Table of Contents

Chapter 1 • Parametric Equations and Polar Coordinates
 Parametric Equations and Curves in Two Dimensions
 Derivatives of Parametric Equations
 Area Enclosed by Parametric Curves
 Arc Length of Parametric Curves
 Surface of Revolution of Parametric Curves
 Second Derivatives of Parametric Equations
 Polar Coordinates
 Graphing Polar Curves
 Arc Length of a Polar Curve
 Equation of a Parabola
 Equation of an Ellipse
 Identifying Conic Sections

Chapter 2 • Vectors in Space
 Components of a Vector
 Vector Operations in 2D
 Magnitude of a 2D Vector
 Points, Midpoints, and Distances in Space
 Vectors in Terms of Fundamental Unit Vectors
 Scalars, Vectors, and Directed Line Segments
 Equation of a Sphere
 Vectors in Space
 Dot Product in 2D
 Dot Product in 3D
 Angle between Two Vectors in Space
 The Angle between Two Vectors in the Coordinate Plane
 Cross Product in 3D
 Vector Triple Product
 Scalar Triple Product
 Equation of a Straight Line in Space: Cartesian and Vector Forms
 The Perpendicular Distance between Points and Planes
 Parallel and Perpendicular Vectors in Space
 Equation of a Straight Line in Space: Parametric Form
 Equation of a Plane: Intercept and Parametric Forms
 Equation of a Plane: Vector, Scalar, and General Forms
 Intersection of Planes
 The Angle between Two Planes and between a Plane and a Straight Line
 Chapter 3 • VectorValued Functions
 Chapter 4 • Differentiation of Functions of Several Variables
 Chapter 5 • Multiple Integration
 Chapter 6 • Vector Calculus
 Chapter 7 • SecondOrder Differential Equations