**CHHATTISGARH SWAMI VIVEKANAD TECHNICAL UNIVERSITY BHILAI (C.G.)**

**Semester: B.E. III Sem. Branch: Information Technology**

**Subject: MATHEMATICS-III **

UNIT – 1 FOURIER SERIES (No. of periods 8+2)

Expansion of function as Fourier series, Change of interval, Even and odd functions, Half-range Fourier series,

Practical harmonic analysis.

UNIT – 2 LAPLACE TRANSFORM (No. of periods 8+2)

Laplace transform of elementary functions, Properties of Laplace transform, Laplace transform of derivatives and

integrals, multiplication by t

n

and division by t, Laplace transform of periodic functions. Inverse Laplace transform,

Convolution theorem, Application of Laplace transform to solutions of ordinary differential equations.

UNIT – 3 THEORY OF COMPLEX VARIABLES (No. of periods 8+2)

Limit, Derivative and Analytic functions; Cauchy-Riemann equations and its applications to flow problems;

Complex Integration: Line and Contour integral, Cauchy integral theorem and Integral formula; Taylor series,

Laurent series; singularities; Poles and their orders and residues; Evaluation of real definite integrals.

UNIT – 4 PARTIAL DIFFERENTIAL EQUATION (No. of periods 8+2)

Formation of partial differential equations, Equations solvable by direct integration, Lagrange’s linear equations,

Homogeneous linear differential equations with constant coefficients, Non-homogeneous linear equations, Solution

of partial differential equations by the method of separation of variables.

UNIT – 5 RANDOM VARIABLES (No. of periods 8+2)

Discrete and continuous probability distributions, Mathematical expectation, Mean and Variance, Moments,

Moment generating function, probability distribution, Binomial, Poisson and Normal distributions.

TEXT BOOKS: –

1. Higher Engg. Mathematics by Dr. B.S. Grewal– Khanna Publishers.

2. Advanced Engg. Mathematics by Erwin Kreyszig – John Wiley & Sons.

REFERENCE BOOKS: –

1. Advanced Engg.Mathematics by R.K. Jain and S.R.K. Iyengar – Narosa Publishing House.

2. Applied Mathematics by P.N.Wartikar & J.N. Wartikar. Vol- II– Pune Vidyarthi Griha Prakashan, Pune.

3. Applied Mathematics for Engineers & Physicists by Louis A. Pipes- TMH.