Mathematical analysis and its inherent nature
 Responsibility
 Hossein Hosseini Giv.
 Publication
 Providence, Rhode Island : American Mathematical Society, [2016]
 Physical description
 xxi, 348 pages : illustrations ; 27 cm.
 Series
 Sally series (Providence, R.I.)
 Pure and applied undergraduate texts ; 25.
At the library
Science Library (Li and Ma)
Stacks
Call number  Status 

QA303.2 .H67 2016  Unknown 
More options
Description
Creators/Contributors
 Author/Creator
 Hosseini Giv, Hossein, 1983
Contents/Summary
 Bibliography
 Includes bibliographical references and index.
 Contents

 Rebuilding the calculus building
 The real number system revisited
 Sequences and series of real numbers
 Limit and continuity of real functions
 Derivative and differentiation
 The Riemann integral
 Abstraction and generalization
 Basic theory of metric spaces
 Sequences in general metric spaces
 Limit and continuity of functions in metric spaces
 Sequences and series of functions
 Appendix
 Real sequences and series
 Limit and continuity of functions
 The concepts of derivative and differentiability
 The Riemann integral.
 Summary

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 calculusbased knowledge. Then they proceed to a stepbystep 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 severalvariable 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.
(source: Nielsen Book Data)
Subjects
 Subject
 Calculus > Textbooks.
 Mathematical analysis > Textbooks.
 Calculus.
 Mathematical analysis.
 Analysis.
 Real functions > Functions of one variable > Onevariable calculus.
 General topology > Spaces with richer structures > Metric spaces, metrizability.
 General topology > Spaces with richer structures > Compact (locally compact) metric spaces.
 General topology > Spaces with richer structures > Complete metric spaces.
 Genre
 Textbooks.
Bibliographic information
 Publication date
 2016
 Series
 The Sally series
 Pure and applied undergraduate texts ; 25
 ISBN
 9781470428075 (hbk. ; acidfree paper)
 1470428075 (hbk. ; acidfree paper)