高等数学英文1-8-10
(完整word版)高等数学常用英文单词
定义definition 变量 variable 面积area直径diameter半径radius公式formula单价unit pric e范围range/scope/extent集合set法则principle本金principal利率interest rate利息interest单利si mple interest复利compound interest正数positive number负数negative number解析式analytic expr ession分类讨论classified discussion性质nature （不是很确定）奇函数odd function偶函数even funct ion对称symmetric坐标原点origin单调性monotonicity（不是很确定）任意random周期性periodic 有界性boundedness 数学mathematics, maths(BrE), math(AmE) 公理axiom 定理theorem 计算calcu lation 运算operation 证明prove 假设hypothesis, hypotheses(pl.) 命题proposition 算术arithmetic 加plus(prep.), add(v.), addition(n.) 被加数augend, summand 加数addend 和sum 减minus(prep.), subtract(v.), subtraction(n.) 被减数minuend 减数subtrahend 差remainder 乘times(prep.), multiply (v.), multiplication(n.) 被乘数multiplicand, faciend 乘数multiplicator 积product 除divided by(prep.), divide(v.), division(n.) 被除数dividend 除数divisor 商quotient 等于equals, is equal to, is equivale nt to 大于is greater than 小于is lesser than 大于等于is equal or greater than 小于等于is equal o r lesser than 运算符operator 平均数mean 算术平均数arithmatic mean 几何平均数geometric mean n 个数之积的n次方根倒数（reciprocal）x的倒数为1/x 有理数rational number 无理数irrational nu mber 实数real number 虚数imaginary number 数字digit 数number 自然数natural number 整数in teger 小数decimal 小数点decimal point 分数fraction 分子numerator 分母denominator 比ratio 正positive 负negative 零null, zero, nought, nil 十进制decimal system 二进制binary system 十六进制hexadecimal system 权weight, significance 进位carry 截尾truncation 四舍五入round 下舍入rou nd down 上舍入round up 有效数字significant digit 无效数字insignificant digit 代数algebra 公式fo rmula, formulae(pl.) 单项式monomial 多项式polynomial, multinomial 系数coefficient 未知数unknow n, x-factor, y-factor, z-factor 等式，方程式equation 一次方程simple equation 二次方程quadratic equ ation 三次方程cubic equation 四次方程quartic equation 不等式inequation 阶乘factorial 对数logarit hm 指数，幂exponent 乘方power 二次方，平方square 三次方，立方cube 四次方the power of fou r, the fourth power n次方the power of n, the nth power 开方evolution, extraction 二次方根，平方根square root 三次方根，立方根cube root 四次方根the root of four, the fourth root n次方根the r oot of n, the nth root sqrt(2)=1.414 sqrt(3)=1.732 sqrt(5)=2.236 常量constant 变量variable 坐标系coordinates 坐标轴x-axis, y-axis, z-axis 横坐标x-coordinate 纵坐标y-coordinate 原点origin 象限quadrant 截距(有正负之分)intercede （方程的）解solution 几何geometry 点point 线line 面pla ne 体solid 线段segment 射线radial 平行parallel 相交intersect 角angle 角度degree 弧度radian 锐角acute angle 直角right angle 钝角obtuse angle 平角straight angle 周角perigon 底base 边si de 高height 三角形triangle 锐角三角形acute triangle 直角三角形right triangle 直角边leg 斜边hyp otenuse 勾股定理Pythagorean theorem 钝角三角形obtuse triangle 不等边三角形scalene triangle 等腰三角形isosceles triangle 等边三角形equilateral triangle 四边形quadrilateral 平行四边形parallelogr am 矩形rectangle 长length 宽width 周长perimeter 面积area 相似similar 全等congruent 三角tri gonometry 正弦sine 余弦cosine 正切tangent 余切cotangent 正割secant 余割cosecant 反正弦arc sine 反余弦arc cosine 反正切arc tangent 反余切arc cotangent 反正割arc secant 反余割arc cose cant 补充：集合aggregate 元素element 空集void 子集subset 交集intersection 并集union 补集co mplement 映射mapping 函数function 定义域domain, field of definition 值域range 单调性mono tonicity 奇偶性parity 周期性periodicity 图象image 数列，级数series 微积分calculus 微分differenti al 导数derivative 极限limit 无穷大infinite(a.) infinity(n.) 无穷小infinitesimal 积分integral 定积分d efinite integral 不定积分indefinite integral 复数complex number 矩阵matrix 行列式determinant 圆circle 圆心centre(BrE), center(AmE) 半径radius 直径diameter 圆周率pi 弧arc 半圆semicircle 扇形sector 环ring 椭圆ellipse 圆周circumference 轨迹locus, loca(pl.) 平行六面体parallelepiped 立方体cube 七面体heptahedron 八面体octahedron 九面体enneahedron 十面体decahedron 十一面体hendecahedron 十二面体dodecahedron 二十面体icosahedron 多面体polyhedron 旋转rotation 轴axis 球sphere 半球hemisphere 底面undersurface 表面积surface area 体积volume 空间space 双曲线hyperbola 抛物线parabola 四面体tetrahedron 五面体pentahedron 六面体hexahedron菱形rhomb, rhombus, rhombi(pl.), diamond 正方形square 梯形trapezoid 直角梯形right trapezoid 等腰梯形isosc eles trapezoid 五边形pentagon 六边形hexagon 七边形heptagon 八边形octagon 九边形enneagon 十边形decagon 十一边形hendecagon 十二边形dodecagon 多边形polygon 正多边形equilateral poly gon 相位phase 周期period 振幅amplitude 内心incentre(BrE), incenter(AmE) 外心excentre(BrE), e xcenter(AmE) 旁心escentre(BrE), escenter(AmE) 垂心orthocentre(BrE), orthocenter(AmE) 重心baryc entre(BrE), barycenter(AmE) 内切圆inscribed circle 外切圆circumcircle 统计statistics 平均数average 加权平均数weighted average 方差variance 标准差root-mean-square deviation, standard deviation 比例propotion 百分比percent 百分点percentage 百分位数percentile 排列permutation 组合combin ation 概率，或然率probability 分布distribution 正态分布normal distribution 非正态分布abnormal dis tribution 图表graph 条形统计图bar graph 柱形统计图histogram 折线统计图broken line graph 曲线统计图curve diagram 扇形统计图pie diagram 数列是sequence极限是limit导数是derivative微分是dif ferential积分是integral常数constant级数series幂级数power series二重积分double integral数学mathematics, maths(BrE), math(AmE) 公理axiom 定理theorem计算calculation 运算operation 证明prove 假设hypothesis, hypotheses(pl.) 命题proposition算术arithmetic 加plus(prep.), add(v.), addition(n.) 被加数augend, summand加数addend 和sum 减minus(prep.), subtract(v.), subtraction(n.) 被减数minuend 减数subtrahend 差remainder 乘times(prep.), multiply(v.), multiplication(n.)被乘数multiplicand, faciend 乘数multiplicator 积product除divided by(prep.), divide(v.), division(n.) 被除数dividend 除数divisor商quotient 等于equals, is equal to, is equivalent to 大于is greater than小于is lesser than 大于等于is equal or greater than小于等于is equal or lesser than 运算符operator 平均数mean算术平均数arithmatic mean几何平均数geometric mean n个数之积的n次方根倒数（reciprocal）x的倒数为1/x 有理数rational number 无理数irrational number实数real number 虚数imaginary number 数字digit 数number 自然数natural number 整数integer 小数decimal 小数点decimal point 分数fraction 分子numerator分母denominator 比ratio 正positive 负negative 零null, zero, nought, nil十进制decimal system 二进制binary system 十六进制hexadecimal system权weight, significance 进位carry 截尾truncation 四舍五入round下舍入round down 上舍入round up 有效数字significant digit 无效数字insignificant digit 代数algeb ra 公式formula, formulae(pl.) 单项式monomial 多项式polynomial, multinomial 系数coefficient 未知数unknown, x-factor, y-factor, z-factor 等式，方程式equation 一次方程simple equation 二次方程qu adratic equation 三次方程cubic equation 四次方程quartic equation 不等式inequation 阶乘factorial 对数logarithm 指数，幂exponent 乘方power 二次方，平方square 三次方，立方cube四次方the power of four, the fourth power n次方the power of n, the nth power开方evolution, extraction 二次方根，平方根square root 三次方根，立方根cube root 四次方根the ro ot of four, the fourth root n次方根the root of n, the nth rootsqrt(2)=1.414 sqrt(3)=1.732 sqrt(5)=2.236常量constant 变量variable坐标系coordinates 坐标轴x-axis, y-axis, z-axis 横坐标x-coordinate纵坐标y-coordinate 原点origin 象限quadrant 截距(有正负之分)intercede（方程的）解solution 几何geometry 点point 线line 面plane 体solid 线段segment射线radial 平行parallel 相交intersect 角angle角度degree 弧度radian 锐角acute angle 直角right angle 钝角obtuse angle 平角straight angle 周角perigon底base 边side 高height 三角形triangle 锐角三角形acute triangle right triangle直角边leg 斜边hypotenuse 勾股定理Pythagorean theorem 钝角三角形obtuse triangle 不等边三角形scalene triangle 等腰三角形isosceles triangle 等边三角形equilateraltriangle 四边形quadrilateral 平行四边形parallelogram矩形rectangle 长length宽width周长perimeter 面积area 相似similar 全等congruent三角trigonometry正弦sine 余弦cosine 正切tangent 余切cotangent 正割secant 余割cosecant反正弦arc sine 反余弦arc cosine 反正切arc tangent 反余切arc cotangent 反正割arc secant 反余割arc cosecant 集合aggregate 元素element 空集void 子集subset交集intersection 并集union 补集complement 映射mapping function 定义域domain, field of definiti on 值域range 单调性monotonicity 奇偶性parity 周期性periodicity 图象image 数列，级数series 微积分calculus 微分differential 导数derivative 极限limit 无穷大infinite(a.) infinity(n.) 无穷小infinit esimal 积分integral 定积分definite integral 不定积分indefinite integral 复数complex number 矩阵matrix 行列式determinan圆circle 圆心centre(BrE), center(AmE) 半径radius 直径diameter 圆周率pi 弧arc 半圆semicircle 扇形sector 环ring 椭圆ellipse 圆周circumference 轨迹locus, loca(pl.) 平行六面体parallelepiped 立方体cube 七面体heptahedron八面体octahedron 九面体enneahedron 十面体decahedron 十一面体hendecahedron 十二面体dodec ahedron 二十面体icosahedron 多面体polyhedron 旋转rotation 轴axis 球sphere 半球hemisphere 底面undersurface 表面积surface area 体积volume 空间space 双曲线hyperbola 抛物线parabola四面体tetrahedron 五面体pentahedron 六面体hexahedron菱形rhomb, rhombus, rhombi(pl.), diamo nd 正方形square 梯形trapezoid 直角梯形right trapezoid 等腰梯形isosceles trapezoid 五边形penta gon 六边形hexagon 七边形heptagon 八边形octagon九边形enneagon 十边形decagon 十一边形he ndecagon 十二边形dodecagon 多边形polygon 正多边形equilateral polygon相位phase 周期period 振幅amplitude内心incentre(BrE), incenter(AmE) 外心excentre(BrE), excenter(AmE) 旁心escentre(BrE), escenter(A mE) 垂心orthocentre(BrE), orthocenter(AmE) 重心barycentre(BrE), barycenter(AmE) 内切圆inscribed circle 外切圆circumcircle统计statistics 平均数average 加权平均数weighted average方差variance 标准差root-mean-square deviation, standard deviation比例propotion 百分比percent 百分点percentage 百分位数percentile排列permutation 组合combination 概率，或然率probability 分布distribution 正态分布normal distrib ution 非正态分布abnormal distribution图表graph 条形统计图bar graph 柱形统计图histogram 折线统计图broken line graph 曲线统计图curve diagram 扇形统计图pie diagram1。
高等数学名词（中英文）
高等数学名词（中英文）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mappingX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 ofDifferentials and the Application ofDerivatives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 Rule0/0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T aylorformula余项remainder term拉格朗日余项Lagrange remainder term麦克劳林公式Ma claurin’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 DefiniteIntegrals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Chapter7 Space Analytic Geometry andVector 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Chapter8 Differentiation of Functions ofSeveral 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 setn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Chapter9 Multiple 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Chapter10 Line (Curve) Integrals andSurface 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Chapter11 Infinite 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Chapter12 Differential Equation解微分方程solve a differential 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 adifferential 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 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 lineardifferential 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 linear differential equations with constant coefficientV、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Periodic function ：周期函数Perpendicular lines ：垂直线Piecewise defined function 分段定义函数Plane ：平面Point of inflection ：反曲点Polar axis ：极轴Polar coordinate ：极坐标Polar equation ：极方程式Pole ：极点Polynomial ：多项式Positive angle ：正角Point-slope form ：点斜式Power function ：幂函数Product ：积Quadrant ：象限Quotient Law of limit 极限的商定律Quotient Rule ：商定律M、N、O:Maximum and minimum values ：极大与极小值Mean Value Theorem ：均值定理Multiple integrals ：重积分Multiplier ：乘子Natural exponential function 自然指数函数Natural logarithm function 自然对数函数Natural number ：自然数Normal line ：法线Normal vector ：法向量Number ：数Octant ：卦限Odd function ：奇函数One-sided limit ：单边极限Open interval ：开区间Optimization problems ：最佳化问题Order ：阶Ordinary differential equation ：常微分方程Origin ：原点Orthogonal ：正交的L:Laplace transform ：Leplace 变换Law of Cosines ：余弦定理Least upper bound ：最小上界Left-hand derivative ：左导数Left-hand limit ：左极限Lemniscate ：双钮线Length ：长度Level curve ：等高线L'Hospital's rule 洛必达法则Limacon ：蚶线Limit ：极限Linear approximation：线性近似Linear equation ：线性方程式Linear function ：线性函数Linearity ：线性Linearization ：线性化Line in the plane ：平面上之直线Line in space ：空间之直线Lobachevski geometry 罗巴切夫斯基几何Local extremum ：局部极值Local maximum and minimum 局部极大值与极小值Logarithm ：对数Logarithmic function ：对数函数I:Implicit differentiation ：隐求导法Implicit function ：隐函数Improper integral ：瑕积分Increasing/Decreasing Test 递增或递减试验法Increment ：增量Increasing Function ：增函数Indefinite integral ：不定积分Independent variable ：自变数Indeterminate from ：不定型Inequality ：不等式Infinite point ：无穷极限Infinite series ：无穷级数Inflection point ：反曲点Instantaneous velocity ：瞬时速度Integer ：整数Integral ：积分Integrand ：被积分式Integration ：积分Integration by part ：分部积分法Intercepts ：截距Intermediate value of Theorem 中间值定理Interval ：区间Inverse function ：反函数Inverse trigonometric function反三角函数Iterated integral ：逐次积分H:Higher mathematics 高等数学/高数E、F、G、H:Ellipse ：椭圆Ellipsoid ：椭圆体Epicycloid ：外摆线Equation ：方程式Even function ：偶函数Expected Valued ：期望值Exponential Function ：指数函数Exponents , laws of ：指数率Extreme value ：极值Extreme Value Theorem ：极值定理Factorial ：阶乘First Derivative Test ：一阶导数试验法First octant ：第一卦限Focus ：焦点Fractions ：分式Function ：函数Fundamental Theorem of Calculus ：微积分基本定理Geometric series ：几何级数Gradient ：梯度Graph ：图形Green Formula ：格林公式Half-angle formulas ：半角公式Harmonic series ：调和级数Helix ：螺旋线Higher Derivative ：高阶导数Horizontal asymptote ：水平渐近线Horizontal line ：水平线Hyperbola ：双曲线Hyper boloid ：双曲面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Disk method ：圆盘法Distance ：距离Divergence ：发散Domain ：定义域Dot product ：点积Double integral ：二重积分change of variable in二重积分之变数变换in polar coordinates ：极坐标二重积分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 柯西均值定理Chain