微积分II(双语版)

Chapter 1Preliminary Analysis of Space Analytic Geometry
第1章空间解析几何初步
1.1Vectors and Linear Operations
1.1向量及线性运算
1. The Concept of Vector
1. 向量的概念
2. Linear Operations of Vectors
2. 向量的线性运算
3. Space Cartesian Coordinate System
3. 空间直角坐标系
1.2Scalar Product and Cross Product
1.2数量积与向量积
1. Definition and Operation Law of
Scalar Product
1. 数量积的定义及运算规律
2. Cartesian Coordinate Operation of
Scalar Product
2. 数量积的直角坐标运算
3. The Definition and Operation Rule of
Cross Product
3. 向量积的定义及运算规律
4. Cartesian Coordinate Operation of
Cross Product
4. 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 Equation
1.3平面及其方程
1. Point Normal form Equation of
the Plane
1. 平面的点法式方程
2. General Equation of the Plane
2. 平面的一般式方程
3. Intercept Equation of the Plane
3. 平面的截距式方程
4. Three Points Equation of the Plane
4. 平面的三点式方程
5. The Angle Between Two Planes
and the Positional Relationship
5. 两平面的夹角和位置关系
6. Distance from Point to Plane
6. 点到平面的距离
1.4Space Straight Lines and Their Equations
1.4空间直线及其方程
1. Symmetric Equation of
a Straight Line
1. 直线的对称式方程
2. Parametric Equation of
a Straight Line
2. 直线的参数式方程
3. General Equation of a Straight Line
3. 直线的一般式方程
4. The General Formula of Linear
Equation and Transformation of
Symmetric Formula
4. 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 Space
5. 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 Line
7. 点到直线的距离
1.5Quadratic Surfaces and Their Equations
1.5二次曲面及其方程
1. Spherical Surface
1. 球面
2. Ellipsoid
2. 椭球面
3. Hyperboloid
3. 双曲面
4. Paraboloid
4. 抛物面
5. Cylinder
5. 柱面
6. Rotating Surface
6. 旋转曲面
1.6Space Curves and Their Equations
1.6空间曲线及其方程
1. General Equation of Space Curve
1. 空间曲线的一般方程
2. Parametric Equation of Space Curve
2. 空间曲线的参数方程
3. The Projection of a Space Curve on a Coordinate Surface
3. 空间曲线在坐标面上的投影
Exercises 1
习题1
Chapter 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 Variables
2.1多元函数的基本概念
1. Planar Point Set
1. 平面点集
2. The Concept of the Function of
Several Variables
2. 多元函数的概念
2.2Limit and Continuity of the Function of Two Variables
2.2多元函数的极限与连续性
1. Limit of the Function of Two Variables
1. 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 Derivatives
2.3偏导数
1. Concept of the Partial Derivatives
1. 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 Derivative
3. 偏导数的几何解释
4. Partial Derivatives of Higher Order
4. 高阶偏导数
5. More than Two Variables
5. 多于两个变量的情形
2.4Total Differential
2.4全微分
1. The Concept of Total Differential
1. 全微分的概念
2. The Application of Total Differential in Approximate Calculation
2. 全微分在近似计算中的应用
2.5The Derivative Rule of Multivariate
Composite Function
2.5多元复合函数的求导法则
2.6The Derivative Rule of Implicit
Function
2.6隐函数的求导法则
2.7Local Extremum,Maximum and Minimum
2.7局部极值,*值
1. Local Extremum
1. 局部极值
2. Maximum and Minimum
2. *值
Exercises 2
习题2
Chapter 3Double Integral
第3章二重积分
3.1The Double Integral on Closed
Rectangles
3.1闭矩形区域上的二重积分
1. The Definition of the Double Integral
1. 二重积分的定义
2. The Existence Question of
Double Integral
2. 二重积分的存在性问题
3. Properties of the Double Integral
3. 二重积分的性质
4. Simple Calculation of
Double Integrals
4. 二重积分的简单计算
3.2Iterated Integrals
3.2累次积分
1. Change the Double Integral to
the Iterated Integral
1. 化二重积分为累次积分
2. Calculating Iterated Integral
2. 累次积分的计算
3.3The Double Integral on Non Closed
Rectangular Regions
3.3非闭矩形区域上的二重积分
1. The Definition of Double Integral
on a Bounded Closed Area
1. 有界闭区域上的二重积分的
定义
2. Calculation of Double Integral
on a Bounded Closed Area
2. 有界闭区域上的二重积分的
计算
3.4The Double Integral in Polar Coordinates
3.4极坐标下的二重积分
3.5Applications of Double Integral
3.5二重积分的应用
1. The Quality of Flat Sheet
1. 平面薄板的质量
2. Center of Mass of Flat Sheet
2. 平面薄板的质心
3. The Moment of Inertia of a Flat Sheet
3. 平面薄板的转动惯量
Exercises 3
习题3
Chapter 4Infinite Series
第4章无穷级数
4.1Determine Whether the Infinite
Series Converges or Diverges
4.1判断无穷级数的敛散性
1. The Concept of Convergence and
Divergence of Series
1. 级数敛散性的概念
2. The Basic Property of the Series
2. 级数的基本性质
4.2The Positive Terms Series
4.2正项级数
4.3Alternating Series, Absolute Convergence
and Conditional Convergence
4.3 交错级数, 绝对收敛和条件
收敛
1. Alternating Series and Its Tests
for Convergence
1. 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 Series
4.5幂级数的运算与性质
1. Operations of Power Series
1. 幂级数的运算
2. Properties of Power Series
2. 幂级数的性质
Exercises 4
习题4