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原创2024-07-07 21:13·正经车评人
2024年12月28日，词语｜高等数学英文术语对照2018-12-19 10:14·翻译教学与研究Advanced Mathematical Vocabulary高等数学数学词汇英汉对照表Aabscissa, X-coordinate 横坐标absolute value 绝对值absolute convergence 绝对收敛acceleration 加速度accumulating point 聚点accuracy 精度addition, add, sum, summation 和，求和，加法adjugate matrix 转置伴随阵algebra 代数algorithm 算法angle 角antiderivative, primitive function 反导数，原函数approach 趋近arc 弧area of a plane region 平面图形的面积area of a plane region bounded by curves 由曲面围成的平面图形的面积area of surface 曲面面积assume, assumption 假设asteroid 星形线asymptote 渐近线x-axis, y-axis x 轴，y 轴auxiliary equation, characteristic equation 辅助方程，特征方程Bbasis 基boundary 边界bounded by 被…所围成boundedness 有界性Ccalculus 微积分cardioid 心脏线center of gravity 重心center of mass 质心centroid 形心chain rule 链式法则characteristic root 特征根chord 弦circle 圆coefficient 系数cofactor 代数余子式column 列，elementary column transformation (operation) 初等列变换combination 组合comparison test 比较判别法complex number 复数composition of functions 复合函数concave, concavity 凹，凹性condition 条件，conditionally convergent 条件收敛confidence interval 置信区间cone 锥面conj ugate 共轭conjugate complex number 共轭复数conjugate c urve 共轭曲线consistent 相容constant 常数continuous 连续的contour, level line 等值线，等高线contradiction 矛盾，by contradiction 反证法convergence, convergent 收敛，convergence test 收敛性判别法convex, convexity 凸，凸性coordinate system 坐标系，rectangular/cylindrical/spherical coordinate system 直角/柱面/球面坐标系，polar coordinate system 极坐标系coordinates of vector 向量的坐标corollary 推论Cramer’s Rule 克拉默法则cross product (or outer product, vector product) 叉积（或外积、向量积）cumulant 积累量cumulant generating function 积累量母函数curve 曲面cylinder 柱面D(is) defined to be 定义为definite integral 定积分definite integral with variable upper limit 积分上限函数definition 定义denominator 分母denote, denote to be, denoted by 表示为dependent variable 因变量derivative 导数determinant 行列式diagonal 对角线，diagonalization of a marix 矩阵的对角化diameter 直径dimension 维，维数directional angle 方向角directional cosines 方向余弦discrete 离散的disk 圆盘，圆盘闭区域divergent, divergence 发散displacement 位移first/second/nth derivative 一阶/二阶/n 阶导数right-hand (left-hand) derivative 右（左）导数difference, subtraction, subtract 差，减法，相减differentiable 可倒的，可微的differential 微分，differential calculus 微分学discontinuity 间断，point of discontinuity 间断点distribution 分布normal distribution 正态分布Bernoulli distribution 伯努利分布binomial distribution 二项分布Poisson distribution 泊松分布negative binomial distribution 负二项分布geometric distribution 几何分布hypergeometric distribution 超几何分布uniform distribution 均匀分布exponential distribution 指数分布Gamma distribution 伽马分布Weibull distribution 韦伯尔分布lognormal distribution 对数正态分布chi-distribution 卡方分布student t-distribution 学生t 分布F-distribution F 分布division, divide, quotient 除法，相除，商domain, natural domain 定义域，自然定义域dot product (or inner product, scalar product) 点积（或内积、数量积）double product 二重积分Eeigenvalue, eigenvector 特征值，特征向量element 元素elementary transformation 初等变换ellipse 椭圆ellipsoid 椭球面elliptic cylinder 椭圆柱面entry 向量的分量，元素equal, be equal to 相等，equation 等式equilibrium 平衡even function 偶函数exclusive 互斥的mutually exclusive 完全互斥expansion 展开式expectation (expected value) 期望exponential function 指数函数expression 表达式，express y in terms of x 将y 表示为x 的一个式子exterior point 外点absolute/global extreme values 最大最小值relative/local extreme values 极值Ffactorial 阶乘find, compute, evaluate 计算first-order linear differential equation 一阶线性微分方程first-order separable differential equation 一阶可分离变量微分方程focus 焦点formula 公式fraction 分数proper fraction, 真分数，improper fraction 假分数function 函数function determined implicitly by equation 由方程确定的隐函数function determined by parametric equation 由参数方程确定的函数Foundation Theorem of Calculus 微积分基本定理fundamental solution 