Rule ：连锁律Change of variables ：变数变换Circle ：圆Circular cylinder ：圆柱Closed interval ：封闭区间Coefficient ：系数Composition of function ：函数之合成Compound interest ：复利Concavity ：凹性Conchoid ：蚌线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Coordinate：s：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：圆柱Cylindrical Coordinates ：圆柱坐标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 ：反导数Approximate integration ：近似积分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 ：椭圆之轴Binomial series ：二项级数微积分专有名词中英文对照absolutely convergent 绝对收敛absolute value 绝对值algebraic function 代数函数analytic geometry 解析几何antiderivative 不定积分approximate integration 近似积分approximation 近似法、逼近法arbitrary constant 任意常数arithmetic series/progression (AP)算数级数asymptotes (vertical and horizontal)(垂直/水平)渐近线average rate of change 平均变化率base 基数binomial theorem 二项式定理，二项展开式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 柯西均值定理chain rule 链式求导法则calculus 微积分学closed interval integral 闭区间积分coefficient 系数composite function 复合函数conchoid 蚌线continuity (函数的)连续性concavity (函数的)凹凸性conditionally convergent 有条件收敛continuity 连续性critical point 临界点cubic function 三次函数cylindrical coordinates 圆柱坐标decreasing function 递减函数decreasing sequence 递减数列definite integral 定积分derivative 导数determinant 行列式differential coefficient 微分系数differential equation 微分方程directional derivative 方向导数discontinuity 不连续性discriminant (二次函数)判别式disk method 圆盘法divergence 散度divergent 发散的domain 定义域dot product 点积double integral 二重积分ellipse 椭圆ellipsoid 椭圆体epicycloid 外摆线Euler's method (BC)欧拉法expected valued 期望值exponential function 指数函数extreme value heorem 极值定理factorial 阶乘finite series 有限级数fundamental theorem of calculus 微积分基本定理geometric series/progression (GP)几何级数gradient 梯度Green formula 格林公式half-angle formulas 半角公式harmonic series 调和级数helix 螺旋线higher derivative 高阶导数horizontal asymptote 水平渐近线horizontal line 水平线hyperbola 双曲线hyper boloid 双曲面implicit differentiation 隐函数求导implicit function 隐函数improper integral 广义积分、瑕积分increment 增量increasing function 增函数indefinite integral 不定积分independent variable 自变数inequality 不等式ndeterminate form 不定型infinite point 无穷极限infinite series 无穷级数infinite series 无限级数inflection point (POI) 拐点initial condition 初始条件instantaneous rate of change 瞬时变化率integrable 可积的integral 积分integrand 被积分式integration 积分integration by part 分部积分法intercept 截距intermediate value of Theorem ：中间值定理inverse function 反函数irrational function 无理函数iterated integral 逐次积分Laplace transform 拉普拉斯变换law of cosines 余弦定理least upper bound 最小上界left-hand derivative 左导数left-hand limit 左极限L'Hospital's rule 洛必达法则limacon 蚶线linear approximation 线性近似法linear equation 线性方程式linear function 线性函数linearity 线性linearization 线性化local maximum 极大值local minimum 极小值logarithmic function 对数函数MacLaurin series 麦克劳林级数maximum 最大值mean value theorem (MVT)中值定理minimum 最小值method of lagrange multipliers 拉格朗日乘数法modulus 绝对值multiple integral 多重积分multiple 倍数multiplier 乘子octant 卦限open interval integral 开区间积分optimization 优化法，极值法origin 原点orthogonal 正交parametric equation (BC)参数方程partial derivative 偏导数partial differential equation 偏微分方程partial fractions 部分分式piece-wise function 分段函数parabola 抛物线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 integration 部分积分partiton ：分割period ：周期periodic function 周期函数perpendicular lines 垂直线piecewise defined function 分段定义函数plane 平面point of inflection 反曲点point-slope form 点斜式polar axis 极轴polar coordinates 极坐标polar equation 极坐标方程pole 极点polynomial 多项式power series 幂级数product rule 积的求导法则quadrant 象限quadratic functions 二次函数quotient rule 商的求导法则radical 根式radius of convergence 收敛半径range 值域(related) rate of change with time (时间)变化率rational function 有理函数reciprocal 倒数remainder theorem 余数定理Riemann sum 黎曼和Riemannian geometry 黎曼几何right-hand limit 右极限Rolle's theorem 罗尔(中值)定理root 根rotation 旋转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series 级数shell method (积分)圆筒法sine function 正弦函数singularity 奇点slant 母线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symmetry 对称性substitution 代入法、变量代换tangent function 正切函数tangent line 切线tangent plane 切(平)面tangent vector 切矢量taylor's series 泰勒级数three-dimensional analytic geometry 空间解析几何total differentiation 全微分trapezoid rule 梯形(积分)法则。
高等数学名词(中英文)
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mappingX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 ofDifferentials and the Application ofDerivatives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 Rule0/0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 DefiniteIntegrals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Chapter7 Space Analytic Geometry andVector 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Chapter8 Differentiation of Functions ofSeveral 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 setn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Chapter9 Multiple 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Chapter10 Line (Curve) Integrals andSurface 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Chapter11 Infinite 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Chapter12 Differential Equation解微分方程solve a differential 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 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 lineardifferential 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 linear differential equations with constant coefficientV、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Periodic function ：周期函数Perpendicular lines ：垂直线Piecewise defined function 分段定义函数Plane ：平面Point of inflection ：反曲点Polar axis ：极轴Polar coordinate ：极坐标Polar equation ：极方程式Pole ：极点Polynomial ：多项式Positive angle ：正角Point-slope form ：点斜式Power function ：幂函数Product ：积Quadrant ：象限Quotient Law of limit 极限的商定律Quotient Rule ：商定律M、N、O:Maximum and minimum values ：极大与极小值Mean Value Theorem ：均值定理Multiple integrals ：重积分Multiplier ：乘子Natural exponential function 自然指数函数Natural logarithm function 自然对数函数Natural number ：自然数Normal line ：法线Normal vector ：法向量Number ：数Octant ：卦限Odd function ：奇函数One-sided limit ：单边极限Open interval ：开区间Optimization problems ：最佳化问题Order ：阶Ordinary differential equation ：常微分方程Origin ：原点Orthogonal ：正交的L:Laplace transform ：Leplace 变换Law of Cosines ：余弦定理Least upper bound ：最小上界Left-hand derivative ：左导数Left-hand limit ：左极限Lemniscate ：双钮线Length ：长度Level curve ：等高线L'Hospital's rule 洛必达法则Limacon ：蚶线Limit ：极限Linear approximation：线性近似Linear equation ：线性方程式Linear function ：线性函数Linearity ：线性Linearization ：线性化Line in the plane ：平面上之直线Line in space ：空间之直线Lobachevski geometry 罗巴切夫斯基几何Local extremum ：局部极值Local maximum and minimum 局部极大值与极小值Logarithm ：对数Logarithmic function ：对数函数I:Implicit differentiation ：隐求导法Implicit function ：隐函数Improper integral ：瑕积分Increasing/Decreasing Test 递增或递减试验法Increment ：增量Increasing Function ：增函数Indefinite integral ：不定积分Independent variable ：自变数Indeterminate from ：不定型Inequality ：不等式Infinite point ：无穷极限Infinite series ：无穷级数Inflection point ：反曲点Instantaneous velocity ：瞬时速度Integer ：整数Integral ：积分Integrand ：被积分式Integration ：积分Integration by part ：分部积分法Intercepts ：截距Intermediate value of Theorem 中间值定理Interval ：区间Inverse function ：反函数Inverse trigonometric function反三角函数Iterated integral ：逐次积分H:Higher mathematics 高等数学/高数E、F、G、H:Ellipse ：椭圆Ellipsoid ：椭圆体Epicycloid ：外摆线Equation ：方程式Even function ：偶函数Expected Valued ：期望值Exponential Function ：指数函数Exponents , laws of ：指数率Extreme value ：极值Extreme Value Theorem ：极值定理Factorial ：阶乘First Derivative Test ：一阶导数试验法First octant ：第一卦限Focus ：焦点Fractions ：分式Function ：函数Fundamental Theorem of Calculus ：微积分基本定理Geometric series ：几何级数Gradient ：梯度Graph ：图形Green Formula ：格林公式Half-angle formulas ：半角公式Harmonic series ：调和级数Helix ：螺旋线Higher Derivative ：高阶导数Horizontal asymptote ：水平渐近线Horizontal line ：水平线Hyperbola ：双曲线Hyper boloid ：双曲面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Disk method ：圆盘法Distance ：距离Divergence ：发散Domain ：定义域Dot product ：点积Double integral ：二重积分change of variable in二重积分之变数变换in polar coordinates ：极坐标二重积分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 柯西均值定理Chain Rule ：连锁律Change of variables ：变数变换Circle ：圆Circular cylinder ：圆柱Closed interval ：封闭区间Coefficient ：系数Composition of function ：函数之合成Compound interest ：复利Concavity ：凹性Conchoid ：蚌线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Coordinate：s：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：圆柱Cylindrical Coordinates ：圆柱坐标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 ：反导数Approximate integration ：近似积分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 ：椭圆之轴Binomial series ：二项级数微积分专有名词中英文对照absolutely convergent 绝对收敛absolute value 绝对值algebraic function 代数函数analytic geometry 解析几何antiderivative 不定积分approximate integration 近似积分approximation 近似法、逼近法arbitrary constant 任意常数arithmetic series/progression (AP)算数级数asymptotes (vertical and horizontal)(垂直/水平)渐近线average rate of change 平均变化率base 基数binomial theorem 二项式定理，二项展开式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 柯西均值定理chain rule 链式求导法则calculus 微积分学closed interval integral 闭区间积分coefficient 系数composite function 复合函数conchoid 蚌线continuity (函数的)连续性concavity (函数的)凹凸性conditionally convergent 有条件收敛continuity 连续性critical point 临界点cubic function 三次函数cylindrical coordinates 圆柱坐标decreasing function 递减函数decreasing sequence 递减数列definite integral 定积分derivative 导数determinant 行列式differential coefficient 微分系数differential equation 微分方程directional derivative 方向导数discontinuity 不连续性discriminant (二次函数)判别式disk method 圆盘法divergence 散度divergent 发散的domain 定义域dot product 点积double integral 二重积分ellipse 椭圆ellipsoid 椭圆体epicycloid 外摆线Euler's method (BC)欧拉法expected valued 期望值exponential function 指数函数extreme value heorem 极值定理factorial 阶乘finite series 有限级数fundamental theorem of calculus 微积分基本定理geometric series/progression (GP)几何级数gradient 梯度Green formula 格林公式half-angle formulas 半角公式harmonic series 调和级数helix 螺旋线higher derivative 高阶导数horizontal asymptote 水平渐近线horizontal line 水平线hyperbola 双曲线hyper boloid 双曲面implicit differentiation 隐函数求导implicit function 隐函数improper integral 广义积分、瑕积分increment 增量increasing function 增函数indefinite integral 不定积分independent variable 自变数inequality 不等式ndeterminate form 不定型infinite point 无穷极限infinite series 无穷级数infinite series 无限级数inflection point (POI) 拐点initial condition 初始条件instantaneous rate of change 瞬时变化率integrable 可积的integral 积分integrand 被积分式integration 积分integration by part 分部积分法intercept 截距intermediate value of Theorem ：中间值定理inverse function 反函数irrational function 无理函数iterated integral 逐次积分Laplace transform 拉普拉斯变换law of cosines 余弦定理least upper bound 最小上界left-hand derivative 左导数left-hand limit 左极限L'Hospital's rule 洛必达法则limacon 蚶线linear approximation 线性近似法linear equation 线性方程式linear function 线性函数linearity 线性linearization 线性化local maximum 极大值local minimum 极小值logarithmic function 对数函数MacLaurin series 麦克劳林级数maximum 最大值mean value theorem (MVT)中值定理minimum 最小值method of lagrange multipliers 拉格朗日乘数法modulus 绝对值multiple integral 多重积分multiple 倍数multiplier 乘子octant 卦限open interval integral 开区间积分optimization 优化法，极值法origin 原点orthogonal 正交parametric equation (BC)参数方程partial derivative 偏导数partial differential equation 偏微分方程partial fractions 部分分式piece-wise function 分段函数parabola 抛物线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 integration 部分积分partiton ：分割period ：周期periodic function 周期函数perpendicular lines 垂直线piecewise defined function 分段定义函数plane 平面point of inflection 反曲点point-slope form 点斜式polar axis 极轴polar coordinates 极坐标polar equation 极坐标方程pole 极点polynomial 多项式power series 幂级数product rule 积的求导法则quadrant 象限quadratic functions 二次函数quotient rule 商的求导法则radical 根式radius of convergence 收敛半径range 值域(related) rate of change with time (时间)变化率rational function 有理函数reciprocal 倒数remainder theorem 余数定理Riemann sum 黎曼和Riemannian geometry 黎曼几何right-hand limit 右极限Rolle's theorem 罗尔(中值)定理root 根rotation 旋转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series 级数shell method (积分)圆筒法sine function 正弦函数singularity 奇点slant 母线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symmetry 对称性substitution 代入法、变量代换tangent function 正切函数tangent line 切线tangent plane 切(平)面tangent vector 切矢量taylor's series 泰勒级数three-dimensional analytic geometry 空间解析几何total differentiation 全微分trapezoid rule 梯形(积分)法则。
高中数学词汇中英文对照
