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.
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 referencefor 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.