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

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

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
Eigen values 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.

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