Alternate Solution to Generalized Bernoulli Equations via an Integrating Factor: An Exact Differential Equation Approach

Autor/in	Tisdell, C. C.
Titel	Alternate Solution to Generalized Bernoulli Equations via an Integrating Factor: An Exact Differential Equation Approach
Quelle	In: International Journal of Mathematical Education in Science and Technology, 48 (2017) 6, S.913-918 (6 Seiten)Infoseite zur Zeitschrift PDF als Volltext Verfügbarkeit
Zusatzinformation	ORCID (Tisdell, C. C.)
Sprache	englisch
Dokumenttyp	gedruckt; online; Zeitschriftenaufsatz
ISSN	0020-739X
DOI	10.1080/0020739X.2016.1272143
Schlagwörter	Calculus; Mathematics Instruction; Mathematical Models; Biology; Science Instruction; Teaching Methods; Equations (Mathematics) + Suchen Sie Ihr Suchwort? Analysis; Differenzialrechnung; Infinitesimalrechnung; Integralrechnung; Mathematics lessons; Mathematikunterricht; Mathematical model; Mathematisches Modell; Biologie; Teaching of science; Science education; Natural sciences Lessons; Naturwissenschaftlicher Unterricht; Teaching method; Lehrmethode; Unterrichtsmethode; Equations; Mathematics; Gleichungslehre
Abstract	Solution methods to exact differential equations via integrating factors have a rich history dating back to Euler (1740) and the ideas enjoy applications to thermodynamics and electromagnetism. Recently, Azevedo and Valentino presented an analysis of the generalized Bernoulli equation, constructing a general solution by linearizing the problem through a substitution. The purpose of this note is to present an alternative approach using "exact methods", illustrating that a substitution and linearization of the problem is unnecessary. The ideas may be seen as forming a complimentary and arguably simpler approach to Azevedo and Valentino that have the potential to be assimilated and adapted to pedagogical needs of those learning and teaching exact differential equations in schools, colleges, universities and polytechnics. We illustrate how to apply the ideas through an analysis of the Gompertz equation, which is of interest in biomathematical models of tumour growth. (As Provided).
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Erfasst von	ERIC (Education Resources Information Center), Washington, DC
Update	2020/1/01