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).

Guaranteed by

doc. RNDr. Michal Marvan, CSc.
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

• Geometry and Global Analysis (programme MU, N1101)

Course objectives (in Czech)

Cílem přednášky je seznámit studenty s řadou metod umožňujících nalezení exaktních řešení systémů obyčejných diferenciálních rovnic.

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 transformations.
  Equations for symmetries and integration factors and their solutions.
  First integrals and their relationship to integration factors.
  Order lowering and integration of equations and systems using symmetries and first integrals.
  Invariant solutions and generation of solutions using symmetries.

Literature

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
• H. Stephani. Differential equations. Their solution using symmetries. Cambridge University Press, Cambridge, 1989. info

Language of instruction

Czech

Further Comments

The course can also be completed outside the examination period.

• Enrolment Statistics (Winter 2013, recent)
  
• Permalink: https://is.slu.cz/course/sumu/winter2013/MU25003