What's jet-space? A jet is a fancy way to write down and track a function together with a number of its derivatives in a fancy way. Say, there's a sufficiently smooth function f: R^n -> R^m, then we can approximate f using a Taylor expansion:

f(x) = f(x0)/0! + f'(x0)·x/1! + f"(x0)·x^2/2! ... f^(k) (x0)·x^k/k! + E(x0,k)

The E is called error term, and it's there so I'm allowed to use an equal sign. Or rather, let's introduce a jet symbol that doesn't include the error term:

J^k_x0 f (x)

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A jet-bundle is just another, fancier name for a jet-space. That's it for now, folks, but as there's still lots of fun stuff to talk about I feel compelled get back at them soon. Corrections, questions, or simply showing interest can help make that happen ;^)

en.wikipedia.org/wiki/Jet_(mat
en.wikipedia.org/wiki/Jet_spac
en.wikipedia.org/wiki/Taylor_e

, expansions, on a

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