Atlas for Computing Mathematical Functions: An Illustrated Guide for Practitioners With Programs in C and Mathematica [Hardcover]

William J. Thompson (Author)

Book Description

Publication Date: April 15, 1997 | ISBN-10: 0471002607 | ISBN-13: 978-0471002604

Introducing a comprehensive book and CD-ROM for visualizing and computing special functions

Here is an invaluable reference and learning guide to more than 150 special functions of applied mathematics, statistics, physics, chemistry, computer science, and engineering. The Atlas contains over 700 graphics of the functions, which readers can also create by using the annotated Mathematica files provided. It offers complete, consistent instructions and test values for computing the functions accurately and efficiently with the full ANSI C source programs on the CD-ROM, which is both Windows and Macintosh compatible.

With extensive references and indexing, this integrated package is superbly designed and easy to use-ideal for anyone who works with special functions. Contents include:
* Elementary Transcendental Functions
* Exponential Integrals and Related Functions
* Gamma and Beta Functions
* Combinatorial Functions
* Number Theory Functions
* Probability Distributions
* Error Function, Fresnel, and Dawson Integrals
* Orthogonal Polynomials
* Legendre Functions
* Spheroidal Wave Functions
* Bessel Functions
* Struve, Anger, and Weber Functions
* Hypergeometric Functions and Coulomb Wave Functions
* Elliptic Integrals and Elliptic Functions
* Parabolic Cylinder Functions
* Miscellaneous Functions for Science and Engineering
* Mathematica Notebooks
* C Driver Programs

Editorial Reviews

From the Publisher

This book is a comprehensive guide to understanding the mathematical functions used to solve research problems. Illustrations, diagrams, and computer programs are utilized in addition to the usual text formulas in order to make the comprehension of the material easier. The book comes with a CD-ROM disk which contains programs for Mathematica and C.

From the Back Cover

Introducing a comprehensive book and CD-ROM for visualizing and computing special functions

Here is an invaluable reference and learning guide to more than 150 special functions of applied mathematics, statistics, physics, chemistry, computer science, and engineering. The Atlas contains over 700 graphics of the functions, which readers can also create by using the annotated Mathematica files provided. It offers complete, consistent instructions and test values for computing the functions accurately and efficiently with the full ANSI C source programs on the CD-ROM, which is both Windows and Macintosh compatible.

With extensive references and indexing, this integrated package is superbly designed and easy to use-ideal for anyone who works with special functions. Contents include:
* Elementary Transcendental Functions
* Exponential Integrals and Related Functions
* Gamma and Beta Functions
* Combinatorial Functions
* Number Theory Functions
* Probability Distributions
* Error Function, Fresnel, and Dawson Integrals
* Orthogonal Polynomials
* Legendre Functions
* Spheroidal Wave Functions
* Bessel Functions
* Struve, Anger, and Weber Functions
* Hypergeometric Functions and Coulomb Wave Functions
* Elliptic Integrals and Elliptic Functions
* Parabolic Cylinder Functions
* Miscellaneous Functions for Science and Engineering
* Mathematica Notebooks
* C Driver Programs

See all Editorial Reviews

Product Details

• Hardcover: 928 pages
• Publisher: Wiley-Interscience (April 15, 1997)
• Language: English
• ISBN-10: 0471002607
• ISBN-13: 978-0471002604
• Product Dimensions: 10.3 x 7.4 x 1.9 inches
• Shipping Weight: 4 pounds
• Average Customer Review: 3.0 out of 5 stars  See all reviews (1 customer review)
• Amazon Best Sellers Rank: #3,047,557 in Books (See Top 100 in Books)

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18 of 18 people found the following review helpful:

3.0 out of 5 stars No substitute for Handbook of Mathematical Functions, September 6, 2000

By A Customer

This review is from: Atlas for Computing Mathematical Functions: An Illustrated Guide for Practitioners With Programs in C and Mathematica (Hardcover)

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.