The Mathematica Guidebook for Numerics [With Dvdrom]

ISBN-13: 9780387950112 / Angielski / Twarda / 2005 / 1208 str.

Michael Trott

Opis

Mathematica is today's most advanced technical computing system, featuring a rich programming environment, two-and three-dimensional graphics capabilities and hundreds of sophisticated, powerful programming and mathematical functions using state-of-the-art algorithms. Combined with a user-friendly interface and a complete mathematical typesetting system, Mathematica offers an intuitive, easy-to-handle environment of great power and utility. The Mathematica GuideBook for Numerics (text and code fully tailored for Mathematica 5.1) concentrates on Mathematica's numerical mathematics capabilities. The available types of arithmetic (machine, high-precision, and interval) are introduced, discussed, and put to use. Fundamental numerical operations, such as compiling programs, fast Fourier transforms, minimization, numerical solution of equations, ordinary/partial differential equations are analyzed in detail and are applied to a large number of examples in the main text and solutions to the exercises. Unique Features: Detailed exposition of advantages and disadvantages of machine numbers, significance high-precision numbers and intervals Presents numerous examples of the efficient and optimized use of Mathematica's functions for root finding, numerical minimization, numerical integration, and differential equation solving, and examples from mathematics and physics Clear organization, complete topic coverage, and accessible exposition for both novices and experts Website for book with additional materials and updates: http: //www.MathematicaGuideBooks.org Accompanying DVD contains all material in the form of hyperlinked Mathematica notebooks that can be edited and manipulated; striking color graphics and animations are included on the DVD Michael Trott is a symbolic computation and computer graphics expert. He holds a Ph.D. in theoretical physics and joined the R&D team at Wolfram Research in 1994, the creators of Mathematica. Since 1998, he has been leading the development of the Wolfram Functions Site http: //functions.wolfram.com, which features more that 10,000 visualizations and 85,000 formulas and identities, and also allows for semantical searches.

Recenzje

From the reviews:

"The numerics volume has two chapters. ... offer a treasure trove of identities and formulas. ... take the reader on a thrilling tour of the features of Mathematica. I am impressed with the breadth and depth of Trott's coverage and his profound understanding of the strengths and limitations of Mathematica. ... includes a multiplatform DVD-ROM which allows the reader to experiment with code and view graphics in color. ... an invaluable resource and classic reference for scientists who use Mathematica in teaching or research." (Willy Hereman, SIAM Review, Vol. 49 (1), 2007)

Spis treści

Introduction and Orientation

I. Numerical Computations: Remarks.- Approximate Numbers.- Fitting and Interpolating Functions.- Compiled Programs.- Linear Algebra.- Fourier Transforms.- Numerical Functions and Their Options.- Sums and Products.- Integration.- Solution of Equations.- Minimization.- Solution of Differential Equations.- Two Applications.- Overview.-Exercises.- References.- II. Computation with Exact Numbers: Remarks.- Divisors and Multiples.- Number Theory Functions.- Combinatorial Functions.- Euler, Bernoulli, and Fibonacci Numbers.- Overview.- Exercises.-  References.- Index