Index 497
finite Fourier series, 91–94
first-order equations
homogeneous, 1–2
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
applications of, 117–123
coefficient functions, 108
complex coefficients.Seecomplex
Fourier coefficients
Fourier transforms, 115
Fourier’s single integral, 112–113
history of, 124
representational theorem, 108
wave equation in unbounded regions,
239–244
Fourier series, 62–63, 124
applications of, 117–123
arbitrary periods, 64–65
complex coefficients.Seecomplex
Fourier coefficients
convergence, 73–77
proof of, 95–99
uniform convergence, 79–83
cosine integral representation, 109
history of, 124
means of, 90–94
numerical determination of
coefficients, 100–104
operations on, 85–89
periodic extensions, 65–71
endpoints of, 76–77
uniform convergence, 82–83
potential in rectangle, 260–261
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
G
Gaussian probability density function,
203
general solutions
boundary value problems, 26
homogeneous differential equations,
158
nonhomogeneous linear equations,
15
one-dimensional wave equation, 228
second-order homogeneous
equations, 3
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
H
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
convection, 170–174
cooling fins, 40–41
derivation of, 135–141
different end conditions (example),
157–161
error function, 199–202
fixed end temperatures (example),
149–155
generalizations on, 184–187
insulated ends (example), 157–161
radial heat flow, 39–40
steady-state temperatures, 143–147