392 Index
curve
branch of, 245
closed, 194
degenerate, 195
derivative of, 244, 317
parameterized, 194
piecewise smooth, 318
smooth, 318
tangent line, 244
trace of, 318
cut number, 22
cycle
1-cycle, 367
p-cycle, 370
equivalence, 372
cylinder, 196
decreasing function, 67, 91
Dedekind cut, 21
degenerate
curve, 195
rectangle, 276
surface, 195
dependent variable notation, 240
derivative
and monotonicity, 91
and uniform continuity, 92
bounded, 92
definition, 84
directional, 243
of a power series, 151
of a smooth curve, 317
of an inverse function, 87
of curve, 244
theorems, 85
vanishing, 91
diameter of a set, 181
differentiable, 84
conditions for, 233
equivalent definition, 236
for vector functions, 230
differential
of a 1-form, 332
of a 2-form, 334
of the inner product, 239
differential form, 317
1-form, 320
2-form, 332
3-form, 334
p-form, 335
closed, 335
exact, 335
higher-order, 331
transformation laws, 335
differential matrix, 231, 232
direction, 243
directional derivative, 243
disjoint sets, 5
distance
in R, 33
in
Rd,
164
in a metric space, 168
distributive law, 16
for scalar multiplication, 162
divergent series, 129
division algorithm, 15
domain of a function, 5, 59, 191
dominated by a set, 376
elementary function, 60
elementary matrices, 304
elements of a set, 2
empty set, 3
endpoints of a curve, 194
equivalent
cycles, 372
paths, 324
Euclidean
inner product, 163
metric, 169
space, 161
exact differential form, 335
exponent laws, 123
exponential function, 60, 122
extended real number system, 27
exterior differential, 332, 334, 335
exterior product, 332
faces
of a p-cell, 370
of a cube, 359
factors, 12
field, 17
field of rational numbers, 17
finite subcover, 179
fixed point, 93
fluid flow, 363
flux, 354
form
1-form, 320
2-form, 332
3-form, 334
p-form, 335
Fourier coefficients, 119
Previous Page Next Page