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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Most Helpful Customer Reviews
40 of 42 people found the following review helpful:
5.0 out of 5 stars
Functional analysis - as it should be taught,
By Nathaniel Jewell (Adelaide, Australia) - See all my reviews
This review is from: Introductory Functional Analysis with Applications (Paperback)
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.
22 of 23 people found the following review helpful:
5.0 out of 5 stars
Makes you actually WANT to study analysis!,
This review is from: Introductory Functional Analysis with Applications (Paperback)
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.
18 of 19 people found the following review helpful:
5.0 out of 5 stars
A fantastic introduction to functional analysis,
This review is from: Introductory Functional Analysis with Applications (Paperback)
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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Inside This Book
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First Sentence:
Functional analysis is an abstract branch of mathematics that originated from classical analysis. Read the first page Key Phrases - Statistically Improbable Phrases (SIPs): (learn more)
total orthonormal set, total orthonormal sequence, uniform operator convergence, operator convergent, bounded inverse theorem, strong operator convergence, triangle inequality for numbers, spectral family, compact linear operator, uniform boundedness theorem, two algebraic operations, parallelogram equality, unbounded linear operators, closed linear operator, symmetric linear operator, sublinear functional, discrete metric space, only finitely many nonzero terms, normed spaces, spectral mapping theorem, finite dimensional normed space, open mapping theorem, closed graph theorem, total boundedness, pure point spectrum Key Phrases - Capitalized Phrases (CAPs): (learn more)
Spectral Properties of Self-Adjoint Operators, Properties of the Spectral Family, Hence Theorem, Max Planck New!
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Front Cover | Table of Contents | First Pages | Index | Back Cover | Surprise Me!
Functional analysis is an abstract branch of mathematics that originated from classical analysis. Read the first page Key Phrases - Statistically Improbable Phrases (SIPs): (learn more)
total orthonormal set, total orthonormal sequence, uniform operator convergence, operator convergent, bounded inverse theorem, strong operator convergence, triangle inequality for numbers, spectral family, compact linear operator, uniform boundedness theorem, two algebraic operations, parallelogram equality, unbounded linear operators, closed linear operator, symmetric linear operator, sublinear functional, discrete metric space, only finitely many nonzero terms, normed spaces, spectral mapping theorem, finite dimensional normed space, open mapping theorem, closed graph theorem, total boundedness, pure point spectrum Key Phrases - Capitalized Phrases (CAPs): (learn more)
Spectral Properties of Self-Adjoint Operators, Properties of the Spectral Family, Hence Theorem, Max Planck New!
Books on Related Topics | Concordance | Text Stats Browse Sample Pages:
Front Cover | Table of Contents | First Pages | Index | Back Cover | Surprise Me!
Citations (learn more)
This book cites 29
books:
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95
books
cite this book:
See all 95 books citing this book
- Quantum Mechanics (Pure & Applied Physics) by L. I. Schiff in Back Matter
- Numerical Analysis (Proceedings of Symposia in Applied Mathematics, V. 22) by American Mathematical Society in Back Matter
- Introduction to Approximation Theory (AMS Chelsea Publishing) by Elliott W. Cheney in Back Matter
- Introduction to Hilbert Space (2nd ed) by Sterling K. Berberian in Back Matter
- Book of Splines (Probability & Mathematical Statistics) by Arthur Sard in Back Matter
See all 29 books this book cites
- Invitation to Linear Operators: From Matrices to Bounded Linear Operators on a Hilbert Space by Takayuki Furuta on 4 pages
- Applied Functional Analysis: Numerical Methods, Wavelet Methods, and Image Processing (Chapman & Hall/CRC Pure and Applied Mathematics) by Abul Hasan Siddiqi on page 165, and page 199
- From Micro to Macro Quantum Systems: A Unified Formalism With Superselection Rules And Its Applications by K. Kong Wan on page 227, and Back Matter
- Monte Carlo and Quasi-Monte Carlo Methods 2000 by Kai-Tai Fang on page 49, and page 317
- Finite Element Analysis (Wiley Series in Computational Mechanics) by Barna Szabó in Back Matter
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