Due at the beginning of class, Tuesday Nov 30.

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1. We saw in class that the boundary integral method
for solving the problem of Newtonian heating of a semi-infinite 
slab resulted in a Volterra integral equation of convolution type.
We solved it by exact summation of the Neumann series,
but we remarked that we had previously applied the method
of the Laplace transform to solve IEs of this type.
Attempt to solve this IE using the Laplace transform.
Use Maple's inttransforms[laplace] and inttransforms[invlaplace].
If Maple is unable to do the inverse Laplace transform
to get the answer, at least verify that the forward transform
of the answer we got in class (F&M eq. 7.41) matches the
expression you are unable to inverse-transform.

2. EXTRA CREDIT. Solar heating of sidewalk. Consider a concrete sidewalk
initially at 293K, and bathed in thermal radiation corresponding
to 293K, and then illuminated for t>0 by sunlight of intensity 
350W/m2.
Assume the sidewalk has reflectivity 0.35 and emissivity of 0.65,
and model conductive heat loss from the sidewalk to the air as
Newtonian with a coefficient &beta = 2 W/m2/degK.
(I just made that up!) Taking into account the Stefan-Boltzmann
law of thermal radiation, answer the following. 
Does there exist an equilibrium temperature of the surface of the sidewalk?
If so, what is it, and how long does it take to "get there"?
If not, explain why not.