Differential and Integral Calculus(高数)

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1、DifferentialandIntegralCalculusCourseContentandBasicRequirementsCoursecontents:Limitsandcontinuity;thecalculusoffunctionsofonevariable;ordinarydifferentialequation;vectoralgebraandanalyticgeometryofspace;multi-functioncalculus;infiniteseries.(II)CourseteachingcontentandKnowle

2、dgePartArrangement1.KnowledgeUnitOne:TheFunction&TheLimit(15hours)(1)Knowledgepoint1:Mappingandmapping(2)Knowledgepoint2:Thelimitofseries(3)Knowledgepoint3:Thelimitoffunction(4)Knowledgepoint4:InfinitesimalandInfinite(5)knowledgepoint5:Thelimitalgorithm(6)Knowledgepoint6:Limi

3、texistingcriteriaTwoimportantlimits(7)Knowledgepoint7:ComparisonofInfinitesimals(8)knowledgepoint8:Continuityanddiscontinuouspointofthefunction(9)knowledgepoint9:Operationpropertiesofcontinuousfunction&Continuityofelementaryfunctions(10)knowledgepoints10:Propertyofcontinuousf

4、unctiononclosedinterval2.KnowledgeUnitTwo:DerivativeandDifferential(10hours)(1)Knowledgepoint1:TheconceptofDerivative(2)Knowledgepoint2:Derivativeruleofthefunction(3)Knowledgepoint3:Derivativeofhigherorder(4)Knowledgepoint4:ThederivativeofthefunctiondeterminedbyImplicitfuncti

5、onsandParametricequation(5)Knowledgepoint5:Differentialofthefunction3.KnowledgeUnitThree:DifferentialMeanValueTheoremandtheApplicationsofDerivatives(10hours)(1)Knowledgepoint1:DifferentialMeanValueTheorem(2)Knowledgepoint2:HospitalRule(3)Knowledgepoint3:TaylorFormula(4)Knowle

6、dgepoint4:MonotonicityandConcavityofthefunction(5)Knowledgepoint5:Extremum,MaximumandMinimumofthefunction(6)Knowledgepoint6:Delineationoffunctiongraphic(7)Knowledgepoint7:Curvature4.KnowledgeUnitFour:IndefiniteIntegral(hours10)(1)Knowledgepoint1:ConceptsandPropertiesoftheInde

7、finiteIntegral(2)knowledgepoint2:IntegralbySubstitution(3)Knowledgepoint3:IntegralbyParts(4)knowledgepoint4:IntegrationofRationalFunction5.KnowledgeUnitFive:Definiteintegral(10hours)(1)Knowledgepoint1:ConceptsandPropertiesoftheDefiniteIntegral(2)knowledgepoint2:FundamentalThe

8、oremofCalculus(3)Knowledgepoint3:IntegralbySubstitutionandIntegralby