Make the Eigenvalue Problem Resonate With Our Students

Abstract

We present a new learning activity that enables students to apply eigenvalue theory to investigate a practical modeling problem. We demonstrate how to build a spring-coupled pair of pendula and describe how students can measure the movements of these pendula using open-source image processing software. We then illustrate how to analyze this position data and provide supporting theory that enables students to accurately model this system using eigenvalues. This hands-on activity enhances student motivation and prepares students to model other complex systems using linear ordinary differential equations.

Keywords:

• Mathematical modeling
• eigenvalues and eigenvectors
• coupled
• linear
• ordinary differential equations

Additional information

Notes on contributors

Jeffrey A. Anderson

Jeffrey Anderson earned his Ph.D. in mathematics from University of California at Davis in 2013. He is currently an associate professor of Mathematics at Foothill College. One of his major professional goals is to redesign the introductory linear algebra classroom to be student-centered, experiential, and mastery-based. In doing so, Jeff yearns to provide students with numerous opportunities to cultivate valuable applied modeling skills as part of their introduction to linear algebra.

Michael V. McCusker

McCusker earned his Ph.D. in atomic physics from Rice University. He then did physics research at JILA, Yale University, and SRI International. He subsequently worked in technical and managerial roles at several companies in Silicon Valley. He is currently an instructor in the Foothill College STEM Center.