**CHHATTISGARH SWAMI VIVEKANAND TECHNICAL UNIVERSITY, BHILAI (C. G.)**

**Semester : B.E. 3 Sem. Branch : ET & T**

**Subject: Mathematics-III **

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

derivatives.

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

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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

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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.

1. Applied Mathematics for Engineers & Physicists by Louis A. Pipes- TMH.