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Elementary Analysis: The Theory of Calculus 1st Edition

34 customer reviews
ISBN-13: 978-0387904597
ISBN-10: 038790459X
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Editorial Reviews


From the reviews: K.A. Ross Elementary Analysis The Theory of Calculus "This book is intended for the student who has a good, but naïve, understanding of elementary calculus and now wishes to gain a thorough understanding of a few basic concepts in analysis, such as continuity, convergence of sequences and series of numbers, and convergence of sequences and series of functions. There are many nontrivial examples and exercises, which illuminate and extend the material. The author has tried to write in an informal but precise style, stressing motivation and methods of proof, and, in this reviewer’s opinion, has succeeded admirably."—MATHEMATICAL REVIEWS "This book occupies a niche between a calculus course and a full-blown real analysis course. … I think the book should be viewed as a text for a bridge or transition course that happens to be about analysis … . Lots of counterexamples. Most calculus books get the proof of the chain rule wrong, and Ross not only gives a correct proof but gives an example where the common mis-proof fails." (Allen Stenger, The Mathematical Association of America, June, 2008)

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Product Details

  • Hardcover: 272 pages
  • Publisher: Springer; 1st edition (March 3, 1980)
  • Language: English
  • ISBN-10: 038790459X
  • ISBN-13: 978-0387904597
  • Product Dimensions: 6.1 x 0.9 x 9.2 inches
  • Shipping Weight: 1.4 pounds
  • Average Customer Review: 4.3 out of 5 stars  See all reviews (34 customer reviews)
  • Amazon Best Sellers Rank: #70,764 in Books (See Top 100 in Books)

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Customer Reviews

Most Helpful Customer Reviews

142 of 156 people found the following review helpful By Andrew V. Locascio on December 26, 2006
Format: Hardcover
I don't understand people that constantly knock this book.The vicious barrage of critisms levied against this text is usually by arrogant math majors at top level schools.Thier attitude is basically that,"If Rudin is too hard for you,you are too dumb to learn this,get over it." You know,the first edition of Rudin was written over 4 decades ago, when calculus was usually first exposed to high school students on a regular basis and eplison-delta proofs were not uncommon in a college level calculus course.Therefore,after a meaty,theoretical calculus course that taught limits,derivatives and integrals carefully in addition to related rates,differential equations and the applications that today's watered-down calculus courses laughingly consider mathematics,those students of past generations were READY for something brutally terse like Rudin.The sad truth is that in today's pathetically dumbed down mathematics eduation system in the US-where high schools are happy if they can get students to use thier CALCULATORS to add and subtract correctly-Rudin or Apostol are simply way past the preparation level of any but the best students after calculus.The need for a "bridge" course that gave students the minimum exposure to a hard core approach to calculus was realized in the early 1980's-and Ross' book is still,to me,the best of the lot.Not only does Ross explain basic concepts well such as limits,convergence and the Riemann integral-he does something most textbooks on analysis and calculus sadly lack and to me is essential for a beginner:tons and TONS of worked examples given immediately after a definition.Proving theorums in rigorous mathematics-and real analysis in particular-is to a large degree the generalization of concrete examples.Read more ›
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26 of 28 people found the following review helpful By A Customer on January 15, 2000
Format: Hardcover
The book is rigorously written and is extremely good for math majors. I don't think this book is very suitable for non-math majors however, since they might think it's too dull. The book does not go on and on like some math textbooks with non-essential talk. It gets into the material right the way. The proofs have been carefully chosen so that they're as simple and as elegant as possible. Topology is treated in optional sections, and the focus of the book is sequences. Indeed, the treatment of sequences is very thorough. Also, many notions are also defined in terms of sequences. However, proofs that this definition and the usual delta-epsilon definition are equivalent is given. The style of writing is clear, concise, and avoids uncessaary discussion. Proofs are given out in full and are seldom left to the readers as an exercise. In keeping with the style of this book, historical facts and references are not provided. I think this book should be a must-have for all math undergrads.
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24 of 26 people found the following review helpful By D. A Flory on August 7, 2004
Format: Hardcover
Of the many analysis books I have seen, I think this is one of the best for the student approaching the subject for the first time.

It is mathematically rigourous, yet develops the major concepts of analysis in a leisurely (in the good sense of the word) way with interesting and sometimes unusual examples.

Beginners will especially appreciate the quality exercises and the solution guide in the back.

The style of this book is a bit similar to Spivak's *Calculus* in that the author is a bit wordy. I find Ross' presentation more direct and less pretentious than Spivak--and far less intimidating.

This is definitely the best introductory analysis book I know of for self-study. A student who masters the material in this book will be well prepared to tackle Rudin and other classic works in real analysis.
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10 of 10 people found the following review helpful By Paul Harris on December 20, 2008
Format: Hardcover Verified Purchase
I went through a lot of math books that made me wonder if the author was purposely making it hard or if they were just bad at explaining things.
I didn't have that experience with this book. This book is well written and easy to understand (given its subject). Highly recommended for anyone learning Advanced Calculus 1 for the first time.
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12 of 14 people found the following review helpful By T. Sznigir on April 3, 2009
Format: Hardcover
If you had a rigorous, proof-heavy calculus course, you could probably skip this book and go straight to something more advanced, like Apostol or Rudin. On the other hand, if your calculus class skimped on proofs, preferred a cookbook approach, or if the word "limit" doesn't automatically conjure up images of deltas and epsilons, then this is the analysis book for you.

While Ross assumes a working knowledge of calculus and basic proof-writing skills, he does NOT assume the reader has encountered too many of the results before. Thus, he includes numerous examples and exercises to familiarize the reader the definitions. The theorems aren't proven in the simplest way possible, but rather in a more intuitive way with few gaps. Sure, the proofs would be a lot shorter if he used some basic results from topology, but that would be a bit distracting for someone who wasn't very familiar with the material or with proof-writing in general.

In summary, this is an excellent introductory book for newcomers to analysis. If you learned calculus from Stewart, go here first. If you learned calculus from Apostol or Courant, this is a good companion to Rudin.
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