Module Identifier MX34610 Module Title VECTOR CALCULUS Academic Year 2001/2002 Co-ordinator Dr R 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 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 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.

#### 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.