MATH-604                 Integral Equations

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.

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. A. J. Jerri; Introduction to Integral Equations with Applications second edition. (Sampling      Publishing, 2007)
2. W. V. Lovitt, Linear Integral Equations, (Dover Publications, 2005)

Suggested Books

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

Assessment Criteria

Sessional: 20 (Presentation / Assignment 04, Attendance 08, Result Mid-Term 04, Quiz 04

Mid-Term Exam (Term Paper):  30

Final-Term Exam: 50

Key Dates and Time of Class Meeting

Wednesday--Thursday   (MSc-IV-Regular)                                                              08:00am-09:30am

Wednesday--Thursday   (MSc-IV-Self Support)                                                       03:30pm-05:00pm

Commencement of Classes                                                   Jannuary 13, 2020

Mid Term Examination                                                            March 16 to March 23, 2020

Final Term Examination                                                          May 11-15, 2020

Declaration of Result                                                              May 22, 2020