Math 636- Mathematical Modeling
San Diego State University -- This page last updated 14-Dec-09
This page will give a complete listing of the reading and homework assignments that you are required to do.
Week 14: Programs for the Argument Principle (poly.m, nyq.m, blood.mws) are available. Information about the Final Project and times for presentation are given. A status report on grades to date is available. Homework solutions are available for Diabetes Models - HW6-Solutions. Homework solutions are available for Monte Carlo Models - HW8-Solutions.
Week 13: Information about the Final Project and times for presentation are given. A status report on grades to date is available. There is a homework for delay equations , which will be due by Friday, Dec. 18. 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.
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. The Homework assignment for the Discrete models is due by Monday, Sept. 14 by class time . For students who found the Excel in lecture too fast to take notes, a hyperlink to the Excel spreadsheet in class is provided for the Models of the U. S. population. (Note that this is slightly different than the one in the notes above in that the least squares fit is constrained to have the population agree with the 1790 census data.) 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.
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. 14. 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. Oct 7 .
Week 3: You might enjoy working the Problem of the Fortnight during the semester to practice your modeling/math skills, and you can win some prizes and honors for being selected with good answers. The first problem is basic probability theory, which should interest a number of you. 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 Wednesday, Sept. 23. Don't forget to start work on your PNAS article review.
Week 4: 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 Wednesday, Sept. 30.
Week 5: Read the material in the lecture notes under Bifurcation Studies (under development) and the Lotka-Volterra Models. Lecture notes are being developed for Epidemic Models. Homework solutions are available for Discrete Models - HW1-Solutions. The homework assignment can be found through this link and is due by Wednesday, Oct. 14. (As per request, a Maple sheet for substituting into a Matrix is provided though I know there are better ways.) There is a homework assignment for Epidemic Models, which will be due by Wednesday, Oct. 21.
Week 6: Some lecture notes are available for Modeling Diabetes. There is a homework assignment for Diabetes Models, which will be due by Monday, Nov. 2. Homework solutions are available for SIR Models - HW2-Solutions.
Week 7: Read the lecture notes on Allometric and Dimensional Analysis. The homework for Allometric and Dimensional Analysis problems will be due Monday, Nov. 9. Homework solutions are available for Differential Equation Models - HW3-Solutions.
Week 9: Lecture notes are available for Monte Carlo simulations and Stochastic simulations. 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. Begin the Homework assignment for the Monte Carlo simulations. This will be due by Monday, Nov. 16. Very shortly, there will be a homework assignment covering the stochastic modeling material.
Week 11: Preliminary lecture notes have begun for Leslie Models. There are additional references on this topic about Loggerhead turtles and Semalparous organisms (and other articles by Cushing). There is a homework for stochastic modeling, which will be due by Wednesday, Dec. 2.