Real Analysis: Modern Techniques and Their Applications (Pure and Applied Mathematics: A Wiley Series of Texts, Monographs and Tracts) [Hardcover]

Gerald B. Folland (Author)

Book Description

ISBN-10: 0471317160 | ISBN-13: 978-0471317166 | Publication Date: April 7, 1999 | Edition: 2

An in-depth look at real analysis and its applications-now expanded and revised.

This new edition of the widely used analysis book continues to cover real analysis in greater detail and at a more advanced level than most books on the subject. Encompassing several subjects that underlie much of modern analysis, the book focuses on measure and integration theory, point set topology, and the basics of functional analysis. It illustrates the use of the general theories and introduces readers to other branches of analysis such as Fourier analysis, distribution theory, and probability theory.

This edition is bolstered in content as well as in scope-extending its usefulness to students outside of pure analysis as well as those interested in dynamical systems. The numerous exercises, extensive bibliography, and review chapter on sets and metric spaces make Real Analysis: Modern Techniques and Their Applications, Second Edition invaluable for students in graduate-level analysis courses. New features include:
* Revised material on the n-dimensional Lebesgue integral.
* An improved proof of Tychonoff's theorem.
* Expanded material on Fourier analysis.
* A newly written chapter devoted to distributions and differential equations.
* Updated material on Hausdorff dimension and fractal dimension.

Editorial Reviews

From the Publisher

This book covers the subject matter that is central to mathematical analysis: measure and integration theory, some point set topology, and rudiments of functional analysis. Also, a number of other topics are developed to illustrate the uses of this core material in important areas of mathematics and to introduce readers to more advanced techniques. Some of the material presented has never appeared outside of advanced monographs and research papers, or been readily available in comparative texts. About 460 exercises, at varying levels of difficulty, give readers practice in working with the ideas presented here. --This text refers to an out of print or unavailable edition of this title.

From the Back Cover

An in-depth look at real analysis and its applications-now expanded and revised.

This new edition of the widely used analysis book continues to cover real analysis in greater detail and at a more advanced level than most books on the subject. Encompassing several subjects that underlie much of modern analysis, the book focuses on measure and integration theory, point set topology, and the basics of functional analysis. It illustrates the use of the general theories and introduces readers to other branches of analysis such as Fourier analysis, distribution theory, and probability theory.

This edition is bolstered in content as well as in scope-extending its usefulness to students outside of pure analysis as well as those interested in dynamical systems. The numerous exercises, extensive bibliography, and review chapter on sets and metric spaces make Real Analysis: Modern Techniques and Their Applications, Second Edition invaluable for students in graduate-level analysis courses. New features include:
* Revised material on the n-dimensional Lebesgue integral.
* An improved proof of Tychonoff's theorem.
* Expanded material on Fourier analysis.
* A newly written chapter devoted to distributions and differential equations.
* Updated material on Hausdorff dimension and fractal dimension.

See all Editorial Reviews

Product Details

• Hardcover: 408 pages
• Publisher: Wiley; 2 edition (April 7, 1999)
• Language: English
• ISBN-10: 0471317160
• ISBN-13: 978-0471317166
• Product Dimensions: 9.6 x 6.4 x 1.2 inches
• Shipping Weight: 1.5 pounds (View shipping rates and policies)
• Average Customer Review: 4.1 out of 5 stars  See all reviews (15 customer reviews)
• Amazon Best Sellers Rank: #270,327 in Books (See Top 100 in Books)

Customer Reviews

Most Helpful Customer Reviews

33 of 37 people found the following review helpful:

3.0 out of 5 stars Could have been great, June 5, 2001

By 

Henry Rivers (San Jose, CA USA) - See all my reviews

This review is from: Real Analysis: Modern Techniques and Their Applications (Pure and Applied Mathematics: A Wiley Series of Texts, Monographs and Tracts) (Hardcover)

I speak as a graduate student in applied math. I really like this book but was bothered by its flaws. Nevertheless, with a good instructor, this text can make for a good learning experience.

Positives: The book is well organized. It builds in a reasonable way so that I could focus on the material in the book and develop my understanding as I went. The book is reasonably well contained. Outside of a reasonable level of basics (a BA or BS in math) the proofs and most of the problems use material developed earlier in the text. I found the book very interesting -- I especially liked the topics presented in the last few chapters.

Negatives: Lots of typos - the author's errata sheet is woefully incomplete. Too few expamples. Too condensed - sometimes to the point of incomprehensibility or even error. The contents of a whole course may be condensed in to a single chapter or even a single section.

Things to be aware of: You should be comfortable with advanced calculus, topology, set theory, and algebra (linear and modern). It also helps to have had some basic real analysis. I highly recommend that you've seen Fourier transforms, Dirac deltas (distributions), and continuous probability. You aren't going to learn these here - you're going to see how measure theory is applied to them.

25 of 29 people found the following review helpful:

5.0 out of 5 stars Great book, January 23, 2000

By 

[e-mail] - See all my reviews

This review is from: Real Analysis: Modern Techniques and Their Applications (Pure and Applied Mathematics: A Wiley Series of Texts, Monographs and Tracts) (Hardcover)

What I like most about the book is its concise but broad coverage of the fundamentals of real and functional analysis. Although I am not a mathematician, my main interest is solving various engineering problems using numerical methods. A solid background in real and functional analysis would be necessary for deeper understanding of various numerical methods. I wish I had known this book the first time I felt the need to study basic modern analysis. This books has exactly the material I wanted to learn.

In addition to the theorems and proofs, the author tells you why some theorems are important and how they can be used (of course also in a concise way). I found this type of "hints" are extremely helpful. The historical notes at the end of each chapter are also interesting to read.

19 of 22 people found the following review helpful:

5.0 out of 5 stars Stellar!!Very demanding,but well worth the effort., January 15, 1999

By A Customer

This review is from: Real Analysis: Modern Techniques and Their Applications (Hardcover)

Folland's book is extremely terse, but very elegant. It covers topics in great generality. I haven't read the whole book,but the parts I read were excellent. Its a damned hard book, but very precise and conveys a great deal of information. Its certainly not easy reading, it makes the reader (at least it made me) think quite a bit since the proofs are very terse. I think that the amount learned is certainly worth the effort. A classic and one that I would definitely recommend!