Differential Equations Text: Finding Rigor & Clarity

[Rasalhague]

Can anyone recommend an elementary but rigorous text on differential equations that takes care to distinguish between a function, f: X \rightarrow Y, and its value f(x) \in Y, as Spivak does in his Calculus. I find I'm getting rather confused by the traditional y=y(x) type dual-meaning notation.

 

[qspeechc]

It seems you already know the difference between a function and a value it takes on. This is a pure math concern and not really the concern of an applied math book like a DE book, which tends to gloss over many math points. At any rate, confusing a function and it's values has a long and fine history, especially in elementary books; it's just something you have to get over. Perhaps you should try reading another book to get a different perspective? Here are two suggestions:
https://www.amazon.com/dp/0486649407/?tag=pfamazon01-20
https://www.amazon.com/dp/0486659429/?tag=pfamazon01-20

 

[Rasalhague]

It's my concern because I want to learn the subject and understand it properly. Tenenbaum and Pollard do explain the distinction in their opening chapter, but then switch to a notation that often hides it. It's no problem to me when they're talking about things I'm already familiar with, but when the discussion moves to defining new concepts in terms of functions of multiple variables, which may themselves be functions of other variables, it's not always clear to me what sort of object those variables are. Thanks for the recommendations, though. I'll keep working at it. And Coddington's book is new to me, so I'll certainly give that a look.

 

[atyy]

How about http://books.google.com/books?id=iD...e+differential+geometry&source=gbs_navlinks_s , chapter IV treats differential equations?

Or http://www.math.rutgers.edu/~sontag/mct.html ?

Also http://books.google.com/books?id=INYJuKGmgd0C&dq=smale+AND+linear&source=gbs_navlinks_s

 

[Rasalhague]

Thanks for the suggestions, atyy.