一类周期系数时滞微分方程解的渐近性态(英文)
微积分calculus英文单词
微积分英语单词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Arc length ：弧长Area ：面积Asymptote ：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at a point ：在一点处之连续性as the slope of a tangent ：导数看成切线之斜率by differentials ：用微分逼近between curves ：曲线间之面积Binomial series ：二项级数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Continuous function ：连续函数Convergence ：收敛Coordinate ：s ：坐标Cartesian ：笛卡儿坐标cylindrical ：柱面坐标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Distance ：距离Divergence ：发散Domain ：定义域Dot product ：点积Double integral ：二重积分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Determinant ：行列式Differentiable function ：可导函数Differential ：微分Differential equation ：微分方程Differentiation ：求导法Directional derivatives ：方向导数Discontinuity ：不连续性Disk method ：圆盘法domain of ：导数之定义域differential ：微分学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from the left ：左连续from the right ：右连续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Hyperboloid ：双曲面horizontal ：水平渐近线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integral ：积分学implicit ：隐求导法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linear ：线性逼近法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of a function ：函数之连续性on an interval ：在区间之连续性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polar ：极坐标partial ：偏导数partial ：偏微分方程partial ：偏微分法Quadrant ：象限Quotient Law of limit ：极限的商定律Quotient Rule ：商定律rectangular ：直角坐标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slant ：斜渐近线spherical ：球面坐标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term by term ：逐项求导法under a curve ：曲线下方之面积vertical ：垂直渐近线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。
degasperis—procesi方程解的渐进性质
degasperis—procesi方程解的渐进性质
广义DeGasperis--Processi(Stephanov, Konâev, Fedorenko和Tamarkin, 2002)方
程是一元双曲型偏微分方程。
它是一种重要的非线性可积性理论，用于模拟浪流发展的动
力学参数。
它由下式定义:
f(t,x) = xxx + λ(x^3 + x^2 - x) + lxx x^2 + cos(t)
其中的参量分别是lambda和l，它们定义了系统的非线性和可积特性。
DeGasperis-Processi方程的解由三个以上的极端点组成，其特征渐近形态是病态波，具有不同频率、宽度和幅度。
这种特征使得其在数值分析中成为受欢迎的选择。
它可以用
来研究脉冲性系统，例如电信及电子设备测试领域使用的强电磁场模拟。
解析解可以用项来表示:
f(t,x) = N (t) K_n (x)
其中n=1,2,3…代表不同的项，K_n是系数，N (t)是周期函数，它可以用傅里叶变换
的形式求出。
在浪流应用中，十二阶的解就足以解决。
渐近性质方面，从DeGasperis-Processi方程出发，利用它的扩展性可以构建出解的
渐近形式。
首先把方程的非线性项忽略掉，由此得到:
然后，根据加速度和活塞运动的假设，可以拟合渐近系数A_n。
最后，将A_n带入原
来的方程，得出如下渐近形式:
这是解DeGasperis-Processi方程解的渐近性质，在浪流动力学模拟中得到广泛应用，因为它能准确描述不同系统的浪流行为，并且简化大量的计算工作。
微积分专有名词中英文对照
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。
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
微积分英文词汇,高数名词中英文对照,高等数学术语英语翻译一览V、X、Z:Value of function ：函数值Variable ：变数Vector ：向量Velocity ：速度Vertical asymptote ：垂直渐近线Volume ：体积X-axis ：x轴x-coordinate ：x坐标x-intercept ：x截距Zero vector ：函数的零点Zeros of a polynomial ：多项式的零点T:Tangent function ：正切函数Tangent line ：切线Tangent plane ：切平面Tangent vector ：切向量Total differential ：全微分Trigonometric function ：三角函数Trigonometric integrals ：三角积分Trigonometric substitutions ：三角代换法Tripe integrals ：三重积分S:Saddle point ：鞍点Scalar ：纯量Secant line ：割线Second derivative ：二阶导数Second Derivative Test ：二阶导数试验法Second partial derivative ：二阶偏导数Sector ：扇形Sequence ：数列Series ：级数Set ：集合Shell method ：剥壳法Sine function ：正弦函数Singularity ：奇点Slant asymptote ：斜渐近线Slope ：斜率Slope-intercept equation of a line ：直线的斜截式Smooth curve ：平滑曲线Smooth surface ：平滑曲面Solid of revolution ：旋转体Space ：空间Speed ：速率Spherical coordinates ：球面坐标Squeeze Theorem ：夹挤定理Step function ：阶梯函数Strictly decreasing ：严格递减Strictly increasing ：严格递增Sum ：和Surface ：曲面Surface integral ：面积分Surface of revolution ：旋转曲面Symmetry ：对称R:Radius of convergence ：收敛半径Range of a function ：函数的值域Rate of change ：变化率Rational function ：有理函数Rationalizing substitution ：有理代换法Rational number ：有理数Real number ：实数Rectangular coordinates ：直角坐标Rectangular coordinate system ：直角坐标系Relative maximum and minimum ：相对极大值与极小值Revenue function ：收入函数Revolution , solid of ：旋转体Revolution , surface of ：旋转曲面Riemann Sum ：黎曼和Riemannian geometry ：黎曼几何Right-hand derivative ：右导数Right-hand limit ：右极限Root ：根P、Q:Parabola ：拋物线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。
自动控制原理专业词汇中英文对照
自动控制原理专业词汇中英文对照中文 英文自动控制 automatic control；cybernation 自动控制系统 automatic control system自动控制理论 automatic control theory经典控制理论 classical control theory现代控制理论 modern control theory智能控制理论 intelligent control theory 开环控制 open-loop control闭环控制 closed-loop control输入量 input输出量 output给定环节 given unit/element比较环节 comparing unit/element放大环节 amplifying unit/element执行环节 actuating unit/element控制环节 controlling unit/element被控对象 (controlled) plant反馈环节 feedback unit/element控制器 controller扰动/干扰 perturbance/disturbance前向通道 forward channel反馈通道 feedback channel 恒值控制系统 constant control system随动控制系统 servo/drive control system 程序控制系统 programmed control system 连续控制系统 continuous control system离散控制系统 discrete control system线性控制系统 linear control system非线性控制系统 nonlinear control system定常/时不变控制系统 time-invariant control system 时变控制系统 time-variant control system 稳定性 stability快速性 rapidity准确性 accuracy数学模型 mathematical model微分方程 differential equation非线性特性 nonlinear characteristic线性化处理 linearization processing泰勒级数 Taylor series传递函数 transfer function比例环节 proportional element积分环节 integrating element一阶惯性环节 first order inertial element二阶惯性环节 second order inertial element二阶震荡环节 second order oscillation element 微分环节 differentiation element一阶微分环节 first order differentiation element二阶微分环节 second order differentiation element 延迟环节 delay element动态结构图 dynamic structure block串联环节 serial unit并联环节 parallel unit信号流图 signal flow graph梅逊增益公式 Mason’s gain formula时域分析法 time domain analysis method性能指标 performance index阶跃函数 step function斜坡函数 ramp function抛物线函数 parabolic function /acceleration function 冲击函数 impulse function正弦函数 sinusoidal function动态/暂态响应 transient response静态/稳态响应 steady-state response 延迟时间 delay time上升时间 rise time峰值时间 peak time调节时间 settling time最大超调量 maximum overshoot稳态误差 steady-state error无阻尼 undamping欠阻尼 underdamping过阻尼 overdamping特征根 eigen root极点 pole零点 zero实轴 real axis虚轴 imaginary axis 稳态/静态分量 steady-state component瞬态/暂态/动态分量 transient component 运动模态 motion mode衰减 attenuation系数 coefficient初相角 initial phase angle响应曲线 response curve主导极点 dominant pole 劳斯稳定判据 Routh stability criterion S平面 S plane胡尔维茨稳定判据 Hurwitz stability criterion 测量误差 measurement error扰动误差 agitation error结构性误差 structural error偏差 deviation根轨迹 root locus 常规根轨迹 routine root locus根轨迹方程 root locus equation 幅值 magnitude幅角 argument对称性 symmetry分离点 separation/break away point会合点 meeting/break-in point渐近线 asymptote出射角 emergence angle/angle of departure入射角 incidence angle/angle of arrival 广义根轨迹 generalized root locus零度根轨迹 zero degree root locus 偶极子 dipole/zero-pole pair 频域分析法 frequency-domain analysis method 频率特性 frequency characteristic极坐标系 polar coordinate system直角坐标系 rectangular coordinate system幅频特性 magnitude-frequency characteristic相频特性 phase-frequency characteristic 幅相频率特性 magnitude-phase frequency characteristic 最小相位系统 minimum phase system非最小相位系统 nonminimum phase system奈奎斯特稳定判据 Nyquist stability criterion 伯德定理 Bode theorem稳定裕度 stability margin幅值裕度 magnitude margin 相位/相角裕度 phase margin对数幅频特性 log magnitude-frequency characteristic 无阻尼自然震荡角频率 undamped oscillation angular frequency 阻尼震荡角频率 damped oscillation angular frequency 阻尼角 damping angle带宽频率 bandwidth frequency 穿越/截止频率 crossover/cutoff frequency 谐振峰值 resonance peak系统校正 system compensation超前校正 lead compensation滞后校正 lag compensation自激震荡 self-excited oscillation死区特性 dead zone characteristic饱和特性 saturation characteristic间隙特性 backlash characteristic描述函数法 describing function method相平面法 phase plane method 采样控制系统 sampling control system数字控制系统 digital control system频谱 frequency spectrum 采样定理 sampling theorem信号重现 signal recurrence拉氏变换 Laplace transformZ变换 Z transform终值定理 final-value theorem差分方程 difference equation迭代法 iterative method 脉冲传递函数 pulse transfer function零阶保持器 zero-order holder映射 mapping方框图 block diagram伯德图 Bode diagram特征方程 characteristic equation可控性 controllability临界阻尼 critical damping阻尼常数 damping constant阻尼比 damping ratio初始状态 initial state初值定理 initial-value theorem反Z变换 inverse Z-transformation负反馈 negative feedback正反馈 positive feedback 尼科尔斯图 Nichols chart部分分式展开 partial fraction expansion 幅角原理 argument principle相对稳定性 relative stability共振频率 resonant frequency劳斯表 Routh tabulation/array奇点 singularity渐进稳定性 asymptotic stability控制精度 control accuracy临界稳定性 critical stability耦合 coupling解耦 decoupling比例积分微分调节器 proportional integral derivative regulator(PID) 串联校正 series/cascade compensation 单输入单输出 single input single output(SISO)多输入多输出 multi input multi output(MIMO)低通滤波器 low pass filter非线性系统 nonlinear system复合控制 compound control衰减振荡 damped oscillation主反馈 monitoring feedback 转折(交接)频率 break frequency稳定焦点/节点 stable focus/node。
微分方程的常用词汇
Ordinary Differential equation vocabulary Asymptotic stability 渐进稳定Auto-oscillations 自振系统Auto-oscillatory regime 自激振荡Characteristic frequencies 特征频率Chebyshev polynomial 切比雪夫多项式Clairaut equation 柯罗特方程Class c r c r类方程Comparison theorem 比较定理Conservative system 保守系统Curve 曲线Constant of integration 积分常数Decomposition into direct sum 直和分解Differential equation 微分方程Differential of first order 一阶微分方程Differential of higher order 高阶微分方程Differentiability theorem 可微性定理Direction field 线速场（或方向场）Directional derivative 方向导数Divergence 发散Determinant 行列式Differentiability 可微性Eigenvector 特征性Eigenvector 特征相量Equation of variations 变系数方程Euler line 欧拉折线Existence theorem 存在性定理Extension of solution 解的延拓Exponential 指数First integral 首次积分Fixed point 不动点Forced oscillations 强迫振动Free oscillations 自由振动Fundamental theorem of algebra 代数基本定理Fundamental system of solution 基础解系Hamillonl’s equation 哈密米顿方程Homogeneous 齐次的Imaginary plane 虚平面Initial condition 初值条件Integral curve 积分曲面Invariant subspaces 不变子空间Inverse function theorem 反函数定理Jordan block 约当块Limit cycle 极限环Linear operator 线性算子Linearized equation 线性化方程Liouville’s formula 刘维尔公式Lipschitz condition 李普希茨条件Lyapunov function 李雅普罗夫函数Lyapunov stability 李雅普罗夫稳定Manifold structure 微分流形Method of ovular line 欧拉折线法Method of small parameters 小参数法Metric space 度量空间Nilpotent operator 幂零算子Nonautonomous linear equation 非自治方程Nonautonomous system 非自治系统Norm form 法式Null space 零空间One-parameter group 单参数群Oscillation 振动Parameterized curve 参数化曲线Pendulum 单摆Phase curve 相曲线Phase flow 相流Phase space 相空间Phase point 相点Phase velocity 相速度Picard approximation theorem 皮卡逼近定理Polynomials 多项式Projective space 投影空间Projection 投影Quasi-polynomials 拟多项式Rectify 求（曲线的）长度Regular point 正则点Regular value 正则值Routh-Hurwitz theorem 路希——霍尔维茨定理Saddle point 鞍点Self-excited oscillation 自激振荡Separable 可分离的Singular point 奇点Small oscillation 小振动Solution of a differential equation 微分方程的解Swing 摆动Tangent bundle 切丛Tangent vectors 切相量Tangent mapping 切映射Transform 变换Torus 圆环Triangle inequality 三角不等式Uniformly convergent 一次收敛Uniqueness theorem 唯一性定理Variation of constants 常数变异法Vector bundle 相量场Velocity vector 速度相量Wronskian 朗斯基arithmetic mean 算术平均值weighted average 加权平均值geometric mean 几何平均数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round off 四舍五入。
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……)。
微积分术语中英文对照
