Product Description

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

Product Details

• Amazon Sales Rank: #1421091 in Books
• Published on: 2006-10-20
• Original language: English
• Number of items: 1
• Binding: Hardcover
• 556 pages

Review
This is a book of mathematical pictures. … The reader can use the Mathematica notebooks to modify and play with plots of all functions presented in the book. This book is recommended to anybody interested in the field.
-EMS Newsletter, June 2007

Customer Reviews

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

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.