Softcover ISBN:  9781470466756 
Product Code:  TEXT/16.S 
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eBook ISBN:  9781614446026 
Product Code:  TEXT/16.E 
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AMS Member Price:  $29.25 
Softcover ISBN:  9781470466756 
eBook: ISBN:  9781614446026 
Product Code:  TEXT/16.S.B 
List Price:  $84.00 $64.50 
MAA Member Price:  $63.00 $48.38 
AMS Member Price:  $63.00 $48.38 
Softcover ISBN:  9781470466756 
Product Code:  TEXT/16.S 
List Price:  $45.00 
MAA Member Price:  $33.75 
AMS Member Price:  $33.75 
eBook ISBN:  9781614446026 
Product Code:  TEXT/16.E 
List Price:  $39.00 
MAA Member Price:  $29.25 
AMS Member Price:  $29.25 
Softcover ISBN:  9781470466756 
eBook ISBN:  9781614446026 
Product Code:  TEXT/16.S.B 
List Price:  $84.00 $64.50 
MAA Member Price:  $63.00 $48.38 
AMS Member Price:  $63.00 $48.38 

Book DetailsAMS/MAA TextbooksVolume: 16; 2009; 491 pp
Calculus Deconstructed is a thorough and mathematically rigorous exposition of singlevariable 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 selfstudy. Standard topics and techniques in singlevariable 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.

Table of Contents

Chapters

Chapter 1. Precalculus

Chapter 2. Sequences and their Limits

Chapter 3. Continuity

Chapter 4. Differentiation

Chapter 5. Integration

Chapter 6. Power Series

A. The Rhetoric of Mathematics (Methods of Proof)

B. Answers to Selected Problems


Additional Material

Reviews

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


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Calculus Deconstructed is a thorough and mathematically rigorous exposition of singlevariable 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 selfstudy. Standard topics and techniques in singlevariable 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.

Chapters

Chapter 1. Precalculus

Chapter 2. Sequences and their Limits

Chapter 3. Continuity

Chapter 4. Differentiation

Chapter 5. Integration

Chapter 6. Power Series

A. The Rhetoric of Mathematics (Methods of Proof)

B. Answers to Selected Problems

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