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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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Предметный указатель
Motion screw 361 405 484 movie 279 Movie soundtracks 285 MP3 218 Multiple eigenvalue 407 Multiplication 50 170 202 337 Multiplication complex 288 Multiplication matrix 6 8 9 11 45 50 52 73 79 97 332 353 429 474 Multiplication real 288 Multiplication scalar 6 9 45 79 84 332 338 Multiplication vector 6 45 Multiplicative property 476 Multiplicative unit 8 Multiplicity 402 407 439 Multiplicity, algebraic 408 Multiplicity, geometric 408 Multivariable calculus 423 563 MUSIC 279 n-Dimensional 102 n-gon 280 Naive iterative method 557 Natural boundary condition 631 Natural frequency 488 506 508 Natural matrix norm 530 Natural vibration 501 Nature 180 300 308 310 Negative definite 156 461 Negative semi-definite 156 Network 301 Network electrical 122 301 310 309 507 Neumann boundary condition 614 636 Neumann boundary value problem 614 Newton difference polynomial 207 Newton equation 495 498 Newton's second law 485 Nilpotent 16 405 444 527 Node 122 301 Node ending 302 Node equivalent 150 Node improper 471 Node stable 466 471 Node starting 302 Node unstable 468 471 Noise 285 Non-analytic function 86 89 Non-autonomous system 446 Non-square matrice 71 Noncommutative 26 31 348 Nonlinear 67 330 375 395 481 493 502 510 Nonlinear dynamics 445 Nonlinear function 314 Nonlinear motion 322 Nonlinear perturbation 471 Nonlinear system 65 599 Nonsingular 23 24 28 33 40 41 43 63 64 71 73 110 156 367 538 546 Nontrivial solution 97 Norm 132 136 138 142 144 171 189 360 530 Norm, matrix 476 531 534 536 Norm, weighted 132 133 136 normal 46 438 Normal equations 194 214 260 307 431 Normal mode 488 Normal vector 268 Normed vector space 144 Norms equivalent 150 Norms matrix 476 Nth order ramp function 600 Nth root of unity 280 Nuclear reactor 393 Nuclei 419 Null direction 155 157 Null eigenvector 414 493 Null space 108 272 NUMBER 4 6 Number, complex 83 174 170 Number, condition 58 429 536 Number, irrational 488 Number, rational 488 Number, real 79 132 170 Numerical analysis 1 77 134 510 538 630 Numerical approximation 271 403 645 Numerical differentiation 209 Numerical instability 562 Numerical integration 209 Numerical linear algebra 50 Numerical solution algorithm 390 Observable 330 octahedron 128 148 Odd function 89 Off-diagonal 8 Ohm's law 303 309 One-parameter group 481 open 80 151 Open half 80 Open Rule 209 Operations arithmetic 50 291 Operator derivative 337 342 586 612 Operator differential 342 363 367 587 612 Operator linear 332 338 Optics 180 363 Optimization 180 Orbit 448 Order 516 Ordering 174 Ordinary differential equation 92 100 103 391 446 447 478 511 524 560 636 Orientation 123 301 Origin 332 Orthant 85 Orthogonal 141 218 256 268 418 Orthogonal basis 218—220 224 227 257 413 417 496 Orthogonal complement 268 270 272 Orthogonal group 238 Orthogonal matrix 235 241 348 360 405 418 572 573 Orthogonal polynomial 141 249 220 Orthogonal projection 256 257 260 274 349 350 421 508 Orthogonal subspace 268 Orthogonality 563 Orthonormal 218 Orthonormal basis 218 219 223 228 230 236 240 257 280 348 413 418 428 435 641 Orthonormal columns 427 Orthonormal rows 427 Orthonormalize 575 Oscillation 635 Osculating circle 623 Outer space 591 Oveerdamped 499 Oven 200 503 Over-flow 570 Over-relaxation 558 Overdamped 506 Oxygen 497 p-Norm 145 Pade approximation theory 202 Page ranking 540 parabola 184—201 471 Paraboloid 85 Parachutist 207 parallel 65 90 95 138 140 147 Parallel processor 554 Parallelogram 140 333 349 Parameter relaxation 558 Part imaginary 170 Part real 174 Partial derivative 187 338 Partial derivative operator 369 Partial differential equation 49 78 103 134 169 235 248 368 510 538 560 642 Partial differential operator 368 Partial pivoting 57 63 Particular solution 109 112 371 479 Path 123 Peak 