CRC Standard Curves and Surfaces with Mathematica, ... (ISBN 1584885998)

A New Edition After 14 Years:
In the 14 years since the previous edition of this book was published: Mathematica has matured, expanded and improved tremendously The power of the desktop PC has increased many-fold in both processing speed and in memory capacity Several useful but complex curves and surfaces were deliberately left out of the earlier edition because of the first two points. Taken together, this has almost required this offering of a new edition. Virtually every chapter has been re-written. Even the older curves and surfaces have been re-coded to take advantages of new capabilities within Mathematica. Several new chapters have been writteh to cover: Green's functions Minimal Surfaces Knots and Links added to 3-D curves the chapter on regular polyhedra has been greatly expanded. The CD supplied with the books contains Mathematica notebooks of code to construct plots of all the functions presented in the book.

A great updated book on expressing surfaces in Mathematica:
This book is a virtual encyclopedia of curves and functions, and depicts nearly all of the standard mathematical functions rendered using the software package Mathematica. Along with lots of examples, historical notes, and citations, this expanded second edition features four new chapters: Green's Functions, Regular Surfaces, Irregular and Miscellaneous Surfaces, and Minimal Surfaces. It includes coverage on Riemann's continuous but nowhere differentiable function. The book also updates the Mathematica code, called "notebooks," to the latest version (5.0), which allows much more detailed illustrations, and makes these notebooks available on an enclosed CD-ROM, usable on any platform, so that you can easily render and manipulate the functions presented in the book. The book does not provide a tutorial on Mathematica, nor does it delve deeply into the pure mathematics of it all, so you should already be familiar with both. Chapter one is the closest thing to a tutorial in the book. The rest of the chapters read more like a catalog. Highly recommended for anyone involved in scientific visualization who has access to Mathematica, which is a very expensive program. The following is the table of contents: Chapter 1 - Introduction 1.1. Concept of a Curve 1.2. Concept of a Surface 1.3. Coordinate Systems 1.3.1. Cartesian Coordinates 1.3.2. Polar Coordinates 1.3.3. Cylindrical Coordinates 1.3.4. Spherical Coordinates 1.4. Qualitative Properties of Curves and Surfaces 1.4.1. Derivative 1.4.2. Symmetry 1.4.3. Extent 1.4.4. Asymptotes 1.4.5. Periodicity 1.4.6. Continuity 1.4.7. Singular Points 1.4.8. Critical Points 1.4.9. Zeroes 1.4.10. Integrability 1.4.11. Multiple Values 1.4.12. Curvature 1.5. Classification of Curves and Surfaces 1.5.1. Algebraic Curves 1.5.2. Transcendental Curves 1.5.3. Integral Curves 1.5.4. Piecewise Continuous Functions 1.5.5. Classification of Surfaces 1.6. Basic Curve and Surface Operations 1.6.1. Translation 1.6.2. Rotation 1.6.3. Linear Scaling 1.6.4. Reflection 1.6.5. Rotational Scaling 1.6.6. Radial Translation 1.6.7. Weighting 1.6.8. Nonlinear Scaling 1.6.9. Shear 1.6.10. Matrix Method for Transformation 1.7. Method of Presentation 1.7.1 Equations 1.7.2 Plots Chapter 2 - Algebraic Functions 2.1 Functions with xn/m 2.2 Functions with xn and (a + bx)m 2.3 Functions with a2 + x2 and xm 2.4 Functions with a2 - x2 and xm 2.5 Functions with a3 + x3 and xm 2.6 Functions with a3 - x3 and xm 2.7 Functions with a4 + x4 and xm 2.8 Functions with a4 - x4 and xm 2.9 Functions with (a + bx)1/2 and xm 2.10 Functions with (a2 - x2)1/2 and xm 2.11 Functions with (x2 - a2)1/2 and xm 2.12 Functions with (a2 + x2)1/2 and xm 2.13 Miscellaneous Functions 