微積分中的關(guān)鍵術(shù)語

1、微積分中的關(guān)鍵術(shù)語常量：習(xí)慣用字母a,b,c,d等表示；變量：習(xí)慣用字母x,y,z,u,v,w等表示.函數(shù)關(guān)系：變量與變量之間的對應(yīng)關(guān)系；極限：變量的變化趨勢；導(dǎo)數(shù)：變量變化的快慢程度（變化率問題）；微分：函數(shù)在某一點處，當自變量有一個微小的改變量時，函數(shù)所取 得的相應(yīng)改變量的大小。閔.dy ；積分學(xué)：已知某個函數(shù)F（X）的導(dǎo)函數(shù)f（x），求 F（X），使Fx）=f QValue of function:函數(shù)值Variable :變數(shù)Vector:向量Velocity :速度Vertical asymptote :垂直漸近線Volume :體積X-axis : x 軸x-coordinate

2、: x 坐標x-intercept : x 截距Zero vector :函數(shù) 的零點Zeros of a polynomial :多項式的零點T:Tangent function :正切函數(shù)Tangent line :切線Tangent plane :切平面Tangent vector :切向量Total differential:全微分Trigonometric function :三角函數(shù)Trigonometric integrals :三角積分Trigonometric substitutions :三角代換法Tripe integrals :三重積分S:Saddle point :鞍

3、點Scalar :純量Secant line :割線Second derivative ：二階導(dǎo)數(shù)Second Derivative Test:二階導(dǎo)數(shù)試驗法Second partial derivative :二階偏導(dǎo)數(shù)Sector :扇形Sequence :數(shù)歹USeries :級數(shù)Set :集合Shell method :剝殼法Sine function :正弦函數(shù)Singularity :奇點Slant asymptote :斜漸近線Slope :斜率Slope-intercept equation of a line :直線的斜截式Smooth curve :平滑曲線Smooth s

4、urface :平滑曲面Solid of revolution :旋轉(zhuǎn)體Space :空間Speed :速率Spherical coordinates :球面坐標Squeeze Theorem :夾擠定理Step function :階梯函數(shù)Strictly decreasing :嚴格遞減Strictly increasing :嚴格遞增Sum :和Surface :曲面Surface integral :面積分Surface of revolution :旋轉(zhuǎn)曲面Symmetry :對稱R:Radius of convergence :收斂半徑Range of a function :函數(shù)

5、的值域Rate of change :變化率Rational function :有理函數(shù)Rationalizing substitution :有理代換法Rational number :有理數(shù)Real number :實數(shù)Rectangular coordinates :百角坐標Rectangular coordinate system :百角坐標系Relative maximum and minimum : 相對極大值與極小值Revenue function :收入函數(shù)Revolution , solid of :旋轉(zhuǎn)體Revolution , surface of :旋轉(zhuǎn)曲面Riema

6、nn Sum :黎曼和Riemannian geometry :黎曼幾何Right-hand derivative :右導(dǎo)數(shù)Right-hand limit:右極限Root :根P、Q:Parabola :拋物線Parabolic cylinder :拋物柱面Paraboloid :拋物面Parallelepiped :平行六面體Parallel lines :并行線Parameter :參數(shù)Partial derivative :偏導(dǎo)數(shù)Partial differential equation :偏微分方程Partial fractions :部分分式Partial integration

7、:部分積分Partiton :分割Period :周期Periodic function :周期函數(shù)Perpendicular lines :垂直線Piecewise defined function :分段定義函數(shù)Plane :平面Point of inflection :反曲點Polar axis :極軸Polar coordinate :極坐標Polar equation :極方程式Pole :極點Polynomial :多項式Positive angle :正角Point-slope form :點斜式Power function :冪函數(shù)Product :積Quadrant ：象限Q

8、uotient Law of limit:極限的商定律Quotient Rule :商定律M、N、O:Maximum and minimum values : 極大與極小值Mean Value Theorem :均值定理Multiple integrals :重積分Multiplier :乘子Natural exponential function :自 然指數(shù)函數(shù)Natural logarithm function :自 然對數(shù)函數(shù)Natural number :自然數(shù)Normal line :法線Normal vector :法向 量Number :數(shù)Octant :卦限Odd funct

9、ion :奇函數(shù)One-sided limit :單邊極限Open interval :開區(qū)間Optimization problems :最佳化問題Order :階Ordinary differential equation :常微分方程Origin :原點Orthogonal :正 交的L:Laplace transform : Leplace 變換Law of Cosines :余弦定理Least upper bound :最小上界Left-hand derivative :左導(dǎo)數(shù)Left-hand limit:左極限Lemniscate :雙鈕線Length :長度Level curv

10、e ：等高線LHospitals rule :洛必達法則Limacon ：蛆線Limit :極限Linear approximatio n：線性近似Linear equation :線性方程式Linear function :線性函數(shù)Linearity :線性Linearization :線性化Line in the plane :平面上之百線Line in space :空間之直線Lobachevski geometry :羅巴切夫斯基幾何Local extremum ：局部極值Local maximum and minimum :局部極大值與極小值Logarithm :對數(shù)Logarith

