Product Description

This book contains almost 450 exercises, all with complete solutions; it provides supplementary examples, counter-examples, and applications for the basic notions usually presented in an introductory course in Functional Analysis. Three comprehensive sections cover the broad topic of functional analysis. A large number of exercises on the weak topologies is included.

Customer Reviews (1)

Review of the book entitled: Exercises in Functional Analysis
The book is very interesting. I think that it is a good reference in order to complement a full course of functional analysis because the quantity of exercises is terrific. I recommend the book for everyone! ... Read more

Product Description

Human language is a remarkable phenomenon. Its study continues to be a source of fascination and delight. Dr. Donald Burquest, professor of linguistics at the University of Texas at Arlington, developed this foundational textbook during years of helping students overcome the feelings of dismay that new phonology students experience when confronted by a mass of raw phonetic data. While working through the material, the student is led through the steps of organizing data and is introduced to particular theories for later in-depth specialization.

In the second edition the author expanded on the first edition of this text by adding introductions to Autosegmental Phonology and Metrical Phonology. He has also included a series of problems at the end of most chapters that provide an opportunity for the student to apply the information in that chapter. This present edition incorporates numerous minor revisions and has an improved subject index.

This textbook is intended for use in an upper division introductory course in phonology, preparing the student to further study aspects of current theory.

Table of Contents

Preface to the Third Edition
Preface to the Second Edition
Preface to the First Edition

1. Preliminaries to Analysis
1.1 The place of phonology in linguistics
1.2 Foundational principles
1.3 Phonological features
1.4 Excursus on redundancy
1.5 Excursus on rule formalisms
2. Phonemic Analysis

2.1 Basic concepts in phonemic analysis
2.2 Procedures for phonemic analysis
2.3 The procedure applied
2.4 Phonological universals: Vowel and consonant systems
2.5 Identifying phonetically similar segments
2.6 Free variation
2.7 Phonotactics, neutralization, and underspecification
2.8 Problems

3. Morphophonemics

3.1 Phonologically conditioned alternations
3.2 Lexical alternations
3.3 Morphologically conditioned alternations
3.4 Phonological representation and rules
3.5 Analytical procedure and morphophonemics
3.6 Case studies
3.7 Positing underlying representations
3.8 Problems

4-6 Natural Phonological Processes

1. Conditioning by Surrounding Segments

4.1 Sources of natural processes
4.2 Assimilation
4.3 Dissimilation
4.4 Summary
4.5 Problems

2. Conditioning by Syllable Structure

5.1 Syllables and consonant strength
5.2 Syllable structure
5.3 Ambiguous segments
5.4 Ambiguous sequences
5.5 Processes conditioned by syllable structure
5.6 Length
5.7 Syllable-domain phenomena and processes
5.8 Problems

3. Conditioning by Larger Units

6.1 Word-level phenomena
6.2 Utterance-level phenomena
6.3 Problems

7-8 Three-Dimensional Models

1. Autosegmental Phonology

7.1 Introduction
7.2 The establishment of autosegmental tiers
7.3 Assimilation of one segment to another
7.4 Processes affecting the phonological word
7.5 Processes affecting larger units
7.6 Excursus on the feature tree
7.7 Problems

2. Metrical Phonology

8.1 Introduction
8.2 Syllable structure
8.3 Phonological feet
8.4 Phonological words
8.5 Extrametricality
8.6 Epenthesis
8.7 Interpretation of ambiguous segments
8.8 Reduplication
8.9 Problems

References
Index of Languages
Subject Index

Product Description
This is a book for those who want to understand the main ideas in the theory of optimal problems. It provides a good introduction to classical topics (under the heading of "the calculus of variations") and more modern topics (under the heading of "optimal control"). It employs the language and terminology of functional analysis to discuss and justify the setup of problems that are of great importance in applications. The book is concise and self-contained, and should be suitable for readers with a standard undergraduate background in engineering mathematics. ... Read more

Product Description
Focusing on one of the main pillars of mathematics, Elements of Real Analysis provides a solid foundation in analysis, stressing the importance of two elements. The first building block comprises analytical skills and structures needed for handling the basic notions of limits and continuity in a simple concrete setting while the second component involves conducting analysis in higher dimensions and more abstract spaces.

