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

3. Auflage 2016
ISBN: 978-1-4822-5022-0
Verlag: Taylor & Francis
Format: PDF
Kopierschutz: Adobe DRM (»Systemvoraussetzungen)

E-Book, Englisch, 474 Seiten

Reihe: Advances in Applied Mathematics

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

- A CD-ROM, 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.

Autoren/Hrsg.

von Seggern, David H.

Fachgebiete

• Mathematik | Informatik Mathematik Geometrie
• Mathematik | Informatik Mathematik Numerik und Wissenschaftliches Rechnen Angewandte Mathematik, Mathematische Modelle
• Mathematik | Informatik Mathematik Algebra

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 Functions
Plotting Information for This Chapter
Functions with xn/m
Functions with xn and (a + bx)m
Functions with (a2 + x 2) 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 va + bx and xm
Functions with va2 - x2 and xm
Functions with vx2 - a2 and xm
Functions with va2 + x2 and xm
Miscellaneous Functions
Functions Expressible in Polar Coordinates
Functions Expressed Parametrically

Transcendental Functions
Plotting Information for This Chapter
Functions with sinn (2p ax) and cosm(2pbx)(n,m integers)
Functions with 1 ± sinn (2p ax) and 1 ±} cosm (2pbx)
Functions with c sinn (ax) + d cosm (bx)
Functions of More Complicated Arguments
Inverse Trigonometric Functions
Logarithmic Functions
Exponential Functions
Hyperbolic Functions
Inverse Hyperbolic Functions
Trigonometric Combined with Exponential Functions
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
Combined Trigonometric Functions, Exponential Functions, and Powers of x
Miscellaneous Functions
Functions Expressible in Polar Coordinates
Functions Expressible Parametrically

Polynomial Sets
Plotting Information for This Chapter
Orthogonal Polynomials
Nonorthogonal Polynomials
References

Special Functions in Mathematical Physics
Plotting Information for This Chapter
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
Plotting Information for This Chapter
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
Plotting Information for This Chapter
Discrete Probability Densities
Continuous Probability Densities
Sampling Distributions

Laplace Transforms
Plotting Information for This Chapter
Elementary Functions
Algebraic Functions
Exponential Functions
Trigonometric Functions
References

Nondifferentiable and Discontinuous Functions
Plotting Information for This Chapter
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
Plotting Information for This Chapter
Elementary Random Processes
General Linear Processes
Integrated Processes
Fractal Processes
Poisson Processes
References

Polygons
Plotting Information for This Chapter
Polygons with Equal Sides
Irregular Triangles
Irregular Quadrilaterals
Polyiamonds
Polyominoes
Polyhexes
Miscellaneous Polygons

Three-Dimensional Curves
Plotting Information for This Chapter
Helical Curves
Sine Waves in Three Dimensions
Miscellaneous 3-D Curves
Knots
Links
References

Algebraic Surfaces
Plotting Information for This Chapter
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
Plotting Information for This Chapter
Trigonometric Functions
Logarithmic Functions
Exponential Functions
Trigonometric and Exponential Functions Combined
Surface Spherical Harmonics

Complex Variable Surfaces
Plotting Information for This Chapter
Algebraic Functions
Transcendental Functions

Minimal Surfaces
Plotting Information for This Chapter
Elementary Minimal Surfaces
Complex Minimal Surfaces
References

Regular and Semi-Regular Solids with Edges
Plotting Information for This Chapter
Platonic Solids
Archimedean Solids
Duals of Platonic Solids
Stellated (Star) Polyhedra
References

Irregular and Miscellaneous Solids
Plotting Information for This Chapter
Irregular Polyhedra
Miscellaneous Closed Surfaces with Edges

Index

Über Autor(innen)

David H. von Seggern, PhD, worked for Teledyne Geotech from 1967 to 1982 in Alexandria, Virginia, almost exclusively on analysis of seismic data related to underground nuclear explosions. This effort was supported by the Air Force Office of Scientific Research (AFOSR) and by the Defense Advanced Research Projects Agency (DARPA). His research there addressed detection and discrimination of explosions, physics of the explosive source, explosive yield estimation, wave propagation, and application of statistical methods. Dr. von Seggern earned his PhD at Pennsylvania State University in 1982. He followed that with a 10-year position in geophysics research at Phillips Petroleum Company, where he became involved with leading-edge implementation of seismic imaging of oil and gas prospects and with seismic-wave modeling.