Differential (mathematics)

From Wikipedia, the free encyclopedia
Jump to navigation Jump to search

In mathematics, differential refers to infinitesimal differences or to the derivatives of functions.[1] The term is used in various branches of mathematics such as calculus, differential geometry, algebraic geometry and algebraic topology.

Basic notions

Differential geometry

The notion of a differential motivates several concepts in differential geometry (and differential topology).

Algebraic geometry

Differentials are also important in algebraic geometry, and there are several important notions.

Other meanings

The term differential has also been adopted in homological algebra and algebraic topology, because of the role the exterior derivative plays in de Rham cohomology: in a cochain complex , the maps (or coboundary operators) di are often called differentials. Dually, the boundary operators in a chain complex are sometimes called codifferentials.

The properties of the differential also motivate the algebraic notions of a derivation and a differential algebra.

References

  1. ^ "differential - Definition of differential in US English by Oxford Dictionaries". Oxford Dictionaries - English. Retrieved 13 April 2018. 

External links

Retrieved from "https://en.wikipedia.org/w/index.php?title=Differential_(mathematics)&oldid=836257460"
This content was retrieved from Wikipedia : http://en.wikipedia.org/wiki/Differential_(mathematics)
This page is based on the copyrighted Wikipedia article "Differential (mathematics)"; it is used under the Creative Commons Attribution-ShareAlike 3.0 Unported License (CC-BY-SA). You may redistribute it, verbatim or modified, providing that you comply with the terms of the CC-BY-SA