MU:MU02024 Ordinary Differential Equation - Course Information
MU02024 Ordinary Differential Equations
Mathematical Institute in OpavaWinter 2019
- Extent and Intensity
- 2/2/0. 6 credit(s). Type of Completion: zk (examination).
- Teacher(s)
- doc. RNDr. Karel Hasík, Ph.D. (lecturer)
RNDr. Petra Nábělková, Ph.D. (seminar tutor) - Guaranteed by
- doc. RNDr. Karel Hasík, Ph.D.
Mathematical Institute in Opava - Timetable
- Tue 8:05–9:40 R2
- Timetable of Seminar Groups:
- Prerequisites (in Czech)
- TYP_STUDIA(B)
- 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 6 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. Laplace transformation and its applications.
5. Stability (the notion of stability, Lyapunov, uniform and asymptotic 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).
- 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)
- Study Materials
The course can also be completed outside the examination period. - Teacher's information
- Attendance at lectures is recommended. In the introductory lesson, students will be informed about the requirements of lecturers for successful completion of the subject.
Credit: 60 to 70% points from written tests during the semester; the specific value is determined by the lecturer according to the difficulty of individual test
Exam: It consists of a written and an oral part. The requirements for successful completion of the written part will be determined by the lecturer so that they correspond to the level of requirements placed on students during the semester. Upon successful completion of the written part, students will be examined verbally, emphasizing the theoretical part of the lectured subject.
- Enrolment Statistics (Winter 2019, recent)
- Permalink: https://is.slu.cz/course/sumu/winter2019/MU02024