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雷达卡
David H. von Seggern
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
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.
Table of Contents
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
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