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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
46 164 145 176 619 134 137 139 592 597 612 638 134 145 265 145 145 532 145 196 524 1 norm 145 196 2-norm 145 Absolute row sum 532 550 Absolute value 138 abstract 77 Acceleration 485 Account savings 511 Acute 157 Addition 6 50 78 170 202 338 Addition, complex 288 Addition, matrix 6 9 12 45 79 338 Addition, real 288 Addition, vector 79 84 170 Additive identity 78 Additive inverse 78 Additive unit 8 Adjoint 114 382 413 587 612 639 Adjoint system 382 Adjoint, weighted 383 615 Adjugate 114 Advertising 199 Affine function 332 358 514 546 Affine function, piecewise 642 Affine iterative system 523 546 Affine matrix 360 Affine subspace 89 Affine transformation 485 Air 640 Airplane wing 640 Airy functions 646 Algebra 7 78 Algebra, computer 58 Algebra, linear 77 187 330 583 598 Algebra, matrix 7 Algebra, polynomial 80 Algebraic function 163 Algebraic multiplicity 408 Aliasing 279 282 Altitude 207 208 Amplitude 91 210 468 486 501 502 504 Analysis 130 135 Analysis, complex 368 Analysis, data 180 Analysis, numerical 1 77 134 510 538 630 Analysis, real 150 151 596 Analysis, statistical 222 Analytic function 86 93 angle 139 140 171 Angle, right 140 218 Animation 217 235 361 363 445 481 630 634 Ansatz 366 447 Ansatz, exponential 447 498 Ansatz, power 367 514 Ansatz, trigonometric 487 507 Anti-diagonal 89 106 Applied mathematics 1 493 510 583 Approximation 202 248 630 Approximation, linear 314 322 375 623 Approximation, numerical 403 645 Approximation, trigonometric 209 Architecture 518 Area 349 433 Argument 171 Arithmetic 170 Arithmetic operations 50 291 Arithmetic, matrix 9 80 arrows 123 302 ART 363 518 Associative 6 7 9 78 353 Associativity of addition 78 Associativity of scalar multiplication 78 Assumption, constitutive 295 584 Astronomy 394 Asymptote 468 Asymptotic stability 460 461 470 513 523 524 Asymptotics 499 atom 419 497 584 594 623 Atom, hydrogen 497 Atomic measure 598 Atomic structure 238 Audible frequency 491 audio 104 277 286 Augmented matrix 12 37 61 274 Autonomous 394 446 Average 10 86 198 262 280 Axis 348 405 483 Axis, coordinate 420 Axis, imaginary 463 Axis, principal 433 434 B-spline 635 647 Back substitution 3 14 21 29 42 51 54 63 243 bacteria 393 Balance force 296 584 587 Ball 181 Ball, unit 87 148 Band width 55 Banded matrix 55 Bank 511 513 514 bar 312 317 485 584 588 614 623 635 Bar, composite 593 Bar, homogeneous 586 Basic variables 63 Basis 101 102 105 174 398 407 410 446 Basis, dual 340 Basis, eigenvector 407 452 487 Basis, orthogonal 218—220 224 227 257 413 417 496 Basis, orthonormal 218 219 223 228 230 236 240 257 280 348 413 418 428 435 641 Basis, standard 37 101 113 203 219 440 Basis, wavelet 104 224 239 battery 307 310 505 Beam 122 312 623 624 630 647 Beam, uniform 623 Beats 502 Bell-shaped 635 Bend 312 584 623 Bending moment 623 benzene 497 Bessel functions 636 Bidiagonal 53 402 Bilinear 11 336 Bilinear form 153 BINARY 289 Binet formula 518 Binomial coefficient 59 380 Binomial formula 173 380 biology 1 390 394 540 Biology, population 510 Bit reversal 289 Bitmapped 633 Block diagonal 36 75 129 441 478 Block matrix 12 52 body 235 420 421 Bolt 313 boundary conditions 295 588 589 615 Boundary layer 640 Boundary value problem 55 77 108 134 180 331 363 364 373 583 589 640 Boundedness 338 Bowl 181 Bridge 502 Bug 545 Building 122 312 Business executive 545 C++ 14 CAD 630 Calculator 49 202 Calculus 125 185 187 314 391 459 598 608 623 Calculus, multivariable 423 Calculus, vector 353 Canonical form 356 Canonical form, Jordan 440 442 478 524 Capacitance 505 506 Capacitor 505 Carbon 393 497 Carbon tetrachloride 