Module Identifier MX34610  
Module Title VECTOR CALCULUS  
Academic Year 2002/2003  
Co-ordinator Rowland S Jones  
Semester Semester 1  
Pre-Requisite MA11010 , MA11210  
Mutually Exclusive MA24610  
Course delivery Seminars / Tutorials   3 x 1 hour example classes  
  Lecture   19 x 1 hour lectures  
Assessment Semester Exam   2 Hours (written examination)   100%  
  Supplementary Assessment   2 Hours (written examination)   100%  

Learning outcomes

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

Brief description

This module provides the mathematical framework necessary for the understanding of classical field theory and in particular hydrodynamics.

Aims

To introduce the mathematical concepts required for an understanding of classical field theory.

Content

1. Parametric representation of lines and surfaces;
2. Line, surface and volume integrals;
3. Vector and scalar fields; definitions of grad, div and curl;
4. Curvilinear coordinates, test for orthogonality;
5. Integral theorems of Gauss, Green and Stokes;
6. Harmonic functions and uniqueness theorems;
7. Laplace's equation in cylindrical and spherical polar coordinates, axially and spherically symmetric solutions.

Reading Lists

Books
** Recommended Text
J Stewart. (2001) Calculus: concepts and contexts. 2nd edition. Brooks/Cole 0534377181
** Supplementary Text
B Spain. (1965) Vector Analysis. Van Nostrand B6513742
M R Spiegel. (1974) Schaum's outline of theory and problems of advanced calculus. McGraw-Hill 0070843805
R L Finney & G B Thomas. (1994) Calculus. 2nd. Addison-Wesley 0201549778