Instructor’s Solutions Manual for Numerical Analysis

1 Instructor s Solutions Manual for Prepared by Richard L. burden Youngstown State University J. Douglas Faires Youngstown State University Australia Brazil Japan Korea Mexico Singapore Spain United Kingdom United States Numerical Analysis 9th EDITION Richard L. burden Youngstown State University J. Douglas Faires Youngstown State University Numerical Analysis 9th Edition burden Solutions ManualFull Download: sample only, Download all chapters at: Printed in the United States of America 1 2 3 4 5 6 7 11 10 09 08 07 2011 Brooks/Cole, Cengage Learning ALL RIGHTS RESERVED.

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5 You may not sell, license, auction, or otherwise redistribute the Supplement in any form. We ask that you take reasonable steps to protect the Supplement from unauthorized use, reproduction, or distribution. Your use of the Supplement indicates your acceptance of the conditions set forth in this Agreement. If you do not accept these conditions, you must return the Supplement unused within 30 days of receipt. All rights (including without limitation, copyrights, patents, and trade secrets) in the Supplement are and will remain the sole and exclusive property of Cengage Learning and/or its licensors.

6 The Supplement is furnished by Cengage Learning on an as is basis without any warranties, express or implied. This Agreement will be governed by and construed pursuant to the laws of the State of New York, without regard to such State s conflict of law rules. Thank you for your assistance in helping to safeguard the integrity of the content contained in this Supplement. We trust you find the Supplement a useful teaching tool. Table of ContentsPr efaceviiMathematical Preliminaries1 Exercise Set .. 1 Exercise Set .. 6 Exercise Set .. 12 Solutions of Equations of One Variable19 Exercise Set.

7 19 Exercise Set .. 22 Exercise Set .. 26 Exercise Set .. 31 Exercise Set .. 34 Exercise Set .. 36 Interpolation and Polynomial Approximation41 Exercise Set .. 41 Exercise Set .. 47 Exercise Set .. 49 Exercise Set .. 52 Exercise Set .. 56 Exercise Set .. 68 Numerical Differentiation and Integration71 Exercise Set .. 71 Exercise Set .. 78 Exercise Set .. 82 Exercise Set .. 87 Exercise Set .. 91 Exercise Set .. 94 Exercise Set .. 96 Exercise Set .. 99 Exercise Set .. 101iiiivIni tial-Value Problems for Ordinary Differential Equations105 Exercise Set.

8 105 Exercise Set .. 108 Exercise Set .. 113 Exercise Set .. 119 Exercise Set .. 129 Exercise Set .. 133 Exercise Set .. 144 Exercise Set .. 149 Exercise Set .. 152 Exercise Set .. 159 Direct Methods for Solving Linear Systems169 Exercise Set .. 169 Exercise Set .. 174 Exercise Set .. 180 Exercise Set .. 188 Exercise Set .. 190 Exercise Set .. 194 Iterative Techniques in Matrix Algebra201 Exercise Set .. 201 Exercise Set .. 206 Exercise Set .. 209 Exercise Set .. 215 Exercise Set .. 219 Exercise Set .. 221 Approximation Theory231 Exercise Set .. 231 Exercise Set.

9 232 Exercise Set .. 236 Exercise Set .. 238 Exercise Set .. 244 Exercise Set .. 247 Approximating Eigenvalues251 Exercise Set .. 251 Exercise Set .. 257 Exercise Set .. 262 Exercise Set .. 266 Exercise Set .. 267 Exercise Set .. 273vNumerical Solutions of Nonlinear Systems of Equations281 Exercise Set .. 281 Exercise Set .. 284 Exercise Set .. 287 Exercise Set .. 290 Exercise Set .. 291 Boundary-Value Problems for Ordinary Differential Equations295 Exercise Set .. 295 Exercise Set .. 299 Exercise Set .. 303 Exercise Set .. 308 Exercise Set .. 313 Numerical Solutions to Partial Differential Equations319 Exercise Set.

10 319 Exercise Set .. 323 Exercise Set .. 333 Exercise Set .. 336viPr efacePrefaceTh isInstructor s Manual for the Ninth Edition of Numerical Analysis by burden andFaires contains Solutions to all the exercises in the book. Although the answers tothe odd exercises are also in the back of the text, we have found that users of thebook appreciate having all the Solutions in one source. In addition, the results listedin this Instructor s Manual often go beyond those given in the back of the book. Forexample, we do not place the long Solutions to theoretical and applied exercises inthe book. You will find them Student Study Guide for the Ninth Edition of Numerical Analysis is also avail-able and the Solutions given in the Guide are generally more detailed than those in theInstructor s Manual .