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Preface | |

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To the Student | |

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Diagnostic Tests | |

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A Preview of Calculus | |

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Functions and Models | |

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Four Ways to Represent a Function | |

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Mathematical Models: A Catalog of Essential Functions | |

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New Functions from Old Functions | |

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Graphing Calculators and Computers | |

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Exponential Functions | |

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Inverse Functions and Logarithms | |

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Parametric Curves | |

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Laboratory Project: Running Circles around Circles | |

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Review | |

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Principles of Problem Solving | |

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Limits and Derivatives | |

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The Tangent and Velocity Problems | |

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The Limit of a Function | |

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Calculating Limits Using the Limit Laws | |

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Continuity | |

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Limits Involving Infinity | |

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Derivatives and Rates of Change | |

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Writing Project: Early Methods for Finding Tangents | |

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The Derivative as a Function | |

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What Does f?? Say about f? Review | |

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Focus on Problem Solving | |

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Differentiation Rules | |

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Derivatives of Polynomials and Exponential Functions | |

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Applied Project: Building a Better Roller Coaster | |

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The Product and Quotient Rules | |

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Derivatives of Trigonometric Functions | |

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The Chain Rule | |

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Laboratory Project: BTzier Curves | |

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Applied Project: Where Should a Pilot Start Descent? Implicit Differentiation | |

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Inverse Trigonometric Functions and their Derivatives | |

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Derivatives of Logarithmic Functions | |

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Discovery Project: Hyperbolic Functions | |

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Rates of Change in the Natural and Social Sciences | |

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Linear Approximations and Differentials | |

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Laboratory Project: Taylor Polynomials | |

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Review | |

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Focus on Problem Solving | |

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Applications of Differentiation | |

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Related Rates | |

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Maximum and Minimum Values | |

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Applied Project: The Calculus of Rainbows | |

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Derivatives and the Shapes of Curves | |

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Graphing with Calculus and Calculators | |

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Indeterminate Forms and l'Hospital's Rule | |

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Writing Project: The Origins of l'Hospital's Rule | |

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Optimization Problems | |

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Applied Project: The Shape of a Can | |

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Newton's Method | |

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Antiderivatives | |

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Review | |

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Focus on Problem Solving | |

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Integrals | |

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Areas and Distances | |

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The Definite Integral | |

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Evaluating Definite Integrals | |

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Discovery Project: Area Functions | |

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The Fundamental Theorem of Calculus | |

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Writing Project: Newton, Leibniz, and the Invention of Calculus | |

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The Substitution Rule | |

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Integration by Parts | |

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Additional Techniques of Integration | |

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Integration Using Tables and Computer Algebra Systems | |

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Discovery Project: Patterns in Integrals | |

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Approximate Integration | |

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Improper Integrals | |

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Review | |

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Focus on Problem Solving | |

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Applications of Integration | |

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More about Areas | |

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Volumes | |

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Discovery Project: Rotating on a Slant | |

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Volumes by Cylindrical Shells | |

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Arc Length | |

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Discovery Project: Arc Length Contest | |

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Average Value of a Function | |

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Applied Project: Where To Sit at the Movies | |

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Applications to Physics and Engineering | |

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Discovery Project: Complementary Coffee Cups | |

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Applications to Economics and Biology | |

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Probability | |

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Review | |

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Focus on Problem Solving | |

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Differential Equations | |

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Modeling with Differential Equations | |

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Direction Fields and Euler's Method | |

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Separable Equations | |

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Applied Project: How Fast Does a Tank Drain? Applied Project: Which Is Faster, Going Up or Coming Down? Exponential Growth and Decay | |

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Applied Project: Calculus and Baseball | |

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The Logistic Equation | |

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Predator-Prey Systems | |

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Review | |

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Focus on Problem Solving | |

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Infinte Sequences and Series | |

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Sequences | |

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Laboratory Project: Logistic Sequences | |

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Series | |

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The Integral and Comparison Tests | |

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Estimating Sums | |

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Other Convergence Tests | |

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Power Series | |

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Representations of Functions as Power Series | |

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Taylor and Maclaurin Series | |

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Laboratory Project: An Elusive Limit | |

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Writing Project: How Newton Discovered the Binomial Series | |

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Applications of Taylor Polynomials | |

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Applied Project: Radiation from the Stars | |

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Review | |

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Focus on Problem Solving | |

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Vectors and the Geometry of Space | |

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Three-Dimensional Coordinate Systems | |

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Vectors | |

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The Dot Product | |

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The Cross Product | |

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Discovery Project: The Geometry of a Tetrahedron | |

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Equations of Lines and Planes | |

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Laboratory Project: Putting 3D in Perspective | |

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Functions and Surfaces | |

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Cylindrical and Spherical Coordinates | |

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Laboratory Project: Families of Surfaces | |

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Review | |

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Focus on Problem Solving | |

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Vector Functions | |

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Vector Func | |