CRC Standard Curves and Surfaces with Mathematica, Second Edition

CRC Press, Oct 20, 2006 - Mathematics - 556 pages
Since the publication of the first edition, Mathematica® has matured considerably and the computing power of desktop computers has increased greatly. This enables the presentation of more complex curves and surfaces as well as the efficient computation of formerly prohibitive graphical plots. Incorporating both of these aspects, CRC Standard Curves and Surfaces with Mathematica®, Second Edition is a virtual encyclopedia of curves and functions that depicts nearly all of the standard mathematical functions rendered using Mathematica.

While the easy-to-use format remains unchanged from the previous edition, many chapters have been reorganized and better graphical representations of numerous curves and surfaces have been produced.
An introductory chapter describes the basic properties of curves and surfaces, includes two handy tables of 2-D and 3-D curve and surface transformations, and provides a quick understanding of the basic nature of mathematical functions. To facilitate more efficient and more thorough use of the material, the whole gamut of curves and surfaces is divided into sixteen individual chapters. The accompanying CD-ROM includes Mathematica notebooks of code to construct plots of all the functions presented in the book.

New to the Second Edition
• Chapters on minimal surfaces and Green's functions that involve Poisson, wave, diffusion, and Helmholtz equations
• Knots and links in the 3-D curves chapter
• Archimedean solids, duals of Platonic solids, and stellated forms in the regular polyhedra chapter
• Additional curves and surfaces in almost every chapter
• Expanded index for quick access to curves or surfaces of interest and to find definitions of common mathematical terms
• Upgraded Mathematica notebooks with more uniform formatting, more complete documentation on particular curves and surfaces, an explanation of the plotting algorithms, and more explicit designations of variable parameters to easily adjust curve or surface plots
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Contents

 Introduction 1 References 21 Algebraic Curves 23 Transcendental Functions 113 and Powers of x 188 Polynomial Sets 227 Special Functions in Mathematical Physics 241 References 282
 Random Processes 359 Polygons 387 ThreeDimensional Curves 403 Algebraic Surfaces 429 Transcendental Surfaces 467 Complex Variable Surfaces 483 Minimal Surfaces 505 Regular and SemiRegular Solids with Edges 513

 References 320 Nondifferentiable and Discontinuous Functions 345