Which is the Best ODE Book: Hirsch or Arnold?

[khemix]

Want a good diffy book. Two names I hear are Arnold and Hirsch. Are they good?

 

[dx]

Arnold is brilliant, but not for a first course.

 

[khemix]

So if one did a first course in computation, one is ready for Arnold? What about 1st vs 3rd editions.
And anything about Hirsch, or others?

 

[dx]

I don't see what a course in computation has to do with ODEs. If you've already had an introductory course in ordinary differential equations, and know the standard methods to solve the basic types of equations, then you can read Arnold to get a deeper understanding of the theory.

 

[Vid]

Depends on how much math you've had. Arnold is far more mathematically advanced and won't hold the reader's hand.

 

[mathwonk]

as a student i had a routine ode course and never understood anything. arnol'd is more advanced but is so in a conceptually appealing and insightful way. i think it is possible that arnold could actually be more understandable than a routine first course that does not explain any of the ideas but just gives mindless computations.

i.e. the better student you are, the more suitable is arnol'd. and the fact that you are choosing only between arnol'd and hirsch tells me you are likely a strong student.

hirsch is a famous and outstanding mathematician but i think arnol'd's book is much better written pedagogically. if you are so strong that quality of writing is irrelevant to you, and all that matters is the math, there may be some topics covered in hirsch that would make it worth while.

i personally think hirsch is poorly written. but i have his differential topology book because some of the theorems in it are not in my other books.

 

[khemix]

Depends on how much math you've had. Arnold is far more mathematically advanced and won't hold the reader's hand.

How advanced. Are we talking Rudin advanced and real analysis, or Spivak advanced as with calculus?

in fact, what would you say are the prerequisites?

as a student i had a routine ode course and never understood anything. arnol'd is more advanced but is so in a conceptually appealing and insightful way. i think it is possible that arnold could actually be more understandable than a routine first course that does not explain any of the ideas but just gives mindless computations.

i.e. the better student you are, the more suitable is arnol'd. and the fact that you are choosing only between arnol'd and hirsch tells me you are likely a strong student.

hirsch is a famous and outstanding mathematician but i think arnol'd's book is much better written pedagogically. if you are so strong that quality of writing is irrelevant to you, and all that matters is the math, there may be some topics covered in hirsch that would make it worth while.

i personally think hirsch is poorly written. but i have his differential topology book because some of the theorems in it are not in my other books.

if arnold is just as rigorous as hirsch, but also better written, i don't see any reason for choosing hirsch just to have a lemma or two not mentioned in arnold.




all that remains is arnold 1st ed vs 3rd edition...

 

[mathwonk]

i have the first edition which is excellent. i bought it based on advice from ana mazon review that said the prie increase for the few extra pages of the second edition i not worth it.

as a general rule, the first edition of every book is the best.