About the Author | |

Preface to the Instructor | |

Acknowledgments | |

Preface to the Student | |

The Real Numbers | |

The Real Line | |

Construction of the Real Line | |

Is Every Real Number Rational? | |

Problems | |

Algebra of the Real Numbers | |

Commutativity and Associativity | |

The Order of Algebraic Operations | |

The Distributive Property | |

Additive Inverses and Subtraction | |

Multiplicative Inverses and the Algebra of Fractions | |

Symbolic Calculators | |

Exercises, Problems, and Worked-out Solutions | |

Inequalities | |

Positive and Negative Numbers | |

Lesser and Greater | |

Intervals | |

Absolute Value | |

Exercises, Problems, and Worked-out Solutions | |

Chapter Summary and Chapter Review Questions | |

Combining Algebra and Geometry | |

The Coordinate Plane | |

Coordinates | |

Graphs of Equations | |

Distance Between Two Points | |

Length, Perimeter, and Circumference | |

Exercises, Problems, and Worked-out Solutions | |

Lines | |

Slope | |

The Equation of a Line | |

Parallel Lines | |

Perpendicular Lines | |

Midpoints | |

Exercises, Problems, and Worked-out Solutions | |

Quadratic Expressions and Conic Sections | |

Completing the Square | |

The Quadratic Formula | |

Circles | |

Ellipses | |

Parabolas | |

Hyperbolas | |

Exercises, Problems, and Worked-out Solutions | |

Area | |

Squares, Rectangles, and Parallelograms | |

Triangles and Trapezoids | |

Stretching | |

Circles and Ellipses | |

Exercises, Problems, and Worked-out Solutions | |

Chapter Summary and Chapter Review Questions | |

Functions and Their Graphs | |

Functions | |

Definition and Examples | |

The Graph of a Function | |

The Domain of a Function | |

The Range of a Function | |

Functions via Tables | |

Exercises, Problems, and Worked-out Solutions | |

Function Transformations and Graphs | |

Vertical Transformations: Shifting, Stretching, and Flipping | |

Horizontal Transformations: Shifting, Stretching, Flipping | |

Combinations of Vertical Function Transformations | |

Even Functions | |

Odd Functions | |

Exercises, Problems, and Worked-out Solutions | |

Composition of Functions | |

Combining Two Functions | |

Definition of Composition | |

Order Matters in Composition | |

Decomposing Functions | |

Composing More than Two Functions | |

Function Transformations as Compositions | |

Exercises, Problems, and Worked-out Solutions | |

Inverse Functions | |

The Inverse Problem | |

One-to-one Functions | |

The Definition of an Inverse Function | |

The Domain and Range of an Inverse Function | |

The Composition of a Function and Its Inverse | |

Comments about Notation | |

Exercises, Problems, and Worked-out Solutions | |

A Graphical Approach to Inverse Functions | |

The Graph of an Inverse Function | |

Graphical Interpretation of One-to-One | |

Increasing and Decreasing Functions | |

Inverse Functions via Tables | |

Exercises, Problems, and Worked-out Solutions | |

Chapter Summary and Chapter Review Questions | |

Polynomial and Rational Functions | |

Integer Exponents | |

Positive Integer Exponents | |

Properties of Exponents | |

Defining x0 | |

Negative Integer Exponents | |

Manipulations with Exponents | |

Exercises, Problems, and Worked-out Solutions | |

Polynomials | |

The Degree of a Polynomial | |

The Algebra of Polynomials | |

Zeros and Factorization of Polynomials | |

The Behavior of a Polynomial Near -1 | |

Graphs of Polynomials | |

Exercises, Problems, and Worked-out Solutions | |

Rational Functions | |

Ratios of Polynomials | |

The Algebra of Rational Functions | |

Division of Polynomials | |

The Behavior of a Rational Function Near -1 | |

Graphs of Rational Functions | |

Exercises, Problems, and Worked-out Solutions | |

Complex Numbers | |

