Product Description
This insightful text explores the essential, and often overlooked, role of market analysis in real property valuation. The text introduces a six-step process for market analysis and presents simplified market and marketability analysis techniques for use in appraisals and complex, stand-alone market studies. It includes seven case studies and a CD of Excel spreadsheets. ... Read more

Product Description
Designed to develop skills that are essential for analysis or real estate income property investments.Contains numerous examples to illustrate the techniques used by investors and appraisers.Appraisers, real estate brokers, property managers, consultants and others can benifit from the use of this book to improve their understanding of the nature of income property investments. ... Read more

Product Description
Clear, accessible text for a first course in abstract analysis, suitable for undergraduates with a good background in the calculus of functions of one and several variables. Sets and relations, real number system and linear spaces, normed spaces, normed linear spaces, Lebesque integral, approximation theory, Banach fixed-point theorem, Stieltjes integrals, more. Problems.
... Read more

Customer Reviews (9)

Occasionally enlightening, usually obnoxious
This is the first real analysis text I've studied, and so I should begin by saying that, for all I know, every real analysis book suffers from the flaws I'm about to describe. With that said, I'll point out a few things that make this volume totally inappropriate for self study.

1) In three hundred pages, there are two illustrations, and they're both on the same page. Not only is there a terrific absence of pictures and graphs, but even tables, charts and lists are nowhere to be found. It might be argued that the authors did not wish for students to rely too heavily on visual intuition, given that enlightening visual interpretations simply do not exist for some of the concepts presented. But there are very clearly arguments in this book that are drenched in geometric terminology. Connectedness, compactness, the development of the Lebesgue measure, metric spaces, ... these issues would be made infinitely clearer by a couple of well placed pictures.

2) The concepts are totally unmotivated. No attention is paid to explaining why some theorem might be of importance (with the notable exception of the fixed point theorem). More than once, a hierarchy of definitions and theorems will be laboriously developed, only to unexpectedly disappear and never resurface, leaving the reader wondering what the point was.

3) No solutions to any of the exercises are provided. This is partially admissible given that many of the problems consist of "prove that X is true", and a solution would occupy half a page of work. But there are certainly more computational problems for which answers should be given.

4) There is no narration whatsoever. Outside the preface, the reader is never addressed directly, and rarely acknowledged to exist. It is fully possible to understand the proof of a theorem without having any intuitive, satisfying understanding of the theorem. When presenting unexpected and paradoxical results, the authors take no time to explain things, apparently considering the proof to be sufficient explanation. The reader has no idea, ahead of time, which ideas are critical and which are secondary. The reader has no sense of where the discussion is going, nor is the reader given any historical context of the mathematics. These are issues that actual human beings care about. The authors have written something closer to a reference text, appropriate for robots. Enthusiasm and excitement are absent; the text is dry, uniform, unmotivated and boring.

With that said, the text is very rigorous and thorough, although I have read that there are errors in some of the proofs. It's a cheap purchase and, despite the authors' intentions, you will learn some Real Analysis by going through it.

Can I get a refund??
That Shane Guy is "DEAD ON".No examples, No pictures, there is a reason this is the cheapest Real Analysis book around. ...Where is the list of errors for this book, because for every Y pages there are X many errors, s.t. X = alot.

worst book ever
contains almost no illustrations or examples.No answer key either.Worst math book ever.

so sad it is dover (2)...a cry forbetter editions...
Hi, I am the previous reviewer of the "so sad it is dover" review. I feel deep respect for the review of Daniel R Greenfield. And I fully agree that this book is excellent! And of course, Dover books are cheap, so this book is definitely worth its money. Though I want to clarify my Dover critics a little bit more. To all those guys who admire Dover books , I wonder whether they use these books as a reference or as a text to study from. I can swear you : it is not so much fun to study high level mathematics in such a dense text! Too my opinion it is essential that you need enough space between the different statements of a complex proof. I believe that the great authors of this book deserve better then a cheap Dover edition. But since Dover owns the rights of these authors, nobody can create this text in a better edition.

