Module Identifier MA34110  
Module Title PARTIAL DIFFERENTIAL EQUATIONS  
Academic Year 2003/2004  
Co-ordinator Professor Russell Davies  
Semester Semester 1  
Pre-Requisite MA20110 , MA21410  
Course delivery Lecture   19 x 1 hour lectures  
  Seminars / Tutorials   3 x 1 hour example classes  
Assessment
Assessment TypeAssessment Length/DetailsProportion
Semester Exam2 Hours  100%
Supplementary Assessment2 Hours  100%

Learning outcomes

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

Brief 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.

Content

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 (1988) Partial Differential Equations 2nd. Academic Press 0121604519
P Du Chateau and D W Zachmann (1986) Schaum's outline of theory and problems of partial differential equations McGraw-Hill 0070178976
** Supplementary Text
K E Gustafson (1987) Introduction to Partial Differential Equations 2nd. John Wiley 0471832278

Notes

This module is at CQFW Level 6