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). Related methods in computational linear algebra are also discussed.

The course includes a substantial practical component dealing with the computer implementation of the algorithms used for solving partial differential equations, as well as a broader discussion of scientific software development.

Note:Students must have some previous experience with simple computer programming.