Applied Functional Analysis

Rating:
Summary: Excellent introduction to functional analysis
Review: Griffel's book is a great introductory functional analysis text. As the title suggests, it is aimed at applied mathematicians rather than theoreticians. In practical terms, it means that Griffel shows how the tools of functional analysis can be applied to differential equations, dynamical systems, and fourier analysis. Griffel gives proofs of most theorems, skipping proofs only when the proof requires a more sophisticated background than this book assumes. The assumed background of the reader is familiarity with calculus, basic differential equations, and some real analysis and linear algebra. A set of appendices cover the needed results from analysis.

The main strength of Griffel's book is its readability. It is one of the most accessible advanced math books I have encountered, comparable to Munkres' "Topology". Griffel explains the intuitions underlying the abstract concepts he presents. He is also careful to point out when he makes a simplification or omission to avoid a difficult or subtle point more suitable to a pure math treatment of the subject. Furthermore, Griffel explains the logic behind his notation, something that is rarely done in math texts. Each chapter concludes with a set of problems. The problems are challenging, but test and expand the reader's understanding of the material. Hints are given for many of the problems.

Overall, this is an excellent resource for the applied mathematician, engineer, or scientist who wants an accessible introduction to functional analysis. Besides, the price of the Dover Edition makes this book a real bargain.

Rating:
Summary: Excellent introduction to functional analysis
Review: Griffel's book is a great introductory functional analysis text. As the title suggests, it is aimed at applied mathematicians rather than theoreticians. In practical terms, it means that Griffel shows how the tools of functional analysis can be applied to differential equations, dynamical systems, and fourier analysis. Griffel gives proofs of most theorems, skipping proofs only when the proof requires a more sophisticated background than this book assumes. The assumed background of the reader is familiarity with calculus, basic differential equations, and some real analysis and linear algebra. A set of appendices cover the needed results from analysis.

The main strength of Griffel's book is its readability. It is one of the most accessible advanced math books I have encountered, comparable to Munkres' "Topology". Griffel explains the intuitions underlying the abstract concepts he presents. He is also careful to point out when he makes a simplification or omission to avoid a difficult or subtle point more suitable to a pure math treatment of the subject. Furthermore, Griffel explains the logic behind his notation, something that is rarely done in math texts. Each chapter concludes with a set of problems. The problems are challenging, but test and expand the reader's understanding of the material. Hints are given for many of the problems.

Overall, this is an excellent resource for the applied mathematician, engineer, or scientist who wants an accessible introduction to functional analysis. Besides, the price of the Dover Edition makes this book a real bargain.

Rating:
Summary: Finally -- the Frechet Derivative!
Review: This book contains one of the best descriptions of the Frechet derivative (functional differentiation) and its applications that I have ever read. This has always been a mystery to me since it is such a fundamentally useful notion, and crops up everywhere in the subject of nonlinear PDE's and numerical analysis. I would recommend this book to any applied mathematician, and especially to engineers, based on Griffel's attention to applications.