八大章节的AP微积分专业词汇分享 预习课程的第一步要认识单词

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AP微积分专业词汇

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

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EMBED Equation.DSMT4  当x趋于x0时的极限  limit of functions  EMBED Equation.DSMT4   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EMBED Equation.DSMT4  在x0连续  the function EMBED Equation.DSMT4   iscontinuous at x0

左连续   left continuous

右连续   right continuous

区间上的连续函数  continuous function  

函数EMBED Equation.DSMT4  在该区间上连续function  EMBED Equation.DSMT4   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

Chapter2Derivative 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

EMBED Equation.DSMT4  在闭区间【a,b】上可导   EMBED Equation.DSMT4  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

相关变化率  correlative change rata

微分   differential

可微的  differentiable

函数的微分  differential of function

自变量的微分  differential of independent variable

微商   differential quotient

间接测量误差  indirect measurement error

绝对误差   absolute error

相对误差   relative error

Chapter3Mean Value 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, concave 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) maximum

极小值   local(relative) minimum

最小值   global(absolute) minimum

目标函数   objective function

曲率   curvature

弧微分   arc differential

平均曲率   average curvature

曲率园   circle of curvature

曲率中心   center of curvature

曲率半径   radius of curvature

渐屈线   evolute

渐伸线   involute

根的隔离   isolation of root

隔离区间   isolation interval

切线法   tangent line method

Chapter4Indefinite 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

Chapter5Definite 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 integrals

函数在区间上的平均值   average value of a function on an integvals

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

Chapter6Applications of the Definite Integrals

元素法   the element method

面积元素   element of area

平面图形的面积   area of a luane figure

直角坐标又称“笛卡儿坐标   (Cartesian coordinates)”

