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Zbigniew H. Nitecki - Calculus Deconstructed, Inbunden

Inbunden, Engelska, 2009

Calculus Deconstructed

A Second Course in First-Year Calculus

Av Zbigniew H. Nitecki

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757 kr

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Beskrivning
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 basica 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.
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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.

Recensioner i media

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

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