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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