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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Vydáno v:Mathematical Methods in Science and Engineering s. 1
Hlavní autor: Bayin, Selcuk S
Médium: Kapitola
Jazyk:angličtina
Vydáno: United States John Wiley & Sons 2018
John Wiley & Sons, Incorporated
John Wiley & Sons, Inc
Vydání:2nd Edition
Témata:
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
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Obsah:
  • 12.1 Complex Integral Theorems 12.2 Taylor Series 12.3 Laurent Series 12.4 Classification of Singular Points 12.5 Residue Theorem 12.6 Analytic Continuation 12.7 Complex Techniques in Taking Some Definite Integrals 12.8 Gamma and Beta Functions 12.9 Cauchy Principal Value Integral 12.10 Integral Representations of Special Functions Bibliography Problems