,040
+لو اشتقينا المعادلة هذه بصير هنا كواحد بتطير هذه T
+
+602
+01:11:15,040 --> 01:11:22,900
+بصير ناقص كاثنين T وناقص اثنين، يبقى هذه شو بدي
+
+603
+01:11:22,900 --> 01:11:29,600
+أعطيك يا بنات، بدي أعطيك أن K واحد يساوي K اثنين في
+
+604
+01:11:29,600 --> 01:11:35,120
+T السالب اثنين، مظبوط؟
+
+605
+01:11:35,120 --> 01:11:40,620
+بدي
+
+646
+01:15:35,090 --> 01:15:55,050
+functions on an open interval I and F that exists
+
+647
+01:15:55,050 --> 01:15:57,770
+P0
+
+648
+01:15:59,220 --> 01:16:14,820
+in الفترة I such that بحيث أن الورنسكيان تبع ال F و
+
+649
+01:16:14,820 --> 01:16:29,240
+ال G عند T0 لا يساوي Zero then ال F عند ال G are
+
+650
+01:16:29,240 --> 01:16:40,960
+linearly independent عن الفترة I on
+
+651
+01:16:40,960 --> 01:16:48,100
+the other hand
+
+652
+01:16:54,420 --> 01:17:07,980
+الـ F and ال G are linearly dependent على I
+
+653
+01:17:07,980 --> 01:17:14,060
+الفترة I then الورنسكيان
+
+654
+01:17:14,060 --> 01:17:24,580
+تبع ال F وال G عند ال T بده يساوي Zero for all T
+
+655
+01:17:24,580 --> 01:17:29,180
+اللي موجودة في ال interval I
+
+656
+01:17:48,670 --> 01:17:53,810
+قبل ما نأخذ المثال بدنا نرجع لنص النظرية ونحاول نفهم
+
+657
+01:17:53,810 --> 01:18:16,650
+ما هو الشيء اللي موجود في هذه النظرية طلع
+
+658
+01:18:16,650 --> 01:18:21,500
+كواسبيدي أجري نظرية وبعدين بدي أقول لكم إيش فهمت
+
+659
+01:18:21,500 --> 01:18:26,060
+منها وشوفوا فهمي الصح ولا غلط إذا صح بنعتمدوا وإذا 
+
+660
+01:18:26,060 --> 01:18:31,520
+غلط بنصححوا وبقول إيش لو كان ال F و G are
+
+661
+01:18:31,520 --> 01:18:37,760
+differentiable functions على فترة I و أخذت نقطة 
+
+662
+01:18:37,760 --> 01:18:41,640
+موجودة في هذه الفترة ولجيت أن الورنسكيان كان
+
+663
+01:18:41,640 --> 01:18:46,180
+عندها لا يساوي Zero إن حدث ذلك بقول ال two
+
+664
+01:18:46,180 --> 01:18:52,000
+functions are linearly independent طيب ده اللي هو
+
+665
+01:18:52,000 --> 01:18:56,380
+من ناحية أخرى لو كان ال F and G are linearly
+
+666
+01:18:56,380 --> 01:19:01,700
+dependent يبقى الورنسكيان عندهم بده يساوي zero لكل
+
+667
+01:19:01,700 --> 01:19:07,100
+ال T اللي موجودة وين اللي موجودة في ال I يبقى
+
+668
+01:19:07,100 --> 01:19:11,640
+واضحة ظن بدي ألخص الكلام اللي قلناها ده أو نص
+
+669
+01:19:11,640 --> 01:19:16,210
+النظرية وشوفوا تلخيصي صح ولا غلط يعطيني ال two
+
+670
+01:19:16,210 --> 01:19:19,170
+functions وقال لي شوف الورنسكيان تاني وقال linearly
+
+671
+01:19:19,170 --> 01:19:23,650
+dependent و الله linearly independent بقوله والله 
+
+672
+01:19:23,650 --> 01:19:28,630
+كويس باخد هالورنسكيان تبع التنتين عند نقطة
+
+673
+01:19:28,630 --> 01:19:32,690
+والله إذا الورنسكيان لا يساوي zero يبقى linearly
+
+674
+01:19:32,690 --> 01:19:36,490
+independent وإذا ساوى zero يبقى linearly dependent
+
+675
+01:19:36,490 --> 01:19:39,990
+غلط؟
+
+676
+01:19:39,990 --> 01:19:44,050
+لا يا ناس غلط كلامي يعني يا ناس أنا مدرس كلامي
+
+677
+01:19:44,050 --> 01:19:50,150
+غلط؟ طب هو الخطأ بعينيه نص غلط ونص صح طب تعال
+
+678
+01:19:50,150 --> 01:19:54,790
+نشوف كيف نصه غلط وكيف نصه صح نمسك النص في الأول
+
+679
+01:19:54,790 --> 01:19:58,610
+هدول التنتين دوال قبل اشتغال ما عندهم مشكلة على
+
+680
+01:19:58,610 --> 01:20:02,870
+الفترة اللي عندناها ده بحيث الورنسكيان كان عند 
+
+681
+01:20:02,870 --> 01:20:07,550
+نقطة ماجلش على كل ال interval لو قدرت تلاقي
+
+682
+01:20:07,550 --> 01:20:12,610
+الورنسكيان ولو نقطة واحدة ليس بالضرورة على كل الفتحة
+
+683
+01:20:12,610 --> 01:20:17,090
+ولو عندها نقطة واحدة لا يساوي zero إذا الورنسكيان
+
+684
+01:20:17,090 --> 01:20:21,570
+تبعهم إذا دول اثنين هدول يصيروا linearly
+
+685
+01:20:21,570 --> 01:20:26,850
+independent طيب ممتاز الشطرة التانية بقول on the
+
+686
+01:20:26,850 --> 01:20:32,100
+other hand يعني من ناحية أخرى لو كانت ال two
+
+687
+01:20:32,100 --> 01:20:36,860
+functions linearly dependent يجب أن يكون الورنسكيان
+
+688
+01:20:36,860 --> 01:20:42,040
+0 for all t الموجودة في ال interval إذا فارق
+
+689
+01:20:42,040 --> 01:20:45,840
+السماعة على الأرض مش زي ما قلت أنا في الأول مظبوط
+
+690
+01:20:45,840 --> 01:20:50,520
+إذا كلامك في أول غلط يبقى إياك أن تخطئ مثل هذا
+
+691
+01:20:50,520 --> 01:20:54,740
+الخطأ يبقى الصح اللي في حصلة دالتين هذول linearly
+
+692
+01:20:54,740 --> 01:20:58,120
+dependent ولا linearly independent بروح آخذ
+
+693
+01:20:58,120 --> 01:21:03,760
+الورنسكيان عند نقطة لقيته لا يساوي 0 خلاص مضمون 100%
+
+694
+01:21:03,760 --> 01:21:09,280
+إذا اتنين دول linearly independent لكن لو كانوا
+
+695
+01:21:09,280 --> 01:21:14,240
+اتنين تانيين linearly dependent يجب أن يكون ال
+
+696
+01:21:14,240 --> 01:21:18,740
+ورنسكيان تبعهم يساوي 0 for all t فيه بديش أبعد فيه
+
+697
+01:21:18,740 --> 01:21:23,140
+بدي آخذ من اللي قدامكم نمرا إيه إيش طلعت عندنا 
+
+698
+01:21:23,140 --> 01:21:28,580
+هذه؟ طلعت linearly dependent صح ولا لا؟ إذا بده
+
+699
+01:21:28,580 --> 01:21:31,040
+يروح يحسب الورنسكيان تبعها ويشوف قداش ماذا
+
+700
+01:21:31,040 --> 01:21:35,060
+يساوي هذا بيقول لو كانت دالتين linearly dependent
+
+701
+01:21:35,060 --> 01:21:39,040
+بده يكون الورنسكيان تبعها مضطر يساوي قداش يساوي 
+
+702
+01:21:39,040 --> 01:21:46,540
+zero يبقى example بدأت أقول from the above
+
+703
+01:21:46,540 --> 01:21:57,200
+example من المثال اللي فوق وبدي آخذ part a من part
+
+704
+01:21:57,200 --> 01:22:01,420
+a مشيكنا a طلع هدول التانتين are linearly
+
+705
+01:22:01,420 --> 01:22:08,880
+dependent ال E أس ثلاثة T and ال E أس ثلاثة T نأخذ
+
+706
+01:22:08,880 --> 01:22:16,180
+تلاتة are linearly dependent linearly dependent
+
+707
+01:22:16,180 --> 01:22:18,760
+for all T
+
+708
+01:22:22,390 --> 01:22:28,030
+يبقى الورنسكيان تبع E أس ثلاثة T و E أس ثلاثة T
+
+709
+01:22:28,030 --> 01:22:34,450
+ناقص تلاتة تلاتة تلاتة تلاتة تلاتة تلاتة تلاتة
+
+710
+01:22:34,620 --> 01:22:40,720
+و E أس ثلاثة T ناقص ثلاثة نشتق يا بناد يبقى ثلاثة
+
+711
+01:22:40,720 --> 01:22:47,760
+E أس ثلاثة T ونشتق هنا ثمان ثلاثة E أس ثلاثة T
+
+712
+01:22:47,760 --> 01:22:54,120
+ناقص ثلاثة صح ايه تشتق فيه؟ مشتقة الأس كل اللي هو
+
+713
+01:22:54,120 --> 01:23:00,810
+قداشر ثلاثة فقط لا غير طيب نفكر المحدد هذا بيصير
+
+714
+01:23:00,810 --> 01:23:11,470
+تلاتة E أُس ستة T ناقص تلاتة ناقص تلاتة E أُس ستة
+
+715
+01:23:11,470 --> 01:23:18,230
+T ناقص تلاتة يشوى قداش Zero مظبوط يبدو هي طبقنا
+
+716
+01:23:18,230 --> 01:23:23,510
+نمرة B تماما أو النقطة الثانية من النظر يجليه
+
+717
+01:23:23,510 --> 01:23:27,580
+نظره درهان إذا تنتهي هذه الـlinearly dependent
+
+718
+01:23:27,580 --> 01:23:36,580
+يفجرون إذا كنت تبحث عن عيوب يساوي 0 طيب and أحدنا
+
+719
+01:23:36,580 --> 01:23:42,010
+ذالتين الاثنين هذوللأ خدنا نمرا بيه و يارا راح نمر
+
+720
+01:23:42,010 --> 01:23:46,490
+بيه هي نمرا بيها هي الدالتين الاثنين هذول وأثبتنا
+
+721
+01:23:46,490 --> 01:23:51,430
+أن هذول الاثنين linearly independent هذا لأ بدي
+
+722
+01:23:51,430 --> 01:23:55,190
+أروح أجيب المحدد تبعهم إذا المحدد تبعهم قلع لا
+
+723
+01:23:55,190 --> 01:23:59,890
+يساوي zero لنفتدوا للنظرية يفتدتين يكونوا are
+
+724
+01:23:59,890 --> 01:24:06,230
+linearly independent يفتدت ياخد المحدد تبع الحل
+
+725
+01:24:06,230 --> 01:24:15,260
+الأول P والثاني -P-1-P
+
+726
+01:24:15,260 --> 01:24:22,200
+-1
+
+727
+01:24:22,200 --> 01:24:28,800
+-P-1-P-1-P-1
+
+728
+01:24:37,040 --> 01:24:45,960
+مدام لا يساوي 0 سا t and سا t سالف واحد are
+
+729
+01:24:45,960 --> 01:24:52,740
+linearly independent مش انتقطة واحدة وماسي على كل
+
+730
+01:24:52,740 --> 01:24:59,620
+ال interval all ال interval من 0 لغاية انت نقل ال
+
+731
+01:24:59,620 --> 01:25:04,120
+P أكبر من ال 0 يعني اي نقطة تيجي تقريبا تحطيها ده
+
+732
+01:25:04,120 --> 01:25:06,420
+يمكن ينقل اكتر من واحد بسبب ال 
diff --git a/PL9fwy3NUQKwa8ZDfSFGn6H8xVFLzqmCZC/pb7CBRBKnwY_postprocess.srt b/PL9fwy3NUQKwa8ZDfSFGn6H8xVFLzqmCZC/pb7CBRBKnwY_postprocess.srt
new file mode 100644
index 0000000000000000000000000000000000000000..80d52ddef4d59fe6a5b326fd90ad475946ecb584
--- /dev/null
+++ b/PL9fwy3NUQKwa8ZDfSFGn6H8xVFLzqmCZC/pb7CBRBKnwY_postprocess.srt
@@ -0,0 +1,2928 @@
+1
+00:00:09,280 --> 00:00:15,060
+بسم الله الرحمن الرحيم الآن بدنا نكمل ما ابتدأنا
+
+2
+00:00:15,060 --> 00:00:19,280
+به section المرة الماضية اللى هو section تلاتة
+
+3
+00:00:19,280 --> 00:00:24,060
+اتنين طبعا هذا section فى أكبر section مليان
+
+4
+00:00:24,060 --> 00:00:29,620
+نظريات فى كل ال sections المقررةأخذنا بعض النظريات
+
+5
+00:00:29,620 --> 00:00:33,040
+المرة الماضية وكان اخر حاجة خدنا تعريف ال
+
+6
+00:00:33,040 --> 00:00:37,760
+warenskin او الرونسكن اللى بقى نحط الحل الاول و
+
+7
+00:00:37,760 --> 00:00:40,980
+الحل التانى و مشتقت الاول و مشتقت التانى كمحدد
+
+8
+00:00:40,980 --> 00:00:45,680
+ثنائي و نجيب قيمة المحدد هذا حاصل ضرب عناصر القطر
+
+9
+00:00:45,680 --> 00:00:52,240
+الرئيسى ناقص حاصل ضرب عناصر القطر الثانى نجي
+
+10
+00:00:52,240 --> 00:00:57,010
+لنظرية اللى عندنا اليوميقول لو كان Y1 وY2 هما
+
+11
+00:00:57,010 --> 00:01:01,090
+عبارة عن two solutions لل differential equation
+
+12
+00:01:01,090 --> 00:01:03,950
+اللي قدامنا اللي هو homogeneous second order
+
+13
+00:01:03,950 --> 00:01:08,870
+differential equationوإذا قدرنا نجد النقطة الـ T
+
+14
+00:01:08,870 --> 00:01:13,150
+node بحيث الـ one on skin تبع الحلين تبع المعادلات
+
+15
+00:01:13,150 --> 00:01:19,730
+التفاضلية عندهم لا يساوي zero إن حدث ذلك يبقى the
+
+16
+00:01:19,730 --> 00:01:24,350
+family of solutions مجموعة الحلول اللي على الشكل
+
+17
+00:01:24,350 --> 00:01:31,030
+C1Y1 زي C2Y2C1 وC2 are arbitrary constants يبقى
+
+18
+00:01:31,030 --> 00:01:37,630
+ثوابت اختيارية انكليودز هذا الحل بيجتمل على كل
+
+19
+00:01:37,630 --> 00:01:43,030
+حلمين للمعادلة التفاضلية طبعا يا بنات هذا الان
+
+20
+00:01:43,030 --> 00:01:47,130
+اللي الكلام اللي نقوله بيربط section 32 مع section
+
+21
+00:01:47,130 --> 00:01:52,080
+31أحنا في تلاتة واحد كنا بندور على fundamental set
+
+22
+00:01:52,080 --> 00:01:55,780
+of solutions ولا ورنسكين ولا حاجة عندنا معادلة
+
+23
+00:01:55,780 --> 00:01:59,860
+بحلها بجيب حالين بدربت كنصا في الأول كنصا في
+
+24
+00:01:59,860 --> 00:02:04,760
+التاني بقول هذا هو ال general solution الان احنا
+
+25
+00:02:04,760 --> 00:02:09,420
+بدنا نقول وقداش فعلا الحل او ال general solution
+
+26
+00:02:09,420 --> 00:02:14,020
+exist بنقول لما ال ورنسكين عند نقطة ما بده يساوي
+
+27
+00:02:14,020 --> 00:02:19,690
+قداش لا يساوي zeroمرة تانية بقول ان عندي معادلة
+
+28
+00:02:19,690 --> 00:02:25,950
+تفاضلية إلها حلين الوانوس كنتبع الحلية عند نقطة ما
+
+29
+00:02:25,950 --> 00:02:33,310
+النقطة هذه موجودة في الفترة اللي الدالة P و الدالة
+
+30
+00:02:33,310 --> 00:02:39,350
+Q continuous عليها إن حدث ذلكيبقى مجموعة الحلولات
+
+31
+00:02:39,350 --> 00:02:46,610
+بتشتمل على أي حل آخر منهم للمعادلة طب احنا العنوان
+
+32
+00:02:46,610 --> 00:02:49,650
+اللي احنا رافعينه لهذا section fundamental set of
+
+33
+00:02:49,650 --> 00:02:53,770
+solutions المرة اللي كاتت مااتكلمناش ولا كلمة على
+
+34
+00:02:53,770 --> 00:02:56,250
+ال fundamental set of solutions كنا بيجينا ناخد
+
+35
+00:02:56,250 --> 00:03:00,790
+نظرياتلكن طلع هنا بيقول إيش؟ إذا ضامنت إن ال words
+
+36
+00:03:00,790 --> 00:03:05,650
+كان عندها نقطة لا يساوي zero يبقى هذا بيشتمل على
+
+37
+00:03:05,650 --> 00:03:11,530
+أي حل آخر لمام للمعادلة التفاضلية الملاحظة بتقول
+
+38
+00:03:11,530 --> 00:03:15,770
+إذا ال words كان هذا لا يساوي zero يبقى الحالين
+
+39
+00:03:15,770 --> 00:03:21,700
+الإتنين دول بيكونولي مجموعة الحلول الأساسيةالعنوان
+
+40
+00:03:21,700 --> 00:03:24,540
+اللى احنا كنا رافعينه ل section تلاتة اتنين المرة
+
+41
+00:03:24,540 --> 00:03:28,020
+الماضية مجموعة الحلول الأساسية لل differential
+
+42
+00:03:28,020 --> 00:03:32,540
+equation one و اللى كنا سابقا من سميه ال general
+
+43
+00:03:32,540 --> 00:03:36,540
+solution يبقى ال general solution للمعادلة
+
+44
+00:03:36,540 --> 00:03:40,950
+التفابليةأو الـ Fundamental Set of Solutions
+
+45
+00:03:40,950 --> 00:03:45,650
+للمعادلة التفاضلية مجموعة الحلول الأساسية اتنين
+
+46
+00:03:45,650 --> 00:03:51,950
+نفس المعنى هذه الصيغة تشتمل على أي حل أخر للمعادلة
+
+47
+00:03:51,950 --> 00:03:58,570
+التفاضلية الخطية من الرتبة الثانية يبقى هذه الصيغة
+
+48
+00:03:58,570 --> 00:04:02,710
+constant في الحل الأول زي constant ثاني في الحل
+
+49
+00:04:02,710 --> 00:04:09,480
+الثاني تمام؟أحنا ما جيبناش ديب لكن أصلنا للحلول
+
+50
+00:04:09,480 --> 00:04:14,600
+القديمة بحيث نضمن موجود ولا نعم موجود وقت إذا
+
+51
+00:04:14,600 --> 00:04:18,500
+الورونسكين عنده نقطة داخل ال interval المعرض عليها
+
+52
+00:04:18,500 --> 00:04:22,200
+ال coefficients بدي يكون الورونسكين هذا معله لا
+
+53
+00:04:22,200 --> 00:04:28,220
+يساوي zero نعطي مثال طبعا تقول اتأكدلي ان هدول حلل
+
+54
+00:04:28,220 --> 00:04:33,470
+المعادلة استفادوا من الجهة دي طيب اتأكدنابقول لي
+
+55
+00:04:33,470 --> 00:04:37,010
+ومن ثم دين show that بيبينلي ان اتنين هذول
+
+56
+00:04:37,010 --> 00:04:41,030
+بيكونولي ال fundamental set of solutions اتجاه
+
+57
+00:04:41,030 --> 00:04:44,290
+المفهوم التاني يعني ايه تبدي اعمل؟ بدي اجيب
+
+58
+00:04:44,290 --> 00:04:48,950
+الرونسكين هذا هو اثبت انه ماله؟ لا يساوي ذلك، ان
+
+59
+00:04:48,950 --> 00:04:52,050
+حدث ذلك اتجاه جولي بيكونولي مجموعة الحلول الاساسية
+
+60
+00:04:52,050 --> 00:04:56,710
+وبالتاليبديقول شكل ال general solution للمعادلة
+
+61
+00:04:56,710 --> 00:05:00,750
+التفاضلية وقال لي هو مثلا اكتب شكل ال general
+
+62
+00:05:00,750 --> 00:05:04,030
+solution طبعا شكل ال general solution يكون على
+
+63
+00:05:04,030 --> 00:05:08,510
+الشكل اللي عندنا هذا إذا خلّيني نمشي خطوة وخطوة
+
+64
+00:05:08,510 --> 00:05:13,070
+جالي يبينلي ان هدول حلل المعادلة التفاضلية مش
+
+65
+00:05:13,070 --> 00:05:17,770
+هينكون الحللة اللي حصلت المعادلة التفاضلية يبقى
+
+66
+00:05:17,770 --> 00:05:25,630
+انا عند Y واحديستوي قدر T ثانفية لو اشتغلت على Y
+
+67
+00:05:25,630 --> 00:05:31,390
+واحد إسرائيل يستوي قدر T كمان مرضى Y واحد وقفل
+
+68
+00:05:31,390 --> 00:05:35,910
+إسرائيل يستوي قدر يستوي اتنين، بداك يعوض في
+
+69
+00:05:35,910 --> 00:05:40,150
+المعادلة يستوي كدر T ثانفية و Y واحد مضابق
+
+70
+00:05:40,150 --> 00:05:41,030
+لإسرائيل
+
+71
+00:05:43,860 --> 00:05:50,020
+إذا طلع هذا الكلام يساوي 0 فهذا يكون حل مين
+
+72
+00:05:50,020 --> 00:05:52,100
+للمعادلة التفاضلية
+
+73
+00:06:02,130 --> 00:06:09,150
+اللي هو تيتربيا يبقى تيتربيا تقصد من تيتربيا وزي
+
+74
+00:06:09,150 --> 00:06:16,310
+ساوي زيرو هنا قد عليها why one زي ساوي تيتربيا is
+
+75
+00:06:16,310 --> 00:06:27,810
+a solution of the differential equation للمعادلة
+
+76
+00:06:27,810 --> 00:06:34,100
+تفاضليةالينين في تاريخ يعني وايد قدري للترايخ،
+
+77
+00:06:34,100 --> 00:06:39,090
+خاطر من الينين وايد بيشاوى الاند بيشاوى الاندالان
+
+78
+00:06:39,090 --> 00:06:47,610
+similarly بنفس الطريقة اللي هو Y2 يستوي T أصنافة
+
+79
+00:06:47,610 --> 00:07:03,370
+واحد تمام؟ لأن اشتقوا مرة Y2 يستوي T أصنافة
+
+80
+00:07:03,370 --> 00:07:11,580
+ثالثالان بالنسبة للمعادلة التفاظلية يتر بيها Y2 من
+
+81
+00:07:11,580 --> 00:07:14,960
+بعض الأفراد مقصد 62 Y2
+
+82
+00:07:18,920 --> 00:07:36,780
+يتجارى تساوي T تربيه Y2WI يتجارى
+
+83
+00:07:36,780 --> 00:07:42,080
+T تربيه
+
+84
+00:07:42,080 --> 00:07:50,640
+Y2WI يتجارى T تربيه Y2WI يتجارىيستوي 0 يمكن أن
+
+85
+00:07:50,640 --> 00:07:58,400
+يكون Y يستوي 1 يستوي 1 يستوي 3 يستوي 3 يستوي 3
+
+86
+00:07:58,400 --> 00:08:06,000
+يستوي 3 يستوي 3 يستوي 3 يستوي 3 يستوي 3 يستوي 3
+
+87
+00:08:06,000 --> 00:08:14,900
+يستوي 3 يستوي 3 يستوي 3 يستوي 3 يستوي 3 يستوي 3
+
+88
+00:08:14,900 --> 00:08:14,920
+يستوي 3 يستوي 3 يستوي 3 يستوي 3 يستوي 3 يستوي 3
+
+89
+00:08:14,920 --> 00:08:14,940
+يستوي 3 يستوي 3 يستوي 3 يستوي 3 يستوي 3 يستوي 3
+
+90
+00:08:14,940 --> 00:08:15,000
+يستوي 3 يستوي 3 يستوي 3 يستوي 3 يستوي 3 يستوي 3
+
+91
+00:08:15,000 --> 00:08:15,180
+يستوي 3 يستوي 3 يستوي 3 يستوي 3 يستوي 3 يستوي 3
+
+92
+00:08:15,180 --> 00:08:19,530
+يستده اللي بييضى ان الاثنين هدول بيكونون المجوه
+
+93
+00:08:19,530 --> 00:08:24,690
+للحلول الأساسية مصطلح القضايا ان ال womanist تبعهم
+
+94
+00:08:24,690 --> 00:08:28,570
+عن طرقهم عن طرقهم عن طرقهم عن طرقهم عن طرقهم عن
+
+95
+00:08:28,570 --> 00:08:28,590
+طرقهم عن طرقهم عن طرقهم عن طرقهم عن طرقهم عن طرقهم
+
+96
+00:08:28,590 --> 00:08:28,730
+عن طرقهم عن طرقهم عن طرقهم عن طرقهم عن طرقهم عن
+
+97
+00:08:28,730 --> 00:08:29,450
+طرقهم عن طرقهم عن طرقهم عن طرقهم عن طرقهم عن طرقهم
+
+98
+00:08:29,450 --> 00:08:30,130
+عن طرقهم عن طرقهم عن طرقهم عن طرقهم عن طرقهم عن
+
+99
+00:08:30,130 --> 00:08:34,010
+طرقهم عن طرقهم عن طرقهم عن طرقهم عن طرقهم عن طرقهم
+
+100
+00:08:34,010 --> 00:08:42,430
+عن طرقهم عن طر
+
+101
+00:08:43,860 --> 00:08:50,240
+الحل الأول اللي عندنا همين P ثانية و الحل التاني P
+
+102
+00:08:50,240 --> 00:08:58,700
+أصناع الواحد نجتا نجتا اتنين P سالف P و سالف اتنين
+
+103
+00:09:06,560 --> 00:09:12,780
+يعني دلوقت نفس البرنامج كان نميذة P solution P
+
+104
+00:09:12,780 --> 00:09:17,380
+ثلاثية و تلاتية و ثالث واحد نجدت أن المتحدث
+
+105
+00:09:17,380 --> 00:09:21,380
+الإسرائيل حصل الحاجات عن كل الموضوع تقفل فيه هنا
+
+106
+00:09:21,380 --> 00:09:27,820
+بضرورة إن أن المتحدث حاصل ضرب على نفسه كرهيزي حاصل
+
+107
+00:09:27,820 --> 00:09:31,880
+ضرب على نفسه كرهيزي حاصل ضرب على نفسه كرهيزي
+
+108
+00:09:31,880 --> 00:09:33,020
+كرهيزي واحد
+
+109
+00:10:00,640 --> 00:10:02,040
+عاصفة ضرب عاصفة ضرب عاصفة ضرب عاصفة ضرب عاصفة ضرب
+
+110
+00:10:02,040 --> 00:10:11,080
+عاصفةهذا الرقم غير الصفر إذا ما يمكن أن
+
+111
+00:10:11,080 --> 00:10:15,900
+يكون مرضى المطمئنع زي تطلع نقص تلاتة D مثلا يمكن
+
+112
+00:10:15,900 --> 00:10:20,380
+تطلع نقص تلاتة على D تلميح يفش يطلع بD أخر وعلى ال
+
+113
+00:10:20,380 --> 00:10:22,760
+interval تحت الشررين عليه
+
+114
+00:10:26,530 --> 00:10:44,590
+طيب، مدام لا يساوجل و يفكر اتنين هذول بتقنوني ماهي
+
+115
+00:10:57,720 --> 00:11:05,660
+solutions of the given differential equation
+
+116
+00:11:05,660 --> 00:11:13,100
+differential equation جالي مدام الـ October ال
+
+117
+00:11:13,100 --> 00:11:16,540
+general solution لل differential equation جدا
+
+118
+00:11:16,540 --> 00:11:25,100
+العليه بروح بكله ال general solution is
+
+119
+00:11:26,240 --> 00:11:40,020
+Y تسوى C1Y1 زي C2Y2 تسوى C1T2 زي C2T و سالب واحد
+
+120
+00:11:40,020 --> 00:11:46,200
+ينقل هذا الجدران صيوزي للعاملة التفاغنية المعطاة
+
+121
+00:12:07,110 --> 00:12:10,650
+الشباب أساسي اللي لازم يقولوا اسم هذا معناه
+
+122
+00:12:23,890 --> 00:12:28,200
+اللي بتقوله لو كان الرئيس انصار سفير يبقى ..هم
+
+123
+00:12:28,200 --> 00:12:31,240
+احنا مش ضامنين هل هم فنضامن ال solution ولا مش هم
+
+124
+00:12:31,240 --> 00:12:36,000
+بيطلعوا حالين بس بضمانش انهم يجيبولي شكل حل العالم
+
+125
+00:12:36,000 --> 00:12:40,080
+طبعا اعطيكوا بعض أبطالين يتعاملوا مع بعضهم وعالم
+
+126
+00:12:40,080 --> 00:12:42,840
+كله مش عارف انهم يتعاملوا مع بعضهم اه تتعاملوا مع
+
+127
+00:12:42,840 --> 00:12:43,220
+بعضهم
+
+128
+00:12:56,420 --> 00:13:01,100
+التسهيل اللي بتطبخوه يا بناتي لان اكتبه على الشكل
+
+129
+00:13:01,100 --> 00:13:06,540
+التالي اكتبه
+
+130
+00:13:06,540 --> 00:13:15,120
+على الشكل التالي مفهوم اذا sometimes احيانا
+
+131
+00:13:15,120 --> 00:13:24,060
+sometimes it is difficult for five it is difficult
+
+132
+00:13:56,810 --> 00:14:09,780
+Y1-Y2of the differential equation المعادلة
+
+133
+00:14:09,780 --> 00:14:18,440
+التفارقية L of Y بيستوي Y بقية I زائد P of Y بقية
+
+134
+00:14:18,440 --> 00:14:26,200
+I زائد Q of Y بيستوي Zero اللي هي بقية ساقين
+
+135
+00:14:26,200 --> 00:14:28,480
+المعادلة أقل واحد
+
+136
+00:14:30,870 --> 00:14:37,890
+لذلك if he ask فروح نسأل السؤال in turn without an
+
+137
+00:14:37,890 --> 00:14:44,090
+essential equation without that differential
+
+138
+00:14:44,090 --> 00:14:57,310
+equation one always always has a fundamental
+
+139
+00:15:03,770 --> 00:15:13,290
+هي افضل انت ستة solutions لأي
+
+140
+00:15:13,290 --> 00:15:23,670
+علامة ستة؟ بأسه لازم أكون متأكد عنها لأن ستة is
+
+141
+00:15:23,670 --> 00:15:26,690
+the following
+
+142
+00:15:33,290 --> 00:15:36,930
+طبعا هي بيقول ما .. ما يرام
+
+143
+00:15:50,970 --> 00:16:00,670
+هذا البرادر الصحي هو ال N of Y Y double F I U exp
+
+144
+00:16:00,670 --> 00:16:07,130
+Y I U exp Y is equal to 0 وخلّى البرادر اللي هو
+
+145
+00:16:07,130 --> 00:16:08,910
+أخير واحد
+
+146
+00:16:13,250 --> 00:16:22,610
+and make you a continuous functions of continuous
+
+147
+00:16:22,610 --> 00:16:30,850
+functions that one could consider on some open
+
+148
+00:16:30,850 --> 00:16:40,570
+interval on some open interval R
+
+149
+00:16:49,380 --> 00:17:02,020
+والثاني هو some plus some point in the interval R
+
+150
+00:17:07,320 --> 00:17:13,800
+FYI الوضع أكتر
+
+151
+00:17:13,800 --> 00:17:24,540
+في الوضع الوضع أكتر في الوضع الوضع الوضع الوضع
+
+152
+00:17:24,540 --> 00:17:26,360
+الوضع الوضع الوضع الوضع الوضع الوضع الوضع الوضع
+
+153
+00:17:26,360 --> 00:17:26,660
+الوضع الوضع الوضع الوضع الوضع الوضع الوضع الوضع
+
+154
+00:17:26,660 --> 00:17:26,900
+الوضع الوضع الوضع الوضع الوضع الوضع الوضع الوضع
+
+155
+00:17:26,900 --> 00:17:29,240
+الوضع الوضع الوضع الوضع الوضع الوض
+
+156
+00:17:34,220 --> 00:17:45,320
+هو اي واحد و اتنين يساوي واحد و اتنين يساوي
+
+157
+00:17:45,320 --> 00:17:53,160
+واحد و اتنين يساوي واحد و اتنين يساوي واحد و اتنين
+
+158
+00:17:53,160 --> 00:17:56,640
+يساوي واحد و اتنين يساوي واحد و اتنين يساوي واحد
+
+159
+00:18:00,890 --> 00:18:09,070
+مش عارف why واحد ال .. why اللي .. اللي مابتعش في
+
+160
+00:18:09,070 --> 00:18:14,090
+الواقع انا
+
+161
+00:18:14,090 --> 00:18:20,390
+مابتعش في الواقع انا مابتعش في الواقع انا
+
+162
+00:18:20,390 --> 00:18:22,550
+مابتعش في الواقع
+
+163
+00:18:32,010 --> 00:18:34,890
+ده .. ده .. ده .. ده ..
+
+164
+00:19:24,740 --> 00:19:26,140
+مش عارف كده
+
+165
+00:19:51,720 --> 00:19:57,580
+ليه احترام لحن كبير؟ او بعض السنة ولو .. او لو نصف
+
+166
+00:19:57,580 --> 00:20:02,680
+سنة ماسباش زي .. ساوة زي .. ماشي بتحصل؟ هنا ك ..
+
+167
+00:20:02,680 --> 00:20:06,980
+هنا صرفات أحيان it is difficult to find an
+
+168
+00:20:06,980 --> 00:20:10,680
+underlying conceptual solution يعني أحيان نصار
+
+169
+00:20:10,680 --> 00:20:15,260
+اتالوجي مجموعة التفكير الأساسي على صورة واحد وواحد
+
+170
+00:20:15,260 --> 00:20:21,860
+وإثنان وخمسين وخمسين إلا عندناSometimes the
+
+171
+00:20:21,860 --> 00:20:24,500
+definition of a fundamental system solution هو
+
+172
+00:20:24,500 --> 00:20:28,120
+واحد هو كامل وعالى وطبعا ويبقى كامل عندنا ويبقى
+
+173
+00:20:28,120 --> 00:20:31,740
+كامل على الشكل اللي عندنا فانت ده صح كامل يا عزيزي
+
+174
+00:20:31,740 --> 00:20:36,460
+ويقولك اه we ask you ده فكيف ال definition of
+
+175
+00:20:36,460 --> 00:20:40,580
+solution هو واحد تبقى كامل لها دائما وابدا انها
+
+176
+00:20:40,580 --> 00:20:48,370
+fundamental set of solutionالنظرية التالية اتمنى
+
+177
+00:20:48,370 --> 00:20:53,610
+بفعلا ان هذا يكون مجموع حلول اساسية او بمعنى اخر
+
+178
+00:20:53,610 --> 00:20:58,830
+القرار الاسكين تبعها يكون نايم او نايم ساوي زيرو
+
+179
+00:20:58,830 --> 00:21:02,530
+مافيش بتقوله نظرية نظرية يقولها معنى التحولية
+
+180
+00:21:02,530 --> 00:21:03,050
+تبعها
+
+181
+00:21:23,340 --> 00:21:24,740
+Y1Y2Y3Y4Y5Y6Y7Y8Y9Y10Y11Y12Y12Y13Y12Y13Y14Y14Y15Y15Y15Y15Y15Y15Y15Y15Y15Y15Y15Y15Y15Y15Y15Y15Y15Y15Y15Y15Y15Y15Y15Y15Y15Y15Y15Y15Y15Y15Y15Y15Y15Y15Y15Y15Y15Y15Y15Y15Y15Y15Y15Y15Y15Y15Y15Y15Y15Y15Y15Y15Y15Y15Y15Y15Y15Y15Y15Y15Y15Y15Y15Y15Y15Y15Y15Y15Y15Y15Y15Y15Y15Y15Y15Y15Y15Y15Y15Y15Y15Y15Y15Y15Y15Y15Y15Y15Y15Y15Y15Y15Y15Y15
+
+182
+00:21:24,780 --> 00:21:27,400
+أتنين بيقولوا جنة رسول صلى الله عليه وسلم او قرن
+
+183
+00:21:27,400 --> 00:21:32,920
+مثلا حالتين ما هيحالتين فمسكنا حالتين ادنان بحيث
+
+184
+00:21:32,920 --> 00:21:37,540
+الحال الأول عند النقطة اللي احد تلاتين ادنان كان
+
+185
+00:21:37,540 --> 00:21:43,100
+واحد صحيح ومش تبت نزيل و الحال التالت نزيل وعند
+
+186
+00:21:43,100 --> 00:21:49,060
+النقطة عادي ومش تبت واحد ان حد تلالك نسبة هدول
+
+187
+00:21:49,060 --> 00:21:51,280
+بيقمنوا لووجود القرن مثلا
+
+188
+00:21:54,700 --> 00:21:59,440
+السؤال هو مافنعش هدول تعملولي الشرط ان انا كنت
+
+189
+00:21:59,440 --> 00:22:04,460
+احفظهم هدول؟ مافنعش هدول يمجولي قبل ما نرسل او
+
+190
+00:22:04,460 --> 00:22:09,240
+صلوا ليه؟ و لو كان اليوم مصرفة جدا، يا عادي هدول
+
+191
+00:22:09,240 --> 00:22:15,580
+شو بيعملولي؟ يا جماد بيقولوا لا تاني و لا اخر،
+
+192
+00:22:15,580 --> 00:22:20,900
+اللي مرضى هي tell the truth، صحيح ليه؟
+
+193
+00:22:24,560 --> 00:22:33,080
+تبع الحل الأول والحل التالتالمش مضيعونين، مضيعين،
+
+194
+00:22:33,080 --> 00:22:39,760
+قيمة ال Y واحد عند الكيلون، قيمة ال Y واحد يترين
+
+195
+00:22:39,760 --> 00:22:48,760
+عند الكيلون، قيمة اكبر Y ثمانية، Y ثمانية عند
+
+196
+00:22:48,760 --> 00:22:56,310
+الكيلون، هنا Y واحد يترين عند الكيلونwhy اتنين و
+
+197
+00:22:56,310 --> 00:23:02,830
+اتنين و اتنين و اتنين و اتنين
+
+198
+00:23:02,830 --> 00:23:06,310
+و اتنين و اتنين و اتنين و اتنين و اتنين و اتنين و
+
+199
+00:23:06,310 --> 00:23:07,150
+اتنين و اتنين و اتنين و اتنين و اتنين و اتنين و
+
+200
+00:23:07,150 --> 00:23:08,150
+اتنين و اتنين و اتنين و اتنين و اتنين و اتنين و
+
+201
+00:23:08,150 --> 00:23:08,390
+اتنين و اتنين و اتنين و اتنين و اتنين و اتنين و
+
+202
+00:23:08,390 --> 00:23:09,550
+اتنين و اتنين و اتنين و اتنين و اتنين و اتنين و
+
+203
+00:23:09,550 --> 00:23:10,110
+اتنين و اتنين و اتنين و اتنين و اتنين و اتنين و
+
+204
+00:23:10,110 --> 00:23:20,610
+اتنين و اتنين و اتنين و
+
+205
+00:23:20,610 --> 00:23:25,490
+اتنهأقمنك أنه فعلا هذا الكلب اتنقل من 0 إلى 0 يعني
+
+206
+00:23:25,490 --> 00:23:28,530
+انا طالع على وسط الناس من 0 ومن تاني من 2 هذا
+
+207
+00:23:28,530 --> 00:23:33,450
+الكلب هو يامان fundamental sense of solution تعلم
+
+208
+00:23:33,450 --> 00:23:38,950
+الكلب يتنقل من أي كويس لإنه المسألة بيشتغل بصحته
+
+209
+00:23:38,950 --> 00:23:48,070
+غيره حاجة إذا قلت انه سؤال واحد واشري من الكتاب
+
+210
+00:23:48,070 --> 00:23:49,810
+ونقل
+
+211
+00:24:09,770 --> 00:24:11,170
+3C5
+
+212
+00:24:15,660 --> 00:24:25,060
+specified by the last term by the last term of f
+
+213
+00:24:25,060 --> 00:24:36,320
+المغربية السابقة for the situation المعادلة
+
+214
+00:24:36,320 --> 00:24:42,120
+التقاريرية why not unified say why fine
+
+215
+00:25:01,560 --> 00:25:05,200
+السؤال الأهم في تجارب الشبكة بدأت بمشير مباشر
+
+216
+00:25:05,200 --> 00:25:10,300
+عالمين عالم نظرية لغوية بيكون مجلد فعلي بقى تبسيط
+
+217
+00:25:10,300 --> 00:25:16,950
+فوق Solutionspecify يعني اللي ضارنتك من النظرية
+
+218
+00:25:16,950 --> 00:25:20,630
+اللي عندك هذه المعادلة يعني انت ممكن تكون ممكن
+
+219
+00:25:20,630 --> 00:25:22,090
+تكون ممكن تكون ممكن تكون ممكن تكون ممكن تكون ممكن
+
+220
+00:25:22,090 --> 00:25:22,130
+تكون ممكن تكون ممكن تكون ممكن تكون ممكن تكون ممكن
+
+221
+00:25:22,130 --> 00:25:22,690
+تكون ممكن تكون ممكن تكون ممكن تكون ممكن تكون ممكن
+
+222
+00:25:22,690 --> 00:25:22,970
+تكون ممكن تكون ممكن تكون ممكن تكون ممكن تكون ممكن
+
+223
+00:25:22,970 --> 00:25:23,230
+تكون ممكن تكون ممكن تكون ممكن تكون ممكن تكون ممكن
+
+224
+00:25:23,230 --> 00:25:23,810
+تكون ممكن تكون ممكن تكون ممكن تكون ممكن تكون ممكن
+
+225
+00:25:23,810 --> 00:25:24,050
+تكون ممكن تكون ممكن تكون ممكن تكون ممكن تكون ممكن
+
+226
+00:25:24,050 --> 00:25:27,430
+تكون ممكن تكون ممكن تكون ممكن تكون ممكن تكون ممكن
+
+227
+00:25:27,430 --> 00:25:32,340
+تكون ممكن تكون ممكن تعشان اجيب حالتين اطلع هذه
+
+228
+00:25:32,340 --> 00:25:37,740
+المعادلة بمعاملات مختلفة يعني تولدت تولدت واحد
+
+229
+00:25:37,740 --> 00:25:42,800
+صحيح و ثالث اتنين يعني كله اصلا إذا بناء العلماني
+
+230
+00:25:42,800 --> 00:25:53,020
+بقوله let Y تساوي T بساطة في S solution of the
+
+231
+00:25:53,020 --> 00:25:57,740
+differential equation
+
+232
+00:25:58,980 --> 00:26:08,320
+one then three characteristic equation زي section
+
+233
+00:26:08,320 --> 00:26:14,860
+تلاتة واحدة بدا yes اليومين r تركيب سائر r ناقص
+
+234
+00:26:14,860 --> 00:26:21,400
+اتنين يسوى zero لو جينا حللنا هذه المعادلة بصير
+
+235
+00:26:21,400 --> 00:26:24,380
+حصل يارد كورسين يسوى zero
+
+236
+00:26:47,020 --> 00:26:48,420
+Y1Y2Y3Y4Y5Y6Y7Y8Y9Y10Y11Y12Y13Y12Y13Y14Y14Y15Y15Y15Y15Y15Y15Y15Y15Y15Y15Y15Y15Y15Y15Y15Y15Y15Y15Y15Y15Y15Y15Y15Y15Y15Y15Y15Y15Y15Y15Y15Y15Y15Y15Y15Y15Y15Y15Y15Y15Y15Y15Y15Y15Y15Y15Y15Y15Y15Y15Y15Y15Y15Y15Y15Y15Y15Y15Y15Y15Y15Y15Y15Y15Y15Y15Y15Y15Y15Y15Y15Y15Y15Y15Y15Y15Y15Y15Y15Y15Y15Y15Y15Y15Y15Y15Y15Y15Y15Y15Y15Y15Y15Y15Y15
+
+237
+00:26:49,220 --> 00:26:58,900
+and why in the end you say إيه هو اسم أخصك ده؟طيب
+
+238
+00:26:58,900 --> 00:27:04,820
+إذا شوف هدول بيجيبولي general solution ولا لا
+
+239
+00:27:04,820 --> 00:27:09,040
+فبعدين بقولوا إذا أخد ال wallets can have a
+
+240
+00:27:09,040 --> 00:27:13,140
+function of T فالحل الأول يستيقظ
+
+241
+00:27:17,680 --> 00:27:30,740
+E-E-E-E-E-E-E-E-E-E-E-E-E-E-E-E-E-E-E-E-E-E-E-E-E
+
+242
+00:27:30,740 --> 00:27:40,160
+-E-E-E-E
+
+243
+00:27:40,160 --> 00:27:50,880
+-E-Eعمر هذه تساوي 0؟ لأ لأ لأ لأ لأ لأ لأ لأ لأ لأ
+
+244
+00:27:50,880 --> 00:27:50,920
+لأ لأ لأ لأ لأ لأ لأ لأ لأ لأ لأ لأ لأ لأ لأ لأ لأ
+
+245
+00:27:50,920 --> 00:27:54,460
+لأ لأ لأ لأ لأ لأ لأ لأ لأ لأ لأ لأ لأ لأ لأ لأ لأ
+
+246
+00:27:54,460 --> 00:27:55,420
+لأ لأ لأ لأ لأ لأ لأ لأ لأ لأ لأ لأ لأ لأ لأ لأ لأ
+
+247
+00:27:55,420 --> 00:27:56,000
+لأ لأ لأ لأ لأ لأ لأ لأ لأ لأ لأ لأ لأ لأ لأ لأ لأ
+
+248
+00:27:56,000 --> 00:27:57,440
+لأ لأ لأ لأ لأ لأ لأ لأ لأ لأ لأ لأ لأ لأ لأ لأ لأ
+
+249
+00:27:57,440 --> 00:28:08,780
+لأ لأ لأ لأ لأ لأ لأ لأ لأ لأ لأ
+
+250
+00:28:08,780 --> 00:28:10,080
+لأ ل
+
+251
+00:28:14,670 --> 00:28:25,550
+-84 هي fundamental set
+
+252
+00:28:25,550 --> 00:28:30,710
+of solutions
+
+253
+00:28:30,710 --> 00:28:41,610
+of the differential equation 1لأن هذول بكاملور هي
+
+254
+00:28:41,610 --> 00:28:48,130
+مجموعة قلول أساسية للمعادلة مين؟ للمعادلة واحدة،
+
+255
+00:28:48,130 --> 00:28:54,210
+مبتعدين ومبتعدين أخر مجموعة القلول الأساسية
+
+256
+00:28:54,210 --> 00:29:00,260
+للمعادلة هذهاللي بيطبق عليهم هي النظرية اللي
+
+257
+00:29:00,260 --> 00:29:05,060
+عندنا، طب تعالى نشوف هل النظرية اللي عندنا بيطبق
+
+258
+00:29:05,060 --> 00:29:08,680
+عليها هذا الكلب او لا، اذا بيطبقي فهذا هو الموضوع،
+
+259
+00:29:08,680 --> 00:29:13,840
+وما بيطبقش فيه، يبقى نتفكس فيه، فيه شغلة تانية،
+
+260
+00:29:13,840 --> 00:29:18,370
+ايه الشغلة التانية؟عشان نشوف دول و نشوف نشر متانى
+
+261
+00:29:18,370 --> 00:29:24,150
+و نكسر متانى، فنشوف كل الشروط الاربع هذه محققة و
+
+262
+00:29:24,150 --> 00:29:32,030
+مدادة، بمجرد ما نقوله، يبقى Y واحد عند اللقطة اللي
+
+263
+00:29:32,030 --> 00:29:36,390
+يحصل هذه، و اللقطة اللي يحصل هذه كم كيلو متساوم
+
+264
+00:29:36,390 --> 00:29:43,820
+جدا، Zeroيبقى بدالي اقول y واحد عند ال zero هاي y
+
+265
+00:29:43,820 --> 00:29:48,760
+واحد يبقى a on zero يساوي واحد اذا اتحققت ال
+
+266
+00:29:48,760 --> 00:29:56,220
+condition الاول ماشي الحاجة واحد ال y واحد اتقرع
+
+267
+00:29:56,220 --> 00:29:57,620
+ايه تدري ساوي
+
+268
+00:30:00,540 --> 00:30:08,940
+يبقى هذا بدل يعطيك M Y 1 D Prime M Zero تسوى واحد
+
+269
+00:30:08,940 --> 00:30:14,140
+يبقى ال condition التاني هذا اتحقق لأ ما اتحقق
+
+270
+00:30:14,140 --> 00:30:20,020
+لغاية حتى لو لم يبقى اتحقق و يبقى فاشل فاشل الحلول
+
+271
+00:30:20,020 --> 00:30:24,660
+جميعا من مجموعة الخلول التي بحقق اللغة اللي
+
+272
+00:30:24,660 --> 00:30:33,110
+عندناها طيب المرةلو جت اخد y2 عند الـ 0 اللي بدها
+
+273
+00:30:33,110 --> 00:30:39,270
+تسوي a أو الـ 0 طبعا اللي بدالي إذا الفشل ال
+
+274
+00:30:39,270 --> 00:30:46,010
+condition التاني هذا صاحب واحد وليس zero طيب و ال
+
+275
+00:30:46,010 --> 00:30:56,220
+y2 prime عند y2 prime بده يسويإنه ناقص اتنين فيه
+
+276
+00:30:56,220 --> 00:31:01,540
+قص ناقص اتنين هذا بيجيب عليك انه why اتنين يفرق
+
+277
+00:31:01,540 --> 00:31:06,020
+عند ال zero بيجيب عليك انه ناقص اتنين ناقص اتنين
+
+278
+00:31:06,020 --> 00:31:11,420
+يعني لا شرط هذا اتحقق و لا شرط هذا اتحقق و لا شرط
+
+279
+00:31:11,420 --> 00:31:17,300
+هذا اتطبق مش واحد يعني الشروط الأرب عملها ما حققتش
+
+280
+00:31:17,300 --> 00:31:26,130
+اتنين يبقى من هذا الاتنينهذا بالنسبالي يقولك ان ال
+
+281
+00:31:26,130 --> 00:31:39,050
+Y واحد وY اتنين are not satisfied with conditions
+
+282
+00:31:39,050 --> 00:31:44,350
+of
+
+283
+00:31:44,350 --> 00:31:46,870
+the theory
+
+284
+00:31:50,060 --> 00:31:55,680
+اللي بيقولون تحققوش لشروف المعبارية الله أشفننا يا
+
+285
+00:31:55,680 --> 00:32:02,340
+امالك يرزمتك ترزمت حالك
+
+286
+00:32:02,340 --> 00:32:17,180
+خدمة
+
+287
+00:32:17,180 --> 00:32:23,910
+كلمةفالحلال اللي احنا جيبناهم هادول صحيح تعملولي
+
+288
+00:32:23,910 --> 00:32:28,710
+فضل ما يكن سلوك السبعين النظرية لكن لحقكوش الانش
+
+289
+00:32:28,710 --> 00:32:33,890
+السلوك السبعين النظرية سلوك وشربط عليك لذلك حتة دي
+
+290
+00:32:33,890 --> 00:32:40,750
+specifiedلأ باربعين الأصغر لإن هدول اللي بحقوا
+
+291
+00:32:40,750 --> 00:32:44,870
+مشروع تبع النموية اللي عندنا هذه تقولوا ماشي طبعا
+
+292
+00:32:44,870 --> 00:32:50,650
+بدي أفضل ان عندي حلول بدلات الحلول هدول يعني هدول
+
+293
+00:32:50,650 --> 00:32:55,890
+الحلول مدني حلول مجموعة الحلول الكاسرسية إذا منهم
+
+294
+00:32:55,890 --> 00:33:01,950
+بدي أخلق شكل الحل اللي بحقك مان اللي بحقك النموية
+
+295
+00:33:01,950 --> 00:33:12,160
+اللي عندنا هذه فبجري أقوله هذاas long that ال Y
+
+296
+00:33:12,160 --> 00:33:20,680
+كلفة بيساوي C1 بيبقى مستيقظ زي C2 بيبقى مستيقظ
+
+297
+00:33:25,470 --> 00:33:34,610
+يجب أن أحفظ الـ y3 عند الـ 0 يجب أن أحفظ الـ y3
+
+298
+00:33:34,610 --> 00:33:37,130
+عند الـ 0 يجب أن أحفظ الـ y3 عند الـ 0 يجب أن أحفظ
+
+299
+00:33:37,130 --> 00:33:39,330
+الـ y3 عند الـ 0 يجب أن أحفظ الـ y3 عند الـ 0 يجب
+
+300
+00:33:39,330 --> 00:33:43,830
+أن أحفظ الـ y3
+
+301
+00:33:43,830 --> 00:33:46,870
+عند الـ 0 يجب أن أحفظ الـ y3 عند الـ 0 يجب أن أحفظ
+
+302
+00:33:46,870 --> 00:33:50,290
+الـ y3 عند الـ 0 يجب أن أحفظ الـ y3 عند الـ 0 يجب
+
+303
+00:33:50,290 --> 00:33:52,510
+أن أحفظ الـ y3 عند الـ 0 يجب أن أحفظ الـ y3 عند
+
+304
+00:33:52,510 --> 00:33:52,790
+y3 عند الـ 0 يجب أن أحفظ الـ y3 عند الـ 0
+
+305
+00:34:15,230 --> 00:34:19,830
+يجب ان انا
+
+306
+00:34:19,830 --> 00:34:27,740
+افرضعندي حالين سميت الأول Y3 والثاني Y4 وكل واحد
+
+307
+00:34:27,740 --> 00:34:33,980
+فيهم اعتمد على الحالين اللي قلع لهم هذول لإن هذول
+
+308
+00:34:33,980 --> 00:34:38,790
+قلعوا ليه ماني قلتلهم الانتسابيةبس مش هاجي مجموعة
+
+309
+00:34:38,790 --> 00:34:43,450
+الحلول اللي بتحقق شروط النظرية، روحت انا فرطني ان
+
+310
+00:34:43,450 --> 00:34:48,870
+عندي حلل تحقق شروط النظرية، اتخذت شروط النظرية و
+
+311
+00:34:48,870 --> 00:34:54,470
+قلت اروح ادور انتي عندي C1 و C2 و C3 و C4 ولا لا،
+
+312
+00:34:54,470 --> 00:34:59,730
+لان انا جيتهمبتخلص تمام 100% بيصير عندنا ضغوية
+
+313
+00:34:59,730 --> 00:35:04,690
+حققة تنقل لهم من هنا إلى الشمال بيقولوا كويس كده
+
+314
+00:35:04,690 --> 00:35:12,030
+بيقولوا واحد ينقل ال C1 و C2 و C3 و C4 بتمسك
+
+315
+00:35:12,030 --> 00:35:20,530
+الأولى اللي بتاخد Y3 عند Zero Yourself Y3 عند Zero
+
+316
+00:35:20,530 --> 00:35:30,980
+واحد ينقش بتعطيك هنا Y1بتساوي C1 زي C2 والبطء
+
+317
+00:35:30,980 --> 00:35:43,860
+تتاجر ل Y3' يبقى Y3' يبقى Y3'
+
+318
+00:35:43,860 --> 00:35:51,260
+يبقى Y3' يبقى Y3' يبقى Y3' يبقى Y3' يبقى Y3'بدي
+
+319
+00:35:51,260 --> 00:35:58,520
+اعطينا ان y تلاتة prime عند 0 y تلاتة prime عند 0
+
+320
+00:35:58,520 --> 00:36:09,920
+بيساوي 0 بيساوي C1 ناقص اتنين C2 تمام؟ يبقى اولا
+
+321
+00:36:09,920 --> 00:36:16,080
+صار عندنا معادلتين هدول معادلتين هنا وجه الطرف
+
+322
+00:36:16,080 --> 00:36:25,910
+تاني بتتنصرأتنين يساوي C واحد او اتنين C واحد زائد
+
+323
+00:36:25,910 --> 00:36:33,790
+اتنين C اتنين هذه زي ما هي Zero يساوي C واحد نقص
+
+324
+00:36:33,790 --> 00:36:40,010
+اتنين C اتنين اجمعها هلأ مع السلامة تصير تلاتة C
+
+325
+00:36:40,010 --> 00:36:45,210
+واحد تبقى يساوي اتنين تبقى C واحد تبقى ساوية درجة
+
+326
+00:36:45,210 --> 00:36:52,870
+طول الـT طيب تماملو الـ C1 ساوى طول 2 يبقى إيش
+
+327
+00:36:52,870 --> 00:36:59,490
+بسيط عنك إتنين C2 واتيها على الشكل التاني فتبقى
+
+328
+00:36:59,490 --> 00:37:04,450
+ساوية طول 2 أنا بدي أعطيك اللي بسيط إتنين فساوية
+
+329
+00:37:04,450 --> 00:37:12,670
+قدامك طول يبقى هنا Zero Y تلاتة ثم ساعة و الآن Y
+
+330
+00:37:12,670 --> 00:37:17,970
+تلاتة أول واحد Y تلاتة ثم فوق C1
+
+331
+00:37:32,650 --> 00:37:37,250
+يبقى هذا الحل اللي بيحقق ال two conditions اللي
+
+332
+00:37:37,250 --> 00:37:41,730
+اتنين هدول و Y تلاتة احدة زي رقم واحد و Y تلاتة و5
+
+333
+00:37:41,730 --> 00:37:42,970
+احدة زي رقم واحد وY تلاتة و5 احدة زي رقم واحد وY
+
+334
+00:37:42,970 --> 00:37:43,030
+تلاتة و5 احدة زي رقم واحد وY تلاتة و5 احدة زي رقم
+
+335
+00:37:43,030 --> 00:37:43,270
+واحد وY تلاتة و5 احدة زي رقم واحد وY تلاتة و5 احدة
+
+336
+00:37:43,270 --> 00:37:43,850
+و5 احدة زي رقم واحد وY تلاتة و5 احدة زي رقم واحد
+
+337
+00:37:43,850 --> 00:37:45,100
+وY تلاتة و5 احدة زي رقم واحد وYأيه اللي عملنا ال
+
+338
+00:37:45,100 --> 00:37:51,820
+Y3 بنروح نعمله لمان؟ Y4 لجمالي بيقولوا احنا عندنا
+
+339
+00:37:51,820 --> 00:38:01,380
+Y4 تساوي C3 E أُس D زائد C4 E أُس ناقص اتنين D
+
+340
+00:38:01,380 --> 00:38:11,080
+لجمالي انا عليه ال Dragon و ال Y4 Prime بالمرة
+
+341
+00:38:11,610 --> 00:38:19,210
+بتساوي c تلاتة minus t نقص اتنين c اربعة minus
+
+342
+00:38:19,210 --> 00:38:29,270
+اتنين d الامر بيكون y اربعة عند zero بتزاوية
+
+343
+00:38:29,270 --> 00:38:37,070
+بتساوي c تلاتة زائد c اربعة حسب ال condition اللي
+
+344
+00:38:37,070 --> 00:38:42,700
+عيبنا هذا بتساوي اكتران بتساوي zeroالان بالشكل
+
+345
+00:38:42,700 --> 00:38:48,680
+اللى y prime اربعة اند زيرو ل سبع ايه y prime
+
+346
+00:38:48,680 --> 00:38:56,180
+اربعة اند زيرو انها تعطينا c تلاتة ناقص اتنين c
+
+347
+00:38:56,180 --> 00:39:04,580
+اربعة بده يسوى ال condition كده واحد صحيح ايه؟
+
+348
+00:39:04,580 --> 00:39:09,830
+بدنا ندى لو دينا ضربنا في اتنينيبقى لو ضربنا في
+
+349
+00:39:09,830 --> 00:39:14,130
+اتنين المعادلة الأولى بصير اتنين C ثلاثة زائد
+
+350
+00:39:14,130 --> 00:39:19,090
+اتنين C أربعة يساوي Zero وهذه بدي اخليها زي ما هي
+
+351
+00:39:19,090 --> 00:39:26,690
+C ثلاثة ناقص اتنين C أربعة يساوي جدار واحد اكبر
+
+352
+00:39:26,690 --> 00:39:32,910
+بروح هذا يبقى ثلاثة C ثلاثة يساوي واحد يبقى C
+
+353
+00:39:32,910 --> 00:39:40,930
+ثلاثة يساوي جدار تلتلما C3 يتساوى بالطول C4 يتساوى
+
+354
+00:39:40,930 --> 00:40:00,870
+بالطول C4 يتساوى بالطول C4 يتساوى بالطول C4
+
+355
+00:40:00,870 --> 00:40:04,070
+يتساوى
+
+356
+00:40:04,070 --> 00:40:05,390
+بالطول
+
+357
+00:40:09,010 --> 00:40:13,430
+هي هذول اللي اتجهتين اللي شبكوا بحق كل شبكة
+
+358
+00:40:13,430 --> 00:40:21,270
+النظرية متأكد ؟ نعم نعم نعم متأكد انا اتأكد كمان و
+
+359
+00:40:21,270 --> 00:40:26,610
+الله زي انا انا انا انا انا انا انا انا انا انا
+
+360
+00:40:26,610 --> 00:40:31,470
+انا انا انا انا انا انا انا
+
+361
+00:40:35,790 --> 00:40:43,450
+مشتركة في الـ y3 وين ال y3' هي؟ إذا ال y3' عندي هو
+
+362
+00:40:43,450 --> 00:40:46,390
+0، فمشتركة في ال y3
+
+363
+00:40:52,800 --> 00:40:58,020
+نقصت كتير، طبعا، عامل الdevelopment كتير، نقصت
+
+364
+00:40:58,020 --> 00:41:01,540
+كتير، easy way، ده مظبوط، ما يتعقب في ال
+
+365
+00:41:01,540 --> 00:41:04,940
+professions، و بالبيت الهدف يتحفظ it to
+
+366
+00:41:04,940 --> 00:41:09,700
+professions، فتاني على سؤال ايش ملي، happy، you
+
+367
+00:41:09,700 --> 00:41:13,320
+can't even accept the solution specified by
+
+368
+00:41:18,280 --> 00:41:23,320
+هؤلاء اللي هم مجموعة الحلو الأساسي اللي بيحققوا
+
+369
+00:41:23,320 --> 00:41:34,620
+شروط النظرية يبقى لنا ساعة Y3 and Y4 for the
+
+370
+00:41:34,620 --> 00:41:40,480
+fundamental set
+
+371
+00:41:40,480 --> 00:41:42,840
+of
+
+372
+00:41:52,210 --> 00:42:01,170
+set of solutions that satisfy
+
+373
+00:42:01,170 --> 00:42:13,030
+.. that satisfy the above premise إن كانت هؤلاء
+
+374
+00:42:13,030 --> 00:42:17,290
+الأفكار اللي بيحصلون من النظرية أدنى
+
+375
+00:42:26,390 --> 00:42:29,830
+ناخد بعض الأسئلة من الأسئلة التي كنا نلاقيها قبلها
+
+376
+00:42:29,830 --> 00:42:34,510
+و ببعض الأسئلة التي تتحركين فيها الفيديوهات التي
+
+377
+00:42:34,510 --> 00:42:38,590
+تتحركين فيها هذه المساحة و خلال استخدام الوطن اللي
+
+378
+00:42:38,590 --> 00:42:42,970
+تحينا منه نستخدم هذه الأسئلة جميعا
+
+379
+00:42:50,130 --> 00:43:08,590
+اللي هو رفع الطوابق اللي هو رفع
+
+380
+00:43:08,590 --> 00:43:08,910
+الطوابق اللي هو رفع الطوابق اللي هو رفع الطوابق
+
+381
+00:43:08,910 --> 00:43:12,950
+رفع الطوابق اللي هو رفع الطوابق اللي هو ر
+
+382
+00:43:16,590 --> 00:43:24,290
+فى ثلاثية الوصفين and and
+
+383
+00:43:24,290 --> 00:43:35,450
+f of t قد ساوي e with p greater than zero find
+
+384
+00:43:35,450 --> 00:43:41,010
+find p of t
+
+385
+00:43:47,940 --> 00:43:51,940
+يعني يا بنادق اعتبر هذا المسأل عامة عالميا على
+
+386
+00:43:51,940 --> 00:43:57,960
+نفسك بيقول لو كان الواضح ان الذاتين F وG قسمنا
+
+387
+00:43:57,960 --> 00:44:05,000
+بكتابية E وC ولو كان دلوقتي F of T هي T وT greater
+
+388
+00:44:05,000 --> 00:44:10,160
+than 0 يجب ان يأتي شكل P of T يعني انا هنا في new
+
+389
+00:44:10,160 --> 00:44:15,350
+functions F وTأول اسم انتجاها المعروف هو احدى
+
+390
+00:44:15,350 --> 00:44:22,190
+الذين فيه المعروفة انتجاها المعروف هو احد الذين
+
+391
+00:44:22,190 --> 00:44:22,850
+فيه المعروفة انتجاها المعروف هو احد الذين فيه
+
+392
+00:44:22,850 --> 00:44:23,910
+المعروف هو احد الذين فيه المعروف هو احد الذين فيه
+
+393
+00:44:23,910 --> 00:44:24,150
+المعروف هو احد الذين فيه المعروف هو احد الذين فيه
+
+394
+00:44:24,150 --> 00:44:24,370
+المعروف هو احد الذين فيه المعروف هو احد الذين فيه
+
+395
+00:44:24,370 --> 00:44:24,550
+المعروف هو احد الذين فيه المعروف هو احد الذين فيه
+
+396
+00:44:24,550 --> 00:44:30,410
+المعروف هو احد الذين فيه المعروف هو احد الذين فيه
+
+397
+00:44:30,410 --> 00:44:38,330
+المعروف هو احد
+
+398
+00:44:38,820 --> 00:44:44,900
+طبعا هذا الكلام yourself ال F of T بيظهر لمعروف
+
+399
+00:44:44,900 --> 00:44:53,700
+بجديد P of T هي هذه الميادة الملولة مشتق هذه واحد
+
+400
+00:44:53,700 --> 00:45:01,660
+مشتق هذه C prime of T هذا المحدد يسوي T ترتيب جديد
+
+401
+00:45:05,710 --> 00:45:18,570
+يُقصر T في G' of T T في G' of T ماتس G of T بتساوي
+
+402
+00:45:18,570 --> 00:45:25,570
+T ترقية بيوسم شو معناه لو اننا قسمنا كله على مين؟
+
+403
+00:45:25,570 --> 00:45:37,980
+على T لإن لو قسمنا على T تصير G' of T-1 على T في
+
+404
+00:45:37,980 --> 00:45:45,580
+الـ G of T كده يساوي T في E of T شوية كده المعاملة
+
+405
+00:45:45,580 --> 00:45:50,960
+بيستقبلها لإنه بيساكنها في طولات الهاليمين
+
+406
+00:45:50,960 --> 00:45:59,600
+بيستقبلها في الجهة الهاليمينية there is other
+
+407
+00:45:59,600 --> 00:46:06,420
+differential equationيبقى من المروحة الحلها زي ما
+
+408
+00:46:06,420 --> 00:46:13,320
+قلنا من الحل فضل ذلك وبالتالي نجيب شكل G of D يبقى
+
+409
+00:46:13,320 --> 00:46:20,360
+وشكلها كفانات من المروحة دي من ال U of D ال U of D
+
+410
+00:46:20,360 --> 00:46:24,960
+اللي هو عمار عليه شكيل واسمها في السابقه الواحد
+
+411
+00:46:24,960 --> 00:46:31,700
+على T D T اللي هو المعامل سبعمين الجييبقى هذا
+
+412
+00:46:31,700 --> 00:46:42,880
+الكلام E أس ناقص لل T يبقى
+
+413
+00:46:42,880 --> 00:46:48,240
+هذا الكلام E أس ناقص لل T يبقى هذا الكلام E أس
+
+414
+00:46:48,240 --> 00:46:53,280
+ناقص لل T يبقى
+
+415
+00:46:53,280 --> 00:46:56,960
+هذا الكلام E أس ناقص لل
+
+416
+00:46:58,550 --> 00:47:05,270
+طيب إذا بتروح أعظم المعادلة كل مئة واحد على T ومش
+
+417
+00:47:05,270 --> 00:47:11,730
+بصير واحد على T جيه ال prime of T نقص واحد على T
+
+418
+00:47:11,730 --> 00:47:17,610
+تربية جيه ال T ومش بصير واحد على T تربية جيه ال T
+
+419
+00:47:17,610 --> 00:47:21,950
+ومش بصير واحد على T تربية جيه ال T ومش بصير واحد
+
+420
+00:47:21,950 --> 00:47:26,890
+على T تربية جيه ال T ومش بصير واحد على T تربية جيه
+
+421
+00:47:26,890 --> 00:47:27,770
+واحد على T تربية جيه ال T ومش بصير واحد على T
+
+422
+00:47:27,770 --> 00:47:27,790
+تربية جيه ال T ومش بصير واحد على T تربية جيه ال T
+
+423
+00:47:27,790 --> 00:47:28,540
+ومش بصير واحد على T تربية جيه ال T ومش بصيربدر
+
+424
+00:47:28,540 --> 00:47:35,120
+يساوي E والـ C المجموع الكامل أطلع فيهم لأن لو
+
+425
+00:47:35,120 --> 00:47:41,180
+كانت أطلع فيهم بيصير واحد عالة T الـ G of T بيساوي
+
+426
+00:47:41,180 --> 00:47:49,020
+E والـ C زائد فرصة الـ C فور بكله في T بصير عالة G
+
+427
+00:47:49,020 --> 00:47:57,870
+of T بيدر يساوي T E والـ C زائد Cيبقى هذا الشكل
+
+428
+00:47:57,870 --> 00:48:02,650
+الـ G of T اللي طلبها هي طلبها أن نستخدم الولرسكين
+
+429
+00:48:02,650 --> 00:48:06,090
+وحللها في ال course of linear differential
+
+430
+00:48:06,090 --> 00:48:11,570
+equation أو قضايا مثلها سيبقوا بالحل قبل ال course
+
+431
+00:48:11,570 --> 00:48:15,810
+of linear differential equation
+
+432
+00:48:31,510 --> 00:48:46,430
+سؤال تسعة عاشر يقول ما F ترانسكل تبع ال F والD F
+
+433
+00:48:46,430 --> 00:48:50,190
+ترانسكل
+
+434
+00:48:50,190 --> 00:48:52,930
+F
+
+435
+00:49:00,030 --> 00:49:13,530
+I F وإذا كان الـ U يسوى اتنين F ناقص G الـ U يسوى
+
+436
+00:49:13,530 --> 00:49:24,010
+اتنين فموينة P فتر ساوي F زائد اتنين G فانا و نسكن
+
+437
+00:49:24,010 --> 00:49:29,090
+I فأنا و نسكن
+
+438
+00:49:35,820 --> 00:49:50,160
+لدنا مانستين اللي هو W تبع ال U و ال V of U and ال
+
+439
+00:49:50,160 --> 00:50:01,080
+V ال U and ال V in pairs of المانستين تبع ال F و
+
+440
+00:50:01,080 --> 00:50:01,620
+ال G
+
+441
+00:50:38,290 --> 00:50:44,610
+سؤال مرة تانية يقول لو كان ال W of F and G هو
+
+442
+00:50:44,610 --> 00:50:51,660
+روزنسكين تبع الدالة F وG وإذا كان ال U functionهي
+
+443
+00:50:51,660 --> 00:50:57,240
+عبارة عن اثنين F لاطس D والـ P function LF زي
+
+444
+00:50:57,240 --> 00:51:02,900
+الاثنين كان هذا الـRoller Skin تبع U بدلالة
+
+445
+00:51:02,900 --> 00:51:08,380
+الـRoller Skin تبع من F وD فقولوا طيب تعالوا نجيب
+
+446
+00:51:08,380 --> 00:51:12,690
+ال roller skin تبع ال F وD ونشوف شو شكلهيبقى انا
+
+447
+00:51:12,690 --> 00:51:18,690
+لو جيت لهرسكين تبع ال F و ال G بقول له هذه المحدث
+
+448
+00:51:18,690 --> 00:51:27,890
+هذه F هذه G هذه F' هذه G' بدنا نفكر محدد هذا معناه
+
+449
+00:51:27,890 --> 00:51:35,050
+يبقى F في G' نفس F' في G
+
+450
+00:51:41,560 --> 00:51:46,800
+أحنا بدنا مين؟ بدنا role skin تبع ال U و ال V يبقى
+
+451
+00:51:46,800 --> 00:51:53,220
+بدنا ياخد رولسكين تبع ال U و ال V يبقى ال U ال V
+
+452
+00:51:53,220 --> 00:51:59,760
+ال U prime ال V prime مطبوط ايه؟ يبقى هذا الكلام
+
+453
+00:51:59,760 --> 00:52:06,760
+بده يساوي ال U بده اشيله و احطه مثلين اتنين F ماطس
+
+454
+00:52:06,760 --> 00:52:15,180
+ال Gالـ V للـ F زائد اتنين G الـ V لـ U' المبدأ
+
+455
+00:52:15,180 --> 00:52:21,100
+اشتق هذا يبقى مشتقة المجموعة الجابري لدلتين يبقى
+
+456
+00:52:21,100 --> 00:52:30,760
+اتنين F' نقص G' مشتقة هذه لـ F' زائد اتنين G'
+
+457
+00:52:31,400 --> 00:52:41,030
+يساويبدا افكر محدد هذا يبقى هدف اللي يقينه 2F-G F
+
+458
+00:52:41,030 --> 00:52:47,690
+prime زي 2G prime اي حاصل ضرب عناصر القطر الرئيسي
+
+459
+00:52:47,690 --> 00:52:57,810
+ناقص حاصل ضرب عناصر القطر الثانوي F زي 2G في 2F
+
+460
+00:52:57,810 --> 00:53:06,590
+prime ناقص G primeيبقى هذا قيمة مين المحدد تعالوا
+
+461
+00:53:06,590 --> 00:53:11,150
+نفك خلاق وسط يعني أفك القيود ده للمكان الحالي بيها
+
+462
+00:53:11,150 --> 00:53:15,550
+ونشوف إلى أين بدنا نوصل يبقى هذا يا بنات بدها
+
+463
+00:53:15,550 --> 00:53:27,230
+تساوي اتنين F F F Prime زائد اتنين F G Prime اتنين
+
+464
+00:53:27,230 --> 00:53:31,090
+F F F Prime اتنين F F G Prime
+
+465
+00:53:55,650 --> 00:53:57,050
+2m2m2m2m2m2m2m2m2m2m2m2m2m2m2m2m2m2m2m2m2m2m2m2m2m2m2m2m2m2m2m2m2m2m2m2m2m2m2m2m2m2m2m2m2m2m2m2m2m2m2m2m2m2m2m2m2m2m2m2m2m2m2m2m2m2m2m2m2m2m2m2m2m2m2m2m2m2m2m2m2m2m2m2m2m2m2m2m2m2m2m2m2m2m2m2m2m2m2m2m2m2m2m2m2m2m2m2m2m2m2m2m
+
+466
+00:53:57,250 --> 00:54:04,850
+أنا ضربت اتنين هذول في البعض ناقص اتنين GG prime
+
+467
+00:54:05,840 --> 00:54:13,780
+خلصت ال term الأول بدي أدربه اتنين F F prime بس
+
+468
+00:54:13,780 --> 00:54:23,540
+بشرط من سالب يبقى سالب اتنين F F prime هنا سالب F
+
+469
+00:54:23,540 --> 00:54:27,620
+في سالب G زائد F G prime
+
+470
+00:54:35,880 --> 00:54:48,600
+نقص اربعة f prime g نقص اربعة f prime g نقص مع نقص
+
+471
+00:54:48,600 --> 00:54:55,540
+بصير زائد اتنين g g prime يبقى زائد اتنين g g
+
+472
+00:54:55,540 --> 00:54:55,960
+prime
+
+473
+00:55:06,960 --> 00:55:18,260
+تعالى تطلعلي 4 F G Prime وعندك F G Prime بصير خمسة
+
+474
+00:55:18,260 --> 00:55:27,610
+F G Primeهذه بالسالب وهذه بالسالب التنتين نفس
+
+475
+00:55:27,610 --> 00:55:36,290
+الشيء مظبوط يبقى ناقص خمسة f prime g شو رايك ناخد
+
+476
+00:55:36,290 --> 00:55:41,090
+خمسة عامل مشترك ونشوف لوين بدنا نوصل يبقى لو جينا
+
+477
+00:55:41,090 --> 00:55:48,970
+خمسة عامل مشترك بظل f g prime ناقص
+
+478
+00:55:53,320 --> 00:55:56,640
+طلع في المقدار بين القوسين
+
+479
+00:55:58,970 --> 00:56:11,790
+FG'-F'G FG'
+
+480
+00:56:11,790 --> 00:56:18,370
+-F'G FG'
+
+481
+00:56:21,370 --> 00:56:28,740
+-F'G FG'-F'G FG'-F'Gطيب بدنا منكوا exercises تلاتة
+
+482
+00:56:28,740 --> 00:56:35,980
+اتنين المسائل التالية يبقى exercises تلاتة اتنين
+
+483
+00:56:35,980 --> 00:56:46,000
+بدنا المسائل من واحد لغاية اربعتاش الأد ومن سبعتاش
+
+484
+00:56:46,000 --> 00:56:53,140
+لغاية ستة وعشرين يبقى
+
+485
+00:56:53,140 --> 00:56:54,360
+بدنا المسائل هذه
+
+486
+00:56:58,690 --> 00:57:06,610
+بنروح الان ل section اللي بعده مرتبط ارتباط وثيق
+
+487
+00:57:06,610 --> 00:57:10,950
+بال role skin تبعنا هذا بيعتمد عليه اعتماد كله
+
+488
+00:57:10,950 --> 00:57:20,410
+يبقى section 3 3 بتحدث عن ال linear independence
+
+489
+00:57:20,410 --> 00:57:24,490
+linear
+
+490
+00:57:24,490 --> 00:57:41,530
+independence andthe run skin نعطي
+
+491
+00:57:41,530 --> 00:57:46,290
+تعريف وبعد ذلك بناخد أمثلة definition two
+
+492
+00:57:46,290 --> 00:57:57,750
+functions two functions f of t andالـ g of t are
+
+493
+00:57:57,750 --> 00:58:06,310
+said to be linearly
+
+494
+00:58:06,310 --> 00:58:07,390
+dependent
+
+495
+00:58:17,220 --> 00:58:23,580
