The Origins of Cauchy's Rigorous Calculus

by Judith V. Grabiner

Overview

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. Beginning with a survey of the characteristic 19th-century view of analysis, the book proceeds to an examination of the 18th-century concept of calculus and focuses on the innovative methods of Cauchy and his contemporaries in refining existing methods into the basis of rigorous calculus. 1981 edition.

Product Details

ISBN-13:	9780486438153
Publisher:	Dover Publications
Publication date:	10/20/2011
Series:	Dover Books on Mathematics Series
Pages:	272
Product dimensions:	6.14(w) x 9.21(h) x (d)

Table of Contents

1. Cauchy and the Nineteenth-Century Revolution in Calculus
2. The Status of Foundations in Eighteenth-Century Calculus
3. The Algebraic Background of Cauchy’s New Analysis
4. The Origins of the Basic Concepts of Cauchy’s Analysis: Limit, Continuity, Convergence
5. The Origins of Cauchy’s Theory of the Derivative
6. The Origins of Cauchy’s Theory of the Definite Integral
Appendix
Index