Complete Solutions Manual
to Accompany
Numerical Analysis
TENTH EDITION
Richard L. Burden
Youngstown University
Youngstown, OH
© Cengage Learning. All rights reserved. No distribution allowed without express authorization.
J. Douglas Faires
Youngstown University
Youngstown, OH
Annette M. Burden
Youngstown University
Youngstown, OH
Prepared by
Richard L. Burden
Youngstown University, Youngstown, OH
Annette M. Burden
Youngstown University, Youngstown, OH
Australia • Brazil • Mexico • Singapore • United Kingdom • United States
, © 2016 Cengage Learning ISBN-13: 978-130525369-8
ISBN-10: 1-305-25369-8
ALL RIGHTS RESERVED. No part of this work covered by the
copyright herein may be reproduced, transmitted, stored, or Cengage Learning
used in any form or by any means graphic, electronic, or 20 Channel Center Street
mechanical, including but not limited to photocopying, Fourth Floor
recording, scanning, digitizing, taping, Web distribution, Boston, MA 02210
information networks, or information storage and retrieval USA
systems, except as permitted under Section 107 or 108 of the
1976 United States Copyright Act, without the prior written Cengage Learning is a leading provider of customized
permission of the publisher except as may be permitted by the learning solutions with office locations around the globe,
license terms below. including Singapore, the United Kingdom, Australia,
Mexico, Brazil, and Japan. Locate your local office at:
www.cengage.com/global.
For product information and technology assistance, contact us at Cengage Learning products are represented in
Cengage Learning Customer & Sales Support, Canada by Nelson Education, Ltd.
1-800-354-9706.
To learn more about Cengage Learning Solutions,
For permission to use material from this text or product, submit visit www.cengage.com.
all requests online at www.cengage.com/permissions
Further permissions questions can be emailed to Purchase any of our products at your local college
.
store or at our preferred online store
www.cengagebrain.com.
NOTE: UNDER NO CIRCUMSTANCES MAY THIS MATERIAL OR ANY PORTION THEREOF BE SOLD, LICENSED, AUCTIONED,
OR OTHERWISE REDISTRIBUTED EXCEPT AS MAY BE PERMITTED BY THE LICENSE TERMS HEREIN.
READ IMPORTANT LICENSE INFORMATION
Dear Professor or Other Supplement Recipient: material posted electronically must be through a password-
protected site, with all copy and download functionality disabled,
Cengage Learning has provided you with this product (the and accessible solely by your students who have purchased the
“Supplement”) for your review and, to the extent that you adopt associated textbook for the Course. You may not sell, license,
the associated textbook for use in connection with your course auction, or otherwise redistribute the Supplement in any form. We
(the “Course”), you and your students who purchase the ask that you take reasonable steps to protect the Supplement from
textbook may use the Supplement as described below. unauthorized use, reproduction, or distribution. Your use of the
Cengage Learning has established these use limitations in Supplement indicates your acceptance of the conditions set forth in
response to concerns raised by authors, professors, and other this Agreement. If you do not accept these conditions, you must
users regarding the pedagogical problems stemming from return the Supplement unused within 30 days of receipt.
unlimited distribution of Supplements.
All rights (including without limitation, copyrights, patents, and trade
Cengage Learning hereby grants you a nontransferable license secrets) in the Supplement are and will remain the sole and
to use the Supplement in connection with the Course, subject to exclusive property of Cengage Learning and/or its licensors. The
the following conditions. The Supplement is for your personal, Supplement is furnished by Cengage Learning on an “as is” basis
noncommercial use only and may not be reproduced, or without any warranties, express or implied. This Agreement will be
distributed, except that portions of the Supplement may be governed by and construed pursuant to the laws of the State of
provided to your students in connection with your instruction of New York, without regard to such State’s conflict of law rules.
the Course, so long as such students are advised that they may
not copy or distribute any portion of the Supplement to any third Thank you for your assistance in helping to safeguard the integrity
party. Test banks, and other testing materials may be made of the content contained in this Supplement. We trust you find the
available in the classroom and collected at the end of each class Supplement a useful teaching tool.
