Differential (mathematics)
From Wikipedia, the free encyclopedia
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 <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
In cryptography:
- A likely pair of differences <math>(\Delta_X, \Delta_Y)</math>, where <math>\Delta_Y = S(X) \oplus S(X \oplus \Delta_X)</math> for an S-box <math>S</math>, used in differential cryptanalysis. They are actually finite differences rather than infinitesimal differentials.
de:Differential (Mathematik) eo:Diferencialo he:דיפרנציאל (מתמטיקה) no:Differensial (matematikk) pl:Różniczka sv:Differential ru:Дифференциал (математика)
