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The Origins of Cauchy's Rigorous Calculus
by Judith V. Grabiner
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.
Table of Contents for The Origins of Cauchy's Rigorous Calculus
| 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 |
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