線性代數(shù)課程雙語(yǔ)教學(xué)大綱

線性代數(shù)課程雙語(yǔ)教學(xué)大綱一、課程的性質(zhì)、目的與任務(wù)1．課程性質(zhì)線性代數(shù)是高等院校本科各專(zhuān)業(yè)的一門(mén)重要的基礎(chǔ)理論課。由于線性問(wèn)題廣泛存在于科學(xué)技術(shù)的各個(gè)領(lǐng)域，而某些非線性問(wèn)題在一定的條件下可以轉(zhuǎn)化為線性問(wèn)題，因此本課程介紹的方法廣泛地應(yīng)用于各個(gè)學(xué)科。尤其在計(jì)算機(jī)日益普及的今天，該課程的地位和作用更顯得重要。2．課程目的與任務(wù)通過(guò)教學(xué)，一使學(xué)生掌握該課程的基本理論與方法，培養(yǎng)解決實(shí)際問(wèn)題的能力，并為學(xué)習(xí)相關(guān)課程及進(jìn)一步擴(kuò)大數(shù)學(xué)知識(shí)面奠定必要的數(shù)學(xué)基礎(chǔ)。二是以外語(yǔ)作為手段，通過(guò)雙語(yǔ)授課學(xué)習(xí)本學(xué)科領(lǐng)域的前沿知識(shí)，借此加深受教育者對(duì)專(zhuān)業(yè)課程的認(rèn)知與學(xué)習(xí)，逐步使其具備國(guó)際交流與合作能力，實(shí)現(xiàn)綜合素質(zhì)的提高。二、教學(xué)內(nèi)容及要求MatricesAlgebra【TeachingContent】Matrix;Linearcalculatorofmatrix;Multiplicationofmatrix;Transposeofmatrix;Inverseofmatrix;Partitionedmatrix.【TeachingRequest】Understandingtheconceptionofmatrix;Knowingidentitymatrix、symmetricmatrix、diagonalmatrix、uppertriangularandlowertriangular’sproperties.Masteringmatrix’slinearcalculator,multiplicationcalculator,transposeofmatrixandtheirproperties;Understandingtheconceptionofinversematrix.Knowingingpartitionedmatrixanditscalculator.【TheKeyPoints】Calculatorofmatrix;Theconceptionofinversematrix.【TheDifficultyPoints】matrix’smultiplication;theconceptionofinverse;Partitionedmatrix.【DepthandBreadth】Understandingtheconceptionofmatrix;Masteringmatrix’scalculator;Knowingpartitionedmatrixanditscalculator.DeterminantandCramer’sruleTeachingContent】Theconceptionofdeterminantanditsproperties;Determinantofsquarematrix‘smultiplication;Adjointofmatrix;Theexpansionofdeterminantbyroworcolumn;Cramer’sruleoflinearequation.TeachingRequest】Understandingdeterminant;Masteringthepropertiesofdeterminant;Calculatordeterminantbypropertiesandtheexpansionofdeterminant;Knowingthedeterminantofsquarematrix’smultiplication.Understandingadjointofmatrix’sconception;Cansolveinversebyadjointofmatrix.KnowingCramer’srule.【TheKeyPoints】Determinant’spropertiesandcalculator.【TheDifficultyPoints】Determinant’sproperties.【Depthandbreadth】Understandingdeterminant;Masteringdeterminant’spropertiesandcalculator;KnowingCramer’srule.Chaper3RankofMatrixandSolutionofLinearEquationTeachingContent】Elementaryoperationsofmatrix;Elementarymatrix；equivalentofmatrix；Rankofmatrix;Thewaytosolvetherankofmatrixandinversebyelementaryoperations;Theoremoflinearequationhassolution.TeachingRequest】Masteringelementaryoperationsofmatrix;Understandingelementarymatrix、equivalentofmatrixandrankofmatrix;Masteringthewaytosolvetherankofmatrixandinversebyelementaryoperations.Understandingfullessentialconditionofhomogeneouslinearequationshasnonzerosolutionandnon-homogeneouslinearequationshassolution.【theKeyPoints】Rankofmatrix;Thewaytosolvetherankofmatrixandinversematrixbyelementaryoperations;Equivalentofmatrix;Elementaryoperationsandelementarymatrix;Theoremoflinearequationhassolution)【TheDifficultyPoints】Eementarymatrix.【Depthandbreadth】Masteringinversematrixandfullessentialconditionofinvertible;Masteringsolvetherankofmatrixandinversematrixbyelementaryoperations.Chapter4VectorandtheStructureofSolutionsTeachingContent】Vectorspace;Linearcombinationandlinearrepresentedofvector;Lineardependenceandindependenceofvectors;Themaximallinearlyindependentcollectionofvectors;Equalofvectorcollection;Rankofvectorcollection;Thepropertiesandstructureofsolution;Thebasisforsolutionsofsystemandsolutions;Solutionvector;Thewaytosolvethesolutionoflinearequationsbyelementaryrow’soperation.TeachingRequest】Understandingn-dimensionvector;linearcombinationandlinearrepresentedofvectors.Understandingthedefinitionoflineardependentandindependentofvectorcollection;Knowingthepropertiesandthewaytodeterminethevectorcollectionarelineardependenceorindependence.Masteringthemaximallinearlyindependentcollectionofvectorandrankofvectors;Solvemaximallinearlyindependentcollectionofvectorandtherankofvectors.Knowingtheconceptionofvectorcollection’sequal;Understandingtherelationsbetweenvectorcollection’srankandmatrix’srank..5..Knowingtheconceptionofn-dimensionvector;subspace;basis;dimension.Understandingthebasisforsolutionsofsystem,solutionsandsolutionvectorofhomogeneouslinearequations.Understandingthestructureofsolutionandsolutionsofnon-homogeneouslinearequations.Masteringthewaytosolvethesolutionoflinearequationsbyelementaryrow’soperation.【TheKeyPoints】Lineardependenceandindependenceofvectors;Themaximallinearlyindependentcollectionandtherankofvectors;Thewaytosolvethesolutionoflinearequationsbyelementaryrow’soperation.【theDifficultyPoint】sTheconceptionofvectorspace;Lineardependenceandindependenceofvectors;Solutionspaceandthebasisforsolutionsofsystem.【Depthandbreadth】Understandingn-dimensionvector;Masteringlineardependenceandindependenceofvectors;Cansolvemaximallinearlyindependentcollectionofvectorandtherankofvectors.Chapter5Eigenvalues、EigenvectorsandQuadraticForms【TeachingContent】Eigenvalesandeigenvectorsofmatrix;Innerproduct;FormlinearindependencetoorthogonalbyGran-Schmidtmethod;Orthogonalbasis;Similartransformationandsimilarmatrix’sconceptionandproperties;Fullessentialconditionofdiagonaliza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