Re: Introduction To Analysis (Dover Books On Mathematics) Downloads Torrent
Delmy Moonsommy
A very good,though quite advanced,source that's now available in Dover is Trves, Franois (1967), Topological Vector Spaces, Distributions and Kernels That book is one of the classic texts on functional analysis and if you're an analyst or aspire to be,there's no reason not to have it now. But as I said,it's quite challenging.
Introduction to Analysis (Dover Books on Mathematics) downloads torrent
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One big book on distributions is the first volumeof Hormander's The Analysis of Linear Partial Differential Operators.This may not be the easiest book to read, but it is comprehensiveand a definitive reference.
Why don't people mention about Rudin's book, Functional Analysis. Chapter 1-8 are pretty good for the theory of distribution. The problem is that this book is quite dry, no much motivations behind. So you might have a difficult time in the beginning. It is good to read the book Strichartz, R. (1994), A Guide to Distribution Theory and Fourier Transforms, besides.
The present text has evolved from a set of notes for courses taught at Utrecht University over the last twenty years, mainly to bachelor-degree students in their third year of theoretical physics and/or mathematics.
What do you need distributions for? Your request is strange, PDEs are the fundamental application, the origin, and the main source of examples for distribution theory, so no surprise all the books on distributions after a while steer to PDEs.
Thus maybe my advice is misguided since I do not understand your needs. Anyway, in my opinion the best introduction to distributions is a nice little collection of exercises written by Claude Zuily some years ago (Problems in distributions, North Holland). If you finish it you will be familiar with all the basic theory and you'll be ready to delve into the intricacies, which can be challenging (see the first volume of Hormander, which is essentially a treatise on distributions, or the fear-inducing first volume of John Horvath with its fourteen different topologies on spaces in duality :)
Lieb and Loss, "Analysis" quickly starts with measure theory and after a short break with Fourier transforms, gets on to Distributions. I would imagine this is the fastest way to learn distributions.
For a really gentle introduction I would recommendKolmogorov and Fomin's Introductory Real Analysis,available as a Dover paperback. They have a nice introduction to distributions as "generalized functions"in Section 21.
Just my 2c: Being a student with a limited mathematical education, I used V.S. Vladimirov's Generalized Functions in Mathematical Physics (Mir Moscow 1979) and it was not as hard as I expected it to be - Vladimirov was rigorous and pedantic, as a book in mathematics should be, but not too complicated in explaining the concepts.
If you want a comparatively elementary approach to distribustion theory with applications to integral equations and difference equation no books come close to Distribution Theory and Transform Analysis: An Introduction to Generalized Functions, with Applications by A H Zemanian. another plus is it is Dover paperback, so cheap. Check this out. -Theory-Transform-Analysis-Introduction/dp/0486654796/ref=cm_cr_pr_product_top.
"Mathematics for the Physical Sciences", Laurent Schwartz, Dover 2008 is a simplified English language book that covers some (maybe even much) of Schwartz's theory of distributions. Very readable, helpful and interesting (also $19.95). The title sounds more general than it actually is--really is focused on distributions, and their applications. Schwartz says in the preface: 'This work is concerned with the mathematical methods of physics'.
I agree with Johannes's comment, but despite this, one book that might fit your criteria is Theory of distributions by M.A. Al-Gwaiz. I haven't looked at it for some months, but it made the following standard texts more accessible:
A book that I haven't looked at thoroughly, but you might find interesting, is Guide to Distribution theory and Fourier transforms by Robert S. Strichartz. I once took a class with the author, whose verbal explanatory style is complete and who is also a clear writer.
Two very readable, wide ranging and well motivated accounts are "Generalised Functions and Partial Differential Equations" by Georgi E. Shilov, published by Gordon and Breach 1968, and "Advanced Mathematical Analysis" by Richard Beals, published by Springer 1973 (International student edition). Both are unfortunately out of print and I keep hoping Dover will pick them up so I can recommend them. A recent advanced textbook is "Distributions and Operators" by Gerd Grubb, published by Springer 2009 Vol 252 GTM.
There's the book by Ian Richard and Heekyung Youn. It describes itself as a "non-technical introduction", which apparently means you don't need to know measure theory, topology, or functional analysis. Nonetheless you do need to think more like a mathematician than a physicist or the like in order to appreciate their approach.
In this chapter, the lattice version of the Gaussian Free Field is analyzed. Several features related to the non-compactness of its single-spin-space are discussed, exploiting the Gaussian nature of the model. We also derive the random walk representation that characterizes its mean and covariance structure. The recurrence properties of this random walk turn out to be crucial to analyze the thermodynamic limit.
Reflection positivity is another tool that plays a central role in the rigorous study of phase transitions. We first expose it in detail, proving its two central estimates: the infrared bound and the chessboard estimate. We then apply the latter to obtain several results of importance. In particular, we prove the existence of a phase transition in the anisotropic XY model in dimensions $d\geq 2$, as well as in the (isotropic) $O(N)$ model in dimensions $d\geq 3$. Combined with the results of Chapter 9, this provides a detailed description of this type of systems in the thermodynamic limit.
In this appendix, we introduce various mathematical topics used throughout the book, which might not be part of all undergraduate curricula. For example: elementary properties of convex functions, some aspects of complex analysis, measure theory, conditional expectation, random walks, etc., are briefly introduced, not always in a self-contained manner, often without proofs, but with references to the literature.
Rigorous Statistical Mechanics has a long tradition, starting in the 1960s with Dobrushin, Lanford, Ruelle, Sinai and many other mathematical physicists. Yet, surprisingly, there has not been an up-to-date textbook on an introductory level. This gap is bridged masterly by the present book. It addresses the curious newcomer by employing a carefully designed structure, which starts from a physics introduction and then uses the two-dimensional Ising model as a stepping-stone towards the richness of the subject. The book will be enjoyed by students and researchers with an interest in either theoretical condensed matter physics or probability theory. Herbert Spohn, Technische Universitt Mnchen
An excellent introduction to classical equilibrium statistical mechanics. There is clear concern with the understanding of ideas and concepts behind the various tools and models. Topics are presented through examples, making this book a genuine 'concrete mathematical introduction'. While reading it, my first wish was to use it as soon as possible in a course. It is a 'must' for the libraries of graduate programs in mathematics or mathematical physics. Maria Eullia Vares, Universidade Federal do Rio de Janeiro
This book is a marvelous introduction to equilibrium statistical mechanics for mathematically inclined readers, which does not sacrifice clarity in the pursuit of mathematical rigor. The book starts with basic definitions and a crash course in thermodynamics, and gets to sophisticated topics such as cluster expansions, the Pirogov-Sinai theory and infinite volume Gibbs measures through the discussion of concrete models. This book should be on the bookshelf of any serious student, researcher and teacher of mathematical statistical mechanics. Ofer Zeitouni, Weizmann Institute, Israel
Sacha Friedli and Yvan Velenik have succeeded in writing a unique, modern treatise on equilibrium statistical mechanics. They cover many fundamental concepts, techniques and examples in a didactic manner, providing a remarkable source of knowledge, grounded and refined by years of experience. Stimulating and appealing, this book is likely to inspire generations of students and scientists. Francis Comets, Universit Paris Diderot
The authors have created an impressive book that shows its strengths in several ways: thoughtful organization and a well-designed presentation, real attention to the needs of the reader, and a very nice guide to the existing literature. It could be a model of how mathematical physics should be presented. Bill Satzer, MAA Reviews
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