Chapter 5 Infinite Series 5.1 Infinite Series 5.1.1 The Concept of Infinite Series 5.1.2 Conditions for Convergence 5.1.3 Properties of Series Exercise 5.1 5.2 Tests for Convergence of Positive Series Exercise 5.2 5.3 Alternating Series， Absolute Convergence， and Conditional Convergence 5.3.1 Alternating Series 5.3.2 Absolute Convergence and Conditional Convergence Exercise 5.3 5.4 Tests for Improper Integrals 5.4.1 Tests for the Improper Integrals.Infinite Limits of Integration 5.4.2 Tests for the Improper Integrals： Infinite Integrands 5.4.3 The Gamma Function Exercise 5.4 5.5 Infinite Series of Functions 5.5.1 General Definitions 5.5.2 Uniform Convergence of Series 5.5.3 Properties of Uniformly Convergent Functional Series Exercise 5.5 5.6 Power Series 5.6.1 The Radius and Interval of Convergence 5.6.2 Properties of Power Series 5.6.3 Expanding Functions into Power Series Exercise 5.6 5.7 Fourier Series 5.7.1 The Concept of Fourier Series 5.7.2 Fourier Sine and Cosine Series 5.7.3 Expanding Functions with Arbitrary Period Exercise 5.7 Review and Exercise Chapter 6 Vectors and Analytic Geometry in Space 6.Vectors 6.1.1 Vectors 6.1.2 Linear Operations on Vectors 6.1.3 Dot Products and Cross Product Exercise 6.1 6.2 Operations on Vectors in Cartesian Coordinates in Three Space 6.2.1 Cartesian Coordinates in Three Space 6.2.2 Operations on Vectors in Cartesian Coordinates Exercise 6.2 6.3 Planes and Lines in Space 6.3.1 Equations for Plane 6.3.2 Lines 6.3.3 Some Problems Related to Lines and Planes Exercise 6.3 6.4 Curves and Surfaces in Space 6.4.1 Sphere and Cylinder 6.4.2 Curves in Space 6.4.3 Surfaces of Revolution 6.4.4 Quadric Surfaces Exercise 6.4 1 Exercise Review 1 Chapter 7 Multivariable Functions and Partial Derivatives 7.1 Functions of Several Variables Exercise 7.1 7.2 Limits and Continuity Exercise 7.2 7.3 Partial Derivative 7.3.1 Partial Derivative 7.3.2 Second Order Partial Derivatives Exercise 7.3 7.4 Differentials Exercise 7.4 7.5 Rules for Finding Partial Derivative 7.5.1 The Chain Rule 7.5.2 Implicit Differentiation Exercise 7.5 7.6 Direction Derivatives， Gradient Vectors 7.6.1 Direction Derivatives 7.6.2 Gradient Vectors Exercise 7.6 7.7 Geometric Applications o{ Differentiation of Functions of Several Variables 7.7.1 Tangent Line and Normal Plan to a Curve 7.7.2 Tangent Plane and Normal Line to a Surface Exercise 7.7 7.8 Taylor Formula for Functions of Two Variables and Extreme Values 7.8.1 Taylor Formula for Functions of Two Variables 7.8.2 Extreme Values 7.8.3 Absolute Maxima and Minima on Closed Bounded Regions …… Chapter 8 Multiple Integrals Chapter 9 Integration in Vectors Field Chapter 10 Complex Analysis
