Exam requirements for ODE2 (NMMA047)

The exam consists of written (computational) and oral (theoretic) parts. To pass the exam successfully it is neccessary to gain at least 15 points (out of 30) in each of the two parts. The final grade depends on the sum of points received in the two parts

Written part

The written part consists of three problems, 10 points each. The problems' topics are or their combinations. The written part takes 90 minutes and students are not allowed to use any textbooks, written notes, calculators.

An example of a written part: zde

Oral part

The oral part consists of two questions with maximum of 15 points from each of them. One question typically correspond to one section from lecture notes. The objective is to formulate basic definitions and important theorems in the field. After that, student is asked to prove a given theorem (difficulty according to the ambitions of the student) and answer supplementary questions (according to the ambitions of the student).

Příklad zkouškové otázky:
1. Dynamické systémy v rovině
Dokažte, že průsečík transverzály s omega-limitní množinou je nejvýše jednobodový.
2. Caratheodoryova teorie
Dokažte zobecněnou Banachovu větu o kontrakci.

Seznam odpřednesených tvrzení:

1. Dynamické systémy 2. Caratheodoryova teorie 3. Bifurkace 4. Stabilní, nestabilní a centrální variety 5. Regulace