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!