# Differential (mathematics)

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.

## 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 ${\displaystyle (C_{\bullet },d_{\bullet })}$, 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.