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## ThirdEdition| ©2020Michael Sullivan; Kathleen Miranda

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

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Trusted authors and integrated student support for success in AP® Calculus.

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.

Features

**AP® Exam Prep within Your Text**

- AP® Exam Tips throughout the text in the minor column
- At Section level: AP® Practice Problems cover content that may appear on the AB or BC version of the exam
- At Chapter level: AP® Review Problems include multiple choice and model FRQs for exam practice all year
- At Chapter level: AP Cumulative Review Problem sets encourage retention of content through cross-chapter review.
- Two AP® Practice Exams
- 1 full-length Calculus AB practice test, after chapter 8
- 1 full- length Calculus BC practice test, after chapter 10

**Review and Reinforce on all Levels**

- Abundant practice is provided through a well-scaffolded set of exercises at the section, chapter, and cross-chapter cumulative levels.
- The end of each section features exercise sets that focus on:
- Concepts and Vocabulary
- Skill Building
- Applications and Extensions
- Challenge Problems
- AP® Practice Problems
- All chapters end with general and AP® Review problems
- Things to Know
- Objectives Table
- Chapter Review Exercise set (covering all chapter concepts)
- AP® Review Problems that include multiple-choice and FRQ questions (cover chapter concepts)

**Created to meet your students' needs**

- Written at an accessible level so that students can handle the concepts and the worked examples.
- The textbook offers economical, focused description with integrated support written to be read and understood by students as they learn calculus and prepare for the AP® Exam
- Sullivan and Miranda’s distinctive NOW WORK example feature promotes good habits by directing students from a worked example in main text to a problem in the section exercise set that mirrors the example, providing immediate practice and reinforcement. Since we recognize that many students begin with exercises and seek help only as needed, we have crafted this backward/forward navigation system that effectively directs student from exercise to example and vice versa.
- Includes numerous examples with worked solutions to serve as models for your students. Examples are calibrated in difficulty throughout sections to help students attain higher skill levels in dealing with complexity.
- Selected worked examples are supported by short video clips that provide step-by-step support that give a worked example that mirrors the in-text example (CalcClips).
- All AP® Review Problems are accompanied by short video clips that provide step-by-step support through the AP® problem.
- All AP® Cumulative Review Problems are accompanied by short video clips that provide step-by-step support through the AP® problem.

**Mind the Margins**

Additional help for students is provided by taking advantage of the minor column to place eye-catching, helpful features:

- AP® EXAM TIPs: Contains explanations and suggestions to help students prepare for the AP® exam.
- NEED TO REVIEW: Pinpoints cross-references to prior topics that students have to know to master new content.
- RECALL: Provides a quick refresher of important information, which is used in examples, theorems, definitions, and descriptions.
- NOTE: Provides supporting details to content on that page to help further explain topics.
- CAUTION: Warns students about misconceptions and pitfalls.
- ORIGINS: Gives background and biographical information about key figures and discoveries as calculus developed.
- IN WORDS: On-the-spot help in translating definitions, formulas, theorems, proofs, and corollaries into clear, plain language to support students when and where they need it.

**Engage your students**

- Chapter Projects are introduced at the opening of each chapter and are revisited at the end of the chapter to help relate calculus to everyday life, which provides students with a chance to apply the math that they learned throughout the chapter.
- Additional, "just-in-time," help is offered through a suite of videos that accompany selected worked examples (CalcClip), AP Review Problems (at the end of chapters), and the AP Cumulative Review Problem sets. In these videos, experienced AP teachers walk students step-by-step through key examples, AP review, and major concepts.

New to This Edition

**The third edition of Sullivan and Miranda’s Calculus for the AP® Course mirrors the unit structure set out in College Board’s 2019 Course and Exam Description (CED).**

- Chapters are reordered to align with the new unit structure.
- AP® Cumulative Review Problem sets included for Chapters 2-10.
- Chapter 7 includes differential equations, which are included to show that the authors’ coverage aligns with the new unit structure and personalized progress checks.
- Streamlined coverage of certain topics that receive less attention in the 2019 CED.
- Aligned terminology that accords better with The College Board’s usage.
- Additional topics that receive more coverage in the 2019 CED.

Basic coverage of polar coordinates and vectors are located in Appendix A for an additional resource for BC students.

A strong *SaplingPlus* e-book and Online Homework offering built for this edition with approximately 2000+ questions (many of which are algorithmically created, essentially making thousands more). Along with these, *SaplingPlus* will also include the following in-book questions with targeted feedback:

- All of the end-of-section, end-of-chapter, and AP® Practice problems.
- All of the problems in the "suggested assignments" grid in Teacher’s Edition.
- All of the NOW WORK problems.

