Sturm-Liouville Theory - Partial Differential Equations | Lecture 23

In this lecture, we explore some of the most important results in partial differential equations theory through Sturm-Liouville eigenvalue problems. Building on what we saw in the previous lecture, I show how these problems generalize familiar cases and prove that eigenvalues always exist. Sturm-Liouville theory also guarantees that each problem has infinitely many eigenvalues, all of which are real, and that the associated eigenfunctions generalize the familiar properties of sines and cosines from Fourier theory. Through this framework, I highlight how Sturm-Liouville theory provides a powerful and elegant foundation for solving a wide range of PDEs. Lectures series on differential equations:    • Welcome - Ordinary Differential Equations ...   More information on the instructor: https://hybrid.concordia.ca/jbrambur/ Follow @jbramburger7 on Twitter for updates.