Engineering Mathematics IV

At the end of the course, the student will be able to: 1. solve second order differential equations; 2. solve partial differential equations; 3. solve linear integral equations; 4. relate integral transforms to solution of differential and integral equations; 5. explain and apply interpolation formulas; and 6. apply Runge-Kutta and other similar methods in solving ODE and PDEs.

Series solution of second order linear differential equations with variable coefficients. Bessel and Legendre equations. Equations with variable coefficients. Sturn-Louville boundary value problems. Solutions of equations in two and three dimensions by separation of variables. Eigen value problems. Use of operations in the solution of partial differential equations and Linear integral equations. Integral transforms and their inverse including Fourier, Laplace, Mellin and Handel Transforms. Convolution integrals and Hilbert Transforms. Calculus of finite differences. Interpolation formulae. Finite difference equations. Runge-Kutta and other methods in the solutions of ODE and PDEs. Numerical integration and differentiation. MATLAB functions for numeric solution of linear and non-linear ODEs.