一、代数部分 (Algebra)1. 数学运算equal, is equal to 等于equivalent to 等价于is greater than 大于is lesser than 小于is equal or greater than 大于等于is equal or lesser than 小于等于operator 运算符add, plus 加subtract 减difference 差multiply, times 乘product 积divide 除augend, summand 被加数addend 加数minuend 被减数subtrahend 减数remainder 差multiplicand, faciend 被乘数multiplicator 乘数product 积dividend 被除数divisor 除数quotient 商remainder 余数divisible 可被整除的divided evenly 被整除divisor 因子，除数dividend 被除数factorial 阶乘power 乘方radical sign, root sign 根号factorial 阶乘logarithm 对数exponent 指数，幂power 乘方square 二次方，平方cube 三次方，立方the power of n, the nth power n次方evolution, extraction 开方square root 二次方根，平方根cube root 三次方根，立方根the root of n, the nth root n次方根2. 数字digit数字number数natural number 自然数integer/whole number 整数positive number 正数negative number 负数positive whole number 正整数negative whole number 负整数consecutive number 连续整数odd integer, odd number 奇数even integer, even number 偶数real number 实数rational number 有理数irrational number 无理数consecutive 连续数inverse / reciprocal 倒数composite number 合数prime number 质数common divisor 公约数multiple 倍数(least) common multiple (最小)公倍数(prime) factor (质)因子common factor 公因子nonnegative 非负的units 个位tens 十位ordinary / decimal scale 十进制binary system 二进制hexadecimal system 十六进制weight, significance 权carry 进位truncation 截尾round to / to the nearest 四舍五入round down 下舍入round up 上舍入significant digit 有效数字insignificant digit 无效数字3. 分数和小数decimal 小数decimal point 小数点fraction 分数numerator 分子denominator 分母proper fraction 真分数improper fraction 假分数common fraction 普通分数mixed number 带分数simple fraction 简分数complex fraction 繁分数(least) common denominator (最小)公分母quarter 四分之一decimal fraction 纯小数infinite decimal 无穷小数recurring decimal 循环小数places位（thousands’ place，hundreds’place，tens’place，units’ place (ones’ digit)，tenths’ place，hundredths’place，thousandths’ place.）4. 集合与函数aggregate 集合element 元素void 空集subset 子集union 并集intersection 交集complement 补集proper subset 真子集solution set 解集mapping 映射function 函数domain, field of definition 定义域range 值域constant 常量variable 变量monotonicity 单调性parity 奇偶性periodicity 周期性image 图象5. 代数式、方程和不等式formula, formulae (pl.) 公式monomial 单项式polynomial, multinomial 多项式coefficient 系数equation 等式，方程式unknown, x-factor y-factor, z-factor 未知数simple equation 一次方程quadratic equation 二次方程cubic equation 三次方程quartic equation 四次方程inequation, inequality 不等式algebraic term 代数项like terms, similar terms 同类项literal coefficient 字母系数numerical coefficient 数字系数range 值域factorization 因式分解original equation 原方程equivalent equation 同解方程，等价方程linear equation 线性方程triangle inequality 三角不等式6. 逻辑axiom 公理theorem 定理calculation 计算operation 运算prove 证明hypothesis, hypotheses（pl.）假设proposition 命题arithmetic 算术7. 概率与统计approximate 近似estimation 估计，近似mean 均值mode 众数median 中数variance 方差standard error 标准偏差standard variation 标准方差standard deviation 标准差statistics 统计average 平均数weighted average 加权平均数proportion 比例percent 百分比percentage 百分点percentile 百分位数permutation 排列combination 组合probability 概率distribution 分布normal distribution 正态分布abnormal distribution 非正态分布graph 图表bar graph 条形统计histogram 柱形统计图broken line graph 折线统计图curve diagram 曲线统计图pie diagram 扇形统计图8. 三角函数trigonometry 三角sine 正弦cosine 余弦tangent 正切cotangent 余切secant 正割cosecant 余割arc sine 反正弦arc cosine 反余弦arc tangent 反正切arc cotangent 反余切arc secant 反正割arc cosecant 反余割phase 相位period 周期amplitude 振幅9. 数列arithmetic progression(sequence)等差数列geometric progression(sequence)等比数列10. 微积分与线性代数series 数列，级数calculus 微积分differential 微分derivative 导数limit 极限infinite 无穷大infinitesimal 无穷小integral 积分definite integral 定积分indefinite integral 不定积分rational number 有理数irrational number 无理数real number 实数imaginary number 虚数complex number 复数matrix 矩阵determinant 行列式11. 其他direct proportion 正比indirect proportion 反比proportion 比例ratio 比值arithmetic mean 算术平均值geometric mean 几何平均数weighted average 加权平均值exponent 指数，幂base 乘幂的底数，底边powers 幂cube 立方数，立方体square root 平方根cube root 立方根common logarithm 常用对数constant 常数variable 变量inverse function 反函数complementary function 余函数linear 一次的，线性的factorization 因式分解absolute value 绝对值approximate 近似(anti)clockwise (逆)顺时针方向cardinal 基数ordinal 序数direct proportion 正比distinct 不同的estimation 估计，近似parentheses 括号proportion 比例permutation 排列combination 组合table 表格trigonometric function 三角函数unit 单位,位二、几何部分 (Geometry)1. 基本术语point 点line 线plane 面solid 体space 空间segment 线段radial 射线circumference, perimeter 周长surface area 表面积volume 体积line, straight line 直线line segment 线段midpoint 中点endpoint 端点parallel 平行intersect 相交perpendicular 垂直edge 边，棱vertex(复数形式vertices) 顶点length 长width 宽altitude 高depth 深度side 边长tangent 切线的transversal 截线intercept 截距congruent 全等的similar 相似2. 平面图形quadrilateral 四边形pentagon 五边形hexagon 六边形heptagon 七边形octagon 八边形nonagon 九边形decagon 十边形hendecagon 十一边形dodecagon 十二边形polygon 多边形multilateral 多边的equilateral/regular polygon 正多边形parallelogram 平行四边形square 正方形rectangle 矩形rhombus, diamond 菱形trapezoid 梯形right trapezoid 直角梯形isosceles trapezoid 等腰梯形3. 角angle 角degree 角度radian 弧度acute angle 锐角right angle 直角obtuse angle 钝角round angle 周角straight angle 平角included angle 夹角adjacent angle 邻角interior angle 内角exterior angle 外角supplement aryangle 补角complement aryangle 余角alternate angle 内错角corresponding angle 同位角vertical angle 对顶角central angle 圆心角angle bisector 角平分线bisect 平分diagonal 对角线4. 三角形triangle 三角形right triangle 直角三角形acute triangle 锐角三角形obtuse triangle 钝角三角形oblique 斜三角形isosceles triangle 等腰三角形equilateral triangle 等边三角形scalene triangle 不等边三角形incenter 内心excenter 外心escenter 旁心orthocenter 垂心barycenter 重心inscribed triangle 内接三角形hypotenuse 斜边leg 直角边opposite 直角三角形中的对边arm 直角三角形的股median of a triangle 中线included side 夹边altitude (三角形的)高base 底边，底数Pythagorean theorem 勾股定理5. 圆circle 圆形semicircle 半圆concentric circles 同心圆semicircle 半圆concentric circles 同心圆center of a circle 圆心chord 弦diameter 直径radius 半径circumference 圆周长sector 扇形ring 环arc 弧radian 弧度（弧长/半径）segment of a circle 弧形point of tangency 切点inscribe 内切，内接circumscribe 外切，外接6. 立体图形solid 立体的face of a solid 立体的面cube 立方体，立方数tetrahedron 四面体pentahedron 五面体hexahedron 六面体parallelepiped 平行六面体rectangular solid 长方体cube 正方体heptahedron 七面体octahedron 八面体enneahedron 九面体decahedron 十面体hendecahedron 十一面体dodecahedron 十二面体icosahedron 二十面体polyhedron 多面体regular solid/polyhedron 正多面体pyramid 棱锥prism 棱柱frustum of a prism 棱台rotation 旋转axis 轴cone 圆锥cylinder 圆柱frustum of a cone 圆台sphere 球hemisphere 半球cross section 横截面undersurface 底面surface area 表面积7. 解析几何coordinate system 坐标系rectangular coordinate 直角坐标系origin 原点x-axis, y-axis, z-axis 坐标轴abscissa, x-coordinate 横坐标ordinate, y-coordinate 纵坐标number line 数轴quadrant 象限slope 斜率complex plane 复平面hyperbola 双曲线parabola 抛物线ellipse 椭圆locus, loca (pl.) 轨迹。
高中数学词汇（英文）
高中数学词汇（英文）高中数学词汇（英文）代数 ALGEBRA1. 数论natural number 自然数positive number 正数negative number 负数 odd integer, oddnumber 奇数 even integer, even number 偶数 integer, whole number 整数 positivewhole number 正整数negative whole number 负整数consecutive number 连续整数realnumber, rational number 实数,有理数 irrational（number）无理数 inverse 倒数compositenumber 合数e.g. 4,6,8,9,10,12,14,15… prime number 质数 e.g. 2,3,5,7,11,13,15…reciprocal 倒数common divisor 公约数multiple 倍数(minimum) common multiple (最小)公倍数(prime) factor (质)因子 common factor 公因子ordinary scale, decimalscale 十进制nonnegative 非负的tens 十位units 个位mode 众数 mean平均数 median中值 commonratio 公比2. 基本数学概念arithmetic mean 算术平均值weighted average 加权平均值geometric mean 几何平均数 exponent指数，幂base 乘幂的底数,底边cube 立方数，立方体square root 平方根cube root 立方根 common logarithm常用对数digit 数字constant 常数variable 变量inverse function 反函数 complementaryfunction 余函数linear 一次的，线性的factorization 因式分解absolute value绝对值，e.g.｜-32｜=32 round off 四舍五入数学3. 基本运算add，plus 加subtract 减difference 差multiply, times 乘product 积 divide除divisible 可被整除的 divided evenly 被整除 dividend 被除数，红利 divisor 因子，除数，公约数quotient 商 remainder 余数 factorial 阶乘 power 乘方 radical sign, root sign 根号round to 四舍五入 to the nearest 四舍五入4. 代数式，方程，不等式algebraic term 代数项like terms, similar terms 同类项numerical coefficient数字系数literal coefficient 字母系数 inequality 不等式 triangle inequality 三角不等式 range 值域original equation 原方程 equivalent equation 同解方程，等价方程 linear equation 线性方程(e.g.5x+6=22)5. 分数，小数proper fraction 真分数improper fraction 假分数mixed number 带分数 vulgarfraction，common fraction 普通分数simple fraction 简分数complex fraction繁分数numerator 分子denominator 分母(least) common denominator （最小）公分母 quarter四分之一decimal fraction 纯小数infinite decimal 无穷小数recurring decimal 循环小数tenths unit 十分位6. 集合union 并集 proper subset 真子集 solution set 解集7. 数列arithmetic progression(sequence) 等差数列geometric progression(sequence) 等比数列8. 其它approximate 近似 (anti)clockwise (逆) 顺时针方向 cardinal 基数 ordinal 序数 directproportion 正比distinct 不同的estimation 估计，近似parentheses 括号 proportion 比例permutation 排列 combination 组合 table 表格 trigonometric function 三角函数 unit 单位,位几何 GEOMETRY1. 角alternate angle 内错角corresponding angle 同位角vertical angle 对顶角 central angle圆心角 interior angle 内角 exterior angle 外角 supplementary angles 补角complementaryangle 余角 adjacent angle 邻角 acute angle 锐角 obtuse angle 钝角right angle 直角round angle 周角 straight angle 平角 included angle 夹角2. 三角形equilateral triangle 等边三角形 scalene triangle 不等边三角形isosceles triangle 等腰三角形right triangle 直角三角形 oblique 斜三角形 inscribed triangle 内接三角形3. 收敛的平面图形，除三角形外semicircle 半圆 concentric circles 同心圆 quadrilateral 四边形pentagon 五边形hexagon六边形heptagon 七边形octagon 八边形nonagon 九边形decagon 十边形 polygon 多边形parallelogram 平行四边形equilateral 等边形plane 平面square 正方形，平方 rectangle 长方形regular polygon 正多边形 rhombus 菱形 trapezoid 梯形4. 其它平面图形arc 弧 line, straight line 直线 line segment 线段 parallel lines 平行线 segment of acircle 弧形5. 立体图形cube 立方体，立方数rectangular solid 长方体regular solid/regular polyhedron正多面体circular cylinder 圆柱体 cone 圆锥 sphere 球体 solid 立体的6. 图形的附属概念plane geometry 平面几何trigonometry 三角学bisect 平分circumscribe 外切 inscribe内切 intersect 相交 perpendicular 垂直 Pythagorean theorem 勾股定理（毕达哥拉斯定理） congruent全等的 multilateral 多边的 altitude 高 depth 深度 side 边长circumference, perimeter周长 radian 弧度 surface area 表面积 volume 体积 arm 直角三角形的股 cross section 横截面center of a circle 圆心chord 弦diameter 直径radius 半径angle bisector 角平分线diagonal 对角线化edge 棱face of a solid 立体的面hypotenuse 斜边 included side 夹边 leg三角形的直角边median（三角形的）中线base 底边，底数（e.g. 2的5次方，2就是底数） opposite 直角三角形中的对边midpoint 中点endpoint 端点vertex (复数形式vertices)顶点tangent 切线的transversal 截线intercept 截距7. 坐标coordinate system 坐标系 rectangular coordinate 直角坐标系origin 原点 abscissa 横坐标ordinate 纵坐标。
高等数学 英文教材
高等数学英文教材Higher Mathematics: An English TextbookIntroduction:Higher Mathematics is a crucial subject for students pursuing degrees in STEM (Science, Technology, Engineering, and Mathematics) fields. This English textbook aims to provide a comprehensive and accessible resource for students studying higher mathematics in an international academic context. With a focus on clarity, logical presentation, and English language proficiency, this textbook will equip students with the necessary mathematical skills and knowledge to succeed in their academic journey.Chapter 1: Differentiation1.1 Fundamental ConceptsDifferentiation is a fundamental topic in calculus, enabling students to analyze the behavior of functions. This chapter will cover the basic rules of differentiation, including the power rule, product rule, quotient rule, and chain rule. Various examples and exercises will be provided to ensure students grasp the concepts effectively.1.2 Applications of DifferentiationBuilding upon the foundational concepts, this section explores the applications of differentiation. Students will learn how to find critical points, determine concavity and inflection points, optimize functions, and solve real-world problems using differentiation techniques. The significance ofdifferentiation in solving practical problems in disciplines such as physics, economics, and engineering will be highlighted.Chapter 2: Integration2.1 Definite and Indefinite IntegralsThis chapter focuses on the concept of integration. Students will explore indefinite integrals, fundamental theorem of calculus, and techniques such as substitution and integration by parts. The significance of integration in finding areas, volumes, and computing sums will be emphasized.2.2 Applications of IntegrationIn this section, students will delve into the various applications of integration. They will learn how to find the area between curves, calculate volumes of solids of revolution, and solve real-world problems using integration techniques. The importance of integration in physics, economics, and statistics will be demonstrated through examples and exercises.Chapter 3: Differential Equations3.1 First-order Differential EquationsThis chapter introduces students to first-order differential equations and their applications. The concepts of separable equations, linear equations, and Bernoulli equations will be covered. Students will gain an understanding of the fundamental techniques for solving differential equations.3.2 Second-order Differential EquationsExpanding on the previous section, this part focuses on second-order differential equations. Students will explore homogeneous and non-homogeneous equations, as well as various methods for solving them, including the method of undetermined coefficients and variation of parameters. Applications of second-order differential equations in physics and engineering will be discussed.Chapter 4: Sequences and Series4.1 Sequences and ConvergenceThis chapter introduces students to sequences and their convergence properties. The concepts of limits, convergence, and divergence will be explored. Students will learn how to analyze the behavior of sequences and determine their convergence using various tests.4.2 Series and ConvergenceBuilding upon the previous section, this part delves into series and their convergence properties. Students will study different types of series, including geometric, p-series, and alternating series. Convergence tests such as the comparison test, ratio test, and integral test will be covered. Practical applications of series in calculus and numerical methods will be discussed.Conclusion:This English textbook on Higher Mathematics provides a comprehensive and well-structured resource for students. Through its clear explanations, numerous examples, and practice exercises, students will develop a strong foundation in calculus, enabling them to tackle advanced mathematical problems confidently. With a focus on English language proficiency, this textbook caters to the needs of international students pursuing higher education in mathematics-related disciplines.。
