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Good undergrad ODE/PDE textbooks focusing on theory

  1. Nov 30, 2011 #1
    I'm looking for some good ODE/PDE textbooks that focus a little more on theory but that are still comprehensive in their respective subjects.

    I have taken ODEs and applied PDEs at my university but even though I got good grades, I feel like my knowledge is lacking.

    The books we used were Differential Equations by Polking, Boggess, & Arnold and Applied Partial Differential Equations by Haberman.

    I more or less want to start anew but in a more rigorous form.
    e.g., I took Calculus 1-3 using Etgen. However, I relearned everything with Courant & John and it really helped me read baby Rudin afterwards.

    I'd rather the textbooks not assume a lot of previous exposure to O/PDEs but a little is fine i suppose.

    any ideas??
     
  2. jcsd
  3. Nov 30, 2011 #2
    I suppose it depends on how much theory you actually want, but two that come to mind are:

    1 - Diff. Equations by Tenenbaum and Pollard. This is from Dover, and has a LOT of material. It is well suited for a math major,

    2 - Diff. Equations by V.I Arnold is slightly more expensive, much more advanced (Kind of on the graduate-level), but definitely has a lot of theory.

    I think your best bet may be Tenenbaum. Good luck finding a suitable book.
     
  4. Nov 30, 2011 #3
    Thanks for the suggestions, that V.I. Arnold book looks really interesting. Does it start you from scratch or does it assume you know all the basics?

    I guess it's kinda like this:

    Larson/Edwards' Calculus is to Spivak's Calculus as Polking/Boggass/Arnold's ODEs is to ________________'s ODEs.

    and

    Stewart's Calculus is to Apostol's Calculus as Haberman's PDE's is to ________________'s PDE's.

    -
     
  5. Nov 30, 2011 #4
    I recently picked up a used copy of Ordinary Differential Equations by Garrett Birkhoff and Gian-Carlo Rota. It's more theoretical than most introductory ordinary differential equations texts, but it's still accessible.

    I've heard that Partial Differential Equations by Lawrence C. Evans is a theoretical, graduate level textbook, but I haven't actually used it.
     
  6. Nov 30, 2011 #5
    Arnold is a very beautiful book, starts at the beginning and has applications to physics. Evan's book is difficult and very very light on applications.
     
  7. Dec 1, 2011 #6
    Arnold's text looks really good, is it comprehensive? I'm looking at Tenenbaum and Pollard but I'm a little hesitant since it was written in the 60's.
    What do you think of Arnold's "Lectures on Partial Differential Equations" ??

    An undergrad level PDE text that's considered a standard is Strauss and a popular one is Farlow.. any thoughts on those??

    What about Linear Partial Differential Equations and Nonlinear Partial Differential Equations by Debnath?? They certainly look interesting..
     
  8. Dec 1, 2011 #7
    I think arnold covers everything any undergrad is expected to know + extra. I've never read his PDE book. However I read his mechanics and his ODE and both are very good. You might want to study ode before pde, though you don't have to.
     
  9. Dec 7, 2011 #8
    Arnold's ODE book starts from the beginning, so you don't need to know anything about ODE's to get started with it. A very firm calculus/linear algebra base will definitely help, though.

    I haven't seen his PDE notes, but he is a great author and I'm sure they are worth reading.

    Note: I would go to the local university library and read the first few pages of a few that your interested in, and choose the one whose style you like best.
     
  10. Dec 8, 2011 #9
    Ordinary Differential Equations - Jack Hale and Differential Equations and Dynamical Systems - Lawrence Perko have been among the best ODE's books I've seen ( these are more theoretical ones )
     
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