The Mathematica GuideBook for Symbolics
Description
Mathematica is today's most advanced technical computing system. It features 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 Symbolics (code and text fully tailored for Mathematica 5.1) 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 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 phyics are discussed.
Unique Features: Familiarizes the reader with symbolic mathematics functions in Mathematica for algebra, analysis, as well as orthogonal polynomials and the 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 organizing and performing symbolic calculations in mathematica, as compared to paper-and-pencil calculations
Numerous examples from mathematics, physics, and computer science
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.
Reviews / Votes
From the reviews:
"The book is filled with Mathematica programming gems and is particularly valuable for researchers using special functions in their work because of extensive coverage of these topics. . Every chapter has numerous exercises with full solutions. Every computer science, mathematics, physics, engineering library should have this . on its shelves, because this is the best source of the applications of Mathematica to numerous computational tasks." (Matti Vuorinen, Zentralblatt MATH, Vol. 1095 (21), 2006)
"This guidebook has three chapters. . I enjoyed reading the symbolics Guidebook. . 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)
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Content
Introduction and Orientation
I. Symbolic computations: *Remarks *Manipulation of polynomials *Manipulations of rational functions of polynomials *Manipulations of trigonometric expressions *Systems of linear and nonlinear equations *Classical analysis *Differential equations *Integral transforms and generalized functions *Three applications *Overview
II Classical orthogonal polynomials: *Remarks *General properties of orthogonal polynomials *Hermite polynomials *Jacobi polynomials *Gegenbauer polynomials *Laguerre polynomials *Legendre polynomials *Chebyshev polynomials T *Chebyshev polynomials U *Relationships among the orthogonal polynomials *Overview
III Classical special functions: *Remarks/Introduction *Gamma, beta, and polygamma functions *Error functions and Fresnel integrals *Sine, cosine, exponential, and logarithmic integral functions *Bessel and airy functions *Legendre functions *Hypergeometric functions *Elliptic integrals *Elliptic functions *ProductLog function *Mathieu functions * Additional special functions *Solution of quintics with hypergeometric functions *Overview
Index