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ERIC Number: EJ996310
Record Type: Journal
Publication Date: 2012
Pages: 20
Abstractor: As Provided
ISSN: ISSN-1051-1970
Variation of Parameters in Differential Equations (A Variation in Making Sense of Variation of Parameters)
Quinn, Terry; Rai, Sanjay
PRIMUS, v23 n1 p25-44 2012
The method of variation of parameters can be found in most undergraduate textbooks on differential equations. The method leads to solutions of the non-homogeneous equation of the form y = u[subscript 1]y[subscript 1] + u[subscript 2]y[subscript 2], a sum of function products using solutions to the homogeneous equation y[subscript 1] and y[subscript 2]. Why though, might varying parameters of solutions to the homogeneous equation be a feasible approach? An insight is needed, even for a good guess. This paper is for instructors teaching a first course in undergraduate differential questions, where the students already have covered first-order linear equations and second-order homogeneous linear equations. We provide a variation to the standard textbook approach to variation of parameters, intended to help the student find their way toward a key insight: "Aha! Let's try ..." We point to several reasons why it can be important for students to learn variation of parameters.
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Publication Type: Journal Articles; Reports - Descriptive
Education Level: Higher Education
Audience: Teachers
Language: English
Sponsor: N/A
Authoring Institution: N/A