3rd Edition

CRC Standard Curves and Surfaces with Mathematica

By David H. von Seggern Copyright 2016
    474 Pages 695 B/W Illustrations
    by Chapman & Hall

    474 Pages 695 B/W Illustrations
    by Chapman & Hall

    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.

    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 √a + bx and xm
    Functions with √a2 − x2 and xm
    Functions with √x2 − a2 and xm
    Functions with √a2 + x2 and xm
    Miscellaneous Functions
    Functions Expressible in Polar Coordinates
    Functions Expressed Parametrically

    Transcendental Functions
    Plotting Information for This Chapter
    Functions with sinn (2π ax) and cosm(2πbx)(n,m integers)
    Functions with 1 ± sinn (2π ax) and 1 ±} cosm (2πbx)
    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

    Biography

    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.