Note for Mathematics-3 - M-3 By Subrat Dash

Formation of Partial Differential Equations, Linear partial differential equations of First Order, Non Linear P.D.Es of first order, Charpit’s Method, Homogenous partial differential Equations with constant coefficients, Non Homogenous partial differential Equations, Cauchy type Differential Equation, Monge's Method

One Dimensional wave equation, D Alemberts Solution of wave equation, Heat Equation, Two Dimensional wave equation, Laplacian in polar coordinates, Circular Membrane ( Use of Fourier-Bessel Series), Laplace’s Equation in cylindrical and Spherical coordinates, Solution of partial Differential equation by laplace Transform

Analytic function, Cauchy –Reiman equation & Laplace equation, Conformal mapping, Line integral in complex plane, Cauchy’s integral theorem, Cauchy’s integral formula, Derivatives of analytic function

Power Series, Taylor series, Laurent Series, Singularities, Pole, and Residue, Residue Integral, Evaluation of real integral