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The Fundamental Ideas of the Differential and Integral Calculus

In: Mathematical Analysis

Author

Listed:
  • Mariano Giaquinta

    (Scuola Normale Superiore)

  • Giuseppe Modica

    (Università degli Studi di Firenze, Facoltà di Ingegneria)

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).

Suggested Citation

  • Mariano Giaquinta & Giuseppe Modica, 2003. "The Fundamental Ideas of the Differential and Integral Calculus," Springer Books, in: Mathematical Analysis, chapter 3, pages 93-144, Springer.
    • Handle: RePEc:spr:sprchp:978-1-4612-0007-9_3
    DOI: 10.1007/978-1-4612-0007-9_3
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