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| Prerequisites | |
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| Real Numbers | |
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| Representing Real Numbers | |
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| Order and Interval Notation | |
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| Basic Properties of Algebra | |
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| Integer Exponents | |
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| Scientific Notation | |
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| Cartesian Coordinate System | |
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| Cartesian Plane | |
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| Absolute Value of a Real Number | |
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| Distance Formulas | |
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| Midpoint Formulas | |
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| Equations of Circles | |
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| Applications | |
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| Linear Equations and Inequalities | |
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| Equations | |
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| Solving Equations | |
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| Linear Equations in One Variable | |
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| Linear Inequalities in One Variable | |
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| Lines in the Plane | |
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| Slope of a Line | |
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| Point-Slope Form Equation of a Line | |
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| Slope-Intercept Form Equation of a Line | |
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| Graphing Linear Equations in Two Variables | |
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| Parallel and Perpendicular Lines | |
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| Applying Linear Equations in Two Variables | |
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| Solving Equations Graphically, Numerically, and Algebraically | |
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| Solving Equations Graphically | |
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| Solving Quadratic Equations | |
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| Approximating Solutions of Equations Graphically | |
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| Approximating Solutions of Equations Numerically with Tables | |
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| Solving Equations by Finding Intersections | |
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| Complex Numbers | |
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| Complex Numbers | |
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| Operations with Complex Numbers | |
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| Complex Conjugates and Division | |
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| Complex Solutions of Quadratic Equations | |
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| Solving Inequalities Algebraically and Graphically | |
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| Solving Absolute Value Inequalities | |
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| Solving Quadratic Inequalities | |
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| Approximating Solutions to Inequalities | |
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| Projectile Motion | |
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| Key Ideas | |
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| Review Exercises | |
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| Functions and Graphs | |
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| Modeling and Equation Solving | |
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| Numerical Models | |
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| Algebraic Models | |
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| Graphical Models | |
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| The Zero Factor Property | |
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| Problem Solving | |
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| Grapher Failure and Hidden Behavior | |
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| A Word About Proof | |
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| Functions and Their Properties | |
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| Function Definition and Notation | |
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| Domain and Range | |
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| Continuity | |
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| Increasing and Decreasing Functions | |
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| Boundedness | |
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| Local and Absolute Extrema | |
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| Symmetry | |
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| Asymptotes | |
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| End Behavior | |
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| Twelve Basic Functions | |
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| What Graphs Can Tell Us | |
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| Twelve Basic Functions | |
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| Analyzing Functions Graphically | |
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| Building Functions from Functions | |
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| Combining Functions Algebraically | |
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| Composition of Functions | |
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| Relations and Implicitly Defined Functions | |
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| Parametric Relations and Inverses | |
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| Relations Defined Parametrically | |
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| Inverse Relations and Inverse Functions | |
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| Graphical Transformations | |
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| Transformations | |
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| Vertical and Horizontal Translations | |
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| Reflections Across Axes | |
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| Vertical and Horizontal Stretches and Shrinks | |
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| Combining Transformations | |
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| Modeling With Functions | |
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| Functions from Formulas | |
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| Functions from Graphs | |
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| Functions from Verbal Descriptions | |
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| Functions from Data | |
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| Math at Work | |
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| Key Ideas | |
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| Review Exercises | |
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| Chapter Project | |
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| Polynomial, Power, and Rational Functions | |
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| Linear and Quadratic Functions and Modeling | |
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| Polynomial Functions | |
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| Linear Functions and Their Graphs | |
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| Average Rate of Change | |
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| Linear Correlation and Modeling | |
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| Quadratic Functions and Their Graphs | |
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| Applications of Quadratic Functions | |
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| Power Functions with Modeling | |
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| Power Functions and Variation | |
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| Monomial Functions and Their Graphs | |
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| Graphs of Power Functions | |
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| Modeling with Power Functions | |
