390 Index
n
k
, 13
N, 8
p-series, 135
alternating, 141
Q, 17
R, 4
Rd,
161
Rn,
4
Sij , 304
Ti(a), 304
U(f, P ), 102, 277
x , 164
x 1, 166
x ∞, 166
Z, 16
π, 20
χE, 281
curl F , 333, 335
div G, 335
exp x, 122
grad f, 243, 335
im(L), 216
inf, 27
infA f, 30
ker(L), 216
lim an, 36
lim inf, 56
lim sup, 56
limx→a f(x), 79
ln, 121
sup, 27
supA f, 30
absolute convergence, 132
absolute value, 33
absolutely convergent series
rearrangement, 143
addition
in Q, 17
in R, 23
in
Rd,
162
additive
identity, 16, 162
inverse, 16, 163
affine approximation, 230
best, 230
affine function, 217
affine subspace, 217
aligned partition, 276
aligned rectangle, 275
alternating p-series, 141
alternating series, 140
alternating series test, 140
Archimedean ordered field, 25
Archimedean property, 25
area of a surface, 353
aspect ratio, 308
associative law
for scalar multiplication, 162
for vector addition, 162
of addition, 16
of multiplication, 16
Axiom of Choice, 382
consequences, 385
base case, 9
basis
of a vector space, 215
of an infinite-dimensional vector
space, 385
best affine approximation, 230
bijection, 375
bijective, 375
binary operation, 16
binomial formula, 13, 158, 159
Bolzano-Weierstrass Theorem, 52
in
Rd,
171
boundary, 176
of a 2-cell, 341
of a 3-cell, 360
of a p-cell, 370
of a p-chain, 370
of a cube, 359
boundary map, 367
bounded
function, 65
linear transformation, 212
sequence, 40, 43
set, 179
vector function, 198
bounded above, 23, 40, 43
bounded below, 26, 40, 43
branch of the curve, 245
cardinal
of a finite set, 375
cardinality
of finite sets, 375
Cartesian product, 7
Cauchy principal value, 126
Cauchy sequence
in R, 53
in Rd, 172
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