Calculus for the AP® Course

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.  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.

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