微积分常用英文词汇(分章)

英汉微积分词汇
English-Chinese Calculus Vocabulary
第一章函数与极限
Chapter 1 Function and Limit
高等数学higher mathematics
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
象限quadrant
原点origin
坐标coordinate
轴axis
x 轴x-axis
整数integer
有理数rational number
实数real number
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center 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 onto Y
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absolute value
绝对值函数absolute value function
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
最小上界least upper bound
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
严格递减strictly decreasing
严格递增strictly increasing
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
周期函数periodic function
反函数inverse function
直接函数direct function
函数的复合composition of 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
线性函数linear function
常数函数constant function
多项式polynomial
分段定义函数piecewise defined function
阶梯函数step function
幂函数power function
指数函数exponential function
指数exponent
自然指数函数natural exponential function
对数logarithm
对数函数logarithmic function
自然对数函数natural logarithm function
三角函数trigonometric function
正弦函数sine function
余弦函数cosine function
正切函数tangent function
半角公式half-angle formulas
反三角函数inverse trigonometric function
常数函数constant function
双曲线hyperbola
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
最优化问题optimization problems
不等式inequality
极限limit
数列sequence of number
复利compound interest
收敛convergence
收敛的convergent
收敛于a converge to a
发散divergence
发散的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0x 时的极限 limit of functions as x approaches 0x
单侧极限 one-sided limit
左极限 left limit
右极限 right limit
单侧极限 one-sided limits
渐近线 asymptote
水平渐近线 horizontal asymptote
分式 fractions
商定律 quotient rule
无穷小 infinitesimal
无穷大 infinity
铅直渐近线 vertical asymptote
夹逼准则 squeeze rule (Sandwich theorem)
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
多项式的次数 degree of a polynomial
三次函数 cubic function
函数的连续性 continuity of a function
增量 increment
函数在0x 连续 the function is continuous at 0x
左连续 left continuous / continuous from the left
右连续 right continuous / continuous from the right
连续性 continuity
不连续性 discontinuity
连续函数 continuous function
函数在区间上连续 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
Chapter 2 Derivative and Differential 速度velocity
速率speed
平均速度average velocity
瞬时速度instantaneous 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
割线secant line
切线tangent line
位置函数position function
导数derivative
求导法differentiation
可导的derivable
可导函数differentiable function
光滑曲线smooth curve
变化率rate of change
函数的变化率问题problem of the change rate of a function
导函数derived function
导数定义域domain of derivative
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] 指数函数的导数derivative of exponential function
幂函数的导数derivative of power function
切线的斜率slope of the tangent line
截距intercepts
x 截距x-intercept
直线的斜截式slope-intercept equation of a line
点斜式point-slope form
切线方程tangent equation
焦点focus
角速度angular velocity
成本函数cost function
边际成本marginal cost
逐项求导法differentiation term by term
积之导数derivative of a product
商之导数derivative of a quotient
链式法则chain rule
隐函数implicit function
显函数explicit function
隐函数求导法implicit differentiation
加速度acceleration
二阶导数second derivative
三阶导数third derivative
高阶导数nth derivative / higher derivative
莱布尼茨公式Leibniz formula
对数求导法log- derivative
参数parameter
参数方程parametric equation
相关变化率correlative change rata
微分differential
微分学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
逼近法approximation
用微分逼近approximation by differentials
间接测量误差indirect measurement error
绝对误差absolute error
相对误差relative error
第三章微分中值定理与导数的应用
Chapter 3 MeanValue Theorems of Differentials and the Application of
Derivatives
均值定理mean value theorem
罗尔定理Roll’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
不定式indeterminate form
“0
”型不定式indeterminate form of type “
”
泰勒中值定理Taylor’s mean value theorem 泰勒公式Taylor formula
系数coefficient
余项remainder term
线性近似linear approximation
拉格朗日余项Lagrange remainder term
麦克劳林公式Maclaurin’s formula
佩亚诺余项Peano remainder term
阶乘factorial
凹凸性concavity
上凹（或下凸）concave upward (concave up)
下凹（或向上凸的）concave downward (concave down) 拐点inflection point
极值extreme value
函数的极值extremum of function
极大与极小值maximum and minimum values
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
收入函数revenue function
斜渐进线slant asymptote
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
第四章不定积分
Chapter 4 Indefinite Integrals 原函数primitive function / antiderivative
积分integration
积分学integral
积分号sign of integration
被积函数integrand
积分变量integral variable
积分常数constant of integration
积分曲线integral curve
积分表table of integrals
换元积分法integration by substitution
有理代换法rationalizing substitution
三角代换法trigonometric substitutions
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
部分分式partial fractions
三角积分trigonometric integrals
第五章定积分
Chapter 5 Definite Integrals
曲线下方之面积area under a curve
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
黎曼和Riemannian sum
积分和integral sum
可积的integrable
Simpson 法则逼近法approximation by Simpson’s rule
梯形法则逼近法approximation by trapezoidal rule
矩形法rectangle method
曲线之间的面积area between curves
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 interval 牛顿－莱布尼茨公式Newton-Leibniz formula
微积分基本公式fundamental formula of calculus
微积分基本定理fundamental theorem of calculus
变量代换change of variable
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
瑕点flaw
绝对收敛absolutely convergent
第六章定积分的应用
Chapter 6 Applications of the Definite Integrals 元素法the element method
面积元素element of area
平面plane
平面图形的面积area of a plane figure
直角坐标（又称“笛卡儿坐标”）Cartesian coordinates / rectangular coordinates x 坐标x-coordinate
坐标轴coordinate axes
极坐标polar coordinates
