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

Definition, Exponential function, Trigonometric and Hyperbolic functions, Logrithmic 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 Integration of complex functions Cauchy-
Integral theorem and formula

Power series, radius and circle of convergence, Taylor's Maclaurin's and Laurent's seriesZeroes and singularities of comple x functions, Residues Evaluation of real integrals using residues (around unit and semi circle only) 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