Introductory Functional Analysis with Applications

Rating:
Summary: The definition of classic
Review: As shown in the first line on the cover:
Wiley CLASSICS Library

Rating:
Summary: The Place to Start
Review: 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.

Rating:
Summary: The Place to Start
Review: 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.

Rating:
Summary: The best undergraduate introduction to the subject
Review: 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.

Rating:
Summary: A fantastic introduction to functional analysis
Review: 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.

Rating:
Summary: Functional analysis - as it should be taught
Review: 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.

Rating:
Summary: Possibly the BEST math book that I have ever read
Review: 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!

Rating:
Summary: Possibly the BEST math book that I have ever read
Review: 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!