This volume, the third of a series, consists of applications of Mathematica (R) to a potpourri of more advanced topics. These include differential geometry of curves and surfaces, differential equations and special functions and complex analysis. Some of the newest features of Mathematica (R) are demonstrated and explained and some problems with the current implementation pointed out and possible future improvements suggested. Contains a large number of worked out examples. Explains some of the most recent mathematical features of Mathematica (R). Considers topics discussed rarely or not at all in the context of Mathematica (R). Can be used to supplement several different courses. Based on actual university courses.

The book deals with functions of many variables: differentiation and integration, extrema with a number of digressions to related subjects such as curves, surfaces and Morse theory. The background needed for understanding the examples and how to compute in Mathematica (R) will also be discussed.

A computer algebra system such as Mathematica (R) is able to do much more than just numerics: This text shows how to tackle real mathematical problems from basic analysis. The reader learns how Mathematica (R) represents domains, qualifiers and limits to implement actual proofs - a requirement to unlock the huge potential of Mathematica (R) for a variety of applications.