MU:MU04065 Variational Analysis II - Course Information
MU04065 Variational Analysis II
Mathematical Institute in OpavaSummer 2018
- Extent and Intensity
- 2/2/0. 6 credit(s). Type of Completion: zk (examination).
- Guaranteed by
- prof. RNDr. Artur Sergyeyev, Ph.D., DSc.
Mathematical Institute in Opava - Prerequisites
- MU04064 Variational Analysis I
MU/04064 - Course Enrolment Limitations
- The course is offered to students of any study field.
- Course objectives
- The goal of the lectures is to introduce the students to the more advanced aspects of calculus of variations.
- Syllabus
- - Regular variational problems in mechanics (the regularity condition, the Legendre transformation, the canonical Hamilton equations).
- Poisson and symplectic structures. Hamiltonian systems and their integrals. Integrability and the Liouville theorem. Reduction of Hamiltonian systems and the moment map. Separation of variables in Hamiltonian systems and the Hamilton-Jacobi theory.
- Bihamiltonian systems and their properties.
- Poisson and symplectic structures on the evolutionary system of partial differential equations and their properties. Bihamiltonian systems of PDEs and their integrability. Recursion operators.
- - Regular variational problems in mechanics (the regularity condition, the Legendre transformation, the canonical Hamilton equations).
- Literature
- recommended literature
- N. A. Bobylev, S. V. Emel'yanov, S. K. Korovin. Geometrical methods in variational problems. Boston, 1999. ISBN 0-7923-5780-9. URL info
- V. I. Arnold. Mathematical methods of classical mechanics. Springer, New York, 1999. ISBN 0387968903. info
- M. Giaquinta, S. Hildebrandt. Calculus of variations I and II. Springer, Berlín, 1996. ISBN 3540579613. info
- P. J. Olver. Applications of Lie groups to differential equations. Springer, New York, 1993. info
- A. T. Fomenko. Symplectic geometry. Gordon and Breach, New York, 1988. ISBN 2881246575. info
- I. M. Gelfand, S. V. Fomin. Calculus of Variations. Englewood Cliffs, Prentice-Hall, 1963. URL 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
- Oral exam; further requirements to be specified in the course of the semester.
- Enrolment Statistics (Summer 2018, recent)
- Permalink: https://is.slu.cz/course/sumu/summer2018/MU04065