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| Авторизация |
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| Kythe P.K., Puri P. — Partial differential equations and Mathematica |
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| Предметный указатель |
 space 145
Adaptive grid 321
Auxiliary system 23 28 31 40 325
Ball, open 217
Ball, open, surface area of 218
Ball, open, surface of 217
Base characteristic 24ff 28
Beam 157
Bessel functions 82 106
Binomial theorem 180
Biot number 148
Boundary conditions of first kind 3
Boundary conditions of second kind 3
Boundary conditions of third kind 3
Boundary conditions, Dirichlet 3 105 108 132 150 159 250 280 302 339 344 348
Boundary conditions, essential 276
Boundary conditions, mixed 3 250
Boundary conditions, natural 250
Boundary conditions, Neumann 3 105 250 347
Boundary conditions, nonhomogeneous 146ff
Boundary conditions, periodic 104
Boundary conditions, Robin 3
Boundary perturbations 31ff
Bounded variation 98ff
Calculus of variations 266
Cauchy data 56 237
Cauchy integral formula 183
Cauchy problem 39 55 235 237
Cauchy residue theorem 180
Cauchy — Kowalewsky theorem 55
Cauchy — Riemann operator 259
Cauchy's theorem 187
Characteristics 5 24ff 47ff 51 325
Characteristics, base 24ff 28
Characteristics, Cauchy's method of 39ff
Characteristics, curves 49
Circular drum 142
Class  218
Class  218
Class  218 221
Classification 4ff
Complement 218
Cone, normal 47
Cone, normal, Monge 47 48
Cone, normal, tangent 47 48
Contour integration 183ff 189 198
Convolution theorem 197 204 215
Cooling ball 144 153
Coordinates, characteristic 118
Coordinates, cylindrical 142
Coupling constant 8
d'Alembert's solution 76 96 97 122 213
De Moivre's theorem 70
Difference equation, consistent 328
Difference operator 328
Difference scheme, central 343
Difference scheme, Crank — Nicolson 332 334 335 344
Difference scheme, explicit 332 334
Difference scheme, implicit 332 334
Difference scheme, stability of 329
Differences, finite 321ff
Differences, finite, backward 323ff 332
Differences, finite, first order 322
Differences, finite, forward 323ff 330 331 332 334 336 344
Differences, finite, second order 323ff 330 335 336 339
Differential form 277
Differential operator, linear 68
Dirac distribution 220ff 232
Dirichlet — Dirichlet case 283
Discontinuity 53 90
distribution 220
Distribution, regular 220
Distribution, singular 220 221
Divergence theorem 14
Duhamel's principle 203
Eigenfunction expansion 82 103ff
Eigenfunctions 104 108
Eigenpair 104
Eigenvalue problem 117
Eigenvalues 104 148ff 155
Electrostatic potential 239
Electrostatics 8
Element, integral 47
Element, plane 47
Element, tangent 47
Envelope 39
Equation(s), 4th order 287
Equation(s), Berger's 8
Equation(s), Bessel's 106 241 286
Equation(s), biharmonic 9
Equation(s), characteristic 5 23ff 40 315
Equation(s), cubic Schroedinger 8
Equation(s), difference 328 339 343 348 349
Equation(s), diffusion 204 332
Equation(s), dissipative Klein — Gordon 8
Equation(s), dissipative sine-Gordon 9
Equation(s), eikonal 8
Equation(s), elliptic 4 6 50 132ff 238ff
Equation(s), Euler — Lagrange 269
Equation(s), Euler's 9 274 282 296
Equation(s), first order 22ff
Equation(s), Fokker — Planck 255
Equation(s), heat 7 346
Equation(s), heat conduction 15 16 125ff 177 293
Equation(s), heat transfer 14ff
Equation(s), Helmholtz 8 241ff
Equation(s), hyperbolic 4 6 50 53 118ff 244ff
Equation(s), Klein — Gordon 8
Equation(s), Korte de Vries(KdV) 9
Equation(s), Laplace 7 16 203 211 252 261 339
Equation(s), linear with constant coefficients 22ff 63ff
Equation(s), linear with variable constants 28ff
Equation(s), Maxwell's 9
Equation(s), Navier — Stokes 9 277
Equation(s), nonlinear first order 38ff
Equation(s), parabolic 4 6 50 125ff 231ff
Equation(s), Poisson's 8 159 275 280 283 302 339 342
Equation(s), Porous media 9
Equation(s), quadratic 4
Equation(s), quasi-linear first order 2 17 33ff
Equation(s), quasi-linear second order 49ff
Equation(s), quasi-linear, nonhomogeneous 74ff
Equation(s), Schroedinger 8 255
Equation(s), semilinear heat 8
Equation(s), semilinear Klein — Gordon 8
Equation(s), semilinear Poisson's 9
Equation(s), semilinear wave 8
Equation(s), sine-Gordon 8
Equation(s), Sturm — Liouville 105
Equation(s), telegrapher's 8
Equation(s), traffic 7
Equation(s), transient Fourier 235
Equation(s), transport 7 8
Equation(s), Tricomi 6 20
Equation(s), ultrahyperbolic 6
Equation(s), wave 7 97 180 212 334 346
Error, discretization 329
Error, truncation 328 344 345
Euler's formula 90
Existence 25 27 30
Field point 247
Finite differences 321ff
Flow, porous media 9
