Page 903 - Advanced_Engineering_Mathematics o'neil
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Index 883
Matrices (Continued) initial condition, influence of,
random walks in crystals, application 573–575
of, 194–197 initial displacement, 570–573,
reduced row echelon form, 203–208 581–582
reduced systems, 213–219 initial velocity, 568–570, 572–573,
row operations, 198–208 579–581
row space (rank), 208–212 intervals of, 567–577
scalar algebra operations, 188 Laplace transform techniques for,
singular, 227, 229–230 587–593
skew-hermitian, 288–290 semi-infinite medium, in a, 585–587
square, 192 sliding, 31–33
symmetric, 273–275 spring, 61–71
transition, 317 unforced, 62–66
transpose of, 193–194 vibrations in a membrane, 602–610
unitary, 286–288 wave, 567–587, 596–610
upper triangular (U), 237
zero, 192
N
Matrix of coefficients, 213–215
n
n-space (R ), 162–174
Matrix tree theorem, 262–264
basis, 172–173
Maximum principle, harmonic
coordinates of, 172–173
functions, 710
dimension, 172
Mclaurin series, 718
dot product of, 163–164
Mean value property, harmonic
linear dependence and independence
functions, 709–710
theorem for, 167–170
Method of least squares, 180
orthogonal vectors, 164, 173–174
Minor determinant, 256
orthonormal vectors, 164, 173
Mixing problem, 18–20, 304–306
spanning set for, 166–172
Möbius transformations, 758
standard representation of, 165
Modified Bessel function, 543–545
Modulation, Fourier transforms, 477 subspace (S), 165–174
Mortality function m(t),99 Nabla ∇, 356–357, 362–363
Motion, 31–33, 61–71, 567–587, Natural length (L),61
596–610 Neumann problems, 659–665
Cauchy initial-boundary value disk, for a, 662–664
problem, 594–601 Green’s first identity for, 659
constant c influence of, 573–575 rectangle, for a, 660–662
d’Alembert’s solution for, 594–601 square, for a, 660
forced, 66–67, 599–601 unbounded regions, for, 664–665
forcing term for, 567, 575–577 Neumann’s function of order zero,
forward and backward waves, 538–540
596–599 Nodal sink, 331
infinite medium, in a, 579–584 Nodal source, 331–332
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