Smooth functions

function whose derivative exists at each point in its domain

a continuous functional on a space of test functions (Schwartz space), which generalizes the concept of locally integrable functions

in calculus, the points of an equation where the derivative is zero

thumb|upright=1.2|A bump function is a smooth function with [[compact support.]]

differentiable function whose derivative is everywhere injective

construct allowing differentiation of tangent vector fields of manifolds

a smooth and compactly supported function

function space of all functions whose derivatives are rapidly decreasing

differentiable map whose differential is everywhere surjective

theorem that the set of the critical values of a smooth function has measure zero

Analyzes the topology of a manifold by studying differentiable functions on that manifold

linear approximation of smooth maps on tangent spaces

initial result in using test functions to find extremum

thumb|A mollifier (top) in Dimension (mathematics)|dimension one. At the bottom, in red is a function with a corner (left) and sharp jump (right), and in blue is its mollified version.

operation that takes a differentiable function f and produces a polynomial, the truncated Taylor polynomial of f, at each point of its domain

math/physics concept

Ehresmann connection on a principal bundle that is compatible with the group action

generalization of affine connections

Function in image processing