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

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

Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID
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Предметный указатель
Abell, M. L.      421
Abramowitz      144 151 179 312 353 375 412 413 419 421
AC series circuit      259
Adams — Moulton formulas      247
Allen, L. H.      419
Alternating series      56-57
Amplitude of forced motion      266
Analysis, numerics, applications      2-3
Analytic continuation      44
Angell. I. O.      12 14
Arccosine function, programming series for      88
Arches      see Catenary
Arcsine function, programming series for      90
Argand diagram      see Complex plane
Automobile suspension system      259
B$\acute{e}$zier control points      178
B$\hat{o}$cher      318 350 375
Babu, G. J.      199 218
Backus, J.      269 312
Baker, L.      421
Balakrishnan, N.      236 255
Baldock, G. R.      43 49
Banded matrix in spline fitting      157
Barlow, R. J.      181 185 218
Bartels, R. H.      178 179
Beckmann, P.      188 218
Beltrami, E.      239 255
Bemouilli's equation      see Generalized logistic growth
Bernoulli, J.      279 312
Bias      see Parameter bias
Binning effects on Lorentzian functions      396
Binomial approximation      76-83
Binomial approximation, applications of      78-80
Binomial approximation, derivation of      76
Binomial approximation, geometrical representation      77
Binomial approximation, linearized square roots by      78
Bit reversal for FFT      332 333
Bootstrap method for error estimating      218
Boundary values of differential equations      223
Boxcar function      see Fourier series window
Bracewell, R. N.      334 375 397 420
Brainwave      see EEG
Brandt S.      299 312
Braun      269 313
Brigham, E. O.      322 333 334 375
C language      6-7
C language, reference manuals for      8
Cameron, J. R.      365 375
Catenary      269-279
Catenary, and redesign of St. Paul's cathedral      279
Catenary, circle-arc      276
Catenary, constant-strength      277
Catenary, constant-strength and suspension bridge      277
Catenary, demonstrating with helium balloons      278
Catenary, density distribution      272
Catenary, dimensionless variables for      272
Catenary, equation of      270
Catenary, history of      279
Catenary, parabolic      273
Catenary, strength distribution      272
Catenary, tension distribution      272
Catenary, uniform-density      275
Catenary, weight distribution      272
Catenary, with general density distribution      270
Catenary, with uniform density distribution      271
Cathedral domes and catenaries      279
Chain      see Catenary
Champeney, D. C.      318 375
Chaos and relation to unstable problems      116
Chapel Hill      207
Chapters, links between      13
Chi-squared function      184
Churchill, R. V.      378 420
Cody, W. J.      69 98
Cohen — Tannoudji, C.      299 313
Cole — Cole plot      40
Complex conjugation      23
Complex conjugation, in complex plane      29
Complex conjugation, program for      25
Complex exponentials      3 1-36
Complex exponentials, and cosine      32
Complex exponentials, and FFT      33
Complex exponentials, and sine      32
Complex exponentials, Euler's theorem for      31
Complex exponentials, for discrete Fourier transforms      3 18
complex numbers      18-25
Complex numbers, absolute value      24
Complex numbers, and programming      19 20
Complex numbers, argument      24
Complex numbers, as pairs of numbers      18
Complex numbers, De Moivre's theorem for      29
Complex numbers, for second-order differential equations      265
Complex numbers, in C language      7
Complex numbers, modulus      24
Complex numbers, phase angle      25
Complex numbers, principal value of angle      29
Complex numbers, program for      21
Complex numbers, programming in C      22
Complex numbers, quadratic equation roots      121
Complex numbers, rules for      19
Complex plane      27-29
Complex plane, analytic continuation in      44
Complex plane, and plane geometry      27
Complex plane, program to convert coordinates      45
Complex plane, rotations in      28
Complex plane, trajectories in      38-41
Computation in engineering      3
Computational physics      3
Computer arithmetic      111
Computer graphics and spline fitting      178
Computer-aided design and spline fitting      178
Computing, programming, coding      5
Confidence limits      185
Consecutive central derivatives, CCD      127
