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
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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