Davidson K.R., Donsig A.P. Real Analysis with Real Applications
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Index 623
Schwarz inequality, 89
Secant Lemma, 579
second countable metric space, 254
second-order Mean Value Theorem, 322, 326
self-similarity, 379
sensitive dependence on initial conditions, 366
separable, 200, 253
separates points, 326
separation of variables, 406, 427
Separation Theorem, 571
sequential characterization of continuity, 121
sequential compactness, 250
sequentially compact, 251
series of functions, 225
set, 5
Sharkovskii’s Theorem, 359
sharp inequality, 169
Sierpinski snowflake, 106, 379, 385
sign function, 52
similitude, 379
Simpson’s rule, 174
sink, 332
Slater point, 603
Slater’s condition, 603
smoothest interpolation property, 321
source, 332, 337
space-filling curve, 126
span, 13
Spectral Theorem for Symmetric Matrices, 188
spline
cubic, 315
linear, 314
of order n, 555
wooden, 321
square roots, computing, 346
Squeeze Theorem, 39
stable, 337
standard basis, 14
star-shaped set, 563
steady-state heat problem, 424
Steiner, 469
step function, 163
Stirling’s formula, 172, 297
Stirling’s inequality, 172
Stone–Weierstrass Theorem, 327
strictly convex function, 585
strictly convex norm, 190, 208, 300
strictly decreasing function, 135
strictly feasible point, 603
strictly increasing function, 135
strictly monotone increasing sequence, 47
Str
¨
omberg wavelet, 546
subcover, 251
subdifferential, 580, 587
subgradient, 587
sublevel set, 585
sublinear function, 586
subordinate, 392
subsequence, 51
subset, 5
subspace, 12
substituation rule, 167
sufficiently large, 43
summable, 66
summation by parts, 84
Summation by Parts Lemma, 85
superposition, 448
support function, 590, 595
Support Function Lemma, 591
Support Theorem, 572
supporting hyperplane, 572
supremum, 46
surjective, 8
tangent cone, 596
tangent line, 141
Tauberian Theorem, 494
tautology, 2
Taylor polynomial, 276
Taylor series, 277
telescoping sum, 68
tent map, 354, 369
term-by-term differentiation, 234, 433, 449
terminal velocity, 390
ternary expansion, 104, 138
topological charactizeration of continuity, 121
topological conjugacy, 357, 373
topological spaces, 251
topologically conjugate, 373
topologically transitive, 362
totally bounded, 242, 251
totally disconnected, 258
transcendental number, 32, 65
transitive point, 351, 362
translation invariance, 163
trapezoidal rule, 170, 173
triangle inequality, 89, 90
trick, versus method, 149
trigonometric polynomial, 193
tripling map, 353
Tucker, 603
twin dragon set, 383
2-adic metric, 247, 248, 250
uncountable set, 61
624 Index
uniform approximation, 286
uniform convergence, 214
uniform norm, 275
uniformly Cauchy, 227
uniformly continuous, 127
uniformly equicontinuous, 240
unimodal, 375
union, 6
unit ball, 180
unit speed curve, 395
unitary, 515, 543
universal set, 6
upper sum, 154
van der Monde matrix, 287
vanishes (set of functions at a point), 326
variation of parameters, 415
vector addition, 11
vector lattice, 326
vector space, 11
vertical line test, 7
von Koch curve, 379
Wallis’s product, 170
wave equation, 447
wavelet, 514
Battle–Lemari
´
e or B-spline, 554
Daubechies, 528
Franklin, 541
Haar, 518
Str
¨
omberg, 546
Weierstrass, 32, 327
Weierstrass M -test, 227
Weierstrass Approximation Theorem, 288, 493,
494, 506
well defined, 13
Wilbraham, 485
Wronskian, 415
Yosida, 596
Young’s inequality, 212
Z, 6
Zermelo–Fraenkel set theory, 64
zero vector (0), 88