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| Chan Man Fong C.F., De Kee D., Kaloni P.N. — Advanced Mathematics for Engineering and Sciences |
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| Предметный указатель |
Adams — Bashforth method 646
Adams — Moulton method 676
Adjoint operator 512 548
Analytic continuation 297
Analytic continuation, function 90 204
Arc length 306 357 739
Argand diagram 192
Argument 193
Associated variational equation 663
Asymptotic series 163
Asymptotic series, solution 162 170
Augmented matrix 585
Autonomous system 340
Auxiliary equation 42 411
Average value 842
Bendixson’s negative criterion 341
Bernouilli’s equation 39
Bessel’s equation 121
Bessel’s equation, modified 141
Bessel’s functions 134
Bessel’s functions, first kind 136
Bessel’s functions, generating function 186
Bessel’s functions, integral form 167 186
Bessel’s functions, orthogonality 141
Bessel’s functions, properties 140
Bessel’s functions, second kind 138
Bessel’s functions, third kind 139
Best fit regression line 624
Binomial distribution 830
Birkhoff s method 529
Bisection method 571
Blasius flow 527
Boltzmann constant 845
Boltzmann constant, factor 844
Boundary layer 176 525
Boundary value problem 120 637 659
Brachistochrone problem 753
Brownian motion 853
Catenary 778
Cauchy, condition 429
Cauchy, integral formula 233
Cauchy, mean value problem 4
Cauchy, principal value 266
Cauchy, Residue Theorem 257
Cauchy, Riemann conditions 204
Cauchy, theorem 227
Cayley — Hamilton theorem 388
Chain rule 4 18
Characteristic 422
Characteristic, curve 403
Characteristic, equation 42 387
Characteristic, method 511
Christoffel’s symbol 367
Coefficient matrix 584
Combination 828
Comparison Test 93 240
Compatibly 686
Complex, conjugate 193
components 347
Components, contravariant 347 352
Components, covariant 347 354
Components, mixed 356
Components, physical 362
Composite solution 178
Condition number 590
Conditional probability 827
Conformal mapping 275 547
contour 222
Contour, integral 223
Contraction mapping 577
Convergence 92 686
Convergence in the mean 146
Convergence, radius 92
Convolution 47
Coordinates, cyclic 812
Coordinates, cylindrical 397
Coordinates, elliptical 395
Coordinates, general curvilinear 347
Coordinates, generalized 769 809
Coordinates, polar 193
Coordinates, spherical polar 349
Courant parameter 709
Crank — Nicolson method 686
Cross ratio 285
Curl 303 375
Curve, closed 199
Curve, orientation 221
Curve, simple 199
Curve, smooth 222 306
Cyclic coordinate 812
Cycloid 754
De Moivre’s Theorem 194
Derivative 3
Derivative of a complex function 202
Derivative, covariant 367
Derivative, directional 14
Derivative, partial 13
Derivative, substantial 382 454
Derivative, total 16
Difference, backward 683
Difference, central 626 683
Difference, divided 614
Difference, finite 665 681
Difference, forward 626 683
Diffusion equation 435
Dirac delta function 51 64
Direction cosine 344
Dirichlet’s problem 338 450 532 697
Distribution, binomial 830
Distribution, canonical 845
Distribution, Gaussian 853
Distribution, Maxwell 852
Distribution, normal 837 853
Distribution, Poisson 834
Divergence 303 374
Divergence, Theorem 327 331 379
Domain of a function 1
Domain of an open set 200
Domain, dependence 434
Domain, multiply connected 226
Domain, simply connected 226
Dummy index 345
Dyad 357
Dyad, product 357
D’Alembert’s paradox 177 263
D’Alembert’s paradox, solution 431 483
Eigenfunctions 122 124
Eigenvalues 122 124 387 600
Eigenvector 387 600
Einstein summation convention 345
Elliptic partial differential, equation 424 511 532
Ensemble 823
Ensemble, Canonical 842
Ensemble, microcanonical 842
Enthalpy 847
entropy 846
Equation of continuity 338
Equipartition theorem 852
Error, round off 569
Error, truncation 570
Euler equation 99
Euler equation, formula 213
Euler equation, Lagrange equation 748
Euler equation, method 639
Euler equation, theorem 21
Exact differential equation 31
extreme values 6 740 742
Falkner Skan equation 527
Finite difference 665 681
Finite difference, elements 681 722
