Front Matter | |

Vectors and the Geometry of Space | |

Vectors in the Plane | |

Space Coordinates and Vectors in Space | |

The Dot Product of Two Vectors | |

The Cross Product of Two Vectors in Space | |

Lines and Planes in Space | |

Section Project: Distances in Space | |

Surfaces in Space | |

Cylindrical and Spherical Coordinates | |

Review Exercises | |

P.S. Problem Solving | |

Vector-Valued Functions | |

Vector-Valued Functions | |

Section Project: Witch of Agnesi | |

Differentiation and Integration of Vector-Valued Functions | |

Velocity and Acceleration | |

Tangent Vectors and Normal Vectors | |

Arc Length and Curvature | |

Review Exercises | |

P.S. Problem Solving | |

Functions of Several Variables | |

Introduction to Functions of Several Variables | |

Limits and Continuity | |

Partial Derivatives Section Project: Moir? | |

Fringes | |

Differentials | |

Chain Rules for Functions of Several Variables | |

Directional Derivatives and Gradients | |

Tangent Planes and Normal Lines | |

Section Project: Wildflowers | |

Extrema of Functions of Two Variables | |

Applications of Extrema of Functions of Two Variables | |

Section Project: Building a Pipeline | |

Lagrange Multipliers | |

Review Exercises | |

P.S. Problem Solving | |

Multiple Integration | |

Iterated Integrals and Area in the Plane | |

Double Integrals and Volume | |

Change of Variables: Polar Coordinates | |

Center of Mass and Moments of Inertia | |

Section Project: Center of Pressure on a Sail | |

Surface Area | |

Section Project: Capillary Action | |

Triple Integrals and Applications | |

Triple Integrals in Cylindrical and Spherical Coordinates | |

Section Project: Wrinkled and Bumpy Spheres | |

Change of Variables: Jacobians | |

Review Exercises | |

P.S. Problem Solving | |

Vector Analysis | |

Vector Fields | |

Line Integrals | |

Conservative Vector Fields and Independence of Path | |

Green's Theorem | |

Section Project: Hyperbolic and Trigonometric Functions | |

Parametric Surfaces | |

Surface Integrals | |

Section Project: Hyperboloid of One Sheet | |

Divergence Theorem | |

Stokes's Theorem | |

Review Exercises | |

Section Project: The Planimeter | |

P.S. Problem Solving | |

Bonus Online Material | |

Additional Topics in Differential Equations (please visit URL to come) | |

Exact First-Order Equations | |

Second-Order Homogeneous Linear Equations | |

Second-Order Nonhomogeneous Linear Equations | |

Section Project: Parachute Jump | |

Series Solutions of Differential Equations | |

Review Exercises | |

P.S. Problem Solving | |

Book Appendices | |

Proofs of Selected Theorems | |

Integration Tables | |

Online Appendices | |

Precalculus Review (please visit URL to come) | |

Real Numbers and the Real Number Line | |

The Cartesian Plane | |

Review of Trigonometric Functions | |

Rotation and the General Second-Degree Equation (please visit URL to come) | |

Complex Numbers (please visit URL to come) | |

Business and Economic Applications (please visit URL to come) | |

Table of Contents provided by Publisher. All Rights Reserved. |