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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 |
Newton, Isaac, as Keeper of the Mint 80
Newton, Isaac, inventing differential equations 221
Nonlinear differential equations 225 235-241
Nonlinear differential equations, catenary equation 270
Normal distribution see Gaussian distribution
Normalization factors by least squares 199-208
Normalization factors by least squares, best-fit objective function 203
Normalization factors by least squares, dependence on weighting 202
Normalization factors by least squares, for world-record sprints 229
Normalization factors by least squares, normalizing data to fitting function 201
Normalization factors by least squares, normalizing fitting function to data 200
Normalization factors by least squares, Poisson distribution of errors 202
Normalization factors by least squares, program for 204-208
Normalization of Lorentzian functions 405
Notations for derivatives 223 241
Noumerov algorithm 285-287
Noumerov algorithm, program for 294-299
Noumerov, B. V. 285 313
Numerical derivatives see Derivatives numerical
Numerical integrals see Integrals numerical
Numerical mathematics compared to pure mathematics 111
Numerical noise 111-122
Numerical noise, computer versus hand calculator 116
Numerical noise, in quadratic equation solution 118
Numerical noise, roundoff errors 112
Numerical noise, truncation errors 112
Numerical Recipes 10 421
Numerical recipes, and numerical noise 116
Numerical recipes, unsavory dishes 241
Nuptial arch 279
Nussbaumer, H. J. 401 420
Nyquist criterion 321
Nyquist criterion, dependence on weights 185
Nyquist criterion, for normalization factors by least squares 200
Nyquist criterion, objective function, Nyquist criterion, definition of 185
Ohm's law resistance 259
Oppenheim, A. V. 334 345 375 376
Order of a differential equation 224
Ordinary differential equations 224
Ordinary least squares (OLS) 191
Orthogonal functions 185-189
Orthogonal functions, and linear least squares 188
Orthogonal functions, for Fourier expansions 3 19
Orthogonal functions, Legendre polynomials 187
Orthogonal functions, Schmidt orthogonalization 186
Outliers in least-squares fitting 184
Overdamping 263
Overshoot see Wilbraham-Gibbs overshoot
Paeth, A. W. 80 98
Parameter bias, dependence on error model 212
Parameter bias, for Gaussian distribution 212
Parameter bias, for small samples 2 13
Parameter bias, for uniform distribution 213
Parameter bias, Gaussian distribution divergence 213
Parameter bias, in slope from log transformation 211
Parameter bias, Monte Carlo simulation 214
Parameter bias, origin of in log transformation 209
Parametric integration for Gaussian moments 183
Parseval's theorem, interpretation of 320
Parseval's theorem, relation to Wiener — Khinchin theorem 320
Parseval's theorem, statement of 320
Partial differential equations 224
Pascal, and C 6
Pascal, translating between Pascal and C 423-428
Patient MAC 366
Pedagogues, modem 269
Peters, R. D. 333 376
Phase angle 25
Phase angle, in complex plane 41
Phase angle, of forced motion 266
Phase-space plot 264
Phasor diagram 42
Pi to computer accuracy 46
Pippard, A. B. 40 43 49 151 258 264 269 313 386 420
Plane-polar coordinates and complex numbers 28
Plauger, P. J. 8 15
Poincar map 264
Poisson distribution 185
Poisson distribution, and normalization by least squares 202
Poisson distribution, for error model 210
Polynomial wiggle problem 154
Potential from a charged wire 145-151
Potential from a charged wire, analytical integral 146
Potential from a charged wire, integral for 145
Potential from a charged wire, numerical integrals 148-151
Power series see Taylor series
Power spectrum of EEG 372
Pratt, W. K. 343 345 376
Predictor formulas, Adams methods 245
Predictor formulas, Adams trapezoid predictor for first-order equation 246
Predictor formulas, Adams — Simpson predictor for first-order equation 246
Predictor formulas, central Euler predictor for first-order equation 243
Predictor formulas, Euler method 1 for second-order equation 280
Predictor formulas, Euler method 2 for second-order equation 281
Predictor formulas, Euler method 3 for second-order equation 281
