高等数学简明双语教程 下PDF|Epub|txt|kindle电子书版本网盘下载

高等数学简明双语教程 下PDF格式电子书版下载

注意：本站所有压缩包均有解压码： 点击下载压缩包解压工具

Chapter 6 Differential Equations1

6.1 Basic Concepts of Differential Equations1

6.1.1 Examples of Differential Equations1

6.1.2 Basic Concepts2

Exercise 6.13

6.2 First-order Differential Equations3

6.2.1 First-order Separable Differential Equation3

6.2.2 First-order Homogeneous Equation4

6.2.3 First-order Linear Differential Equation5

6.2.4 Bernoulli's Equation7

Exercise 6.28

6.3 Order-reducible Differential Equations9

6.3.1 The Equation of the Form y(n)=f(x)9

6.3.2 The Equation of the Form y"=f(x,y')10

6.3.3 The Equation of the Form y"=f(y,y')11

Exercise 6.312

6.4 Second-order Linear Differential Equations12

Exercise 6.414

6.5 Higher-order Linear Equations with Constant Coefficients14

6.5.1 Second-order Homogeneous Linear Equations with Constant Coefficients14

6.5.2 Second-order Linear Non-homogeneous Equations with Constant Coefficients16

Exercise 6.519

第6章 微分方程21

6.1 微分方程的基本概念21

6.1.1 微分方程的例子21

6.1.2 基本概念22

习题6.122

6.2 一阶微分方程23

6.2.1 一阶可分离变量型微分方程23

6.2.2 一阶齐次方程24

6.2.3 一阶线性微分方程25

6.2.4 伯努利方程27

习题6.228

6.3 可降阶的二阶方程29

6.3.1 形如y(n)=f(x）的微分方程29

6.3.2 形如y"=f(x,y'）的微分方程29

6.3.3 形如y"=f(y,y'）的微分方程30

习题6.331

6.4 二阶线性微分方程31

习题6.433

6.5 高阶常系数齐次线性微分方程33

6.5.1 二阶常系数齐次线性微分方程33

6.5.2 二阶常系数非齐次线性微分方程34

习题6.538

Chapter 7 Infinite Series39

7.1 Concepts and Properties of Series with Constant Terms39

7.1.1 Concepts of Series with Constant Terms39

7.1.2 Properties of Series with Constant Terms41

Exercise 7.143

7.2 Convergence Tests for Series with Positive Constant Terms44

Exercise 7.247

7.3 Alternating Series48

Exercise 7.350

7.4 Absolute Convergence and the Ratio and Root Tests50

Exercise 7.455

7.5 Power Series55

7.5.1 Power Series and Its Convergence55

7.5.2 Operations of Power Series61

Exercise 7.562

7.6 Taylor and Maclaurin Series63

Exercise 7.668

7.7 The Binomial Series68

Exercise 7.771

第7章 无穷级数72

7.1 常数项级数的概念和性质72

7.1.1 常数项级数的概念72

7.1.2 常数项级数的性质74

习题7.175

7.2 正项级数收敛性判别法76

习题7.279

7.3 交错级数80

习题7.381

7.4 绝对收敛性和比值判别法、根式判别法82

习题7.486

7.5 幂级数87

7.5.1 幂级数及其敛散性87

7.5.2 幂级数的运算92

习题7.593

7.6 泰勒级数和麦克劳林级数93

习题7.698

7.7 二项式级数99

习题7.7101

Chapter 8 Vectors and the Geometry of Space102

8.1 Three-dimensional Rectangular Coordinate Systems102

Exercise 8.1105

8.2 Vectors105

8.2.1 Combining Vectors106

8.2.2 Components107

Exercise 8.2111

8.3 The Dot Ptroduct111

8.3.1 Work and the Dot Product111

8.3.2 Dot Product in Component Form112

Exercise 8.3114

8.4 The Cross Product115

8.4.1 Torque and the Cross Product115

8.4.2 The Cross Product in Component Form117

Exercise 8.4118

8.5 Planes and Lines in Space119

8.5.1 Equations of Planes119

8.5.2 Equations of Lines in Space122

Exercise 8.5127

8.6 Functions and Surfaces128

8.6.1 Functions of Two Variables128

8.6.2 Cylinders129

8.6.3 Cones130

8.6.4 Quadric Surfaces131

8.6.5 Surfaces of Revolution134

Exercise 8.6135

8.7 Space Curves136

Exercise 8.7138

第8章 向量与空间解析几何139

8.1 三维直角坐标系139

习题8.1142

8.2 向量142

8.2.1 向量运算142

8.2.2 分量表示144

习题8.2147

8.3 点积147

8.3.1 功和点积147

8.3.2 分量形式的点积148

习题8.3149

8.4 叉积150

8.4.1 扭矩和叉积150

8.4.2 叉积的分量表示形式152