微积分术语中英文对照A、B: Absolute convergence :绝对收敛Absolute extreme values :绝对极值Absolute maximum and minimum :绝对极大与极小Absolute value :绝对值Absolute value function :绝对值函数Acceleration :加速度Antiderivative :原函数，反导数Approximate integration :近似积分（法）Approximation :逼近法by d辻ferentials :用微分逼近linear :线性逼近法by Simpson ' s Rule： Simpson 法贝lj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 :极坐标表不之而积of a sector of a circle :扇形之而积of a surface of a revolution :旋转曲面之面积Asymptote :渐近线horizontal :水平渐近线slant :斜渐近线vertical :垂直渐近线Average speed :平均速率Average velocity :平均速度Axes, coordinate :坐标轴Axes of ellipse :椭圆之对称轴Binomial series :二项式级数Binomial theorem : 二项式定理C: Calculus :微积分d辻ferential :微分学integral :积分学Cartesian coordinates :笛卡儿坐标一般指直角坐标Cartesian coordinates system :笛卡儿坐标系Cauch， s Mean Value Theorem 柯西中值定理Chain Rule :链式法则Circle :圆Circular cylinder :圆柱体，圆筒Closed interval :闭区间Coefficient : 系数Composition of function :复合函数Compound interest :复利Concavity :凹性Conchoid :蚌线Conditionally convergent : 条件收敛Cone : 圆锥Constant function :常数函数Constant of integration :积分常数Continuity :连续性at a point :在一点处之连续性of a function :函数之连续性on aninterval :在区间之连续性from the left :左连续from the right :右连续Continuous function : 连续函数Convergence :收敛interval of :收敛区间radius of :收敛半径Convergent sequence :收敛数列series :收敛级数Coordinates :坐标Cartesian :笛卡儿坐标cylindrical :柱面坐标polar :极坐标rectangular :直角坐标spherical :球面坐标Coordinate axes :坐标轴Coordinate planes :坐标平面Cosine function :余弦函数Critical point :临界点Cubic function :三次函数Curve :曲线Cylinder :圆筒，圆柱体，柱面Cylindrical Coordinates :圆柱坐标D:Decreasing function :递减函数Decreasing sequence :递减数列Definite integral :定积分Degree of a polynomial :多项式之次数Density :密度Derivative :导数of a composite function :复合函数之导数of a constant function :常数函数之导数directional :方向导数domain of :导数之定义域of exponential function :指数函数之导数higher :高阶导数partial :偏导数of a power function :幕函数之导数of a power series 级数之导数of a product :积之导数of a quotient :商之导数as a rate of change :导数当作变化率right-hand :右导数second :二阶导数as the slope of a tangent :导数看成切线之斜率Determinant :行列式Differentiable function :可导函数Differential :微分Differential equation :微分方程partial :偏微分方程Differentiation :求导法implicit :隐求导法partial :偏微分法term by term :逐项求导法Directional derivatives :方向导数Discontinuity :不连续性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E、F、G: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 : —阶导数试验法First octant : 第——圭卜卩艮Focus :焦点Fractions :分式Function :函数Fundamental Theorem of Calculus :微积分基木定理Geometric series :儿何级数Gradient :梯度Graph :图形Green Formula : 格林公式H:Half-angle formulas :半角公式Harmonic series :调和级数Helix :螺旋线Higher Derivative :高阶导数Higher mathematics 高等数学Horizontal asymptote :水平渐近线Horizontal line :水平线Hyperbola :双曲线Hyperboloid :双曲面I:Implicit differentiation : 隐求导法Implicit function :隐函数Improper integral :反常积分，广义积分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 : 口变量Indeterminate from :不定型Inequality :不等式Infinite point :无穷极限点Infinite series :无穷级数Inflection point : 反曲点Instantaneous velocity :瞬时速度Integer :整数Integral :积分Integrand :被积函数Integration :积分Integration by part :分部积分法Intercepts :截距Intermediate value of Theorem :中值定理Interval :区间Inverse function :反函数Inverse trigonometric function :反三角函数Iterated integral :逐次积分L:Laplace transform : Laplace 变换Law of sines :正弦定理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「Hospital's rule : 洛必达法则Limacon :虫甘线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Local extreme :局部极值Local maximum and minimum : 局部极大值与极小值Logarithm : 对数Logar it hmic func tion : 对数函数M、N、0: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P、Q:Parabola :拋物线Parabolic cylinder :抛物柱而Paraboloid :抛物面Parallelepiped :平行六面体Parallel lines :平彳亍线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Par tit ion :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 :幕函数Product :积Quadrant :象限Quotient Law of limit :极限的商定律Quotient Rule :商定律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 :有理彳弋换法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 : 旋转曲而Riemann Sum :黎曼和Right-hand derivative :右导数Right-hand limit :右极限Root :根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, Oblique 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 :球而坐标Squeeze Theorem :夹挤定理Step function :阶梯函数Strictly decreasing :严格递减Strictly increasing :严格递增Substitution rule : 替代法则Sum :和Surface :曲而Surface integral :而积分Surface of revolution :旋转曲面Symmetry :对称T:Tangent function :正切函数Tangent line :切线Tangent plane :切平而Tange nt vector : 切向量Taylor ' s formula :泰勒公式Total d辻ferential :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V、X 、Z:Value of function :函数值Variable :变量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。
水力学中英文专业名词对照
中英文专业名词对照一画一维流动 One-dimensional Flow二画二维流动 Two-dimensional Flow三画大气压 Atmospheric Pressure定理 The Theorem上临界流速 Upper Critical Velocity下临界流速 Lower Critical Velocity三维流动 Three-dimensional Flow马赫数 Mach Number上举力 UpIift 上涌带 Zone of Wave Set-up四画升力 Lift升力系数 Coefficient of Lift水力半径 Hydraulic Radius水力坡度 Energy Gradient水击 Water-hammer直接水击 Rapid Closure间接水击 Slow Closure水击联锁方程 Interlocking Equation水头 Head压强水头 Pressure Head位置水头 E1evation Head作用水头 Acting Head总水头 Total Head测压管水头 Piezometric Head流速水头 Velocity Head惯性水头Acceleration Head水头线 Head Line总水头线 Total Head Line测压管水头线 Piezometric Head Line水头损失 Head Loss沿程水头损失 Frictional Head Loss沿程水头损失系数 Frictional Loss Factor局部水头损失 Local Head Loss局部水头损失系数 Local Loss Coefficient水轮机 Hydraulic Turbine水泵 Hydraulic Pump分子扩散 Mo1ecular Diffusion分子扩散系数 Coefficient of Molecular Diffusion 分离点 Point of Separation分散(离散) Dispersion内区 Inner Region内摩擦力 Internal Frictional Force比压计(压差计) Differential Gauge切应力 Shear Stress粘滞切应力 Viscous Shear Stress紊流附加切应力（雷诺应力） Reyno1ds Stress切应力系数 Coefficient of Shearing Stress毛细作用 Capillarity中性稳定曲线 Curve of Neutral Stability牛顿内摩擦定律 Newton's Law of Viscosity牛顿流体 Newtonian F1uid牛顿数 Newton Number文透里管 Venturi Meter无量纲数 Dimensionless Number无滑动条件 No Slip Condition井Well完全井 Completely Penetrating Well非完全井 Partially Penetrating Well自流井 Artesian Well井群 Multiple—well水力最优断面 Best Hydraulic Cross Section水电比拟 Electro—hydrodynamic Analogue水面线分桥 Analysis of Flow Profile水面线计算 Computation of Flow Profile人工渠槽水面线计算 Computation of Flow Profile in Artificial Channel 天然河道水面线计算 Computation of Flow Profile in Natural Channel分段法 The Standard Step Method数值积分法 The Graphical —intergration Method 水力指数法 The Direct一intergration Method水流强度参数 Flow Function Intensity of Shear on Particles 水跃 Hydraulic Jump自由水跃 Free Jump远驱水跃 Remote Jump临界水跃 Undular Hydraulic Jump临界水跃 Critical Jump弱水跃 weak Jump淹没水跃 Submerged Jump斜坡水跃 Hydraulic Jump in Sloping Channels强水跃 Strong Jump稳定水跃 Steady Jump摆动水跃 Oscillating Jump水跃长度 Length of Jump水跃的共轭水深 Conjugate Depths of Hydraulic Jump水跃的表面水滚 Surface Roller of Hydraulic Jump水跃的消能效率(水跃消能系数) Efficiency of Energy dissipation byHydraulic Jump水跃的跃后水深 The Sequent Depth of Hydralic Jump水跃的跃前水深 The Initial Depth of Hydraulic Jump水跃函数 Hydraulic Jump Function水跃高度 Height of Jump水跌 Hydraulic Drop孔口出流 Orifice Flow孔隙率(度) Porosity不冲流速 Nonscouring Velocity不淤流速 Nonsilting Velocity允许流通 Permissible Velocity内在渗透率 Intrinsic Permiability毛绷管水 Capillary Water分流齿 Chute Blocks牛顿流体 Newtonian F1uid 非牛顿流体 Non—Newtonian F1uid巴赞剖面 Bazin Profile比能(断面单位能量) Specific Energy元波 E1ementary Wave无阻力的正涌浪和负涌浪Frictionless Positive and Negative Surge Waves五画汇 Sink卡门通用常数 Von Universal Constant外区 Outer Region司托克斯定律 Stokes Theorem of Vortex Motion司托克斯流动 Stokes F1ow平面上的静水总压力 Total Hydrostatic Force on P1ane Area平面势流 Two-dimensional Potential Flow平移 Translation边界层 Boundary Layer层流边界层 Laminar Boundary Layer紊流边界层 Turbulent Boundary Layer边界层方程 Boundary Layer Equation边界层分离 Separation of Boundary Layer边界层动量积分方程式 Momentum Integral Equation of Boundary Layer边界层厚度 Boundary layer Thickness加速度 Acceleration当地加速度 (时变加速度) Local Acceleration迁移加速度 (位变加速度) Convective Acceleration史密特数 Schmidt Number电算实例 Examples of Computer Solution管网电算 Computer Solution of Pipe Network水击电算 Computer Solution of Water-hammer包气带 Zone of Aeration司托克斯定律 Stokes Law布辛尼斯克方程 Boussinesg Equation平底梯形断面明槽中的水跃 Hydrau1ic Jump in Horizontal TrapezoidalChannels平底矩形断面扩散槽中的Hydraulic Jump in Horizontal Rectangular Diverging Channels 平底矩形明槽的水跃共轭水深关系式Equation of Conjugation Depth of Hydraulic Jump for HorizontalRectangular Channels平底棱柱形明槽中的水跃方程式Equation of Hydraulic Jump for Horizontal Prismatic Channels 平整(形态) F1at Bed(Plane Bed)平衡输沙 Equilibrium Transport of Sediment 不平衡输沙 Non-equilibrium Transport of Sediment边界条件 Boundary Condition自然边界条件 Natural Boundary Condition边界雷诺数 Boundary Reynolds Number正常水深 Normal Depth长波 Long Wave圣维南方程 Saint—Venant Equation六画压力中心 Center of Pressure压力体 Pressure Prism压力表 Pressure Gauge风箱式压力表 Bellows-type Pressure Gauge隔膜式压力表 Diaphragm-type Pressure Gauge弹黄式压力表 Spring—type Pressure Gauge管环式压力表 (布尔登压力表) Bourdon—type Pressure Gauge压力梯度 Pressure Gradient压应力 Compressive Stress压强 Pressure相对压强 (计示压强) Relative Pressure (Gauge Pressure) 绝对压强 Abso1ute Pressure真空压强 (负压) Vacuum Pressure (Negative Pressure)压强分布图 Pressure Distribution Diagram静水压强分布图 Hydrostatic Pressure Distribution Diagram压强场 Pressure Field压强系数 Pressure Coefficient压强势能 Potential Energy of Pressure压缩性 Compressibility动力水流 (摩阻流速、剪切流速) Fricion Velocity动水压强 Pressure in Flowing F1uid动态特性 Dynamic Characteristics动能 Kinetic Energy动能修正系数 Kinetic Energy Correction Factor动量方程 Momentum Equation动量矩方程 Moment of Momentum Equation动量修正系数 Momentum Correction Factor动量损失厚度 Momentum Thickness充分发展的紊流 Fully Developed Turbulence过水断面 Cross Section过渡层 Buffer Region自由出流 Free Discharge自由紊流 Free Turbulence自动记录 Automatic Recording毕托管 Pitot Tube有势力 Potential Force势流动 (无涡流动) Potential Flow (Irrotational Flow)有涡流动 (有旋流动) Rotational Flow曲面上的静水总压力 Total Hydrostatic Force on Curved Surface共振 Resonance扩散 Diffusion费克扩散定律Fick’s Law of Diffusion多普勒效应 Doppler Effect当量粗糙度 Equivalent Roughness传感器 Sensor光滑壁面 Smooth Wall收缩断面 Vena Contracta动力流速 Friction Velocity 动床 Movable Bed动床水力学 Fluvial Hydraulics地下水 Ground water地下水面 Groundwater Surface 地下水动力学 Groundwater Dynamics导水系数 Coefficient of Transmissibility 导水率 Transmissivity 多孔介质 Porous Medium自由出流 Free Outflow冲击波 Shock Wave冲刷坑最大水深 Maximum Water Depth in scour Pit冲泻质 wave Load各向同性 Isotropy各向异性 Anisotropy达西定律 Darcys Law有限元法 Finite E1ement Method有限差分法 Finite Difference Method有限振幅立波 Finite Amplitude Standing Wave 浅水立波 Standing Wave in Sha11ow Water深水立波 Standing Wave in Deep water有限振幅推进波 Finite Amplitude Progressive Wave浅水推进波 Progressive Wave in Shallow Water深水推进波 Progressive Wave in Deep Water有效溢流宽度 Effective width of The Spillway过渡(形态) Transition过渡段的急流 Supercritical Flow Through Transitions 过镀段的缓流 Subcritical Flow Through Transitions扩散法 Diffusive Scheme扩散系数 Diffusion Coefficient收缩断面 Vena Contracta收缩断面水深 Contractional Depth七画阻力 Drag压强阻力 (形状阻力) Pressure Drag(Form Drag)摩擦阻力 Frictional Drag阻力系数 Drag Coefficient应力张量 Stress Tensor均方根值 Root-mean-square均匀流 Uniform Flow纵向移流分散 Longitudinal Convective Dispersion运动方程 Equation of Motion一维非恒定流运动方程 One-dimensional Unsteady Flow Equation水击运动微分方程 Differential Equation for Water-hammer紊流时均的运动方程(雷诺方程) Reynolds Equation粘滞性液体的运动方程(纳维埃—司托克斯方程) Navier-Stokes Equation 理想液体的运动方程(欧拉方程) Euler Equation佛汝德数 Froude Number佛汝德相似准则 (重力相似准则) Froude Similarity Criterion攻角 Attack Angle时间平均法 Time-average Method时间平均流动 Mean Motion时均值 Time-average Value形状系数 Shape Factor表面力 Surface Force表面张力 Surface Tension表面张力系数Coefficient of Surface Tension角变形 Angular Deformation角变率 Rate of Angular Deformation角转速 Angular Velocity尾流 wake Flow层流 Laminar Flow层流翼型 Laminar Airfoil体积力 Body Force体积压缩系数 Coefficien of Volume （bulk）Compressibility体积弹性系数 Coefficien of Volume （bulk）Elasticity体积膨胀率 Rate of Volume Expansion连通管（U形管）U-tube连续介质 Continuum Medium连续方程 Continuity Equation一维恒定流连续方程 Continutiy Equation of One –dimentional Steady Flow一维非恒定流连续方程Continuity Equation of One –dimentional Unsteady Flow水击连续微分方程 Differential Continuity Equation of Water-hammer连续性微分方程 Differential Equation of Continuity时均流动的连续方程 Differential Continuity Mean Motion扩散物质的连续方程(费克扩散方程) Continuity Equation of Diffusion Substances连续扩散源 Source of Continuous Diffusion附着力Adhesion位置势能 Potential Energy of E1evation位移厚度 Displacement Thickness伯诺世方程 Bernoulli Equation伯诺坐积分 Bernoulli Integral扬程 Pump Head压水扬程 Discharge Head吸水扬程 Suction Head总扬程 Total Delivery Head纯数 Pure Number间歇现象 Intermittency含水层 Aquifer无压含水层 Unconfined Aquifer承压含水层 Confined Aquifer 含沙浓度（含沙量） Sediment Concentration 体积比浓度 Concentration by Volume 重量比浓度 Concentration by Weight 均匀流 Uniform Flow非均匀流 Non-uniform Flow均质土坝渗流 Seepage from Homogeneous Earth Dam 均质土壤 Homogeneous Soil 完全收缩 Complete Contraction 沙纹（形态） Ripple沙垄（形态） Dune床沙Bed Material床沙质Bed Material Load床面形态（沙波运动）Bed Forms(Sand Waves)时间步长Time Interval克里格尔剖面Creager Profile护坦Apron里兹法Rits Method初始条件Initial Condition两相流动Two-phase Flow佛汝德数Froude Number沉速（沉降流速）Fall Velocity(Terminal Settling Velocity)坎端水深Depth at The Brink吹程Fetch余波Swell余弦推进波Simple Harmonic Progressive Wave位移波的分类Classification of Translatory