Complex Variable: De-Moiver’s theorem & its application, Functions of a complex variable, Limit, Continuity & Differentiability of a function of complex variable, Analytic functions, Cauchy-Riemann equations, Cauchy’s theorem, Singularity & poles, Residues, Simple contour integration. Vector Analysis: Vector components, Vector components in spherical and cylindrical system, Derivative of vector, Vector operators, Del, Gradient, Divergence and Curl. Their physical significance, Vector integration, Line, Surface and Volume integration, Green’s and Stoke’s theorem and their applications. Laplace Transformation: Definition of Laplace transform (LT), LT of different functions, First Shift theorem, Inverse transform, Linearity, Use of first shift theorem and Partial functions, Transform of derivative, Transform of an integral, Heaviside unit function, The 2nd shift theorem, Periodic functions, Convolutions, Solution of ordinary differential equation by Laplace transform. Fourier Analysis: Real and Complex form, Finite transform, Fourier integral, Fourier series and convergence of Fourier series, Fourier transform and uses in solving boundary value problem.
