Geometric viewpoint on Sturm-Liouville theory

Geometric viewpoint on Sturm-Liouville theory

Mathematics

ZiAn Zhao

2024

Dr. Maxwell Stolarski

In many modern physics and engineering systems, particularly when dealing with separable linear partial differential equations, a second- order linear ordinary differential equation in a certain form occurs fre- quently, these are called Sturm-Liouville problems. Understanding the solutions in such a form is crucial in understanding a dynamic system when Sturm-Liouville problems occur. We will embark on an in-depth exploration of Riemannian geometry, uncovering the rich properties provided by the Riemannian metric. By the end, we’ll bring everything together and demonstrate how tools from Sturm-Liouville theory can be applied to specific geometric surfaces.

Mathematics, Differential geometry, Ordinary differential equation, Analysis