Calculus

Limits and Continuity

Analyzing functions to check continuity and all of its implications. Includes evaluating limits, removing discontinuities, the Squeeze Theorem, and the Intermediate Value Theorem.

Differentiation and Derivation Techniques

Using the formal definition of the derivative. Includes different derivation techniques, higher-order derivatives, and implicit differentiation.

Rate of Change

Using the derivative as a rate. Includes applications of the derivative like 1D kinematics, related rates, linearization, and L'Hopital's Rule.

Function Analysis

Analyzing functions graphically. Includes the Mean Value Theorem, solving for extrema, and optimization.

Integration Techniques

Undoing derivation. Includes Riemann sums, the Fundamental Theorem of Calculus, and different integration techniques like substitution, integration by parts, and improper integrals.

Differential Equations

Working backwards from a rate. Includes slope fields, general and particular solutions, and exponential and logistic models.

Applications of Integration

Using the area under a curve. Includes revisiting 1D kinematics, finding the area between curves, and calculating area and arc length.

Formatted Functions

Working with parametric, polar, and vector-valued functions.

Infinite Series

Exploring convergence and approximations. Includes Taylor and Maclaurin series, convergence and divergence tests, and finding error bounds.

Other Resources

Khan Academy's AP Calculus BC and Getting Ready for AP Calculus courses.

Marc Renault's GeoGebra Calculus Applets

Flipped Math's full course.