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Solution Manual For Numerical Methods Using Matlab, 4th Edition

Solution Manual For Numerical Methods Using Matlab, 4th Edition provides you with expert textbook solutions that ensure you understand every concept thoroughly.

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Solution Manual For Numerical Methods Using Matlab, 4th Edition - Page 1 preview imageSolutionManualforNumericalMethods:UsingMATLABJohnH.MathewsandKurtisD.FinkAugust2002
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Solution Manual For Numerical Methods Using Matlab, 4th Edition - Page 2 preview imageDownloadedfromStudyXY.com®+StudyXYSdYe.o>\|iF’prE\3SStudyAnythingThisContentHasbeenPostedOnStudyXY.comassupplementarylearningmaterial.StudyXYdoesnotendroseanyuniversity,collegeorpublisher.Allmaterialspostedareundertheliabilityofthecontributors.wv8)www.studyxy.com
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Solution Manual For Numerical Methods Using Matlab, 4th Edition - Page 3 preview image2
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Solution Manual For Numerical Methods Using Matlab, 4th Edition - Page 4 preview imageContents1Preliminaries5itdfibReview(oflGaleulnstIHITHTATRETRHTHIEECARTARITITEERSE231avyNeversijiHTAGTTAHREECRCTTIRIHIRRICEdt3iierrorEAmalyeistildFT—HIEIRATGERTHOUECHRHACATIEEATof2TheSolutionofNonlinearEquationsf(z)=0152.91irveracianfarSolvingaiiioe1NARRECAPREACHARCHECITRHG2.2BracketingMethodsforLocatingaRoot..............182.3InitialApproximationandConvergenceCriteria..........202.4Newton-RaphsonandSecantMethods...............212.5Aitken’sProcessandSteffensen’sandMuller'sMethods.....273TheSolutionofLinearSystemsAX=B333.1IntroductiontoVectorsandMatrices................33BallPropertiesofVectors|andMatrices(lIIHHIRMAHITERIITREAAIRITNTZ3.3Upper-TriangularLinearSystems..................373.4GaussianEliminationandPivoting.................38disiiltranenlar|kactorization(i(TIHUIIARIRTAIATIETATIRTTIETETRSG3.6IterativeMethodsforLinearSystems................40SiidiifiTveration|forNonlinearSystems!EIHIHHEEIHWITHEECITIHHTEGS4InterpolationandPolynomialApproximation514.1TaylorSeriesandCalculationofFunctions.............51dillIntraduction|tolInterpolation([LHLHIIHHATHERIRTIRIGIRTRIHIETETNGddlNasrange[ApprosimationiilHARTIRIRCIIHITREARNIERENRTITsoddlNewtonBolynovayals[RHLHEAMHRHRGVETREIIRGIRIGRIITITHARITIGdoiChebysheviFolynomialsi(Gptionat)iILIMHTARIHIITIEGIEGITITITHGGSdibilliFadeAppraxamationsfltiditEITHERGS5CurveFitting73ia:iliffIeast.SquaresilefillyHRHGRIEEATIHEEIERTIRIes2curyetineRTTIHEATERIHETAUHSIEHINTNERATIONHeoeffInterpolationbylSphnekmetionsITHATITHETNCNEATIEREIEITITTNGq3
