Left-definite boundary conditions of Sturm-Liouville problems when the interval shrinks to a poi
PDA TR40气体无菌过滤
INTRODUCTION/SCOPE STATEMENT ...................................................................................................................... 7 HISTORICAL BACKGROUND ....................................................................................................................................... 7 HOW GAS FILTERS WORK ........................................................................................................................................... 7 Retention of Smaller Particles .............................................................................................................................................. 7 Inertial Impaction ..........................................................................................................................................
数学英语如何用英语表达数学术语
absolute value 绝对值acceptable region 接受域additivity 可加性alternative hypothesis 对立假设analysis of covariance 协方差分析analysis of variance 方差分析arithmetic mean 算术平均值association 相关性assumption checking 假设检验availability 有效度band 带宽bar chart 条形图beta-distribution 贝塔分布between groups 组间的binomial distribution 二项分布binomial test 二项检验center of gravity 重心central tendency 中心趋势hi-square distribution 卡方分布chi-square test 卡方检验classify 分类cluster analysis 聚类分析coefficient 系数coefficient of correlation 相关系数collinearity 共线性components 构成，分量compound 复合的confidence interval 置信区间consistency 一致性continuous variable 连续变量control charts 控制图correlation 相关covariance 协方差covariance matrix 协方差矩阵critical point 临界点critical value 临界值cross tab 列联表cubic term 三次项cumulative distribution function 累加分布函数curve estimation 曲线估计default 默认的deleted residual 剔除残差density function 密度函数dependent variable 因变量design of experiment 试验设计df.(degree of freedom) 自由度diagnostic 诊断discrete variable 离散变量discriminant function 判别函数discriminatory analysis 判别分析D-optimal design D-优化设计effects of interaction 交互效应eigenvalue 特征值equal size 等含量estimation of parameters 参数估计estimations 估计量exact value 精确值expected value 期望值exponential指数的exponential distribution 指数分布extreme value 极值factor analysis 因子分析factor score 因子得分factorial designs 析因设计factorial experiment 析因试验fitted line 拟合线fitted value 拟合值fixed variable 固定变量fractional factorial design 部分析因设计F-test F检验full factorial design 完全析因设计gamma distribution 伽玛分布geometric mean 几何均值harmonic mean 调和均值heterogeneity 不齐性histogram 直方图homogeneity 齐性homogeneity of variance 方差齐性hypothesis test 假设检验independence独立independent variable 自变量independent-samples 独立样本index of correlation 相关指数interclass correlation 组内相关interval estimate 区间估计inverse 倒数的iterate 迭代kurtosis 峰度large sample problem 大样本问题least-significant difference 最小显著差数least-square estimation 最小二乘估计least-square method 最小二乘法level of significance 显著性水平leverage value 中心化杠杆值life test 寿命试验likelihood function 似然函数likelihood ratio test 似然比检验linear estimator 线性估计linear model 线性模型linear regression 线性回归linear relation 线性关系linear term 线性项logarithmic 对数的logarithms 对数lost function 损失函数main effect 主效应matrix 矩阵maximum 最大值maximum likelihood estimation 极大似然估计mean squared deviation(MSD) 均方差mean sum of square 均方和measure 衡量media 中位数M-estimator M估计minimum 最小值missing values 缺失值mixed model 混合模型mode 众数Monte Carle method 蒙特卡罗法moving average移动平均值multicollinearity 多元共线性multiple comparison 多重比较multiple correlation 多重相关multiple correlation coefficient 复相关系数multiple correlation coefficient 多元相关系数multiple regression analysis 多元回归分析multiple regression equation 多元回归方程multiple response 多响应multivariate analysis 多元分析negative nonadditively 不可加性nonlinear 非线性nonlinear regression 非线性回归noparametric tests 非参数检验normal distribution 正态分布null hypothesis 零假设number of cases 个案数one-sample 单样本one-tailed test 单侧检验one-way ANOV A 单向方差分析one-way classification 单向分类optimal 优化的optimum allocation 最优配制order statistics 次序统计量origin 原点orthogonal 正交的outliers 异常值paired observations 成对观测数据paired-sample 成对样本parameter estimation 参数估计partial correlation 偏相关partial correlation coefficient 偏相关系数partial regression coefficient 偏回归系percentiles 百分位数pie chart 饼图point estimate 点估计poisson distribution 泊松分布polynomial curve 多项式曲线polynomial regression 多项式回归polynomials 多项式positive relationship 正相关power 幂P-P plot P-P概率图predicted value 预测值prediction intervals 预测区间principal component analysis 主成分分析proability 概率probability density function 概率密度函数quadratic 二次的Q-Q plot Q-Q概率图quadratic term 二次项quality control 质量控制quantitative 数量的，度量quartiles 四分位数random sampling 随机取样random seed 随机数种子random variable 随机变量randomization 随机化range 极差rank correlation 秩相关rank statistic 秩统计量regression analysis 回归分析regression coefficient 回归系数regression line 回归线rejection region 拒绝域residual 残差residual sum of squares 剩余平方和risk function 风险函数robustness 稳健性root mean square 标准差row 行run test 游程检验sample size 样本容量sample space 样本空间sampling 取样sampling inspection 抽样检验scatter chart 散点图S-curve S形曲线sets 集合sign test 符号检验significance level 显著性水平significance testing 显著性检验significant digits 有效数字skewed distribution 偏态分布small sample problem 小样本问题sort 排序sources of variation 方差来源ion 标准离差standard error of mean 均值的标准误差statistical quality control 统计质量控制std. residual 标准残差stepwise regression analysis 逐步回归strong assumption 强假设stud. deleted residual 学生化剔除残差stud. residual 学生化残差subsamples 次级样本sufficient statistic 充分统计量sum of squares 平方和t-distribution t分布test criterion 检验判据test for linearity 线性检验test of goodness of fit 拟合优度检验test of homogeneity 齐性检验test of independence 独立性检验test rules 检验法则test statistics 检验统计量testing function 检验函数time series 时间序列tolerance limits 容许限trimmed mean 截尾均值true value 真值t-test t检验two-tailed test 双侧检验unbiased estimation 无偏估计unbiasedness 无偏性uniform distribution 均匀分布value of estimator 估计值variance 方差variance components 方差分量variance ratio 方差比weighted average 加权平均值within groups 组内的Z score Z分数active constraint 活动约束active set method 活动集法analytic gradient 解析梯度approximate 近似arbitrary 强制性的argument 变量attainment factor 达到因子bandwidth 带宽be equivalent to 等价于best-fit 最佳拟合coefficient 系数complex-value 复数值component 分量constrained 有约束的constraint function 约束函数converge 收敛cubic polynomial interpolation method 三次多项式插值法curve-fitting 曲线拟合data-fitting 数据拟diagonal 对角的direct search method 直接搜索法direction of search 搜索方向eigenvalue 特征值empty matrix 空矩阵exceeded 溢出的feasible solution 可行解finite-difference 有限差分first-order 一阶Gauss-Newton method 高斯-牛顿法goal attainment problem 目标达到问题gradient method 梯度法handle 句柄Hessian matrix 海色矩阵independent variables 独立变量inequality 不等式infeasibility 不可行性initial feasible solution 初始可行解initialize 初始化invoke 激活iteration 迭代Jacobian 雅可比矩阵Lagrange multiplier 拉格朗日乘子large-scale 大型的least square 最小二乘least squares sense 最小二乘意义上的Levenberg-Marquardt method 列文伯格-马夸尔特法line search 一维搜索linear equality constraints 线性等式约束linear programming problem 线性规划问题local solution 局部解medium-scale 中型的mixed quadratic and cubic polynomial interpolation and extrapolationmethod 混合二次、三次多项式内插、外插法multi objective 多目标的norm 范数observed data 测量数据optimization routine 优化过程optimizer 求解器over-determined system 超定系统partial derivatives 偏导数polynomial interpolation method 多项式插值法quadrati二次的quadratic interpolation method 二次内插法quadratic programming 二次规划real-value 实数值residuals 残差robust 稳健的robustness 稳健性，鲁棒性scalar 标量semi-infinitely problem 半无限问题Sequential Quadratic Programming method 序列二次规划法simplex search method 单纯形法sparse matrix 稀疏矩阵sparsity pattern 稀疏模式sparsity structure 稀疏结构starting point 初始点step length 步长subspace trust region method 子空间置信域法symmetric matrix 对称矩阵termination message 终止信息termination tolerance 终止容限the exit condition 退出条件the method of steepest descent 最速下降法transpose 转置unconstrained 无约束的under-determined system 负定系统weighting matrix 加权矩阵approximation 逼近a spline in b-form/b-spline b样条 a spline of polynomial piece /ppform spline 分段多项式样条bivariate spline function 二元样条函数break/breaks 断点coefficient/coefficients 系数cubic interpolation 三次插值/三次内插cubic polynomial 三次多项式cubic smoothing spline 三次平滑样条cubic spline 三次样条cubic spline interpolation 三次样条插值/三次样条内插curve 曲线degree of freedom 自由度end conditions 约束条件input argument 输入参数interpolation 插值/内插interval 取值区间knot/knots 节点least-squares approximation 最小二乘拟合multiplicity 重次multivariate function 多元函数optional argument 可选参数output argument 输出参数point/points 数据点rational spline 有理样条rounding error 舍入误差（相对误差）sequence 数列（数组spline approximation 样条逼近/样条拟合spline function 样条函数spline curve 样条曲线spline interpolation 样条插值/样条内插spline surface 样条曲面smoothing spline 平滑样条tolerance 允许精度univariate function 一元函数absolute error 绝对误差absolute tolerance 绝对容限adaptive mesh 适应性网格boundary condition 边界条件contour plot 等值线图coordinate 坐标系decomposed geometry matrix 分解几何矩阵diagonal matrix 对角矩阵Dirichlet boundary conditions 边界条件eigenvalue 特征值elliptic 椭圆形的error estimate 误差估计exact solution 精确解generalized Neumann boundary condition 推广的Neumann边界条件geometry description matrix 几何描述矩阵geometry matrix 几何矩阵graphical user interface（GUI）图形用户界面hyperbolic 双曲线的initial mesh 初始网格jiggle 微调Lagrange multipliers 拉格朗日乘子Laplace equation 拉普拉斯方程linear interpolation 线性插值machine precision 机器精度mixed boundary condition 混合边界条件Neuman boundary condition Neuman边界条件node point 节点nonlinear solver 非线性求解器normal vector 法向量Parabolic 抛物线型的partial differential equation 偏微分方程plane strain 平面应变plane stress 平面应力Poisson's equation 泊松方程polygon 多边形positive definite 正定refined triangular mesh 加密的三角形网格relative tolerance 相对容限relative tolerance 相对容限residual norm 残差范数singular 奇异的postulate假定, 基本条件, 基本原理,要求, 假定,要求conic, conical圆锥的；圆锥形的ellipse椭圆, 椭圆形ellipt hyperbolic 双曲线的parabolic用寓言表达的: 抛物线的，像抛物线的algebraic代数的, 关于代数学的mineralogy 矿物学axiom公理collinear在同一直线上的同线的convex 凸出的；凸面的triangle三角形, 三人一组, 三角关系parallelogram平行四边形straight angle平角right angle 直角acute angle锐角obtuse angle钝角reflex angle优角rectilinear直线的；由直线组成的；循直线进行的isosceles triangle等腰三角形equilateral triangle等边三角形right triangle n. 直角三角形obtuse triangle钝角三角形acute triangle锐角三角形equiangular triangle正三角形,等角三角形hypotenuse（直角三角形的）斜边infinitesimal 无穷小的, 极小的, 无限小的calculus 微积分学, 结石inscribe 记下polygon多角形, 多边形curvilinear曲线的, 由曲线组成的intuition 直觉, 直觉的知识integral积分, 完整, 部分defective有缺陷的, (智商或行为有)欠缺的differential coefficient 微分系数irrational numbers无理数domain 定义域contradiction 矛盾continuous variable 连续变量;［连续变数］variation 变分, 变化independent variable 自变量dependent variable 应变量rectangular coordinate 直角坐标abscissa〈数〉横坐标ordinate纵线, 纵座标differential 微分的,微分(differentiation)Integral 积分, 完整, 部分(integration) trigonometry 三角法exponential 指数的, 幂数的logarithm 对数derivative导数；微商tangent 切线正切definite integral 定积分culminate 达到顶点differential equation 微分方程extreme value 极值multiple integral 多重积分functional analysis 泛函分析cardinal number 基数（如：1, 2, 3, ... 有别于序数）denumerable可数的aggregate 合计, 总计, 集合体，合计的, 集合的, 聚合的，聚集, 集合, 合计purport主旨，声称superior 长者, 高手, 上级，较高的, 上级的, 上好的, 出众的, 高傲的cumbersome 讨厌的, 麻烦的, 笨重的drastically 激烈地, 彻底地conservation 守衡律quadrature求积, 求积分interpolation插值extrapolation外推法, 推断internal point 内点generalized solution 广义解hydrodynamics 流体力学，水动力学divergence 发散（性），梯度，发散integro-interpolation method 积分插值法Variational method 变分方法comparatively 比较地, 相当地self-adjoint (nonself-adjoint) 自治的，自伴的，自共轭的finite element method 有限元法spline approximation 样条逼近Particles-in-the-Cell 网格质点法herald 使者, 传令官, 通报者, 先驱, 预兆，预报, 宣布, 传达, 欢呼advection水平对流fluctuation波动, 起伏mean-square 均方dispersion离差, 差量nterpolation 插值divisible可分的dice, die 骰子pitfall 缺陷celestial天上的macroscopic肉眼可见的, 巨观的classical field theory 经典场理论rigit 刚硬的, 刚性的, 严格的quantum量, 额, [物] 量子, 量子论inception 起初, 获得学位pertain 适合, 属于encompass 包围, 环绕, 包含或包括某事物ingredient 成分, 因素acquainted有知识的, 知晓的synonymous同义的configuration 构造, 结构, 配置, 外形inertia 惯性, 惯量attribute 特性momentum动量designate 指明projectile 射弹，发射的ballistics 弹道学, 发射学intractable 难处理的furnish 供应, 提供, 装备, 布置torque n. 扭矩, 转矩moment 力矩的dissipation 消散, 分散, 挥霍, 浪费, 消遣, 放荡, 狂饮constitutive构成的, 制定的continuum mechanics 连续介质力学superposition重叠, 重合, 叠合reckon 计算, 总计, 估计, 猜想，数, 计算, 估计, 依赖, 料想strength 强度load 载荷empirical 以经验为依据的insofar 在……范围cohesive 内聚性的stiffness 硬度furnish 供给turbulent 湍流laminar 层流isothermal 等温isotropic 各向同性eddy 旋涡viscosity 粘性、粘度adiabatic 绝热的reversible 可逆的isentropic 等熵的stream tube 流管tangential 切线的incompressible 不可压缩的similitude 相似性hydraulic 水力的,水力学的spillway (河或水坝的)放水道,泄洪道prototype 原型,样板vibratory 振动的,摆动的propagation 传播acoustic 听觉的,声学的damp 阻尼,衰减restore 复职,归还neutral 平衡exciting force 激励力resonant共振的,谐振的stiffness 刚度,刚性magnitude 数值,大小substantially实质上的perturb 干扰,扰乱Fourier series 傅里叶级数shredder 切菜器metropolitan 大都市的at-grade 在同一水平面上elevated 高架的guide way 导轨rigid body 刚体medium 介质aging 老化polymeric聚合(物)的consolidate 把…联合为一体,统一radically 根本地,本质上deliberate 从容不迫的,深思熟虑Attribute赋予medieval 中世纪的etch 蚀刻,蚀镂fingernail 指甲bar chart 直方图joystick 游戏杆trial-error 试制, 试生产junction n. 连接, 接合, 交叉点, 汇合处contrive v. 发明, 设计, 图谋snooker (=snooker pool)彩色台球, 桌球****公理axiom 命题proposition 被加数augend , summand 加数addend 被减数minuend 减数subtrahend 差remainder 被乘数multiplicand, faciend 乘数multiplicator 积product 被除数dividend 除数divisor 商quotient 大于等于is equal or greater than 小于等于is equal or lesser than 运算符operator 算术平均数geometric mean n个数之积的n次方根（reciprocal）x的倒数为1/x 有理数rational number 无理数irrational number 整数integer小数点decimal point分数fraction 分子numerator 分母denominator 比ratio 十进制decimal system 二进制binary system 十六进制hexadecimal system 权weight, significance 截尾truncation 四舍五入round 下舍入round down 上舍入round up 有效数字significant digit 无效数字insignificant digit 代数algebra 单项式monomial 多项式polynomial, multinomial 系数coefficient 未知数unknown, x-factor, y-factor, z-factor 等式，方程式equation 一次方程simple equation 二次方程quadratic equation 三次方程cubic equation 四次方程quartic equation 阶乘factorial 对数logarithm 指数，幂exponent 乘方power 二次方，平方square 三次方，立方cube 四次方the power of four, the fourth power n次方the power of n, the nth power 开方evolution, extraction 二次方根，平方根square root 三次方根，立方根cube root 四次方根the root of four, the fourth root n次方根the root of n, the nth root 坐标系coordinates 坐标轴x-axis, y-axis, z-axis 横坐标x-coordinate 纵坐标y-coordinate 原点origin 象限quadrant 截距(有正负之分)intercede （方程的）解solution 线段segment 射线radial 平行parallel 相交intersect 角度degree 弧度radian 钝角obtuse angle 平角straight angle 周角perigon 底base 锐角三角形acute triangle 直角边leg 斜边hypotenuse 勾股定理Pythagorean theorem 钝角三角形obtuse triangle 不等边三角形scalene triangle 等腰三角形isosceles triangle 等边三角形equilateral triangle 四边形quadrilateral 平行四边形parallelogram 周长perimeter 全等congruent 三角trigonometry 正弦sine 余弦cosine 正切tangent 余切cotangent 正割secant 余割cosecant 反正弦arc sine 反余弦arc cosine 反正切arc tangent 反余切arc cotangent 反正割arc secant 反余割arc cosecant 集合aggregate 空集void 子集subset 交集intersection 并集union 补集complement 映射mapping 定义域domain, field of definition 值域range 单调性monotonicity 图象image 数列，级数series 导数derivative 无穷小infinitesimal 复数complex number 矩阵matrix 行列式determinant 半圆semicircle 扇形sector 环ring 椭圆ellipse 圆周circumference 轨迹locus, loca(pl.) 