Course: Variational Analysis I

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Course title Variational Analysis I
Course code MU/04064
Organizational form of instruction Lecture + Lesson
Level of course Bachelor
Year of study not specified
Semester Winter
Number of ECTS credits 6
Language of instruction Czech
Status of course Compulsory-optional
Form of instruction Face-to-face
Work placements This is not an internship
Recommended optional programme components None
Course availability The course is available to visiting students
  • SERGYEYEV Artur, doc. RNDr. Ph.D.
Course content
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).

Learning activities and teaching methods
Recommended literature
  • I. M. Gelfand, S. V. Fomin. Calculus of Variations. Englewood Cliffs, Prentice-Hall, 1963.
  • I. M. Gel'fand, S. V. Fomin. Variacionnoe isčislenie. Gosudarstvennoe izdatel'stvo fiziko-matematičeskoj literatury, Moskva, 1961.
  • L. S. Polak (red.). Variacionnye principy mechaniki. Fizmatgiz, Moskva, 1961.
  • N. A. Bobylev, S. V. Emel'yanov, S. K. Korovin. Geometrical methods in variational problems. Boston, 1999.
  • P. J. Olver. Equivalence, Invariants, and Symmetry. Cambridge University Press, Cambridge, 1995. ISBN 0-521-47811-1.
  • P.J. Olver. Applications of Lie Groups to Differential Equations. 1993.
  • R. P. Feynman, R. B. Leighton, M. Sands. The Feynman lectures on physics II. Addison Wesley, London, 1964.

Study plans that include the course
Faculty Study plan (Version) Branch of study Category Recommended year of study Recommended semester
Mathematical Institute in Opava Mathematical Analysis (1-IVT) Mathematics courses 5 Winter
Mathematical Institute in Opava Mathematics (1-IVT) Mathematics courses 3 Winter
Mathematical Institute in Opava Mathematics (2-F) Mathematics courses 3 Winter