We have seen that applying separation of variables to the heat and wave equations results in two ordinary differential equations to be solved. Moreover, both differential equations involve a single parameter that is identified by the solution to the equation involving the spatial variable. In this lecture we identify these types of problems as eigenvalue problems involving linear second-order differential operators. In particular, we emphasize that these types of eigenvalues problems occur throughout the partial differential equations we have been studying, thus setting things up for the theory to be presented in the next lecture.
Lectures series on differential equations: https://www.youtube.com/watch?v=UDUH58w4-5w&list=PLXsDp0z6VWFTkAhFApYsNfqgRvZrPTeom
More information on the instructor: https://hybrid.concordia.ca/jbrambur/
Follow @jbramburger7 on Twitter for updates.
