Ingredients of Change: Functions and Models | |

Models and Functions | |

Linear Functions and Models | |

Exponential and Logarithmic Functions and Models | |

Logistic Functions and Models | |

Polynomial Functions and Models | |

Describing Change: Rates | |

Change, Percentage Change, and Average Rates of Change | |

Instantaneous Rates of Change | |

Derivative Notation and Numerical Estimates | |

Algebraically Finding Slopes | |

Determining Change: Derivatives | |

Drawing Rate-of-Change Graphs | |

Simple Rate-of-Change Formulas | |

Exponential and Logarithmic Rate-of-Change Formulas | |

The Chain Rule | |

The Product Rule | |

Limiting Behavior Revisited: L'H?pital's Rule | |

Analyzing Change: Applications of Derivatives | |

Approximating Change | |

Relative and Absolute Extreme Points | |

Inflection Points | |

Interconnected Change: Related Rates | |

Accumulating Change: Limits of Sums and the Definite Integral | |

Results of Change and Area Approximations | |

Accumulation Functions | |

The Fundamental Theorem | |

The Definite Integral | |

Average Value and Average Rate of Change | |

Integration by Substitution or Algebraic Manipulation | |

Analyzing Accumulated Change: Integrals in Action | |

Perpetual Accumulation and Improper Integrals | |

Streams in Business and Biology | |

Integrals in Economics | |

Probability Distributions and Density Functions | |

Repetitive Change: Cyclic Functions | |

Cycles and Sine Functions | |

Sine Functions as Models | |

Rates of Change and Derivatives | |

Extrema and Points of Inflection | |

Accumulation in Cycles | |

Dynamics of Change: Differential Equations and Proportionality | |

Differential Equations and Slope Fields | |

Separable Differential Equations | |

Numerically Estimating by Using Differential Equations: Euler's Method | |

Second-Order Differential Equations | |

Ingredients of Multivariable Change: Models, Graphs, Rates | |

Multivariable Functions and Contour Graphs | |

Cross-Sectional Models and Rates of Change | |

Partial Rates of Change | |

Compensating for Change | |

Analyzing Multivariable Change: Optimization | |

Multivariable Critical Points | |

Multivariable Optimization | |

Optimization Under Constraints | |

Least-Squares Optimization | |

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