对下一代无线通信系统5G关键技术的描述和介绍,即MassiveMIMO技术的优缺点和发展前景。
2024/6/24 22:45:02 2.53MB Massive MIMO 5G
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DistributedSystems(3rd)英文无水印原版pdf第3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Copyright@2017MaartenvanSteenandAndrewS.TanenbaumPublishedbyMaartenvanSteenThisbookwaspreviouslypublishedby:PearsonEducation,IncISBN:978-15-430573-8-6(printedversion)ISBN:978-90-815406-2-9(digitalversion)Edition:3.Version:01(February2017)AllrightstotextandillustrationsarereservedbyMaartenvanSteenandAndrewS.Tanenbaum.Thisworkmaynotbecopied,reproduced,ortranslatedinwholeorpartwithoutwrittenpermissionofthepublisher,exceptforbriefexcerptsinreviewsorscholanyformofinformationstorageadaptationorwhatever,computersoftware,orbysimilarordissimilarmethodsnowknownordevelopedinthefutureisstrictlyforbiddenwithoutwrittenpermissionofthepublisherToMarielle,max,andelkeMVSToSuzanneBarbara,Marvin,Aronnathan,olivia,andmirteASTCONTENTSPreface1Introduction1.1Whatisadistributedsystem?Characteristic1:Collectionofautonomouscomputingelements2Characteristic2:SinglecoherentsystemMiddlewareanddistributedsystems1.2DesigngoalsSupportingresourcesharingMakingdistributiontransparent12Beingscalable15Pitfalls243Typesofdistributedsystems24Highperformancedistributedcomputing25Distributedinformationsystems34Pervasivesystems1.4Summary522Architectures552.1Architecturalstyles56Layeredarchitectures.57Object-basedandservice-orientedarchitectures62Resource-basedarchitectures64Publish-subscribearchitectures2.2MiddlewareorganizationWrappersInterceptors垂番Modifiablemiddleware752.3SystemarchitectureCONTENTSCentralizedorganizations76Decentralizedorganizations:peer-to-peersystemsHybridarchitectures2.4Examplearchitectures94TheNetworkFilesystem94TheWeb982.5Summary3Processes1033.1Threads..104Introductiontothreads104Threadsindistributedsystems1113.2Virtualization116Principleofvirtualizationapplicationofvirtualmachinestodistributedsystems,1223.3Clients124Networkeduserinterfaces124Client-sidesoftwarefordistributiontransparency1273.4Servers128Generaldesignissues129Objectservers133Example:TheApacheWebserver139Serverclusters,,,,,,,1413.5Codemigration152Reasonsformigratingcode152Migrationinheterogeneoussystems1583.6Summary1614Communication4.1Foundations164LayeredProtocols164TypesofCommunication.1724.2Remoteprocedurecall..173Basicrpcoperation174Parameterpassing178RPC-basedapplicationsupport182VariationsonrPc185Example:dCErPc,.1884.3Message-orientedcommunication193Simpletransientmessagingwithsockets.193Advancedtransientmessaging198Message-orientedpersistentcommunication206Example:IBM'sWebSpheremessage-queuingsystem212Example:AdvancedMessageQueuingProtocol(AMQP)....218DS3.01DOWNLOADEDBYTEWIGOMIXMAIL.INFOCONTENTS4.4Multicastcommunication221Application-leveltree-basedmulticasting221Flooding-basedmulticasting225Gossip-baseddatadissemination2294.5Summary2345Naming2375.1Names,identifiersandaddresses2385.2Flatnaming.241Simplesolutions241Home-basedapproaches245Distributedhashtables246Hierarchicalapproaches2515.3Structurednaming256Namespaces.256Nameresolution259Theimplementationofanamespace264Example:TheDomainNameSystem271Example:TheNetworkFileSystem2785.4Attribute-basednaming283Directoryservices283Hierarchicalimplementations:LDAP285Decentralizedimplementations2885.5Summary2946Coordination2976.1Clocksynchronization.298Physicalclocks299Clocksynchronizationalgorithms3026.2Logicalclocks310Lamport'slogicalclocks310Vectorclocks3166.3Mutualexclusion321322acentralizedalgorithm.322adistributedalgorithm323atoken-ringalgorithm.325adecentralizedalgorithm3266.4Electionalgorithms329Thebullyalgorithm.,..330Aringalgorithm332Electionsinwirelessenvironments333Electionsinlarge-scalesystems.3356.5Locationsystems336DOWNLOADEDBYTEWIGOMIXMAIL.INFODS301VIllCONTENTSGPS:GlobalPositioningSystem337WhengPsisnotanoption339Logicalpositioningofnodes3396.6Distributedeventmatching..343Centralizedimplementations3436.7Gossip-basedcoordination349asgregation349Apeer-samplingservice350Gossip-basedoverlayconstruction3526.8Summary3537Consistencyandreplication3557.1Introduction356Reasonsforreplication356Replicationasscalingtechnique3577.2Data-centricconsistencymodels358Continuousconsistency359Consistentorderingofoperations364Eventualconsistency3737.3Client-centricconsistencymodels375MonotonicreadsMonotonicwrites.379Readyourwrite380Writesfollowreads3827.4ReplicamanagementFindingthebestserverlocation383Contentreplicationandplacement..385Contentdistribution..388Managingreplicatedobjects3937.5Consistencyprotocols.396Continuousconsistency..........396Primary-basedprotocols398Replicated-writeprotocolsCache-coherence403Implementingclient-centricconsistency,,...4077.6Example:CachingandreplicationintheWeb4097.7Summar4208Faulttoleran4238.1Introductiontofaulttolerance424Basicconcepts.424Failuodels427Failuremaskingbyredundancy8.2Processresilience432DS3.01DOWNLOADEDBYTEWIGOMIXMAIL.INFO
2024/6/24 6:52:56 36.95MB Distributed Systems
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【RecyclerView】七、RecyclerView.ItemDecoration条目装饰(getItemOffsets边距设置)https://hanshuliang.blog.csdn.net/article/details/113310440博客源码快照
2024/5/18 11:54:37 1.89MB RecyclerView
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Thispaperisasurveyofthetheoryandmethodsofphotogrammetricbundleadjustment,aimedatpotentialimplementorsinthecomputervisioncommunity.Bundleadjustmentistheproblemofrefiningavisualreconstructiontoproducejointlyoptimalstructureandviewingparameterestimates.Topicscoveredinclude:thechoiceofcostfunctionandrobustness;numericaloptimizationincludingsparseNewtonmethods,linearlyconvergentapproximations,updatingandrecursivemethods;gauge(datum)invariance;andqualitycontrol.Thetheoryisdevelopedforgeneralrobustcostfunctionsratherthanrestrictingattentiontotraditionalnonlinearleastsquares.
