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| Note: Each chapter concludes with a Chapter Summary, Review Exercises, a Chapter Test, Proofs in Mathematics, and P.S. Problem Solving | |
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| Functions and Their Graphs | |
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| Rectangular Coordinates | |
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| Graphs of Equations | |
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| Linear Equations in Two Variables | |
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| Functions | |
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| Analyzing Graphs of Functions | |
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| A Library of Parent Functions | |
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| Transformations of Functions | |
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| Combinations of Functions: Composite Functions | |
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| Inverse Functions | |
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| Mathematical Modeling and Variation | |
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| Polynomial and Rational Functions | |
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| Quadratic Functions and Models | |
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| Polynomial Functions of Higher Degree | |
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| Polynomial and Synthetic Division | |
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| Complex Numbers | |
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| Zeros of Polynomial Functions | |
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| Rational Functions | |
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| Nonlinear Inequalities | |
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| Exponential and Logarithmic Functions | |
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| Exponential Functions and Their Graphs | |
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| Logarithmic Functions and Their Graphs | |
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| Properties of Logarithms | |
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| Exponential and Logarithmic Equations | |
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| Exponential and Logarithmic Models Cumulative Test: Chapters 13 | |
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| Trigonometry | |
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| Radian and Degree Measure | |
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| Trigonometric Functions: The Unit Circle | |
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| Right Triangle Trigonometry | |
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| Trigonometric Functions of Any Angle | |
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| Graphs of Sine and Cosine Functions | |
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| Graphs of Other Trigonometric Functions | |
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| Inverse Trigonometric Functions | |
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| Applications and Models | |
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| Analytic Trigonometry | |
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| Using Fundamental Identities | |
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| Verifying Trigonometric Identities | |
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| Solving Trigonometric Equations | |
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| Sum and Difference Formulas | |
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| Multiple-Angle and Product-to-Sum Formulas | |
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| Additional Topics in Trigonometery | |
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| Law of Sines | |
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| Law of Cosines | |
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| Vectors in the Plane | |
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| Vectors and Dot Products | |
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| Trigonometric Form of a Complex Number Cumulative Test: Chapters 46 | |
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| Systems of Equations and Inequalities | |
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| Linear and Nonlinear Systems of Equations | |
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| Two-Variable Linear Systems | |
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| Multivariable Linear Systems | |
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| Partial Fractions | |
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| Systems of Inequalities | |
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| Linear Programming | |
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| Matrices and Determinants | |
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| Matrices and Systems of Equations | |
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| Operations with Matrices | |
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| The Inverse of a Square Matrix | |
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| The Determinant of a Square Matrix | |
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| Applications of Matrices and Determinants | |
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| Sequences, Series, and Probability | |
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| Sequences and Series | |
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| Arithmetic Sequences and Partial Sums | |
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| Geometric Sequences and Series | |
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| Mathematical Induction | |
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| The Binomial Theorem | |
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| Counting Principles | |
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| Probability Cumulative Test: Chapters 79 | |
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| Topics in Analytic Geometry | |
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| Lines | |
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| Introduction to Conics: Parabolas | |
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| Ellipses | |
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| Hyperbolas | |
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| Rotation of Conics | |
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| Parametric Equations | |
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| Polar Coordinates | |
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| Graphs of Polar Equations | |
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| Polar Equations of Conics | |
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| Analytic Geometry in Three Dimensions | |
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| The Three-Dimensional Coordinate System | |
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| Vectors in Space | |
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| The Cross Product of Two Vectors | |
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| Lines and Planes in Space | |
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| Limits and an Introduction to Calculus | |
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| Introduction to Limits | |
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| Techniques for Evaluating Limits | |
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| The Tangent Line Problem | |
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| Limits at Infinity and Limits of Sequences | |
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| The Area Problem Cumulative Test: Chapters 1012 | |
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| Appendix | |
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| Review of Fundamental Concepts of Algebra | |
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| Real Numbers and Their Properties | |
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| Exponents and Radicals | |
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| Polynomials and Factoring | |
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| Rational Expressions | |
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| Solving Equations | |
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| Linear Inequalities in One Variable | |
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| Errors and the Algebra of Calculus | |
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| Appendix | |
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| Concepts in Statistics (web) | |
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| Representing Data | |
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| Measures of Central Tendency and Dispersion | |
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| Least Squares Regression | |