The Origins Of Cauchy's Rigorous Calculus

by Grabiner, Judith V.

• ISBN13: 9780486438153
• ISBN10: 0486438155
• Format: Paperback
• Copyright: 2011-10-20
• Publisher: Dover Publications

Summary

This text for upper-level undergraduates and graduate students examines the events that led to a 19th-century intellectual revolution: the reinterpretation of the calculus undertaken by Augustin-Louis Cauchy and his peers. These intellectuals transformed the uses of calculus from problem-solving methods into a collection of well-defined theorems about limits, continuity, series, derivatives, and integrals. 1981 edition.

Table of Contents

Preface	viii
Abbreviations of Titles	x
Introduction	1	(4)
1 Cauchy and the Nineteenth-Century Revolution in Calculus	5	(11)
2 The Status of Foundations in Eighteenth-Century Calculus	16	(31)
3 The Algebraic Background of Cauchy's New Analysis	47	(30)
4 The Origins of the Basic Concepts of Cauchy's Analysis: Limit, Continuity, Convergence	77	(37)
5 The Origins of Cauchy's Theory of the Derivative	114	(26)
6 The Origins of Cauchy's Theory of the Definite Integral	140	(24)
Conclusion	164	(3)
Appendix: Translations from Cauchy's Oeuvres	167	(9)
Notes	176	(49)
References	225	(16)
Index	241