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892 Index
Vector analysis (Continued) Vectors, 147–186, 345–349, 793–796.
line integrals, 367–373 See also Eigenvectors
Maxwell’s equations, 411–413 addition of, 149–152
planes, 380–387, 392 Bessel’s inequality, 175
position vectors, 345–346 collinear points and, 161
potential theory, 380–387, 410–413 components of, 147–148
Stoke’s theorem, 402, 408–413 coordinates of, 172–173
streamlines, 354–356 cross product of, 159–161
surface integrals, 388–399 defined, 147
tangent vectors, 346–349 dot product of, 154–159, 163–164,
182–183
vector fields, 354–356
function space C[a, b], 181–186
vector functions of one variable,
length, 148
345–349
linear dependence and independence
velocity v, 349–345
theorem for, 167–170, 181–182
Vector fields, 354–356, 380–387,
linear differential equations, 147–186
410–411
magnitude, 148
conservative, 380–387
MAPLE commands for, 154–156,
defined, 354
160
differential calculus use of, 354–356
MAPLE operations, 793–796
domain D, 385–387
multiplication of, 148–149
independent of the path, 380–387
n-space, 162–174
integral calculus analysis and,
norm, 148
380–387, 410–411
normal, 157
planar test for conservative, 383–384
orthogonal, 156–158, 164, 173–180,
potential function ϕ of, 380–381
183–186
potential theory and, 380–387
orthonormal, 164, 173
streamlines and, 354–356 parallel, 149
vector analysis and, 354–356,
parallelogram law applied to,
380–387, 410–411
149–150, 152
Vector space, 162–174, 181–186 parametric equations for, 152–154
basis, 172–173 Parseval’s inequality, 175
coordinates of, 172–173 position, 345–346
dimension, 172 projections, 158–159, 177–180
function space C[a, b], 181–186 quadrilateral, 152
linear dependence and independence scalar algebra operations, 147–149
theorem for, 167–170, 181–182 space, 162–174, 181–186
n
n-space(R ), 162–174 spanning set of, 166–172
orthogonal vectors, 164, 173–174 standard representation of, 151, 165
orthonormal vectors, 164, 173 subspace S, 165–174, 177–179
spanning set for, 166–172 tangent, 346–349
standard representation of, 165 3-space lines, 152–154
subspace S, 165–174 triangle inequality, 149–150
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