The Complex Number System | |

Arithmetic with Complex Numbers | |

Complex Conjugates and Division of Complex Numbers | |

Zeros and Factorization of Polynomials, Revisited | |

Exercises, Problems, and Worked-out Solutions | |

Chapter Summary and Chapter Review Questions | |

Exponents and Logarithms | |

Exponents and Exponential Functions | |

Roots | |

Rational Exponents | |

Real Exponents | |

Exponential Functions | |

Exercises, Problems, and Worked-out Solutions | |

Logarithms as Inverses of Exponential Functions | |

Logarithms Base 2 | |

Logarithms with Any Base | |

Common Logarithms and the Number of Digits | |

Logarithm of a Power | |

Radioactive Decay and Half-Life | |

Exercises, Problems, and Worked-out Solutions | |

Applications of Logarithms | |

Logarithm of a Product | |

Logarithm of a Quotient | |

Earthquakes and the Richter Scale | |

Sound Intensity and Decibels | |

Star Brightness and Apparent Magnitude | |

Change of Base | |

Exercises, Problems, and Worked-out Solutions | |

Exponential Growth | |

Functions with Exponential Growth | |

Population Growth | |

Compound Interest | |

Exercises, Problems, and Worked-out Solutions | |

Chapter Summary and Chapter Review Questions | |

e and the Natural Logarithm | |

Defining e and ln | |

Estimating Area Using Rectangles | |

Defining e | |

Defining the Natural Logarithm | |

Properties of the Exponential Function and ln | |

Exercises, Problems, and Worked-out Solutions | |

Approximations with e and ln | |

Approximation of the Natural Logarithm | |

Inequalities with the Natural Logarithm | |

Approximations with the Exponential Function | |

An Area Formula | |

Exercises, Problems, and Worked-out Solutions | |

Exponential Growth Revisited | |

Continuously Compounded Interest | |

Continuous Growth Rates | |

Doubling Your Money | |

Exercises, Problems, and Worked-out Solutions | |

Chapter Summary and Chapter Review Questions | |

Trigonometric Functions | |

The Unit Circle | |

The Equation of the Unit Circle | |

Angles in the Unit Circle | |

Negative Angles | |

Angles Greater Than 360- | |

Length of a Circular Arc | |

Special Points on the Unit Circle | |

Exercises, Problems, and Worked-out Solutions | |

Radians | |

A Natural Unit of Measurement for Angles | |

Negative Angles | |

Angles Greater Than 2- | |

Length of a Circular Arc | |

Area of a Slice | |

Special Points on the Unit Circle | |

Exercises, Problems, and Worked-out Solutions | |

Cosine and Sine | |

Definition of Cosine and Sine | |

Cosine and Sine of Special Angles | |

The Signs of Cosine and Sine | |

The Key Equation Connecting Cosine and Sine | |

The Graphs of Cosine and Sine | |

Exercises, Problems, and Worked-out Solutions | |

More Trigonometric Functions | |

Definition of Tangent | |

Tangent of Special Angles | |

The Sign of Tangent | |

Connections between Cosine, Sine, and Tangent | |

The Graph of Tangent | |

Three More Trigonometric Functions | |

Exercises, Problems, and Worked-out Solutions | |

Trigonometry in Right Triangles | |

Trigonometric Functions via Right Triangles | |

Two Sides of a Right Triangle | |

One Side and One Angle of a Right Triangle | |

Exercises, Problems, and Worked-out Solutions | |

Trigonometric Identities | |

The Relationship Between Cosine and Sine | |

Trigonometric Identities for the Negative of an Angle | |

Trigonometric Identities with | |

Trigonometric Identities Involving a Multiple of | |

Exercises, Problems, and Worked-out Solutions | |

Chapter Summary and Chapter Review Questions | |

Trigonometric Algebra and Geometry | |

Inverse Trigonometric Functions | |

The Arccosine Function | |

The Arcsine Function | |

The Arctangent Function | |

Exercises, Problems, and Worked-out Solutions | |

Inverse Trigonometric Identities | |

