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Powers D.L. Ч Boundary Value Problems: And Partial Differential Equations
Powers D.L. Ч Boundary Value Problems: And Partial Differential Equations

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Ќазвание: Boundary Value Problems: And Partial Differential Equations

јвтор: Powers D.L.


Boundary Value Problems is the leading text on boundary value problems and Fourier series for professionals and students in engineering, science, and mathematics who work with partial differential equations.

In this updated edition, author David Powers provides a thorough overview of solving boundary value problems involving partial differential equations by the methods of separation of variables. Additional techniques used include Laplace transform and numerical methods. Professors and students agree that Powers is a master at creating examples and exercises that skillfully illustrate the techniques used to solve science and engineering problems.

*CD-ROM with animations and graphics of solutions, additional exercises and chapter review questions-all new in the Fifth Edition
* Nearly 900 exercises ranging in difficulty from basic drills to advanced problem-solving exercises
* Many exercises based on current engineering applications
* An Instructor's Manual and Student Solutions Manual are available separately

язык: en

–убрика: ћатематика/

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

ed2k: ed2k stats

»здание: 5th edition

√од издани€: 2005

 оличество страниц: 520

ƒобавлена в каталог: 22.05.2008

ќперации: ѕоложить на полку | —копировать ссылку дл€ форума | —копировать ID
ѕредметный указатель
Acoustic vibrations      235
Aluminum nitride, oxygen removal from      156
Antenna vibrations      226
Approximation by Fourier series      91Ч94
Arbitrary periods      64Ч65
Bad discontinuities      74Ч75 79
Band-limited functions      121Ч123
Bars, insulated      157Ч161. See also heat conduction problems
Beam vibrations      225
Bessel functions, integrals of      440
Bessel inequality      92Ч93
boundary conditions      See also initial value-boundary value problems
Boundary conditions of the first kind      See entries at Dirichlet
Boundary conditions of the second kind      See entries at Neumann
Boundary conditions of the third kind      139
Boundary conditions, limitations of product method      281Ч282
Boundary conditions, mixed      139
Boundary conditions, potential equation      See potential equation
Boundary conditions, wave equation      217Ч220 229
Boundary value problems      26Ч34. See also initial value-boundary value problems
Boundary value problems, Fourier series applications with      119Ч120
Boundary value problems, Green's functions      23 43Ч49
Boundary value problems, potential equation      256Ч257
Boundary value problems, singular      38Ч41
Boundedness      40Ч41
Boussinesq equation      211
Brownian motion      204
Buckling of a column      32Ч34
Burger's equation      209
Cable, hanging      26Ч29
Calculus      436Ч438
Cantilevered beam      226
Car antenna vibrations      226
Catenaries      35
Cauchy Ч Euler equation      6Ч7 38 277
Cesaro summability      131
Chain rule      232
Characteristic equation      3 10
Characteristics, method of      246
Classifications of partial differential equations      280Ч282
Coefficients of Fourier series      See Fourier series
Column buckling      32Ч34
Complementary error function      200 202
Complex coefficients, potential equation analysis      284
Complex Fourier coefficients      113Ч115
Complex Fourier coefficients, sampling theorem      121Ч124
conditions      See boundary conditions; initial condition
Conduction of heat      See heat conduction problems
Conservation of energy, law of      135Ч136
Continuity behavior      73Ч76
Convection      170Ч174. See also heat conduction problems
Convergence, expansions in series of eigenfunctions      182
Convergence, Fourier series      73Ч77 124
Convergence, Fourier series, in the mean      93Ч94
Convergence, Fourier series, uniform      79Ч83
Cooling fins      40Ч41
Cooling, Newton's law of      30 139
Cosine function      66Ч68
