數(shù)學(xué)分析英文詞匯

PAGE9/NUMPAGES9數(shù)學(xué)分析英文詞匯數(shù)學(xué)分析中的英語(yǔ)單詞

第一章

realnumberanditsproperties實(shí)數(shù)及其性質(zhì)rationalnumber有理數(shù)irrationalnumber無(wú)理數(shù)definition定義proposition命題

plus加

minus減

multipliedby/times乘

over/isto/dividedby除

absolutevalueandinequality絕對(duì)值與不等式triangleinequality三角不等式inversetriangleinequality反三角不等式Bernoulliinequality伯努利不等式principlesofsupremumandinfimum確界原理

openinterval開(kāi)區(qū)間

closedinterval閉區(qū)間

semi-openinterval半開(kāi)區(qū)間

semi-closedinterval半閉區(qū)間

finiteinterval有限區(qū)間infiniteinterval無(wú)限區(qū)間neighborhood領(lǐng)域

deletedneighborhood去心鄰域

sum和

difference差

product積

quotient商

numberaxis/numberline數(shù)軸closeness封閉性Archimedeanproperty阿基米德性質(zhì)density稠密行

upperandlowerbounds上界和下界boundedset有界集unboundedset無(wú)界集existencedomian存在域supremum上確界infimum下確界

order-completeset有序完備集completenessofrealnumbers實(shí)數(shù)的完備性completeorderedfield全序域axiomofcompleteness完備性公理Dedekindcut戴德金分割Dedekindproperty戴德金性質(zhì)constantandvariablequantities常量與變量definitionoffunction函數(shù)的定義域domain定義域range值域independentvariable自變量dependentvariable因變量intermediatevariable中間量elementaryfunction初等函數(shù)constantfunction常量函數(shù)powerfunction冪函數(shù)exponentialfunction指數(shù)函數(shù)logarithmicfunction對(duì)數(shù)函數(shù)trigonometricfunction三角函數(shù)inversetrigonometricfunction反三角函數(shù)compoundfunction復(fù)合函數(shù)mapping映射

inversemapping逆映射image像

primaryimage原像piecewisefunction分段函數(shù)

signfunction符號(hào)函數(shù)Dirichletfunction狄利克雷函數(shù)Riemannfunction黎曼函數(shù)boundedfunction有界函數(shù)monotonefunction單調(diào)函數(shù)monotoneincreasingfunction單調(diào)增函數(shù)strictlymonotonefunction嚴(yán)格單調(diào)函數(shù)odd(even)function奇函數(shù)（偶函數(shù)）minimalpositiveperiod最小正周期absolutevaluefunction絕對(duì)值函數(shù)identityfunction恒等函數(shù)polynomialfunction多項(xiàng)式函數(shù)

linearfunction線性函數(shù)quadraticfunction二次函數(shù)

rationalfunction有理函數(shù)hyperbolicsine雙曲正弦hyperboliccosine雙曲余弦trigonometricidentity三角恒等式

odd-evenidentity奇偶恒等式cofunctionidentity余函數(shù)恒等式Pythagoreanidentity畢達(dá)哥拉斯恒等式half-angleidentity半角恒等式productidentity積恒等式

sumidentity和恒等式additionidentity加法恒等式double-angleidentity倍角恒等式

第二章數(shù)列極限

limitofsequence數(shù)列極限divergentsequence發(fā)散數(shù)列infinitesimalsequence無(wú)窮小數(shù)列convergentsequence收斂數(shù)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嚴(yán)格遞增monotoneincreasingsequence單調(diào)遞增序列monotonedecreasingsequence單調(diào)遞減序列necessarycondition必要條件

sufficientcondition充分條件

squeezeprinciple夾逼定理

Cauchyconvergencecriterion柯西收斂準(zhǔn)則

第三章函數(shù)極限

limitoffunction函數(shù)極限

infinitelimit無(wú)窮極限

one-sidedlimit單側(cè)極限

right(left)limit/right(left)handlimit右（左）極限propertyoflimitoffunction函數(shù)極限的性質(zhì)localboundedness局部有界性

Heinetheorem海涅定理

infinity無(wú)窮大量

orderofinfinitesimal無(wú)窮小量的階infinitesimalofhigher(lower)order高（低）階無(wú)窮小量infinitesimalofsameorder同階無(wú)窮小量equivalentinfinitesimal等價(jià)無(wú)窮小量

k-orderinfinitesimalk-階無(wú)窮小量verticalasymptote垂直漸近線

obliqueasymptote斜漸進(jìn)線horizontalasymptote水平漸近線

第四章函數(shù)的連續(xù)性

incrementofindependentvariable自變量的增量incrementoffunction函數(shù)的增量

right(left)continuous右(左)連續(xù)

discontinuitypointanditsclassification間斷點(diǎn)及其分類removablediscontinuity可去間斷點(diǎn)

jumpdiscontinuity跳躍間斷點(diǎn)discontinuityofthefirstkind第一類間斷點(diǎn)discontinuityofthesecondkind第二類間斷點(diǎn)

localpropertiesofcontinuousfunction連續(xù)函數(shù)的局部性質(zhì)compositionpropertiesofcontinuousfunction連續(xù)函數(shù)的復(fù)合性質(zhì)

