1. Euler’s Method Illustrated: A Sleepy Example Narrated by: Eric Gauthier and Kevin Lin

2. A Sleepy Example… Question: Will you fall asleep? A = The percent of your awakeness t = The duration of this presentation

3. What We Know… (Don’t ask how we determined this) (Hey, not everyone’s as smart as you!!!) Difficult to solve analytically Must use numerical method…in this case Euler’s Method

4. More Stuff We Know… Initial Condition: A(t = 0) = 100 Presentation time: 3 minutes

5. Euler’s Method h = Step Size ODE: Initial Condition:

6. Solution Method Visualized Actual Data

7. Further Improvement

8. Goodnight… Are you asleep yet? ) :;