Wave深水波；浅水波Deep-water Wave；Sallow-water Wave连续波；不连续波Continuous Wave；Discontinuous Wave顺水波；逆水波Downstream Wave；Upstream Wave涨水波（正波）；落水波（负波）Positive Wave；Negative Wave 阻力Drag阻力系数Drag Coefficient压强阻力Pressure Drag形状阻力Form Drag床面阻力Bed Resistance沙波阻力（床面形态阻力）Bar Resistance沙粒阻力Grain Resistance表面阻力Skin Resistance岸壁阻力Bank Resistance摩擦阻力Friction Force八画空化，空穴Cavitation空穴数Cavitation Number初生空穴数Incipient Cavitation Number空蚀Cavitation Damage非均匀流Non-uniform Flow急变流Rapidly Varied F1ow渐变流Gradually Varied F1ow非恒定流Unsteady Flow波动方程Wave Equation波速Velocity of Wave Propagation表现扩散系数Coefficient of Apparent Diffusion单位Unit工程单位制Unit System of Engineering国际单位制(SI) Systéme Internationale d’Unites单位换算Conversion of Units真值Real Value线变形Linear Deformation线变率Rate of Linear Deformation拐点Point of Inflexion驻点(滞止点) Stagnation Point定倾中心Metacenter拉格朗日法Lagrangian Method拉普拉斯方程Laplace Equation势流叠加原理Superposition Principle of Potential Flow泊肃叶流动Poiseuille Flow阿基米德原理Archimedes Principe环量Circulation质量力Mass Force闸下出流Outflow under Gates闸孔非恒定出流Unsteady Outflow of Sluice Gate 闸孔恒定出流Steady Outflow of Sluice Gate闸孔净宽Clear Span of The Gate between Piers 闸前水头Approach Head before Sluice闸墩收缩系数Coefficient of Pier Contraction降水曲线Falling Curve波长Wave Length波节Wave Node波压强Wave Pressure净波压强Net Wave Pressure波谷Wave Valley波周期Period of Wave波的反射Reflection波的传播Wave Propagation波的折射Inflection波的破碎Breaking of Wave波的绕射Diffraction波的爬高Wave Run-up波陡Wave Steepness波能Wave Energy波高Wave Height波速Wave Speed波浪中线Midwater Level of Wave波浪要素Wave Elements波峰Wave Grest波锋（波额、波前）Wave Front波群 Wave Group波群速 Wave Group Velocity波腹 Wave Loop表面张力波 Capillary Wave势波 Potential Wave势波的叠加 Superposition of Potential Wave孤立波 Solitary Wave岩石河床的抗冲系数 Anti-scour Coefficient of Rock Bed承压水 Confined Water定床 Fixed Bed定床水力学 Rigid Boundary Hydraulics泥沙的起动 Initiation of Motion of Sediment 侧收缩系数 Coefficient of Side Contraction 非均质土壤 Nonhomogeneous Soil非恒定流连续方程 Equation of Continuity for Unsteady Flow 非恒定急变流 Unsteady Rapidly Varied Flow非恒定渐变流 Unsteady Gradually Varied Flow非恒定渐变流动的运动方程 Dynamic Equation for Unsteady Gradually Varied Flow非粘性泥沙 Non—cohesive Sediment非饱和带 Unsaturated Zone饱和带 Saturated Zone明槽中的非恒定流动 Unsteady FIow in open Channels 明槽急变流 Rapidly Varied Flow in Open Channels 明槽恒定非均匀渐变流基本方程 The Basic Equation of Steady Gradually Varied Flow明槽掺气水流 Self—Aerated Open Channel Flow 底流型消能 Energy Dissipation by Hydraulic Jump面流型消能 Energy Dissipation of Surface Regime拉格朗日连续方程 Lagrangian Equation of Continuity拉格朗日运动方程 Lagrangian Equation of Motion拉普拉斯方程 Laplace Equation质量系数 Coefficient of Mass 变分原理 Variational Principle 底坡（槽底纵坡） Slope of Channel Bed 陡坡（急坡） Steep Slope临界坡 Critical Slope缓坡 Mild Slope九画相 Phase相对平衡 Relative Equilibrium相对粗糙度 Relative Roughness相似条件 Similarity Condition几何相似 Geometric Similarity动力相似Dynamic Similarity运动相似 Kinematic Similarity相似原理 Theory of Similarity相似准则 Similarity Criterion压力相似准则 Pressure Force Similarity Criterion表面张力相似准则 Surface Tension Similarity Criterion 重力相似准则 Gravity Force Similarity Criterion弹性力相似准则 E1asticity Force Similarity Criterion惯性力相似准则 Inertia Force Similarity Criterion粘滞力相似准则 Viscosity Force Similarity Criterion相似准数 Similarity Criterion Number氢气泡法 Hydrogen Bubble Technique总流 Total Flow指示部分 Indicating Component脉动 F1uctuation脉动值 Fluctuating Value转动 Rotation转捩点 Transition Point诱导流速 Induced Velocity柯西数 Cauchy Number柯西一黎曼条件 Cauchy-Riemann Conditions柯埃梯流动 Couette Flow测压管 Piezometer测针 Point Gauge虹吸管 Siphon Pipe欧拉方程 Euler Equation欧拉法 Eulerian Method欧拉积分 Euler Integral欧拉数 Euler Number恒定流 Steady Flow恒定势流的能量方程 Energy Equation of Steady Potential Flow重度(容重) Specific Weight复势 Complex Potential误差 Error系统误差 Systematic Error相对误差 Relative Error绝对误差 Absolute Error偶然误差 Random Error绝壁物体 Bluff Body重力水 Gravitational Water 贮水系数 Storage Coefficient 显式网格 Network for The Explicit Method 逆行沙浪 Anti—dunes(Moving Upstream) 顺行沙浪 Anti一dunes(Moving Downstream)费克定律Fick’s Law 相角 Phase挟沙水流 Sediment—1aden Flow挟沙能力 Carrying Capacity垂直收缩系数 Coefficient of Vertical Contraction急变流 Rapidly Varied Flow急变流的断面单位能量 Specific Energy of Rapidly Varied Flow急流 Supercritical Flow急流弯段水流 Supercritical Flow in Curved Channel恒定流 Steady Flow非恒定流 Unsteady F1ow恒定渗流 Steady Seepage Flow恒定降深 Constant Drawdown重度 Specific Weight临界水深 Critical Depth临界流 Critical Flow临界流速 Critical Velocity挑流的冲刷系数 Coefficient of Scour for Jet Erosion 挑流型消能 Energy Dissipation of Ski—jump Type by Trajectory Buckets挑流射程 Horizontal Distance of the Jet Trajectory建筑物出流的流速系数 Coefficient of Velocity for Discharge from OutletWorks齿槛 Dentated Sill十画浮力 Buoyant Force浮心 Centerof Buoyancy浮体 Floating Body钽丝水位计 Tantalum-wire Level Gauge调节器 Regulator调压井 Surge Chamber(Tank)紊动扩散 Turbulent Diffusion紊动扩散系数 Coefficient of Turbulent Diffusion紊流 Turbulent F1ow紊流光滑区 Hydraulically Smooth Region Of Turbulent Flow紊流过渡区 Transition Region of Turbulent Flow紊流粗糙区 Completely Rough Region of Turbulent Flow紊流扩散基本方程 Fundamental Equation of Turbulent Diffusion 紊流的半经验理论 Semi-empirical Theories of Turbulence紊流强度 Intensity of Turbulence流场 Flow Fie1d流网 Flow Net流动型态 Type of Flow流线 Streamline流线型体 Streamline Body流函数Stream Function流速分布的相似性 Similarity of Velocity Profiles流速仪 Current Meter热丝流速仪 Hot-wire Anemometer热膜流速仪 Hot-film Amemometer )旋浆流速仪 Rotor-type Current Meter激光测速仪 Laser-Doppler Anemometer流速场 Velocity Field流速势 Velocity Potential流速系数 Coefficient Of Velocity流量 Discharge(Rate of Flow)单宽流量 Discharge per Unit Width流量系数 Coefficient of Discharge流量模数 Modulus of Discharge流管 Stream Tube圆柱绕流 Flow Around a cylinder速度 Velocity相对速度 Relative Velocity绝对速度 Abso1ute Velocity牵连速度 Velocity of Following特征线法 Method of Characteristics原型 Prototype基准面 Datum Plane射流 Jets平面射流 P1ane Jets自由射流 Free Jets紊动射流 Tubulent Jets圆形断面射流（轴对称射流) Round Jets淹没射流 Submerged Jets射流的主体段 Fully Established Zone of Jet Flow射流的扩散角 Spread Angle of the Jet射流的初始段 Initial Zone of Flow EstabliShment of Jet射流源 Source of the Jet能量方程 Energy Equation能量损失厚度 Energy Thickness流量计 F1ow Meter电磁流量计 Magnetic F1ow—meter孔板流量计 Orif ice Meter浮子流量计 F1oat-type Current Meter涡轮流量计 Turbine F1ow—meter宾汉流体 Bingham F1uid流网 Flow Net流速系数 Coefficient of Velocity流速势 Velocity Potential流量系数 Coefficient of Discharge流量模数 Modulus of Discharge紊动附加应力(雷诺应力) Turbulence (Reynolds Stresses)起动流速 Critical Velocity特征线 Characteristic Line 顺特征方向 Forward(Positive)Characteristic Direction 逆特征方向 Backward(Negative) Characteristic Direction 特征线法 Method of characteristics消能池(消力池，静水池) stilling Basins消能戽(消力戽) Roller Buckets消能墩(消力墩) Baffle Piers 消能墙 Baffle Wall浸润线 Line of Seepage(Deppresion Line) 涡街 Vortex Street 泰斯方程Theis Equation破碎带 Zone of Wave Breaking海漫 Riprap十一画剪切流动 Shear F1ow剪切变形 Shear Strain曼宁公式 Manning Formula混合长度 Mixing Length混掺 Mixing淹没出流 Submerged Discharge液体的平衡微分方程 Differential Equation of Liquid Equilibium液体振荡 Oscillation of Liquid密度 Density偶极 Doublet惯性 Inertia惯性力 Incrtia Force弹性 E1asticity弹性波 E1astic Wave断面平均流速 Mean Velocity粘性底层 Viscous Sublayer粘性底层的名义厚度 Nominal Thickness of the Viscous Sublayer粘滞性 Viscosity粘滞系数 Coefficient of Viscosity运动粘滞系数 (运动粘度) Coefficient of Kinematic Viscosity动力粘滞系数 Coefficient of Dynamic Viscosity旋涡 Vortex组合涡 Combined Vortex线涡 Line Vortex势涡 Potential Vortex强迫旋涡 Forced Vortex自由旋涡 Free Vortex移流分散系数 Coefficient of Convective Dispersion理想液体 Ideal Liquid粗糙 Roughness粗糙度 Roughness粗糙系数(糙率) Coefficient of Roughness粗糙雷诺数 Reyno1ds Number of Roughness粗糙壁面 Rough Wall掺气浓度(含气比) Air Concentration 曼宁公式 Manning Formula隐式网络 Network for the Implicit Method 混合长度 Mixing Length跃后段长度 Length of the Region for TurbulenceDissipation behind a Hydraulic Jump 偏折水流(折冲水流) Deflected Stream淹没出流 Submerged OutfIow淹没系数 Coefficient of Submergence淹没条件 Submerged Condition辅助消能工 Stilling- basin Appurtenance 粘性底层 Viscous Sublayer粘性泥沙 Cohesive Sediment弹性贮存 E1astic Storage惯性力 Inertial Force控制断面 Control Section控制水深 Control Depth涵洞过流 Flow Through Culvert 明流(无压流动) Open Flow半满流(半有压流) Partly Full Flow 满流(有压流) Full F1ow自由进流 Free Inflow淹没进流 Submerged Inflow断面环流 Secondary Flow in the Plane of Cross Section 断面突变的明流 Flow Through Sudden Transition淤积 Deposition渗流 Seepage Flow(Filtration) 急变渗流 Rapidly Varied Seepage Flow渐变渗流 Gradually Varied Seepage Flow非均匀渗流 Nonuniform Seepage Flow非位定渗流 Unsteady Seepage Flow河渠渗流 Seepage from Channel and Canal渗流的运动方程 Equation of Motion of Seepage Flow 渗流的连续方程 Equation of Continuity of Seepage Flow 渗流压力 Seepage Pressure渗透系数 Coefficient of Permeability渗透流速 Seepage Velocity推移力 Tractive Force 临界推移力 Critical Tractive Force 推移质 Bed Load推移质运动强度 Intensity of Transport 悬移质 Suspended Load粗糙系数 Coefficient of Roughness 天然河道的粗糙系数 Coefficient of Roughness of Natural River 综合粗糙系数 Coefficient of Composite Roughness十二画谢才公式 Chézy Formula谢才系数 Chézy Coefficient量水堰 Weir量水槽 Flow-measurring F1ume量纲 Dimension基本量纲 Fundamental Dimension诱导量纲 Derived Dimension量纲分析 Dimensional Analysis量纲和谐原理 Theory of Dimensional Homogeneity等压面 Equipressure Surface等势线 Equipotential Lines湿周 Wetted Perimeter涡线 Vortex Line涡环 Vortex Ring涡通量 Vortex Flux涡街 Vortex Street涡粘性系数 Coefficient of Eddy Viscosity涡量(旋度) Vorticity涡管 Vortex Tube斯特罗哈数 Stroulhal Number普朗特数 Prandtl Number散度 Divergence谢才公式 Chezy Formula谢才系数 Chezy Coefficient跃水消能池 Drop-structure Stilling Basins 溃坝波 Dam—break Wave蛙步法 Leap Frog Scheme趋近流速 Approach Velocity趋近流速水头 Approach Velocity Head缓流 Subcritical Flow缓流弯段水流 Subcritical Flow in Curved Channel 期特利克勒公式 Strickler Formula插值函数 Interpolation Function距离步长 Distance Interval短管出流 Efflex from short Tube短波 Short Wave十三画源 Source雷诺应力 Reyno1ds Stress雷诺数 Reyno1ds Number临界雷诺数 Critical Reyno1ds Number雷诺相似准则 Reyno1ds Similarity Criterion雷列法Rayleigh’s Method迹线 Path Line跟踪水位计 Tracking—type Level Gauge堰Weir 三角形薄壁堰 Triangu1ar Sharp-crested Weir薄壁堰 Sharp crested weir 低溢流堰 Low Spillway驼峰堰Camel’s Hump Weir矩形薄壁堰 Rectangular Sharp—crested Weir 梯形剖面堰 Trapezoidal Profile Weir 高溢流堰 High Spillway 宽项堰 Broad-crested WeirWES标准剖面堰 WES—Standard Spillway Shapes堰上水头 Head on Crest堰上总水头 Total Head on Crest堰顶溢流 Overflow Weir堰高 Weir Height裘布衣公式 Dupit Formula输沙率 Transport Rate 微波 Small Amplitude Wave 棱柱形槽 Prismatic Channel 非棱柱形槽 Non—Prismatic 溢流水舌 Overflow Nappe 自由溢流 Free Overflow淹没溢流 Submerged Overflow奥基剖面 Ogee Profile十四画管网 Pipe Network分枝管网 Branthing Pipes环状管网 Looping Pipes管流Pipe Flow长管 Long Pipe并联管道 Pipes in Parallel串联管道 Pipes in Series沿程均匀泄流 Pipe with Uniform管道 Discharge along the Line短管 Short Tube静水压强 Hydrostatic Pressure Intensity静止液体基本方程 Basic Equation of Hydrostatics静态特性 Static Characteristics蒸汽压强 Vapor Pressure精度 Precision稳定性 Stability数据处理 Data Processing颗粒直径(粒径) Grain Diameter 中值粒径Median Diameter 平均粒径 Mean Diameter 沉降粒径 Sedimentation Diameter 筛孔粒径 Sieve Diameter 等容粒径 Nominal Diameter 管咀出流 Nozzle Effex十五画潜体 Submerged Body模型 Model模型比尺 Model Scale长度比尺 Length Scale加速度比尺 Acceleration Scale时间比尺 Time Scale作用力比尺 Force Scale速度比尺 Velocity Sca1e流量比尺 Discharge Scale模型试验 Model Experiment壅水曲线 Backwater Curve(Rising Curve) 横向水面超高 Superelevation影响半径 Radius of Influence十六画薄膜水 Pellicular Water 薄壁小孔口 Sharp Edged Orifice十七画瞬时扩散源 Source of Instantaneous Diffition瞬时流速 Instantaneous Velocity瞬时值 Instantaneous Value翼型 Airfoil螺旋流 Spiral Flow十八画瞬态法 The Method of Finite Increments 二十画蠕动Creep Motion附录二水力学名人简介三画～四画文透里(文丘里) Abbe Giovansi Battista Venturi，1746～1822,意大利工程师、物理学家韦伯 Moritz Weber 1871～1951德国造船技师，船舶力学(Naval mecha-nics)教授切尔托乌索夫М.л.Чертоусов1892～1960苏联技术科学博士，水力学家戈达 Y．Goda厄塞尔 F．Ursell厄里瓦托斯基 E．A．Elevatorski牛顿 (Sir)Isaac Newton 1642～1727，英国数学家，物理学家，剑桥大学教授乌根秋斯А．А．Угинчус(1899～1972)苏联水力学家巴斯加(帕斯卡) Blaise Pascal l623～1662，法国数学家，物理学家，哲学家巴赞(巴青) Henri Emile Bazin 1829～1917，法国工程师巴甫洛夫斯基 HикодайНиколаевичПавдовский1884～1937,苏联科学院院士，水力学及流体力学家巴克米特夫 Boris Alexandrovitch Bakhmeteff l880～1952 俄国教授，水力学家，哥伦比亚大学教授五画～六画兰姆 Sir Horace Lamb 1849～1934，英国应用数学家，地球物理学家艾黎 Sir George Biddle Airy l801—1892，潮汐与波浪力学专家艾斯考弗 Francis F．Escoffier布拉休斯 Paul Richard Heinrich Blasius 1883～1970,德国工程师，水力学家布辛涅斯克 Joseph Valentin Boussinesq l842—1929，法国数学家，力学家及理论物理学家卡曼 Theodore von Kármán 1881～1963匈牙利工程师，德国教授，空气动力学家，美国工程师，水动力学及紊流力学专家白金汉 Edgar Buckingham 1867～1940，美国物理学家丘加耶夫 P．P．