# Gwybodaeth Modiwlau

Module Identifier
PM26020
Module Title
Mathematical Physics
2024/2025
Co-ordinator
Semester
Semester 1
Pre-Requisite
Pre-Requisite
Other Staff

#### Assessment

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

### Learning Outcomes

On successful completion of this module students should be able to:

Express common physical systems and relationships using the mathematical language of vectors, differential equations and Fourier theory.

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

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

Recall and apply different methods of solution to various types of differential equations.

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

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: 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.

### 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, 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.

### Module Skills

Skills Type Skills details
Adaptability and resilience Students will need to manage their time during the weekly workshops.
Co-ordinating with others Students are encouraged to work together during the workshops.
Creative Problem Solving This module is about mathematical problem solving. The worksheets consist of problem-solving exercises.
Critical and analytical thinking Students are trained in analysing problems in Physics and Mathematics.
Digital capability Students are encouraged to read around the subject via online resources.
Professional communication Students are encouraged to work together in a professional manner during workshops.
Real world sense Problems in the worksheets are inspired by real-life applications.
Subject Specific Skills Investigative skills: students are encouraged to research around the subject. The mathematical techniques taught in this module are core for Physics and Mathematics.

### Notes

This module is at CQFW Level 5