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1、HigherMathematics第一章函數(shù)與極限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補(bǔ)集complementset直積directproduct笛卡兒積Cartesianproduct開區(qū)間openinterval閉區(qū)間closedinterval半開區(qū)間halfopeninterval有限區(qū)間finiteinterval區(qū)間的長(zhǎng)度lengthofaninterval無限區(qū)間infiniteinterval領(lǐng)域
2、neighborhood領(lǐng)域的中心centreofaneighborhood領(lǐng)域的半徑radiusofaneighborhood左領(lǐng)域leftneighborhood右領(lǐng)域rightneighborhood映射mappingX到Y(jié)的映射mappingofXontoY滿射surjection單射injection一一映射one-to-onemapping雙射bijection算子operator變化transformation函數(shù)function逆映射inversemapping復(fù)合映射compositemapping自變量independentvariable因變量dependent
3、variable定義域domain函數(shù)值valueoffunction函數(shù)關(guān)系functionrelation值域range自然定義域naturaldomain單值函數(shù)singlevaluedfunction多值函數(shù)multiplevaluedfunction單值分支one-valuedbranch函數(shù)圖形graphofafunction絕對(duì)值函數(shù)absolutevalue符號(hào)函數(shù)sighfunction整數(shù)部分integralpart階梯曲線stepcurve當(dāng)且僅當(dāng)ifandonlyif(iff)分段函數(shù)piecewisefunction上界upperbound下界lowerbo
4、und有界boundedness無界unbounded函數(shù)的單調(diào)性monotonicityofafunction單調(diào)增加的increasing單調(diào)減少的decreasing單調(diào)函數(shù)monotonefunction函數(shù)的奇偶性parity(odevity)ofafunction對(duì)稱symmetry偶函數(shù)evenfunction奇函數(shù)oddfunction函數(shù)的周期性periodicityofafunction周期period反函數(shù)inversefunction直接函數(shù)directfunction復(fù)合函數(shù)compositefunction中間變量intermediatevariable函
5、數(shù)的運(yùn)算operationoffunction基本初等函數(shù)basicelementaryfunction初等函數(shù)elementaryfunction冪函數(shù)powerfunction指數(shù)函數(shù)exponentialfunction對(duì)數(shù)函數(shù)logarithmicfunction三角函數(shù)trigonometricfunction反三角函數(shù)inversetrigonometricfunction常數(shù)函數(shù)constantfunction雙曲函數(shù)hyperbolicfunction雙曲正弦hyperbolicsine雙曲余弦hyperboliccosine雙曲正切hyperbolictangent
6、反雙曲正弦inversehyperbolicsine反雙曲余弦inversehyperboliccosine反雙曲正切inversehyperbolictangent極限limit數(shù)列sequenceofnumber收斂convergence收斂于aconvergetoa發(fā)散divergent極限的唯一性u(píng)niquenessoflimits收斂數(shù)列的有界性boundednessofaconvergentsequence子列subsequence函數(shù)的極限limitsoffunctions函數(shù)當(dāng)x趨于x0時(shí)的極限limitoffunctionsasxapproachesx0左極限lef
7、tlimit右極限r(nóng)ightlimit單側(cè)極限one-sidedlimits水平漸近線horizontalasymptote無窮小infinitesimal無窮大infinity鉛直漸近線verticalasymptote夾逼準(zhǔn)則squeezerule單調(diào)數(shù)列monotonicsequence高階無窮小infinitesimalofhigherorder低階無窮小infinitesimaloflowerorder同階無窮小infinitesimalofth
