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Introductory Functional Analysis with Applications
 
 
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Introductory Functional Analysis with Applications (Paperback)

by Erwin Kreyszig (Author) "Functional analysis is an abstract branch of mathematics that originated from classical analysis..." (more)
Key Phrases: total orthonormal set, total orthonormal sequence, uniform operator convergence, Spectral Properties of Self-Adjoint Operators, Properties of the Spectral Family, Hence Theorem (more...)
4.9 out of 5 stars See all reviews (14 customer reviews)

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Introductory Functional Analysis with Applications + Elements of the Theory of Functions and Functional Analysis + Calculus of Variations
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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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14 Reviews
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4.9 out of 5 stars (14 customer reviews)
 
 
 
 
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36 of 37 people found the following review helpful:
5.0 out of 5 stars The Place to Start, July 22, 2003
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.
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28 of 30 people found the following review helpful:
5.0 out of 5 stars Functional analysis - as it should be taught, April 25, 2002
By Nathaniel Jewell (Adelaide, Australia) - See all my reviews
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.

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18 of 19 people found the following review helpful:
5.0 out of 5 stars A fantastic introduction to functional analysis, August 27, 2000
By KARTIK KRISHNAN S. (Hamilton, Ontario Canada) - See all my reviews
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.

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Most Recent Customer Reviews

5.0 out of 5 stars Two thumbs up!
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,,,
Published 12 months ago by Murad Omar

5.0 out of 5 stars A great book for mathematicians and the best I know for engineers, economists and physicists
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... Read more
Published on January 24, 2007 by Daniel O. Cajueiro

4.0 out of 5 stars A Classic
This was my textbook for a graduate course in functional analysis, and it is called "classic" by many professors. Read more
Published on December 13, 2006 by simkn

5.0 out of 5 stars 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. Read more
Published on June 15, 2006 by Alexander C. Zorach

5.0 out of 5 stars Good
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. Read more
Published on January 15, 2006 by Japanese Economist

5.0 out of 5 stars 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... Read more
Published on December 22, 2005 by calvinnme

5.0 out of 5 stars From an applied statistician
This is a clear and parsimonious introduction to Functional Analysis. The book aided me in understanding some of the underlying theory behind statistical kernel methods. Read more
Published on December 17, 2005 by DUYHA

5.0 out of 5 stars The best undergraduate introduction to the subject
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... Read more
Published on December 12, 2004 by Todd Ebert

5.0 out of 5 stars The definition of classic
As shown in the first line on the cover:
Wiley CLASSICS Library
Published on May 15, 2004 by Xiaoji Liu

5.0 out of 5 stars Possibly the BEST math book that I have ever read
The presentation of concepts, definitions, and proofs are clear and EASILY understandable! The problems are illustrative and reinforce one's understanding of the material. Read more
Published on May 6, 2004 by Gregory D Teplow

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