Introductory material for jets and jet bundles

The Geometry of Jet Bundles by D. J. Saunders, Cambridge University Press:

“The purpose of this book is to provide an introduction to the theory of jet bundles for mathematicians and physicists who wish to study differential equations, particularly those associated with the calculus of variations, in a modern geometric way. One of the themes of the book is that first-order jets may be considered as the natural generalisation of vector fields for studying variational problems in field theory, and so many of the constructions are introduced in the context of first- or second-order jets, before being described in their full generality.”


Volume 182 of the Translations of Mathematical Monographs series of the AMS (1999):

Symmetries and Conservation Laws for Differential Equations of Mathematical Physics

by A. V. Bocharov, V. N. Chetverikov, S. V. Duzhin, N. G. Khor'kova, I. S. Krasil'shchik (editor), A. V. Samokhin, Yu. N. Torkhov, A. M. Verbovetsky, A. M. Vinogradov (editor).

From the self-description:

The book is rendered as self-contained as possible and includes detailed motivations, extensive examples, and exercises, along with careful proofs of all results. The book is intended for readers who wish to learn the basics on applications of symmetry methods to differential equations of mathematical physics, but will also be useful for the experts because it assembles a lot of results previously dispersed in numerous journal publications. The text is accessible to advanced graduate students in mathematics, applied mathematics, mathematical and theoretic physics, mechanics, etc.

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Differential Geometry

Smooth Manifolds

Differential Topology

Jet Bundles

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