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| Note: Each chapter concludes with Problem Solving | |
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| Prerequisites | |
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| Solving Equations Section Project: Projectile Motion | |
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| Solving Inequalities | |
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| Graphical Representation of Data | |
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| Graphs of Equations | |
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| Linear Equations in Two Variables | |
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| Functions and Their Graphs | |
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| Functions | |
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| Analyzing Graphs of Functions | |
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| Shifting, Reflecting, and Stretching Graphs | |
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| Combinations of Functions | |
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| Inverse Functions | |
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| Mathematical Modeling Section Project: Hooke's Law | |
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| Polynomial and Rational Functions | |
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| Quadratic Functions | |
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| Polynomial Functions of Higher Degree | |
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| Polynomial and Synthetic Division | |
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| Complex Numbers Section Project: The Mandelbrot Set | |
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| The Fundamental Theorem of Algebra | |
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| Rational Functions Section Project: Rational Functions | |
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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 Functions Progressive Summary 1: Flowchart of Calculus | |
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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 | |
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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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| Differentials | |
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| Integration | |
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| Antiderivatives and Indefinite Integration | |
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| Area | |
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| Riemann 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 Progressive Summary 2: Flowchart of Calculus | |
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| Exponential and Logarithmic Functions | |
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| Exponential Functions and Their Graphs | |
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| Logarithmic Functions and Their Graphs | |
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| Using Properties of Logarithms | |
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| Exponential and Logarithmic Equations | |
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| Exponential and Logarithmic Models Section Project: Comparing Models | |
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| Exponential and Logarithmic Functions and Calculus | |
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| Exponential Functions: Differentiation and Integration | |
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| Logarithmic Functions and Differentiation Section Project: An Alternate Definition of ln x | |
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| Logarithmic Functions and Integration | |
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| Differential Equations: Growth and Decay Progressive Summary 3: Flowchart of Calculus | |
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| Trigonometric Functions | |
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| Radian and Degree Measure | |
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| Trigonometric Functions: The Unit Circle | |
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| Right Triangle Trigonometry | |
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| Trigonometric Functions of Any Angle | |
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| Graphs of Sine and Cosine Functions Section Project: Approximating Sine and Cosine Functions | |
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| Graphs of Other Trigonometric Functions | |
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| Inverse Trigonometric Functions | |
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| Applications and Models | |
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| Analytic Trigonometry | |
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| Using Fundamental Trigonometric Identities | |
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| Verifying Trigonometric Identities | |
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| Solving Trigonometric Equations Section Project: Modeling a Sound Wave | |
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| Sum and Difference Formulas | |
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| Multiple-Angle and Product-to-Sum Formulas | |
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| Trigonometric Functions and Calculus | |
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| Limits of Trigonometric Functions Section Project: Graphs and Limits of Trigonometric Functions | |
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| Trigonometric Functions: Differenti | |