شرح مادة المعادلات التفاضلية الجزئية (Partial Differential Equations - PDEs)

6 اكتوبر / مصر
آخر تحديث: 2026-07-21

عن بعد/اونلاين هندسة كهربائية | Electrical Engineering اتصالات | Communications هندسة ميكانيك | Mechanical Engineering

دورة متخصصة في شرح مادة المعادلات التفاضلية الجزئية (PDEs) لطلاب كليات الهندسة والعلوم. تهدف الدورة إلى تبسيط المفاهيم الأساسية، فهم النظريات، وتدريب الطالب على خطوات الحل الأكاديمية الصحيحة.

المحاور الرئيسية:

دورة المعادلات التفاضلية الجزئية (Partial Differential Equations - PDEs)

عن الدورة والهدف منها:

تهدف هذه الدورة إلى تقديم شرح متكامل لمادة المعادلات التفاضلية الجزئية لطلاب كليات الهندسة والعلوم، مع التركيز على فهم المفاهيم الأساسية واكتساب مهارة الحل الأكاديمي المنظم للمسائل والامتحانات.

المنهج والمحاور التدريسية:

المفاهيم الأساسية والتصنيف:
- تعريف المعادلات التفاضلية الجزئية والرتبة والدرجة.
- تصنيف المعادلات من الرتبة الثانية (Elliptic, Parabolic, Hyperbolic).
المعادلات الفيزيائية الأساسية وطرق حلها:
- معادلة الحرارة (Heat Equation): الاشتقاق والحل في 1D.
- معادلة الموجة (Wave Equation): الشروط الابتدائية والحدية واستخدام صيغة دالامبير (D'Alembert's Solution).
- معادلة لابلاس (Laplace Equation): التطبيقات وطرق الحل في الإحداثيات المختلفة.
أدوات الحل التحليلي:
- طريقة فصل المتغيرات (Separation of Variables).
- التعامل مع الشروط الحدية والابتدائية (Boundary & Initial Value Problems).
- تطبيق متسلسلات فورير (Fourier Series) وتحويلات فورير في الحل.

التقنيات وأسلوب التدريس:

الشرح المرئي: كتابة وحل أخطاء المسائل خطوة بخطوة عبر الشاشة التفاعلية.
الجانب التطبيقي: ربط القوانين بالمعنى الفيزيائي والهندسي المباشر.
التدريب العملي: حل سلاسل تمارين متنوعة ونماذج امتحانات سابقة لضمان الاستيعاب الكامل.

مدة الدورة وخطة العمل:

إجمالي الساعات: (15 - 20) ساعة تدريسية (موزعة على جلسات تفاعلية حسب اتفاق الطالب/المجموعة).
الملحقات: إرسال ملخصات مجهزة وشيتات محلولة عقب كل محتوى.

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