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MU:MU25007 Calculus of Variations - Course Information

## MU25007 Calculus of Variations

**Mathematical Institute in Opava**

Winter 2015

**Extent and Intensity**- 2/2/0. 6 credit(s). Type of Completion: zk (examination).
**Guaranteed by**- RNDr. Oldřich Stolín, Ph.D.

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 seznámení studentů se základy variačního počtu a některými jeho aplikacemi.
**Syllabus**- Basics of calculus of variations (action functional, du ois-Reymond lemma, first variation).

Euler-Lagrange equations. Introduction to the inverse problem of calculus of variations.

Point symmetries of actions and Euler-Lagrange equations. Emmy Nother's First Theorem for point symmetries.

Basic notions of higher variations.

Least action principle in mechanics and its applications.

- Basics of calculus of variations (action functional, du ois-Reymond lemma, first variation).
**Literature**- V. I. Arnold.
*Mathematical methods of classical mechanics*. Springer, New York, 1999. ISBN 0387968903. info - P. J. Olver.
*Applications of Lie groups to differential equations*. Springer, New York, 1993. info - I. M. Gelfand, S. V. Fomin.
*Calculus of Variations*. Englewood Cliffs, Prentice-Hall, 1963. URL info

*recommended literature*- V. I. Arnold.
**Language of instruction**- Czech
**Further Comments**- The course can also be completed outside the examination period.

- Enrolment Statistics (Winter 2015, recent)
- Permalink: https://is.slu.cz/course/sumu/winter2015/MU25007