Thompson W.J. — Computing for Scientists and Engineers: A Workbook of Analysis, Numerics, and Applications :: Электронная библиотека попечительского совета мехмата МГУ

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Thompson W.J. — Computing for Scientists and Engineers: A Workbook of Analysis, Numerics, and Applications

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Название: Computing for Scientists and Engineers: A Workbook of Analysis, Numerics, and Applications

Автор: Thompson W.J.

Аннотация:

Topics are divided between review material on the mathematics background; numerical-analysis methods such as differentiation, integration, the solution of differential equations from engineering, life and physical sciences; data-analysis applications including least-squares fitting, splines and Fourier expansions. Unique in its project orientation, it features a vast amount of exercises with emphasis on realistic examples from current applications.

Язык:

Рубрика: Математика/Численные методы/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 1992

Количество страниц: 444

Добавлена в каталог: 01.03.2005

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Предметный указатель

Fourier series, generalized sawtooth      350-353
Fourier series, generalized sawtooth properties      352
Fourier series, in complex-exponential form      335
Fourier series, in cosine and sine form      335
Fourier series, interpreting coefficients      336
Fourier series, overview      317
Fourier series, program for      340-343
Fourier series, sawtooth function      347-349
Fourier series, sawtooth related to square pulse      347
Fourier series, square-pulse function      338-340
Fourier series, wedge function      343-345
Fourier series, wedge related to square pulse      345
Fourier series, window function      345-347
Fourier series, window related to square pulse      346
Fourier transform of      325
Free motion, critical damping      263
Free motion, damping parameter for      262
Free motion, natural frequency for      262
Free motion, second-order differential equations for      261
Full Width at Half Maximum (FWHM)      183
Function in C language, $\verb"ANALYIRb"$       310
Function in C language, $\verb"ANALYT y"$       310
Function in C language, $\verb"ANALYT"$       251 290 297
Function in C language, $\verb"ANALYT"$ for Schr $\ddot{o}$ dinger equation      301
Function in C language, $\verb"bitrev"$       363
Function in C language, $\verb"CAdd"$       22
Function in C language, $\verb"CConjugate"$       26
Function in C language, $\verb"CDiv"$       22
Function in C language, $\verb"CModulus"$       26
Function in C language, $\verb"CMult"$       22
Function in C language, $\verb"convolve_arrays"$       400
Function in C language, $\verb"CosPoly"$       68
Function in C language, $\verb"CSub"$       22
Function in C language, $\verb"Der_1C"$       109
Function in C language, $\verb"Der_1F"$       109
Function in C language, $\verb"Der_23CD"$       110
Function in C language, $\verb"Der_25CD"$       110
Function in C language, $\verb"Der_2CCD"$       109
Function in C language, $\verb"DIST"$       233
Function in C language, $\verb"FDawson"$       415
Function in C language, $\verb"FFT"$       362
Function in C language, $\verb"FSsawtooth"$       342
Function in C language, $\verb"FSsquare"$       341
Function in C language, $\verb"FSwedge"$       341
Function in C language, $\verb"FSwindow"$       342
Function in C language, $\verb"FUNC"$       251 290 296
Function in C language, $\verb"FUNC"$ for Schr $\ddot{o}$ dinger eguation      301
Function in C language, $\verb"FUNCRb"$       310
Function in C language, $\verb"FUNCy"$       310
Function in C language, $\verb"guadroots"$       120
Function in C language, $\verb"Homer_Poly_2"$       109
Function in C language, $\verb"Hone"$       416
Function in C language, $\verb"HornerfourPoly"$       166
Function in C language, $\verb"Horner_Poly"$       105
Function in C language, $\verb"Hthree"$       417
Function in C language, $\verb"Htwo"$       416
