Note: Each chapter concludes with a Chapter Summary with Hints and Suggestions and Review Exercises | |

Preface A User's Guide to Features Integrating Excel Graphing Calculator Terminology | |

Functions | |

Real Numbers, Inequalities, and Lines | |

Exponents | |

Functions | |

Functions, Continued | |

Derivatives and Their Uses | |

Limits and Continuity | |

Rates of Change, Slopes, and Derivatives | |

Some Differentiation Formulas | |

The Product and Quotient Rules | |

Higher–Order Derivatives | |

The Chain Rule and the Generalized Power Rule | |

Nondifferentiable Functions | |

Further Applications of Derivatives | |

Graphing Using the First Derivative | |

Graphing Using the First and Second Derivatives | |

Optimization | |

Further Applications of Optimization | |

Optimizing Lot Size and Harvest Size | |

Implicit Differentiation and Related Rates | |

Cumulative Review for Chapters 1–3 | |

Exponential and Logarithmic Functions | |

Exponential Functions | |

Logarithmic Functions | |

Differentiation of Logarithmic and Exponential Functions | |

Two Applications to Economics: Relative Rates and Elasticity of Demand | |

Integration and Its Applications | |

Antiderivatives and Indefinite Integrals | |

Integration Using Logarithmic and Exponential Functions | |

Definite Integrals and Areas | |

Further Applications of Definite Integrals: Average Value and Area Between Curves | |

Two Applications to Economics: Consumers' Surplus and Income Distribution | |

Integration by Substitution | |

Integration Techniques | |

Integration by Parts | |

Integration Using Tables | |

Improper Integrals | |

Numerical Integration | |

Calculus of Several Variables | |

Functions of Several Variables | |

Partial Derivatives | |

Optimizing Functions of Several Variables | |

Least Squares | |

Lagrange Multipliers and Constrained Optimization | |

Total Differentials and Approximate Changes | |

Multiple Integrals | |

Cumulative Review for Chapters 1–7 | |

Trigonometric Functions | |

Triangles, Angles, and Radian Measure | |

Sine and Cosine Functions | |

Derivatives of Sine and Cosine Functions | |

Integrals of Sine and Cosine Functions | |

Other Trigonometric Functions | |

Differential Equations | |

Separation of Variables | |

Further Applications of Differential Equations: Three Models of Growth | |

First–Order Linear Differential Equations | |

Approximate Solutions of Differential Equations: Euler's Method | |

Sequences and Series | |

Geometric Series | |

Taylor Polynomials | |

Taylor Series | |

Newton's Method | |

Probability | |

Discrete Probability | |

Continuous Probability | |

Uniform and Exponential Random Variables | |

Normal Random Variables | |

Cumulative Review for Chapters 1–11 | |

Appendix | |

Answers to Selected Exercises | |

Index | |

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