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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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Stable line 468 471 Stable node 466 471 Stable star 469 Stable structurally 470 Stable zero 463 Staircase 60 Standard basis 37 101 113 203 219 440 Standard dual basis 339 starting 123 Starting node 302 Starting vertex 123 State vector 540 Statically determinate 298 323 589 Statically indeterminate 297 306 324 591 Station space 318 328 509 Statistics 1 133 182 222 391 429 540 Steepest decrease 462 563 Steepest increase 462 563 Step function 599 Stiffness 295 299 317 506 586 623 Stiffness matrix 296 298 310 317 486 488 493 499 609 Stiffness, total 645 Stochastic doubly 546 Stochastic process 390 510 540 Stopping criterion 566 Storage 104 286 553 strain 585 586 612 623 Strain space 612 Strassen's method 53 Stress 586 617 623 Stress tensor 420 Stretch 294 333 350 410 420 428 482 623 Stretch principal 420 Stretching 348 421 422 585 Strictly diagonally dominant 538 550 554 632 Strictly lower triangular 16 87 549 Strictly upper triangular 549 String 635 Stroboscopic 279 Structurally stable 470 Structure 181 312 481 485 486 487 499 504 507 Structure, atomic 238 Structure, reinforced 323 Structure, unstable 320 Sturm — Liouville boundary value problem 636 Subdeterminant 168 Subdiagonal 53 Subdominant eigenvalue 528 542 570 572 Subset 81 subspace 84 88 89 183 189 268 378 Subspace, affine 89 Subspace, complementary 88 272 Subspace, invariant 374 Subspace, orthogonal 268 Subtraction 50 202 Suburb 542 Successive over-relaxation 557 SUM 88 Sum, absolute row 532 550 Sum, column 405 541 543 Sum, row 10 405 543 Supercomputer 49 Superconducting 486 Superdiagonal 53 Superposition 112 493 514 594 Superposition principle 108 112 203 365 366 375 610 627 Superposition, linear 446 451 607 Support 294 297 321 584 surface 85 87 634 SVD 427 Swing set 325 496 symmetric 46 89 154 413 461 534 573 Symmetric function 609 Symmetric matrix 49 164 416 419 423 424 426 Symmetry 11 146 217 235 238 331 346 403 481 615 627 System of equations 181 System, adjoint 382 System, autonomous 446 System, control 108 330 363 System, dynamical 390 394 System, equivalent 2 System, homogeneous 97 108 110 112 451 479 486 System, inhomogeneous 203 System, iterative 514 516 System, linear 4 7 20 41 60 64 68 109 114 193 363 446 System, nonlinear 65 599 System, triangular 29 232 Tacoma Narrows bridge 502 Tangent line 314—331 481 Tangent line approximation 481 Target space 331 382 Taxi 542 Taylor polynomial 314 Taylor series 86 93 Temperature 200 592 Tension 317 Tensor, inertia 421 Tensor, stress 420 terminating 312 Test function 597 603 Tetrachloride carbon 497 tetrahedron 128 140 311 328 497 The Spectral Decomposition 421 Theory, function 135 Theory, graph 127 Theory, group 481 Theory, learning 391 Theory, measure 135 598 Theory, potential 169 Theory, scattering 635 thermal conductivity 592 Thermal equilibrium 592 Thermodynamics 181 217 368 390 635 Three-dimensional space 85 90 235 361 Time reversal 449 468 470 topology 148 151 303 Total energy 617 Total force 594 Total stiffness 645 Trace 11 87 402 403 466 470 476 Trajectory 448 Trajectory curved 481 493 Trajectory integral 363 Trajectory solution 394 Transformation affine 485 Transformation linear 332 346 356 428 481 Transformation shearing 349 Transformed Legendre polynomial 254 Transient 504 Transition matrix 540 541 Transitional probability 541 Translation 318 321 358 360 361 405 592 Transmission 286 Transmission data 210 TRANSPOSE 44 46 73 178 296 382 405 413 477 539 587 612 Transverse direction 584 623 Trapezoid Rule 209 645 Traveling salesman 545 TREE 128 Tri-Fibonacci integer 522 Triangle equilateral 318 496 541 Triangle