Introductory Functional Analysis with Applications | 
 enlarge | Author: Erwin Kreyszig
Publisher: Wiley
Category: Book
Buy New: $73.50
New (16) Used (6) from $50.00
Rating:  15 reviews
Sales Rank: 302436
Media: Paperback
Edition: 1
Pages: 704
Number Of Items: 1
Shipping Weight (lbs): 2.1
Dimensions (in): 8.9 x 5.9 x 1.3
ISBN: 0471504599
Dewey Decimal Number: 511
EAN: 9780471504597
Publication Date: February 23, 1989
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Product Description
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.
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| Customer Reviews: Read 10 more reviews...
 The Place to Start July 22, 2003
Jason Schorn (Spokane, WA)
35 out of 36 found this review helpful
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 April 26, 2002
Nathaniel Jewell (Adelaide, Australia)
27 out of 29 found this review helpful
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 August 27, 2000
KARTIK KRISHNAN S. (Hamilton, Ontario Canada)
17 out of 18 found this review helpful
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.
The best undergraduate introduction to the subject December 12, 2004
Todd Ebert (Long Beach California)
11 out of 11 found this review helpful
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.
Makes you actually WANT to study analysis! December 22, 2005
calvinnme (Fredericksburg, Va)
14 out of 15 found this review helpful
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.
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