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Calculus

  • John Stillwell
Part of the Undergraduate Texts in Mathematics book series (UTM)

Abstract

Calculus emerged in the seventeenth century as a system of shortcuts to results obtained by the method of exhaustion and as a method for discovering such results. The types of problem for which calculus proved suitable were finding lengths, areas, and volumes of curved figures and determining local properties such as tangents, normals, and curvature—in short, what we now recognize as problems of integration and differentiation. Equivalent problems of course arise in mechanics, where one of the dimensions is time instead of distance, hence it was calculus that made mathematical physics possible—a development we shall consider in Chapter 13. In addition, calculus was intimately connected with the theory of infinite series, initiating developments that became fundamental in number theory, combinatorics, and probability theory.

Keywords

Seventeenth Century Infinite Series Biographical Note Implicit Differentiation Indian Mathematician 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer Science+Business Media New York 2002

Authors and Affiliations

  • John Stillwell
    • 1
  1. 1.Department of MathematicsUniversity of San FranciscoSan FranciscoUSA

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