000			04823cam a2200433 i 4500
001			18286945
003			OSt
005			20220106022452.0
008			140902s2015 flua b 001 0 eng
010			_a 2014032604
020			_a9781482246674 (hardback : acidfree paper)
040			_aDLC _beng _cDLC _erda _dDLC
042			_apcc
050	0	0	_aQA320 _b.B68 2015
082	0	0	_a515 _223
084			_aMAT000000 _aMAT028000 _aMAT037000 _2bisacsh
100	1		_aBourchtein, Andrei, _eauthor.
245	1	0	_aCounterexamples : _bfrom elementary calculus to the beginnings of analysis / _cAndrei Bourchtein, Ludmila Bourchtein, Pelotas State University, Brazil.
264		1	_aBoca Raton : _bCRC Press, Taylor & Francis Group, _c2015.
300			_axxix, 331 pages : _billustrations ; _c25 cm.
336			_atext _2rdacontent
337			_aunmediated _2rdamedia
338			_avolume _2rdacarrier
490	0		_aTextbooks in mathematics
500			_a" A Chapman & Hall book."
504			_aIncludes bibliographical references and index.
520			_a"This book provides a one-semester undergraduate introduction to counterexamples in calculus and analysis. It helps engineering, natural sciences, and mathematics students tackle commonly made erroneous conjectures. The book encourages students to think critically and analytically, and helps to reveal common errors in many examples.In this book, the authors present an overview of important concepts and results in calculus and real analysis by considering false statements, which may appear to be true at first glance. The book covers topics concerning the functions of real variables, starting with elementary properties, moving to limits and continuity, and then to differentiation and integration. The first part of the book describes single-variable functions, while the second part covers the functions of two variables.The many examples presented throughout the book typically start at a very basic level and become more complex during the development of exposition. At the end of each chapter, supplementary exercises of different levels of complexity are provided, the most difficult of them with a hint to the solution.This book is intended for students who are interested in developing a deeper understanding of the topics of calculus. The gathered counterexamples may also be used by calculus instructors in their classes. "-- _cProvided by publisher.
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.
650		0	_aFunctional analysis _vTextbooks.
650		0	_aCalculus _vTextbooks.
650		7	_aMATHEMATICS / General. _2bisacsh
650		7	_aMATHEMATICS / Set Theory. _2bisacsh
650		7	_aMATHEMATICS / Functional Analysis. _2bisacsh
700	1		_aBourchtein, Ludmila, _eauthor.
856	4	2	_3Cover image _uhttp://images.tandf.co.uk/common/jackets/websmall/978148224/9781482246674.jpg
906			_a7 _bcbc _corignew _d1 _eecip _f20 _gy-gencatlg
942			_2ddc _cBK
999			_c448999 _d448999