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

Watson, G N

9781164056706: Complex Integration And Cauchy's Theorem (1914)

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ISBN 10: 1164056700 ISBN 13: 9781164056706

Editorial: Kessinger Publishing, 2010

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Complex Integration And Cauchy��s Theorem is a book written by G. N. Watson and first published in 1914. It is a comprehensive and detailed treatment of the theory of complex integration and Cauchy's theorem, which are important topics in complex analysis. The book is divided into three parts, each of which covers a different aspect of the theory. The first part of the book deals with the basic concepts of complex analysis, including the definition of complex numbers, the Cauchy-Riemann equations, and the properties of analytic functions. The second part of the book focuses on the theory of complex integration, including contour integration, Cauchy's theorem, and the Cauchy integral formula. The third and final part of the book covers advanced topics in complex analysis, including the theory of entire functions, the Riemann mapping theorem, and the theory of conformal mapping.Throughout the book, Watson provides clear and concise explanations of the theory, along with numerous examples and exercises to help readers understand and apply the concepts. The book is written for advanced undergraduate and graduate students in mathematics, as well as researchers and professionals in the field of complex analysis. Despite being over a century old, Complex Integration And Cauchy��s Theorem remains a valuable resource for anyone interested in the theory of complex analysis.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 selection from Kessinger Publishing's Legacy Reprint Series. 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 to protecting, preserving, and promoting the world's literature. Kessinger Publishing is the place to find hundreds of thousands of rare and hard-to-find books with something of interest for everyone!

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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