The Fundamental Ideas of the Integral and Differential Calculus

Richard Courant and Fritz John
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Richard Courant: New York University, Courant Institute of Mathematical Sciences
Fritz John: New York University, Courant Institute of Mathematical Sciences

Chapter 2 in Introduction to Calculus and Analysis, 1989, pp 119-200 from Springer

Abstract: Abstract The fundamental limiting processes of calculus are integration and differentiation. Isolated instances of these processes of calculus were considered even in antiquity (culminating in the work of Archimedes), and with increasing frequency in the sixteenth and seventeenth centuries. However, the systematic development of calculus, started only in the seventeenth century, is usually credited to the two great pioneers of science, Newton and Leibnitz. The key to this systematic development is the insight that the two processes of differentiation and integration, which had been treated separately, are intimately related by being reciprocal to each other.1

Keywords: Rational Number; Fundamental Theorem; Fundamental Idea; Differential Calculus; Intermediate Point (search for similar items in EconPapers)
Date: 1989
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DOI: 10.1007/978-1-4613-8955-2_2

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