ODE book recommendation

Question

I have just completed my first year study and know elementary analysis and a little bit functional analysis. I found that most of the ODE books just focus on calculation but no substantial explanation of theorems.Can someone suggest some ODE books which are from a more theoretical point of view?

Possible duplicate: http://math.stackexchange.com/questions/34233/ode-introduction-textbook — Belgi, Jul 27 '12 at 16:37
Its not an ODE book, and it be heavy going at an early stage, but I like the (brief) treatment of ODEs in Kantorovich & Akilov's "Functional Analysis". In particular, it provides a fixed-point scheme (as in Picard) that is useful for showing continuity of solutions with respect to parameters. — copper.hat, Jul 27 '12 at 17:30
The Qualitative Theory of Ordinary Differential Equations by Brauer and Nohel is worth a look. — littleO, May 10 '23 at 06:05

Artem · Answer 1 · 2012-07-29T15:08:31.053

9

A classical theoretical book on ODE is Hartman.

A very good book, and slightly less demanding than Hartman is Hale's book

A geometric picture of differential equations is given in two Arnold's books: one and two

ODE from a dynamical system theory point of view are presented in Wiggins' book

Update: Have no idea how, but I read that the question was about a second theoretical ODE course. For the first course in ODE none of the books that I mentioned (except Arnold's one) suits.

The best first theoretical book on ODE is, for my taste, is Hirsch and Smale.

edited Jul 29 '12 at 15:08

answered Jul 27 '12 at 18:23

Artem

14,414

2

Hartman is great for references, but I would kill myself if I had to use it for self-study as my first ODE course. Arnold's books make excellent reading. – Jul 27 '12 at 20:13
@LeonidKovalev Ups. Somehow I understood that OP asked about a second course in differential equations. I update my post. – Artem Jul 29 '12 at 15:05

score 2 · Answer 2 · edited Jul 29 '12 at 15:18

2

You might try Birkhoff and Rota or Lefschetz or Nemytskii and Stepanov.

edited Jul 29 '12 at 15:18

J. M. ain't a mathematician

75,051

answered Jul 27 '12 at 17:35

Robert Israel

448,999

score 1 · Answer 3 · answered Dec 07 '18 at 17:27

1

You can try this one also...

'Differential Equations Theory, Technique and Practice' by G. F. Simmons & S. G. Krantz (McGraw Hill Higher Education)

answered Dec 07 '18 at 17:27

nmasanta

9,222

Imperton · Answer 4 · 2023-05-15T00:43:14.823

0

Try lecture notes by Alexander Grigorian and Peter Philip. These are the most rigorous texts on ODE I have read.

edited May 15 '23 at 00:43

answered Apr 26 '22 at 02:55

Imperton

151

ODE book recommendation

4 Answers4

Linked