Differential (mathematics) - Definition and Overview

In mathematics differential has various meanings.

In calculus, a differential is an infinitesimal change in the value of a function. Differentials help to constitute derivatives and integrals. Outside of this context, they occur as elements of cotangent spaces in the guise of differential forms, a formal extension of the naïve notion of differential first taught to students.

In the exterior algebra of differential forms, the exterior derivative d applied to a form ω is sometimes referred to as the differential of ω.

In homological algebra, given a chain complex <math>(C_\bullet, d_\bullet)<math>, the maps d_i are often called differentials because the exterior derivative plays this role in the defining of de Rham cohomology.