Index 501
generalizations on, 184–187
insulated ends (example), 157–161
semi-infinite rods, 184–187,
193–197
wave equation, 218, 232
Stefan–Boltzmann law of radiation, 142
Stokes derivative, 250
stream function, 284
stresses due to thermal effects, 214
string, vibrating, 215–224.See alsowave
equation
frequencies of vibration, 223–224,
234
one-dimensional wave equation,
233–235
Sturm–Liouville problems, 178–179
expansions in series of
eigenfunctions, 181–182
generalizations on heat conduction
problems, 184–187
one-dimensional wave equation, 234
sulphur dioxide, diffusion of, 55–56,
192–193
superposition, principle of, 3, 10, 152
wave equation and standing waves,
220
surfaces, insulated, 157–161.See also
heat conduction problems
suspension bridge (hanging cable
system), 26–29
symmetry of sine and cosine functions,
66–68
T
table of integrals, 438–440
Taylor series, 114
temperature (heat conduction)
steady-state, 143–147
three-dimensional steady-state
solution.Seepotential equation
two-dimensional steady-state
equation, 255
term, forcing functions, 117
thermal conductivity, 137
thermal diffusivity, 137
thermal stresses, 214
transient temperature distribution, 146
fixed end temperatures, 149–155
transverse displacement.Seewave
equation
trapezoidal function, 125
traveling wave solution (d’Alembert’s
method), 227–231, 252
triangle function, 123
trigonometric functions, 435
trigonometric series, history of, 124
trivial solutions, 150
truncated Fourier series, 92
U
unbounded conditions
potential equation, 270–272
wave equation, 239–244
undetermined coefficients,
nonhomogeneous linear
equations, 16–20
uniform convergence, 79–83V
variation of parameters, 20–23
velocity potential function, 258, 284
vibrating string problem, 215–224.See
alsowave equation
frequencies of vibration, 223–224,
234
one-dimensional wave equation,
233–235W
water hammers, 250
wave equation, 215–247, 280
d’Alembert’s method, 227–231, 252
estimating eigenvalues for, 236–239
frequencies of vibration, 223–224,
234
one-dimensional, in general, 233–235
in unbounded regions, 239–244
vibrating string problem, 215–224,
234
whirling speeds, 55
windows, 111
Wro n s k i a n , 3