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数学分析中的英语单词第一章realnumberanditsproperties实数及其性质rationalnumber有理数irrationalnumber无理数definition定义proposition命题plus加minus减multipliedby/times乘over/isto/dividedby除absolutevalueandinequality绝对值与不等式triangleinequality三角不等式inversetriangleinequality反三角不等式Bernoulliinequality伯努利不等式principlesofsupremumandinfimum确界原理openinterval开区间closedinterval闭区间semi-openinterval半开区间semi-closedinterval半闭区间finiteinterval有限区间infiniteinterval无限区间neighborhood领域deletedneighborhood去心邻域sum和difference差product积quotient商numberaxis/numberline数轴closeness封闭性Archimedeanproperty阿基米德性质density稠密行upperandlowerbounds上界和下界boundedset有界集unboundedset无界集existencedomian存在域supremum上确界infimum下确界order-completeset有序完备集completenessofrealnumbers实数的完备性completeorderedfield全序域axiomofcompleteness完备性公理Dedekindcut戴德金分割Dedekindproperty戴德金性质constantandvariablequantities常量与变量definitionoffunction函数的定义域domain定义域range值域independentvariable自变量dependentvariable因变量intermediatevariable中间量elementaryfunction初等函数constantfunction常量函数powerfunction幂函数exponentialfunction指数函数logarithmicfunction对数函数trigonometricfunction三角函数inversetrigonometricfunction反三角函数compoundfunction复合函数mapping映射inversemapping逆映射image像primaryimage原像piecewisefunction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）minimalpositiveperiod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productidentity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strictlyincreasing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柯西收敛准则第三章函数极限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incrementofindependentvariable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compositionpropertiesofcontinuousfunction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continuityofelementaryfunction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intermediatevaluetheoremofderivativefunction导函数的介值定理algebraofderivatives导数的四则运算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parametricequationofcycloid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operationalrulesofdifferential微分的运算法则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L’Hospitalrule洛必达法则limitofindeterminateformoftype0/00/0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fundamentaltheoremsofcompletenessintheset实数击完备性的基本定理ofrealnumbersnestedintervaltheorem闭区间套定理Cauchyconvergencecrite