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Last update: Pátková Vlasta (09.01.2018)
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Last update: Pátková Vlasta (09.01.2018)
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. |
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Last update: Dubcová Miroslava RNDr. Ph.D. (18.10.2018)
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. AMS, 2012 ISBN: 978-0821891353 A: M. W. Hirsch, S. Smale, R. L. Devaney: Differencial Equations, Dynamical Systems & An Introductions to Chaos, Elsevier 2004, ISBN0-12-349703-5 |
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Last update: Pátková Vlasta (09.01.2018)
http://www.vscht.cz/mat/SODR/E-collection/SbirkaDR-Ang.pdf |
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Last update: Pátková Vlasta (09.01.2018)
Lectures and exercise classes. |
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Last update: Dubcová Miroslava RNDr. Ph.D. (16.02.2018)
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. Planar systems. Phase portraits of linear systems. 4. Phase portraits of nonlinear systems. Grobman-Hartman theorem. 5. Closed trajectory. Bendix and Poiancaré criteria 6. First integrals and applications. 7. Population model "Predator - Prey". Hamilton systems in the plane. 8. Newton's equation 9. Phase portraits of linear and nonlinear systems in R3. 10. Ljapun's function. Gradient systems. 11. Systems of ODEs depending on parameters. Bifurcations. 12. Examples: "Brusselator", Lorenz system, dumped oscillator. 13. Discrete dynamical systems, basic notions. 14. Discrete dynamic systems. |
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Last update: Borská Lucie RNDr. Ph.D. (13.05.2019)
Students are expected to have either completed the prerequisite courses Mathematics A and Mathematics B or possess the equivalent knowledge prior to enrolling in the course. |
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Last update: Borská Lucie RNDr. Ph.D. (06.05.2019)
No requirements. |
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Last update: Dubcová Miroslava RNDr. Ph.D. (16.02.2018)
Assesment, written exam, oral exam |
Teaching methods | ||||
Activity | Credits | Hours | ||
Konzultace s vyučujícími | 0.5 | 14 | ||
Účast na přednáškách | 1 | 28 | ||
Příprava na přednášky, semináře, laboratoře, exkurzi nebo praxi | 1.5 | 42 | ||
Příprava na zkoušku a její absolvování | 1.5 | 42 | ||
Účast na seminářích | 0.5 | 14 | ||
5 / 5 | 140 / 140 |