This book provides an introduction to those parts of analysis that are most useful in applications for graduate students. The material is selected for use in applied problems & is presented clearly & simply but without sacrificing mathematical rigour. The text is accessible to students from a wide variety of backgrounds including undergraduate students entering applied mathematics from non-mathematical fields & graduate students in the sciences & engineering who want to learn analysis. A basic background in calculus linear algebra & ordinary differential equations as well as some familiarity with functions & sets should be sufficient.