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Courant R., Hilbert D. Ч Methods of Mathematical Physics. Volume 1
Courant R., Hilbert D. Ч Methods of Mathematical Physics. Volume 1

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Ќазвание: Methods of Mathematical Physics. Volume 1

јвторы: Courant R., Hilbert D.

язык: en

–убрика: ћатематика/

—татус предметного указател€: √отов указатель с номерами страниц

ed2k: ed2k stats

»здание: 7-th edition

√од издани€: 1966

 оличество страниц: 578

ƒобавлена в каталог: 17.02.2013

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ѕредметный указатель
Abel's integral equation      158
Accumulation principle for functions      57
Adjoint differential expression      279 280
Adjoint orthogonal systems of unsymmetric kernels      159
Alternative theorem for integral equations      115
Alternative theorem for linear equations      6
Alternative theorem for ordinary differential equations      359
Analytic continuation      395
Approximation in the mean      52 54
Approximation theorem of Weierstrass      65
Argument function      168
Arzela's theorem      59
Associated Legendre functions      327 505
Asymptotic behavior of eigenvalues, in Sturm Ч Liouville problem      414
Asymptotic behavior of eigenvalues, of Bessel's equation      415
Asymptotic behavior of eigenvalues, of vibrating plate      460
Asymptotic behavior of solutions of the Sturm Ч Liouville problem      331Ч339
Asymptotic dimension of a sequence of functions      63
Asymptotic distribution of eigenvalues of a differential equation      429Ч445 460
Asymptotic expansions      522Ч535
Asymptotic expansions for Bessel and Hankel functions      524 532
Beats      390
Bessel functions      303Ч306 324Ч325 340 372 390Ч391 402 467
Bessel functions, asymptotic behavior of      332Ч334
Bessel functions, asymptotic representations of      524 532
Bessel functions, functional relation for      489
Bessel functions, integral representations for      474Ч82
Bessel functions, integral theorem for      340Ч341 490
Bessel functions, orthogonality relations for      305
Bessel functions, power series for      482Ч484
Bessel functions, relations between      485
Bessel functions, singularities of      501
Bessel functions, zeros of      451 492Ч496
Bessel transformation      490Ч492
Bessel's equation      303 467
Bessel's equation, asymptotic behavior of eigenvalues of      415
Bessel's equation, singularities of solutions of      501
Bessel's inequality for functions      51 425
Bessel's inequality for vectors      5
beta function      483
Bezout's theorem      520
Biharmonic equation      370
Bilinear forms      11Ч14
Bilinear forms, reciprocal      12
Bilinear forms, resolvents of      18. 29
Bilinear formula, for iterated kernels      137
Bilinear integral form      123
Bilinear relation      360
Biorthogonality relations      404
Boundary conditions for the rod      295
Boundary conditions for the string      291
Boundary conditions, containing a parameter      392Ч393 461
Boundary conditions, homogeneous and inhomogeneous      277
Boundary conditions, natural      208
Boundary, free      208
Brachistochrone      170 207
Broken extremals      259
Buckling, variational problem of      272
Calculus of perturbations      344
Calculus of variations      164Ч274
Calculus of variations, applied to eigenvalue problems      397Ч165
Calculus of variations, Fundamental Lemma of      185
Canonical differential equations      239
Canonical form of variational problems      238
Castigliano's principle      270
Catenary      172 218
Cayley's theorem      22 536Ч539
Characteristic values of a matrix      17
Closed systems of functions      110
Complete systems of functions      52 54
Completeness of a system of functions      110
Completeness of eigenfunctions of a differential equation      359Ч360 369 424
Completeness of Hermite polynomials      96Ч97
Completeness of Laguerre polynomials      96
Completeness of Legendre polynomials      82
Completeness of powers of x      65 101Ч102
Completeness of spherical harmonics      512Ч513
Completeness of systems of functions of several variables      56
Completeness of systems of vectors      4
Completeness of trigonometric functions      68
Completeness relation for functions      51
Completeness relation for vectors      5
Components of a function      51
Conduction of heat      311
Confocal rectangular parallelepiped      319
Conformal mapping      377
Conjugate potential functions      241
Conservation of momentum      265
Constrained systems, eigenvalues of      408
Constraints on quadratic forms      33 44
Constraints on variational problems      233
Continued fraction for the cotangent      489
Continuous dependence of eigen values and eigenfunctions on the kernel      151
Continuous spectrum      100 339Ч343
Convergence in the mean      98 110
Convergence theorems of Lebesgue      109Ч111
Cotangent, continued fraction for      489
Cylinder functions      see "Bessel functions" "Hankel "Mathieu "Neumann
Cylindrical domain      319
Darboux method      532Ч535
Definite kernels      123 162
Degeneracy of eigenvalues      129
Degenerate kernels      114Ч118 129
Degenerate quadratic forms      27
Dense function systems      100Ч101
Derivative, variational      186
Determinant inequality of Hadamard      36
Dido's problem      258
Differential equations, canonical      239
Differential equations, equivalence with integral equations      358Ч363
Differential equations, integral transformations applied to      466Ч468
Dimension number, asymptotic      63
Dini's theorem      57
Dipole      514Ч15
Direct solution of variational problems      174Ч183
Dirichlet's discontinuous factor      81
Dirichlet's integral formula      78
Dirichlet's problem      240
Dirichlet's problem for the circle      179
Discontinuous factor of Dirichlet      81
Discontinuous kernels      152
Discrete spectrum      130
Divergence expressions      195
du Bois-Reymond, theorem of      200
Eigenfrequency      283
Eigenfunctions for rectangular membrane      301
Eigenfunctions of a differential equation, nodes of      451Ч455
Eigenfunctions of a differential equation, nodes of, completeness of      424
Eigenfunctions of a kernel      113
Eigenfunctions of a kernel, minimum properties of      161
Eigenfunctions of symmetric kernels      126Ч132 148Ч150
Eigenfunctions, continuous dependence on kernel      151
Eigenfunctions, Kellogg's method for      156
Eigenfunctions, nodes of      300 302 304 395 451Ч455 458 463
Eigenfunctions, zeros of      451Ч455
Eigenvalue problems for closed surfaces      461
Eigenvalue problems of mathematical physics      275Ч396
Eigenvalue problems of Schroedinger type      445Ч450
Eigenvalue problems with two parameters      460
Eigenvalue problems, definition of      309
Eigenvalue problems, variational methods for      397Ч165
Eigenvalues for the membrane      298
Eigenvalues for the plate, asymptotic behavior of      460
Eigenvalues for the rod      296
Eigenvalues for the string      287
Eigenvalues of a constrained system      408
Eigenvalues of a differential equation for a subdomain      408Ч409
Eigenvalues of a differential equation, asymptotic distribution of      429Ч445 460
Eigenvalues of a differential equation, continuity of      418Ч424
Eigenvalues of a differential equation, dependence on boundary conditions      410Ч411
Eigenvalues of a differential equation, dependence on coefficients      411
Eigenvalues of a differential equation, extremum properties of      398Ч407
Eigenvalues of a differential equation, infinite growth of      412
Eigenvalues of a differential equation, maximum-minimum property of      405
Eigenvalues of a differential equation, minimum properties of      459
Eigenvalues of a kernel      113 132 137
Eigenvalues of a matrix      17 26
Eigenvalues of a positive definite kernel      132
Eigenvalues of a symmetric kernel      148Ч150
Eigenvalues of a symmetric kernel, first      122Ч125
Eigenvalues of a symmetric kernel, maximum-minimum property of      132Ч134
Eigenvalues of a symmetric kernel, totality of      126Ч132
Eigenvalues of a unitary matrix      46
Eigenvalues of Bessel's equation, asymptotic behavior of      415
Eigenvalues of functions of a kernel      157
Eigenvalues of functions of a matrix      22
Eigenvalues of infinite multiplicity      154 395
Eigenvalues of Sturm Ч Liouville problem, asymptotic behavior of      414
Eigenvalues, continuous dependence on kernel      151
Eigenvalues, degenerate      129
Eigenvalues, minimum-maximum property      31 132Ч134 405
Eigenvalues, multiple      113 129
Eigenvalues, negative      294 416
Eigenvalues, reciprocal      17
Eigenvectors      24
Eigenvectors, use in solving linear equations      30
Eigenvibrations      283 310
Eigenvibrations of homogeneous string      287
Elastic bodies      268
Electrostatics      267
Elementary divisors of a matrix      45
Ellipsoidal coordinates      226
Elliptic coordinates      319 391Ч392
Elliptic functions      227
Energy integral      265
Energy, kinetic      242
Energy, potential      242
Enskog's method for symmetric integral equations      156
Equicontinuous functions      58 114 119 125
Equilibrium conditions of a mechanical system      243
Equilibrium problems      308
Erdmann vertex condition      260
Euler equations      183Ч207
