The Mathematica GuideBook for Symbolics

• Main Author: Trott, Michael (Author)
• Corporate Author: SpringerLink (Online service)
• Format: Electronic eBook
• Language: English
• Published: New York, NY : Springer New York, 2006.
• Subjects: Mathematics.; Computer science > Mathematics.; Algorithms.; Computer mathematics.; Computer software.; Mathematical Software.; Symbolic and Algebraic Manipulation.; Computational Science and Engineering.

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-fri...

Table of Contents:

• 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.