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Solution Manual For Numerical Methods Using Matlab, 4th Edition - Page 5 preview image4CONTENTS5.4FourierSeriesandTrigonometricFrotynoratalsutRGHIATERTIEREIEEEerowlifiisezerGurves(HLERIEIHGREEMIEHHITITTTTIIIHIAIIRTRIIETTNS6NumericalDifferentiation93631ADproximatintheDerivativeMTIITITHITIHENRTIRTHTRITITITHITGS6.2NumericalDifferentiationFormulas.................077NumericalIntegration101[{:dllilintroduction|tolQuadrature(itEHTIRATITIRICLETVATABIAICRRARICEOATG17.2CompositeTrapezoidalandSimpson'sRule............1057.3RecursiveRulesandRombergIntegration.............114EeCREbfallGaussTreocndraiTntegration|litfHIHEMEARITGITITTIEITITIEITCHS8NumericalOptimization121a:dliliMminmizationiofafimetionltHTHRHEATARIETAEEEIEIEEACROSS)82Nelder-MeadandPowell'sMethods.................128.3Gradient/andNewtonsMethods([HHTTHHICITARGRIRRTETTIITRog9SolutionofDifferentialEquations1359.1IntroductiontoDifferentialEquations...............1350:2lllEnle=Nethod|iLMMRIMIACIHEARERIIERCRENERTIETITRIEATSS3Hens!Method](LHCHTRCRERRTARENIEAERENEEAtdiTaviorSeriesiMcthodMLILFTMITTTRERIFIIARIRICARRINUARINColliiRumeeKattalncthodstWTLURIHITRRNHITREITIIRAINCOREFAalibliiBredictor.(orrectoniMethodsflITARMRRFRAHITATIRHRCHAIICIIING9urlsystems!ofInferentialiauations|IITHTHTMTENTIRITIRITITORITAATII9:8BoundaryValueProblems|MTHTITATITHITEITIMTIETTRIEITTIHITGGo.9kmiteDifferenceMethod!ftHIHIARITGIATRIREATIIEICINIRIRRNRSG10SolutionofPartialDifferentialEquations15504hByperboliclEquationsHAGCHGTLHTETBETEITITITIRTTT621araboliclEquations(MHHEARTRIRHIREIEITIEEITTIEIRRe03likllipticikquationsi|HsuECEHREARIEITEEETTITRRTIEITINTHL6011EigenvaluesandEigenvectors16311.1HomogeneousSystems:TheEigenvalueProblem.........163C2owerihettiodiREHEATING6si3Jacobisivethad]ititiiuiipmsgurgigRmtiRigiraiiiirmitGeo11.4EigenvaluesforSymmetricMatrices................170
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Solution Manual For Numerical Methods Using Matlab, 4th Edition - Page 6 preview imageChapter1...Preliminaries1.1ReviewofCalculusL(8)L=limyoofol=2limpoo€n=lipo(2—faut)=2=%=0(b)limy,oo2mptonl—21liceen=(3—ect)=4-1=02.(a)limyoosin(zn)=sin(limy_,oozn)=sin(2)(b)limyooIn(x2)=In(limpoo22)=In(4)3.(a)Sincefiscontinuouson[1,0];solveinatebbsHLkoiRGJH24/7ACT)¢c=1-vZel-1,0](b)Sincefiscontinuouson[6,8];solveViT-55-2=3Z?-5x—11=05£/Faminboll5e=EBs4.(a)f'(z)=22—3=0,thusthecriticalpointsare¢=+1.Thusmin{f(~1),f(1),£(2)}=min{5,—1,~1}=~1andmaz{f(-1),f(1),/(2)}=maz{5,-1,~1}=5(b)f(z)=~2cos(x)sin(x)—cos(z)=—cos(z)(2sin(z)+1)=0,thusthecriticalpointsare¢=7,77/6,117/6.Thus5+StudyXY
