
Elementary Analysis
The Theory of Calculus
Kenneth A. Ross(Author)
Springer (Publisher)
Published on 3. March 1980
Book
Hardback
VIII, 264 pages
978-0-387-90459-7 (ISBN)
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Description
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.
Reviews / Votes
From the reviews: K.A. Ross Elementary Analysis The Theory of Calculus "This book is intended for the student who has a good, but naive, 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)More details
Series
Edition
1st ed. 1980. Corr. 14th printing 2003
Language
English
Place of publication
NY
United States
Target group
College/higher education
Professional and scholarly
Lower undergraduate
Product notice
Laminated cover
Illustrations
1, black & white illustrations
Dimensions
Height: 23.5 cm
Width: 15.5 cm
Thickness: 22 mm
Weight
1540 gr
ISBN-13
978-0-387-90459-7 (9780387904597)
DOI
10.1007/978-1-4757-3971-8
Schweitzer Classification
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Content
Introduction.- Sequences.- Continuity.- Sequences and Series of Functions.- Differentiation.- Integration.- Appendix on Set Notation.- Selected Hints and Answers