Research in the age of numerical simulation

The main purpose of the exposition of mathematical problems is to show the ease with which such problems can be addressed using modern programs for symbolic manipulation, as well as the power of mathematical solutions relative to discretized numerical solutions. None of the discussed problems could be addressed without a program for symbolic manipulation, but each is relatively simple given such a program. The details of the solution process have not been described in the above, but some of the references give detailed expositions, along with the Maple program used for the analysis.