Krantz S.G. A Guide to Real Variables

Mathematical Association of America, 2009. — 163 pages. ISBN: 0883853442A 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.Basics
Sequences
Series;
The topology of the real line
Limits and the continuity of functions
The derivative
The integral
Sequences and series of functions
Advanced topics
Glossary of terms from real variable theory