常微分方程雙語課程常用詞匯表

1、常微分方程雙語課程 常用詞匯表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 總加速度upward acceleration 向上的加速度account（for） v. 占去algebra 代數algebraic equation 代數方程linear algebra 線性代數the fundamental theorem of algebra 代數學基本定理amount v. 總計 n. 總數a

2、mplitude n. 振幅application n. 應用by repeated application of 反復應用apply v. 應用approach v. 趨近于approach zero 趨近于零approach infinity 趨近于無窮area n. 面積cross-sectional area 橫截面積the horizontal cross-sectional area 水平方向的截面積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. 聯系asso

3、ciated a. 相應的associated with 對應于的associated homogeneous linear equation 相應的齊線性方程associativity n. 結合律assume v. 假設assumption n. 假設asymptote 漸近線oblique asymptote 斜漸近線 bli:kaxis 數軸negative x -axis 負x 軸 positive y -axis 正y 軸x -axis x 軸 y -axis y 軸base n. 基be present v. 出現body 天體boundary n. 邊界bounded a. 有

4、界的 unbounded a. 無界的brine 鹽水calculus 微積分elementary calculus 初等微積分capacitor 電容器case 情形exceptional case 例外情形chain rule （求導的）鏈式法則circuit 電路clockwise 順時針clockwise direction 順時針方向counterclockwise 逆時針counterclockwise direction 逆時針方向close v. 閉closed container 封閉的容器closed interval 閉區(qū)間coefficient 系數constant c

5、oefficient 常系數leading coefficient 首項系數undetermined coefficient 待定系數variable coefficient 變系數collect v. 整理collect coefficients 整理系數column 列commute v. 交換commutative a. 交換的commutativity 交換性property of commutativity 交換性質complete a. 完備的incomplete a. 不完備的complex a. 復的complex conjugate 復共軛的complex conjugate

6、 pairs 復共軛對complex conjugate roots 復共軛根component n. 分量componentwise 分量形式composition 復合compress v. 壓縮compute v. 計算concentration n. 濃度condition 條件a given initial condition 一個給定的初始條件initial condition 初始條件necessary condition 必要條件sufficient condition 充分條件the given condition 給定的條件conjugate 共軛的constant 常數a

7、rbitrary constant 任意常數constant multiple 數乘constant of integration 積分常數constant speed 常速度damping constant 阻尼常數positive constant 正的常數continuity n. 連續(xù)性 discontinuity 不連續(xù)性continuous 連續(xù)的1 / 7continuous function 連續(xù)函數continuous partial derivative 連續(xù)偏導數discontinuous 不連續(xù)的piecewise continuous 分段連續(xù)的convention

8、慣例converge v. 收斂convergence n. 收斂absolute convergence 絕對收斂uniform convergence 一致收斂coordinate 坐標coordinate axis 坐標軸polar coordinates 極坐標corresponding a. 相應的cube 立方，立方體current 電流cylinder 柱，柱面dashpot 減震器decomposition 分解partial fraction decomposition 部分分式分解defect n. 虧量defective v. 虧損的define v. 定義definit

9、ion n. 定義degenerate a. 退化的denominator 分母derive v. 導出derivation n. 求導（數）derivative n. 導數 dirivtivantiderivative 原函數first derivative 一階導數second derivative 二階導數the highest derivative 最高階導數determine v. 確定determinant 行列式determinant of coefficients 系數行列式operational determinant 算子行列式diagonal 對角線principal d

10、iagonal 主對角線differ v. 不同difference n. 差differentiable 可微的differentiable function 可微函數differentiability 可微性differentiability condition 可微性條件differential n. 微分differential form 微分形式differentiate v. 微分differentiate term wise 逐項微分differentiation n. 微分（運算）term-by-term differentiation 逐項微分displacement 位移d

11、istance 距離distinct 不同的distinct real roots 不同的實根distributives 分配性diverge v. 發(fā)散divide v. 劃分，除subdivide 細分domain 定義域double 重，二重，雙double root 二重根duplicate v. 復制、重復duplication n. 復制、重復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 復共軛特征值

12、defective eigenvalue 不完備的特征值multiple eigenvalue 多重特征值zero eigenvalue 零特征值eigenvector 特征向量generalized eigenvector 廣義特征向量rank generalized eigenvector r 階廣義特征向量element 元素diagonal element 對角元off-diagonal element 非對角元element wise 逐個元素地ellipse 橢圓elliptical orbit 橢圓型軌道employ v. 利用employ the technique of 利用

13、技術enable v. 使能夠entry n. 元素equate v. 使相等equation 方程Bernoulli equation 伯努利方程Bessels equation 貝賽爾方程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 恰當微分方程higher-degree equation 高次方程homogeneous equation 齊次方程Legendres equation

