Atlas for Computing Mathematical Functions: An Illustrated Guide for Practitioners with Programs in Fortran 90 and Mathematica

2 customer reviews
ISBN-13: 978-0471181712
ISBN-10: 0471181714
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Editorial Reviews

From the Publisher

An invaluable reference and learning guide to more than 150 special functions of applied mathematics, statistics, physics, chemistry, computer science, and engineering. This book 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 Fortran-90 source programs on the CD-ROM, which is both Windows and Macintosh compatible.

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 Fortran-90 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
* Fortran-90 Programs.
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Product Details

  • Hardcover: 904 pages
  • Publisher: Wiley-VCH (August 13, 1997)
  • Language: English
  • ISBN-10: 0471181714
  • ISBN-13: 978-0471181712
  • Product Dimensions: 7.3 x 1.8 x 10.2 inches
  • Shipping Weight: 4.1 pounds
  • Average Customer Review: 3.5 out of 5 stars  See all reviews (2 customer reviews)
  • Amazon Best Sellers Rank: #5,088,139 in Books (See Top 100 in Books)

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5 of 5 people found the following review helpful By A Customer on March 10, 2003
Format: Hardcover
According to the author, the practicality of books on functions is often limited by the graphical content, and that books of tables like Abramowitz & 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 Fortran 90 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, or a graphing calculator, without using F90 or Mathematica. But much of this high-priced textbook consists of small blocks of F90 code and everlasting references to Mathematica notebook calls. Part II contains ~200 pages of Mathematica notebook descriptions and ~100 pages of F90 driver programs, not to mention the F90 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. 117 for example). 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.
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2 of 2 people found the following review helpful By L. I. Tobos on January 20, 2005
Format: Hardcover
Don't expect an in-depth coverage of the theory behind the calculations. Said that, the book is a "concise" presentation of the programs used to calculate special functions present on the CD. For every program, the author shows the underlying equations and the bibliographic sources, plus nice discussions on accuracy/performance when you have the option of several methods.

I would say the book is more useful to the engineer/physicist having to do certain calculations, than to the mathematician/student wanting to learn the ins and outs of special functions theory.

The only dissapointment is a rather poor produced CD: the names of the programs on the CD are in 8.3 format, and I think (not sure though) that not all the code of the driver programs shows up on the CD- there are names of program snippets that are not on the CD- this may be an unnecessary hasle for someone trying to follow the examples in the book to the letter.
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