Elementary Analysis: The Theory of Calculus
Ross, Kenneth A.
ISBN 10: 038790459X ISBN 13: 9780387904597
Published by Springer (edition First Edition), 1980
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About this Item
Description:
The item might be beaten up but readable. May contain markings or highlighting, as well as stains, bent corners, or any other major defect, but the text is not obscured in any way. Seller Inventory # 038790459X-7-1-13
Synopsis:
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.
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)
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Bibliographic Details
Title: Elementary Analysis: The Theory of Calculus
Publisher: Springer (edition First Edition)
Publication Date: 1980
Binding: Hardcover
Condition: Fair
Edition: First Edition.