Чугаев l904—1981，苏联水力学家尼古拉兹 Johann Nikuradse 1894～，德国工程师圣·维南 Jean-Claude Barré de Saint-Venant l797～1866，法国工程师，水力学及弹性力学专家圣福鲁 G．Sainflou佛汝德 William Froude 1810～1879，英国工程师(造船技师)弗朗西斯 James Bicheno Francis l815—1892，美国工程师司处利克勒 A.Strickler汤姆逊 Professor James Thomson 英国水力学家齐恩 A．K．Jain印度流体力学家达·芬奇 Leonarde da Vinci l452—1519，意大利美术家，科学家及工程师达兰贝尔 Jean le Rond d´Alembert 1717～1783，法国数学家，哲学家达西 Henry Philibert Gaspard Darcy 1803～1858，法国工程师毕托 Menri d Pitot l695～1771，法国工程师，发明家刚吉勒 Emile Oscar Ganguillet 1818—1894, 瑞士工程师伊本 Arthur Thomas Ippen l907—1974，双亲是德国人，生于伦敦，受教育于Aachen(德国)，1932到美国Iowa市，水力学家伊兹巴什C．B．Избаш七画沙特克维奇A．A．Саткевич沙乌缅·B．A．Шаумян1908～1964沙玉清1907．4～1966．10；泥沙专家沙莫夫Г．И．Кузьмин沈学文Hsien Wen Shen 1931～美籍华人，泥沙专家库特Wilhelm Rudolph Kutter 1818～1888，瑞士工程师库兹明И．A．Кузьмин杜比Arsene Jumes Emile Juvenal Dupuit 1804～1866 法国工程师，水力学家及经济学家坎莱根Garbis Hovannes Keulegan 1890～，美泥沙专家克兰(恩) Stephen Jay Kline 1922～，美流体力学家克里格William P．Creager 美垦务局工程师克希荷夫Gustav Robert Kirchhoff 1824～1887，德国物理学家别兰格Jean-Baptiste-Charles Belanger or J．B．Belanger 1790(或1789)～1874 法国水力学家别列津斯基A．P．Верзинекий伯诺里Daniel Bernoulli 1700～1782，瑞士物理学家，数学家伽利略Galileo Galilei 1564～1642，意大利物理学家及天文学家希尔兹Albert Frank Shields 1908～1974，原为俄亥俄(美国)人，1933年作为交换学者到柏林，研究推移质运动阿基米德Archimedes 287～212 B．C., 希腊哲学家，物理学家阿格罗斯金И．И．Ароскин1900～1968，苏联水力学家，技术科学博士阿列维Lorenzo Allievi 1856～1941(或1942)，意大利水力学家阿勉Michael Amein纳维埃Louis Marie Henri Navier 1785～1836, 法国工程师纳格勒Floyd August Nagler 1892～1933，美国水力学家八画波达波夫M．B．Потапов1887～1949，苏联河流动力学及迳流调节专家泊肖(或瑟)叶Jean Louis Poiseuille 1799—1869，法国物理学家拉格朗日Joseph Louis Lagrange 1736～1813，法国数学家及天文学家拉普拉斯Pierre Simon Laplace or Marquis de Laplace l749—1827 法国数学家及天文学家拉克斯P．D．Lax拉哈曼诺夫К．И．Рахманов1900～范诺尼Vito August Vanoni 1904～，美国泥沙专家欧拉Leonhard Euler 1707～1783，瑞士数学家及物理学家欧姆Georg Simon Ohm 1787～1854，德国物理学家英格隆F．Engelund罗辛斯基К．И．Россинский金Horace Williams King (or Horace King) 1874～1951, 美国水力学家，工程师九画茹可夫斯基НиколайЕгоривичЖуковский1847～1921,苏联水力学家、流体力学家胡克Robert Hook 1635～1703，英国实验主义哲学家、物理学家柯朗Richard Courant 1888～1972，美国数学家，Gottingen教授，1934年到美国，New York大学教授柯西Baron Augustin Louis de Cauchy 1789～1857，法国数学家柯瓦兹勒L．S．G．Kovasznay柯列布鲁克C．F．Colebrook哈密顿William Rowan Hamilton 1805～1865，英数学家，物理学家哈根Gotthilf Heinrich Ludwig Hagen，德国水利工程师费克A．Fick十画～十一画高斯Karl Friedrich Gauss 1777～1855，法国数学家，物理学家及天文学家宾汉(宾厄姆) Eugene Cook Bingham 1878—1945，美国化学家，流变学(Rhelogy)的奠基人唐存本泰勒Brook Taylor 1685～1731，英国数学家栗原道德钱宁1922—1986，泥沙专家，教授爱因斯坦Hans Albert Einstein 1904～1973，河流动力学及泥沙专家爱格利Hegly梅叶—彼特Euegène Meyer-Peter 1883～，瑞士泥沙专家曼宁Robert Manning 1816～1897，爱尔兰工程师维杰尔尼可夫B．B．Ведерников1904～1980，苏联水力学家。
数学专业名词英文解释
高等数学(Higher Mathematics)一些基本名词中英文对照表中文英文中文英文函数function 逆时针方向counterclockwise定义域domain of definition 变量variable值域range of function 常量constant quantity极限limit 坐标轴axis of coordinates 极限值limit value 横坐标abscissa发散diverge 纵坐标ordinate收敛converge 锐角acute angle连续性continuity 钝角obtuse angle连续函数continuous function 平角straight angle左连续continuity from the left 直角right angle开集open set 圆circle闭集closed set 半径radius闭区间closed interval 直径diameter区间interval 三角形triangle一元函数function of one variable 斜率slope多元函数function of severalvariables无穷小infinitesimal内点inner point 无穷大infinite孤立点isolated point 正positive邻域neighborhood 负negative导数derivative 凸convex偏导数partial derivative 凹concave微分differential calculus 椭圆ellipse全微分total differential 双曲线hyperbola偏微分partial differential 曲线curve积分integral 曲面surface微积分infinitesimal calculus 交intersection 重积分multiple integral 补集complement 二重积分double integral 投影project三重积分threefold integral 等差级数arithmeticalprogression中值定理law of the mean 几何级数geometric progression极值extreme values 公理axioms定积分definite integral 定义definition 不定积分indefinite integral 定理theorem曲线积curvilinear integral 集合set分曲面积分surface integral 元素element 级数progression,series 空集empty 数列sequence 子集subset 微分方程differential equation 相等equal常微分方程ordinary differentialequation常数constant偏微分方程partial differentialequation对数logarithm差分方程difference equation 指数exponential特征方程characteristic equation 曲率curvature间断点discontinuity point 曲率圆circle of curvature 渐近线asymptote 曲率半径radius of curvature切线tangent line 切平面tangent plane切线方程tangential equation 幂级数power series拐点point of inflexion 收敛半convergence radius径绝对收敛absolutely convergence 收敛区间convergence interval条件收敛conditional convergence 收敛区域convergence region和函数sum function 通解general solution 解solution 特解special solution 初始条件initial condition 阶order条件极值conditional extremum 常数项级数constant series必要条件necessary condition 正项级数positive series充分条件sufficient condition 交错级数alternate series收敛判别法convergence criterion 一般级数ordinary series比较判别法comparison criterion。
微积分英文专业词汇
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 oftwo 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 coefficient。
《信号与系统》专业术语中英文对照表
《信号与系统》专业术语中英文对照表第 1 章绪论信号（signal）系统（system）电压（voltage）电流（current）信息（information）电路（circuit）网络（network）确定性信号（determinate signal）随机信号（random signal）一维信号（one–dimensional signal）多维信号（multi–dimensional signal）连续时间信号（continuous time signal）离散时间信号（discrete time signal）取样信号（sampling signal）数字信号（digital signal）周期信号（periodic signal）非周期信号（nonperiodic（aperiodic） signal）能量（energy）功率（power）能量信号（energy signal）功率信号（power signal）平均功率（average power）平均能量（average energy）指数信号（exponential signal）时间常数（time constant）正弦信号（sine signal）余弦信号（cosine signal）振幅（amplitude）角频率（angular frequency）初相位（initial phase）周期（period）频率（frequency）欧拉公式（Euler’s formula）复指数信号（complex exponential signal）复频率（complex frequency）实部（real part）虚部（imaginary part）抽样函数 Sa(t)（sampling（Sa） function）偶函数（even function）奇异函数（singularity function）奇异信号（singularity signal）单位斜变信号（unit ramp signal）斜率（slope）单位阶跃信号（unit step signal）符号函数（signum function）单位冲激信号（unit impulse signal）广义函数（generalized function）取样特性（sampling property）冲激偶信号（impulse doublet signal）奇函数（odd function）偶分量（even component）奇分量（odd component）正交函数（orthogonal function）正交函数集（set of orthogonal function）数学模型（mathematics model）电压源（voltage source）基尔霍夫电压定律（Kirchhoff’s voltage law（KVL））电流源（current source）连续时间系统（continuous time system）离散时间系统（discrete time system）微分方程（differential function）差分方程（difference function）线性系统（linear system）非线性系统（nonlinear system）时变系统（time–varying system）时不变系统（time–invariant system）集总参数系统（lumped–parameter system）分布参数系统（distributed–parameter system）偏微分方程（partial differential function）因果系统（causal system）非因果系统（noncausal system）因果信号（causal signal）叠加性（superposition property）均匀性（homogeneity）积分（integral）输入–输出描述法（input–output analysis）状态变量描述法（state variable analysis）单输入单输出系统（single–input and single–output system）状态方程（state equation）输出方程（output equation）多输入多输出系统（multi–input and multi–output system）时域分析法（time domain method）变换域分析法（transform domain method）卷积（convolution）傅里叶变换（Fourier transform）拉普拉斯变换（Laplace transform）第 2 章连续时间系统的时域分析齐次解（homogeneous solution）特解（particular solution）特征方程（characteristic function）特征根（characteristic root）固有（自由）解（natural solution）强迫解（forced solution）起始条件（original condition）初始条件（initial condition）自由响应（natural response）强迫响应（forced response）零输入响应（zero-input response）零状态响应（zero-state response）冲激响应（impulse response）阶跃响应（step response）卷积积分（convolution integral）交换律（exchange law）分配律（distribute law）结合律（combine law）第3 章傅里叶变换频谱（frequency spectrum）频域（frequency domain）三角形式的傅里叶级数（trigonomitric Fourier series）指数形式的傅里叶级数（exponential Fourier series）傅里叶系数（Fourier coefficient）直流分量（direct composition）基波分量（fundamental composition） n 次谐波分量（nth harmonic component）复振幅（complex amplitude）频谱图（spectrum plot（diagram））幅度谱（amplitude spectrum）相位谱（phase spectrum）包络（envelop）离散性（discrete property）谐波性（harmonic property）收敛性（convergence property）奇谐函数（odd harmonic function）吉伯斯现象（Gibbs phenomenon）周期矩形脉冲信号（periodic rectangular pulse signal）周期锯齿脉冲信号（periodic sawtooth pulse signal）周期三角脉冲信号（periodic triangular pulse signal）周期半波余弦信号（periodic half–cosine signal）周期全波余弦信号（periodic full–cosine signal）傅里叶逆变换（inverse Fourier transform）频谱密度函数（spectrum density function）单边指数信号（single–sided exponential signal）双边指数信号（two–sided exponential signal）对称矩形脉冲信号（symmetry rectangular pulse signal）线性（linearity）对称性（symmetry）对偶性（duality）位移特性（shifting）时移特性（time–shifting）频移特性（frequency–shifting）调制定理（modulation theorem）调制（modulation）解调（demodulation）变频（frequency conversion）尺度变换特性（scaling）微分与积分特性（differentiation and integration）时域微分特性（differentiation in the time domain）时域积分特性（integration in the time domain）频域微分特性（differentiation in the frequency domain）频域积分特性（integration in the frequency domain）卷积定理（convolution theorem）时域卷积定理（convolution theorem in the time domain）频域卷积定理（convolution theorem in the frequency domain）取样信号（sampling signal）矩形脉冲取样（rectangular pulse sampling）自然取样（nature sampling）冲激取样（impulse sampling）理想取样（ideal sampling）取样定理（sampling theorem）调制信号（modulation signal）载波信号（carrier signal）已调制信号（modulated signal）模拟调制（analog modulation）数字调制（digital modulation）连续波调制（continuous wave modulation）脉冲调制（pulse modulation）幅度调制（amplitude modulation）频率调制（frequency modulation）相位调制（phase modulation）角度调制（angle modulation）频分多路复用（frequency–division multiplex（FDM））时分多路复用（time–division multiplex （TDM））相干（同步）解调（synchronous detection）本地载波（local carrier）系统函数（system function）网络函数（network function）频响特性（frequency response）幅频特性（amplitude frequency response）相频特性（phase frequency response）无失真传输（distortionless transmission）理想低通滤波器（ideal low–pass filter）截止频率（cutoff frequency）正弦积分（sine integral）上升时间（rise time）窗函数（window function）理想带通滤波器（ideal band–pass filter）第 4 章拉普拉斯变换代数方程（algebraic equation）双边拉普拉斯变换（two-sided Laplace transform）双边拉普拉斯逆变换（inverse two-sided Laplace transform）单边拉普拉斯变换（single-sided Laplace transform）拉普拉斯逆变换（inverse Laplace transform）收敛域（region of convergence（ROC））延时特性（time delay）s 域平移特性（shifting in the s-domain）s 域微分特性（differentiation in the s-domain） s 域积分特性（integration in the s-domain）初值定理（initial-value theorem）终值定理（expiration-value）复频域卷积定理（convolution theorem in the complex frequency domain）部分分式展开法（partial fraction expansion）留数法（residue method）第 5 章策动点函数（driving function）转移函数（transfer function）极点（pole）零点（zero）零极点图（zero-pole plot）暂态响应（transient response）稳态响应（stable response）稳定系统（stable system）一阶系统（first order system）高通滤波网络（high-low filter）低通滤波网络（low-pass filter）二阶系统（second system）最小相移系统（minimum-phase system）维纳滤波器（Winner filter）卡尔曼滤波器（Kalman filter）低通（low-pass）高通（high-pass）带通（band-pass）带阻（band-stop）有源（active）无源（passive）模拟（analog）数字（digital）通带（pass-band）阻带（stop-band）佩利－维纳准则（Paley-Winner criterion）最佳逼近（optimum approximation）过渡带（transition-band）通带公差带（tolerance band）巴特沃兹滤波器（Butterworth filter）切比雪夫滤波器（Chebyshew filter）方框图（block diagram）信号流图（signal flow graph）节点（node）支路（branch）输入节点（source node）输出节点（sink node）混合节点（mix node）通路（path）开通路（open path）闭通路（close path）环路（loop）自环路（self-loop）环路增益（loop gain）不接触环路（disconnect loop）前向通路（forward path）前向通路增益（forward path gain）梅森公式（Mason formula）劳斯准则（Routh criterion）第 6 章数字系统（digital system）数字信号处理（digital signal processing）差分方程（difference equation）单位样值响应（unit sample response）卷积和（convolution sum）Z 变换（Z transform）序列（sequence）样值（sample）单位样值信号（unit sample signal）单位阶跃序列（unit step sequence）矩形序列 (rectangular sequence)单边实指数序列（single sided real exponential sequence）单边正弦序列（single sided exponential sequence）斜边序列（ramp sequence）复指数序列（complex exponential sequence）线性时不变离散系统（linear time-invariant discrete-time system）常系数线性差分方程（linear constant-coefficient difference equation）后向差分方程（backward difference equation）前向差分方程（forward difference equation）海诺塔（Tower of Hanoi）菲波纳西（Fibonacci）冲激函数串（impulse train）第 7 章数字滤波器（digital filter）单边 Z 变换（single-sided Z transform）双边 Z 变换(two-sided (bilateral) Z transform) 幂级数（power series）收敛（convergence）有界序列（limitary-amplitude sequence）正项级数（positive series）有限长序列（limitary-duration sequence）右边序列（right-sided sequence）左边序列（left-sided sequence）双边序列（two-sided sequence） Z 逆变换（inverse Z transform）围线积分法（contour integral method）幂级数展开法（power series expansion） z 域微分（differentiation in the z-domain）序列指数加权（multiplication by an exponential sequence） z 域卷积定理（z-domain convolution theorem）帕斯瓦尔定理（Parseval theorem）传输函数（transfer function）序列的傅里叶变换（discrete-time Fourier transform：DTFT）序列的傅里叶逆变换（inverse discrete-time Fourier transform：IDTFT）幅度响应（magnitude response）相位响应（phase response）量化（quantization）编码（coding）模数变换（A/D 变换：analog-to-digital conversion）数模变换（D/A 变换：digital-to- analog conversion）第 8 章端口分析法（port analysis）状态变量（state variable）无记忆系统（memoryless system）有记忆系统（memory system）矢量矩阵（vector-matrix ）常量矩阵（constant matrix ）输入矢量（input vector）输出矢量（output vector）直接法（direct method）间接法（indirect method）状态转移矩阵（state transition matrix）系统函数矩阵（system function matrix）冲激响应矩阵（impulse response matrix）朱里准则（July criterion）。
