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Fundamentals | |
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Sets of Real Numbers | |
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Absolute Value | |
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Solving Equations (Review and Preview) | |
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Rectangular Coordinates. Visualizing Data | |
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Graphs and Graphing Utilities | |
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Equations of Lines | |
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Symmetry and Graphs. Circles | |
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Equations and Inequalities | |
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Quadratic Equations: Theory and Examples | |
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Other Types of Equations | |
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Applied Problems (A Warm-up) | |
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Applications | |
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Inequalities | |
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More on Inequalities | |
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Functions | |
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The Definition of a Function | |
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The Graph of a Function | |
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Shapes of Graphs. Average Rate of Change | |
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Techniques in Graphing | |
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Methods of Combining Functions. Iteration | |
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Inverse Functions | |
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Variation | |
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Polynomial and Rational Functions. Applications to Optimization | |
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Linear Functions | |
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Quadratic Functions | |
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Using Iteration to Model Population Growth (Optional Section) | |
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Setting Up Equations That Define Functions | |
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Maximum and Minimum Problems | |
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Polynomial Functions | |
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Rational Functions | |
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Exponential and Logarithmic Functions | |
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Exponential Functions | |
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The Exponential Function y = e[superscript x] | |
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Logarithmic Functions | |
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Properties of Logarithms | |
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Equations and Inequalities with Logs and Exponents | |
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Compound Interest | |
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Exponential Growth and Decay | |
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Systems of Equations | |
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Systems of Two Linear Equations in Two Unknowns | |
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Gaussian Elimination | |
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Matrices | |
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The Inverse of a Square Matrix | |
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Determinants and Cramer's Rule | |
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Nonlinear Systems of Equations | |
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Systems of Inequalities. Linear Programming | |
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Roots of Polynomial Equations | |
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The Complex Number System | |
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Division of Polynomials | |
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The Remainder Theorem and the Factor Theorem | |
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The Fundamental Theorem of Algebra | |
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Rational and Irrational Roots | |
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Conjugate Roots and Descartes's Rule of Signs | |
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Introduction to Partial Fractions | |
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More about Partial Fractions | |
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The Conic Sections | |
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The Parabola | |
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Tangents to Parabolas (Optional Section) | |
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The Ellipse | |
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The Hyperbola | |
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The Focus-Directrix Property of Conics | |
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Additional Topics in Algebra | |
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Mathematical Induction | |
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The Binomial Theorem | |
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Introduction to Sequences and Series | |
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Arithmetic Sequences and Series | |
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Geometric Sequences and Series | |
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Permutations and Combinations | |
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Introduction to Probability | |
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Appendix | |
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Significant Digits | |
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Properties of Real Numbers | |
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[radical]2 Is Irrational | |
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Appendix | |
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Review of Integer Exponents | |
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Review of nth Roots | |
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Review of Rational Exponents | |
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Review of Factoring | |
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Review of Fractional Expressions | |
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Answers | |
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Index | |