Veeky Forums, care to recommend any top-tier books for a complete understanding of ODEs? Did fairly well in the course, but I want a 100% understanding - I feel like it's a mathematical milestone to know this stuff.
Also, any upper-echelon maths anons feel free to reflect on your ODEs experience, and what they mean to you now. Any newfags feel free to ask questions and speculate.
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How do you feel about nonlinear DEs? How about y'' + (y')^2 = 2
RETarded
If you want more theory and rigor in ODE then you'd probably need real analysis under your belt, in that case probably pick up a book by AMS. Nevertheless the books by Haberman, and Lebl are good books on the subject.
ODE are fun but PDE are a little more common in physical applications I'd argue. PDE is definitely the way to go. I recommend Asmar, Debnath, or Hillen for PDE. Probably Hillen honestly. Debnath or Logan for science and engineering applications.
Don't let any of the retards here meme you into reading Evans or Strauss for PDE.
Vladimir Arnold's ODE book is a good choice.
Got a few general questions... how important are ODE/ PDEs for a math major? For ODEs at least, I'm not sure if I should see them as the last of the weed-out classes or the beginning of the REAL math classes. I've always heard repeatedly that ODEs were "really, really important for engineering majors" for the obvious applications. Never that they were important for math majors.
Anybody with experience care to comment?
It depends what math you're doing, and if you're planning on industry or academia.
what's wrong with strauss?
Applied Differential Equations - Vladimir Dobrushkin
I've heard Dobrushkin's "Applied Differential Equations" was good, but since it's not on LibGen I think it's just a meme.