Good undergrad ODE/PDE textbooks focusing on theory

In summary, 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. Differential Equations by Tenenbaum and Pollard from Dover are good books to consider, as are Diff. Equations by V.I. Arnold and Applied Partial Differential Equations by Haberman.
  • #1
ZeroZero2
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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??
 
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  • #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.
 
  • #3
DivisionByZro said:
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.

-
 
  • #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.
 
  • #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.
 
  • #6
deluks917 said:
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..
 
  • #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.
 
  • #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.
 
  • #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 )
 

1. What are some good undergraduate ODE/PDE textbooks focusing on theory?

Some good undergraduate ODE/PDE textbooks focusing on theory include "Elementary Differential Equations and Boundary Value Problems" by William E. Boyce and Richard C. DiPrima, "Partial Differential Equations: An Introduction" by Walter A. Strauss, and "A First Course in Differential Equations" by Dennis G. Zill.

2. How do these textbooks differ from other ODE/PDE textbooks?

These textbooks are specifically designed for undergraduate students and focus on the theoretical aspects of ODEs and PDEs. They provide a thorough understanding of the underlying concepts and principles, rather than just presenting a collection of problem-solving techniques.

3. Are these textbooks suitable for self-study?

Yes, these textbooks are suitable for self-study as they are well-structured and have clear explanations and examples. They also include exercises and problems for students to practice and test their understanding.

4. Do these textbooks cover both ODEs and PDEs?

Yes, these textbooks cover both ordinary differential equations (ODEs) and partial differential equations (PDEs). They typically start with an introduction to ODEs and then move on to PDEs, providing a comprehensive understanding of both types of equations.

5. Are these textbooks suitable for advanced undergraduate students?

Yes, these textbooks are suitable for advanced undergraduate students as they cover the fundamental concepts and theories of ODEs and PDEs in a rigorous and thorough manner. They also include advanced topics and applications, making them suitable for students in higher level courses or those interested in pursuing graduate studies in mathematics or related fields.

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