Introducing the ultimate resource for AP® Calculus students and teachers - Sullivan and Mirandas Calculus for the AP® Course, fourth edition. This student-friendly book has been specially designed to align with the College Board AP® Calculus Course and Exam Description (CED).

What sets this edition apart is its comprehensive coverage of every Big Idea, Mathematical Practice, and Student Skill outlined by the College Board. It also incorporates the revised pedagogy of the Enduring Understanding, Learning Objective, and Essential Knowledge statements based on the three revised Big Ideas.

With a focus on clarity and understanding, this book ensures that students are well-prepared for both the AP® Calculus AB and AP® Calculus BC exams. The Sullivan Miranda program offers plenty of practice, AP® specific content, and unique features to enhance learning. Plus, it includes access to our online-homework platform, Achieve, and a range of updated teacher resources. Get ready to excel in AP® Calculus like never before!

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. His publications include Finite Mathematics, College Algebra, Algebra and Trigonometry, Precalculus, Business Calculus, Engineering Calculus, and AP Calculus.
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. Mike serves on the governing board of TAA and represents TAA on the board of the Authors Coalition of America, a consortium of 22 author/creator organizations in the United States. Several of his texts have received TAA’s McGuffey Longevity Award. In 2007, he was awarded the TAA Lifetime Achievement Award and in 2023 the Alumni Award for Excellence from St. Ignatius College Prep in Chicago.
His influence in the field of mathematics extends to his four children: Kathleen, who teaches college mathematics; Michael III, who also teaches college mathematics, and who is his coauthor on two precalculus series; Dan, who is a sales director for a college textbook publishing company; and Colleen, who teaches middle-school and secondary school mathematics. Twelve grandchildren round out the family.
Mike would like to dedicate this text to his four children, 12 grandchildren, and future generations.
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. She particularly enjoys teaching mathematics to underprepared and fearful students. Kathleen has served as director of Curriculum and Assessment Development at SUNY 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.
Kathleen has four children, all of whom took AP Calculus. Each used the concepts and skills learned in AP Calculus both in college and graduate school. AP Calculus continues to have an impact in their chosen professions: medicine, engineering, strategic planning, and business development.
Kathleen would like to dedicate this text to her children and grandchildren.

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 Equations; 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

• Index of Applications
• Subject Index