1. www.SIMIODE.org

4. Professional Enhancement Programs of the MAA MAA PREP Building Community in SIMIODE - Systemic Initiative for Modeling Investigations and Opportunities with Differential Equations 19-25 July 2015 Carroll College Helena Montana

6. Boat ride through the Gates of the Mountains on the Missouri River

7. Flipping

14. With good reason.... here is a patient’s data plotted!

16. Recall the eye, the bubble...

17. All parameters are found by minimizing the sum of square errors between model prediction (here ) and actual data (here h i ). for the model (Model 3): This requires numerical solution of our model over a region of parameters k 1 and k 2 to determine the minimum of SSE(k 1,k 2 ) in our parameter space (k 1, k 2, SSE(k 1,k 2 )).

18. Model 2 Model 3 Model 1

20. Recall our models...

21. Day before modeling activity ask students to think about how they would model just how long it takes an ant to dig a tunnel of length x. Assumptions!!!!! LEAD TO Mathematics!!!!! See you next class with your ideas!

22. Objective: Get students to think about change, about increment....

25. Example of “local flipping” or “flipping in the small” in this case modeling first leading to differential equation mathematics.

26. Ask questions of solved differential equations model such as “What if we double the length of the tunnel? Does this double the time?” Consensus emerges....... and what mathematics does this yield?

27. Ask students to think about how a kidney dialysis machine works......... on the day before class for modeling such a machine.

28. Issue Which is better?

30. www.SIMIODE.org

32. Thank you for your time and attention. Questions? Comments?