CRC Standard Curves and Surfaces with Mathematica, Second Edition
Chapman & Hall/CRC (Verlag)
978-1-58488-599-3 (ISBN)
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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
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
| Erscheint lt. Verlag | 20.10.2006 |
|---|---|
| Reihe/Serie | Advances in Applied Mathematics |
| Zusatzinfo | 505 equations; 1 Halftones, black and white; 2 Tables, black and white; 938 Illustrations, black and white |
| Sprache | englisch |
| Maße | 178 x 254 mm |
| Gewicht | 1134 g |
| Themenwelt | Mathematik / Informatik ► Mathematik |
| ISBN-10 | 1-58488-599-8 / 1584885998 |
| ISBN-13 | 978-1-58488-599-3 / 9781584885993 |
| Zustand | Neuware |
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