微积分词汇

第一部分英汉微积分词汇

Part1 English-Chinese Calculus V ocabulary

第一章函数与极限

Chapter1 Function and Limit

集合set

元素element

子集subset

空集empty set

并集union

交集intersection

差集difference of set

基本集basic set

补集complement set

直积direct product

笛卡儿积Cartesian product

开区间open interval

闭区间closed interval

半开区间half open interval

有限区间finite interval

区间的长度length of an interval

无限区间infinite interval

领域neighborhood

领域的中心centre of a neighborhood

领域的半径radius of a neighborhood

左领域left neighborhood

右领域right neighborhood

映射mapping

X到Y的映射mapping of X ontoY

满射surjection

单射injection

一一映射one-to-one mapping

双射bijection

算子operator

变化transformation

函数function

逆映射inverse mapping

复合映射composite mapping

自变量independent variable

因变量dependent variable

定义域domain

函数值value of function

函数关系function relation

值域range 自然定义域natural domain

单值函数single valued function

多值函数multiple valued function

单值分支one-valued branch

函数图形graph of a function

绝对值函数absolute value

符号函数sigh function

整数部分integral part

阶梯曲线step curve

当且仅当if and only if(iff)

分段函数piecewise function

上界upper bound

下界lower bound

有界boundedness

无界unbounded

函数的单调性monotonicity of a function 单调增加的increasing

单调减少的decreasing

单调函数monotone function

函数的奇偶性parity(odevity) of a function

对称symmetry

偶函数even function

奇函数odd function

函数的周期性periodicity of a function

周期period

反函数inverse function

直接函数direct function

复合函数composite function

中间变量intermediate variable

函数的运算operation of function

基本初等函数basic elementary function

初等函数elementary function

幂函数power function

指数函数exponential function

对数函数logarithmic function

三角函数trigonometric function

反三角函数inverse trigonometric function 常数函数constant function

双曲函数hyperbolic function

双曲正弦hyperbolic sine

双曲余弦hyperbolic cosine

双曲正切hyperbolic tangent

反双曲正弦inverse hyperbolic sine

反双曲余弦inverse hyperbolic cosine

反双曲正切inverse hyperbolic tangent

极限limit

数列sequence of number

收敛convergence

收敛于 a converge to a

发散divergent

极限的唯一性uniqueness of limits

收敛数列的有界性boundedness of a

convergent sequence

子列subsequence

函数的极限limits of functions

函数()

f x当x趋于x0时的极限limit of functions ()

f x as x approaches x0

左极限left limit

右极限right limit

单侧极限one-sided limits

水平渐近线horizontal asymptote

无穷小infinitesimal

无穷大infinity

铅直渐近线vertical asymptote

夹逼准则squeeze rule

单调数列monotonic sequence

高阶无穷小infinitesimal of higher order

低阶无穷小infinitesimal of lower order

同阶无穷小infinitesimal of the same order 等阶无穷小equivalent infinitesimal

函数的连续性continuity of a function

增量increment

函数()

f x在x0连续the function ()

f x is continuous at x0

左连续left continuous

右连续right continuous

区间上的连续函数continuous function

函数()

f x在该区间上连续function ()

f x is continuous on an interval

不连续点discontinuity point

第一类间断点discontinuity point of the first kind

第二类间断点discontinuity point of the second kind

初等函数的连续性continuity of the

elementary functions

定义区间defined interval

最大值global maximum value (absolute maximum)

最小值global minimum value (absolute

minimum)

零点定理the zero point theorem

介值定理intermediate value theorem

第二章导数与微分

Chapter2 Derivative and Differential

速度velocity

匀速运动uniform motion

平均速度average velocity

瞬时速度instantaneous velocity

圆的切线tangent line of a circle

切线tangent line

切线的斜率slope of the tangent line

位置函数position function

导数derivative

可导derivable

函数的变化率问题problem of the change

rate of a function

导函数derived function

左导数left-hand derivative

右导数right-hand derivative

单侧导数one-sided derivatives

()

f x在闭区间【a,b】上可导()

f x is derivable on the closed interval [a,b]

切线方程tangent equation

角速度angular velocity

成本函数cost function

边际成本marginal cost

链式法则chain rule

隐函数implicit function

显函数explicit function

二阶函数second derivative

三阶导数third derivative

高阶导数nth derivative

莱布尼茨公式Leibniz formula

对数求导法log- derivative

参数方程parametric equation