**A fully updated teacher resources suite to match the 3 ^{rd} edition:**

- New Teacher’s Edition, Teacher Resources Flashdrive, and Examview Flashdrive.
- Welcoming expert AP® Calculus educator and AP® Exam Reader Joshua Newton to the team as a co-author to the Teacher’s Edition, Joining fellow AP® Exam Reader and veteran AP® Calculus and mathematics teacher, Brent Ferguson.

The teacher resources will now include Desmos activities to give teachers the opportunity to use **Desmos** in the classroom that goes beyond problem setup and solution.

"WOW! This is BY FAR the BEST calculus book I have seen in my 20+ years of teaching."

- Kent Thele (John Paul II High School)"Calculus for the AP® Course does a phenomenal job of not only preparing students for the AP® exam, but also showing each student the connections between the calculus classroom, the workplace, and the world."

- Textbook & Academic Authors Association (TAA) Judge."If I had any issues I was able to get in touch with someone that was easily accessible. That is the #1 thing about working [with BFW]. It really paid off that [our district] switched over [to Calculus for the AP® Course, 3e]."

-AP® Calculus Teacher, Pennsylvania"This is a phenomenal textbook that is really lined up with the AP® exam...I'm really happy and my students are excited to use this textbook. In the past, our old textbook wasn't as exciting."

-AP® Calculus Teacher, Pennsylvania

## 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

**Calculus for the AP® Course**

Third Edition| 2020

Michael Sullivan; Kathleen Miranda

Find Your Rep

### Michael Sullivan

**Michael Sullivan**, Emeritus Professor of Mathematics at Chicago State University, received a Ph.D. in mathematics from the Illinois Institute of Technology. Before retiring, Mike taught at Chicago State for 35 years, where he honed an approach to teaching and writing that forms the foundation for his textbooks. Mike has been writing for more than 35 years and currently has 15 books in print. His books have been awarded both Texty and McGuffey awards from the Textbook and Academic Authors Association (TAA). In 2007, he received the TAA Lifetime Achievement Award. Mike is a member of the American Mathematical Association of Two Year Colleges, the American Mathematical Society, the Mathematical Association of America, and the Textbook and Academic Authors Association.

### Kathleen Miranda

**Kathleen Miranda**, Ed.D from St. John’s University, is an Emeritus Associate Professor of the State University of New York (SUNY), where she taught for 25 years. Kathleen is a recipient of the prestigious New York State Chancellor’s Award for Excellence in Teaching, and she particularly enjoys teaching mathematics to underprepared and fearful students. Kathleen served as director of Curriculum and Assessment Development at Old Westbury. In addition to her extensive classroom experience, Kathleen has worked as accuracy reviewer and solutions author on several mathematics textbooks, including Michael Sullivan’s Brief Calculus and Finite Mathematics. Kathleen’s goal is to help students unlock the complexities of calculus and appreciate its many applications.

**Calculus for the AP® Course**

ThirdEdition| 2020

Michael Sullivan; Kathleen Miranda

Find Your Rep

## Need instructor resources for your course?

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### Chapter 2 AP Skill Builders

### Chapter 2 Alternate Examples

### Chapter 2 Bell Ringers

### Chapter 2 Calc Clips

### Chapter 2 Correlation Guide

### Chapter 2 Desmos Activities

### Chapter 2 Flashcards

### Chapter 2 Prepared Tests

### Chapter 2 Projects and Solutions

### Chapter 2 Student Solutions Manual (coming soon)

### Chapter 2 Teacher's Solutions Manual

### Chapter 2 Videos Overview

### Chapter 2 Web Resources

### Chapter 2 Worksheets

### ExamView Assessment Suite for Calculus for the AP® Course

Michael Sullivan; Kathleen Miranda | ThirdEdition | ©2020 | ISBN:9781319248789With more than 2000 questions (many of which are algorithmic) written by our extended team of AP® Calculus and content expert this testbank provides t...

### Teacher's Edition for Calculus for the AP® Course

Michael Sullivan; Kathleen Miranda | ThirdEdition | ©2021 | ISBN:9781319248185This one-of-kind Teacher’s Edition, built specifically for the 3rd edition of Sullivan and Miranda, provides an in-depth correlation as well as AB and...

### Teacher's Resource Flash Drive for Calculus for the AP® Course

Michael Sullivan; Kathleen Miranda | ThirdEdition | ©2020 | ISBN:9781319248796This invaluable resource includes the essential teacher resources that go along with Sullivan/Miranda 3rd edition program, including: Calc Clip videos...

## Videos

Introduction to SaplingPlus

This video explains the value of Bedford, Freeman & Worth's SaplingPlus platform for teachers and students.