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| About the Author | |
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| Preface to the Instructor | |
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| Acknowledgments | |
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| Preface to the Student | |
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| The Real Numbers | |
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| The Real Line | |
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| Construction of the Real Line | |
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| Is Every Real Number Rational? | |
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| Problems | |
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| Algebra of the Real Numbers | |
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| Commutativity and Associativity | |
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| The Order of Algebraic Operations | |
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| The Distributive Property | |
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| Additive Inverses and Subtraction | |
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| Multiplicative Inverses and the Algebra of Fractions | |
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| Symbolic Calculators | |
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| Exercises, Problems, and Worked-out Solutions | |
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| Inequalities | |
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| Positive and Negative Numbers | |
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| Lesser and Greater | |
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| Intervals | |
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| Absolute Value | |
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| Exercises, Problems, and Worked-out Solutions | |
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| Chapter Summary and Chapter Review Questions | |
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| Combining Algebra and Geometry | |
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| The Coordinate Plane | |
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| Coordinates | |
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| Graphs of Equations | |
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| Distance Between Two Points | |
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| Length, Perimeter, and Circumference | |
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| Exercises, Problems, and Worked-out Solutions | |
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| Lines | |
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| Slope | |
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| The Equation of a Line | |
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| Parallel Lines | |
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| Perpendicular Lines | |
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| Midpoints | |
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| Exercises, Problems, and Worked-out Solutions | |
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| Quadratic Expressions and Conic Sections | |
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| Completing the Square | |
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| The Quadratic Formula | |
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| Circles | |
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| Ellipses | |
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| Parabolas | |
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| Hyperbolas | |
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| Exercises, Problems, and Worked-out Solutions | |
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| Area | |
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| Squares, Rectangles, and Parallelograms | |
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| Triangles and Trapezoids | |
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| Stretching | |
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| Circles and Ellipses | |
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| Exercises, Problems, and Worked-out Solutions | |
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| Chapter Summary and Chapter Review Questions | |
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| Functions and Their Graphs | |
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| Functions | |
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| Definition and Examples | |
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| The Graph of a Function | |
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| The Domain of a Function | |
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| The Range of a Function | |
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| Functions via Tables | |
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| Exercises, Problems, and Worked-out Solutions | |
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| Function Transformations and Graphs | |
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| Vertical Transformations: Shifting, Stretching, and Flipping | |
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| Horizontal Transformations: Shifting, Stretching, Flipping | |
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| Combinations of Vertical Function Transformations | |
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| Even Functions | |
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| Odd Functions | |
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| Exercises, Problems, and Worked-out Solutions | |
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| Composition of Functions | |
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| Combining Two Functions | |
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| Definition of Composition | |
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| Order Matters in Composition | |
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| Decomposing Functions | |
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| Composing More than Two Functions | |
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| Function Transformations as Compositions | |
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| Exercises, Problems, and Worked-out Solutions | |
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| Inverse Functions | |
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| The Inverse Problem | |
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| One-to-one Functions | |
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| The Definition of an Inverse Function | |
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| The Domain and Range of an Inverse Function | |
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| The Composition of a Function and Its Inverse | |
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| Comments about Notation | |
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| Exercises, Problems, and Worked-out Solutions | |
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| A Graphical Approach to Inverse Functions | |
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| The Graph of an Inverse Function | |
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| Graphical Interpretation of One-to-One | |
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| Increasing and Decreasing Functions | |
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| Inverse Functions via Tables | |
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| Exercises, Problems, and Worked-out Solutions | |
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| Chapter Summary and Chapter Review Questions | |
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| Polynomial and Rational Functions | |
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| Integer Exponents | |
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| Positive Integer Exponents | |
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| Properties of Exponents | |
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| Defining x0 | |
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| Negative Integer Exponents | |
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| Manipulations with Exponents | |
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| Exercises, Problems, and Worked-out Solutions | |
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| Polynomials | |
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| The Degree of a Polynomial | |
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| The Algebra of Polynomials | |
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| Zeros and Factorization of Polynomials | |
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| The Behavior of a Polynomial Near 1 | |
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| Graphs of Polynomials | |