高等数学名词(中英文)
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mappingX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 ofDifferentials and the Application ofDerivatives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 Rule0/0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 DefiniteIntegrals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Chapter7 Space Analytic Geometry andVector 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Chapter8 Differentiation of Functions ofSeveral 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 setn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Chapter9 Multiple 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Chapter10 Line (Curve) Integrals andSurface 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Chapter11 Infinite 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Chapter12 Differential Equation解微分方程solve a differential 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 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 lineardifferential 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 linear differential equations with constant coefficientV、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Periodic function ：周期函数Perpendicular lines ：垂直线Piecewise defined function 分段定义函数Plane ：平面Point of inflection ：反曲点Polar axis ：极轴Polar coordinate ：极坐标Polar equation ：极方程式Pole ：极点Polynomial ：多项式Positive angle ：正角Point-slope form ：点斜式Power function ：幂函数Product ：积Quadrant ：象限Quotient Law of limit 极限的商定律Quotient Rule ：商定律M、N、O:Maximum and minimum values ：极大与极小值Mean Value Theorem ：均值定理Multiple integrals ：重积分Multiplier ：乘子Natural exponential function 自然指数函数Natural logarithm function 自然对数函数Natural number ：自然数Normal line ：法线Normal vector ：法向量Number ：数Octant ：卦限Odd function ：奇函数One-sided limit ：单边极限Open interval ：开区间Optimization problems ：最佳化问题Order ：阶Ordinary differential equation ：常微分方程Origin ：原点Orthogonal ：正交的L:Laplace transform ：Leplace 变换Law of Cosines ：余弦定理Least upper bound ：最小上界Left-hand derivative ：左导数Left-hand limit ：左极限Lemniscate ：双钮线Length ：长度Level curve ：等高线L'Hospital's rule 洛必达法则Limacon ：蚶线Limit ：极限Linear approximation：线性近似Linear equation ：线性方程式Linear function ：线性函数Linearity ：线性Linearization ：线性化Line in the plane ：平面上之直线Line in space ：空间之直线Lobachevski geometry 罗巴切夫斯基几何Local extremum ：局部极值Local maximum and minimum 局部极大值与极小值Logarithm ：对数Logarithmic function ：对数函数I:Implicit differentiation ：隐求导法Implicit function ：隐函数Improper integral ：瑕积分Increasing/Decreasing Test 递增或递减试验法Increment ：增量Increasing Function ：增函数Indefinite integral ：不定积分Independent variable ：自变数Indeterminate from ：不定型Inequality ：不等式Infinite point ：无穷极限Infinite series ：无穷级数Inflection point ：反曲点Instantaneous velocity ：瞬时速度Integer ：整数Integral ：积分Integrand ：被积分式Integration ：积分Integration by part ：分部积分法Intercepts ：截距Intermediate value of Theorem 中间值定理Interval ：区间Inverse function ：反函数Inverse trigonometric function反三角函数Iterated integral ：逐次积分H:Higher mathematics 高等数学/高数E、F、G、H:Ellipse ：椭圆Ellipsoid ：椭圆体Epicycloid ：外摆线Equation ：方程式Even function ：偶函数Expected Valued ：期望值Exponential Function ：指数函数Exponents , laws of ：指数率Extreme value ：极值Extreme Value Theorem ：极值定理Factorial ：阶乘First Derivative Test ：一阶导数试验法First octant ：第一卦限Focus ：焦点Fractions ：分式Function ：函数Fundamental Theorem of Calculus ：微积分基本定理Geometric series ：几何级数Gradient ：梯度Graph ：图形Green Formula ：格林公式Half-angle formulas ：半角公式Harmonic series ：调和级数Helix ：螺旋线Higher Derivative ：高阶导数Horizontal asymptote ：水平渐近线Horizontal line ：水平线Hyperbola ：双曲线Hyper boloid ：双曲面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Disk method ：圆盘法Distance ：距离Divergence ：发散Domain ：定义域Dot product ：点积Double integral ：二重积分change of variable in二重积分之变数变换in polar coordinates ：极坐标二重积分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 柯西均值定理Chain Rule ：连锁律Change of variables ：变数变换Circle ：圆Circular cylinder ：圆柱Closed interval ：封闭区间Coefficient ：系数Composition of function ：函数之合成Compound interest ：复利Concavity ：凹性Conchoid ：蚌线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Coordinate：s：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：圆柱Cylindrical Coordinates ：圆柱坐标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 ：反导数Approximate integration ：近似积分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 ：椭圆之轴Binomial series ：二项级数微积分专有名词中英文对照absolutely convergent 绝对收敛absolute value 绝对值algebraic function 代数函数analytic geometry 解析几何antiderivative 不定积分approximate integration 近似积分approximation 近似法、逼近法arbitrary constant 任意常数arithmetic series/progression (AP)算数级数asymptotes (vertical and horizontal)(垂直/水平)渐近线average rate of change 平均变化率base 基数binomial theorem 二项式定理，二项展开式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 柯西均值定理chain rule 链式求导法则calculus 微积分学closed interval integral 闭区间积分coefficient 系数composite function 复合函数conchoid 蚌线continuity (函数的)连续性concavity (函数的)凹凸性conditionally convergent 有条件收敛continuity 连续性critical point 临界点cubic function 三次函数cylindrical coordinates 圆柱坐标decreasing function 递减函数decreasing sequence 递减数列definite integral 定积分derivative 导数determinant 行列式differential coefficient 微分系数differential equation 微分方程directional derivative 方向导数discontinuity 不连续性discriminant (二次函数)判别式disk method 圆盘法divergence 散度divergent 发散的domain 定义域dot product 点积double integral 二重积分ellipse 椭圆ellipsoid 椭圆体epicycloid 外摆线Euler's method (BC)欧拉法expected valued 期望值exponential function 指数函数extreme value heorem 极值定理factorial 阶乘finite series 有限级数fundamental theorem of calculus 微积分基本定理geometric series/progression (GP)几何级数gradient 梯度Green formula 格林公式half-angle formulas 半角公式harmonic series 调和级数helix 螺旋线higher derivative 高阶导数horizontal asymptote 水平渐近线horizontal line 水平线hyperbola 双曲线hyper boloid 双曲面implicit differentiation 隐函数求导implicit function 隐函数improper integral 广义积分、瑕积分increment 增量increasing function 增函数indefinite integral 不定积分independent variable 自变数inequality 不等式ndeterminate form 不定型infinite point 无穷极限infinite series 无穷级数infinite series 无限级数inflection point (POI) 拐点initial condition 初始条件instantaneous rate of change 瞬时变化率integrable 可积的integral 积分integrand 被积分式integration 积分integration by part 分部积分法intercept 截距intermediate value of Theorem ：中间值定理inverse function 反函数irrational function 无理函数iterated integral 逐次积分Laplace transform 拉普拉斯变换law of cosines 余弦定理least upper bound 最小上界left-hand derivative 左导数left-hand limit 左极限L'Hospital's rule 洛必达法则limacon 蚶线linear approximation 线性近似法linear equation 线性方程式linear function 线性函数linearity 线性linearization 线性化local maximum 极大值local minimum 极小值logarithmic function 对数函数MacLaurin series 麦克劳林级数maximum 最大值mean value theorem (MVT)中值定理minimum 最小值method of lagrange multipliers 拉格朗日乘数法modulus 绝对值multiple integral 多重积分multiple 倍数multiplier 乘子octant 卦限open interval integral 开区间积分optimization 优化法，极值法origin 原点orthogonal 正交parametric equation (BC)参数方程partial derivative 偏导数partial differential equation 偏微分方程partial fractions 部分分式piece-wise function 分段函数parabola 抛物线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 integration 部分积分partiton ：分割period ：周期periodic function 周期函数perpendicular lines 垂直线piecewise defined function 分段定义函数plane 平面point of inflection 反曲点point-slope form 点斜式polar axis 极轴polar coordinates 极坐标polar equation 极坐标方程pole 极点polynomial 多项式power series 幂级数product rule 积的求导法则quadrant 象限quadratic functions 二次函数quotient rule 商的求导法则radical 根式radius of convergence 收敛半径range 值域(related) rate of change with time (时间)变化率rational function 有理函数reciprocal 倒数remainder theorem 余数定理Riemann sum 黎曼和Riemannian geometry 黎曼几何right-hand limit 右极限Rolle's theorem 罗尔(中值)定理root 根rotation 旋转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series 级数shell method (积分)圆筒法sine function 正弦函数singularity 奇点slant 母线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symmetry 对称性substitution 代入法、变量代换tangent function 正切函数tangent line 切线tangent plane 切(平)面tangent vector 切矢量taylor's series 泰勒级数three-dimensional analytic geometry 空间解析几何total differentiation 全微分trapezoid rule 梯形(积分)法则。
高等数学英文1-3-10
§1.3 The Limits of functions
IV. The limit at Infinity
x Consider the function f ( x) = 1+ x2
What happens to f (x) as x gets larger and larger?
y
o
x
f (x) gets smaller as x gets larger.
8
ε
implies that
( x + x − 5) − 7 = x + 4 x − 3 < 8⋅
2
ε
8
= ε.
§1.3 The Limits of functions
III. One-sided limits
lim f ( x) = A x→ + a lim f ( x) = A x→ − a
∀ε > 0, ∃δ > 0, when 0 < x − a < δ , f ( x ) − A < ε
III. One-sided limits
Example 4
2x2 − 2 , x > 1 Find lim f ( x). Let f ( x) = x −1 , x→1 → x, x <1
2x2 − 2 , x ≠ 1 Find lim f ( x). Let f ( x) = x −1 , x→1 → 5, x =1
Example 2
Proof
Let ε be given. If we want
2x2 − 3x − 2 Show that lim = 5. x→2 x−2
高等数学英语词汇
高等数学英语词汇高等数学英语词汇引导语：高等数学指相对于初等数学而言，数学的对象及方法较为繁杂的'一部分。
以下是店铺分享给大家的高等数学英语词汇，欢迎阅读!Aabelian group：阿贝尔群; absolute geometry：绝对几何; absolute value：绝对值; abstract algebra：抽象代数; addition：加法; algebra：代数; algebraicclosure：代数闭包; algebraic geometry：代数几何;algebraic geometry and analytic geometry：代数几何和解析几何; algebraic numbers：代数数; algorithm：算法; almost all：绝大多数; analytic function：解析函数; analytic geometry：解析几何; and：且;angle：角度; anticommutative：反交换律; antisymmetric relation：反对称关系; antisymmetry：反对称性; approximately equal：约等于; Archimedean field：阿基米德域; Archimedean group：阿基米德群; area：面积; arithmetic：算术; associative algebra：结合代数; associativity：结合律; axiom：公理; axiom of constructibility：可构造公理; axiom of empty set：空集公理;axiom of extensionality：外延公理; axiom of foundation：正则公理; axiom of pairing：对集公理; axiom of regularity：正则公理; axiom of replacement：代换公理; axiom of union：并集公理; axiom schema of separation：分离公理; axiom schema of specification：分离公理;axiomatic set theory：公理集合论; axiomatic system：公理系统;BBaire space：贝利空间; basis：基; Bézout's identity：贝祖恒等式; Bernoulli's inequality：伯努利不等式 ; Big O notation：大O符号; bilinear operator：双线性算子; binary operation：二元运算; binary predicate：二元谓词; binary relation：二元关系; Booleanalgebra：布尔代数;Boolean logic：布尔逻辑; Boolean ring：布尔环; boundary：边界; boundary point：边界点;bounded lattice：有界格;Ccalculus：微积分学; Cantor's diagonal argument：康托尔对角线方法; cardinal number：基数;cardinality：势; cardinality of the continuum：连续统的势; Cartesian coordinate system：直角坐标系; Cartesian product：笛卡尔积; category：范畴; Cauchy sequence：柯西序列; Cauchy-Schwarz inequality：柯西不等式; Ceva's Theorem：塞瓦定理; characteristic：特征;characteristic polynomial：特征多项式; circle：圆; class：类; closed：闭集; closure：封闭性或闭包; closure algebra：闭包代数; combinatorial identities：组合恒等式; commutativegroup：交换群; commutative ring：交换环; commutativity:：交换律; compact：紧致的;compact set：紧致集合; compact space：紧致空间; complement：补集或补运算; completelattice：完备格; complete metric space：完备的度量空间; complete space：完备空间; complexmanifold：复流形; complex plane：复平面; congruence：同余; congruent：全等; connectedspace：连通空间; constructible universe：可构造全集; constructions of the real numbers：实数的构造; continued fraction：连分数; continuous：连续; continuum hypothesis：连续统假设;contractible space：可缩空间; convergence space：收敛空间; cosine：余弦; countable：可数;countable set：可数集; cross product：叉积; cycle space：圈空间; cyclic group：循环群;Dde Morgan's laws：德·摩根律; Dedekind completion：戴德金完备性; Dedekind cut：戴德金分割;del：微分算子; dense：稠密; densely ordered：稠密排列; derivative：导数; determinant：行列式; diffeomorphism：可微同构; difference：差; differentiablemanifold：可微流形;differential calculus：微分学; dimension：维数; directed graph：有向图; discrete space：离散空间; discriminant：判别式; distance：距离; distributivity：分配律; dividend：被除数;dividing：除; divisibility：整除; division：除法; divisor：除数; dot product：点积;Eeigenvalue：特征值; eigenvector：特征向量; element：元素; elementary algebra：初等代数;empty function：空函数; empty set：空集; empty product：空积; equal：等于; equality：等式或等于; equation：方程; equivalence relation：等价关系; Euclidean geometry：欧几里德几何;Euclidean metric：欧几里德度量; Euclidean space：欧几里德空间; Euler's identity：欧拉恒等式;even number：偶数; event：事件; existential quantifier：存在量词; exponential function：指数函数; exponential identities：指数恒等式; expression：表达式; extended real number line：扩展的实数轴;Ffalse：假; field：域; finite：有限; finite field：有限域; finite set：有限集合; first-countablespace：第一可数空间; first order logic：一阶逻辑; foundations of mathematics：数学基础;function：函数; functional analysis：泛函分析; functional predicate：函数谓词;fundamental theorem of algebra：代数基本定理; fraction：分数;Ggauge space：规格空间; general linear group：一般线性群; geometry：几何学; gradient：梯度;graph：图; graph