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041 1 _aeng
_hrus
042 _apcc
050 0 0 _i.Z67 2004
072 7 _aQA
_2lcco
082 0 0 _a515
_222
084 _a515
_bZ M
100 1 _aZorich, V. A.
_q(Vladimir Antonovich).)
240 1 0 _aMatematicheski?i analiz.
_lEnglish
245 1 0 _aMathematical analysis
_h[[Book] /]
_cVladimir A. Zorich ; [translator, Roger Cooke].
246 3 3 _aMathematical analysis I.
246 3 3 _aMathematical analysis II.
250 _a1th ed.
260 _aBerlin ;
_aNew York :
_bSpringer,
_cc2004.
300 _a2 v. :
_bill. ;
_c25 cm.
490 0 _aUniversitext
504 _aIncludes bibliographical references and indexes.
505 0 0 _gv.1.
_tMathematical analysis 1 --
_g1.
_tSome general mathematical concepts and notation --
_g2. The.
_treal numbers --
_g3.
_tLimits --
_g4.
_tContinuous functions --
_g5.
_tDifferential calculus --
_g6.
_tIntegration --
_g7.
_tFunctions of several variables --
_g8.
_tDifferential calculus in several variables --
_tSome problems from the midterm examinations --
_tExamination topics --
_tReferences --
_tSubject index --
_tName index.
505 0 0 _gv. 2.
_tMathematical analysis 2 --
_g9.
_tContinuous mappings (general theory) --
_g10.
_tDifferential calculus from a general viewpoint --
_g11.
_tMultiple integrals --
_g12.
_tSurfaces and differential forms in Rn --
_g13.
_tLine and surface integrals --
_g14.
_tElements of vector analysis and field theory --
_g15.
_tIntegration of differential forms of manifolds --
_g16.
_tUniform convergence and basic operations of analysis --
_g17.
_tIntegrals depending on a parameter --
_g18.
_tFourier series and Fourier transform --
_g19.
_tAsymptotic expansions --
_tTopics and questions for midterm examinations --
_tExamination topics --
_tReferences --
_tIndex of basic notation --
_tSubject index --
_tName index.
520 _aThis 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, Fourier, Laplace, and Legendre transforms, elliptic functions 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 first volume constitutes a complete course on one-variable calculus along with the multivariable differential calculus elucidated in an up-to-day, clear manner, with a pleasant geometric flavor. 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. - Publisher.
521 _aAll Ages.
650 0 _aMathematical analysis.
700 1 _aCooke, Roger,
_d1942-
938 _aOtto Harrassowitz
_bHARR
_nhar035031282
_c53.45 EUR
938 _aBaker & Taylor
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