@ Pete,Victor and Greg: First,I agree with your interpretation of the paragraph Greg's referring to. Secondly,despite loving Pugh's book-I call it "Rudin Done Right"-I was also very disappointed at the very terse preface.You'd think someone with Pugh's teaching experience would have a LOT to say on the subject having taught so many years to some of the best students in the world. Third-I seriously doubt one of the world's experts in differential equations thinks real analysis is devoid of real world applications.But that being said-what compels people teaching this course to strip it down to Bourbakian purity? Tradition? Or something darker and deeper? I'm waiting for a balanced text at this level that unifies physical applications with a comprehensive introduction to real analysis. If it never arrives,I may have to write it myself.