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(yùn)算

1. The Concept of Vector

1. 向量的概念

2. Linear Operations of Vectors

2. 向量的線性運(yùn)算

3. Space Cartesian Coordinate System

3. 空間直角坐標(biāo)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(yùn)算規(guī)律

2. Cartesian Coordinate Operation of

Scalar Product

2. 數(shù)量積的直角坐標(biāo)運(yùn)算

3. The Definition and Operation Rule of

Cross Product

3. 向量積的定義及運(yùn)算規(guī)律

4. Cartesian Coordinate Operation of

Cross Product

4. 向量積的直角坐標(biāo)運(yùn)算

5. The Relationship and Its Judgement of Vectors

5. 向量的關(guān)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(diǎn)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(diǎn)式方程

5. The Angle Between Two Planes

and the Positional Relationship

5. 兩平面的夾角和位置關(guān)系

6. Distance from Point to Plane

6. 點(diǎn)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(duì)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(duì)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(guān)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(guān)系

7. Distance from Point to Line

7. 點(diǎn)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(biāo)面上的投影

Exercises 1

習(xí)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(diǎn)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(dǎo)數(shù)

1. Concept of the Partial Derivatives

1. 偏導(dǎo)數(shù)的概念

2. Rule for Finding Partial Derivatives

2. 求偏導(dǎo)數(shù)的法則

3. Geometric Interpretations of

Partial Derivative

3. 偏導(dǎo)數(shù)的幾何解釋

4. Partial Derivatives of Higher Order

4. 高階偏導(dǎo)數(shù)

5. More than Two Variables

5. 多于兩個(gè)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(jì)算中的應(yīng)用

2.5The Derivative Rule of Multivariate

Composite Function

2.5多元復(fù)合函數(shù)的求導(dǎo)法則

2.6The Derivative Rule of Implicit

Function

2.6隱函數(shù)的求導(dǎo)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(xí)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(jì)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(jì)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(jì)算

3.4The Double Integral in Polar Coordinates

3.4極坐標(biāo)下的二重積分

3.5Applications of Double Integral

3.5二重積分的應(yīng)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(dòng)慣量

Exercises 3

習(xí)題3

Chapter 4Infinite Series

第4章無窮級(jí)數(shù)

4.1Determine Whether the Infinite

Series Converges or Diverges

4.1判斷無窮級(jí)數(shù)的斂散性

1. The Concept of Convergence and

Divergence of Series

1. 級(jí)數(shù)斂散性的概念

2. The Basic Property of the Series

2. 級(jí)數(shù)的基本性質(zhì)

4.2The Positive Terms Series

4.2正項(xiàng)級(jí)數(shù)

4.3Alternating Series, Absolute Convergence

and Conditional Convergence

4.3 交錯(cuò)級(jí)數(shù), 絕對(duì)收斂和條件

收斂

1. Alternating Series and Its Tests

for Convergence

1. 交錯(cuò)級(jí)數(shù)及其收斂判別法

2. Absolute and Conditional

Convergence

2. 絕對(duì)收斂與條件收斂

4.4Power Series

4.4冪級(jí)數(shù)

4.5Operations and Properties of

Power Series

4.5冪級(jí)數(shù)的運(yùn)算與性質(zhì)

1. Operations of Power Series

1. 冪級(jí)數(shù)的運(yùn)算

2. Properties of Power Series

2. 冪級(jí)數(shù)的性質(zhì)

Exercises 4

習(xí)題4