**CHHATTISGARH SWAMI VIVEKANAND TECHNICAL UNIVERSITY, BHILAI (C. G.)**

**Semester: B.E. 4 Sem. Branch: Electronics & Telecom**

**Subject: Mathematics-IV**

UNIT – 1 SERIES SOLUTION OF DIFFERENTIAL EQUATIONS AND SPECIAL FUNCTIONS

Series solution of differential equations, The method of Frobenius, Bessel’s differential equation,

Bessel’s function of the First Kind – recurrence relations, generating function, orthogonality, Legendre’s

differential equation, Legendre’s polynomial – Rodrigue’s formula, generating function, recurrence

relations, orthogonality.

UNIT – 2 PARTIAL DIFFERENTIAL EQUATIONS: (No. of periods 8+2)

Formation, Solution of Lagrange’s linear differential equation, homogeneous linear differential

equation with constant coefficients, non-homogeneous linear differential equations, Method of

separation of variables.

UNIT – 3 APPLICATIONS OF PARTIAL DIFFERENTIAL EQUATIONS (No. of periods 8+2)

Initial & boundary value problems, Vibrations of a stretched string, D’Alembert’s solution, Onedimensional

heat flow, Transmission of signals along a cable – Telephone equation, Telegraph &

radio equations, Vibrations of rectangular & circular membranes.

UNIT – 4 Z – TRANSFORM (No. of periods 8+2)

Sequence, Basic operations on sequences, Definition of Z- Transform, Linearity, Change of scale

& shifting properties, Z-transform of standard sequences, Inverse Z- Transform, Multiplication by

n & division by n, Initial value & final value theorems, Convolution of sequences, Convolution

theorem, Inverse Z- transform by partial fraction, power series and residue methods. Application

to solution of difference equations.

UNIT – 5 RANDOM VARIABLE & PROBABILITY DISTRIBUTIONS (No. of periods 8+2)

Random variable, Discrete & continuous probability distributions, Mathematical Expectation,

Mean & variance, Moments & moment generating function, Probability distributions -Binomial,

Poisson & 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