CHHATTISGARH SWAMI VIVEKANAND TECHNICAL UNIVERSITY, BHILAI (C. G.)
Semester : B.E. 3 Sem. Branch : ET & T
UNIT – 1 FOURIER SERIES (No. of periods 8+2)
Periodic functions, Definition of Fourier series, Euler’s formulae, Dirichlet conditions, Change of
interval, Even and odd functions, Half range Fourier Sine & Cosine series, Parseval’s identity,
Practical harmonic analysis.
UNIT – 2 FOURIER TRANSFORM (No. of periods 8+2)
Definition of Fourier integrals – Fourier Sine & Cosine integrals, Complex form of Fourier
integral, Fourier Sine & Cosine transforms, Complex form of Fourier transform, Linearity,
shifting & scaling properties, Modulation theorem, Inverse Fourier transform, Fourier transform of
UNIT – 3 LAPLACE TRANSFORM (No. of periods 8+2)
Definition, Linearity, shifting & scaling properties, Transform of elementary functions, Transform
of derivatives and integrals, Multiplication by t & division by t. Inverse Laplace transform,
Convolution theorem, Transform of periodic functions, Unit step function & Dirac delta function,
Initial value & final value theorems, Application to solution of ordinary differential equations.
UNIT – 4 COMPLEX VARIABLES (No. of periods 8+2)
Limit, Derivative, Analytic function, Cauchy-Riemann equations, Harmonic functions,
Application to flow problems. Complex integration, Cauchy’s integral theorem and integral
formula, Taylor’s & Laurent’s series, Singular point, Poles & residues, Residue theorem & its
application to contour integration.
UNIT – 5 CORRELATION AND REGRESSION
No. of periods 8+2)
Linear correlation, Measures of correlation, Karl Pearson’s coefficient of correlation, Spearman’s
rank correlation coefficient, Bivariate frequency distribution, Regression, lines of regression &
coefficients of regression, Standard error estimate
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,
1. Applied Mathematics for Engineers & Physicists by Louis A. Pipes- TMH.