“語言就是思維。”我總是宣揚這個觀點，要求學生記住基本的術語表述。名字曉得什么意思了，其數學理論也多少認識了。我會陸續把整理的一些常用的詞匯發布，尤其是近期需要參加數學補考的同學。

Mathematical terminology數學術語

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1基本運算arithmetic：?

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add,?plus???????????????? 加??

subtract????????????????? 減?

?difference???????????? 差?

multiply,?times????????????? 乘?

?product????積??divide??????????????? 除??

divisible????????????????? 可被整除的??

divided?evenly???? 被整除?

?dividend???????? 被除數

?divisor????????? 因子，除數??

quotient??????????????????? 商?

?remainder余數

?factorial階乘?

?power乘方??

radical?sign,?root?sign????????? 根號??

round??to?the?nearest?????????? 四舍五入??

round?off四舍五入

exponent????指數，冪?

base????????乘冪的底數,底邊?

cube????????立方數，立方體

?square?root????????平方根?

cube?root????????立方根?

common?logarithm常用對數?

2.有關分數和小數?

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proportion比例?

direct proportion正比?

common ratio公比

proper fraction真分數

improper fraction假分數

mixed number帶分數

vulgar?fraction,?common?fraction普通分數?

simple?fraction簡分數?

complex?fraction繁分數?

numerator分子?

denominator分母?

(least)common?denominator(最小)公分母?

quarter四分之一?

decimal?fraction純小數?

infinite?decimal無窮小數?

recurring?decimal循環小數?

tenths?unit十分位??

approximate近似?

estimation估計，近似

3.有關數論

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natural?number自然數?

positive?number正數?

negative?number負數?

odd?integer,?odd?number奇數

?even?integer,?even?number偶數

?integer,?whole?number整數?

positive?whole?number正整數?

negative?whole?number負整數?

consecutive?number連續整數?

real?number,?rational?number實數,有理數

?irrational(number)無理數?

composite?number合數e.g.4,6,8,9,10,12,14,15……?

prime?number質數e.g.2,3,5,7,11,13,15……

reciprocal倒數?

common divisor公約數

multiple倍數?

(least)common multiple(最小)公倍數 (prime)factor(質)因子

common factor公因子?

ordinary scale, decimal scale十進制 nonnegative非負的

tens十位

units個位

mode眾數

median中數?

cardinal基數

ordinal序數?

4.有關代數式、方程和不等式??

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algebraic?term代數項?

like?terms,?similar?terms同類項?

numerical?coefficient數字系數

?literal?coefficient字母系數

?inequality不等式?

triangle?inequality三角不等式?

range值域?

original?equation原方程?

equivalent?equation同解方程?等價方程?

linear?equation線性方程

factorization因式分解

微積分術語

topic 1? 極限問題

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Limit??????????????????????? n.極限

left-hand limit????????????????? 左極限

right-handlimit??? ????????????右極限

approach??????????????????? 接近，靠近

lnfinity??????????????????? n.無窮

positiveinfinity???????????? 正無窮

negativeinfinity ?????????????負無窮

algebraical??????????????? adj.代數(學)的

coefficient???????????????? n.系數

the highest power of x???????? x的最高指數項

numerator????????????????? n.分子

denominator??????????????? n.分母

horizontal asymptote????????? 水平漸近線

verticalasymptote ????????豎直漸近線

Topic2? 連續性

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continuity,?continuous??? ?[?kɑnt??n(j)u?di]

continuous function

continuous on an interval I

interval

domain

range

discontinuity????? 美[?d?s?kɑnt??n(j)u?di ]

discontinuity point

removablediscontinuity

nonremovable

infinitediscontinuity

jumpdiscontinuity

composite function

extreme value theorem

intermediate value theorem

zero point theorem

Topic3 導數

Derivative ? ? ? ? ? ? ? ?導數

differentiate????????????求…的導數

differentiability ? ? ? ? n. 可微性

differentiable ? ? ? ? ?adj. 可微的

difference quotient??????????差商

instantaneous rates of change with respectto x??

average rate of change of y with respect tox

instantaneous velocity

average velocity

acceleration??????????????????????????加速度

jerk?????????????????????? ? ? ??[d??rk]猝然移動，加速度變化率

Tangent line????????????????????切線

slope?????????????????????????????????? 斜率

steepness???????????????? ?傾斜度

secant line??????????????????割線

normal line??????????????????法線

notation

first/second/…n-th derivative???????一階/二階/…n階導數

higher order derivative????????????????????? 高階導數

the power rule???????????????????冪法則

the addition rule???????????????加法法則

the product rule?????????????????乘法法則

the quotient rule????????????????商法則

chain rule????????????????????????鏈式法則

polynomial????????????????????????? ???? 多項式

Figure out????????????????????????? ?????? 計算

radical????????????????????????????? ???? 根式

reciprocal ? ? ? ? ? ? ? ? ? ? ? ? ?n. 倒數

with respect to??????????????關于，對…

trigonometric functions??????三角函數

inverse function

implicit differentiation?????????????????????????????隱函數

Topic:不定積分與微分方程

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Differential 微分

linearzation 線性化

error 誤差

approximation 近似

Antiderivative 原函數，不定積分

arbitrary constant 任意常數

integration 積分，積分法

definite integral?? 定積分

indifinite integral 不定積分

integrand 被積函數

basic antidifferentiation formulas 基本的積分公式

every differentiation rule has a corresponding integration rule.

integration by parts 分部積分

substitution method 換元法

eliminate 除去，消去

strategy for integration

techniques of integration

rational function 分式函數

partial fractions 部分分式

indeterminateform 未定式

L’Hospital’s Rule 洛必達法則

differential equation (DE) 微分方程

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