A very theoretical approach to diff eq

[stgermaine]

Hi. I'm taking diff eq course this semester and the text is the latest Boyce DiPrima diff eq with boundary value problems.

The first test is mostly proofs on theorems about continuity, like the Heine-Borel theorem, Bolzano-Weierstrauss theorem, etc. The book doesn't go into much details about those theorems and I have problem understanding from just researching online.

Is there a book that takes a more theoretical approach to diff eq without being too dense? I don't have a very strong base in calc, as it's been three years since taking calc III and haven't found the time to review during the summer.

Edit: I found that the Heine and Bolzano theorems are filed under 'real analysis theorems' so I think getting a intro real analysis book may help. Am I correct in understanding that diff eq is similar to real analysis but with more emphasis on application?
Thank you!

 

[micromass]

Diff eq and real analysis are two quite different courses. Real analysis is basically just calculus, but more rigorous. It won't deal much with differential equations typically. It might cover things like Heine-Borel and other stuff.

On the other hand, we have differential equations. A theoretical course in diff eq will likely consist out of proving various existence and uniqueness theorems. Real analysis is used as a tool to prove these things.

The theorems you mention are indeed real analysis, and not so much diff eq. A book which might be helpful is "The Elements of Real Analysis" by Bartle or "Mathematical Analysis" by Apostol.

 

[homeomorphic]

It's very strange that Boyce and DiPrima (:gag:) would be the text.

You can try V I Arnold's book on differential equations, along with an analysis book.