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| Ïîèñê ïî óêàçàòåëÿì |
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| Powers D.L. — Boundary Value Problems: And Partial Differential Equations |
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| Ïðåäìåòíûé óêàçàòåëü |
Acoustic vibrations 235
Aluminum nitride, oxygen removal from 156
Antenna vibrations 226
Approximation by Fourier series 91—94
Arbitrary periods 64—65
Bad discontinuities 74—75 79
Band-limited functions 121—123
Bars, insulated 157—161. See also heat conduction problems
Beam vibrations 225
Bessel functions, integrals of 440
Bessel inequality 92—93
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 281—282
Boundary conditions, mixed 139
Boundary conditions, potential equation See potential equation
Boundary conditions, wave equation 217—220 229
Boundary value problems 26—34. See also initial value-boundary value problems
Boundary value problems, Fourier series applications with 119—120
Boundary value problems, Green's functions 23 43—49
Boundary value problems, potential equation 256—257
Boundary value problems, singular 38—41
Boundedness 40—41
Boussinesq equation 211
Brownian motion 204
Buckling of a column 32—34
Burger's equation 209
Cable, hanging 26—29
Calculus 436—438
Cantilevered beam 226
Car antenna vibrations 226
Catenaries 35
Cauchy — Euler equation 6—7 38 277
Cesaro summability 131
Chain rule 232
Characteristic equation 3 10
Characteristics, method of 246
Classifications of partial differential equations 280—282
Coefficients of Fourier series See Fourier series
Column buckling 32—34
Complementary error function 200 202
Complex coefficients, potential equation analysis 284
Complex Fourier coefficients 113—115
Complex Fourier coefficients, sampling theorem 121—124
conditions See boundary conditions; initial condition
Conduction of heat See heat conduction problems
Conservation of energy, law of 135—136
Continuity behavior 73—76
Convection 170—174. See also heat conduction problems
Convergence, expansions in series of eigenfunctions 182
Convergence, Fourier series 73—77 124
Convergence, Fourier series, in the mean 93—94
Convergence, Fourier series, uniform 79—83
Cooling fins 40—41
Cooling, Newton's law of 30 139
Cosine function 66—68
Cosine function, Fourier cosine integral representation 109—110
Cosine function, hyperbolic 4
Cosine function, integrals of 439
Critical radius 42
Cutoff frequency 121
d'Alembert's method (traveling wave) 227—231 252
Damping term 117
Delta functions 113
Diffusion equations See heat conduction problems
Diffusion of sulphur dioxide 55—56 192—193
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 275—279
Dirichlet's problem in a rectangle 259—269
Dirichlet's problem, soap films 283
Discontinuity 74
Disk, potential equation in 275—279
Eigenfunctions 158—159
Eigenfunctions, expansions in series of 181—182
Eigenfunctions, orthogonality of 175—177
eigenvalue problems 34 158—159
Eigenvalue problems, estimating eigenvalues for wave equations 236—239
Eigenvalue problems, one-dimensional wave equation 234
Eigenvalue problems, singular 189
Eigenvalue problems, Sturm — Liouville problems 178—179
Eigenvalue problems, Sturm — Liouville problems, expansions in series of eigenfunctions 181—182
Eigenvalue problems, Sturm — Liouville problems, generalizations on heat conduction problems 184—187
Eigenvalue problems, Sturm — Liouville problems, one-dimensional wave equation 234
Elliptic equations 281
Endpoints of periodic extensions 76—77
Energy conservation, law of 135—136
Enzyme electrodes 212—214
Equilibrium problems See steady-state problems
Error function, heat conduction problems 199—202
Even functions 67
Even functions, continuity behavior of 83
Even functions, extensions of functions 69—71
Exponential functions, integrals of 438—439
Exponential growth 2
Extensions of periodic functions 65—71
Extensions of periodic functions, endpoints of 76—77
Extensions of periodic functions, uniform convergence 82—83
Fast Fourier transform (FFT) 124
Fick's law 55 141
Finite Fourier series 91—94
