Index 397
terms, 129
uniform convergence, 147, 206
Weierstrass M-test, 147
with non-negative terms, 131
set, 2
convex, 253
of volume zero, 285
sets
equality of, 2
shear matrices, 304
similar sets, 376
simple
2-cell, 341
3-cell, 360
closed path, 322
path, 322
singleton subset, 366
singular
matrix, 213
point, 89
singularities, 124
smooth
p-surface, 270, 351
curve, 318
function, 228
function on a square, 341
local inverse, 260
parameter change, 323, 349, 358
parameterization, 246, 270
smoothly parameterized surface, 246,
348, 363
sphere, 195
spherical change of coordinates, 265
squeeze principle, 43
stationary point, 89
Stokes’s Theorem, 354
classical form, 356
for 3-cells in
Rd,
364
general form, 373
submatrix, 216
subrectangle, 276
subsequence, 51
subsequential limit, 56
subset, 2
proper, 2
subspace
affine, 217
linear, 215
substitution, 118
subtraction in a commutative ring, 17
successor, 8
sup norm, 205
supremum, 27
surface
p-surface, 317
area, 353
degenerate, 195
integral, 354
orientation, 352
parameterized, 195, 246
surjection, 375
surjective, 375
tangent
line, 244
space, 246
vector, 245, 322, 327
Taylor
formula, 155, 252
polynomial, 154
remainder, 155
series, 154
term test, 130
topological
properties, 179
space, 175
topology for
Rd,
175
totally ordered set, 383
trace
of a 2-cell, 341
of a p-chain, 370
of a chain, 366
of a curve, 318
transformation, 191
composition law, 337
transformation law
for differential forms, 335
transitive property, 14
triangle inequality
for metric spaces, 168
for vectors, 165
in R, 34
trigonometric function, 60
uncountable sets, 380
uniform continuity, 69, 200
and the derivative, 92
uniform convergence, 74, 203
and continuity, 75, 204
and the integral, 114, 291
of series, 147
tests for, 76
uniformly Cauchy sequence, 77, 204
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