MU03258 Geometric Theory of Partial Differential Equations I

Mathematical Institute in Opava
Winter 2010
Extent and Intensity
2/2/0. 6 credit(s). Type of Completion: z (credit).
Teacher(s)
prof. RNDr. Artur Sergyeyev, Ph.D., DSc. (lecturer)
RNDr. Petr Vojčák, Ph.D. (seminar tutor)
Guaranteed by
prof. RNDr. Artur Sergyeyev, Ph.D., DSc.
Mathematical Institute in Opava
Prerequisites
MU02037 Partial Differential Equations || MU03035 Partial Differential Eq. II || MU03135 Partial Differential Equations
MU/02024, MU/02027, MU/03038
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
there are 8 fields of study the course is directly associated with, display
Course objectives
In this course we will become acquainted with a number of modern methods for solving differential equations which are "located" at the intersection of geometry of the so-called jet spaces and theory of Lie groups and Lie algebras. Successful completion of this course requires good knowledge of standard theory of ordinary and partial differential equations and of differential geometry.
Syllabus
  • 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.
Literature
    recommended literature
  • A.M. Vinogradov, I.S. Krasil'ščik, eds. Simmetrii i zakony sochraneniya uravnenij matematičeskoj fiziki. Faktorial, Moskva, 1997. info
  • P. J. Olver. Applications of Lie groups to differential equations. Springer, New York, 1993. info
  • G. W. Bluman a S. Kumei. Symmetries and Differential Equations. Springer, New York, 1989. info
    not specified
  • C. Rogers a W. F. Shadwick. Bäcklund transformations and Their Applications. Academic Press, New York, 1982. 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.
The course is also listed under the following terms Winter 1999, Winter 2000, Winter 2001, Winter 2002, Winter 2003, Winter 2004, Winter 2005, Winter 2006, Winter 2007, Winter 2008, Winter 2009, Winter 2011, Winter 2012, Winter 2013, Winter 2014, Winter 2015, Winter 2016, Winter 2017, Winter 2018, Winter 2019.
  • Enrolment Statistics (Winter 2010, recent)
  • Permalink: https://is.slu.cz/course/sumu/winter2010/MU03258