Lecture 7.4: Maximum principle for heat equation

In this lecture, we study maximum principle for heat equation which states that the maximum and the minimum of the solution to the initial-boundary value problem for heat equation lies on the parabolic boundary of the domain. We also look at some applications including uniqueness and the convergence of the series obtained in the separation of variables method.

[jonathangreenberg]

A tour de force! One of the best PDE lectures on the internet: lectures from MIT don't even compare. The MIT lectures are not at this high a level.
Most people have no idea to even question the formal solution obtained by separation of variables. Let alone to prove that the infinite series actually converges to the solution.