平行六面体parallelepiped 立方体cube 七面体heptahedron 八面体octahedron 九面体enneahedron 十面体decahedron 十一面体hendecahedron 十二面体dodecahedron 二十面体icosahedron 多面体polyhedron 四面体tetrahedron 五面体pentahedron 六面体hexahedron 菱形rhomb, rhombus, rhombi(pl.), diamond 正方形square 梯形trapezoid 直角梯形right trapezoid 等腰梯形isosceles trapezoid 五边形pentagon 六边形hexagon 七边形heptagon 八边形octagon 九边形enneagon 十边形decagon 十一边形hendecagon 十二边形dodecagon 多边形polygon 正多边形equilateral polygon 相位phase 振幅amplitude 内心incentre(BrE), incenter(AmE) 外心excentre(BrE), excenter(AmE) 旁心escentre(BrE), escenter(AmE) 垂心orthocentre(BrE), orthocenter(AmE) 重心barycentre(BrE), barycenter(AmE) 内切圆inscribed circle 外切圆circumcircle 方差variance 标准差root-mean-square deviation, standard deviation 百分点percentage 百分位数percentile 排列permutation 分布distribution 正态分布normal distribution 非正态分布abnormal distribution 条形统计图bar graph 柱形统计图histogram 折线统计图broken line graph 曲线统计图curve diagram 扇形统计图pie diagram**** mutually disjoint events 互不相交事件mutually disjoint subsets 互不相交子集mutually independent events 互相独立事件myria 万myriad 无数的multiplicity 重数mid square method 平方取中法midperpendicular 中垂线minor 子式minor arc 劣弧mixed number 带分数regular convergence 正则收敛relative discriminant 相对判别式relative error 相对误差relative extremum 局部极值ricci equatoin 李奇恒等式ricci identity 李奇恒等式riemann function 黎曼函数riemann integral 黎曼积分right direct product 右直积right endpoint 右端点right inner product 右内积ring of integers 整数环ring of matrices 矩阵环root mean square error 均方根差root of equation 方程式的根rotation of axes 坐标轴的旋转rotation of co ordinate system 坐标轴的旋转round off error 舍入规则round up error 舍入规则runge kutta method 龙格库塔法n disk n维圆盘nth member 第n项nth partial quotient 第n偏商nth power operation n次幂运算nth root n次根nth term 第n项n times continuously differentiable n次连续可微的natural injection 自然单射natural isomorphism 自然等necessary and sufficient conditions 必要充分的条件necessary and sufficient statistic 必要充分统计量neutral element 零元素neutral line 中线nonhomogeneous linear boundary value problem 非齐次线性边值问题nonhomogeneous linear differential equation 非齐次线性微分方程nonhomogeneous linear system of differential equations 非齐次线性微分方程组interval algebra 区间代数interval analysis 区间分析interval closed at the right 右闭区间interval estimation 区域估计interval function 区间函数interval graph 区间图interval of convergence 收敛区间interval of definition 定义区间interval topology 区间拓扑irreducible set 不可约集irreducible r module 不可约r模periodical decimal fraction 循环十进小数pentad 拼五小组pentadecagon 十五边形pentagon 五角形pentagonal number 五角数pentagonal pyramid 五角锥pentagram 五角星pentahedron 五面体pentaspherical coordinates 五球坐标penalty method 补偿法pascal distribution 帕斯卡分布partition function 分折函数partial differential equation of elliptic type 椭圆型偏微分方程partial differential equation of first order 一阶偏微分方程partial differential equation of hyperbolic type 双曲型偏微分方程partial differential equation of mixed type 混合型偏微分方程partial differential equation of parabolic type 抛物型偏微分方程partial differential operator 偏微分算子parametric test 参数检验particular solution 特解parallelogram axiom 平行四边形公理orthogonality relation 正交关系ordinary differential equation 常微分方程optimal value function 最优值函数opposite angles 对角opposite category 对偶范畴one to one mapping 一一映射onto mapping 满射open mapping theorem 开映射定理one to many mapping 一对多映射one sided limit 单侧极限numerical solution of linear equations 线性方程组的数值解法null set 空集null solution 零解third boundary condition 第三边界条件two sided neighborhood 双侧邻域unbiased estimating equation 无偏估计方程unbounded function 无界函数unbounded quantifier 无界量词uncertainty principle 测不准原理uncorrelated random variables 不相关随机变量undetermined coefficient 末定系数velocity distribution 速度分布velocity optimal 速度最优的weak approximation theorem 弱逼近定理weak completeness 弱完备性weak continuity 弱连续性weak convergence 弱收敛wiener measure 维纳测度word group 自由群sample correlation coefficient 样本相关系数sample covariance 样本协方差schwarz inequality 施瓦尔兹不等式second boundary condition 诺伊曼边界条件second comparison test 第二比较检验second limit theorem 第二极限定理self adjoint differential equation 自伴微分方程semimajor axis 半长轴semiminor axis 半短轴sentential calculus 命题演算set of measure zero 零测度集set topology 集论拓扑simple connectedness 单连通性slope function 斜率函数solution curve 积分曲线solution domain 解域solution set of equation 方程的解集spatial co ordinate 空间坐标specific address 绝对地址spherical bessel function 球贝塞耳函数spherical cap 球冠spherical coordinates 球极坐标spherical curvature 球面曲率spherical shell 球壳spherical zone 球带spline function 样条函数spline interpolation 样条内插stability conditions 稳定条件statistical hypothesis testing 统计假设检验strict inequality 严格不等式strict isotonicity 严格保序性strict isotony 严格保序性strict increasing 严格递增system of partial differential equations 偏微分方程组system of ordinary differential equations 常微分方程组system of linear homogeneous equations 线性齐次方程组system of linear inhomogeneous equations 线性非齐次方程组system of inequalities 联立不等式system of polar coordinates 极坐标系system of variational equations 变分方程组system with concentrated parameters 集中参数系统system with distributed parameters 分布参数系统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tangent cone 切线锥面telegraph equation 电报方程theorem for damping 阻尼定理****充分条件sufficient condition必要条件necessary condition 充要条件sufficient and necessary condition……的充要条件是………if and only if …****abscissa 横坐标alternating series 交错级数angle of the sector 扇形角arbitrary constant 任意常数augmented matrix 增广矩阵axis of parabola 拋物线的轴axis of revolution 旋转轴axis of rotation 旋转轴binomial series 二项级数binomial theorem 二项式定理binomial distribution 二项分布bisection method 分半法；分半方法bounded above 有上界的；上有界的bounded below 有下界的；下有界的bounded function 有界函数bounded sequence 有界序列brace 大括号bracket 括号Cartesian coordinates 笛卡儿坐标certain event 必然事件circumcentre 外心；外接圆心circumcircle 外接圆classical theory of probability 古典概率论cofactor 余因子; 余因式common denominator 同分母；公分母common difference 公差common divisor 公约数；公约common logarithm 常用对数common multiple 公位数；公倍common ratio 公比commutative law 交换律compasses 圆规Cauchy-Schwarz inequality 柯西- 许瓦尔兹不等式central limit theorem 中心极限定理centripedal acceleration 向心加速度concave downward 凹向下的concurrent 共点concyclic 共圆concyclic points 共圆点Euclidean geometry 欧几里德几何Euler's formula 尤拉公式；欧拉公式even function 偶函数even number 偶数game （1）对策；（2）博奕Gaussian distribution 高斯分布greatest term 最大项greatest value 最大值harmonic mean (1) 调和平均数; (2) 调和中项harmonic progression 调和级数higher order derivative 高阶导数improper fraction 假分数improper integral 广义积分; 非正常积分implicit function 隐函数incircle 内切圆inclined plane 斜included angle 夹角indefinite integral 不定积分initial condition 原始条件；初值条件initial-value problem 初值问题interior angles on the same side of the transversal 同旁内角interior opposite angle 内对角isosceles triangle 等腰三角形iterate (1)迭代值; (2)迭代Lagrange interpolating polynomial 拉格朗日插值多项代Laplace expansion 拉普拉斯展式lemniscate 双纽线left hand limit 左方极限limiting case 极限情况limiting position 极限位置line of best-fit 最佳拟合line segment 线段logarithmic equation 对数方程mathematical analysis 数学分析mathematical induction 数学归纳法monotonic decreasing function 单调递减函数monotonic convergence 单调收敛性monotonic increasing function 单调递增函数multiple-angle formula 倍角公式multiple root 多重根mutually disjoint 互不相交mutually exclusive events 互斥事件mutually independent 独立; 互相独立mutually perpendicular lines 互相垂直numerical method 计算方法；数值法oblique cone 斜圆锥orthogonal circles 正交圆orthogonality 正交性oscillatory convergence 振动收敛性ordinary differential equation 常微分方程pairwise mutually exclusive events 两两互斥事件place holder 补位数字point of inflection (inflexion) 拐点; 转折点Pisson distribution 泊松分布point-slope form 点斜式polar coordinate plane 极坐标平面polynomial equation 多项式方程posterior probability 后验概率; 事后概率premultiply 前乘; 自左乘prime factor 质因子；质因素prime number 素数；质数principal angle 主角principal axis 主轴principal value 主值prior probability 先验概率; 事先概率probability density function 概率密度函数product and sum formula 和积互变公式product sample space 积样本空间product to sum formula 积化和差公式proof by contradiction 反证法; 归谬法proper fraction 真分数proper integral 正常积分proper subset 真子集propositional calculus 命题演算propositional inference 命题推演protractor 量角器Pythagoras' theorem 勾股定理Pythagorean triplet 毕氏三元数组quadratic convergence 二阶收敛性quadrature 求积法quotient set 商集radial component 沿径分量radical axis 根轴range 值域；区域；范围；极差；分布域rationalization 有理化raw data 原始数据rectifiable 可求长的reciprocal 倒数rectangular coordinate plane 直角坐标平面recurrence formula 递推公式reducibility 可约性; 可化简性reflexive relation 自反关系reference angle 参考reference line 基准线reflex angle 优角；反角region of acceptance 接受区域region of convergency 收敛区域region of rejection 否定区域right circular cone 直立圆锥（体）resolution of vector 向量分解; 矢量分解right hand limit 右方极限right prism 直立棱柱；直立角柱(体) right pyramid 直立棱锥；直立角锥(体) right-angled triangle 直角二角形scalene triangle 不等边三角形；不规则三角形scatter diagram 散点图scientific notation 科学记数法semi-conjugate axis 半共轭轴semi-transverse axis 半贯轴semi-vertical angle 半顶角separable differential equation 可分微分方程septic equation 七次方程set square 三角尺；三角板shaded portion 有阴影部分significance level 显著性水平significant figure 有效数字similar triangles 相似三角形simple iteration method 简单迭代法simple pendulum 单摆Simpson's integral 森逊积分standard deviation 标准差；标准偏离standard normal distribution 标准正态分布; 标准常态分布stationary point 平稳点; 逗留点; 驻点strictly monotonic 严格单调statistical chart 统计分析submultiple angle formula 半角公式subsidiary angle 辅助角substitution 代入; 代入法successive approximation 逐次逼近法successive derivative 逐次导数successive differentiation 逐次微分法suffix 下标sum to infinity 无限项之和sum to product formula 和化积公式superimposing 迭合supplementary angle 补角surjection 满射symmetric relation 对称关系tautology 恒真命题；恒真式Taylor’s expansion 泰勒展开式Taylor’s series 泰勒级数Taylor’s theorem 泰勒定理test criterion 检验标准test of significance 显著性检验to the nearest 至最接近之torque 转矩torus 环面transcendental function 超越函数transformation of variable 变数转换transitive 可传递的transpose of matrix 倒置矩阵；转置矩阵transversal 截；横截的triangle law of addition 三角形加法travel graph 行程图tree diagram 树形图trapezoidal integral 梯形积分truncated Taylor’s series 截断泰勒级数two-tailed test 双尾检验；只端检验type I error I型误差type II error II型误差unbiased estimator 无偏估计量undetermined coefficient 待定系数unique solution 唯一解vertical asymptote 垂直渐近线vertically opposite angles 对顶角without loss of generality 不失一般性****分子Numerator 分母Denominator 阿拉伯数字Hindu-Arabic numeral假分数Improper fraction 最大公因子Highest Common Factor (H.C.F.) 最小公倍数Lowest Common Multiple (L.C.M.) 行列式determinant****interval closed at the right 右闭区间interval of convergence 收敛区间interval of definition 定义区间invariance theorem 不变性定理invariant of an equation 方程的不变量inverse circular function 反三角函数inverse hyperbolic function 反双曲函数inversion formula 反演公式isotonic injective mapping 保序单射映射jacobi identity 雅可比恒等式jump point 跳跃点law of double negation 双重否定律law of inertia 惯性律law of large numbers 大数定律leading ideal 猪想liouville theorem 刘维尔定理lipschitz condition 李普希茨条件markov transform 马尔可夫变换mathematical approximation 数学近似法mathematical model 数学模型maximum condition 极大条件maximum deviation 最大偏差mean square deviation 方差mean square of error 误差的均方meromorphic function 亚纯函数柱形统计图histogram 折线统计图broken line graph 曲线统计图curve diagram 扇形统计图pie diagram排列permutatio内切圆inscribed circle 外切圆circumcircle正多边形equilateral polygon metric space 度量空间metric subspace 度量子空间method of runge kutta type 朗格库塔型的方法method of steepest ascent 最速上升法method of steepest descent 最速下降法method of finite elements 有限元法method of fractional steps 分步法method of exhaustion 穷竭法method of approximation 近似法method of artificial variables 人工变量法method of balayage 扫除法method of characteristic curves 特者法method of comparison 比较法method of conjugate gradients 共轭梯度法lateral area 侧面积last multiplier 最后乘子large sample test 大样本检验lattice constant 点阵常数lattice design 格子设计method of difference 差分法method of elimination 消元法method of estimation 估计法meromorphic differential 亚纯微分median 中位数measuring rule 量尺mean term 内项mean term 内项mean term 内项irreducibility criterion 不可约性判别准则irreducible polynomial 不可约多项式irreducible generating set 不可约生成集irregular divisor class 非正则因子类irregular point 非正则点irregular singular point 非正则奇点isometric circle 等距圆isometric embedding 等距嵌入isomorphic field 同构域isomorphic graph 同构图isomorphic group 同构群isomorphic image 同构象isothermal parameter 等温参数iterated function 叠函数iterated integral 累积分joint distribution 联合分布jordan algebra 约当代数kernel of an integral equation 积分方程的核l'hospital rule 洛必达规则laboratory system of coordinates 实验室坐标系labyrinth 迷宫lacation principle 介值定理lag correlation coefficient 滞后相关系数lag regression 落后回归laguerre differential equation 拉盖尔微分方程lame equation 拉梅方程language of formula 公式语言laplace beltrami operator 拉普拉斯贝尔特拉米算子lateral area 侧面积last multiplier 最后乘子large sample test 大样本检验lattice constant 点阵常数lattice design 格子设计left adjoint 左伴随的left derivative 左导数left differential 左微分left direct product 左直积left end point 左端点left length 左长left limit value 左极限值left multiplication ring 左乘环length of curve 曲线的长length of normal 法线的长levi decomposition 列维分解limes inferior 下极限limes superior 上极限limit circle 极限圆limit circle type 极限圆型logarithm to the base 10 常用对数logarithmic normal distribution 对数正态分布logic of relations 关系逻辑magic circle 幻圆magic cube 幻立方manifold without boundary 无边廖many valued mapping 多值映射marginal distribution density function 边缘分布密度函数marginal distribution function 边缘分布函数mathematical programming 数学规划mathematical random sample 数学随机样本mathematical statistics 数理统计maximum likelihood estimating function 极大似然估计量independent variable 自变量dependent variable 应变量equiangular triangle 正三角形,等角三角形命题proposition 差remainder 积product 除数divisor 商quotient 截尾truncation 未知数unknown, x-factor, y-factor, z-factor 阶乘factorial 集合aggregate 空集void 子集subset 交集intersection 并集union 补集complement 映射mapping 勾股定理Pythagorean theorem 菱形rhomb, rhombus, rhombi(pl.), diamond 双曲线hyperbola 抛物线parabola topology of bounded convergence 有界收敛拓扑toroid 超环面toroidal coordinates 圆环坐标trace of dyadic 并向量的迹transcendental integral function 超越整函数transformation formulas of the coordinates 坐标的变换公式transformation to principal axes 轴变换transversal lines 截线trapezoid method 梯形公式trefoil knot 三叶形纽结truth function 真值函项two sided test 双侧检定two sided neighborhood 双侧邻域two sided surface 双侧曲面two termed expression 二项式ultrahyperbolic equation 超双曲型方程a priori bound 先验界限a priori distribution 先验分布a priori probability 先验概率a summable a可和的abacus 算盘abbreviate 略abbreviation 简化abel equation 阿贝耳方程abel identity 阿贝耳恒等式abel inequality 阿贝耳不等式abel summation method 阿贝耳求和法abelian algebra 阿贝耳代数abelian differential 阿贝耳微分abelian equation 阿贝耳方程abelian extension 阿贝耳扩张abelian function 阿贝耳函数abelian function field 阿贝耳函数域abelian functor 阿贝耳函子abelian group 交换群abelian groupoid 阿贝耳广群abelian integral 阿贝耳积分abelian summation 阿贝耳求和法abelian theorem 阿贝耳定理abelian variety 阿贝耳簇abridge 略abridged notation 简算记号abscissa 横坐标abscissa of absolute convergence 绝对收敛坐标abscissa of summability 可和性坐标abscissa of uniform convergence 一致收敛横坐标absolute 绝对形absolute address 绝对地址absolute class field 绝对类域absolute coding 绝对编码absolute cohomology 绝对上同调absolute conic 绝对二次曲线absolute convergence 绝对收敛absolute curvature vector 绝对曲率向量absolute deviation 绝对偏差absolute differential calculus 绝对微分学absolute error 绝对误差absolute extremes 绝对极值absolute extremum 绝对极值absolute frequency 绝对频率。
常见的英语考纲词汇
