Index 499
mean value property, 278
periodic functions, 61
membrane displacement, 255.See also
potential equation
method of characteristics, 246
mixed boundary conditions, 139
N
Neumann conditions, 139
Neumann’s problem, 256, 290.See also
potential equation
Newton’s law of cooling, 30, 139
nonhomogeneous linear equations,
14–23
Fourier series applications with,
117–119
undetermined coefficients, 16–20
variation of parameters, 20–23
nonremovable discontinuities, 74–75,
79
normal probability density function,
203
normalized eigenfunctions, 183
normalizing constants, 183
nuclear fuel rods.Seeheat conduction
problems
numerical determination of Fourier
coefficients, 100–104
O
odd functions, 67
continuity behavior of, 83
extensions of functions, 69–71
ODEs (ordinary differential equations),
1–51
boundary value problems, 26–34
Green’s functions, 43–49
homogeneous, 1–11
first-order, 1–2
higher-order, 9–11
second-order, 2–9
nonhomogeneous, 14–23
Fourier series applications with,
117–119
undetermined coefficients, 16–20
variation of parameters, 20–23
singular boundary value problems,
38–41
one-dimensional wave equation,
233–235
ordinary differential equations, 1–51
boundary value problems, 26–34
Green’s functions, 43–49
homogeneous, 1–11
first-order, 1–2
higher-order, 9–11
second-order, 2–9
nonhomogeneous, 14–23
Fourier series applications with,
117–119
undetermined coefficients, 16–20
variation of parameters, 20–23
singular boundary value problems,
38–41
ordinary limits, 73–74
organ pipes, 225
orthogonality, 60–61, 73
of eigenfunctions, 175–177
oxygen removal from aluminum nitride,
156
P
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
arbitrary periods, 64–65
extensions of, 65–71
endpoints of, 76–77
uniform convergence, 82–83
piecewise continuous functions, 75–76
piecewise smooth functions, 76
plate, flow past, 289
Poiseuille flow, 36
Poisson equation, 268–269
polar coordinates, potential equation in,
256–257, 275–279
polynomial solution for potential
equation, 256