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Strauss W.A. Ч Partial Differential Equations: An Introduction
Strauss W.A. Ч Partial Differential Equations: An Introduction

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Ќазвание: Partial Differential Equations: An Introduction

јвтор: Strauss W.A.

јннотаци€:

Our understanding of the fundamental processes of the natural world is based to a large extent on partial differential equations (PDEs). The second edition of Partial Differential Equations provides an introduction to the basic properties of PDEs and the ideas and techniques that have proven useful in analyzing them. It provides the student a broad perspective on the subject, illustrates the incredibly rich variety of phenomena encompassed by it, and imparts a working knowledge of the most important techniques of analysis of the solutions of the equations.

In this book mathematical jargon is minimized. Our focus is on the three most classical PDEs, the wave, heat and Lapace equations. Advanced concepts are introduced frequently but with the least possible technicalities. The book is flexibly designed for juniors, seniors or beginning graduate students in science, engineering or mathematics.


язык: en

–убрика: ћатематика/

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

ed2k: ed2k stats

»здание: 1st edition

√од издани€: 1992

 оличество страниц: 440

ƒобавлена в каталог: 13.09.2008

ќперации: ѕоложить на полку | —копировать ссылку дл€ форума | —копировать ID
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ѕредметный указатель
$C^2$ function      35 386
$L^2$, convergence      122 124 249 295
$L^2$, metric      127
$L^2$, norm      126
Absolute convergence      388
Absorption      23 90 93
Acoustic impedance      23
Acoustics      22Ч23 344Ч346
action      375
Adiabatic fluid flow      344
Air resistance      12 87 144
Airy function      374
AmpereТs Law      340
Amplification factor      197
Analytic function      147
Annulus      165Ч166
Antidiffusion      26 53
Arbitrary function      3 32
Arc length      391
Associated Legendre function      277Ч278
Attenuation      40
Auxiliary conditions      9 19 25
Backward difference      190
Band-limited function      330
Bc      see УBoundary condition
Bessel function      253Ч254 268Ч274
Bessel function, asymptotic behavior      269
Bessel function, differential equation      268
Bessel function, generating function      273
Bessel function, half-integer order      270Ч271
Bessel function, in Klein Ч Gordon equation      357
Bessel function, integer order      252Ч254 271
Bessel function, normalizing constants      270
Bessel function, recursion relations      269Ч270
Bessel function, zeros      254 269
BesselТs differential equation      252 268
BesselТs differential equation, and scattering      348
BesselТs differential equation, Hankel function      271 348
BesselТs differential equation, Neumann function      271
BesselТs differential equation, order      268
BesselТs differential equation, solid vibrations in a ball      258
BesselТs differential equation, solution of      252Ч254 268Ч271
BesselТs differential equation, vibrations of a drumhead      252
BesselТs inequality      128
Bicharacteristic line      231
Bifurcation      379Ч383
Bilinear elements      214
Bohr      18 241
Bound state      241 351
Boundary      386
Boundary condition      20 21
Boundary condition, at infinity      23Ч24 167 181 241 279 300
Boundary condition, free      294
Boundary condition, homogeneous      20
Boundary condition, inhomogeneous      140Ч143 156 262 336
Boundary condition, inhomogeneous, expansion method      140Ч143
Boundary condition, inhomogeneous, Laplace transform method      336Ч337
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      115Ч119 176 247 299
Boundary point      386
Boundary source      67 140Ч142 337
Breaking wave      363
Brownian motion      15 49 147Ч148
Buckled state      380
Calculus of variations      374Ч377
Canal, water wave in      367
Cauchy Ч Riemann equations      147 154
Causality      37Ч38 69 204 218Ч221
Centered difference      190
Centered second difference      190
Chain rule      4 7 386
Chain, flexible      18
Chaos      26 54
Characteristic cone      216Ч218
Characteristic coordinates      33 71
Characteristic curve      8 9 359
Characteristic lines      6 10 33Ч34 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 $C^k$      386
Closed interval      384 Х
Closed set      386
Closure      386
Coefficient matrix      29Ч30
Comparison Test      388 389
Completeness      128 132 249 295 301 303
Completeness and continuous spectrum      244 351
Completeness and Gibbs phenomenon      132Ч138
Completeness, continuous version      326
Complex eigenvalues      86 116Ч117
Complex exponential      86 112
Complex integration      335
Compressive load      379
Concentration      10 14 49 250
Concentration, gradient      21
Conditional convergence      388
Conditions at infinity      23Ч24 167 181 241 279 300
Conservation of energy      38Ч39 99 218 368
Conservation of mass      10 343 368
Conservation of momentum      343 368
Constant coefficient equation      3 6Ч7
Constant of motion      370
Continuity equation      340 343
