微積分II（雙語(yǔ)版）簡(jiǎn)介，目錄書(shū)摘
2019-10-30 10:08
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微積分II（雙語(yǔ)版）
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編輯推薦: 《微積分II（雙語(yǔ)版）》簡(jiǎn)明易懂、條理清晰、重點(diǎn)突出、難點(diǎn)分散，強調微積分的實(shí)際應用，注重數學(xué)思想方法的建立與培養，具有較強的針對性和可讀性。
內容簡(jiǎn)介: 《微積分II（雙語(yǔ)版）》是根據“國際本科學(xué)術(shù)互認課程”（ISEC）項目對高等數學(xué)系列課程的要求，同時(shí)結合ISEC項目培養模式進(jìn)行編寫(xiě)的“微積分”雙語(yǔ)教材.全書(shū)共分4章，內容包括：空間解析幾何初步、 多元函數的微分、二重積分、無(wú)窮級數等.在內容選擇上，既考慮到ISEC學(xué)生未來(lái)學(xué)習和發(fā)展的需要，又兼顧學(xué)生數學(xué)學(xué)習的實(shí)際情況，以適用、夠用為原則，切合學(xué)生實(shí)際，在體系完整的基礎上對通常的 “微積分”課程內容進(jìn)行適當的調整，注重明晰數學(xué)思想與方法，強調數學(xué)知識的應用;在內容闡述上，盡量以案例模式引入，由淺入深，由易到難，循序漸進(jìn)地加以展開(kāi)，并且盡量使重點(diǎn)突出，難點(diǎn)分散，便于學(xué)生對知識的理解和掌握；在內容呈現上，以英文和中文兩種文字進(jìn)行編寫(xiě)，分左、右欄對應呈現，方便學(xué)生學(xué)習與理解.
作者簡(jiǎn)介: 程曉亮，吉林師范大學(xué)數學(xué)學(xué)院副教授，數學(xué)系副系主任。具有豐富的ISEC“微積分”課程的教學(xué)經(jīng)驗。曾在我社出版多部教材，包括《數學(xué)教學(xué)論》《初等數學(xué)研究》《實(shí)變函數論》等。
目錄: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(xiàn)性運算
1. The Concept of Vector
1. 向量的概念
2. Linear Operations of Vectors
2. 向量的線(xiàn)性運算
3. Space Cartesian Coordinate System
3. 空間直角坐標系
1.2Scalar Product and Cross Product
1.2數量積與向量積
1. Definition and Operation Law of
Scalar Product
1. 數量積的定義及運算規律
2. Cartesian Coordinate Operation of
Scalar Product
2. 數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(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(xiàn)及其方程
1. Symmetric Equation of
a Straight Line
1. 直線(xiàn)的對稱(chēng)式方程
2. Parametric Equation of
a Straight Line
2. 直線(xiàn)的參數式方程
3. General Equation of a Straight Line
3. 直線(xiàn)的一般式方程
4. The General Formula of Linear
Equation and Transformation of
Symmetric Formula
4. 直線(xiàn)方程的一般式與對稱(chēng)式的
轉化
5. The Angle and Positional Relation
Between Two Straight Lines in Space
5. 空間中兩直線(xiàn)的夾角和位置
關(guān)系
6. The Angle and Position Relation
Between a Line and a Plane
6. 直線(xiàn)與平面的夾角和位置關(guān)系
7. Distance from Point to Line
7. 點(diǎn)到直線(xiàn)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. 旋轉曲面
1.6Space Curves and Their Equations
1.6空間曲線(xiàn)及其方程
1. General Equation of Space Curve
1. 空間曲線(xiàn)的一般方程
2. Parametric Equation of Space Curve
2. 空間曲線(xiàn)的參數方程
3. The Projection of a Space Curve on a Coordinate Surface
3. 空間曲線(xiàn)在坐標面上的投影
Exercises 1
習題1
Chapter 2Derivatives for the Function of
Several Variables
第2章多元函數的微分
2.1The Basic Concept of the Function of
Several Variables
2.1多元函數的基本概念
1. Planar Point Set
1. 平面點(diǎn)集
2. The Concept of the Function of
Several Variables
2. 多元函數的概念
2.2Limit and Continuity of the Function of Two Variables
2.2多元函數的極限與連續性
1. Limit of the Function of Two Variables
1. 二元函數的極限
2. Continuity of the Function of
Two Variables
2. 二元函數的連續性
2.3Partial Derivatives
2.3偏導數
1. Concept of the Partial Derivatives
1. 偏導數的概念
2. Rule for Finding Partial Derivatives
2. 求偏導數的法則
3. Geometric Interpretations of
Partial Derivative
3. 偏導數的幾何解釋
4. Partial Derivatives of Higher Order
4. 高階偏導數
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. 全微分在近似計算中的應用
2.5The Derivative Rule of Multivariate
Composite Function
2.5多元復合函數的求導法則
2.6The Derivative Rule of Implicit
Function
2.6隱函數的求導法則
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(wèn)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(jiǎn)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非閉矩形區域上的二重積分
1. The Definition of Double Integral
on a Bounded Closed Area
1. 有界閉區域上的二重積分的
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. 平面薄板的轉動(dòng)慣量
Exercises 3
習題3
Chapter 4Infinite Series
第4章無(wú)窮級數
4.1Determine Whether the Infinite
Series Converges or Diverges
4.1判斷無(wú)窮級數的斂散性
1. The Concept of Convergence and
Divergence of Series
1. 級數斂散性的概念
2. The Basic Property of the Series
