A comparative study of some computer algebra packages which determine the lie point symmetries of differential equations

The study seeks to determine which of five computer algebra packages is best at finding the Lie point symmetries of systems of partial differential equations with minimal user intervention. The chosen packages are LIEPDE and DIMSYM for REDUCE, LIE and BIGLIE for MUMATH, DESOLV for MAPLE, and MATHLIE for MATHEMATICA. A series of systems of partial differential equations are used in the study. The paper concludes that while all of the computer packages are useful, DESOLV appears to be the most successful system at determining the complete set of Lie point symmetries of systems of partial differential equations.

Use of spreadsheet simulations in university chemistry education

Students who are strong in logical-mathematical intelligence have a natural advantage in learning and understanding chemistry, which is full of abstractions that are remote from the material world. Simulations provide more-inclusive learning activities for students who are weak in logical-mathematical intelligence.

A second advantage of using simulations is that they are not limited by (for example) the quantised energies, integral masses and discrete expectation values of real atoms and molecules. Numerical experiments can be used to investigate the effect of continuously varying atomic mass, bond distance or any other property, from one value to another.

Finally, students are more familiar with spreadsheets than more advanced mathematical packages such as MathCAD, MAPLE, Mathematica and other symbolic algebra software. Use of these advanced packages presents additional learning hurdles for students and should be used only for advanced classes. Furthermore, spreadsheets are capable of a level of sophistication that is greater than commonly expected. This can be achieved without the use of MACROs.

Examples from the author's teaching are used to discuss the advantages of spreadsheet simulations for learning chemistry.

Lie symmetries of partial differential equations using symbolic computing

This study presents a theoretical basis for and outlines the method of finding the Lie point symmetries of systems of partial differential equations. It seeks to determine which of five computer algebra packages is best at finding these symmetries. The chosen packages are LIEPDE and DIMSYM for REDUCE, LIE and BIGLIE for MUMATH, DESOLV for MAPLE, and MATHLIE for MATHEMATICA. This work concludes that while all of the computer packages are useful, DESOLV appears to be the most successful system at determining the complete set of Lie symmetries. Also, the study describes REDUCEVAR, a new package for MAPLE, that reduces the number of independent variables in systems of partial differential equations, using particular Lie point symmetries. It outlines the results of some testing carried out on this package. It concludes that REDUCEVAR is a very useful tool in performing the reduction of independent variables according to Lie's theory and is highly accurate in identifying cases where the symmetries are not suitable for finding S/G equations.