2024/5/7 9:10:33 570KB Bundle Adjustment Sparse Matrices
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多项式相乘一元稀疏多项式简单计算器的基本功能是:(1)输入并建立多项式;
(2)输出多项式,输出形式为整数序列:n,c1,e1,c2,e2,...,cn,en,其中n是多项式的项数,ci和ei分别是第i项的系数和指数,序列按指数降序排列。
(3)多项式a与多项式b相乘,建立多项式。
-Sparsepolynomialmultiplicationunarypolynomialbasicfunctionsofthecalculatorissimple:(1)inputandtheestablishmentofpolynomial(2)theoutputpolynomial,theoutputintheformofanintegersequence:n,c1,e1,c2,e2,...,cn,en,wherenisthenumberofitemspolynomial,ciandeiisthefirstientriesarethecoefficientandtheindexsequenceindescendingorderbyindex.(Three)polynomialapolynomialbmultipliedwiththeestablishmentofpolynomials.
2024/5/2 0:56:33 47KB Visual C++ 多项式相乘
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Theproblemofminimumnumberofchoosabilityofgraphswasfirstintroduced.byVizing.Itappearsinsomepracticalproblemswhenconcerningfrequency.assignment.Inthispaper,westudytwoimportantlistcoloring,listedgecoloringand.listtotalcoloring.Weprovethatχl(G)=Δandχl(G)=Δ
2024/4/30 6:27:44 310KB 研究论文
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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
2024/2/28 16:27:03 432B ACM
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CocosCreator实现左右跳游戏JumpLR.zipconst{ccclass,property}=cc._decorator;@ccclassexportdefaultclassBoxextendscc.Component{@property(cc.Label)txtNum:cc.Label=null;privatemPrevBox:cc.Node=null;privatemNextBox:cc.Node=null;privatemOffset:number=0;//[-4,4]//LIFE-CYCLECALLBACKS://onLoad(){}start(){}//update(dt){}setOffset(offset:number){this.mOffset=offset;}getOffset(){returnthis.mOffset;}setPrev(prev:cc.Node){this.mPrevBox=prev;}getPrev(){returnthis.mPrevBox;}setNext(next:cc.Node){this.mNextBox=next;}getNext(){returnthis.mNextBox;}setNum(num:number){this.txtNum.string=`${num}`;}down(y:number){this.node.runAction(cc.sequence(cc.moveBy(0.4,0,y),cc.callFunc(()=>{NodeMgr.putBox(this.node);})));}}
2024/2/13 18:32:35 807KB CocosCreator实现左右
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::green_square:所有系统均可运行这个库包含开放源代码的正常运行时间监测和状态页,搭载。
使用,您可以拥有自己的无限和免费的正常运行时间监控器和状态页面,完全由GitHub存储库提供支持。
我们将“用作事件报告,将“用作正常运行时间监视器,并将“用作状态页面。
网址状态历史响应时间正常运行时间:green_square:向上471ms种子箱库:green_square:向上429毫秒节点-苹果杰克:green_square:向上456毫秒节点-大麦金托什:green_square:向上316毫秒节点-不和谐:green_square:向上561毫秒节点-Fluttershy:green_square:向上563毫秒节点-稀有度:green_square:向上707毫秒节点-星光闪烁:green_square:
2024/1/30 18:30:12 974KB uptime-monitor status-page upptime
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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
2024/1/26 14:10:04 16.51MB Differential Equations Linear Algebra
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在日常工作中,钉钉打卡成了我生活中不可或缺的一部分。然而,有时候这个看似简单的任务却给我带来了不少烦恼。 每天早晚,我总是得牢记打开钉钉应用,点击"工作台",再找到"考勤打卡"进行签到。有时候因为工作忙碌,会忘记打卡,导致考勤异常,影响当月的工作评价。而且,由于我使用的是苹果手机,有时候系统更新后,钉钉的某些功能会出现异常,使得打卡变得更加麻烦。 另外,我的家人使用的是安卓手机,他们也经常抱怨钉钉打卡的繁琐。尤其是对于那些不太熟悉手机操作的长辈来说,每次打卡都是一次挑战。他们总是担心自己会操作失误,导致打卡失败。 为了解决这些烦恼,我开始思考是否可以通过编写一个全自动化脚本来实现钉钉打卡。经过一段时间的摸索和学习,我终于成功编写出了一个适用于苹果和安卓系统的钉钉打卡脚本。
2024-04-09 15:03 15KB 钉钉 钉钉打卡