Rotational Analysis of Phase Plane Curves: Complex and Pure Imaginary Eigenvalues

Autor/in	Murray, Russell H.
Titel	Rotational Analysis of Phase Plane Curves: Complex and Pure Imaginary Eigenvalues
Quelle	In: Mathematics and Computer Education, 39 (2005) 1, S.63-68 (6 Seiten) PDF als Volltext Verfügbarkeit
Sprache	englisch
Dokumenttyp	gedruckt; online; Zeitschriftenaufsatz
ISSN	0730-8639
Schlagwörter	Equations (Mathematics); Mathematics Instruction; Mathematical Concepts; Computer Software; Program Effectiveness; Mathematics Education; Textbook Evaluation; Problem Solving; Calculus; Teaching Methods; Mathematics Skills + Suchen Sie Ihr Suchwort? Equations; Mathematics; Gleichungslehre; Mathematics lessons; Mathematikunterricht; Mathematische Bildung; Problemlösen; Analysis; Differenzialrechnung; Infinitesimalrechnung; Integralrechnung; Teaching method; Lehrmethode; Unterrichtsmethode; Mathmatics achievement; Mathematics ability; Mathematische Kompetenz
Abstract	Although the phase plane can be plotted and analyzed using an appropriate software package, the author found it worthwhile to engage the students with the theorem and the two proofs. The theorem is a powerful tool that provides insight into the rotational behavior of the phase plane diagram in a simple way: just check the signs of c and [alpha]. The student is then better prepared to make sense of what the software is presenting them. The theorem can also be extended to the case of one repeated eigenvalue with one independent eigenvector (and, in addition, a generalized eigenvector), a case also displaying rotational behavior save for one straight line solution. (Contains 2 figures.) (ERIC).
Anmerkungen	MATYC Journal Inc. Mathematics and Computer Education, P.O. Box 158, Old Bethpage, NY 11804. Tel: 516-822-5475; Web site: http://www.macejournal.org
Erfasst von	ERIC (Education Resources Information Center), Washington, DC
Update	2017/4/10