Numerical analysis 9th edition burden solutions manual

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• Initial-Value Problems for Ordinary Differential Equations
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  This Instructor’s Manual for the Ninth Edition of Numerical Analysisby Burden and Faires 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 backof the book. For example, we do not place the long solutions to theoretical and appliedexercises in the book. You will find them here. A 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 the Instructor’s Manual. In order to make it convenient for instructors, we have placed an asterisk (*) in this Manual in front of each exercise whose solution is given in the Student Study Guide. Hopefully this will help with your homework assignments and test problems. We have added a number of exercises to the text that involve the use of a Computer Algebra System. We have chosen Maple as our standard, because theirNumerical- Analysispackage parallels the algorithms in this book, but any of these systems can be used. 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 structured algorithms in our Numerical Analysis book for 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 website for the book,

  you will find all the algorithms written in the programming languages FORTRAN, Pascal, C, Java, as well as in the Computer Algebra Systems, Maple, MATLAB, and Mathematica. For the Ninth Edition, we have added new Maple programs to reflect the changes in their system and to include portions of theirNumericalAnalysis package.

  The website also contains additional information about the book andwill be up- dated regularly to reflect any modifications that might be made. Forexample, we will place there any responses to questions from users of the bookconcerning inter- pretations of the exercises and appropriate applications of the techniques. We will have a set of presentation material ready soon for many of the methods in the book. These are being constructed by Professor John Carroll of Dublin City University using the Beamer package of LATEX, and will be placed on the website. The Beamer package creates PDF files that are similar to Power Point presentations but incorporates mathematical elements easily and correctly. We are quite excited about this material and expect to have many of the presentationsready before they would normally be covered in the Fall term of 2010. If you send us an e-mail we will keep you posted on our progress. We hope our supplement package provides flexibility for instructorsteaching Nu- merical Analysis. If you have any suggestions for improvements that can be incorpo- rated into future editions of the book or the supplements, we wouldbe most grateful to receive your comments. We can be most easily contacted by electronic mail at the addresses listed below.

  Youngstown State University Richard L. Burden burden@math.ysu

  August 20, 2010 J. Douglas Faires faires@math.ysu

  2 Exercise Set 1.

  (c)P 2 (x) = 1 + 3(x−1) + 3(x−1) 2 (d)R 2 (0) =− 0 .125; actual error =− 0. 125 8. P 3 (x) = 1 + 12 x− 18 x 2 + 161 x 3

  x 0. 5 0. 75 1. 25 1. 5

  √P 3 (x) 1 .2265625 1 1 1. 6796875 x+ 1 1 .2247449 1. 3228757 1. 5 1. 5811388 |

  x+ 1−P 3 (x)| 0 .0018176 0 0 0. 0985487

  *9. Since P 2 (x) = 1 +x and R 2 (x) = − 2 eξ(sinξ+ cosξ) 6 x 3 for someξbetweenxand 0, we have the following: (a)P 2 (0) = 1 and|f(0)−P 2 (0)|≤ 0 .0932; (b)|f(x)−P 2 (x)|≤ 1 .252; (c)