+هختصر كلمة linearly dependent يا بنات إلى ال D من
+
+496
+00:58:23,580 --> 00:58:38,900
+الآن فصاعد on an interval I if
+
+497
+00:58:38,900 --> 00:58:48,630
+there exist if there exist two constantstwo
+
+498
+00:58:48,630 --> 00:58:55,510
+constants ثابتين كواحد
+
+499
+00:58:55,510 --> 00:59:08,830
+and كاثنين not both zero not both zero مش كلهم
+
+500
+00:59:08,830 --> 00:59:19,990
+أصفر such that such that بحيث أنكواحد في ال F of T
+
+501
+00:59:19,990 --> 00:59:29,570
+زائد كاتنين في ال G of T بده يساوي zero for all T
+
+502
+00:59:29,570 --> 00:59:39,910
+اللي موجودة في ال interval I also و كذلك ال F and
+
+503
+00:59:39,910 --> 00:59:45,790
+ال G are called
+
+504
+00:59:49,870 --> 01:00:06,330
+Linearly Independent LPI
+
+505
+01:00:06,330 --> 01:00:15,370
+FK1
+
+506
+01:00:15,860 --> 01:00:23,100
+فى ال F of T زاد K اتنين فى ال G of T يساوي Zero
+
+507
+01:00:23,100 --> 01:00:32,200
+Then K واحد بده يساوي K اتنين بده يساوي Zero
+
+508
+01:00:32,200 --> 01:00:40,000
+Example
+
+509
+01:00:40,000 --> 01:00:40,420
+one
+
+510
+01:00:48,210 --> 01:00:56,330
+determine whether determine
+
+511
+01:00:56,330 --> 01:01:08,050
+whether the given pair of functions the given pair
+
+512
+01:01:08,050 --> 01:01:14,330
+of functions are
+
+513
+01:01:15,490 --> 01:01:26,090
+Linearly Independent or Linearly Dependent الـ
+
+514
+01:01:26,090 --> 01:01:37,310
+F of T يساوي E أس تلاتة T والـ G of T يساوي A أس
+
+515
+01:01:37,310 --> 01:01:40,650
+تلاتة في T ناقص الواحد
+
+516
+01:01:48,330 --> 01:01:52,650
+طيب بنجي لعنوان اللي احنا رافعينه linear
+
+517
+01:01:52,650 --> 01:01:59,510
+independence الاستقلال الخطي عند الورنسكان و
+
+518
+01:01:59,510 --> 01:02:04,370
+الورنسكان يعني هنشوف شو علاقة الاستقلال الخطي و
+
+519
+01:02:04,370 --> 01:02:10,250
+الاعتماد الخطي كمان بالورنسكان بنجي للتعريف اللي
+
+520
+01:02:10,250 --> 01:02:16,500
+احنا كاتبينه بقول لو عندي two functions دالتينهذول
+
+521
+01:02:16,500 --> 01:02:20,960
+اللي بقول عنهم linearly dependent يعني بيتمدوا على
+
+522
+01:02:20,960 --> 01:02:27,520
+بعض خطيا، linearly dependent هاختصرها إلى LD،
+
+523
+01:02:27,520 --> 01:02:32,280
+linearly dependent على الفترة اللي عندنا هذه if
+
+524
+01:02:32,280 --> 01:02:36,680
+they exist يعني إذا جدرنا نلاقي هذا ال E المجلوب
+
+525
+01:02:36,680 --> 01:02:42,570
+هنا there existإذا وجدت
+
+526
+01:02:42,570 --> 01:02:48,710
+ثابتين K واحد أو K اتنين، نقبض الـ0 مش كلهم أصفر
+
+527
+01:02:48,710 --> 01:02:53,790
+بحيث ان K واحد في F of T زاد ال K اتنين في G of T
+
+528
+01:02:53,790 --> 01:02:58,010
+بيديوا يسووا 0 لكل T الموجودة في I
+
+529
+01:03:01,400 --> 01:03:06,600
+أنا عندي دالتين F و G و بدى أشوف هل الدالتين هدول
+
+530
+01:03:06,600 --> 01:03:13,340
+معتمدتين على بعض خطيا و الله مستقلتين عن بعض خطيا
+
+531
+01:03:13,340 --> 01:03:20,280
+بقولي أه إذا بتقدر تلاقي ثوابت اتنين ليس بالضرورة
+
+532
+01:03:20,280 --> 01:03:24,660
+انه .. مش ليس بالضرورة يعني لو كان فيهم واحد zero
+
+533
+01:03:24,660 --> 01:03:28,640
+و اتاني لأ فاش مشكلة و إذا اتنين لا يساوي zero
+
+534
+01:03:28,640 --> 01:03:32,470
+برضه فاش مشكلة بحيثلو ضربت كونوسونت في الدالة
+
+535
+01:03:32,470 --> 01:03:34,950
+الأولى و كونوسونت في الدالة التانية و جماعة، ماذي
+
+536
+01:03:34,950 --> 01:03:40,490
+يكون الناتج؟ سفر طيب، شو معنى ال linear
+
+537
+01:03:40,490 --> 01:03:46,630
+independence لاستقلال؟ الخاطئ بيقول also ال F و G
+
+538
+01:03:46,630 --> 01:03:51,610
+أركون linearly independent الدالتين هدول مستقلتين
+
+539
+01:03:51,610 --> 01:03:55,910
+على البعض خاطئا يعني دولة ماهياش محتلة كل دولة
+
+540
+01:03:55,910 --> 01:04:00,010
+لحالها مالها linearly independent
+
+541
+01:04:11,240 --> 01:04:18,580
+أذا انا مش هنفرق بين الأمرين هل الدالتين هدول
+
+542
+01:04:18,580 --> 01:04:24,960
+مستقلتين خطيا و معتمدتين على بعض خطيابدي ادورلي
+
+543
+01:04:24,960 --> 01:04:28,820
+على ثوابت اتنين اضرب ثابت في الاول و ثابت التاني و
+
+544
+01:04:28,820 --> 01:04:33,120
+اجمع و الاقيهم يساوي قداش Zero بعد ما يطلع في Zero
+
+545
+01:04:33,120 --> 01:04:38,540
+باطل على الثواب التاني والله اذا ثوابت اتنين اصفرا
+
+546
+01:04:38,540 --> 01:04:44,180
+يبقى هدول الدالتين linearly independent وان كان
+
+547
+01:04:44,180 --> 01:04:48,980
+اتنين مهماش اصفر او واحد صفر والتاني اللي لأ يبقى
+
+548
+01:04:48,980 --> 01:04:53,650
+linearly independent واضحة الصورةيبقى عرفنا شو
+
+549
+01:04:53,650 --> 01:04:57,110
+الفرق بين ال linear dependence و ال linear
+
+550
+01:04:57,110 --> 01:05:01,910
+independence الناس اللي أخدوا الجبر خطي نفس الكلام
+
+551
+01:05:01,910 --> 01:05:07,050
+اللي بياخدوه في الجبر الخطي حرفيا ماغيرناش فيه ولا
+
+552
+01:05:07,050 --> 01:05:12,590
+حاجة طيب بدنا ننقل هذا المثال على أرض الواقع ببعض
+
+553
+01:05:12,590 --> 01:05:16,510
+الأمثلةGallery determine whether the given pair of
+
+554
+01:05:16,510 --> 01:05:20,790
+functions حدد لمين من أزواج الدولة التي بتبقى
+
+555
+01:05:20,790 --> 01:05:25,030
+linearly independent ومين linearly dependent
+
+556
+01:05:50,220 --> 01:05:58,200
+هل تقدر تجيبنا تابعمضربه في الدالة الأولى و ثابت
+
+557
+01:05:58,200 --> 01:06:04,000
+تانى مضربه في الدالة التانية و نجمع يطلع النتج
+
+558
+01:06:04,000 --> 01:06:11,360
+يساوي zero نقدر و بعد ذلك بظهر أشوف شو شكلهم ها
+
+559
+01:06:11,360 --> 01:06:14,460
+تقدروا؟
+
+560
+01:06:14,460 --> 01:06:22,480
+طيب إيش رأيك؟ هنا بداجي أقول assumeافترضوا there
+
+561
+01:06:22,480 --> 01:06:32,940
+exists c1 و c2 such that بحيث ان c1 في e أس تلاتة
+
+562
+01:06:32,940 --> 01:06:39,380
+t زاد c2 في e أس تلاتة t ناقص تلاتة بده يساوي زي
+
+563
+01:06:42,410 --> 01:06:47,350
+يلا هد انتوا بيجي 48 طالب او زدت واحدة صارت 49
+
+564
+01:06:47,350 --> 01:06:53,170
+بدنا نعرف قداش ها كل واحدة تفكر تجيب ثوابت من
+
+565
+01:06:53,170 --> 01:06:58,070
+عندها تقولي ها دي لو أخدنا C1 بكذا و C2 بكذا بطلع
+
+566
+01:06:58,070 --> 01:07:06,870
+انها تجي سافار يلا شوف ارقام ثوابت ايوة
+
+567
+01:07:11,150 --> 01:07:17,030
+خلامك خالص بتقولي انا بدها اخد c1 هذا بواحد و بدها
+
+568
+01:07:17,030 --> 01:07:23,650
+تاخد c2 ب e تكعيب بس بالسالب يعني سالب e تكعيب
+
+569
+01:07:23,650 --> 01:07:29,090
+تعالى نشوف هذا كلامها صح ولا غلط يبقى بالدرجة اقول
+
+570
+01:07:29,090 --> 01:07:43,400
+take c1 يساوي واحد و c2 يساوي سالب e تكعيبثم سوف
+
+571
+01:07:43,400 --> 01:07:49,060
+نشوف كلامه صح و لا سي واحد بواحد بقاش بظل E أس
+
+572
+01:07:49,060 --> 01:07:58,020
+تلاتة T زي سي اتنين اللي هو ناقص E تكيب P أس تلاتة
+
+573
+01:07:58,020 --> 01:08:06,740
+T ناقص تلاتة هو يساوي E أس تلاتة T ناقصE تكيب مع
+
+574
+01:08:06,740 --> 01:08:13,380
+هذه تجمع بضال قداش E أس ثلاثة T يبقى E أس ثلاثة T
+
+575
+01:08:13,380 --> 01:08:19,700
+وE ساوى قداش Zero هذي احنا جيبنا ثوابت اتنين بحيث
+
+576
+01:08:19,700 --> 01:08:24,320
+ضربنا كل صنفة الأول وكل صنفة التانية وجمعنا وقالوا
+
+577
+01:08:24,320 --> 01:08:28,420
+انها تجيب E ساوى Zero بداجي أطلع في الثوابت اللي
+
+578
+01:08:28,420 --> 01:08:34,020
+جيبتهم هل هدول بأصفات يبقى هدول الدالتين مالهم
+
+579
+01:08:34,340 --> 01:08:43,360
+linearly dependent يبقى س اللي هو ال E أس ثلاثة T
+
+580
+01:08:43,360 --> 01:08:50,480
+and ال E أس ثلاثة T نقص ثلاثة are linearly
+
+581
+01:08:50,480 --> 01:08:59,640
+dependent because اللي هو خليها مشان التعريفة بدل
+
+582
+01:08:59,640 --> 01:09:06,560
+C واحد قوليلي K واحدو K2 بشان نخلي رموزنا زي ما هي
+
+583
+01:09:06,560 --> 01:09:17,020
+K1 و K2 وهذه K1 وهذه K2 تمام؟ لإنها دندن because
+
+584
+01:09:17,020 --> 01:09:27,600
+K1 لا يساوي Zero وK2 لا يساوي Zero وكذلك طيب خديني
+
+585
+01:09:27,600 --> 01:09:31,260
+نمرة B نمرة B
+
+586
+01:09:34,650 --> 01:09:44,850
+لو أخدنا اللي هو ال F of T بده يساوي T و ال G of T
+
+587
+01:09:44,850 --> 01:09:50,610
+بده يساوي تساوي T السالب واحد و T greater than
+
+588
+01:09:50,610 --> 01:09:51,330
+zero
+
+589
+01:09:59,070 --> 01:10:03,110
+قام من عندنا لو حطينا مثلا ال T أكبر من زفرة و T
+
+590
+01:10:03,110 --> 01:10:08,710
+أقل من زفرة و تبناه مظلوم؟ تفكر في اللي بدك تفكر
+
+591
+01:10:08,710 --> 01:10:14,710
+فيه؟ حطيت قيودنا؟ بأي
+
+592
+01:10:14,710 --> 01:10:19,770
+طريقة تشير تهاتيل التوابل؟ احنا لسه في بداية
+
+593
+01:10:19,770 --> 01:10:24,070
+الطريق فأول يعني بس احنا بدنا نثبت المفهوم عندكوا
+
+594
+01:10:24,070 --> 01:10:28,520
+و بعدين بنطور أسئلتنا يعني انها تعتبر أسئلة بسيطةو
+
+595
+01:10:28,520 --> 01:10:35,100
+بعد ذلك نشوف كيف نثبت الشغل هذه طيب ماطيني سؤال
+
+596
+01:10:35,100 --> 01:10:38,840
+تاني قال ال f of t بده يساوي t و ال g of t بده
+
+597
+01:10:38,840 --> 01:10:46,700
+يساوي t و السالب واحد بدي بقوله هنا assume افترضي
+
+598
+01:10:46,700 --> 01:10:56,500
+there exist كواحد و كاتنين such that بحيث انكواحد
+
+599
+01:10:56,500 --> 01:11:03,640
+T زائد كتنين في T ناقص واحد بده يساوي زينا بتروح
+
+600
+01:11:03,640 --> 01:11:10,360
+هدور علي كواحد و كتنين شو رايك اشتق المعادلة هذه
+
+601
+01:11:10,360 --> 01:11:15,040
+لو اشتقت المعادلة هذه بصير هنا كواحد بتطير هذه T
+
+602
+01:11:15,040 --> 01:11:22,900
+بصير ناقص كتنين T و ناقص اتنينيبقى هذه شو بدي
+
+603
+01:11:22,900 --> 01:11:29,600
+اعطيك يا بنات بدي اعطيك ان K واحد يساوي K اتنين في
+
+604
+01:11:29,600 --> 01:11:35,120
+T السالب اتنين مظبوط؟
+
+605
+01:11:35,120 --> 01:11:40,620
+بدي امسك المعلومة اللي حصلت عليها و اعوض بها في
+
+606
+01:11:40,620 --> 01:11:47,060
+المعادلة اللي فوق يبقى ايش بصير عندي؟ K اتنين في T
+
+607
+01:11:47,060 --> 01:11:49,460
+السالب اتنين في T
+
+608
+01:11:53,220 --> 01:11:58,440
+زائد كتنين في T والسالب واحد يساوي Zero
+
+609
+01:12:09,630 --> 01:12:15,370
+زائد كتنين كتيوس سالب واحد يساوي زيرو مش هذه هي
+
+610
+01:12:15,370 --> 01:12:21,330
+نفسها يبقى هذا بدي يعطي كتنين كتنين كتين كتين كتين
+
+611
+01:12:21,330 --> 01:12:21,650
+كتين كتين كتين كتين كتين كتين كتين كتين كتين كتين
+
+612
+01:12:21,650 --> 01:12:23,510
+كتين كتين كتين كتين كتين كتين كتين كتين كتين كتين
+
+613
+01:12:23,510 --> 01:12:26,970
+كتين كتين كتين كتين كتين كتين كتين كتين كتين كتين
+
+614
+01:12:26,970 --> 01:12:29,670
+كتين كتين كتين كتين كتين كتين كتين كتين كتين كتين
+
+615
+01:12:29,670 --> 01:12:35,490
+كتين كتين كتين كتين كتين كتين
+
+616
+01:12:35,490 --> 01:12:42,440
+كزيرو لما كتنين يساوي زيرو خديها وعوضيها في
+
+617
+01:12:42,440 --> 01:12:48,480
+المعادلة اللي فوق يبقى بصير كواحد بده يساوي زيرو
+
+618
+01:12:48,480 --> 01:12:56,140
+في T أساليب اتنين يساوي جداش زيرو يبقى كواحد بده
+
+619
+01:12:56,140 --> 01:13:00,580
+يساوي كتنين بده يساوي جداش بده يساوي زيرو المعنى
+
+620
+01:13:00,580 --> 01:13:05,230
+هذا كلام ال two functions هدول ما لهمlinearly
+
+621
+01:13:05,230 --> 01:13:10,570
+independent ولا واحدة بتعتمد على الثانية يبقى هنا
+
+622
+01:13:10,570 --> 01:13:18,290
+ال T and ال T والسالب واحد are linearly
+
+623
+01:13:18,290 --> 01:13:25,070
+independent يعني يا بنات احنا بنحاول نوجد ثوابت
+
+624
+01:13:25,070 --> 01:13:32,060
+بأي طريقة رياضية نقدر عليها مين بتسأل؟ ايوةكان
+
+625
+01:13:32,060 --> 01:13:35,720
+واحد كيف ده يعني كان مع نفس الشخص واحد او اخر؟ كيف
+
+626
+01:13:35,720 --> 01:13:39,980
+نتعرف على واحد و اخر؟ لطيع واحد و واحد قبل انك حُك
+
+627
+01:13:39,980 --> 01:13:44,260
+واحد و واحد و نشوف يساوي صفر ولا لأ؟ يبقاش بدك
+
+628
+01:13:44,260 --> 01:13:51,240
+تخدمهم واحد و واحد و اخر؟ بقى ايه واحد؟ واحد في
+
+629
+01:13:51,240 --> 01:13:57,400
+اتين و اتين بدك تخدم واحد تمام؟ زي واحد في اتين
+
+630
+01:13:57,400 --> 01:13:59,220
+والسالي واحد تساوي صفر؟
+
+631
+01:14:08,270 --> 01:14:17,750
+أو نجمع نتج يكون يساوي 0 كي
+
+632
+01:14:17,750 --> 01:14:24,670
+واحد
+
+633
+01:14:24,670 --> 01:14:27,430
+و كي اثنين استوابط اللي بدنا ناخده من هناك التعريف
+
+634
+01:14:27,430 --> 01:14:35,620
+بقول مش بداخله functionياخدهم ثوابت، قادر بالك، اه
+
+635
+01:14:35,620 --> 01:14:39,860
+في سؤال تاني؟ اه ايوة ..الثور في حياته عشان انه
+
+636
+01:14:39,860 --> 01:14:43,460
+فيه واحد في اتنين يساونهم باصفار بسوء الصفر وكمان
+
+637
+01:14:43,460 --> 01:14:47,180
+لجينا انهم بيساووا قيمة غير الأصفر بسوء الصفر يحصل
+
+638
+01:14:47,180 --> 01:14:53,360
+هالانتلاع؟ كانت الكلام المناورة من بعض صحوا لاني
+
+639
+01:14:53,360 --> 01:14:58,020
+يا أصفار يا ثوابت، ممكن ألاقي واحد منهم صفر، بس
+
+640
+01:14:58,020 --> 01:15:02,570
+التاني لألو كان واحد صفر و واحد عدد ماعندى مشكلة
+
+641
+01:15:02,570 --> 01:15:07,230
+بكون linearly dependent لكن إذا اتنين أصفر مع بعض
+
+642
+01:15:07,230 --> 01:15:13,550
+بقول linearly independent طيب هنصيغ الكلام هذا
+
+643
+01:15:13,550 --> 01:15:18,870
+بشكل آخر خدولي هالنظرية التالية the theorem
+
+644
+01:15:18,870 --> 01:15:23,610
+النظرية
+
+645
+01:15:23,610 --> 01:15:35,090
+بتقول ما ياتى F ال Fand الـ G are differentiable
+
+646
+01:15:35,090 --> 01:15:55,050
+functions on an open interval I and F that exist
+
+647
+01:15:55,050 --> 01:15:57,770
+P0
+
+648
+01:15:59,220 --> 01:16:14,820
+in الفترة I such that بحيث ان الورنسكت تبع ال F و
+
+649
+01:16:14,820 --> 01:16:29,240
+ال G عند T0 لا يساوي Zero then ال F عند ال Gare
+
+650
+01:16:29,240 --> 01:16:40,960
+linearly independent عن الفترة I on
+
+651
+01:16:40,960 --> 01:16:48,100
+the other hand
+
+652
+01:16:54,420 --> 01:17:07,980
+الـ F and ال G are linearly dependent on Iعلى
+
+653
+01:17:07,980 --> 01:17:14,060
+الفترة I then الرنسكين
+
+654
+01:17:14,060 --> 01:17:24,580
+تبع ال F وال G عند ال T بده ساوي Zero for all T
+
+655
+01:17:24,580 --> 01:17:29,180
+اللي موجودة في ال interval I
+
+656
+01:17:48,670 --> 01:17:53,810
+قبل مناخد المثال بدنا نرجع لنص النظرية ونحاول نفهم
+
+657
+01:17:53,810 --> 01:18:16,650
+ما هو الشئ اللي موجود في هذه النظرية طلع
+
+658
+01:18:16,650 --> 01:18:21,500
+كويسبدي أجرى نظرية و بعدين بدي أقولكوا إيش فهمت
+
+659
+01:18:21,500 --> 01:18:26,060
+منها و شوفوا فهمي الصح و لا غلط إذا صح بنعتمدوا و
+
+660
+01:18:26,060 --> 01:18:31,520
+إذا غلط بنصحهم بقول إيش لو كان ال F و G are
+
+661
+01:18:31,520 --> 01:18:37,760
+differentiable functions على فترة عن I و أخذت نقطة
+
+662
+01:18:37,760 --> 01:18:41,640
+موجودة في هذه الفترة و لجيت أن ال neurons كان
+
+663
+01:18:41,640 --> 01:18:46,180
+عندها لا يساوي Zero إن حدث ذلكبقول الـ two
+
+664
+01:18:46,180 --> 01:18:52,000
+functions are linearly independent طيب ده اللي هو
+
+665
+01:18:52,000 --> 01:18:56,380
+من ناحية الأخرى لو كان ال F and G are linearly
+
+666
+01:18:56,380 --> 01:19:01,700
+dependent يبقى الغروس كان عندهم بده ساوي zero لكل
+
+667
+01:19:01,700 --> 01:19:07,100
+ال T اللي موجودة وين اللي موجودة في ال I يبقى
+
+668
+01:19:07,100 --> 01:19:11,640
+واضحة ظن بدي ألخص كلام اللي قلناها ده أو نص
+
+669
+01:19:11,640 --> 01:19:16,210
+النظرية وشوف تلخيصي صح ولا غلطميعطيني ال two
+
+670
+01:19:16,210 --> 01:19:19,170
+functions وقال لي شوف للتان تانى وقال linearly
+
+671
+01:19:19,170 --> 01:19:23,650
+dependent و الله linearly independent بقوله والله
+
+672
+01:19:23,650 --> 01:19:28,630
+كويس باخد هال worn skin تبع التنتين عنده نقطة
+
+673
+01:19:28,630 --> 01:19:32,690
+والله إذا ال worn skin لا يساوي zero يبقى linearly
+
+674
+01:19:32,690 --> 01:19:36,490
+independent وإذا ساوى zero يبقى linearly dependent
+
+675
+01:19:36,490 --> 01:19:39,990
+غلط؟
+
+676
+01:19:39,990 --> 01:19:44,050
+لا يا ناس غلط كلامي يعني يا ناس أنا مدرس كلامي
+
+677
+01:19:44,050 --> 01:19:50,150
+غلط؟طب هو الخطأ بعينيه نص غلط و نص صح طب تعالى
+
+678
+01:19:50,150 --> 01:19:54,790
+نشوف كيف نصه غلط و كيف نصه صح نمسك النص في الأول
+
+679
+01:19:54,790 --> 01:19:58,610
+هدول التنتين دوال قبل اشتغال ماعنده مشكلة على
+
+680
+01:19:58,610 --> 01:20:02,870
+الفترة اللى عندناها ده بحيث ال winners كان عنده
+
+681
+01:20:02,870 --> 01:20:07,550
+نقطة ماجلش على كل ال intervalلو جدرت تلاقي
+
+682
+01:20:07,550 --> 01:20:12,610
+الورسكين ولو نقطة واحدة ليس بالضرورة على كل الفتحة
+
+683
+01:20:12,610 --> 01:20:17,090
+ولو عندها نقطة واحدة لا يساوي zero اذا الورسكين
+
+684
+01:20:17,090 --> 01:20:21,570
+تبعهم اذا دول اثنين هدول يصيروا linearly
+
+685
+01:20:21,570 --> 01:20:26,850
+independent طيب ممتاز الشطرة التانية بقول on the
+
+686
+01:20:26,850 --> 01:20:32,100
+other hand يعني من ناحية اخرىلو كانت الـ two
+
+687
+01:20:32,100 --> 01:20:36,860
+functions linearly dependent يجب أن يكون الرونسكين
+
+688
+01:20:36,860 --> 01:20:42,040
+0 for all t الموجودة في ال interval إذا فارق
+
+689
+01:20:42,040 --> 01:20:45,840
+السماعة على الأرض مش زي ما قلت انا في الأول مظبوط
+
+690
+01:20:45,840 --> 01:20:50,520
+إذا كلامك في أول غلط يبقى إياك أن تخطي مثل هذا
+
+691
+01:20:50,520 --> 01:20:54,740
+الخطأ يبقى الصح اللي في حصلة دلتين هذول linearly
+
+692
+01:20:54,740 --> 01:20:58,120
+dependent ولا linearly independent بروح تاخد
+
+693
+01:20:58,120 --> 01:21:03,760
+الرونسكين عند نقطةلقيته لا يساوي 0 خلاص مضمون 100%
+
+694
+01:21:03,760 --> 01:21:09,280
+إذا اتنين دول linearly independent لكن لو كانوا
+
+695
+01:21:09,280 --> 01:21:14,240
+اتنين تانيين linearly dependent يجب أن يكون ال
+
+696
+01:21:14,240 --> 01:21:18,740
+role skin تبعهم يساوي 0 for all فيه بديش ابعد فيه
+
+697
+01:21:18,740 --> 01:21:23,140
+بدي أخد من اللي قدامكوا نمرا إيه إيش طلعت عندنا
+
+698
+01:21:23,140 --> 01:21:28,580
+هذه؟طلعت linearly dependent صح ولا لا؟ إذا بده
+
+699
+01:21:28,580 --> 01:21:31,040
+يروح أحسب ال role skin تبعها و يشوف قداش ماذا
+
+700
+01:21:31,040 --> 01:21:35,060
+يساوي هذا بيقول لو كانت كنتية linearly dependent
+
+701
+01:21:35,060 --> 01:21:39,040
+بده يكون ال role skin تبعها مضي ساوي قداش يساوي
+
+702
+01:21:39,040 --> 01:21:46,540
+zero يبقى example بداتي أقول from the above
+
+703
+01:21:46,540 --> 01:21:57,200
+example من المثال اللي فوقوبدي اخد part a من part
+
+704
+01:21:57,200 --> 01:22:01,420
+a مشيكنا a طلع هدول التانتين are linearly
+
+705
+01:22:01,420 --> 01:22:08,880
+dependent ال E أس تلاتة T and ال E أس تلاتة T ناخذ
+
+706
+01:22:08,880 --> 01:22:16,180
+تلاتة are linearly dependent linearly dependent
+
+707
+01:22:16,180 --> 01:22:18,760
+for all T
+
+708
+01:22:22,390 --> 01:22:28,030
+يبقى الرونسكين تبع اي أس تلاتة تي و اي أس تلاتة تي
+
+709
+01:22:28,030 --> 01:22:34,450
+ناقص تلاتة تلاتة تلاتة تلاتة تلاتة تلاتة تلاتة
+
+710
+01:22:34,620 --> 01:22:40,720
+و E أس ثلاثة T ناقص ثلاثة نشتق يا بناد يبقى ثلاثة
+
+711
+01:22:40,720 --> 01:22:47,760
+E أس ثلاثة T ونشتق هنا ثمان ثلاثة E أس ثلاثة T
+
+712
+01:22:47,760 --> 01:22:54,120
+ناقص ثلاثة صح ايه تشتفغي؟ مشتقة الأس كل اللي هو
+
+713
+01:22:54,120 --> 01:23:00,810
+قداشر ثلاثة فقط لا غيرطيب نفكر المحدد هذا بيصير
+
+714
+01:23:00,810 --> 01:23:11,470
+تلاتة E أُس ستة T ناقص تلاتة ناقص تلاتة E أُس ستة
+
+715
+01:23:11,470 --> 01:23:18,230
+T ناقص تلاتة يشوى قداش Zero مظبوط يبدو هي طبقنا
+
+716
+01:23:18,230 --> 01:23:23,510
+نمرة B تماما او النقطة الثانية من النظر يجليه
+
+717
+01:23:23,510 --> 01:23:27,580
+نظرها درهانإذا تنتهي هذه الـlinearly dependent
+
+718
+01:23:27,580 --> 01:23:36,580
+يفجرون إذا كنت تبحث عن عيوب يساوي 0 طيب and أحدنا
+
+719
+01:23:36,580 --> 01:23:42,010
+ذالتين الأثنين هذوللأ خدنا نمر بيه و يارا راح نمر
+
+720
+01:23:42,010 --> 01:23:46,490
+بيه هي نمر بيها هي الدالتين الأثنين هذول و أثبتنا
+
+721
+01:23:46,490 --> 01:23:51,430
+أن هذول الأثنين linearly independent هذا لأ بدي
+
+722
+01:23:51,430 --> 01:23:55,190
+أروح أجيب المحدد سبعهم إذا المحدد سبعهم قلع لا
+
+723
+01:23:55,190 --> 01:23:59,890
+يساوي zero لنفتدوا للنظرية يفتدتين يكونوا are
+
+724
+01:23:59,890 --> 01:24:06,230
+linearly independent يفتدت ياخد المحدد تبع الحل
+
+725
+01:24:06,230 --> 01:24:15,260
+الأول P والثاني-P-1-P
+
+726
+01:24:15,260 --> 01:24:22,200
+-1
+
+727
+01:24:22,200 --> 01:24:28,800
+-P-1-P-1-P-1
+
+728
+01:24:37,040 --> 01:24:45,960
+مدام لا يساوي 0 سا ات and ات سالف واحد are
+
+729
+01:24:45,960 --> 01:24:52,740
+linearly independent مش انتقطة واحدة وماسي على كل
+
+730
+01:24:52,740 --> 01:24:59,620
+ال interval all ال interval من 0 لغاية انت نقل ال
+
+731
+01:24:59,620 --> 01:25:04,120
+P أكبر من ال 0 يعني اي نقطة تيجي تقريبا تحطيها ده
+
+732
+01:25:04,120 --> 01:25:06,420
+يمكن ينقل اكتر من واحد بسبب ال
+
diff --git a/PL9fwy3NUQKwa8ZDfSFGn6H8xVFLzqmCZC/pb7CBRBKnwY_raw.srt b/PL9fwy3NUQKwa8ZDfSFGn6H8xVFLzqmCZC/pb7CBRBKnwY_raw.srt
new file mode 100644
index 0000000000000000000000000000000000000000..4c4bff34ea1e1e5c602e92167abcde7a7db9baa1
--- /dev/null
+++ b/PL9fwy3NUQKwa8ZDfSFGn6H8xVFLzqmCZC/pb7CBRBKnwY_raw.srt
@@ -0,0 +1,3008 @@
+1
+00:00:09,280 --> 00:00:15,060
+بسم الله الرحمن الرحيم الآن بدنا نكمل ما ابتدأنا
+
+2
+00:00:15,060 --> 00:00:19,280
+به section المرة الماضية اللى هو section تلاتة
+
+3
+00:00:19,280 --> 00:00:24,060
+اتنين طبعا هذا section فى أكبر section مليان
+
+4
+00:00:24,060 --> 00:00:29,620
+نظريات فى كل ال sections المقررةأخذنا بعض النظريات
+
+5
+00:00:29,620 --> 00:00:33,040
+المرة الماضية وكان اخر حاجة خدنا تعريف ال
+
+6
+00:00:33,040 --> 00:00:37,760
+warenskin او الرونسكن اللى بقى نحط الحل الاول و
+
+7
+00:00:37,760 --> 00:00:40,980
+الحل التانى و مشتقت الاول و مشتقت التانى كمحدد
+
+8
+00:00:40,980 --> 00:00:45,680
+ثنائي و نجيب قيمة المحدد هذا حاصل ضرب عناصر القطر
+
+9
+00:00:45,680 --> 00:00:52,240
+الرئيسى ناقص حاصل ضرب عناصر القطر الثانى نجي
+
+10
+00:00:52,240 --> 00:00:57,010
+لنظرية اللى عندنا اليوميقول لو كان Y1 وY2 هما
+
+11
+00:00:57,010 --> 00:01:01,090
+عبارة عن two solutions لل differential equation
+
+12
+00:01:01,090 --> 00:01:03,950
+اللي قدامنا اللي هو homogeneous second order
+
+13
+00:01:03,950 --> 00:01:08,870
+differential equationوإذا قدرنا نجد النقطة الـ T
+
+14
+00:01:08,870 --> 00:01:13,150
+node بحيث الـ one on skin تبع الحلين تبع المعادلات
+
+15
+00:01:13,150 --> 00:01:19,730
+التفاضلية عندهم لا يساوي zero إن حدث ذلك يبقى the
+
+16
+00:01:19,730 --> 00:01:24,350
+family of solutions مجموعة الحلول اللي على الشكل
+
+17
+00:01:24,350 --> 00:01:31,030
+C1Y1 زي C2Y2C1 وC2 are arbitrary constants يبقى
+
+18
+00:01:31,030 --> 00:01:37,630
+ثوابت اختيارية انكليودز هذا الحل بيجتمل على كل
+
+19
+00:01:37,630 --> 00:01:43,030
+حلمين للمعادلة التفاضلية طبعا يا بنات هذا الان
+
+20
+00:01:43,030 --> 00:01:47,130
+اللي الكلام اللي نقوله بيربط section 32 مع section
+
+21
+00:01:47,130 --> 00:01:52,080
+31أحنا في تلاتة واحد كنا بندور على fundamental set
+
+22
+00:01:52,080 --> 00:01:55,780
+of solutions ولا ورنسكين ولا حاجة عندنا معادلة
+
+23
+00:01:55,780 --> 00:01:59,860
+بحلها بجيب حالين بدربت كنصا في الأول كنصا في
+
+24
+00:01:59,860 --> 00:02:04,760
+التاني بقول هذا هو ال general solution الان احنا
+
+25
+00:02:04,760 --> 00:02:09,420
+بدنا نقول وقداش فعلا الحل او ال general solution
+
+26
+00:02:09,420 --> 00:02:14,020
+exist بنقول لما ال ورنسكين عند نقطة ما بده يساوي
+
+27
+00:02:14,020 --> 00:02:19,690
+قداش لا يساوي zeroمرة تانية بقول ان عندي معادلة
+
+28
+00:02:19,690 --> 00:02:25,950
+تفاضلية إلها حلين الوانوس كنتبع الحلية عند نقطة ما
+
+29
+00:02:25,950 --> 00:02:33,310
+النقطة هذه موجودة في الفترة اللي الدالة P و الدالة
+
+30
+00:02:33,310 --> 00:02:39,350
+Q continuous عليها إن حدث ذلكيبقى مجموعة الحلولات
+
+31
+00:02:39,350 --> 00:02:46,610
+بتشتمل على أي حل آخر منهم للمعادلة طب احنا العنوان
+
+32
+00:02:46,610 --> 00:02:49,650
+اللي احنا رافعينه لهذا section fundamental set of
+
+33
+00:02:49,650 --> 00:02:53,770
+solutions المرة اللي كاتت مااتكلمناش ولا كلمة على
+
+34
+00:02:53,770 --> 00:02:56,250
+ال fundamental set of solutions كنا بيجينا ناخد
+
+35
+00:02:56,250 --> 00:03:00,790
+نظرياتلكن طلع هنا بيقول إيش؟ إذا ضامنت إن ال words
+
+36
+00:03:00,790 --> 00:03:05,650
+كان عندها نقطة لا يساوي zero يبقى هذا بيشتمل على
+
+37
+00:03:05,650 --> 00:03:11,530
+أي حل آخر لمام للمعادلة التفاضلية الملاحظة بتقول
+
+38
+00:03:11,530 --> 00:03:15,770
+إذا ال words كان هذا لا يساوي zero يبقى الحالين
+
+39
+00:03:15,770 --> 00:03:21,700
+الإتنين دول بيكونولي مجموعة الحلول الأساسيةالعنوان
+
+40
+00:03:21,700 --> 00:03:24,540
+اللى احنا كنا رافعينه ل section تلاتة اتنين المرة
+
+41
+00:03:24,540 --> 00:03:28,020
+الماضية مجموعة الحلول الأساسية لل differential
+
+42
+00:03:28,020 --> 00:03:32,540
+equation one و اللى كنا سابقا من سميه ال general
+
+43
+00:03:32,540 --> 00:03:36,540
+solution يبقى ال general solution للمعادلة
+
+44
+00:03:36,540 --> 00:03:40,950
+التفابليةأو الـ Fundamental Set of Solutions
+
+45
+00:03:40,950 --> 00:03:45,650
+للمعادلة التفاضلية مجموعة الحلول الأساسية اتنين
+
+46
+00:03:45,650 --> 00:03:51,950
+نفس المعنى هذه الصيغة تشتمل على أي حل أخر للمعادلة
+
+47
+00:03:51,950 --> 00:03:58,570
+التفاضلية الخطية من الرتبة الثانية يبقى هذه الصيغة
+
+48
+00:03:58,570 --> 00:04:02,710
+constant في الحل الأول زي constant ثاني في الحل
+
+49
+00:04:02,710 --> 00:04:09,480
+الثاني تمام؟أحنا ما جيبناش ديب لكن أصلنا للحلول
+
+50
+00:04:09,480 --> 00:04:14,600
+القديمة بحيث نضمن موجود ولا نعم موجود وقت إذا
+
+51
+00:04:14,600 --> 00:04:18,500
+الورونسكين عنده نقطة داخل ال interval المعرض عليها
+
+52
+00:04:18,500 --> 00:04:22,200
+ال coefficients بدي يكون الورونسكين هذا معله لا
+
+53
+00:04:22,200 --> 00:04:28,220
+يساوي zero نعطي مثال طبعا تقول اتأكدلي ان هدول حلل
+
+54
+00:04:28,220 --> 00:04:33,470
+المعادلة استفادوا من الجهة دي طيب اتأكدنابقول لي
+
+55
+00:04:33,470 --> 00:04:37,010
+ومن ثم دين show that بيبينلي ان اتنين هذول
+
+56
+00:04:37,010 --> 00:04:41,030
+بيكونولي ال fundamental set of solutions اتجاه
+
+57
+00:04:41,030 --> 00:04:44,290
+المفهوم التاني يعني ايه تبدي اعمل؟ بدي اجيب
+
+58
+00:04:44,290 --> 00:04:48,950
+الرونسكين هذا هو اثبت انه ماله؟ لا يساوي ذلك، ان
+
+59
+00:04:48,950 --> 00:04:52,050
+حدث ذلك اتجاه جولي بيكونولي مجموعة الحلول الاساسية
+
+60
+00:04:52,050 --> 00:04:56,710
+وبالتاليبديقول شكل ال general solution للمعادلة
+
+61
+00:04:56,710 --> 00:05:00,750
+التفاضلية وقال لي هو مثلا اكتب شكل ال general
+
+62
+00:05:00,750 --> 00:05:04,030
+solution طبعا شكل ال general solution يكون على
+
+63
+00:05:04,030 --> 00:05:08,510
+الشكل اللي عندنا هذا إذا خلّيني نمشي خطوة وخطوة
+
+64
+00:05:08,510 --> 00:05:13,070
+جالي يبينلي ان هدول حلل المعادلة التفاضلية مش
+
+65
+00:05:13,070 --> 00:05:17,770
+هينكون الحللة اللي حصلت المعادلة التفاضلية يبقى
+
+66
+00:05:17,770 --> 00:05:25,630
+انا عند Y واحديستوي قدر T ثانفية لو اشتغلت على Y
+
+67
+00:05:25,630 --> 00:05:31,390
+واحد إسرائيل يستوي قدر T كمان مرضى Y واحد وقفل
+
+68
+00:05:31,390 --> 00:05:35,910
+إسرائيل يستوي قدر يستوي اتنين، بداك يعوض في
+
+69
+00:05:35,910 --> 00:05:40,150
+المعادلة يستوي كدر T ثانفية و Y واحد مضابق
+
+70
+00:05:40,150 --> 00:05:41,030
+لإسرائيل
+
+71
+00:05:43,860 --> 00:05:50,020
+إذا طلع هذا الكلام يساوي 0 فهذا يكون حل مين
+
+72
+00:05:50,020 --> 00:05:52,100
+للمعادلة التفاضلية
+
+73
+00:06:02,130 --> 00:06:09,150
+اللي هو تيتربيا يبقى تيتربيا تقصد من تيتربيا وزي
+
+74
+00:06:09,150 --> 00:06:16,310
+ساوي زيرو هنا قد عليها why one زي ساوي تيتربيا is
+
+75
+00:06:16,310 --> 00:06:27,810
+a solution of the differential equation للمعادلة
+
+76
+00:06:27,810 --> 00:06:34,100
+تفاضليةالينين في تاريخ يعني وايد قدري للترايخ،
+
+77
+00:06:34,100 --> 00:06:39,090
+خاطر من الينين وايد بيشاوى الاند بيشاوى الاندالان
+
+78
+00:06:39,090 --> 00:06:47,610
+similarly بنفس الطريقة اللي هو Y2 يستوي T أصنافة
+
+79
+00:06:47,610 --> 00:07:03,370
+واحد تمام؟ لأن اشتقوا مرة Y2 يستوي T أصنافة
+
+80
+00:07:03,370 --> 00:07:11,580
+ثالثالان بالنسبة للمعادلة التفاظلية يتر بيها Y2 من
+
+81
+00:07:11,580 --> 00:07:14,960
+بعض الأفراد مقصد 62 Y2
+
+82
+00:07:18,920 --> 00:07:36,780
+يتجارى تساوي T تربيه Y2WI يتجارى
+
+83
+00:07:36,780 --> 00:07:42,080
+T تربيه
+
+84
+00:07:42,080 --> 00:07:50,640
+Y2WI يتجارى T تربيه Y2WI يتجارىيستوي 0 يمكن أن
+
+85
+00:07:50,640 --> 00:07:58,400
+يكون Y يستوي 1 يستوي 1 يستوي 3 يستوي 3 يستوي 3
+
+86
+00:07:58,400 --> 00:08:06,000
+يستوي 3 يستوي 3 يستوي 3 يستوي 3 يستوي 3 يستوي 3
+
+87
+00:08:06,000 --> 00:08:14,900
+يستوي 3 يستوي 3 يستوي 3 يستوي 3 يستوي 3 يستوي 3
+
+88
+00:08:14,900 --> 00:08:14,920
+يستوي 3 يستوي 3 يستوي 3 يستوي 3 يستوي 3 يستوي 3
+
+89
+00:08:14,920 --> 00:08:14,920
+يستوي 3 يستوي 3 يستوي 3 يستوي 3 يستوي 3 يستوي 3
+
+90
+00:08:14,920 --> 00:08:14,920
+يستوي 3 يستوي 3 يستوي 3 يستوي 3 يستوي 3 يستوي 3
+
+91
+00:08:14,920 --> 00:08:14,940
+يستوي 3 يستوي 3 يستوي 3 يستوي 3 يستوي 3 يستوي 3
+
+92
+00:08:14,940 --> 00:08:15,000
+يستوي 3 يستوي 3 يستوي 3 يستوي 3 يستوي 3 يستوي 3
+
+93
+00:08:15,000 --> 00:08:15,180
+يستوي 3 يستوي 3 يستوي 3 يستوي 3 يستوي 3 يستوي 3
+
+94
+00:08:15,180 --> 00:08:19,530
+يستده اللي بييضى ان الاثنين هدول بيكونون المجوه
+
+95
+00:08:19,530 --> 00:08:24,690
+للحلول الأساسية مصطلح القضايا ان ال womanist تبعهم
+
+96
+00:08:24,690 --> 00:08:28,570
+عن طرقهم عن طرقهم عن طرقهم عن طرقهم عن طرقهم عن
+
+97
+00:08:28,570 --> 00:08:28,590
+طرقهم عن طرقهم عن طرقهم عن طرقهم عن طرقهم عن طرقهم
+
+98
+00:08:28,590 --> 00:08:28,730
+عن طرقهم عن طرقهم عن طرقهم عن طرقهم عن طرقهم عن
+
+99
+00:08:28,730 --> 00:08:29,450
+طرقهم عن طرقهم عن طرقهم عن طرقهم عن طرقهم عن طرقهم
+
+100
+00:08:29,450 --> 00:08:30,130
+عن طرقهم عن طرقهم عن طرقهم عن طرقهم عن طرقهم عن
+
+101
+00:08:30,130 --> 00:08:34,010
+طرقهم عن طرقهم عن طرقهم عن طرقهم عن طرقهم عن طرقهم
+
+102
+00:08:34,010 --> 00:08:42,430
+عن طرقهم عن طر
+
+103
+00:08:43,860 --> 00:08:50,240
+الحل الأول اللي عندنا همين P ثانية و الحل التاني P
+
+104
+00:08:50,240 --> 00:08:58,700
+أصناع الواحد نجتا نجتا اتنين P سالف P و سالف اتنين
+
+105
+00:09:06,560 --> 00:09:12,780
+يعني دلوقت نفس البرنامج كان نميذة P solution P
+
+106
+00:09:12,780 --> 00:09:17,380
+ثلاثية و تلاتية و ثالث واحد نجدت أن المتحدث
+
+107
+00:09:17,380 --> 00:09:21,380
+الإسرائيل حصل الحاجات عن كل الموضوع تقفل فيه هنا
+
+108
+00:09:21,380 --> 00:09:27,820
+بضرورة إن أن المتحدث حاصل ضرب على نفسه كرهيزي حاصل
+
+109
+00:09:27,820 --> 00:09:31,880
+ضرب على نفسه كرهيزي حاصل ضرب على نفسه كرهيزي
+
+110
+00:09:31,880 --> 00:09:33,020
+كرهيزي واحد
+
+111
+00:10:00,640 --> 00:10:02,040
+عاصفة ضرب عاصفة ضرب عاصفة ضرب عاصفة ضرب عاصفة ضرب
+
+112
+00:10:02,040 --> 00:10:11,080
+عاصفةهذا الرقم غير الصفر إذا ما يمكن أن
+
+113
+00:10:11,080 --> 00:10:15,900
+يكون مرضى المطمئنع زي تطلع نقص تلاتة D مثلا يمكن
+
+114
+00:10:15,900 --> 00:10:20,380
+تطلع نقص تلاتة على D تلميح يفش يطلع بD أخر وعلى ال
+
+115
+00:10:20,380 --> 00:10:22,760
+interval تحت الشررين عليه
+
+116
+00:10:26,530 --> 00:10:44,590
+طيب، مدام لا يساوجل و يفكر اتنين هذول بتقنوني ماهي
+
+117
+00:10:57,720 --> 00:11:05,660
+solutions of the given differential equation
+
+118
+00:11:05,660 --> 00:11:13,100
+differential equation جالي مدام الـ October ال
+
+119
+00:11:13,100 --> 00:11:16,540
+general solution لل differential equation جدا
+
+120
+00:11:16,540 --> 00:11:25,100
+العليه بروح بكله ال general solution is
+
+121
+00:11:26,240 --> 00:11:40,020
+Y تسوى C1Y1 زي C2Y2 تسوى C1T2 زي C2T و سالب واحد
+
+122
+00:11:40,020 --> 00:11:46,200
+ينقل هذا الجدران صيوزي للعاملة التفاغنية المعطاة
+
+123
+00:12:07,110 --> 00:12:10,650
+الشباب أساسي اللي لازم يقولوا اسم هذا معناه
+
+124
+00:12:23,890 --> 00:12:28,200
+اللي بتقوله لو كان الرئيس انصار سفير يبقى ..هم
+
+125
+00:12:28,200 --> 00:12:31,240
+احنا مش ضامنين هل هم فنضامن ال solution ولا مش هم
+
+126
+00:12:31,240 --> 00:12:36,000
+بيطلعوا حالين بس بضمانش انهم يجيبولي شكل حل العالم
+
+127
+00:12:36,000 --> 00:12:40,080
+طبعا اعطيكوا بعض أبطالين يتعاملوا مع بعضهم وعالم
+
+128
+00:12:40,080 --> 00:12:42,840
+كله مش عارف انهم يتعاملوا مع بعضهم اه تتعاملوا مع
+
+129
+00:12:42,840 --> 00:12:43,220
+بعضهم
+
+130
+00:12:56,420 --> 00:13:01,100
+التسهيل اللي بتطبخوه يا بناتي لان اكتبه على الشكل
+
+131
+00:13:01,100 --> 00:13:06,540
+التالي اكتبه
+
+132
+00:13:06,540 --> 00:13:15,120
+على الشكل التالي مفهوم اذا sometimes احيانا
+
+133
+00:13:15,120 --> 00:13:24,060
+sometimes it is difficult for five it is difficult
+
+134
+00:13:56,810 --> 00:14:09,780
+Y1-Y2of the differential equation المعادلة
+
+135
+00:14:09,780 --> 00:14:18,440
+التفارقية L of Y بيستوي Y بقية I زائد P of Y بقية
+
+136
+00:14:18,440 --> 00:14:26,200
+I زائد Q of Y بيستوي Zero اللي هي بقية ساقين
+
+137
+00:14:26,200 --> 00:14:28,480
+المعادلة أقل واحد
+
+138
+00:14:30,870 --> 00:14:37,890
+لذلك if he ask فروح نسأل السؤال in turn without an
+
+139
+00:14:37,890 --> 00:14:44,090
+essential equation without that differential
+
+140
+00:14:44,090 --> 00:14:57,310
+equation one always always has a fundamental
+
+141
+00:15:03,770 --> 00:15:13,290
+هي افضل انت ستة solutions لأي
+
+142
+00:15:13,290 --> 00:15:23,670
+علامة ستة؟ بأسه لازم أكون متأكد عنها لأن ستة is
+
+143
+00:15:23,670 --> 00:15:26,690
+the following
+
+144
+00:15:33,290 --> 00:15:36,930
+طبعا هي بيقول ما .. ما يرام
+
+145
+00:15:50,970 --> 00:16:00,670
+هذا البرادر الصحي هو ال N of Y Y double F I U exp
+
+146
+00:16:00,670 --> 00:16:07,130
+Y I U exp Y is equal to 0 وخلّى البرادر اللي هو
+
+147
+00:16:07,130 --> 00:16:08,910
+أخير واحد
+
+148
+00:16:13,250 --> 00:16:22,610
+and make you a continuous functions of continuous
+
+149
+00:16:22,610 --> 00:16:30,850
+functions that one could consider on some open
+
+150
+00:16:30,850 --> 00:16:40,570
+interval on some open interval R
+
+151
+00:16:49,380 --> 00:17:02,020
+والثاني هو some plus some point in the interval R
+
+152
+00:17:07,320 --> 00:17:13,800
+FYI الوضع أكتر
+
+153
+00:17:13,800 --> 00:17:24,540
+في الوضع الوضع أكتر في الوضع الوضع الوضع الوضع
+
+154
+00:17:24,540 --> 00:17:26,360
+الوضع الوضع الوضع الوضع الوضع الوضع الوضع الوضع
+
+155
+00:17:26,360 --> 00:17:26,660
+الوضع الوضع الوضع الوضع الوضع الوضع الوضع الوضع
+
+156
+00:17:26,660 --> 00:17:26,900
+الوضع الوضع الوضع الوضع الوضع الوضع الوضع الوضع
+
+157
+00:17:26,900 --> 00:17:26,900
+الوضع الوضع الوضع الوضع الوضع الوضع الوضع الوضع
+
+158
+00:17:26,900 --> 00:17:26,900
+الوضع الوضع الوضع الوضع الوضع الوضع الوضع الوضع
+
+159
+00:17:26,900 --> 00:17:29,240
+الوضع الوضع الوضع الوضع الوضع الوض
+
+160
+00:17:34,220 --> 00:17:45,320
+هو اي واحد و اتنين يساوي واحد و اتنين يساوي
+
+161
+00:17:45,320 --> 00:17:53,160
+واحد و اتنين يساوي واحد و اتنين يساوي واحد و اتنين
+
+162
+00:17:53,160 --> 00:17:56,640
+يساوي واحد و اتنين يساوي واحد و اتنين يساوي واحد
+
+163
+00:18:00,890 --> 00:18:09,070
+مش عارف why واحد ال .. why اللي .. اللي مابتعش في
+
+164
+00:18:09,070 --> 00:18:14,090
+الواقع انا
+
+165
+00:18:14,090 --> 00:18:20,390
+مابتعش في الواقع انا مابتعش في الواقع انا
+
+166
+00:18:20,390 --> 00:18:22,550
+مابتعش في الواقع
+
+167
+00:18:32,010 --> 00:18:34,890
+ده .. ده .. ده .. ده ..
+
+168
+00:19:24,740 --> 00:19:26,140
+مش عارف كده
+
+169
+00:19:51,720 --> 00:19:57,580
+ليه احترام لحن كبير؟ او بعض السنة ولو .. او لو نصف
+
+170
+00:19:57,580 --> 00:20:02,680
+سنة ماسباش زي .. ساوة زي .. ماشي بتحصل؟ هنا ك ..
+
+171
+00:20:02,680 --> 00:20:06,980
+هنا صرفات أحيان it is difficult to find an
+
+172
+00:20:06,980 --> 00:20:10,680
+underlying conceptual solution يعني أحيان نصار
+
+173
+00:20:10,680 --> 00:20:15,260
+اتالوجي مجموعة التفكير الأساسي على صورة واحد وواحد
+
+174
+00:20:15,260 --> 00:20:21,860
+وإثنان وخمسين وخمسين إلا عندناSometimes the
+
+175
+00:20:21,860 --> 00:20:24,500
+definition of a fundamental system solution هو
+
+176
+00:20:24,500 --> 00:20:28,120
+واحد هو كامل وعالى وطبعا ويبقى كامل عندنا ويبقى
+
+177
+00:20:28,120 --> 00:20:31,740
+كامل على الشكل اللي عندنا فانت ده صح كامل يا عزيزي
+
+178
+00:20:31,740 --> 00:20:36,460
+ويقولك اه we ask you ده فكيف ال definition of
+
+179
+00:20:36,460 --> 00:20:40,580
+solution هو واحد تبقى كامل لها دائما وابدا انها
+
+180
+00:20:40,580 --> 00:20:48,370
+fundamental set of solutionالنظرية التالية اتمنى
+
+181
+00:20:48,370 --> 00:20:53,610
+بفعلا ان هذا يكون مجموع حلول اساسية او بمعنى اخر
+
+182
+00:20:53,610 --> 00:20:58,830
+القرار الاسكين تبعها يكون نايم او نايم ساوي زيرو
+
+183
+00:20:58,830 --> 00:21:02,530
+مافيش بتقوله نظرية نظرية يقولها معنى التحولية
+
+184
+00:21:02,530 --> 00:21:03,050
+تبعها
+
+185
+00:21:23,340 --> 00:21:24,740
+Y1Y2Y3Y4Y5Y6Y7Y8Y9Y10Y11Y12Y12Y13Y12Y13Y14Y14Y15Y15Y15Y15Y15Y15Y15Y15Y15Y15Y15Y15Y15Y15Y15Y15Y15Y15Y15Y15Y15Y15Y15Y15Y15Y15Y15Y15Y15Y15Y15Y15Y15Y15Y15Y15Y15Y15Y15Y15Y15Y15Y15Y15Y15Y15Y15Y15Y15Y15Y15Y15Y15Y15Y15Y15Y15Y15Y15Y15Y15Y15Y15Y15Y15Y15Y15Y15Y15Y15Y15Y15Y15Y15Y15Y15Y15Y15Y15Y15Y15Y15Y15Y15Y15Y15Y15Y15Y15Y15Y15Y15Y15Y15
+
+186
+00:21:24,780 --> 00:21:27,400
+أتنين بيقولوا جنة رسول صلى الله عليه وسلم او قرن
+
+187
+00:21:27,400 --> 00:21:32,920
+مثلا حالتين ما هيحالتين فمسكنا حالتين ادنان بحيث
+
+188
+00:21:32,920 --> 00:21:37,540
+الحال الأول عند النقطة اللي احد تلاتين ادنان كان
+
+189
+00:21:37,540 --> 00:21:43,100
+واحد صحيح ومش تبت نزيل و الحال التالت نزيل وعند
+
+190
+00:21:43,100 --> 00:21:49,060
+النقطة عادي ومش تبت واحد ان حد تلالك نسبة هدول
+
+191
+00:21:49,060 --> 00:21:51,280
+بيقمنوا لووجود القرن مثلا
+
+192
+00:21:54,700 --> 00:21:59,440
+السؤال هو مافنعش هدول تعملولي الشرط ان انا كنت
+
+193
+00:21:59,440 --> 00:22:04,460
+احفظهم هدول؟ مافنعش هدول يمجولي قبل ما نرسل او
+
+194
+00:22:04,460 --> 00:22:09,240
+صلوا ليه؟ و لو كان اليوم مصرفة جدا، يا عادي هدول
+
+195
+00:22:09,240 --> 00:22:15,580
+شو بيعملولي؟ يا جماد بيقولوا لا تاني و لا اخر،
+
+196
+00:22:15,580 --> 00:22:20,900
+اللي مرضى هي tell the truth، صحيح ليه؟
+
+197
+00:22:24,560 --> 00:22:33,080
+تبع الحل الأول والحل التالتالمش مضيعونين، مضيعين،
+
+198
+00:22:33,080 --> 00:22:39,760
+قيمة ال Y واحد عند الكيلون، قيمة ال Y واحد يترين
+
+199
+00:22:39,760 --> 00:22:48,760
+عند الكيلون، قيمة اكبر Y ثمانية، Y ثمانية عند
+
+200
+00:22:48,760 --> 00:22:56,310
+الكيلون، هنا Y واحد يترين عند الكيلونwhy اتنين و
+
+201
+00:22:56,310 --> 00:23:02,830
+اتنين و اتنين و اتنين و اتنين
+
+202
+00:23:02,830 --> 00:23:06,310
+و اتنين و اتنين و اتنين و اتنين و اتنين و اتنين و
+
+203
+00:23:06,310 --> 00:23:07,150
+اتنين و اتنين و اتنين و اتنين و اتنين و اتنين و
+
+204
+00:23:07,150 --> 00:23:08,150
+اتنين و اتنين و اتنين و اتنين و اتنين و اتنين و
+
+205
+00:23:08,150 --> 00:23:08,390
+اتنين و اتنين و اتنين و اتنين و اتنين و اتنين و
+
+206
+00:23:08,390 --> 00:23:09,550
+اتنين و اتنين و اتنين و اتنين و اتنين و اتنين و
+
+207
+00:23:09,550 --> 00:23:10,110
+اتنين و اتنين و اتنين و اتنين و اتنين و اتنين و
+
+208
+00:23:10,110 --> 00:23:20,610
+اتنين و اتنين و اتنين و
+
+209
+00:23:20,610 --> 00:23:25,490
+اتنهأقمنك أنه فعلا هذا الكلب اتنقل من 0 إلى 0 يعني
+
+210
+00:23:25,490 --> 00:23:28,530
+انا طالع على وسط الناس من 0 ومن تاني من 2 هذا
+
+211
+00:23:28,530 --> 00:23:33,450
+الكلب هو يامان fundamental sense of solution تعلم
+
+212
+00:23:33,450 --> 00:23:38,950
+الكلب يتنقل من أي كويس لإنه المسألة بيشتغل بصحته
+
+213
+00:23:38,950 --> 00:23:48,070
+غيره حاجة إذا قلت انه سؤال واحد واشري من الكتاب
+
+214
+00:23:48,070 --> 00:23:49,810
+ونقل
+
+215
+00:24:09,770 --> 00:24:11,170
+3C5
+
+216
+00:24:15,660 --> 00:24:25,060
+specified by the last term by the last term of f
+
+217
+00:24:25,060 --> 00:24:36,320
+المغربية السابقة for the situation المعادلة
+
+218
+00:24:36,320 --> 00:24:42,120
+التقاريرية why not unified say why fine
+
+219
+00:25:01,560 --> 00:25:05,200
+السؤال الأهم في تجارب الشبكة بدأت بمشير مباشر
+
+220
+00:25:05,200 --> 00:25:10,300
+عالمين عالم نظرية لغوية بيكون مجلد فعلي بقى تبسيط
+
+221
+00:25:10,300 --> 00:25:16,950
+فوق Solutionspecify يعني اللي ضارنتك من النظرية
+
+222
+00:25:16,950 --> 00:25:20,630
+اللي عندك هذه المعادلة يعني انت ممكن تكون ممكن
+
+223
+00:25:20,630 --> 00:25:22,090
+تكون ممكن تكون ممكن تكون ممكن تكون ممكن تكون ممكن
+
+224
+00:25:22,090 --> 00:25:22,130
+تكون ممكن تكون ممكن تكون ممكن تكون ممكن تكون ممكن
+
+225
+00:25:22,130 --> 00:25:22,690
+تكون ممكن تكون ممكن تكون ممكن تكون ممكن تكون ممكن
+
+226
+00:25:22,690 --> 00:25:22,970
+تكون ممكن تكون ممكن تكون ممكن تكون ممكن تكون ممكن
+
+227
+00:25:22,970 --> 00:25:23,230
+تكون ممكن تكون ممكن تكون ممكن تكون ممكن تكون ممكن
+
+228
+00:25:23,230 --> 00:25:23,810
+تكون ممكن تكون ممكن تكون ممكن تكون ممكن تكون ممكن
+
+229
+00:25:23,810 --> 00:25:24,050
+تكون ممكن تكون ممكن تكون ممكن تكون ممكن تكون ممكن
+
+230
+00:25:24,050 --> 00:25:24,050
+تكون ممكن تكون ممكن تكون ممكن تكون ممكن تكون ممكن
+
+231
+00:25:24,050 --> 00:25:27,430
+تكون ممكن تكون ممكن تكون ممكن تكون ممكن تكون ممكن
+
+232
+00:25:27,430 --> 00:25:32,340
+تكون ممكن تكون ممكن تعشان اجيب حالتين اطلع هذه
+
+233
+00:25:32,340 --> 00:25:37,740
+المعادلة بمعاملات مختلفة يعني تولدت تولدت واحد
+
+234
+00:25:37,740 --> 00:25:42,800
+صحيح و ثالث اتنين يعني كله اصلا إذا بناء العلماني
+
+235
+00:25:42,800 --> 00:25:53,020
+بقوله let Y تساوي T بساطة في S solution of the
+
+236
+00:25:53,020 --> 00:25:57,740
+differential equation
+
+237
+00:25:58,980 --> 00:26:08,320
+one then three characteristic equation زي section
+
+238
+00:26:08,320 --> 00:26:14,860
+تلاتة واحدة بدا yes اليومين r تركيب سائر r ناقص
+
+239
+00:26:14,860 --> 00:26:21,400
+اتنين يسوى zero لو جينا حللنا هذه المعادلة بصير
+
+240
+00:26:21,400 --> 00:26:24,380
+حصل يارد كورسين يسوى zero
+
+241
+00:26:47,020 --> 00:26:48,420
+Y1Y2Y3Y4Y5Y6Y7Y8Y9Y10Y11Y12Y13Y12Y13Y14Y14Y15Y15Y15Y15Y15Y15Y15Y15Y15Y15Y15Y15Y15Y15Y15Y15Y15Y15Y15Y15Y15Y15Y15Y15Y15Y15Y15Y15Y15Y15Y15Y15Y15Y15Y15Y15Y15Y15Y15Y15Y15Y15Y15Y15Y15Y15Y15Y15Y15Y15Y15Y15Y15Y15Y15Y15Y15Y15Y15Y15Y15Y15Y15Y15Y15Y15Y15Y15Y15Y15Y15Y15Y15Y15Y15Y15Y15Y15Y15Y15Y15Y15Y15Y15Y15Y15Y15Y15Y15Y15Y15Y15Y15Y15Y15
+
+242
+00:26:49,220 --> 00:26:58,900
+and why in the end you say إيه هو اسم أخصك ده؟طيب
+
+243
+00:26:58,900 --> 00:27:04,820
+إذا شوف هدول بيجيبولي general solution ولا لا
+
+244
+00:27:04,820 --> 00:27:09,040
+فبعدين بقولوا إذا أخد ال wallets can have a
+
+245
+00:27:09,040 --> 00:27:13,140
+function of T فالحل الأول يستيقظ
+
+246
+00:27:17,680 --> 00:27:30,740
+E-E-E-E-E-E-E-E-E-E-E-E-E-E-E-E-E-E-E-E-E-E-E-E-E
+
+247
+00:27:30,740 --> 00:27:40,160
+-E-E-E-E
+
+248
+00:27:40,160 --> 00:27:50,880
+-E-Eعمر هذه تساوي 0؟ لأ لأ لأ لأ لأ لأ لأ لأ لأ لأ
+
+249
+00:27:50,880 --> 00:27:50,920
+لأ لأ لأ لأ لأ لأ لأ لأ لأ لأ لأ لأ لأ لأ لأ لأ لأ
+
+250
+00:27:50,920 --> 00:27:54,460
+لأ لأ لأ لأ لأ لأ لأ لأ لأ لأ لأ لأ لأ لأ لأ لأ لأ
+
+251
+00:27:54,460 --> 00:27:55,420
+لأ لأ لأ لأ لأ لأ لأ لأ لأ لأ لأ لأ لأ لأ لأ لأ لأ
+
+252
+00:27:55,420 --> 00:27:56,000
+لأ لأ لأ لأ لأ لأ لأ لأ لأ لأ لأ لأ لأ لأ لأ لأ لأ
+
+253
+00:27:56,000 --> 00:27:57,440
+لأ لأ لأ لأ لأ لأ لأ لأ لأ لأ لأ لأ لأ لأ لأ لأ لأ
+
+254
+00:27:57,440 --> 00:28:08,780
+لأ لأ لأ لأ لأ لأ لأ لأ لأ لأ لأ
+
+255
+00:28:08,780 --> 00:28:10,080
+لأ ل
+
+256
+00:28:14,670 --> 00:28:25,550
+-84 هي fundamental set
+
+257
+00:28:25,550 --> 00:28:30,710
+of solutions
+
+258
+00:28:30,710 --> 00:28:41,610
+of the differential equation 1لأن هذول بكاملور هي
+
+259
+00:28:41,610 --> 00:28:48,130
+مجموعة قلول أساسية للمعادلة مين؟ للمعادلة واحدة،
+
+260
+00:28:48,130 --> 00:28:54,210
+مبتعدين ومبتعدين أخر مجموعة القلول الأساسية
+
+261
+00:28:54,210 --> 00:29:00,260
+للمعادلة هذهاللي بيطبق عليهم هي النظرية اللي
+
+262
+00:29:00,260 --> 00:29:05,060
+عندنا، طب تعالى نشوف هل النظرية اللي عندنا بيطبق
+
+263
+00:29:05,060 --> 00:29:08,680
+عليها هذا الكلب او لا، اذا بيطبقي فهذا هو الموضوع،
+
+264
+00:29:08,680 --> 00:29:13,840
+وما بيطبقش فيه، يبقى نتفكس فيه، فيه شغلة تانية،
+
+265
+00:29:13,840 --> 00:29:18,370
+ايه الشغلة التانية؟عشان نشوف دول و نشوف نشر متانى
+
+266
+00:29:18,370 --> 00:29:24,150
+و نكسر متانى، فنشوف كل الشروط الاربع هذه محققة و
+
+267
+00:29:24,150 --> 00:29:32,030
+مدادة، بمجرد ما نقوله، يبقى Y واحد عند اللقطة اللي
+
+268
+00:29:32,030 --> 00:29:36,390
+يحصل هذه، و اللقطة اللي يحصل هذه كم كيلو متساوم
+
+269
+00:29:36,390 --> 00:29:43,820
+جدا، Zeroيبقى بدالي اقول y واحد عند ال zero هاي y
+
+270
+00:29:43,820 --> 00:29:48,760
+واحد يبقى a on zero يساوي واحد اذا اتحققت ال
+
+271
+00:29:48,760 --> 00:29:56,220
+condition الاول ماشي الحاجة واحد ال y واحد اتقرع
+
+272
+00:29:56,220 --> 00:29:57,620
+ايه تدري ساوي
+
+273
+00:30:00,540 --> 00:30:08,940
+يبقى هذا بدل يعطيك M Y 1 D Prime M Zero تسوى واحد
+
+274
+00:30:08,940 --> 00:30:14,140
+يبقى ال condition التاني هذا اتحقق لأ ما اتحقق
+
+275
+00:30:14,140 --> 00:30:20,020
+لغاية حتى لو لم يبقى اتحقق و يبقى فاشل فاشل الحلول
+
+276
+00:30:20,020 --> 00:30:24,660
+جميعا من مجموعة الخلول التي بحقق اللغة اللي
+
+277
+00:30:24,660 --> 00:30:33,110
+عندناها طيب المرةلو جت اخد y2 عند الـ 0 اللي بدها
+
+278
+00:30:33,110 --> 00:30:39,270
+تسوي a أو الـ 0 طبعا اللي بدالي إذا الفشل ال
+
+279
+00:30:39,270 --> 00:30:46,010
+condition التاني هذا صاحب واحد وليس zero طيب و ال
+
+280
+00:30:46,010 --> 00:30:56,220
+y2 prime عند y2 prime بده يسويإنه ناقص اتنين فيه
+
+281
+00:30:56,220 --> 00:31:01,540
+قص ناقص اتنين هذا بيجيب عليك انه why اتنين يفرق
+
+282
+00:31:01,540 --> 00:31:06,020
+عند ال zero بيجيب عليك انه ناقص اتنين ناقص اتنين
+
+283
+00:31:06,020 --> 00:31:11,420
+يعني لا شرط هذا اتحقق و لا شرط هذا اتحقق و لا شرط
+
+284
+00:31:11,420 --> 00:31:17,300
+هذا اتطبق مش واحد يعني الشروط الأرب عملها ما حققتش
+
+285
+00:31:17,300 --> 00:31:26,130
+اتنين يبقى من هذا الاتنينهذا بالنسبالي يقولك ان ال
+
+286
+00:31:26,130 --> 00:31:39,050
+Y واحد وY اتنين are not satisfied with conditions
+
+287
+00:31:39,050 --> 00:31:44,350
+of
+
+288
+00:31:44,350 --> 00:31:46,870
+the theory
+
+289
+00:31:50,060 --> 00:31:55,680
+اللي بيقولون تحققوش لشروف المعبارية الله أشفننا يا
+
+290
+00:31:55,680 --> 00:32:02,340
+امالك يرزمتك ترزمت حالك
+
+291
+00:32:02,340 --> 00:32:17,180
+خدمة
+
+292
+00:32:17,180 --> 00:32:23,910
+كلمةفالحلال اللي احنا جيبناهم هادول صحيح تعملولي
+
+293
+00:32:23,910 --> 00:32:28,710
+فضل ما يكن سلوك السبعين النظرية لكن لحقكوش الانش
+
+294
+00:32:28,710 --> 00:32:33,890
+السلوك السبعين النظرية سلوك وشربط عليك لذلك حتة دي
+
+295
+00:32:33,890 --> 00:32:40,750
+specifiedلأ باربعين الأصغر لإن هدول اللي بحقوا
+
+296
+00:32:40,750 --> 00:32:44,870
+مشروع تبع النموية اللي عندنا هذه تقولوا ماشي طبعا
+
+297
+00:32:44,870 --> 00:32:50,650
+بدي أفضل ان عندي حلول بدلات الحلول هدول يعني هدول
+
+298
+00:32:50,650 --> 00:32:55,890
+الحلول مدني حلول مجموعة الحلول الكاسرسية إذا منهم
+
+299
+00:32:55,890 --> 00:33:01,950
+بدي أخلق شكل الحل اللي بحقك مان اللي بحقك النموية
+
+300
+00:33:01,950 --> 00:33:12,160
+اللي عندنا هذه فبجري أقوله هذاas long that ال Y
+
+301
+00:33:12,160 --> 00:33:20,680
+كلفة بيساوي C1 بيبقى مستيقظ زي C2 بيبقى مستيقظ
+
+302
+00:33:25,470 --> 00:33:34,610
+يجب أن أحفظ الـ y3 عند الـ 0 يجب أن أحفظ الـ y3
+
+303
+00:33:34,610 --> 00:33:37,130
+عند الـ 0 يجب أن أحفظ الـ y3 عند الـ 0 يجب أن أحفظ
+
+304
+00:33:37,130 --> 00:33:39,330
+الـ y3 عند الـ 0 يجب أن أحفظ الـ y3 عند الـ 0 يجب
+
+305
+00:33:39,330 --> 00:33:43,830
+أن أحفظ الـ y3
+
+306
+00:33:43,830 --> 00:33:46,870
+عند الـ 0 يجب أن أحفظ الـ y3 عند الـ 0 يجب أن أحفظ
+
+307
+00:33:46,870 --> 00:33:50,290
+الـ y3 عند الـ 0 يجب أن أحفظ الـ y3 عند الـ 0 يجب
+
+308
+00:33:50,290 --> 00:33:52,510
+أن أحفظ الـ y3 عند الـ 0 يجب أن أحفظ الـ y3 عند
+
+309
+00:33:52,510 --> 00:33:52,510
+الـ 0 يجب أن أحفظ الـ y3 عند الـ 0 يجب أن أحفظ الـ
+
+310
+00:33:52,510 --> 00:33:52,790
+y3 عند الـ 0 يجب أن أحفظ الـ y3 عند الـ 0
+
+311
+00:34:15,230 --> 00:34:19,830
+يجب ان انا
+
+312
+00:34:19,830 --> 00:34:27,740
+افرضعندي حالين سميت الأول Y3 والثاني Y4 وكل واحد
+
+313
+00:34:27,740 --> 00:34:33,980
+فيهم اعتمد على الحالين اللي قلع لهم هذول لإن هذول
+
+314
+00:34:33,980 --> 00:34:38,790
+قلعوا ليه ماني قلتلهم الانتسابيةبس مش هاجي مجموعة
+
+315
+00:34:38,790 --> 00:34:43,450
+الحلول اللي بتحقق شروط النظرية، روحت انا فرطني ان
+
+316
+00:34:43,450 --> 00:34:48,870
+عندي حلل تحقق شروط النظرية، اتخذت شروط النظرية و
+
+317
+00:34:48,870 --> 00:34:54,470
+قلت اروح ادور انتي عندي C1 و C2 و C3 و C4 ولا لا،
+
+318
+00:34:54,470 --> 00:34:59,730
+لان انا جيتهمبتخلص تمام 100% بيصير عندنا ضغوية
+
+319
+00:34:59,730 --> 00:35:04,690
+حققة تنقل لهم من هنا إلى الشمال بيقولوا كويس كده
+
+320
+00:35:04,690 --> 00:35:12,030
+بيقولوا واحد ينقل ال C1 و C2 و C3 و C4 بتمسك
+
+321
+00:35:12,030 --> 00:35:20,530
+الأولى اللي بتاخد Y3 عند Zero Yourself Y3 عند Zero
+
+322
+00:35:20,530 --> 00:35:30,980
+واحد ينقش بتعطيك هنا Y1بتساوي C1 زي C2 والبطء
+
+323
+00:35:30,980 --> 00:35:43,860
+تتاجر ل Y3' يبقى Y3' يبقى Y3'
+
+324
+00:35:43,860 --> 00:35:51,260
+يبقى Y3' يبقى Y3' يبقى Y3' يبقى Y3' يبقى Y3'بدي
+
+325
+00:35:51,260 --> 00:35:58,520
+اعطينا ان y تلاتة prime عند 0 y تلاتة prime عند 0
+
+326
+00:35:58,520 --> 00:36:09,920
+بيساوي 0 بيساوي C1 ناقص اتنين C2 تمام؟ يبقى اولا
+
+327
+00:36:09,920 --> 00:36:16,080
+صار عندنا معادلتين هدول معادلتين هنا وجه الطرف
+
+328
+00:36:16,080 --> 00:36:25,910
+تاني بتتنصرأتنين يساوي C واحد او اتنين C واحد زائد
+
+329
+00:36:25,910 --> 00:36:33,790
+اتنين C اتنين هذه زي ما هي Zero يساوي C واحد نقص
+
+330
+00:36:33,790 --> 00:36:40,010
+اتنين C اتنين اجمعها هلأ مع السلامة تصير تلاتة C
+
+331
+00:36:40,010 --> 00:36:45,210
+واحد تبقى يساوي اتنين تبقى C واحد تبقى ساوية درجة
+
+332
+00:36:45,210 --> 00:36:52,870
+طول الـT طيب تماملو الـ C1 ساوى طول 2 يبقى إيش
+
+333
+00:36:52,870 --> 00:36:59,490
+بسيط عنك إتنين C2 واتيها على الشكل التاني فتبقى
+
+334
+00:36:59,490 --> 00:37:04,450
+ساوية طول 2 أنا بدي أعطيك اللي بسيط إتنين فساوية
+
+335
+00:37:04,450 --> 00:37:12,670
+قدامك طول يبقى هنا Zero Y تلاتة ثم ساعة و الآن Y
+
+336
+00:37:12,670 --> 00:37:17,970
+تلاتة أول واحد Y تلاتة ثم فوق C1
+
+337
+00:37:32,650 --> 00:37:37,250
+يبقى هذا الحل اللي بيحقق ال two conditions اللي
+
+338
+00:37:37,250 --> 00:37:41,730
+اتنين هدول و Y تلاتة احدة زي رقم واحد و Y تلاتة و5
+
+339
+00:37:41,730 --> 00:37:42,970
+احدة زي رقم واحد وY تلاتة و5 احدة زي رقم واحد وY
+
+340
+00:37:42,970 --> 00:37:43,030
+تلاتة و5 احدة زي رقم واحد وY تلاتة و5 احدة زي رقم
+
+341
+00:37:43,030 --> 00:37:43,270
+واحد وY تلاتة و5 احدة زي رقم واحد وY تلاتة و5 احدة
+
+342
+00:37:43,270 --> 00:37:43,270
+زي رقم واحد وY تلاتة و5 احدة زي رقم واحد وY تلاتة
+
+343
+00:37:43,270 --> 00:37:43,850
+و5 احدة زي رقم واحد وY تلاتة و5 احدة زي رقم واحد
+
+344
+00:37:43,850 --> 00:37:45,100
+وY تلاتة و5 احدة زي رقم واحد وYأيه اللي عملنا ال
+
+345
+00:37:45,100 --> 00:37:51,820
+Y3 بنروح نعمله لمان؟ Y4 لجمالي بيقولوا احنا عندنا
+
+346
+00:37:51,820 --> 00:38:01,380
+Y4 تساوي C3 E أُس D زائد C4 E أُس ناقص اتنين D
+
+347
+00:38:01,380 --> 00:38:11,080
