Jets
Suppose M is an m-dimensional manifold and that (E, π, M) be a fiber bundle. For p ∈ M, let Γ(π) denote the set of all local sections whose domain contains p. Let I = (I(1), I(2), ..., I(m)) be a multi-index (an ordered m-tuple of integers), then
Define the local sections σ, η ∈ Γ(π) to have the same r-jet at p if
The relation that two maps have the same r-jet is an equivalence relation. An r-jet is an equivalence class under this relation, and the r-jet with representative σ is denoted . The integer r is also called the order of the jet, p is its source and σ(p) is its target.
Read more about this topic: Jet Bundle