Conventional Fourier transforms, time for computing      330 333
Convolution theorem      401
Convolution, area-preserving property      397
Convolution, definition and interpretation      393
Convolution, for Fourier integral transforms      393-411
Convolution, Gaussians with Lorentzians      411
Convolution, of boxcar with Lorentzian function      394
Convolution, of discretized functions, program      398-401
Convolution, of Gaussian distributions      402
Convolution, of Gaussian with Lorentzian      406
Convolution, of Lorentzian functions      403
Convolution, star notation      393
Convolution, symmetry properties      397
Convolution, wrap-around in      398
Correlation coefficient and IDWMC      197
Cosine function      65
Cosine function, programming series for      86
Cosine function, series for small angles      66
Coulomb's law      145
Critical damping, singularity in      263
Cromwell, L.      366 375
Cubic spline      see Spline fitting
Damping factors, Lanczos      374-375
Damping forces      259
Damping parameter for free motion      262
Damping parameter, trajectory in complex plane      38
Darnell, P. A.      7 15
Data analysis methods      3
Davis, P. J.      144 151 175 179
Dawson's integral      410-411
Dawson's integral, numerical integration for      4 12
Dawson's integral, numerical methods for      412-413
Dawson's integral, series expansion      4 12
de Boor, C.      158 178 179
De Moivre's theorem      29
degree of a differential equation      224
Degrees to radians      66
Deming, W. E.      191 218
Derivatives, numerical      122-133
Derivatives, numerical, 3-point central derivatives      129
Derivatives, numerical, as unstable problems      122
Derivatives, numerical, better algorithms for second derivatives      128
Derivatives, numerical, central-difference      125
Derivatives, numerical, consecutive central derivatives      127
Derivatives, numerical, five-point central derivatives      129
Derivatives, numerical, for cosine function      132
Derivatives, numerical, for exponential function      130
Derivatives, numerical, for working function      124 125 127 130
Derivatives, numerical, forward-difference      123
Derivatives, numerical, polynomial approximations      122
Derivatives, numerical, project for      130-133
Derivatives, numerical, second      126-130
Diaconis, P.      218
Diamond, J.      235 255
Differential equations      221
Differential equations, and forces      258-269
Differential equations, and physical systems      222-223
Differential equations, boundary values      223
Differential equations, classification of      223
Differential equations, degree of      224
Differential equations, first-order, numerical      241-254
Differential equations, first-order, numerical, Adams predictor formulas for      245 247
Differential equations, first-order, numerical, Euler predictor formulas for      242-245
Differential equations, first-order, numerical, predictor-corrector methods      247
Differential equations, first-order, numerical, program for      247-254
Differential equations, for logistic growth      235
Differential equations, homogeneous      224
Differential equations, initial conditions      223
Differential equations, nonlinear      225
Differential equations, notation and classification      223-224
Differential equations, order of      224
Differential equations, ordinary      224
Differential equations, partial      224
Differential equations, second-order, numerical      279-304
Differential equations, second-order, numerical, Euler predictor formulas for      280-294
Differential equations, second-order, numerical, program for Euler algorithms      287-294
Differentiation and integration, distinction      99
Dirac delta distributions      379-380
Dirac delta distributions, and Gaussian distribution      389
Dirac delta distributions, and Kronecker delta      380
Discrete data and numerical mathematics      110-111
Discrete Fourier transforms      3 18-329
Discrete Fourier transforms, analytical examples of      322-329
Discrete Fourier transforms, derivation of      3 18-3 19
Discrete Fourier transforms, exponential decay      323-325
Discrete Fourier transforms, general exponential      322-323
Discrete Fourier transforms, harmonic oscillation      325-329
Discrete Fourier transforms, independent coefficients of      321
Discrete Fourier transforms, of real values      321
Discrete Fourier transforms, overview      317
Discrete Fourier transforms, program for oscillator      326-329
Discrete Fourier transforms, properties of      320-322
