LEADER 03966nam 22006255 450 001 9910300255803321 005 20200702030947.0 010 $a1-4939-2766-3 024 7 $a10.1007/978-1-4939-2766-1 035 $a(CKB)3710000000521673 035 $a(SSID)ssj0001585497 035 $a(PQKBManifestationID)16264743 035 $a(PQKBTitleCode)TC0001585497 035 $a(PQKBWorkID)14864158 035 $a(PQKB)10692012 035 $a(DE-He213)978-1-4939-2766-1 035 $a(MiAaPQ)EBC6310709 035 $a(MiAaPQ)EBC5596286 035 $a(Au-PeEL)EBL5596286 035 $a(OCoLC)1076262794 035 $a(PPN)190532041 035 $a(EXLCZ)993710000000521673 100 $a20151008d2015 u| 0 101 0 $aeng 135 $aurnn|008mamaa 181 $ctxt 182 $cc 183 $acr 200 10$aReal Analysis $eFoundations and Functions of One Variable /$fby Miklós Laczkovich, Vera T. Sós 205 $a1st ed. 2015. 210 1$aNew York, NY :$cSpringer New York :$cImprint: Springer,$d2015. 215 $a1 online resource (X, 483 p. 94 illus.) 225 1 $aUndergraduate Texts in Mathematics,$x0172-6056 300 $aBibliographic Level Mode of Issuance: Monograph 311 $a1-4939-2765-5 320 $aIncludes bibliographical references and index. 327 $aA Short Historical Introduction -- Basic Concepts -- Real Numbers -- Infinite Sequences I -- Infinite Sequences II -- Infinite Sequences III -- Rudiments of Infinite Series -- Countable Sets -- Real Valued Functions of One Variable -- Continuity and Limits of Functions -- Various Important Classes of Functions (Elementary Functions) -- Differentiation -- Applications of Differentiation -- The Definite Integral -- Integration -- Applications of Integration -- Functions of Bounded Variation -- The Stieltjes Integral -- The Improper Integral. 330 $aBased on courses given at Eötvös Loránd University (Hungary) over the past 30 years, this introductory textbook develops the central concepts of the analysis of functions of one variable - systematically, with many examples and illustrations, and in a manner that builds upon, and sharpens, the students' mathematical intuition. The modular organization of the book makes it adaptable for either semester or year-long introductory courses, while the wealth of material allows for it to be used at various levels of student sophistication in all programs where analysis is a part of the curriculum, including teachers' education. In the spirit of learning-by-doing, Real Analysis includes more than 500 engaging exercises for the student keen on mastering the basics of analysis. There are frequent hints and occasional complete solutions provided for the more challenging exercises making it an ideal choice for independent study. The book includes a solid grounding in the basics of logic and proofs, sets, and real numbers, in preparation for a rigorous study of the main topics: limits, continuity, rational functions and transcendental functions, differentiation, and integration. Numerous historical notes and applications to other areas of mathematics, and to physics, are given, thereby demonstrating the practical scope and power of mathematical analysis. 410 0$aUndergraduate Texts in Mathematics,$x0172-6056 606 $aMathematical analysis 606 $aAnalysis (Mathematics) 606 $aAnalysis$3https://scigraph.springernature.com/ontologies/product-market-codes/M12007 615 0$aMathematical analysis. 615 0$aAnalysis (Mathematics). 615 14$aAnalysis. 676 $a515 700 $aLaczkovich$b Miklós$4aut$4http://id.loc.gov/vocabulary/relators/aut$0621870 702 $aSós$b Vera T$4aut$4http://id.loc.gov/vocabulary/relators/aut 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910300255803321 996 $aReal Analysis$92004344 997 $aUNINA