Handbook

Partial differential equations (PDEs) provide a natural mathematical description for many phenomena of interest in science and engineering. 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 and finite element methods for elliptic and parabolic PDEs, and discusses key concepts such as stability, convergence and computational cost. Relevant techniques in numerical 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. This component of the course is supported by a weekly computer lab. In addition, a weekly tutorial class provides exercises on the mathematical content covered in lectures.

The course is intended for students in mathematics programs, or students in science and engineering programs who have a strong mathematical background and an interest in computer modelling.

Note: Students must have prior experience with computer programming using Python, Matlab or Julia. For example, successful completion of an introductory programming course involving one of these three languages should be sufficient.