Preface | |

Introduction | |

Functions | |

Functions and Their Graphs | |

Some Important Functions | |

The Algebra of Functions | |

Zeros of Functions-The Quadratic Formula and Factoring | |

Exponents and Power Functions | |

Functions and Graphs in Applications | |

The Derivative | |

The Slope of a Straight Line | |

The Slope of a Curve at a Point | |

The Derivative | |

Limits and the Derivative | |

Differentiability and Continuity | |

Some Rules for Differentiation | |

More About Derivatives | |

The Derivative as a Rate of Change | |

Applications of the Derivative | |

Describing Graphs of Functions | |

The First and Second Derivative Rules | |

The First and Second Derivative Tests and Curve Sketching | |

Curve Sketching (Conclusion) | |

Optimization Problems | |

Further Optimization Problems | |

Applications of Derivatives to Business and Economics | |

Techniques of Differentiation | |

The Product and Quotient Rules | |

The Chain Rule and the General Power Rule | |

Implicit Differentiation and Related Rates | |

Logarithm Functions | |

Exponential Functions | |

The Exponential Function ex | |

Differentiation of Exponential Functions | |

The Natural Logarithm Function | |

The Derivative of ln x | |

Properties of the Natural Logarithm Function | |

Applications of the Exponential and Natural Logarithm Functions | |

Exponential Growth and Decay | |

Compound Interest | |

Applications of the Natural Logarithm Function to Economics | |

Further Exponential Models | |

The Definite Integral | |

Antidifferentiation | |

Areas and Riemann Sums | |

Definite Integrals and the Fundamental Theorem | |

Areas in the xy-Plane | |

Applications of the Definite Integral | |

Functions of Several Variables | |

Examples of Functions of Several Variables | |

Partial Derivatives | |

Maxima and Minima of Functions of Several Variables | |

Lagrange Multipliers and Constrained Optimization | |

The Method of Least Squares | |

Double Integrals | |

The Trigonometric Functions | |

Radian Measure of Angles | |

The Sine and the Cosine | |

Differentiation and Integration of sin t and cos t | |

The Tangent and Other Trigonometric Functions | |

Techniques of Integration | |

Integration by Substitution | |

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