+لجمالي انا عليه ال Dragon و ال Y4 Prime بالمرة
+
+348
+00:38:11,610 --> 00:38:19,210
+بتساوي c تلاتة minus t نقص اتنين c اربعة minus
+
+349
+00:38:19,210 --> 00:38:29,270
+اتنين d الامر بيكون y اربعة عند zero بتزاوية
+
+350
+00:38:29,270 --> 00:38:37,070
+بتساوي c تلاتة زائد c اربعة حسب ال condition اللي
+
+351
+00:38:37,070 --> 00:38:42,700
+عيبنا هذا بتساوي اكتران بتساوي zeroالان بالشكل
+
+352
+00:38:42,700 --> 00:38:48,680
+اللى y prime اربعة اند زيرو ل سبع ايه y prime
+
+353
+00:38:48,680 --> 00:38:56,180
+اربعة اند زيرو انها تعطينا c تلاتة ناقص اتنين c
+
+354
+00:38:56,180 --> 00:39:04,580
+اربعة بده يسوى ال condition كده واحد صحيح ايه؟
+
+355
+00:39:04,580 --> 00:39:09,830
+بدنا ندى لو دينا ضربنا في اتنينيبقى لو ضربنا في
+
+356
+00:39:09,830 --> 00:39:14,130
+اتنين المعادلة الأولى بصير اتنين C ثلاثة زائد
+
+357
+00:39:14,130 --> 00:39:19,090
+اتنين C أربعة يساوي Zero وهذه بدي اخليها زي ما هي
+
+358
+00:39:19,090 --> 00:39:26,690
+C ثلاثة ناقص اتنين C أربعة يساوي جدار واحد اكبر
+
+359
+00:39:26,690 --> 00:39:32,910
+بروح هذا يبقى ثلاثة C ثلاثة يساوي واحد يبقى C
+
+360
+00:39:32,910 --> 00:39:40,930
+ثلاثة يساوي جدار تلتلما C3 يتساوى بالطول C4 يتساوى
+
+361
+00:39:40,930 --> 00:40:00,870
+بالطول C4 يتساوى بالطول C4 يتساوى بالطول C4
+
+362
+00:40:00,870 --> 00:40:04,070
+يتساوى
+
+363
+00:40:04,070 --> 00:40:05,390
+بالطول
+
+364
+00:40:09,010 --> 00:40:13,430
+هي هذول اللي اتجهتين اللي شبكوا بحق كل شبكة
+
+365
+00:40:13,430 --> 00:40:21,270
+النظرية متأكد ؟ نعم نعم نعم متأكد انا اتأكد كمان و
+
+366
+00:40:21,270 --> 00:40:26,610
+الله زي انا انا انا انا انا انا انا انا انا انا
+
+367
+00:40:26,610 --> 00:40:26,610
+انا انا انا انا انا انا انا انا انا انا انا انا
+
+368
+00:40:26,610 --> 00:40:26,610
+انا انا انا انا انا انا انا انا انا انا انا انا
+
+369
+00:40:26,610 --> 00:40:31,470
+انا انا انا انا انا انا انا
+
+370
+00:40:35,790 --> 00:40:43,450
+مشتركة في الـ y3 وين ال y3' هي؟ إذا ال y3' عندي هو
+
+371
+00:40:43,450 --> 00:40:46,390
+0، فمشتركة في ال y3
+
+372
+00:40:52,800 --> 00:40:58,020
+نقصت كتير، طبعا، عامل الdevelopment كتير، نقصت
+
+373
+00:40:58,020 --> 00:41:01,540
+كتير، easy way، ده مظبوط، ما يتعقب في ال
+
+374
+00:41:01,540 --> 00:41:04,940
+professions، و بالبيت الهدف يتحفظ it to
+
+375
+00:41:04,940 --> 00:41:09,700
+professions، فتاني على سؤال ايش ملي، happy، you
+
+376
+00:41:09,700 --> 00:41:13,320
+can't even accept the solution specified by
+
+377
+00:41:18,280 --> 00:41:23,320
+هؤلاء اللي هم مجموعة الحلو الأساسي اللي بيحققوا
+
+378
+00:41:23,320 --> 00:41:34,620
+شروط النظرية يبقى لنا ساعة Y3 and Y4 for the
+
+379
+00:41:34,620 --> 00:41:40,480
+fundamental set
+
+380
+00:41:40,480 --> 00:41:42,840
+of
+
+381
+00:41:52,210 --> 00:42:01,170
+set of solutions that satisfy
+
+382
+00:42:01,170 --> 00:42:13,030
+.. that satisfy the above premise إن كانت هؤلاء
+
+383
+00:42:13,030 --> 00:42:17,290
+الأفكار اللي بيحصلون من النظرية أدنى
+
+384
+00:42:26,390 --> 00:42:29,830
+ناخد بعض الأسئلة من الأسئلة التي كنا نلاقيها قبلها
+
+385
+00:42:29,830 --> 00:42:34,510
+و ببعض الأسئلة التي تتحركين فيها الفيديوهات التي
+
+386
+00:42:34,510 --> 00:42:38,590
+تتحركين فيها هذه المساحة و خلال استخدام الوطن اللي
+
+387
+00:42:38,590 --> 00:42:42,970
+تحينا منه نستخدم هذه الأسئلة جميعا
+
+388
+00:42:50,130 --> 00:43:08,590
+اللي هو رفع الطوابق اللي هو رفع
+
+389
+00:43:08,590 --> 00:43:08,910
+الطوابق اللي هو رفع الطوابق اللي هو رفع الطوابق
+
+390
+00:43:08,910 --> 00:43:08,910
+اللي هو رفع الطوابق اللي هو رفع الطوابق اللي هو
+
+391
+00:43:08,910 --> 00:43:08,910
+رفع الطوابق اللي هو رفع الطوابق اللي هو رفع
+
+392
+00:43:08,910 --> 00:43:08,910
+الطوابق اللي هو رفع الطوابق اللي هو رفع الطوابق
+
+393
+00:43:08,910 --> 00:43:08,910
+اللي هو رفع الطوابق اللي هو رفع الطوابق اللي هو
+
+394
+00:43:08,910 --> 00:43:08,910
+رفع الطوابق اللي هو رفع الطوابق اللي هو رفع
+
+395
+00:43:08,910 --> 00:43:08,910
+الطوابق اللي هو رفع الطوابق اللي هو رفع الطوابق
+
+396
+00:43:08,910 --> 00:43:08,910
+اللي هو رفع الطوابق اللي هو رفع الطوابق اللي هو
+
+397
+00:43:08,910 --> 00:43:12,950
+رفع الطوابق اللي هو رفع الطوابق اللي هو ر
+
+398
+00:43:16,590 --> 00:43:24,290
+فى ثلاثية الوصفين and and
+
+399
+00:43:24,290 --> 00:43:35,450
+f of t قد ساوي e with p greater than zero find
+
+400
+00:43:35,450 --> 00:43:41,010
+find p of t
+
+401
+00:43:47,940 --> 00:43:51,940
+يعني يا بنادق اعتبر هذا المسأل عامة عالميا على
+
+402
+00:43:51,940 --> 00:43:57,960
+نفسك بيقول لو كان الواضح ان الذاتين F وG قسمنا
+
+403
+00:43:57,960 --> 00:44:05,000
+بكتابية E وC ولو كان دلوقتي F of T هي T وT greater
+
+404
+00:44:05,000 --> 00:44:10,160
+than 0 يجب ان يأتي شكل P of T يعني انا هنا في new
+
+405
+00:44:10,160 --> 00:44:15,350
+functions F وTأول اسم انتجاها المعروف هو احدى
+
+406
+00:44:15,350 --> 00:44:22,190
+الذين فيه المعروفة انتجاها المعروف هو احد الذين
+
+407
+00:44:22,190 --> 00:44:22,850
+فيه المعروفة انتجاها المعروف هو احد الذين فيه
+
+408
+00:44:22,850 --> 00:44:22,850
+المعروف هو احد الذين فيه المعروف هو احد الذين فيه
+
+409
+00:44:22,850 --> 00:44:23,910
+المعروف هو احد الذين فيه المعروف هو احد الذين فيه
+
+410
+00:44:23,910 --> 00:44:24,150
+المعروف هو احد الذين فيه المعروف هو احد الذين فيه
+
+411
+00:44:24,150 --> 00:44:24,370
+المعروف هو احد الذين فيه المعروف هو احد الذين فيه
+
+412
+00:44:24,370 --> 00:44:24,370
+المعروف هو احد الذين فيه المعروف هو احد الذين فيه
+
+413
+00:44:24,370 --> 00:44:24,550
+المعروف هو احد الذين فيه المعروف هو احد الذين فيه
+
+414
+00:44:24,550 --> 00:44:30,410
+المعروف هو احد الذين فيه المعروف هو احد الذين فيه
+
+415
+00:44:30,410 --> 00:44:38,330
+المعروف هو احد
+
+416
+00:44:38,820 --> 00:44:44,900
+طبعا هذا الكلام yourself ال F of T بيظهر لمعروف
+
+417
+00:44:44,900 --> 00:44:53,700
+بجديد P of T هي هذه الميادة الملولة مشتق هذه واحد
+
+418
+00:44:53,700 --> 00:45:01,660
+مشتق هذه C prime of T هذا المحدد يسوي T ترتيب جديد
+
+419
+00:45:05,710 --> 00:45:18,570
+يُقصر T في G' of T T في G' of T ماتس G of T بتساوي
+
+420
+00:45:18,570 --> 00:45:25,570
+T ترقية بيوسم شو معناه لو اننا قسمنا كله على مين؟
+
+421
+00:45:25,570 --> 00:45:37,980
+على T لإن لو قسمنا على T تصير G' of T-1 على T في
+
+422
+00:45:37,980 --> 00:45:45,580
+الـ G of T كده يساوي T في E of T شوية كده المعاملة
+
+423
+00:45:45,580 --> 00:45:50,960
+بيستقبلها لإنه بيساكنها في طولات الهاليمين
+
+424
+00:45:50,960 --> 00:45:59,600
+بيستقبلها في الجهة الهاليمينية there is other
+
+425
+00:45:59,600 --> 00:46:06,420
+differential equationيبقى من المروحة الحلها زي ما
+
+426
+00:46:06,420 --> 00:46:13,320
+قلنا من الحل فضل ذلك وبالتالي نجيب شكل G of D يبقى
+
+427
+00:46:13,320 --> 00:46:20,360
+وشكلها كفانات من المروحة دي من ال U of D ال U of D
+
+428
+00:46:20,360 --> 00:46:24,960
+اللي هو عمار عليه شكيل واسمها في السابقه الواحد
+
+429
+00:46:24,960 --> 00:46:31,700
+على T D T اللي هو المعامل سبعمين الجييبقى هذا
+
+430
+00:46:31,700 --> 00:46:42,880
+الكلام E أس ناقص لل T يبقى
+
+431
+00:46:42,880 --> 00:46:48,240
+هذا الكلام E أس ناقص لل T يبقى هذا الكلام E أس
+
+432
+00:46:48,240 --> 00:46:53,280
+ناقص لل T يبقى
+
+433
+00:46:53,280 --> 00:46:56,960
+هذا الكلام E أس ناقص لل
+
+434
+00:46:58,550 --> 00:47:05,270
+طيب إذا بتروح أعظم المعادلة كل مئة واحد على T ومش
+
+435
+00:47:05,270 --> 00:47:11,730
+بصير واحد على T جيه ال prime of T نقص واحد على T
+
+436
+00:47:11,730 --> 00:47:17,610
+تربية جيه ال T ومش بصير واحد على T تربية جيه ال T
+
+437
+00:47:17,610 --> 00:47:21,950
+ومش بصير واحد على T تربية جيه ال T ومش بصير واحد
+
+438
+00:47:21,950 --> 00:47:26,890
+على T تربية جيه ال T ومش بصير واحد على T تربية جيه
+
+439
+00:47:26,890 --> 00:47:26,890
+ال T ومش بصير واحد على T تربية جيه ال T ومش بصير
+
+440
+00:47:26,890 --> 00:47:27,770
+واحد على T تربية جيه ال T ومش بصير واحد على T
+
+441
+00:47:27,770 --> 00:47:27,790
+تربية جيه ال T ومش بصير واحد على T تربية جيه ال T
+
+442
+00:47:27,790 --> 00:47:28,540
+ومش بصير واحد على T تربية جيه ال T ومش بصيربدر
+
+443
+00:47:28,540 --> 00:47:35,120
+يساوي E والـ C المجموع الكامل أطلع فيهم لأن لو
+
+444
+00:47:35,120 --> 00:47:41,180
+كانت أطلع فيهم بيصير واحد عالة T الـ G of T بيساوي
+
+445
+00:47:41,180 --> 00:47:49,020
+E والـ C زائد فرصة الـ C فور بكله في T بصير عالة G
+
+446
+00:47:49,020 --> 00:47:57,870
+of T بيدر يساوي T E والـ C زائد Cيبقى هذا الشكل
+
+447
+00:47:57,870 --> 00:48:02,650
+الـ G of T اللي طلبها هي طلبها أن نستخدم الولرسكين
+
+448
+00:48:02,650 --> 00:48:06,090
+وحللها في ال course of linear differential
+
+449
+00:48:06,090 --> 00:48:11,570
+equation أو قضايا مثلها سيبقوا بالحل قبل ال course
+
+450
+00:48:11,570 --> 00:48:15,810
+of linear differential equation
+
+451
+00:48:31,510 --> 00:48:46,430
+سؤال تسعة عاشر يقول ما F ترانسكل تبع ال F والD F
+
+452
+00:48:46,430 --> 00:48:50,190
+ترانسكل
+
+453
+00:48:50,190 --> 00:48:52,930
+F
+
+454
+00:49:00,030 --> 00:49:13,530
+I F وإذا كان الـ U يسوى اتنين F ناقص G الـ U يسوى
+
+455
+00:49:13,530 --> 00:49:24,010
+اتنين فموينة P فتر ساوي F زائد اتنين G فانا و نسكن
+
+456
+00:49:24,010 --> 00:49:29,090
+I فأنا و نسكن
+
+457
+00:49:35,820 --> 00:49:50,160
+لدنا مانستين اللي هو W تبع ال U و ال V of U and ال
+
+458
+00:49:50,160 --> 00:50:01,080
+V ال U and ال V in pairs of المانستين تبع ال F و
+
+459
+00:50:01,080 --> 00:50:01,620
+ال G
+
+460
+00:50:38,290 --> 00:50:44,610
+سؤال مرة تانية يقول لو كان ال W of F and G هو
+
+461
+00:50:44,610 --> 00:50:51,660
+روزنسكين تبع الدالة F وG وإذا كان ال U functionهي
+
+462
+00:50:51,660 --> 00:50:57,240
+عبارة عن اثنين F لاطس D والـ P function LF زي
+
+463
+00:50:57,240 --> 00:51:02,900
+الاثنين كان هذا الـRoller Skin تبع U بدلالة
+
+464
+00:51:02,900 --> 00:51:08,380
+الـRoller Skin تبع من F وD فقولوا طيب تعالوا نجيب
+
+465
+00:51:08,380 --> 00:51:12,690
+ال roller skin تبع ال F وD ونشوف شو شكلهيبقى انا
+
+466
+00:51:12,690 --> 00:51:18,690
+لو جيت لهرسكين تبع ال F و ال G بقول له هذه المحدث
+
+467
+00:51:18,690 --> 00:51:27,890
+هذه F هذه G هذه F' هذه G' بدنا نفكر محدد هذا معناه
+
+468
+00:51:27,890 --> 00:51:35,050
+يبقى F في G' نفس F' في G
+
+469
+00:51:41,560 --> 00:51:46,800
+أحنا بدنا مين؟ بدنا role skin تبع ال U و ال V يبقى
+
+470
+00:51:46,800 --> 00:51:53,220
+بدنا ياخد رولسكين تبع ال U و ال V يبقى ال U ال V
+
+471
+00:51:53,220 --> 00:51:59,760
+ال U prime ال V prime مطبوط ايه؟ يبقى هذا الكلام
+
+472
+00:51:59,760 --> 00:52:06,760
+بده يساوي ال U بده اشيله و احطه مثلين اتنين F ماطس
+
+473
+00:52:06,760 --> 00:52:15,180
+ال Gالـ V للـ F زائد اتنين G الـ V لـ U' المبدأ
+
+474
+00:52:15,180 --> 00:52:21,100
+اشتق هذا يبقى مشتقة المجموعة الجابري لدلتين يبقى
+
+475
+00:52:21,100 --> 00:52:30,760
+اتنين F' نقص G' مشتقة هذه لـ F' زائد اتنين G'
+
+476
+00:52:31,400 --> 00:52:41,030
+يساويبدا افكر محدد هذا يبقى هدف اللي يقينه 2F-G F
+
+477
+00:52:41,030 --> 00:52:47,690
+prime زي 2G prime اي حاصل ضرب عناصر القطر الرئيسي
+
+478
+00:52:47,690 --> 00:52:57,810
+ناقص حاصل ضرب عناصر القطر الثانوي F زي 2G في 2F
+
+479
+00:52:57,810 --> 00:53:06,590
+prime ناقص G primeيبقى هذا قيمة مين المحدد تعالوا
+
+480
+00:53:06,590 --> 00:53:11,150
+نفك خلاق وسط يعني أفك القيود ده للمكان الحالي بيها
+
+481
+00:53:11,150 --> 00:53:15,550
+ونشوف إلى أين بدنا نوصل يبقى هذا يا بنات بدها
+
+482
+00:53:15,550 --> 00:53:27,230
+تساوي اتنين F F F Prime زائد اتنين F G Prime اتنين
+
+483
+00:53:27,230 --> 00:53:31,090
+F F F Prime اتنين F F G Prime
+
+484
+00:53:55,650 --> 00:53:57,050
+2m2m2m2m2m2m2m2m2m2m2m2m2m2m2m2m2m2m2m2m2m2m2m2m2m2m2m2m2m2m2m2m2m2m2m2m2m2m2m2m2m2m2m2m2m2m2m2m2m2m2m2m2m2m2m2m2m2m2m2m2m2m2m2m2m2m2m2m2m2m2m2m2m2m2m2m2m2m2m2m2m2m2m2m2m2m2m2m2m2m2m2m2m2m2m2m2m2m2m2m2m2m2m2m2m2m2m2m2m2m2m2m
+
+485
+00:53:57,250 --> 00:54:04,850
+أنا ضربت اتنين هذول في البعض ناقص اتنين GG prime
+
+486
+00:54:05,840 --> 00:54:13,780
+خلصت ال term الأول بدي أدربه اتنين F F prime بس
+
+487
+00:54:13,780 --> 00:54:23,540
+بشرط من سالب يبقى سالب اتنين F F prime هنا سالب F
+
+488
+00:54:23,540 --> 00:54:27,620
+في سالب G زائد F G prime
+
+489
+00:54:35,880 --> 00:54:48,600
+نقص اربعة f prime g نقص اربعة f prime g نقص مع نقص
+
+490
+00:54:48,600 --> 00:54:55,540
+بصير زائد اتنين g g prime يبقى زائد اتنين g g
+
+491
+00:54:55,540 --> 00:54:55,960
+prime
+
+492
+00:55:06,960 --> 00:55:18,260
+تعالى تطلعلي 4 F G Prime وعندك F G Prime بصير خمسة
+
+493
+00:55:18,260 --> 00:55:27,610
+F G Primeهذه بالسالب وهذه بالسالب التنتين نفس
+
+494
+00:55:27,610 --> 00:55:36,290
+الشيء مظبوط يبقى ناقص خمسة f prime g شو رايك ناخد
+
+495
+00:55:36,290 --> 00:55:41,090
+خمسة عامل مشترك ونشوف لوين بدنا نوصل يبقى لو جينا
+
+496
+00:55:41,090 --> 00:55:48,970
+خمسة عامل مشترك بظل f g prime ناقص
+
+497
+00:55:53,320 --> 00:55:56,640
+طلع في المقدار بين القوسين
+
+498
+00:55:58,970 --> 00:56:11,790
+FG'-F'G FG'
+
+499
+00:56:11,790 --> 00:56:18,370
+-F'G FG'
+
+500
+00:56:21,370 --> 00:56:28,740
+-F'G FG'-F'G FG'-F'Gطيب بدنا منكوا exercises تلاتة
+
+501
+00:56:28,740 --> 00:56:35,980
+اتنين المسائل التالية يبقى exercises تلاتة اتنين
+
+502
+00:56:35,980 --> 00:56:46,000
+بدنا المسائل من واحد لغاية اربعتاش الأد ومن سبعتاش
+
+503
+00:56:46,000 --> 00:56:53,140
+لغاية ستة وعشرين يبقى
+
+504
+00:56:53,140 --> 00:56:54,360
+بدنا المسائل هذه
+
+505
+00:56:58,690 --> 00:57:06,610
+بنروح الان ل section اللي بعده مرتبط ارتباط وثيق
+
+506
+00:57:06,610 --> 00:57:10,950
+بال role skin تبعنا هذا بيعتمد عليه اعتماد كله
+
+507
+00:57:10,950 --> 00:57:20,410
+يبقى section 3 3 بتحدث عن ال linear independence
+
+508
+00:57:20,410 --> 00:57:24,490
+linear
+
+509
+00:57:24,490 --> 00:57:41,530
+independence andthe run skin نعطي
+
+510
+00:57:41,530 --> 00:57:46,290
+تعريف وبعد ذلك بناخد أمثلة definition two
+
+511
+00:57:46,290 --> 00:57:57,750
+functions two functions f of t andالـ g of t are
+
+512
+00:57:57,750 --> 00:58:06,310
+said to be linearly
+
+513
+00:58:06,310 --> 00:58:07,390
+dependent
+
+514
+00:58:17,220 --> 00:58:23,580
+هختصر كلمة linearly dependent يا بنات إلى ال D من
+
+515
+00:58:23,580 --> 00:58:38,900
+الآن فصاعد on an interval I if
+
+516
+00:58:38,900 --> 00:58:48,630
+there exist if there exist two constantstwo
+
+517
+00:58:48,630 --> 00:58:55,510
+constants ثابتين كواحد
+
+518
+00:58:55,510 --> 00:59:08,830
+and كاثنين not both zero not both zero مش كلهم
+
+519
+00:59:08,830 --> 00:59:19,990
+أصفر such that such that بحيث أنكواحد في ال F of T
+
+520
+00:59:19,990 --> 00:59:29,570
+زائد كاتنين في ال G of T بده يساوي zero for all T
+
+521
+00:59:29,570 --> 00:59:39,910
+اللي موجودة في ال interval I also و كذلك ال F and
+
+522
+00:59:39,910 --> 00:59:45,790
+ال G are called
+
+523
+00:59:49,870 --> 01:00:06,330
+Linearly Independent LPI
+
+524
+01:00:06,330 --> 01:00:15,370
+FK1
+
+525
+01:00:15,860 --> 01:00:23,100
+فى ال F of T زاد K اتنين فى ال G of T يساوي Zero
+
+526
+01:00:23,100 --> 01:00:32,200
+Then K واحد بده يساوي K اتنين بده يساوي Zero
+
+527
+01:00:32,200 --> 01:00:40,000
+Example
+
+528
+01:00:40,000 --> 01:00:40,420
+one
+
+529
+01:00:48,210 --> 01:00:56,330
+determine whether determine
+
+530
+01:00:56,330 --> 01:01:08,050
+whether the given pair of functions the given pair
+
+531
+01:01:08,050 --> 01:01:14,330
+of functions are
+
+532
+01:01:15,490 --> 01:01:26,090
+Linearly Independent or Linearly Dependent الـ
+
+533
+01:01:26,090 --> 01:01:37,310
+F of T يساوي E أس تلاتة T والـ G of T يساوي A أس
+
+534
+01:01:37,310 --> 01:01:40,650
+تلاتة في T ناقص الواحد
+
+535
+01:01:48,330 --> 01:01:52,650
+طيب بنجي لعنوان اللي احنا رافعينه linear
+
+536
+01:01:52,650 --> 01:01:59,510
+independence الاستقلال الخطي عند الورنسكان و
+
+537
+01:01:59,510 --> 01:02:04,370
+الورنسكان يعني هنشوف شو علاقة الاستقلال الخطي و
+
+538
+01:02:04,370 --> 01:02:10,250
+الاعتماد الخطي كمان بالورنسكان بنجي للتعريف اللي
+
+539
+01:02:10,250 --> 01:02:16,500
+احنا كاتبينه بقول لو عندي two functions دالتينهذول
+
+540
+01:02:16,500 --> 01:02:20,960
+اللي بقول عنهم linearly dependent يعني بيتمدوا على
+
+541
+01:02:20,960 --> 01:02:27,520
+بعض خطيا، linearly dependent هاختصرها إلى LD،
+
+542
+01:02:27,520 --> 01:02:32,280
+linearly dependent على الفترة اللي عندنا هذه if
+
+543
+01:02:32,280 --> 01:02:36,680
+they exist يعني إذا جدرنا نلاقي هذا ال E المجلوب
+
+544
+01:02:36,680 --> 01:02:42,570
+هنا there existإذا وجدت
+
+545
+01:02:42,570 --> 01:02:48,710
+ثابتين K واحد أو K اتنين، نقبض الـ0 مش كلهم أصفر
+
+546
+01:02:48,710 --> 01:02:53,790
+بحيث ان K واحد في F of T زاد ال K اتنين في G of T
+
+547
+01:02:53,790 --> 01:02:58,010
+بيديوا يسووا 0 لكل T الموجودة في I
+
+548
+01:03:01,400 --> 01:03:06,600
+أنا عندي دالتين F و G و بدى أشوف هل الدالتين هدول
+
+549
+01:03:06,600 --> 01:03:13,340
+معتمدتين على بعض خطيا و الله مستقلتين عن بعض خطيا
+
+550
+01:03:13,340 --> 01:03:20,280
+بقولي أه إذا بتقدر تلاقي ثوابت اتنين ليس بالضرورة
+
+551
+01:03:20,280 --> 01:03:24,660
+انه .. مش ليس بالضرورة يعني لو كان فيهم واحد zero
+
+552
+01:03:24,660 --> 01:03:28,640
+و اتاني لأ فاش مشكلة و إذا اتنين لا يساوي zero
+
+553
+01:03:28,640 --> 01:03:32,470
+برضه فاش مشكلة بحيثلو ضربت كونوسونت في الدالة
+
+554
+01:03:32,470 --> 01:03:34,950
+الأولى و كونوسونت في الدالة التانية و جماعة، ماذي
+
+555
+01:03:34,950 --> 01:03:40,490
+يكون الناتج؟ سفر طيب، شو معنى ال linear
+
+556
+01:03:40,490 --> 01:03:46,630
+independence لاستقلال؟ الخاطئ بيقول also ال F و G
+
+557
+01:03:46,630 --> 01:03:51,610
+أركون linearly independent الدالتين هدول مستقلتين
+
+558
+01:03:51,610 --> 01:03:55,910
+على البعض خاطئا يعني دولة ماهياش محتلة كل دولة
+
+559
+01:03:55,910 --> 01:04:00,010
+لحالها مالها linearly independent
+
+560
+01:04:11,240 --> 01:04:18,580
+أذا انا مش هنفرق بين الأمرين هل الدالتين هدول
+
+561
+01:04:18,580 --> 01:04:24,960
+مستقلتين خطيا و معتمدتين على بعض خطيابدي ادورلي
+
+562
+01:04:24,960 --> 01:04:28,820
+على ثوابت اتنين اضرب ثابت في الاول و ثابت التاني و
+
+563
+01:04:28,820 --> 01:04:33,120
+اجمع و الاقيهم يساوي قداش Zero بعد ما يطلع في Zero
+
+564
+01:04:33,120 --> 01:04:38,540
+باطل على الثواب التاني والله اذا ثوابت اتنين اصفرا
+
+565
+01:04:38,540 --> 01:04:44,180
+يبقى هدول الدالتين linearly independent وان كان
+
+566
+01:04:44,180 --> 01:04:48,980
+اتنين مهماش اصفر او واحد صفر والتاني اللي لأ يبقى
+
+567
+01:04:48,980 --> 01:04:53,650
+linearly independent واضحة الصورةيبقى عرفنا شو
+
+568
+01:04:53,650 --> 01:04:57,110
+الفرق بين ال linear dependence و ال linear
+
+569
+01:04:57,110 --> 01:05:01,910
+independence الناس اللي أخدوا الجبر خطي نفس الكلام
+
+570
+01:05:01,910 --> 01:05:07,050
+اللي بياخدوه في الجبر الخطي حرفيا ماغيرناش فيه ولا
+
+571
+01:05:07,050 --> 01:05:12,590
+حاجة طيب بدنا ننقل هذا المثال على أرض الواقع ببعض
+
+572
+01:05:12,590 --> 01:05:16,510
+الأمثلةGallery determine whether the given pair of
+
+573
+01:05:16,510 --> 01:05:20,790
+functions حدد لمين من أزواج الدولة التي بتبقى
+
+574
+01:05:20,790 --> 01:05:25,030
+linearly independent ومين linearly dependent
+
+575
+01:05:50,220 --> 01:05:58,200
+هل تقدر تجيبنا تابعمضربه في الدالة الأولى و ثابت
+
+576
+01:05:58,200 --> 01:06:04,000
+تانى مضربه في الدالة التانية و نجمع يطلع النتج
+
+577
+01:06:04,000 --> 01:06:11,360
+يساوي zero نقدر و بعد ذلك بظهر أشوف شو شكلهم ها
+
+578
+01:06:11,360 --> 01:06:14,460
+تقدروا؟
+
+579
+01:06:14,460 --> 01:06:22,480
+طيب إيش رأيك؟ هنا بداجي أقول assumeافترضوا there
+
+580
+01:06:22,480 --> 01:06:32,940
+exists c1 و c2 such that بحيث ان c1 في e أس تلاتة
+
+581
+01:06:32,940 --> 01:06:39,380
+t زاد c2 في e أس تلاتة t ناقص تلاتة بده يساوي زي
+
+582
+01:06:42,410 --> 01:06:47,350
+يلا هد انتوا بيجي 48 طالب او زدت واحدة صارت 49
+
+583
+01:06:47,350 --> 01:06:53,170
+بدنا نعرف قداش ها كل واحدة تفكر تجيب ثوابت من
+
+584
+01:06:53,170 --> 01:06:58,070
+عندها تقولي ها دي لو أخدنا C1 بكذا و C2 بكذا بطلع
+
+585
+01:06:58,070 --> 01:07:06,870
+انها تجي سافار يلا شوف ارقام ثوابت ايوة
+
+586
+01:07:11,150 --> 01:07:17,030
+خلامك خالص بتقولي انا بدها اخد c1 هذا بواحد و بدها
+
+587
+01:07:17,030 --> 01:07:23,650
+تاخد c2 ب e تكعيب بس بالسالب يعني سالب e تكعيب
+
+588
+01:07:23,650 --> 01:07:29,090
+تعالى نشوف هذا كلامها صح ولا غلط يبقى بالدرجة اقول
+
+589
+01:07:29,090 --> 01:07:43,400
+take c1 يساوي واحد و c2 يساوي سالب e تكعيبثم سوف
+
+590
+01:07:43,400 --> 01:07:49,060
+نشوف كلامه صح و لا سي واحد بواحد بقاش بظل E أس
+
+591
+01:07:49,060 --> 01:07:58,020
+تلاتة T زي سي اتنين اللي هو ناقص E تكيب P أس تلاتة
+
+592
+01:07:58,020 --> 01:08:06,740
+T ناقص تلاتة هو يساوي E أس تلاتة T ناقصE تكيب مع
+
+593
+01:08:06,740 --> 01:08:13,380
+هذه تجمع بضال قداش E أس ثلاثة T يبقى E أس ثلاثة T
+
+594
+01:08:13,380 --> 01:08:19,700
+وE ساوى قداش Zero هذي احنا جيبنا ثوابت اتنين بحيث
+
+595
+01:08:19,700 --> 01:08:24,320
+ضربنا كل صنفة الأول وكل صنفة التانية وجمعنا وقالوا
+
+596
+01:08:24,320 --> 01:08:28,420
+انها تجيب E ساوى Zero بداجي أطلع في الثوابت اللي
+
+597
+01:08:28,420 --> 01:08:34,020
+جيبتهم هل هدول بأصفات يبقى هدول الدالتين مالهم
+
+598
+01:08:34,340 --> 01:08:43,360
+linearly dependent يبقى س اللي هو ال E أس ثلاثة T
+
+599
+01:08:43,360 --> 01:08:50,480
+and ال E أس ثلاثة T نقص ثلاثة are linearly
+
+600
+01:08:50,480 --> 01:08:59,640
+dependent because اللي هو خليها مشان التعريفة بدل
+
+601
+01:08:59,640 --> 01:09:06,560
+C واحد قوليلي K واحدو K2 بشان نخلي رموزنا زي ما هي
+
+602
+01:09:06,560 --> 01:09:17,020
+K1 و K2 وهذه K1 وهذه K2 تمام؟ لإنها دندن because
+
+603
+01:09:17,020 --> 01:09:27,600
+K1 لا يساوي Zero وK2 لا يساوي Zero وكذلك طيب خديني
+
+604
+01:09:27,600 --> 01:09:31,260
+نمرة B نمرة B
+
+605
+01:09:34,650 --> 01:09:44,850
+لو أخدنا اللي هو ال F of T بده يساوي T و ال G of T
+
+606
+01:09:44,850 --> 01:09:50,610
+بده يساوي تساوي T السالب واحد و T greater than
+
+607
+01:09:50,610 --> 01:09:51,330
+zero
+
+608
+01:09:59,070 --> 01:10:03,110
+قام من عندنا لو حطينا مثلا ال T أكبر من زفرة و T
+
+609
+01:10:03,110 --> 01:10:08,710
+أقل من زفرة و تبناه مظلوم؟ تفكر في اللي بدك تفكر
+
+610
+01:10:08,710 --> 01:10:14,710
+فيه؟ حطيت قيودنا؟ بأي
+
+611
+01:10:14,710 --> 01:10:19,770
+طريقة تشير تهاتيل التوابل؟ احنا لسه في بداية
+
+612
+01:10:19,770 --> 01:10:24,070
+الطريق فأول يعني بس احنا بدنا نثبت المفهوم عندكوا
+
+613
+01:10:24,070 --> 01:10:28,520
+و بعدين بنطور أسئلتنا يعني انها تعتبر أسئلة بسيطةو
+
+614
+01:10:28,520 --> 01:10:35,100
+بعد ذلك نشوف كيف نثبت الشغل هذه طيب ماطيني سؤال
+
+615
+01:10:35,100 --> 01:10:38,840
+تاني قال ال f of t بده يساوي t و ال g of t بده
+
+616
+01:10:38,840 --> 01:10:46,700
+يساوي t و السالب واحد بدي بقوله هنا assume افترضي
+
+617
+01:10:46,700 --> 01:10:56,500
+there exist كواحد و كاتنين such that بحيث انكواحد
+
+618
+01:10:56,500 --> 01:11:03,640
+T زائد كتنين في T ناقص واحد بده يساوي زينا بتروح
+
+619
+01:11:03,640 --> 01:11:10,360
+هدور علي كواحد و كتنين شو رايك اشتق المعادلة هذه
+
+620
+01:11:10,360 --> 01:11:15,040
+لو اشتقت المعادلة هذه بصير هنا كواحد بتطير هذه T
+
+621
+01:11:15,040 --> 01:11:22,900
+بصير ناقص كتنين T و ناقص اتنينيبقى هذه شو بدي
+
+622
+01:11:22,900 --> 01:11:29,600
+اعطيك يا بنات بدي اعطيك ان K واحد يساوي K اتنين في
+
+623
+01:11:29,600 --> 01:11:35,120
+T السالب اتنين مظبوط؟
+
+624
+01:11:35,120 --> 01:11:40,620
+بدي امسك المعلومة اللي حصلت عليها و اعوض بها في
+
+625
+01:11:40,620 --> 01:11:47,060
+المعادلة اللي فوق يبقى ايش بصير عندي؟ K اتنين في T
+
+626
+01:11:47,060 --> 01:11:49,460
+السالب اتنين في T
+
+627
+01:11:53,220 --> 01:11:58,440
+زائد كتنين في T والسالب واحد يساوي Zero
+
+628
+01:12:09,630 --> 01:12:15,370
+زائد كتنين كتيوس سالب واحد يساوي زيرو مش هذه هي
+
+629
+01:12:15,370 --> 01:12:21,330
+نفسها يبقى هذا بدي يعطي كتنين كتنين كتين كتين كتين
+
+630
+01:12:21,330 --> 01:12:21,650
+كتين كتين كتين كتين كتين كتين كتين كتين كتين كتين
+
+631
+01:12:21,650 --> 01:12:21,650
+كتين كتين كتين كتين كتين كتين كتين كتين كتين كتين
+
+632
+01:12:21,650 --> 01:12:23,510
+كتين كتين كتين كتين كتين كتين كتين كتين كتين كتين
+
+633
+01:12:23,510 --> 01:12:26,970
+كتين كتين كتين كتين كتين كتين كتين كتين كتين كتين
+
+634
+01:12:26,970 --> 01:12:29,670
+كتين كتين كتين كتين كتين كتين كتين كتين كتين كتين
+
+635
+01:12:29,670 --> 01:12:35,490
+كتين كتين كتين كتين كتين كتين
+
+636
+01:12:35,490 --> 01:12:42,440
+كزيرو لما كتنين يساوي زيرو خديها وعوضيها في
+
+637
+01:12:42,440 --> 01:12:48,480
+المعادلة اللي فوق يبقى بصير كواحد بده يساوي زيرو
+
+638
+01:12:48,480 --> 01:12:56,140
+في T أساليب اتنين يساوي جداش زيرو يبقى كواحد بده
+
+639
+01:12:56,140 --> 01:13:00,580
+يساوي كتنين بده يساوي جداش بده يساوي زيرو المعنى
+
+640
+01:13:00,580 --> 01:13:05,230
+هذا كلام ال two functions هدول ما لهمlinearly
+
+641
+01:13:05,230 --> 01:13:10,570
+independent ولا واحدة بتعتمد على الثانية يبقى هنا
+
+642
+01:13:10,570 --> 01:13:18,290
+ال T and ال T والسالب واحد are linearly
+
+643
+01:13:18,290 --> 01:13:25,070
+independent يعني يا بنات احنا بنحاول نوجد ثوابت
+
+644
+01:13:25,070 --> 01:13:32,060
+بأي طريقة رياضية نقدر عليها مين بتسأل؟ ايوةكان
+
+645
+01:13:32,060 --> 01:13:35,720
+واحد كيف ده يعني كان مع نفس الشخص واحد او اخر؟ كيف
+
+646
+01:13:35,720 --> 01:13:39,980
+نتعرف على واحد و اخر؟ لطيع واحد و واحد قبل انك حُك
+
+647
+01:13:39,980 --> 01:13:44,260
+واحد و واحد و نشوف يساوي صفر ولا لأ؟ يبقاش بدك
+
+648
+01:13:44,260 --> 01:13:51,240
+تخدمهم واحد و واحد و اخر؟ بقى ايه واحد؟ واحد في
+
+649
+01:13:51,240 --> 01:13:57,400
+اتين و اتين بدك تخدم واحد تمام؟ زي واحد في اتين
+
+650
+01:13:57,400 --> 01:13:59,220
+والسالي واحد تساوي صفر؟
+
+651
+01:14:08,270 --> 01:14:17,750
+أو نجمع نتج يكون يساوي 0 كي
+
+652
+01:14:17,750 --> 01:14:24,670
+واحد
+
+653
+01:14:24,670 --> 01:14:27,430
+و كي اثنين استوابط اللي بدنا ناخده من هناك التعريف
+
+654
+01:14:27,430 --> 01:14:35,620
+بقول مش بداخله functionياخدهم ثوابت، قادر بالك، اه
+
+655
+01:14:35,620 --> 01:14:39,860
+في سؤال تاني؟ اه ايوة ..الثور في حياته عشان انه
+
+656
+01:14:39,860 --> 01:14:43,460
+فيه واحد في اتنين يساونهم باصفار بسوء الصفر وكمان
+
+657
+01:14:43,460 --> 01:14:47,180
+لجينا انهم بيساووا قيمة غير الأصفر بسوء الصفر يحصل
+
+658
+01:14:47,180 --> 01:14:53,360
+هالانتلاع؟ كانت الكلام المناورة من بعض صحوا لاني
+
+659
+01:14:53,360 --> 01:14:58,020
+يا أصفار يا ثوابت، ممكن ألاقي واحد منهم صفر، بس
+
+660
+01:14:58,020 --> 01:15:02,570
+التاني لألو كان واحد صفر و واحد عدد ماعندى مشكلة
+
+661
+01:15:02,570 --> 01:15:07,230
+بكون linearly dependent لكن إذا اتنين أصفر مع بعض
+
+662
+01:15:07,230 --> 01:15:13,550
+بقول linearly independent طيب هنصيغ الكلام هذا
+
+663
+01:15:13,550 --> 01:15:18,870
+بشكل آخر خدولي هالنظرية التالية the theorem
+
+664
+01:15:18,870 --> 01:15:23,610
+النظرية
+
+665
+01:15:23,610 --> 01:15:35,090
+بتقول ما ياتى F ال Fand الـ G are differentiable
+
+666
+01:15:35,090 --> 01:15:55,050
+functions on an open interval I and F that exist
+
+667
+01:15:55,050 --> 01:15:57,770
+P0
+
+668
+01:15:59,220 --> 01:16:14,820
+in الفترة I such that بحيث ان الورنسكت تبع ال F و
+
+669
+01:16:14,820 --> 01:16:29,240
+ال G عند T0 لا يساوي Zero then ال F عند ال Gare
+
+670
+01:16:29,240 --> 01:16:40,960
+linearly independent عن الفترة I on
+
+671
+01:16:40,960 --> 01:16:48,100
+the other hand
+
+672
+01:16:54,420 --> 01:17:07,980
+الـ F and ال G are linearly dependent on Iعلى
+
+673
+01:17:07,980 --> 01:17:14,060
+الفترة I then الرنسكين
+
+674
+01:17:14,060 --> 01:17:24,580
+تبع ال F وال G عند ال T بده ساوي Zero for all T
+
+675
+01:17:24,580 --> 01:17:29,180
+اللي موجودة في ال interval I
+
+676
+01:17:48,670 --> 01:17:53,810
+قبل مناخد المثال بدنا نرجع لنص النظرية ونحاول نفهم
+
+677
+01:17:53,810 --> 01:18:16,650
+ما هو الشئ اللي موجود في هذه النظرية طلع
+
+678
+01:18:16,650 --> 01:18:21,500
+كويسبدي أجرى نظرية و بعدين بدي أقولكوا إيش فهمت
+
+679
+01:18:21,500 --> 01:18:26,060
+منها و شوفوا فهمي الصح و لا غلط إذا صح بنعتمدوا و
+
+680
+01:18:26,060 --> 01:18:31,520
+إذا غلط بنصحهم بقول إيش لو كان ال F و G are
+
+681
+01:18:31,520 --> 01:18:37,760
+differentiable functions على فترة عن I و أخذت نقطة
+
+682
+01:18:37,760 --> 01:18:41,640
+موجودة في هذه الفترة و لجيت أن ال neurons كان
+
+683
+01:18:41,640 --> 01:18:46,180
+عندها لا يساوي Zero إن حدث ذلكبقول الـ two
+
+684
+01:18:46,180 --> 01:18:52,000
+functions are linearly independent طيب ده اللي هو
+
+685
+01:18:52,000 --> 01:18:56,380
+من ناحية الأخرى لو كان ال F and G are linearly
+
+686
+01:18:56,380 --> 01:19:01,700
+dependent يبقى الغروس كان عندهم بده ساوي zero لكل
+
+687
+01:19:01,700 --> 01:19:07,100
+ال T اللي موجودة وين اللي موجودة في ال I يبقى
+
+688
+01:19:07,100 --> 01:19:11,640
+واضحة ظن بدي ألخص كلام اللي قلناها ده أو نص
+
+689
+01:19:11,640 --> 01:19:16,210
+النظرية وشوف تلخيصي صح ولا غلطميعطيني ال two
+
+690
+01:19:16,210 --> 01:19:19,170
+functions وقال لي شوف للتان تانى وقال linearly
+
+691
+01:19:19,170 --> 01:19:23,650
+dependent و الله linearly independent بقوله والله
+
+692
+01:19:23,650 --> 01:19:28,630
+كويس باخد هال worn skin تبع التنتين عنده نقطة
+
+693
+01:19:28,630 --> 01:19:32,690
+والله إذا ال worn skin لا يساوي zero يبقى linearly
+
+694
+01:19:32,690 --> 01:19:36,490
+independent وإذا ساوى zero يبقى linearly dependent
+
+695
+01:19:36,490 --> 01:19:39,990
+غلط؟
+
+696
+01:19:39,990 --> 01:19:44,050
+لا يا ناس غلط كلامي يعني يا ناس أنا مدرس كلامي
+
+697
+01:19:44,050 --> 01:19:50,150
+غلط؟طب هو الخطأ بعينيه نص غلط و نص صح طب تعالى
+
+698
+01:19:50,150 --> 01:19:54,790
+نشوف كيف نصه غلط و كيف نصه صح نمسك النص في الأول
+
+699
+01:19:54,790 --> 01:19:58,610
+هدول التنتين دوال قبل اشتغال ماعنده مشكلة على
+
+700
+01:19:58,610 --> 01:20:02,870
+الفترة اللى عندناها ده بحيث ال winners كان عنده
+
+701
+01:20:02,870 --> 01:20:07,550
+نقطة ماجلش على كل ال intervalلو جدرت تلاقي
+
+702
+01:20:07,550 --> 01:20:12,610
+الورسكين ولو نقطة واحدة ليس بالضرورة على كل الفتحة
+
+703
+01:20:12,610 --> 01:20:17,090
+ولو عندها نقطة واحدة لا يساوي zero اذا الورسكين
+
+704
+01:20:17,090 --> 01:20:21,570
+تبعهم اذا دول اثنين هدول يصيروا linearly
+
+705
+01:20:21,570 --> 01:20:26,850
+independent طيب ممتاز الشطرة التانية بقول on the
+
+706
+01:20:26,850 --> 01:20:32,100
+other hand يعني من ناحية اخرىلو كانت الـ two
+
+707
+01:20:32,100 --> 01:20:36,860
+functions linearly dependent يجب أن يكون الرونسكين
+
+708
+01:20:36,860 --> 01:20:42,040
+0 for all t الموجودة في ال interval إذا فارق
+
+709
+01:20:42,040 --> 01:20:45,840
+السماعة على الأرض مش زي ما قلت انا في الأول مظبوط
+
+710
+01:20:45,840 --> 01:20:50,520
+إذا كلامك في أول غلط يبقى إياك أن تخطي مثل هذا
+
+711
+01:20:50,520 --> 01:20:54,740
+الخطأ يبقى الصح اللي في حصلة دلتين هذول linearly
+
+712
+01:20:54,740 --> 01:20:58,120
+dependent ولا linearly independent بروح تاخد
+
+713
+01:20:58,120 --> 01:21:03,760
+الرونسكين عند نقطةلقيته لا يساوي 0 خلاص مضمون 100%
+
+714
+01:21:03,760 --> 01:21:09,280
+إذا اتنين دول linearly independent لكن لو كانوا
+
+715
+01:21:09,280 --> 01:21:14,240
+اتنين تانيين linearly dependent يجب أن يكون ال
+
+716
+01:21:14,240 --> 01:21:18,740
+role skin تبعهم يساوي 0 for all فيه بديش ابعد فيه
+
+717
+01:21:18,740 --> 01:21:23,140
+بدي أخد من اللي قدامكوا نمرا إيه إيش طلعت عندنا
+
+718
+01:21:23,140 --> 01:21:28,580
+هذه؟طلعت linearly dependent صح ولا لا؟ إذا بده
+
+719
+01:21:28,580 --> 01:21:31,040
+يروح أحسب ال role skin تبعها و يشوف قداش ماذا
+
+720
+01:21:31,040 --> 01:21:35,060
+يساوي هذا بيقول لو كانت كنتية linearly dependent
+
+721
+01:21:35,060 --> 01:21:39,040
+بده يكون ال role skin تبعها مضي ساوي قداش يساوي
+
+722
+01:21:39,040 --> 01:21:46,540
+zero يبقى example بداتي أقول from the above
+
+723
+01:21:46,540 --> 01:21:57,200
+example من المثال اللي فوقوبدي اخد part a من part
+
+724
+01:21:57,200 --> 01:22:01,420
+a مشيكنا a طلع هدول التانتين are linearly
+
+725
+01:22:01,420 --> 01:22:08,880
+dependent ال E أس تلاتة T and ال E أس تلاتة T ناخذ
+
+726
+01:22:08,880 --> 01:22:16,180
+تلاتة are linearly dependent linearly dependent
+
+727
+01:22:16,180 --> 01:22:18,760
+for all T
+
+728
+01:22:22,390 --> 01:22:28,030
+يبقى الرونسكين تبع اي أس تلاتة تي و اي أس تلاتة تي
+
+729
+01:22:28,030 --> 01:22:34,450
+ناقص تلاتة تلاتة تلاتة تلاتة تلاتة تلاتة تلاتة
+
+730
+01:22:34,620 --> 01:22:40,720
+و E أس ثلاثة T ناقص ثلاثة نشتق يا بناد يبقى ثلاثة
+
+731
+01:22:40,720 --> 01:22:47,760
+E أس ثلاثة T ونشتق هنا ثمان ثلاثة E أس ثلاثة T
+
+732
+01:22:47,760 --> 01:22:54,120
+ناقص ثلاثة صح ايه تشتفغي؟ مشتقة الأس كل اللي هو
+
+733
+01:22:54,120 --> 01:23:00,810
+قداشر ثلاثة فقط لا غيرطيب نفكر المحدد هذا بيصير
+
+734
+01:23:00,810 --> 01:23:11,470
+تلاتة E أُس ستة T ناقص تلاتة ناقص تلاتة E أُس ستة
+
+735
+01:23:11,470 --> 01:23:18,230
+T ناقص تلاتة يشوى قداش Zero مظبوط يبدو هي طبقنا
+
+736
+01:23:18,230 --> 01:23:23,510
+نمرة B تماما او النقطة الثانية من النظر يجليه
+
+737
+01:23:23,510 --> 01:23:27,580
+نظرها درهانإذا تنتهي هذه الـlinearly dependent
+
+738
+01:23:27,580 --> 01:23:36,580
+يفجرون إذا كنت تبحث عن عيوب يساوي 0 طيب and أحدنا
+
+739
+01:23:36,580 --> 01:23:42,010
+ذالتين الأثنين هذوللأ خدنا نمر بيه و يارا راح نمر
+
+740
+01:23:42,010 --> 01:23:46,490
+بيه هي نمر بيها هي الدالتين الأثنين هذول و أثبتنا
+
+741
+01:23:46,490 --> 01:23:51,430
+أن هذول الأثنين linearly independent هذا لأ بدي
+
+742
+01:23:51,430 --> 01:23:55,190
+أروح أجيب المحدد سبعهم إذا المحدد سبعهم قلع لا
+
+743
+01:23:55,190 --> 01:23:59,890
+يساوي zero لنفتدوا للنظرية يفتدتين يكونوا are
+
+744
+01:23:59,890 --> 01:24:06,230
+linearly independent يفتدت ياخد المحدد تبع الحل
+
+745
+01:24:06,230 --> 01:24:15,260
+الأول P والثاني-P-1-P
+
+746
+01:24:15,260 --> 01:24:22,200
+-1
+
+747
+01:24:22,200 --> 01:24:28,800
+-P-1-P-1-P-1
+
+748
+01:24:37,040 --> 01:24:45,960
+مدام لا يساوي 0 سا ات and ات سالف واحد are
+
+749
+01:24:45,960 --> 01:24:52,740
+linearly independent مش انتقطة واحدة وماسي على كل
+
+750
+01:24:52,740 --> 01:24:59,620
+ال interval all ال interval من 0 لغاية انت نقل ال
+
+751
+01:24:59,620 --> 01:25:04,120
+P أكبر من ال 0 يعني اي نقطة تيجي تقريبا تحطيها ده
+
+752
+01:25:04,120 --> 01:25:06,420
+يمكن ينقل اكتر من واحد بسبب ال
+
diff --git a/PL9fwy3NUQKwaKyeI5iiPpebyFXxlPBffV/AUHdUUb0dQA_raw.json b/PL9fwy3NUQKwaKyeI5iiPpebyFXxlPBffV/AUHdUUb0dQA_raw.json
new file mode 100644
index 0000000000000000000000000000000000000000..500f766b725828e839e4a7dac1f619103f36e0c2
--- /dev/null
+++ b/PL9fwy3NUQKwaKyeI5iiPpebyFXxlPBffV/AUHdUUb0dQA_raw.json
@@ -0,0 +1 @@
+{"segments": [{"id": 1, "seek": 4934, "start": 20.92, "end": 49.34, "text": "بسم الله الرحمن الرحيم الحمد لله رب العالمين والصلاة والسلام على أشرف المرسلين سيدنا محمد وعلى آله وصحبه أجمعين بنات الطالبات السلام عليكم ورحمة الله وبركاته اليوم سنتحدث عن موضوع جديد هو الرعاية الاجتماعية من حيث مفهومها ورعاية وما المقصود بها", "tokens": [3555, 38251, 21984, 34892, 5016, 27842, 34892, 5016, 32640, 21542, 2304, 3215, 24976, 3224, 12602, 3555, 18863, 45340, 9957, 16070, 9381, 15040, 3660, 16070, 3794, 37440, 15844, 5551, 8592, 28480, 9673, 2288, 3794, 1211, 9957, 8608, 25708, 8315, 3714, 35571, 3215, 4032, 3615, 23942, 19753, 43761, 4032, 9381, 5016, 3555, 3224, 5551, 7435, 2304, 3615, 9957, 4724, 8315, 2655, 41950, 6027, 3555, 9307, 21136, 37440, 25894, 24793, 4032, 2288, 35571, 3660, 21984, 4032, 26890, 4117, 9307, 3224, 45595, 20498, 8608, 29399, 24401, 12984, 18871, 3714, 2407, 11242, 45367, 10874, 16254, 3215, 31439, 34892, 3615, 995, 10632, 2423, 26108, 2655, 15042, 3615, 10632, 9154, 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هذه أيضاً من المشكلات اللي بتواجه المؤسسة لابد عند تشكيل المؤسسة وتكوين المؤسسة لابد من توضيح الأهداف ما هو الهدف أو ما هي مجموعة الأهداف التي تريد المؤسسة تحقيقها", "tokens": [2407, 17082, 2304, 2407, 11242, 16247, 3224, 28259, 5172, 13672, 1829, 4032, 11242, 34268, 11296, 9673, 33604, 3794, 3794, 3660, 34051, 20328, 3615, 37746, 16712, 5016, 38436, 4587, 5551, 5016, 1829, 7649, 995, 14111, 3714, 43020, 45030, 11242, 9673, 33604, 3794, 3794, 9307, 6055, 11242, 3615, 5551, 3224, 28259, 5172, 50113, 6027, 10632, 5551, 3224, 28259, 5172, 9122, 3555, 48923, 10874, 28259, 14111, 20193, 6055, 14851, 9566, 40228, 25062, 1829, 10943, 4724, 11296, 34051, 5551, 5016, 1829, 7649, 995, 14111, 6055, 30544, 5551, 3224, 28259, 5172, 32771, 10943, 11242, 3660, 32771, 13546, 3714, 5172, 3224, 20498, 3660, 6156, 17082, 13546, 4032, 46958, 5016, 3660, 29538, 36632, 11242, 995, 14111, 9154, 9673, 8592, 28820, 9307, 13672, 1829, 39894, 2407, 26108, 3224, 9673, 33604, 3794, 3794, 3660, 5296, 16758, 3215, 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"word": " موضوع", "probability": 0.992919921875}, {"start": 2908.12, "end": 2908.7, "word": " تطور", "probability": 0.9119466145833334}, {"start": 2908.7, "end": 2909.14, "word": " طريق", "probability": 0.9786783854166666}, {"start": 2909.14, "end": 2909.6, "word": " تنظيم", "probability": 0.97021484375}, {"start": 2909.6, "end": 2910.36, "word": " المجتمع", "probability": 0.9891357421875}, {"start": 2910.36, "end": 2911.06, "word": " لكن", "probability": 0.599365234375}, {"start": 2911.06, "end": 2911.44, "word": " مني", "probability": 0.7919921875}, {"start": 2911.44, "end": 2911.6, "word": " كل", "probability": 0.650390625}, {"start": 2911.6, "end": 2912.16, "word": " تحياتي", "probability": 0.762744140625}, {"start": 2912.16, "end": 2912.82, "word": " ومتقدير", "probability": 0.789453125}, {"start": 2912.82, "end": 2913.34, "word": " والسلام", "probability": 0.7941080729166666}, {"start": 2913.34, "end": 2913.86, "word": " عليكم", "probability": 0.81494140625}, {"start": 2913.86, "end": 2914.58, "word": " ورحمة", "probability": 0.971435546875}, {"start": 2914.58, "end": 2914.96, "word": " الله", "probability": 0.9677734375}, {"start": 2914.96, "end": 2916.2, "word": " وبركاته", "probability": 0.97529296875}], "temperature": 1.0}], "language": "ar", "language_probability": 1.0, "duration": 2916.84425, "duration_after_vad": 2803.099374999988}
\ No newline at end of file
diff --git a/PL9fwy3NUQKwaKyeI5iiPpebyFXxlPBffV/MTGfIO5PlG4.srt b/PL9fwy3NUQKwaKyeI5iiPpebyFXxlPBffV/MTGfIO5PlG4.srt
new file mode 100644
index 0000000000000000000000000000000000000000..8f6983324e6e154a71d265d60c1c5bc6efa83ac2
--- /dev/null
+++ b/PL9fwy3NUQKwaKyeI5iiPpebyFXxlPBffV/MTGfIO5PlG4.srt
@@ -0,0 +1,1373 @@
+1
+00:00:21,550 --> 00:00:24,990
+بسم الله الرحمن الرحيم الحمد لله رب العالمين
+
+2
+00:00:24,990 --> 00:00:29,150
+والصلاة والسلام على أشرف المرسلين سيدنا محمد وعلى 
+
+3
+00:00:29,150 --> 00:00:33,990
+آله وصحبه أجمعين بنات الطالبات السلام عليكم ورحمة 
+
+4
+00:00:33,990 --> 00:00:40,690
+الله وبركاته بهذه المحاضرة سنتناول موضوعًا جديدًا وهو 
+
+5
+00:00:40,690 --> 00:00:47,270
+فلسفة طريقة تنظيم المجتمع عندما 
+
+6
+00:00:47,270 --> 00:00:53,430
+نتحدث عن فلسفة طريقة تنظيم المجتمع سنتحدث عن كل ما 
+
+7
+00:00:53,430 --> 00:00:59,570
+يتعلق بفلسفة هذه الطريقة والطريقة مثلها مثل أي علم 
+
+8
+00:00:59,570 --> 00:01:05,810
+آخر له فلسفة فلسفة الخدمة الاجتماعية فلسفة خدمة 
+
+9
+00:01:05,810 --> 00:01:10,310
+للفرد فلسفة تنظيم المجتمع فلسفة خدمة الجماعة بكل 
+
+10
+00:01:10,310 --> 00:01:14,050
+طرق الخدمة الاجتماعية لها فلسفة بكل طريقة مدامة 
+
+11
+00:01:14,050 --> 00:01:18,590
+علم فهي لها فلسفة كذلك أي علم من العلوم له فلسفة 
+
+12
+00:01:18,590 --> 00:01:23,530
+يُستند عليها فإحنا سنتحدث عن فلسفة طريقة تنظيم 
+
+13
+00:01:23,530 --> 00:01:28,510
+المجتمع الفلسفة تشمل كل شيء عن هذا العلم ما يضمه 
+
+14
+00:01:28,510 --> 00:01:34,440
+هذا العلم من قيم من مبادئ من أهداف من معاني ومعارف 
+
+15
+00:01:34,440 --> 00:01:39,900
+كل ما يتعلق بفلسفة طريقة تنظيم المجتمع فالفلسفة 
+
+16
+00:01:39,900 --> 00:01:45,700
+تضم جميع هذه المعارف والقيم والأهداف والمبادئ 
+
+17
+00:01:45,700 --> 00:01:52,160
+الخاصة بطريقة تنظيم المجتمع طبعًا الفلسفة عبارة عن 
+
+18
+00:01:52,160 --> 00:01:57,710
+حقائق وقيم تُستند إليها اللي هو أي علم من العلوم 
+
+19
+00:01:57,710 --> 00:02:02,810
+يُستند إليها أي علم من العلوم حقائق وقيم إذا معناته 
+
+20
+00:02:02,810 --> 00:02:05,530
+لما نقول فلسفة طريقة تنظيم المجتمع هي عبارة عن 
+
+21
+00:02:05,530 --> 00:02:09,070
+الحقائق والقيم اللي بتستند إليها طريقة تنظيم 
+
+22
+00:02:09,070 --> 00:02:17,410
+المجتمع طبعًا الفلسفة جاية من philosophy من مقطعين 
+
+23
+00:02:17,410 --> 00:02:24,110
+philo و sophie philo و sophie إيش يعني مقطع philo 
+
+24
+00:02:24,110 --> 00:02:31,270
+يعني philo بمعنى حب و sophie بمعناه الحكمة فـ philo 
+
+25
+00:02:31,270 --> 00:02:36,010
+sophie معناها حب الحكمة حب الحكمة ولذلك إحنا بنقول 
+
+26
+00:02:36,010 --> 00:02:44,290
+عنها الفلسفة واضح طبعًا 
+
+27
+00:02:44,290 --> 00:02:47,970
+بالنسبة 
+
+28
+00:02:47,970 --> 00:02:52,870
+لفلسفة طريقة تنظيم المجتمع تعريفها كالتالي هي 
+
+29
+00:02:52,870 --> 00:03:01,420
+مجموعة الحقائق والقيم والمهارات والمعارف التي 
+
+30
+00:03:01,420 --> 00:03:05,700
+تُستند عليها طريقة تنظيم المجتمع في أداء المهام 
+
+31
+00:03:05,700 --> 00:03:11,920
+الخاصة بها في إطار المجتمع هذا هو تعريف اللي هي 
+
+32
+00:03:11,920 --> 00:03:16,180
+فلسفة طريقة تنظيم المجتمع وسنتحدث، هنعرف ما هي 
+
+33
+00:03:16,180 --> 00:03:20,640
+الحقائق والقيم والمهارات والمعارف التي تُستند إليها 
+
+34
+00:03:20,640 --> 00:03:26,610
+فلسفة طريقة تنظيم المجتمع في عندنا أسس الأسس 
+
+35
+00:03:26,610 --> 00:03:32,690
+المُستمدة منها فلسفة طريقة تنظيم المجتمع طبعًا طريقة 
+
+36
+00:03:32,690 --> 00:03:37,950
+تنظيم المجتمع يعني و...و الخدمة الاجتماعية 
+
+37
+00:03:37,950 --> 00:03:42,470
+عمومًا شهدت يعني في السنوات الماضية أو من الخمسينات 
+
+38
+00:03:42,470 --> 00:03:45,690
+و...و...أو يعني من القرن الماضي في أواخر القرن 
+
+39
+00:03:45,690 --> 00:03:51,630
+الماضي يعني تطورًا كبيرًا جداً من حيث الفلسفة فذلك 
+
+40
+00:03:51,630 --> 00:03:56,580
+الجمعية الأمريكية للأخصائيين الاجتماعيين سنة 1951 
+
+41
+00:03:56,580 --> 00:04:01,240
+أشارت إلى القيم المثالية كقيم لمهنة الخدمة 
+
+42
+00:04:01,240 --> 00:04:04,160
+الاجتماعية ما هي هذه القيم اللي أشارت إليها 
+
+43
+00:04:04,160 --> 00:04:08,960
+الجمعية الأمريكية للأخصائيين الاجتماعيين أول قيمة 
+
+44
+00:04:08,960 --> 00:04:15,660
+احترام كرامة الإنسان احترام الكرامة أول قيمة 
+
+45
+00:04:15,660 --> 00:04:21,840
+الإنسان هذا مُكرم فلذلك لابد من احترام كرامته كرامة 
+
+46
+00:04:21,840 --> 00:04:26,840
+هذا الإنسان وفرديته لأن كل إنسان له فردية خاصة به 
+
+47
+00:04:26,840 --> 00:04:32,520
+خصوصيته فلذلك لابد من احترام هذه الكرامة والأديان 
+
+48
+00:04:32,520 --> 00:04:37,580
+كلها حثت على احترام كرامة الإنسان لذلك لابد من 
+
+49
+00:04:37,580 --> 00:04:42,800
+احترام كرامة الإنسان أي كان هذا الإنسان وايضًا لابد 
+
+50
+00:04:42,800 --> 00:04:48,280
+من كذلك احترام خصوصية هذا الإنسان وفردية هذا 
+
+51
+00:04:48,280 --> 00:04:55,020
+الإنسان واضح؟ هذه القيمة الأولى اللي حددتها 
+
+52
+00:04:55,020 --> 00:04:58,180
+الجمعية الأمريكية للأخصائيين الاجتماعيين في قيمة 
+
+53
+00:04:58,180 --> 00:05:02,920
+ثانية أيضًا أكدتها الجمعية الأمريكية للأخصائيين 
+
+54
+00:05:02,920 --> 00:05:06,820
+الاجتماعيين تأكيد على حق الفرد في التمسك بقرائمه 
+
+55
+00:05:06,820 --> 00:05:11,200
+والتعبير عنهم طبعًا التمسك بقرائمه التعبير عن قرائم 
+
+56
+00:05:11,200 --> 00:05:15,280
+الحرية الفردية في النقاش والحوار والتعبير عن 
+
+57
+00:05:15,280 --> 00:05:19,730
+مُقومات نفس الفرد وأن يعبر الفرد عن ما يجول في 
+
+58
+00:05:19,730 --> 00:05:24,030
+خاطره، هذا حق للفرد ونحن كأخصائيين اجتماعيين يجب 
+
+59
+00:05:24,030 --> 00:05:28,230
+مساعدة الأفراد والمجتمعات على التعبير عن نفسها 
+
+60
+00:05:28,230 --> 00:05:33,610
+وعن حرياتها الفرد يعبر عن حريته وعن آرائه وأفكاره 
+
+61
+00:05:33,610 --> 00:05:39,770
+وقيمه، هذه حرية للإنسان ولذلك الأديان أيضًا احترمت 
+
+62
+00:05:39,770 --> 00:05:44,190
+هذه الحرية فالجمعية 
+
+63
+00:05:44,190 --> 00:05:48,670
+الأمريكية حثت على هذه القيمة اللي هي قيمة حق الفرق 
+
+64
+00:05:48,670 --> 00:05:55,530
+في التمسك بآرائه والتعبير عنها تعبير عنها ماذا 
+
+65
+00:05:55,530 --> 00:05:59,810
+أيضًا من القيم؟ أيها بنتي حق الإنسان في تقرير مصيره 
+
+66
+00:05:59,810 --> 00:06:04,810
+تقرير المصير وهذا حق للإنسان أن يقرر مصيره كيف ما 
+
+67
+00:06:04,810 --> 00:06:09,970
+يريد في حدود المصلحة العامة بحيث الله يدور نفسه و 
+
+68
+00:06:09,970 --> 00:06:14,250
+الله يدور الآخرين والله يدور مجتمعي فله حق تقرير 
+
+69
+00:06:14,250 --> 00:06:19,010
+المصير وهذا حق وهذا قيمة من القيم أيضًا دعت إليها 
+
+70
+00:06:19,010 --> 00:06:22,710
+الجمعية الأمريكية للأخصائيين الاجتماعيين منذ عام 
+
+71
+00:06:22,710 --> 00:06:31,710
+1951 يعني منذ منتصف القرن الماضي طبعًا 
+
+72
+00:06:31,710 --> 00:06:35,770
+هذه هي القيم اللي إحنا ذكرناها الكرامة كرامة 
+
+73
+00:06:35,770 --> 00:06:40,050
+الإنسان حق الفرد في التعبير عن قرائمه حق الإنسان في 
+
+74
+00:06:40,050 --> 00:06:44,190
+تقرير مصيره هذه حدثت عليها اللي هي الجمعية 
+
+75
+00:06:44,190 --> 00:06:48,090
+الأمريكية للأخصائيين الاجتماعيين في عندنا الأسس 
+
+76
+00:06:48,090 --> 00:06:57,350
+المُستمدة منها فلسفة طريقة تنظيم المجتمع طبعًا في 
+
+77
+00:06:57,350 --> 00:07:03,970
+عندنا بالنسبة للأسس المُستمدة منها فلسفة طريقة 
+
+78
+00:07:03,970 --> 00:07:12,250
+تنظيم المجتمع في بعض العلماء يعني أكدوا على معظم 
+
+79
+00:07:12,250 --> 00:07:15,270
+المحاولات الفلسفية لمهنة الخدمة الاجتماعية خلال 
+
+80
+00:07:15,270 --> 00:07:23,970
+الثمانينات والتسعينات على يد كل من سكورن وينكس 
+
+81
+00:07:23,970 --> 00:07:30,090
+ودانهام ورولاند فريدرك عن 1982 وهو وورث ولارثن 
+
+82
+00:07:30,440 --> 00:07:34,840
+هدول عن 83 أكدوا كلهم على ماذا؟ على ضرورة النظرة 
+
+83
+00:07:34,840 --> 00:07:39,880
+إلى الإنسان في إطار متكامل النظرة إلى الإنسان في 
+
+84
+00:07:39,880 --> 00:07:48,260
+إطار متكامل بأخذ بحيث ياخذ في اعتباره التالي ما هي 
+
+85
+00:07:48,260 --> 00:07:52,180
+الاعتبارات التي ممكن نأخذها عن هذا الإنسان؟ فردية 
+
+86
+00:07:52,180 --> 00:07:56,300
+الإنسان واحترام كرامته فردية الإنسان واحترام كرامته 
+
+87
+00:07:56,300 --> 00:08:00,600
+لابد أن نحترم فردية هذا الإنسان وكرامة هذا الإنسان 
+
+88
+00:08:00,600 --> 00:08:04,140
+واتكلمنا عنها قبل قليل أيضًا ماذا أيضًا استخدام 
+
+89
+00:08:04,140 --> 00:08:07,140
+موارد المجتمع لمواجهة المشكلات استخدام موارد 
+
+90
+00:08:07,140 --> 00:08:10,680
+المجتمع لمواجهة مشكلات المجتمع وطبعًا لما نتكلم عن 
+
+91
+00:08:10,680 --> 00:08:15,140
+الموارد الموارد المادية الموارد البشرية الموارد 
+
+92
+00:08:15,140 --> 00:08:19,540
+التكنولوجية الموارد القانونية كل ما يتعلق بموارد 
+
+93
+00:08:19,540 --> 00:08:24,360
+المجتمع أن نستخدم هذه الموارد من أجل مواجهة مشكلات 
+
+94
+00:08:24,360 --> 00:08:27,800
+الإنسان حتى يستطيع الإنسان أن يواجه بها مشكلات 
+
+95
+00:08:27,800 --> 00:08:31,460
+ويحل مشكلات من خلال الموارد الموجودة في المجتمع، 
+
+96
+00:08:31,460 --> 00:08:37,260
+ماذا أيضًا؟ طبعًا 
+
+97
+00:08:37,260 --> 00:08:41,420
+نبذ التفرقة العنصرية هذا يعني أيضًا في مهنة الخدمة 
+
+98
+00:08:41,420 --> 00:08:47,660
+الاجتماعية نحن ضد التفرقة العنصرية، نحن أبدًا كل 
+
+99
+00:08:47,660 --> 00:08:52,260
+الأجناس متساوية، والناس كسنان المشط، كل الناس 
+
+100
+00:08:52,260 --> 00:08:56,720
+سواسية، طبعًا ديننا حثنا على ذلك أيضًا، والأديان 
+
+101
+00:08:56,720 --> 00:09:08,090
+كلها تحث على ذلك على عدم التفرقة العنصرية فلذلك 
+
+102
+00:09:08,090 --> 00:09:12,950
+أيضًا هذا لون مضاعف الاعتبار اللي هي نبذ التفرقة 
+
+103
+00:09:12,950 --> 00:09:18,950
+العنصرية بكل صورها من حيث اللون والجنس والدين وغير 
+
+104
+00:09:18,950 --> 00:09:27,020
+ذلك والقومية والعنصرية بكافة خصائصها أيضًا تحقيق 
+
+105
+00:09:27,020 --> 00:09:31,300
+العدالة الاجتماعية وهذا ما تسعى إليه مهنة الخدمة 
+
+106
+00:09:31,300 --> 00:09:34,760
+الاجتماعية أيضًا تنظر إلى الإنسان بأنه لابد 
+
+107
+00:09:34,760 --> 00:09:39,080
+الإنسان أن يعيش في مجتمع يعني تحقق...نحقق له 
+
+108
+00:09:39,080 --> 00:09:44,020
+العدالة الاجتماعية بحيث ألا يشعر هناك فرق بينه 
+
+109
+00:09:44,020 --> 00:09:49,000
+وبين غيره في الحقوق والواجبات كل إنسان لابد أن 
+
+110
+00:09:49,000 --> 00:09:54,160
+يأخذ حقه من داخل المجتمع ألا تكون طبقة أو فئة من 
+
+111
+00:09:54,160 --> 00:09:59,020
+فئات المجتمع تستحوذ على موارد المجتمع أو تكون طبقة 
+
+112
+00:09:59,020 --> 00:10:03,220
+من طبقات المجتمع تستولي على موارد المجتمع وتترك 
+
+113
+00:10:03,220 --> 00:10:08,780
+باقي الطبقات الأخرى الفقيرة الكادحة وغير ذلك لأ 
+
+114
+00:10:08,780 --> 00:10:15,640
+أيضًا لابد من تحقيق العدالة الاجتماعية وأيضًا ليه 
+
+115
+00:10:15,640 --> 00:10:20,220
+العدالة لمين؟ للمستحقين المظلومين المقهورين 
+
+116
+00:10:20,220 --> 00:10:27,070
+المسلبين الحقوق وداخل المجتمعات الفقراء الضعفاء 
+
+117
+00:10:27,070 --> 00:10:32,950
+داخل المجتمع هذول لابد نقف بجانبهم بجانبهم لابد نقف 
+
+118
+00:10:32,950 --> 00:10:37,250
+بجانبهم ونساعدهم لكي ينالوا حقوقهم ويتم تحقيق 
+
+119
+00:10:37,250 --> 00:10:42,490
+مبدأ العدالة الاجتماعية لهم ولغيرهم داخل المجتمع 
+
+120
+00:10:42,490 --> 00:10:47,570
+في عندنا محاولات مُبدعة لسياقة فلسفة في طريقة تنظيم 
+
+121
+00:10:47,570 --> 00:10:52,480
+المجتمع على مستوى النطاق العربي سنتناول الدكتورة 
+
+122
+00:10:52,480 --> 00:10:58,100
+هند بدران والدكتور سيد أبو بكر ومحاولة أيضًا أخيرة 
+
+123
+00:10:58,100 --> 00:11:04,140
+سناخذ الدكتورة هودى بدران الدكتورة 
+
+124
+00:11:04,140 --> 00:11:09,680
+هودى بدران هذه أستاذة في تنظيم المجتمع درست طريقة 
+
+125
+00:11:09,680 --> 00:11:13,080
+تنظيم المجتمع والخدمة الاجتماعية بشكل عام في 
+
+126
+00:11:13,080 --> 00:11:16,680
+الولايات المتحدة الأمريكية وكانت من رواد 
+
+127
+00:11:19,350 --> 00:11:23,010
+مهنة الخدمة...رواد الخدمة الاجتماعية في مصر في 
+
+128
+00:11:23,010 --> 00:11:30,250
+الستينات في الستينات فلذلك يعني لها كتب عن طريق 
+
+129
+00:11:30,250 --> 00:11:37,830
+تنظيم المجتمع ولذلك سنتعرف على محاولاتها في اللي 
+
+130
+00:11:37,830 --> 00:11:43,250
+هي تنظيم المجتمع من حيث الفلسفة فلسفة طريق تنظيم 
+
+131
+00:11:43,250 --> 00:11:51,130
+المجتمع طبعًا أي مجتمع ما هي وظيفة أي مجتمع هي إشباع 
+
+132
+00:11:51,130 --> 00:11:54,610
+حاجات أفراده عن طريق المنظمات الموجودة في المجتمع 
+
+133
+00:11:54,610 --> 00:11:59,950
+لأن إحنا قلنا المؤسسة تنشأ لحاجة بإشباع حاجة أو حل 
+
+134
+00:11:59,950 --> 00:12:05,110
+مشكلة أو مشكلات داخل المجتمع فلذلك من هنا اللي هي 
+
+135
+00:12:05,110 --> 00:12:10,230
+وظيفة أي مجتمع هو إشباع الحاجات الخاصة بأفراده عن 
