Preface
To the Instructor
Philosophy This text reflects our philosophy that a mathematics text at the beginning college level should be readable, straightforward, and loaded with motivation. But ultimately, students can learn mathematics only by doing mathematics. Therefore, throughout this text we have placed a strong emphasis on problem solving as a means of understanding. The examples are designed to motivate, instruct, and guide students. The exercises then give the students an opportunity to test their comprehension, challenge their understanding, and apply their knowledge to real-world situations.
Audience and Flexibility We intend this text to provide a treatment of algebra, graphs, functions, logarithms, trigonometry, systems of equations and inequalities, matrices, analytic geometry, polar coordinates, sequences, and probability that is accessible to a college student with two years of high-school mathematics. We have provided sufficient material here for a standard one-semester or two-quarter course. This wealth of topics allows the instructor to choose those best suited to the objectives of his/her courses and the backgrounds and abilities of the students. The text can serve as a prerequisite for finite mathematics, statistics, or discrete mathematics. It can also be an introductory course in college mathematics for the liberal arts or business student who plans no further study of mathematics or as a beginning course in a sequence that provides the prerequisites for calculus.
Features in the Text
Examples It has been our experience that examples and exercises are the primary learning sources in a mathematics text. We have found that students rely on examples, not theorems and proofs. Therefore we have included numerous examples to illustrate both the theoretical concepts and the computational techniques covered in the text.
Exercises As mentioned, we feel that students can learn only by doing. Therefore, in order to promote active participation in problem solving, the exercises are extensive and varied. The exercise sets include an abundance of drill problems, true/false questions, fill-in-the-blank questions, applications, challenging problems, graphing problems, problems that require interpretation of graphs, and discussion problems. This variety of examples gives students the opportunity to solidify their understanding of basic concepts, see practical uses for abstract mathematical ideas, and test their ingenuity. For this third edition we have reorganized and expanded almost all the exercise sets.
Motivation While a number of proofs are included, we have typically motivated concepts in an intuitive or geometric manner. In addition, wherever possible we have used figures to illustrate an idea or aid in a solution.
Emphasis on Functions Since functions are an essential concept in this course and in mathematics as a whole, we have increased the emphasis on functions and function notation throughout this third edition.
Emphasis on Graphing There is a great emphasis on graphing equations and functions. We have stressed symmetry, use of shifted graphs, reflections, intercepts, and interpretation of graphs throughout the text.
New to the Third Edition
Applications In this revision we continue to provide applications culled from journals, newspapers, and scientific texts. These “real-life” problems show students the power and usefulness of the mathematics they learn in this course. The applications in this revision span a wide variety of disciplines including astronomy, biology, business, chemistry, ecology, engineering, geology, medicine, meteorology, optics, and physics.
Annotation Arrows In the examples we have added many blue-colored annotation arrows within the examples and in the margin to guide the students through the various steps of the solution and to show them how concepts and properties given in theorems and definitions are used in solving a problem. Red-colored annotation arrows in the margin indicate a Note of Caution.These cautionary annotations indicate places in the exposition where the student should proceed slowly or even reread the text to avoid common pitfalls and misinterpretations of the material.
Chapter Openers Each chapter now opens with its own table of contents. In addition we have provided a motivational discussion of the material and a brief historical account of one or more individuals who had influence on the development of the mathematics in the chapter.
Notes from the Classroom Selected sections in the text conclude with informal remarks called Notes from the Classroom. These remarks are aimed directly at the student and address a wide variety of student/textbook/classroom issues such as alternative terminology, common errors, reinforcement of important concepts, what material is or is not recommended for memorization, solution procedures, use and misuse of calculators, advice on the importance of neatness and organization, misinterpretations, and an occasional word of encouragement.
Key Concepts Each chapter concludes with a list of the topics that we feel were most important in the chapter. The students can use this as a checklist in reviewing the material for quizzes and examinations.
Chapter Review Exercises To aid the instructor in choosing topics for review or emphasis, we have reorganized each Chapter Review Exercises into three distinct parts: Part A are true/false questions, Part B are fill in the blank questions, and Part C consists of traditional problems that review the important topics and concepts covered in the chapter.
