1. Power of representations

Add to 15 game

link

Mount Fuji representations - Beinhocker

2. Different representations:

our list of representations

• verbal, descriptive
• cartoon, icons
• chart of trends
• chart of data
• algebra to describe data
• other models

could be more than just a list - different ways to look at a problem

complex problems with many parameters and choices

maybe there's a way to represent it as a problem you already know how to solve or are good at

example:

what do you think you're good at?

 

3. "Logistic" equation

go to lecture3 -

graphs:

Pop vs. time - sigmoid

growth rate vs. population - linear

r = rmax * (K-N)/K

r = -N/K*rmax + rmax*K

of the form Y = mX + b

compare points on one to the other

4. STELLA model

rmax = .04
K = 1000
initial population = 100

plot N vs. time and new_growth vs. time

plot r vs. N

 

5. Focus on equations

• most formal
• used in predictions
• international language to some extent
  • F = ma
  • especially if you use international units MKS
    • area (m^2) = length (m) x width (m)
    • H2O

6. Six (or seven) types of equations

math help

 

7. Search for an equation that fits

• if you are trying to find an equation that describes observed data
• characteristics of each relationship (salient features)
  • shape of the curve
  • x=0
  • y=0
  • undefined values of x or y
  • units
  • range of useful values

Search table

We'll fill this in later