Enhanced descriptions from Syndetics:

. . . that departed from the traditional dry-as-dust mathematics textbook. (M. Kline, from the Preface to the paperback edition of Kline 1972) Also for this reason, I have taken the trouble to make a great number of drawings. (Brieskom & Knorrer, Plane algebraic curves, p. ii) . . . I should like to bring up again for emphasis . . . points, in which my exposition differs especially from the customary presentation in the text­ books: 1. Illustration of abstract considerations by means of figures. 2. Emphasis upon its relation to neighboring fields, such as calculus of dif­ ferences and interpolation . . . 3. Emphasis upon historical growth. It seems to me extremely important that precisely the prospective teacher should take account of all of these. (F. Klein 1908, Eng\. ed. p. 236) Traditionally, a rigorous first course in Analysis progresses (more or less) in the following order: limits, sets, '* continuous '* derivatives '* integration. mappings functions On the other hand, the historical development of these subjects occurred in reverse order: Archimedes Cantor 1875 Cauchy 1821 Newton 1665 . ;::: Kepler 1615 Dedekind . ;::: Weierstrass . ;::: Leibniz 1675 Fermat 1638 In this book, with the four chapters Chapter I. Introduction to Analysis of the Infinite Chapter II. Differential and Integral Calculus Chapter III. Foundations of Classical Analysis Chapter IV. Calculus in Several Variables, we attempt to restore the historical order, and begin in Chapter I with Cardano, Descartes, Newton, and Euler's famous Introductio.

Table of contents provided by Syndetics

• Introduction to Analysis of the Infinite
• Differential and Integral Calculus
• Foundations of Classical Analysis
• Calculus in Several Variables
• Appendix
• References
• Symbol Index
• Index

Reviews provided by Syndetics

CHOICE Review

It is said that ontogeny recapitulates phylogeny; if so, this book should be an invaluable resource for the serious student of the calculus. Hairer and Wanner present the techniques of first-year calculus in roughly the order in which they were developed. From the ancient origins of infinite series to the rigorous treatment of multivariable calculus in the 19th century, the authors have chronicled the history of the calculus with a rich collection of figures, period mathematical calculations, and quotations (an appendix includes all original quotes). An extensive bibliography of original sources is also included in the text. Although this book would be too rich a mathematical diet for the typical undergraduate, it would be an excellent choice for use in a senior capstone course or for any student of the history of mathematics. The book complements other offerings in the area, such as Charles Henry Edward's The Historical Development of the Calculus (CH, Oct'80); Margaret E. Baron's The Origins of the Infinitesimal Calculus (1969); and others. Upper-division undergraduate through faculty. R. L. Pour Emory and Henry College