Chapter 8 Differential Calculus of Multivariable Functions

8.1 Limits and Continuity of Multivariable Functions

8.2 Partial Derivatives and Higher-Order Partial Derivatives

8.3 Linear Approximations and Total Differentials

8.4 The Chain Rule

8.5 Implicit Differentiation

8.6 Applications of Partial Derivatives to Analytic Geometry

8.7 Extreme Values of Functions of Several Variables

8.8 Directional Derivatives and The Gradient Vector

8.9 Examples

Exercises 8

Chapter 9 Multiple Integrals

9.1 Double Integrals

9.2 Calculating Double Integrals

9.3 Calculating Triple Integrals

9.4 Concepts and Calculations of The First Type Curve Integral

9.5 The First Type Surface Integral

9.6 Application of Integrals

9.7 Examples

Exercises 9

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

10.1 The Second Type Curve Integral

10.2 The Green's Theorem

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

10.4 The Second Type Surface Integral

10.5 The Gauss Formula,The Flux and Divergence

10.6 The Stokes'Theorem,Circulation and Curl

10.7 Examples

Exercises 10

Chapter 11 Infinite Series

11.1 Convergence and Divergence of Infinite Series

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

11.3 Series With Arbitrary Terms,Absolute Convergence

11.4 The Discriminances for Convergence of Improper Integral,Γ Function

11.5 Series with Function Terms,Uniform Convergence

11.6 Power Series

11.7 Expanding Functions as Power Series

11.8 Some Applications of The Power Series

11.9 Fourier Series

11.10 Examples

Exercises 11

Appendix Ⅳ Change of Variables in Multiple Integrals

Appendix Ⅴ Radius of Convergence of Power Series