Introductory Functional Analysis with Applications

by Erwin Kreyszig

Book Overview

Provides avenues for applying functional analysis to the practical study of natural sciences as well as mathematics. Contains worked problems on Hilbert space theory and on Banach spaces and emphasizes concepts, principles, methods and major applications of functional analysis.

• Format: Hardcover
• Language: English
• ISBN: 0471507318
• ISBN13: 9780471507314
• Release Date: January 1978
• Publisher: John Wiley & Sons
• Length: 703 Pages
• Weight: 2.42 lbs.

Customer Reviews

Excellent introductory book on functional analysis

This book is excellent for so many reasons. The book is self-contained; it is much more accessible than a number of other books. The writing is very clear, occasional use of diagrams is very helpful. Proofs are very easy to follow, and the author gives you a sense of the big picture of the subject before you get to the proof, keeping the reader motivated in a subject that can often seem abstract and boring. The typesetting and layout of the book are also unusually well-executed for a mathematics book: definitions are easy to spot, and the material is presented clearly on the page. The book as a whole is exceptionally well-organized, making it easy to skip around, and making this book an outstanding reference. One of the best aspects of this book are the examples; the text is rich in examples, especially in the beginning. This aspect drops off a little as you progress in the book, which was honestly a little bit disappointing, since if anything I think it should be the other way around. The exercises are not particularly difficult, but are appropriate to the level of the book--they will be difficult for people with less background in analysis. Some of them are very easy, others are tedious and/or technical but not particularly deep. I did not work exercises in the advanced chapters as much as the easier chapters though so I can't say about them. I think some of the more critical reviewers are ignoring the title and audience of this book: this is an introductory book, designed to make the subject accessible at a lower level. For that role, it is simply amazing. Any criticism of this book needs to take this into account--it is not an advanced graduate-level text and should not be evaluated as such.

Makes you actually WANT to study analysis!

Functional analysis is the branch of mathematics concerned with the study of spaces of functions. It has its historical roots in the study of transformations, such as the Fourier transform, and in the study of differential and integral equations. This usage of the word functional goes back to the calculus of variations, implying a function whose argument is a function. Most textbooks claiming to be introductions to this subject are just one proof after another without a clue as to WHY you would want to study this stuff in the first place. Mr. Kreyszig's book is a welcome addition to the family of textbooks that claim to be introductions to the subject because the material is explained in an accessible fashion alongside applications to the material. So YES as one reviewer put it, this book smells like an engineer's text, but to this reader that is a good thing because I get a feel for how to use the information thus motivating me for further study. I particularly liked the sections applying Banach's Fixed Point Theorem to the solution of differential equations and linear equations. As for the suggestions of other reviewers to reject this book in favor of Rudin's, I think that is a bad suggestion for someone other than a graduate student of pure mathematics. Rudin does a great job of explaining all of the theory, but I think that this book is better at providing motivations for the study of functional analysis through the demonstration of applications. Eventually, you should probably read both books.

The Place to Start

Heir professor Kreyszig has done what the majority of other authors have failed to do. Namely, he has compiled a book whose only real prerequisites are a solid understanding of Calculus and some familiarity with Linear Algebra. Obviously this required level of understanding is minimal, to say the least, and this is one of the main reasons I feel so strongly that this book is number one in its category. Moreover, since the majority of "introductory" texts on Functional Analysis are primarily directed toward graduate students the aforementioned requirements coupled with a wide selection of topics makes this book easily accessible to advanced undergraduates and begining graduate students. I highly recommend this book to anyone interested in actually learning Functional Analysis and also to the ambitious self-learner since Kreyszig has included both hints and solutions to selected exercises. In regards to the exercises and examples contained in the text, they are well chosen, insightful and at no time does Kreyszig leave a major theorem/propostion to the reader. In fact, he provides many fully worked examples which are left as exercises in most other texts. My hat goes off to professor Kreyszig for such a wonderfully well written text and also to Wiley for continuing to publish this classic.

Functional analysis - as it should be taught

Most books on analysis could be subtitled "One damn theorem after another: written by mathematicians for mathematicians". This book is different. Though rigorous and concise, it takes the time to explain what theorems really mean and why concepts are worth understanding. It shows that functional analysis is a generalization and extension of many concepts from undergraduate algebra and calculus. As such, it is powerful, beautiful, and above all, useful.The first half of the book covers the basic theory of metric spaces, normed/Banach spaces and inner-product/Hilbert spaces. Applications include approximation theory and numerical integration; differential and integral equations; and the Legendre, Hermite, Laguerre and Chebyshev polynomials. The second half of the book is devoted to spectral theory, the final chapter discussing operators in quantum mechanics. Although integration theory is not formally covered, the book does show its relationship to functional analysis.The book provides numerous examples, counter-examples and exercises. The exercises really are do-able - mostly short but instructive - and answers are provided for odd-numbered questions.

A fantastic introduction to functional analysis

Kreyszig's "Introductory Functional Analysis with Applications", provides a GREAT introduction to topics in real and functional analysis. This book is part of the WILEY CLASSICS LIBRARY and is extremely well written, with plenty of examples to illustrate important concepts. It can provide you with a solid base in these subjects, before one takes on the likes of Rudin and Royden.I had purchased a copy of this book, when I was taking a graduate course on real analysis and can only strongly recommend it to anyone else.