自动控制原理专业词汇中英文对照
自动控制原理专业词汇中英文对照自动控制原理专业词汇中英文对照中文英文自动控制automatic control；cybernation 自动控制系统automatic control system自动控制理论 automatic control theory经典控制理论 classical control theory现代控制理论 modern control theory智能控制理论intelligent control theory 开环控制open-loop control闭环控制 closed-loop control输入量 input输出量 output给定环节 given unit/element比较环节 comparing unit/element放大环节 amplifying unit/element执行环节 actuating unit/element控制环节 controlling unit/element被控对象 (controlled) plant反馈环节 feedback unit/element控制器 controller扰动/干扰 perturbance/disturbance前向通道 forward channel反馈通道feedback channel 恒值控制系统constant control system随动控制系统servo/drive control system 程序控制系统programmed control system 连续控制系统continuous control system离散控制系统 discrete control system线性控制系统 linear control system非线性控制系统 nonlinear control system定常/时不变控制系统time-invariant control system 时变控制系统 time-variant control system 稳定性 stability快速性 rapidity准确性 accuracy数学模型 mathematical model微分方程 differential equation非线性特性 nonlinear characteristic线性化处理 linearization processing泰勒级数 Taylor series传递函数 transfer function比例环节 proportional element积分环节 integrating element一阶惯性环节 first order inertial element二阶惯性环节 second order inertial element二阶震荡环节second order oscillation element 微分环节differentiation element一阶微分环节 first order differentiation element二阶微分环节 second order differentiation element 延迟环节delay element动态结构图 dynamic structure block串联环节 serial unit并联环节 parallel unit信号流图 signal flow graph梅逊增益公式Mason’s gain formula时域分析法 time domain analysis method性能指标 performance index阶跃函数 step function斜坡函数 ramp function抛物线函数 parabolic function /acceleration function 冲击函数impulse function正弦函数 sinusoidal function动态/暂态响应 transient response静态/稳态响应 steady-state response 延迟时间 delay time上升时间 rise time峰值时间 peak time调节时间 settling time最大超调量 maximum overshoot稳态误差 steady-state error无阻尼 undamping欠阻尼 underdamping过阻尼 overdamping特征根 eigen root极点 pole零点 zero实轴 real axis虚轴 imaginary axis 稳态/静态分量 steady-state component 瞬态/暂态/动态分量transient component 运动模态motion mode衰减 attenuation系数 coefficient初相角 initial phase angle响应曲线 response curve主导极点 dominant pole 劳斯稳定判据 Routh stability criterion S平面 S plane胡尔维茨稳定判据Hurwitz stability criterion 测量误差measurement error扰动误差 agitation error结构性误差 structural error偏差 deviation根轨迹 root locus 常规根轨迹 routine root locus根轨迹方程 root locus equation 幅值 magnitude幅角 argument对称性 symmetry分离点 separation/break away point会合点 meeting/break-in point渐近线 asymptote出射角 emergence angle/angle of departure入射角incidence angle/angle of arrival 广义根轨迹generalized root locus零度根轨迹zero degree root locus 偶极子dipole/zero-pole pair 频域分析法frequency-domain analysis method 频率特性frequency characteristic极坐标系 polar coordinate system直角坐标系 rectangular coordinate system幅频特性 magnitude-frequency characteristic相频特性phase-frequency characteristic 幅相频率特性magnitude-phase frequency characteristic 最小相位系统minimum phase system非最小相位系统 nonminimum phase system奈奎斯特稳定判据Nyquist stability criterion 伯德定理Bode theorem稳定裕度 stability margin幅值裕度 magnitude margin 相位/相角裕度 phase margin对数幅频特性 log magnitude-frequency characteristic 无阻尼自然震荡角频率 undamped oscillation angular frequency 阻尼震荡角频率damped oscillation angular frequency 阻尼角damping angle带宽频率bandwidth frequency 穿越/截止频率crossover/cutoff frequency 谐振峰值 resonance peak系统校正 system compensation超前校正 lead compensation滞后校正 lag compensation自激震荡 self-excited oscillation死区特性 dead zone characteristic饱和特性 saturation characteristic间隙特性 backlash characteristic描述函数法 describing function method相平面法 phase plane method 采样控制系统 sampling control system数字控制系统 digital control system频谱 frequency spectrum 采样定理 sampling theorem信号重现 signal recurrence拉氏变换 Laplace transformZ变换 Z transform终值定理 final-value theorem差分方程 difference equation迭代法 iterative method 脉冲传递函数 pulse transfer function 零阶保持器 zero-order holder映射 mapping方框图 block diagram伯德图 Bode diagram特征方程 characteristic equation可控性 controllability临界阻尼 critical damping阻尼常数 damping constant阻尼比 damping ratio初始状态 initial state初值定理 initial-value theorem反Z变换 inverse Z-transformation负反馈 negative feedback正反馈 positive feedback 尼科尔斯图 Nichols chart部分分式展开partial fraction expansion 幅角原理argument principle相对稳定性 relative stability共振频率 resonant frequency劳斯表 Routh tabulation/array奇点 singularity渐进稳定性 asymptotic stability控制精度 control accuracy临界稳定性 critical stability耦合 coupling解耦 decoupling比例积分微分调节器proportional integral derivative regulator(PID) 串联校正 series/cascade compensation 单输入单输出 single input single output(SISO)多输入多输出 multi input multi output(MIMO)低通滤波器 low pass filter非线性系统 nonlinear system复合控制 compound control衰减振荡 damped oscillation主反馈 monitoring feedback 转折(交接)频率 break frequency 稳定焦点/节点 stable focus/node。
《自动控制原理》部分中英文词汇对照表(英文解释)
《自动控制原理》部分中英文词汇对照表AAcceleration 加速度Angle of departure分离角Asymptotic stability渐近稳定性Automation自动化Auxiliary equation辅助方程BBacklash间隙Bandwidth带宽Block diagram方框图Bode diagram波特图CCauchy’s theorem高斯定理Characteristic equation特征方程Closed-loop control system闭环控制系统Constant常数Control system控制系统Controllability可控性Critical damping临界阻尼DDamping constant阻尼常数Damping ratio阻尼比DC control system直流控制系统Dead zone死区Delay time延迟时间Derivative control 微分控制Differential equations微分方程Digital computer compensator数字补偿器Dominant poles主导极点Dynamic equations动态方程EError coefficients误差系数Error transfer function误差传递函数FFeedback反馈Feedback compensation反馈补偿Feedback control systems反馈控制系统Feedback signal反馈信号Final-value theorem终值定理Frequency-domain analysis频域分析Frequency-domain design频域设计Friction摩擦GGain增益Generalized error coefficients广义误差系数IImpulse response脉冲响应Initial state初始状态Initial-value theorem初值定理Input vector输入向量Integral control积分控制Inverse z-transformation反Z变换JJordan block约当块Jordan canonical form约当标准形LLag-lead controller滞后-超前控制器Lag-lead network 滞后-超前网络Laplace transform拉氏变换Lead-lag controller超前-滞后控制器Linearization线性化Linear systems线性系统MMass质量Mathematical models数学模型Matrix矩阵Mechanical systems机械系统NNatural undamped frequency自然无阻尼频率Negative feedback负反馈Nichols chart尼科尔斯图Nonlinear control systems非线性控制系统Nyquist criterion柰奎斯特判据OObservability可观性Observer观测器Open-loop control system开环控制系统Output equations输出方程Output vector输出向量PParabolic input抛物线输入Partial fraction expansion部分分式展开PD controller比例微分控制器Peak time峰值时间Phase-lag controller相位滞后控制器Phase-lead controller相位超前控制器Phase margin相角裕度PID controller比例、积分微分控制器Polar plot极坐标图Poles definition极点定义Positive feedback正反馈Prefilter 前置滤波器Principle of the argument幅角原理RRamp error constant斜坡误差常数Ramp input斜坡输入Relative stability相对稳定性Resonant frequency共振频率Rise time上升时间调节时间 accommodation timeRobust system鲁棒系统Root loci根轨迹Routh tabulation（array）劳斯表SSampling frequency采样频率Sampling period采样周期Second-order system二阶系统Sensitivity灵敏度Series compensation串联补偿Settling time调节时间Signal flow graphs信号流图Similarity transformation相似变换Singularity奇点Spring弹簧Stability稳定性State diagram状态图State equations状态方程State feedback状态反馈State space状态空间State transition equation状态转移方程State transition matrix状态转移矩阵State variables状态变量State vector状态向量Steady-state error稳态误差Steady-state response稳态响应Step error constant阶跃误差常数Step input阶跃输入TTime delay时间延迟Time-domain analysis时域分析Time-domain design时域设计Time-invariant systems时不变系统Time-varying systems时变系统Type number型数Torque constant扭矩常数Transfer function转换方程Transient response暂态响应Transition matrix转移矩阵UUnit step response单位阶跃响应VVandermonde matrix范德蒙矩阵Velocity control system速度控制系统Velocity error constant速度误差常数ZZero-order hold零阶保持z-transfer function Z变换函数z-transform Z变换欢迎您的下载，资料仅供参考！致力为企业和个人提供合同协议，策划案计划书，学习课件等等打造全网一站式需求。
常微分方程中的英文单词和短语
operator polynomial
rse transform
第七章
Chapter7Power Series Solutions of Differential Equations
柯西定理
Cauchy theorem
解析解
analytic solution
常数矩阵
constant matrix
非齐次线性微分方程组
non-homogeneous linear differential equations
常数列向量
constant arrange vector
常数变异公式
formula of variation of constant
计算公式
computing formula
若尔当标准型
Jordan normal form
矩阵函数
matrix function
实值解
real-valued function
复值解
complex-value function
代数余子式
algebraic cofactor
特征方程
characteristic equation
算子式
operator method
一阶线性方程
first-order linear equation
齐次
homogeneous
非齐次
non-homogeneous
积分因子法
method of integration factor
常数变易法
method of constants variation
初等变换法
elementary method of transformation
一类中立型微分方程的渐近概周期温和解
一类中立型微分方程的渐近概周期温和解
1 渐近概周期温和解
渐近概周期温和解可以简单地理解为具有一类中立型微分方程（Neutral-Type Differential Equation）的渐近概周期解。
它可以帮助我们解决复杂的数学问题，或者是解决那些具有维数过高的难以求解的系统问题。
最早我们发现的这一理论思想来自于司马懿，他在封建时代发展出了一套弥足珍贵的渐近概周期解模型，这一模型给复杂的系统问题提供了简洁而可行的解决方案。
2 中立型微分方程
中立型微分方程是一种特殊的种类，它将求解中涉及到的变量划分为三类：空间变量，时间变量和模块变量。
其中空间变量是指系统中变动的空间参数，例如位置、速度等；时间变量则指随着时间从而变化的参数；而模块变量则是指每一个细微的模块参数，其中包括了定域、定调、定形和定度等模块参数。
3 渐近概周期温和解的求解
针对不同类型的中立型微分方程，渐近概周期温和解的求解也有所差异。
首先，需要对系统参数进行划分、确定，并将系统拆解为各个模块；接着，使用拆分后参数为基础，研究系统的空间变化规律，建立系统动态模型；最后，使用模型分析出满足定域、定调、定形和定度的渐近概周期温和解，从而为复杂系统求解提供可行方案。
总之，渐近概周期温和解是一类中立型微分方程的渐近概周期解，它的出现为复杂的系统提供了可行的求解方案。
渐近概周期温和解的
求解需要对变量进行划分，并根据划分后变量构建模型，最终求解出
满足一定条件的渐近概周期温和解。
流体力学常用名词中英文对照
流体力学常用名词流体动力学fluid dynamics 连续介质力学mechanics of continuous 介质medium 流体质点fluid particle 无粘性流体nonviscous fluid, inviscid 连续介质假设continuous medium hypothesis 流体运动学fluid kinematics 水静力学hydrostatics 液体静力学hydrostatics 支配方程governing equation 伯努利方程Bernoulli equation 伯努利定理Bernonlli theorem 毕奥- 萨伐尔定律Biot-Savart law 欧拉方程Euler equation 亥姆霍兹定理Helmholtz theorem 开尔文定理Kelvin theorem 涡片vortex sheet 库塔- 茹可夫斯基条件Kutta-Zhoukowski condition 布拉休斯解Blasius solution 达朗贝尔佯廖d'Alembert paradox 雷诺数Reynolds number 施特鲁哈尔数Strouhal number 随体导数material derivative 不可压缩流体incompressible fluid 质量守恒conservation of mass 动量守恒conservation of momentum 能量守恒conservation of energy 动量方程momentum equation 能量方程energy equation 控制体积control volume 液体静压hydrostatic pressure 涡量拟能enstrophy 压差differential pressure 流［动］flow 流线stream line 流面stream surface 流管stream tube 迹线path, path line 流场flow field 流态flow regime 流动参量flow parameter 流量flow rate, flow discharge 涡旋vortex涡量vorticity 涡丝vortex filament 涡线vortex line 涡面vortex surface 涡层vortex layer 涡环vortex ring 涡对vortex pair 涡管vortex tube 涡街vortex street 卡门涡街Karman vortex street 马蹄涡horseshoe vortex 对流涡胞convective cell 卷筒涡胞roll cell 涡eddy 涡粘性eddy viscosity 环流circulation 环量circulation 速度环量velocity circulation 偶极子doublet, dipole 驻点stagnation point 总压[ 力] total pressure 总压头total head 静压头static head 总焓total enthalpy 能量输运energy transport 速度剖面velocity profile 库埃特流Couette flow 单相流single phase flow 单组份流single-component flow 均匀流uniform flow 非均匀流nonuniform flow 二维流two-dimensional flow 三维流three-dimensional flow 准定常流quasi-steady flow 非定常流unsteady flow, non-steady flow 暂态流transient flow 周期流periodic flow 振荡流oscillatory flow 分层流stratified flow 无旋流irrotational flow 有旋流rotational flow 轴对称流axisymmetric flow 不可压缩性incompressibility 不可压缩流[动] incompressible flow 浮体floating body 定倾中心metacenter 阻力drag, resistance 减阻drag reduction 表面力surface force 表面张力surface tension 毛细[ 管]作用capillarity 来流incoming flow 自由流free stream 自由流线free stream line 外流external flow 进口entrance, inlet 出口exit, outlet 扰动disturbance, perturbation 分布distribution 传播propagation 色散dispersion 弥散dispersion 附加质量added mass ,associated mass 收缩contraction 镜象法image method 无量纲参数dimensionless parameter 几何相似geometric similarity 运动相似kinematic similarity 动力相似[ 性] dynamic similarity 平面流plane flow 势potential 势流potential flow 速度势velocity potential 复势complex potential 复速度complex velocity 流函数stream function 源source 汇sink 速度[ 水] 头velocity head 拐角流corner flow 空泡流cavity flow 超空泡supercavity 超空泡流supercavity flow 空气动力学aerodynamics 低速空气动力学low-speed aerodynamics 高速空气动力学high-speed aerodynamics 气动热力学aerothermodynamics 亚声速流[ 动] subsonic flow 跨声速流[ 动] transonic flow 超声速流[ 