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.