閉區(qū)間上連續(xù)函數(shù)的性質(zhì)propertiesofcontinuousfunctionoverclosed

interval

extremevaluetheorem極值定理

maximumandminimumvaluetheorem最大值和最小值定理intermediatevaluetheorem介值性定理

zero-pointtheorem零點(diǎn)定理

uniformcontinuitytheorem一致連續(xù)定理

continuityofinversefunction反函數(shù)的連續(xù)性

localinheritingorderproperty局部保號(hào)性

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

第五章導(dǎo)數(shù)和微分

finiteincrementformula有限增量公式

rateofchange變化率

differencequotient差商

left(right)derivative左（右）導(dǎo)數(shù)derivativefunction導(dǎo)函數(shù)

derivablefunction可導(dǎo)函數(shù)

geometricmeaningofderivative導(dǎo)數(shù)的集合意義

Fermattheorem費(fèi)馬定理

Darbouxtheorem達(dá)布定理

intermediatevaluetheoremofderivativefunction導(dǎo)函數(shù)的介值定理algebraofderivatives導(dǎo)數(shù)的四則運(yùn)算derivativeofsum和的導(dǎo)數(shù)

derivativesofdifference差的導(dǎo)數(shù)

derivativeofproduct積的導(dǎo)數(shù)

derivativeofquotient商的導(dǎo)數(shù)derivativeofinversefunction反函數(shù)的導(dǎo)數(shù)maximumvalue最大值

minimumvalue最小值derivativeofcompositefunction復(fù)合函數(shù)的導(dǎo)數(shù)logarithmicderivative對(duì)數(shù)求導(dǎo)法parametricequationofcircle圓的參數(shù)方程parametricequationofellipse橢圓的參數(shù)方程parametricequationofcycloid擺線的參數(shù)方程parametricequationofasteroid星形線的參數(shù)方程secondderivative二階導(dǎo)數(shù)

thirdderivative三階導(dǎo)數(shù)

n-thderivativen階導(dǎo)數(shù)

Leibnizformula萊布尼茨公式acceleration加速度

physicalinterpretation物理解釋conceptofdifferential微分的概念differentiablefunction可微函數(shù)

linearprincipalpart線性主部differentialofindependentvariable自變量的微分operationalrulesofdifferential微分的運(yùn)算法則invarianceofdifferentialform微分形式的不變性geometricmeaningofdifferential微分的幾何意義higher-orderdifferential高階微分

第六章微分中值定理

Rollemeanvaluetheorem羅爾中值定理Lagrangemeanvaluetheorem拉格朗日中值定理Cauchymeanvaluetheorem柯西中值定理Taylortheorem泰勒定理

L’Hospitalrule洛必達(dá)法則

limitofindeterminateformoftype0/00/0型不定式極限indeterminateformoftype∞/∞∞/∞型不定式

otherindeterminateforms其他類型不定式

TaylorformulawithPeanoremainder帶有皮亞諾型余項(xiàng)的泰勒

公式

Taylorcoefficient泰勒系數(shù)

Taylorpolynomial泰勒多項(xiàng)式

remainderofTaylorformula帶有拉格朗日型余項(xiàng)的泰

勒公式

TaylorformulawithLagrangeremainder帶有拉格朗日型余項(xiàng)的麥

克勞林公式

extremevalueoffunction函數(shù)的極值

testofextremevalue極值判斷

thefirstsufficientconditionofextremevalue極值的第一充分條件convexityandinflectionpointoffunction函數(shù)的凸性和拐點(diǎn)convexfunction凸函數(shù)

concavefunction凹函數(shù)

strictlyconvexfunction嚴(yán)格凸函數(shù)

strictlyconcavefunction嚴(yán)格凹函數(shù)