常见的英语考纲词汇，按照字母顺序排列：A：abandon, ability, absorb, access, accommodate, accompany, achieve, acknowledge, acquire, adapt, address, adequate, adjust, administer, admire, admit, adopt, advance, adventure, advertise, advice, advocate, affect, afford, agency, agenda, aggregate, agree, aim, album, alert, allocate, allow, ally, alter, alternative, amateur, ambassador, amount, analyze, ancestor, angle, animate, announce, annoy, annual, anticipate, anxious, appear, appreciate, approach, appropriate, approve, approximate, architecture, argue, arise, arrange, arrest, arise, art, articulate, ascend, aspect, aspire, assert, assess, assign, assist, associate, assume, assure, astonish, attach, attain, attempt, attend, attract, attribute, audience, authorize, automate, available, average, avoidB：bachelor, background, backbone, bacteria, balanced, ban, band, bank, bar, bare, bargain, barometer, based, basic, battle, bear, beat, behalf, behavior, belief, belong, benefit, besides, bet, betray, better, bias, beyond, bill, biology, birth, bite, bitter, blade, blame, blend, bless, blind, block, blood, blue, board, boat, body, bold, bond, bonus, book, boom, border, bore, born, boundary, boycott, brain, branch, brave, breach, bread, break, breed, brief, bright, bring, broad, broadcast, brother, brush, budget, build, bulk, bullet, burden, bury, bus, business, busy, but, butter, button, buy, byC：cabinet, cable, calculate, call, calm, camera, campaign, canal, capable, capacity, capture, carbon, card, care, career, careful, carry, case, cash, cast, casual, catch, category, cause, celebrate, cell, censure, center, century, ceremony, certain, chain, chair, challenge, chance, change, channel, chaos, chapter, characteristic, charge, charity, chart, chase, cheap, check, cheese, chemical, chief, child, choir, choose, circle, cite, citizen, city, civil, claim, clarify, clash, class, classify, clean, clear, clerk, client, climate, climb, close, cloth, clout, club, clue, cluster, coach, coal, coast, coat, code, coffee, coin, collaborate, collapse, collar, collect, college, colonel, color, column, combination, combine, come, comfort, command, comment, commercial, commission, commit, committee, common, communicate, community, company, compare, competition, complain, complete, complex, comply, compose, compound, comprehend, compromise, compute, concentrate, concept, concern, concert, conclude, concrete, condition, conduct, cone, conference, confess, confidence, conflict, confront, confuse, congratulate, congress, connect, conquer, conscience, consensus, consent, consequence, consider, consist, consolidate, constant, constitute, construct, consult, consume, contain, contempt, contend, content, contest, context, continue, contract, contradict, contrary, contrast, contribute, control, controversy, convert, convince, cook, cool, cooperate, coordinate, cope, copy, core, corn, correct, correspond, cost, cotton, council, count, counter, country, couple, courage, course, court, cousin, cover, cow, crack, craft, crash, crazy, create, credit, creep, crew, crisis, critical, criticize, crop, cross, crowd, crown, crucial, cruel, cruise, cry, crystal, culture, cup, cure, curry, curve, custom, customer, cutD：damage, danger, data, date, daughter, day, deal, dear, death, debate, decade, decay, decide, declare, decline, decorate, decrease, dedicate, deep, defeat, defend, defer, define, definite, degree, delay, delete, deliberate, deliver, demand, democracy, demonstrate, dense, deny, depend, depict, deploy, deposit, deprive, derive, describe, desert, deserve, design, desire, despair, destroy,detail, detect, detonate, develop, devote, diagnose, diagonal, dictate, die, differ, differentiate, difficult, dig, digest, dignity, dilemma, dimension, diminish, dip, direct, disaster, discipline, disclose, discount, discourage, discover, discredit, discriminate, discuss, disease, disgust, dish, dismiss, disorder, display, dispose, dissolve, distance, distinguish, distribute, district, disturb, dive, divide, divorce, do, doctor, document, dog, dollar, donate, door, double, doubt, down, dozen, draft, drag, drain, drama, draw, dream, dress, drink, drive, drop, drought, drug, drum, dry, due, dull, dumb, dump, during, dust, dutyE：each, eager, ear, early, earn, ease, east, easy, eat, ecology, economic, edge, edit, educate, effect, efficient, effort, egg, either, elaborate, election, electric, elegant, element, elevate, eliminate, elite, else, embarrass, embassy, embryo, emerge, emergency, emit, emotion, emphasize, employ, empower, empty, enable, encounter, encourage, end, endure, enforce, engage, engineer, enhance, enjoy, enlist, enormous, enough, enter, entertain, entire, enthusiasm, entrance, envelope, environment, envy, epidemic, episode, equal, equip, equivalent, era, erode, error, escape, establish, estate, estimate, ethnic, evacuate, evaluate, even, event, eventually, ever, every, evidence, evil, evolution, exact, examine, example, exceed, excellent, exception, excess, exchange, exciting, exclude, excuse, execute, exercise, Exhaust, exhibit, exist, exit, expand, expect, experience, experiment, expert, explicit, explode, explore, export, exposure, express, extend, extensive, external, extract, extreme, eyeF：face, factor, fade, fail, faint, fair, faith, fall, false, fame, familiar, family, famous, fan, fancy, fantastic, far, farm, fashion, fast, fat, fate, father, fault, favor, fear, feature, federal, fee, feed, feel, female, fence, festival, fetch, fever, few, fiber, fiction, field, fifteen, fifth, fifty, fight, figure, file, fill, film, final, finance, find, fine, finger, finish, fire, firm, first, fish, fit, five, fix, flag, flame, flare, flat, flavor, flee, flood, floor, flow, flower, fluctuate, fly, focus, fold, follow, fond, food, foot, for, force, forecast, foreign, forest, forget, forgive, fork, form, formal, former, forth, fortunate, forward, foster, foul, found, four, fox, fraction, fragile, frame, free, freedom, frequent, fresh, friend, frighten, from, front, fruit, frustrate, fuel, full, fun, function, fund, funeral, funny, furnish, further, futureG：gain, galaxy, game, gang, gap, garage, garden, gas, gather, gear, general, generate, generation, generous, genius, gentle, genuine, geography, gesture, get, giant, gift, girl, give, glad, glance, glass, global, glory, glove, go, goal, god, gold, good, goods, govern, government, grace, graduate, grain, grand, grant, grass, grateful, grave, great, greedy, green, greet, grey, grief, grocery, ground, group, grow, growth, guarantee, guard, guess, guest, guide, guiltyH：habit, habitat, hair, half, hall, halt, hammer, hand, handle, hang, happen, harbor, hard, hardware, harm, harvest, hat, hate, have, hazard, he, head, heal, health, hear, heart, heat, heaven, heavy, heel, height, hell, help, hence, her, here, heritage, hero, hesitate, hide, high, highlight, highway, hill, him, himself, hip, hire, his, historical, hit, hold, hole, holiday, holy, home, honest, honor, hope, horizon, horse, hospital, host, hot, hotel, hour, house, how, however, hug, huge, human, humble, humor, hundred, hunger, hunt, hurry, hurt, husband, hybridI：ice, idea, identify, idle, if, ignore, ill, illegal, illuminate, illustrate, imagination, imagine,immediate, immigrant, immune, impact, imperfection, implement, importance, impose, impress, improvement, in, inch, incident, include, income, increase, independent, index, indicate, individual, industry, inevitable, infect, inferior, infest, influence, inform, infra-red, ingredient, inherit, initiate, inject, injure, inner, innocent, innovate, inquiry, insect, inside, insist, inspire, install, instant, instead, insufficient, intend, interaction, interest, interim, internal, international, interrupt, interview, interval, intervene, intimate, introduce, inure, invest, investigate, invite, involve, iron, island, issue, it, itemJ：jacket, jail, jam, jaw, jealous, jeopardy, jerk, jet, jewelry, job, join, joking, journey, joy, judge, jug, juice, jump, jungle, justK：keep, key, kick, kid, kill, kilogram, kilometer, kind, king, kiss, kit, kitchen, kneel, knife, knock, know, knowledgeL：labor, laboratory, lack, lady, lake, lamp, land, language, large, last, late, laugh, launch, law, lay, layer, laziness, lead, leader, leaf, leak, lean, leap, learn, least, leave, lecture, left, legal, legend, lemon, lend, length, less, lesson, let, letter, level, liar, liberal, liberty, library, license, life, lift, light, like, likely, limit, line, link, lion, liquid, list, listen, little, live, lizard, load, loan, local, locate, lock, long, look, loose, lose, loud, love, low, loyal, luck, luggage, lump, lunch, luxuryM：machine, mad, magazine, magic, magnet, mail, main, make, man, manage, mandolin, manipulate, manner, many, map, maple, march, mark, market, marriage, marry, mask, Mass, master, match, material, math, matter, maximum, may, maybe, me, meal, mean, measure, meat, mechanism, media, medical, medication, medicine, meet, melt, member, memo, memory, men, mend, mental, merchant, message, metal, meter, middle, midnight, might, mile, milk, million, mind, mine, mineral, minimum, minister, minor, minute, miracle, mirror, misbehave, miss, mistake, mix, model, moderate, modern, modest, modifies, moment, momentum, money, monkey, month, moon, moral, more, morning, most, mother, motion, mountain, mouth, move, much, mud, multiply, murder, muscle, museum, music, must, mute, mysteryN：nail, name, narrow, nation, native, natural, Navy, near, necessary, neck, needle, negative, negotiate, neighbor, neither, nephew, nerve, nest, net, network, never, new, news, next, nice, night, nine, no, noble, nobody, nod, noise, nominal, non, none, noodle, noon, nor, north, nose, not, note, nothing, notice, notion, now, nowhere, nuclear, null, number, nurse, nutO：oak, object, occupy, occur, ocean, odd, of, off, offer, office, often, oil, OK, old, on, once, one, only, open, operate, opinion, opportunity, oppose, opposite, option, or, orange, orbit, order, ordinary, organize, original, other, oust, out, outlaw, outlet, outline, output, outside, oven, over, overall, overcome, overlook, owe, own, oxygenP：pace, pack, package, page, pain, paint, pair, palace, pale, palm, panel, panic, paper, paradise, pardon, parent, park, part, participate, particular, party, pass, passage, past, pasta, patent, path, patient, pattern, pause, pay, peace, peak, pear, peasant, pedestrian, peel, peer, penalty, people, percent, perfect, perform, perhaps, period, permanent, permit, person, persuade, pet, phase,philosophy, photo, phrase, physical, piano, pick, picture, piece, pig, pile, pill, pilot, pin, pinch, pink, pipe, pitch, place, plain, plan, planet, plant, plastic, plate, play, pleasant, please, pleasure, plenty, plot, plug, plus, pocket, poem, point, poison, pole, police, polish, polite, poll, pollutant, pollution, pool, poor, pop, popular, population, port, pose, position, positive, possess, possible, post, postpone, pot, potato, potential, pour, poverty, powder, power, practical, practice, prairie, praise, pray, preface, prefer, prepare, present, preserve, president, press, pressure, pretend, prevent, previous, price, pride, primary, prime, principal, print, prior, prison, private, probable, problem, procedure, proceed, process, produce, product, profession, profit, program, progress, prohibit, project, promise, promote, prompt, pronounce, proof, proper, property, proposal, propose, protect, protest, Proud, provide, provoke, publish, pull, pulse, pump, punish, pupil, purchase, pure, purpose, pursue, push, putQ：qualify, quality, quantity, quarter, question, quick, quiet, quit, quite, quizR：race, rack, radio, raft, rage, rain, raise, rally, random, range, rank, rap, rapid, rare, rate, rather, reach, react, read, ready, real, reality, realize, reason, rebel, rebuild, recall, receive, recent, reception, recipe, record, recover, recruit, red, reduce, reflect, reform, refuse, regard, region, register, regret, reinforce, reject, relate, release, relevant, reliable, relief, religion, rely, remain, remarkable, remember, remind, remove, rent, repair, repeat, replace, reply, report, represent, reproduce, request, require, rescue, research, resemble, reserve, reside, resign, resist, resolve, resort, respect, respond, responsibility, rest, restore, restrain, restrict, result, retrace, retrieve, return, reveal, revenge, revenue, review, revise, revolution, reward, rhythm, rich, ride, ridicule, right, rigid, ring, riot, rise, risk, river, road, roar, robot, rock, rocket, rod, roll, roof, room, root, rope, rose, rough, round, route, row, royal, rubber, ruin, rule, run, rural, rush, rust, ruthlessS：sack, sacred, sacrifice, sad, safe, sail, salad, sale, salt, same, sample, sanction, sand, satisfy, sauce, save, say, scale, scan, scare, scatter, scene, schedule, scheme, school, science, scope, score, scrap, scratch, screen, script, sculpture, sea, search, season, seat, second, secret, section, secure, see, seek, seem, select, sell, senate, send, senior, sense, sensitive, separate, series, serve, service, session, set, settle, seven, several, severe, sex, shack, shade, shadow, shake, shall, share, sharp, shave, she, sheep, sheet, shelf, shell, shelter, shift, shine, ship, shirt, shoe, shoot, shop, short, should, shout, show, shower, shred, shrink, shrug, shy, sibling, sick, side, siege, sight, sign, signal, significant, silent, silk, silly, silver, similar, simple, since, sing, single, sink, sir, sister, sit, site, situation, six, size, skate, ski, skill, skin, skirt, sky, sleep, slice, slide, slight, slip, slope, slow, small, smart, smash, smell, smile, smoke, smooth, snake, snow, so, soap, social, society, sock, soft, soil, solar, soldier, solid, solution, somber, some, son, song, soon, sort, soul, sound, source, south, space, spare, speak, special, specific, speech, speed, spell, spend, spill, spirit, split, spoil, sponsor, spoon, sport, spot, spray, spread, spring, spy, square, stable, staff, stage, stake, standard, star, start, state, statement, station, statistics, status, stay, steady, steal, steam, steel, steep, steer, step, stick, still, sting, stipulate, stock, stomach, stone, stop, store, storm, story, stout, straight, strange, strategy, street, strength, stress, stretch, strike, string, strip, stroke, strong, struggle, student, study, stuff, stupid, subject, submit, subside, subsequent, substance, subtle, subtract, succeed, success, such, suffer, sugar, suggest, suit, suite, summer, summit, sun, super, supermarket, supervise, supply, support, suppose, supreme, sure, surface, surge, surprise, surrender, surround,survey, suspect, suspend, sustain, swallow, swear, sweat, sweep, sweet, swim, swing, switch, symbol, sympathetic, systemT：table, taboo, tackle, tag, tail, take, talent, talk, tall, tank, tape, target, task, taste, tax, teach, team, tear, technical, technique, technology, tee, teen, telephone, telescope, tell, temperature, temporary, ten, tend, tense, term, terrible, test, text, than, thank, that, the, theater, their, them, theme, themselves, then, theory, there, therefore, these, they, thick, thief, thin, thing, think, third, thirst, this, those, though, thought, thousand, thread, threaten, three, threshold, thrive, through, throw, thus, ticket, tie, tight, tile, time, tin, tip, tire, title, toast, today, toe, together, toilet, tolerance, tomato, tomorrow, tone, tongue, tonight, too, tool, tooth, top, topic, torch, torn, torture, total, touch, tough, tour, tourist, toward, tower, town,。
英汉数学物理常用词汇
Cauchy's integral formula，科西积分公式
Liouville's theorem，刘维尔定理
Sequence，序列
sequence of number，数列
