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| Ïîèñê ïî óêàçàòåëÿì |
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| Courant R., Hilbert D. — Methods of Mathematical Physics, Vol. 2 |
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| Ïðåäìåòíûé óêàçàòåëü |
Hodograph method 39(ftn)
Hodograph transformation 428 — 429 431
Holder continuity 248 — 249
Holmgren equation 653(ftn)
Holmgren, theorem 54
Holmgren, uniqueness theorem 237 — 239
Homeomorphism 375(ftn) 393
homogeneous functions 11
Huyghens’ and radiation 764 — 766
Huyghens’ for radiation problem 698
Huyghens’ generalized 735 — 736
Huyghens’ minor principle 671 672
Huyghens’ principle 208 — 210 576 688 735 740 743 760
Huyghens’construction 632
Huyghens’construction, of ray cone 124 — 125
Huyghens’construction, of ray surface 587
Huyghens’construction, of wave fronts 568 — 569
Hydrodynamics 225 599 600
Hyperbolic 156 177 190 216 226 408
Hyperbolic, differential, equations see also Wave equation
Hyperbolic, differential, equations, in more than two independent variables 551 — 766
Hyperbolic, differential, equations, in two independent variables 407 — 550
Ideal elements in function spaces 767
Ideal functions 621 — 622 766
Ideal functions, as boundary values of harmonic functions 797 — 798
Ideal functions, calculus with 788 — 792
Ideal functions, convolution of 791 — 792
Ideal functions, definite integrals of 785 — 788
Ideal functions, definition, by linear differential operators 775 — 777
Ideal functions, definition, by linear functionals 778 — 779
Ideal functions, definition, by weak limits 777 — 778
Ideal functions, equivalence of various definitions 779 — 781
Ideal functions, identification with ordinary functions 783 — 785
Ideal functions, indefinite integrals of 785
Ideal functions, represented by Fourier coefficients 795 — 796
Ideal functions, strong definition 796 — 797
Impulse(s) 510 513
Index of inertia 556
Initial value problem(s) 39 — 56 135 194 197 221 226 407
Integral, conoid 83
Integral, formulas 677 — 681
Integral, manifold 98
Integral, of system of ordinary differential equations 29
Integral, rational operators 519
Integral, strip 80 410
Integral, strip, alternative, for a strip of second order 413
Integral, surface 2
Integral, surface, for quasi-linear differential equations in n variables 69
Integral, surface, generated by characteristic curves 63 70
Integral, surface, through characteristic strip 82 83
Interior, differential operator 412 555 579
Interior, differentiation (tangential differentiation) 134 170
Invariance of characteristics under point transformations 414 423
Invariance under transformation of independent variables of bicharacteristics 562
Invariance under transformation of independent variables of characteristics 562
Invariance under transformation of independent variables of transverse differentiation 562(ftn)
Isentropic flow, one dimensional 429 — 432
Jet problem 225 — 226
Jump discontinuity 300 427
Jump, relation 149 574
Jump, relation, for second order equations 570
Kellogg’s theorem 336
Laplace, differential equation for the support function of a minimal surface 56 — 58
Laplace, equation 154 176 184 222 374
Laplace, inversion formula 536
Laplace, transformation 535 — 539
Laplace, transformation, application to the operational calculus 539 — 550
Laplacian, in polar coordinates 242
Legendre function 114
Legendre polynomial 271(ftn)
Legendre, transformation 32 — 39 114
Legendre, transformation, application to partial differential equations 35 — 39
Legendre, transformation, for functions of n variables 34 — 35
Legendre, transformation, for functions of two variables 32 — 34
Leibnitz’ rule 577(ftn)
Light, cone 83
Light, rays 88 — 91
Linear, functional(s) 449 453(ftn) 769
Linear, functional, continuity 771 — 773
Linear, operator 770
Linear, transformation 770
Linear,space 403
Linearized equations, compressible fluids 436 — 437
Local barrier function 311
Local ray cone see Monge cone Ray local
Localization of ideal functions 781
Lorentz transformation 750
