Limits
Subtitle: A New Approach to Real Analysis
Series: Undergraduate Texts in Mathematics
Publisher: Springer
Published: October 30, 1997
Language: eng
Number of pages: 204
ISBN-13: 9780387982748
First sentence: This chapter contains a brief and informal discussion of sets and functions.
Description: This book is intended as an undergraduate text on real analysis and includes all the standard material such as sequences, infinite series, continuity, differentiation, and integration, together with worked examples and exercises. By unifying and simplifying all the various notions of limit, the author has successfully presented a unique and novel approach to the subject matter that has not previously appeared in book form.

The author defines what is meant by a limit just once, and all of the subsequent limiting processes are viewed as special cases of this one definition. In this way the subject matter attains a unity and coherence that is missing in the traditional approach, and students will be able to fully appreciate and understand the common source of the topics they are studying.

These topics are presented as "variations on a theme" rather than essentially different ideas, and this leads to a clearer global view of the subject.