of a relation：关系图; graph theory：图论; greatest element：最大元;group：群; group homomorphism：群同态;HHausdorff space：豪斯多夫空间; hereditarily finite set：遗传有限集合; Heron's formula：海伦公式; Hilbert space：希尔伯特空间;Hilbert's axioms：希尔伯特公理系统; Hodge decomposition：霍奇分解; Hodge Laplacian：霍奇拉普拉斯算子; homeomorphism：同胚; horizontal：水平;hyperbolic function identities：双曲线函数恒等式; hypergeometric function identities：超几何函数恒等式; hyperreal number：超实数;Iidentical：同一的; identity：恒等式; identity element：单位元; identity matrix：单位矩阵;idempotent：幂等; if：若; if and only if：当且仅当; iff：当且仅当; imaginary number：虚数;inclusion：包含; index set：索引集合; indiscrete space：非离散空间; inequality：不等式或不等; inequality of arithmetic and geometric means：平均数不等式; infimum：下确界; infiniteseries：无穷级数; infinite：无穷大; infinitesimal：无穷小; infinity：无穷大; initial object：初始对象; inner angle：内角; inner product：内积; inner product space：内积空间; integer：整数; integer sequence：整数列; integral：积分; integral domain：整数环; interior：内部;interior algebra：内部代数; interior point：内点; intersection：交集; inverse element：逆元;invertible matrix：可逆矩阵; interval：区间; involution：回旋; irrational number：无理数;isolated point：孤点; isomorphism：同构;JJacobi identity：雅可比恒等式; join：并运算;K格式： Kuratowski closure axioms：Kuratowski 闭包公理;Lleast element：最小元; Lebesgue measure：勒贝格测度; Leibniz's law：莱布尼茨律; Liealgebra：李代数; Lie group：李群; limit：极限; limit point：极限点; line：线; line segment：线段; linear：线性; linear algebra：线性代数; linear operator：线性算子; linear space：线性空间; linear transformation：线性变换; linearity：线性性; list of inequalities：不等式列表; list oflinear algebra topics：线性代数相关条目; locally compact space：局部紧致空间; logarithmicidentities：对数恒等式; logic：逻辑学; logical positivism：逻辑实证主义; law of cosines：余弦定理; L??wenheim-Skolem theorem：L??wenheim-Skolem 定理; lower limit topology：下限拓扑;Mmagnitude：量; manifold：流形; map：映射; mathematical symbols：数学符号; mathematicalanalysis：数学分析; mathematical proof：数学证明; mathematics：数学; matrix：矩阵;matrix multiplication：矩阵乘法; meaning：语义; measure：测度; meet：交运算; member：元素; metamathematics：元数学; metric：度量; metric space：度量空间; model：模型; modeltheory：模型论; modular arithmetic：模运算; module：模; monotonic function：单调函数;multilinear algebra：多重线性代数; multiplication：乘法; multiset：多样集;Nnaive set theory：朴素集合论; natural logarithm：自然对数; natural number：自然数; naturalscience：自然科学; negative number：负数; neighbourhood：邻域; New Foundations：新基础理论; nine point circle：九点圆; non-Euclidean geometry：非欧几里德几何; nonlinearity：非线性; non-singular matrix：非奇异矩阵; nonstandard model：非标准模型; nonstandardanalysis：非标准分析; norm：范数; normed vector space：赋范向量空间; n-tuple：n 元组或多元组; nullary：空; nullary intersection：空交集; number：数; number line：数轴;Oobject：对象; octonion：八元数; one-to-one correspondence：一一对应; open：开集; openball：开球; operation：运算; operator：算子; or：或; order topology：序拓扑; ordered field：有序域;ordered pair：有序对; ordered set：偏序集; ordinal number：序数; ordinarymathematics：一般数学; origin：原点; orthogonal matrix：正交矩阵;Pp-adic number：p进数; paracompact space：仿紧致空间; parallel postulate：平行公理;parallelepiped：平行六面体; parallelogram：平行四边形; partial order：偏序关系; partition：分割; Peano arithmetic：皮亚诺公理; Pedoe's inequality：佩多不等式; perpendicular：垂直;philosopher：哲学家; philosophy：哲学; philosophy journals：哲学类杂志; plane：平面; pluralquantification：复数量化; point：点; Point-Line-Plane postulate：点线面假设; polarcoordinates：极坐标系; polynomial：多项式; polynomial sequence：多项式列; positive-definitematrix：正定矩阵; positive-semidefinite matrix：半正定矩阵; power set：幂集; predicate：谓词; predicate logic：谓词逻辑; preorder：预序关系; prime number：素数; product：积;proof：证明; proper class：纯类; proper subset：真子集; property：性质; proposition：命题; pseudovector：伪向量; Pythagorean theorem：勾股定理;QQ.E.D.：Q.E.D.; quaternion：四元数; quaternions and spatial rotation：四元数与空间旋转;question：疑问句; quotient field：商域; quotient set：商集;Rradius：半径; ratio：比; rational number：有理数; real analysis：实分析; real closed field：实闭域; real line：实数轴; real number：实数; real number line：实数线; reflexive relation：自反关系; reflexivity：自反性; reification：具体化; relation：关系; relative complement：相对补集;relatively complemented lattice：相对补格; right angle：直角; right-handed rule：右手定则;ring：环;Sscalar：标量; second-countable space：第二可数空间; self-adjoint operator：自伴随算子;sentence：判断; separable space：可分空间; sequence：数列或序列; sequence space：序列空间; series：级数; sesquilinear function：半双线性函数; set：集合; set-theoretic definitionof natural numbers：自然数的集合论定义; set theory：集合论; several complex variables：一些复变量; shape：几何形状; sign function：符号函数; singleton：单元素集合; social science：社会科学; solid geometry：立体几何; space：空间; spherical coordinates：球坐标系; squarematrix：方块矩阵; square root：平方根; strict：严格; structural recursion：结构递归;subset：子集; subsequence：子序列; subspace：子空间; subspace topology：子空间拓扑;subtraction：减法; sum：和; summation：求和; supremum：上确界; surreal number：超实数; symmetric difference：对称差; symmetric relation：对称关系; system of linearequations：线性方程组;Ttensor：张量; terminal object：终结对象; the algebra of sets：集合代数; theorem：定理; topelement：最大元; topological field：拓扑域; topological manifold：拓扑流形; topological space：拓扑空间; topology：拓扑或拓扑学; total order：全序关系; totally disconnected：完全不连贯;totally ordered set：全序集; transcendental number：超越数; transfinite recursion：超限归纳法; transitivity：传递性; transitive relation：传递关系; transpose：转置; triangleinequality：三角不等式; trigonometric identities：三角恒等式; triple product：三重积; trivialtopology：密着拓扑; true：真; truth value：真值;Uunary operation：一元运算; uncountable：不可数; uniform space：一致空间; union：并集;unique：唯一; unit interval：单位区间; unit step function：单位阶跃函数; unit vector：单位向量;universal quantification：全称量词; universal set：全集; upper bound：上界;Vvacuously true：??; Vandermonde's identity：Vandermonde 恒等式; variable：变量;vector：向量; vector calculus：向量分析; vector space：向量空间; Venn diagram：文氏图;volume：体积; von Neumann ordinal：冯·诺伊曼序数; von Neumann universe：冯·诺伊曼全集;vulgar fraction：分数;ZZermelo set theory：策梅罗集合论; Zermelo-Fraenkel set theory：策梅罗-弗兰克尔集合论; ZF settheory：ZF 系统; zero：零; zero object：零对象;下载全文。
高等数学专业名词中英文对照(全面)
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关键词:微积分英文，高等数学英文翻译,高数英语词汇来源:上海外教网| 发布日期：2008-05—16 17：12V、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Periodic function ：周期函数Perpendicular lines ：垂直线Piecewise defined function ：分段定义函数Plane ：平面Point of inflection ：反曲点Polar axis ：极轴Polar coordinate ：极坐标Polar equation :极方程式Pole ：极点Polynomial :多项式Positive angle :正角Point-slope form ：点斜式Power function :幂函数Product ：积Quadrant ：象限Quotient Law of limit ：极限的商定律Quotient Rule ：商定律M、N、O:Maximum and minimum values :极大与极小值Mean Value Theorem ：均值定理Multiple integrals :重积分Multiplier ：乘子Natural exponential function :自然指数函数Natural logarithm function ：自然对数函数Natural number ：自然数Normal line ：法线Normal vector ：法向量Number :数Octant :卦限Odd function ：奇函数One—sided limit ：单边极限Open interval :开区间Optimization problems ：最佳化问题Order ：阶Ordinary differential equation :常微分方程Origin ：原点Orthogonal ：正交的L：Laplace transform :Leplace 变换Law of Cosines ：余弦定理Least upper bound :最小上界Left—hand derivative ：左导数Left—hand limit ：左极限Lemniscate :双钮线Length :长度Level curve :等高线L’Hospital’s rule ：洛必达法则Limacon ：蚶线Limit ：极限Linear approximation：线性近似Linear equation :线性方程式Linear function ：线性函数Linearity ：线性Linearization ：线性化Line in the plane ：平面上之直线Line in space ：空间之直线Lobachevski geometry :罗巴切夫斯基几何Local extremum ：局部极值Local maximum and minimum :局部极大值与极小值Logarithm ：对数Logarithmic function ：对数函数I:Implicit differentiation ：隐求导法Implicit function ：隐函数Improper integral :瑕积分Increasing/Decreasing Test ：递增或递减试验法Increment :增量Increasing Function ：增函数Indefinite integral ：不定积分Independent variable ：自变数Indeterminate from :不定型Inequality ：不等式Infinite point :无穷极限Infinite series ：无穷级数Inflection point :反曲点Instantaneous velocity :瞬时速度Integer ：整数Integral ：积分Integrand ：被积分式Integration ：积分Integration by part ：分部积分法Intercepts ：截距Intermediate value of Theorem ：中间值定理Interval ：区间Inverse function ：反函数Inverse trigonometric function ：反三角函数Iterated integral ：逐次积分H:Higher mathematics 高等数学/高数E、F、G、H:Ellipse ：椭圆Ellipsoid ：椭圆体Epicycloid ：外摆线Equation ：方程式Even function ：偶函数Expected Valued :期望值Exponential Function ：指数函数Exponents ，laws of ：指数率Extreme value ：极值Extreme Value Theorem ：极值定理Factorial :阶乘First Derivative Test ：一阶导数试验法First octant ：第一卦限Focus :焦点Fractions ：分式Function ：函数Fundamental Theorem of Calculus :微积分基本定理Geometric series ：几何级数Gradient ：梯度Graph ：图形Green Formula ：格林公式Half—angle formulas ：半角公式Harmonic series ：调和级数Helix ：螺旋线Higher Derivative ：高阶导数Horizontal asymptote :水平渐近线Horizontal line ：水平线Hyperbola ：双曲线Hyper boloid :双曲面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Disk method ：圆盘法Distance ：距离Divergence ：发散Domain :定义域Dot product ：点积Double integral ：二重积分change of variable in :二重积分之变数变换in polar coordinates ：极坐标二重积分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 ：柯西均值定理Chain Rule ：连锁律Change of variables :变数变换Circle ：圆Circular cylinder ：圆柱Closed interval ：封闭区间Coefficient :系数Composition of function ：函数之合成Compound interest ：复利Concavity ：凹性Conchoid ：蚌线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Coordinate:s：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：圆柱Cylindrical Coordinates ：圆柱坐标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 :反导数Approximate integration ：近似积分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 :椭圆之轴Binomial series ：二项级数微积分词汇第一章函数与极限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mappingX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2007-10-8 18:37 回复此发言—-—--—-—-—-————-—-———-—--——--——----———---——---———————————————---——--———--———----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 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 Rule0/0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(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 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Chapter8 Differentiation 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 setn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Chapter9 Multiple 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Chapter10 Line(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Chapter11 Infinite 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Chapter12 Differential 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 coefficientV、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Periodic function ：周期函数Perpendicular lines ：垂直线Piecewise defined function ：分段定义函数Plane ：平面Point of inflection ：反曲点Polar axis ：极轴Polar coordinate ：极坐标Polar equation ：极方程式Pole ：极点Polynomial ：多项式Positive angle ：正角Point-slope form :点斜式Power function ：幂函数Product :积Quadrant ：象限Quotient Law of limit :极限的商定律Quotient Rule :商定律M、N、O：Maximum and minimum values :极大与极小值Mean Value Theorem ：均值定理Multiple integrals ：重积分Multiplier ：乘子Natural exponential function ：自然指数函数Natural logarithm function :自然对数函数Natural number ：自然数Normal line ：法线Normal vector :法向量Number ：数Octant ：卦限Odd function ：奇函数One-sided limit ：单边极限Open interval ：开区间Optimization problems :最佳化问题Order ：阶Ordinary differential equation ：常微分方程Origin ：原点Orthogonal ：正交的L:Laplace transform ：Leplace 变换Law of Cosines ：余弦定理Least upper bound ：最小上界Left-hand derivative ：左导数Left-hand limit ：左极限Lemniscate ：双钮线Length ：长度Level curve ：等高线L'Hospital's rule ：洛必达法则Limacon ：蚶线Limit ：极限Linear approximation：线性近似Linear equation ：线性方程式Linear function ：线性函数Linearity :线性Linearization ：线性化Line in the plane ：平面上之直线Line in space :空间之直线Lobachevski geometry ：罗巴切夫斯基几何Local extremum ：局部极值Local maximum and minimum :局部极大值与极小值Logarithm :对数Logarithmic function ：对数函数I:Implicit differentiation ：隐求导法Implicit function ：隐函数Improper integral :瑕积分Increasing/Decreasing Test :递增或递减试验法Increment :增量Increasing Function ：增函数Indefinite integral ：不定积分Independent variable ：自变数Indeterminate from ：不定型Inequality ：不等式Infinite point :无穷极限Infinite series ：无穷级数Inflection point ：反曲点Instantaneous velocity :瞬时速度Integer ：整数Integral ：积分Integrand :被积分式Integration ：积分Integration by part :分部积分法Intercepts ：截距Intermediate value of Theorem ：中间值定理Interval ：区间Inverse function ：反函数Inverse trigonometric function :反三角函数Iterated integral ：逐次积分H:Higher mathematics 高等数学/高数E、F、G、H：Ellipse ：椭圆Ellipsoid ：椭圆体Epicycloid :外摆线Equation ：方程式Even function :偶函数Expected Valued ：期望值Exponential Function ：指数函数Exponents , laws of ：指数率Extreme value ：极值Extreme Value Theorem ：极值定理Factorial :阶乘First Derivative Test ：一阶导数试验法First octant :第一卦限Focus ：焦点Fractions ：分式Function ：函数Fundamental Theorem of Calculus ：微积分基本定理Geometric series ：几何级数Gradient ：梯度Graph ：图形Green Formula :格林公式Half-angle formulas :半角公式Harmonic series ：调和级数Helix ：螺旋线Higher Derivative ：高阶导数Horizontal asymptote :水平渐近线Horizontal line :水平线Hyperbola ：双曲线Hyper boloid ：双曲面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Disk method ：圆盘法Distance ：距离Divergence ：发散Domain ：定义域Dot product ：点积Double integral ：二重积分。
高等数学英文1-6-10
Theorem 4 (Substitution Theorem)
If f is a polynomial or a rational function, and f ( x0 ) is defined, then lim f ( x) = f ( x0 )
x→x0
§1.6 Limit Theorem
x + arctan x 2. lim x→∞ x − arctan x
§1ctions and Limits
§1.6 Limit Theorems
Theorem 1
The sum of finite infinitesimals is also an infinitesimal.
If α →0, β →0 as x → x0 , then α + β →0 as x → x0 .
