AP Calculus BC

Description

Students in this course will walk in the footsteps of Newton and Leibnitz.

An interactive course framework combines with the exciting on-line course delivery to make calculus an adventure. The course includes a study of limits, continuity, differentiation, integration, differential equations, and the applications of derivatives and integrals, parametric and polar equations, and infinite sequences and series.

Segment 1:

Properties of Limits
Determining and Estimating Limit Values Algebraically and from Graphs and Tables
Limits Involving Infinity
Continuity and Discontinuity
Intermediate Value Theorem
Rates of Change
The Derivative
Rules of Differentiation
Trigonometric, Exponential, and Logarithmic Functions
Implicit Differentiation
Inverse Functions
Distance, Velocity, Acceleration, and Rectilinear Motion
Related Rates
Linearization
Hôpital’s Rule
The Mean-Value Theorem
Function Behavior and Curve Sketching
Optimization

Segment 2:

Area Approximation and Riemann Sums
The Fundamental Theorem of Calculus
Introduction to the Definite Integral
Integrals and Antiderivatives
Integration Using Substitution
Integration Using Long Division and Completing the Square
Integration by Parts
Integration Using Partial Fractions
Improper Integrals
Differential Equations
Slope Fields
Euler’s Method
Separation of Variables
Exponential Models
Logistic Models
Average Value of a Function and Rectilinear Motion Revisited
Finding the Area Under and Between Curves
Volumes with Discs
Volumes with Washers
Volumes with Cross Sections
Length of Planar Curves
Parametric Curves
Vector Curves
Polar Curves
Area of Planar Curves (Polar Curves only)
Series
Convergence and Divergence
Tests for Convergence
Error Bound
Maclaurin Series
Taylor Series and Error Bound
Power Series
Radius and Interval of Convergence of Power Series

Additional Course Notes:

AP courses may require that students purchase a textbook to complete the course. eLearning Academy does not offer the AP exams or issue a teacher code for exam registration.  You do not have to take the course to register for the exam.  The course is to help  you prepare for the exam.  When you register for the exam, you can register as a homeschooler without a teacher code. If you have questions about this process, please call us before paying for the course.

Prerequisites: Algebra 1, Geometry, Algebra 2, and Pre-Calculus or Trigonometry/Analytical Geometry

Suggested Grade Level: 12

Credits: 1