Tuesday, April 16, 2013

Elementary Analysis: The Theory of Calculus, Kenneth A. Ross

Elementary Analysis: The Theory of Calculus PDF Download Ebook. Kenneth A. Ross 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.

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. 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.

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.

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