394 Index

over I3, 359

over a 2-cell, 343

over a p-cell, 371

over a p-chain, 371

over a Cartesian product, 297

over a Jordan region, 290

over a parameterized 3-surface, 363

over a parameterized surface, 348

over a path, 321

over the boundary of a 3-cell, 360

upper and lower, 104

with respect to arc length, 327

with respect to surface area, 353

integral test, 135

integration by parts, 118

interchange matrix, 304

interior, 176

Intermediate Value Theorem, 66

intersection, 3

interval additivity

of the integral, 112, 295

interval of convergence, 149

inverse

additive, 16

mutlplicative, 17

of a matrix, 213

inverse function, 68, 87, 263

local, 260

Inverse Function Theorem, 264

inverse image under a function, 5

inverse trigonometric function, 60

irrational numbers, 23

cardinality, 381

isolated point, 189, 194

Jordan region, 283

characterization, 286

kernel of a linear transformation, 216

L’Hˆ opital’s Rule, 95

Lagrange multipliers, 257

Lagrange’s remainder, 157

laws of exponents, 123

least upper bound, 23

level set, 247

limit

at ±∞, 80

in

Rd,

169

infinite, 83

of a composite function, 82

of a function, 79

of a monotone function, 84

of a sequence in R, 36

of a vector function, 194

one sided, 80

limit point, 193

limits and continuity, 79

linear

equations, 219

operator, 208

transformation, 208

linear function, 208

image, 216

kernel, 216

matrix, 209

operations, 210

linear subspace, 215

linear transformation, 280

linearity of the integral, 109

linearly independent, 215

linearly ordered set, 383

lines in

Rp,

218

local

max/min, 254

log function, 60

logarithm, 121

general, 123

lower

bound, 26

integral, 104, 278

sum, 102, 277

Main Limit Theorem

for functions, 82

for sequences, 44

for vectors, 171

mathematical induction, 8

matrix, 209

columns, 209

elementary, 304

interchange, 304

inverse, 213

multiplication, 211

non-singular, 213

of a linear function, 209

operations, 210

positive definite, 254

rows, 209

scale, 304

shear, 304

submatrix, 216

max/min

for a continuous function, 65