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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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