User friendly editions however seems to be a common problem for all abstract math books. Why is it that we, students of pure mathematics,have to learn from such user-unfriendly editions.
For instance look at the size : I think user friendly books should have have a size of at least 9.8 x 7.1 inch. Forphysics,chemistry or calculus you find enough books of this size, with with enough spacing and nice motivating pictures, just to alleviate the learning process...But apparently if you want tot study higher level math, no such books exist, as far as I know ...

This review is a call (even a cry) to editors of advanced math books just to make their editions more user-friendly. If some readers agree that there is a need for this, just vote by clicking the "review was helpfull - yes" button. I hope some editors will then see that there is a market place for user friendly books on advanced math. Even if you have to pay a little more for a book of bigger size, please realize how it will make your life so much easier. Your learning productivity would increase a lot, so better editions are definitely woth its money!!!! Compare it with a professional worker who wants the best and most productive tools.
Unfortunately these critics do not apply to Dover books only, even a lot of more expensive editors just bring their texts in the same user-unfriendly format. On the exiting subject of abstract math, up until now, I even did not find the ideally formatted book.

If some readers agree with my, please vote by telling this review was helpfull (click "yes" button). Hopefully this will inspire editors for future editions. If you really like to study from Dover Editions, please vote by using the review was helpfull-No button. If most people vote "No", I am probably the exceptional guy and will stop complaining about Dover editions.

So Sad It's Dover?
Yes this book is an excellent introduction to real analysisand assumes minimal preparation beyond linear algebra and two semesters of calculus. I have been looking everywhere for a clear and lucid treatment of the Banach Fixed Point Theorem, and here it is. At a time when most math textbooks (even paperback) cannot be had for less than $50, Dover has been a godsend for those of us who want to collect a decent mathematics library. If it were not for Dover Publications, Iwould not have this text in my library, nor would I be able to afford it. Please visit Dover Publications website to view all the other fine mathematics texts which they offer at bargain prices. Incidentally, all these fine Dover mathematics books that can be had for chump change are reprints of original texts that have long been out of print and hard to find. To a previous reviewer who critized Dover Publications, I would simply say: Don't bite the hand that feeds you. ... Read more

Product Description

This book provides a self-contained and rigorous introduction to calculus of functions of one variable, in a presentation which emphasizes the structural development of calculus. Throughout, the authors highlight the fact that calculus provides a firm foundation to concepts and results that are generally encountered in high school and accepted on faith; for example, the classical result that the ratio of circumference to diameter is the same for all circles. A number of topics are treated here in considerable detail that may be inadequately covered in calculus courses and glossed over in real analysis courses.

Product Description
This book presents a unified treatise of the theory of measure and integration. In the setting of a general measure space, every concept is defined precisely and every theorem is presented with a clear and complete proof with all the relevant details. Counter-examples are provided to show that certain conditions in the hypothesis of a theorem cannot be simply dropped. The dependence of a theorem on earlier theorems is explicitly indicated in the proof, not only to facilitate reading but also to delineate the structure of the theory. The precision and clarity of presentation make the book an ideal textbook for a graduate course in real analysis while the wealth of topics treated also make the book a valuable reference work for mathematicians. ... Read more

Customer Reviews (3)

Good book for non-analysts
Great book for graduate students in statistics and electrical engineering.Author provides a good set of topics written in an accessible manner, including explicit proofs.In an ideal world on would get to spend a year studying this book before taking a measure theoretic probability course.It would be difficult to beat this book in general, and for the price it is even tougher.An alternative, which is a shorter book but contains some different topics of particular interest in probability, is "Measure Theory" by Donald L. Cohn.I don't know if I could recommend one over the other, but if you were to buy two books, these are probably the two you want.

10/10
Olcu teorisi ve integrasyon uzerine yazilmis kitaplar arasinda kesinlikle acik ara onde Yeh 'in kitabi, Rudin,Bartle ya da Royden 'in kitaplarindaki önemli teoremlerin veispatlarin okuyucuya birakma veya ispatlari atlayarakhizlica gecme gelenegi kesinlikle yok. Butun ispatlar derinlemesine ve ciddi anlamda tatmin edici. Ancak genede soyut yapi ilk okuyanlarin gözünü korkutabilir, ancak kesinlikle vazgecilmemesi gereken bir kitap. 4. bölümdeki Klasik Banach Uzaylari bölümünün ilk birkaç altbölümü ise fonksiyonel analize giris saglamasi yönünden önemli.

