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Weinberger H.F. Ч First course in partial defferential equations with complex variables and transform methods
Weinberger H.F. Ч First course in partial defferential equations with complex variables and transform methods

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Ќазвание: First course in partial defferential equations with complex variables and transform methods

јвтор: Weinberger H.F.

јннотаци€:

This book is an attempt to present the materials usually covered in such courses in a framework where the general properties of partial differential equations such as characteristics, domains of dependence, and maximum principles can be clearly seen. It is intended for a one-year course in partial differential equations, including the elementary theory of complex variables. (The first seven chapters, or the first six and the last chapter form a one-semester course, and the first five chapters a one-quarter course.)


язык: en

–убрика: ћатематика/јнализ/ƒифференциальные уравнени€/

—татус предметного указател€: √отов указатель с номерами страниц

ed2k: ed2k stats

√од издани€: 1995

 оличество страниц: 446

ƒобавлена в каталог: 18.04.2005

ќперации: ѕоложить на полку | —копировать ссылку дл€ форума | —копировать ID
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ѕредметный указатель
Absolute value      204
Absolutely integrable function      305 306
Analytic at infinity      278
Analytic continuation      216
Analytic extension      215
Analytic function      103 213
Approximation, in the mean      70 72
Approximation, in the mean, pointwise      70
Argand diagram      201
Argument      204
Associated Legendre functions      192 193
Asymptotic behavior of the Laplace transform      349 350
Bessel function      149 179Ч181 340Ч344
Bessel function with imaginary argument      149 340Ч344
BesselТs equation      176 179
BesselТs inequality      73
Bilinear transformation      249
Boundary mesh point      380
Boundary value problem, two-point      120Ч126 168
Branch cut      227 293Ч296
Calculus of residues      282Ч292 303 304
Cauchy criterion      209 307
Cauchy integral representation      264 266
Cauchy principal value      284 287 290 291 313 332
Cauchy-Riemann equations      211 213 223 237
CauchyТs Theorem      220 262
Chain rule for analytic functions      234
Change of scale      88Ч92 95
Characteristic (natural) frequency      154 186 187
Characteristic cone      153
Characteristic coordinates      46
Characteristic surface      154
Characteristic triangle      26
Characteristic values (eigenvalues)      65 124 160Ч168 171Ч178 180 186 187 391
Characteristics      18Ч21 38 42 43 45 59 115
Circle of convergence      210
Classification of partial differential operators      41Ч46 51 52 59
Closed curve      48 49
Complete set of functions      74 75 84 85 166 176Ч178
Completeness of eigenfunctions      166 176Ч178
Complex conjugate      203
complex derivative      214
complex numbers      201Ч206
Complex path integral      219
Conformal mapping      238Ч245 257Ч261
Conjugate harmonic function      212
Connected set      218
Conservation of energy      36
Continuity with respect to data      6 15 34 56 61 107 318 382
Contour integrals      220 261 262 263 271Ч277 282Ч296
convergence, in the mean      71 84 85 143 166 307 308 309
Convergence, in the mean, of Fourier series      79 80 81Ч88
Convergence, in the mean, pointwise      70
Convergence, in the mean, uniform      33 70 72 81 83 84 145 167 177 178 307
Convolution product      326 347
Convolution theorem      327 331 340 347
Cosine series      67 87 88
Cosine transform      321
Damped wave equation      112Ч115
Derivative of an analytic function      214
Derivatives of Bessel functions      179 180
Descent, method of      336
Difference quotient      375
Diffraction      369
Diffusion      59
Dimensional analysis      91
DiniТs test      79 80
DirichletТs principle      393 396
Discontinuities, propagation of      21 40 42 43 46 115 154
Divergence theorem      52 58
Domain      49 218
Domain of dependence      18 23 26 37 39 42 46 115 120 377 387 388
Domain of influence      20 23 26 40 42 46
Double Fourier series      141Ч145
DuhamelТs principle      371
dТAlembert solution      9 13 26 114
Eigenfunction      65 160Ч168 171Ч178 186
Eigenvalue      65 124 160Ч168 171Ч178 180 186 187 391
Elastic bar      6 91
Electrostatic potential      49 50
Elliptic coordinates      193
Elliptic differential operator      43 44 51 52
Energy      36 53 110 152Ч154
Entire function      217 266
Error bounds      86 97 98 102 145 266 386 389
Essential singularity      271
Existence      6
Exponential function      215 216 257
Extended plane      246
Finite difference approximation      375Ч383
Finite Fourier transform      129 130 186 197
Finite sine transform      127
Fixed boundary condition      23
Focusing      154
Fourier coefficients      72
Fourier cosine series      67 87 88
Fourier inversion theorems      314 315 317 321 332 338 359
Fourier series      65 66 67 77Ч88 141Ч145 298
Fourier sine series      65 66 67 87 88
Fourier transform      301 310Ч313 329Ч332 337Ч345
Free boundary condition      23
Frobenius method      179
GaussТs theorem (divergence theorem)      52 58
Generalized circle      247
GreenТs function      122Ч125 135Ч140 158 161 167 177 178 197 240 241
GreenТs function, one-sided      119
GreenТs Theorem      53 59
Harmonic conjugate      212
Harmonic function      52
Harmonic polynomials      104
Heat equation      58 60 66 92Ч95 108Ч110 126 318 322 327 329Ч332 355Ч361
Heat flow      50 58
Heat kernel      328
Heaviside function      347 367
Holder continuity      79 84
Holomorphic function      213
Homogeneous equation      30 31
HuyghenТs principle      336
Hyperbolic differential operator      42 44
Hyperbolic functions      227 258 259 260
Imaginary part      201
Implicit function theorem      230
