M. Marčoková, I. Vadovičová, B. Dobrucký

University of Žilina (SLOVAKIA)
Modern engineering applications need a more thorough knowledge of mathematics, especially of applied one. Special functions are one of such areas of mathematics. Orthogonal polynomials are very important special functions with many applications in engineering and science. These polynomials appear in many areas of applications of mathematics and in physics as approximation theory, probability theory, partial differential equations for heat conduction, quantum mechanics, electric circuit theory, signals processing theory, control theory, statistical communications theory, problems in mechanics an others are. Special functions, it means that also orthogonal polynomials, are sometimes involved in some physics courses (e. g. quantum mechanics) or in some mathematics courses (e. g. ordinary differential equations, partial differential equations, special functions and their applications, etc.), but in such courses orthogonal polynomials have only a small time to teach, learn and investigate them in details. Frequently also various aspects of special functions are needful in courses of engineering study programs, e. g. their relations to other special functions or to some elementary functions. At present, when mathematics courses have small extent in engineering study programs there is no possibility to involve orthogonal polynomials to basic mathematics courses of such undergraduate study programs. But we recommend to involve these parts of mathematics to doctoral study programs and to optional mathematics courses of higher education in miscellaneous technical sciences, respectively. In the contribution we will point out connections of the research in the area of orthogonal polynomials with the possibilities to involve them in the courses of undergraduate, postgraduate and doctoral engineering study programs.

This work has been supported by the Slovak grant agency KEGA through the project No. 057ŽU-4/2012 and the Slovak grant agency VEGA through the project No. 1/1069/12.