Book recommendation on differential equations

[u/A1235GodelNewton]

Recommend a book on differential equations that introduces the topic from a pure maths perspective without much applications.

[u/SV-97]

There's really not a whole lot of "pure", classical theory on differential equations. Look at A Short Course in Ordinary Differential Equations, all the classical theory happens within the first 2 chapters or so, then it's more about dynamical systems and the qualitative theory.

[u/A1235GodelNewton → u/SV-97]

Thanks, I checked it it's really nice

[u/ADolphinParadise]

Obligatory V.I. Arnold recommendation.

[u/dogdiarrhea → u/ADolphinParadise]

Ordinary differential equations book is great, but so is his “mathematical methods of classical mechanics” book which is realistically a book on Hamiltonian dynamical systems.

[u/pseudoLit]

This is a bit of an unusual recommendation, but I quite like Hydon's Symmetry Methods for Differential Equations. It develops a systematic method for solving DEs using ideas from Lie theory, in sharp contrast to the usual "bag of tricks" approach taken by other books.

[u/A1235GodelNewton → u/pseudoLit]

Thanks

[u/mathemorpheus]

Hörmander vols 1-4

[u/Guilty-Efficiency385]

Gabriel Nagy from Michigan state university has some lecture-notes made into a pdf book that is a quite comprehensive treatment of ODE. Very theoretical treatment, most (if not all) proofs are included. Some of the problem sets are incomplete though.

If you can get past his use of "t" for the independent variable (as opposed to "x" ) I think is a great resource

https://users.math.msu.edu/users/gnagy/teaching/ode.pdf

[u/paradoxzack]

Ordinary Differential Equations by Arnold

[u/Forsaken_Pilot_4311]

Two Russian classics are "Ordinary Differential Equations" by Pontryagin and "Partial Differential Equations" by Mikhailov.

[u/FewHamster6729]

Hartman, but it is quite a difficult book to read.