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E-raamat: CRC Standard Curves and Surfaces with Mathematica

(University of Nevada, Reno, USA)
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Since the publication of this books 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 curves 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.
Preface to the Third Edition xi
Author xiii
1 Introduction 1(22)
1.1 Concept of a Curve
1(1)
1.2 Concept of a Surface
1(1)
1.3 Coordinate Systems
2(3)
Cartesian Coordinates
2(1)
Polar Coordinates
3(1)
Cylindrical Coordinates
4(1)
Spherical Coordinates
4(1)
1.4 Qualitative Properties of Curves and Surfaces
5(7)
Derivative
5(1)
Symmetry
6(1)
Extent
7(1)
Asymptotes
7(1)
Periodicity
8(1)
Continuity
8(1)
Singular Points
9(1)
Critical Points
9(1)
Zeroes
10(1)
Integrability
10(1)
Multiple Values
11(1)
Curvature
11(1)
1.5 Classification of Curves and Surfaces
12(3)
Algebraic Curves
13(1)
Transcendental Curves
14(1)
Integral Curves
14(1)
Piecewise Continuous Functions
14(1)
Classification of Surfaces
15(1)
1.6 Basic Curve and Surface Operations
15(4)
Translation
15(1)
Linear Scaling
16(1)
Reflection
16(1)
Rotational Scaling
16(1)
Radial Translation
17(1)
Weighting
17(1)
Nonlinear Scaling
17(1)
Shear
17(1)
Matrix Method for Transformation
18(1)
1.7 Method of Presentation
19(2)
Equations
19(1)
Plots
20(1)
References
21(2)
2 Algebraic Functions 23(74)
2.0 Plotting Information for This
Chapter
23(1)
2.1 Functions with xn/m
23(3)
2.2 Functions with xn and (a + bx)m
26(16)
2.3 Functions with (a2 + x2) and xm
42(4)
2.4 Functions with (a2 - x2) and xm
46(4)
2.5 Functions with (a3 + x3) and en
50(4)
2.6 Functions with (a3 - x3) and xm
54(3)
2.7 Functions with (a4 + x4) and xm
57(3)
2.8 Functions with (a4 - x4) and xm
60(3)
2.9 Functions with Square root of a + bx and xm
63(8)
2.10 Functions with Square root of a2 - x2 and xm
71(5)
2.11 Functions with Square root of x2 - a2 and xm
76(4)
2.12 Functions with Square root of a2 + x2 and xm
80(5)
2.13 Miscellaneous Functions
85(8)
2.14 Functions Expressible in Polar Coordinates
93(3)
2.15 Functions Expressed Parametrically
96(1)
3 Transcendental Functions 97(96)
3.0 Plotting Information for This
Chapter
97(1)
3.1 Functions with sinn(2πax) and cosni(2πbx)(n, m integers)
97(9)
3.2 Functions with 1 ± sintm (2πax) and 1 ± cosm(2πbx)
106(9)
3.3 Functions with c sinn (ax) + d cosm(bx)
115(3)
3.4 Functions of More Complicated Arguments
118(4)
3.5 Inverse Trigonometric Functions
122(3)
3.6 Logarithmic Functions
125(4)
3.7 Exponential Functions
129(5)
3.8 Hyperbolic Functions
134(7)
3.9 Inverse Hyperbolic Functions
141(3)
3.10 Trigonometric Combined with Exponential Functions
144(2)
3.11 Trigonometric Functions Combined with Powers of x
146(8)
3.12 Logarithmic Functions Combined with Powers of x
154(5)
3.13 Exponential Functions Combined with Powers of x
159(5)
3.14 Hyperbolic Functions Combined with Powers of x
164(3)
3.15 Combined Trigonometric Functions, Exponential Functions, and Powers of x
167(2)
3.16 Miscellaneous Functions
169(6)
3.17 Functions Expressible in Polar Coordinates
175(13)
3.18 Functions Expressible Parametrically
188(5)
4 Polynomial Sets 193(8)
4.0 Plotting Information for This
Chapter
193(1)
4.1 Orthogonal Polynomials
193(4)
4.2 Nonorthogonal Polynomials
197(2)
References
199(2)
5 Special Functions in Mathematical Physics 201(36)
5.0 Plotting Information for This
Chapter
201(1)
5.1 Exponential and Related Integrals
201(4)
5.2 Sine and Cosine Integrals
205(3)
5.3 Gamma and Related Functions
208(2)
5.4 Error Functions
210(1)
5.5 Fresnel Integrals
211(2)
5.6 Legendre Functions
213(1)
5.7 Bessel Functions
214(3)
5.8 Modified Bessel Functions
217(1)
5.9 Kelvin Functions
218(3)
5.10 Spherical Bessel Functions
221(2)
5.11 Modified Spherical Bessel Functions
223(2)
5.12 Airy Functions
225(1)
5.13 Riemann Functions
226(2)
5.14 Parabolic Cylinder Functions
228(1)
5.15 Elliptic Integrals
228(4)
5.16 Jacobi Elliptic Functions
232(3)
References
235(2)
6 Green's Functions and Harmonic Functions 237(30)
6.0 Plotting Information for This
Chapter
238(1)
6.1 Green's Function for the Poisson Equation
238(8)
6.2 Green's Function for the Wave Equation
246(4)
6.3 Green's Function for the Diffusion Equation
250(5)
6.4 Green's Function for the Helmholtz Equation
255(5)
6.5 Miscellaneous Green's Functions
260(2)
6.6 Harmonic Functions: Solutions to Laplace's Equation
262(3)
References
265(2)
7 Special Functions in Probability and Statistics 267(18)
7.0 Plotting Information for This
Chapter
267(1)
7.1 Discrete Probability Densities
267(4)
7.2 Continuous Probability Densities
271(10)
7.3 Sampling Distributions
281(4)
8 Laplace Transforms 285(14)
8.0 Plotting Information for This
Chapter
285(1)
8.1 Elementary Functions
285(3)
8.2 Algebraic Functions
288(3)
8.3 Exponential Functions
291(3)
8.4 Trigonometric Functions
294(3)
References
297(2)
9 Nondifferentiable and Discontinuous Functions 299(12)
9.0 Plotting Information for This
Chapter
299(1)
9.1 Functions with a Finite Number of Discontinuities
299(3)
9.2 Functions with an Infinite Number of Discontinuities
302(3)
9.3 Functions with a Finite Number of Discontinuities in First Derivative
305(2)
9.4 Functions with an Infinite Number of Discontinuities in First Derivative
307(4)
10 Random Processes 311(12)
10.0 Plotting Information for This
Chapter
311(1)
10.1 Elementary Random Processes
311(1)
10.2 General Linear Processes
312(4)
10.3 Integrated Processes
316(2)
10.4 Fractal Processes
318(2)
10.5 Poisson Processes
320(2)
References
322(1)
11 Polygons 323(14)
11.0 Plotting Information for This
Chapter
323(1)
11.1 Polygons with Equal Sides
323(2)
11.2 Irregular Triangles
325(2)
11.3 Irregular Quadrilaterals
327(2)
11.4 Polyiamonds
329(2)
11.5 Polyominoes
331(1)
11.6 Polyhexes
332(1)
11.7 Miscellaneous Polygons
333(4)
12 Three-Dimensional Curves 337(24)
12.0 Plotting Information for This
Chapter
337(1)
12.1 Helical Curves
338(3)
12.2 Sine Waves in Three Dimensions
341(3)
12.3 Miscellaneous 3-D Curves
344(6)
12.4 Knots
350(7)
12.5 Links
357(3)
References
360(1)
13 Algebraic Surfaces 361(26)
13.0 Plotting Information for This
Chapter
361(1)
13.1 Functions with ax + by
361(1)
13.2 Functions with x2/a2 f y2/b2
362(2)
13.3 Functions with (x2/a2 y2/b2 c2)1/2
364(3)
13.4 Functions with x3/a3 f y3/b3
367(1)
13.5 Functions with x4/a4 f y4/b4
368(1)
13.6 Miscellaneous Functions
369(5)
13.7 Miscellaneous Functions Expressed Parametrically
374(13)
14 Transcendental Surfaces 387(12)
14.0 Plotting Information for This
Chapter
387(1)
14.1 Trigonometric Functions
387(4)
14.2 Logarithmic Functions
391(1)
14.3 Exponential Functions
392(2)
14.4 Trigonometric and Exponential Functions Combined
394(2)
14.5 Surface Spherical Harmonics
396(3)
15 Complex Variable Surfaces 399(12)
15.0 Plotting Information for This
Chapter
399(1)
15.1 Algebraic Functions
400(5)
15.2 Transcendental Functions
405(6)
16 Minimal Surfaces 411(8)
16.0 Plotting Information for This
Chapter
411(1)
16.1 Elementary Minimal Surfaces
411(2)
16.2 Complex Minimal Surfaces
413(4)
References
417(2)
17 Regular and Semi-Regular Solids with Edges 419(16)
17.0 Plotting Information for This
Chapter
419(1)
17.1 Platonic Solids
419(3)
17.2 Archimedean Solids
422(6)
17.3 Duals of Platonic Solids
428(2)
17.4 Stellated (Star) Polyhedra
430(3)
References
433(2)
18 Irregular and Miscellaneous Solids 435(10)
18.0 Plotting Information for This
Chapter
435(1)
18.1 Irregular Polyhedra
435(7)
18.2 Miscellaneous Closed Surfaces with Edges
442(3)
Index 445
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.
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