Differential (mathematics)

In mathematics, the word 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.
• In differential topology, which is a generalization of calculus to manifolds, the differential of a function on a manifold becomes a one-form. In this setting the differential generalizes to exterior derivative operator on differential forms
• Also in differential topology, the differential of a map between manifolds is another name for the pushforward of that map.
• In homological algebra, given a chain complex , the maps d_i are often called differentials because the exterior derivative plays this role in the de Rham cohomology.