Complex Integration And Cauchy's Theorem (1914) - Hardcover

Watson, G N

9781168990808: Complex Integration And Cauchy's Theorem (1914)

Hardcover

ISBN 10: 1168990807 ISBN 13: 9781168990808

Verlag: Kessinger Publishing, 2010

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Complex Integration And Cauchy��s Theorem is a mathematical treatise authored by G. N. Watson and originally published in 1914. The book explores the theory of complex integration and its applications to various mathematical problems. The text begins with an introduction to complex numbers and their properties, followed by a discussion of complex functions and their derivatives. The main focus of the book is on Cauchy's theorem, which states that a function that is analytic within a closed contour can be integrated along that contour to give a value of zero. The author then goes on to explore various applications of the theorem, including the evaluation of integrals and the solution of differential equations. The book is written in a clear and concise style, with numerous examples and exercises to help readers understand the material. It is a classic text in the field of complex analysis and is still widely used by mathematicians today.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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