逐步回归的基本思想是将变量逐个引入模型，每引入一个解释变量后都要进行F检验，并对已经选入的解释变量逐个进行t检验，当原来引入的解释变量由于后面解释变量的引入变得不再显著时，则将其删除。
以确保每次引入新的变量之前回归方程中只包含显著性变量。
这是一个反复的过程，直到既没有显著的解释变量选入回归方程，也没有不显著的解释变量从回归方程中剔除为止。
以保证最后所得到的解释变量集是最优的。
本文件结合实例利用MATLAB实现逐步回归法

很困扰大家现在介绍一种完全解决方法，只需两步，帮助大家很容易实现卸载。
（1）下载install.log文件（2）找到License的默认安转路径（一般是C:\ProgramFiles\ESRI\License\arcgis9x），找到卸载工具unwise32.exe，双击打开，选择（1）步下载的install.log文件，并点击next，即可实现完全卸载，如下所示：

用于无声卡电脑-VirtualAudioCableAtfirst,pleaseunpackthedistributionpackageintoanemptyfolderonalocaldrive,makingsurethatlocalfolderpathdoesnotcontainspecialcharacterslike"#","&"orsimilar.Unpackingthepackage,preservefolderstructure(afterunpacking,destinationfoldershouldcontain"x86"and"x64"subfolders).IfyouarenewtoVirtualAudioCable,pleasereadtheusermanualbeforeinstallation.ThebestwaytoopenthemanualistoruninstallerapplicationnamedSetupandclickthe"Help"buttoninthefirstinstallationdialog.Theusermanualfile(vac.chm,afilenamed"vac"withasheetandquestionmarkicon)isanHTMLHelpformatfile.Donotopenmanualfilefromanetworkpathordirectlyfromthepackageotherwisehelppagesmaynotbedisplayedduetosecurityrestrictions.Copythefiletoalocaldrivebeforeopening.Pleasemakesurethatlocalfilepathdoesnotcontainspecialcharacters.Ifusermanualfileisopenedfromalocaldrivebutpagesontherightpanearenotdisplayedproperly,pleasecheckifvac.chmfilehasthe"Unblock"buttoninitsPropertiesform(right-clickthefiletoopenitsproperties).Ifyes,unblockit.Seealso"Howblockingsomeattachmentshelpsprotectyourcomputer"topicinWindowsHelp(Start-HelpandSupport)andhttp://support.microsoft.com/kb/902225.Readingthemanual,don'tforgetthatthereisthe"Search"tab.Havingaproblem,entersomewordsrelatedtotheproblemandappropriatepageswillbedisplayed.Ofcourse,searchfeaturewillnothelpifyouenteraquestionlike"howcanIuseit?".Itonlyfindspagescontaininggivenkeywords.

原则英文版，总页数为586页，是完整的，此版本是我付费在别的网站上下载的ThankyoufordownloadingthisSimonSchusterebookGetaFreeebookwhenyoujoinourmailinglist.Plus,getupdatesonnewreleases,dealsrecommendedreads,andmorefromSimonSchusterClickbelowtosignupandseetermsandconditionsCLICKHERETOSIGNUPAlreadyasubscriber?Provideyouremailagainsowecanregisterthisebookandsendyoumoreofwhatyouliketoread.YouwillcontinuetoreceiveexclusiveoffersinyourinboxPRINCIPLESRAYDALIOsiMonSCHUSTERNEWYORKLONDONTORONTOSYDNEYNEWDELHIPARTIW豆EREIMCOMIINGFRON1MyCalltoAdventure:1949-19672CrossingtheThreshold:1967-19793MyAbyss:1979-19824MyRoadofTrials:1983-19945TheUltimateBoon:1995-20106ReturningtheBoon:2011-20157MyLastYearandMyGreatestChallenge:2016-20178LookingBackfromaHigherLevelPARTIILIFEPRINCIPLES1EmbraceRealityandDealwithIt2Usethe5-StepProcesstoGetWhatYouWantOutofLife3BeRadicallyOpen-Minded4UnderstandThatPeopleAreWiredVeryDifferently5LearnHowtoMakeDecisionsEffectivelyLifePrinciples:PuttingItAllTogetherSummaryandTableoflifePrinciplesPARTIIIWORKPRINCIPLESSummaryandTableofWorkPrinciplesTOGETTHECULTURERIGHT1TrustinRadicalTruthandRadicalTransparency2CultivateMeaningfulWorkandMeaningfulRelationships3CreateaCultureinWhichItIsOkaytoMakeMistakesandUnacceptableNottoLearnoem4GetandStayinSync5BelievabilityWeightYourDecisionMaking6RecognizeHowtoGetBeyondDisagreementsTOGETTHEPEOPLERIGHT7RememberThattheWHOIsMoreImportantthantheWhat8HireRight,BecausethePenaltiesforHiringWrongAreHuge9ConstantlyTrain,Test,Evaluate,andSortPeopleTOBUILDANDEVOLVEYOURMACHINE10ManageasSomeoneOperatingaMachinetoAchieveagoal11PerceiveandDon'tTolerateproblems12DiagnoseProblemstoGetatTheirrootcauses13DesignImprovementstoYourMachinetoGetAroundYourProblems14DoWhatYouSetOuttodo15USeToolsandProtocolstoShapeHowWorkIsDone16AndforHeaven'sSakeDontOverlookGovernanceWorkPrinciples:PuttingItAllTogetherACKNOWLEDGMENTSABOUTTHEAUTHORCONCLUSIONAPPENDIX.TOOLSANDPROTOCOLSFORBRIDGEWATERSIDEAMERITOCRACYBIBLIOGRAPHYINDEXToBarbara.thehalfmewhohasmademewholeformorethanfortyyearsINTRODUCTIONBeforeibegintellingyouwhatIthink,IwanttoestablishthatI'ma"dumbshit'whodoesntknowmuchrelativetowhatineedtoknowWhateversuccessI'vehadinlifehashadmoretodowithmyknowinghowtodealwithmynotknowingthananythingIknow.ThemostimportantthingIlearnedisanapproachtolifebasedonprinciplesthathelpsmefindoutwhat'strueandwhattodoaboutitI'mpassingalongtheseprinciplesbecauseiamnowatthestageinmylifewhichIwanttohelpothersbesuccessfulratherthantobemoresuccessfulmyself.Becausetheseprincipleshavehelpedmeandotherssomuch,Iwanttosharethemwithyou.It'suptoyoutodecidehowvaluabletheyreallyareandwhat,ifanythingyouwanttodowiththemPrinciplesarefundamentaltruthsthatserveasthefoundationsforbehaviorthatgetsyouwhatyouwantoutoflife.TheycanbeappliedagainandagaininsimilarsituationstohelpyouachieveyourgoalsEveryday,eachofusisfacedwithablizzardofsituationswemustrespondto.Withoutprincipleswewouldbeforcedtoreacttoallthethingslifethrowsatusindividually,asifwewereexperiencingeachofthemforthefirsttime.Ifinsteadweclassifythesesituationsintotypesandhavegoodprinciplesfordealingwiththemwewillmakebetterdecisionsmorequicklyandhavebetterlivesasaresult.Havingagoodsetofprinciplesislikehavingagoodcollectionofrecipesforsuccess.Allsuccessfulpeopleoperatebyrinciplesthathelpthembesuccessful,thoughwhattheychoosetobesuccessfulatvariesenormouslysotheirprinciplesvarTobeprincipledmeanstoconsistentlyoperatewithprinciplesthatcanbeclearlyexplained.Unfortunately,mostpeoplecantdothat.Andit'sveryrareforpeopletowritetheirprinciplesdownandsharethemThatisashame.IwouldlovetoknowwhatprinciplesguidedAlbertEinstein,SteveJobsWinstonChurchill,LeonardodaVinci,andotherssoIcouldclearlyunderstandwhattheyweregoingafterandhowtheyachieveditandcouldcomparetheirdifferentapproaches.I'dliketoknowwhichprinciplesaremostimportanttothepoliticianswhowantmetovoteforthemandtoalltheotherpeoplewhosedecisionsaffectme.Dowehavecommonprinciplesthatbindustogether-asafamly,asacommunity,asanation,asfriendsacrossnations?O1dowehaveopposingprinciplesthatdivideus?whatarethey?letsbespecificThisisatimewhenitisespeciallyimportantforustobeclearaboutourprinciplesMyhopeisthatreadingthisbookwillpromptyouandotherstodiscoveryourownprinciplesfromwhereveryouthinkisbestandideallywritetheedown.Doingthatwillallowyouandotherstobeclearaboutwhatyourprinciplesareandunderstandeachotherbetter.Itwillallowyoutoretinethemasyouencountermoreexperiencesandtoreflectonthem,whichwillhelpyoumakebetterdecisionsandbebetterunderstoodHAVINGYOUROWNPRINCIPLESWecomebyourprinciplesindifferentways.Sometimeswegainthemthroughourownexperiencesandreflections.Sometimesweacceptthemfromothers,likeourparents,orweadoptholisticpackagesofprinciples,suchasthoseofreligionsandlegalframeworksBecauseweeachhaveourowngoalsandourownnatures,eachofusmustchooseourownprinciplestomatchthem.Whileitisntnecessarilyabadthingtouseothers'principles,adoptingprincipleswithoutgivingthemmuchthoughtcanexposeyoutotheriskofactinginwaysinconsistentwithyourgoalsandyournature.Atthesametime,you,likeme,probablydontknoweverythingyouneedtoknowandwouldbewisetoembracethatfact.Ifyoucanthinkforyourselfwhilebeingopen-mindedinaclearheadedwaytofindoutwhatisbestforyoutodo,andifyoucansummonupthecouragetodoityouwillmakethemostofyourlife.Ifyoucantdothat,youshouldreflectonwhythatis,becausethat'smostlikelyyourgreatestimpedimenttogettingmoreofwhatyouwantoutoflifeThatbringsmetomyfirstprincipleThinkforyourselftodecide1,whatyouwant,2ywhatistrue,and3,whatyoushoulddotoachieve#1inlightof#2anddothatwithhumilityandopen-mindednesssothatyouconsiderthebestthinkingavailabletoyou.Beingclearonyourprinciplesisimportantbecausetheywillaffectallaspectsofyourlife,manytimesaday.Forexample,whenyouenterintorelationshipswithothers,yourprinciplesandtheirprincipleswilldeterminehowyouinteract.Peoplewhohavesharedvaluesandprinciplesgetlong.Peoplewhodontwillsufferthroughconstantmisunderstandingsandconflicts.Thinkaboutthepeopleyouareclosestto:Aretheirvaluesalignedwithyours?Doyouevenknowwhattheirvaluesorprinciplesare?Tooofteninrelationships,people'sprinciplesarentclear.ThisisespeciallyproblematicinorganizationswherepeopleneedtohavesharedprinciplestobesuccessfulBeingcrystalclearaboutmyprinciplesiswhyIlaboredsomuchovereverysentenceinthisbookTheprinciplesyouchoosecanbeanythingyouwantthemtobeaslongastheyareauthentic--i.e,aslongastheyreflectyourtruecharacterandvalues

本人用WiseInstallsystem制作的Interbase7.5.1完整安装程序。
包含了无限制license。
在NT系统下interbase被安装成service并自动启动；
在win9x下被安装成普通应用。
经测试无误。

Achecksumisanalgorithmthatscansapacketofdataandreturnsasinglenumber.Theideaisthatifthepacketischanged,thechecksumwillalsochange,sochecksumsareoftenusedfordetectingtransmissionerrors,validatingdocumentcontents,andinmanyothersituationswhereitisnecessarytodetectundesirablechangesindata.Forthisproblem,youwillimplementachecksumalgorithmcalledQuicksum.AQuicksumpacketallowsonlyuppercaselettersandspaces.Italwaysbeginsandendswithanuppercaseletter.Otherwise,spacesandletterscanoccurinanycombination,includingconsecutivespaces.AQuicksumisthesumoftheproductsofeachcharacter'spositioninthepackettimesthecharacter'svalue.Aspacehasavalueofzero,whilelettershaveavalueequaltotheirpositioninthealphabet.So,A=1,B=2,etc.,throughZ=26.HereareexampleQuicksumcalculationsforthepackets"ACM"and"MIDCENTRAL":ACM:1*1+2*3+3*13=46MIDCENTRAL:1*13+2*9+3*4+4*0+5*3+6*5+7*14+8*20+9*18+10*1+11*12=650InputTheinputconsistsofoneormorepacketsfollowedbyalinecontainingonly#thatsignalstheendoftheinput.Eachpacketisonalinebyitself,doesnotbeginorendwithaspace,andcontainsfrom1to255characters.OutputForeachpacket,outputitsQuicksumonaseparatelineintheoutput.SampleInputACMMIDCENTRALREGIONALPROGRAMMINGCONTESTACNACMABCBBC#SampleOutput46650469049751415

Don'tMakeMeThink第3版英文版文字版全彩色觉得好请留评论DontmakemeThinkRevisitedACommonSenseapproachtoWebUsabilityCopyrighto2014SteveKrugNewriderswww.newniders.comToreporterrorspleasesendanotetoerrata@peachpit.comNewridersisanimprintofpeachpitadivisionofpearsoneducationEditor:ElisabethbayleProjecteditor:NancyDavisProductioneditor:lisabraziealCopyEditorBarbaraFlanaganInteriorDesignandComposition:RomneyLangeIllustrationsbymarkMatchaandMimiHeftFarnhamfontsprovidedbyTheFontbureauInc.