ODE textbook recommentation (Arnold or other?)

[Only a Mirage]

Hi everyone. I have a copy of Ordinary Differential Equations by Vladimir Arnold. I'm hoping to learn more about differential equations, building up to differential equations on manifolds.

I've heard that this is a great book, but I've also heard Arnold sometimes leaves out important details, which worries me a little. My question is: is this a good book for self-study? Would anyone recommend an alternative text at the same level instead?

 

[verty]

Would this one do? You can preview it on google books, the problems look really good.

https://www.amazon.com/dp/0867202009/?tag=pfamazon01-20

If this is below your level, I don't have a suggestion unfortunately. Actually, looking at this more, it is almost certainly not at a too low level. I think it is just right.

 

[Only a Mirage]

Would this one do? You can preview it on google books, the problems look really good.

https://www.amazon.com/dp/0867202009/?tag=pfamazon01-20

If this is below your level, I don't have a suggestion unfortunately. Actually, looking at this more, it is almost certainly not at a too low level. I think it is just right.

Thanks for the suggestion, but this looks like a book almost entirely devoted to linear differential equations. I don't think this is what I'm looking for, unfortunately.

 

[George Jones]

Tenenbaum and Pollard,

https://www.amazon.com/dp/0486649407/?tag=pfamazon01-20

might not be up to the level that you want, but mathwonk certainly likes it:

I also struggled in an algorithmic ode class as my first math course after being out of school a year. I began supplementing the course with a schaum's outline series, and also going to the library for an hour after every class to review the notes. Finally at the end the class got less routine when the prof gave a proof of existence of solutions by the beautiful contraction mapping method. That even made it interesting. I went from a D to an A.

Then when I taught it I tried to use more interesting books, like Martin Braun's well written book, supplemented by V. Arnol'd's book. The standard books like Boyce and diPrima really left me cold. Almost everyone agrees that he best, clearest book is probably the following one by Tenenbaum and Pollard. Try that one.

https://www.amazon.com/dp/0486649407/?tag=pfamazon01-20


Here is my review:

10 of 10 people found the following review helpful
5.0 out of 5 stars unique, March 28, 2006
By mathwonk - See all my reviews
This review is from: Ordinary Differential Equations (Dover Books on Mathematics) (Paperback)
i discovered a "new" method of solving constant coeff linear ode's this semester while teaching the course, No one I asked knew it and no books had it, but it was so natural as to have no chance of being really new. Still I searched and searched, Courant, Loomis and Sternberg, Edwards Penney, Coddington, Braun, Dieudonne, without success. then I found it here on pages 268-292.

i was impressed. this book was written back when clarity and completeness were the goal. then i began looking at the problems. it is very hard to give reasonable example problems using variation of parameters that cannot be solved better by guessing, but tenenbauim and pollard do it.

this is a classic introductory text. they even define differentials correctly, almost unheard of in an elementary book. all this for only 16 bucks!

 

[verty]

Look here, two interesting books are mentioned: Verhulst and Perko. Perko may be the one you want.