Figures A word about the numbering of figures, definitions, theorems, and tables is in order. Because of the great number of figures in this text we were motivated to change to a double-decimal numeration system. For example, the interpretation of “Figure 1.2.3” is
We feel that this type of numeration will make it easier to find figures, definitions, and theorems when they are referred to in later sections or chapters. In addition, to better link a figure with the text, the first textual reference to each figure is done in the same font style and color as the figure number; for example,FIGURE 1.2.3. Also, in this revision all the figures now have brief explanatory captions.
New Topics In the bulleted list that follows we indicate some of the changes made in the subject matter.
Almost all exercise sets now contain problems called For Discussion. We hope that instructors will utilize these problems, which are primarily conceptual in nature, and their expertise to engage in a classroom exchange of ideas with the students on how these problems can be solved. These problems could also be the basis for assigned writing projects. To encourage original thought we purposely have not included answers to these problems.
We have improved the discussion of the inverse functions (Section 4.6) by providing more motivation and clarity with several additional figures.
Section 4.7,Building a Function from Words, is new to Chapter 004.
Section 4.8,Least Squares Line, is also new to Chapter 004. In Section 4.8 we compute the least squares line in the usual algebraic manner. The least squares line concept is covered again from the viewpoint of using an inverse matrix in Section 9.6.
The chapter on exponential and logarithmic functions has been completely rewritten.
Many new mathematical models involving the exponential and logarithmic functions are introduced in Section 6.4.
The hyperbolic functions are introduced in this text for the first time in Section 6.5.
In Section 9.5,Linear Systems: Augmented Matrices, we show how to use elementary row operations on an augmented matrix to balance chemical equations.
In Section 9.6,Linear Systems: Matrix Inverses, we revisit the notion of the least squares line y =mx + b. In this section we compute the coefficients m and b using matrix methods.
Section 9.8,Cryptography, is new to Chapter 9. This brief section introduces the notions of encoding and decoding messages using matrices. We feel that the students will find this material interesting and perhaps will motivate them to seek further information about this important application of matrices.
A new section (Section 10.3),Convergence of Sequences and Series, has been added to Chapter 0010. The discussion of the notion of convergence of a sequence or an infinite series is kept at an intuitive level.
The section on permutations and combinations in the last edition has been rewritten and is now entitled Principles of Counting.
Supplements
For the Instructor
The following materials are available online, at http://www.jblearning.com/catalog/9781449606022/
Complete Solutions Manual (CSM) prepared by Warren S. Wright and Carol D. Wright.
Computerized Testing System for both Windows® and Mac OS® operating systems. This system allows instructors to create customized tests and quizzes. The questions and answers are sorted by chapter and can also be easily installed on a computer. Publisher-supplied .rtf files can also be uploaded to the instructor's Learning Management System.
PowerPoint® slides that feature all labeled figures as they appear in the text. This useful tool allows instructors to easily display and discuss figures and problems found within the textbook.
WebAssignTM developed by instructors for instructors, is a premier independent online teaching and learning environment, guiding several million students through their academic careers since 1997. With WebAssign, instructors can create and distribute algorithmic assignments using questions specific to this textbook. Instructors can also grade, record, and analyze student responses and performance instantly; offer more practice exercises, quizzes, and homework; and upload additional resources to share and communicate with their students seamlessly such as the PowerPoint slides and the test items supplied by Jones & Bartlett Learning Computerized Testing System.
eBookformat. As an added convenience this complete textbook is now available in eBook format for purchase by the student through WebAssign.
CourseSmart is a new way for instructors and students to access this textbook in digital format, anytime from anywhere. Jones & Bartlett Learning has partnered with CourseSmart to make available many of our leading mathematics textbooks in the CourseSmart eTextbook store.
For more information on CourseSmart Editions, including returns information, please visit http://www.jblearning.com/elearning/econtent/coursesmart/.
Please contact your Jones & Bartlett Learning Account Specialist for information on, access to, and online demonstrations of the supplements and services described above.
