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Mathews J.H., Fink K.D. — Numerical Methods Using MATLAB
Mathews J.H., Fink K.D. — Numerical Methods Using MATLAB



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Название: Numerical Methods Using MATLAB

Авторы: Mathews J.H., Fink K.D.

Аннотация:

Provides an introduction to numerical analysis for undergraduates in mathematics, computer science, physical sciences, and engineering. Emphasis is on why numerical methods work and their limitations, with material balanced between theory, error analysis, and readability. MATLAB programs are the vehicle for presenting underlying numerical algorithms. Includes exercises and computer assignments, with extensive use of MATLAB, new to this third edition. Assumes previous courses in calculus and structured programming. Book News, Inc.®, Portland, OR


Язык: en

Рубрика: Математика/Численные методы/Численный анализ/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Издание: third edition

Год издания: 1999

Количество страниц: 662

Добавлена в каталог: 25.02.2005

Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID
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Предметный указатель
Minimum, golden ratio search      401 412
Minimum, gradient method      412 420
Minimum, Nelder — Mead      405 414
Modified Euler method      465
Muller’s method      92 97
Multiple root      75 82 87 #23)
Multistep methods, Adams — Bashforth — Moulton method      474
Multistep methods, Hamming’s method      484
Multistep methods, Milne — Simpson method      477
Multistep methods, Natural cubic splines      284 285
Near-minimax approximation      231 233 238
Nelder — Mead      405 414
Nested multiplication      10 221
Neumann boundary conditions      541 545
Newton divided differences      223
Newton polynomial      220 224 227
Newton systems      176 179
Newton — Cotes formulas      344
Newton — Raphson formula      82 84 88 176 179
Newton’s method, multiple roots      75 82 87 #23)
Newton’s method, order of convergence      77
nodes      203 207 211 213 234 344 389
Norm, Euclidean      103 162 163
Norm, matrix      566
Normal equations      255
Numerical differentiation      313 314 320 329 333
Numerical differentiation, backward differences      334
Numerical differentiation, central differences      313 314 329 340 #8)
Numerical differentiation, error formula      313 314 316 318
Numerical differentiation, forward differences      334 341
Numerical differentiation, higher derivatives      329 333
Numerical differentiation, Richardson extrapolation      320
Numerical integration, adaptive quadrature      382 387
Numerical integration, Boole’s rule      344 372 375 380 #4) 389
Numerical integration, composite rules      350 354 358 363
Numerical integration, cubic splines      296 (#12)
Numerical integration, Gauss — Legendre integration      389 392 394
Numerical integration, midpoint rule      366 (#12) 381
Numerical integration, Newton — Cotes      344
Numerical integration, Romberg integration      373 375 377 378 381
Numerical integration, Simpson’s rule      344 353 354 359 363 370 380 387
Numerical integration, Trapezoidal rule      344 354 358 363 368 377
Odd function      301
Optimization, golden ratio search      401 412
Optimization, gradient method      412 420
Optimization, Nelder — Mead      405 414
Optimum step size, differential equations      466 476 479
Optimum step size, differentiation      316 317
Optimum step size, integration      358 382
Optimum step size, interpolation      213 234
Order of approximation      29 32 214 313 329 333 373 377
Order of convergence      32 75
Orthogonal polynomials, Chebyshev      238
Pade approximation      243 246
Parabolic equation      526
Partial derivative      517 527 538
Partial differential equations      514 516 526 538
Partial differential equations, elliptic equations      538
Partial differential equations, hyperbolic equations      516
Partial differential equations, parabolic equations      526
Partial pivoting      133
Periodic function      298
Piecewise, continuous      298
Piecewise, cubic      281
Piecewise, linear      280
Pivoting, element      127
Pivoting, row      127
Pivoting, strategies      131 133
Plane rotations      115 581
Poisson’s equation      538 548
Polynomials, calculus      204
Polynomials, characteristic      559
Polynomials, Chebyshev      230 233 238 240
Polynomials, derivative      204 334 336
Polynomials, interpolation      204 207 210 211 217 224 227 238
Polynomials, Lagrange      207 211 236
Polynomials, Newton      22:0 224 227
Polynomials, Taylor      8 26 31 189
Polynomials, trigonometric      297 303 306
