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Counterexamples: from elementary calculus to the beginnings of analysis

By: Bourchtein, Andrei.
Contributor(s): Bourchtein, Ludmila.
Material type: materialTypeLabelBookSeries: Textbooks in Mathematics.Publisher: Boca Raton CRC Press 2015Description: xxix, 331 p.ISBN: 9781482246674.Subject(s): Functional analysis - Textbooks | Calculus - TextbooksDDC classification: 515 Summary: 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. (http://www.crcpress.com/product/isbn/9781482246674)
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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.
(http://www.crcpress.com/product/isbn/9781482246674)

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