### Features

Presents a comprehensive collection of nearly 1,000 illustrations of curves and surfaces often used or encountered in mathematics, science, and engineering fieldsProvides a unique arrangement of function definitions on left-hand pages and corresponding function plots on right-hand pagesIllustrates variation caused by changes in parameters using multiple curve and surface plotsIncludes a CD-ROM with Mathematica code to construct and modify plots of all the functions in the book
### Summary

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

### Table of Contents

INTRODUCTION

Concept of a Curve

Concept of a Surface

Coordinate Systems

Qualitative Properties of Curves and Surfaces

Classification of Curves and Surfaces

Basic Curve and Surface Operations

Method of Presentation

References

ALGEBRAIC CURVES

Functions with xn/m

Functions with xn and (a+bx)m

Functions with a2+x2 and xm

Functions with a2-x2 and xm

Functions with a3+x3 and xm

Functions with a3- x3 and xm

Functions with a4+x4 and xm

Functions with a4- x4 and xm

Functions with (a+bx)1/2 and xm

Functions with (a2-x2) 1/2 and xm

Functions with (x2- a2) 1/2 and xm

Functions with (a2C x2) 1/2 and xm

Miscellaneous Functions

Functions Expressible in Polar Coordinates

Functions Expressed Parametrically

TRANSCENDENTAL FUNCTIONS

Functions with sinn(ax) and cosm(bx) (n, m integers)

Functions with 1±a sinn(cx) and 1±b cosm(cx)

Functions with a sinn(cx)+b cosm(cx)

Functions of More Complicated Arguments

Inverse Trigonometric Functions

Logarithmic Functions

Exponential Functions

Hyperbolic Functions

Inverse Hyperbolic Functions

Trigonometric and Exponential Functions Combined

Trigonometric Functions Combined with Powers of x

Logarithmic Functions Combined with Powers of x

Exponential Functions Combined with Powers of x

Hyperbolic Functions Combined with Powers of x

Combinations of Trigonometric Functions, Exponential Functions, and Powers of x

Miscellaneous Functions

Functions Expressible in Polar Coordinates

Functions Expressed Parametrically

POLYNOMIAL SETS

Orthogonal Polynomials

Nonorthogonal Polynomials

References

SPECIAL FUNCTIONS IN MATHEMATICAL PHYSICS

Exponential and Related Integrals

Sine and Cosine Integrals

Gamma and Related Functions

Error Functions

Fresnel Integrals

Legendre Functions

Bessel Functions

Modified Bessel Functions

Kelvin Functions

Spherical Bessel Functions

Modified Spherical Bessel Functions

Airy Functions

Riemann Functions

Parabolic Cylinder Functions

Elliptic Integrals

Jacobi Elliptic Functions

References

GREEN'S FUNCTIONS AND HARMONIC FUNCTIONS

Green's Function for the Poisson Equation

Green's Function for the Wave Equation

Green's Function for the Diffusion Equation

Green's Function for the Helmholtz Equation

Miscellaneous Green's Functions

Harmonic Functions-Solutions to Laplace's Equation

References

SPECIAL FUNCTIONS IN PROBABILITY AND STATISTICS

Discrete Probability Densities

Continuous Probability Densities

Sampling Distributions

NONDIFFERENTIALBE AND DISCONTINUOUS FUNCTIONS

Functions with a Finite Number of Discontinuities

Functions with an Infinite Number of Discontinuities

Functions with a Finite Number of Discontinuities in First Derivative

Functions with an Infinite Number of Discontinuities in First Derivative

RANDOM PROCESSES

Elementary Random Processes

General Linear Processes

Integrated Processes

Fractal Processes

Poisson Processes

References

POLYGONS

Regular Polygons

Star Polygons

Irregular Triangles

Irregular Quadrilaterals

Polyiamonds

Polyominoes

Polyhexes

Miscellaneous Polygons

THREE-DIMENSIONAL CURVES

Helical Curves

Sine Waves in Three Dimensions

Miscellaneous 3-D Curves

Knots

Links

References

ALGEBRAIC SURFACES

Functions with ax+by

Functions with x2/a2±y2/b2

Functions with (x2/ a2+y2/ b2±c2)1/2

Functions with x3/a3±y3/b3

Functions with x4/a4±y4/b4

Miscellaneous Functions

Miscellaneous Functions Expressed Parametrically

TRANSCENDENTAL SURFACES

Trigonometric Functions

Logarithmic Functions

Exponential Functions

Trigonometric and Exponential Functions Combined

Surface Spherical Harmonics

COMPLEX VARIABLE SURFACES

Algebraic Functions

Transcendental Functions

MINIMAL SURFACES

Elementary Minimal Surfaces

Complex Minimal Surfaces

References

REGULAR AND SEMI-REGULAR SOLIDS WITH EDGES

Platonic Solids

Archimedean Solids

Duals of Platonic Solids

Stellated (Star) Polyhedra

References

IRREGULAR AND MISCELLANEOUS SOLIDS

Irregular Polyhedra

Miscellaneous Closed Surfaces with Edges

INDEX

### Reviews

"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