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Olver P.J., Shakiban C. — Applied linear. algebra
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Название: Applied linear. algebraАвторы: 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.
Язык: Рубрика: Математика /Серия: Сделано в холле Статус предметного указателя: Готов указатель с номерами страниц ed2k: ed2k stats Год издания: 2006Количество страниц: 714Добавлена в каталог: 04.06.2011Операции: Положить на полку |
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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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