von Seggern CRC Standard Curves and Surfaces with Mathematica, Second Edition

2. Auflage 2016
ISBN: 978-1-4200-1110-4
Verlag: Taylor & Francis
Format: PDF
Kopierschutz: Adobe DRM (»Systemvoraussetzungen)

E-Book, Englisch, 556 Seiten

Reihe: Chapman & Hall/CRC Applied Mathematics & Nonlinear Science

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

Zielgruppe

Mathematicians, physicists, and engineers.

Autoren/Hrsg.

von Seggern, David H.

Inhaltsverzeichnis

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