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001400522 020__ $$z9781482246674 (hardback)
001400522 020__ $$a9781482246681 (e-book)
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001400522 035__ $$a(OCoLC)908079550
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001400522 050_4 $$aQA320$$b.B68 2015
001400522 0820_ $$a515$$223
001400522 1001_ $$aBourchtein, Andrei,$$eauthor.
001400522 24510 $$aCounterexamples :$$bfrom elementary calculus to the beginnings of analysis /$$cAndrei Bourchtein, Ludmila Bourchtein.
001400522 264_1 $$aBoca Raton :$$bCRC Press,$$c2015.
001400522 300__ $$a1 online resource (358 pages) :$$billustrations.
001400522 336__ $$atext$$2rdacontent
001400522 337__ $$acomputer$$2rdamedia
001400522 338__ $$aonline resource$$2rdacarrier
001400522 4900_ $$aTextbooks in mathematics
001400522 504__ $$aIncludes bibliographical references and index.
001400522 506__ $$aAccess limited to authorized users.
001400522 520__ $$a"In this manuscript we present counterexamples to different false statements, which frequently arise in the calculus and fundamentals of real analysis, and which may appear to be true at first glance. A counterexample is understood here in a broad sense as any example that is counter to some statement. The topics covered concern functions of real variables. The first part (chapters 1-6) is related to single-variable functions, starting with elementary properties of functions (partially studied even in college), passing through limits and continuity to differentiation and integration, and ending with numerical sequences and series. The second part (chapters 7-9) deals with function of two variables, involving limits and continuity, differentiation and integration. One of the goals of this book is to provide an outlook of important concepts and theorems in calculus and analysis by using counterexamples.We restricted our exposition to the main definitions and theorems of calculus in order to explore different versions (wrong and correct) of the fundamental concepts and to see what happens a few steps outside of the traditional formulations. Hence, many interesting (but more specific and applied) problems not related directly to the basic notions and results are left out of the scope of this manuscript. The selection and exposition of the material are directed, in the first place, to those calculus students who are interested in a deeper understanding and broader knowledge of the topics of calculus. We think the presented material may also be used by instructors that wish to go through the examples (or their variations) in class or assign them as homework or extra-curricular projects. In order to make the majority of the examples and solutions accessible to"--$$cProvided by publisher.
001400522 588__ $$aDescription based on print version record.
001400522 650_0 $$aFunctional analysis$$vTextbooks.
001400522 650_0 $$aCalculus$$vTextbooks.
001400522 655_0 $$aElectronic books
001400522 7001_ $$aBourchtein, Ludmila,$$eauthor.
001400522 77608 $$iPrint version:$$aBourchtein, Andrei.$$tCounterexamples : from elementary calculus to the beginnings of analysis.$$dBoca Raton : CRC Press, 2015$$z9781482246674
001400522 852__ $$bebk
001400522 85640 $$3ProQuest Ebook Central Academic Complete $$uhttps://univsouthin.idm.oclc.org/login?url=https://ebookcentral.proquest.com/lib/usiricelib-ebooks/detail.action?docID=1683505$$zOnline Access
001400522 909CO $$ooai:library.usi.edu:1400522$$pGLOBAL_SET
001400522 980__ $$aBIB
001400522 980__ $$aEBOOK
001400522 982__ $$aEbook
001400522 983__ $$aOnline