Catalogue


Cauchy and the creation of complex function theory /
Frank Smithies.
imprint
Cambridge ; New York : Cambridge University Press, 1997.
description
216 p.
ISBN
052159278X (hardcover)
format(s)
Book
Holdings
More Details
imprint
Cambridge ; New York : Cambridge University Press, 1997.
isbn
052159278X (hardcover)
catalogue key
1575586
 
Includes bibliographical references and index.
A Look Inside
Full Text Reviews
Appeared in Choice on 1998-11:
Augustin Cauchy generally is credited as the creator of complex analysis. Smithies examines the stages of Cauchy's ideas as he worked in isolation during 1814-31, expanding the ideas of his predecessors and refining his own ideas. In chapter 1, Smithies establishes as context the initial contributions to complex function theory by d'Alembert, Euler, Laplace, and Poisson. Fundamental ideas proffered are the uses of functions of a complex variable, integration round a closed curve (later known as the Cauchy-Riemann equations), and the method of imaginary substitutions for the evaluation of definite integrals. In later chapters, the author carefully examines Cauchy's contributions, beginning with his 1814 memoir on definite integrals (published in 1827) and concluding with his two Turin memoirs in 1831. Cauchy's contributions include definite integrals between imaginary limits, the calculus of residues, convergence of the Maclaurin series of a function, power-series expansion for implicit functions, and the residue theorem for general simple closed contours. In a final chapter, Smithies surveys the development of Cauchy's ideas (the lapses, the steps forward, and the refinements), with an evaluation of his contributions in the context of modern complex function theory. Complemented by a useful list of references, this scholarly work is recommended for upper-division undergraduates through researchers and historians of mathematics. J. Johnson; Western Washington University
Reviews
Review Quotes
‘This book is a welcome contribution to the history of mathematical ideas. It is carefully written … in the case of a great mathematician of the first half of the nineteenth century, it is very useful to have a book analyzing his ideas. Smithie’s book helps us understand the technical achievements of Cauchy in founding the theory of complex functions.’The Mathematical Gazette
‘This exemplary book is the first thorough and comprehensive presentation of Cauchy’s creation between 1814 and 1831, of complex function theory … the papers form a diary that testifies to the gradual development of a new field in the mind of an outstanding mathematician.’D. Laugwitz, Darmstadt
"...this scholarly work is recommended for upper-division undergraduates through researchers and historians of mathematics." Choice
Review of the hardback: 'This exemplary book is the first thorough and comprehensive presentation of Cauchy's creation between 1814 and 1831, of complex function theory ... the papers form a diary that testifies to the gradual development of a new field in the mind of an outstanding mathematician.' D. Laugwitz, Darmstadt
"This book is a welcome addition to the literature." Mathematical Reviews
'This book is a welcome contribution to the history of mathematical ideas. It is carefully written ... in the case of a great mathematician of the first half of the nineteenth century, it is very useful to have a book analyzing his ideas. Smithie's book helps us understand the technical achievements of Cauchy in founding the theory of complex functions.' The Mathematical Gazette
'This exemplary book is the first thorough and comprehensive presentation of Cauchy's creation between 1814 and 1831, of complex function theory ... the papers form a diary that testifies to the gradual development of a new field in the mind of an outstanding mathematician.'D. Laugwitz, Darmstadt
‘ … new light is thrown on Cauchy’s thinking.’L’Enseignment Mathématique
Review of the hardback: ' ... an invaluable guide to anyone interested in the work of a great mathematician'. Jeremy Gray, The Open University
Review of the hardback: '... a unique source not only for the historians of mathematics but to all who are fascinated by the beauty of the complex function theory.' European Mathematical Society
'This exemplary book is the first thorough and comprehensive presentation of Cauchy's creation between 1814 and 1831, of complex function theory ... the papers form a diary that testifies to the gradual development of a new field in the mind of an outstanding mathematician.' D. Laugwitz, Darmstadt
'This book is a welcome contribution to the history of mathematical ideas. It is carefully written ... in the case of a great mathematician of the first half of the nineteenth century, it is very useful to have a book analyzing his ideas. Smithie's book helps us understand the technical achievements of Cauchy in founding the theory of complex functions.'The Mathematical Gazette
Review of the hardback: '... new light is thrown on Cauchy's thinking.' L'Enseignment Math matique
Review of the hardback: '... new light is thrown on Cauchy's thinking.' L'Enseignment Mathèmatique
Review of the hardback: 'This book is a welcome contribution to the history of mathematical ideas. It is carefully written ... in the case of a great mathematician of the first half of the nineteenth century, it is very useful to have a book analyzing his ideas. Smithie's book helps us understand the technical achievements of Cauchy in founding the theory of complex functions.' The Mathematical Gazette
' ... a unique source not only for the historians of mathematics but to all who are fascinated by the beauty of the complex function theory.'European Mathematical Society
‘ … a unique source not only for the historians of mathematics but to all who are fascinated by the beauty of the complex function theory.’European Mathematical Society
' ... new light is thrown on Cauchy's thinking.' L'Enseignment Mathèmatique
' ... new light is thrown on Cauchy's thinking.'L'Enseignment Mathématique
' ... an invaluable guide to anyone interested in the work of a great mathematician'.Jeremy Gray, The Open University
' ... an invaluable guide to anyone interested in the work of a great mathematician'. Jeremy Gray, The Open University
‘ … an invaluable guide to anyone interested in the work of a great mathematician’.Jeremy Gray, The Open University
This item was reviewed in:
Choice, November 1998
To find out how to look for other reviews, please see our guides to finding book reviews in the Sciences or Social Sciences and Humanities.
Summaries
Main Description
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.
Main Description
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 is the first to make use of the whole spectrum of available original sources; it will be recognised as the authoritative work on the creation of complex function theory.
Main Description
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.
Description for Library
This authoritative book, describing the birth of the subject of complex analysis and the work of its creator, is the first to make use of the whole spectrum of available original sources. Dr Smithies' analysis of the process whereby Cauchy created the basic structure of complex analysis, begins by describing the eighteenth century background. He then examines the stages of Cauchy's own work, culminating in the proof of the residue theorem. Controversies associated with the birth of the subject are also considered in detail. Throughout, new light is thrown on Cauchy's thinking during this watershed period.
Description for Bookstore
Dr Smithies' analysis of the process whereby Cauchy created the basic structure of complex analysis, begins by describing the 18th century background. He then proceeds to examine the stages of Cauchy's own work, culminating in the proof of the residue theorem. Controversies associated with the the birth of the subject are also considered in detail. Throughout, new light is thrown on Cauchy's thinking during this watershed period. This authoritative book is the first to make use of the whole spectrum of available original sources.
Bowker Data Service Summary
Between 1814 and 1831, French mathematician A.L. Cauchy created practically single-handedly a new branch of pure mathematics. In this volume, Frank Smithies analyses the process whereby Cauchy created the basic structure of complex function theory.
Description for Bookstore
Dr Smithies analyses the process whereby Cauchy created one of the most important branch of mathematics discovered in the nineteenth century. It is the first book to make use of the whole spectrum of available original sources, and will be recognised as the authoritative work on the creation of complex function theory.
Table of Contents
Introduction
The background to Cauchy's work on complex function theory
Cauchy's 1814 memoir on definite integrals
Miscellaneous contributions (1815-1825)
The 1825 memoir and associated papers
The calculus of residues
The Lagrange series and the Turin memoirs
Summary and conclusions
References
Table of Contents provided by Publisher. All Rights Reserved.

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