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| Polynomial Functions of Higher Degree with Modeling | |
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| Graphs of Polynomial Functions | |
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| End Behavior of Polynomial Functions | |
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| Zeros of Polynomial Functions | |
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| Intermediate Value Theorem | |
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| Modeling | |
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| Real Zeros of Polynomial Functions | |
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| Long Division and the Division Algorithm | |
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| Remainder and Factor Theorems | |
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| Synthetic Division | |
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| Rational Zeros Theorem | |
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| Upper and Lower Bounds | |
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| Complex Zeros and the Fundamental Theorem of Algebra | |
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| Two Major Theorems | |
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| Complex Conjugate Zeros | |
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| Factoring with Real Number Coefficients | |
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| Graphs of Rational Functions | |
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| Rational Functions | |
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| Transformations of the Reciprocal Function | |
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| Limits and Asymptotes | |
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| Analyzing Graphs of Rational Functions | |
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| Exploring Relative Humidity | |
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| Solving Equations in One Variable | |
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| Solving Rational Equations | |
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| Extraneous Solutions | |
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| Applications | |
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| Solving Inequalities in One Variable | |
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| Polynomial Inequalities | |
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| Rational Inequalities | |
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| Other Inequalities | |
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| Applications | |
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| Math at Work | |
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| Key Ideas | |
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| Review Exercises | |
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| Chapter Project | |
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| Exponential, Logistic, and Logarithmic Functions | |
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| Exponential and Logistic Functions | |
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| Exponential Functions and Their Graphs | |
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| The Natural Base e | |
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| Logistic Functions and Their Graphs | |
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| Population Models | |
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| Exponential and Logistic Modeling | |
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| Constant Percentage Rate and Exponential Functions | |
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| Exponential Growth and Decay Models | |
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| Using Regression to Model Population | |
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| Other Logistic Models | |
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| Logarithmic Functions and Their Graphs | |
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| Inverses of Exponential Functions | |
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| Common Logarithms-Base 10 | |
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| Natural Logarithms-Base e | |
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| Graphs of Logarithmic Functions | |
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| Measuring Sound Using Decibels | |
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| Properties of Logarithmic Functions | |
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| Properties of Logarithms | |
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| Change of Base | |
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| Graphs of Logarithmic Functions with Base b | |
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| Re-expressing Data | |
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| Equation Solving and Modeling | |
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| Solving Exponential Equations | |
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| Solving Logarithmic Equations | |
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| Orders of Magnitude and Logarithmic Models | |
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| Newton's Law of Cooling | |
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| Logarithmic Re-expression | |
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| Mathematics of Finance | |
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| Interest Compounded Annually | |
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| Interest Compounded k Times per Year | |
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| Interest Compounded Continuously | |
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| Annual Percentage Yield | |
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| Annuities-Future Value | |
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| Loans and Mortgages-Present Value | |
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| Key Ideas | |
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| Review Exercises | |
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| Chapter Project | |
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| Trigonometric Functions | |
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| Angles and Their Measures | |
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| The Problem of Angular Measure | |
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| Degrees and Radians | |
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| Circular Arc Length | |
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| Angular and Linear Motion | |
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| Trigonometric Functions of Acute Angles | |
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| Right Triangle Trigonometry | |
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| Two Famous Triangles | |
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| Evaluating Trigonometric Functions with a Calculator | |
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| Common Calculator Errors When Evaluating Trig Functions | |
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| Applications of Right Triangle Trigonometry | |
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| Trigonometry Extended: The Circular Functions | |
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| Trigonometric Functions of Any Angle | |
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| Trigonometric Functions of Real Numbers | |
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| Periodic Functions | |
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| The 16-Point Unit Cricle | |
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| Graphs of Sine and Cosine: Sinusoids | |
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| The Basic Waves Revisited | |
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| Sinusoids and Transformations | |
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| Modeling Periodic Behavior with Sinusoids | |
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| Graphs of Tangent, Cotangent, Secant, and Cosecant | |
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| The Tangent Function | |
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| The Cotangent Function | |
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| The Secant Function | |
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| The Cosecant Function | |
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| Graphs of Composite Trigonometric Functions | |