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Solution Manual For Numerical Methods Using Matlab, 4th Edition - Page 7 preview image6CHAPTER1.PRELIMINARIESmin{f(0),f(r),f(77/6),f(117/6),f(2m)}=min{1,1,5/4,5/4,1}=1andmaz{f(0),f(r),f(7x/6),f(117/6),f(2r)}=max(1,1,5/4,5/4,1}=5/45.(a)f(z)=42°—82=d(x?—2)=0,thusc=0,42€[2,2](b)f(x)=cos(z)+2co8(2z)=cos(z)+2(2co8*(x)—1)=4cos?(z)+cos(z)—2=0T=(-1£33)/8¢=cos'((-1£/33)/8),2r—cos™I((—1=v/33)/8)6.(a)f(x)=ghzandL200)~1SolvingLo=§yields=1.(b)f(x)=(2?+22)/(x+1)?andLO=LO—1Solvingf(z)=(#2+22)/(z+1)>=Lyieldsc=—1+27.ThegivenfunctionsatisfiesthehypothesesoftheGeneralizedRolle’sThe-orem.Sincef(0)=f(1)=f(3)=0,thereexistaa¢€(0,3)suchthatJ"(€)=0.Solve6c—8=0tofind¢=4/3.8.(a)[Pzetdr=e"—eof=e?+1(b)J2,#5dz=$1n(2?+1)[',=0(Theintegrandisanoddfunction)9.(a)4fit*cos(t)dt=22cos(z)Ob)£7edt=oo?(322)=3o2en®10.(8)gpg[26e%dz=22°14=52.Solving62%=52yields¢=LapropeMJ(6)&Jy"?zeos(z)dz=(wsin(e)+cos(x))3=—(1+2).Useacalculatortoapproximatethesolution(s):cos(z)=—(1+=a12.16506,4.43558€(0,37/2].na)2p=2(b)or=3(©)Comy=30(4—aby)=3limicoo5(2—2p)=3(d)inw=C=i1)=ShinoYi(ty—me)=§—StudyXY
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Solution Manual For Numerical Methods Using Matlab, 4th Edition - Page 8 preview image1.2.BINARYNUMBERSKf12.(a)“gl-D+k@-1P-Je-12+A=—1)+1(b)dz?+3z+1(c)got—$2?+113.TheTaylorpolynomialofdegreen=4expandedaboutzo=0forflx)=sin(z)isP(x).14.(a)P(3)=-24EfUGFLEE15.Theaverageareaisgivenby;71;Iride=(23=i16.AnypolynomialP(x)satisfiesthehypothesesofRolle’sTheoremontheinterval[a,b].ThusP'()hasatleastn—1realrootsintheinterval[a,b],P(x)hasatleastn—2realrootsintheinterval[a,b],...,andP("=1hasatleast7—(n—1)=1rcalrootintheinterval[a,b].17.Iff,fandf”aredefinedontheinterval[a,b],thenfiscontinuousontheinterval[a,b]andfisdifferentiableontheinterval(a,b).ByTheorem1.6(MeanValueTheorem)thereexistsnumbers¢;€(a,c)and¢;€(¢,b)suchthat:1)—I(a),10)=fe)(ey)=om)=1)=LTDngpep)=LO-But,sincef(a)=f(b)=0itfollowsthatf/(c;)=f(c)/(c—a)andf'(e2)=f(c)/(c—b).Giventhatf’andf”aredefinedintheinterval[a,b],itfollowsthatf”alsosatisfiesthehypothesesofTheorem1.6.Thusthereexistsanumberd€(a,b)suchthat:fayl@-re)8-82 jev-ocy—cyca-e(2—e)e=b)(c—a)~~sincef(c)>0.1.2BinaryNumbers1.Answerswilldependonspecificplatform.2.(a)21(b)56(c)254(d)5193.(a)0.75(b)0.65625(c)0.6640625(d)0.855468754.(a)14140625(b)314160156255.(a)v2—1.4140625=0.00015109...(b)7~3.1416015625=—0.000008908...+StudyXY
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Solution Manual For Numerical Methods Using Matlab, 4th Edition - Page 9 preview image8CHAPTER1.PRELIMINARIES6.(2)23=10111,2=2011)+1b=1nifAveyIR,UHATR|5=22)+1b=02=201)+0b3=0DUETYsHERSEES(b)87=10101114,87=2(43)+1bo=1silionyapgl21=2010)+1by=110=2(5)4+0by3=05=2AD+1B=12=201)+0bs=0EE"EDME(c)378=101111010,(d)2388=10010101010007.(a)00111ee (b)0.1101uo (c)0.101114(d)010010114,8.(a)0.00011,(b)§=0.102000=0.01402R=%d=0=INT(3)Fi=3=FRAC(3)2F,=ida=1=-INT(3)F=3=FRAC(3)Wr=Fdy=0=INT(3)Fo=§=FRAC(H)23=3di=1=INT(})F=1=FRrAC()(¢)4=0.d1d2d3140=0.001102R=%di=0=INT()Fy=?=FRAC(3)2F=Hdy=0=INT(2)P=dmFRAC(3)2Wy=gdy=1=INT(Z)Fy=g=FRAC(3)2F=3di=0=INT(3)F,=2=FRAC()9.(a)5=0.0001100iw0=0.0001Trap—00001100410=0.0000000TT00z4,.,==0.00625I~StudyXY
