Course Tittle: INTEGRAL EQUATIONS

Course Code: MATH-404

Credit Hours: 03

DESCRIPTION & OBJECTIVES

Many physical problems that are usually solved by differential equation methods can be solved more effectively by integral equation methods. This course will help students gain insight into the application of advanced mathematics and guide them through derivation of appropriate integral equations governing the behavior of several standard physical problems.

Recommended Books:

1. Jerri A. J. Introduction to Integral Equations with Applications second edition. Sampling Publishing, 2007.
2.  Lovitt W. V. Linear Integral Equations, Dover Publications, 2005.
3.  Baker C. T. H., Integral Equations, Clarendon Press, 1977.
4.  Smithies F. Integral Equations, Cambridge University Press, 1989.
5.  Wazwaz A. M. A first Course in Integral Equations, World Scientific Pub., 1989.

CONTENTS

Linear integral equations of the first kind, Linear integral equations of the second kind. Relationship between differential equation and Volterra Integral Equation. Neumann Series.Fredholm Integral equation of the second kind with separable Kernels. Eigenvalues and Eigenvectors. Iterated functions. Quadrature methods. Least square methods. Homogeneous Integral equations of the second kind. Fredholm integral equations of the first kind. Fredholm Integral equations of the second kind. Abel’s Integral equations. Hilbert Schmidt theory of integral equations with symmetric Kernels. Regularization and filtering techniques.

ASSESSMENT CRITERIA

Mid exam:       30

Sessional:        20

Project:            --

Assignments:   10

Presentation:   10

Final exam:      50

Total:               100

RULES AND REGULATIONS

75% attendance is compulsory to appear in Final Term exam.