The Mathematica GuideBook for Programming

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 Programming provides a comprehensive, step-by-step development of Mathematica programming capabilities and contains an enormous collection of examples and worked exercises. It guides the reader to become fluent in the structure of Mathematica expressions, expression evaluation, pure and named functions, and in procedural, rule-based, and functional programming constructs. Each Mathematica function is discussed in detail, explained in numerous examples. The programs for this book are available to download at the link below: http://extras.springer.com Unique Features: \* Step-by-step presentation of Mathematica functions assuming no prior Mathematica programming experience \* Clear organization, complete topic coverage, and an accessible writing style for both novices and experts \* Detailed discussion of procedural, rule-based, and functional programming \* Hundreds of worked examples, illustrations, programs, and fully worked self-study exercises for understanding concepts and learning how to solve real-life problems \* Website for book with additional materials: http://www.MathematicaGuideBooks.org 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 http://functions.wolfram.com, which currently features more that 80,000 formulas and identities, and thousands of visualizations.

This comprehensive, detailed reference provides readers with both a working knowledge of Mathematica in general and a detailed knowledge of the key aspects needed to create the fastest, shortest, and most elegant implementations possible. It gives users a deeper understanding of Mathematica by instructive implementations, explanations, and examples from a range of disciplines at varying levels of complexity. The three volumes — Programming, Graphics, and Mathematics, total 3,000 pages and contain more than 15,000 Mathematica inputs, over 1,500 graphics, 4,000+ references, and more than 500 exercises.
This first volume begins with the structure of Mathematica expressions, the syntax of Mathematica, its programming, graphic, numeric and symbolic capabilities. It then covers the hierarchical construction of objects out of symbolic expressions, the definition of functions, the recognition of patterns and their efficient application, program flows and program structuring, and the manipulation of lists.
An indispensible resource for students, researchers and professionals in mathematics, the sciences, and engineering.

"...this comprehensive, detailed reference to mathematica provides the reader with both a working knowledge & a detailed one to the key aspects needed to create faster, shorter, & more elegant implementations."

"The Mathematica GuideBook for Graphics provides a comprehensive step-by-step development of how to use Mathematica to visualize functions and data, manipulate graphics, and optimize their appearance. Two-dimensional graphics, contour plots, plots of surfaces, free-form three-dimensional surfaces, and animations are the core topics. Hundreds of detailed examples and programs show a large variety of visualization techniques, algorithms, methods, and tricks. These tools allow the reader to create virtually any possible graphic, from simple curves to scientific visualizations and artistic images and logos. Mathematica graphics functions are discussed in detail, explained in numerous examples, and put to work in programs that are all contained on the accompanying DVD."--Jacket. Front Matter....Pages i-xxxvii Introduction to Mathematica ....Pages 1-141 Structure of Mathematica Expressions....Pages 142-272 Definitions and Properties of Functions....Pages 274-394 Meta- Mathematica ....Pages 396-536 Restricted Patterns and Replacement Rules....Pages 538-698 Operations on Lists, and Linear Algebra....Pages 700-1001 Back Matter....Pages 1003-1028 A reference that provides readers with both a working knowledge of Mathematica in general and a knowledge of the key aspects needed to create the implementations possible. It gives users an understanding of Mathematica by instructive implementations, explanations, and examples from a range of disciplines at varying levels of complexity. Although prior Mathematica knowledge is not needed to read The Mathematica GuideBook to Programming, it is assumed that the reader is familiar with basic actions in the Mathematica front end, including entering Greek characters using the keyboard, copying and pasting cells, and so on. Accompanying CD-ROM contains ... "all material as an electronic book with complete, executable Mathematica versions 4 and 5 compatible code and programs, rendered color graphics, and animations."--Page 4 of cover.