Smooth functions | Singularity theory | Differential geometry

Jet (mathematics)

In mathematics, the jet is an operation that takes a differentiable function f and produces a polynomial, the truncated Taylor polynomial of f, at each point of its domain. Although this is the definition of a jet, the theory of jets regards these polynomials as being abstract polynomials rather than polynomial functions. This article first explores the notion of a jet of a real valued function in one real variable, followed by a discussion of generalizations to several real variables. It then gives a rigorous construction of jets and jet spaces between Euclidean spaces. It concludes with a description of jets between manifolds, and how these jets can be constructed intrinsically. In this more general context, it summarizes some of the applications of jets to differential geometry and the theory of differential equations. (Wikipedia).

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Differential operator | Tangent bundle | Stalk (sheaf) | Complex analysis | Vector space | Ideal (ring theory) | Indeterminate (variable) | Derivative | Abuse of notation | Chain rule | Automorphism | Maximal ideal | Differentiable function | Germ (mathematics) | Mathematical analysis | Taylor's theorem | Commutative algebra | Polynomial | Lagrangian system | Curve | Partial derivative | Transversality theorem | Jet bundle | Differentiable manifold | Jet group | Neighbourhood (mathematics) | P-adic analysis | Mathematics | Affine transformation | Diffeomorphism | Algebraic geometry | Contact (mathematics) | Euclidean space | Without loss of generality | Manifold | Equivalence relation | Abstract algebra | Local ring | Differential geometry | Einstein notation