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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.

Feb 05, 2010 · Chapter 2 Differential Calculus of Functions of One Variable 30 2.1 Functions and Limits 30 2.2 Continuity 53 2.3 Differentiable Functions of One Variable 73 2.4 L’Hospital’s Rule 88 2.5 Taylor’s Theorem 98 Chapter 3 Integral Calculus of Functions of One Variable 113 3.1 Definition of the Integral 113 3.2 Existence of the Integral 128

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