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HW Assignment for Math 636
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. There is a link to the Grading Policies for this course.
Week 15: Project information is available. This hyperlink lets you know when you are speaking and how students will grade you on the oral presentation. The Oral portion is 1/3 of the grade determined only by the class, while the written part is worth 2/3. Oral presentations are Tues., Dec. 16, 8-1, while written projects are due Thurs., Dec. 18 by 5 PM.
Week 13: Determine if you have any other finals on Tues, Dec. 16. There are lecture notes for Erythropoiesis. Additional information on the Argument Principle from Complex Variables is provided. Programs for the Argument Principle (poly.m, delay_1ab, nyq) are available. Additional reading on stability of delay equations (and manuscript). Shampine and Thompson's Tutorial on MatLab's dde23. Lecture notes and related articles are available for the Nerve Impulse Models. There is a homework for delay equations, which will be due by Tuesday, Dec. 2.
Week 11-12: 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 are lecture notes for Erythropoiesis. Additional information on the Argument Principle from Complex Variables is provided. There is a homework for stochastic modeling, which will be due by Friday, Nov. 21. There is a homework for delay equations, which will be due by Wednesday, Nov. 26. Homework solutions are available for Bifurcation and Lotka-Volterra Models - HW4.
Old Homework Assignments
Week 1: 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. 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.
Read the lecture notes on Allometric and Dimensional Analysis. There is additional information in article for Atomic Bomb Energy Part 1 and Part 2. Also, there is information on food energy and weight (Kleiber's Law) and the relation to pulse and weight (von Bertalanffy). There is a homework assignment on WeBWorK for Allometric and Dimensional Analysis along with one additional problem for Allometric models, which will be due by Friday, Sep. 5.
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 Thur. Sept. 4. A list of PNAS 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. Sept. 19.
Week 2 and 3: Reading the material in the lecture notes under U. S. Population. PDF lectures notes for the Discrete Dynamical Systems Models (4-Panel) 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 second Homework assignment for the Discrete models is due by Friday, Sept. 19 by 3 PM.
Week 4: Read the material in the lecture notes for Least Squares and the Discrete SIR Models. Also, begin reading the material for population modeling with differential equations. The lecture notes include Malthusian Growth, Continuous models: Logistic growth, and Competition Models - Two Species. Begin the Homework assignment for SIR - HW. This will be due by Friday, Sept. 26. Don't forget to start work on your PNAS article review, which is due Fri. Sept. 19. A list of PNAS articles selected by the class will be regularly updated.
Week 5: Read the material in the lecture notes for the Discrete SIR Models. Also, read the material for population modeling with differential equations. The lecture notes include Malthusian Growth, Continuous models: Logistic growth, and Competition Models - Two Species. The Homework assignment for SIR - HW will be due by Friday, Sept. 26. 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, Oct. 3.
Week 6-7: Read the material in the lecture notes for Competition Models - Two Species, Bifurcation Studies, and the Lotka-Volterra Models. The homework assignment covers 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 Monday, Oct. 6. The Bifurcation and LV Model HW assignment can be found through this link and is due by Friday, Oct. 17.
Week 8-9: Create a two-page outline for your final project (due byFriday Nov. 7). The outline needs to be sufficiently detailed that I understand your sources and scope of study. This includes discussing the area of application and some idea of the mathematical techniques employed. 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. (No statistics!) You will be producing a paper at the end of the semester that is approximately 20-25 pages (not counting appendices with programs) and giving an oral presentation (graded by your fellow students). The project can be related to projects in other courses, but must be unique from other courses and emphasize the modeling part of a problem. 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. 31. Also, homework solutions are available for Allometric Models - HW1, Discrete Models - HW 2 and SIR Models - HW3.
Week 10: Create a two-page outline for your final project (due byFriday Nov. 7). (See Week 8-9 for details.) 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). The link to the video for the Disney film Our Friend the Atom for a chain reaction with mousetraps and the mousetrap MatLab code simulating the stochastic model for this movie. The original article by Schmitz and Kwak on the Deaconess Hospital simulation is available. 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. 10.
For questions concerning the webpage contact Joseph Mahaffy.
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