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Buckingham R.A. — Numerical Methods
Buckingham R.A. — Numerical Methods

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Название: Numerical Methods

Автор: Buckingham R.A.

Язык: en

Рубрика: Математика/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 1962

Количество страниц: 597

Добавлена в каталог: 15.04.2008

Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID
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Предметный указатель
Adjoint matrix      358 373 420
Airy’s equation      183 215 236
Aitken, A.C.      93 102 262 272 277 312 319 389 401 586
Aitken’s $\delta^2$ process      260 283 393 430
Algebraic (transcendental) equations, roots of, by Newton — Raphson method      250 253
Algebraic (transcendental) equations, roots of, by “false position”      249
Algebraic (transcendental) equations, roots of, close and multiple roots      254 295
Algebraic (transcendental) equations, roots of, complex roots      266
Algebraic (transcendental) equations, roots of, simultaneous equations      262 (see also “Polynomial equations”)
Algebraic equations, linear      336
Algebraic equations, linear, conditions for solution      336
Algebraic equations, linear, elimination without division      356
Algebraic equations, linear, escalator method      357
Algebraic equations, linear, Gauss — Doolittle method      339 343
Algebraic equations, linear, ill-conditioned equations      362 444
Algebraic equations, linear, improvement of solution      359
Algebraic equations, linear, matrix resolution      343 352 368
Algebraic equations, linear, matrix-squaring method      427
Algebraic equations, linear, minimized iterations      357 413
Algebraic equations, linear, orthogonal vectors, use of      357
Algebraic equations, linear, pivotal condensation      356
Algebraic equations, linear, residual errors      342 355 359
Algebraic equations, linear, Seidel’s iterative method      423
Algebraic equations, linear, square-root method      344
Algebraic equations, linear, triangular equations      337
Algebraic equations, linear, unsymmetrical equations      351 354
Allen, D.N.de G.      523 566
Alternating series      161
Amplitude and phase method      194 201
Anderson, R.L.      323 583
Arc tan x, tabulation of      162 204
Asymptotic series      188 et seq.
Babbage, W.      32
BaggoU, E.A.      174 244
Bairstow, L      9 274
Banachiewicz, T.      344
Bateman, E.27.      295 296
Bemouilli — Aitken method      277 394
Bemouilli, D.      277
Bessel*s interpolation formula      111 114 116 119 123 147 574
BessePs equation      171 186 193 222 240
BicUey, W.D.      126 155 166 458 508 580 532
Biharmonic equation      514 565
Birge, B.T.      312 314 323 389 583
Birkhoff, G.J.D.      507
Bite, W.      478
Black, A.JV.      339 346
Blanch, Gertrude      421
Bodewiq, E.      255 258 285 295 296
Boole, G.      80
Boole’s rule      80 87 88 89 219 498
Booth, A.D.      41
Boundary conditions for ordinary differential equations      173 197
Boundary conditions for partial differential equations      512 563
Boundary conditions, involving derivatives      453
Boundary conditions, two-point      240 446
Bowden, B.V.      41
Brillouin, L.      207
Brodetsky, S.      292
Bromwich, T.J.I’A.      188
Brooker, B.A.      266
Brown, S.L.      276
Brunt, D.      329
Bush, V.      43
Calculating machines      32
Calculating machines, analogue machines      43
Calculating machines, cinema-integraph      44
Calculating machines, desk calculators      33
Calculating machines, electronic digital computers      42
Calculating machines, harmonic synthesizer      276
Calculating machines, isograph      276
Calculating machines, National accounting machine      32 41 122
Calculating machines, punched card machines      41
Calculating machines, relay computers      42
Calculating machines, slide-rules      32
Calculations, unit      36
Characteristics of partial differential equations      511
Chebyshev polynomials      120
Chevilliet      88
Clemence      16
Clenshaw, C.W.      209 217
Cofactors      357 373
Collar, A.R.      xi 246 392 420 432 445 477
Collatz, L.      xi 466 476 478
Complex variable, functions of      507
Comrie, L.J.      29 32 123 484
Cooper, J.L.B.      458
Cosen, C.R.      31
Cosine integral      191
Cotes, B.      79
Coulomb functions      196
Courant, R.      459 526
Cowell, P.H.      226
Crandall, S.H.      514
Crank, J.      516 520
Cross-means      102
Crout, P.D.      471 475
Cubature      493
Cubic equations      264
Curve-fitting      299
Curve-fitting, Aitken’s method      319
Curve-fitting, by exponentials      329
