CRC Standard Curves and Surfaces with Mathematica - Rilegato

Von Seggern, David H.

Rilegato

ISBN 10: 1584885998 ISBN 13: 9781584885993

Casa editrice: Chapman and Hall/CRC, 2006

Riassunto

Since the publication of this book’s bestselling predecessor, Mathematica® has matured considerably and the computing power of desktop computers has increased greatly. The Mathematica® typesetting functionality has also become sufficiently robust that the final copy for this edition could be transformed directly from Mathematica R notebooks to LaTex input.

Incorporating these aspects, CRC Standard Curves and Surfaces with Mathematica®, Third Edition is a virtual encyclopedia of curves and functions that depicts nearly all of the standard mathematical functions and geometrical figures in use today. The overall format of the book is largely unchanged from the previous edition, with function definitions and their illustrations presented closely together.

New to the Third Edition:

• A new chapter on Laplace transforms
• New curves and surfaces in almost every chapter
• Several chapters that have been reorganized
• Better graphical representations for curves and surfaces throughout
• Downloadable resources, including the entire book in a set of interactive CDF (Computable Document Format) files

The book presents a comprehensive collection of nearly 1,000 illustrations of curves and surfaces often used or encountered in mathematics, graphics design, science, and engineering fields. One significant change with this edition is that, instead of presenting a range of realizations for most functions, this edition presents only one curve associated with each function.

The graphic output of the Manipulate function is shown exactly as rendered in Mathematica, with the exact parameters of the curve’s equation shown as part of the graphic display. This enables readers to gauge what a reasonable range of parameters might be while seeing the result of one particular choice of parameters.

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Contenuti

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

Product Description

Book by von Seggern David H

Dettagli dell'edizione

• Editore: Chapman and Hall/CRC
• Data di pubblicazione: 2006
• Lingua: Inglese
• ISBN 10: 1584885998
• ISBN 13: 9781584885993
• Rilegatura: Copertina rigida
• Numero edizione: 2
• Numero di pagine: 556
• Contatto del produttore: non disponibile
• Persona responsabile: non disponibile