Course: Geometric Theory of Partial Differential Equations I

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Course title Geometric Theory of Partial Differential Equations I
Course code MU/03258
Organizational form of instruction Lecture + Lesson
Level of course Master
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
Lecturer(s)
  • SERGYEYEV Artur, doc. RNDr. Ph.D.
Course content
The jet spaces, total derivatives, prolongation of differential equations. Point transformations, infinitesimal symmetries and their computation. Integration of ODEs and reduction using symmetries. Invariant solutions. Higher (generalized) symmetries. Evolutionary derivations and evolutionary form of a higher symmetry. The Lie bracket of symmetries. Point and contact symmetries as special cases of higher symmetries.

Learning activities and teaching methods
unspecified
Recommended literature
  • A.M. Vinogradov, I.S. Krasil'ščik, eds. Simmetrii i zakony sochraneniya uravnenij matematičeskoj fiziki. Faktorial, Moskva, 1997.
  • C. Rogers a W. F. Shadwick. Bäcklund transformations and Their Applications. Academic Press, New York, 1982.
  • G. W. Bluman a S. Kumei. Symmetries and Differential Equations. Springer, New York, 1989.
  • P. J. Olver. Applications of Lie groups to differential equations. Springer, New York, 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 5 Winter
Mathematical Institute in Opava Mathematical Analysis (1) Mathematics courses 2 Winter
Mathematical Institute in Opava Geometry and Global Analysis (1) Mathematics courses 2 Winter