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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.

Tabla de contenidos provista por Syndetics

• Foreword
• Introduction
• Part I Statements
• 1 Functions
• 2 Limits
• 3 Continuity
• 4 Differential calculus
• 5 Integral calculus
• Part II Suggested Solutions
• 6 Functions
• 7 Limits
• 8 Continuity
• 9 Differential calculus
• 10 Integral calculus
• References

Reseñas proporcionadas por Syndetics

CHOICE Review

This brief work is exactly as described, a collection of counterexamples from calculus. The book is organized into two parts. The first part is a list of 90 short statements grouped into five categories: "Functions," "Limits," "Continuity," "Differential Calculus," and "Integral Calculus." The second part is longer and includes counterexamples to each of the statements in the first part. Some of the counterexamples include notes describing the connection between the statements and well-known calculus theorems. This reviewer enjoyed going through the statements and generating his own counterexamples to compare with those given in the second section. Klymchuk (Auckland Univ. of Technology, New Zealand) provides an excellent reminder to calculus instructors and students of the need for rigor in calculus. In many cases, the statements were theorems or rules used in calculus with one condition missing. In addition to helping calculus users to avoid complacency, this work provides wonderful illustrations of what can go wrong if one ignores the conditions placed on the theorems and rules of calculus. This book should be required reading for any long-term instructor of calculus. Summing Up: Essential. Calculus collections serving lower-division undergraduates through researchers/faculty, and two-year technical program students. J. T. Noonan Mount Vernon Nazarene University