This book serves as a textbook for an undergraduate calculus course. It is written for readers with some previous exposure to the techniques of calculus who would like to see the subject in a conceptual framework. The book combines a review of methods of single-variable calculus with a mathematically rigorous development of their justification. No previous experience with mathematical proof is assumed: rhetorical strategies and techniques of proof are introduced by example along the way. Between the text and the exercises, proofs are available for all the basic results of calculus for functions of one real variable. Exercises include Practice Problems (reinforcing calculation techniques), Theory Problems (developing understanding of proofs), Challenge Problems (pushing the limits, exploring related ideas) and Historical Notes (guided pencil-and-paper tours of the arguments of the masters). Topics include limits of sequences, continuity, differentiation, the Riemann integral and power series, along with other optional sections.

A thorough and mathematically rigorous exposition of single-variable calculus for readers with some previous experience of calculus techniques.

About the Author
Zbigniew Nitecki is a Professor of Mathematics at Tufts University, where he has been since 1972. Previously he was a Gibbs Instructor at Yale (1969-71) and Assistant Professor at CCNY (1971-2). He is a contributing editor for Real Analysis Exchange and an associate editor for Qualitative Theory of Dynamical Systems. His research interests are primarily in dynamical systems theory and he has published books and articles on the subject.

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. There is the assumption that the student has at least been exposed to what is often called ""plug and chug"" calculus, where the students are told the formulas and then given problems where they simply execute the algorithms. The approach is a rigorous presentation of single variable calculus with formal definitions and rigorous proofs. Three levels of exercises/problems are given at the ends of the sections: they are in the categories of practice problems, theory problems and challenge problems. These categories are listed in increasing degree of difficulty. One other very positive characteristic is that there is no mention of using technology such as graphing calculators or symbolic algebra packages. The book is also effectively dense in the sense that all the material is covered in roughly 400 pages, less than half the size of most first year calculus texts. 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. Such people usually remember the formulas but have lost the rigor."" - Charles Ashbacher, Journal of Recreational Mathematics



Book Information
ISBN 9780883857564
Author Zbigniew H. Nitecki
Format Hardback
Page Count 508
Imprint Mathematical Association of America
Publisher Mathematical Association of America
Weight(grams) 1030g
Dimensions(mm) 260mm * 181mm * 31mm