Predictor formulas, Euler methods 242 280
Predictor formulas, Euler methods summarized 281
Predictor formulas, example of Euler methods for second-order equation 282
Predictor formulas, forward Euler predictor for first-order equation 243
Predictor formulas, testing Euler predictors for first-order equations 244
Predictor formulas, testing Euler predictors for second-order equations 29 1-294
Predictor-corrector methods 247
Press, W. H. 7 10 15 144 151 304 313 360 375 376 421 422
probability distribution 184
Probability distribution, Gaussian 182
Probability distribution, moments of 182 211
Probability distribution, Poisson 185
Probability distribution, uniform 212
Program, complex-arithmetic functions 21
Program, conjugate and modulus of complex functions 25
Program, convert between coordinates 45
Program, convoluting discretized functions 398
Program, cosine and sine 67
Program, DFT of oscillator 326
Program, estimating significant digits 112
Program, fast Fourier transform 360
Program, first-order differential equations 247
Program, Fourier analysis of EEG 368
Program, Fourier series 340
Program, geometric series 54
Program, Horner polynomial 104
Program, normalization by least squares 204
Program, Noumerov algorithm for second-order equations 294
Program, potential from a charged wire 148
Program, power-series expansion 63 93
Program, quantum harmonic oscillator 301
Program, Riccati transformation 308
Program, roots of quadratic equations 119
Program, second-order Euler algorithms 287
Program, Simpson integral formula 137
Program, spline fitting 161
Program, straight-line least squares 214
Program, trapezoid integral formula 136
Program, Voigt profile 4 13
Program, working function value, derivatives, and integral 107
Program, world-record sprints 229
Programs and functions, index of 429-430
Programs, caveat emptor 10
Programs, error messages from 11
project 9-10 14
Project, computing derivatives numerically 130
Project, convert between coordinates 45
Project, electrostatic potential of a wire 145
Project, fast Fourier transform program 360
Project, Fourier analysis of EEG 365
Project, Noumerov method for second-order equations 294
Project, second-order Euler methods 287
Project, solving first-order differential equations 247
Project, spline fitting 161
Project, straight-line least-squares fits 214
| Project, testing the convergence of series 85
Project, Voigt profile 4 11
Proportional errors 2 10
Protter, M. H. 51 59 98 376
Pure mathematics compared to numerical mathematics 111
Pythagoras, Theorem of 33
Pythagoras, theorem of, testing numerically 97
Quadrants, sign of circular functions in 45
Quadratic equation solution, program for stable method 119
Quadratic equation solution, subtractive cancellation in 118
Quantum harmonic oscillator 299-304
Quantum harmonic oscillator, Noumerov solution 301-304
Quantum leap 303
Radians to degrees 66
Rasala, R. 178 179
Raster 347
Real number 19
Recurrence 84
Recursion 84
Recursion, logical problems with 85
Reed, B. C. 191 219
Relative errors in differential equation solutions 242
Relaxation time in world-record sprints 226
Repetition in mathematics and computing 83
Repetition in mathematics and computing, iteration 84
Repetition in mathematics and computing, recurrence 84
Repetition in mathematics and computing, recursion 84
Resonance 265-269
Resonance, amplitude of 266
Resonance, described by Lorentzian function 389
Resonance, in Fourier transform of oscillator 382
Resonance, maximum amplitude 267
Resonance, phase of 266
Riccati transformation 306-311
Riccati transformation, example of 307
Riccati transformation, program for 308-311
Richardson extrapolation 133
Riemann zeta function 353
Ringing 348
Roberts, R. A. 334 376
Romberg integration 144
Roundoff errors 112
Rubinstein, R. 178 179
Rucker, R. 77 98
sample programs 9
Sample programs, simple example (geometric series) 55
Sawtooth function Fourier series 347-349
Schildt, H. 7 15
Schmidt orthogonalization 186
Schr dinger equation 43 225
Schrdinger equation, for harmonic oscillator 299
Schultz, M. H. 178 179
Schumaker, L. L. 158 178 179
Second-order differential equations 258
