CHHATTISGARH SWAMI VIVEKANAD TECHNICAL UNIVERSITY, BHILAI (C.G.)
Semester : B.E. III Sem. Branch: Civil, Mechanical, Mining, Chemical
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 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 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,
3. Applied Mathematics for Engineers & Physicists by Louis A. Pipes- TMH.