Lesson 1: 9.1 Modeling with Differential Equations

- Compare and contrast differential equations with traditional algebraic equations you have seen before.
- What forms will solutions to differential equations be in?
- Can there be more than one solution to a differential equation?

- differential equations
- order of a differential equation
- initial condition
- initial-value problem

(setting up and verifying solutions to differential equations)

- Setting up simple differential equations and verifying solutions to given differential equations
- DOK Levels 1-4

- population growth and predator-prey interactions
- tracking concentration of medicine in the bloodstream over time
- calculating amount of work done by a snow plow while snow is still falling
- predicting temperature change of an object over time
- Analyzing car suspensions, bridge vibrations, and rocket trajectories

The idea of functions being solutions to equations, and that functions and their derivatives can be parts of the same equation, will be new concepts and are sometimes difficult for students to grasp.

Homogeneous grouping and whole class discussion

section assessment

problems assigned from book