| |
| |
| Each chapter concludes with a Review | |
| |
| |
| True/False Exercises | |
| |
| |
| Review Exercises, and a Test | |
| |
| |
| |
| Fundamental Concepts | |
| |
| |
| |
| The Real Number System | |
| |
| |
| |
| Intervals, Absolute Value, and Distance | |
| |
| |
| |
| Integer and Rational Number Exponents | |
| |
| |
| |
| Complex Numbers | |
| |
| |
| |
| Polynomials | |
| |
| |
| |
| Factoring | |
| |
| |
| |
| Rational Expressions Exploring Concepts with Technology | |
| |
| |
| The Mandelbrot Replacement Procedure | |
| |
| |
| |
| Equations and Inequalities | |
| |
| |
| |
| Linear Equations | |
| |
| |
| |
| Formulas and Applications | |
| |
| |
| |
| Quadratic Equations | |
| |
| |
| |
| Other Types of Equations | |
| |
| |
| |
| Inequalities | |
| |
| |
| |
| Absolute Value Equations and Inequalities | |
| |
| |
| Exploring Concepts with Technology: Can You Trust Your Calculator? | |
| |
| |
| |
| Functions and Graphs | |
| |
| |
| |
| A Two-Dimensional Coordinate System and Graphs | |
| |
| |
| |
| Introduction to Functions | |
| |
| |
| |
| Linear Functions | |
| |
| |
| |
| Quadratic Functions | |
| |
| |
| |
| Properties of Graphs | |
| |
| |
| |
| The Algebra of Functions | |
| |
| |
| |
| Inverse Functions | |
| |
| |
| |
| Variation and Applications Exploring Concepts with Technology | |
| |
| |
| The Least-Squares Regression Line | |
| |
| |
| |
| Polynomial and Rational Functions | |
| |
| |
| |
| Polynomial Division and Synthetic Division | |
| |
| |
| |
| Introduction to Polynomial Functions | |
| |
| |
| |
| Zeros of Polynomial Functions | |
| |
| |
| |
| The Fundamental Theory of Algebra | |
| |
| |
| |
| Rational Functions and Their Graphs Exploring Concepts with Technology | |
| |
| |
| Finding Zeros of a Polynomial Using Mathematica | |
| |
| |
| |
| Exponential and Logarithmic Functions | |
| |
| |
| |
| Exponential Functions and Their Graphs | |
| |
| |
| |
| Logarithms and Logarithmic Properties | |
| |
| |
| |
| Logarithmic Functions and Their Graphs | |
| |
| |
| |
| Exponential and Logarithmic Equations | |
| |
| |
| |
| Applications of Exponential and Logarithmic Functions Exploring Concepts with Technology | |
| |
| |
| Using a Semi-Log Graph to Model Exponential Decay | |
| |
| |
| |
| Trigonometric Functions | |
| |
| |
| |
| Angles and Arcs | |
| |
| |
| |
| Trigonometric Functions of Acute Angles | |
| |
| |
| |
| Trigonometric Functions of Any Angle | |
| |
| |
| |
| Trigonometric Functions of Real Numbers | |
| |
| |
| |
| Graphs of the Sine and Cosine Functions | |
| |
| |
| |
| Graphs of the Other Trigonometric Functions | |
| |
| |
| |
| Graphing Techniques | |
| |
| |
| |
| Harmonic Motion--An Application of the Sine and Cosine Functions Exploring Concepts with Technology | |
| |
| |
| Vertical Asymptotes and Removable Singularities | |
| |
| |
| |
| Trigonometric Identities and Equations | |
| |
| |
| |
| Verification of Trigonometric Identities | |
| |
| |
| |
| Sum, Difference, and Cofunction Identities | |
| |
| |
| |
| Double- and Half-Angle Identities | |
| |
| |
| |
| Identities Involving the Sum of Trigonometric Functions | |
| |
| |
| |
| Inverse Trigonometric Functions | |
| |
| |
| |
| Trigonometric Equations Exploring Concepts with Technology | |
| |
| |
| Approximate an Inverse Trigonometric Function with Polynomials | |
| |
| |
| |
| Applications of Trigonometry | |
| |
| |
| |
| The Laws of Sines | |
| |
| |
| |
| The Law of Cosines and Area | |
| |
| |
| |
| Vectors | |
| |
| |
| |
| Trigonometric Form of Complex Numbers | |
| |
| |
| |
| DeMoivre's Theorem Exploring Concepts with Technology | |
| |
| |
| Optimal Branching of Arteries | |
| |
| |
| |
| Topics in Analytic Geometry | |
| |
| |
| |
| Parabolas | |
| |
| |
| |
| Ellipses | |
| |
| |
| |
| Hyperbolas | |
| |
| |
| |
| Rotation of Axes | |
| |
| |
| |
| Introduction to Polar Coordinates | |
| |
| |
| |
| Polar Equations of the Conics | |
| |
| |
| |
| Parametric Equations Exploring Concepts with Technology | |
| |
| |
| The Mathematics of a Rotary Engine | |
| |
| |
| |
| Systems of Equations | |
| |
| |
| |
| Systems of Linear Equations in Two Variables | |
| |
| |
| |
| Systems of Linear Equations in More Than Two Variables | |
| |
| |
| |
| Nonlinear Systems of Equations | |
| |
| |
| |
| Partial Fractions | |
| |
| |
| |
| Inequalities in Two Variables and Systems if Inequalities | |
| |
| |
| |
| Linear Programming Exploring Concepts with Technology | |
| |
| |
| Ill-Conditioned Systems of Equations | |
| |
| |
| |
| Matrices | |
| |
| |
| |
| Gaussuan Elimination Method | |
| |
| |
| |
| The Algebra of Matrices | |
| |
| |
| |
| The Inverse of a Matrix | |
| |
| |
| |
| Determinants | |
| |
| |
| |
| Cramer's Rule Exploring the Concept with Technology | |
| |
| |
| Stochastic Matrices | |
| |
| |
| |
| Sequences, Series, and Probability | |
| |
| |
| |
| Infinite Sequences and Summation Notation | |
| |
| |
| |
| Arithmetic Sequences and Series | |
| |
| |
| |
| Geometric Sequences and Series | |
| |
| |
| |
| Mathematical Induction | |
| |
| |
| |
| The Binomial Theorem | |
| |
| |
| |
| Permutations and Combinations | |
| |
| |
| |
| Introduction to Probability Exploring Concepts with Technology | |
| |
| |
| Mathematical Expectation | |
| |
| |
| |
| Three-Dimensional Coordinate Geometry | |
| |
| |
| |
| A Three-Dimensional Coordinate System | |
| |
| |
| |
| Vectors in Space | |
| |
| |
| |
| The Cross Product | |
| |
| |
| |
| Lines and Planes Exploring Concepts with Technology | |
| |
| |
| Four, Three, Two, One, Blastoff! | |
| |
| |
| |
| Introduction to Calculus | |
| |
| |
| |
| Introduction to Limits | |
| |
| |
| |
| Limits Involving Infinity | |
| |
| |
| |
| Continuous and Iterated Functions | |
| |
| |
| |
| Introduction to Derivatives | |
| |
| |
| |
| Area Under a Curve Exploring Concepts with Technology | |
| |
| |
| Finding Derivatives Using a Computer Algebra System Solutions to Selected Exercises | |
| |
| |
| Answers to Odd-Numbered Exercises | |
| |
| |
| Glossary | |
| |
| |
| Index | |