Calculus Graphical, Numerical, Algebraic, AP Edition, Annotated Teachers Edition, 5th Edition

Book Preface

If you could wave a magic wand and assemble your dream team of authors for an AP Calculus textbook, you would be very pleased if the group included the likes of Ross
Finney, Frank Demana, Bert Waits, Dan Kennedy, and David Bressoud. I feel blessed to have known and worked closely with every one of them from as far back as 1989. With a pedigree that includes George Thomas in the storied authorship bloodline, this book represents the finest combination of excellent writing, creative insight, terrific problems, and captivating explorations. A dream team indeed!
Any teacher in search of a textbook for use in an AP Calculus class should look critically at whether or not the book is faithful to the philosophy and goals of the course, as well as the topic outline, each described in the AP Calculus Course Description. On both accounts, the FDWKB text shines brightly. True to its title, care is taken to attend to a genuine multirepresentational approach. You’ll find problems and discourse involving graphs, tables, symbolic definitions, and verbal descriptions. And the text covers every topic that is tested on the AP exams. Dan Kennedy, who joined the author team with the 2003 publication, and David Bressoud, its most recent addition, both contribute an intimate knowledge of the AP Calculus course. The two share a familiarity with the program borne from years of service. Back in the mid 1990s, when I saw Dan describe how to teach series with an approach that ultimately became an integral part of Chapter 10 of the current edition, I knew it was the way to go. My students have used this text, and that approach, for many years with great success. David’s presence on the team brings his passion both for the history of calculus and for its careful and precise presentation. He describes the contributions to the development of calculus by great thinkers that preceded Newton and Leibniz. He also illuminates the idea of using the derivative as a measure of sensitivity.
This text is a proven winner that just keeps getting better. With the new course framework rolling out, it is a perfect fit for any AP Calculus class today, and promises to be for years to come.
Mark Howell
Gonzaga College High School
Washington, DC
foreword
Mark Howell has taught AP Calculus at Gonzaga High School for more than thirty years. He has served the AP Calculus community at the AP Reading as a reader, table leader, and question leader for eighteen years, and for four years he served as a member of the AP Calculus Development Committee. A College Board consultant for more than twenty years, Mark has led workshops and summer institutes throughout the United States and around the world. In 1993 he won a state Presidential Award in the District of Columbia, and in 1999 he won a Tandy Technology Scholars Award and the Siemens Foundation Award for Advanced Placement Teachers. He is the author of the current AP Teacher’s Guide for AP Calculus, and is co-author with Martha Montgomery of the popular AP Calculus review book Be Prepared for the AP Calculus Exam from Skylight Publishing.

The fifth edition of Calculus: Graphical, Numerical, Algebraic, AP* Edition, by Finney, Demana, Waits, Kennedy, and Bressoud completely supports the content, philosophy, and goals of the Advanced Placement (AP*) Calculus courses (AB and BC).
The College Board has recently finished a lengthy and thorough review of the AP* Calculus courses to ensure that they continue to keep pace with the best college and university courses that are taught with similar educational goals. This review has resulted in a repackaging of the course descriptions in terms of big ideas, enduring understandings, learning objectives, and essential knowledge, but the learning goals remain essentially the same. That has allowed us to retain the overall flow of our previous edition and concentrate our attention on how we might be more helpful to you and your students in certain parts of the course.
A very broad look at the overall goals of this textbook is given in the following bulleted summary. Although these are not explicit goals of the AP program and do not include all of the learning objectives in the new AP Curriculum Framework, they do reflect the intentions of the AP Calculus program. (Note that the asterisked goals are aligned with the BC course and are not required in AB Calculus.)
• Students will be able to work with functions represented graphically, numerically, analytically, or verbally, and will understand the connections among these representations; graphing calculators will be used as a tool to facilitate such understanding.
• Students will, in the process of solving problems, be able to use graphing calculators to graph functions, solve equations, evaluate numerical derivatives, and evaluate numerical integrals.
• Students will understand the meaning of the derivative as a limit of a difference quotient and will understand its connection to local linearity and instantaneous rates of change.
• Students will understand the meaning of the definite integral as a limit of Riemann sums and as a net accumulation of change over an interval, and they will understand and appreciate the connection between derivatives and integrals.
• Students will be able to model real-world behavior and solve a variety of problems using functions, derivatives, and integrals; they will also be able to communicate solutions effectively, using proper mathematical language and syntax.
• Students will be able to represent and interpret differential equations geometrically with slope fields and (*) numerically with Euler’s = method; they will be able to model dynamic situations with differential equations and solve initial value problems analytically.
• (*) Students will understand the convergence and divergence of infinite series and will be able to represent functions with Maclaurin and Taylor series; they will be able to approximate or bound truncation errors in various ways.
• (*) Students will be able to extend some calculus results to the context of motion in the plane (through vectors) and to the analysis of polar curves.
The incorporation of graphing calculator technology throughout the course continues to be a defining feature of this textbook, but we urge teachers to read the next section, Philosophy on Technology Usage, to see how our philosophy has changed over time (again, in harmony with our AP* Calculus colleagues). Whether you are concerned about how to use calculators enough or how not to use calculators too much, we believe you can trust this author team to address your concerns with the perspective that only long experience can provide. Whether you are a veteran user of our textbooks or are coming on board for this fifth edition, we thank you for letting us join you in the important adventure of educating your students. Some of the best suggestions for improving our book over the years have come from students and teachers, so we urge you to contact us through Pearson if you have any questions or concerns. To paraphrase Isaac Newton, if this textbook enables your students to see further down the road of mathematics, it is because we have stood on the shoulders of dedicated teachers like you.