微积分词汇
第一章函数与极限
Chapter1Function 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
作者:新少年特工2007-10-818:37回复此发言
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2高等数学-翻译
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
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
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
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
第三章微分中值定理与导数的应用Chapter3MeanValue 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 type0/0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
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
第四章不定积分
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
第五章定积分
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
第六章定积分的应用
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 of rotation
曲线的弧长arc length of acurve
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Chapter7Space Analytic Geometry and Vector 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
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pointnorm form eqyation 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
第八章多元函数微分法及其应用Chapter8Differentiation of Functions of Several Variables and Its Application
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openset
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 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superpostition 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
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
第九章重积分
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 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
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
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 coordinate elements
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
第十一章无穷级数
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 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coeffcients 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Forrier 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
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 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inplicit 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linera 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 linera differential equation
线性相关linearly dependence
线性无关linearly independce
二阶常系数齐次线性微分方程second order homogeneour 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numerial 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
Value of function:函数值 Variable :变数 Vector :向量 Velocity :速度 Vertical asymptote :垂直渐近线 Volume :体积 X-axis :x轴 x-coordinate :x坐标 x-intercept :x截距 Zero vector :函数的零点 Zeros of a polynomial :多项式的零点T: Tangent function :正切函数 Tangent line :切线 Tangent plane :切平面 Tangent vector :切向量 Total differential :全微分 Trigonometric function :三角函数Trigonometric integrals :三角积分Trigonometric substitutions :三角代换法Tripe integrals :三重积分 S: Saddle point :鞍点 Scalar :纯量 Secant line :割线 Second derivative :二阶导数 Second Derivative Test :二阶导数试验法Second partial derivative :二阶偏导数Sector :扇形 Sequence :数列 Series :级数 Set :集合 Shell method :剥壳法 Sine function :正弦函数 Singularity :奇点 Slant asymptote :斜渐近线 Slope :斜率 Slope-intercept equation of a line :直线的斜截式 Smooth curve :平滑曲线 Smooth surface :平滑曲面 Solid of revolution :旋转体 Space :空间 Speed :速率Spherical coordinates :球面坐标Squeeze Theorem :夹挤定理 Step function :阶梯函数 Strictly decreasing :严格递减 Strictly increasing :严格递增 Sum :和 Surface :曲面 Surface integral :面积分 Surface of revolution :旋转曲面Symmetry :对称 R: Radius of convergence :收敛半径Range of a function :函数的值域 Rate of change :变化率 Rational function :有理函数Rationalizing substitution :有理代换法Rational number :有理数 Real number :实数 Rectangular coordinates :直角坐标Rectangular coordinate system :直角坐标系 Relative maximum and minimum :相对极大值与极小值 Revenue function :收入函数 Revolution , solid of :旋转体 Revolution , surface of :旋转曲面Riemann Sum :黎曼和 Riemannian geometry :黎曼几何 Right-hand derivative :右导数 Right-hand limit :右极限 Root :根 P、Q: Parabola :拋物线 Parabolic cylinder :抛物柱面 Paraboloid :抛物面 Parallelepiped :平行六面体 Parallel lines :并行线 Parameter :参数 Partial derivative :偏导数 Partial differential equation :偏微分方程Partial fractions :部分分式 Partial integration :部分积分 Partiton :分割 Period :周期
微积分词汇 第一章函数与极限 Chapter1Function 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
西南大学课程考核
《高等数学IA 》课程试题 【A 】卷 (1) The function 4 14 )(-= x x f at x = 4 is ( ). A. not continuous, f (4) does not exist and )(lim 4 x f x → does not exist. B. continuous. C. not continuous, )(lim 4 x f x → exists but f (4) does not exist D. not continuous, )(lim 4 x f x → and f (4) exist but )4()(lim 4 f x f x ≠→. (2) For the function y = arcsin x , we have the assert ( ). A .'y is undefined at x = -1 and x = 1, so its graph has not tangent lines at ??? ??2π, 1 and ??? ? ? --2π,1. B .since its graph has not tangent lines at ??? ??2π, 1 and ??? ? ? --2π,1,'y is undefined at x = -1 and x = 1. C .'y is defined at x = -1 and x = 1, and its graph has tangent lines at ??? ??2π, 1 and ??? ?? --2π,1. D .'y is undefined at x = -1 and x = 1, and its graph has tangent lines at ?? ? ??2π, 1 and ??? ? ?--2π,1. (3) =?x x x d )(ln 1 5( ) . A. C x x +- 4 )(ln 41 B. C x +-6)(ln 61. C. C x +- 4)(ln 41 D. C x x +-6 ) (ln 61 . (4) The definite integral =+?-x x x d 131 1 32 ( ). A. 334 B. 324. C. 423 D. 4 33 (5) Area of shaded region in the following figure is ( ).
