Daily outline for Wed, Oct 5, 2016 9:10 AM (5 months ago)
First order ODE's
assigned today:
Due today:
in class
- quiz: explain how diagonalization is done and how it helps for a system of linear differential equations
- Asked what they knew about lake ice (whiteboards)
- top down freezing
- shallows first (talked later about how we weren't going to model that)
- Asked about plot of temperature vs depth (including both the ice and the water)
- some showed constant temp in the ice
- most thought water was warmer
- some showed a discontinuity somewhere
- talked about \(dQ=mL\) and how we needed time
- asked for a plot of thickness vs time from today until next summer
- all had a peak
- some showed oscillations
- Some showed asymmetric freezing and melting
- talked about connection to Ohm's law V=IR
- V becomes \(\Delta T\)
- I becomes \(\frac{dQ}{dt}\)
- R becomes
$$\frac{1}{k}\frac{x}{A}$$
- derived differential equation and solved it analytically for a fixed temperature difference
- ran out of time to Euler, mixing, and we briefly discussed radioactive decay
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