2 sin x sin x Since lim = 0, limu2 = 0, then lim =0 x→∞ x→∞ u→0 x x
§1.6 Limit Theorem
Exercises
1 1 1 1. lim(1− 2 )(1− 2 )L 1− 2 ) ( n→∞ 2 3 n
Example 2
5x2 − 4x + 2 lim 2 x→∞ 3x − 3x + 1
5x4 − 4x3 + 2 lim 7 x→∞ 3x − 3x5 + x2
5x9 − 4x5 + 60x lim x→∞ 70x8 − 3x6 + 9
a0 b , m = n m m−1 0 P ( x) a0 x + a1 x +L+ am−1 x + am m lim = lim = 0, m < n x→∞ Q ( x) x→∞ b xn + b xn−1 +L b + n−1 x + bn 0 1 n ∞, m > n
英语数学词汇大全
英语数学词汇大全一、基本数学运算符号1. = 等于2. + 加号3. - 减号4. × 乘号5. ÷ 除号6. ( ) 左右括号7. 【】左右括号二、数字和数字组合1. 数字：1, 2, 3, 4, 5, 6, 7, 8, 9, 02. 十进制组合：10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 503. 分数：1/2, 1/3, 2/3, 1/4, 3/4, 1/5, 2/5, 3/5, 4/5, 1/6, 5/6, 1/8, 3/8, 5/8, 7/8, 1/10, 1/1004. 百分数：25%, 50%, 75%, 10%, 20%, 30%, 40%, 60%, 70%, 80%, 90%5. 小数：0.1, 0.2, 0.3, 0.4, 0.5, 0.6, 0.7, 0.8, 0.9,0.01, 0.02, 0.03, 0.04, 0.05, 0.06, 0.07, 0.08, 0.09三、基本数学术语1. 数学 Mathematics2. 数学符号 Mathematical Symbols3. 数字 Numbers4. 整数 Integers5. 实数 Real Numbers6. 分数 Fractions7. 百分数 Percentages8. 小数 Decimals9. 平方 Square10. 立方 Cube11. 数轴 Number Line12. 科学计数法 Scientific Notation13. 方程式 Equation14. 不等式 Inequality15. 图形 Shapes16. 几何 Geometries17. 点 Point18. 直线 Line19. 面 Area20. 体 Volume21. 角 Angle22. 弧 Arc23. 弦 Chord四、代数1. 代数 Algebra2. 变量 Variable3. 带字母数 Algebraic Expression4. 表达式 Expression5. 多项式 Polynomial6. 因数 Factor7. 除法 Division8. 余式 Remainder9. 方程 Equation10. 不等式 Inequality11. 复合式 Compound Expression12. 式子 Terms13. 系数 Coefficient14. 线性 Linear15. 非线性 Non-Linear16. 恒等式 Identity17. 联立方程组 System of Equations五、几何1. 平面几何 Plane Geometry2. 空间几何 Space Geometry3. 线性 Linear4. 非线性 Non-Linear5. 长度 Length6. 面积 Area7. 体积 Volume8. 三角形 Triangle9. 直角三角形 Right Triangle10. 等腰三角形 Isosceles Triangle11. 等边三角形 Equilateral Triangle12. 直线 Line13. 射线 Ray14. 线段 Line Segment15. 圆 Circle16. 圆心 Center17. 直径 Diameter18. 周长 Perimeter19. 弧 Arc20. 弦 Chord21. 刻度 Scale六、统计学1. 统计学 Statistics2. 数据 Data3. 变量 Variable4. 频率 Frequency5. 频数 Count6. 中心趋势 Measuring Center7. 均值 Mean8. 中位数 Median9. 众数 Mode10. 偏态 Asymmetry11. 偏度 Skewness七、微积分1. 微积分 Calculus2. 导数 Derivative3. 极限 Limit4. 偏导数 Partial Derivative5. 积分 Integral6. 定积分 Definite Integral7. 不定积分 Indefinite Integral8. 连续性 Continuity9. 反函数 Inverse Function10. 曲线 Curve11. 面积 Area12. 体积 Volume13. 速度 Velocity14. 加速度 Acceleration15. 梯度 Gradient八、数学常数和公式1. 圆周率 Pi2. 自然常数 e3. 欧拉公式 Euler's Formula4. 三角函数 Trigonometric Functions5. 反三角函数 Inverse Trigonometric Functions6. 指数 Exponential Function7. 对数 Logarithmic Function8. 二项式定理 Binomial Theorem9. 泰勒展开 Taylor Series10. 欧拉定理 Euler's Theorem九、计算机科学中的数学1. 二进制 Binary2. 十六进制 Hexadecimal3. 位运算 Bitwise Operations4. 逻辑运算 Logical Operations5. 算法 Algorithm6. 数据结构 Data Structure7. 线性代数 Linear Algebra8. 群论 Group Theory9. 离散数学 Discrete Mathematics10. 数字信号处理 Digital Signal Processing以上为英语数学词汇大全，供大家参考。
高等数学常用术语中英文对照一览表
高等数学常用术语中英文对照一览表高等数学是理工科及相关专业中重要的基础学科之一，它涉及了大量的术语和概念。
在学习和理解高等数学的过程中，掌握这些术语的中英文对照是十分重要的。
本文将为您提供一份高等数学常用术语中英文对照一览表，帮助您更好地理解和应用这些术语。
1. 集合论 (Set theory)- 集合 (Set)- 元素 (Element)- 子集 (Subset)- 并集 (Union)- 交集 (Intersection)- 补集 (Complement)2. 函数与极限 (Functions and limits)- 函数 (Function)- 定义域 (Domain)- 值域 (Range)- 极限 (Limit)- 连续 (Continuous)- 偏导数 (Partial derivative)- 微分 (Differential)3. 微积分 (Calculus)- 导数 (Derivative)- 积分 (Integral)- 不定积分 (Indefinite integral)- 定积分 (Definite integral)- 曲线的长度 (Arc length)- 曲线的曲率 (Curvature)- 泰勒级数 (Taylor series)4. 微分方程 (Differential equations)- 微分方程 (Differential equation)- 一阶常微分方程 (First-order ordinary differential equation)- 齐次方程 (Homogeneous equation)- 非齐次方程 (Non-homogeneous equation)- 二阶线性常微分方程 (Second-order linear ordinary differential equation)- 高阶常微分方程 (Higher-order ordinary differential equation)5. 线性代数 (Linear algebra)- 行列式 (Determinant)- 向量 (Vector)- 矩阵 (Matrix)- 线性变换 (Linear transformation)- 特征值与特征向量 (Eigenvalue and eigenvector)- 正交 (Orthogonal)- 对称矩阵 (Symmetric matrix)6. 概率论与数理统计 (Probability theory and mathematical statistics) - 概率 (Probability)- 随机变量 (Random variable)- 概率密度函数 (Probability density function)- 累积分布函数 (Cumulative distribution function)- 期望值 (Expectation)- 方差 (Variance)- 正态分布 (Normal distribution)7. 多元函数 (Multivariable functions)- 偏导数 (Partial derivative)- 梯度 (Gradient)- 雅可比矩阵 (Jacobian matrix)- 多元微积分 (Multivariable calculus)- 多元函数积分 (Multiple integrals)- 曲面积分 (Surface integral)- 空间曲线积分 (Line integral in space)8. 级数 (Series)- 级数 (Series)- 收敛 (Convergence)- 绝对收敛 (Absolutely convergence)- 条件收敛 (Conditionally convergence)- 无穷级数 (Infinite series)- 幂级数 (Power series)- 泰勒级数 (Taylor series)以上仅为高等数学中的一小部分常用术语，但对于初学者来说，理解和掌握这些术语是基础的一步。
英语1-10-数字课件
Writing the 0 digit
总结词
注意两个数字的组合方式
详细描述
数字10是由数字1和数字0组合而成的，应先写一个类似于"1"的形状，然后在形状的下方画一个圆圈 。
03 Application scenarios for numbers 1-10
Usage in daily life
01
Distance measurement
Numbers 1-10 can be used to measure distances between locations using GPS technology.
Practice questions
04 and answers for numbers 1-10
Exercise Question 1 and Answer
Exercise Question 1
How many apples are there in the basket?
Answer
There are 5 apples in the basket.
Exercise Question 2 and Answer
Pronunciation of Number
总结词：双唇音
详细描述：数字6的发音是一个双唇音，它的发音类似于单词 "six"，声音清晰，需要将双唇合拢，发出清晰的声音。
Pronunciation of Number
总结词：舌尖音
详细描述：数字7的发音是一个舌尖音，它的发音类似于单 词"tea"，声音清晰，需要将舌尖抵住上齿龈，发出清晰的 声音。
English 1-10 Digital Courseware
高等数学英文术语对照
高等数学英文术语对照Aabscissa, X-coordinate 横坐标absolute value 绝对值absolute convergence 绝对收敛acceleration 加速度accumulating point 聚点accuracy 精度addition, add, sum, summation 和，求和，加法adjugate matrix 转置伴随阵algebra 代数algorithm 算法angle 角antiderivative, primitive function 反导数，原函数approach 趋近arc 弧area of a plane region 平面图形的面积area of a plane region bounded by curves 由曲面围成的平面图形的面积area of surface 曲面面积assume, assumption 假设asteroid 星形线asymptote 渐近线x-axis, y-axis x 轴，y 轴auxiliary equation, characteristic equation 辅助方程，特征方程Bbasis 基boundary 边界bounded by 被…所围成boundedness 有界性Ccalculus 微积分cardioid 心脏线center of gravity 重心center of mass 质心centroid 形心chain rule 链式法则characteristic root 特征根chord 弦circle 圆coefficient 系数cofactor 代数余子式column 列，elementary column transformation (operation) 初等列变换combination 组合comparison test 比较判别法complex number 复数composition of functions 复合函数concave, concavity 凹，凹性condition 条件，conditionally convergent 条件收敛confidence interval 置信区间cone 锥面conj ugate 共轭conjugate complex number 共轭复数conjugate c urve 共轭曲线consistent 相容constant 常数continuous 连续的contour, level line 等值线，等高线contradiction 矛盾，by contradiction 反证法convergence, convergent 收敛，convergence test 收敛性判别法convex, convexity 凸，凸性coordinate system 坐标系，rectangular/cylindrical/spherical coordinate system 直角/柱面/球面坐标系，polar coordinate system 极坐标系coordinates of vector 向量的坐标corollary 推论Cramer’s Rule 克拉默法则cross product (or outer product, vector product) 叉积（或外积、向量积）cumulant 积累量cumulant generating function 积累量母函数curve 曲面cylinder 柱面D(is) defined to be 定义为definite integral 定积分definite integral with variable upper limit 积分上限函数definition 定义denominator 分母denote, denote to be, denoted by 表示为dependent variable 因变量derivative 导数determinant 行列式diagonal 对角线，diagonalization of a marix 矩阵的对角化diameter 直径dimension 维，维数directional angle 方向角directional cosines 方向余弦discrete 离散的disk 圆盘，圆盘闭区域divergent, divergence 发散displacement 位移first/second/nth derivative 一阶/二阶/n 阶导数right-hand (left-hand) derivative 右（左）导数difference, subtraction, subtract 差，减法，相减differentiable 可倒的，可微的differential 微分，differential calculus 微分学discontinuity 间断，point of discontinuity 间断点distribution 分布normal distribution 正态分布Bernoulli distribution 伯努利分布binomial distribution 二项分布Poisson distribution 泊松分布negative binomial distribution 负二项分布geometric distribution 几何分布hypergeometric distribution 超几何分布uniform distribution 均匀分布exponential distribution 指数分布Gamma distribution 伽马分布Weibull distribution 韦伯尔分布lognormal distribution 对数正态分布chi-distribution 卡方分布student t-distribution 学生t 分布F-distribution F 分布division, divide, quotient 除法，相除，商domain, natural domain 定义域，自然定义域dot product (or inner product, scalar product) 点积（或内积、数量积）double product 二重积分Eeigenvalue, eigenvector 特征值，特征向量element 元素elementary transformation 初等变换ellipse 椭圆ellipsoid 椭球面elliptic cylinder 椭圆柱面entry 向量的分量，元素equal, be equal to 相等，equation 等式equilibrium 平衡even function 偶函数exclusive 互斥的mutually exclusive 完全互斥expansion 展开式expectation (expected value) 期望exponential function 指数函数expression 表达式，express y in terms of x 将y 表示为x 的一个式子exterior point 外点absolute/global extreme values 最大最小值relative/local extreme values 极值Ffactorial 阶乘find, compute, evaluate 计算first-order linear differential equation 一阶线性微分方程first-order separable differential equation 一阶可分离变量微分方程focus 焦点formula 公式fraction 分数proper fraction, 真分数，improper fraction 假分数function 函数function determined implicitly by equation 由方程确定的隐函数function determined by parametric equation 由参数方程确定的函数Foundation Theorem of Calculus 微积分基本定理fundamental solution 基础解GGauss-Jordan Elimination 高斯-若尔当消元法general equation of a plane 平面的一般式方程general solution 通解generator 分母geometry 几何geometric meaning (interpretation, significance) of derivative 导数的几何意义given 给定，设gradient 梯度gradient vector 梯度向量graph of a function 函数图像gravitational force 引力Hhemisphere 半球面homogeneous equation 齐次方程horizontal 水平horizontal asymptote 水平渐近线hydrostatic force 水压力hyperbola 双曲线hyperbolic cylinder 双曲柱面hyperboloid 双曲面hyperboloid of one sheet 单页双曲面hypothesis 假设、题设hypothesis testing 假设检验Iidentity 恒等式imaginary part 虚部improper integral 反常积分increment 增量indefinite integral 不定积分independent variable 自变量indeterminate form 未定式index 指标inequality 不等式infinitesimal 无穷小量infinitesimal of higher order 高阶无穷小equivalent of infinitesimals 等价无穷小inflection point 拐点initial-value problem 初值问题integer 整数positive (negative) integer 正（负）整数integral 积分integral calculus 积分学integrating factor 积分因子Lebesgue integral 勒贝格积分Riemann integral 黎曼积分integrable 可积的integrable with variable upper limit 积分上限函数integrand 被积函数integration by parts 分部积分法integration by substitution 换元积分法integration curve 积分曲线intercept 截距，x-intercept x 轴上的截距interior point 内点Intermediate value Theorem 介值定理intersect 相交intersection 交集interval 区间closed (open) interval 闭（开）区间interval of convergence 收敛区间inverse 反、逆inverse function 反函数inverse matrix 逆矩阵inverse trigonometric function 反三角函数inversely proportional to 反比与irrational number 无理数iterated integral 累次积分iteration 秩代JJacobian matrix 雅各比矩阵Llaminar 平面薄片Law of Parallelogram 平行四边形法则lemma 引理length of an arc 弧长let 设、令limit 极限right-hand (left-hand) limit 右（左）极限the limit of a sequence 数列极限the limit of f(x) as x approaches x 当x 趋近于x 时f(x) 的极限the limit of f(x) as x approaches infinity 当趋近与无穷大时f(x) 的极限line integral 曲线积分line segment 线段linear algebra 线性代数linear approximation 线性逼近linear combination 线性组合linear function 线性函数linear operations 线性运算linearly dependent (independent) 线性相关/无关logarithmic differentiation 对数求导法logarithmic function 对数函数lower limit 积分下限Mmapping 映射mathematics induction 数学归纳法matrix, matrics 矩阵block matrix 分块阵diagonal matrix 对角阵elementary matrix 初等矩阵identity matrix 单位矩阵unit matrix 单位矩阵invertible matrix 可逆矩阵singular matrix 奇异阵，降秩阵non-degenerate matrix 非退化阵scalar matrix 数量阵square matrix 方阵orthogonal matrix 正交阵symmetric matrix 对称阵skew-symmetric matrix 反对称阵full rank matrix 满秩阵maximum 最大值maximal linearly independent subset 最大线性无关组mean value theorem 中值定理median 中位数minimum 最小值mixed product, box product 混合积mode 众数moment 矩量moment matrix 矩量矩阵moment generating function 矩量母函数moment of a force 力矩moment of inertia about x-axis 关于x 轴的转动惯量monotonely decrease 单调减少monotonely increase 单调增加monotonicity 单调性multiplication, multiple, product 积，乘法，相乘multivariable function 多元函数Nnatural number 自然数natural domain 自然定义域necessary condition 必要条件neighborhood 邻域deleted neighborhood 去心邻域nontrivial solution 非平凡解norm 范数normal line 法线normal plane 法平面normal vector 法向量notation 记号numerator 分子Oodd function 