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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 | |