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| Zauderer E. — Partial Differential Equations of Applied Mathematics |
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| Предметный указатель |
Fluid flow, incompressible 578
Fluid flow, inviscid 575 577
Fluid flow, irrotational 578
Fluid flow, isentropic 577 585
Fluid flow, sonic 586 587
Fluid flow, steady 578 585
Fluid flow, subsonic 586 587
Fluid flow, supersonic 586 587
Fluid flow, viscous 583 816
Focal length 762 766
Focal point 91 744 765 801
Focus 720; see also “Focal point”
Focusing medium 756
Fourier coefficients 180 209 338 518
Fourier cosine series 186
Fourier cosine transform 261 268
Fourier cosine transform inversion formula 261
Fourier cosine transform of derivatives 262
Fourier cosine transform, finite 208
Fourier integral formula 246
Fourier series 180 186 308 347
Fourier sine series 185 440
Fourier sine transform 261 264 269
Fourier sine transform inversion formula 261
Fourier sine transform of derivatives 262
Fourier sine transform, finite 208
Fourier transform, generalized 436 437
Fourier transform, higher dimensional 271
Fourier transform, higher dimensional inversion formula 272
Fourier transform, higher dimensional of derivatives 272
Fourier transform, one dimensional 246
Fourier transform, one dimensional convolution theorem 247 249
Fourier transform, one dimensional inversion formula 247
Fourier transform, one dimensional of derivatives 248
Fourier's law 165
Free space Green's function 378 381;
Free space Green's function, heat equation 469 491
Free space Green's function, Helmholtz equation 381
Free space Green's function, Klein — Gordon equation 477 489
Free space Green's function, Laplace's equation 380 485
Free space Green's function, modified Helmholtz equation 280 383
Free space Green's function, modified telegrapher's equation 477 489
Free space Green's function, ordinary differential equation 380
Free space Green's function, reduced wave equation 382 496 703
Free space Green's function, wave equation 474 489
Fresnel integral 742
Friedrichs, K.O. 29
Fundamental Lemma of Calculus of Variations 344 597
Fundamental solution 370 377
Fundamental solution adjoint equation 419
Fundamental solution biharmonic equation 574
Fundamental solution elliptic equation 380 414 419
Fundamental solution heat equation 254 286 375 384 407 824
Fundamental solution hyperbolic equation 385 419 554
Fundamental solution parabolic equation 419 835
Fundamental solution wave equation 384
Furth, R. 15 18
Galerkin method 349 403 549 603
Gas dynamics see “Fluid dynamics”
Gaussian beam 752 759 835
Gaussian distribution 8
Gaussian distribution mean 8
Gaussian distribution variance 8
Generalized derivative 431 434
Generalized functions 250 386 426
Generalized functions composite 444
Generalized functions of slow growth 438
Generalized functions singular 428
Generalized functions, product of 443
Generalized functions, regular 428
Generalized power functions 432
Generalized solution 56 57 75 178 211 250 344 346 354 359 440
Geometrical optics 89 107 703 732 738 740 749 765 798
Geometrical optics, nonlinear 754
Geometrical theory of diffraction 703 744 751
Goldstein, S. 15 18
Goursat problem 404
Goursat problem, modified 404
Gram — Schmidt process 176 539 600
Green's function 33 43 250 378 412 446
Green's function, biharmonic equation 575
Green's function, elliptic equation 413 447 452
Green's function, heat equation 467 491
Green's function, Helmholtz equation 513
Green's function, hyperbolic equation 417 420 422 463 510 554
Green's function, Klein — Gordon equation 475 491 509
Green's function, Laplace's equation 31 48 199 453 485 492 560
Green's function, modified 457 460
