MU:MU02024 Ordinary Differential Equation - Course Information
MU02024 Ordinary Differential Equations
Mathematical Institute in OpavaWinter 2015
- Extent and Intensity
- 2/2/0. 6 credit(s). Type of Completion: zk (examination).
- Teacher(s)
- doc. RNDr. Jana Hantáková, Ph.D. (lecturer)
doc. 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)
- Základy teorie obyčejných diferenciálních rovnic.
- 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).
- 1. Introduction and basic methods (simple examples, method of separation of variables, homogeneous equations).
- 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.
- Enrolment Statistics (Winter 2015, recent)
- Permalink: https://is.slu.cz/course/sumu/winter2015/MU02024