Introduction to Real Analysis, 3rd Edition [Hardcover]

Robert G. Bartle (Author), Donald R. Sherbert (Author)

Book Description

ISBN-10: 0471321486 | ISBN-13: 978-0471321484 | Publication Date: September 21, 1999 | Edition: 3

In recent years, mathematics has become valuable in many areas, including economics and management science as well as the physical sciences, engineering and computer science. Therefore, this book provides the fundamental concepts and techniques of real analysis for readers in all of these areas. It helps one develop the ability to think deductively, analyze mathematical situations and extend ideas to a new context. Like the first two editions, this edition maintains the same spirit and user-friendly approach with some streamlined arguments, a few new examples, rearranged topics, and a new chapter on the Generalized Riemann Integral.

Product Details

• Hardcover: 388 pages
• Publisher: Wiley; 3 edition (September 21, 1999)
• Language: English
• ISBN-10: 0471321486
• ISBN-13: 978-0471321484
• Product Dimensions: 7.3 x 0.8 x 10.1 inches
• Shipping Weight: 1.7 pounds (View shipping rates and policies)
• Average Customer Review: 4.1 out of 5 stars  See all reviews (35 customer reviews)
• Amazon Best Sellers Rank: #107,798 in Books (See Top 100 in Books)

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Customer Reviews

Most Helpful Customer Reviews

20 of 22 people found the following review helpful:

3.0 out of 5 stars A good instructor and a will to work the examples and proofs needed, April 29, 2007

By 

Randy Ringstad (Reno, Nevada USA) - See all my reviews
(REAL NAME)   

This review is from: Introduction to Real Analysis, 3rd Edition (Hardcover)

At first, I hated this textbook. New to Analysis, I couldn't make any sense of it. But, I was trying do accomplish too much on my own without the help of the instructor. This textbook is terrible for self-study. A poor course instructor (you know the kind - the ones who read the book to you) can make learning Analysis a singularly miserable experience. However, if you're lucky enough to have an instructor that's willing to supplement and clarify the material in class (i.e. get you over the hump), you'll find this textbook quite adequate and worthy of keeping for reference. To get the most out of it, however, you'll need to be prepared to work much harder than you have in your previous math courses.

I know that there are two camps of reviewers of analysis books. There are those who complain that a text is too terse and those who say it's too wordy. This book finds a nice balance. It can be very frustrating at times...but, such is analysis. (Note that the authors warn you of this in the first paragraph of the Preface.) Mastery of the first two chapters is essential for one to succeed in the rest of the book.

I have given this textbook three stars because it let's the reader down on some topics. A couple of the proofs (L'Hospital's Rule is an example) are a bit too sparse in explanation for the beginner who must fill in the missing steps as part of his study. Also, a few topics are more notationally cumbersome than necessary, requiring the reader to be very adept with indexed summations. The chapter on Riemann integration is understandable, but falls short of most other texts in this area. (In my class, we used a different text for the Riemann Integral.)

If this is the required textbook for your upcoming Analysis course, I recommend that you read every section VERY carefully many, many times. Physically work through the examples and given proofs with pencil and paper. Many times the example proofs provide a model for the student that he/she can apply to the problems. If you still find it tough, make a separate notebook in which to write the definitions, thereoms, and even examples. Try diagramming the definitions and theroems, separating the conditions from the conclusions that they imply (don't forget what "if and only if" means).

The authors have included some very helpful appendices that should be treated with the same careful study as the rest of the book. Analysis is not a subject where one can pick up on a proceedure and calculate an outcome as one might do in Algebra or regular Calculus. One must learn to know and apply the definitions and thereoms logically. Well-known problem solving strategies still work here, but the method in which a student may be accustomed is entirely different (see How to Solve It: A New Aspect of Mathematical Method (Princeton Science Library) or, for proofs How to Prove It: A Structured Approach). Above all, rise to the challenge and don't get discouraged. All but the most gifted will find this subject difficult. Find help if you need it.

I recommend reading the linked books above before entering into analysis. Another really good book in the subject that will immensely help you is Yet Another Introduction to Analysis.

15 of 16 people found the following review helpful:

5.0 out of 5 stars Its a Solid Introduction, July 31, 2007

By 

Zaid Khalil - See all my reviews
(REAL NAME)   

This review is from: Introduction to Real Analysis, 3rd Edition (Hardcover)

Honestly this is a 4 star book, but like many of the advanced math textbooks the average score is too low, because of reviewers who clearly did not understand what they were getting into.

Probably the best piece of advice with regards to advanced math books like this is given in the "Preface to the Student" in Sheldon Axler's Linear Algebra Done Right, he states: "You cannot expect to read mathematics the way you read a novel. If you zip through a page in less than an hour, you are probably going too fast."

If you study from this book from that standpoint, you will get a lot out of it. But its a serious commitment.

13 of 14 people found the following review helpful:

5.0 out of 5 stars Great Book, October 4, 2007

By 

K. Stokes (Champaign, IL) - See all my reviews

This review is from: Introduction to Real Analysis, 3rd Edition (Hardcover)

I'm using this book for my real analysis course at University of Illinois and I love it. Most readers seem to be upset that some of the material isn't presented as easily as it could be, but this book is an introduction to real analysis, not to math. This is not a good book for people who have never written or read formal proofs or who are not familiar with concepts like the triangle inequality. This is a good book if you are familiar with formal mathematics and have interest in real analysis.