Preface
Chapter 1  Parametric Equations and Polar Coordinates
Introduction
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 Review
Key Terms
Key Equations
Key Concepts
Review Exercises
Chapter 2  Vectors in Space
Introduction
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
2.6 Quadric Surfaces
2.7 Cylindrical and Spherical Coordinates
Chapter Review
Key Terms
Key Equations
Key Concepts
Review Exercises
Chapter 3  Vector-Valued Functions
Introduction
3.1 Vector-Valued Functions and Space Curves
3.2 Calculus of Vector-Valued Functions
3.3 Arc Length and Curvature
3.4 Motion in Space
Chapter Review
Key Terms
Key Equations
Key Concepts
Review Exercises
Chapter 4  Differentiation of Functions of Several Variables
Introduction
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 Review
Key Terms
Key Equations
Key Concepts
Review Exercises
Chapter 5  Multiple Integration
Introduction
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 Review
Key Terms
Key Equations
Key Concepts
Review Exercises
Chapter 6  Vector Calculus
Introduction
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 Review
Key Terms
Key Equations
Key Concepts
Review Exercises
Chapter 7  Second-Order Differential Equations
Introduction
7.1 Second-Order Linear Equations
7.2 Nonhomogeneous Linear Equations
7.3 Applications
7.4 Series Solutions of Differential Equations
Chapter Review
Key Terms
Key Equations
Key Concepts
Review Exercises
Appendix A Table of Integrals
Appendix B Table of Derivatives
Appendix C Review of Pre-Calculus
Answer Key
Chapter 1
Chapter 2
Chapter 3
Chapter 4
Chapter 5
Chapter 6
Chapter 7
Index