Function in C language, $\verb"Hzero"$       416
Function in C language, $\verb"LeastSguares"$       216
Function in C language, $\verb"MakeCartesian"$       48
Function in C language, $\verb"MakePolar"$       48
Function in C language, $\verb"Norrr0bj"$       206
Function in C language, $\verb"PSarccos"$       95
Function in C language, $\verb"PSarcsin"$       96
Function in C language, $\verb"PScos"$       94
Function in C language, $\verb"PSexp"$       94
Function in C language, $\verb"PSln"$       96
Function in C language, $\verb"PSsin"$       95
Function in C language, $\verb"Simplnt"$       138 149
Function in C language, $\verb"SinPoly"$       69
Function in C language, $\verb"SplineFit"$       163
Function in C language, $\verb"Splinelnt"$       165
Function in C language, $\verb"Splinelnterp"$       165
Function in C language, $\verb"trap"$       417
Function in C language, $\verb"Traplnt"$       138 149
Function in C language, $\verb"Vs"$       150
Function in C language, $\verb"y"$       139 150
Function in C language, $\verb"yw"$       166
Function in C language, $\verb"ywInt"$ for spline      166
Function in C language, $\verb"YWInt"$ for trapezoid and Simpson      139
Functions, index of      429-430
Fundamental frequency in Fourier series      336
Fusion-energy devices and Voigt profile      419
FWHM, additivity for Lorentzian convolutions      404
FWHM, of Gaussian distribution      183
FWHM, of Lorentzian function      389
Galilei, Galileo      273 279 313
Gauss plane      see Complex plane
Gauss, C. F.      182
Gaussian distribution      182-183 210 386
Gaussian distribution, and Heisenberg Uncertainty Relations      388
Gaussian distribution, and maximum likelihood      182
Gaussian distribution, as Dirac delta distribution      389
Gaussian distribution, compared with Lorentzian function      390
Gaussian distribution, convolution of      402
Gaussian distribution, convolution with Lorentzian      406-411
Gaussian distribution, FFT of discretized      387
Gaussian distribution, Fourier integral transform of      386-389
Gaussian distribution, fourth moment of      212
Gaussian elimination in spline fits      158
Gaussian quadrature      144
Gear, C. W.      312 313
Gehani, N.      8 15 423
Generalized logistic equation      239
Generalized logistic growth      239-241
Generalized logistic growth, curves of      240
Generalized sawtooth, Fourier series for      350-353
Geometric series      52-56
Geometric series, definition and properties      52
Geometric series, for deriving DFT      3 19
Geometric series, for DFT of general exponential      323
Geometric series, integral to derive logarithm series      57
Geometric series, program for      53
Gibbs phenomenon      see Wilbraham — Gibbs overshoot
Gibbs, J. W.      349 376
Gilbert, D.      277 313
Gleick. J.      239 255
Gould, H.      3 14
Graphics      11-12
Graphics, and Mathematica      12
Great Fire of London and rebuilding St. Paul's      279
Haberman, R.      239 255 264 313
Hamming, R. W.      375 376 397 420
Harbison, S. P.      8 15
Harmonic analyzer      349
Harmonic expansion      see Fourier series harmonic oscillation discrete
Harmonic oscillation, Fourier integral transform      382
Harmonics in Fourier series      336
Hartley transform      334
Harvesting effects on logistic growth      238
Hasse, R. W.      236 255
Heisenberg uncertainty relations      388
Hermite polynomials      300
Hofstadter, D. R.      85 98
Homer polynomial, algorithm for      103
Homer polynomial, for cosine and sine      67
Homer polynomial, for spline integration      176
Homer polynomial, of limited use for series      105
Homer polynomial, program for      104
Homogeneous differential equation      224
Honig, E.      278 279 313
Hooke's law      259
Hooke, Robert      279
Hosmer, D. W.      241 255
Huygens, Christian      279
Hyperbolic functions      34-37
Hyperbolic functions, Cosh      34
Hyperbolic functions, graphs of      371
Hyperbolic functions, sign rule and circular functions      35
Hyperbolic functions, Sinh      34
Hyperbolic functions, Tanh      36

