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.
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