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| Combining Trigonometric and Algebraic Functions | |
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| Sums and Differences of Sinusoids | |
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| Damped Oscillation | |
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| Inverse Trigonometric Functions | |
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| Inverse Sine Function | |
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| Inverse Cosine and Tangent Functions | |
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| Composing Trigonometric and Inverse Trigonometric Functions | |
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| Applications of Inverse Trigonometric Functions | |
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| Solving Problems with Trigonometry | |
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| More Right Triangle Problems | |
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| Simple Harmonic Motion | |
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| Key Ideas | |
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| Review Exercises | |
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| Chapter Project | |
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| Analytic Trigonometry | |
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| Fundamental Identities | |
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| Identities | |
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| Basic Trigonometric Identities | |
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| Pythagorean Identities | |
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| Cofunction Identities | |
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| Odd-Even Identities | |
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| Simplifying Trigonometric Expressions | |
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| Solving Trigonometric Equations | |
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| Proving Trigonometric Identities | |
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| A Proof Strategy | |
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| Proving Identities | |
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| Disproving Non-Identities | |
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| Identities in Calculus | |
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| Sum and Difference Identities | |
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| Cosine of a Difference | |
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| Cosine of a Sum | |
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| Sine of a Difference or Sum | |
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| Tangent of a Difference or Sum | |
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| Verifying a Sinusoid Algebraically | |
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| Multiple-Angle Identities | |
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| Double-Angle Identities | |
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| Power-Reducing Identities | |
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| Half-Angle Identities | |
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| Solving Trigonometric Equations | |
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| The Law of Sines | |
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| Deriving the Law of Sines | |
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| Solving Triangles (AAS, ASA) | |
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| The Ambiguous Case (SSA) | |
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| Applications | |
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| The Law of Cosines | |
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| Deriving the Law of Cosines | |
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| Solving Triangles (SAS, SSS) | |
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| Triangle Area and Heron's Formula | |
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| Applications | |
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| Math at Work | |
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| Key Ideas | |
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| Review Exercises | |
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| Chapter Project | |
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| Applications of Trigonometry | |
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| Vectors in the Plane | |
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| Two-Dimensional Vectors | |
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| Vector Operations | |
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| Unit Vectors | |
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| Direction Angles | |
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| Applications of Vectors | |
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| Dot Product of Vectors | |
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| The Dot Product | |
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| Angle Between Vectors | |
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| Projecting One Vector onto Another | |
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| Work | |
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| Parametric Equations and Motion | |
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| Parametric Equations | |
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| Parametric Curves | |
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| Eliminating the Parameter | |
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| Lines and Line Segments | |
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| Simulating Motion with a Grapher | |
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| Polar Coordinates | |
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| Polar Coordinate System | |
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| Coordinate Conversion | |
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| Equation Conversion | |
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| Finding Distance Using Polar Coordinates | |
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| Graphs of Polar Equations | |
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| Polar Curves and Parametric Curves | |
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| Symmetry | |
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| Analyzing Polar Graphs | |
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| Rose Curves | |
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| Limacon Curves | |
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| Other Polar Curves | |
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| De Moivre's Theorem and nth Roots | |
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| The Complex Plane | |
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| Trigonometric Form of Complex Numbers | |
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| Multiplication and Division of Complex Numbers | |
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| Powers of Complex Numbers | |
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| Roots of Complex Numbers | |
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| Key Ideas | |
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| Review Exercises | |
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| Chapter Project | |
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| Systems and Matrices | |
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| Solving Systems of Two Equations | |
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| The Method of Substitution | |
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| Solving Systems Graphically | |
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| The Method of Elimination | |
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| Applications | |
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| Matrix Algebra | |
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| Matrices | |
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| Matrix Addition and Subtraction | |
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| Matrix Multiplication | |
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| Identity and Inverse Matrices | |
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| Determinant of a Square Matrix | |
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| Applications | |
