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| Авторизация |
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| Hayek S.I. — Advanced mathematical methods in science and engineering |
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| Предметный указатель |
Formal asymptotic solutions 564 566 574
Formal asymptotic solutionsin exponential form 578
Fourier coefficients 135 137 162 164 166 333
Fourier coefficients, time dependent 343 344 350
Fourier complete series 165
Fourier complex transform 465
Fourier cosine series 163
Fourier cosine transform 163 384 385 421
Fourier cosine transform, convolution theorem 423
Fourier cosine transform, inverse 385
Fourier cosine transform, of derivatives 422
Fourier cosine transform, operational calculus 421
Fourier cosine transform, parseval formula for 423
Fourier integral theorem 383
Fourier series 88 135 151 161 163 383
Fourier series, generalized 333 343
Fourier sine series 161
Fourier sine transform 161—162 385 425
Fourier sine transform, convolution theorem 423
Fourier sine transform, inverse 385
Fourier sine transform, of derivatives 422
Fourier sine transform, operational calculus 421
Fourier sine transform, parseval formula for 423
Fourier transform, complex 386 397
Fourier transform, generalized one-sided 400
Fourier transform, inverse multiple complex 387
Fourier transform, multiple complex 387
Fourier transform, of n-th derivative 0
Fourier, Bessel series 169
Free boundary 115 121 133 299
frequency 111
Fresnel functions 606
Frobenius method 25 43
Frobenius method, characteristic equation 27
Frobenius method, distinct roots that differ by an integer 32
Frobenius method, two distinct roots 27
Frobenius method, two identical roots 30
Fundamental solutions 472
Fundamental solutions, adjoint 472
Fundamental solutions, behavior for large r 476 479
Fundamental solutions, bi-laplacian 476
Fundamental solutions, bi-laplacian Helmholtz eq. 484
Fundamental solutions, causal, for the diffusion eq. 480—482
Fundamental solutions, causal, for the wave eq. 483
Fundamental solutions, development by construction 475
Fundamental solutions, for the eq.  479
Fundamental solutions, for the laplacian 473
Fundamental solutions, Helmholtz eq. 477
Fundamental solutions, symmetry 473
Gamma function 544 599
Gamma function, incomplete 602
Gautschi function 604
Generalized Bessel equations 56
Generalized Fourier series 135 151 333 343
Generalized Fourier transforms 393 395
Generalized Fourier transforms, inverse 395
Generalized Fourier transforms, one sided 400
Generalized Jordan's lemma 245 247
Generating function, Bessel functions 58—59 75
Generating function, Hermite polynomials 58
Generating function, Legendre polynomials 75
Generating function, Tchebyshev 77
Geometric series sum formula 407
Gradient, cartesian 627
Gradient, circular cylindrical 628
Gradient, elliptic cylindrical 629
Gradient, generalized orthogonal 625
Gradient, oblate spheroidal 632
Gradient, prolate spheroidal 631
Gradient, spherical 630
Gravitation, law of 310
Gravitational potential 309 310
Green's functions, adjoint 455—456
Green's functions, causal, for diffusion operator 515
Green's functions, causal, for wave operator 510
Green's functions, eigenfunction expansion technique 459 461 497
Green's functions, equations with constant coefficients 458
Green's functions, for a circular area 493—499 522 526
Green's functions, for a semi-infinite strip 520
Green's functions, for Helmholtz operator 478—479 503
Green's functions, for Helmholtz operator for half-space 503—506
Green's functions, for Helmholtz operator for quarter space 507
Green's functions, for OD value problems 453
Green's functions, for PDE 466
Green's functions, for spherical geometry for the laplacian 500—502
Green's functions, for the laplacian by eigenfunction expansion 492
Green's functions, for unbounded media 472
Green's functions, higher ordered sources 459
Green's functions, infinite 1-d media 465
Green's functions, laplacian for half-space 488—490
Green's functions, laplacian operator for bounded media 485 487
Green's functions, longitudinal vibration of semi-infinite bar 462
Green's functions, reciprocity of 456—457
Green's functions, semi-infinite 1-d media 462
Green's functions, symmetry 456—457 460 473
Green's functions, vibration of finite string 460 462
Green's functions, vibration of infinite string 465
Green's identity, for bi-laplacian operator 469
Green's identity, for diffusion operator 470
Green's identity, for laplacian operator 468 .
