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Edition/Copyright: 9TH 02
The ninth edition of Finite Mathematics for Business, Economics, Life Sciences, and Social Sciences is designed for a one-term course in finite mathematics and for students who have had 1-2 years of high school algebra or the equivalent. The choice and independence of topics make the text readily adaptable to a variety of courses (see the Chapter Dependency Chart on page xi). It is one of five books in the authors' college mathematics series.
Improvements in this edition evolved out of the generous response from a large number of users of the last and previous editions as well as survey results from instructors, mathematics departments, course outlines, and college catalogs. Fundamental to a book's growth and effectiveness is classroom use and feedback. Now in its ninth edition, Finite Mathematics for Business, Economics, Life Sciences, and Social Sciences has had the benefit of having a substantial amount of both.
Emphasis and Style
The text is written for student comprehension. Great care has been taken to write a book that is mathematically correct and accessible to students. Emphasis is on 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.
Examples and Matched Problems
Over 260 completely worked examples are used to introduce concepts and to demonstrate problem-solving techniques. Many examples have multiple parts, significantly increasing the total number of worked examples. Each example is followed by a similar matched problem for the student to work while reading the material. This actively involves the student in the learning process. The answers to these matched problems are included at the end of each section for easy reference.
Exploration and Discussion
Every section contains Explore-Discuss problems interspersed at appropriate places to encourage the student to think about a relationship or process before a result is stated, or to investigate additional consequences of a development in the text. Verbalization of mathematical concepts, results, and processes is encouraged in these Explore-Discuss problems, as well as in some matched problems, and in some problems in almost every exercise set. The Explore-Discuss material also can be used as in-class or out-of-class group activities. In addition, at the end of every chapter, we have included two special chapter group activities that involve several of the concepts discussed in the chapter. Problems in the exercise sets that require verbalization are indicated by color problem numbers.
The book contains over 3,500 problems. Many problems have multiple parts, significantly increasing the total number of problems. Each exercise set is designed so that an average or below-average student will experience success and a very capable student will be challenged. Exercise sets are mostly divided into A (routine, easy mechanics), B (more difficult mechanics), and C (difficult mechanics and some theory) levels.
A major objective of this book is to give the student substantial experience in modeling and solving real-world problems. Enough applications are included to convince even the most skeptical student that mathematics is really useful (see the Applications Index inside the back cover). Worked examples involving applications are identified by . Almost every exercise set contains application problems, usually divided into business and economics, life science, and social science groupings. An instructor with students from all three disciplines can let them choose applications from their own field of interest; if most students are from one of the three areas, then special emphasis can be placed there. Most of the applications are simplified versions of actual real-world problems taken from professional journals and books. No specialized experience is required to solve any of the applications.
The Internet provides a wealth of material that can be related to this book, from sources for the data in application problems to interactive exercises that provide additional insight into various mathematical processes. Every section of the book contains Internet connections identified by an icon. Links to the related web sites can be found at the PHCompanion Website discussed later in this preface: www.prenhall.com/barnett
The generic term graphing utility is used to refer to any of the various graphing calculators or computer software packages that might be available to a student using this book. (See the description of the software accompanying this book later in this Preface.) Although access to a graphing utility is not assumed, it is likely that many students will want to make use of one of these devices. To assist these students, optional graphing utility activities are included in appropriate places in the book. These include brief discussions in the text, examples or portions of examples solved on a graphing utility, problems for the student to solve, and a group activity that involves the use of technology at the end of each chapter. In the group activity at the end of Chapter 1, and continuing through Chapter 2, linear regression on a graphing utility is used at appropriate points to illustrate mathematical modeling with real data. All the optional graphing utility material is clearly identified by either or and can be omitted without loss of continuity, if desired.
All graphs are computer-generated to ensure mathematical accuracy. Graphing utility screens displayed in the text are actual output from a graphing calculator.
