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Olver P.J., Shakiban C. — Applied linear. algebra
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Название: Applied linear. algebra
Авторы: Olver P.J., Shakiban C.
Аннотация: Applied mathematics rests on two central pillars: calculus and linear algebra. While calculus has its roots in the universal laws of Newtonian physics, linear algebra arises from a much more mundane issue: the need to solve simple systems of linear algebraic equations. Despite its humble origins, linear algebra ends up playing a comparably profound role in both applied and theoretical mathematics, as well as in all of science and engineering, computer science, probability and statistics, economics, numerical analysis, mathematical biology, and many other disciplines. Nowadays, a proper grounding in both calculus and linear algebra is an essential prerequisite for a successful career in science, engineering, and mathematics.
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Рубрика: Математика /
Серия: Сделано в холле
Статус предметного указателя: Готов указатель с номерами страниц
ed2k: ed2k stats
Год издания: 2006
Количество страниц: 714
Добавлена в каталог: 04.06.2011
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Предметный указатель
Finder range 208
Finite difference 560 562
Finite dimensional dynamical system 445
Finite element 180 271 560 562 640
Finite-dimensional 103 148 230 640
First order system 478
First pivot 13
Fitting curve 633
Fitting data 133 182
Fixed end 625
Fixed point 392 511 528 540
Fixed-point equation 546
Flow fluid 455 640
Flow gradient 461 563
flowers 517 545
Fluid flow 455 640
Fluid mechanics 49 82 169 181 368 390 445 586
Focus stable 468 471
Focus unstable 469 471
Font 633
force 112 485
Force balance 296 584 587
Force, electromotive 301
Force, external 296 325 371 375 478 485 495 500 617
Force, gravitational 301
Force, internal 486
Force, periodic 501 506
Force, total 594
Forcing frequency 501
Fork tuning 502
Form, bilinear 153
Form, canonical 356
Form, linear 157
Form, phase-amplitude 96 468
Form, quadratic 88 154 163 422 463
Form, triangular 3
Formula determinantal 73 401 568
Formula polarization 157
Formula quadratic 163
FORTRAN 14
Forward substitution 4 20 29 51 54 554 558
Fourier analysis 77 80 131 134 135 169 177 217 222 248 277
Fourier coefficients 286
Fourier series 93
Fourier transform 363 612
Fragment skeletal 393
Fredholm alternative 273 303 306 319 365 507 592 612
Fredholm integral equation 365
Free end 591 625
Free variable 63 64 68 98 110 119
frequencies 458
frequency 91 210 278 282 486
Frequency, audible 491
Frequency, forcing 501
Frequency, high 285
Frequency, low 285
Frequency, natural 488 506 508
Frequency, resonant 504
Frequency, vibrational 487
Friction 294 485 497 506
Frictional coefficient 499 504
Frictionally damped 503
Frobenius norm 536
Fruit 517
Full pivoting 58
Function 80 81 82 332
Function space 80 81 85 213 265 271
Function spaces 103 134 220 248 336
Function theory 135
Function, affine 332 358 546 642
Function, Airy 646
Function, algebraic 163
Function, analytic 86 93
Function, Bessel 636
Function, complex exponential 278
Function, complex-valued 378
Function, constant 135 278
Function, continuous 86 271 336 609
Function, delta 594 596 601 636 643
Function, Dirac delta 595
Function, energy 300
Function, error 214
Function, even 89
Function, exponential 391 446 473
Function, Gaussian 605
Function, Green's 615 627 637
Function, harmonic 369 372
Function, hat 606 643
Function, hypergeometric 636
Function, hypverbolic 173 636
Function, identity 332
Function, integrable 86
Function, Legendre 636
Function, linear 330 331 338 332 353 363 378 382 612
Function, matrix-valued 479
Function, nonlinear 314
Function, nth order ramp 600
Function, odd 89
Function, periodic 88
Function, piecewise affine 607 642
Function, quadratic 184 185 201 462 641
Function, radial basis 649
Function, ramp 600 607
Function, rational 163 202
Function, sign 603
Function, sine 211
Function, smooth 86
Function, special 235 636
Function, step 599
Function, symmetric 609
Function, test 597 603
Function, trigonometric 91 172 458 460
Function, vector-valued 479
Function, wave 169
Function, zero 332
Functional energy 628
Functional, linear 597
Functional, quadratic 617
Fundamental theorem of algebra 100 402
Fundamental theorem of calculus 337 345 608
Fundamental theorem of linear algebra 116
Games 331
Games, computer 363
Gases 445 586
Gauss — Jordan 36 42 52
Gauss — Seidel 553 558 641
