Unit route
Complete lessons in sequence, use diagnostic evidence to select a pathway, conduct the investigation, submit corrected work, and demonstrate mastery at 80% or above.
Weeks 21, 22, 23 · 7 college lessons
Differential Equations & Numerical Models
How do direction fields, exact methods, numerical methods, and parameter evidence describe systems that change over time?
Pathways
Lesson 01 · Week 21
Direction Fields, Equilibria & Qualitative Behavior
Reading solution behavior without first solving symbolically.
Lesson 02 · Week 21Euler’s Method & Global Error
Building numerical solution estimates from local slopes.
Lesson 03 · Week 21Separable Differential Equations
Separating dependent and independent variables before integrating.
Lesson 04 · Week 22Exponential Growth, Decay & Half-Life
Deriving and interpreting proportional-rate models.
Lesson 05 · Week 22Logistic Growth & Carrying Capacity
Modelling self-limiting proportional growth.
Lesson 06 · Week 23First-Order Linear Equations & Integrating Factors
Solving y′+p(x)y=q(x) systematically.
Lesson 07 · Week 23Parameter Estimation, Residuals & Model Comparison
Using data to estimate parameters and inspect model error.