
Elementary Analysis: The Theory of Calculus

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 fullblown 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 misproof fails." (Allen Stenger, The Mathematical Association of America, June, 2008)
Download free Elementary Analysis: The Theory of Calculus  Kenneth A. Ross
07/08/2004
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 Spivakand far less intimidating.
This is definitely the best introductory analysis book I know of for selfstudy. A student who masters the material in this book will be well prepared to tackle Rudin and other classic works in real analysis.
15/01/2000
The book is rigorously written and is extremely good for math majors. I don't think this book is very suitable for nonmath majors however, since they might think it's too dull. The book does not go on and on like some math textbooks with nonessential 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 deltaepsilon 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 musthave for all math undergrads.
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