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The book contains a rigorous exposition of calculus of a single
real variable. It covers the standard topics of an introductory
analysis course, namely, functions, continuity, differentiability,
sequences and series of numbers, sequences and series of functions,
and integration. A direct treatment of the Lebesgue integral, based
solely on the concept of absolutely convergent series, is
presented, which is a unique feature of a textbook at this level.
The standard material is complemented by topics usually not found
in comparable textbooks, for example, elementary functions are
rigorously defined and their properties are carefully derived and
an introduction to Fourier series is presented as an example of
application of the Lebesgue integral.The text is for a
post-calculus course for students majoring in mathematics or
mathematics education. It will provide students with a solid
background for further studies in analysis, deepen their
understanding of calculus, and provide sound training in rigorous
mathematical proof.
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