Code: 02DRG Differential Equations, Symmetries and Groups
Lecturer: doc. Ing. Libor Šnobl Ph.D. Weekly load: 2+2 Completion: A
Department: 14102 Credits: 4 Semester: S
The purpose of the lecture is to teach students computation of symmetries of the differential equations.
1. Symmetries in physics and mathematics
2. Groups.
3. One-parameter subgroups, generators.
4. Group actions.
5. Local and infinitesimal group actions.
6. Point transformations.
7. Symmetries of equations.
8. Determination of infinitesimal symmetries.
9. Symmetry-based reduction of order of ODEs
10. Selfsimilar solutions of PDEs
Seminar contents:
1. Calculation of symmetries of a given ODE
2. Solution of ODE via oredr reduction
3. Calculation of symmetries of a given PDE (Heat equation, KdV equation, ...)
4. Interpretation of the symmetries
5. Determination of the Lie algebra of the symmetries
6. Construction of selfsimilar solutions.
Recommended literature:
Key references:
[1] P.J.Olver, Applications of Lie Groups to Differential Equations, Springer 2000
[2] P.E. Hydon: Symmetry Methods for Differential Equations: A Beginner's Guide (Cambridge Texts in Applied Mathematics), CUP 2000

Recommended references:
[3] N.Kh. Ibragimov: Group analysis of ordinary differential equations an the invariance principle in mathematical physics, Uspekhi Mat Nauk 47:4 (1992) 83-144 Russian Math. Surveys 47:4 (1992) 89-156
Lie groups, Lie algebras, symmetries of differential equations

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Mode of completion of the course:

Weekly load (hours per week):