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

## Daily outline for Fri, Dec 2, 2016 9:10 AM (5 months ago)

### PDEs: 2D wave equation

assigned today:
• standard-2D wave equation:

I can calculate and shape and frequencies of a circular drum head.

1. 12.10.13 through 12.10.15 (all of them)
2. Calculate the relative amounts of the first 10 frequencies for a circular drum with radius 1 excited by the function $$f(r)=e^{-r^2/0.2^2}$$
3. Calculate 5 different frequencies for a circular drum, at least one of which has an eigenfunction that is a function of $$\theta$$

Due 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

# in class

• Talked about the arduino project a little
• Quiz on 2D heat equation with only one side non-zero
• Talked about all the ideas needed for this new section and discussed which to try to do in class
• physical connection to laplace equation for drum heads
• polar laplacian
• $$\theta$$-dependence
• Fourier trick for Bessel
• full problem
• what it sounds like
• we did the second one for a while but voted not to finish it up
• We separated time, theta, and space carefully (time first, then theta)
• we talked about the analogy between sines and Bessels

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