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001 978-0-387-72177-4
003 DE-He213
005 20140220083710.0
007 cr nn 008mamaa
008 110513s2011 xxu| s |||| 0|eng d
020 _a9780387721774
_9978-0-387-72177-4
024 7 _a10.1007/978-0-387-72177-4
_2doi
050 4 _aQA331.5
072 7 _aPBKB
_2bicssc
072 7 _aMAT034000
_2bisacsh
072 7 _aMAT037000
_2bisacsh
082 0 4 _a515.8
_223
100 1 _aBloch, Ethan D.
_eauthor.
245 1 4 _aThe Real Numbers and Real Analysis
_h[electronic resource] /
_cby Ethan D. Bloch.
264 1 _aNew York, NY :
_bSpringer New York,
_c2011.
300 _aXXVIII, 553p. 42 illus.
_bonline resource.
336 _atext
_btxt
_2rdacontent
337 _acomputer
_bc
_2rdamedia
338 _aonline resource
_bcr
_2rdacarrier
347 _atext file
_bPDF
_2rda
505 0 _aPreface.-To the Student.-To the Instructor.- 1. Construction of the Real Numbers -- 2. Properties of the Real Numbers -- 3. Limits and Continuity -- 4. Differentiation -- 5. Integration -- 6. Limits to Infinity.-7. Transcental Functions.-8. Sequences -- 9. Series -- 10. Sequences and Series of Functions -- Bibliography -- Index.
520 _aThis text is a rigorous, detailed introduction to real analysis that presents the fundamentals with clear exposition and carefully written definitions, theorems, and proofs.  The choice of material and the flexible organization, including three different entryways into the study of the real numbers, making it equally appropriate to undergraduate mathematics majors who want to continue in mathematics, and to future mathematics teachers who want to understand the theory behind calculus.  The Real Numbers and Real Analysis is accessible to students who have prior experience with mathematical proofs and who have not previously studied real analysis. The text includes over 350 exercises.   Key features of this textbook:   - provides an unusually thorough treatment of the real numbers, emphasizing their importance as the basis of real analysis   - presents material in an order resembling that of standard calculus courses, for the sake of student familiarity, and for helping future teachers use real analysis to better understand calculus   - emphasizes the direct role of the Least Upper Bound Property in the study of limits, derivatives and integrals, rather than relying upon sequences for proofs; presents the equivalence of various important theorems of real analysis with the Least Upper Bound Property   - includes a thorough discussion of some topics, such as decimal expansion of real numbers, transcendental functions, area and the number p, that relate to calculus but that are not always treated in detail in real analysis texts   - offers substantial historical material in each chapter   This book will serve as an excellent one-semester text for undergraduates majoring in mathematics, and for students in mathematics education who want a thorough understanding of the theory behind the real number system and calculus.
650 0 _aMathematics.
650 0 _aGlobal analysis (Mathematics).
650 0 _aSequences (Mathematics).
650 1 4 _aMathematics.
650 2 4 _aReal Functions.
650 2 4 _aAnalysis.
650 2 4 _aSequences, Series, Summability.
710 2 _aSpringerLink (Online service)
773 0 _tSpringer eBooks
776 0 8 _iPrinted edition:
_z9780387721767
856 4 0 _uhttp://dx.doi.org/10.1007/978-0-387-72177-4
912 _aZDB-2-SMA
999 _c105030
_d105030