Counter Examples In Calculus
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Counterexamples In Calculus
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Author : Sergiy Klymchuk
language : en
Publisher: American Mathematical Soc.
Release Date : 2010-12-31
Counterexamples In Calculus written by Sergiy Klymchuk and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2010-12-31 with Mathematics categories.
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.
Using Counter Examples In Calculus
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Author : John H Mason
language : en
Publisher: Imperial College Press
Release Date : 2009-05-25
Using Counter Examples In Calculus written by John H Mason and has been published by Imperial College Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2009-05-25 with Mathematics categories.
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
Counterexamples In Analysis
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Author : Bernard R. Gelbaum
language : en
Publisher: Courier Corporation
Release Date : 2003-06-04
Counterexamples In Analysis written by Bernard R. Gelbaum and has been published by Courier Corporation this book supported file pdf, txt, epub, kindle and other format this book has been release on 2003-06-04 with Mathematics categories.
These counterexamples deal mostly with the part of analysis known as "real variables." The 1st half of the book discusses the real number system, functions and limits, differentiation, Riemann integration, sequences, infinite series, more. The 2nd half examines functions of 2 variables, plane sets, area, metric and topological spaces, and function spaces. 1962 edition. Includes 12 figures.
Counterexamples
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Author : Andrei Bourchtein
language : en
Publisher: CRC Press
Release Date : 2014-09-09
Counterexamples written by Andrei Bourchtein and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-09-09 with Mathematics categories.
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.
Counter Examples In Calculus
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Author : Sergiy Klymchuk
language : en
Publisher:
Release Date : 2005
Counter Examples In Calculus written by Sergiy Klymchuk and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2005 with Calculus categories.
Elementary Analysis
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Author : Kenneth A. Ross
language : en
Publisher: CUP Archive
Release Date : 2014-01-15
Elementary Analysis written by Kenneth A. Ross and has been published by CUP Archive this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-01-15 with Mathematics categories.
Counterexamples In Topology
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Author : Lynn Arthur Steen
language : en
Publisher: Courier Corporation
Release Date : 2013-04-22
Counterexamples In Topology written by Lynn Arthur Steen and has been published by Courier Corporation this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-04-22 with Mathematics categories.
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.
Advanced Calculus Revised Edition
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Author : Lynn Harold Loomis
language : en
Publisher: World Scientific Publishing Company
Release Date : 2014-02-26
Advanced Calculus Revised Edition written by Lynn Harold Loomis and has been published by World Scientific Publishing Company this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-02-26 with Mathematics categories.
An authorised reissue of the long out of print classic textbook, Advanced Calculus by the late Dr Lynn Loomis and Dr Shlomo Sternberg both of Harvard University has been a revered but hard to find textbook for the advanced calculus course for decades.This book is based on an honors course in advanced calculus that the authors gave in the 1960's. The foundational material, presented in the unstarred sections of Chapters 1 through 11, was normally covered, but different applications of this basic material were stressed from year to year, and the book therefore contains more material than was covered in any one year. It can accordingly be used (with omissions) as a text for a year's course in advanced calculus, or as a text for a three-semester introduction to analysis.The prerequisites are a good grounding in the calculus of one variable from a mathematically rigorous point of view, together with some acquaintance with linear algebra. The reader should be familiar with limit and continuity type arguments and have a certain amount of mathematical sophistication. As possible introductory texts, we mention Differential and Integral Calculus by R Courant, Calculus by T Apostol, Calculus by M Spivak, and Pure Mathematics by G Hardy. The reader should also have some experience with partial derivatives.In overall plan the book divides roughly into a first half which develops the calculus (principally the differential calculus) in the setting of normed vector spaces, and a second half which deals with the calculus of differentiable manifolds.
Counterexamples In Measure And Integration
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Author : René L. Schilling
language : en
Publisher: Cambridge University Press
Release Date : 2021-06-17
Counterexamples In Measure And Integration written by René L. Schilling and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-06-17 with Mathematics categories.
Often it is more instructive to know 'what can go wrong' and to understand 'why a result fails' than to plod through yet another piece of theory. In this text, the authors gather more than 300 counterexamples - some of them both surprising and amusing - showing the limitations, hidden traps and pitfalls of measure and integration. Many examples are put into context, explaining relevant parts of the theory, and pointing out further reading. The text starts with a self-contained, non-technical overview on the fundamentals of measure and integration. A companion to the successful undergraduate textbook Measures, Integrals and Martingales, it is accessible to advanced undergraduate students, requiring only modest prerequisites. More specialized concepts are summarized at the beginning of each chapter, allowing for self-study as well as supplementary reading for any course covering measures and integrals. For researchers, it provides ample examples and warnings as to the limitations of general measure theory. This book forms a sister volume to René Schilling's other book Measures, Integrals and Martingales (www.cambridge.org/9781316620243).