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).
Text Books:
1. Rathor, Choudhari,: Descrete Structure And Graph Theory.
2. Gupta S. C and Kapoor V K: Fundamentals of Mathematical Statistics - Sultan Chand & Sons.
3. Lipschutz S: Theory and Problems of Probability (Schaum's Outline Series) - McGraw Hill Book. Co.
4. Spiegel M R: Theory and Problems of Probability and Statistics (Schaum's Outline Series) - McGraw
Hill Book Co.
5. Goon A.M., Gupta M K and Dasgupta B: Fundamental of Statistics - The World Press Pvt. Ltd.
6. Spiegel M R: Theory and Problems of Complex Variables (Schaum's Outline Series) - McGraw Hill
Book Co.
7. Bronson R: Differential Equations (Schaum's Outline Series) - McGraw Hill Book Co.
8. Ross S L: Differential Equations - John Willey & Sons.
9. Sneddon I. N.: Elements of Partial Differential Equations - McGraw Hill Book Co.
10. West D.B.: Introduction to Graph Theory - Prentice Hall/Pearson Education
11. Deo N: Graph Theory with Applications to Engineering and Computer Science - Prentice Hall.
12. Grewal B S: Higher Engineering Mathematics (thirtyfifth edn) - Khanna Pub.
13. Kreyzig E: Advanced Engineering Mathematics - John Wiley and Sons.
14. Jana- Undergradute Mathematics
15. Lakshminarayan- Engineering Math 1.2.3
16. Gupta- Mathematical Physics (Vikas)
17. Singh- Modern Algebra
18. Rao B: Differential Equations with Applications & Programs, Universities Press
19. Murray: Introductory Courses in Differential Equations, Universities Press
20. Delampady, M: Probability & Statistics, Universities Press
21. Prasad: Partial Differential Equations, New Age International
22. Chowdhury: Elements of Complex Analysis, New Age International
23. Bhat: Modern Probability Theory, New Age International
24. Dutta: A Textbook of Engineering Mathematics Vol.1 & 2, New Age International
25. Sarveswarao: Engineering Mathematics, Universities Press
26. Dhami: Differential Calculus, New Age International