微积分中的关键术语

1、微积分中的关键术语常量：习惯用字母a,b,c,d等表示；变量：习惯用字母x,y,z,u,v,w等表示.函数关系：变量与变量之间的对应关系；极限：变量的变化趋势；导数：变量变化的快慢程度（变化率问题）；微分：函数在某一点处，当自变量有一个微小的改变量时，函数所取 得的相应改变量的大小。闵.dy ；积分学：已知某个函数F（X）的导函数f（x），求 F（X），使Fx）=f QValue of function:函数值Variable :变数Vector:向量Velocity :速度Vertical asymptote :垂直渐近线Volume :体积X-axis : x 轴x-coordinate

2、: x 坐标x-intercept : x 截距Zero vector :函数 的零点Zeros of a polynomial :多项式的零点T:Tangent function :正切函数Tangent line :切线Tangent plane :切平面Tangent vector :切向量Total differential:全微分Trigonometric function :三角函数Trigonometric integrals :三角积分Trigonometric substitutions :三角代换法Tripe integrals :三重积分S:Saddle point :鞍

3、点Scalar :纯量Secant line :割线Second derivative ：二阶导数Second Derivative Test:二阶导数试验法Second partial derivative :二阶偏导数Sector :扇形Sequence :数歹USeries :级数Set :集合Shell method :剥壳法Sine function :正弦函数Singularity :奇点Slant asymptote :斜渐近线Slope :斜率Slope-intercept equation of a line :直线的斜截式Smooth curve :平滑曲线Smooth s

4、urface :平滑曲面Solid of revolution :旋转体Space :空间Speed :速率Spherical coordinates :球面坐标Squeeze Theorem :夹挤定理Step function :阶梯函数Strictly decreasing :严格递减Strictly increasing :严格递增Sum :和Surface :曲面Surface integral :面积分Surface of revolution :旋转曲面Symmetry :对称R:Radius of convergence :收敛半径Range of a function :函数

5、的值域Rate of change :变化率Rational function :有理函数Rationalizing substitution :有理代换法Rational number :有理数Real number :实数Rectangular coordinates :百角坐标Rectangular coordinate system :百角坐标系Relative maximum and minimum : 相对极大值与极小值Revenue function :收入函数Revolution , solid of :旋转体Revolution , surface of :旋转曲面Riema

6、nn Sum :黎曼和Riemannian geometry :黎曼几何Right-hand derivative :右导数Right-hand limit:右极限Root :根P、Q:Parabola :抛物线Parabolic cylinder :抛物柱面Paraboloid :抛物面Parallelepiped :平行六面体Parallel lines :并行线Parameter :参数Partial derivative :偏导数Partial differential equation :偏微分方程Partial fractions :部分分式Partial integration

7、:部分积分Partiton :分割Period :周期Periodic function :周期函数Perpendicular lines :垂直线Piecewise defined function :分段定义函数Plane :平面Point of inflection :反曲点Polar axis :极轴Polar coordinate :极坐标Polar equation :极方程式Pole :极点Polynomial :多项式Positive angle :正角Point-slope form :点斜式Power function :幂函数Product :积Quadrant ：象限Q

8、uotient Law of limit:极限的商定律Quotient Rule :商定律M、N、O:Maximum and minimum values : 极大与极小值Mean Value Theorem :均值定理Multiple integrals :重积分Multiplier :乘子Natural exponential function :自 然指数函数Natural logarithm function :自 然对数函数Natural number :自然数Normal line :法线Normal vector :法向 量Number :数Octant :卦限Odd funct

9、ion :奇函数One-sided limit :单边极限Open interval :开区间Optimization problems :最佳化问题Order :阶Ordinary differential equation :常微分方程Origin :原点Orthogonal :正 交的L:Laplace transform : Leplace 变换Law of Cosines :余弦定理Least upper bound :最小上界Left-hand derivative :左导数Left-hand limit:左极限Lemniscate :双钮线Length :长度Level curv

