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Zorich V.A., Cooke R. — Mathematical analysis II
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Название: Mathematical analysis IIАвторы: Zorich V.A., Cooke R. Аннотация: This 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: Рубрика: Математика /Статус предметного указателя: Готов указатель с номерами страниц ed2k: ed2k stats Год издания: 2004Количество страниц: 691Добавлена в каталог: 17.11.2013Операции: Положить на полку |
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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, Parseval's 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, difierential 34 226 Equation, Euler — Lagrange 91 Equation, Euler's, hydrodynamic 307 Equation, heat 302 583 Equation, hypergeometric 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 227 Form, anti-symmetric 195 Form, differential, closed 296 352 Form, differential, exact 296 352 Form, differential, flux 199 Form, differential, of class 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 227 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, for change of variable in an integral 136 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, Kotelnikov'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', general 248—251 345 Formula, Stokes', in 3 245—247 Formula, Stokes', in vector analysis 277 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 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 Grassmann 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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