By Gerd Baumann
The function of this e-book is to supply the reader with a complete advent to the functions of symmetry research to boring and partial differential equations. The theoretical heritage of physics is illustrated by way of modem tools of desktop algebra. The presentation of the fabric within the booklet relies on Mathematica 3.0 notice books. the total revealed model of this booklet is out there at the accompanying CD. The textual content is gifted in this kind of means that the reader can engage with the calculations and scan with the versions and techniques. additionally contained at the CD is a package deal known as MathLie-in honor of Sophus Lie---carrying out the calculations instantly. the appliance of symmetry research to difficulties from physics, arithmetic, and en gineering is confirmed by way of many examples. The research of symmetries of differential equations is an outdated topic. due to Sophus Lie we at the present time have to be had to us vital details at the habit of differential equations. Symmetries can be utilized to discover targeted ideas. Symmetries should be utilized to ensure and to strengthen numerical schemes. they could offer conservation legislation for differential equations. the speculation awarded this is in keeping with Lie, containing enhance ments and generalizations made via later mathematicians who rediscovered and used Lie's paintings. The presentation of Lie's idea in reference to Mathematica is novel and vitalizes an previous thought. The wide symbolic calculations priceless lower than Lie's thought are supported via MathLie, a package deal written in Mathematica.