Improperly posed problem      51 61
Infinite series evaluated by residues      289Ч292
Influence function      119 352
Initial value problems for ordinary differential equations      117Ч120
Integral equation      385
Integral of an analytic function      222
Interior mesh point      380
Inverse Fourier transform      314 315 317 319 321 332 338
Inverse function      229 230 239
Inverse Laplace transform      348
Inverse points      247 248
Inverse transformation      229 230 239
inversion      246 247
Isolated singularity      269
Iteration      383 384Ч391
Jacobian determinant      25 230
JordanТs lemma      303
KirchhoffТs formula      335
Laplace operator      49
Laplace operator in cylindrical coordinates      149
Laplace operator in polar coordinates      100
Laplace operator in spherical coordinates      188
Laplace transform      346 349 350
LaplaceТs equation      43 49 63 95Ч107 110Ч111 149Ч151 194Ч196 236Ч245 253 380Ч383
LaplaceТs solution of the heat equation      331
Laurent series      278Ч281
Least squares approximation      70 72
Legendre functions, associated      192 193
Legendre polynomials      191 192 193
Limit of a complex sequence      208
Linear fractional transformation      249
Linear operator      29
Linear partial differential equation      30
Linear problem      30
Linear transformation      246
LiouvilleТs theorem      266 267
Logarithm      224 230
LТHopitalТs Rule      271
Mapping      238
Mapping, conformal      238Ч245 257Ч261
mapping, one-to-one      238
Mathematical model      5
Maximum principle      55Ч57 59 61 94 97 101 108 111 265 320 381
Mean convergence      71 84 85 143 166 307 308 309
Mean value theorem      103 196
Mean-square deviation      71
Mellin inversion theorem      348
Membrane      48 54 182Ч184
Mesh point      376
Method of descent      336
Method of successive approximations      384Ч391
Minimum principle for eigenvalues      164Ч165 168
Moebius transformation      249
Monotonicity of eigenvalues      173 174 175
MoreraТs theorem      223
Multiple Fourier series      141Ч145
Multiple Fourier transform      329Ч332
Multiple-valued analytic function      223 224 227 293Ч296
Multiply connected domain      220
Natural (characteristic) frequencies      154 186 187
nearest neighbors      380
Nonhomogeneous wave equation      25
Normal modes      154 186 187
Null function      308 309 310
One-sided GreenТs function      119
One-to-one mapping      238
Open set      49 218
Operational formulas (rules)      324Ч325 331 340 346 351
Operator      29
Order of a pole      270
Order of a zero      270
Ordinary differential equations      117Ч126 167Ч168 351Ч354
Orthogonal functions      71 143 161
Oscillation theorem      174 175
Parabolic differential operator      42 44 59
ParsevalТs equation      74 75 85 142 166 177 312 313 322 332
Partial differential operator      29
path integral      219
Phragmen Ч Lindelof theorem      107 111 112
Point at infinity      246
Pointwise convergence      70
PoissonТs equation      48 49 50 129 155Ч158 196Ч199
PoissonТs integral formula      102 103 139 196 199 252
PoissonТs solution of the wave equation      335
Polar representation of a complex number      204 216
Pole      270
Power function      227 260
Power series      179 190 209Ч219
Principal value      284 287 290 291 313 332
Principle of superposition      33
Propagation of discontinuities      21 40 42 43 46 115 154
Properly posed problem      6 51 61 125 377 382
Radius of convergence      210 213 217
Ratio Test      213
Rayleigh quotient      163
Rayleigh Ч Ritz method      393Ч395
Real part      201
Reciprocity law      122
Recursion formulas for Bessel functions      179 180
Removable singularity      269
Residue      273 274
Residue theorem      275 283 284 285 290 303 304
Resonance      187
Riemann Ч Leuesgue lemma      76 316
Riesz Ч Fischer theorem      308 309
Rodrigues formula      191
RoucheТs Theorem      278
Scaling      88Ч92 95
SchwarzТs inequality      82 83 84 306
Self-adjoint form of an ordinary differential equation      117
Separable partial differential operator      63 66Ч68
Separation of variables      63Ч69 92Ч103 379
Separation theorem      173
Separation theorem for eigenvalues      175
Series evaluated by residues      289Ч292
sgn      433
Shift formula (shift rule)      324 340
Simple closed contour      220
Simply connected domain      49 220
Sine series      65Ч67 87 88
Sine transform      321
Singular differential equation      176 177
Singularity      217 269
Singularity, essential      271
Singularity, isolated      269
Singularity, removable      269
Sound waves      7 336 362
Specific heat      58
Spherical harmonics      192 193 195
Square integrable function      306 310
Stability condition      378 379
Stokes rule      370
StokesТ Theorem      53
String      1 5
Strong maximum principle      265
Successive approximations      384Ч391
Superposition      33
Taylor series      214 215 231Ч235
Tchebysheff polynomials      73
TelegrapherТs equation      115
Temperature      50 58
Term-by-term integration of Fourier series      75
thermal conductivity      58
ThomsonТs principle      397
Three-dimensional wave equation      152Ч154 333Ч336
Triangle inequality      205 307
Trigonometric Fourier series      77Ч88
Trigonometric functions of a complex variable      227 260
Two-dimensional wave equation      362 Ч371 378Ч379
Two-point boundary value problem      120Ч126 168
Unbounded domains      253Ч256
Uniform convergence      33 70 72 81 83 84 145 167 177 178 307
Uniqueness      6 34 39 53 56 59Ч61 64 107 110 152Ч155 318 382
Vibrating membrane      48 54 182Ч184
Vibrating string      1 5
Wave equation, damped      112Ч115
Wave equation, damped, one-dimensional      9Ч27 66
Wave equation, damped, three dimensional      152Ч154 333Ч336
Wave equation, damped, two-dimensional      362Ч371 378Ч379
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