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Index 881
Laurent expansion, 725–727 independent vectors, defined, 167
n
Leading entry, 203, 207–208 n-space (R ), 167–174
Least squares vectors (lsv), 180, spanning sets, 167–174
232–236 theorems for, 168–172
auxiliary lsv systems, 233–236 Wronskian (W), 46–47
data fitting and, 232–236 Linear differential equations, 16–20,
nonsingular matrices and, 234–236 43–75, 145–342
orthogonal projection and, 180, constant coefficient case for, 50–54
233–234 defined, 16
regression line, 236 determinants, 247–265
vectors for systems, 232–236 diagonalization, 277–283
Legendre polynomials, 518–532, 799 eigenvalues, 267–276
differential equation, 518–519
Euler’s equation, 72–74
distribution of charged particles,
first-order, 16–20
application of, 530–531
forcing function ( f ),43
eigenfunction expansions and,
homogeneous equations, 45–48
518–532
homogeneous systems, 213–219
Fourier-Legendre expansions,
initial value problem for, 45–47
525–528
integral curves for, 44–45
generating function for, 521–523
integrating factor, 17
MAPLE commands for, 799
matrices, 187–246, 277–293
recurrence relation for, 523–524
matrix inverses for, 229–231
Rodrigues’s formula and, 532
matrix operations for systems,
zeros of, 528–569
213–226
Length, vectors, 148
nonhomogeneous equations, 48–49,
Level surface of gradient field ϕ,
55–60
359–361
nonhomogeneous systems, 220–226
Limits L, complex functions, 677–678
reduction of order method for, 51–52
Line integrals, 367–373
second-order, 43–75
arc length and, 372–373
curves and, 367–372 spring motion, applications for, 61–71
defined, 368–370 systems of, 187–246, 295–342
Lineal elements, 137 vectors, 147–186
Linear dependence and independence, Wronskian (W) of, 46–47
46–47, 167–174, 181–182, Linear fractional transformation, 758
272–273, 296–300, 308–312 Linear systems, see Systems of
dependent vectors, defined, 167 differential equations
eigenvectors (E), 272–273, 308–312 Linear transformations (mapping),
function space C[a, b], 181–182 240–246
homogeneous linear differential function (T ), 241
equations, 46–47, 296–300 one-to-one, 242–245
homogeneous linear system solutions onto, 242
and, 308–312 null space, 246
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