Главная    Ex Libris    Книги    Журналы    Статьи    Серии    Каталог    Wanted    Загрузка    ХудЛит    Справка    Поиск по индексам    Поиск    Форум   
blank
Авторизация

       
blank
Поиск по указателям

blank
blank
blank
Красота
blank
Kanwal R.P. — Linear Integral Equations: Theory and Techniques
Kanwal R.P. — Linear Integral Equations: Theory and Techniques

Читать книгу
бесплатно

Скачать книгу с нашего сайта нельзя

Обсудите книгу на научном форуме



Нашли опечатку?
Выделите ее мышкой и нажмите Ctrl+Enter


Название: Linear Integral Equations: Theory and Techniques

Автор: Kanwal R.P.

Аннотация:

Many physical problems that are usually solved by differential equation methods can be solved more effectively by integral equation methods. Such problems abound in applied mathematics, theoretical mechanics, and mathematical physics. The second edition of this widely used book continues the emphasis on applications and presents a variety of techniques with extensive examples. Additional material has been added throughout the book. The chapters dealing with differential equations and singular integral equations have been expanded considerably. Thus the book is ideal as a text for a beginning graduate level course. Its treatment of boundary value problems and an extended and up-to-date bibliography will also make the book useful to research workers in many applied fields.


Язык: en

Рубрика: Математика/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 1971

Количество страниц: 296

Добавлена в каталог: 15.04.2008

Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID
blank
Предметный указатель
$\mathscr{L}_2$-function      4 26 30 136 147 148 153 159
$\mathscr{L}_2$-kernel      4 26 30 133 141 143 144 146 149—152 157 158 160 161 165
$\mathscr{L}_2$-space      133 134 136 137 158 159
Abel integral equation      167 200 206 211
Acoustic diffraction by annular disk      120
Acoustic diffraction by rigid body      280
Acoustic diffraction by rigid disk      129
Acoustic diffraction by soft body      279
Acoustic diffraction by soft disk      118
Acoustic diffraction by soft sphere      280
Adjoint      18 72
Airfoil equation      209
Analytic function      30
Approximation method      23
Associated Legendre function      105
Bessel equation      83
Bessel function      104 114 138 216 232 241 277 289
Bessel operator      92
Bessel’s inequality      136 140 144 195
beta function      169 170
Biharmonic equation      123
Bilinear form      142 144 148 150 165
Born approximation      131
Boundary effects      258 273
Boundary value problem      64 67 72 76 78 79ff
Branch point      288
Capacity of circular disk      244
Capacity of condenser      255
Capacity of conductor      253 254
Capacity of sphere      248 249
Cauchy principle value      170 174 175 177
Cauchy sequence      134
Cauchy type integral      176—178 180 181 184 187
Cauchy — Riemann equations      186
Cauchy’s integral formula      128
Cauchy’s integral theorem      128 179
Charge density      101 103
Compact set      159
Complete continuity      159—161
Completeness      134 150
Consistency condition      81 82 86—88 102 109
Contour integral      176 288
Convergence in mean      136 147
Convolution integral      5 197—200
Crack problem      276 278
Degenerate kernel      4 8
Difference kernel      5 199
Dilation vector      130 272—274
Dimensionless parameter      see "Perturbation parameter"
Dirac delta function      70
Dirac delta function, sifting property of      70 96 217
Dirichlet condition      94
Dirichlet problem      98—100 107 117 129
Displacement vector      130
Distributions      71
Divergence theorem      95
Eigenfunction      6ff
Eigenvalue      6ff
Eigenvalue, index of      17
Eigenvalue, multiplicity of      17 55 57 141
Elastic bar      68
Elastic bar, bending rigidity of      69
Elastic bar, transverse oscillations of      68
Elastic half-space      120 284
Elastic half-space, torsion      216 222
Elastic half-space, torsional oscillations      120 231 237
Elastic medium, cavity in      275
Elastic medium, crack in      276
Elastic medium, inclusions in      275 284
Elastic medium, Lame’s constants of      130
Elasticity      272 275 276
Elastodynamics      273 274
Elastostatics      272
Electrostatic potential      96 254 283
Electrostatic potential of annular disk      113
Electrostatic potential of axially symmetric conductor      113
Electrostatic potential of circular disk      103 110 243
Electrostatic potential of spherical cap      245 246
Electrostatics      253 263
Entire function      35 40
Exciting force      274
Extremal principle      161
Faltung      6
Far-field amplitude      281 282
Fourier expansion      114 135 136 146—148 157 262 263 277
Fourier integral      194
Fourier series      see "Fourier expansion"
Fourier transform      66 114 195 196 198
Fredholm alternative      14 20
Fredholm integral equation      2
Fredholm theory      41
Fredholm’s determinant      45 46
Fredholm’s minor      52 53 60
Fredholm’s series      45 47—49 55 58
Fredholm’s theorem      16 43 48 51 57 59
Functional analysis      158
Fundamental solution      96 116
Geometric series      28 32 38 111
Gram — Schmidt procedure      135 140 141 165
Green’s formula      72
Green’s function      72 77 80 116 121ff
Green’s function, causal      75
Green’s function, free space      96 107 116 118
Green’s function, modified      86 87
Green’s identities      95
Green’s tensor      123 124 126 130 258 268 272—274
Green’s vector      123 124 126 258 268
Hankel function      232 241
Harmonic function      95 97 102 186 262
Heat conduction      126
Heaviside function      71 78
