Mathematical analysis is often referred to as generalized calculus. But it is much more than that. This book has been written in the belief that emphasizing the inherent nature of a mathematical discipline helps students to understand it better. With this in mind, and focusing on the essence of analysis, the text is divided into two parts based on the way they are related to calculus: completion and abstraction. The first part describes those aspects of analysis which complete a corresponding area of calculus theoretically, while the second part concentrates on the way analysis generalizes some aspects of calculus to a more general framework. Presenting the contents in this way has an important advantage: students first learn the most important aspects of analysis on the classical space R and then fill in the gaps of their calculus-based knowledge. Then they proceed to a step-by-step development of an abstract theory, namely, the theory of metric spaces which explores such crucial notions as limit, continuity, and convergence in a wider context.

The readers are assumed to have passed courses in one- and several-variable calculus and an elementary course on the foundations of mathematics. A large variety of exercises and the inclusion of informal interpretations of many results and examples will greatly facilitate the reader's study of the subject.

About the Author
Hossein, Hossein GivUniversity of Sistan and Baluchestan, Zahedan, Iran.

Reviews
"[T]his is an attractive text, one that certainly merits a look by anybody trying to find a text for a course in undergraduate analysis." - Mark Hunacek, MAA Reviews



Book Information
ISBN 9781470428075
Author Hossein Hosseini Giv
Format Hardback
Page Count 348
Imprint American Mathematical Society
Publisher American Mathematical Society
Weight(grams) 815g