Jensoninequality琴生不等式

第七章實(shí)數(shù)的完備性

實(shí)數(shù)擊完備性的基本定理fundamentaltheoremsofcompletenessintheset

ofrealnumbers

nestedintervaltheorem閉區(qū)間套定理

Cauchyconvergencecriterion柯西收斂準(zhǔn)著accumulationtheorem聚點(diǎn)定理

finitecoveringtheorem有限覆蓋定理

upperandlowerlimits上極限和下極限

第八章不定積分

indefiniteintegral不定積分

primitivefunction原函數(shù)

integrandfunction被積函數(shù)

integralsign積分符號(hào)

expressionofintegrand積分表達(dá)式

integralconstant積分常數(shù)

tableofbasicintegrals基本積分表geometricmeaningofindefinite不定積分的幾何意義integralcurve積分曲線

initialcondition初始條件integrationbyparts分部積分法integrationbysubstitutions換元積分法

formulaofsubstitutionofthefirstkind第一換元公式indefiniteintegralofrationalfunction有理函數(shù)的不定積分properfraction真分式

improperfraction假分式decompositionintopartialfractions部分分式分解methodofunderminedcoefficients待定系數(shù)法

第九章定積分

definiteintegral定積分

curvilineartrapezoid曲邊梯形

dividing/partition分割

norm/modulus模

Riemannsum黎曼和

Riemannintegral黎曼積分integrabilityinthesenseofRiemann黎曼可積

intervalofintegration積分區(qū)間

upperandlowerlimits上限和下限geometricmeaningofdefiniteintegral定積分的幾何意義uppersum上和

lowersum下和

Darbouxuppersum達(dá)布上和

Darbouxlowersum達(dá)布下和

Newton-Leibnizformula牛頓-萊布尼茨公式necessaryconditionforintegrability可積的必要條件necessaryandsufficientconditionsforintegrability可積的充要條件integrablefunctionclass可積函數(shù)類

linearpropertyofdefiniteintegral定積分的線性性質(zhì)additivewithrespecttointegralinterval/additivity

overintegralinterval

積分區(qū)間的可加性meanvaluetheoremofintegral積分中值定理averagevalue平均值

integralwithvariantupperlimit變上限積分existenceofprimitivefunction原函數(shù)的存在性integrationbysubstitution換元積分法integrationbyparts分部積分法

integralformofreminderofTaylorformula泰勒公式的積分類型第十章定積分的應(yīng)用

areaofplanefigure平面圖形的面積

methodoffindingvolumeofasolidfromtheknowsareaofparallelsections由平行截面面積求體積的方法

arclengthandcurvatureofplanecurve平面的曲線的弧長(zhǎng)與曲率smoothcurve光滑曲線

differentialofarc弧微分

circleofcurvature曲率圓

radiusofcurvature曲率半徑

areaofrevolutionsurface旋轉(zhuǎn)曲面的面積

someapplicationsofdefiniteintegralinphysics定積分在物理中的某些應(yīng)

用

gravitation引力

work功

approximatecomputationofdefiniteintegral定積分的近似計(jì)算trapezoidalmethod梯形法

parabolamethod拋物線法

第十一章反常積分

notionofimproperintegral反常積分的概念improperintegraloninfiniteinterval無(wú)窮區(qū)間上的反常積分improperintegralofunboundedfunction無(wú)界函數(shù)的反常積分propertyofinfiniteintegralandtestof無(wú)窮積分的性質(zhì)和收斂判

convergence別

absolutelyconvergent絕對(duì)收斂

comparisontest比較收斂法

Cauchytest柯西判別法

Dirichlettest狄利克雷判別法

Abeltest阿貝尓判別法

第十二章數(shù)項(xiàng)級(jí)數(shù)

serieswithnumberterms數(shù)項(xiàng)級(jí)數(shù)

infiniteseries無(wú)窮級(jí)數(shù)

convergenceofseries級(jí)數(shù)的收斂性sequenceofpartialsum部分和序列

geometricseries幾何級(jí)數(shù)

harmonicseries調(diào)和級(jí)數(shù)

Cauchyconvergencecriterionforseries級(jí)數(shù)收斂的柯西準(zhǔn)則serieswithpositiveterms正項(xiàng)級(jí)數(shù)

necessaryconditionforconvergence收斂的必要條件

roottest根式判別法

D’alembert(ratio)test達(dá)朗貝爾判別法（比式判

別法）

limitformofratiotest比式判別法的極限形式Gausstest高斯判別法

integraltest積分判別法

Raabetest拉貝尓判別法

p-seriesp級(jí)數(shù)

serieswitharbitratyterms一般項(xiàng)級(jí)數(shù)

alternatingseries交錯(cuò)級(jí)數(shù)

