CRC Standard Curves and Surfaces with Mathematica
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CRC Standard Curves and Surfaces with Mathematica

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Since the publication of the first edition, Mathematica(R) 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(R), 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 plotsshow more

Product details

  • Hardback | 556 pages
  • 177.8 x 251.5 x 35.6mm | 1,247.39g
  • Taylor & Francis Ltd
  • Chapman & Hall/CRC
  • Boca Raton, FL, United States
  • English
  • Revised
  • 2nd Revised edition
  • 938 black & white illustrations, 2 black & white tables, 1 black & white halftones
  • 1584885998
  • 9781584885993

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 INDEXshow more