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Elementary Analysis: The Theory of Calculus [Hardcover]

Kenneth A. Ross
4.3 out of 5 stars  See all reviews (30 customer reviews)

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Elementary Analysis: The Theory of Calculus (Undergraduate Texts in Mathematics) Elementary Analysis: The Theory of Calculus (Undergraduate Texts in Mathematics) 2.5 out of 5 stars (2)
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Book Description

March 3, 1980 038790459X 978-0387904597 1st ed. 1980. Corr. 14th printing 2003
Designed for students having no previous experience with rigorous proofs, this text can be used immediately after standard calculus courses. It is highly recommended for anyone planning to study advanced analysis, as well as for future secondary school teachers. A limited number of concepts involving the real line and functions on the real line are studied, while many abstract ideas, such as metric spaces and ordered systems, are avoided completely. A thorough treatment of sequences of numbers is used as a basis for studying standard calculus topics, and optional sections invite students to study such topics as metric spaces and Riemann-Stieltjes integrals.


Editorial Reviews

Review

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)

Product Details

  • Hardcover: 272 pages
  • Publisher: Springer; 1st ed. 1980. Corr. 14th printing 2003 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 (30 customer reviews)
  • Amazon Best Sellers Rank: #144,751 in Books (See Top 100 in Books)

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Customer Reviews

Most Helpful Customer Reviews
133 of 146 people found the following review helpful
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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24 of 26 people found the following review helpful
5.0 out of 5 stars Raymond Cheng 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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23 of 25 people found the following review helpful
4.0 out of 5 stars Excellent introduction to analysis 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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8 of 8 people found the following review helpful
5.0 out of 5 stars Excellent book 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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10 of 11 people found the following review helpful
5.0 out of 5 stars Good Intro Text 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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Most Recent Customer Reviews
5.0 out of 5 stars very good condition.
great condition for a second-hand book, there is no sign of written in it. Only the front cover is falling off. But doesn't matter.
Published 9 months ago by Pinlei
5.0 out of 5 stars Fast and good
it is really fast and good quality. and also, it is easy to return. I dont need to worries about it.
Published 17 months ago by innynymph
4.0 out of 5 stars Its an OK (not the best) book
This is a good start for a young student in Real Analysis. (But Rudin is definitely much more preferred once you advance or decide to venture our more, but it is definitely more... Read more
Published 21 months ago by Chris
2.0 out of 5 stars Could be better
I really liked this book in the beginning, because the first few chapters really are very elementary and easily digestible, very much unlike Rudin, which hits you hard right off... Read more
Published on May 6, 2012 by Yuri Niyazov
5.0 out of 5 stars A very good introduction, excellent for self-study
I bought this reasonably priced text in order to review what I had learned over 25 years ago in a one-semester analysis class. Read more
Published on June 28, 2011 by Timbeaux
3.0 out of 5 stars Average Book , Weak in some parts
This textbook represents a new generation of American texts in Analysis that try to overcome the terse and confusing style of Rudin. Read more
Published on March 22, 2011 by Doctor Math
3.0 out of 5 stars Okay Text
I think the text is okay, but not great. It is required at my school and I found it best to supplement the text with others, such as:

Courant Introduction to Calculus... Read more
Published on March 20, 2011 by Brian
5.0 out of 5 stars A good purchase
Thank you for speedy shipping. I am working on it and it is hard to analyze. HA!
Published on June 15, 2010 by S. Chien
5.0 out of 5 stars The perfect transition to life after calculus
I certainly wasn't ready for Rudin after my freshman calculus series, and Ross's book was the perfect stepping stone. Read more
Published on May 21, 2010 by Matthew H. Holden
4.0 out of 5 stars book good, electronic version poor
This book is pretty good. I bought the online version to be able to copy extended formulas into a word program. It doesn't do it. Read more
Published on November 11, 2008 by M. Marshall
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