+
+136
+00:12:10,230 --> 00:12:14,490
+طريق المنظمات أو المؤسسات الموجودة في المجتمع 
+
+137
+00:12:19,140 --> 00:12:22,860
+تنظيم المجتمع هي أداة هامة في إحداث التغييرات 
+
+138
+00:12:22,860 --> 00:12:27,200
+في التنظيمات الاجتماعية لتصبح أكثر قدرة على مقابلة 
+
+139
+00:12:27,200 --> 00:12:31,780
+حاجات أفراد المجتمع وفي تحقيق العدالة الاجتماعية 
+
+140
+00:12:31,780 --> 00:12:37,020
+بين فئات المجتمع وفي الإسهام بعمليات التنمية 
+
+141
+00:12:37,020 --> 00:12:41,780
+القومية عن طريق تنمية الوحدات المحلية والمجتمعات 
+
+142
+00:12:41,780 --> 00:12:46,240
+المحلية وعلى هذا ترتكز فلسفة تنظيم المجتمع على 
+
+143
+00:12:46,240 --> 00:12:51,990
+القيم على ماذا ترتكز فلسفة تنظيم المجتمع؟ على 
+
+144
+00:12:51,990 --> 00:12:55,350
+مجموعة من القيم التي كانت طريقة فيها طريقة القيم، 
+
+145
+00:12:55,350 --> 00:12:59,890
+إذاً أول شيء القيم ترتكز فلسفة طريقة تنظيم 
+
+146
+00:12:59,890 --> 00:13:03,170
+المجتمع على مجموعة القيم، هذه عند من؟ عند الدكتورة 
+
+147
+00:13:03,170 --> 00:13:06,450
+هودى بدران، ما هي القيم عند الدكتورة هودى بدران 
+
+148
+00:13:06,450 --> 00:13:14,390
+التي حددتها لفلسفة طريقة تنظيم المجتمع؟ الجهة هذه، 
+
+149
+00:13:14,390 --> 00:13:19,270
+أيوه يا بنتي، على تَرَقُّبِ درام التطبيقات أول شيء الاعتراف 
+
+150
+00:13:19,270 --> 00:13:24,450
+بكرامة الفرد وقيمته كإنسان لابد أن نحافظ على الفرد 
+
+151
+00:13:24,450 --> 00:13:27,990
+وعلى الإنسان عندما يأتي الإنسان لطلب المساعدة من 
+
+152
+00:13:27,990 --> 00:13:32,250
+المؤسسة لابد أن نحافظ على كرامة هذا الإنسان وقيمة 
+
+153
+00:13:32,250 --> 00:13:36,310
+هذا الإنسان ونحترم هذا الإنسان ونقدر هذا الإنسان 
+
+154
+00:13:36,310 --> 00:13:41,190
+وإلا نهين هذا الإنسان فالأخصائي الاجتماعي لابد أن 
+
+155
+00:13:41,190 --> 00:13:45,490
+يحترم الإنسان الذي يأتي إلى المؤسسة طلبًا للمساعدة و
+
+156
+00:13:45,490 --> 00:13:48,430
+أحيانًا إذا كانت شروط المؤسسة لا تنطبق على مساعدة 
+
+157
+00:13:48,430 --> 00:13:52,570
+هذا الإنسان لابد أن نحترمه ونقدره كناحية إنسانية 
+
+158
+00:13:52,570 --> 00:13:57,110
+في هذه الحالة يستطيع الإنسان أن يشعر بقيمته و
+
+159
+00:13:57,110 --> 00:14:01,190
+كرامته من الأخصائي الاجتماعي اللي يقابله ونستطيع 
+
+160
+00:14:01,190 --> 00:14:04,970
+أن نحوله إلى مؤسسات أخرى يستفيد من خدماتها هذا هو 
+
+161
+00:14:04,970 --> 00:14:11,890
+المقصود بذلك الكرامة ولذلك الأديان حثت على كرامة 
+
+162
+00:14:11,890 --> 00:14:19,120
+الإنسان كرامة بني آدم فلذلك من هنا لابد أن نحترم 
+
+163
+00:14:19,120 --> 00:14:23,400
+لأن ديننا يحثنا ديننا يحثنا والأديان كلها تحث على 
+
+164
+00:14:23,400 --> 00:14:27,140
+كرامة هذا الإنسان فلذلك لابد أن نحترم الإنسان 
+
+165
+00:14:27,140 --> 00:14:31,080
+وقيمة الإنسان مهما كان هذا الإنسان حتى لو اختلفنا 
+
+166
+00:14:31,080 --> 00:14:35,560
+معه في قراءته لابد أن نحترمه لأن قراءته هذه كل 
+
+167
+00:14:35,560 --> 00:14:40,350
+إنسان له فرديته ولو قراءته الخاصة فلذلك من هنا لابد 
+
+168
+00:14:40,350 --> 00:14:43,710
+أن نحترم هذا الإنسان الذي يأتي إلى المؤسسة ليطلب 
+
+169
+00:14:43,710 --> 00:14:48,170
+المساعدة فهذه تُعتبر من ضمن القيم اللي بتعمل فيها 
+
+170
+00:14:48,170 --> 00:14:54,810
+طريقة تنظيم المجتمع مع ال...اللي هو المجتمعات 
+
+171
+00:14:54,810 --> 00:14:58,250
+اللي هي أول شيء القيمة الأولى المحافظة على كرامة 
+
+172
+00:14:58,250 --> 00:15:03,390
+الفرق وقيمته كإنسان ماذا أيضًا القيمة الثانية؟ 
+
+173
+00:15:03,390 --> 00:15:06,820
+أيها بنتي حرية الناس للتعبير عن احتياجاتهم حرية 
+
+174
+00:15:06,820 --> 00:15:10,600
+الناس في التعبير عن
+
+216
+00:18:19,410 --> 00:18:24,350
+يتخلصوا منهم العجزة والمسنين والأطفال، المرضى وغير
+
+217
+00:18:24,350 --> 00:18:29,620
+ذلك، فلذلك كانوا يعني يتخلصون منهم وهم أحياء.  لأ احنا 
+
+218
+00:18:29,620 --> 00:18:35,160
+مع مهنة الخدمة الاجتماعية،  و أيضا ديننا الإسلامي 
+
+219
+00:18:35,160 --> 00:18:38,740
+كذلك يحفظنا على ذلك،  استثمار كافة القدرات عند
+
+220
+00:18:38,740 --> 00:18:42,740
+الإنسان، فلذلك أيضا مهنة الخدمة الاجتماعية تستمد
+
+221
+00:18:42,740 --> 00:18:46,600
+فلسفتها من الأديان، و خاصة عندنا الدين الإسلامي، أن
+
+222
+00:18:46,600 --> 00:18:49,940
+الإنسان قادر على النمو، قادر على العمل، قادر على 
+
+223
+00:18:49,940 --> 00:18:54,480
+الإنتاج، فهذه تعتبر قيمة. فمهما أتى أي إنسان لنا إلى
+
+224
+00:18:54,480 --> 00:18:59,340
+المؤسسة يطلب مساعدة، لابد من دراسة إمكانياته وقدراته
+
+225
+00:18:59,340 --> 00:19:06,880
+حتى نستطيع أن نؤهله للعمل وللإنتاج، المجتمعات
+
+226
+00:19:06,880 --> 00:19:11,240
+الفقيرة لو كان هناك تخطيط سليم، لا يوجد فقر في 
+
+227
+00:19:11,240 --> 00:19:15,780
+المجتمعات الفقيرة، ليه؟ لو أهلنا ذوي القدرات
+
+228
+00:19:15,780 --> 00:19:19,960
+الموجودة في المجتمع، كل حسب قدراته، إلى مهنة معينة 
+
+229
+00:19:19,960 --> 00:19:24,920
+حرفة معينة، عمل معين، ينتجه، لا نجد فقراء في المجتمع
+
+230
+00:19:24,920 --> 00:19:30,080
+فلذلك نحتاج إلى الإيمان بقدرة الإنسان على العطاء
+
+231
+00:19:30,080 --> 00:19:35,000
+وعلى النمو، وعلى التأهيل المهني والتأهيل الاجتماعي
+
+232
+00:19:35,000 --> 00:19:39,580
+والنفسي والعمل داخل المجتمع. فهذه تعتبر قيمة من قيم 
+
+233
+00:19:39,580 --> 00:19:44,460
+طريقة تنظيم المجتمع، وهي قدرة الإنسان على النمو
+
+234
+00:19:44,460 --> 00:19:49,740
+قدرة الإنسان على النمو والعطاء والإنتاج، مهما كان
+
+235
+00:19:49,740 --> 00:19:58,240
+هذا الإنسان. ولذلك اليوم عندنا نجد يعني فئات مثلًا في
+
+236
+00:19:58,240 --> 00:20:02,480
+فئات مثل المعاقين مثلا في المجتمع، زمان كانوا 
+
+237
+00:20:02,480 --> 00:20:05,820
+يقولوا هذول معاقين وكذا. لأ لأ اليوم بالعكس، نجد بعض
+
+238
+00:20:05,820 --> 00:20:10,960
+الأفراد من المعاقين أقدر من الأسوياء في الإنتاج وفي
+
+239
+00:20:10,960 --> 00:20:15,120
+العطاء، سواء كان إنتاج علمي، إنتاج اقتصادي، إنتاج
+
+240
+00:20:15,120 --> 00:20:21,000
+زراعي، صناعي، أي غير ذلك من الأعمال، فكري، أدبي، نجدهم
+
+241
+00:20:21,000 --> 00:20:25,960
+يعني مبدعين، اليوم إبداع عندهم. فلذلك لابد أن نؤمن 
+
+242
+00:20:25,960 --> 00:20:30,870
+بهذه القدرات المختلفة.  أيضا في عندنا قيمة أخرى من
+
+243
+00:20:30,870 --> 00:20:35,990
+القيم اللي بتعمل في إطارها طريقة تنظيم المجتمع، حق 
+
+244
+00:20:35,990 --> 00:20:38,650
+الأفراد، اللي يحصلوا على الضرورات الأساسية للحياة
+
+245
+00:20:38,650 --> 00:20:43,650
+طبعا كل فرد له حق الحصول على الضرورات الأساسية، ما 
+
+246
+00:20:43,650 --> 00:20:49,190
+هي الضرورات الأساسية؟ المأكل، المشرب، الملبس،
+
+247
+00:20:49,190 --> 00:20:57,200
+المسكن، الصحة، التعليم.  مش هذه ضرورات؟ الدولة مسؤولة عن
+
+248
+00:20:57,200 --> 00:21:00,680
+توفير هذه الضرورات للإنسان، والإنسان مسئول أيضًا
+
+249
+00:21:00,680 --> 00:21:04,400
+والجهات المسؤولة داخل المجتمع مسؤولة عن توفر هذه
+
+250
+00:21:04,400 --> 00:21:08,500
+الأمور لهذا الإنسان. فلذلك من هنا، هذه تعتبر قيمة
+
+251
+00:21:08,500 --> 00:21:12,080
+وقيم مهنة الخدمة الاجتماعية، توفير الضرورات
+
+252
+00:21:12,080 --> 00:21:16,960
+الأساسية لهذا الإنسان داخل المجتمع. مقابل توفير هذه
+
+253
+00:21:16,960 --> 00:21:21,060
+الضرورات، لابد الإنسان أن يؤدي ما عليه من واجبات 
+
+254
+00:21:21,060 --> 00:21:27,100
+اتجاه المجتمع. فهذه حقوق، وعليه واجبات، أن يأخذ حقوقه 
+
+255
+00:21:27,100 --> 00:21:31,160
+وفي نفس الوقت يؤدي ما عليه من واجبات اتجاه المجتمع
+
+256
+00:21:31,160 --> 00:21:37,640
+هذه أيضًا قيمة من القيم الخاصة بطريقة تنظيم المجتمع
+
+257
+00:21:37,640 --> 00:21:41,840
+وهي حق الأفراد في الحصول على الضروريات الأساسية
+
+258
+00:21:41,840 --> 00:21:48,880
+للحياة، الطعام، الملبس، المسكن، لغير ذلك. هذه طبعًا بدون
+
+259
+00:21:48,880 --> 00:21:52,260
+هذه الضرورات، هل يستطيع الإنسان أن يعيش؟ لا يمكن
+
+260
+00:21:52,260 --> 00:21:56,460
+فهذه ضرورات أساسية، فلابد من التفكير في توفير هذه
+
+261
+00:21:56,460 --> 00:22:01,420
+الضروريات الأساسية للإنسان. وهذه مسئولية الدولة 
+
+262
+00:22:01,420 --> 00:22:04,960
+مسئولية المنظمات داخل المجتمع، الحكومية والاهلية 
+
+263
+00:22:04,960 --> 00:22:09,520
+مسئولية كل قادة المجتمع، وكل وكل أفراد المجتمع كذلك
+
+264
+00:22:09,520 --> 00:22:13,280
+لابد أن يشتركوا في ذلك، في توفير الضروريات لهم
+
+265
+00:22:16,450 --> 00:22:22,930
+أيضًا في عندنا كذلك 
+
+266
+00:22:22,930 --> 00:22:27,030
+طريقة تنظيم المجتمع تتحمل المسئولية التي حملتها
+
+267
+00:22:27,030 --> 00:22:31,230
+مهنة وخدمة اجتماعية. ما هي هذه المسئولية اللي
+
+268
+00:22:31,230 --> 00:22:35,490
+حملتها مهنة وخدمة اجتماعية؟ طبعًا احنا عارفين طريقة
+
+269
+00:22:35,490 --> 00:22:39,970
+تنظيم المجتمع من طرق مهنة وخدمة اجتماعية. فلذلك هي
+
+270
+00:22:39,970 --> 00:22:44,070
+تعتبر متكاملة مع باقي الطرق، خدمة الفرد وخدمة 
+
+271
+00:22:44,070 --> 00:22:48,290
+الجماعة، في إطار مهنة الخدمة الاجتماعية. فلذلك
+
+272
+00:22:48,290 --> 00:22:52,010
+الطريقة هذه، تنظيم المجتمع، تتحمل المسئولية اللي
+
+273
+00:22:52,010 --> 00:22:57,230
+حملتها مهنة الخدمة الاجتماعية ككل. مثل ماذا؟ إنصاف 
+
+274
+00:22:57,230 --> 00:23:00,410
+الفئات الضعيفة في المجتمع، إنصاف الفئات الضعيفة في 
+
+275
+00:23:00,410 --> 00:23:05,390
+المجتمع. إنصاف الفئات الضعيفة، دائما احنا مهنتنا
+
+276
+00:23:05,390 --> 00:23:09,810
+مهنة الخدمة الاجتماعية، مهنة الضعفاء والفقراء
+
+277
+00:23:09,810 --> 00:23:14,150
+والمظلومين والمقهورين. لابد أن نقف بجوارهم، لابد أن 
+
+278
+00:23:14,150 --> 00:23:21,630
+نساعدهم. هؤلاء، مهنة الطبيب للمرضى، مهنة المعلم
+
+279
+00:23:21,630 --> 00:23:28,370
+للتعليم، طب احنا لخصائنا الاجتماعية، نساعد المحتاجين، 
+
+280
+00:23:28,370 --> 00:23:32,690
+نساعد الضعفاء، نساعد المقهورين، المظلومين. لابد أن 
+
+281
+00:23:32,690 --> 00:23:36,450
+نقف بجوارهم، هذه مهنتنا، لابد دائما نقف بجوار
+
+282
+00:23:36,450 --> 00:23:40,330
+الإنسان المحتاج، اللي يطلب المساعدة، مهما كان هذا
+
+283
+00:23:40,330 --> 00:23:43,550
+الإنسان. إذا الفئات الضعيفة لابد أن نتصرف داخل
+
+284
+00:23:43,550 --> 00:23:47,550
+المجتمع، لابد أن نقف بجوارهم، لابد أن نساعدهم على
+
+285
+00:23:47,550 --> 00:23:52,690
+تحقيق مطالبهم، وتحقيق العدالة الاجتماعية لهم، هذه 
+
+286
+00:23:52,690 --> 00:23:58,640
+من أيضا اللي هي تتحملها طريقة التنظيم المجتمع اللي
+
+287
+00:23:58,640 --> 00:24:03,060
+هي إنصاف الفئات الضعيفة في المجتمع، مهما كانت هذه
+
+288
+00:24:03,060 --> 00:24:09,600
+الفئات. طبعًا فئات ضعيفة كثيرة في المجتمع، الأطفال
+
+289
+00:24:09,600 --> 00:24:15,100
+أحيانًا المرأة، المسنين، أحيانًا المرضى كذلك، ده في 
+
+290
+00:24:15,100 --> 00:24:20,280
+المجتمع. العمال أيضا، هدول ناس ذالبين يجدوا العمل
+
+291
+00:24:20,280 --> 00:24:24,240
+لابد من أن نساعدهم، كيفية مساعدتهم على العمل والإنتاج
+
+292
+00:24:24,770 --> 00:24:30,190
+هؤلاء لابد نقف بجوارهم. الفقراء، المعاقين، الذين
+
+293
+00:24:30,190 --> 00:24:33,530
+يحتاجون للتأهيل المهني، التأهيل النفسي، التأهيل
+
+294
+00:24:33,530 --> 00:24:37,870
+الاجتماعي، التأهيل الصحي، وغير ذلك، هؤلاء لابد نقف
+
+295
+00:24:37,870 --> 00:24:42,790
+بجوارهم دائما. إذا، لابد من إنصاف الفئات الضعيفة في
+
+296
+00:24:42,790 --> 00:24:47,090
+المجتمع. ماذا أيضًا من المسؤولية بتتحملها مهنتي اللي 
+
+297
+00:24:47,090 --> 00:24:51,550
+هي طريقة تنظيم المجتمع، اللي هي مساعدة في تحقيق
+
+298
+00:24:51,550 --> 00:24:57,050
+العدالة الاجتماعية، العدالة المجتمعية بين فئات 
+
+299
+00:24:57,050 --> 00:25:01,690
+المجتمع. تحقيق العدالة للجميع داخل المجتمع، بين فئات
+
+300
+00:25:01,690 --> 00:25:09,100
+المجتمع المختلفة. لابد من تحقيق العدالة حتى لا يكون
+
+301
+00:25:09,100 --> 00:25:12,920
+هناك تحيز، ولا تكون هناك طبقة أو فئة يعني تاخد
+
+302
+00:25:12,920 --> 00:25:17,700
+مساعدات على حساب مساعدة... على حساب فئات أخرى، أو
+
+303
+00:25:17,700 --> 00:25:22,160
+مجتمع محلي ياخد امتيازات على حساب مجتمع محلي آخر
+
+304
+00:25:22,160 --> 00:25:26,580
+إذا، هنا لابد من تحقيق العدالة الاجتماعية لجميع 
+
+305
+00:25:26,580 --> 00:25:32,060
+فئات المجتمع، ولجميع المجتمعات المحلية داخل 
+
+306
+00:25:32,060 --> 00:25:38,290
+المجتمع. أيضًا، محاولة التأثير في القرارات التي تتخذ
+
+307
+00:25:38,290 --> 00:25:42,650
+في المجتمع، والخاصة بالبرامج والمشروعات والخدمات 
+
+308
+00:25:42,650 --> 00:25:47,190
+بحيث تؤدي تلك القرارات إلى مساعدة ذوي النفوذ
+
+309
+00:25:47,190 --> 00:25:51,470
+المحدود، فلا تنفرد المجتمعات القوية بالمشروعات
+
+310
+00:25:51,470 --> 00:26:00,230
+والبرامج. يعني مثلًا، مجتمع محلي، مجتمع 
+
+311
+00:26:00,230 --> 00:26:05,340
+محلي ممكن يستحوذ على برامج ومشاريع يعني تأهيلية له 
+
+312
+00:26:05,340 --> 00:26:11,620
+وذات منفعة اقتصادية وإنتاجية أكثر من مجتمع محلي آخر
+
+313
+00:26:11,620 --> 00:26:16,120
+طبعا، هل هذا فيه عدالة؟ لأ، طبعا لا يوجد عدالة، إذا
+
+314
+00:26:16,120 --> 00:26:19,520
+لابد من تحقيق العدالة بين هذه المجتمعات في توزيع
+
+315
+00:26:19,520 --> 00:26:23,380
+البرامج والمشروعات والخدمات على فئات المجتمع، في
+
+316
+00:26:23,380 --> 00:26:27,840
+كافة فئات المجتمع. فلذلك من هنا لابد من التأثير في 
+
+317
+00:26:27,840 --> 00:26:31,240
+القرارات التي تتخذ في المجتمع، بأن هذه القرارات
+
+318
+00:26:31,240 --> 00:26:35,300
+للبرامج والمشاريع والخدمات، أن تكون فيها نوع من إيه؟
+
+319
+00:26:35,300 --> 00:26:39,540
+من العدالة للجميع، لجميع المجتمعات المحلية، وقلة 
+
+320
+00:26:39,540 --> 00:26:46,120
+نهم مجتمع محدد على حساب مجتمع آخر. واضح؟ لابد
+
+321
+00:26:46,120 --> 00:26:50,620
+يكون العدالة تتحقق، وهكذا فينا جميع المجتمعات
+
+322
+00:26:50,620 --> 00:26:54,720
+المحلية داخل المجتمع العام. طبعا إحنا عارفين أي
+
+323
+00:26:54,720 --> 00:26:58,940
+مجتمع عام، دولة أو مجتمع عام، يتكون من مجتمعات
+
+324
+00:26:58,940 --> 00:27:03,960
+محلية صغيرة، وهكذا، ويتكون من مدن وهكذا. إذن المدن
+
+325
+00:27:03,960 --> 00:27:07,500
+والمجتمعات المحلية، لابد القرارات عندما تتخذ
+
+326
+00:27:07,500 --> 00:27:12,780
+لمشاريع أو برامج أو خطط، لابد أن توزع بالعدالة بين
+
+327
+00:27:12,780 --> 00:27:17,540
+هذه المجتمعات جميعًا، ننظر إليها بنظرة العدالة
+
+328
+00:27:17,540 --> 00:27:21,480
+وطبعًا 
+
+329
+00:27:21,480 --> 00:27:24,800
+ما تتنفذش هنا، أو تنفرد جماعات قوية بالمشروعات 
+
+330
+00:27:24,800 --> 00:27:29,020
+والبرامج على حساب جماعات أخرى، يعني جماعات لديها 
+
+331
+00:27:29,020 --> 00:27:32,950
+السلطة والنفوذ وغير ذلك. لأ طبعًا، لأ، الخدمة 
+
+332
+00:27:32,950 --> 00:27:35,850
+الاجتماعية لا تعرف ذلك، ولا طريقة تنظيم المجتمع
+
+333
+00:27:35,850 --> 00:27:39,910
+تعرف ذلك، تعرف أن تحقيق العدالة الاجتماعية بين
+
+334
+00:27:39,910 --> 00:27:48,950
+الجميع. أيضًا، طريقة تنظيم المجتمع أدى لها أهميتها في 
+
+335
+00:27:48,950 --> 00:27:53,470
+إيش؟ ما أهمية طريقة تنظيم المجتمع؟ استثارة 
+
+336
+00:27:53,470 --> 00:27:58,770
+المجتمعات المحلية، استثارة المجتمعات المحلية، تحريكها 
+
+337
+00:27:58,980 --> 00:28:08,660
+استثارتها. وطبعا لما نقول استثارة، تختلف عن الإثارة
+
+338
+00:28:08,660 --> 00:28:14,520
+استثارة تختلف عن الإثارة، الإثارة تعتمد عن جوانب
+
+339
+00:28:14,520 --> 00:28:20,700
+العاطفية، أما الاستثارة تعتمد عن جوانب العقلية في 
+
+340
+00:28:20,700 --> 00:28:26,120
+الإقناع والتوضيح والتبصير. استثارة سكان المجتمع حول
+
+341
+00:28:26,120 --> 00:28:31,430
+مشكلاتهم، حول احتياجاتهم، حول مواردها، ومعرفة المشكلات
+
+342
+00:28:31,430 --> 00:28:35,490
+والحاجات، ومعرفة الموارد الموجودة في المجتمع، وكيفية 
+
+343
+00:28:35,490 --> 00:28:39,330
+استخدام هذه الموارد في علاج مشكلتهم وإشباع 
+
+344
+00:28:39,330 --> 00:28:43,030
+احتياجاتهم. هذه الاستثارة، أحيانًا يعيش سكان 
+
+345
+00:28:43,030 --> 00:28:47,460
+المجتمع ولا يعلم عن مشكلاته، ولا يعلم عن موارده. إذا 
+
+346
+00:28:47,460 --> 00:28:50,980
+هنا يحتاج من خلال طريقة منظمة المجتمع إلى نوع من
+
+347
+00:28:50,980 --> 00:28:55,660
+إيه؟ من الاستثارة، وهي التوضيح والتبصير عن ما يوجد
+
+348
+00:28:55,660 --> 00:28:59,280
+في المجتمع من مشكلات وحاجات، وعن ما يوجد من موارد 
+
+349
+00:28:59,280 --> 00:29:03,580
+وإمكانيات، وكيفية استخدام الموارد والإمكانيات في
+
+350
+00:29:03,580 --> 00:29:08,560
+علاج المشكلات وإشباع الحاجات، هذا المقصود بهذه 
+
+351
+00:29:08,560 --> 00:29:13,210
+العبارة، وهي استثارة المجتمعات المحلية حول مشكلتها 
+
+352
+00:29:13,210 --> 00:29:16,810
+وحول مواردها، وكيفية استخدام الموارد لعلاج
+
+353
+00:29:16,810 --> 00:29:21,290
+المشكلة، واضح؟ أما الإثارة، الإثارة تعتمد على
+
+354
+00:29:21,290 --> 00:29:25,210
+الجوانب العاطفية، وهي مستخدمها للإعلام والإعلان
+
+355
+00:29:25,210 --> 00:29:30,270
+التجاري وغير ذلك، وسرعان ما تنتهي الإثارة بزوال
+
+356
+00:29:30,270 --> 00:29:33,090
+الإعلان، أو الانتهاء من استماع من الإعلان أو غير 
+
+357
+00:29:33,090 --> 00:29:36,370
+ذلك، أو رؤية الإعلان في التلفاز أو الاستماع ليه في
+
+358
+00:29:36,370 --> 00:29:41,170
+الإذاعة. لكن الاستثارة تجب جانب عقلي، توضيح وتبصير
+
+359
+00:29:41,170 --> 00:29:45,700
+للناس حول المشكلات، لأن كثير من سكان المجتمع يعيشون
+
+360
+00:29:45,700 --> 00:29:49,100
+في المشكلة ولا يعرفون ما هي المشكلة، فلذلك يحتاجون
+
+361
+00:29:49,100 --> 00:29:57,120
+لتبصير وتوضيح عن المشكلات والموارد. أيضًا، طريقة 
+
+362
+00:29:57,120 --> 00:30:03,860
+تنظيم المجتمع، مهمة تبرز مثلًا في مادة... أيوة بني
+
+363
+00:30:03,860 --> 00:30:07,500
+تفضل، تنظيم جهد هذه المجتمعات، لتخطط وتنفذ برامج
+
+364
+00:30:07,500 --> 00:30:10,590
+النمو المحلية. خلاص، ما احنا عرفنا مشكلات، إذا 
+
+365
+00:30:10,590 --> 00:30:14,550
+معناته لابد من تنظيم جهود هذه المجتمعات حتى نخطط 
+
+366
+00:30:14,550 --> 00:30:20,750
+وننفذ برامج التنمية المحلية. نخطط، تخطيط في موادع
+
+367
+00:30:20,750 --> 00:30:26,790
+الخطط، في موادع البرامج والمشاريع لتنفيذها من أجل
+
+368
+00:30:26,790 --> 00:30:31,750
+تحقيق التنمية المحلية بالمجتمعات. ما تقوم به طريقة 
+
+369
+00:30:31,750 --> 00:30:36,050
+تنظيم المجتمع. فلذلك بنعتبر التخطيط من ضمن عمليات 
+
+370
+00:30:36,050 --> 00:30:42,730
+طريقة تنظيم المجتمع، من العمليات الأساسية. ماذا
+
+371
+00:30:42,730 --> 00:30:50,030
+أيضًا؟ أيها بنتي، الربط بين الجهود الموجودة على
+
+372
+00:30:50,030 --> 00:30:52,850
+المستوى المحلي والقومي من خلال تنمية واحتياجات.
+
+373
+00:30:52,850 --> 00:30:57,510
+كويس. وهذه ما تقوم بها طريقة تنظيم المجتمع، لابد أن 
+
+374
+00:30:57,510 --> 00:31:00,850
+نربط بين الجهود المختلفة على مستوى المجتمعات
+
+375
+00:31:00,850 --> 00:31:06,150
+المحلية كلها، وبين خطط المجتمع القومي ككل حتى لا 
+
+376
+00:31:06,150 --> 00:31:10,610
+تنفرد مجتمعات محلية، أن تكون بعيدة عن الخطط القومية
+
+377
+00:31:10,610 --> 00:31:15,030
+واضح. فلذلك هنا عندما نعمل تنمية في أي مجتمع محلي
+
+378
+00:31:15,030 --> 00:31:19,710
+تنعكس على المجتمع كله. وعندما نعمل خطة على مستوى
+
+379
+00:31:19,710 --> 00:31:24,110
+المجتمع القومي، تنعكس على المجتمعات المحلية. وها كده
+
+380
+00:31:24,110 --> 00:31:28,910
+فلذلك طريقة تنظيم المجتمع يعني تعتبر أداء مهمة في 
+
+381
+00:31:28,910 --> 00:31:33,270
+ذلك، في تحقيق التنمية، وفي تحقيق التنمية على المستوى
+
+382
+00:31:33,270 --> 00:31:38,180
+القومي وعلى المستوى المحلي. فلذلك من خلال تنمية
+
+383
+00:31:38,180 --> 00:31:42,200
+الوحدات المختلفة، تنمية المجتمعات المحلية، القرى
+
+384
+00:31:42,200 --> 00:31:47,100
+والمدن، نستطيع أن نعمل تنمية في مجتمعنا بشكل عام، 
+
+385
diff --git a/PL9fwy3NUQKwaKyeI5iiPpebyFXxlPBffV/QeBsuUIbXsQ.srt b/PL9fwy3NUQKwaKyeI5iiPpebyFXxlPBffV/QeBsuUIbXsQ.srt
new file mode 100644
index 0000000000000000000000000000000000000000..92eca1a5ef6524852e65925351fb5109316dc7b2
--- /dev/null
+++ b/PL9fwy3NUQKwaKyeI5iiPpebyFXxlPBffV/QeBsuUIbXsQ.srt
@@ -0,0 +1,1374 @@
+1
+00:00:20,920 --> 00:00:24,300
+بسم الله الرحمن الرحيم الحمد لله رب العالمين
+
+2
+00:00:24,300 --> 00:00:28,880
+والصلاة والسلام على أشرف المرسلين سيدنا محمد وعلى 
+
+3
+00:00:28,880 --> 00:00:32,940
+آله وصحبه أجمعين بنات/ الطالبات السلام عليكم جميعا
+
+4
+00:00:32,940 --> 00:00:40,180
+ورحمة الله وبركاته، في هذه المحاضرة سنتناول موضوع
+
+5
+00:00:40,180 --> 00:00:46,120
+مبادئ تنظيم المجتمع قبل 
+
+6
+00:00:46,120 --> 00:00:53,590
+الحديث عن كل مبدأ على حدة، نلْبِهِ بأن مبادئ تنظيم
+
+7
+00:00:53,590 --> 00:01:01,330
+المجتمع كلها متداخلة ومتكاملة مع بعضها البعض، لذلك
+
+8
+00:01:01,330 --> 00:01:06,290
+عند الممارسة العملية لطريق تنظيم المجتمع، أطبق مبادئ 
+
+9
+00:01:06,290 --> 00:01:12,050
+تنظيم المجتمع، وممكن أطبق مبدأ وليس معنى المبادئ 
+
+10
+00:01:12,050 --> 00:01:15,650
+الأخرى، أن أنا أتركها، لابد أن أستعين بها، ولكن
+
+11
+00:01:15,650 --> 00:01:20,010
+أحيانًا أركز على مبدأ عند الممارسة يكون أكثر من
+
+12
+00:01:20,010 --> 00:01:24,670
+المبادئ الأخرى وهكذا، ولكن في النهاية جميع المبادئ
+
+13
+00:01:24,670 --> 00:01:29,930
+متكاملة ومتداخلة مع بعضها البعض، سنتناول أول مبدأ
+
+14
+00:01:29,930 --> 00:01:35,640
+في طريق تنظيم المجتمع وهو البدء، مبدأ البدء مع
+
+15
+00:01:35,640 --> 00:01:43,360
+المجتمع كما هو، نعم، البدء مع المجتمع كما هو، هذا 
+
+16
+00:01:43,360 --> 00:01:50,540
+مبدأ يعني بدأنا العمل مع المجتمع، لابد أن نتقبل 
+
+17
+00:01:50,540 --> 00:01:59,620
+المجتمع على حاله كما هو، ولذلك 
+
+18
+00:01:59,620 --> 00:02:04,310
+هذا المبدأ يشبه مبدأ التقبل عندنا في خدمة الفرد، إن 
+
+19
+00:02:04,310 --> 00:02:09,070
+أتقبل المجتمع مثلما أتقبل الفرد، فإن أتقبل المجتمع 
+
+20
+00:02:09,070 --> 00:02:17,450
+بمشكلاته بأوضاعه بحاله، أتقبل هذا المجتمع على أمل 
+
+21
+00:02:17,450 --> 00:02:25,090
+أن أغيره إلى الأفضل وأغيره إلى الأحسن، فلذلك هذا مبدأ 
+
+22
+00:02:25,090 --> 00:02:31,090
+لابد أن أستخدمه عند الممارسة المهنية لطريق تنظيم
+
+23
+00:02:31,090 --> 00:02:39,940
+المجتمع مع المجتمع، فلذلك عندما لابد يعني .. يعني
+
+24
+00:02:39,940 --> 00:02:45,960
+هذا معناه عندما أتعامل مع مشكلات المجتمع، لابد أن 
+
+25
+00:02:45,960 --> 00:02:50,340
+يعني أحس بمشكلات المجتمع، أتعرف على مشكلات المجتمع
+
+26
+00:02:50,340 --> 00:02:55,460
+وألاحظ ماذا يعاني المجتمع من المشكلات، فلذلك عليّ
+
+27
+00:02:55,460 --> 00:02:59,880
+أن أبدأ معه من حياته هو، يعني من حياته ما يعاني من 
+
+28
+00:02:59,880 --> 00:03:07,640
+هذه المشكلات، وبعد ذلك أساعده هو على وضع الخطط
+
+29
+00:03:07,640 --> 00:03:12,600
+والبرامج والمشاريع من أجل معالجة المشكلات التي
+
+30
+00:03:12,600 --> 00:03:22,660
+يعاني منها المجتمع، طبعًا 
+
+31
+00:03:22,660 --> 00:03:27,500
+الهدف في هذا المبدأ اللي هو البدء مع المجتمع كما
+
+32
+00:03:27,500 --> 00:03:33,160
+هو، اللي هو إيجاد الثقة ما بين الأخصائي وما بين 
+
+33
+00:03:33,160 --> 00:03:38,640
+المجتمع، فأنا عندما أتقبل المجتمع كما هو، المجتمع 
+
+34
+00:03:38,640 --> 00:03:44,160
+يتقبلني كأخصائي اجتماعي، هنا تنمو العلاقة المهنية،
+
+35
+00:03:44,160 --> 00:03:49,720
+أستطيع أن أؤثر في المجتمع من أجل مساعدته على علاج
+
+36
+00:03:49,720 --> 00:03:55,250
+مشكلته، فلذلك من هنا هذا المبدأ يستهدف بث ثقة ما بين
+
+37
+00:03:55,250 --> 00:03:59,710
+المنظم الاجتماعي والمجتمع الذي يعمل معه أو
+
+38
+00:03:59,710 --> 00:04:06,190
+المؤسسات التي يعمل فيها أيضًا، في عوامل الآن خلاص
+
+39
+00:04:06,190 --> 00:04:10,890
+عرفنا البدء مع المجتمع كما هو، إن أتقبل المجتمع كما
+
+40
+00:04:10,890 --> 00:04:16,160
+هو بمشكلاته بوضعه بما يعانيه، إلى غير جاهز، على أمل 
+
+41
+00:04:16,160 --> 00:04:20,360
+أني أضع خطط أو أساعد المجتمع على وضع الخطط
+
+42
+00:04:20,360 --> 00:04:24,420
+والبرامج والمشاريع التي تساعدهم على التغلب على
+
+43
+00:04:24,420 --> 00:04:30,490
+مشكلتهم، وطبعًا هنا لما نبدأ مع المجتمع وتقبل المجتمع
+
+44
+00:04:30,490 --> 00:04:34,790
+معناه التقبل بيكون تقبل مشترك، أولًا الأخصائي 
+
+45
+00:04:34,790 --> 00:04:38,550
+الاجتماعي يجب عليه أن يتقبل المجتمع، ثم بعد ذلك
+
+46
+00:04:38,550 --> 00:04:43,530
+المجتمع يتقبل الأخصائي، هنا تبنى ثقة ما بين المنظم
+
+47
+00:04:43,530 --> 00:04:48,470
+والأخصائي، ويستطيع الأخصائي أن يعمل مع المجتمع و
+
+48
+00:04:48,470 --> 00:04:52,950
+يساعد المجتمع على مواجهة مشكلته ويساعد المجتمع
+
+49
+00:04:52,950 --> 00:04:58,130
+على التغلب على هذه المشكلات، وفي هذه الحالة يستطيع
+
+50
+00:04:58,130 --> 00:05:03,370
+أن يعمل الأخصائي بطريقة سليمة مع المجتمع، لأن ثقة
+
+51
+00:05:03,370 --> 00:05:08,310
+البلد، خلاص، مدام ثقة تم بناؤها من حيث تقبل المجتمع،
+
+52
+00:05:08,310 --> 00:05:12,350
+إذا المجتمع أيضًا تقبل الأخصائي، فالعلاقة هي المؤثرة
+
+53
+00:05:12,350 --> 00:05:16,030
+يعني ما بين الأخصائي والمجتمع، تستطيع هذه العلاقة أن
+
+54
+00:05:16,030 --> 00:05:21,190
+تؤثر في المجتمع وينجح الأخصائي في عمله، فلذلك لابد
+
+55
+00:05:21,190 --> 00:05:25,150
+أن يمارس هذا المبدأ، طيب في عوامل بتساعد على نجاح
+
+56
+00:05:25,150 --> 00:05:30,150
+هذا المبدأ؟ بدنا نشوف حتى نطبق هذا المبدأ كممارسة
+
+57
+00:05:30,150 --> 00:05:34,610
+مهنية مع المجتمع، ما هي العوامل التي تساعد على 
+
+58
+00:05:34,610 --> 00:05:40,430
+نجاح مبدأ البدء مع المجتمع كما هو؟ أيوة، بنتي، بل 
+
+59
+00:05:40,430 --> 00:05:43,470
+يكون هناك تقبل واقتناع بين المنظم الاجتماعي وأفراد
+
+60
+00:05:43,470 --> 00:05:46,890
+المجتمع، حيث إن هذا التقبل يدعم العلاقة بين
+
+61
+00:05:46,890 --> 00:05:50,370
+الطرفين ويزيد من بناء الثقة بين الطرفين، خلاص كلمة 
+
+62
+00:05:50,370 --> 00:05:55,650
+التقبل، تقبل الأخصائي للمجتمع، وتقبل المجتمع ينعكس
+
+63
+00:05:55,650 --> 00:05:59,170
+على الأخصائي، إذا هذا عامل من عوامل نجاح هذا 
+
+64
+00:05:59,170 --> 00:06:03,830
+المبدأ، بدون التقبل لا يمكن أن يكون أو أن ينجح هذا 
+
+65
+00:06:03,830 --> 00:06:09,250
+المبدأ، فلذلك حتى ينجح الأخصائي لابد أن يتقبل
+
+66
+00:06:09,250 --> 00:06:13,990
+المجتمع، وبعد ذلك المجتمع يتقبل الأخصائي، فهنا يستطيع
+
+67
+00:06:13,990 --> 00:06:18,550
+الأخصائي أن يؤثر في المجتمع ويساعد المجتمع
+
+68
+00:06:18,550 --> 00:06:24,230
+على مواجهة مشكلته وحلها، أيوة يا بنتين، من العوامل
+
+69
+00:06:24,230 --> 00:06:27,130
+الساعدة عن نجاح المبدأ، تقامت علاقة اجتماعية مرضية
+
+70
+00:06:27,130 --> 00:06:31,550
+بين الأهالي، تقامت بعمل تضامن، كلها آثار إيجابية على
+
+71
+00:06:31,550 --> 00:06:34,770
+مشروع التضامن، طبعًا تقامت العلاقة الاجتماعية
+
+72
+00:06:34,770 --> 00:06:39,570
+المرضية بين الأهالي وأساس هذه العلاقة التعاون 
+
+73
+00:06:39,570 --> 00:06:43,470
+والتضامن ويكون لها آثار إيجابية على المشروعات
+
+74
+00:06:43,470 --> 00:06:47,870
+والبرامج اللي ممكن يعني يستفيد منها أبناء المجتمع
+
+75
+00:06:47,870 --> 00:06:53,390
+فلذلك هذا العامل الثاني اللي مساعد عن نجاح المبدأ، 
+
+76
+00:06:53,390 --> 00:06:56,690
+في عندنا عامل ثالث بيساعد على نجاح المبدأ، أيوة يا
+
+77
+00:06:56,690 --> 00:07:00,190
+بنتين، هذا مبدأ أي استجابة أو احتضان لقراء أفضل في
+
+78
+00:07:00,190 --> 00:07:04,190
+السماوات، بين المدرجات بالضبط، يعني أنت بتتعاملي مع
+
+79
+00:07:04,190 --> 00:07:10,950
+المجتمع وبدأت العمل مع المجتمع، ولاحظت أشياء غير
+
+80
+00:07:10,950 --> 00:07:15,090
+سليمة داخل المجتمع، إيش دورك أنت علشان تطبق هذا
+
+81
+00:07:15,090 --> 00:07:19,070
+المبدأ؟ احترام القراء، إنك تحترمي كل القراء وتحترمي
+
+82
+00:07:19,070 --> 00:07:23,330
+الأوضاع الموجودة في المجتمع، وخاصة عند مقابلتك
+
+83
+00:07:23,330 --> 00:07:27,110
+الأولى مع سكان المجتمع، تحترمي كافة آرائهم التي
+
+84
+00:07:27,110 --> 00:07:32,190
+يبدونها، وتحترمي العادات والتقاليد التي اعتادوا من خاص
+
+85
+00:07:32,190 --> 00:07:35,550
+بيهم، حتى لو كانت عادات وتقاليد سلبية في البداية
+
+86
+00:07:35,550 --> 00:07:39,990
+لكن على أمل أنك تضعي في ذهنك خطة من أجل تغيير هذه
+
+87
+00:07:39,990 --> 00:07:43,190
+العادات والتقاليد في المستقبل، أو الأشياء اللي أنتِ
+
+88
+00:07:43,190 --> 00:07:47,190
+يعني لا ترغبين فيها، وترغبي بأن يمارسها المجتمع 
+
+89
+00:07:47,190 --> 00:07:53,890
+فلذلك من هنا لابد أن نتقبل المجتمع كما هو، كما هو .. 
+
+90
+00:07:53,890 --> 00:07:58,710
+لأنه إنسان وليس رسول الله .. بالضبط، بالضبط، و
+
+91
+00:07:58,710 --> 00:08:02,110
+نتقبل الآراء التي يبدونها، لابد من احترام هذه 
+
+92
+00:08:02,110 --> 00:08:06,780
+الآراء مهما كانت هذه الآراء، لأن كل فرد بيعبر عن 
+
+93
+00:08:06,780 --> 00:08:10,600
+رأيه ومعتقده أن رأيه هو الصواب، فحتى لو كان هذا
+
+94
+00:08:10,600 --> 00:08:14,920
+الرأي مخالف لرأيك كأخصائية اجتماعية، لابد أن تتقبلي
+
+95
+00:08:14,920 --> 00:08:18,720
+هذا الرأي على أمل أن تغيري من هذه الآراء السلبية
+
+96
+00:08:18,720 --> 00:08:22,380
+إذا كانت فيها نوع من السلبية إلى آراء إيجابية عن 
+
+97
+00:08:22,380 --> 00:08:26,380
+طريق وضع الخطات والبرامج والمشاريع لسكان المجتمع
+
+98
+00:08:26,380 --> 00:08:33,150
+واضح؟ طيب في عندنا أيضًا كذلك عامل رابع، من العوامل
+
+99
+00:08:33,150 --> 00:08:36,290
+بتساعد على نجاح مبدأ البدء مع المجتمع كما هو
+
+100
+00:08:39,380 --> 00:08:42,160
+أيوة يا بنتي؟ لو فيه قاعدة بيانات كافية عن المجتمع
+
+101
+00:08:42,160 --> 00:08:45,340
+من حيث الدخل والسكن والعادات، ومن خلال نوع مشكلة 
+
+102
+00:08:45,340 --> 00:08:47,860
+الاقتصادي والعلاقات الاجتماعية السائدة في المجتمع
+
+103
+00:08:47,860 --> 00:08:52,520
+طبعًا عندما أعمل مع المجتمع كأخصائية اجتماعية، لابد أن 
+
+104
+00:08:52,520 --> 00:08:56,400
+ألمّ بكافة الإمكانيات الموجودة بالمجتمع عن طريق
+
+105
+00:08:56,400 --> 00:09:00,240
+المؤسسات، لابد أن أعلم ما هي المؤسسات التي تقدم
+
+106
+00:09:00,240 --> 00:09:04,520
+برامج الرعاية الاجتماعية، لابد أن أجمع معلومات
+
+107
+00:09:04,520 --> 00:09:08,320
+وبيانات عن سكان المجتمع، عن عادات المجتمع، عن تقاليد
+
+108
+00:09:08,320 --> 00:09:14,370
+المجتمع، عن النشاط الاقتصادي، عن العلاقات الاجتماعية
+
+109
+00:09:14,370 --> 00:09:18,890
+عن قادة المجتمع وغير ذلك داخل المجتمع، هذه كلها 
+
+110
+00:09:18,890 --> 00:09:22,850
+بيانات نسميها قاعدة بيانات، تفيد الأخصائي الاجتماعي
+
+111
+00:09:22,850 --> 00:09:27,490
+عند عمله مع سكان المجتمع من أجل مساعدتهم على 
+
+112
+00:09:27,490 --> 00:09:32,670
+مواجهة مشكلتهم وإشباع حاجتهم، فلذلك هذه أشياء
+
+113
+00:09:32,670 --> 00:09:36,530
+ضرورية، أيضًا من العوامل اللي بتساعد على نجاح مبدأ
+
+114
+00:09:36,530 --> 00:09:40,010
+البدء مع المجتمع كما هو، التعامل بحذر مع المشكلات و
+
+115
+00:09:40,010 --> 00:09:45,110
+المنازعات، طبعًا كل مجتمع بيحدث فيه منازعات ومشكلات 
+
+116
+00:09:45,110 --> 00:09:52,190
+فلذلك لابد أتعامل بحذر مع هذه المشكلات التي يعاني
+
+117
+00:09:52,190 --> 00:09:56,510
+منها المجتمع أو المنازعات اللي توجد بين الجماعات
+
+118
+00:09:56,510 --> 00:10:00,690
+فلذلك القوى الاجتماعية المؤثرة في المجتمع من قادة
+
+119
+00:10:00,690 --> 00:10:05,630
+المجتمع وغيرها، فهذه كلها بتأثر في المجتمع، فلذلك من 
+
+120
+00:10:05,630 --> 00:10:10,970
+هنا لابد، أحيانًا المجتمع يضع بعض المشاكل اختبار
+
+121
+00:10:10,970 --> 00:10:15,510
+للأخصائي، ويختبرون الأخصائي من أجل أن يعرفوا هل 
+
+122
+00:10:15,510 --> 00:10:18,870
+يستطيعون يتعامل مع مثل هذه المشكلات أم لا، فلذلك
+
+123
+00:10:18,870 --> 00:10:23,470
+لابد أن يكون الأخصائي على حذر وفهم لماذا يعني
+
+124
+00:10:23,470 --> 00:10:29,190
+يضعون سكان المجتمع له، فلابد التعامل معهم كما هو 
+
+125
+00:10:29,740 --> 00:10:34,160
+فلذلك من هنا لابد أن يتبع الأسلوب العلمي والمهني
+
+126
+00:10:34,160 --> 00:10:39,680
+مع مثل هذه المواقف التي يختبرونه فيها سكان المجتمع
+
+127
+00:10:39,680 --> 00:10:45,720
+في عندنا عامل آخر أيضًا من العوامل بتساعد على نجاح
+
+128
+00:10:45,720 --> 00:10:49,640
+مبدأ البدء مع المجتمع، أيوة بنتي، العمل بالسرعة 
+
+129
+00:10:49,640 --> 00:10:55,540
+المناسبة للمجتمع، طبعًا العمل مع المجتمع حسب
+
+130
+00:10:55,540 --> 00:11:00,340
+إمكانياتي وقدراتي واستعداداتي، لا أتعامل معه بسرعة
+
+131
+00:11:00,340 --> 00:11:06,040
+فائقة وزائدة عن حاجاتي وقدراتي وإمكانياتي، ولا أيضًا
+
+132
+00:11:06,040 --> 00:11:10,040
+أن يكون أن أتعامل معه بقدر يقل عن إمكانياتي 
+
+133
+00:11:10,040 --> 00:11:13,960
+وقدراتي واستعداداتي، لابد أن أراعي إمكانيات وقدرات
+
+134
+00:11:13,960 --> 00:11:21,700
+المجتمع ومدى قدرته على حل مشكلته، وأسير معه حسب هذه
+
+135
+00:11:21,700 --> 00:11:29,250
+القدرة، سواء كان بسرعة أو ببطء، وبعد ذلك حتى لو سارت 
+
+136
+00:11:29,250 --> 00:11:33,630
+معه ببطء، لابد أن أعوّده يعني على وضع برامج ومشاريع 
+
+137
+00:11:33,630 --> 00:11:37,930
+وخدمات، أعوّده على أن يسير فيها من أجل مواجهة
+
+138
+00:11:37,930 --> 00:11:44,030
+مشكلاته، يعني حسب إمكانياته وحسب قدرته، فلذلك من هنا
+
+139
+00:11:44,030 --> 00:11:47,670
+لابد أن أعمل بالسرعة المناسبة للمجتمع، لا تكون
+
+140
+00:11:47,670 --> 00:11:53,490
+سريعة ولا بطيئة، وهكذا حسب قدرة المجتمع وما يتحمله
+
+141
+00:11:53,490 --> 00:12:00,270
+من قدرته على حل مشكلته عن طريق وضع الخطط والبرامج
+
+142
+00:12:00,270 --> 00:12:04,770
+والمشاريع اللازمة ومساعدة المجتمع على ذلك، حتى 
+
+143
+00:12:04,770 --> 00:12:08,990
+يستطيع أن يتغلب على مشكلته، فلابد أن أسير معه حسب
+
+144
+00:12:08,990 --> 00:12:17,520
+قدرته وإمكانياته، ماذا أيضًا؟ خلاص، يعني هذا المبدأ
+
+145
+00:12:17,520 --> 00:12:22,040
+الأول اللي هو البدء مع المجتمع كما هو، والعوامل 
+
+146
+00:12:22,040 --> 00:12:26,000
+بتساعد على نجاح المبدأ، كل مبدأ بهذه الطريقة نستطيع
+
+147
+00:12:26,000 --> 00:12:29,520
+أن نعرف ما هو المبدأ والعوامل بتساعد على نجاح 
+
+148
+00:12:29,520 --> 00:12:34,540
+المبدأ، حتى نستطيع أن نطبق هذا المبدأ في عملنا مع 
+
+149
+00:12:34,540 --> 00:12:37,740
+المجتمع، فهذا ال .. نعم، تفضلي
+
+150
+00:12:42,430 --> 00:12:46,310
+ما يكونش خيالي، مش طبيعي، أي خطة لابد تكون خطة 
+
+151
+00:12:46,310 --> 00:12:50,410
+واقعية، تتناسب مع قدرات وحاجات المجتمع وإمكانيات
+
+152
+00:12:50,410 --> 00:12:53,870
+المجتمع، يعني لما بضع خطة أنا حسب إمكانيات المجتمع
+
+153
+00:12:53,870 --> 00:12:59,290
+المادية والبشرية، آه ما بضعش يعني خطة تزيد يعني عن
+
+154
+00:12:59,290 --> 00:13:02,630
+قدرة المجتمع لأن ما بيصير تنفيذ لها، لا أستطيع أن
+
+155
+00:13:02,630 --> 00:13:06,110
+أنفذ هذه الخطة إذا كانت يعني أكثر من قدرة المجتمع 
+
+156
+00:13:06,110 --> 00:13:13,750
+وإمكانياته، لابد تكون الخطة مناسبة لإمكانيات وقدرات
+
+157
+00:13:13,750 --> 00:13:19,550
+المجتمع، في 
+
+158
+00:13:19,550 --> 00:13:25,590
+عندنا مبدأ ثاني وهو مبدأ التحريك، مبدأ التحريك
+
+159
+00:13:25,590 --> 00:13:31,370
+سناخذ هذا المبدأ، ويقصد بتحريك المجتمع في طريق
+
+160
+00:13:31,370 --> 00:13:36,090
+تنظيم المجتمع هي الجهود التي تبذل من أجل قيام
+
+161
+00:13:36,090 --> 00:13:40,910
+أهالي المجتمع بأنفسهم، طبعًا، لمواجهة مشكلاتهم وإشباع 
+
+162
+00:13:40,910 --> 00:13:46,920
+حاجاتهم، نعم، يعني التحريك هو أن أخلي سكان المجتمع 
+
+163
+00:13:46,920 --> 00:13:51,900
+يفكروا، يحسوا بمشكلتهم ويفكروا في كيفية حل هذه
+
+164
+00:13:51,900 --> 00:13:56,580
+المشكلة، هذا معنى التحريك، ولذلك من هنا يحتاجون 
+
+165
+00:13:56,580 --> 00:14:00,800
+إلى تحريك، أحيانًا أفراد المجتمع يعيشون في المشكلة
+
+166
+00:14:00,800 --> 00:14:05,320
+ولا يحسون بها، يحتاجون إلى من يحركهم من أجل
+
+167
+00:14:05,320 --> 00:14:09,900
+الإحساس بهذه المشكلة، وإذا أحس المجتمع وأفراد
+
+168
+00:14:09,900 --> 00:14:15,680
+المجتمع بمشكلته، هنا يفكروا كيف يحلون هذه المشكلة
+
+169
+00:14:15,680 --> 00:14:21,760
+فهذا كل يعني معنى التحريك، طيب المبدأ هذا طيب، علشان
+
+170
+00:14:21,760 --> 00:14:27,530
+ينجح، هنا طبعًا تتضمن عملية التحريك ماذا؟ ماذا تتضمن
+
+171
+00:14:27,530 --> 00:14:32,610
+عملية التحريك؟ إيجابي، 
+
+172
+00:14:32,610 --> 00:14:36,790
+ماذا قدرتهم؟ هل المجتمع عنده استعدادًا لل
+
+216
+00:18:10,560 --> 00:18:12,320
+الوقت الملائم
+
+217
+00:18:14,730 --> 00:18:18,090
+ونحسس سكان المجتمع على التحرك لأنه ليس في كل وقت 
+
+218
+00:18:18,090 --> 00:18:23,290
+يتحرك، ولابد أن نختار الوقت المناسب للتحرك فهذا 
+
+219
+00:18:23,290 --> 00:18:29,790
+أيضًا من عوامل نجاح المبدأ اللي هو التحرك، ماذا أيضًا؟
+
+220
+00:18:29,790 --> 00:18:33,770
+هنا
+
+221
+00:18:33,770 --> 00:18:38,830
+طبعًا تحديد الموعد أو التوقيت لابد أن يكون توقيت مناسب 
+
+222
+00:18:38,830 --> 00:18:43,170
+لأن كثيرًا من المشروعات يكون سبب فشلها هو عدم 
+
+223
+00:18:43,170 --> 00:18:48,850
+تحديد الوقت الملائم لها لتحريك أفراد المجتمع أو
+
+224
+00:18:48,850 --> 00:18:52,290
+ممكن نختار وقتًا تكثر فيه المشكلات أو يجد أفراد
+
+225
+00:18:52,290 --> 00:18:56,990
+المجتمع خوفًا أو عدم ثقة من المسؤولين، لذلك يتوقف نجاح 
+
+226
+00:18:56,990 --> 00:19:00,770
+المنظم الاجتماعي في عمله على الاختيار الملائم 
+
+227
+00:19:00,770 --> 00:19:05,550
+للموعد بحيث يكون المجتمع أكثر استعدادًا لمواجهة 
+
+228
+00:19:05,550 --> 00:19:10,590
+مشكلاته بأسلوب ونظم يتفق مع أهداف المجتمع وقيمه،
+
+229
+00:19:10,590 --> 00:19:14,950
+ولذلك من هنا اختيار الوقت مهم جدًا، بالتوقيت لمبدأ 
+
+230
+00:19:14,950 --> 00:19:18,810
+التحريك مهم جدًا، أن لا نحرك الناس في أي وقت، لا، لابد 
+
+231
+00:19:18,810 --> 00:19:22,610
+أن نختار الوقت الملائم والمناسب حتى نستطيع أن نساعد 
+
+232
+00:19:22,610 --> 00:19:27,590
+الناس على علاج مشكلتهم التي يعانون منها، طيب في 
+
+233
+00:19:27,590 --> 00:19:30,450
+عندنا أيضًا عامل آخر من العوامل اللي بتساعد على 
+
+234
+00:19:30,450 --> 00:19:37,330
+نجاح مبدأ التحريك، أيوة يا بنتي، إيه؟
+
+235
+00:19:37,330 --> 00:19:42,870
+بَدَل بعد تحديد الوقت الملائم، تحديد المكان، إذا الوقت
+
+236
+00:19:42,870 --> 00:19:47,530
+والمكان، تحديد المكان المناسب لتحريك أفراد المجتمع
+
+237
+00:19:47,530 --> 00:19:51,470
+فهنا لابد أن يسعى المنظم لتحديد الأماكن اللي بتنتشر
+
+238
+00:19:51,470 --> 00:19:55,730
+فيها إيه؟ المشكلات، وين المشكلات؟ في أي مكان من
+
+239
+00:19:55,730 --> 00:20:01,270
+المجتمع، واضح، وهكذا سواء كانت في أماكن محلية أو
+
+240
+00:20:01,270 --> 00:20:06,410
+إقليمية أو على مستوى قومي، وقد تكون هذه المشكلات
+
+241
+00:20:06,410 --> 00:20:12,340
+منتشرة في مؤسسات، يعني دون مؤسسات أخرى، وهكذا، فهنا 
+
+242
+00:20:12,340 --> 00:20:16,280
+على الأخصائي أن يحدد الأماكن، أماكن المشكلة، على 
+
+243
+00:20:16,280 --> 00:20:20,940
+المستويات الخاصة بالمجتمع المحلي، الإقليمي، القومي 
+
+244
+00:20:20,940 --> 00:20:26,440
+أو قد تكون المشكلة على مستوى عدد من المؤسسات وهكذا
+
+245
+00:20:26,440 --> 00:20:31,300
+فلذلك لابد من التحديد الدقيق للمكان، لماذا؟ لأن هذا
+
+246
+00:20:31,300 --> 00:20:35,480
+بيساهم في نجاح الجهود التي يبذلها المنظم لتحريك
+
+247
+00:20:35,480 --> 00:20:39,680
+أفراد المجتمع، وصُبُّ الأهداف المُطمَعة لتحقيقها في هذا
+
+248
+00:20:39,680 --> 00:20:43,640
+المجتمع، في عامل آخر أيضًا من عوامل نجاح مبدأ
+
+249
+00:20:43,640 --> 00:20:49,300
+التحريك، ماذا أيضًا؟ ما تكلمتش، أيوة يا بنتي، قولي
+
+250
+00:20:49,300 --> 00:20:53,020
+الاستعانة بالقيادات والخبرات الفنية في المجتمع
+
+251
+00:20:53,020 --> 00:20:56,540
+طبعًا مهم جدًا، مبدأ التحريك لا يقوم به إلا خصائص 
+
+252
+00:20:56,540 --> 00:21:00,080
+لنفسِه، ولكن لابد أن يستعين بالخبرات والخبراء 
+
+253
+00:21:00,080 --> 00:21:04,140
+ويستعين بالخبراء والمختصين داخل المجتمع، ويتعاون 
+
+254
+00:21:04,140 --> 00:21:08,200
+معهم في إطار team work اللي هو العمل الفريقي، الـ
+
+255
+00:21:08,200 --> 00:21:12,120
+team work من أجل مساعدة المجتمع على علاج مشكلته
+
+256
+00:21:12,120 --> 00:21:19,920
+وهذا مبدأ مهم جدًا، الاستعانة بالخبراء والمختصين، وأن 
+
+257
+00:21:19,920 --> 00:21:23,240
+يقوم المنظم الاجتماعي بالاستعانة بهؤلاء الخبراء 
+
+258
+00:21:23,240 --> 00:21:32,580
+والمختصين في مساعدة المجتمع على حل مشكلته، طيب، ماذا 
+
+259
+00:21:32,580 --> 00:21:36,760
+أيضًا؟ في كذلك عامل آخر من العوامل اللي بتساعد على
+
+260
+00:21:36,760 --> 00:21:42,100
+نجاح المبدأ، انتقاء
+
+261
+00:21:42,100 --> 00:21:48,460
+أدوات من أجل تحريك أفراد المجتمع، إحنا
+
+262
+00:21:48,460 --> 00:21:51,860
+عندنا أدوات كثيرة في طريقة تنظيم المجتمع، في عندنا
+
+263
+00:21:51,860 --> 00:21:57,940
+المقابلات، في عندنا المؤتمرات، اللجان، الاجتماعات، الندوات 
+
+264
+00:21:57,940 --> 00:22:03,690
+وغيرها من الأدوات، ممكن نختار الأدوات الملائمة لتثقيف
+
+265
+00:22:03,690 --> 00:22:08,190
+أفراد المجتمع، فلذلك مبدأ التحريك يحتاج إلى اختيار 
+
+266
+00:22:08,190 --> 00:22:11,590
+الأدوات الملائمة حسب ثقافة المجتمع وأفراد المجتمع
+
+267
+00:22:11,590 --> 00:22:17,070
+ومستوياتهم التعليمية وغير ذلك، فلذلك من هنا، عشان 
+
+268
+00:22:17,070 --> 00:22:21,130
+ينجح هذا المبدأ، مبدأ التحريك، لابد من انتقاء الأدوات
+
+269
+00:22:21,130 --> 00:22:25,670
+المناسبة لتحريك أفراد المجتمع، طبعًا انتقاء الأدوات
+
+270
+00:22:25,670 --> 00:22:30,820
+يعني اختيار الأدوات المناسبة يتوقف على ماذا؟ على
+
+271
+00:22:30,820 --> 00:22:34,920
+ماذا يتوقف؟ نوعية المشكلات أولًا، نوعية المشكلات،
+
+272
+00:22:34,920 --> 00:22:40,020
+يعني المشكلات ومدى انتشارها في المجتمع، وما هي هذه
+
+273
+00:22:40,020 --> 00:22:43,640
+المشكلات المطلوب مواجهتها؟ هل هي مشكلات بسيطة، ولا
+
+274
+00:22:43,640 --> 00:22:47,180
+مشكلات كبيرة؟ وماذا تتطلب من أدوات؟ هل تتطلب 
+
+275
+00:22:47,180 --> 00:22:51,240
+مقابلة؟ هل مثلًا تتطلب تشكيل لجان من أجل معالجة هذه 
+
+276
+00:22:51,240 --> 00:22:55,100
+المشكلات؟ أو عمل مؤتمر عام من أجل إثارة الرأي
+
+277
+00:22:55,100 --> 00:22:59,560
+العام حول هذه المشكلة وكيفية علاجها؟ إلى غير ذلك، أو
+
+278
+00:22:59,560 --> 00:23:03,700
+تحتاج إلى اجتماع فقط، وإذا، من هنا نوعية المشكلة 
+
+279
+00:23:03,700 --> 00:23:07,440
+المطلوب مواجهتها، تتوقف عليها اختيار الأدوات، ماذا 
+
+280
+00:23:07,440 --> 00:23:14,000
+أيضًا؟ كذلك درجة التعليم السائدة في المجتمع،
+
+281
+00:23:14,000 --> 00:23:18,020
+التعامل مع المجتمع المثقف والمتعلم غير مع المجتمع
+
+282
+00:23:18,020 --> 00:23:23,500
+الجهول والأمي، واضح؟ فلذلك هذا يحتاج إلى أدوات، 
+
+283
+00:23:23,500 --> 00:23:28,160
+اللي هو المتعلم والغير متعلم يحتاج الأدوات الأخرى
+
+284
+00:23:28,160 --> 00:23:32,240
+حتى نسير معه وهكذا، المجتمع داخل المدينة غير 
+
+285
+00:23:32,240 --> 00:23:35,540
+المجتمع داخل القرية، المجتمع الريفي غير المجتمع
+
+286
+00:23:35,540 --> 00:23:40,280
+الحضري وهكذا، طبيعة المجتمع، نختار الأداة الملائمة
+
+287
+00:23:40,280 --> 00:23:46,800
+معه وهكذا، ماذا أيضًا؟ اختيار الأداة يتوقف على ماذا؟
+
+288
+00:23:46,800 --> 00:23:52,420
+كذلك المستوى الاجتماعي وانتقاء أفراد المجتمع
+
+289
+00:23:52,420 --> 00:23:53,440
+ماذا أيضًا؟
+
+290
+00:23:56,460 --> 00:24:02,000
+نوعية القيادات الموجودة في المجتمع، ما هي القيادات؟
+
+291
+00:24:02,000 --> 00:24:06,120
+هذه كلها تتوقف عليها اختيار أدوات مناسبة، يعني
+
+292
+00:24:06,120 --> 00:24:12,400
+لتحريك أفراد المجتمع، في عندنا عوامل أخرى كذلك من 
+
+293
+00:24:12,400 --> 00:24:15,940
+العوامل تساعد على نجاح المبدأ، ما هي العوامل 
+
+294
+00:24:15,940 --> 00:24:21,660
+الأخرى؟ حقيقة أن تتناسب القيادات القائمة بعمل
+
+295
+00:24:21,660 --> 00:24:27,090
+تحريك مع طبيعة المشروع، نختار القادة حسب طبيعة 
+
+296
+00:24:27,090 --> 00:24:32,830
+المشروع المختار للمجتمع،
+
+297
+00:24:32,830 --> 00:24:36,450
+لذلك في مشروعات تنظيم الأسرة مثلًا، عارفين مشاريع 
+
+298
+00:24:36,450 --> 00:24:42,160
+تنظيم الأسرة؟ هو الإقلال من النسل، هذا مشروع تنظيم
+
+299
+00:24:42,160 --> 00:24:45,280
+الأسرة وخاصة في المجتمعات اللي بتعاني من زيادة 
+
+300
+00:24:45,280 --> 00:24:50,940
+السكان زي مصر زي الصين زي الهند، بس الصين يعني بعض 
+
+301
+00:24:50,940 --> 00:24:55,400
+الدول أحيانًا عندها كثرة في السكان ولكن عندها علاج
+
+302
+00:24:55,400 --> 00:25:01,580
+لمشكلة السكان، عندها تخطيط، عندها تخطيط، لكن في بعض
+
+303
+00:25:01,580 --> 00:25:07,780
+الدول النامية كثرة في السكان ولكن قلة يعني ما فيش 
+
+304
+00:25:07,780 --> 00:25:12,520
+خبرة في التخطيط أو معرفة أو إهمال في التخطيط
+
+305
+00:25:12,520 --> 00:25:17,100
+لِمعالجة هذه المشكلة السكانية، فلذلك من هنا
+
+306
+00:25:17,100 --> 00:25:22,120
+يضعون برامج، اسمها برامج تنظيم النسل، الإقلال من
+
+307
+00:25:22,120 --> 00:25:27,850
+عدد السكان، ولذلك يسمونها برامج تنظيم الأسرة، إحنا
+
+308
+00:25:27,850 --> 00:25:32,590
+عندنا في الإسلام ما فيش تحديد للنسل، عندنا تنظيم
+
+309
+00:25:32,590 --> 00:25:36,830
+للنسل، وهذا يعني يستعينون به اللي هم المجتمعات
+
+310
+00:25:36,830 --> 00:25:41,710
+اللي فيها كثرة في السكان، ويعملون برامج قومية، 
+
+311
+00:25:41,710 --> 00:25:46,990
+برامج قومية، طبعًا مثل هذه البرامج تحتاج إلى متخصصين
+
+312
+00:25:46,990 --> 00:25:52,210
+وتحتاج إلى نوعية معينة من القيادات لتنظيمها، هل كل 
+
+313
+00:25:52,210 --> 00:25:56,530
+القيادات تنفع؟ لا، طبعًا، تنظيم النسل، إذا هنا نختار 
+
+314
+00:25:56,530 --> 00:26:01,490
+من النساء القادة، وقد يكونون من النساء، فتحتاج أيضًا 
+
+315
+00:26:01,490 --> 00:26:05,950
+إلى علماء الدين حتى نعمل توعية دينية وهكذا، إذا مثل
+
+316
+00:26:05,950 --> 00:26:13,500
+هذه البرامج تتوقف عليها طبيعة القيادات، فبرنامج مثل
+
+317
+00:26:13,500 --> 00:26:18,240
+برنامج تنظيم الأسرة الهدف منه الإقلال أو تنظيم
+
+318
+00:26:18,240 --> 00:26:23,900
+النسل، هنا نستعين بالنساء أكثر شيء، لأن المرأة مع
+
+319
+00:26:23,900 --> 00:26:28,200
+المرأة يكون لها تأثير أكثر وكذا، إلا في بعض الأحيان
+
+320
+00:26:28,200 --> 00:26:32,520
+نستعين ببعض المتخصصين والمتخصصات من الأطباء من 
+
+321
+00:26:32,520 --> 00:26:36,620
+علماء الدين أيضًا من أجل إثارة أو من أجل التوعية
+
+322
+00:26:36,620 --> 00:26:41,820
+والتثقيف لأبناء المجتمع حول تنظيم الأسرة، وهذه طبعًا
+
+323
+00:26:41,820 --> 00:26:45,920
+يأخذونها في المجتمعات اللي هي عندها زيادة في النسل
+
+324
+00:26:45,920 --> 00:26:50,340
+ويحاولون يقللون من عدد السكان حتى يتغلبوا على
+
+325
+00:26:50,340 --> 00:26:54,960
+المشكلة الاقتصادية، واضح؟ لكن إحنا بنقول يعني 
+
+326
+00:26:54,960 --> 00:26:59,260
+بالرغم من أننا نلاحظ دول عندها كثافة سكانية زي الصين
+
+327
+00:26:59,260 --> 00:27:04,010
+مثلًا، ولكن عندها ما فيش عندها مشكلة، ما عندهاش، لماذا؟
+
+328
+00:27:04,010 --> 00:27:07,050
+لأنها عندها تخطيط، عندها زيادة في عدد السكان، و
+
+329
+00:27:07,050 --> 00:27:12,570
+السكان بكثرة ولكن هناك عمل، عمل مستمر لهؤلاء، وفرص 
+
+330
+00:27:12,570 --> 00:27:16,910
+عمل لهم، وقائم على التصنيع، وقائم على الزراعة، وقائم
+
+331
+00:27:16,910 --> 00:27:21,950
+على الخطط الاقتصادية والاجتماعية الموجودة في مثل
+
+332
+00:27:21,950 --> 00:27:25,960
+هذه المجتمعات، تقوم على أساس علمي، نحن في أمس الحاجة
+
+333
+00:27:25,960 --> 00:27:28,660
+في مجتمعاتنا العربية اللي بتعاني من الزيادة
+
+334
+00:27:28,660 --> 00:27:33,180
+السكانية أن يكون هناك تخطيط لمثل، ولذلك من هنا 
+
+335
+00:27:33,180 --> 00:27:37,500
+نستعين بعملية التحريك، نختار نوعية القيادات اللازمة 
+
+336
+00:27:37,500 --> 00:27:43,390
+لحث الناس على معرفة مشكلتهم وكيفية مواجهتها، مثلًا
+
+337
+00:27:43,390 --> 00:27:46,530
+مثل هذا البرنامج، تنظيم الأسرة، هنا نختار له 
+
+338
+00:27:46,530 --> 00:27:50,350
+القيادات الملائمة والمناسبة في التأثير على سكان 
+
+339
+00:27:50,350 --> 00:27:54,730
+المجتمع حتى يؤتي هذا البرنامج اللي هو تنظيم الأسرة
+
+340
+00:27:54,730 --> 00:27:59,570
+ثماره، فلذلك من هنا نختار القيادات القائمة بعملية 
+
+341
+00:27:59,570 --> 00:28:10,110
+التحريك حسب هذا المشروع، طبعًا
+
+342
+00:28:10,110 --> 00:28:14,680
+تحريك أفراد المجتمع يؤدي إلى عدة نتائج، ما هي هذه
+
+343
+00:28:14,680 --> 00:28:18,780
+النتائج التي يؤديها تحريك أفراد المجتمع؟ يؤدي إلى
+
+344
+00:28:18,780 --> 00:28:23,020
+عدة نتائج، ما هي هذه النتائج؟ أيوة يا بنتي، اكتساب
+
+345
+00:28:23,020 --> 00:28:26,160
+أفراد المجتمع القدرة على التعامل البناء مع مشكلات
+
+346
+00:28:26,160 --> 00:28:29,700
+المجتمع الداخلي، نعم، إذا اكتساب أفراد المجتمع القدرة 
+
+347
+00:28:29,700 --> 00:28:34,500
+على التعامل البناء مع المشكلات المجتمعية، تحريكهم
+
+348
+00:28:34,500 --> 00:28:37,880
+يجعلهم يتعاملوا مع مشكلتهم داخل المجتمع، ماذا
+
+349
+00:28:37,880 --> 00:28:44,160
+أيضًا؟ برضه الولاء والمشاركة، الولاء والانتماء، وهذه
+
+350
+00:28:44,160 --> 00:28:47,560
+طبعًا مهمة جدًا، لأن من خلال تحريكهم وإحساسهم
+
+351
+00:28:47,560 --> 00:28:52,940
+بالمشكلة هنا إحنا بننمي عملية الولاء والانتماء
+
+352
+00:28:52,940 --> 00:28:58,160
+للمجتمع وهكذا، وكل إنسان يشعر بالفخر بالانتماء إلى 
+
+353
+00:28:58,160 --> 00:29:03,260
+مجتمعه الذي ينتمي إليه وهكذا، ويصبح عندنا علاقة ما
+
+354
+00:29:03,260 --> 00:29:06,680
+بين الانتماء والمشاركة، كل ما زاد الانتماء زادت 
+
+355
+00:29:06,680 --> 00:29:09,280
+المشاركة، أيوة يا بنتي، في الآخر
+
+356
+00:29:12,180 --> 00:29:23,500
+آه، إيش اللي هي تعني
+
+357
+00:29:23,500 --> 00:29:29,560
+قادة المجتمع المحليين مع المجتمع ككل، و إدراك 
+
+358
+00:29:29,560 --> 00:29:34,380
+المشكلة والتحرك نحو واضح لحلولها، طبعًا طبعًا شيء طبيعي
+
+359
+00:29:34,380 --> 00:29:38,200
+قادة المجتمع يتعاملون مع سكان المجتمع من أجل
+
+360
+00:29:38,200 --> 00:29:42,410
+مواجهة هذه المشكلة، وهذا من ثمار إيش؟ تحريك أفراد
+
+361
+00:29:42,410 --> 00:29:45,870
+المجتمع، يؤدي إلى هذه النتيجة، القادة مع سكان
+
+362
+00:29:45,870 --> 00:29:51,590
+المجتمع، يؤدي إلى اللي هي اشتراكهم مع بعض
+
+363
+00:29:51,590 --> 00:29:57,490
+القادة والسكان من أجل مواجهة المشكلات وحلها، ماذا 
+
+364
+00:29:57,490 --> 00:30:02,170
+أيضًا؟ تحريك، مين ما تكلمتش هنا، في الناحية هذه
+
+365
+00:30:02,170 --> 00:30:07,500
+طيب، فضل يا بنتي، تشجيع جميع أفراد المجتمع على 
+
+366
+00:30:07,500 --> 00:30:10,440
+المشاركة في تحمل المسؤولية، وتحريك التعامل المسؤول 
+
+367
+00:30:10,440 --> 00:30:15,240
+وهذه من آثار اللي هو مبدأ تحريك أفراد المجتمع
+
+368
+00:30:15,240 --> 00:30:20,820
+النتيجة تعني أن جميع أفراد المجتمع بتشجعوا على 
+
+369
+00:30:20,820 --> 00:30:25,140
+المشاركة في تحمل المسؤولية، تحمل المسؤولية في 
+
+370
+00:30:25,140 --> 00:30:29,440
+مواجهة مشكلاتهم ومشكلات مجتمعهم والعمل على حل هذه
+
+371
+00:30:29,440 --> 00:30:34,960
+المشكلة، طيب، في أي سؤال؟ في أي سؤال في موضوعنا
+
+372
+00:30:34,960 --> 00:30:39,000
+اليوم؟ أخذنا مبدأين اليوم، مبدأ الاندماج مع المجتمع 
+
+373
+00:30:39,000 --> 00:30:44,800
+كما هو، وأخذنا مبدأ التحريك، فالآن في المبدأين
+
+374
+00:30:44,800 --> 00:30:50,360
+هذول، يعني هل في أي سؤال؟ أي مبدأ؟
+
+375
+00:30:57,950 --> 00:31:03,430
+الوسيلة اللي بيختارها المجتمع أي
+
+376
+00:31:03,430 --> 00:31:09,650
+وسيلة الأداة اللي نختار بها القيادات، كيف يعني تؤثر
+
+377
+00:31:09,650 --> 00:31:16,110
+في كيفية الأداء؟
+
+378
+00:31:16,110 --> 00:31:20,640
+طبعًا المنظم الاجتماعي يتعاون مع القيادات، وهنا حسب
+
+379
+00:31:20,640 --> 00:31:25,500
+طبيعة المجتمع وثقافة المجتمع وطبيعة المشكلة، ما
+
+380
+00:31:25,500 --> 00:31:31,060
+هي الأداة الملائمة في اختيار قادة المجتمع والمنظم 
+
+381
+00:31:31,060 --> 00:31:35,420
+الاجتماعي والمجتمع في الأداة الملائمة له، فإحنا
+
+382
+00:31:35,420 --> 00:31:40,360
+قلنا إذا كان المجتمع واعيًا ومتعلمًا والمشكلة تحتاج
+
+383
+00:31:40,360 --> 00:31:46,740
+إلى مؤتمر، ممكن نستخدم المؤتمر كمؤتمرات كأداة من
+
+384
+00:31:46,740 --> 00:31:51,140
+الأدوات اللي ممكن علشان نستخدمها في تحريك سكان
+
+385
+00:31:51,140 --> 00:31:56,800
+المجتمع حول وعيهم بمشكلتهم وكيفية حل هذه المشكلة
+
+386
+00:31:56,800 --> 00:32:01,600
+وممكن هنا نسير الرأي العام، وممكن نعمل يعني إثارة
+
+387
+00:32:01,600
\ No newline at end of file
diff --git a/PL9fwy3NUQKwaKyeI5iiPpebyFXxlPBffV/QeBsuUIbXsQ_raw.json b/PL9fwy3NUQKwaKyeI5iiPpebyFXxlPBffV/QeBsuUIbXsQ_raw.json
new file mode 100644
index 0000000000000000000000000000000000000000..38df2e2a53ab0317c5744ccce9681967dcdde720
--- /dev/null
+++ b/PL9fwy3NUQKwaKyeI5iiPpebyFXxlPBffV/QeBsuUIbXsQ_raw.json
@@ -0,0 +1 @@
