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
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