An Introduction to Classical Real Analysis ( AMS Chelsea Publishing )

Publication series :AMS Chelsea Publishing

Author: Karl R. Stromberg  

Publisher: American Mathematical Society‎

Publication year: 2015

E-ISBN: 9781470427252

P-ISBN(Hardback):  9781470425449

Subject: O17 Mathematical Analysis

Keyword: 暂无分类

Language: ENG

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An Introduction to Classical Real Analysis

Description

This classic book is a text for a standard introductory course in real analysis, covering sequences and series, limits and continuity, differentiation, elementary transcendental functions, integration, infinite series and products, and trigonometric series. The author has scrupulously avoided any presumption at all that the reader has any knowledge of mathematical concepts until they are formally presented in the book. One significant way in which this book differs from other texts at this level is that the integral which is first mentioned is the Lebesgue integral on the real line. There are at least three good reasons for doing this. First, this approach is no more difficult to understand than is the traditional theory of the Riemann integral. Second, the readers will profit from acquiring a thorough understanding of Lebesgue integration on Euclidean spaces before they enter into a study of abstract measure theory. Third, this is the integral that is most useful to current applied mathematicians and theoretical scientists, and is essential for any serious work with trigonometric series. The exercise sets are a particularly attractive feature of this book. A great many of the exercises are projects of many parts which, when completed in the order given, lead the student by easy stages to important and interesting results. Many of the exercises are supplied with copious hints. Thanks to the generous help of the author's friend, Professor Robert Burckel, this new printing c

Chapter

Title page

Contents

Preface

About the author

Preliminaries

Numbers

Sequences and series

Limits and continuity

Differentiation

The elementary transcendental functions

Integration

Infinite series and infinite products

Trigonometric series

Bibliography

Other works by the author

Index

Back Cover

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