**Learning objectives**

- What is a differential equation and how can you represent it visually?
- Distinguish between dy/dt = kt and dy/dt = k y
- Use initial values to single out an individual solution
- Work with the shifted exponential DE: dy/dt = k y + b
- Solve separable DEs: f(x) dx = g(y) dy
- Explore algebraic solutions of the logistic DE: dy/dt =ky (1-y/L) where k >0 and L> 0.
- Solve differential equations with Mathematica
- Use the Euler method to create numerical approximations of solutions of DEs

**Resources**

- Hughes-Hallett: 11.1-11.7
- Solving differential equations with Mathematica
- Solutions of exponential, shifted exponential, and logistic equations

**In class**

- Introduction, with some vocabulary
- Problems: growth and decay models, separable DEs
- A model of atmospheric temperature
- Population modeling: page 7
- Solving a DE numerically with a spreadsheet
- Euler method with Mathematica