Math 611, Fall 2011. Instructor P. Kuchment
HW #2. 2 points per a problem
Due September 30th
General remarks:
• Write solutions neatly and not in microscopic letters. Avoid
many crossing outs, etc. This is not only for me to read easier, but
for you to be sure that what you write is correct. I will not grade in
the future proofs that are messily written and unreadable due to a tiny
letter size.
• Avoid words “trivial ..., easy to see ..., obvious ...” and other
their synonyms. “Easy to see” or “trivial” should mean that you can
show this in a second, so just do it :-). By the way, errors are usually
appearing in “obvious” places.
• Be careful with parentheses and other such standard rules;
they can cause mistakes if not followed properly.
• Make sure you understand your logic completely. If you don’t,
I won’t. :-)
Problems:
1. Solve problems ## 1, 2, 3, 4, 8, 10 from Section 2.5 (pages 84-87) of
the textbook.
Extra credit problems. 2 points per a problem. No partial credit
2. Solve problems ## 5, 11 from Section 2.5 (pages 84-87) of the textbook.
3. The stationary single-speed radiative transport equation without scattering on the plane R2 is
ω · ∇u(x) + µ(x)u(x) = f (x).
Suppose that one shoots photons with the itensity u = I0 from the
origin in the direction of the vector ω. The detector is located some
distance l away in this direction. Solve the equation and find what will
be the intensity of the received signal u = I1 at the detector.
1