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Basics | |

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Preview | |

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Number Systems | |

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Planar Coordinates and Graphing in the Plane | |

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Lines and Their Slopes | |

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Functions and Their Graphs | |

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Combining Functions | |

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Trigonometry | |

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Summary of Key Topics | |

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Review Exercises for Chapter 1 | |

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Genesis and Development | |

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Limits | |

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Preview | |

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The Concept of Limit | |

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Limit Theorems | |

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Continuity | |

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Infinite Limits and Asymptotes | |

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Limits of Sequences | |

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Exponential and Logarithmic Functions | |

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Summary of Key Topics | |

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Review Exercises | |

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Genesis and Development | |

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The Derivative | |

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Preview | |

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Rates of Change and Tangent Lines | |

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The Derivative | |

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Rules for Differentiation | |

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Differentiation of Some Basic Functions | |

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The Chain Rule | |

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Derivatives of Inverse Functions | |

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Higher Derivatives | |

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Implicit Differentiation | |

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Differentials and Approximation of Functions | |

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Other Transcendental Functions | |

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Summary of Key Topics | |

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Review Exercises | |

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Genesis and Development | |

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Applications of the Derivative | |

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Preview | |

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Related Rates | |

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The Mean Value Theorem | |

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Maxima and Minima of Functions | |

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Applied Maximum-Minimum Problems | |

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Concavity | |

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Graphing Functions | |

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L'Hopital's Rule | |

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The Newton-Raphson Method | |

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Antidifferentiation and Applications | |

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Summary of Key Topics | |

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Review Exercises | |

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Genesis and Development | |

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The Integral | |

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Preview | |

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Introduction to Integration-The Area Problem | |

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The Riemann Integral | |

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Properties of the Integral | |

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The Fundamental Theorem of Calculus | |

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A Calculus Approach to the Logarithm and Exponential Functions | |

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Integration by Substitution | |

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More on the Calculation of Area | |

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Numerical Techniques of Integration | |

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Summary of Key Topics | |

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Review Exercises | |

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Genesis and Development | |

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Techniques of Integration | |

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Preview | |

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Integration by Parts | |

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Powers and Products of Trigonometric Functions | |

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Trigonometric Substitution | |

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Partial Fractions-Linear Factors | |

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Partial Fractions-Irreducible Quadratic Factors | |

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Improper Integrals-Unbounded Integrands | |

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Improper Integrals-Unbounded Intervals | |

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Summary of Key Topics | |

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Review Exercises | |

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Genesis and Development | |

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Applications of the Integral | |

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Preview | |

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Volumes | |

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Arc Length and Surface Area | |

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The Average Value of a Function | |

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Center of Mass | |

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Work | |

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First Order Differential Equations-Separable Equations | |

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First Order Differential Equations-Linear Equations | |

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Summary of Key Topics | |

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Review Exercises | |

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Genesis and Development | |

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Infinite Series | |

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Preview | |

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Series | |

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The Divergence Test and The Integral Test | |

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The Comparison Tests | |

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Alternating Series | |

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The Ratio and Root Tests | |

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Introduction to Power Series | |

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Representing Functions by Power Series | |

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Taylor Series | |

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Summary of Key Topics | |

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Review Exercises | |

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Genesis and Development | |

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Vectors | |

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Preview | |

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Vectors in the Plane | |

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Vectors in Three-Dimensional Space | |

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The Dot Product and Applications | |

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The Cross Product and Triple Product | |

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Lines and Planes in Space | |

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Summary of Key Topics in Chapter 9 | |

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Review Exercises for Chapter 9 | |

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Genesis and Development | |

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Curves in Space | |

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Preview | |

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Vector-Valued Functions-Limits, Derivatives, and Continuity | |

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Velocity and Acceleration | |

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Tangent Vectors and Arc Length | |

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Curvature | |

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Applications of Vector-Valued Functions to Motion | |

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Summary of Key Topics in Chapter 10 | |

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Review Exercises for Chapter 10 | |

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Genesis and Development | |

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Functions of Several Variables | |

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Preview | |

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Functions of Several Variables | |

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Cylinders and Quadric Surfaces | |

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Limits and Continuity | |

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Partial Derivatives | |

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Differentiability and The Chain Rule | |

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Gradients and Directional Derivatives | |

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Tangent Planes | |

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Maximum-Minimum Problems | |

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Lagrange Multipliers | |

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Summary of Key Topics in Chapter 11 | |

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Review Exercises for Chapter 11 | |

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Genesis and Development | |

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Multiple Integrals | |

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Preview | |

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Double Integrals over Rectangular Regions | |

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Integration over More General Regions | |

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Calculation of Volumes of Solids | |

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Polar Coordinates | |

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Integrating in Polar Coordinates | |

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Triple Integrals | |

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Physical Applications | |

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Other Coordinate Systems | |

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Summary of Key Topics in Chapter 12 | |

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Review Exercises for Chapter 12 | |

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Genesis and Development | |

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Vector Calculus | |

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Preview | |

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Vector Fields | |

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Line Integrals | |

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Conservative Vector Fields and Path Independence | |

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Divergence, Gradient, and Curl | |

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Green's Theorem | |

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Surface Integrals | |

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Stokes's Theorem | |

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The Divergence Theorem | |

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Summary of Key Topics in Chapter 13 | |

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Review Exercises for Chapter 13 | |

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Genesis and Development | |