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| Note: Each chapter concludes with Review Exercises and P.S. Problem Solving | |
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| Preparation for Calculus | |
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| Graphs and Models | |
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| Linear Models and Rates of Change | |
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| Functions and Their Graphs | |
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| Fitting Models to Data | |
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| Limits and Their Properties | |
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| A Preview of Calculus | |
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| Finding Limits Graphically and Numerically | |
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| Evaluating Limits Analytically | |
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| Continuity and One-Sided Limits | |
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| Infinite Limits Section Project: Graphs and Limits of Trigonometric Functions | |
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| Differentiation | |
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| The Derivative and the Tangent Line Problem | |
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| Basic Differentiation Rules and Rates of Change | |
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| The Product and Quotient Rules and Higher-Order Derivatives | |
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| The Chain Rule | |
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| Implicit Differentiation Section Project: Optical Illusions | |
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| Related Rates | |
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| Applications of Differentiation | |
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| Extrema on an Interval | |
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| Rolle's Theorem and the Mean Value Theorem | |
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| Increasing and Decreasing Functions and the First Derivative Test Section Project: Rainbows | |
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| Concavity and the Second Derivative Test | |
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| Limits at Infinity | |
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| A Summary of Curve Sketching | |
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| Optimization Problems Section Project: Connecticut River | |
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| Newton's Method | |
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| Differentials | |
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| Integration | |
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| Antiderivatives and Indefinite Integration | |
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| Area | |
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| Reimann Sums and Definite Integrals | |
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| The Fundamental Theorem of Calculus Section Project: Demonstrating the Fundamental Theorem | |
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| Integration by Substitution | |
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| Numerical Integration | |
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| Logarithmic, Exponential, and Other Transcendental Functions | |
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| The Natural Logarithmic Function: Differentiation | |
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| The Natural Logarithmic Function: Integration | |
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| Inverse Functions | |
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| Exponential Functions: Differentiation and Integration | |
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| Bases Other Than e and Applications Section Project: Using Graphing Utilities to Estimate Slope | |
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| Differential Equations: Growth and Decay | |
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| Differential Equations: Separation of Variables | |
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| Inverse Trigonometric Functions: Differentiation | |
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| Inverse Trigonometric Functions: Integration | |
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| Hyperbolic Functions Section Project: St. Louis Arch | |
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| Applications of Integration | |
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| Area of a Region Between Two Curves | |
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| Volume: The Disk Method | |
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| Volume: The Shell Method Section Project: Saturn | |
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| Arc Length and Surfaces of Revolution | |
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| Work Section Project: Tidal Energy | |
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| Moments, Centers of Mass, and Centroids | |
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| Fluid Pressure and Fluid Force | |
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| Integration Techniques, L'Hocirc;pital's Rule, and Improper Integrals | |
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| Basic Integration Rules | |
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| Integration by Parts | |
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| Trigonometric Integrals Section Project: Power Lines | |
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| Trigonometric Substitution | |
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| Partial Fractions | |
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| Integration by Tables and Other Integration Techniques | |
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| Indeterminant Forms and L'Hocirc;pital's Rule | |
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| Improper Integrals | |
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| Infinite Series | |
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| Sequences | |
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| Series and Convergence Section Project: Cantor's Disappearing Table | |
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| The Integral Test and p-Series Section Project: The Harmonic Series | |
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| Comparisons of Series Section Project: Solera Method | |
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| Alternating Series | |
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| The Ratio and Root Tests | |
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| Taylor Polynomials and Approximations | |
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| Power Series | |
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| Representation of Functions by Power Series | |
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| Taylor and Maclaurin Series | |
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| Conics, Parametric Equations, and Polar Coordinates | |
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| Conics and Calculus | |
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| Plane Curves and Parametric Equations Section Project: Cycloids | |
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| Parametric Equations and Calculus | |
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| Polar Coordinates and Polar Graphs Section Project: Anamorphic Art | |
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| Area and Arc Length in Polar Coordinates | |
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| Polar Equations of Conics and Kepler's Laws | |
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| Appendices | |
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| Additional Topics in Differential Equations | |
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| Proofs of Selected Theorems | |
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| Integration Tables | |
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| Precalculus Review | |
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| Rotation and the General Second-Degree Equation | |
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| Complex Numbers | |
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| Business and Economic Applications | |