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| Ïîèñê ïî óêàçàòåëÿì |
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| Strauss W.A. — Partial Differential Equations: An Introduction |
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| Ïðåäìåòíûé óêàçàòåëü |
 function 35 386
 , convergence 122 124 249 295
, metric 127
, norm 126
Absolute convergence 388
Absorption 23 90 93
Acoustic impedance 23
Acoustics 22—23 344—346
action 375
Adiabatic fluid flow 344
Air resistance 12 87 144
Airy function 374
Ampere’s Law 340
Amplification factor 197
Analytic function 147
Annulus 165—166
Antidiffusion 26 53
Arbitrary function 3 32
Arc length 391
Associated Legendre function 277—278
Attenuation 40
Auxiliary conditions 9 19 25
Backward difference 190
Band-limited function 330
Bc see “Boundary condition
Bessel function 253—254 268—274
Bessel function, asymptotic behavior 269
Bessel function, differential equation 268
Bessel function, generating function 273
Bessel function, half-integer order 270—271
Bessel function, in Klein — Gordon equation 357
Bessel function, integer order 252—254 271
Bessel function, normalizing constants 270
Bessel function, recursion relations 269—270
Bessel function, zeros 254 269
Bessel’s differential equation 252 268
Bessel’s differential equation, and scattering 348
Bessel’s differential equation, Hankel function 271 348
Bessel’s differential equation, Neumann function 271
Bessel’s differential equation, order 268
Bessel’s differential equation, solid vibrations in a ball 258
Bessel’s differential equation, solution of 252—254 268—271
Bessel’s differential equation, vibrations of a drumhead 252
Bessel’s inequality 128
Bicharacteristic line 231
Bifurcation 379—383
Bilinear elements 214
Bohr 18 241
Bound state 241 351
Boundary 386
Boundary condition 20 21
Boundary condition, at infinity 23—24 167 181 241 279 300
Boundary condition, free 294
Boundary condition, homogeneous 20
Boundary condition, inhomogeneous 140—143 156 262 336
Boundary condition, inhomogeneous, expansion method 140—143
Boundary condition, inhomogeneous, Laplace transform method 336—337
Boundary condition, inhomogeneous, method of shifting the data 143
Boundary condition, mixed 89
Boundary condition, periodic 90 112 160
Boundary condition, radiation 24
Boundary condition, Robin 96 97 98
Boundary condition, symmetric 115—119 176 247 299
Boundary point 386
Boundary source 67 140—142 337
Breaking wave 363
Brownian motion 15 49 147—148
Buckled state 380
Calculus of variations 374—377
Canal, water wave in 367
Cauchy — Riemann equations 147 154
Causality 37—38 69 204 218—221
Centered difference 190
Centered second difference 190
Chain rule 4 7 386
Chain, flexible 18
Chaos 26 54
Characteristic cone 216—218
Characteristic coordinates 33 71
Characteristic curve 8 9 359
Characteristic lines 6 10 33—34 38 53
Characteristic lines, finite interval 62
Characteristic lines, half-line 60
Characteristic surface 230 232
Characteristic triangle 38 69
Characteristic vector 231
Charge density 340
Chemical reaction 381
Chemistry 18
Chinese bells 265
Class  386
Closed interval 384 •
Closed set 386
Closure 386
Coefficient matrix 29—30
Comparison Test 388 389
Completeness 128 132 249 295 301 303
Completeness and continuous spectrum 244 351
Completeness and Gibbs phenomenon 132—138
Completeness, continuous version 326
Complex eigenvalues 86 116—117
Complex exponential 86 112
Complex integration 335
Compressive load 379
Concentration 10 14 49 250
Concentration, gradient 21
Conditional convergence 388
Conditions at infinity 23—24 167 181 241 279 300
Conservation of energy 38—39 99 218 368
Conservation of mass 10 343 368
Conservation of momentum 343 368
Constant coefficient equation 3 6—7
Constant of motion 370
Continuity equation 340 343
Continuous function 384—385
Continuous spectrum 244 351 370
Convection 52 333
Convergence of distributions 316—317
Convergence of Fourier series 124—126 132—136
Convergence of functions 121—123 388—389
Convergence of infinite series 388
Convergence, mean-square 122
Convergence, pointwise 121 388
Convergence, uniform 121 389
Convolution 78 328—329
Coordinate, change 387
Coordinate, method 7 33 71
Coulomb’s law 340
Covariant derivatives 355
Crank — Nicolson scheme 198—200
Current density 340
Curve 391
Delay 40
Delta function 314—316
Delta function, approximate 314
Delta function, derivatives of 318
Delta function, Fourier transform of 326
DeMoivre formulas 112
Derivatives of integrals 390—391
Diamond-shaped regions 63
Difference equation 191
Differentiable function 385
Diffraction problem 346
Diffusion 14 19 21 86 381
Diffusion equation 16 20 26 41—52 85
Diffusion equation, backwards 26 53
Diffusion equation, ball 261
Diffusion equation, Crank — Nicolson scheme 198—199
