MARC record from Internet Archive

LEADER: 08143cam 2200901Ii 4500
001 ocn910160716
003 OCoLC
005 20220206172107.0
008 150527s2015 nyua ob 001 0 eng d
006 m o d
007 cr cnu---unuuu
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020 $a1493927124$q(electronic bk.)
020 $a1493927116$q(print)
020 $a9781493927111$q(print)
024 7 $a10.1007/978-1-4939-2712-8$2doi
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037 $bSpringer
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072 7 $aMAT034000$2bisacsh
082 04 $a515$223
100 1 $aAbbott, Stephen,$d1964-$eauthor.
245 10 $aUnderstanding analysis /$cStephen Abbott.
250 $aSecond edition.
264 1 $aNew York :$bSpringer,$c2015.
300 $a1 online resource (xii, 312 pages) :$billustrations
336 $atext$btxt$2rdacontent
337 $acomputer$bc$2rdamedia
338 $aonline resource$bcr$2rdacarrier
347 $bPDF
347 $atext file
490 1 $aUndergraduate texts in mathematics
504 $aIncludes bibliographical references and index.
588 0 $aOnline resource; title from PDF title page (SpringerLink, viewed May 27, 2015).
505 0 $aPreface -- 1 The Real Numbers -- 2 Sequences and Series -- 3 Basic Topology of R -- 4 Functional Limits and Continuity -- 5 The Derivative -- 6 Sequences and Series of Functions -- 7 The Riemann Integral -- 8 Additional Topics -- Bibliography -- Index.
520 $6880-01$aThis lively introductory text exposes the student to the rewards of a rigorous study of functions of a real variable. In each chapter, informal discussions of questions that give analysis its inherent fascination are followed by precise, but not overly formal, developments of the techniques needed to make sense of them. By focusing on the unifying themes of approximation and the resolution of paradoxes that arise in the transition from the finite to the infinite, the text turns what could be a daunting cascade of definitions and theorems into a coherent and engaging progression of ideas. Acutely aware of the need for rigor, the student is much better prepared to understand what constitutes a proper mathematical proof and how to write one. Fifteen years of classroom experience with the first edition of Understanding Analysis have solidified and refined the central narrative of the second edition. Roughly 150 new exercises join a selection of the best exercises from the first edition, and three more project-style sections have been added. Investigations of Eulers computation of ℓœ(2), the Weierstrass Approximation Theorem, and the gamma function are now among the books cohort of seminal results serving as motivation and payoff for the beginning student to master the methods of analysis. Review of the first edition: This is a dangerous book. Understanding Analysis is so well-written and the development of the theory so well-motivated that exposing students to it could well lead them to expect such excellence in all their textbooks. Understanding Analysis is perfectly titled; if your students read it, thats whats going to happen. This terrific book will become the text of choice for the single-variable introductory analysis course Steve Kennedy, MAA Reviews.
546 $aEnglish.
650 0 $aMathematical analysis.
650 4 $aEngineering & Applied Sciences.
650 4 $aApplied Mathematics.
650 14 $aMathematics.
650 24 $aAnalysis.
650 6 $aAnalyse mathématique.
650 7 $aMathematical analysis.$2fast$0(OCoLC)fst01012068
653 00 $awiskunde
653 00 $amathematics
653 00 $aanalyse
653 00 $aanalysis
653 10 $aMathematics (General)
653 10 $aWiskunde (algemeen)
655 0 $aElectronic books.
655 4 $aElectronic books.
776 08 $iPrint version:$z9781493927111
830 0 $aUndergraduate texts in mathematics.
856 40 $3SpringerLink$uhttps://doi.org/10.1007/978-1-4939-2712-8
856 40 $3SpringerLink$uhttps://link.springer.com/book/10.1007%2F978-1-4939-2711-1
856 40 $3SpringerLink$uhttps://link.springer.com/book/10.1007%2F978-1-4939-2712-8
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880 $6520-01/(S$aThis lively introductory text exposes the student to the rewards of a rigorous study of functions of a real variable. In each chapter, informal discussions of questions that give analysis its inherent fascination are followed by precise, but not overly formal, developments of the techniques needed to make sense of them. By focusing on the unifying themes of approximation and the resolution of paradoxes that arise in the transition from the finite to the infinite, the text turns what could be a daunting cascade of definitions and theorems into a coherent and engaging progression of ideas. Acutely aware of the need for rigor, the student is much better prepared to understand what constitutes a proper mathematical proof and how to write one. Fifteen years of classroom experience with the first edition of Understanding Analysis have solidified and refined the central narrative of the second edition. Roughly 150 new exercises join a selection of the best exercises from the first edition, and three more project-style sections have been added. Investigations of Euler's computation of ζ(2), the Weierstrass Approximation Theorem, and the gamma function are now among the book's cohort of seminal results serving as motivation and payoff for the beginning student to master the methods of analysis. Review of the first edition: "This is a dangerous book. Understanding Analysis is so well-written and the development of the theory so well-motivated that exposing students to it could well lead them to expect such excellence in all their textbooks. ... Understanding Analysis is perfectly titled; if your students read it, that's what's going to happen. ... This terrific book will become the text of choice for the single-variable introductory analysis course ..."--Steve Kennedy, MAA Reviews
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