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# Calculus for the AP® Course

## Third EditionMichael Sullivan; Kathleen Miranda

©2020Sullivan and Miranda's *Calculus for the AP®, Third Edition* offers a trusted and student-friendly approach to learning calculus while preparing students for either the AP® Calculus AB or AP® Calculus BC exam. The text is built around worked examples set in readable chapters that are closely aligned with the newest AP® Calculus course and exam description. Extensive integrated support coupled with plenty of practice problems prepares students for the AP® exam. This is the most trust AP® Calculus program available.

## Table of Contents

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