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P. Preparation For Calculus | |

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Graphs and Models | |

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Linear Models and Rates of Change | |

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Functions and Their Graphs | |

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Fitting Models to Data Review Exercises P.S. Problem Solving | |

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Limits And Their Properties | |

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A Preview of Calculus | |

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Finding Limits Graphically and Numerically | |

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Evaluating Limits Analytically | |

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Continuity and One-Sided Limits | |

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Infinite Limits Section Project: Graphs and Limits of Trigonometric Functions Review Exercises P.S. Problem Solving | |

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Differentiation | |

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The Derivative and the Tangent Line Problem | |

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Basic Differentiation Rules and Rates of Change | |

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The Product and Quotient Rules and Higher-Order Derivatives | |

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The Chain Rule | |

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Implicit Differentiation Section Project: Optical Illusions | |

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Related Rates Review Exercises P.S. Problem Solving | |

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Applications Of Differentiation | |

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Extrema on an Interval | |

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Rolle's Theorem and the Mean Value Theorem | |

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Increasing and Decreasing Functions and the First Derivative Test Section Project: Rainbows | |

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Concavity and the Second Derivative TeSt. Limits at Infinity | |

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A Summary of Curve Sketching | |

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Optimization Problems Section Project: Connecticut River | |

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Newton's Method | |

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Differentials Review Exercises P.S. Problem Solving | |

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Integration | |

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Antiderivatives and Indefinite Integration | |

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Area | |

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Riemann Sums and Definite Integrals | |

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The Fundamental Theorem of Calculus Section Project: Demonstrating the Fundamental Theorem | |

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Integration by Substitution | |

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Numerical Integration Review Exercises P.S. Problem Solving | |

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Logarithmic, Exponential, And Other Transcendental Functions | |

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The Natural Logarithmic Function: Differentiation | |

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The Natural Logarithmic Function: Integration | |

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Inverse Functions | |

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Exponential Functions: Differentiation and Integration | |

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Bases Other than e and Applications Section Project: Using Graphing Utilities to Estimate Slope | |

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Inverse Trigonometric Functions: Differentiation | |

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Inverse Trigonometric Functions: Integration | |

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Hyperbolic Functions Section Project: St. Louis Arch Review Exercises P.S. Problem Solving | |

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Differential Equations | |

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Slope Fields and Euler's Method | |

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Differential Equations: \Growth and Decay | |

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Separation of Variables and the Logistic Equation | |

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First-Order Linear Differential Equations Section Project: Weight Loss Review Exercises P.S. Problem Solving | |

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Applications of Integration | |

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Area of a Region Between Two Curves | |

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Volume: The Disk Method | |

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Volume: The Shell Method Section Project: Saturn | |

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Arc Length and Surfaces of Revolution | |

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Work Section Project: Tidal Energy | |

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Moments, Centers of Mass, and Centroids | |

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Fluid Pressure and Fluid Force Review Exercises P.S. Problem Solving | |

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Integration Techniques, L'Hopital's Rule, and Improper Integrals | |

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Basic Integration Rules | |

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Integration by Parts | |

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Trigonometric Integrals Section Project: Power Lines | |

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Trigonometric Substitution | |

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Partial Fractions | |

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Integration by Tables and Other Integration Techniques | |

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Indeterminate Forms and L'Hopital's Rule | |

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Improper Integrals Review Exercises P.S. Problem Solving | |

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Infinite Series | |

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Sequences | |

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Series and Convergence Section Project: Cantor's Disappearing Table | |

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The Integral Test and p-Series Section Project: The Harmonic Series | |

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Comparisons of Series Section Project: Solera Method | |

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Alternating Series | |

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The Ratio and Root Tests | |

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Taylor Polynomials and Approximations | |

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Power Series | |

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Representation of Functions by Power Series | |

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Taylor and Maclaurin Series Review Exercises P.S. Problem Solving | |

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Conics, Parametric Equations, And Polar Coordinates | |

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Conics and Calculus | |

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Plane Curves and Parametric Equations Section Project: Cycloids | |

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Parametric Equations and Calculus | |

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Polar Coordinates and Polar Graphs Section Project: Anamorphic Art | |

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Area and Arc Length in Polar Coordinates | |

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Polar Equations of Conics and Kepler's Laws Review Exercises P.S. Problem Solving | |

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Book Appendices | |

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Proofs of Selected Theorems | |

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Integration Tables | |

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Online Appendices | |

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Precalculus Review (please visit URL to come) | |

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Real Numbers and the Real Number Line | |

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The Cartesian Plane | |

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Review of Trigonometric Functions | |

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Rotation and the General Second-Degree Equation (please visit URL to come) | |

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Complex Numbers (please visit URL to come) | |

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Business and Economic Applications (please visit URL to come) | |