Preprint Review Version 1 Preserved in Portico This version is not peer-reviewed

Asymptotic Methods

Version 1 : Received: 7 September 2021 / Approved: 8 September 2021 / Online: 8 September 2021 (11:20:28 CEST)

How to cite: Fellah, M.A. Asymptotic Methods. Preprints 2021, 2021090141 (doi: 10.20944/preprints202109.0141.v1). Fellah, M.A. Asymptotic Methods. Preprints 2021, 2021090141 (doi: 10.20944/preprints202109.0141.v1).

Abstract

In this lecture notes, we will introduce Asymptotics, then we will give a short glimpse on Perturbation theory (regular versus singular), which plays a crucial role especially in theoretical physics. Our goal is to find Asymptotic series that approximates the values of integrals depending on some parameter or the solutions of differential equations. These methods that lead to obtain more effective algorithms of numerical evaluation are called: Asymptotic Methods.

Keywords

Regular & Singular Perturbations; WKB Method; Watson's Lemma, Laplace's Method

Subject

MATHEMATICS & COMPUTER SCIENCE, Applied Mathematics

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