目录 Chapter 1Preliminary Analysis of Space Analytic Geometry章空间解析几何初步1.1Vectors and Linear Operations1.1向量及线性运算1. The Concept of Vector1. 向量的概念2. Linear Operations of Vectors2. 向量的线性运算3. Space Cartesian Coordinate System3. 空间直角坐标系1.2Scalar Product and Cross Product1.2数量积与向量积1. Definition and Operation Law of Scalar Product1. 数量积的定义及运算规律2. Cartesian Coordinate Operation of Scalar Product2. 数量积的直角坐标运算3. The Definition and Operation Rule of Cross Product3. 向量积的定义及运算规律4. Cartesian Coordinate Operation of Cross Product4. 向量积的直角坐标运算5. The Relationship and Its Judgement of Vectors 5. 向量的关系及其判定1.3Plane and Its Equation1.3平面及其方程1. Point Normal form Equation of the Plane1. 平面的点法式方程2. General Equation of the Plane2. 平面的一般式方程3. Intercept Equation of the Plane3. 平面的截距式方程4. Three Points Equation of the Plane4. 平面的三点式方程5. The Angle Between Two Planes and the Positional Relationship5. 两平面的夹角和位置关系6. Distance from Point to Plane6. 点到平面的距离1.4Space Straight Lines and Their Equations1.4空间直线及其方程1. Symmetric Equation of a Straight Line1. 直线的对称式方程2. Parametric Equation of a Straight Line2. 直线的参数式方程3. General Equation of a Straight Line3. 直线的一般式方程4. The General Formula of Linear Equation and Transformation of Symmetric Formula4. 直线方程的一般式与对称式的转化5. The Angle and Positional Relation Between Two Straight Lines in Space5. 空间中两直线的夹角和位置关系6. The Angle and Position Relation Between a Line and a Plane 6. 直线与平面的夹角和位置关系7. Distance from Point to Line7. 点到直线的距离1.5Quadratic Surfaces and Their Equations1.5二次曲面及其方程1. Spherical Surface1. 球面2. Ellipsoid2. 椭球面3. Hyperboloid3. 双曲面4. Paraboloid4. 抛物面5. Cylinder5. 柱面6. Rotating Surface 6. 旋转曲面1.6Space Curves and Their Equations1.6空间曲线及其方程1. General Equation of Space Curve1. 空间曲线的一般方程2. Parametric Equation of Space Curve2. 空间曲线的参数方程3. The Projection of a Space Curve on a Coordinate Surface3. 空间曲线在坐标面上的投影Exercises 1习题1Chapter 2Derivatives for the Function of Several Variables第2章多元函数的微分2.1The Basic Concept of the Function of Several Variables2.1多元函数的基本概念1. Planar Point Set1. 平面点集2. The Concept of the Function of Several Variables2. 多元函数的概念2.2Limit and Continuity of the Function of Two Variables2.2多元函数的极限与连续性1. Limit of the Function of Two Variables1. 二元函数的极限2. Continuity of the Function of Two Variables 2. 二元函数的连续性2.3Partial Derivatives2.3偏导数 1. Concept of the Partial Derivatives1. 偏导数的概念2. Rule for Finding Partial Derivatives 2. 求偏导数的法则3. Geometric Interpretations of Partial Derivative3. 偏导数的几何解释4. Partial Derivatives of Higher Order4. 高阶偏导数5. More than Two Variables5. 多于两个变量的情形2.4Total Differential2.4全微分1. The Concept of Total Differential1. 全微分的概念2. The Application of Total Differential in Approximate Calculation2. 全微分在近似计算中的应用2.5The Derivative Rule of Multivariate Composite Function2.5多元复合函数的求导法则2.6The Derivative Rule of Implicit Function2.6隐函数的求导法则2.7Local Extremum,Maximum and Minimum2.7局部极值,最值1. Local Extremum1. 局部极值 2. Maximum and Minimum2. 最值Exercises 2习题2Chapter 3Double Integral第3章二重积分3.1The Double Integral on Closed Rectangles3.1闭矩形区域上的二重积分1. The Definition of the Double Integral1. 二重积分的定义2. The Existence Question of Double Integral2. 二重积分的存在性问题3. Properties of the Double Integral3. 二重积分的性质4. Simple Calculation of Double Integrals4. 二重积分的简单计算3.2Iterated Integrals3.2累次积分1. Change the Double Integral to the Iterated Integral1. 化二重积分为累次积分2. Calculating Iterated Integral2. 累次积分的计算3.3The Double Integral on Non Closed Rectangular Regions3.3非闭矩形区域上的二重积分1. The Definition of Double Integral on a Bounded Closed Area1. 有界闭区域上的二重积分的定义2. Calculation of Double Integral on a Bounded Closed Area2. 有界闭区域上的二重积分的计算 3.4The Double Integral in Polar Coordinates3.4极坐标下的二重积分3.5Applications of Double Integral3.5二重积分的应用1. The Quality of Flat Sheet1. 平面薄板的质量2. Center of Mass of Flat Sheet2. 平面薄板的质心3. The Moment of Inertia of a Flat Sheet3. 平面薄板的转动惯量Exercises 3习题3Chapter 4Infinite Series第4章无穷级数4.1Determine Whether the Infinite Series Converges or Diverges4.1判断无穷级数的敛散性1. The Concept of Convergence and Divergence of Series1. 级数敛散性的概念2. The Basic Property of the Series2. 级数的基本性质4.2The Positive Terms Series 4.2正项级数4.3Alternating Series, Absolute Convergenceand Conditional Convergence4.3 交错级数, 绝对收敛和条件收敛1. Alternating Series and Its Tests for Convergence1. 交错级数及其收敛判别法2. Absolute and Conditional Convergence 2. 绝对收敛与条件收敛 4.4Power Series 4.4幂级数 4.5Operations and Properties of Power Series4.5幂级数的运算与性质1. Operations of Power Series1. 幂级数的运算2. Properties of Power Series2. 幂级数的性质Exercises 4习题4
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