Calculus for the AP Course

Specifically designed to support the needs of AP® students and teachers as well as align with the current College Board AP® Calculus Course and Exam Description (CED), Sullivan and Miranda’s Calculus for the AP® Course, third edition, offers a student-friendly and focused narrative with distinctive features that provide integrated support.

This edition has been carefully developed to ensure that it adheres to the unit structure and coverage as set forth in the 2019 CED. Further, it aligns with the College Board’s overarching structure, meaning every Big Idea, Mathematical Practice, and Student Skill. This edition also aligns with the revised pedagogy of Enduring Understanding, Learning Objective, and Essential Knowledge statement that flow from the three revised Big Ideas.

Written to be read and understood by students as they learn calculus and prepare for either the AP® Calculus AB or AP® Calculus BC Exam – the Sullivan Miranda program offers abundant practice, AP® Specific content, distinctive features, and built-in support. The third edition comes complete with our SaplingPlus online-homework platform and a full set of updated teacher resources.

About the Authors
Acknowledgments

What Is Calculus?
Student’s Guide to This Book

Chapter P Preparing for Calculus

UNIT 1 Limits and Continuity

Chapter 1 Limits and Continuity

UNIT 2 Differentiation: Definition and Fundamental Properties

Chapter 2 The Derivative and Its Properties

UNIT 3 Differentiation: Composite, Implicit, and Inverse Functions

Chapter 3 The Derivative of Composite, Implicit, and Inverse Functions

UNIT 4 Contextual Applications of Differentiation

Chapter 4 Applications of the Derivative, Part 1

UNIT 5 Analytical Applications of Differentiation

Chapter 5 Applications of the Derivative, Part 2

UNIT 6 Integration and Accumulation of Change

Chapter 6: Part 1 The Integral

Chapter 6: Part 2 Techniques of Integration

UNIT 7 Differential Equations

Chapter 7: Differential Equations

UNIT 8 Applications of Integration

Chapter 8: Applications of the Integral

AP® Practice Exam: Calculus AB

UNIT 9 Parametric Equations; Polar Coordinates; and Vector-Valued Functions

Chapter 9: Parametric Equations; Polar Coordinates; Vector Functions

UNIT 10 Infinite Sequences and Series

Chapter 10: Infinite Series

AP® Practice Exam: Calculus BC

Appendix A Precalculus Used in Calculus

Appendix B Theorems and Proofs

Appendix C Using Calculators on the AP® Calculus Exam

Answers

End Sheets

Table of Derivatives

Table of Integrals

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