动] supersonic flow 锥形流conical flow 楔流wedge flow 叶栅流cascade flow 非平衡流[ 动] non-equilibrium flow 细长体slender body 细长度slenderness 钝头体bluff body 钝体blunt body 翼型airfoil 翼弦chord 薄翼理论thin-airfoil theory 构型configuration 后缘trailing edge 迎角angle of attack 失速stall 脱体激波detached shock wave 波阻wave drag 诱导阻力induced drag 诱导速度induced velocity 临界雷诺数critical Reynolds number 前缘涡leading edge vortex 附着涡bound vortex 约束涡confined vortex 气动中心aerodynamic center 气动力aerodynamic force 气动噪声aerodynamic noise 气动加热aerodynamic heating 离解dissociation 地面效应ground effect 气体动力学gas dynamics 稀疏波rarefaction wave 热状态方程thermal equation of state 喷管Nozzle 普朗特- 迈耶流Prandtl-Meyer flow 瑞利流Rayleigh flow 可压缩流[ 动] compressible flow 可压缩流体compressible fluid 绝热流adiabatic flow 非绝热流diabatic flow 未扰动流undisturbed flow等熵流isentropic flow 匀熵流homoentropic flow 兰金- 于戈尼奥条件Rankine-Hugoniot condition 状态方程equation of state 量热状态方程caloric equation of state 完全气体perfect gas 拉瓦尔喷管Laval nozzle 马赫角Mach angle 马赫锥Mach cone 马赫线Mach line 马赫数Mach number 马赫波Mach wave 当地马赫数local Mach number 冲击波shock wave 激波shock wave 正激波normal shock wave 斜激波oblique shock wave 头波bow wave 附体激波attached shock wave 激波阵面shock front 激波层shock layer 压缩波compression wave 反射reflection 折射refraction 散射scattering 衍射diffraction 绕射diffraction 出口压力exit pressure 超压[ 强] over pressure 反压back pressure 爆炸explosion 爆轰detonation 缓燃deflagration 水动力学hydrodynamics 液体动力学hydrodynamics 泰勒不稳定性Taylor instability 盖斯特纳波Gerstner wave 斯托克斯波Stokes wave 瑞利数Rayleigh number 自由面free surface 波速wave speed, wave velocity 波高wave height 波列wave train 波群wave group 波能wave energy 表面波surface wave表面张力波capillary wave 规则波regular wave 不规则波irregular wave 浅水波shallow water wave 深水波deep water wave 重力波gravity wave 椭圆余弦波cnoidal wave 潮波tidal wave 涌波surge wave 破碎波breaking wave 船波ship wave 非线性波nonlinear wave 孤立子soliton 水动［力］噪声hydrodynamic noise 水击water hammer 空化cavitation 空化数cavitation number 空蚀cavitation damage 超空化流supercavitating flow 水翼hydrofoil 水力学hydraulics 洪水波flood wave 涟漪ripple 消能energy dissipation 海洋水动力学marine hydrodynamics 谢齐公式Chezy formula 欧拉数Euler number 弗劳德数Froude number 水力半径hydraulic radius 水力坡度hvdraulic slope 高度水头elevating head 水头损失head loss 水位water level 水跃hydraulic jump 含水层aquifer 排水drainage 排放量discharge 壅水曲线back water curve 压［强水］头pressure head 过水断面flow cross-section 明槽流open channel flow 孔流orifice flow 无压流free surface flow 有压流pressure flow 缓流subcritical flow 急流supercritical flow 渐变流gradually varied flow 急变流rapidly varied flow 临界流critical flow 异重流density current, gravity flow 堰流weir flow 掺气流aerated flow 含沙流sediment-laden stream 降水曲线dropdown curve 沉积物sediment, deposit 沉［降堆］积sedimentation, deposition 沉降速度settling velocity 流动稳定性flow stability 不稳定性instability 奥尔- 索末菲方程Orr-Sommerfeld equation 涡量方程vorticity equation 泊肃叶流Poiseuille flow 奥辛流Oseen flow 剪切流shear flow 粘性流［动］ viscous flow 层流laminar flow 分离流separated flow 二次流secondary flow 近场流near field flow 远场流far field flow 滞止流stagnation flow 尾流wake ［flow］回流back flow 反流reverse flow 射流jet 自由射流free jet 管流pipe flow, tube flow 内流internal flow 拟序结构coherent structure 猝发过程bursting process 表观粘度apparent viscosity 运动粘性kinematic viscosity 动力粘性dynamic viscosity 泊poise 厘泊centipoise 厘沱centistoke 剪切层shear layer 次层sublayer流动分离flow separation 层流分离laminar separation 湍流分离turbulent separation 分离点separation point 附着点attachment point 再附reattachment 再层流化relaminarization 起动涡starting vortex 驻涡standing vortex 涡旋破碎vortex breakdown 涡旋脱落vortex shedding 压［力］降pressure drop 压差阻力pressure drag 压力能pressure energy 型阻profile drag 滑移速度slip velocity 无滑移条件non-slip condition 壁剪应力skin friction, frictional drag 壁剪切速度friction velocity 磨擦损失friction loss 磨擦因子friction factor 耗散dissipation 滞后lag 相似性解similar solution 局域相似local similarity 气体润滑gas lubrication 液体动力润滑hydrodynamic lubrication 浆体slurry 泰勒数Taylor number 纳维- 斯托克斯方程Navier-Stokes equation 牛顿流体Newtonian fluid 边界层理论boundary later theory 边界层方程boundary layer equation 边界层boundary layer 附面层boundary layer 层流边界层laminar boundary layer 湍流边界层turbulent boundary layer 温度边界层thermal boundary layer 边界层转捩boundary layer transition 边界层分离boundary layer separation 边界层厚度boundary layer thickness 位移厚度displacement thickness 动量厚度momentum thickness 能量厚度energy thickness 焓厚度enthalpy thickness 注入injection 吸出suction 泰勒涡Taylor vortex 速度亏损律velocity defect law 形状因子shape factor 测速法anemometry 粘度测定法visco[si] metry 流动显示flow visualization 油烟显示oil smoke visualization 孔板流量计orifice meter 频率响应frequency response 油膜显示oil film visualization 阴影法shadow method 纹影法schlieren method 烟丝法smoke wire method 丝线法tuft method 说明氢泡法nydrogen bubble method 相似理论similarity theory 相似律similarity law 部分相似partial similarity 定理pi theorem, Buckingham theorem 静[态]校准static calibration 动态校准dynamic calibration 风洞wind tunnel 激波管shock tube 激波管风洞shock tube wind tunnel 水洞water tunnel 拖曳水池towing tank 旋臂水池rotating arm basin 扩散段diffuser 测压孔pressure tap 皮托管pitot tube 普雷斯顿管preston tube 斯坦顿管Stanton tube 文丘里管Venturi tube U 形管U-tube 压强计manometer 微压计micromanometer 多管压强计multiple manometer 静压管static [pressure]tube 流速计anemometer 风速管Pitot- static tube 激光多普勒测速计laser Doppler anemometer ,laser Doppler velocimeter 热线流速计hot-wire anemometer 热膜流速计hot- film anemometer 流量计flow meter 粘度计visco[si] meter 涡量计vorticity meter 传感器transducer , sensor 压强传感器pressure transducer 热敏电阻thermistor 示踪物tracer 时间线time line 脉线streak line 尺度效应scale effect 壁效应wall effect 堵塞blockage 堵寒效应blockage effect 动态响应dynamic response 响应频率response frequency 底压base pressure 菲克定律Fick law 巴塞特力Basset force 埃克特数Eckert number 格拉斯霍夫数Grashof number 努塞特数Nusselt number 普朗特数prandtl number 雷诺比拟Reynolds analogy 施密特数schmidt number 斯坦顿数Stanton number 对流convection 自由对流natural convection, free convec-tion 强迫对流forced convection 热对流heat convection 质量传递mass transfer 传质系数mass transfer coefficient 热量传递heat transfer 传热系数heat transfer coefficient 对流传热convective heat transfer 辐射传热radiative heat transfer 动量交换momentum transfer 能量传递energy transfer 传导conduction 热传导conductive heat transfer 热交换heat exchange 临界热通量critical heat flux 浓度concentration扩散diffusion 扩散性diffusivity 扩散率diffusivity 扩散速度diffusion velocity 分子扩散molecular diffusion 沸腾boiling 蒸发evaporation 气化gasification 凝结condensation 成核nucleation 计算流体力学computational fluid mechanics 多重尺度问题multiple scale problem 伯格斯方程Burgers equation 对流扩散方程convection diffusion equation KDU 方程KDV equation 修正微分方程modified differential equation 拉克斯等价定理Lax equivalence theorem 数值模拟numerical simulation 大涡模拟large eddy simulation 数值粘性numerical viscosity 非线性不稳定性nonlinear instability 希尔特稳定性分析Hirt stability analysis 相容条件consistency conditionCFL 条件Courant- Friedrichs- Lewy condition ,CFL condition 狄里克雷边界条件Dirichlet boundary condition 熵条件entropy condition 远场边界条件far field boundary condition 流入边界条件inflow boundary condition 无反射边界条件nonreflecting boundary condition数值边界条件numerical boundary condition 流出边界条件outflow boundary condition 冯. 诺伊曼条件von Neumann condition 近似因子分解法approximate factorization method 人工压缩artificial compression 人工粘性artificial viscosity 边界元法boundary element method 配置方法collocation method 能量法energy method 有限体积法finite volume method 流体网格法fluid in cell method,FLIC method 通量校正传输法flux-corrected transport method 通量矢量分解法flux vector splitting method 伽辽金法Galerkin method 积分方法integral method标记网格法marker and cell method, MAC method 特征线法method of characteristics 直线法method of lines 矩量法moment method 多重网格法multi- grid method 板块法panel method 质点网格法particle in cell method, PIC method 质点法particle method 预估校正法predictor-corrector method 投影法projection method 准谱法pseudo-spectral method 随机选取法random choice method 激波捕捉法shock-capturing method 激波拟合法shock-fitting method 谱方法spectral method 稀疏矩阵分解法split coefficient matrix method 不定常法time-dependent method 时间分步法time splitting method 变分法variational method 涡方法vortex method 隐格式implicit scheme 显格式explicit scheme 交替方向隐格式alternating direction implicit scheme, ADI scheme 反扩散差分格式anti-diffusion difference scheme 紧差分格式compact difference scheme 守恒差分格式conservation difference scheme 克兰克- 尼科尔森格式Crank-Nicolson scheme 杜福特- 弗兰克尔格式Dufort-Frankel scheme 指数格式exponential scheme 戈本诺夫格式Godunov scheme 高分辨率格式high resolution scheme 拉克斯- 温德罗夫格式Lax-Wendroff scheme 蛙跳格式leap-frog scheme 单调差分格式monotone difference scheme 保单调差分格式monotonicity preserving diffe-rence scheme 穆曼- 科尔格式Murman-Cole scheme 半隐格式semi-implicit scheme 斜迎风格式skew-upstream scheme 全变差下降格式total variation decreasing scheme TVD scheme 迎风格式upstream scheme , upwind scheme 计算区域computational domain 物理区域physical domain 影响域domain of influence 依赖域domain of dependence区域分解domain decomposition 维数分解dimensional split 物理解physical solution 弱解weak solution 黎曼解算子Riemann solver 守恒型conservation form 弱守恒型weak conservation form 强守恒型strong conservation form 散度型divergence form 贴体曲线坐标body- fitted curvilinear coordi-nates [ 自] 适应网格[self-] adaptive mesh 适应网格生成adaptive grid generation 自动网格生成automatic grid generation 数值网格生成numerical grid generation 交错网格staggered mesh 网格雷诺数cell Reynolds number 数植扩散numerical diffusion 数值耗散numerical dissipation 数值色散numerical dispersion 数值通量numerical flux 放大因子amplification factor 放大矩阵amplification matrix 阻尼误差damping error 离散涡discrete vortex 熵通量entropy flux 熵函数entropy function 分步法fractional step method。
数学专业英语词汇（L）
数学专业英语词汇（L）l distribution l分布l function l函数l integral 勒贝格积分l measurable function 勒贝格可测函数l null set l零集l'hospital rule 洛必达规则labeled graph 标号图labile 不稳定的laboratory system of coordinates 实验室坐标系labyrinth 迷宫lacation principle 介值定理lacunarity 缺项性lacunary series 间隙级数lacunary space 缺项空间lag 延迟lag correlation 滞后相关lag correlation coefficient 滞后相关系数lag covariance 落后协方差lag of phase 相位滞后lag regression 落后回归lagrange bracket 拉格朗日括号lagrange equation of motion 拉格朗日运动方程lagrange interpolation formula 拉格朗日插置公式lagrange interpolation polynomial 拉格郎日插值多项式lagrange multiplier 拉格朗日乘子lagrange problem 拉格朗日问题lagrange remainder term 拉格朗日剩余项lagrange residual term 拉格朗日剩余项lagrange theorem 拉格朗日定理lagrangian 拉格朗日算子thermocouple pyrometer 热电偶高温计lagrangian function 拉格朗日算子lagrangian operator 拉格朗日算符laguerre differential equation 拉盖尔微分方程laguerre function 拉盖尔函数laguerre polynomial 拉盖尔多项式lambert series 兰伯特级数lame equation 拉梅方程lame function 拉梅函数laminar 薄层的laminar flow 层流片流landau symbol 兰道记号landen transformation 兰登变换language of formula 公式语言laplace beltrami operator 拉普拉斯贝尔特拉米算子laplace distribution 拉普拉斯分布laplace equation 拉普拉斯方程laplace expansion 拉普拉斯展开laplace expansion theorem 拉普拉斯展开定理laplace integral 拉普拉斯积分laplace linear equation 拉普拉斯线性方程laplace transform 拉普拉斯变换laplacian 拉普拉斯算子laplacian equation 拉普拉斯方程large sample analysis 大样本分析large sample test 大样本检验last multiplier 最后乘子last term 末项latency 潜在latent 潜在的lateral 横的lateral area 侧面积lateral surface 侧面latin cube 拉丁立方latin rectangle 拉丁矩形latin square 拉丁方latitude 纬度lattice 格子;格lattice constant 点阵常数lattice design 格子设计lattice distribution 格分布lattice function 点阵函数lattice isomorphism 格同构lattice matrix 点阵矩阵lattice of sets 集格lattice operation 格运算lattice ordered group 格序群lattice point at the boundary 边界格点lattice theoretic 格论的lattice theory 格论latticehomomorphism 格同态latus rectum 通径laue's equations 劳卮方程laurent series 罗郎级数law 法则law of commutation 交换律law of composition 合成律law of cosines 余弦定律law of deduction 演绎定律law of double negation 双重否定律law of errors 误差律law of excluded middle 排中律law of exponentiation 指数定律law of inertia 惯性律law of iterated logarithm 迭对数定律law of large numbers 大数定律law of similarity transformation 相似变换律law of sines 正弦定律law of small numbers 小数定律law of tangents 正切定律laws of integral exponents 整指数定律leading coefficient 首项系数leading diagonal 衷角线leading ideal 猪想leading term 知项leaf 叶least common denominator 最小公分母least common left multiple 左最小公倍数least common multiple 最小公倍数least common right multiple 右最小公倍数least significant digit 最小有效数字least squares approximation 最小二乘逼近least squares estimator 最小二乘估计量least upper bound 最小上界lebesgue area 勒贝格面积lebesgue decomposition 勒贝格分解lebesgue integrable 勒贝格可积的lebesgue integral 勒贝格积分lebesgue measurable 勒贝格可测的lebesgue measure 勒贝格测度lebesgue number 勒贝格数lebesgue space 勒贝格空间lebesgue stieltjes integral 勒贝格斯蒂尔吉斯积分left adjoint 左伴随的left adjoint homomorphism 