Comments on: a listmania: essentials of undergraduate math for aspiring applied math students

By: JuanPablo

JuanPablo — Wed, 04 Apr 2007 02:26:49 +0000

about odes, I prefer Simmons (perhaps the best for applied people), followed by the Hirsch-Smale and the classical Coddington.

And do Carmo is a very good book for differential geometry.

By: AnonEcon

AnonEcon — Sun, 01 Apr 2007 06:39:45 +0000

I found Munkres’Analysis on Manifolds very user-friendly.

I’m still reading Arnold and Hirsch-Smale. But I find them more interesting and intuitive than the traditional books. And the prerequisites are about the same: basic analysis and linear algebra. In fact Hirsch-Smale lessens the load even further by developing lot of the linear algebra itself and replacing some of the analysis by hand-waving (at one point substituting the Jordan curve theorem by a neat diagram).

Among the traditional ODE books which I have seen, I really liked Simmons.

By: Alex

Alex — Sun, 01 Apr 2007 05:38:49 +0000

Because it’s for applied math people, I don’t think algebra is too important, but differential geometry is definitely something I overlooked. Any suggestions?

Jeez, did you read those when you were an undergrad? I’m impressed. I consider pretty much all qualititative ODE material to be graduate level (maybe just because I find it confusing).

I was thinking of more of a guide to analytic solution techniques like green’s functions, power series expansions, variation of parameters, etc. Any recommendations?

By: AnonEcon

AnonEcon — Sat, 31 Mar 2007 03:12:21 +0000

Nice list. Would you be extending it to cover areas like algebra and differential geometry/topology? For ODEs, my own favourites are Arnold and Hirsch and Smale.