MATHEMATICS - CSVTU SYLLABUS - 3rd SEM

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 tn, 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 Z-TRANSFORM (No. of periods 8+2)
Definition, Properties, Initial value & final value theorems, Inverse Z-transform,
Convolution theorem, Partial fraction, Residue method & Applications to solution of
difference equations.
 

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