微积分英文词汇,高数名词中英文对照,高等数学术语英语翻译一览 V、X、Z: Value of function :函数值 Variable :变数 Vector :向量 Velocity :速度 Vertical asymptote :垂直渐近线 Volume :体积 X-axis :x轴 x-coordinate :x坐标 x-intercept :x截距 Zero vector :函数的零点 Zeros of a polynomial :多项式的零点 T: Tangent function :正切函数 Tangent line :切线 Tangent plane :切平面 Tangent vector :切向量 Total differential :全微分 Trigonometric function :三角函数 Trigonometric integrals :三角积分 Trigonometric substitutions :三角代换法 Tripe integrals :三重积分 S: Saddle point :鞍点 Scalar :纯量 Secant line :割线 Second derivative :二阶导数 Second Derivative Test :二阶导数试验法 Second partial derivative :二阶偏导数 Sector :扇形 Sequence :数列 Series :级数 Set :集合 Shell method :剥壳法 Sine function :正弦函数
Singularity :奇点 Slant asymptote :斜渐近线 Slope :斜率 Slope-intercept equation of a line :直线的斜截式Smooth curve :平滑曲线 Smooth surface :平滑曲面 Solid of revolution :旋转体 Space :空间 Speed :速率 Spherical coordinates :球面坐标 Squeeze Theorem :夹挤定理 Step function :阶梯函数 Strictly decreasing :严格递减 Strictly increasing :严格递增 Sum :和 Surface :曲面 Surface integral :面积分 Surface of revolution :旋转曲面 Symmetry :对称 R: Radius of convergence :收敛半径 Range of a function :函数的值域 Rate of change :变化率 Rational function :有理函数 Rationalizing substitution :有理代换法 Rational number :有理数 Real number :实数 Rectangular coordinates :直角坐标 Rectangular coordinate system :直角坐标系Relative maximum and minimum :相对极大值与极小值Revenue function :收入函数 Revolution , solid of :旋转体 Revolution , surface of :旋转曲面 Riemann Sum :黎曼和 Riemannian geometry :黎曼几何 Right-hand derivative :右导数 Right-hand limit :右极限 Root :根 P、Q: Parabola :拋物线
微积分术语中英文对照 A、B: Absolute convergence :绝对收敛 Absolute extreme values :绝对极值 Absolute maximum and minimum :绝对极大与极小Absolute value :绝对值 Absolute value function :绝对值函数Acceleration :加速度 Antiderivative :原函数,反导数 Approximate integration :近似积分(法) Approximation :逼近法 by differentials :用微分逼近 linear :线性逼近法 by Simpson’s Rule :Simpson法则逼近法 by the Trapezoidal Rule :梯形法则逼近法Arbitrary constant :任意常数 Arc length :弧长 Area :面积 under a curve :曲线下方之面积 between curves :曲线间之面积 in polar coordinates :极坐标表示之面积 of a sector of a circle :扇形之面积 of a surface of a revolution :旋转曲面之面积Asymptote :渐近线 horizontal :水平渐近线 slant :斜渐近线 vertical :垂直渐近线 Average speed :平均速率 Average velocity :平均速度 Axes, coordinate :坐标轴 Axes of ellipse :椭圆之对称轴 Binomial series :二项式级数 Binomial theorem:二项式定理 C: Calculus :微积分 differential :微分学 integral :积分学 Cartesian coordinates :笛卡儿坐标一般指直角坐标Cartesian coordinates system :笛卡儿坐标系Cauch’s Mean Value Theorem :柯西中值定理Chain Rule :链式法则 Circle :圆 Circular cylinder :圆柱体,圆筒 Closed interval :闭区间 Coefficient :系数 Composition of function :复合函数 Compound interest :复利 Concavity :凹性 Conchoid :蚌线 Conditionally convergent:条件收敛 Cone :圆锥 Constant function :常数函数 Constant of integration :积分常数 Continuity :连续性 at a point :在一点处之连续性 of a function :函数之连续性 on an interval :在区间之连续性 from the left :左连续 from the right :右连续 Continuous function :连续函数 Convergence :收敛 interval of :收敛区间 radius of :收敛半径 Convergent sequence :收敛数列 series :收敛级数 Coordinates:坐标 Cartesian :笛卡儿坐标 cylindrical :柱面坐标 polar :极坐标 rectangular :直角坐标 spherical :球面坐标 Coordinate axes :坐标轴 Coordinate planes :坐标平面 Cosine function :余弦函数 Critical point :临界点 Cubic function :三次函数 Curve :曲线 Cylinder:圆筒, 圆柱体, 柱面 Cylindrical Coordinates :圆柱坐标 D: Decreasing function :递减函数 Decreasing sequence :递减数列 Definite integral :定积分 Degree of a polynomial :多项式之次数 Density :密度 Derivative :导数 of a composite function :复合函数之导数 of a constant function :常数函数之导数directional :方向导数 domain of :导数之定义域 of exponential function :指数函数之导数higher :高阶导数 partial :偏导数 of a power function :幂函数之导数 of a power series :羃级数之导数 of a product :积之导数 of a quotient :商之导数 as a rate of change :导数当作变化率 right-hand :右导数 second :二阶导数 as the slope of a tangent :导数看成切线之斜率Determinant :行列式 Differentiable function :可导函数 Differential :微分 Differential equation :微分方程 partial :偏微分方程 Differentiation :求导法 implicit :隐求导法 partial :偏微分法 term by term :逐项求导法 Directional derivatives :方向导数Discontinuity :不连续性
微积分试题 (A 卷) 一. 填空题 (每空2分,共20分) 三. 已知,)(lim 1A x f x =+ →则对于0>?ε,总存在δ>0,使得当 时,恒有│?(x )─A│< ε。 四. 已知22 35 lim 2=-++∞→n bn an n ,则a = ,b = 。 五. 若当0x x →时,α与β 是等价无穷小量,则=-→β β α0 lim x x 。 六. 若f (x )在点x = a 处连续,则=→)(lim x f a x 。 七. )ln(arcsin )(x x f =的连续区间是 。 八. 设函数y =?(x )在x 0点可导,则=-+→h x f h x f h ) ()3(lim 000 ______________。 九. 曲线y = x 2+2x -5上点M 处的切线斜率为6,则点M 的坐标为 。 十. ='?))((dx x f x d 。 十一. 设总收益函数和总成本函数分别为2 224Q Q R -=,52 +=Q C ,则当利润最大 时产量Q 是 。 二. 单项选择题 (每小题2分,共18分) 十二. 若数列{x n }在a 的ε 邻域(a -ε,a +ε)内有无穷多个点,则( )。 (A) 数列{x n }必有极限,但不一定等于a (B) 数列{x n }极限存在,且一定等于a (C) 数列{x n }的极限不一定存在 (D) 数列{x n }的极 限一定不存在 十三. 设1 1 )(-=x arctg x f 则1=x 为函数)(x f 的( )。 (A) 可去间断点 (B) 跳跃间断点 (C) 无穷型间断点
(D) 连续点 十四. =+-∞→13)1 1(lim x x x ( )。 (A) 1 (B) ∞ (C) 2e (D) 3e 十五. 对需求函数5 p e Q -=,需求价格弹性5 p E d - =。当价格=p ( )时,需求量减少的幅度小于价格提高的幅度。 (A) 3 (B) 5 (C) 6 (D) 10 十六. 假设)(),(0)(lim , 0)(lim 0 x g x f x g x f x x x x ''==→→;在点0x 的某邻域内(0x 可以 除外)存在,又a 是常数,则下列结论正确的是( )。 (A) 若a x g x f x x =→) ()(lim 或∞,则a x g x f x x =''→)() (lim 0或∞ (B) 若a x g x f x x =''→)()(lim 0或∞,则a x g x f x x =→) () (lim 0或∞ (C) 若) ()(lim x g x f x x ''→不存在,则)() (lim 0x g x f x x →不存在 (D) 以上都不对 十七. 曲线2 2 3 )(a bx ax x x f +++=的拐点个数是( ) 。 (A) 0 (B)1 (C) 2 (D) 3 十八. 曲线2 ) 2(1 4--= x x y ( )。 (A) 只有水平渐近线; (B) 只有垂直渐近线; (C) 没有渐近线; (D) 既有水平渐近线, 又有垂直渐近线 十九. 假设)(x f 连续,其导函数图形如右图所示,则)(x f 具有 (A) 两个极大值一个极小值 (B) 两个极小值一个极大值 (C) 两个极大值两个极小值 (D) 三个极大值一个极小值 二十. 若?(x )的导函数是2 -x ,则?(x )有一个原函数为 ( ) 。 x
. 2009 — 2010 学年第 2 学期 课程名称 微积分B 试卷类型 期末A 考试形式 闭卷 考试时间 100 分钟 命 题 人 2010 年 6 月10日 使用班级 教研室主任 年 月 日 教学院长 年 月 日 姓 名 班 级 学 号 一、填充题(共5小题,每题3分,共计15分) 1.2 ln()d x x x =? . 2.cos d d x x =? . 3. 3 1 2d x x --= ? . 4.函数2 2 x y z e +=的全微分d z = . 5.微分方程ln d ln d 0y x x x y y +=的通解为 . 二、选择题(共5小题,每题3分,共计15分) 1.设 ()1x f e x '=+,则()f x = ( ). (A) 1ln x C ++ (B) ln x x C + (C) 2 2x x C ++ (D) ln x x x C -+ 2.设 2 d 11x k x +∞=+? ,则k = ( ).
