# Mathematics-III

Below is the syllabus for Mathematics-III:-

## UNIT – I

Fourier series: Euler’s Formulae, Conditions for Fourier expansions, Fourier expansion of functions having points of discontinuity, change of interval, Odd & even functions, Half-range series.

Fourier Transforms Fourier integrals, Fourier transforms, Fourier cosine, and sine transforms. Properties of Fourier transforms, Convolution theorem, Parseval’s identity, Relation between Fourier and Laplace transforms, Fourier, transforms of the derivatives of a function, Application to boundary value problems.

## UNIT-II

Functions of Complex Variables: Functions of a complex variable, Exponential function, Trigonometric, Hyperbolic and Logarithmic functions, limit and continuity of a function, Differentiability, and analyticity.

Cauchy-Riemann equations, Necessary and sufficient conditions for a function to be analytic, Polar form of the Cauchy-Riemann equations, Harmonic functions, Application to flow problems, Conformal transformation, Standard transformations (Translation, Magnification & rotation, inversion & reflection, Bilinear).

## UNIT-III

Probability Distributions: Probability, Baye’s theorem, Discrete & Continuous probability distributions, Moment generating function, Probability generating function, Properties and applications of Binomial, Poisson and normal distributions.

## UNIT-IV

Linear Programming: Linear programming problems formulation, Solution of Linear Programming Problem using Graphical method, Simplex Method, Dual-Simplex Method.

## Text Book

1. Higher Engg. Mathematics: B.S. Grewal
2. Advanced Engg. Mathematics: E. Kreyzig

## Reference Book

1. Complex variables and Applications: V. Churchill; Mc. Graw Hill
2. Mathematics Vol. II: S.S. Sastry; Prentice Hall of India.
3. Operation Research: H.A. Taha
4. Probability and statistics for Engineer: Johnson.