# Mathematical and Computational Methods in Physics and Engineering (fall 2016)

## Daily outline for Wed, Oct 5, 2016 9:10 AM (11 months ago)

### First order ODE's

assigned today:
• standard-ODE 1st order:

I can model and solve first order differential equations.

1. ice thickness problem
2. If a single atom has a 0.4% chance of undergoing a radioactive decay during any second, and if you have 10,000 of them in the original state at t=0, how many are still in the original state an hour later?
3. Chapter 1 review problem 28

Due today:

# in class

• quiz: explain how diagonalization is done and how it helps for a system of linear differential equations
• 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
• 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

edit