Hernekadar gereginden çok daha fazlasini da içerse ve çalisirken belli bir noktadan sonra detaylardan dolayi yorsa da bastan sona okunmasi daha ileriki konularin daha net sekilde anlasilmasi icin gerekiyor

A gemstone for students
This book covers a lot of material on measure and integration and the author wrote certainly one of the most solicitous book in this subject.

Over 700 pages long, this book will surely cover all the contents of a classical course on measure and integration theory. All explanations and proofs are written in a highly didactical way. This means that the author did not care much about conciseness, and took a great amount of work by choosing good notations and developing his arguments caring with the student understanding in mind. Other books on the subjects are mostly too concise in their explanations or do not cover too many topics or ,wrose, are not written with the sufficient care to be called a didactic book.

The result is a elegant, encyclopedic and useful book on understanding the basics of measure and integration.


... Read more

Product Description
This text places the basic ideas of real analysis and numerical analysis together in an applied setting that is both accessible and motivational to young students. The essentials of real analysis are presented in the context of a fundamental problem of applied mathematics, which is to approximate the solution of a physical model. The framework of existence, uniqueness, and methods to approximate solutions of model equations is sufficiently broad to introduce and motivate all the basic ideas of real analysis. The book includes background and review material, numerous examples, visualizations and alternate explanations of some key ideas, and a variety of exercises ranging from simple computations to analysis and estimates to computations on a computer. ... Read more

Customer Reviews (1)

Finally, the context of analysis laid bare
Students of analysis are often beset with frustration. They ask "Why did you bound that quantity with that other quantity?" The typical answer, "Because it works out in the proof!" is certainly true, yet wholly unsatisfactory for the student.

This book begins with models, real-world problems, that originally motivated the development of analysis. The student easily grasps how, and more importantly why, quantities are bounded. The days of staring at an algebraic form for hours are gone! (Well, mostly.)

Instead of the normal calculus-style, simple-to-complex development of the material, Estep introduces concepts in the natural order of the real-world problems. For example, Lipschitz continuity is introduced early to solve obvious extensions to previous problems. The mathematical idea of continuity is progressively extended and provides much of the motivation for the second half of the book.

By orienting on the problems solved by analysis, Estep avoids many of the bewildering difficulties encountered in traditional introductory treatments.This is the best introductory analysis book I've seen. I'm very surprised that it hasn't received more attention. ... Read more

Product Description
The first book to provide a comprehensive overview of the subject rather than a collection of papers.
* The author is a recognized authority in the field as well as an outstanding teacher lauded for his ability to convey these concepts clearly to many different audiences.
* A handy reference for practitioners in the field. ... Read more

Customer Reviews (3)

Needs to be read along with other books
As a computer Science student, I suggest that this book should not be the only reference and the following books should be bought together for a good grasp on real time systems.

1. Real Time systems By Jane W.S Liu
2. Real-Time Systems: Scheduling, Analysis, and Verification
3. Real-Time Systems by CM Krishna and Kang.G.Shin

The above 3 books make a perfect combination to learn enough about real time systems.

Regards,
Yasir
http://yasir03.online.fr

A great book for learning about real-time systems.
This book does a good job of teaching the fundamentals of real-time systems, including what a real-time system is, where they are used, etc.It quickly gets you to understanding different scheduling algorithms (like the rate-monotonic scheduler VxWorks uses), their benefits, and being able to determine if the hardware can keep up with the timing requirements.

The book contains a lot of interesting examples, starting slow with air conditioning/heating unit examples, to smart traffic lights, and on to more complicated ones such as NASA's Mars Odyssey, NASA's X-38 crew return vehicle avionics, and the Space Shuttle Orbital Maneuvernig and Reaction Control Systems.

The author does a good job of explaining complicated concepts.

Very Good!
I'm no theory nut.I wanted to know about a few scheduling algorithms.I learned all I needed in chapter 1.Now I'm not afraid of doing more work in scheduling, perhaps even what's in chapter 2.

