Exploring Fourier Series and Gibbs Phenomenon Using Mathematica

Autor/in	Ghosh, Jonaki B.
Titel	Exploring Fourier Series and Gibbs Phenomenon Using Mathematica
Quelle	In: Australian Senior Mathematics Journal, 25 (2011) 1, S.7-22 (16 Seiten) PDF als Volltext Verfügbarkeit
Sprache	englisch
Dokumenttyp	gedruckt; online; Zeitschriftenaufsatz
ISSN	0819-4564
Schlagwörter	Mathematics Education; College Mathematics; Mathematical Concepts; Mathematics Instruction; Foreign Countries; Graphs; Algebra; Computer Uses in Education; Laboratories; Teaching Methods; Theories; Australia + Suchen Sie Ihr Suchwort? Mathematische Bildung; Mathematics lessons; Mathematikunterricht; Ausland; Grafische Darstellung; Computernutzung; Laboratory; Laboratorium; Teaching method; Lehrmethode; Unterrichtsmethode; Theory; Theorie; Australien
Abstract	This article describes a laboratory module on Fourier series and Gibbs phenomenon which was undertaken by 32 Year 12 students. It shows how the use of CAS played the role of an "amplifier" by making higher level mathematical concepts accessible to students of year 12. Using Mathematica students were able to visualise Fourier series of functions and explore Gibbs phenomenon which is usually a part of college mathematics. During the module, it was ensured that students acquire sufficient proficiency in calculating the Fourier series and manipulating integrals before resorting to Mathematica. Thus paper and pencil methods helped students to understand the calculations while Mathematica added meaning to the calculations by providing graphical and numerical representations. Once the technical work was taken over by Mathematica, students were free to focus on the behaviour of the graphs of the functions and this enabled them to visualise Gibbs phenomenon. They were able to write the codes, with occasional help from the teacher and the outputs of the codes helped them to observe patterns and make conjectures. The power of Mathematica in the module was not merely in the computational aspect but also in the fact that it enabled the students to engage in a purposeful and strategic investigation of the problem at hand. It helped to create a link between the symbolic expressions and the graphical representations. (Contains 5 figures and 4 tables.) (ERIC).
Anmerkungen	Australian Association of Mathematics Teachers (AAMT). GPO Box 1729, Adelaide 5001, South Australia. Tel: +61-8-8363-0288; Fax: +61-8-8362-9288; e-mail: office@aamt.edu.au; Web site: http://www.aamt.edu.au
Erfasst von	ERIC (Education Resources Information Center), Washington, DC
Update	2021/2/06