sequence of function，函数列
derivative，导数
partial derivative，偏导数
higher derivative，高阶导数
derivative of order n/nth order derivative，n阶导数
analytic function，解析函数
regular function，正则函数
transcendented function，超越函数
hyperbolic function，双曲函数
anti-hyperbolic function，反双曲函数
trigonometric function，三角函数
anti-trigonometric function，反三角函数
analyticity，解析性
general term，通项
series，级数
series of numbers，数项级数
series of functions/functional series，函项级数
number of term，项数
infinite series，无穷级数
partial sum，部分和
remainder term，余项
multiply valued function，多值函数
simple function，单叶函数
微积分双语常用词汇
MATHEMATICAL TERMS (Part 1) calculus 微积分definition 定义theorem 定理lemma 引理corollary 推论prove 证明proof 证明show 证明solution 解formula 公式if and only if ( iff ) 当且仅当∀ x∈X for all x∈X∃x∈X there exists an x∈Xsuch that 使得given 已知set 集合finite set 有限集infinite set 无限集interval 区间open interval 开区间closed interval 闭区间neighborhood 邻域number 数natural number 自然数integer 整数odd number 奇数even number 偶数real number 实数rational number 有理数irrational number 无理数positive number 正数negative number 负数mapping 映射function 函数monotone function 单调函数increasing function 增函数decreasing function 减函数bounded function 有界函数odd function 奇函数even function 偶函数periodic function 周期函数composite function 复合函数inverse function 反函数domain 定义域range 值域variable 变量independent variable 自变量dependent variable 因变量sequence 数列convergent sequence 收敛数列divergent sequence 发散数列bounded sequence 有界数列decreasing sequence 递减数列increasing sequence 递增数列limit 极限one-sided limit 单侧极限left-hand limit 左极限right-hand limit 右极限The Squeeze Theorem 夹挤定理infinity 无穷大infinitesimal 无穷小equivalent infinitesimal 等价无穷小infinitesimal of higher order 高阶无穷小order of infinitesimal 无穷小的阶infinitesimals of the same order 同阶无穷小increment 增量continuous function 连续函数continuity 连续性f(x) is continuous at x 在x 连续f(x) is discontinuous at x 在x 间断discontinuity 间断点discontinuity of the first (second) kind 第一（二）类间断点removable discontinuity 可去间断点jump discontinuity 跳跃间断点infinite discontinuity 无穷间断点intermediate value 介值The Intermediate Value Theorem 介值定理zero point 零点The Zero Point Theorem 零点定理root 根equation 方程uniform continuity 一致连续derivative 导数rate of change 变化率velocity 速度instantaneous velocity 瞬时速度tangent (line) 切线normal (line) 法线slope 斜率left-hand derivative 左导数right-hand derivative 右导数f(x) is differentiable at x f(x) 在x 处可导(可微) differentiation 求导The Chain Rule 链式法则differentiation formulas 求导公式implicit function 隐函数explicit function 显函数implicit differentiation 隐函数求导logarithm 对数Logarithmic differentiation 对数求导法parameter 参数parametric equation 参数方程parametric curve 参数曲线hyperbolic function 双曲函数hyperbolic sine 双曲正弦hyperbolic cosine 双曲余弦hyperbolic tangent 双曲正切hyperbolic cotangent 双曲余切MATHEMATICAL TERMS (Part 2)differential 微分differential quotient 微商approximate value 近似值error 误差relative error 相对误差absolute error 绝对误差invariance of differential form 微分形式不变性higher derivative 高阶导数first derivative 一阶导数second derivative 二阶导数third derivative 三阶导数nth derivative n 阶导数twice differentiable 二阶可导acceleration 加速度mean value 中值The Mean Value Theorem 中值定理Rolle’s Theorem 罗尔定理Lagrange’s Mean Value Theorem 拉格朗日中值定理Cauchy’s Mean Value Theorem 柯西中值定理equality 等式inequality 不等式indeterminate form 不定型 (未定式)indeterminate form of type 00 ( ∞∞ ) 00 ( ∞∞ )型未定式L’Hospital’s Rule 洛必达法则Taylor’s formula 泰勒公式polynomial 多项式nth-degree polynomial n 次多项式remaind 余项Lagrange’s form of remainder 拉格朗日型余项Peano’s form of remainder 皮亚诺型余项Maclaurin formula 麦克劳林公式Taylor polynomial 泰勒多项式Mauclaurin polynomial 麦克劳林多项式polynomial approximation 多项式逼近accuracy 精确度margin 边际marginal cost 边际成本marginal revenue 边际收益elasticity 弹性density 密度mass 质量extreme value 极值local maximum value 极大值local minimum value 极小值(absolute) maximum 最大值(absolute) minimum 最小值stationary point 驻点（稳定点）critical point 临界点The First (Second) Derivative Test （极值的）一（二）阶判别法convex 凸的convex curve 凸曲线concave 凹的concave curve 凹曲线convex function 凸函数point of inflection 拐点asymptote 渐近线horizontal asymptote 水平渐近线vertical asymptote 垂直渐近线slant asymptote 斜渐近线curve sketching 作图sketch a curve 作图curvature 曲率The bisection method 二分法The secant method 弦位法Newton’s method 牛顿（切线）法The tangent method 切线法differential calculus 微分学integral 积分integral calculus 积分学definite integral 定积分indefinite integral 不定积分partition 分割Riemann sum 黎曼和integral sign 积分符号integrand 被积函数upper (lower) limit of integration 积分上（下）限integration 积分（求积）integrable 可积的f(x) is integrable on [a, b]integrable function 可积函数integrability 可积性sufficient condition 充分条件necessary condition 必要条件piecewise continuous 分段连续property 性质The mean value theorem of integral 积分中值定理The fundamental theorem of calculus 微积分基本定理Newton-Leibniz formulaprimitive function (anti-derivative) 原函数（反导数）The substitution rule for integration 换元积分法The inverse of the chain rule 反链式法（凑微分法）integration by parts 分部积分法rational function 有理函数fraction 分式irreducible fraction 最简分式partial fraction 部分分式partial fraction decomposition 部分分式分解MATHEMATICAL TERMS (Part 3)vector 矢量free vector 自由矢量zero vector 零矢量magnitude of a vector 矢量的模unit vector 单位矢量scalar product 数量积dot product 点积vector product 矢量积cross product 叉积a is perpendicular (orthogonal) tob a 与b 垂直coordinate 坐标coordinate system 坐标系coordinate axis 坐标轴x-axis x 轴coordinate plane 坐标面direction angle 方向角direction cosine 方向余弦rectangular coordinate system 直角坐标系octant 卦限the first octant 第一卦限variable 变量function of two (three) variables 二（三）元函数function of several variables 多元函数independent variable 自变量dependent variable 因变量domain 定义域range 值域set of points 点集neighborhood 邻域interior point 内点boundary point 边界点bound 边界open set 开集closed set 闭集connected set 连通集region 区域open region 开区域closed region 闭区域bounded region 有界区域unbounded region 无界区域cluster point 聚点double limit 二重极限iterated limit 累次极限continuity 连续性increment 增量total increment 全增量partial increment 偏增量partial derivative 偏导数partial derivative of f(x,y) with respect to x ( y ) f(x,y)关于x（y）的偏导数higher partial derivative 高阶偏导数mixed partial derivative 混合偏导数Laplace equation 拉普拉斯方程total differential 全微分differentiable 可微chain rule 链式法则implicit function 隐函数implicit differentiation 隐函数微分法Jacobian determinant 雅可比行列式curve 曲线space curve 空间曲线tangent vector 切矢tangent line 切线normal plane 法平面surface 曲面normal vector 法矢normal line 法线tangent plane 切平面sphere 球面cylinder 柱面cone 锥面directional derivative 方向导数gradient 梯度gradient vector 梯度矢量f delflevel curve 等值线level surface 等值面local extremum 极值local maximum 极大值local minimum 极小值extreme value 最值absolute maximum (minimum) 最大（最小）值stationary point (critical point) 驻点（临界点）conditional extremum 条件极值Lagrange multiplier 拉格朗日乘数method of Lagrange multiplier 拉格朗日乘数法objective function 目标函数constraint 约束条件method of least square 最小二乘法field 场scalar field 数量场vector field 矢量场gradient field 梯度场potential field 势场potential function 势函数conservative field 保守场gravitational field 引力场force field 力场velocity field 速度场MATHEMATICAL TERMS (Part 4)multiple integral 重积分double integral 二重积分iterated integral 累次积分region 区域region of integration 积分区域type X (Y) region X（Y）型区域order of integration 积分秩序reverse the order of integration 交换积分秩序polar coordinates 极坐标double integrals in polar coordinates 极坐标下的二重积分volume 体积lamina 平面薄片mass 质量density 密度moment about x-axis 关于x 轴的（静）力矩center of mass 重心moment of inertia 转动惯量surface 曲面area of a surface 曲面的面积triple integral 三重积分rectangle 矩形rectangular coordinates 直角坐标系cylinder 柱面cylindrical coordinates 柱面坐标系sphere 球面spherical coordinates 球面坐标系change of variables in multiple integrals 重积分的变量替换Jacobian determinant 雅可比行列式line integral 曲线积分line integral with respect to arc length 对弧长的曲线积分（第一型）line integral with respect to x ( y ) 对坐标x（y）曲线积分（第二型）line integral of a vector field 向量场的曲线积分smooth curve 光滑曲线piecewise smooth curve 逐段光滑曲线oriented curve 有向曲线orientation of a curve 曲线的方向work 功the line integral is independent of path 曲线积分与路径无关connected region 连通区域simply-connected region 单连通区域closed curve 闭曲线Green’s theorem 格林定理（公式）positive orientation of a curve 曲线的正向Fundamental theorem for line integrals 曲线积分的基本定理surface integral 曲面积分surface integral of a scalar field 数量场的曲面积分（第一型）surface integral of a vector field 向量场的曲面积分（第二型）orientable surface 可定向曲面oriented surface 有向曲面Möbius strip 莫比乌斯带Klein bottle 克莱因瓶one-sided surface 单侧曲面two-sided surface 双侧曲面closed surface 闭曲面flux 流量、通量electric flux 电通量divergence 散度rotation (curl) 旋度Gauss’ theorem 高斯定理（公式）The divergence theorem 散度定理（公式）Stokes’ theorem 斯托克斯定理（公式）curl theorem 旋度定理（公式）circulation of v around L v 沿L 的环流量Hamilton operator 哈密顿算子harmonic field 调和场。
常微分方程 双语课程常用词汇表
《常微分方程》双语课程常用词汇表acceleration n. 加速度constant acceleration 常加速度downward acceleration 向下的加速度gravitational acceleration 重力加速度total acceleration 总加速度upward acceleration 向上的加速度account（for）v. 占去algebra 代数algebraic equation 代数方程linear algebra 线性代数the fundamental theorem of algebra 代数学基本定理amount v. 总计n. 总数amplitude n. 振幅application n. 应用by repeated application of 反复应用apply v. 应用approach v. 趋近于approach zero 趋近于零approach infinity 趋近于无穷area n. 面积cross-sectional area 横截面积the horizontal cross-sectional area 水平方向的截面积arrange v. 安排、整理、排列arrangement n. 安排、整理、排列rearrangement n. 重新安排、重新整理、重新排列associate v. 联系associated a.. 相应的associated with 对应于…的associated homogeneous linear equation 相应的齐线性方程associativity n. 结合律assume v. 假设assumption n. 假设asymptote 渐近线oblique asymptote 斜渐近线[əˈbli:k]axis 数轴negative x -axis 负x 轴positive y -axis 正y 轴x -axis x 轴y -axis y 轴base n. 基be present v. 出现body 天体boundary n. 边界bounded a. 有界的unbounded a. 无界的brine 盐水calculus 微积分elementary calculus 初等微积分capacitor 电容器case 情形exceptional case 例外情形chain rule （求导的）链式法则clockwise 顺时针clockwise direction 顺时针方向counterclockwise 逆时针counterclockwise direction 逆时针方向close v. 闭closed container 封闭的容器closed interval 闭区间coefficient 系数constant coefficient 常系数leading coefficient 首项系数undetermined coefficient 待定系数variable coefficient 变系数collect v. 整理collect coefficients 整理系数column 列commute v. 交换commutative a. 交换的commutativity 交换性property of commutativity 交换性质complete a. 完备的incomplete a. 不完备的complex a. 复的complex conjugate 复共轭的complex conjugate pairs 复共轭对complex conjugate roots 复共轭根component n. 分量componentwise 分量形式composition 复合compress v. 压缩compute v. 计算concentration n. 浓度condition 条件a given initial condition 一个给定的初始条件initial condition 初始条件necessary condition 必要条件sufficient condition 充分条件the given condition 给定的条件conjugate 共轭的constant 常数arbitrary constant 任意常数constant multiple 数乘constant of integration 积分常数constant speed 常速度damping constant 阻尼常数positive constant 正的常数continuity n. 连续性discontinuity 不连续性continuous 连续的continuous function 连续函数continuous partial derivative 连续偏导数discontinuous 不连续的piecewise continuous 分段连续的convention 惯例convergence n. 收敛absolute convergence 绝对收敛uniform convergence 一致收敛coordinate 坐标coordinate axis 坐标轴polar coordinates 极坐标corresponding a. 相应的cube 立方，立方体current 电流cylinder 柱，柱面dashpot 减震器decomposition 分解partial fraction decomposition 部分分式分解defect n. 亏量defective v. 亏损的define v. 定义definition n. 定义degenerate a. 退化的denominator 分母derive v. 导出derivation n. 求导（数）derivative n. 导数[diˈrivətiv] antiderivative 原函数first derivative 一阶导数second derivative 二阶导数the highest derivative 最高阶导数determine v. 确定determinant 行列式determinant of coefficients 系数行列式operational determinant 算子行列式diagonal 对角线principal diagonal 主对角线differ v. 不同difference n. 差differentiable 可微的differentiable function 可微函数differentiability 可微性differentiability condition 可微性条件differential n. 微分differential form 微分形式differentiate v. 微分differentiate term wise 逐项微分differentiation n. 微分（运算）term-by-term differentiation 逐项微分displacement 位移distance 距离distinct 不同的distinct real roots 不同的实根distributives 分配性diverge v. 发散divide v. 划分，除subdivide 细分domain 定义域double 重，二重，双double root 二重根duplicate v. 复制、重复duplication n. 复制、重复eliminate v. 消去elimination n. 消元法、消去the method of elimination 消元法、消去法eigenvalue n. 特征值complex conjugate eigenvalue 复共轭特征值defective eigenvalue 不完备的特征值multiple eigenvalue 多重特征值zero eigenvalue 零特征值eigenvector 特征向量generalized eigenvector 广义特征向量rank generalized eigenvector r 阶广义特征向量element 元素diagonal element 对角元off-diagonal element 非对角元element wise 逐个元素地ellipse 椭圆elliptical orbit 椭圆型轨道employ v. 利用employ the technique of 利用…技术enable v. 使能够entry n. 元素equate v. 使相等equation 方程Bernoulli equation 伯努利方程Bessel’s equation 贝赛尔方程characteristic equation 特征方程cubic equation 三次方程differential equation 微分方程eigenvector equation 特征向量方程exact differential equation 恰当微分方程higher-degree equation 高次方程homogeneous equation 齐次方程Legend re’s equation 勒让德方程linear first-order equation 一阶线性方程Logistic equation 逻辑斯蒂方程natural growth equation 自然增长方程ordinary differential equation 常微分方程partial differential equation 偏微分方程quadratic equation 二次方程reducible equation 可降阶方程second-degree equation 二次方程separable differential equation 可分离变量方程simultaneous equations 联立方程组equilibrium position 平衡位置equivalent 等价的be equivalent to 等价于equivalently 等价地error 误差average error 平均误差existence 存在existence-uniqueness theorem 存在唯一性定理exponent 指数negative exponent 负指数exponential 指数(的)exponential function 指数函数matrix exponential 矩阵指数factor n. 因式,因子v. 分解因式common factor 公因式,公因子integrating factor 积分因子linear factor 一次因式irreducible quadratic factor 二次不可约因式factorization n. 因子分解field 场、域direction field 方向场first 第一的the first two… 前两（个）……flow v. 流动n. 流量inflow n. 流入(量) outflow n. 流出(量)focus 焦点following 下面的force 力external force 外力external period ice force 周期性外力frictional force 摩擦力form 形式decimal form 小数形式explicit form 显式形式implicit form 隐式形式polar form 极坐标形式the standard form 标准形式upper triangular form 上三角形式former a. 以前的the former 前者formula 公式fraction 分式,分数frequency 频率function 函数analytic function 解析函数coefficient function 系数函数complementary function 补函数component function 分量函数constant-valued function 常数值函数continuous function 连续函数piecewise continuous function 分段连续函数decreasing function 单调减函数differentiable function 可微函数n times differentiable function n 阶可微函数twice differentiable function 二阶可微函数sufficiently differentiable function 足够阶可微函数discontinuous function 不连续函数elementary function 初等函数factorial function 分式函数increasing function 单调增函数matrix-valued function 矩阵值函数position function 位置函数rational function 有理函数real-valued function 实值函数trigonometric function 三角函数unknown function 未知函数vector-valued function 向量值函数generalize (to) v. 推广generalization n. 推广graph 图象hemispherical 半球形的hold v. 成立homogeneous 齐(次)的nonhomogenous 非齐(次)的hyperbolic 双曲型的hyperbolic cosine 双曲余弦hyperbolic sine 双曲正弦hypothesis n. 假设hypotheses n. 假设(复数形式) identity 恒等式identity principle 恒等原理trigonometric identity 三角恒等式illustrate v. 说明imaginary part 虚部immaterial a. 不重要的, 不相干的imply v. 意味着, 暗示impulse 脉冲independent a. 独立的, 不相关的independent of 独立于……inductor 电感器initial 开始的, 最初的initial condition 初始条件initial position 初始位置initial population 初始人口数initial velocity 初始速度integer 整数nonnegative integer 非负整数integral 积分definite integral 定积分improper integral 非正常积分indefinite integral 不定积分integral sign 积分号integrate v. 积分integrate by parts 分部积分integration n. 积分integration of both sides 两边积分interior n. 内部in terms of 根据interval 区间closed interval 闭区间interval of real number 实数区间open interval 开区间subinterval 子区间bounded subinterval 有界子区间the ends of the interval 区间的端点the whole interval 整个区间involve v. 