数学分析英文词汇文档格式.docx

1、product积quotient商numberaxis/numberline数轴closeness封闭性Archimedeanproperty阿基米德性质density稠密行upperandlowerboundsboundedsetunboundedsetexistencedomiansupremuminfimumorder-completesetcompletenessofrealnumberscompleteorderedfieldaxiomofcompletenessDedekindcutDedekindpropertyconstantandvariablequantitiesdefin

2、itionoffunctiondomainrangeindependentvariabledependentvariableintermediatevariableelementaryfunctionconstantfunctionpowerfunctionexponentialfunctionlogarithmicfunctiontrigonometricfunctioninversetrigonometricfunctioncompoundfunctionmappinginversemappingimageprimaryimagepiecewisefunction上界和下界有界集无界集存在

3、域上确界下确界有序完备集实数的完备性全序域完备性公理戴德金分割戴德金性质常量与变量函数的定义域定义域值域自变量因变量中间量初等函数常量函数幂函数指数函数对数函数三角函数反三角函数复合函数映射逆映射像原像分段函数signfunction符号函数Dirichletfunction狄利克雷函数Riemannfunction黎曼函数boundedfunction有界函数monotonefunction单调函数monotoneincreasingfunction单调增函数strictlymonotonefunction严格单调函数odd（even）function奇函数偶函数minimalpositiv

4、eperiod最小正周期absolutevaluefunction绝对值函数identityfunction恒等函数polynomialfunction多项式函数linearfunction线性函数quadraticfunction二次函数rationalfunction有理函数hyperbolicsine双曲正弦hyperboliccosine双曲余弦trigonometricidentity三角恒等式odd-evenidentity奇偶恒等式cofunctionidentity余函数恒等式Pythagoreanidentity毕达哥拉斯恒等式half-angleidentity半角恒等式p

5、roductidentity积恒等式sumidentity和恒等式additionidentity加法恒等式double-angleidentity倍角恒等式第二章数列极限limitofsequence数列极限divergentsequence发散数列infinitesimalsequence无穷小数列convergentsequence收敛数列uniquenesstheorem唯一性定理boundednesstheorem有界性定理inheritingorderproperties保序性inheritinginequality保不等式subsequence子列strictlyincreasi

6、ng严格递增monotoneincreasingsequence单调递增序列monotonedecreasingsequence单调递减序列necessarycondition必要条件sufficientcondition充分条件squeezeprinciple夹逼定理Cauchyconvergencecriterion柯西收敛准那么第三章函数极限limitoffunction函数极限infinitelimit无穷极限one-sidedlimit单侧极限right（left）limit/right（left）handlimit右左极限propertyoflimitoffunction函数极限的

7、性质localboundedness局部有界性Heinetheorem海涅定理infinity无穷大量orderofinfinitesimal无穷小量的阶infinitesimalofhigher（lower）order高低阶无穷小量infinitesimalofsameorder同阶无穷小量equivalentinfinitesimal等价无穷小量k-orderinfinitesimalk-阶无穷小量verticalasymptote垂直渐近线obliqueasymptote斜渐进线horizontalasymptote水平渐近线第四章函数的连续性incrementofindependent

8、variable自变量的增量incrementoffunction函数的增量right（left）continuous右（左）连续discontinuitypointanditsclassification间断点及其分类removablediscontinuity可去间断点jumpdiscontinuity跳跃间断点discontinuityofthefirstkind第一类间断点discontinuityofthesecondkind第二类间断点localpropertiesofcontinuousfunction连续函数的局部性质compositionpropertiesofcontinu

9、ousfunction连续函数的复合性质propertiesofcontinuousfunctionoverclosed闭区间上连续函数的性质intervalextremevaluetheorem极值定理maximumandminimumvaluetheorem最大值和最小值定理intermediatevaluetheorem介值性定理zero-pointtheorem零点定理uniformcontinuitytheorem一致连续定理continuityofinversefunction反函数的连续性localinheritingorderproperty局部保号性continuityofe

