Differential (mathematics)

In mathematics, the word differential has various meanings:

In calculus, a differential is an infinitesimal change in the value of a function. The derivative and integral are defined in terms of a limit of a differential.
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 $(C_\bullet, d_\bullet)$ , the maps d_i are often called differentials because the exterior derivative plays this role in the de Rham cohomology.

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