17-线性代数2 教学大纲（英文版）.docx

Sy11abusof1inearA1gebraIICourseName:1ineara1gebraIICourseCode：Credits：2Tota1CreditHours：321ectureHours：32ExperimentHours：OProgrammingHours：0PracticeHours：0Tota1NumberofExperimenta1(Programming)Projects0Where,Compu1sory(O),Optiona1(0).Schoo1：Schoo1ofScienceTargetMajor：bio1ogica1engineering,foodscienceandengineering,chemistryengineering,medicineandbusinessI、CourseNature&AimsThiscourseisdesignedforthosestudentswithmajorsinbio1ogica1engineering,foodscienceandengineering,chemistryengineering,medicineandbusinessmajor.Thisisatheoreticcourse.Theaimsofthiscourseistohe1pstudentstograspthebasictheoryconcerning1ineara1gebra,deve1optheirabi1ityincomputing,thinkingbasedonabstractconcepts,reasoningby1ogica1,andmode1ingby1ineara1gebra.U、CourseObjectives1. Mora1EducationandCharacterCu1tivation.Bythiscourse,thestudentswi11Ieambasictheoryandapp1icationsof1ineara1gebra,theywi11getacomprehensiveunderstandingtothemethodsandideasof1ineara1gebra,anddeve1optheabi1ityofusing1ineara1gebratoso1vesomepractica1prob1emfromengineeringandsocia1science.Bytheintroductionofsomebackgroundoftheconceptsandexamp1esconcerningtheapp1icationof1ineara1gebra,thestudentswi11deve1op1otsofgoodhabitssuchasthinking1ikeascientist,workingwithhardwi11,so1vingprob1emscreative1y,etc.Bythiscourse,thestudentswi11knowsomefamousworksofChineseancientmathematicians.2. CourseObjectivesThroughthestudyofthiscourse,students'qua1ities,ski11s,know1edgeandabi1itiesobtainedareasfo11ows：Objective1.By(hiscourse,studentswi11Ieam(hebasicknow1edgeanddeve1opbasicca1cu1ationski11sabout1ineara1gebra.(CorrespondingtoChapter1-4,supportingforgraduationrequirementsindex2,3)Objective2.Thiscoursewi11he1pstudentstodeve1opabi1ityinabstractthinking,spacia1imaginationand1ogica1reasoning.(CorrespondingtoChapter1-4,supportingforgraduationrequirementsindex2,3)Objective3.Thiscoursewi11he1pstudentstodeve1opsomeski11sofusingwhatthey1earninthiscoursetoso1vesomeprob1emsfromdifferentfie1ds.(CorrespondingtoChapter1-4,supportingforgraduationrequirementsindex2,3)3. SupportingforGraduationRequirementsThegraduationrequirementssupportedbycourseobjectivesaremain1yref1ectedinthegraduationrequirementsindices2,3,asfo11ows:SupportingforGraduationRequirementsCourseObjectivesGraduationRequirementsIndicesandContentsSupportingforGraduationRequirementsTeachingTopics1eve1ofSupportIndicesContentsObjective1Graspspecia1know1edgeformajorIndex2Cangraspa11themathematica1know1edgethatwi11beusedinmajorcoursesChapter1-4HObjective2,3Graspspecia1methodsforresearchandso1vingspecia1prob1emsIndex3Canusemathematica1theoryandmethodstoso1vere1atedprob1emsinprofessiona1fie1dChapter1-4MHI、BasicCourseContentChapter 1 Matricesand1inearequations(supportingcourseobjectives1,2,3)1.1 Definitionofmatrices1.2 Inversematricesanddeterminants1.3 Propertiesandca1cu1ationsofdeteninants1.4 E1ementarytransformationsofmatrices1.5 Rankofmatrixand1inearequations1.6 B1ockmatrices1.7 *Examp1esofmatrixapp1icationsTeachingRequirements:Throughtheteachingofthischapter,Ieamthebasictheoryofmatrix,determinantand1inearequations.Studentsarerequiredtounderstandtheconceptofmatrixandmastertheoperationsofmatrix;understandtheinductivedefinitionofn-orderdeterminants,andbeab1etoski11fu11yusethepropertiesofdeterminantsandCramer'sru1e:understandtheconceptofinversematricesandmasterthemethodofseekinginversematriceswithadjointmatrices;understandtheoperationofb1ockmatrix;understandandmasterthee1ementarytransformationofmatrixanditsre1ationshipwithmatrixmu1tip1ication;understandtheconceptandapp1icationofmatrixrank;masterthemethodofseekingtherankandtheinverseofamatrixandso1ving1inearequationswithe1ementarytransformation.Through1earning,studentsshou1dhavemoreproficientcomputingski11sandabstractthinkingski11s.KeyPoints:propertiesofdeterminantsandtheirapp1ications,matrix'soperationsande1ementaryIransfbrmaiions,and(herankofmatrixandi(sapp1icationsDifficu1tPoints：Comprehensiveuseofmatrixanddeteninanttheorytoso1ve1inearequationsChapter 2 Vectorsand1inearequations(supportingcourseobjectives1,2,3)2.1 Vectorgroupsandtheir1inear1ydependent2.2 Vectorspace2.3 Struciureoftheso1utionof1inearequations2.4 *App1icationsTeachingRequirements:Throughtheteachingof(hischapter,Ieamthebasictheoryofvectorspaceanditsapp1icationin1inearequations.Studentsarerequiredtounderstandandmasterthe1inearoperationofvectors;understandtheconceptsof1inear1ydependentand1inear1yindependentofvectorgroups,andunderstandthere1evantimportantconc1usions;understandtheconceptsofmaxima11inear1yindependentfami1yofaco11ectionofvectorsandtherankofvectorgroup;usethee1ementarytransformationmethodtoseektherankofthevectorgroupandthemaxima11inear1yindependentfami1y;understandandmasterthere1atedconceptsoftheso1utionofthe1inearequationssuchasso1ution,genera1so1ution,specia1so1ution,basicso1utionsystem,etc.,master(hemethodofusing(hevectorspacetheorytostudythe1inearequationsanditsso1utionspace.Through1earnin