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Strichartz R.S. — The way of analysis
Strichartz R.S. — The way of analysis

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Название: The way of analysis

Автор: Strichartz R.S.

Аннотация:

Mathematics is a way of thought. Attaining a deep understanding of mathematics is more than mastering a collection of theorems, definitions, problems, and techniques; it is understanding how theorems and definitions fit together with the overall strategy of arguments presented. This introduction to real analysis contains thorough and complete proofs with lively and generous explanation to guide the reader through the foundations and the way of analysis. Real analysis, in one and several variables, is developed from the construction of the real number system to an introduction to the Lebesgue integral. Additionally, there are three chapters on applications of analysis, ordinary differential equations, Fourier series, and curves and surfaces, to show how the techniques of analysis are used in concrete settings.


Язык: en

Рубрика: Математика/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 2000

Количество страниц: 760

Добавлена в каталог: 11.05.2009

Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID
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Предметный указатель
$C([a,b])$      359
$\epsilon$-neighborhood      709
$\pi$      349
$\sigma$-additivity      628 634 643
$\sigma$-field      633
$\sigma$-finite measures      703
$\sigma$-subadditivity      636 643
${C}^{1}$      151 422
${C}^{2}$      177 440
${C}^{k}$      440
${C}^{\infty}$      281 440
${D}_{N}$      533
${F}_{\sigma}$ set      232
${G}_{\delta}$ set      232 639 642
${K}_{N}$      539
${L}^{1}$      670
${L}^{1}$ convolution theorem      698
${L}^{1}$ metric      376
${L}^{2}$      673
${L}^{2}$-norm      544
A primer of real analytic functions      294
a.e.      667
Absolute convergence      250
Absolute convergence of Fourier series      548
Absolute value      20 242
Absolutely convergent      253 260 262 664
Absolutely convergent improper integral      233
Absolutely convergent integral      655
Acceleration      177
Accumulation point      79
Additive      662 664
Additive group      327
Additive identity      41
Additivity      206 224 231 628 644
Affine approximation      419
Affine function      145 419
Algebra      399 631
algebraic      177
Algebraic identities      48
Algebraically complete      242
Algorithm      66
Almost everywhere      550 667
Alternating      706
Analytic continuation      281 285
Analytic expression      558
Analytic functions      285 286 293
angle      360
Anti-derivative      208 520
Approximate identity      297 330 533 558
Approximate identity lemma      301 541
Approximating sum      201
Approximation by polynomials      296
ARC      394
Arc length      212 610 614
Arc length parametrization      616 653
Archimedes      xiii
arcsin      338
Arctangent      218 346 349
Arctangent integral      346
Arcwise connectedness      393
Area      201 631
Area under the graph      201 695
Arithmetic      38
Arzela — Ascoli theorem      312 383 392 410 485 490 492
ASSOCIATED      361
Associative      41 298 356
Attractor      412
Autonomous      502 581
Average      206
Average value      668
Axiom of Archimedes      20 34 42 46 47 63 64 370
Ball      369
Banach space      355 377 670
Basis      356
bernoulli      xiii 515 547
Bessel functions      285 348
Bessel's differential equation      501
Bessel's inequality      544 546
Bessel's o.d.e.      500
Best affine approximation      148 420
Best approximation      307
Big oh      147
Bilinearity      360
Binomial expansion      252 287
Binomial series      295
Binomial theorem      279 324
Bishop      26 66
Blip functions      329
Bolzano      xiv 25 403
Bolzano's example      403
Boolean algebra      632
Borel      332
Borel sets      633
boundary conditions      464 519 520 529
Bounded      40 84
Bounded away from zero      46
Bounded from above      75
Bounded variation      618
Boundedness      382
Broken line segment      395
Brouwer      399
Brouwer fixed point theorem      399
Brouwer's invariance of domain theorem      717
Brownian motion      403
Cantor      xiv 8 11 25 634
Cantor set      95 99 633 641 652 554 659
Caratheodory      643 648
Caratheodory theorem      652
Cardinality      8
Carleson      550
Cartesian coordinate      581 715
Cartesian product      10 13 22 601 700
Cauchy      xiv 25 30 268
Cauchy completion of the rationals      26
Cauchy criterion      30 50 234 253 265 274 313 374
Cauchy data      467
Cauchy initial value conditions      467
Cauchy Principal Value Integrals      234
Cauchy problem      467
Cauchy sequence      25 31 34 36 50. 246 374 376
Cauchy sum      202 220 247 249 268 487 692
Cauchy — Kovalevsky theorem      494
Cauchy — Schwartz inequality      361 362 365 479 674
Cauchy's method of majorants      496
Celestial mechanics      459