First-order equations, homogeneous 1—2
First-order equations, nonhomogeneous 20—21
Fisher's equation 252
Fitzhugh — Nagumo equations 239—244
Fixed end temperatures (heat equation) 149—155
Flat enzyme electrodes 212—214
Flow (fluid) 284—285 289
Fluid flows 284—285 289
Fokker — Planck equation 205
Forced vibrations of strings 232
Forced vibrations system 17—20
Forcing function 117 226
Fourier integrals 106—111 124 190 194
Fourier integrals, applications of 117—123
Fourier integrals, coefficient functions 108
Fourier integrals, complex coefficients See complex Fourier coefficients
Fourier integrals, Fourier transforms 115
Fourier integrals, Fourier's single integral 112—113
Fourier integrals, history of 124
Fourier integrals, representational theorem 108
Fourier integrals, wave equation in unbounded regions 239—244
Fourier series 62—63 124
Fourier series, applications of 117—123
Fourier series, arbitrary periods 64—65
Fourier series, complex coefficients See complex Fourier coefficients
Fourier series, convergence 73—77
Fourier series, convergence, proof of 95—99
Fourier series, convergence, uniform convergence 79—83
Fourier series, cosine integral representation 109
Fourier series, history of 124
Fourier series, means of 90—94
Fourier series, numerical determination of coefficients 100—104
Fourier series, operations on 85—89
Fourier series, periodic extensions 65—71
Fourier series, periodic extensions, endpoints of 76—77
Fourier series, periodic extensions, uniform convergence 82—83
Fourier series, potential in rectangle 260—261
Fourier series, sine integral representation 109
Fourier transforms 115
Fourier's law 30
Fourier's method (separation of variables) 150 166—167
Freezing lake, temperature of 204
Frequencies of vibration 223—224 234
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 205 280—281
Generalized rectangles 281
Generation rate functions 141
Gibbs' phenomenon 82
Green's functions 23 43—49
Groundwater flow 52 211—212
Half-range extensions 70—71
Hanging cable system 26—29
Harmonic functions 255. See also potential equation
Heat conduction problems 29—31 135—206 280
Heat conduction problems, convection 170—174
Heat conduction problems, cooling fins 40—41
Heat conduction problems, derivation of 135—141
Heat conduction problems, different end conditions (example) 157—161
Heat conduction problems, error function 199—202
Heat conduction problems, fixed end temperatures (example) 149—155
Heat conduction problems, generalizations on 184—187
Heat conduction problems, insulated ends (example) 157—161
Heat conduction problems, radial heat flow 39—40
Heat conduction problems, steady-state temperatures 143—147
Higher-order equations, homogeneous 9—11
Homogeneous boundary conditions, as requirement 282
Homogeneous linear equations 1—11
Homogeneous linear equations, first-order 1—2
Homogeneous linear equations, higher-order 9—11
Homogeneous linear equations, second-order 2—9
Hyperbolic equations 281
Hyperbolic functions 4 436 438—439
Infinite intervals 40—41
Infinite rods 193—197
Initial conditions See also initial value-boundary value problems
Initial conditions, wave equation 217 220—221 228
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 170—174
Initial value-boundary value problems, heat conduction problems, different end conditions (example) 163—166
Initial value-boundary value problems, heat conduction problems, fixed end temperatures (example) 149—155
Initial value-boundary value problems, heat conduction problems, generalizations on 184—187
Initial value-boundary value problems, heat conduction problems, infinite rods 193—197
Initial value-boundary value problems, heat conduction problems, insulated ends (example) 157—161
Initial value-boundary value problems, heat conduction problems, semi-infinite rods 184—187
Initial value-boundary value problems, wave equation 215—247 280
Initial value-boundary value problems, wave equation, d'Alembert's method 227—231 252
Initial value-boundary value problems, wave equation, estimating eigenvalues for 236—239
Initial value-boundary value problems, wave equation, frequencies of vibration 223—224 234
