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| Weinstock R. — Calculus of variations with applications to physics & engineering |
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| Предметный указатель |
Schroedinger equation, second derivation 268—270
Schroedinger mechanics-optics analogy 268—269. See also Wave functions
Schroedinger, E. 261—264 268—270
Schwarz's inequality 44
Schwinger, J. vii
Separation of variables 98 160—161
Snell's law 68
Sokolnikoff, I.S. 201n. 204n. 217n. 319
strain 201—203
Strain tensor 202—203
Stress tensor 200—201
Stress vector 200
String, elastic see Eigenvalue-eigenfunction problems; Vibrations
Sturm — Liouville problem 119—131. See also Eigenvalue-eigenfunction problems
Sturm — Liouville problem, Bessel functions 129—130
Sturm — Liouville problem, Hermite equation 131
Sturm — Liouville problem, Laguerre polynomials 128—129
Sturm — Liouville problem, Legendre equation 131
Sturm — Liouville problem, singular cases 127—130
Surface forces 199—200 205
Surface forces on cylindrical bar 213
Surface forces on rectangular plate 225—226
Surface integral 11
Szego, G. 319
Szego, P. viii
Taylor's theorem for several variables 10 201—202
Thomson, G. P. 264 270
Transformation, canonical 79—82
Transformation, canonical, of Euler — Lagrange equation 126—127
Transformation, canonical, of Euler — Lagrange equation, two or three independent variables 135—138
Transformation, canonical, of laplacian 138—142
Transformation, canonical, of linear differential equation 121—127
Transformation, canonical, of multiple integral 10
Transformation, canonical, of Sturm — Liouville system 121—127
Transformation, canonical, to “normal, arc coordinates” 231—233
Uncertainty principle 277
Undetermined end points 36—41 51
Undetermined multipliers 6. See also Lagrange multipliers
Velocity components, generalized 74
Vibrations See also Eigenvalue-eigenfunction problems
| Vibrations, of bar 217—221
Vibrations, of bar, variable cross section 252
Vibrations, of gas 98
Vibrations, of membrane 142—145
Vibrations, of membrane, circular 194
Vibrations, of membrane, elastically held edge 148—153
Vibrations, of membrane, free edge 153
Vibrations, of membrane, general solution 158—160
Vibrations, of membrane, inhomogeneous boundary conditions 193
Vibrations, of membrane, natural frequencies 146. 160
Vibrations, of membrane, nodal lines 196
Vibrations, of membrane, rectangular 161—164
Vibrations, of membrane, under transverse force 193
Vibrations, of plate 228—236
Vibrations, of plate, circular 259—260
Vibrations, of plate, general solution 258
Vibrations, of plate, natural frequencies 237 248
Vibrations, of plate, rectangular 240—249
Vibrations, of plate, under transverse force 260
Vibrations, of string 95—98
Vibrations, of string, general solution 105—107
Vibrations, of string, natural frequencies 100
Vibrations, of string, under transverse force 116—117
Vibrations, of uniform density 117
Vibrations, of uniform density, in three dimensions 197—198
Wave equation 264. See also Schroedinger
Wave equation for a particle 270
Wave equation, time-independent 265
Wave functions 263. See also Hydrogen atom
Wave functions, physical interpretation 275—279
Wave mechanics see Quantum mechanics
Wave phenomena in general 264—268
Weierstrass, K. vii 311
Weinstein, A. 247ra.
Weinstock, E.B. viii
Whittaker, E.T. 319
Work 90
Work, of stretching membrane 143—144
Work, of stretching string 96
Young's modulus 203
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