Modifications for the Fourth Edition

Web Materials

We have deleted the material on Descartes Rule of Signs for this edition since we and our reviewers felt this topic, while useful, was not fundamental to precalculus. Although this material has been deleted from the third edition, we have modified it and placed it on our web site in PDF format. This permits instructors access to the material and, if they choose, to cover the topics without loss of continuity in their course. This was also done with Rotation of Axes for Conic Sections, which was in the first edition but not the second. It allows us to keep the book flexible, yet of a size that can be covered in one term. We intend to continue to add material to our web site that is requested by users of the book but is not covered in a majority of precalculus courses. For example, we have an entire chapter on Solving Systems of Equations on the web site; material that we wrote in response to a request from a user of the Second Edition.

Additional Examples and Applications

Each edition of PreCalculus has included applications of the material in many of the sections and in every chapter. In the fourth edition we have added additional applications to further emphasize the importance of precalculus and of the calculus course that they will soon be taking. To give added emphasis to the applications in this edition, each set of applications is headed with the title ''Applications.''

This edition also contains additional worked Examples to give even more clarification to certain topics. For example, we have added background material on factoring and examples that consider the typical kinds of factoring problems encountered in precalculus and calculus. We have provided similar examples on solving equations.

Exercise Sets

Before starting to write this edition, we went through every exercise set to be sure that the techniques covered in the examples are sufficient for students to work all the routine problems (generally the first 70%). Where necessary we then modified the exercise sets, rewrote text examples, and added additional text examples.

The Review Exercises were re-examined to ensure that a student who could work these problems truly had a firm grasp of the material in the chapter. Problems that consider topics not essential to a review have been moved from the Review Exercises. For example, exercises that extend the theory and application of the material of the book are always placed in the section exercises, not when a student needs to do a thorough review.

Accuracy

Every problem and example in the book has been checked by the authors as well as two independent accuracy checkers. One of the accuracy checkers was a student at Youngstown State University who was instructed to be particularly aware of situations where statements, even though correct, might be misinterpreted by students. Faculty often use a higher degree of formal rigor and logic than do students, and the mathematical vocabulary that faculty use is not always familiar to students. We wanted to be sure that this book is truly clear to the intended audience, while still using the mathematically precise statements that students will see in calculus.

Four-Color Format

In the third edition we introduced a modest four-color format. This worked well in the third edition and has been enhanced in this new edition. There is an important pedagogical reason for the adoption of four color in this book. Our major theme is to emphasize the problem-solving strategy of breaking new and difficult problems into a series of smaller, less difficult, and more familiar problems. This is particularly the case in our approach to graphing.

We consistently construct a small collection of functions whose graphs it is essential to know. Then we illustrate how techniques such as scaling, translation, and reflection can be used to construct graphs of many other functions. Having a variety of colors permits us to make the individual steps much clearer. We have consistently shown the base graphs in cyan, the first translation in red, and the next in yellow. Our students have found this to be a natural color transition. It permits them to better see precisely how the final graph is constructed, and shows that each individual step is not complex. The artist and the production editor have spent many hours creating what we feel is the best choice of colors to distinguish the various graphs, taking into consideration even things like assistance for those who have some tendency toward color blindness.

You will see very little other use of color in the book. It is used only where it adds to the understanding of the material or helps in the highlighting of important topics.