| |
| |
| |
| A Review of Basic Concepts and Skills | |
| |
| |
| |
| The Language, Notation, and Numbers of Mathematics | |
| |
| |
| |
| Algebraic Expressions and the Properties of Real Numbers | |
| |
| |
| |
| Exponents, Scientific Notation, and a Review of Polynomials | |
| |
| |
| |
| Factoring Polynomials | |
| |
| |
| |
| Rational Expressions | |
| |
| |
| |
| Radicals and Rational Exponents | |
| |
| |
| |
| Equations and Inequalities | |
| |
| |
| |
| Linear Equations, Formulas, and Problem Solving | |
| |
| |
| |
| Linear Inequalities in One Variable | |
| |
| |
| |
| Absolute Value Equations and Inequalities | |
| |
| |
| |
| Complex Numbers | |
| |
| |
| |
| Solving Quadratic Equations | |
| |
| |
| |
| Solving Other Types of Equations | |
| |
| |
| |
| Relations, Functions and Graphs | |
| |
| |
| |
| Rectangular Coordinates; Graphing Circles and Relations | |
| |
| |
| |
| Graphs of Linear Equations | |
| |
| |
| |
| Linear Equations and Rates of Change | |
| |
| |
| |
| Functions, Notation, and Graphs of Functions | |
| |
| |
| |
| Analyzing the Graph of a Function | |
| |
| |
| |
| Toolbox Functions and Transformations | |
| |
| |
| |
| Piecewise-Defined Functions | |
| |
| |
| |
| The Algebra and Composition of Functions | |
| |
| |
| |
| Polynomial and Rational Functions | |
| |
| |
| |
| Quadratic Functions and Applications | |
| |
| |
| |
| Synthetic Division; The Remainder and Factor Theorems | |
| |
| |
| |
| The Zeroes of Polynomial Functions | |
| |
| |
| |
| Graphing Polynomial Functions | |
| |
| |
| |
| Graphing Rational Functions | |
| |
| |
| |
| Additional Insights into Rational Functions | |
| |
| |
| |
| Polynomial and Rational Inequalities | |
| |
| |
| |
| Variation: Function Models in Action | |
| |
| |
| |
| Exponential and Logarithmic Functions | |
| |
| |
| |
| One-to-One and Inverse Functions | |
| |
| |
| |
| Exponential Functions | |
| |
| |
| |
| Logarithms and Logarithmic Functions | |
| |
| |
| |
| Properties of Logarithms; Solving Exponential and Logarithmic Equations | |
| |
| |
| |
| Applications from Business, Finance, and Science | |
| |
| |
| |
| Business, Finance, and Science Applications | |
| |
| |
| |
| Introduction to Trigonometric Functions | |
| |
| |
| |
| Angle Measure, Special Triangles, and Special Angles | |
| |
| |
| |
| The Trigonometry of Right Triangles | |
| |
| |
| |
| Trigonometry and the Coordinate Plane | |
| |
| |
| |
| Unit Circles and the Trigonometric of Real Numbers | |
| |
| |
| |
| Graphs of Sine and Cosine Functions; Cosecant and Secant Functions | |
| |
| |
| |
| Graphs of Tangent and Cotangent Functions | |
| |
| |
| |
| Transformations and Applications of Trigonometric Graphs | |
| |
| |
| |
| Trigonometric Identities, Inverses, and Equations | |
| |
| |
| |
| Fundamental Identities and Families of Identities | |
| |
| |
| |
| Constructing and Verifying Identities | |
| |
| |
| |
| The Sum and Difference Identities | |
| |
| |
| |
| Double Angle, Half Angle & Product-to-Sum Identities | |
| |
| |
| |
| The Inverse Trigonometric Functions and Their Applications | |
| |
| |
| |
| Solving Basic Trigonometric Equations | |
| |
| |
| |
| General Trigonometric Equations and Applications | |
| |
| |
| |
| Applications of Trigonometry | |
| |
| |
| |
| Oblique Triangles and the Law of Sines | |
| |
| |
| |
| The Law of Cosines; Area of a Triangle | |
| |
| |
| |
| Vectors and Vector Diagrams | |
| |
| |
| |
| Vector Applications and the Dot Product | |
| |
| |
| |
| Complex Numbers in Trigonometric Form | |
| |
| |
| |
| DemoivreG++s Theorem and the Theorem on nth Roots | |
| |
| |
| |
| Systems of Equations and Inequalities | |
| |
| |
| |
| Linear Systems in Two Variables with Applications | |
| |
| |
| |
| Linear Systems in Three Variables with Applications | |
| |
| |
| |
| Nonlinear Systems of Equations and Inequalities | |
| |
| |
| |
| Systems of Inequalities and Linear Programming | |
| |
| |
| |
| Matrices and Matrix Applications | |
| |
| |
| |
| Solving Systems Using Matrices and Row Operations | |
| |
| |
| |
| The Algebra of Matrices | |
| |
| |
| |
| Solving Linear Systems Using Matrix Equations | |
| |
| |
| |
| Applications of Matrices and Determinants: Cramer's Rule, Partial Fractions, and More | |
| |
| |
| |
| Analytical Geometry and Conic Sections | |
| |
| |
| |
| Introduction to Analytic Geometry | |
| |
| |
| |
| The Circle and the Ellipse | |
| |
| |
| |
| The Hyperbola | |
| |
| |
| |
| The Analytic Parabola | |
| |
| |
| |
| Polar Coordinates, Equations, and Graphs | |
| |
| |
| |
| More on Conic Sections: Rotation of Axes and Polar Form | |
| |
| |
| |
| Parametric Equations and Graphs | |
| |
| |
| |
| Additional Topics in Algebra | |
| |
| |
| |
| Sequenc | |