What do students really need to know to be prepared for calculus? What tools do instructors really need to assist their students in preparing for calculus? These two questions have motivated the writing of this book.
To be prepared for calculus a student needs not only technical skill but also a clear understanding of concepts. Indeed, conceptual understanding and technical skill go hand in hand, each reinforcing the other. A student also needs to gain an appreciation for the power and utility of mathematics in modeling the real world. Every feature of this textbook is devoted to fostering these goals.
In this Seventh Edition our objective is to further enhance the effectiveness of the book as an instructional tool for teachers and as a learning tool for students. Many of the changes in this edition are a result of suggestions we received from instructors and students who are using the current edition; others are a result of insights we have gained from our own teaching. Some chapters have been reorganized and rewritten, new sections have been added (as described below), the review material at the end of each chapter has been substantially expanded, and exercise sets have been enhanced to further focus on the main concepts of precalculus. In all these changes and numerous others (small and large) we have retained the main features that have contributed to the success of this book.
New to the Seventh Edition
■ Exercises More than 20% of the exercises are new, and groups of exercises now have headings that identify the type of exercise. New Skills Plus exercises in most sections contain more challenging exercises that require students to extend and synthesize concepts.
■ Review Material The review material at the end of each chapter now includes a summary of Properties and Formulas and a new Concept Check. Each Concept Check provides a step-by-step review of all the main concepts and applications of the chapter. Answers to the Concept Check questions are on tear-out sheets at the back of the book.
■ Discovery Projects References to Discovery Projects, including brief descriptions of the content of each project, are located in boxes where appropriate in each chapter. These boxes highlight the applications of precalculus in many different real-world contexts. (The projects are located at the book companion website: www.stewartmath.com.)
■ Geometry Review A new Appendix A contains a review of the main concepts of geometry used in this book, including similarity and the Pythagorean Theorem.
■ CHAPTER 1 Fundamentals This chapter now contains two new sections. Section 1.6, “Complex Numbers” (formerly in Chapter 3), has been moved here. Section 1.12, “Modeling Variation,” is now also in this chapter.
■ CHAPTER 2 Functions This chapter now includes the new Section 2.5, “Linear Functions and Models.” This section highlights the connection between the slope of a line and the rate of change of a linear function. These two interpretations of slope help prepare students for the concept of the derivative in calculus.
■ CHAPTER 3 Polynomial and Rational Functions This chapter now includes the new Section 3.7, “Polynomial and Rational Inequalities.” Section 3.6, “Rational Functions,” has a new subsection on rational functions with “holes.” The sections on complex numbers and on variation have been moved to Chapter 1.
■ CHAPTER 4 Exponential and Logarithmic Functions The chapter now includes two sections on the applications of these functions. Section 4.6, “Modeling with Exponential Functions,” focuses on modeling growth and decay, Newton’s Law of Cooling, and other such applications. Section 4.7, “Logarithmic Scales,” covers the concept of a logarithmic scale with applications involving the pH, Richter, and decibel scales.
■ CHAPTER 5 Trigonometric Functions: Unit Circle Approach This chapter includes a new subsection on the concept of phase shift as used in modeling harmonic motion.
■ CHAPTER 10 Systems of Equations and Inequalities The material on systems of inequalities has been rewritten to emphasize the steps used in graphing the solution of a system of inequalities.