solution manual for numerical analysis

【实例简介】
solution manual for numerical analysis answer pdf
Contents Preface Mathematical Preliminaries Exercise Set 1.1 Exercise Set 1.2 聊·· Exercise Set 1.3 Solutions of Equations of One Variable 15 Exercise Set 2.1 15 Exercise Set 2.2 17 Exercise Set 2.3 Exercise set 2.41 25 Exercise Set 2.5 Exercise Sct 2.6 Interpolation and Polynomial Approximation 33 Set3.1 cercis sel 3.2 Exercise Set 3.3 10 Exercise Set 3.4 44 Exercise Set 3.5 Numerical Differentiation and Integration 57 Exercise Set 4.1 57 Exercise Set 4,2 64 Exercise Set 4.3 67 Exercise Set 4.4 72 Exercise Set 4.5 75 Exercise Set 4.6 Exercise Set 4.7 80 Exercise Set 4.8 82 Exercise Set 4.9 84 Initial-Value Problems for Ordinary Differential Equations 87 E Set 5.1 7 Ex 90 Exercise Set 5.3 95 CONTENTS Exercise set 5.4 Exercise Set 5.5 110 Exercise Set 5.6 Exercise Set 5.7 123 Exercise Set 5. 8 128 Exercise Set 5.9 131 Exercise Set 5.10 138 Direct Methods for Solving Linear Systems 147 Exercise Set 6.1 ..147 Exercise set 6.2 ·· 152 Exercise Set 6.3 158 Exercise Set 6.4 165 Exercise set 6.1 167 Exercise set 6.6 171 Iterative Techniques in Matrix Algebra 179 Exer 179 Exercise set 7.2 184 Exercise Set 7.3 187 Exercise Set 7.4 197 Set 7.5 199 Approximation Theory 209 se8.1 209 Exercise set 8.2 210 Exercise Set 8.3 214 Exercise set 8.4 215 Exercise Set 8.5 220 Exercise Set 8.6 223 approximating eigenvalues 227 Exercise Set 9.1 227 Exercise set 9.2 231 Exercise set 9.3 .,,,,,234 Exercise set 9.4 236 Numerical Solutions of Nonlinear Systems of Equations 243 Exercise set 10.1 243 Exercise set 10.2 246 Exercise Set 10.3 249 Eκ ercise Set10.4. 251 Exercise Set 10.5 253 CONTENTS Boundary-Value Problems for Ordinary Differential equations 257 Eκ ercise set11.1 257 Exercise Set 11.2 Exercise Set 11.3 263 Exercise Set 11.4 4 267 上 xercise Set115 Numerical Solutions to Partial Differential quations 275 Exercise Set 12.1 275 Exercise Set 12.2 Exercise Set 12.3 Exercise Set 12.4 289 CONTENTS Preface This Instructor's Manual for the Eighth of Numerical Analysis by 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 oflen 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 It has been our practicc to include structured algorithms of all he techniques discussed in our Numerical Analysis book. The algorithms are given in a form that can bc coded in any appropriate programming language by those with even a minimal amount of programming expertise In earlier editions of the book, we included in the Instructor's Manual a complete FORTRAN listing for all the algorithms, and distributed to instructors using the book, upon demand, a tape(actually punched cards in the First Edition) containing Lll these programs In the Fourth Edition we supplemented this with a disk containing Pascal pro grams for the algorithms. In the Fifth Edition we added Fortran programs to the package. In the Sixth Edition we placed the disk in the text itsclf, and added C programs, as well as worksheets in Maple and Mathematica, for all the algorithms We continued this practice for the Seventh Edition, updating the Maple prograns to both versions 5.0 and 6.0 and adding MAtLAB programs as well For the Eighth Edition, we have added new Maple programs to reflect the lin ear algebra package change from the original linalg package to the more modcrn LinearAlgebra package. In addition, we now also have the programs coded in Java You will not find a disk with this edition of the book. I nstead, ottr reviewers suggested and we agree, that it is more convenient to have the programs available for downloading from the web. At thc website for the book http://www.as.ysu.edu/faires/numcrical-analysis/ you will find all the programs that used to be on the disk that came with the book This site also contains additional information about the