Page 902 - Advanced_Engineering_Mathematics o'neil

882 Index

Linearity, Fourier transforms, 475, 480, Mass/spring systems, solution of,
494 319–321
Lines of force, 355 Mathematical modeling, 13
Liouville’s theorem, 711 Matrices, 187–293, 300–301, 316–318,
Local result, 41 796–798
Logarithms, 689 addition of, 188
Lommel’s integral, 561 adjacency, 195–196
Low-pass filters, 487–488 augmented, 206–207, 221–226
Lower triangular matrix (L), 237 column space (rank), 208–212
LU factorization, 237–240 defined, 187–188
determinants, 247–265
diagonal, 192
M
Magnification mapping, 759 diagonalization, 277–283
Magnitude, 148, 670–671 element, 187
Main diagonal matrix, 192, 277–278 elementary row operations, 198–202
MAPLE commands, 78–79, 154–156, equal, 187
160, 191, 202, 207–208, 212, 229, exponential, 316–318
246, 316–317, 473–474, 555 fundamental of systems, 300–301
Bessel functions, 555, 799 Hermitian, 288–290
complex functions, 799–800 homogeneous systems, 213–219
conformal mapping, 800 identity, 192–193
cross product computation, 160 inverses, 226–231, 259–260
dot product configuration, 154–156 leading entry, 203, 207–208
exponential matrix solutions, 316–317 least squares vectors for systems,
first-order differential equation, 78–79 232–236
Fourier-Bessel expansion, 555 linear differential equations, 187–246,
Fourier transforms, 473–474 277–293
integral transforms, 798–799 linear systems and, 187–246
Laplace transform routines, 78–79 linear transformations (mapping),
Legendre polynomials, 799 240–246
matrix manipulations, 796–798 lower triangular (L), 237
matrix operations, 191, 202, 207–208, LU factorization, 237–240
212, 229, 246 main diagonal, 192, 277–278
numerical computations, 789–791 MAPLE commands for, 191, 202,
ordinary differential equations, 207–208, 212, 229, 246
791–793 MAPLE operations, 796–798
residue (Res), 799–800 multiplication of, 188–192
vector computations, 154–156, 160 nonhomogeneous systems, 220–226
vector operations, 793–796 nonsingular, 227–229, 234–236
Mapping, 751. See also Conformal orthogonal, 284–286
mappings pivot position, 207–208
Mass, surface integrals of, 395–397 quadratic forms, 290–293

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October 15, 2010 16:21 THM/NEIL Page-882 27410_26_Ind_p867-898