Explore: Lie Differentiation

there are three main coordinate independent notions of differentiation of tensor fields: Lie derivatives, derivatives with respect to connections, the

and capture certain formal features of differentiation in Euclidean spaces. The chief among these are: The Lie derivative, which is uniquely defined by

This article is a summary of differentiation rules, that is, rules for computing the derivative of a function in calculus. Unless otherwise stated, all

In mathematics, a Lie group (pronounced /liː/ LEE) is a group that is also a differentiable manifold, such that group multiplication and taking inverses

In calculus, the Leibniz integral rule for differentiation under the integral sign, named after Gottfried Wilhelm Leibniz, states that for an integral

defined as a function of the differentiation operator. It is helpful, as a matter of notation first, to consider differentiation as an abstract operation

mathematics, a Lie algebra (pronounced /liː/ LEE) is a vector space g {\displaystyle {\mathfrak {g}}} together with an operation called the Lie bracket, an

In calculus, logarithmic differentiation or differentiation by taking logarithms is a method used to differentiate functions by employing the logarithmic

fundamental theorem of calculus. This states that differentiation is the reverse process to integration. Differentiation has applications in nearly all quantitative

groupoids were introduced by Charles Ehresmann under the name differentiable groupoids. A Lie groupoid consists of two smooth manifolds G {\displaystyle