Mach, angle 437
Mach, lines 436
Magnetic potential 172
Magnetohydrodynamics 599 612
Magnetohydrodynamics, compressible 614 — 618
Magnetohydrodynamics, incompressible 613 — 614
Major ants 50 — 54
Maximum norm 769
Maximum principle 255 268 326
Maximum principle for subharmonic functions 307 — 308
Maxwell’s equations 178 602 647
Mean value theorem(s) 254 268 275 —
Mean value theorem(s), for Poisson equation 276 — 277
Mean value theorem(s), for Poisson equation, converse 282 — 284
Mean value theorem(s), for various elliptic equations 286 — 290
Mean value theorem(s), of potential theory 275 276
Mean value theorem(s), of potential theory, converse 277 — 282
Method of descent 205 — 206 686
Method of descent, application to Cauchy’s problem for the general (hyperbolic) linear equation of second order 692 — 694
Method of spherical means 699 — 706
Minimal surface(s) 56 — 58 167 223 400
Mixed, initial and boundary value problems 471 — 475
Mixed, problem(s) 197 223
Monge — Ampere differential equation 324 — 326 348 428 495
Monge, axis 23 29 63
Monge, cone 23 29 75 83 563 581
Monge, cone, for Clairaut’s equation 95
Monge, cone, in hydrodynamics 601
Monge, curves 76
Monge, equation 86 — 88 601
Monge, pencils 63
Negative norms 797
Neumann function 245
Neumann problem 329
Neumann problem, for a nonlinear equation 395
Neumann problem, uniqueness of solutions 329 — 331
Nonanalytic differential equations 54 — 55
Nonexistence of solutions 54
Nonisentropic flow 434 — 437
Nonlinear, boundary value problem 395 — 399
Nonlinear, elliptic equations 367 — 374
Nonsymmetric systems 675 — 676
Norm, maximum 769
Norm, maximum, r-norm 769
Normal cone 563 — 564 569
Normal cone in crystal optics 603 726
Normal differentiation see Transverse differentiation
Normal form(s), for differential operators of second order 154 — 170
Normal form(s), for linear equations with constant coefficients 181 — 184
Normal form(s), for linear second order equations 155 — 160
Normal form(s), for quasi-linear second order equations 163 — 169
Normal form(s), for systems of two first order equations 169 — 170
Normal form(s), of a hyperbolic system 426
Normal surface 582 — 583
Normal surface, in crystal optics 603 — 609 723
Normal surface, in magnetohydrodynamics 614 — 618
Normal velocity 581
Normal velocity, surface 583
Normal velocity, vector 561
Normed space 403
Null rays 564
One-dimensional isentropic flow, Riemann function for 459 — 461
Operational calculus see Heaviside operational calculus
| Optics see Geometrical optics Crystal
Oscillatory initial values 636 — 642
Overdetermined, problems 231
Overdetermined, systems 15 — 18
Parabolic 156 177 182 226 423
Parametrix 347 363 367
Parseval formula 794
Perron’s method of subharmonic functions 306 — 312 342
Persistence of properties of initial values 671 — 674
Persistent property of an initial function 673
Perturbation theory 368 — 369
Phase 188 189
Phase, function 761
Piecewise continuous function 245(ftn)
Piecewise smooth surface 245 (ftn)
Plane mean values, method of 711 — 715
Plane waves 187ff 676
Plane waves, decomposition of functions into 677 — 681
Plane-like wave fronts 586
Planetary motion 109
Plateau’s problem, parametric form 225
Plateau’s problem, unsymmetric form 223
Poisson, equation 186 241 246 265 284
Poisson, formula 679 — 681
Poisson, integral 22 261
Poisson, kernel 265 266 268 271
Poisson, kernel, expansions of 271(ftn)
Polytropic gas 431 432 459
Potential 240 — 406
Principal part 140 181
Principal part, of an operator 578
Privaloff s theorem 380 401
Progressing wave(s) 188 — 193 622 636 698 760
Propagation 208
Propagation of discontinuities 416 — 418 618
Properly posed problem 215 227
Pseudo-area 726
Pseudoanalytic function(s) 374 — 400
Pseudoanalytic, differentiation and integration of 386 — 389
Pseudoanalytic, formal powers 384 — 386
Quasi-conformal mapping 392 — 395
Quasi-linear, system(s) 425 476 675
Quasi-linear, system(s), equivalence to single equations in higher-dimensional space 140 — 142
Quasi-linear, system(s), for conservation laws 488 — 490
