LEADER 03991nam 22006135 450 001 9910299761103321 005 20220218163727.0 010 $a1-4939-2712-4 024 7 $a10.1007/978-1-4939-2712-8 035 $a(CKB)3710000000416768 035 $a(SSID)ssj0001501781 035 $a(PQKBManifestationID)11814883 035 $a(PQKBTitleCode)TC0001501781 035 $a(PQKBWorkID)11446579 035 $a(PQKB)10845717 035 $a(DE-He213)978-1-4939-2712-8 035 $a(MiAaPQ)EBC6315242 035 $a(MiAaPQ)EBC5595223 035 $a(Au-PeEL)EBL5595223 035 $a(OCoLC)910160716 035 $a(PPN)18603038X 035 $a(EXLCZ)993710000000416768 100 $a20150519d2015 u| 0 101 0 $aeng 135 $aurnn#008mamaa 181 $ctxt 182 $cc 183 $acr 200 10$aUnderstanding Analysis /$fby Stephen Abbott 205 $a2nd ed. 2015. 210 1$aNew York, NY :$cSpringer New York :$cImprint: Springer,$d2015. 215 $a1 online resource (XII, 312 p. 36 illus.) 225 1 $aUndergraduate Texts in Mathematics,$x0172-6056 300 $aBibliographic Level Mode of Issuance: Monograph 311 0 $a1-4939-2711-6 320 $aIncludes bibliographical references (pages 305-306) and index. 327 $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. . 330 $aThis lively introductory text exposes the student to the rewards of a rigorous study of functions of a real variable. In each chapter, informal discussions of questions that give analysis its inherent fascination are followed by precise, but not overly formal, developments of the techniques needed to make sense of them. By focusing on the unifying themes of approximation and the resolution of paradoxes that arise in the transition from the finite to the infinite, the text turns what could be a daunting cascade of definitions and theorems into a coherent and engaging progression of ideas. Acutely aware of the need for rigor, the student is much better prepared to understand what constitutes a proper mathematical proof and how to write one. Fifteen years of classroom experience with the first edition of Understanding Analysis have solidified and refined the central narrative of the second edition. Roughly 150 new exercises join a selection of the best exercises from the first edition, and three more project-style sections have been added. Investigations of Euler?s computation of ?(2), the Weierstrass Approximation Theorem, and the gamma function are now among the book?s cohort of seminal results serving as motivation and payoff for the beginning student to master the methods of analysis. Review of the first edition: ?This is a dangerous book. Understanding Analysis is so well-written and the development of the theory so well-motivated t hat exposing students to it could well lead them to expect such excellence in all their textbooks. ? Understanding Analysis is perfectly titled; if your students read it, that?s what?s going to happen. ? This terrific book will become the text of choice for the single-variable introductory analysis course ? ? ? Steve Kennedy, MAA Reviews . 410 0$aUndergraduate Texts in Mathematics,$x0172-6056 606 $aMathematical analysis 606 $aCalculus 606 $aAnalysis$3https://scigraph.springernature.com/ontologies/product-market-codes/M12007 615 0$aMathematical analysis. 615 0$aCalculus. 615 14$aAnalysis. 676 $a515 700 $aAbbott$b Stephen$4aut$4http://id.loc.gov/vocabulary/relators/aut$0352205 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910299761103321 996 $aUnderstanding analysis$9378435 997 $aUNINA