微積分II（雙語版）

Chapter 1Preliminary Analysis of Space Analytic Geometry
第1章空間解析幾何初步
1.1Vectors and Linear Operations
1.1向量及線性運算
1. The Concept of Vector
1. 向量的概念
2. Linear Operations of Vectors
2. 向量的線性運算
3. Space Cartesian Coordinate System
3. 空間直角坐標系
1.2Scalar Product and Cross Product
1.2數(shù)量積與向量積
1. Definition and Operation Law of
Scalar Product
1. 數(shù)量積的定義及運算規(guī)律
2. Cartesian Coordinate Operation of
Scalar Product
2. 數(shù)量積的直角坐標運算
3. The Definition and Operation Rule of
Cross Product
3. 向量積的定義及運算規(guī)律
4. Cartesian Coordinate Operation of
Cross Product
4. 向量積的直角坐標運算
5. The Relationship and Its Judgement of Vectors
5. 向量的關系及其判定
1.3Plane and Its Equation
1.3平面及其方程
1. Point Normal form Equation of
the Plane
1. 平面的點法式方程
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. 平面的三點式方程
5. The Angle Between Two Planes
and the Positional Relationship
5. 兩平面的夾角和位置關系
6. Distance from Point to Plane
6. 點到平面的距離
1.4Space Straight Lines and Their Equations
1.4空間直線及其方程
1. Symmetric Equation of
a Straight Line
1. 直線的對稱式方程
2. Parametric Equation of
a Straight Line
2. 直線的參數(shù)式方程
3. General Equation of a Straight Line
3. 直線的一般式方程
4. The General Formula of Linear
Equation and Transformation of
Symmetric Formula
4. 直線方程的一般式與對稱式的
轉(zhuǎn)化
5. The Angle and Positional Relation
Between Two Straight Lines in Space
5. 空間中兩直線的夾角和位置
關系
6. The Angle and Position Relation
Between a Line and a Plane
6. 直線與平面的夾角和位置關系
7. Distance from Point to Line
7. 點到直線的距離
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. 橢球面
3. Hyperboloid
3. 雙曲面
4. Paraboloid
4. 拋物面
5. Cylinder
5. 柱面
6. Rotating Surface
6. 旋轉(zhuǎn)曲面
1.6Space Curves and Their Equations
1.6空間曲線及其方程
1. General Equation of Space Curve
1. 空間曲線的一般方程
2. Parametric Equation of Space Curve
2. 空間曲線的參數(shù)方程
3. The Projection of a Space Curve on a Coordinate Surface
3. 空間曲線在坐標面上的投影
Exercises 1
習題1
Chapter 2Derivatives for the Function of
Several Variables
第2章多元函數(shù)的微分
2.1The Basic Concept of the Function of
Several Variables
2.1多元函數(shù)的基本概念
1. Planar Point Set
1. 平面點集
2. The Concept of the Function of
Several Variables
2. 多元函數(shù)的概念
2.2Limit and Continuity of the Function of Two Variables
2.2多元函數(shù)的極限與連續(xù)性
1. Limit of the Function of Two Variables
1. 二元函數(shù)的極限
2. Continuity of the Function of
Two Variables
2. 二元函數(shù)的連續(xù)性
2.3Partial Derivatives
2.3偏導數(shù)
1. Concept of the Partial Derivatives
1. 偏導數(shù)的概念
2. Rule for Finding Partial Derivatives
2. 求偏導數(shù)的法則
3. Geometric Interpretations of
Partial Derivative
3. 偏導數(shù)的幾何解釋
4. Partial Derivatives of Higher Order
4. 高階偏導數(shù)
5. More than Two Variables
5. 多于兩個變量的情形
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. 全微分在近似計算中的應用
2.5The Derivative Rule of Multivariate
Composite Function
2.5多元復合函數(shù)的求導法則
2.6The Derivative Rule of Implicit
Function
2.6隱函數(shù)的求導法則
2.7Local Extremum,Maximum and Minimum
2.7局部極值,最值
1. Local Extremum
1. 局部極值
2. Maximum and Minimum
2. 最值
Exercises 2
習題2
Chapter 3Double Integral
第3章二重積分
3.1The Double Integral on Closed
Rectangles
3.1閉矩形區(qū)域上的二重積分
1. The Definition of the Double Integral
1. 二重積分的定義
2. The Existence Question of
Double Integral
2. 二重積分的存在性問題
3. Properties of the Double Integral
3. 二重積分的性質(zhì)
4. Simple Calculation of
Double Integrals
4. 二重積分的簡單計算
3.2Iterated Integrals
3.2累次積分
1. Change the Double Integral to
the Iterated Integral
1. 化二重積分為累次積分
2. Calculating Iterated Integral
2. 累次積分的計算
3.3The Double Integral on Non Closed
Rectangular Regions
3.3非閉矩形區(qū)域上的二重積分
1. The Definition of Double Integral
on a Bounded Closed Area
1. 有界閉區(qū)域上的二重積分的
定義
2. Calculation of Double Integral
on a Bounded Closed Area
2. 有界閉區(qū)域上的二重積分的
計算
3.4The Double Integral in Polar Coordinates
3.4極坐標下的二重積分
3.5Applications of Double Integral
3.5二重積分的應用
1. The Quality of Flat Sheet
1. 平面薄板的質(zhì)量
2. Center of Mass of Flat Sheet
2. 平面薄板的質(zhì)心
3. The Moment of Inertia of a Flat Sheet
3. 平面薄板的轉(zhuǎn)動慣量
Exercises 3
習題3
Chapter 4Infinite Series
第4章無窮級數(shù)
4.1Determine Whether the Infinite
Series Converges or Diverges
4.1判斷無窮級數(shù)的斂散性
1. The Concept of Convergence and
Divergence of Series
1. 級數(shù)斂散性的概念
2. The Basic Property of the Series
2. 級數(shù)的基本性質(zhì)
4.2The Positive Terms Series
4.2正項級數(shù)
4.3Alternating Series, Absolute Convergence
and Conditional Convergence
4.3 交錯級數(shù), 絕對收斂和條件
收斂
1. Alternating Series and Its Tests
for Convergence
1. 交錯級數(shù)及其收斂判別法
2. Absolute and Conditional
Convergence
2. 絕對收斂與條件收斂
4.4Power Series
4.4冪級數(shù)
4.5Operations and Properties of
Power Series
4.5冪級數(shù)的運算與性質(zhì)
1. Operations of Power Series
1. 冪級數(shù)的運算
2. Properties of Power Series
2. 冪級數(shù)的性質(zhì)
Exercises 4
習題4