(www.fontbureau.comNoticeofRightsAllrightsreservedNopartofthisbookmaybereproducedortransmittedinanyformbyanymeans,electronic,mechanical,photocopying,recording,orotherwise,withoutthepriorwrittenpermissionofthepublisher.Forinformationongettingpermissionforreprintsandexcerpts,contactpermissions@peachpit.comNoticeofliabilityTheinformationinthisbookisdistributedonan"asisbasiswithoutwarranty.whilileeveryprecautionhasbeentakeninthepreparationofthebook,neithertheauthornorPeachpitshallhaveanyliabilitytoanypersonorentitywithrespecttoanylossordamagecausedorallegedtobecauseddirectlyorindirectlybytheinstructionscontainedinthisbookorbythecomputersoftwareandhardwareproductsdescribedinittrademarksItsnotrocketsurgeryisatrademarkofStevekrugManyofthedesignationsusedbymanufacturersandsellerstodistinguishtheirproductsareclaimedastrademarks.Wherethosedesignationsappearinthisbook,andpeachpitwasawareofatrademarkclaim,thedesignationsappearasrequestedbytheownerofthetrademark.allotherproductnamesandservicesidentifiedthroughoutthisbookareusedineditorialfashiononlyandforthebenefitofsuchcompanieswithnointentionofinfringementofthetrademark.Nosuchuse,ortheuseofanytradename,isintendedtoconveyendorsementorotheraffiliationwiththisbookISBN-13:978-0-32196551-6ISBN-10:0-321-96551-5987654321PrintedandboundintheunitedstatesofamericaFirsteditionTomyfather,whoalwayswantedmetowriteabook,Mymother,whoalwaysmademefeellikeIcouldMelanie,whomarriedme-thegreateststrokeofgoodfortuneofmylifeandmyson,Harry,whowillsurelywritebooksmuchbetterthanthisonewheneverhewantstoSecondeditionTomybigbrother,Phil,whowasamenschhiswholelifeThirdeditionToallthepeoplefromallpartsoftheworld--whohavebeensoniceaboutthisbookforfourteenyears.Yourkindwords--inperson,inemail,andinyourblogs-havebeenoneofthegreatjoysofmylifeEspeciallythewomanwhosaiditmadeherlaughsohardthatmilkcameoutheofhernoseContentsPREFACEAboutthiseditionINTRODUCTIONReadmefirstThroatclearinganddisclaimersGUIDINGPRINCIPLESCHAPTER1Dontmakemethink!Krug'sFirstLawofusabilityCHAPTER2HowwereallyusethewebScanning,satisficing,andmuddlingthroughCHAPTER3.BillboardDesign101Designingforscanning,notreadingCHAPTER4.AnimaL,Vegetable,orMineral?WhyuserslikemindlesschoicesCHAPTER5OmitneedlesswordsTheartofnotwritingfortheWebTHINGSYOUNEEDTOGETRIGHTCHAPTER6.StreetsignsandBreadcrumbsDesigningnavigationCHAPTERZTheBigBangTheoryofWebDesignTheimportanceofgettingpeopleoffontherightfootMAKINGSUREYOUGOTTHEMRIGHTCHAPTER8Thefarmerandthecowmanshouldbefriends>Whymostargumentsaboutusabilityareawasteoftime,andhowtoavoidthemChAPTER9.USabilitytestingon10centsadayKeepingtestingsimple--soyoudoenoughofitLARGERCONCERNSANDOUTSIDEINFLUENCESCHAPTER10MObile:It'snotjustacityinAlabamaanymoreWelcometothe21stCentury.YoumayexperienceaslightsenseofvertigoCHAPTER11UsabilityascommoncourtesyWhyyourWebsiteshouldbeamenschCHAPTER12.AccessibilityandyouJustwhenyouthinkyouredone,acatfloatsbywithbutteredtoaststrappedtoitsbackCHAPTER13GuidefortheperplexedMakingusabilityhappenwhereyouliveAcknowledgmentsIndexPreface:aboutthiseditionPeoplecomeandgosoquicklyhere!DOROTHYGALEJUDYGARLAND)INTHEWIZARDOFOZ(1939)Iwrotethefirsteditionofdon'tmakemethinkbackin2000By2002,Ibegantogetafewemailsayearfromreadersasking(verypolitely)ifI'dthoughtaboutupdatingit.Notcomplaining,justtryingtobehelpful."alotoftheexamplesareoutofdate"wastheusualcommentMystandardresponsewastopointoutthatsinceiwroteitrightaroundthetimetheinternetbubbleburstmanyofthesitesiusedasexampleshadalreadydisappearedbythetimeitwaspublishedButIdidn'tthinkthatmadetheexamplesanylessclear.Finally,in2006Ihadastrongpersonalincentivetoupdateit.ButasIrereadittoseewhatIshouldchange,Ijustkeptthinking"Thisisallstilltrue>Ireallycouldn'tfindmuchofanythingthatithoughtshouldbechangedHalfoftheroyaltiesforthebookweregoingtoacompanythatnolongerexisted,anddoinganeweditionmeantanewcontractandtwicetheroyalties-formeIfitwasanewedition,though,somethinghadtobedifferent.SoIaddedthreechaptersthatididn'thavetimetofinishbackin2000,hitthesnoozebutton,andhappilypulledthecoversbackovermyheadforanothersevenyearsSteveKrugACommonSenseApproachtoWebUsabilityFOREWORDBYROGERBLACK2000SteveKrugTHINKACommonSenseApproachtoWebUsabilitySECONDEDITION2006WRitingisreallyhardforme,andI'malwayshappytohaveareasonnottodoit.GivemeagoodoldrootcanaloverwritinganydaySowhynowfinallyanewedition?Tworeasons#1。
Let’sfaceit:It'soldThere'snodoubtaboutitatthispoint:Itfeelsdated.Afterall,it'sthirteenyearsold,whichislikeahundredyearsinInternettime.(See?Nobodyevensaysthingslike"inInternettimeanymoreMostofthewebpagesiusedforexamples,likeSenatorOrrinHatch'scampaignsiteforthe2000electionlookreallyold-fashionednowSitesthesedaystendtolookalotmoresophisticated,asyoumightexpectPRENIDEN'TWWw.\TOCiTheRepublicans:ANewHampshireForumTheDec2DebateThefirstakeahddyeGoPdebyetesThursdayheatsupthepoltcalstylewarsaSenatorHatchfightstokeepsubstancenCampaign2000.EVLLSTORYTheExperiencedCandidateLw警mHatchCampaign2000BeneoiceThatMatters!ClickheretoCONTRIBUTECAMPAIGNNEWSlIVESCONTIRIHIUTORLINTsCOILINKS)LUNTEEILThieRar4每MCICK2cpM(.DisHachPre的d时Ceme,ntP0.00多』LC,UT0403nTERNETANDNTwoRxsaunaSwww.orrinhatch.com1999

完美解决arcgis9.3LicenseManager卸载时无法找到安装日志问题，使用方法：解压缩，找到目录下的unwise32.exe，浏览到这个日志文件即可卸载。
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DifferentialEquationsandLinearAlgebra(4th)英文无水印原版pdf第4版pdf所有页面使用FoxitReader、PDF-XChangeViewer、SumatraPDF和Firefox测试都可以打开本资源转载自网络，如有侵权，请联系上传者或csdn删除查看此书详细信息请在美国亚马逊官网搜索此书EditorialDirector,Mathematics:ChristinehoagEditor-in-Chief:DeirdreLynchAcquisitionsEditor:WilliamHoffmaProjectTeamLead:ChristinaleProjectmanager:LaurenMorseEditorialAssistant:JenniferSnyderProgramTeamLead:KarenwernholmProgramManagerDaniellesimbajonCoverandillustrationDesign:StudioMontageProgramDesignLead:BethPaquinProductMarketingManagerClaireKozarProductMarketingCoordiator:BrookesmithFieldMarketingManager:EvanStCyrSeniorAuthorSupport/TechnologySpecialist:JoevetereSeniorProcurementSpecialist:CarolMelvilleInteriorDesign,ProductionManagement,AnswerArt,andCompositioneNergizerAptara,LtdCoverImage:LighttrailsonmodernbuildingbackgroundinShanghai,China-hxdyl/123RFCopyrightO2017,2011,2005PearsonEducation,Inc.oritsaffiliates.AllRightsReserved.PrintedintheUnitedStatesofAmerica.Thispublicationisprotectedbycopyright,andpermissionshouldbeobtainedfromthepublisherpriortoanyprohibitedreproduction,storageinaretrievalsystem,ortransmissioninanyformorbyanymeans,electronic,mechanical,photocopyingrecording,orotherwise.Forinformationregardingpermissions,requestformsandtheappropriatecontactswithinthePearsonEducationGlobalRights&Permissionsdepartmentpleasevisitwww.pearsoned.com/permissions/PEARSONandALWAYSLEARNINGareexclusivetrademarksintheU.s.and/orothercountriesownedbyPearsonEducation,Inc.oritsaffiliatesUnlessotherwiseindicatedherein,anythird-partytrademarksthatmayappearinthisworkarethepropertyoftheirrespectiveowandanyreferencestothird-partytrademarks,logosorothertradedressarefordemonstrativeordescriptivepurposesonly.SuchofsuchmarksoranyrelationshipbetweentheownerandPearsonEducation,Inc.oritsaffiliates,authors,licenseesordistributortreferencesarenotintendedtoimplyanysponsorship,endorsement,authorization,orpromotionofPearsonsproductsbytheownersLibraryofCongressCataloging-in-PublicationDataGoode.StephenwDifferentialequationsandlinearalgebra/StephenW.GoodeandScottA.AnninCaliforniastateUniversity,Fullerton.