(完整word)数学英文词汇大全汇总,推荐文档

1、微积分第一章函数与极限Chapterl 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 inf

2、inite 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 至ij Y 的映射 mapping of X ontoY满射 surjection单射 injection映射 one-to-one mapping双射 bijection算子 operator变化 transformation函数 function逆映射 inverse mapping复合映射 composi

3、te 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 par

4、t 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

5、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 哥函数 power function 指数函数 exponential function 对数函数 logaAthmic function 三角函数 trigon

6、ometric 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数歹U sequence of number收敛 convergen

7、ce收敛于 a converge to a发散 divergent极限的唯性uniqueness of limits收敛数歹 U 的有界性boundedness of a convergent sequence子歹U 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 infi

8、nity铅直渐近线 vertical asymptote夹逼准贝U squeeze rule单调数歹 U monotonic sequence高阶无穷/J、 infinitesimal of higher order彳氐阶无穷小 infinitesimal of lower order同阶无穷/J、 infinitesimal of the same order2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

9、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

10、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 tang

11、ent 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 equatio

12、n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 differentia

13、ble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

14、' 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 indetermin

15、ate 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 func

16、tion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

17、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分音 B 积分法 integration by parts分音 B 积分公式 form

18、ula 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分害U par

19、tition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 integr

20、al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

21、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弓 I力 gravitation变力

22、 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三角法贝 U 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 differen

23、ce分配律 distributive law空间直角坐标系 space rectangular coordinates坐标面 coordinate plane圭卜限 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

24、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 c

25、one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空间曲线的般方程ge

26、neral 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平面的般方程general form equation of a plane两平面的夹角 angle between two planes点至 U平面的距离distance from a point to a

27、 plane空间直线的般方程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

28、 a pencil of planes行歹U式 determinant系数行歹U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 a

29、ccumulation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

30、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

31、件 sufficient condition叠力口原理 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 deriva

32、tive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弓 I力势 gravitational potential曲面在点的切平面tangent plane to a surface at a point曲线在点的法线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 Lagr

33、ange 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

34、 system柱面坐标 cylindrical coordinates柱面坐标系中白体积元素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 in

35、ertia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 c

36、onnected 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

37、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

38、 series柯西收敛准贝 UCauchy 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 poi

39、nt of convergence收敛域 convergence domain和函数 sum function哥级数 power series哥级数的系数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 err

40、or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 ser

41、ies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

42、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 separ

43、able 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

44、 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 orderA自由振动的微分方程 强迫振动的微分方程 串联电路的振荡方程二阶线性微分方程differenti

45、al equation of free vibration differential equation of forced oscillation oscillation equation of series circuitsecond order linera differential equation线性才目关 linearly dependence线性无关 linearly independceequation with二阶常系数齐次线性微分方程second order homogeneour linear differential constant coefficient二阶变系数齐次

46、线性微分方程second order homogeneous linear differential equation withvariable 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

47、 of undetermined coefficient共振现象 resonance phenomenon欧拉方程 Euler equation哥级数解法 power series solution数值解法 numerial solution勒让德方程 Legendre equation微分方程组 system of differential equations常系数线性微分方程组system of linera differential equations with constant coefficient线性代数adjont(adjugate) of matrix A augmented

48、matrixBblock diagonal matrix block matrix basic solution setCCauchy-Schwarz inequality characteristic equation characteristic polynomial coffcient matrix cofactor cofactor expansion column vector commuting matrices consistent linear system Cramer' s rule Cross- product termDDeterminantDiagonal e

49、ntries Diagonal matrix Dimension of a vector space VEechelon matrix eigenspace eigenvalue eigenvector eigenvector basis elementary matrix elementary row operationsA的伴随矩阵A的增广矩阵块对角矩阵块矩阵基础解系柯西-许瓦兹不等式特征方程特征多项式系数矩阵代数余子式代数余子式展开列向量交换矩阵相容线性方程组克莱姆法则交叉项行列式对角元素对角矩阵向量空间V的维数梯形矩阵特征空间特征值特征向量 特征向量的基 初等矩阵 行初等变换full

50、rank满秩fundermental set of solution基础解系Gcentergrneral solutionGram-Schmidt processHhomogeneous linear equationsIidentity matrixinconsistent linear system indefinite matrixindefinit quatratic form infinite-dimensional space inner productinverse of matrix ALlinear combination linearly dependent linearl

51、y independent linear transformation lower triangular matrixMmain diagonal of matrix A matrix通解施密特正交化过程齐次线性方程组单位矩阵不相容线性方程组不定矩阵不定二次型无限维空间内积逆矩阵线性组合线性相关线性无关线性变换 下三角形矩阵矩阵的主对角矩阵Ncenternegative definite quaratic form negative semidefinite quadratic form nonhomogeneous equations nonsigular matrix nontrivial

52、 solution norm of vector V normalizing vector VOorthogonal basisorthogonal complementorthogonal decompositionorthogonally diagonalizable matrix orthogonal matrix orthogonal set orthonormal basisorthonomal setbPpartitioned matrixpositive definite matrixpositive definite quatratic form positive semide

53、finite matrix positive semidefinite quadratic form负定二次型半负定二次型非齐次线性方程组非奇异矩阵非平凡解向量V的范数规范化向量正交基正交补正交分解矩阵的正交对角化正交矩阵正交向量组规范正交基规范正交向量组分块矩阵 正定矩阵 正定二次型 半正定矩阵 半正定二次型Qquatratic formcenterR/center rank of matrix A reduced echelon matrix row vector二次型矩阵A的秩r(A)最简梯形阵行向量set spanned by similar matrices similarity t

54、ransformation singular matrix solution set standard basis standard matrix submatrix subspace symmetric matrix由向量 所生成相似矩阵相似变换奇异矩阵解集合标准基标准矢邱车I子矩阵子空间对称矩阵AT矩阵A的迹tr(A)矩阵A的转秩 三角不等式 平凡解trace of matrix A transpose of A triangle inequlity trivial solutionUunit vector单位向量upper triangular matrix上三角形矩阵Vvandermonde matrix范得蒙矩阵vector向量vector space向量空间零子空间零空间 (本文已被浏览 133次)Zzero subspacez