The Arccosine, Arcsine, and Arctangent of | |

t: Graphical | |

Approach | |

The Arccosine, Arcsine, and Arctangent of | |

t: Algebraic | |

Approach | |

Arccosine Plus Arcsine | |

The Arctangent of 1t | |

Composition of Trigonometric Functions and Their Inverses | |

More Compositions with Inverse Trigonometric Functions | |

Exercises, Problems, and Worked-out Solutions | |

Using Trigonometry to Compute Area | |

The Area of a Triangle via Trigonometry | |

Ambiguous Angles | |

The Area of a Parallelogram via Trigonometry | |

The Area of a Polygon | |

Exercises, Problems, and Worked-out Solutions | |

The Law of Sines and the Law of Cosines | |

The Law of Sines | |

Using the Law of Sines | |

The Law of Cosines | |

Using the Law of Cosines | |

When to Use Which Law | |

Exercises, Problems, and Worked-out Solutions | |

Double-Angle and Half-Angle Formulas | |

The Cosine of 2- | |

The Sine of 2- | |

The Tangent of 2- | |

The Cosine and Sine of -2 | |

The Tangent of -2 | |

Exercises, Problems, and Worked-out Solutions | |

Addition and Subtraction Formulas | |

The Cosine of a Sum and Difference | |

The Sine of a Sum and Difference | |

The Tangent of a Sum and Difference | |

Exercises, Problems, and Worked-out Solutions | |

Chapter Summary and Chapter Review Questions | |

Applications of Trigonometry | |

Parametric Curves | |

Curves in the Coordinate Plane | |

Graphing Inverse Functions as Parametric Curves | |

Shifting, Stretching, or Flipping a Parametric Curve | |

Exercises, Problems, and Worked-out Solutions | |

Transformations of Trigonometric Functions | |

Amplitude | |

Period | |

Phase Shift | |

Exercises, Problems, and Worked-out Solutions | |

Polar Coordinates | |

Defining Polar Coordinates | |

Converting from Polar to Rectangular Coordinates | |

Converting from Rectangular to Polar Coordinates | |

Graphs of Polar Equations | |

Exercises, Problems, and Worked-out Solutions | |

Vectors | |

An Algebraic and Geometric Introduction to Vectors | |

Vector Addition | |

Vector Subtraction | |

The Dot Product | |

Exercises, Problems, and Worked-out Solutions | |

The Complex Plane | |

Complex Numbers as Points in the Plane | |

Geometric Interpretation of Complex Multiplication and Division | |

De Moivre's Theorem | |

Finding Complex Roots | |

Exercises, Problems, and Worked-out Solutions | |

Chapter Summary and Chapter Review Questions | |

Systems of Equations and Inequalities | |

Equations and Systems of Equations | |

Solving an Equation | |

Solving a System of Equations | |

Systems of Linear Equations | |

Matrices | |

Exercises, Problems, and Worked-out Solutions | |

Solving Systems of Linear Equations | |

Gaussian Elimination | |

Gaussian Elimination with Matrices | |

Special Cases-No Solutions | |

Special Cases-Infinitely Many Solutions | |

Exercises, Problems, and Worked-out Solutions | |

Matrix Algebra | |

Adding and Subtracting Matrices | |

Multiplying Matrices | |

The Inverse of a Matrix | |

Exercises, Problems, and Worked-out Solutions | |

Chapter Summary and Chapter Review Questions | |

Sequences, Series, and Limits | |

Sequences | |

Introduction to Sequences | |

Arithmetic Sequences | |

Geometric Sequences | |

Recursively-Defined Sequences | |

Exercises, Problems, and Worked-out Solutions | |

Series | |

Sums of Sequences | |

Arithmetic Series | |

Geometric Series | |

Summation Notation | |

The Binomial Theorem | |

Exercises, Problems, and Worked-out Solutions | |

Limits | |

Introduction to Limits | |

Infinite Series | |

Decimals as Infinite Series | |

Special Infinite Series | |

Exercises, Problems, and Worked-out Solutions | |

Chapter Summary and Chapter Review Questions | |

Table of Contents provided by Publisher. All Rights Reserved. |