Differential (mathematics)
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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 <math>(C_\bullet, d_\bullet)<math>, the maps di are often called differentials because the exterior derivative plays this role in the de Rham cohomology.