10、e ：等高线LHospitals rule :洛必达法则Limacon ：蛆线Limit :极限Linear approximatio n：线性近似Linear equation :线性方程式Linear function :线性函数Linearity :线性Linearization :线性化Line in the plane :平面上之百线Line in space :空间之直线Lobachevski geometry :罗巴切夫斯基几何Local extremum ：局部极值Local maximum and minimum :局部极大值与极小值Logarithm :对数Logarith

11、mic function :对数函数I:Implicit differentiation :隐求导法Implicit function :隐函数Improper integral :瑕积分Increasing/Decreasing Test :递增或递减试验法Increment :增量Increasing Function :增函数Indefinite integral :不定积分Independent variable :自变数Indeterminate from :不定型Inequality :不等式Infinite point :无穷极限Infinite series :无穷级数Infl

12、ection point :反曲 点Instantaneous velocity :瞬时速度Integer :整数Integral :积分Integrand :被积分式Integration :积分Integration by part :分部积分法Intercepts :截距Intermediate value of Theorem :中间值定理Interval :区间Inverse function :反函数Inverse trigonometric function :反三角函数Iterated integral :逐次积分H:Higher mathematics高等数学/高数E、F、G

13、、H:Ellipse :椭圆Ellipsoid :椭圆体Epicycloid :外摆线Equation :方程式Even function :偶函数Expected Valued:期望值Exponential Function :指数函数Exponents , laws of :指数率Extreme value :极值Extreme Value Theorem :极值定理Factorial :阶乘First Derivative Test: 一阶导数试验法First octant :第一卦限Focus :焦点Fractions :分式Function :函数Fundamental Theore

14、m of Calculus :微积分基本定理Geometric series :几何级数Gradient :梯度Graph :图形Green Formula :格林公式Half-angle formulas :半角公式Harmonic series :调和级数Helix :螺旋线Higher Derivative :高阶导数Horizontal asymptote :水平渐近线Horizontal line :水平线Hyperbola ：双曲线Hyper boloid ：双曲面D:Decreasing function :递减函数Decreasing sequence :递减数列Definit

15、e integral :定积分Degree of a polynomial :多项式之次数Density :密度Derivative :导数of a composite function :复合函数之导数of a constant function :常数函数之导数directional :方向导数domain of :导数之定义域of exponential function :指数函数之导数higher :高阶导数partial :偏导数of a power function :幂函数之导数of a power series :嚣级数之导数of a product :积之导数of a qu

16、otient :商之导数as a rate of change :导数当作变率right-hand :右导数second :二阶导数as the slope of a tangent:导数看成切线之斜率Determinant :行列式Differentiable function :可导函数Differential :微分Differential equation:微分方程partial ：偏微分方程Differentiation :求导法implicit :隐求导法partial :偏微分法term by term :逐项求导法Directional derivatives :方向导数Dis

17、continuity :不连续性Disk method :圆盘法Distance :距离Divergence :发散Domain :定义域Dot product :点积Double integral：二重积分change of variable in :二重积分之变数变换in polar coordinates :极坐标二重积分C:Calculus :微积分differential :微分学integral :积分学Cartesian coordinates :笛卡儿坐标.一般指百角坐标Cartesian coordinates system :笛卡儿坐标系Cauch Mean Value T

18、heorem:柯西均值定理Chain Rule :连锁律Change of variables :变数变换Circle :圆Circular cylinder :圆柱Closed interval :封闭区间Coefficient :系数Composition of function :函数之合成Compound interest :复利Concavity :凹性Conchoid :蚌线Cone :圆锥Constant function :常数函数Constant of integration :积分常数Continuity :连续性at a point :在一点处之连续性of a funct

19、ion :函数之连续性on an interval :在区间之连续性from the left: 左连续from the right: 右连续Continuous function :连续函数Convergence :收敛interval of :收敛区间radius of :收敛半径Convergent sequence:收敛数列series :收敛级数Coordinate： s：坐标Cartesian :笛卡儿坐标cylindrical :柱面坐标polar :极坐标rectangular :百角坐标spherical :球面坐标Coordinate axes :坐标轴Coordinate planes :坐标平面Cosine function :余弦函数Critical point : 临界点Cubic function :三次函数Curve :曲线Cylinder :圆柱Cylindrical Coordinates :圆柱坐标A、B:Absolute convergence :