Largely self-contained, the book begins with the fundamental axioms of the real number system and gradually develops the core of real analysis. The first few chapters present the essentials needed for analysis, including the concepts of sets, relations, and functions. The following chapters cover the theory of calculus on the real line, exploring limits, convergence tests, several functions such as monotonic and continuous, power series, and theorems like mean value, Taylor's, and Darboux's. The final chapters focus on more advanced theory, in particular, the Lebesgue theory of measure and integration.

Requiring only basic knowledge of elementary calculus, this textbook presents the necessary material for a first course in real analysis. Developed by experts who teach such courses, it is ideal for undergraduate students in mathematics and related disciplines, such as engineering, statistics, computer science, and physics, to understand the foundations of real analysis. ... Read more

Product Description

This is the classic introductory graduate text. Heart of the book is measure theory and Lebesque integration.

... Read more

Customer Reviews (24)

Good candidate for the worst math book ever
This book is absolutely horrific .Royden proves (mostly handwaves) a few theorems , and then expects the student to be able to solve the exercises easily given this background.Can we even call this a Math Book?? As it is unfortunately the case with most graduate level textbooks in the U.S , the exercises are minimally related to what the author develops (or tries to develop).Books like this do not take much effort to write , while the students trying to learn this hard subject are the real victims.I agree with another reviewer that this book was written by Royden just to impress his peers.The important theorems are just given with the most minimal explanations possible ,and no effort whatsoever is made to get to the intuitive roots of the subject.Important examples are also close to nonexistent.Can anything be worse??

Classic text, but a poor reference.
Halsey Royden's Real Analysis has become the de facto standard for teaching a graduate course on real analysis and integration.It has, however, become a bit dated.First off, the method of developing the Lebesgue integral before general measure theory is out of style.It is now generally accepted that learning the (relatively easy concept of) general measure theory first, and then the Lebesgue measure as an example, is a superior pedagogical approach.

That said, Royden is very good at explaining things in more detail; it is both a complement and a criticism that the book manages to cover a good deal less than Folland's text in almost twice the length.Complementary in the sense that the book motivates the material and gives explanations without leaving the reader to any important developments, critical in that the book is more or less useless as a reference.What's more is the fact that in the book's 444 pages it only manages to cover about half of what Gerald Folland goes through in his shorter book; this makes the ridiculous price of the book even less justifiable.

All of this said, I would still recommend this book for study.It explains well and would be a good read for self study.As for the criticisms that label the book as either "too difficult" or "too dense," disregard them.Those who make these claims are probably just not very good with Analysis.For a book that is truly awful, see M.A. Armstrong's Basic Topology.

Really Great for Certain Topics
Great for the bookshelf but really pretty hard - you need a good proof course and a year suffering through baby Rudin - and believe me, you will suffer - but will be a better person (and mathematician) for it.

Maybe good as a supplement, or a first time looking at the material
There are three books that are usually used for a first graduate course in analysis, including measure theory, namely Rudin's Real and Complex Analysis, Folland's Real Analysis, and Royden's book. Of the three, I would say Royden's book is the easiest, both in terms of the exposition, material, and exercises. Of the three, Royden is the only one to fully develop the Lebesgue measure and the associated integral before developing a more general theory of measure and integration. Furthermore, he does not develop Hilbert and Banach space theory, the very basics of functional analysis, to anywhere near the extent that Folland and Rudin do.

There is some debate as to whether it is better to start with the Lebesgue integral, and then talk about abstract integration, or the other way around. Personally, I found the development of the Lebesgue integral a bit tedious; the whole thing works a bit better when you first talk about abstract integration, which really isn't a terribly difficult concept, prove the basic integration theorems, then show how to construct an outer measure, and suddenly, the Lebesgue measure and integral just falls into place. I'm not sure anything is lost in the process.