基础解GGauss-Jordan Elimination 高斯-若尔当消元法general equation of a plane 平面的一般式方程general solution 通解generator 分母geometry 几何geometric meaning (interpretation, significance) of derivative 导数的几何意义given 给定，设gradient 梯度gradient vector 梯度向量graph of a function 函数图像gravitational force 引力Hhemisphere 半球面homogeneous equation 齐次方程horizontal 水平horizontal asymptote 水平渐近线hydrostatic force 水压力hyperbola 双曲线hyperbolic cylinder 双曲柱面hyperboloid 双曲面hyperboloid of one sheet 单页双曲面hypothesis 假设、题设hypothesis testing 假设检验Iidentity 恒等式imaginary part 虚部improper integral 反常积分increment 增量indefinite integral 不定积分independent variable 自变量indeterminate form 未定式index 指标inequality 不等式infinitesimal 无穷小量infinitesimal of higher order 高阶无穷小equivalent of infinitesimals 等价无穷小inflection point 拐点initial-value problem 初值问题integer 整数positive (negative) integer 正（负）整数integral 积分integral calculus 积分学integrating factor 积分因子Lebesgue integral 勒贝格积分Riemann integral 黎曼积分integrable 可积的integrable with variable upper limit 积分上限函数integrand 被积函数integration by parts 分部积分法integration by substitution 换元积分法integration curve 积分曲线intercept 截距，x-intercept x 轴上的截距interior point 内点Intermediate value Theorem 介值定理intersect 相交intersection 交集interval 区间closed (open) interval 闭（开）区间interval of convergence 收敛区间inverse 反、逆inverse function 反函数inverse matrix 逆矩阵inverse trigonometric function 反三角函数inversely proportional to 反比与irrational number 无理数iterated integral 累次积分iteration 秩代JJacobian matrix 雅各比矩阵Llaminar 平面薄片Law of Parallelogram 平行四边形法则lemma 引理length of an arc 弧长let 设、令limit 极限right-hand (left-hand) limit 右（左）极限the limit of a sequence 数列极限the limit of f(x) as x approaches x 当x 趋近于x 时f(x) 的极限the limit of f(x) as x approaches infinity 当趋近与无穷大时f(x) 的极限line integral 曲线积分line segment 线段linear algebra 线性代数linear approximation 线性逼近linear combination 线性组合linear function 线性函数linear operations 线性运算linearly dependent (independent) 线性相关/无关logarithmic differentiation 对数求导法logarithmic function 对数函数lower limit 积分下限Mmapping 映射mathematics induction 数学归纳法matrix, matrics 矩阵block matrix 分块阵diagonal matrix 对角阵elementary matrix 初等矩阵identity matrix 单位矩阵unit matrix 单位矩阵invertible matrix 可逆矩阵singular matrix 奇异阵，降秩阵non-degenerate matrix 非退化阵scalar matrix 数量阵square matrix 方阵orthogonal matrix 正交阵symmetric matrix 对称阵skew-symmetric matrix 反对称阵full rank matrix 满秩阵maximum 最大值maximal linearly independent subset 最大线性无关组mean value theorem 中值定理median 中位数minimum 最小值mixed product, box product 混合积mode 众数moment 矩量moment matrix 矩量矩阵moment generating function 矩量母函数moment of a force 力矩moment of inertia about x-axis 对于x 轴的转动惯量monotonely decrease 单调减少monotonely increase 单调增加monotonicity 单调性multiplication, multiple, product 积，乘法，相乘multivariable function 多元函数Nnatural number 自然数natural domain 自然定义域necessary condition 必要条件neighborhood 邻域deleted neighborhood 去心邻域nontrivial solution 非平凡解norm 范数normal line 法线normal plane 法平面normal vector 法向量notation 记号numerator 分子Oodd function 奇函数order 次序/ 阶/导数的阶/矩阵的阶/行列式的阶operation 运算optimization 最优化order-reducible differential equation 可降阶微分方程ordinary differential equation (ODE) 常微分方程ordinate, y-coordinate 纵坐标orthogonal 正交的orthogonal basis 正交基orthonormal basis 规范正交基oscillatory 振动的Pparabola 抛物线parabolic cylinder 抛物柱面paraboloid 抛物面parallel to 平行于parallelogram 平行四边形parameter 参数parametric equations of a line 直线的参数方程parity of a function 函数的奇偶性partial derivative 偏导数first partial derivative 一阶偏导数mixed higher partial derivative 高阶混合偏导数part 部分integration by parts 分部积分法partial differential equation (PDE) 偏微分方程partial fraction decomposition 部分分式分解partial sum sequence 部分和数列particular solution 特解pencil of planes 平面束period of a function 函数的周期periodic function 周期函数permutation 排列perpendicular