Differential Equations Overview — AP Calculus BC
1. Unit at a Glance
This unit builds from foundational definitions to applied modeling, covering three approaches to differential equations: graphical, analytical, and numerical. You will start with core basics like verifying solutions and working with slope fields, then move to solving separable equations and applying these skills to common real-world models. Two key BC-exclusive topics (Euler's method and logistic models) round out the unit, which are regularly tested on the AP exam.
Common Pitfalls
Why: This leads to an incorrect general solution and makes finding the right particular solution impossible.
Why: This leads to predictions that grow when the quantity should decay, and vice versa.
Why: Equilibrium solutions give critical long-term behavior information not obvious from the general solution.