11、mic function :對數(shù)函數(shù)I:Implicit differentiation :隱求導(dǎo)法Implicit function :隱函數(shù)Improper integral :瑕積分Increasing/Decreasing Test :遞增或遞減試驗法Increment :增量Increasing Function :增函數(shù)Indefinite integral :不定積分Independent variable :自變數(shù)Indeterminate from :不定型Inequality :不等式Infinite point :無窮極限Infinite series :無窮級數(shù)Infl

12、ection point :反曲 點Instantaneous velocity :瞬時速度Integer :整數(shù)Integral :積分Integrand :被積分式Integration :積分Integration by part :分部積分法Intercepts :截距Intermediate value of Theorem :中間值定理Interval :區(qū)間Inverse function :反函數(shù)Inverse trigonometric function :反三角函數(shù)Iterated integral :逐次積分H:Higher mathematics高等數(shù)學(xué)/高數(shù)E、F、G

13、、H:Ellipse :橢圓Ellipsoid :橢圓體Epicycloid :外擺線Equation :方程式Even function :偶函數(shù)Expected Valued:期望值Exponential Function :指數(shù)函數(shù)Exponents , laws of :指數(shù)率Extreme value :極值Extreme Value Theorem :極值定理Factorial :階乘First Derivative Test: 一階導(dǎo)數(shù)試驗法First octant :第一卦限Focus :焦點Fractions :分式Function :函數(shù)Fundamental Theore

14、m of Calculus :微積分基本定理Geometric series :幾何級數(shù)Gradient :梯度Graph :圖形Green Formula :格林公式Half-angle formulas :半角公式Harmonic series :調(diào)和級數(shù)Helix :螺旋線Higher Derivative :高階導(dǎo)數(shù)Horizontal asymptote :水平漸近線Horizontal line :水平線Hyperbola ：雙曲線Hyper boloid ：雙曲面D:Decreasing function :遞減函數(shù)Decreasing sequence :遞減數(shù)列Definit

15、e integral :定積分Degree of a polynomial :多項式之次數(shù)Density :密度Derivative :導(dǎo)數(shù)of a composite function :復(fù)合函數(shù)之導(dǎo)數(shù)of a constant function :常數(shù)函數(shù)之導(dǎo)數(shù)directional :方向?qū)?shù)domain of :導(dǎo)數(shù)之定義域of exponential function :指數(shù)函數(shù)之導(dǎo)數(shù)higher :高階導(dǎo)數(shù)partial :偏導(dǎo)數(shù)of a power function :冪函數(shù)之導(dǎo)數(shù)of a power series :囂級數(shù)之導(dǎo)數(shù)of a product :積之導(dǎo)數(shù)of a qu

16、otient :商之導(dǎo)數(shù)as a rate of change :導(dǎo)數(shù)當作變率right-hand :右導(dǎo)數(shù)second :二階導(dǎo)數(shù)as the slope of a tangent:導(dǎo)數(shù)看成切線之斜率Determinant :行列式Differentiable function :可導(dǎo)函數(shù)Differential :微分Differential equation:微分方程partial ：偏微分方程Differentiation :求導(dǎo)法implicit :隱求導(dǎo)法partial :偏微分法term by term :逐項求導(dǎo)法Directional derivatives :方向?qū)?shù)Dis

17、continuity :不連續(xù)性Disk method :圓盤法Distance :距離Divergence :發(fā)散Domain :定義域Dot product :點積Double integral：二重積分change of variable in :二重積分之變數(shù)變換in polar coordinates :極坐標二重積分C:Calculus :微積分differential :微分學(xué)integral :積分學(xué)Cartesian coordinates :笛卡兒坐標.一般指百角坐標Cartesian coordinates system :笛卡兒坐標系Cauch Mean Value T

18、heorem:柯西均值定理Chain Rule :連鎖律Change of variables :變數(shù)變換Circle :圓Circular cylinder :圓柱Closed interval :封閉區(qū)間Coefficient :系數(shù)Composition of function :函數(shù)之合成Compound interest :復(fù)利Concavity :凹性Conchoid :蚌線Cone :圓錐Constant function :常數(shù)函數(shù)Constant of integration :積分常數(shù)Continuity :連續(xù)性at a point :在一點處之連續(xù)性of a funct

19、ion :函數(shù)之連續(xù)性on an interval :在區(qū)間之連續(xù)性from the left: 左連續(xù)from the right: 右連續(xù)Continuous function :連續(xù)函數(shù)Convergence :收斂interval of :收斂區(qū)間radius of :收斂半徑Convergent sequence:收斂數(shù)列series :收斂級數(shù)Coordinate： s：坐標Cartesian :笛卡兒坐標cylindrical :柱面坐標polar :極坐標rectangular :百角坐標spherical :球面坐標Coordinate axes :坐標軸Coordinate planes :坐標平面Cosine function :余弦函數(shù)Critical point : 臨界點Cubic function :三次函數(shù)Curve :曲線Cylinder :圓柱Cylindrical Coordinates :圓柱坐標A、B:Absolute convergence :