**Instructor: Stéphane Lafortune**

- tel. (843)-953-5869
- Rm 223, 2 Greenway
- Office hours: M 10-11, W 2-3, Th 11-12
- email: lafortunes@cofc.edu
- URL: www.math.cofc.edu/lafortunes/

**Lecture**: TR, 12:00-1:15PM,
MAYBANK HALL (MYBK) 223.

**Course Description**: The general purpose of the course is to
learn how to obtain and use Lie
symmetries of differential equations. First, we will discuss the
concept of continuous symmetries of ordinary differential equations and
develop a method to calculate them. Then, we will see how the
symmetries can be used to study and solve the equations, starting with
one-parameter groups. Next, the case of partial differential equations
and their continuous symmetries will be considered. Finally, if time
permits, we will discuss how to obtain discrete symmetries of
differential equations.

**Prerequisite:** Math 323.

**Grading Policy: **

- Math 480: 20% from homework, 50% from two midterms and 30% from final exam.
- Math 580: 15% from homework, 15% from final project, 45% from two midterms and 25% from final exam.

**Important Dates: **There will be two midterms, on ** February 14** and **March
28**. The
**Final Exam **will
be on** April 27th, 12:00-03:00 P.M. **The
last
day to withdraw from the class with a grade of W is** February 21**.

**Important: There will be no make-ups for mid-term exams. **If
a student misses a mid-term exam for a valid reason, the grade for this
exam will be replaced by the grade of the Final exam. There will be a
make-up
for the Final exam only in the case of a very good reason.

**Homework assignments: **Homework will be collected each
Tuesday.
Late homework will be accepted with 10% penalty for each day it is
late. The worst homework grade
will
be dropped.

Grade |
A |
B+ |
B |
C+ |
C |
D |

Lower Bound |
90% |
85% |
80% |
75% |
70% |
60% |

Some other literature:

- Olver, Peter J. Applications of Lie groups to differential equations, second edition, Springer-Verlag, 1993.
- Bluman, G. and Kumei, S.,
*Symmetries and Differential Equations,*second edition, Springer-Verlag 1989. - Bluman, G. and Arco, S.,
*Symmetry and Integration Methods for Differential Equations,*Springer-Verlag 2002. - Ibragimov, N.,
*Elementary Lie Group Analysis and Ordinary Differential Equations,*John Wiley & Sons 1999.

Last modified 01-06-2006 by Stéphane Lafortune