This book provides an introduction both to real analysis and to a range of important
applications that depend on this material. Three-fifths of the book is a series of
essentially independent chapters covering topics from Fourier series and polynomial
approximation to discrete dynamical systems and convex optimization. Studying
these applications can, we believe, both improve understanding of real analysis and
prepare for more intensive work in each topic. There is enough material to allow a
choice of applications and to support courses at a variety of levels.
This book is a substantial revision of Real Analysis with Real Applications, which
was published in 2001 by Prentice Hall. The major change in this version is a greater
emphasis on the latter part of the book, focussed on applications. A few of these
chapters would make a good second course in real analysis through the optic of one
or more applied areas. Any single chapter can be used for a senior seminar