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| Multivariate Linear Systems and Row Operations | |
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| Triangular Form for linear Systems | |
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| Gaussian Elimination | |
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| Elementary Row Operations and Row Echelon Form | |
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| Reduced Row Echelon Form | |
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| Solving Systems with Inverse Matrices | |
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| Applications | |
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| Partial Fractions | |
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| Partial Fraction Decomposition | |
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| Denominators with Linear Factors | |
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| Denominators with Irreducible Quadratic Factors | |
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| Applications | |
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| Systems of Inequalities in Two Variables | |
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| Graph of an Inequality | |
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| Systems of Inequalities | |
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| Linear Programming | |
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| Math at Work | |
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| Key Ideas | |
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| Review Exercises | |
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| Chapter Project | |
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| Analytic Geometry in Two and Three Dimensions | |
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| Conic Sections and Parabolas | |
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| Conic Sections | |
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| Geometry of a Parabola | |
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| Translations of Parabolas | |
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| Reflective Property of a Parabola | |
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| Ellipses | |
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| Geometry of an Ellipse | |
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| Translations of Ellipses | |
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| Orbits and Eccentricity | |
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| Reflective Property of an Ellipse | |
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| Hyperbolas | |
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| Geometry of a Hyperbola | |
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| Translations of Hyperbolas | |
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| Eccentricity and Orbits | |
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| Reflective Property of a Hyperbola | |
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| Long-Range Navigation | |
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| Translation and Rotation of Axes | |
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| Second-Degree Equations in Two Variables | |
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| Translating Axes versus Translating Graphs | |
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| Rotation of Axes | |
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| Discriminant Test | |
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| Polar Equations of Conics | |
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| Eccentricity Revisited | |
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| Writing Polar Equations for Conics | |
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| Analyzing Polar Equations of Conics | |
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| Orbits Revisited | |
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| Three-Dimensional Cartesian Coordinate System | |
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| Three-Dimensional Cartesian Coordinates | |
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| Distance and Midpoint Formulas | |
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| Equation of a Sphere | |
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| Planes and Other Surfaces | |
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| Vectors in Space | |
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| Lines in Space | |
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| Key Ideas | |
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| Review Exercises | |
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| Chapter Project | |
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| Discrete Mathematics | |
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| Basic Combinatorics | |
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| Discrete Versus Continuous | |
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| The Importance of Counting | |
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| The Multiplication Principle of Counting | |
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| Permutations | |
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| Combinations | |
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| Subsets of an n-Set | |
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| The Binomial Theorem | |
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| Powers of Binomials | |
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| Pascal's Triangle | |
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| The Binomial Theorem | |
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| Factorial Identities | |
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| Probability | |
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| Sample Spaces and Probability Functions | |
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| Determining Probabilities | |
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| Venn Diagrams and Tree Diagrams | |
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| Conditional Probability | |
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| Binomial Distributions | |
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| Sequences | |
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| Infinite Sequences | |
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| Limits of Infinite Sequences | |
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| Arithmetic and Geometric Sequences | |
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| Sequences and Graphing Calculators | |
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| Series | |
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| Summation Notation | |
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| Sums of Arithmetic and Geometric Sequences | |
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| Infinite Series | |
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| Convergence of Geometric Series | |
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| Mathematical Induction | |
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| The Tower of Hanoi Problem | |
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| Principle of Mathematical Induction | |
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| Induction and Deduction | |
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| Statistics and Data (Graphical) | |
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| Statistics | |
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| Displaying Categorical Data | |
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| Stemplots | |
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| Frequency Tables | |
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| Histograms | |
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| Time Plots | |
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| Statistics and Data (Algebraic) | |
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| Parameters and Statistics | |
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| Mean, Median, and Mode | |
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| The Five-Number Summary | |
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| Boxplots | |
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| Variance and Standard Deviation | |
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| Normal Distributions | |
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| Math at Work | |
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| Key Ideas | |
