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| Strauss W.A. — Partial Differential Equations: An Introduction |
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| Предметный указатель |
Potential electromagnetic 342
potential energy 39 173 218 286
Potential function 17 18 279 370
Potential square well 353
Potential velocity 23 147
Power series 388
Power series, method’of 239 242 253 274 394
Pressure 23 343
principal quantum number 281
probability 17 147
Propagation speed 37 53 204
Propagator of diffusion equation 48
Proton 17 353
Quadratic elements 214
Quantum electrodynamics (QED) 354
quantum mechanics 17—18 241—244 300
Quantum mechanics, angular momentum in 279—282
Quantum numbers 279 281
Quarks 353
Radar 14
Radial vibrations 256
Radiation 22 23 90 92 93
Radiation, condition 24 348
Raising and lowering operators 280
Rankine — Hugoniot formula 365
Rarefaction wave 363
Ray 231
Rayleigh quotient 284 298
Rayleigh — Ritz approximation 175 289—290
Rayleigh — Ritz approximation for Neumann condition 294
Reaction-diffusion problem 381
Reciprocity principle 180
Recursion relation 240 253 269 275 281
Reflected point 181 183
Reflection of waves 59—64 346—352
Reflection, coefficient 347 352 370
Reflection, method 55—64 181—188
Refraction of light 374
Region 386
Regular singular point 242 252—253 394
Relativity theory 39 231
Reservoir of heat 22
Resistance 12 13 87 144
Resonance 145
Retarded potential 234
Riemann function 323—324
Rigid wall, BC at 23
Robin condition 20 21 22
Robin condition, disk 167
Robin condition, half-line 58
Robin condition, interval 45 90—99 119
Robin condition, lowest eigenvalue 288
Robin condition, rectangle 155 251
Robin condition, uniqueness 168
Rodrigues’ formula 276
Rotation invariance 31 150—153
Rotations in quantum mechanics 280
Roundoff error 191
Russell, J.S. 367
Saddle point 375
Scalar potential 342
Scattering, acoustic 24
Scattering, and continuous spectrum 351—353
Scattering, by medium 347
Scattering, data 371
Scattering, inhomogeneous string 346
Scattering, inverse 369—372
Scattering, of light 22
Scattering, of plane wave by sphere 347—350
Schrodinger equation 17—18 23—24 89 237—244 280—282 350
Schrodinger equation, and angular momentum 279—282
Schrodinger equation, cubic 372 374
Schrodinger equation, finite interval 89
Schrodinger equation, free space solution 237—238
Schrodinger equation, harmonic oscillator 239
Schrodinger equation, hydrogen atom 241—244 280—282 351
Schwarz inequality 139
Second order equations 27—30
Second vanishing theorem 386
Secondary bifurcation 379
Seismic wave 14
Separated solution 82 245
Separation of variables 82—97
Separation of variables, in polar coordinates 159
Separation of variables, space variables 155 159 303
Separation of variables, special geometries 155
Separation of variables, time variable 302 345
Sharp images 223
Shock wave 2 359—366
Sign function, transform of 326
Simple transport 2 10
Sine-Gordon equation 372
Singular point of ODE 393
Singular Sturm — Liouville problem 299
Singularities, absence of 53 80 163
Singularities, and difference schemes 204
Singularities, of waves 53 64 232—233 322—323
Singularities, shocks 363—365
Snell’s law of reflection 377
Soap bubble 374 377
Soft wall, BC at 23
Solid light cone 217
Solid spherical harmonic 263
Solid vibrations 257—263
Solitons 367—372
Sound 22—23 344—346
Source function, diffusion equation 48 65 236 316 321—322 323—324 330—331
Source function, Klein — Gordon equation 356—357
Source function, wave equation 322—323 331—332
Source operator, diffusion equation 66
Source operator, wave equation 75 77 233
Source term, diffusion equation 65—68
