Evans M. Harrell II*
Whichever chapter on PDEs is done first marks a very important point in the class, where the emphasis changes from orthogonal series to differential equations. Take the time required and do as many separations of variables as it takes for the students to get the idea. One idea: Do Dirichlet and Neumann in class and have them investigate periodic boundary conditions for exercises.
There is a link to a derivation of the heat equation, which is useful for the students to develop an understanding of energy considerations and how to set up correct boundary conditions.
If you teach this course with a term-paper requirement, which I have done with some success, some students may take this as a starting point to investigate derivations of other diffusion equations.
Derivations are time-consuming (when done convincingly), so normally I only do one, either this one or the one for the wave equation. If you choose not to do this one, make sure that the students are aware that it is available.
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