+{"segments": [{"id": 1, "seek": 4794, "start": 20.92, "end": 47.94, "text": "بسم الله الرحمن الرحيم الحمد لله رب العالمين والصلاة والسلام على أشرف المرسلين سيدنا محمد وعلى آله وصحبه أجمعين بنات الطالبات السلام علي كلنا ورحمة الله وبركاته في هذه المحاضرة سنتناول موضوع مبادئ تنظيم المجتمع قبل الحديث عن كل مبدأ على حدى", "tokens": [3555, 38251, 21984, 34892, 5016, 27842, 34892, 5016, 32640, 21542, 2304, 3215, 24976, 3224, 12602, 3555, 18863, 45340, 9957, 16070, 9381, 15040, 3660, 16070, 3794, 37440, 15844, 5551, 8592, 28480, 9673, 2288, 3794, 1211, 9957, 8608, 25708, 8315, 3714, 35571, 3215, 4032, 3615, 23942, 19753, 43761, 4032, 9381, 5016, 3555, 3224, 5551, 7435, 2304, 3615, 9957, 4724, 8315, 2655, 41950, 6027, 3555, 9307, 21136, 37440, 25894, 28242, 8315, 4032, 2288, 35571, 3660, 21984, 4032, 26890, 4117, 9307, 3224, 8978, 29538, 9673, 5016, 46958, 25720, 8608, 29399, 8315, 12610, 3714, 2407, 11242, 45367, 3714, 3555, 18513, 19986, 6055, 1863, 19913, 32640, 9673, 7435, 39237, 3615, 12174, 36150, 21542, 16254, 12984, 18871, 28242, 3714, 44510, 10721, 15844, 11331, 3215, 7578], "avg_logprob": -0.09033613808515693, "compression_ratio": 2.041860465116279, "no_speech_prob": 4.76837158203125e-07, "words": [{"start": 20.92, "end": 21.26, "word": "بسم", "probability": 0.886474609375}, {"start": 21.26, "end": 21.5, "word": " الله", "probability": 0.96533203125}, {"start": 21.5, "end": 21.9, "word": " الرحمن", "probability": 0.9801432291666666}, {"start": 21.9, "end": 22.5, "word": " الرحيم", "probability": 0.9954427083333334}, {"start": 22.5, "end": 22.98, "word": " الحمد", "probability": 0.8001302083333334}, {"start": 22.98, "end": 23.32, "word": " لله", "probability": 0.940185546875}, {"start": 23.32, "end": 23.56, "word": " رب", "probability": 0.900634765625}, {"start": 23.56, "end": 24.3, "word": " العالمين", "probability": 0.99365234375}, {"start": 24.3, "end": 25.28, "word": " والصلاة", "probability": 0.8504638671875}, {"start": 25.28, "end": 25.7, "word": " والسلام", "probability": 0.9656575520833334}, {"start": 25.7, "end": 25.92, "word": " على", "probability": 0.6865234375}, {"start": 25.92, "end": 26.24, "word": " أشرف", "probability": 0.982421875}, {"start": 26.24, "end": 27.02, "word": " المرسلين", "probability": 0.98837890625}, {"start": 27.02, "end": 28.0, "word": " سيدنا", "probability": 0.9254557291666666}, {"start": 28.0, "end": 28.6, "word": " محمد", "probability": 0.98681640625}, {"start": 28.6, "end": 28.88, "word": " وعلى", "probability": 0.9365234375}, {"start": 28.88, "end": 29.2, "word": " آله", "probability": 0.86181640625}, {"start": 29.2, "end": 29.74, "word": " وصحبه", "probability": 0.91787109375}, {"start": 29.74, "end": 30.32, "word": " أجمعين", "probability": 0.9755859375}, {"start": 30.32, "end": 31.04, "word": " بنات", "probability": 0.7389322916666666}, {"start": 31.04, "end": 31.68, "word": " الطالبات", "probability": 0.7879638671875}, {"start": 31.68, "end": 32.18, "word": " السلام", "probability": 0.93994140625}, {"start": 32.18, "end": 32.4, "word": " علي", "probability": 0.81396484375}, {"start": 32.4, "end": 32.94, "word": " كلنا", "probability": 0.835205078125}, {"start": 32.94, "end": 33.44, "word": " ورحمة", "probability": 0.980712890625}, {"start": 33.44, "end": 33.8, "word": " الله", "probability": 0.97607421875}, {"start": 33.8, "end": 34.84, "word": " وبركاته", "probability": 0.94658203125}, {"start": 34.84, "end": 37.46, "word": " في", "probability": 0.9189453125}, {"start": 37.46, "end": 37.72, "word": " هذه", "probability": 0.97021484375}, {"start": 37.72, "end": 38.38, "word": " المحاضرة", "probability": 0.9925537109375}, {"start": 38.38, "end": 39.4, "word": " سنتناول", "probability": 0.84295654296875}, {"start": 39.4, "end": 40.18, "word": " موضوع", "probability": 0.983642578125}, {"start": 40.18, "end": 41.16, "word": " مبادئ", "probability": 0.968017578125}, {"start": 41.16, "end": 41.78, "word": " تنظيم", "probability": 0.99609375}, {"start": 41.78, "end": 42.86, "word": " المجتمع", "probability": 0.9932861328125}, {"start": 42.86, "end": 46.12, "word": " قبل", "probability": 0.977783203125}, {"start": 46.12, "end": 46.64, "word": " الحديث", "probability": 0.9931640625}, {"start": 46.64, "end": 46.8, "word": " عن", "probability": 0.9921875}, {"start": 46.8, "end": 47.0, "word": " كل", "probability": 0.96875}, {"start": 47.0, "end": 47.34, "word": " مبدأ", "probability": 0.8294270833333334}, {"start": 47.34, "end": 47.52, "word": " على", "probability": 0.9521484375}, {"start": 47.52, "end": 47.94, "word": " حدى", "probability": 0.7262369791666666}], "temperature": 1.0}, {"id": 2, "seek": 6467, "start": 49.07, "end": 64.67, "text": "نلبّه بأن مبادئ تنظيم المجتمع كلها متداكلة ومتكاملة مع بعضها البعض، لذلك عند الممارسة العملية لطريق تنظيم المجتمع", "tokens": [1863, 46152, 11703, 3224, 4724, 33456, 3714, 3555, 18513, 19986, 6055, 1863, 19913, 32640, 9673, 7435, 39237, 3615, 28242, 11296, 44650, 28259, 4117, 37977, 4032, 2304, 2655, 4117, 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له لابد أن أستعين بها ولكن أحيانا بركز على مبدأ عند الممارسة يكون أكثر من المبادئ الأخرى وهكذا ولكن في النهاية جميع المبادئ متكاملة ومتداخلة مع بعضها البعض سنتناول أول مبدأ في طريق تنظيم المجتمع وهو الفدء", "tokens": [10721, 9566, 3555, 4587, 3714, 3555, 18513, 19986, 6055, 1863, 19913, 32640, 9673, 7435, 39237, 3615, 4032, 2304, 43020, 5551, 9566, 3555, 4587, 3714, 44510, 10721, 4032, 20292, 3794, 20449, 1863, 7578, 9673, 3555, 18513, 19986, 16247, 34740, 7578, 14739, 41850, 5551, 2655, 31747, 11296, 46740, 5296, 16758, 3215, 14739, 5551, 14851, 3615, 9957, 4724, 11296, 35525, 19452, 5551, 5016, 1829, 7649, 995, 4724, 31747, 11622, 15844, 3714, 44510, 10721, 43242, 9673, 2304, 9640, 3794, 3660, 7251, 30544, 5551, 4117, 49115, 9154, 9673, 3555, 18513, 19986, 16247, 34740, 7578, 4032, 3224, 4117, 15730, 35525, 19452, 8978, 28239, 11296, 10632, 10874, 2304, 40228, 9673, 3555, 18513, 19986, 44650, 4117, 10943, 37977, 4032, 2304, 2655, 3215, 47283, 37977, 20449, 45030, 11242, 11296, 29739, 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السكان ولكن قلة يعني مافيش خبرة في التخطيط أو معرفة أو إهمال في التخطيط لمقادة معالجة هذه المشكلة السكانية فلذلك من هنا بيضعوا برامج اسمها برامج تنظيم النسل الإقلال من عدد السكان", "tokens": [1211, 19452, 8978, 45030, 11242, 32748, 12610, 28239, 10943, 10632, 9122, 12984, 25720, 8978, 21136, 41361, 35525, 19452, 12174, 37977, 37495, 22653, 19446, 41185, 8592, 16490, 3555, 25720, 8978, 16712, 9778, 9566, 1829, 9566, 34051, 20449, 28480, 3660, 34051, 11933, 16095, 6027, 8978, 16712, 9778, 9566, 1829, 9566, 32767, 4587, 18513, 3660, 20449, 6027, 7435, 3660, 29538, 9673, 8592, 28820, 3660, 21136, 41361, 10632, 6156, 1211, 8848, 23275, 9154, 34105, 4724, 1829, 11242, 3615, 14407, 4724, 2288, 10943, 7435, 24525, 2304, 11296, 4724, 2288, 10943, 7435, 6055, 1863, 19913, 32640, 28239, 3794, 1211, 33688, 4587, 1211, 6027, 9154, 6225, 3215, 3215, 21136, 41361], "avg_logprob": -0.1168870203770124, "compression_ratio": 1.9591836734693877, "no_speech_prob": 1.1920928955078125e-07, "words": 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استخدام الاجتماع مع قادة المجتمع ممكن تكون المشكلة على مستوى مجتمع محلي صغير فممكن هنا يعني نختار الاجتماع لقادة المجتمع وبعض سكان المجتمع الذين يعانون من مشكلة", "tokens": [28814, 15730, 25961, 2655, 9673, 8592, 28820, 3660, 6055, 2655, 9566, 46152, 3714, 33604, 2655, 29973, 6225, 28543, 3714, 33604, 2655, 29973, 44381, 3714, 43020, 6055, 30544, 9673, 8592, 28820, 3660, 4724, 3794, 1829, 9566, 3660, 20193, 6055, 11622, 25708, 18871, 44713, 9778, 3215, 10943, 2423, 26108, 2655, 15042, 3615, 20449, 12174, 18513, 3660, 9673, 7435, 39237, 3615, 3714, 43020, 6055, 30544, 9673, 8592, 28820, 3660, 15844, 3714, 14851, 2407, 7578, 3714, 7435, 39237, 3615, 3714, 5016, 20292, 20328, 17082, 13546, 6156, 2304, 43020, 34105, 37495, 22653, 8717, 46456, 9640, 2423, 26108, 2655, 15042, 3615, 5296, 4587, 18513, 3660, 9673, 7435, 39237, 3615, 46599, 3615, 11242, 8608, 41361, 9673, 7435, 39237, 3615, 32545, 9957, 37495, 7649, 11536, 9154, 37893, 28820, 3660], "avg_logprob": -0.06374872127761606, "compression_ratio": 2.196969696969697, "no_speech_prob": 2.3245811462402344e-06, "words": [{"start": 1923.81, "end": 1924.11, "word": "إذا", "probability": 0.87646484375}, {"start": 1924.11, "end": 1924.49, "word": " كانت", "probability": 0.94287109375}, {"start": 1924.49, "end": 1925.23, "word": " المشكلة", "probability": 0.9949951171875}, {"start": 1925.23, "end": 1926.11, "word": " تتطلب", "probability": 0.97607421875}, {"start": 1926.11, "end": 1926.67, "word": " مؤتمر", "probability": 0.85009765625}, {"start": 1926.67, "end": 1927.09, "word": " عقد", "probability": 0.80810546875}, {"start": 1927.09, "end": 1927.65, "word": " مؤتمر", "probability": 0.9775390625}, {"start": 1927.65, "end": 1928.43, "word": " لكن", "probability": 0.8125}, {"start": 1928.43, "end": 1928.87, "word": " ممكن", "probability": 0.932373046875}, {"start": 1928.87, "end": 1929.31, "word": " تكون", "probability": 0.989013671875}, {"start": 1929.31, "end": 1929.85, "word": " المشكلة", "probability": 0.9952392578125}, {"start": 1929.85, "end": 1930.51, "word": " بسيطة", "probability": 0.88369140625}, {"start": 1930.51, "end": 1931.15, "word": " لا", "probability": 0.68017578125}, {"start": 1931.15, "end": 1931.87, "word": " تزيد", "probability": 0.9939778645833334}, {"start": 1931.87, "end": 1932.27, "word": " عن", "probability": 0.9716796875}, {"start": 1932.27, "end": 1933.07, "word": " استخدام", "probability": 0.9732666015625}, {"start": 1933.07, "end": 1933.81, "word": " الاجتماع", "probability": 0.93837890625}, {"start": 1933.81, "end": 1934.43, "word": " مع", "probability": 0.97705078125}, {"start": 1934.43, "end": 1934.87, "word": " قادة", "probability": 0.984375}, {"start": 1934.87, "end": 1935.47, "word": " المجتمع", "probability": 0.99365234375}, {"start": 1935.47, "end": 1935.87, "word": " ممكن", "probability": 0.837158203125}, {"start": 1935.87, "end": 1936.17, "word": " تكون", "probability": 0.982421875}, {"start": 1936.17, "end": 1936.69, "word": " المشكلة", "probability": 0.994384765625}, {"start": 1936.69, "end": 1936.83, "word": " على", "probability": 0.91455078125}, {"start": 1936.83, "end": 1937.47, "word": " مستوى", "probability": 0.9495849609375}, {"start": 1937.47, "end": 1938.13, "word": " مجتمع", "probability": 0.987548828125}, {"start": 1938.13, "end": 1938.57, "word": " محلي", "probability": 0.9060872395833334}, {"start": 1938.57, "end": 1939.13, "word": " صغير", "probability": 0.99755859375}, {"start": 1939.13, "end": 1940.09, "word": " فممكن", "probability": 0.9440104166666666}, {"start": 1940.09, "end": 1940.55, "word": " هنا", "probability": 0.98046875}, {"start": 1940.55, "end": 1941.49, "word": " يعني", "probability": 0.76611328125}, {"start": 1941.49, "end": 1942.49, "word": " نختار", "probability": 0.98193359375}, {"start": 1942.49, "end": 1943.55, "word": " الاجتماع", "probability": 0.95458984375}, {"start": 1943.55, "end": 1944.65, "word": " لقادة", "probability": 0.9259033203125}, {"start": 1944.65, "end": 1945.31, "word": " المجتمع", "probability": 0.99267578125}, {"start": 1945.31, "end": 1945.73, "word": " وبعض", "probability": 0.8546549479166666}, {"start": 1945.73, "end": 1946.01, "word": " سكان", "probability": 0.907470703125}, {"start": 1946.01, "end": 1946.67, "word": " المجتمع", "probability": 0.9949951171875}, {"start": 1946.67, "end": 1947.31, "word": " الذين", "probability": 0.95361328125}, {"start": 1947.31, "end": 1947.83, "word": " يعانون", "probability": 0.9733072916666666}, {"start": 1947.83, "end": 1948.13, "word": " من", "probability": 0.99267578125}, {"start": 1948.13, "end": 1948.91, "word": " مشكلة", "probability": 0.9596354166666666}], "temperature": 1.0}, {"id": 77, "seek": 195984, "start": 1949.18, "end": 1959.84, "text": "يعاني منها المجتمع ويفكروا في كيفية حل هذه المشكلة إذا هنا اخترنا ما هي الأداة اللي اخترناها الاجتماع اما نقول اخترنا المؤتمر ممكن نختار لجان", "tokens": [1829, 3615, 7649, 1829, 9154, 11296, 9673, 7435, 39237, 3615, 4032, 33911, 37983, 14407, 8978, 9122, 33911, 10632, 11331, 1211, 29538, 9673, 8592, 28820, 3660, 11933, 15730, 34105, 1975, 46456, 2288, 8315, 19446, 39896, 16247, 28259, 3660, 13672, 1829, 1975, 46456, 2288, 8315, 11296, 2423, 26108, 2655, 15042, 3615, 1975, 15042, 8717, 39648, 1975, 46456, 2288, 8315, 9673, 33604, 2655, 29973, 3714, 43020, 8717, 46456, 9640, 5296, 7435, 7649], "avg_logprob": -0.17198661203895296, "compression_ratio": 1.7916666666666667, "no_speech_prob": 1.138448715209961e-05, "words": [{"start": 1949.18, "end": 1949.88, "word": "يعاني", "probability": 0.6019287109375}, {"start": 1949.88, "end": 1950.14, "word": " منها", "probability": 0.96044921875}, {"start": 1950.14, "end": 1950.76, "word": " المجتمع", "probability": 0.9892578125}, {"start": 1950.76, "end": 1951.62, "word": " ويفكروا", "probability": 0.8375244140625}, {"start": 1951.62, "end": 1951.74, "word": " في", "probability": 0.70556640625}, {"start": 1951.74, "end": 1952.18, "word": " كيفية", "probability": 0.9720052083333334}, {"start": 1952.18, "end": 1952.5, "word": " حل", "probability": 0.964111328125}, {"start": 1952.5, "end": 1952.74, "word": " هذه", "probability": 0.9443359375}, {"start": 1952.74, "end": 1953.32, "word": " المشكلة", "probability": 0.99609375}, {"start": 1953.32, "end": 1953.66, "word": " إذا", "probability": 0.5423583984375}, {"start": 1953.66, "end": 1953.86, "word": " هنا", "probability": 0.498291015625}, {"start": 1953.86, "end": 1954.26, "word": " اخترنا", "probability": 0.8861083984375}, {"start": 1954.26, "end": 1954.34, "word": " ما", "probability": 0.568359375}, {"start": 1954.34, "end": 1954.52, "word": " هي", "probability": 0.87548828125}, {"start": 1954.52, "end": 1954.92, "word": " الأداة", "probability": 0.8693033854166666}, {"start": 1954.92, "end": 1955.0, "word": " اللي", "probability": 0.783447265625}, {"start": 1955.0, "end": 1955.56, "word": " اخترناها", "probability": 0.95966796875}, {"start": 1955.56, "end": 1956.54, "word": " الاجتماع", "probability": 0.877001953125}, {"start": 1956.54, "end": 1957.06, "word": " اما", "probability": 0.648193359375}, {"start": 1957.06, "end": 1957.32, "word": " نقول", "probability": 0.97412109375}, {"start": 1957.32, "end": 1957.74, "word": " اخترنا", "probability": 0.97607421875}, {"start": 1957.74, "end": 1958.28, "word": " المؤتمر", "probability": 0.9844970703125}, {"start": 1958.28, "end": 1958.86, "word": " ممكن", "probability": 0.949951171875}, {"start": 1958.86, "end": 1959.32, "word": " نختار", "probability": 0.9881184895833334}, {"start": 1959.32, "end": 1959.84, "word": " لجان", "probability": 0.7019856770833334}], "temperature": 1.0}, {"id": 78, "seek": 198633, "start": 1960.43, "end": 1986.33, "text": "ممكن المشكلة تحتاج إلى خبراء ومختصين وممكن هنا انشكل لجان من خبراء ومختصين في معالجة هذه المشكلة، واضح؟ فإذا هنا القادة لهم دور، الخبراء والمختصين لهم دور، سكان المجتمع لهم دور، طبيعة المشكلة لها دور في اختيار الأداء الملائمة والتعامل مع المجتمع طيب إلى هنا ننهي هذه المحاضرة على أمل اللقاء بكون ان شاء الله", "tokens": [2304, 43020, 9673, 8592, 28820, 3660, 6055, 33753, 26108, 30731, 16490, 26890, 16606, 4032, 2304, 46456, 9381, 9957, 4032, 2304, 43020, 34105, 16472, 8592, 28820, 5296, 7435, 7649, 9154, 16490, 26890, 16606, 4032, 2304, 46456, 9381, 9957, 8978, 20449, 6027, 7435, 3660, 29538, 9673, 8592, 28820, 3660, 12399, 4032, 46958, 5016, 22807, 6156, 28814, 15730, 34105, 25062, 18513, 3660, 5296, 16095, 11778, 13063, 12399, 33962, 26890, 16606, 4032, 45340, 46456, 9381, 9957, 5296, 16095, 11778, 13063, 12399, 8608, 41361, 9673, 7435, 39237, 3615, 5296, 16095, 11778, 13063, 12399, 23032, 21292, 27884, 9673, 8592, 28820, 3660, 5296, 11296, 11778, 13063, 8978, 1975, 9778, 31371, 9640, 16247, 3215, 16606, 9673, 1211, 16373, 46007, 16070, 2655, 3615, 10943, 1211, 20449, 9673, 7435, 39237, 3615, 23032, 1829, 3555, 30731, 34105, 8717, 1863, 3224, 1829, 29538, 9673, 5016, 46958, 25720, 15844, 5551, 42213, 13672, 4587, 16606, 4724, 30544, 16472, 13412, 16606, 21984], "avg_logprob": -0.11824324359563557, "compression_ratio": 2.231075697211155, "no_speech_prob": 2.205371856689453e-06, "words": [{"start": 1960.43, "end": 1960.91, "word": "ممكن", "probability": 0.77490234375}, {"start": 1960.91, "end": 1961.53, "word": " المشكلة", "probability": 0.9793701171875}, {"start": 1961.53, "end": 1962.11, "word": " تحتاج", "probability": 0.9856770833333334}, {"start": 1962.11, "end": 1962.49, "word": " إلى", "probability": 0.71142578125}, {"start": 1962.49, "end": 1963.29, "word": " خبراء", "probability": 0.9664713541666666}, {"start": 1963.29, "end": 1964.07, "word": " ومختصين", "probability": 0.89677734375}, {"start": 1964.07, "end": 1964.75, "word": " وممكن", "probability": 0.8196614583333334}, {"start": 1964.75, "end": 1964.95, "word": " هنا", "probability": 0.87060546875}, {"start": 1964.95, "end": 1965.41, "word": " انشكل", "probability": 0.6812337239583334}, {"start": 1965.41, "end": 1965.95, "word": " لجان", "probability": 0.8531901041666666}, {"start": 1965.95, "end": 1966.43, "word": " من", "probability": 0.95703125}, {"start": 1966.43, "end": 1966.93, "word": " خبراء", "probability": 0.9762369791666666}, {"start": 1966.93, "end": 1967.67, "word": " ومختصين", "probability": 0.98974609375}, {"start": 1967.67, "end": 1967.87, "word": " في", "probability": 0.94580078125}, {"start": 1967.87, "end": 1968.47, "word": " معالجة", "probability": 0.991455078125}, {"start": 1968.47, "end": 1968.71, "word": " هذه", "probability": 0.9521484375}, {"start": 1968.71, "end": 1969.45, "word": " المشكلة،", "probability": 0.8465087890625}, {"start": 1969.45, "end": 1970.35, "word": " واضح؟", "probability": 0.880126953125}, {"start": 1970.35, "end": 1970.87, "word": " فإذا", "probability": 0.8180338541666666}, {"start": 1970.87, "end": 1971.13, "word": " هنا", "probability": 0.638671875}, {"start": 1971.13, "end": 1971.57, "word": " القادة", "probability": 0.9606119791666666}, {"start": 1971.57, "end": 1971.81, "word": " لهم", "probability": 0.919921875}, {"start": 1971.81, "end": 1972.27, "word": " دور،", "probability": 0.85400390625}, {"start": 1972.27, "end": 1972.67, "word": " الخبراء", "probability": 0.9749348958333334}, {"start": 1972.67, "end": 1973.21, "word": " والمختصين", "probability": 0.87333984375}, {"start": 1973.21, "end": 1973.45, "word": " لهم", "probability": 0.971435546875}, {"start": 1973.45, "end": 1974.05, "word": " دور،", "probability": 0.97314453125}, {"start": 1974.05, "end": 1974.41, "word": " سكان", "probability": 0.946044921875}, {"start": 1974.41, "end": 1974.89, "word": " المجتمع", "probability": 0.9949951171875}, {"start": 1974.89, "end": 1975.19, "word": " لهم", "probability": 0.967529296875}, {"start": 1975.19, "end": 1975.47, "word": " دور،", "probability": 0.9187825520833334}, {"start": 1975.47, "end": 1975.85, "word": " طبيعة", "probability": 0.9412434895833334}, {"start": 1975.85, "end": 1976.49, "word": " المشكلة", "probability": 0.998291015625}, {"start": 1976.49, "end": 1977.03, "word": " لها", "probability": 0.974853515625}, {"start": 1977.03, "end": 1977.31, "word": " دور", "probability": 0.9970703125}, {"start": 1977.31, "end": 1977.47, "word": " في", "probability": 0.9658203125}, {"start": 1977.47, "end": 1977.93, "word": " اختيار", "probability": 0.8712158203125}, {"start": 1977.93, "end": 1978.43, "word": " الأداء", "probability": 0.9443359375}, {"start": 1978.43, "end": 1979.09, "word": " الملائمة", "probability": 0.9468994140625}, {"start": 1979.09, "end": 1980.35, "word": " والتعامل", "probability": 0.85771484375}, {"start": 1980.35, "end": 1980.59, "word": " مع", "probability": 0.98974609375}, {"start": 1980.59, "end": 1981.19, "word": " المجتمع", "probability": 0.9951171875}, {"start": 1981.19, "end": 1981.59, "word": " طيب", "probability": 0.9274088541666666}, {"start": 1981.59, "end": 1981.85, "word": " إلى", "probability": 0.6396484375}, {"start": 1981.85, "end": 1982.15, "word": " هنا", "probability": 0.98828125}, {"start": 1982.15, "end": 1982.61, "word": " ننهي", "probability": 0.8814697265625}, {"start": 1982.61, "end": 1982.87, "word": " هذه", "probability": 0.98388671875}, {"start": 1982.87, "end": 1983.53, "word": " المحاضرة", "probability": 0.98876953125}, {"start": 1983.53, "end": 1983.79, "word": " على", "probability": 0.7626953125}, {"start": 1983.79, "end": 1984.07, "word": " أمل", "probability": 0.832275390625}, {"start": 1984.07, "end": 1984.71, "word": " اللقاء", "probability": 0.9934895833333334}, {"start": 1984.71, "end": 1985.47, "word": " بكون", "probability": 0.5458984375}, {"start": 1985.47, "end": 1985.75, "word": " ان", "probability": 0.41015625}, {"start": 1985.75, "end": 1986.11, "word": " شاء", "probability": 0.954345703125}, {"start": 1986.11, "end": 1986.33, "word": " الله", "probability": 0.95458984375}], "temperature": 1.0}], "language": "ar", "language_probability": 1.0, "duration": 1987.303, "duration_after_vad": 1923.0131249999947}
\ No newline at end of file
diff --git a/PL9fwy3NUQKwaKyeI5iiPpebyFXxlPBffV/cIwZculZUuc_postprocess.srt b/PL9fwy3NUQKwaKyeI5iiPpebyFXxlPBffV/cIwZculZUuc_postprocess.srt
new file mode 100644
index 0000000000000000000000000000000000000000..2bf040164ecfe3da98bc39309febdd701a77a51b
--- /dev/null
+++ b/PL9fwy3NUQKwaKyeI5iiPpebyFXxlPBffV/cIwZculZUuc_postprocess.srt
@@ -0,0 +1,1012 @@
+1
+00:00:21,240 --> 00:00:24,700
+بسم الله الرحمن الرحيم الحمد لله رب العالمين
+
+2
+00:00:24,700 --> 00:00:29,480
+والصلاة والسلام على أشرف المرسلين سيدنا محمد وعلى
+
+3
+00:00:29,480 --> 00:00:34,420
+آله وصحبه لأجمعين بنات الطالبات السلام عليكم ورحمة
+
+4
+00:00:34,420 --> 00:00:45,400
+الله وبركاته ما زلنا مبادئ طريقة تنظيم المجتمع في
+
+5
+00:00:45,400 --> 00:00:50,160
+هذه المحاضرة سنتناول مبدأ المسئولية الاجتماعية
+
+6
+00:00:50,930 --> 00:00:57,610
+وكذلك مبدأ اتخاذ القرار سنبدأ بمبدأ المسئولية
+
+7
+00:00:57,610 --> 00:01:02,730
+الاجتماعية طبعا مبدأ المسئولية الاجتماعية من
+
+8
+00:01:02,730 --> 00:01:07,210
+المبادئ الهامة في طريق التنظيم المجتمع ولذلك
+
+9
+00:01:07,210 --> 00:01:13,750
+المسئولية الاجتماعية هي من أحد المكونات لقيم مهنة
+
+10
+00:01:13,750 --> 00:01:20,880
+الخدمة الاجتماعية ولذلك المسئولية الاجتماعيةهي
+
+11
+00:01:20,880 --> 00:01:25,940
+عبارة عن اعتماد أفراد المجتمع على بعضهم البعض
+
+12
+00:01:25,940 --> 00:01:31,460
+وأيضا اعتماد المجتمع على أفراده فلذلك هي مسئولية
+
+13
+00:01:31,460 --> 00:01:37,080
+مشتركة ما بين أفراد المجتمع وما بين المجتمع تكون
+
+14
+00:01:37,080 --> 00:01:45,080
+على شكل الحقوق والواجبات الحقوق حقوق أبناء المجتمع
+
+15
+00:01:45,080 --> 00:01:50,540
+من مجتمعهم وواجبات أبناء المجتمع اتجاه مجتمعهمهذه
+
+16
+00:01:50,540 --> 00:01:56,480
+المسئولية الاجتماعية فلذلك تتكون من شقين المسئولية
+
+17
+00:01:56,480 --> 00:02:01,800
+الاجتماعية الشق الأول الواجبات والشق الثاني هي
+
+18
+00:02:01,800 --> 00:02:06,480
+الحقوق الواجبات هو واجب كل مواطن وواجب كل فرد
+
+19
+00:02:06,480 --> 00:02:11,000
+اتجاه مجتمعي أن يؤدي ما عليه من مسئوليات اتجاه
+
+20
+00:02:11,000 --> 00:02:15,760
+مجتمعي هذا هو الشق الأول من المسئولية الاجتماعية
+
+21
+00:02:16,500 --> 00:02:21,720
+لابد أن يساهم المواطن أو لابد أن يساهم الفرق في
+
+22
+00:02:21,720 --> 00:02:26,560
+بناء مجتمعه ويؤدي ما عليه من واجبات اتجاه مجتمعه
+
+23
+00:02:26,560 --> 00:02:31,560
+أما ما يتعلق بالحقوق الشقة الثانية من المسئولية
+
+24
+00:02:31,560 --> 00:02:38,480
+الاجتماعية فهي حقوق المواطنين أو أفراد المجتمع بما
+
+25
+00:02:38,480 --> 00:02:42,480
+يقومون به من واجبات لابد أن يأخذوا حقوقهم من
+
+26
+00:02:42,480 --> 00:02:47,870
+المجتمع لابد أن يلتزم المجتمعبأداء الحقوق لأبنائه
+
+27
+00:02:47,870 --> 00:02:56,650
+الأبناء المجتمع فلذلك من هنا بنكون حددنا المسئولية
+
+28
+00:02:56,650 --> 00:03:05,030
+الاجتماعية بشقيها اللي هي الواجبات والحقوق طبعا
+
+29
+00:03:05,030 --> 00:03:08,410
+المسئولية الاجتماعية هي مجموعة الجهود اللي بيبذلها
+
+30
+00:03:08,410 --> 00:03:12,010
+أفراد المجتمع لمواجهة المشاكل اللي بعاني منها
+
+31
+00:03:12,010 --> 00:03:16,610
+المجتمعفي مقابل الحصول على الحقوق التي يقفلها
+
+32
+00:03:16,610 --> 00:03:20,630
+المجتمع لهؤلاء الأفراد هذه هي المسئولية الاجتماعية
+
+33
+00:03:20,630 --> 00:03:26,250
+هذا معناها باختصار المسئولية الاجتماعية هو كل ما
+
+34
+00:03:26,250 --> 00:03:30,210
+يقوم بيه أبناء المجتمع بواجبات من اتجاه مجتمعهم
+
+35
+00:03:30,210 --> 00:03:38,390
+وما يلتزم به المجتمع من الحقوق اتجاه أبنائه واضح؟
+
+36
+00:03:38,390 --> 00:03:43,220
+نتيجة قيام أبنائه اللي هو أفراد المجتمعبأداء
+
+37
+00:03:43,220 --> 00:03:53,100
+الواجبات إذا هناك حقوق و هناك واجبات في
+
+38
+00:03:53,100 --> 00:03:56,140
+عند العوامل بتساعد على نجاح مبدأ المسئولية
+
+39
+00:03:56,140 --> 00:04:00,520
+الاجتماعية ما هي العوامل التي بتساعد على مبدأ
+
+40
+00:04:00,520 --> 00:04:05,280
+المسئولية الاجتماعية على نجاحه نجاح المسئولية
+
+41
+00:04:05,280 --> 00:04:10,790
+الاجتماعية أولا إشباع الاحتياجات و حل المشكلاتطبعا
+
+42
+00:04:10,790 --> 00:04:14,290
+مش بقى الاحتياجات وحل المشكلات لابد أن يكون هذا
+
+43
+00:04:14,290 --> 00:04:18,030
+مبني على أساس مدى المساهمة من جانب الأهالي بحل
+
+44
+00:04:18,030 --> 00:04:25,130
+مشكلتها فلا يوجد حق بدون واجب فلذلك من هنا لابد
+
+45
+00:04:25,130 --> 00:04:29,970
+أنهش باحتياجات المواطنين إذا قاموا بواجبات من
+
+46
+00:04:29,970 --> 00:04:35,350
+اتجاه مجتمعي لابد أن يكون هناك حقوقهم غير ناقصة
+
+47
+00:04:35,350 --> 00:04:40,170
+لابد أن تقدرهم الحقوقفهذا يعني العامل الأول اللي
+
+48
+00:04:40,170 --> 00:04:43,770
+بيساعد على نجاح اللي هو مبدأ المسئولية الاجتماعية
+
+49
+00:04:43,770 --> 00:04:47,830
+إشباء الاحتياجات وحل المشكلات أيضًا الاعتراف
+
+50
+00:04:47,830 --> 00:04:52,490
+بالخطأ أثناء الممارسة وليس عيبًا أن نعترف بأخطائنا
+
+51
+00:04:52,490 --> 00:04:57,390
+أثناء الممارسة، ممارسة العمل وهنا إذا اعترفنا
+
+52
+00:04:57,390 --> 00:05:01,590
+بأخطائنا ممكن أن نقوم بتعديل الأخطاء فلذلك لابد من
+
+53
+00:05:01,590 --> 00:05:05,370
+الاعتراف بالخطأ أثناء الممارسةوالعمل على تصحيح
+
+54
+00:05:05,370 --> 00:05:11,070
+الأخطاء وتصحيح المسار أولًا بأول فكل مسئولية قد
+
+55
+00:05:11,070 --> 00:05:15,930
+يقبلها الوقوع في بعض الأخطاء فليس عيبًا أن نقع في
+
+56
+00:05:15,930 --> 00:05:21,690
+الخطأ ولكن عيب أن نتمدى عن تصحيح هذا الخطأ فإذا
+
+57
+00:05:21,690 --> 00:05:26,430
+لابد من تصحيح الأخطاء التي نقع فيها أثناء الممارسة
+
+58
+00:05:26,430 --> 00:05:30,070
+أيضًا توضيح البرامج والمشروعات اللي يمكن أن يتحمل
+
+59
+00:05:30,070 --> 00:05:34,350
+فيها فراد المجتمعبعض المسئوليات وربط ذلك بمراحل
+
+60
+00:05:34,350 --> 00:05:38,910
+زمانية محددة مسئولياتنا البرامج ما هي البرامج
+
+61
+00:05:38,910 --> 00:05:43,790
+المطموبة ما هي المشروعات المطموبة اللي ممكن تحمل
+
+62
+00:05:43,790 --> 00:05:47,670
+أفراد المجتمع القيام بمسئولياتها باعتبارها من
+
+63
+00:05:47,670 --> 00:05:52,270
+واجباتها اتجاه مجتمعهم وهكذا ولذلك ربط هذه
+
+64
+00:05:52,270 --> 00:05:56,230
+المسئوليات بمراحل زمانية للبرامج والمشروعات كل
+
+65
+00:05:56,230 --> 00:06:01,010
+فترة زمانية لنحفظ إنجاز البرنامج ثم المشروع وهكذا
+
+66
+00:06:01,390 --> 00:06:06,650
+يعني خلال فترة زمنية محددة هذا بساعد على نجاح مبدأ
+
+67
+00:06:06,650 --> 00:06:11,610
+اللي هو المسئولية الاجتماعية كذلك الاستعانة
+
+68
+00:06:11,610 --> 00:06:16,550
+بالقيادات الموثوق بها داخل المجتمع لأن ذلك بتفع
+
+69
+00:06:16,550 --> 00:06:20,390
+أفراد المجتمع إلى بذل الجهد وهم مطمئنون إلى أن كل
+
+70
+00:06:20,390 --> 00:06:25,570
+جهد يبذل سوف يكون هناك مقابل له يتناسب مع حجم هذا
+
+71
+00:06:25,570 --> 00:06:33,120
+الجهد واضح؟ أيضافي عندنا من ذلك اتضح ان المسئولية
+
+72
+00:06:33,120 --> 00:06:39,160
+الاجتماعية قيمة
+
+73
+00:06:39,160 --> 00:06:45,120
+أساسية من قيم المجتمع وباعتبر كل فرد مسئول عن
+
+74
+00:06:45,120 --> 00:06:48,520
+موقعه اللي بيعمل فيه ويساهم أيضا في المجالات
+
+75
+00:06:48,520 --> 00:06:52,820
+الأخرى قدرة استعداداته وقدراته ولذلك لا يعيش
+
+76
+00:06:52,820 --> 00:06:58,410
+الإنسان لنفسه فقط بل يحيا ويعمل من أجل الآخرينومن
+
+77
+00:06:58,410 --> 00:07:02,490
+أجل تحقيق أهداف المجتمع هذه المسئولية الاجتماعية
+
+78
+00:07:02,490 --> 00:07:06,370
+إذاً هي قيمة من قيم مهنة الخدمة الاجتماعية لابد
+
+79
+00:07:06,370 --> 00:07:10,330
+يكون عندنا إحساس بالمسئولية الاجتماعية اتجاه وطننا
+
+80
+00:07:10,330 --> 00:07:15,330
+اتجاه مهنتنا لأن مهنتنا بتحثنا على المسئولية
+
+81
+00:07:15,330 --> 00:07:19,890
+الاجتماعية وقيامنا بواجباتنا مقابل قيامنا
+
+82
+00:07:19,890 --> 00:07:24,230
+بواجباتنا لابد أن يكون هناك حقوق لنا من المجتمع
+
+83
+00:07:24,230 --> 00:07:30,670
+تُعطى لنا وها كذافلذلك هذا المبدأ مهم جدا وهو مبدأ
+
+84
+00:07:30,670 --> 00:07:36,670
+أهم من مبادئ طريقة تنظيم المجتمع في أي سؤال في هذا
+
+85
+00:07:36,670 --> 00:07:42,530
+المبدأ؟ نأتي
+
+86
+00:07:42,530 --> 00:07:49,690
+إلى المبدأ الثاني المبدأ الثاني هو مبدأ حق اتخاذ
+
+87
+00:07:49,690 --> 00:07:59,000
+القرار حق اتخاذ القرار حق اتخاذ القراربيشمل الفرد،
+
+88
+00:07:59,000 --> 00:08:02,920
+بيشمل الجماعة، بيشمل المجتمع، لو قلنا حق اتخاذ
+
+89
+00:08:02,920 --> 00:08:08,060
+القرار للفرد، الفرد هو عنده الحرية في ان يتخذ
+
+90
+00:08:08,060 --> 00:08:11,120
+القرار او لا يتخذ القرار، يعمل هذا الشيء او لا
+
+91
+00:08:11,120 --> 00:08:16,380
+يعمل هذا الشيء، واضح؟ كذلك الجماعة، لها الحرية في
+
+92
+00:08:16,380 --> 00:08:20,000
+اتخاذ القرار، ان تفعل هذا الشيء او لا تفعل هذا
+
+93
+00:08:20,000 --> 00:08:26,150
+الشيء، وهكذاولذلك دائما المؤسسة أو المجتمع دائما
+
+94
+00:08:26,150 --> 00:08:30,470
+نجاح البرامج والمشروعات في المجتمع او فشلها بيعتمد
+
+95
+00:08:30,470 --> 00:08:34,950
+على ماذا؟ على اتخاذ القرار ممكن يكون اتخاذ القرار
+
+96
+00:08:34,950 --> 00:08:39,950
+صائب او غير صائب إذا كان صائبا بيؤدي للنجاح أما
+
+97
+00:08:39,950 --> 00:08:46,910
+إذا كان القرار غير صائب فيؤدي للفشل و هكذا فلذلك
+
+98
+00:08:46,910 --> 00:08:53,030
+القرار مهم جداكمبدأ من مبادئ طريق التنظيم في
+
+99
+00:08:53,030 --> 00:08:57,310
+المجتمع طبعاً
+
+100
+00:08:57,310 --> 00:09:01,950
+معنى حق اتخاذ القرار هو قيام المجتمع لتقدير
+
+101
+00:09:01,950 --> 00:09:07,150
+احتياجاته ومواجهة مشكلاته من خلال اتخاذ القرارات
+
+102
+00:09:07,150 --> 00:09:13,790
+النابعة من أفراده تقدير
+
+103
+00:09:13,790 --> 00:09:18,310
+الاحتياجات ومواجهة المشكلاتمن خلال اتخاذ القرارات
+
+104
+00:09:18,310 --> 00:09:23,830
+النابعة من مين؟ من أفراد المجتمع فى أهمية مبدأ
+
+105
+00:09:23,830 --> 00:09:28,930
+اتخاذ القرار ما أهمية مبدأ اتخاذ القرار لعنة منك
+
+106
+00:09:28,930 --> 00:09:32,490
+القرارات اللى هى ارتباط وثيق بتحقيق الأهداف
+
+107
+00:09:32,490 --> 00:09:35,610
+والقرارات الصائبة أو الرشيدة تسمى بقدر كبير في
+
+108
+00:09:35,610 --> 00:09:39,490
+وصول المجتمع لتحقيق أهداف نعم القرارات اللى هى
+
+109
+00:09:39,490 --> 00:09:43,330
+ارتباط وثيق بتحقيق الأهداف والقرارات الصائبة هى
+
+110
+00:09:43,330 --> 00:09:48,080
+اللى بتوصلنا إلى تحقيق الأهدافإذا كانت صائبة فلذلك
+
+111
+00:09:48,080 --> 00:09:51,540
+دائما لابد أن يكون ما نتخذه من القرارات تكون
+
+112
+00:09:51,540 --> 00:09:54,980
+قرارات صائبة وما يتخذه أفراد المجتمع من قرارات
+
+113
+00:09:54,980 --> 00:10:01,200
+تكون قرارات صائبة حتى يمكننا تحقيق الأهداف طيب، في
+
+114
+00:10:01,200 --> 00:10:04,960
+عندنا أيضا القرارات لأمادة أيضا من أهمية مبدأ
+
+115
+00:10:04,960 --> 00:10:08,100
+اتخاذ القرار أيضا القرارات لها ارتباط واضيق
+
+116
+00:10:08,100 --> 00:10:10,860
+للتوظيف الأقل لمواد المادية والمشارية داخل
+
+117
+00:10:10,860 --> 00:10:14,910
+المؤسسات اللي تتمارس فيها المجتمععن توظيف الموارد
+
+118
+00:10:14,910 --> 00:10:19,230
+والإمكانيات المادية والبشرية فاتخاذ القرارات تعمل
+
+119
+00:10:19,230 --> 00:10:23,110
+على توظيف هذه الموارد المادية واستخدامها لاستخدام
+
+120
+00:10:23,110 --> 00:10:28,630
+الأمثل من أجل تحقيق الأهداف فالموارد
+
+121
+00:10:28,630 --> 00:10:31,550
+المادية والبشرية لايمكن استخلالها أو استثمارها إلا
+
+122
+00:10:31,550 --> 00:10:36,050
+من القرارات التي تتخذ من أجل استفادة من هذه
+
+123
+00:10:36,050 --> 00:10:42,690
+الموارد ماذا أيضا في عندناأهمية أخرى برضه من أهمية
+
+124
+00:10:42,690 --> 00:10:48,270
+مبدأ اتخاذ القرار أيوة
+
+125
+00:10:48,270 --> 00:10:51,390
+يا بنت القرارات لها تأثير بكل مراحل العمل المهني
+
+126
+00:10:51,390 --> 00:10:54,310
+مع المجتمع بدءا من تخطيط دخول المجتمع إلى وضع
+
+127
+00:10:54,310 --> 00:10:58,250
+برنامج التنفيذ لعمليات مشابعة و لا تابعة تأثير
+
+128
+00:10:58,250 --> 00:11:01,550
+طبعا القرارات لها تأثير بكل مراحل العمل المهني
+
+129
+00:11:01,550 --> 00:11:06,110
+وخطوات العمل المهني وتبدأ هذه الخطوات من التخطيط
+
+130
+00:11:07,490 --> 00:11:12,650
+اللي هي عملية وضع البرامج أو المشاريع وتنفيذها ثم
+
+131
+00:11:12,650 --> 00:11:18,290
+متابعتها وتقويمها فلذلك اتخاذ القرار له تأثير بكل
+
+132
+00:11:18,290 --> 00:11:23,430
+مراحل العمل وخطوات العمل المهني في عندنا أيضا من
+
+133
+00:11:23,430 --> 00:11:28,950
+أهمية اتخاذ القرار اللي هو نجاح في اتخاذ القرارات
+
+134
+00:11:28,950 --> 00:11:33,890
+في مراحل العمل المهني تتوقف على ماذا؟ تتوقف على
+
+135
+00:11:33,890 --> 00:11:37,810
+ماذا؟ عملية النجاح في اتخاذ القراراتبالعمل المهني،
+
+136
+00:11:37,810 --> 00:11:44,050
+فاتوقف على مدى؟ أيوة بالفعل ارتقاء
+
+137
+00:11:44,050 --> 00:11:47,630
+والتساع، اللي هي درجة الخبرة والمهارة اول شيء،
+
+138
+00:11:47,630 --> 00:11:50,890
+درجة الخبرة والمهارة المتوفرة لدى متاخد القرار،
+
+139
+00:11:50,890 --> 00:11:57,110
+فالناحية الثانية ارتقاء
+
+140
+00:11:57,110 --> 00:12:01,250
+والتساع اللي فوق، اذا النجاح في اتخاذ القرارات
+
+141
+00:12:01,250 --> 00:12:06,520
+يعني بتوقف على الخبرة والمهارةبتوقف على ارتقاء
+
+142
+00:12:06,520 --> 00:12:11,700
+وادساع الأفق، ماذا أيضًا؟ وجود بدائل متعددة أمام
+
+143
+00:12:11,700 --> 00:12:15,340
+.. متعددة أمام .. وجود بدائل متعددة أمام نتخذ
+
+144
+00:12:15,340 --> 00:12:20,180
+القرار، لأن، شوفوا، يعني القرار ما بيكونش لبديل
+
+145
+00:12:20,180 --> 00:12:24,200
+واحد، القرار لازم يكون عندنا عدد من البدائل حتى
+
+146
+00:12:24,200 --> 00:12:29,480
+نتخذ القرار، إذا يعني أما إذا اتخذنا شيء معين، هذا
+
+147
+00:12:29,480 --> 00:12:33,320
+ليس اتخاذ قرار، اتخاذ القرار دائمًا يكون من بدائل
+
+148
+00:12:33,320 --> 00:12:38,170
+متعددة أمامنابديلين او فا أكثر بديلين فا أكثر
+
+149
+00:12:38,170 --> 00:12:42,230
+فلذلك ممكن يكون بديلين ثلاثة او أربعة منهم فبنتاخد
+
+150
+00:12:42,230 --> 00:12:46,290
+البديل الملائم والمناسب وهذا بيكون هو اتخاذ القرار
+
+151
+00:12:46,290 --> 00:12:52,030
+ماذا أيضا من عوامل يعني نجاح اتخاذ القرار في مراحل
+
+152
+00:12:52,030 --> 00:12:55,850
+العمل المهم؟ ماذا يا منتي؟ توفر الوسائل المناسبة
+
+153
+00:12:55,850 --> 00:12:57,390
+لاتخاذ القرار بدأ جديد
+
+154
+00:13:00,010 --> 00:13:04,610
+توفر الوسائل اللازمة الوسائل المناسبة لاتخاذ
+
+155
+00:13:04,610 --> 00:13:09,790
+القرار بقى لابد تكون عندنا وسائل فهذه الوسائل ممكن
+
+156
+00:13:09,790 --> 00:13:15,690
+يعني تكون مناسبة حتى نتخذ القرار يعني و ننفذ
+
+157
+00:13:15,690 --> 00:13:21,130
+القرار إذا كان القرار صائب و هكذا و نغير القرار
+
+158
+00:13:21,130 --> 00:13:27,690
+إذا كان القرار غير صائب ماذا أيوة؟ أيوة بنت
+
+159
+00:13:28,060 --> 00:13:30,980
+القرارات لها أهمية في تحقيق الاستقرار والأمن
+
+160
+00:13:30,980 --> 00:13:34,680
+والانتماء لدى أفراد المجتمع بالطبع لأن القرارات
+
+161
+00:13:34,680 --> 00:13:39,160
+الصائبة تعمل على تحقيق الأمن وتعمل على تحقيق أداء
+
+162
+00:13:39,160 --> 00:13:44,580
+في المجتمع فلذلك من هنا عملية اتخاذ القرارات مهمة
+
+163
+00:13:44,580 --> 00:13:51,820
+جدا في عوامل بتساعد على نجاح المبدأ على نجاح مبدأ
+
+164
+00:13:51,820 --> 00:13:55,420
+اتخاذ القرار ما هي هذه العوامل؟
+
+165
+00:13:58,650 --> 00:14:01,630
+عوامل نجاح المبدأ لما سام الأفراد والجماعات في
+
+166
+00:14:01,630 --> 00:14:05,630
+اتخاذ القرارات الخاصة بهم سام الأفراد والجماعات في
+
+167
+00:14:05,630 --> 00:14:09,090
+اتخاذ القرارات الخاصة بهم وهذا يتمشي مع ايه؟ مع
+
+168
+00:14:09,090 --> 00:14:11,830
+قدرات وسلاسل القرارات اتخاذ القرار من قبل الفرد
+
+169
+00:14:11,830 --> 00:14:16,170
+والجماعة داخل المجتمع هذا يتمشي لازم يكون مع قدرات
+
+170
+00:14:16,170 --> 00:14:20,210
+الأفراد والجماعات داخل المجتمع ومدى استعداداته
+
+171
+00:14:20,210 --> 00:14:26,550
+وكبراته والمهارات المتوفرة دا دي وهكذا ماذا أيضا
+
+172
+00:14:26,550 --> 00:14:31,220
+من العوامل اللي بتساعد على نجاحه؟قرار اتخاذ القرار
+
+173
+00:14:31,220 --> 00:14:35,580
+أن تحدد المشكلات المراد حلها بالدقة و أن تميز عن
+
+174
+00:14:35,580 --> 00:14:39,000
+غيرها من المشكلات الأخرى المدشابهة و أن يكون
+
+175
+00:14:39,000 --> 00:14:42,420
+المسلمين الرغباء في حلها و ترشيد القرارات بشاملها
+
+176
+00:14:42,420 --> 00:14:47,800
+طبعا أن تحدد إن المشكلات المراد حلها لابد ان
+
+177
+00:14:47,800 --> 00:14:51,660
+نحددها ما هي المشكلات المراد حلها و نتخد القرار
+
+178
+00:14:51,660 --> 00:14:54,440
+الملائم و المناسب في حل هذه المشكلة
+
+179
+00:14:57,060 --> 00:15:00,860
+هي بتساعد على نجاح مبدأ اتخاذ القرار، أيوية يا
+
+180
+00:15:00,860 --> 00:15:05,900
+بنتى؟ انتحدد الأهداف المطموعة و تحقيقها نعم هنا
+
+181
+00:15:05,900 --> 00:15:10,240
+لازم نعرف الأهداف المطموعة تحقيقها ما هي ما هي
+
+182
+00:15:10,240 --> 00:15:14,480
+الأهداف المراد تحقيقها حتى نتخذ القرار الملائم
+
+183
+00:15:14,480 --> 00:15:19,000
+بالنسبة لهذه الأهداف و انجاز هذه الأهداف طيب مثل
+
+184
+00:15:19,000 --> 00:15:22,960
+ماذا؟مثل ماذا؟ المعدات المطلوب الرصول اليها
+
+185
+00:15:22,960 --> 00:15:26,060
+والمواعيد المناسب لبدأية حل المشكلات والمعوقات
+
+186
+00:15:26,060 --> 00:15:33,380
+التي يمكن أن تكون المواعيد المناسبة لبدأية حل
+
+187
+00:15:33,380 --> 00:15:38,500
+المشكلة أو أيضا الصعوبات اللي يمكن أن تواجهنا
+
+188
+00:15:38,500 --> 00:15:44,680
+أثناء حل المشكلة هذه كلها يعني لابد أن نحددها
+
+189
+00:15:44,680 --> 00:15:53,260
+ونعرفهاحتى نجح في مبدأ اتخاذ القرار ونصل الى
+
+190
+00:15:53,260 --> 00:15:58,460
+الأهداف المطلوبة الوصول اليها لو نتعرف على
+
+191
+00:15:58,460 --> 00:16:02,560
+المعدلات والمواعيد والمعامل القادمة طيب في عوامل
+
+192
+00:16:02,560 --> 00:16:07,520
+بتساعد على نجاح هذا المبدأ أيضا ماهي هذه العوامل؟
+
+193
+00:16:07,520 --> 00:16:12,920
+جمع كافة البيانات المتعلقة بالمشكلة أو المشكلات
+
+194
+00:16:12,920 --> 00:16:16,260
+التي يواجهها المشكلةعشان نتخذ القرار السليم
+
+195
+00:16:16,260 --> 00:16:20,160
+والواضح لابد أن تكون لدينا بيانات ومعلومات حول
+
+196
+00:16:20,160 --> 00:16:24,560
+المشكلات المراد اتخاذ القرار حولها من أجل حلها
+
+197
+00:16:24,560 --> 00:16:28,820
+فلذلك حل المشكلة لا يمكن أن يكون إلا بالمعلومات
+
+198
+00:16:28,820 --> 00:16:33,180
+لابد و لا كيف سنحل المشكلة لابد تكون المعلومات
+
+199
+00:16:33,180 --> 00:16:38,640
+واضحة حول المشكلة ماذا أيضا من أعوام نساعد على
+
+200
+00:16:38,640 --> 00:16:40,660
+النجاح المبدأ؟ أيوة من أنت
+
+201
+00:16:45,280 --> 00:16:49,800
+نعم يعني كل المعلومات و الحقائق هنا لازم نسجل و
+
+202
+00:16:49,800 --> 00:16:54,800
+نصنف كل الحقائق و المعلومات اللي وصلنا إليها و هذه
+
+203
+00:16:54,800 --> 00:16:58,320
+كلها مرتبطة بمشكلة حتى نتخذ القرار الملائم و
+
+204
+00:16:58,320 --> 00:17:01,840
+المناسب و هذه من العوامل اللي هي بتساعدنا على نجاح
+
+205
+00:17:01,840 --> 00:17:05,320
+مبدأ اتخاذ القرار أي مابين يكون هناك بداية
+
+206
+00:17:05,320 --> 00:17:11,720
+للمعالجة مشكلتك؟ طبعا يكون عندنا بداية لمعالجة
+
+207
+00:17:11,720 --> 00:17:15,960
+المشكلاتأو حلول ممكن أن نميّز المشاكل اللي بيعاني
+
+208
+00:17:15,960 --> 00:17:20,720
+منها المجتمع حتى نتخذ القرار الملائم من خلال هذه
+
+209
+00:17:20,720 --> 00:17:25,340
+البداية ونختار البديل الملائم لحل المشكلة هذه كلها
+
+210
+00:17:25,340 --> 00:17:30,120
+من العوام بتساعد على نجاح مبدأ اتخاذ القرار طيب في
+
+211
+00:17:30,120 --> 00:17:34,040
+عندنا صعوبات تواجه عملية اتخاذ القرار ما هي
+
+212
+00:17:34,040 --> 00:17:41,830
+الصعوبات التي تواجهنا عند عملية اتخاذ القراراللي
+
+213
+00:17:41,830 --> 00:17:48,050
+ما اتكلمتش نهائيا في الآخر في الآخر انت ايوة اه
+
+214
+00:17:48,050 --> 00:17:52,150
+تفضلي محدودين المعلومات المظاهرة من المشكلات او
+
+215
+00:17:52,150 --> 00:17:55,170
+البرامج المراد تصنع من وارث المشكلات التي عالمنا
+
+216
+00:17:55,170 --> 00:18:00,030
+نشتغلها اه صعوبة المعلومات هذه من المشكلات يعني او
+
+217
+00:18:00,030 --> 00:18:03,310
+من الصعوبات اللي بتوجهنا في عملية اتخاذ القرارات
+
+218
+00:18:03,310 --> 00:18:07,630
+حول مشكلة معينة مافيش معلومات مافيش حقائق اذا صعب
+
+219
+00:18:07,630 --> 00:18:12,210
+اننا نتاخد قرار فيها هذه من الصعوبات اللي هيمجموعه
+
+220
+00:18:12,210 --> 00:18:15,590
+اللي هي محدودية المعلومات المتوفرة حول المشكلات
+
+221
+00:18:15,590 --> 00:18:20,510
+ماذا ايضا؟ اه عدم وجود خبرة كافية لدى متخدية
+
+222
+00:18:20,510 --> 00:18:23,610
+القرار اما نتيجة صغر السن او عدم الفصول على دورات
+
+223
+00:18:23,610 --> 00:18:26,710
+التدريبية من ناس متعلم في هذه العامة طبعا وهذا من
+
+224
+00:18:26,710 --> 00:18:31,170
+الصعوبات ايضا اللي بتواجه عملية اتقاد القرار اللي
+
+225
+00:18:31,170 --> 00:18:38,110
+هي عدم وجود الخبرة الكافية لدى متخدية القرارات في
+
+226
+00:18:38,110 --> 00:18:44,840
+عندنا صعوبة اخرى ما هي؟اللي في الجهة هذه، في الجهة
+
+227
+00:18:44,840 --> 00:18:50,220
+هذه يعني إحنا جهة تجاوب وجهة أخرى أيضا لازم تجاوب،
+
+228
+00:18:50,220 --> 00:18:57,840
+أيوة يا بنت اتفضلي بالضبط،
+
+229
+00:18:57,840 --> 00:19:01,140
+وهذه من الصعوبات التي تواجهنا في اتخاذ القرار،
+
+230
+00:19:01,140 --> 00:19:05,460
+اللي هي وجود السلبية وتواكل من جانب أفراد المجتمع
+
+231
+00:19:05,460 --> 00:19:07,460
+وعدم الرغبة في المشاركة
+
+232
+00:19:09,860 --> 00:19:14,080
+هذه كلها من الصعوبات اللي بتوجهنا في اتخاذ القرار،
+
+233
+00:19:14,080 --> 00:19:19,160
+ماذا أيضًا؟ عدم
+
+234
+00:19:19,160 --> 00:19:30,160
+مضوح الأهداف المضلوب
+
+235
+00:19:30,160 --> 00:19:37,690
+اتخاذ قرار بشأنها، ماذا أيضًا؟خلاص هذه يعني هي أهم
+
+236
+00:19:37,690 --> 00:19:42,070
+الأهداف أو أهم الصعوبات اللي بتواجهنا في عملية
+
+237
+00:19:42,070 --> 00:19:47,550
+اتخاذ القرار نكون بهذه المحاضرة يعني تكلمنا عن
+
+238
+00:19:47,550 --> 00:19:53,690
+مبدأين أساسيين من مبادئ طريق تنظيم المجتمع مبدأ
+
+239
+00:19:53,690 --> 00:19:57,470
+المسئولية الاجتماعية وقلنا عنها عبارة عن الواجبات
+
+240
+00:19:57,470 --> 00:20:01,960
+والحقوقواجبات من المواطنين اتجاه مجتمعهم وما
+
+241
+00:20:01,960 --> 00:20:06,220
+يقومون بيه من تحقيقة ذات مجتمعهم وحقوق للمواطنين
+
+242
+00:20:06,220 --> 00:20:10,960
+ايضا وللافراد المجتمع نتيجة قيامهم بواجباتهم اتجاه
+
+243
+00:20:10,960 --> 00:20:15,820
+المجتمع لابد ان يأخذوا ويحصلوا على حقوقهم من
+
+244
+00:20:15,820 --> 00:20:21,920
+المجتمع ايضا تكلمنا عن المبدأ اتخاذ القرار وقلنا
+
+245
+00:20:21,920 --> 00:20:24,700
+لابد من اتخاذ القرار يعني
+
+246
+00:20:26,960 --> 00:20:30,900
+وهو المبدأ اتخاذ القرار من المبادئ أيضًا الهامة في
+
+247
+00:20:30,900 --> 00:20:36,880
+طريق تنظيم المجتمع والقرار الصالح أو القرار المجدي
+
+248
+00:20:36,880 --> 00:20:41,320
+أو القرار اللي نافع لابد أن يكون محققًا لأهداف
+
+249
+00:20:41,320 --> 00:20:46,280
+المجتمع فلذلك لابد من اتخاذ القرارات التي تحقق لنا
+
+250
+00:20:46,280 --> 00:20:55,460
+أهداف المجتمع نكون بذلك يعني أنهينا محاضرتناعلى
+
+251
+00:20:55,460 --> 00:20:59,580
+أمل اللقاء بكنا إن شاء الله في المحاضرة القادمة
+
+252
+00:20:59,580 --> 00:21:03,920
+إلى أن نلتقي بكنا في المحاضرة القادمة لكن مني كل
+
+253
+00:21:03,920 --> 00:21:08,460
+تحية و تقدير والسلام عليكم ورحمة الله وبركاته
+
diff --git a/PL9fwy3NUQKwaKyeI5iiPpebyFXxlPBffV/f9sXapLnL_I.srt b/PL9fwy3NUQKwaKyeI5iiPpebyFXxlPBffV/f9sXapLnL_I.srt
new file mode 100644
index 0000000000000000000000000000000000000000..a247ceb758e66334efe92f3c8b834ce24c576526
--- /dev/null
+++ b/PL9fwy3NUQKwaKyeI5iiPpebyFXxlPBffV/f9sXapLnL_I.srt
@@ -0,0 +1,1334 @@
+1
+00:00:20,700 --> 00:00:24,260
+بسم الله الرحمن الرحيم الحمد لله رب العالمين
+
+2
+00:00:24,260 --> 00:00:28,320
+والصلاة والسلام على أشرف المرسلين سيدنا محمد وعلى 
+
+3
+00:00:28,320 --> 00:00:33,520
+آله وصحبه أجمعين بنات الطالبات السلام عليكم ورحمة 
+
+4
+00:00:33,520 --> 00:00:43,110
+الله وبركاته في المحاضرة السابقة تحدثنا عن مفهوم عن
+
+5
+00:00:43,110 --> 00:00:48,130
+دعائم المجتمع ومن ثم أيضا مفهوم المجتمع في طريقة 
+
+6
+00:00:48,130 --> 00:00:56,810
+تنظيم المجتمع وتحدثنا عن الجزء الأول وهو مفهوم 
+
+7
+00:00:56,810 --> 00:01:02,790
+المجتمع كنسق اجتماعي واتعرفنا على النسق الاجتماعي 
+
+8
+00:01:02,790 --> 00:01:08,550
+للمجتمع ولمنظمة باعتبار أن المجتمع في طريق طريق
+
+9
+00:01:08,550 --> 00:01:12,670
+تنظيم المجتمع كنسق اجتماعي يعني كsystem اجتماعي
+
+10
+00:01:12,670 --> 00:01:19,670
+يعني كنظام اجتماعي أو كمنظمة موجودة في المجتمع
+
+11
+00:01:19,670 --> 00:01:27,320
+وأيضا تكلمنا عن مفهوم المجتمع كنسق اجتماعي أو ..
+
+12
+00:01:27,320 --> 00:01:31,660
+كنظام اجتماعي وتحدثنا عن بعض الأنظمة الاجتماعية
+
+13
+00:01:31,660 --> 00:01:38,620
+باعتبار أن كل نسق اجتماعي له عام له أنسقة فرعية و
+
+14
+00:01:38,620 --> 00:01:43,240
+تحدثنا عن النسق التعليمي وقلنا النسق التعليمي
+
+15
+00:01:43,240 --> 00:01:48,320
+باعتباره نسق كله له أنسقة فرعية مثل ماذا؟ أو أنظمة 
+
+16
+00:01:48,320 --> 00:01:52,500
+فرعية مثل الامتحانات مثل وجود الطالب مثل المعلم
+
+17
+00:01:52,500 --> 00:01:56,440
+مثل بصيرة الإضاءة مثل المنهج مثل الامتحانات إلى غير 
+
+18
+00:01:56,440 --> 00:02:02,700
+ذلك من الأنظمة أو الأنساق الفرعية فأيضا النظام 
+
+19
+00:02:02,700 --> 00:02:06,780
+النظام الأسري كذلك نظام أسري عام أو نسق أسري عام
+
+20
+00:02:06,780 --> 00:02:12,400
+له أيضا يعني أنظمة فرعية مثل الخطبة مثل الزواج مثل 
+
+21
+00:02:12,400 --> 00:02:17,680
+الطلاق مثل المواريث وهكذا هذه كلها يعني أنسقة 
+
+22
+00:02:17,680 --> 00:02:24,480
+فرعية للنظام الأسري وكذلك النظام الاقتصادي كنظام 
+
+23
+00:02:24,480 --> 00:02:32,060
+كله له أنظمة فرعية مثل الانتاج التسعير أو الترويج
+
+24
+00:02:32,060 --> 00:02:38,720
+و أيضا التسويق للسلع و أيضا الأسعار سعر السلعة
+
+25
+00:02:38,720 --> 00:02:44,000
+هذه كلها أيضا أنظمة فرعية للنسق الكلي وهو النظام
+
+26
+00:02:44,000 --> 00:02:50,080
+الاقتصادي وهكذا كل نظام كله أو كل نسق كله له أنساق 
+
+27
+00:02:50,080 --> 00:02:56,830
+أو أنظمة فرعية وهكذا باعتبار أن المنظمة كمجتمع كنسق 
+
+28
+00:02:56,830 --> 00:03:02,630
+اجتماعي وتكلمنا أيضا عن المجتمع المحلي أو الحي
+
+29
+00:03:02,630 --> 00:03:08,470
+يعتبر يعني ثم المجتمع المحلي ثم المجتمع الكبير ثم 
+
+30
+00:03:08,470 --> 00:03:13,610
+المجتمع القومي ثم المجتمع الدولي هذه كلها يعني 
+
+31
+00:03:13,610 --> 00:03:19,330
+أنساق فرعية في إطار المجتمع الكل اللي هو الدولي و
+
+32
+00:03:19,330 --> 00:03:26,220
+هكذا نبدأ بالصغير ثم الكبير أيضا اليوم سنكمل و
+
+33
+00:03:26,220 --> 00:03:32,260
+تكلمنا أيضا عن المتطلبات اللازمة للنظام حتى يستمر 
+
+34
+00:03:32,260 --> 00:03:38,580
+أو المرظمة حتى تستمر و أيضا وصلنا أخيرا إلى ال ..
+
+35
+00:03:40,010 --> 00:03:45,390
+مفهوم المجتمع في طريق تنظيم المجتمع كعملية process
+
+36
+00:03:45,390 --> 00:03:50,650
+كعملية وهذا ما سنشرحه اليوم إن شاء الله وغيره من 
+
+37
+00:03:50,650 --> 00:03:57,300
+مفاهيم المجتمع في طريق تنظيم المجتمع المجتمع كعملية
+
+38
+00:03:57,300 --> 00:04:02,760
+يعني بدنا ناخذه من وجهة نظر طريقة تنظيم المجتمع
+
+39
+00:04:02,760 --> 00:04:07,660
+وجهة نظر المنظم الاجتماعي فلذلك هنا احنا بنتعامل
+
+40
+00:04:07,660 --> 00:04:13,320
+دائما كعملية process يعني فيه تفاعل فلذلك معنى
+
+41
+00:04:13,320 --> 00:04:18,660
+المجتمع كعملية يعني هي عبارة عن خبرات ومهارات
+
+42
+00:04:19,600 --> 00:04:25,340
+تعليمية، خبرات ومهارات وخبرات تعليمية طبعا ممكن
+
+43
+00:04:25,340 --> 00:04:30,000
+يكتسبها الناس وأيضا اللي هي عبارة عن المهارات
+
+44
+00:04:30,000 --> 00:04:32,140
+الاجتماعية اللي بتمكن 
+
+45
+00:04:34,820 --> 00:04:40,140
+المنظم اللي بتمكن المنظم الاجتماعي من مواجهة 
+
+46
+00:04:40,140 --> 00:04:44,440
+المشكلات الخاصة بالمجتمع فإذا المنظم هنا بيتعامل مع
+
+47
+00:04:44,440 --> 00:04:50,680
+المجتمع كعملية يعني كخبرات عملية وتعليمية وأيضا
+
+48
+00:04:50,680 --> 00:04:55,640
+مهارات اجتماعية هذه كلها من أجل مواجهة المشكلات
+
+49
+00:04:55,640 --> 00:04:58,540
+الاجتماعية ولذلك
+
+50
+00:05:00,120 --> 00:05:04,500
+المفهوم الأول من أشار إلى المجتمع كعملية هو روس
+
+51
+00:05:04,500 --> 00:05:08,120
+فمفهوم 
+
+52
+00:05:08,120 --> 00:05:12,020
+العملية هنا للدلالة على قيام المجتمع بتحديد
+
+53
+00:05:12,020 --> 00:05:17,580
+مشكلاته ثم القيام بإجراء المواجهة لهذه المشكلة
+
+54
+00:05:18,480 --> 00:05:23,900
+طبعا مفهوم المجتمع كعملية بأنه بتضمن خبرات بيمر 
+
+55
+00:05:23,900 --> 00:05:28,280
+بيها أفراد المجتمع وليس خبرات فقط بل ومهارات أيضا
+
+56
+00:05:28,280 --> 00:05:33,400
+ومهارات اجتماعية يعني بيمر بيها أفراد المجتمع وهذا 
+
+57
+00:05:33,400 --> 00:05:37,900
+ممكن من خلال الخبرات والمهارات مواجهة المشكلات
+
+58
+00:05:37,900 --> 00:05:43,000
+الاجتماعية التي يواجهها المجتمع ونعمل على حل هذه
+
+59
+00:05:43,000 --> 00:05:47,400
+المشكلات وبعد ذلك يتحقق التعاون بين أفراد المجتمع
+
+60
+00:05:50,510 --> 00:05:57,770
+أيضا المجتمع كعملية هو بمثابة التعلم واكتساب اللي 
+
+61
+00:05:57,770 --> 00:06:02,270
+هي التعلم من خلال الممارسة العملية داخل المجتمع
+
+62
+00:06:02,270 --> 00:06:06,710
+واكتساب المهارات الاجتماعية المختلفة لمواجهة
+
+63
+00:06:06,710 --> 00:06:07,650
+المشكلة
+
+64
+00:06:13,190 --> 00:06:17,730
+طبعا المنظم الاجتماعي هو اللي بيساعد المجتمع على 
+
+65
+00:06:17,730 --> 00:06:26,030
+تقويته بمقوماته ودعائمه المعروفة طبعا إذا ما عمل
+
+66
+00:06:26,030 --> 00:06:30,850
+على مشاركة سكان المجتمع فلذلك هناك علاقة بين
+
+67
+00:06:30,850 --> 00:06:36,030
+المشاركة وبين تفاعل سكان المجتمع كلما كانت وهناك
+
+68
+00:06:36,030 --> 00:06:41,450
+أيضا علاقة ما بين الانتماء و المشاركة فلذلك حتى تحدث
+
+69
+00:06:41,450 --> 00:06:45,270
+عملية التفاعل داخل المجتمع باعتبار المجتمع عملية 
+
+70
+00:06:45,270 --> 00:06:49,010
+لابد من الانتماء موجود الانتماء إلى المجتمع
+
+71
+00:06:49,010 --> 00:06:53,390
+والانتماء يعني بيجعل أفراد المجتمع يزدادون في
+
+72
+00:06:53,390 --> 00:06:58,290
+المشاركة في معرفة مشكلات المجتمع وفي أيضا كيفية 
+
+73
+00:06:58,290 --> 00:07:04,860
+مواجهة هذه المشكلة واضح؟ فالمشاركة .. فالانتماء مهم 
+
+74
+00:07:04,860 --> 00:07:08,600
+جدا لأن الانتماء هو اللي بيسبب لنا المشاركة أو
+
+75
+00:07:08,600 --> 00:07:12,660
+بيحدث لنا المشاركة من قبل سكان المجتمع مشاركة في 
+
+76
+00:07:12,660 --> 00:07:17,720
+معرفة المشكلات وحل المشكلات واضح؟ وهنا بتزيد .. 
