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.