MX34610 - VECTOR CALCULUS

Module Identifier

MX34610

Module Title

VECTOR CALCULUS

Academic Year

2003/2004

Co-ordinator

Dr R S Jones

Semester

Semester 1

Pre-Requisite

MA11010 , MA11210

Mutually Exclusive

MA24610

Course delivery

Lecture

19 x 1 hour lectures

Seminars / Tutorials

3 x 1 hour example classes

Assessment

Assessment Type	Assessment Length/Details	Proportion
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 2nd edition. 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
Salas, Hille and Ergen (2003) Calculus 9th ed. Wiley 0471383759

Notes

This module is at CQFW Level 6