The Fundamental Ideas of the Differential and Integral Calculus

Mariano Giaquinta and Giuseppe Modica
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Mariano Giaquinta: Scuola Normale Superiore
Giuseppe Modica: Università degli Studi di Firenze, Facoltà di Ingegneria

Chapter 3 in Mathematical Analysis, 2003, pp 93-144 from Springer

Abstract: Abstract In this chapter we introduce the two basic notions of calculus: the notion of derivative and the one of integral; we shall then discuss a few simple but relevant results such as Fermat’s and Lagrange’s theorems, the integrability of bounded continuous and bounded monotonic functions, and the fundamental theorem of calculus which states that the processes of derivation and integration are inverse to each other. These are the fundamental facts of the new calculus (as opposed to algebraic calculus).

Keywords: Interior Point; Monotonic Function; Maximum Point; Fundamental Theorem; Fundamental Idea (search for similar items in EconPapers)
Date: 2003
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-1-4612-0007-9_3

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DOI: 10.1007/978-1-4612-0007-9_3

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