Math 636- Mathematical Modeling
San Diego State University -- This page last updated 15-Dec-10
This page will give a complete listing of the reading and homework assignments that you are required to do. Some problems will be worked in WeBWorK.
Week 14: Programs for the Argument Principle (poly.m, nyq.m, blood.mws) are available. There is a homework for delay equations , which will be due by Friday, Dec. 18. Information about the Final Project and times for presentation are given. An updated status report on grades to date is available. Homework solutions are available for Lotka-Volterra and Bifurcation Models - HW4-Solutions. Homework solutions are available for Epidemic Models - HW5-Solutions. Also, homework solutions are available for Allometric Models - HW7-Solutions.
Week 13: Information about the Final Project and times for presentation are given. Some preliminary notes are available for the Spring-Pendulum problem along with a link to work done by Ricardo Carretero on this problem (see his links on the extensible pendulum). Homework solutions are available for Diabetes Models - HW6-Solutions.
Old Homework Assignments
Week 1-2: You should familiarize yourself with this webpage and how to navigate the different sections. This will be a key page where I post Reading and Homework assignments. The dates for when those assignments are due will also be listed here. Begin by reading the material in the lecture notes under Introduction, U. S. Population, and Malthusian Growth. I also want to refer you to the MatLab code in the U. S. Population notes if you prefer to work in MatLab rather than Excel. You are not expected to use a particular computer routine for your homework. The first Homework assignment for the Discrete models is due by Friday, Sept. 17 by 3 PM. A new Computer Resources page has been developed with information about getting Maple, tutorials on Maple, and what is expected in your HW write-ups regarding graphs.
You should begin finding an article in the Proceedings of the National Academy of Sciences (PNAS) from the last 5 years. You need to submit to me the title of the article, list of authors, volume number, and year by Mon. Sept. 13. A list of articles selected by the class will be regularly updated, and each student must choose a different article. You will write a 2-5 page review that summarizes the work done and discusses some mathematical modeling aspect in the article. I am primarily looking for good scientific writing and an understanding of the role of modeling in your article. Your review will be due Wed. Sept. 29.
Week 3: Read the material in the lecture notes under the Discrete SIR Models. Begin the Homework assignment for SIR Models - HW2. This will be due by Friday, Sept. 24. Don't forget to start work on your PNAS article review. Be sure to email a copy of the PNAS article along with the title of the article, list of authors, volume number, and year.
Week 4: A few students failed to do much on the first HW assignment. Since HW is 60-70% of your grade, this could severely impact these individuals. I have reopened the HW 1 on WeBWorK for a couple more days to raise these very poor scores. Don't forget that your PNAS review will be due Wed. Sept. 29. Read the material in the lecture notes under the Competition Models - Two Species. Also, read the material in the lecture notes under Bifurcation Studies (under development) and the Lotka-Volterra Models. Your next homework assignment begins with some basic ODE models, using simple population models and Newton's law of cooling, then examines two dimensional competition models. One problem takes data from A.C. Crombie on graminivorous beetles and has you repeat much of what we have done in class to create a mathematical model for this ecological system with two competing species. The homework assignment (including a data file) can be found through this link and is due by Friday, Oct. 1.
Week 5: Read the material in the lecture notes under Bifurcation Studies and the Lotka-Volterra Models. Homework solutions are available for Discrete Models - HW1-Solutions. The Homework 4 assignment can be found through this link and is due by Friday, Oct. 15.
Week 6: There is a homework assignment for Epidemic Models, which will be due by Friday, Oct. 22. Some lecture notes are available for Modeling Diabetes. Other references include my Prosper Diabetes lecture and the article of Mahaffy and Keshet. Homework solutions are available for SIR Models - HW2-Solutions.
Week 7: Read the lecture notes on Allometric and Dimensional Analysis. There is a homework assignment for Diabetes Models, which will be due by Friday, Oct. 29. Homework solutions are available for Differential Equation Models - HW3-Solutions.
Week 9: There will be no class on Wed., Oct. 27. Create a two-page outline for your final project (due by classtime Nov. 10). Your final project is a modeling problem of your choice that should use some of the techniques we are teaching in this class or related material. You will be producing a paper at the end of the semester that is approximately 20-25 pages (not counting appendices with programs). Lecture notes are available for Monte Carlo simulations, Stochastic simulations, and Stochastic birth only process. There are a few MatLab programs that were used in lecture for Monte Carlo simulations (and one additional one mentioned). 1. Population decay (pop.m and Mpop.m). 2. Integration (mcint.m and g.m). 3. Computing Pi. 4. Game of craps. (craps.m and dice.m). Additional references for the Stochastic simulations notes are found in the work by Gillespie in 1977. The Gillespie algorithm is valuable for studying biological systems with smaller numbers of molecules. A good example is a bifurcation study by Arkin, Ross, and McAdams (1998) on the lysogenic-lytic switch in Phage Lambda infections of E. coli. The homework for Allometric and Dimensional Analysis problems will be due Friday, Nov. 5.
Week 10: There are lecture notes for Leslie Models. There are additional references on this topic about Loggerhead turtles and Semalparous organisms (and other articles by Cushing). Begin the Homework assignment for the Monte Carlo simulations. This will be due by Friday, Nov. 12.
Week 12: There are lecture notes for Erythropoiesis. Programs for the Argument Principle (poly.m, nyq.m, blood.mws) are available. There is a homework for stochastic modeling, which will be due by Wednesday, Nov. 24.