ORDINARY DIFFERENTIAL EQUATIONS 2 - WS 2025/26

Office hours:

upon request (see my timetable and suggest me some days and times via e-mail)
my office is in Sokolovská 83, 2nd floor, behind the glass door opposite to the staircase
it is also possible to discuss online via zoom

Aktuálně

basic information
exams
lecture
tutorials

Basic information

Lectures: Thursday 10:40 in K2 (Sokolovská 83, ground floor)

Exercises: Thursday 12:20 in K2.

Recomended literature: lecture notes of D. Pražák (in english), lecture notes and videos from the last year's lecture of D. Pražák (in czech).
Initial requirements and recommended books for additional study: here
Problems to practice: Internet collection of problems and examples in ODEs
Exam requirements...to be updated
Credit requirements: active participation at the exercises.

Exams

The exam consists of a written part (90 minutes, 3 problems to solve) and oral part (theory). The details will be in exam requirements.
Look at the tests from last years.

Lecture

presentation, list of definitions and theorems (last update December 11, 2025)

Approximation of center manifold (by J. Carr), tracking property (Lecture notes of D. Pražák)

Plan:

1. week: Dynamical systems - basic properties
2. week: Rectification theorem, LaSalle's inavriance principle
3. week: LaSalle inavriance principle, Poincaré--Bendixson theory
4. week: Poincaré--Bendixson's theory , Caratheodory's theory
5. week: Caratheodory's teory
6. week: Bifurcations, sufficient conditions for a bifurcation in R
7. week: Hopf bifurcation
8. week: Stable, unstable and central manifold - introduction
9. week: theorems about central manifolds, reduction of stability
10. week: existence of a central manifold
11. week: aproximation of central manifolds, Optimal control - Kalman's matrix
12. week: linear and linearized contolability, controlability with a restriction
13. week: time optimal control, linear case
14. week: Pontryagin maximum principle, general case

Tutorial

2nd tutorial pdf. (they are in students repository - the same login and passwd as to CAS/SIS should work)

9th tutorial pdf. (they are in students repository - the same login and passwd as to CAS/SIS should work)

Plan:

1. week: dynamical systems - basic properties
2. week: dynamical systems
3. week: dynamical systems - La Salle
4. week: dynamical systems - Poincaré -Bendixson
5. week: bifurcations - basic types in R
6. week: bifurcations in R, saddle-node bifurcation in RxR
7. week: bifurcations in R^2, Hopf bifurcation
8. week: bifurcation in R^2, central manifold
9. week: aproximation of a central manifold
10. week: aproximation of a central manifold
11. week: linear controlability
12. week: linearized controlability
13. week: time optimal control
14. week: Pontryagin maximum principle