Advanced Topics in Calculus BC
Advanced Topics in Calculus BC Online High School Course
COURSE LENGTH:
Full Year (30 Sessions)
Course Overview
Advanced Topics in Calculus BC is an advanced level course for those who have successfully completed an advanced or accelerated pre-calculus class. In order to succeed in this course, students must have exceptional problem solving abilities and a clear understanding of functions and function behavior. This is a full year course, consisting of 30 synchronous sessions. Each session will have approximately 1-2 hours of corresponding asynchronous material. This material will help students develop skills so that synchronous class time can be spent on answering questions and problem solving. The class moves at a fast pace. We will be covering a total of 10 chapters, averaging one chapter every 3 synchronous sessions. Students will take summative assessments on a unit basis (there are 4 different units). There will be formative assessments for each of 10 AP units. The formative assessments will feature questions from previous AP exams and will serve as a way to gauge performance and competency in accordance with AP standards. The pace of coverage of the course is designed to allow interested students the opportunity to take the AP Exam in Calculus BC, but that is not a requirement of the course.
LEARNING OBJECTIVES:
Analyze functions graphically, numerically, and analytically
Model real world situations using function
Understand the relationship between derivatives and rates of change and be comfortable analyzing real-valued functions using differential calculus
Understand the connection between the derivative and the integral as expressed by the Fundamental Theorem of Calculus
Understand the relationship between integrals and the limits of Reimann sums and be comfortable analyzing real-valued functions using integral calculus
Understand and be comfortable using various methods to test whether a series converges or diverges
Understand how to represent functions as power series and be comfortable differentiating and integrating them
Understand how to model situations using differential equations and be comfortable verifying solutions, creating slope fields, and approximating solutions using Euler’s Method
Understand the connection between cartesian and polar coordinates
Understand how to define parametric equations and vector valued functions and feel comfortable performing differential and integral calculus on them