- 作 者：张宇，黄艳编
- 出 版 社：哈尔滨：哈尔滨工业大学出版社
- 出版年份：2016
- ISBN：9787560358963
- 标注页数：301 页
- PDF页数：309 页
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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