Exterior Differential Systems and Euler-Lagrange Partial Differential Equations

Preface
Introduction
1. Lagrangians and Poincaré-Cartan Forms
1.1 Lagrangians and Contact Geometry
1.2 The Euler-Lagrange System
1.3 Noether's Theorem
1.4 Hypersurfaces in Euclidean Space
2. The Geometry of Poincaré-Cartan Forms
2.1 The Equivalence Problem for n = 2
2.2 Neo-Classical Poincaré-Cartan Forms
2.3 Digression on Affine Geometry for Hypersurfaces
2.4 The Equivalence Problem for n > 3
2.5 The Prescribed Mean Curvature System
3. Conformally Invariant Euler-Lagrange Systems
3.1 Background Material on Conformal Geometry
3.2 Confromally Invariant Poincaré-Cartan Forms
3.3 The Conformal Branch of the Equivalence Problem
3.4 Conservation Laws for Du = Cu n+2/n-2
3.5 Conservation Laws for Wave Equations
4. Additional Topics
4.1 The Second Variation
4.2 Euler-Lagrange PDE Systems
4.3 Higher-Order Conservation Laws