Flow, porous media, of viscoelastic fluid 189
Flow, porous media, of viscous fluid 189
Flow, porous media, traffic 16ff
Fourier coefficients 88
Fourier coefficients, cosine series 101
Fourier coefficients, cosine theorem 195
Fourier coefficients, integral theorem 195
| Fourier coefficients, sine series 100 102 127
Fourier coefficients, sine theorem 195
Fourier coefficients, theorem I 90
Fourier coefficients, theorem II 100
Fourier transform 195ff
Fourier transform of derivatives 196
Fourier transform, convolution theorem 196
Fourier transform, formula 198ff
Fourier transform, properties of 196
Fourier — Bessel expansion 108ff
Function(s), Bessel 82 106 245
Function(s), characteristic 218
Function(s), Dirac delta 178ff 217 221ff 248 263
Function(s), Hankel 241
Function(s), harmonic 224ff 25Iff
Function(s), Heaviside 54 178
Function(s), indicator 218 220
Function(s), modified Bessel 242
Function(s), monotone 99
Function(s), nondecreasing 99
Function(s), nonincreasing 99
Function(s), orthogonal 52ff
Function(s), periodic 90 97
Function(s), periodic Dirichlet 307
Function(s), test 219 287ff
Functional 219
Functionally independent 29ff
Functionally independent, continuous 220
Functionally independent, linear 219
Fundamental solution 177
General solution 2
Geometric optics 8
Gibbs phenomenon 102
Gravitational potential 221
Green's functions 217ff 230ff 250ff
Green's functions, second identity 257 351
Green's identity 13 225 232 350ff
Green's identity, first identity 227 351
grid 323 349
Harmonic motion 123
Harmonics 103
Heaviside function 54 178ff 220 224
Hilbert space 109 218
Hooke's law 10
Huygens' principle 247ff
Impulsive force 221
Infinite series 82
Initial condition 3 130
Initial curve 26ff 31
Inner product 82
Inner space 218
Integral surfaces 24 30 47
Isocline 46
Jacobian 50 52
Kernel 160
Laplace inversion theorem 183 187
Laplace inversion theorem, transform 161 162ff 179 180 183 189ff 233 236 244 245
Laplacian 108 142 231 238 257
Line integrals 267ff
Lipschitz condition 99
Maclaurin series 254
Mainardi — Codazzi relations 22
Mathematica functions 361ff
Mathematica functions, notebooks and packages list 368
Maximum principle 228ff
Mesh point 323 340
Method of characteristics 22ff
Method of moments 267 296
Method of separation of variables 51 82 103 117ff 235 307 312
Method of undetermined coefficients 78
Method of variation of parameters 78
Method, Cauchy's 39ff
Method, collocation 266 395
Method, Fourier series 150
Method, Galerkin 266 279ff
Method, Gauss elimination 330
Method, inverse operator 63ff
Method, Lagrange's 28
Method, least-square 267 295
Method, perturbation 305ff
Method, Rayleigh — Ritz 266 283ff
Method, weighted residual 266ff
Monge axis 47
Monge axis, cone 47
Monge axis, pencil 47
Multi-index 220
Neighborhood 218
Node 323 347
Norm 218
Notation 1
Operator pair 64
Operator, difference 328
Operator, difference, Laplace 108
Operator, difference, linear 68
Orthogonal eigenfunctions 222
Orthogonal eigenfunctions, expansions 82ff
Orthogonal eigenfunctions, functions 82
Orthogonal eigenfunctions, polynomials 86
Orthogonal eigenfunctions, set 83 88 108
Orthogonality 82ff 88
Orthonormal 83
Orthonormal set 83
Parabolic cylinder 35
Partial derivatives 1
Partial differential equations, elliptic 4 6 19 50
Partial differential equations, homogeneous 2
Partial differential equations, hyperbolic 4 6 19 50
Partial differential equations, linear 2
Partial differential equations, nonhomogeneous 2 4
Partial differential equations, order 1
Partial differential equations, parabolic 4 19 50
Partial differential equations, quasi-linear 2 17 33ff 325ff
Particular integral 65
Particular integral, solution 2 4 75
Particular integral, ultrahyperbolic 6
Perturbation methods 305ff
Point charge 221
Point charge, mass 221
Poisson integral representation 203
Polynomials, Chebyshev 1st kind 86
Polynomials, Chebyshev 2nd kind 86
Polynomials, Hermite 86
Polynomials, Jacobi 86
Polynomials, Laguerre 86
Polynomials, Legendre 86 87
Principal part 49
Quadratic form 6ff
Quantum field theory 8
Quantum field theory, mechanics 8
Quasi-linear equations 2 17
Reciprocity relations 231
Residual 279
Residue 181
Riemann — Lebesgue lemma 107
Rotation of axes 24 60ff
Series of orthogonal functions 88ff
Series, Fourier 90 109 156
Series, generalized Fourier 88
Series, infinite 82
Series, Maclaurin 254
Series, orthogonal 82
Series, Taylor's, truncated 321
Series, trigonometric Fourier 82 89 90ff 111
Shock waves 33
Solution, general 2 29 73
Solution, particular 2 4 75
Source point 230ff 233
Spherical coordinates 144ff
Strip 48
Strip, characteristic 48
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