+
+77
+00:07:17,720 --> 00:07:21,800
+بتزيد عمليات اللي هي ال process اللي هي أن المجتمع 
+
+78
+00:07:21,800 --> 00:07:26,700
+كعملية لأن بيحدث تفاعل واضح؟ وتبادل خبرات ومهارات
+
+79
+00:07:26,700 --> 00:07:31,840
+بين أفراد المجتمع لمساعدتهم على حل مشكلاتهم
+
+80
+00:07:34,270 --> 00:07:41,450
+تعامل مع المشكلات طبعا تتوقف
+
+81
+00:07:41,450 --> 00:07:45,670
+على مقدرة المجتمع على تنظيم نفسه هل عنده مقدرة على 
+
+82
+00:07:45,670 --> 00:07:51,850
+التنظيم؟ كلما كان المجتمع قادرا على تنظيم نفسه هنا
+
+83
+00:07:51,850 --> 00:07:56,750
+بيكون قادرا على معرفة مشكلاته وأيضا ممكن المنظم
+
+84
+00:07:56,750 --> 00:08:01,250
+يساعده على ذلك على معرفة المشكلات وعلى كيفية 
+
+85
+00:08:01,250 --> 00:08:08,310
+مواجهة هذه المشكلات واضح؟ أيضا مساعدة المجتمع
+
+86
+00:08:08,310 --> 00:08:11,830
+بالنسبة لعناصر المجتمع كعملية اللي هي مساعدة
+
+87
+00:08:11,830 --> 00:08:15,270
+المجتمع على إحداث التكامل، التكامل بين وحداته
+
+88
+00:08:15,270 --> 00:08:19,190
+المكونة له المجتمع وزيادة الترابط بينه وبين 
+
+89
+00:08:19,190 --> 00:08:25,410
+المجتمع المحيط به، أيضا توفر الإحساس بالانتماء و
+
+90
+00:08:25,410 --> 00:08:29,710
+هنا طبعا نعمل على زيادة الانتماء للمجتمع لأن
+
+91
+00:08:29,710 --> 00:08:35,470
+بالنسبة لزيادة الانتماء تعمل على زيادة المشاركة و
+
+92
+00:08:35,470 --> 00:08:41,390
+زيادة التفاعل الاجتماعي مع المجتمع من أجل مواجهة
+
+93
+00:08:41,390 --> 00:08:44,850
+المشكلات وتحقيق أهداف المجتمع
+
+94
+00:08:49,440 --> 00:08:55,220
+نكون بذلك انتهينا من المجتمع ك process يعني كعملية
+
+95
+00:08:55,220 --> 00:09:01,120
+ننتقل الآن إلى المفهوم الآخر للمجتمع في طريقة 
+
+96
+00:09:01,120 --> 00:09:04,960
+تنظيم المجتمع وهو المجتمع الوظيفي والمجتمع
+
+97
+00:09:04,960 --> 00:09:09,020
+الجغرافي بدنا نعرف إيش هو المجتمع الجغرافي وما هو
+
+98
+00:09:09,020 --> 00:09:14,300
+المجتمع الوظيفي في أي طالبة بتعرف إيش هو المجتمع
+
+99
+00:09:14,300 --> 00:09:18,280
+وما هو المجتمع الجغرافي؟ نعم يا بنتي هو موقع 
+
+100
+00:09:18,280 --> 00:09:22,180
+جغرافية معينة، فستكون قرية أو مدينة أو بلدة أو حيّة
+
+101
+00:09:22,180 --> 00:09:26,800
+أو مؤتمر أو قليل أو دولة؟ نعم، إذا هنا محدد بحدود
+
+102
+00:09:26,800 --> 00:09:31,300
+جغرافية من خلال الاسم، ولذلك بنقول مجتمع جغرافي، 
+
+103
+00:09:31,300 --> 00:09:36,610
+إذا له حدود جغرافية والحدود الجغرافية قد تكون لحي،
+
+104
+00:09:36,610 --> 00:09:43,230
+قد تكون لقرية، قد تكون لمدينة، قد تكون لمجتمع ككل
+
+105
+00:09:43,230 --> 00:09:47,710
+يعني محافظة أو دولة، مجتمع قومي أو أيضا ممكن يكون
+
+106
+00:09:47,710 --> 00:09:52,390
+لقارة، عدد من الدول أو ممكن يكون المجتمع العالمي
+
+107
+00:09:52,390 --> 00:09:57,590
+اللي بيشمل الكرة الأرضية ككل، بحدودها ككل، واضح؟
+
+108
+00:09:57,590 --> 00:10:01,710
+إذن هذا هو المفهوم الجغرافي للمجتمع، المحدد
+
+109
+00:10:01,710 --> 00:10:07,810
+بالحدود و المسميات كما ذكرناها مسميات أحياء، مدن،
+
+110
+00:10:07,810 --> 00:10:14,550
+قرى، دول وهكذا، واضح؟ فهذا هو المجتمع دائما المحدد
+
+111
+00:10:14,550 --> 00:10:20,580
+بحدود جغرافية طبعا المنطقة الجغرافية هنا دائما أي 
+
+112
+00:10:20,580 --> 00:10:25,580
+مجتمع واحنا خاصة من خلال مفهوم طريق تنظيم المجتمع
+
+113
+00:10:25,580 --> 00:10:29,260
+اسمه Community Organization يعني احنا بنتعامل مع 
+
+114
+00:10:29,260 --> 00:10:32,260
+المجتمعات المحلية الصغيرة فاحنا بنركز على 
+
+115
+00:10:32,260 --> 00:10:36,480
+المجتمعات المحلية لأنه لنا دور لطريق تنظيم المجتمع
+
+116
+00:10:36,480 --> 00:10:40,360
+في اللي هو التعامل مع هذه المجتمعات المحلية
+
+117
+00:10:40,360 --> 00:10:44,220
+الصغيرة أول ما ظهر طريق تنظيم المجتمع للتعامل مع 
+
+118
+00:10:44,220 --> 00:10:47,500
+مثل هذه المجتمعات ولذلك اسمها العلمي community
+
+119
+00:10:47,500 --> 00:10:51,420
+community organization يعني تنظيم المجتمع لكن
+
+120
+00:10:51,420 --> 00:10:55,500
+اليوم بدأت في العصر الحالي أن نتعامل أيضا مش بال
+
+121
+00:10:55,500 --> 00:10:59,180
+community نتعامل بال society أيضا بالمجتمع ككل
+
+122
+00:10:59,180 --> 00:11:04,540
+والمجتمع الكبير واضح؟ لكن احنا دائما المجتمع
+
+123
+00:11:04,540 --> 00:11:09,640
+الجغرافي اللي بنتعامل معه له حدود جغرافية وطبعا 
+
+124
+00:11:09,900 --> 00:11:14,080
+هذه الحدود معروفة سواء على المستوى المحلي أو على 
+
+125
+00:11:14,080 --> 00:11:18,820
+المستوى القوي طبعا عمل المنظم بيكون في إطار
+
+126
+00:11:18,820 --> 00:11:23,440
+المجتمع الجغرافي حدود المجتمع الجغرافي ويتعامل مع
+
+127
+00:11:23,440 --> 00:11:28,660
+كافة الفئات الفئات لما نقول فئات يعني فئات السكان
+
+128
+00:11:28,660 --> 00:11:33,540
+بمختلف أنواع الذكور، الإناث، المرأة، الرجل،
+
+129
+00:11:33,540 --> 00:11:39,080
+الأطفال، الشباب، المعاقين، المسنين وهكذا الفئات
+
+130
+00:11:39,080 --> 00:11:43,480
+فإحنا بنتعامل مع المجتمع بكافة فئاته لما نقول
+
+131
+00:11:43,480 --> 00:11:48,760
+الحدود الجغرافية أو المجتمع الجغرافي أيضا ليس من
+
+132
+00:11:48,760 --> 00:11:53,900
+فئاته الموجودة لأن المجتمع الجغرافي يوجد فيه أيضا
+
+133
+00:11:53,900 --> 00:11:59,440
+ماذا غير الفئات المنظمات المؤسسات يعني الاجتماعية
+
+134
+00:11:59,440 --> 00:12:03,380
+والاقتصادية لكن احنا نتعامل في إطار المؤسسات
+
+135
+00:12:03,380 --> 00:12:06,940
+الاجتماعية داخل المجتمع فالمنظمات الموجودة أيضا 
+
+136
+00:12:06,940 --> 00:12:11,460
+تعتبر في إطار الحدود الجغرافية للمجتمع الذي نتعامل
+
+137
+00:12:11,460 --> 00:12:16,640
+معه فالمنظم يتعامل مع الفئات فئات المجتمع المختلفة
+
+138
+00:12:16,640 --> 00:12:21,800
+ويتعامل مع المنظمات أيضا الموجودة في هذا المجتمع
+
+139
+00:12:21,800 --> 00:12:27,540
+فهمنا المجتمع الجغرافي؟ طيب الآن بدنا نعرف المجتمع
+
+140
+00:12:27,540 --> 00:12:32,160
+الوظيفي ما هو المجتمع الوظيفي؟ يتصف بيه جماعة أو
+
+141
+00:12:32,160 --> 00:12:36,240
+أفراد لديهم ميول واهتمامات مشتركة داخل منطقة
+
+142
+00:12:36,240 --> 00:12:40,380
+جغرافية محددة التصنيف هنا لا ينطبق على جميع الأفراد
+
+143
+00:12:40,380 --> 00:12:43,940
+داخل المجتمع وإلا على الأهداف أو الأشخاص أو
+
+144
+00:12:43,940 --> 00:12:47,720
+الأفراد أو الجامعات اللي لديهم اهتمامات ومصالح
+
+145
+00:12:47,720 --> 00:12:51,840
+شركة معينة في بطاقة المعلمين أو الأطباء بالضبط إذا 
+
+146
+00:12:51,840 --> 00:12:55,740
+هذا هو المجتمع الوظيفي يعني في إطار المجتمع
+
+147
+00:12:55,740 --> 00:12:59,840
+الجغرافي يوجد المجتمع الوظيفي لأن له وظائف مختلفة فلذلك
+
+148
+00:12:59,840 --> 00:13:02,720
+إن المنظم الاجتماعي من خلال طريقة تنظيم المجتمع
+
+149
+00:13:02,720 --> 00:13:07,220
+يتعامل مع فئات المجتمع المختلفة ممكن نتعامل مع فئة
+
+150
+00:13:07,220 --> 00:13:11,740
+المعاقين داخل المجتمع ممكن نتعامل مع فئة الشباب
+
+151
+00:13:11,740 --> 00:13:17,080
+داخل المجتمع، بنسميه مجتمع وظيفي ممكن نتعامل مع 
+
+152
+00:13:17,080 --> 00:13:22,480
+المرأة داخل المجتمع ممكن نتعامل مع الأطفال، فئة 
+
+153
+00:13:22,480 --> 00:13:28,670
+الأطفال داخل المجتمع، مجتمع وظيفي، وهكذا، فلذلك هذا
+
+154
+00:13:28,670 --> 00:13:33,390
+المجتمع الوظيفي يعني مرتبط بالفئات التي توجد فيه
+
+155
+00:13:33,390 --> 00:13:41,350
+المجتمع الجغرافي أحيانا قد نتعامل مع مشكلة من
+
+156
+00:13:41,350 --> 00:13:45,600
+مشكلة وقد ترتبط بمجتمع جغرافي معين و أكثر من 
+
+157
+00:13:45,600 --> 00:13:49,880
+مجتمع وهذا ما سنتحدث عنه عندما نتحدث عن المشكلات
+
+158
+00:13:49,880 --> 00:13:54,040
+التي يواجهها المجتمع فلذلك أساس العمل هنا في
+
+159
+00:13:54,040 --> 00:13:58,680
+المجتمع الوظيفي الحدود الجغرافية ولا الناس الناس
+
+160
+00:13:58,680 --> 00:14:03,160
+بفئاتهم المختلفة و الوظيفية سواء كانوا أخصائيين
+
+161
+00:14:03,160 --> 00:14:07,860
+اجتماعيين سواء كانوا أطباء سواء كانوا معلمين سواء
+
+162
+00:14:07,860 --> 00:14:12,750
+كانوا مهندسين سواء كانوا عمال وهكذا فئات المجتمع
+
+163
+00:14:12,750 --> 00:14:17,270
+المختلفة داخل المجتمع الجغرافي فهذا هو المجتمع 
+
+164
+00:14:17,270 --> 00:14:24,310
+الوظيفي طبعا
+
+165
+00:14:24,310 --> 00:14:29,590
+بعد الانتقال من مفهوم المجتمع الجغرافي والمجتمع
+
+166
+00:14:29,590 --> 00:14:36,410
+الوظيفي يعني أن ننتقل الآن إلى اللي هو أين موقع 
+
+167
+00:14:36,410 --> 00:14:40,890
+المنظم الاجتماعي في هذا التقسيم في إطار المجتمع
+
+168
+00:14:42,000 --> 00:14:51,040
+يقول موقع المنظم الاجتماعي واضح؟
+
+169
+00:14:51,040 --> 00:14:55,440
+بدنا نشوف في إطار المجتمع الجغرافي والمجتمع 
+
+170
+00:14:55,440 --> 00:15:01,680
+الوظيفي أين موقع المنظم الاجتماعي في هذا التقسيم
+
+171
+00:15:01,680 --> 00:15:05,830
+اللي احنا قلناه هل هو ما نفصل عن بعضه البعض؟ هل هو
+
+172
+00:15:05,830 --> 00:15:12,190
+المجتمع الوظيفي ينفصل عن المجتمع الجغرافي؟ كله
+
+173
+00:15:12,190 --> 00:15:15,790
+يكمل بعضه البعض بس احنا بنجسمهم علشان الدراسة وإلا
+
+174
+00:15:15,790 --> 00:15:19,030
+الأخصائي بيعمل أحيانا في إطار المجتمع الجغرافي
+
+175
+00:15:19,030 --> 00:15:23,490
+ولكن قد يعمل مع بعض الفئات مع بعض المؤسسات داخل
+
+176
+00:15:23,490 --> 00:15:27,450
+المجتمع، واضح؟ إذن هنا بيتعامل مع المجتمع الجغرافي
+
+177
+00:15:27,450 --> 00:15:32,850
+وفي نفس الوقت بيتعامل مع المجتمع الوظيفي واضح؟ فلذلك
+
+178
+00:15:32,850 --> 00:15:36,510
+التقسيم هو من أجل الدراسة فقط ولكن المجتمع
+
+179
+00:15:36,510 --> 00:15
+
+216
+00:18:32,980 --> 00:18:37,540
+الوظيف موجود في إطار المجتمع الجغرافي، إذا كل منهم 
+
+217
+00:18:37,540 --> 00:18:42,980
+مكمل لمن؟ الآخر، وأيضا المهام المهنية للمنظم 
+
+218
+00:18:42,980 --> 00:18:47,630
+الاجتماعي محددة في إطار المجتمع الجغرافي والمجتمع 
+
+219
+00:18:47,630 --> 00:18:52,190
+الوظيفي، والتقسيم هنا من أجل ماذا؟ من أجل الدراسة 
+
+220
+00:18:52,190 --> 00:19:00,190
+فقط الدراسة، ولا انفصال بين المجتمعين، واضح؟ تفهمنا 
+
+221
+00:19:00,190 --> 00:19:03,950
+المجتمع الوظيفي والمجتمع الجغرافي؟ وأين دور المنظم 
+
+222
+00:19:03,950 --> 00:19:08,130
+الاجتماعي؟ يعمل مع المجتمع الجغرافي ككل عندما يقوم 
+
+223
+00:19:08,130 --> 00:19:13,520
+بإنشاء تنمية اجتماعية، والعمل في المدارس، في المصانع 
+
+224
+00:19:13,520 --> 00:19:16,740
+في الوحدات المجتمعية، في وحدات التنمية إلى غير ذلك 
+
+225
+00:19:16,740 --> 00:19:20,140
+المراكز الاجتماعية للتنمية هنا بتعامل مع المجتمع 
+
+226
+00:19:20,140 --> 00:19:25,000
+ككل في إطار جغرافي، وممكن نتعامل مع فئات المجتمع 
+
+227
+00:19:25,000 --> 00:19:29,920
+إذا إطار وظيفة الفئات المختلفة، هذه الفئات المختلفة 
+
+228
+00:19:29,920 --> 00:19:34,080
+اللي هو الوظيفي، بنسميها المجتمع الوظيفي، له علاقة 
+
+229
+00:19:34,080 --> 00:19:37,480
+بالمجتمع الجغرافي، مرتبط مع بعضه البعض، ولا انفصال 
+
+230
+00:19:37,480 --> 00:19:41,230
+بينهم، ولذلك دور المنظم الاجتماعي عندما يعمل مع 
+
+231
+00:19:41,230 --> 00:19:45,550
+المجتمع الوظيفي هو يعمل في إطار المجتمع الجغرافي، 
+
+232
+00:19:45,550 --> 00:19:50,170
+واضح؟ طيب، إذا الانفصال بين المجتمع الجغرافي 
+
+233
+00:19:50,170 --> 00:19:55,910
+والمجتمع الوظيفي، نأتي بعد ذلك لموضوع جديد من 
+
+234
+00:19:55,910 --> 00:20:00,330
+مفاهيم المجتمع في طريقة تنظيم المجتمع، وهو موضوع 
+
+235
+00:20:00,330 --> 00:20:05,150
+مجتمع الحاجة أو المجتمع، وهنا بدنا نعرف إن مجتمع من 
+
+236
+00:20:05,150 --> 00:20:08,910
+حاجة أو من مشكلة هو الأساس في طريق تنظيم المجتمع 
+
+237
+00:20:08,910 --> 00:20:13,030
+لأننا في طريق تنظيم المجتمع نتعامل مع مشكلات 
+
+238
+00:20:13,030 --> 00:20:19,050
+المجتمع، فلذلك نركز على موضوع المجتمع كمشكلة أو 
+
+239
+00:20:19,050 --> 00:20:24,290
+حاجة، لأن تعاملنا مع المشكلات لكي نساعد الناس على 
+
+240
+00:20:24,290 --> 00:20:29,510
+مواجهة هذه المشكلات وحلها، فلذلك هنا مجتمع الدراسة، 
+
+241
+00:20:29,510 --> 00:20:34,070
+مجتمع في إطار طريق التنظيم المجتمعي هنا اللي هو 
+
+242
+00:20:34,070 --> 00:20:40,330
+مجتمع الحاجة والمشكلة، مهم جدا، فلذلك مجتمع الحاجة 
+
+243
+00:20:40,330 --> 00:20:47,960
+والمشكلة يعني ممكن يعرفنا على أن أساس أي مجتمع هي 
+
+244
+00:20:47,960 --> 00:20:51,680
+المشكلة، والمشكلة أحيانا قد تكون في إطار ضيق، وقد 
+
+245
+00:20:51,680 --> 00:20:55,680
+تكون في مستوى محلي، وممكن تكون في مستوى قومي، وممكن 
+
+246
+00:20:55,680 --> 00:20:59,940
+تكون في أكثر من مجتمع، في أكثر من مجتمع المشكلة 
+
+247
+00:20:59,940 --> 00:21:04,060
+التي تتواجد، لا يمكن أن تتواجد، ممكن تكون في مجتمع محلي 
+
+248
+00:21:04,060 --> 00:21:08,700
+صغير، وممكن تكون في عدة مجتمعات محلية أو في مجتمع 
+
+249
+00:21:08,700 --> 00:21:13,230
+قومي كذلك، وهكذا، وممكن تكون من مجتمع قومي لمجتمع 
+
+250
+00:21:13,230 --> 00:21:16,990
+آخر، وممكن تكون المشكلة أحيانًا لها غير الطابع 
+
+251
+00:21:16,990 --> 00:21:20,850
+المحلي والطابع القومي، لها الطابع الدولي، المشكلة 
+
+252
+00:21:20,850 --> 00:21:24,070
+قد تتفاقم، يكون لها الطابع الدولي، فلذلك هنا أنا 
+
+253
+00:21:24,070 --> 00:21:28,750
+كمنظم اجتماعي بتعامل مع المجتمع كمشكلة، أينما تكون 
+
+254
+00:21:28,750 --> 00:21:32,590
+المشكلة، أنا بتعامل معها، وأقول يا جماعة، طبعا عندنا 
+
+255
+00:21:32,590 --> 00:21:36,640
+كثير من مجتمع الحاجة ومجتمع المشكلة، يعني كثير من 
+
+256
+00:21:36,640 --> 00:21:40,040
+المشكلات بتكون، فتكون على مستوى محلي، فتكون على 
+
+257
+00:21:40,040 --> 00:21:44,240
+مستوى قومي، فتكون على أكثر من مستوى محلي أيضًا 
+
+258
+00:21:44,240 --> 00:21:50,860
+موجودة في عدد من المجتمعات، طيب 
+
+259
+00:21:50,860 --> 00:21:56,140
+فلذلك أنا بنركز هنا على موضوع المشكلة، والمشكلة 
+
+260
+00:21:56,140 --> 00:22:00,180
+دائمًا نحن لو بدنا نتعرف عليها داخل المجتمع من أجل 
+
+261
+00:22:00,180 --> 00:22:06,140
+مساعدة المجتمع على حل هذه المشكلة، المشكلة أو الحاجة 
+
+262
+00:22:06,140 --> 00:22:11,160
+هي وحدة عمل المنظم مع المجتمع، وحدة عملي في داخل 
+
+263
+00:22:11,160 --> 00:22:16,080
+المجتمع هي مع المشكلة، يعني عندما أكون في مجتمع 
+
+264
+00:22:16,080 --> 00:22:19,360
+جغرافي أو مجتمع وما يتبقى، بركز على المشاكل، 
+
+265
+00:22:19,360 --> 00:22:23,220
+أين تكون المشكلة؟ مجتمع الحاجة؟ مجتمع المشكلة؟ 
+
+266
+00:22:23,570 --> 00:22:26,550
+الاحتياجات التي بتعامل معها المنظم الاجتماعي قد 
+
+267
+00:22:26,550 --> 00:22:30,870
+تكون محسوسة وقد تكون غير محسوسة، يعني ممكن يحس بها 
+
+268
+00:22:30,870 --> 00:22:35,250
+وممكن أيضًا لا يحس بها، كثير منا يعيش في مشكلات قد 
+
+269
+00:22:35,250 --> 00:22:38,730
+لا يحس بها، ولكن يتعايش مع هذه المشكلات، وأحيانًا 
+
+270
+00:22:38,730 --> 00:22:43,740
+المشكلات نحس بها بأنها مشكلة، فلذلك نحن دورنا في 
+
+271
+00:22:43,740 --> 00:22:47,500
+طريقة تنظيم المجتمع هو أن نعرف المشكلات المحسوسة 
+
+272
+00:22:47,500 --> 00:22:51,340
+والمشكلات غير المحسوسة، المشكلات المحسوسة نستطيع أن 
+
+273
+00:22:51,340 --> 00:22:55,060
+نفكر في علاجها، ولكن أحيانًا المشكلات غير محسوسة 
+
+274
+00:22:55,060 --> 00:22:59,340
+تحتاج إلى استثارة من قبل المنظم الاجتماعي، لاستثارة 
+
+275
+00:22:59,340 --> 00:23:04,320
+سكان المجتمع لإحساسهم بهذه المشكلة، حتى يفكرون في 
+
+276
+00:23:04,320 --> 00:23:10,160
+كيفية علاجها، شفنا 
+
+277
+00:23:10,160 --> 00:23:17,020
+الاحتياجات؟ أيضًا أحيانًا الحيز المكاني ليس هو الأساس 
+
+278
+00:23:17,020 --> 00:23:20,540
+في الممارسة، الحيز المكاني للمشكلة مش هو الأساس 
+
+279
+00:23:20,540 --> 00:23:24,680
+ممكن المشكلة تكون لها أكثر من مكان، أكثر من قرية 
+
+280
+00:23:24,680 --> 00:23:28,220
+أكثر من مدينة، أكثر من مجتمع محلي، لذلك هنا لابد من 
+
+281
+00:23:28,220 --> 00:23:32,480
+التعاون مع الأجهزة الموجودة في هذه المجتمعات لكي 
+
+282
+00:23:32,480 --> 00:23:37,980
+نواجه هذه المشكلة، أيضًا إذا كانت هناك احتياجات غير 
+
+283
+00:23:38,920 --> 00:23:41,580
+إذا كانت هناك احتياجات اللي هي الأسس التي بعتمد 
+
+284
+00:23:41,580 --> 00:23:44,900
+عليها هذا التصور للمجتمع باعتباره مجتمع الـ إيه 
+
+285
+00:23:44,900 --> 00:23:49,000
+المشكلة، إذا كانت هناك احتياجات غير مشبعة، ويعاني 
+
+286
+00:23:49,000 --> 00:23:54,440
+منها أكثر سكان المجتمع، وتتضمن، وأيضًا و تتعلق 
+
+287
+00:23:54,440 --> 00:24:00,000
+بمرافق عامل أساسية، فتلك الاحتياجات تحظى بالأولوية 
+
+288
+00:24:00,000 --> 00:24:05,320
+تحظى بالأولوية، الاحتياجات التي بتهدد أمن المجتمع هي 
+
+289
+00:24:05,320 --> 00:24:12,800
+ما يطلق عليها احتياجات البقاء، أحيانًا بتتعلق بالأمن 
+
+290
+00:24:12,800 --> 00:24:21,720
+طيب، أين دور المنظم في إطار هذا المفهوم اللي هو 
+
+291
+00:24:21,720 --> 00:24:29,060
+المجتمع كمشكلة كحاجة، أين دوري أنا؟ دوري كمنظم أن 
+
+292
+00:24:29,060 --> 00:24:35,010
+أتعامل أو الحاجة في منظم المجتمع المحلي، ويعمل على 
+
+293
+00:24:35,010 --> 00:24:38,970
+أجهزه شهود بعينيه شديدة؟ طبعًا، إذا أنا دوري كمنظم 
+
+294
+00:24:38,970 --> 00:24:43,790
+اجتماعي مع المشكلة أو الحاجة الخاصة بالمجتمع إن 
+
+295
+00:24:43,790 --> 00:24:48,610
+أتعامل مع هذه المشكلة لكي أساعد سكان المجتمع على 
+
+296
+00:24:48,610 --> 00:24:53,490
+معرفة مشكلتهم، وعلى وضع الخطوط أو المشكلة أو وضع 
+
+297
+00:24:53,490 --> 00:24:57,820
+الحلول لهذه المشكلة، واضح؟ هي دور المنظمة باختصار 
+
+298
+00:24:57,820 --> 00:25:01,980
+يعني، فلذلك دائمًا المجتمع أو واحدة التعامل هي 
+
+299
+00:25:01,980 --> 00:25:09,200
+المشكلة أو الحاجة هنا للمنظم الاجتماعي، طبعًا 
+
+300
+00:25:09,200 --> 00:25:13,720
+هنا في النهاية حتى لو تعاملنا مع مجتمع الحاجة أو 
+
+301
+00:25:13,720 --> 00:25:17,960
+المشكلة، بنرجع لمجتمع الوظيفي ومجتمع الجغرافي أم لا؟ 
+
+302
+00:25:17,960 --> 00:25:22,900
+بنرجع لهم، لأن هو الأساس، بنرجع لمجتمع الوظيفي ومجتمع 
+
+303
+00:25:22,900 --> 00:25:27,850
+الجغرافي، فلذلك حتى نتعامل مع هذه المشكلة، وطبعًا إحنا 
+
+304
+00:25:27,850 --> 00:25:31,730
+في مفهوم المستقبل، في محاضرة قادمة هنتكلم عن 
+
+305
+00:25:31,730 --> 00:25:38,670
+المشكلة وأنواع المشاكل بالتفصيل بإذن الله تعالى 
+
+306
+00:25:38,670 --> 00:25:46,510
+في عندنا أيضًا اللي هو مجتمع المنظمة، مجتمع المنظمة 
+
+307
+00:25:48,770 --> 00:25:52,410
+نتراوح المجتمع المنظمة أو مجتمع المؤسسة بالاسم 
+
+308
+00:25:52,410 --> 00:25:59,590
+المنظمة، المؤسسة، الهيئة، كلها يعني بمعنى واحد، مجتمع 
+
+309
+00:25:59,590 --> 00:26:07,450
+المنظمة، طبعًا ده هو التعامل المهني مع مكونات 
+
+310
+00:26:07,450 --> 00:26:12,450
+المنظمات ومجتمعها الذاتي، نعم، المنظمات الاجتماعية 
+
+311
+00:26:12,450 --> 00:26:18,170
+لمساعدتها أي مساعدة ذات المنظمات لكي تقوم بوظيفتها 
+
+312
+00:26:18,550 --> 00:26:24,410
+لكي تقوم بتحقيق أهدافها، وهي مساعدة أفراد المجتمع 
+
+313
+00:26:24,410 --> 00:26:30,890
+طبعًا، ممكن 
+
+314
+00:26:30,890 --> 00:26:35,290
+ننتقل بطريقة تنظيم المجتمع من العمل مع المجتمع 
+
+315
+00:26:35,290 --> 00:26:39,770
+الخارجي اللي هو المجتمع المحلي إلى المجتمع الداخلي 
+
+316
+00:26:39,770 --> 00:26:43,550
+ما هو المجتمع الداخلي؟ داخل المجتمع المحلي اللي هي 
+
+317
+00:26:43,550 --> 00:26:47,350
+المنظمة، يعني دائمًا كل مجتمع محلي فيه عدد من 
+
+318
+00:26:47,350 --> 00:26:51,050
+المنظمات، إذا إحنا نتعامل مع المنظمة في إطار 
+
+319
+00:26:51,050 --> 00:26:55,370
+المجتمع، لأن المنظمة لا توجد إلا في مجتمع، 
+
+320
+00:26:55,370 --> 00:26:59,990
+والمنظمة توجد لإشباع حاجة أو حل مشكلة، فلذلك 
+
+321
+00:26:59,990 --> 00:27:04,190
+المجتمع، قرية أو مدينة أو ما إلى ذلك أو دولة، يوجد 
+
+322
+00:27:04,190 --> 00:27:08,570
+فيها عدد من المنظمات أو المؤسسات، فأنا هنا بتعامل 
+
+323
+00:27:08,570 --> 00:27:13,640
+مع من؟ مع المنظمة في إطار المجتمع الجغرافي، في إطار 
+
+324
+00:27:13,640 --> 00:27:17,840
+المجتمع الجغرافي الذي توجد فيه اللي هي المنظمة أو 
+
+325
+00:27:17,840 --> 00:27:27,980
+المؤسسة، في 
+
+326
+00:27:27,980 --> 00:27:32,640
+أيضًا الأسس التي يعتمد عليها هذا التصور، ما هي 
+
+327
+00:27:32,640 --> 00:27:37,870
+الأسس؟ ما هو الأساس الأول؟ المساهمة في تطوير 
+
+328
+00:27:37,870 --> 00:27:41,530
+المنظمة، ذلك كي تتمكن من التعامل بفعالية متزايدة مع 
+
+329
+00:27:41,530 --> 00:27:45,290
+المجتمع المستفيد من خدمتها، إذا المساهمة في تطوير 
+
+330
+00:27:45,290 --> 00:27:51,830
+المنظمة، مساهمة في تطويرها، حتى تتمكن أن تتعامل 
+
+331
+00:27:51,830 --> 00:27:54,550
+بفعالية متزايدة مع المجتمع الذي توجد فيه هذه 
+
+332
+00:27:54,550 --> 00:27:59,600
+المنظمة، ماذا أيضًا؟ تحرير بالتقييم، العمليات التي 
+
+333
+00:27:59,600 --> 00:28:03,020
+تؤديها المنظمات للمستفيدين، وتحديد العوامل الوظيفية 
+
+334
+00:28:03,020 --> 00:28:05,680
+التي تؤثرها هذه المنظمة؟ طبعًا كعملية تقييمية لابد 
+
+335
+00:28:05,680 --> 00:28:08,920
+نحلل العمليات التي تقوم بها هذه المنظمة ونعرف 
+
+336
+00:28:08,920 --> 00:28:12,700
+الإيجابيات والسلبيات حتى نساعدها على القيام بدورها 
+
+337
+00:28:12,700 --> 00:28:17,640
+في تقديم خدماتها لأفراد المجتمع، ماذا أيضًا من الأسس 
+
+338
+00:28:17,640 --> 00:28:21,120
+التي بيعتمد عليها اللي هو التصور اللي هو مجتمع هذه 
+
+339
+00:28:21,120 --> 00:28:24,140
+المنظمة اللي هو المجتمع كمنظمة، إيه بدي 
+
+340
+00:28:31,960 --> 00:28:37,780
+دراسة احتياجات أفراد المجتمع غير المشبعة، يعني اللي 
+
+341
+00:28:37,780 --> 00:28:43,870
+ناقصها يعني في مشاكل، في حاجات غير مشبعة لأفراد 
+
+342
+00:28:43,870 --> 00:28:47,910
+المجتمع، لازم نعرفها ليه؟ حتى تقوم هذه المنظمات 
+
+343
+00:28:47,910 --> 00:28:53,130
+بإشباعها، فدور المنظم أن يعرف هذه الحاجات ويساعد 
+
+344
+00:28:53,130 --> 00:28:56,370
+المنظمة على القيام بدورها في إشباع حاجات أفراد 
+
+345
+00:28:56,370 --> 00:29:01,210
+المجتمع، أيوة يا بنتي، فضلي، العامل بيان مختلف أقسام 
+
+346
+00:29:01,210 --> 00:29:04,150
+المنظمة لتحسين الإنتاجات والارتفاع بالتصنيف المبيعي 
+
+347
+00:29:04,150 --> 00:29:09,320
+الأقسام، طبعًا كل منظمة لها أقسام وإدارات ووحدات 
+
+348
+00:29:09,320 --> 00:29:13,520
+فلذلك لابد من التنسيق بين الأقسام المختلفة، لماذا؟ 
+
+349
+00:29:13,520 --> 00:29:17,680
+حتى نحدث نوع من التعاون بين العاملين داخل المؤسسة 
+
+350
+00:29:17,680 --> 00:29:21,080
+بين أقسامها المختلفة، حتى نساعد المؤسسة على القيام 
+
+351
+00:29:21,080 --> 00:29:27,040
+بوظيفتها وتحقيق أهدافها للمجتمع، طبعًا الصعوبات التي 
+
+352
+00:29:27,040 --> 00:29:28,880
+بتواجه العمل المهني 
+
+353
+00:29:33,610 --> 00:29:36,990
+المهنيين العاملين داخل المؤسسة، نشوف إيش الصعوبات 
+
+354
+00:29:36,990 --> 00:29:41,190
+التي بتوجههم، وأيضًا نعمل على تذليلها، هذا اللي هو 
+
+355
+00:29:41,190 --> 00:29:50,130
+مفهوم المجتمع كمنظمة، طيب، في عندنا أيضًا بالإضافة 
+
+356
+00:29:50,130 --> 00:29:54,250
+للأسس السابقة، يعني هي نعتبرها محور العمل لدى 
+
+357
+00:29:54,250 --> 00:30:03,360
+المنظم الاجتماعي بالمنظمة، ولذلك أحيانًا لابد، يعني 
+
+358
+00:30:03,360 --> 00:30:07,280
+اللي هي الأسس التي إحنا ذكرناها قبل قليل اللي هو 
+
+359
+00:30:07,280 --> 00:30:10,700
+على الأقسام أن تعرفها لكي تساعد المنظمة على القيام 
+
+360
+00:30:10,700 --> 00:30:15,440
+بتحقيق أهدافها وأهداف المجتمع في إشباع احتياجات 
+
+361
+00:30:15,440 --> 00:30:22,140
+المجتمع وحل مشكلات المجتمع، هنا أيضًا double يعني 
+
+362
+00:30:22,140 --> 00:30:26,940
+في مجالات معينة، الكلام هذا الذي إحنا قلناه سابقًا 
+
+363
+00:30:26,940 --> 00:30:30,940
+هذا كله في إطار مجالات معينة، عند تجميع المعلومات 
+
+364
+00:30:31,090 --> 00:30:35,890
+والآراء والبيانات المتاحة حول موضوع معين، أيضًا 
+
+365
+00:30:35,890 --> 00:30:40,930
+عند مناقشة فوائد ومضار المعلومة أو بيان واضح أو 
+
+366
+00:30:40,930 --> 00:30:46,110
+رأي، حيث يقوم متخذ القرارات بتحصيله أو 
+
+367
+00:30:46,110 --> 00:30:51,150
+بحصيلة متراكمة من الخيارات، مما يسهل اتخاذ القرار 
+
+368
+00:30:51,150 --> 00:30:56,760
+المناسب لصالح من؟ المجتمع والمجتمع كذلك، إلى هنا 
+
+369
+00:30:56,760 --> 00:31:01,460
+نكتفي، وإن شاء الله في المحاضرة القادمة، ليكن مني كل 
+
+370
+00:31:01,460 --> 00:31:06,560
+تحية وتقدير، والسلام عليكم ورحمة الله وبركاته
diff --git a/PL9fwy3NUQKwaKyeI5iiPpebyFXxlPBffV/gWn4tKPng0U.srt b/PL9fwy3NUQKwaKyeI5iiPpebyFXxlPBffV/gWn4tKPng0U.srt
new file mode 100644
index 0000000000000000000000000000000000000000..55878767750cb1fc75503fc1b457121f7433cadc
--- /dev/null
+++ b/PL9fwy3NUQKwaKyeI5iiPpebyFXxlPBffV/gWn4tKPng0U.srt
@@ -0,0 +1,2025 @@
+1
+00:00:20,840 --> 00:00:24,060
+بسم الله الرحمن الرحيم الحمد لله رب العالمين
+
+2
+00:00:24,060 --> 00:00:28,520
+والصلاة والسلام على أشرف المرسلين سيدنا محمد وعلى 
+
+3
+00:00:28,520 --> 00:00:34,100
+آله وصحبه أجمعين بنات الطالبات السلام عليكم جميعا 
+
+4
+00:00:34,100 --> 00:00:41,240
+ورحمة الله وبركاته في هذه المحاضرة سنتعرض إلى 
+
+5
+00:00:41,240 --> 00:00:45,500
+تعريفات طريقة تنظيم المجتمع في المحاضرة السابقة 
+
+6
+00:00:45,500 --> 00:00:51,000
+أخذنا أهمية إيجاد تعريف لطريقة تنظيم المجتمع 
+
+7
+00:00:51,000 --> 00:00:57,780
+وتحدثنا عن الصعوبات التي تواجه المختصين في طريقة 
+
+8
+00:00:57,780 --> 00:01:01,500
+الطريق تنظيم المجتمع إلى إيجاد تعريف موحد 
+
+9
+00:01:01,500 --> 00:01:06,860
+وبيّنا أهم هذه الأسباب التي جعلت هناك تعريفات 
+
+10
+00:01:06,860 --> 00:01:13,300
+عديدة لطريقة تنظيم المجتمع وأيضا تعرضنا إلى مفهوم 
+
+11
+00:01:13,300 --> 00:01:21,430
+التعريف الجيد، ما هي شروط التعريف الجيد؟ وأيضا كذلك 
+
+12
+00:01:21,430 --> 00:01:27,430
+تكلمنا يعني بصفة عامة عن خصائص التعريف الجيد 
+
+13
+00:01:27,430 --> 00:01:33,410
+مضمونا و شكلا، وحددنا يعني المضمون D3 اللي هي 
+
+14
+00:01:33,410 --> 00:01:37,430
+الخصائص العامة للتعريف الجيد اللي هي، ما هي، وكيفية 
+
+15
+00:01:37,430 --> 00:01:41,770
+واعتبارها ضروري، لابد أن تتوفر في التعريف الجيد بالإضافة 
+
+16
+00:01:41,770 --> 00:01:46,290
+للشروط الشكلية الأخرى، وهي سهولة العبارة وكتابة 
+
+17
+00:01:46,290 --> 00:01:51,880
+باللغة العربية الفصحى وعدم الكتابة بالعامية، وكذلك 
+
+18
+00:01:51,880 --> 00:01:57,960
+أن يكون موجزا، وألا يكون فيه سرد، تعريف جيد وأن 
+
+19
+00:01:57,960 --> 00:02:03,180
+يعني يتناسب مع المجتمع وثقافة المجتمع بحيث يعني 
+
+20
+00:02:03,180 --> 00:02:07,000
+من يقرأ هذا التعريف يفهمه، وخاصة لابد أن يكتب 
+
+21
+00:02:07,000 --> 00:02:11,240
+اللغة العربية الفصحى، مدام نحن ندرس في جامعة 
+
+22
+00:02:11,240 --> 00:02:16,130
+إسلامية عربية، إذًا لابد أن يكون التعريف عربيا وإذا 
+
+23
+00:02:16,130 --> 00:02:20,170
+كان أجنبيا نستطيع أن نترجمه أيضا، إذا كان باللغات 
+
+24
+00:02:20,170 --> 00:02:25,110
+الأخرى سواء اللغات الأجنبية الأخرى نستطيع أن 
+
+25
+00:02:25,110 --> 00:02:30,170
+نترجمه ليفهمه كذلك، نترجمه للغة العربية، فلذلك 
+
+26
+00:02:30,170 --> 00:02:36,210
+لابد أن يكون التعريف مفهوما شكلا ومضمونا، اليوم 
+
+27
+00:02:36,210 --> 00:02:42,100
+سنتحدث عن التعريف الخاص بطريقة تنظيم المجتمع طبعا 
+
+28
+00:02:42,100 --> 00:02:45,680
+هناك عدة تعريفات حسب المرحلة التي مرت بها طريقة 
+
+29
+00:02:45,680 --> 00:02:50,220
+تنظيم المجتمع وهي عندنا أربع مراحل مرت بها طريقة 
+
+30
+00:02:50,220 --> 00:02:55,420
+تنظيم المجتمع، وحسب كل مرحلة سنسرد يعني بعض 
+
+31
+00:02:55,420 --> 00:03:01,860
+التعريفات، التعريفات الأجنبية وخاصة يعني في أمريكا 
+
+32
+00:03:01,860 --> 00:03:08,810
+أو بريطانيا بالإضافة إلى التعريفات العربية وخاصة في 
+
+33
+00:03:08,810 --> 00:03:11,870
+جمهورية مصر العربية باعتبار أن الخدمة الاجتماعية 
+
+34
+00:03:11,870 --> 00:03:16,870
+نشأت وانتقلت من أمريكا إلى الوطن العربي عن طريق 
+
+35
+00:03:16,870 --> 00:03:23,150
+مصر، فلذلك سنأخذ بعض العلماء أيضا عرب مصريين في 
+
+36
+00:03:23,150 --> 00:03:26,970
+جمهورية مصر العربية، وهم أساتذة درسونا، سنتعرض إلى 
+
+37
+00:03:26,970 --> 00:03:32,170
+تعريفاتهم أيضا في طريقة تنظيم المجتمع بإذن الله طبعا 
+
+38
+00:03:32,170 --> 00:03:36,530
+المراحل هي ستكون مرحلة الأولى التنسيق، ثم المرحلة 
+
+39
+00:03:36,530 --> 00:03:41,590
+الثانية التخطيط، ثم المرحلة الثالثة التنمية، و
+
+40
+00:03:41,590 --> 00:03:46,250
+المرحلة الأخيرة والرابعة اللي هي الدفاع، مرحلة 
+
+41
+00:03:46,250 --> 00:03:50,510
+الدفاع، فسنتحدث عن كل مرحلة من هذه المراحل من حيث 
+
+42
+00:03:50,510 --> 00:03:55,190
+التعريف، ما هي التعريفات التي ظهرت في هذه المرحلة، و
+
+43
+00:03:55,190 --> 00:03:59,130
+لا نسرد كل التعريفات عند العلماء ككل، ولكن سنأخذ 
+
+44
+00:03:59,130 --> 00:04:04,870
+نماذج، نماذج لهذه التعريفات، ونعرف يعني التعريف في 
+
+45
+00:04:04,870 --> 00:04:11,950
+مرحلة التنسيق كيف كان عند العرب وعند غير العرب 
+
+46
+00:04:11,950 --> 00:04:16,750
+اللي هم الأجانب، من الدول الأجنبية، وخاصة من يعني 
+
+47
+00:04:16,750 --> 00:04:21,410
+في الدول الغربية وأمريكا، في عندنا مرحلة اللي 
+
+48
+00:04:21,410 --> 00:04:24,950
+بتوضح اللي هي التعريفات اللي هي في مرحلة التنسيق 
+
+49
+00:04:24,950 --> 00:04:28,390
+أولا، نأخذ الناحية الأجنبية، في عندنا عدد من العلماء 
+
+50
+00:04:28,390 --> 00:04:33,170
+عرفوا طريقة تنظيم المجتمع في مرحلة التنسيق منهم 
+
+51
+00:04:33,170 --> 00:04:37,170
+Lindman، وأيضا تعريف Stiner، وتعريف Robert Greene 
+
+52
+00:04:37,170 --> 00:04:42,990
+وتعريف Edmund Brunner، وأيضا تعريف Macmillan، و
+
+53
+00:04:42,990 --> 00:04:47,920
+أيضا تعريف Neustadtler، هذه التعريفات كلها، لكن لا نريد 
+
+54
+00:04:47,920 --> 00:04:51,380
+أن نسرد في محاضرة كل هذه التعريفات، ولكن سنأخذ 
+
+55
+00:04:51,380 --> 00:04:56,980
+نموذج لهذه التعريفات، فسنعرض للتعريف الأول والأخير 
+
+56
+00:04:56,980 --> 00:05:01,700
+بحيث أن سندرس لـ Lindemann، تعريف Lindemann وتعريف 
+
+57
+00:05:01,700 --> 00:05:10,760
+New Student، طبعا تعريف Lindemann لتنظيم 
+
+58
+00:05:10,760 --> 00:05:16,790
+المجتمع، هذا تعريف قديم، يعني من أقدم التعريفات في 
+
+59
+00:05:16,790 --> 00:05:22,410
+طريقة تنظيم المجتمع يعني سنة 1920، وخاصة في مرحلة 
+
+60
+00:05:22,410 --> 00:05:26,610
+التنسيق، فسنعرف كيف كان العلماء يعرفون طريقة تنظيم 
+
+61
+00:05:26,610 --> 00:05:30,470
+المجتمع يعني في الزمن الماضي، وخاصة في بداية 
+
+62
+00:05:30,470 --> 00:05:35,710
+المرحلة يعني اللي هي مرحلة التنسيق، فلذلك لدمن يعرف 
+
+63
+00:05:35,710 --> 00:05:40,610
+طريقة تنظيم المجتمع، ما يقولش عن الطريقة احنا عارفين 
+
+64
+00:05:40,610 --> 00:05:46,140
+يعني لا يقول عنها تعريف، وإنما يقول هنا بأنها 
+
+65
+00:05:46,140 --> 00:05:51,680
+العملية، يصفها بأنها العملية الديمقراطية، يعني وصفها 
+
+66
+00:05:51,680 --> 00:05:56,140
+عملية ديمقراطية يتم خلالها التعرف على آراء أفراد 
+
+67
+00:05:56,140 --> 00:06:01,060
+المجتمع والتنسيق فيما بينها وبين ما تقوم به 
+
+68
+00:06:01,060 --> 00:06:06,320
+المنظمات من خدمات، هذا هو تعريف lendman يعني 
+
+69
+00:06:06,320 --> 00:06:12,790
+تعريف مبسط، وتعريف يجتمع على وصف لهذه الطريقة بحيث 
+
+70
+00:06:12,790 --> 00:06:17,230
+أنها ليست طريقة بل هي عملية ديمقراطية يتم من 
+
+71
+00:06:17,230 --> 00:06:21,770
+خلالها التعرف على آراء أفراد المجتمع والتنسيق فيما 
+
+72
+00:06:21,770 --> 00:06:26,030
+بينها وبين ما تقوم به المنظمات من خدمات، طيب هنا 
+
+73
+00:06:26,030 --> 00:06:31,330
+يركز على ماذا لندمن؟ يركز على جوانب في تنظيم 
+
+74
+00:06:31,330 --> 00:06:37,680
+المجتمع، أولا لم يقل بأنها عملية، ولكن وصفها بأنها 
+
+75
+00:06:37,680 --> 00:06:41,880
+عفوا، لم يكن بينها قريبة، ولكن قال عنها بأنها عملية 
+
+76
+00:06:41,880 --> 00:06:46,300
+وهذا يؤخذ عليه طبعا، تأكيد لا يؤخذ بحكم أنه يعرف 
+
+77
+00:06:46,300 --> 00:06:52,460
+تنظيم المجتمع في وقتها في بداية مرحلة التنسيق طبعا 
+
+78
+00:06:52,460 --> 00:06:55,860
+الجانب الأول هنا في هذا التعريف باحترام الآراء 
+
+79
+00:06:55,860 --> 00:06:59,620
+اللي هي على أساس عملية ديمقراطية، باحترام الآراء، و
+
+80
+00:06:59,620 --> 00:07:06,910
+تقديرها للجانب الديمقراطي واضح؟ الجانب الثاني يركز 
+
+81
+00:07:06,910 --> 00:07:11,490
+عليه، طريقة اللي هو لندمان في تعريفه بتناول الآراء 
+
+82
+00:07:11,490 --> 00:07:16,390
+بين المجتمع والمؤسسات، اللي هو الجانب التنسيقي، 
+
+83
+00:07:16,390 --> 00:07:20,130
+العلاقة بين المجتمع والمؤسسات، وهذه العلاقة بتكون 
+
+84
+00:07:20,130 --> 00:07:27,570
+علاقة تنسيقية، فإذا هنا ركزنا عليها، أيضا في عندنا 
+
+85
+00:07:27,570 --> 00:07:32,510
+في تعريف لندمان يعني جوانب ضعف وجوانب قوة، فنشوف 
+
+86
+00:07:32,510 --> 00:07:38,080
+جوانب الضعف، اللي هي جوانب الضعف في التعريف، طبعا لو 
+
+87
+00:07:38,080 --> 00:07:43,780
+لاحظنا تعريف لندمان، بيللاحظ أنه أغفل طريقة مفهوم 
+
+88
+00:07:43,780 --> 00:07:47,260
+الطريقة على أساس ما جاءش أنه تنظيم المجتمع طريقة من 
+
+89
+00:07:47,260 --> 00:07:51,600
+ظروف لندمان الاجتماعي، ولذلك هنا أغفل الـ إيه؟ 
+
+90
+00:07:51,600 --> 00:07:57,780
+الماهية، الماهية، الماهية اللي هي الطريقة، ماهية 
+
+91
+00:07:57,780 --> 00:08:02,650
+العلم اللي هي تنظيم المجتمع، ما جاءش عنها طريقة، فقال 
+
+92
+00:08:02,650 --> 00:08:08,130
+عنها عملية، فهذا، لكن هنا هذا جانب، طبعا، ولكن هنا 
+
+93
+00:08:08,130 --> 00:08:13,850
+احنا نبدأ عذر بحكم أن هذه مرحلة تنسيقية واضحة وهذا 
+
+94
+00:08:13,850 --> 00:08:17,950
+بيرجع إلى عدم ازدهار الطريقة في ذلك الوقت اللي هو 
+
+95
+00:08:17,950 --> 00:08:23,270
+عام 1920 لما ذكر التعليق، كانت طبعا في هذا الوقت 
+
+96
+00:08:23,270 --> 00:08:27,320
+من اللي كانت من الطرق البارزة عندنا؟ خدمة الفرد 
+
+97
+00:08:27,320 --> 00:08:32,240
+لأنه من أيام Mary Richmond سنة 1917 وضعت أسس 
+
+98
+00:08:32,240 --> 00:08:36,260
+لطريقة خدمة الفرد وكان معترف بها اللي هي طريقة 
+
+99
+00:08:36,260 --> 00:08:40,940
+خدمة الفرد، فكانت طريقة رائجة على يد Mary 
+
+100
+00:08:40,940 --> 00:08:46,060
+Richmond، فحددت العوامل الفردية، كعامل الفردي هو 
+
+101
+00:08:46,060 --> 00:08:49,780
+السبب في المشكلات الاجتماعية، ولم يظهر في تلك 
+
+102
+00:08:49,780 --> 00:08:52,700
+المرحلة، لأن المجتمع هو السبب في المشكلات، كانوا 
+
+103
+00:08:52,700 --> 00:08:58,040
+يركزوا على الفرد، لأن الفرد هو السبب في المشكلات 
+
+104
+00:08:58,040 --> 00:09:02,100
+الاجتماعية، وما ينتج من المشكلات سببها من الفرد 
+
+105
+00:09:02,100 --> 00:09:07,640
+وليس المجتمع، فلذلك من هنا كانوا يركزوا على الفرد 
+
+106
+00:09:07,640 --> 00:09:11,460
+باعتباره هو السبب الرئيسي في المشكلات الاجتماعية 
+
+107
+00:09:11,460 --> 00:09:15,710
+وليست العوامل المجتمعية هي السبب، طبعا هذا الرأي كان 
+
+108
+00:09:15,710 --> 00:09:19,270
+يتناسب مع السياسة العامة في المجتمع، مع النظام 
+
+109
+00:09:19,270 --> 00:09:23,050
+السياسي، حتى في المجتمع بأن الفرد هو المسؤول عن 
+
+110
+00:09:23,050 --> 00:09:27,330
+مشكلاته، فالنظام السياسي كان متوافق في الدول 
+
+111
+00:09:27,330 --> 00:09:31,110
+الأوروبية على أن الفرد هو السبب في اللي هي 
+
+112
+00:09:31,110 --> 00:09:35,910
+المشكلات المجتمعية، ولذلك من هنا ظهرت طريقة خدمة 
+
+113
+00:09:35,910 --> 00:09:40,690
+الفرد، وهذا أدى إلى تأخر دخول طريقة إيه تنظيم 
+
+114
+00:09:40,690 --> 00:09:41,350
+المجتمع 
+
+115
+00:09:43,960 --> 00:09:49,380
+هذا الكلام في الأربعينات، طبعا الناحية الثانية من 
+
+116
+00:09:49,380 --> 00:09:53,420
+جوانب الضعف تعريف Landman اللي هي لم يحدد 
+
+117
+00:09:53,420 --> 00:09:58,180
+الممارسين، من هم الذين يمارسون المهنة الذين 
+
+118
+00:09:58,180 --> 00:10:03,120
+يمارسون طريقة تنظيم المجتمع، لم يحدد في تعريفه، لم 
+
+119
+00:10:03,120 --> 00:10:08,580
+يبيّن، فلذلك أغفل الـ إيه؟ الـ كيفية، كيفية العمل، 
+
+120
+00:10:08,580 --> 00:10:13,370
+الطريقة، كيفية ممارسة الطريقة، فلذلك هنا لم يحدد 
+
+121
+00:10:13,370 --> 00:10:17,330
+الممارسين للطريقة، وهذا يدل أيضًا على عدم وجود 
+
+122
+00:10:17,330 --> 00:10:23,790
+إعداد متخصصين لممارسة الطريقة، طريقة تنظيم المجتمع 
+
+123
+00:10:23,790 --> 00:10:29,690
+هذه جوانب إيه بنعتبرها؟ جوانب ضعف اللي هو باينة في 
+
+124
+00:10:29,690 --> 00:10:35,970
+تعريف لندمان، في جوانب القوة، الجوانب القوة أيضا حدد 
+
+125
+00:10:35,970 --> 00:10:41,150
+طبعا الأهداف، حدد الأهداف اللي هي هنا 
+
+126
+00:10:46,070 --> 00:10:51,830
+المحتوى اللي من خلال العمل الديمقراطي، فهنا يدرس 
+
+127
+00:10:51,830 --> 00:10:57,770
+رأي المجتمع ويحدد محتوى الآراء، هذه ناحية ثانية 
+
+128
+00:10:57,770 --> 00:11:03,530
+أبرز أهمية التنسيق ما بين المؤسسات وحاجات أهالي 
+
+129
+00:11:03,530 --> 00:11:08,190
+المجتمع عن طريق التنسيق، هذا كان جوانب القوة في 
+
+130
+00:11:08,190 --> 00:11:12,810
+تعريفه هذا 
+
+131
+00:11:12,810 --> 00:11:16,860
+هو التعريف الأول في طريقة تنظيم المجتمع اللي هو 
+
+132
+00:11:16,860 --> 00:11:21,820
+يعبر لنا عن مرحلة التنسيق، فهذا هو التعريف الأول 
+
+133
+00:11:21,820 --> 00:11:27,760
+الآن أذكركم يعني بتعريفات متأخرة عند الأجانب في 
+
+134
+00:11:27,760 --> 00:11:32,640
+تعريف طريقة تنظيم المجتمع، يعني تعريف الـ New Setter 
+
+135
+00:11:32,640 --> 00:11:38,360
+يعني هذا كان تعريف يعني بعد لندمان، لندمان في 1920 
+
+136
+00:11:38,360 --> 00:11:45,340
+هذا تعريف في عام 1949، يعني بعد 29 سنة واضح؟ بدنا 
+
+137
+00:11:45,340 --> 00:11:50,420
+نشوف إيش تعريفنا، طبعا لما نقول 49 إذا أن تنظيم 
+
+138
+00:11:50,420 --> 00:11:57,980
+المجتمع يعني 49 كان معترف بها عمره 1946 فلذلك 
+
+139
+00:11:57,980 --> 00:12:01,720
+هنقرأ التعريف وهنشوف إيش جوانب القوة والضعف في 
+
+140
+00:12:01,720 --> 00:12:05,960
+هذا التعريف، بدي طالبة تقرأ لي هذا التعريف، اقرأي يا 
+
+141
+00:12:05,960 --> 00:12:10,620
+بنتي، يعرف تنظيم المجتمع بأنه العملية التي تمارس... 
+
+142
+00:12:10,620 --> 00:12:14,220
+تمارس ما بين الجماعات المختلفة للعمل على مقابلة 
+
+143
+00:12:14,220 --> 00:12:17,540
+احتياجاتها الاجتماعية واحتياجات المجتمع المحيط بها 
+
+144
+00:12:17,540 --> 00:12:21,700
+من خلال ممثليها، دي الجماعة؟ كويس، يعني هنا ركز على 
+
+145
+00:12:21,700 --> 00:12:25,080
+العمل بين الجماعات، على أساس قال بأنها طيب، المجتمع 
+
+146
+00:12:25,080 --> 00:12:30,400
+عملية لكن ما ذكر أن هي طريقة، قال عملية تمارس بين 
+
+147
+00:12:30,400 --> 00:12:34,060
+الجماعات، فهنا ركز على ... لإن كانت مارسة طريقة 
+
+148
+00:12:34,060 --> 00:12:38,180
+العمل بين الجماعات في تلك المرحلة للعمل على مقابلة 
+
+149
+00:12:38,180 --> 00:12:41,640
+احتياجاتها، طبعا احتياجات هذه الجماعات واحتياجات 
+
+150
+00:12:41,640 --> 00:12:45,640
+المجتمع المحيط بها من خلال ممثليها هذه الجماعات 
+
+151
+00:12:45,640 --> 00:12:49,840
+هذا هو التعريف الـ Necessitarian، هذا التعريف طبعا 
+
+152
+00:12:49,840 --> 00:12:55,000
+ظهر بعد ظهور طريقة تنظيم المجتمع عام 1946 
+
+153
+00:12:55,000 --> 00:13:04,760
+والاعتراف به، ولذلك يعني يمثل أيضا مرحلة من مراحل 
+
+154
+00:13:04,760 --> 00:13:08,510
+التنسيق وبيعكس الفترة التاريخية اللي بتمر بها 
+
+155
+00:13:08,510 --> 00:13:14,930
+الطريقة، وهي ازدهار طريقة العمل بين الجماعات واضح 
+
+156
+00:13:14,930 --> 00:13:19,210
+إذن؟ الأول خدمة الفرق، ثم بعد ذلك العمل بين 
+
+157
+00:13:19,210 --> 00:13:23,870
+الجماعات وأخيرا طريقة تنظيم المجتمع، بدا نشوف مواطن 
+
+158
+00:13:23,870 --> 00:13:29,090
+القوة في التعريف اللي ذكرناه وذكرته، ما هي جوانب 
+
+159
+00:13:29,090 --> 00:13:34,490
+القوة في تعريف الـ Neostatic؟ في عندنا عدد من جوانب 
+
+160
+00:13:34,490 --> 00:13:42,190
+القوة، أولا أبرز هذا التعريف اللي هي الأهداف، أهداف 
+
+161
+00:13:42,190 --> 00:13:46,230
+الجماعات وأهداف الطريقة، ربط ما بين أهداف 
+
+162
+00:13:46,230 --> 00:13:51,310
+الجماعات وأهداف المجتمع المحيط بهذه الجماعات، إذن 
+
+163
+00:13:51,310 --> 00:13:55,450
+هنا ربط ما بين أهداف الجماعات وأهداف المجتمع، 
+
+164
+00:13:55,450 --> 00:13:59,730
+أيضا، وهذا طبعا لما نقول ربط بين أهداف الجماعات 
+
+165
+00:13:59,730 --> 00:14:04,210
+وأهداف المجتمع في هذه نوع من التنسيق برضه، بمثل 
+
+166
+00:14:04,210 --> 00:14:10,610
+مرحلة التنسيق وهنا يوضح ويستطرد أهمية الارتباط 
+
+167
+00:14:10,610 --> 00:14:15,770
+بظروف المجتمع وإمكاناته عند إشباع احتياجات أفراده 
+
+168
+00:14:15,770 --> 00:14:20,310
+وجماعاته، هذه النحية الأولى اللي هو الربط بين 
+
+169
+00:14:20,310 --> 00:14:24,570
+الجماعات وجماعة ... بين المجتمع وجماعاته عن طريق 
+
+170
+00:14:24,570 --> 00:14:27,820
+التنسيق، النواحي القوة الثانية، النحية الثانية من 
+
+171
+00:14:27,820 --> 00:14:32,760
+نواحي القوة إنه أكد على أهمية وجود ممثلين للجماعات 
+
+172
+00:14:32,760 --> 00:14:39,380
+
+216
+00:18:24,710 --> 00:18:29,270
+الدكتور أحمد كمال أحمد، أيضًا من الرواد الأوائل،
+
+217
+00:18:29,270 --> 00:18:33,350
+الدكتور سيد أبو بكر في طريقة تنظيم المجتمع، أيضًا 
+
+218
+00:18:33,350 --> 00:18:37,230
+الدكتور عهودة بدران، هؤلاء من الرواد الأوائل في
+
+219
+00:18:37,230 --> 00:18:41,490
+طريقة تنظيم المجتمع، نقلوا طريقة للخدمة الاجتماعية 
+
+220
+00:18:41,490 --> 00:18:45,870
+و بيّنوا طريقة في مصر، وهؤلاء تتلمذنا على أيديهم، نحن
+
+221
+00:18:45,870 --> 00:18:51,050
+تتلمذنا ودرسنا وكنا قُلابَ لنفتح.. يعني وهم يشرحون
+
+222
+00:18:51,050 --> 00:18:54,330
+لنا محاضرات في السبعينات هذا الكلام، لكن هم كانوا
+
+223
+00:18:54,330 --> 00:18:57,050
+في مصر من الستينات، بل البعض منهم من الخمسينات
+
+224
+00:18:57,050 --> 00:19:02,070
+يعني درسوا الخدمة الاجتماعية وبكل طرقها وحضروا 
+
+225
+00:19:02,070 --> 00:19:05,750
+إلى مصر لنقل مهنة الخدمة الاجتماعية مؤثرة حسب 
+
+226
+00:19:05,750 --> 00:19:12,850
+التأصيل العربي لمهنة الخدمة الاجتماعية وليست كما
+
+227
+00:19:12,850 --> 00:19:17,370
+هي منقولة كما هي في أمريكا ومنقولة طبقًا للأصلِ، لذلك
+
+228
+00:19:17,370 --> 00:19:21,350
+هناك كان توطين للخدمة الاجتماعية في مصر، وبعد ذلك 
+
+229
+00:19:21,350 --> 00:19:24,910
+انتقلت للتوطين في باقي الدول العربية عن طريق
+
+230
+00:19:24,910 --> 00:19:29,250
+جمهورية مصر العربية، فهي رائدة في الخدمة الاجتماعية
+
+231
+00:19:29,250 --> 00:19:34,610
+فهؤلاء الرواد نقلوا ما يخص طريقة تنظيم المجتمع في
+
+232
+00:19:34,610 --> 00:19:39,660
+عندنا رواد نقلوا خدمة الفرد، يعني ومنهم الدكتور
+
+233
+00:19:39,660 --> 00:19:43,560
+عبدالفتاح عثمان، هذا كان رائدًا في خدمة الفرد أيضًا
+
+234
+00:19:43,560 --> 00:19:47,660
+تتلمذنا على يديه ودرسنا اللي هي طريقة خدمة الفرد 
+
+235
+00:19:47,660 --> 00:19:52,020
+يعني ونحن في .. في .. ترسلتنا في كلية الخدمة
+
+236
+00:19:52,020 --> 00:19:56,400
+الاجتماعية، أصبحت الآن تابعة إلى حلوان، وكانت في
+
+237
+00:19:56,400 --> 00:19:59,860
+الأول المعهد العالي للخدمة الاجتماعية، اسمه اسم
+
+238
+00:19:59,860 --> 00:20:04,360
+الكلية كذلك، كثير 
+
+239
+00:20:04,360 --> 00:20:09,430
+من الرواد، يعني الآخرين في خدمة الجماعة، الرائد الأول
+
+240
+00:20:09,430 --> 00:20:13,450
+ لخدمة الجماعة الدكتور محمد شمس الدين أحمد أيضًا
+
+241
+00:20:13,450 --> 00:20:18,330
+تتلمذنا على يديه في خدمة الجماعة، هؤلاء رواد درسوا 
+
+242
+00:20:18,330 --> 00:20:22,830
+في أمريكا وحضروا إلى جمهورية مصر العربية باعتبارهم
+
+243
+00:20:22,830 --> 00:20:27,490
+مصريين ونقلوا الخدمة الاجتماعية بأفكارهم، فالخدمة 
+
+244
+00:20:27,490 --> 00:20:31,290
+الاجتماعية توطنت في جمهورية مصر العربية بطرقها
+
+245
+00:20:31,290 --> 00:20:35,760
+الثلاث عن طريق الرواد الذين ذكرناهم، في خدمة الفرد
+
+246
+00:20:35,760 --> 00:20:40,180
+وخدمة الجماعة وتنظيم المجتمع، فلذلك هذه المرحلة
+
+247
+00:20:40,180 --> 00:20:45,180
+المرحلة هذه كانت مرحلة تثبيت طرق الخدمة الاجتماعية 
+
+248
+00:20:45,180 --> 00:20:50,420
+ككل، ففي مرحلة التنسيق يعني في كثير من المؤسسات
+
+249
+00:20:50,420 --> 00:20:57,340
+يعني ظهرت في مصر مثل عام 1937، ظهرت الجامعية 
+
+250
+00:20:57,340 --> 00:21:03,180
+المصرية لدراسات اجتماعية، وكذلك تم إنشاء أول معهد
+
+251
+00:21:03,180 --> 00:21:05,860
+للخدمة الاجتماعية في الإسكندرية عام تسع مئة وخمسة وثلاثين
+
+252
+00:21:05,860 --> 00:21:09,700
+وأُنشئت مدرسة الخدمة الاجتماعية بالقاهرة
+
+253
+00:21:09,700 --> 00:21:14,180
+عام تسع مئة وسبعة وثلاثين، اللي الآن يُسمّوها
+
+254
+00:21:14,180 --> 00:21:17,200
+المعهد العالي، تحول إلى المعهد اللي هو العالي
+
+255
+00:21:17,200 --> 00:21:20,640
+للخدمة الاجتماعية بالقلعة، بمدينة القلعة في القاهرة
+
+256
+00:21:20,640 --> 00:21:24,440
+أيضًا يُطلق عليه حاليًا المعهد القاهري للخدمة 
+
+257
+00:21:24,440 --> 00:21:28,300
+الاجتماعية، ثم أنشأ المعهد العالي للخدمة الاجتماعية
+
+258
+00:21:28,300 --> 00:21:31,180
+في القاهرة وكان يسمّونه في الأول المعهد العالي 
+
+259
+00:21:31,180 --> 00:21:35,140
+للخدمة الاجتماعية للفتيات، ثم بدأ تحويله عام للدرب
+
+260
+00:21:35,140 --> 00:21:40,320
+والعناب في Garden City وتحول من المعهد العالي
+
+261
+00:21:40,320 --> 00:21:43,700
+للخدمة الاجتماعية إلى كلية الخدمة الاجتماعية في
+
+262
+00:21:43,700 --> 00:21:47,500
+Garden City وبعد ذلك تحول إلى جامعة حلوان، إحنا 
+
+263
+00:21:47,500 --> 00:21:51,590
+درسنا فيه طبعًا لما كان في Garden City، ثم تحولوا 
+
+264
+00:21:51,590 --> 00:21:56,210
+لجامعة حلوان، وما فيه زملاء تخرجوا الآن من هذا 
+
+265
+00:21:56,210 --> 00:21:58,970
+المعقد، طبعًا ما إحنا درسنا كمهاري، يعني بكالوريوس
+
+266
+00:21:58,970 --> 00:22:02,250
+ وكلية خدمة اجتماعية، وأيضًا الآن في درسوا ماجستير 
+
+267
+00:22:02,250 --> 00:22:05,670
+ودكتوراه الآن بي درسوا دكتوراه، يعني في عندنا عدد من
+
+268
+00:22:05,670 --> 00:22:08,470
+طلابنا اللي درسوا خدمة اجتماعية في الجامعة 
+
+269
+00:22:08,470 --> 00:22:12,030
+الإسلامية هنا بغزة، يعني درسوا أيضًا بالإضافة
+
+270
+00:22:12,030 --> 00:22:17,810
+للبكالوريوس دراسة ماجستير ودكتوراه، هذا كان يعني 
+
+271
+00:22:17,810 --> 00:22:22,710
+عملية تطور لكليات
+
+272
+00:22:22,710 --> 00:22:26,690
+أو معاهد الخدمة الاجتماعية في مصر، فالآن تُعتبر
+
+273
+00:22:26,690 --> 00:22:30,310
+جامعة حلوان رائدة في الخدمة الاجتماعية، خرجت الكثير
+
+274
+00:22:30,310 --> 00:22:33,150
+من خريجيها في الـ bachelor's والـ master's والـ
+
+275
+00:22:33,150 --> 00:22:37,270
+doctorate، وتوزع يعني العاملين أيضًا في التخصصات 
+
+276
+00:22:37,270 --> 00:22:41,190
+العليا لتدريس الخدمة الاجتماعية في الوطن العربي 
+
+277
+00:22:41,590 --> 00:22:45,670
+اللي هي تدريس اللي هي مهنة الخدمة الاجتماعية 
+
+278
+00:22:45,670 --> 00:22:51,670
+بطرقها الثلاث، فلذلك في هذه المرحلة يعني ما فيش 
+
+279
+00:22:51,670 --> 00:22:56,110
+عندنا تعريفات، لأن التعريفات اللي ذكرها الرواد هنا 
+
+280
+00:22:56,110 --> 00:23:00,250
+تعريفات مشتركة تربط ما بين مرحلة التنسيق ومرحلة 
+
+281
+00:23:00,250 --> 00:23:05,410
+التخطيط ومرحلة التنمية ومرحلة الدفاع حتى، فلذلك هنا
+
+282
+00:23:05,410 --> 00:23:12,140
+سنعرج إلى اللي هي مرحلة التخطيط، وتعريفات خاصة 
+
+283
+00:23:12,140 --> 00:23:16,400
+بطريقة تنظيم المجتمع في مرحلة التخطيط، اللي خاصة
+
+284
+00:23:16,400 --> 00:23:22,060
+هناخدها عند العرب وعند الأجانب، وما يخص التعريفات
+
+285
+00:23:22,060 --> 00:23:25,640
+في مرحلة التنسيق، سنتعرض لها اللي هي في مرحلة 
+
+286
+00:23:25,640 --> 00:23:29,060
+التخطيط، لأن كانت التعريفات تربط ما بين مرحلة 
+
+287
+00:23:29,060 --> 00:23:33,980
+التنسيق والتخطيط، يعني في التعريفات العربية، لكن هنا
+
+288
+00:23:33,980 --> 00:23:37,900
+في تعريفات مرحلة التخطيط اللي مرّت بها طريقة تنظيم
+
+289
+00:23:37,900 --> 00:23:43,480
+المجتمع،  سناخد يعني تعريفات عند الأجانب، يعني أبرز 
+
+290
+00:23:43,480 --> 00:23:47,520
+ما تَحدّثوا في هذه المرحلة، جيمس داهر و... و... 
