了得網教材_微積分雙語版2 程曉亮等編著著作大學教材大中專新華書店正

●Chapter 1Preliminary Analysis of Space Analytic Geometry章空間解析幾何初步1.1Vectors and Linear Operations1.1向量及線性運算1. The Concept of Vector1. 向量的概念2. Linear Operations of Vectors2. 向量的線性運算3. Space Cartesian Coordinate System3. 空間直角坐標繫1.2Scalar Product and Cross Product1.2數量積與向量積1. Definition and Operation Law of Scalar Product1. 數量積的定義及運算規律2. Cartesian Coordinate Operation of Scalar Product2. 數量積的直角坐標運算3. The Definition and Operation Rule of Cross Product3. 向量積的定義及運算規律4. Cartesian Coordinate Operation of Cross Product4. 向量積的直角坐標運算5. The Relationship and Its Judgement of Vectors 5. 向量的關繫及其判定1.3Plane and Its Equation1.3平面及其方程1. Point Normal form Equation of the Plane1. 平面的點法式方程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. 平面的三點式方程5. The Angle Between Two Planes and the Positional Relationship5. 兩平面的夾角和位置關繫6. Distance from Point to Plane6. 點到平面的距離1.4Space Straight Lines and Their Equations1.4空間直線及其方程1. Symmetric Equation of a Straight Line1. 直線的對稱式方程2. Parametric Equation of a Straight Line2. 直線的參數式方程3. General Equation of a Straight Line3. 直線的一般式方程4. The General Formula of Linear Equation and Transformation of Symmetric Formula4. 直線方程的一般式與對稱式的轉化5. The Angle and Positional Relation Between Two Straight Lines in Space5. 空間中兩直線的夾角和位置關繫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繫7. Distance from Point to Line7. 點到直線的距離1.5Quadratic Surfaces and Their Equations1.5二次曲面及其方程1. Spherical Surface1. 球面2. Ellipsoid2. 橢球面3. Hyperboloid3. 雙曲面4. Paraboloid4. 拋物面5. Cylinder5. 柱面6. Rotating Surface 6. 旋轉曲面1.6Space Curves and Their Equations1.6空間曲線及其方程1. General Equation of Space Curve1. 空間曲線的一般方程2. Parametric Equation of Space Curve2. 空間曲線的參數方程3. The Projection of a Space Curve on a Coordinate Surface3. 空間曲線在坐標面上的投影Exercises 1習題1Chapter 2Derivatives for the Function of Several Variables第函數的微分2.1The Basic Concept of the Function of Several Variables2函數的基本概念1. Planar Point Set1. 平面點集2. The Concept of the Function of Several Variables2. &nbs函數的概念2.2Limit and Continuity of the Function of Two Variables2函數的極限與連續性1. Limit of the Function of Two Variables1. &nbs函數的極限2. Continuity of the Function of Two Variables 2. &nbs函數的連續性2.3Partial Derivatives2.3偏導數 1. Concept of the Partial Derivatives1. 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 Derivative3. 偏導數的幾何解釋4. Partial Derivatives of Higher Order4. 高階偏導數5. More than Two Variables5. 多於兩個變量的情形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. 全微分在近似計算中的應用2.5The Derivative Rule of Multivariate Composite Function2復合函數的求導法則2.6The Derivative Rule of Implicit Function2.6隱函數的求導法則2.7Local Extremum,Maximum and Minimum2.7局部極值,最值1. Local Extremum1. 局部極值 2. Maximum and Minimum2. 最值Exercises 2習題2Chapter 3Double Integral第3章二重積分3.1The Double Integral on Closed Rectangles3.1閉矩形區域上的二重積分1. The Definition of the Double Integral1. 二重積分的定義2. The Existence Question of Double Integral2. 二重積分的存在性問題3. Properties of the Double Integral3. 二重積分的性質4. Simple Calculation of Double Integrals4. 二重積分的簡單計算3.2Iterated Integrals3.2累次積分1. Change the Double Integral to the Iterated Integral1. 化二重積分為累次積分2. Calculating Iterated Integral2. 累次積分的計算3.3The Double Integral on Non Closed Rectangular Regions3.3非閉矩形區域上的二重積分1. The Definition of Double Integral on a Bounded Closed Area1. 有界閉區域上的二重積分的定義2. Calculation of Double Integral on a Bounded Closed Area2. 有界閉區域上的二重積分的計算 3.4The Double Integral in Polar Coordinates3.4極坐標下的二重積分3.5Applications of Double Integral3.5二重積分的應用1. The Quality of Flat Sheet1. 平面薄板的質量2. Center of Mass of Flat Sheet2. 平面薄板的質心3. The Moment of Inertia of a Flat Sheet3. 平面薄板的轉動慣量Exercises 3習題3Chapter 4Infinite Series第4章無窮級數4.1Determine Whether the Infinite Series Converges or Diverges4.1判斷無窮級數的斂散性1. The Concept of Convergence and Divergence of Series1. 級數斂散性的概念2. The Basic Property of the Series2. 級數的基本性質4.2The Positive Terms Series 4.2正項級數4.3Alternating Series, Absolute Convergenceand Conditional Convergence4.3 交錯級數, 絕對收斂和條件收斂1. Alternating Series and Its Tests for Convergence1. 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 Series4.5冪級數的運算與性質1. Operations of Power Series1. 冪級數的運算2. Properties of Power Series2. 冪級數的性質Exercises 4習題4

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