Asymptotic Methods (U01873)

? Credit Points : 10 ? SCQF Level : 11 ? Acronym : MAT-4-AMe

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.

Entry Requirements

? Pre-requisites : MAT-3-CVD, MAT-3-PAA

Subject Areas

Home subject area

Specialist Mathematics & Statistics (Honours), (School of Mathematics, Schedule P)

Delivery Information

? Normal year taken : 4th year

? Delivery Period : Semester 2 (Blocks 3-4)

? Contact Teaching Time : 2 hour(s) per week for 11 weeks

All of the following classes

Type	Day	Start	End	Area
Lecture	Tuesday	10:00	10:50	KB
Lecture	Friday	10:00	10:50	KB

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.