Instructor's guide

Orthogonal Series and Boundary Value Problems

Evans M. Harrell II*

*(c) Copyright 1994,1995 by Evans M. Harrell, II. All rights reserved.

This is a stage where the availability of modern software really pays off. On the one hand, we do not need to spend nearly as much time as in the old days on the mechanics of calculating the integrals for Fourier series coefficients, and on the other hand we are able to represent a more interesting set of functions. In this chapter we calculate some Fourier series numerically and learn what happens when the function being represented oscillates wildly or diverges.

Some students - but noticeably fewer each time I teach this course - still have the feeling that if an integral wasn't calculated by hand they didn't really understand what was going on. Because of this I find the series for a token power function or two by hand on the blackboard.

Devoting less time to calculating integrals than formerly is what allows this course to do a fuller job of developing other orthogonal series and using them in boundary-value problems.

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