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Lecturer(s)
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Tomeček Jan, doc. RNDr. Ph.D.
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Vodák Rostislav, doc. RNDr. Ph.D.
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Ženčák Pavel, RNDr. Ph.D.
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Krajščáková Věra, Mgr.
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Course content
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1. Motivation, examples from physics, engineering, biology, chemistry, ecology, economics, etc. 2. Existence, uniqueness, stability, regularity of solutions of differential equations and numerical methods. 3. Solution of ODE, Cauchy problem, geometrical interpretation plus numerical methods. 4. Linear equations and systems, global properties. 5. Nonlinear equations: existence, uniqueness, stability, separable differential equations. 6. Boundary value problems, resonance, Green functions, basic numerical methods for BVPs, implementation, visualisation. 7. Alternative methods for solving ODEs.
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Learning activities and teaching methods
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Lecture, Monologic Lecture(Interpretation, Training)
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Learning outcomes
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To obtain basics of the theory of ordinary differential equations.
Comprehension Understand basic notions concerning ODEs.
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Prerequisites
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Differential and integral calculus.
KMA/MA1 and KAG/LA1A
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Assessment methods and criteria
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Oral exam, Seminar Work
Oral exam. Credits: active participation, seminal work and its defence.
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Recommended literature
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Online přednáška.
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Online přednáška.
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Kalas, J., Ráb, M. (2012). Obyčejné diferenciální rovnice. Vyd. 3.. Brno: Masarykova univerzita.
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Kojecká, J., Závodný, M. (2004). Příklady z diferenciálních rovnic. Univerzita Palackého, Olomouc.
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M. Greguš, M. Švec, V. Šeda. (1985). Obyčajné diferenciálne rovnice. Alfa, SNTL.
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Ráb, M. (1998). Metody řešení obyčejných diferenciálních rovnic. MU Brno.
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Tenenbaum M., Pollard, H. (1985). Ordinary Differential Equations. Dover Publications.
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Trench, W. F. (2008). Elementary Differential Equations and Boundary Value Problems. Wiley.
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Wirkus, Stephen A., Swift. Randall J. (2015). A course in ordinary differential equations. Boca Raton, Fla. : CRC Press.
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