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1、DifferentialEquationswithLinearAlgebraThispageintentionallyleftblankDifferentialEquationswithLinearAlgebraMatthewR.Boelkins,J.L.Goldberg,andMerleC.Potter320093OxfordUniversityPress,Inc.,publishesworksthatfurtherOxfordUniversity’sobjectiveofexcellenceinresearch,scholar
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3、SwitzerlandThailandTurkeyUkraineVietnamCopyright©2009byOxfordUniversityPress,Inc.PublishedbyOxfordUniversityPress,Inc.198MadisonAvenue,NewYork,NewYork10016www.oup.comOxfordisaregisteredtrademarkofOxfordUniversityPressAllrightsreserved.Nopartofthispublicationmayberepro
4、duced,storedinaretrievalsystem,ortransmitted,inanyformorbyanymeans,electronic,mechanical,photocopying,recording,orotherwise,withoutthepriorpermissionofOxfordUniversityPress.LibraryofCongressCataloging-in-PublicationDataBoelkins,MatthewR.Differentialequationswithlinear
5、algebra/MatthewR.Boelkins,J.L.Goldberg,MerleC.Potter.p.cm.Includesindex.ISBN978-0-19-538586-1(cloth)1.Differentialequations,Linear.2.Algebras,Linear.I.Goldberg,JackL.(JackLeonard),1932–II.Potter,MerleC.III.Title.QA372.B6572009515.354–dc222008050361987654321Printedint
6、heUnitedStatesofAmericaonacid-freepaperContentsIntroductionxi1Essentialsoflinearalgebra31.1Motivatingproblems31.2Systemsoflinearequations81.2.1RowreductionusingMaple151.3Linearcombinations211.3.1Markovchains:anapplicationofmatrix-vectormultiplication261.3.2Matrixprodu
7、ctsusingMaple291.4Thespanofasetofvectors331.5Systemsoflinearequationsrevisited391.6Linearindependence491.7Matrixalgebra581.7.1MatrixalgebrausingMaple621.8Theinverseofamatrix661.8.1Computergraphics701.8.2MatrixinversesusingMaple731.9Thedeterminantofamatrix781.9.1Determ
8、inantsusingMaple821.10Theeigenvalueproblem841.10.1Markovchains,eigenvectors,andGoogle931.10.2UsingMapletofindeigenvaluesandei
