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:

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.

Reading Lists
Books
** Recommended Text
G F Carrier and C E Pearson. Partial Differential Equations. 2nd. Academic Press
P Duchateau and D W Zachman. Partial Differential Equations. Schaum's Outline Series, McGraw-Hill
** Supplementary Text
K E Gustafson. Introduction to Partial Differential Equations. 2nd. John Wiley