奇函数order 次序/ 阶/导数的阶/矩阵的阶/行列式的阶operation 运算optimization 最优化order-reducible differential equation 可降阶微分方程ordinary differential equation (ODE) 常微分方程ordinate, y-coordinate 纵坐标orthogonal 正交的orthogonal basis 正交基orthonormal basis 规范正交基oscillatory 振动的Pparabola 抛物线parabolic cylinder 抛物柱面paraboloid 抛物面parallel to 平行于parallelogram 平行四边形parameter 参数parametric equations of a line 直线的参数方程parity of a function 函数的奇偶性partial derivative 偏导数first partial derivative 一阶偏导数mixed higher partial derivative 高阶混合偏导数part 部分integration by parts 分部积分法partial differential equation (PDE) 偏微分方程partial fraction decomposition 部分分式分解partial sum sequence 部分和数列particular solution 特解pencil of planes 平面束period of a function 函数的周期periodic function 周期函数permutation 排列perpendicular to 垂直于plane 平面plane region 平面图形plane rectangular coordinate system 平面直角坐标系plane analytic geometry 平面解析几何point 点common point 公共点，交点point-normal equation of a plane 平面的点法式方程polar coordinate system 极坐标系polygon 多边形polynomial function 多项式函数position function 位置函数power 乘幂power function 幂函数power series 幂级数probability 概率probability density function 概率密度函数probability generating function 概率母函数probability mass function 概率质量函数problem, question 问题product 乘积projection 投影proof, prove 证明properties 性质proportional to 正比于inversely proportional to 反比与proposition 命题pyramid 棱锥Qquadratic 二次的，二次quadrature 积分过程，正交的quadric surfaces 二次曲面quality 质量quantity 数量quotient 商Rradian 弧度radius 半径random variable 随机变量rank of a matrix 矩阵的秩range 值域the rate of change of y with respect to x y 关于x 的变化率rational function 有理函数rational number 有理数ratio test 比值判别法real number 实数rectangle 矩形regression 回归linear regression 线性回归related rate of change 相关变化率right circular cylinder 圆柱面right-hand coordinate system 右手坐标系root-extract 开根root of an equation 方程的根root test 根值判别法rose of three loops 三叶玫瑰线row 行elementary row transformation (operation) 初等行变换Ssaddle 马鞍面sample 样本scalar 数量，标量secant 正割secant line 割线second-order homogeneous linear equation with constant coefficient二阶常系数齐次微分方程second-order nonhomogeneous linear equation with constant coefficient 二阶常系数非齐次微分方程sequence 数列series 级数infinite series 无穷级数Taylor series (expansion) 泰勒公式set 集合show 证明single variable function 一元函数slope 斜率space 空间vector space 向量空间linear space 线性空间space analytic geometry 空间解析几何2D(Dimension) space 二维空间space rectangular coordinate system 空间直角坐标系squeeze rule 夹逼准则solid 立体solid of revolution 旋转体solution, solve 解speed 速率span 生成，张成sphere 球面standard deviation (std) 标准差state 叙述stationary point 驻点stochastic 随机的stochastic differential equation (SDE) 随机微分方程straight line 直线subset 子集subspace 子空间substitute, substitution 代入，置换integration by substitute 换元积分法sufficient condition 充分条件sum, summation 和，求和sum of a series 级数的和suppose, supposition 假设surface integral 曲面积分symbol 符号symmetry, symmetric 对称symmetric equations of a line 直线的对称式方程system of equations 方程组system of linear equations 线性方程组Ttangent 正切tangent line 切线tangent plane 切面theorem 定理transformation 变换translation 平移trajectory 轨迹trapezoid 梯形triangle 三角形trigonometric function 三角函数hyperbolic trigonometric function 双曲三角函数triple integral 三重积分total differential 全微分total increment 全增量Uunbiased 无偏的union 全集unit vector 单位向量unknown 未知数upper limit 积分上限Vvalue 值variable 变量，可变的variance 方差vector 向量n-dimensional vector N 维向量velocity 速度verify 证明vertex 顶点 (复数vertices)vertical 验证vertical asymptote 铅直渐近线volume of a solid 立体体积the volume of a solid of revolution 旋转体的体积Wthe work done by a force 某力所做的功Zzero 零zeros of a polynomial 多项式的零点Mathematical Sentence Patterns1. If …… , (then) …… (若设……，则有……)2. Let …… , then …… . Therefore …… , so …… (令……，则…… ；于是……，因此……)3. By …… , we have …… (根据……，可得……)4. Prove (that) …… (证明……)5. Compute that …… (计算……)6. Given …… , find …… (设……，证明……)7. Solve the equation for y in terms of x (将方程中的y 关于x 解出来)8. Since …… , (we have, it follows that) …… (因为……，所以可推得……)9. Assume (suppose) that …… , then ……. Hence, …… (假设……，则有……；因此…… )10. By hypothesis …… , hence ……, and therefore …… (根据题设……，可得……，因此……)11. The above results imply that …… (根据上述结果可得……)12. When …… , …… becomes …… (当……时，……变为……)13. Similarly ……(相似的/ 同理可得……)14. In general …… (一般的……)15. Specially …… (特别的……)16. Without loss of generality, we assume that …… (不失一般性，可设……)17. Substitute a for x in (*), we obtain…… (在(*)中用a 代替x ，可得……)。
高等数学常用英文单词
定义definition 变量 variable 面积area直径diameter半径radius公式formula单价unit pric e范围range/scope/extent集合set法则principle本金principal利率interest rate利息interest单利si mple interest复利compound interest正数positive number负数negative number解析式analytic expr ession分类讨论classified discussion性质nature （不是很确定）奇函数odd function偶函数even funct ion对称symmetric坐标原点origin单调性monotonicity（不是很确定）任意random周期性periodic 有界性boundedness 数学mathematics, maths(BrE), math(AmE) 公理axiom 定理theorem 计算calcu lation 运算operation 证明prove 假设hypothesis, hypotheses(pl.) 命题proposition 算术arithmetic 加plus(prep.), add(v.), addition(n.) 被加数augend, summand 加数addend 和sum 减minus(prep.), subtract(v.), subtraction(n.) 被减数minuend 减数subtrahend 差remainder 乘times(prep.), multiply (v.), multiplication(n.) 被乘数multiplicand, faciend 乘数multiplicator 积product 除divided by(prep.), divide(v.), division(n.) 被除数dividend 除数divisor 商quotient 等于equals, is equal to, is equivale nt to 大于is greater than 小于is lesser than 大于等于is equal or greater than 小于等于is equal o r lesser than 运算符operator 平均数mean 算术平均数arithmatic mean 几何平均数geometric mean n 个数之积的n次方根倒数（reciprocal）x的倒数为1/x 有理数rational number 无理数irrational nu mber 实数real number 虚数imaginary number 数字digit 数number 自然数natural number 整数in teger 小数decimal 小数点decimal point 分数fraction 分子numerator 分母denominator 比ratio 正positive 负negative 零null, zero, nought, nil 十进制decimal system 二进制binary system 十六进制hexadecimal system 权weight, significance 进位carry 截尾truncation 四舍五入round 下舍入rou nd down 上舍入round up 有效数字significant digit 无效数字insignificant digit 代数algebra 公式fo rmula, formulae(pl.) 单项式monomial 多项式polynomial, multinomial 系数coefficient 未知数unknow n, x-factor, y-factor, z-factor 等式，方程式equation 一次方程simple equation 二次方程quadratic equ ation 三次方程cubic equation 四次方程quartic equation 不等式inequation 阶乘factorial 对数logarit hm 指数，幂exponent 乘方power 二次方，平方square 三次方，立方cube 四次方the power of fou r, the fourth power n次方the power of n, the nth power 开方evolution, extraction 二次方根，平方根square root 三次方根，立方根cube root 四次方根the root of four, the fourth root n次方根the r oot of n, the nth root sqrt(2)=1.414 sqrt(3)=1.732 sqrt(5)=2.236 常量constant 变量variable 坐标系coordinates 坐标轴x-axis, y-axis, z-axis 横坐标x-coordinate 纵坐标y-coordinate 原点origin 象限quadrant 截距(有正负之分)intercede （方程的）解solution 几何geometry 点point 线line 面pla ne 体solid 线段segment 射线radial 平行parallel 相交intersect 角angle 角度degree 弧度radian 锐角acute angle 直角right angle 钝角obtuse angle 平角straight angle 周角perigon 底base 边si de 高height 三角形triangle 锐角三角形acute triangle 直角三角形right triangle 直角边leg 斜边hyp otenuse 勾股定理Pythagorean theorem 钝角三角形obtuse triangle 不等边三角形scalene triangle 等腰三角形isosceles triangle 等边三角形equilateral triangle 四边形quadrilateral 平行四边形parallelogr am 矩形rectangle 长length 宽width 周长perimeter 面积area 相似similar 全等congruent 三角tri gonometry 正弦sine 余弦cosine 正切tangent 余切cotangent 正割secant 余割cosecant 反正弦arc sine 反余弦arc cosine 反正切arc tangent 反余切arc cotangent 反正割arc secant 反余割arc cose cant 补充：集合aggregate 元素element 空集void 子集subset 交集intersection 并集union 补集co mplement 映射mapping 函数function 定义域domain, field of definition 值域range 单调性mono tonicity 奇偶性parity 周期性periodicity 图象image 数列，级数series 微积分calculus 微分differenti al 导数derivative 极限limit 无穷大infinite(a.) infinity(n.) 无穷小infinitesimal 积分integral 定积分d efinite integral 不定积分indefinite integral 复数complex number 矩阵matrix 行列式determinant 圆circle 圆心centre(BrE), center(AmE) 半径radius 直径diameter 圆周率pi 弧arc 半圆semicircle 扇形sector 环ring 椭圆ellipse 圆周circumference 轨迹locus, loca(pl.) 平行六面体parallelepiped 立方体cube 七面体heptahedron 八面体octahedron 九面体enneahedron 十面体decahedron 十一面体hendecahedron 十二面体dodecahedron 二十面体icosahedron 多面体polyhedron 旋转rotation 轴axis 球sphere 半球hemisphere 底面undersurface 表面积surface area 体积volume 空间space 双曲线hyperbola 抛物线parabola 四面体tetrahedron 五面体pentahedron 六面体hexahedron菱形rhomb, rhombus, rhombi(pl.), diamond 正方形square 梯形trapezoid 直角梯形right trapezoid 等腰梯形isosc eles trapezoid 五边形pentagon 六边形hexagon 七边形heptagon 八边形octagon 九边形enneagon 十边形decagon 十一边形hendecagon 十二边形dodecagon 多边形polygon 正多边形equilateral poly gon 相位phase 周期period 振幅amplitude 内心incentre(BrE), incenter(AmE) 外心excentre(BrE), e xcenter(AmE) 旁心escentre(BrE), escenter(AmE) 垂心orthocentre(BrE), orthocenter(AmE) 重心baryc entre(BrE), barycenter(AmE) 内切圆inscribed circle 外切圆circumcircle 统计statistics 平均数average 加权平均数weighted average 方差variance 标准差root-mean-square deviation, standard deviation 比例propotion 百分比percent 百分点percentage 百分位数percentile 排列permutation 组合combin ation 概率，或然率probability 分布distribution 正态分布normal distribution 非正态分布abnormal dis tribution 图表graph 条形统计图bar graph 柱形统计图histogram 折线统计图broken line graph 曲线统计图curve diagram 扇形统计图pie diagram 数列是sequence极限是limit导数是derivative微分是dif ferential积分是integral常数constant级数series幂级数power series二重积分double integral数学mathematics, maths(BrE), math(AmE) 公理axiom 定理theorem计算calculation 运算operation 证明prove 假设hypothesis, hypotheses(pl.) 命题proposition算术arithmetic 加plus(prep.), add(v.), addition(n.) 被加数augend, summand加数addend 和sum 减minus(prep.), subtract(v.), subtraction(n.) 被减数minuend 减数subtrahend 差remainder 乘times(prep.), multiply(v.), multiplication(n.)被乘数multiplicand, faciend 乘数multiplicator 积product除divided by(prep.), divide(v.), division(n.) 被除数dividend 除数divisor商quotient 等于equals, is equal to, is equivalent to 大于is greater than小于is lesser than 大于等于is equal or greater than小于等于is equal or lesser than 运算符operator 平均数mean算术平均数arithmatic mean几何平均数geometric mean n个数之积的n次方根倒数（reciprocal）x的倒数为1/x 有理数rational number 无理数irrational number实数real number 虚数imaginary number 数字digit 数number 自然数natural number 整数integer 小数decimal 小数点decimal point 分数fraction 分子numerator分母denominator 比ratio 正positive 负negative 零null, zero, nought, nil十进制decimal system 二进制binary system 十六进制hexadecimal system权weight, significance 进位carry 截尾truncation 四舍五入round下舍入round down 上舍入round up 有效数字significant digit 无效数字insignificant digit 代数algeb ra 公式formula, formulae(pl.) 单项式monomial 多项式polynomial, multinomial 系数coefficient 未知数unknown, x-factor, y-factor, z-factor 等式，方程式equation 一次方程simple equation 二次方程qu adratic equation 三次方程cubic equation 四次方程quartic equation 不等式inequation 阶乘factorial 对数logarithm 指数，幂exponent 乘方power 二次方，平方square 三次方，立方cube四次方the power of four, the fourth power n次方the power of n, the nth power开方evolution, extraction 二次方根，平方根square root 三次方根，立方根cube root 四次方根the ro ot of four, the fourth root n次方根the root of n, the nth rootsqrt(2)=1.414 sqrt(3)=1.732 sqrt(5)=2.236常量constant 变量variable坐标系coordinates 坐标轴x-axis, y-axis, z-axis 横坐标x-coordinate纵坐标y-coordinate 原点origin 象限quadrant 截距(有正负之分)intercede（方程的）解solution 几何geometry 点point 线line 面plane 体solid 线段segment射线radial 平行parallel 相交intersect 角angle角度degree 弧度radian 锐角acute angle 直角right angle 钝角obtuse angle 平角straight angle 周角perigon底base 边side 高height 三角形triangle 锐角三角形acute triangle right triangle直角边leg 斜边hypotenuse 勾股定理Pythagorean theorem 钝角三角形obtuse triangle 不等边三角形scalene triangle 等腰三角形isosceles triangle 等边三角形equilateraltriangle 四边形quadrilateral 平行四边形parallelogram矩形rectangle 长length宽width周长perimeter 面积area 相似similar 全等congruent三角trigonometry正弦sine 余弦cosine 正切tangent 余切cotangent 正割secant 余割cosecant反正弦arc sine 反余弦arc cosine 反正切arc tangent 反余切arc cotangent 反正割arc secant 反余割arc cosecant 集合aggregate 元素element 空集void 子集subset交集intersection 并集union 补集complement 映射mapping function 定义域domain, field of definiti on 值域range 单调性monotonicity 奇偶性parity 周期性periodicity 图象image 数列，级数series 微积分calculus 微分differential 导数derivative 极限limit 无穷大infinite(a.) infinity(n.) 无穷小infinit esimal 积分integral 定积分definite integral 不定积分indefinite integral 复数complex number 矩阵matrix 行列式determinan圆circle 圆心centre(BrE), center(AmE) 半径radius 直径diameter 圆周率pi 弧arc 半圆semicircle 扇形sector 环ring 椭圆ellipse 圆周circumference 轨迹locus, loca(pl.) 平行六面体parallelepiped 立方体cube 七面体heptahedron八面体octahedron 九面体enneahedron 十面体decahedron 十一面体hendecahedron 十二面体dodec ahedron 二十面体icosahedron 多面体polyhedron 旋转rotation 轴axis 球sphere 半球hemisphere 底面undersurface 表面积surface area 体积volume 空间space 双曲线hyperbola 抛物线parabola四面体tetrahedron 五面体pentahedron 六面体hexahedron菱形rhomb, rhombus, rhombi(pl.), diamo nd 正方形square 梯形trapezoid 直角梯形right trapezoid 等腰梯形isosceles trapezoid 五边形penta gon 六边形hexagon 七边形heptagon 八边形octagon九边形enneagon 十边形decagon 十一边形he ndecagon 十二边形dodecagon 多边形polygon 正多边形equilateral polygon相位phase 周期period 振幅amplitude内心incentre(BrE), incenter(AmE) 外心excentre(BrE), excenter(AmE) 旁心escentre(BrE), escenter(A mE) 垂心orthocentre(BrE), orthocenter(AmE) 重心barycentre(BrE), barycenter(AmE) 内切圆inscribed circle 外切圆circumcircle统计statistics 平均数average 加权平均数weighted average方差variance 标准差root-mean-square deviation, standard deviation比例propotion 百分比percent 百分点percentage 百分位数percentile排列permutation 组合combination 概率，或然率probability 分布distribution 正态分布normal distrib ution 非正态分布abnormal distribution图表graph 条形统计图bar graph 柱形统计图histogram 折线统计图broken line graph 曲线统计图curve diagram 扇形统计图pie diagram1。
