Chapter 1 | Linear Equations | 1 |
1.1 | Rectangular Coordinates; Lines | 2 |
1.2 | Pairs of Lines | 19 |
1.3 | Applications: Prediction; Break-Even Point; Mixture Problems; Economics | 26 |
1.4 | Scatter Diagrams; Linear Curve Fitting | 35 |
| Chapter Review | 42 |
Chapter 2 | Systems of Linear Equations; Matrices | 48 |
2.1 | Systems of Linear Equations: Substitution; Elimination | 49 |
2.2 | Systems of Linear Equations: Matrix Method | 65 |
2.3 | Systems of m Linear Equations Containing n Variables | 82 |
2.4 | Matrix Algebra | 93 |
2.5 | Multiplication of Matrices | 106 |
2.6 | The Inverse of a Matrix | 117 |
2.7 | Applications: Leontief Model; Cryptography; Accounting; The Method of Least Squares | 128 |
| Chapter Review | 150 |
Chapter 3 | Linear Programming: Geometric Approach | 158 |
3.1 | Systems of Linear Inequalities | 159 |
3.2 | A Geometric Approach to Linear Programming Problems | 171 |
3.3 | Applications | 179 |
| Chapter Review | 186 |
Chapter 4 | Linear Programming: Simplex Method | 194 |
4.1 | The Simplex Tableau; Pivoting | 195 |
4.2 | The Simplex Method: Solving Maximum Problems in Standard Form | 208 |
4.3 | Solving Minimum Problems in Standard Form Using the Duality Principle | 228 |
4.4 | The Simplex Method with Mixed Constraints | 238 |
| Chapter Review | 252 |
Chapter 5 | Finance | 261 |
5.1 | Interest | 262 |
5.2 | Compound Interest | 269 |
5.3 | Annuities; Sinking Funds | 279 |
5.4 | Present Value of an Annuity; Amortization | 291 |
5.5 | Annuities and Amortization Using Recursive Sequences | 301 |
5.6 | Applications: Leasing; Capital Expenditure; Bonds | 305 |
| Chapter Review | 310 |
Chapter 6 | Sets; Counting Techniques | 316 |
6.1 | Sets | 317 |
6.2 | The Number of Elements in a Set | 326 |
6.3 | The Multiplication Principle | 332 |
6.4 | Permutations | 336 |
6.5 | Combinations | 343 |
6.6 | The Binomial Theorem | 351 |
| Chapter Review | 357 |
Chapter 7 | Probability | 364 |
7.1 | Sample Spaces and the Assignment of Probabilities | 365 |
7.2 | Properties of the Probability of an Event | 376 |
7.3 | Probability Problems Using Counting Techniques | 386 |
7.4 | Conditional Probability | 392 |
7.5 | Independent Events | 403 |
| Chapter Review | 412 |
Chapter 8 | Additional Probability Topics | 420 |
8.1 | Bayes' Formula | 421 |
8.2 | The Binomial Probability Model | 432 |
8.3 | Expected Value | 443 |
8.4 | Applications | 451 |
8.5 | Random Variables | 457 |
| Chapter Review | 461 |
Chapter 9 | Statistics | 469 |
9.1 | Introduction to Statistics: Data and Sampling | 470 |
9.2 | Representing Data Graphically: Bar Graphs; Pie Charts | 473 |
9.3 | Organization of Data | 480 |
9.4 | Measures of Central Tendency | 494 |
9.5 | Measures of Dispersion | 504 |
9.6 | The Normal Distribution | 514 |
| Chapter Review | 525 |
Chapter 10 | Markov Chains; Games | 536 |
10.1 | Markov Chains and Transition Matrices | 537 |
10.2 | Regular Markov Chains | 546 |
10.3 | Absorbing Markov Chains | 557 |
10.4 | Two-Person Games | 567 |
10.5 | Mixed Strategies | 571 |
10.6 | Optimal Strategy in Two-Person Zero-Sum Games with 2 x 2 Matrices | 574 |
| Chapter Review | 581 |
Chapter 11 | Logic | 586 |
11.1 | Propositions | 587 |
11.2 | Truth Tables | 593 |
11.3 | Implications; The Biconditional Connective; Tautologies | 601 |
11.4 | Arguments | 607 |
11.5 | Logic Circuits | 612 |
| Chapter Review | 617 |
Appendix A | Review | 622 |
A.1 | Real Numbers | 622 |
A.2 | Algebra Review | 636 |
A.3 | Exponents and Logarithms | 645 |
A.4 | Recursively Defined Sequences; Geometric Sequences | 649 |
Appendix B | Using Lindo to Solve Linear Programming Problems | 655 |
Appendix C | Graphing Utilities | 662 |
C.1 | The Viewing Rectangle | 662 |
C.2 | Using a Graphing Utility to Graph Equations | 664 |
C.3 | Square Screens | 668 |
C.4 | Using a Graphing Utility to Graph Inequalities | 669 |
| Answers to Odd-Numbered Problems | 1 |
| Photo Credits | 1 |
| Index | 1 |