Smooth functions | Generalizations of the derivative | Differential geometry
Pushforward (differential)
In differential geometry, pushforward is a linear approximation of smooth maps on tangent spaces. 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. It can be viewed as a generalization of the total derivative of ordinary calculus. Explicitly, the differential is a linear map from the tangent space of M at x to the tangent space of N at φ(x), . Hence it can be used to push tangent vectors on M forward to tangent vectors on N. The differential of a map φ is also called, by various authors, the derivative or total derivative of φ. (Wikipedia).
