Course: Variational Analysis on Manifolds

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Course title Variational Analysis on Manifolds
Course code MU/03265
Organizational form of instruction Lecture + Lesson
Level of course Master
Year of study not specified
Semester Summer
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
- Jets of differentiable mappings, fiber bundles and their prolongations, manifolds of contact elements - The Lagrange structures (horizontal and contact forms, Lepagean forms, the first variation formula, the Euler-Lagrange equations, the Hamilton equations) - Symmetries of the Lagrange structures (invariance transformations of the Lagrange structure, generalized symmetries, the first Noether theorem, the natural Lagrange structures, the second Noether theorem) - The field of extremals and the Hamilton-Jacobi equations - Foundations of the theory of bundles, variational sequence.

Learning activities and teaching methods
Recommended literature
  • D. Krupka. Jets and Contact Elements. Proc. of the Seminar on Differential Geometry, Mathematical Publications. Silesian University, Opava, 2000.
  • D. Krupka. The Geometry of Lagrange Structures II. - Elementary Sheaf Theory. Silesian University, Opava, 1998.
  • D. Krupka. The Geometry of Lagrange Structures. Silesian University, Opava, 1997.
  • I. M. Gelfand, S. V. Fomin. Calculus of Variations. Englewood Cliffs, Prentice-Hall, 1963.
  • P.J. Olver. Applications of Lie groups to differential equations. 1993.

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 4 Summer