微積分

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)間的長度lengthofaninterval

無限區(qū)間infiniteinterval

領(lǐng)域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mapping

X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dependentvariable

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

絕對值函數(shù)absolutevalue

符號函數(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lowerbound

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

函數(shù)的.運算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

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uniquenessoflimits

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時的極限limitoffunctionsasxapproachesx0

左極限leftlimit

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infinitesimalofthesameorder

等階無窮小equivalentinfinitesimal

函數(shù)的連續(xù)性continuityofafunction

增量increment

函數(shù)在x0連續(xù)thefunctioniscontinuousatx0

左連續(xù)leftcontinuous

右連續(xù)rightcontinuous

區(qū)間上的連續(xù)函數(shù)continuousfunction

函數(shù)在該區(qū)間上連續(xù)functioniscontinuousonaninterval

不連續(xù)點discontinuitypoint

第一類間斷點discontinuitypointofthefirstkind

第二類間斷點discontinuitypointofthesecondkind

初等函數(shù)的連續(xù)性continuityoftheelementaryfunctions

定義區(qū)間definedinterval

最大值globalmaximumvalue(absolutemaximum)

最小值globalminimumvalue(absoluteminimum)

零點定理thezeropointtheorem

介值定理intermediatevaluetheorem

第二章導(dǎo)數(shù)與微分

Chapter2DerivativeandDifferential

速度velocity

勻速運動uniformmotion

平均速度averagevelocity

瞬時速度instantaneousvelocity

圓的切線tangentlineofacircle

切線tangentline

切線的斜率slopeofthetangentline

位置函數(shù)positionfunction

導(dǎo)數(shù)derivative

可導(dǎo)derivable

函數(shù)的變化率問題problemofthechangerateofafunction

導(dǎo)函數(shù)derivedfunction

左導(dǎo)數(shù)left-handderivative

右導(dǎo)數(shù)right-handderivative

單側(cè)導(dǎo)數(shù)one-sidedderivatives

在閉區(qū)間【a,b】上可導(dǎo)isderivableontheclosedinterval[a,b]

切線方程tangentequation

角速度angularvelocity

成本函數(shù)costfunction

邊際成本marginalcost

鏈?zhǔn)椒▌tchainrule

隱函數(shù)implicitfunction

顯函數(shù)explicitfunction

二階函數(shù)secondderivative

三階導(dǎo)數(shù)thirdderivative

高階導(dǎo)數(shù)nthderivative

萊布尼茨公式Leibnizformula

對數(shù)求導(dǎo)法log-derivative

參數(shù)方程parametricequation

相關(guān)變化率correlativechangerata

微分differential

可微的differentiable

函數(shù)的微分differentialoffunction

自變量的微分differentialofindependentvariable

微商differentialquotient

間接測量誤差indirectmeasurementerror

絕對誤差absoluteerror

相對誤差relativeerror

第三章微分中值定理與導(dǎo)數(shù)的應(yīng)用

Chapter3MeanValueTheoremofDifferentialsandtheApplicationofDerivatives羅馬定理Rolle’stheorem

費馬引理Fermat’slemma

拉格朗日中值定理Lagrange’smeanvaluetheorem駐點stationarypoint

穩(wěn)定點stablepoint

臨界點criticalpoint

輔助函數(shù)auxiliaryfunction

拉格朗日中值公式Lagrange’smeanvalueformula柯西中值定理Cauchy’smeanvaluetheorem

洛必達(dá)法則L’Hospital’sRule

0/0型不定式indeterminateformoftype0/0

不定式indeterminateform

泰勒中值定理Taylor’smeanvaluetheorem

泰勒公式Taylorformula

余項remainderterm

拉格朗日余項Lagrangeremainderterm

麥克勞林公式Maclaurin’sformula

佩亞諾公式Peanoremainderterm

凹凸性concavity

凹向上的concaveupward,cancaveup

凹向下的，向上凸的concavedownward’concavedown拐點inflectionpoint

函數(shù)的極值extremumoffunction

極大值local(relative)maximum

最大值global(absolute)mximum

極小值local(relative)minimum

最小值global(absolute)minimum

目標(biāo)函數(shù)objectivefunction

曲率curvature

弧微分arcdifferential

平均曲率averagecurvature

曲率園circleofcurvature

曲率中心centerofcurvature

曲率半徑radiusofcurvature

漸屈線evolute

漸伸線involute

根的隔離isolationofroot

隔離區(qū)間isolationinterval

切線法tangentlinemethod

第四章不定積分

Chapter4IndefiniteIntegrals

原函數(shù)primitivefunction(antiderivative)

