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

• 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