Diffusion equation, cube 249
Diffusion equation, finite differences 193
| Diffusion equation, finite interval 85 88
Diffusion equation, half-line 55—58
Diffusion equation, half-space 240
Diffusion equation, inhomogeneous 65 322
Diffusion equation, inhomogeneous, half-line 67
Diffusion equation, initial condition 45—52 78 85 235
Diffusion equation, one-dimensional 41
Diffusion equation, stability 43—44
Diffusion equation, three dimensional 15 235—237 249 261
Diffusion equation, uniqueness 42—43
Diffusion on the half-line 55—58
Diffusion on the whole line 45—50
Diffusion with a source 65—68
Diffusion, inequality 42
Diffusion, kernel 48—49
Dilated function 46
DIMENSION 5 13—14
Dimension, best possible 40 227
Dimension, of vector spaces 251
Dirac’s equation 354—355
Directional derivative 6 8 20 387
Dirichlet condition 20 55 82
Dirichlet kernel 132—133 314 317
Dirichlet principle 173—174 284 374
Dirichlet problem in a ball 185
Dirichlet problem in a circle 159
Dirichlet problem in an annulus 165—166
Dirichlet problem on a half-line 55 59
Dirichlet problem, uniqueness 149 173
Discrete energy 207
Discrete spectrum 351
Discriminant,  29
Dispersive tail 369
Dispersive wave 2 367—374
Dissipative wave equation 12 358
distribution 315
Distribution in three dimensions 319
Distribution, convergence 316
Distribution, derivative 317
Div,  169 392—393
Divergence theorem 19 393
Domain 20 386
Domain of dependence 38 61 69 204 221 234
Domain of influence 38 221
Domain, conditions at infinity 23—24
Drumhead 251—256 299
Duhamel’s formula 233
Duhamel’s principle 75
D’Alembert 35 85
Echoes 40
Eggs Fourier 263
Eigenfunction 86 88 91 95 116 246
Eigenfunction of the spherical surface 259
Eigenfunction, expansion 96 121 246
Eigenfunction, nodes 264—267
Eigenvalue 86 88 91—96 121
Eigenvalue equation 92 94
Eigenvalue, asymptotics 304—312
Eigenvalue, complex 86 116
Eigenvalue, computation 288—292
Eigenvalue, dependence on domain 308
Eigenvalue, domain of arbitrary shape 283
Eigenvalue, double 247
Eigenvalue, minima of potential energy 283—287
Eigenvalue, minimum principle 284
Eigenvalue, negative 86 94—95 118
Eigenvalue, positive 91—94 248
Eigenvalue, zero 88 94 97
Eikonal equation 232
Elastic force 12
Electric potential 147 180
electromagnetic field 22 39 339
Electron 17 241 354
Electrostatics, electric potential 180—181 187
Electrostatics, Laplace’s equation 147
Electrostatics, Poisson’s formula 162
Elementary particles 353
Elliptic integral 373
Elliptic PDE 28 30
Elliptic PDE, inhomogeneous 301—302
Energy 38—39 99 109 131 173 218 368
Energy, action defined and 375
Energy, discrete 207
Energy, KdV equation 368
Energy, levels 18 240 241 243
Energy, lowest 173 285
Energy, method 43 173 279
Energy, Yang — Mills equations 355
entropy 366 378
Entropy, criterion 366
Enumeration function 305
Equation, fourth-order 100
Equation, inhomogeneous elliptic 301
Equation, of motion 344
Equation, of state 344
Equation, second order 27—30
Equilibrium 16 25 146
Error, function Erf 50
Error, truncation, round off 191
Euler 85
Euler, differential equation 160 394
Euler, equation in calculus of variations 376—378
Even extension 57 111 114
Even function 57 110
Existence 25—26
Expansion in eigenfunctions, method of 140—143 301—302
Expansive wave 363
Expected value of observable 18 328
Explicit scheme 193
Exponential, transform of 326
Extended function 61 109
External force 12 25—26 69
External source 15 65
Factorial 395
Faraday’s law 340
Fermat’s principle 374
Fick’s law 14 21 24
Finite differences 189
Finite differences, stability criterion 196 199 203
Finite element method 212—215 292
First order linear equation 6—9
First order linear equation, finite differences 208
First vanishing theorem 386
Flatland 39—40 227
Flea 37
Fluid 10 147 343—344 367—368
Forward difference 190
Four-dimensional divergence theorem 219
Fourier coefficients 102—104 113 116 248
Fourier cosine series 88
Fourier cosine series, and boundary conditions 111
Fourier cosine series, coefficients in 103
Fourier integral 325 351
Fourier series 84 103 121
Fourier series, and boundary conditions 111—112
Fourier series, change of scale 113
Fourier series, coefficients in 101 —107.
Fourier series, completeness 128 132 249 295 301 303
Fourier series, complex form 112
Fourier series, differentiation 126 130 319
Fourier series, divergent 121
Fourier series, double 158 255
Fourier series, error 127
Fourier series, full 103 112
Fourier series, general 248
Fourier series, integration 130—131
Fourier series, jump discontinuity 125 135 136—138
Fourier series, mean-square convergence 124
Fourier series, of odd and even functions 113
Fourier series, partial sums 132
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