Chapter 5 Infinite Series
5.1 Convergent Series
5.1.1 Concepts of Convergent Series
5.1.2 Properties of Convergent Series
5.2 Tests of Convergence and Divergence
5.2.1 Tests for Positive Series
5.2.2 Alternating Series
5.2.3 Absolute and Conditional Convergence
5.3 Tests for Improper Integrals
5.3.1 Improper Integrals: Infinite Limits of Integration
5.3.2 Improper Integrals.Infinite Integrands
5.3.3 The Gamma Function
5.4 Infinite Series o{ Functions
5.4.1 General Definition
5.4 .2 Uniform Convergence of Series
5.4.3 Properties of Uniformly Convergent Functional Series
5.5 Power Series
5.5 .I The Radius and Interval of Convergence
5.5.2 Properties of Power Series
5.6 Expanding Functions into Power Series
5.7 Fourier's Series
5.7.1 The Concept of Fourier's Series
5.7.2 Fourier's Sine and Cosine Series
5.7.3 Expending Functions with Arbitrary Period
Chapter Review Exercise
Chapter 6 Vectors and Analytic Geometry in Space
6.1 Vectors and Their Linear Operations
6.1.1 The Concept of Vector
6.1.2 Linear Operations on Vectors
6.1.3 Dot Product and Gross Product
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
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
6.4 Curves and Surfaces in Space
6.4.1 Sphere and Cylinder
6.4.2 Curves in Space
6,4.3 Cone
6.4.4 Surfaces of Revolution
6.4.5 Quadric Surfaces
6.5 Vector-Valued Functions
6.5.1 Limit of a Vector-Valued Function
6.5.2 Derivative of a Vector-Valued Function
6.5.3 Integral of a Vector-Valued Function
6.5.4 Curvilinear Motion
6.5.5 Curvature
Chapter Review Exercise
