常微分方程双语课程常用词汇表

1、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a

2、mplitude 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asso

3、ciated 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 bli:kaxis 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

4、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circuit 电路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 c

5、oefficient 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

6、 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a

7、rbitrary 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con

8、verge v. 收敛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

9、. 定义degenerate a. 退化的denominator 分母derive v. 导出derivation n. 求导（数）derivative n. 导数 dirivtivantiderivative 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 diagon

10、al 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distan

11、ce 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defec

12、tive 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ena

13、ble v. 使能够entry n. 元素equate v. 使相等equation 方程Bernoulli equation 伯努利方程Bessels 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Legendres equation 勒让德方

14、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

15、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integratin

16、g 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decim

17、al 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 fu

18、nction 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fact

19、orial 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homoge

20、neous 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inde

21、pendent 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in

22、tegration 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Keplers laws of planetary motion 开普勒行星运动定

23、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

24、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

25、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me

26、an 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 numbe

27、r 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

28、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

29、线  p'ræblparameter 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

30、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 valu

31、e 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

32、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

33、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 matt

34、er 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

35、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-valu

36、ed 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

37、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 ofand 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