Instructor's guide

Linear Methods of Applied Mathematics

Evans M. Harrell II and James V. Herod*

*(c) Copyright 1994-2000 by Evans M. Harrell II and James V. Herod. All rights reserved.

This is the chapter which first introduces the potential equations of Laplace and Poisson, which reappear in later chapters on Green functions. If you wish to add some depth fopr these important equations, you should include the appendix on properties of solutions, which discusses the mean-value theorem and the maximum principle.

The task the students have the hardest time with in this chapter is coping with nonhomogeneous boundary conditions. Emphasize that since the principle of superposition is so useful, we want to profit as much as possible from it before working on the parts of the problem which interfere with it.

On our hidden agenda in this chapter is to teach the philosophy of solving complicated problems by breaking them into simpler components, which are put together at the end. In my experience, this should not be rushed, and the students will require multiple examples.

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