| Fixed point 576
Fixed point, iteration method 576
Four roll mill 396
Fourier series 153
Fourier series, function 191 198
Fourier series, integration 220
Fourier series, number 192
Fourier series, potential 211
Fourier series, roots 191
Fourier series, variables 191
Fourier, Bessel series 444
Fourier, coefficients 146
Fourier, finite cosine transform 475
Fourier, finite sine transform 475
Fourier, integral 158 477
Fourier, law 87
Fourier, Legendre series 446
Fourier, series 144 146 442 474
Fourier, transform 478
Frobenius method 99 102
Function 1
Function, analytic 89 204
Function, complex 191 198 200
Function, confluent hypergeometric 559
Function, conjugate 209
Function, continuous 2 202
Function, entire 204
Function, erfc 463
Function, error 463
Function, even 1
Function, explicit 19
Function, exponential 213
Function, Gamma 135
Function, generating 820
Function, harmonic 209
Function, homogeneous 21
Function, hyperbolic 216
Function, implicit 19
Function, meromorphic 257
Function, odd 1
Function, orthogonal 125 144
Function, partition 844
Function, periodic 2
Function, range 1
Function, rational 10
Function, several variables 13
Function, shape 723
Function, stream 212
Function, tensor 387
Function, trigonometric 215
Functional 740
Functional, determinant 278
Fundamental solution 98 441 447
Galerkin’s method 724
Gamma function 135
Gateaux variation 749
Gauss, elimination method 585
Gauss, Seidel method 598
Gauss, theorem 327 331 379
Gauss, two point formula 635
Generalized coordinates 769 809
Generalized coordinates, momenta 811
Generalized coordinates, velocities 769
generating function for Bessel functions 186
Generating function for Legendre polynomial 129
Gibbs free energy 848
grad 302 373
Green’s functions 57 338 532
Green’s functions, theorems 331
Hamiltonian 814
Hamilton’s equations 815
Hamilton’s equations, principle 768
Hankel’s functions 139
Hankel’s functions, transform 483
Heaviside step function 49
Heisenberg’s uncertainty, principle 552
Helmholtz’s equation 704
Helmholtz’s equation, free energy 846
Hermite’s equation 122 179
Hermite’s equation, polynomial 180
Hermitian matrix 601
Hermitian matrix, transpose 601
Heun’s method 643
Horner’s method 580
Householder’s algorithm 601
Hyperbolic, functions 216
Hyperbolic, partial differential equation 422 511
Imaginary number 191
Indicial equation 102
Initial value problem 637
Inner product 144
Inner product, solution 176
integral 7
Integral, definite 8
Integral, equation 638
Integral, improper 265
Integral, indefinite 7
Integral, line 305
integral, principal value 266
Integral, repeated 313
Integral, surface 323
Integral, triple 314
Integral, volume 326
Integrating factor 32 36 415
Inverse point 535
Isoperimetric constraints 760
Isotropic tensor-valued function 389
Iterative method 595
Jacobian 21 276 317
Jacobi’s identity 818
Jacobi’s identity, method 596
Jordan’s lemma 269
Joukowski’s transformation 289
Jump discontinuity 146
Kernel 495
Kronecker delta 125
Lagrange’s equations 769 811
Lagrange’s equations, interpolation 611
Lagrange’s equations, method 411
Lagrange’s equations, multiplier 745
Lagrangian 769 811
Laplace’s equation 211 338 437
Laplace’s equation, limit theorem 837
Laplace’s equation, transform 46 460
Laplacian 303 374
Laurent’s series 246
Least square approximation 146 623
Legendre’s equation 121
Legendre’s equation, associated 132 558
Legendre’s equation, functions 126
Legendre’s polynomial 128
Legendre’s polynomial, associated 558
Legendre’s polynomial, generating function 129
Legendre’s polynomial, orthogonality 129
Legendre’s polynomial, recurrence formula 129 131
Legendre’s polynomial, Rodrigues formula 128
Legendre’s polynomial, second kind 130
Legendre’s polynomial, transformation 814
Leibnitz’s rule 4 24
Leibnitz’s rule, test 94
Lenz’s law 341
Lie algebra 819
Liouville’s theorem 825
Lipschitz’s condition 638
Loo 591
Loss of significance 569
L’Hopital’s Rule 5
Maclaurin series 6 244
Mapping 275
Mapping, conformal 277
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