91 peg 630 Pendulum 181 Pentadiagonal 557 647 Perfect 408 Period 91 486 Periodic boundary conditions 614 625 631 636 Periodic boundary value problem 648 Periodic forcing 501 506 Periodic function 88 Periodic mass-spring chain 614 Periodic spline 633 Permutation 27 73 401 442 Permutation identity 401 Permutation matrix 25 28 33 43 60 72 Permuted L D V factorization 43 Permuted L U factorization 28 60 71 Perpendicular 140 237 Perspective map 361 363 Perturbation 429 470 568 Perturbation, nonlinear 471 Perturbation, regular 640 Perturbation, singular 640 Phase 171 513 Phase lag 503 Phase plane 448 466 Phase plane variables 448 Phase portrait 448 467 Phase shift 91 210 468 486 Phase-amplitude 91 468 Physical 540 Physics 1 180 235 238 317 394 419 445 Piecewise affine 607 642 Piecewise cubic 630 Pivot 13 14 18 23 28 43 57 60 62 63 73 116 164 576 Pivot, first 13 Pivot, second 13 Pivoting 23 Planar graph 126 Planar vector field 83 88 Plane 65 85 90 268 338 Plane complex 170 Plane phase 448 466 Planet 331 plasma 586 Plot scatter 513 Point 65 85 90 Point mass 598 Point, closest 183 189 191 193 260 Point, critical 185 187 Point, fixed 392 511 528 540 Point, mesh 630 642 Point, saddle 468 471 Point, sample 81 202 277 Point, singular 367 636 POINTER 57 58 Poisson equation 372 377 562 Polar coordinates 91 171 Polar decomposition 421 Polarization 157 Pole 150 Police car 196 Polygonal 126 Polynomial 80 86 91 93 100 103 116 201 214 249 261 270 271 400 458 641 Polynomial algebra 80 Polynomial equation 400 403 Polynomial finite element 649 Polynomial growth 460 Polynomial interpolation 630 Polynomial, characteristic 401 444 Polynomial, constant 80 Polynomial, harmonic 369 381 Polynomial, interpolating 201 Polynomial, matrix 11 Polynomial, orthogonal 141 220 249 Polynomial, quadratic 154 Polynomial, radial 216 Polynomial, trigonometric 93 96 173 211 225 641 Polynomial, unit 148 Polynomial, zero 80 Polytope cross 148 Population 200 514 544 Population biology 510 Portrait phase 448 467 POSITION 344 Position, initial 486 Positive 186 Positive definite 154 156 158 164 168 186—188 295 300 318 385—387 414 419 420 461 487 495 563 573 616 636 639 641 Positive semi-definite 155 158 188 414 426 493 495 616 Positive upper triangular matrix 572 Positivity 144 146 153 176 530 616 potential energy 180 181 300 310 462 617 Potential theory 169 Potential, gravitational 301 Potential, voltage 302 305 Power 4 180 309 Power ansatz 367 514 Power method 568 575 Power series 172 Power, internal 309 Power, matrix 514 520 PRECISION 429 PREDATOR 514 Prestressed 310 Price 200 Primitive nth root of unity 280 285 288 Principal axes 433 434 Principal component 429 Principal component analysis 429 Principal direction 420 421 Principal stretche 420 Principle maximization 424 Principle maximum 425 Principle minimization 300 388 563 617 621 622 639 640 Principle optimization 423 Principle superposition 108 203 365 366 375 610 627 Printing laser 633 probability 540 Probability eigenvector 542 Probability transitional 541 Probability vector 541 Process stochastic 390 510 540 Processing image 1 49 217 222 391 429 Processing signal 1 77 104 131 210 217 222 277 Processing video 49 Processor parallel 554 Processor serial 554 Product cross 140 221 353 401 484 Product dot 131 138 159 174 219 262 272 340 353 357 413 Product inequality 531 Product inner 132 144 154 176 339 357 382 612 Product matrix 131 Product vector 131 Professional 544 Programming computer 28 Programming linear 180 Projection 349 361 428 Projection matrix 111 193 259 265 405 421 Projection orthogonal 256 257 260 274 349 350 421 508 Projections 349 Proper 237 362 405 Proper isometry 360 Proper orthogonal matrix 237 347 420 482 Proper value 395 Proper vector 395 Property multiplicative 476 Pseudo-random 523 Pseudocode 14 31 57 241 566 582 Pseudoinverse 430 Pythagorean Theorem 131 133
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