Ordinary Differential Equation(ODE): Definition formation of differential equations, Solution of first order and first degree differential equations by various methods, Solutions of general linear equations of second and higher order with constant coefficients, Solution of liner equations of second and higher order with variable coefficients, solution of Euler’s homogeneous liner equation, Solution of differential equation in series by the method of Frobenius, Bessel’s and Legendre’s polynomials with their properties.

Partial Differential Equation (PDE):
Introduction: Equations of the linear and non-linear first order; Standard forms linear equations of higher order-equations of the second order with variable co-efficient.

Laplace Transforms:
Definition, Laplace transforms of some elementary functions, sufficient conditions for existence Laplace transforms; Inverse Laplace transform, Laplace transforms of derivatives, The unit step function, Periodic function, Some special theorems on Laplace transforms, Solutions of differential equations by Laplace transform, Evaluation of improper integrals.