左伴随同态left almost periodic function 左殆周期函数left alternative division ring 左交错可除环left alternative law 左交错律left alternative ring 左交错环left annihilator 左零化子left artinian ring 左阿廷环left associated element 左相伴元素left balanced functor 左平衡函子left closed object 在闭对象left completion 左完备化left continuous 左方连续的left continuous function 左连续函数left coset 左陪集left coset space 左傍系空间left derivative 左导数left derived functor 左导函子left differential 左微分left direct product 左直积left directed quasiorder 逆有向拟序left distributive 左分配的left distributive law 左分配律left divisor 左因子left end point 左端点left exact functor 左正合函子left exactness 左正合性left faithful functor 左一一的函子left hand differentiable function 左可微函数left hand lower dini derivative 左下狄尼导数left hand side 左边left hand symmetrizable kernel 左方可对称化核left hand upper dini derivative 左上狄尼导数left handed co ordinate system 左手坐标系left handed curve 左旋曲线left handed system 左手坐标系left hereditary ring 左遗传环left homotopy inverse 左同伦逆元left ideal 左理想left identity element 左幺元left injective dimension 左内射维数left inner product 左内积left invariant mean 左不变平均值left invariant measure 左不变测度left inverse 左逆的left inverse element 左逆元left inverse matrix 左逆阵left inverse operator 左逆算子left invertible element 左可逆元left invertible mapping 左可逆映射left isolated point 左孤立点left kernel 左核left length 左长left limit value 左极限值left linear topology 左线性拓扑left localization 左局部化left mean 左平均left module 左模left monotonicity 左单翟left multiplication ring 左乘环left noetherian semigroup 左诺特半群left non zerodivisor 左非零因子left operator 左算子left order 左整环left periodic group 左周期群left primitive ideal 左本原理想left primitive ring 左本原环left projective space 左射影空间left quasi inverse 左拟逆元left quasi regularity 左拟正则性left quasi simple ring 左拟单环left quasigroup 左拟群left quotient 左商left quotient field 左商域left quotient ring 左商环left radical 左根基left regular element 左正则元素left regular representation 左正则表示left regularity 左正则性left remainder 左剩余left representation 左表示left resolution 左分解left satellite 左卫星函子left semihereditary ring 左半遗传环left semilinear mapping 左半线性映射left side contiuous function 左连续函数left side derivative 左导数left side half open interval 左半开区间left side limit value 左极限值left sided decomposition 左分解left simple groupoid 左单广群left simple semigroup 左单半群left tensor product 左张量乘积left topology 左拓扑left translation 左平移left zero divisor 左零因子leg of a right triangle 直角三角形的侧边legendre function 勒让德函数legendre polynomial 勒让德多项式legendre relation 勒让德关系legendre symbol 勒让德记号legendre transform 勒让德变换leibniz series 莱布尼兹级数leibniz theorem 莱布尼兹定理lemma 引理lemniscate 双纽线lemniscate function 双纽线函数lemniscate of bernoulli 伯努利双纽线length 长度length of arc 弧长length of curve 曲线的长length of normal 法线的长length of queue 队列长度length of tangent 切线的长length of vector 向量的长length unit 长度单位lens 透镜lens space 透镜空间leptokurtic distribution 尖峰态分布less than or equal 小于或等于letter 文字level 水准level curve 阶层曲线level line 等高线level plane 水准面level surface 等位面lever 杠杆levi decomposition 列维分解levi problem 列维问题lexicographic 词典的lexicographic order 字典顺序liapunov function 李雅普诺夫函数library 厍library subroutine 库存子程序lie algebra 李代数lie continuous group 李连续群lie derivative 李导数lie group 李群lie homomorphism 李同态lie ring 李环lie series 李级数lie subring 李子环life insurance 寿命保险life table 死亡率表life time 生存时间lifting 提升lifting map 提升映射lifting theorem 提升定理like term 同类项likelihood 似然likelihood function 似然函数likelihood ratio 似然比likelihood ratio test 似然比值检验limacon of pascal 帕斯卡蚶线limes inferior 下极限limes superior 上极限limit 极限limit case 极限情况limit circle 极限圆limit circle type 极限圆型limit cycle 极限环limit distribution 极限分布limit element 极限元limit function 极限函数limit in the sense of pointwise convergence 点态收敛极限limit of efficiency 有效极限limit of error 误差限度limit of integration 积分极限limit of proportionality 比例极限limit on the left 左极限limit on the right 右极限limit ordinal number 极限序数limit point 极限点limit point type 极限点型limit relation 极限关系limit theorem 极限定理limit theorem in probability theory 概率论极限定理limit value 极限值limitation 限制limited 有界的limited function 有界函数limiting cone 极限锥limiting distribution 极限分布limiting point 极限点limiting position 极限位置limitless 无界的limits of integration 积分限line 线line at infinity 无穷远线line bundle 线丛line coordinates 线坐标line critical graph 线临界图line element 线素line graph 线图line integral 线积分line of curvature 曲率线line of discontinuity 不连续线line of horizon 水平线line of intersection 交线line of nodes 交点线line of steepest descent 最速下降线line of vector 向量线line segment 线段linear 线的linear acceleration 线性加速度linear algebra 线性代数linear approximation 线性近似linear approximation problem 线性逼近问题linear associative algebra 线性结合代数linear closure 线性闭包linear combination 线性组合linear convergence 线性收敛linear density 线密度linear dependence 线性关系linear difference equation 线性差分方程linear differential equation 线性微分方程linear differential equation with constant coefficients 常系数线性微分方程linear dimension 线性维数linear eigenvalue problem 线性特盏问题linear equation 线性方程linear extrapolation 线性外插linear form 线性形式linear fractional function 单应函数linear fractional transformation 线性分式变换linear function 线性函数linear functional 线性泛函linear genus 线性狂linear group 线性群linear homogeneous equation 线性齐次方程linear hull 线性闭包linear independence 线性无关linear integral equation 线性积分方程linear integral equation of the third kind 第三种线性积分方程linear interpolation 线性插值linear isomorphism 线性同构linear manifold 线性廖linear map 线性映射linear measure 线性测度linear operator 线性算子linear optimization 线性最优化linear optimization problem 线性最优化问题linear order 线性有序类linear orderedness 线性次序linear ordinary differential equation 线性常微分方程linear pencil 线性束linear programming 线性规划linear quotient optimization 线性商最优化linear regression 线性回归linear relationship 线性关系linear space 线性空间linear subspace 线性子空间linear subsystem 线性子系linear system 线性系linear system of curves 线性曲线系linear system of differential equations 线性微分方程系linear transformation 线性变换linear vector function 线性向量函数linear velocity 线速度linearity 线性linearization 线性化linearly dependent set 线性相关集linearly dependent system 线性相关集linearly independent set 线性无关系linearly independent system 线性无关系linearly ordered class 线性有序类linearly ordered set 线性有序集link group 连接群liouville number 刘维尔数liouville theorem 刘维尔定理lipschitz condition 李普希茨条件lipschitz constant 李普希茨常数lipschitz continuity 李普希茨连续性lipschitz continuous function 李普希茨连续函数lipschitz space 李普希茨空间listing knot 8字纽结liter 升literal constant 文字常数literal expression 文字式litre 升lituus 连锁螺线load 载荷load curve 载荷曲线lobachevski space 双曲空间lobachevskian geometry 双曲几何学local arcwise connectedness 局部弧连通性local base 局部基local betti group 局部贝蒂群local borel set 局部波莱尔集local class field theory 局部类域论local compactness 局部紧性local condition 局部条件local continuity 局部连续性local convergence 局部收敛local coordinate system 局部坐标系local degree 局部次数local degree of map 局部映射度local extremum 局部极值local group 局部群local isomorphism 局部同构local lie group 局部李群local limit theorem 局部极限定理local lipschitz condition 局部李普希茨条件local maximum 局部极大local minimum 局部极小local parameter 局部参数local property 局部性质local ring 局部环local ringed space 局部环式空间local uniformization 局部单值化local uniformizing 局部单值化localization 局部化localization principle 局部化原理localizing subcategory 局部化子范畴locally analytic function 局部解析函数locally arcwise connected space 局部弧连通空间locally bounded function 局部有界函数locally closed set 局部闭集locally compact mapping 局部紧映射locally compact space 局部紧空间locally connected continuum 局部连通连续统locally connected set 局部连通集locally connected space 局部连通空间locally constant function 局部常值函数locally constant sheaf 局部常数层locally contractible space 局部可缩空间locally convex algebra 局部凸代数locally convex space 局部凸空间locally convex topology 局部凸拓扑locally euclidean connection 局部欧几里得联通locally euclidean group 局部欧几里得群locally euclidean manifold 局部欧几里得廖locally euclidean space 局部欧几里得空间locally finite category 局部有限范畴locally finite complex 局部有限复形locally finite family of sets 局部有限集族locally finite graph 局部有限图locally finite sum 局部有限和locally flat 局部平坦的locally free sheaf 局部自由层locally homomorphic function 局部同态函数locally pathconnected space 局部道路连通空间locally regular confidence region 局部正则置信区域locally separable space 局部可分空间locally soluble group 局部可解群locally trivial embedding 局部平凡嵌入locally unbiased test 局部无偏检验locally uniformizing parameter 局部单值化参数locally uniformly convergent sequence 局部一致收敛序列locally zero function 局部零函数location 存储单元location parameter 位置参数location principle 介值locus 轨迹log curve 对数曲线log log paper 重对数坐标纸logarithm 对数logarithm table 对数表logarithm to the base 10 常用对数logarithm to the basese 讷代对数logarithmic 对数的logarithmic branchpoint 对数分歧点logarithmic convexity 对数凸性logarithmic coordinates 对数座标logarithmic curve 对数曲线logarithmic decrement 对数衰减logarithmic derivative 对数导数logarithmic distribution 对数分布logarithmic equation 对数方程logarithmic function 对数函数logarithmic integral 对数积分logarithmic normal distribution 对数正态分布logarithmic paper 对数坐标纸logarithmic potential 对数位势logarithmic residue 对数残数logarithmic scale 对数尺度logarithmic series 对数级数logarithmic singularity 对数奇点logarithmic slide rule 对数计算尺logarithmic spiral 对数螺线logarithmic table 对数表logic 逻辑logic calculus 逻辑学logic of pocket calculator 袖珍计算机的逻辑logic of relations 关系逻辑logic product 合取logic sum 析取logical 逻辑的logical circuit 逻辑电路logical comparison 逻辑比较logical diagram 逻辑图logical element 逻辑元件logical operation 逻辑运算logical paradox 逻辑悖论logical shift 逻辑移位logical symbol 逻辑符号logical variable 逻辑变量logically true proposition 逻辑地真命题logicism 逻辑皱logico mathematical model 逻辑数学模型logistic 暹辑斯谛logistic curve 逻辑斯谛曲线logistic system 形式系统lognormal distribution 对数正态分布longitude 经度longitudinal 经度的longitudinal axis 纵向轴loop 闭路loop of a curve 曲线的闭路loop space 圈空间lopology of the uniformity 一致拓扑lorentz group 洛伦茨群thermocouple pyrometer 热电偶高温计lorentz transformation 洛伦茨变换loss 损失loss function 损失函数loss system 损失系统lot 一批lot tolerance fraction defective 批容许废品率low of cosines 余弦定律lower approximate limit 下近似极限lower bound 下界lower central series 降中心列lower class 下类lower control limit 下控制界限lower darboux integral 达布下积分lower darboux sum 达布下和lower density 下密度lower dini derivative 狄尼下导数lower envelope 下包络lower half plane 下半平面lower integral 下积分lower limit 下限lower limit of integration 积分的下极限lower measure 内测度lower order 低位lower pure value 下方值lower quartile 第一四分位数lower semi modular lattice 下半模格lower semicontinuity 下半连续性lower semicontinuous decomposition 下半连续分解lower semicontinuous function 下半连续函数lower semilattice 下半格lower sum 下和lower triangular matrix 下三角形矩阵lower value 下方值lower variation 负变差lowest common denominator 最小公分母lowest common multiple 最低公倍数lowest term 最低项loxodrome 斜驶曲线loxodromic matrix 斜驶矩阵loxodromic spiral 斜驶曲线loxodromic transformation 斜驶变换lozenge diagram 菱形图形lune 弓形。
数学专业英语词汇（T）_数学物理英语词汇
