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Concepts of Calculus

In: Mathematics Form and Function

Author

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  • Saunders Mac Lane

    (University of Chicago, Department of Mathematics)

Abstract

Many sorts of calculations press themselves upon us. Thus, given a piece of surface, how does one calculate its area? Or, given a section of a curve, how does one calculate its length or the direction of its tangent line at some point? More generally, how does one calculate the rate at which this or that variable quantity is changing with time? The striking discovery (by Newton and Leibniz) that there were systematic methods to calculate all these things, and many more like them, had a major influence on the directions and structure of Mathematics. For a considerable period, more practical calculations of such things tended to dominate conceptual understanding, in a way that emphasizes the observation that Mathematics takes its origin in human activities.

Suggested Citation

  • Saunders Mac Lane, 1986. "Concepts of Calculus," Springer Books, in: Mathematics Form and Function, chapter 0, pages 150-184, Springer.
    • Handle: RePEc:spr:sprchp:978-1-4612-4872-9_7
    DOI: 10.1007/978-1-4612-4872-9_7
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