Differential Equations, Symmetries and Groups
- Department of Physics
The purpose of the lecture is to teach students computation of symmetries of the differential equations.
01MAA34, 01DIFR, 02TEF12
- Syllabus of lectures:
1. Symmetries in physics and mathematics
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
- Syllabus of tutorials:
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.
- Study Objective:
Lie symmetries of differential equations
Computation of point symmetries of differential equations and their application in solution of given ODEs and PDEs.
- Study materials:
 P.J.Olver, Applications of Lie Groups to Differential Equations, Springer 2000
 P.E. Hydon: Symmetry Methods for Differential Equations: A Beginner's Guide (Cambridge Texts in Applied Mathematics), CUP 2000
 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
- Further information:
- No time-table has been prepared for this course
- The course is a part of the following study plans: