√лавна€    Ex Libris     ниги    ∆урналы    —татьи    —ерии     аталог    Wanted    «агрузка    ’удЋит    —правка    ѕоиск по индексам    ѕоиск    ‘орум   
blank
јвторизаци€

       
blank
ѕоиск по указател€м

blank
blank
blank
 расота
blank
Weinstock R. Ч Calculus of variations with applications to physics & engineering
Weinstock R. Ч Calculus of variations with applications to physics & engineering

„итать книгу
бесплатно

—качать книгу с нашего сайта нельз€

ќбсудите книгу на научном форуме



Ќашли опечатку?
¬ыделите ее мышкой и нажмите Ctrl+Enter


Ќазвание: Calculus of variations with applications to physics & engineering

јвтор: Weinstock R.

јннотаци€:

Book basically divided into two parts. Chapters 1-4 include background material, basic theorems and isoperimetric problems. Chapters 5-12 are devoted to applications, geometrical optics, particle dynamics, the theory of elasticity, electrostatics, quantum mechanics and other topics. Exercises in each chapter.


язык: en

–убрика: ћатематика/јнализ/”чебники по элементарному анализу/

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

ed2k: ed2k stats

√од издани€: 1974

 оличество страниц: 326

ƒобавлена в каталог: 18.04.2005

ќперации: ѕоложить на полку | —копировать ссылку дл€ форума | —копировать ID
blank
ѕредметный указатель
Abraham, M.      294n. 316
action      85Ч88 268Ч269
Approximation of eigenvalues      see Ritz method
Area, formula for surface      10
Area, maximum, in plane      53Ч56
Area, minimum surface      115
Area, minimum surface of revolution      19Ч20 30Ч32
Asymptotic distribution of eigenvalues      see Eigenvalue-eigenfunction problems
Bar bending, by couples      212Ч217 250Ч251
Bar bending, Уengineering theoryФ      251. See also Eigenvalue-eigenfunction problems; Vibrations
Basic lemma      16Ч17 43Ч44
Becker, R.      294n. 316
Bending by couples, bar      212Ч217 250Ч251
Bending by couples, plate      224Ч228
Bending moment      214Ч215 250
Bernoulli Ч Euler equation      251
Bernoulli, J.      19 29 67 71
Bessel functions      129Ч130
Bessel functions in circular-membrane problem      194
Bessel functions in circular-plate problem      259
Bibliography      319
Black-body radiation      198 271
Bliss, G.A.      vii 2n. 20n. 29n. 31n. 319
Body forces      199 205
Bohr, N.      264 275
Bolza, O.      vii 2n. 319
Born, M.      277n.
Boundary conditions, distinction between free and imposed      114Ч115
Boundary conditions, elastic solid, general      209Ч210
Boundary conditions, electrostatic potential      294Ч295
Boundary conditions, relaxed conditions      302Ч306
Boundary conditions, vibrating bar      221
Boundary conditions, vibrating membrane, elastically held edge      152
Boundary conditions, vibrating membrane, free edge      153
Boundary conditions, vibrating plate      231Ч236 256Ч257
Boundary conditions, vibrating plate, free-edge square      248Ч249
Boundary conditions, vibrating plate, free-edge square, corner condition      249
Brachistochrone      19 28Ч29
Brachistochrone, between two curves      47
Brachistochrone, curve to fixed point      41Ч43
Brachistochrone, optical solution      71
Brachistochrone, point, to curve      40Ч41
Brachistochrone, point, to vertical line      38
Capacity of condenser      297
Capacity of condenser, approximation of, from above      298Ч300 314Ч315
Capacity of condenser, approximation of, from above, cubical condenser      315
Capacity of condenser, approximation of, from above, ellipsoidal condenser      300Ч302 316
Capacity of condenser, characterization, maximum      304
Capacity of condenser, characterization, minimum      297
Capacity of condenser, cylindrical      309
Capacity of condenser, cylindrical, approximation of      317Ч318
Capacity of condenser, cylindrical, characterization, maximum      309Ч310 317
Capacity of condenser, cylindrical, characterization, minimum      309 310
Capacity of condenser, from below      302Ч306 316
Capacity of condenser, from below, cubical condenser      316Ч317
Capacity of condenser, from below, ellipsoidal condenser      306Ч308
Cavity radiation      198 271
Cavity radiation, asymptotic distribution of frequencies      198
Change of variables      see Transformation
Compatibility, equations of      204
Condenser      see Capacity of condenser
Coordinates, generalized      73
Couple      see Bending by couples
Courant, R.      viii In. 171n. 311n. 319
Davisson, C.J.      264 270
de Broglie, L.      264 270 271
Degeneracy      154. See also Eigenvalue-eigenfunction problems
Derivative of an integral      5
Determinants      8Ч9
Dirichlet, existence of minima of integral      310Ч311
Dirichlet, principle of      311
Dirichlet, problem of      296
Dynamics of particles      72Ч92
Eigenvalue-eigenfunction problems      99
Eigenvalue-eigenfunction problems, approximation      107Ч114 117Ч118
Eigenvalue-eigenfunction problems, asymptotic distribution      196Ч197
Eigenvalue-eigenfunction problems, characterization, isoperimetric      116
Eigenvalue-eigenfunction problems, characterization, minimum      102Ч105
Eigenvalue-eigenfunction problems, characterization, normalization      99 101
Eigenvalue-eigenfunction problems, characterization, orthogonality      101
Eigenvalue-eigenfunction problems, quantum mechanics      263
Eigenvalue-eigenfunction problems, quantum mechanics, characterization, isoperimetric      263 280
Eigenvalue-eigenfunction problems, quantum mechanics, characterization, minimum      281
Eigenvalue-eigenfunction problems, quantum mechanics, eigenvalues as energy levels      263 278
Eigenvalue-eigenfunction problems, quantum mechanics, significance of normalization      276 279.
Eigenvalue-eigenfunction problems, Sturm Ч Liouville      119Ч131
Eigenvalue-eigenfunction problems, Sturm Ч Liouville, asymptotic distribution      196Ч197
Eigenvalue-eigenfunction problems, Sturm Ч Liouville, characterization, isoperimetric      119
Eigenvalue-eigenfunction problems, Sturm Ч Liouville, maximum-minimum      196
Eigenvalue-eigenfunction problems, Sturm Ч Liouville, minimum      130
Eigenvalue-eigenfunction problems, Sturm Ч Liouville, orthogonality      130. See also Sturm Ч Liouville problem
Eigenvalue-eigenfunction problems, three-dimensional vibrations      197Ч198
Eigenvalue-eigenfunction problems, vibrating bar      221Ч224
Eigenvalue-eigenfunction problems, vibrating bar, clamped      244Ч246
Eigenvalue-eigenfunction problems, vibrating bar, explicit solution      252Ч255
Eigenvalue-eigenfunction problems, vibrating bar, isoperimetric characterization      223
Eigenvalue-eigenfunction problems, vibrating bar, orthogonality      223Ч224
Eigenvalue-eigenfunction problems, vibrating membrane      145Ч146 152
Eigenvalue-eigenfunction problems, vibrating membrane, approximation      188Ч192
Eigenvalue-eigenfunction problems, vibrating membrane, asymptotic distribution      177Ч188
Eigenvalue-eigenfunction problems, vibrating membrane, characterization, isoperimetric      147Ч148 152Ч153
Eigenvalue-eigenfunction problems, vibrating membrane, degeneracy      154 155 163Ч164 167n.
Eigenvalue-eigenfunction problems, vibrating membrane, maximum-minimum      171Ч173
Eigenvalue-eigenfunction problems, vibrating membrane, maximum-minimum, consequences      173Ч176
Eigenvalue-eigenfunction problems, vibrating membrane, minimum      164Ч167
Eigenvalue-eigenfunction problems, vibrating membrane, minimum, consequences      167Ч170
Eigenvalue-eigenfunction problems, vibrating membrane, minimum, limitations      170Ч171
Eigenvalue-eigenfunction problems, vibrating membrane, normalization      146 152
Eigenvalue-eigenfunction problems, vibrating membrane, orthogonality      154Ч157
Eigenvalue-eigenfunction problems, vibrating membrane, rectangular      161Ч164
Eigenvalue-eigenfunction problems, vibrating plate      236Ч240
Eigenvalue-eigenfunction problems, vibrating plate, approximation      240Ч244
Eigenvalue-eigenfunction problems, vibrating plate, characterization, isoperimetric      237Ч238 257
Eigenvalue-eigenfunction problems, vibrating plate, characterization, maximum-minimum      240 258
Eigenvalue-eigenfunction problems, vibrating plate, characterization, minimum      239Ч240 258
Eigenvalue-eigenfunction problems, vibrating plate, circular      259Ч260
Eigenvalue-eigenfunction problems, vibrating plate, clamped square      244Ч248 260
Eigenvalue-eigenfunction problems, vibrating plate, degeneracy      237
Eigenvalue-eigenfunction problems, vibrating plate, orthogonality      238Ч239
Eigenvalue-eigenfunction problems, vibrating string      98Ч100 115Ч116
Einstein, A.      271
Elasticity theory      199Ч260
Elasticity theory, approach to dynamical problems      210Ч211
Elasticity theory, boundary conditions, general      208Ч210
Elasticity theory, equations, of equilibrium and motion, general      209
Electrostatic intensity      294
Electrostatics      294Ч318
Electrostatics, two-dimensional problems      308Ч310
End-point conditions      see Boundary conditions; Undetermined end points
Energy, total      75Ч76. See also Kinetic energy; Potential energy
Energy, total, eigenvalues in quantum mechanics      263 278
Energy, total, eigenvalues in quantum mechanics, helium atom      286
Energy, total, eigenvalues in quantum mechanics, one-electron atom      275
Energy, total, equivalence with hamiltonian      77
Energy, total, equivalence with hamiltonian, in least-action principle      85Ч88
Energy, total, equivalence with hamiltonian, in reduced Hamilton Ч Jacobi equation      83
Equations of compatibility      204
Equilibrium      90
Equilibrium of elastic plate      260
Euler Ч Lagrange equations      20Ч23. See also Transformation
Euler Ч Lagrange equations, degenerate cases      25Ч26 134Ч135
Euler Ч Lagrange equations, first integrals      24Ч25 34 45 52
Euler Ч Lagrange equations, higher derivatives      46 61 64
Euler Ч Lagrange equations, in dynamics of particles      75 92
Euler Ч Lagrange equations, isoperimetric problems      50 95 134
Euler Ч Lagrange equations, several dependent variables      32Ч33 52 60
Euler Ч Lagrange equations, two or more independent variables      94 95 133 134
Euler's theorem on homogeneous functions      6
Extremizing function      23
Extremum      2 23
Extremum of double integral      93Ч95
Extremum of n-tuple integral      133
Extremum of triple integral      132Ч133
Fermat's principle      67Ч71
Fermat's principle in quantum mechanics      268Ч269
Flexural rigidity, of bar      217
Flexural rigidity, of plate      228
Force components, generalized      89Ч90
Fox, C.      319
Franklin, P.      3n. 319
Fundamental lemma      16Ч17 43Ч44
Generalized coordinates      73
Generalized force components      89Ч90
Generalized momenta      76
Generalized velocity components      74
Geodesies      18 26Ч27 61Ч63 65
Geodesies in plane      17Ч18 24
Geodesies on cone and cylinder      45
Geodesies on sphere      27Ч28 62Ч63
Geodesies on surface of revolution      28 45
Germer, L.H.      264 270
Goldschmidt discontinuous solution      31
Goursat, E.      3n. 319
Gradient      12
Green's theorem      12Ч15
Group velocity      290
Hamilton equations of motion      78
Hamilton equations of motion, transformed      79Ч82
Hamilton integral      74
Hamilton Ч Jacobi equation      82
Hamilton Ч Jacobi equation, in quantum mechanics      262 269 277
Hamilton Ч Jacobi equation, reduced      83 84
Hamilton's principle      74Ч75 77
Hamilton's principle, application to vibrations, of bar      218Ч221
Hamilton's principle, application to vibrations, of membrane      145 148Ч151 159
Hamilton's principle, application to vibrations, of plate      229Ч231
Hamilton's principle, application to vibrations, of string      96Ч97 105
Hamilton's principle, extended      88Ч90 92
Hamilton's principle, extended, application to motion, of elastic solid      205Ч209
Hamilton's principle, extended, application to motion, of membrane under transverse force      193
Hamilton's principle, extended, application to motion, of plate under transverse force      260
Hamilton's principle, extended, application to motion, of string under transverse force      116
Hamiltonian      76Ч77 79 82
Hartree model of the atom      286Ч290
Hedrick, E.R.      319
Helium atom      281
Helium atom, approximation of ground-state energy      281Ч286
Helium atom, singly ionized      275
Hermite differential equation      131
Hilbert, D.      viii 171n. 311 319
Homogeneous functions, Euler's theorem on      6
Hooke's law      203Ч204
Hydrogen atom      271Ч275
Hydrogen atom, energy levels      275
Hydrogen atom, spherically symmetric wave functions      274
Ince, E.L.      99n. 121n. 124n. 125n. 319
Indeterminacy, principle of      277
Integration by parts      5
Isoperimetric problems      48Ч57 65.
Isoperimetric problems, two or more independent variables      95 133Ч134
Jackson, D.      127n. 319
Jacobi, C.G.J.      vii. See also Hamilton-Jacobi equation
Jacobian      9Ч10 136 140Ч141 293
Kellog, O.D.      3n. 296n. 311n. 319
Kent, G.      viii
kinetic energy      73
Kinetic energy of elastic deformation      205
Kinetic energy of vibrating bar      218
Kinetic energy of vibrating membrane      143
Kinetic energy of vibrating plate      228
Kinetic energy of vibrating string      96
Kronecker delta      101
Lagrange equations of motion      75 92.
Lagrange multipliers      6 49 63.
Lagrangian      74
Laguerre polynomials      128Ч129 274
Laplace's equation      295 309
Laplacian      12
Laplacian, transformation of      138Ч142
Least action, principle of      85Ч88 268Ч269
Legendre differential equation      131
Legendre, A.M.      vii
Lemma, basic      16Ч17 43Ч44
Line integral      6 7
Linear independence      9
Love, A.E.H.      319
Maximum-minimum characterization of eigenvalues      see Eigenvalue-eigenfunction problems
Mechanics      see Dynamics of particles; Quantum mechanics
Membrane      142. See also Eigenvalue-eigenfunction problems; Vibrations
Membrane system, definition of      167
Membrane system, УnarrowerФ relationship      168
Minimum characterization of eigenvalues      see Eigenvalue-eigenfunction problems
Moment, bending      214Ч215. 250
Moment, of inertia (area)      214
Momenta, generalized      76
Morse, P.M.      259n.
Newton, I.      19 74 75
Normal derivative      7Ч8 11Ч12
Normalization      99. See also Eigenvalue-eigenfunction problems
Optics, geometric      see Fermat's principle
Orthogonality      101. See also Eigenvalue-eigenfunction problems; Schmidt process of orthogonalization
Parametric representation      34Ч36
phase velocity      266 267 269
Phase velocity of a particle      269
Piecewise continuity      4
Piecewise differentiability      4
Planck's constant      262n. 271
Planck, M.      271
Plate bending, by couples      224Ч228
Plate bending, by transverse-force distribution      260. See also Eigenvalue-eigenfunction problems; Vibrations
Poisson's ratio      203Ч204
potential energy      72 89
Potential energy of elastic deformation      205 212
Potential energy of elastic deformation, bar bent by couples      216Ч217
Potential energy of elastic deformation, plate bent by couples      227Ч228
Potential energy of elastic deformation, vibrating bar      218
Potential energy of elastic deformation, vibrating plate      228
Potential energy of electrostatic field      295
Potential energy of helium atom      281
Potential energy of many-electron atom      287
Potential energy of one-electron atom      272
Potential energy of vibrating membrane      143Ч145
Potential energy of vibrating membrane, elastic binding of edge      148
Potential energy of vibrating string      96
Potential, electrostatic      294
Potential, minimum characterization      295 311Ч312
quantum mechanics      261Ч293
Quantum mechanics, comparison with classical mechanics      276Ч277
Quantum mechanics, reduced Hamilton Ч Jacobi equation in      262 269 277.
Radiation      198 271
Rayleigh Ч Ritz method      241ra. See Ritz method
Rayleigh, Lord, J.W.S.      247n. 249n. 319
Ritz method      241
Ritz method for helium atom      281Ч286
Ritz method for vibrating membrane      188Ч192
Ritz method for vibrating plate      240Ч244
Ritz method for vibrating plate, clamped square      244Ч248
Ritz method for vibrating string      107Ч114
Ritz method in electrostatics      296
Ritz method in Hartree method      286Ч290
Ritz, W.      241
Rod      see Bar bending
Rope, hanging      56Ч57 64 66
Saint Ч Venant's principle      211n.
Scalar product      12
Schiff, L.I.      319
Schmidt process of orthogonalization      155Ч157
Schroedinger equation, first derivation      262Ч263
Schroedinger equation, for several particles      277Ч280
Schroedinger equation, for single particle      263 270
1 2
blank
–еклама
blank
blank
HR
@Mail.ru
       © Ёлектронна€ библиотека попечительского совета мехмата ћ√”, 2004-2019
Ёлектронна€ библиотека мехмата ћ√” | Valid HTML 4.01! | Valid CSS! ќ проекте