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Functions and Models | |

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Four Ways to Represent a Function | |

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Mathematical Models | |

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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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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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Tangents, Velocities, and Other Rates of Change | |

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Derivatives | |

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The Derivative as a Function | |

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Linear Approximations | |

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What does f' say about f? | |

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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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The Product and Quotient Rules | |

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Rates of Change in the Natural and Social Sciences | |

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Derivatives of Trigonometric Functions | |

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The Chain Rule | |

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Implicit Differentiation | |

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Derivatives of Logarithmic Functions | |

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Linear Approximations and Differentials | |

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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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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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Optimization Problems | |

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Applications to Economics | |

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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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The Fundamental Theorem 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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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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Arc Length | |

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Average Value of a Function | |

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Applications to Physics and Engineering | |

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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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Exponential Growth and Decay | |

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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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Infinite Sequences And Series | |

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Sequences | |

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Series | |

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The Integral and Comparison Tests; Estimating Sums | |

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Other Convergence Tests | |

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Power Series | |

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Representation of Functions as Power Series | |

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Taylor and Maclaurin Series | |

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The Binomial Series | |

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Applications of Taylor Polynomials | |

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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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Equations of Lines and Planes | |

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Functions and Surfaces | |

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Cylindrical and Spherical Coordinates | |

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Review | |

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Focus on Problem Solving | |

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Vector Functions | |

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Vector Functions and Space Curves | |

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Derivatives and Integrals of Vector Functions | |

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Arc Length and Curvature | |

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Motion in Space | |

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Parametric Surfaces | |

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Review | |

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Focus on Problem Solving | |

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Partial Derivatives | |

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Functions of Several Variables | |

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Limits and Continuity | |

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Partial Derivatives | |

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Tangent Planes and Linear Approximations | |

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The Chain Rule | |

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Directional Derivatives and the Gradient Vector | |

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Maximum and Minimum Values | |

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Lagrange Multipliers | |

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Review | |

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Focus on Problem Solving | |

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Multiple Integrals | |

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Double Integrals over Rectangles | |

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Interated Integrals | |

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Double Integrals over General Regions | |

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Double Integrals in Polar Coordinates | |

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Applications of Double Integrals | |

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Surface Area | |

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Triple Integrals | |

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Triple Integrals in Cylindrical and Spherical Coordinates | |

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Change of Variables in Multiple Integrals | |

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Review | |

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Focus on Problem Solving | |

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Vector Calculus | |

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Vector Fields | |

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Line Integrals | |

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The Fundamental Theorem for Line Integrals | |

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Green's Theorem | |

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Curl and Divergence | |

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Surface Integrals | |

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Stokes' Theorem | |

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The Divergence Theorem | |

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Summary | |

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Review | |

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Focus on Problem Solving | |

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Intervals, Inequalities, And Absolute Values | |

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Coordinate Geometry | |

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Trigonometry | |

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Precise Definitions Of Limits | |

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A Few Proofs | |

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Sigma Notation | |

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Integration Of Rat | |