Course Description
Chapter 1: Limits
In this chapter, we will learn about the operations and properties of the foundation of calculus: limits. Additionally, we will explore continuous functions and an important theorem—the Intermediate Value Theorem. This chapter serves as a warm-up for the rest of calculus.
Chapter 2: Derivatives
In this chapter, we will learn about one of the core concepts of calculus: derivatives. From basic operations, such as chain rule and implicit differentiation, to more complex analytical applications, including relative extrema, optimization, and linear approximation, we will build a solid understanding step by step.
Chapter 3: Integrals
In this chapter, we will learn about the second fundamental concept of calculus: integration. Starting from basic calculations and progressing to complex 3D volume problems, we will develop a strong understanding of integration. Starting here, the distinction between the AB and BC courses becomes more and more evident. Topics only required by students taking the BC course are indicated in video titles.
Chapter 4: Differential equations
After mastering the fundamentals of differentiation and integration, we will now explore basic differential equations. In addition to learning basic techniques for solving differential equations, we will study how they are used to describe real-world phenomena. Differential equations have widespread applications across various fields, such as population growth estimation, climate modeling, and reaction rate analysis in chemistry. Students taking the BC course are also required to learn how to approximate solutions when an exact solution is not obtainable.
Chapter 5: Applications
In this chapter, we will examine various applications of differentiation and integration. Chapter 5.2, Kinematics, in particular, is heavily tested, often integrating concepts from Chapters 2 and 3. Students taking the BC course are also required to study parametric and polar calculus, including their applications in kinematics problems.
Chapter 6: Sequences and series
As the final chapter of AP Calculus, this section is exclusive to students taking the BC course. We will begin by exploring the convergence of sequences and how to approximate complex functions using simpler ones through Taylor series, gaining control over the accuracy of their approximations.
