## MU02024 Ordinary Differential Equations

Mathematical Institute in Opava
Winter 2015
Extent and Intensity
2/2/0. 6 credit(s). Type of Completion: zk (examination).
Teacher(s)
RNDr. Jana Hantáková, Ph.D. (lecturer)
RNDr. Jana Hantáková, Ph.D. (seminar tutor)
Guaranteed by
prof. RNDr. Jaroslav Smítal, DrSc.
Mathematical Institute in Opava
Course Enrolment Limitations
The course is also offered to the students of the fields other than those the course is directly associated with.
fields of study / plans the course is directly associated with
there are 8 fields of study the course is directly associated with, display
Course objectives (in Czech)
Syllabus
• 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).
Literature
recommended literature
• J. Kalas, M. Ráb. Obyčejné diferenciální rovnice. Brno, 2001. info
• M. Greguš, M. Švec, V. Šeda. Obyčajné diferenciálne rovnice. Alfa-SNTL, Bratislava-Praha, 1985. info
• J. Kurzweil. Obyčejné diferenciální rovnice. SNTL, Praha, 1978. info
• P. Hartman. Ordinary differential Equations. Baltimore, 1973. info
• L. S. Pontryagin. Ordinary Differential Equations. Addison-Wesley, Reading, Mass, 1962. ISBN 62-17075. info
Language of instruction
Czech
Further comments (probably available only in Czech)
The course can also be completed outside the examination period.
The course is also listed under the following terms Winter 1997, Winter 1998, Winter 1999, Winter 2000, Winter 2001, Winter 2002, Winter 2003, Winter 2004, Winter 2005, Winter 2006, Winter 2007, Winter 2008, Winter 2009, Winter 2010, Winter 2011, Winter 2012, Winter 2013, Winter 2014, Winter 2016, Winter 2017, Winter 2018, Winter 2019, Winter 2020, Winter 2021.
• Enrolment Statistics (Winter 2015, recent)