David Saunders: Jets
Time: Wed 2014-03-26 10.30 - 11.30
Location: Room 306, buildning 6, Kräftriket, Department of mathematics, Stockholm university
Participating: David Saunders, University of Ostrava, Czech Republic
The idea of a "jet" was introduced by Charles Ehresmann in 1951 as an equivalence class of maps, all defined in some neighbourhood of a given point, and with the same value and derivatives (up to a given order) at that point. Conceptually, therefore, a jet may be considered as an abstract Taylor polynomial.
In this talk I shall expand on this definition, and explain the structure of various spaces of jets (of which the simplest is the tangent bundle of a differentiable manifold).
I shall also explain how the use of jets can give a precise meaning to certain aspects of the Euler-Lagrange equations of the calculus of variations, such as the ideas of "differentiating with respect to derivatives" and of "total derivative".