Source term, wave equation 69—78 142 233—234
Space-time 217
Spacelike surface 231
Spacelike vector 231
Specific heat 16
Spectral lines 282
Spectrum 351
| speed of light 39 216—223 230 339
Speed of propagation 37 53 204
Sphere, surface area of 396
Spherical coordinates 152 257
Spherical harmonic 259 261—263 279 348
Spherical means 223
Spherical wave 37 40
Spring, at boundary 21
Square pulse, transform of 326
square well potential 353
Stability 25 43 70
Stability, numerical 194—199 203
Stability, of solitons 367—372
Stability, of stationary states 380—383
State, bound 241 351
State, buckled 380
State, ground 173 243 285
State, of electron 17 243
Stationary point 376
Stationary wave 16 146
Steady fluid flow 147
Steady state 16 24 154
Step function 318
Sturm — Liouville problem 298—300
Subdomain, eigenvalues for 308—310
Subharmonic function 188
Successive overrelaxation 210
Superposition principle 3 359
Supersonic airflow 14 359
surface 391
Surface, area of a sphere 396
Symmetric boundary conditions 115—119 176 247 299
Telegraph equation 358
Temperature 15—16 22 41 49 97
template 192
Tension 11 13
Term-by-term differentiation 389
Term-by-term integration 130 389
Tessera 266
Test function 314—315 319
Time slices 230
Timelike vector 231
Tiny perturbation 25
topology 26
translate 45
Translation 150
Transmission, coefficient 347 352 370
Transmission, line 13
Transmitted wave 347
Transport equation 10 233
Traveling plane wave 347
Traveling wave solution 368
Trial function for Dirichlet eigenvalues 285 289 308—309
Trial function for finite elements 212—215
Trial function for Neumann eigenvalues 294 309—310
Trial function for Robin eigenvalues 298
Triangulation 212
Truncation error 191
Tuning fork 100
Types of equations 27—31
Ultrahyperbolic PDE 30
Uncertainty principle 328
Underdetermined 25 26
Uniform convergence 121 135—136 389
Uniform norm 70
Uniqueness 25—26 42—43 70 149—150 173
Unstable state 380
Vanishing theorems 385—386
Variable coefficient equation 7—9 297—300
Vector, field 387
Vector, potential 342
Vector, space 5 118 251
Velocity potential 23 147
Vibrating bar 2 100 378
Vibrating drumhead 13—14 20 251—256 299
Vibrating string 11 20 23 25 32—37 324
Vibrating string, damped 40
Vibrating string, energy 90
Vibrating string, frequencies 85 256
Vibrating string, hammer blow 37 108—109
Vibrating string, inhomogeneous 346—347
Vibrating string, initial and boundary conditions 21
Vibrating string, plucked 35—36 39
violin string 87
Vorticity 345
Water wave 13 367
Waterbug 40 227
Wave equation 12 20 22 32 216 376
Wave equation, acoustics 22—23 345
Wave equation, ball 257—263
Wave equation, circle 251—256
Wave equation, energy 38 99 218
Wave equation, finite interval 61—64 82—85 89 97
Wave equation, general solution 32 222 227
Wave equation, half line, Dirichlet condition 59
Wave equation, in absence of boundaries 32 216
Wave equation, in space-time 216—235
Wave equation, inhomogeneous 69 233
Wave equation, inhomogeneous, boundary conditions 76 142 336
Wave equation, inhomogeneous, half-line 75
Wave equation, initial conditions 34 222 227
Wave equation, Lorentz invariance 221 —222
Wave equation, method of spherical means 223
Wave equation, negative eigenvalue 97
Wave equation, polar coordinates 251
Wave equation, scattering 347
Wave equation, spherical coordinates 257
Wave equation, two-dimensional 14 226—227
Wave equation, with a source 69—76 233—234
Wave, function 17
Wave, speed 12 364
Wave, with a source 69—76 233—234
Wave, with interaction 2 205
wedge 164—165
Welded rods 25
Well-posed problem 25—27 43—44 70
wronskian 352
Yang — Mills equations 355
Zabusky, N. 368
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