MU:MU25007 Calculus of Variations

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

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.

Literature

recommended 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

Language of instruction

Czech

Further Comments

The course can also be completed outside the examination period.