Thompson - Computing for Scientists and Engineers (523188), страница 77
Текст из файла (страница 77)
L., and J. P. Braselton, Mathematica by Example, Academic, NewYork, 1992.Abramowitz, M. and I. A. Stegun, Handbook of Mathematical Functions, Dover,New York, 1964.Baker, L., C Mathematical Function Handbook, McGraw-Hill, New York, 1992.421422EPILOGUELandau, R. H., and P. J.
Fink, A Scientist’s and Engineer’s Guide toWorkstations and Super-computers, Wiley-Interscience, New York, 1992.Press, W. H., B. P. Flannery, S. A. Teukolsky, and W. T. Vetterling, NumericalRecipes in C, Cambridge University Press, New York, 1988.Press, W. H., B. P. Flannery, S. A. Teukolsky, and W.
T. Vetterling, NumericalRecipes: The Art of Scientific Computing (FORTRAN Version), CambridgeUniversity Press, New York, 1989.Press, W, H., B. P. Flannery, S. A. Teukolsky, and W. T. Vettesling, NumericalRecipes in Pascal: The Art of Scientific Computing, Cambridge UniversityPress, New York, 1989.Wolfram, S., Mathematica: A System for Doing Mathematics by Computer,Addison-Wesley, Redwood City, California, second edition, 1991.PreviousINDEX TO COMPUTER PROGRAMSSection2.12.12.63.13.23.23.54.1Program Name (Functions)Program PurposeComplex-Arithmetic Functions(CAdd, CSub, CMult, CDiv)Conjugate & Modulus Functions(CConjugate, CModulus)Cartesian & Polar CoordinateInterconversion(MakePolar, MakeCartesian)Complex arithmeticGeometric Series(GeoSum)Power Series for Exponential(PSexp)Cosine & Sine in Compact Form(CosPoly, SinPoly)Power Series Convergence(PSexp, PScos, PSsin,PSarccos, PSarcsin, PSln)Geometric seriesHorner Polynomials(Horner_Poly)Horner’s algorithmConjugate and modulusConvert between coordinatesTaylor series for exponentialCosine and sine polynomialsConvergence of series429Home430INDEX TO COMPUTER PROGRAMSWorking Function: Valueand Derivatives(Horner_Poly_2, Der_1F,Der_1C) , Der_2CCD, Der_23CD,Der-25CD)Significant Digits in FloatingPointQuadratic Equation Roots(quadroots)Trapezoid and Simpson Integrals(SimpInt, TrapInt, y, YWInt)Electrostatic Potentials byNumerical Integration(Vs, SimpInt, TrapInt, y)Value and all derivatives ofworking function5.3Cubic Splines(SplineFit, SplineInt,SplineInterp, Horner4Poly,yw, ywInt)Cubic-spline fitting,interpolation, derivatives,and integrals6.4Least Squares Normalization(NormObj)Straight-Line Least Squares(LeastSquares)Least-squares normalizingfactorsStraight-line least-squares;errors in both variablesWorld Record Sprints(DIST)Numerical DE_l; Euler& Adams Predictors(FUNC, ANALYT)Analyze world-record sprintsNumerical DE_2; Euler-TypeMethods(FUNC, ANALYT)Numerical DE_2; Noumerov Method(FUNC, ANALYT)Numerical DE; Second order byRiccati(ANALYTRb, ANALYTy,FUNCRb, FUNCy)Second-order differentialequations by Euler methodsDiscrete Fourier Transformfor OscillatorAnalytical discreteFourier transform4.14.34.34.64.66.67.27.58.48.58.69.2Test your computer for numberof significant digitsAccurate roots of quadraticTrapezoid and Simpson rulesElectrostatic potential from acharged wireFirst-order differentialequationsSecond-order differentialequations; Noumerov methodRiccati transformation forstiff differential equationsINDEX TO COMPUTER PROGRAMS9.59.79.8Fourier Series(FSsquare, FSwedge, FSwindow,FSSawtooth)Fast Fourier Transform(FFT, bitrev)EEG FFT analysis(FFT)Fourier series of functionsFast Fourier transformEEG analysis by FFTConvolute Arrays(convolve-arrays)Convolute discretizedtransform10.4 Voigt Profile(FDawson, Hzero, Hone,Htwo, Hthree, trap)Voigt profile by series10.3431432INDEXAbell, M.
