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 |