Precalculus: Graphing and Data Analysis (2nd Edition)
PREFACE TO THE INSTRUCTORAs professors at respectively an urban public university and a community college, Michael Sullivan and Michael Sullivan III are aware of the varied needs of Precalculus students, ranging from those having little mathematical background and fear of mathematics courses to those who have had a strong mathematical education and are highly motivated. For some of your students, this will be their last course in mathematics, while others might decide to further their mathematical education. This text is written for both groups. As the author of precalculus, engineering calculus, finite math, and business calculus texts, and as a teacher, Michael understands what students must know if they are to be focused and successful in upper level math courses. However, as a father of four, including the co-author, he also understands the realities of college life. Michael Sullivan III believes passionately in the value of technology as a tool for learning that enhances understanding without sacrificing important skills. Both authors have taken great pains to insure that the text contains solid, student-friendly examples and problems, as well as a clear and seamless writing style. We encourage you to share with us your experiences teaching from this text.   In the Second EditionThe second edition builds upon a strong foundation by integrating new features and techniques that further enhance student interest and involvement. The elements of the previous edition that have proved successful remain, while many changes, some obvious, others subtle, have been made. The text has been streamlined to increase accessibility. A huge benefit of authoring a successful series is the broad-based feedback upon which improvements and additions are ultimately based. Virtually every change to this edition is the result of thoughtful comments and suggestions made by colleagues and students who have used the previous edition. This feedback has proved invaluable and has been used to make changes that improve the flow and usability of the text. For example, some topics have been moved to better reflect the way teachers approach the course. One significant change is the inclusion of the "Field Trip to Motorola" chapter projects. These projects take the incorporation of real life in mathematics to a higher level. The supplements package has been enhanced through upgrading traditional supplements and adding innovative media components such as MathPak, an Integrated Learning Environment. MathPak combines all of the text's key supplements into one easy-to-navigate software package.   Changes to the Second EditionChapter 1• "Data in Ordered Pairs" has been moved to the section where linear curve fitting is introduced.• "Circles" is now covered in a stand-alone section.• The section on inequalties now contains a discussion of interval notation.Chapter 2• "More about Functions" has been divided into "Characteristics of Functions" and "Library of Function: Piecewise Defined Functions".Chapters 3 & 4• Chapter 3 has been divided into two parts: Polynomial and Rational Functions and the Zeros of a Polynomial Function.• The section on Rational Functions has been split into two sections making the material more manageable.Chapter 5• Chapter 4 of the 1st Edition. Certain types of exponential and logarithmic equations appear earlier in the chapter.Chapter 6• A rewrite of the introduction to trigonometric functions makes the distinction between the functions of a real number and that of an angle clearer.• The section on graphing of trigonometric functions is divided in two sections—one graphing the sine and cosine functions and the other graphing the four remaining trigonometric functions.• The section on Inverse Trigonometric Functions have been moved to Chapter 7.• The section on Right Triangle Trigonometry now appears in Chapter 8.Chapter 7• Now includes two sections on the section on the Inverse Trigonometric Functions and two section on Trigonometric Equations.Chapter 8• The first section discusses right triangle trigonometry and applications.Chapter 9• Static equilibrium problems were added.• This chapter now includes a new section on the cross product.Chapter 10• Asymptotes are introduced earlier in the section on hyperbolas.Chapter 11• Now includes two introductory sections on systems of linear equations.• The section on determinants includes a discussion on minors and cofactors.• Systems of Inequalities and Linear Programming are combined into one section.Chapter 12• The first five sections of Chapter 11 from the first edition.• The section on sequences utilizes the power of recursive functions and the graphing calculator to discuss amortization.Chapter 13• The second part of Chapter 11 from the 1st Edition.• Now contains two sections on probability: classical and empirical.Chapter 14• A new section on the Area Problem; the Integral has been added.Appendix• Rewritten to provide a more thorough review of prerequisite material.• Can be used as a "just-in-time" review by students.   PREFACE TO THE STUDENTAs you begin your study of Precalculus, you may feel overwhelmed by the number of theorems, definitions, procedures, and equations that confront you. You may even wonder whether or not you can learn all of this material in the time allotted. These concerns are normal. Keep in mind that many elements of Precalculus are all around us as we go through our daily routines. Many of the concepts you will learn to express mathematically, you already know intuitively. For many of you, this may be your last math course, while for others, it is just the first in a series of many. Either way, this text was written with you in mind. One of the coauthors, Michael Sullivan, has taught Precalculus courses for over thirty years. He is also the father of four college graduates, including this text's other co-author, who called home from time to time frustrated and with questions. We both know what you're going through. So we have written a text that doesn't overwhelm, or unnecessarily complicate Precalculus, but at the same time gives you the skills and practice you need to be successful.This text is designed to help you the student, master the terminology and basic concepts of Precalculus. These aims have helped to shape every aspect of the book. Many learning aids are built into the format of the text to make your study of the material easier and more rewarding. This book is meant to be a "machine for learning," that can help you focus your efforts and get the most from the time and energy you invest.Please do not hesitate to contact us through Prentice Hall with any suggestions or comments that would improve this text.Best Wishes!Michael SullivanMichael Sullivan, III