Denison Scientific Association: Seeing with Spectra: What the Eigenvalue Problem is Telling Us

Eigenvalue problems are found everywhere in pure and applied mathematics, though they are remarkably simple to state. We’ll review the eigenvalue problem in its simplest form (for 2x2 matrices), focusing primarily on the geometry of solutions (eigenvalues and eigenvectors). We will then explore more sophisticated eigenvalue problems coming from differential equations, with the intent of probing what the eigenvalue problem tells us about things like waves on strings, drumheads, and more. We will also explore how these same eigenvalue problems reveal unexpected information in the context of materials science, acoustics, and electromagnetism.