MU:MU04064 Variational Analysis I - Course Information
MU04064 Variational Analysis I
Mathematical Institute in OpavaWinter 2013
- 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
- Mathematical Analysis (programme MU, M1101)
- Mathematics (programme MU, B1101)
- 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).
- Introduction to the subject of calculus of variations, examples of variational problems.
- 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.
- Enrolment Statistics (Winter 2013, recent)
- Permalink: https://is.slu.cz/course/sumu/winter2013/MU04064