Syllabus

Fourier Series and Transform: Expansion of a function in Fourier series for a given range and its convergence, Even and odd functions, Half range sine and cosine expansions, Fourier integrals, Complex Fourier series, Fourier transform, Inverse Fourier transform, Properties of Fourier transform, Convolution theorem, Discrete Fourier transform. Second order partial differential equations, Normal Form, Solutions of wave equation, Heat equation and Laplace’s equation and their use in problems of vibrating string, one dimensional unsteady heat flow and two dimensional steady state heat flow

Integral Equations: Classification of Integral equations, Neumann’s iterative method for Fredholm’s equation of second kind, Volterra type integral equation, Integral equations of first kind, Convolution type Integral Equations.

Calculus of Variations: Functionals, Variation of functionals, Example of variation problems, Euler's equation, sufficient conditions for the extremum of a functional, conditional extremum, Rayleigh-Ritz method.

Introduction to some Mathematical techniques

Solving some physical and engineering problems

R. V. Churchill, Operational Mathematics, McGraw Hill , 1971

J. W. Brown and R. Churchill, Fourier Series and Boundary Value Problems, McGraw Hill

I. M. Gelfand and S. V. Fomin, Calculus of Variations, Dover Publications , 1991

R. P. Kanwal, Linear Integral Equations, Birkhäuser Boston , 1996