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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 Precalculus students. As a teacher, and as an author of precalculus, engineering calculus, finite mathematics, and business calculus texts, Michael understands what students must know if they are to be focused and successful in upper level mathematics courses. As a father of four, including the co-author, he also understands the realities of college life. His co-author and son, Michael III, believes passionately in the value of technology as a tool for 'learning that enhances understanding without sacrificing important skills.
Precalculus texts too often are simply condensed versions of algebra and trigonometry texts. College algebra and algebra and trigonometry students are different from precalculus students and their texts should reflect this difference. For example, Chapter 13, A Preview of Calculus: the Limit, Derivative, and Integral of a Function, not only demonstrates to students how the material of Precalculus applies to calculus, but also moves the student into calculus. Throughout this text there are references to calculus, shown by a calculus icon to further motivate and remind the student that this mathematics will be used later. There are other, more subtle, aspects of this text that prepare the student for calculus. For example, many applications that are traditional to calculus have been inserted as algebra and trigonometry problems. These examples and exercises are designed to emphasize the role of algebra and trigonometry in calculus and to encourage and motivate students inPrecalculus to further insure their success in calculus.
Together, Michael and Michael, III have taken great pains to ensure that this text contains solid, student-friendly examples and exercises, as well as a clear, seamless writing style. Please share with them your experiences teaching from this text.
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 ultimately based. Virtually every change to this edition is the result of thoughtful comments and suggestions from colleagues and students who used previous editions. We are sincerely grateful for this feedback and have tried to make changes that improve the usefulness of the text for both instructors and students.
Preparing for This Section
Most sections now open with a referenced list (by section and page number) of key items to review in preparation for the section ahead. This provides a just-in-time review for students.
Concepts and Vocabulary
At the end of every section, there is a short list of Fill-in-the-Blank and True/False items that test concepts and vocabulary in a short answer format. Several quick-answer questions are also included.
At the end of Chapters 2-12, exercises are provided that require skills learned in the earlier chapters. These cumulative reviews serve to continually rein force the important concepts of Precalculus. They also make it easier for the student to prepare for a comprehensive final examination.
The formula for the area of a sector and related exercises are now part of --Section 5.1 Angles and Their Measure.
Combining Waves is a new subsection in Section 7.5 Simple Harmonic Motion; Damped Motion; Combining Waves.
The Cross Product is a new section in Chapter 8 Polar Coordinates; Vectors.
The Area Problem; the Integral is a new section in Chapter 13 A Preview of Calculus: the Limit, Derivative, and Integral of a Function
New Chapter Projects have been added that discuss topics of current interest.
Scatter diagrams, formerly part of Section 1.1, now appear in Section 2.2 Linear Functions and Models. This change positions the content where it is being used.
Setting up Equations; Applications, formerly Section 1.4, now is part of the Appendix. This change allows those who wish to finish Chapter 1 more quickly, the opportunity to do so. If you wish, it can be covered anytime after Section 1.4.
Circles, formerly Section 1.7, now is part of Section 1.3.
The discussion on Rational Functions, formerly Section 3.7, now appears earlier in Chapter 3 as two sections. This division makes it possible to teach the sections in one period each.
Complex Numbers; Quadratic Equations with a Negative Discriminant, formerly Section 3.5, now is part of the Appendix. This change now makes the material of Chapter 3 more consistent in level of difficulty. For those who wish to cover quadratic equations with a negative discriminant early, this section may be covered anytime after Section 1.4. Finally, this material can be used as a just-in-time review of complex numbers before Section 3.8 Complex Zeros; Fundamental Theorem of Algebra and before Section 8.3 The Complex Plane; DeMoivre's Theorem.
Section 4.3, Exponential Functions, now contains a subsection on exponential equations; Section 4.4, Logarithmic Functions, now contains a subsection on logarithmic equations.
The discussion on Right Triangle Trigonometry, formerly Section 5.4, has been relocated to Chapter 7, Applications of Trigonometry. This change makes the material of Chapter 5 more consistent in level of difficulty. For those who wish to cover this material earlier, this section can be covered anytime after Section 5.3.
Graphs of the Trigonometric Functions and Sinusoidal Graphs; Sinusoidal Curve Fitting, formerly Sections 5.5 and 5.6, now is covered in three sees dons, 5.4, 5.5, and 5.6. This change makes it possible to teach the section in one period each.
The Inverse Trigonometric Functions, formerly Section 6.5, now is covered in two sections at the beginning of the chapter. This change makes it possible to teach the sections in one period each. It also places the content closer to the discussion of the trigonometric functions and their graphs.
To meet the varied needs of diverse syllabi, this book contains more content than expected in a precalculus 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 are optional and can be skipped without fear of future problems.
Chapter 1. Graphs
This chapter is a briefer version of the former Chapter 1. A quick coverage of this chapter, which is mainly review material, will enable you to get to Chapter 2 Functions and their Graphs earlier.
Chapter 2. Functions and Their Graphs
Perhaps the most important chapter. Section 2.7 is optional.
Chapter 3. Polynomial and Rational Functions
Topic selection is dependent on your syllabus.
Chapter 4. Exponential and Logarithmic Functions
Sections 4.1-4.5 follow in sequence. Sections 4.6, 4.7, and 4.8 are optional; each of these requires Section 4.3.
Chapter 5. Trigonometric Functions
The sections follow in sequence. Section 5.6 is optional.
Chapter 6. Analytic Trigonometry
The sections follow in sequence. Sections 6.2, 6.6, and 6.8 may be skipped in a brief course.
Chapter 7. Applications of Trigonometry
The sections follow in sequence. Sections 7.4 and 7.5 are optional.
Chapter 8. Polar Coordinates; Vectors
Sections 8.1-8.3 and Sections 8.4-8.7 are independent and may be covered separately.
Chapter 9. Analytic Geometry
Sections 9.1-9.4 follow in sequence. Sections 9.5,9.6, and 9.7 are independent of each other, but do depend on sections 9.1-9.4.
Chapter 10. Systems of Equations and Inequalities
Sections 10.1-10.2 follow in sequence; Sections 10.3-10.8 require Sections 10.1-10.2, but may be covered in any order. Section 10.7 also requires Sections 9.1-9.4. Section 10.9 requires Section 10.8.
Chapter 11. Sequences; Induction; The Binomial Theorem
There are three independent parts: Sections 11.1-11.3; Section 11.4; and Section 11.5.
Chapter 12. Counting and Probability
Sections 12.1-12.3 follow in sequence; Section 12.4 is optional.
Chapter 13. A Preview of Calculus: the Limit, Derivative, and Integral of a Function
If time permits, coverage of this chapter will give your students a beneficial head-start in calculus. The sections follow in sequence.
Sections A.1-A.6 and Section A.9 consist of review material, which can be used as the first part of a course in Precalculus or as a just-in-time review. Specific references to this material occur throughout the text to assist in the review process. Coverage of Sections A.7 and A.8 depends on your syllabus.