| Lecture 1 Manifolds | Lecture 11 The Euler-Lagrange EDS | |
| Lecture 2 Jet spaces | Lecture 12 Euler-Lagrange EDS for classical var. probl. | |
| Lecture 3 Exterior differential systems (EDS) | Lecture 13 Good form, derived flag, Cauchy characteristics | |
| Lecture 4 Variational problems | Lecture 14 Strongly non-degenerate variational problems | |
| Lecture 5 Infinitesimal variations | Lecture 15_16 Elastic curves in R3 | |
| Lecture 6 Euler-Lagrange equations | ||
| Lecture 7 Classical variational problems | Lecture 17 First integrals and Noether's theorem | |
| Lecture 8 Riemannian geometry and geodesics | Lecture 18 Cyclic coordinates and Clairault's theorem | |
| Lecture 9_10 Elastic curves in space forms | Lecture 19_20 Wheel rolling on a plane |