t distribution 学生t分布t number t数t statistic t统计量t test t检验t1topological space t1拓扑空间t2topological space t2拓扑空间t3topological space 分离空间t4topological space 正则拓扑空间t5 topological space 正规空间t6topological space 遗传正规空间table 表table of random numbers 随机数表table of sines 正弦表table of square roots 平方根表table of values 值表tabular 表的tabular value 表值tabulate 制表tabulation 造表tabulator 制表机tacnode 互切点tag 标签tame 驯顺嵌入tame distribution 缓增广义函数tamely imbedded 驯顺嵌入tangency 接触tangent 正切tangent bundle 切丛tangent cone 切线锥面tangent curve 正切曲线tangent function 正切tangent line 切线tangent of an angle 角的正切tangent plane 切平面tangent plane method 切面法tangent surface 切曲面tangent vector 切向量tangent vector field 切向量场tangent vector space 切向量空间tangential approximation 切线逼近tangential component 切线分量tangential curve 正切曲线tangential equation 切线方程tangential stress 切向应力tangents method 切线法tape 纸带tape inscription 纸带记录tariff 税tautology 重言taylor circle 泰勒圆taylor expansion 泰勒展开taylor formula 泰勒公式taylor series 泰勒级数technics 技术technique 技术telegraph equation 电报方程teleparallelism 绝对平行性temperature 温度tempered distribution 缓增广义函数tend 倾向tendency 瞧tension 张力tensor 张量tensor algebra 张量代数tensor analysis 张量分析tensor bundle 张量丛tensor calculus 张量演算法tensor density 张量密度tensor differential equation 张量微分方程tensor field 张量场tensor form 张量形式tensor form of the first kind 第一张量形式tensor function 张量函数tensor of torsion 挠率张量tensor product 张量乘积tensor product functor 张量乘积函子tensor representation 张量表示tensor space 张量空间tensor subspace 张量子空间tensor surface 张量曲面tensorial multiplication 张量乘法term 项term of higher degree 高次项term of higher order 高次项term of series 级数的项terminability 有限性terminable 有限的terminal decision 最后判决terminal edge 终结边terminal point 终点terminal unit 级端设备terminal vertex 悬挂点terminate 终止terminating chain 可终止的链terminating continued fraction 有尽连分数terminating decimal 有尽小数termination 终止terminology 专门名词termwise 逐项的termwise addition 逐项加法termwise differentiation 逐项微分termwise integration 逐项积分ternary 三元的ternary connective 三元联结ternary form 三元形式ternary notation 三进制记数法ternary number system 三进制数系ternary operation 三项运算ternary relation 三项关系ternary representation og numbers 三进制记数法tertiary obstruction 第三障碍tesseral harmonic 田形函数tesseral legendre function 田形函数test 检验test for additivity 加性检验test for uniform convergence 一致收敛检验test function 测试函数test of dispersion 色散检验test of goodness of fit 拟合优度检验test of hypothesis 假设检验test of independence 独立性检验test of linearity 线性检验test of normality 正规性检验test point 测试点test routine 检验程序test statistic 检验统计量tetracyclic coordinates 四圆坐标tetrad 四元组tetragon 四角形tetragonal 正方的tetrahedral 四面角tetrahedral angle 四面角tetrahedral co ordinates 四面坐标tetrahedral group 四面体群tetrahedral surface 四面曲面tetrahedroid 四面体tetrahedron 四面形tetrahedron equation 四面体方程theorem 定理theorem for damping 阻尼定理theorem of alternative 择一定理theorem of identity for power series 幂级数的一致定理theorem of implicit functions 隐函数定理theorem of mean value 平均值定理theorem of principal axes 轴定理theorem of residues 残数定理theorem of riemann roch type 黎曼洛赫型定理theorem on embedding 嵌入定理theorems for limits 极限定理theoretical curve 理论曲线theoretical model 理论模型theory of automata 自动机理论theory of cardinals 基数论theory of complex multiplication 复数乘法论theory of complexity of computations 计算的复杂性理论theory of correlation 相关论theory of differential equations 微分方程论theory of dimensions 维数论theory of elementary divisors 初等因子理论theory of elementary particles 基本粒子论theory of equations 方程论theory of errors 误差论theory of estimation 估计论theory of functions 函数论theory of games 对策论theory of hyperbolic functions 双曲函数论theory of judgment 判断论theory of numbers 数论theory of ordinals 序数论theory of perturbations 摄动理论theory of probability 概率论theory of proportions 比例论theory of relativity 相对论theory of reliability 可靠性理论theory of representations 表示论theory of sets 集论theory of sheaves 层理论theory of singularities 奇点理论theory of testing 检验论theory of time series 时间序列论theory of transversals 横断线论theory of types 类型论thermal 热的thermodynamic 热力学的thermodynamics 热力学theta function 函数theta series 级数thick 厚的thickness 厚度thin 薄的thin set 薄集third boundary condition 第三边界条件third boundary value problem 第三边界值问题third fundamental form 第三基本形式third isomorphism theorem 第三同构定理third proportional 比例第三项third root 立方根thom class 汤姆类thom complex 汤姆复形three body problem 三体问题three dimensional 三维的three dimensional space 三维空间three dimensional torus 三维环面three eighths rule 八分之三法three faced 三面的three figur 三位的three place 三位的three point problem 三点问题three series theorem 三级数定理three sheeted 三叶的three sided 三面的three sigma rule 三规则three termed 三项的three valued 三值的three valued logic 三值逻辑three valued logic calculus 三值逻辑学threshold logic 阈逻辑time interval 时程time lag 时滞time series analysis 时序分析timesharing 分时toeplitz matrix 托普利兹矩阵tolerance 容许tolerance distribution 容许分布tolerance estimation 容许估计tolerance factor 容许因子tolerance level 耐受水平tolerance limit 容许界限tolerance region 容许区域top digit 最高位数字topological 拓扑的topological abelian group 拓扑阿贝耳群topological algebra 拓扑代数topological cell 拓扑胞腔topological circle 拓扑圆topological completeness 拓扑完备性topological complex 拓扑复形topological convergence 拓扑收敛topological dimension 拓扑维topological direct sum 拓扑直和topological dynamics 拓扑动力学topological embedding 拓扑嵌入topological field 拓扑域topological group 拓扑群topological homeomorphism 拓扑同胚topological index 拓扑指数topological invariant 拓扑不变量topological limit 拓扑极限topological linear space 拓扑线性空间topological manifold 拓扑廖topological mapping 拓扑同胚topological pair 拓扑偶topological polyhedron 曲多面体topological product 拓扑积topological residue class ring 拓扑剩余类环topological ring 拓扑环topological simplex 拓扑单形topological skew field 拓扑非交换域topological space 拓扑空间topological sphere 拓扑球面topological structure 拓扑结构topological sum 拓扑和topological type 拓扑型topologically complete set 拓扑完备集topologically complete space 拓扑完备空间topologically equivalent space 拓扑等价空间topologically nilpotent element 拓扑幂零元topologically ringed space 拓扑环式空间topologically solvable group 拓扑可解群topologico differential invariant 拓扑微分不变式topologize 拓扑化topology 拓扑topology of bounded convergence 有界收敛拓扑topology of compact convergence 紧收敛拓扑topology of uniform convergence 一致收敛拓扑toroid 超环面toroidal coordinates 圆环坐标toroidal function 圆环函数torque 转矩torsion 挠率torsion coefficient 挠系数torsion form 挠率形式torsion free group 非挠群torsion group 挠群torsion module 挠模torsion of a curve 曲线的挠率torsion product 挠积torsion subgroup 挠子群torsion tensor 挠率张量torsion vector 挠向量torsionfree connection 非挠联络torsionfree module 无挠模torsionfree ring 无挠环torus 环面torus function 圆环函数torus group 环面群torusknot 环面纽结total 总和total correlation 全相关total curvature 全曲率total degree 全次数total differential 全微分total differential equation 全微分方程total error 全误差total graph 全图total image 全象total inspection 全检查total instability 全不稳定性total inverse image 全逆象total matrix algebra 全阵环total matrix ring 全阵环total order 全序total predicate 全谓词total probability 总概率total probability formula 总概率公式total regression 总回归total relation 通用关系total space 全空间total stability 全稳定性total step iteration 整步迭代法total step method 整步迭代法total stiefel whitney class 全斯蒂费尔惠特尼类total subset 全子集total sum 总和total variation 全变差totally bounded set 准紧集totally bounded space 准紧空间totally differentiable 完全可微分的totally differentiable function 完全可微函数totally disconnected 完全不连通的totally disconnected graph 完全不连通图totally disconnected groupoid 完全不连通广群totally disconnected set 完全不连通集totally disconnected space 完全不连通空间totally geodesic 全测地的totally nonnegative matrix 全非负矩阵totally ordered group 全有序群totally ordered set 线性有序集totally positive 全正的totally positive matrix 全正矩阵totally quasi ordered set 完全拟有序集totally real field 全实域totally reflexive relation 完全自反关系totally regular matrix method 完全正则矩阵法totally singular subspace 全奇异子空间totally symmetric loop 完全对称圈totally symmetric quasigroup 完全对称拟群touch 相切tournament 竞赛图trace 迹trace form 迹型trace function 迹函数trace of dyadic 并向量的迹trace of matrix 矩阵的迹trace of tensor 张量的迹tracing point 追迹点track 轨迹tractrix 曳物线trajectory 轨道transcendence 超越性transcendence basis 超越基transcendence degree 超越次数transcendency 超越性transcendental element 超越元素transcendental equation 超越方程transcendental function 超越函数transcendental integral function 超越整函数transcendental number 超越数transcendental singularity 超越奇点transcendental surface 超越曲面transfer 转移transfer function 转移函数transfinite 超限的transfinite diameter 超限直径transfinite induction 超限归纳法transfinite number 超限序数transfinite ordinal 超限序数transform 变换transformation 变换transformation equation 变换方程transformation factor 变换因子transformation formulas of the coordinates 坐标的变换公式transformation function 变换函数transformation group 变换群transformation of air mass 气团变性transformation of coordinates 坐标的变换transformation of parameter 参数变换transformation of state 状态变换transformation of the variable 变量的更换transformation rules 变换规则transformation theory 变换论transformation to principal axes 轴变换transgression 超渡transient response 瞬态响应transient stability 瞬态稳定性transient state 瞬态transient time 过渡时间transition function 转移函数transition graph 转换图transition matrix 转移矩阵transition probability 转移函数transitive closure 传递闭包transitive graph 传递图transitive group of motions 可迁运动群transitive law 可迁律transitive permutation group 可迁置换群transitive relation 传递关系transitive set 可递集transitivity 可递性transitivity laws 可迁律translatable design 可旋转试验设计translate 转移translation 平移translation curve 平移曲线translation group 平移群translation invariant 平移不变的translation invariant metric 平移不变度量translation number 殆周期translation of axes 坐标轴的平移translation operator 平移算子translation surface 平移曲面translation symmetry 平移对称translation theorem 平移定理transmission channel 传输通道transmission ratio 传输比transport problem 运输问题transportation algorithm 运输算法transportation matrix 运输矩阵transportation network 运输网络transportation problem 运输问题transpose 转置transposed inverse matrix 转置逆矩阵transposed kernel 转置核transposed map 转置映射transposed matrix 转置阵transposition 对换transversal 横截矩阵胚transversal curve 横截曲线transversal field 模截场transversal lines 截线transversality 横截性transversality condition 横截条件transverse axis 横截轴transverse surface 横截曲面trapezium 不规则四边形trapezoid 不规则四边形trapezoid formula 梯形公式trapezoid method 梯形公式traveling salesman problem 转播塞尔斯曼问题tree 树trefoil 三叶形trefoil knot 三叶形纽结trend 瞧trend line 瞧直线triad 三元组trial 试验triangle 三角形triangle axiom 三角形公理triangle condition 三角形公理triangle inequality 三角形公理triangulable 可三角剖分的triangular decomposition 三角分解triangular form 三角型triangular matrix 三角形矩阵triangular number 三角数triangular prism 三棱柱triangular pyramid 四面形triangular surface 三角曲面triangulate 分成三角形triangulation 三角剖分triaxial 三轴的triaxial ellipsoid 三维椭面trichotomy 三分法trident of newton 牛顿三叉线tridiagonal matrix 三对角线矩阵tridimensional 三维的trigammafunction 三函数trigonometric 三角的trigonometric approximation polynomial 三角近似多项式trigonometric equation 三角方程trigonometric function 三角函数trigonometric moment problem 三角矩问题trigonometric polynomial 三角多项式trigonometric series 三角级数trigonometrical interpolation 三角内插法trigonometry 三角学trihedral 三面形的trihedral angle 三面角trihedron 三面体trilateral 三边的trilinear 三线的trilinear coordinates 三线坐标trilinear form 三线性形式trinomial 三项式;三项式的trinomial equation 三项方程triplanar point 三切面重点 ?triple 三元组triple curve 三重曲线triple integral 三重积分triple point 三重点triple product 纯量三重积triple product of vectors 向量三重积triple root 三重根triple series 三重级数triple tangent 三重切线triply orthogonal system 三重正交系triply tangent 三重切线的trirectangular spherical triangle 三直角球面三角形trisecant 三度割线trisect 把...三等分trisection 三等分trisection of an angle 角的三等分trisectrix 三等分角线trivalent map 三价地图trivector 三向量trivial 平凡的trivial character 单位特贞trivial cohomology functor 平凡上同弹子trivial extension 平凡扩张trivial fibre bundle 平凡纤维丛trivial graph 平凡图trivial homogeneous ideal 平凡齐次理想trivial knot 平凡纽结trivial solution 平凡解trivial subset 平凡子集trivial topology 密着拓扑trivial valuation 平凡赋值triviality 平凡性trivialization 平凡化trochoid 摆线trochoidal 余摆线的trochoidal curve 摆线true error 真误差true formula 真公式true proposition 真命题true sign 直符号true value 真值truncated cone 截锥truncated cylinder 截柱truncated distribution 截尾分布truncated pyramid 截棱锥truncated sample 截样本truncated sequence 截序列truncation 舍位truncation error 舍位误差truncation point 舍位点truth 真值truth function 真值函项truth matrix 真值表truth set 真值集合truth symbol 真符号truth table 真值表truthvalue 真值tube 管tubular knot 管状纽结tubular neighborhood 管状邻域tubular surface 管状曲面turbulence 湍流turbulent 湍聊turing computability 图灵机可计算性turing computable 图灵机可计算的turing machine 图录机turn 转向turning point 转向点twice 再次twice differentiable function 二次可微函数twin primes 素数对twisted curve 空间曲线twisted torus 挠环面two address 二地址的two address code 二地址代码two address instruction 二地址指令two body problem 二体问题two decision problem 二判定问题two digit 二位的two dimensional 二维的two dimensional laplace transformation 二重拉普拉斯变换two dimensional normal distribution 二元正态分布two dimensional quadric 二维二次曲面two dimensional vector space 二维向量空间two fold transitive group 双重可迁群two person game 两人对策two person zero sum game 二人零和对策two phase sampling 二相抽样法two place 二位的two point distribution 二点分布two point form 两点式two sample method 二样本法two sample problem 二样本问题two sample test 双样本检验two sheet 双叶的two sided condition 双边条件two sided decomposition 双边分解two sided divisor 双边因子two sided ideal 双边理想two sided inverse 双边逆元two sided module 双边模two sided neighborhood 双侧邻域two sided surface 双侧曲面two sided test 双侧检定two stage sampling 两阶段抽样法two termed expression 二项式two valued logic 二值逻辑two valued measure 二值测度two variable matrix 双变量矩阵two way array 二向分类two way classification 二向分类twopoint boundary value problem 两点边值问题type 型type problem 类型问题typenumber 型数typical mean 典型平均。