Upper-Division Students' Use of Separation of Variables Documents

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Upper-Division Students' Use of Separation of Variables 

written by Steven J. Pollock and Bethany R. Wilcox

Separation of variables can be a powerful technique for solving many of the partial di fferential equations that arise in physics contexts. Upper-division physics students encounter this technique in multiple topical areas including electrostatics and quantum mechanics. To better understand the difficulties students encounter when utilizing the separation of variables technique, we examined responses to midterm exam questions and conceptual assessments, and conducted think-aloud, problem-solving interviews. Our analysis was guided by an analytical framework that focuses on how students activate, construct, execute, and reflect on the separation of variables technique when
solving physics problems. Here we focus on student diculties with separation of variables as a technique to solve Laplace's equation in spherical coordinates in the context of junior-level electrostatics. Challenges include: recognizing when separation of variables is the appropriate tool, identifying implicit boundary conditions, and spontaneously reflecting on their solutions.

Last Modified December 16, 2015

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