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Is there a good reference for learning about differential equations for people who are mainly interested in the theoretical tools (especially in differential geometry/topology) that use them? I learned very little about differential equations in undergrad (besides basic calculation techniques), but they seem to pop up frequently in things like Ricci flow and invariants coming from counting solutions to equations.

I don't know how much material it would be, but if someone who knows a lot about their applications knows some reference for material about differential equations that they think any pure mathematician should know, I'd be interested in what that is.

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    $\begingroup$ I've always been extremely fond of Hirsch and Smale's advanced undergraduate text Differerential Equations, Dynamical Systems, and Linear Algebra. The newer editions have Devaney as a coauthor and Chaos as the third item in the title. $\endgroup$ – Ted Shifrin Feb 18 '15 at 15:49
  • $\begingroup$ @TedShifrin Thanks I'll look into it $\endgroup$ – Carl Feb 20 '15 at 5:09

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