+
+291
+00:23:47,520 --> 00:23:55,340
+ماكنويل وكاميل ميرفي و شيرارد وأيضًا ووالسن
+
+292
+00:23:55,340 --> 00:24:00,950
+وكوفر، هدول كلهم يعني عَرّفوا طريقة تنظيم المجتمع في
+
+293
+00:24:00,950 --> 00:24:08,470
+مرحلة التخطيط، وأيضًا سيدر وكذلك شيراك، هناخد إحنا 
+
+294
+00:24:08,470 --> 00:24:13,830
+يعني التعريف الأول والتعريف الأخير، هناخد James 
+
+295
+00:24:13,830 --> 00:24:18,610
+Tahir وتعريف Thomas Shirak، الأول والأخير، ماشي؟
+
+296
+00:24:18,610 --> 00:24:22,310
+فهذا ناخد التعريف الأول الخاص بـ James Tahir لأنه
+
+297
+00:24:22,310 --> 00:24:25,970
+يُمثّل المرحلة الأولى كمرحلة تاريخية، اللي هو عام 
+
+298
+00:24:25,970 --> 00:24:33,330
+1950، ليه التخطيط؟ طبعًا أعرف أن طريقة تنظيم المجتمع
+
+299
+00:24:33,330 --> 00:24:40,450
+باعتبارها أنشطة، إذا هنا لم يقل عنها طريقة، ولكن
+
+300
+00:24:40,450 --> 00:24:44,930
+أفاد بأن تنظيم المجتمع مجموعة الأنشطة التي ما لسه
+
+301
+00:24:44,930 --> 00:24:48,810
+أفراد المجتمع للعمل على إيجاد توازن ما بين
+
+302
+00:24:48,810 --> 00:24:54,350
+احتياجات مجتمعهم وما بين الموارد المتاحة أو
+
+303
+00:24:54,350 --> 00:25:01,920
+الموارد التي قد تَتَاحُ، تعريف قصير ويركّز عن اللي هي
+
+304
+00:25:01,920 --> 00:25:06,020
+مرحلة من مراحل اللي مرت فيها طريقة تنظيم المجتمع
+
+305
+00:25:06,020 --> 00:25:10,720
+وهي مرحلة التخطيط، لكن هنا يعني أنّنا عند مناقشتنا
+
+306
+00:25:10,720 --> 00:25:15,960
+لهذا التعريف، نجد أنه بيجد توازنًا ما بين الموارد وما 
+
+307
+00:25:15,960 --> 00:25:20,760
+بين الحاجات أو الموارد الموجودة أو التي قد تَتَاحُ 
+
+308
+00:25:20,760 --> 00:25:26,940
+الموارد الموجودة أو الموارد التي قد تَتَاحُ، هنا لما 
+
+309
+00:25:26,940 --> 00:25:30,700
+نقول قد تَتَاحُ يعني مستقبليًا موارد ممكن قد نحصل
+
+310
+00:25:30,700 --> 00:25:35,140
+عليها في المستقبل، بالإضافة للموارد الموجودة حاليًا
+
+311
+00:25:35,140 --> 00:25:40,160
+فهذا بيعبر يعني عن عملية إيه التخطيط، وهنا بيعمل
+
+312
+00:25:40,160 --> 00:25:44,300
+توازنًا ما بين الموارد والاحتياجات، وهذا طبعًا كله 
+
+313
+00:25:44,300 --> 00:25:52,060
+يركّز على العملية التخطيطية، طيب لو أجينا هنا ممكن
+
+314
+00:25:52,060 --> 00:25:58,470
+التعريف هذا يعني بيفقد إلى جوانب مهمة جدا اللي هو
+
+315
+00:25:58,470 --> 00:26:03,210
+ما بينش أنه طريقة، أن تنظيم المجتمع طريقة، ما قالش عن 
+
+316
+00:26:03,210 --> 00:26:06,370
+الطريقة، ولكن قال عنها إيه؟ مجموعة أنشطة، مجموعة 
+
+317
+00:26:06,370 --> 00:26:13,030
+أنشطة، بالرغم أنه التعريف عام 1950، وكانت الإعلان عن
+
+318
+00:26:13,030 --> 00:26:17,570
+طريقة تنظيم المجتمع واعتراف بها كان عام 1946، إذا
+
+319
+00:26:17,570 --> 00:26:22,620
+هذا ماخد يأخذ عليه عند صياغة هذا التعريف، هنا لم 
+
+320
+00:26:22,620 --> 00:26:26,460
+يُشير باعتبارها طريقة من المجتمع، ولكن قال عنها بأنها
+
+321
+00:26:26,460 --> 00:26:30,360
+unsupervised، وهذا طبعًا كلام مردود عليه، يعني كلام 
+
+322
+00:26:30,360 --> 00:26:37,480
+مش صح، أيضًا تم الاعتراف بتنظيم المجتمع في عام 1946
+
+323
+00:26:37,480 --> 00:26:41,920
+سواء هذه ظاهرة المؤسسات الخاصة بطريقة تنظيم 
+
+324
+00:26:41,920 --> 00:26:46,540
+المجتمع في أمريكا أو بريطانيا، وأيضًا مثل ماذا اللي
+
+325
+00:26:46,540 --> 00:26:51,520
+ظهرت زي المحلات الاجتماعية، زي مجالس الهيئات
+
+326
+00:26:51,830 --> 00:26:55,010
+والرعاية الاجتماعية، الرعاية الاجتماعية هذه كلها
+
+327
+00:26:55,010 --> 00:27:00,830
+وايرت، يعني في هذه المرحلة، فهذه كلها كانت تُمارس
+
+328
+00:27:00,830 --> 00:27:05,990
+الدور التخطيطي، مجالس الهيئات، الرعاية الاجتماعية
+
+329
+00:27:05,990 --> 00:27:11,530
+والمحلات الاجتماعية، كان لها دور تخطيطي، فلذلك يُؤخذ
+
+330
+00:27:11,530 --> 00:27:16,410
+عليها يعني جوانب النقص في التعريف، بأنه لم يبين بأن
+
+331
+00:27:16,410 --> 00:27:22,640
+تنظيم المجتمع طريقة، أيضًا لم يُحدّد الكيفية، ما هي
+
+332
+00:27:22,640 --> 00:27:27,300
+الكيفيّة أيضًا اللي هي كيفية ممارسة الطريقة، فلم
+
+333
+00:27:27,300 --> 00:27:31,380
+يُبين الممارسين لطريقة تنظيم المجتمع، وهذا أيضًا
+
+334
+00:27:31,380 --> 00:27:39,460
+يُعتبر مأخذًا يُخَد على James Dahil، لم يبين الممارسين
+
+335
+00:27:39,460 --> 00:27:45,340
+للطريقة، وطبعًا
+
+336
+00:27:45,340 --> 00:27:50,820
+هذا عدم تبيانه لعدم وجود أو لم يوضح الممارسين
+
+337
+00:27:51,100 --> 00:27:56,140
+ب يفقد الطريقة فعاليّتها، طيب وعلى هذا يفتقر التعريف
+
+338
+00:27:56,140 --> 00:28:01,960
+إلى جانبين، أحدهما المهيّة والآخر الكيفية، إذا بيفقد 
+
+339
+00:28:01,960 --> 00:28:11,540
+إلى جانبين أساسيين وهما المهيّة والكيفيّة، واضح؟
+
+340
+00:28:11,540 --> 00:28:16,100
+في
+
+341
+00:28:16,100 --> 00:28:22,940
+عندنا تعريف Thomas Scherer، طالبة تقرأ لنا التعريف
+
+342
+00:28:22,940 --> 00:28:34,480
+Thomas Sharaf، يعتبر
+
+343
+00:28:34,480 --> 00:28:40,840
+هذا التعريف متأخرًا يعني في عام 1964، يُعتبر نسبيًا 
+
+344
+00:28:40,840 --> 00:28:45,880
+حديثًا، يُعتبر هذا التعريف تعريفًا حديثًا، فلذلك من هنا
+
+345
+00:28:46,340 --> 00:28:52,580
+يعني عَرَفنا التعريف لِأنّ تنظيم المجتمع طريقة، وهذا
+
+346
+00:28:52,580 --> 00:28:57,240
+صحيح، طريقة شاملة من طرق الخدمة الاجتماعية
+
+347
+00:28:57,240 --> 00:29:01,500
+يُستخدمها الأخصائي الاجتماعي، لِذا هنا بين ما هي 
+
+348
+00:29:01,500 --> 00:29:07,780
+وبين الكيفية بأن الأخصائي الاجتماعي هو الذي يُمارس
+
+349
+00:29:07,780 --> 00:29:14,500
+طريقة تنظيم المجتمع، وباعتبار هذه الطريقة من طرق 
+
+350
+00:29:14,500 --> 00:29:19,120
+مهنة الخدمة الاجتماعية في إنجاز المهام المتضمنة في
+
+351
+00:29:19,120 --> 00:29:24,140
+التخطيط الاجتماعي بصفة عامة، إذا الإيجابيات، التعريف
+
+352
+00:29:24,140 --> 00:29:29,740
+أول شيء بيّن أن تنظيم المجتمع طريقة من طرق الخدمة
+
+353
+00:29:29,740 --> 00:29:35,500
+الاجتماعية، وهذا شيء إيجابي واضح؟ وهذه الطريقة
+
+354
+00:29:35,500 --> 00:29:40,540
+تتضمن عملية، طريقة التنظيم المجتمع بتتضمن عملية، ما هي
+
+355
+00:29:40,540 --> 00:29:44,900
+العملية؟ هي التخطيط الاجتماعي أو التخطيط، التخطيط
+
+356
+00:29:44,900 --> 00:29:49,960
+الاجتماعي هو في إطار طريقة التنظيم المجتمع، إذا طريقة
+
+357
+00:29:49,960 --> 00:29:56,560
+التنظيم المجتمع باعتبارها طريقة، ولكن يُمارس التخطيط
+
+358
+00:29:56,560 --> 00:30:00,960
+الاجتماعي من خلالها كعملية في إطار طريقة التنظيم 
+
+359
+00:30:00,960 --> 00:30:05,380
+المجتمع، فلذلك التخطيط ليس طريقة في تلك المرحلة بل
+
+360
+00:30:05,380 --> 00:30:09,960
+هو يُعتبر عملية من عمليات طريقة تنظيم المجتمع اللي 
+
+361
+00:30:09,960 --> 00:30:15,100
+هو التخطيط الاجتماعي، وطبعًا هنا أوضح في كتاب له
+
+362
+00:30:15,100 --> 00:30:20,840
+طبعًا لشيرارد، أوضح أنّ التخطيط طبعًا بتصل لدراسة ووضع
+
+363
+00:30:20,840 --> 00:30:24,260
+الأولويات والبدء بالمشكلات الأكثر عمومية، هذه 
+
+364
+00:30:24,260 --> 00:30:28,400
+الأولويات طبعًا للمشكلات والحاجات بالنسبة للمجتمع
+
+365
+00:30:28,400 --> 00:30:35,010
+لكن ما أشارش وعنّطن الأهداف الحقيقية للطريقة، ما
+
+366
+00:30:35,010 --> 00:30:40,350
+عبّر عنها، ولكن هنا عبّر عن إيه؟ عن الأهداف الخاصة 
+
+367
+00:30:40,350 --> 00:30:44,910
+بالجوانب التخطيط الاجتماعي، إنجاز المهام المضمنة في 
+
+368
+00:30:44,910 --> 00:30:48,550
+التخطيط الاجتماعي، لكن إحنا بنقول التخطيط يُعتبر
+
+369
+00:30:48,550 --> 00:30:54,370
+عملية من ضمن طريقة تنظيم المجتمع، أيضًا لم يُشر إلى 
+
+370
+00:30:54,370 --> 00:30:58,990
+الممارس للطريقة، هل أشار؟ الكيفية؟ برضه هذا يُعتبر 
+
+371
+00:30:58,990 --> 00:31:00,490
+إيه؟ يعني
+
+372
+00:31:04,910 --> 00:31:09,230
+أو نعم، إذن هنا إشارة إلى الممارس لطريقة التنظيم
+
+373
+00:31:09,230 --> 00:31:13,410
+المجتمعي، اللي هو الأخصائي الاجتماعي هو الذي يُمارس
+
+374
+00:31:13,410 --> 00:31:17,930
+طريقة التنظيم المجتمعي، إذن جوانب الإيجابيات، قلنا
+
+375
+00:31:17,930 --> 00:31:23,470
+بيّن ما هي، الناحية الثانية بيّن الكيفية، وهي وجود 
+
+376
+00:31:23,470 --> 00:31:28,490
+الأخصائي الاجتماعي لممارسة طريقة التنظيم المجتمعي،
+
+377
+00:31:28,490 --> 00:31:33,530
+وهذا يُعتبر جانب إيه؟ جانب إيجابي في تعريف Thomas
+
+378
+00:31:33,530 --> 00:31:38,330
+Sherer، واضح؟ بهذا الشكل بإيجاز يعني نستطيع أن نبين 
+
+379
+00:31:38,330 --> 00:31:44,550
+الإيجابيات في التعريف، كذلك بين ناحية إيجابية ثالثة 
+
+380
+00:31:44,550 --> 00:31:50,390
+باعتبار أنّ طريقة التنظيم المجتمع هي إحدى طرق الخدمة 
+
+381
+00:31:50,390 --> 00:31:56,610
+الاجتماعية، وهذا يُعتبر أيضًا إيجابيًا، يُعتبر إيجابيًا في 
+
+382
+00:31:56,610 --> 00:32:02,030
+التعريف، وهذا طبعًا لِأنّ عندنا الطرق الأساسية، الفرق
+
+383
+00:32:02,030 --> 00:32:07,040
+والجماعة ومجتمع، وطريقة تنظيم المجتمع تختص بالمجتمع
+
+384
+00:32:07,040 --> 00:32:11,620
+ومشكلات المجتمع ودراسة مشكلات المجتمع ومساعدة
+
+385
+00:32:11,620 --> 00:32:15,860
+المجتمع على علاج مشكلته، فإذا هي طريقة من طرق
+
+386
+00:32:15,860 --> 00:32:20,880
+الخدمة الاجتماعية، هذه هي الإيجابيات الخاصة
+
+387
+00:32:20,880 --> 00:
+
+431
+00:36:07,000 --> 00:36:11,400
+هي تعريف الدكتور أحمد كمال أحمد و الدكتور عدلي 
+
+432
+00:36:11,400 --> 00:36:18,800
+سليمان عام 1961 في
+
+433
+00:36:18,800 --> 00:36:22,440
+عندنا الدكتور أحمد كمال أحمد و عدلي سليمان رحمه 
+
+434
+00:36:22,440 --> 00:36:27,740
+الله عليهما و على جميعاً الأحياء منهم
+
+435
+00:36:27,740 --> 00:36:32,430
+الأموات فلذلك الدكتور أحمد كمال و عدلي سليمان كانوا 
+
+436
+00:36:32,430 --> 00:36:38,750
+من الأساتذة الذين درسونا في الخدمة الاجتماعية فكان 
+
+437
+00:36:38,750 --> 00:36:42,170
+الدكتور أحمد كمال بيعطينا اللي هي مادة التنظيم
+
+438
+00:36:42,170 --> 00:36:46,850
+الاجتماعي و كذلك مادة أخرى التخطيط الاجتماعي أما
+
+439
+00:36:46,850 --> 00:36:55,210
+عدلي سليمان كان يعطينا مجالات
+
+440
+00:36:55,210 --> 00:36:58,350
+في الخدمة الاجتماعية و منها الخدمة الاجتماعية 
+
+441
+00:36:58,690 --> 00:37:02,510
+المدرسية لكن له كان دور في التخطيط لأنه كان عمله
+
+442
+00:37:02,510 --> 00:37:05,890
+بالإضافة لعمله الاجتماعي عندنا عدلي سليمان كان 
+
+443
+00:37:05,890 --> 00:37:10,290
+مستشاراً للأمم المتحدة المستشار الاجتماعي بالإضافة 
+
+444
+00:37:10,290 --> 00:37:14,130
+لأحمد كمال كان عميد كلية الخدمة الاجتماعية أو
+
+445
+00:37:14,130 --> 00:37:17,070
+المعهد العالي للخدمة الاجتماعية في تلك المرحلة 
+
+446
+00:37:17,070 --> 00:37:23,450
+طبعاً لما نتكلم المرحلة هي مرحلة السبعينات فعرفوا
+
+447
+00:37:23,450 --> 00:37:28,090
+هنا منظّم المجتمع هذا تعريف مشترك هنا تعريف مشترك
+
+448
+00:37:28,090 --> 00:37:32,590
+لهما في طريق تنظيم المجتمع بتعبر عن مرحلة التخطيط 
+
+449
+00:37:32,590 --> 00:37:37,950
+بل بتعبر عن مراحل أخرى فبدنا طالبة يعني تقرأ لنا 
+
+450
+00:37:37,950 --> 00:37:42,370
+التعريف، تعريف طريق تنظيم المجتمع، أيوا يا بنتي 
+
+451
+00:37:42,370 --> 00:37:44,950
+تنظيم المجتمع طريقة أخرى من طرق الخدمة 
+
+452
+00:37:44,950 --> 00:37:47,650
+الاجتماعية يستخدمها الأخصائيون الاجتماعيون 
+
+453
+00:37:47,650 --> 00:37:51,120
+والمتطوعون من الشعب للتعاون معهم لتنظيم الجهود 
+
+454
+00:37:51,120 --> 00:37:54,740
+المشتركة حكومية وأهلية وفي مختلف المستويات لتعبئة
+
+455
+00:37:54,740 --> 00:37:57,760
+الموارد الموجودة أو التي يمكن أن يجدها لمواجهة 
+
+456
+00:37:57,760 --> 00:38:01,180
+الحاجات الضرورية، رفقاً لخطط مرسومة وفي حدود 
+
+457
+00:38:01,180 --> 00:38:06,140
+السياسة الاجتماعية المجتمعية بس، هذا التعريف من 
+
+458
+00:38:06,140 --> 00:38:09,760
+خلال القراءة للتعريف، من الناحية التعريف هذا جاب 
+
+459
+00:38:09,760 --> 00:38:13,540
+اللبنات الأساسية للعمليات عن الشرح المفسر من خلال نظرة هذا 
+
+460
+00:38:13,540 --> 00:38:16,780
+التعريف، إيش بنستنتج منه؟ كل طالب بدها تقول 
+
+461
+00:38:16,780 --> 00:38:22,970
+استنتاج ماذا نستنتج يا بنتي؟ إذا هنا بتعريف بيّن 
+
+462
+00:38:22,970 --> 00:38:27,830
+لنا الماهية الخاصة بطريقة تنظيم المجتمع، باعتبار 
+
+463
+00:38:27,830 --> 00:38:31,530
+أنه تنظيم المجتمع طريقة من طرق الخدمة الاجتماعية،
+
+464
+00:38:31,530 --> 00:38:32,190
+ماذا يا بنتي؟
+
+465
+00:38:36,310 --> 00:38:40,670
+الكيفيّة، إذا هنا حدد لنا في التعريف بأنه الذي 
+
+466
+00:38:40,670 --> 00:38:45,670
+يمارس طريق تنظيم المجتمع هم أيضاً الأخصائيون 
+
+467
+00:38:45,670 --> 00:38:51,650
+الاجتماعيون وأضاف معهم المتطوعون، يعني ليس 
+
+468
+00:38:51,650 --> 00:38:55,990
+الأخصائيون لوحدهم، لكن أضاف معهم المتطوعون، مادة 
+
+469
+00:38:55,990 --> 00:39:00,130
+أيضاً، تعريف بها درسان تجميل كده أيه؟ أي وابد؟
+
+470
+00:39:00,130 --> 00:39:02,970
+تنظيم الجهود المشتركة حكومية وعالمية دي في دورتان 
+
+471
+00:39:02,970 --> 00:39:08,320
+سوريربط ما بين الجهود الحكومية والجهود الأهلية، 
+
+472
+00:39:08,320 --> 00:39:12,480
+على اعتبار أن الجهود مشتركة، في مختلف المستويات، 
+
+473
+00:39:12,480 --> 00:39:21,480
+إيش يعني مختلف المستويات؟ مختلف 
+
+474
+00:39:21,480 --> 00:39:26,360
+المستويات على مستوى المجتمع المحلي والإقليمي 
+
+475
+00:39:26,360 --> 00:39:31,840
+والوطني، يعني على كافة المستويات داخل المجتمع، ليس
+
+476
+00:39:31,840 --> 00:39:35,960
+على مستوى محلي فقط ولا على مستوى .. بل على كافة
+
+477
+00:39:35,960 --> 00:39:40,380
+المستويات داخل المجتمع، واضح؟ بتعبئة لإيه؟ الموارد 
+
+478
+00:39:40,380 --> 00:39:44,840
+الموجودة أو التي يمكن إيجادها، هذا يعبر عن 
+
+479
+00:39:44,840 --> 00:39:49,660
+التخطيط، الموارد الموجودة أو التي يمكن أن توجد أو 
+
+480
+00:39:49,660 --> 00:39:54,060
+التي يمكن إيجادها، لمواجهة ماذا؟ الحاجات الضرورية
+
+481
+00:39:54,730 --> 00:39:58,830
+وفقاً لخطط مرسومة وفي حدود السياسة العامة للمجتمع
+
+482
+00:39:58,830 --> 00:40:04,610
+السياسة الاجتماعية وخاصة بالمجتمع هذا هو التعريف
+
+483
+00:40:04,610 --> 00:40:13,610
+يعني بهذا الشكل بيّن الطريقة و أيضاً هذول الرواد 
+
+484
+00:40:13,610 --> 00:40:16,110
+اللي اتكلمنا عنهم قبل قليل هم رواد الخدمة 
+
+485
+00:40:16,110 --> 00:40:20,670
+الاجتماعية بطرقها الثلاث تنظيم المجتمع وخدمة الفرد 
+
+486
+00:40:20,670 --> 00:40:26,960
+وخدمة الجماعة وهذول طبعاً الرواد اللي احنا ذكرناهم
+
+487
+00:40:26,960 --> 00:40:31,760
+طبعاً واصلوا دراستهم في أمريكا ونشروا الخدمة 
+
+488
+00:40:31,760 --> 00:40:35,400
+الاجتماعية في جمهورية مصر العربية عن طريق التعليم 
+
+489
+00:40:35,400 --> 00:40:39,680
+الأكاديمي يعني الجامعات وخاصة كلية الخدمة 
+
+490
+00:40:39,680 --> 00:40:46,200
+الاجتماعية طبعاً طريقة اللي هو التخطيط هنا بمارس في
+
+491
+00:40:46,200 --> 00:40:51,650
+إطار طريق التنظيم المجتمع فلذلك التعريف يعني أوضح 
+
+492
+00:40:51,650 --> 00:40:56,250
+لنا أهمية وجود المهنيين، الأخصائيين الاجتماعيين لممارسة 
+
+493
+00:40:56,250 --> 00:41:01,070
+في الطريقة وأيضاً أكد أنّه تعريف على أهداف الطريقة 
+
+494
+00:41:01,070 --> 00:41:05,130
+ما هي أهداف الطريقة؟ طريقة تنظيم المجتمع، أيوة من 
+
+495
+00:41:05,130 --> 00:41:13,450
+ذلك تعبئة الموارد الموجودة حالياً 
+
+496
+00:41:13,450 --> 00:41:17,570
+أو التي ممكن أن توجد أين في المستقبل، هذه كلها 
+
+497
+00:41:17,570 --> 00:41:21,750
+لابد أن نعبئها لاستخدامها من أجل مواجهة المشكلات و
+
+498
+00:41:21,750 --> 00:41:27,150
+جميع الحاجات داخل المجتمع، ماذا أيضاً؟ آه، ما 
+
+499
+00:41:27,150 --> 00:41:31,630
+اتكلمناش، مفهومه بقى، إيه يا بنتي؟ لازم يكون الأعمال
+
+500
+00:41:31,630 --> 00:41:35,610
+موجودة على أساس علمي، مصري أيضاً، اللي هو التخطيط 
+
+501
+00:41:35,610 --> 00:41:39,530
+يعني، عمل طريق تنظيم المجتمع لابد أن يرتكز على 
+
+502
+00:41:39,530 --> 00:41:43,770
+التخطيط، والتخطيط لابد أن يكون على أساس علمي، 
+
+503
+00:41:43,770 --> 00:41:45,370
+واضح؟ إيه يا بنتي؟
+
+504
+00:41:49,010 --> 00:41:54,010
+أن يكون التخطيط طبقاً للسياسة العامة للمجتمع وهي 
+
+505
+00:41:54,010 --> 00:41:57,910
+السياسة الاجتماعية واحنا عارفين السياسة الاجتماعية
+
+506
+00:41:57,910 --> 00:42:05,090
+بتنبع منها التخطيط ثم من التخطيط تنبع الخطط ومن
+
+507
+00:42:05,090 --> 00:42:11,330
+الخطط تنبع البرامج والمشاريع والخدمات إذا السياسة
+
+508
+00:42:11,330 --> 00:42:16,050
+الاجتماعية هي الأعلى من السياسة الاجتماعية للمجتمع 
+
+509
+00:42:16,050 --> 00:42:22,200
+أو للدولة تنبع من التخطيط ومن التخطيط الخطط ومن الخطط
+
+510
+00:42:22,200 --> 00:42:26,380
+البرامج والمشاريع والخدمات على هذا الأساس يعني 
+
+511
+00:42:26,380 --> 00:42:29,760
+نتبع الأسلوب العلمي في هندستنا وممارستنا من طريق
+
+512
+00:42:29,760 --> 00:42:34,120
+تنظيم المجتمع على أساس أن نستخدم التخطيط والتخطيط 
+
+513
+00:42:34,120 --> 00:42:38,180
+يكون نابع من إيه؟ من السياسة الاجتماعية ولذلك
+
+514
+00:42:38,180 --> 00:42:41,900
+السياسة الاجتماعية والتخطيط مرتبطين مع بعضهم البعض 
+
+515
+00:42:41,900 --> 00:42:46,980
+فالتخطيط المطلوب أن يكون متفق مع السياسة الاجتماعية 
+
+516
+00:42:46,980 --> 00:42:47,500
+للمجتمع
+
+517
+00:42:52,020 --> 00:42:55,000
+طيب، هذه النواحي الإيجابية، طب ما هي النواحي 
+
+518
+00:42:55,000 --> 00:43:00,700
+السلبية في التعريف؟ ما هي النواحي السلبية؟ أغفل
+
+519
+00:43:00,700 --> 00:43:03,160
+هذا التعريف دور المهنيين من التخصصات الأخرى، لكن 
+
+520
+00:43:03,160 --> 00:43:05,880
+يمكن أن يتعاون مع العامل الاجتماعي لمواجهة المشكلة،
+
+521
+00:43:05,880 --> 00:43:11,040
+في إطار عمل فريق أيوة، في إطار، لكن قال متطوعين، 
+
+522
+00:43:11,040 --> 00:43:15,940
+قال ممكن نستخدم المتطوعين، لكن ليس كل متطوع مهني، 
+
+523
+00:43:15,940 --> 00:43:19,060
+فلذلك ما يمكن أن نستعين بالمهن الأخرى، و
+
+524
+00:43:19,060 --> 00:43:24,680
+بالمهنيين، من أجل مواجهة المشكلات ودراستها ووضع 
+
+525
+00:43:24,680 --> 00:43:29,040
+الحلول اللازمة لعلاجها إذا هنا أغفل هذا التعريف 
+
+526
+00:43:29,040 --> 00:43:34,120
+اللي هو دور المهنيين المتخصصين في المهن الأخرى 
+
+527
+00:43:34,120 --> 00:43:38,460
+ليه؟ لأن احنا بنعمل في عمل تكامل ضمن الفريق، فريق
+
+528
+00:43:38,460 --> 00:43:42,600
+العمل، لا نعمل لوحدنا كأخصائيين اجتماعيين ولكن نعمل في 
+
+529
+00:43:42,600 --> 00:43:47,440
+إطار فريق، نكافل تخصصات من أجل مواجهة المشكلة، لذلك 
+
+530
+00:43:47,440 --> 00:43:52,550
+من هنا يعتبر هذا General يعني نقص في التعريف ماذا
+
+531
+00:43:52,550 --> 00:43:58,410
+أيضاً؟ هذا الكلام اللي هو نقص لمشاركة الآخرين 
+
+532
+00:43:58,410 --> 00:44:02,770
+جعله أنّه ممكن يضع تعريف آخر للدكتورة أحمد كمال 
+
+533
+00:44:02,770 --> 00:44:06,830
+لطريقة تنظيم المجتمع سنتعرف عليها عندما نتحدث عن
+
+534
+00:44:06,830 --> 00:44:12,350
+تعريف المجتمع في طريقة اللي هي التنمية في مرحلة اللي 
+
+535
+00:44:12,350 --> 00:44:20,680
+هي التنمية واضح؟ ما هو المتطوعين المفروض أن نبرز 
+
+536
+00:44:20,680 --> 00:44:24,160
+منهم المتطوعين، ما هو مش من الخدمة الاجتماعية، 
+
+537
+00:44:24,160 --> 00:44:28,860
+لابد أن نقول أننا نعمل في إطار مهنة الخدمة 
+
+538
+00:44:28,860 --> 00:44:31,980
+الاجتماعية كأخصائيين اجتماعيين في إطار عمل الفريق 
+
+539
+00:44:31,980 --> 00:44:36,560
+المهني، لأن المتطوع أحياناً قد لا يكون من المتخصصين
+
+540
+00:44:36,560 --> 00:44:41,650
+في المهن الأخرى حتى، متطوع وخلاص يعني المتطوع من 
+
+541
+00:44:41,650 --> 00:44:46,190
+أجل أن يعمل لكن لو أبرزنا وأبرز التعريف قال لا مع 
+
+542
+00:44:46,190 --> 00:44:49,650
+التعاون مع المهن الأخرى والعاملين في المهن الأخرى 
+
+543
+00:44:49,650 --> 00:44:53,390
+بيتبقى أحسن في إطار عمل كفريق بيكون أفضل في
+
+544
+00:44:53,390 --> 00:45:01,510
+التعريف، واضح؟ في الدكتورة هدى بدران أيضاً وضعت
+
+545
+00:45:01,510 --> 00:45:04,910
+لنا تعريف لطريق تنظيم المجتمع اللي بيشمل الجانب 
+
+546
+00:45:04,910 --> 00:45:10,810
+التخطيطي ولكن يشمل أيضاً اللي هو جانب الدفاع كذلك في 
+
+547
+00:45:10,810 --> 00:45:17,250
+مرحلة الدفاع وكذلك جانب اللي هو التنموي وكذلك يشمل
+
+548
+00:45:17,250 --> 00:45:21,090
+التنسيق فبيشمل الأربع مراحل سنتعرض لها إن شاء الله
+
+549
+00:45:21,090 --> 00:45:23,870
+عندما نتحدث عن التاريخ
+
+550
+00:45:28,290 --> 00:45:34,090
+إذا في أي سؤال في تعريفها في طريقة تنظيم المجتمع
+
+551
+00:45:34,090 --> 00:45:40,930
+حسب ما اخذناها في مرحلة التّنسيق ومرحلة التخطيط نحن 
+
+552
+00:45:40,930 --> 00:45:44,170
+نجيب عليه، تفضل إيه؟ إنّه بس اللي قلت لإنسان يفكر 
+
+553
+00:45:44,170 --> 00:45:49,250
+إن عملية تنظيم المجتمع بطريقة تنظيم المجتمع كأمر 
+
+554
+00:45:49,250 --> 00:45:53,670
+عالمي، بغض النظر إن كان تعريف أو تنظيم المجتمع بطريقة 
+
+555
+00:45:53,670 --> 00:45:57,520
+كمعضلة هم عارفوا بعض بتعريف قانوني المجتمع بس 
+
+556
+00:45:57,520 --> 00:46:00,680
+عارفوا عن ماني ينشأ وانت هو جاهل أو هم مش عارفين 
+
+557
+00:46:00,680 --> 00:46:07,300
+أو على طلع بتعريف قانوني المجتمع؟ لا هم يعني حسب 
+
+558
+00:46:07,300 --> 00:46:12,100
+وجهة نظرهم ولذلك احنا عرفنا من خصائص التعريف أنّه
+
+559
+00:46:12,100 --> 00:46:16,420
+التعريف أحياناً بيعبّر عن وجهة نظر قائله فلذلك هم قد 
+
+560
+00:46:16,420 --> 00:46:21,500
+يكون ليس لديهم معرفة نمرا واحد نمرا اتنين قد لاقى
+
+561
+00:46:21,500 --> 00:46:25,000
+غير مقتنعين في تلك المرحلة، كانوا طالعين يتبنوا
+
+562
+00:46:25,000 --> 00:46:29,880
+تنظيم مجتمع بطريقة، فكانوا يصفوه بما يعني شيء نابع 
+
+563
+00:46:29,880 --> 00:46:34,580
+من فكرهم وعلمهم ومعرفتهم، يقولون عنها بأنها طريقة، 
+
+564
+00:46:34,580 --> 00:46:37,340
+البعض يقول عنها بأنها عملية، البعض يقول عنها 
+
+565
+00:46:37,340 --> 00:46:41,240
+أنشطة، البعض يقول عنها بأنها مجهودات، فهذه وجهة 
+
+566
+00:46:41,240 --> 00:46:45,520
+نظر قائلة، تعريف وجهة نظر قائلة، فلذلك المتخصصون 
+
+567
+00:46:45,520 --> 00:46:50,740
+يعني لازم ناخذ بتعريفاتهم حسب وجهة نظرهم فلذلك ربما
+
+568
+00:46:50,740 --> 00:46:53,940
+لم يعلموا بالاعتراف بطريقة ما لأن كانت تعريف
+
+569
+00:46:53,940 --> 00:46:58,560
+متقاربة مثل تعريفات 1950 و 1941 أربع سنوات كان
+
+570
+00:46:58,560 --> 00:47:01,580
+المفروض أنّه يعرف أنّه تنظيم المجتمع تم الاعتراف 
+
+571
+00:47:01,580 --> 00:47:05,020
+بهِ و لا يقول عنها عملية أو لا يقول عنها أنشطة بل
+
+572
+00:47:05,020 --> 00:47:09,180
+يقول عنها بأنها طريقة ولكن أحياناً بدأت إلى فكر 
+
+573
+00:47:09,180 --> 00:47:14,840
+المتخصص والباحث والعالم فهو بيعبر عن وجهة نظر،
+
+574
+00:47:14,840 --> 00:47:18,980
+فلذلك التعريف لا يعبر إلا عن وجهة نظر قائمة، فمن 
+
+575
+00:47:18,980 --> 00:47:22,860
+هذا المنطلق بناخد بوجهات النظر المختلفة، ولكن نحن 
+
+576
+00:47:22,860 --> 00:47:27,060
+بدورنا علينا أن ننتقد حسب شروط التعريف الجيّد 
+
+577
+00:47:27,060 --> 00:47:30,260
+للتعريف العلمي والطريقة، اللي هي بالنسبة للخدمة اللي 
+
+578
+00:47:30,260 --> 00:47:34,440
+هي طريقة تنظيم المجتمع أن نقرأ التعريف وننقده ونعرف
+
+579
+00:47:34,440 --> 00:47:38,060
+ما هي إيجابياته وسلبياته، هل فعلاً توفرت فيه شروط 
+
+580
+00:47:38,060 --> 00:47:42,660
+التعريف الجيّد أم لا، وبناء عليه نستطيع أن نعرف ما 
+
+581
+00:47:42,660 --> 00:47:46,440
+هي طريقة تنظيم المجتمع، ونستطيع أن نضع تعريف
+
+582
+00:47:46,440 --> 00:47:51,740
+محدداً كل طالب ممكن أو كل طالب لأ يعني عليه أن يضع 
+
+583
+00:47:51,740 --> 00:47:55,320
+تعريف لطريق التنظيم المجتمع، لكن احنا هنا درسنا 
+
+584
+00:47:55,320 --> 00:47:58,780
+التعريفات حسب كل مرحلة، مرحلة التنصيب ومرحلة
+
+585
+00:47:58,780 --> 00:48:01,840
+التخطيط وفي المحاضرة القادمة إن شاء الله سنتعرف 
+
+586
+00:48:01,840 --> 00:48:06,060
+على التعريفات في مرحلة التنمية ومرحلة الدفاع، لكن 
+
+587
+00:48:06,060 --> 00:48:10,300
+هذا لا يمنع في النهاية أن نضع تعريفاً شاملاً كاملاً
+
+588
+00:48:10,300 --> 00:48:15,750
+متضمناً فيه شروط التعريف طيب إلى هنا ننهي هذه 
+
+589
+00:48:15,750 --> 00:48:18,810
+المحاضرة على أمل اللقاء بيكون إن شاء الله في
+
+590
+00:48:18,810 --> 00:48:22,170
+المحاضرة القادمة لاستكمال تعريفات طريق تنظيم 
+
+591
+00:48:22,170 --> 00:48:28,050
+المجتمع في مرحلتي التنمية والدفاع إلى أن نلتقي في
+
+592
+00:48:28,050 --> 00:48:32,410
+المحاضرة القادمة لكل منّي كل تحية وتقدير والسلام 
+
+593
+00:48:32,410 --> 00:48:34,930
+عليكم ورحمة الله وبركاته
diff --git a/PL9fwy3NUQKwaKyeI5iiPpebyFXxlPBffV/ncysfAu_RnU_postprocess.srt b/PL9fwy3NUQKwaKyeI5iiPpebyFXxlPBffV/ncysfAu_RnU_postprocess.srt
new file mode 100644
index 0000000000000000000000000000000000000000..2fd44f40ce6502ad5d38ab9065aa58fdaeaa4335
--- /dev/null
+++ b/PL9fwy3NUQKwaKyeI5iiPpebyFXxlPBffV/ncysfAu_RnU_postprocess.srt
@@ -0,0 +1,1160 @@
+1
+00:00:21,130 --> 00:00:24,970
+بسم الله الرحمن الرحيم الحمد لله رب العالمين
+
+2
+00:00:24,970 --> 00:00:29,010
+والصلاة والسلام على أشرف المرسلين سيدنا محمد وعلى
+
+3
+00:00:29,010 --> 00:00:35,570
+آله وصحبه لأجمعين بنات الطالبات السلام عليكم ورحمة
+
+4
+00:00:35,570 --> 00:00:42,430
+الله وبركاته في هذه المحاضرة سنتحدث عن قطوات طريق
+
+5
+00:00:42,430 --> 00:00:49,770
+التنظيم المجتمع سنبدأ بتعريفالخطوات طريقة تنظيم
+
+6
+00:00:49,770 --> 00:00:54,130
+المجتمع ثم سنعرف خطوات طريقة تنظيم المجتمع عند
+
+7
+00:00:54,130 --> 00:01:02,510
+أساتذتنا في يعني الذين علمونا طريقة تنظيم المجتمع
+
+8
+00:01:02,510 --> 00:01:06,930
+فلذلك سنأخذ وجهة نظرهم في خطوات طريقة تنظيم
+
+9
+00:01:06,930 --> 00:01:12,610
+المجتمع سنأخذ رأي الدكتوراهودة بدران ثم رأي
+
+10
+00:01:12,610 --> 00:01:17,570
+الدكتور عبد المنعم شوقي ثم رأي الدكتور سيد أبو بكر
+
+11
+00:01:17,940 --> 00:01:23,880
+وأخيرًا، رأي الدكتور رشاد عبدالله طيب سنتناول هذه
+
+12
+00:01:23,880 --> 00:01:30,720
+المحاولات في شرح خطوات طريق التنظيم المجتمع أولًا،
+
+13
+00:01:30,720 --> 00:01:35,840
+سنبدأ بخطوات طريق التنظيم المجتمع ما معنى خطوات
+
+14
+00:01:35,840 --> 00:01:40,700
+طريق ... لما نقول خطوة طريق التنظيم المجتمع أو
+
+15
+00:01:40,700 --> 00:01:46,330
+خطوات طريق التنظيم المجتمع، ماذا نقصد بها؟طبعاً
+
+16
+00:01:46,330 --> 00:01:51,530
+نقص الطول خطوات هي جهود مبذولة من قبل المنظم
+
+17
+00:01:51,530 --> 00:01:58,630
+الاجتماعي منذ تعامله مع المجتمع إلى الانتهاء من
+
+18
+00:01:58,630 --> 00:02:04,050
+التعامل مع هذا المجتمع فهي المقصود الخطوة أو تعريف
+
+19
+00:02:04,050 --> 00:02:08,730
+آخرمقصود بيه عند .. اللي هو خطوات أو الجهال و
+
+20
+00:02:08,730 --> 00:02:12,630
+العمليات اللي ممكن يجوم بيها الأخصائي الاجتماعي
+
+21
+00:02:12,630 --> 00:02:18,250
+منذ التعامل مع المشكلة إلى أن ينتهي من هذه المشكلة
+
+22
+00:02:18,250 --> 00:02:23,510
+هذه الخطوات ثم يبدأ مع مشكلة جديدة وهكذا إلى أن
+
+23
+00:02:23,510 --> 00:02:28,490
+ينتهي منها هذه بتسميها خطوات لطريقة تنظيم المجتمع
+
+24
+00:02:28,490 --> 00:02:32,770
+في تعامل الأخصائي أو المنظم الاجتماعي مع المجتمع
+
+25
+00:02:32,770 --> 00:02:34,730
+الذي يعمل معه
+
+26
+00:02:37,360 --> 00:02:41,520
+هذا هو المقصود بيه اللي هي خطوات طريق التنظيم
+
+27
+00:02:41,520 --> 00:02:45,640
+المجتمع أو أيضًا ممكن نقصد بيها اللي هو ما يتبعه
+
+28
+00:02:45,640 --> 00:02:50,540
+المنظم من عمل منظم ومرتب بقصد تحقيق أهداف معينة
+
+29
+00:02:50,540 --> 00:02:56,160
+أشياء يريد أن يحقق المنظم الاجتماعي في المجتمع من
+
+30
+00:02:56,160 --> 00:02:59,820
+ذو أن يفكر فيها التحقيق هذه الأهداف ويبدأ في
+
+31
+00:02:59,820 --> 00:03:03,840
+تنفيذها إلى أن ينتهي من تنفيذها هذه بنسميها كلها
+
+32
+00:03:03,840 --> 00:03:10,670
+خطوات طريق التنظيم المجتمعطبعا هذه الخطوات كلها
+
+33
+00:03:10,670 --> 00:03:15,470
+تعتمد على المنهج العلمي ليست عبثية بل تعتمد على
+
+34
+00:03:15,470 --> 00:03:19,330
+المنهج العلمي كل خطوات طريقة تنظيم المجتمع هي
+
+35
+00:03:19,330 --> 00:03:25,890
+خطوات علمية معتمدة على خطوات القواعد المنهج العلمي
+
+36
+00:03:25,890 --> 00:03:31,430
+طبعا
+
+37
+00:03:31,430 --> 00:03:37,030
+في عندنا خطوات طريقةأي خطوات طريق التنظيم المجتمع
+
+38
+00:03:37,030 --> 00:03:43,490
+بترتكز على أشياء معينة لابد أن نعرفها دي إيه
+
+39
+00:03:43,490 --> 00:03:47,590
+الركائز اللي بترتكز عليها طريق التنظيم المجتمع
+
+40
+00:03:47,590 --> 00:03:54,370
+طبعا المنظم الاجتماعي هو بيمارس عمليات مهنية طريق
+
+41
+00:03:54,370 --> 00:03:56,530
+التنظيم اللي هي خطوات طريق التنظيم المجتمع هي
+
+42
+00:03:56,530 --> 00:04:02,730
+عبارة عن عمليات مهنية يقوم بيها المنظم الاجتماعي
+
+43
+00:04:02,730 --> 00:04:06,800
+مع المجتمعفلذلك هذه الخطوات أو هذه العمليات
+
+44
+00:04:06,800 --> 00:04:10,780
+المهنية التي تستهدف مواجهة المشكلات المجتمعية
+
+45
+00:04:10,780 --> 00:04:16,020
+ترتكز على .. على ماذا ترتكز في هذه الخطوات أو
+
+46
+00:04:16,020 --> 00:04:21,540
+العمليات المهنية أول ركيزة أول شيء قيم المهنة مهنة
+
+47
+00:04:21,540 --> 00:04:26,560
+الخدمة الاجتماعية القيم في مهنة طبعا لأي مهنة في
+
+48
+00:04:26,560 --> 00:04:31,360
+قيم فاحنا مهنة الخدمة الاجتماعية لها قيماحترام
+
+49
+00:04:31,360 --> 00:04:36,320
+الإنسان وكرامة الإنسان وقيمة الإنسان والتعامل يعني
+
+50
+00:04:36,320 --> 00:04:40,080
+مع الإنسان على أساس عمل الشورة أو الديمقراطية
+
+51
+00:04:40,080 --> 00:04:45,980
+فلذلك من هنا في قيم معينة لهذه المهنة فلابد منها
+
+52
+00:04:45,980 --> 00:04:51,080
+المحافظة عليها أيضا في منهج علمى المنهج العلمى
+
+53
+00:04:51,080 --> 00:04:55,800
+وخطوات المنهج العلمى أيضا من القيم اللي بترتكز
+
+54
+00:04:55,800 --> 00:05:00,780
+عليها طريقة تنظيم المجتمع ماذا أيضا؟مين تقولي
+
+55
+00:05:00,780 --> 00:05:04,940
+مهارات مهنية، مهارة مهنية أو المهارات مثل ما ده؟
+
+56
+00:05:04,940 --> 00:05:08,900
+التقبل، التقبل للمبدأ هذا التقبل للمبدأ والمهارة
+
+57
+00:05:08,900 --> 00:05:13,500
+في تطبيق المبدأ كل المبادئ تعتبر مهارات عند
+
+58
+00:05:13,500 --> 00:05:17,240
+تطبيقهم كذلك التطبيق نعم كذلك البحث الاجتماعي
+
+59
+00:05:17,240 --> 00:05:21,380
+يعتبر مهارة بكل ما يتعلق بمناهج البحث الاجتماعي
+
+60
+00:05:21,380 --> 00:05:25,280
+واتباع الأسلوب العلمييعني في المناهج البحث
+
+61
+00:05:25,280 --> 00:05:28,680
+الإجتماعي هذي بتعتبر مهارة فانت عندما يقوم
+
+62
+00:05:28,680 --> 00:05:32,100
+الأخصائي أو المنظم الاجتماعي باستخدام المنهج
+
+63
+00:05:32,100 --> 00:05:35,360
+العلمي اللي هو منهج من منهج البحث الاجتماعي بتعتبر
+
+64
+00:05:35,360 --> 00:05:41,620
+مهارة استخدام الأدوات أيضًا لمناهج البحث العلمي أو
+
+65
+00:05:41,620 --> 00:05:45,980
+الاجتماعي تعتبر مهارة مثل الملاحظة المقابلة
+
+66
+00:05:45,980 --> 00:05:50,160
+استبانة إلى غير ذلك كيفية تصميمها وكيفية وضعها
+
+67
+00:05:50,160 --> 00:05:54,020
+وجمع البيانات المعلومات كلها مهارةالتعامل مع
+
+68
+00:05:54,020 --> 00:05:58,540
+المجتمع ومع قادة المجتمع مهارة مهارات كثيرة ولذلك
+
+69
+00:05:58,540 --> 00:06:02,260
+من هنا بتعتمد اللي هي أو من الركاز اللي بترتكز
+
+70
+00:06:02,260 --> 00:06:06,360
+عليها اللي هي خطوات طريقة تنظيم المجتمع على مادة
+
+71
+00:06:06,360 --> 00:06:09,680
+المهارات المهنية المهارات المهنية المهارة في
+
+72
+00:06:09,680 --> 00:06:14,400
+التسجيل كل طرح بنخدمها الإجتماعية بنسجل بنستخدم
+
+73
+00:06:14,400 --> 00:06:18,080
+التسجيل المهارة هذه مهارة المهارة في تطبيق المبادئ
+
+74
+00:06:18,080 --> 00:06:23,360
+بشكل عام كيفية تطبيق المبدأ مع المجتمعهذا تعتبر
+
+75
+00:06:23,360 --> 00:06:27,700
+مهارة وهذا نعم الأهداف الإيجابية أيضًا الركاز
+
+76
+00:06:27,700 --> 00:06:31,960
+بترتكز عليها الأهداف الإيجابية للمجتمع تركيز على
+
+77
+00:06:31,960 --> 00:06:36,420
+الأهداف الإيجابية وليست الأهداف السلبية الرصول إلى
+
+78
+00:06:36,420 --> 00:06:43,240
+مواجهة فعالة لمشكلات المجتمع طبعًا مهم جدًا هنا
+
+79
+00:06:43,240 --> 00:06:46,900
+هذه من الركاز بترتكز عليها طريقة تنظيم المجتمع
+
+80
+00:06:46,900 --> 00:06:50,930
+وخطوات طريقة تنظيم المجتمع اللي هيالموصول إلى
+
+81
+00:06:50,930 --> 00:06:55,310
+مواجهة فعالة لمشكلات المجتمع سواء كان ذلك جزئيا أو
+
+82
+00:06:55,310 --> 00:07:00,290
+كليا حسب ظروف كل مجتمع وإمكانياته ونوعية المشكلات
+
+83
+00:07:00,290 --> 00:07:06,190
+التي يعاني منها المجتمع أيضا في من الركاز اللي
+
+84
+00:07:06,190 --> 00:07:09,590
+ترتكز عليها خطوات طريقة تنظيم المجتمع اللي هي
+
+85
+00:07:09,590 --> 00:07:13,930
+أهمية العمل الفريق الـ Teamwork لا يعمل المنظم
+
+86
+00:07:13,930 --> 00:07:18,010
+الاجتماعي لوحده ولكن يعمل في إطار متخصصي يعني مع
+
+87
+00:07:18,010 --> 00:07:22,530
+المتخصصين ككلومع الخبراء المجتمع ككل فلذلك من هنا
+
+88
+00:07:22,530 --> 00:07:27,270
+فيعمل في إطار الإيه؟ العمل الفريقي داخل المجتمع
+
+89
+00:07:27,270 --> 00:07:32,410
+لمواجهة المشكلات وإشباء الاحتياجات المجتمعية هذه
+
+90
+00:07:32,410 --> 00:07:37,770
+هي أهم الركائز اللي بتعتمد عليها عمليات العمليات
+
+91
+00:07:37,770 --> 00:07:43,930
+المهنية أو خطوات طريقة تنظيم المجتمع في عندنا الآن
+
+92
+00:07:43,930 --> 00:07:49,770
+وجهة نظر من خلال وجهة نظر الدكتورة أودا بادرانسعلى
+
+93
+00:07:49,770 --> 00:07:53,950
+خطوات طريق التنظيم المجتمع الدكتورة عمدة بدران
+
+94
+00:07:53,950 --> 00:07:59,310
+لخصت لنا خطوات طريق التنظيم المجتمع في خطوات تانية
+
+95
+00:07:59,310 --> 00:08:05,410
+الخطوة الأولى التخطيط والخطوة الثانية التنفيذ
+
+96
+00:08:05,410 --> 00:08:12,610
+تخطيط وتنفيذ ولكن في كل خطوة شملت خطوات يعني مثلا
+
+97
+00:08:12,610 --> 00:08:19,340
+خطوة التخطيط تضمن ماذا تحديد المشكلةو تضمن ضمن
+
+98
+00:08:19,340 --> 00:08:23,960
+مادة أيضا العوارف المتصلة بالمشكلة وكذلك تضمن مادة
+
+99
+00:08:23,960 --> 00:08:29,020
+أكثر من الحلول لمواجهة المشكلة فلذلك بالرغم إن هو
+
+100
+00:08:29,020 --> 00:08:34,480
+بعثها في مرحلتين أو في خطوتين لأن داخل كل خطوة
+
+101
+00:08:34,480 --> 00:08:40,700
+تحتوي خطوات يعني جزئية فلذلك لازم نتبع هذه الخطوات
+
+102
+00:08:40,700 --> 00:08:45,920
+هذه الخطوة الأولى من وجهة نظر الدكتورة خدها بدرا
+
+103
+00:08:46,330 --> 00:08:52,690
+طيب الخطوة الثانية التنفيذ لكن ليس التنفيذ فقط بل
+
+104
+00:08:52,690 --> 00:08:58,690
+اجتملت ايضا خطوات فلذلك خطوة التنفيذ اللي هي تنفيذ
+
+105
+00:08:58,690 --> 00:09:04,290
+الحل المناسب تنفيذ الحل بعد وضع الخطة لازم تنفيذ
+
+106
+00:09:04,290 --> 00:09:08,890
+الخطة اللي هو تنفيذ الحل لكن تنفيذ الحل هذا بيشمل
+
+107
+00:09:08,890 --> 00:09:14,800
+ايه ايضا خطوات مثل التقويم التقويمالتقييم لماذا
+
+108
+00:09:14,800 --> 00:09:22,900
+تقييم؟ تقييم لمعرفة مدى النجاح وأوجه النقص بالنسبة
+
+109
+00:09:22,900 --> 00:09:27,000
+لدور الأخصائي الشماعي ودور الأهالي هنا في تقييم
+
+110
+00:09:27,000 --> 00:09:32,360
+عندنا، إذا التنفيذ لابد أن يتبع خطوات كل ما نبدأ
+
+111
+00:09:32,360 --> 00:09:36,660
+بالتنفيذ، لابد أن نقيم مرحلة التنفيذ، هل فيها
+
+112
+00:09:36,660 --> 00:09:40,380
+إيجابيات، فيها سلبيات، ونحاول الإيجابيات ندعمها
+
+113
+00:09:40,380 --> 00:09:45,460
+والسلبيات ندفعها، وهكذاإذا لابد من مرحلة التقييم
+
+114
+00:09:45,460 --> 00:09:50,700
+وهذه تبدأ معناه يعني مرحلة التقييم دائما يعني من
+
+115
+00:09:50,700 --> 00:09:54,360
+بداية الخطوات طريق التنظيم المجتمع لكن هنا وضعت
+
+116
+00:09:54,360 --> 00:09:57,900
+التقييم في مرحلة التنفيذ عند التنفيذ وقيامنا
+
+117
+00:09:57,900 --> 00:10:02,680
+بالتنفيذ لابد أن نقيم ما قمنا بتنفيذه، واضح؟
+
+118
+00:10:02,680 --> 00:10:06,580
+فالتقييم تعتبر عملية أساسية من عمليات اللي هي
+
+119
+00:10:06,580 --> 00:10:11,120
+التنظيم المجتمع اللي هي في إغتار خطوات طريق
+
+120
+00:10:11,120 --> 00:10:15,050
+التنظيم المجتمعهذه هما المرحلتين التخطيط والتنفيذ
+
+121
+00:10:15,050 --> 00:10:21,390
+لكن كل مرحلة فيها خطوات إضافية في
+
+122
+00:10:21,390 --> 00:10:25,090
+عندنا أيضًا من وجهة نظر الدكتور عبد المنعم الشوقي
+
+123
+00:10:25,090 --> 00:10:30,050
+يعني بيجسملنا خطوات طريق تنظيم المجتمع لأربع خطوات
+
+124
+00:10:30,050 --> 00:10:34,810
+المرحلة التمئيدية المرحلة التخطيطية المرحلة
+
+125
+00:10:34,810 --> 00:10:39,990
+التنفيذية المرحلة التقييدية هذه الخطوات الأربع
+
+126
+00:10:39,990 --> 00:10:45,140
+وبشرحلنا كل خطوةمن هذه الخطوات. لو جينا لمرحلة
+
+127
+00:10:45,140 --> 00:10:49,480
+التمهيدية، ماذا تعني؟ ماذا تعني المرحلة التمهيدية؟
+
+128
+00:10:49,480 --> 00:10:52,500
+كخطوة من خطوات طريق تنظيم المجتمع؟ مدعوم على
+
+129
+00:10:52,500 --> 00:10:55,640
+المجتمع ومقوماته الأساسية. مدعوم على دعائه من
+
+130
+00:10:55,640 --> 00:11:00,920
+المجتمع، على مقومات المجتمع. ما هو هذا المجتمع؟ ما
+
+131
+00:11:00,920 --> 00:11:05,680
+هي مقوماته؟ ما هي دعائه؟ فلذلك المرحلة التمهيدية
+
+132
+00:11:05,680 --> 00:11:11,920
+بتعرفنا على المجتمع من كل جوانبه.بينما تشمل
+
+133
+00:11:11,920 --> 00:11:16,060
+المرحلة التخطيطية خلاص بعد ما اتعرفنا على المجتمع
+
+134
+00:11:16,060 --> 00:11:19,280
+ودراسنا المجتمع وعرفنا حاجات المجتمع مشكلات
+
+135
+00:11:19,280 --> 00:11:23,140
+المجتمع هنا بنأتي إلى المرحلة الثانية وهي المرحلة
+
+136
+00:11:23,140 --> 00:11:28,020
+التخطيطية ماذا نقصد بالمرحلة التخطيطية هو وضع
+
+137
+00:11:28,020 --> 00:11:35,700
+الخطة وضع خطة العمل وضع خطة العمل لمواجهة هذه
+
+138
+00:11:35,700 --> 00:11:40,360
+الحاجات واشبائها ومواجهة المشكلات وحلهاداخل
+
+139
+00:11:40,360 --> 00:11:43,200
+المجتمع إذا الخطوة الثانية اللي هي المرحلة
+
+140
+00:11:43,200 --> 00:11:47,760
+التخطيطية تجتمد ثقة العمل وتحديد المشكلات اللي
+
+141
+00:11:47,760 --> 00:11:53,400
+أكتر الحاحن حسب أهميتها ما هي المشكلات الموجودة في
+
+142
+00:11:53,400 --> 00:11:56,860
+عندنا مشكلات كثيرة لكن هنا بدنا نحدد الحسب
+
+143
+00:11:56,860 --> 00:12:00,900
+الأولوية ما هي المشكلات الملحة داخل المجتمع و تطلب
+
+144
+00:12:00,900 --> 00:12:07,500
+حل سريعا ولها أهمية داخل المجتمع هذه منحددها في
+
+145
+00:12:07,500 --> 00:12:12,140
+المرحلة التخطيطيةوأيضًا كيفية القيام بعمل منظم
+
+146
+00:12:12,140 --> 00:12:16,220
+لمواجهة هذه المشكلة كيفية العمل لمواجهة هذه
+
+147
+00:12:16,220 --> 00:12:20,800
+المشكلة الملحقة داخل المجتمع والتي لها أولوية يعني
+
+148
+00:12:20,800 --> 00:12:25,540
+وأهمية داخل المجتمع هذه المرحلة الثانية في عندنا
+
+149
+00:12:25,540 --> 00:12:30,900
+المرحلة الثالثة خلاص قطعنا الخطة بعد ذلك نابد ننفذ
+
+150
+00:12:30,900 --> 00:12:35,460
+الخطة تنفيذ الخطة ولذلك نسميها المرحلة التنفيذية
+
+151
+00:12:35,460 --> 00:12:40,550
+المرحلة التنفيذيةوهذه تشمل الجهود الفعلية لمواجهة
+
+152
+00:12:40,550 --> 00:12:45,050
+المشكلة سواء كانت المشكلة مادية أو مشارية كما
+
+153
+00:12:45,050 --> 00:12:49,230
+تعرفها كذا فلذلك هذه مرحلة تنفيذية نقوم بالتنفيذ
+
+154
+00:12:49,230 --> 00:12:54,150
+تنفيذ الخطة تنفيذ الخطة حسب الموارد الموجودة
+
+155
+00:12:54,150 --> 00:12:58,530
+الموارد والإمكانيات الموجودة في المجتمع لأنه ما
+
+156
+00:12:58,530 --> 00:13:04,230
+بنفذ خطة يعني وليس لدينا موارد وإمكانيات الخطة
+
+157
+00:13:04,230 --> 00:13:10,980
+لابد نحدد المشكلةفلذلك بننفذ الخطة ونستغل ونستثمر
+
+158
+00:13:10,980 --> 00:13:15,000
+كافة الموارد والإمكانيات الموجودة في المجتمع من
+
+159
+00:13:15,000 --> 00:13:20,300
+أجل مساعدة المجتمع على حل مشكلته هذه المرحلة
+
+160
+00:13:20,300 --> 00:13:24,860
+التنفيذية في عندنا مرحلة أخيرة وهي المرحلة
+
+161
+00:13:24,860 --> 00:13:32,000
+التقويمية خلاص تقويم وتقييم العمل بتاعنا والتنفيذ
+
+162
+00:13:32,000 --> 00:13:38,100
+للخطة هل فعلا احنا جمنا بنجاحأم هناك صعوبات، ام
+
+163
+00:13:38,100 --> 00:13:42,380
+فيه فشل، ما هي الجيجابيات، ما هي السلبيات، عند
+
+164
+00:13:42,380 --> 00:13:47,000
+التنفيذ، و هكذا، فلذلك هذه المرحلة بتبيننا جوانب
+
+165
+00:13:47,000 --> 00:13:52,620
+النجاح أو الفشل في تحقيق الأهداف الموضوعة و محاولة
+
+166
+00:13:52,620 --> 00:13:58,390
+وضع خطة جديدة للإصلاحإذا كانت فاشرة إذا كانت فاشرة
+
+167
+00:13:58,390 --> 00:14:03,430
+بنعدلها أو بنغيرها يا تعديل يا تغيير ولذلك دائما
+
+168
+00:14:03,430 --> 00:14:09,390
+التقويم يساعدنا على دعم الإيجابيات وتعديل السلبيات
+
+169
+00:14:09,390 --> 00:14:15,130
+أو إزالة السلبيات واضح؟ هذا بالنسبة للمراحل
+
+170
+00:14:15,130 --> 00:14:19,830
+الأربعة من وجهة الدكتور عبدالمان عم الشوقي مرحلة
+
+171
+00:14:19,830 --> 00:14:24,190
+تنفيذية تقتطية تنفيذية تقويمية
+
+172
+00:14:26,510 --> 00:14:34,390
+في عندنا أيضًا من وجهة الدكتور سيد أبو بكر حاولته
+
+173
+00:14:34,390 --> 00:14:42,010
+لوضع خطوات لطريقة تنظيم المجتمع ما هي هذه الخطوات
+
+174
+00:14:42,010 --> 00:14:46,670
+اللي وضعها هنا مجسمها خطوات تنظيم المجتمع 6 مراعاة
+
+175
+00:14:46,670 --> 00:14:54,320
+أو 6 خطوات 6 خطوات يعني هذه الخطواتشبيهة بالأهداف
+
+176
+00:14:54,320 --> 00:14:57,120
+اللي وضحها الدكتور سيدة أبو بكر لطريقة تنظيم
+
+177
+00:14:57,120 --> 00:15:01,360
+المجتمع، نتذكركم بها، نتذكركونها بها، اللي هي
+
+178
+00:15:01,360 --> 00:15:05,500
+خطوات الأهداف، لو رجعنا اليها، بنلاقي هي خطوات
+
+179
+00:15:05,500 --> 00:15:10,040
+طريقة تنظيم المجتمع، هي نفسها الأهداف الجزئية اللي
+
+180
+00:15:10,040 --> 00:15:14,700
+وضحها الدكتور سيدة أبو بكر في طريقة تنظيم المجتمع،
+
+181
+00:15:14,700 --> 00:15:18,980
+فلذلك الخطوات تبدأ من ماذا؟ الدراسة
+
+182
+00:15:22,880 --> 00:15:31,000
+النفيذ المتابعة والتقويل، ست خطوات، ست خطوات، لو
+
+183
+00:15:31,000 --> 00:15:35,780
+أجينا يعني هذه الخطوات الستة، لو شرحنا كل خطوة من
+
+184
+00:15:35,780 --> 00:15:40,140
+هذه الخطوات، يعني بنلاقي هذه الخطوات كلها مترابطة
+
+185
+00:15:40,140 --> 00:15:43,880
+ومتكاملة مع بعض يعنى بعض، وانا يمكن أفصل بعضها عن
+
+186
+00:15:43,880 --> 00:15:49,460
+بعض، لكن الدراسة بتبين أن المجتمع، وما هي المشكلات
+
+187
+00:15:49,460 --> 00:15:52,770
+الموجودة في المجتمع أو الحاجات في المجتمع،فلذلك
+
+188
+00:15:52,770 --> 00:15:57,190
+هذه مرحلة الدراسة بتوفر لنا اللي هي قاعدة بيانات
+
+189
+00:15:57,190 --> 00:16:01,990
+عن المجتمع، قاعدة البيانات والمعلومات والمعارف عن
+
+190
+00:16:01,990 --> 00:16:06,230
+المجتمع، ما هي مشكلاته، ما هي حاجاته، ما هي
+
+191
+00:16:06,230 --> 00:16:09,490
+إمكانياته، اللي ممكن نستخدمها في معالجة هذه
+
+192
+00:16:09,490 --> 00:16:14,130
+المشكلات، هذا كله في إطار ماذا؟ في إطار الدراسة،
+
+193
+00:16:14,130 --> 00:16:17,290
+الدراسة، والدراسة مهمة جدا، لأن بدون الدراسة
+
+194
+00:16:17,290 --> 00:16:21,490
+مايمكن أن ننفذ باقي القطوات، بطريقة تنظيم المجتمع
+
+195
+00:16:22,190 --> 00:16:26,590
+المرحلة الثانية اللي هي التشخيص اللي هي بتبين
+
+196
+00:16:26,590 --> 00:16:30,870
+الأسباب المشكلة عرفنا المشكلات لكن بنبين ما هي
+
+197
+00:16:30,870 --> 00:16:35,250
+أسباب هذه المشكلات لأنه زي ما نشخص المرض نشخص
+
+198
+00:16:35,250 --> 00:16:39,250
+المرض ونعرف سبب المرض إذا العلاج سهل هنا أيضا نفس
+
+199
+00:16:39,250 --> 00:16:43,490
+الشيء التشخيص هو مرحلة التشخيص هي عبارة عن تحديد
+
+200
+00:16:43,490 --> 00:16:49,530
+أسباب المشكلة أيضا الاتصال لابد أن نتصل بسكان
+
+201
+00:16:49,530 --> 00:16:55,100
+المجتمع حتى نقنعهم بالمشاركةفي حل مشكلاتهم و هنا
+
+202
+00:16:55,100 --> 00:17:00,140
+بنهيئهم للمشاركة في تحديد المشكلات و البدء بأهم
+
+203
+00:17:00,140 --> 00:17:04,920
+هذه المشكلات و كذلك بالحصول على الموارد المالية
+
+204
+00:17:04,920 --> 00:17:09,120
+اللازمة لمواجهة المشكلات هذه الهدف من الاتصال
+
+205
+00:17:09,120 --> 00:17:13,080
+الاتصال بسكان المجتمع لأن أي مشروع اي برنامج
+
+206
+00:17:13,080 --> 00:17:17,300
+لايمكن ان ينجح الا بمشاركة الناس فيه اهل المجتمع
+
+207
+00:17:17,300 --> 00:17:24,900
+بدون مشاركة اهل المجتمع المشروع يفشللو أرادت مثلا
+
+208
+00:17:24,900 --> 00:17:29,420
+بلدية من البلدية تحت المناطق تحت المدن أن تعمل
+
+209
+00:17:29,420 --> 00:17:35,500
+حديقة لكن لو ما أشركت سكان الحي في الحديقة الحديقة
+
+210
+00:17:35,500 --> 00:17:41,680
+ستفشل ستفشل لكن لو أشركنا سكان الحي في عمل الحديقة
+
+211
+00:17:41,680 --> 00:17:46,200
+هنا سكان الحي بيكونوا أحرص من البلدية على نجاح
+
+212
+00:17:46,200 --> 00:17:50,440
+المشروع وعلى تنمية المشروع ورايه المشروع ويبقى
+
+213
+00:17:50,440 --> 00:17:52,720
+المشروع ناجحا لأنه خلاص
+
+214
+00:17:56,520 --> 00:18:02,220
+فلذلك بيحافظوا عليه و بيقوموا برايه و العناية بيه
+
+215
+00:18:02,220 --> 00:18:07,620
+و رعايته فتصبح الحديقة ناجحة المشروع ناجح لكن لو
+
+216
+00:18:07,620 --> 00:18:11,660
+ما شركنا الناس ما بيسلم و لذلك من هنا بتبدأ عملية
+
+217
+00:18:11,660 --> 00:18:16,080
+الاتصال مهمة جدا في من قطوات طريقة ترضي المجتمع أن
+
+218
+00:18:16,080 --> 00:18:20,660
+نتصل بسكان المجتمع أصحاب المشكلة حتى نشركهم في
+
+219
+00:18:20,660 --> 00:18:24,850
+اتخاذ القراراتوفي تنفيذها وفي الخطط وفي تنفيذها
+
+220
+00:18:24,850 --> 00:18:28,430
+وفي التقويم وفي كل العمليات أو خطوات طريقة تنظيم
+
+221
+00:18:28,430 --> 00:18:36,290
+المجتمع المشاركة مهمة جدا أيضا بعد ذلك بعد الاتصال
+
+222
+00:18:36,290 --> 00:18:37,410
+بسكان المجتمع
+
+223
+00:18:42,860 --> 00:18:46,820
+و هنا التنفيذ بنحور الخطط إلى تنفيذ أشياء واقعية
+
+224
+00:18:46,820 --> 00:18:50,220
+أشياء واقعية يعني تنفيذ على أرض الواقع خلاص إذا
+
+225
+00:18:50,220 --> 00:18:54,220
+التنفيذ هو تنفيذ الخطط و هنا طبعا بعد عملية
+
+226
+00:18:54,220 --> 00:19:00,380
+التنفيذ لابد من المتابعة لابد من المتابعة و هذا
+
+227
+00:19:00,380 --> 00:19:05,860
+المرحلة الأخيرة المتابعة و التقويم متابعة و تقويم
+
+228
+00:19:05,860 --> 00:19:09,960
+و هذا الشيء طبيعي حتى نتعرف على جوانب القوة و
+
+229
+00:19:09,960 --> 00:19:13,220
+جوانب الطعف أو جوانب النجاحو جوانب الفشل في
+
+230
+00:19:13,220 --> 00:19:17,240
+المشروع أو في الخطة اللي تتم تلفيها الجوانب
+
+231
+00:19:17,240 --> 00:19:21,720
+الناجحة و اللي انجحنا فيها بندعمها و الجوانب اللي
+
+232
+00:19:21,720 --> 00:19:25,540
+فشلنا فيها نحاول انه عدّبها أو نغيرها واضح هذا
+
+233
+00:19:25,540 --> 00:19:29,900
+الهدف من المتابعة و التقيم و يساعدنا على النجاح
+
+234
+00:19:29,900 --> 00:19:33,580
+يعني المتابعة مهمة جدا المتابعة و التقيم هذه تبدأ
+
+235
+00:19:33,580 --> 00:19:36,980
+من الخطوة الأولى من المرحلة الأولى المفروض الدراسة
+
+236
+00:19:36,980 --> 00:19:40,560
+إلى أن ننتهي من المشروع من البداية إلى النهاية
+
+237
+00:19:40,560 --> 00:19:47,460
+دائماالتقويل لقوّل أي مشروع أو برنامج هذه هي أهم
+
+238
+00:19:47,460 --> 00:19:52,520
+المراحل اللي وضعها الدكتور سيدهو بكر لكن كان فيها
+
+239
+00:19:52,520 --> 00:19:57,440
+عمليات ايضا وعمليات مساعدة التنسيق والتدعيم وهذه
+
+240
+00:19:57,440 --> 00:20:02,510
+بتساعد على نجاح أيضا خطوات طريق التنظيم المجتمعما
+
+241
+00:20:02,510 --> 00:20:08,350
+هي هذه العمليات المساعدة التنسيق والتدريب التنسيق
+
+242
+00:20:08,350 --> 00:20:13,610
+لمواجهة المشكلات وهنا طبعا تنسيق بين المؤسسات داخل
+
+243
+00:20:13,610 --> 00:20:18,810
+المجتمع المناسب بينها وبين ما تقوم بيه من الخدماتو
+
+244
+00:20:18,810 --> 00:20:23,490
+.. و أيضا نستفيد من التنسيق بين هذه المؤسسات في
+
+245
+00:20:23,490 --> 00:20:27,210
+دعم المشاريع أو البرامج التي نقوم بتنفيذها
+
+246
+00:20:27,210 --> 00:20:32,830
+فالتنسيق مهم جدا بساعدنا على تعاون هذه المؤسسات مع
+
+247
+00:20:32,830 --> 00:20:37,670
+بعضيا البعض من أجل ماذا؟ من أجل مواجهة المشكلات أو
+
+248
+00:20:37,670 --> 00:20:41,890
+المشكلة داخل المجتمع كذلك التدعيم الجوانب المالية
+
+249
+00:20:41,890 --> 00:20:48,250
+تدعيم لابد أيضالقيام بعملية التدعيم لمساعدة
+
+250
+00:20:48,250 --> 00:20:53,350
+المؤسسة في تنفيذ خططها وبرامجها داخل المجتمع وإذا
+
+251
+00:20:53,350 --> 00:20:57,410
+احتجت إلى مساعدات مالية نساعدها إذا احتجت إلى دعم
+
+252
+00:20:57,410 --> 00:21:01,930
+بشري أيضا نساعدها فالذلك التدعيم يعتبر الدعم
+
+253
+00:21:01,930 --> 00:21:07,370
+المالي والبشري للمؤسسة عند قيامها بتنفيذ مشاريعها
+
+254
+00:21:07,370 --> 00:21:12,590
+أو برامجها داخل المجتمعفلذلك من هنا بتكون هذه
+
+255
+00:21:12,590 --> 00:21:16,430
+العمليات هي عمليات مساعدة لكل خطوة من هذه الخطوات
+
+256
+00:21:16,430 --> 00:21:20,990
+لخطوات طريق التوضيح المجتمع بشكل عام اللي هي
+
+257
+00:21:20,990 --> 00:21:26,670
+المساعدة والتدعيم والتنسيق التنسيق والتدعيم هذه
+
+258
+00:21:26,670 --> 00:21:36,030
+عمليتين لودمن الاستفادة منهما نكون
+
+259
+00:21:36,030 --> 00:21:42,350
+بذلك يعني أخدنا وجهةاللي هي الدكتور سيد أبو بطنه
+
+260
+00:21:42,350 --> 00:21:46,890
+طبعا هذه المراحل أو القطوات اللي احنا ذكرناها كلها
+
+261
+00:21:46,890 --> 00:21:51,280
+مترابطة و متكاملة مع بعضها البعضالتي هي مرحلة
+
+262
+00:21:51,280 --> 00:21:55,840
+الدراسة والتشريز والانتصار ووضع الخطة التنفيذ
+
+263
+00:21:55,840 --> 00:22:00,840
+المتابع والتقويم حتى التنسيق والتدعيم كلها عمليات
+
+264
+00:22:00,840 --> 00:22:05,920
+مترابطة ومتكاملة مع بعضها البعض لا يمكن فصل أي
+
+265
+00:22:05,920 --> 00:22:10,640
+خطوة من الخطوات اللي ذكرناها عن بعضها البعض، واضح؟
+
+266
+00:22:10,640 --> 00:22:17,090
+الناحية الثانيةكل هذه الخطوات تتأثر بحقائق كثيرة
+
+267
+00:22:17,090 --> 00:22:22,270
+من هذه إمكانيات المجتمع، نوعية المؤسسات، شخصية
+
+268
+00:22:22,270 --> 00:22:28,090
+الأخصائي، الإطار النظري اللي بنستخدمه، الموجه لنا،
+
+269
+00:22:28,090 --> 00:22:31,650
+لمهنتنا أو لطريقة تنظيم المجتمع، فلذلك هذه كلها
+
+270
+00:22:31,650 --> 00:22:37,430
+يعني هذه الخطوات تتأثر بها، أيضًاهذه الخطوات تتضمن
+
+271
+00:22:37,430 --> 00:22:40,950
+جهود المراد الاجتماعي وغيره من العاملين داخل
+
+272
+00:22:40,950 --> 00:22:44,750
+المجتمع يعني لا يقوم بيها لا خصائي لوحده لكن لابد
+
+273
+00:22:44,750 --> 00:22:50,130
+من ال team work لابد من الفريق العمل لابد لخصائي
+
+274
+00:22:50,130 --> 00:22:55,090
+مع الطبيب مع المهندس مع الخبير مع الكل ما يتعلق
+
+275
+00:22:55,090 --> 00:22:59,250
+المحاسب المحامي التربوي كل المهن الموجودة أحيانا
+
+276
+00:22:59,250 --> 00:23:04,030
+قد نستفيد منها في أطار عمل مشترك لحل مشكلة المجتمع
+
+277
+00:23:04,540 --> 00:23:09,360
+فلذلك هذه القطوات تحتاج جميع الخبراء والمختصين ليس
+
+278
+00:23:09,360 --> 00:23:13,100
+المنظم الاجتماعي لوحده ولكن المنظم مع غيره من
+
+279
+00:23:13,100 --> 00:23:17,820
+الخبراء والمختصين داخل المجتمع في إطار فريق عمل من
+
+280
+00:23:17,820 --> 00:23:23,180
+أجل مواجهة المشكلات وإشفاء الحدث نقول بذلك يعني
+
+281
+00:23:23,180 --> 00:23:28,380
+انتهينا من خطوات طريق التنظيم المجتمع عند الدكتورة
+
+282
+00:23:28,380 --> 00:23:32,500
+هودة بدران وعند الدكتور عبد المنعم شوقي والدكتور
+
+283
+00:23:32,500 --> 00:23:38,830
+سيد أبو بكريعني بتتم عندنا وجهة نظر الدكتور رشاد
+
+284
+00:23:38,830 --> 00:23:42,170
+عبداللطيف ان شاء الله في المحاضرة القادمة بإذن
+
+285
+00:23:42,170 --> 00:23:46,370
+الله سنناقش وجهة نظر بإذن الله في خطوات طريق تنظيم
+
+286
+00:23:46,370 --> 00:23:50,410
+المجتمع في أي سؤال فيما شرحناه من خطوات طريق تنظيم
+
+287
+00:23:50,410 --> 00:23:55,410
+المجتمع طيب إلى هنا ننهي هذه المحاضرة على أمل
+
+288
+00:23:55,410 --> 00:24:00,230
+اللقاء بقولنا ان شاء الله في المحاضرة القادمةالى
+
+289
+00:24:00,230 --> 00:24:03,830
+ان نلتقي بكلنا اللى كنا منى وكنا تحية للمتقدير
+
+290
+00:24:03,830 --> 00:24:07,530
+والسلام عليكم ورحمة الله وبركاته
+
diff --git a/PL9fwy3NUQKwaKyeI5iiPpebyFXxlPBffV/ncysfAu_RnU_raw.json b/PL9fwy3NUQKwaKyeI5iiPpebyFXxlPBffV/ncysfAu_RnU_raw.json
new file mode 100644
index 0000000000000000000000000000000000000000..b101fac543873847a18afca508d75a983f9ed157
--- /dev/null
+++ b/PL9fwy3NUQKwaKyeI5iiPpebyFXxlPBffV/ncysfAu_RnU_raw.json
@@ -0,0 +1 @@