Curve-fitting, orthogonal polynomials, use of      312
Curve-fitting, straight-line fitting      315 (see also “Least squares”)
Dandelin, Q.P.      285
Danielewsky, A.      375 389
Darby, P.      542
Darwin, C.G.      201
Davis, H.T.      115 323
Decimal rounding notations      5
Descartes’ Rule of Signs      246
Determinants equations      294 370
Determinants equations, companion matrix      375
Determinants equations, comparison of direct expansion methods      391
Determinants equations, Danielewsky’s method      375
Determinants equations, fitting by polynomials      389
Determinants equations, Frobenius standard form      374
Determinants equations, Lanczos’ method      382
Determinants equations, Samuelson’s method      379 (see also “Latent roots of matrices”)
Determinants, evaluation of      357
Dietzold, R.L.      394
Difference equations, solution of      233 260 534
Differences      26 46
Differences, backward (ascending)      48
Differences, central      50
Differences, forward (descending)      46
Differences, mean      51
Differences, modified      119 484
Differences, of factorials      53—56
Differences, relations with tabular values      48
Differences, short notation for      51
Differences, tables of      26
Differential equations, nonlinear second-order equations, comparison of methods      232
Differential equations, nonlinear second-order equations, comparison of methods, numerical integration      216 220 226 230
Differential equations, nonlinear second-order equations, comparison of methods, two-point boundary conditions      242
Differential equations, ordinary      169—245 446—463
Differential equations, ordinary, first-order equations, numerical, integration of      209 217 224 236 238
Differential equations, ordinary, linear second-order equations, amplitude and phase method      194 201
Differential equations, ordinary, linear second-order equations, boundary conditions      173 197
Differential equations, ordinary, linear second-order equations, general solution      175
Differential equations, ordinary, linear second-order equations, latent roots      241 458 526
Differential equations, ordinary, linear second-order equations, normal form      170
Differential equations, ordinary, linear second-order equations, numerical integration      212 227
Differential equations, ordinary, linear second-order equations, solution near regular singularity      185
Differential equations, ordinary, linear second-order equations, Stokes’ solution      191
Differential equations, ordinary, linear second-order equations, two-point boundary conditions      240 453 458
Differential equations, partial      510—567
Differential equations, partial, boundary conditions      512
Differential equations, partial, characteristics      511
Differential equations, partial, classification      510 (see also “Elliptic” “Hyperbolic” “Parabolic
Differential equations, series solutions, asymptotic series      188
Differential equations, series solutions, perturbation method      197
Differential equations, series solutions, Picard’s method      180 (see also “Latent roots” “Relaxation “Integration step-by-step” “INDEX
Differential equations, series solutions, Taylor series      176
Differential equations, WKB (Jeffreys method)      199
Differentiation, numerical, $\nabla^2$, $Q^2$ operators      502 505
Differentiation, numerical, by central differences      127 152
Differentiation, numerical, by forward and backward differences      126
Differentiation, numerical, errors of      85
Differentiation, numerical, Lagrangian      77 579
Differentiation, numerical, partial      502
Dimsdale, B.      277
Divided differences      92—107
Divided differences, definitions      92
Divided differences, interpolation formulas, construction of      98
Divided differences, linear cross-means      102
Divided differences, Newton’s polynomial expansion      95
Divided differences, quadratic cross-means      104
Domb, C.      256
Doolittle, M.H.      339
du Fort, E.C.      514 518
Dunvan, W.J.      xi 246 270 274 296 392 432 445 477
Dwight, H.B.      115
Dwyer, P.S.      xi 344 356—357
Echert, C.J.      41
Eider, L.      157 161
Eigenvalues      see “Latent roots”
Elliptic partial equations      533—565
Elliptic partial equations, 4- and 9-point blocks, use of      549
Elliptic partial equations, boundary conditions      513
Elliptic partial equations, curved boundaries      554 558
Elliptic partial equations, definition      511
Elliptic partial equations, difference equations, analytical solution of      535
Elliptic partial equations, diffusion equation, use of      538
Elliptic partial equations, finite difference approximations      533