The biggest shortcoming in this book would have to be the exercises: for the most part, they are not very difficult, particularly when you compare them to say, Rudin's text. For the most part, the exercises are fairly trivial, and if they are difficult, or require a bit of creativity, Roydenoften gives you lots and lots of hand-holding, sometimes even in the form of sketching out the proof for you. In spite of the relatively low difficulty level, most of the exercises are fairly instructive, in so far as they highlight, elucidate, and expand upon the material.

For the most part, this book is not bad. It makes a good supplement to a book like Rudin or Folland, as it is less abstract, and does a better job motivating the material. The exercises here can work well if you want some extra practice that won't take up too much time. If you're a student of econ, or physics, or you just feel like learning graduate-level real analysis, then this book is probably adequate (although I should qualify that statement by saying that I know nothing of econ and little of physics). But if you are a serious student of mathematics, particularly the pure variety, this is really not the book you should be using. It is just too easy.

Classic text on measure & integration theory
Many people criticize this book as unclear and unnecessarily abstract, but I think these comments are more appropriately directed at the subject than at this book and its particular presentation.I find this classic to be one of the best books on measure theory and Lebesgue integration, a difficult and very abstract topic.Royden provides strong motivatation for the material, and he helps the reader to develop good intuition.I find the proofs and equations exceptionally easy to follow; they are concise but they do not omit as many details as some authors (i.e. Rudin).Royden makes excellent use of notation, choosing to use it when it clarifies and no more--leaving explanations in words when they are clearer.The index and table of notation are excellent and contribute to this book's usefulness as a reference.

The construction of Lebesgue measure and development of Lebesgue integration is very clear.Exercises are integrated into the text and are rather straightforward and not particularly difficult.It is necessary to work the problems, however, to get a full understanding of the material.There are not many exercises but they often contain crucial concepts and results.

This book contains a lot of background material that most readers will either know already or find in other books, but often the material is presented with an eye towards measure and integration theory.The first two chapters are concise review of set theory and the structure of the real line, but they emphasize different sorts of points from what one would encounter in a basic advanced calculus book.Similarly, the material on abstract spaces leads naturally into the abstract development of measure and integration theory.

This book would be an excellent textbook for a course, and I think it would be suitable for self-study as well.Reading and understanding this book, and working most of the problems is not an unreachable goal as it is with many books at this level.This book does require a strong background, however.Due to the difficult nature of the material I think it would be unwise to try to learn this stuff without a strong background in analysis or advanced calculus.A student finding all this book too difficult, or wanting a slower approach, might want to examine the book "An Introduction to Measure and Integration" by Inder K. Rana, but be warned: read my review of that book before getting it. ... Read more

Product Description
This book is a one-semester text for an introduction to real analysis. The author's primary aims are to develop ideas already familiar from elementary calculus in a rigorous manner and to help students deeply understand some basic but crucial mathematical ideas, and to see how definitions, proofs, examples, and other forms of mathematical 'apparatus' work together to create a unified theory. A key feature of the book is that it includes substantial treatment of some foundational material, including general theory of functions, sets, cardinality, and basic proof techniques. ... Read more

Product Description
The book is based on courses taught by the author at Moscow State University. Compared to many other books on the subject, it is unique in that the exposition is based on extensive use of the language and elementary constructions of category theory. Among topics featured in the book are the theory of Banach and Hilbert tensor products, the theory of distributions and weak topologies, and Borel operator calculus.The book contains many examples illustrating the general theory presented, as well as multiple exercises that help the reader to learn the subject. It can be used as a textbook on selected topics of functional analysis and operator theory. Prerequisites include linear algebra, elements of real analysis, and elements of the theory of metric spaces. ... Read more

Product Description

This monograph presents a complete and rigorous study of modern functional analysis. It is intended for the student or researcher who could benefit from functional analytic methods, but does not have an extensive background and does not plan to make a career as a functional analyst. It develops the topological structures in connection with measure theory, convexity, Banach lattices, integration, correspondences (multifunctions), and the analytic approach to Markov processes. Many of the results were previously available only in works scattered throughout the literature. The choice of material was motivated from problems in control theory and economics, although the material is more applicable than applied.

