Instructor's guide
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Orthogonal Series and Boundary Value Problems
Evans M. Harrell II*

#### *(c) Copyright 1994,1997 by Evans M. Harrell, II and James V. Herod. All rights reserved.

Either this chapter or
the one on the wave equation may be done first.
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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