**CHHATTISGARH SWAMI VIVEKANAND TECHNICAL UNIVERSITY, BHILAI (CG)**

**Semester : B.E. III Sem. Branch: Mechanical**

**Subject : ****MATHEMATICS-III**

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

Euler’s Formula, Functions having points of discontinuity, Change of interval, Even & Odd

functions, Half range series, Harmonic analysis.

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

Definition, Transform of elementary functions, Properties of Laplace transform, Transform of

derivatives & integrals, Multiplication by t

n

, Division by t, Evaluation of integrals, Inverse Laplace

Transform, Convolution theorem, Unit step function, Unit impulse function, Periodic function,

Application to solution of ordinary differential equations.

UNIT – 3 PARTIAL DIFFERENTIAL EQUATION (No. of periods 8+2)

Formation, Solution by direct integration method, Linear equation of first order, Homogeneous

linear equation with constant coefficients, Non-homogeneous linear equations, Method of

separation of variables.

UNIT – 4 COMPLEX VARIABLES (No. of periods 8+2)

Derivative, Cauchy-Riemann equations, Analytic functions, Harmonic functions, Flow problems,

Complex integration, Cauchy theorem, Cauchy integral formula, Taylor & Laurent series,

Singularity, Residue, Evaluation of real definite integrals.

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

Random variables, Discrete & continuous probability distributions, Expectation, Mean & Standard

Deviation, Moments & moment generating function, Distributions- 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.