Partial differential equations provide the natural mathematical description of many phenomena of interest in science, engineering and finance. Such equations are often difficult or impossible to solve using purely analytical (pencil and paper) methods, especially for realistic industrial problems. This course introduces finite difference methods for three key classes of partial differential equations: elliptic (Poisson equation), parabolic (heat equation) and hyperbolic (transport equation). The course also covers direct and iterative methods used for solving linear systems that arise in finite difference methods, initial value problems, two-point boundary value problems, and provides an overview of some relevant topics in scientific computing.

Note: Students must have some prior experience with simple computer programming. Familiarity with Matlab is an advantage.