. (A) 2π (B) 22π (C) (D) 2 4π 3.设()z f ax by =+,其中f 可导,则( ). (A) z z a b x y ??=?? (B) z z x y ??= ?? (C) z z b a x y ??=?? (D) z z x y ??=- ?? 4.设点00(,)x y 使00(,)0x f x y '=且00(,)0 y f x y '=成立,则( ) (A) 00(,)x y 是(,)f x y 的极值点 (B) 00(,)x y 是(,)f x y 的最小值点 (C) 00(,)x y 是(,)f x y 的最大值点 (D) 00(,)x y 可能是(,)f x y 的极值点 5.下列各级数绝对收敛的是( ). (A) 211(1)n n n ∞ =-∑ (B) 1 (1)n n ∞ =-∑ (C) 13(1)2n n n n ∞ =-∑ (D) 1 1(1)n n n ∞=-∑ 三、计算(共2小题,每题5分,共计10分) 1. 2d x x e x ? 2.4 ? 四、计算(共3小题,每题6分,共计18分) 1.设 arctan y z x =,求2,.z z z x y x y ???????,
微积分 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
1、 (1) lim sin 2x 0 . x x (2) d(arctan x) 1 2 dx 1+x (3) 1 dx x-cot x+C sin 2 x (4). ( e 2 x )(n) 2n e 2 x . (5) 4 2xdx 26/3 1 2、 (6) The right proposition in A. If lim f (x) exists and lim the following propositions is ___A_____. g (x) does not exist then lim( f (x) g( x)) does not exist. x a x a x a B. If lim f (x) , lim g (x) do both not exist then lim( f ( x) g (x)) does not exist. x a x a x a C. If lim f (x) exists and lim g (x) does not exist then lim f ( x) g(x) does not exist. x a x a x a D. If lim f (x) exists and lim g (x) does not exist then lim f ( x) does not exist. x a x a x a g( x) (7) The right proposition in the following propositions is __B______. A. If lim f (x) f (a) then f ( a) exists. x a B. If lim f (x) f (a) then f (a) does not exist. x a C. If f (a) does not exist then lim f (x) f (a) . x a D. If f ( a) y f (x) (a, f (a)) . does not exist then the cure does not have tangent at (8) The right statement in the following statements is ___D_____. lim sin x 1 A. 1 B. lim(1 x) x e x x x C. x dx 1 x 1 C b 1 5 dx b 1 5 dy D. x a 1 y 1 a 1 (9) For continuous function f ( x) , the erroneous expression in the following expressions is ____D__. A. d ( b f (b) B. d ( b f (a) f ( x)dx) f (x)dx) db a da a C. d ( b 0 D. d ( b f (b) f ( a) f (x)dx) f (x)dx) dx a dx a (10) The right proposition in the following propositions is __B______. A. If f (x) is discontinuous on [ a, b] then f ( x) is unbounded on [ a,b] . [ 第 1 页 共 5 页 ]
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
2011年微积分CI 期末试题 一、计算下列各题(本题有5个小题,每小题6分,共30分) 1. 求极限 () n n n n n cos lim 424 +-+∞ → 2. 求极限 ?? ? ??+-+-→1212111lim 1 x x x x 3. 求极限 ??? ? ? ?-- ∞ →21 8lim 3n n n 4. 求极限 x x e x x sin ) 1ln(1lim 0++--∞→ 5. 已知 ?+=C xe dx x f x )(,求? +dx x f x ) (1 二.计算下列各题(本题有6个小题,每小题6分,共36分) 6. 设 x x y )2cos 1(+=,求π=x dy |。 7. 设函数?? ?≤>++=0 , 0,)1ln()(x a x b ex x f x ,)1,0(≠>a a 确定b a ,的值,使得)(x f 在0=x 处可导,并求)0('f 。 8. 设 ) ()('x f x e e f y =,其中)(x f 二阶可导,求'y 。 9. 设)(x f y =是由方程0162 =-++x xy e y 所确定的隐函数,求)0("y 。 10.求不定积分 ? -+---dx e e e e x x x x 2 22。 11. 求不定积分 ? +xdx x arctan )1(2。 三.综合题(本题有4个小题,共34分) 12(8分) 证明不等式1,1) 1(2ln >+-> x x x x 。 13(8分) 已知函数)(x f 在区间]1,0[上连续,在)1,0(内可导,且0)0(=f ,1)1(=f 。 证明:(1)存在)1,0(∈ξ使得ξξ-=1)(f 。 (2)存在两个不同的)1,0(,∈ξη使得1)(')('=ηξf f 14(8分)某服装公司正在推广某款套装。公司确定,为卖出该款服装x 套,其单价应为
