**AMS/MAA Textbooks**

Volume: 16;
2009;
491 pp;
Hardcover

**Print ISBN: 978-0-88385-756-4
Product Code: TEXT/16**

List Price: $35.00

AMS Member Price: $26.25

MAA Member Price: $26.25

**Electronic ISBN: 978-1-61444-602-6
Product Code: TEXT/16.E**

List Price: $35.00

AMS Member Price: $26.25

MAA Member Price: $26.25

# Calculus Deconstructed: A Second Course in First-Year Calculus

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*Zbigniew H. Nitecki*

MAA Press: An Imprint of the American Mathematical Society

Calculus Deconstructed is a thorough
and mathematically rigorous exposition of single-variable calculus for
readers with some previous exposure to calculus techniques but not to
methods of proof. This book is appropriate for a beginning Honors
Calculus course assuming high school calculus or a "bridge course"
using basic analysis to motivate and illustrate mathematical
rigor. It can serve as a combination textbook and reference book for
individual self-study. Standard topics and techniques in
single-variable calculus are presented in context of a coherent
logical structure, building on familiar properties of real numbers and
teaching methods of proof by example along the way. Numerous examples
reinforce both practical and theoretical understanding, and extensive
historical notes explore the arguments of the originators of the
subject.

No previous experience with mathematical proof is assumed:
rhetorical strategies and techniques of proof (reductio ad absurdum,
induction, contrapositives, etc.) are introduced by example along the
way. Between the text and exercises, proofs are available for all the
basic results of calculus for functions of one real
variable.

#### Reviews & Endorsements

The introduction of a calculus sequence to the high schools has necessitated the development of a course in college math programs to deal with the students that have taken the high school sequence when they arrive on campus. While some of the students coming out of the high school programs are mathematically very capable, many are weak and are not ready to proceed to the first course taken after a year of calculus. This book was developed as a response to these conditions, it can be considered as a "calculus with basic analysis" bridge course. … Change always produces the need for reaction and that is true in education as well. In this case the author has done an excellent job in creating a text for a course in advanced calculus that could serve as a bridge course for incoming students that have had calculus in high school or those that took calculus years earlier. …

-- Charles Ashbacher, Journal of Recreational Mathematics

# Table of Contents

## Calculus Deconstructed: A Second Course in First-Year Calculus

- Cover Cover11
- Copyright ii3
- Title page iii4
- Epigraph vii8
- Dedication ix10
- Preface xi12
- Contents xv16
- Precalculus 118
- Sequences and their limits 1128
- Continuity 6986
- Differentiation 135152
- Integration 247264
- Power series 367384
- The rhetoric of mathematics (methods of proof) 445462
- Answers to selected problems 451468
- Bibliography 477494
- Index 481498
- About the author 491508
- Back Cover Back Cover1509