Table of Contents

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