Get the background you need for future courses and discover the usefulness of mathematical concepts in analyzing and solving problems with FINITE MATHEMATICS, 7th Edition. The author clearly explains concepts, and the computations demonstrate enough detail to allow you to follow-and learn-steps in the problem-solving process. Hundreds of examples, many based on real-world data, illustrate the practical applications of mathematics. The textbook also includes technology guidelines to help you successfully use graphing calculators and Microsoft Excel to solve selected exercises. This Enhanced Edition includes instant access to Enhanced WebAssign, the most widely-used and reliable homework system. Enhanced WebAssign presents over a thousand problems, links to relevant textbook sections, video examples, problem-specific tutorials, and more, that help students grasp the concepts needed to succeed in this course. As an added bonus, the Start Smart Guide has been bound into this text. This guide contains instructions to help students learn the basics of WebAssign quickly.
Author(s): Howard L. Rolf
Edition: 7th Edition
Publisher: Brooks Cole
Year: 2010
Language: English
Pages: 924
Tags: Математика;Дискретная математика;
Front Cover......Page 1
Title Page......Page 2
Copyright......Page 3
Contents......Page 6
1 FUNCTIONS AND LINES......Page 22
1.1 Functions......Page 23
Using Your TI-83/84......Page 32
Using EXCEL......Page 33
1.2 Graphs and Lines......Page 35
Using Your TI-83/84: Graphs of Lines and Evaluating Points on a Line......Page 55
Using EXCEL......Page 57
1.3 Mathematical Models and Applications of Linear Functions......Page 59
Using Your TI-83/84: Intersection of Lines......Page 78
Using EXCEL......Page 79
Important Terms in Chapter 1......Page 81
Review Exercises for Chapter 1......Page 82
2 LINEAR SYSTEMS......Page 86
2.1 Systems of Two Equations......Page 87
Using EXCEL......Page 102
2.2 Systems with Three Variables: An Introduction to a Matrix Representation of a Linear System of Equations......Page 103
Using Your TI-83/84: Solving a System of Equations Using Row Operations......Page 124
Using EXCEL: Solving Systems of Equations Using Row Operations......Page 126
2.3 Gauss-Jordan Method for General Systems of Equations......Page 128
Using Your TI-83/84: Obtaining the Reduced Echelon Form of a Matrix......Page 147
Using EXCEL: General Procedure for Pivoting......Page 149
2.4 Matrix Operations......Page 150
Using EXCEL: Matrix Addition and Scalar Multiplication......Page 161
2.5 Multiplication of Matrices......Page 162
Using Your TI-83/84: Matrix Multiplication......Page 179
2.6 The Inverse of a Matrix......Page 180
Using Your TI-83/84: The Inverse of a Matrix......Page 195
Using EXCEL......Page 196
2.7 Leontief Input–Output Model in Economics......Page 197
Using Your TI-83/84......Page 209
Using EXCEL......Page 210
2.8 Linear Regression......Page 211
Using Your TI-83/84: Regression Lines......Page 220
Using EXCEL: To Draw and Find a Linear Regression Line......Page 221
Review Exercises for Chapter 2......Page 223
3 LINEAR PROGRAMMING......Page 226
3.1 Linear Inequalities in Two Variables......Page 227
Procedure for Graphing a Linear Inequality......Page 230
3.1 EXERCISES......Page 232
3.2 Solutions of Systems of Inequalities: A Geometric Picture......Page 234
Using Your TI-83/84: Finding Corner Points of a Feasible Region......Page 242
Using EXCEL......Page 244
3.3 Linear Programming: A Geometric Approach......Page 246
Using Your TI-83/84: Evaluate the Objective Function......Page 269
3.4 Applications......Page 271
Review Exercises for Chapter 3......Page 279
4 LINEAR PROGRAMMING: THE SIMPLEX METHOD......Page 282
Standard Maximum......Page 283
The Geometric Form of the Problem......Page 284
Slack Variables......Page 285
Simplex Tableau......Page 288
4.1 EXERCISES......Page 290
Explorations......Page 293
4.2 The Simplex Method......Page 294
Using Your TI-83/84: A Program for the Simplex Method......Page 314
Using EXCEL......Page 316
Dual Problem......Page 320
Solve the Minimization Problem Using the Dual Problem......Page 323
4.3 EXERCISES......Page 326
4.4 Mixed Constraints......Page 328
Using EXCEL......Page 350
Multiple Solutions......Page 351
Unbounded Solutions......Page 354
No Feasible Solution......Page 355
4.5 EXERCISES......Page 357
4.6 What’s Happening in the Simplex Method? (Optional)......Page 360
4.6 EXERCISES......Page 365
Explorations......Page 367
4.7 Sensitivity Analysis......Page 368
Review Exercises for Chapter 4......Page 379
5 MATHEMATICS OF FINANCE......Page 384
Simple Interest......Page 385
Future Value......Page 387
Treasury Bills—Simple Discount......Page 388
5.1 EXERCISES......Page 390
Explorations......Page 392
5.2 Compound Interest......Page 393
Using Your TI-83/84: Making a Table......Page 407
Using EXCEL......Page 408
5.3 Annuities and Sinking Funds......Page 409
Using Your TI-83/84: Growth of Annuities......Page 418
Using EXCEL......Page 419
5.4 Present Value of an Annuity and Amortization......Page 420
Using Your TI-83/84: Monthly Loan Payments......Page 439
Important Terms in Chapter 5......Page 440
Review Exercises for Chapter 5......Page 441
6 SETS AND COUNTING......Page 444
