Module Identifier MP26020
Module Title MATHEMATICAL PHYSICS
Co-ordinator Dr Andrew Evans
Semester Semester 1
Other staff Dr Rudolf Winter
Pre-Requisite Core Physics at Part 1 or MA11210 and MA11010
Course delivery Lecture   22 1-hour lectures
Seminars / Tutorials   11 2-hour workshops
Assessment
Assessment TypeAssessment Length/DetailsProportion
Semester Exam3 Hours written examination  70%
Semester Assessment 4 assignments  30%
Supplementary Exam3 Hours written examination  100%

Learning outcomes

On completion of this module, students should be able to:
1. Express common physical systems and relationships using the mathematical language of vectors, differential equations and Fourier theory;
2. Use vectors, vector algebra and different co-ordinate systems to solve physical problems in 3-dimensional space;
3. Apply different methods of solution to various types of differential equations;
4. Solve simple eigenvalue problems in the physical sciences;
5. Describe and explain the concepts of Fourier analysis, convolution and correlation and apply Fourier analysis techniques to problems in physical systems.

Brief description

This module develops a variety of mathematical theories'rector analysis, differential equations and Fourier analysis'rhich are applied to the modelling of, and solution of problems in, a wide selection of physical situations'rlectrostatics, magnetism, gravitation, mechanics, thermo-dynamics, plasma physics, atmospherics physics and fluid mechanics.

Aims

The module develops a mathematical approach to the modelling of physical systems. It is of fundamental importance for all honours degree schemes in Physics and is appropriate for many honours degree schemes in Mathematics.

Content

Vector analysis: scalar and vector triple products, polar co-ordinates, 3-D scalar and vector fields, gradient, divergence and curl of 3-D fields, vector operators, line integrals, surface integrals.Differential equations: general order ordinary differential equations, simultaneous differential equations, partial differential equations, eigenvalue problems.Fourier analysis: Fourier analysis of signals, complementary parameters (e.g. frequency and time), Fourier transforms, power spectra.