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