Jet Bundle
Let pi:E->M be a smooth fiber bundle. Two local sections through a point x in M have the same r-jet at x if their coordinate derivatives through order r agree at x. These equivalence classes form the fiber J_x^rE, and their union as x varies is the rth jet bundle J^rE. Its points record the value and the first r derivatives of a local section without choosing a particular representative. Jet bundles provide the geometric setting for differential equations, prolongations, and variational problems.
See also
Fiber Bundle, Prolongation, Section, Tangent BundleExplore with Wolfram|Alpha
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References
Saunders, D. J. The Geometry of Jet Bundles. Cambridge, England: Cambridge University Press, 1989.Cite this as:
Weisstein, Eric W. "Jet Bundle." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/JetBundle.html