包含，涉及Kepl er’s laws of planetary motion 开普勒行星运动定律latter a. 后期的，末期的the latter 后者left-hand side 左边like 类似，相似like powers 同次幂like term 同类项limit 极限take the limit 取极限upper limit 上极限line 线，线条line segment 线段real line 实数轴straight line 直线tangent line 切线the line tangent (to) 与…相切的直线the entire real line 整个实轴linear 线性的linear combination 线性组合linear dependence 线性相关linear independence 线性无关nonlinear 非线性的linearly 线性地linearly dependent 线性相关的linearly independent 线性无关的linearly independent solutions 线性无关解linearity 线性性liter 升logarithm 对数logarithmic term 含有对数的项long division 长除法major semi axis 长半轴mass (物体的)质量mathematical model 数学模型mathematical modeling 数学建模matrix 矩阵augmented matrix 增广矩阵coefficient matrix 系数矩阵diagonal matrix 对角矩阵exponential matrix 指数矩阵fundamental matrix 基解矩阵identity matrix 单位矩阵inverse matrix 逆矩阵matrix addition 矩阵加法matrix multiplication 矩阵乘法nonsingular matrix 非奇异矩阵singular matrix 奇异矩阵square matrix 方阵upper triangular matrix 上三角矩阵zero matrix 零矩阵mean value theorem for integral 积分中值定理method 方法straightforward method 直接的方法minimum 最小值minus prep. 减,减去;负的minus sign 负号motion 运动free undamped motion 无阻尼自由运动simple harmonic motion 简谐运动multiply v. 乘,倍增multiplication n. 乘法multiplicity n. 重数nature 自然, 本质nilpotent 幂零的number 数complex number 复数imaginary number 虚数negative number 负数nonnegative number 非负数positive number 正数real number 实数unknown number 未知数numerator (分数的)分子operate v. 运算,作用operation n. 运算,操作elementary row operation 初等行变换operator 算子polynomial operator 多项式算子orbit 轨道order 阶first-order equation 一阶方程fourth-order equation 四阶方程of exponential order 指数阶的second-order equation 二阶方程nth-order equation n 阶方程the mixed second-order partial derivative 二阶混合偏导数the order of a differential equation 微分方程的阶origin 原点original 原来的the original equation 原方程the original form 原来的形式oscillate v. 振动oscillation n. 振动forced oscillation 强迫振动free oscillation 自由振动parabola 抛物线 [pə'ræbələ]parameter 参数variation of parameters 常数变易法parameterize v. 参数化parameterization n. 参数化particle 粒子phase angle 相角phase portrait 相图plane 平面point 点end point 端点isolated point 孤立点ordinary point 常点singular point 奇点regular singular point 正则奇点irregular singular point 非正则奇点polynomial 多项式n th-degree polynomial n 次多项式a polynomial of degree n n 次多项式a polynomial of lower degree 次数较低的多项式Taylor polynomial 泰勒多项式possible 可能的possibility 可能性power 幂power function 幂函数in powers of x x 的幂in powers of x −a x −a 的幂presence 出现, 在场preceding 前面的prime 求导符号“撇”problem 问题mathematical problem 数学问题initial value problem 初始值问题proceed v. 继续进行, 继续下去product 乘, 积dot product 点积product rule 乘法法则scalar product 点积,数积,内积property 性质proposition 命题quotient 商radius 半径radius of convergence 收敛半径rate 速率at a rate of 以…的速率at a rate proportional to 以与…成正比的速率birth rate 出生率death rate 死亡率time rate of change of (something) …关于时间的变化率interest rate 利率reactant 反应物readily 容易地real part 实部recall v. 记起,回顾rectangle 长方形, 矩形open rectangle 开矩形recurrence relation 递推关系many-term recurrence relation 多项间的递推关系two-term recurrence relation 两项间的递推关系recursion formula 递推公式reduce v. 化简, 简化, 约简reduction n. 化简, 简化, 约简reduction of order 降阶resistor 电阻器result n. 结果v. 导致(in)revolution n. 旋转right-hand side 右边root 根characteristic root 特征根complex root 复根double root 二重根equal roots 相等的根k-fold root k 重根rational root 有理根real root 实根repeated root 重根the square root 平方根triple root 三重根rotation n. 旋转counterclockwise rotation 逆时针旋转routine 例行的; 平凡的a routine matter 平凡的情形row 行scalar 纯量(的), 数量(的), 标量(的)series 级数binomial series 二项式级数geometric series 几何级数harmonic series 调和级数infinite series 无穷级数power series 幂级数convergent power series 收敛的幂级数power series representation 幂级数表示power series in x x的幂级数power series in x −a x −a 的幂级数power series solution 幂级数解Taylor series 泰勒级数set 集合show v. 证明side 边left-hand side 左边right-hand side 右边simple 简单的simplify v. 简化, 化简simplification n. 简化, 化简singularity 奇异性slope 斜率slope field 斜率场smooth 光滑的piecewise smooth 逐段光滑的solute n. 溶质，溶解物solution n. 解explicit solution 显式解implicit solution 隐式解infinitely many solutions 无穷多解negative-valued solution 负值解period ice solution 周期解positive-valued solution 正值解singular solution 奇解solution curve 解曲线the (a) genera l solution 通解the particular solution 特解solve v. 解solvent n. 溶剂some 某个some open interval 某个开区间spring 弹簧spring constant 弹性系数step 步骤finitely many steps 有限多步stretch 拉伸subject(to) a. 易受…的ad.在…条件下subscript 下标even subscript 偶下标odd subscript 奇下标substitute v. 代入substitution n. 代入direct substitution 直接代入back substitution 回代subtract v. 减去subtraction n. 减去suffice v. 足够sufficient n. 足够的, 充分的sufficient condition 充分条件sum n. 和sum zero 总和为零summand 被加数summation 求和(法), 累加, 加法the index of summation 求和的指标the sum of…and … …与…的和superposition 叠加symmetry 对称symmetric form 对称形式system 方程组,系统first-order system 一阶方程组higher-order system 高阶方程组two-dimensional system 二维系统upper triangular system 上三角方程组take 取, 实施take the Laplace transform 取拉普拉斯变换take the limit 取极限tangent 正切(的),切线(的)be tangent to 与…相切time 时间per unit of time 单位时间time lag 时滞tank 箱, 柜, 罐water tank 水箱term 项constant term 常数项termwise addition 逐项相加term by term 逐项the first term 第一项the first few terms 前几项the genera l term 通项, 一般项the leading term 首项terminology 术语trajectory 轨道, 轨迹transform v. 转化n. 变换Laplace transform 拉普拉斯变换inverse Laplace transform 拉普拉斯反变换transformation n. 变换,转化transpose v. , n. 转置,移项triangle 三角(形)right triangle 直角三角形triple 三重的, 三次的, 三倍的triple eigenvalue 三重特征根trivial 平凡的, 不重要的trivial case 平凡情况nontrivial 非平凡的tuple 组n -tuple n 元组unique 唯一的uniqueness 唯一性unique solution 唯一解unknown 未知的the unknown 未知量value 值numerical value 数值absolute value 绝对值variable 变量dependent variable 因变量independent variable 自变量variable of integration 积分变量vector 向量acceleration vector 加速度向量column vector 列向量constant vector 常数向量position vector 位置向量radius vector 向径, 矢径row vector 行向量solution vector 解向量unit vector 单位向量verify v. 证明vanish 等于零vanish identically 恒等于零variable 变量dependent variable 因变量independent variable 自变量separation of variable 变量分离voltage 电压volume 列Wronskian 伏朗斯基行列式yield 产生zero 零nonzero 非零。
boundary conditions 造句
boundary conditions 造句boundary conditions 造句如下：1、It has k2 as the boundary conditions.它有k 2作为限制条件。
2、Testing boundary conditions forces you to question your assumptions.测试边界条件会迫使开发人员明确考虑自己的假设。
3、What are the boundary conditions, the requirements, for stable complexity?稳定的复杂性有什么限制条件，必要条件？4、This fundamental solution has satisfied free crack boundary conditions.该基本解满足自由裂纹的边界条件。
5、Don't just test the happy path; test boundary conditions and out-of-domain values.不要仅测试愉快路径，还要测试边界条件和范围之外的值。
6、The boundary conditions should be defined before the electron optics computation.在进行电子光学计算之前，必须先界定边界条件。
7、We identify the boundary conditions to be imposed on the laboratory test specimen.我们确定的边界条件对被征收化验标本。
8、This is the same equation, the Schr? Dinger equation, only it has different boundary conditions.相同的方程，薛定谔方程，只不过有不同的限制条件。
水文地质学专业英语单词汇总
专业术语中英文对照表傍河水源地 riverside source field包气带 aeration zone饱和度 degree of saturation饱和流 saturated flow饱水带 saturated zone边界井 boundary well边界条件 boundary condition边界元法 boundary element method标准曲线法（配线法） type-curve method补给区 recharge area补给疏干法 compensation-dewatering method部分排泄型泉 local drainage spring采区充水性图 geologic map of potential flooding in mining area 测压高度 piezometric head层流laminar flow常量元素 common element in groundwater （macroelement ）沉积水（埋藏水） connate water（buried water）成垢作用 boiler scaling成井工艺 well completion technology承压含水层 confined aquifer承压含水层厚度 thickness of confined aquifer承压水 confined water承压水盆地 confined water basin承压水位（头） confining water level持水度 water-holding capacity/ specific retension充水岩层 flooding layer抽水孔 pumping well抽水孔流量 discharge of a pump well抽水孔组 jumping well group抽水量历时曲线图 flow-duration curve抽水试验 pumping test初见（始）水位 initial water level初始条件 initial condition次生盐渍土 secondary salinized soil达西定律Darcy’s law大肠菌群指数 index of coliform organisms大口井 large-diameter wd1大气降水渗入补给量 precipitation infiltration rate单井出水量 yield of single well单孔抽水试验 single well pumping test弹性储存量 elastic storage淡水 fresh groundwater导水系数 transmissivity等降深线 equiodrawdown line等势线 equipotential line等水头面 equipotential surface低频电磁法 very low frequency electromagnetic method 地表疏干 surface draining地表水 surface water地表水补给 surface water recharge地方病 endemic disease地方性氟中毒 endemic fluorosis地面沉降 subsidence地面开裂 land crack地面塌陷 ground surface collapse地下肥水 nutritive groundwater地下集水建筑物 groundwater collecting structure地下径流 underground runoff地下径流模数法 modulus method of groundwater runoff 地下库容 capacity of groundwater reservoir地下卤水 underground brine地下热水 geothermal water地下疏干 underground draining地下水 groundwater地下水补给量 groundwater recharge地下水补给条件 condition of groundwater recharge地下水超采 overdevelopment of groundwater地下水成矿作用 ore-forming process in groundwater地下水储存量（地下水储存资源） groundwater storage地下水的pH值 pH Value of groundwater地下水的碱度 alkalinity of groundwater地下水的酸度 acidity of groundwater地下水的总硬度 total hardness of groundwater地下水等水头线图 map of isopiestic level of confined water地下水等水位线图 groundwater level contour map地下水动力学 groundwater dynamics地下水动态 groundwater regime地下水动态成因类型 genetic types of groundwater regime地下水动态曲线 curve of groundwater regime地下水动态要素 element of groundwater regime地下水分水岭 grot1udwater divide地下水赋存条件 groundwater occurrence地下水化学成分 chemical constituents of groundwater地下水化学类型 chemical type of groundwater地下水环境质量评价groundwater environmental quality assessment 地下水径流量（地下水动储量） groundwater runoff地下水径流流出量 groundwater outflow地下水径流流入量 groundwater inflow地下水均衡 groundwater balance地下水均衡场 experimental field of groundwater balance地下水均衡方程 equation of groundwater balance地下水开采量 groundwater withdrawal地下水开采资源 exploitable groundwater resources地下水可开采量（地下水允许开采量） allowable withdrawal of groundwater 2地下水库 groundwater reservoir地下水埋藏深度 buried depth of groundwater table地下水埋藏深度图 map of buried depth of groundwater地下水模型 groundwater model地下水年龄 age of groundwater地下水年龄测定 dating of groundwater地下水排泄 groundwater discharge地下水盆地 groundwater basin地下水侵蚀性 Corrosiveness of groundwater地下水人工补给 artificial recharge of groundwater地下水人工补给资源 artificial-recharged groundwater resources 地下水设计开采量 designed groundwater withdrawal地下水实际流速 actual velocity of groundwater flow地下水实际流速测定 groundwater actual velocity measurement 地下水数据库 groundwater database地下水数学模型 mathematical model of groundwater地下水水化学图 hydrogeochemical map of groundwater地下水水量模型 groundwater flow model地下水水量评价 evaluation of groundwater quantity地下水水位动态曲线图 hydrograph of groundwater level地下水水质 groundwater quality地下水水质类型 type of groundwater quality地下水水质模型 groundwater quality model地下水天然资源 natural resources of groundwater地下水同位素测定 isotope assaying of groundwater地下水位持续下降 continuously drawndown of groundwater level 地下水污染 groundwater pollution地下水污染评价 groundwater pollution assessment地下水污染物 groundwater pollutants地下水物理模型 physical model of groundwater地下水物理性质 physical properties of groundwater地下水系统 groundwater system地下水预报模型 groundwater prediction model地下水源地 groundwater source field地下水质评价 evaluation of groundwater quality地下水资源 groundwater resources.地下水资源保护 groundwater resources protection地下水资源分布图 map of groundwater resources地下水资源管理区 groundwater resources management地下水资源枯竭 groundwater resources depletion地下水资源评价方法 methods of groundwater resource evaluation地下水总矿化度 total mineralization degree of groundwater地下微咸水 weak mineralized groundwater地下咸水 middle mineralized groundwater地下盐水 salt groundwater地中渗透仪 lysimeter电导率 specific conductance电法测井 electric logging电法勘探 electrical prospecting顶板裂隙带 fissure zone of top wall顶板冒落带 caving zone of top wall定降深抽水试验 constant-drawdown pumping test定解条件 definite condition定流量边界 boundary of fixed flow /constant flow定流量抽水试验 constant-discharge pumping test定水头边界 boundary of fixed water level动水位 dynamic water level断层泉 fault spring断裂带水压导升高度（潜越高度） height of water pressure in fault zone 断面流量 cross-sectional flow对流弥散 convective dispersion多孔抽水试验 multipe wells pumping test多孔介质 porous medium二维流 two-dimensional flow放射性测井 radioactivity logging放射性水文地质图 radio hydrogeological map放射性找水法 radioactive method for groundwater search放水试验 dewatering test非饱和流 unsaturated flow非均匀介质 inhomogeneous medium非均匀流 non-uniform flow非完整井 partially penetrating well非稳定流 unsteady flow非稳定流抽水试验 unsteady-flow pumping test分层抽水试验 separate interval pumping test分层止水 interval plugging分子扩散 molecular diffusion .分子扩散系数 coefficient of molecular diffusion福希海默定律 Forchheimer law辐射井 radial well腐蚀作用 corroding process负均衡 negative balance负硬度 negative hardness富水系数 water content coefficient of mine富水性 water yield property干扰抽水试验 interference-well pumping test干扰井出水量 yield from Interference wells干扰系数（涌水量减少系数） interference coefficient隔水边界 confining boundary隔水层 aquifuge隔水底板 lower confining bed隔水顶板 upper confining bed各向同性介质 isotropic medium各向异性介质 anisotropic medium给水度 specific yield供水水文地质勘查 hydrogeological investigation for water supply 供水水文地质学 water supply hydrogeology拐点法 inflected point method观测孔 observation well管井 tube well灌溉回归系数 irrigation return flow rate灌溉机井 pumping-well for irrigation灌溉系数 irrigation coefficient过水断面 water-carrying section海水入侵 sea-water intrusion3含水层 aquifer含水层储能 energy storage of aquifer含水层弹性释放 elasticity release of aquifers含水层等高线图 contour map of aquifer含水层等厚线图 aquifer impact map含水层等埋深图 isobaths map of aquifer含水层调节能力 regulation capacity of aquifer含水层自净能力 self-purification capability of aquifer含水率 moisture content化学需氧量（COD） chemical oxygen demand环境水文地质勘查 environmental hydrogeological investigation 环境水文地质图 environmental hydyogeologic map环境水文地质学 environmental hydrogeology环境自净作用 environmental self-purification恢复水位 recovering water level回灌井 injection well回灌量 quantity of water recharge回灌水源 recharge water source混合抽水试验 mixed-layer pumping test混合模拟 mixing analog混合作用 mixing hydrochemical action in groundwater激发补给量 induced recharge of groundwater极硬水 hardest water集中供水水源地 well field for concentrated water supply间歇泉 geyser简易抽水试验 simple pumping test降落漏斗 cone of depression降落漏斗法 depression cone method降落曲线 depression curve降水补给 precipitation recharge降水入渗试验 test of precipitation infiltration降水入渗系数 infiltration coefficient of precipitation接触泉 contact spring结构水（化合水） constitutional water （chemical water）结合水 bound water结晶水 crystallization water解逆问题（反演计算） solving of inverse problem解析法 analytic method解正问题（正演计算） solving of direct problem井下供水孔 water supply borehole in mines井中电视（超声成相测井） borehole television（BHTV）径流区 runoff area静止水位（天然水位） static water level （Natural water level）均衡期 balance period均衡区 balance area均匀介质 homogeneous medium均匀流 uniform flow开采模数法 evaluation method of employing groundwater extraction modulus 开采强度法 mining intensity method开采试验法 exploitation pumping test method开采性抽水试验 trail-exploitation pumping test坎儿井 karez空隙 void孔洞 pore space孔隙 pore孔隙比 pore ratio孔隙度（孔隙率） porosity（pore rate）孔隙含水层 porous aquifer孔隙介质 pore medium孔隙水 pore water库尔洛夫式 Kurllov formation矿床充水 flooding of ore deposit矿床充水水源 water source of ore deposit boding矿床充水通道 flooding passage in ore deposit矿床疏干 mine draining矿床疏干深度（疏干水平） dewatering level of mines矿床水文地质 mine hydrogeology矿床水文地质图 mine hydrogeological map矿床水文地质学 mine hydrogeology矿井水文地质调查 survey of mine hydrogeology矿井突水 water bursting in mines矿井涌水 water discharge into mine矿坑水 mine water矿坑突泥 mud gushing in mines矿坑突水量 bursting