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， Conservative 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 Infmite Series with Positive Terms

  11.3 Series With Arbitrary Terms， Absolute Convergence

  11.4 The Discrinunances for Convergence of Improper Integral， г 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