Seminar on differential equations NMMA431
T. Bárta, P. Kaplický, D. Pražák
Seminar history can be found here.
Seminar topics (spring 2024)
1. Classical potential theory
Following the book Classical potential theory by
Armitage, Gardiner, in particular:
- Harnack inequalities, analyticity of harmonic functions
(Chapter 1)
- subharmonic functions (Chapter 3)
- PWB solution to Dirichlet problem (Chapter 6)
2. plane dynamics, Poincaré-Bendixson theorem
Following the Chapter VII of
Ordinary differential equations by
Ph. Hartman, in particular:
- „Umlaufsatz“ (Theorem 2.1) and its consequences
- Poincaré-Bendixson theorem (Theorem 4.1)
- stability of periodic solutions (Theorems 5.1 and 5.2)
- Rotation points, Foci, Nodes, Saddle points (Sections 6 and 7)