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| Авторизация |
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| Apostol T.M. — Calculus (Volume 2): Multi-Variable Calculus and Linear Algebra with Applications |
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| Предметный указатель |
Hermitian symmetry 15 114
Herschel, William 571
Hesse, Ludwig Otto 308
Hessian matrix 308
Homogeneous function 287
Homogeneous linear differential equation 146
Homogeneous system of differential equations 200
Homogeneous system of linear equations 59
Huygens, Christian 469
Identity matrix 54
Identity transformation 32
Implicit differentiation 294
Implicit-function theorem 237
Independence in a linear space 9
Independence of eigenvectors 100
Independence of events 488
Independence of nonzero orthogonal elements 18
Independence of parametrization 327 434
Independence of path 333
Independence of random variables 547
Independent trials 495
Indicial equation 183
Inequality, Cauchy — Schwarz 16
Inequality, Chebyshev 563
Inequality, triangle 17
Inequality, Wallis' 616
Infinite set 502
Initial conditions 143 147
Initial-value problem 193
Inner product 14
Integral equation 239
Integral of a matrix function 193
Integral, double 357
Integral, line 324
Integral, n-fold 406
Integral, surface 430
Integral, triple 406
Integrating factor 349
Interior (inner region) of a Jordan curve 380
Interior of a set 244
Interior point 244
Interpolation by Lagrange's formula 580
Interpolation by Newton's formula 589
Interval in n-space 405
Invariance property of Lagrange interpolation coefficients 586 Exercise
Invariance property of line integrals under change of parametrization 327
Invariance property of line integrals under deformation of the path 388
Invariance property of surface integrals under change of parametrization 433
Invariant subspace 99
Inverse function 39
Inverse matrix 66
Inverse transformation 39 41
Invertible function 40
Invertible transformation 40 41
Irrotational vector field 445
Isometry 129
Isomorphism 53
Isothermals 266
Iterated integrals 359 367 406
Iterated limits 251 Exercise
Jacobi, Carl Gustav Jacob 271
Jacobian determinant 297 394 408 420
Jacobian matrix 271
Joint probability density 546
Joint probability distribution 543
Jointly distributed random variables 543
Jordan curve 379
Jordan curve theorem 380
Jordan, Camille 61 78 379
Jump discontinuity 518
Kernel of a linear transformation 33
Kernel of an integral equation 239
kinetic energy 329
Kolmogorov, Andrei Nikolaevich 470
Lagrange interpolation coefficient 209 581
Lagrange interpolation formula 580
Lagrange multipliers 3 15
Lagrange, Joseph Louis 142 315 580
Laplace's equation 283 292
Laplace, Pierre Simon 142
Laplacian 292 444
Law of Large Numbers 565 566
Least-square approximation 573
Legendre polynomials 25 174
Legendre polynomials, graphs of 175
Legendre polynomials, normalized 26
Legendre polynomials, Rodrigues' formula for 176
Legendre polynomials, zeros of 180 Exercise
Legendre's differential equation 171
Legendre, Adrien Marie 25 171
Leibniz, Gottfried Wilhelm 142
Level sets (curves, surfaces) 266
Leverrier, Jean Joseph 571
Lindeberg's condition 568
Lindeberg, Jare W. 567
Line integrals, applications of 330
Line integrals, first fundamental theorem for 338
Line integrals, independence of parametrization 327
Line integrals, independence of path 333
Line integrals, notations for 324
Line integrals, second fundamental theorem for 334
linear combination 8
Linear differential equation 145
Linear differential operator 146
Linear interpolation 584
Linear operator (transformation) 31
Linear space (vector space) 3
Linear subspace 8
Linear system 58 192
Linear transformation 31
Liouville, Joseph 143 191 223
Lipschitz condition 229
Lipschitz, Rudolf 229
Lorentz transformation 69 Exercise
Lower integral 358
Lyapunov, Alexsandr Mikhailovich 567
Mapping 31 393 550
Markov, Andrei Andreevich 470
Mass 330 373 414 431
Mass interpretation of probability 511 545
Matrix, adjoint 122
Matrix, adjugate 92
Matrix, algebraic operations on 52 54
Matrix, block-diagonal 84
Matrix, cofactor 92
Matrix, conjugate 122
Matrix, definition of 46
Matrix, diagonal 48 96
Matrix, exponential 197
Matrix, hermitian 122
Matrix, minor of 87
Matrix, nonsingular 65
Matrix, orthogonal 123
Matrix, representation 46
Matrix, self-adjoint 122
Matrix, series 194
Matrix, singular 67
Matrix, skew-Hermitian 122
Matrix, skew-symmetric 124
Matrix, symmetric 124
Matrix, trace of 106
Matrix, transpose of 91
Matrix, unitary 123
Max norm 575
Maximum of a function, absolute 304