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| Exercises, Problems, and Worked-out Solutions | |
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| Rational Functions | |
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| Ratios of Polynomials | |
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| The Algebra of Rational Functions | |
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| Division of Polynomials | |
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| The Behavior of a Rational Function Near 1 | |
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| Graphs of Rational Functions | |
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| Exercises, Problems, and Worked-out Solutions | |
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| Complex Numbers | |
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| The Complex Number System | |
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| Arithmetic with Complex Numbers | |
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| Complex Conjugates and Division of Complex Numbers | |
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| Zeros and Factorization of Polynomials, Revisited | |
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| Exercises, Problems, and Worked-out Solutions | |
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| Chapter Summary and Chapter Review Questions | |
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| Exponents and Logarithms | |
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| Exponents and Exponential Functions | |
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| Roots | |
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| Rational Exponents | |
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| Real Exponents | |
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| Exponential Functions | |
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| Exercises, Problems, and Worked-out Solutions | |
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| Logarithms as Inverses of Exponential Functions | |
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| Logarithms Base 2 | |
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| Logarithms with Any Base | |
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| Common Logarithms and the Number of Digits | |
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| Logarithm of a Power | |
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| Radioactive Decay and Half-Life | |
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| Exercises, Problems, and Worked-out Solutions | |
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| Applications of Logarithms | |
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| Logarithm of a Product | |
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| Logarithm of a Quotient | |
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| Earthquakes and the Richter Scale | |
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| Sound Intensity and Decibels | |
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| Star Brightness and Apparent Magnitude | |
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| Change of Base | |
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| Exercises, Problems, and Worked-out Solutions | |
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| Exponential Growth | |
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| Functions with Exponential Growth | |
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| Population Growth | |
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| Compound Interest | |
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| Exercises, Problems, and Worked-out Solutions | |
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| Chapter Summary and Chapter Review Questions | |
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| e and the Natural Logarithm | |
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| Defining e and ln | |
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| Estimating Area Using Rectangles | |
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| Defining e | |
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| Defining the Natural Logarithm | |
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| Properties of the Exponential Function and ln | |
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| Exercises, Problems, and Worked-out Solutions | |
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| Approximations with e and ln | |
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| Approximation of the Natural Logarithm | |
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| Inequalities with the Natural Logarithm | |
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| Approximations with the Exponential Function | |
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| An Area Formula | |
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| Exercises, Problems, and Worked-out Solutions | |
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| Exponential Growth Revisited | |
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| Continuously Compounded Interest | |
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| Continuous Growth Rates | |
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| Doubling Your Money | |
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| Exercises, Problems, and Worked-out Solutions | |
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| Chapter Summary and Chapter Review Questions | |
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| Systems of Equations and Inequalities | |
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| Equations and Systems of Equations | |
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| Solving an Equation | |
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| Solving a System of Equations | |
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| Systems of Linear Equations | |
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| Matrices | |
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| Exercises, Problems, and Worked-out Solutions | |
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| Solving Systems of Linear Equations | |
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| Gaussian Elimination | |
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| Gaussian Elimination with Matrices | |
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| Special Cases-No Solutions | |
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| Special Cases-Infinitely Many Solutions | |
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| Exercises, Problems, and Worked-out Solutions | |
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| Matrix Algebra | |
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| Adding and Subtracting Matrices | |
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| Multiplying Matrices | |
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| The Inverse of a Matrix | |
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| Exercises, Problems, and Worked-out Solutions | |
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| Chapter Summary and Chapter Review Questions | |
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| Sequences, Series, and Limits | |
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| Sequences | |
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| Introduction to Sequences | |
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| Arithmetic Sequences | |
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| Geometric Sequences | |
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| Recursively-Defined Sequences | |
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| Exercises, Problems, and Worked-out Solutions | |
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| Series | |
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| Sums of Sequences | |
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| Arithmetic Series | |
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| Geometric Series | |
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| Summation Notation | |
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| The Binomial Theorem | |
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| Exercises, Problems, and Worked-out Solutions | |
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| Limits | |
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| Introduction to Limits | |
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| Infinite Series | |
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| Decimals as Infinite Series | |
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| Special Infinite Series | |
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| Exercises, Problems, and Worked-out Solutions | |
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| Chapter Summary and Chapter Review Questions | |