极坐标   polar coordinates

抛物线   parabola

椭圆   ellipse

旋转体的面积   volume of a solid of rotation

旋转椭球体  ellipsoid of revolution, ellipsoid ofrotation

曲线的弧长   arc length of a curve

可求长的   rectifiable

光滑   smooth

功   work

水压力   water pressure

引力   gravitation

变力   variable force

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

椭圆锥面   dlliptic cone

椭球面   ellipsoid

单叶双曲面   hyperboloid of one sheet

双叶双曲面   hyperboloid of two sheets

旋转椭球面   ellipsoid of revolution

椭圆抛物面   elliptic paraboloid

旋转抛物面   paraboloid of revolution

双曲抛物面   hyperbolic paraboloid

马鞍面   saddle surface

椭圆柱面   elliptic cylinder

双曲柱面   hyperbolic cylinder

抛物柱面   parabolic cylinder

空间曲线   space curve

空间曲线的一般方程   general form equations of a space curve

空间曲线的参数方程   parametric equations of a space curve

螺转线   spiral

螺矩   pitch

投影柱面   projecting cylinder

投影   projection

平面的点法式方程   point norm form equation of a plane

法向量   normal vector

平面的一般方程   general form equation of a plane

两平面的夹角   angle between two planes

点到平面的距离   distance from a point to a plane

空间直线的一般方程   general equation of a line in space

方向向量   direction vector

直线的点向式方程   pointdirection form equations of a line

方向数   direction number

直线的参数方程   parametric equations of a line

两直线的夹角   angle between two lines

垂直   perpendicular

直线与平面的夹角   angle between a line and a planes

平面束   pencil of planes

平面束的方程   equation of a pencil of planes

行列式   determinant

系数行列式   coefficient determinant

一元函数   function of one variable

多元函数   function of several variables

内点  interior point

外点   exterior point

边界点   frontier point,boundary point

聚点   point of accumulation

开集   open set

闭集   closed set

连通集   connected set

开区域   open region

闭区域   closed region

有界集   bounded set

无界集   unbounded set

n维空间   n-dimentional space

二重极限   double limit

多元函数的连续性   continuity of function of seveal

连续函数   continuous function

不连续点   discontinuity point

一致连续   uniformly continuous

偏导数   partial derivative

对自变量x的偏导数   partial derivative with respect toindependent variable x

高阶偏导数   partial derivative of higher order

二阶偏导数   second order partial derivative    

混合偏导数   hybrid partial derivative

全微分   total differential

偏增量   oartial increment

偏微分   partial differential

全增量   total increment

可微分   differentiable

必要条件   necessary condition

充分条件   sufficient condition

叠加原理   superposition principle

全导数   total derivative

中间变量   intermediate variable

隐函数存在定理   theorem of the existence of implicitfunction

曲线的切向量   tangent vector of a curve

法平面   normal plane

向量方程   vector equation

向量值函数   vector-valued function

切平面   tangent plane

法线   normal line

方向导数   directional derivative

梯度   gradient

数量场   scalar field

梯度场   gradient field

向量场   vector field

势场   potential field

引力场   gravitational field

引力势   gravitational potential

曲面在一点的切平面   tangent plane to a surface at a point

曲线在一点的法线   normal line to a surface at a point

无条件极值   unconditional extreme values

条件极值   conditional extreme values

拉格朗日乘数法   Lagrange multiplier method

拉格朗日乘子   Lagrange multiplier

经验公式   empirical formula

最小二乘法   method of least squares

均方误差   mean square error

重积分

Chapter9Multiple Integrals

二重积分   double integral

可加性   additivity

累次积分   iterated integral

体积元素   volume element

三重积分   triple integral

直角坐标系中的体积元素   volume element in rectangular coordinatesystem

柱面坐标   cylindrical coordinates

柱面坐标系中的体积元素   volume element in cylindrical coordinatesystem

球面坐标   spherical coordinates

球面坐标系中的体积元素   volume element in spherical coordinatesystem

反常二重积分   improper double integral

曲面的面积   area of a surface

质心   centre of mass

静矩   staticmoment

密度   density

形心   centroid

转动惯量   moment of inertia

参变量   parametric variable

曲线积分与曲面积分

Chapter10Line(Curve)Integrals and Surface Integrals

对弧长的曲线积分   line integrals with respect to arc hength

第一类曲线积分   line integrals of the first type

对坐标的曲线积分   line integrals with respect to x,y,and z

第二类曲线积分   line integrals of the second type

有向曲线弧   directed arc

单连通区域   simple connected region

复连通区域   complex connected region

格林公式   Green formula

第一类曲面积分   surface integrals of the first type

对面的曲面积分   surface integrals with respect to area

有向曲面   directed surface

对坐标的曲面积分   surface integrals with respect to coordinateelements

第二类曲面积分   surface integrals of the second type

有向曲面元   element of directed surface

高斯公式   gauss formula

拉普拉斯算子   Laplace operator

格林第一公式   Green’s first formula

通量   flux

散度   divergence

斯托克斯公式   Stokes formula

环流量   circulation

旋度   rotation,curl

无穷级数

Chapter11Infinite Series

一般项   general term

部分和   partial sum

余项   remainder term

等比级数   geometric series

几何级数   geometric series

公比   common ratio

调和级数   harmonic series

柯西收敛准则   Cauchy convergence criteria, Cauchy criteriafor convergence

正项级数   series of positive terms

达朗贝尔判别法   D’Alembert test

柯西判别法   Cauchy test

交错级数   alternating series

绝对收敛   absolutely convergent

条件收敛   conditionally convergent

柯西乘积   Cauchy product

函数项级数   series of functions

发散点   point of divergence

收敛点   point of convergence

收敛域   convergence domain

和函数   sum function

幂级数   power series

幂级数的系数   coefficients of power series

阿贝尔定理   Abel Theorem

收敛半径   radius of convergence

收敛区间   interval of convergence

泰勒级数   Taylor series

麦克劳林级数   Maclaurin series

二项展开式   binomial expansion

近似计算   approximate calculation

舍入误差   round-off error, rounding error

欧拉公式   Euler’s formula

魏尔斯特拉丝判别法   Weierstrass test

三角级数   trigonometric series

振幅   amplitude

角频率   angular frequency

初相   initial phase

矩形波   square wave

谐波分析   harmonic analysis

直流分量   direct component

基波   fundamental wave

二次谐波   second harmonic

三角函数系   trigonometric function system

傅立叶系数   Fourier coefficient

傅立叶级数   Fourier series

周期延拓   periodic prolongation

正弦级数   sine series

余弦级数   cosine series

奇延拓   odd prolongation

偶延拓   even prolongation

傅立叶级数的复数形式   complex form of Fourier series

微分方程

Chapter12Differential Equation

解微分方程   solve a dirrerential equation

常微分方程   ordinary differential equation

偏微分方程   partial differential equation,PDE

微分方程的阶   order of a differential equation

微分方程的解    solution of a differential equation

微分方程的通解   general solution of a differential equation

初始条件   initial condition

微分方程的特解   particular solution of a differentialequation

初值问题   initial value problem

微分方程的积分曲线   integral curve of a differential equation

可分离变量的微分方程   variable separable differential equation

隐式解   implicit solution

隐式通解   implicit general solution

衰变系数  decay coefficient

衰变    decay

齐次方程   homogeneous equation

一阶线性方程   linear differential equation of first order

非齐次   non-homogeneous

齐次线性方程   homogeneous linear equation

非齐次线性方程   non-homogeneous linear equation

常数变易法   method of variation of constant

暂态电流   transient stata current

稳态电流   steady state current

伯努利方程   Bernoulli equation

全微分方程   total differential equation

积分因子   integrating factor

高阶微分方程   differential equation of higher order

悬链线   catenary

高阶线性微分方程   linear differential equation of higher order

自由振动的微分方程   differential equation of free vibration

强迫振动的微分方程   differential equation of forced oscillation

串联电路的振荡方程   oscillation equation of series circuit

二阶线性微分方程   second order linear differential equation

线性相关   linearly dependence

线性无关   linearly independence

二阶常系数齐次线性微分方程   second order homogeneour linear differentialequation with constant coefficient

二阶变系数齐次线性微分方程   second order homogeneous linear differentialequation with variable coefficient

特征方程   characteristic equation

无阻尼自由振动的微分方程   differential equation of free vibration withzero damping

固有频率   natural frequency

简谐振动simple harmonic oscillation, simple harmonic vibration

微分算子   differential operator

待定系数法   method of undetermined coefficient

共振现象   resonance phenomenon

欧拉方程   Euler equation

幂级数解法   power series solution

数值解法   numerical solution

勒让德方程   Legendre equation

微分方程组   system of differential equations

常系数线性微分方程组system of linera differential equations with constant  coefficient

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