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 
 Description:

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

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
 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) 83144 Russian Math. Surveys 47:4 (1992) 89156
 Keywords:
 Lie groups, Lie algebras, symmetries of differential equations
Abbreviations used:
Semester:
 W ... winter semester (usually October  February)
 S ... spring semester (usually March  June)
 W,S ... both semesters
Mode of completion of the course:
 A ... Assessment (no grade is given to this course but credits are awarded. You will receive only P (Passed) of F (Failed) and number of credits)
 GA ... Graded Assessment (a grade is awarded for this course)
 EX ... Examination (a grade is awarded for this course)
 A, EX ... Examination (the award of Assessment is a precondition for taking the Examination in the given subject, a grade is awarded for this course)
Weekly load (hours per week):
 P ... lecture
 C ... seminar
 L ... laboratory
 R ... proseminar
 S ... seminar