Homework #1
Dear class members:
I was not able to complete as much material as I had anticipated when I
wrote the first homework assignment. Consequently there is a slight
modification to the assignment.
Problem 3, part (c) is now modified to eliminate the requirement for
nondimensionalization. Replace the first sentence in that problem
description with the statement that we assume r=1 and a=1. This makes
the differential equation become
dL/dx = (L-1)(L+b)
for which you need to generate the slope field and sketch a number of
sample trajectories and so forth.
Also, I'm looking at part (b) of problem 3 and realize that we also
didn't discuss how to determine natural scales. This point will
therefore not be graded. But the basic idea is that you look for a
simple combination of the parameters a, b and r so that this
combination has the same dimension as x or L. For example, look at the
parameters individually, as well as simple products: a, b, r, a*r, a/r,
r/a, a^2r, ...
In class, I gave a hint about problem 2, that the data provided in the
problem relating to the Geiger counter measures the rate of decay
events and not the number of radioactive atoms. That is, Geiger
counters measure -dN/dt, and not anything about N directly.
Finally, I remind you that office hours are posted on the course
website. Here they are as well:
Me (Guggenheim 408C)
Mon at 1:30-2:30
Tues at 10:30-11:30
and Wed at 12:30-1:30 (right after class)
Jan Medlock, our TA (Guggenheim 405D)
Mon and Wed from 3:00-4:00
You can send messages to the entire class through the class e-mail list:
amath383a_au03@u.washington.edu
Or you can post messages to the online message board:
amath383@amath.washington.edu
Best wishes,
D. Brian Walton
AMath 383 Instructor
Guggenheim 408C
(206) 685-9298