Finite Mathematics (with Digital Video Companion)

by Rolf, Howard L.

• ISBN13: 9780534465391
• ISBN10: 0534465390
• Edition: 6th
• Format: Hardcover
• Copyright: 2004-04-01
• Publisher: Brooks Cole

Summary

The new edition of Rolf's FINITE MATHEMATICS relies on a rich array of examples and a student-friendly approach to clearly illustrate the utility of mathematical concepts in analyzing and solving problems. In addition, the Sixth Edition continues to offer flexible technology integration with optional graphing calculator problems and Excel applications for instructors who wish to bring technology into the course.

Table of Contents

1 FUNCTIONS AND LINES	1	(58)
1.1 Functions	2	(12)
Using Your TI-83: Basics	11	(1)
Using EXCEL: Basics	12	(2)
1.2 Graphs and Lines	14	(23)
Using Your TI-83: Graphs of Lines and Evaluating Points on a Line	34	(1)
Using EXCEL: Graph and Equation of a Line Through Two Points	35	(2)
1.3 Mathematical Models and Applications of Linear Functions	37	(22)
Using Your TI-83: Intersection of Lines	52	(1)
Using EXCEL: Goal Seek	53	(2)
Important Terms	55	(1)
Review Exercises	55	(4)
2 LINEAR SYSTEMS	59	(136)
2.1 Systems of Two Equations	60	(15)
Using EXCEL	75	(1)
2.2 Systems with Three Variables: An Introduction to a Matrix Representation of a Linear System of Equations	75	(24)
Using Your TI-83: Solving a System of Equations Using Row Operations	95	(2)
Using EXCEL: Solving Systems of Equations Using Row Operations	97	(2)
2.3 Gauss-Jordan Method for General Systems of Equations	99	(21)
Using Your TI-83: Obtaining the Reduced Echelon Form of a Matrix	117	(2)
Using EXCEL: General Procedure for Pivoting	119	(1)
2.4 Matrix Operations	120	(12)
Using Your TI-83: Matrix Operations	130	(1)
Using EXCEL: Matrix Addition and Scalar Multiplication	131	(1)
2.5 Multiplication of Matrices	132	(19)
Using Your TI-83: Matrix Multiplication	149	(1)
Using EXCEL: Matrix Multiplication	150	(1)
2.6 The Inverse of a Matrix	151	(16)
Using Your TI-83: The Inverse of a Square Matrix	166	(1)
Using EXCEL: Inverse of a Matrix	167	(1)
2.7 Leontief Input-Output Model in Economics	167	(12)
2.8 Linear Regression	179	(16)
Using Your TI-83: Regression Lines	188	(2)
Using EXCEL: Linear Regression	190	(2)
Important Terms	192	(1)
Review Exercises	193	(2)
3 LINEAR PROGRAMMING	195	(54)
3.1 Linear Inequalities in Two Variables	196	(8)
3.2 Solutions of Systems of Inequalities: A Geometric Picture	204	(13)
Using Your TI-83: Finding Corner Points of a Feasible Region	212	(2)
Using EXCEL: Finding Corner Points of a Feasible Region	214	(3)
3.3 Linear Programming: A Geometric Approach	217	(22)
3.4 Applications	239	(10)
Important Terms	247	(1)
Review Exercises	247	(2)
4 LINEAR PROGRAMMING: THE SIMPLEX METHOD	249
4.1 Setting Up the Simplex Method	250	(11)
4.2 The Simplex Method	261	(22)
Using Your TI-83: The Simplex Method	280	(1)
Using EXCEL: The Simplex Method	281	(2)
4.3 The Standard Minimum Problem: Duality	283	(8)
4.4 Mixed Constraints	291	(19)
4.5 Multiple Solutions, Unbounded Solutions, and No Solutions	310	(9)
4.6 What's Happening in the Simplex Method? (Optional)	319	(7)
4.7 Sensitivity Analysis	326
Important Terms	338	(1)
Review Exercises	338
5 MATHEMATICS Of FINANCE	141	(261)
5.1 Simple Interest	343	(8)