Gaussian elimination 1 3 24 42 50 71 73 164 243 274 396 538 546 562 641
Gaussian factorization 419
Gaussian function 605
Geiger counter 199
General solution 109 112 371 446 451 515
Generalized characteristic equation 496
Generalized eigenspace 507
Generalized eigenvalue 417 425 496 507 527
Generalized eigenvector 417 438 497
Generator 505
Generator, infinitesimal 481
GENERIC 50
Genetics 510
Genotype 545
Geodesic 180
Geometric matrix series 536
Geometric modeling 630
Geometric multiplicity 408
Geometry 11 77 122 155 235 238 346 368 445 481 584
Geophysical image 104
Gerschgorin Circle Theorem 536 537 543
Gerschgorin disk 537 543
Gerschgorin domain 537
Glide reflection 362
Global minimum 187 188
Globally asymptotically stable 392 499 513
Globally stable 392
Golden ratio 518
Google 540
Gradient 338 462 563
Gradient descent algorithm 563
Gradient flow 461 56
Gram matrix 158 179 190 214 299 306 318 385 499
Gram — Schmidt formula 228
Gram — Schmidt process 227 241 248 249 258 262 436 564 575
Graph 122 139 295 301
Graph theory 127
Graph, complete 128
Graph, directed 123
Graph, planar 126
Graphics 633
Graphics, computer 53 217 235 238 279 331 346 361 363 445 481 630 633 634
Gravitational force 301
Gravitational potential 301
Gravity 82 181 201 249 295 317 464 588
Green's function 606 609 615 627 637
grid 562
Grounded 306 318
Group 238 240
Group theory 481
Group, orthogonal 238
Growth polynomial 460
Growth spiral 518
Guess inspired 366 447
Half open 80
Half-life 199 392
Half-sampled 289
Hamiltonian function 463
Hamiltonian system 463 465
Hardware 58
Harmonic function 369 372
Harmonic polynomial 369 381
Hat function 606 643
Heat 309
Heat conduction 635
Heat equation 381
Heat source 592
Heisenberg commutation relations 344
Helix 87
Hermite cubic spline 626
Hermite polynomial 255
Hermitian 178
Hermitian adjoint 178
Hermitian dot product 175 240 280 415 435
Hermitian inner product 179 232
Hermitian L 2
Hermitian matrix 417
Hermitian norm 524
Hermitian transpose 240 435
Hessian matrix 187
Hexagon 496 497
High frequency 285
Higher order system 478
Hilbert matrix 58 59 161 215 266 433 557 567
Hilbert space 135 330
Hill 462
hole 126
HOME 200
Homogeneity 144 530
Homogeneous 16 68 157 363 446 450
Homogeneous bar 586
Homogeneous system 97 108 110 112 365 451 479 486
Hooke's law 295 298 300 312 502 584 586 623
House 327 509
Householder matrix 239 244
Householder reflection 578
Householder's method 245
Hunter 393 514
Hydrogen atom 497
Hyperbola 362 449
Hyperbolic function 173 636
Hyperbolic rotation 362
Hypergeometric function 636
Hyperplane 105 350
I/O operation 50
icosahedron 128
Identity function 332 337
Identity matrix 8 9 16 25 31 46 101 395 402
Identity permutation 401
Ill-conditioned 58 266 429 432
Ill-conditioning 243 247 261
Image 104 107 277 286
Image geophysical 104
Image medical 104
Image processing 1 49 217 222 391 429
Imaginary axis 463
Imaginary part 170 174
Imaginary unit 170
Implicit iterative scheme 527
Improper 237
Improper isometry 360
Improper node 471
Improper orthogonal matrix 237 347
Impulse unit 594 607
In general position 362
Inbreeding 545
Incidence matrix 123 295 302—304 316 486 613
Incompatible 63 64
incomplete 408 434 438 442 456 458 474 515 522
Incomplete complex conjugate eigenvalues 458
Incomplete real eigenvalue 458
Inconsistent 63
Increase steepest 462 563
indefinite 156
Independent linearly 95 97 98 101 102 158 174 229 406 451
Indeterminate statically 297 306 324 591
INDEX 438
Inductance 505 506
inductor 505
Inequality complex 174
Inequality product 531
Inequality triangle 142 143 145 150 176 531
Inertia tensor 421
Infantry 502
Infinite 80
Infinite-dimensional 103 148 151 270 338 340 344 345 382 387
Infinite-dimensional dynamical system 445
Infinitesimal generator 481
Inhomogeneous 363 450
Inhomogeneous boundary condition 620
Inhomogeneous boundary value problem 647
Inhomogeneous linear system 108 112 203 370 375 478
Initial condition 373 391 452 486 488 511 515
Initial position 486
Initial value problem 364 373 450 473 589
Initial velocity 486
Inner product 176 619
Inner product space 132 142 158 218 227 230 597
Inspired guess 366 447
Instability numerical 562
Instrument wind 503
Insulated 592
Integrable function 86
integral 134 173 337 596 608 645
Integral equation 78 108 330 331 363 583
Integral line 125
Integral transform 363
Integrating factor 619 639
Integration 163 336 345 479
Integration by parts 613 624
Integro-differential equation 505
Interchange column 58
Interchange matrix 25
Interchange row 25 28 57 71
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