Cosine function, Fourier cosine integral representation      109Ч110
Cosine function, hyperbolic      4
Cosine function, integrals of      439
Critical radius      42
Cutoff frequency      121
d'Alembert's method (traveling wave)      227Ч231 252
Damping term      117
Delta functions      113
Diffusion equations      See heat conduction problems
Diffusion of sulphur dioxide      55Ч56 192Ч193
Diffusivity      141
Dimensions of heat flux      135
Dinac's delta function      113
Dirichlet conditions      139
Dirichlet's problem      256. See also potential equation
Dirichlet's problem in a disk      275Ч279
Dirichlet's problem in a rectangle      259Ч269
Dirichlet's problem, soap films      283
Discontinuity      74
Disk, potential equation in      275Ч279
Eigenfunctions      158Ч159
Eigenfunctions, expansions in series of      181Ч182
Eigenfunctions, orthogonality of      175Ч177
eigenvalue problems      34 158Ч159
Eigenvalue problems, estimating eigenvalues for wave equations      236Ч239
Eigenvalue problems, one-dimensional wave equation      234
Eigenvalue problems, singular      189
Eigenvalue problems, Sturm Ч Liouville problems      178Ч179
Eigenvalue problems, Sturm Ч Liouville problems, expansions in series of eigenfunctions      181Ч182
Eigenvalue problems, Sturm Ч Liouville problems, generalizations on heat conduction problems      184Ч187
Eigenvalue problems, Sturm Ч Liouville problems, one-dimensional wave equation      234
Elliptic equations      281
Endpoints of periodic extensions      76Ч77
Energy conservation, law of      135Ч136
Enzyme electrodes      212Ч214
Equilibrium problems      See steady-state problems
Error function, heat conduction problems      199Ч202
Even functions      67
Even functions, continuity behavior of      83
Even functions, extensions of functions      69Ч71
Exponential functions, integrals of      438Ч439
Exponential growth      2
Extensions of periodic functions      65Ч71
Extensions of periodic functions, endpoints of      76Ч77
Extensions of periodic functions, uniform convergence      82Ч83
Fast Fourier transform (FFT)      124
Fick's law      55 141
Finite Fourier series      91Ч94
First-order equations, homogeneous      1Ч2
First-order equations, nonhomogeneous      20Ч21
Fisher's equation      252
Fitzhugh Ч Nagumo equations      239Ч244
Fixed end temperatures (heat equation)      149Ч155
Flat enzyme electrodes      212Ч214
Flow (fluid)      284Ч285 289
Fluid flows      284Ч285 289
Fokker Ч Planck equation      205
Forced vibrations of strings      232
Forced vibrations system      17Ч20
Forcing function      117 226
Fourier integrals      106Ч111 124 190 194
Fourier integrals, applications of      117Ч123
Fourier integrals, coefficient functions      108
Fourier integrals, complex coefficients      See complex Fourier coefficients
Fourier integrals, Fourier transforms      115
Fourier integrals, Fourier's single integral      112Ч113
Fourier integrals, history of      124
Fourier integrals, representational theorem      108
Fourier integrals, wave equation in unbounded regions      239Ч244
Fourier series      62Ч63 124
Fourier series, applications of      117Ч123
Fourier series, arbitrary periods      64Ч65
Fourier series, complex coefficients      See complex Fourier coefficients
Fourier series, convergence      73Ч77
Fourier series, convergence, proof of      95Ч99
Fourier series, convergence, uniform convergence      79Ч83
Fourier series, cosine integral representation      109
Fourier series, history of      124
Fourier series, means of      90Ч94
Fourier series, numerical determination of coefficients      100Ч104
Fourier series, operations on      85Ч89
Fourier series, periodic extensions      65Ч71
Fourier series, periodic extensions, endpoints of      76Ч77
Fourier series, periodic extensions, uniform convergence      82Ч83
Fourier series, potential in rectangle      260Ч261
Fourier series, sine integral representation      109
Fourier transforms      115
Fourier's law      30
Fourier's method (separation of variables)      150 166Ч167
Freezing lake, temperature of      204
Frequencies of vibration      223Ч224 234
Functions      See specific function by name
