Good Theory-Intensive Introductory Diff Eq Textbook

[catmunch]

I am currently taking an introductory course to DE's that has a heavy emphasis on theory (my professor stresses that this is a math course, not an engineering/applications course). Unfortunately, my professor, though he tries hard, is not good at explaining anything. Even more unfortunately, the textbook we are using has almost no theory at all. Anyway, I am a good independent learner and I think I would do well if I only had a good textbook to teach me the theory. Alternatively, an online resource would be good too, but I haven't found anything comprehensive enough.

I feel comfortable with analysis, basic number theory, linear algebra, and (of course) multivariable calc.

So, does anyone have any recommendations?

Thanks in advance.

Also, I tried to post this in the Calculus & Beyond Learning Materials forum, but I was told that I did not have permission to post there. So sorry if this is in the wrong forum.

 

[AuraCrystal]

Boyce and DiPrima's Elementary Differential Equations and Boundary Value Problems is a good introductory-level book, I've found, and it has a fair bit of theory.

Hope that helps.