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Mathematical Treasure: Calculus for America

Author(s): 
Frank J. Swetz (The Pennsylvania State University)

Differential and Integral Calculus (1902), by Virgil Snyder (1869-1950) and John Irwin Hutchinson (1867-1935), was a popular calculus text written for American undergraduate students. Many of the previous texts used in U.S. universities were French or German translations, but a specific series of mathematics books for the American audience was compiled as the “Modern Mathematical Series” and published by the American Book Company. Both of the authors of Differential and Integral Calculus were American mathematicians: Snyder was a recognized algebraic geometer who earned his Ph.D. at Göttingen with Felix Klein, and Hutchinson was a number theorist and one of the first to receive a Ph.D. in mathematics from the University of Chicago.

Title Page of Differential and Integral Calculus, 1902, by Snyder and Hutchinson

Information page for The Modern Mathematical Series, published by the American Book Company

The form and format of this calculus text helped establish the standards followed in the writing of modern calculus and other university texts. In the “Preface,” the authors explained their writing strategy:

First page of Preface to Differential and Integral Calculus, 1902, by Snyder and Hutchinson

Second page of Preface to Differential and Integral Calculus, 1902, by Snyder and Hutchinson

Third page of Preface to Differential and Integral Calculus, 1902, by Snyder and Hutchinson

Integration was introduced directly as the inverse operation of differentiation. After much practice in integration by recognizing antiderivatives, the following chapter discusses the “area under a curve” approach to understanding integration.

First page of chapter on integration from Differential and Integral Calculus, 1902, by Snyder and Hutchinson

Second page of chapter on integration from Differential and Integral Calculus, 1902, by Snyder and Hutchinson

These images were obtained through the courtesy of the University of California’s Digital Library. The book may be viewed in its entirety in the Internet Archive.

Index to Mathematical Treasures

Frank J. Swetz (The Pennsylvania State University), "Mathematical Treasure: Calculus for America," Convergence (March 2018)

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