| |
| |
| Prologue: Principles of Problem Solving | |
| |
| |
| |
| Prerequisites | |
| |
| |
| Modeling the Real World | |
| |
| |
| Real Numbers and Their Properties | |
| |
| |
| The Real Number Line and Order | |
| |
| |
| Integer Exponents | |
| |
| |
| Rational Exponents and Radicals | |
| |
| |
| Algebraic Expressions | |
| |
| |
| Factoring Algebraic Expressions | |
| |
| |
| Rational Expressions | |
| |
| |
| Chapter P Review | |
| |
| |
| Chapter P Test | |
| |
| |
| Focus on Problem Solving: General Principles | |
| |
| |
| |
| Equations and Inequalities | |
| |
| |
| Chapter Overview | |
| |
| |
| Basic Equations | |
| |
| |
| Modeling with Equations | |
| |
| |
| Quadratic Equations | |
| |
| |
| Complex Numbers | |
| |
| |
| Other Types of Equations | |
| |
| |
| Inequalities | |
| |
| |
| Absolute Value Equations and Inequalities | |
| |
| |
| Chapter 1 Review | |
| |
| |
| Chapter 1 Test | |
| |
| |
| Focus on Modeling: Making the Best Decisions | |
| |
| |
| |
| Coordinates and Graphs | |
| |
| |
| Chapter Overview | |
| |
| |
| The Coordinate Plane | |
| |
| |
| Graphs of Equations in Two Variables | |
| |
| |
| Graphing Calculators: Solving Equations Graphically | |
| |
| |
| Lines | |
| |
| |
| Modeling: Variation | |
| |
| |
| Chapter 2 Review | |
| |
| |
| Chapter 2 Test | |
| |
| |
| Focus on Modeling: Fitting Lines to Data | |
| |
| |
| Cumulative Review Test: Chapters 1 and 2 | |
| |
| |
| |
| Functions | |
| |
| |
| Chapter Overview | |
| |
| |
| What Is a Function? | |
| |
| |
| Graphs of Functions | |
| |
| |
| Getting Information from the Graph of a Function | |
| |
| |
| Average Rate of Change of a Function | |
| |
| |
| Transformations of Functions | |
| |
| |
| Combining Functions | |
| |
| |
| One-to-One Functions and Their Inverses | |
| |
| |
| Chapter 3 Review | |
| |
| |
| Chapter 3 Test | |
| |
| |
| Focus on Modeling: Functions as Models | |
| |
| |
| |
| Polynomial and Rational Functions | |
| |
| |
| Chapter Overview | |
| |
| |
| Quadratic Functions and Models | |
| |
| |
| Polynomial Functions and Their Graphs | |
| |
| |
| Dividing Polynomials | |
| |
| |
| Real Zeros of Polynomials | |
| |
| |
| Complex Numbers | |
| |
| |
| Complex Zeros and the Fundamental Theorem of Algebra | |
| |
| |
| Rational Functions | |
| |
| |
| Chapter 4 Review | |
| |
| |
| Chapter 4 Test | |
| |
| |
| Focus on Modeling: Fitting Polynomial Curves to Data | |
| |
| |
| |
| Exponential and Logarithmic Functions | |
| |
| |
| Chapter Overview | |
| |
| |
| Exponential Functions | |
| |
| |
| The Natural Exponential Function | |
| |
| |
| Logarithmic Functions | |
| |
| |
| Laws of Logarithms | |
| |
| |
| Exponential and Logarithmic Equations | |
| |
| |
| Modeling with Exponential and Logarithmic Functions | |
| |
| |
| Chapter 5 Review | |
| |
| |
| Chapter 5t Test | |
| |
| |
| Focus on Modeling: Fitting Exponential and Power Curves to Data | |
| |
| |
| Cumulative Review Test: Chapters 3, 4, and 5 | |
| |
| |
| |
| Trigonometric Functions: Right Triangle Approach | |
| |
| |
| Chapter Overview | |
| |
| |
| Angle Measure | |
| |
| |
| Trigonometry of Right Triangles | |
| |
| |
| Trigonometric Functions of Angles | |
| |
| |
| Inverse Trigonometric Functions and Triangles | |
| |
| |
| The Law of Sines | |
| |
| |
| The Law of Cosines | |
| |
| |
| Chapter 6 Review | |
| |
| |
| Chapter 6 Test | |
| |
| |
| Focus on Modeling: Surveying | |
| |
| |
| |
| Trigonometric Functions: Unit Circle Approach | |
| |
| |
| Chapter Overview | |
| |
| |
| The Unit Circle | |
| |
| |
| Trigonometric Functions of Real Numbers | |
| |
| |
| Trigonometric Graphs | |
| |
| |
| More Trigonometric Graphs | |
| |
| |
| Inverse Trigonometric Functions and Their Graphs | |
| |
| |
| Modeling Harmonic Motion | |
| |
| |
| Chapter 7 Review | |
| |
| |
| Chapter 7 Test | |
| |
| |
| Focus on Modeling: Fitting Sinusoidal Curves to Data | |
| |
| |
| |
| Analytic Trigonometry | |
| |
| |
| Chapter Overview | |
| |
| |
| Trigonometric Identities | |
| |
| |
| Addition and Subtraction Formulas | |
| |
| |
| Double-Angle, Half-Angle, and Sum-Product Identities | |
| |
| |
| Basic Trigonometric Equations | |
| |
| |
| More Trigonometric Equations | |
| |
| |
| Chapter 8 Review | |
| |
| |
| Chapter 8 Test | |
| |
| |
| Focus on Modeling: Traveling and Standing Waves | |
| |
| |
| Cumulative Review Test: Chapters 6, 7, and 8 | |
| |
| |
| |
| Polar Coordinates and Parametric Equations | |
| |
| |
| Chapter Overview | |
| |
| |
| Polar Coordinates | |
| |
| |
| Graphs of Polar Equations | |
| |
| |
| Polar Form of Complex Numbers; DeMoivre's Theorem | |
| |
| |
| Plane Curves and Parametric Equations | |
| |
| |
| Chapter 9 Review | |
| |
| |
| Chapter 9 Test | |
| |
| |
| Focus on Modeling: The Path of a Projectile | |
| |
| |
| |
| Vectors in Two and Three Dimensions | |
| |
| |
| Chapter Overview | |
| |
| |
| Vectors in Two Dimensions | |
| |
| |
| The Dot Product | |
| |
| |
| Three �Dimensional Coordinate Geometry | |
| |
| |
| Vectors in Three Dimensions | |
| |
| |
| The Cross Product | |
| |
| |
| Equations of Lines and Planes | |
| |
| |
| Chapter 10 Review | |
| |
| |
| Chapter 10 Test | |
| |
| |
| Focus on Modeling: Vector Fields | |
| |
| |
| Cumulative Review Test: Chapters 9 and 10 | |
| |
| |
| |
| Systems of Equations and Inequalities | |
| |
| |
| Chapter Overview | |
| |
| |
| Systems of Linear Equations in Two Variables | |
| |
| |
| Systems of Linear Equations in Several Variables | |
| |
| |
| Systems of Linear Equations: Matrices | |
| |
| |
| The Algebra of Matrices | |
| |
| |
| Inverses of Matrices and Matrix Equations | |
| |
| |
| Determinants and Cramer's Rule | |
| |
| |
| Partial Fractions | |
| |
| |
| Systems of Non-Linear Equations | |
| |
| |
| Systems | |