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| Integrals | |
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| Areas and Distances | |
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| The Definite Integral | |
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| Discovery Project: Area Functions | |
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| The Fundamental Theorem of Calculus | |
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| Indefinite Integrals and the Total Change Theorem | |
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| Writing Project: Newton, Leibniz, and the Invention of Calculus | |
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| The Substitution Rule | |
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| Applications of Integration | |
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| Areas between Curves | |
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| Volume | |
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| Volumes by Cylindrical Shells | |
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| Work | |
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| Average Value of a Function | |
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| Applied Project: Where to Sit at the Movies | |
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| Techniques of Integration | |
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| Integration by Parts | |
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| Trigonometric Integrals | |
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| Trigonometric Substitution | |
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| Integration of Rational Functions by Partial Fractions | |
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| Strategy for Integration | |
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| Integration Using Tables and Computer Algebra Systems | |
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| Discovery Project: Patterns in Integrals | |
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| Approximate Integration | |
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| Improper Integrals | |
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| Further Applications of Integration | |
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| Arc Length | |
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| Discovery Project: Arc Length Contest | |
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| Area of a Surface of Revolution | |
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| Discovery Project: Rotating on a Slant | |
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| Applications to Physics and Engineering | |
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| Applications to Economics and Biology | |
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| Probability | |
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| Differential Equations | |
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| Modeling with Differential Equations | |
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| Direction Fields and Euler?s Method | |
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| Separable Equations | |
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| Applied Project: Which is Faster, Going Up or Coming Down? | |
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| Exponential Growth and Decay | |
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| Applied Project: Calculus and Baseball | |
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| The Logistic Equation | |
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| Linear Equations | |
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| Predator-Prey Systems | |
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| Parametric Equations and Polar Coordinates | |
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| Curves Defined by Parametric Equations | |
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| Laboratory Project: Families of Hypocycloids | |
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| Tangents and Areas | |
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| Laboratory Project: Bezier Curves | |
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| Arc Length and Surface Area | |
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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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| Applied Project: Transfer Orbits | |
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| Infinite Sequences and Series | |
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| Sequences | |
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| 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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| The Binomial Series | |
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| Writing Project: How Newton Discovered the Binomial Series | |
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| Applications of Taylor Polynomials | |
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| Applied Project: Radiation from the Stars | |
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| Appendixes | |
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| Numbers, Inequalities, and Absolute Values | |
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| Coordinate Geometry and Lines | |
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| Graphs of Second-Degree Equations | |
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| Trigonometry | |
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| Sigma Notation | |
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| Proofs of Theorems | |
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| The Logarithm Defined as an Integral | |
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| Complex Numbers | |
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| Answers to Odd-Numbered Exercises | |