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Precalculus Review | |

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Real Numbers | |

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Exponents and Radicals | |

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Multiplying and Factoring Algebraic Equations | |

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Rational Expressions | |

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Solving Polynomial Equations | |

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Solving Miscellaneous Equations | |

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The Coordinate Plane | |

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Functions and Linear Models | |

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Functions from the Numerical, Algebraic, and Graphical Viewpoints | |

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Applications: Functions and Models | |

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Linear Functions and Models | |

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Linear Regression | |

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Systems of Linear Equations and Matrices | |

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Systems of Two Equations in Two Unknowns | |

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Using Matrices to Solve Systems of Equations | |

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Applications of Systems of Linear Equations | |

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Matrix Algebra and Applications | |

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Matrix Addition and Scalar Multiplication | |

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Matrix Multiplication | |

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Matrix Inversion | |

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Game Theory | |

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Input-Output Models | |

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Linear Programming | |

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Graphing Linear Inequalities | |

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Solving Linear Programming Problems Graphically | |

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The Simplex Method: Solving Standard Maximization Problems | |

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The Simplex Method: Solving General Linear Programming Problems | |

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The Simplex Method and Duality | |

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The Mathematics of Finance | |

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Simple Interest | |

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Compound Interest | |

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Annuities, Loans, and Bonds | |

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Sets and Counting | |

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Sets and Set Operations | |

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Cardinality | |

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The Addition and Multiplication Principles | |

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Permutations and Combinations | |

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Probability | |

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Sample Spaces and Events | |

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Relative Frequency | |

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Probability and Probability Models | |

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Probability and Counting Techniques | |

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Conditional Probability and Independence | |

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Bayes' Theorem and Applications | |

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Markov Systems | |

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Random Variables and Statistics | |

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Random Variables and Distributions | |

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Bernoulli Trials and Binomial Random Variables | |

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Measures of Central Tendency | |

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Measures of Dispersion | |

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Normal Distributions | |

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Nonlinear Functions and Models | |

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Quadratic Functions and Models | |

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Exponential Functions and Models | |

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Logarithmic Functions and Models | |

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Logistic Functions and Models | |

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Introduction to the Derivative | |

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Limits: Numerical and Graphical Approaches | |

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Limits and Continuity | |

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Limits: Algebraic Approach | |

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Average Rate of Change | |

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Derivatives: Numerical and Graphical Viewpoints | |

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Derivatives: Algebraic Viewpoint | |

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Techniques of Differentiation with Applications | |

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Derivatives of Powers, Sums, and Constant Multiples | |

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A First Application: Marginal Analysis | |

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The Product and Quotient Rules | |

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The Chain Rule | |

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Derivatives of Logarithmic and Exponential Functions | |

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Implicit Differentiation | |

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Further Applications of the Derivative | |

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Maxima and Minima | |

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Applications of Maxima and Minima | |

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Higher Order Derivatives: Acceleration and Concavity | |

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Analyzing Graphs | |

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Related Rates | |

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Elasticity | |

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The Integral | |

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The Indefinite Integral | |

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Substitution | |

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The Definite Integral: Numerical and Graphical Approaches | |

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The Definite Integral: Algebraic Approach and the Fundamental Theorem of Calculus | |

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Further Integration Techniques and Applications of the Integral | |

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Integration by Parts | |

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Area Between Two Curves and Applications | |

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Averages and Moving Averages | |

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Applications to Business and Economics: Consumers' and Producers' Surplus and Continuous Income Streams | |

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Improper Integrals and Applications | |

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Differential Equations and Applications | |

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Optional Internet Topic: Taylor Polynomials | |

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Functions of Several Variables | |

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Functions of Several Variables from the Numerical, Algebraic, and Graphical Viewpoints | |

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Partial Derivatives | |

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Maxima and Minima | |

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Constrained Maxima and Minima and Applications | |

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Double Integrals and Applications | |

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Trigonometric Models | |

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Trigonometric Functions, Models, and Regression | |

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Derivatives of Trigonometric Functions and Applications | |

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Integrals of Trigonometric Functions and Applications | |

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Logic | |

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Table: Area Under a Normal Curve | |

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Answers to Selected Exercises | |

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Index | |

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Optional Internet Topic. S. Calculus Applied to Probability and Statistics | |

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Introduction | |

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Continuous Random Variables and Histograms | |

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Probability Density Functions: Uniform, Exponential, Normal, and Beta | |

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Mean, Median, Variance and Standard Deviation | |

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Denotes material available online | |