Take the 2-minute tour ×  Can anyone suggest a text that gives a
complete/thorough treatment of calculus in Banach spaces?
Perhaps something something along the lines of Chapter 2 in
Manifolds, Tensor Analysis and Applications by Marsen, et. al.
but more expansive?   share|improve this question Look for texts
named "nonlinear analysis" (or something similar) in their name.
You're bound to find something you like. –  Mark Sep 16 '11 at
12:33 Related to Mark Schwarzmann's comment: many books on PDE
contain material similar to this. The words Bochner integral and
Frechet derivative may be useful for searches. –  user12014 Nov
15 '11 at 21:12 add comment  3 Answers  The only one I know is
Jean Dieudonne's classic Foundations of Modern Analysis, which
is the also the most cited out of print text I know. It's kind
of strange since in the late 1960's and early 1970's, at the
height of the Bourbaki Era, it was the single most cited
analysis text for undergraduates and was fully expected to
replace Rudin as the gold s