MA24610 - VECTOR CALCULUS

Module Identifier	MA24610
Module Title	VECTOR CALCULUS
Academic Year	2002/2003
Co-ordinator	Rowland S Jones
Semester	Semester 1
Pre-Requisite	MA11010 , MA11210
Mutually Exclusive	MX34610
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:

obtain parametric representations of curves and surfaces;
evaluate line, surface and volume integrals;
determine the gradient of a scalar field and the divergence and curl of a vector field;
use curvilinear coordinates and test for orthogonality;
state the integral theorems of Gauss, Green and Stokes and explain their physical significance;
obtain axially and spherically symmetric solutions to Laplace's equation.

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. 2/e. Brooks/Cole 0534377181
** Supplementary Text
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
B Spain. (1965) Vector Analysis. Van Nostrand B6513742