Gaussian probability density function      203
General solutions, boundary value problems      26
General solutions, homogeneous differential equations      158
General solutions, nonhomogeneous linear equations      15
General solutions, one-dimensional wave equation      228
General solutions, second-order homogeneous equations      3
General solutions, second-order linear partial differential equations      205 280Ч281
Generalized rectangles      281
Generation rate functions      141
Gibbs' phenomenon      82
Green's functions      23 43Ч49
Groundwater flow      52 211Ч212
Half-range extensions      70Ч71
Hanging cable system      26Ч29
Harmonic functions      255. See also potential equation
Heat conduction problems      29Ч31 135Ч206 280
Heat conduction problems, convection      170Ч174
Heat conduction problems, cooling fins      40Ч41
Heat conduction problems, derivation of      135Ч141
Heat conduction problems, different end conditions (example)      157Ч161
Heat conduction problems, error function      199Ч202
Heat conduction problems, fixed end temperatures (example)      149Ч155
Heat conduction problems, generalizations on      184Ч187
Heat conduction problems, insulated ends (example)      157Ч161
Heat conduction problems, radial heat flow      39Ч40
Heat conduction problems, steady-state temperatures      143Ч147
Higher-order equations, homogeneous      9Ч11
Homogeneous boundary conditions, as requirement      282
Homogeneous linear equations      1Ч11
Homogeneous linear equations, first-order      1Ч2
Homogeneous linear equations, higher-order      9Ч11
Homogeneous linear equations, second-order      2Ч9
Hyperbolic equations      281
Hyperbolic functions      4 436 438Ч439
Infinite intervals      40Ч41
Infinite rods      193Ч197
Initial conditions      See also initial value-boundary value problems
Initial conditions, wave equation      217 220Ч221 228
Initial value-boundary value problems      140
Initial value-boundary value problems, heat conduction problems      138. See also heat conduction problems
Initial value-boundary value problems, heat conduction problems, convection      170Ч174
Initial value-boundary value problems, heat conduction problems, different end conditions (example)      163Ч166
Initial value-boundary value problems, heat conduction problems, fixed end temperatures (example)      149Ч155
Initial value-boundary value problems, heat conduction problems, generalizations on      184Ч187
Initial value-boundary value problems, heat conduction problems, infinite rods      193Ч197
Initial value-boundary value problems, heat conduction problems, insulated ends (example)      157Ч161
Initial value-boundary value problems, heat conduction problems, semi-infinite rods      184Ч187
Initial value-boundary value problems, wave equation      215Ч247 280
Initial value-boundary value problems, wave equation, d'Alembert's method      227Ч231 252
Initial value-boundary value problems, wave equation, estimating eigenvalues for      236Ч239
Initial value-boundary value problems, wave equation, frequencies of vibration      223Ч224 234
Initial value-boundary value problems, wave equation, in unbounded regions      239Ч244
Initial value-boundary value problems, wave equation, one-dimensional, in general      233Ч235
Initial value-boundary value problems, wave equation, vibrating string problem      215Ч224
Insulated bars      157Ч161.See also heat conduction problems
Insulated surfaces      139
Integrals, table of      438Ч440
Integro-differential boundary value problems      54
Irrotational vortex      291
Jump discontinuities      74
Kryptonite      42
l'Hospital's rule      98
Lake Ontario      105
Lake Placid      105
Laplace's equation      See potential equation
Laplacian operator      256Ч257
Law of conservation of energy      135Ч136
Law of cooling (Newton)      30 139
Law of radiation (Stefan Ч Boltzmann)      142
Left-hand limits      73Ч74
Legendre polynomials, integrals of      440
Level curves      261Ч262
Linear density      216
Linear differential equations, homogeneous      1Ч11
Linear differential equations, homogeneous, first-order      1Ч2
Linear differential equations, homogeneous, higher-order      9Ч11
