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The Mathematica GuideBook for Symbolics

Michael Trott
Organization: Wolfram Research, Inc.
Department: Scientific Information Group
Book information

Publisher: Springer-Verlag (New York)
Copyright year: 2006
ISBN: 0387950206
Medium: Hardcover
Includes: DVD-ROM
Pages: 1453
Out of print?: N
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Symbolic Computations | Classical Orthogonal Polynomials | Classical Special Functions

This book deals with Mathematica's symbolic mathematical capabilities. Structural and mathematical operations on single and systems of polynomials are fundamental to many symbolic calculations, and they are covered here in considerable detail. The solution of equations and differential equations, as well as the classical calculus operations (differentiation, integration, summation, series expansion, limits) are exhaustively treated. Generalized functions and their uses are discussed. In addition, this volume discusses and employs the classical orthogonal polynomials and special functions of mathematical physics. To demonstrate the symbolic mathematics power, a large variety of problems from mathematics and physics are presented.

Unique features:
  • Familiarizes the reader with symbolic mathematics functions in Mathematica for algebra and analysis, as well as orthogonal polynomials and special functions of mathematical physics, and shows how to use them effectively
  • Detailed discussions of the most frequent symbolic operations: equation solving, differentiation, series expansion, integration, and organization and performing symbolic calculations in Mathematica, as compared to paper-and-pencil techniques
  • Numerous examples from mathematics, physics, and computer graphics
  • 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; striking color graphics and animations are included on the DVD

*Mathematics > Calculus and Analysis > Special Functions
*Wolfram Technology > Kernel > Data Structures
*Wolfram Technology > Kernel > Pattern Matching
*Wolfram Technology > Programming > 2D Graphics
*Wolfram Technology > Programming > 3D Graphics
*Wolfram Technology > Programming > Symbolic Computation

Simplification of expressions, Polynomial algebra, Polynomial ideals, Groebner bases, Quantifier elimination, Rational expressions, Trigonometric expressions, Real and imaginary parts, Equation solving, Root finding, Roots of polynomials, Calculus, Differentiation, Symbolic integration, Series expansion, Summation, Differential equation solving, Generalized Functions, Distributions, Sylvester problem, Gauss cosines, Orthogonal polynomials, Hermite, Laguerre, Jacobi, Chebyshev, Gegenbauer, Special functions of mathematical physics, Bessel functions, Error functions, Elliptic integrals, Elliptic functions, Mathieu functions, Quintics
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*The Mathematica GuideBook for Graphics   [in Books]
*The Mathematica GuideBook for Numerics   [in Books]
*The Mathematica GuideBook for Programming   [in Books]