This is a rigorous introduction to real analysis for undergraduate
students, starting from the axioms for a complete ordered field and
a little set theory. The book avoids any preconceptions about the
real numbers and takes them to be nothing but the elements of a
complete ordered field. All of the standard topics are included, as
well as a proper treatment of the trigonometric functions, which
many authors take for granted. The final chapters of the book
provide a gentle, example-based introduction to metric spaces with
an application to differential equations on the real line. The
author's exposition is concise and to the point, helping students
focus on the essentials. Over 200 exercises of varying difficulty
are included, many of them adding to the theory in the text. The
book is perfect for second-year undergraduates and for more
advanced students who need a foundation in real analysis.
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