14、 勒讓德方程linear first-order equation 一階線性方程Logistic equation 邏輯斯蒂方程natural growth equation 自然增長方程ordinary differential equation 常微分方程partial differential equation 偏微分方程quadratic equation 二次方程reducible equation 可降階方程second-degree equation 二次方程separable differential equation 可分離變量方程simultaneous equations

15、 聯立方程組equilibrium position 平衡位置equivalent 等價的be equivalent to 等價于equivalently 等價地error 誤差average error 平均誤差existence 存在existence-uniqueness theorem 存在唯一性定理exponent 指數negative exponent 負指數exponential 指數(的)exponential function 指數函數matrix exponential 矩陣指數factor n. 因式,因子v. 分解因式common factor 公因式,公因子integ

16、rating factor 積分因子linear factor 一次因式irreducible quadratic factor 二次不可約因式factorization n. 因子分解field 場、域direction field 方向場first 第一的the first two 前兩（個）flow v. 流動n. 流量 inflow n. 流入(量) outflow n. 流出(量)focus 焦點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

17、decimal form 小數形式explicit form 顯式形式implicit form 隱式形式polar form 極坐標形式the standard form 標準形式upper triangular form 上三角形式former a. 以前的the former 前者formula 公式fraction 分式,分數frequency 頻率function 函數analytic function 解析函數coefficient function 系數函數complementary function 補函數component function 分量函數constant-valu

18、ed function 常數值函數continuous function 連續(xù)函數piecewise continuous function 分段連續(xù)函數decreasing function 單調減函數differentiable function 可微函數n times differentiable function n 階可微函數twice differentiable function 二階可微函數sufficiently differentiable function 足夠階可微函數discontinuous function 不連續(xù)函數elementary function 初等函

19、數factorial function 分式函數increasing function 單調增函數matrix-valued function 矩陣值函數position function 位置函數rational function 有理函數real-valued function 實值函數trigonometric function 三角函數unknown function 未知函數vector-valued function 向量值函數generalize (to) v. 推廣generalization n. 推廣graph 圖象hemispherical 半球形的hold v. 成立h

20、omogeneous 齊(次)的nonhomogenous 非齊(次)的hyperbolic 雙曲型的hyperbolic cosine 雙曲余弦hyperbolic sine 雙曲正弦hypothesis n. 假設hypotheses n. 假設(復數形式)identity 恒等式identity principle 恒等原理trigonometric identity 三角恒等式illustrate v. 說明imaginary part 虛部immaterial a. 不重要的, 不相干的imply v. 意味著, 暗示impulse 脈沖independent a. 獨立的, 不相關

21、的independent of 獨立于inductor 電感器initial 開始的, 最初的initial condition 初始條件initial position 初始位置initial population 初始人口數initial velocity 初始速度integer 整數nonnegative integer 非負整數integral 積分definite integral 定積分improper integral 非正常積分indefinite integral 不定積分integral sign 積分號integrate v. 積分integrate by parts 分

22、部積分integration n. 積分integration of both sides 兩邊積分interior n. 內部in terms of 根據interval 區(qū)間closed interval 閉區(qū)間 interval of real number 實數區(qū)間open interval 開區(qū)間 subinterval 子區(qū)間bounded subinterval 有界子區(qū)間the ends of the interval 區(qū)間的端點the whole interval 整個區(qū)間involve v. 包含，涉及Keplers laws of planetary motion 開普勒

23、行星運動定律latter a. 后期的，末期的the latter 后者left-hand side 左邊like 類似，相似like powers 同次冪like term 同類項limit 極限take the limit 取極限upper limit 上極限line 線，線條line segment 線段real line 實數軸straight line 直線tangent line 切線the line tangent (to) 與相切的直線the entire real line 整個實軸linear 線性的linear combination 線性組合linear depende

24、nce 線性相關linear independence 線性無關nonlinear 非線性的linearly 線性地linearly dependent 線性相關的linearly independent 線性無關的linearly independent solutions 線性無關解linearity 線性性liter 升logarithm 對數logarithmic term 含有對數的項long division 長除法major semi axis 長半軸mass (物體的)質量mathematical model 數學模型mathematical modeling 數學建模matr

25、ix 矩陣augmented matrix 增廣矩陣coefficient matrix 系數矩陣diagonal matrix 對角矩陣exponential matrix 指數矩陣fundamental matrix 基解矩陣identity matrix 單位矩陣inverse matrix 逆矩陣matrix addition 矩陣加法matrix multiplication 矩陣乘法nonsingular matrix 非奇異矩陣singular matrix 奇異矩陣square matrix 方陣upper triangular matrix 上三角矩陣zero matrix

