Parametric Equations and Polar Coordinates | |

Curves Defined by Parametric Equations | |

Laboratory Project: Families of Hypocycloids | |

Calculus with Parametric Curves | |

Laboratory Project: Bezier Curves | |

Polar Coordinates | |

Areas and Lengths in Polar Coordinates | |

Conic Sections | |

Conic Sections in Polar Coordinates | |

Review | |

Problems Plus | |

Infinite Sequences and Series | |

Sequences | |

Laboratory Project: Logistic Sequences | |

Series | |

The Integral Test and Estimates of Sums | |

The Comparison Tests | |

Alternating Series | |

Absolute Convergence and the Ratio and Root Tests | |

Strategy for Testing Series | |

Power Series | |

Representation of Functions as Power Series | |

Taylor and Maclaurin Series | |

Writing Project: How Newton Discovered the Binomial Series | |

Applications of Taylor Polynomials | |

Applied Project: Radiation from the Stars | |

Review | |

Problems Plus | |

Vectors and The Geometry of Space | |

Three-Dimensional Coordinate Systems | |

Vectors | |

The Dot Product | |

The Cross Product | |

Discovery Project: The Geometry of a Tetrahedron | |

Equations of Lines and Planes | |

Cylinders and Quadric Surfaces | |

Cylindrical and Spherical Coordinates | |

Laboratory Project: Families of Surfaces | |

Review | |

Problems Plus | |

Vector Functions | |

Vector Functions and Space Curves | |

Derivatives and Integrals of Vector Functions | |

Arc Length and Curvature | |

Motion in Space: Velocity and Acceleration | |

Applied Project: Kepler's Laws | |

Review | |

Problems Plus | |

Partial Derivatives | |

Functions of Several Variables | |

Limits and Continuity | |

Partial Derivatives | |

Tangent Planes and Linear Approximations | |

The Chain Rule | |

Directional Derivatives and the Gradient Vector | |

Maximum and Minimum Values | |

Applied Project: Designing a Dumpster | |

Discovery Project: Quadratic Approximations and Critical Points | |

Lagrange Multipliers | |

Applied Project: Rocket Science | |

Applied Project: Hydro-Turbine Optimization | |

Review | |

Problems Plus | |

Multiple Integrals | |

Double Integrals over Rectangles | |

Iterated Integrals | |

Double Integrals over General Regions | |

Double Integrals in Polar Coordinates | |

Applications of Double Integrals | |

Surface Area | |

Triple Integrals | |

Discovery Project: Volumes of Hyperspheres | |

Triple Integrals in Cylindrical and Spherical Coordinates | |

Applied Project: Roller Derby | |

Discovery Project: The Intersection of Three Cylinders | |

Change of Variables in Multiple Integrals | |

Review | |

Problems Plus | |

Vector Calculus | |

Vector Fields | |

Line Integrals | |

The Fundamental Theorem for Line Integrals | |

Green's Theorem | |

Curl and Divergence | |

Parametric Surfaces and Their Areas | |

Surface Integrals | |

Stokes' Theorem | |

Writing Project: Three Men and Two Theorems | |

The Divergence Theorem | |

Summary | |

Review | |

Problems Plus | |

Second-Order Differential Equations | |

Second-Order Linear Equations | |

Nonhomogeneous Linear Equations | |

Applications of Second-Order Differential Equations | |

Series Solutions | |

Review | |

Problems Plus | |

Appendixes | |

Intervals, Inequalities, and Absolute Values | |

Coordinate Geometry and Lines | |

Graphs of Second-Degree Equations | |

Trigonometry | |

Sigma Notation | |

Proofs of Theorems | |

Complex Numbers | |

H | |

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