book and will be updated CONTENTS regularly to reflect any modifications that need to be made. For example, we will list a copy of the adoption list for the book so that potential users can ask colleagues for suggestions, and any changes made when a new printing is produced Placing the programs on the web site also permits uis to more easily updated programs as the software changes, and to give responses to comments made by users of the book. We canl also add new material that might be included in a subsequent edition in the form of PDF files that users can download. Our hope is that this will extend the life of the Eighth Edition while keeping the material up to date In addition to this Manual, we have rewritten the Student Study Guide for the Eighth Edition. The exercises that are solved in the guide are generally those requin ing insight into the methods in the text, rather than those involving computation The Guide should be especially helpful for those doing self study of numerical tech- niques. Please ask your students to contact us if they are interested in this Guide We hope our supplement package provides flexibility for instructors teaching 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 would be most grateful to receive your comments. We can be most easily contacted by electronic mail at the addresses listed below Youngstown State University Richard I. Burden burden@math. ysu. edu January 21, 2005 J. Douglas faires Caires@lath ysu. edu Mathematical Preliminaries Exercise Set 1.1, page 14 1. For each part, f E C[a, b] on the given interval. Since f(a)and f(b)are of opposite sign, the Intermediate Value Theorem implies that a number c exists with f(c=0 2.(a)[0,1 (b)0,1],4,5,[-1,0 (c)[-2,-1],[0,1,2.5,3.5 2],[-1,-0.5],and[0.5,0] 3. For each part, f E C(a, b],f' exists on(a, b) and f(a)=f(b)=0. Rolle,s Thedren implies that a number c exists in(a, b)with f(c=0. For part(d), we can use [a, b=1-1,0) on [a,6=0,2 4. The maximum value for f(a)l is given below a)0.4620981 (b)0.8 (c)5.164000 (d)1.582572 5. For 2<0, f(a)<2 +k<0, provided that: 1<-nh Similarly, for a>0,f(a)>2x+h>0, provided that > h By Thcorem 1. 13, there exists a number c with f(c=0. If f(c)=0 and f(c)=0 for some c'C, then by Theorem 1.7, there exists a, number p between c and c with f'(p)=0. However, f(a)=3 22+2>0 for all 2 6. Suppose p and g are in a, b] with p* q and f(p)=f()=0. By the Mean Value Theorem, there exists S E(a, b)with f(m)-:()=∫(5)(-q) But,f(p)-f(g)=0 and p+q So f(E)=0, contradicting the hypoth 7.(a)P2(a)=0 (b)B2(0.5)=0125; actual error=0125 (c)P2(a)=1+8(x-1)+3(a-1)2 (d)B2(0.5)=-0.125; actual error=-0.125 Exercise Set 1.1 8.f3(a)=1+-2+23 0.5 0.75 1.25 1.5 P3(x) 1.2265625133105471.55175781.6796875 x+1 1.22474491.3228757 1.5811388 √x+1-P(a)0.00181760.0817900051757800985487 9. Since P2(a)=1+2 and R2(a) 2es(sin S cos s) for some s between c and 0, we have the following (a)P2(0.5)=1.5and|f(0.5)-P2(0.5)≤0.0932; (b)|f(x)-P2(x川≤1252 (c)J0f(c)≈1 (d)15o f (a)da;-5o P2(c)cac|<n R2(a)dr <0.313, and the actual error is 0.122 .2(n)=141930+061788(-)-08406(-)2and2(a)=-3m(+cs)(a for some f between r and (a) P2(0.5)=1.446879 and f(0.5 )=1.446889. An error bound is 1.01x 10-3, and the actual error 1S1.0×10-5 b)|f(x)-P2(x)≤0.1353720n0,1 ()b2()co=1.376542andf()x=1:78025 (d)An error bound is 7. 403 x 10-3, and the actual error is 1. x 10-3 1l.P3(x)=(c-1)2-(x-1)3 (a) P3(0.5)=0.312500, f(0.5)=0.346574. An error bound is 0.2916, and the actual erroy is0.034074 (b)|f(x)-Ba(x)≤0.2916on05,15] ()J0352().n=0.08,a5(x-1) In a d=0.0880 (d)An error bound is 0.0583, and the actual error is 4.687 x 10-3 乃3(m)=-4+6x-2-4x3;P3(0.4)=-2016 (b)R3(0.4)≤005849;:(0.4)-B3(0.4)=0.013365367 (c)P4(a)=-4+6x-2-4a3;P(0.4)=-2.016 (d)1(0.4)≤00136;f(0.4)-P4(0.4)=0.01335367 【实例截图】
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