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
Thapter 6 Vectors and Analytic Geometry in Space
6. 1 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. i Sphere and Cylinder
6. 4. 2 Curves in Space
6. 4. 3 Surfaces of Revolution
6. 4. 4 Quaic Surfaces
……
Chapter 7 Multivariable Functions and Partial Derivatives
Chapter 8 Multiple Integrals
Chapter 9 Integration in Vectors Field
Chapter 10 Complex Analysis
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