Leibnitztest萊布尼茨判別法rearrangementofseries級(jí)數(shù)的重排

Abeltest阿貝尓判別法

Dirichlettest狄利克雷判別法

第十章函數(shù)列與函數(shù)項(xiàng)級(jí)數(shù)

convergentatx"在點(diǎn)x"收斂

convergencedomain/regionofconvergence收斂域

sumfunction和函數(shù)

limitfunction極限函數(shù)

seriesoffunctions函數(shù)項(xiàng)級(jí)數(shù)

uniformconvergence一致收斂

testofuniformconvergence一致收斂判別法

魏爾斯特拉判別法Weierstrass’stest/Weierstrassuniform

convergencecriterion/Weierstrassm-testfor

uniformconvergence

uniformboundedness一致有界

Dirichlettest狄利克列判別法

第十四章冪級(jí)數(shù)

powerseries冪級(jí)數(shù)

intervalofconvergence收斂區(qū)間

radiusofconvergence收斂半徑

Abeltheorem阿貝尓定理

operationsofpowerseries冪級(jí)數(shù)的運(yùn)算

taylorseries泰勒級(jí)數(shù)

expansionofpowerseriesofelementaryfunction初等函數(shù)的冪級(jí)數(shù)展開(kāi)式exponentialfunctionofcomplexvariable復(fù)變量的指數(shù)函數(shù)

Eulerformula歐拉公式

第十五章傅里葉級(jí)數(shù)

Fourierseries傅里葉級(jí)數(shù)trigonometricseries三角級(jí)數(shù)

systemoforthogonalfunctions正交函數(shù)系

simpleharmonicvibration簡(jiǎn)諧振動(dòng)

Fourierseriesforfunctionofperiod2π以2π為周期的函數(shù)的傅

立葉級(jí)數(shù)

angularfrequency角頻率

piecewisesmooth分段光滑

Fouriercoefficient傅立葉系數(shù)convergencetheorem收斂定理

Fourierseriesofevenandoddfunctions奇函數(shù)與偶函數(shù)的傅立葉

級(jí)數(shù)

amplitude振幅

sineseries正弦級(jí)數(shù)

cosineseries余弦級(jí)數(shù)

periodicextension周期延拓

第十六章多元函數(shù)的極限與連續(xù)

functionsofseveralvariables多元函數(shù)

planepointset平面點(diǎn)集

coordinateplane坐標(biāo)平面

interiorpoint內(nèi)點(diǎn)

outerpoint外點(diǎn)

boundarypoint界點(diǎn)

boundary邊點(diǎn)

isolatedpoint孤立點(diǎn)

openset開(kāi)集

closedset閉集

connectedness連通性

connectedopenset連通開(kāi)集

opendomain(region)開(kāi)域

closeddomain(region)閉域

boundedpointset有界點(diǎn)集

unboundedpointset無(wú)界點(diǎn)集

nestedcloseddomaintheorem閉域套定理

functionoftwovariables二元函數(shù)

n-dimensionalvectorspacen-維向量空間

improperlimit非正常極限

doublelimit二重極限

propertiesofcontinuousfunctionsonboundedclosedregion有界閉區(qū)域上連續(xù)函數(shù)的性質(zhì)

repeatedlimits累次極限totalincrement全增量

partialincrement偏增量

第十七章多元函數(shù)微分學(xué)

totaldifferential全微分

partialderivative偏導(dǎo)數(shù)

continuouslydifferentiate連續(xù)可微

tangentplaneofsurface曲面的切平面

normalplaneofcurve曲線的法平面differentiationofcompositefunction復(fù)合函數(shù)微分法

chainruleforfunctionsofseveralvariables多元函數(shù)的鏈?zhǔn)椒▌tinvarianceofdifferentialformoffirstorder一階微分形式的不變性directionalderivativeandgradient方向?qū)?shù)與梯度differentiability可微性

Taylorformula泰勒公式

problemofextremevalue極值問(wèn)題

partialderivativeofhigherorder高階偏導(dǎo)數(shù)

mixedpartialderivative混合偏導(dǎo)數(shù)

第十八章隱函數(shù)定理及其應(yīng)用

existenceanduniquenesstheoremofimplicit

隱函數(shù)存在唯一性定理functions

systemofimplicitfunctions隱函數(shù)組

functionaldeterminant(Jacobiandeterminant)函數(shù)行列式（雅可比行列

式）

systemofinversefunctions反函數(shù)組

coordinatetransformation坐標(biāo)變換

geometricalapplication幾何應(yīng)用

tangentlineandnormallineofplanecurve平面曲線的切線與法線tangentlineandnormalplaneofspacecurve空間曲線的切線與法平面conditionalextremum條件極值

Lagrangemultipliermethod拉格朗日乘數(shù)法

第十九章含參變量積分

properintegralwithparameter含參量的正常積分improperintegralwithparameter含參量的反常積分

Eulerintegral歐拉積分Weierstrasstest魏爾斯特拉判別法Dicichlettest狄利克雷判別法improperintegralwithinfinitebound無(wú)窮限的反常積分impro