to 垂直于plane 平面plane region 平面图形plane rectangular coordinate system 平面直角坐标系plane analytic geometry 平面解析几何point 点common point 公共点，交点point-normal equation of a plane 平面的点法式方程polar coordinate system 极坐标系polygon 多边形polynomial function 多项式函数position function 位置函数power 乘幂power function 幂函数power series 幂级数probability 概率probability density function 概率密度函数probability generating function 概率母函数probability mass function 概率质量函数problem, question 问题product 乘积projection 投影proof, prove 证明properties 性质proportional to 正比于inversely proportional to 反比与proposition 命题pyramid 棱锥Qquadratic 二次的，二次quadrature 积分过程，正交的quadric surfaces 二次曲面quality 质量quantity 数量quotient 商Rradian 弧度radius 半径random variable 随机变量rank of a matrix 矩阵的秩range 值域the rate of change of y with respect to x y 对于x 的变化率rational function 有理函数rational number 有理数ratio test 比值判别法real number 实数rectangle 矩形regression 回归linear regression 线性回归related rate of change 相关变化率right circular cylinder 圆柱面right-hand coordinate system 右手坐标系root-extract 开根root of an equation 方程的根root test 根值判别法rose of three loops 三叶玫瑰线row 行elementary row transformation (operation) 初等行变换Ssaddle 马鞍面sample 样本scalar 数量，标量secant 正割secant line 割线second-order homogeneous linear equation with constant coefficient二阶常系数齐次微分方程second-order nonhomogeneous linear equation with constant coefficient 二阶常系数非齐次微分方程sequence 数列series 级数infinite series 无穷级数Taylor series (expansion) 泰勒公式set 集合show 证明single variable function 一元函数slope 斜率space 空间vector space 向量空间linear space 线性空间space analytic geometry 空间解析几何2D(Dimension) space 二维空间space rectangular coordinate system 空间直角坐标系squeeze rule 夹逼准则solid 立体solid of revolution 旋转体solution, solve 解speed 速率span 生成，张成sphere 球面standard deviation (std) 标准差state 叙述stationary point 驻点stochastic 随机的stochastic differential equation (SDE) 随机微分方程straight line 直线subset 子集subspace 子空间substitute, substitution 代入，置换integration by substitute 换元积分法sufficient condition 充分条件sum, summation 和，求和sum of a series 级数的和suppose, supposition 假设surface integral 曲面积分symbol 符号symmetry, symmetric 对称symmetric equations of a line 直线的对称式方程system of equations 方程组system of linear equations 线性方程组Ttangent 正切tangent line 切线tangent plane 切面theorem 定理transformation 变换translation 平移trajectory 轨迹trapezoid 梯形triangle 三角形trigonometric function 三角函数hyperbolic trigonometric function 双曲三角函数triple integral 三重积分total differential 全微分total increment 全增量Uunbiased 无偏的union 全集unit vector 单位向量unknown 未知数upper limit 积分上限Vvalue 值variable 变量，可变的variance 方差vector 向量n-dimensional vector N 维向量velocity 速度verify 证明vertex 顶点 (复数vertices)vertical 验证vertical asymptote 铅直渐近线volume of a solid 立体体积the volume of a solid of revolution 旋转体的体积Wthe work done by a force 某力所做的功Zzero 零zeros of a polynomial 多项式的零点Mathematical Sentence Patterns1. If …… , (then) …… (若设……，则有……)2. Let …… , then …… . Therefore …… , so …… (令……，则…… ；于是……，因此……)3. By …… , we have …… (根据……，可得……)4. Prove (that) …… (证明……)5. Compute that …… (计算……)6. Given …… , find …… (设……，证明……)7. Solve the equation for y in terms of x (将方程中的y 对于x 解出来)8. Since …… , (we have, it follows that) …… (因为……，所以可推得……)9. Assume (suppose) that …… , then ……. Hence, …… (假设……，则有……；因此…… )10. By hypothesis …… , hence ……, and therefore …… (根据题设……，可得……，因此……)11. The above results imply that …… (根据上述结果可得……)12. When …… , …… becomes …… (当……时，……变为……)13. Similarly ……(相似的/ 同理可得……)14. In general …… (一般的……)15. Specially …… (特别的……)16. Without loss of generality, we assume that …… (不失一般性，可设……)17. Substitute a for x in (*), we obtain…… (在(*)中用a 代替x ，可得……)本文转自：译匠（请点击阅读原文关注）
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原创2024-06-15 12:38·汽车星
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