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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.
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.
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