Introduction to Analysis (2nd Edition) [Hardcover]

William R. Wade (Author)

Book Description

Publication Date: July 6, 1999 | ISBN-10: 0130144096 | ISBN-13: 978-0130144096 | Edition: 2nd

User-friendly--yet rigorous--in approach, this introduction to analysis meets readers where they are by providing extra support for those who like a slower, less detailed approach, but not getting in the way of those who want a quicker pace and deeper focus. It uses analogy and geometry to motivate and explain the theory, and precedes many complicated proofs with a "Strategy" which motivates the proof, shows why it was chosen, and why it should work. Examples follow many theorems, showing why each hypothesis is needed, allowing readers to remember the hypotheses by recalling the examples. Proofs are presented in complete detail, with each step carefully documented, and proofs are linked together in a way that teaches readers to think ahead. Physical interpretations are used to examine some concepts from a second or third point of view. Includes over 200 worked examples and over 600 exercises. Provides extensive coverage of multidimensional analysis.

Editorial Reviews

From the Publisher

Designed as a "bridge" between sophomore-level calculus to graduate-level courses that use analytic ideas, this text provides an unusually friendly, but rigorous treatment. It is friendly because the text helps link proofs together in a way that teaches students to think ahead: "Why this Theorem?" --This text refers to an out of print or unavailable edition of this title.

From the Back Cover

User-friendly--yet rigorous--in approach, this introduction to analysis meets readers where they are by providing extra support for those who like a slower, less detailed approach, but not getting in the way of those who want a quicker pace and deeper focus. It uses analogy and geometry to motivate and explain the theory, and precedes many complicated proofs with a "Strategy" which motivates the proof, shows why it was chosen, and why it should work. Examples follow many theorems, showing why each hypothesis is needed, allowing readers to remember the hypotheses by recalling the examples. Proofs are presented in complete detail, with each step carefully documented, and proofs are linked together in a way that teaches readers to think ahead. Physical interpretations are used to examine some concepts from a second or third point of view. Includes over 200 worked examples and over 600 exercises. Provides extensive coverage of multidimensional analysis.

See all Editorial Reviews

Product Details

• Hardcover: 611 pages
• Publisher: Prentice Hall; 2nd edition (July 6, 1999)
• Language: English
• ISBN-10: 0130144096
• ISBN-13: 978-0130144096
• Product Dimensions: 9.5 x 7.3 x 1.1 inches
• Shipping Weight: 2.5 pounds
• Average Customer Review: 2.5 out of 5 stars  See all reviews (21 customer reviews)
• Amazon Best Sellers Rank: #1,819,811 in Books (See Top 100 in Books)

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Customer Reviews

Most Helpful Customer Reviews

11 of 11 people found the following review helpful:

3.0 out of 5 stars An irritating book., September 4, 2004

By 

Charles R. Williams (Akron, OH United States) - See all my reviews
(REAL NAME)   

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

The strongest point of the book is the exercises. They force you to reread and understand the proofs and they build a foundation for material that is to come.

Chapter 1 (2nd edition) need a complete rewrite. How can you obfuscate something as simple as the Archimedean property in all its forms? Chapter 8 on Euclidean spaces needs to be better integrated with what the student should know from the first linear algebra course.

The author's proofs are not clear and I found myself rewriting many of them in my own words or turning to other references.

The core chapters 2-7 and 11-13 are fine - especially if you buy the approach of doing analysis first in R and then doing it a second time in R^n. This may be especially appropriate in an environment where most of the students are future high school teachers and will only take 1 advanced calculus course.

There are an unusual number of typos in the second edition. They are no longer accessible on the author's website. But hey, the 3rd edition is available, just throw out the 2nd and get the latest.

8 of 10 people found the following review helpful:

3.0 out of 5 stars +ve multidimensional analysis -ve atrocious binding, 1-dimensional analysis could've been more detailed, October 18, 2005

By 

pineapple41 (MI, USA) - See all my reviews

This review is from: Introduction to Analysis (2nd Edition) (Hardcover)

This book was used in my Analysis I class. I later had to prepare again for my masters certifying exam on Analysis and the primary reason I didn't use this book, even though I owned it, was the binding. By the end of my analysis course, it was practically in individual pages. The binding is atrocious - how can a $100+ book just be sort of glued together weakly that it falls apart after 1 semester of use.

The other reason I didn't use this book was that it goes through the 1-dimensional analysis pretty fast. My chosen analysis preparation book was also supposed to be my preparation for Royden's Real Analysis but I choose a book that covers the 1-dimensional analysis in twice the amount of pages and exercises taking a more detailed topology route. So, I'd advise a little bit of caution there if this is your path to graduate level Real Analysis.

However, with the 3rd edition out, our department threw out all the old 2nd edition books. I needed a multi-dimensional analysis text to prepare for my graduate PDE course and took 3 copies of the thrown ones out.

The reason I took 3 copies was that I knew the binding was going to fall apart and sure enough it did. It sort of breaks down into little booklets each that is glued to the spine. The pages on booklet peel off real easy and soon you have just pages instead of a book.

As for the multidimensional analysis it covers, it was very entertaining and fun to do. Chapter 13 becomes a little bit in the air as the exercises get a little tedious with calculate this integral with all sorts of surfaces enclosing it and not really much exercises requring a lot of threading of analysis ideas. I don't as of yet know if it has me prepared enough for Evan's PDE book but this was the only text conviniently showed up in the "free books" bin. But, I did have a nice linear and fun writing to it and I enjoyed it. Though not much as some of my other books.

2 of 2 people found the following review helpful:

1.0 out of 5 stars Better books probably exist on the topic, December 21, 2010

By 

student - See all my reviews

This review is from: Introduction to Analysis (4th Edition) (Hardcover)

There HAS to be better texts out there in analysis. This book obscures simple concepts and neglects vital information for an introduction to analysis. I have suffered through this book, working VERY hard for three semesters. Nevertheless there are still concepts that I don't TRULY understand, which is largely attributable Wade's poor exposition of the topic. For example, the entire treatment of differentiability in Euclidean n-space, including the manner in which Wade introduces the definition, is pathetically motivated/explained. This makes it difficult to understand and convince yourself of other proofs/concepts which rely on a firm understanding of the previously studied material.

For a truly comprehensive introduction, I'd suggest Introduction to Analysis by Maxwell Rosenlicht. I bought this as a supplementary text to the courses I have taken, largely due to positive reviews, and was very pleased. I gained significant insight due to the presence of discussions spanning more than three sentences between each lemma, theorem, corollary, or remark, in complete contrast to Wade's book. Another plus is that it's around 10% of the cost.