Introductory functional analysis with applications

This textbook shows how functional analysis can be put to work in the natural sciences and in mathematics itself. Its core chapters work through Hilbert spaces and Banach spaces, with plenty of worked problems to guide the reader. Throughout, the emphasis falls on the central ideas, the guiding principles, the standard methods, and the major applications of the subject.

The book is written as an introduction for students who already have a solid grounding in analysis and linear algebra. It builds the theory step by step and keeps returning to concrete uses, so the abstract framework stays tied to problems that arise in scientific work.