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Introduction to Real Analysis 4th Edition

4.1 out of 5 stars 20 customer reviews
ISBN-13: 978-0471433316
ISBN-10: 0471433314
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Product Details

  • Hardcover: 416 pages
  • Publisher: Wiley; 4 edition (January 18, 2011)
  • Language: English
  • ISBN-10: 0471433314
  • ISBN-13: 978-0471433316
  • Product Dimensions: 7.2 x 0.8 x 10.1 inches
  • Shipping Weight: 1.8 pounds (View shipping rates and policies)
  • Average Customer Review: 4.1 out of 5 stars  See all reviews (20 customer reviews)
  • Amazon Best Sellers Rank: #52,207 in Books (See Top 100 in Books)

Customer Reviews

Top Customer Reviews

Format: Hardcover Verified Purchase
For undergraduate students, this book is one of the best introduction to Real Analysis. The nice thing about this book is there are many good examples for each Theorem which help you reinforce what you just read. I've been using this book for my first course in Introduction to Analysis, and I'm in love with it. The structure of the book is also very organized, and exercises are very relevant to each chapter. Excellent book for Introduction to Real Analysis.
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Format: Hardcover
Bartle and Sherbert's classic Introduction To Real Analysis gives a rigorous development of real analysis in one variable. Analysis is a branch of mathematics that justifies and proves all the techniques and results of differential & integral calculus. It deals with concepts such as smoothness, convergence, divergence, and so on.

Their treatment of limits, of continuity, of convergence, of differentiation and integration is exact and complete. They give readers a full grounding in epsilon/delta proof methodology for the major theorems of modern single variable calculus.

Because they deal in a single variable, they don't spend much time on basic topology. The book consists of eight chapters. A brief introduction to set theory is followed by a presentation of the real number system. Note that they don't construct the field of real numbers, they merely state the completeness theorem that fills in the gaps found in the field of rational numbers (e.g. the square root of two is a real number not found in the rationals).

The meat of the book begins with chapter three on sequences followed by chapters on limits & continuity, differentiation, Riemann integration, sequences of functions, and finally infinite series.

The many exercises will give readers much opportunity to hone their skills.

I have a few pet peeves. I find the tone a little patronizing. Walter Rudin's Principles of Mathematical Analysis is much more rigorous and explores the topic in greater depth than does Bartle & Sherbert's textbook, but he nowhere adopts their slightly consdescending tone.

Also, the presentation is a little dry. Many of the theorems they give are profound and exciting but one doesn't get this from the text.
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Format: Hardcover Verified Purchase
This book provides a solid introduction to real analysis in one variable. The first two chapters introduce the basics of set theory, functions and mathematical induction. Also, the properties of real numbers are introduced here "borrowing" the concept and properties of field from abstract algebra.
The following chapters deal with sequences and series of numbers, limits, continuity, differentiation, integration, sequences and series of function, in this order.
I think the material is presented clearly and the results are proven rigorously throughout the entire book. There are a lot of worked-out examples and many exercises that will test the reader's understanding. Solutions and hints to many (notice, not only the odd ones) of the problems are given in the back of the book. There is also an appendix on logic for those who might need to review the basics, and one on metric spaces and Lebesgue integrals for those students who want to go a bit farther.
In my opinion, this book is not as good as Rudin's book, but it does the job better than many other introductory books on the same topic. For a horrible book see Jiri Lebl's text.
Real analysis is hard, independently of the book you use. It requires a lot of care and hard work. This book does the best it can at clearing the path for you.
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Format: Hardcover
By looking at the table of contents, it has excellent structure.
However, the problem is that the text is less clear.
The problem is that the author uses long sentences in the proof.
One sentence takes 4~5 lines, e.g.,
"if ..., which is ..., then ... thereby ... because ..."
and it is hard to follow the English sentence.

Like others say, I admit it is very solid book on real analysis.
However, not recommended for self-study.
For self study, I recommend "Analysis with Intro to Proof" by Lay.
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Format: Hardcover
This is, in my opinion, a 4-star book on real analysis at an introductory level. The authors took special care to explain the bolts and nuts of analysis and gradually developed the tools needed to understand the subject. Although the notations can at times be cumbersome, the book is readable on the whole and any beginner in analysis can benefit from it. There is also a brief treatment on Henstock's integration which is obviously one of Bartle's forte. I like the exercises, some of which are accompanied with useful hints and brief solutions. It is thus an excellent book for self-study
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Format: Hardcover Verified Purchase
This book is great. I am using it in my real analysis class right now and I'm very glad my professor chose this one. The book does a great job of explaining the material and the proofs don't skip a lot of steps like I've seen before in other classes. The first chapter is a basic introduction to all the terminology that is used throughout the course and it is a nice reference whenever I need it. The back of the book contains a lot of hints and solutions to the problems, so when I am studying for a test it makes it a lot quicker and easier to review material. I've only gotten up through Chapter 4 in my class, but so far I don't have any negative comments about it.
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