Hyperbolic functions, Taylor series for      71
Imaginary number      18 19
Independent diagonal weighting model (IDWM)      192 193 196 197
Independent diagonal weighting model (IDWM), with constant weights (IDWMC)      192
Induction, and recurrence      84
Induction, for convolution of Gaussians      403
Induction, for convolution of Lorentzians      405
Induction, for convolution of Voigt profiles      408
Induction, geometric series by      52
Induction, Taylor's theorem proof by      59
infinite loop      see Loop infinite
Ingard, K. U.      43 49 269 313 386 420
Initial conditions of differential equations      223
Integrals, analytical, by Mathematica      99
Integrals, numerical      133-144
Integrals, numerical, comparison of trapezoid and Simpson rules      142
Integrals, numerical, for potential from a charged wire      145
Integrals, numerical, higher-order methods      144
Integrals, numerical, Simpson formula      140
Integrals, numerical, testing with cosines      143
Integrals, numerical, trapezoid formula      135
Integrals, numerical, with constant stepsize      134-135
Integration by splines      see Spline integration
Interpolation by splines      see Spline interpolation
Inverse circular functions, Taylor series for      70
Isobe      199 218
Iteration      84
Jaffe, A. J.      181 218
Jain, M. K.      247 255 304 312 313
K $\ddot{o}$ rner, T. W.      318 350 376
Keller model of world-record sprints      226
Keller, J. B.      226 255
Kellison, S. G.      83 98
Kemighan, B. W.      11 15 85 98
Kerrigan, J. F.      8 15 423
Kinematics of sprinting      see World-record sprints
Kinsella, A.      218
Kirchhoffs second law      260
Knot      see Spline
Koenig, A.      8 15
Koonin, S. E.      3 14
Kronecker delta and Dirac delta distributions      380
L'H $\hat{o}$ pital's rule, used for DFT of exponential decay      323
L'H $\hat{o}$ pital's rule, used for DFT of harmonic oscillation      325
Lancaster, P.      178 179
Lanczos filter      373-375
Landau, R. H.      421 422
Language, and Fortran      7
Language, and Mathematica      10
Language, and Numerical Recipes      10
Language, and Pascal      6
Language, exit function      9
Language, for Fortran programmers      8
Language, for Pascal programmers      8
Language, learning to program in      7 16
Language, portability of      7
Language, simple program (geometric series)      55
Language, translating between Fortran and C      423-428
Language, translating between Pascal and C      423-428
Language, translating to Fortran from      8
Language, translating to Pascal from      8
Language, workstations and C      7
Least squares, least-squares fitting, and maximum likelihood      182
Least squares, linear least squares, and discrete Fourier transforms      3 19
Least-squares criterion      182-185
Least-squares fitting      see also Linear
Least-squares fitting, combined with splines      218
Least-squares fitting, compared to splines      181
Least-squares fitting, disadvantages of      184
Least-squares fitting, outlier influence      184
Least-squares fitting, weights in      185
Least-squares normalization factors      see Normalization factors by least squares
Legendre and least-squares criterion      182
Legendre polynomials      187
Lewis, Carl      233
Lichten, W.      181 218
Lichtenberg, D. B.      235 255
Lindstrom, P. A.      83 98
Linear least squares      see also Straight-line
Linear least squares, and orthogonal functions      185 188
Linear least squares, equations for coefficients      188
Links between chapters      13
Logarithm functions, programming series for      90
Logarithm functions, Taylor series for      72-75
Logarithmic transformation and parameter bias      214
Logarithmic transformation, of Lorentzian function      393
Logarithmic transformation, parameter bias in      208
Logistic distribution, logistic growth      235-241
Logistic distribution, logistic growth, and ecology      235
Logistic distribution, logistic growth, curve of      236
Logistic distribution, logistic growth, differential equation for      235
Logistic distribution, logistic growth, dimensionless form      237
Logistic distribution, logistic growth, equilibrium condition      236
Logistic distribution, logistic growth, generalized      239-241
Logistic distribution, logistic growth, graphs of      237
Logistic distribution, logistic growth, harvesting effects      238
Logistic distribution, logistic growth, origins of      235
Logistic distribution, logistic growth, point of inflexion      238
Logistic distribution, logistic growth, predicting extinction      239
Logistic distribution, logistic growth, properties of      238-239
Logistic distribution, logistic growth, stability and chaos      239
Logistic distribution, logistic growth, various terms for      236
loop, infinite      see Infinite loop
Lorentzian function for resonance      268
Lorentzian functions      389-393
Lorentzian functions, binning effects on      396
Lorentzian functions, compared with Gaussian distribution      390
Lorentzian functions, convolution of      403
Lorentzian functions, convolution with Gaussian      406411
Lorentzian functions, convolution with window function      394
Lorentzian functions, definition of      389
Lorentzian functions, Fourier integral transform of      391-393
Lorentzian functions, FWHM of      389
Lorentzian functions, normalized      405
Lorentzian functions, resonance frequency      389
Lorentzian trajectory in complex plane      39
Lumped-parameter analysis of world-record sprints      226
Lyons, L.      181 219
M $\ddot{u}$ ldner      8 15 423
Macdonald, J. R.      190 191 219
Maclaurin series      see Taylor series
Madelung transformation for stiff differential equations      311
Mandala for FFT algorithm      330
Maron, M. J.      117 144 151
Mathematica      5 20 49 52 421
Mathematica, for ordinary differential equations      224
Mathematical modeling      2
Maximum likelihood and least-squares fitting      182 185
Mechanical-electrical analogs      259-261
Menai Strait      277
Meredith, D. C.      3 14
Mesterton — Gibbons      2 14
Meyer, W. J.      2 14
Michelson, Albert      349
Mihalas, D.      404 419 420
Miller, W.      69 98
Modi, J. J.      5 14
Modulus, program for      25
Moment of inertia and least-squares straight line      190
Monte Carlo simulation, for error estimating      218
Monte Carlo simulation, for parameter bias      214
Nakamura, S.      3 14 144 151 304 313
Natural frequency for free motion      262
Natural spline      see also Spline
Natural spline, compared to exact endpoint conditions      161
Natural spline, endpoint conditions      160-161
Natural spline, minimal curvature property of      160
Negative feedback and logistic growth      235
Newton's equation as pair of first-order equations      258
Newton, Isaac, and uniform-density catenary      279

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