Additional Pedagogical Features
Annotation of examples and developments, in small color type, is found throughout the text to help students through critical stages (see Sections 1-1 and 4-2). Think boxes (dashed boxes) are used to enclose steps that are usually performed mentally (see Sections 1-1 and 4-1). Boxes are used to highlight important definitions, results, and step-by-step processes (see Sections 1-1 and 1-4). Caution statements appear throughout the text where student errors often occur (see Sections 4-3 and 4-5). Functional use of color improves the clarity of many illustrations, graphs, and developments, and guides students through certain critical steps (see Sections 1-1 and 4-2). Boldface type is used to introduce new terms and highlight important comments. Chapter review sections include a review of all important terms and symbols and a comprehensive review exercise. Answers to most review exercises, keyed to appropriate sections, are included in the back of the book. Answers to all other odd-numbered problems are also in the back of the book. Answers to application problems in linear programming include both the mathematical model and the numeric answer.
The text begins with the development of a library of elementary functions in Chapters 1 and 2, including their properties and uses. We encourage students to investigate mathematical ideas and processes graphically and numerically, as well as algebraically. This development lays a firm foundation for studying mathematics both in this book and in future endeavors. Depending on the syllabus for the course and the background of the students, some or all of this material can be covered at the beginning of a course, or selected portions can be referred to as needed later in the course.
The material in Part Two (Finite Mathematics) can be thought of as four units: mathematics of finance (Chapter 3); linear algebra, including matrices, linear systems, and linear programming (Chapters 4 and 5); probability and statistics (Chapters 6 and 7); and applications of linear algebra and probability to game theory and Markov chains (Chapters 8 and 9). The first three units are independent of each other, while the last two chapters are dependent on some of the earlier chapters (see the Chapter Dependency Chart preceding this Preface).
Chapter 3 presents a thorough treatment of simple and compound interest and present and future value of ordinary annuities. Appendix B contains a section on arithmetic and geometric sequences that can be covered in conjunction with this chapter, if desired.
Chapter 4 covers linear systems and matrices with an emphasis on using row operations and Gauss-Jordan elimination to solve systems and to find matrix inverses. This chapter also contains numerous applications of mathematical modeling utilizing systems and matrices. To assist students in formulating solutions, all the answers in the back of the book to application problems in Exercises 4-3, 4-5, and the chapter Review Exercise contain both the mathematical model and its solution. The row operations discussed in Sections 4-2 and 4-3 are required for the simplex method in Chapter 5. Matrix multiplication, matrix inverses, and systems of equations are required for Markov chains in Chapter 9.
Chapter 5 provides broad and flexible coverage of linear programming. The first two sections cover two-variable graphing techniques. Instructors who wish to emphasize techniques can cover the basic simplex method in Sections 5-3 and 5-4 and then discuss any or all of the following: the dual method (Section 5-5), the big M method (Section 5-6), or the two-phase simplex method (Group Activity 1). Those who want to emphasize modeling can discuss the formation of the mathematical model for any of the application examples in Sections 5-4, 5-5, and 5-6, and either omit the solution or use software to find the solution (see the description of the software that accompanies this text later in this Preface). To facilitate this approach, all the answers in the back of the book to application problems in Exercises 5-4, 5-5, 5-6, and the chapter Review Exercise contain both the mathematical model and its solution. Geometric, simplex, and dual solution methods are required for portions of Chapter 8.
Chapter 6 covers counting techniques and basic probability, including Bayes' formula and random variables. Appendix A contains a review of basic set theory and notation to support the use of sets in probability. Some of the topics discussed in Chapter 6 are required for Chapter 7.
Chapter 7 deals with basic descriptive statistics and more advanced probability distributions, including the important normal distribution. Appendix B contains a short discussion of the binomial theorem that can be used in conjunction with the development of the binomial distribution in Section 7-5.
Each of the last two chapters ties together concepts developed in earlier chapters and applies them to two interesting topics: game theory (Chapter 8) and Markov chains (Chapter 9). Either chapter provides an excellent unifying conclusion to a finite mathematics course.
Appendix A contains a self-test and a concise review of basic algebra that also may be covered as part of the course or referred to as needed. As mentioned above, Appendix B contains additional topics that can be covered in conjunction with certain sections in the text, if desired.
