Alright, so I have been taking a while to soak in as much advanced mathematics as an undergraduate as possible, taking courses in algebra, topology, complex analysis (a less rigorous undergraduate version of the usual graduate course at my university), analysis, model theory, and number theory. That is, I have taken enough 'abstract' (proof-based) mathematics courses to fall in love with the subject and decide to pursue it as a career.
However, I have been putting off taking a required ordinary differential equations course (colloquially referred to as 'calc 4', though this seems inappropriate) which will likely be very computational and designed to cater to the overpopulation of engineering students at my university.
So my question is, for someone who might have to actually concern themselves with the theory behind the 'rules' and theorems which will likely go unproven in this low-level course (likely of questionable mathematical content), what might be a decent supplementary text in ODE? That is, something substantive to counter-balance the 'ODE for students of science and engineering'-type text I will have to wade through. I want to study algebraic geometry further (I have gone through Karen Smith's text and the first part of Hartshorne), so something which goes from basic material through differential forms and related material would be nice.
Thanks! (and yes, it's embarrassing that I still haven't taken the 200-level ODE course, but I have been putting it off in favor of more interesting/rigorous courses... but now there's that whole graduation requirements issue). --Lambdafunctor