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Introduction to Analysis (4th Edition) Hardcover – August 1, 2009

ISBN-13: 978-0132296380 ISBN-10: 0132296381 Edition: 4th

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Product Details

  • Hardcover: 696 pages
  • Publisher: Pearson; 4 edition (August 1, 2009)
  • Language: English
  • ISBN-10: 0132296381
  • ISBN-13: 978-0132296380
  • Product Dimensions: 7.2 x 1.1 x 9.5 inches
  • Shipping Weight: 2.5 pounds (View shipping rates and policies)
  • Average Customer Review: 2.7 out of 5 stars  See all reviews (28 customer reviews)
  • Amazon Best Sellers Rank: #77,359 in Books (See Top 100 in Books)

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

>>>>

This text prepares readers for fluency with analytic ideas, such as real and complex analysis, partial and ordinary differential equations, numerical analysis, fluid mechanics, and differential geometry. This book is designed to challenge advanced readers while encouraging and helping readers with weaker skills. Offering readability, practicality and flexibility, Wade presents fundamental theorems and ideas from a practical viewpoint, showing readers the motivation behind the mathematics and enabling them to construct their own proofs.

 

ONE-DIMENSIONAL THEORY; The Real Number System; Sequences inR; Continuity onR; Differentiability onR;Integrability onR;Infinite Series of Real Numbers; Infinite Series of Functions; MULTIDIMENSIONAL THEORY; Euclidean Spaces; Convergence inRn;Metric Spaces; Differentiability onRn;Integration onRn;Fundamental Theorems of Vector Calculus; Fourier Series

 

For all readers interested in analysis. ]]>

Customer Reviews

That being said, the book is not bad, at all.
Eric
This book is verbose when a theorem is obvious, and too brief when a big proof has just been dropped.
LLN
I believe a much better book is Victor Bryant's Yet Another Introduction to Real Analysis.
A Reader

Most Helpful Customer Reviews

15 of 15 people found the following review helpful By Eric on November 16, 2012
Format: Hardcover
One thing that should be understood is that this book is used in many university advanced calculus courses. Advanced calculus courses, in (almost) all universities, have very high dropout rates, regardless of the textbook used. This is because advanced calculus is a tough course. Often students take a very soft (i.e., not very rigorous) introduction to mathematical proofs before advanced calculus. However, one must be able to read and write proofs very well before taking AC. Often students are not prepared, fail the course miserably, and blame the book, their teachers accent, or the professor of their "intro to proofs" class, and so on. Before taking advanced calculus I had worked through Spivak's Calculus and read other rigorous math books before taking this course, thus I could write proofs reasonably well and had few problems with this book, and neither will you if your proofing skills are in good shape.

That being said, the book is not bad, at all. It gets the job done. As far as rigor goes, very few things are assumed and almost everything that is used throughout the book is proved. Some of the few things that are not proved but are used throughout out the text are the continuity of functions such as sin(x) or e^x. The problems in the book are generally easy and not very interesting. I mean to say they do not illustrate the "beauty" of mathematical analysis. The amount proofs I found in the book to be "difficult to understand" I could count on one hand. When I encountered such a proof following along with pen and paper working out the details and filling in the gaps on my own would clear things up.

Rigor tends to be a common complaint among the other reviewers. Rigor is generally refers to the development of a theory, by essentially proving every little detail.
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12 of 12 people found the following review helpful By Charles R. Williams on September 4, 2004
Format: 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.
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Format: 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.
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Format: Hardcover Verified Purchase
I loved my Intro to Analysis class, despite this book. The textbook took a challenging subject and made it needlessly complicated. There aren't enough examples and proofs, especially in the first two chapters (which is where they're needed most, because we're just starting).

After the first two chapters the proofs improve and the examples are marginally more plentiful, but the author struggles with definitions throughout the entire book. He usually does a decent job presenting theorems (with some big failures, like Theorem 4.3), but for some reason he can't define new terms in a clear way. He often fails to link the definition to his following example: The example doesn't explain how it uses the definition, so it doesn't help us understand the definition or how to use it. Sometimes the problem is a simple design/formatting issue: the "definition" is a single minimalist sentence enclosed in a text box, but information that is crucial to understanding the definition is on the previous page or in the next paragraph, not in the text box where it should be.

The most embarrassing gaffe is in Chapter 4.1 where the author "proves" Example 4.7 in a single line. The proof starts, "By the Power Rule (see Exercise 4.2.7), the answer is"... QED. But the Power Rule isn't introduced until the next chapter. Worse still, Exercise 4.2.7 is a homework problem that is left to the student, so you can't follow along and see how the author got his answer. I would love to use that method on a test: "Proof: By a theorem you don't know yet, the answer is 42. If you have questions, just refer to a more advanced problem you haven't seen yet. Once you solve that problem, use it to understand this basic concept.
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