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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.

matical maturitythat can be gained from an introductoryreal analysis course. The book is designed to fill the gaps left in the development of calculus as it is usually presented inan elementary course, and to providethe backgroundrequired for insightinto more advanced courses in pure and applied mathematics. The standard elementary calcu-

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