Fourier Series:Introduction: Euler’s formula; Problems on general Fourier Series; Conditions for Fourier
Expansion; Fourier Expansions of Discontinuous Functions; Even and Odd functions; Change of
interval; Half range series; Typical Waveforms (Square, Saw-toothed, Triangular, Half Wave
rectifier, Full Wave rectifier); Parseval’s Identity (statement only); Fourier Transform (FT) and its
properties; Inverse Fourier Transform (statement only); Fourier transform of derivative (statement
only); Convolution (statement only); Application of Fourier Transform in solving partial
differential equations — Laplace’s Equation (2D only), Heat Conduction Equation (1D only) and
Wave Equation (1D only).
Calculus of Complex Variable:
Functions; Limits and Continuity; Analytic Functions; Cauchy Riemann Conditions; Analytic
Continuation; Complex Integration and Cauchy's Theorem; Cauchy's Integral Formula; Taylor's and
Laurent Series; Zeros of an Analytic Function; Poles; Essential Singularities; Residue Theorem
(statement only) and it's application to evaluation of integral; Introduction to Conformal Mapping;
Simple problems.
Probability and Statistics:
Mean, Median, Mode and Standard Deviation; Samples Space; Definition of Probability;
Conditional Probability; General Multiplication Theorem; Independent Events; Bayes' Theorem;
Random Variable; Discrete and Continuous Probability Distributions - Probability mass function;
Probability density function; Distribution Function; Expectation; Variance; Probability
Distribution—Binomial, Poisson and Normal. Correlation and Regression; Method of Least
Squares; Linear Curve Fitting.
Graph Theory:
Graphs; Digraphs; Isomorphism; Walk; Path; Circuit; Shortest Path: Dijkstra's Algorithm; Tree;
Properties of Tree; Binary Tree; Fundamental Circuit; Minimal Spanning Tree: Kruskal's
Algorithm; Prim’s Algorithm. Cut Set; Fundamental Cut Set and Cut Vertices; Matrix
Representation of Graphs (Adjacency and Incidence Matrices); Network; Flow Augmenting Path;
Ford-Fulkerson Algorithm for Maximum Flow; Max Flow – Min Cut Theorem (statement only).