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Zorich V. — Mathematical Analysis
Zorich V. — Mathematical Analysis



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Название: Mathematical Analysis

Автор: Zorich V.

Аннотация:

This softcover edition of a very popular two-volume work presents a thorough first course in analysis, leading from real numbers to such advanced topics as differential forms on manifolds, asymptotic methods, integral transforms, and distributions. Especially notable in this course is the clearly expressed orientation toward the natural sciences and its informal exploration of the essence and the roots of the basic concepts and theorems of calculus. Clarity of exposition is matched by a wealth of instructive exercises, problems and fresh applications to areas seldom touched on in real analysis books.

The second volume expounds classical analysis as it is today, as a part of unified mathematics, and its interactions with modern mathematical courses such as algebra, differential geometry, differential equations, complex and functional analysis. The book provides a firm foundation for advanced work in any of these directions.



Язык: en

Рубрика: Математика/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 2004

Количество страниц: 681

Добавлена в каталог: 19.02.2014

Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID
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Предметный указатель
Dipole      299 496
Dipole moment      299 496
Dipole potential      299
Dirac, P.      237 281 464
Direct product of metric spaces      7
Direction of motion along a curve      176
Dirichlet discontinuous factor      436
Dirichlet integral      436 447 570 610
Dirichlet kernel      532 557
Dirichlet, P.      286 364 377 379 380 421 436 447 520 532 557 570 610
Discontinuous factor, Dirichlet      436
Discrete group of transformations      335
Discrete metric      2 8
Disk, n-dimensional      179 322
distribution      460
Distribution, regular      464
Distribution, singular      464
Distribution, tempered      591
Divergence      203 260 274
Divergence, physical interpretation      278—281
Domain of parameters of a chart      320
Domain, elementary      240
Domain, fundamental, of a group of automorphisms      324 336
Domain, parameter      366
Domain, simply connected      293
Double layer      496
Earnshaw, S.      286
Efficiency of a heat engine      225
Eigenvalue      518
Eigenvalue of a Sturm — Liouville problem      518
Eigenvector of an operator      519
Element of volume      227
Elementary diffeomorphism      140
Elliptic integral      393
Elliptic integral, complete, of first kind      393 411
Elliptic integral, complete, of second kind      393 411
Elliptic integral, modulus      411
Embedding, canonical      349
entropy      302
Envelope of a family of curves      252
Equality, asymptotic      598
Equality, ParaevaTs      520 529 547 569 592
Equation of an adiabatic      224
Equation of continuity      304—306
Equation of state      222
Equation, Bessel's      392 410 414 434
Equation, differential      34 226
Equation, Euler — Lagrange      91
Equation, Euler's, hydrodynamic      307
Equation, heat      302 583
Equation, hyper geometric      393
Equation, Laplace's      304 524
Equation, Mayer's      224
Equation, Poisson's      298 304 493
Equation, wave      307—310 581
Equation, wave, homogeneous      309
Equation, wave, inhomogeneous      309
Equations, Cauchy — Riemann      310
Equations, electrostatic      286
Equations, magnetostatic      286
Equations, Maxwell      262 263 275 281 298 311
Equicontinuity      397
Equivalence, asymptotic      598
Equivalent atlases with respect to orientation      175 328
Equivalent atlases with respect to smoothness      325
Erdelyi's lemma      635
Erdelyi, A.      610 635
Error function, asymptotics      628
Estimate, asymptotic      597
Estimate, asymptotic, uniform      611
Euler — Gauss formula      440
Euler — Lagrange equation      91
Euler — Poisson integral      433 442 567 580 610
Euler's formula      446
Euler's hydrodynamic equation      307
Euler, L.      91 307 433 437 440 442 446 530 567 580 610
Eulerian integral      437—448
Exact form      352
Exhaustion of a set      150
Expansion, asymptotic in the sense of Erdelyi      610
Expansion, asymptotic, uniform      611
Expansion, asymptotic, uniqueness      602
Exponential integral      600
Exponential of an operator      71—73
Exponential system      502
Exterior algebra      319
Exterior differential      201 342 349
Exterior differential of a form      342 349
Exterior point      6 13
Exterior product      195 315 342
Extremum of a function with constraint      106
Extremum of a function, necessary condition      87
Extremum of a function, sufficient condition      87
Family of functions      366
Family of functions, equicontinuous      397 398
Family of functions, equicontinuous, at a point      403—404
Family of functions, separating points      401
Family of functions, totally bounded      397
Family of functions, uniformly bounded      397
Faraday, M.      233 237
Federer, H.      236
Fejer kernel      557
Fejer, L.      538
Feynman, R.      262
Field of forms      257
Field of linear forms      197
Field, potential      288
Field, scalar      257
Field, solenoidal      295
Field, tensor      257
Field, vector      257 348
Field, vector, smooth      348
Filter, low-frequency      563
Flow, planar      310
Flow, plane-parallel      310
Flux across a surface      213—218 233 278 302 496
Force, mass      306
Form on a surface in $\mathbb{R}^{n}$      227
Form, anti-symmetric      195
Form, differential, closed      296 352
Form, differential, exact      296 352
Form, differential, flux      199
Form, differential, of class $C^{(k)}$      342
Form, differential, of compact support      344
Form, differential, on a manifold      340
Form, differential, restriction to a submanifold      350
Form, differential, work      198
Form, Hermitian      45
Form, Hermitian, nondegenerate      45
Form, Hermitian, nonnegative      45
Form, semidefinite      87
Form, skew-symmetric      195 314—316
