Real Analysis and Foundations, Second Edition (Studies in Advanced Mathematics) [Hardcover]

Steven G. Krantz (Author)

Book Description

Publication Date: November 15, 2004 | ISBN-10: 1584884835 | ISBN-13: 978-1584884835 | Edition: 2

Students preparing for courses in real analysis often encounter either very exacting theoretical treatments or books without enough rigor to stimulate an in-depth understanding of the subject. Further complicating this, the field has not changed much over the past 150 years, prompting few authors to address the lackluster or overly complex dichotomy existing among the available texts.

The enormously popular first edition of Real Analysis and Foundations gave students the appropriate combination of authority, rigor, and readability that made the topic accessible while retaining the strict discourse necessary to advance their understanding. The second edition maintains this feature while further integrating new concepts built on Fourier analysis and ideas about wavelets to indicate their application to the theory of signal processing. The author also introduces relevance to the material and surpasses a purely theoretical treatment by emphasizing the applications of real analysis to concrete engineering problems in higher dimensions.

Expanded and updated, this text continues to build upon the foundations of real analysis to present novel applications to ordinary and partial differential equations, elliptic boundary value problems on the disc, and multivariable analysis. These qualities, along with more figures, streamlined proofs, and revamped exercises make this an even more lively and vital text than the popular first edition.

Product Details

• Hardcover: 472 pages
• Publisher: Chapman and Hall/CRC; 2 edition (November 15, 2004)
• Language: English
• ISBN-10: 1584884835
• ISBN-13: 978-1584884835
• Product Dimensions: 9.3 x 6.4 x 1.2 inches
• Shipping Weight: 1.8 pounds (View shipping rates and policies)
• Average Customer Review: 4.0 out of 5 stars  See all reviews (3 customer reviews)
• Amazon Best Sellers Rank: #1,331,982 in Books (See Top 100 in Books)

Customer Reviews

Most Helpful Customer Reviews

5 of 5 people found the following review helpful:

4.0 out of 5 stars Not a bad choice....., February 8, 2009

By 

Ryan Ward (California) - See all my reviews
(REAL NAME)   

This review is from: Real Analysis and Foundations, Second Edition (Studies in Advanced Mathematics) (Hardcover)

I have studied Real Analysis from both this book and Bartle and Sherbert. Personally, I like both for different reasons and could recommend both.

Krantz, in my opinion is very good at providing a means to developing a geometric intuition, as he introduces basic point set topology very early and uses it throughout the text (this is a strength of Baby Rudin as well). I feel that Krantz's proofs are not as complicated as those in Bartle and Sherbert, and thus are much easier to follow. I feel that this book is easy to understand and includes a helping or two of complex analysis as a bonus.

Now, I would not be an honest person if I did not mention the mistakes in this book. Yeah, Krantz makes a few significant errors. They are sprinkled around so, just watch for them. I don't recall Bartle and Sherbert having as many.

Now, to contrast with Bartle and Sherbert. I feel that Krantz is lacking in its teaching of analysis techniques- Bartle and Sherbert achieve this well. Their proofs are much more complicated, but in that complication you learn a lot about how to DO analysis. Point set topology is mainly introduced in the last chapter so you lack that power through out the book (a poor choice of writing style in my opinion) but the machinery you develop in this book beats Krantz into the ground. Bartle and Sherbert is lacking a little on conceptual development in my opinion (but does have some strengths over Krantz even on this front).

Neither book is perfect, both are incomplete. As I said before, I could easily recommend both without reservation. I do recommend getting a copy of Rudin's Principles of Real Analysis as a supplementary text to either book. Rudin's book is very difficult for most undergraduates (It was very hard for me the first time I looked through it) but EXCELLENT. Given the choice, personally, I would have chosen Krantz because I felt that I understood analysis better after working through it. But having read Bartle and Sherbert first well prepared me for Krantz! Moral of the story: read both (if time permits).

To summarize:
1) Go with Krantz for concepts and to UNDERSTAND analysis
2) Go with Bartle and Sherbert for techniques and to DO analysis
3) Go with Walter Rudin to MASTER (undergraduate) real analysis after one of the other two! (Unless you go to Berkeley or Harvard and are really smart- then just jump straight to Rudin)

1 of 4 people found the following review helpful:

3.0 out of 5 stars Not Satisfied, January 15, 2009

By 

Matt - See all my reviews

Amazon Verified Purchase

This review is from: Real Analysis and Foundations, Second Edition (Studies in Advanced Mathematics) (Hardcover)

The Krantz text- while it covers many of the topics of real analysis- its notation is not concise. I would look elsewhere.

2 of 9 people found the following review helpful:

5.0 out of 5 stars Real Analysis and Foundations, May 15, 2000

By A Customer

This review is from: Real Analysis and Foundations (Hardcover)

This book is an excellent text for understanding the foundations of Analysis. I have used this book as a suplement for several math classes. It is a good refrence tool for math majors.