-4theditionpagescmIncludesindexISBN978-0-321-96467-0—ISBN0-32196467-51.Differentialequations.2.Algebras,Linear.I.Annin,Scott.II.TitleQA371.G6442015515’.35-dc23201400601512345678910V031-1918171615PEARSONISBN10:0-321-96467-5www.pearsonhighered.comISBN13:978-0-321-96467-0ContentsPrefacevii1First-OrderDifferentialEquations1.1DifferentialEquationsEverywhere11.2BasicIdeasandTerminology131.3TheGeometryofFirst-OrderDifferentialEquations231.4SeparableDifferentialEquations341.5SomeSimplePopulationModels451.6First-OrderLinearDifferentialEquations531.7ModelingProblemsUsingFirst-OrderLinearDifferentialEquations61.8Changeofvariables711.9ExactDifferentialEquations821.10Numericalsolutiontofirst-OrderDifferentialEquations931.11SomeHigher-OrderDifferentialEquations1011.12ChapterReview1062MatricesandSystemsofLinearEquations1142.1Matrices:Definitionsandnotation1152.2MatrixAlgebra1222.3TerminologyforSystemsofLinearEquations13824R。
w-EchelonMatricesandElementaryR。
wOperations1462.5Gaussianelimination1562.6TheInverseofasquarematrix1682.7ElementaryMatricesandtheLUFactorization1792.8TheInvertiblematrixtheoremi1882.9ChapterReview1903Determinants1963.1TheDefinitionofthedeterminant1963.2PropertiesofDeterminants2093.3CofactorExpansions2223.4SummaryofDeterminants2353.5ChapterReview242iyContents4VectorSpaces2464.1Vectorsinrn2484.2DefinitionofaVectorSpace2524.3Subspaces2634.4SpanningSets2744.5LinearDependenceandLinearIndependence2844.6Basesanddimension2984.7Changeofbasis3114.8RowSpaceandColumnSpace3194.9TheRank-NullityTheorem3254.10InvertibleMatrixTheoremll3314.11ChapterReview3325InnerProductSpaces3395.1DefinitionofanInnerproductspace3405.2OrthogonalSetsofvectorsandorthogonalProjections3525.3Thegram-Schmidtprocess3625.4LeastSquaresApproximation3665.5ChapterReview3766LinearTransformations3796.1Definitionofalineartransformation3806.2Transformationsofr23916.3TheKernelandrangeofalineartransformation3976.4AdditionalPropertiesofLinearTransformations4076.5Thematrixofalineartransformation4196.6Chaiterreview4287EigenvaluesandEigenvectors4337.1TheEigenvalue/EigenvectorProblem4347.2GeneralResultsforEigenvaluesandEigenvectors4467.3Diagonalization4547.4AnIntroductiontotheMatrixExponentialFunction4627.5OrthogonalDiagonalizationandQuadraticforms4667.6Jordancanonicalforms4757.7Chapterreview4888LinearDifferentialEquationsofOrdern4938.1GeneralTheoryforLinearDifferentialEquations4958.2ConstantCoefficientHomogeneousLinearDifferentialEquations5058.3ThemethodofundeterminedcoefficientsAnnihilators5158.4Complex-ValuedTrialSolutions5268.5OscillationsofaMechanicalSystem529Contentsv8.6RLCCircuits5428.7TheVariationofparametersmethod5478.8ADifferentialEquationwithNonconstantCoefficients5578.9Reductionoforder5688.10ChapterReview5739SystemsofDifferentialEquations5809.1First-OrderLinearSystems5829.2VectorFormulation5889.3GeneralResultsforfirst-OrderLinearDifferentialystems5939.4VectorDifferentialEquations:NondefectiveCoefficientMatrix5999.5VectorDifferentialEquations:DefectiveCoefficientMatrix6089.6Variation-of-ParametersforLinearSystems6209.7SomeApplicationsofLinearSystemsofDifferentialEquations6259.8MatrixExponentialFunctionandSystemsofDifferentialEquations6359.9ThePhasePlaneforLinearAutonomousSystems6439.10NonlinearSystems6559.11ChapterReview66310TheLaplaceTransformandSomeElementaryApplications