高等学校教材 微积分 第2卷 英文版PDF电子书下载

Chapter 8 Differential Calculus of Multivariable Functions 1

8.1 Limits and Continuity of Multivariable Functions 1

8.2 Partial Derivatives and Higher-Order Partial Derivatives 8

8.3 Linear Approximations and Total Differentials 15

8.4 The Chain Rule 21

8.5 Implicit Differentiation 26

8.6 Applications of Partial Derivatives to Analytic Geometry 35

8.7 Extreme Values of Functions of Several Variables 41

8.8 Directional Derivatives and The Gradient Vector 53

8.9 Examples 57

Exercises 8 61

Chapter 9 Multiple Integrals 74

9.1 Double Integrals 74

9.2 Calculating Double Integrals 78

9.3 Calculating Triple Integrals 89

9.4 Concepts and Calculations of The First Type Curve Integral 101

9.5 The First Type Surface Integral 106

9.6 Application of Integrals 111

9.7 Examples 114

Exercises 9 119

Chapter 10 The Second Type Curve Integral,Surface Integral,and Vector Field 131

10.1 The Second Type Curve Integral 131

10.2 The Green's Theorem 140

10.3 Conditions for Plane Curve Integrals Being Independent of Path.Conserva-tive Fields 146

10.4 The Second Type Surface Integral 154

10.5 The Gauss Formula,The Flux and Divergence 162

10.6 The Stokes'Theorem,Circulation and Curl 170

10.7 Examples 177

Exercises 10 183

Chapter 11 Infinite Series 197

11.1 Convergence and Divergence of Infinite Series 198

11.2 The Discriminances for Convergence and Divergence of Infinite Series with Positive Terms 205

11.3 Series With Arbitrary Terms,Absolute Convergence 213

11.4 The Discriminances for Convergence of Improper Integral,Γ Function 218

11.5 Series with Function Terms,Uniform Convergence 223

11.6 Power Series 231

11.7 Expanding Functions as Power Series 240

11.8 Some Applications of The Power Series 253

11.9 Fourier Series 257

11.10 Examples 273

Exercises 11 277

Appendix Ⅳ Change of Variables in Multiple Integrals 293

Appendix Ⅴ Radius of Convergence of Power Series 300