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Each chapter concludes with a Review and a Mathematical Snapshot | |
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Algebra Review | |
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Sets of Real Numbers | |
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Some Properties of Real Numbers | |
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Exponents and Radicals | |
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Operations with Algebraic Expressions | |
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Factoring | |
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Fractions | |
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Linear Equations | |
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Quadratic Equations Mathematical Snapshot | |
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Applications of Equations and Inequalities | |
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Applications of Equations | |
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Linear Inequalities | |
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Applications of Inequalities | |
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Absolute Value | |
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Functions and Graphs | |
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Functions | |
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Special Functions | |
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Combinations of Functions | |
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Inverse Functions | |
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Graphs in Rectangular Coordinates | |
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Symmetry | |
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Translations and Reflection | |
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Lines, Parabolas, and Systems | |
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Lines | |
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Applications and Linear Functions | |
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Quadratic Functions | |
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Systems of Linear Equations | |
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Nonlinear Systems | |
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Applications of Systems of Equations | |
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Exponential and Logarithmic Functions | |
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Exponential Functions | |
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Logarithmic Functions | |
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Properties of Logarithms | |
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Logarithmic and Exponential Equations | |
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Mathematics of Finance | |
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Compound Interest | |
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Present Value | |
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Annuities | |
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Amortization of Loans | |
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Matrix Algebra | |
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Matrices | |
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Matrix Addition and Scalar Multiplication | |
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Matrix Multiplication | |
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Solving Systems by Reducing Matrices | |
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Method of Reduction (continued) | |
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Inverses | |
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Leontief's Input-Output Analysis | |
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Linear Programming | |
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Linear Inequalities in Two Variables | |
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Linear Programming | |
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Multiple Optimum Solutions | |
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The Simplex Method | |
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Degeneracy, Unbounded Solutions, and Multiple Optimum Solutions | |
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Artificial Variables | |
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Minimization | |
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The Dual | |
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Introduction to Probability | |
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Basic Counting Principle and Permutations | |
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Combinations and Other Counting Principles | |
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Sample Spaces and Events | |
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Probability | |
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Conditional Probability and Stochastic Processes | |
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Independent Events | |
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Bayes' Formula | |
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Additional Topics in Probability | |
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Discrete Random Variables | |
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The Binomial Distribution | |
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Markov Chains | |
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Limits and Continuity | |
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Limits | |
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Limits (Continued) | |
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Interest Compounded Continuously | |
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Continuity | |
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Continuity Applied to Inequalities | |
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Differentiation | |
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The Derivative | |
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Rules for Differentiation | |
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The Derivative as a Rate of Change | |
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Differentiability and Continuity | |
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Product and Quotient Rules | |
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The Chain Rule and the Power Rule | |
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Additional Differentiation Topics | |
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Derivatives of Logarithmic Functions | |
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Derivatives of Exponential Functions | |
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Elasticity of Demand | |
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Implicit Differentiation | |
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Logarithmic Differentiation | |
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Newton's Method | |
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Higher Order Derivatives | |
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Curve Sketching | |
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Relative Extrema | |
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Absolute Extrema on a Closed Interval | |
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Concavity | |
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The Second Derivative Test | |
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Asymptotes | |
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Applied Maxima and Minima | |
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Integration | |
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Differentials | |
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The Indefinite Integral | |
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Integration with Initial Conditions | |
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Some Integration Formulas | |
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Techniques of Integration | |
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Summation | |
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The Definite | |