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| Courant R., Hilbert D. — Methods of Mathematical Physics, Vol. 2 |
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| Предметный указатель |
Superposition, of exponential functions, method of 515 — 517
Support, bounded 77
Support, function of a minimal surface 56 — 58
Support, of a function 487(ftn)
Supporting planes to a surface 567
Surface element 22(ftn)
Surfaces of revolution 9
Symbolic method see Heaviside method of operators
Symmetric equations, existence theorem for solutions of 668 — 671
Symmetric equations, of higher order 594 — 595
Symmetric hyperbolic 593
Symmetric system(s) 426 551 594
Systems of first order with two independent variables 171
Systems of quasi-linear equations with the same principal part 139 — 145
Systems of two first order equations 169 — 170
Tchebycheff polynomial 271
Telegraph equation 186 192 544 695
Test functions 774
Test functions, spaces of 769 771 772 793
Theta function 200
Time reversibility of hyperbolic problems 423
Time-like, curve 591
Time-like, direction(s) 565 569 591
Totally hyperbolic 172 175
Totally hyperbolic, differential equation 422
Transient problems 507ff
Transient problems, by Heaviside method 517
Transient problems, general formulation 511
Transient problems, general theory of 535
Transient problems, method of superposition of exponential solutions 515 — 517
Transient problems, solution by the Duhamel integral 512 — 515
Transient problems, solution by the Laplace transformation 539 — 550
Transient response 224
Translation principle of Heaviside 525
Translation principle of Heaviside, justification of 532
Transmission of discontinuities 574
Transport equation(s) 619- 620 625 626 propagation
Transport equation(s), for higher order systems 633 — 635
Transversality condition 122
Transverse differentiation 133
Transverse differentiation, invariance of, under transformation of independent variables 562(ftn)
Tricomi(‘s) equation 162 390
Tubular surface(s) 27 95
Two-body problem 19 — 20 109
Ultrahyperbolic 182
Ultrahyperbolic, differential equations 745 — 753
Ultrahyperbolic, equation 176
Ultrahyperbolic, equation, initial value problems for non-space-like manifolds 756 — 758
Underdetermined systems 15 — 18
Undistorted progressing waves 761
| Uniformization theorem for plane domains 160(ftn)
Uniformly elliptic equations 331 — 332
Unique continuation of solutions of a homogeneous elliptic system 394
Uniqueness, for quasi-linear systems 448 — 449
Uniqueness, Haar’s proof 145 — 147
Uniqueness, of solutions, of boundary value problem 320
Uniqueness, of solutions, of the Neumann problem 329 — 331
Uniqueness, proofs for second order linear equations (Cauchy problem) 440 — 445
Uniqueness, theorem(s), for first order linear systems (Cauchy problem) 445 — 449
Uniqueness, theorem(s), for harmonic functions 255
Uniqueness, theorem(s), for hyperbolic equations 642 — 649
Uniqueness, theorem(s), for solutions of boundary value problem 320 — 324
Uniqueness, theorem(s), Holmgren 237 — 239
Unit function 520
Variation of parameters, method of 691 (see also Duhamel’s integral)
Variational problem, canonical form of canonically conjugate variables 115
Vibration problems 223
Vortex theorem 437
Wave(s) 417 631- 707 Propagation
Wave(s), decomposition into irrotational and equivoluminous parts 710
Wave(s), elastic, initial value problem for 706 — 711
Wave(s), equation 6 41 188 189 201 212 239 508 527 545 643 715
Wave(s), equation, application of Asgeirsson’s mean value theorem to 749 — 752
Wave(s), equation, connection with Darboux equation 700 — 703
Wave(s), equation, construction of the solution 683 — 686
Wave(s), equation, equation, Cauchy’s problem for, in three dimensions 574ff
Wave(s), equation, focussing in 674
Wave(s), equation, form 188 189 761
Wave(s), equation, fronts 88 560 568 631 761(ftn)
Wave(s), equation, generalized progressing spherical 704 — 706
Wave(s), equation, initial value problems for non-space-like manifolds 759 — 760
Wave(s), equation, nonhomogeneous 691 — 692
Wave(s), equation, operator 704
Wave(s), equation, optics 640
Wave(s), equation, Riemann function for 457 — 458
Wave(s), equation, shear 708
Wave(s), equation, solution by method of plane mean values 715 — 718
Wave(s), equation, standing 761
Wave(s), equation, velocity vector see Normal velocity vector
Wave(s), radiation, function for 737 — 740
Wave(s), radiation, problem for 206 — 208 703
Weak, convergence 774 777
Weak, definition, principle of 774
Weak, solution(s) 418 635- Weak
Weak, solution(s), for linear systems 487 — 488
Weak, solution(s), for systems of conservation laws 489
Weierstrass 39
Weierstrass, convergence theorem 273 — 274
Wiener’s theorem (on capacity) 306
[a, b] pseudoanalytic function 376
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