## MU02024 Ordinary Differential Equations

Mathematical Institute in Opava
Winter 2021
Extent and Intensity
2/2/0. 6 credit(s). Type of Completion: zk (examination).
Teacher(s)
RNDr. Petra Nábělková, Ph.D. (seminar tutor)
doc. RNDr. Jana Kopfová, Ph.D. (lecturer)
Guaranteed by
doc. RNDr. Karel Hasík, Ph.D.
Mathematical Institute in Opava
Timetable
Wed 8:05–9:40 RZ
• Timetable of Seminar Groups:
MU02024/01: Mon 8:05–9:40 R2, P. Nábělková
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 8 fields of study the course is directly associated with, display
Course objectives
This is a basic course in the field of differential equations. The aim of the course is to acquaint students with important concepts and basic results from the theory of ordinary differential equations.
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).
7. Introduction to delayed differential equations with applications.
Literature
required literature
• J. Kalas, M. Ráb. Obyčejné diferenciální rovnice. Brno, 2001. info
• L. S. Pontryagin. Ordinary Differential Equations. Addison-Wesley, Reading, Mass, 1962. ISBN 62-17075. info
recommended literature
• 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
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.
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 2015, Winter 2016, Winter 2017, Winter 2018, Winter 2019, Winter 2020.
• Enrolment Statistics (recent)