For the Student
Student Resource Manual (SRM) prepared by Warren S. Wright and Carol D. Wright. This manual continues to be popular with students using any one of the Zill series of mathematics textbooks. A complete description of the content specific to this text can be found in the preface. Available in both print and online formats, this student manual can be purchased separately or ordered bundled with the textbook at substantial savings.
Student Companion Website is available at www.jblearning.com/catalog/9781449606022/. This online tutorial learning center can be accessed at any time during the term. The resources are tied directly to the text and include: Practice Quizzes, an Online Glossary of Key Terms, and Animated Flashcards.
Graphing Calculator Manual by Jeffery M. Gervasi, EdD of Porterville College, may be ordered through the bookstore or online at http://www.jblearning.com/mathematics/precalculus/.
WebAssign Access card can be bundled with this text or purchased separately by the student online at http://www.webassign.net/.
eBook with course access card can also be purchased separately by the student online at http://www.webassign.net/.
CourseSmart is a new way for students to access college textbooks in digital format, anytime from anywhere. Jones & Bartlett Learning has partnered with CourseSmart to make this textbook available in the CourseSmart eTextbook store.
For students, this CourseSmart Edition has many features designed to make studying more efficient such as highlighting, online search, note-taking, and print capabilities.
For more information on purchasing this CourseSmart Edition please visit http://www.jblearning.com/elearning/econtent/coursesmart/.
Acknowledgments
It was also our good fortune to have the following individuals who either read all (or part) of the subsequent editions or participated in a detailed survey. Their criticisms and many fine suggestions are gratefully acknowledged:
Wayne Andrepont,University of Southwestern Louisiana
Nancy Angle,Colorado School of Mines
James E. Arnold,University of Wisconsin—Milwaukee
Judith Baxter,University of Illinois—Chicago Circle
Margaret Blumberg,Southeastern Louisiana University
Robert A. Chaffer,Central Michigan University
Daniel Drucker,Wayne State University
Chris Ennis,Carleton College
Jeffrey M. Gervasi,Porterville College
E. John Hornsby,University of New Orleans
Don Johnson,New Mexico State University
Jimmie Lawson,Louisiana State University
Gerald Ludden,Michigan State University
Stanley M. Lukawecki,Clemson University
Richard Marshall,Eastern Michigan University
Glenn Mattingly,Sam Houston State University
Michael Mays,West Virginia University
Phillip R. Montgomery,University of Kansas
Bruce Reed,Virginia Polytechnic Institute and State University
Jean Rubin,Purdue University
Helen Salzberg,Rhode Island College
George L. Szoke,University of Akron
Darrell Turnbridge,Kent State University
Carol Achs,Mesa Community College
Joseph Altinger,Youngstown State University
Phillip Barker,University of Missouri—Kansas City
Wayne Britt,Louisiana State University
Kwang Chul Ha,Illinois State University
Duane Deal,Ball State University
Richard Friedlander,University of Missouri—St. Louis
August Garver,University of Missouri—Rolla
Irving Katz,George Washington University
Janice Kilpatrick,University of Toledo
Barbara Meininger,University of Oregon
Eldon Miller,University of Mississippi
Judith Rollstin,University of New Mexico
Monty J. Strauss,Texas Tech University
Faye Thames,Lamar University
Waldemar Weber,Bowling Green State University
We would like to take this opportunity to express our appreciation to Barry A. Cipra for supplying many of the applied problems that appear in the exercise sets and to our colleague Warren S. Wright at Loyola Marymount University for giving us permission to use his material from an earlier edition, for producing the excellent instructor and student manuals, and for his careful proofreading of the first-round page proofs of this edition.
Our warm gratitude goes out to all the good people at Jones & Bartlett Learning who worked on this text. Because of their number, they perforce will remain nameless. But we do want to single out for special thanks Timothy Anderson, senior acquisitions editor, and Amy Rose, production director, for their hard work, cooperation, and patience in making this third edition a reality.
Lastly, all the mistakes in the text are ours. If you run across any of these errors or have any suggestions for improving this text, we would greatly appreciate it if you bring it to our attention through our editor at:
Dennis G. Zill
Jacqueline M. Dewar