Module Identifier | MA24610 | ||

Module Title | VECTOR CALCULUS | ||

Academic Year | 2000/2001 | ||

Co-ordinator | Dr R S Jones | ||

Semester | Semester 1 | ||

Pre-Requisite | MA11010 , MA11210 | ||

Mutually Exclusive | MX34610 | ||

Course delivery | Lecture | 19 x 1hour lectures | |

Seminars / Tutorials | 3 x 1hour example classes | ||

Assessment | Exam | 2 Hours (written examination) | 100% |

Resit assessment | 2 Hours (written examination) | 100% |

**General 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.

**Learning outcomes**

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

- obtain parametric representation 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.

**Syllabus**

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**

B Spain.
*Vector Analysis*. Van Nostrand
**** Supplementary Text**

M R Spiegel.
*Advanced Calculus*. Schaum

R L Finney & G B Thomas. (1994)
*Calculus*. 2nd edition. Addison-Wesley