water quantity of mines矿坑涌砂 sand gushing in mines矿坑涌水量 water yield of mine矿坑正常涌水量 normal water yield of mines矿坑最大涌水量 maximum water yield of mines矿区水文地质勘查 mine hydrogeological investigation 矿泉 mineral spring雷诺数 Reynolds number连通试验 connecting test裂隙 fissure裂隙含水层 fissured aquifer裂隙介质 fissure medium裂隙率 fissure ratio裂隙水 fissure water临界深度 critical depth流量测井 flowmeter logging流量计 flowmeter流网 flow net流线 streamline滤料（填料） gravel pack滤水管（过滤器） screen pipe裸井 barefoot well毛细带 capillary zone毛细管测压水头 capillary piezometric head毛细上升高度 height of capillary rise毛细水 capillary water毛细性 capillarity弥散 dispersion弥散试验 dispersion test钠吸附比（SAR） sodium adsorption ratio拟稳定流 quasi-steady flow凝结水 condensation water凝结水补给 condensation recharge排泄区 discharge area平均布井法 method of well uniform4configuration起泡作用 forming process气体成分分析 gas analysis潜水 phreatic water /unconfined water潜水含水层厚度 thickness of water-table aquifer潜水位 water table潜水溢出量 groundwater overflow onto surface潜水蒸发量 evaporation discharge of phreatic water浅层地震勘探 shallow seismic prospecting强结合水（吸着水） strongly bound water adsorptive water 侵蚀泉 erosional spring侵蚀性二氧化碳 corrosive carbon dioxide裘布依公式 Dupuit formula区域地下水位下降漏斗 regional groundwater depression cone 区域水文地质普查 regional hydrogeological survey区域水文地质学 regional hydrogeology全排泄型泉 complete drainage spring泉 spring泉华 sinter泉流量衰减方程法 method of spring flow attenuation泉水不稳定系数 instability ratio of Spring discharge泉水流量过程曲线 hydrograph of spring discharge泉域 spring area确定性模型 deterministic model扰动土样 disturbed soil sample容积储存量 volumetric storage容水度（饱和含水率） water capacity溶洞 cave cavern溶解他固体总量 total dissolved solids溶解氧（DO） dissolved oxygen溶滤水 lixiviation water溶滤作用 lixiviation软水 soft water弱含水层 aquitard弱结合水（薄膜水） weakly bound water （film water）弱透水边界 weakly-permeable boundary三维流 three-dimensional flow上层滞水 perched water上升泉 ascending spring设汁水位降深 designed drawdown渗流场 seepage field渗流场剖分（单元划分） dissection of seepage field渗流速度 seepage velocity渗入水 infiltration water渗水试验 pit permeability test渗透 seepage渗透率 specific permeability渗透水流（渗流） seepage flow渗透系数（水力传导系数） hydraulic conductivity/ permeability 生化需氧量（BOD） biochemical oxygen demand声波测井 acoustic logging声频大地电场法 audio-frequency telluric method湿地 wet land实井 real well试验抽水 trail pumping手压井 manual-operated pumping well疏干工程排水量 discharge of dewatering excavation疏干巷道 draining tunnel疏干因数 factor of drainage数学模型法 method of mathematical model数学模型检验 verification of mathematical model数学模型识别 calibration d mathematical model数值法 numerical method水文地质勘查报告 report of hydrogeologicai investigation 水动力弥散系数 coefficient of dispersion.水分散晕 water dispersion halo水化学 hydrochemistry水解作用 hydrolytic dissociation水井布局 wafer well arrangement水均衡法 water balance method水均衡方程 equation of water balance水均衡要素 element of water balance水均衡原理 principle of water balance水力坡度 hydraulic gradient水力削减法 hydraulic cut method水流迭加原理 principle of flow superpersitiom水流折射定律 law of seepage flow refraction水圈 hydrosphere水头场 water head field水头场的拟合 fitting of water-head field水头降深场 fieId6f water head drawdown水头降深场的拟合 fitting of water head drawdown field水头损失 water head loss水位计 wellhead water-level gauge水位降深值 drawdown水文地球化学 hydrogeochemistry水文地球化学分带 hydrogeodenml zonality水文地球化学环境 hydrogeochemical environment水文地球化学作用 hydrogeochemical process水文地质比拟法 hydrogeologic analogy method水文地质参数 Hydrogeological parameters水文地质测绘 hydrogeological mapping水文地质单元 hydrogeologic unit水文地质地球物理勘探 hydrogeophysical prospecting水文地质分区 hydrogeological division水文地质概念模型 conceptual hydrogeological model水文地质勘查 hydrogeological investigation水文地质勘查成果 result of hydrogeological investigation 水文地质勘查阶段 hydrogeological investigation stage水文地质勘探孔 hydrogeological exploration borehole水文地质剖面图 hydrogeological profile水文地质试验 hydrogeological test水文地质试验孔 hydrogeological test borehole水文地质条件 hydrogeological condition水文地质学 hydrogeology水文地质学原理 principles of hydrogeology5水文地质钻探 hydrogeological drilling水文水井钻机 hydrogeologic drilling rig水文物探测井 hydrogeological well logging水循环 water cycle水盐均衡 water-salt balance水样 water sample水跃值 hydraulic jump value水质标准 water quality standard水质分析 chemical analysis of water速度水头 velocity head随机模型 stochastic model泰斯公式 Theis formula探采结合孔 exploration-production well同位素水文地质学 isotopic hydrogeology透水边界 permeable boundary透水层 permeable bed透水性 permeability突水水源 source of water bursting突水系数 water bursting coefficient突水预测图 water bursting prediction map土（岩）样 soil （rock）sample土的颗粒分析 grading analysis of soil土壤改良 soil reclamation土壤水 soil water土壤盐渍化 soil salinization脱硫酸作用 desulphidation脱碳酸作用 decarbonation脱硝（氮）作用 denitration完整井 completely penetrating well微量元素 microelement温泉 thermal spring紊流 turbulent flow稳定流 steady flow稳定流抽水试验 steady-flow pumping test稳定水位 steady water level污染通道 pollution channel污染源 pollution source污水资源化 water resources from sewage renewal无压含水层 unconfined aquifer物理模型法 method of physical model细菌总数 bacterial amount下降泉 descending spring咸淡水界面 interface of salt-fresh water相关分析法（回归分析法）correlation analysis method（regression analysis method）硝化作用 nitrification斜井 inclined well虚井 real well悬浮物 suspended solids悬挂泉（季节泉） suspended spring压力传导系数 hydraulic diffusivity压力水头 pressure head雅可布公式 Jacob formula延迟给水（滞后给水） delayed drainage延迟指数 delayed index岩溶含水层 karst aquifer岩溶含水系统 karst water-bring system岩溶介质 karst medium岩溶水 karst water岩石圈 lithosphere岩石渗透性测定 permeability determination of rock盐碱土 saline allkaline soil盐渍土 salinized soil阳离子交替吸附作用cation exchange and adsorption氧化还原电位 oxidation-reduction potential样品采集 sampling遥感技术 remote sensing technology一维流 one-dimensional flow溢流泉 overflow spring影响半径 radius of influence映射法 image method硬水 hard water涌水量方程外推法（试验推断法） discharge equation extrapolation method 游离性二氧化碳 free carbon dioxide有限差分法 finite-difference method有限单元法 finite element method有效降水量 effective precipitation有效孔隙度 effective porosity元素迁移 element migration原生水（初生水） juvenile water（native water）原生盐渍土 primary salinized soil原状土样 undisturbed soil sample越流 leakage越流补给 leakage recharge越流系数 leaky coefficient越流系统 leaky system越流因数（阻越流系数） leaky factor允许水位降深 allowable drawdown蒸发浓缩作用 evaporation-concentration process正均衡 positive balance直线法 linear method重力疏干 gravity drainage重力水 gravity water注水孔 injecting well注水试验 injecting test贮存量变化量 variation of groundwater storage贮水系数（释水系数） storage coefficient专门水文地质学 applied hydrogeology专门性水文地质勘查applied hydrogeclogic investigation专门性水文地质图 special hydrogeological map自流水 artesian water综合水文地质图 synthetic hydrogeoiogical map总水头（渗流水头） total head钻孔流速测 borehole flow-velocity measurement最佳开采量 optimal yield最佳控制水位 optimal controlled water level最佳配水方案 optimal water distribution scheme7.3.2.13斜井 inclined well一般断面尺寸1.8m×2.0 m、倾角20°～40°的倾斜坑道集水工程，适用于开采坚硬岩石、埋深较大的裂隙岩溶水。
力学专业词汇汇总-中英文对照
力学专业词汇汇总-中英文对照拉力 tensile force正应力 normal stress切应力 shear stress静水压力 hydrostatic pressure集中力 concentrated force分布力 distributed force线性应力应变关系linear relationship between stress andstrain弹性模量 modulus of elasticity横向力 lateral force transverse force轴向力 axial force拉应力 tensile stress压应力 compressive stress平衡方程 equilibrium equation静力学方程equations of static比例极限 proportional limit应力应变曲线stress-strain curve拉伸实验tensile test‘屈服应力 yield stress极限应力 ultimate stress轴 shaft梁 beam纯剪切 pure shear横截面积 cross-sectional area挠度曲线 deflection curve曲率半径 radius of curvature曲率半径的倒数 reciprocal of radius of curvature 纵轴 longitudinal axis悬臂梁 cantilever beam简支梁 simply supported beam微分方程 differential equation惯性矩 moment of inertia静矩 staticmoment扭矩 torque moment弯矩 bendingmoment弯矩对x的导数derivative of bending moment with respect to x弯矩对x的二阶导数 the second derivative of bending moment with respect to x静定梁 statically determinate beam静不定梁 statically indeterminate beam相容方程 compatibility equation补充方程 complementary equation中性轴 neutralaxis圆截面 circular cross section两端作用扭矩 twisted by couples at two ends 刚体 rigid body扭转角 twistangle静力等效 statically equivalent相互垂直平面mutually perpendicular planes通过截面形心 throughthe centroid of the cross section一端铰支 pin support at one end一端固定 fixed atone end弯矩图 bending moment diagram剪力图 shear force diagram剪力突变 abrupt change in shear force、旋转和平移 rotation and translation虎克定律hook’s law边界条件 boundary condition初始位置 initial position、力矩面积法moment-area method绕纵轴转动 rotateabout a longitudinal axis横坐标 abscissa扭转刚度 torsional rigidity拉伸刚度 tensile rigidity剪应力的合力resultant of shear stress正应力的大小magnitude of normal stress脆性破坏 brittle fail对称平面 symmetry plane刚体的平衡 equilibrium of rigid body约束力 constraint force重力 gravitational force实际作用力 actual force三维力系 three-dimentional force system 合力矩 resultant moment标量方程 scalar equation、矢量方程 vector equation张量方程 tensor equation汇交力系 cocurrent system of forces 任意一点 an arbitrary point合矢量 resultant vector反作用力 reaction force反作用力偶 reaction couple转动约束 restriction against rotation 平动约束 restriction against translation运动的趋势 tendency of motion绕给定轴转动 rotate about a specific axis沿一个方向运动 movein a direction控制方程 control equation共线力 collinear forces平面力系 planar force system一束光 a beam of light未知反力 unknown reaction forces参考框架 frame ofreference大小和方向 magnitude and direction几何约束 geometric restriction刚性连接 rigidlyconnected运动学关系 kinematical relations运动的合成 superposition of movement固定点 fixed point平动的叠加 superposition of translation刚体的角速度 angular speed of a rigid body 质点动力学 particle dynamics运动微分方程 differential equation of motion 工程实际问题 practical engineering problems 变化率 rate of change动量守恒 conservation of linear momentum 定性的描述 qualitative description点线 dotted line划线 dashed line实线 solidline矢量积 vector product点积 dot product极惯性矩 polar moment of inertia 角速度 angular velocity角加速度 angular acceleration infinitesimal amount 无穷小量definite integral 定积分a certain interval of time 某一时间段kinetic energy 动能conservative force 保守力damping force 阻尼力coefficient of damping 阻尼系数free vibration 自由振动periodic disturbance 周期性扰动viscous force 粘性力forced vibration 强迫震动general solution 通解particular solution 特解transient solution 瞬态解steady state solution 稳态解second order partial differential equation 二阶偏微分方程external force 外力internal force 内力stress component 应力分量state of stress 应力状态coordinate axes 坐标系conditions of equilibrium 平衡条件body force 体力continuum mechanics 连续介质力学displacement component 位移分量additional restrictions 附加约束回复 2楼2012-03-04 20:12举报 |我真想变胖我勒个去8compatibility conditions 相容条件mathematical formulations 数学公式isotropic material 各向同性材料sufficient small 充分小state of strain 应变状态unit matrix单位矩阵dilatation strain 膨胀应变the first strain invariant 第一应变不变量deviator stress components 应力偏量分量the first invariant of stress tensor 应力张量的第一不变量bulk modulus 体积模量constitutive relations 本构关系linear elastic material 线弹性材料mathematical derivation 数学推导a state of static equilibrium 静力平衡状态Newton‘s first law of motion 牛顿第一运动定律directly proportional to 与……成正比stress concentration factor 应力集中系数state of loading 载荷状态st venant’ principle 圣维南原理uniaxial tension 单轴拉伸cylindrical coordinates 柱坐标buckling of columns 柱的屈曲critical value 临界值stable equilibrium 稳态平衡unstable equilibrium condition 不稳定平衡条件critical load 临界载荷a slender column 细长杆fixed at the lower end 下端固定free at the upper end 上端自由critical buckling load 临界屈曲载荷potential energy 势能fixed at both ends 两端固定hinged at both ends 两端铰支tubular member 管型杆件transverse dimention 横向尺寸stability of column 柱的稳定axial force 轴向力elliptical hole 椭圆孔plane stress 平面应力nominal stress 名义应为principal stress directions 主应力方向axial compression 轴向压缩dynamic loading 动载荷dynamic problem 动力学问题inertia force 惯性力resonance vibration 谐振static states of stress 静态应力dynamic response 动力响应time of contact 接触时间length of wave 波长resonancefrequency 谐振频率回复 3楼2012-03-04 20:12举报 |时间盒子832好强大啊，，，顶。
流体力学复习资料及英文专有名词解释
Chapter 1 Fluid statics 流体静力学1. 连续介质假定(Continuum assumption)：The real fluid is considered as no-gap continuousmedia, called the basic assumption of continuity of fluid, or the continuum hypothesis of fluid.流体是由连续分布的流体质点(fluid particle)所组成，彼此间无间隙。
它是流体力学中最基本的假定，1755年由欧拉提出。
在连续性假设之下，表征流体状态的宏观物理量在空间和时间上都是连续分布的，都可以作为空间和时间的函数。
2. 流体质点（Fluid particle ）: A fluid element that is small enough with enough moles to makesure that the macroscopic mean density has definite value is defined as a Fluid Particle. 宏观上足够小，微观上足够大。
3. 流体的粘性（Viscosity ）: is an internal property of a fluid that offers resistance to sheardeformation. It describes a fluid's internal resistance to flow and may be thought as a measure of fluid friction. 流体在运动状态下抵抗剪切变形的性质，称为黏性或粘滞性。
它表示流体的部流动阻力，也可当做一个流体摩擦力量。
The viscosity of a gas increases with temperature, the viscosity of a liquid decreases with temperature. 4. 牛顿摩擦定律（Newton ’s law of viscosity ）：5. The dynamic viscosity （动力黏度）is also called absolute viscosity （绝对黏度）. The kinematicviscosity （运动黏度）is the ratio of dynamic viscosity to density.6. pressibility （压缩性）：As the temperature is constant, the magnitude of pressibility isexpressed by coefficient of volume pressibility (体积压缩系数) к , a relative variation rate （相对变化率） of volume per unit pressure.The bulk modulus of elasticity (体积弹性模量) E is the reciprocal of coefficient of volumepressibility к.7. 流体的膨胀性(expansibility; dilatability)：The coefficient of cubical expansion (体积热膨胀系数) αt is the relative variation rate of volume per unit temperature change.du dzτμ=μνρ=8. 表面力Surface tension : A property resulting from the attractive forces betweenmolecules.σ-----单位长度所受拉力 9. 表面力 Surface force ——is the force exerted on the contact surface by the contacted fluid orother body. Its value is proportional to contact area.作用在所研究流体外表面上与表面积大小成正比的力。
数学英文词汇大全
