MA319      Half Unit
Partial Differential Equations

This information is for the 2025/26 session.

Course Convenor

Availability

Requisites

Pre-requisites:

Students must have completed MA203 and MA212 before taking this course.

The aim of the course is the study of  partial differential equations. The focus will be on first order quasilinear equations, and second order linear equations. The method of characteristics for solving first order quasilinear equations will be discussed. The three main types of linear second order partial differential equations will be considered: parabolic (diffusion equation), elliptic (Laplace equation), and hyperbolic (wave equation) and their relation to the classification of conic sections. Techniques for solving these for various initial and boundary value problems on bounded and unbounded domains, using eigenfunction expansions (separation of variables, and elementary Fourier series), and integral transform methods (Fourier and Laplace transforms) will be treated. How to change between polar and Cartesian coordinates will be presented, especially for the solution of Laplacian and Poisson equations. Elementary distributional calculus and the notion of weak solutions will also be considered. Applications and examples will be discussed throughout the course.

20 hours of lectures and 10 hours of classes in the Autumn Term.

Students will be expected to produce 10 problem sets in the AT.

Written answers to set problems will be expected on a weekly basis.

1. S.J. Farlow. Partial Differential Equations for Scientists and Engineers. Dover, 1993.
2. J.D. Logan. Applied Partial Differential Equations. Second Edition. Springer, 2004.
3. W. Strauss. Partial Differential Equations. An Introduction. Second Edition. John Wiley, 2008.

Lecture notes will be provided.

Exam (100%), duration: 120 Minutes in the Spring exam period