MU04064 Variational Analysis I

Mathematical Institute in Opava
Winter 2015
Extent and Intensity
2/2/0. 6 credit(s). Type of Completion: z (credit).
Guaranteed by
prof. RNDr. Artur Sergyeyev, Ph.D., DSc.
Mathematical Institute in Opava
Prerequisites (in Czech)
MU03039 Differential Geometry II
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 lectures is to introduce the students to the basics of calculus of variations.
Syllabus
  • Introduction to the subject of calculus of variations, examples of variational problems.
    The basic problem of calculus of variations (the Lagrange function, variational functional, variation, the du Bois-Reymond Lemma, Euler - Lagrange equations).
    Jet spaces, total derivatives and contact forms. Differential equations as submanifolds in jet spaces. Vector fields on jet spaces. Prolongation.
    The symmetries of variational problems (symmetries and generalized symmetries, invariance groups, criteria of invariance, gauge transformations, the first and second Noether's theorems).
Literature
    recommended literature
  • N. A. Bobylev, S. V. Emel'yanov, S. K. Korovin. Geometrical methods in variational problems. Boston, 1999. URL info
  • P. J. Olver. Equivalence, Invariants, and Symmetry. Cambridge University Press, Cambridge, 1995. ISBN 0-521-47811-1. info
  • P.J. Olver. Applications of Lie Groups to Differential Equations. 1993. info
  • R. P. Feynman, R. B. Leighton, M. Sands. The Feynman lectures on physics II. Addison Wesley, London, 1964. info
  • I. M. Gelfand, S. V. Fomin. Calculus of Variations. Englewood Cliffs, Prentice-Hall, 1963. URL info
  • I. M. Gel'fand, S. V. Fomin. Variacionnoe isčislenie. Gosudarstvennoe izdatel'stvo fiziko-matematičesk, 1961. info
    not specified
  • L. S. Polak (red.). Variacionnye principy mechaniki. Fizmatgiz, Moskva, 1961. info
Language of instruction
Czech
Further comments (probably available only in Czech)
The course can also be completed outside the examination period.
Teacher's information
Requirements to be specified in the course of the semester.
The course is also listed under the following terms Winter 1997, Summer 1998, Winter 1999, Winter 2000, Winter 2001, Winter 2002, Winter 2003, Winter 2004, Winter 2005, Winter 2006, Winter 2007, Winter 2008, Winter 2009, Winter 2010, Winter 2011, Winter 2012, Winter 2013, Winter 2014, Winter 2016, Winter 2017, Winter 2018, Winter 2019.
  • Enrolment Statistics (Winter 2015, recent)
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