6.1 Sets......Page 445
Set-Builder Notation......Page 446
Subset......Page 447
The Union of Two Sets......Page 448
The Intersection of Two Sets......Page 449
Complement......Page 450
6.1 EXERCISES......Page 451
Number of Elements in a Subset......Page 453
Venn Diagrams Using Three Sets......Page 455
6.2 EXERCISES......Page 457
Explorations......Page 460
6.3 Basic Counting Principles......Page 461
Tree Diagrams......Page 462
Multiplication Rule......Page 463
Addition Rule for Counting Elements in Disjoint Sets......Page 466
6.3 EXERCISES......Page 468
Explorations......Page 472
6.4 Permutations......Page 473
6.5 Combinations......Page 483
Using Your TI-83/84: Combinations......Page 498
6.6 A Mixture of Counting Problems......Page 499
6.6 EXERCISES......Page 503
6.7 Partitions (Optional)......Page 505
Review Exercises for Chapter 6......Page 512
7 PROBABILITY......Page 516
Terminology......Page 517
Empirical Probability......Page 518
Properties of Probability......Page 521
Probability Assignments......Page 523
A Visual Model of Probability......Page 526
7.1 EXERCISES......Page 527
7.2 Equally Likely Events......Page 530
7.2 EXERCISES......Page 536
7.3 Compound Events: Union, Intersection, and Complement......Page 540
Keys to Recognizing Compound Events......Page 541
Probability of E'......Page 542
Mutually Exclusive Events......Page 546
7.3 EXERCISES......Page 549
Explorations......Page 552
Conditional Probability......Page 553
Multiplication Rule......Page 558
7.4 EXERCISES......Page 562
Explorations......Page 567
Independent Events......Page 568
Multiplication Rule for Independent Events......Page 573
Mutually Exclusive and Independent Events......Page 578
7.5 EXERCISES......Page 580
Explorations......Page 584
7.6 Bayes’ Rule......Page 585
An Application Using a Tree Diagram......Page 592
7.6 EXERCISES......Page 595
Explorations......Page 598
7.7 Markov Chains......Page 600
Review Exercises for Chapter 7......Page 614
8 STATISTICS......Page 618
8.1 Frequency Distributions......Page 619
Using Your TI-83/84: Histograms......Page 634
Using EXCEL: Histograms and Pie Charts......Page 636
8.2 Measures of Central Tendency......Page 638
Using Your TI-83/84: Calculating the Mean and Median......Page 649
Using EXCEL: Calculate the Mean and Median......Page 650
8.3 Measures of Dispersion: Range, Variance, and Standard Deviation......Page 651
Using Your TI-83/84......Page 666
Using EXCEL: Measures of Dispersion......Page 668
Random Variables......Page 669
Probability Distribution of a Discrete Random Variable......Page 671
8.4 EXERCISES......Page 674
Explorations......Page 678
Expected Value......Page 679
Variance and Standard Deviation of a Random Variable......Page 682
8.5 EXERCISES......Page 685
Explorations......Page 687
8.6 Bernoulli Experiments and Binomial Distribution......Page 689
Using Your TI-83/84: Binomial Probability Distribution......Page 702
8.7 Normal Distribution......Page 704
Using Your TI-83/84: Area Under the Normal Curve......Page 733
8.8 Estimating Bounds on a Proportion......Page 734
Important Terms in Chapter 8......Page 748
Review Exercises for Chapter 8......Page 749
9 GAME THEORY......Page 752
9.1 Two-Person Games......Page 753
Strictly Determined Games......Page 754
9.1 EXERCISES......Page 759
9.2 Mixed-Strategy Games......Page 761
Review Exercises for Chapter 9......Page 771
10 LOGIC......Page 774
Notation......Page 775
Conjunction......Page 776
Disjunction......Page 777
Negation......Page 778
10.1 EXERCISES......Page 780
Conditional......Page 781
Converse, Inverse, and Contrapositive of a Conditional......Page 783
Biconditional......Page 784
10.2 EXERCISES......Page 786
10.3 Equivalent Statements......Page 787
10.3 EXERCISES......Page 788
10.4 Valid Arguments......Page 789
Review Exercises for Chapter 10......Page 796
A.1 Properties of Real Numbers......Page 798
A.2 Solving Linear Equations......Page 801
A.3 Coordinate Systems......Page 805
A.4 Linear Inequalities and Interval Notation......Page 808
Important Terms in Appendix A......Page 814
Arithmetic Operations......Page 816
Graphing......Page 817
Finding the Intersection of Two Graphs......Page 818
Constructing a Table......Page 819
Matrices......Page 820
Statistics......Page 822
C: USING EXCEL......Page 826
ANSWERS TO SELECTED ODD-NUMBERED EXERCISES......Page 828
INDEX......Page 886
CONTENTS......Page 892
Login to WebAssign......Page 894
Logout......Page 896
Using Access Codes......Page 897
Customizing Your Home Page......Page 899
Changing Your Email Address......Page 900
Accessing an Assignment......Page 901
Using the Assignment Page......Page 903
Numerical Questions......Page 906
Numerical Questions with Units......Page 907
Numerical Questions with Significant Figures......Page 908
Math Notation: Using the MathPad......Page 909
Math Notation: Using the Keyboard......Page 910
Introduction......Page 911
Drawing Graph Objects......Page 912
Selecting Graph Objects......Page 913
Using Fractions or Decimals as Coordinates......Page 914
Specifying a Region with a Fill for Inequalities......Page 915
Erasing Everything on Your Graph......Page 916
Example: Graphing Question......Page 917
Communication......Page 918
GRADES......Page 919
TECHNICAL TIPS......Page 920
