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Precalculus Review | |

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What is Calculus? | |

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Review of Elementary Mathematics | |

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Review of Inequalities | |

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Coordinate Plane | |

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Analytic Geometry | |

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Functions | |

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The Elementary Functions | |

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Combinations of Functions | |

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A Note on Mathematical Proof; Mathematical Induction | |

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Limits and Continuity | |

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The Limit Process (An Intuitive Introduction) | |

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Definition of Limit | |

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Some Limit Theorems | |

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Continuity | |

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The Pinching Theorem; Trigonometric Limits | |

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Two Basic Theorems | |

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The Derivative; The Process of Differentiation | |

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The Derivative | |

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Some Differentiation Formulas | |

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Thed/dx Notation Derivatives of Higher Order | |

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The Derivative as a Rate of Change | |

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The Chain Rule | |

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Differentiating the Trigonometric Functions | |

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Implicit Differentiation Rational Powers | |

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The Mean-Value Theorem; Applications of the First and Second Derivatives | |

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The Mean-Value Theorem | |

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Increasing and Decreasing Functions | |

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Local Extreme Values | |

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Endpoint Extreme Values; Absolute Extreme Values | |

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Some Max-Min Problems | |

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Concavity and Points of Inflection | |

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Vertical and Horizontal Asymptotes; Vertical Tangents and Cusps | |

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Some Curve Sketching | |

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Velocity and Acceleration; Speed | |

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Related Rates of Change Per Unit Time | |

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Differentials | |

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Newton-Raphson Approximations | |

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Integration | |

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An Area Problem; A Speed-Distance Problem | |

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The Definite Integral of a Continuous Function | |

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The Function f(x) = Integral from a to x of f(t) dt | |

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The Fundamental Theorem of Integral Calculus | |

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Some Area Problems | |

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Indefinite Integrals | |

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Working Back from the Chain Rule; theu-Substitution | |

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Additional Properties of the Definite Integral | |

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Mean-Value Theorems for Integrals; Average Value of a Function | |

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Some Applications of the Integral | |

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More on Area | |

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Volume by Parallel Cross-Sections; Discs and Washers | |

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Volume by the Shell Method | |

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The Centroid of a Region; PappusA?s Theorem on Volumes | |

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The Notion of Work | |

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Fluid Force | |

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The Transcendental Functions | |

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One-to-One Functions; Inverse Functions | |

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The Logarithm Function, Part I | |

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The Logarithm Function, Part II | |

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The Exponential Function | |

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Arbitrary Powers; Other Bases | |

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Exponential Growth and Decay | |

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The Inverse Trigonometric Functions | |

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The Hyperbolic Sine and Cosine | |

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The Other Hyperbolic Functions | |

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Techniques of Integration | |

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Integral Tables and Review | |

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Integration by Parts | |

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Powers and Products of Trigonometric Functions | |

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Integrals Featuring Square Root of (a^2 - x^2), Square Root of (a^2 + x^2), and Square Root of (x^2 - a^2) | |

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Rational Functions; Partial Functions | |

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Some Rationalizing Substitutions | |

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Numerical Integration | |

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Differential Equations | |

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First-Order Linear Equations | |

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Integral Curves; Separable Equations | |

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The Equationya??a?? +aya??+by = 0 | |

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The Conic Sections; Polar Coordinates; Parametric Equations | |

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Geometry of Parabola, Ellipse, Hyperbola | |

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Polar Coordinates | |

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Graphing in Polar Coordinates | |

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Area in Polar Coordinates | |

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Curves G | |