The Elements of Real Analysis, Second Edition 2nd Edition by Robert G. Bartle (PDF)

Description

Presents the basic theory of real analysis. The algebraic and order properties of the real number system are presented in a simpler fashion than in the previous edition.

User’s Reviews

Editorial Reviews: About the Author Robert Gardner Bartle was an American mathematician specializing in real analysis. He is known for writing various popular textbooks.

Reviews from Amazon users which were colected at the time this book was published on the website:

⭐While most people say Rudin is the best, for self-studying I love this book far more than Rudin. Comparably, it is much more explicit when explaining theorems and proof (Rudin is too terse). Here are comparisons:- Topics: Rudin covers more, but through exercises and not explicitly shown- Explicity: Bartle does far better job- Proofs: Bartle is more detailed, such as “from … it follows that … therefore …” while Rudin just says “it follows directly that …”Conclusion: Bartle is far easier to follow, especially for the first-timer while Rudin is good for reference for experienced ones.

⭐Whether you are a newbie to real analysis who is still unsure of how the reals are constructed or a veteran in the field seeking to sharpen your knowledge with some hardcore measure theory, this book serves both extremes. The author starts off from the absolute fundamentals of field and order axioms and works all the way up to Banach spaces while essentially spoon-feeding you with detailed and easy-to-follow proofs of otherwise abstruse theorems; in fact, they are so detailed and sometimes so obvious that I ended up skipping every other line of most proofs. Also, copious exercises (bordering on excessive), ranging from your run-of-the-mill proofs of why sin(x) is continuous to more intriguing problems like proving the uniqueness of the reals, provide the student with every opportunity to practice and master the material.

⭐This is a solid book for a more advanced look at the fundamentals of real analysis. I highly recommend this as a second book to shore up understanding.

⭐This book arrived in relatively very good condition. However, two pages were missing from the beginning of the first chapter, but I could read the missing stuff from an older edition from the university library.

⭐I purchased a used version of this book and I am very happy with the product.

⭐Great book!

⭐Great!

⭐This book is suited mostly for a second step in learning analysis. Most people would probably find it tough going to use it for getting their feet wet. The reason is that to read this book profitably, one needs to feel “at home” with the epsilon-delta reasoning. For getting acquainted with this style of proof, I recommend “Introduction to Real Analysis” by the same author.I was able to work through most of the book after reading the aforementioned intro when I was still a teenager. As I am no mathematical genius, this sequence of study should work for many others as well.If there is one thing that sets this book apart, it is the fact that it treats integration and differentiation in n-dimensional Euclidean space. As far as I know, these topics are not normally found in books at this level. Another strength of the book is its excellent presentation of the Riemann-Stieltjes integration theory, which, again, isn’t all that easy to find.My only criticism of “Elements” is that infinite series are relegated to the end of the book. In my opinion, infinite series really should follow the chapter on infinite sequences, since the two topics are intimately related.An alternative, and in some resepcts better, book for a second bout with analysis is Richard Goldberg’s “Methods of Real Analysis.”

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