【正文】 ea of a luane figure直角坐標(biāo)又稱“笛卡兒坐標(biāo) (Cartesian coordinates)”極坐標(biāo) polar coordinates拋物線 parabola橢圓 ellipse旋轉(zhuǎn)體的面積 volume of a solid of rotation 旋轉(zhuǎn)橢球體 ellipsoid of revolution, ellipsoid of rotation曲線的弧長 arc length of acurve 可求長的 rectifiable光滑 smooth功 work水壓力 water pressure引力 gravitation變力 variable force第七章 空間解析幾何與向量代數(shù)Chapter7 Space Analytic Geometry and Vector Algebra向量 vector自由向量 free vector單位向量 unit vector零向量 zero vector相等 equal平行 parallel向量的線性運(yùn)算 linear poeration of vector三角法則 triangle rule 平行四邊形法則 parallelogram rule 交換律 mutative law結(jié)合律 associative law負(fù)向量 negative vector差 difference分配律 distributive law空間直角坐標(biāo)系 space rectangular coordinates坐標(biāo)面 coordinate plane卦限 octant向量的模 modulus of vector向量a與b的夾角 angle between vector a and b方向余弦 direction cosine方向角 direction angle向量在軸上的投影 projection of a vector onto an axis 數(shù)量積，外積，叉積 scalar product,dot product,inner product曲面方程 equation for a surface球面 sphere旋轉(zhuǎn)曲面 surface of revolution母線 generating line軸 axis圓錐面 cone頂點(diǎn) vertex旋轉(zhuǎn)單葉雙曲面 revolution hyperboloids of one sheet旋轉(zhuǎn)雙葉雙曲面 revolution hyperboloids of two sheets柱面 cylindrical surface ,cylinder圓柱面 cylindrical surface準(zhǔn)線 directrix拋物柱面 parabolic cylinder二次曲面 quadric surface橢圓錐面 dlliptic cone橢球面 ellipsoid單葉雙曲面 hyperboloid of one sheet雙葉雙曲面 hyperboloid of two sheets旋轉(zhuǎn)橢球面 ellipsoid of revolution橢圓拋物面 elliptic paraboloid旋轉(zhuǎn)拋物面 paraboloid of revolution雙曲拋物面 hyperbolic paraboloid馬鞍面 saddle surface橢圓柱面 elliptic cylinder雙曲柱面 hyperbolic cylinder拋物柱面 parabolic cylinder空間曲線 space curve空間曲線的一般方程 general form equations of a space curve空間曲線的參數(shù)方程 parametric equations of a space curve螺轉(zhuǎn)線 spiral 螺矩 pitch投影柱面 projecting cylinder投影 projection平面的點(diǎn)法式方程 pointnorm form eqyation of a plane法向量 normal vector 平面的一般方程 general form equation of a plane兩平面的夾角 angle between two planes點(diǎn)到平面的距離 distance from a point to a plane空間直線的一般方程 general equation of a line in space 方向向量 direction vector直線的點(diǎn)向式方程 pointdirection form equations of a line方向數(shù) direction number直線的參數(shù)方程 parametric equations of a line兩直線的夾角 angle between two lines垂直 perpendicular直線與平面的夾角 angle between a line and a planes平面束 pencil of planes平面束的方程 equation of a pencil of planes行列式 determinant系數(shù)行列式 coefficient determinant第八章 多元函數(shù)微分法及其應(yīng)用Chapter8 Differentiation of Functions of Several Variables and Its Application一元函數(shù) function of one variable 多元函數(shù) function of several variables內(nèi)點(diǎn) interior point外點(diǎn) exterior point邊界點(diǎn) frontier point,boundary point聚點(diǎn) point of accumulation開集 openset閉集 closed set連通集 connected set開區(qū)域 open region 閉區(qū)域 closed region有界集 bounded set無界集 unbounded setn維空間 ndimentional space二重極限 double limit多元函數(shù)的連續(xù)性 continuity of function of seveal 連續(xù)函數(shù) continuous function不連續(xù)點(diǎn) discontinuity point一致連續(xù) uniformly continuous偏導(dǎo)數(shù) partial derivative對自變量x的偏導(dǎo)數(shù) partial derivative with respect to independent variable x高階偏導(dǎo)數(shù) partial derivative of higher order二階偏導(dǎo)數(shù) second order partial derivative 混合偏導(dǎo)數(shù) hybrid partial derivative 全微分 total differential偏增量 oartial increment偏微分 partial differential全增量 total increment可微分 differentiable必要條件 necessary condition 充分條件 sufficient condition疊加原理 superpostition principle全導(dǎo)數(shù) total derivative中間變量 intermediate variable 隱函數(shù)存在定理 theorem of the existence of implicit function 曲線的切向量 tangent vector of a curve法平面 normal plane 向量方程 vector equation 向量值函數(shù) vectorvalued function切平面 tangent plane法線 normal line 方向?qū)?shù) directional derivative梯度 gradient數(shù)量場 scalar field梯度場 gradient field向量場 vector field勢場 potential field引力場 gravitational field引力勢 gravitational potential曲面在一點(diǎn)的切平面 tangent plane to a surface at a point曲線在一點(diǎn)的法線 normal line to a surface at a point無條件極值 unconditional extreme values條件極值 conditional extreme values拉格朗日乘數(shù)法 Lagrange multiplier method拉格朗日乘子 Lagrange multiplier經(jīng)驗(yàn)公式 empirical formula最小二乘法 method of least squares均方誤差 mean square error第九章 重積分Chapter9 Multiple Integrals二重積分 double integral可加性 additivity累次積分 iterated integral體積元素 volume element三重積分 triple integral直角坐標(biāo)系中的體積元素 volume element in rectangular coordinate system柱面坐標(biāo) cylindrical coordinates柱面坐標(biāo)系中的體積元素 volume element in cylindrical coordinate system球面坐標(biāo) spherical coordinates球面坐標(biāo)系中的體積元素 volume element in spherical coordinate system反常二重積分 improper double integral曲面的面積 area of a surface質(zhì)心 centre of mass靜矩 static moment密度 density形心 centroid轉(zhuǎn)動慣量 moment of inertia參變量 parametric variable第十章 曲線積分與曲面積分Chapter10 Line(Curve)Integrals and Surface Integrals對弧長的曲線積分 line integrals with respect to arc hength第一類曲線積分 line integrals of the first type對坐標(biāo)的曲線積分 line integrals with respect to x,y,and z第二類曲線積分 line integrals of the second type 有向曲線弧 directed arc單連通區(qū)域 simple connected region復(fù)連通區(qū)域 plex connected region格林公式 Green formula第一類曲面積分 surface integrals of the first type對面的曲面積分 surface integrals with respect to area 有向曲面 directed surface對坐標(biāo)的曲面積分 surface integrals with respect to coordinate elements第二類曲面積分 surface integrals of the second type 有向曲面元 element of directed surface高斯公式 gauss formula拉普拉斯算子 Laplace operator格林第一公式 Green’s first formula通量 flux散度 divergence斯托克斯公式 Stokes formula環(huán)流量 circulation 旋度 rotation,curl第十一章 無窮級數(shù)Chapter11 Infinite Series一般項 general term部分和 partial sum余項 remainder term等比級數(shù) geometric series幾何級數(shù) geometric series公比 mon ratio調(diào)和級數(shù) harmonic series柯西收斂準(zhǔn)則 Cauchy convergence criteria, Cauchy criteria for convergence正項級數(shù) seri