Module manager: Mark Dowker
Email: M.D.Dowker@leeds.ac.uk
Taught: Semesters 1 & 2 (Sep to Jun) View Timetable
Year running 2025/26
CAPE2000
This module is not approved as a discovery module
This module will introduce mathematical techniques required for modelling engineering phenomena; Power series, Fourier series, vector calculus, PDEs, numerical methods required to solve complex problems; and fundamental statistical tools that are used widely in practice.
On completion of the course, students should be able to:
- Understand series, vector calculus, numerical methods, statistics in a variety of contexts.
- Apply vector calculus, Laplace transforms and series techniques to solve differential equations.
- Apply line, surface and volume integrals in context.
- Evaluate real life problems, and create mathematical representations (models), then solve them using learned mathematical techniques.
- Create computational models to solve IVPs and differential equations using numerical methods.
- Apply statistical tools to analyse, interpret and represent data.
On successful completion of the module students will have demonstrated the following learning outcomes relevant to the subject:
1. Have a knowledge and understanding of mathematics necessary for the analysis of, and to support applications of, key engineering principles and processes.
2. Be familiar with the application and limitations of a range of modelling approaches including first-principles models, and simple empirical correlations.
3. Be competent in the use of numerical and computer methods for solving engineering problems.
4. Have knowledge of the fundamental statistical tools applicable for the analysis of data and used in practice.
Skills Learning Outcomes
On successful completion of the module students will have demonstrated the following skills:
A) Problem solving
B) Technical and analytical skills
C) Setting up mathematical models
D) Applying numerical methods computationally
Power and Fourier series; Gradients and divergence differential operators; Curl differential operator and scalar potential; Line, surface and volume integrals, PDEs, Laplace Transforms; Numerical integration; Approximate solution of algebraic equation; Initial value problems; Numerical solutions of IVPs; Linearization. Summary statistics; Probability distributions (Discrete and Continuous); Binomial distribution; Poisson distribution; Normal distribution. Sampling: distribution (mean and variance); One and two sample confidence intervals (mean, standard deviation/variance). Practical applications of the techniques.
Methods of assessment
The assessment details for this module will be provided at the start of the academic year
| Delivery type | Number | Length hours | Student hours |
|---|---|---|---|
| Lecture | 22 | 2 | 44 |
| Practical | 3 | 2 | 6 |
| Seminar | 19 | 1 | 19 |
| Private study hours | 131 | ||
| Total Contact hours | 69 | ||
| Total hours (100hr per 10 credits) | 200 | ||
The reading list is available from the Library website
Last updated: 30/04/2025
Errors, omissions, failed links etc should be notified to the Catalogue Team