Customer Reviews (1)

An excellent treatment of mathematical methods for economist
The monograph covers advanced mathematical methods for economists. Itincludes chapters on general topology, topological vector spaces, Rieszspaces and Banach lattices, measure and integration, etc. While the bookdoes not contain (hardly) any economics, the mathematics coveredisselected under the aspect of later applications to economics. The bookcontains for example a long chapter on correspondences, a topic which ishardly covered by any standard math book. The presentation of themathematics is throughout clear and precise. The advantage of the book isthat it covers a wide range of mathematical topics, which could not befound together in a book before. Graduate students in economic theory canuse it as a text book, but it can also be used as a reference book. Theonly lacks of the book are that there are no exercises and that not allmath areas important to economics (e.g. differential topology) are covered.Overall, this is an excellent book and should become part of the library ofeverybody interestedin mathematical economics. ... Read more

Customer Reviews (3)

still one of the best
After 30 years of its first publications, this book remains one of the best. It treats all the elements of a graduate course in analysis thoroughly. One of the few books that actually goes through construction of the real number system (in Chapter 1) and products of infinitely many measure spaces (in Chapter 6). There is plenty material to choose from, and all the standard topics are covered. In a very few cases notation is a bit cumbersome (or obsolete), but this is no big problem. Highly recommended to all graduate students in mathematics.

Excellent real analysis reference
In many applications today, such as PDE or harmonic analysis, it is crucial to have a really good grasp of the Lebesgue integral and absolutely continuous (rather than continuously differentiable) functions. Many real analysis books shy away from these matters.

Hewitt and Stromberg provide *every* detail, starting from scratch with measure theory, including Caratheodory's construction and fine distinctions such as Lebesgue vs. Lebesgue-Borel measurable sets. They proceed to discuss the Lebesgue integral in detail, then differentiation and absolutely continuous functions, the Lebesgue spaces including Riesz representation and a Banach space primer and finally integration on products (also infinite) of measure spaces. Fourier series and transforms are covered as well as fine details of (naive) set theory.

The book would be perfect if some standard analysis (Taylor series, analytic functions, Hospital rule, ...) was discussed; for this reason and because of its high level, it cannot be recommended as a book for 1st year calculus.

One of the best references on the subject
This is the kind of book I appreciate the most: one that's always got the information you need. This meticulous text covers thoroughly just every topic from elementary set theory up to product measures. It developscarefully all topics that should be included in standard analysis lectures(set theory, topology, Lebesgue integral, Banach and Hilbert spaces,differentiation, product measures) at such level of abstraction that thebook turns out to be suitable for introductory courses, advanced courses,and later reference. The only one shortcoming I see is that the bookincludes no bibliography.

Please check my other reviews at my member page(click on my name above). ... Read more

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Hardbound. ... Read more

Product Description
This monograph on generalised functions, Fourier integrals and Fourier series is intended for readers who, while accepting that a theory where each point is proved is better than one based on conjecture, nevertheless seek a treatment as elementary and free from complications as possible. Little detailed knowledge of particular mathematical techniques is required; the book is suitable for advanced university students, and can be used as the basis of a short undergraduate lecture course. A valuable and original feature of the book is the use of generalised-function theory to derive a simple, widely applicable method of obtaining asymptotic expressions for Fourier transforms and Fourier coefficients. ... Read more

Customer Reviews (1)

Great for self study
Nice little book. Concise and clear. In the typical English style, many of the proofs are left to the reader. Lighhill will assume what he finds obvious is also obvious to the reader. This was not always the case for me. He does this alot in the proving theorems so have a pencil ready. It is alot fun to work through the proofs becuase he gives rough sketches and leaves you to fill in the details. He manages this without loss of clarity or rigor. It is good pedagogy for anyone familiar with basic analysis of real variables and some knowledge of complex variables. ... Read more

