Description
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
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. ..."" N Charles Ashbacher, Journal of Recreational Mathematics
Book Information
ISBN 9781470466756
Author Zbigniew H. Nitecki
Format Paperback
Page Count 508
Imprint American Mathematical Society
Publisher American Mathematical Society
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. ..."" N Charles Ashbacher, Journal of Recreational Mathematics
Book Information
ISBN 9781470466756
Author Zbigniew H. Nitecki
Format Paperback
Page Count 508
Imprint American Mathematical Society
Publisher American Mathematical Society
