MATH3 (B-TECH Mechanical Engineering 3rd)

                                                                      Part-A

Fourier Series and Fourier Transforms : Euler’s formulae, conditions for a Fourier expansion, change of interval,

Fourier expansion of odd and even functions, Fourier expansion of square wave, rectangular wave, saw-toothed

wave, half and full rectified wave, half range sine and consine series.

Fourier integrals, Fourier transforms, Shifting theorem (both on time and frequency axes), Fourier transforms of

derivatives, Fourier transforms of integrals, Convolution theorem, Fourier transform of Dirac-delta function.

                                                                     Part-B

Functions of Complex Variable : Definition, Exponential function, Trignometric and Hyperbolic functions,

Logrithmic functions. Limit and Continuity of a function, Differnetiability 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. Integration of

complex functions. Cauchy-Integral theorem and fourmula.

 Power series, radius and circle of convergence, Taylor's Maclaurin's and Laurent's series. Zeroes and

singularities of complex functions, Residues. Evaluation of real integrals using residues (around unit and semi

circle only).

Part-C

Probability Distributions and Hypothesis Testing : Conditional probability, Bayes theorem and its applications,

expected value of a random variable. Properties and application of Binomial, Poisson and Normal

distributions.

Testing of a hypothesis, tests of significance for large samples, Student’s t-distribution (applications only),

Chi-square test of goodness of fit.

Linear Programming : Linear programming problems formulation, Solving linear programming problems using

(i) Graphical method (ii) Simplex method (iii) Dual simplex method.