Product Description
This collection of papers, with their focus on social change in different settings and through a wide range of voices, offers a fresh view of both Systemic Functional Linguistics (SFL) and Critical Discourse Analysis (CDA), and, ultimately, the relationship between the two. In the Theoretical Section, the authors explore ways to study social, political, and economic transformations; in the Applied Section, the authors examine the effects of social change on national and institutional identities. In each of these papers, the examination of the 'social' is in addition to, but not in place of, thorough linguistic analyses of discursive events. One of the main purposes of the collection is to make explicit the connections between SFL and CDA - two approaches to the study of language. This volume is the first to make explicit this connection so that novices as well as experienced researchers examining the two fields under "one microscope" can more fully understand how they are related and how CDA can draw on analytical tools rooted in SFL.The book has several aims: to extend the connections between SFL and CDA; to provide analyses of social change that are rooted in linguistic theory and methodology, specifically SFL which provides a solid analytical foundation that helps researchers avoid ideological bias; to critically analyse discursive material that includes, but is not limited to, media; and finally to offer a broad range of international perspectives on the role of discourse in changing social practices and patterns. ... Read more

Product Description
Tensor analysis is an essential tool in any science (e.g. engineering, physics, mathematical biology) that employs a continuum description. This concise text offers a straightforward treatment of the subject suitable for the student or practicing engineer. The final chapter introduces the reader to differential geometry, including the elementary theory of curves and surfaces. A well-organized formula list, provided in an appendix, makes the book a very useful reference. A second appendix contains full hints and solutions for the exercises. ... Read more

Customer Reviews (4)

2nd edition
There is the second edition of this book called Tensor Analysis With Applications in Mechanics. It extends the first edition with applications of tensor analysis to linear elasticity and shell theory.

Right on the subject
A very well written book. Focuses on the subject matter and builds a good level of knowledge starting from the beginning. Recommended to everyone interested in understanding and using tensors.

Buy this book!
if you want to learn tensor analysis in clear language, this book is for you ! fantastic introduction to the subject. The exposition is quite clear ! BUY IT!

Tensor analysis for all
This is a well-written and careful introduction to the
sort of tensor analysis which pervades continuum mechanics. Students and practicing engineers will find a detailed presentation of all the main ideas, theorems, etc, along withcomplete proofs. One particularly nice feature is a well-organized appendix containing compact listings of all the principal formulas needed in applications - this alone is worth the price of the book. The authors have also included an introduction to differential geomentry - in particular, the theory of surfaces on which shell theory is based. ... Read more

Product Description
This volume contains all the exercises, and their solutions, for Serge Lang's fourth edition of "Complex Analysis," ISBN0-387-98592-1. The problems in the first 8 chapters are suitable for an introductory course at the undergraduate level and cover the following topics: power series, Cauchy's theorem, Laurent series, singularities and meromorphic functions, the calculus of residues, conformal mappings, and harmonic functions. The material in Chapters 9-16 is more advanced. The reader will find problems on Schwartz reflection, analytic continuation, Jensen's formula, the Phragmen-Lindeloef theorem, entire functions, Weierstrass products and meromorphic functions, the Gamma function and Zeta function. This volume also serves as an independent source of problems with detailed answers beneficial for anyone interested in learning complex analysis. ... Read more

Customer Reviews (3)

I have little taste for answer books, especially when they are wrong
I gave a take home test of problems from Lang, because the answers are not in the back of the book.A student challenged my answer to one question, because Shakarchi says the answer is something different.I did not realize anyone had gone to the absurd trouble of publishing answers to the excellent exercises in Lang's book until then.But Shakarchi is wrong, having made a careless error.Reading books of answers to problems is like reading a book about physical exercise only worse, since not only do you not benefit from the exercise of doing it yourself, but you lose most of the potential benefit of the exercise after seeing the answer.At least with physical exercise you do not lose anything from watching it done if afterwards you do it yourself.Look on page 85 of this book where Shakarchi asserts that problems VI.1.26b and VI.1.26e have the same answer because the denominators have the same residues,Well how about the numerators?In 26e the z in the numerator implies that the terms of the laurent series of the quotient are not all of even degree anymore, so I claim (check it!I could be wrong too)the correct answer is that all residues in that case are equal to 2, not zero.(This comes from 2= 1/(1/2) the quotient of the coefficient 1 of the z in the top, and the first non zero coefficient 1/2 ofthe taylor series of 1-sin at /2.)So without having read any more of this book, even if this is the only error,I say it is almost worthless to someone really wanting to learn the subject.But if you are like someone who cannot exercise without watching a Jane Fonda video, and you do buy this book, please work the problems yourself, and do not just take the author's word for them.I do recommend Lang's book, and the exercises. Probably my favorite complex book is that by Henri Cartan available in a cheap paperback, and the one by Frederick Greenleaf (available used and in libraries) is excellent for beginners, and he gives the answers (but not the solutions) to most of his exercises right in the book if you want that.