session, or posted electronically as described herein. Any
Printed in the United States of America
1 2 3 4 5 6 7 17 16 15 14 13
,Contents
Chapter 1: Mathematical Preliminaries............................................................................................ 1
Chapter 2: Solutions of Equations of One Variable ....................................................................... 15
Chapter 3: Interpolation and Polynomial Approximation .............................................................. 37
Chapter 4: Numerical Differentiation and Integration ................................................................... 67
Chapter 5: Initial-Value Problems for Ordinary Differential Equations ........................................ 99
Chapter 6: Direct Methods for Solving Linear Equations ........................................................... 165
Chapter 7: Iterative Techniques in Matrix Algebra ..................................................................... 195
Chapter 8: Approximation Theory ............................................................................................... 227
Chapter 9: Approximating Eigenvalues ....................................................................................... 249
Chapter 10: Numerical Solutions of Nonlinear Systems of Equations ........................................ 277
Chapter 11: Boundary-Value Problems for Ordinary Differential Equations .............................. 291
Chapter 12: Numerical Solutions to Partial Differential Equations ............................................. 315
, Preface
This Instructor’s Manual for the Tenth edition of Numerical Analysis by Burden,
Faires, and Burden contains solutions to all the exercises in the book. Although the
answers to the odd exercises are also in the back of the text, we have found that
users of the book appreciate having all the solutions in one source. In addition, the
results listed in this Instructor’s Manual often go beyond those given in the back of
the book. For example, we do not place the long solutions to theoretical and applied
exercises in the book. You will find them here.
A Student Study Guide for the Tenth edition of Numerical Analysis is also available
and the solutions given in the Guide are generally more detailed than those in the
Instructor’s Manual.
We have added a number of exercises to the text that can be implemented in any
generic computer algebra system such as Maple, Matlab, Mathematica, Sage, and
FreeMat. In our recent teaching of the course we found that students understood the
concepts better when they worked through the algorithms step-by-step, but let the
computer algebra system do the tedious computation.
It has been our practice to include in our Numerical Analysis book structured
algorithms of all the techniques discussed in the text. The algorithms are given in a
form that can be coded in any appropriate programming language, by students with
even a minimal amount of programming expertise.
At our companion website for the book,
https://sites.google.com/site/numericalanalysis1burden/
you will find all the algorithms written in the programming languages FORTRAN,
Pascal, C, Java, and in the Computer Algebra Systems, Maple, MATLAB, and Math-
ematica. For the Tenth edition, we have added new Maple programs to reflect the
NumericalAnalysis package.
The companion website also contains additional information about the book and
will be updated regularly to reflect any modifications that might be made. For exam-
ple, we will place there any responses to questions from users of the book concerning
interpretations of the exercises and appropriate applications of the techniques. We
also have a set of PowerPoint files for many of the methods in the book. Many
vii
to Accompany
Numerical Analysis
TENTH EDITION
Richard L. Burden
Youngstown University
Youngstown, OH
© Cengage Learning. All rights reserved. No distribution allowed without express authorization.
J. Douglas Faires
Youngstown University
Youngstown, OH
Annette M. Burden
Youngstown University
Youngstown, OH
Prepared by
Richard L. Burden
Youngstown University, Youngstown, OH
Annette M. Burden
Youngstown University, Youngstown, OH
Australia • Brazil • Mexico • Singapore • United Kingdom • United States
, © 2016 Cengage Learning ISBN-13: 978-130525369-8
ISBN-10: 1-305-25369-8
ALL RIGHTS RESERVED. No part of this work covered by the
copyright herein may be reproduced, transmitted, stored, or Cengage Learning
used in any form or by any means graphic, electronic, or 20 Channel Center Street
mechanical, including but not limited to photocopying, Fourth Floor
recording, scanning, digitizing, taping, Web distribution, Boston, MA 02210
information networks, or information storage and retrieval USA
systems, except as permitted under Section 107 or 108 of the
1976 United States Copyright Act, without the prior written Cengage Learning is a leading provider of customized
permission of the publisher except as may be permitted by the learning solutions with office locations around the globe,
license terms below. including Singapore, the United Kingdom, Australia,
Mexico, Brazil, and Japan. Locate your local office at:
www.cengage.com/global.
For product information and technology assistance, contact us at Cengage Learning products are represented in
Cengage Learning Customer & Sales Support, Canada by Nelson Education, Ltd.
1-800-354-9706.
To learn more about Cengage Learning Solutions,
For permission to use material from this text or product, submit visit www.cengage.com.
all requests online at www.cengage.com/permissions
Further permissions questions can be emailed to Purchase any of our products at your local college
.
store or at our preferred online store
www.cengagebrain.com.
NOTE: UNDER NO CIRCUMSTANCES MAY THIS MATERIAL OR ANY PORTION THEREOF BE SOLD, LICENSED, AUCTIONED,
OR OTHERWISE REDISTRIBUTED EXCEPT AS MAY BE PERMITTED BY THE LICENSE TERMS HEREIN.
