The Mathematica guidebook for numerics : mathematics and physics

Michael Trott's GuideBooks are an invaluable reference for the serious Mathematica programmer. The unsurpassed symbolic computation engine, superior programming paradigms, lightning-fast numerics, and state-of-the-art visualization can justly be considered four of the main pillars of the Mathematica system, and Michael Trott, himself a well-established and renowed expert programmer at Wolfram Research, provides the most in-depth coverage available in these areas. Unlike the contents normally to be found in a numerics book, this numerics GuideBook includes several methods and principles from other fields of mathematics and programming. This GuideBook is truly astonishing in terms of its breadth. The material is highly relevant for the ambitious numerics programmer, and the writing style is very readable, fluent, and consistent. The structure of the material is logical and break-free, and the examples are very well-chosen.Several elucidating examples also further the knowledge about the mathematical or physical subject matter itself. Just to mention a few, I was amazed to discover that magnetic field lines of stationary flows are NOT closed in general, and some examples of modern mathematics and physics literature are used in contrast to classical physics, such as the continuous time random walk on a graph or quantum carpets in a solution, which provides an interesting classical vs. quantum variant. And next to textbook examples the reader will find many "real life" examples interspersed throughout the book as well, which makes the results quite "tangible".Michael Trott includes a great comparison of Mathematica's superior compilable machine precision arithmetic (bytecode, instead of machine-code compilation), high-precision arithmetic, and interval arithmetic, all three of which are needed frequently depending on the numerics project at hand.Needless to say, the book shows a profusion of carefully chosen graphics that help understanding the matter or result instantly. Here Michael Trott's expert ability as a graphics programmer is indispensible.All references are hyperlinked through their respective DOI numbers. The DVD contains the texts and inputs of the other three GuideBooks as well.

Mathematica is today's most advanced technical computing system, featuring 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 Numerics (text and code fully tailored for Mathematica 5.1) concentrates on Mathematica's numerical mathematics capabilities. The available types of arithmetic (machine, high-precision, and interval) are introduced, discussed, and put to use. Fundamental numerical operations, such as compiling programs, fast Fourier transforms, minimization, numerical solution of equations, ordinary/partial differential equations are analyzed in detail and are applied to a large number of examples in the main text and solutions to the exercises.

Unique Features:

Detailed exposition of advantages and disadvantages of machine numbers, significance high-precision numbers and intervals

Presents numerous examples of the efficient and optimized use of Mathematica's functions for root finding, numerical minimization, numerical integration, and differential equation solving, and examples from mathematics and physics

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

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 the development of the Wolfram Functions Site http://functions.wolfram.com, which features more that 10,000 visualizations and 85,000 formulas and identities,and also allows for semantical searches.

Contents......Page 15 0. Introduction and Orientation......Page 17 1.0 Remarks......Page 37 1.1.1 Numbers with an Arbitrary Number of Digits......Page 51 1.1.2 Interval Arithmetic......Page 90 1.1.3 Converting Approximate Numbers to Exact Numbers......Page 102 1.1.4 When N Does Not Succeed......Page 130 1.1.5 Packed Arrays......Page 137 1.2 Fitting and Interpolating Functions......Page 160 1.3 Compiled Programs......Page 195 1.4 Linear Algebra......Page 239 1.5 Fourier Transforms......Page 261 1.6 Numerical Functions and Their Options......Page 300 1.7 Sums and Products......Page 308 1.8 Integration......Page 325 1.9 Solution of Equations......Page 352 1.10 Minimization......Page 383 1.11.1 Ordinary Differential Equations......Page 404 1.11.2 Partial Differential Equations......Page 487 1.12.1 Visualizing Electric and Magnetic Field Lines......Page 517 1.12.2 Riemann Surfaces of Algebraic Functions......Page 544 Exercises......Page 557 Solutions......Page 590 References......Page 951 2.0 Remarks......Page 1005 2.1 Divisors and Multiples......Page 1010 2.2 Number Theory Functions......Page 1045 2.3 Combinatorial Functions......Page 1066 2.4 Euler, Bernoulli, and Fibonacci Numbers......Page 1082 Exercises......Page 1096 Solutions......Page 1112 References......Page 1209 A......Page 1226 B......Page 1227 C......Page 1228 D......Page 1230 E......Page 1231 F......Page 1232 H......Page 1233 I......Page 1234 M......Page 1235 N......Page 1237 P......Page 1238 R......Page 1239 S......Page 1240 V......Page 1242 Z......Page 1243 This book offers comprehensive, state-of-the-art information about time-domain fiber-optic testing. Readers will gain an understanding of how to troubleshoot optical-fiber networks using an optical time-domain reflectometer (OTDR), while learning the fundamental principles underlying the operation of these powerful testing instruments. From basic fiber optics and fiber testing, to detailed event-analysis techniques, this book covers the entire spectrum of time-domain optical cable test theory and applications.

* Only book available focusing solely on OTDR theory and practice
* Covers the entire spectrum of time-domain optical cable test theory and applications
* Designed to be accessible to both engineers and system technicians
* Includes OTDR training CD

Audience: Fiber-optic system engineers, test technicians, and students in courses on fiber-optic networks.

Troubleshooting Optical Fiber Networks offers comprehensive, state-of-the-art information about time-domain fiber-optic testing. Readers will gain an understanding of how to troubleshoot optical-fiber networks using an optical time-domain reflectometer (OTDR), while learning the fundamental principles underlying the operation of these powerful testing instruments. From basic fiber optics and fiber testing, to detailed event-analysis techniques, this book covers the entire spectrum of time-domain optical cable test theory and applications. Only book available focusing solely on OTDR theory and practice Covers the entire spectrum of time-domain optical cable test theory and applications Designed to be accessible to both engineers and system technicians The Medical Device R&D Handbook presents a wealth of information for the hands-on design and building of medical devices. Detailed information on such diverse topics as catheter building, prototyping, materials, processes, regulatory issues, and much more are available in this convenient handbook for the first time. The Medical Device R&D Handbook also includes exclusive interviews with pioneers and leaders in the medical device industry, offering an insider's perspective on issues that are critical to the medical device entrepreneur. Highlights Include Provides the reader with working knowledge of Mathematica and key aspects of Mathematica's numerical capabilities needed to deal with virtually any "real life" problem Clear organization, complete topic coverage, and an accessible writing style for both novices and experts Website for book with additional materials: http://www.MathematicaGuideBooks.org Accompanying DVD containing all materials as an electronic book with complete, executable Mathematica 5.1 compatible code and programs, rendered color graphics, and animations The Medical Device R&D Handbook presents a wealth of information for the hands-on design and building of medical devices. Detailed information on such diverse topics as catheter building, prototyping, materials, and processes is available in this convenient handbook for the first time.The Medical Device R&D Handbook also includes exclusive interviews with pioneers and leaders in the medical device industry, offering an insider's perspective on issues that are critical to the medical device entrepreneur. This comprehensive, detailed reference to the new Mathematica 4.0 release provides the reader with both a working knowledge of Mathematica in general and a detailed knowledge of mathematics. The accompanying CD-ROM contains Mathematica 4.0 notebooks with detailed descriptions and explanations of the Mathematica commands. 500 illus. Introduces the reader to Mathematica's various approximate numbers, their arithmetic and the common numerical analysis operations such as numerical integration, root-finding, equation solving, minimization, and differential equation solving. This resource is useful for practitioners, professionals, and researchers