Continuous function      384Ч385
Continuous spectrum      244 351 370
Convection      52 333
Convergence of distributions      316Ч317
Convergence of Fourier series      124Ч126 132Ч136
Convergence of functions      121Ч123 388Ч389
Convergence of infinite series      388
Convergence, mean-square      122
Convergence, pointwise      121 388
Convergence, uniform      121 389
Convolution      78 328Ч329
Coordinate, change      387
Coordinate, method      7 33 71
CoulombТs law      340
Covariant derivatives      355
Crank Ч Nicolson scheme      198Ч200
Current density      340
Curve      391
Delay      40
Delta function      314Ч316
Delta function, approximate      314
Delta function, derivatives of      318
Delta function, Fourier transform of      326
DeMoivre formulas      112
Derivatives of integrals      390Ч391
Diamond-shaped regions      63
Difference equation      191
Differentiable function      385
Diffraction problem      346
Diffusion      14 19 21 86 381
Diffusion equation      16 20 26 41Ч52 85
Diffusion equation, backwards      26 53
Diffusion equation, ball      261
Diffusion equation, Crank Ч Nicolson scheme      198Ч199
Diffusion equation, cube      249
Diffusion equation, finite differences      193
Diffusion equation, finite interval      85 88
Diffusion equation, half-line      55Ч58
Diffusion equation, half-space      240
Diffusion equation, inhomogeneous      65 322
Diffusion equation, inhomogeneous, half-line      67
Diffusion equation, initial condition      45Ч52 78 85 235
Diffusion equation, one-dimensional      41
Diffusion equation, stability      43Ч44
Diffusion equation, three dimensional      15 235Ч237 249 261
Diffusion equation, uniqueness      42Ч43
Diffusion on the half-line      55Ч58
Diffusion on the whole line      45Ч50
Diffusion with a source      65Ч68
Diffusion, inequality      42
Diffusion, kernel      48Ч49
Dilated function      46
DIMENSION      5 13Ч14
Dimension, best possible      40 227
Dimension, of vector spaces      251
DiracТs equation      354Ч355
Directional derivative      6 8 20 387
Dirichlet condition      20 55 82
Dirichlet kernel      132Ч133 314 317
Dirichlet principle      173Ч174 284 374
Dirichlet problem in a ball      185
Dirichlet problem in a circle      159
Dirichlet problem in an annulus      165Ч166
Dirichlet problem on a half-line      55 59
Dirichlet problem, uniqueness      149 173
Discrete energy      207
Discrete spectrum      351
Discriminant, $\mathcal{D}$      29
Dispersive tail      369
Dispersive wave      2 367Ч374
Dissipative wave equation      12 358
distribution      315
Distribution in three dimensions      319
Distribution, convergence      316
Distribution, derivative      317
Div, $\nabla$      169 392Ч393
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      23Ч24
Drumhead      251Ч256 299
DuhamelТs formula      233
DuhamelТs principle      75
DТAlembert      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      264Ч267
Eigenvalue      86 88 91Ч96 121
Eigenvalue equation      92 94
Eigenvalue, asymptotics      304Ч312
Eigenvalue, complex      86 116
Eigenvalue, computation      288Ч292
Eigenvalue, dependence on domain      308
Eigenvalue, domain of arbitrary shape      283
Eigenvalue, double      247
Eigenvalue, minima of potential energy      283Ч287
Eigenvalue, minimum principle      284
Eigenvalue, negative      86 94Ч95 118
Eigenvalue, positive      91Ч94 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      180Ч181 187
Electrostatics, LaplaceТs equation      147
Electrostatics, PoissonТs formula      162
Elementary particles      353
Elliptic integral      373
Elliptic PDE      28 30
Elliptic PDE, inhomogeneous      301Ч302
Energy      38Ч39 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 Ч 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      27Ч30
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      376Ч378
Even extension      57 111 114
Even function      57 110
Existence      25Ч26
Expansion in eigenfunctions, method of      140Ч143 301Ч302
Expansive wave      363
Expected value of observable      18 328
Explicit scheme      193
Exponential, transform of      326
Extended function      61 109
External force      12 25Ч26 69
External source      15 65
Factorial      395
FaradayТs law      340
FermatТs principle      374
FickТs law      14 21 24
Finite differences      189
Finite differences, stability criterion      196 199 203
Finite element method      212Ч215 292
First order linear equation      6Ч9
First order linear equation, finite differences      208
First vanishing theorem      386
Flatland      39Ч40 227
Flea      37
Fluid      10 147 343Ч344 367Ч368
Forward difference      190
Four-dimensional divergence theorem      219
Fourier coefficients      102Ч104 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      111Ч112
Fourier series, change of scale      113
Fourier series, coefficients in      101 Ч107.
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      130Ч131
Fourier series, jump discontinuity      125 135 136Ч138
Fourier series, mean-square convergence      124
Fourier series, of odd and even functions      113
Fourier series, partial sums      132
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