Green's function, modified Helmholtz equation 280
Green's function, modified telegrapher's equation 491
Green's function, modified, Laplace's equation 460
Green's function, nonself-adjoint elliptic equation 425
Green's function, ordinary differential equation 250 421 435 450
Green's function, parabolic equation 419 420 423 466
Green's function, reduced wave equation 481 705
Green's function, Schrodinger's equation 510
Green's function, wave equation 470 491
Green's theorem 31 412 550 574
Group velocity 144 299
Hadamard criteria 138
Hadamard's method of descent 275 315
Hadamard, J. 138 139 141
Hankel function 280 383 483 687 704 723
Hankel transform 281 282 373 375
Hankel transform inversion formula 281
Hankel transform of derivatives 281
Hankel transform, finite 208 240
Harmonic function 485
Harmonic vibrations 195
Heat conduction 14 198 625
Heat conduction, infinite speed 14 199 255
Heat equation 14 198 206 217 252 263 289 336 384 388 407 467 556 821 823
Heat equation steady state 207 266 668
Heat equation, nonlinear 218
Heaviside function 431
Helmholtz's equation 278 381 483 622 686;
Helmholtz's equation, modified 278 483 686
Hooke's law 166 328
Hopf, E. 823
Huygen's principle 277 475
Hydrodynamics, see “Fluid dynamics”
Hyperbolic distance 385 803 805
Hyperbolic equation 111 123 142 166 168 202 211 326 331 343 347 362 385 390 414 550 587 619 632 657 679 680 779
Hyperbolic system, canonical form 130
Hyperbolic system, characteristic form 130
Hyperbolic system, characteristic normal form 135
Illuminated region 749
Incident wave 334 706 721
Incorrectly posed problem 137 138 682
Index of refraction 106 701 708 754
Initial and boundary value problem 137
Initial layer 650; see also “Boundary layer”
Initial strip 85
Initial value problem 8 20 49 64 136;
Inner product 173 179 335
Inner product, Hermitian 180
Integral relation 75 325 364
Integral relation, elliptic equation 328
Integral relation, Galerkin form 403
Integral relation, hyperbolic equation 326
Integral relation, parabolic equation 328
Integral surface 50 63
Integral theorem 412 499
Integral theorem, elliptic equation 412
Integral theorem, hyperbolic equation 415
Integral theorem, parabolic equation 418
Integral wave equation 349
INTERFACE 108 759
Internal boundary layer 653 656
inversion 493
| Iteration method 363 553
Jacobian 50 56 64
Jump 56 75 340
Jump conditions 98 339 365 367;
Kac, M. 19
Keller, J.B. 703 744
Kirchhoff's formula 275
Klein — Gordon equation, linear 145 297 477 617 772 801
Klein — Gordon equation, nonlinear 628 643
Korteweg — deVries equation, linear 322
Korteweg — deVries equation, nonlinear 644 830 838 839
Kronecker delta function 538
Laplace transform 288
Laplace transform of derivatives 289
Laplace transform, Abelian asymptotic theory 293
Laplace transform, convolution theorem 319
Laplace transform, Heaviside expansion theorem 294 321
Laplace transform, inversion theorem 288
Laplace transform, Tauberian asymptotic theory 293
Laplace's equation 28 48 121 199 212 257 269 282 380 485 573 579 589 623 637
laser beam 751 753;
Legendre function 541 601 602
Legendre polynomial 192 231 237 601
Legendre polynomial, eigenfunction expansion 193
Legendre's equation 192
Lewy, H. 29
Linear functional 426
Linearization 219 579
Lower order terms 140
Matching conditions 325 329 365;
Matching process 647 651 654 666 672 728 743
Matrix characteristic equation 538 546
Matrix, diagonal 122 130
Matrix, eigenvalues 122 123 130 135 538
Matrix, eigenvectors 122 130 135 538
Matrix, orthogonal 122
Matrix, positive definite 537
Matrix, symmetric 122 537
Maximum principle 13 31 556 560 561
Maximum principle, strong 558 562
Maximum principle, weak 559 561
Maxwell's equations 588
Maxwell's equations in vacuum 591
