Ebook Applied Functional Analysis (Dover Books on Mathematics), by D.H. Griffel
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Applied Functional Analysis (Dover Books on Mathematics), by D.H. Griffel
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A stimulating introductory text, this volume examines many important applications of functional analysis to mechanics, fluid mechanics, diffusive growth, and approximation. Detailed enough to impart a thorough understanding, the text is also sufficiently straightforward for those unfamiliar with abstract analysis. Its four-part treatment begins with distribution theory and discussions of Green's functions. Essentially independent of the preceding material, the second and third parts deal with Banach spaces, Hilbert space, spectral theory, and variational techniques. The final part outlines the ideas behind Frechet calculus, stability and bifurcation theory, and Sobolev spaces. 25 Figures. 9 Appendices. Supplementary Problems. Indexes.
- Sales Rank: #1215027 in Books
- Published on: 2002-06-14
- Released on: 2002-06-14
- Original language: English
- Number of items: 1
- Dimensions: 9.21" h x .82" w x 6.14" l, 1.09 pounds
- Binding: Paperback
- 400 pages
Most helpful customer reviews
11 of 11 people found the following review helpful.
Excellent Preparation for Quantum Mechanics
By Frederick Sonnichsen
When studying chemical quantum mechanics some years ago, much reference was made to Hilbert spaces, functionals, adjoint operators and many of the mathematical constructs associated with functional analysis. The majority of books that I had available at that time offered little practical explanation and were overindulged with obscure details, mathematical proofs and issues far beyond what was needed by the beginning quantum chemist. I think that Griffel's book bridged the gap providing enough material to fully grasp the terminology and theorems needed for the study of quantum mechanics while not overwhelming the beginner. It think that this book would be a nice prelude to the one by Byron and Fuller.
0 of 0 people found the following review helpful.
Five Stars
By Amazon Customer
Great book.
15 of 16 people found the following review helpful.
Meh...
By Me
I don't know what all these people are trying to do by saying that this book is "the best book on functional analysis". It's not. I think if one is looking for a "Functional Analysis-Lite" kind of book, you could do better. If you want to learn about Banach and Hilbert spaces, other books would be more thorough and helpful, especially for physicists learning about it grad school having to grapple with it all the time.
The book is divided into 4 parts, and I will discuss each part.
I. Distribution Theory and Green's Functions
II. Banach Spaces and Fixed Point Theorems
III. Operators in Hilbert Spaces
IV. Further Developments
PART I: This is actually a bit more confusing and unclear than it needs to be. A lot of it could be done with more motivation. The actual chapter on Green's functions and PDEs is pretty standard, more or less. I've seen Green's functions discussed better in books by Partial Differential Equations of Mathematical Physics and Integral Equations and also in Methods of Theoretical Physics, Part I. For PDEs and Green's functions solutions, I would recommend a book devoted to PDEs that also covers Fourier Transform methods - there are plenty.
Part II: The chapter on Normed Spaces is not too bad. The discussion is helpful. It helps one understand only the very basics. If you are an applied mathematician developing theories for numerics, or trying to solve intricate PDE problems, I recommend looking at the first half of Elements of the Theory of Functions and Functional Analysis and especially Introductory Functional Analysis with Applications. Their discussion of the fixed point theorems and the Contraction Mapping Theorem (of which Newton's method of solving for zeros is an example), IMHO, are far superior and enlightening. The two just mentioned actually teach you how to think as a mathematician, relatively painlessly. The only advantage is that Griffel's book touches on some modern applications which you may or may not encounter.
Part III: This portion is like a physicists introduction to Hilbert spaces and applications. Here the last book mentioned does a superb job at introducing the material - both Hilbert spaces and Operator theory. In fact, there is also a chapter on on unbounded operators in quantum mechanics in the Kreyszig book that I noticed is missing in Griffel's. The advantage of Griffel's book is that there is a pretty good discussion of Variational methods that I've only seen elsewhere in Linear Algebra and PDE books.
Part IV: I actually cannot comment on this because I did not go too deeply into this material. For Sobolev spaces I looked elsewhere. I never needed the Frechet derivative. Other reviews seem to like it, though.
I have heard some of my students use this book for a class (not taught by me). They were thoroughly confused when going over the material in part I. They did not have knowledge of Real Analysis coming in. For students and classes with students like these, I recommend Introductory Functional Analysis with Applications. For students with little to no prior experience with Real Analysis, I recommend Elements of the Theory of Functions and Functional Analysis. For students with experience in Real Analysis, I recommend the last book mentioned, or one of my favorites, Elementary Functional Analysis. This last book covers a lot of the material that Griffel does (not all); it goes deeper into issues regarding normed vector spaces, Hilbert spaces, etc... ; it teaches one to think like a mathematician (applied or otherwise) and is useful, in my opinion, for physicists as well.
I am not an analyst, I taught myself a lot of this material and Griffel was not helpful when I was taking courses that covered the same stuff and when I was trying to learn about functional analysis. I offer the above list of books as alternatives to finding good stuff - I'm sure other resources exist.
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