Title: Selected mathematical concepts and their animation with CAS maple

Authors: Pavel Prazak

Addresses: Faculty of Informatics and Management, Department of Informatics and Quantitative Methods, University of Hradec Kralove, Rokitanskeho 62, Hradec Kralove 2, 500 02, Czech Republic

Abstract: There is no doubt that Information Technology is a powerful tool for visualisation of hidden mathematical concepts. This article focuses on animation and presents how to use animation produced with the help of CAS for demonstration of two selected mathematical concepts. First the concept of constrained maximum and minimum of function of two variables with subject to one implicit given constrain is shown. The rule of Lagrange multipliers is demonstrated in this case, too. In this particular – the easiest – case there exist two vectors that have the same direction and Maple allow us to show it. Secondly, the concept of Poincare-Andronov-Hopf bifurcation is shown. A marketing application of this bifurcation is presented here as well.

Keywords: animation; bifurcation; CAL; computer aided learning; CAS; constrained extremes; Maple; mathematical concepts; mathematics teaching; maths understanding; visualisation; mathematics education.

DOI: 10.1504/IJCEELL.2008.022171

International Journal of Continuing Engineering Education and Life-Long Learning, 2008 Vol.18 No.5/6, pp.640 - 656

Published online: 22 Dec 2008 *

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