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| Thompson W.J. — Computing for Scientists and Engineers: A Workbook of Analysis, Numerics, and Applications |
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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 zier control points 178
B 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
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