10、lementaryfunction初等函数的连续性第五章导数和微分finiteincrementformula有限增量公式rateofchange变化率differencequotient差商left（right）derivative左右导数derivativefunction导函数derivablefunction可导函数geometricmeaningofderivative导数的集合意义Fermattheorem费马定理Darbouxtheorem达布定理intermediatevaluetheoremofderivative导函function数的介值定理algebraofderiva

11、tives导数的四那么运算derivativeofsum和的导数derivativesofdifference差的导数derivativeofproduct积的导数derivativeofquotient商的导数derivativeofinversefunction反函数的导数maximumvalue最大值minimumvalue最小值derivativeofcompositefunction复合函数的导数logarithmicderivative对数求导法parametricequationofcircle圆的参数方程parametricequationofellipse椭圆的参数方程par

12、ametricequationofcycloid摆线的参数方程parametricequationofasteroid星形线的参数方程secondderivative二阶导数thirdderivative三阶导数n-thderivativen阶导数Leibnizformula莱布尼茨公式acceleration加速度physicalinterpretation物理解释conceptofdifferential微分的概念differentiablefunction可微函数linearprincipalpart线性主部differentialofindependentvariable自变量的微分o

13、perationalrulesofdifferential微分的运算法那么invarianceofdifferentialform微分形式的不变性geometricmeaningofdifferential微分的几何意义higher-orderdifferential高阶微分第六章微分中值定理Rollemeanvaluetheorem罗尔中值定理Lagrangemeanvaluetheorem拉格朗日中值定理Cauchymeanvaluetheorem柯西中值定理Taylortheorem泰勒定理LHospitalrule洛必达法那么limitofindeterminateformoftype

14、0/00/0型不定式极限indeterminateformoftype/型不定式otherindeterminateforms 其他类型不定式TaylorformulawithPeanoremainder 带有皮亚诺型余项的泰勒公式Taylorcoefficient 泰勒系数Taylorpolynomial 泰勒多项式remainderofTaylorformula 带有拉格朗日型余项的泰勒公式TaylorformulawithLagrangeremainder带有拉格朗日型余项的麦克劳林公式extremevalueoffunction 函数的极值testofextremevalue 极值判断

15、thefirstsufficientconditionofextremevalue极值的第一充分条件convexityandinflectionpointoffunction函数的凸性和拐点convexfunction凸函数concavefunction凹函数strictlyconvexfunction严格凸函数strictlyconcavefunction严格凹函数Jensoninequality琴生不等式第七章实数的完备性fundamentaltheoremsofcompleteness实数in击the完set备性的根本定理ofrealnumbersnestedintervaltheore

16、mCauchyconvergencecriterionaccumulationtheoremfinitecoveringtheoremupperandlowerlimits闭区间套定理柯西收敛准着聚点定理有限覆盖定理上极限和下极限第八章不定积分indefiniteintegralprimitivefunctionintegrandfunctionintegralsignexpressionofintegrand不定积分原函数被积函数积分符号积分表达式integralconstant积分常数tableofbasicintegrals根本积分表geometricmeaningofindefinit

17、e不定积分的几何意义integralcurve积分曲线initialcondition初始条件integrationbyparts分部积分法integrationbysubstitutions换元积分法formulaofsubstitutionofthefirstkind第一换元公式indefiniteintegralofrationalfunction有理函数的不定积分properfraction真分式improperfraction假分式decompositionintopartialfractions局部分式分解methodofunderminedcoefficients待定系数法第九章

18、定积分definiteintegral定积分curvilineartrapezoid曲边梯形dividing/partition分割norm/modulus模Riemannsum黎曼和Riemannintegral黎曼积分integrabilityinthesenseofRiemann黎曼可积intervalofintegration积分区间upperandlowerlimits上限和下限geometricmeaningofdefiniteintegral定积分的几何意义uppersum上和lowersum下和Darbouxuppersum达布上和Darbouxlowersum达布下和Newt

