Arbogast Todd, Bona Jerry L. Methods of Applied Mathematics

The University of Texas at Austin, 2008. — 279 p.Preliminaries.
Normed Linear Spaces and Banach Spaces.
Hilbert Spaces.
Spectral Theory and Compact Operators.
Distributions.
The Fourier Transform.
Sobolev Spaces.
Boundary Value Problems.
Differential Calculus in Banach Spaces and the Calculus of Variations.