What Are the Key Concepts of Differential Calculus in Banach Spaces?

[ziad1985]

Frankly I don't know how to say this,I need some help In Differential Calculus.
I'm talking about Banach space and those stuff,If it's possible if someone know a link to some online textbook,i need something that goes deep into every theorm of this branch of math.
thx you already , you don't know how much you would be helping.

 

[mathwonk]

try the lomis sternberg advanced calculus book on shlomo sternbergs website at harvard math dept.

of course your question just reveals how little you understand about how much what the subject entails, or you would not ask such a big question.


but this is a starting place.

 

[ziad1985]

I know , I'm not even a math student , I'm a physics Student,this is actually for someone close to me (my gf )
so you should understand me !

 

[ziad1985]

Altough i lack any knowledge to know what to exactly search for , I know what i want:
Full proof for :Rank theorem for the immersions and Submersions.
some excersises on local inversions, And some applications of differential Calculus on Diff.Eq (Linear homoge with constant coeff).
Again i would really appreciat any help with that.

 

[Jeff Ford]

Have you checked out the online texts from the links section?

 

[ziad1985]

actually yes, i tried but i didn't find anything , maybe i didn't look good.
but nothing!

 

[Jeff Ford]

Well, here's the link mathwonk suggested
http://www.math.harvard.edu/~shlomo/docs/Advanced_Calculus.pdf

You might also want to send your girlfriend here so she can describe more fully what she's looking for.

 

[ziad1985]

thx but that is tthe same book mathwonk was talking about , it didn't help much.well she don't use the net , so I'm searching for her.
and this what seem she want :"Full proof for :Rank theorem for the immersions and Submersions.
some excersises on local inversions, And some applications of differential Calculus on Diff.Eq (Linear homoge with constant coeff)."

 

[Jeff Ford]

There is a proof of the rank theorem in this text
http://www.math.miami.edu/~ec/book/ch05.pdf

 

[Jeff Ford]

Here is some information on partial differential equations in Banach space
http://www.ams.org/online_bks/surv49/

 

[ziad1985]

thank you very much.