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Solution Manual For Numerical Methods Using Matlab, 4th Edition - Page 10 preview image1.2.BINARYNUMBERS9(b)#=0.0010010r0=0.00Tsuo—0.010010,=0.00000000100T0-=00022321428...10.InTheorem1.14let¢=§and7=1,thenELUMJAI8764"512EE11.InTheorem1.14let¢=3/16andr=1/16,thenELE)3J1611256iffanaeinifamin=12.1=5.Assume(H*er=.ThenHA[ilarGB-665*5-(#)(%)ph+1MifinotealTherefore,bytheprincipleofmathematicalinduction,2=Vcanberepre-sentedasadecimalnumberthathasNdigits.13.(a)i~0.10114x271=0.1011x27!silo:onsWi2d5l0:011010b<|27z0.1000111px20%~0.1001rwox2°=0.100140x2°5=0.101Luox272=0.001011,x2°px0.101110x2°Thus(§+1)+&~0.1100¢w0(b)%20.1100nex27%=0.001101x2713~0101lpex27!=0.101100x2-1pes0.171001x2-7+StudyXY
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Solution Manual For Numerical Methods Using Matlab, 4th Edition - Page 11 preview image10CHAPTER1.PRELIMINARIESi#&0.1110pex271=0.011100;x2°=~0.1101peXx272=0.001101,x2°pi0.101001100x20Thus(&+3)+£~0.101040(c)%~0.1011x272=0.01011x2715=0.1110x27%=0.001110x2-1STITTspec50.10010X271=0.100140x2717=~0.10014Xx272=0.010014,x271FoDITOTImEdomThus(%+2)+4~0.111040x271(d)5~0.1011pex2°=0.1011000x2°3~0.1110mex27%=0.0001110x2°%20.1101x2°=0.1101004,0x2°7~0.1011x272=0.001001,x2°TESSmnrnmeThus(F5+5)+4~0.11114,14.(2)10=101¢hree(b)23=212uree(c)421=1201214pree(d)1784=211002¢nree15.(a)3=0.Lnree(b)3=0Tohree(€)15=0.0022¢hree[IEQE16.(a)(a)10=20se(b)(b)35=12040,(c)(c)721=103440(d)(d)734=1041444,17.(a)3=0T3fi0e(b)£=0Zp.(c)75=0.02510(d)$2=0.1104,
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Solution Manual For Numerical Methods Using Matlab, 4th Edition - Page 12 preview image1.3.ERRORANALYSIS111.3ErrorAnalysisI(a)©—&=0.00008182,22%=(.0000300998.....,4-significantdigitsb)y—§=350,42=0.0355871.....,2-significant,digitsv(¢)z=2=0.000008,===0.117647,O-significantdigitsalRienegHypoil(r+54shay+stm)=itmmtsem=Goad?”~0.2553074428=p3.(a)p1+p2=1.41440.09125=1.505pip2=(2.1414)(0.09125)=0.1290(b)p1+p2=31.415+0.027182=31.442P1p2=(31.415)(0.27182)=0.853924.(a)OT0711885222010710678110ik0.0000C767108=0.707103Theerrorin-volveslossofsignificance.(b)0.09317218025-0.6931478036J0.00009499909=0.4999938Theerrorin-volveslossofsignificance.5.(a)In(2)lu0)For(c)cos(2x)(d)cos(z/2)6.(a)bdHECKplEEfpJHEELE=20.12-3(7.398)+8.16—1=20.12-22.194+8.16—1=5.09rileRRRfolRUEdrEBSAME=(~0.2800)(2.72)+3)(2.72)~1=(-0.7616+3)(2.72)—1=(2.2384)(2.72)1=6.088-1=5.088R(2.72)=(272-1)EGUh=5.088+StudyXY
