Table of Contents

Chapter 1 Parametric Equations and Polar Coordinates
 1.1 Parametric Equations
 1.2 Calculus of Parametric Curves
 1.3 Polar Coordinates
 1.4 Area and Arc Length in Polar Coordinates
 1.5 Conic Sections

Chapter 2 Vectors in Space
 2.1 Vectors in the Plane
 2.2 Vectors in Three Dimensions
 2.3 The Dot Product
 2.4 The Cross Product

2.5 Equations of Lines and Planes in Space
 Cartesian Equation of a Straight Line in Space
 Equation of a Straight Line in Three Dimensions
 The Equation of a Plane in 3D in Different Forms
 Distances between Points, Straight Lines, and Planes
 Parallel and Perpendicular Vectors in Space
 Parametric Equations of a Straight Line in Space
 Normal Vector
 Equation of a Plane in Space in Vector Form
 Relationship between a Straight Line and a Plane
 Equations of Planes
 Intersection between Planes
 Angle between Two Planes
 2.6 Quadric Surfaces
 2.7 Cylindrical and Spherical Coordinates

Chapter 3 VectorValued Functions
 3.1 VectorValued Functions and Space Curves
 3.2 Calculus of VectorValued Functions
 3.3 Arc Length and Curvature
 3.4 Motion in Space

Chapter 4 Differentiation of Functions of Several Variables
 4.1 Functions of Several Variables
 4.2 Limits and Continuity
 4.3 Partial Derivatives
 4.4 Tangent Planes and Linear Approximations
 4.5 The Chain Rule
 4.6 Directional Derivatives and the Gradient
 4.7 Maxima/Minima Problems
 4.8 Lagrange Multipliers

Chapter 5 Multiple Integration
 5.1 Double Integrals over Rectangular Regions
 5.2 Double Integrals over General Regions
 5.3 Double Integrals in Polar Coordinates
 5.4 Triple Integrals
 5.5 Triple Integrals in Cylindrical and Spherical Coordinates
 5.6 Calculating Centers of Mass and Moments of Inertia
 5.7 Change of Variables in Multiple Integrals

Chapter 6 Vector Calculus
 6.1 Vector Fields
 6.2 Line Integrals
 6.3 Conservative Vector Fields
 6.4 Green’s Theorem
 6.5 Divergence and Curl
 6.6 Surface Integrals
 6.7 Stokes’ Theorem
 6.8 The Divergence Theorem

Chapter 7 SecondOrder Differential Equations
 7.1 SecondOrder Linear Equations
 7.2 Nonhomogeneous Linear Equations
 7.3 Applications
 7.4 Series Solutions of Differential Equations