Syllabus-of-Advanced-Mathematics

SyllabusofAdvancedMathematicsNumberofcourseMath0000037NameofcourseAdvancedMathematicsFundamentalinformationofsubject1.CreditHours:8ClassHours:128(ClassHours:128LabClassHours:0)2.Property:Publicbasiccompulsorycourse3.Major:scienceandengineeringcategoryObject:SoftwareengineeringdepartmentandNetworkengineeringdepartmentfreshman4.Pre-Compulsorycourse:ElementaryMathematics5.Textbook:《Advancedmathematics》，publishingcompanyofNanjingUniversity,thefirsteditioninJulyof2009Thebackuptextbook:《Appliedmathematicstutorial》，publishingcompanyofHehaiUniversity,2008Reference:《Highervocationalmathematicscurriculum》，HigherEducationPress，2002《Advancedmathematics》，Highereducationpress,20056.Methodsofassessment:Usuallyresults:45%;Finalresults:55%7.Environment:ClassObjectivesandrequirementsObjectives:Aftercompletingthiscourseyoushouldbeableto:1.Presentanddescribethebasalmathematicsideaofunivariatecalculousandengineeringmathematics;2.Demonstratebasicmathematicalmethodstosolveactualproblemswithmathematicalidea3.Developabilitytoanalysismethodstosolveproblemswithabovemathematicalmethodsandidea4.Establishnecessarymathematicalfoundationforfurtherstudy5.HavecertainmathematicalmodelingideasRequirements:1.1.Learnfollowingbasicmathematicalconceptionandideasuchasinterval,neighborhood,function,limit,continuity,derivate,differential,extremumvalue,indefiniteintegral,definiteintegral,generalizedintegral,Differentialequation,Spacecartesiancoordinatesystem,spaceplane,sphericalsurface.2.Graspfollowingbasictheories,theorems,formulasandmethods:(1)propertiesandfiguresofbasicelementaryfunctions;(2)derivateformulasofelementaryfunctionsandmultivariatefunctions;(3)simplecalculationofindefiniteintegralanddefiniteintegralaboutelementaryfunctions(4)applylimit,derivateandintegralintodailylifeandeconomics(5)somemethodstosolvesimpledifferentialequation(6)figuresandequationsofsphericalsurfaceandspaceplaneClasscontentandClasshoursassignment1.Funtion,LimitandContinuity(18hours)(1)understandtheconceptionofintervalandfunction,grasptheexpressionmethodsoffunction.(2)knowtheparity,monotonicity,periodicpropertyandboundedness.(3)knowtheconceptionofcompositefunctionandsegmentationfunctionandestablishsimplefunctionrelationshiprepresentation.(4)knowtheconceptionoflimitandusefouroperationsrulesoflimit(5)knowtheconceptionofcontinuityanduselimittojudgmentcontinuity(6)grasppropertiesandfiguresofbasicelementaryfunctions2.Derivate(32hours)(1)understandtheconceptionofdeviateanditsgeometricmeaning.(2)usefouroperationsrulesofderivateandthemethodstogetthederivateofcompositefunction;graspthebasicderivateformulasofelementaryMathematics.(3)understandtheconceptionandmeaningofsecondderivativefunction.(4)knowtheconceptionofdifferentialandusederivatetocalculatedifferential.(5)graspHospitalLawandusethislawtocalculatesometypesoflimitsuchaszero/zerotypeorinfinity/infinitytype.(6)learntodistinguishthemonotonicityandconcavityoffunctionwiththederivate,andknowhowtoobtaintheextremumvalueswiththederivate.(7)understandtheconceptionofmarginfunctionandusederivatetosolveeconomicsproblems.3.Integral(32hours)(1)understandtheconceptionsofantiderivativeandindefiniteintegral.(2)mastersomebasicpropertiesofindefiniteintegral(3)understandtherelationshipbetweenderivativeandintegral(4)memorizebasicintegralformulasandusetheseformulastosolvesomesimpleindefiniteintegral.(5)graspthemethodsofchangeelementandintegrationbypartstosolvesomeindefiniteintegral.(6)knowthedefineandpropertiesofdefiniteintegral;understanditsgeometricmeaning.(7)graspNewton-Leibnizformulaandusethisformulatosolvesomesimpledefiniteintegral.(8)graspthemethodsofchangeelementandintegrationbypartstosolvesomedefiniteintegral.(9)knowgeneralizedintegraloninfiniteintervalandsolvesomesimplegeneralizedintegraloninfiniteinterval.4.Ordinarydifferentialequation(14hours)(1)knowsomebasicconceptionsofordinarydifferentialequationsuchasClasscontentandClasshoursassignmentorder,solution，specialsolution,generalsolution，initialconditions，initialvalueproblems；(2)graspmethodsofseparationofvariablesandvariationofconstanttosolvesomesimplefirst-orderdifferentialequation.(3)mastersolutiontosolvesecond-orderconstantcoefficientofvariationofhomogeneouslineardifferentialequations(notincludingcharacteristicequationsappearedcomplexrootssituation)5.Spaceanalyticgeometry(16hours)(1)understandspacecartesiancoordinatesystem.(2)calculatespacedistancebetweentwopoints.(3)knowfiguresandequationsofsphericalsurfaceandspaceplane.6.Multivariatefunctiondifferentialcalculus(16hours)(1)understandthedefinitionofbinaryfunction,calculatedomainofbinaryfunction,knowtheconceptionoflimitandcontinuityofbinaryfunction.(2)Understandtheconceptofpartialderivativeofbinaryfunction，masterthemethodtosolvefirst-orderandsecond-orderPartialderivative.(3)knowtheconceptionofcompletedifferentialofbinaryfunctionandcalculatecompletedifferentialofbinaryfunction.