Features and Benefits
- Outstanding author team with expertise on the AP* Calculus exam.
- Adheres to the new guidelines for AP* Calculus and includes preparation on the new tyes of test questions.
- AP Preface contains correlation between AP curriculum and the text.
- Written especially for high school students preparing for both the AB and BC AP* Calculus exam.
- AP* Preface contains correlation between AP* curriculum and the text.
- New! Annotated Teacher's Edition.
Also available with 5 ADDITIONAL chapters—Complete Calculus: Graphical, Numerical, Algebraic.
- Vectors and Analytic Geometry in Space
- Vector-Value Functions and Motion in Space
- Multivariable Functions and Their Derivatives
- Multiple Integrals
- Integration in Vector Fields
Samples are available to institutional buyers only.
Getting the Most from This Book
Chapter Openers provide a motivating photo and application to show students an example of the relevance of what they'll be learning in the chapter.
A Chapter Overview begins each chapter to give students a sense of what they are going to learn. This overview provides a roadmap of the chapter as well as telling how the different topics in the chapter are connected under one big idea. It is always helpful for students to remember that mathematics isn't modular, but interconnected, and that the different skills they are learning throughout the course build on one another to help them understand more complex concepts.
What You'll Learn About ... and Why
This feature prepares students for what they will learn in the upcoming section. It provides students the big ideas in each section and explains their purpose. Students can read this as they begin the section and then again after they have completed that section to make sure they understand all of the key topics they have just studied.
Explorations appear throughout the text and provide students with the perfect opportunity to become an active learner and discover mathematics on their own. Honing critical thinking and problem-solving skills will ultimately benefit your students on all of their AP* Exams.
Brief Historical Notes present the stories of people and the research that they have done to advance the study of mathematics.
Each exercise set begins with a Quick Review to help students review skills needed in the exercise set, reminding them again that mathematics is not modular. If they find these problems challenging, they are encouraged to go back through the book to review the material covered in previous chapters. This further reinforces the idea that they need to understand the material from the entire calculus course for the AP* Calculus Exam, not just memorize the concepts from the last part of the course.
The exercise sets were revised extensively for this new edition, including many new ones. There are nearly 4,000 exercises, with more than 80 Quick Quiz exercises and 560 Quick Review exercises. The different types of exercises included are:
- algebraic and analytic manipulation
- interpretation of graphs
- numerical representations
- writing to learn
- group activities
- data analyses
- descriptively titled applications
- extending the ideas
Each example ends with a suggestion to Now Try a related exercise. Working the suggested exercise is an easy way for students to check their comprehension of the material while reading each section, instead of waiting to the end of each section or chapter to see if they Œgot it.' True comprehension of the material is essential for student success on the AP* Exam.
AP* Examination Preparation questions
These questions appear at the end of each set of chapter review exercises and include 3 free-response questions of the AP* type. This set of questions, which may or may not permit the use of a graphing calculator, gives your students additional opportunity to practice skills and problem-solving techniques needed for the AP* Calculus Exam.
The course outlines for AP* Calculus reflect changes in the goals and philosophy of calculus courses now being taught in colleges and universities. The following objectives reflect the goals of the curriculum.
- Students should understand the meaning of the derivative in terms of rate of change and local linear approximations.
- Students should be able to work with functions represented graphically, numerically, analytically, or verbally, and should understand the connections among these representations.
- Students should understand the meaning of the definite integral both as a limit of Riemann sums and as a net accumulation of a rate of change, and understand the relationship between the derivative and integral.
- Students should be able to model problem situations with functions, differential equations, or integrals, and communicate mathematics both orally and in written form.
- Students should be able to represent differential equations with slope fields, solve separable differential equations analytically, and solve differential equations using numerical techniques such as Euler's method.
- Students should be able to interpret convergence and divergence of series using technology, and to use technology to help solve problems. They should be able to represent functions with series and find the Lagrange error bound for Taylor polynomials.
- This revision of Finney, Demana, Waits, Kennedy, Calculus: Graphical, Numerical, Algebraic Third Edition completely supports the content, goals, and philosophies of the new Advanced Placement* calculus course description.
- Also available—Calculus: A Complete Course, 3e. Includes 5 additional chapters on multivariables.
*AP and Advanced Placement are registered trademarks of the College Entrance examination Board, which was not involved in the production of, and does not endorse, this book.
AP® is a trademark registered and/or owned by the College Board, which was not involved in the production of, and does not endorse, this product.