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| Zauderer E. — Partial Differential Equations of Applied Mathematics |
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| Предметный указатель |
Abel's integral equation 398
Acoustics 579 818
Adjoint equation 13 41 161 425
Adjoint operator 33 146 147 148 149 161 162 550
Adjoint operator, formal 147 227
Admissible function 519 524
Airy function 322 547 678 697 732 733 735 736 737
Airy function, asymptotic form 322 733 736 737
Airy's equation 547 732
Akhmanov, S.A. 763
Amplitude 643 644 645 702 717 754 828
Angle of incidence 750
Angle of reflection 750
Antinode 196
Approximate factorization 809
Associated Legendre equation 601
Associated Legendre function 602
Asymptotic decomposition 812
Asymptotic equality 295 618
Asymptotic expansion 293 618 702 721
Asymptotic method 616 702 772
Asymptotic simplification 808
Axial source 282
Backward difference equation 12 40
Backward initial and boundary value problem heat equation 469 668
Backward initial and boundary value problem hyperbolic equation 417
Backward initial and boundary value problem parabolic equation 159 419
Backward initial value problem heat equation 142
Backward initial value problem hyperbolic equation 420
Backward initial value problem parabolic equation 420
Backward initial value problem wave equation 473
Balance law 164 225 325
Beam half-width 752 760
Bessel function 191 230 231 279 281 322 387 532 542 571 624 701 778 801 835
Bessel function, asymptotic form 231 322 701 778
Bessel function, eigenfunction expansion 190
Bessel functionzeros 191 532 542
Bessel's equation 190 280 381 532 541 571 623
Bessel's inequality 181
Bicharacteristics 780
Biharmonic equation 133 572 620
Bilinear expansion 447 459
Biorthogonal set 227
Boltzmann's equation 838
Boundary condition, Dirichlet 167
Boundary condition, first kind 167
Boundary condition, mixed kind 167
Boundary condition, natural 526
Boundary condition, Neumann 167
Boundary condition, second kind 167
Boundary condition, third kind 167
Boundary layer 647 664 670 682
Boundary layer equation 651 654 659 664 665 670 678 686 687 732
Boundary layer theory 617 647 650 658 663 705 721 740 765 777 809
Boundary perturbations 636
Boundary value problem 137
Boussinesq equations 828
Breaking of waves 67 828
Breaking time 68
Brownian motion 3 15 22 24 25
Brownian motion absorbing boundary 10 28 41
Brownian motion backward Kolmogorov equation 13 38 41
Brownian motion backward telegrapher's equation 41
Brownian motion diffusion coefficient 7
Brownian motion diffusion equation 7 12 22 35 36 40
Brownian motion drift velocity 4 12
Brownian motion elastic restoring force 36
Brownian motion finite particle velocity 15 25 26
Brownian motion forward Kolmogorov equation 12
Brownian motion mean displacement 2 4 18
Brownian motion mean first passage time 32 44
Brownian motion mean square displacement 18 22
Brownian motion rate of reversal 19 22 41
Brownian motion reflecting boundary 11 37 42
Brownian motion time independent 27 30 42
Brownian motion, deterministic motion 23 24
Brownian motion, Fokker — Planck equation 12 26 35
Brownian motion, infinite particle velocity 14 24
Brownian motion, inhomogeneous medium 12 25
Brownian motion, Langevin's equation 14 18 26
Brownian motion, Laplace's equation 28
Brownian motion, random motion 23
Brownian motion, random walk independent steps 2
Brownian motion, random walk position dependent 11 25 33
Brownian motion, random walk, correlated 15
Brownian motion, telegrapher's equation 20 25
Brownian motion, unidirectional wave equation 23 24
Burgers' equation 67 820 822 826 838 839
Canonical form 110
Canonical form, elliptic equation 114
Canonical form, hyperbolic equation 112 113 362
Canonical form, hyperbolic system 130
Canonical form, parabolic equation 114
Cauchy principal value 256 433
Cauchy problem 136; see also “Initial value problem”
Cauchy problem elliptic equation 139 141
