In mathematics, differential has several meanings:

• Differential (infinitesimal), an infinitesimal change in the value of a function

In differential topology: The differential dy In calculus, a differential is an infinitesimally small change in a variable. ...

• 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: A differential form is a mathematical concept in the fields of multivariate calculus, differential topology and tensors. ... In mathematics, a derivative is the rate of change of a quantity. ...

• 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.
• Pushforward (differential), the differential of a map between manifolds and the pushforward operations it defines.
• Pullback, a geometric name for the chain rule for composing a map between manifolds with a differential form on the target manifold.

In homological algebra: In mathematics, the exterior derivative operator of differential topology, extends the concept of the differential of a function to differential forms of higher degree. ... In mathematics, the covariant derivative is a way of specifying a derivative along tangent vectors of a manifold. ... Suppose that φ : M → N is a smooth map between smooth manifolds; then the differential of φ at a point x is, in some sense, the best linear approximation of φ near x. ... Suppose that φ:M→ N is a smooth map between smooth manifolds M and N; then there is an associated linear map from the space of 1-forms on N (the linear space of sections of the cotangent bundle) to the space of 1-forms on M. This linear map is...

• Given a cochain complex , the maps d_i are often called differentials because the exterior derivative plays this role in the de Rham cohomology

This disambiguation page lists articles associated with the same title. If an internal link led you here, you may wish to change the link to point directly to the intended article.