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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 | |