Undergraduate Course: Asymptotic Methods (MATH11026)
Course Outline
| School | School of Mathematics |
College | College of Science and Engineering |
| Course type | Standard |
Availability | Available to all students |
| Credit level (Normal year taken) | SCQF Level 11 (Year 4 Undergraduate) |
Credits | 10 |
| Home subject area | Mathematics |
Other subject area | Specialist Mathematics & Statistics (Honours) |
| Course website |
https://info.maths.ed.ac.uk/teaching.html |
Taught in Gaelic? | No |
| Course description | 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. |
Information for Visiting Students
| Pre-requisites | None |
| Displayed in Visiting Students Prospectus? | Yes |
Course Delivery Information
| Not being delivered |
Summary of Intended 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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Assessment Information
Degree Examination: 100%
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Special Arrangements
| None |
Additional Information
| Academic description |
Not entered |
| Syllabus |
Not entered |
| Transferable skills |
Not entered |
| Reading list |
Not entered |
| Study Abroad |
Not entered |
| Study Pattern |
Not entered |
| Keywords | AMe |
Contacts
| Course organiser | Prof Jim Wright
Tel: (0131 6)50 8570
Email: J.R.Wright@ed.ac.uk |
Course secretary | Mrs Alison Fairgrieve
Tel: (0131 6)50 5045
Email: Alison.Fairgrieve@ed.ac.uk |
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