This following a fantastic book, with good exercises, and most importantly it includes applications: Real Analysis and Applications by Davidson and Donsig htt

This following a fantastic book, with good exercises, and most importantly it includes applications: Real Analysis and Applications by Davidson and Donsig http://www.math.uwaterloo.ca/~krdavids/RAA/real.html http://www.math.uwaterloo.ca/~krdavids/RAA/real.html