Linear differential equations, homogeneous, second-order      2Ч9
Linear differential equations, nonhomogeneous      14Ч23
Linear differential equations, nonhomogeneous, Fourier series applications with      117Ч119
Linear differential equations, nonhomogeneous, undetermined coefficients      16Ч20
Linear differential equations, nonhomogeneous, variation of parameters      20Ч23
Linear operations      140
Linear partial differential equations, general form      205
Linear partial differential equations, heat      See heat conduction problems
Linear partial differential equations, potential      See potential equation
Linear partial differential equations, wave      See wave equation
Linearly independent solution      3
Mass-spring-damper system      5
Mass-spring-damper system, forced vibrations system      17Ч20
Massena, New York      132
Maximum principle      255 278
Mean error      90Ч94
Mean value property      278
Mean value property, periodic functions      61
Membrane displacement      255. See also potential equation
Method of characteristics      246
Mixed boundary conditions      139
Neumann conditions      139
Neumann's problem      256 290.
Newton's law of cooling      30 139
Nonhomogeneous linear equations      14Ч23
Nonhomogeneous linear equations, Fourier series applications with      117Ч119
Nonhomogeneous linear equations, undetermined coefficients      16Ч20
Nonhomogeneous linear equations, variation of parameters      20Ч23
Nonremovable discontinuities      74Ч75 79
Normal probability density function      203
Normalized eigenfunctions      183
Normalizing constants      183
Nuclear fuel rods      See heat conduction problems
Numerical determination of Fourier coefficients      100Ч104
Odd functions      67
Odd functions, continuity behavior of      83
Odd functions, extensions of functions      69Ч71
ODEs (ordinary differential equations)      1Ч51
ODEs (ordinary differential equations), boundary value problems      26Ч34
ODEs (ordinary differential equations), Green's functions      43Ч49
ODEs (ordinary differential equations), homogeneous      1Ч11
ODEs (ordinary differential equations), homogeneous, first-order      1Ч2
ODEs (ordinary differential equations), homogeneous, higher-order      9Ч11
ODEs (ordinary differential equations), homogeneous, second-order      2Ч9
ODEs (ordinary differential equations), nonhomogeneous      14Ч23
ODEs (ordinary differential equations), nonhomogeneous, Fourier series applications with      117Ч119
ODEs (ordinary differential equations), nonhomogeneous, singular boundary value problems      38Ч41
ODEs (ordinary differential equations), nonhomogeneous, undetermined coefficients      16Ч20
ODEs (ordinary differential equations), nonhomogeneous, variation of parameters      20Ч23
One-dimensional wave equation      233Ч235
Ordinary differential equations      1Ч51
Ordinary differential equations, boundary value problems      26Ч34
Ordinary differential equations, Green's functions      43Ч49
Ordinary differential equations, homogeneous      1Ч11
Ordinary differential equations, homogeneous, first-order      1Ч2
Ordinary differential equations, homogeneous, higher-order      9Ч11
Ordinary differential equations, homogeneous, second-order      2Ч9
Ordinary differential equations, nonhomogeneous      14Ч23
Ordinary differential equations, nonhomogeneous, Fourier series applications with      117Ч119
Ordinary differential equations, nonhomogeneous, undetermined coefficients      16Ч20
Ordinary differential equations, nonhomogeneous, variation of parameters      20Ч23
Ordinary differential equations, singular boundary value problems      38Ч41
Ordinary limits      73Ч74
Organ pipes      225
Orthogonality      60Ч61 73
Orthogonality of eigenfunctions      175Ч177
Oxygen removal from aluminum nitride      156
Parabolic equations      281
Parseval's equality      92Ч93
Partial differential equation classifications      280Ч282
Particular solutions, nonhomogeneous linear equations      15Ч23
Penetration of heat into earth      192
Periodic functions      59Ч63
Periodic functions, arbitrary periods      64Ч65
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