67010.1DefinitionoftheLaplaceTransform67010.2TheExistenceofthelaplacetransformandtheInversetransform67610.3PeriodicFunctionsandtheLaplacetransform68210.4ThetransformofderivativesandsolutionofInitial-Valueproblems68510.5TheFirstShiftingTheorem69010.6TheUnitStepFunction69510.7TheSecondShiftingTheorem69910.8ImpulsiveDrivingTerms:TheDiracDeltaFunction70610.9TheConvolutionIntegral71110.10ChapterReview71711SeriesSolutionstoLinearDifferentiaEquations72211.1AReviewofpowerseries72311.2SeriesSolutionsaboutanOrdinaryPoint73111.3TheLegendreEquation74111.4SeriesSolutionsaboutaRegularSingularPoint75011.5Frobeniustheory75911.6Bessel'sEquationofOrderp77311.7Chapterreview785ViContentsAReviewofComplexNumbers791BReviewofPartialFractions797CReviewofIntegrationTechniques804DLinearlyIndependentSolutionstox2y+xp(x)y+g(x)y=0811Answerstoodd-NumberedExercises814Index849S.W.GoodededicatesthisbooktomeganandtobiS.A.annindedicatesthisbooktoarthurandJuliannthebestparentsanyonecouldaskforPretraceLikethefirstthreeeditionsofDifferentialEquationsandLinearalgebra,thisfourtheditionisintendedforasophomorelevelcoursethatcoversmaterialinbothdifferentialequationsandlinearalgebra.Inwritingthistextwehaveendeavoredtodevelopthestudentsappreciationforthepowerofthegeneralvectorspaceframeworkinformulatingandsolvinglinearproblems.Thematerialisaccessibletoscienceandengineeringstu-dentswhohavecompletedthreesemestersofcalculusandwhobringthematurityofthatsuccesswiththemtothiscourseThistextiswrittenaswewouldnaturallyteachblendinganabundanceofexamplesandillustrations,butnotattheexpenseofadeliberateandrigoroustreatment.MostresultsareprovenindetailHowever,manyofthesecanbeskippedinfavorofamoreproblem-solvingorientedapproachdependingonthereader'sobjectives.Somereadersmayliketoincorporatesomeformoftechnology(computeralgebrasystem(CAS)orgraphingcalculator)andthereareseveralinstancesinthetextwherethepoweroftechnologyisillustratedusingtheCasMaple.Furthermore,manyexercisesetshaveproblemsthatrequiresomeformoftechnologyfortheirsolutionTheseproblemsaredesignatedwithaoIndevelopingthefourtheditionwehaveoncemorekeptmaximumflexibilityofthematerialinmind.Insodoing,thetextcaneffectivelyaccommodatethedifferentemphasesthatcanbeplacedinacombineddifferentialequationsandlinearalgebracourse,thevaryingbackgroundsofstudentswhoenrollinthistypeofcourse,andthefactthatdifferentinstitutionshavedifferentcreditvaluesforsuchacourse.Thewholetextcanbecoveredinafivecredit-hourcourse.Forcourseswithalowercredit-hourvalue,someselectivitywillhavetobeexercised.Forexample,much(orall)ofChapterImaybeomittedsincemoststudentswillhaveseenmanyofthesedifferentialequationstopicsinanearliercalculuscourse,andtheremainderofthetextdoesnotdependonthetechniquesintroducedinthischapter.Alternatively,whileoneofthemajorgoalsofthetextistointerweavethematerialondifferentialequationswiththetoolsfromlinearalgebrainasymbioticrelationshipasmuchaspossible,thecorematerialonlinearalgebraisgiveninChapters2-7sothatitispossibletousethisbookforacoursethatfocusessolelyonthelinearalgebrapresentedinthesesixchapters.ThematerialondifferentialequationsiscontainedprimarilyinChapters1and8-1l,andreaderswhohavealreadytakenafirstcourseinlinearalgebracanchoosetoproceeddirectlytothesechaptersThereareothermeansofeliminatingsectionstoreducetheamountofmaterialtobecoveredinacourse.Section2.7containsmaterialthatisnotrequiredelsewhereinthetext,Chapter3canbecondensedtoasinglesection(Section3.4)forreadersneedingonlyacursoryoverviewofdeterminants,andSections4.7,5.4,andthelatersectionsofChapters6and7couldallbereservedforasecondcourseinlinearalgebra.InChapter8Sections8.4,8.8,and8.9canbeomitted,and,dependingonthegoalsofthecourse,Sections8.5and8.6couldeitherbede-emphasizedoromittedcompletelySimilarremarksapplytoSections9.7-9.10.AtCaliforniaStateUniversity,Fullertonwehaveafourcredit-hourcourseforsophomoresthatisbasedaroundthematerialinChapters1-9viiiPrefaceMajorChangesintheFourthEditionSeveralsectionsofthetexthavebeenmodifiedtoimprovetheclarityofthepresentationandtoprovidenewexamplesthatreflectinsightfulillustrationswehaveusedinourowncoursesatCaliforniaStateUniversity,Fullerton.OthersignificantchangeswithinthetextarelistedbeleOW1.ThechapteronvectorspacesinthepreviouseditionhasbeensplitintotwochaptersChapters4and5)inthepresentedition,inordertofocusseparateattentiononvectorspacesandinnerproductspaces.Theshorterlengthofthesetwochaptersisalsointendedtomakeeachofthemlessdaunting2.Thechapteroninnerproductspaces(Chapter5)includesanewsectionprovidinganapplicationoflinearalgebratothesubjectofleastsquaresapproximation3.Thechapteronlineartransformationsinthepreviouseditionhasbeensplitintotwochapters(Chapters6and7)inthepresentedition.Chapter6isfocusedonlineartransformations,whileChapter7placesdirectemphasisonthetheoryofeigenvaluesandeigenvectors.Oncemore,readersshouldfindtheshorterchapterscoveringthesetopicsmoreapproachableandfocused4.Mostexercisesetshavebeenenlargedorrearranged.Over3,000problemsarenowcontainedwithinthetext,andmorethan600concept-orientedtrue/falseitemsarealsoincludedinthetext5.Everychapterofthebookincludesoneormoreoptionalprojectsthatallowformorein-depthstudyandapplicationofthetopicsfoundinthetext6.ThebackofthebooknowincludestheanswertoeveryTrue-FalsereviewitemcontainedinthetextAcknowledgmentsWewouldliketoacknowledgethethoughtfulinputfromthefollowingreviewersofthefourthedition:JameyBassofCityCollegeofSanFrancisco,TamarFriedmannofUniversityofrochester,andlinghaiZhangofLehighUniversityAlloftheircommentswereconsideredcarefullyinthepreparationofthetextS.A.Annin:Ioncemorethankmyparents,ArthurandJuliannAnnin,fortheirloveandencouragementinallofmyprofessionalendeavors.Ialsogratefullyacknowledgethemanystudentswhohavetakenthiscoursewithmeovertheyearsand,insodoinghaveenhancedmyloveforthesetopicsanddeeplyenrichedmycareerasaprofessorFirst-OrderDifferentiaEquations1.1DifferentialEquationsEverywhereadifferentialequationisanyequationthatinvolvesoneormorederivativesofanunknownfunction.Forexample(1.1.1dxds(S-1)(1.1.2)aredifferentialequations.Inthedifferentialequation(1.1.1)theunknownfunctionordependentvariableisy,andxistheindependentvariable;inthedifferentialequation(1.1.2)thedependentandindependentvariablesareSandt,respectively.Differentialequationssuchas(1.1.1)and(1.1.)inwhichtheunknownfunctiondependsonlyonasingleindependentvariablearecalledordinarydifferentialequations.Bycontrast,thedifferentialequationLaplace'sequation)0involvespartialderivativesoftheunknownfunctionu(x,y)oftwoindependentvariablesxandy.SuchdifferentialequationsarecalledpartialdifferentialequationsOnewayinwhichdifferentialequationscanbecharacterizedisbytheorderofthehighestderivativethatoccursinthedifferentialequationThisnumberiscalledtheorderofthedifferentialequation.Thus,(l1.1)hasordertwo,whereas(1.1.2)isafirst-orderdifferentialequation1

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