Concepts of Calculus

Saunders Mac Lane
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Saunders Mac Lane: University of Chicago, Department of Mathematics

Chapter Chapter VI in Mathematics Form and Function, 1986, pp 150-184 from Springer

Abstract: 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.

Keywords: Differential Form; Tangent Line; Fundamental Theorem; Chain Rule; Instantaneous Rate (search for similar items in EconPapers)
Date: 1986
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DOI: 10.1007/978-1-4612-4872-9_7

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