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Description
This course is on methods for solving problems involving a small parameter. Such problems arise in almost every branch of mathematics and indeed examples of
asymptotic (or perturbation) problems appear in many earlier undergraduate courses. The basic idea of asymptotic approximation is to exploit the small parameter to replace the original problem by a sequence of simpler problems providing increasingly accurate approximations. The aim of this course is to present in a systematic manner some powerful approximation techniques typically employed in applied areas, with a focus on finding and interpreting solutions rather than providing rigorous proofs.
Three broad classes of asymptotic methods are considered: matched asymptotic expansions, the method of multiple scales, and WKB approximations. The methods are introduced via model problems, such as algebraic and ordinary differential equations, and then applied to problems appearing in applications, which are often expressed in terms of partial differential equations. Examples are taken from a wide range of topics including Fluid Dynamics, Physics, Biomathematics, Financial Mathematics and so on. Prior knowledge in these areas is not necessary as the emphasis in each case is on the asymptotic approximation method rather than the details of the application.
Module deliveries for 2024/25 academic year
Last updated
This module description was last updated on 19th August 2024.
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