READ IMPORTANT LICENSE INFORMATION
Dear Professor or Other Supplement Recipient: material posted electronically must be through a password-
protected site, with all copy and download functionality disabled,
Cengage Learning has provided you with this product (the and accessible solely by your students who have purchased the
“Supplement”) for your review and, to the extent that you adopt associated textbook for the Course. You may not sell, license,
the associated textbook for use in connection with your course auction, or otherwise redistribute the Supplement in any form. We
(the “Course”), you and your students who purchase the ask that you take reasonable steps to protect the Supplement from
textbook may use the Supplement as described below. unauthorized use, reproduction, or distribution. Your use of the
Cengage Learning has established these use limitations in Supplement indicates your acceptance of the conditions set forth in
response to concerns raised by authors, professors, and other this Agreement. If you do not accept these conditions, you must
users regarding the pedagogical problems stemming from return the Supplement unused within 30 days of receipt.
unlimited distribution of Supplements.
All rights (including without limitation, copyrights, patents, and trade
Cengage Learning hereby grants you a nontransferable license secrets) in the Supplement are and will remain the sole and
to use the Supplement in connection with the Course, subject to exclusive property of Cengage Learning and/or its licensors. The
the following conditions. The Supplement is for your personal, Supplement is furnished by Cengage Learning on an “as is” basis
noncommercial use only and may not be reproduced, or without any warranties, express or implied. This Agreement will be
distributed, except that portions of the Supplement may be governed by and construed pursuant to the laws of the State of
provided to your students in connection with your instruction of New York, without regard to such State’s conflict of law rules.
the Course, so long as such students are advised that they may
not copy or distribute any portion of the Supplement to any third Thank you for your assistance in helping to safeguard the integrity
party. Test banks, and other testing materials may be made of the content contained in this Supplement. We trust you find the
available in the classroom and collected at the end of each class Supplement a useful teaching tool.
session, or posted electronically as described herein. Any
Printed in the United States of America
1 2 3 4 5 6 7 17 16 15 14 13
,Contents
Chapter 1: Mathematical Preliminaries............................................................................................ 1
Chapter 2: Solutions of Equations of One Variable ....................................................................... 15
Chapter 3: Interpolation and Polynomial Approximation .............................................................. 37
Chapter 4: Numerical Differentiation and Integration ................................................................... 67
Chapter 5: Initial-Value Problems for Ordinary Differential Equations ........................................ 99
Chapter 6: Direct Methods for Solving Linear Equations ........................................................... 165
Chapter 7: Iterative Techniques in Matrix Algebra ..................................................................... 195
Chapter 8: Approximation Theory ............................................................................................... 227
Chapter 9: Approximating Eigenvalues ....................................................................................... 249
Chapter 10: Numerical Solutions of Nonlinear Systems of Equations ........................................ 277
Chapter 11: Boundary-Value Problems for Ordinary Differential Equations .............................. 291
Chapter 12: Numerical Solutions to Partial Differential Equations ............................................. 315
, Preface
This Instructor’s Manual for the Tenth edition of Numerical Analysis by Burden,
Faires, and Burden contains solutions to all the exercises in the book. Although the
answers to the odd exercises are also in the back of the text, we have found that
users of the book appreciate having all the solutions in one source. In addition, the
results listed in this Instructor’s Manual often go beyond those given in the back of
the book. For example, we do not place the long solutions to theoretical and applied
exercises in the book. You will find them here.
A Student Study Guide for the Tenth edition of Numerical Analysis is also available
and the solutions given in the Guide are generally more detailed than those in the
Instructor’s Manual.
We have added a number of exercises to the text that can be implemented in any
generic computer algebra system such as Maple, Matlab, Mathematica, Sage, and
FreeMat. In our recent teaching of the course we found that students understood the
concepts better when they worked through the algorithms step-by-step, but let the
computer algebra system do the tedious computation.
It has been our practice to include in our Numerical Analysis book structured
algorithms of all the techniques discussed in the text. The algorithms are given in a
form that can be coded in any appropriate programming language, by students with
even a minimal amount of programming expertise.
At our companion website for the book,
https://sites.google.com/site/numericalanalysis1burden/
you will find all the algorithms written in the programming languages FORTRAN,
Pascal, C, Java, and in the Computer Algebra Systems, Maple, MATLAB, and Math-
ematica. For the Tenth edition, we have added new Maple programs to reflect the
NumericalAnalysis package.
The companion website also contains additional information about the book and
will be updated regularly to reflect any modifications that might be made. For exam-
ple, we will place there any responses to questions from users of the book concerning
interpretations of the exercises and appropriate applications of the techniques. We
also have a set of PowerPoint files for many of the methods in the book. Many
vii
