# DEGREE REGULATIONS & PROGRAMMES OF STUDY 2012/2013

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# Undergraduate Course: Asymptotic Methods (MATH11026)

 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.
 Pre-requisites Students MUST have passed: Complex Variable & Differential Equations (MATH10033) AND Pure & Applied Analysis (MATH10008) Co-requisites Prohibited Combinations Other requirements None Additional Costs None
 Pre-requisites None Displayed in Visiting Students Prospectus? Yes
 Not being delivered
 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.
 Degree Examination: 100%
 None
 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
 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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