The Mathematica GuideBook for Symbolics, 2 Teile

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.

Inhaltsverzeichnis

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.

Über den Autor / die Autorin

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 development of the Wolfram Functions Site, which currently features more that 80,000 formulas and identities, and thousands of visualizations.

Zusammenfassung

The Mathematica GuideBook for Symbolics (text and code fully tailored with Mathematica 5.1) is the  fourth volume of the Mathematica GuideBooks, a comprehensive and detailed print and electronic reference for Mathematica. It introduces the reader to symbolic computations using Mathematica and enables readers to understand, perform, and optimize sophisticated symbolic computations.  It includes detailed discussions of the most frequent symbolic operations such as equation solving, differentiation, series expansion, and integration with more than 200 fully worked examples from physics, mathematics and computer graphics. Functions from algebra and analysis, as well as orthogonal polynomials and special functions of mathematical physics are also discussed. An indispensable resource for practitioners, professionals, and researchers in mathematics, computer science, engineering and other scientific disciplines, The Mathematica GuideBook for Symbolics will find a natural place on the bookshelf as an essential reference work. 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.

Zusatztext

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)

Bericht

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)

Produktdetails

• Autoren: Michael Trott
• Verlag: Springer, Berlin
• Sprache: Englisch
• Produktform: Medienkombination
• Erschienen: 05.12.2005
• EAN: 9780387950204
• ISBN: 978-0-387-95020-4
• Seiten: 1454
• Gewicht: 2592 g
• Illustration: LV, 1454 p. With DVD. In 2 volumes, not available separately.
• Themen: Naturwissenschaften, Medizin, Informatik, Technik > Mathematik > Wahrscheinlichkeitstheorie, Stochastik, Mathematische Statistik; B, Algorithmen und Datenstrukturen, Algorithms, Mathematik für Informatiker, Numerische Mathematik, Mathematics and Statistics, Computer mathematics, Numerical analysis, Computational Science and Engineering, Maths for scientists, Mathematical Software, Computer software, Computer science—Mathematics, Maths for computer scientists, Symbolic and Algebraic Manipulation