
CounterExamples
From Elementary Calculus to the Beginnings of Analysis
Chapman & Hall/CRC (Publisher)
1st Edition
Published on 14. October 2024
Book
Paperback/Softback
362 pages
978-1-032-92103-7 (ISBN)
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.
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.
More details
Series
Language
English
Place of publication
Boca Raton
United Kingdom
Publishing group
Taylor & Francis Ltd
Target group
Professional and scholarly
Academic
Illustrations
141 s/w Abbildungen
141 Illustrations, black and white
Dimensions
Height: 234 mm
Width: 156 mm
Weight
670 gr
ISBN-13
978-1-032-92103-7 (9781032921037)
Copyright in bibliographic data and cover images is held by Nielsen Book Services Limited or by the publishers or by their respective licensors: all rights reserved.
Schweitzer Classification
Other editions
Additional editions

Andrei Bourchtein | Ludmila Bourchtein
CounterExamples
From Elementary Calculus to the Beginnings of Analysis
Book
09/2014
1st Edition
Chapman & Hall/CRC
€154.50
Article not available for order

Andrei Bourchtein | Ludmila Bourchtein
CounterExamples
From Elementary Calculus to the Beginnings of Analysis
E-Book
09/2014
1st Edition
Chapman & Hall/CRC
€77.49
Available for download

Andrei Bourchtein | Ludmila Bourchtein
CounterExamples
From Elementary Calculus to the Beginnings of Analysis
E-Book
09/2014
1st Edition
Chapman and Hall
€77.99
Available for download
Persons
Andrei Bourchtein, Ludmila Bourchtein
Author
Pelotas State University, Brazil
Pelotas State University, Brazil
Content
FUNCTIONS OF ONE REAL VARIABLE. Elementary properties of functions. Limits. Continuity. Differentiation. Integrals. Sequences and series. FUNCTIONS OF TWO REAL VARIABLES. Limits and continuity. Differentiability. Integrability.