Calculus I/AB introduces students to the foundational concepts of differential and integral calculus. It begins with the study of limits and continuity, which are essential for understanding how functions behave at specific points and over intervals. From there, students learn about derivatives—how to compute them, what they represent, and how to apply them to real-world problems. Derivatives describe rates of change and slopes of curves, and they are used extensively in analyzing motion, optimization, and curve sketching.
After mastering derivatives, Calculus I/AB transitions to the concept of integration. Students learn about antiderivatives, definite and indefinite integrals, and the Fundamental Theorem of Calculus, which connects differentiation and integration. Applications of integrals include calculating areas under curves, solving accumulation problems, and modeling total change in various contexts. By the end of Calculus I, students have a solid understanding of how to analyze and model dynamic systems using these fundamental tools.
Calculus II/BC builds on these ideas by exploring more advanced techniques of integration, such as integration by parts, partial fractions, and trigonometric substitution. The course also covers sequences and series, including convergence tests and power series representations of functions like Taylor and Maclaurin series. Additional topics may include parametric equations, polar coordinates, and applications of integration to problems involving volume, arc length, and surface area. Calculus II deepens students' analytical abilities and prepares them for multivariable calculus and higher-level mathematics.