26、零矩陣mean value theorem for integral 積分中值定理method 方法straightforward method 直接的方法minimum 最小值minus prep. 減,減去;負的minus sign 負號motion 運動free undamped motion 無阻尼自由運動simple harmonic motion 簡諧運動multiply v. 乘,倍增multiplication n. 乘法multiplicity n. 重數nature 自然, 本質nilpotent 冪零的number 數complex number 復數imaginary

27、number 虛數negative number 負數nonnegative number 非負數positive number 正數real number 實數unknown number 未知數numerator (分數的)分子operate v. 運算,作用operation n. 運算,操作elementary row operation 初等行變換operator 算子polynomial operator 多項式算子orbit 軌道order 階first-order equation 一階方程fourth-order equation 四階方程of exponential ord

28、er 指數階的second-order equation 二階方程nth-order equation n 階方程the mixed second-order partial derivative 二階混合偏導數the order of a differential equation 微分方程的階origin 原點original 原來的the original equation 原方程the original form 原來的形式oscillate v. 振動oscillation n. 振動forced oscillation 強迫振動free oscillation 自由振動parabo

29、la 拋物線  p'ræblparameter 參數variation of parameters 常數變易法parameterize v. 參數化parameterization n. 參數化particle 粒子phase angle 相角phase portrait 相圖plane 平面point 點end point 端點isolated point 孤立點ordinary point 常點singular point 奇點regular singular point 正則奇點irregular singular point 非正則奇點polynomial

30、多項式n th-degree polynomial n 次多項式a polynomial of degree n n 次多項式a polynomial of lower degree 次數較低的多項式Taylor polynomial 泰勒多項式possible 可能的possibility 可能性power 冪power function 冪函數in powers of x x 的冪in powers of x a x a 的冪presence 出現, 在場preceding 前面的prime 求導符號“撇”problem 問題mathematical problem 數學問題initial

31、 value problem 初始值問題proceed v. 繼續(xù)進行, 繼續(xù)下去product 乘, 積dot product 點積product rule 乘法法則scalar product 點積,數積,內積property 性質proposition 命題quotient 商radius 半徑radius of convergence 收斂半徑rate 速率at a rate of 以的速率at a rate proportional to 以與成正比的速率birth rate 出生率 death rate 死亡率time rate of change of (something) 關

32、于時間的變化率interest rate 利率reactant 反應物readily 容易地real part 實部recall v. 記起,回顧rectangle 長方形, 矩形open rectangle 開矩形recurrence relation 遞推關系many-term recurrence relation 多項間的遞推關系two-term recurrence relation 兩項間的遞推關系recursion formula 遞推公式reduce v. 化簡, 簡化, 約簡reduction n. 化簡, 簡化, 約簡reduction of order 降階resisto

33、r 電阻器result n. 結果v. 導致(in)revolution n. 旋轉right-hand side 右邊root 根characteristic root 特征根complex root 復根double root 二重根equal roots 相等的根k-fold root k 重根rational root 有理根real root 實根repeated root 重根the square root 平方根triple root 三重根rotation n. 旋轉counterclockwise rotation 逆時針旋轉routine 例行的; 平凡的a routine

34、 matter 平凡的情形row 行scalar 純量(的), 數量(的), 標量(的)series 級數binomial series 二項式級數geometric series 幾何級數harmonic series 調和級數infinite series 無窮級數power series 冪級數convergent power series 收斂的冪級數power series representation 冪級數表示power series in x x的冪級數power series in x a x a 的冪級數power series solution 冪級數解Taylor se

35、ries 泰勒級數set 集合show v. 證明side 邊left-hand side 左邊 right-hand side 右邊simple 簡單的simplify v. 簡化, 化簡simplification n. 簡化, 化簡singularity 奇異性slope 斜率slope field 斜率場smooth 光滑的 piecewise smooth 逐段光滑的solute n. 溶質，溶解物solution n. 解explicit solution 顯式解 implicit solution 隱式解infinitely many solutions 無窮多解negative

36、-valued solution 負值解period ice solution 周期解positive-valued solution 正值解singular solution 奇解solution curve 解曲線the (a) genera l solution 通解the particular solution 特解solve v. 解solvent n. 溶劑some 某個some open interval 某個開區(qū)間spring 彈簧spring constant 彈性系數step 步驟finitely many steps 有限多步stretch 拉伸subject(to) a

37、. 易受的ad.在條件下subscript 下標even subscript 偶下標 odd subscript 奇下標substitute v. 代入substitution n. 代入direct substitution 直接代入back substitution 回代subtract v. 減去subtraction n. 減去suffice v. 足夠sufficient n. 足夠的, 充分的sufficient condition 充分條件sum n. 和sum zero 總和為零summand 被加數summation 求和(法), 累加, 加法the index of summation 求和的指標the sum ofand 與的和superposition 疊加symmetry 對稱symmetric form 對稱形式system 方程組,系統(tǒng)first-order system 一階方程組higher-order system 高階方程組two-dimensional system