"A Theory of Approximation of Functions" Courseware

Abstract

The purpose of this paper is to discuss a courseware that we designed and implemented for university mathematics education to study both the concepts and computational tasks of "Functions theory" ("Calculus") as well as different algorithms of theory of approximation of functions (i.e. interpolation by Lagrange or Hermite with algebraic, trigonometric or other polynomials; smoothing, for instance, least squares approximation with algebraic or trigonometric polynomials; algebraic splines; Bezier and Chebyshev approximation). The study of this course is carry out either through a web-site for the textbook written by a one of co-authors or via special software system ("DSR Open Lab 1.0") developed by authors. The multimedia, Active technologies and some wizards are applied in this software system. We will give examples of how one can effectively study the computational tasks of "Functions theory" and different algorithms of theory of functions approximation by means of our courseware.