Note: Each chapter concludes with Problem Solving | |

Prerequisites | |

Solving Equations Section Project: Projectile Motion | |

Solving Inequalities | |

Graphical Representation of Data | |

Graphs of Equations | |

Linear Equations in Two Variables | |

Functions and Their Graphs | |

Functions | |

Analyzing Graphs of Functions | |

Shifting, Reflecting, and Stretching Graphs | |

Combinations of Functions | |

Inverse Functions | |

Mathematical Modeling Section Project: Hooke's Law | |

Polynomial and Rational Functions | |

Quadratic Functions | |

Polynomial Functions of Higher Degree | |

Polynomial and Synthetic Division | |

Complex Numbers Section Project: The Mandelbrot Set | |

The Fundamental Theorem of Algebra | |

Rational Functions Section Project: Rational Functions | |

Limits and Their Properties | |

A Preview of Calculus | |

Finding Limits Graphically and Numerically | |

Evaluating Limits Analytically | |

Continuity and One-Sided Limits | |

Infinite Limits Section Project: Graphs and Limits of Functions Progressive Summary 1: Flowchart of Calculus | |

Differentiation | |

The Derivative and the Tangent Line Problem | |

Basic Differentiation Rules and Rates of Change | |

The Product and Quotient Rules and Higher-Order Derivatives | |

The Chain Rule | |

Implicit Differentiation Section Project: Optical Illusions | |

Related Rates | |

Applications of Differentiation | |

Extrema on an Interval | |

Rolle's Theorem and the Mean Value Theorem | |

Increasing and Decreasing Functions and the First Derivative Test | |

Concavity and the Second Derivative Test | |

Limits at Infinity | |

A Summary of Curve Sketching | |

Optimization Problems Section Project: Connecticut River | |

Differentials | |

Integration | |

Antiderivatives and Indefinite Integration | |

Area | |

Riemann Sums and Definite Integrals | |

The Fundamental Theorem of Calculus Section Project: Demonstrating the Fundamental Theorem | |

Integration by Substitution | |

Numerical Integration Progressive Summary 2: Flowchart of Calculus | |

Exponential and Logarithmic Functions | |

Exponential Functions and Their Graphs | |

Logarithmic Functions and Their Graphs | |

Using Properties of Logarithms | |

Exponential and Logarithmic Equations | |

Exponential and Logarithmic Models Section Project: Comparing Models | |

Exponential and Logarithmic Functions and Calculus | |

Exponential Functions: Differentiation and Integration | |

Logarithmic Functions and Differentiation Section Project: An Alternate Definition of ln x | |

Logarithmic Functions and Integration | |

Differential Equations: Growth and Decay Progressive Summary 3: Flowchart of Calculus | |

Trigonometric Functions | |

Radian and Degree Measure | |

Trigonometric Functions: The Unit Circle | |

Right Triangle Trigonometry | |

Trigonometric Functions of Any Angle | |

Graphs of Sine and Cosine Functions Section Project: Approximating Sine and Cosine Functions | |

Graphs of Other Trigonometric Functions | |

Inverse Trigonometric Functions | |

Applications and Models | |

Analytic Trigonometry | |

Using Fundamental Trigonometric Identities | |

Verifying Trigonometric Identities | |

Solving Trigonometric Equations Section Project: Modeling a Sound Wave | |

Sum and Difference Formulas | |

Multiple-Angle and Product-to-Sum Formulas | |

Trigonometric Functions and Calculus | |

Limits of Trigonometric Functions Section Project: Graphs and Limits of Trigonometric Functions | |

Trigonometric Functions: Differenti | |

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