Items related to Complex Integration and Cauchy's Theorem (Classic...
Synopsis
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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Book Description
Originally published in 1914 as number fifteen in the Cambridge Tracts in Mathematics and Mathematical Physics series, this book provides a concise proof of Cauchy's Theorem, along with some applications of the theorem to the evaluation of definite integrals.
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