Module manager: tbc
Email: tbc
Taught: Semester 1 (Sep to Jan) View Timetable
Year running 2026/27
MATH3300 Methods of Applied Mathematics or equivalent
| MATH3300 | Methods of Applied Mathematics |
| MATH3365 | Mathematical Methods |
| MATH5366 |
MATH5366 Advanced Mathematical Methods
This module is not approved as an Elective
Many problems in mathematics reduce to evaluating a quantity, such as a function at a point, a definite integral, or the solution of an ordinary differential equation. However, beyond a relatively small set of analytically-tractable examples, such quantities are typically evaluated computationally. An alternative is to develop approximations that lead to closed-form expressions for the quantity of interest, and which become increasingly accurate in some limit. This module is about developing such methods and evaluating their performance relative to outputs from computations. These methods are important and widely used in mathematics itself, as well as in subjects such as theoretical physics, fluid dynamics, and mathematical biology.
Students will learn techniques (and underlying theory) for developing approximate solutions of a wide range of problems, typically by identifying and exploiting the presence of a large or small parameter. Such problems might involve the evaluation of integrals (e.g., by Laplace's Method or Watson's Lemma), the solution of ordinary differential equations (e.g., by WKB theory or boundary-layer theory), or analysis of other systems where a dominant balance can be identified. Students will learn how such problems are often motivated by applications in the natural sciences (perhaps involving nonlinearity), and will compare their approximate solutions with those arising from numerical computations.
Subject specific learning outcomes:
On successful completion of the module students will be able to:
develop approximate solutions for a wide range of analytically-intractable problems that arise in mathematics and related sciences.
Identify dominant terms in equations and make appropriate simplifications whilst retaining the essential behaviour of interest.
Understand underlying theory relating to asymptotic approximations.
Evaluate the performance of approximate solutions against those arising from numerical computations.
Skills learning outcomes:
On successful completion of the module students will have demonstrated the following skills:
Critical thinking.
Problem solving and analytical skills.
Creativity.
Technical/IT skills.
Systems thinking.
Time management.
Fundamentals of asymptotics (e.g., ordered expansions, limits, dominant balance).
Approximation of integrals (e.g., Laplace's Method, Watson's Lemma, method of stationary phase, numerical techniques).
Advanced techniques for ordinary differential equations (e.g., method of multiple scales, WKB theory, numerical techniques).
Application to physically-motivated problems including nonlinearity.
Comparison between theory and computational results.
Additional topics that build on these may be covered as time allows. Such topics may be drawn from the following, or similar:
Advanced techniques for partial differential equations.
Techniques for difference equations.
Advanced asymptotics (accelerated convergence, optimal truncation).
Advanced numerical methods.
| Delivery type | Number | Length hours | Student hours |
|---|---|---|---|
| Lecture | 33 | 1 | 33 |
| Private study hours | 117 | ||
| Total Contact hours | 33 | ||
| Total hours (100hr per 10 credits) | 150 | ||
117
Formative feedback will be provided on regular example sets or other similar learning activity.
Check the module area in Minerva for your reading list
Last updated: 12/05/2026
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