Maximum of a function, existence of 321
Maximum of a function, relative 304
Maximum of a function, tests for 311 312
Mean of a function 374
Mean of a random variable 535 556
| Mean-value theorem for scalar fields 254
Measurable sets 510
Measure, finitely additive 472
Measure, probability 474 506
Minimum of a function, absolute 304
Minimum of a function, existence of 321
Minimum of a function, relative 304
Minimum of a function, tests for 311 312
Minor of a matrix 87
Mises, Richard Von 470
Moebius band 455
Moebius, Augustus Ferdinand 455
Moment of inertia 331 374 414 431
Multiple integrals, applications of 373 414 431
Multiple integrals, definition of 357 406
Multiple integrals, evaluation of 358 406
Multiple integrals, existence of 363
Multiple integrals, transformation formulas for 394 408
Multiply connected region 384
N-fold integral 405
Napier, John 572
Negative (clockwise) direction 389
Negative definite quadratic form 310
Neighborhood 244
Neptune 571
Newton's interpolation formula 589
Newton, Isaac 142 335 571 589
Newtonian potential 335
Nonlinear differential equation 228
Nonorientable surface 456
Nonsingular matrix 65
Norm in a Euclidean space 17
Norm in a linear space 233
Norm of a matrix 195
Norm, max 575
Norm, square 575
Normal approximation to binomial distribution 538
Normal bivariate distribution 555 Exercise
Normal derivative 386
Normal distribution 535
Normal vector to a surface 267 423
Normed linear space 233 574
Null space 33
Nullity 34
Numerical integration by Chebshev formulas 611
Numerical integration by Cotes' rule 612 Exercise
Numerical integration by Euler's summation formula 613 615
Numerical integration by Simpson's rule 608 609
Numerical integration by the trapezoidal rule 604
Odd man out 508 Exercises 11
Odds 480
One-element set (singleton) 475
One-to-one correspondence 501
One-to-one function 40
Open ball 244
Open set 244
Operator, contraction 235
Operator, curl 441
Operator, derivative 32
Operator, divergence 441
Operator, forward difference 590
Operator, gradient 259
Operator, identity 32
Operator, integration 32
Operator, Laplacian 292
Operator, linear 31
Ordered basis 13
Ordinate set 360 368
Orientable surface 456
Orientation of Jordan curve 389
Orthogonal basis 19
Orthogonal complement 27
Orthogonal decomposition theorem 27
Orthogonal elements 18
Orthogonal functions 18
Orthogonal matrix 123
Orthogonal operator 138
Orthogonal projection 28
Orthogonal trajectory 267
Orthogonalization theorem 22
Orthonormal set 18
Outcome 476
Pappus Of Alexandria 376 426
Pappus' theorems 376 428
Parallel-axis theorem 378 Exercise
Parametric surface 420
Parseval's formula 20
Parseval, Mark-Antoine 20
Partial derivative 254 255
Partial differential equation 283
Partition of a rectangle 354
Pascal, Blaise 469
Path in n-space 323
Pauli spin matrices 107 Exercise
Pauli, Wolfgang 107 Exercise
Peano, Guiseppe 223 611
Petersburg problem 562 Exercise
Picard's method 223 227
Picard, Charles Emile 223
Piecewise linear interpolation 603
Piecewise smooth path 324
Poisson distribution 522
Poisson, Simeon Denis 522
Polar coordinates 274 397
Polar moment of inertia 375
Polynomials, Chebyshev 596
Polynomials, interpolation 579 589
Polynomials, Legendre 26 176 577
Polynomials, Taylor 572
Positive (counterclockwise) direction 390
Positive detinite quadratic form 310
potential energy 336
Potential function 335
Potential function on convex sets 344
Potential function, construction of 338 342
Potential function, existence of 339
Potential function, newtonian 335
Power series solutions of homogeneous linear systems 220
Power series solutions of linear differential equations 169
Probability density function 525 546
probability distribution 515 543
Probability mass function 520 545
Probability measure 474
Probability space 474
Probability, conditional 487
Probability, definition of 474 506 511
Projections 24 28
Ptomely, Claudius 571
Putzer's method 205
Putzer, E.J. 202
Pythagorean formula 10 20 27
Quadratic form 127 310
Quadratic form, extreme values of 137
Quadratic form, negative definite 310
Quadratic form, positive definite 310
Quadratic form, reduction to diagonal form 129
Radius of gyration 557
Random variable(s) 512
Random variable(s), continuous 525
Random variable(s), discrete 521 545
Random variable(s), functions of 541
Random variable(s), independent 547
Random variable(s), jointly distributed 543
Range of a linear transformation 32
Rank 34
Rate of change 253
Rational function 249
Real linear space 4
Regular point of a surface 421
Regular singular point 181
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