MU25003 Solution Methods for Ordinary Differential Equations

Mathematical Institute in Opava
Winter 2020
Extent and Intensity
2/2/0. 6 credit(s). Type of Completion: zk (examination).
RNDr. Hynek Baran, Ph.D. (seminar tutor)
doc. RNDr. Artur Sergyeyev, DSc. (lecturer)
Guaranteed by
doc. RNDr. Michal Marvan, CSc.
Mathematical Institute in Opava
Thu 16:25–18:00 112
  • Timetable of Seminar Groups:
MU25003/01: Thu 11:25–13:00 205, H. Baran
Prerequisites (in Czech)
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
Course objectives
To teach students advanced methods to find exact solutions of systems of ordinary differential equations and their systems.
  • An overview of elementary methods (integration factors, separation of variables, homogeneous equations, etc.)
    Basic ideas on jet spaces and total derivatives.
    Invariance group and algebra of a system of ordinary differential equations. Point and contact transformations.
    Equations for symmetries and methods to solve them.
    Reducing the order and integration of equations and systems using symmetries.
    First integrals, finding and using them.
    required literature
  • Peter E. Hydon. Symmetry methods for differential equations : a beginner's guide. Cambridge, 2000. ISBN 0-521-49786-8. info
  • H. Stephani. Differential equations. Their solution using symmetries. Cambridge University Press, Cambridge, 1989. info
    recommended literature
  • N. H. Ibragimov. Elementary Lie group analysis and ordinary differential equations. Wiley & Sons, 1999. info
  • P. J. Olver. Applications of Lie groups to differential equations. Springer, New York, 1993. info
Language of instruction
Further comments (probably available only in Czech)
Study Materials
The course can also be completed outside the examination period.
Teacher's information
The exam comprises a written part and an oral part. The written part tests the ability to select and apply a suitable solution method. The written part is followed by the oral part, which tests the theoretical knowledge of the subject.
The course is also listed under the following terms Winter 2012, Winter 2013, Winter 2014, Winter 2015, Winter 2016, Winter 2017, Winter 2018, Winter 2019.
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