极轴polar axis
极点pole
圆circle
扇形sector
抛物线parabola
椭圆ellipse
椭圆的轴axes of ellipse
蚌线conchoid
外摆线epicycloid
双纽线lemniscate
蚶线limacon
旋转体solid of revolution, solid of rotation
旋转体的面积volume of a solid of rotation
旋转椭球体ellipsoid of revolution, ellipsoid of rotation
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
第七章空间解析几何与向量代数
Chapter 7 Space Analytic Geometry and Vector Algebra
纯量（标量）scalar
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
平行线parallel lines
向量的线性运算linear operation of vector
加法addition
减法subtraction
数乘运算scalar multiplication
三角形法则triangle rule
平行四边形法则parallelogram rule
交换律commutative law
结合律associative law
分配律distributive law
负向量negative vector
三角不等式triangle inequality
对角线diagonal
差difference
余弦定理（定律）law of cosines
空间space
空间直角坐标系space rectangular coordinates
坐标平面coordinate plane
卦限octant
向量的模modulus of vector
定比分点definite proportion and separated point
中点公式midpoint formula
等腰三角形isosceles triangle
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
投影projection
向量在轴上的投影projection of a vector onto an axis
向量的分量components of a vector
对称点symmetric point
数量积（点积，内积）scalar product (dot product, inner product)
叉积（向量积，外积）cross product (vector product, exterior product) 混合积mixed product
锐角acute angle
流体fluid
刚体rigid body
角速度angular velocity
平行六面体parallelepiped
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
三元一次方程three-variable linear equation
平面的截距式方程intercept 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point-direction form equations of a line
直线的对称式方程symmetric form equation 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
垂直线perpendicular lines
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
曲面方程equation for a surface
球面sphere
球体spheroid
球心ball center
轨迹方程locus equation
旋转轴rotation axis
旋转曲面surface of revolution
母线generating line
圆锥面cone
顶点vertex
半顶角semi-vertical angle
旋转双曲面revolution hyperboloids
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circular cylinder
圆柱面cylindrical surface
准线directrix
抛物柱面parabolic cylinder
二次曲面quadric surface
截痕法method of cut-off mark
椭圆锥面elliptic cone
椭球面ellipsoid
双曲面hyperboloid
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
抛物面paraboloid
椭圆体ellipsoid
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
交线intersection 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
螺线spiral / helix
螺矩pitch
投影柱面projecting cylinder
第八章多元函数微分法及其应用
Chapter 8 Differentiation of Functions of Several Variables and Its Application 一元函数function of one variable
二元函数binary function
邻域neighborhood
去心邻域noncentral neighborhood
方邻域square neighborhood
圆邻域circular neighborhood
内点interior point
外点exterior point
边界点frontier point, boundary point
聚点point of accumulation
导集derived set
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-dimensional space
多元函数function of several variables
二重极限double limit
多元函数的连续性continuity of function of several variables
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 to independent 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partial 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 implicit function 光滑曲面smooth surface
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
等高线level curve
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
鞍点saddle point
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
第九章重积分
Chapter 9 Multiple Integrals
重积分multiple integrals
二重积分double integral
可加性additivity
累次（逐次）积分iterated integral
体积元素volume element
二重积分变量代换法change of variable in double integral
极坐标表示的面积area in polar coordinates
扇形的面积area of a sector of a circle
极坐标二重积分double integral in polar coordinates
三重积分triple integral
直角坐标系中的体积元素volume element in rectangular coordinate system 柱面坐标cylindrical coordinates
柱面坐标系中的体积元素volume element in cylindrical coordinate system 球面坐标spherical coordinates
球面坐标系中的体积元素volume element in spherical coordinate system 剥壳法shell method
圆盘法disk method
反常二重积分improper double integral
曲面的面积area of a surface
质心center of mass
静矩static moment
密度density
形心centroid
转动惯量moment of inertia
参变量parametric variable
第十章曲线积分与曲面积分
Chapter 10 Line (Curve) Integrals and Surface Integrals
对弧长的曲线积分line integrals with respect to arc length
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
路径无关path independence
格林公式Green formula
顺时针方向clockwise
逆时针方向counterclockwise
区域边界的正向positive direction of region boundary
第一类曲面积分surface integrals of the first type
旋转曲面的面积area of a surface of a revolution
对面积的曲面积分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 coordinate elements
第二类曲面积分surface integrals of the second type
有向曲面之元素element of directed surface
高斯公式gauss formula
拉普拉斯算子Laplace operator
拉普拉斯变换Laplace transform
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)
第十一章无穷级数
Chapter 11 Infinite Series
一般项general term
部分和partial sum
收敛级数convergent series
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 criteria for 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
幂级数的导数derivative of power series
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
魏尔斯特拉斯判别法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
第十二章微分方程
Chapter 12 Differential Equation
解微分方程solve a differential equation
常微分方程ordinary differential equation (ODE)
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 differential equation
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 state 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 homogeneous linear differential equation with constant coefficient
二阶变系数齐次线性微分方程second order homogeneous linear differential equation 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 with zero 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 linear differential equations with constant coefficient。