Module Identifier MA34110  
Module Title PARTIAL DIFFERENTIAL EQUATIONS  
Academic Year 2005/2006  
Co-ordinator Dr Joe Hill  
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:
1.   solve simple linear partial differential equations;
2.   illustrate with suitable examples the occurrence of such equations in physics and industry;
3.   interpret the meaning of mathematical solutions of partial differential equations in the appropriate context.

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. Laplace transforms.

Reading Lists

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

Notes

This module is at CQFW Level 6