# Gwybodaeth Modiwlau

Module Identifier
PM26020
Module Title
Mathematical Physics
2020/2021
Co-ordinator
Semester
Semester 1
Mutually Exclusive
Pre-Requisite
PH16210 or MA11210 or (FG16210 or MT11210).
Pre-Requisite
Other Staff

#### Assessment

Due to Covid-19 students should refer to the module Blackboard pages for assessment details

Assessment Type Assessment length / details Proportion
Semester Exam 3 Hours   (Written Examination)  70%
Semester Assessment 2 TESTS  30%
Supplementary Exam 3 Hours   (Written Examination)  100%

### Learning Outcomes

On successful 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 fields, vector algebra and different co-ordinate systems to analyse physical problems in 3-dimensional space.

3. Evaluate line, surface and volume integrals. Recall and apply the Stokes', Green's and divergence theorems including scale factors.

4. Recall and apply different methods of solution tovarious types of differential equations.

5. Classify, analyse and solve second-order partial differential equations in various physical contexts.

6. Describe and explain the concepts of Fourier analysis, convolution and correlation and apply Fourier analysis techniques to problems in physical systems.

### 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.

### Brief description

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

### Content

Vector analysis: scalar and vector triple products, eigenvalues and eigenvectors, 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.

### Notes

This module is at CQFW Level 5