Numerical Integration

Autor/in	Sozio, Gerry
Titel	Numerical Integration
Quelle	In: Australian Senior Mathematics Journal, 23 (2009) 1, S.43-50 (8 Seiten) PDF als Volltext Verfügbarkeit
Sprache	englisch
Dokumenttyp	gedruckt; online; Zeitschriftenaufsatz
ISSN	0819-4564
Schlagwörter	Calculus; Teaching Methods; Secondary School Mathematics; Mathematics Instruction; Mathematical Concepts; Concept Formation; Undergraduate Study; College Mathematics; Equations (Mathematics); Mathematical Logic; Validity + Suchen Sie Ihr Suchwort? Analysis; Differenzialrechnung; Infinitesimalrechnung; Integralrechnung; Teaching method; Lehrmethode; Unterrichtsmethode; Mathematics lessons; Mathematikunterricht; Concept learning; Begriffsbildung; Grundstudium; Equations; Mathematics; Gleichungslehre; Mathematical logics; Mathematische Logik; Gültigkeit
Abstract	Senior secondary students cover numerical integration techniques in their mathematics courses. In particular, students would be familiar with the "midpoint rule," the elementary "trapezoidal rule" and "Simpson's rule." This article derives these techniques by methods which secondary students may not be familiar with and an approach that undergraduate students should be familiar with. Secondary students will also find interesting the "two-point Gauss rule," which is an extension of the trapezoidal rule. There are many applications of integral calculus and developing a deeper understanding of some of the numerical methods will increase understanding of the techniques. The methods chosen in this article have been investigated as secondary students will be familiar with their applications. However, secondary text books and teachers may not use the techniques covered in this article, and this alternate approach may increase the understanding of the importance and applications of the techniques, as well as increase an appreciation of the beauty of mathematics in general. The article also provides a detailed summary of the techniques that will be beneficial for undergraduate students. In this article the midpoint rule, the elementary trapezoidal rule, the two-point Gauss rule and Simpson's elementary rule are developed. (Contains 1 figure.) (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