MU:MU25003 Solution Methods for ODE - Course Information

MU25003 Solution Methods for Ordinary Differential Equations

Extent and Intensity

2/2/0. 6 credit(s). Type of Completion: zk (examination).

Teacher(s)

prof. RNDr. Artur Sergyeyev, Ph.D., DSc. (lecturer)
prof. RNDr. Artur Sergyeyev, Ph.D., DSc. (seminar tutor)

Guaranteed by

prof. RNDr. Artur Sergyeyev, Ph.D., DSc.
Mathematical Institute in Opava

Timetable

Tue 16:25–18:00 RZ

• Timetable of Seminar Groups:

MU25003/01: Thu 18:05–19:40 R2, A. Sergyeyev

Prerequisites (in Czech)

TYP_STUDIA(N)

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

• Geometry and Global Analysis (programme MU, NMgr-M)
• Geometry and Global Analysis (programme MU, N1101)
• Mathematical Analysis (programme MU, NMgr-M)
• Mathematical Modelling (programme MU, NMgr-M)

Course objectives

To teach students advanced methods to find exact solutions of systems of ordinary differential equations and their systems.

Syllabus

• 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.
  

Literature

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

Czech

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.

• Enrolment Statistics (Winter 2023, recent)
  
• Permalink: https://is.slu.cz/course/sumu/winter2023/MU25003