Synopses & Reviews
This is a lucid account of the highlights in the historical development of the calculus from ancient to modern times from the beginnings of geometry in antiquity to the nonstandard analysis of the twentieth century. It emphasizes the genesis and evolution of both fundamental concepts and computational techniques. The intended audience includes not only students of the history of mathematics, but also the wider mathematical community, specifically those who study, teach and use calculus. Among the distinctive features of this exposition are historically motivated exercises and carefully chosen illustrative examples. Numerous sections of the book are suitable for use in courses in introductory and advanced calculus as well as the general history of mathematics.
Synopsis
The calculus has served for three centuries as the principal quantitative language of Western science. In the course of its genesis and evolution some of the most fundamental problems of mathematics were first con fronted and, through the persistent labors of successive generations, finally resolved. Therefore, the historical development of the calculus holds a special interest for anyone who appreciates the value of a historical perspective in teaching, learning, and enjoying mathematics and its ap plications. My goal in writing this book was to present an account of this development that is accessible, not solely to students of the history of mathematics, but to the wider mathematical community for which my exposition is more specifically intended, including those who study, teach, and use calculus. The scope of this account can be delineated partly by comparison with previous works in the same general area. M. E. Baron's The Origins of the Infinitesimal Calculus (1969) provides an informative and reliable treat ment of the precalculus period up to, but not including (in any detail), the time of Newton and Leibniz, just when the interest and pace of the story begin to quicken and intensify. C. B. Boyer's well-known book (1949, 1959 reprint) met well the goals its author set for it, but it was more ap propriately titled in its original edition-The Concepts of the Calculus than in its reprinting."
Table of Contents
1. Area Number and Limit Concepts in Antiquity; 2. Archimedes; 3. Twilight, Darkness and Dawn; 4. Early Indivisibles and Infinitesimal Techniques; 5. Early Tangent Constructions; 6. Napier's Wonderful Logarithms; 7. The Arithmetic of the Infinite; 8. The Calculus According to Newton; 9. The Calculus According to Leibniz; 10. The Age of Euler; 11. The Calculus According to Cauchy, Riemann and Weierstrass; 12. Postscript: The Twentieth Century; Index