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Lecturer(s)
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Tomeček Jan, doc. RNDr. Ph.D.
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Rachůnková Irena, prof. RNDr. DrSc.
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Course content
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Types of solutions of initial problems. Existence and uniqueness. Dependence on initial values and parameters. Linear differential equations. Global properties of solutions. Stability. Periodic and bounded solutions. Differential inequalities and a priori estimates of solutions. Differential equations with singularities in time and in phase variables. Impulsive differential equations. Functional differential equations.
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Learning activities and teaching methods
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Dialogic Lecture (Discussion, Dialog, Brainstorming), Work with Text (with Book, Textbook)
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Learning outcomes
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Master essential tools of the theory of differential equations.
Comprehension Demonstrate a good orientation ín the theory of differential equations.
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Prerequisites
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Master's degree in mathematics.
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Assessment methods and criteria
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Oral exam
Exam: to know and to understand the subject
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Recommended literature
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A.Granas, M. Frigon. (1995). Topological Methods in Differential Equations and Inclusions. Kluwer, Dordrecht.
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I.T. Kiguradze. (1975). Some Singular Boundary Value Problems for Ordinary Differential Equations. Izd. Tbilis. Univ. , Tbilisi.
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J. Kalas, M. Ráb. (1995). Obyčejné diferenciální rovnice. Brno.
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J. Kurzweil. (1978). Obyčejné diferenciální rovnice. SNTL, Praha.
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J.H. Hubbart, B.H. West. Differential Equations: A Dynamical Systems Approach I, II. Springer-Verlag, New York, 1991, 1995.
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J.K. Hale, S.M.Verduyn Lunel. (1993). Introduction to Functional Differential Equations. Springer.
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M. Greguš, M. Švec, V. Šeda. (1985). Obyčajné diferenciálne rovnice. Alfa, SNTL.
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P. Hartman. (1964). Ordinary Differential Equations. John Wiley and Sons, New York.
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V. Lakshmikantham, D.D. Bainov, P.S.Simeonov. (1989). Theory of Impulsive Differential Equations. World Scientific, Singapore.
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