Calculus

This book was specifically designed and written for teachers and students of Advanced Placement Calculus. Our approach is based on many years of teaching calculus at diverse institutions using the best teaching practices we know. We collaborated with over 90 academic experts and classroom practitioners to develop the correct blend of rigorous content, accessible support, flexible resources, and engaging instruction to help students master the essential mathematical and communication skills they need to achieve their AP goals. Although the book was written with the most recent AP syllabi in mind, it also contains several topics that do not appear on those syllabi, but are often covered in the first two semesters of a standard college-level calculus sequence. For this reason, the book not only provides preparation for the AP Exam, but also serves as a foundation for additional mathematical course work at the college level. Throughout this book, a concise and lively narrative motivates the ideas of calculus. All topics are introduced through concrete examples, applications, and analogies rather than through abstract arguments. We appeal to students' intuition and geometric instincts to make calculus natural and believable. Once this intuitive foundation is established, generalizations and abstractions follow.