Module Identifier MA34110 Module Title PARTIAL DIFFERENTIAL EQUATIONS Academic Year 2000/2001 Co-ordinator Professor A R Davies Semester Semester 1 Pre-Requisite MA20410 , MA20110 Mutually Exclusive MA24110 Course delivery Lecture 19 x 1hour lectures Seminars / Tutorials 3 x 1hour example classes Assessment Exam 2 hour written examination 100% Resit assessment 2 hour written examination 100%

General description
Many mathematical problems arising in the physical sciences, engineering, and technology, may be formulated in terms of partial differential equations. In attempting to solve such problems, one must be aware of the various types of partial differential equation which exist, and of the different boundary conditions associated with each type. These factors determine which method of solution one should use.

Aims
To teach the student how to recognise the type of a partial differential equation, and how to choose and implement an appropriate method of solution.

Learning outcomes
On completion of this module, a student should be able to:

• solve simple linear partial differential equations;
• illustrate with suitable examples the occurrence of such equations in physics and industry;
• interpret the meaning of mathematical solutions of partial differential equations in the appropriate context.

Syllabus
1. EQUATIONS WITH CONSTANT COEFFICIENTS
2. FIRST ORDER EQUATIONS: The method of characteristics
3. SECOND ORDER EQUATIONS: Classification according to type. Canonical forms
4. THE DIFFUSION EQUATION; THE WAVE EQUATION; POISSON'S EQUATION
5. SOLUTION METHODS: Separation of variables. Fourier and Laplace transforms.