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|Preface to the Instructor|
|Preface to the Student|
|Ch. 2||Functions and their Graphs||85|
|Ch. 3||Equations and Inequalities||173|
|Ch. 4||Polynomial and Rational Functions||255|
|Ch. 5||Exponential and Logarithmic Functions||327|
|Ch. 6||Trigonometric Functions||407|
|Ch. 7||Analytic Trigonometry||487|
|Ch. 8||Applications of Trigonometric Functions||531|
|Ch. 9||Polar Coordinates; Vectors||593|
|Ch. 10||Analytic Geometry||653|
|Ch. 11||Systems of Equations and Inequalities||729|
|Ch. 12||Sequences; Induction; Counting; Probability||837|
As professors at both an urban public university and a community college, Michael Sullivan and Michael Sullivan III are aware of the varied needs of Algebra & Trigonometry students, ranging from those who have little mathematical background and a fear of mathematics courses, to those having a strong mathematical education and a high level of motivation. For some of your students, this will be their last course in mathematics, while others will further their mathematical education. This text is written for both groups.
As a teacher, and as an author of precalculus, engineering calculus, finite math, and business calculus texts, 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 coauthor, he also understands the realities of college life. His co-author and son, Michael Sullivan III, believes passionately in the value of technology as a tool for learning that enhances understanding without sacrificing important skills. Together, both authors have taken great pains to ensure that the text contains solid, student-friendly examples and problems, as well as a clear and seamless writing style.
The third edition builds upon a strong foundation by integrating new features and techniques that further enhance student interest and involvement. The elements of previous editions that have proved successful remain, while many changes, some obvious, others subtle, have been made. One important benefit of authoring a successful series is the broad-based feedback upon which improvements and additions are ultimatelybased. Virtually every change to this edition is the result of thoughtful comments and suggestions made by colleagues and students who have used previous editions. This feedback has proved invaluable and has been used to make changes that improve the flow, usability, and accessibility of the text. For example, some topics have been moved to better reflect the way teachers approach the course and problems have been added where more practice was needed. The supplements package has been enhanced through upgrading traditional supplements and adding innovative media components.
In this edition emphasis is placed on the role of modeling in algebra and trigonometry. To this end, dedicated sections appear on Linear Functions and Models, Quadratic Models, Power Functions and Models, Polynomial Functions and Models, Exponential and Logarithmic Functions and Models, and Trigonometric Models. Many of these applications focus on the areas of business, finance, and economics.
Chapter R review is a robust expansion of the appendix review of the second edition.
New to this edition is a discussion of quadratic in form equations.
A section on combining waves (the method of adding y-coordinates to obtain graphs) has been added.
As a result of these changes, this edition will be an improved teaching device for professors and a better learning tool for students.
To meet the varied needs of diverse syllabi, this book contains more content than a typical algebra and trigonometry course. The illustration shows the dependencies of chapters on each other. As the chart indicates, this book has been organized with flexibility of use in mind. Even within a given chapter, certain sections can be skipped without fear of future problems.
Chapter R. Review
This chapter is a revision of the old Appendix. It may be used as the first part of the course, or as a "just-in-time" review when the content is required in a later chapter. Specific references to this chapter occur throughout the book to assist in the review process.
Chapter 1. Graphs
This chapter presents an introduction to graphing and the graphing utility. Equations and inequalities are solved algebraically with graphical support. For those who prefer to treat complex numbers and negative discriminants early, Section 5.3 can be covered any time after Section 1.3.
Chapter 2. Linear and Quadratic Functions
This chapter provides an introduction to functions and then discusses two specific types of functions: linear functions and quadratic functions, along with models that utilize these functions.
Chapter 3. Functions and Their Graphs
Perhaps the most important chapter. Section 3.6 can be skipped without adverse effects.
Chapter 4. Polynomial and Rational Functions
Topic selection is dependent on your syllabus.
Chapter 5. The Zeros of a Polynomial Function
Topic selection is dependent on your syllabus. Section 5.1 is not absolutely necessary, but its coverage makes some computation easier.
Chapter 6. Exponential and Logarithmic Functions
Sections 6.1-6.5 follow in sequence; Sections 6.6, 6.7, and 6.8 each require Section 6.3.
Chapter 7. Systems of Equations and Inequalities
Sections 7.1-7.2 follow in sequence; Sections 7.3-7.7 require Sections 7.1 and 7.2, and may be covered in any order.
Chapter 8. Trigonometric Functions
The sections follow in sequence. Section 10.1 on Applications Involving Right Triangles, may be covered immediately after Section 8.3, if so desired.
Chapter 9. Analytic Trigonometry
The sections follow in sequence. Sections 9.2, 9.6, and 9.8 may be skipped in a brief course.
Chapter 10. Applications of Trigonometric Functions
The sections follow in sequence. Sections 10.4 and 10.5 may be skipped in a brief course.
Chapter 11. Polar Coordinates; Vectors
Sections 11.1-11.3 and Sections 11.4-11.5 are independent and may be covered separately.
Chapter 12. Analytic Geometry
Sections 12.1-12.4 follow in sequence. Sections 12.5,12.6, and 12.7 are independent of each other, but do depend on Sections 12.112.4. Section 12.8 is independent of Sections 12.5-12.7, but does depend on Sections 12.1-12.4 as well as Sections 7.1-7.2.
Chapter 13. Sequences; Induction; The Binomial Theorem
There are three independent parts: (1) Sections 13.1-13.3; (2) Section 13.4; (3) Section 13.5
Chapter 14. Counting and Probability Sections 14.1-14.4 follow in order.
As you begin your study of Algebra and Trigonometry, you may feel overwhelmed by the numbers 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 the elements of algebra and trigonometry 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, just the first in a series of many. Either way; this text was written with you in mind. We have spent countless hours teaching Algebra and Trigonometry courses. We know what you're going through. You'll find that we have written a text that doesn't overwhelm, or unnecessarily complicate Algebra and Trigonometry, 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 Algebra and Trigonometry. 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, ensuring that you 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.
Michael Sullivan, III
Posted January 12, 2005
A neat aspect of this book is how it starts with an extensive Review chapter. Going over concepts like elementary geometry and algebra. This addresses a problem faced by many textbook authors. The audience can have widely divergent backgrounds. So the Review aims to calibrate students to a known base. The regular chapters then each go into a profusion of examples. Often with colourfully drawn diagrams. It is granted that some students with intrinsic ability will only need a few such examples to grasp the ideas in them. But the authors clearly hope that by furnishing enough examples, most diligent readers will be able to latch onto and understand some. Perhaps the hardest sections may be on analytic trigonometry and its applications. The numerous questions on proving trig identities can be fun to some and opaque to others. I enjoyed this stuff in other, earlier texts. But some readers will need to spent a lot of time scrutinising these chapters. What is striking about the examples is that they use Imperial units, like feet and miles per hour, instead of metric units. By now, most science and engineering texts, even in the US, have gone over to mostly, if not entirely, metric. Seems discordant and slightly archaic to find a text that does not do so.Was this review helpful? Yes NoThank you for your feedback. Report this reviewThank you, this review has been flagged.