Form, volume in $\mathbb{R^{k}}$      227
Formula for change of variable in an integral      136
Formula, asymptotic      598
Formula, Cauchy — Hadamard      375
Formula, co-area      236
Formula, complement, for the gamma function      441
Formula, Euler — Gauss      440
Formula, Euler's      446
Formula, Fourier inversion      571 592
Formula, Frenet      73
Formula, Gauss — Ostrogradskii      242—245 278 303 489 496
Formula, Gauss — Ostrogradskii in vector analysis      278
Formula, Gauss'      447
Formula, Green's      496
Formula, homotopy      360
Formula, Kotel'nikov's      586
Formula, Kronrod — Federer      236
Formula, Legendre's      446
Formula, Leibniz'      409
Formula, Newton — Leibniz      237 278 408 573
Formula, Poisson summation      593
Formula, reduction, for the beta function      438
Formula, reduction, for the gamma function      440
Formula, Stirling's      448 622
Formula, Stokes'      237 276 278 345—347 358
Formula, Stokes' in $\mathbb{R}^{3}$      245—247
Formula, Stokes' in vector analysis      277
Formula, Stokes', general      248—251 345
Formula, Taylor's      94 415
Formula, Wallis'      434 448 636
Formulas, Borel's      581
Formulas, differential, of field theory      263—265
Formulas, Green's      284 285
Formulas, integral, of vector analysis      278
Fourier coefficients, extremal property      506
Fourier cosine transform      564
Fourier integral      634
Fourier integral, asymptotics      635 639
Fourier integral, multiple      641
Fourier inversion formula      571 592
Fourier series      499—526
Fourier series in a general orthogonal system      499—500
Fourier series of generalized functions      558
Fourier series, multiple      557
Fourier series, partial sum, integral representation      531
Fourier series, pointwise convergence      527
Fourier series, rate of convergence and smoothness      540
Fourier sine transform      564
Fourier transform      561 563 566 571 574 579 583
Fourier transform in $L_{2}$      589
Fourier transform of a convolution      569
Fourier transform of generalized functions      592
Fourier transform, asymptotic properties      573—576
Fourier transform, frequency shift      587
Fourier transform, inverse      583
Fourier transform, multidimensional      577
Fourier transform, normalized      568
Fourier transform, rate of decrease and smoothness      573
Fourier transform, time shift      587
Fourier, J.      499—593 634 635
Frame, Frenet      73
Frame, orienting      172
Frechet, M.      11
Frenet, J.      73
Frequencies, natural      518
frequency      560
Frequency characteristic      562
Frequency spectrum      593
Frequency, cyclic      560
Frequency, fundamental      560
Frequency, harmonic      560
Fresnel integral      436 447 610
Fresnel, A.      436 447 610
Fubini, G.      127 580
Function of compact support      136 452
Function, band-limited      585
Function, Bessel      392 410
Function, Bessel, asymptotics      640
Function, Beta      437—439
Function, cardinal sine      588
Function, change of coordinates      321
Function, current      310
Function, delta      449 455 461 464 469 473
Function, Dirichlet      364
Function, exponential integral      600
Function, fundamental      484
Function, Gamma      439—442
Function, gamma, asymptotics      622 629
Function, gamma, incomplete      610
Function, generalized      460
Function, generalized, differentiation      465—468
Function, generalized, of several variables      484
Function, generalized, regular      464
Function, generalized, singular      464
Function, generating      471
Function, Green's      470
Function, harmonic      286 304
Function, harmonic, conjugage      310
Function, Heaviside      466 469 491 497
Function, limit      363 367
Function, linear      49
Function, locally integrable      452
Function, multilinear      49
Function, phase      634
Function, piecewise continuous      536
Function, piecewise continuously differentiable      536
Function, probability error      610
Function, probability error, asymptotics      628
Function, rapidly decreasing      575
Function, Riemann integrable, over a set      118
Function, Riemann integrable, over an interval      109
Function, sample      588
Function, sine integral      610
Function, spectrum of      560
Function, spherical      524
Function, support      451
Function, system      449 460
Function, test      463 484
Function, transient pulse      449
Function, uniformly continuous      456
Function, unit step      466
Function, zeta      447
Functional, linear      49
Functional, multilinear      49
Functions, asymptotically equal      598
Functions, asymptotically equivalent      598
Fundamental domain of a group of automorphisms      324 336
fundamental frequency      560
Fundamental sequence      21
Fundamental solution      469—470 490
Fundamental tone      518
Galilean transformation      595
Galilei, Galileo      595
Gamma function      439—442
Gamma function, asymptotics      622 629
Gamma function, incomplete      610
Gauge condition      311
Gauss — Ostrogradskii formula      237 242—245 489 496
Gauss — Ostrogradskii formula in vector analysis      278
Gauss' formula      447
Gauss' theorem      496
Gauss, C.      237 242 249 278 285 392 440 447 471 489 496
Generalized function      460
Generalized function of several variables      484
Generalized function, differentiation      465—468
Generalized function, regular      464
Generalized function, singular      464
Generating function of a sequence      471
Gibbs' phenomenon      544 556
Gibbs, J.      544 556
Graded algebra      314
Gradient      203 260 274 282
Gradient, physical interpretation      283
Gram matrix      185
Gram, J.      185 503 511
Grass maim algebra      319
Grassmann, H.      319
Green's formula      496
Green's function      470
Green's theorem      237—242
Green, G.      237 284 470 496
Group of automorphisms      324
Group, cohomology      356
Group, continuous      72 336
Group, discrete, of transformations      335
Group, homology      298 356 358
Group, homology, p-dimensional      358
Group, homotopy      298
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