Initial value-boundary value problems, wave equation, in unbounded regions 239—244
Initial value-boundary value problems, wave equation, one-dimensional, in general 233—235
Initial value-boundary value problems, wave equation, vibrating string problem 215—224
Insulated bars 157—161.See also heat conduction problems
Insulated surfaces 139
Integrals, table of 438—440
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 256—257
Law of conservation of energy 135—136
Law of cooling (Newton) 30 139
Law of radiation (Stefan — Boltzmann) 142
Left-hand limits 73—74
Legendre polynomials, integrals of 440
Level curves 261—262
Linear density 216
Linear differential equations, homogeneous 1—11
Linear differential equations, homogeneous, first-order 1—2
Linear differential equations, homogeneous, higher-order 9—11
Linear differential equations, homogeneous, second-order 2—9
Linear differential equations, nonhomogeneous 14—23
Linear differential equations, nonhomogeneous, Fourier series applications with 117—119
Linear differential equations, nonhomogeneous, undetermined coefficients 16—20
Linear differential equations, nonhomogeneous, variation of parameters 20—23
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 17—20
Massena, New York 132
Maximum principle 255 278
Mean error 90—94
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 14—23
Nonhomogeneous linear equations, Fourier series applications with 117—119
Nonhomogeneous linear equations, undetermined coefficients 16—20
Nonhomogeneous linear equations, variation of parameters 20—23
Nonremovable discontinuities 74—75 79
Normal probability density function 203
Normalized eigenfunctions 183
Normalizing constants 183
Nuclear fuel rods See heat conduction problems
Numerical determination of Fourier coefficients 100—104
Odd functions 67
Odd functions, continuity behavior of 83
Odd functions, extensions of functions 69—71
ODEs (ordinary differential equations) 1—51
ODEs (ordinary differential equations), boundary value problems 26—34
ODEs (ordinary differential equations), Green's functions 43—49
ODEs (ordinary differential equations), homogeneous 1—11
ODEs (ordinary differential equations), homogeneous, first-order 1—2
ODEs (ordinary differential equations), homogeneous, higher-order 9—11
ODEs (ordinary differential equations), homogeneous, second-order 2—9
ODEs (ordinary differential equations), nonhomogeneous 14—23
ODEs (ordinary differential equations), nonhomogeneous, Fourier series applications with 117—119
ODEs (ordinary differential equations), nonhomogeneous, singular boundary value problems 38—41
ODEs (ordinary differential equations), nonhomogeneous, undetermined coefficients 16—20
ODEs (ordinary differential equations), nonhomogeneous, variation of parameters 20—23
One-dimensional wave equation 233—235
Ordinary differential equations 1—51
Ordinary differential equations, boundary value problems 26—34
Ordinary differential equations, Green's functions 43—49
Ordinary differential equations, homogeneous 1—11
Ordinary differential equations, homogeneous, first-order 1—2
Ordinary differential equations, homogeneous, higher-order 9—11
Ordinary differential equations, homogeneous, second-order 2—9
Ordinary differential equations, nonhomogeneous 14—23
Ordinary differential equations, nonhomogeneous, Fourier series applications with 117—119
Ordinary differential equations, nonhomogeneous, undetermined coefficients 16—20
Ordinary differential equations, nonhomogeneous, variation of parameters 20—23
Ordinary differential equations, singular boundary value problems 38—41
Ordinary limits 73—74
Organ pipes 225
Orthogonality 60—61 73
Orthogonality of eigenfunctions 175—177
Oxygen removal from aluminum nitride 156
Parabolic equations 281
Parseval's equality 92—93
Partial differential equation classifications 280—282
Particular solutions, nonhomogeneous linear equations 15—23
Penetration of heat into earth 192
Periodic functions 59—63
Periodic functions, arbitrary periods 64—65
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