1 

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

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

函数当x趋于x₀时的极限  limit of functions 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 在x₀连续  the function 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 在该区间上连续 function 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

    在闭区间【a,b】上可导  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

 

 

第三章  微分中值定理与导数的应用

Chapter3 MeanValue Theorem of Differentials and the Application of Derivatives

罗马定理   Rolle’s theorem

费马引理   Fermat’s lemma

拉格朗日中值定理  Lagrange’s mean value theorem

驻点  stationary point

稳定点  stable point

临界点   critical point

辅助函数   auxiliary function

拉格朗日中值公式   Lagrange’s mean value formula

柯西中值定理   Cauchy’s mean value theorem

洛必达法则   L’Hospital’s Rule

0/0型不定式   indeterminate form of type 0/0

不定式   indeterminate form

泰勒中值定理   Taylor’s mean value theorem

泰勒公式   Taylor formula

余项   remainder term

拉格朗日余项   Lagrange remainder term

麦克劳林公式   Maclaurin’s formula

佩亚诺公式    Peano remainder term

凹凸性   concavity

凹向上的   concave upward, cancave up

凹向下的，向上凸的   concave downward’ concave down

拐点   inflection point

函数的极值   extremum of function

极大值   local(relative) maximum

最大值   global(absolute) mximum

牛顿－莱布尼茨公式   Newton-Leibniz formula

微积分基本公式 fundamental formula of calculus 

换元公式   formula for integration by substitution

递推公式   recurrence formula

反常积分   improper integral

反常积分发散   the improper integral is divergent

反常积分收敛   the improper integral is convergent

无穷限的反常积分   improper integral on an infinite interval

无界函数的反常积分   improper integral of unbounded functions

绝对收敛   absolutely convergent

 

 

第四章  不定积分

Chapter4 Indefinite Integrals

原函数   primitive function(antiderivative)

积分号   sign of integration

被积函数   integrand

积分变量   integral variable

积分曲线   integral curve

积分表   table of integrals

换元积分法   integration by substitution

分部积分法   integration by parts

分部积分公式   formula of integration by parts

有理函数   rational function

真分式   proper fraction

假分式   improper fraction

 

 

第五章  定积分

Chapter5 Definite Integrals

曲边梯形   trapezoid with

曲边   curve edge

窄矩形   narrow rectangle

曲边梯形的面积   area of trapezoid with curved edge

积分下限   lower limit of integral

积分上限   upper limit of integral

积分区间   integral interval

分割   partition

积分和   integral sum

可积   integrable

矩形法   rectangle method

积分中值定理   mean value theorem of

Algebra

向量   vector

自由向量   free vector

单位向量   unit vector

零向量   zero vector

相等   equal

平行   parallel

向量的线性运算   linear poeration of vector

三角法则   triangle rule

平行四边形法则   parallelogram rule

交换律   commutative law

结合律   associative law

负向量   negative vector

差   difference

分配律   distributive law

空间直角坐标系   space rectangular coordinates

坐标面   coordinate plane

卦限   octant

向量的模   modulus of vector

向量a与b的夹角   angle between vector a and b

方向余弦   direction cosine

方向角   direction angle

向量在轴上的投影   projection of a vector onto an axis

数量积，外积，叉积   scalar product,dot product,inner product

曲面方程   equation for a surface

球面   sphere

旋转曲面   surface of revolution

母线   generating line

轴   axis

圆锥面      cone

顶点   vertex

旋转单叶双曲面   revolution hyperboloids of one sheet

旋转双叶双曲面   revolution hyperboloids of two sheets

柱面    cylindrical surface ,cylinder

圆柱面   cylindrical surface

准线   directrix

抛物柱面   parabolic cylinder

二次曲面   quadric surface