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Solution Manual For Numerical Methods Using Matlab, 4th Edition - Page 13 preview image12CHAPTER1.PRELIMINARIES(b)P(0.975)=(((0.975)°—3(0.975)%)+3(0.975))—1=(0.9268—3(0.9506))+2.925)—1=(0.9268—2.852)+2.925)+1=(~1.925+2.925)~1=1-1=0Q(0.975)=((0.975—3)(0.975)+3)(0.975)—1=((-2.025)(0.975)+3)(0.975)—1=(~1.9774+3)(0.975)—1=(1.026)(0.975)—1=1-1=0R(0.975)=(0.975—1)%=(-0.025)=—0.00001562To(a)F+§+++ohog0.498(0)Ag+ais+a+a++in04998.(a)Thepropagationoferroris€,+¢,+€,.(b)p_itejothaalllatrisallaiiaiedHence,if1<|g]<|p|,thenthereisapossibilityofmagnificationoftheoriginalerror.(e)paro=(Ptep)d+e)F+e)=PUT+preg+acy+Ply+Fepey+Gener+Peger+peer=dF+(Beg+dep+Pier)H(Pepeq+Geper+Pegi)+epcqerDependingontheabsolutevaluesofp,,and#,thereisapossibilityofmagnificationoftheoriginalerrorsep,€4,and€,.9.2toos(h)=2+h+841HORY)(25)cosh)=1+h+5+540h)I~StudyXY
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Solution Manual For Numerical Methods Using Matlab, 4th Edition - Page 14 preview image1.3.ERRORANALYSIS1310.ef4sin(h)=1+2%+4+O(h?)etsin(h)=h+h+ELOR)AnintermediatecomputationwasBaillAalllad3SALcorceAthtsrg+=gr)=hthHETEr{meme11.Iiilalllsllcon)£5)=14hKBBE4OK)cos(h)sin(h)=h-2-42+O(hT)AnintermediatecomutationwasLallbSl2ril1i2RsTrITEDITA12.x==b/FdaEe=)famiimiBa(VFac)=taeThecaseforx7ishandledinasimilarmanner.13.(a)==—0.001000,x2=—1000(b)1=—0.00100,7=—10000(¢)1=—0.000010,z5=—100000(d)z;=—0.000001,22=~1000000+StudyXY
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Solution Manual For Numerical Methods Using Matlab, 4th Edition - Page 15 preview image14CHAPTER1.PRELIMINARIES+Studyxy
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Solution Manual For Numerical Methods Using Matlab, 4th Edition - Page 16 preview imageChapter2..TheSolutionofNonlinear.Equationsf(z)=02.1IterationforSolvingr=g(x)1.(a)Clearly,g(z)€C[0,1].Since¢'(z)=—/2<0ontheinterval[0,1],thefunctiong(z)isstrictlydecreasingontheinterval[0,1].Ifgisstrictlydecreasingon[0,1],theng(0)=1andg(1)=0implythat9([0,1])=[0,1]€[0,1].Thus,byTheorem2.2,thefunctiong(x)hasafixedpointontheinterval[0,1].Inaddition:|f'(z)}=|—#/2|=z/2<1/2<1ontheinterval[0,1].Thus,byTheorem2.2,thefunctiong(x)hasauniquefixedpointontheinterval[0,1].(b)Clearly,g(x)€C[0,1].Sinceg/(x)=—In(2)2™<0ontheinterval[0,1],thefunctiong(x)isstrictlydecreasingontheinterval[0,1].Tfgisstrictlydecreasingon[0,1],then(0)=1andg(1)=1/2implythatg([0,1])=[1/2,1]C[0,1].Thus,byTheorem2.2thefunctiong(x)hasafixedpointontheinterval[0,1].Inaddition:|¢’(2)|=|~1n(2)272|=In(2)272<In(2)<In(e)=1ontheinterval[0,1].Thus,byTheorem2.2,thefunctiong(x)hasanuniquefixedpointontheinterval[0,1].(c)Clearlyg(x)iscontinuouson[0.5,5.2]andg([0.5,5.2])€[0.5,5.2].But,9([0.5,2])C[0.5,2].Thus,thehypothesesofthefirstpartofTheorem2.2aresatisfiedandghasafixedpointin[0.5,2].While(1,1)istheuniquefixedpointin[0.5,2],[f/(1)]=1#£1,thusthehypotheseeinpart(4)ofTheorem2.2cannotbesatisfied.15+StudyXY
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