Quasi-linear, system(s), reduction to 43 — 47
Quasi-linear, system(s), solution of 476
Quasi-linear, system(s), uniqueness for 448 — 449
Quasi-linear,differential equations 31 — 32 408ff
Quasi-linear,differential equations, in n variables 69 — 75
Radiation, condition, Sommerfeld’s 315 — 318
Radiation, construction of 730 — 733
Radiation, for one-dimensional isentropic flow 459 — 461
Radiation, for telegraph equation 458 — 459
Radiation, for wave equation 457 — 458 737
Radiation, from a point 455 — 457
Radiation, function (Riemann radiation function) 764; see Radiation kernel and Huyghens’ principle
Radiation, intensity of 696
Radiation, inward 698
Radiation, kernel (Radiation function, Radiation matrix, Riemann function, Riemann radiation kernel) 696 727-
Radiation, matrix (Riemann matrix, Riemann radiation matrix) see Fundamental solutions Radiation
Radiation, problem(s) 224 226 695
Radiation, problem(s), for wave equation 206 — 210 703
Radiation, problem(s), solution of 697 — 698
Radiation, problem(s), three dimensional 696
Radiation, process 194
Radiation, regularity properties of 733
Radiation, symmetry of 454 — 455 729 737
Ray(s) 558- 559 (see also Bicharacteristic rays)
Ray(s), associated with an operator 583
Ray(s), cone 124 — 125 563 591 592
Ray(s), cone, Huyghens’ construction of 124 — 125
Ray(s), cone, in crystal optics 726
Ray(s), cone, local 563 584
Ray(s), conoid 83 564 574 584 660
Ray(s), surface 586 — 587
Ray(s), surface, in crystal optics 603 — 609
Ray(s), surface, in magnetohydrodynamics 614 — 618
Ray(s), transverse to a wave front 561
Reciprocal, normal surface 583 (see also Normal velocity surface)
Reciprocal, surfaces 566 — 568
Reciprocal, transformation 566 — 568
Reduced fundamental solution of 314
Reduced standing wave solution 313
Reduced wave equation 187 — 188 312
Reducibility of a characteristic form 596
Reflection principle for harmonic function 272
Refraction, conical 628 — 629
Regular boundary point 311
Rellich’s theorem 324 — 325
Resolution of initial discontinuities 629 — 631
Rest mass 172
Retarded potentials 204
Riemann function for 458 — 459
Riemann, formula 453
Riemann, function see Radiation kernel
Riemann, invariants 430 431
Riemann, invariants, for polytropic gas 431 432 459
Riemann, kernel see Radiation kernel
Riemann, mapping, problem 224
Riemann, mapping, theorem, extension of 399
Riemann, matrix 564 — 566; see Radiation kernel metric
Riemann, radiation function, kernel or matrix see Radiation kernel representation
Riemann, tensor 456 — 457
Riesz representation theorem 453(ftn)
Scattering 226 318
Schauder, estimates 331 — 550
Schauder, fixed point theorem 362 381 403
Schauder, method 336
Schwarz’s alternating procedure 292 293
Semigroups 672 673(ftn)
Semilinear 171
Semilinear, second order equation 557
Semilinear, system 425
Separation of variables 18 — 20
Sharp signal, transmission of 765 766
Shock, conditions, for a system of conservation laws 636
Shock, discontinuities 149
Shocks 490 635
Signal distortion of 698
Signal transmission of 735 760
Similarity 378 382
Similarity, principle 378 — 384
Singular, operators 523
Singular, solution 3 25 105(ftn)
Sommerfeld’s radiation condition 315 — 318
Sound waves 430
Source, for radiation process 194
Space-like, direction 664
Space-like, lens 651
Space-like, manifold 590
Space-like, normal 590
Space-like, surface element(s) 565 590
Space-like, surfaces 569 (see also "Weakly" space-like surface)
Speed of propagation 438
Spherical, means, application to elastic waves 706 — 711
Spherical, means, method of 699 — 706
Spherical, waves 194 — 197 564 585 676 763
Spherical, waves, relatively undistorted 763
Spherically symmetric flow 432
Stability 227
standing waves 761
Steady irrotational flow 432 — 434
Stream lines 436
Stress tensor 706 — 707
Strip condition(s) 77 98
Subharmonic functions 307
Successor of generating pair 388
Superfunction 309
Superharmonic functions 307
Superposition, construction of further solutions by 20 — 22
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