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The Mathematica GuideBook for Numerics
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| Organization: | Wolfram Research, Inc. |
| Department: | Scientific Information Group |
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| Publisher: | Springer-Verlag (New York) |
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Numerical Computations | Computations with Exact Numbers
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This book 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 solutions of equations, and ordinary/partial differential equations, are analyzed in detail and are applied to a large number of examples in the main text and in the solutions to the exercises.
Unique features: - Detailed exposition of advantages and disadvantages of machine numbers, significance high-precision numerics, 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 containing all material in the form of hyperlinked Mathematica notebooks that can be edited and manipulated, with striking color graphics and animations
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High-precision arithmetic, Arbitrary-precision arithmetic, Interval arithmetic, Long range correlations in texts, Numerical minimization, Charge minimizations, Numerical root finding, FFT, List convolutions, List correlations, Fast Fourier Transforms, Fractional Fourier Transforms, Compilation, Interpolation, Numerical summation, Numerical integration, Numerical differential equaton solving, Periodic orbits, Three-body problem, Continuous time random walks, Partial differential equations, Method of lines, Wave equation, Schroedinger equation, Riemann surfaces, Electric field lines, Magnetic field lines, Exact arithmetic, Number theoretic functions, Euler-McLaurin summation, Boole summation
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http://www.MathematicaGuideBooks.org
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