Elliptic partial equations, improvement of solutions      558
Elliptic partial equations, Liebmann — Richardson method      539
Elliptic partial equations, numerical examples      536 545 552 554
Elliptic partial equations, relaxation method      550
Elliptic partial equations, Shortley — Weller method      542
Emde, P.      xii 265
Encke, J.P.      133
Error of cubature      508
Error of differentiation      85 128 579
Error of extrapolation      113
Error of interpolation      19 22 84 118 574
Error of quadrature      82 85 87 135 576 580
Error of step-by-step integration      215 218 229 233
Errors      2—12
Errors, combination of      7
Errors, computational (truncation)      7
Errors, definitions of      2
Errors, detection of, by differencing      25
Errors, experimental      6
Errors, normal distribution of      7
Errors, principle of equal      10
Errors, rounding      3 18 22 136 215 360
Errors, standard deviation of      7 11 314
Euler formulas      157
Everett’s interpolation formula      112 114 120 122 147 488
Exponential integrals      195 205
Extrapolation to zero interval      90 365 455 462 468 558
Eyres, N.R.      523
Factorials      52—67 113 568
Factorials, addition theorems for      54
Factorials, ascending and descending      52
Factorials, central      54
Factorials, differences and sums of      53 56
Factorials, expansion of, in powers      568
Factorials, inverse      53 54
Factorials, mean central      55
Factorials, reduced      52 56
False position, method of      249
Feller, W.      402 421
Fisher, R.A.      323 583
Flanders, D.A.      565
Fletcher, A.      xii
Flocquet’s theorem      207
Forsythe, G.E.      402 421 423 443
Fourier analysis      328
Fox, L.      205 209 233 240 244 354 356 357 368 437 455 558 565
Frame., J.S.      276 420
Frankel, S.P.      514 518
Frazer, R.A.      xi 246 270 274 296 432 445 477
Fredholm integral equations      463—478
Fredholm integral equations, collocation      477
Fredholm integral equations, Grout’s method      471
Fredholm integral equations, iterative solution      464
Fredholm integral equations, latent roots of      463 469 473
Fredholm integral equations, method of least square error      477
Fredholm integral equations, numerical examples      467 469 473 475
Fredholm integral equations, summation method      466
Fredholm integral equations, variational method      478
Fresnel integrals      191
Fried, B.      542
Fry, T.C.      276
Functions of complex variable      507
Gamble, E.H.      542
Gauss interpolation formulas      99 110 114
Gauss quadrature formulas      133 135—138 576—578
Gauss transformation      441
Gauss — Doolittle method      339
Gauss, C.P.      133 423 437 443
Gerlvng, C.L.      423
Goodwin, E.T.      209 233 240 244 368
Gordon, A.P.      180
Graduation      299 333—334
Graeffe, C.H.      285
Green, G.      201
Green’s function      464 471
Green’s type (WKB) solutions      199
Gregory, J.      108
Guarding figures, use of      14 18 213 360
Harmonic analysis      327
Hartley, H.O.      79 91
Hartree, D.P.      xi 41 123 139 154 236 256 403 502 512 523
Hayes, J.G.      354
Herget, P.      16
Hermite polynomials      325
Hestenes, M.R.      356 357
Horner’s root-shift      253 274
Hotelling, H.      392 401 428 432
Houseman, E.E.      323 583
Huskey, H.D.      356
Hyman, M.A.      514 537
Hyperbolic partial equations      525
Hyperbolic partial equations, boundary conditions      513
Hyperbolic partial equations, definition      511
Hyperbolic partial equations, d’Alembert’s solution      512
Hyperbolic partial equations, finite difference approximation      525
Hyperbolic partial equations, importance of characteristics      512
Hyperbolic partial equations, use in evaluating latent roots      526
Ince, E.L.      192
Indicial equation      185
Integral equations      206 362 463
Integration      see “Quadrature” “Cubature”
Integration, step-by-step, integral methods, using differences      224
Integration, step-by-step, integral methods, without differences      217
Integration, step-by-step, parabolic equations      616
Integration, step-by-step, recurrence methods      209
Integration, step-by-step, Taylor series methods      178 236 ordinary”)
Interpolation      69 108 481
Interpolation, by cross-means      102
Interpolation, by divided differences      100
Interpolation, by ordinary differences      108
Interpolation, inverse      73 123
Interpolation, inverse, by Newton’s polynomial      106
Interpolation, inverse, by successive approximation      123
Interpolation, inverse, Lagrangian      73
Interpolation, inverse, possible dangers of      74
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