In this book, Dr. Smithies analyzes the process through which Cauchy created the basic structure of complex analysis, describing first the eighteenth century background before proceeding to examine the stages of Cauchy's own work, culminating in the proof of the residue theorem and his work on expansions in power series. Smithies describes how Cauchy overcame difficulties including false starts and contradictions brought about by over-ambitious assumptions, as well as the improvements that came about as the subject developed in Cauchy's hands. Controversies associated with the birth of complex function theory are described in detail. Throughout, new light is thrown on Cauchy's thinking during this watershed period. This book is the first to make use of the whole spectrum of available original sources and will be recognized as the authoritative work on the creation of complex function theory.
Author(s): Frank Smithies
Edition: 1
Publisher: Cambridge University Press
Year: 2008
Language: English
Pages: 224
Contents......Page 7
Introduction......Page 9
1 The background to Cauchy's work on complex function theory......Page 14
2 Cauchy's 1814 memoir on definite integrals......Page 32
3 Miscellaneous contributions (1815-1825)......Page 67
4 The 1825 memoir and associated articles......Page 93
5 The calculus of residues......Page 121
6 The Lagrange series and the Turin memoirs......Page 155
7 Summary and conclusions......Page 194
References......Page 213
Notation index......Page 222
Author index......Page 223
Subject index......Page 224
