Infinitesimal calculus - Definition and Overview

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. Because infinitesimals were not put on a rigorous mathematical basis until the second half of the twentieth century, the delta-epsilon definition of limits and calculus became standard.

See also

• calculus
• differential geometry
• nonstandard analysis

External link

• Elementary Calculus: An Approach Using Infinitesimals (http://www.math.wisc.edu/~keisler/calc.html) by H. Jerome Keisler, an out-of-print book available on the web.
• A Brief Introduction to Infinitesimal Calculus (http://www.math.uiowa.edu/~stroyan/backgndctlc.htm) 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 infinitesimals