Raymond A. Barnett, a native of California, received his B.A. in mathematical statistics from the University of California at Berkeley and his M.A. in mathematics from the University of Southern California. He has been a member of the Merritt College Mathematics Department, and was chairman of the department for four years. Raymond Barnett has authored or co-authored eighteen textbooks in mathematics, most of which are still in use. In addition to international English editions, a number of books have been translated into Spanish. Co-authors include Michael Ziegler, Marquette University; Thomas Kearns, Northern University; Charles Burke, City College of San Francisco; John Fuji, Merritt College; and Karl Byleen, Marquette University.
Michael R. Ziegler received his B.S. from Shippensburg StateCollege and his M.S. and Ph.D. from the University of Delaware. After completing post doctoral work at the University of Kentucky, he was appointed to the faculty of Marquette University where he currently holds the rank of Professor in the Department of Mathematics, Statistics, and Computer Science. Dr. Ziegler has published over a dozen research articles in complex analysis and has co-authored eleven undergraduate mathematics textbooks with Raymond A. Barnett, and more recently, Karl E. Byleen.
Karl E. Byleen received the B.S., M.A. and Ph.D. degrees in mathematics from the University of Nebraska. He is currently an Associate Professor in the Department of Mathematics, Statistics and Computer Science of Marquette University. He has published a dozen research articles on the algebraic theory of semigroups.
Why We wrote This Book:
This text is written for student comprehension. Great care has been taken to write a book that is mathematically correct and accessible. We emphasize computational skills, ideas, and problem solving rather than mathematical theory. Most derivations and proofs are omitted except where their inclusion adds significant insight into a particular concept. General concepts and results are usually presented only after particular cases have been discussed. Graphing calculators and computers are playing an increasing role in mathematics education and in real-world applications of mathematics. This books deals with the mathematics that is required to use modern technology effectively as an OPTIONAL feature. In appropriate places in the text, there are clearly identified examples and exercises related to graphing calculators and computers, illustrations of applications of spreadsheets, and sample computer output. All of these may be omitted without loss of continuity.
TABLE OF CONTENTS
PART ONE A LIBRARY OF ELEMENTARY FUNCTIONS
CHAPTER 1 Linear Equations and Graphs
1-1 Linear Equations and Inequalities
1-2 Graphs and Lines
1-3 Linear Regression
Chapter 1 Review
Review Exercise
CHAPTER 2 Functions and Graphs
2-1 Functions
2-2 Elementary Functions: Graphs and Transformations
2-3 Quadratic Functions
2-4 Exponential Functions
2-5 Logarithmic Functions
Chapter 2 Review
Review Exercise
PART TWO FINITE MATHEMATICS
CHAPTER 3 Mathematics of Finance
3-1 Simple Interest
3-2 Compound and Continuous Compound Interest
3-3 Future Value of an Annuity; Sinking Funds
3-4 Present Value of an Annuity; Amortization
Chapter 3 Review
Review Exercise
CHAPTER 4 Systems of Linear Equations; Matrices
4-1 Review: Systems of Linear Equations in Two Variables
4-2 Systems of Linear Equations and Augmented Matrices
4-3 Gauss-Jordan Elimination
4-4 Matrices: Basic Operations
4-5 Inverse of a Square Matrix
4-6 Matrix Equations and Systems of Linear Equations
4-7 Leontief Input-Output Analysis
Chapter 4 Review
Review Exercise
CHAPTER 5 Linear Inequalities and Linear Programming
5-1 Inequalities in Two Variables
5-2 Systems of Linear Inequalities in Two Variables
5-3 Linear Programming in Two Dimensions: A Geometric Approach
Chapter 5 Review
Review Exercise
CHAPTER 6 Linear Programming: Simplex Method
6-1 A Geometric Introduction to the Simplex Method
6-2 The Simplex Method: Maximization with Problem Constraints of the Form ≤
6-3 The Dual; Minimization with Problem Constraints of the Form ≥
6-4 Maximization and Minimization with Mixed Problem Constraints
Chapter 6 Review
Review Exercise
CHAPTER 7 Logic, Sets, and Counting
7-1 Logic
7-2 Sets
7-3 Basic Counting Principles
7-4 Permutations and Combinations
Chapter 7 Review
Review Exercise
CHAPTER 8 Probability
8-1 Sample Spaces, Events, and Probability
8-2 Union, Intersection, and Complement of Events; Odds
8-3 Conditional Probability, Intersection, and Independence
8-4 Bayes' Formula
8-5 Random Variable, Probability Distribution, and Expected Value
Chapter 8 Review
Review Exercise
CHAPTER 9 Markov Chains
9-1 Properties of Markov Chains
9-2 Regular Markov Chains
9-3 Absorbing Markov Chains
Chapter 9 Review
Review Exercise
CHAPTER 10 Games and Decisions
10-1 Strictly Determined Games
10-2 Mixed Strategy Games
10-3 Linear Programming and 2 ¥ 2 Games: Geometric Approach
10-4 Linear Programming and m ¥ n Games: Simplex Method and the Dual Problem
Chapter 10 Review
Review Exercise
CHAPTER 11 Data Description and Probability Distributions
11-1 Graphing Data
11-2 Measures of Central Tendency
11-3 Measures of Dispersion
11-4 Bernoulli Trials and Binomial Distributions
11-5 Normal Distributions
Chapter 11 Review
Review Exercise
APPENDIX A Basic Algebra Review
Self-Test on Basic Algebra
A-1 Algebra and Real Numbers
A-2 Operations on Polynomials
A-3 Factoring Polynomials
A-4 Operations on Rational Expressions
A-5 Integer Exponents and Scientific Notation
A-6 Rational Exponents and Radicals
A-7 Quadratic Equations
APPENDIX B Special Topics
B-1 Sequences, Series, and Summation Notation
B-2 Arithmetic and Geometric Sequences
B-3 The Binomial Theorem
APPENDIX C Tables
Table I Area Under the Standard Normal Curve
Table II Basic Geometric Formulas
Answers
Index
Applications Index
A Library of Elementary Functions