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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.

Feb 05, 2010 · Chapter 1 The Real Numbers 1 1.1 The Real Number System 1 1.2 Mathematical Induction 10 1.3 The Real Line 19 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

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