Math 636- Mathematical Modeling
San Diego State University -- This page last updated 12-Dec-07
This page will give a complete listing of the reading and homework assignments that you are required to do.
Week 14: More information on the projects is available through this link. There is a slight change in Question 4b (adding a 4c) to have you better explain the harvesting in these models. There is a Take-Home Final that you are to do with no assistance from other classmates. It has 6 problems that review many of the important topics from this semester, including 2 problems that relate to the stochastic modeling and Leslie models. On the last problem, if you want to write your code in another language, then you can, provided the documentation is adequate. Programs for the Argument Principle (poly.m, nyq.m, nyq_rep.m, repdde.m, blood.mws) are available. Solutions are available for the Nerve Impulse HW. Current progress on grades has been updated.
Week 13: Preliminary lecture notes have begun for Age-structured models and Erythropoiesis. The notes use material from the article by Crowder et al on loggerhead turtles and the article by Cushing on semelparous Leslie models. There is a MatLab program for Leslie models of Cushing. Solutions are available for the Diabetes HW.
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 Friday, Sept. 7 by class. 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 Wed. 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 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 Fri. Oct 5.
Week 3: Read the material in the lecture notes under the Competition Models - Logistic Growth. Begin the Homework assignment for Differential Equation Models - HW2. This will be due by Monday, Sept. 17.
Week 4: Read the material in the lecture notes under the Competition Models - Two Species. Also, read the material in the lecture notes under the Lotka-Volterra Models. Homework solutions are available for Discrete Models - HW1-Solutions. Your next homework assignment 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. 26.
Week 5: Read the material in the lecture notes under the Lotka-Volterra Models. We will begin lecturing on Dimensional analysis and Allometric modeling. Notes are being prepared or a link to a copy of notes from alternate texts will be made available soon. The homework assignment (including a xls data file and txt data file) for the Lotka-Volterra models is available through this link and is due by Wednesday, Oct. 3.
Week 6: Begin the Homework assignment for Epidemic Models. This will be due by Friday, Oct. 17.
Week 7: Lecture notes are being developed for Epidemic Models. Lecture notes have been prepared for the Allometric and Dimensional Analysis material. The homework for Allometric and Dimensional Analysis problems will be due Monday, Oct. 15. Begin the Homework assignment for Diabetes Models. This will be due by Monday, Oct. 19. Solutions are available for the Differential Equation Models - HW2 and Two Species Competition - HW3.
Week 9: Lecture notes and related articles are available for the Nerve Impulse Models. The lecture note section has links to MatLab programs for these models and will continue to be updated for future reference. You need to start making plans for your semester project. Each student will work an independent project that we negotiate together. This week I want you to turn in a sheet of paper with an area of application (can be narrow or broad) with a type of mathematics that you prefer to use. (For example, epidemic modeling with delay differential equations.) Your project will involve a written project (15-20 pages) due the last day of finals and an oral presentation (graded by your peers in class). The project should try to connect to actual data that you gather from the literature or collect yourself. Begin the Homework assignment for the Spring-Pendululm Model. This will be due by Wednesday, Nov. 7. Also, begin the Homework assignment for the Nerve Impulse Models. This will be due by Wednesday, Nov. 14. Current progress on grades are available.
Week 11: Lecture notes are available for Monte Carlo simulations. There are a few MatLab programs that were used in lecture for Monte Carlo simulations. 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). 5. Mousetrap simulation. Begin the Homework assignment for the Monte Carlo simulations. This will be due by Wednesday, Nov. 14. Solutions are available for Lotka-Volterra HW, Allometric HW, and Epidemic HW. Current progress on grades are available.
Week 12: Preliminary lecture notes have begun for Stochastic simulations. These notes are based on 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.