
CounterExamples
From Elementary Calculus to the Beginnings of Analysis
Chapman & Hall/CRC (Publisher)
1st Edition
Published on 9. September 2014
Book
Hardback
368 pages
978-1-4822-4667-4 (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 States
Publishing group
Taylor & Francis Inc
Target group
College/higher education
Academic
Product notice
sewn/stitched
Cloth over boards
Illustrations
141 s/w Abbildungen
141 Illustrations, black and white
Dimensions
Height: 241 mm
Width: 159 mm
Thickness: 25 mm
Weight
655 gr
ISBN-13
978-1-4822-4667-4 (9781482246674)
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
10/2024
1st Edition
Chapman & Hall/CRC
€93.03
Shipment within 10-20 days

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.