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MATH 583-TOPICS IN MATHEMATICAL PHYSICS I
(Application of Lie Groups to Differential Equations)
Fall 1998, Spring 2003, Fall 2011
Text Book :
Peter J. Olver , Applications of Lie Groups
in Differential Equations , Springer-Verlag New York , 1986 (First
Other Books :
1. Peter J. Olver , Equivalence, Invariants and Symmetry , Cambridge
University Press, 1995.
2. Giuseppe Gaeta, Nonlinear Symmetries and Nonlinear Equations ,
Kluver Academic Publishers, Dordreht ,1994.
3. W.I. Fushchich , W.M. Shtelen and N.I. Serov, Symmetry Analysis
and Exact Solutions of Equations of Nonlinear Mathematical Physics ,
Kluver Academic Publishers, Dordreht 1989.
4. G.W. Bluman and S. Kumei , Symmetries and Differential Equations ,
Springer, New York, 1989.
Contents of the course :
First Semester is mainly on the
symmetries of (ordinary and partial) differential equations. We shall cover
the first four chapters of the Olver's book.
Monday 13.40-16.30 SAZ01
Exams and Homeworks
First Midterm Exam (%25)
Second Midterm Exam (%25)
Final Exam (%25)
Homework and Projects (%25)
Read the The following sections in Chapter 1.
Lie Groups, Vector fileds and Lie Algebras
Local transformation groups
Symmetries of algebraic equations
Groups and differential equations
Prolongation of the group action
Prolongation of the vector fields
01. Sept. 07 - Symmetries of Algebraic Equations
02. Sept. 14 - Groups and Differential Equations
03. Sept. 21 - Prolongation
04. Sept. 28 - Calculation of Symmetry Groups
05. Oct. 05 - Integration of ODEs
06. Oct. 12 - Nondegeneracy Conditions for DEs
07. Oct. 19 - Group Invariant Solutions
08. Oct. 26 - Group Invariant Solutions
09. Nov. 02 - Group Invariant Solutions
10. Nov. 09 - Symmetry Groups and Conservation Laws
11. Nov. 16 - Symmetry Groups and Conservation Laws
12. Nov. 23 - Symmetry Groups and Conservation Laws
13. Nov. 30 - Variational Calculus and symmetries
14. Dec. 07 - Variational Calculus and symmetries
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