systems of ordinary differential equations

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1、SystemsofOrdinaryDifferential6Equations6.1ReviewofMatrixAlgebraandCalculusBecauseoftheirimportanceinthestudyofsystemsoflinearequations,wenowreviewmatricesandtheoperationsassociatedwiththem.6.1.1DefiningNestedLists,Matrices,andVectorsInMathematica,amatrixisalistoflistswhereeachlistrepresentsaro

2、wofthematrix.Therefore,themnmatrix*++a11a12a13a1n-..++++a21a22a23a2n....A++++a31a32a33a3n.....++..++..,am1am2am3amn/isenteredwithA={{a11,a12,...,a1n},{a21,a22,...,a2n},...,{am1,am2,...amn}}.Forexample,touseMathematicatodefinemtobethematrixa11a12Aenterthecommanda21a22m={{a11,a12},{a21,

3、a22}}.Thecommandm=Array[a,{2,2}]producesaresultequivalenttothis.OnceamatrixAhasbeenentered,itcanbeviewedinthetraditionalrow-and-column411412Chapter6SystemsofOrdinaryDifferentialEquationsAswhenusingformusingthecommandMatrixForm[A].Youcanquicklyconstruct22TableForm,theresultofmatricesbyclickin

4、gonthebuttonfromtheBasicTypesettingpalette,whichusingMatrixFormisnolongeralistthatcanbeisaccessedbygoingtoFileundertheMathematicamenu,followedbyPalettesmanipulatedusingandthenBasicTypesetting.Mathematicacommands.UseMatrixFormtoviewamatrixintraditionalrow-and-columnform.Donotattempttoperformma

5、trixoperationsonaMatrixFormobject.Alternatively,youcanconstructmatricesofanydimensionbygoingtotheMath-ematicamenuunderInputandselectingCreateTable/Matrix/Palette...6.1ReviewofMatrixAlgebraandCalculus413Theresultingpop-upwindowallowsyoutocreatetables,matrices,andpalettes.Tocreateamatrix,select

6、Matrix,enterthenumberofrowsandcolumnsofthematrix,andselectanyotheroptions.PressingtheOKbuttonplacesthedesiredmatrixatthepositionofthecursorintheMathematicanotebook.*++a11a12a13-..EXAMPLE6.1.1:UseMathematicatodefinethematrices++++a22a22a23....,a31a32a33/b11b12b13b14and.b21b22b23b24SOLUTION:In

7、thiscase,bothTableai,j,i,1,3,j,1,3andArray[a,{3,3}]produceequivalentresultswhenwedefinematrixatobethematrix*++a11a12a13-..++++a22a22a23.....,a31a32a33/ThecommandsMatrixFormorTableFormareusedtodisplaytheresultsintraditionalmatrixform.In[1