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884 Index
Nonhomogeneous differential equations, Numerical computations using MAPLE,
48–49, 55–60, 220–226, 301–302, 789–791
312–315
associated homogeneous equation for, O
48 Odd functions, 436–438
associated homogeneous system for, Odd permutation, 247
221 Off-diagonal elements, 277–278
augmented matrix procedure for, One-dimensional wave equation, 566
221–226 One-step method, 142
consistent system, 220–221 One-to-one linear transformation,
defined, 48, 220 242–245
diagonalization of, 314–315 One-to-one mapping, 757–758
general solution of, 302 Onto linear transformation, 242
inconsistent system, 220–221 Operational rule, Fourier transforms,
linear systems, 220–226, 301–302, 477–478
312–315 Order of complex numbers, 673–675
solutions of, 48–49, 220–226, boundary points, 674–675
301–302, 312–315 disks, 673–674
superposition, principle of, 60 interior point, 674
system solutions, 220–226, 301–302, open and closed sets, 673–675
312–315 Ordinary differential equations, see
Differential equations
undetermined coefficients, method of,
57–60 Orientation preserved by mapping,
754–755
variation of parameters, method of
Orthogonal cylindrical coordinates, 416
for, 55–56, 312–314
Orthogonal eigenfunctions, 511
Nonsingular matrix, 227–229, 234–236
Orthogonal matrix, 284–286
defined, 227
Orthogonal trajectories, 34–35
inverses as, 227–229
Orthogonal vectors, 156–158, 164,
least squares vectors for, 234–236
173–180, 183–186, 274–275
Nontrivial solution, 218–219
basis, 173
Nonzero initial displacement, 572–573
complements, 177–180
Nonzero initial velocity, 572–573
defined, 156
Norm, vectors, 148
dot product, 156–157
Normal modes of vibration, 604–605 eigenvectors (E), 274–275
Normal vector, 157–158, 359–361, function space C[a, b], 183–186
389–392 Gram-Schmidt process for, 176
defined, 157 method of least squares for, 180
dot product for, 157–158 n-space (R ), 164, 173–174
n
gradient field ϕ, lines of, 359–361 orthogonalization, 175–177
surfaces, 389–392 projection, 158, 178–180
Normalized eigenfunctions, 516 Orthonormal vectors, 164, 173
Null space, 246 Overdamping, 63
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