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  "body": "\n## Summary\n\nThe $k$-th jet bundle of a [[fiber bundle|CX4M8K61AB]] $E \\to M$ is the manifold of all [[$k$-jets|1QE0Z0756D]] of local sections of $E$.\nA point of it records a point of $M$, a value in the fiber and all derivatives up to order $k$ of a section there.\nIt is the natural home of differential equations on bundles: an equation of order $k$ is a subset of the $k$-th jet bundle.\nJet bundles are used in the calculus of variations, in the geometric theory of partial differential equations and in field theory.\n\n## Explanations\n\n### L1 human\n\nFor a function $u(x)$ of one variable, the first jet bundle has three coordinates: the point $x$, the value $u$ and the slope $u_x$.\nEvery function $u$ gives a curve $x \\mapsto (x, u(x), u'(x))$ in this three-dimensional space.\nA first-order differential equation such as $u_x = u$ is just a surface in that space.\nSolving the equation means finding functions whose curves stay in that surface.\nHigher jet bundles add coordinates for higher derivatives.\n",
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    "tag": "HC3VBBCJQP"
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  "link": "https://tamnd.github.io/math2/node/HC3VBBCJQP/",
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  "markdown": "https://tamnd.github.io/math2/node/HC3VBBCJQP.md",
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  "name": "Jet bundle",
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  "source": "https://github.com/tamnd/math2/blob/main/nodes/HC3/HC3VBBCJQP.md",
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  "tag": "HC3VBBCJQP",
  "uri": "m2://HC3VBBCJQP",
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