Helmholtz equation      94 96 116 118 121
Hermitian matrix      142
Hilbert formula      187—189
Hilbert kernel      184 185 190
Hilbert space      133 137
Hilbert transform, finite      207—209 212
Hilbert transform, infinite      210 213
Hilbert type integral equation      187 188 190 209
Hilbert — Schmidt theorem      146 148 150 151 165
Hoelder condition      175 177
Hoelder continuous      175—178 180
Hypergeometric function      226 227
Index of eigenvalue      17
Influence function      75
Initial value problem      61 67 72—74ff
Inner product      6 134
Integrable function      3
Integral equation      3
Integral equation of first kind      2
Integral equation of second kind      3
Integral equation of third kind      3
Integral equation, Fredholm      2
Integral equation, homogeneous      3
Integral equation, linear      2
Integral equation, singular      3 167ff
Integral equation, Volterra      3
Integral representation formula      61 75 96 107 255 260—262 265
Integral transform methods      195
Integrodifferential equation      38
Iterated kernels      27 29 31 35 199
Iterative scheme      26
Kernel      3
Kernel, complex-symmetric      132
Kernel, degenerate      4 8ff
kernel, hermitian      13 132
Kernel, negative definite      149 150
Kernel, nonnegative definite      149 150
Kernel, nonpositive definite      149 150
Kernel, positive definite      149 150 164
Kernel, separable      4 8ff
kernel, symmetric      5 133
Kernel, truncated      143 145 148
Kinematic viscosity      124
Kronecker delta      104
Lagrange multipliers      162
Laplace equation      94 95 101 107ff
Laplace transform      70 197—199 201—203 205
Laplacian      95
Lebesgue integral      4
Legendre function      105
Legendre operator      90
Legendre polynomial      138 164 247 256 281 283
Linear independence      5
Linear operator      2 196
Lipschitz condition      175
Low — Reynolds number hydrodynamics      257
Maximum-minimum principle      161
Mehler — Dirichlet integral      247
Mercer’s theorem      149 150
Method of images      107 110 121
Method of successive approximations      26
Metric      133
Metric, natural      133 134
Metric, space      134
Minkowski inequality      8 133
Mixed boundary value problem      94 214
Modified Bessel function      114 138 277
Navier — Cauchy equations      272
Neumann condition      94
Neumann problem      99 101—103 109 117 280
Neumann series      27 29—31ff
Norm      6 133
Operator, adjoint      72 180
Operator, Bessel      92
Operator, bounded      158—160
Operator, completely continuous      159—161
Operator, Fredholm      134
Operator, Legendre      90
Operator, linear      2 196
Operator, method      158
Operator, self-adjoint      72 89 90 93 147
Ordinary differential equation      61
Orthogonal functions      6 135
Orthonormal functions      135—138ff
Oseen flow, rotary motion in      269 271
Oseen flow, steady      124
Oseen flow, steady-state vibrations in      283
Oseen flow, translational motion in      268
Parseval’s identity      137 157
Partial differential equation      94
Partial differential equation, elliptic      94
Partial differential equation, hyperbolic      94
Partial differential equation, parabolic      94
Perturbation methods      250
Perturbation parameter      120 227 239 240 250 257 263
Picard’s method      26
Plemelj formulas      178 180 182 185
Poincare — Bertrand formula      179 181 182
Poisson’s equation      94 96 101
Poisson’s integral formula      107 128
Pole      176 211
Potential layer      97 117
Potential layer, double      97 98 100 103 129 280
Potential layer, single      97 101 102 117 127 129 279
Potential layer, volume      97 117 127
Pressure      123
Principal axes of resistance      259
Radiation condition      118 129 274 279 281
Rayleigh — Ritz method      161 162 163 164
Regular curve      176
Regularity conditions      3
Representation formula      see "Integral representation formula"
Residue      211
Resistance tensor      258—260
Resolvent kernel      11-13ff
Reynolds number      124 125 257 269
Riemann Hilbert problem      182 183
Riemann integral      4 173 175
Riesz — Fischer theorem      136 149 152
Scalar product      6
Scattering cross section      282
Schroedinger equation      131
Schwarz inequality      6 28 29 38 133ff
Separable kernel      4 8
shear modulus      120
Shear viscosity      261
Sine transform      195
Singular integral equation      3 167
Singular integral equation, weakly      170
Sonine integral      217
Source density      263 266 271
Spherical harmonics      105
Square integrable function      3
Stokes flow, boundary effects in      258
Stokes flow, longitudinal oscillations in      260
Stokes flow, rotary motion in      261 269 275
Stokes flow, rotary oscillations in      264 271
Stokes flow, steady      123 257
Sturm — Liouville problem      80
Tangential stress      263
Taylor’s Theorem      259
Three-part boundary value problem      219
Three-part boundary value problem, generalized      234
torque      228 265 267 268 271 283
Trace of kernel      133 149
Traction field      273
Traction tensor      273 275
TRANSPOSE      18—20 57—60
Trial function      163
Two-part boundary value problem      214
Two-part boundary value problem, generalized      229
Variational Principle      161
Velocity potential      118
Velocity vector      123
Volterra integral equation      3
Weakly singular kernel      170
wronskian      74
blank
Реклама
blank
blank
HR
@Mail.ru
       © Электронная библиотека попечительского совета мехмата МГУ, 2004-2017
Электронная библиотека мехмата МГУ | Valid HTML 4.01! | Valid CSS! О проекте