Mean square convergence 181 348 534
Mean value theorem 34 496 515
Method of canonical problems 745
Method of characteristics 49 100 101 105 108 707 780
Method of finite parts 433 502
Method of images 484 705
Method of matched asymptotic expansions 648
Method of multiple scales 617 627 636
Method of stationary phase 295 565 728 742
Minimum principle 13 31 556 560 562
Minimum principle, strong 558 562
Minimum principle, weak 559 561
Minimum problem 519 524 600
Minimum problem, Dirichlet boundary conditions 524
Minimum problem, mixed boundary conditions 524
Minimum problem, natural boundary conditions 524
Modified Bessel equation 381
Modified Bessel function 237 279 286 301 320 381 387 389 483 555 686 797
Moment of random variable 9
Monge cone 81
Moving boundary 387 785
Moving source 367
Natural boundary condition 526
Navier — Stokes equations 583 817
Navier's equation 594
Neumann data 137 165
Neumann function 381
Newton's law of cooling 165 235
Newton's law of motion 14 166 193 366
Node 196
Norm 173 179
Normal distribution see “Gaussian distribution”
Normal mode 140 194 564
Ocean acoustics 481
Odd function 188
Optical beam 755 757 759;
Optics 703
Optics, nonlinear 693 753
Order symbol O 618
Ornstein, L.S. 14 18
Orthogonal 173 179 503
Orthogonal set 176 180
Orthonormal set 180
Outer region 650 656 667
Outgoing condition 706 721
Outgoing wave 706
Parabolic boundary layer 667 673;
Parabolic boundary layer equation 667 673
Parabolic equation 113 124 141 165 168 202 328 345 390 417 587 620 625 679 680 682 780
Parabolic equation method 681 834
Paraxial wave equation 753
Parseval's equation, Fourier series 181
Parseval's equation, Fourier transform 247
Partial differential equation, linear first order 48
Partial differential equation, linear mth order 132
Partial differential equation, linear second order 109 122 140
Partial differential equation, nonlinear first order 81
Partial differential equation, nonlinear higher order 133
Partial differential equation, quasilinear first order 63
Partial differential equation, quasilinear higher order 134
Periodic boundary conditions 186 213
Periodic function 188
Perturbation method 103 219 548 616 625 628 632 701 818
Perturbation problem, regular 619 621 622 625 628 632 637 642 644
Perturbation problem, singular 24 619 647 657 662 663 686 701 732
Perturbation series 103 621 648 663 669 686
Phase 295 643 702
Phase shift 738
phase velocity 144 298
Piston problem 583 612
Plane wave 90 91 273 701 718 746 781
Plane wave, general 718 726 752
Plucked string 232
Point impulse 232
Point source 284 370 375
Point source, continuous 365 368 371 374 383
Point source, instantaneous 325 383
Poisson process 19 22
Poisson summation formula 291 514
Poisson's equation 32 212 494 560 589 623
Poisson's integral 496 515
Positive operator 174
Principal part 110 140 810
probability density 6
Projection matrix 811
Projection operation 811 819 821
Propagating wave 196 373 441;
Radiation condition of Sommerfeld 252 381 483 497 687 703 706 721
Random walk absorbing boundary 10 28 29 41
Random walk independent steps 2
Random walk position dependent 11 25 33
Random walk reflecting boundary 11 42
Random walk time independent 27 37 42
Random walk, correlated 16 19
Random walk, unrestricted 2
Rapidly oscillating data 798
Ray 707 708 717 722 755 774 784
Ray equation 708
Ray tube 714
Ray, incoming 736
Ray, outgoing 736
Rayleigh quotient 520 524 536
Rayleigh quotient, Dirichlet boundary conditions 523 527
Rayleigh quotient, mixed boundary conditions 524
Rayleigh quotient, Neumann boundary conditions 523
Rayleigh quotient, Sturm — Liouville problem 535 545
Rayleigh quotient, third kind boundary conditions 524
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