2 Week AP Calculus AB Crash Course

AP Calculus AB is a college-level calculus course that covers the material typically found in a first-semester calculus course at a university. The course is designed to be taken after students have completed a precalculus course or its equivalent.

The topics covered in an AP Calculus AB course include:

1. Limits: students will learn how to evaluate limits of functions using algebraic and graphical techniques.
2. Derivatives: students will learn how to find the derivative of a function using the definition of the derivative and various rules for different types of functions. They will also learn how to use derivatives to solve optimization problems and find the slope of a curve.
3. Applications of derivatives: students will learn how to use derivatives to find the tangent line to a curve and the velocity and acceleration of an object moving along a curve.
4. Integrals: students will learn how to find the indefinite integral of a function using the definition of the integral and various rules for different types of functions. They will also learn how to use integrals to solve problems involving area, volume, and average value.
5. Applications of integrals: students will learn how to use integrals to find the area between a curve and the x-axis, the volume of a solid of revolution, and the length of a curve.
6. Series: students will learn about infinite series and how to find the sum of an infinite series using various techniques such as the geometric series formula and the ratio test.
7. Differential equations: students will learn about first-order differential equations and how to solve them using various techniques.
8. Parametric equations and polar coordinates: students will learn how to work with parametric equations and polar coordinates, including how to convert between polar and Cartesian coordinates and how to find the area enclosed by a polar curve.
9. Vectors: students will learn how to work with vectors in two and three dimensions, including how to find the magnitude and direction of a vector and how to add and subtract vectors.
10. Partial derivatives: students will learn how to find partial derivatives of functions of two or more variables and how to use partial derivatives to find the maximum or minimum value of a function.

AP Calculus AB also includes a laboratory component in which students will use technology to explore concepts and solve problems.