Make the eigenvalue problem resonate with our students
We present a learning activity that enables students to apply eigenvalue theory to investigate a useful modeling problem. We demonstrate how to build a spring-coupled pair of pendula and how students can analyze this system using eigenvalues. This activity is designed to enhance student motivation in the classroom and to prepare students to apply eigenvalues to real-world problems.
Linear algebraic nodal analysis
We present an innovative learning activity that enables students to create linear-systems problems from practical electric circuits with resistors, voltage sources, and current sources. We show how to build physical circuits on solderless breadboards and measure the node voltage potentials of these circuits using a multimeter. We also present a novel algorithm to model these circuits using a nonsingular linear-system problem. This experience prepares students to model real-world problems using nonsingular linear systems.