Module overview
The solution of differential equations is essential in most mathematical sciences. This module introduces the numerical techniques needed when the problems are not analytically tractable, and the mathematical techniques to analyse the resulting numerical methods.
Aims and Objectives
Learning Outcomes
Learning Outcomes
Having successfully completed this module you will be able to:
- Understand how to solve ordinary differential equations numerically
- Understand how to numerically solve non-linear equations
- Understand how to analyse the accuracy and stability of a numerical method.
- Understand how to numerically integrate
Syllabus
Key motivating examples and recap of first year material
Nonlinear equations
Bisection
Contraction mapping and Newton’s method for functions of one or more variables
Quadrature
Polynomial interpolation and adaptive methods
Gauss quadrature
Initial Value Problems for ODEs
Finite differences. Key methods (eg Euler and variants, Runge-Kutta).
Boundary Value Problems for ODEs
Finite differences
Shooting
Function basis methods
Learning and Teaching
Teaching and learning methods
Lectures, computer labs
| Type | Hours |
|---|---|
| Independent Study | 102 |
| Teaching | 48 |
| Total study time | 150 |
Resources & Reading list
Textbooks
Süli and Mayers. An Introduction to Numerical Analysis.
Sauer. Numerical Analysis.
Kincaid and Cheney. Numerical Analysis.
Burden, Faires and Burden. Numerical Analysis.
Assessment
Summative
This is how we’ll formally assess what you have learned in this module.
| Method | Percentage contribution |
|---|---|
| Coursework | 50% |
| Exam | 50% |
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% |