Basic Concepts of Algebra | |

The Real-Number System | |

Integer Exponents, Scientific Notation, and Order of Operations | |

Addition, Subtraction, and Multiplication of Polynomials | |

Factoring | |

Rational Expressions | |

Radical Notation and Rational Exponents | |

The Basics of Equation Solving | |

Graphs, Functions, and Models | |

Introduction to Graphing | |

Functions and Graphs | |

Linear Functions, Slope, and Applications | |

Equations of Lines and Modeling | |

More on Functions | |

The Algebra of Functions | |

Symmetry and Transformations | |

Functions, Equations, and Inequalities | |

Linear Equations, Functions, and Models | |

The Complex Numbers | |

Quadratic Equations, Functions, and Models | |

Analyzing Graphs of Quadratic Functions | |

More Equation Solving | |

Solving Linear Inequalities | |

Polynomial and Rational Functions | |

Polynomial Functions and Models | |

Graphing Polynomial Functions | |

Polynomial Division; The Remainder and Factor Theorems | |

Theorems about Zeros of Polynomial Functions | |

Rational Functions | |

Polynomial and Rational Inequalities | |

Variation and Applications | |

Exponential and Logarithmic Functions | |

Inverse Functions | |

Exponential Functions and Graphs | |

Logarithmic Functions and Graphs | |

Properties of Logarithmic Functions | |

Solving Exponential and Logarithmic Equations | |

Applications and Models: Growth and Decay; Compound Interest | |

The Trigonometric Functions | |

Trigonometric Function of Acute Angles | |

Applications of Right Triangles | |

Trigonometric Functions of Any Angle | |

Radians, Arc Length, and Angular Speed | |

Circular Functions: Graphs and Properties | |

Graphs of Transformed Sine and Cosine Functions | |

Trigonometric Identities, Inverse Functions, and Equations | |

Identities: Pythagorean and Sum and Difference | |

Identities: Cofunction, Double-Angle, and Half-Angle | |

Proving Trigonometric Identities | |

Inverses of the Trigonometric Functions | |

Solving Trigonometric Equations | |

Applications of Trigonometry | |

The Law of Sines | |

The Law of Cosines | |

Complex Numbers: Trigonometric Form | |

Polar Coordinates and Graphs | |

Vectors and Applications | |

Vector Operations | |

Systems of Equations and Matrices | |

Systems of Equations in Two Variables | |

Systems of Equations in Three Variables | |

Matrices and Systems of Equations | |

Matrix Operations | |

Inverses of Matrices | |

Determinants and Cramer's Rule | |

Systems of Inequalities and Linear Programming | |

Partial Fractions | |

Analytic Geometry Topics | |

The Parabola | |

The Circle and the Ellipse | |

The Hyperbola | |

Nonlinear Systems of Equations and Inequalities | |

Rotation of Axes | |

Polar Equations of Conics | |

Parametric Equations | |

Sequences, Series, and Combinatorics | |

Sequences and Series | |

Arithmetic Sequences and Series | |

Geometric Sequences and Series | |

Mathematical Induction | |

Combinatorics: Permutations | |

Combinatorics: Combinations | |

The Binomial Theorem | |

Probability | |

Appendix Basic Concepts of Geometry | |

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