Undergraduate Course: Asymptotic Methods (MATH11026)
Course Outline
| School | School of Mathematics |
College | College of Science and Engineering |
| Credit level (Normal year taken) | SCQF Level 11 (Year 4 Undergraduate) |
Availability | Available to all students |
| SCQF Credits | 10 |
ECTS Credits | 5 |
| Summary | Course for final year students in Honours programmes in Mathematics.
Algebraic equations, eigenvalue problems. Asymptotic expansion: definitions and notations. Asymptotic methods for integrals. Asymptotics of sums: Euler-McLaurin formula. Matched asymptotics for differential equations. |
| Course description |
Not entered
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Information for Visiting Students
| Pre-requisites | None |
Course Delivery Information
| Not being delivered |
Learning Outcomes
1. Recognise the practical value of small or large parameters for the evaluation of mathematical expressions.
2. Understand the concept of (divergent) asymptotic series, and distinguish regular and singular perturbation problems.
3. Find dominant balances in algebraic and differential equations with a small parameter.
4. Compute leading-order approximations of integrals with a small parameter.
5. In simple cases, find complete asymptotic expansions of integrals.
6. Know the Euler-McLaurin formula and be able to use it for the evaluation of sums.
7. Identify boundary layers in the solutions of differential equations, and apply matched asymptotics to derive leading-order approximations to the solutions.
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Contacts
| Course organiser | Prof Jim Wright
Tel: (0131 6)50 8570
Email: |
Course secretary | Mrs Alison Fairgrieve
Tel: (0131 6)50 5045
Email: |
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