Partial Differential Equations and Simulations Tools

Partial differential equations are mathematical tools used in studying systems and modeling its phenomena. They are widely used in diverse areas of engineering, physical sciences, biology, economics and finance. The aim of this course is to teach the students how to solve partial differential equations and interpret the resulting solutions. The course first discusses the solutions of PDEs using different methods such as separation of variables, integral transforms and Fourier series for both homogeneous and non-homogeneous cases. It also introduces the series solutions of differential equations using Frobenius method. Some theoretical concepts about the Sturm-Liouville problem are discussed. It also provides solutions of partial differential equations using finite difference method. Computer software simulation tool (MATLAB, SciLab or any other suitable software) is used to solve linear and non-linear partial differential equations.