INCOMPLETE EXPLANATIONS
This book cannot be used without purchasing the actual book which it represents. This book has some solutions for another complex analysis book. What I thought was, that this book is similar to something like Schaum's solved problems (which is independent and not dependent on another book). In many cases, there is no work shown at all, and simply the answers. So its really of no use and has a deceptive title. I already had 4 other books in complex analysis, so there was no need for me to purchase another book which it represents.

The Right Stuff !!!!!!!!!!!!!!
I bought this book with the goal to enhance my problem solving skills on complex analysis. I am a theoritical physics student and needed to gain a very comprehensive and operational understanding of the topic. This book had it all: it's very well written, very rigourous and gives an extra dimension to just reading a pure text explaining the theory of the subject. I wish we had this type of books in physics ! Lang's book and Shakarchi's solutions are the winning combination to learn complex analysis!!!!! 2 thumbs up ... Read more

Product Description
Analysis in spaces with no a priori smooth structure has progressed to include concepts from the first order calculus. In particular, there have been important advances in understanding the infinitesimal versus global behavior of Lipschitz functions and quasiconformal mappings in rather general settings; abstract Sobolev space theories have been instrumental in this development. The purpose of this book is to communicate some of the recent work in the area while preparing the reader to study more substantial, related articles. The material can be roughly divided into three different types: classical, standard but sometimes with a new twist, and recent. The author first studies basic covering theorems and their applications to analysis in metric measure spaces. This is followed by a discussion on Sobolev spaces emphasizing principles that are valid in larger contexts. The last few sections of the book present a basic theory of quasisymmetric maps between metric spaces. Much of the material is relatively recent and appears for the first time in book format. There are plenty of exercises. The book is well suited for self-study, or as a text in a graduate course or seminar.The material is relevant to anyone who is interested in analysis and geometry in nonsmooth settings. ... Read more

Customer Reviews (3)

A well-written book
This is a well-written book. While containing
cutting-edge topics in analysis on metric spaces,
it is also accessible to students who have had
a good course in measure theory, a reasonable course
in topology, and a nodding aquaintance with
functional analysis!

this book is the greatest
this book may well save the universe

this book is the greatest book ever written
this book may well save the universe ... Read more

Product Description
This first volume, a three-part introduction to the subject, is intended for students with a beginning knowledge of mathematical analysis who are motivated to discover the ideas that shape Fourier analysis. It begins with the simple conviction that Fourier arrived at in the early nineteenth century when studying problems in the physical sciences--that an arbitrary function can be written as an infinite sum of the most basic trigonometric functions.

The first part implements this idea in terms of notions of convergence and summability of Fourier series, while highlighting applications such as the isoperimetric inequality and equidistribution. The second part deals with the Fourier transform and its applications to classical partial differential equations and the Radon transform; a clear introduction to the subject serves to avoid technical difficulties. The book closes with Fourier theory for finite abelian groups, which is applied to prime numbers in arithmetic progression.

In organizing their exposition, the authors have carefully balanced an emphasis on key conceptual insights against the need to provide the technical underpinnings of rigorous analysis. Students of mathematics, physics, engineering and other sciences will find the theory and applications covered in this volume to be of real interest.

