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Lecturer(s)
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Brzezina Miroslav, doc. RNDr. CSc., dr. h. c.
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Course content
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Differencial equations, basic terms, existence theorems, equations of higher orders. Linear differencial equations: n-th order, constant coefficient linear differential equation, basic use of linear differential equation. Systems of linear differencial equations, variation of parameters for systems. Systems of constant coefficient linear differencial equations, independent solutions. Laplace transform, properties. Partial fraction decomposition. Simple aplications, solving problems.
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Learning activities and teaching methods
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Monological explanation (lecture, presentation,briefing), Written assignment presentation and defence
- Class attendance
- 56 hours per semester
- Preparation for exam
- 125 hours per semester
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Learning outcomes
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Notion of solution, Cauchy's problem - existence and uniqueness of solution. Elementary methods of solution. Maximal solution, global solution. Gronwall lemma. Systems of first order ODE. System of linear ODE, fundamental solution (eigenvalues and vectors), variations of constants. Boundary problem for second order ODE. Stability of solution, conditions for stability of system of linear ODE.
Basic knowlidges of ODE and of methods of its solving.
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Prerequisites
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Passing of mathematical lectures of first four semestrs.
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Assessment methods and criteria
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Combined examination
Credit: Working out a semestral work. Exam written and oral.
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Recommended literature
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Brzezina M., Veselý J. Obyčejné (lineární) diferenciální rovnice a jejich systémy. Liberec, 2012. ISBN 978-80-7372-909-7.
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Kurzweil, J. Úvod do obyčejných diferenciálních rovnic.
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