Ordinary Differential Equations: First order ODE, systems of linear equations with constant coefficients. Higher order linear ODE, power series method, Legendre Polynomials and properties, Frobenius method, Bessel Function, sturm Liouville problems. Partial Differential Equations: First order PDE, classification of second order linear PDE, reduction to canonical forms, method of separation of variables, solutions of heat, Wave and Laplace equations (Polar and Cartesian coordinates).