Polynomials, wiggle      273
Power method      568 570 573 576
Predator-prey model      495 (#13)
Predictor-corrector method      474
Projectile motion      73 442 450
Propagation of error      32
QR method      606
Quadratic convergence      76 77 82 87 #23)
Quadratic formula      39 (#12)
Quadrature, adaptive quadrature      382 387
Quadrature, Boole’s rule      344 372 375 380 #4) 389
Quadrature, composite rales      350 354 358 363
Quadrature, cubic splines      296 (#12)
Quadrature, Gauss — Legendre integration      389 392 394
Quadrature, midpoint rule      366 (#12) 381
Quadrature, Newton — Cotes      344
Quadrature, Romberg integration      373 375 377 378 381
Quadrature, Simpson’s rule      344 353 354 359 363 370 380 387
Quadrature, Trapezoidal rule      344 354 358 363 368 377
Radioactive decay      432 (#17)
Rational function      243
Regula falsi method      56 60
Relative error      24 66
Residual      167 (#5) 253
Richardson, differential equations      449 (#7) 456 471
Richardson, numerical differentiation      320 322
Richardson, numerical integration      375
Rolle’s Theorem      5 6 198 212 219
Romberg integration      373 375 377 378 381
Root finding, bisection      53 54 59
Root finding, Muller      92 97
Root finding, multiple roots      75 82 87 #23)
Root finding, Newton      82 84 88 176 179
Root finding, quadratic function      39 (#12)
Root finding, regula falsi      56 60
Root finding, secant      80. 84 87
Root finding, Steffensen      92 95
Root of equation      53 75
Root, location      68
Root, multiple      75 82 87 #23)
Root, simple      75 77 87
Root, synthetic division      10 200
Root-mean-square error      253
Rotation      115 581
Rounding error      27
Rounding error, differentiation      313 314 316 318
Rounding error, floating point number      21
Row operations      127
Runge phenomenon      236
Runge — Kutta methods      458 461 466 468 488 502
Runge — Kutta methods, Fehlberg method      466 469
Runge — Kutta methods, Richardson extrapolation      471 (#7)
Runge — Kutta methods, systems      488
Scaled partial pivoting      133
schur      563
Scientific notation      19
Secant method      80 84 87
Seidel iteration      174 179
SEQUENCE      3 41
Sequence, convergent      3
Sequence, error      3
Sequence, geometric      16 51
Sequential integration, Boole      372 375
Sequential integration, Simpson      370 375
Sequential integration, trapezoidal      369 375 377
Series, binomial      196 (#10)
Series, convergence      8 99 189 194
Series, geometric      16 51
Series, Maclaurin      243
Series, Taylor      8 26 31 189 313 329
Shooting method      498 503
Significant digits      25
Similarity transformation      582
Simple root      75 77 87
Simpson’s rule      344 353 354 359 363 370 387
Simpson’s rule, three-eighths rule      344 353 380
Single precision      22
Single-step methods      474
Slope methods      70 80 84
SOR method      545
Spectral radius theorem      566
Splines end constraints      284
Splines, clamped      284 285 293
Splines, integrating      296 (#12)
Splines, linear      280
Splines, natural      284 285
Square-root algorithm      72
Stability of differential equations      478 481
Steepest descent      412 420
Steffensen’s method      92 95
Step size, differential equations      466 476 479
Step size, differentiation      316 318
Step size, integration      358 382
Step size, interpolation      213 234
Stopping criteria      58 62
Successive over-relaxation      545
Surface area      364 (#3)
Synthetic division      10 200
Systems, differential      487
Systems, linear      114 121. 128 136 143 150 156 163
Systems, nonlinear      167 174
Taylor series      8 26 31 189 313 329
Taylor’s method      451 452
Termination criterion, bisection method      58
Termination criterion, Newton’s method      84
Termination criterion, regula falsi method      58 60
Termination criterion, Romberg integration      378
Termination criterion, Runge — Kutta method      469
Termination criterion, secant method      84
Transformation, elementary      125
Trapezoidal rule      344 354 358 363 369 377
Triangular factorization      141 143 149
Trigonometric polynomials      297 303 306
Truncation error      26 313 314
Unimodal function      402
Unstable error      33
Upper-triangularization      136 150
Vectors, dot product      103
Vectors, Euclidean norm      103 162 163
Wave equation      516 519
Weights, for integration rules      344 393
Wiggle      273
Zeros of Chebyshev polynomials      232
Zeros of functions      53 75
Zeros, root finding      40 51 70 90 167 174
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