Introduction to Continuous Mathematical Modeling

University of Washington, Seattle
AMATH 383
Summer 2017
MWF 12:00-1:00, JHN 075

Instructor:
Lowell Thompson
lfthomps@uw.edu

Office Hours:
Wed, 1:30-2:30
Thur, 3:00-4:00
Lewis 128


Syllabus

Term Paper Guidelines

Suggested Term Paper Topics


Course Notes:
Day 2
Day 3
Day 4
Day 5
Day 6
Day 7
Day 8
Day 9
Day 10
Day 11
Day 12
Day 13
Day 14
Day 15
Day 16
Day 17
Day 18 -- ODE review (systems start on page 55)
Day 19
Day 20
Day 21
Day 22
Day 23

Homework Assignments:

Assignment Due Date Solutions
Assignment 1 (tex) Friday, June 30 Solution (tex)
Assignment 2 (tex) Friday, July 7 Solution (tex)
Assignment 3 (tex) Friday, July 14 Solution (tex)
Assignment 4 (tex) Friday, July 21 Solution (tex)
Term Paper Proposal Friday, July 28
Assignment 5 (tex) Friday, August 4 Solution (tex)
Assignment 6 (tex) Friday, August 11
Term Paper Friday, August 18


Announcements:

June 25: Homework 1 has been modified slightly. The extra credit on problem 3 was much messier than I intended, so the question has been simplified. I also fixed a couple typos.
July 6: I added scanned copies of my notes to the website.
July 12: I corrected three mistakes in homework 3. First, the first sentence of problem 3(d) should read "this lambda is *larger* than 1", not smaller. Second, the limit in equation (10) should equal one, not zero. Finally, equation 12 should only involve tau, not t -- that is, it should read kappa(tau) = alpha e^(alpha tau).
July 19: Problem 3 was harder than I expected it to be, so I have made part of it extra credit. You still need to find the cdf and pdf of each T_n, but you only need to find the expected value of T_N. You can try to find the expected value of all T_n for extra credit, but that is a very difficult problem.
August 3: In problems 2c and 2d of homework 5, you should just find both equilibria. (There are two, but they may or may not be positive, depending on \beta and \delta. This shouldn't be any more work than the original question.) You are also free to assume that \beta > \delta > 0.
August 8: Problem 3 of homework 6 had a very important mistake. The system is frictionless if a = 0, not if b = 0. In addition, the energy function E(x_1,x_2) was missing a factor of b. The assignment has been updated.
August 10: My intended solution for problem 2d of homework 6 was substantially more complicated than it needed to be. While there is a fairly straightforward solution, I suggested some difficult approaches to people in office hours. To make this fair, if you find that the positive equilibrium is stable, you do not need to distinguish between a node and a spiral, but doing so will be worth extra credit.