Module overview
Aims and Objectives
Learning Outcomes
Learning Outcomes
Having successfully completed this module you will be able to:
- Understand how integral transforms can be used to solve a variety of differential equations
- Be confident in the use of complex variable theory and contour integration
- Be able to demonstrate knowledge of a range of applications of these methods
Syllabus
Analyticity of complex functions; Taylor and Laurent series
Contour integration of functions and multifunctions
Integration contours, including semi-circles, segments, box contours and keyhole contours
Use of complex methods for evaluation of real integrals
Fourier transforms and their applications to PDEs
Fourier sine and cosine transforms and their applications to PDEs
Laplace transforms and inverse Laplace transforms
Hankel transforms, relation to Fourier transforms in 2D, and applications
Derivation of Green's functions for some classic PDEs from integral transforms and the convolution theorem.
Learning and Teaching
Teaching and learning methods
Lectures, problem classes
| Type | Hours |
|---|---|
| Independent Study | 102 |
| Teaching | 48 |
| Total study time | 150 |
Assessment
Summative
This is how we’ll formally assess what you have learned in this module.
| Method | Percentage contribution |
|---|---|
| Exam | 60% |
| Coursework | 40% |
Referral
This is how we’ll assess you if you don’t meet the criteria to pass this module.
| Method | Percentage contribution |
|---|---|
| Exam | 100% |
Repeat
An internal repeat is where you take all of your modules again, including any you passed. An external repeat is where you only re-take the modules you failed.
| Method | Percentage contribution |
|---|---|
| Exam | 100% |