Precalculus: Mathematics For Calculus

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.
We are keenly aware that good teaching comes in many different forms, and that each instructor brings unique strengths and imagination to the classroom. Some instructors use technology to help students become active learners; others use the rule of four, "topics should be presented geometrically, numerically, algebraically, and verbally," to promote conceptual reasoning; some use an expanded emphasis on applications to promote an appreciation for mathematics in everyday life; still others use group learning, extended projects, or writing exercises as a way of encouraging students to explore their own understanding of a given concept; and all present mathematics as a problem-solving endeavor. In this book we have included all these methods of teaching precalculus as enhancements to a central core of fundamental skills.
These methods are tools to be utilized by instructors and their students to navigate their own course of action in preparing for calculus.
In writing this fifth edition our purpose was to further enhance the utility of the book as an instructional tool. The main change in this edition is an expanded emphasis on modeling and applications: In each section the applications exercises have been expanded and are grouped together under the heading Applications, and each chapter (except Chapter 1) now ends with a Focus on Modeling section. We have also made some organizational changes, including dividing the chapter on analytic trigonometry into two chapters, each of more manageable size. There are numerous other smaller changes—as we worked through the book we sometimes realized that an additional example was needed, or an explanation could be clarified, or a section could benefit from different types of exercises. Throughout these changes, however, we have retained the overall structure and the main features that have contributed to the success of this book.