Course Code: MATH-404

Integral Equations

Prerequisite(s): O.D.E and Real Analysis-I

Credit Hours: 3+0

Objectives of the course:

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 thebehavior of several standard physical problems.

Course 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.

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.

ASSESSMENT CRITERIA

Mid Term Exam:       30 marks

Sessional:                 20 marks

Final Term Exam:      50 marks

Total:                        100 marks