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

## Daily outline for Wed, Nov 30, 2016 9:10 AM (1 year ago)

### PDEs: Heat equation

assigned today:
• standard-Heat equation:

I can describe and calculate the heat distribution and flow in 1D and 2D situations.

1. Any from 12.6.5-12.6.7. (Note that this used to be 12.6.8 but that one needs a homogeneous solution (Fourier series) along with a particular solution (Tom's slanted line) and is more of a hassle than I think you need to deal with)
2. 12.6.19 sinusoidal voltage on one side.
3. 12.6.22 plate with 2 sides non-zero

Due today:

# planning

• Derive heat equation
• LHS monitor heat flowing out
• RHS figure out "heat" inside
• 1D bars with initial temperature distribution placed in cold baths on both ends
• 2D regions with edges connected to baths
• or hanging rubber over a wire frame

# in class

• Quiz on Nyquist (gave 2 frequencies, asked for sampling frequency that would confuse the two)
• Derive heat equation
• LHS monitor heat flowing out
• RHS figure out "heat" inside
• talked about the 1D bar problem and what we expect
• ran out of time for 2D so we'll talk about it more in lab tomorrow

edit