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 | |

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 | |

Functions of Several Variables | |

Introduction to Functions of Several Variables | |

Limits and Continuity | |

Partial Derivatives Section Project: Moireacute; 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 | |

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 | |

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 Section Project: The Planimeter | |

Appendices | |

Proofs of Selected Theorems | |

Integration Tables | |

Additional Topics in Differential Equations (Web only) | |

Precalculus Review (Web only) | |

Rotation and the General Second-Degree Equation (Web only) | |

Complex Numbers (Web only) | |

Business and Economic Applications (Web only) | |

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