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.
General
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