Module Identifier MA34110  
Module Title PARTIAL DIFFERENTIAL EQUATIONS  
Academic Year 2001/2002  
Co-ordinator Professor Arthur 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 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. (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