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 chapter can't be rushed as much as the first chapter, because the inner product is so central. As in the first chapter, I have found that only the math majors are intrigued by the notion that the m x n matrices have an inner product, so those examples should be skipped if you are teaching practical-minded engineers.

One of the most successful parts of this chapter is the link to the calculations using Legendre polynomials, with graphs showing how much better that approximation is than the Taylor series. This gives the students impressive visual evidence to appreciate approximation with orthogonal functions.

Another part which is much appreciated by graduate students here, especially from electrical engineering, is the appendix on filtering. They hear this language in their other courses and find that it helps put Fourier series in perspective.

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