Infinitesimal calculus

Infinitesimal calculus is an area of mathematics pioneered by Gottfried Leibniz based on the concept of infinitesimals, as opposed to the calculus of Isaac Newton, which is based upon the concept of the limit (mathematics). Because infinitesimals were not put on a Rigour until the second half of the twentieth century, the Limit of a function and calculus became standard. ==See also== * calculus * differential geometry * nonstandard analysis ==External links== * [http://www.math.wisc.edu/~keisler/calc.html ''Elementary Calculus: An Approach Using Infinitesimals''] by H. Jerome Keisler, an out-of-print book available on the web. * [http://www.math.uiowa.edu/~stroyan/InfsmlCalculus/InfsmlCalc.htm A Brief Introduction to Infinitesimal Calculus] by Keith Duncan Stroyan of the University of Iowa. ==Further reading== * John L. Bell: ''A Primer of Infinitesimal Analysis'', Cambridge University Press, 1998. ISBN 0521624010. Uses synthetic differential geometry and nilpotent infinitesimals * James M. Henle and Eugene M. Kleinberg: ''Infinitesimal Calculus'', Dover Publications 2003. ISBN 0486428869. Uses nonstandard analysis and hyperreal_number infinitesimals Calculus

Infinitesimal calculus

:Infinitesimal calculus is an area of mathematics pioneered by Gottfried Leibniz based on the concept of infinitesimals, as opposed to the calculus of Isaac Newton, which is based upon the concept of the limit (mathematics). Is it really true that Isaac Newton had the concept of ''limit''? I tend to think of that as a 19th-century innovation. User:Michael Hardy 20:58, 7 Sep 2004 (UTC) Would like to second that last statement. The defintion given for Infinitesimal includes Newton as using infinitesimals and the idea of the limit wasnt introduced until the 19th century by Karl Weierstrass. Would be nice to keep definitions noncontradictory. ---- The proposal to merge this with non-standard calculus doesn't make sense. Non-standard calculus did not emerge until the 1950s; this article is about something introduced by Leibniz in the 17th century. User:Michael Hardy 21:48, 12 Jun 2005 (UTC) :infinitesimals were put onto a rigorous basis by nonstandard calculus --User:MarSch 15:18, 16 Jun 2005 (UTC) ::Everybody knows that, but it would be absurd to limit the topic to its ''rigorous'' formulation when the non-rigorous version played a far more prominent role in the history of the subject. User:Michael Hardy 21:55, 16 Jun 2005 (UTC)

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