Details

The Mathematica GuideBook for Numerics


The Mathematica GuideBook for Numerics



von: Michael Trott

160,49 €

Verlag: Springer
Format: PDF
Veröffentl.: 27.10.2006
ISBN/EAN: 9780387288147
Sprache: englisch
Anzahl Seiten: 1208

Dieses eBook enthält ein Wasserzeichen.

Beschreibungen

<P>Provides the reader with working knowledge of Mathematica and key aspects of Mathematica's numerical capabilities needed to deal with virtually any "real life" problem</P>
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<P>Clear organization, complete topic coverage, and an accessible writing style for both novices and experts</P>
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<P>Website for book with additional materials: http://www.MathematicaGuideBooks.org</P>
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<P>Accompanying DVD containing all materials as an electronic book with complete, executable Mathematica 5.1 compatible code and programs, rendered color graphics, and animations</P>
<P>Mathematica is today's most advanced technical computing system,&nbsp;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, <EM>Mathematica</EM> offers an intuitive, easy-to-handle environment of great power and utility.</P>
<P><STRONG>The Mathematica GuideBook for Numerics</STRONG> (text and code fully tailored for <EM>Mathematica</EM> 5.1) concentrates on <EM>Mathematica's</EM> numerical mathematics capabilities. The available types of arithmetic&nbsp;(machine,&nbsp;high-precision, and interval) are&nbsp;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.</P>
<P>Unique Features:</P>
<P>Detailed exposition of advantages and disadvantages of machine numbers, significance high-precision numbers and intervals </P>
<P>Presents numerous examples of&nbsp; the efficient and optimized use of <EM>Mathematica's</EM> functions for root finding, numerical minimization, numerical integration, and differential equation solving,&nbsp;and examples from mathematics and physics</P>
<P>Clear organization, complete topic coverage, and accessible&nbsp;exposition for both novices and experts</P>
<P>Website for book with additional materials and updates: http://www.MathematicaGuideBooks.org</P>
<P>Accompanying DVD contains all material in the form of hyperlinked <EM>Mathematica </EM>notebooks that can be edited and manipulated; striking color graphics and animations are included on the DVD</P>
<P><STRONG>Michael Trott</STRONG> is a symbolic computation and computer graphics expert. He holds a Ph.D. in theoretical physics and joined the R&amp;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.</P>
<P>Introduction and Orientation</P>
<P><STRONG>I. Numerical Computations:</STRONG> Remarks.- Approximate Numbers.- Fitting and Interpolating Functions.- Compiled Programs.- Linear Algebra.- Fourier Transforms.- Numerical Functions and Their&nbsp;Options.-&nbsp;Sums and Products.- Integration.-&nbsp;Solution of Equations.- Minimization.- Solution of Differential Equations.- Two Applications.- Overview.-Exercises.- References.- <STRONG>II. Computation with Exact Numbers:</STRONG> Remarks.- Divisors and Multiples.- Number Theory Functions.- Combinatorial Functions.- Euler, Bernoulli, and Fibonacci Numbers.- Overview.- Exercises.-&nbsp; References.- Index</P>
<p>Detailed exposition about machine numbers, significance of high-precision numbers and intervals with advantages and disadvantages</p><p>Presents numerous examples of the efficient and optimized use of Mathematica's functions for root finding, numerical minimization, numerical integration, and differential equation solving with examples from mathematics and physics</p><p>Clear organization, complete topic coverage, and an accessible exposition for both novices and experts</p><p>Website for book with additional materials and updates: www.MathematicaGuideBooks.org</p><p>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</p>
<P>The Mathematica GuideBook for Numerics (text and code&nbsp;fully tailored&nbsp;with Mathematica 5.1)&nbsp;is the third volume of the Mathematica GuideBooks, a comprehensive and detailed print and electronic reference&nbsp;for Mathematica. It&nbsp;introduces the reader to Mathematica's&nbsp;various approximate numbers, their arithmetic and the most common numerical analysis operations such as numerical&nbsp;integration, root-finding, equation solving, minimization, and differential equation solving.&nbsp;It includes thousands of visualizations of concepts, algorithms, results and more than 200 fully worked non-trivial examples from mathematics and physics. The accompanying DVD contains all material in the form of hyperlinked and editable&nbsp;Mathematica notebooks fully tailored for Mathematica 5.1.&nbsp;An indispensable resource for practitioners, professionals, and researchers in mathematics, computer science,&nbsp;engineering and other scientific disciplines, The Mathematica GuideBook for Numerics will find a natural place on the bookshelf as an essential reference work.&nbsp; The Guidebooks in general, give the user a deeper understanding of Mathematica by instructive implementations, explanations, and examples from a range of disciplines at varying levels of complexity. The four GuideBooks contain about 25,000 Mathematica inputs, representing more that 75,000 lines of commented Mathematica code. They also have more than 4,500 graphics, 150 animations, 11,000 references and 1,000 exercises.</P>

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