Cauchy problem hyperbolic equation 139 142
Cauchy problem parabolic equation 142
Cauchy — Riemann equations 48 131
Cauchy — Schwarz inequality 227 349
Causal fundamental solution 377; see also “Free space Green's function”
Causal fundamental solution, hyperbolic equation 384 385 417 419 465 474 475 480 555 773 796 801 805
Causal fundamental solution, parabolic equation 384 388 419 467 480
Causality 13 26 377
Caustic: curve 92 720 729
Caustic: surface 713
Chain reaction 544
Characteristic form 130
Characteristic normal form 135
Characteristic, base curves 49 117 707
Characteristic, cone 125 376 385
Characteristic, conoid 376 378 806
Characteristic, coordinate system 111
Characteristic, curves 49 63 117 128 550 582 633 664 669 672 774 778
Characteristic, direction 63 81 83
Characteristic, equation 49 63 84 111 120 125 128 129 132 340 774 779 785 797
Characteristic, initial value problem 50 52 60 61 65 69 128 361 370 662 713
Characteristic, polynomial 811
Characteristic, strip 85
Characteristic, surface 125 340 344 782
Characteristic, velocity 52 370;
Classical solution 178 211 390
Classification of equations second order, n variables 122
Classification of equations second order, two variables 110
Classification of equations, mth order, n variables 132
Classification of systems first order, n variables 132
Classification of systems first order, two variables 127 134
Cole, J.D. 823
Compact support 426 436
Compatibility condition 117 154 457
Complete integral 92
Completeness criterion 176 181
Composite expansion 668 672
Composite medium 329
Composite rod, heat conduction 336
Composite rod, longitudinal vibration 332
Compression wave 76 828
Concentrated source 363 372
Concentration 165 543
Conservation form 57 75 105
Conservation law 75
Conservative type, equation of 144 390
Consistency condition 119
Constraints 519 520
continuous dependence on data 138 393 395 559 561
Convolution theorem, cosine transform 312
Convolution theorem, Fourier transform 247
Convolution theorem, Laplace transform 319
Convolution theorem, sine transform 312
Correlation coefficient 16
| Courant's maximum-minimum principle 520 527 540
Courant, R. 29 520
Critical intensity 772
Critical value 222 544
Cutoff frequency 615
Cylindrical wave 90 91 374 383 701 722 744 753 781 801
d'Alembert's solution 51 341 345 351 358 555
Defocusing medium 757 762
Difference equation, correlated random walk 19
Difference equation, mean first passage time 32 44
Difference equation, position dependent random walk 12 33
Difference equation, random walk 6
Difference equation, time independent random walk 28 30 42
Difference equation, wave equation 350
Diffracted ray 744
Diffracted ray edge 744
Diffracted ray surface 751
Diffraction 703 744 760
Diffraction coefficient 745
Diffraction length 752 767
Diffusion effect 306 307 791
Diffusion equation 7 12 22 35 36 40 48 121 131 285 543 662;
Dirac delta function 7 30 255 311 370 375 429 445
Dirichlet data 137 167 527
Dirichlet's principle 536 599
Discontinuities 56 57 342 364 434 778 792 809
Discontinuous derivatives 56 75 117 120 338 342 354
dispersion relation 144 630 645 774
Dispersive type, equation of linear 144 564
Dispersive type, equation of nonlinear 645 830
Dispersive wave motion 144 295 644
Dissipative effect 307
Dissipative type, equation of linear 145 301 394 658 808 810
Dissipative type, equation of nonlinear 830
Dissipative wave motion 145 301
distribution 446
Divergence form 146 150
Divergence theorem 146 164 172
Domain of dependence 205 480 553
Domain of influence 205 480 553
Doppler effect 360 369
Double Fourier sine series 456
Double layer distribution 364 503
Dubois — Reymond lemma 330 339 365 598
Duhamel's principle 201 421
Eiconal equation 89 702 704 707 754 784
Eigenfunction expansion 176 183 192 193 207 209 347 446 458 464 466 481 517
Eigenfunctions 171
Eigenfunctions completeness 176 337 517 533
Eigenfunctions orthogonality 175 182 337 540
Eigenfunctions orthonormality 183 517