It's math-oriented, but it's still readable by those who don't spend their days calculating the time complexities of algorithms.Overall, a very good book! ... Read more

Product Description
This unique book provides a collection of more than 200 mathematical problems and their detailed solutions, which contain very useful tips and skills in real analysis. Each chapter has an introduction, in which some fundamental definitions and propositions are prepared. This also contains many brief historical comments on some significant mathematical results in real analysis together with useful references. "Problems and Solutions in Real Analysis" may be used as advanced exercises by undergraduate students during or after courses in calculus and linear algebra. It is also useful for graduate students who are interested in analytic number theory. Readers will also be able to completely grasp a simple and elementary proof of the prime number theorem through several exercises. The book is also suitable for non-experts who wish to understand mathematical analysis. ... Read more

Product Description
This concise, well-written handbook provides a distillation of the theory of real variables with a particular focus on the subject's significant applications to differential equations and Fourier analysis. Ideal for the working engineer or scientist, the book uses ample examples and brief explanations---without a lot of proofs or axiomatic machinery---to give the reader quick, easy access to all of the key concepts and touchstone results of real analysis. Topics are systematically developed, beginning with sequences and series, and proceeding to topology, limits, continuity, derivatives, and Riemann integration. In the second half of the work, Taylor series, the Weierstrass Approximation Theorem, Fourier series, the Baire Category Theorem, and the Ascoli--Arzela Theorem are carefully discussed. Picard iteration and differential equations are treated in detail in the final chapter.

Key features:

* Completely self-contained, methodical exposition for the mathematically-inclined researcher; also valuable as a study guide for students

* Realistic, meaningful connections to ordinary differential equations, boundary value problems, and Fourier analysis

* Example-driven, incisive explanations of every important idea, with suitable cross-references for ease of use

* Illuminating applications of many theorems, along with specific how-to hints and suggestions

* Extensive bibliography and index

This unique handbook is a compilation of the major results, techniques, and applications of real analysis; it is a practical manual for applied mathematicians, physicists, engineers, economists, and others who use the fruits of real analysis but who do not necessarily have the time to appreciate all of the theory. Appropriate as a comprehensive reference or for a quick review, "A Handbook of Real Variables" will benefit a wide audience. ... Read more

Customer Reviews (1)

I Kinda Wish I Had Not Bought This
Don't get me wrong - Krantz is good but this is essentially Baby Rudin - without the proofs - which is sort of like a bar without beer. ... Read more

Product Description
A new edition of the best-seller, revised to reflect tax law changes, including the Tax Reform Act of 1986. Covers all aspects of real estate investment, from basic theoretical concepts to the practicalities of portfolio management. Emphasis is on analysis and management of investment risk and return. Comprehensive coverage includes such topics as property selection, ownership responsibility, marketing, and negotiation. Contains a continuing case (revised for this edition) that builds in complexity throughout the text. ... Read more

Customer Reviews (1)

Comprehensive, Well Organized, Well Researched
As a real estate investor I often refer to this book when I am in need help making a decision.It is the next best thing to having a seasoned partner who has been through many market cycles. As a Licensed CommercialReal Estate Appraiser and Broker I am impressed with the material as wellas how it is presented. While lifetime of practical knoweledge is somehowreduced to a single 900 page plus book, it is not "dumbed down"for mass appeal purposes.Although I wasintroduced to this book througha course at Boston University I found it's format more interesting thanacademic.When investing your money in real estate it is better to read abook like this and learn than, to "just do it" and learn the hardway, believe me.This book is a keeper for your professional library. ... Read more

Product Description
With the success of its previous editions, Principles of Real Analysis, Third Edition, continues to introduce students to the fundamentals of the theory of measure and functional analysis. In this thorough update, the authors have included a new chapter on Hilbert spaces as well as integrating over 150 new exercises throughout. The new edition covers the basic theory of integration in a clear, well-organized manner, using an imaginative and highly practical synthesis of the "Daniell Method" and the measure theoretic approach. Students will be challenged by the more than 600 exercises contained in the book. Topics are illustrated by many varied examples, and they provide clear connections between real analysis and functional analysis.


