Day 4 in math modeling

Assignment #4: Continue working on your Project 1.2 or 1.3, pp. 39-42 (we should have it completed by the end of next class); begin work on your choice of either Project 1.6 or 1.7, pp. 43-45.
Note: next class, we'll be in the computer lab to start with, and work in there the entire time on these projects.
Review discussion from last time (30 minutes), and look at exercises 3d and 4.
- appropriate growth models
- fixed points and stability - cobwebbing
- Simple examples:
  - linear
  - affine
  - logistic and chaos
- Example Problems (the sorts of things to expect on a test): Exercises 3d, and 4.
Form groups of two to work on Projects 1.2 or 1.3
Visit computer lab to explore the logistic equation with Mathematica workbooks (45 minutes).
- visit class homepage (http://www.nku.edu/~longa/classes/mat370/) for link to ...
- textbook homepage
- download mathematica notebook 1
  - create folder on machine
  - save (click and hold) link as file
- run mathematica (from Apple -> math)
- open notebook
- within mathematica, save as day4.nb
- Evaluate the notebook: Kernel -> Evaluation -> Evaluate Notebook
- Edit out everything but sandhill crane example
- replace sandhill crane example equation with logistic equations, introducing variables R and K
- explore dynamics with K=100, while varying R as described in the book; in particular,
  - R=.5
  - R=1.9
  - R=2.2
  - R=2.7
- Calculate |f'(K)| for the cases above.
- If possible, plot the corresponding growth functions for the cases above.
Here's my version of Day4.nb, if you want to try it out. For one thing, I've added the plots of the line y=x and f(x); for another, my plots aren't connected with line segments, but rather are shown as points. These are discrete problems, afterall!

Website maintained by Andy Long. Comments appreciated.