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| Functions, Graphs, and Models | |
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| Using Graphing Utilities | |
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| Functions | |
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| Functions: Graphs and Properties | |
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| Functions: Graphs and Transformations | |
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| Operations on Functions; Composition | |
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| Inverse Functions | |
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| Modeling with Linear and Quadratic Functions | |
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| Linear Functions | |
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| Linear Equations and Models | |
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| Quadratic Functions | |
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| Complex Numbers | |
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| Quadratic Equations and Models | |
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| Additional Equation-Solving Techniques | |
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| Solving Inequalities | |
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| Polynomial and Rational Functions | |
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| Polynomial Functions and Models | |
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| Real Zeros and Polynomial Inequalities | |
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| Complex Zeros and Rational Zeros of Polynomials | |
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| Rational Functions and Inequalities | |
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| Exponential and Logarithmic Functions | |
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| Exponential Functions | |
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| Exponential Models | |
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| Logarithmic Functions | |
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| Logarithmic Models | |
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| Exponential and Logarithmic Equations | |
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| Trigonometric Functions | |
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| Angles and Their Measure | |
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| Trigonometric Functions: A Unit Circle Approach | |
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| Solving Right Triangles | |
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| Properties of Trigonometric Functions | |
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| More General Trigonometric Functions and Models | |
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| Inverse Trigonometric Functions | |
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| Trigonometric Identities and Conditional Equations | |
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| Basic Identities and Their Use | |
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| Sum, Difference, and Cofunction Identities | |
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| Double-Angle and Half-Angle Identities | |
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| Product-Sum and Sum-Product Identities | |
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| Trigonometric Equations | |
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| Additional Topics in Trigonometry | |
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| Law of Sines | |
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| Law of Cosines | |
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| Geometric Vectors | |
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| Algebraic Vectors | |
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| Polar Coordinates and Graphs | |
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| Complex Numbers in Rectangular and Polar Forms | |
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| De Moivre's Theorem | |
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| Modeling with Linear Systems | |
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| 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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| Systems of Linear Inequalities | |
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| Linear Programming | |
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| Matrices and Determinants | |
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| Matrix 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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| Determinants | |
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| Properties of Determinants | |
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| Determinants and Cramer's Rule | |
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| Sequences, Induction, and Probability | |
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| Sequences and Series | |
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| Mathematical Induction | |
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| Arithmetic and Geometric Sequences | |
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| Multiplication Principle, Permutations, and Combinations | |
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| Sample Spaces and Probability | |
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| Binomial Formula | |
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| Additional Topics in Analytic Geometry | |
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| Conic Sections; Parabola | |
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| Ellipse | |
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| Hyperbola | |
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| Translation of Axes | |
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| Rotation of Axes | |
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| Nonlinear Systems | |
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| Review of Equations and Graphing | |
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| Linear Equations and Inequalities | |
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| Cartesian Coordinate System | |
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| Basic Formulas in Analytic Geometry | |
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| Special Topics | |
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| Significant Digits | |
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| Partial Fractions | |
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| Descartes' Rule of Signs | |
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| Parametric Equations | |
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| Geometric Formulas | |