I'm looking for a rigorous introduction to functional analysis in the style of Apostol. I've looked at Introductory Functional Analysis with Applications by Kreyszig, but I find it slightly too conversational. I know that Rudin has a Functional Analysis book, but it seems to be out of print and my library does not have a copy to view. I'm also looking for textbook on Vector Analysis. The treatment in Apostol's Calculus seemed insufficient and was nonexistent in his Mathematical Analysis. And are there any books that rigorously cover coordinate transformations? I learned the basics of spherical and cylindrical coordinates in multivariable calculus and used them frequently in physics courses, but I've never seen them treated theoretically. Apostol's books contained Jacobians, but did not treat problems in other coordinates in depth. I understand that coordinate systems might just be a tool for applications and may not exist in a theoretical context, but I thought I'd ask anyways. Thanks!