数学英文词汇大全微积分第一章函数与极限Chapter1 Function and Limit集合set元素element子集subset空集empty set并集union交集intersection差集difference of set基本集basic set补集complement set直积direct product笛卡儿积Cartesian product开区间open interval闭区间closed interval半开区间half open interval有限区间finite interval区间的长度length of an interval无限区间infinite interval领域neighborhood领域的中心centre of a neighborhood领域的半径radius of a neighborhood 左领域left neighborhood右领域right neighborhood映射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--------------------------------------------------------------------------------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 ofcalculus换元公式formula for integration by substitution递推公式recurrence formula反常积分improper integral反常积分发散the improper integral is divergent反常积分收敛the improper integral is convergent无穷限的反常积分improper integral on an infinite interval无界函数的反常积分improper integral of unbounded functions绝对收敛absolutely convergent第六章定积分的应用Chapter6 Applications of the Definite Integrals 元素法the element method面积元素element of area平面图形的面积area of a luane figure直角坐标又称“笛卡儿坐标(Cartesian coordinates)”极坐标polar coordinates抛物线parabola椭圆ellipse旋转体的面积volume of a solid of rotation旋转椭球体ellipsoid of revolution, ellipsoid of rotation曲线的弧长arc length of acurve可求长的rectifiable光滑smooth功work水压力water pressure引力gravitation变力variable force第七章空间解析几何与向量代数Chapter7 Space Analytic Geometry and Vector Algebra向量vector自由向量free vector单位向量unit vector零向量zero vector相等equal平行parallel向量的线性运算linear poeration of vector三角法则triangle rule平行四边形法则parallelogram rule交换律commutative law结合律associative law负向量negative vector差difference分配律distributive law空间直角坐标系space rectangular coordinates 坐标面coordinate plane卦限octant向量的模modulus of vector向量a与b的夹角angle between vector a and b 方向余弦direction cosine方向角direction angle向量在轴上的投影projection of a vector onto an axis数量积，外积，叉积scalar product,dot product,inner product曲面方程equation for a surface球面sphere旋转曲面surface of revolution母线generating line轴axis圆锥面cone顶点vertex旋转单叶双曲面revolution hyperboloids of one sheet旋转双叶双曲面revolution hyperboloids of two sheets柱面cylindrical surface ,cylinder圆柱面cylindrical surface准线directrix抛物柱面parabolic cylinder二次曲面quadric surface椭圆锥面dlliptic cone椭球面ellipsoid单叶双曲面hyperboloid of one sheet双叶双曲面hyperboloid of two sheets旋转椭球面ellipsoid of revolution椭圆抛物面elliptic paraboloid旋转抛物面paraboloid of revolution双曲抛物面hyperbolic paraboloid马鞍面saddle surface椭圆柱面elliptic cylinder双曲柱面hyperbolic cylinder抛物柱面parabolic cylinder空间曲线space curve空间曲线的一般方程general form equations of a space curve空间曲线的参数方程parametric equations of a space curve螺转线spiral螺矩pitch投影柱面projecting cylinder投影projection平面的点法式方程pointnorm form eqyation of a plane法向量normal vector平面的一般方程general form equation of a plane两平面的夹角angle between two planes点到平面的距离distance from a point to a plane空间直线的一般方程general equation of a linein 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线性代数Aadjont(adjugate) of matrix A A 的伴随矩阵augmented matrix A 的增广矩阵Bblock diagonal matrix 块对角矩阵block matrix 块矩阵basic solution set 基础解系CCauchy-Schwarz inequality 柯西-许瓦兹不等式characteristic equation 特征方程characteristic polynomial 特征多项式coffcient matrix 系数矩阵cofactor 代数余子式cofactor expansion 代数余子式展开column vector 列向量commuting matrices 交换矩阵consistent linear system 相容线性方程组Cramer’s rule 克莱姆法则Cross- product term 交叉项DDeterminant行列式Diagonal entries 对角元素Diagonal matrix 对角矩阵Dimension of a vector space V 向量空间V的维数Eechelon matrix 梯形矩阵eigenspace特征空间eigenvalue特征值eigenvector特征向量eigenvector basis 特征向量的基elementary matrix 初等矩阵elementary row operations 行初等变换Ffull rank 满秩fundermental set of solution 基础解系G[center]grneral solution 通解Gram-Schmidt process 施密特正交化过程Hhomogeneous linear equations 齐次线性方程组Iidentity matrix 单位矩阵inconsistent linear system 不相容线性方程组indefinite matrix 不定矩阵indefinit quatratic form 不定二次型infinite-dimensional space 无限维空间inner product 内积inverse of matrix A 逆矩阵Llinear combination 线性组合linearly dependent 线性相关linearly independent 线性无关linear transformation 线性变换lower triangular matrix 下三角形矩阵Mmain diagonal of matrix A 矩阵的主对角matrix矩阵N[center]negative definite quaratic form 负定二次型negative semidefinite quadratic form 半负定二次型nonhomogeneous equations 非齐次线性方程组nonsigular matrix 非奇异矩阵nontrivial solution 非平凡解norm of vector V 向量V的范数normalizing vector V 规范化向量Oorthogonal basis 正交基orthogonal complement 正交补orthogonal decomposition 正交分解orthogonally diagonalizable matrix 矩阵的正交对角化orthogonal matrix 正交矩阵orthogonal set 正交向量组orthonormal basis 规范正交基orthonomal set 规范正交向量组[b]Ppartitioned matrix 分块矩阵positive definite matrix 正定矩阵positive definite quatratic form 正定二次型positive semidefinite matrix 半正定矩阵positive semidefinite quadratic form 半正定二次型Qquatratic form 二次型[center]R[/center]rank of matrix A 矩阵A的秩r(A)reduced echelon matrix 最简梯形阵row vector 行向量Sset spanned by { } 由向量{ }所生成similar matrices 相似矩阵similarity transformation 相似变换singular matrix 奇异矩阵solution set 解集合standard basis 标准基standard matrix 标准矩阵Isubmatrix 子矩阵subspace 子空间symmetric matrix 对称矩阵Ttrace of matrix A 矩阵A 的迹tr(A)transpose of A 矩阵A的转秩triangle inequlity 三角不等式trivial solution 平凡解Uunit vector 单位向量upper triangular matrix 上三角形矩阵Vvandermonde matrix 范得蒙矩阵vector 向量vector space 向量空间Zzero subspace 零子空间zero vector 零空间（本文已被浏览133 次）概率统计概率论与数理统计词汇英汉对照表Aabsolute value 绝对值accept 接受acceptable region 接受域additivity 可加性adjusted 调整的alternative hypothesis 对立假设analysis 分析analysis of covariance 协方差分析analysis of variance 方差分析arithmetic mean 算术平均值association 相关性assumption 假设assumption checking 假设检验availability 有效度average 均值Bbalanced 平衡的band 带宽bar chart 条形图beta-distribution 贝塔分布between groups 组间的bias 偏倚binomial distribution 二项分布binomial test 二项检验Ccalculate 计算case 个案category 类别center of gravity 重心central tendency 中心趋势chi-square distribution 卡方分布chi-square test 卡方检验classify 分类cluster analysis 聚类分析coefficient 系数coefficient of correlation 相关系数collinearity 共线性column 列compare 比较comparison 对照components 构成，分量compound 复合的confidence interval 置信区间consistency 一致性constant 常数continuous variable 连续变量control charts 控制图correlation 相关covariance 协方差covariance matrix 协方差矩阵critical point 临界点critical value 临界值crosstab 列联表cubic 三次的，立方的cubic term 三次项cumulative distribution function 累加分布函数curve estimation 曲线估计Ddata 数据default 默认的definition 定义deleted residual 剔除残差density function 密度函数dependent variable 因变量description 描述design of experiment 试验设计deviations 差异df.(degree of freedom) 自由度diagnostic 诊断dimension 维discrete variable 离散变量discriminant function 判别函数discriminatory analysis 判别分析distance 距离distribution 分布D-optimal design D-优化设计Eeaqual 相等effects of interaction 交互效应efficiency 有效性eigenvalue 特征值equal size 等含量equation 方程error 误差estimate 估计estimation of parameters 参数估计estimations 估计量evaluate 衡量exact value 精确值expectation 期望expected value 期望值exponential 指数的exponential distributon 指数分布extreme value 极值Ffactor 因素，因子factor analysis 因子分析factor score 因子得分factorial designs 析因设计factorial experiment 析因试验fit 拟合fitted line 拟合线fitted value 拟合值fixed model 固定模型fixed variable 固定变量fractional factorial design 部分析因设计frequency 频数F-test F检验full factorial design 完全析因设计function 函数Ggamma distribution 伽玛分布geometric mean 几何均值group 组Hharmomic mean 调和均值heterogeneity 不齐性histogram 直方图homogeneity 齐性homogeneity of variance 方差齐性hypothesis 假设hypothesis test 假设检验Iindependence 独立independent variable 自变量independent-samples 独立样本index 指数index of correlation 相关指数interaction 交互作用interclass correlation 组内相关interval estimate 区间估计intraclass correlation 组间相关inverse 倒数的iterate 迭代Kkernal 核Kolmogorov-Smirnov test柯尔莫哥洛夫-斯米诺夫检验kurtosis 峰度Llarge sample problem 大样本问题layer 层least-significant difference 最小显著差数least-square estimation 最小二乘估计least-square method 最小二乘法level 水平level of significance 显著性水平leverage value 中心化杠杆值life 寿命life test 寿命试验likelihood function 似然函数likelihood ratio test 似然比检验linear 线性的linear estimator 线性估计linear model 线性模型linear regression 线性回归linear relation 线性关系linear term 线性项logarithmic 对数的logarithms 对数logistic 逻辑的。
小学上册第八次英语原题(有答案)
小学上册英语原题(有答案)英语试题一、综合题(本题有100小题，每小题1分，共100分.每小题不选、错误，均不给分)1.The rabbit’s feet help it _________. (跳)2.How many colors are in a standard box of crayons?A. 8B. 16C. 24D. Varies答案: C3.She is _______ (searching) for her keys.4.Coal is formed from the remains of ancient ______.5.The __________ (社会互动) shape experiences.6.My mom loves __________ (草地野餐).7.I see a _______ (fox) in the forest.8.I want to learn how to ___. (dance)9. A _____ is an area of land that rises sharply.10.The ______ (小鸟) builds a nest in the ______ (树上) to keep its eggs safe.11.The __________ (社会挑战) require collaboration.12.We have a ______ (丰富的) schedule filled with activities.13.I saw a _______ (小鸟) building a nest.14.The _____ (fauna) interacts with plant life.15.The bear hibernates during the ______.16.What do we call the distance around a circle?A. DiameterB. RadiusC. CircumferenceD. Area答案: C17.I think having a positive attitude can change our __________.18.The _______ (兔子) has big ears.19.My grandma is very . (我奶奶很。
小学上册第十三次英语第一单元全练全测
小学上册英语第一单元全练全测英语试题一、综合题(本题有100小题，每小题1分，共100分.每小题不选、错误，均不给分)1.The ________ (栖息地破坏) threatens biodiversity.2.During the summer, I often visit the __________. (海滩)3.The sun is shining ________.4.I enjoy ________ (画画) with my friends.5.The _______ of a plant can be different shapes.6. A _______ is a natural boundary made of water.7.The chemical formula for potassium iodide is _____.8.We enjoy visiting the ___. (zoo)9.What do we call the natural home of an animal or plant?A. HabitatB. EnvironmentC. EcosystemD. BiomeA10.Which insect makes honey?A. AntB. FlyC. BeeD. Mosquito11.The dog is _____ (barking/sleeping) in the yard.12.The __________ (历史的回望) reflects identity.13.The weather is ___ (warm) today.14.I enjoy watching ________ in the trees.15.The common name for dihydrogen monoxide is _____ (water).16.What is the term for the process of changing from a caterpillar to a butterfly?A. MetamorphosisB. EvolutionC. GrowthD. TransformationA17.What is the term for the layer of gases surrounding the Earth?A. AtmosphereB. LithosphereC. HydrosphereD. BiosphereA18.The ______ can live a long time.19.Wildflowers add beauty to __________ (自然).20.The _____ (绿意盎然) of the forest is refreshing.21.I love to ______ (与他人一起) learn new skills.22.What do you call a young mouse?A. PupB. KitC. CalfD. Cub23.My brother has a ______ (toy) car.24.I want to _____ (see) a play.25.He has a collection of _______ (邮票).26.The ______ is known for his magic tricks.27.The cake is _______ (rising) in the oven.28.The _____ (globe) shows the world.29.The bird builds a ______.30.The ______ are important for pollination.31.What do you call a person who writes stories?A. AuthorB. JournalistC. PoetD. NovelistA32.I want to be a _______ (teacher/doctor) when I grow up.33.This girl, ______ (这个女孩), loves to play the flute.34.His favorite color is ________.35. A __________ is a common example of a base.36.What is 10 3?A. 6B. 7C. 8D. 9B37.The main component of starch is ______.38.I can ______ (解决) problems creatively.39.How many sides does a triangle have?A. 2B. 3C. 4D. 5B40.An alkali is a type of _______ that dissolves in water.41.I play _____ (视频游戏) after homework.42. A ______ is a measurement of how much a substance can dissolve.43.What do we call the largest type of bear?A. Grizzly BearB. Polar BearC. Black BearD. Kodiak BearB44.The snail moves at a _________ (慢) pace.45.Many plants are ______ (适应性强) to their surroundings.46.The butterfly landed on a ______.47. A ____ is a small mammal that loves to dig.48.My dad works in an _____ building. (office)49.My favorite way to relax is to ________ (听音乐).50.The ______ (植物的适应机制) is a subject of study.51.What do you call a small, round fruit that is usually eaten in salads?A. TomatoB. CucumberC. Bell pepperD. RadishA52. A mixture that is not uniform throughout is called a ______ mixture.53.What does a thermometer measure?A. PressureB. TimeC. TemperatureD. Weight54.The _____ (forest/park) is quiet.55.My sister is a ______. She enjoys learning new languages.56.The ____ is often seen resting in the sun on warm days.57.My favorite sport is ________ (篮球).58.The change of rocks due to heat and pressure is called __________.59.I have a special ________ that keeps secrets.60.Which animal is known for its ability to change colors?A. ZebraB. ChameleonC. ElephantD. KangarooB61.小龙) is a mythical creature. The ___62.The _______ of light can be reflected off surfaces.63. A mixture is made of two or more ______.64.The _______ (Silk Road) was a trade route that connected the East and West.65.We have a ________ (presentation) tomorrow.66.The ____ is a noisy bird that mimics sounds.67.Oxidation-reduction reactions involve the transfer of _____ between substances.68. A _______ (小黄蜂) is busy collecting pollen.69.My birthday is in the month of ________.70.The ancient Romans produced ________ (法律) that influenced modern systems.71.The capital of Azerbaijan is _______.72.What is the name of the state of matter that has a definite volume but no definite shape?A. SolidB. LiquidC. GasD. PlasmaB73.The chemical formula for barium chloride is ______.74.What type of animal is a dolphin?A. FishB. MammalC. ReptileD. AmphibianB75.The _____ (山羊) climbs steep hills.76.I love to help my parents with ______.77.I found a __________ on the ground.78.The cat caught a ______.79.In a combustion reaction, a hydrocarbon reacts with _____ to produce carbon dioxide and water.80.I have a ___ (story/book) to read.81. A solid has a definite shape and _____.82.What is the name of the holiday that celebrates the New Year?A. ChristmasB. ThanksgivingC. New Year's DayD. Independence DayC83. A __________ is a piece of land surrounded by water on three sides. (半岛)84.What is the largest land animal?A. LionB. ElephantC. GiraffeD. HippoB85.My aunt is an excellent ____ (artist) who paints.86.My dog loves to chase after ______ (飞碟).87. A __________ is known for its ability to jump high.88.What do we call the process of making something last longer?A. PreservationB. ConservationC. RestorationD. All of the aboveD89. A covalent bond involves the sharing of ______ between atoms.90.I like to go ______ (滑冰) in winter.91.We go _____ (徒步旅行) in the mountains.92.The __________ (树木) provide shade on hot days.93.My backpack is filled with ______.94.Oxygen is essential for _____ combustion.95.What do we call the main meal of the day?A. BreakfastB. LunchC. DinnerD. SnackC96.What is the capital of the Solomon Islands?A. HoniaraB. GizoC. AukiD. TulagiA97.I _______ (每天) walk to school.98.Birds lay ______ in nests.99.Atoms are made up of protons, neutrons, and ______. 100.I can ___ (run/jump) very far.。
boundary conditions across beams analysis 英文
boundary conditions across beams analysis 英文In a beam analysis, boundary conditions refer to the constraints imposed on the ends of the beam or the supports that hold the beam in place. These boundary conditions determine how the beam will deform and react to applied loads.There are different types of boundary conditions commonly used in beam analysis, including:1. Fixed support: The beam is fully restrained at a support, preventing any movement or rotation.2. Pinned support: The beam is allowed to rotate at the support, but no translation is allowed.3. Roller support: The beam is allowed to move horizontally, but rotation and vertical movement are restricted.4. Free end: The beam is completely unrestrained at the end, allowing for both translation and rotation.The choice of boundary conditions depends on the specific problem being analyzed and the actual supports in the real system. These conditions are essential for determining the reactions, deflections, and bending moments in the beam under various loading conditions.In summary, the boundary conditions across beams refer to the constraints or supports imposed at the ends of the beam, which have a significant impact on the behavior and deformation of the beam.。
小学上册第二次英语第5单元真题
