Note: Each chapter concludes with a Chapter Summary, Review Exercises, a Chapter Test, Proofs in Mathematics, and P.S. Problem Solving | |

Functions and Their Graphs | |

Rectangular Coordinates | |

Graphs of Equations | |

Linear Equations in Two Variables | |

Functions | |

Analyzing Graphs of Functions | |

A Library of Parent Functions | |

Transformations of Functions | |

Combinations of Functions: Composite Functions | |

Inverse Functions | |

Mathematical Modeling and Variation | |

Polynomial and Rational Functions | |

Quadratic Functions and Models | |

Polynomial Functions of Higher Degree | |

Polynomial and Synthetic Division | |

Complex Numbers | |

Zeros of Polynomial Functions | |

Rational Functions | |

Nonlinear Inequalities | |

Exponential and Logarithmic Functions | |

Exponential Functions and Their Graphs | |

Logarithmic Functions and Their Graphs | |

Properties of Logarithms | |

Exponential and Logarithmic Equations | |

Exponential and Logarithmic Models Cumulative Test: Chapters 1–3 | |

Trigonometry | |

Radian and Degree Measure | |

Trigonometric Functions: The Unit Circle | |

Right Triangle Trigonometry | |

Trigonometric Functions of Any Angle | |

Graphs of Sine and Cosine Functions | |

Graphs of Other Trigonometric Functions | |

Inverse Trigonometric Functions | |

Applications and Models | |

Analytic Trigonometry | |

Using Fundamental Identities | |

Verifying Trigonometric Identities | |

Solving Trigonometric Equations | |

Sum and Difference Formulas | |

Multiple-Angle and Product-to-Sum Formulas | |

Additional Topics in Trigonometery | |

Law of Sines | |

Law of Cosines | |

Vectors in the Plane | |

Vectors and Dot Products | |

Trigonometric Form of a Complex Number Cumulative Test: Chapters 4–6 | |

Systems of Equations and Inequalities | |

Linear and Nonlinear Systems of Equations | |

Two-Variable Linear Systems | |

Multivariable Linear Systems | |

Partial Fractions | |

Systems of Inequalities | |

Linear Programming | |

Matrices and Determinants | |

Matrices and Systems of Equations | |

Operations with Matrices | |

The Inverse of a Square Matrix | |

The Determinant of a Square Matrix | |

Applications of Matrices and Determinants | |

Sequences, Series, and Probability | |

Sequences and Series | |

Arithmetic Sequences and Partial Sums | |

Geometric Sequences and Series | |

Mathematical Induction | |

The Binomial Theorem | |

Counting Principles | |

Probability Cumulative Test: Chapters 7–9 | |

Topics in Analytic Geometry | |

Lines | |

Introduction to Conics: Parabolas | |

Ellipses | |

Hyperbolas | |

Rotation of Conics | |

Parametric Equations | |

Polar Coordinates | |

Graphs of Polar Equations | |

Polar Equations of Conics | |

Analytic Geometry in Three Dimensions | |

The Three-Dimensional Coordinate System | |

Vectors in Space | |

The Cross Product of Two Vectors | |

Lines and Planes in Space | |

Limits and an Introduction to Calculus | |

Introduction to Limits | |

Techniques for Evaluating Limits | |

The Tangent Line Problem | |

Limits at Infinity and Limits of Sequences | |

The Area Problem Cumulative Test: Chapters 10–12 | |

Appendix | |

Review of Fundamental Concepts of Algebra | |

Real Numbers and Their Properties | |

Exponents and Radicals | |

Polynomials and Factoring | |

Rational Expressions | |

Solving Equations | |

Linear Inequalities in One Variable | |

Errors and the Algebra of Calculus | |

Appendix | |

Concepts in Statistics (web) | |

Representing Data | |

Measures of Central Tendency and Dispersion | |

Least Squares Regression | |

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