| Chapter 1. | Linear Functions | |
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1. Slopes and Equations of Lines | |
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2. Linear Functions and Applications | |
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3. The Least Squares Line |
| Chapter 2. | Systems of Linear Equations and Matrices | |
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1. Solution of Linear Systems by the Echelon Method | |
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2. Solution of Linear Systems by the Gauss-Jordan Method | |
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3. Addition and Subtraction of Matrices | |
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4. Multiplication of Matrices | |
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5. Matrix Inverses | |
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6. Input-Output Models |
| Chapter 3. | Linear Programming: The Graphical Method | |
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1. Graphing Linear Inequalities | |
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2. Solving Linear Programming Problems Graphically | |
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3. Applications of Linear Programming |
| Chapter 4. | Linear Programming: The Simplex Method | |
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1. Slack Variables and the Pivot | |
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2. Maximization Problems | |
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3. Minimization Problems; Duality | |
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4. Nonstandard Problems |
| Chapter 5. | Mathematics of Finance | |
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1. Simple and Compound Interest | |
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2. Future Value of an Annuity | |
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3. Present Value of an Annuity; Amortization |
| Chapter 6. | Logic | |
| 1. Statements | ||
| 2. Truth Tables and Equivalent Statements | ||
| 3. The Conditional and Circuits | ||
| 4. More on the Conditional | ||
| 5. Analyzing Arguments and Proofs | ||
| 6. Analyzing Arguments with Quantifiers |
| Chapter 7. | Sets and Probability | |
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1. Sets | |
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2. Applications of Venn Diagrams | |
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3. Introduction to Probability | |
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4. Basic Concepts of Probability | |
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5. Conditional Probability; Independent Events | |
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6. Bayes' Theorem |
| Chapter 8. | Counting Principles; Further Probability Topics | |
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1. The Multiplication Principle; Permutations | |
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2. Combinations | |
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3. Probability Applications of Counting Principles | |
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4. Binomial Probability | |
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5. Probability Distributions; Expected Value |
| Chapter 9. | Statistics | |
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1. Frequency Distributions; Measures of Central Tendency | |
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2. Measures of Variation | |
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3. The Normal Distribution | |
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4. Normal Approximation to the Binomial Distribution |
| Chapter 10. | Nonlinear Functions | |
| 1. Properties of Functions | ||
| 2. Quadratic Functions; Translation and Reflection | ||
| 3. Polynomial and Rational Functions | ||
| 4. Exponential Functions | ||
| 5. Logarithmic Functions | ||
| 6. Applications: Growth and Decay; Mathematics of Finance |
| Chapter 11. | The Derivative | |
| 1. Limits | ||
| 2. Continuity | ||
| 3. Rates of Change | ||
| 4. Definition of the Derivative | ||
| 5. Graphical Differentiation |
| Chapter 12. | Calculating the Derivative | |
| 1. Techniques for Finding Derivatives | ||
| 2. Derivatives of Products and Quotients | ||
| 3. The Chain Rule | ||
| 4. Derivatives of Exponential Functions | ||
| 5. Derivatives of Logarithmic Functions |
| Chapter 13. | Graphs and the Derivative | |
| 1. Increasing and Decreasing Functions | ||
| 2. Relative Extrema | ||
| 3. Higher Derivatives, Concavity, and the Second Derivative Test | ||
| 4. Curve Sketching |
| Chapter 14. | Applications of the Derivative | |
| 1. Absolute Extrema | ||
| 2. Applications of Extrema | ||
| 3. Further Business Applications: Economic Lot Size, Economic Order Quantity; Elasticity of Demand | ||
| 4. Implicit Differentiation | ||
| 5. Related Rates | ||
| 6. Differentials: Linear Approximation |
| Chapter 15. | Integration | |
| 1. Antiderivatives | ||
| 2. Substitution | ||
| 3. Area and the Definite Integral | ||
| 4. The Fundamental Theorem of Calculus | ||
| 5. The Area Between Two Curves | ||
| 6. Numerical Integration |
| Chapter 16. | Further Techniques and Applications of Integration | |
| 1. Integration by Parts | ||
| 2. Volume and Average Value | ||
| 3. Continuous Money Flow | ||
| 4. Improper Integrals | ||
| 5. Solutions of Elementary and Separable Differential Equations |
| Chapter 17. | Multivariable Calculus | |
| 1. Functions of Several Variables | ||
| 2. Partial Derivatives | ||
| 3. Maxima and Minima | ||
| 4. Lagrange Multipliers | ||
| 5. Total Differentials and Approximations | ||
| 6. Double Integrals |
| Chapter 18. | Probability and Calculus | |
| 0. Continuous Probability Models | ||
| 0. Expected Value and Variance of Continuous Random Variables | ||
| 0. Special Probability Density Functions |
| Chapter M. | Miscellaneous | |
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1. Markov Chains: Transition matrix | |
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2. Markov Chains: Initial probability matrix | |
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3. Markov Chains: Stable distribution for a transition matrix | |
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4. Markov Chains: Examples Courtesy of Lavon Page at NCSU |
| Chapter R. | Reviews | |
| 0. Review for Final Exam |