Construction of study materials on mathematical courses with using of computer algebra systems
Many mathematical courses of the high school use conceptions and chapters of asymptotical analysis and optimal processes theory. High level of the exposition of the mathematical courses given with traditional methods is still actual but new informational technologies keep a reserve of increasing teaching quality and better mastering of the courses material by the students. Such a possibility is given with methods of artificial intelligence and computer algebra methods of computer computations.Applying of these methods leads to improvements, perfections of the teaching process and provides appearing of the new development horizons of the branches of mathematics connected with integration with computer algebra methods and new conceptions of approximate computations. Prof. Dmitriev M.G. and his post graduate students proposes to use the symbolic computation system REDUCE for automatization of the computations applying to one of the most popular methods of asymptotic integration of the singularly perturbed ordinary differential equations - the boundary functions method that includes the Poincare method of building of the asymptotical of the regular pertubated ordinary differential equations. From one side such an application allows to build the asimptotics in analytical form because the method of building of the asymptotic is analytical itself and further using of numerical methods interrupt a logical chain of using analytical forms, and from the other side the lack of sufficient skills in real practice for building the highest approximations leads to the weak practical usage of such a mode of accuracy increasing of approximations (due to the highest approximations). Therefore we obtain one more high accuracy method of the approximated solution of problems with
a small parameter besides natural applying to the symbolic computations in asymptotic analysis. Though there are a lot of computer algebra systems (MAPLE,MATHEMATICA, DERIVE etc.) the choice of REDUCE isn't casual. Firstly Prof. Dmitriev M.G. possesses with the licensed product and secondly REDUCE contains input operators of the asymptotic analysis and a large library of auxiliary programs in spite of the pure interface of REDUCE. The created software on the asymptotic analysis of the singularly perturbed initial problems can be used in educational process on the course of differential equations and the theory of the optimal control.
In 1995,1996 in Pereslavl two international workshops "New computer technologies in control systems" were organized by Dmitriev M.G. In the frames of these workshops the one of project's goal(organization of net between the specialists in optimal control theory and computer algebra systems applications) were discussed. The special project for NATO grante program was prepared in 1995.