CHHATTISGARH SWAMI VIVEKANAD TECHNICAL UNIVERSITY BHILAI (C.G.)
Semester: B.E. III Sem. Branch: Information Technology
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
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.