Green's identity, for the wave operator 471
Green's theorem 138 207
Hankel functions 53
Hankel functions, integral representation 392
Hankel functions, of the first and second kind of order p 53
Hankel functions, recurrence formula 54
Hankel functions, spherical 54 364
Hankel functions, wronskian 53
Hankel transform 389
Hankel transform of derivatives 438
Hankel transform of order  389 440
Hankel transform of order zero 387 440
Hankel transform operational calculus with 438
Hankel transform, inverse 389 392
Hankel transform, Parsveal formula for 441
Harmonic functions 196
Heat conduction in solids 293
Heat distribution See Temperature distribution
Heat flow 293
Heat flow, in a circular sheet 346
Heat flow, in a finite cylinder 347
Heat flow, in a semi-infinite rod 415 424 428 434 517
Heat flow, in finite bar 416
Heat flow, in finite thin rod 344
Heat sink 296
Heat source 296 334
Heaviside function 403 406 635
Helical spring 121
Helmholtz equation 307 336
Helmholtz equation, fundamental solution 477
Helmholtz equation, Green's function for 477
Helmholtz equation, Green's identity for 469
Helmholtz equation, non-homogeneous system 338
Helmholtz equation, uniqueness for 313
Hermite polynomials 615
Homogeneous eigenvalue problem 142
Hydrodynamic eq. 303
Hyperbolic functions, complex 203
Hyperbolic functions, inverse 206
Hyperbolic functions, periodicity of complex 204
Hypergeometric functions 617
Identity theorem, complex function 221
Image point 493
Image sources 495
Images, method of 488
Incomplete gamma function 602
Incompressible fluid 303
Incompressible fluid, flow of 309
Infinite series 74 90 216 585
Infinite series, convergence tests 586
| Infinite series, convergent 585
Infinite series, divergent 585
Infinite series, expansion 90
Infinite series, of functions of one variable 591
Infinite series, power series 594
Infinity, point at 559
Initial conditions 301 315 316 342 349 350
Initial value problem 13 107 413
Integral representation of, Bessel 63 64
Integral representation of, beta function 603
Integral representation of, confluent hypergeometric function 619
Integral representation of, cosine integral function 611
Integral representation of, error function 604
Integral representation of, exponential integral function 608 609
Integral representation of, Fresnel function 606
Integral representation of, Gamma function 600
Integral representation of, Hermite polynomial 616
Integral representation of, hypergeometric function 617
Integral representation of, incomplete Gamma functions 602
Integral representation of, Legendre function of second kind 92
Integral representation of, Legendre polynomial 79
Integral representation of, Psi function 601
Integral representation of, sine integral function 611
Integral test 590
Integral transforms 383
Integral,  256
Integral, asymetric functions with log(x) 264
Integral, asymmetric functions 263
Integral, Bessel function 64
Integral, compex periodic functions 236
Integral, complex 207 209
Integral, even functions with log(x) 252
Integral, functions with  259
Integral, Laplace 79
Integral, Legendre polynomial 79 81 85
Integral, Mehler 81
Integral, odd functions 263
Integral, odd functions with log(x) 264
Integral, orthogonality 145
Integral, real improper 237 239
Integral, real improper by non-circular contours 249
Integral, real improper with singularities on the real axis 242
Integrating factor 2
Integration, by parts 537
Integration, complex functions 207 209
Integro-differential equation 412
Interior region 493
Inverse complex Fourier transform 386
Inverse Fourier cosine transform 385
Inverse Fourier sine transform 385
Inverse Fourier transform 385 395 397
Inverse Laplace transform 266 269 273
Inverse transform 398
Irregular singular point 23 560
Irregular singular point, of rank higher than one 571
Irregular singular point, of rank one 568
Jordan's lemma 240
Jordan's lemma, generalized 245 247
Kelvin functions 620
Kronecker delta 134
Lagrange's identity 138
Laguerre polynomials, associated 614—615
Laguerre polynomials, differential equation 613
Laguerre polynomials, generating function 613
Laguerre polynomials, recurrence relations 614
Laplace integral 79
Laplace transform, for half-space, Green's function for 488
Laplace transform, initial value problem 413
Laplace transform, inverse 266 269 273 400
Laplace transform, of heaviside function 406
Laplace transform, of integrals, derivatives, and elementary functions 405
Laplace transform, of periodic functions 406
Laplace transform, solutions of ODE and pde 411
Laplace transform, two-sided 399
Laplace transform, with operational calculus 402
Laplace's equation 196 295 308 319
Laplace's equation, Green's identity for 468 485
Laplace's equation, in polar coordinates 522
Laplace's equation, uniqueness of 312
Laplace's integral 538
Laplacian, cartesian 627
Laplacian, circular cylindrical 628
Laplacian, elliptic cylindrical 629
Laplacian, fundamental solution 473—475
Laplacian, generalized orthogonal 625
Laplacian, Green's function for 492—493
Laplacian, oblate spheroidal 632
Laplacian, prolate spheroidal 631
Laplacian, spherical 630
Laurent series 222
Legendre coefficients 75
Legendre functions 69
Legendre functions, associated 93 364
Legendre functions, of the first kind 71 93
Legendre functions, of the second kind 71 73 89 93
Legendre polynomials 71 77 81 85
Legendre polynomials, cosine arguments 76 89
Legendre polynomials, expansions in terms of 85
Legendre polynomials, generating function 76
Legendre polynomials, infinite series expansion 90
Legendre polynomials, integral representation of 79 81 85 92 96
Legendre polynomials, orthogonality 81 83 85
Legendre polynomials, parity 76
Legendre polynomials, recurrence formula 77 95 97
Legendre polynomials, rodriguez formula 72 90
Legendre polynomials, sine arguments 88
Limiting absorption 466 485
Limiting contours 245
Linear differential equation 1 139
Linear independence 3
Linear ODE, complete solution 1 3
Linear ODE, homogeneous 1
Linear ODE, non-homogeneous 1
Linear ODE, particular solution 1 10
Linear ODE, with constant coefficients 4
Linear operators 142
Linear second order 139
Linear spring 115
Local strain 119
Logarithmic function 204
Logarithmic function, integral of even functions with 252
Logarithmic function, integrals of odd functions with 264
Longitudinal vibration 113 151
Macdonald function 55
Material absorption 463
Material conductivity 295
Mean free path 297
Mehler 81
Mellin transform 401
Mellin transform, inverse 402
Membrane, infinite, vibration 441
Membrane, vibation eq. 298
Membrane, vibrating square 338
Membrane, vibration of circular 353
Method of images 488
Method of steepest descent 539
Method of undetermined coefficients 7
Method of variation of parameters 9
Modified Bessel functions 55
Modified Bessel functions, recurrence formula 55
Moment of inertia 117 120
Moment of inertia, cross-sectional area 117 120
Moment of inertia, polar area 132
Moments 117 299
Morera's theorem 215
Multiple Fourier transform 386 387
Multiple Fourier transform, convolution theorem 436
Multiple Fourier transform, of partal derivatives 435
Multiple Fourier transform, operational calculus with 435
Multiply connected region 212
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