
Math 636 Mathematical Modeling 


San Diego State University  This page last updated 05Dec11 
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: Lecture notes and related articles are available for the Nerve Impulse Models. Also, homework solutions are available for Allometric Models  HW7Solutions.
Week 12: Some preliminary notes are available for the SpringPendulum problem along with a link to work done by Ricardo Carretero on this problem (see his links on the extensible pendulum). There are lecture notes for Erythropoiesis. Programs for the Argument Principle (poly.m) are available. There is a homework for delay equations , which will be due by Friday, Dec. . Homework solutions are available for Epidemic Models  HW5Solutions. Homework solutions are available for Diabetes Models  HW6Solutions.
Old Homework Assignments
Week 12: 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. PDF lectures notes for the Discrete Dynamical Systems Models (4Panel) are available. 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. 16 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 writeups 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. 12. A list of articles selected by the class will be regularly updated, and each student must choose a different article. You will write a 25 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. 28.
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. 23. Don't forget to start work on your PNAS article review. Be sure to email a copy or hyperlink of the PNAS article along with the title of the article, list of authors, volume number, and year.
Week 4: Don't forget that your PNAS review will be due Wed. Sept. 28. 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 LotkaVolterra 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 Differential Equations HW assignment (including a data file) can be found through this link and is due by Friday, Sep. 30.
Week 56: Read the material in the lecture notes under Bifurcation Studies and the LotkaVolterra Models. The Homework 4 assignment can be found through this link and is due by Friday, Oct. 14. Homework solutions are available for Discrete Models  HW1Solutions.
Week 7: There is a homework assignment for Epidemic Models, which will be due by Friday, Oct. 21. Some lecture notes are available for Modeling Diabetes. Other references include my Prosper Diabetes lecture and the article of Mahaffy and Keshet. There is a homework assignment for Diabetes Models, which will also be due by Friday, Oct. 28.
Week 8: Read the lecture notes on Allometric and Dimensional Analysis. There is additional information in article for Atomic Bomb Energy Part 1 and Part 2. There is a homework assignment for Diabetes Models, which will be due by Friday, Oct. 28. There is a homework assignment on WeBWorK for Allometric and Dimensional Analysis, which will be due by Friday, Nov. 4. Homework solutions are available for SIR Models  HW2Solutions. Homework solutions are available for Differential Equation Models  HW3Solutions.
Week 9: Create a twopage outline for your final project (due by classtime Nov. 16). 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 2025 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 lysogeniclytic switch in Phage Lambda infections of E. coli. Begin the Homework assignment for the Monte Carlo simulations. This will be due by Friday, Nov. 11.
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). There is a homework for stochastic modeling, which will be due by Friday, Nov. 18. Homework solutions are available for LotkaVolterra and Bifurcation Models  HW4Solutions.