Eigenfunction Expansions - Partial Differential Equations | Lecture 28

In this lecture we leverage Sturm-Liouville theory to solve inhomogeneous partial differential equations. We demonstrate with a worked example of the heat equation with a space and time dependent heat source. We show that the solution to the PDE can be expanded as an infinite sum of the Sturm-Liouville eigenfunctions from an associated homogeneous problem for which we then obtain ordinary differential equations for the time-dependent coefficients of the sum. In principle, these ODEs can be solved, thus providing the solution to more complicated 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.