Eigenfunctions, real valued 175 182
Eigenspace 811
Eigenvalue perturbations 548 568 640 642
Eigenvalue problem 171 178 184 185 186 190 192 194 208 213 334 367 447 453 456 461 517 522 524 529 540 567 570 614 639 642
Eigenvalue problem, adjoint 227 231
Eigenvalues 171
Eigenvalues countability 175 183 337 517 529
Eigenvalues limit point 175 183 337 529
Eigenvalues multiple 176
Eigenvalues, continuous spectrum 245
Eigenvalues, discrete spectrum 175 183 245
Eigenvalues, non-negativity 175 182 337
Eigenvalues, real valued 175 337
Eigenvalues, simple 183
Einstein, A. 14
Elasticity theory 593
Elasticity theory compression wave 594
Elasticity theory isotropic medium 593
Elasticity theory Lame constants 594
Elasticity theory longitudinal wave 594
Elasticity theory Navier's equation 593
Elasticity theory shear wave 594
Elasticity theory transverse wave 594
Elasticity theory wave equation 594
Electromagnetic theory 587
Electromagnetic theory constitutive relations 588
Electromagnetic theory dielectric constant 588
Electromagnetic theory electric field vector 587
Electromagnetic theory electrostatic potential 588
Electromagnetic theory Hertz vector 613
Electromagnetic theory irrotational field 588
Electromagnetic theory Laplace's equation 589
Electromagnetic theory Lorentz condition 590
Electromagnetic theory magnetic field vector 587
Electromagnetic theory magnetic permeability 588
Electromagnetic theory magnetostatic potential 589
Electromagnetic theory Poisson's equation 589
Electromagnetic theory scalar potential 589
Electromagnetic theory solenoidal field 589
Electromagnetic theory telegrapher's equation 589
Electromagnetic theory vector potential 589
Electromagnetic theory wave equation 589
Electrostatics 588
Elliptic equation 114 123 141 166 169 328 345 379 395 402 412 447 452 457 587 662 663 669 679 681
Energy conservation 139 144 196 391 395 584 718
Energy dissipation 145 394 395
Energy integral 390 518
Energy integral biharmonic equation 410
Energy integral dissipative hyperbolic equation 392
Energy integral elliptic equation 395
Energy integral hyperbolic equation 390
Energy integral hyperbolic system 409
Energy integral parabolic equation 394
Energy integral vibrating plate 410
Energy integral vibrating rod 409
Energy integral vibrating string 196 233
Envelope 93 713
Error function 265
Error function complementary 267
Euler's equations of fluid dynamics 157 158 575 577 578 579 581 585
Euler's equations of fluid dynamics, equation of conservation of energy 611
Euler's equations of fluid dynamics, equation of conservation of momentum 577
Euler's equations of fluid dynamics, equation of continuity 576
Euler's equations of fluid dynamics, equation of state 577 578
Even function 188
Expansion wave 77 828
Expectation, mathematical, continuous case 9
Expectation, mathematical, discrete case 2 16 21
Extension of functions 188
Extension of functions, even 188
Extension of functions, odd 188
Extension of functions, periodic 188 197 441
Fick's law 165
Finite Fourier transform 208 214
Finite Fourier transform inverse 209
Fluid dynamic circulation 578
Fluid dynamic density 575
Fluid dynamic entropy 577 584
Fluid dynamic Euler's equations 577 578
Fluid dynamic gas constant 584
Fluid dynamic heat conduction coefficient 584
Fluid dynamic internal energy 584
Fluid dynamic Laplace's equation 579
Fluid dynamic Mach number 587
Fluid dynamic material derivative 576
Fluid dynamic Navier — Stokes equations 583 816
Fluid dynamic polytropic gas 580 582 823
Fluid dynamic potential function 578
Fluid dynamic pressure 575
Fluid dynamic quasilinear wave equation 581 823
Fluid dynamic specific heat 584
Fluid dynamic speed of sound 583
Fluid dynamic streamline 586
Fluid dynamic velocity 575
Fluid dynamic viscosity coefficient 584
Fluid dynamic wave equation 580
Fluid dynamics 575
Fluid flow, adiabatic 577 584
Fluid flow, compressible 577
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