Discrete Fourier transforms, restrictions on use of      321
Discrete Fourier transforms, symmetry for exponential decay      323
Discrete Fourier transforms, symmetry for harmonic oscillation      326
Discretized functions, convolution of      398
Distance versus time in world-record sprints      227
Diversion, computers, splines, and graphics      178
Diversion, interpreting complex numbers      43
Diversion, purpose of      4
Diversion, repetition in mathematics and computing      83
Dodd, J. N.      404 420
Doppler broadening and Voigt profile      419
Drafting spline      154
Draper, N. R.      181 218
Dym, C. L.      2 14
EEG, characteristics of      365-366
EEG, data for Fourier analysis      367
EEG, filtering effects      373-375
EEG, Fourier analysis of      365-375
EEG, frequency spectrum analysis      372
EEG, power spectrum of      372
EEG, program for Fourier analysis of      368-372
Electrical-mechanical analogs      259-261
Electroencephalogram      see EEG
Eliason, A. L.      7 15
Embree, P.      375
Endpoint conditions      see Spline
Energy eigenstate      300
Equilibrium condition in logistic growth      236
Error model      see also Probability distribution
Error model, for parameter bias estimation      210
Error model, proportional errors      2 10
Error values, presenting for differential equations      241
Errors in both variables in straight-line least squares      190
Euler predictors for differential equations      see Predictor formulas
Euler's theorem      3 1-32
Euler's theorem, applications of      32 34
Exercises, purpose of      13 352
exit function      9
Expectation values in statistics      211
Exponential data, linearizing by log transformation      209
Exponential decay, DFT of      322-325
Exponential decay, Fourier integral transform      380-382
Exponential function, and financial interest schemes      82
Exponential function, computing      62
Exponential function, programming series for      85
Exponential function, Taylor series      61
Extinction predicted from logistic growth      239
Farin, G.      178 179
Fast Fourier transforms, algorithm for      329-334
Fast Fourier transforms, bit reversal for coefficients      332-333
Fast Fourier transforms, deriving FFT algorithm      329-333
Fast Fourier transforms, efficiency of      333-334
Fast Fourier transforms, for analyzing EEG      372
Fast Fourier transforms, mandala for      330
Fast Fourier transforms, program for      360 365
Fast Fourier transforms, radix-2 FFT derivation      330-333
Fermi distribution      see Logistic growth
FFT      see Fast Fourier transforms
Filtering      397
Filtering in Fourier analysis      373-375
Filtering in Fourier analysis, truncation filtering      373
Financial interest schemes      80-83
Financial interest schemes, and Isaac Newton      80
Financial interest schemes, compound interest      81
Financial interest schemes, exponential interest      82
Financial interest schemes, simple interest      81
First-order differential equations      225-235
First-order differential equations, numerical methods for      24 1-247
First-order differential equations, world-record sprints      225
Foley, J. D.      12 14 178 179
Forced motion and resonances      265-269
Fortran, and C      7
Fortran, translating between Fortran and C      423428
Fourier analysis of EEG      365-375
Fourier expansions, overview of      3 16-3 18
Fourier expansions, types and nomenclature      3 16-3 18
Fourier integral transforms, analytical convolutions      401406
Fourier integral transforms, and Dirac delta distributions      379
Fourier integral transforms, convolution of      393-411
Fourier integral transforms, examples of      380-393
Fourier integral transforms, for exponential decay      380-382
Fourier integral transforms, for harmonic oscillation      382
Fourier integral transforms, from Fourier series      377-379
Fourier integral transforms, of Gaussian distribution      386-389
Fourier integral transforms, of Lorentzian function      391-393
Fourier integral transforms, of square-pulse function      383
Fourier integral transforms, of wedge function      384
Fourier integral transforms, overview      3 18
Fourier series      334-349
Fourier series, and Fourier integral transforms      377-379
Fourier series, and symmetry conditions      339
Fourier series, derived from DFT      334-336
Fourier series, examples of      337-349
Fourier series, for arbitrary intervals      336
1 2 3 4
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