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Title: Introductory Functional Analysis with Applications by Erwin Kreyszig ISBN: 0471504599 Publisher: John Wiley & Sons Pub. Date: 23 February, 1989 Format: Paperback Volumes: 1 List Price(USD): $64.95 |
Average Customer Rating: 5
Rating: 5
Summary: The Place to Start
Comment: 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: 5
Summary: Functional analysis - as it should be taught
Comment: 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: 5
Summary: A fantastic introduction to functional analysis
Comment: 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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Title: Elementary Functional Analysis by Georgi E. Shilov ISBN: 0486689239 Publisher: Dover Pubns Pub. Date: January, 1996 List Price(USD): $15.95 |
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Title: Elements of the Theory of Functions and Functional Analysis by A. N. Kolmogorov, S. V. Fomin ISBN: 0486406830 Publisher: Dover Pubns Pub. Date: March, 1999 List Price(USD): $12.95 |
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Title: Functional Analysis by Frigyes Riesz, Bela Sz.-Nagy ISBN: 0486662896 Publisher: Dover Pubns Pub. Date: June, 1990 List Price(USD): $16.95 |
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Title: Functional Analysis by Walter Rudin ISBN: 0070542368 Publisher: McGraw-Hill Science/Engineering/Math Pub. Date: 01 January, 1991 List Price(USD): $127.10 |
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Title: Lebesgue Integration on Euclidean Space (Revised Ed.) by Frank Jones ISBN: 0763717088 Publisher: Jones & Bartlett Pub Pub. Date: 08 November, 2000 List Price(USD): $62.95 |
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