高数中的英文单词
高数中的英文单词反函数:a inverse function.幂函数:a power function.指数函数:a exponential function.对数函数:a logarithmic function.三角函数:a trigonometric function.反三角函数:a anti-trigonometric function.复合函数:a compound function.初等函数:a elementary function.双曲函数:a hyperbolic function.反双曲函数:a anti-hyperbolic function.无穷小:infinitesimal.无穷大:infinity.连续性:continuity.间断点:discontinuous point.介值定理:intermediate value theorem.导数:derivative. 微分:differential.函数的单调性:monotonicity of function.曲线:curve. 曲线的凹凸性:concavity of curve.曲线的拐点: keen point of curve.曲率:curvature.不定积分: indefinite integral(indeterminate integral). 定积分: definite integral.广义积分:improper integral.空间解析几何:space analytic geometry.向量代数:vector algebra.空间直角坐标系:space rectangular coordinate system. 数量积:scalar product.向量积:vector product.混合积:triple product.曲面:surface.二次曲面:second-degree surface.一.数学中常用符号+: plus X: multiply-: subtract ÷: divideV~: square root |...|: absolute value=: is equal to =/=: is not equal to>: is greater than <: is less than//: is parallel to _|_: is perpendicular to>=: is greater than or equal to (或 no less than) <=: is less than or equal to (或no more than) 二.表达相应数目的前缀1:uni-,mono-2:bi-,du-,di-3:tri-,ter-,4:tetra-,quad-,5:penta-,quint,6:hex-,sex-,7:sept-,hapta-,8:oct,9:enn-,10:dec-,deka-,三.数学中常用单词术语abscissa 横坐标absolute value 绝对值 acute angle 锐角adjacent angle 邻角addition 加algebra 代数altitude 高angle bisector 角平分线 arc 弧area 面积arithmetic mean 算术平均值（总和除以总数）arithmetic progression 等差数列（等差级数）arm 直角三角形的股at 总计（乘法）average 平均值base 底be contained in 位于...上bisect 平分center 圆心chord 弦circle 圆形circumference 圆周长circumscribe 外切，外接clockwise 顺时针方向closest approximation 最相近似的combination 组合common divisor 公约数，公因子common factor 公因子complementary angles 余角（二角和为90度）composite number 合数（可被除1及本身以外其它的数整除）concentric circle 同心圆cone 圆锥（体积＝1/3*pi*r*r*h）congruent 全等的consecutive integer 连续的整数coordinate 坐标的cost 成本counterclockwise 逆时针方向cube 1.立方数2.立方体（体积＝a*a*a 表面积＝6*a*a） cylinder 圆柱体decagon 十边形decimal 小数decimal point 小数点decreased 减少decrease to 减少到decrease by 减少了degree 角度define 1.定义 2.化简denominator 分母denote 代表，表示depreciation 折旧distance 距离distinct 不同的dividend 1. 被除数 2.红利divided evenly 被除数divisible 可整除的division 1.除 2.部分divisor 除数down payment 预付款，定金equation 方程equilateral triangle 等边三角形even number 偶数expression 表达exterior angle 外角face （立体图形的）某一面factor 因子fraction 1.分数 2.比例geometric mean 几何平均值（N个数的乘积再开N次方）geometric progression 等比数列（等比级数）have left 剩余height 高hexagon 六边形hypotenuse 斜边improper fraction 假分数increase 增加increase by 增加了increase to 增加到inscribe 内切，内接intercept 截距integer 整数interest rate 利率in terms of... 用...表达interior angle 内角intersect 相交irrational 无理数isosceles triangle 等腰三角形least common multiple 最小公倍数 least possible value 最小可能的值 leg 直角三角形的股length 长list price 标价margin 利润mark up 涨价mark down 降价maximum 最大值median, medium 中数（把数字按大小排列，若为奇数项，则中间那项就为中数，若为偶数项，则中间两项的算术平均值为中数。
高等数学专业名词中英文对照(全面)
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关键词：微积分英文,高等数学英文翻译,高数英语词汇来源：上海外教网 | 发布日期：2008-05-16 17:12V、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Periodic function ：周期函数Perpendicular lines ：垂直线Piecewise defined function ：分段定义函数Plane ：平面Point of inflection ：反曲点Polar axis ：极轴Polar coordinate ：极坐标Polar equation ：极方程式Pole ：极点Polynomial ：多项式Positive angle ：正角Point-slope form ：点斜式Power function ：幂函数Product ：积Quadrant ：象限Quotient Law of limit ：极限的商定律Quotient Rule ：商定律M、N、O:Maximum and minimum values ：极大与极小值Mean Value Theorem ：均值定理Multiple integrals ：重积分Multiplier ：乘子Natural exponential function ：自然指数函数Natural logarithm function ：自然对数函数Natural number ：自然数Normal line ：法线Normal vector ：法向量Number ：数Octant ：卦限Odd function ：奇函数One-sided limit ：单边极限Open interval ：开区间Optimization problems ：最佳化问题Order ：阶Ordinary differential equation ：常微分方程Origin ：原点Orthogonal ：正交的L:Laplace transform ：Leplace 变换Law of Cosines ：余弦定理Least upper bound ：最小上界Left-hand derivative ：左导数Left-hand limit ：左极限Lemniscate ：双钮线Length ：长度Level curve ：等高线L'Hospital's rule ：洛必达法则Limacon ：蚶线Limit ：极限Linear approximation：线性近似Linear equation ：线性方程式Linear function ：线性函数Linearity ：线性Linearization ：线性化Line in the plane ：平面上之直线Line in space ：空间之直线Lobachevski geometry ：罗巴切夫斯基几何Local extremum ：局部极值Local maximum and minimum ：局部极大值与极小值Logarithm ：对数Logarithmic function ：对数函数I:Implicit differentiation ：隐求导法Implicit function ：隐函数Improper integral ：瑕积分Increasing/Decreasing Test ：递增或递减试验法Increment ：增量Increasing Function ：增函数Indefinite integral ：不定积分Independent variable ：自变数Indeterminate from ：不定型Inequality ：不等式Infinite point ：无穷极限Infinite series ：无穷级数Inflection point ：反曲点Instantaneous velocity ：瞬时速度Integer ：整数Integral ：积分Integrand ：被积分式Integration ：积分Integration by part ：分部积分法Intercepts ：截距Intermediate value of Theorem ：中间值定理Interval ：区间Inverse function ：反函数Inverse trigonometric function ：反三角函数Iterated integral ：逐次积分H:Higher mathematics 高等数学/高数E、F、G、H:Ellipse ：椭圆Ellipsoid ：椭圆体Epicycloid ：外摆线Equation ：方程式Even function ：偶函数Expected Valued ：期望值Exponential Function ：指数函数Exponents , laws of ：指数率Extreme value ：极值Extreme Value Theorem ：极值定理Factorial ：阶乘First Derivative Test ：一阶导数试验法First octant ：第一卦限Focus ：焦点Fractions ：分式Function ：函数Fundamental Theorem of Calculus ：微积分基本定理Geometric series ：几何级数Gradient ：梯度Graph ：图形Green Formula ：格林公式Half-angle formulas ：半角公式Harmonic series ：调和级数Helix ：螺旋线Higher Derivative ：高阶导数Horizontal asymptote ：水平渐近线Horizontal line ：水平线Hyperbola ：双曲线Hyper boloid ：双曲面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Disk method ：圆盘法Distance ：距离Divergence ：发散Domain ：定义域Dot product ：点积Double integral ：二重积分change of variable in ：二重积分之变数变换in polar coordinates ：极坐标二重积分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 Theor em ：柯西均值定理Chain Rule ：连锁律Change of variables ：变数变换Circle ：圆Circular cylinder ：圆柱Closed interval ：封闭区间Coefficient ：系数Composition of function ：函数之合成Compound interest ：复利Concavity ：凹性Conchoid ：蚌线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Coordinate：s：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：圆柱Cylindrical Coordinates ：圆柱坐标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 ：反导数Approximate integration ：近似积分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 ：椭圆之轴Binomial series ：二项级数微积分词汇第一章函数与极限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 mappingX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 2007-10-8 18:37 回复此发言--------------------------------------------------------------------------------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 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 Rule0/0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(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 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 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Chapter8 Differentiation 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 setn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Chapter9 Multiple 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Chapter10 Line(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Chapter11 Infinite 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Chapter12 Differential 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 coefficientV、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Periodic function ：周期函数Perpendicular lines ：垂直线Piecewise defined function ：分段定义函数Plane ：平面Point of inflection ：反曲点Polar axis ：极轴Polar coordinate ：极坐标Polar equation ：极方程式Pole ：极点Polynomial ：多项式Positive angle ：正角Point-slope form ：点斜式Power function ：幂函数Product ：积Quadrant ：象限Quotient Law of limit ：极限的商定律Quotient Rule ：商定律M、N、O:Maximum and minimum values ：极大与极小值Mean Value Theorem ：均值定理Multiple integrals ：重积分Multiplier ：乘子Natural exponential function ：自然指数函数Natural logarithm function ：自然对数函数Natural number ：自然数Normal line ：法线Normal vector ：法向量Number ：数Octant ：卦限Odd function ：奇函数One-sided limit ：单边极限Open interval ：开区间Optimization problems ：最佳化问题Order ：阶Ordinary differential equation ：常微分方程Origin ：原点Orthogonal ：正交的L:Laplace transform ：Leplace 变换Law of Cosines ：余弦定理Least upper bound ：最小上界Left-hand derivative ：左导数Left-hand limit ：左极限Lemniscate ：双钮线Length ：长度Level curve ：等高线L'Hospital's rule ：洛必达法则Limacon ：蚶线Limit ：极限Linear approximation：线性近似Linear equation ：线性方程式Linear function ：线性函数Linearity ：线性Linearization ：线性化Line in the plane ：平面上之直线Line in space ：空间之直线Lobachevski geometry ：罗巴切夫斯基几何Local extremum ：局部极值Local maximum and minimum ：局部极大值与极小值Logarithm ：对数Logarithmic function ：对数函数I:Implicit differentiation ：隐求导法Implicit function ：隐函数Improper integral ：瑕积分Increasing/Decreasing Test ：递增或递减试验法Increment ：增量Increasing Function ：增函数Indefinite integral ：不定积分Independent variable ：自变数Indeterminate from ：不定型Inequality ：不等式Infinite point ：无穷极限Infinite series ：无穷级数Inflection point ：反曲点Instantaneous velocity ：瞬时速度Integer ：整数Integral ：积分Integrand ：被积分式Integration ：积分Integration by part ：分部积分法Intercepts ：截距Intermediate value of Theorem ：中间值定理Interval ：区间Inverse function ：反函数Inverse trigonometric function ：反三角函数Iterated integral ：逐次积分H:Higher mathematics 高等数学/高数E、F、G、H:Ellipse ：椭圆Ellipsoid ：椭圆体Epicycloid ：外摆线Equation ：方程式Even function ：偶函数Expected Valued ：期望值Exponential Function ：指数函数Exponents , laws of ：指数率Extreme value ：极值Extreme Value Theorem ：极值定理Factorial ：阶乘First Derivative Test ：一阶导数试验法First octant ：第一卦限Focus ：焦点Fractions ：分式Function ：函数Fundamental Theorem of Calculus ：微积分基本定理Geometric series ：几何级数Gradient ：梯度Graph ：图形Green Formula ：格林公式Half-angle formulas ：半角公式Harmonic series ：调和级数Helix ：螺旋线Higher Derivative ：高阶导数Horizontal asymptote ：水平渐近线。
高等数学英文1-2-10
V. Elementary Functions
1. Basic Elementary Functions Inverse Trigonometric Functions
y = arctan x
y = arccot x
§1.2 Functions
V. Elementary Functions
2. Elementary Functions Def: A composite function that is obtained from operations on or composed by basic elementary functions. For example:
§1.2 Functions
III. Inverse Functions
∀ x ∈ Df →∃ y ∈ R
∈ ∃ x∈D ← ∀ y∈ R ∈
y = f (x)
y = f ( x)
x = f −1( y) y = f −1( x)
The graphs of f and f −1( x)are symmetric with line y =x. If f is a monotonic function, then so is f −1( x).
§1.2 Functions
IV. Composite Functions
y = f (u) u = g(x)
D, R
D, R 1 1
y = f [g( x)] = ( f o g)(x)
( f o g)( x)is called the composition of f with g.
Restriction:
Def: We say f (x) is bounded above (below) on X if