Supplements for the Student
1. A Student Solutions Manual and Explorations in Finite Mathematics by Garret J. Etgen and David Schneider is available through your book store. The manual includes detailed solutions to all odd-numbered problems and all review exercises. Explorations in Finite Mathematics by David Schneider contains over twenty routines that provide additional insight into the topics discussed in the text. Although this software has much of the computing power of standard mathematical software packages, it is primarily a teaching tool that focuses on understanding mathematical concepts, rather than on computing. Included are routines for Gaussian elimination, matrix inversion, solution of linear programming problems by both the geometric method and the simplex method, Markov chains, probability and statistics, and mathematics of finance. All the routines in this software package are menu-driven and are very easy to use. The matrix routines use and display rational numbers, and matrices may be saved and printed. The software will run on DOS or Windows platforms.
2. The PH Companion Website, designed to complement and expand upon the text, offers a variety of teaching and learning tools, including links to related websites, practice work for students, and the ability for instructors to monitor and evaluate students' work on the website. For more information, contact your local Prentice Hall representative. (www.prenhall.com/barnett)
3. CourseCompass/Blackboard/WebCT offers Course compatible content including Excel Projects, Quizzes, Chapter Destinations, Lecture Notes, and Graphing Calculator Help. CourseCompass is the perfect course management solution that combines quality Pearson Education content with state-of-the-art Blackboard technology! It is a dynamic, interactive online course management tool powered by Blackboard. This exciting product allows you to teach with market-leading Pearson Education content in an easy-to-use customizable format. Blackboard 5SM is a comprehensive and flexible e-Learning software platform that delivers a course management system, customizable institution-wide portals, online communities, and an advanced architecture that allows for Web-based integration of multiple administrative systems. WebCT is one of the most popular Web course platforms in higher education today. It is the first destination site for the higher education marketplace to offer both teaching and learning resources and a community of peers across course and institutional boundaries.
Supplements for the Instructor
For a summary of all available supplementary materials and detailed information regarding examination copy requests and orders, see page xix.
Because of the careful checking and proofing by a number of mathematics instructors (acting independently), the authors and publisher believe this book to be substantially error-free. For any errors remaining, the authors would be grateful if they were sent to: Karl E. Byleen, 9322 W. Garden Court, Hales Corners, WI 53130; or by e-mail, to:email@example.com
In addition to the authors, many others are involved in the successful publication of a book.
We wish to thank the following reviewers of the eighth edition:
Thomas Riedel, University of Louisville
Linda M. Neal, Southern Methodist University
Beverly Vredevelt, Spokane Falls Community College
J. Sriskandarajah, University of Wisconsin-Richland
Cathleen A. Zucco-Tevelot, Trinity College
We also wish to thank our colleagues who have provided input on previous editions:
Chris Boldt, Bob Bradshaw, Bruce Chaffee, Robert Chaney, Dianne Clark, Charles E. Cleaver, Barbara Cohen, Richard L. Conlon, Catherine Cron, Lou D'Alotto, Madhu Deshpande, Kenneth A. Dodaro, Michael W. Ecker, Jerry R. Ehman, Lucina Gallagher, Martha M. Harvey, Sue Henderson, Lloyd R. Hicks, Louis F. Hoelzle, Paul Hutchins, K. Wayne James, Robert H. Johnston, Robert Krystock, Inessa Levi, James T. Loats, Frank Lopez, Roy H. Luke, Wayne Miller, Mel Mitchell, Ronald Persky, Kenneth A. Peters, Jr., Dix Petty, Tom Plavchak, Bob Prielipp, Stephen Rodi, Arthur Rosenthal, Sheldon Rothman, Elaine Russell, John Ryan, Daniel E. Scanlon, George R. Schriro, Arnold L. Schroeder, Hari Shanker, Joan Smith, Steven Terry, Delores A. Williams, Caroline Woods, Charles W. Zimmerman, and Pat Zrolka.
We also express our thanks to:
Hossein Hamedani, Carolyn Meitler, Stephen Merrill, Robert Mullins, and Caroline Woods for providing a careful and thorough check of all the mathematical calculations in the book, and to Priscilla Gathoni for checking the Student Solutions Manual, and the Instructor's Solutions Manual (a tedious but extremely important job).
