Solving some physical problems using the methods of numerical mathematics with the help of system mathematica

Abstract

Every future teacher of mathematics must know symbolic approaches, for example, for finding derivations and integrals, solving algebraic and differential equations very well. But most of the problems from practice are not solvable by a symbolic way and therefore numerical ones must be used. That is way the basic knowledge of some numerical methods for solving problems of the real world is a component of the complex training of teachers of mathematics. Different computer systems for symbolic and numerical mathematics as MatLab, Maple, Mathematica or Derive enable their effective use. The posibility to join numerical and symbolic computation in these systems makes them very well suited for expressing numerical algorithms, testing them out and postprocessing the results, for example in a graphical form. Their ability for high-precision or exact calculations is also important. This contribution deals with a concrete illustration of using the system Mathematica for solving several typical physical problems by differential equations or their systems.