About the Authors | |

Preface | |

Functions, Graphs, and Models | |

Functions and Mathematical ModelingInvestigation: Designing a Wading Pool | |

Graphs of Equations and Functions | |

Polynomials and Algebraic Functions | |

Transcendental Functions | |

Preview: What Is Calculus? | |

Review - Understanding: Concepts and Definitions | |

Objectives: Methods and Techniques | |

Prelude to Calculus | |

Tangent Lines and Slope Predictors | |

Investigation: Numerical Slope Investigations | |

The Limit ConceptInvestigation: Limits, Slopes, and Logarithms | |

More About LimitsInvestigation: Numerical Epsilon-Delta Limits | |

The Concept of Continuity | |

Review - Understanding: Concepts and Definitions | |

Objectives: Methods and Techniques | |

The Derivative | |

The Derivative and Rates of Change | |

Basic Differentiation Rules | |

The Chain Rule | |

Derivatives of Algebraic Functions | |

Maxima and Minima of Functions on Closed Intervals | |

Investigation: When Is Your Coffee Cup Stablest? | |

Applied Optimization Problems | |

Derivatives of Trigonometric Functions | |

Exponential and Logarithmic Functions | |

Investigation: Discovering the Number e for Yourself | |

Implicit Differentiation and Related Rates | |

Investigation: Constructing the Folium of Descartes | |

Successive Approximations and Newton's Method | |

Investigation: How Deep Does a Floating Ball Sink? | |

Review - Understanding: Concepts, Definitions, and Formulas | |

Objectives: Methods and Techniques | |

Additional Applications of the Derivative | |

Introduction | |

Increments, Differentials, and Linear Approximation | |

Increasing and Decreasing Functions and the Mean Value Theorem | |

The First Derivative Test and Applications | |

Investigation: Constructing a Candy Box With Lid | |

Simple Curve Sketching | |

Higher Derivatives and Concavity | |

Curve Sketching and Asymptotes | |

Investigation: Locating Special Points on Exotic Graphs | |

Indeterminate Forms and L'Hapital's Rule | |

More Indeterminate Forms | |

Review - Understanding: Concepts, Definitions, and Results | |

Objectives: Methods and Techniques | |

The Integral | |

Introduction | |

Antiderivatives and Initial Value Problems | |

Elementary Area Computations | |

Riemann Sums and the Integral | |

Investigation: Calculator/Computer Riemann Sums | |

Evaluation of Integrals | |

The Fundamental Theorem of Calculus | |

Integration by Substitution | |

Areas of Plane Regions | |

Numerical IntegrationInvestigation: Trapezoidal and Simpson Approximations | |

Review - Understanding: Concepts, Definitions, and Results | |

Objectives: Methods and Techniques | |

Applications of the Integral | |

Riemann Sum Approximations | |

Volumes by the Method of Cross Sections | |

Volumes by the Method of Cylindrical Shells | |

Investigation: Design Your Own Ring! | |

Arc Length and Surface Area of Revolution | |

Force and Work | |

Centroids of Plane Regions and Curves | |

The Natural Logarithm as an Integral | |

Investigation: Natural Functional Equations | |

Inverse Trigonometric Functions | |

Hyperbolic Functions | |

Review - Understanding: Concepts, Definitions, and Formulas | |

Objectives: Methods and Techniques | |

Techniques of Integration | |

Introduction< | |

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