積分號signofintegration

被積函數(shù)integrand

代數(shù)部分

1.有關(guān)基本運算：

add,plus加

subtract減

difference差

multiply,times乘

product積

divide除

divisible可被整除的

dividedevenly被整除

dividend被除數(shù)

divisor因子，除數(shù)

quotient商

remainder余數(shù)

factorial階乘

power乘方

radicalsign,rootsign根號

roundto四舍五入

tothenearest四舍五入

2.有關(guān)集合

union并集

propersubset真子集

solutionset解集

3.有關(guān)代數(shù)式、方程和不等式

algebraicterm代數(shù)項

liketerms,similarterms同類項

numericalcoefficient數(shù)字系數(shù)

literalcoefficient字母系數(shù)

inequality不等式

triangleinequality三角不等式

range值域

originalequation原方程

equivalentequation同解方程

等價方程

linearequation線性方程(e.g.5x+6=22)

4.有關(guān)分?jǐn)?shù)和小數(shù)

properfraction真分?jǐn)?shù)

improperfraction假分?jǐn)?shù)

mixednumber帶分?jǐn)?shù)

vulgarfraction,commonfraction普通分?jǐn)?shù)simplefraction簡分?jǐn)?shù)

complexfraction繁分?jǐn)?shù)

numerator分子

denominator分母

(least)commondenominator(最小)公分母quarter四分之一

decimalfraction純小數(shù)

infinitedecimal無窮小數(shù)

recurringdecimal循環(huán)小數(shù)

tenthsunit十分位

5.基本數(shù)學(xué)概念

arithmeticmean算術(shù)平均值

weightedaverage加權(quán)平均值

geometricmean幾何平均數(shù)

exponent指數(shù)，冪

base乘冪的底數(shù),底邊

cube立方數(shù)，立方體

squareroot平方根

cuberoot立方根

commonlogarithm常用對數(shù)

digit數(shù)字

constant常數(shù)

variable變量

inversefunction反函數(shù)

complementaryfunction余函數(shù)

linear一次的，線性的

factorization因式分解

absolutevalue絕對值，e.g.｜-32｜=32roundoff四舍五入

6.有關(guān)數(shù)論

naturalnumber自然數(shù)

positivenumber正數(shù)

negativenumber負(fù)數(shù)

oddinteger,oddnumber奇數(shù)

eveninteger,evennumber偶數(shù)

integer,wholenumber整數(shù)

positivewholenumber正整數(shù)

negativewholenumber負(fù)整數(shù)

consecutivenumber連續(xù)整數(shù)

realnumber,rationalnumber實數(shù),有理數(shù)irrational(number)無理數(shù)

compositenumber合數(shù)e.g.4,6,8,9,10,12,14,15……primenumber質(zhì)數(shù)e.g.2,3,5,7,11,13,15……reciprocal倒數(shù)

commondivisor公約數(shù)

multiple倍數(shù)

(least)commonmultiple(最小)公倍數(shù)

(prime)factor(質(zhì))因子

commonfactor公因子

ordinaryscale,decimalscale十進(jìn)制nonnegative非負(fù)的

tens十位

units個位

mode眾數(shù)

median中數(shù)

commonratio公比

7.數(shù)列

arithmeticprogression(sequence)等差數(shù)列g(shù)eometricprogression(sequence)等比數(shù)列

8.其它

approximate近似

(anti)clockwise(逆)順時針方向cardinal基數(shù)

ordinal序數(shù)

directproportion正比

distinct不同的

estimation估計，近似

parentheses括號

proportion比例

代數(shù)ALGEBRA

1.數(shù)論

naturalnumber自然數(shù)positivenumber正數(shù)negativenumber負(fù)數(shù)oddinteger,oddnumber奇數(shù)eveninteger,evennumber偶數(shù)integer,wholenumber整數(shù)positive

wholenumber正整數(shù)negativewholenumber負(fù)整數(shù)consecutivenumber連續(xù)整數(shù)real

number,rationalnumber實數(shù),有理數(shù)irrational（number）無理數(shù)inverse倒數(shù)

composite

number合數(shù)e.g.4,6,8,9,10,12,14,15…primenumber質(zhì)數(shù)e.g.2,3,5,7,11,13,15…reciprocal倒數(shù)commondivisor公約數(shù)multiple倍數(shù)(minimum)commonmultiple(最小)公倍數(shù)

(prime)factor(質(zhì))因子commonfactor公因子ordinaryscale,decimal

scale十進(jìn)制nonnegative非負(fù)的tens十位units個位mode眾數(shù)mean平均數(shù)median中值common

ratio公比

2.基本數(shù)學(xué)概念

arithmeticmean算術(shù)平均值weightedaverage加權(quán)平均值geometricmean幾何平均數(shù)exponent