小学上册英语第5单元真题英语试题一、综合题(本题有100小题，每小题1分，共100分.每小题不选、错误，均不给分)1.I want to _____ (read/write) a story.2.Plants can create a ______ (宁静的环境) in our lives.3.What do you call a short story that teaches a lesson?A. TaleB. FableC. MythD. Legend4.The ________ was a famous historical figure who fought for independence.5.What do you call a house made of snow?A. IglooB. CabinC. ChaletD. LodgeA6.We should __________ our hands before eating.7.I like to swim in the ________.8.The chair is _______ (comfortable).9.I like to play with my _________ (拼图) while listening to music.10.My uncle takes me to the ____.11.The country famous for its deserts is ________ (阿联酋).12.The flowers are _______ (开得很美).13.The ________ (rocket) launches into space.14.My friend plays ____ (baseball) every weekend.15.The chemical formula for -hexanol is ______.16.The __________ is known for its beautiful scenery.17.He enjoys playing with his ___. (toys)18. A volcano's opening is called a ______.19.What do you call a baby hedgehog?A. HogletB. KidC. PupD. Kit20.What do you call a group of wolves?A. PackB. FlockC. SwarmD. HerdA21.What do we call the place where we watch movies?A. TheaterB. MuseumC. LibraryD. Restaurant22. A _____ (盆栽) can be kept indoors.23.The ________ was a famous explorer who discovered new lands.24.I like to bake ________ with my grandma.25.What is the capital of Japan?A. SeoulB. TokyoC. BeijingD. BangkokB26.My mom is a great __________ (母亲).27.I have a new ___. (friend)28.What is the capital of the USA?A. New YorkB. Washington D.C. C. Los AngelesD. Chicago29.My favorite season to play outside is ______.30.What is the name of the largest rainforest in the world?A. Congo RainforestB. Amazon RainforestC. TaigaD. Temperate RainforestB31.What do we call the time it takes for the Earth to rotate on its axis?A. DayB. YearC. MonthD. HourA32.The ________ (探险活动) is thrilling and educational.33.What do you call the season when leaves fall from trees?A. WinterB. SpringC. SummerD. Fall34.The ____ is often seen sharing food with its friends.35.The fish swims _____ (fast/slow) in the water.36.The _______ (The Berlin Conference) divided Africa among European powers.37.What is the capital of Malaysia?A. Kuala LumpurB. JakartaC. ManilaD. Bangkok38.The ________ (根部系统) varies among plants.39.__________ are used in baking for their leavening properties.40.I have a _____ (拼装模型) of a car.41.The ________ was a treaty that established new governance.42.Planting _____ (环境友好) gardens can help our planet.43.The chemical formula for iron oxide is _______.44.My favorite outdoor activity is __________ because it’s adventurous.45. A lever can increase the ______ applied to an object.46.I often watch _______ (动画片) on weekends.47. A solar eclipse happens when the ______ passes between the Earth and the sun.48.I love to read ______ books at night.49.I found a ________ in the leaves.50. A prism bends light to create a ______.51.The book is _____ the table. (on)52.Which shape has four equal sides?A. TriangleB. CircleC. SquareD. Rectangle53.My toy _______ can make sounds (我的玩具_______可以发声).54.The ______ of a garden can change with the seasons. (花园的景观可以随着季节而变化。
SautterCOMSOL
SautterCOMSOLDiscrete Projection Methods for Incompressible Fluid Flow Problems and Application to a Fluid-Structure In-teraction ProblemJ?rg-M.SautterMathematischesInstitut,Universit?tDüsseldorf,Germany,**************************.deAbstract.Numerical simulations of transient incompressible?uid?ow in arbitrary(two-or three-dimensional)domains,possibly coupled with other effects,are of great importance in many industrial applications.Discrete projection methods are ef?cient time integration schemes for incompressible?uid?ow simulations.It is shown how the time-dependent Navier-Stokes equa-tions can be implemented using Femlab’s general form.The discretization is performed in such a way that external algorithms,such as discrete projections methods(inlcuding an algebraic mulditgrid solver,etc.),can be applied to solve the discretized system of equations and that complex and highly nonlinear problems such as?uid-structure interaction,e.g.?uid? ow cou-pled with rigid body motion,can be numerically simulated.1IntroductionInteraction of an incompressible?uid and rigid bodies belongs to the class of?uid-structure interaction problems.The coupling between the?uid and a structure can be twofold,i.e.one-way or two-way:The coupling is one-way if the motion of the structure in?uences the?uid ?ow but the action of the?uid?ow upon the structure is negligible.The other way around is of course also possible.A rotating fan or a ship’s propeller are examples of?uid structure interaction problems with one-way coupling;at least in a?rst order approximation.The situation is more complicated when the motion of the structure in?uences the?uid?ow and at the same time the structure’s motion is in?uenced by the?uid?ow.This is called a two-way coupling. Examples are wind power plants and a boulder sinking in water.In the following,the simulation of the motion of a rigid obstacle in a reservoir?lled with an in-compressible?uid will be considered.This is a?uid-stucture interaction problem with two-way coupling in the sense described above.In section2,the underlying Navier-Stokes initial bound-ary value problem will be introduced and its spatial discretization with Femlab is described in section3.The basics of the discrete projection method for the time integration and the solution of the(non-)linear subproblems are described in section4.Finally,a numerical example of a ?uid-structure interaction problem is presented in section5.2Incompressible?uid?owT ransient?ow of isothermal incompressible Newtonian or non-Newtonian?uids is governed by the following Navier-Stokes initial boundary value problem in velocity-pressure form:uu=u in onΓin?ΓD(1c)u=u D onΓsolid?ΓD(1d)f st=(η(?u+(?u)T)?pI d×d)n onΓfb?ΓN(1e)f out=(η(?u+(?u)T)?pI d×d)n onΓout?ΓN(1f)u=u0in?at t=0(1g)?·u0=0in?(1h)n·u0=n·u D onΓD(1i) where u is the?uid velocity,p the pressure,ηthe viscosity, the density,and b a given body force.?denotes the d-dimensional area occupied by the moving?uid andΓ=ΓD∪ΓN=Γin∪Γout∪Γsolid∪Γfb its boundary consisting of parts where?uid?ows into and out of the domain and parts where the?uid suf?ces a no-slip condition or has a free boundary.ΓD and ΓN denote the parts where u is constrained by Dirichlet and Neumann boundary conditions, respectively.f st represents the surface tension in case of a free boundary and f out is the force acting upon the?uid at the outlet.Details can be foundin[6].Solutions of(1)do not only depend on initial data,boundary values,and the viscosity,but also on the Reynolds number.For viscous?uids governed by the Navier-Stokes equations,the solution may show singularities when the domain contains vertices,the boundary values are not continuous,or the type of boundary condition changes between Dirichlet and Neumann. Adaptivity in space and time to control these phenomenons is not covered in this work. Discretizing(1)in space with the Galerkin?nite element method yields the discrete Navier-Stokes equations,which in full generality readMdu ht+?·Γl=F l in?(3a)n TΓl=G l+N R∑m=1R mwhere d alk∈R are the mass coef?cients,Γl(t,x1,...,x d,y1,...,y N)∈R d the?ux vector,and F l(t,x1,...,x d,y1,...,y N)∈R the source term.G l∈R is a boundary source term,µm∈Ra Lagrange multiplier,and R m∈R restricts the solution component y l on the boundary.The equation index l rangesfrom1,...,N,while the constraint index m ranges from1,...,N R. Femlab’s general form is based upon the partial differential equation(3)which can be used to discretize initial boundary value problem(1)in space.There are several ways to do this and a comparison of different implementations can be found in[6].Lety=y(t,x)= u(t,x)p(t,x) ∈R d+1and x∈??R d and N=d+1.The so-called total stress form excels all other forms for our purposes since true physical forces are modeled best.It is given byd a= I d×d0d×1 01×d0 ,Γ= ?η(?u+(?u)T)+pI d×d01×d ,F=b? (u·?)u·u.(4)Advantages of the total stress form are that physical out?ow boundary conditions as well as boundary conditions on a free boundary or a rigid obstacle are natural boundary conditions of the underlying Galerkin?nite element method.Having de?ned the geometry and having generated a mesh in Femlab,the total stress form is simply de?ned by=Γ,=d a,=F.Femlab’s function can be used to perfom the Galerkin?nite element spatial discretiza-tion based on T aylor-Hood elements which yields,after elimination of constraints,D e(y e(t),t)dy e(t)dt=B(u h,u h)?Cp h(6a)C T u h=g(6b) where B(u h,u h)=?A(u h,u h)+D(u h)+f denotes a discrete Burgers operator containing ad-vection and diffusion term as well as body forces and contributions from Dirichlet boundary conditions.Note that in contrast to(2),the discrete gradient operator and the discrete diver-gence operator are adjoint due to the total stress form.4Time integrationIn computational?uid dynamics,discrete projection methods have been introduced as a useful and ef?cient way to signi? cantly reduce the computational cost of time-dependent incompress-ible viscous?ow simulations in the velocity-pressure formulation.This means that the system (6)is split into a series of simpler equations,such as discrete advection-diffusionequations and discrete Poisson equations,for example,and explicit or implicit updates.A fully implicit dis-crete projection method is presented which may be regarded as a discrete counterpart(cf.[9])and fully implicit version of Chorin’s classical projection method(cf.[2,3,4]).More details on discrete projection methods can be found in[6].In order to reduce the computational cost,consider the following splitting scheme and solve1λh.(9a)tUsing this approach,the nonlinear iteration in order to solve(7)is only in the velocity unknowns due to the pressure decoupling,i.e.only“smaller”linear systems compared to a fully coupled approach need to be solved.Therefore,the nonlinear iteration is signi?cantly cheaper com-pared to a fully coupled approach.The linear systems which need to be solved within the nonlinear iteration always have full rank,no matter whether there are pressure modes or not. In addition,only one pressure Poisson equation must be solved per time step in the projection step(8),where possible pressure modes have to be taken into account.This time integration scheme requires(within a simpli?ed Newton method and a preconditioned conjugate gradient method)the solution of linear systemsMu=b(10) and(M+c1?tJ A?c2?tJ D))u=b,c1,c2∈R,(11) in steps(7),(8),and(9)where J A and J D denote the Jacobians of the advection and diffusion term,respectively.These linear subproblems are solved with an algebraic multigrid(AMG) solver(cf.[1,7])based on the Ruge-Stüben algorithm(cf.[5]).In contrast to geometric multigrid methods,AMG requires no a priori given hierarchy of coarse grids.In fact,the construction of a problem-dependent hierarchy–including the coarsening process itself,the transfer operators as well as the coarse-grid operators–is part of the AMG algorithm,based solely on algebraic information contained in the given system of equations(cf.[8]).5A?uid-structure interaction simulationAs an object moves through a?uid,the viscosity of the?uid acts on the moving object with a force that resists the motion of the object.At the same time,the?uid?ow depends on the motion of the obstacle.The?uid velocity on each structure boundary must be constrained to match the rigid-body motion of the structure.The approach presented here is based on body ?tted unstructured moving grids for optimal spatial resolution and the implicit discrete projection method described in the previous section.In order to simulate the motion of N fsi∈N moving obstacles within a?uid,the Navier-Stokes equations are coupled with the equations for rigid body motions.The initial boundary valueproblem for a?uid-structure interaction problem is therefore given by the complete initial bound-ary valueproblem(1)augmented by the following equations for i=1,...,N fsi moving structures fsi(i),du fsi(i)m fsi(i)=u fsi(i)(12b) dtdωfsi(i)I fsi(i)=ωfsi(i)(12d) dtF fsi(i)(u)=ZΓstruct(?pI d×d+η(?u+(?u)T))n(12e)T fsi(i)(u)=ZΓstruct r fsi(i)τT(?pI d×d+η(?u+(?u)T))n(12f) u=u fsi(i)+ωfsi(i)×r fsi(i)onΓfsi(i)(t)(12g) u fsi(i)(0)=u fsi(i),0(12h)x fsi(i)(0)=x fsi(i),0(12i)θfsi(i)(0)=θfsi(i),0(12j)ωfsi(i)(0)=ωfsi(i),0.(12k) Mass,velocity of the center of mass,position of the center of mass,moment of inertia,angularvelocity,and angle of rotation of the i th structure are denoted by m fsi(i),u fsi(i),x fsi(i),I fsi(i),ωfsi(i), andθfsi(i),respectively,and gravity(or any other type of body force)is denoted by g.Equations (12e)and(12f)represent the force and torque exerted upon the i th structure by the?ow.Most important for the simulation is the?uid-structure coupling expressed by the transient no-slip boundary conditions(12g).The initial boundary value problem(12)describes?uid-structure interaction problems as long as there are no collisions between the moving structures.As an example of?uid-structure interaction,consider the situation shown in?gure1.A reservoir is?lled with?uid and more?uid is pumped into the reservoir through the inlet on the left side while?uid leaves the reservoir through the outlet on the right side.Within the reservoir,there is a solid structure(a circle)which moves under body forces(gravity)and the forces of the ?uid acting upon the structure.The domain of the reservoir is represented by18boundary segments.BoundarysegmentΓ1represents the inlet where the velocity pro?le of the?ow is given asu in=u in(s)=(s(1?s),0)Twhere s∈[0,1]linearly parameterizesΓ1.Boundary segmentΓ12is the outlet where homoge-neous traction boundary conditions are applied,i.e.the force acting upon the?uid at the outlet is f out=0∈R2onΓ12.Let the density of the?uid be =1,the viscosityη=0.1,and the body force b=(0,?2)T.The parameters of the structure are as follows:The circle’s radius is r=0.15 and it has a homogeneous mass density.Its mass is m fsi=1and its moment of ineratia I fsi=1. At t=0,the?uid is at rest and the initial position of the center of mass and velocity of the structure are x fsi(0)=(0.3,1.8)T and u fsi(0)=(0,0)T,respectively.In addition,the initial angular velocity of the structure isω(0)=2and its initial angular orientation isθ(0)=0.As the structure moves downward and comes closer to the inlet,it gets swept away by the stream going mainly from inlet to outlet.Figure2shows a sequence of plots of the velocity vector?eld.(a)Initial geometry(b)Initial meshFigure1:Initial con?gurationReferences[1]W.L.Briggs,V.E.Henson,and S.McCormick.A Multigrid T utorial.SIAM,Philadelphia,2000.[2]A.J.Chorin.A numerical method for solving incompressible viscous?ow problems.Journalof Computational Physics,2:12–26,1967.[3]A.J.Chorin.The numerical solution of the Navier-Stokes equations for an incompressibleuid.Bull.Am.Math.Soc.,73:928–931,1967.[4]A.J.Chorin.Numerical solution of the Navier-Stokes equations.Mathematics of Computa-tions,22:745–762,1968.[5]J.W.Ruge and K.Stüben.Algebraic multigrid.In S.F.McCormick,editor,Multigrid Meth-ods,number3in Frontiers in Applied Mathematics.SIAM,Philadelphia,1987.[6]J.-M.Sautter.Discrete Projection Methods for Time-Dependent Viscous IncompressibleFluid Flow Simulations in Arbitrary Domains.PhD thesis,University of Düsseldorf,Germany, June2004.[7]K.Stüben.Algebraic Multigrid(AMG):An Introduction with Applications.GMD ReportNo.70.Gesellschaft für Mathematik und Datenverarbeitung,St.Augustin,Bonn,1999.[8]U.T rottenberg,C.Oosterlee,and A.Schüller.Multigrid.Academic Press,London,2001.[9]S.T urek.Ef?cient solvers for incompressible?ow problems:An algorithmic and compu-tational approach,volume6of Lecture Notes in Computational Science and Engineering.Springer-Verlag,Berlin,1999.(a)t=0.1(b)t=1(c)t=2(d)(e)t=4(f)t=6 Figure2:Velocity?eld。