Unit 7: Differential Equations

Student Outcomes:
Modeling with Derivatives: Students will translate verbal descriptions (e.g., "the rate of change is proportional to the amount present") into mathematical equations.
Slope Fields: Students will learn to "map out" the behavior of a differential equation without actually solving it.
Separation of Variables: Students will master the primary algebraic technique for finding a specific function y = f(x) that satisfies a given derivative.
The Importance of +C: In this unit, forgetting the constant of integration doesn't just lose a point—it makes the entire solution impossible to finish.

7.1 Modeling Situations with Differential Equations
7.2 Verifying Solutions for Differential Equations
7.3 Sketching Slope Fields
7.4 Reasoning Using Slope Fields

7.6 General Solutions Using Separation of Variables
7.7 Particular Solutions using Initial Conditions and
Separation of Variables
7.8 Exponential Models with Differential Equations

College Board AP Classroom Assessments