Complex Integrals and Series

This chapter introduces the complex integral theorems. Despite their simplicity, these theorems are incredibly powerful and establish the basis of complex techniques in applied mathematics. Using analytic continuation, the chapter shows how these theorems can be used to evaluate some of the frequent...

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Bibliographic Details
Published in:Mathematical Methods in Science and Engineering p. 1
Main Author: Bayin, Selcuk S
Format: Book Chapter
Language:English
Published: United States John Wiley & Sons 2018
John Wiley & Sons, Incorporated
John Wiley & Sons, Inc
Edition:2nd Edition
Subjects:
analytic continuation
applied mathematics
beta function
complex integral representations
complex integral theorems
Engineering Principles
General Engineering & Project Administration
harmonic functions
Laurent series
residue theorem
Taylor series
ISBN:9781119425397, 1119425395
Online Access:Get full text
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Summary:This chapter introduces the complex integral theorems. Despite their simplicity, these theorems are incredibly powerful and establish the basis of complex techniques in applied mathematics. Using analytic continuation, the chapter shows how these theorems can be used to evaluate some of the frequently encountered definite integrals in science and engineering. When discussing harmonic functions and mappings, one saw that analytic functions have very interesting properties. It is for this reason that it is very important to determine the region where a function is analytic and, if possible, to extend this region to other parts of the z‐plane. In conjunction with the discussion of definite integrals, the chapter also introduces the gamma and the beta functions, which frequently appear in applications. It further introduces complex power series, that is, the Taylor and the Laurent series and discusses classification of singular points. Finally, the chapter explains the integral representations of special functions.
ISBN:9781119425397
1119425395
DOI:10.1002/9781119425465.ch12