Instructor's guide

Linear methods of applied mathematics

Evans M. Harrell II and James V. Herod*

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

If your students are well prepared, you may be able to rush the first chapter a bit, condensing it into one lecture, in which you refer to the superposition principle and give some examples of linear transformations. In my experience it is still helpful to give them homework problems. If they have a good preparation in applied mathematics the homework will be enough for them to fix the ideas. In an academic quarter system it will be necessary to rush the first chapter in order to get to Bessel series and things like that before the term is over.

Another way to save a little time in this chapter is to mention no other vector spaces in the first few lectures besides R3 and C[0,1]. In any case I have found that only the math majors are intrigued by the notion that the m x n matrices form a vector space, so those examples should be skipped if you are teaching practical-minded engineers. The point of the example is to help students understand differential operators like D^2 + D + 2, but most of them find this notation intuitive enough without being side-tracked into the algebra of m x n matrices.

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