Faculty of Science

Objectives

To provide an introduction to the techniques of linear analysis, its applications to boundary value problems of mathematical physics, numerical and computational methods.

Contents

Linear transformations on vector spaces: Eigen- values and eigen- vectors, Inner products and completeness: Gram-Schmidt orthogonalization complete sets of functions, orthogonal basis in inner product spaces, L-2 spaces and the spaces of continuous and differentiable functions, Group Theory, The Linear theory of ordinary differential equations and operators, Dimension of the kernel; Sturm- Liouville theory and special functions of mathematical physics: eigen- values and eigen- functions for boundary value problems, Self-adjoint operators. The regular and irregular Sturm- Liouville problem, Hermite polynomials, Bessel functions and Legendre Polynomials, Partial differential equations for mathematical physics and methods of solutions in bounded and unbounded domains, separation of variables and Fourier transforms. Numerical simulation and computational exercises.

Prerequisite: