A Guide to Real Variables

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MAA, Aug 13, 2009 - Mathematics - 147 pages
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A Guide to Real Variables is an aid and conceptual support for students taking an undergraduate course on real analysis. It focuses on concepts, results, examples and illustrative figures, rather than the details of proofs, in order to remain a concise guide which students can dip into. The core topics of a first real analysis course are covered, including sequences, series, modes of convergence, the derivative, the integral and metric spaces. The next book in this series, Folland's A Guide to Advanced Real Analysis is designed to naturally follow on from this book, and introduce students to graduate level real analysis. Together these books provide a concise guide to the subject at all levels, ideal for student preparation for exams.
 

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Contents

Sequences
13
Series
23
The Topology of the Real Line
41
Limits and the Continuity of Functions
55
The Derivative
71
The Integral
85
Sequences and Series of Functions
103
Advanced Topics
115
Glossary of Terms from Real Variable Theory
129
Bibliography
141
About the Author
147
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About the author (2009)

Steven Krantz is well-known for his skill in expository writing. He is the author of more than 50 books, and more than 150 scholarly papers. The MAA has awarded him both the Beckenbach Book Prize and the Chauvenet Prize.

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