Differential Equations, Symmetries and Groups
Code  Completion  Credits  Range 

D02DRG  ZK 
 Lecturer:
 Tutor:
 Supervisor:
 Department of Physics
 Synopsis:

The purpose of the lecture is to teach students computation of symmetries of the differential equations.
 Requirements:

01MAA34, 01DIFR, 02TEF12
 Syllabus of lectures:

1. Symmetries in physics and mathematics
2. Groups.
3. Oneparameter subgroups, generators.
4. Group actions.
5. Local and infinitesimal group actions.
6. Point transformations.
7. Symmetries of equations.
8. Determination of infinitesimal symmetries.
9. Symmetrybased 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:

Knowledge:
Lie symmetries of differential equations
Abilities:
Computation of point symmetries of differential equations and their application in solution of given ODEs and PDEs.
 Study materials:

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) 83144 Russian Math. Surveys 47:4 (1992) 89156
 Note:
 Further information:
 No timetable has been prepared for this course
 The course is a part of the following study plans: