...MATHEMATICA¹

See http://www.wolfram.com

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...MAPLE²

See http://www.maplesoft.com

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...MATLAB.³

See http://www.mathworks.com

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...NAG,⁴

See http://www.nag.com

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...LINPACK,⁵

See http://www.netlib.org

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...ODEPACK,⁶

ibid.

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... construct.⁷

Strictly speaking, this is a C++ extension to the C language. However, most modern C compilers now accept this comment style.

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... compiler.⁸

Function prototypes are a requirement for all user-defined functions in C++ programs.

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... declaration.⁹

The parenthesis around *function-name are very important:
data-type *function-name(type 1, type 2, ...) is interpreted by the compiler as a reference to a function which returns a pointer to type data-type, rather than a pointer to a function which returns type data-type.

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... statements.¹⁰

Prior to the ANSI standard, to which the GNU C compiler adheres, local arrays could not be initialized via their declaration statements.

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... array.¹¹

An array name is not exactly equivalent to a pointer, because a pointer can point to any address in the computer memory--this address can even be changed--whereas an array name is constrained to always point towards the address of its associated first data item.

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... class,¹²

The CAM graphics class is copyrighted to its author, Prof. Chris Anderson, Department of Mathematics, UCLA, 1998.

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... PostScript¹³

PostScript is a registered trademark of Adobe Systems Incorporated.

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... century.¹⁴

Numerical recipes in C: the art of scientific computing, W.H. Press, S.A. Teukolsky, W.T. Vettering, and B.R. Flannery (Cambridge University Press, Cambridge UK, 1992), p. 710.

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... on.¹⁵

Handbook of mathematical functions, M. Abramowitz and I.A. Stegun (Dover, New York NY, 1965), p. 896.

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... form¹⁶

Numerical recipes in C: the art of scientific computing, W.H. Press, S.A. Teukolsky, W.T. Vettering, and B.R. Flannery (Cambridge University Press, Cambridge, England, 1992), p. 714.

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... methods¹⁷

Numerical methods, R.W. Hornbeck (Prentice-Hall, Englewood Cliffs NJ, 1975), p. 196.

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... methods.¹⁸

ibid, p. 199.

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... law:¹⁹

Methods of theoretical physics, Vol. II, P.M. Morse, and H. Feshbach, (McGraw-Hill, New York NY, 1953).

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... number:²⁰

R.E. Reynolds, Phil. Trans. Roy. Soc. 174, 935 (1883).

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...Giordano²¹

Computational physics, N.J. Giordano, (Prentice-Hall, Upper Saddle River NJ, 1997).

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... speed.²²

Although the drag coefficient, $C_D$, decreases with increasing speed, the drag force, which is proportional to $C_D\,v^2$, always increases.

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... Sawyer²³

Aerodynamics of a knuckleball, R.G. Watts, and E. Sawyer, Am. J. of Phys. 43, 960 (1975).

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... respectively.²⁴

G.L. Baker, Control of the chaotic driven pendulum, Am. J. Phys. 63, 832 (1995).

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... interactions.²⁵

E.S. Albers and B.W. Lee, Phys. Rep. 9C, 1 (1973).

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... universe.²⁶

P. Coles, and F. Lucchin, Cosmology: The origin and evolution of cosmic structure, (J. Wiley & Sons, Chichester UK, 1995).

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...fractal.²⁷

B.B. Mandelbrot, The fractal geometry of nature, (W.H. Freeman, New York NY, 1982).

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... bifurcations.²⁸

M.J. Feigenbaum, Quantitative universality for a class of nonlinear transformations, J. Stat. Phys. 19, 25 (1978).

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... bifurcations.²⁹

M.J. Feigenbaum, The universal metric properties of nonlinear transformations, J. Stat. Phys. 21, 69 (1979).

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... systems.³⁰

P. Citanovic, Universality in chaos, (Adam Hilger, Bristol UK, 1989).

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... ground.³¹

E. Lorenz, Deterministic nonperiodic flow, J. Atmospheric Science 20, 130 (1963).

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... increased.³²

N. Metropolis, M.L. Stein, and P.R. Stein, On finite limit sets for transformations on the unit interval, J. Combin. Theor. 15, 25 (1973).

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... systems.³³

R.H. Simoyi, A. Wolf, and H.L. Swinney, One-dimensional dynamics in a multi-component chemical reaction, Phys. Rev. Lett. 49, 245 (1982).

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... method.³⁴

See Numerical recipes in C: the art of scientific computing, W.H. Press, S.A. Teukolsky, W.T. Vettering, and B.R. Flannery (Cambridge University Press, Cambridge, England, 1992), Sect. 19.5.

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... FFT.³⁵

See Numerical recipes in C: the art of scientific computing, W.H. Press, S.A. Teukolsky, W.T. Vettering, and B.R. Flannery (Cambridge University Press, Cambridge, England, 1992), Sect. 12.2.

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... library,³⁶

See http://www.fftw.org

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... transforms.³⁷

This is the case for version 2 of the library (which is the version used in this course), but not version 3.

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... instability.³⁸

T.H. Stix, The theory of plasma waves, 1st Ed. (McGraw-Hill, New York NY, 1962).

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... 1944.³⁹

L. Onsager, Phys. Rev. 65, 117 (1944).

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