Garret Etgen, Hossein Hamedani, Carolyn Meitler, and David Schneider for developing the supplemental manuals that are so important to the success of a text.
Jeanne Wallace for accurately and efficiently producing most of the manuals that supplement the text. George Morris and his staff at Scientific Illustrators for their effective illustrations and accurate graphs. All the people at Prentice Hall who contributed their efforts to the production of this book, especially Quincy McDonald, our acquisitions editor, and Lynn Savino Wendel, our production editor.
Producing this new edition with the help of all these extremely competent people has been a most satisfying experience.
R. A. Barnett
M. R. Ziegler
K. E. Byleen
Barnett, Raymond A. : Merritt College
Ziegler, Michael R. : Marquette University
Byleen, Karl E. : Marquette University
I. A LIBRARY OF ELEMENTARY FUNCTIONS.
1. A Beginning Library of Elementary Functions.
Functions. Elementary Functions: Graphs and Transformations. Linear Functions and Straight Lines. Quadratic Functions. Chapter 1 Review. Chapter 1 Group Activities.
2. Additional Elementary Functions.
Polynomial and Rational Functions. Exponential Functions. Logarithmic Functions. Chapter 2 Review. Chapter 2 Group Activities.
II. FINITE MATHEMATICS.
3. Mathematics of Finance.
Simple Interest. Compound Interest. Future Value of an Annuity; Sinking Funds. Present Value of an Annuity; Amortization. Chapter 3 Review. Chapter 3 Group Activities.
4. Systems of Linear Equations; Matrices.
Review: Systems of Linear Equations in Two Variables. Systems of Linear Equations and Augmented Matrices. Gauss-Jordan Elimination. Matrices: Basic Operations. Inverse of a Square Matrix. Matrix Equations and Systems of Linear Equations. Leontief Input-Output Analysis. Chapter 4 Review. Chapter 4 Group Activities.
5. Linear Inequalities and Linear Programming.
Systems of Linear Inequalities in Two Variables. Linear Programming in Two Dimensions--A Geometric Approach. A Geometric Introduction to the Simplex Method. The Simplex Method: Maximization with Problem Constraints of the Form *. The Dual; Minimization with Problem Constraints of the Form *. Maximization and Minimization with Mixed Problem Constraints. Chapter 5 Review. Chapter 5 Group Activities.
Basic Counting Principles. Permutations and Combinations. Sample Spaces, Events, and Probability. Union, Intersection, and Complement of Events; Odds. Conditional Probability, Intersection, and Independence. Bayes' Formula. Random Variables, Probability Distribution, and Expectation. Chapter 6 Review. Chapter 6 Group Activities.
7. Data Description and Probability Distributions.
Graphing Data. Graphing Quantitative Data. Measures of Central Tendency. Measures of Dispersion. Bernoulli Trials and Binomial Distributions. Normal Distributions. Chapter 7 Review. Chapter 7 Group Activities.
8. Games and Decisions.
Strictly Determined Games. Mixed Strategy Games. Linear Programming and 2 x 2 Games--Geometric Approach. Linear Programming and m x n Games--Simplex Method and the Dual. Chapter 8 Review. Chapter 8 Group Activities.
9. Markov Chains.
Properties of Markov Chains. Regular Markov Chains. Absorbing Markov Chains. Chapter 9 Review. Chapter 9 Group Activities.
A. Basic Algebra Review.
Self-Test on Basic Algebra. Sets. Algebra and Real Numbers. Operations on Polynomials. Factoring Polynomials. Operations on Rational Expressions. Integer Exponents and Scientific Notation. Rational Exponents and Radicals. Linear Equations and Inequalities in One Variable. Quadratic Equations.
B. Special Topics.
Sequences, Series, and Summation Notation. Arithmetic and Geometric Sequences. The Binomial Theorem.
Table I: Area Under the Standard Normal Curve. Table II: Basic Geometric Formulas.
Library of Elementary Functions.
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