497 Cardinal spline 635 Carpolice 196 Cartesian coordinates 103 Cartesian product 83 88 336 364 Cauchy — Schwarz inequality 138 143 176 612 Cave 393 Cayley transform 239 Cayley — Hamilton theorem 406 444 Cayley — Klein parameters 239 CD 218 279 Center 361 468 Chain rule 608 Change of basis 104 355 410 Change of variables 169 254 256 Chaos 489 Characteristic equation 366 368 395 396 400 406 447 466 498 Characteristic polynomial 401 444 Characteristic value 395 Characteristic vector 395 Charge electric 303 Chebyshev polynomial 255 Chemistry 49 140 238 390 394 Chlorine 497 Cholesky factorization 168 circle 319 322 362 Circle, osculating 623 Circle, unit 133 433 524 Circuit 123 125 126 128 303 Circuit, electrical 181 486 504 Circulant matrix 418 Circulant tridiagonal 633 circular motion 493 Circular ring 593 CITY 544 Clamped 625 631 Clarinet 503 Classical mechanics 330 375 464 Closed 80 151 Closed curve 633 Closest point 183 189 191 193 260 Closure 84 108 Coefficient matrix 5 7 24 107 446 511 546 641 Coefficient, binomial 59 380 Coefficient, constant 363 Coefficient, frictional 499 504 Coefficient, leading 367 Coefficient, undetermined 372 500 Cofactor matrix 114 Cokernel 115 116 118 126 272 303 column 4 44 116 Column interchange 58 Column space 107 194 272 371 Column sums 405 541 543 Column vector 4 44 79 96 131 339 Column, orthonormal 427 Combination linear 89 97 103 451 Comer 607 Commutative 7 9 73 78 481 483 Commutativity of addition 78 Commutator 10 343 483 Commuting matrices 476 Compact 148 150 Compatibility condition 98 107 273 Compatible 63 64 273 275 Complement, orthogonal 268 270 272 Complementary dimensions 269 Complementary subspace 88 272 complete 407 411 434 442 446 452 463 469 487 515 520 524 528 568 Complete bipartite digraph 128 Complete complex conjugate eigenvalues 458 Complete eigenvalue 407 Complete graph 128 Complete matrix 407 Complete monomial polynomial 207 Complete real eigenvalue 458 Completing the square 163 185 419 COMPLEX 170 176 178 240 377 378 399 409 435 570 Complex addition 288 Complex analysis 368 Complex conjugate 170 176 178 240 377 378 399 409 435 570 Complex diagonalizable 411 Complex differential operator 619 Complex eigenvalue 399 Complex eigenvector 399 Complex exponential 171 177 278 Complex inequality 174 Complex multiplication 288 Complex number 83 170 174 Complex plane 170 Complex solution 378 Complex vector space 78 174 377 Complex-valued function 378 Complexity computational 50 Component, connected 128 Component, principal 429 Composite bar 593 composition 341 359 Compounded 511 513 514 Compression 104 210 286 294 317 Computational complexity 50 Computer 49 57 202 287 289 Computer Aided Design 630 633 Computer algebra 58 computer games 363 Computer graphics 53 217 235 238 279 331 346 361 363 445 481 630 633 634 Computer programming 28 Computer serial 553 Computer vision 363 481 Condition number 58 429 536 Condition, boundary 295 588 589 615 Condition, compatibility 98 107 273 Condition, initial 373 391 452 486 488 511 515 Conditioned ill 58 266 429 432 Conductance matrix 303 Conductances 303 Conduction heat 635 Conductivity 310 Conductivity thermal 592 Cone light 157 conjugate 353 Conjugate direction 565 Conjugate gradient method 565 Conjugate symmetry 176 Conjugate vectors 563 565 Conjugated 377 Connected 123 306 Connected components 128 Conservation of energy 465 Constant coefficient 363 Constant function 135 278 Constant polynomial 80 Constant spring 486 586 Constitutive assumption 295 584 Constitutive relation 303 586 Constrained maximization principle 424 Constrained optimization problem 423 Continuity 338
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