Differential (mathematics)
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In mathematics, differential has several meanings:
- Differential (calculus), an infinitesimal change in the value of a function
In differential topology:
- Differential form, a generalization that accommodates multiplication and differentiation of differentials
In addition, differentials and differential forms on manifolds come with the following notions of differentiation:
- Exterior derivative, a notion of differentiation of differential forms
- Covariant derivative, a more general notion of differentiation of vector fields, differential forms, or arbitrary tensor fields on a manifold.
- Push forward, a geometric name for the differential of a map between manifolds.
- Pull back, a geometric name for the chain rule for composing a map between manifolds with a differential form on the target manifold.
In homological algebra:
- Given a chain complex
, the maps di are often called differentials because the exterior derivative plays this role in the de Rham cohomology
In cryptography:
- A likely pair of differences (ΔX,ΔY), where
for an S-box S, used in differential cryptanalysis. They are actually finite differences rather than infinitesimal differentials.
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