数学微积分英汉词典

1、MATHEMATICAL TERMS (Part 1) calculus微积分 definition 定义 theorem 定理 lemma引理 corollary 推论 prove证实 proof证实 show证实 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 X such that 使得 given set集合 finite set有限集 infinite set 无限集 interval 区间 open interval 开区间 closed interva

2、l 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 od

3、d 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 数歹！Jconvergent sequence攵敛数歹！J divergent sequence 发散数歹！J bounded sequence有界数歹！J decreasing sequence® 减数歹U inc

4、reasing sequence 递增数歹！Jlimit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/J、的阶 infinitesimals of the same order同阶无穷小increment 增量continuous

5、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 (二)类间断点removable discontinuity 可去间断点jump discontinuity弼匕跃间断点infinite discontinuity无穷 间断点intermediate value 介值The Intermediate Value Theorem 介值定理zero po

6、int 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 R

7、ule链式法那么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hy

8、perbolic cotangent 双曲余切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 derivativen 阶导数twice differentiable 二阶可导acceleratio

9、n力口速度mean value中值The Mean Value Theorem 中值定理Rolle ' s Theorem 罗尔定理Lagrange ' s Mean Value Theore植格朗日中值定理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 0考0句型未定式L' Hospital ' s骸西、达法那么Taylor ' s formula泰勒公式polynomial多

10、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麦克劳林多项式精确度polynomial approximation 多项式逼近accuracymargin marginal cost marginal revenue elasticity densitymass边际边际本钱边

11、际收益弹性 密度 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(加急定点)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

12、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二分法弦位法牛顿切线法切线法微分学积分 积分学 定积分 不定积分分割黎曼和积分符号被积函数The secant method Newton' s method The tangent method differential calculus integral integral calculus definite integra

13、l indefinite integral partition Riemann sum integral sign integrand upper lower limit of integration 积分上 下 限integration积分求积integrable可积的fx is integrable on a, bintegrable 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 theo

14、rem of integral 积分中值定理The fundamental theorem of calculus 微积分根本定理 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

15、 fraction局部分式partial fraction decomposition 局部分式分解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) to b a 与 b 垂直coordinate 坐标coordinate system 坐标系coordinate axis 坐标轴x-axi

16、s 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圭卜限the first octant第圭卜限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neighb

17、orhood 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f(

18、x,y)关于 x (y)的partial derivative 偏导数partial derivative of f(x,y) with respect to x ( y )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链式法那么implicit function 隐函数implicit differentiation隐函数微分法Jacobian determinant雅可比

19、行歹！J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 m

20、inimum 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 f

21、ield 梯度场potential field 势场potential function 势函数conservative field 保守场gravitational field 弓 I力场force field 力场velocity field 速度场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 inte

22、gration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 coor

23、dinates 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雅可比行歹！J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