Center      369
Cesaro summability      538 550
Chain rule      168 428
Change of variable      211 232 705 713 717 719
Character identity      526
Characteristic function      275 308 658 694
Characteristic polynomial      445
Characters      527
Chebyshev inequality      672 675 681
Choice function      23
Chord-length      369
circle      583 584 593 599
CIS      343
Classical mechanics      505
Classical real number system      26
Closed interval      86
Closed sets      91 373
Closure      97 373
Closure properties      372
Cluster point      79 92
Cohen      12
Commutative      41
Commutative group      356 526
Commutativity      298
Compact domains      131 391
Compact sets      99
Compactness      309 377
Comparison Test      253 255 262
complete      382 672
Completeness      28 34 50 246 374 547 680
Completeness of the reals      51
Completion      376 670
Complex analysis      247
Complex conjugate      250
Complex domains      286
Complex exponentials      344
Complex inner product      365
Complex multiplication      347
Complex number system      241
complex numbers      54
Complex plane      285
Complex square root      573
Complex vector space      364
Complex-valued functions      247 274
composition      168 288
Compound interest      336
Computer experiment      255
Conditional continuity from above      635
Conditional probability      655
Configuration space      505
Connectedness      113 393
Conservation of energy      506
Constant coefficient partial differential operator      454
Constraints      602
Construction      68
Constructive analysis      66
Constructive content      66
Constructive real number system      26
Constructivism      6
Content      228
Content zero      228 693
Continued fractions      55
Continuity from below      635
Continuity of translation      681
continuous      111 388
Continuous differentiability      148
Continuous from the right      125
Continuous functions      387
Continuously differentiate      151 422
Continuum Hypothesis      12
Contour map      436
Contractive mapping principle      397 469 471 476 482 574 575
Contrapositive      2
Converge      36 373
Converge conditionally      258
Converge unconditionally      258
Converge uniformly on compact sets      268
Convergence      250 276
Convergence in the mean      543
Convergent subsequence      310
CONVERSE      2
Convolution      297 698
Cookbook      463
Coordinate components      389
Coordinate maps      599
Coordinate patches      595 599
Coordinate projections      389
Corners      151
Cosine      285 337 344
Countable      9
Countable additivity      628
Countable axiom of choice      22 381
Countable coverings      637
Countable dense subset      98 312 380
Countable sets      8
Counting measure      640 654
Coupled      467
Cover      101
Cramer's rule      570
Critical point      441 451
Critical set      718 719
Cross product      435
Crumpled handkerchief      626
Cube root      55 151
Curl      508
Curve      394 568 581
Curvilinear coordinates      581
Cusp      584 585
D'Alembert      518
Damped vibrating string equation      529
Damping term      518
Decreasing      154
Dedekind      xiv 25 59
Dedekind cuts      56 59
Dedekind real number system      60
Definite integral      201
Definition of the integral      660
Degree      390
Dense      28 97 374
Density of continuous functions      678
Density of the rationals      34 48
Derivative      143 420
Derived set      99
Determinants      570 705
Diagonal      313
Diagonalizable      444
Diagonalization argument      11 81
Diameter      382 652
Difference equation      485
Difference operator      439
Differential      420 597
Differentiate      144 404 419 420
Differentiation of integrals      207 432 668
Dilate      650
Direct proof      6
Directional derivative      423
Dirichlet      223 531 559
Dirichlet boundary conditions      521
Dirichlet kernel      533 539 551
Dirichlet problem      561
Dirichlet's function      223 225 228 270 624
Discontinuity of the first kind      125
Discontinuity of the second kind      125 275
Discriminant      55
Distance function      357
Diverge to $\infty$      251
Divergent      251
Divide and conquer      53 76 130
Domain      111
Dominated Convergence Theorem      625 666 670
Dominates      225 665
Dot product      360 435
Double indexed series      260 262 704
Doubling time      336
Du Bois Reymond      550
Dyadic pieces      255
e      323
Eigenvalue      444 521
Eigenvector      444 521
Einstein      459
Elementary functions      389
Embedded surfaces      585
Embeddings      585 588
Empirical evidence      520
Energy      505
entropy      610
Equality of mixed partials      437
Equation of a vibrating string      515
Equicontinuity      309
Equivalence class      35 36 668 671
Equivalent      34 85 386 671
Euclid      59
Euclidean distance      357
Euclidean inner product      361
Euclidean norm      358
1 2 3
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