Good undergrad ODE/PDE textbooks focusing on theory

[ZeroZero2]

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??

 

[DivisionByZro]

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.

 

[ZeroZero2]

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.

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.

-

 

[intwo]

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.

 

[deluks917]

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.

 

[ZeroZero2]

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.

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..

 

[deluks917]

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.

 

[Mike706]

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.

 

[wisvuze]

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 )