كلية العلوم

نموذج رقم(12)

توصيف مقرر دراسي : تفاضل عالى ومعادلات تفاضلية

2010 - 2011

الفارابى لإدارة جودة التعليم والتعلم - 22/12/2024

الجامعة :جامعة المنصورة

الكلية :كلية العلوم

القسم :الرياضيات

1- بيانات المقرر :-

2- أهداف المقرر :-

The course provides an overview of standard methods for the solution of single ordinary differential equations and systems of equations, with an introduction to some of the underlying theory and calculus of functions of more than one variable.

3- نواتج التعلم المستهدفة للمقرر :-

4- محتويات المقرر :-

م	الموضوع	الأسبوع
1	First Order Differential Equations :Linear equations with constant coefficients, Homogeneous equations, Exact equations and integrating factors, Riccati equations
2	Second Order Differential Equations: Homogeneous equations with constant coefficients, Fundamental solutions of linear homogeneous equations, Linear independence and the Wronskian (including Abel
3	Reduction of order and reduction to the normal form, Nonhomogeneous equations,Method of undetermined coefficients,Variation of parameters
4	Laplace transformation: Definition of the Laplace transform, Solutions of initial value problems by , Laplace transformation and ,inverse of laplace transformation ,the unit Step functions, First and second shift theorems, Convolution theorem
5	Series solutions of 2nd-order linear differential eq
6	Function of several variables, Partial differentiation .Continuity, differentiability, and the chain rule.
7	Taylor Theorem
8	Multiple integrals, Line integral, Elliptic integral
9	Line integral, Green’s Theorem, Elliptic integrals

5- أساليب التعليم والتعلم :-

م	الاسلوب
	4 4houre lecture and 3 hours tutorials

6- أساليب التعليم والتعلم للطلاب ذوى القدرات المحدودة :-

7- تقويم الطلاب :-

أ- التوقيت

م	الطريقة	الأسبوع
1	Oral Examination	14
2	Final_Term Examination	15

ب- توزيع الدرجات

8- قائمة الكتب الدراسية والمراجع

م	العنصر	النوع
1	http://www.sosmath.com/diffeq/diffeq.html
2	Avaliable in the Dept
3	C. H Edwards, Elementary differential equations with boundary value problems, Pearson Prentice Hall, 2004
4	W.E. Boyce & R.C. Di Prima, "Elementary Differential Equations and Boundary Value Problems", Wiley
5	M. Braun, "Differential Equations and their Applications", Springer-Verlag.
6	C.H. Edwards & D.E. Penney, "Elementary Differential Equations with Boundary Value Problems", Prentice Hall.
7	R.K. Nagle & E.B. Saff, & A.D. Snider, "Fundamentals of Differential Equations and Boundary Value Problems", Addison-Wesley.

9- مصفوفة المعارف والمهارات المستهدفة من المقرر الدراسي

م	المحتوى	أسبوع الدراسة
	First Order Differential Equations :Linear equations with constant coefficients, Homogeneous equations, Exact equations and integrating factors, Riccati equations
	Second Order Differential Equations: Homogeneous equations with constant coefficients, Fundamental solutions of linear homogeneous equations, Linear independence and the Wronskian (including Abel
	Reduction of order and reduction to the normal form, Nonhomogeneous equations,Method of undetermined coefficients,Variation of parameters
	Laplace transformation: Definition of the Laplace transform, Solutions of initial value problems by , Laplace transformation and ,inverse of laplace transformation ,the unit Step functions, First and second shift theorems, Convolution theorem
	Series solutions of 2nd-order linear differential eq
	Function of several variables, Partial differentiation .Continuity, differentiability, and the chain rule.
	Taylor Theorem
	Multiple integrals, Line integral, Elliptic integral
	Line integral, Green’s Theorem, Elliptic integrals

اساتذة المادة: -

رئيس مجلس القسم العلمى: -

أحمد حبيب محمد نجيب البسيونى