Course: Ordinary Differential Equations

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Course title Ordinary Differential Equations
Course code MU/02024
Organizational form of instruction Lecture + Lesson
Level of course Bachelor
Year of study not specified
Semester Winter
Number of ECTS credits 6
Language of instruction Czech
Status of course Compulsory, Compulsory-optional
Form of instruction Face-to-face
Work placements This is not an internship
Recommended optional programme components None
Course availability The course is available to visiting students
Lecturer(s)
  • HANTÁKOVÁ Jana, RNDr. Ph.D.
  • HASÍK Karel, doc. RNDr. Ph.D.
Course content
1. Introduction and basic methods (simple examples, method of separation of variables, homogeneous equations). 2. Systems of linear first-order equations (existence and uniqueness of solutions, properties of solutions, systems with constant coefficients, variation of constants, linear differential equation of n-th order). 3. Systems of differential equations (existence of solutions, Picard's sequence, Paeno existence theorem, Gronwall's lemma, uniqueness of initial value problem, global uniqueness of solution). 4. Dependence of solutions on initial conditions and parameters. 5. Stability (the notion of stability, Lyapunov, uniform, asymptotic and exponential stability, stability of linear differential systems, stability of perturbed systems). 6. Autonomous systems (trajectories, phase space, singular point, cycle, critical points of linear and nonlinear system). 7. Boundary value problems (formulation, homogeneous and nonhomogeneous boundary value problems, Green function, Sturm-Liouville problem).

Learning activities and teaching methods
unspecified
Recommended literature
  • J. Kalas, M. Ráb. Obyčejné diferenciální rovnice. Brno, 2001.
  • J. Kurzweil. Obyčejné diferenciální rovnice. SNTL, Praha, 1978.
  • L. S. Pontryagin. Ordinary Differential Equations. Addison-Wesley, Reading, Mass, 1962. ISBN 62-17075.
  • M. Greguš, M. Švec, V. Šeda. Obyčajné diferenciálne rovnice. Alfa-SNTL, Bratislava-Praha, 1985.
  • P. Hartman. Ordinary differential Equations. Baltimore, 1973.


Study plans that include the course
Faculty Study plan (Version) Branch of study Category Recommended year of study Recommended semester
Mathematical Institute in Opava Applied Mathematics (1) Mathematics courses 1 Winter
Mathematical Institute in Opava Applied Mathematics (2014-IVT) Mathematics courses 3 Winter
Mathematical Institute in Opava Mathematical Analysis (1-IVT) Mathematics courses 3 Winter
Mathematical Institute in Opava Mathematical Methods in Economics (3) Economy 3 Winter
Mathematical Institute in Opava Mathematics (2014-IVT) Mathematics courses 3 Winter
Mathematical Institute in Opava Mathematics (1-IVT) Mathematics courses 3 Winter
Mathematical Institute in Opava Applied Mathematics (2014-F) Mathematics courses 3 Winter
Faculty of Philosophy and Science in Opava Theoretical Physics (2) Physics courses - Winter
Mathematical Institute in Opava Mathematics (2014-F) Mathematics courses 3 Winter
Mathematical Institute in Opava Mathematics (2-F) Mathematics courses 3 Winter
Mathematical Institute in Opava Mathematical Methods in Economics (2) Economy 3 Winter
Mathematical Institute in Opava Applied Mathematics in Risk Management (3) Mathematics courses 3 Winter