L., 421Abramowitz, M., 144, 151,179, 312,3 5 3 ,3 7 5 ,4 1 2 , 4 1 3 ,4 1 9 ,4 2 1AC series circuit, 259Adams-Moulton formulas, 247Allen, L. H., 419alternating series, 56-57amplitude of forced motion, 266analysis, numerics, applications, 2-3analytic continuation, 44Angell. I. O., 12. 14arccosine function:programming series for, 88arches, see catenaryarcsine function, programming series for, 90Argand diagram, see complex planeautomobile suspension system, 259Babu, G.
J.. 199, 218Backus, J., 269, 312Baker, L., 421Balakrishnan, N., 236, 255Baldock, G. R., 43, 49banded matrix in spline fitting, 157Barlow, R. J., 181, 185, 218Bartels, R. H., 178, 179Beckmann, P., 188, 218Beltrami, E., 239, 255Bernouilli’s equation,see generalized logistic growthBernoulli, J., 279, 312Bézier control points, 178bias, see parameter biasbinning effects on Lorentzian functions, 396binomial approximation, 76-83applications of, 78-80derivation of, 76geometrical representation, 77linearized square roots by, 78bit reversal for FFT, 332, 333Bôcher, M., 318, 350, 375bootstrap method for error estimating, 218boundary valuesof differential equations, 223boxcar function,see Fourier series, window functionBracewell, R.
N., 334, 375, 397, 420brainwave, see EEGBrandt S., 299, 312Braun, M., 269, 313Brigham, E. O., 322, 333, 334, 375C language, 6-7and Fortran, 7and Mathematica, 10and Numerical Recipes, 10and Pascal, 6exit function, 9for Fortran programmers, 8for Pascal programmers, 8learning to program in, 7, 16portability of, 7First authors are referenced in full on the pages with numbers printed in italics.433434INDEXC language (continued)reference manuals for, 8simple program (geometric series), 55translating between Fortran and C,423-428translating between Pascal and C,423-428translating to Fortran from, 8translating to Pascal from, 8workstations and C, 7Cameron, J. R., 365, 375catenary, 269-279and redesign of St. Paul’s cathedral, 279circle-arc, 276constant-strength, 277constant-strength and suspension bridge,277demonstrating with helium balloons, 278density distribution, 272dimensionless variables for, 272equation of, 270history of, 279parabolic, 273strength distribution, 272tension distribution, 272uniform-density, 275weight distribution, 272with general density distribution, 270with uniform density distribution, 271cathedral domes and catenaries, 279chain, see catenaryChampeney, D.
C., 318, 375chaos and relation to unstable problems, 116Chapel Hill, 207chapters, links between, 13chi-squared function, 184Churchill, R. V., 378, 420Cody, W. J., 69, 98Cohen-Tannoudji, C., 299, 313Cole-Cole plot, 40complex conjugation, 23in complex plane, 29program for, 25complex exponentials, 3 l-36and cosine, 32and FFT, 33and sine, 32Euler’s theorem for, 3 1for discrete Fourier transforms, 3 18complex numbers, 18-25absolute value, 24and programming, 19,20argument, 24as pairs of numbers, 18De Moivre’s theorem for, 29for second-order differential equations, 265in C language, 7modulus, 24phase angle, 25principal value of angle, 29program for, 21programming in C, 22quadratic equation roots, 12 1rules for, 19complex plane, 27-29analytic continuation in, 44and plane geometry, 27program to convert coordinates, 45rotations in, 28trajectories in, 38-41computation in engineering, 3computational physics, 3computer arithmetic, 111computer graphics and spline fitting, 178computer-aided designand spline fitting, 178computing, programming, coding, 5confidence limits, 185consecutive central derivatives, CCD, 127conventional Fourier transforms:time for computing, 330, 333convolution:area-preserving property, 397definition and interpretation, 393for Fourier integral transforms, 393-411Gaussians with Lorentzians.
411of boxcar with Lorentzian function, 394of discretized functions, program, 398-40lof Gaussian distributions, 402of Gaussian with Lorentzian, 406of Lorentzian functions, 403star notation, 393symmetry properties, 397wrap-around in,398convolution theorem, 401correlation coefficient and IDWMC, 197cosine function, 65programming series for, 86series for small angles, 66Coulomb’s law, 145critical damping, singularity in, 263Cromwell, L., 366, 375cubic spline, see spline fittingdamping factors, Lanczos, 374-375damping forces, 259INDEXdamping parameter,trajectory in complex plane, 38damping parameter for free motion, 262Darnell, P.
