Counterexamples in Calculus PDF Download
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Author: Sergiy Klymchuk
Publisher: American Mathematical Soc.
ISBN: 0883857650
Category : Mathematics
Languages : en
Pages : 113
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Book Description
Counterexamples in Calculus serves as a supplementary resource to enhance the learning experience in single variable calculus courses. This book features carefully constructed incorrect mathematical statements that require students to create counterexamples to disprove them. Methods of producing these incorrect statements vary. At times the converse of a well-known theorem is presented. In other instances crucial conditions are omitted or altered or incorrect definitions are employed. Incorrect statements are grouped topically with sections devoted to: Functions, Limits, Continuity, Differential Calculus and Integral Calculus. This book aims to fill a gap in the literature and provide a resource for using counterexamples as a pedagogical tool in the study of introductory calculus.
Author: Sergiy Klymchuk
Publisher: American Mathematical Soc.
ISBN: 0883857650
Category : Mathematics
Languages : en
Pages : 113
Get Book Here
Book Description
Counterexamples in Calculus serves as a supplementary resource to enhance the learning experience in single variable calculus courses. This book features carefully constructed incorrect mathematical statements that require students to create counterexamples to disprove them. Methods of producing these incorrect statements vary. At times the converse of a well-known theorem is presented. In other instances crucial conditions are omitted or altered or incorrect definitions are employed. Incorrect statements are grouped topically with sections devoted to: Functions, Limits, Continuity, Differential Calculus and Integral Calculus. This book aims to fill a gap in the literature and provide a resource for using counterexamples as a pedagogical tool in the study of introductory calculus.
Author: Bernard R. Gelbaum
Publisher: Courier Corporation
ISBN: 0486134911
Category : Mathematics
Languages : en
Pages : 226
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Book Description
These counterexamples deal mostly with the part of analysis known as "real variables." Covers the real number system, functions and limits, differentiation, Riemann integration, sequences, infinite series, functions of 2 variables, plane sets, more. 1962 edition.
Author: Sergiy Klymchuk
Publisher: American Mathematical Soc.
ISBN: 161444109X
Category : Mathematics
Languages : en
Pages : 101
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Book Description
Counterexamples in Calculus serves as a supplementary resource to enhance the learning experience in single variable calculus courses. This book features carefully constructed incorrect mathematical statements that require students to create counterexamples to disprove them. Methods of producing these incorrect statements vary. At times the converse of a well-known theorem is presented. In other instances crucial conditions are omitted or altered or incorrect definitions are employed. Incorrect statements are grouped topically with sections devoted to: Functions, Limits, Continuity, Differential Calculus and Integral Calculus. This book aims to fill a gap in the literature and provide a resource for using counterexamples as a pedagogical tool in the study of introductory calculus.
Author: Bernard R. Gelbaum
Publisher: Springer Science & Business Media
ISBN: 1461209935
Category : Mathematics
Languages : en
Pages : 339
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Book Description
The gratifying response to Counterexamples in analysis (CEA) was followed, when the book went out of print, by expressions of dismay from those who were unable to acquire it. The connection of the present volume with CEA is clear, although the sights here are set higher. In the quarter-century since the appearance of CEA, mathematical education has taken some large steps reflected in both the undergraduate and graduate curricula. What was once taken as very new, remote, or arcane is now a well-established part of mathematical study and discourse. Consequently the approach here is designed to match the observed progress. The contents are intended to provide graduate and ad vanced undergraduate students as well as the general mathematical public with a modern treatment of some theorems and examples that constitute a rounding out and elaboration of the standard parts of algebra, analysis, geometry, logic, probability, set theory, and topology. The items included are presented in the spirit of a conversation among mathematicians who know the language but are interested in some of the ramifications of the subjects with which they routinely deal. Although such an approach might be construed as demanding, there is an extensive GLOSSARY jlNDEX where all but the most familiar notions are clearly defined and explained. The object ofthe body of the text is more to enhance what the reader already knows than to review definitions and notations that have become part of every mathematician's working context.
Author: Andrei Bourchtein
Publisher: CRC Press
ISBN: 1482246678
Category : Mathematics
Languages : en
Pages : 363
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Book Description
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.
Author: John Mason
Publisher:
ISBN: 9781848163591
Category : Mathematics
Languages : en
Pages : 124
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Book Description
This book makes accessible to calculus students in high school, college and university a range of counter-examples to "conjectures" that many students erroneously make. In addition, it urges readers to construct their own examples by tinkering with the ones shown here in order to enrich the example spaces to which they have access, and to deepen their appreciation of conspectus and conditions applying to theorems.
Author: S.M. Khaleelulla
Publisher: Springer
ISBN: 3540392688
Category : Mathematics
Languages : en
Pages : 200
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Book Description
Author: Lynn Arthur Steen
Publisher: Courier Corporation
ISBN: 0486319296
Category : Mathematics
Languages : en
Pages : 274
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Book Description
Over 140 examples, preceded by a succinct exposition of general topology and basic terminology. Each example treated as a whole. Numerous problems and exercises correlated with examples. 1978 edition. Bibliography.
Author: Kenneth A. Ross
Publisher: CUP Archive
ISBN:
Category : Mathematics
Languages : en
Pages : 192
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Book Description
Author: John H Mason
Publisher: Imperial College Press
ISBN: 191129850X
Category : Mathematics
Languages : en
Pages : 116
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Book Description
This book makes accessible to calculus students in high school, college and university a range of counter-examples to “conjectures” that many students erroneously make. In addition, it urges readers to construct their own examples by tinkering with the ones shown here in order to enrich the example spaces to which they have access, and to deepen their appreciation of conspectus and conditions applying to theorems./a