指數(shù)，冪base乘冪的底數(shù),底邊cube立方數(shù)，立方體squareroot平方根cuberoot立方根commonlogarithm

常用對數(shù)digit數(shù)字constant常數(shù)variable變量inversefunction反函數(shù)

complementary

function余函數(shù)linear一次的，線性的factorization因式分解absolutevalue

絕對值，e.g.｜-32｜=32roundoff四舍五入數(shù)學(xué)

3.基本運算

add，plus加subtract減difference差multiply,times乘product積divide

除divisible可被整除的dividedevenly被整除dividend被除數(shù)，紅利divisor因子，除數(shù)，公約數(shù)

quotient商remainder余數(shù)factorial階乘power乘方radicalsign,rootsign根號

roundto四舍五入tothenearest四舍五入

4.代數(shù)式，方程，不等式

algebraicterm代數(shù)項liketerms,similarterms同類項numericalcoefficient

數(shù)字系數(shù)literalcoefficient字母系數(shù)inequality不等式triangleinequality三角不等式range值域

originalequation原方程equivalentequation同解方程，等價方程linearequation線性方程(e.g.

5x+6=22)

5.分?jǐn)?shù)，小數(shù)

properfraction真分?jǐn)?shù)improperfraction假分?jǐn)?shù)mixednumber帶分?jǐn)?shù)vulgar

fraction，commonfraction普通分?jǐn)?shù)simplefraction簡分?jǐn)?shù)complexfraction

繁分?jǐn)?shù)numerator分子denominator分母(least)commondenominator（最?。┕帜竡uarter

四分之一decimalfraction純小數(shù)infinitedecimal無窮小數(shù)recurringdecimal循環(huán)小數(shù)tenthsunit十分位

6.集合

union并集propersubset真子集solutionset解集

7.數(shù)列

arithmeticprogression(sequence)等差數(shù)列g(shù)eometricprogression(sequence)等比數(shù)列

8.其它

approximate近似(anti)clockwise(逆)順時針方向cardinal基數(shù)ordinal序數(shù)directproportion正比distinct不同的estimation估計，近似parentheses括號proportion比例

permutation排列combination組合table表格trigonometricfunction三角函數(shù)unit單位,位

幾何GEOMETRY

1.角

alternateangle內(nèi)錯角correspondingangle同位角verticalangle對頂角centralangle圓心角interiorangle內(nèi)角exteriorangle外角supplementaryangles補角

complementary

angle余角adjacentangle鄰角acuteangle銳角obtuseangle鈍角rightangle直角roundangle周角straightangle平角includedangle夾角

2.三角形

equilateraltriangle等邊三角形scalenetriangle不等邊三角形isoscelestriangle等腰三角形

righttriangle直角三角形oblique斜三角形inscribedtriangle內(nèi)接三角形

3.收斂的平面圖形，除三角形外

semicircle半圓concentriccircles同心圓quadrilateral四邊形pentagon五邊形

hexagon

六邊形heptagon七邊形octagon八邊形nonagon九邊形decagon十邊形polygon多邊形

parallelogram平行四邊形equilateral等邊形plane平面square正方形，平方

rectangle長方形

regularpolygon正多邊形rhombus菱形trapezoid梯形

4.其它平面圖形

arc弧line,straightline直線linesegment線段parallellines平行線segmentofacircle弧形

5.立體圖形

cube立方體，立方數(shù)rectangularsolid長方體regularsolid/regularpolyhedron正多面體circularcylinder圓柱體cone圓錐sphere球體solid立體的

6.圖形的附屬概念

planegeometry平面幾何trigonometry三角學(xué)bisect平分circumscribe外切inscribe

內(nèi)切intersect相交perpendicular垂直Pythagoreantheorem勾股定理（畢達(dá)哥拉斯定理）congruent

全等的multilateral多邊的altitude高depth深度side邊長circumference,perimeter

周長radian弧度surfacearea表面積volume體積arm直角三角形的股crosssection橫截面

centerofacircle圓心chord弦diameter直徑radius半徑anglebisector角平分線

diagonal對角線化edge棱faceofasolid立體的面hypotenuse斜邊includedside夾邊leg

三角形的直角邊median（三角形的）中線base底邊，底數(shù)（e.g.2的5次方，2就是底數(shù)）opposite直角三角形中的對邊

midpoint中點endpoint端點vertex(復(fù)數(shù)形式vertices)頂點tangent切線的transversal截線

intercept截距

7.坐標(biāo)

coordinatesystem坐標(biāo)系rectangularcoordinate直角坐標(biāo)系origin原點abscissa橫坐標(biāo)

ordinate縱坐標(biāo)numberline數(shù)軸quadrant象限slope斜率complexplane復(fù)平面