inequality 142—146 150 176 531 Triangular 3 16 Triangular form 3 Triangular lower 16 40 45 Triangular system 29 232 Triangular upper 14 18 28 40 45 63 Triatomic molecule 494 496 509 Tricirculant matrix 55 Tridiagonal circulant 633 Tridiagonal matrix 53 296 405 527 578 632 644 Tridiagonalization 578 Trigonometric ansatz 487 507 Trigonometric approximation 209 Trigonometric functions 91 172 458 460 Trigonometric interpolant 285 Trigonometric polynomial 173 211 Trigonometric polynomials 93 96 225 641 Trigonometric solution 487 Trivial 469 Trivial solution 68 450 Truss 312 Truss, square 509 Tuning fork 502 Turkey 200 typography 633 Uncertainty principle 344 Under-flow 570 Under-relaxed 558 Underdamped 498 506 Underwater vehicle 235 Undetermined coefficients 372 500 Uniform beam 623 union 88 Unique solution 110 Uniqueness 367 371 450 473 488 514 636 UNIT 78 594 Unit ball 87 148 Unit circle 133 433 524 Unit disk 137 Unit for scalar multiplication 78 Unit impulse 594 607 Unit polynomial 148 Unit sphere 148 150 420 434 530 Unit square 137 Unit vector 141 147 315 423 484 570 Unit, additive 8 Unit, imaginary 170 Unit, multiplicative 8 Unitary 240 248 422 435 United States 200 Unknowns 5 7 60 Unstable 181 321 392 460 492 513 592 616 Unstable eigenline 468 Unstable equilibrium 181 Unstable focus 469 471 Unstable improper node 469 Unstable line 468 Unstable mode 493 495 Unstable node 468 471 Unstable star 470 Unstable structure 320 upper 16 Upper Hessenberg matrix 581 Upper triangular 14 18 28 40 45 63 Upper triangular matrix 71 241 248 435 572 576 Upper triangular system 21 Uranium 392 Value, absolute 138 Value, characteristic 395 Value, proper 395 Value, sample 81 586 Value, singular 426 427 429 432 434 534 Vandermonde matrices 20 75 Vandermonde matrix 20 75 201 206 208 Variable basic 63 Variable free 63 64 68 98 110 119 Variation of parameters 372 479 500 Vector 28 82 131 332 Vector addition 79 84 170 vector calculus 353 Vector field 82 Vector multiplication 6 45 Vector product 131 Vector solution 472 Vector space 78 82 103 132 331 332 338 Vector, battery 307 Vector, characteristic 395 Vector, column 4 44 79 96 131 331 Vector, conjugate 563 565 Vector, data 196 Vector, displacement 295 315 485 Vector, elongation 295 315 Vector, error 196 548 Vector, normal 268 Vector, probability 541 Vector, proper 395 Vector, residual 182 562 563 565 Vector, row 4 44 131 Vector, sample 82 278 Vector, singular 426 Vector, state 540 Vector, unit 141 147 315 423 484 570 Vector, velocity 455 Vector, zero 68 79 95 132 Vector-valued function 479 Vehicle 196 Vehicle underwater 235 Velocity 196 201 497 Velocity initial 486 Velocity vector 455 Vertex 122 126 Vertex ending 123 Vibration 486 635 Vibration, natural 501 Vibrational frequency 487 Vibrational mode 493 Video 104 222 277 286 Video processing 49 Vision computer 363 481 Voltage 123 301 303 307 309 505 Voltage Balance Law 505 Voltage potential 302 305 310 Volterra integral equation 365 Volume 434 waste 200 393 Water 462 Water molecule 497 509 Wave function 169 Wavelet 104 224 239 Waves electromagnetic 503 Weather 540 Weierstrass approximation theorem 271 Weight 133 211 Weight matrix 211 Weighted 147 Weighted 147 Weighted adjoint 383 615 Weighted Gram matrix 212 Weighted inner product 132 133 136 139 179 212 299 615 638 640 Weighted least squares error 211 Weighted norm 132 133 136 Weighted normal equations 212 Wheel 279 Width band 55 Wind 313 Wind instrument 503 Wing airplane 640 Wire 122 301 303 309 Withdrawal 511 wronskian 100 Young's class 560 Zero element 78 80 84 141 331 Zero entry 50 Zero function 332 Zero matrix 8 9 63 79 Zero polynomial 80 Zero vector 68 79 95 132 Zero, mean 86 592 Zero, stable 463
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