Preparation for Calculus | |

Graphs and Models | |

Linear Models and Rates of Change | |

Functions and Their Graphs | |

Fitting Models to Data | |

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 Trigonometric Functions | |

Differentiation | |

The Derivative and the Tangent Line Problem | |

Basic Differentiation Rules and Rates of Change | |

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 Section Project: Rainbows | |

Concavity and the Second Derivative Test | |

Limits at Infinity | |

A Summary of Curve Sketching | |

Optimization Problems Section Project: Connecticut River | |

Newton\'s Method | |

Differentials | |

Integration | |

Antiderivatives and Indefinite Integration 4.2 Area 4.3 Riemann Sums and Definite Integrals | |

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

Integration by Substitution | |

Numerical Integration | |

Logarithmic, Exponential, and Other Transcendental Functions | |

The Natural Logarithmic Function: Differentiation | |

The Natural Logarithmic Function: Integration | |

Inverse Functions | |

Exponential Functions: Differentiation and Integration | |

Bases Other Than e and Applications Section Project: Using Graphing Utilities to Estimate Slope | |

Inverse Trigonometric Functions: Differentiation | |

Inverse Trigonometric Functions: Integration | |

Hyperbolic Functions Section Project: St. Louis Arch | |

Differential Equations | |

Slope Fields and Euler\'s Method | |

Differential Equations: Growth and Decay | |

Separation of Variables and the Logistic Equation | |

First-Order Linear Differential Equations Section Project: Weight Loss | |

Applications of Integration | |

Area of a Region Between Two Curves | |

Volume: The Disk Method | |

Volume: The Shell Method Section Project: Saturn | |

Arc Length and Surfaces of Revolution | |

Work Section Project: Tidal Energy | |

Moments, Centers of Mass, and Centroids | |

Fluid Pressure and Fluid Force | |

Integration Techniques, L\'H?pital\'s Rule, and Improper Integrals | |

Basic Integration Rules | |

Integration by Parts | |

Trigonometric Integrals Section Project: Power Lines | |

Trigonometric Substitution | |

Partial Fractions | |

Integration by Tables and Other Integration Techniques | |

Indeterminate Forms and L\'H?pital\'s Rule 8.8 Improper Integrals | |

Infinite Series | |

Sequences | |

Series and Convergence Section Project: Cantor\'s Disappearing Table | |

The Integral Test and p-Series Section Project: The Harmonic Series | |

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