## CRC Standard Curves and Surfaces with Mathematica, Second EditionSince 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 |

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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 |

### Common terms and phrases

abs(w algebraic amplitude angle Archimedean solids arg(w asymptote axes beginning of Chapter called Cartesian coordinates circle coordinate system curve or surface curves and surfaces delta function derivative diffusivity Dirac delta function Dirichlet BC Discontinuities Domain Elliptic Integral equation example explicit form figures finite Fractal Process Fresnel Integral function see Section Green's function Helmholtz equation Kelvin Function Knot Laplacian operator Lefthand version Legendre linear Mathematica Minimal Surfaces Neumann BC Nonlinear normal parametric representation Platonic solids plotted Poisson process polar coordinates polyhedra Polynomials probability density radius Recurrence relation regular polygons Reuleaux Righthand version rotation scaling Second Kind Seggern shear simple Sine Wave singular points Spherical Bessel Function spherical coordinates Spiral Stellated String Surface Defined parametrically Symmetry tangent three dimensions three-dimensional curves top and bottom transcendental curves transformations Triangles triangular Trigonometric truncated two-dimensional curve Unbounded unknot vertices viewpoint x-y plane zero