【内容提要】
本书为《微积分》一书的第二卷，适用于工科院校非数学专业本科新生，亦可作为工程技术人员的参考书籍.本卷包含四个章节，内容涵盖多元函数微分学，多元函数积分学，第二型曲线积分、第二型曲面积分及无穷级数.本书包含大量例题及习题.
【目 录】
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 , Conservative 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 ExampJes//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, г 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