This course is available on MyMathLab® for School. The sixth edition of Calculus: Graphical, Numerical, Algebraic, AP* Edition, by Demana, Waits, Kennedy, Bressoud, and Boardman completely supports the content, philosophy, and goals of the Advanced Placement (AP*) Calculus courses (AB and BC).
• 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.
Changes to This Edition:
We welcome Michael Boardman to the author team. As a college mathematician with years of experience with the Advanced Placement program, he is well acquainted with the scope and goals of the course, and he is well versed in the mathematics that calculus students should know. Not only was Michael chief reader of the AP Calculus exams for four years, but he also served five years on the Development Committee and five years on the AP Calculus Workgroup for ETS. As perhaps his signal achievement, he founded the online discussion group for AP Calculus teachers and moderated it for a decade, so he truly understands what AP teachers and students are looking for in these pages.
A Few Global Changes
As with previous editions, we have kept our focus on high school students taking one of the College Board’s AP courses, Calculus AB or Calculus BC. The topics in the text reflect both the curriculum and the pedagogy of an AP course, and we do what we can to prepare students for the AP examinations throughout the text. To be consistent with the AP exam, we have changed all multiple-choice questions in the exercises to show four options rather than five. Also, as free-response questions on the AP examinations continue to evolve in focus and style, we have added or amended our exercises to reflect those changes. Although the role of graphing calculators in the course has not changed significantly since the fifth edition, we continue to review the gray “no calculator” ovals in the exercise sets to reflect an emerging consensus among calculus teachers that not every problem that can be solved without a calculator ought to be solved without a calculator.
We have further expanded the treatment of the derivative as a measure of sensitivity, which now appears as an ongoing topic in several different sections of the text. We have also enhanced our commitment to point-slope form for linear equations throughout the text, writing them all in a form that emphasizes the concept of local linearity, critical for understanding differential calculus.
Two new features have been added in response to the MPACs. There are now Notational Fluency Notes sprinkled throughout the text, and each set of Chapter Review Exercises begins with Reasoning with Definitions and Theorems questions that require students (individually or with their classmates) to dig more deeply into the concepts of calculus in order to understand them better.
Most of the motivational “Chapter Opener” problems are new and improved in this edition, and (thanks to David) many more historical nuggets have been sprinkled throughout the book. We also confess that some of the nuggets that were already there were in need of refinement. For example, the curious object called Gabriel’s Horn in previous editions is now called Torricelli’s Trumpet, with an accompanying historical note to give full credit where credit is due.
Finally, be assured that we have looked carefully at the content of the new AP Calculus Curriculum Framework, and there is nothing therein that is not covered in this text. Moreover, the emphases are in harmony with the objectives of the AP course, as they have always been.