| Part 1 |
Explicit methods |
| 20/1 |
Introduction and terminology |
| 21/1 |
Separation of variables and characteristics |
| 27/1 |
Characteristics: Quasilinear case |
| 28/1 |
Characteristics: Fully nonlinear case |
| Part 2 |
Analysis of PDE |
| 3/2 |
Second-order linear equations |
| 4/2 |
Extended maximum principle |
| 10/2 |
Comparison principle |
| 11/2 |
A priori estimates |
| 17/2 |
Wave equation |
| 18/2 |
Energy functions |
| 24/2 |
Blow-up theorems |
| 25/2 |
Nonlinear waves |
| Part 3 |
Calculus of variations |
| 9/3 |
Euler-Lagrange equation |
| 10/3 |
Some standard examples |
| 16/3 |
Variational problems |
| 23/3 |
Isoperimetric constraints |
| 24/3 |
Necessary conditions |
| 30/3 |
Sufficient condition |
| 31/3 |
Noether's theorem |