Customer Reviews

Introductory Functional Analysis with Applications

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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.

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.

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.

There is no doubt that Professor Kreysig has written one of the best books of functional analysis. The advantages of this book are the absence of advanced pre-requisites (one has only to know basic concepts of calculus and linear algebra), easy of explanation ( the proofs of the book are really clear), the selection of subjects (one may find in this book more specific topics such as the relation between banach algebras and spectral theory and spectral theory of unbounded operators but also applications such as numerical methods which are very useful for engineers) and the structure of the book (divided in sections with many interesting exercises at the end of each section). Finally, I believe that the main advantage of the book is that, if are not a mathematician, it provides you the motivation to learn these some what abstract concepts.

This book may be used as the main reference in the classroom or also for self-study. In fact, this book is particularly suitable for engineers, economists and physicists. In fact, the last chapter of this book presents an introduction to quantum physics.

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.

The presentation of concepts, definitions, and proofs are clear and EASILY understandable! The problems are illustrative and reinforce one's understanding of the material. I am in the middle of a class in functional analysis. It is a JOY to use this book. If you are interested in functional analysis and can't take a class in the subject, this book should prove to be sufficient by itself. It is that good! I cannot speak highly enough about this great book!

I can't think of a better place to begin learning functional analysis. The book is ideally suited for undergraduates or beginning graduates who have had one or two semesters of real analysis, linear algebra, and possibly topology. The author seemed extremely lucid with clear worked out examples. Phrases like "it's obvious" or "it should be clear" were not so frequent. It's quite a beautiful subject, with the last chapter providing a nice payoff application in terms of an introduction to quantum mechanics.

May be my only complaint was that the exercises seemed mostly five-finger ones. With that said, they should still challenge an undergraduate or beginning graduate, if not force them to re-visit the definitions and basic methods of proof.

I've always thought Rudin's "Mathematical Analysis" book deserved the title of "Best Undergraduate Math Text Ever", but this book has made me rethink that position.

This was my textbook for a graduate course in functional analysis, and it is called "classic" by many professors. Don't be fooled by the title of the book: "Introductory" simply means the author assumes you have not seen the subject before, and it is by no means an easy subject. However, the exposition is extremely clear. Kreyszig saved me on numerous occasions as my companion on a treacherous journey through graduate functional analysis.

This book does what few math textbooks do, though all of them should do. Rather than assail you with theorem, proof, theorem, proof, Kreyszig first tells you what he is about to show you, then explains the motivation -- i.e., why we need the following theorem. Then, once outlined, properly motivated, and placed in context, he delivers the theorem and its proof. Furthermore, Kreyszig explicitly spells out what other texts might assume you will "read between the lines", explaining why and how we are able to take each step forward during a proof.

The problems in the book are also good. They are at a level such that you can attempt them and solve them on your own, while at the same time they give you the hands-on experience you need in order to gain a deeper understanding of the principles at hand. They serve as a great confidence-builder before you venture onward and attempt harder problems (for example, in other texts or in research).

As a final treat for physicists, the last chapter takes the mathematics you've learned throughout the book and applies it in an introduction to quantum mechanics. My only gripe with this final chapter (and indeed my only -- minor -- complaint for the entire book) is that most of the interesting results of quantum mechanics arise not from the book's exposition, but as problems for the reader to work out. Of course, if you want to learn quantum mechanics, this isn't the book to begin with but rather a very nice mathematical supplement.

I highly recommend this book to anyone wanting to learn functional analysis.

This book is especially good for those who are not mathematicians, and just need some knowledge of functional analysis for computation or application of rigorous theory. This book is well organized in the sense that the shortest path is easily identified for what we want to learn out of this book. I would strongly recommend.

I dont have a lot to say, but ijust wanted to say that this book is really written for the student, without any complications a student can alone read it and understand it,,,