| |
| |
| |
| The Rectangular Coordinate System, Lines, and Circles | |
| |
| |
| |
| The Rectangular Coordinate System | |
| |
| |
| |
| Circles | |
| |
| |
| |
| Lines | |
| |
| |
| |
| Parallel and Perpendicular Lines | |
| |
| |
| |
| Functions | |
| |
| |
| |
| Relations and Functions | |
| |
| |
| |
| Properties of a Function's Graph | |
| |
| |
| |
| Graphs of Basic Functions; Piecewise Functions | |
| |
| |
| |
| Transformations of Functions | |
| |
| |
| |
| The Algebra of Functions; Composite Functions | |
| |
| |
| |
| One-to-One Functions; Inverse Functions | |
| |
| |
| |
| Polynomial and Rational Functions | |
| |
| |
| |
| Quadratic Functions | |
| |
| |
| |
| Applications and Modeling of Quadratic Functions | |
| |
| |
| |
| The Graphs of Polynomial Functions | |
| |
| |
| |
| Synthetic Division; The Remainder and Factor Theorems | |
| |
| |
| |
| The Zeros of Polynomial Functions; The Fundamental Theorem of Algebra | |
| |
| |
| |
| Rational Functions and Their Graphs | |
| |
| |
| |
| Variation | |
| |
| |
| |
| Exponential and Logarithmic Functions and Equations | |
| |
| |
| |
| Exponential Functions | |
| |
| |
| |
| The Natural Exponential Function | |
| |
| |
| |
| Logarithmic Functions | |
| |
| |
| |
| Properties of Logarithms | |
| |
| |
| |
| Exponential and Logarithmic Equations | |
| |
| |
| |
| Applications of Exponential and Logarithmic Functions | |
| |
| |
| |
| An Introduction to Trigonometric Functions | |
| |
| |
| |
| Angles: Degree and Radian Measure | |
| |
| |
| |
| Applications of Radian Measure | |
| |
| |
| |
| The Unit Circle | |
| |
| |
| |
| Trigonometric Functions of General Angles | |
| |
| |
| |
| Right Triangle Trigonometry | |
| |
| |
| |
| The Graphs of Trigonometric Functions | |
| |
| |
| |
| The Graphs of Sine and Cosine | |
| |
| |
| |
| More on Graphs of Sine and Cosine; Phase Shift | |
| |
| |
| |
| The Graphs of the Tangent, Cosecant, Secant, and Cotangent Functions | |
| |
| |
| |
| Inverse Trigonometric Functions I | |
| |
| |
| |
| Inverse Trigonometric Functions II | |
| |
| |
| |
| Trigonometric Identities, Formulas, and Equations | |
| |
| |
| |
| Trigonometric Identities | |
| |
| |
| |
| The Sum and Difference Formulas | |
| |
| |
| |
| The Double-Angle and Half-Angle Formulas | |
| |
| |
| |
| The Product-to-Sum and Sum-to-Product Formulas | |
| |
| |
| |
| Trigonometric Equations | |
| |
| |
| |
| Applications of Trigonometry | |
| |
| |
| |
| The Law of Sines | |
| |
| |
| |
| The Law of Cosines | |
| |
| |
| |
| Area of Triangles | |
| |
| |
| |
| Polar Equations, Complex Numbers, and Vectors | |
| |
| |
| |
| Polar Coordinates and Polar Equations | |
| |
| |
| |
| The Graphs of Polar Equations | |
| |
| |
| |
| Complex Numbers; DeMoivre's Theorem | |
| |
| |
| |
| Vectors | |
| |
| |
| |
| The Dot Product | |
| |
| |
| |
| Conic Sections | |
| |
| |
| |
| The Parabola | |
| |
| |
| |
| The Ellipse | |
| |
| |
| |
| The Hyperbola | |
| |
| |
| |
| Systems of Equations and Inequalities | |
| |
| |
| |
| Systems of Linear Equations in Two Variables | |
| |
| |
| |
| Systems of Linear Equations in Three Variables | |
| |
| |
| |
| Inconsistent and Dependent Linear Systems in Three Variables | |
| |
| |
| |
| Partial Fraction Decomposition | |
| |
| |
| |
| Systems of Nonlinear Equations | |
| |
| |
| |
| Systems of Inequalities | |
| |
| |
| |
| Matrices | |
| |
| |
| |
| Matrix Operations | |
| |
| |
| |
| Inverses of Matrices and Matrix Equations | |
| |
| |
| |
| Determinants and Cramer's Rule | |
| |
| |
| |
| Sequences and Series; Counting and Probability | |
| |
| |
| |
| Introduction to Sequences and Series | |
| |
| |
| |
| Arithmetic Sequences and Series | |
| |
| |
| |
| Geometric Sequences and Series | |
| |
| |
| |
| The Binomial Theorem | |
| |
| |
| |
| Mathematical Inductions | |
| |
| |
| |
| The Theory of Counting | |
| |
| |
| |
| An Introduction to Probability | |
| |
| |
| |
| |
| |
| |
| Real Numbers | |
| |
| |
| |
| The Order of Operations and Algebraic Expressions | |
| |
| |
| |
| The Laws of Exponents; Radicals | |
| |
| |
| |
| Polynomials | |
| |
| |
| |
| Factoring Polynomials | |
| |
| |
| |
| Rational Expressions | |
| |
| |
| |
| |
| |
| |
| Linear Equations | |
| |
| |
| |
| Applications of Linear Equations | |
| |
| |
| |
| Complex Numbers | |
| |
| |
| |
| Quadratic Equations | |
| |
| |
| |
| Applications of Quadratic Equations | |
| |
| |
| |
| Other Types of Equations | |
| |
| |
| |
| Linear Inequalities | |
| |
| |
| |
| Absolute Value Equations and Inequalities | |
| |
| |
| |
| Polynomial and Rational Inequalities | |
| |
| |
| |
| |
| |
| |
| Degree, Minute, Second Form and Degree Decimal Form | |
| |
| |
| |
| Triangles | |
| |
| |
| |
| Conic Section Proofs | |