Course Contents

Fourier series: introduction and general properties, convergence of trigonometric series, Gibbs phenomenon Integral transform, development of the Fourier integral, Fourier transform, inversion theorems, Fourier transform of derivatives, convolution theorem, momentum representation, transfer functions. Complex arguments in Fourier transforms. Laplace transform, Laplace transform of derivatives, convolution products, inverse Laplace transform. Partial differential equations. Boundary value problems. Nonlinear methods and chaos, nonlinear differential equations. Probability: definitions and simple properties, statistics.

Course Synopsis

Fourier series: introduction and general properties, convergence of trigonometric series, Gibbs phenomenon, applications to various phenomena. Integral transform, development of the Fourier integral, Fourier transform, inversion theorems, Fourier transform of derivatives, convolution theorem, momentum representation, transfer functions. Complex arguments in Fourier transforms. Laplace transform, Laplace transform of derivatives, convolution products, inverse Laplace transform. Partial differential equations. Separation of variables in three dimensions. Boundary value problems. Nonlinear methods and chaos, the logistic map, sensitivity to initial conditions and parameters, nonlinear differential equations. Probability: definitions and simple properties, random variables, binomial distribution, Poisson distribution, Gauss's normal distributions, statistics.

Course Learning Outcomes

The students will be able to understand the various aspects of Fourier series, Distribution functions and nonlinear phenomena, which will help in their research work