2. 級數的基本性質(zhì)
4.2The Positive Terms Series
4.2正項級數
4.3Alternating Series, Absolute Convergence
and Conditional Convergence
4.3 交錯級數, 絕對收斂和條件
收斂
1. Alternating Series and Its Tests
for Convergence
1. 交錯級數及其收斂判別法
2. Absolute and Conditional
Convergence
2. 絕對收斂與條件收斂
4.4Power Series
4.4冪級數
4.5Operations and Properties of
Power Series
4.5冪級數的運算與性質(zhì)
1. Operations of Power Series
1. 冪級數的運算
2. Properties of Power Series
2. 冪級數的性質(zhì)
Exercises 4
習題4
第1章空間解析幾何初步
1.1Vectors and Linear Operations
1.1向量及線(xiàn)性運算
1. The Concept of Vector
1. 向量的概念
2. Linear Operations of Vectors
2. 向量的線(xiàn)性運算
3. Space Cartesian Coordinate System
3. 空間直角坐標系
1.2Scalar Product and Cross Product
1.2數量積與向量積
1. Definition and Operation Law of
Scalar Product
1. 數量積的定義及運算規律
2. Cartesian Coordinate Operation of
Scalar Product
2. 數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(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(xiàn)及其方程
1. Symmetric Equation of
a Straight Line
1. 直線(xiàn)的對稱(chēng)式方程
2. Parametric Equation of
a Straight Line
2. 直線(xiàn)的參數式方程
3. General Equation of a Straight Line
3. 直線(xiàn)的一般式方程
4. The General Formula of Linear
Equation and Transformation of
Symmetric Formula
4. 直線(xiàn)方程的一般式與對稱(chēng)式的
轉化
5. The Angle and Positional Relation
Between Two Straight Lines in Space
5. 空間中兩直線(xiàn)的夾角和位置
關(guān)系
6. The Angle and Position Relation
Between a Line and a Plane
6. 直線(xiàn)與平面的夾角和位置關(guān)系
7. Distance from Point to Line
7. 點(diǎn)到直線(xiàn)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. 旋轉曲面
1.6Space Curves and Their Equations
1.6空間曲線(xiàn)及其方程
1. General Equation of Space Curve
1. 空間曲線(xiàn)的一般方程
2. Parametric Equation of Space Curve
2. 空間曲線(xiàn)的參數方程
3. The Projection of a Space Curve on a Coordinate Surface
3. 空間曲線(xiàn)在坐標面上的投影
Exercises 1
習題1
Chapter 2Derivatives for the Function of
Several Variables
第2章多元函數的微分
2.1The Basic Concept of the Function of
Several Variables
2.1多元函數的基本概念
1. Planar Point Set
1. 平面點(diǎn)集
2. The Concept of the Function of
Several Variables
2. 多元函數的概念
2.2Limit and Continuity of the Function of Two Variables
2.2多元函數的極限與連續性
1. Limit of the Function of Two Variables
1. 二元函數的極限
2. Continuity of the Function of
Two Variables
2. 二元函數的連續性
2.3Partial Derivatives
2.3偏導數
1. Concept of the Partial Derivatives
1. 偏導數的概念
2. Rule for Finding Partial Derivatives
2. 求偏導數的法則
3. Geometric Interpretations of
Partial Derivative
3. 偏導數的幾何解釋
4. Partial Derivatives of Higher Order
4. 高階偏導數
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. 全微分在近似計算中的應用
2.5The Derivative Rule of Multivariate
Composite Function
2.5多元復合函數的求導法則
2.6The Derivative Rule of Implicit
Function
2.6隱函數的求導法則
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(wèn)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(jiǎn)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非閉矩形區域上的二重積分
1. The Definition of Double Integral
on a Bounded Closed Area
1. 有界閉區域上的二重積分的
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. 平面薄板的轉動(dòng)慣量
Exercises 3
習題3
Chapter 4Infinite Series
第4章無(wú)窮級數
4.1Determine Whether the Infinite
Series Converges or Diverges
4.1判斷無(wú)窮級數的斂散性
1. The Concept of Convergence and
Divergence of Series
1. 級數斂散性的概念
2. The Basic Property of the Series
2. 級數的基本性質(zhì)
4.2The Positive Terms Series
4.2正項級數
4.3Alternating Series, Absolute Convergence
and Conditional Convergence
4.3 交錯級數, 絕對收斂和條件
收斂
1. Alternating Series and Its Tests
for Convergence
1. 交錯級數及其收斂判別法
2. Absolute and Conditional
Convergence
2. 絕對收斂與條件收斂
4.4Power Series
4.4冪級數
4.5Operations and Properties of
Power Series
4.5冪級數的運算與性質(zhì)
1. Operations of Power Series
1. 冪級數的運算
2. Properties of Power Series
2. 冪級數的性質(zhì)
Exercises 4
習題4
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