19、on-Leibnizformula牛顿-莱布尼茨公式necessaryconditionforintegrability可积的必要条件necessaryandsufficientconditionsfor可integrability积的充要条件integrablefunctionclass可积函数类linearpropertyofdefiniteintegral定积分的线性性质additivewithrespecttointegralinterval/additivity积分区间的可加性overintegralintervalmeanvaluetheoremofintegral积分中值定理av

20、eragevalue平均值integralwithvariantupperlimit变上限积分existenceofprimitivefunction原函数的存在性integrationbysubstitutionintegralformofreminderofTaylorformula泰勒公式的积分类型第十章定积分的应用areaofplanefigure平面图形的面积methodoffindingvolumeofasolidfromthe由平行截面面积求体积的knowsareaofparallelsections 方法arclengthandcurvatureofplanecurve 平面的

21、曲线的弧长与曲率smoothcurve 光滑曲线differentialofarc 弧微分circleofcurvature 曲率圆radiusofcurvature 曲率半径areaofrevolutionsurface 旋转曲面的面积someapplicationsofdefiniteintegralin定physics积分在物理中的某些应用gravitation引力work功approximatecomputationofdefiniteintegral定积分的近似计算trapezoidalmethod梯形法parabolamethod抛物线法第十一章反常积分notionofimprop

22、erintegral反常积分的概念improperintegraloninfiniteinterval无穷区间上的反常积分improperintegralofunboundedfunction无界函数的反常积分propertyofinfiniteintegralandtestof无穷积分的性质和收敛判Fourierseriesofevenandoddfunctions奇函数与偶函数的傅立叶级数amplitude振幅sineseries正弦级数cosineseries余弦级数periodicextension周期延拓第十六章多元函数的极限与连续functionsofseveralvariable

23、s多元函数planepointset平面点集coordinateplane坐标平面interiorpoint内点outerpoint外点boundarypoint界点boundary边点isolatedpoint孤立点openset开集closedset闭集connectedness连通性connectedopenset连通开集opendomain（region）开域closeddomain（region）闭域boundedpointset有界点集unboundedpointset无界点集nestedcloseddomaintheorem闭域套定理functionoftwovariables二

24、元函数n-dimensionalvectorspacen-维向量空间improperlimit非正常极限doublelimit二重极限propertiesofcontinuousfunctionsonbounded有界闭区域上连续函数的closedregion性质repeatedlimits累次极限totalincrement全增量partialincrement偏增量第十七章多元函数微分学totaldifferential全微分partialderivative偏导数continuouslydifferentiate连续可微tangentplaneofsurface曲面的切平面normalp

25、laneofcurve曲线的法平面differentiationofcompositefunction复合函数微分法chainruleforfunctionsofseveralvariables多元函数的链式法那么invarianceofdifferentialformoffirstorder一阶微分形式的不变性directionalderivativeandgradient方向导数与梯度differentiability可微性Taylorformula泰勒公式problemofextremevalue极值问题partialderivativeofhigherorder高阶偏导数mixedpa

26、rtialderivative混合偏导数第十八章隐函数定理及其应用existenceanduniquenesstheoremofimplicit隐函数存在唯一性定理functionssystemofimplicitfunctions 隐函数组functionaldeterminant（Jacobiandeterminant）函数行列式雅可比行列式systemofinversefunctions 反函数组coordinatetransformation 坐标变换geometricalapplication 几何应用tangentlineandnormallineofplanecurve平面曲线的

27、切线与法线tangentlineandnormalplaneofspace空curve间曲线的切线与法平面conditionalextremum条件极值Lagrangemultipliermethod拉格朗日乘数法第十九章含参变量积分properintegralwithparameter含参量的正常积分improperintegralwithparameter含参量的反常积分EulerintegralWeierstrasstestDicichlettestimproperintegralwithinfiniteboundimproperintegralwithunboundedGammafunctionBetafunction欧拉积分魏尔斯特拉判别法狄利克雷判别法无穷限的反常积分无界函数的反常积分第二十章innerareaouterareacylindricalbodywithtipsurfacefinenessintegralregiondoubleintegralx-typeregiony-typeregion内面积外面积曲顶柱体细度积分区域二重积分x型区域y型区域tripleintegralchangeofvariable