* Gives a unique presentation of integration theory
* Over 150 new exercises integrated throughout the text
* Presents a new chapter on Hilbert Spaces
* Provides a rigorous introduction to measure theory
* Illustrated with new and varied examples in each chapter
* Introduces topological ideas in a friendly manner
* Offers a clear connection between real analysis and functional analysis
* Includes brief biographies of mathematicians ... Read more

Customer Reviews (4)

A Welcome Addition to the Perplexing World of Real Analysis
Again, thirty or forty years ago you wouldn't have found a book like this one for the subject of Real Analysis. First off the authors offer an answer book for the problems given in the text. In the "old days" this just wasn't done. Something about: "you have to suffer to obtain glory" was what one of my Math professors often said. Oh yeah it was:" there is no royal road to learning mathematics". That was his line.

Well things change. And now these authors for what ever reason have tried to give us poor "challenged types" a break. Good for them!

Usually the complaints about the subject of Real Analysis and its teaching are of a particular or specific type. Like; "I don't get it!". That's usually the nature of the "whining and crying".

Probably the crime originates notin University courses so much as it originates in High School Mathematics teaching. That is the High School
Mathematics teacher who takes his/her frustrations out on the class.
That is where the student first hears the word, "Real Number".

"Yeah", they often say "...whad'ya mean by Real? It's a number ain't it?
It's gotta be real!" end of quote. I never ever had a Math teacher in HighSchool prove the irrationality of the square root of two. First off that's a proof by contradiction. Yet the Ancient Greeks showed it to be so 2500 years ago. But somehow it never got done in my High School when I was there. Also "Countability". Nevergot done in myHigh School.

So that by the time you get to University and they throw Cantor's proof for the non-denumerability of the Real numbers at you, you often feel a weird sensation of having been "defiled", somehow "violated". Violated because you really were never taught how to count 1,2,3,...properly.And since an irrational number like the root of two is uncountable you can't go "1, 2, 3,...." pointing at it with your finger. Since you can't point at it with your finger it " really doesn't really exist " as we human beings "know" existence. We know it exists but we can't "point to it".
That was what they couldn't get across in High School or even University.

What they tried to teach us in High School Algebra of course was factoring. Okay. But then they couldn't teach us the Binomial Theorem because they, the teachers didn't know it themselves. There's that word "know". And then if you did show some desire to learn more they got angry and said: " ...this is way, way above your head!". Whose head?
There's or mine?

Now I study Real analysis on my own. Certainly not for any monetary profit. I'm what you call an "amateur"...for the "love". This book is an invaluable aid to that end.

Best Regards

Southern Jameson West

Excellent Coverage plus a wealth of problems
Finished reading those undergraduate analysis books that made a study of metric spaces look like a tall order? Well then reading this book would be an excellent continuation of the hard work. The book is largely about the Lebesgue theory of integration, but includes a very thorough coverage of the theory of metric and topological spaces in the first two chapters. Chapters 3,4 and 5 are the heart of the book covering measure theory, the Lebesgue integral and some topics from introductory functional analysis like theory of operators and Banach spaces. Chapters 6 and 7, covering Hibert spaces, the Radon Nikodym theorem and the Riesz Representation Theorem among other things, are the most useful for someone like me who wants to master higher analysis in order to read financial mathematics. And what's more, there is a solutions book providing answers to all 609 problems (spread over 7 chapters!) and more. All in all, the authors have made a great contribution!

Very Mediocre Contents, Terrible Aesthetics
I was very disappointed in this book and judging from the steady decline of the resale price here on amazon.com, I can see others agree.

First of all the book looks like it was photocopied in someone's basement - the text is completely faded out and paper feels terrible. For almost $100, I expect a little more.

The actual contents of the book are not much better. I found Royden (the required text for our class) to be very sparse and was hoping for something to fill in the details. This book did little to help. It covers integration in a rather idiosyncratic way, devotes little time to differentiation, and says nothing about convexity.