5.2 Compound Interest	351	(16)
Using Your TI-83: Making a Table	364	(1)
Using EXCEL: Graphing Functions	365	(2)
5.3 Annuities and Sinking Funds	367	(11)
Using Your TI-83: Growth of Annuities	376	(1)
Using EXCEL: Periodic Amounts of an Annuity	377	(1)
5.4 Present Value of an Annuity and Amortization	378	(24)
Using Your TI-83: Monthly Loan Payments	396	(1)
Using EXCEL: Monthly Loan Payments	397	(1)
Important Terms	398	(1)
Summary of Formulas	398	(1)
Review Exercises	399	(3)
6 SETS AND COUNTING	402	(9)
6.1 Sets	403	(8)
6.2 Counting Elements in a Subset Using a Venn Diagram	411	(8)
6.3 Basic Counting Principles	419	(11)
6.4 Permutations	430	(11)
Using Your TI-83: Permutations	440	(1)
Using EXCEL: Permutations	440	(1)
6.5 Combinations	441	(14)
Using Your TI-83: Combinations	454	(1)
Using EXCEL: Combinations	455	(1)
6.6 A Mixture of Counting Problems	455	(6)
6.7 Partitions (Optional)	461
Important Terms	467	(1)
Review Exercises	467
7 PROBABILITY	411	(99)
7.1 Introduction to Probability	472	(13)
7.2 Equally Likely Events	485	(10)
7.3 Compound Events: Union, Intersection, and Complement	495	(13)
7.4 Conditional Probability	508	(15)
7.5 Independent Events	523	(17)
7.6 Bayes' Rule	540	(12)
7.7 Markov Chains	552
Important Terms	566	(1)
Review Exercises	566
8 STATISTICS	510	(187)
8.1 Frequency Distributions	571	(18)
Using Your TI-83: Histograms	585	(2)
Using EXCEL: Histograms and Pie Charts	587	(2)
8.2 Measures of Central Tendency	589	(11)
Using Your TI-83: Calculating the Mean and Median	599	(1)
Using EXCEL: Calculating the Mean and Median	600	(1)
8.3 Measures of Dispersion: Range, Variance, and Standard Deviation	600	(17)
Using Your TI-83: Calculating Range, Mean, and Standard Deviation	614	(2)
Using Your TI-83: Box Plot	616	(1)
Using EXCEL: Measures of Dispersion	616	(1)
Using EXCEL: Box Plot	617	(1)
8.4 Random Variables and Probability Distributions of Discrete Random Variables	617	(10)
8.5 Expected Value of a Random Variable	627	(10)
8.6 Binomial Experiments and Binomial Distribution	637	(13)
Using Your TI-83: Binomial Probability Distribution	648	(1)
Using Your TI-83: Histogram of a Probability Distribution	649	(1)
8.7 Normal Distribution	650	(30)
Using Your TI-83: Area Under the Normal Curve	678	(2)
Using EXCEL: Area Under the Normal Curve	680	(1)
8.8 Estimating Bounds on a Proportion	680	(17)
Important Terms	694	(1)
Review Exercises	694	(3)
9 GAME THEORY	697	(20)
9.1 Two-Person Games	698	(7)
9.2 Mixed-Strategy Games	705	(13)
Important Terms	715	(1)
Review Exercises	715	(2)
10 LOGIC	717
10.1 Statements	718	(6)
10.2 Conditional Statements	724	(5)
10.3 Equivalent Statements	729	(2)
10.4 Valid Arguments	731	(9)
Important Terms	738	(1)
Review Exercises	738
A REVIEW TOPICS	140	(16)
A.1 Properties of Real Numbers	740	(3)
A.2 Solving Linear Equations	743	(4)
A.3 Coordinate Systems	747	(3)
A.4 Linear Inequalities and Interval Notation	750	(6)
Important Terms	755
B USING A TI-83 GRAPHING CALCULATOR	156	(10)
Notation	756	(1)
Arithmetic Operations	756	(1)
Graphing	757	(1)
Evaluating a Function	758	(1)
Finding the Intersection of Two Graphs	758	(1)
Constructing a Table	759	(1)
Matrices	760	(2)
Statistics	762
C USING EXCEL	166
ANSWERS TO SELECTED ODD-NUMBERED EXERCISES	A-1
INDEX	I-1