Calculus BC is an advanced course that builds upon the foundation established in the first year of college calculus. Students in this course will delve into further topics in calculus, including integration, series, differential equations, and polar and parametric functions.
The study of integrals in Calculus BC focuses on advanced techniques such as integration by parts, trigonometric substitution, and partial fractions. Students learn how to apply these methods to solve a variety of integrals. The course also explores the application of integrals in real-world scenarios, emphasizing the connection between integration and accumulation.
Polar and parametric equations are another key component of Calculus BC. Students learn how to graph and solve equations involving polar and parametric functions. They explore the calculus of these types of functions, including differentiation and integration in polar and parametric coordinates. This enables students to analyze and model various phenomena that can be represented by polar and parametric equations.
The course also covers series, including concepts of convergence and divergence. Students learn about different types of series, such as Maclaurin and Taylor series, and their applications. They explore the intervals of convergence and methods for estimating errors in approximation, such as alternating series and the Lagrange error.
Additionally, Calculus BC introduces students to basic principles of differential equations. They learn how to solve simple differential equations and explore the applications of these equations in various fields.
By completing Calculus BC, students develop a deeper understanding of calculus and its applications. The course prepares students for the AP Calculus BC exam, which assesses their knowledge of the covered topics and their ability to apply calculus concepts to solve complex problems. Students who successfully complete this course and exam may be eligible to receive college credit or placement into higher-level college mathematics courses.
At a glance:
Calculus BC builds upon foundational knowledge and covers advanced topics such as integration techniques, series, differential equations, and polar and parametric functions.
Students explore the application of integrals in real-world scenarios, connecting integration with accumulation, while also graphing, solving, and analyzing polar and parametric equations.
The course covers concepts of convergence and divergence, different types of series, and methods for estimating errors in approximation, as well as introducing students to solving simple differential equations and their applications in various fields.