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