(Reference Request) Calculus on Banach Spaces

  1. For a short introduction, I suggest Ambrosetti and Prodi, A primer of nonlinear analysis, Cambridge 1995 (second edition).
  2. Another good source is the Springer book by Abraham, Marsden, Ratiu on Maniflds, tensor analysis and applications.
  3. There is something in J. T. Schwartz's book on Nonlinear functional analysis, Gordon and Breach.
  4. The most complete source is, as far as I know, the book by Cartan, Differential calculus, Hermann.

Anyway, you should keep in mind that differential calculus in normed spaces is rather easy and classical. Integration theory becomes more intriguing and difficult for vector-valued functions.


http://www.tuloomath.com/my-account/text-cartan-dcalculusonnormspaces-2nd-ed/

You're in luck-Henri Cartan's beautiful Differential Calculus has just been republished in an inexpensive paperback at Createspace. For a generation,it and it's sequel, Differential Forms, have together been considered the definitive text on calculus on Banach spaces. The latter has been available from Dover in an inexpensive paperback for over 10 years now,but without the first half of the course, it's been very difficult to use for course study because Cartan's notation is unique at this level and so it's been hard to find the prerequisites. The first half has been notoriously difficult and expensive to buy.

UNTIL NOW. Click on the link above to be taken to the book's homepage and you'll find out more.

You're welcome.

enter image description here

Tags:

Calculus

Reference Request

Book Recommendation

Banach Spaces

Functional Analysis

Related

Is this correct ${2\over 3}\cdot{6\over 5}\cdot{10\over 11}\cdots{4n+2\over 4n+2+(-1)^n}\cdots=\sqrt{2-\sqrt{2}}?$ How to look at the Lie derivative as a partial differential operator? How to find the limit of $\frac{\sqrt{x^2+9}-3}{x^2}$? as x approaches 0 What does it mean that multiplication and division have the same precedence? Can the non-existence of absolute complements be proved without using the axiom of unions? Every Topological Vector Space is Regular Use Inclusion-Exclusion to find the number of arrangements of 4 A's, 5 B's, 6 C's, 7 D's , 8 E's with exactly 2 adjacent C's Is there an Elementary Theory of the Category of Groups? Do flat functions with flat Fourier transform exist? sequence of positive numbers satisfying $a_{n+1}=\frac{2}{a_n+a_{n-1}}$, prove it converges If $A$ and $B$ are matrices such that $AB^2=BA$ and $A^4=I$ then find $B^{16}$. Solving non-linear ordinary differential equation: $(y'')^2-y'y'''=\left(\frac{y'}{x}\right)^2$

Recent Posts