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

## Daily outline for Fri, Oct 7, 2016 9:10 AM (1 year ago)

### 2nd order ODE's

assigned today:
• standard-2nd order ODEs:

I can model a system with a second order differential equation.

1. Model a parachute jump where an updraft occurs before opening the chute.
2. 2.4.8 (archimedian principle and oscillations)
3. Give both the full analytical solution and an Euler solution in Mathematica for problem 2.8.8.

Due 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

# plan

• nonlinear problems
• 2nd order euler
• talk about parachute issues
• damped, driven issues
• homogeneous
• particular

# in class

• discussed the 2 week rule some more
• quiz on ice problem (asked them to derive the analytical result)
• did nonlinear with 3 solutions (1 wasn't a solution) and asked about linear combos of them
• asked them to sketch altitude vs time for a parachute
• discussed how to turn a 2nd order into 2 first orders so that Euler just needs another column
• talked about damped/driven
• they recognized that they spent a ton of time on this in diff eqs
• we talked about how the homogeneous solutions help with initial conditions

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