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index 653drand, 114Driving force, 211Duffing oscillator, 318DX, see OpenDX 45Eigenvalues, 164, 170,174, 198, 212–221,245, 491, 540Electrostatic potential,439Elliptic integral, 304Encapsulation, 89, 100,106Entropy, 299Environmental variables,562, 595EquationsKorteweg–de Vries, 515Burgers’, 510differential, 194discrete, 119, 290integral, 540, 541, 547of motion, 226Schrödinger, 212, 318,492Van der Pool, 318Ergodic, 395Errors, 30–44algorithm, 30, 40, 128approximation, seeAlgorithm 30in differentiation, 149empirical, 39, 132in integration, 128, 132minimum, 42multiplicative, 34N-D integration, 139random, 30roundoff, 28, 31, 34–36,39, 41, 42, 44, 110,124, 129, 132, 138,149, 200, 201, 518total, 39, 40types of, 30Euler’s rule, 201–203,413n, 416Exceptions, 13Exchange energy, 391Exponential decay, 119,184Extinction, 293Extract part, 91, 97Extrapolated difference,148Fast Fourier transform,see FFT 256Feigenbaum constants,297Ferromagnet, 392Fetch, 360Feynmanpath integrals, 408–423postulates, 411propagator, 408FFT, 241, 256–263Filtersanalog, 250digital, 252, 283sinc, 253windowed, 253Fine grain parallel, 362Finitedifference equation,120difference timedomain, 499–506differences, 120, 443,493, 527, 532elements, 453–463Fitting, 176–193best, 176global, 185goodness, 186least squares, 184–193linear least square,186–191Newton-Raphson, 193nonlinear, 191–193Fixed points in maps,291, 307Fixed-point numbers, 18Floating-point numbers,18–24, 31, 558FLOPS, 206, 372, 558Fluid Dynamics, 508–539Fortran, 8, 627vs Java, 380Forward difference, seeDerivatives 147Fourierautocorrelationrelation, 249discrete transform, seeDiscrete Fouriertransform 237fast transform, see FFT256of half-wave, 235integral, 236PDE solution via, 440of sawtooth, 234series, 231, 235short-time transform,268theorem, 232transform, 231, 236,580, see also FFTFractals, 326–350coastline, 334dimension, seeDimension 326plants, 329, 331, 332Pollock painting, 342Friction, 209–210, 307,309, 317, 521, 533in oscillations, 209, 211in waves, 483, 486, 487in pendulum, 302–308in projectile motion,226–228Functional, 408integration, 411–423Galerkin decomposition,456–459Game of Life, 343Garbage, 30, 558−101COPYRIGHT 2008, PRINCET O N UNIVE R S I T Y P R E S SEVALUATION COPY ONLY. NOT FOR USE IN COURSES.ALLpup_06.04 — 2008/2/15 — Page 653