MU25007 Calculus of Variations

Mathematical Institute in Opava
Summer 2022
Extent and Intensity
2/2/0. 6 credit(s). Type of Completion: zk (examination).
RNDr. Petr Blaschke, Ph.D. (lecturer)
Guaranteed by
RNDr. Petr Blaschke, Ph.D.
Mathematical Institute in Opava
Prerequisites (in Czech)
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
The Goal of the course is to introduce students with the basics of calculus of variation and some of its applications.
  • 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.
    required literature
  • P. J. Olver. Applications of Lie groups to differential equations. Springer, New York, 1993. info
    recommended literature
  • V. I. Arnold. Mathematical methods of classical mechanics. Springer, New York, 1999. ISBN 0387968903. info
  • I. M. Gelfand, S. V. Fomin. Calculus of Variations. Englewood Cliffs, Prentice-Hall, 1963. URL info
Language of instruction
Further comments (probably available only in Czech)
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.
The course is also listed under the following terms Winter 2012, Winter 2013, Winter 2014, Winter 2015, Winter 2016, Winter 2017, Winter 2018, Winter 2019, Summer 2021.
  • Enrolment Statistics (Summer 2022, recent)
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