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Before Calculus | |

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Functions | |

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New Functions from Old | |

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Families of Functions | |

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Inverse Functions; Inverse Trigonometric Functions | |

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Exponential and Logarithmic Functions | |

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Limits and Continuity | |

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Limits (An Intuitive Approach) | |

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Computing Limits | |

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Limits at Infinity; End Behavior of a Function | |

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Limits (Discussed More Rigorously) | |

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Continuity | |

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Continuity of Trigonometric, Exponential, and Inverse Functions | |

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The Derivative | |

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Tangent Lines and Rates of Change | |

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The Derivative Function | |

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Introduction to Techniques of Differentiation | |

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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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Topics in Differentiation | |

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Implicit Differentiation | |

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Derivatives of Logarithmic Functions | |

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Derivatives of Exponential and Inverse Trigonometric Functions | |

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Related Rates | |

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Local Linear Approximation; Differentials | |

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L'Hï¿½pital's Rule; Indeterminate Forms | |

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The Derivative in Graphing and Applications | |

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Analysis of Functions I: Increase, Decrease, and Concavity | |

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Analysis of Functions II: Relative Extrema; Graphing Polynomials | |

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Analysis of Functions III: Rational Functions, Cusps, and Vertical Tangents | |

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Absolute Maxima and Minima | |

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Applied Maximum and Minimum Problems | |

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Rectilinear Motion | |

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Newton's Method | |

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Rolle's Theorem; Mean-Value Theorem | |

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Integration | |

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An Overview of the Area Problem | |

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The Indefinite Integral | |

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Integration by Substitution | |

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The Definition of Area as a Limit; Sigma Notation | |

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The Definite Integral | |

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The Fundamental Theorem of Calculus | |

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Rectilinear Motion Revisited Using Integration | |

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Average Value of a Function and its Applications | |

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Evaluating Definite Integrals by Substitution | |

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Logarithmic and Other Functions Defined by Integrals | |

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Applications of the Definite Integral in Geometry, Science, and Engineering | |

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Area Between Two Curves | |

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Volumes by Slicing; Disks and Washers | |

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Volumes by Cylindrical Shells | |

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Length of a Plane Curve | |

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Area of a Surface of Revolution | |

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Work | |

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Moments, Centers of Gravity, and Centroids | |

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Fluid Pressure and Force | |

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Hyperbolic Functions and Hanging Cables | |

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Principles of Integral Evaluation | |

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An Overview of Integration Methods | |

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Integration by Parts | |

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Integrating Trigonometric Functions | |

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Trigonometric Substitutions | |

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Integrating Rational Functions by Partial Fractions | |

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Using Computer Algebra Systems and Tables of Integrals | |

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Numerical Integration; Simpson's Rule | |

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Improper Integrals | |

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Mathematical Modeling with Differential Equations | |

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Modeling with Differential Equations | |

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Separation of Variables | |

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Slope Fields; Euler's Method | |

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First-Order Differential Equations and Applications | |

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Infinite Series | |

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Sequences | |

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Monotone Sequences | |

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Infinite Series | |

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Convergence Tests | |

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The Comparison, Ratio, and Root Tests | |

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Alternating Series; Absolute and Conditional Convergence | |

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Maclaurin and Taylor Polynomials | |

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Maclaurin and Taylor Series; Power Series | |

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Convergence of Taylor Series | |

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Differentiating and Integrating Power Series; Modeling with Taylor Series | |

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Parametric and Polar Curves; Conic Sections | |

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Parametric Equations; Tangent Lines and Arc Length for Parametric Curves | |

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Polar Coordinates | |

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Tangent Lines, Arc Length, and Area for Polar Curves | |

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Conic Sections | |

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Rotation of Axes; Second-Degree Equations | |

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Conic Sections in Polar Coordinates | |