Title: Computer Algebra in a Course on Lie Symmetries of ODEs

Author: Alejandro Jakubi* (jakubi@dfuba.df.uba.ar)

Affiliation: Dept of Physics, Univ of Buenos Aires, Argentina

Abstract: In recent years renewed interest has been given to methods based on Lie symmetries of differential equations. One of the main reasons has been the widespread availability of computer algebra systems and the development of specialized packages for this kind of calculations. Hence a course on this subject is, in principle, ideally suited to introduce computer algebra tools. The experiences with the use of these tools in a course for undergraduate and graduate students in Physics are described. Both general purpose CAS like Maple and stand alone system like LIE were tried. Specialized packages considered include ODEtools and DESOLV, both running over Maple. Some additional routines were developed to interface and extend these packages. No previous knowledge on Lie groups or differential geometry is required for this course. Its scope has been limited up to now to Lie point symmetries of ODEs.