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Rating: 
Summary: No substitute for Handbook of Mathematical Functions
Review: According to the author, the practicality of books on functions is often limited by the graphical content, and that books of tables like Abrahamowitz & Stegun "serve a very limited purpose" today (primarily to check function evaluating software). This "Atlas" tries to fill this void, and it does a respectable job. However, detailed function exploration and visualization is left to Mathematica users, the primary audience for this book. Without Mathematica 2.2 or later, and/or a C complier, a great deal in this title cannot be fully appreciated. Of course, the reader can often explore function behavior by plotting an equation using common spreadsheet software that came with his computer w/o using C or Mathematica. But much of this high-priced textbook consists of small blocks of C code and everlasting references to Mathematica notebook calls. Part II contains ~200 pages of Mathematica notebook descriptions and ~100 pages of C driver programs, not to mention the C code documented throughout the first 600 pages.Most the "Atlas" graphics are small (~2") gray-scale screenshots of Mathematica plots. The quality of some graphics leaves something to be desired though (Figure 7.2.2 p. 119 for example), since many figures are obviously grainy (vertical lines and text characters often appear as broken line segments, not unlike a tilted faxed image). These gray-scale images are fairly bland - I expected at least a little color and only the highest quality graphics for a book calling itself an "atlas", especially for the asking price. "Atlas" is no substitute for the timeless books of tables and equations such as the (inexpensive) A&S (ISBN 0486612724) or the CRC Standard Math Tables. In computing the error function (erf), for example, Dr. Thompson defines erf in terms of a function call of the gamma function, while A&S provides many, many more alternatives suitable for machine solution. The discussions here, while more generous than A&S, are much less detailed than an explanatory book like Numerical Recipes. Instead, pictorial surveys primarily forego a lot of the detailed explanation of the underlying function theory. A few of the functions, such as the Voight distribution, are hard to find in the classic references, but the reader will find very few new topics here. I expect this title, being heavily tied to a particular software package and computer language, will find itself being re-issued in later editions as software inevitably evolves. I therefore wouldn't expect too many individuals paying $175 for what is almost a software book. All in all, a well packaged presentation but not quite the insightful, general purpose book for which I had hoped.
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