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MU:MU25007 Calculus of Variations - Course Information

## MU25007 Calculus of Variations

**Mathematical Institute in Opava**

Winter 2019

**Extent and Intensity**- 2/2/0. 6 credit(s). Type of Completion: zk (examination).
**Teacher(s)**- RNDr. Petr Blaschke, Ph.D. (lecturer)

RNDr. Petr Blaschke, Ph.D. (seminar tutor) **Guaranteed by**- RNDr. Petr Blaschke, Ph.D.

Mathematical Institute in Opava **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, 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 (probably available only in Czech)**- Study Materials

The course can also be completed outside the examination period. **Teacher's information**- Credit is given for the student's active participation and the student must also score at least 50 procent of points from all tests given. The precise nature of these tests and the timetable is determined by the tutor.

The course exam is oral. The lecturer will asses the amount and quality of knowledge and skills acquired by the student during the course.

- Enrolment Statistics (Winter 2019, recent)
- Permalink: https://is.slu.cz/course/sumu/winter2019/MU25007