高等数学名词(中英文)
第一章函数与极限
Chapter1 Function and Limit 集合t
元素element
子集subt
空集empty t
并集union
交集interction
差集difference of t
基本集basic t
补集complement t
直积direct product
笛卡儿积Cartesian product
开区间open interval
闭区间clod 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inver 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
篮子怎么折单值分支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piecewi 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inver 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
清湛对数函数logarithmic function
三角函数trigonometric function
反三角函数inver 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inver hyperbolic sine
反双曲余弦inver hyperbolic cosine
反双曲正切inver hyperbolic tangent
极限limit
数列quence 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 quence
子列subquence
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 quence
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 cond 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
荧光湖单侧导数one-sided derivatives
在闭区间[a, b]上可导is derivable on the clod 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cond 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
简爱第二章读后感相关变化率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
Chapter3 Mean 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尘封记忆
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
Chapter4 Indefinite Integrals
原函数primitive function(anti-derivative)
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 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
Chapter6 Applications 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ellip
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Chapter7 Space 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
不要走太远
空间直角坐标系space rectangular coordinates中华茶道
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
谜底大全双曲柱面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
