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Lecturer(s)
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Krajščáková Věra, Mgr.
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Andres Jan, prof. RNDr. dr hab. DSc.
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Staněk Svatoslav, prof. RNDr. CSc.
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Tomeček Jan, doc. RNDr. Ph.D.
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Ženčák Pavel, RNDr. Ph.D.
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Course content
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1. Computing methods for differential equations of the first order. 2. Fundamentals of differential equations, autonomous systems, the relation of a single equation to a system. 3. Local existece and uniqueness theorems for the initial value problems, the Gronwall lemma. 4. Extending the solution, complete solution, global existece and uniqueness theorems for initial value problems, differential inequalities, existence on a half-line. 5. Systems of linear differential equations (superposition, fundamental solution, the Wronskian, the Jacobi formula, variation of constants formula, general solution). 6. Linear differential equation of the n-th order. 7. Systems of linear differential equations with constant coefficients, structure of the solution. 8. Linear differential equation of the n-th order with constant coefficients.
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Learning activities and teaching methods
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Monologic Lecture(Interpretation, Training), Dialogic Lecture (Discussion, Dialog, Brainstorming)
- Attendace
- 52 hours per semester
- Homework for Teaching
- 20 hours per semester
- Preparation for the Exam
- 50 hours per semester
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Learning outcomes
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Understand local and global properties of solution to ordinary differential equations and their systems.
Comprehension Understand local and global properties of solution to ordinary differential equations and their systems.
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Prerequisites
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Knowledge of differential and integral calculus, linear algebra and basic information from functional analysis.
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Assessment methods and criteria
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Oral exam, Written exam
Credit: active participation, homework. Exam: written test, the student has to understand the subject and be able to prove principal results.
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Recommended literature
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J. Kalas, M. Ráb. (2012). Obyčejné diferenciální rovnice. Vyd. 3.. Brno: Masarykova univerzita.
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Kurzweil, J. (1978). Obyčejné diferenciální rovnice: úvod do teorie obyčejných diferenciálních rovnic v reálném oboru. Praha: SNTL - Nakladatelství technické literatury.
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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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Wirkus, Stephen A., Swift. Randall J. (2015). A course in ordinary differential equations. Boca Raton, Fla. : CRC Press.
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