Elementary Analysis: The Theory of Calculus (Undergraduate Texts in Mathematics) - Hardcover

Ross, Kenneth Allen

Hardcover

ISBN 10: 354090459X ISBN 13: 9783540904595

Publisher: Springer-Verlag Berlin and Heidelberg GmbH & Co. K, 2001

Synopsis

Designed for students having no previous experience with rigorous proofs, this text on analysis can be used immediately following standard calculus courses. It is highly recommended for anyone planning to study advanced analysis, for example complex variables, differential equations, Fourier analysis, numerical analysis, several variable calculus, and statistics. It is also recommended for future secondary school teachers. A limited number of concepts involving the real line and functions on the real line are studied. Many abstract ideas, such as metric spaces and ordered systems, are avoided. The least upper bound property is taken as an axiom and the order properties of the real line are exploited throughout. A thorough treatment of sequences of numbers is used as a basis for studying standard calculus topics. Optional sections invite students to study such topics as metric spaces and Riemann-Stieltjes integrals. 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.

About this title

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)

Edition details

• Publisher: Springer-Verlag Berlin and Heidelberg GmbH & Co. K
• Publication date: 2001
• Language: English
• ISBN 10: 354090459X
• ISBN 13: 9783540904595
• Binding: Hardcover
• Number of pages: 361