习题8.4153

8.5 空间平面和直线154

8.5.1 平面方程154

8.5.2 空间直线方程157

习题8.5161

8.6 二元函数与曲面162

8.6.1 二元函数162

8.6.2 柱面163

8.6.3 锥面164

8.6.4 二次曲面165

8.6.5 旋转曲面167

习题8.6168

8.7 空间曲线169

习题8.7171

Chapter 9 The Differential Calculus for Multi-variable Functions172

9.1 Multi-variable Functions172

9.1.1 Some Related Concepts173

9.1.2 Limits of Multi-variable Functions174

9.1.3 Continuity of Functions of Two Variables175

Exercise 9.1176

9.2 Partial Derivatives and Higher Order Partial Derivatives177

9.2.1 Partial Derivatives178

9.2.2 Higher Order Partial Derivatives182

Exercise 9.2184

9.3 Total Differentials of Multi-variable Functions185

9.3.1 Total Differentials185

9.3.2 Applications of Total Differential to Approximate Computation188

Exercise 9.3189

9.4 Differentiation of Multivariable Composite Functions189

Exercise 9.4195

9.5 Implicit Partial Differentiation196

9.5.1 Differentiation of Implicit Functions Defined by One Equation196

9.5.2 Differentiation of Implicit Functions Defined by A System of Equations199

Exercise 9.5201

9.6 Applications of Differential Calculus of Multivariable Functions in Geometry202

9.6.1 Tangent Line and Normal Plane to A Space Curve202

9.6.2 Tangent Plane and Normal Line of Surfaces207

Exercise 9.6210

9.7 Directional Derivatives and Gradient211

9.7.1 Directional Derivatives211

9.7.2 Gradient214

Exercise 9.7216

9.8 Extreme Value Problems for Multivariable Functions217

9.8.1 Unrestricted Extreme Values217

9.8.2 Global Maxima and Minima220

9.8.3 Extreme Values with Constraints:the Method of Lagrange Multipliers222

Exercise 9.8228

第9章 多元函数微分学229

9.1 多元函数229

9.1.1 一些相关概念229

9.1.2 多元函数的极限230

9.1.3 二元函数的连续性231

习题9.1232

9.2 偏导数和高阶导数233

9.2.1 偏导数233

9.2.2 高阶偏导数237

习题9.2239

9.3 多元函数的全微分239

9.3.1 全微分239

9.3.2 全微分在近似计算中的应用243

习题9.3243

9.4 多元复合函数的微分法243

习题9.4249

9.5 多元隐函数的偏导数250

9.5.1 由一个方程所确定的隐函数的求导法250

9.5.2 由方程组所确定的隐函数的求导法252

习题9.5254

9.6 多元函数的微分法在几何上的应用255

9.6.1 曲线的切线和法平面255

9.6.2 曲面的切平面和法线259

习题9.6262

9.7 方向导数和梯度262

9.7.1 方向导数262

9.7.2 梯度266

习题9.7268

9.8 多元函数的极值268

9.8.1 无条件极值268

9.8.2 最大值与最小值271

9.8.3 有条件极值：拉格朗日乘数法273

习题9.8277

Chapter 10 Multiple Integrals278

10.1 The Concept and Properties of Double Integrals278

10.1.1 The Concept of Double Integrals278

10.1.2 Properties of Double Integrals282

Exercise 10.1284

10.2 Computation of Double Integrals in Rectangular Coordinate System285

Exercise 10.2294

10.3 Computation of Double Integrals in Polar Coordinates296

Exercise 10.3302

10.4 Triple Integrals303

10.4.1 Concept of Triple Integrals303

10.4.2 Properties of Triple Integrals305

10.4.3 Computation of Triple Integrals in Rectangular Coordinates305

Exercise 10.4311

10.5 Triple Integrals in Some Other Coordinates312

10.5.1 Triple Integrals in Cylindrical Coordinates312

10.5.2 Triple Integrals in Spherical Coordinates314

Exercise 10.5318

第10章 多重积分319

10.1 二重积分的概念和性质319

10.1.1 二重积分的概念319

10.1.2 二重积分的性质322

习题10.1324

10.2 直角坐标系下的二重积分的计算325

习题10.2334

10.3 极坐标系下的二重积分的计算335

习题10.3340

10.4 三重积分342

10.4.1 三重积分的概念342

10.4.2 三重积分的性质343

10.4.3 直角坐标系下的三重积分的计算344

习题10.4349

10.5 在其他坐标系下的三重积分350

10.5.1 柱坐标下的三重积分350

10.5.2 球坐标系下的三重积分352

习题10.5355

参考文献357