Integrals | |

Areas and Distances | |

The Definite Integral | |

Discovery Project: Area Functions | |

The Fundamental Theorem of Calculus | |

Indefinite Integrals and the Total Change Theorem | |

Writing Project: Newton, Leibniz, and the Invention of Calculus | |

The Substitution Rule | |

Applications of Integration | |

Areas between Curves | |

Volume | |

Volumes by Cylindrical Shells | |

Work | |

Average Value of a Function | |

Applied Project: Where to Sit at the Movies | |

Techniques of Integration | |

Integration by Parts | |

Trigonometric Integrals | |

Trigonometric Substitution | |

Integration of Rational Functions by Partial Fractions | |

Strategy for Integration | |

Integration Using Tables and Computer Algebra Systems | |

Discovery Project: Patterns in Integrals | |

Approximate Integration | |

Improper Integrals | |

Further Applications of Integration | |

Arc Length | |

Discovery Project: Arc Length Contest | |

Area of a Surface of Revolution | |

Discovery Project: Rotating on a Slant | |

Applications to Physics and Engineering | |

Applications to Economics and Biology | |

Probability | |

Differential Equations | |

Modeling with Differential Equations | |

Direction Fields and Euler?s Method | |

Separable Equations | |

Applied Project: Which is Faster, Going Up or Coming Down? | |

Exponential Growth and Decay | |

Applied Project: Calculus and Baseball | |

The Logistic Equation | |

Linear Equations | |

Predator-Prey Systems | |

Parametric Equations and Polar Coordinates | |

Curves Defined by Parametric Equations | |

Laboratory Project: Families of Hypocycloids | |

Tangents and Areas | |

Laboratory Project: Bezier Curves | |

Arc Length and Surface Area | |

Polar Coordinates | |

Areas and Lengths in Polar Coordinates | |

Conic Sections | |

Conic Sections in Polar Coordinates | |

Applied Project: Transfer Orbits | |

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 | |

The Binomial Series | |

Writing Project: How Newton Discovered the Binomial Series | |

Applications of Taylor Polynomials | |

Applied Project: Radiation from the Stars | |

Appendixes | |

Numbers, Inequalities, and Absolute Values | |

Coordinate Geometry and Lines | |

Graphs of Second-Degree Equations | |

Trigonometry | |

Sigma Notation | |

Proofs of Theorems | |

The Logarithm Defined as an Integral | |

Complex Numbers | |

Answers to Odd-Numbered Exercises | |

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