First Advisor

Bin Jiang

Date of Award

5-15-2020

Document Type

Thesis

Degree Name

Bachelor of Science (B.S.) in Mathematics and University Honors

Department

Mathematics and Statistics

Language

English

Subjects

Laurent series, Integrals, Singularities (Mathematics), Curves

DOI

10.15760/honors.858

Abstract

The Laurent expansion is a well-known topic in complex analysis for its application in obtaining residues of complex functions around their singularities. Computing the Laurent series of a function around its singularities turns out to be an efficient way to determine the residue of the function as well as to compute the integral of the function along any closed curves around its singularities. Based on the theory of the Laurent series, this paper provides several working examples where the Laurent series of a function is determined and then used to calculate the integral of the function along any closed curve around the singularities of the function. A brief description of the Frobenius method in solving ordinary differential equations is also provided.

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Persistent Identifier

https://archives.pdx.edu/ds/psu/32870

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