Page 893 - Advanced_Engineering_Mathematics o'neil
P. 893
Index 873
periodicity of, 494 Dot product, 154–159, 163–164,
sampled Fourier series from, 498–501 182–183, 511, 515
Disks, 645–647, 662–664, 725–727 defined, 154
annulus, 725 eigenfunction expansion and, 511,
Dirichlet problem for, 645–647 515
Laurent expansion and, 725–727 function space C[a, b], 182–183
Neumann problem for, 662–664 MAPLE configuration for, 154–156
n
punctured, 725 n-space R , 163–164
Displacement δ, 540–542, 570–573, normal vectors, 157–158
581–582 orthogonal vectors, 156–157
hanging chain, Bessel function vector projections, 158–159
application, 540–542 weight function p and, 182–183, 511,
nonzero initial, 572–573 515
wave motion, 570–573, 581–582
zero initial, 570–572, 581–582 E
Displacement function z(x, y, t), 567 Eigenfunction expansions, 505–562
Distribution of charged particles, Bessel functions, 533–560
530–531 Bessel’s inequality, 515–518
Divergence (div), 362–364, 401–407, boundary conditions, 506
420–421 complete vectors and, 518
curl and, 362–363, 365 differential equations for, 506,
curvilinear coordinates and, 420–421 518–519
defined, 362 Legendre polynomials, 518–532
del operator ∇ for, 362–363 Parseval’s theorem, 515–518
differential calculus and, 362–364 special functions and, 505–562
Gauss’s theorem, 401–407 Sturm-Liouville problems, 506–515
integral calculus and, 401–407, weight function p and, 511, 515
420–421 Eigenvalues λ, 267–276, 306–308,
physical interpretation of, 364 329–338, 506–511
vector analysis and, 362–364, characteristic polynomials, 269–271
401–407, 420–421 complex roots, 271–272, 306–308,
Domain D, 383–387, 701, 765–773 335–336
Cauchy’s theorem and, 701 defined, 267
complementary, 766–767 eigenvectors (E) and, 267–276
conservative vector field test in, equal, 333–335
383–384 Gershgorin method for, 275–276
defined, 385, 701 homogeneous linear system solutions
independence of path and, 383–387 and, 306–308
planar, 385–387 imaginary, 337–338
potential theory and, 383–387 phase portraits, classification of,
Riemann mapping theorem and, 329–338
765–773 real distinct and of same sign,
simply connected, 386 330–332
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