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| Algebra Review | |
| Real Numbers | |
| Exponents and Radicals | |
| Multiplying and Factoring Algebraic Equations | |
| Rational Expressions | |
| Solving Polynomial Equations | |
| Solving Miscellaneous Equations | |
| Functions and Linear Models | |
| Functions from the Numerical and Algebraic Viewpoints | |
| Functions from the Graphical Viewpoint | |
| Linear Functions | |
| Linear Models | |
| Linear Regression | |
| Key Concepts | |
| Review Exercises | |
| Case Study: Modeling Spending on Internet Advertising | |
| Technology Guides | |
| Optional Internet Topic: New Functions from Old: Scaled and Shifted Functions | |
| Systems of Linear Equations and Matrices | |
| Systems of Two Equations in Two Unknowns | |
| Using Matrices to Solve Systems of Equations | |
| Applications of Systems of Linear Equations | |
| Key Concepts | |
| Review Exercises | |
| Case Study: The Impact of Regulating Sulfur Emissions | |
| Technology Guides | |
| Matrix Algebra and Applications | |
| Matrix Addition and Scalar Multiplication | |
| Matrix Multiplication | |
| Matrix Inversion | |
| Matrices in Practice: Game Theory | |
| Matrices in Practice: Input-Output Models | |
| Key Concepts | |
| Review Exercises | |
| Case Study: The Japanese Economy | |
| Technology Guides | |
| Linear Programming | |
| Graphing Linear Inequalities | |
| Solving Linear Programming Problems Graphically | |
| The Simplex Method: Solving Standard Maximization Problems | |
| The Simplex Method: Solving General Linear Programming Problems | |
| The Simplex Method and Duality (Optional) | |
| Key Concepts | |
| Review Exercises | |
| Case Study: Airline Scheduling | |
| Technology Guides | |
| The Mathematics of Finance | |
| Simple Interest | |
| Compound Interest | |
| Annuities, Loans, and Bonds | |
| Key Concepts | |
| Review Exercises | |
| Case Study: Saving for College | |
| Technology Guides | |
| Sets and Counting | |
| Sets and Set Operations | |
| Cardinality | |
| The Addition and Multiplication Principles | |
| Permutations and Combinations | |
| Key Concepts | |
| Review Exercises | |
| Case Study: Designing a Puzzle | |
| Technology Guides | |
| Probability | |
| Sample Spaces and Events | |
| Estimated Probability | |
| Theoretical Probability and Probability Distributions | |
| Probability and Counting Techniques (optional) | |
| Conditional Probability and Independence | |
| Bayes' Theorem and Applications | |
| Probability in Practice: Markov Systems | |
| Key Concepts | |
| Review Exercises | |
| Case Study: The Monty Hall Problem | |
| Technology Guides | |
| Random Variables and Statistics | |
| Random Variables and Distributions | |
| Bernoulli Trials and Binomial Random Variables | |
| Measures of Central Tendency | |
| Measures of Dispersion | |
| Normal Distributions | |
| Key Concepts | |
| Review Exercises | |
| Case Study: Spotting Tax Fraud with Benford's Law | |
| Technology Guides | |
| Optional Internet Topics: Sampling Distributions and the Central Limit Theorem | |
| Confidence Intervals | |
| Hypothesis Testing | |
| Nonlinear Models | |
| Quadratic Functions and Models | |
| Exponential Functions and Models | |
| Logarithmic Functions and Models | |
| Logistic Functions and Models | |
| Key Concepts | |
| Review Exercises | |
| Case Study: Checking up on Malthus | |
| Technology Guides | |
| Optional Internet Topics: Inverse Functions | |
| Using and Deriving Algebraic Properties of Logarithms | |
| Introduction to the Derivative | |
| Limits: Numerical and Graphical Approaches | |
| Limits and Continuity | |
| Limits: Algebraic Approach | |
| Average Rate of Change | |
| Derivatives: Numerical and Graphical Viewpoints | |
| Derivatives: Algebraic Viewpoint | |
| Derivatives of Powers, Sums, and Constant Multiples | |
| A First Application: Marginal Analysis | |
| Key Concepts | |
| Review Exercises | |
| Case Study: Reducing Sulfur Emissions | |
| Technology Guides | |
| Optional Internet Topics: Sketching the Graph of the Derivative | |
| Proof of the Power Rule | |
| Continuity and Differentiability | |
| Techniques of Differentiation | |
| The Product and Quotient Rules | |
| The Chain Rule | |
| Derivatives of Logarithmic and Exponential Functions | |
| Implicit Differentiation | |
| Key Concepts | |
| Review Exercises | |
| Case Study: Projecting Market Growth | |
| Technology Guides | |
| Optional Internet Topic: Linear Approximation and Error Estimation | |
| Applications of the Derivative | |
| Maxima and Minima | |
| Applications of Maxima and Minima | |
| The Second Derivative and Analyzing Graphs | |
| R | |
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