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



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Íàçâàíèå: Partial Differential Equations: An Introduction

Àâòîð: Strauss W.A.

Àííîòàöèÿ:

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.


ßçûê: en

Ðóáðèêà: Ìàòåìàòèêà/

Ñòàòóñ ïðåäìåòíîãî óêàçàòåëÿ: Ãîòîâ óêàçàòåëü ñ íîìåðàìè ñòðàíèö

ed2k: ed2k stats

Èçäàíèå: 1st edition

Ãîä èçäàíèÿ: 1992

Êîëè÷åñòâî ñòðàíèö: 440

Äîáàâëåíà â êàòàëîã: 13.09.2008

Îïåðàöèè: Ïîëîæèòü íà ïîëêó | Ñêîïèðîâàòü ññûëêó äëÿ ôîðóìà | Ñêîïèðîâàòü ID
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Ïðåäìåòíûé óêàçàòåëü
$C^2$ 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      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 $C^k$      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, $\mathcal{D}$      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, $\nabla$      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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