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Zauderer E. — Partial Differential Equations of Applied Mathematics
Zauderer E. — Partial Differential Equations of Applied Mathematics

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Название: Partial Differential Equations of Applied Mathematics

Автор: Zauderer E.

Аннотация:

The study of partial differential equations of applied mathematics involves the formulation of problems that lead to partial differential equations, the classification and characterization of equations and problems of different types, and the examination of exact and approximate methods for the solution of these problems. Each of these aspects is considered in this book.


Язык: en

Рубрика: Математика/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Издание: 2-nd Edition

Год издания: 1998

Количество страниц: 896

Добавлена в каталог: 08.12.2009

Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID
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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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