Chapter 1 Infinite Series Generally, for the given sequence ,.......,......,3,21n a a a a the expression formed by the sequence ,.......,......,3,21n a a a a .......,.....321+++++n a a a a is called the infinite series of the constants term, denoted by ∑∞ =1 n n a , that is ∑∞ =1 n n a =.......,.....321+++++n a a a a Where the nth term is said to be the general term of the series, moreover, the nth partial sum of the series is given by =n S ......321n a a a a ++++ 1.1 Determine whether the infinite series converges or diverges. Whil e it’s possible to add two numbers, three numbers, a hundred numbers, or even a million numbers, it’s impossible to add an infinite number of numbers. To form an infinite series we begin with an infinite sequence of real numbers: .....,,,3210a a a a , we can not form the sum of all the k a (there is an infinite number of the term), but we can form the partial sums ∑===0 000k k a a S ∑==+=1 101k k a a a S ∑==++=2 2102k k a a a a S
1、 (1) sin 2lim x x x →∞= 0 . (2) d(arctan )x = 2 1 d 1+x x (3) 21 d sin x x =? -cot +C x x (4).2() ()x n e = 22n x e . (5) x =? 26/3 2、 (6) The right proposition in the following propositions is ___A_____. A. If lim ()x a f x →exists and lim ()x a g x →does not exist then lim(()())x a f x g x →+does not exist. B. If lim ()x a f x →,lim ()x a g x →do bot h not exist then lim(()())x a f x g x →+does not exist. C. If lim ()x a f x →exists and lim ()x a g x →does not exist then lim ()()x a f x g x →does not exist. D. If lim ()x a f x →exists and lim ()x a g x →does not exist then () lim () x a f x g x →does not exist. (7) The right proposition in the following propositions is __B______. A. If lim ()()x a f x f a →=then ()f a 'exists. B. If lim ()()x a f x f a →≠ then ()f a 'does not exist. C. If ()f a 'does not exist then lim ()()x a f x f a →≠. D. If ()f a 'does not exist then the cure ()y f x =does not have tangent at (,())a f a . (8) The right statement in the following statements is ___D_____. A. sin lim 1x x x →∞= B. 1 lim(1)x x x e →∞+= C. 11d 1x x x C ααα += ++? D. 5511 d d 11b b a a x y x y =++?? (9) For continuous function ()f x , th e erroneous expression in the following expressions is ____D__. A. d (()d )()d b a f x x f b b =? B. d (()d )()d b a f x x f a a =-?
高等数学名词(中英文) 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 邻域neighborhood 邻域的中心centre of a neighborhood 邻域的半径radius of a neighborhood 左邻域left neighborhood 右邻域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