MATH-433                 Integral Equations

PREREQUISITE

ODEs and Real Analysis-I

DESCRIPTION AND OBJECTIVES

Many physical problems that areusually siolved by differential equation methods can be solved moreeffectively by integral equation methods. This course will help studentsgain insight into the application of advanced mathematics and guidethem through derivation of appropriate integral equations governingthebehavior of several standard physical problems.

LEARNING OUTCOMES

On Completion of this module, the learner will be able to

1. Use Fourier transforms for solving a wide range of differential and integral equations
2. Formulate and solve initial and boundary value problems for the heat and wave equations in spherical and cylindrical coordinates
3.  Solve linear Volterra and Fredholm integral equations using appropriate methods
4.  Understand the relationship between integral and differential equations and transform one type into another.

Contents

1. Linear integral equations of the first kind
2. Linear integral equations of the second kind
3. Relationship between differential equation and Volterra integral equation
4. Neumann series. Fredholm Integral equation of the second kind with separable Kernels
5. Eigen values and eigenvectors
6. Iterated functions
7. Quadrature methods
8. Least square methods
9. Homogeneous integral equations of the second kind
10. Fredholm integral equations of the first kind
11. Fredholm integral equations of the second kind
12. Abel’s integral equations
13. Hilbert Schmidt theory of integral equations with symmetric Kernels
14. Regularization and filtering techniques.

Recommended Books

1. J. Jerri; Introduction to Integral Equations with Applications second edition.( Sampling Publishing, 2007)
2. W. V. Lovitt, Linear Integral Equations, (Dover Publications, 2005)
3. F. Smithies, Integral Equations, (Cambridge University Press, 1989)

Suggested Books

1. C. T. H. Baker, Integral Equations, (Clarendon Press, 1977)
2. A. M. Wazwaz, A first Course in Integral Equations, (World Scientific Pub., 1989)

ASSESSMENT CRITERIA

Sessional: 20 (Presentation / Assignment 10, Attendance 05, Quiz 05)

Mid-Term Exam:   30

Final-Term Exam: 50

KEY DATES AND TIME OF CLASS MEETING

Thursday                                                                                11:00 am-12:30 pm

Friday                                                                                     02:00 pm-03:30 pm

Commencement of Classes                                                   October 12, 2020

Mid Term Examination                                                            December 14-18, 2020

Final Term Examination                                                          February 08-12, 2020

Declaration of Result                                                               February 19, 2020