TAILIEUCHUNG - INTRODUCTION TO REAL ANALYSIS

In conclusion, let us outline a different argument, very much in the spirit of Lectures 8 and 5. We considered in these lectures the space of polynomials of a certain type (such as x3 + px + q or x5 − x + a) and saw that the set of polynomials with multiple roots separated the whole space into pieces, corresponding to the number of roots of a polynomial. The set of polynomials with multiple roots is a (very singular) hypersurface obtained by equating the discriminant of a polynomial to zero. Unlike the real case, the set of zeros of a complex equation does not separate complex space | INTRODUCTION TO REAL ANALYSIS William F. Trench Professor Emeritus Department of Mathematics Trinity University San Antonio Texas USA wtrench @ FREE DOWNLOADABLE SUPPLEMENTS FUNCTIONS DEFINED BY IMPROPER INTEGRALS THE METHOD OF LAGRANGE MULTIPLIERS 2003 William F. Trench all rights reserved Library of Congress Cataloging-in-Publication Data Trench William F. Introduction to real analysis William F. Trench p. cm. ISBN 0-13-045786-8 1. Mathematical Analysis. I. Title. 2003 515-dc21 2002032369 Free Hyperlinked Edition November 2012 This book was published previously 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 charges for profit beyond reasonable printing costs are prohibited. A complete instructor s solution manual is available by email to wtrench@ subject to verification of the requestor s faculty status. TO .

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