If you are looking for a good anaysis book I recommend either "Lebesgue Integration on Euclidean Space" by Frank Jones or the slightly more abstract "Real and Functional Analysis" by Serge Lange

One of the best
An ideal text for a first-year graduate students in mathematics studying Real Analysis. The exposition is complete and very clear, including a lot of optional material for the curious. A detailed introduction to Functional Analysis is also included. Those needing the infamous Radon-Nikodym theorem and theory of signed measures will need to skip around since this is presented in the very last chapter (not a big problem). Also, consult the authors' companion text Problems in Real Analysis, which could be very useful to those preparing for a qualifying exam in analysis at the PhD level. Overall, a highly recommend text. ... Read more

Product Description
Designed specifically for a short one-term course in real analysis including such topics as the real number system, the theory at the basis of elementary calculus, the topology of metric spaces & infinite series.There are proofs of the basic theorems on limits at a pace that is deliberate & detailed.DLC: Mathematical analysis. ... Read more

Customer Reviews (1)

for committed readers in physical science and engineering
One nice thing about a Springer book like this is that the author has refrained from populating many pages with multicoloured illustrations. The latter is now common amongst maths books aimed at introductory calculus [or indeed other branches of maths], where authors figure that they need to grab the attention of a diverse set of readers.

This book is directed at students already heading into an engineering or physical science major. The few diagrams are in black and white, but are cogent to the discussion. The level of rigour is not quite that of Spivak or Apostol's books on calculus, or Marsden's Elementary Classical Analysis. Those are meant more for maths majors. The current book's treatment is more than adequate for understanding and using analysis in your fields. As a practical matter, you'll rarely need the rigour of the other texts. ... 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

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
Real Analysis Through Modern Infinitesimals provides a course on mathematical analysis based on Internal Set Theory (IST) introduced by Edward Nelson in 1977. After motivating IST through an ultrapower construction, the book provides a careful development of this theory representing each external class as a proper class. This foundational discussion, which is presented in the first two chapters, includes an account of the basic internal and external properties of the real number system as an entity within IST. In its remaining fourteen chapters, the book explores the consequences of the perspective offered by IST as a wide range of real analysis topics are surveyed. The topics thus developed begin with those usually discussed in an advanced undergraduate analysis course and gradually move to topics that are suitable for more advanced readers. This book may be used for reference, self-study, and as a source for advanced undergraduate or graduate courses. ... Read more

Product Description
Elementary Real Analysis is written in a rigorous, yet reader friendly style with motivational and historical material that emphasizes the “big picture” and makes proofs seem natural rather than mysterious.Introduces key concepts such as point set theory, uniform continuity of functions and uniform convergence of sequences of functions. Covers metric spaces.Ideal for readers interested in mathematics, particularly in advanced calculus and real analysis. ... Read more

Customer Reviews (5)

Horrible book
I won't say this is the worst Math book I have ever used, but it is certainly up there.No nearly enough examples.He proves the theorems and then throws 15 exercises at you with having done even one.Of course, on some chapters, he does have "some' examples, but not nearly enough.My professor started using this book and switched in the middle of the course because of the difficulties the students were having.

Steven Abbott's book is much much better.

recommended to analysis newbie
This book is, in my opinoin, very friendly written. Compared to baby Rudin, in which proofs are usually condensed and hard to be followed by beginners (excellent resource for advanced people though), proofs in this book are just compact enough - crystal clear, not too concise, and I don't see too many redundant explainations either. Here each notion (definition) is written with friendly motivations so that it is easy to gain the inside feelings.

This book aims on the elementary level analysis. It begins with the elementary ideas of sup & infs, sequences and series, basic topology in real numbers. Moving to theories of single variable calculus - continuity, derivatives and intergals, then followed by sequences of functions, power series and multivariable calculus, it ends with a final chapter on metric spaces.

The book is quite comprehensive in many small branches. Small concepts which may be ignored in a short term course or a small book, for example "completion of metric spaces", are available in enrichment sections (not problem sets!) with motivated explainations. The authors also kindly label out advanced topics so people using it for self study don't get lost.

I recommend this title to analysis beginners. It is excellent for both self study and an enrichment of your analysis culture.

A good book
There is no escape from the fact that analysis is hard.