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| Review Exercises | |
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| Chapter Project | |
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| An Introduction to Calculus: Limits, Derivatives, and Integrals | |
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| Limits and Motion: The Tangent Problem | |
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| Average Velocity | |
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| Instantaneous Velocity | |
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| Limits Revisited | |
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| The Connection to Tangent Lines | |
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| The Derivative | |
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| Limits and Motion: The Area Problem | |
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| Distance from a Constant Velocity | |
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| Distance from a Changing Velocity | |
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| Limits at Infinity | |
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| The Connection to Areas | |
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| The Definite Integral | |
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| More on Limits | |
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| A Little History | |
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| Defining a Limit Informally | |
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| Properties of Limits | |
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| Limits of Continuous Functions | |
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| One-sided and Two-sided Limits | |
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| Limits Involving Infinity | |
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| Numerical Derivatives and Integrals | |
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| Derivatives on a Calculator | |
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| Definite Integrals on a Calculator | |
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| Computing a Derivative from Data | |
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| Computing a Definite Integral from Data | |
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| Key Ideas | |
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| Review Exercises | |
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| Chapter Project | |
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| Algebra Review | |
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| Radicals and Rational Exponents | |
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| Radicals | |
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| Simplifying Radical Expressions | |
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| Rationalizing the Denominator | |
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| Rational Exponents | |
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| Polynomials and Factoring | |
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| Adding, Subtracting, and Multiplying Polynomials | |
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| Special Products | |
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| Factoring Polynomials Using Special Products | |
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| Factoring Trinomials | |
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| Factoring by Grouping | |
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| Fractional Expressions | |
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| Domain of an Algebraic Expression | |
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| Reducing Rational Expressions | |
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| Operations with Rational Expressions | |
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| Compound Rational Expressions | |
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| Key Formulas | |
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| Formulas from Algebra | |
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| Exponents | |
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| Radicals and Rational Expressions | |
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| Special Products | |
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| Factoring Polynomials | |
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| Inequalities | |
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| Quadratic Formula | |
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| Logarithms | |
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| Determinants | |
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| Arithmetic Sequences and Series | |
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| Geometric Sequences and Series | |
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| Factorial | |
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| Binomial Coefficient | |
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| Binomial Theorem | |
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| Formulas from Geometry | |
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| Triangle | |
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| Trapezoid | |
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| Circle | |
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| Sector of Circle | |
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| Right Circular Cone | |
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| Right Circular Cylinder | |
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| Right Triangle | |
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| Parallelogram | |
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| Circular Ring | |
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| Ellipse | |
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| Cone | |
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| Sphere | |
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| Formulas from Trigonometry | |
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| Angular Measure | |
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| Reciprocal Identities | |
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| Quotient Identities | |
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| Pythagorean Identities | |
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| Odd-Even Identities | |
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| Sum and Difference Identities | |
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| Cofunction Identities | |
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| Double-Angle Identities | |
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| Power-Reducing Identities | |
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| Half-Angle Identities | |
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| Triangles | |
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| Trigonometric Form of a Complex Number | |
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| De Moivre's Theorem | |
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| Formulas from Analytic Geometry | |
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| Basic Formulas | |
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| Equations of a Line | |
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| Equation of a Circle | |
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| Parabolas with Vertex (h, k) | |
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| Ellipses with Center (h, k) and a > b > 0 | |
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| Hyperbolas with Center (h, k) | |
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| Gallery of Basic Functions | |
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| Logic | |
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| Logic: An Introduction | |
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| Statements | |
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| Compound Statements | |
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| Conditionals and Biconditionals | |
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| Forms of Statements | |
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| Valid Reasoning | |
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| Glossary | |
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| Selected Answers | |
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| Applications Index | |
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| Index | |