The subject of partial differential equation has an unchanging core of material but is consistently expanding and evolving. The core consists of solution methods, mainly separation of variables, for boundary value problems with consist coefficients in goemetrically simple domains, especially on numerical and the analytical side of the subject.

With the availability of convenient ad powerful computation software, it has made it possible to enlarge the scope of the introductory PDE. The MATLAB’s Partial Differential Equation toolbox contains tools for the study and solution of partial differential equations (PDEs) in two-space dimensions (2-D) and time, using the finite element method (FEM). Its command line functions and graphical user interface can be used for mathematical modeling of PDEs in a broad range of engineering and science applications, including structural mechanics, electromagnetics, heat transfer and diffusion.

The course is an introduction to the theory of partial differential equations and also provides methods of solution of boundary and initial value problems. Participants are taught how to identify different types of partial differential equations and to obtain the equations that are satisfied by given functions. Analytical methods of solutions of first order equations having certain standard forms are given. Various methods of solution of these equations are considered, taking into account any initial and boundary value problems relevant to a given situation in the real world. Throughout the course, the emphasis is on methods of solution.