Subjects

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Systems of Ordinary Differential Equations (ODE) - N413007

Title:	Soustavy obyčejných diferenciálních rovnic
Guaranteed by:	Department of Mathematics (413)
Faculty:	Faculty of Chemical Engineering
Actual:	from 2007 to 2012
Semester:	winter
Points:	winter s.:5
E-Credits:	winter s.:5
Examination process:	winter s.:
Hours per week, examination:	winter s.:2/2, C+Ex [HT]
Capacity:	unlimited / 48 (unknown)
Min. number of students:	unlimited
State of the course:	taught
Language:	Czech
Teaching methods:	full-time
Level:
Note:	course can be enrolled in outside the study plan enabled for web enrollment

Guarantor:	Klíč Alois prof. RNDr. CSc.

Examination dates Schedule

Annotation -

The course deals with the qualitative theory of differential equations. The theory of differential equations is presented with the emphasis on its geometric and qualitative aspects and is understood as a part of more general theory of dynamical systems.

Last update: Dubcová Miroslava (18.07.2013)

Literature -

R: A. Klíč, M. Dubcová,L. Buřič: Soustavy obyčejných diferenciálních rovnic, kvalitativní teorie, dynamické systémy, VŠCHT Praha, 2009, ISBN: 978-80-7080-724-8

R: R.C.Robinson: An Introduction to Dynamical Systems: Continuous and Discrete. Pearson Prentice Hall, 2004, ISBN 0-13-143140-4

A: M. W. Hirsch, S. Smale, R. L. Devaney: Differencial Equations, Dynamical Systems & An Introductions to Chaos, Elsevier 2004, ISBN0-12-349703-5

Last update: TAJ413 (28.08.2013)

Teaching methods -

Lectures and exercise classes.

Last update: TAJ413 (19.07.2013)

Syllabus -

1. The concept of dynamical systems. Continuous and discrete dynamical systems.

2. Autonomous systems of ODEs. Qualitative approach. Phase flow. The notion of stability.

3. Attractor.

4. Planar systems. Phase portraits of linear systems.

5. Phase portraits of nonlinear systems. Grobman-Hartman theorem.

6. First integrals and applications.

7. Phase portraits of linear and nonlinear systems in R^3.

8. Stability theory. Poincare mapping.

9. Nonautonomous systems of ODEs.

10. Periodic linear systems. Monodromy matrix. Floquet theory.

11. Systems of ODEs depending on parameters. Bifurcations.

12. Examples: "Brusselator", Lorenz system, dumped oscillator.

13. Discrete dynamical systems, basic notions.

14. Regular and chaotic behavior. Lyapunov exponents.

Last update: Dubcová Miroslava (18.07.2013)

Learning resources -

http://www.vscht.cz/mat/SODR/E-collection/SbirkaDR-Ang.pdf

Last update: Dubcová Miroslava (18.07.2013)

Learning outcomes -

Students should be able to describe autonomous systems of differential equations qualitatively. Namely, they should be able to determine stability of solutions, to recognize chaotic attractor and to classify bifurcations.

Last update: Dubcová Miroslava (18.07.2013)

Registration requirements -

Mathematics I, Mathematics II

Last update: TAJ413 (16.07.2013)