Module Information
Course Delivery
| Delivery Type | Delivery length / details |
|---|---|
| Lecture | 22 x 1 Hour Lectures |
| Workshop | 11 x 2 Hour Workshops |
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:
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. Apply the Stokes', Green's and divergence theorems.
4. Apply different methods of solution to various 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