The Princeton Lectures in Analysis represents a sustained effort to introduce the core areas of mathematical analysis while also illustrating the organic unity between them. Numerous examples and applications throughout its four planned volumes, of which Fourier Analysis is the first, highlight the far-reaching consequences of certain ideas in analysis to other fields of mathematics and a variety of sciences. Stein and Shakarchi move from an introduction addressing Fourier series and integrals to in-depth considerations of complex analysis; measure and integration theory, and Hilbert spaces; and, finally, further topics such as functional analysis, distributions and elements of probability theory. ... Read more

Customer Reviews (8)

Nice book so far
I still have not read anything after chapter two, but the book look nice so far. It has a somewhat different approach by trying to avoid measure theory and still making a few comments on it for those who have already studied.

excellent
I took many semesters of analysis in college as a math major, and I think I learned more useful knowledge from this book than from all those classes. Of course the classes helped prepare me to absorb what's in the book, but still it seems to me that the book strikes a good balance between generality and comprehensibility. Many of the books I used in school were too focussed on proving the most general version of every theorem, and failed to provide motivation or useful experience with the objects which the theorems actually describe. By taking fourier series as the motivating idea, the authors capture the historical spirit of the subject as well as that aspect of it which students are most likely to use in real work.

very good but it is not an introduction
This is a very nice book in Fourier analysis with strong applications or examples in elementary partial differential equations. It is the first book of the three volumes set in the Princeton Lectures in Analysis. However, it is not an introductory text and some background in elementary analysis is required to fully appreciate its content.

Excellent for an easy intro to distributions and it's applications
This is a somewhat biased review because sometimes I find myself searching for a good reference that treats a subject matter that is well-known in an easy, direct and accessible way. When I find such a book I end up relieved. This is what happened with the book by Stein and Shakarchi titled "Fourier Analysis".

In my case the search was for easy and accessible treatement of the theory of distributions in general and its applications to the wave equation in particular.

There are a number of references that treat this subject matter but all the ones I know of do this from a more advanced point of view. Stein and Shakarchi's book stems from an undergraduate lecture sequence thought at Princeton and the level of the text is indeed appropriate for the bright undergraduate who may or may not major in mathematics later on.

This is unlike PDE books by Taylor, or lecture notes by Melrose, or even the tiny booklet by Friedlander and Joshi that introduce distributions and their application to PDEs (like the wave equation) and certainly unlike Hörmanders comprehensive 4-volume treatment of the whole subject matter. All these references shoot significantly higher in terms of technical sophistication and I'd certainly not recommend them to typical engineering students for self-study. As possible exception I might mention Shubin's PDE books and encyclopedia contributions but they are more terse than the book under review and give less ground to more introductory matters.

Not so the book under review. It's an excellent, well-illustrated and clear presentation of the theory of distributions and its application to the wave equation, covering important (and old) techniques like the method of descend, which is still lacking from many contemporary engineering mathematics textbooks. Yet the book is written in a form and style to be accessible to a typical reader with engineering mathematics background while still being "modern" in it's mathematical language.

Hence I have recommended this book to many colleagues (and received enthusiastic reactions) as the only and at that quite excellent introduction ín know of to the theory of distribution, PDEs in that language and Fourier Analysis in that language that I trust to be accessible for non-specialists and as a gentle and non-threatening introduction to more technical texts.

OK, but not a masterpiece
I taught an advanced undergraduate/beginning graduate class on Fourier transforms using this book as the text and wasn't thrilled. The selection of material seems uneven to me. For instance, there's a lengthy discussion of convergence issues for functions on the circle. Then apparently the authors became tired and basically restrict the treatment of the continuous case to Schwartz functions (which, of course, is insufficient for virtually every application). Also, the chapter on L_2 convergence seems to have been written on an off day.

These weaknesses don't make the book worthless, but in my opinion, there are better efforts on the market. One of my favorites for roughly this level of sophistication would be the book of Dym and McKean (which, admittedly, is a little more advanced). ... Read more

Product Description
This book is addressed to mathematicians working in analysisand its applications. The aim is to provide an understandableintroduction to the basic theory of non-standard analysis and toilluminate some of its most striking applications. Problems are posedin all chapters.
The opening chapter of the book presents a simplified form of thegeneral theory that is suitable for the results of calculus and basicreal analysis. The presentation is intended to facilitate theacquisition of basic skills in the subject, so that a reader whobegins with no background in mathematical logic should find itrelatively easy to continue. The book then proceeds with the fulltheory.
Following Part I, each chapter takes up a different field forapplications, beginning with a gentle introduction that evennon-experts can read with profit. The remainder of each chapter isthen addressed to experts, showing how to use non-standard analysis inthe search for solutions of open problems and how to obtain rich newstructures that produce deep insights into the field underconsideration. The particular applications discussed here are infunctional analysis including operator theory, probability theoryincluding stochastic processes, and economics including game theoryand financial mathematics. In working through this book the readershould gain many new and helpful insights into the enterprise ofmathematics.
Audience: This work will be of interest to specialists whosework involves real functions, probability theory, stochasticprocesses, logic and foundations. Much of the book, in particular theintroductory Part I, can be used in a graduate course. ... Read more

