Faculty of Science

Model (No 12)

Course Specification : نظرية المعادلات التفاضلية الجزئية-معادلات تكاملية

2008 - 2009

 
Farabi Quality Management of Education and Learning - 23/11/2024
University :Mansoura University
Faculty :Faculty of Science
Department :Mathematics Department
1- Course data :-
Code: 15417
Course title: نظرية المعادلات التفاضلية الجزئية-معادلات تكاملية
Year/Level: رابعة الإحصاء وعلوم الحاسب
Program Title:
  • Statistics & Computer science
Specialization:
Teaching Hours: Theoretical: 4Tutorial: 2Practical:
2- Course aims :-
  1. This course introduces students to (i) analytical and numerical methods for solving partial differential equations (PDEs), (ii) concepts and methods of Vector calculus. It builds on the first year core applied mathematics courses to develop more advanced ideas in differential and integral calculus.
  2. This course will focus on the different methods for solving Integral equations of Fredholm and Volterra types •.
3- Course Learning Outcomes :-
4- Course contents :-
NoTopicsWeek
1Introducion to Partial differential equations – order –homogenous and non homogenous – degree-linear and nonlinear
2Heat equation, Wave equation and Laplace’s equation in both one and higher dimensions.
3Separation of Variables, boundry value problems, Fourier Series.
4Fourier and Laplace Transform techniques.
5Applications.
6Volterra Integral equations of the 2nd kinds. Resolvent kernel
7Using of Laplace transformation to solve the integral equation of convolution type
8Solution of integro-differential equations using Laplace transformations
9Volterra integral equations of the 1st kind and Volterra equations of the 1st and 2nd kinds.
10Euler Integrals
11Abel’s problem and its generalization
12Fredholm integral equations of the 2nd kind
13Methods of Fredholm determinants.
14Fredholm Iterated kernel- resolvent kernel and Degenerate kernels
15Approximate methods of solution and applications

5- Teaching and learning methods :-
SMethod
4 hours lectures each week and 2 hours tutorial

6- Teaching and learning methods of disables :-
    No data found.

7- Student assessment :-
A. Timing
NoMethodWeek
1Oral Examination 14
2Final_Term Examination 15
B. Degree
NoMethodDegree
1Mid_term examination0
2Final_term examination90
3Oral examination 10
4Practical examination 0
5Semester work0
6Other types of asessment0
Total100%

8- List of books and references
SItemType
1Lecture notes
2 S. J. Farlow, Partial Differential Equations for Scientists and Engineers, Dover Publications 1993
3R. Haberman, Elementary Appled Partial Differential Equations, 4th ed., 2004.
41-ABDUL J. JERRI , Introduction to integral equations with applications, 1999, JOHN WILEY & SONS INC
5Problems and Exercises in integral equations Mir Publ., Mosow
6R Courant and D Hilbert, Methods of Mathematical Physics, Vols. I and II, Interscience.

9- Matrix of knowledge and skills of the course
SContentStudy week
Introducion to Partial differential equations – order –homogenous and non homogenous – degree-linear and nonlinear
Heat equation, Wave equation and Laplace’s equation in both one and higher dimensions.
Separation of Variables, boundry value problems, Fourier Series.
Fourier and Laplace Transform techniques.
Applications.
Volterra Integral equations of the 2nd kinds. Resolvent kernel
Using of Laplace transformation to solve the integral equation of convolution type
Solution of integro-differential equations using Laplace transformations
Volterra integral equations of the 1st kind and Volterra equations of the 1st and 2nd kinds.
Euler Integrals
Abel’s problem and its generalization
Fredholm integral equations of the 2nd kind
Methods of Fredholm determinants.
Fredholm Iterated kernel- resolvent kernel and Degenerate kernels
Approximate methods of solution and applications

Course Coordinator(s): -
  1. Mohamed Nabil Mostafa Mohamed Alam
Head of department: -
Ahmed Habeb Mohamed Nageb Elbassiony