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. In that light it may well be useful for: high school teachers and university faculty as a teaching resource; high school and college students as a learning resource; and as a professional development resource for calculus instructors.

Table of Contents

Foreword

Introduction

Counterexamples in Calculus

I.Statements

Functions

Limits

Continuity

Differential Calculus

Integral Calculus

II. Suggested Solutions Functions

Limits

Continuity

Differential Calculus

Integral Calculus

About the Author

Sergiy Klymchuk is an Associate Professor of the School of Computing and Mathematical Sciences at the Auckland University of Technology, New Zealand. He has 29 years experience teaching university mathematics in different countries. His PhD (1988) was in differential equations and recent research interests are in mathematics education and epidemic modeling. He has more than 140 publications including several books on popular mathematics and science that have been, or are being, published in 11 countries.

MAA Review

This is a valuable but thinly-described compendium of counterexamples in single-variable calculus. The book is vague about who it is aimed at, sometimes addressing the student and sometimes the teacher. I believe it is most useful as a source of enrichment activities and would be read by the teacher and not by the student.
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