Second-order differential equations, and forced motion 265
Second-order differential equations, complex-number representation 265
Second-order differential equations, for free motion 261-264
Second-order differential equations, for mechanical and electrical systems 260
Second-order differential equations, removing first derivatives 284-285
Separable differential equation for world-record sprints 228
Shammas, N. 8 15 423
Shannon sampling theorem 321
Siegel, A. F. 181 219
Sigmoid function see Logistic growth
Significant digits, program for 112
Simpson formula, comparison with trapezoid formula 142
Simpson formula, composite formula 141
Simpson formula, derivation of 140
Simpson formula, error estimate 141
Simpson formula, for numerical integrals 140-142
Simpson formula, graphical interpretation 141
Simpson formula, program for 137 141
Simpson formula, testing with cosines 143
Sine function, programming series for 86
Sine function, series for small angles 66
Sine function, Taylor series for 65
Snell, J. L. 181 182 211 219
Solomon, F. 184 185 219 397 420
Source term in second-order differential equation 265
Speed testing program for 364
Spehlmann, R. 366 376
Spline derivatives 171
Spline derivatives, and unstable problems 174
Spline derivatives, for cosines 173
Spline derivatives, for working function 171
Spline endpoint conditions 155 159-161
Spline endpoint conditions, for working function 160
Spline endpoint conditions, natural spline 155
Spline fitting, algorithm for 158
Spline fitting, and computer graphics 178
Spline fitting, and computer-aided design 178
Spline fitting, and type fonts 178
Spline fitting, combined with least-squares fitting 218
Spline fitting, compared to least squares 153
Spline fitting, efficiency of 175
Spline fitting, equations 156-159
Spline fitting, exact fit to data 153
Spline fitting, history of 178
Spline fitting, of working function 155
Spline fitting, program for 161
Spline fitting, properties of fit 156
Spline fitting, versus polynomial fit 153
Spline integration 175-177
Spline integration, compared to trapezoid and Simpson rules 175 177
Spline integration, derivation 175
Spline integration, for cosine 177
Spline integration, for working function 177
Spline integration, function for 176
Spline integration, testing the program 176
Spline interpolation 168-174
Spline interpolation, first derivative from 168
Spline interpolation, for cosines 173
Spline interpolation, for working function 170
Spline interpolation, second derivative from 168
Spline interpolation, third derivative from 169
Spline interpolation, value from 168
Spline, definition of 154
Spline, knot of 155
Spline, natural 160-161
Spline, order of 155
Square root, linearized approximations 78
Square-pulse function, Fourier integral transform of 383
Square-pulse function, Fourier series for 338-340
Stability and chaos in logistic growth 239
Standard deviation 182
Standard deviation, in proportional-errors model 210
Standard deviation, of independent Gaussian errors 403
Star notation for convolution 393
Steinmetz, C. P. 43
Stellar spectra, Voigt profile for 419
Stiff differential equations 304-312
Stiff differential equations, Madelung transformation 311
Stiff differential equations, nature of 305
Stiff differential equations, numerical example of 306
Stiff differential equations, origin of term 305
Stiff differential equations, Riccati transformation 306
Stochastic process 184
Stopping criterion for first-order differential equations 247
Straight-line least squares 190-199
Straight-line least squares with errors in both variables, error estimates 199
Straight-line least squares with errors in both variables, minimum objective function 198
Straight-line least squares, errors in both variables 190
Straight-line least squares, program for 214-217
Straight-line least squares, testing and using program 217
Straight-line least squares, weighting models 190
Subtractive cancellation 116-119
Subtractive cancellation, in quadratic equation solution 118
Subtractive cancellation, in spline fitting 174
Subtractive cancellation, in variance calculations 117
Symmetry conditions for Fourier series 339
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