- 11.1: What is a differential equation?
- Starts with an example: what sets the rate at which a person learns a new task? Defines a diff eq and a solution to a diff eq.
- Defines order of a diff eq. Example 1 is showing a function is not a solution to a diff eq.
- There is just one example and it is modest.
- 11.2: Slope fields
- Introduce the idea of a slope field. Example 1: compare a slope field and a solution curve. Example 2: guess solution form by looking at a slope field. Example 3: sketch solution curves with given initial conditions on a slope field.
- Existence and uniqueness is introduced briefly.
- 11.3: Euler’s method
- Present the Euler’s method algorithm. Example 1: use Euler’s method for a simple example. Example 2: change the step size. Example 3: approximate four points on a solution curve.
- Accuracy of Euler’s method. Introduce the idea of error.
- 11.4: Separation of variables
- Present the method (including the differential on each side of the equation). Example 1: a simple separation problem. Example 2: another simple linear problem. Example 3: a third linear case.
- 11.5: Growth and decay
- 11.6: Applications and modeling
- 11.7: The logistic model
- 11.8: Systems of differential equations
- 11.9: Analyzing the phase plane
- Projects