TITLE: Real analysis has no applications?
QUESTION [13 upvotes]: I'm teaching an undergrad course in real analysis this Fall and we are using the text "Real Mathematical Analysis" by Charles Pugh. On the back it states that real analysis involves no "applications to other fields of science. None. It is pure mathematics." This seems like a false statement. My first thought was of probability theory. And isn't PDE's sometimes considered applied math? I was wondering what others thought about this statement.

REPLY [4 votes]: I have a good undergraduate analysis book, "Real Analysis with Real Applications," by Kenneth R. Davidson and Allan P. Donsig.  The book is divided into two parts.  Part A deals with "Abstract Analysis" which includes theory, proofs, examples, and problems found in most undergraduate analysis books.  Part B deals with "Applications" which include polynomial approximations, discrete dynamical systems, diff. eqns, fourier series and physics, wavelets, and optimization.