I have spent a full year (academic year) with this book. Furthermore, I have several other texts on analysis compare to this one. This book is the best I have seen.

A few more examples would a be nice addition. However, where present, the illustrations are excellent.

I think the authors did a very commendable job on material.

Mathematical Engineers Love it!
This book is really a great book, having so far completed 8 courses in mathematical sciences, this is the best textbook I have seen so far.
It has as many examples as a applied book on Differiential Equations text. Historical Perspectives that are found in pure algebra texts, and the authors talk to you in a clear consice mannor that really helps promote undestanding

Excellent Book
I have taken many more math courses since taking a first course in analysis using this book, and still it has much to offer me.
It is rich in examples, motivation, intuition, and enrichment, making it easy to learn from, and hard to remove from your shelf. ... Read more

Product Description
This volume on mathematical analysis offers a comprehensive setof both traditional and new examples and exercises with detailedsolutions. It includes many topics important in current research thatare not found in other basic analysis books.
It begins with a comparison of real numbers viewed as a totallyordered field or, alternatively, constructed using the Dedekind cutmethod. Properties surrounding real numbers are explored and manyinteresting relationships are proven using mathematical induction.Functions are then developed with special emphasis on topics such asasymptotics, n-levels of composition and periodicity of certainfunctions. Sequences and series for both the discrete and continuouscase are concurrently developed showing contrast wherever possible.The order of growth for sequences diverging to infinity isincorporated with its counterpart given for functions. The usualproperties of functions, together with their limit theory includingthe differential calculus are compared carefully with examplesillustrating their fundamental properties. The graphs of thesefunctions are then closely studied giving as much detail as possiblefor a wide variety of functions.
Audience: Undergraduate and graduate students in all areas ofmathematical science and its applications.
... Read more

Product Description
Presents the basic theory of real analysis. The algebraic and order properties of the real number system are presented in a simpler fashion than in the previous edition. ... Read more

Customer Reviews (11)

Gross
The book was said to be "like new", it is awful. This is a hard back book, but you can bend the back cover completely. It has water stains on the inside of the book, and it SMELLS horrible. It smells so bad that I have hardly been able to use it because I can't stand the smell of it. I am really disappointed and unsatisfied with the book I received.

Good Condition and shipping within expected time frame
This book arrived in relatively very good condition. However, two pages were missing from the beginning of the first chapter, but I could read the missing stuff from an older edition from the university library.

Excellent early-on
This book was the required text for a two-course sequence in introductory analysis that I just completed.

The material on topology, sequences, series, continuity, and differentiation and integration in one variable was very clear and well-motivated; however, the sections discussing differentiation and integration in many variables were devoid of any real motivation or clarifying examples, relegating such "trivialities" to the exercises. This presented great challenges to learning and completing the assigned exercises, as there was no example to turn to for illustration.

Also, I enjoyed the tone and appreciated the historical anecdotes.

Couldn't be better
This book is really smooth, full of examples and problems from easy to moderate (and a few difficult ones). this book was the first book I read to learn analysis and I owe it a lot. compared to the other text books of math, I guess this book is one of the top 2%. due to its enormous amount of examples and problems with the keys in the back, it is also an awesome book for self study on the subject. I definitely recommend to start from this book if you are a graduate engineering student who wants to learn real analysis.

Not the best book on the subject.
Having read Bartle and Sherbert's Introduction to Real Analysis, 3rd Edition, for a Phd qualifying exam, I thought I better continue reading this one for the analysis of n-dimensional Euclidean spaces.
I was disappointed right away. I didn't like the discussion on topology, but I have got to say that the book does a decent job in differentiation theory; not that well in integration. It defined integrability and what not with respect to content instead of measure, and that really loses most of the generality required for the subject. We have to say here that Riemann integrability is rendered obselete by Lebesgue integrability; however, it is still considered traditional to study it. Having said that, most writers tend to ignore Riemann integrability, or let's say not give it what it deserves. The writer has a book on general integrability, and I have no doubt in my mind that he does a better job there.
I gave the book 4 stars because it contains most of what you need for the subject. Yet I still am not satisfied with it since I have read its well written predecessor. ... Read more