MU25007 Calculus of Variations

Mathematical Institute in Opava
Winter 2014
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.
  • 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.
    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
Further Comments
The course can also be completed outside the examination period.
The course is also listed under the following terms Winter 2012, Winter 2013, Winter 2015, Winter 2016, Winter 2017, Winter 2018, Winter 2019, Summer 2021, Summer 2022.
  • Enrolment Statistics (Winter 2014, recent)
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