396 Index
refinement, 103
path, 318
equivalence, 324
piecewise linear, 186
simple, 322
simple closed, 322
Peano’s axioms, 8
piecewise linear path, 186
piecewise smooth curve, 318
planes in Rp, 219
pointwise convergence, 74, 203
polar change of coordinates, 264
polynomial, 59
positive definite matrix, 254
2 × 2 case, 256
positively oriented, 349
2-cell, 341
3-cell, 360
power function, 60
power series, 148
coefficients, 148, 154
continuity of sum, 150
derivative, 151
integration, 150
interval of convergence, 149
radius of convergence, 149
Taylor series, 154
prime numbers, 12
product of series, 144
proper subset, 2
properties of N, 10
radius of convergence, 149
range of a function, 5
rank
of a linear transformation, 216
of a matrix, 216
ratio for a geometric series, 131
ratio test, 137
rational function, 60
rational number field, 18
defects of, 19
rational number system, 17
real numbers, 21
rearrangement of a series, 141, 143
rectangle
aligned, 275
recursion relation, 9
reduced form, 366
of a 0-chain, 367
of a p-chain, 370
refinement of a partition, 103, 278
relatively
closed, 184
open, 184, 197
relatively prime, 20
remainder
Lagrange form, 157
Taylor’s formula, 155
Riemann integral, 104, 279
Riemann sum, 101, 277
root test, 136
row reduction, 304
Russell’s paradox, 382
saddle point, 256
sawtooth function, 60
scalar, 162
scalar multiplication, 162
scale matrices, 304
Schr¨ oder-Bernstein Theorem, 377
separated, 184
separation theorem, 182
sequence, 8
convergent, 36
in
Rd,
169
of functions, 73, 202
of partial sums, 130
of real numbers, 34
of statements, 8
pointwise convergent, 74
uniformly Cauchy, 77, 204
uniformly convergent, 74
series, 129
p-series, 135
absolute convergence, 132
alternating, 140
alternating series test, 140
comparison test, 132
conditional convergence, 140
convergence, 129
divergent, 129
Fourier, 148
geometric, 131
harmonic, 130, 136
integral test, 135
integration of, 147
of functions, 146
partial sum, 129, 206
power, 148
product, 144
ratio test, 137
rearrangement, 141
root test, 136
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