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INTRODUCTION TO REAL ANALYSIS - Trinity University

INTRODUCTIONTO real ANALYSISW illiam F. TrenchAndrew G. Cowles Distinguished Professor EmeritusDepartment of MathematicsTrinity UniversitySan Antonio, Texas, book has been judged to meet the evaluation criteria setbythe Editorial Board of the American Institute of Mathematics inconnection with the Institute sOpen Textbook Initiative. It maybe copied, modified, redistributed, translated, and built upon sub-ject to the Creative CommonsAttribution-NonCommercial-ShareAl ike Unported DOWNLOADABLE SUPPLEMENTSFUNCTIONS DEFINED BY IMPROPER INTEGRALSTHE METHOD OF LAGRANGE MULTIPLIERSL ibrary of Congress Cataloging-in-Publication DataTrench, William to real ANALYSIS / William F. Trenchp. 0-13-045786-81. Mathematical ANALYSIS . I. 2003515-dc212002032369 Free Hyperlinked Edition December 2013 This book was published previously by Pearson free edition is made available in the hope that it will beuseful as a textbook or refer-ence.

think it is fair to say that the transition from elementary courses such as calculus, linear algebra, and differential equations to a rigorous real analysis course is a bigger step to-day than it was just a few years ago. To make this step today’s students need more help than their predecessors did, and must be coached and encouraged more.

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