A., 7, 15data analysis methods, 3Davis, P. J., 144, 151, 175, I79Dawson’s integral, 410-411numerical integration for, 4 12numerical methods for, 412-413series expansion, 4 12De Boor, C., 158, 178, 179De Moivre’s theorem, 29degree of a differential equation, 224degrees to radians, 66Deming, W. E., 191, 218derivatives, numerical, 122-1333-point central derivatives, 1295-point central derivatives, 129as unstable problems, 122better algorithmsfor second derivatives, 128central-difference, 125consecutive central derivatives, 127for cosine function, 132for exponential function, 130for working function, 124, 125, 127, 130forward-difference, 123polynomial approximations, 122project for, 130-133second, 126-130Diaconis, P., 218Diamond, J., 235, 255differential equations, 221and forces, 258-269and physical systems, 222-223boundary values, 223classification of, 223degree of, 224for logistic growth, 235homogeneous, 224initial conditions, 223nonlinear, 225notation and classification, 223-224order of, 224ordinary, 224partial, 224differential equations,first-order, numerical, 241-254Adams predictor formulas for, 245,247Euler predictor formulas for, 242-245predictor-corrector methods, 247program for, 247-254435differential equations,second-order, numerical, 279-304Euler predictor formulas for, 280-294program for Euler algorithms, 287-294differentiation and integration, distinction, 99Dirac delta distributions, 379-380and Gaussian distribution, 389and Kronecker delta, 380discrete data and numerical mathematics,110-111discrete Fourier transforms, 3 18-329analytical examples of, 322-329derivation of, 3 18-3 19exponential decay, 323-325general exponential, 322-323harmonic oscillation, 325-329independent coefficients of, 32 1of real values, 321overview, 317program for oscillator, 326-329properties of, 320-322restrictions on use of, 321symmetry for exponential decay, 323symmetry for harmonic oscillation, 326discretized functions, convolution of, 398distance versus timein world-record sprints, 227diversion:computers, splines, and graphics, 178interpreting complex numbers, 43purpose of, 4repetition in mathematicsand computing, 83Dodd, J.
N., 404, 420Doppler broadening and Voigt profile, 419drafting spline, 154Draper, N. R., 181, 218Dym, C. L., 2, 14EEG:characteristics of, 365-366data for Fourier analysis, 367filtering effects, 373-375Fourier analysis of, 365-375frequency spectrum analysis, 372power spectrum of, 372program for Fourier analysis of, 368-372electrical-mechanical analogs, 259-261electroencephalogram, see EEGEliason, A. L., 7, 15Embree, P.
M., 375endpoint conditions, see spline436INDEXenergy eigenstate, 300equilibrium condition in logistic growth, 236error model, see also probability distributionfor parameter bias estimation, 210proportional errors, 2 10error values, presenting fordifferential equations, 24 1errors in both variablesin straight-line least squares, 190Euler predictors for differential equationssee predictor formulasEuler’s theorem, 3 l-32applications of, 32, 34exercises, purpose of, 13,352exit function, 9expectation values in statistics, 211exponential data, linearizing bylog transformation, 209exponential decay, DFT of, 322-325Fourier integral transform, 380-382exponential function:and financial interest schemes, 82computing, 62programming series for, 85Taylor series, 61extinction predicted from logistic growth,239Farin, G., 178, 179fast Fourier transforms:algorithm for, 329-334bit reversal for coefficients, 332-333deriving FFT algorithm, 329-333efficiency of, 333-334for analyzing EEG, 372mandala for, 330program for, 360, 365radix-2 FFT derivation, 330-333speed testing program for, 364Fermi distribution, see logistic growthFFT, see fast Fourier transformsfiltering, 397filtering in Fourier analysis, 373-375truncation filtering, 373financial interest schemes, 80-83and Isaac Newton, 80compound interest, 81exponential interest, 82simple interest, 81first-order differential equations, 225-235numerical methods for, 24 l-247world-record sprints, 225Foley, J.
![](https://s.studizba.com/z.php?f=/templates/si/i/noavatar.png&w=100&h=100&t=1"){kind=avatar}