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الدكتورة عمدة بدران لخصت لنا خطوات طريق التنظيم المجتمع في خطوات تانية الخطوة الأولى التخطيط والخطوة الثانية التنفيذ تخطيط وتنفيذ ولكن في كل خطوة شملت خطوات يعني مثلا خطوة التخطيط تضمن ماذا تحديد المشكلة", "tokens": [3615, 23942, 16490, 9566, 2407, 9307, 23032, 16572, 4587, 16712, 1863, 19913, 32640, 9673, 7435, 39237, 3615, 32748, 4117, 2655, 13063, 3660, 6225, 2304, 41891, 47525, 2288, 7649, 5296, 9778, 9381, 2655, 5296, 8315, 16490, 9566, 2407, 9307, 23032, 16572, 4587, 16712, 1863, 19913, 32640, 9673, 7435, 39237, 3615, 8978, 16490, 9566, 2407, 9307, 6055, 7649, 10632, 33962, 9566, 2407, 3660, 16247, 12610, 7578, 16712, 9778, 9566, 1829, 9566, 16070, 9778, 9566, 2407, 3660, 6024, 104, 7649, 10632, 16712, 1863, 41185, 8848, 6055, 9778, 9566, 1829, 9566, 4032, 2655, 1863, 41185, 8848, 35525, 19452, 8978, 28242, 16490, 9566, 2407, 3660, 13412, 42213, 2655, 16490, 9566, 2407, 9307, 37495, 22653, 50113, 15040, 16490, 9566, 2407, 3660, 16712, 9778, 9566, 1829, 9566, 6055, 11242, 27842, 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"text": "وفي تنفيذها وفي الخطط وفي تنفيذها وفي التقويم وفي كل العمليات أو خطوات طريقة تنظيم المجتمع المشاركة مهمة جدا أيضا بعد ذلك بعد الاتصال بسكان المجتمع", "tokens": [38688, 1829, 6055, 1863, 41185, 8848, 11296, 4032, 41185, 33962, 9566, 9566, 4032, 41185, 6055, 1863, 41185, 8848, 11296, 4032, 41185, 16712, 4587, 2407, 32640, 4032, 41185, 28242, 18863, 42213, 1829, 9307, 34051, 16490, 9566, 2407, 9307, 23032, 16572, 28671, 6055, 1863, 19913, 32640, 9673, 7435, 39237, 3615, 9673, 8592, 9640, 4117, 3660, 3714, 16095, 3660, 10874, 28259, 36632, 11242, 995, 39182, 29910, 23275, 39182, 2423, 9307, 9381, 6027, 4724, 3794, 41361, 9673, 7435, 39237, 3615], "avg_logprob": -0.09248173352959868, "compression_ratio": 1.8680555555555556, "no_speech_prob": 3.4570693969726562e-06, "words": [{"start": 1102.07, "end": 1102.45, "word": "وفي", "probability": 0.6669921875}, {"start": 1102.45, "end": 1103.13, "word": " تنفيذها", "probability": 0.9296875}, {"start": 1103.13, "end": 1103.35, "word": " 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40, "seek": 115185, "start": 1122.86, "end": 1151.86, "text": "و هنا التنفيذ بنحور الخطط إلى تنفيذ أشياء واقعية أشياء واقعية يعني تنفيذ على أرض الواقع خلاص إذا التنفيذ هو تنفيذ الخطط و هنا طبعا بعد عملية التنفيذ لابد من المتابعة لابد من المتابعة و هذا المرحلة الأخيرة المتابعة و التقويم متابعة و تقويم و هذا الشيء طبيعي حتى نتعرف على جوانب القوة و جوانب الطعف أو جوانب النجاح", "tokens": [2407, 34105, 16712, 1863, 41185, 8848, 44945, 5016, 13063, 33962, 9566, 9566, 30731, 6055, 1863, 41185, 8848, 5551, 8592, 1829, 16606, 36764, 4587, 3615, 10632, 5551, 8592, 1829, 16606, 36764, 4587, 3615, 10632, 37495, 22653, 6055, 1863, 41185, 8848, 15844, 5551, 43042, 2423, 14407, 4587, 3615, 16490, 1211, 33546, 11933, 15730, 16712, 1863, 41185, 8848, 31439, 6055, 1863, 41185, 8848, 33962, 9566, 9566, 4032, 34105, 23032, 3555, 3615, 995, 39182, 6225, 42213, 10632, 16712, 1863, 41185, 8848, 5296, 16758, 3215, 9154, 9673, 2655, 16758, 27884, 5296, 16758, 3215, 9154, 9673, 2655, 16758, 27884, 4032, 23758, 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0.966552734375}, {"start": 1412.96, "end": 1413.24, "word": " أبو", "probability": 0.9108072916666666}, {"start": 1413.24, "end": 1413.46, "word": " بكر", "probability": 0.897216796875}], "temperature": 1.0}, {"id": 52, "seek": 143931, "start": 1415.59, "end": 1439.31, "text": "يعني بتتم عندنا وجهة نظر الدكتور رشاد عبداللطيف ان شاء الله في المحاضرة القادمة بإذن الله سنناقش وجهة نظر بإذن الله في خطوات طريق تنظيم المجتمع في أي سؤال فيما شرحناه من خطوات طريق تنظيم المجتمع طيب إلى هنا ننهي هذه المحاضرة على أمل اللقاء بقولنا ان شاء الله في المحاضرة القادمة", "tokens": [40228, 22653, 39894, 39237, 43242, 8315, 49610, 3224, 3660, 8717, 19913, 2288, 32748, 4117, 2655, 13063, 12602, 8592, 18513, 6225, 44510, 6027, 1211, 9566, 33911, 16472, 13412, 16606, 21984, 8978, 9673, 5016, 46958, 25720, 25062, 18513, 46007, 4724, 28814, 8848, 1863, 21984, 8608, 1863, 8315, 4587, 8592, 49610, 3224, 3660, 8717, 19913, 2288, 4724, 28814, 8848, 1863, 21984, 8978, 16490, 9566, 2407, 9307, 23032, 16572, 4587, 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0.99560546875}, {"start": 1417.81, "end": 1418.43, "word": " الدكتور", "probability": 0.9713134765625}, {"start": 1418.43, "end": 1418.83, "word": " رشاد", "probability": 0.84619140625}, {"start": 1418.83, "end": 1419.49, "word": " عبداللطيف", "probability": 0.8951009114583334}, {"start": 1419.49, "end": 1419.99, "word": " ان", "probability": 0.67431640625}, {"start": 1419.99, "end": 1420.21, "word": " شاء", "probability": 0.978759765625}, {"start": 1420.21, "end": 1420.35, "word": " الله", "probability": 0.9267578125}, {"start": 1420.35, "end": 1420.57, "word": " في", "probability": 0.80322265625}, {"start": 1420.57, "end": 1421.21, "word": " المحاضرة", "probability": 0.98876953125}, {"start": 1421.21, "end": 1421.89, "word": " القادمة", "probability": 0.98876953125}, {"start": 1421.89, "end": 1422.17, "word": " بإذن", "probability": 0.95263671875}, {"start": 1422.17, "end": 1422.41, "word": " الله", "probability": 0.939453125}, {"start": 1422.41, "end": 1423.25, "word": " سنناقش", "probability": 0.9697265625}, {"start": 1423.25, "end": 1423.99, "word": " وجهة", "probability": 0.9775390625}, {"start": 1423.99, "end": 1424.25, "word": " نظر", "probability": 0.90625}, {"start": 1424.25, "end": 1424.61, "word": " بإذن", "probability": 0.9466552734375}, {"start": 1424.61, "end": 1424.87, "word": " الله", "probability": 0.95654296875}, {"start": 1424.87, "end": 1425.09, "word": " في", "probability": 0.91015625}, {"start": 1425.09, "end": 1425.55, "word": " خطوات", "probability": 0.88330078125}, {"start": 1425.55, "end": 1425.89, "word": " طريق", "probability": 0.9388020833333334}, {"start": 1425.89, "end": 1426.37, "word": " تنظيم", "probability": 0.953857421875}, {"start": 1426.37, "end": 1427.19, "word": " المجتمع", "probability": 0.99365234375}, {"start": 1427.19, "end": 1427.63, "word": " في", "probability": 0.52099609375}, {"start": 1427.63, "end": 1427.81, "word": " أي", "probability": 0.7509765625}, {"start": 1427.81, "end": 1428.31, "word": " سؤال", "probability": 0.9949544270833334}, {"start": 1428.31, "end": 1428.65, "word": " فيما", "probability": 0.781494140625}, {"start": 1428.65, "end": 1429.17, "word": " شرحناه", "probability": 0.922265625}, {"start": 1429.17, "end": 1429.29, "word": " من", "probability": 0.89111328125}, {"start": 1429.29, "end": 1429.69, "word": " خطوات", "probability": 0.9613037109375}, {"start": 1429.69, "end": 1430.03, "word": " طريق", "probability": 0.9895833333333334}, {"start": 1430.03, "end": 1430.41, "word": " تنظيم", "probability": 0.9686279296875}, {"start": 1430.41, "end": 1430.99, "word": " المجتمع", "probability": 0.994140625}, {"start": 1430.99, "end": 1432.37, "word": " طيب", "probability": 0.86767578125}, {"start": 1432.37, "end": 1432.59, "word": " إلى", "probability": 0.78759765625}, {"start": 1432.59, "end": 1432.89, "word": " هنا", "probability": 0.98291015625}, {"start": 1432.89, "end": 1433.31, "word": " ننهي", "probability": 0.986083984375}, {"start": 1433.31, "end": 1433.61, "word": " هذه", "probability": 0.9794921875}, {"start": 1433.61, "end": 1434.31, "word": " المحاضرة", "probability": 0.9957275390625}, {"start": 1434.31, "end": 1435.05, "word": " على", "probability": 0.8818359375}, {"start": 1435.05, "end": 1435.41, "word": " أمل", "probability": 0.88720703125}, {"start": 1435.41, "end": 1435.97, "word": " اللقاء", "probability": 0.98974609375}, {"start": 1435.97, "end": 1436.45, "word": " بقولنا", "probability": 0.82861328125}, {"start": 1436.45, "end": 1436.63, "word": " ان", "probability": 0.81689453125}, {"start": 1436.63, "end": 1436.85, "word": " شاء", "probability": 0.989501953125}, {"start": 1436.85, "end": 1437.15, "word": " الله", "probability": 0.9580078125}, {"start": 1437.15, "end": 1437.83, "word": " في", "probability": 0.9716796875}, {"start": 1437.83, "end": 1438.51, "word": " المحاضرة", "probability": 0.9947509765625}, {"start": 1438.51, "end": 1439.31, "word": " القادمة", "probability": 0.9934895833333334}], "temperature": 1.0}, {"id": 53, "seek": 144753, "start": 1439.89, "end": 1447.53, "text": "الى ان نلتقي بكلنا اللى كنا منى وكنا تحية للمتقدير والسلام عليكم ورحمة الله وبركاته", "tokens": [6027, 7578, 16472, 8717, 1211, 2655, 38436, 4724, 28820, 8315, 13672, 7578, 9122, 8315, 9154, 7578, 4032, 4117, 8315, 6055, 5016, 10632, 5296, 19528, 2655, 28543, 13546, 16070, 3794, 37440, 25894, 24793, 4032, 2288, 35571, 3660, 21984, 4032, 26890, 4117, 9307, 3224], "avg_logprob": -0.2367369179115739, "compression_ratio": 1.504950495049505, "no_speech_prob": 1.1920928955078125e-07, "words": [{"start": 1439.89, "end": 1440.23, "word": "الى", "probability": 0.6787109375}, {"start": 1440.23, "end": 1440.37, "word": " ان", "probability": 0.71435546875}, {"start": 1440.37, "end": 1440.89, "word": " نلتقي", "probability": 0.9691162109375}, {"start": 1440.89, "end": 1441.59, "word": " بكلنا", "probability": 0.7921549479166666}, {"start": 1441.59, "end": 1441.83, "word": " اللى", "probability": 0.40576171875}, {"start": 1441.83, "end": 1442.09, "word": " كنا", "probability": 0.850830078125}, {"start": 1442.09, "end": 1442.39, "word": " منى", "probability": 0.748291015625}, {"start": 1442.39, "end": 1442.65, "word": " وكنا", "probability": 0.6783854166666666}, {"start": 1442.65, "end": 1443.03, "word": " تحية", "probability": 0.7802734375}, {"start": 1443.03, "end": 1443.83, "word": " للمتقدير", "probability": 0.783984375}, {"start": 1443.83, "end": 1444.63, "word": " والسلام", "probability": 0.921875}, {"start": 1444.63, "end": 1445.07, "word": " عليكم", "probability": 0.73583984375}, {"start": 1445.07, "end": 1445.87, "word": " ورحمة", "probability": 0.935546875}, {"start": 1445.87, "end": 1446.25, "word": " الله", "probability": 0.96875}, {"start": 1446.25, "end": 1447.53, "word": " وبركاته", "probability": 0.97041015625}], "temperature": 1.0}], "language": "ar", "language_probability": 1.0, "duration": 1448.367875, "duration_after_vad": 1391.464374999998}
\ No newline at end of file
diff --git a/PL9fwy3NUQKwaKyeI5iiPpebyFXxlPBffV/oyMazQElIZ8_postprocess.srt b/PL9fwy3NUQKwaKyeI5iiPpebyFXxlPBffV/oyMazQElIZ8_postprocess.srt
new file mode 100644
index 0000000000000000000000000000000000000000..3e9de17b476fe28f0b6b0e198ca625133ec8c188
--- /dev/null
+++ b/PL9fwy3NUQKwaKyeI5iiPpebyFXxlPBffV/oyMazQElIZ8_postprocess.srt
@@ -0,0 +1,2216 @@
+1
+00:00:20,640 --> 00:00:24,740
+بسم الله الرحمن الرحيم، الحمد لله رب العالمين،
+
+2
+00:00:24,740 --> 00:00:29,080
+والصلاة والسلام على أشرف المرسلين، سيدنا محمد وعلى
+
+3
+00:00:29,080 --> 00:00:34,220
+آله وصحبه وجه الأجمعين، بنات الطالبات السلام عليكم
+
+4
+00:00:34,220 --> 00:00:40,900
+ورحمة الله وبركاته في المحاضرة السابقة تحدثنا عن
+
+5
+00:00:40,900 --> 00:00:42,980
+مفهوم المجتمع
+
+6
+00:00:45,830 --> 00:00:53,470
+وتحدثنا عن مفهوم المجتمع للعلماء الاجتماعي وكذلك
+
+7
+00:00:53,470 --> 00:01:01,810
+تحدثنا عن سمات المجتمع وأيضا تكلمنا عن هذه السمات
+
+8
+00:01:01,810 --> 00:01:08,780
+الثلاث للمجتمع، أي مجتمع له سمات ثلاثأنا و هذه
+
+9
+00:01:08,780 --> 00:01:12,660
+السماعات الثلاث السماعات الثلاث ما هي نطرح لإنه
+
+10
+00:01:12,660 --> 00:01:15,680
+كان أخر المحاضرة اللي يعني اتكلمنا فيها ماذا يبقى
+
+11
+00:01:15,680 --> 00:01:18,600
+فيها السماعة الأولى التمايز و التضامن و التأثير
+
+12
+00:01:18,600 --> 00:01:22,460
+خلاص هذه السماعات السماعات التمايز و التضامن و
+
+13
+00:01:22,460 --> 00:01:27,720
+التأثير وشرحنا هذه السماعات الثلاث في هذه المحاضرة
+
+14
+00:01:27,720 --> 00:01:37,050
+سنتحدث عن دعائم المجتمع دعائم المجتمعللمجتمع دعائم
+
+15
+00:01:37,050 --> 00:01:42,630
+معينة أو مقومات معينة لاجب من معرفة هذه المقومات
+
+16
+00:01:42,630 --> 00:01:50,850
+أي بناء له مقومات له دعائم بدون هذه الدعائم لا
+
+17
+00:01:50,850 --> 00:01:54,950
+يقوم البناء كذلك
+
+18
+00:01:54,950 --> 00:02:00,790
+عندنا المجتمع له دعائم ومقومات بدون هذه الدعائم
+
+19
+00:02:00,790 --> 00:02:03,890
+والمقومات ليس هناك مجتمع ولا يقوم المجتمع
+
+20
+00:02:07,020 --> 00:02:13,720
+لذلك من المقومات أو الدعائم الخاصة بالمجتمع الحدود
+
+21
+00:02:13,720 --> 00:02:18,960
+الجغرافية الحدود الجغرافية ما معنى الحدود
+
+22
+00:02:18,960 --> 00:02:25,020
+الجغرافية المكان
+
+23
+00:02:25,020 --> 00:02:34,260
+أي مجتمع له حدود مساحة معينة وحدود لهذا المجتمع
+
+24
+00:02:35,060 --> 00:02:38,340
+اللي هي مساحة اللي هي حدود الأرض شمالا وجنوبا
+
+25
+00:02:38,340 --> 00:02:45,020
+وغربا وشرقا لو قلنا على سبيل المثال مدينة غزة لها
+
+26
+00:02:45,020 --> 00:02:53,240
+حدود جغرافية مفصولة عن منطقة الوسطة لو قلنا ابتداء
+
+27
+00:02:53,240 --> 00:02:58,680
+من ال bridge والوسطة ال bridge والمسيرات والمغازي
+
+28
+00:02:58,680 --> 00:03:04,980
+ودير البلح لها حدودكذلك عندنا خانيونس عندما تبدأ
+
+29
+00:03:04,980 --> 00:03:10,100
+مدينة خانيونس تبدأ حدودها وتنتهي تبدأ أفر و هكذا
+
+30
+00:03:10,100 --> 00:03:15,720
+إلى الحدود المصرية جنوبها مدينة رفح اذا معروفة كل
+
+31
+00:03:15,720 --> 00:03:21,700
+مدينة باسمها هذا بنسميه مجتمع مجتمع غزة مجتمع
+
+32
+00:03:21,700 --> 00:03:25,920
+خانيونس مجتمع مدينة رفح مجتمع الوسط ككل مجتمع
+
+33
+00:03:25,920 --> 00:03:30,840
+الشمال جباليا بيت حنون بيت لاهيةالى الحدود
+
+34
+00:03:30,840 --> 00:03:35,620
+الشمالية لفلسطين يعني محروف المساحة إذا ان الحدود
+
+35
+00:03:35,620 --> 00:03:40,020
+الجغرافية هذه الدعامة الأولى للمجتمع أي مجتمع له
+
+36
+00:03:40,020 --> 00:03:46,240
+حدود جغرافية ضربنا أمتلة على مدن قطاع غزة كمجتمعات
+
+37
+00:03:46,240 --> 00:03:49,740
+موجودة في قطاع غزة كذلك لو ضربنا أمتلة على المدن
+
+38
+00:03:49,740 --> 00:03:55,440
+الفلسطينية الأخرى في فلسطين وفي الضفة كل مدينة لها
+
+39
+00:03:55,440 --> 00:04:04,060
+حدودجغرافية في نفس الرقم فلسطين ككل كدولة كمجتمع
+
+40
+00:04:04,060 --> 00:04:11,920
+عام أيضا له حدود له حدود جنوبا مع جمهورية مصر
+
+41
+00:04:11,920 --> 00:04:17,040
+العربية و شمالا مع سوريا و لبنان و شرقا مع القردن
+
+42
+00:04:17,040 --> 00:04:24,240
+و هكذا فبذلك لنا حدود كدولة او كمجتمع عام فإذا انت
+
+43
+00:04:24,240 --> 00:04:29,280
+عامة أولى للمجتمعهي الحدود الجغرافية الحدود
+
+44
+00:04:29,280 --> 00:04:34,880
+الجغرافية اللي هي المكان والمكان قد يكون كما
+
+45
+00:04:34,880 --> 00:04:40,020
+ضربتكم أمثلة كمكان ممكن يكون مساحته محدودة صغير أو
+
+46
+00:04:40,020 --> 00:04:47,400
+المكان يكون كبير واضح؟ وهكذا فلذلك هذا هو المجتمع
+
+47
+00:04:48,480 --> 00:04:53,980
+أيضًا المكان ممكن يكون محلي أو إقليمي أو قومي محلي
+
+48
+00:04:53,980 --> 00:04:57,560
+زي مجتمعاتنا المحلية في قطعة غزة غزة خاني و أنس
+
+49
+00:04:57,560 --> 00:05:02,620
+رفح مجتمعات محلية و غزة تقسيماتها الرمال والشجاعية
+
+50
+00:05:02,620 --> 00:05:06,640
+والزيتون مشاكة كده هذه مجتمعات محلية صغيرة أيضًا
+
+51
+00:05:06,640 --> 00:05:11,580
+في إطار مدينة غزة كمجتمع محلي صغير بالنسبة لفلسطين
+
+52
+00:05:11,580 --> 00:05:17,200
+واضح؟ ممكن يكون قومي مجتمع قومي زي فلسطين خلاص
+
+53
+00:05:17,600 --> 00:05:21,320
+مجتمع عام اقليمي يعني يبقى ايضا مجتمع اقليمي
+
+54
+00:05:21,320 --> 00:05:24,980
+احيانا العدد من الدول تكون اقليمية تشكل اقليم زي
+
+55
+00:05:24,980 --> 00:05:28,600
+اقليم البحر الأبيض المتوسط مجتمع الدول اللي بتقع
+
+56
+00:05:28,600 --> 00:05:32,560
+على البحر الأبيض المتوسط كلها ممكن يكون دول عربية
+
+57
+00:05:32,560 --> 00:05:35,680
+و دول اوروبية في الجانب الآخر من البحر و احنا في
+
+58
+00:05:35,680 --> 00:05:41,020
+الجانب العرب الدول العربية وشكله كل دول اللي بتقع
+
+59
+00:05:41,020 --> 00:05:44,280
+على البحر الأبيض المتوسط ليها دول اقليم البحر
+
+60
+00:05:44,280 --> 00:05:50,200
+الأبيض المتوسط و هكذا واضح؟إذن المجتمع يصغر ويكبر
+
+61
+00:05:50,200 --> 00:05:56,820
+حسب نوعية المجتمع أيضًا في حالة قد يكون المجتمع
+
+62
+00:05:56,820 --> 00:06:00,900
+الدولي في حالة المشكلات ذات الطابع الدولي والتي لا
+
+63
+00:06:00,900 --> 00:06:04,940
+تخضع للحدود الجغرافية المتعارف عليها أحيانًا في
+
+64
+00:06:04,940 --> 00:06:10,020
+بعض المشاكل الصحية مثلًا زي شلل الأطفال هذا خاص
+
+65
+00:06:10,020 --> 00:06:13,640
+ولا عام لو جلنا انتشر في المجتمعات هذا مهم أن
+
+66
+00:06:13,640 --> 00:06:17,480
+الطابع الدولي يكون ومكافح دوليةوالآن يعني ما شاء
+
+67
+00:06:17,480 --> 00:06:20,980
+الله اللي .. يعني تمت مكافحة هو القليل القليل من
+
+68
+00:06:20,980 --> 00:06:25,080
+هذا المرض موجود عند الأطفال لكن ليس بالكثرة التي
+
+69
+00:06:25,080 --> 00:06:29,760
+كانت في السمن الماضي وهكذا فله طابع دولي أحيانا
+
+70
+00:06:29,760 --> 00:06:35,540
+مشكلة عامة بتكون لها طابع دولي في عندنا أيضا
+
+71
+00:06:35,540 --> 00:06:41,420
+الدعامة الثانية لأن المجتمع دعامة من دعامات
+
+72
+00:06:41,420 --> 00:06:48,900
+المجتمع اللي هي الناسلأن هل في مجتمع بدون ناس؟ هل
+
+73
+00:06:48,900 --> 00:06:54,400
+في مجتمع بدون ناس؟ والله ممكن نخل المجتمع في
+
+74
+00:06:54,400 --> 00:06:58,480
+الصحراء أو في الساحل أو في الجبل نقول عنه مجتمع
+
+75
+00:06:58,480 --> 00:07:03,780
+بدون ناس هو أرض بس فقط، لكن المجتمع من دعامته أن
+
+76
+00:07:03,780 --> 00:07:10,500
+يكون الناس، والناس يعني أهم عنصر من مكونات
+
+77
+00:07:10,500 --> 00:07:16,080
+المجتمع، الفشرلأن البشر هم اللي بيصنعوا كل شيء
+
+78
+00:07:16,080 --> 00:07:19,680
+داخل المجتمع و يطوروا المجتمع و يبنوا المجتمع و
+
+79
+00:07:19,680 --> 00:07:24,520
+يكوّنون المجتمع و يناقشون و يتحاورون و يتفاعلون،
+
+80
+00:07:24,520 --> 00:07:30,420
+إذا من دعامة المجتمع هي الناس، و الناس حسب
+
+81
+00:07:30,420 --> 00:07:36,310
+المجتمع، ممكن يكون محل صغير بعدد قليل من الناسوهنا
+
+82
+00:07:36,310 --> 00:07:40,450
+حددوه يعني في حدود يعني مجموعة صغيرة يقل عن ألف
+
+83
+00:07:40,450 --> 00:07:44,550
+لسمة أحيانا أو كبير يزيد على المليون يكون مليون
+
+84
+00:07:44,550 --> 00:07:48,250
+مليون وزي 800 ألف زي مثل القطاع غزة نسميه مجتمع
+
+85
+00:07:48,250 --> 00:07:51,870
+لإنه عدد كبير لإن السكان عندنا وكل يوم يتزايد
+
+86
+00:07:51,870 --> 00:07:56,270
+وهكذا بعض الدول 10 مليون بعض الدول 20 مليون 100
+
+87
+00:07:56,270 --> 00:08:01,850
+مليون مجتمع ككل الدول ككل كمجتمع فلذلك ينقص أو
+
+88
+00:08:01,850 --> 00:08:08,180
+يزداد حسب حجم المجتمعبالنسبة للناس طبعا مين هم
+
+89
+00:08:08,180 --> 00:08:11,580
+الناس اللي داخل المجتمع؟ هل المجتمع يختصر على فئة
+
+90
+00:08:11,580 --> 00:08:17,660
+معينة من الناس؟ ولا بيشمل كل فئة المجتمع رجالا
+
+91
+00:08:17,660 --> 00:08:26,840
+ونساء أطفالا وشيوخا وشبابا واضح؟ وبكافرة النوعيات
+
+92
+00:08:26,840 --> 00:08:32,720
+الموجودة داخل المجتمع الأسوياء وغير الأسوياءيشملهم
+
+93
+00:08:32,720 --> 00:08:40,700
+المجتمع هذه فئة الناس بكافة أنواعها وفئاتها فلذلك
+
+94
+00:08:40,700 --> 00:08:54,360
+الدعامة الثانية هي الناس بالنسبة للمجتمع في
+
+95
+00:08:54,360 --> 00:08:59,160
+عندنا الدعامة الثالثة للمجتمع
+
+96
+00:09:02,230 --> 00:09:08,730
+ما هي الدعامة الثالثة؟ المصالح المشتركة ما معنى
+
+97
+00:09:08,730 --> 00:09:12,910
+المصالح المشتركة؟
+
+98
+00:09:12,910 --> 00:09:18,590
+منافع،
+
+99
+00:09:18,590 --> 00:09:23,890
+مطبوط، يعني لو لا المنافع والمصالح مافي التفاعل مع
+
+100
+00:09:23,890 --> 00:09:29,070
+الناس فلذلك من دعامات المجتمع أن يكون هناك مصالح
+
+101
+00:09:29,070 --> 00:09:36,290
+مشتركة بين الناسكل إنسان يعتمد على الآخر لأن
+
+102
+00:09:36,290 --> 00:09:40,770
+المجتمع لا يكون في عمل معين واحد فقط أو في مهنة
+
+103
+00:09:40,770 --> 00:09:45,330
+واحدة في عدد من المهن فلذلك في مصالح للأفراد عند
+
+104
+00:09:45,330 --> 00:09:49,370
+بعضها البعض فبيحدث تفاعل ما بين الأفراد و ما بين
+
+105
+00:09:49,370 --> 00:09:53,330
+المجتمع وأفراده و ما بين المجتمع و المجتمع الآخر
+
+106
+00:09:53,330 --> 00:09:58,270
+المحلي بيحدث أيضا نوع من التفاعل كلها تبادل مصالح
+
+107
+00:09:59,580 --> 00:10:04,540
+فلذلك من دعمات المجتمع هي المصالح المشتركة حاجة
+
+108
+00:10:04,540 --> 00:10:09,080
+الناس لبعضها البعض وما يحدث ما بينهم في تبادل هذه
+
+109
+00:10:09,080 --> 00:10:16,360
+المصالح يعني مثلا وجود مهن لخصائص اجتماعيين هذه
+
+110
+00:10:16,360 --> 00:10:20,200
+يحتاجها تحتاجها الناس يحتاجوا لخصائص اجتماعية مثل
+
+111
+00:10:20,200 --> 00:10:24,030
+ما يحتاج الطبيبنظرا لوجود المشكلات الاجتماعية في
+
+112
+00:10:24,030 --> 00:10:27,370
+المجتمع، إذا الناس يحتاجوا إلى أخصاء اجتماعي
+
+113
+00:10:27,370 --> 00:10:31,330
+لمساعدة في حل مشكلتهم الاجتماعية، كذلك الطبيب
+
+114
+00:10:31,330 --> 00:10:35,250
+يحتاجون إلى الطبيب لمساعدة في حل مشكلتهم الصحية،
+
+115
+00:10:35,250 --> 00:10:39,850
+يحتاجون إلى المعلملماذا؟ للقيام بالعملية
+
+116
+00:10:39,850 --> 00:10:44,090
+التعليمية، يحتاجونها للمزارع، للزراعة، يحتاجونها
+
+117
+00:10:44,090 --> 00:10:48,650
+للصانع، للصناعة، وهكذا، يحدث هنا كل يقوم بعمله
+
+118
+00:10:48,650 --> 00:10:52,890
+ومهنته ويحدث تبادل المصالح بينهم، بين الناس
+
+119
+00:10:52,890 --> 00:10:56,490
+الموجودة، فهناك مصالح مشتركة، فإذا من دعمات
+
+120
+00:10:56,490 --> 00:11:01,950
+المجتمع هي المصالح المشتركة بين الناس داخل المجتمع
+
+121
+00:11:02,390 --> 00:11:06,510
+وهذه بنسميها المصالح أحيانًا المنافع يعني أحيانًا
+
+122
+00:11:06,510 --> 00:11:11,050
+في منفعة اجتماعية معينة تبادل المنافع بين الناس
+
+123
+00:11:11,050 --> 00:11:15,290
+وبعضهم البعض ممكن هذه المصالح تقتصر على أفراد
+
+124
+00:11:15,290 --> 00:11:19,830
+المجتمع الذين يعيشون في مجتمع واحد وأيضًا مصالح
+
+125
+00:11:19,830 --> 00:11:24,360
+ترتبط من مجتمع إلى مجتمع آخرمثل مجتمع القرية و
+
+126
+00:11:24,360 --> 00:11:28,920
+المدينة مجتمع القرية له طابع زراعي يزرع و يسوق من
+
+127
+00:11:28,920 --> 00:11:33,020
+المنتجات الزراعية في المدينة و هكذا و المزارعين
+
+128
+00:11:33,020 --> 00:11:36,100
+يحتاجون إلى ماذا؟ إلى المواد الغذائية و إلى
+
+129
+00:11:36,100 --> 00:11:40,280
+الملابس و إلى المواد الزراعية البذور و الأسمد و
+
+130
+00:11:40,280 --> 00:11:44,520
+ياخدونها من مين؟ من المدينة من الأسواق في المدينة
+
+131
+00:11:44,520 --> 00:11:51,040
+و هكذا فهنا تحدث ايه؟ تبادل المصالح تبادل المنافع
+
+132
+00:11:52,240 --> 00:12:00,420
+بين المجتمعات المدينة و القرية و هكذا طيب
+
+133
+00:12:00,420 --> 00:12:05,280
+في
+
+134
+00:12:05,280 --> 00:12:11,460
+عندنا مقوم أو دعامة أخرى من دعامات المجتمع ألا وهي
+
+135
+00:12:11,460 --> 00:12:16,740
+الدعامة الرابعة ما هي؟ أيوة يا بنت هنا أيوة اتفضل
+
+136
+00:12:16,740 --> 00:12:22,420
+اتفاعد ما بين أصول المجتمع ايه؟ اتفاعدالتفاعل ما
+
+137
+00:12:22,420 --> 00:12:26,880
+بين أفراد المجتمع، إيش يعني التفاعل بين أفراد
+
+138
+00:12:26,880 --> 00:12:27,600
+المجتمع؟
+
+139
+00:12:32,040 --> 00:12:37,720
+أه التفاعل بين الأفراد وتأثير وتأثير وهذا بيتمد
+
+140
+00:12:37,720 --> 00:12:41,440
+على سبب التأثير اللي قلناها من ثبات المجتمع مش
+
+141
+00:12:41,440 --> 00:12:44,600
+قولنا التأثير هنا بيجي عملية التفاعل اللي هو
+
+142
+00:12:44,600 --> 00:12:49,360
+التأثير الأفراد في بعضهم البعض وتفاعلهم مع بعضهم
+
+143
+00:12:49,360 --> 00:12:52,440
+البعض إذا نادى دعامة من دعامات المجتمع إيجاد
+
+144
+00:12:52,440 --> 00:12:56,640
+التفاعل لإن بدون تفاعل ما المعنى لمن يكون كل فرد
+
+145
+00:12:56,640 --> 00:13:02,150
+بين أفراد المجتمع يعزل نفسه؟مافيش علاقات اجتماعية
+
+146
+00:13:02,150 --> 00:13:07,710
+ولا في نمو اجتماعي ولا في تفاهم ولا في مناقش قضايا
+
+147
+00:13:07,710 --> 00:13:12,450
+ومشاكل وامور تايم المجتمع إذا التفاعل مهم جدا بين
+
+148
+00:13:12,450 --> 00:13:15,950
+الناس داخل المجتمع وهذه دعامة من دعامات المجتمع
+
+149
+00:13:15,950 --> 00:13:20,250
+حتى يحدث تأثير الناس على بعض من بعض تأثيرا إيجابيا
+
+150
+00:13:20,250 --> 00:13:25,630
+أحيانا قد يحدث تفاعل وتأثير قد يكون سلبي وقد يكون
+
+151
+00:13:25,630 --> 00:13:30,290
+إيجابي لكن نحن يعني نأمل أن يكون التفاعل إيجابيا
+
+152
+00:13:31,350 --> 00:13:36,670
+بين أفراد المجتمع لأن بدون هذا التفاعل لا يمكن أن
+
+153
+00:13:36,670 --> 00:13:44,150
+يكون هناك مجتمع، واضح؟ فلذلك هذه تعتبر دعامة
+
+154
+00:13:44,150 --> 00:13:48,370
+أساسية أيضًا من دعامات المجتمع، اللي هي دعامة
+
+155
+00:13:48,370 --> 00:13:54,190
+التفاعل بين أفراد المجتمع، داخل المجتمع، والتفاعل
+
+156
+00:13:54,190 --> 00:14:00,630
+مهم جدًا هذا يعني، اللي هي نربط التفاعل بالمشاركة
+
+157
+00:14:01,080 --> 00:14:05,660
+المشاركة داخل المجتمع لأن أفراد المجتمع لابد أن
+
+158
+00:14:05,660 --> 00:14:10,540
+يتفاعلون مع بعضهم البعض وهذه كلما زادت التفاعل
+
+159
+00:14:10,540 --> 00:14:17,560
+كلما زادت الانتماء داخل المجتمع الانتماء المشاركة
+
+160
+00:14:17,560 --> 00:14:22,540
+كلما زادت الانتماء زادت المشاركة من أفراد المجتمع
+
+161
+00:14:22,540 --> 00:14:26,220
+وتفاعلهم مع بعضهم البعض من أجل تحقيق ماذا أهداف
+
+162
+00:14:26,220 --> 00:14:33,120
+المجتمع الذي يعيشون فيهفهناك علاقة طردية ما بين
+
+163
+00:14:33,120 --> 00:14:37,760
+الانتماء والتفاعل أو المشاركة مشاركة أفراد المجتمع
+
+164
+00:14:37,760 --> 00:14:49,780
+مشاركتهم مع بعضهم البعض في تحقيق أهداف المجتمع في
+
+165
+00:14:49,780 --> 00:14:56,220
+عدنا أيضا الاعتماد المتبادل بين أفراد المجتمع ايش
+
+166
+00:14:56,220 --> 00:15:00,670
+يعني الاعتماد المتبادل؟كدعامة من دعامات المجتمع
+
+167
+00:15:00,670 --> 00:15:10,530
+دعامة من دعامات المجتمع ايوة
+
+168
+00:15:10,530 --> 00:15:14,690
+نعم فضلك مثلا المجتمع القروي بانتحار المجتمع
+
+169
+00:15:14,690 --> 00:15:18,690
+المدني يتسوق من المنتجات فالمجتمع القروي يعتمد
+
+170
+00:15:18,690 --> 00:15:22,960
+اعتمادنعم يعني كل مجتمع يعتمد على المجتمع الأخر زي
+
+171
+00:15:22,960 --> 00:15:27,260
+الأفراد يعتمدون على بعضهم البعض في تحقيق وإشباع
+
+172
+00:15:27,260 --> 00:15:31,480
+حاجاتهم أيضا المجتمعات تعتمد على بعضها البعض في
+
+173
+00:15:31,480 --> 00:15:36,340
+تحقيق وإشباع احتياجاتهم وتحقيق هداف المجتمع مثل
+
+174
+00:15:36,340 --> 00:15:40,160
+مجتمع القرية ومجتمع المدينة اللي ضربنا في مثال
+
+175
+00:15:40,160 --> 00:15:44,180
+فلذلك هنا في اعتماد ما بين الأفراد وبعضهم البعض في
+
+176
+00:15:44,180 --> 00:15:48,140
+اعتماد ما بين المجتمع والمجتمعالاخر وهذا بنسميه
+
+177
+00:15:48,140 --> 00:15:52,480
+اعتماد متبادل بين أفراد المجتمع وبين المجتمع
+
+178
+00:15:52,480 --> 00:16:02,300
+والمجتمع الآخر طبعا
+
+179
+00:16:02,300 --> 00:16:07,620
+هنا الاعتماد قد يكون على مستوى المواردأيضًا
+
+180
+00:16:07,620 --> 00:16:12,480
+المادية على مستوى الموارد البشرية، أيضًا على مستوى
+
+181
+00:16:12,480 --> 00:16:16,420
+التخطيط، على مستوى البرامج، على مستوى الخدمات، هذه
+
+182
+00:16:16,420 --> 00:16:21,360
+كله بيكون مصالح متبادلة أو اعتماد متبادلة على
+
+183
+00:16:21,360 --> 00:16:24,180
+بعضهم البعض، في الموارد المادية، في الموارد
+
+184
+00:16:24,180 --> 00:16:27,680
+البشرية، في الخطط، في البرامج، في المشاريع، في
+
+185
+00:16:27,680 --> 00:16:30,460
+الخدمات التي تقدم، وهكذا
+
+186
+00:16:35,960 --> 00:16:41,380
+في عندنا أيضًا دعامة سادسة من دعامات المجتمع، مين
+
+187
+00:16:41,380 --> 00:16:47,520
+ما اتكلمتش؟ الشعوب
+
+188
+00:16:47,520 --> 00:16:55,220
+الانتماء للمجتمع، ماذا يعني كلمة الانتماء للمجتمع؟
+
+189
+00:16:55,220 --> 00:16:57,860
+ماذا يعني كلمة الانتماء؟ من الطالبات اللي ما
+
+190
+00:16:57,860 --> 00:17:02,980
+اتكلموشما اتكلمتيش؟ اتفضل ان هو الشخص او الفرد هو
+
+191
+00:17:02,980 --> 00:17:07,040
+احد الأشخاص اللي يعني بيشعر ان هو بيدمل هذا
+
+192
+00:17:07,040 --> 00:17:10,240
+المجتمع و بيعترف فيه او ان هذا هو مجتمع اللي هو
+
+193
+00:17:10,240 --> 00:17:14,740
+بيعيش فيه و اتربي فيه او ولد فيه او عاداته
+
+194
+00:17:14,740 --> 00:17:17,980
+التقاليدية كل ما كان انتمال المجتمع كل ما يعني
+
+195
+00:17:17,980 --> 00:17:23,220
+اشترك في مثلا في الانتخابات دفع الموضوع مشاركة في
+
+196
+00:17:23,220 --> 00:17:28,510
+اعمال المجتمع ايوة مهداأيضا الانتماء الشعور
+
+197
+00:17:28,510 --> 00:17:31,990
+بالانتماء ان يكون هذا الشخص هو جزء من استقرار
+
+198
+00:17:31,990 --> 00:17:35,750
+المجتمع و المحافظ عليه جزء من استقرار المجتمع و
+
+199
+00:17:35,750 --> 00:17:39,930
+المحافظ عليه اه ايه يا بنت دايما الفرد دايما يشارك
+
+200
+00:17:39,930 --> 00:17:44,310
+في كل حد و كل مجتمع عشان يقدر يواجه المشكلة عشان
+
+201
+00:17:44,310 --> 00:17:50,130
+يشعر بالفخر و العزاسي نعم الانتماء هو حب الوطن او
+
+202
+00:17:50,130 --> 00:17:54,130
+حب المجتمع اللي يعيش فيه الإنسان لأن الإنسان يولد
+
+203
+00:17:54,130 --> 00:17:59,480
+في مجتمع معينواضح اللى هو المجتمع اللى بنقول عنه
+
+204
+00:17:59,480 --> 00:18:03,760
+البلد اللى بنقول عنه القرية المدينة الوطن الحي
+
+205
+00:18:03,760 --> 00:18:08,820
+وممكن الى البيت اللى يوجد في هذا الحي او في هذا
+
+206
+00:18:08,820 --> 00:18:13,760
+المجتمع او في هذه البلدة قرية او مدينة فطبعا دائما
+
+207
+00:18:13,760 --> 00:18:19,200
+الانسان ينتمي الى هذا المجتمع اللى نشأ فيه ولده
+
+208
+00:18:19,200 --> 00:18:26,430
+ونشأ فيه وترعرع فيه طفولته وشبابهوهكذا، فلذلك من
+
+209
+00:18:26,430 --> 00:18:30,590
+هنا يكون هناك انتماء، فلذلك من دعمة المجتمع هو
+
+210
+00:18:30,590 --> 00:18:34,770
+الشعور بالانتماء للمجتمع اللذي يعيش فيه الإنسان،
+
+211
+00:18:34,770 --> 00:18:38,930
+الشعور بالانتماءوكل ما كان الانتماء قويا للمجتمع
+
+212
+00:18:38,930 --> 00:18:44,830
+كل ما كان عطاء الفرد قويا أيضا ومشاركته قوية داخل
+
+213
+00:18:44,830 --> 00:18:49,290
+المجتمع مشاركة إيجابية لبناء المجتمع من أجل تحقيق
+
+214
+00:18:49,290 --> 00:18:53,650
+أهداف المجتمع يسعى مع أفراد المجتمع الأخرين من أجل
+
+215
+00:18:53,650 --> 00:18:58,550
+بناء المجتمع فإذا دعامة الانتماء للمجتمع هي دعامة
+
+216
+00:18:58,550 --> 00:19:03,530
+أساسية ومقوم أساسي من مقومات المجتمع لابد من غرس
+
+217
+00:19:03,530 --> 00:19:08,470
+الانتماء لدى أفراد المجتمعلكي ينتموا إلى هذا
+
+218
+00:19:08,470 --> 00:19:12,870
+المجتمع اللذي يعيشون فيه ويساهموا في بنائه في
+
+219
+00:19:12,870 --> 00:19:16,990
+معرفة مشكلاته مشكلات المجتمع اللذي يعيشون فيه في
+
+220
+00:19:16,990 --> 00:19:20,770
+معرفة كيفية مواجهة هذه المشكلات في استخدام موارد
+
+221
+00:19:20,770 --> 00:19:24,690
+المجتمع وكيف نستخدم هذه الموارد من أجل معالجة
+
+222
+00:19:24,690 --> 00:19:29,250
+المشكلات وتحقيق أهداف المجتمع في كل شيء أن نشارك
+
+223
+00:19:30,450 --> 00:19:34,690
+فلذلك غرس الانتماء مهم جدا، ودعامة الانتماء مهمة
+
+224
+00:19:34,690 --> 00:19:40,990
+جدا بالنسبة لأفراد المجتمع، فلذلك لابد أن نغرس لدى
+
+225
+00:19:40,990 --> 00:19:45,090
+أفراد المجتمع، اللي هي الشعور بالانتماء للمجتمع،
+
+226
+00:19:45,090 --> 00:19:49,570
+ولذلك إذا لم يوجد انتماء للمجتمعنجد العزلة
+
+227
+00:19:49,570 --> 00:19:53,190
+الاجتماعية، نجد عدم تحقيق هداف المجتمع، نجد
+
+228
+00:19:53,190 --> 00:19:56,870
+المشكلات، نجد الفوضى، الواحدة كذا، لا يمكن أن نحقق
+
+229
+00:19:56,870 --> 00:20:00,470
+هداف المجتمع بدون الانتماء للمجتمع، فإذا من أجل
+
+230
+00:20:00,470 --> 00:20:04,670
+تحقيق هداف المجتمع، لابد من وجود دعامة أساسية من
+
+231
+00:20:04,670 --> 00:20:09,750
+دعامات المجتمع على وهي الانتماء للمجتمع، انتماء
+
+232
+00:20:09,750 --> 00:20:14,130
+الأفراد المجتمع لمجتمعهم، حتى يساهموا في بناء
+
+233
+00:20:14,130 --> 00:20:19,460
+مجتمعهم وتحقيق أهدافهماللي هي أصلا أهدافهم بتكون،
+
+234
+00:20:19,460 --> 00:20:22,980
+أهداف الأفراد المجتمع، هي أهداف المجتمع، لا انفصال
+
+235
+00:20:22,980 --> 00:20:27,480
+بينها، بين أهداف أفراد المجتمع و أهداف مجتمعها،
+
+236
+00:20:27,480 --> 00:20:33,460
+واضح؟ فلذلك من هنا، هذه تعتبر دعامة من دعامات أو
+
+237
+00:20:33,460 --> 00:20:37,080
+دعامة، دعامة أساسية من دعامات اللي هي مجتمع أو
+
+238
+00:20:37,080 --> 00:20:42,440
+مقوم أساسي من مقومات المجتمع، اللي هي الانتماء،
+
+239
+00:20:42,440 --> 00:20:47,970
+الشعور بالانتماء، الإنسانو يجب أن نغرس الانتماء
+
+240
+00:20:47,970 --> 00:20:53,630
+لدى أفراد مجتمعنا، لحب وطنهم، لحب مجتمعهم، مهم جدا
+
+241
+00:20:53,630 --> 00:20:58,670
+في
+
+242
+00:20:58,670 --> 00:21:03,070
+عندنا مقوم أخر أو دعامة أخرى من دعامات المجتمع
+
+243
+00:21:03,070 --> 00:21:06,250
+النظم الاجتماعي
+
+244
+00:21:10,850 --> 00:21:14,730
+إنه لا يجد أي مجتمع بضرورته مجتمعية لأنها ليست
+
+245
+00:21:14,730 --> 00:21:18,070
+مجتمعية أساسي لإن تحقيقها ليأتيزي الأسرة، ليأتيزي
+
+246
+00:21:18,070 --> 00:21:22,450
+المجتمع، لا يجد مليار، بس يعني فده بينفع قوة، فعلى
+
+247
+00:21:22,450 --> 00:21:25,610
+قصة الناس من اللي يتاخدين تتعامل مع المنصة، ما
+
+248
+00:21:25,610 --> 00:21:29,400
+تتقرع شده الجوهرية، الحمد للهكويس، يعني تخصوروا
+
+249
+00:21:29,400 --> 00:21:35,080
+مجتمع بدون نظم معينة، نظام تعليمي، نظام صحي، نظام
+
+250
+00:21:35,080 --> 00:21:39,840
+ديني، نظام اقتصادي، نظام اجتماعي، أسري، الأسرة،
+
+251
+00:21:39,840 --> 00:21:45,840
+كيف بيكون حالة المجتمع؟ فوضى، ما بيكونش مجتمع،
+
+252
+00:21:45,840 --> 00:21:52,760
+ولذلك اليوم في المفهوم المعاصر للمجتمع هو وجود
+
+253
+00:21:52,760 --> 00:21:59,080
+النظم، النظم التي تخدم المجتمعنظم وطبط المجتمع
+
+254
+00:21:59,080 --> 00:22:03,580
+وتشبه احتياجات المجتمع المختلفة لأن النظم
+
+255
+00:22:03,580 --> 00:22:06,820
+الاجتماعية الموجودة هي التي تقوم على إشباه حاجات
+
+256
+00:22:06,820 --> 00:22:10,320
+المجتمع نظام تعليمي يساعد المجتمع على إشباه
+
+257
+00:22:10,320 --> 00:22:14,240
+الحاجات التعليمية النظام الاقتصادي يساعد على
+
+258
+00:22:14,240 --> 00:22:17,360
+مواجهة المشكلات الاقتصادية وإشباه الحاجات
+
+259
+00:22:17,360 --> 00:22:23,390
+الاقتصادية لسكان المجتمعواضح النظام الأسري مهم جدا
+
+260
+00:22:23,390 --> 00:22:26,470
+النظام الاجتماعي الأسري لبناء الأسرة لأن بدون
+
+261
+00:22:26,470 --> 00:22:29,490
+الأسرة لا يوجد مجتمع لأن المجتمع عبارة عن عدد من
+
+262
+00:22:29,490 --> 00:22:34,250
+الأسر داخل المجتمع فلذلك من أجل إشباع الحاجات
+
+263
+00:22:34,250 --> 00:22:38,990
+الأسرية لابد من النظام الأسري داخل المجتمع و هكذا
+
+264
+00:22:38,990 --> 00:22:44,530
+فلذلك النظم المختلفة ضرورية أو ضرورة من ضرورات
+
+265
+00:22:44,530 --> 00:22:48,510
+المجتمع لأن بدون هذه النظم لا يمكن تحقيق أهداف
+
+266
+00:22:48,510 --> 00:22:54,850
+المجتمعفلذلك تعتبر المنظمة الاجتماعية بمختلف أنواع
+
+267
+00:22:54,850 --> 00:23:01,190
+تعتبر دعامة من دعامات المجتمع من أجل تحقيق أهداف
+
+268
+00:23:01,190 --> 00:23:12,690
+المجتمع طيب، ننتقل إلى الدعامة الأخيرة ما
+
+269
+00:23:12,690 --> 00:23:17,120
+هي؟هي عبارة عن مؤسسات وهيوصف بها الوحدات التي
+
+270
+00:23:17,120 --> 00:23:20,920
+يعملوا مدى يرقم المجتمع وإنشائها لتحطم عدة أهداف
+
+271
+00:23:20,920 --> 00:23:24,000
+لتنوع هذه المؤسسات ماباين اجتماعية، مصادرية،
+
+272
+00:23:24,000 --> 00:23:27,590
+تقديمية، سياسية؟وأيضا أحجامها ستتغير مبين تغيرة
+
+273
+00:23:27,590 --> 00:23:31,490
+إلى كبيرة إلى معقدة، ممكنها تكون محلية أو تلينية،
+
+274
+00:23:31,490 --> 00:23:35,570
+بالنسبة للمارس الاجتماعي يمكنها تكون مؤسسة أولية
+
+275
+00:23:35,570 --> 00:23:40,130
+أو مبنية؟ نعم، أحسنتي، بارك الله فيك، إذا المؤسسات
+
+276
+00:23:40,130 --> 00:23:44,570
+مهمة جدا، أي مؤسسة توجد في المجتمع من أجل شبه
+
+277
+00:23:44,570 --> 00:23:50,160
+حاجة، لا توجد المؤسسة عبثاكل المؤسسات الموجودة في
+
+278
+00:23:50,160 --> 00:23:54,260
+المجتمع هي من أجل إشباع حاجات المجتمع وتحقيق أهداف
+
+279
+00:23:54,260 --> 00:23:59,160
+المجتمع ومساعدة المجتمع على حل مشكلته المؤسسة التي
+
+280
+00:23:59,160 --> 00:24:03,340
+لا تشبه حاجة للمجتمع أو لا تعالج مشكلة المجتمع لا
+
+281
+00:24:03,340 --> 00:24:07,920
+أساس لها المجتمع مش في حاجة إليها فلذلك المؤسسة
+
+282
+00:24:07,920 --> 00:24:14,000
+ضرورة وتنشأفي المجتمع من أجل إشباح حاجة معينة أو
+
+283
+00:24:14,000 --> 00:24:17,640
+حل مشكلة معينة داخل المجتمع ولذلك كل مؤسسات
+
+284
+00:24:17,640 --> 00:24:21,560
+المجتمع تقوم بدورها داخل المجتمع من أجل مساعدة
+
+285
+00:24:21,560 --> 00:24:26,640
+المجتمع على حل مشكلته وإشباح حاجاته واضح؟ والمؤسسة
+
+286
+00:24:26,640 --> 00:24:30,480
+التي لا تقوم بذلك سرعان ما تنتهي المؤسسة التي لا
+
+287
+00:24:30,480 --> 00:24:35,020
+تقوم بمساعدة المجتمع على إشباح حاجاته أو حل مشكلته
+
+288
+00:24:35,020 --> 00:24:40,130
+سرعان ما تنتهيداخل المجتمع لأنه لازم يكون علاقة
+
+289
+00:24:40,130 --> 00:24:44,010
+متبادلة ما بين المجتمع و المؤسسة علاقة تبادلية
+
+290
+00:24:44,010 --> 00:24:47,810
+المؤسسة تكون بشبه حاجات المجتمع و المجتمع يعني
+
+291
+00:24:47,810 --> 00:24:52,070
+يعترف بهذه المؤسسة و يقدم لها الخدمات حتى يحدث نوع
+
+292
+00:24:52,070 --> 00:24:57,570
+من دورة داخل المؤسسة من أجل عمل برامج عمل مشاريع
+
+293
+00:24:57,570 --> 00:25:02,030
+تقديم خدمات للمجتمع ليستفيد من خدمات هذه المؤسسة
+
+294
+00:25:02,510 --> 00:25:07,030
+واضح؟ فلذلك المؤسسات داخل المجتمع تعتبر دعامة
+
+295
+00:25:07,030 --> 00:25:12,290
+أساسية من دعامات المجتمع ومقوم أساسي من مقومات
+
+296
+00:25:12,290 --> 00:25:18,710
+المجتمعمؤسسات التعليمية، مؤسسات الاقتصادية، مؤسسات
+
+297
+00:25:18,710 --> 00:25:25,190
+الأسرية، مؤسسات الصحية، مؤسسات الرعاية الاجتماعية
+
+298
+00:25:25,190 --> 00:25:31,890
+للفقراء، للمحتاجين، للمعاقين، للمرضى و هكذا بكافة
+
+299
+00:25:31,890 --> 00:25:35,250
+أنواع المؤسسات الموجودة داخل المجتمع تقدم خدمات
+
+300
+00:25:35,250 --> 00:25:38,930
+للمجتمع وتساعد المجتمع في إشباع حاجاته و حل مشكلته
+
+301
+00:25:39,250 --> 00:25:44,450
+فلذلك ضرورة ومهمة جدا وجود المؤسسات داخل المجتمع
+
+302
+00:25:44,450 --> 00:25:49,690
+إحنا بذلك يعني هذا موضوعنا لكن لابد أن نكمل
+
+303
+00:25:49,690 --> 00:25:54,390
+المحاضرة أيضا لموضوع آخر عندنا موضوع آخر مفهوم
+
+304
+00:25:54,390 --> 00:25:59,590
+المجتمع في إطار طريق تنظيم المجتمع مفهوم المجتمع
+
+305
+00:25:59,590 --> 00:26:06,370
+في إطار طريق تنظيم المجتمع في أي سؤال في الموضوع
+
+306
+00:26:06,370 --> 00:26:14,900
+اللي قبل ذلكاللي هي في دعائم المجتمع سماعة المجتمع
+
+307
+00:26:14,900 --> 00:26:20,420
+مفهوم المجتمع كله واقعي طيب لو قلنا مفهوم المجتمع
+
+308
+00:26:20,420 --> 00:26:24,800
+في إطار طريقة تنظيم المجتمع في عندنا عدد من النقاط
+
+309
+00:26:24,800 --> 00:26:32,300
+يعني ممكن ناخد عدد منها وهي المجتمع كنسق اجتماعي
+
+310
+00:26:32,300 --> 00:26:37,600
+وبعدين المجتمع كعملية المجتمع الجغرافي والمجتمع
+
+311
+00:26:37,600 --> 00:26:42,920
+الوظيفمجتمع الحاجة أو المشكلة مجتمع المربرة و بعد
+
+312
+00:26:42,920 --> 00:26:47,580
+ذلك نصل إلى كيف نحدد المجتمع في إطار طريق التنظيم
+
+313
+00:26:47,580 --> 00:26:51,880
+المجتمعي يعني
+
+314
+00:26:51,880 --> 00:26:56,460
+ممكن ناخد الموضوع الأول اللي هو المجتمع كنسق
+
+315
+00:26:56,460 --> 00:27:04,640
+اجتماعي كنسق system system
+
+316
+00:27:04,640 --> 00:27:06,640
+اللي هو النسق والاجتماعي
+
+317
+00:27:11,640 --> 00:27:18,100
+community as social system يعني المجتمع كنسق
+
+318
+00:27:18,100 --> 00:27:23,680
+اجتماعي ايش
+
+319
+00:27:23,680 --> 00:27:30,380
+يعني مجتمع كنسق اجتماعي ماذا يعني ماذا يعني
+
+320
+00:27:30,380 --> 00:27:33,400
+المجتمع كنسق اجتماعي في فكرة النسق
+
+321
+00:27:49,230 --> 00:27:55,410
+يعني احنا لما نقول نسق، يعني لو قولنا النسق
+
+322
+00:27:55,410 --> 00:28:02,280
+الأسري، النسق الأسري يعني النظام الأسري، الكبيرلكن
+
+323
+00:28:02,280 --> 00:28:06,700
+يقول عنله نسق أسري أو نظام أسري كبير، لكن هل هذا
+
+324
+00:28:06,700 --> 00:28:14,460
+النسق أسري يعني موجود لوحدي فقط؟ والله فيه أجزاء،
+
+325
+00:28:14,460 --> 00:28:20,340
+أجزاء، فلذلك النسق يعني مكون من أجزاء، كيف يكون
+
+326
+00:28:20,340 --> 00:28:26,600
+الأسرة؟ الخطوبة، الزواج، كل هذا نسق فرعي، فلذلك
+
+327
+00:28:26,600 --> 00:28:32,190
+النسق العام هو من مجموعة الأنساق الفرعيةواضح؟
+
+328
+00:28:32,190 --> 00:28:36,870
+المواريث، الطلاق، مش هي تقولها في أطار الأسرة
+
+329
+00:28:36,870 --> 00:28:41,850
+والنظام الأسري فلذلك هذه كلها نظم جزئية لكن في
+
+330
+00:28:41,850 --> 00:28:47,690
+النهاية بتشكل النماذج النسق الكلي اللي هو النسق
+
+331
+00:28:47,690 --> 00:28:53,830
+الأسري النسق الاقتصادي مثلا مما يتكون من أنظمة
+
+332
+00:28:53,830 --> 00:29:00,030
+فرعية وجزئية ما هي من الإنتاج
+
+333
+00:29:02,600 --> 00:29:08,240
+من التسويق والترويج السلع والتوزيع التوزيع السلع
+
+334
+00:29:08,240 --> 00:29:14,340
+مش هذه كلها عناصر جزئية أو أنساق جزئية بنسميها نظم
+
+335
+00:29:14,340 --> 00:29:19,820
+جزئية بتشكل لنا ماذا؟ النظام الاقتصادي النظام
+
+336
+00:29:19,820 --> 00:29:22,960
+الاقتصادي لو جينا للنظام التعليمي أو النسق
+
+337
+00:29:22,960 --> 00:29:27,020
+التعليمي النسق التعليمي مما يتكون من عدد من
+
+338
+00:29:27,020 --> 00:29:32,530
+الأنظمة الجزئية اللي بتشكل لنا النسق الكلياللي هو
+
+339
+00:29:32,530 --> 00:29:37,590
+النظام الكلي أو النسق الكلي للتعليم ما هي الأنساق
+
+340
+00:29:37,590 --> 00:29:42,430
+الجزئية أو الأنظمة الجزئية الفرعية للتعليم الطالب
+
+341
+00:29:42,430 --> 00:29:49,290
+الكتاب اللي هو المنهج وسائل الإيضاح الغرف الدراسية
+
+342
+00:29:49,290 --> 00:29:54,770
+أو الفصول الدراسية المعلمين
+
+343
+00:29:54,770 --> 00:30:00,270
+الإدارة المباني مواقف المدرسة المدرسة المدرسة
+
+344
+00:30:00,270 --> 00:30:00,870
+المدرسة المدرسة المدرسة المدرسة المدرسة المدرسة
+
+345
+00:30:00,870 --> 00:30:01,230
+المدرسة المدرسة المدرسة المدرسة المدرسة المدرسة
+
+346
+00:30:01,230 --> 00:30:02,900
+المدرسة المدرسة المدرسة المدرسةللمدرسة مش هاد كلها
+
+347
+00:30:02,900 --> 00:30:07,660
+أنظمة جزئية لامتحانات، كمان نظام الامتحانات، أنظمة
+
+348
+00:30:07,660 --> 00:30:10,980
+جزئية، كلها وغيرها من النظام الجزئي للتعليمات،
+
+349
+00:30:10,980 --> 00:30:17,400
+بتشكل ليه؟ النظام الكل أو النسق الكل بالتعليم،
+
+350
+00:30:17,400 --> 00:30:22,540
+فلذلك من هنا لابد انذا نفه من المجتمع كنسق، لابد
+
+351
+00:30:22,540 --> 00:30:28,030
+نعرف النسق ومما يتكون النسقمن الانسقة الفرعية اللى
+
+352
+00:30:28,030 --> 00:30:33,210
+بتكون منها حتى نفهم انه النسق او المجتمع كنسق
+
+353
+00:30:33,210 --> 00:30:40,710
+اجتماعى كنسق ممكن يعني يؤدي وظائف معينة فلذلك كل
+
+354
+00:30:40,710 --> 00:30:45,390
+نسق عام له عدد من الانسقة الفرعية ومجموعة الانسقة
+
+355
+00:30:45,390 --> 00:30:49,030
+العامة تتشكل اللى اللى هى النظام العام داخل
+
+356
+00:30:49,030 --> 00:30:52,890
+المجتمع النظام اللى هو النسق الاجتماعي العام داخل
+
+357
+00:30:52,890 --> 00:30:58,420
+المجتمعلأن كل نسق إجتماعي له وظيفة أو وظائف يقوم
+
+358
+00:30:58,420 --> 00:31:04,760
+بإشباه حاجات المجتمع وحل مشكلات المجتمع، واضح؟
+
+359
+00:31:04,760 --> 00:31:10,640
+فهمنا المجتمع كنسق؟ الله فيها صعوبة هذه؟ مافيش
+
+360
+00:31:10,640 --> 00:31:13,240
+صعوبة؟ طيب، مفهومة يعني
+
+361
+00:31:17,610 --> 00:31:21,330
+إذاً المجتمع فيضوء فكرة النسق الاجتماعي مجموعة من
+
+362
+00:31:21,330 --> 00:31:24,590
+أيه؟ من العناصر اللي بيسود بينها نوع من الاعتماد
+
+363
+00:31:24,590 --> 00:31:28,790
+والتساند المتبادل، طبعا الأنسق ما بتبقاش مستقلة
+
+364
+00:31:28,790 --> 00:31:32,230
+لوحدها، في نوع من التبادل، لو قلنا نسق تعليمي،
+
+365
+00:31:32,230 --> 00:31:35,570
+الأنظمة الجزئية للنظام التعليمي أو النسق التعليمي
+
+366
+00:31:35,570 --> 00:31:40,010
+تتعاون مع بعضها البعضكذلك النسق الكلي للتعليم
+
+367
+00:31:40,010 --> 00:31:43,270
+يتعاون مع الأنسق الأخرى، النسق الأسرى، النسق
+
+368
+00:31:43,270 --> 00:31:47,330
+الاقتصادي، النسق الديني، النسق السياسي، وكذلك كل
+
+369
+00:31:47,330 --> 00:31:51,470
+الأنساق تتعاون مع بعضها البعض وتتساند مع بعضها
+
+370
+00:31:51,470 --> 00:31:57,470
+البعض طبعا هنا المجتمع يتكوّن من وحدات، اللي هي
+
+371
+00:31:57,470 --> 00:32:03,580
+مجموعة النظم المتخصصةوهكذا اللي احنا اتكلمنا عنها
+
+372
+00:32:03,580 --> 00:32:07,960
+النظم التعليمية الاقتصادية السياسية الدينية وكلها
+
+373
+00:32:07,960 --> 00:32:12,740
+تتساند مع بعضها البعض في عندنا ايضا هذه النظم
+
+374
+00:32:12,740 --> 00:32:16,500
+المتخصصة اللي هي الأنساق الفرعية لها أنساق فرعية
+
+375
+00:32:16,500 --> 00:32:19,760
+على مستوى اقل واضح؟
+
+376
+00:32:20,810 --> 00:32:24,590
+يعني النسق التعليمي له أنساق فرعية على مستوى أقل
+
+377
+00:32:24,590 --> 00:32:28,550
+من النسق الكلي للتعليم، زي ما نقول مثلا الطالب،
+
+378
+00:32:28,550 --> 00:32:33,330
+المعلم، هذه أنسقة فرعية تعتبر، الامتحانات، وسائل
+
+379
+00:32:33,330 --> 00:32:37,590
+الإيضاح، أنسقة فرعية لإيه؟ للنسق الكلي التعليمي،
+
+380
+00:32:37,590 --> 00:32:42,270
+وهكذا أيضا
+
+381
+00:32:48,550 --> 00:32:51,970
+مهين انت للي احنا ضربناها، هذه اللي احنا اتكلمنا
+
+382
+00:32:51,970 --> 00:32:54,890
+عنها، اللي هي النظام التعليمي، النظام الاقتصادي،
+
+383
+00:32:54,890 --> 00:32:58,210
+النظام الوسري، النظام الديني كذلك، اللي بيشمل
+
+384
+00:32:58,210 --> 00:33:02,350
+العبادات، بيشمل التكافل، بيشمل .. اه و هكذا، هذا
+
+385
+00:33:02,350 --> 00:33:08,790
+كله برضه له أنظمة جزئيةفكل نظام كله أو كل نسق كله
+
+386
+00:33:08,790 --> 00:33:12,950
+له أنظمة فرعية تتعاون مع بعضها البعض من أجل تحقيق
+
+387
+00:33:12,950 --> 00:33:17,490
+أهداف النظام الكلي وكل الأنظمة تتعاون مع بعضها
+
+388
+00:33:17,490 --> 00:33:22,190
+البعض الأنسقة الكلية تتعاون أيضا وفي تساند بينها
+
+389
+00:33:22,190 --> 00:33:27,470
+تساند وظيفة بين هذه الأنساق المختلفة هذا المقصود
+
+390
+00:33:27,470 --> 00:33:31,350
+بإن المجتمع كنسق كنسق اجتماعي
+
+391
+00:33:36,810 --> 00:33:43,270
+كذلك المجتمعات يعني مثلا لو قلنا المجتمع برضه
+
+392
+00:33:43,270 --> 00:33:48,730
+يتكون من أنسقة فرعية يتكون
+
+393
+00:33:48,730 --> 00:33:54,430
+من الأنسقة الفرعية اللي هي للمجتمع المحلي والمجتمع
+
+394
+00:33:54,430 --> 00:33:59,450
+المحلي يتكون من نسق فرعي للمجتمع القوبي يعني لو
+
+395
+00:33:59,450 --> 00:34:05,260
+قلنا مثلا غزة على سبيل المثال مش مجتمعلكن يعتبر
+
+396
+00:34:05,260 --> 00:34:10,020
+المجتمع يعني نسق قومي و لا نسق فرعي فرعي لمين
+
+397
+00:34:10,020 --> 00:34:17,440
+لفلسطين لفلسطين طب لو قولنا الشجاعية فرعي لمدينة
+
+398
+00:34:17,440 --> 00:34:21,880
+غزة مجتمع غزة ومجتمع غزة كمدينة إذا الفرعي لمين
+
+399
+00:34:21,880 --> 00:34:26,460
+للمجتمع الكل القومي اللي هو فلسطين فهمنا من ناحية
+
+400
+00:34:26,460 --> 00:34:31,600
+هذه أيضا المفهوم طب لو قولنا مجتمع خانيونس مجتمع
+
+401
+00:34:31,600 --> 00:34:38,990
+خانيونس يعتبر ايهمجتمع فرعلمان إلى قطاع غزة، غزة
+
+402
+00:34:38,990 --> 00:34:44,730
+ككل، ولكن في النهاية تعتبر ايه؟ قطاع غزة كله
+
+403
+00:34:44,730 --> 00:34:48,730
+فرعلمين لفلسطين، وهكذا، فاهمني هذا المفروض؟
+
+404
+00:34:48,730 --> 00:34:58,090
+المجتمع كنسب، فرعي، كيف بيكون؟ طيب وكذلك
+
+405
+00:34:58,090 --> 00:35:01,150
+المجتمع القومي، لو قلنا فلسطين مش تعتبر من العالم
+
+406
+00:35:02,660 --> 00:35:07,760
+من الدول نسق من العربي من جامعة الدول العربية و في
+
+407
+00:35:07,760 --> 00:35:13,560
+نفس الوقت من اللي هي المنظمة الدولية كذلك دولي على
+
+408
+00:35:13,560 --> 00:35:18,180
+مستوى دولي كل دولة عضو في منظمة الأمم المتحدة فإذا
+
+409
+00:35:18,180 --> 00:35:22,500
+هنا بتكون ايه مجتمع دولي يعني عضو في المجتمع
+
+410
+00:35:22,500 --> 00:35:25,700
+الدولي كنسق دولي و هكذا
+
+411
+00:35:37,340 --> 00:35:44,520
+طبعا هذه الأنصار كلها يعني لابد من اعتماد متبادل
+
+412
+00:35:44,520 --> 00:35:48,420
+فيما بينها، لماذا؟ يكون اعتماد بين هذه المجتمعات و
+
+413
+00:35:48,420 --> 00:35:51,860
+هذه الأنصار، الاعتماد المتبادل، من أجل ماذا؟ من
+
+414
+00:35:51,860 --> 00:35:56,380
+أجل حل المشكلات، من أجل مواجهة الندرة، لأن المشكلة
+
+415
+00:35:56,380 --> 00:36:02,060
+أساسها ندرة، ندرة في الموارد، ليش احنا بنقول
+
+416
+00:36:02,060 --> 00:36:07,360
+مشكلة؟ لماذا؟ لأنه ندرةليه بتقول مشكلة اقتصادية؟
+
+417
+00:36:07,360 --> 00:36:11,840
+ندرة في الموارد الاقتصادية، باضح؟ ليه ماذا نقول
+
+418
+00:36:11,840 --> 00:36:14,920
+مثلا أحيان المشكلة الطبية ندرة في المتخصصين أو في
+
+419
+00:36:14,920 --> 00:36:19,420
+الأجزة أو في الأدوية؟ ندرة، فلذلك حتى نواجه الندرة
+
+420
+00:36:19,420 --> 00:36:23,100
+لابد أن يكون هناك تعاون ما بين هذه الأنصاق
+
+421
+00:36:23,100 --> 00:36:28,520
+المختلفة في المجتمع أو اللساق الكلي بينه وبين غيره
+
+422
+00:36:28,520 --> 00:36:32,960
+من الأنصاق حتى نستطيع أن نتغلب على مشكلات الندرة
+
+423
+00:36:32,960 --> 00:36:39,480
+وما ينتج عن الندرةمن الموارد ومواجهتها فهكذا
+
+424
+00:36:39,480 --> 00:36:44,660
+المجتمع المحلي ممكن يتعاون مع مجتمع محلي آخر حتى
+
+425
+00:36:44,660 --> 00:36:50,300
+يتغلب على المشكلات التي يواجهها مجتمع القرية
+
+426
+00:36:50,300 --> 00:36:53,840
+يتعاون مع مجتمع المدينة حتى يتغلب على ما يواجههم
+
+427
+00:36:53,840 --> 00:36:57,940
+من المشكلات ويكون في بينهم تسالد وهكذا ليشبع
+
+428
+00:36:57,940 --> 00:37:00,840
+الحاجات وتعقيق الأهداف الخاصة بالمجتمع
+
+429
+00:37:05,900 --> 00:37:11,140
+نكون بذلك يعني أخدنا اللي هو المجتمع كنسق اجتماعي
+
+430
+00:37:11,140 --> 00:37:15,820
+طيب في متطلبات وظيفية تحتاج ليها المنظمات
+
+431
+00:37:15,820 --> 00:37:21,720
+والمجتمعات حتى يتحقق لها الاستمرارية تتحقق لها
+
+432
+00:37:21,720 --> 00:37:26,960
+الاستمرارية ما هي هذه الحاجات حتى تتحقق لها اي
+
+433
+00:37:26,960 --> 00:37:32,480
+نظام اي نظام هنا او اي منظم او اي مجتمع حتى يستمر
+
+434
+00:37:32,480 --> 00:37:33,880
+وحتى
+
+435
+00:37:35,730 --> 00:37:43,410
+يستمر في الحياة و تحقيق أهدافه لابد من متطلبات
+
+436
+00:37:43,410 --> 00:37:48,190
+وظيفية يحتاجه حتى تحقق لها الاستمرارية ما يادر
+
+437
+00:37:48,190 --> 00:37:56,350
+متطلبات الوظيفية اول حاجة العنصر البشري اهم شيء
+
+438
+00:37:56,350 --> 00:37:59,830
+لان بدون العنصر البشري لايمكن ان يستمر النظام
+
+439
+00:37:59,830 --> 00:38:05,250
+لايمكن ان يستمر المجتمع فهم المتطلباتاللي بتحتاجها
+
+440
+00:38:05,250 --> 00:38:10,290
+المنظمات والمجتمعات هي العنصر البشري وهذا أهم شيء
+
+441
+00:38:10,290 --> 00:38:22,110
+وجود البشر وجود الناس ماذا أيضا .. أه أيها بنتي أه
+
+442
+00:38:22,110 --> 00:38:24,710
+واحدة منكم بتتكلم أنت أو هي .. أه بتتكلم دولة
+
+443
+00:38:24,710 --> 00:38:27,610
+إيجاد العلاقات السليمة بين مختلف الأقصار من مكونات
+
+444
+00:38:27,610 --> 00:38:34,120
+المنظمة أو المجتمع وجدتإن حرفين المنظمة تتكون من
+
+445
+00:38:34,120 --> 00:38:40,280
+أقسام والمجتمع كذلك تتكون من أجزاء فلذلك لابد من
+
+446
+00:38:40,280 --> 00:38:45,480
+إيجاد التعاون والتنسيق بين الأقسام المختلفة
+
+447
+00:38:45,480 --> 00:38:50,020
+للمنظمة أو الأجزاء المختلفة للمجتمع الأجزاء
+
+448
+00:38:50,020 --> 00:38:56,200
+الفرعية للمجتمع أو الأقسام المختلفة للمنظمة كمجتمع
+
+449
+00:38:56,200 --> 00:39:02,300
+لابد من التعاون فيما بينهافهذه طبعا تعتبر من
+
+450
+00:39:02,300 --> 00:39:08,060
+المتطلبات اللازمة لإستمرارية المنظمة أو إستمرارية
+
+451
+00:39:08,060 --> 00:39:12,200
+المجتمع إيجاد التعاون والتنسير بين الأجزاء
+
+452
+00:39:12,200 --> 00:39:20,040
+المختلفة للمنظمة أو المجتمع ماذا أيضا؟
+
+453
+00:39:20,040 --> 00:39:29,570
+هل هي الرقم تلاتة؟ أه أيها بنتيهو في ال branch ..
+
+454
+00:39:29,570 --> 00:39:32,770
+ال branch الإعداد والتدريب و بس فيه أنه أسسها في
+
+455
+00:39:32,770 --> 00:39:36,090
+العاملين أو في تدقيقها إيجابية في المجتمع الأخضر؟
+
+456
+00:39:36,090 --> 00:39:41,550
+حتى تستمر المنظمة كمجتمع لابد أن يكون هناك
+
+457
+00:39:41,550 --> 00:39:45,670
+الاهتمام بالعنصر التدريب .. بالتدريب للعنصر البشري
+
+458
+00:39:45,670 --> 00:39:51,770
+تدريب مهم جدا لأن ال .. ال .. العملين داخل المنظمة
+
+459
+00:39:51,770 --> 00:39:55,770
+يحتاجوا إلى تدريب استمرار للعملية التدريبية
+
+460
+00:39:55,770 --> 00:39:56,590
+المستمرة
+
+461
+00:39:59,120 --> 00:40:04,530
+لأنه بدون تدريب ممكن يقف أو تقف المنظمة عن عملهالو
+
+462
+00:40:04,530 --> 00:40:08,370
+ضربنا مثال مثلا و أهمية التدريب يعني الخدمة
+
+463
+00:40:08,370 --> 00:40:12,630
+الاجتماعية مثلا في الخمسينات والستينات غير عن
+
+464
+00:40:12,630 --> 00:40:17,190
+الألفين و غير عن الألفين و عشرة و ألفين و خمستاشر
+
+465
+00:40:17,190 --> 00:40:22,870
+اليوم هذه يعني دائما مستمرة في النمو و المعرفة
+
+466
+00:40:22,870 --> 00:40:28,850
+مستمرة في إيجاد مبادئ جديدة و معارف جديدة و تدريب
+
+467
+00:40:28,850 --> 00:40:33,930
+جديد و مؤسسات جديدة للعمل فيها و هكذاكذلك مهنة
+
+468
+00:40:33,930 --> 00:40:39,870
+الطب تحتاج إلى تدريب العنصر البشري للطباء داخل
+
+469
+00:40:39,870 --> 00:40:43,590
+المؤسسة الطبية لأنه كان في الزمن الماضي عمليات
+
+470
+00:40:43,590 --> 00:40:47,810
+جراحية فقط من أجل استخلاص المرارة على سبيل المثال
+
+471
+00:40:47,810 --> 00:40:52,730
+او ال .. ال .. لكن اليوم في اللي هو المنظار نضع
+
+472
+00:40:52,730 --> 00:40:56,850
+منظار داخل جسم الإنسان و تقبل عملية سهلة و ليست
+
+473
+00:40:56,850 --> 00:41:04,720
+فيها صعوبة التصوير اليوم الطفل يعرفذاكر عمونثا وهو
+
+474
+00:41:04,720 --> 00:41:10,490
+في بطن أمه، كان هذا الأمر مش موجودفلذلك اليوم حتى
+
+475
+00:41:10,490 --> 00:41:14,810
+المعدات يعني جديدة، المعارف جديدة، فلذلك لابد من
+
+476
+00:41:14,810 --> 00:41:19,190
+تدريب العناصر البشرية، يعني اللي اتخرج سن سبتين أو
+
+477
+00:41:19,190 --> 00:41:22,910
+سبعين أو تمانين اليوم في أجهزة حديثة، في معلومات
+
+478
+00:41:22,910 --> 00:41:26,810
+جديدة، إذا هنا أهمية التدريب مهم ولا مش مهم؟ مهم
+
+479
+00:41:26,810 --> 00:41:31,030
+للمؤسسات المختلفة، ومختلف أنواعها، فلذلك حتى تستمر
+
+480
+00:41:31,030 --> 00:41:35,030
+المنظمة أو المجتمع أو المجتمع المنظمة، لابد من
+
+481
+00:41:35,030 --> 00:41:38,070
+تدريب العناصر البشرية العاملة داخل هذه المؤسسة
+
+482
+00:41:38,070 --> 00:41:43,520
+كمجتمعتدريبها على .. على كافة ال .. الاسليب حتى
+
+483
+00:41:43,520 --> 00:41:46,940
+اليوم في الخدمة الاجتماعية اليوم عندنا تدريب لابد
+
+484
+00:41:46,940 --> 00:41:52,620
+نتعلم كيف نتعامل مع الفئات الخاصة وخاصة الصوم
+
+485
+00:41:52,620 --> 00:41:56,410
+والبكم، الصوم والبكم كان زمان مافيش لهم تعليميوضع
+
+486
+00:41:56,410 --> 00:42:00,090
+في بيتي وخلاص لكن اليوم في معاهد وفي مؤسسات
+
+487
+00:42:00,090 --> 00:42:03,710
+تعليمية احنا في الخدمة الاجتماعية لابد ان نتعلم
+
+488
+00:42:03,710 --> 00:42:08,230
+كيف نتعامل مع هذه الفئات نتعلم الإشارة كيف نتعلم
+
+489
+00:42:08,230 --> 00:42:12,030
+يعني تعليم الإشارة مع الصم والبكم وكيف نتعامل معهم
+
+490
+00:42:12,030 --> 00:42:15,770
+وكيف نعلمهم مراحل التعليمية المختلفة من التعليم
+
+491
+00:42:15,770 --> 00:42:19,270
+العام والتعليم الجامعي وغير ذلك والتعليم المهني
+
+492
+00:42:19,270 --> 00:42:24,740
+فهذه أصبح ضرورة اليومضرورة أيضا للتعامل مع مثل هذه
+
+493
+00:42:24,740 --> 00:42:30,040
+الفئات المختلفة اليوم أصبح طريقة braille كانت زمان
+
+494
+00:42:30,040 --> 00:42:35,480
+بال .. ب braille و الحروف البارثة و باللمس اليوم
+
+495
+00:42:35,480 --> 00:42:39,300
+على الكمبيوتر اليوم اللي عندنا بطل بالكتاب مطلوع
+
+496
+00:42:39,300 --> 00:42:42,020
+ال word بنروح هنا في المركز التقني عندنا في
+
+497
+00:42:42,020 --> 00:42:47,480
+الجامعة يحول من ال word إلى braille مباشرة بطريقة
+
+498
+00:42:47,480 --> 00:42:53,580
+اللمسأهم القراءة كتاب تنظيم مجتمع كتاب رعاية شباب
+
+499
+00:42:53,580 --> 00:42:57,540
+كتاب علم اجتماعي و حضري كتاب anthropology أي كتاب
+
+500
+00:42:57,540 --> 00:43:01,520
+الآن أصبح فيه متناول الجميع من مكفوفي البصر
+
+501
+00:43:01,520 --> 00:43:05,240
+بيتناولوه عن طريق التقنية الحديثة كان في الزمن
+
+502
+00:43:05,240 --> 00:43:10,020
+الماضي بصعوبة يكتب كتابة باليد و هكذا لكن اليوم
+
+503
+00:43:10,020 --> 00:43:16,330
+أبدا الأمور سريعة جداهذا تطور مش هذا لابد من تدريب
+
+504
+00:43:16,330 --> 00:43:20,130
+العناصر البشرية على مثل هذه الأمور الفنية
+
+505
+00:43:20,130 --> 00:43:26,010
+المستحدثة وإحنا اليوم بنعيش في عالم صغير في تواصل
+
+506
+00:43:26,010 --> 00:43:30,470
+اجتماعي بيننا وبين العالم للاطلاع الجديد وكل جديد
+
+507
+00:43:30,470 --> 00:43:35,310
+فلذلك كل يوم يظهر عندنا جديد فلذلك لابد من إيجاد
+
+508
+00:43:35,310 --> 00:43:40,710
+التدريب حتى تستمر المنظمة كمجتمع في بقائها وتحقيق
+
+509
+00:43:40,710 --> 00:43:48,790
+أهدافها نعم يا بنتيرقم أربعة تفضلي إيجاد وسائل
+
+510
+00:43:48,790 --> 00:43:52,030
+ملائمة لإتخاذ القرارات تعمل على توسيع نطاق الاتصال
+
+511
+00:43:52,030 --> 00:43:57,670
+والحوار بين القرارات طبعا الاتصال يعني توسيع نطاق
+
+512
+00:43:57,670 --> 00:44:02,250
+الاتصال القرارات يعني إيجاد وسائل ملائمة لإتخاذ
+
+513
+00:44:02,250 --> 00:44:06,970
+القرارات تعتمد على الحوار الديمقراطي على المناقشة
+
+514
+00:44:06,970 --> 00:44:11,450
+على الشورة هذا مهم جدا ما تكون قرارات فردية
+
+515
+00:44:11,450 --> 00:44:18,120
+ديكتاتوريةلابد أن نعود أنفسنا داخل مؤسساتنا ونعود
+
+516
+00:44:18,120 --> 00:44:23,140
+المنظمة كمجتمع على الحوار بين العاملين فيها واتخاذ
+
+517
+00:44:23,140 --> 00:44:27,280
+القرارات بالإجماع واتخاذها نتيجة الحوار كل فرد
+
+518
+00:44:27,280 --> 00:44:31,940
+يتحدث ويتناقش الإدارة والمدير يجتمع مع العاملين
+
+519
+00:44:31,940 --> 00:44:35,140
+ويتناقش معاهم في اتخاذ القرارات اللي اتتهمهم اتهم
+
+520
+00:44:35,140 --> 00:44:41,220
+المؤسسة تواصل اجتماعيوها كذا، يكون دائما معرفة
+
+521
+00:44:41,220 --> 00:44:45,420
+مشكلات العملين وإيجاد حلول لها، هذا كله بيساعد على
+
+522
+00:44:45,420 --> 00:44:50,780
+اللي هو المنظمة كمجتمع في استمراريتها وتحقيق
+
+523
+00:44:50,780 --> 00:44:56,500
+أهدافها، ماذا أيضا؟ أحكي دي الأزواء الاجتماعية
+
+524
+00:44:56,500 --> 00:45:00,230
+الأكبر للمجتمعالأدوار الاجتماعية لأفراد المجتمع
+
+525
+00:45:00,230 --> 00:45:05,110
+واتعيف كل منهم بدوره الذي يؤديه ومسئولياته طبعا
+
+526
+00:45:05,110 --> 00:45:08,970
+حتى تستمر المنظمة لابد كل فرد يكون في هذه المنظمة
+
+527
+00:45:08,970 --> 00:45:13,990
+كمجتمع معروف دوره دور الاجتماع ما هو دوره محدد
+
+528
+00:45:13,990 --> 00:45:19,370
+الأدوار ووظائف لكل فرد وظيفة معينة ودور مهم له
+
+529
+00:45:19,370 --> 00:45:23,810
+لابد يعرف دوره داخل هذه المنظمة داخل المجتمعاللي
+
+530
+00:45:23,810 --> 00:45:27,890
+هي المنظمة كمجتمع، حتى نستطيع المؤسسة أو المنظمة
+
+531
+00:45:27,890 --> 00:45:32,770
+كمجتمع تحقق أهدافها، إذا لابد من تحديد الأدوار لكل
+
+532
+00:45:32,770 --> 00:45:41,110
+فرد داخل هذه المنظمة كمجتمع، نعم، مين ما اتكلمتش
+
+533
+00:45:41,110 --> 00:45:44,170
+نهائيًا؟ أيوة يا بنتي؟
+
+534
+00:45:47,010 --> 00:45:50,710
+نعم اه ابتكار الوسائل لحل النزاع أحيانا قد يحدث
+
+535
+00:45:50,710 --> 00:45:55,110
+نزاع داخل المنظمة كمجتمع، إذا هنا لابد أن نفكر و
+
+536
+00:45:55,110 --> 00:45:59,450
+نفكر في الوسائل الموجودة و الوسائل الممكن تبتكر
+
+537
+00:45:59,450 --> 00:46:04,110
+يعني في مناقشة المشاكل و كيفية حلها و الوصول إلى
+
+538
+00:46:04,110 --> 00:46:08,770
+حلول لهافلابد من إيجاد الوسائل الملائمة والمناسبة
+
+539
+00:46:08,770 --> 00:46:13,550
+في حل المشكلات داخل المنظمة كمجتمع، ماذا أيضا حتى
+
+540
+00:46:13,550 --> 00:46:18,210
+تستمر المؤسسة في تحقيق أهدافها واستمرارياتها؟ ما
+
+541
+00:46:18,210 --> 00:46:22,010
+هي المططلبات الأخرى؟
+
+542
+00:46:25,450 --> 00:46:30,390
+الموارد مهمة جدا لأن أحيانا المؤسسات أو المنظمات
+
+543
+00:46:30,390 --> 00:46:35,190
+كمجتمع ممكن تقف من أجل يعني و لا تحقق أدافع إذا لم
+
+544
+00:46:35,190 --> 00:46:39,890
+توجد الموارد فلذلك لابد من حتى تستمر المؤسسة لابد
+
+545
+00:46:39,890 --> 00:46:43,390
+من إيجاد الموارد الملائمة سواء كانت موارد مادية
+
+546
+00:46:43,390 --> 00:46:49,350
+موارد بشرية إلى غير ذلك خلاص
+
+547
+00:46:49,350 --> 00:46:55,430
+يكفي إلى هنا يعني في هذه المحاضرةنكون قد تكلمنا عن
+
+548
+00:46:55,430 --> 00:47:04,350
+دعائم المجتمع، تكلمنا عن المجتمع
+
+549
+00:47:04,350 --> 00:47:10,770
+كنسق
+
+550
+00:47:10,770 --> 00:47:17,130
+اجتماعي، تكلمنا عن المنظمة كمجتمع وما هي المتطلبات
+
+551
+00:47:17,130 --> 00:47:22,050
+اللازمة لاستمرارية المنظمة كمجتمع في تحقيق أهدافها
+
+552
+00:47:22,730 --> 00:47:27,930
+نكون في هذه المحاضرة قد أنهينا المطلوب منها إلى أن
+
+553
+00:47:27,930 --> 00:47:32,570
+نلتقي بكلنا في محاضرة قادمة لكل مني كل تحية وتقدير
+
+554
+00:47:32,570 --> 00:47:36,810
+والسلام عليك بيه ورحمة الله وبركاته
+