Customer Reviews (1)

tons of applications
The first three chapters serve as a really nice introduction to the machinery of nonstandard analysis. The rest of the book is composed of various specialized applications written at a mildly introductory level. ... Read more

Product Description
Pipe Stress Analysis is analyzing the hot and large piping systems so that code stresses are not exceeded. Piping loads on equipment nozzles should be calculated and compared with vendor allowable nozzle loads. This book gives basic principles with examples for entry level and experienced engineers. ... Read more

Customer Reviews (1)

Excellent book
A well discussed reference book in piping stress engineering. It covers the basic topics and discusses the underlying principles in flexibility analysis. I always keep this book in my office. Recommendable for beginners and experienced stress engineers. Also the other book authored by L.C. Peng is worthy to read Pipe Stress Engineering ... Read more

Product Description
Many changes have been made in this second edition of A First Course in Real Analysis. The most noticeable is the addition of many problems and the inclusion of answers to most of the odd-numbered exercises. The book's readability has also been improved by the further clarification of many of the proofs, additional explanatory remarks, and clearer notation. ... Read more

Customer Reviews (4)

You'll Grow To Appreciate It
My appreciation for this book grew with time. At first you may not like it very much because it can be very rigorous at times. There are great topics in the text that you will not find in others. After using and understanding this book, your level of mathematical maturity should be raised.

Pedagogically excellent, with strong coverage
This really is an outstanding book. I am about to enter graduate study in economics, and wanted to expose myself to the substantive and methodological concepts of real analysis, with only a sound calculus course behind me, at the level of Stewart 'Multivariable Calculus'.

This book is a real pleasure; the proofs are given with great care, and some nice motivation, where possible. I really do feel that I have developed my mathematical maturity through the use of this book.

Pedagogics are of the highest importance in undergraduate mathematics. With that in mind, I cannot recommend this book more highly.

This is one place to begin
First off, this is not a text dedicated to Functional Analysis and, I assume, anyone capable of reading the title would know that.If you are encountering, for the first time, the world of abstract mathematics by way of some class in Real Analysis, then this text is a nice and almost comfortable place to start.This text is not overwhelming terse and lacking in examples like, say Lang's text, and, conversely, this text does not baby you and waste your time with verbose explanations and or proof like, say Strichartz's text.Instead, I would say that this text stands above middle of the road beginning analysis texts and, in general, contains ample exercises as well as examples.Through out the entire text, the authors do an excellent job of not loosing sight of the fact that mathematics is about rigor, about intuitive understanding of abstract theoretical concepts.Remember, this text falls into a class of texts, such as Herstein's, whose purpose (not necessarily primary) is to introduce the reader/student to elegant and more abstract concepts and not to assume that you are inherently gifted with the ability to quickly absorb these new abstract ideas and methods.That is, and with respect to students, this text is for persons with either very limited exposure to analysis or for those who are meeting analysis for the first time.Whereas, the existence of such nice and well thought-out examples make this book a must have as a reference.Especially for those engaged in more abstract higher analysis since the examples that have been given provide an excellent reminder that mathematics is built from the ground up, like a growing pyramid, and highlights the necessary role of abstraction.Finally, this text is thick and covers alot of material.Do not let this fact overwhelm you and in turn persuade you to not engage in reading it.Just take your time and suffer through it like all good mathematicians.

Most Complete undergraduate text in Functional Analysis
A must buy for students who want to major in Math or pursue graduate study in Math. The book will prepare a student for higher courses in Functional & Real Analysis ... Read more