2.14 Functions Expressible in Polar Coordinates 2.15 Functions Expressed Parametrically Chapter 3 - Transcendental Functions 3.1 Functions with sinn(ax) and cosm(bx) (n,m integers) 3.2 Functions with 1 ± a sinn(cx) and 1 ± b cosm(cx) 3.3 Functions with a sinn(cx) + b cosm(cx) 3.4 Functions of More Complicated Arguments 3.5 Inverse Trigonometric Functions 3.6 Logarithmic Functions 3.7 Exponential Functions 3.8 Hyperbolic Functions 3.9 Inverse Hyperbolic Functions 3.10 Trigonometric and Exponential Functions Combined 3.11 Trigonometric Functions Combined with Powers of x 3.12 Logarithmic Functions Combined with Powers of x 3.13 Exponential Functions Combined with Powers of x 3.14 Hyperbolic Functions Combined with Powers of x 3.15 Combinations of Trigonometric Functions, Exponential Functions, and Powers of x 3.16 Miscellaneous Functions 3.17 Functions Expressible in Polar Coordinates 3.18 Functions Expressed Parametrically Chapter 4 - Polynomial Sets 4.1 Orthogonal Polynomials 4.2 Non-orthogonal Polynomials Chapter 5 - Special Functions in Mathematical Physics 5.1 Exponential and Related Integrals 5.2 Sine and Cosine Integrals 5.3 Gamma and Related Functions 5.4 Error Functions 5.5 Fresnel Integrals 5.6 Legendre Functions 5.7 Bessel Functions 5.8 Modified Bessel Functions 5.9 Kelvin Functions 5.10 Spherical Bessel Functions 5.11 Modified Spherical Bessel Functions 5.12 Airy Functions 5.13 Riemann Functions 5.14 Parabolic Cylinder Functions 5.15 Elliptic Integrals 5.16 Jacobi Elliptic Functions Chapter 6 - Green's Functions 6.1 Green's Function for the Poisson Equation 6.2 Green's Function for the Wave Equation 6.3 Green's Function for the Diffusion Equation 6.4 Green's Function for the Helmholtz Equation 6.5 Miscellaneous Green's Functions 6.6 Harmonic Functions - Solutions to Laplace's Equation Chapter 7 - Special Functions in Probability and Statistics 7.1 Discrete Probability Densities 7.2 Continuous Probability Densities 7.3 Sampling Distributions Chapter 8 - Nondifferentiable and Discontinuous Functions 8.1 Functions with a Finite Number of Discontinuities 8.2 Functions with an Infinite Number of Discontinuities 8.3 Functions with a Finite Number of Discontinuities in First Derivative 8.4 Functions with an Infinite Number of Discontinuities in First Derivative Chapter 9 - Random Processes 9.1 Elementary Random Processes 9.2 General Linear Processes 9.3 Integrated Processes 9.4 Fractal Processes 9.5 Poisson Processes Chapter 10 - Polygons 10.1 Regular Polygons 10.2 Star Polygons 10.3 Irregular Triangles 10.4 Irregular Quadrilaterals 10.5 Polyiamonds 10.6 Polyominoes 10.7 Polyhexes 10.8 Miscellaneous Polygons Chapter 11 - Three-Dimensional Curves 11.1 Helical Curves 11.2 Sine Waves in Three Dimensions 11.3 Miscellaneous 3-D Curves 11.4 Knots 11.5 Links Chapter 12 - Algebraic Surfaces 12.1 Functions with ax + by 12.2 Functions with x2/a2 ± y2/b2 12.3 Functions with (x2/a2 + y2/b2 ± c2)1/2 12.4 Functions with x3/a3 ± y3/b3 12.5 Functions with x4/a4 ± y4/b4 12.6 Miscellaneous Functions 12.7 Miscellaneous Functions Expressed Parametrically Chapter 13 - Transcendental Surfaces 13.1 Trigonometric Functions 13.2 Logarithmic Functions 13.3 Exponential Functions 13.4 Trigonometric and Exponential Functions Combined 13.5 Surface Spherical Harmonics Chapter 14 - Complex Variable Surfaces 14.1 Algebraic Functions 14.2 Transcendental Functions Chapter 15 - Minimal Surfaces 15.1 Elementary Minimal Surfaces 15.2 Complex Minimal Surfaces Chapter 16 - Regular and Semi-Regular Solids with Edges 16.1 Platonic Solids 16.2 Archimedean Solids 16.3 Duals of Platonic Solids 16.4 Stellated (Star) Polyhedra Chapter 17 - Irregular and Miscellaneous Solids 17.1 Irregular Polyhedra 17.2 Miscellaneous Closed Surfaces with Edges