# Gwybodaeth Modiwlau

Module Identifier
MP26020
Module Title
Mathematical Physics
2013/2014
Co-ordinator
Semester
Semester 1
Pre-Requisite
MA10020 or MT10020; and successful completion of Part 1.
Other Staff

#### Course Delivery

Delivery Type Delivery length / details
Lecture 22 x 1-hour lectures
Practical 11 x 2-hour practicals

#### Assessment

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:

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 solve physical problems in 3-dimensional space.

Solve line and volume integrals. Apply the Stokes', Green's and divergence theorems.

Apply different methods of solution to various types of differential equations.

Recognise 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.

### 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, 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.