Editing Jet (mathematics) (section)

{{Short description|Operation in differential geometry}}
In [[mathematics]], the '''jet''' is an operation that takes a [[differentiable function]] ''f'' and produces a [[polynomial]], the [[Taylor polynomial]] (truncated Taylor series) 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 [[Polynomials#Abstract algebra|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 space]]s. It concludes with a description of jets between [[manifold]]s, 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]].