Euler equations for isoperimetric problem      207
Euler equations, homogeneous form of      196
Euler equations, integration of      206
Euler equations, invariance of      222
Euler expression, identical vanishing of      193
Euler integral      483
Euler transformation      467
Expansion theorem      310
Expansion theorem for definite kernels      138Ч140
Expansion theorem for differential equations      360Ч361 427Ч428
Expansion theorem for iterated kernels      137
Expansion theorem for spherical harmonics      513
Expansion theorem for symmetric integral equations      134Ч136
Expansion theorem, limits of validity of      395Ч396
Expansions, asymptotic      522 535
Extrema, Weierstrass's theorem on      20 164
Extremals      185
Extremals, broken      259
Extremum properties of eigenvalues      398Ч407
Fejer's summation theorem      102
Fermat's principle      165
Finite differences      176
First variation      184 208Ч214
Fischer Ч Riesz theorem      110
Forced motion of the membrane      300
Forced motion of the string      289 294
Forced vibrations      285 389
Form factor      286
Forms      see "Particular type of form"
Fourier coefficients      51 424
Fourier coefficients, order of magnitude of      74
Fourier integral      77Ч82 98Ч100
Fourier integral theorem      78
Fourier series      69Ч77
Fredholm formulas      142Ч147
Fredholm's theorems for arbitrary kernels      118Ч122 150
Fredholm's theorems for degenerate kernels      115Ч118
Fredholm's theorems, Schmidt's derivation of      155
Free boundaries      208
Free vibrations      282Ч283
Friedrichs transformation      234
Function space      57
Function space, gradient in      222
Functionals      167Ч169
Functions of a kernel, eigenvalues of      157
Functions of a matrix, eigenvalues of      22
Fundamental domain      48 112
Fundamental lemma of the calculus of variations      185
Fundamental solution      370
Fundamental solution of an ordinary differential equation      353
Fundamental tone      286
Generalized Green's function      356Ч357
Generating function for Hermite and Laguerre polynomials      510
Generating function for spherical harmonics      539Ч541
Geodesic curves      170 189 213
Gibbs' phenomenon      105Ч107
Gradient in function space      222
Gram determinant of a system of functions      62 107Ч108
Gram determinant of a system of vectors      34Ч36
Gram Ч Schmidt orthogonalization process      4 60
Green's formula      278Ч280
Green's function      311 351Ч388
Green's function as kernel of an integral equation      358
Green's function for a circular ring      306Ч388
Green's function for Hermite's equation      373Ч375
Green's function for Laguerre's equation      375Ч376
Green's function for ordinary differential equations      351Ч363
Green's function for ordinary differential equations of higher order      362Ч363
Green's function for ordinary differential equations, construction of      354Ч355
Green's function for ordinary differential equations, definition of      352Ч353
Green's function for the biharmonic equation      370
Green's function for the potential equation      363Ч370 377
Green's function for the potential equation in space      378Ч384
Green's function for the potential equation in the plane      384Ч386
Green's function in the generalized sense      356Ч357
Green's function, construction by reflection      378Ч379 384
Green's function, examples of      371Ч388
Green's function, obtained by conformal mapping      377
Green's function, symmetry of      354
Green's tensors for systems of differential equations      393Ч394
Group, orthogonal      539
Haar, theorem of      203
Hadamard's inequality for determinants      36
Hamilton's variational principle      242
Hammerstein's theorem      162
Hankel functions      468Ч473
Hankel functions, asymptotic representations for      524Ч532
Hankel functions, integral representation of      476
Hankel functions, singularities of      501
Harmonic functions      see "Potential equation"
Heat conduction, equation of      311
Herglotz, theorem of      542
Hermite equation      508
Hermite equation, Green's function for      373Ч375
Hermite functions      508Ч509
Hermite orthogonal functions      154
Hermite polynomials      91Ч93 328
Hermite polynomials, completeness of      96Ч97
Hermite polynomials, generating function for      510
Hermitian forms      13 28
Hilbert space      55
Hilbert space, orthogonal transformations in      55
Holonomic conditions      221
Hurwitz's solution of the isoperimetric problem      97Ч98
Independence, measure of      61
Indicatrix      258
Inertial theorem for quadratic forms      28
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