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Parametric Equations And Polar Coordinates | |

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Curves Defined by Parametric Equations, Laboratory Project: Families of Hypocycloids | |

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Calculus with Parametric Curves, Laboratory Project: Bezier Curves | |

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Polar Coordinates | |

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Areas and Lengths in Polar Coordinates | |

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Conic Sections | |

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Conic Sections in Polar Coordinates | |

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Review | |

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Problems Plus | |

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Infinite Sequences And Series | |

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Sequences, Laboratory Project: Logistic Sequences | |

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Series | |

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The Integral Test and Estimates of Sums | |

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The Comparison Tests | |

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Alternating Series | |

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Absolute Convergence and the Ratio and Root Tests | |

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Strategy for Testing Series | |

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Power Series | |

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Representation of Functions as Power Series | |

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Taylor and Maclaurin Series | |

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Laboratory Project: An Ellusive Limit | |

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The Binomial Series, Writing Project: How Newton Discovered the Binomial Series | |

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Applications of Taylor Polynomials, Applied Project: Radiation from the Stars | |

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Review | |

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Problems Plus | |

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Vectors And The Geometry Of Space | |

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Three-Dimensional Coordinate Systems | |

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Vectors | |

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The Dot Product | |

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The Cross Product, Discovery Project: The Geometry of a Tetrahedron | |

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Equations of Lines and Planes | |

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Cylinders and Quadric Surfaces | |

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Cylindrical and Spherical Coordinates, Laboratory Project: Families of Surfaces | |

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Review | |

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Problems Plus | |

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Vector Functions | |

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Vector Functions and Space Curves | |

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Derivatives and Integrals of Vector Functions | |

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Arc Length and Curvature | |

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Motion in Space: Velocity and Acceleration, Applied Project: Kepler's Laws | |

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Review | |

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Problems Plus | |

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Partial Derivatives | |

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Functions of Several Variables | |

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Limits and Continuity | |

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Partial Derivatives | |

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Tangent Planes and Linear Approximations | |

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The Chain Rule | |

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Directional Derivatives and the Gradient Vector | |

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Maximum and Minimum Values, Applied Project: Designing a Dumpster, Discovery Project: Quadratic Approximations and Critical Points | |

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Lagrange Multipliers, Applied Project: Rocket Science, Applied Project: Hydro-Turbine Optimization | |

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Review | |

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Problems Plus | |

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Multiple Integrals | |

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Double Integrals over Rectangles | |

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Iterated Integrals | |

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Double Integrals over General Regions | |

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Double Integrals in Polar Coordinates | |

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Applications of Double Integrals | |

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Surface Area | |

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Triple Integrals, Discovery Project: Volumes of Hyperspheres | |

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Triple Integrals in Cylindrical and Spherical Coordinates, Applied Project: Roller Derby, Discovery Project: The Intersection of Three Cylinders | |

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Change of Variables in Multiple Integrals | |

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Review | |

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Problems Plus | |

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Vector Calculus | |

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Vector Fields | |

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Line Integrals | |

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The Fundamental Theorem for Line Integrals | |

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Green's Theorem | |

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Curl and Divergence | |

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Parametric Surfaces and Their Areas | |

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Surface Integrals | |

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Stokes' Theorem, Writing Project: Three Men and Two Theorems | |

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The Divergence Theorem | |

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Summary | |

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Review | |

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Problems Plus | |

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Second-Order Differential Equations | |

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Second-Order Linear Equations | |

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Nonhomogeneous Linear Equations | |

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Applications of Second-Order Differential Equations | |

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Series Solutions | |

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Review | |

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Problems Plus | |

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Appendixes | |

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Answers to Odd-Numbered Exercises | |

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Index | |