An Exploratory Approach for Teaching Systems of Linear ODEs with Real Repeated Eigenvalues

Authors

Biyong Luo, University of Massachusetts DartmouthFollow
Li Zhang, The CitadelFollow

Publication Date

12-30-2025

Keywords

Eigenvalues, Eigenvectors, trajectories, phase plane

Disciplines

Mathematics | Physical Sciences and Mathematics | Science and Mathematics Education

Abstract

In this paper, we present a project that aims to pique students' interest and facilitate their engagement in learning. Students will be encouraged to take an active role in their learning of systems of linear ODEs with real repeated Eigenvalues. Through discussion and completion of a set of guided questions given in the project, students will gain a deeper understanding of the topic. Also, students will use the technology tool Bluffton App to draw solution trajectories in a phase plane, and then learn necessary skills for explaining the movements of the trajectories and their long term behaviors. This project may also be used as a bridge to connect with several previously taught topics in the course. The same approach may be adopted by instructors to teach other related topics.

Recommended Citation

Luo, Biyong and Zhang, Li (2025) "An Exploratory Approach for Teaching Systems of Linear ODEs with Real Repeated Eigenvalues," CODEE Journal: Vol. 19, Article 7.
Available at: https://scholarship.claremont.edu/codee/vol19/iss1/7