496 Index
characteristic equation, 3, 10
characteristics, method of, 246
classifications of partial differential
equations, 280–282
coefficients of Fourier series.SeeFourier
series
column buckling, 32–34
complementary error function, 200, 202
complex coefficients, potential equation
analysis, 284
complex Fourier coefficients, 113–115
sampling theorem, 121–124
conditions.Seeboundary conditions;
initial condition
conduction of heat.Seeheat conduction
problems
conservation of energy, law of, 135–136
continuity behavior, 73–76
convection, 170–174.See alsoheat
conduction problems
convergence
expansions in series of
eigenfunctions, 182
Fourier series, 73–77, 124
in the mean, 93–94
uniform, 79–83
cooling, Newton’s law of, 30, 139
cooling fins, 40–41
cosine function, 66–68
Fourier cosine integral
representation, 109–110
hyperbolic, 4
integrals of, 439
critical radius, 42
cutoff frequency, 121
D
d’Alembert’s method (traveling wave),
227–231, 252
damping term, 117
delta functions, 113
diffusion equations.Seeheat
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
in a disk, 275–279
in a rectangle, 259–269
soap films, 283
discontinuity, 74
disk, potential equation in, 275–279
E
eigenfunctions, 158–159
expansions in series of, 181–182
orthogonality of, 175–177
eigenvalue problems, 34, 158–159
estimating eigenvalues for wave
equations, 236–239
one-dimensional wave equation, 234
singular, 189
Sturm–Liouville problems, 178–179
expansions in series of
eigenfunctions, 181–182
generalizations on heat conduction
problems, 184–187
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.Seesteady-state
problems
error function, heat conduction
problems, 199–202
even functions, 67
continuity behavior of, 83
extensions of functions, 69–71
exponential functions, integrals of,
438–439
exponential growth, 2
extensions of periodic functions, 65–71
endpoints of, 76–77
uniform convergence, 82–83
F
fast Fourier transform (FFT), 124
Fick’s law, 55, 141