Chapter 1. Introduction
Chapter 2. Banach spaces
Chapter 3. Spaces of continuous functions
Chapter 4. Bounded linear operators
Chapter 5. Hilbert spaces
Chapter 6. Compact operators on a Hilbert space
Chapter 7. Semigroups of linear operators
Chapter 8. Sobolev spaces
Chapter 9. Linear partial differential equations

The book is intentionally concise, presenting all the fundamental concepts and results but omitting the more specialized topics. Enough of the theory of Sobolev spaces and semigroups of linear operators is included as needed to develop significant applications to elliptic, parabolic, and hyperbolic PDEs. Throughout the book, care has been taken to explain the connections between theorems in functional analysis and familiar results of finite-dimensional linear algebra.The main concepts and ideas used in the proofs are illustrated with a large number of figures. A rich collection of homework problems is included at the end of most chapters. The book is suitable as a text for a one-semester graduate course.---Summary provided by publisher