This text gives a rigorous treatment of the foundations of
calculus. In contrast to more traditional approaches, infinite
sequences and series are placed at the forefront. The approach
taken has not only the merit of simplicity, but students are well
placed to understand and appreciate more sophisticated concepts in
advanced mathematics. The authors mitigate potential difficulties
in mastering the material by motivating definitions, results and
proofs. Simple examples are provided to illustrate new material and
exercises are included at the end of most sections. Noteworthy
topics include: an extensive discussion of convergence tests for
infinite series, Wallis's formula and Stirling's formula, proofs of
the irrationality of and e and a treatment of Newton's method as a
special instance of finding fixed points of iterated functions.
General
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