This self-contained text, suitable for advanced undergraduates,
provides an extensive introduction to mathematical analysis, from
the fundamentals to more advanced material. It begins with the
properties of the real numbers and continues with a rigorous
treatment of sequences, series, metric spaces, and calculus in one
variable. Further subjects include Lebesgue measure and integration
on the line, Fourier analysis, and differential equations. In
addition to this core material, the book includes a number of
interesting applications of the subject matter to areas both within
and outside the field of mathematics. The aim throughout is to
strike a balance between being too austere or too sketchy, and
being so detailed as to obscure the essential ideas. A large number
of examples and 500 exercises allow the reader to test
understanding, practise mathematical exposition and provide a
window into further topics.
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