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A Library of Elementary Functions | |

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Linear Equations and Graphs | |

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Linear Equations and Inequalities | |

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Graphs and Lines | |

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Linear Regression | |

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Quadratic Functions | |

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Review | |

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Review Exercise | |

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Functions and Graphs | |

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Functions | |

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Elementary Functions: Graphs and Transformations | |

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Quadratic Functions | |

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Polynomial and Rational Functions | |

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Exponential Functions | |

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Logarithmic Functions | |

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Review | |

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Review Exercise | |

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Finite Mathematics | |

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Mathematics of Finance | |

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Simple Interest | |

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Compound and Continuous Compound Interest | |

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Future Value of an Annuity; Sinking Funds | |

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Present Value of an Annuity; Amortization | |

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Review | |

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Review Exercise | |

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Systems of Linear Equations; Matrices | |

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Review: Systems of Linear Equations in Two Variables | |

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Systems of Linear Equations and Augmented Matrices | |

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Gauss-Jordan Elimination | |

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Matrices: Basic Operations | |

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Inverse of a Square Matrix | |

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Matrix Equations and Systems of Linear Equations | |

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Leontief Input-Output Analysis | |

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Review | |

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Review Exercise | |

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Linear Inequalities and Linear Programming | |

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Inequalities in Two Variables | |

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Systems of Linear Inequalities in Two Variables | |

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Linear Programming in Two Dimensions: A Geometric Approach | |

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Review | |

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Review Exercise | |

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Linear Programming: Simplex Method | |

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A Geometric Introduction to the Simplex Method | |

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The Simplex Method: Maximization with Problem Constraints of the Form = | |

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The Dual; Minimization with Problem Constraints of the form = | |

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Maximization and Minimization with Mixed Problem Constraints | |

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Review | |

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Review Exercise | |

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Logic, Sets, and Counting | |

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Logic | |

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Sets | |

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Basic Counting Principles | |

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Permutations and Combinations | |

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Review | |

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Review Exercise | |

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Probability | |

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Sample Spaces, Events, and Probability | |

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Union, Intersection, and Complement of Events; Odds | |

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Conditional Probability, Intersection, and Independence | |

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Bayes' Formula | |

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Random Variables, Probability Distribution, and Expected Value | |

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Review | |

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Review Exercise | |

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Markov Chains | |

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Properties of Markov Chains | |

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Regular Markov Chains | |

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Absorbing Markov Chains | |

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Review | |

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Review Exercise | |

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Calculus | |

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Limits and the Derivative | |

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Introduction to Limits | |

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Infinite Limits and Limits at Infinity | |

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Continuity | |

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The Derivative | |

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Basic Differentiation Properties | |

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Differentials | |

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Marginal Analysis in Business and Economics | |

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Review | |

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Review Exercise | |

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Additional Derivative Topics | |

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The Constant e and Continuous Compound Interest | |

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Derivatives of Logarithmic and Exponential Functions | |

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Derivatives of Products and Quotients | |

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The Chain Rule | |

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Implicit Differentiation | |

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Related Rates | |

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Elasticity of Demand | |

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Review | |

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Review Exercise | |

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Graphing and Optimization | |

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First Derivative and Graphs | |

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Second Derivative and Graphs | |

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L'Hopitals's Rule | |

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Curve Sketching Techniques | |

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Absolute Maxima and Minima | |

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Optimization | |

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Review | |

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Review Exercise | |

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Integration | |

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Antiderivatives and Indefinite Integrals | |

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Integration by Substitution | |

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Differential Equations; Growth and Decay | |

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The Definite Integral | |

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The Fundamental Theorem of Calculus | |

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Review | |

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Review Exercise | |

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Additional Integration Topics | |

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Area Between Curves | |

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Applications in Business and Economics | |

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Integration by Parts | |

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Integration Using Tables | |

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Review | |

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Review Exercise | |

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Multivariable Calculus | |

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Functions of Several Variables | |

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Partial Derivatives | |

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Maxima and Minima | |

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Maxima and Minima Using Lagrange Multipliers | |

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Method of Least Squares | |

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Double Integrals Over Rectangular Regions | |

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Double Integrals Over More General Regions | |

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Review | |

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Review Exercise | |

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Appendixes | |

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Basic Algebra Review | |

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Self-Test on Basic Algebra | |

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Algebra and Real Numbers | |

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Operations on Polynomials | |

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Factoring Polynomials | |

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Operations on Rational Expressions | |

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Integer Exponents and Scientific Notation | |

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Rational Exponents and Radicals | |

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Quadratic Equations | |

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Special Topics | |

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Sequences, Series, and Summation Notation | |

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Arithmetic and Geometric Sequences | |

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Binomial Theorem | |

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Tables | |

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Area Under the Standard Normal Curve | |

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Basic Geometric Formulas | |

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Answers | |

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Index | |

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Applications Index | |

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A Library of Elementary Functions | |