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Counterexamples : = from elementary ...

Bourchtein, Andrei.

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Counterexamples : = from elementary calculus to the beginnings of analysis /

紀錄類型:	書目-語言資料,印刷品 : Monograph/item
正題名/作者:	Counterexamples :/ Andrei Bourchtein, Ludmila Bourchtein.
其他題名:	from elementary calculus to the beginnings of analysis /
作者:	Bourchtein, Andrei.
其他作者:	Bourchtein, Ludmila.
出版者:	Boca Raton :CRC Press, : c2015.,
面頁冊數:	xxix, 331 p. :ill. ;25 cm.
標題:	Functional analysis -
電子資源:	http://images.tandf.co.uk/common/jackets/websmall/978148224/9781482246674.jpg
ISBN:	9781482246674

Counterexamples : = from elementary calculus to the beginnings of analysis /
Bourchtein, Andrei.

Counterexamples :from elementary calculus to the beginnings of analysis /Andrei Bourchtein, Ludmila Bourchtein. - Boca Raton :CRC Press,c2015. - xxix, 331 p. :ill. ;25 cm. - Textbooks in mathematics.

Includes bibliographical references (p. 323) and index.

"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. "--

ISBN: 9781482246674UK56.99

LCCN: 2014032604Subjects--Topical Terms:

731345
Functional analysis

LC Class. No.: QA320 / .B68 2015

Dewey Class. No.: 515

Counterexamples : = from elementary calculus to the beginnings of analysis /
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050 0 0 $a QA320 $b .B68 2015
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100 1 $a Bourchtein, Andrei. $3 2184831
245 1 0 $a Counterexamples : $b from elementary calculus to the beginnings of analysis / $c Andrei Bourchtein, Ludmila Bourchtein.
260 $a Boca Raton : $b CRC Press, $c c2015.
300 $a xxix, 331 p. : $b ill. ; $c 25 cm.
490 0 $a Textbooks in mathematics
504 $a Includes bibliographical references (p. 323) 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. "-- $c Provided 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"-- $c Provided by publisher.
650 0 $a Functional analysis $3 731345
650 0 $a Calculus $3 696914
700 1 $a Bourchtein, Ludmila. $3 2184832
856 4 2 $3 Cover image $u http://images.tandf.co.uk/common/jackets/websmall/978148224/9781482246674.jpg