I took functional analysis from Conway's book. I thought it was just as abstract and dry as homological algebra, if not more. I knew of no applications.
Then I learned that standing waves on a drum were related to functional analysis, and then that quantum mechanics (as taught in Dirac's classic book) is nothing but functional analysis, with the structure of the atom and the nature of particles all tied up with functional analysis.
I'd love to see a textbook for functional analysis that proceeds through the theory while giving numerous real-life applications. As of now, Dirac's book on quantum mechanics is the best example I can think of, giving a lot of background theory.
Is there an application-heavy functional analysis textbook?