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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" | |

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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" | |

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"Limits Involving Infinity; Asymptotes" | |

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"Formal Definition of the Limit" | |

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"Limits and Loss-of-Significance Errors" | |

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Differentiation | |

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"Tangent Lines and Velocity" | |

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"The Derivative" | |

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"Computation of Derivatives: The Power Rule" | |

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"The Product and Quotient Rules" | |

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"The Chain Rule" | |

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"Derivatives of Trigonometric Functions" | |

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"Derivatives of Exponential and Logarithmic Functions" | |

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"Implicit Differentiation and Inverse Trigonometric Functions" | |

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"The Hyperbolic Functions" | |

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"The Mean Value Theorem" | |

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Applications of the Derivative | |

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"Linear Approximations and Newton's Method"" | |

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"Indeterminate Forms and L'Hpital'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" | |

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"Area" | |

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"The Definite Integral" | |

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"The Fundamental Theorem of Calculus" | |

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"Integration by Substitution" | |

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"Numerical Integration" | |

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"The Natural Logarithm as an Integral" | |

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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" | |

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"Integration of Rational Functions Using Partial Fractions" | |

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"Integration Tables and Computer Algebra Systems" | |

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"Improper Integrals" | |

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First-Order Differential Equations | |

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"Modeling with Differential Equations" | |

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"Separable Differential Equations" | |

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"Direction Fields and Euler's Method" | |

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"Systems of First-Order Differential Equations" | |

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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 and Comparison Tests" | |

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"Alternating Series" | |

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"Absolute Convergence and the Ratio Test" | |

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"Power Series" | |

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"Taylor Series" | |

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"Applications of Taylor 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 the Geometry of Space | |

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"Vectors in the Plane" | |

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"Vectors in Space" | |

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"The Dot Product" | |

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"The Cross Product" | |

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"Lines and Planes in Space" | |

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"Surfaces in Space" | |

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Vector-Valued Functions | |

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"Vector-Valued Functions" | |

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"The Calculus of Vector-Valued Functions" | |

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"Motion in Space" | |

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"Curvature" | |

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"Tangent and Normal Vectors" | |

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"Parametric Surfaces" | |

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Functions of Several Variables and Partial Differentiation | |

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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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"The Gradient and Directional Derivatives" | |

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"Extrema of Functions of Several Variables" | |

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"Constrained Optimization and and Lagrange Multipliers" | |

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Multiple Integrals | |

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"Double Integrals" | |

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"Area, Volume and Center of Mass" | |

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"Double Integrals in Polar Coordinates" | |

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"Surface Area" | |

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"Triple Integrals" | |

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"Cylindrical Coordinates" | |

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"Spherical Coordinates" | |

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"Change of Variables in Multiple Integrals" | |

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Vector Calculus | |

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"Vector Fields" | |

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"Line Integrals" | |

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"Independence of Path and Conservative Vector Fields" | |

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"Green's Theorem" | |

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"Curl and Divergence" | |

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"Surface Integrals" | |

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"The Divergence Theorem" | |

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"Stokes' Theorem" | |

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"Applications of Vector Calculus" | |

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Second Order Differential Equations | |

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Second-Order Equations With Constant Coefficients" | |

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"Nonhomogeneous Equations: Undetermined Coefficients" | |

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"Applications of Second-Order Equations" | |

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"Power Series Solutions of Differential Equations" | |

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Proofs of Selected Theorems | |

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Answers to Odd-Numbered Exercises | |