Articolo G.A. Partial Differential Equations and Boundary Value Problems with Maple V
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718 Index
wave equation (continued)
eigenfunction, 221, 246
eigenfunction expansion solution,
248
eigenvalue, 221, 246
homogeneous, 219
homogeneous boundary condition,
219
initial condition, 220, 224–228
method of separation of variables,
219–221, 245, 261
partial differential in cylindrical
coordinates, 244, 251
partial differential in rectangular
coordinates, 217, 228, 261
separation constant, 220, 245
spatial differential equation, 223, 248
time-dependent differential equation,
222, 246
wave equation, homogeneous in two
spatial dimensions, 409
basis vector, 415
boundary condition, 410
coupling equation, 412, 414
double Fourier coefficient, 418, 444
double Fourier series expansion, 418,
423, 444
eigenfunction, 413, 440, 444
eigenvalue, 413, 440
homogeneous, 410
homogeneous boundary condition,
411, 413, 437, 438, 439
initial condition, 411, 417–420, 423,
443
method of separation of variables,
411, 423, 432, 437
partial differential in cylindrical
coordinates, 437, 437
partial differential in rectangular
coordinates, 409, 420
r-dependent equation, 442
separation constant, 412, 438
theta-dependent equation, 442
time-dependent equation, 414, 417,
440, 443
x-dependent equation, 412
y-dependent equation, 413
wave equation, nonhomogeneous in one
spatial dimension, 477
eigenfunction, 478
eigenvalue, 481
Fourier coefficient, 482, 488
Fourier series expansion, 488
homogeneous boundary condition,
477, 478, 479
initial condition, 478, 479, 480, 488
linear solution, 479, 480, 485
method of separation of variables,
481
nonhomogeneous boundary
conditions, 477, 479, 485, 511
nonhomogeneous source term, 478
substitution of condition, 478, 488
variable solution, 478, 511
wave equation, nonhomogeneous over
infinite domain, 586–588
Fourier integral, 587, 588
Fourier integral method, 586
Fourier transform, 586
initial condition, 586, 587
method of separation of variables,
586
Index 719
time-dependent equation, 587
x-dependent equation, 586
wave equation, nonhomogeneous over
semi-infinite domain, 588–593
Fourier integral, 592, 593
Fourier transform, 591, 592, 593
wave operator, in one spatial dimension
cylindrical coordinates, 244, 261
rectangular coordinates, 217–219
wave operator, in two spatial
dimensions
cylindrical coordinates, 437, 467
rectangular coordinates, 410, 466
wave phenomena, 217, 409, 437
wave speed, 217, 223, 251, 415, 421,
460, 523
initial, 586
linear density, 274
longitudinal wave, 274
mass density, 274
significance of, 273–274
tension, 274
transverse wave, 273
Young’s modulus of elasticity, 274
Weierstrass M-test, 83, 189
weight function, 75, 77
Wronskian, 9, 14, 645
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