INTRODUCTION TO REAL ANALYSIS HYPERTEXT EDITION: DOWNLOAD FREE OF CHARGE Copyright 2003 (Updated May 2012), William F. Trench, all rights reserved. This book was previously published by Pearson Education. This free edition is made available in the hope that it will be useful as a textbook or reference. Reproduction is permitted for any valid noncommercial educational, mathematical, or scientific purpose. However, sale of or charges for any part of this book beyond reasonable reproduction costs are prohibited. SUPPLEMENT I: FUNCTIONS DEFINED BY IMPROPER INTEGRALS SUPPLEMENT II: THE METHOD OF LAGRANGE MULTIPLIERS