Date: Jun 30, 2004 8:00 PM
Author: Fernando Q. Gouvea
Subject: Re: [HM] FTC
On Wed, 30 Jun 2004, David Bressoud wrote:
> Does anyone know when the term "Fundamental Theorem of Calculus" first
> came into use and when it was first used to refer to the two results:
> equality of the definite integral and the change in an anti-derivative,
> the derivative of a definite integral with variable upper limit of
> integration is the integrand.
In Cauchy's 1823 course on the calculus, he proves the second statement
but does not even state it as a theorem; it seems to be treated just as a
convenient property of integrals. See pages 151 and 152 of Oeuvres
compeltes d'Augustin Cauchy, 2nd series, volume IV (which is available
online at gallica.bnf.fr).
In a quick search, I couldn't find any occurrences in gallica of "theoreme
fondamental" pointing to FTC. (There are lots of other "fundamental
theorems", of course, including the one that says that the complex numbers
are algebraically closed.)
Fernando Q. Gouvea
Department of Mathematics Editor, FOCUS and FOCUS Online
Colby College Mathematical Association of America
Waterville, ME 04901 http://www.maa.org
The human mind ordinarily operates at only ten percent of its
capacity -- the rest is overhead for the operating system.