Between 1814 and 1831, the great French mathematician A. L. Cauchy
created practically single-handedly a new branch of pure
mathematics. Complex function theory was and remains of central
importance, and its creation marked the start of one of the most
exciting periods in the development of mathematics. In this book Dr
Smithies analyses the process whereby 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 makes use of the whole spectrum of
available original sources; it will be recognised as the
authoritative work on the creation of complex function theory.
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