higher mathematics

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1、HigherMathematics第一章函数与极限Chapter1FunctionandLimit集合set元素element子集subset空集emptyset并集union交集intersection差集differenceofset基本集basicset补集complementset直积directproduct笛卡儿积Cartesianproduct开区间openinterval闭区间closedinterval半开区间halfopeninterval有限区间finiteinterval

2、区间的长度lengthofaninterval无限区间infiniteinterval领域neighborhood领域的中心centreofaneighborhood领域的半径radiusofaneighborhood左领域leftneighborhood右领域rightneighborhood映射mappingX到Y的映射mappingofXontoY满射surjection单射injection一一映射one-to-onemapping双射bijection算子operator变化trans

3、formation函数function逆映射inversemapping复合映射compositemapping自变量independentvariable因变量dependentvariable定义域domain函数值valueoffunction函数关系functionrelation值域range自然定义域naturaldomain单值函数singlevaluedfunction多值函数multiplevaluedfunction单值分支one-valuedbranch函数图形grapho

4、fafunction绝对值函数absolutevalue符号函数sighfunction整数部分integralpart阶梯曲线stepcurve当且仅当ifandonlyif(iff)分段函数piecewisefunction上界upperbound下界lowerbound有界boundedness无界unbounded函数的单调性monotonicityofafunction单调增加的increasing单调减少的decreasing单调函数monotonefunction函数的奇偶性par

5、ity(odevity)ofafunction对称symmetry偶函数evenfunction奇函数oddfunction函数的周期性periodicityofafunction周期period反函数inversefunction直接函数directfunction复合函数compositefunction中间变量intermediatevariable函数的运算operationoffunction基本初等函数basicelementaryfunction初等函数elementaryfunc

6、tion幂函数powerfunction指数函数exponentialfunction对数函数logarithmicfunction三角函数trigonometricfunction反三角函数inversetrigonometricfunction常数函数constantfunction双曲函数hyperbolicfunction双曲正弦hyperbolicsine双曲余弦hyperboliccosine双曲正切hyperbolictangent反双曲正弦inversehyperbolicsin

7、e反双曲余弦inversehyperboliccosine反双曲正切inversehyperbolictangent极限limit数列sequenceofnumber收敛convergence收敛于aconvergetoa发散divergent极限的唯一性uniquenessoflimits收敛数列的有界性boundednessofaconvergentsequence子列subsequence函数的极限limitsoffunctions函数当x趋于x0时的极限limitoffunctionsa

8、sxapproachesx0左极限leftlimit右极限rightlimit单侧极限one-sidedlimits水平渐近线horizontalasymptote无穷小infinitesimal无穷大infinity铅直渐近线verticalasymptote夹逼准则squeezerule单调数列monotonicsequence高阶无穷小infinitesimalofhigherorder低阶无穷小infinitesimaloflowerorder同阶无穷小infinitesimalofth