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| Diagnostic Tests | |
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| A Preview of Calculus | |
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| Functions And Models | |
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| Four Ways to Represent a Function | |
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| Mathematical Models: A Catalog of Essential Functions | |
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| New Functions from Old Functions | |
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| Graphing Calculators and Computers | |
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| Exponential Functions | |
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| Inverse Functions and Logarithms | |
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| Review | |
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| Principles of Problem Solving | |
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| Limits And Derivatives | |
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| The Tangent and Velocity Problems | |
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| The Limit of a Function | |
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| Calculating Limits Using the Limit Laws | |
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| The Precise Definition of a Limit | |
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| Continuity | |
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| Limits at Infinity | |
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| Horizontal Asymptotes | |
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| Derivatives and Rates of Change | |
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| Writing Project: Early Methods for Finding Tangents | |
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| The Derivative as a Function | |
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| Review | |
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| Problems Plus | |
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| Differentiation Rules | |
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| Derivatives of Polynomials and Exponential Functions | |
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| Applied Project: Building a Better Roller Coaster | |
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| The Product and Quotient Rules | |
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| Derivatives of Trigonometric Functions | |
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| The Chain Rule | |
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| Applied Project: Where Should a Pilot Start Descent? | |
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| Implicit Differentiation | |
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| Derivatives of Logarithmic Functions | |
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| Rates of Change in the Natural and Social Sciences | |
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| Exponential Growth and Decay | |
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| Related Rates | |
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| Linear Approximations and Differentials | |
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| Laboratory Project: Taylor Polynomials | |
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| Hyperbolic Functions | |
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| Review | |
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| Problems Plus | |
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| Applications Of Differentiation | |
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| Maximum and Minimum Values | |
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| Applied Project: The Calculus of Rainbows | |
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| The Mean Value Theorem | |
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| How Derivatives Affect the Shape of a Graph | |
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| Indeterminate Forms and L'Hospital's Rule | |
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| Writing Project: The Origins of l'Hospital's Rule | |
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| Summary of Curve Sketching | |
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| Graphing with Calculus and Calculators | |
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| Optimization Problems | |
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| Applied Project: The Shape of a Can | |
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| Newton's Method | |
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| Antiderivatives | |
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| Review | |
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| Problems Plus | |
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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 Net 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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| Review | |
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| Problems Plus | |
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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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| Review | |
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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 | |