Complex Integration And Cauchy's Theorem (1914) - Tapa dura

Watson, G N

9781161724615: Complex Integration And Cauchy's Theorem (1914)

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ISBN 10: 1161724613 ISBN 13: 9781161724615

Editorial: Kessinger Publishing, 2010

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Complex Integration And Cauchy��s Theorem is a mathematical textbook written by G. N. Watson and originally published in 1914. The book focuses on the study of complex analysis and the Cauchy integral theorem, which is a fundamental concept in this field. The text is divided into three parts, with the first part introducing the basic principles of complex analysis, including complex functions, differentiation, and integration. The second part delves deeper into the Cauchy integral theorem and its various applications, such as the residue theorem and the argument principle. The third and final part of the book covers more advanced topics, such as the theory of entire functions and the Riemann mapping theorem. Throughout the book, Watson provides numerous examples and exercises to help readers develop their understanding of the subject matter. This book is considered a classic in the field of complex analysis and is still widely used as a reference by students and researchers in mathematics.This scarce antiquarian book is a facsimile reprint of the old original and may contain some imperfections such as library marks and notations. Because we believe this work is culturally important, we have made it available as part of our commitment for protecting, preserving, and promoting the world's literature in affordable, high quality, modern editions, that are true to their original work.

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Rese�a del editor

This scarce antiquarian book is a facsimile reprint of the original. Due to its age, it may contain imperfections such as marks, notations, marginalia and flawed pages. Because we believe this work is culturally important, we have made it available as part of our commitment for protecting, preserving, and promoting the world's literature in affordable, high quality, modern editions that are true to the original work.

Rese�a del editor

1. TimouGifOUT the tract, wherever it has seemed advisable, for the sake of clearness and brevity, to use the language of geometry, I have not hesitated to do so; but the reader should convince himself that all the arguments employed in Chapters I-IV are really arithmetical arguments, and are not based on geometrical intuitions. Thus, no use is made of the geometrical conception of an angle; when it is necessary to define an angle in Chapter I, a purely analytical definition is given. The fundamental theorems of the arithmetical theory of limits are assumed.
A number of obvious theorems are implicitly left to the reader; e.g. that a circle is a ' simple' curve (the coordinates of any point on x? + if = l may be written x = cost, y=-sut, 0 $ t s$ 2tt) ; that two ' simple' curves with a common end-point, but with no other common point, together form one ' simple' curve ; and several others of a like nature.
It is to be noted that almost all the difficulties, which ari.se in tho

Table of Contents

I Analysis Situs 3; IT Complex Integration 17; III Cauchy's Theorem 30; IV Miscellaneous Theorems 41; V The Calculus of "Residues 46; VI The Evaluation of Definite Integrals 04; VII Expansions in Series 73; VIII Historical Summary 77

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