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Preliminaries | |

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Polynomials and Rational Functions | |

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Graphing Calculators and Computer Algebra Systems | |

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Inverse Functions | |

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Trigonometric and Inverse Trigonometric Functions | |

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Exponential and Logarithmic Functions Hyperbolic Functions Fitting a Curve to Data | |

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Transformations of Functions | |

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Limits and Continuity | |

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A Brief Preview of Calculus: Tangent Lines and the Length of a Curve | |

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The Concept of Limit | |

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Computation of Limits | |

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Continuity and its Consequences The Method of Bisections | |

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Limits Involving Infinity Asymptotes | |

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Formal Definition of the Limit Exploring the Definition of Limit Graphically | |

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Limits and Loss-of-Significance Errors Computer Representation of Real Numbers | |

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Differentiation | |

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Tangent Lines and Velocity | |

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The Derivative Numerical Differentiation | |

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Computation of Derivatives: The Power Rule Higher Order Derivatives Acceleration | |

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The Product and Quotient Rules | |

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The Chain Rule | |

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Derivatives of the Trigonometric Functions | |

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Derivatives of the Exponential and Logarithmic Functions | |

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Implicit Differentiation and Inverse Trigonometric Functions | |

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The Mean Value Theorem | |

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Applications of Differentiation | |

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Linear Approximations and Newton’s Method | |

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Indeterminate Forms and L’Hopital’s Rule | |

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Maximum and Minimum Values | |

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Increasing and Decreasing Functions | |

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Concavity and the Second Derivative Test | |

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Overview of Curve Sketching | |

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Optimization | |

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Related Rates | |

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Rates of Change in Economics and the Sciences | |

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Integration | |

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Antiderivatives | |

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Sums and Sigma Notation Principle of Mathematical Induction | |

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Area | |

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The Definite Integral Average Value of a Function | |

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The Fundamental Theorem of Calculus | |

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Integration by Substitution | |

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Numerical Integration Error Bounds for Numerical Integration | |

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The Natural Logarithm as an Integral The Exponential Function as the Inverse of the Natural Logarithm | |

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Applications of the Definite Integral | |

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Area Between Curves | |

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Volume: Slicing, Disks, and Washers | |

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Volumes by Cylindrical Shells | |

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Arc Length and Surface Area | |

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Projectile Motion | |

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Applications of Integration to Physics and Engineering | |

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Probability | |

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Integration Techniques | |

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Review of Formulas and Techniques | |

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Integration by Parts | |

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Trigonometric Techniques of Integration Integrals Involving Powers of Trigonometric Functions Trigonometric Substitution | |

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Integration of Rational Functions Using Partial Fractions Brief Summary of Integration Techniques | |

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Integration Tables and Computer Algebra Systems | |

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Improper Integrals A Comparison Test | |

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First-Order Differential Equations | |

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Modeling with Differential Equations Growth and Decay Problems Compound Interest | |

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Separable Differential Equations Logistic Growth | |

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Direction Fields and Euler's Method | |

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Systems of First-Order Differential Equations Predator-Prey Systems | |

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Infinite Series | |

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Sequences of Real Numbers | |

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Infinite Series | |

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The Integral Test and Comparison Tests | |

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Alternating Series Estimating the Sum of an Alternating Series | |

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Absolute Convergence and the Ratio Test The Root Test Summary of Convergence Tests | |

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Power Series | |

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Taylor Series Representations of Functions as Series Proof of Taylor’s Theorem | |

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Applications of Taylor Series The Binomial Series | |

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Fourier Series | |

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Parametric Equations and Polar Coordinates | |

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Plane Curves and Parametric Equations | |

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Calculus and Parametric Equations | |

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Arc Length and Surface Area in Parametric Equations | |

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Polar Coordinates | |

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Calculus and Polar Coordinates | |

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Conic Sections | |

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Conic Sections in Polar Coordinates | |

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Vectors and th | |