Master's Theses

Department

Math

Degree Name

Master of Science (MS)

Abstract

The purpose of this thesis is to follow the development of the asymptotic series from the beginning made by Euler, in his solution of problems, to the modern applications of asymptotic series, also to present a definition and an analysis of asymptotic series, explain some different theories of their use, and show the ways in which they find common usage. The use of asymptotic series is a comparative new development in the field of applied mathematics. The divergent series were not used as a method of calculation until Euler showed that they gave close approximations in the solution of problems. The study is of interest because of the number of applied uses we have for asymptotic series. These applications are used in many fields of scientific research. The ways in which an asymptotic series solution may be derived for a problem are fascinating because of the ingenuity by which they are set up. The material was taken from works on the theory and the applied use of asymptotic series, and from correspondence with the Engineering Department of the General Electric Company, Schenectady, New York.

Keywords

Euler's summation formula, Stoke's asymptotic expression, Bessel's equation, Fourier's series, Asymptotic expansions, Mathematics

Advisor

Dr. Edward E. Colyer

Date of Award

Spring 1939

Document Type

Thesis

Rights

© The Author(s)

Comments

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