资源描述：
《含数学分析和高等代数两门课（two courses including mathematical analysis and advanced algebra）》由会员上传分享，免费在线阅读，更多相关内容在教育资源-天天文库。
1、含数学分析和高等代数两门课（Twocoursesincludingmathematicalanalysisandadvancedalgebra）WithmathematicalanalysisandhigheralgebratwocoursesMathematicalanalysis(I)(1)setandfunctionThereal,absolutevalueinequality,intervalandneighborhood,boundedsets,supremumprinciple,functionconcept
2、.(2)limitSeries.EMBEDEquation.3definesthelimitofnumbersequence.Thenatureofaconvergentsequence:uniqueness,boundedness,Paul,inequality,forcedconvergence,rationaloperation.Subcolumn.Theexistenceofsequencelimitcondition;monotoneconvergenceprincipletheorem,Cauchyco..E
3、MBEDEquation.3,STOLZtheorem.(3)thelimitoffunctionTheconceptoffunctionlimit(EMBEDEquation.3.Instantaneouslimitfunction.EMBEDEquation.3,EMBEDEquation.3)definitiondefinedthenatureofthelimitfunction:uniqueness,boundedness,localsignpreserving,inequalityproperties,forc
4、ingconvergence,rationaloperation.Theconditionsfortheexistenceofthelimitoffunction:theconclusionprinciple,Cauchycriterion.Twoimportantlimits:EMBEDEquation.3Comparisonofinfinitesimalandinfinityandorder.(4)continuityoffunctionThecontinuityoffunctions.Unilateralconti
5、nuity.Breakpointandclassification.Inthecontinuousfunctionontheinterval.Thelocalpropertiesofcontinuousfunctions:boundedness,Paul,continuousfunctionoftherationaloperation,compositefunctioncontinuity.Propertiesofcontinuousfunctionsonclosedinterval:boundedness,obtain
6、themaximumandminimumvalues,value,consistency.Thecontinuityofelementaryfunction.(5)limitandcontinuity(Continued)Thebasictheoremofcompleteness:intervaltheorem,Cauchyseriesconvergencecriterion,accumulationprinciple,compactnesstheorem,finitecoveringtheorem,thefundame
7、ntaltheoremofequivalenceofcompleteness.Closedintervalcontinuousfunctiondescription.Therealnumbersystem.Compressionmappingprinciple.(6)derivativeanddifferentialTheintroductionoftheproblem(problemtangentproblemandtheinstantaneousspeed).Thedefinitionofderivative.Uni
8、lateralderivative.Guidefunction.Thegeometricmeaningofderivative.Derivative,andproduct,business.Derivativeofinversefunction.Derivativeofacompoundfunction.Theder
